Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(25,546)]
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, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bk (of order \(6\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 415.6 | ||
Root | \(0.385124 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.415 |
Dual form | 546.2.bk.b.25.6 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 2.25312 | + | 1.30084i | 1.00763 | + | 0.581753i | 0.910496 | − | 0.413519i | \(-0.135700\pi\) |
0.0971303 | + | 0.995272i | \(0.469034\pi\) | |||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −1.49160 | − | 2.18521i | −0.563772 | − | 0.825931i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.30084 | + | 2.25312i | 0.411362 | + | 0.712499i | ||||
\(11\) | 3.11915 | − | 1.80084i | 0.940458 | − | 0.542974i | 0.0503540 | − | 0.998731i | \(-0.483965\pi\) |
0.890104 | + | 0.455758i | \(0.150632\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 3.60168 | − | 0.167055i | 0.998926 | − | 0.0463328i | ||||
\(14\) | −0.199160 | − | 2.63824i | −0.0532279 | − | 0.705101i | ||||
\(15\) | − | 2.60168i | − | 0.671751i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.41647 | + | 2.45340i | 0.343545 | + | 0.595037i | 0.985088 | − | 0.172049i | \(-0.0550389\pi\) |
−0.641543 | + | 0.767087i | \(0.721706\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −1.15537 | − | 0.667055i | −0.265061 | − | 0.153033i | 0.361580 | − | 0.932341i | \(-0.382237\pi\) |
−0.626641 | + | 0.779308i | \(0.715571\pi\) | |||||||
\(20\) | 2.60168i | 0.581753i | ||||||||
\(21\) | −1.14664 | + | 2.38437i | −0.250218 | + | 0.520312i | ||||
\(22\) | 3.60168 | 0.767881 | ||||||||
\(23\) | −1.46789 | + | 2.54247i | −0.306077 | + | 0.530141i | −0.977501 | − | 0.210933i | \(-0.932350\pi\) |
0.671423 | + | 0.741074i | \(0.265683\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0.884367 | + | 1.53177i | 0.176873 | + | 0.306354i | ||||
\(26\) | 3.20267 | + | 1.65617i | 0.628096 | + | 0.324801i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.14664 | − | 2.38437i | 0.216695 | − | 0.450603i | ||||
\(29\) | 8.97209 | 1.66608 | 0.833038 | − | 0.553216i | \(-0.186600\pi\) | ||||
0.833038 | + | 0.553216i | \(0.186600\pi\) | |||||||
\(30\) | 1.30084 | − | 2.25312i | 0.237500 | − | 0.411362i | ||||
\(31\) | −3.46410 | + | 2.00000i | −0.622171 | + | 0.359211i | −0.777714 | − | 0.628619i | \(-0.783621\pi\) |
0.155543 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −3.11915 | − | 1.80084i | −0.542974 | − | 0.313486i | ||||
\(34\) | 2.83294i | 0.485846i | ||||||||
\(35\) | −0.518152 | − | 6.86387i | −0.0875836 | − | 1.16021i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −0.144674 | − | 0.0835276i | −0.0237843 | − | 0.0137319i | 0.488061 | − | 0.872810i | \(-0.337704\pi\) |
−0.511845 | + | 0.859078i | \(0.671038\pi\) | |||||||
\(38\) | −0.667055 | − | 1.15537i | −0.108211 | − | 0.187426i | ||||
\(39\) | −1.94551 | − | 3.03562i | −0.311531 | − | 0.486088i | ||||
\(40\) | −1.30084 | + | 2.25312i | −0.205681 | + | 0.356250i | ||||
\(41\) | − | 3.03630i | − | 0.474191i | −0.971486 | − | 0.237095i | \(-0.923805\pi\) | ||
0.971486 | − | 0.237095i | \(-0.0761954\pi\) | |||||||
\(42\) | −2.18521 | + | 1.49160i | −0.337185 | + | 0.230159i | ||||
\(43\) | 2.33411 | 0.355948 | 0.177974 | − | 0.984035i | \(-0.443046\pi\) | ||||
0.177974 | + | 0.984035i | \(0.443046\pi\) | |||||||
\(44\) | 3.11915 | + | 1.80084i | 0.470229 | + | 0.271487i | ||||
\(45\) | −2.25312 | + | 1.30084i | −0.335875 | + | 0.193918i | ||||
\(46\) | −2.54247 | + | 1.46789i | −0.374866 | + | 0.216429i | ||||
\(47\) | −8.43580 | − | 4.87041i | −1.23049 | − | 0.710423i | −0.263357 | − | 0.964699i | \(-0.584830\pi\) |
−0.967132 | + | 0.254276i | \(0.918163\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −2.55026 | + | 6.51891i | −0.364322 | + | 0.931273i | ||||
\(50\) | 1.76873i | 0.250137i | ||||||||
\(51\) | 1.41647 | − | 2.45340i | 0.198346 | − | 0.343545i | ||||
\(52\) | 1.94551 | + | 3.03562i | 0.269794 | + | 0.420964i | ||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 9.37041 | 1.26351 | ||||||||
\(56\) | 2.18521 | − | 1.49160i | 0.292011 | − | 0.199323i | ||||
\(57\) | 1.33411i | 0.176707i | ||||||||
\(58\) | 7.77006 | + | 4.48605i | 1.02026 | + | 0.589047i | ||||
\(59\) | −10.0232 | + | 5.78689i | −1.30491 | + | 0.753388i | −0.981241 | − | 0.192783i | \(-0.938249\pi\) |
−0.323666 | + | 0.946172i | \(0.604915\pi\) | |||||||
\(60\) | 2.25312 | − | 1.30084i | 0.290877 | − | 0.167938i | ||||
\(61\) | −2.01815 | + | 3.49554i | −0.258398 | + | 0.447558i | −0.965813 | − | 0.259240i | \(-0.916528\pi\) |
0.707415 | + | 0.706798i | \(0.249861\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 2.63824 | − | 0.199160i | 0.332388 | − | 0.0250919i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.33233 | + | 4.30881i | 1.03350 | + | 0.534442i | ||||
\(66\) | −1.80084 | − | 3.11915i | −0.221668 | − | 0.383940i | ||||
\(67\) | 10.1679 | − | 5.87041i | 1.24220 | − | 0.717185i | 0.272659 | − | 0.962111i | \(-0.412097\pi\) |
0.969542 | + | 0.244926i | \(0.0787635\pi\) | |||||||
\(68\) | −1.41647 | + | 2.45340i | −0.171773 | + | 0.297519i | ||||
\(69\) | 2.93579 | 0.353428 | ||||||||
\(70\) | 2.98320 | − | 6.20336i | 0.356561 | − | 0.741443i | ||||
\(71\) | − | 5.76873i | − | 0.684623i | −0.939587 | − | 0.342311i | \(-0.888790\pi\) | ||
0.939587 | − | 0.342311i | \(-0.111210\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −9.93411 | + | 5.73546i | −1.16270 | + | 0.671285i | −0.951950 | − | 0.306255i | \(-0.900924\pi\) |
−0.210751 | + | 0.977540i | \(0.567591\pi\) | |||||||
\(74\) | −0.0835276 | − | 0.144674i | −0.00970988 | − | 0.0168180i | ||||
\(75\) | 0.884367 | − | 1.53177i | 0.102118 | − | 0.176873i | ||||
