Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, 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("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.2 | ||
Root | \(-0.780776 + 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.l.295.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.56155 | 0.698348 | 0.349174 | − | 0.937058i | \(-0.386462\pi\) | ||||
0.349174 | + | 0.937058i | \(0.386462\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.780776 | − | 1.35234i | −0.246903 | − | 0.427649i | ||||
\(11\) | 1.28078 | + | 2.21837i | 0.386169 | + | 0.668864i | 0.991931 | − | 0.126782i | \(-0.0404650\pi\) |
−0.605762 | + | 0.795646i | \(0.707132\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.500000 | + | 3.57071i | −0.138675 | + | 0.990338i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.780776 | + | 1.35234i | 0.201596 | + | 0.349174i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.0615528 | + | 0.106613i | −0.0149287 | + | 0.0258574i | −0.873393 | − | 0.487016i | \(-0.838085\pi\) |
0.858465 | + | 0.512873i | \(0.171419\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.28078 | − | 2.21837i | 0.293830 | − | 0.508929i | −0.680882 | − | 0.732393i | \(-0.738403\pi\) |
0.974712 | + | 0.223464i | \(0.0717366\pi\) | |||||||
\(20\) | −0.780776 | + | 1.35234i | −0.174587 | + | 0.302393i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.28078 | − | 2.21837i | 0.273062 | − | 0.472958i | ||||
\(23\) | 0.561553 | + | 0.972638i | 0.117092 | + | 0.202809i | 0.918614 | − | 0.395156i | \(-0.129309\pi\) |
−0.801522 | + | 0.597965i | \(0.795976\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 3.34233 | − | 1.35234i | 0.655485 | − | 0.265217i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | 3.06155 | + | 5.30277i | 0.568516 | + | 0.984699i | 0.996713 | + | 0.0810133i | \(0.0258156\pi\) |
−0.428197 | + | 0.903685i | \(0.640851\pi\) | |||||||
\(30\) | 0.780776 | − | 1.35234i | 0.142550 | − | 0.246903i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.28078 | + | 2.21837i | −0.222955 | + | 0.386169i | ||||
\(34\) | 0.123106 | 0.0211124 | ||||||||
\(35\) | −0.780776 | + | 1.35234i | −0.131975 | + | 0.228588i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 1.21922 | + | 2.11176i | 0.200439 | + | 0.347171i | 0.948670 | − | 0.316268i | \(-0.102430\pi\) |
−0.748231 | + | 0.663438i | \(0.769096\pi\) | |||||||
\(38\) | −2.56155 | −0.415539 | ||||||||
\(39\) | −3.34233 | + | 1.35234i | −0.535201 | + | 0.216548i | ||||
\(40\) | 1.56155 | 0.246903 | ||||||||
\(41\) | 5.62311 | + | 9.73950i | 0.878182 | + | 1.52106i | 0.853335 | + | 0.521364i | \(0.174577\pi\) |
0.0248471 | + | 0.999691i | \(0.492090\pi\) | |||||||
\(42\) | 0.500000 | + | 0.866025i | 0.0771517 | + | 0.133631i | ||||
\(43\) | 4.00000 | − | 6.92820i | 0.609994 | − | 1.05654i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | −2.56155 | −0.386169 | ||||||||
\(45\) | −0.780776 | + | 1.35234i | −0.116391 | + | 0.201596i | ||||
\(46\) | 0.561553 | − | 0.972638i | 0.0827964 | − | 0.143408i | ||||
\(47\) | −0.315342 | −0.0459973 | −0.0229986 | − | 0.999735i | \(-0.507321\pi\) | ||||
−0.0229986 | + | 0.999735i | \(0.507321\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 1.28078 | + | 2.21837i | 0.181129 | + | 0.313725i | ||||
\(51\) | −0.123106 | −0.0172382 | ||||||||
\(52\) | −2.84233 | − | 2.21837i | −0.394160 | − | 0.307633i | ||||
\(53\) | 7.00000 | 0.961524 | 0.480762 | − | 0.876851i | \(-0.340360\pi\) | ||||
0.480762 | + | 0.876851i | \(0.340360\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 2.00000 | + | 3.46410i | 0.269680 | + | 0.467099i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | 2.56155 | 0.339286 | ||||||||
\(58\) | 3.06155 | − | 5.30277i | 0.402002 | − | 0.696287i | ||||
\(59\) | −2.56155 | + | 4.43674i | −0.333486 | + | 0.577614i | −0.983193 | − | 0.182570i | \(-0.941558\pi\) |
0.649707 | + | 0.760185i | \(0.274892\pi\) | |||||||
\(60\) | −1.56155 | −0.201596 | ||||||||
\(61\) | 5.62311 | − | 9.73950i | 0.719965 | − | 1.24702i | −0.241048 | − | 0.970513i | \(-0.577491\pi\) |
0.961013 | − | 0.276503i | \(-0.0891755\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | − | 0.866025i | −0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.780776 | + | 5.57586i | −0.0968434 | + | 0.691600i | ||||
\(66\) | 2.56155 | 0.315305 | ||||||||
\(67\) | −4.56155 | − | 7.90084i | −0.557282 | − | 0.965241i | −0.997722 | − | 0.0674592i | \(-0.978511\pi\) |
0.440440 | − | 0.897782i | \(-0.354823\pi\) | |||||||
\(68\) | −0.0615528 | − | 0.106613i | −0.00746437 | − | 0.0129287i | ||||
\(69\) | −0.561553 | + | 0.972638i | −0.0676030 | + | 0.117092i | ||||
\(70\) | 1.56155 | 0.186641 | ||||||||
\(71\) | 5.68466 | − | 9.84612i | 0.674645 | − | 1.16852i | −0.301928 | − | 0.953331i | \(-0.597630\pi\) |
0.976573 | − | 0.215188i | \(-0.0690365\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −2.43845 | −0.285399 | −0.142699 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142699 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(74\) | 1.21922 | − | 2.11176i | 0.141732 | − | 0.245487i | ||||
\(75\) | −1.28078 | − | 2.21837i | −0.147891 | − | 0.256155i | ||||
\(76\) | 1.28078 | + | 2.21837i | 0.146915 | + | 0.254464i | ||||
\(77\) | −2.56155 | −0.291916 | ||||||||
\(78\) | 2.84233 | + | 2.21837i | 0.321830 | + | 0.251181i | ||||
\(79\) | −6.56155 | −0.738232 | −0.369116 | − | 0.929383i | \(-0.620340\pi\) | ||||
−0.369116 | + | 0.929383i | \(0.620340\pi\) | |||||||
\(80\) | −0.780776 | − | 1.35234i | −0.0872935 | − | 0.151197i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 5.62311 | − | 9.73950i | 0.620968 | − | 1.07555i | ||||
\(83\) | −5.12311 | −0.562334 | −0.281167 | − | 0.959659i | \(-0.590721\pi\) | ||||
−0.281167 | + | 0.959659i | \(0.590721\pi\) | |||||||
\(84\) | 0.500000 | − | 0.866025i | 0.0545545 | − | 0.0944911i | ||||
\(85\) | −0.0961180 | + | 0.166481i | −0.0104255 | + | 0.0180574i | ||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | −3.06155 | + | 5.30277i | −0.328233 | + | 0.568516i | ||||
\(88\) | 1.28078 | + | 2.21837i | 0.136531 | + | 0.236479i | ||||
\(89\) | −1.71922 | − | 2.97778i | −0.182237 | − | 0.315644i | 0.760405 | − | 0.649449i | \(-0.225001\pi\) |
−0.942642 | + | 0.333805i | \(0.891667\pi\) | |||||||
\(90\) | 1.56155 | 0.164602 | ||||||||
\(91\) | −2.84233 | − | 2.21837i | −0.297957 | − | 0.232548i | ||||
\(92\) | −1.12311 | −0.117092 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.157671 | + | 0.273094i | 0.0162625 | + | 0.0281675i | ||||
\(95\) | 2.00000 | − | 3.46410i | 0.205196 | − | 0.355409i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.438447 | − | 0.759413i | 0.0445176 | − | 0.0771067i | −0.842908 | − | 0.538058i | \(-0.819158\pi\) |
0.887426 | + | 0.460951i | \(0.152492\pi\) | |||||||
\(98\) | −0.500000 | + | 0.866025i | −0.0505076 | + | 0.0874818i | ||||
\(99\) | −2.56155 | −0.257446 | ||||||||
\(100\) | 1.28078 | − | 2.21837i | 0.128078 | − | 0.221837i | ||||
\(101\) | 2.90388 | + | 5.02967i | 0.288947 | + | 0.500471i | 0.973559 | − | 0.228437i | \(-0.0733615\pi\) |
−0.684612 | + | 0.728908i | \(0.740028\pi\) | |||||||
\(102\) | 0.0615528 | + | 0.106613i | 0.00609464 | + | 0.0105562i | ||||
\(103\) | 6.24621 | 0.615457 | 0.307729 | − | 0.951474i | \(-0.400431\pi\) | ||||
0.307729 | + | 0.951474i | \(0.400431\pi\) | |||||||
\(104\) | −0.500000 | + | 3.57071i | −0.0490290 | + | 0.350137i | ||||
\(105\) | −1.56155 | −0.152392 | ||||||||
\(106\) | −3.50000 | − | 6.06218i | −0.339950 | − | 0.588811i | ||||
\(107\) | −6.96543 | − | 12.0645i | −0.673374 | − | 1.16632i | −0.976941 | − | 0.213508i | \(-0.931511\pi\) |
0.303567 | − | 0.952810i | \(-0.401822\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −12.2462 | −1.17297 | −0.586487 | − | 0.809959i | \(-0.699490\pi\) | ||||
−0.586487 | + | 0.809959i | \(0.699490\pi\) | |||||||
\(110\) | 2.00000 | − | 3.46410i | 0.190693 | − | 0.330289i | ||||
\(111\) | −1.21922 | + | 2.11176i | −0.115724 | + | 0.200439i | ||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −0.780776 | + | 1.35234i | −0.0734493 | + | 0.127218i | −0.900411 | − | 0.435041i | \(-0.856734\pi\) |
0.826962 | + | 0.562258i | \(0.190067\pi\) | |||||||
\(114\) | −1.28078 | − | 2.21837i | −0.119956 | − | 0.207769i | ||||
\(115\) | 0.876894 | + | 1.51883i | 0.0817708 | + | 0.141631i | ||||
\(116\) | −6.12311 | −0.568516 | ||||||||
\(117\) | −2.84233 | − | 2.21837i | −0.262773 | − | 0.205088i | ||||
\(118\) | 5.12311 | 0.471620 | ||||||||
\(119\) | −0.0615528 | − | 0.106613i | −0.00564254 | − | 0.00977316i | ||||
\(120\) | 0.780776 | + | 1.35234i | 0.0712748 | + | 0.123452i | ||||
\(121\) | 2.21922 | − | 3.84381i | 0.201748 | − | 0.349437i | ||||
\(122\) | −11.2462 | −1.01818 | ||||||||
\(123\) | −5.62311 | + | 9.73950i | −0.507018 | + | 0.878182i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8078 | −1.05612 | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | −6.24621 | − | 10.8188i | −0.554262 | − | 0.960009i | −0.997961 | − | 0.0638334i | \(-0.979667\pi\) |
0.443699 | − | 0.896176i | \(-0.353666\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 5.21922 | − | 2.11176i | 0.457756 | − | 0.185213i | ||||