\(76\) | − | 1.33411i | − | 0.153033i | ||||||
\(77\) | −8.58773 | − | 4.12985i | −0.978662 | − | 0.470640i | ||||
\(78\) | −0.167055 | − | 3.60168i | −0.0189153 | − | 0.407810i | ||||
\(79\) | −3.37041 | + | 5.83773i | −0.379201 | + | 0.656796i | −0.990946 | − | 0.134259i | \(-0.957134\pi\) |
0.611745 | + | 0.791055i | \(0.290468\pi\) | |||||||
\(80\) | −2.25312 | + | 1.30084i | −0.251906 | + | 0.145438i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.51815 | − | 2.62952i | 0.167652 | − | 0.290381i | ||||
\(83\) | − | 8.10051i | − | 0.889147i | −0.895742 | − | 0.444573i | \(-0.853355\pi\) | ||
0.895742 | − | 0.444573i | \(-0.146645\pi\) | |||||||
\(84\) | −2.63824 | + | 0.199160i | −0.287856 | + | 0.0217302i | ||||
\(85\) | 7.37041i | 0.799434i | ||||||||
\(86\) | 2.02140 | + | 1.16706i | 0.217973 | + | 0.125847i | ||||
\(87\) | −4.48605 | − | 7.77006i | −0.480955 | − | 0.833038i | ||||
\(88\) | 1.80084 | + | 3.11915i | 0.191970 | + | 0.332502i | ||||
\(89\) | −7.07288 | − | 4.08353i | −0.749723 | − | 0.432853i | 0.0758705 | − | 0.997118i | \(-0.475826\pi\) |
−0.825594 | + | 0.564265i | \(0.809160\pi\) | |||||||
\(90\) | −2.60168 | −0.274241 | ||||||||
\(91\) | −5.73732 | − | 7.62123i | −0.601434 | − | 0.798922i | ||||
\(92\) | −2.93579 | −0.306077 | ||||||||
\(93\) | 3.46410 | + | 2.00000i | 0.359211 | + | 0.207390i | ||||
\(94\) | −4.87041 | − | 8.43580i | −0.502345 | − | 0.870087i | ||||
\(95\) | −1.73546 | − | 3.00591i | −0.178055 | − | 0.308400i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 0.139148i | 0.0141283i | 0.999975 | + | 0.00706416i | \(0.00224861\pi\) | ||||
−0.999975 | + | 0.00706416i | \(0.997751\pi\) | |||||||
\(98\) | −5.46804 | + | 4.37041i | −0.552356 | + | 0.441478i | ||||
\(99\) | 3.60168i | 0.361982i | ||||||||
\(100\) | −0.884367 | + | 1.53177i | −0.0884367 | + | 0.153177i | ||||
\(101\) | −1.78269 | − | 3.08771i | −0.177384 | − | 0.307238i | 0.763600 | − | 0.645690i | \(-0.223430\pi\) |
−0.940984 | + | 0.338452i | \(0.890097\pi\) | |||||||
\(102\) | 2.45340 | − | 1.41647i | 0.242923 | − | 0.140252i | ||||
\(103\) | −9.53747 | + | 16.5194i | −0.939755 | + | 1.62770i | −0.173827 | + | 0.984776i | \(0.555613\pi\) |
−0.765928 | + | 0.642927i | \(0.777720\pi\) | |||||||
\(104\) | 0.167055 | + | 3.60168i | 0.0163811 | + | 0.353174i | ||||
\(105\) | −5.68521 | + | 3.88067i | −0.554819 | + | 0.378714i | ||||
\(106\) | − | 3.00000i | − | 0.291386i | ||||||
\(107\) | 4.03630 | − | 6.99108i | 0.390204 | − | 0.675853i | −0.602272 | − | 0.798291i | \(-0.705738\pi\) |
0.992476 | + | 0.122437i | \(0.0390711\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −11.1451 | + | 6.43462i | −1.06751 | + | 0.616325i | −0.927499 | − | 0.373825i | \(-0.878046\pi\) |
−0.140007 | + | 0.990150i | \(0.544713\pi\) | |||||||
\(110\) | 8.11502 | + | 4.68521i | 0.773736 | + | 0.446717i | ||||
\(111\) | 0.167055i | 0.0158562i | ||||||||
\(112\) | 2.63824 | − | 0.199160i | 0.249291 | − | 0.0188189i | ||||
\(113\) | −19.8800 | −1.87015 | −0.935075 | − | 0.354449i | \(-0.884668\pi\) | ||||
−0.935075 | + | 0.354449i | \(0.884668\pi\) | |||||||
\(114\) | −0.667055 | + | 1.15537i | −0.0624754 | + | 0.108211i | ||||
\(115\) | −6.61469 | + | 3.81899i | −0.616823 | + | 0.356123i | ||||
\(116\) | 4.48605 | + | 7.77006i | 0.416519 | + | 0.721432i | ||||
\(117\) | −1.65617 | + | 3.20267i | −0.153113 | + | 0.296087i | ||||
\(118\) | −11.5738 | −1.06545 | ||||||||
\(119\) | 3.24838 | − | 6.75478i | 0.297779 | − | 0.619210i | ||||
\(120\) | 2.60168 | 0.237500 | ||||||||
\(121\) | 0.986046 | − | 1.70788i | 0.0896406 | − | 0.155262i | ||||
\(122\) | −3.49554 | + | 2.01815i | −0.316471 | + | 0.182715i | ||||
\(123\) | −2.62952 | + | 1.51815i | −0.237095 | + | 0.136887i | ||||
\(124\) | −3.46410 | − | 2.00000i | −0.311086 | − | 0.179605i | ||||
\(125\) | − | 8.40672i | − | 0.751920i | ||||||
\(126\) | 2.38437 | + | 1.14664i | 0.212416 | + | 0.102151i | ||||
\(127\) | −10.0386 | −0.890785 | −0.445392 | − | 0.895335i | \(-0.646936\pi\) | ||||
−0.445392 | + | 0.895335i | \(0.646936\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −1.16706 | − | 2.02140i | −0.102753 | − | 0.177974i | ||||
\(130\) | 5.06160 | + | 7.89770i | 0.443932 | + | 0.692674i | ||||
\(131\) | −4.05562 | + | 7.02454i | −0.354341 | + | 0.613737i | −0.987005 | − | 0.160690i | \(-0.948628\pi\) |
0.632664 | + | 0.774427i | \(0.281962\pi\) | |||||||
\(132\) | − | 3.60168i | − | 0.313486i | ||||||
\(133\) | 0.265702 | + | 3.51971i | 0.0230393 | + | 0.305198i | ||||
\(134\) | 11.7408 | 1.01425 | ||||||||
\(135\) | 2.25312 | + | 1.30084i | 0.193918 | + | 0.111958i | ||||
\(136\) | −2.45340 | + | 1.41647i | −0.210378 | + | 0.121462i | ||||
\(137\) | 4.00934 | − | 2.31479i | 0.342541 | − | 0.197766i | −0.318854 | − | 0.947804i | \(-0.603298\pi\) |
0.661395 | + | 0.750038i | \(0.269965\pi\) | |||||||
\(138\) | 2.54247 | + | 1.46789i | 0.216429 | + | 0.124955i | ||||
\(139\) | −0.935789 | −0.0793726 | −0.0396863 | − | 0.999212i | \(-0.512636\pi\) | ||||
−0.0396863 | + | 0.999212i | \(0.512636\pi\) | |||||||
\(140\) | 5.68521 | − | 3.88067i | 0.480488 | − | 0.327976i | ||||
\(141\) | 9.74083i | 0.820326i | ||||||||
\(142\) | 2.88437 | − | 4.99587i | 0.242051 | − | 0.419244i | ||||
\(143\) | 10.9333 | − | 7.00712i | 0.914290 | − | 0.585964i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 20.2152 | + | 11.6713i | 1.67878 | + | 0.969245i | ||||
\(146\) | −11.4709 | −0.949341 | ||||||||
\(147\) | 6.92067 | − | 1.05087i | 0.570807 | − | 0.0866741i | ||||
\(148\) | − | 0.167055i | − | 0.0137319i | ||||||
\(149\) | 7.04871 | + | 4.06957i | 0.577453 | + | 0.333392i | 0.760120 | − | 0.649782i | \(-0.225140\pi\) |
−0.182668 | + | 0.983175i | \(0.558473\pi\) | |||||||
\(150\) | 1.53177 | − | 0.884367i | 0.125068 | − | 0.0722083i | ||||
\(151\) | 17.3278 | − | 10.0042i | 1.41011 | − | 0.814130i | 0.414716 | − | 0.909951i | \(-0.363881\pi\) |
0.995399 | + | 0.0958208i | \(0.0305476\pi\) | |||||||
\(152\) | 0.667055 | − | 1.15537i | 0.0541053 | − | 0.0937132i | ||||
\(153\) | −2.83294 | −0.229030 | ||||||||
\(154\) | −5.37227 | − | 7.87041i | −0.432910 | − | 0.634216i | ||||
\(155\) | −10.4067 | −0.835888 | ||||||||
\(156\) | 1.65617 | − | 3.20267i | 0.132599 | − | 0.256419i | ||||
\(157\) | −10.6724 | − | 18.4852i | −0.851752 | − | 1.47528i | −0.879626 | − | 0.475666i | \(-0.842207\pi\) |
0.0278743 | − | 0.999611i | \(-0.491126\pi\) | |||||||
\(158\) | −5.83773 | + | 3.37041i | −0.464425 | + | 0.268136i | ||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | −2.60168 | −0.205681 | ||||||||
\(161\) | 7.74533 | − | 0.584693i | 0.610418 | − | 0.0460803i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −0.890194 | − | 0.513954i | −0.0697254 | − | 0.0402560i | 0.464732 | − | 0.885451i | \(-0.346151\pi\) |
−0.534457 | + | 0.845195i | \(0.679484\pi\) | |||||||
\(164\) | 2.62952 | − | 1.51815i | 0.205331 | − | 0.118548i | ||||
\(165\) | −4.68521 | − | 8.11502i | −0.364743 | − | 0.631753i | ||||
\(166\) | 4.05026 | − | 7.01525i | 0.314361 | − | 0.544489i | ||||
\(167\) | − | 5.96976i | − | 0.461954i | −0.972959 | − | 0.230977i | \(-0.925808\pi\) | ||
0.972959 | − | 0.230977i | \(-0.0741922\pi\) | |||||||
\(168\) | −2.38437 | − | 1.14664i | −0.183958 | − | 0.0884655i | ||||
\(169\) | 12.9442 | − | 1.20336i | 0.995707 | − | 0.0925660i | ||||
\(170\) | −3.68521 | + | 6.38297i | −0.282642 | + | 0.489551i | ||||
\(171\) | 1.15537 | − | 0.667055i | 0.0883536 | − | 0.0510110i | ||||
\(172\) | 1.16706 | + | 2.02140i | 0.0889871 | + | 0.154130i | ||||
\(173\) | 8.29108 | − | 14.3606i | 0.630359 | − | 1.09181i | −0.357119 | − | 0.934059i | \(-0.616241\pi\) |
0.987478 | − | 0.157756i | \(-0.0504258\pi\) | |||||||
\(174\) | − | 8.97209i | − | 0.680173i | ||||||
\(175\) | 2.02811 | − | 4.21731i | 0.153311 | − | 0.318799i | ||||
\(176\) | 3.60168i | 0.271487i | ||||||||
\(177\) | 10.0232 | + | 5.78689i | 0.753388 | + | 0.434969i | ||||
\(178\) | −4.08353 | − | 7.07288i | −0.306073 | − | 0.530135i | ||||
\(179\) | 9.37041 | + | 16.2300i | 0.700378 | + | 1.21309i | 0.968334 | + | 0.249659i | \(0.0803184\pi\) |
−0.267956 | + | 0.963431i | \(0.586348\pi\) | |||||||
\(180\) | −2.25312 | − | 1.30084i | −0.167938 | − | 0.0969589i | ||||
\(181\) | −0.426228 | −0.0316813 | −0.0158406 | − | 0.999875i | \(-0.505042\pi\) | ||||
−0.0158406 | + | 0.999875i | \(0.505042\pi\) | |||||||
\(182\) | −1.15804 | − | 9.46884i | −0.0858400 | − | 0.701877i | ||||
\(183\) | 4.03630 | 0.298372 | ||||||||
\(184\) | −2.54247 | − | 1.46789i | −0.187433 | − | 0.108215i | ||||
\(185\) | −0.217312 | − | 0.376395i | −0.0159771 | − | 0.0276731i | ||||
\(186\) | 2.00000 | + | 3.46410i | 0.146647 | + | 0.254000i | ||||
\(187\) | 8.83637 | + | 5.10168i | 0.646179 | + | 0.373072i | ||||
\(188\) | − | 9.74083i | − | 0.710423i | ||||||
\(189\) | −1.49160 | − | 2.18521i | −0.108498 | − | 0.158950i | ||||
\(190\) | − | 3.47093i | − | 0.251808i | ||||||
\(191\) | 4.43462 | − | 7.68099i | 0.320878 | − | 0.555777i | −0.659791 | − | 0.751449i | \(-0.729355\pi\) |
0.980669 | + | 0.195672i | \(0.0626887\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −6.06945 | + | 3.50420i | −0.436888 | + | 0.252238i | −0.702277 | − | 0.711904i | \(-0.747833\pi\) |
0.265388 | + | 0.964142i | \(0.414500\pi\) | |||||||
\(194\) | −0.0695739 | + | 0.120505i | −0.00499511 | + | 0.00865179i | ||||
\(195\) | −0.434624 | − | 9.37041i | −0.0311241 | − | 0.671029i | ||||
\(196\) | −6.92067 | + | 1.05087i | −0.494334 | + | 0.0750620i | ||||
\(197\) | 17.8050i | 1.26856i | 0.773105 | + | 0.634278i | \(0.218703\pi\) | ||||
−0.773105 | + | 0.634278i | \(0.781297\pi\) | |||||||
\(198\) | −1.80084 | + | 3.11915i | −0.127980 | + | 0.221668i | ||||
\(199\) | 13.5545 | + | 23.4770i | 0.960850 | + | 1.66424i | 0.720374 | + | 0.693585i | \(0.243970\pi\) |
0.240475 | + | 0.970655i | \(0.422697\pi\) | |||||||
\(200\) | −1.53177 | + | 0.884367i | −0.108312 | + | 0.0625342i | ||||
\(201\) | −10.1679 | − | 5.87041i | −0.717185 | − | 0.414067i | ||||
\(202\) | − | 3.56538i | − | 0.250859i | ||||||
\(203\) | −13.3828 | − | 19.6059i | −0.939287 | − | 1.37606i | ||||
\(204\) | 2.83294 | 0.198346 | ||||||||
\(205\) | 3.94974 | − | 6.84116i | 0.275862 | − | 0.477807i | ||||
\(206\) | −16.5194 | + | 9.53747i | −1.15096 | + | 0.664507i | ||||
\(207\) | −1.46789 | − | 2.54247i | −0.102026 | − | 0.176714i | ||||
\(208\) | −1.65617 | + | 3.20267i | −0.114834 | + | 0.222065i | ||||
\(209\) | −4.80504 | −0.332371 | ||||||||
\(210\) | −6.86387 | + | 0.518152i | −0.473652 | + | 0.0357559i | ||||
\(211\) | 22.6743 | 1.56096 | 0.780481 | − | 0.625179i | \(-0.214974\pi\) | ||||
0.780481 | + | 0.625179i | \(0.214974\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | −4.99587 | + | 2.88437i | −0.342311 | + | 0.197634i | ||||
\(214\) | 6.99108 | − | 4.03630i | 0.477901 | − | 0.275916i | ||||
\(215\) | 5.25903 | + | 3.03630i | 0.358663 | + | 0.207074i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 9.53747 | + | 4.58658i | 0.647446 | + | 0.311357i | ||||
\(218\) | −12.8692 | −0.871615 | ||||||||
\(219\) | 9.93411 | + | 5.73546i | 0.671285 | + | 0.387567i | ||||
\(220\) | 4.68521 | + | 8.11502i | 0.315877 | + | 0.547114i | ||||
\(221\) | 5.51153 | + | 8.59974i | 0.370746 | + | 0.578481i | ||||
\(222\) | −0.0835276 | + | 0.144674i | −0.00560600 | + | 0.00970988i | ||||
\(223\) | 9.19496i | 0.615740i | 0.951428 | + | 0.307870i | \(0.0996162\pi\) | ||||
−0.951428 | + | 0.307870i | \(0.900384\pi\) | |||||||
\(224\) | 2.38437 | + | 1.14664i | 0.159312 | + | 0.0766134i | ||||