\(131\) | 14.2462 | 1.24470 | 0.622349 | − | 0.782740i | \(-0.286179\pi\) | ||||
0.622349 | + | 0.782740i | \(0.286179\pi\) | |||||||
\(132\) | −1.28078 | − | 2.21837i | −0.111477 | − | 0.193084i | ||||
\(133\) | 1.28078 | + | 2.21837i | 0.111057 | + | 0.192357i | ||||
\(134\) | −4.56155 | + | 7.90084i | −0.394058 | + | 0.682529i | ||||
\(135\) | −1.56155 | −0.134397 | ||||||||
\(136\) | −0.0615528 | + | 0.106613i | −0.00527811 | + | 0.00914195i | ||||
\(137\) | −6.21922 | + | 10.7720i | −0.531344 | + | 0.920315i | 0.467987 | + | 0.883736i | \(0.344980\pi\) |
−0.999331 | + | 0.0365795i | \(0.988354\pi\) | |||||||
\(138\) | 1.12311 | 0.0956051 | ||||||||
\(139\) | 2.71922 | − | 4.70983i | 0.230642 | − | 0.399483i | −0.727356 | − | 0.686261i | \(-0.759251\pi\) |
0.957997 | + | 0.286778i | \(0.0925842\pi\) | |||||||
\(140\) | −0.780776 | − | 1.35234i | −0.0659877 | − | 0.114294i | ||||
\(141\) | −0.157671 | − | 0.273094i | −0.0132783 | − | 0.0229986i | ||||
\(142\) | −11.3693 | −0.954092 | ||||||||
\(143\) | −8.56155 | + | 3.46410i | −0.715953 | + | 0.289683i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.78078 | + | 8.28055i | 0.397022 | + | 0.687662i | ||||
\(146\) | 1.21922 | + | 2.11176i | 0.100904 | + | 0.174770i | ||||
\(147\) | 0.500000 | − | 0.866025i | 0.0412393 | − | 0.0714286i | ||||
\(148\) | −2.43845 | −0.200439 | ||||||||
\(149\) | 7.78078 | − | 13.4767i | 0.637426 | − | 1.10405i | −0.348570 | − | 0.937283i | \(-0.613332\pi\) |
0.985996 | − | 0.166771i | \(-0.0533342\pi\) | |||||||
\(150\) | −1.28078 | + | 2.21837i | −0.104575 | + | 0.181129i | ||||
\(151\) | −21.9309 | −1.78471 | −0.892354 | − | 0.451335i | \(-0.850948\pi\) | ||||
−0.892354 | + | 0.451335i | \(0.850948\pi\) | |||||||
\(152\) | 1.28078 | − | 2.21837i | 0.103885 | − | 0.179934i | ||||
\(153\) | −0.0615528 | − | 0.106613i | −0.00497625 | − | 0.00861912i | ||||
\(154\) | 1.28078 | + | 2.21837i | 0.103208 | + | 0.178761i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.500000 | − | 3.57071i | 0.0400320 | − | 0.285886i | ||||
\(157\) | −1.31534 | −0.104976 | −0.0524878 | − | 0.998622i | \(-0.516715\pi\) | ||||
−0.0524878 | + | 0.998622i | \(0.516715\pi\) | |||||||
\(158\) | 3.28078 | + | 5.68247i | 0.261005 | + | 0.452073i | ||||
\(159\) | 3.50000 | + | 6.06218i | 0.277568 | + | 0.480762i | ||||
\(160\) | −0.780776 | + | 1.35234i | −0.0617258 | + | 0.106912i | ||||
\(161\) | −1.12311 | −0.0885131 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −12.2462 | + | 21.2111i | −0.959197 | + | 1.66138i | −0.234741 | + | 0.972058i | \(0.575424\pi\) |
−0.724457 | + | 0.689320i | \(0.757909\pi\) | |||||||
\(164\) | −11.2462 | −0.878182 | ||||||||
\(165\) | −2.00000 | + | 3.46410i | −0.155700 | + | 0.269680i | ||||
\(166\) | 2.56155 | + | 4.43674i | 0.198815 | + | 0.344358i | ||||
\(167\) | −6.24621 | − | 10.8188i | −0.483346 | − | 0.837180i | 0.516471 | − | 0.856305i | \(-0.327245\pi\) |
−0.999817 | + | 0.0191244i | \(0.993912\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −12.5000 | − | 3.57071i | −0.961538 | − | 0.274670i | ||||
\(170\) | 0.192236 | 0.0147438 | ||||||||
\(171\) | 1.28078 | + | 2.21837i | 0.0979434 | + | 0.169643i | ||||
\(172\) | 4.00000 | + | 6.92820i | 0.304997 | + | 0.528271i | ||||
\(173\) | 9.00000 | − | 15.5885i | 0.684257 | − | 1.18517i | −0.289412 | − | 0.957205i | \(-0.593460\pi\) |
0.973670 | − | 0.227964i | \(-0.0732068\pi\) | |||||||
\(174\) | 6.12311 | 0.464191 | ||||||||
\(175\) | 1.28078 | − | 2.21837i | 0.0968176 | − | 0.167693i | ||||
\(176\) | 1.28078 | − | 2.21837i | 0.0965422 | − | 0.167216i | ||||
\(177\) | −5.12311 | −0.385076 | ||||||||
\(178\) | −1.71922 | + | 2.97778i | −0.128861 | + | 0.223194i | ||||
\(179\) | 0.876894 | + | 1.51883i | 0.0655422 | + | 0.113522i | 0.896934 | − | 0.442164i | \(-0.145789\pi\) |
−0.831392 | + | 0.555686i | \(0.812456\pi\) | |||||||
\(180\) | −0.780776 | − | 1.35234i | −0.0581956 | − | 0.100798i | ||||
\(181\) | 13.2462 | 0.984583 | 0.492292 | − | 0.870430i | \(-0.336159\pi\) | ||||
0.492292 | + | 0.870430i | \(0.336159\pi\) | |||||||
\(182\) | −0.500000 | + | 3.57071i | −0.0370625 | + | 0.264679i | ||||
\(183\) | 11.2462 | 0.831344 | ||||||||
\(184\) | 0.561553 | + | 0.972638i | 0.0413982 | + | 0.0717038i | ||||
\(185\) | 1.90388 | + | 3.29762i | 0.139976 | + | 0.242446i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.315342 | −0.0230601 | ||||||||
\(188\) | 0.157671 | − | 0.273094i | 0.0114993 | − | 0.0199174i | ||||
\(189\) | 0.500000 | − | 0.866025i | 0.0363696 | − | 0.0629941i | ||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 2.56155 | − | 4.43674i | 0.185347 | − | 0.321031i | −0.758346 | − | 0.651852i | \(-0.773992\pi\) |
0.943694 | + | 0.330821i | \(0.107326\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −0.0615528 | − | 0.106613i | −0.00443067 | − | 0.00767414i | 0.863802 | − | 0.503832i | \(-0.168077\pi\) |
−0.868232 | + | 0.496158i | \(0.834744\pi\) | |||||||
\(194\) | −0.876894 | −0.0629573 | ||||||||
\(195\) | −5.21922 | + | 2.11176i | −0.373756 | + | 0.151226i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −6.28078 | − | 10.8786i | −0.447487 | − | 0.775070i | 0.550735 | − | 0.834680i | \(-0.314348\pi\) |
−0.998222 | + | 0.0596103i | \(0.981014\pi\) | |||||||
\(198\) | 1.28078 | + | 2.21837i | 0.0910208 | + | 0.157653i | ||||
\(199\) | 8.00000 | − | 13.8564i | 0.567105 | − | 0.982255i | −0.429745 | − | 0.902950i | \(-0.641397\pi\) |
0.996850 | − | 0.0793045i | \(-0.0252700\pi\) | |||||||
\(200\) | −2.56155 | −0.181129 | ||||||||
\(201\) | 4.56155 | − | 7.90084i | 0.321747 | − | 0.557282i | ||||
\(202\) | 2.90388 | − | 5.02967i | 0.204316 | − | 0.353886i | ||||
\(203\) | −6.12311 | −0.429758 | ||||||||
\(204\) | 0.0615528 | − | 0.106613i | 0.00430956 | − | 0.00746437i | ||||
\(205\) | 8.78078 | + | 15.2088i | 0.613276 | + | 1.06223i | ||||
\(206\) | −3.12311 | − | 5.40938i | −0.217597 | − | 0.376889i | ||||
\(207\) | −1.12311 | −0.0780612 | ||||||||
\(208\) | 3.34233 | − | 1.35234i | 0.231749 | − | 0.0937682i | ||||
\(209\) | 6.56155 | 0.453872 | ||||||||
\(210\) | 0.780776 | + | 1.35234i | 0.0538787 | + | 0.0933206i | ||||
\(211\) | −2.56155 | − | 4.43674i | −0.176345 | − | 0.305438i | 0.764281 | − | 0.644883i | \(-0.223094\pi\) |
−0.940626 | + | 0.339445i | \(0.889761\pi\) | |||||||
\(212\) | −3.50000 | + | 6.06218i | −0.240381 | + | 0.416352i | ||||
\(213\) | 11.3693 | 0.779013 | ||||||||
\(214\) | −6.96543 | + | 12.0645i | −0.476147 | + | 0.824711i | ||||
\(215\) | 6.24621 | − | 10.8188i | 0.425988 | − | 0.737833i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.12311 | + | 10.6055i | 0.414709 | + | 0.718297i | ||||
\(219\) | −1.21922 | − | 2.11176i | −0.0823875 | − | 0.142699i | ||||
\(220\) | −4.00000 | −0.269680 | ||||||||
\(221\) | −0.349907 | − | 0.273094i | −0.0235373 | − | 0.0183703i | ||||
\(222\) | 2.43845 | 0.163658 | ||||||||
\(223\) | −4.87689 | − | 8.44703i | −0.326581 | − | 0.565655i | 0.655250 | − | 0.755412i | \(-0.272563\pi\) |
−0.981831 | + | 0.189757i | \(0.939230\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | 1.28078 | − | 2.21837i | 0.0853851 | − | 0.147891i | ||||
\(226\) | 1.56155 | 0.103873 | ||||||||
\(227\) | 5.43845 | − | 9.41967i | 0.360962 | − | 0.625205i | −0.627157 | − | 0.778893i | \(-0.715782\pi\) |
0.988119 | + | 0.153688i | \(0.0491149\pi\) | |||||||
\(228\) | −1.28078 | + | 2.21837i | −0.0848215 | + | 0.146915i | ||||
\(229\) | 17.0540 | 1.12696 | 0.563479 | − | 0.826130i | \(-0.309462\pi\) | ||||
0.563479 | + | 0.826130i | \(0.309462\pi\) | |||||||
\(230\) | 0.876894 | − | 1.51883i | 0.0578207 | − | 0.100148i | ||||
\(231\) | −1.28078 | − | 2.21837i | −0.0842689 | − | 0.145958i | ||||
\(232\) | 3.06155 | + | 5.30277i | 0.201001 | + | 0.348144i | ||||
\(233\) | 1.36932 | 0.0897069 | 0.0448535 | − | 0.998994i | \(-0.485718\pi\) | ||||
0.0448535 | + | 0.998994i | \(0.485718\pi\) | |||||||
\(234\) | −0.500000 | + | 3.57071i | −0.0326860 | + | 0.233425i | ||||
\(235\) | −0.492423 | −0.0321221 | ||||||||
\(236\) | −2.56155 | − | 4.43674i | −0.166743 | − | 0.288807i | ||||
\(237\) | −3.28078 | − | 5.68247i | −0.213109 | − | 0.369116i | ||||
\(238\) | −0.0615528 | + | 0.106613i | −0.00398988 | + | 0.00691067i | ||||
\(239\) | 19.3693 | 1.25290 | 0.626448 | − | 0.779463i | \(-0.284508\pi\) | ||||
0.626448 | + | 0.779463i | \(0.284508\pi\) | |||||||
\(240\) | 0.780776 | − | 1.35234i | 0.0503989 | − | 0.0872935i | ||||
\(241\) | 0.0961180 | − | 0.166481i | 0.00619150 | − | 0.0107240i | −0.862913 | − | 0.505352i | \(-0.831363\pi\) |
0.869105 | + | 0.494628i | \(0.164696\pi\) | |||||||
\(242\) | −4.43845 | −0.285314 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 5.62311 | + | 9.73950i | 0.359982 | + | 0.623508i | ||||
\(245\) | −0.780776 | − | 1.35234i | −0.0498820 | − | 0.0863981i | ||||
\(246\) | 11.2462 | 0.717032 | ||||||||
\(247\) | 7.28078 | + | 5.68247i | 0.463265 | + | 0.361567i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.56155 | − | 4.43674i | −0.162332 | − | 0.281167i | ||||
\(250\) | 5.90388 | + | 10.2258i | 0.373394 | + | 0.646738i | ||||
\(251\) | 6.80776 | − | 11.7914i | 0.429702 | − | 0.744266i | −0.567144 | − | 0.823618i | \(-0.691952\pi\) |