\(225\) | −1.76873 | −0.117916 | ||||||||
\(226\) | −17.2166 | − | 9.93999i | −1.14523 | − | 0.661198i | ||||
\(227\) | −11.7238 | + | 6.76873i | −0.778135 | + | 0.449257i | −0.835769 | − | 0.549081i | \(-0.814978\pi\) |
0.0576337 | + | 0.998338i | \(0.481644\pi\) | |||||||
\(228\) | −1.15537 | + | 0.667055i | −0.0765165 | + | 0.0441768i | ||||
\(229\) | 15.9407 | + | 9.20336i | 1.05339 | + | 0.608175i | 0.923597 | − | 0.383366i | \(-0.125235\pi\) |
0.129794 | + | 0.991541i | \(0.458569\pi\) | |||||||
\(230\) | −7.63798 | −0.503634 | ||||||||
\(231\) | 0.717312 | + | 9.50211i | 0.0471957 | + | 0.625193i | ||||
\(232\) | 8.97209i | 0.589047i | ||||||||
\(233\) | 5.86505 | − | 10.1586i | 0.384232 | − | 0.665510i | −0.607430 | − | 0.794373i | \(-0.707800\pi\) |
0.991662 | + | 0.128863i | \(0.0411329\pi\) | |||||||
\(234\) | −3.03562 | + | 1.94551i | −0.198445 | + | 0.127182i | ||||
\(235\) | −12.6713 | − | 21.9473i | −0.826581 | − | 1.43168i | ||||
\(236\) | −10.0232 | − | 5.78689i | −0.652453 | − | 0.376694i | ||||
\(237\) | 6.74083 | 0.437864 | ||||||||
\(238\) | 6.19057 | − | 4.22562i | 0.401275 | − | 0.273906i | ||||
\(239\) | 11.1731i | 0.722729i | 0.932425 | + | 0.361365i | \(0.117689\pi\) | ||||
−0.932425 | + | 0.361365i | \(0.882311\pi\) | |||||||
\(240\) | 2.25312 | + | 1.30084i | 0.145438 | + | 0.0839688i | ||||
\(241\) | −12.7659 | + | 7.37041i | −0.822326 | + | 0.474770i | −0.851218 | − | 0.524812i | \(-0.824135\pi\) |
0.0288920 | + | 0.999583i | \(0.490802\pi\) | |||||||
\(242\) | 1.70788 | − | 0.986046i | 0.109787 | − | 0.0633855i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −4.03630 | −0.258398 | ||||||||
\(245\) | −14.2261 | + | 11.3704i | −0.908872 | + | 0.726429i | ||||
\(246\) | −3.03630 | −0.193588 | ||||||||
\(247\) | −4.27272 | − | 2.20951i | −0.271867 | − | 0.140588i | ||||
\(248\) | −2.00000 | − | 3.46410i | −0.127000 | − | 0.219971i | ||||
\(249\) | −7.01525 | + | 4.05026i | −0.444573 | + | 0.256675i | ||||
\(250\) | 4.20336 | − | 7.28043i | 0.265844 | − | 0.460455i | ||||
\(251\) | 22.9465 | 1.44837 | 0.724186 | − | 0.689605i | \(-0.242216\pi\) | ||||
0.724186 | + | 0.689605i | \(0.242216\pi\) | |||||||
\(252\) | 1.49160 | + | 2.18521i | 0.0939620 | + | 0.137655i | ||||
\(253\) | 10.5738i | 0.664767i | ||||||||
\(254\) | −8.69371 | − | 5.01932i | −0.545492 | − | 0.314940i | ||||
\(255\) | 6.38297 | − | 3.68521i | 0.399717 | − | 0.230777i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.370413 | − | 0.641575i | 0.0231058 | − | 0.0400203i | −0.854241 | − | 0.519877i | \(-0.825978\pi\) |
0.877347 | + | 0.479856i | \(0.159311\pi\) | |||||||
\(258\) | − | 2.33411i | − | 0.145315i | ||||||
\(259\) | 0.0332708 | + | 0.440732i | 0.00206735 | + | 0.0273858i | ||||
\(260\) | 0.434624 | + | 9.37041i | 0.0269542 | + | 0.581128i | ||||
\(261\) | −4.48605 | + | 7.77006i | −0.277679 | + | 0.480955i | ||||
\(262\) | −7.02454 | + | 4.05562i | −0.433978 | + | 0.250557i | ||||
\(263\) | 10.5042 | + | 18.1938i | 0.647717 | + | 1.12188i | 0.983667 | + | 0.179998i | \(0.0576092\pi\) |
−0.335950 | + | 0.941880i | \(0.609057\pi\) | |||||||
\(264\) | 1.80084 | − | 3.11915i | 0.110834 | − | 0.191970i | ||||
\(265\) | − | 7.80504i | − | 0.479460i | ||||||
\(266\) | −1.52975 | + | 3.18101i | −0.0937950 | + | 0.195040i | ||||
\(267\) | 8.16706i | 0.499816i | ||||||||
\(268\) | 10.1679 | + | 5.87041i | 0.621101 | + | 0.358593i | ||||
\(269\) | 15.5587 | + | 26.9484i | 0.948628 | + | 1.64307i | 0.748319 | + | 0.663339i | \(0.230861\pi\) |
0.200308 | + | 0.979733i | \(0.435806\pi\) | |||||||
\(270\) | 1.30084 | + | 2.25312i | 0.0791666 | + | 0.137121i | ||||
\(271\) | 1.73932 | + | 1.00420i | 0.105656 | + | 0.0610007i | 0.551897 | − | 0.833912i | \(-0.313904\pi\) |
−0.446241 | + | 0.894913i | \(0.647237\pi\) | |||||||
\(272\) | −2.83294 | −0.171773 | ||||||||
\(273\) | −3.73152 | + | 8.77928i | −0.225842 | + | 0.531346i | ||||
\(274\) | 4.62959 | 0.279684 | ||||||||
\(275\) | 5.51694 | + | 3.18521i | 0.332684 | + | 0.192075i | ||||
\(276\) | 1.46789 | + | 2.54247i | 0.0883569 | + | 0.153039i | ||||
\(277\) | −7.68404 | − | 13.3091i | −0.461689 | − | 0.799669i | 0.537356 | − | 0.843356i | \(-0.319423\pi\) |
−0.999045 | + | 0.0436862i | \(0.986090\pi\) | |||||||
\(278\) | −0.810417 | − | 0.467895i | −0.0486056 | − | 0.0280625i | ||||
\(279\) | − | 4.00000i | − | 0.239474i | ||||||
\(280\) | 6.86387 | − | 0.518152i | 0.410194 | − | 0.0309655i | ||||
\(281\) | − | 16.6682i | − | 0.994343i | −0.867652 | − | 0.497171i | \(-0.834372\pi\) | ||
0.867652 | − | 0.497171i | \(-0.165628\pi\) | |||||||
\(282\) | −4.87041 | + | 8.43580i | −0.290029 | + | 0.502345i | ||||
\(283\) | −8.90252 | − | 15.4196i | −0.529200 | − | 0.916601i | −0.999420 | − | 0.0340519i | \(-0.989159\pi\) |
0.470220 | − | 0.882549i | \(-0.344174\pi\) | |||||||
\(284\) | 4.99587 | − | 2.88437i | 0.296450 | − | 0.171156i | ||||
\(285\) | −1.73546 | + | 3.00591i | −0.102800 | + | 0.178055i | ||||
\(286\) | 12.9721 | − | 0.601679i | 0.767056 | − | 0.0355780i | ||||
\(287\) | −6.63495 | + | 4.52895i | −0.391649 | + | 0.267336i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 4.48721 | − | 7.77208i | 0.263954 | − | 0.457181i | ||||
\(290\) | 11.6713 | + | 20.2152i | 0.685360 | + | 1.18708i | ||||
\(291\) | 0.120505 | − | 0.0695739i | 0.00706416 | − | 0.00407849i | ||||
\(292\) | −9.93411 | − | 5.73546i | −0.581350 | − | 0.335643i | ||||
\(293\) | − | 26.4733i | − | 1.54658i | −0.634050 | − | 0.773292i | \(-0.718609\pi\) | ||
0.634050 | − | 0.773292i | \(-0.281391\pi\) | |||||||
\(294\) | 6.51891 | + | 2.55026i | 0.380191 | + | 0.148734i | ||||
\(295\) | −30.1112 | −1.75314 | ||||||||
\(296\) | 0.0835276 | − | 0.144674i | 0.00485494 | − | 0.00840901i | ||||
\(297\) | 3.11915 | − | 1.80084i | 0.180991 | − | 0.104495i | ||||
\(298\) | 4.06957 | + | 7.04871i | 0.235744 | + | 0.408321i | ||||
\(299\) | −4.86215 | + | 9.40237i | −0.281186 | + | 0.543753i | ||||
\(300\) | 1.76873 | 0.102118 | ||||||||
\(301\) | −3.48156 | − | 5.10051i | −0.200674 | − | 0.293989i | ||||
\(302\) | 20.0084 | 1.15135 | ||||||||
\(303\) | −1.78269 | + | 3.08771i | −0.102413 | + | 0.177384i | ||||
\(304\) | 1.15537 | − | 0.667055i | 0.0662652 | − | 0.0382582i | ||||
\(305\) | −9.09428 | + | 5.25058i | −0.520737 | + | 0.300647i | ||||
\(306\) | −2.45340 | − | 1.41647i | −0.140252 | − | 0.0809743i | ||||
\(307\) | 23.2783i | 1.32856i | 0.747483 | + | 0.664281i | \(0.231262\pi\) | ||||
−0.747483 | + | 0.664281i | \(0.768738\pi\) | |||||||
\(308\) | −0.717312 | − | 9.50211i | −0.0408726 | − | 0.541433i | ||||
\(309\) | 19.0749 | 1.08514 | ||||||||
\(310\) | −9.01248 | − | 5.20336i | −0.511875 | − | 0.295531i | ||||
\(311\) | −8.27293 | − | 14.3291i | −0.469115 | − | 0.812531i | 0.530262 | − | 0.847834i | \(-0.322094\pi\) |
−0.999377 | + | 0.0353031i | \(0.988760\pi\) | |||||||
\(312\) | 3.03562 | − | 1.94551i | 0.171858 | − | 0.110143i | ||||
\(313\) | 5.01395 | − | 8.68442i | 0.283405 | − | 0.490873i | −0.688816 | − | 0.724936i | \(-0.741869\pi\) |
0.972221 | + | 0.234064i | \(0.0752025\pi\) | |||||||
\(314\) | − | 21.3448i | − | 1.20456i | ||||||
\(315\) | 6.20336 | + | 2.98320i | 0.349520 | + | 0.168084i | ||||
\(316\) | −6.74083 | −0.379201 | ||||||||
\(317\) | 18.5408 | + | 10.7045i | 1.04135 | + | 0.601226i | 0.920216 | − | 0.391410i | \(-0.128012\pi\) |
0.121137 | + | 0.992636i | \(0.461346\pi\) | |||||||
\(318\) | −2.59808 | + | 1.50000i | −0.145693 | + | 0.0841158i | ||||
\(319\) | 27.9853 | − | 16.1573i | 1.56687 | − | 0.904635i | ||||
\(320\) | −2.25312 | − | 1.30084i | −0.125953 | − | 0.0727191i | ||||
\(321\) | −8.07261 | −0.450569 | ||||||||
\(322\) | 7.00000 | + | 3.36631i | 0.390095 | + | 0.187597i | ||||
\(323\) | − | 3.77946i | − | 0.210295i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 3.44110 | + | 5.36920i | 0.190878 | + | 0.297830i | ||||
\(326\) | −0.513954 | − | 0.890194i | −0.0284653 | − | 0.0493033i | ||||
\(327\) | 11.1451 | + | 6.43462i | 0.616325 | + | 0.355836i | ||||
\(328\) | 3.03630 | 0.167652 | ||||||||
\(329\) | 1.93999 | + | 25.6987i | 0.106955 | + | 1.41681i | ||||
\(330\) | − | 9.37041i | − | 0.515824i | ||||||
\(331\) | −31.0561 | − | 17.9302i | −1.70700 | − | 0.985535i | −0.938235 | − | 0.345998i | \(-0.887540\pi\) |
−0.768761 | − | 0.639536i | \(-0.779126\pi\) | |||||||
\(332\) | 7.01525 | − | 4.05026i | 0.385012 | − | 0.222287i | ||||
\(333\) | 0.144674 | − | 0.0835276i | 0.00792809 | − | 0.00457728i | ||||
\(334\) | 2.98488 | − | 5.16997i | 0.163325 | − | 0.282888i | ||||
\(335\) | 30.5459 | 1.66890 | ||||||||
\(336\) | −1.49160 | − | 2.18521i | −0.0813735 | − | 0.119213i | ||||
\(337\) | 6.73850 | 0.367069 | 0.183535 | − | 0.983013i | \(-0.441246\pi\) | ||||
0.183535 | + | 0.983013i | \(0.441246\pi\) | |||||||
\(338\) | 11.8117 | + | 5.42995i | 0.642470 | + | 0.295351i | ||||
\(339\) | 9.93999 | + | 17.2166i | 0.539866 | + | 0.935075i | ||||
\(340\) | −6.38297 | + | 3.68521i | −0.346165 | + | 0.199858i | ||||
\(341\) | −7.20336 | + | 12.4766i | −0.390084 | + | 0.675645i | ||||
\(342\) | 1.33411 | 0.0721404 | ||||||||
\(343\) | 18.0491 | − | 4.15077i | 0.974561 | − | 0.224121i | ||||
\(344\) | 2.33411i | 0.125847i | ||||||||
\(345\) | 6.61469 | + | 3.81899i | 0.356123 | + | 0.205608i | ||||
\(346\) | 14.3606 | − | 8.29108i | 0.772029 | − | 0.445731i | ||||
\(347\) | −17.2869 | − | 29.9418i | −0.928009 | − | 1.60736i | −0.786650 | − | 0.617400i | \(-0.788186\pi\) |
−0.141359 | − | 0.989958i | \(-0.545147\pi\) | |||||||
\(348\) | 4.48605 | − | 7.77006i | 0.240477 | − | 0.416519i | ||||
\(349\) | 21.7771i | 1.16570i | 0.812579 | + | 0.582852i | \(0.198063\pi\) | ||||
−0.812579 | + | 0.582852i | \(0.801937\pi\) | |||||||
\(350\) | 3.86505 | − | 2.63824i | 0.206596 | − | 0.141020i | ||||
\(351\) | 3.60168 | − | 0.167055i | 0.192243 | − | 0.00891675i | ||||
\(352\) | −1.80084 | + | 3.11915i | −0.0959851 | + | 0.166251i | ||||
\(353\) | 17.6244 | − | 10.1755i | 0.938052 | − | 0.541585i | 0.0487029 | − | 0.998813i | \(-0.484491\pi\) |
0.889349 | + | 0.457229i | \(0.151158\pi\) | |||||||
\(354\) | 5.78689 | + | 10.0232i | 0.307570 | + | 0.532726i | ||||
\(355\) | 7.50420 | − | 12.9977i | 0.398281 | − | 0.689844i | ||||
\(356\) | − | 8.16706i | − | 0.432853i | ||||||
\(357\) | −7.47400 | + | 0.564211i | −0.395566 | + | 0.0298612i | ||||
\(358\) | 18.7408i | 0.990483i | ||||||||
\(359\) | 1.24040 | + | 0.716146i | 0.0654659 | + | 0.0377968i | 0.532376 | − | 0.846508i | \(-0.321299\pi\) |
−0.466910 | + | 0.884305i | \(0.654633\pi\) | |||||||
\(360\) | −1.30084 | − | 2.25312i | −0.0685603 | − | 0.118750i | ||||
\(361\) | −8.61007 | − | 14.9131i | −0.453162 | − | 0.784899i | ||||
\(362\) | −0.369125 | − | 0.213114i | −0.0194008 | − | 0.0112010i | ||||
\(363\) | −1.97209 | −0.103508 | ||||||||
\(364\) | 3.73152 | − | 8.77928i | 0.195585 | − | 0.460159i | ||||
\(365\) | −29.8437 | −1.56209 | ||||||||
\(366\) | 3.49554 | + | 2.01815i | 0.182715 | + | 0.105490i | ||||
\(367\) | −12.1755 | − | 21.0885i | −0.635553 | − | 1.10081i | −0.986398 | − | 0.164377i | \(-0.947439\pi\) |
0.350844 | − | 0.936434i | \(-0.385895\pi\) | |||||||
\(368\) | −1.46789 | − | 2.54247i | −0.0765193 | − | 0.132535i | ||||
\(369\) | 2.62952 | + | 1.51815i | 0.136887 | + | 0.0790318i | ||||
\(370\) | − | 0.434624i | − | 0.0225950i | ||||||
\(371\) | −3.43993 | + | 7.15310i | −0.178592 | + | 0.371371i | ||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | −15.9763 | + | 27.6717i | −0.827221 | + | 1.43279i | 0.0729891 | + | 0.997333i | \(0.476746\pi\) |