0.996847 | + | 0.0793522i | \(0.0252852\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −1.43845 | + | 2.49146i | −0.0904344 | + | 0.156637i | ||||
\(254\) | −6.24621 | + | 10.8188i | −0.391922 | + | 0.678829i | ||||
\(255\) | −0.192236 | −0.0120383 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 12.1847 | + | 21.1044i | 0.760058 | + | 1.31646i | 0.942820 | + | 0.333302i | \(0.108163\pi\) |
−0.182762 | + | 0.983157i | \(0.558504\pi\) | |||||||
\(258\) | −4.00000 | − | 6.92820i | −0.249029 | − | 0.431331i | ||||
\(259\) | −2.43845 | −0.151518 | ||||||||
\(260\) | −4.43845 | − | 3.46410i | −0.275261 | − | 0.214834i | ||||
\(261\) | −6.12311 | −0.379011 | ||||||||
\(262\) | −7.12311 | − | 12.3376i | −0.440067 | − | 0.762218i | ||||
\(263\) | −2.56155 | − | 4.43674i | −0.157952 | − | 0.273581i | 0.776178 | − | 0.630514i | \(-0.217156\pi\) |
−0.934130 | + | 0.356933i | \(0.883822\pi\) | |||||||
\(264\) | −1.28078 | + | 2.21837i | −0.0788263 | + | 0.136531i | ||||
\(265\) | 10.9309 | 0.671478 | ||||||||
\(266\) | 1.28078 | − | 2.21837i | 0.0785294 | − | 0.136017i | ||||
\(267\) | 1.71922 | − | 2.97778i | 0.105215 | − | 0.182237i | ||||
\(268\) | 9.12311 | 0.557282 | ||||||||
\(269\) | −13.5616 | + | 23.4893i | −0.826862 | + | 1.43217i | 0.0736251 | + | 0.997286i | \(0.476543\pi\) |
−0.900488 | + | 0.434882i | \(0.856790\pi\) | |||||||
\(270\) | 0.780776 | + | 1.35234i | 0.0475165 | + | 0.0823011i | ||||
\(271\) | 11.3693 | + | 19.6922i | 0.690637 | + | 1.19622i | 0.971630 | + | 0.236508i | \(0.0760030\pi\) |
−0.280993 | + | 0.959710i | \(0.590664\pi\) | |||||||
\(272\) | 0.123106 | 0.00746437 | ||||||||
\(273\) | 0.500000 | − | 3.57071i | 0.0302614 | − | 0.216109i | ||||
\(274\) | 12.4384 | 0.751434 | ||||||||
\(275\) | −3.28078 | − | 5.68247i | −0.197838 | − | 0.342666i | ||||
\(276\) | −0.561553 | − | 0.972638i | −0.0338015 | − | 0.0585459i | ||||
\(277\) | 9.78078 | − | 16.9408i | 0.587670 | − | 1.01787i | −0.406867 | − | 0.913487i | \(-0.633379\pi\) |
0.994537 | − | 0.104387i | \(-0.0332879\pi\) | |||||||
\(278\) | −5.43845 | −0.326176 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.780776 | + | 1.35234i | −0.0466603 | + | 0.0808180i | ||||
\(281\) | 12.9309 | 0.771391 | 0.385696 | − | 0.922626i | \(-0.373962\pi\) | ||||
0.385696 | + | 0.922626i | \(0.373962\pi\) | |||||||
\(282\) | −0.157671 | + | 0.273094i | −0.00938916 | + | 0.0162625i | ||||
\(283\) | 10.0000 | + | 17.3205i | 0.594438 | + | 1.02960i | 0.993626 | + | 0.112728i | \(0.0359589\pi\) |
−0.399188 | + | 0.916869i | \(0.630708\pi\) | |||||||
\(284\) | 5.68466 | + | 9.84612i | 0.337322 | + | 0.584260i | ||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 7.28078 | + | 5.68247i | 0.430521 | + | 0.336012i | ||||
\(287\) | −11.2462 | −0.663843 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.49242 | + | 14.7093i | 0.499554 | + | 0.865253i | ||||
\(290\) | 4.78078 | − | 8.28055i | 0.280737 | − | 0.486251i | ||||
\(291\) | 0.876894 | 0.0514045 | ||||||||
\(292\) | 1.21922 | − | 2.11176i | 0.0713497 | − | 0.123581i | ||||
\(293\) | 3.46543 | − | 6.00231i | 0.202453 | − | 0.350659i | −0.746865 | − | 0.664975i | \(-0.768442\pi\) |
0.949318 | + | 0.314317i | \(0.101775\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −4.00000 | + | 6.92820i | −0.232889 | + | 0.403376i | ||||
\(296\) | 1.21922 | + | 2.11176i | 0.0708659 | + | 0.122743i | ||||
\(297\) | −1.28078 | − | 2.21837i | −0.0743182 | − | 0.128723i | ||||
\(298\) | −15.5616 | −0.901457 | ||||||||
\(299\) | −3.75379 | + | 1.51883i | −0.217087 | + | 0.0878360i | ||||
\(300\) | 2.56155 | 0.147891 | ||||||||
\(301\) | 4.00000 | + | 6.92820i | 0.230556 | + | 0.399335i | ||||
\(302\) | 10.9654 | + | 18.9927i | 0.630990 | + | 1.09291i | ||||
\(303\) | −2.90388 | + | 5.02967i | −0.166824 | + | 0.288947i | ||||
\(304\) | −2.56155 | −0.146915 | ||||||||
\(305\) | 8.78078 | − | 15.2088i | 0.502786 | − | 0.870851i | ||||
\(306\) | −0.0615528 | + | 0.106613i | −0.00351874 | + | 0.00609464i | ||||
\(307\) | −9.93087 | −0.566785 | −0.283392 | − | 0.959004i | \(-0.591460\pi\) | ||||
−0.283392 | + | 0.959004i | \(0.591460\pi\) | |||||||
\(308\) | 1.28078 | − | 2.21837i | 0.0729790 | − | 0.126403i | ||||
\(309\) | 3.12311 | + | 5.40938i | 0.177667 | + | 0.307729i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.9309 | 1.24359 | 0.621793 | − | 0.783182i | \(-0.286405\pi\) | ||||
0.621793 | + | 0.783182i | \(0.286405\pi\) | |||||||
\(312\) | −3.34233 | + | 1.35234i | −0.189222 | + | 0.0765614i | ||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 0.657671 | + | 1.13912i | 0.0371145 | + | 0.0642842i | ||||
\(315\) | −0.780776 | − | 1.35234i | −0.0439918 | − | 0.0761960i | ||||
\(316\) | 3.28078 | − | 5.68247i | 0.184558 | − | 0.319664i | ||||
\(317\) | 12.4384 | 0.698613 | 0.349306 | − | 0.937009i | \(-0.386417\pi\) | ||||
0.349306 | + | 0.937009i | \(0.386417\pi\) | |||||||
\(318\) | 3.50000 | − | 6.06218i | 0.196270 | − | 0.339950i | ||||
\(319\) | −7.84233 | + | 13.5833i | −0.439086 | + | 0.760520i | ||||
\(320\) | 1.56155 | 0.0872935 | ||||||||
\(321\) | 6.96543 | − | 12.0645i | 0.388773 | − | 0.673374i | ||||
\(322\) | 0.561553 | + | 0.972638i | 0.0312941 | + | 0.0542030i | ||||
\(323\) | 0.157671 | + | 0.273094i | 0.00877304 | + | 0.0151953i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.28078 | − | 9.14657i | 0.0710447 | − | 0.507361i | ||||
\(326\) | 24.4924 | 1.35651 | ||||||||
\(327\) | −6.12311 | − | 10.6055i | −0.338609 | − | 0.586487i | ||||
\(328\) | 5.62311 | + | 9.73950i | 0.310484 | + | 0.537774i | ||||
\(329\) | 0.157671 | − | 0.273094i | 0.00869267 | − | 0.0150561i | ||||
\(330\) | 4.00000 | 0.220193 | ||||||||
\(331\) | −9.68466 | + | 16.7743i | −0.532317 | + | 0.922000i | 0.466971 | + | 0.884273i | \(0.345345\pi\) |
−0.999288 | + | 0.0377275i | \(0.987988\pi\) | |||||||
\(332\) | 2.56155 | − | 4.43674i | 0.140583 | − | 0.243498i | ||||
\(333\) | −2.43845 | −0.133626 | ||||||||
\(334\) | −6.24621 | + | 10.8188i | −0.341777 | + | 0.591976i | ||||
\(335\) | −7.12311 | − | 12.3376i | −0.389177 | − | 0.674074i | ||||
\(336\) | 0.500000 | + | 0.866025i | 0.0272772 | + | 0.0472456i | ||||
\(337\) | −13.4924 | −0.734979 | −0.367490 | − | 0.930028i | \(-0.619783\pi\) | ||||
−0.367490 | + | 0.930028i | \(0.619783\pi\) | |||||||
\(338\) | 3.15767 | + | 12.6107i | 0.171755 | + | 0.685930i | ||||
\(339\) | −1.56155 | −0.0848119 | ||||||||
\(340\) | −0.0961180 | − | 0.166481i | −0.00521273 | − | 0.00902871i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.28078 | − | 2.21837i | 0.0692565 | − | 0.119956i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.00000 | − | 6.92820i | 0.215666 | − | 0.373544i | ||||
\(345\) | −0.876894 | + | 1.51883i | −0.0472104 | + | 0.0817708i | ||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | −7.52699 | + | 13.0371i | −0.404070 | + | 0.699870i | −0.994213 | − | 0.107429i | \(-0.965738\pi\) |
0.590143 | + | 0.807299i | \(0.299071\pi\) | |||||||
\(348\) | −3.06155 | − | 5.30277i | −0.164116 | − | 0.284258i | ||||
\(349\) | 9.00000 | + | 15.5885i | 0.481759 | + | 0.834431i | 0.999781 | − | 0.0209364i | \(-0.00666475\pi\) |
−0.518022 | + | 0.855367i | \(0.673331\pi\) | |||||||
\(350\) | −2.56155 | −0.136921 | ||||||||
\(351\) | 0.500000 | − | 3.57071i | 0.0266880 | − | 0.190591i | ||||
\(352\) | −2.56155 | −0.136531 | ||||||||
\(353\) | 16.9039 | + | 29.2784i | 0.899703 | + | 1.55833i | 0.827874 | + | 0.560914i | \(0.189550\pi\) |
0.0718288 | + | 0.997417i | \(0.477116\pi\) | |||||||
\(354\) | 2.56155 | + | 4.43674i | 0.136145 | + | 0.235810i | ||||
\(355\) | 8.87689 | − | 15.3752i | 0.471137 | − | 0.816033i | ||||
\(356\) | 3.43845 | 0.182237 | ||||||||
\(357\) | 0.0615528 | − | 0.106613i | 0.00325772 | − | 0.00564254i | ||||
\(358\) | 0.876894 | − | 1.51883i | 0.0463453 | − | 0.0802724i | ||||
\(359\) | −1.75379 | −0.0925614 | −0.0462807 | − | 0.998928i | \(-0.514737\pi\) | ||||
−0.0462807 | + | 0.998928i | \(0.514737\pi\) | |||||||
\(360\) | −0.780776 | + | 1.35234i | −0.0411505 | + | 0.0712748i | ||||
\(361\) | 6.21922 | + | 10.7720i | 0.327328 | + | 0.566948i | ||||
\(362\) | −6.62311 | − | 11.4716i | −0.348103 | − | 0.602932i | ||||
\(363\) | 4.43845 | 0.232958 | ||||||||
\(364\) | 3.34233 | − | 1.35234i | 0.175186 | − | 0.0708821i | ||||
\(365\) | −3.80776 | −0.199307 | ||||||||
\(366\) | −5.62311 | − | 9.73950i | −0.293924 | − | 0.509092i | ||||
\(367\) | −6.80776 | − | 11.7914i | −0.355362 | − | 0.615506i | 0.631818 | − | 0.775117i | \(-0.282309\pi\) |
−0.987180 | + | 0.159611i | \(0.948976\pi\) | |||||||
\(368\) | 0.561553 | − | 0.972638i | 0.0292730 | − | 0.0507023i | ||||
\(369\) | −11.2462 | −0.585454 | ||||||||
\(370\) | 1.90388 | − | 3.29762i | 0.0989781 | − | 0.171435i | ||||
\(371\) | −3.50000 | + | 6.06218i | −0.181711 | + | 0.314733i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.53457 | − | 2.65794i | 0.0794568 | − | 0.137623i | −0.823559 | − | 0.567231i | \(-0.808015\pi\) |
0.903016 | + | 0.429608i | \(0.141348\pi\) | |||||||
\(374\) | 0.157671 | + | 0.273094i | 0.00815296 | + | 0.0141213i | ||||
\(375\) | −5.90388 | − | 10.2258i | −0.304875 | − | 0.528059i | ||||
\(376\) | −0.315342 | −0.0162625 | ||||||||