−0.900210 | + | 0.435456i | \(0.856587\pi\) | |||||||
\(374\) | 5.10168 | + | 8.83637i | 0.263802 | + | 0.456918i | ||||
\(375\) | −7.28043 | + | 4.20336i | −0.375960 | + | 0.217060i | ||||
\(376\) | 4.87041 | − | 8.43580i | 0.251172 | − | 0.435043i | ||||
\(377\) | 32.3146 | − | 1.49883i | 1.66429 | − | 0.0771939i | ||||
\(378\) | −0.199160 | − | 2.63824i | −0.0102437 | − | 0.135697i | ||||
\(379\) | − | 2.79664i | − | 0.143654i | −0.997417 | − | 0.0718269i | \(-0.977117\pi\) | ||
0.997417 | − | 0.0718269i | \(-0.0228829\pi\) | |||||||
\(380\) | 1.73546 | − | 3.00591i | 0.0890274 | − | 0.154200i | ||||
\(381\) | 5.01932 | + | 8.69371i | 0.257147 | + | 0.445392i | ||||
\(382\) | 7.68099 | − | 4.43462i | 0.392994 | − | 0.226895i | ||||
\(383\) | 8.52487 | + | 4.92184i | 0.435600 | + | 0.251494i | 0.701730 | − | 0.712443i | \(-0.252411\pi\) |
−0.266129 | + | 0.963937i | \(0.585745\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −13.9769 | − | 20.4763i | −0.712329 | − | 1.04357i | ||||
\(386\) | −7.00840 | −0.356718 | ||||||||
\(387\) | −1.16706 | + | 2.02140i | −0.0593247 | + | 0.102753i | ||||
\(388\) | −0.120505 | + | 0.0695739i | −0.00611774 | + | 0.00353208i | ||||
\(389\) | −8.19057 | − | 14.1865i | −0.415278 | − | 0.719283i | 0.580179 | − | 0.814489i | \(-0.302982\pi\) |
−0.995458 | + | 0.0952056i | \(0.969649\pi\) | |||||||
\(390\) | 4.30881 | − | 8.33233i | 0.218185 | − | 0.421924i | ||||
\(391\) | −8.31693 | −0.420605 | ||||||||
\(392\) | −6.51891 | − | 2.55026i | −0.329255 | − | 0.128807i | ||||
\(393\) | 8.11124 | 0.409158 | ||||||||
\(394\) | −8.90252 | + | 15.4196i | −0.448502 | + | 0.776829i | ||||
\(395\) | −15.1879 | + | 8.76873i | −0.764186 | + | 0.441203i | ||||
\(396\) | −3.11915 | + | 1.80084i | −0.156743 | + | 0.0904956i | ||||
\(397\) | −4.71379 | − | 2.72151i | −0.236579 | − | 0.136589i | 0.377025 | − | 0.926203i | \(-0.376947\pi\) |
−0.613603 | + | 0.789615i | \(0.710281\pi\) | |||||||
\(398\) | 27.1089i | 1.35885i | ||||||||
\(399\) | 2.91531 | − | 1.98996i | 0.145948 | − | 0.0996226i | ||||
\(400\) | −1.76873 | −0.0884367 | ||||||||
\(401\) | 15.2214 | + | 8.78805i | 0.760118 | + | 0.438854i | 0.829338 | − | 0.558747i | \(-0.188718\pi\) |
−0.0692201 | + | 0.997601i | \(0.522051\pi\) | |||||||
\(402\) | −5.87041 | − | 10.1679i | −0.292790 | − | 0.507126i | ||||
\(403\) | −12.1425 | + | 7.78205i | −0.604860 | + | 0.387652i | ||||
\(404\) | 1.78269 | − | 3.08771i | 0.0886920 | − | 0.153619i | ||||
\(405\) | − | 2.60168i | − | 0.129278i | ||||||
\(406\) | −1.78689 | − | 23.6706i | −0.0886817 | − | 1.17475i | ||||
\(407\) | −0.601679 | −0.0298241 | ||||||||
\(408\) | 2.45340 | + | 1.41647i | 0.121462 | + | 0.0701258i | ||||
\(409\) | −16.4618 | + | 9.50420i | −0.813981 | + | 0.469952i | −0.848337 | − | 0.529457i | \(-0.822396\pi\) |
0.0343552 | + | 0.999410i | \(0.489062\pi\) | |||||||
\(410\) | 6.84116 | − | 3.94974i | 0.337861 | − | 0.195064i | ||||
\(411\) | −4.00934 | − | 2.31479i | −0.197766 | − | 0.114180i | ||||
\(412\) | −19.0749 | −0.939755 | ||||||||
\(413\) | 27.5961 | + | 13.2710i | 1.35792 | + | 0.653023i | ||||
\(414\) | − | 2.93579i | − | 0.144286i | ||||||
\(415\) | 10.5375 | − | 18.2514i | 0.517264 | − | 0.895928i | ||||
\(416\) | −3.03562 | + | 1.94551i | −0.148833 | + | 0.0953867i | ||||
\(417\) | 0.467895 | + | 0.810417i | 0.0229129 | + | 0.0396863i | ||||
\(418\) | −4.16128 | − | 2.40252i | −0.203535 | − | 0.117511i | ||||
\(419\) | 5.48165 | 0.267796 | 0.133898 | − | 0.990995i | \(-0.457250\pi\) | ||||
0.133898 | + | 0.990995i | \(0.457250\pi\) | |||||||
\(420\) | −6.20336 | − | 2.98320i | −0.302693 | − | 0.145565i | ||||
\(421\) | − | 3.16472i | − | 0.154239i | −0.997022 | − | 0.0771196i | \(-0.975428\pi\) | ||
0.997022 | − | 0.0771196i | \(-0.0245723\pi\) | |||||||
\(422\) | 19.6365 | + | 11.3371i | 0.955890 | + | 0.551883i | ||||
\(423\) | 8.43580 | − | 4.87041i | 0.410163 | − | 0.236808i | ||||
\(424\) | 2.59808 | − | 1.50000i | 0.126174 | − | 0.0728464i | ||||
\(425\) | −2.50536 | + | 4.33942i | −0.121528 | + | 0.210493i | ||||
\(426\) | −5.76873 | −0.279496 | ||||||||
\(427\) | 10.6488 | − | 0.803872i | 0.515329 | − | 0.0389021i | ||||
\(428\) | 8.07261 | 0.390204 | ||||||||
\(429\) | −11.5350 | − | 5.96498i | −0.556915 | − | 0.287992i | ||||
\(430\) | 3.03630 | + | 5.25903i | 0.146424 | + | 0.253613i | ||||
\(431\) | −13.3688 | + | 7.71848i | −0.643952 | + | 0.371786i | −0.786135 | − | 0.618054i | \(-0.787921\pi\) |
0.142183 | + | 0.989840i | \(0.454588\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 13.9419 | 0.670003 | 0.335001 | − | 0.942218i | \(-0.391263\pi\) | ||||
0.335001 | + | 0.942218i | \(0.391263\pi\) | |||||||
\(434\) | 5.96640 | + | 8.74083i | 0.286396 | + | 0.419573i | ||||
\(435\) | − | 23.3425i | − | 1.11919i | ||||||
\(436\) | −11.1451 | − | 6.43462i | −0.533753 | − | 0.308163i | ||||
\(437\) | 3.39193 | − | 1.95833i | 0.162258 | − | 0.0936798i | ||||
\(438\) | 5.73546 | + | 9.93411i | 0.274051 | + | 0.474670i | ||||
\(439\) | 13.6936 | − | 23.7180i | 0.653560 | − | 1.13200i | −0.328693 | − | 0.944437i | \(-0.606608\pi\) |
0.982253 | − | 0.187562i | \(-0.0600586\pi\) | |||||||
\(440\) | 9.37041i | 0.446717i | ||||||||
\(441\) | −4.37041 | − | 5.46804i | −0.208115 | − | 0.260383i | ||||
\(442\) | 0.473258 | + | 10.2034i | 0.0225106 | + | 0.485324i | ||||
\(443\) | −12.0556 | + | 20.8809i | −0.572780 | + | 0.992084i | 0.423499 | + | 0.905896i | \(0.360802\pi\) |
−0.996279 | + | 0.0861872i | \(0.972532\pi\) | |||||||
\(444\) | −0.144674 | + | 0.0835276i | −0.00686593 | + | 0.00396404i | ||||
\(445\) | −10.6240 | − | 18.4014i | −0.503627 | − | 0.872308i | ||||
\(446\) | −4.59748 | + | 7.96307i | −0.217697 | + | 0.377062i | ||||
\(447\) | − | 8.13915i | − | 0.384968i | ||||||
\(448\) | 1.49160 | + | 2.18521i | 0.0704715 | + | 0.103241i | ||||
\(449\) | 2.59095i | 0.122275i | 0.998129 | + | 0.0611373i | \(0.0194728\pi\) | ||||
−0.998129 | + | 0.0611373i | \(0.980527\pi\) | |||||||
\(450\) | −1.53177 | − | 0.884367i | −0.0722083 | − | 0.0416895i | ||||
\(451\) | −5.46789 | − | 9.47067i | −0.257473 | − | 0.445957i | ||||
\(452\) | −9.93999 | − | 17.2166i | −0.467538 | − | 0.809799i | ||||
\(453\) | −17.3278 | − | 10.0042i | −0.814130 | − | 0.470038i | ||||
\(454\) | −13.5375 | −0.635345 | ||||||||
\(455\) | −3.01286 | − | 24.6349i | −0.141245 | − | 1.15490i | ||||
\(456\) | −1.33411 | −0.0624754 | ||||||||
\(457\) | −9.06607 | − | 5.23430i | −0.424093 | − | 0.244850i | 0.272734 | − | 0.962089i | \(-0.412072\pi\) |
−0.696827 | + | 0.717239i | \(0.745405\pi\) | |||||||
\(458\) | 9.20336 | + | 15.9407i | 0.430045 | + | 0.744859i | ||||
\(459\) | 1.41647 | + | 2.45340i | 0.0661153 | + | 0.114515i | ||||
\(460\) | −6.61469 | − | 3.81899i | −0.308411 | − | 0.178061i | ||||
\(461\) | 30.0168i | 1.39802i | 0.715111 | + | 0.699011i | \(0.246376\pi\) | ||||
−0.715111 | + | 0.699011i | \(0.753624\pi\) | |||||||
\(462\) | −4.12985 | + | 8.58773i | −0.192138 | + | 0.399537i | ||||
\(463\) | − | 19.4649i | − | 0.904609i | −0.891864 | − | 0.452304i | \(-0.850602\pi\) | ||
0.891864 | − | 0.452304i | \(-0.149398\pi\) | |||||||
\(464\) | −4.48605 | + | 7.77006i | −0.208259 | + | 0.360716i | ||||
\(465\) | 5.20336 | + | 9.01248i | 0.241300 | + | 0.417944i | ||||
\(466\) | 10.1586 | − | 5.86505i | 0.470586 | − | 0.271693i | ||||
\(467\) | 0.150069 | − | 0.259927i | 0.00694437 | − | 0.0120280i | −0.862532 | − | 0.506002i | \(-0.831123\pi\) |
0.869477 | + | 0.493974i | \(0.164456\pi\) | |||||||
\(468\) | −3.60168 | + | 0.167055i | −0.166488 | + | 0.00772213i | ||||
\(469\) | −27.9944 | − | 13.4626i | −1.29266 | − | 0.621643i | ||||
\(470\) | − | 25.3425i | − | 1.16896i | ||||||
\(471\) | −10.6724 | + | 18.4852i | −0.491759 | + | 0.851752i | ||||
\(472\) | −5.78689 | − | 10.0232i | −0.266363 | − | 0.461354i | ||||
\(473\) | 7.28043 | − | 4.20336i | 0.334755 | − | 0.193271i | ||||
\(474\) | 5.83773 | + | 3.37041i | 0.268136 | + | 0.154808i | ||||
\(475\) | − | 2.35969i | − | 0.108270i | ||||||
\(476\) | 7.47400 | − | 0.564211i | 0.342570 | − | 0.0258605i | ||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | −5.58656 | + | 9.67621i | −0.255523 | + | 0.442579i | ||||
\(479\) | 20.4248 | − | 11.7922i | 0.933232 | − | 0.538802i | 0.0453996 | − | 0.998969i | \(-0.485544\pi\) |
0.887832 | + | 0.460167i | \(0.152211\pi\) | |||||||
\(480\) | 1.30084 | + | 2.25312i | 0.0593749 | + | 0.102840i | ||||
\(481\) | −0.535023 | − | 0.276671i | −0.0243950 | − | 0.0126151i | ||||
\(482\) | −14.7408 | −0.671426 | ||||||||
\(483\) | −4.37902 | − | 6.41531i | −0.199253 | − | 0.291907i | ||||
\(484\) | 1.97209 | 0.0896406 | ||||||||
\(485\) | −0.181009 | + | 0.313517i | −0.00821919 | + | 0.0142361i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 29.6544 | − | 17.1210i | 1.34377 | − | 0.775826i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
0.987359 | + | 0.158502i | \(0.0506666\pi\) | |||||||
\(488\) | −3.49554 | − | 2.01815i | −0.158236 | − | 0.0913574i | ||||
\(489\) | 1.02791i | 0.0464836i | ||||||||
\(490\) | −18.0054 | + | 2.73402i | −0.813399 | + | 0.123510i | ||||
\(491\) | −39.7553 | −1.79413 | −0.897065 | − | 0.441898i | \(-0.854305\pi\) | ||||
−0.897065 | + | 0.441898i | \(0.854305\pi\) | |||||||
\(492\) | −2.62952 | − | 1.51815i | −0.118548 | − | 0.0684436i | ||||
\(493\) | 12.7087 | + | 22.0122i | 0.572372 | + | 0.991377i | ||||
\(494\) | −2.59553 | − | 4.04985i | −0.116778 | − | 0.182211i | ||||
\(495\) | −4.68521 | + | 8.11502i | −0.210584 | + | 0.364743i | ||||
\(496\) | − | 4.00000i | − | 0.179605i | ||||||
\(497\) | −12.6059 | + | 8.60465i | −0.565451 | + | 0.385971i | ||||
\(498\) | −8.10051 | −0.362993 | ||||||||
\(499\) | 10.6091 | + | 6.12519i | 0.474931 | + | 0.274201i | 0.718301 | − | 0.695732i | \(-0.244920\pi\) |
−0.243371 | + | 0.969933i | \(0.578253\pi\) | |||||||
\(500\) | 7.28043 | − | 4.20336i | 0.325591 | − | 0.187980i | ||||
\(501\) | −5.16997 | + | 2.98488i | −0.230977 | + | 0.133355i | ||||
\(502\) | 19.8723 | + | 11.4733i | 0.886943 | + | 0.512077i | ||||
\(503\) | 2.12842 | 0.0949016 | 0.0474508 | − | 0.998874i | \(-0.484890\pi\) | ||||
0.0474508 | + | 0.998874i | \(0.484890\pi\) | |||||||
\(504\) | 0.199160 | + | 2.63824i | 0.00887131 | + | 0.117517i | ||||
\(505\) | − | 9.27596i | − | 0.412775i | ||||||
\(506\) | −5.28689 | + | 9.15715i | −0.235031 | + | 0.407085i | ||||
\(507\) | −7.51423 | − | 10.6083i | −0.333719 | − | 0.471132i | ||||
\(508\) | −5.01932 | − | 8.69371i | −0.222696 | − | 0.385721i | ||||
\(509\) | 29.1741 | + | 16.8437i | 1.29312 | + | 0.746583i | 0.979206 | − | 0.202869i | \(-0.0650266\pi\) |
0.313913 | + | 0.949452i | \(0.398360\pi\) | |||||||
\(510\) | 7.37041 | 0.326367 | ||||||||
\(511\) | 27.3509 | + | 13.1531i | 1.20993 | + | 0.581858i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.15537 | − | 0.667055i | −0.0510110 | − | 0.0294512i | ||||
\(514\) | 0.641575 | − | 0.370413i | 0.0282987 | − | 0.0163382i | ||||
\(515\) | −42.9781 | + | 24.8134i | −1.89384 | + | 1.09341i | ||||
\(516\) | 1.16706 | − | 2.02140i | 0.0513767 | − | 0.0889871i | ||||
\(517\) | −35.0833 | −1.54296 | ||||||||
\(518\) | −0.191553 | + | 0.398321i | −0.00841635 | + | 0.0175012i | ||||
\(519\) | −16.5822 | −0.727876 | ||||||||
\(520\) | −4.30881 | + | 8.33233i | −0.188954 | + | 0.365397i | ||||
\(521\) | 0.130752 | + | 0.226469i | 0.00572835 | + | 0.00992180i | 0.868875 | − | 0.495031i | \(-0.164843\pi\) |
−0.863147 | + | 0.504953i | \(0.831510\pi\) | |||||||
\(522\) | −7.77006 | + | 4.48605i | −0.340086 | + | 0.196349i | ||||