\(377\) | −20.4654 | + | 8.28055i | −1.05402 | + | 0.426470i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −18.8078 | − | 32.5760i | −0.966090 | − | 1.67332i | −0.706658 | − | 0.707556i | \(-0.749798\pi\) |
−0.259432 | − | 0.965761i | \(-0.583535\pi\) | |||||||
\(380\) | 2.00000 | + | 3.46410i | 0.102598 | + | 0.177705i | ||||
\(381\) | 6.24621 | − | 10.8188i | 0.320003 | − | 0.554262i | ||||
\(382\) | −5.12311 | −0.262121 | ||||||||
\(383\) | 6.40388 | − | 11.0918i | 0.327223 | − | 0.566767i | −0.654737 | − | 0.755857i | \(-0.727220\pi\) |
0.981960 | + | 0.189090i | \(0.0605538\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | −0.0615528 | + | 0.106613i | −0.00313296 | + | 0.00542644i | ||||
\(387\) | 4.00000 | + | 6.92820i | 0.203331 | + | 0.352180i | ||||
\(388\) | 0.438447 | + | 0.759413i | 0.0222588 | + | 0.0385533i | ||||
\(389\) | −5.31534 | −0.269499 | −0.134749 | − | 0.990880i | \(-0.543023\pi\) | ||||
−0.134749 | + | 0.990880i | \(0.543023\pi\) | |||||||
\(390\) | 4.43845 | + | 3.46410i | 0.224750 | + | 0.175412i | ||||
\(391\) | −0.138261 | −0.00699214 | ||||||||
\(392\) | −0.500000 | − | 0.866025i | −0.0252538 | − | 0.0437409i | ||||
\(393\) | 7.12311 | + | 12.3376i | 0.359313 | + | 0.622349i | ||||
\(394\) | −6.28078 | + | 10.8786i | −0.316421 | + | 0.548057i | ||||
\(395\) | −10.2462 | −0.515543 | ||||||||
\(396\) | 1.28078 | − | 2.21837i | 0.0643614 | − | 0.111477i | ||||
\(397\) | −13.9654 | + | 24.1888i | −0.700905 | + | 1.21400i | 0.267244 | + | 0.963629i | \(0.413887\pi\) |
−0.968149 | + | 0.250374i | \(0.919446\pi\) | |||||||
\(398\) | −16.0000 | −0.802008 | ||||||||
\(399\) | −1.28078 | + | 2.21837i | −0.0641190 | + | 0.111057i | ||||
\(400\) | 1.28078 | + | 2.21837i | 0.0640388 | + | 0.110918i | ||||
\(401\) | 0.903882 | + | 1.56557i | 0.0451377 | + | 0.0781808i | 0.887712 | − | 0.460400i | \(-0.152294\pi\) |
−0.842574 | + | 0.538581i | \(0.818961\pi\) | |||||||
\(402\) | −9.12311 | −0.455019 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.80776 | −0.288947 | ||||||||
\(405\) | −0.780776 | − | 1.35234i | −0.0387971 | − | 0.0671985i | ||||
\(406\) | 3.06155 | + | 5.30277i | 0.151942 | + | 0.263172i | ||||
\(407\) | −3.12311 | + | 5.40938i | −0.154807 | + | 0.268133i | ||||
\(408\) | −0.123106 | −0.00609464 | ||||||||
\(409\) | 5.78078 | − | 10.0126i | 0.285841 | − | 0.495091i | −0.686972 | − | 0.726684i | \(-0.741060\pi\) |
0.972813 | + | 0.231593i | \(0.0743937\pi\) | |||||||
\(410\) | 8.78078 | − | 15.2088i | 0.433652 | − | 0.751107i | ||||
\(411\) | −12.4384 | −0.613543 | ||||||||
\(412\) | −3.12311 | + | 5.40938i | −0.153864 | + | 0.266501i | ||||
\(413\) | −2.56155 | − | 4.43674i | −0.126046 | − | 0.218318i | ||||
\(414\) | 0.561553 | + | 0.972638i | 0.0275988 | + | 0.0478025i | ||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | −2.84233 | − | 2.21837i | −0.139357 | − | 0.108765i | ||||
\(417\) | 5.43845 | 0.266322 | ||||||||
\(418\) | −3.28078 | − | 5.68247i | −0.160468 | − | 0.277939i | ||||
\(419\) | −11.6847 | − | 20.2384i | −0.570833 | − | 0.988712i | −0.996481 | − | 0.0838227i | \(-0.973287\pi\) |
0.425648 | − | 0.904889i | \(-0.360046\pi\) | |||||||
\(420\) | 0.780776 | − | 1.35234i | 0.0380980 | − | 0.0659877i | ||||
\(421\) | −22.3002 | −1.08684 | −0.543422 | − | 0.839459i | \(-0.682872\pi\) | ||||
−0.543422 | + | 0.839459i | \(0.682872\pi\) | |||||||
\(422\) | −2.56155 | + | 4.43674i | −0.124694 | + | 0.215977i | ||||
\(423\) | 0.157671 | − | 0.273094i | 0.00766622 | − | 0.0132783i | ||||
\(424\) | 7.00000 | 0.339950 | ||||||||
\(425\) | 0.157671 | − | 0.273094i | 0.00764816 | − | 0.0132470i | ||||
\(426\) | −5.68466 | − | 9.84612i | −0.275423 | − | 0.477046i | ||||
\(427\) | 5.62311 | + | 9.73950i | 0.272121 | + | 0.471328i | ||||
\(428\) | 13.9309 | 0.673374 | ||||||||
\(429\) | −7.28078 | − | 5.68247i | −0.351519 | − | 0.274352i | ||||
\(430\) | −12.4924 | −0.602438 | ||||||||
\(431\) | −9.68466 | − | 16.7743i | −0.466494 | − | 0.807991i | 0.532774 | − | 0.846258i | \(-0.321150\pi\) |
−0.999268 | + | 0.0382670i | \(0.987816\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 10.6577 | − | 18.4596i | 0.512175 | − | 0.887113i | −0.487725 | − | 0.872997i | \(-0.662173\pi\) |
0.999900 | − | 0.0141160i | \(-0.00449340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.78078 | + | 8.28055i | −0.229221 | + | 0.397022i | ||||
\(436\) | 6.12311 | − | 10.6055i | 0.293244 | − | 0.507913i | ||||
\(437\) | 2.87689 | 0.137621 | ||||||||
\(438\) | −1.21922 | + | 2.11176i | −0.0582568 | + | 0.100904i | ||||
\(439\) | 13.1231 | + | 22.7299i | 0.626332 | + | 1.08484i | 0.988282 | + | 0.152641i | \(0.0487777\pi\) |
−0.361950 | + | 0.932197i | \(0.617889\pi\) | |||||||
\(440\) | 2.00000 | + | 3.46410i | 0.0953463 | + | 0.165145i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.0615528 | + | 0.439575i | −0.00292777 | + | 0.0209085i | ||||
\(443\) | −27.0540 | −1.28537 | −0.642687 | − | 0.766129i | \(-0.722180\pi\) | ||||
−0.642687 | + | 0.766129i | \(0.722180\pi\) | |||||||
\(444\) | −1.21922 | − | 2.11176i | −0.0578618 | − | 0.100220i | ||||
\(445\) | −2.68466 | − | 4.64996i | −0.127265 | − | 0.220429i | ||||
\(446\) | −4.87689 | + | 8.44703i | −0.230928 | + | 0.399978i | ||||
\(447\) | 15.5616 | 0.736036 | ||||||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | 3.31534 | − | 5.74234i | 0.156461 | − | 0.270998i | −0.777129 | − | 0.629341i | \(-0.783325\pi\) |
0.933590 | + | 0.358343i | \(0.116658\pi\) | |||||||
\(450\) | −2.56155 | −0.120753 | ||||||||
\(451\) | −14.4039 | + | 24.9483i | −0.678252 | + | 1.17477i | ||||
\(452\) | −0.780776 | − | 1.35234i | −0.0367246 | − | 0.0636089i | ||||
\(453\) | −10.9654 | − | 18.9927i | −0.515201 | − | 0.892354i | ||||
\(454\) | −10.8769 | −0.510478 | ||||||||
\(455\) | −4.43845 | − | 3.46410i | −0.208078 | − | 0.162400i | ||||
\(456\) | 2.56155 | 0.119956 | ||||||||
\(457\) | −14.4654 | − | 25.0549i | −0.676665 | − | 1.17202i | −0.975979 | − | 0.217863i | \(-0.930091\pi\) |
0.299315 | − | 0.954154i | \(-0.403242\pi\) | |||||||
\(458\) | −8.52699 | − | 14.7692i | −0.398440 | − | 0.690118i | ||||
\(459\) | 0.0615528 | − | 0.106613i | 0.00287304 | − | 0.00497625i | ||||
\(460\) | −1.75379 | −0.0817708 | ||||||||
\(461\) | −3.02699 | + | 5.24290i | −0.140981 | + | 0.244186i | −0.927866 | − | 0.372913i | \(-0.878359\pi\) |
0.786885 | + | 0.617099i | \(0.211692\pi\) | |||||||
\(462\) | −1.28078 | + | 2.21837i | −0.0595871 | + | 0.103208i | ||||
\(463\) | 12.3153 | 0.572342 | 0.286171 | − | 0.958178i | \(-0.407617\pi\) | ||||
0.286171 | + | 0.958178i | \(0.407617\pi\) | |||||||
\(464\) | 3.06155 | − | 5.30277i | 0.142129 | − | 0.246175i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.684658 | − | 1.18586i | −0.0317162 | − | 0.0549341i | ||||
\(467\) | −36.9848 | −1.71145 | −0.855727 | − | 0.517427i | \(-0.826890\pi\) | ||||
−0.855727 | + | 0.517427i | \(0.826890\pi\) | |||||||
\(468\) | 3.34233 | − | 1.35234i | 0.154499 | − | 0.0625121i | ||||
\(469\) | 9.12311 | 0.421266 | ||||||||
\(470\) | 0.246211 | + | 0.426450i | 0.0113569 | + | 0.0196707i | ||||
\(471\) | −0.657671 | − | 1.13912i | −0.0303039 | − | 0.0524878i | ||||
\(472\) | −2.56155 | + | 4.43674i | −0.117905 | + | 0.204217i | ||||
\(473\) | 20.4924 | 0.942243 | ||||||||
\(474\) | −3.28078 | + | 5.68247i | −0.150691 | + | 0.261005i | ||||
\(475\) | −3.28078 | + | 5.68247i | −0.150532 | + | 0.260730i | ||||
\(476\) | 0.123106 | 0.00564254 | ||||||||
\(477\) | −3.50000 | + | 6.06218i | −0.160254 | + | 0.277568i | ||||
\(478\) | −9.68466 | − | 16.7743i | −0.442966 | − | 0.767240i | ||||
\(479\) | 0.965435 | + | 1.67218i | 0.0441118 | + | 0.0764040i | 0.887238 | − | 0.461311i | \(-0.152621\pi\) |
−0.843126 | + | 0.537715i | \(0.819288\pi\) | |||||||
\(480\) | −1.56155 | −0.0712748 | ||||||||
\(481\) | −8.15009 | + | 3.29762i | −0.371612 | + | 0.150359i | ||||
\(482\) | −0.192236 | −0.00875611 | ||||||||
\(483\) | −0.561553 | − | 0.972638i | −0.0255515 | − | 0.0442566i | ||||
\(484\) | 2.21922 | + | 3.84381i | 0.100874 | + | 0.174719i | ||||
\(485\) | 0.684658 | − | 1.18586i | 0.0310887 | − | 0.0538473i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −11.8423 | + | 20.5115i | −0.536627 | + | 0.929466i | 0.462456 | + | 0.886642i | \(0.346968\pi\) |
−0.999083 | + | 0.0428230i | \(0.986365\pi\) | |||||||
\(488\) | 5.62311 | − | 9.73950i | 0.254546 | − | 0.440887i | ||||
\(489\) | −24.4924 | −1.10759 | ||||||||
\(490\) | −0.780776 | + | 1.35234i | −0.0352719 | + | 0.0610927i | ||||
\(491\) | 8.24621 | + | 14.2829i | 0.372146 | + | 0.644576i | 0.989895 | − | 0.141799i | \(-0.0452886\pi\) |
−0.617749 | + | 0.786375i | \(0.711955\pi\) | |||||||
\(492\) | −5.62311 | − | 9.73950i | −0.253509 | − | 0.439091i | ||||
\(493\) | −0.753789 | −0.0339489 | ||||||||
\(494\) | 1.28078 | − | 9.14657i | 0.0576249 | − | 0.411524i | ||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.68466 | + | 9.84612i | 0.254992 | + | 0.441659i | ||||
\(498\) | −2.56155 | + | 4.43674i | −0.114786 | + | 0.198815i | ||||
\(499\) | 30.2462 | 1.35401 | 0.677003 | − | 0.735980i | \(-0.263278\pi\) | ||||
0.677003 | + | 0.735980i | \(0.263278\pi\) | |||||||
\(500\) | 5.90388 | − | 10.2258i | 0.264030 | − | 0.457313i | ||||
\(501\) | 6.24621 | − | 10.8188i | 0.279060 | − | 0.483346i | ||||
\(502\) | −13.6155 | −0.607691 | ||||||||
\(503\) | 14.2462 | − | 24.6752i | 0.635207 | − | 1.10021i | −0.351264 | − | 0.936276i | \(-0.614248\pi\) |
0.986471 | − | 0.163935i | \(-0.0524186\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | 4.53457 | + | 7.85410i | 0.201786 | + | 0.349503i | ||||
\(506\) | 2.87689 | 0.127894 | ||||||||
\(507\) | −3.15767 | − | 12.6107i | −0.140237 | − | 0.560060i | ||||
\(508\) | 12.4924 | 0.554262 | ||||||||
\(509\) | 20.9039 | + | 36.2066i | 0.926548 | + | 1.60483i | 0.789052 | + | 0.614326i | \(0.210572\pi\) |
0.137496 | + | 0.990502i | \(0.456094\pi\) | |||||||
\(510\) | 0.0961180 | + | 0.166481i | 0.00425618 | + | 0.00737191i | ||||
\(511\) | 1.21922 | − | 2.11176i | 0.0539353 | − | 0.0934186i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.28078 | + | 2.21837i | −0.0565477 | + | 0.0979434i | ||||
\(514\) | 12.1847 | − | 21.1044i | 0.537442 | − | 0.930877i | ||||
\(515\) | 9.75379 | 0.429803 | ||||||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | −0.403882 | − | 0.699544i | −0.0177627 | − | 0.0307659i | ||||
\(518\) | 1.21922 | + | 2.11176i | 0.0535696 | + | 0.0927853i | ||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | −0.780776 | + | 5.57586i | −0.0342393 | + | 0.244518i | ||||
\(521\) | 25.8769 | 1.13369 | 0.566844 | − | 0.823825i | \(-0.308164\pi\) | ||||
0.566844 | + | 0.823825i | \(0.308164\pi\) | |||||||
\(522\) | 3.06155 | + | 5.30277i | 0.134001 | + | 0.232096i | ||||
\(523\) | 8.40388 | + | 14.5560i | 0.367476 | + | 0.636487i | 0.989170 | − | 0.146773i | \(-0.0468886\pi\) |
−0.621694 | + | 0.783260i | \(0.713555\pi\) | |||||||
\(524\) | −7.12311 | + | 12.3376i | −0.311174 | + | 0.538970i | ||||
\(525\) | 2.56155 | 0.111795 | ||||||||
\(526\) | −2.56155 | + | 4.43674i | −0.111689 | + | 0.193451i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.56155 | 0.111477 | ||||||||
\(529\) | 10.8693 | − | 18.8262i | 0.472579 | − | 0.818531i | ||||
\(530\) | −5.46543 | − | 9.46641i | −0.237403 | − | 0.411195i | ||||
\(531\) | −2.56155 | − | 4.43674i | −0.111162 | − | 0.192538i | ||||
\(532\) | −2.56155 | −0.111057 | ||||||||
\(533\) | −37.5885 | + | 15.2088i | −1.62814 | + | 0.658764i | ||||
\(534\) | −3.43845 | −0.148796 | ||||||||
\(535\) | −10.8769 | − | 18.8393i | −0.470249 | − | 0.814495i | ||||
\(536\) | −4.56155 | − | 7.90084i | −0.197029 | − | 0.341264i | ||||
\(537\) | −0.876894 | + | 1.51883i | −0.0378408 | + | 0.0655422i | ||||
\(538\) | 27.1231 | 1.16936 | ||||||||
\(539\) | 1.28078 | − | 2.21837i | 0.0551669 | − | 0.0955520i | ||||
\(540\) | 0.780776 | − | 1.35234i | 0.0335993 | − | 0.0581956i | ||||
\(541\) | 19.1771 | 0.824487 | 0.412244 | − | 0.911074i | \(-0.364745\pi\) | ||||
0.412244 | + | 0.911074i | \(0.364745\pi\) | |||||||
\(542\) | 11.3693 | − | 19.6922i | 0.488354 | − | 0.845854i | ||||
\(543\) | 6.62311 | + | 11.4716i | 0.284225 | + | 0.492292i | ||||
\(544\) | −0.0615528 | − | 0.106613i | −0.00263906 | − | 0.00457098i | ||||
\(545\) | −19.1231 | −0.819144 | ||||||||
\(546\) | −3.34233 | + | 1.35234i | −0.143038 | + | 0.0578750i | ||||
\(547\) | −33.6155 | −1.43730 | −0.718648 | − | 0.695374i | \(-0.755239\pi\) | ||||
−0.718648 | + | 0.695374i | \(0.755239\pi\) | |||||||
\(548\) | −6.21922 | − | 10.7720i | −0.265672 | − | 0.460158i | ||||
\(549\) | 5.62311 | + | 9.73950i | 0.239988 | + | 0.415672i | ||||
\(550\) | −3.28078 | + | 5.68247i | −0.139893 | + | 0.242301i | ||||
\(551\) | 15.6847 | 0.668189 | ||||||||
\(552\) | −0.561553 | + | 0.972638i | −0.0239013 | + | 0.0413982i | ||||
\(553\) | 3.28078 | − | 5.68247i | 0.139513 | − | 0.241643i | ||||
\(554\) | −19.5616 | −0.831091 | ||||||||
\(555\) | −1.90388 | + | 3.29762i | −0.0808153 | + | 0.139976i | ||||
\(556\) | 2.71922 | + | 4.70983i | 0.115321 | + | 0.199741i | ||||
\(557\) | −6.06155 | − | 10.4989i | −0.256836 | − | 0.444853i | 0.708556 | − | 0.705654i | \(-0.249347\pi\) |
−0.965393 | + | 0.260801i | \(0.916013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.7386 | + | 17.7470i | 0.961742 | + | 0.750616i | ||||
\(560\) | 1.56155 | 0.0659877 | ||||||||
\(561\) | −0.157671 | − | 0.273094i | −0.00665687 | − | 0.0115300i | ||||
\(562\) | −6.46543 | − | 11.1985i | −0.272728 | − | 0.472379i | ||||
\(563\) | 2.87689 | − | 4.98293i | 0.121247 | − | 0.210005i | −0.799013 | − | 0.601314i | \(-0.794644\pi\) |
0.920260 | + | 0.391309i | \(0.127977\pi\) | |||||||
\(564\) | 0.315342 | 0.0132783 | ||||||||
\(565\) | −1.21922 | + | 2.11176i | −0.0512931 | + | 0.0888423i | ||||
\(566\) | 10.0000 | − | 17.3205i | 0.420331 | − | 0.728035i | ||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 5.68466 | − | 9.84612i | 0.238523 | − | 0.413134i | ||||
\(569\) | 11.0000 | + | 19.0526i | 0.461144 | + | 0.798725i | 0.999018 | − | 0.0443003i | \(-0.0141058\pi\) |
−0.537874 | + | 0.843025i | \(0.680772\pi\) | |||||||
\(570\) | −2.00000 | − | 3.46410i | −0.0837708 | − | 0.145095i | ||||
\(571\) | −21.1231 | −0.883974 | −0.441987 | − | 0.897021i | \(-0.645726\pi\) | ||||
−0.441987 | + | 0.897021i | \(0.645726\pi\) | |||||||
\(572\) | 1.28078 | − | 9.14657i | 0.0535520 | − | 0.382437i | ||||
\(573\) | 5.12311 | 0.214021 | ||||||||
\(574\) | 5.62311 | + | 9.73950i | 0.234704 | + | 0.406519i | ||||
\(575\) | −1.43845 | − | 2.49146i | −0.0599874 | − | 0.103901i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −35.5616 | −1.48045 | −0.740223 | − | 0.672361i | \(-0.765280\pi\) | ||||
−0.740223 | + | 0.672361i | \(0.765280\pi\) | |||||||
\(578\) | 8.49242 | − | 14.7093i | 0.353238 | − | 0.611827i | ||||
\(579\) | 0.0615528 | − | 0.106613i | 0.00255805 | − | 0.00443067i | ||||
\(580\) | −9.56155 | −0.397022 | ||||||||
\(581\) | 2.56155 | − | 4.43674i | 0.106271 | − | 0.184067i | ||||
\(582\) | −0.438447 | − | 0.759413i | −0.0181742 | − | 0.0314787i | ||||
\(583\) | 8.96543 | + | 15.5286i | 0.371310 | + | 0.643128i | ||||
\(584\) | −2.43845 | −0.100904 | ||||||||
\(585\) | −4.43845 | − | 3.46410i | −0.183507 | − | 0.143223i | ||||
\(586\) | −6.93087 | −0.286312 | ||||||||
\(587\) | −1.12311 | − | 1.94528i | −0.0463555 | − | 0.0802901i | 0.841917 | − | 0.539608i | \(-0.181427\pi\) |
−0.888272 | + | 0.459317i | \(0.848094\pi\) | |||||||
\(588\) | 0.500000 | + | 0.866025i | 0.0206197 | + | 0.0357143i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 8.00000 | 0.329355 | ||||||||
\(591\) | 6.28078 | − | 10.8786i | 0.258357 | − | 0.447487i | ||||
\(592\) | 1.21922 | − | 2.11176i | 0.0501098 | − | 0.0867927i | ||||
\(593\) | −33.9848 | −1.39559 | −0.697795 | − | 0.716297i | \(-0.745835\pi\) | ||||
−0.697795 | + | 0.716297i | \(0.745835\pi\) | |||||||
\(594\) | −1.28078 | + | 2.21837i | −0.0525509 | + | 0.0910208i | ||||
\(595\) | −0.0961180 | − | 0.166481i | −0.00394045 | − | 0.00682506i | ||||
\(596\) | 7.78078 | + | 13.4767i | 0.318713 | + | 0.552027i | ||||
\(597\) | 16.0000 | 0.654836 | ||||||||
\(598\) | 3.19224 | + | 2.49146i | 0.130540 | + | 0.101884i | ||||
\(599\) | 23.8617 | 0.974964 | 0.487482 | − | 0.873133i | \(-0.337915\pi\) | ||||
0.487482 | + | 0.873133i | \(0.337915\pi\) | |||||||
\(600\) | −1.28078 | − | 2.21837i | −0.0522875 | − | 0.0905646i | ||||
\(601\) | −14.1501 | − | 24.5087i | −0.577194 | − | 0.999730i | −0.995799 | − | 0.0915616i | \(-0.970814\pi\) |
0.418605 | − | 0.908168i | \(-0.362519\pi\) | |||||||
\(602\) | 4.00000 | − | 6.92820i | 0.163028 | − | 0.282372i | ||||
\(603\) | 9.12311 | 0.371522 | ||||||||
\(604\) | 10.9654 | − | 18.9927i | 0.446177 | − | 0.772802i | ||||
\(605\) | 3.46543 | − | 6.00231i | 0.140890 | − | 0.244029i | ||||
\(606\) | 5.80776 | 0.235924 | ||||||||
\(607\) | 24.4924 | − | 42.4221i | 0.994117 | − | 1.72186i | 0.403256 | − | 0.915087i | \(-0.367878\pi\) |
0.590861 | − | 0.806774i | \(-0.298788\pi\) | |||||||
\(608\) | 1.28078 | + | 2.21837i | 0.0519423 | + | 0.0899668i | ||||
\(609\) | −3.06155 | − | 5.30277i | −0.124060 | − | 0.214879i | ||||
\(610\) | −17.5616 | −0.711046 | ||||||||
\(611\) | 0.157671 | − | 1.12599i | 0.00637868 | − | 0.0455529i | ||||
\(612\) | 0.123106 | 0.00497625 | ||||||||
\(613\) | −10.7808 | − | 18.6729i | −0.435431 | − | 0.754189i | 0.561899 | − | 0.827206i | \(-0.310071\pi\) |
−0.997331 | + | 0.0730162i | \(0.976738\pi\) | |||||||
\(614\) | 4.96543 | + | 8.60039i | 0.200389 | + | 0.347083i | ||||
\(615\) | −8.78078 | + | 15.2088i | −0.354075 | + | 0.613276i | ||||
\(616\) | −2.56155 | −0.103208 | ||||||||
\(617\) | −11.5885 | + | 20.0719i | −0.466537 | + | 0.808066i | −0.999269 | − | 0.0382179i | \(-0.987832\pi\) |
0.532732 | + | 0.846284i | \(0.321165\pi\) | |||||||
\(618\) | 3.12311 | − | 5.40938i | 0.125630 | − | 0.217597i | ||||
\(619\) | 2.06913 | 0.0831654 | 0.0415827 | − | 0.999135i | \(-0.486760\pi\) | ||||
0.0415827 | + | 0.999135i | \(0.486760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.561553 | − | 0.972638i | −0.0225343 | − | 0.0390306i | ||||
\(622\) | −10.9654 | − | 18.9927i | −0.439674 | − | 0.761537i | ||||
\(623\) | 3.43845 | 0.137758 | ||||||||
\(624\) | 2.84233 | + | 2.21837i | 0.113784 | + | 0.0888059i | ||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | 3.00000 | + | 5.19615i | 0.119904 | + | 0.207680i | ||||
\(627\) | 3.28078 | + | 5.68247i | 0.131022 | + | 0.226936i | ||||
\(628\) | 0.657671 | − | 1.13912i | 0.0262439 | − | 0.0454558i | ||||
\(629\) | −0.300187 | −0.0119692 | ||||||||
\(630\) | −0.780776 | + | 1.35234i | −0.0311069 | + | 0.0538787i | ||||
\(631\) | 5.03457 | − | 8.72012i | 0.200423 | − | 0.347143i | −0.748242 | − | 0.663426i | \(-0.769102\pi\) |
0.948665 | + | 0.316283i | \(0.102435\pi\) | |||||||
\(632\) | −6.56155 | −0.261005 | ||||||||
\(633\) | 2.56155 | − | 4.43674i | 0.101813 | − | 0.176345i | ||||
\(634\) | −6.21922 | − | 10.7720i | −0.246997 | − | 0.427811i | ||||
\(635\) | −9.75379 | − | 16.8941i | −0.387067 | − | 0.670420i | ||||
\(636\) | −7.00000 | −0.277568 | ||||||||
\(637\) | 3.34233 | − | 1.35234i | 0.132428 | − | 0.0535818i | ||||
\(638\) | 15.6847 | 0.620962 | ||||||||
\(639\) | 5.68466 | + | 9.84612i | 0.224882 | + | 0.389506i | ||||
\(640\) | −0.780776 | − | 1.35234i | −0.0308629 | − | 0.0534561i | ||||
\(641\) | −4.21922 | + | 7.30791i | −0.166649 | + | 0.288645i | −0.937240 | − | 0.348686i | \(-0.886628\pi\) |
0.770590 | + | 0.637331i | \(0.219961\pi\) | |||||||
\(642\) | −13.9309 | −0.549808 | ||||||||
\(643\) | −23.8423 | + | 41.2961i | −0.940250 | + | 1.62856i | −0.175256 | + | 0.984523i | \(0.556075\pi\) |
−0.764994 | + | 0.644037i | \(0.777258\pi\) | |||||||
\(644\) | 0.561553 | − | 0.972638i | 0.0221283 | − | 0.0383273i | ||||
\(645\) | 12.4924 | 0.491889 | ||||||||
\(646\) | 0.157671 | − | 0.273094i | 0.00620347 | − | 0.0107447i | ||||
\(647\) | 4.47301 | + | 7.74748i | 0.175852 | + | 0.304585i | 0.940456 | − | 0.339916i | \(-0.110399\pi\) |
−0.764604 | + | 0.644501i | \(0.777065\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −13.1231 | −0.515127 | ||||||||
\(650\) | −8.56155 | + | 3.46410i | −0.335812 | + | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.2462 | − | 21.2111i | −0.479599 | − | 0.830689i | ||||
\(653\) | −10.2808 | − | 17.8068i | −0.402318 | − | 0.696835i | 0.591687 | − | 0.806168i | \(-0.298462\pi\) |
−0.994005 | + | 0.109333i | \(0.965129\pi\) | |||||||
\(654\) | −6.12311 | + | 10.6055i | −0.239432 | + | 0.414709i | ||||
\(655\) | 22.2462 | 0.869231 | ||||||||
\(656\) | 5.62311 | − | 9.73950i | 0.219545 | − | 0.380264i | ||||
\(657\) | 1.21922 | − | 2.11176i | 0.0475664 | − | 0.0823875i | ||||
\(658\) | −0.315342 | −0.0122933 | ||||||||
\(659\) | −1.03457 | + | 1.79192i | −0.0403009 | + | 0.0698033i | −0.885472 | − | 0.464692i | \(-0.846165\pi\) |
0.845171 | + | 0.534495i | \(0.179498\pi\) | |||||||
\(660\) | −2.00000 | − | 3.46410i | −0.0778499 | − | 0.134840i | ||||
\(661\) | 10.0270 | + | 17.3673i | 0.390005 | + | 0.675508i | 0.992450 | − | 0.122653i | \(-0.0391401\pi\) |
−0.602445 | + | 0.798160i | \(0.705807\pi\) | |||||||
\(662\) | 19.3693 | 0.752810 | ||||||||
\(663\) | 0.0615528 | − | 0.439575i | 0.00239051 | − | 0.0170717i | ||||
\(664\) | −5.12311 | −0.198815 | ||||||||
\(665\) | 2.00000 | + | 3.46410i | 0.0775567 | + | 0.134332i | ||||
\(666\) | 1.21922 | + | 2.11176i | 0.0472440 | + | 0.0818289i | ||||
\(667\) | −3.43845 | + | 5.95557i | −0.133137 | + | 0.230600i | ||||
\(668\) | 12.4924 | 0.483346 | ||||||||
\(669\) | 4.87689 | − | 8.44703i | 0.188552 | − | 0.326581i | ||||
\(670\) | −7.12311 | + | 12.3376i | −0.275190 | + | 0.476642i | ||||
\(671\) | 28.8078 | 1.11211 | ||||||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | 1.37689 | + | 2.38485i | 0.0530754 | + | 0.0919293i | 0.891342 | − | 0.453331i | \(-0.149764\pi\) |
−0.838267 | + | 0.545260i | \(0.816431\pi\) | |||||||
\(674\) | 6.74621 | + | 11.6848i | 0.259854 | + | 0.450081i | ||||
\(675\) | 2.56155 | 0.0985942 | ||||||||
\(676\) | 9.34233 | − | 9.03996i | 0.359320 | − | 0.347691i | ||||
\(677\) | −24.7386 | −0.950783 | −0.475391 | − | 0.879774i | \(-0.657694\pi\) | ||||
−0.475391 | + | 0.879774i | \(0.657694\pi\) | |||||||
\(678\) | 0.780776 | + | 1.35234i | 0.0299855 | + | 0.0519365i | ||||
\(679\) | 0.438447 | + | 0.759413i | 0.0168261 | + | 0.0291436i | ||||
\(680\) | −0.0961180 | + | 0.166481i | −0.00368596 | + | 0.00638426i | ||||
\(681\) | 10.8769 | 0.416803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.2462 | + | 35.0675i | −0.774700 | + | 1.34182i | 0.160263 | + | 0.987074i | \(0.448766\pi\) |
−0.934963 | + | 0.354745i | \(0.884568\pi\) | |||||||
\(684\) | −2.56155 | −0.0979434 | ||||||||
\(685\) | −9.71165 | + | 16.8211i | −0.371063 | + | 0.642700i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | 8.52699 | + | 14.7692i | 0.325325 | + | 0.563479i | ||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | −3.50000 | + | 24.9950i | −0.133339 | + | 0.952234i | ||||
\(690\) | 1.75379 | 0.0667656 | ||||||||
\(691\) | 16.4924 | + | 28.5657i | 0.627401 | + | 1.08669i | 0.988071 | + | 0.153997i | \(0.0492148\pi\) |
−0.360670 | + | 0.932694i | \(0.617452\pi\) | |||||||
\(692\) | 9.00000 | + | 15.5885i | 0.342129 | + | 0.592584i | ||||
\(693\) | 1.28078 | − | 2.21837i | 0.0486527 | − | 0.0842689i | ||||
\(694\) | 15.0540 | 0.571441 | ||||||||
\(695\) | 4.24621 | − | 7.35465i | 0.161068 | − | 0.278978i | ||||
\(696\) | −3.06155 | + | 5.30277i | −0.116048 | + | 0.201001i | ||||
\(697\) | −1.38447 | −0.0524406 | ||||||||
\(698\) | 9.00000 | − | 15.5885i | 0.340655 | − | 0.590032i | ||||
\(699\) | 0.684658 | + | 1.18586i | 0.0258962 | + | 0.0448535i | ||||
\(700\) | 1.28078 | + | 2.21837i | 0.0484088 | + | 0.0838465i | ||||
\(701\) | −39.3002 | −1.48435 | −0.742174 | − | 0.670207i | \(-0.766205\pi\) | ||||
−0.742174 | + | 0.670207i | \(0.766205\pi\) | |||||||
\(702\) | −3.34233 | + | 1.35234i | −0.126148 | + | 0.0510410i | ||||
\(703\) | 6.24621 | 0.235580 | ||||||||
\(704\) | 1.28078 | + | 2.21837i | 0.0482711 | + | 0.0836080i | ||||
\(705\) | −0.246211 | − | 0.426450i | −0.00927285 | − | 0.0160611i | ||||
\(706\) | 16.9039 | − | 29.2784i | 0.636186 | − | 1.10191i | ||||
\(707\) | −5.80776 | −0.218423 | ||||||||
\(708\) | 2.56155 | − | 4.43674i | 0.0962690 | − | 0.166743i | ||||
\(709\) | 19.1501 | − | 33.1689i | 0.719197 | − | 1.24569i | −0.242122 | − | 0.970246i | \(-0.577843\pi\) |
0.961318 | − | 0.275440i | \(-0.0888234\pi\) | |||||||
\(710\) | −17.7538 | −0.666288 | ||||||||
\(711\) | 3.28078 | − | 5.68247i | 0.123039 | − | 0.213109i | ||||
\(712\) | −1.71922 | − | 2.97778i | −0.0644306 | − | 0.111597i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −0.123106 | −0.00460711 | ||||||||
\(715\) | −13.3693 | + | 5.40938i | −0.499984 | + | 0.202299i | ||||
\(716\) | −1.75379 | −0.0655422 | ||||||||
\(717\) | 9.68466 | + | 16.7743i | 0.361680 | + | 0.626448i | ||||
\(718\) | 0.876894 | + | 1.51883i | 0.0327254 | + | 0.0566821i | ||||
\(719\) | −0.403882 | + | 0.699544i | −0.0150623 | + | 0.0260886i | −0.873458 | − | 0.486899i | \(-0.838128\pi\) |
0.858396 | + | 0.512988i | \(0.171461\pi\) | |||||||
\(720\) | 1.56155 | 0.0581956 | ||||||||
\(721\) | −3.12311 | + | 5.40938i | −0.116311 | + | 0.201456i | ||||
\(722\) | 6.21922 | − | 10.7720i | 0.231456 | − | 0.400893i | ||||
\(723\) | 0.192236 | 0.00714933 | ||||||||
\(724\) | −6.62311 | + | 11.4716i | −0.246146 | + | 0.426337i | ||||
\(725\) | −7.84233 | − | 13.5833i | −0.291257 | − | 0.504472i | ||||
\(726\) | −2.21922 | − | 3.84381i | −0.0823631 | − | 0.142657i | ||||
\(727\) | 40.0000 | 1.48352 | 0.741759 | − | 0.670667i | \(-0.233992\pi\) | ||||
0.741759 | + | 0.670667i | \(0.233992\pi\) | |||||||
\(728\) | −2.84233 | − | 2.21837i | −0.105344 | − | 0.0822183i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.90388 | + | 3.29762i | 0.0704658 | + | 0.122050i | ||||
\(731\) | 0.492423 | + | 0.852901i | 0.0182129 | + | 0.0315457i | ||||
\(732\) | −5.62311 | + | 9.73950i | −0.207836 | + | 0.359982i | ||||
\(733\) | −28.8617 | −1.06603 | −0.533016 | − | 0.846105i | \(-0.678942\pi\) | ||||
−0.533016 | + | 0.846105i | \(0.678942\pi\) | |||||||
\(734\) | −6.80776 | + | 11.7914i | −0.251279 | + | 0.435228i | ||||
\(735\) | 0.780776 | − | 1.35234i | 0.0287994 | − | 0.0498820i | ||||
\(736\) | −1.12311 | −0.0413982 | ||||||||
\(737\) | 11.6847 | − | 20.2384i | 0.430410 | − | 0.745492i | ||||
\(738\) | 5.62311 | + | 9.73950i | 0.206989 | + | 0.358516i | ||||
\(739\) | −7.68466 | − | 13.3102i | −0.282685 | − | 0.489624i | 0.689360 | − | 0.724419i | \(-0.257892\pi\) |
−0.972045 | + | 0.234794i | \(0.924558\pi\) | |||||||
\(740\) | −3.80776 | −0.139976 | ||||||||
\(741\) | −1.28078 | + | 9.14657i | −0.0470505 | + | 0.336008i | ||||
\(742\) | 7.00000 | 0.256978 | ||||||||
\(743\) | 2.24621 | + | 3.89055i | 0.0824055 | + | 0.142731i | 0.904283 | − | 0.426934i | \(-0.140406\pi\) |
−0.821877 | + | 0.569665i | \(0.807073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.1501 | − | 21.0446i | 0.445145 | − | 0.771014i | ||||
\(746\) | −3.06913 | −0.112369 | ||||||||
\(747\) | 2.56155 | − | 4.43674i | 0.0937223 | − | 0.162332i | ||||
\(748\) | 0.157671 | − | 0.273094i | 0.00576501 | − | 0.00998530i | ||||
\(749\) | 13.9309 | 0.509023 | ||||||||
\(750\) | −5.90388 | + | 10.2258i | −0.215579 | + | 0.373394i | ||||
\(751\) | 20.4039 | + | 35.3406i | 0.744548 | + | 1.28960i | 0.950406 | + | 0.311013i | \(0.100668\pi\) |
−0.205857 | + | 0.978582i | \(0.565998\pi\) | |||||||
\(752\) | 0.157671 | + | 0.273094i | 0.00574966 | + | 0.00995871i | ||||
\(753\) | 13.6155 | 0.496177 | ||||||||
\(754\) | 17.4039 | + | 13.5833i | 0.633812 | + | 0.494675i | ||||
\(755\) | −34.2462 | −1.24635 | ||||||||
\(756\) | 0.500000 | + | 0.866025i | 0.0181848 | + | 0.0314970i | ||||
\(757\) | −26.3693 | − | 45.6730i | −0.958409 | − | 1.66001i | −0.726366 | − | 0.687308i | \(-0.758792\pi\) |
−0.232043 | − | 0.972706i | \(-0.574541\pi\) | |||||||
\(758\) | −18.8078 | + | 32.5760i | −0.683129 | + | 1.18321i | ||||
\(759\) | −2.87689 | −0.104425 | ||||||||
\(760\) | 2.00000 | − | 3.46410i | 0.0725476 | − | 0.125656i | ||||
\(761\) | −25.4924 | + | 44.1542i | −0.924100 | + | 1.60059i | −0.131097 | + | 0.991370i | \(0.541850\pi\) |
−0.793003 | + | 0.609218i | \(0.791483\pi\) | |||||||
\(762\) | −12.4924 | −0.452553 | ||||||||
\(763\) | 6.12311 | − | 10.6055i | 0.221671 | − | 0.383946i | ||||
\(764\) | 2.56155 | + | 4.43674i | 0.0926737 | + | 0.160516i | ||||
\(765\) | −0.0961180 | − | 0.166481i | −0.00347515 | − | 0.00601914i | ||||
\(766\) | −12.8078 | −0.462763 | ||||||||
\(767\) | −14.5616 | − | 11.3649i | −0.525787 | − | 0.410364i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −2.43845 | − | 4.22351i | −0.0879327 | − | 0.152304i | 0.818704 | − | 0.574215i | \(-0.194693\pi\) |
−0.906637 | + | 0.421911i | \(0.861359\pi\) | |||||||
\(770\) | 2.00000 | + | 3.46410i | 0.0720750 | + | 0.124838i | ||||
\(771\) | −12.1847 | + | 21.1044i | −0.438820 | + | 0.760058i | ||||
\(772\) | 0.123106 | 0.00443067 | ||||||||
\(773\) | −10.3693 | + | 17.9602i | −0.372958 | + | 0.645983i | −0.990019 | − | 0.140933i | \(-0.954990\pi\) |
0.617061 | + | 0.786915i | \(0.288323\pi\) | |||||||
\(774\) | 4.00000 | − | 6.92820i | 0.143777 | − | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.438447 | − | 0.759413i | 0.0157393 | − | 0.0272613i | ||||
\(777\) | −1.21922 | − | 2.11176i | −0.0437394 | − | 0.0757589i | ||||
\(778\) | 2.65767 | + | 4.60322i | 0.0952821 | + | 0.165033i | ||||
\(779\) | 28.8078 | 1.03215 | ||||||||
\(780\) | 0.780776 | − | 5.57586i | 0.0279563 | − | 0.199648i | ||||
\(781\) | 29.1231 | 1.04211 | ||||||||
\(782\) | 0.0691303 | + | 0.119737i | 0.00247209 | + | 0.00428179i | ||||
\(783\) | −3.06155 | − | 5.30277i | −0.109411 | − | 0.189505i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | −2.05398 | −0.0733095 | ||||||||
\(786\) | 7.12311 | − | 12.3376i | 0.254073 | − | 0.440067i | ||||
\(787\) | 0.0885405 | − | 0.153357i | 0.00315613 | − | 0.00546657i | −0.864443 | − | 0.502731i | \(-0.832329\pi\) |
0.867599 | + | 0.497264i | \(0.165662\pi\) | |||||||
\(788\) | 12.5616 | 0.447487 | ||||||||
\(789\) | 2.56155 | − | 4.43674i | 0.0911937 | − | 0.157952i | ||||
\(790\) | 5.12311 | + | 8.87348i | 0.182272 | + | 0.315704i | ||||
\(791\) | −0.780776 | − | 1.35234i | −0.0277612 | − | 0.0480838i | ||||
\(792\) | −2.56155 | −0.0910208 | ||||||||
\(793\) | 31.9654 | + | 24.9483i | 1.13513 | + | 0.885939i | ||||
\(794\) | 27.9309 | 0.991229 | ||||||||
\(795\) | 5.46543 | + | 9.46641i | 0.193839 | + | 0.335739i | ||||
\(796\) | 8.00000 | + | 13.8564i | 0.283552 | + | 0.491127i | ||||
\(797\) | −25.2462 | + | 43.7277i | −0.894267 | + | 1.54892i | −0.0595571 | + | 0.998225i | \(0.518969\pi\) |
−0.834710 | + | 0.550690i | \(0.814364\pi\) | |||||||
\(798\) | 2.56155 | 0.0906780 | ||||||||
\(799\) | 0.0194102 | − | 0.0336194i | 0.000686682 | − | 0.00118937i | ||||
\(800\) | 1.28078 | − | 2.21837i | 0.0452823 | − | 0.0784312i | ||||
\(801\) | 3.43845 | 0.121492 | ||||||||
\(802\) | 0.903882 | − | 1.56557i | 0.0319172 | − | 0.0552822i | ||||
\(803\) | −3.12311 | − | 5.40938i | −0.110212 | − | 0.190893i | ||||
\(804\) | 4.56155 | + | 7.90084i | 0.160874 | + | 0.278641i | ||||
\(805\) | −1.75379 | −0.0618129 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.1231 | −0.954779 | ||||||||
\(808\) | 2.90388 | + | 5.02967i | 0.102158 | + | 0.176943i | ||||
\(809\) | −4.46543 | − | 7.73436i | −0.156996 | − | 0.271926i | 0.776788 | − | 0.629762i | \(-0.216848\pi\) |
−0.933784 | + | 0.357837i | \(0.883514\pi\) | |||||||
\(810\) | −0.780776 | + | 1.35234i | −0.0274337 | + | 0.0475165i | ||||
\(811\) | 24.0000 | 0.842754 | 0.421377 | − | 0.906886i | \(-0.361547\pi\) | ||||
0.421377 | + | 0.906886i | \(0.361547\pi\) | |||||||
\(812\) | 3.06155 | − | 5.30277i | 0.107439 | − | 0.186091i | ||||
\(813\) | −11.3693 | + | 19.6922i | −0.398739 | + | 0.690637i | ||||
\(814\) | 6.24621 | 0.218930 | ||||||||
\(815\) | −19.1231 | + | 33.1222i | −0.669853 | + | 1.16022i | ||||
\(816\) | 0.0615528 | + | 0.106613i | 0.00215478 | + | 0.00373219i | ||||
\(817\) | −10.2462 | − | 17.7470i | −0.358470 | − | 0.620887i | ||||
\(818\) | −11.5616 | −0.404240 | ||||||||
\(819\) | 3.34233 | − | 1.35234i | 0.116790 | − | 0.0472547i | ||||
\(820\) | −17.5616 | −0.613276 | ||||||||
\(821\) | −13.6501 | − | 23.6427i | −0.476392 | − | 0.825134i | 0.523243 | − | 0.852184i | \(-0.324722\pi\) |
−0.999634 | + | 0.0270494i | \(0.991389\pi\) | |||||||
\(822\) | 6.21922 | + | 10.7720i | 0.216920 | + | 0.375717i | ||||
\(823\) | 19.1231 | − | 33.1222i | 0.666590 | − | 1.15457i | −0.312262 | − | 0.949996i | \(-0.601087\pi\) |
0.978852 | − | 0.204571i | \(-0.0655799\pi\) | |||||||
\(824\) | 6.24621 | 0.217597 | ||||||||
\(825\) | 3.28078 | − | 5.68247i | 0.114222 | − | 0.197838i | ||||
\(826\) | −2.56155 | + | 4.43674i | −0.0891278 | + | 0.154374i | ||||
\(827\) | 34.2462 | 1.19086 | 0.595429 | − | 0.803408i | \(-0.296982\pi\) | ||||
0.595429 | + | 0.803408i | \(0.296982\pi\) | |||||||
\(828\) | 0.561553 | − | 0.972638i | 0.0195153 | − | 0.0338015i | ||||
\(829\) | 0.184658 | + | 0.319838i | 0.00641345 | + | 0.0111084i | 0.869214 | − | 0.494436i | \(-0.164625\pi\) |
−0.862801 | + | 0.505544i | \(0.831292\pi\) | |||||||
\(830\) | 4.00000 | + | 6.92820i | 0.138842 | + | 0.240481i | ||||
\(831\) | 19.5616 | 0.678583 | ||||||||
\(832\) | −0.500000 | + | 3.57071i | −0.0173344 | + | 0.123792i | ||||
\(833\) | 0.123106 | 0.00426536 | ||||||||
\(834\) | −2.71922 | − | 4.70983i | −0.0941590 | − | 0.163088i | ||||
\(835\) | −9.75379 | − | 16.8941i | −0.337544 | − | 0.584643i | ||||
\(836\) | −3.28078 | + | 5.68247i | −0.113468 | + | 0.196532i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.6847 | + | 20.2384i | −0.403640 | + | 0.699125i | ||||
\(839\) | −9.12311 | + | 15.8017i | −0.314965 | + | 0.545535i | −0.979430 | − | 0.201784i | \(-0.935326\pi\) |
0.664465 | + | 0.747319i | \(0.268659\pi\) | |||||||
\(840\) | −1.56155 | −0.0538787 | ||||||||
\(841\) | −4.24621 | + | 7.35465i | −0.146421 | + | 0.253609i | ||||
\(842\) | 11.1501 | + | 19.3125i | 0.384258 | + | 0.665554i | ||||
\(843\) | 6.46543 | + | 11.1985i | 0.222681 | + | 0.385696i | ||||
\(844\) | 5.12311 | 0.176345 | ||||||||
\(845\) | −19.5194 | − | 5.57586i | −0.671488 | − | 0.191815i | ||||
\(846\) | −0.315342 | −0.0108417 | ||||||||
\(847\) | 2.21922 | + | 3.84381i | 0.0762534 | + | 0.132075i | ||||
\(848\) | −3.50000 | − | 6.06218i | −0.120190 | − | 0.208176i | ||||
\(849\) | −10.0000 | + | 17.3205i | −0.343199 | + | 0.594438i | ||||
\(850\) | −0.315342 | −0.0108161 | ||||||||
\(851\) | −1.36932 | + | 2.37173i | −0.0469396 | + | 0.0813017i | ||||
\(852\) | −5.68466 | + | 9.84612i | −0.194753 | + | 0.337322i | ||||
\(853\) | 30.3693 | 1.03983 | 0.519913 | − | 0.854219i | \(-0.325964\pi\) | ||||
0.519913 | + | 0.854219i | \(0.325964\pi\) | |||||||
\(854\) | 5.62311 | − | 9.73950i | 0.192419 | − | 0.333279i | ||||
\(855\) | 2.00000 | + | 3.46410i | 0.0683986 | + | 0.118470i | ||||
\(856\) | −6.96543 | − | 12.0645i | −0.238074 | − | 0.412356i | ||||
\(857\) | 16.4384 | 0.561527 | 0.280763 | − | 0.959777i | \(-0.409412\pi\) | ||||
0.280763 | + | 0.959777i | \(0.409412\pi\) | |||||||
\(858\) | −1.28078 | + | 9.14657i | −0.0437250 | + | 0.312259i | ||||
\(859\) | 17.9309 | 0.611793 | 0.305897 | − | 0.952065i | \(-0.401044\pi\) | ||||
0.305897 | + | 0.952065i | \(0.401044\pi\) | |||||||
\(860\) | 6.24621 | + | 10.8188i | 0.212994 | + | 0.368916i | ||||
\(861\) | −5.62311 | − | 9.73950i | −0.191635 | − | 0.331921i | ||||
\(862\) | −9.68466 | + | 16.7743i | −0.329861 | + | 0.571336i | ||||
\(863\) | 41.1231 | 1.39985 | 0.699923 | − | 0.714218i | \(-0.253217\pi\) | ||||
0.699923 | + | 0.714218i | \(0.253217\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 14.0540 | − | 24.3422i | 0.477849 | − | 0.827660i | ||||
\(866\) | −21.3153 | −0.724325 | ||||||||
\(867\) | −8.49242 | + | 14.7093i | −0.288418 | + | 0.499554i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.40388 | − | 14.5560i | −0.285082 | − | 0.493777i | ||||
\(870\) | 9.56155 | 0.324167 | ||||||||
\(871\) | 30.4924 | − | 12.3376i | 1.03320 | − | 0.418043i | ||||
\(872\) | −12.2462 | −0.414709 | ||||||||
\(873\) | 0.438447 | + | 0.759413i | 0.0148392 | + | 0.0257022i | ||||
\(874\) | −1.43845 | − | 2.49146i | −0.0486562 | − | 0.0842750i | ||||
\(875\) | 5.90388 | − | 10.2258i | 0.199588 | − | 0.345696i | ||||
\(876\) | 2.43845 | 0.0823875 | ||||||||
\(877\) | 14.2732 | − | 24.7219i | 0.481972 | − | 0.834799i | −0.517814 | − | 0.855493i | \(-0.673254\pi\) |
0.999786 | + | 0.0206937i | \(0.00658747\pi\) | |||||||
\(878\) | 13.1231 | − | 22.7299i | 0.442883 | − | 0.767096i | ||||
\(879\) | 6.93087 | 0.233772 | ||||||||
\(880\) | 2.00000 | − | 3.46410i | 0.0674200 | − | 0.116775i | ||||
\(881\) | −9.97301 | − | 17.2738i | −0.335999 | − | 0.581968i | 0.647677 | − | 0.761915i | \(-0.275741\pi\) |
−0.983676 | + | 0.179947i | \(0.942407\pi\) | |||||||
\(882\) | −0.500000 | − | 0.866025i | −0.0168359 | − | 0.0291606i | ||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0.411460 | − | 0.166481i | 0.0138389 | − | 0.00559937i | ||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | 13.5270 | + | 23.4294i | 0.454448 | + | 0.787127i | ||||
\(887\) | 4.47301 | + | 7.74748i | 0.150189 | + | 0.260135i | 0.931297 | − | 0.364261i | \(-0.118678\pi\) |
−0.781108 | + | 0.624396i | \(0.785345\pi\) | |||||||
\(888\) | −1.21922 | + | 2.11176i | −0.0409145 | + | 0.0708659i | ||||
\(889\) | 12.4924 | 0.418982 | ||||||||
\(890\) | −2.68466 | + | 4.64996i | −0.0899900 | + | 0.155867i | ||||
\(891\) | 1.28078 | − | 2.21837i | 0.0429076 | − | 0.0743182i | ||||
\(892\) | 9.75379 | 0.326581 | ||||||||
\(893\) | −0.403882 | + | 0.699544i | −0.0135154 | + | 0.0234094i | ||||
\(894\) | −7.78078 | − | 13.4767i | −0.260228 | − | 0.450728i | ||||
\(895\) | 1.36932 | + | 2.37173i | 0.0457712 | + | 0.0792781i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −3.19224 | − | 2.49146i | −0.106586 | − | 0.0831875i | ||||
\(898\) | −6.63068 | −0.221269 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.28078 | + | 2.21837i | 0.0426925 | + | 0.0739457i | ||||
\(901\) | −0.430870 | + | 0.746288i | −0.0143544 | + | 0.0248625i | ||||
\(902\) | 28.8078 | 0.959194 | ||||||||
\(903\) | −4.00000 | + | 6.92820i | −0.133112 | + | 0.230556i | ||||
\(904\) | −0.780776 | + | 1.35234i | −0.0259682 | + | 0.0449783i | ||||
\(905\) | 20.6847 | 0.687581 | ||||||||
\(906\) | −10.9654 | + | 18.9927i | −0.364302 | + | 0.630990i | ||||
\(907\) | 0.561553 | + | 0.972638i | 0.0186461 | + | 0.0322959i | 0.875198 | − | 0.483765i | \(-0.160731\pi\) |
−0.856552 | + | 0.516061i | \(0.827398\pi\) | |||||||
\(908\) | 5.43845 | + | 9.41967i | 0.180481 | + | 0.312603i | ||||
\(909\) | −5.80776 | −0.192631 | ||||||||
\(910\) | −0.780776 | + | 5.57586i | −0.0258825 | + | 0.184838i | ||||
\(911\) | 13.6155 | 0.451103 | 0.225551 | − | 0.974231i | \(-0.427582\pi\) | ||||
0.225551 | + | 0.974231i | \(0.427582\pi\) | |||||||
\(912\) | −1.28078 | − | 2.21837i | −0.0424107 | − | 0.0734576i | ||||
\(913\) | −6.56155 | − | 11.3649i | −0.217156 | − | 0.376125i | ||||
\(914\) | −14.4654 | + | 25.0549i | −0.478474 | + | 0.828741i | ||||
\(915\) | 17.5616 | 0.580567 | ||||||||
\(916\) | −8.52699 | + | 14.7692i | −0.281740 | + | 0.487987i | ||||
\(917\) | −7.12311 | + | 12.3376i | −0.235226 | + | 0.407423i | ||||
\(918\) | −0.123106 | −0.00406309 | ||||||||
\(919\) | 22.9654 | − | 39.7773i | 0.757560 | − | 1.31213i | −0.186532 | − | 0.982449i | \(-0.559725\pi\) |
0.944092 | − | 0.329683i | \(-0.106942\pi\) | |||||||
\(920\) | 0.876894 | + | 1.51883i | 0.0289104 | + | 0.0500742i | ||||
\(921\) | −4.96543 | − | 8.60039i | −0.163617 | − | 0.283392i | ||||
\(922\) | 6.05398 | 0.199377 | ||||||||
\(923\) | 32.3153 | + | 25.2213i | 1.06367 | + | 0.830171i | ||||
\(924\) | 2.56155 | 0.0842689 | ||||||||
\(925\) | −3.12311 | − | 5.40938i | −0.102687 | − | 0.177859i | ||||
\(926\) | −6.15767 | − | 10.6654i | −0.202354 | − | 0.350487i | ||||
\(927\) | −3.12311 | + | 5.40938i | −0.102576 | + | 0.177667i | ||||
\(928\) | −6.12311 | −0.201001 | ||||||||
\(929\) | 1.37689 | − | 2.38485i | 0.0451744 | − | 0.0782444i | −0.842554 | − | 0.538612i | \(-0.818949\pi\) |
0.887729 | + | 0.460367i | \(0.152282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.56155 | −0.0839515 | ||||||||
\(932\) | −0.684658 | + | 1.18586i | −0.0224267 | + | 0.0388442i | ||||
\(933\) | 10.9654 | + | 18.9927i | 0.358992 | + | 0.621793i | ||||
\(934\) | 18.4924 | + | 32.0298i | 0.605091 | + | 1.04805i | ||||
\(935\) | −0.492423 | −0.0161039 | ||||||||
\(936\) | −2.84233 | − | 2.21837i | −0.0929044 | − | 0.0725097i | ||||
\(937\) | −34.4384 | −1.12506 | −0.562528 | − | 0.826779i | \(-0.690171\pi\) | ||||
−0.562528 | + | 0.826779i | \(0.690171\pi\) | |||||||
\(938\) | −4.56155 | − | 7.90084i | −0.148940 | − | 0.257972i | ||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | 0.246211 | − | 0.426450i | 0.00803053 | − | 0.0139093i | ||||
\(941\) | −10.6307 | −0.346550 | −0.173275 | − | 0.984873i | \(-0.555435\pi\) | ||||
−0.173275 | + | 0.984873i | \(0.555435\pi\) | |||||||
\(942\) | −0.657671 | + | 1.13912i | −0.0214281 | + | 0.0371145i | ||||
\(943\) | −6.31534 | + | 10.9385i | −0.205656 | + | 0.356206i | ||||
\(944\) | 5.12311 | 0.166743 | ||||||||
\(945\) | 0.780776 | − | 1.35234i | 0.0253987 | − | 0.0439918i | ||||
\(946\) | −10.2462 | − | 17.7470i | −0.333133 | − | 0.577003i | ||||
\(947\) | −29.2808 | − | 50.7158i | −0.951497 | − | 1.64804i | −0.742187 | − | 0.670192i | \(-0.766212\pi\) |
−0.209310 | − | 0.977849i | \(-0.567122\pi\) | |||||||
\(948\) | 6.56155 | 0.213109 | ||||||||
\(949\) | 1.21922 | − | 8.70700i | 0.0395777 | − | 0.282641i | ||||
\(950\) | 6.56155 | 0.212885 | ||||||||
\(951\) | 6.21922 | + | 10.7720i | 0.201672 | + | 0.349306i | ||||
\(952\) | −0.0615528 | − | 0.106613i | −0.00199494 | − | 0.00345533i | ||||
\(953\) | −6.43845 | + | 11.1517i | −0.208562 | + | 0.361240i | −0.951262 | − | 0.308385i | \(-0.900212\pi\) |
0.742700 | + | 0.669624i | \(0.233545\pi\) | |||||||
\(954\) | 7.00000 | 0.226633 | ||||||||
\(955\) | 4.00000 | − | 6.92820i | 0.129437 | − | 0.224191i | ||||
\(956\) | −9.68466 | + | 16.7743i | −0.313224 | + | 0.542520i | ||||
\(957\) | −15.6847 | −0.507013 | ||||||||
\(958\) | 0.965435 | − | 1.67218i | 0.0311918 | − | 0.0540258i | ||||
\(959\) | −6.21922 | − | 10.7720i | −0.200829 | − | 0.347846i | ||||
\(960\) | 0.780776 | + | 1.35234i | 0.0251995 | + | 0.0436467i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 6.93087 | + | 5.40938i | 0.223460 | + | 0.174405i | ||||
\(963\) | 13.9309 | 0.448916 | ||||||||
\(964\) | 0.0961180 | + | 0.166481i | 0.00309575 | + | 0.00536200i | ||||
\(965\) | −0.0961180 | − | 0.166481i | −0.00309415 | − | 0.00535922i | ||||
\(966\) | −0.561553 | + | 0.972638i | −0.0180677 | + | 0.0312941i | ||||
\(967\) | −28.4924 | −0.916255 | −0.458127 | − | 0.888887i | \(-0.651480\pi\) | ||||
−0.458127 | + | 0.888887i | \(0.651480\pi\) | |||||||
\(968\) | 2.21922 | − | 3.84381i | 0.0713285 | − | 0.123545i | ||||
\(969\) | −0.157671 | + | 0.273094i | −0.00506512 | + | 0.00877304i | ||||
\(970\) | −1.36932 | −0.0439661 | ||||||||
\(971\) | −20.8078 | + | 36.0401i | −0.667753 | + | 1.15658i | 0.310778 | + | 0.950482i | \(0.399410\pi\) |
−0.978531 | + | 0.206100i | \(0.933923\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 2.71922 | + | 4.70983i | 0.0871743 | + | 0.150990i | ||||
\(974\) | 23.6847 | 0.758905 | ||||||||
\(975\) | 8.56155 | − | 3.46410i | 0.274189 | − | 0.110940i | ||||
\(976\) | −11.2462 | −0.359982 | ||||||||
\(977\) | 20.5885 | + | 35.6604i | 0.658686 | + | 1.14088i | 0.980956 | + | 0.194230i | \(0.0622207\pi\) |
−0.322270 | + | 0.946648i | \(0.604446\pi\) | |||||||
\(978\) | 12.2462 | + | 21.2111i | 0.391591 | + | 0.678255i | ||||
\(979\) | 4.40388 | − | 7.62775i | 0.140749 | − | 0.243784i | ||||
\(980\) | 1.56155 | 0.0498820 | ||||||||
\(981\) | 6.12311 | − | 10.6055i | 0.195496 | − | 0.338609i | ||||
\(982\) | 8.24621 | − | 14.2829i | 0.263147 | − | 0.455784i | ||||
\(983\) | 18.7386 | 0.597670 | 0.298835 | − | 0.954305i | \(-0.403402\pi\) | ||||
0.298835 | + | 0.954305i | \(0.403402\pi\) | |||||||
\(984\) | −5.62311 | + | 9.73950i | −0.179258 | + | 0.310484i | ||||
\(985\) | −9.80776 | − | 16.9875i | −0.312501 | − | 0.541268i | ||||
\(986\) | 0.376894 | + | 0.652800i | 0.0120028 | + | 0.0207894i | ||||
\(987\) | 0.315342 | 0.0100374 | ||||||||
\(988\) | −8.56155 | + | 3.46410i | −0.272379 | + | 0.110208i | ||||
\(989\) | 8.98485 | 0.285701 | ||||||||
\(990\) | 2.00000 | + | 3.46410i | 0.0635642 | + | 0.110096i | ||||
\(991\) | 14.3348 | + | 24.8285i | 0.455358 | + | 0.788704i | 0.998709 | − | 0.0508022i | \(-0.0161778\pi\) |
−0.543350 | + | 0.839506i | \(0.682844\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.3693 | −0.614667 | ||||||||
\(994\) | 5.68466 | − | 9.84612i | 0.180306 | − | 0.312300i | ||||
\(995\) | 12.4924 | − | 21.6375i | 0.396036 | − | 0.685955i | ||||
\(996\) | 5.12311 | 0.162332 | ||||||||
\(997\) | 20.9924 | − | 36.3599i | 0.664837 | − | 1.15153i | −0.314493 | − | 0.949260i | \(-0.601834\pi\) |
0.979330 | − | 0.202271i | \(-0.0648322\pi\) | |||||||
\(998\) | −15.1231 | − | 26.1940i | −0.478714 | − | 0.829156i | ||||
\(999\) | −1.21922 | − | 2.11176i | −0.0385745 | − | 0.0668130i |
(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 | 546.2.l.l.211.2 | ✓ | 4 | |
3.2 | odd | 2 | 1638.2.r.y.757.1 | 4 | |||
13.3 | even | 3 | 7098.2.a.bt.1.2 | 2 | |||
13.9 | even | 3 | inner | 546.2.l.l.295.2 | yes | 4 | |
13.10 | even | 6 | 7098.2.a.bi.1.1 | 2 | |||
39.35 | odd | 6 | 1638.2.r.y.1387.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.l.211.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
546.2.l.l.295.2 | yes | 4 | 13.9 | even | 3 | inner | |
1638.2.r.y.757.1 | 4 | 3.2 | odd | 2 | |||
1638.2.r.y.1387.1 | 4 | 39.35 | odd | 6 | |||
7098.2.a.bi.1.1 | 2 | 13.10 | even | 6 | |||
7098.2.a.bt.1.2 | 2 | 13.3 | even | 3 |