\(523\) | −5.23966 | + | 9.07536i | −0.229114 | + | 0.396838i | −0.957546 | − | 0.288281i | \(-0.906916\pi\) |
0.728432 | + | 0.685119i | \(0.240250\pi\) | |||||||
\(524\) | −8.11124 | −0.354341 | ||||||||
\(525\) | −4.66635 | + | 0.352262i | −0.203656 | + | 0.0153740i | ||||
\(526\) | 21.0084i | 0.916010i | ||||||||
\(527\) | −9.81361 | − | 5.66589i | −0.427488 | − | 0.246810i | ||||
\(528\) | 3.11915 | − | 1.80084i | 0.135743 | − | 0.0783715i | ||||
\(529\) | 7.19057 | + | 12.4544i | 0.312633 | + | 0.541497i | ||||
\(530\) | 3.90252 | − | 6.75936i | 0.169515 | − | 0.293608i | ||||
\(531\) | − | 11.5738i | − | 0.502259i | ||||||
\(532\) | −2.91531 | + | 1.98996i | −0.126395 | + | 0.0862757i | ||||
\(533\) | −0.507230 | − | 10.9358i | −0.0219706 | − | 0.473682i | ||||
\(534\) | −4.08353 | + | 7.07288i | −0.176712 | + | 0.306073i | ||||
\(535\) | 18.1886 | − | 10.5012i | 0.786360 | − | 0.454005i | ||||
\(536\) | 5.87041 | + | 10.1679i | 0.253563 | + | 0.439184i | ||||
\(537\) | 9.37041 | − | 16.2300i | 0.404363 | − | 0.700378i | ||||
\(538\) | 31.1173i | 1.34156i | ||||||||
\(539\) | 3.78489 | + | 24.9260i | 0.163027 | + | 1.07364i | ||||
\(540\) | 2.60168i | 0.111958i | ||||||||
\(541\) | −18.8112 | − | 10.8607i | −0.808757 | − | 0.466936i | 0.0377670 | − | 0.999287i | \(-0.487976\pi\) |
−0.846524 | + | 0.532350i | \(0.821309\pi\) | |||||||
\(542\) | 1.00420 | + | 1.73932i | 0.0431340 | + | 0.0747103i | ||||
\(543\) | 0.213114 | + | 0.369125i | 0.00914560 | + | 0.0158406i | ||||
\(544\) | −2.45340 | − | 1.41647i | −0.105189 | − | 0.0607308i | ||||
\(545\) | −33.4817 | −1.43420 | ||||||||
\(546\) | −7.62123 | + | 5.73732i | −0.326159 | + | 0.245534i | ||||
\(547\) | −33.3593 | −1.42634 | −0.713170 | − | 0.700991i | \(-0.752741\pi\) | ||||
−0.713170 | + | 0.700991i | \(0.752741\pi\) | |||||||
\(548\) | 4.00934 | + | 2.31479i | 0.171270 | + | 0.0988831i | ||||
\(549\) | −2.01815 | − | 3.49554i | −0.0861326 | − | 0.149186i | ||||
\(550\) | 3.18521 | + | 5.51694i | 0.135818 | + | 0.235243i | ||||
\(551\) | −10.3661 | − | 5.98488i | −0.441611 | − | 0.254964i | ||||
\(552\) | 2.93579i | 0.124955i | ||||||||
\(553\) | 17.7840 | − | 1.34251i | 0.756251 | − | 0.0570892i | ||||
\(554\) | − | 15.3681i | − | 0.652927i | ||||||
\(555\) | −0.217312 | + | 0.376395i | −0.00922438 | + | 0.0159771i | ||||
\(556\) | −0.467895 | − | 0.810417i | −0.0198432 | − | 0.0343694i | ||||
\(557\) | 33.2612 | − | 19.2034i | 1.40932 | − | 0.813672i | 0.413999 | − | 0.910277i | \(-0.364132\pi\) |
0.995323 | + | 0.0966049i | \(0.0307983\pi\) | |||||||
\(558\) | 2.00000 | − | 3.46410i | 0.0846668 | − | 0.146647i | ||||
\(559\) | 8.40672 | − | 0.389925i | 0.355566 | − | 0.0164921i | ||||
\(560\) | 6.20336 | + | 2.98320i | 0.262140 | + | 0.126063i | ||||
\(561\) | − | 10.2034i | − | 0.430786i | ||||||
\(562\) | 8.33411 | − | 14.4351i | 0.351553 | − | 0.608908i | ||||
\(563\) | −1.93346 | − | 3.34885i | −0.0814856 | − | 0.141137i | 0.822403 | − | 0.568906i | \(-0.192633\pi\) |
−0.903888 | + | 0.427769i | \(0.859300\pi\) | |||||||
\(564\) | −8.43580 | + | 4.87041i | −0.355211 | + | 0.205081i | ||||
\(565\) | −44.7920 | − | 25.8607i | −1.88441 | − | 1.08797i | ||||
\(566\) | − | 17.8050i | − | 0.748402i | ||||||
\(567\) | −1.14664 | + | 2.38437i | −0.0481545 | + | 0.100134i | ||||
\(568\) | 5.76873 | 0.242051 | ||||||||
\(569\) | 13.8371 | − | 23.9666i | 0.580083 | − | 1.00473i | −0.415386 | − | 0.909645i | \(-0.636353\pi\) |
0.995469 | − | 0.0950882i | \(-0.0303133\pi\) | |||||||
\(570\) | −3.00591 | + | 1.73546i | −0.125904 | + | 0.0726906i | ||||
\(571\) | 20.0470 | + | 34.7225i | 0.838942 | + | 1.45309i | 0.890780 | + | 0.454435i | \(0.150159\pi\) |
−0.0518379 | + | 0.998656i | \(0.516508\pi\) | |||||||
\(572\) | 11.5350 | + | 5.96498i | 0.482303 | + | 0.249408i | ||||
\(573\) | −8.86925 | −0.370518 | ||||||||
\(574\) | −8.01051 | + | 0.604711i | −0.334352 | + | 0.0252402i | ||||
\(575\) | −5.19263 | −0.216548 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 0.352227 | − | 0.203358i | 0.0146634 | − | 0.00846592i | −0.492650 | − | 0.870227i | \(-0.663972\pi\) |
0.507314 | + | 0.861761i | \(0.330639\pi\) | |||||||
\(578\) | 7.77208 | − | 4.48721i | 0.323276 | − | 0.186643i | ||||
\(579\) | 6.06945 | + | 3.50420i | 0.252238 | + | 0.145629i | ||||
\(580\) | 23.3425i | 0.969245i | ||||||||
\(581\) | −17.7013 | + | 12.0827i | −0.734374 | + | 0.501276i | ||||
\(582\) | 0.139148 | 0.00576786 | ||||||||
\(583\) | −9.35744 | − | 5.40252i | −0.387545 | − | 0.223749i | ||||
\(584\) | −5.73546 | − | 9.93411i | −0.237335 | − | 0.411077i | ||||
\(585\) | −7.89770 | + | 5.06160i | −0.326530 | + | 0.209271i | ||||
\(586\) | 13.2366 | − | 22.9265i | 0.546800 | − | 0.947086i | ||||
\(587\) | 22.0131i | 0.908576i | 0.890855 | + | 0.454288i | \(0.150106\pi\) | ||||
−0.890855 | + | 0.454288i | \(0.849894\pi\) | |||||||
\(588\) | 4.37041 | + | 5.46804i | 0.180233 | + | 0.225498i | ||||
\(589\) | 5.33644 | 0.219884 | ||||||||
\(590\) | −26.0771 | − | 15.0556i | −1.07358 | − | 0.619830i | ||||
\(591\) | 15.4196 | − | 8.90252i | 0.634278 | − | 0.366201i | ||||
\(592\) | 0.144674 | − | 0.0835276i | 0.00594607 | − | 0.00343296i | ||||
\(593\) | −27.0080 | − | 15.5931i | −1.10909 | − | 0.640331i | −0.170494 | − | 0.985359i | \(-0.554536\pi\) |
−0.938593 | + | 0.345027i | \(0.887870\pi\) | |||||||
\(594\) | 3.60168 | 0.147779 | ||||||||
\(595\) | 16.1059 | − | 10.9937i | 0.660277 | − | 0.450698i | ||||
\(596\) | 8.13915i | 0.333392i | ||||||||
\(597\) | 13.5545 | − | 23.4770i | 0.554747 | − | 0.960850i | ||||
\(598\) | −8.91194 | + | 5.71162i | −0.364436 | + | 0.233565i | ||||
\(599\) | 3.17009 | + | 5.49075i | 0.129526 | + | 0.224346i | 0.923493 | − | 0.383615i | \(-0.125321\pi\) |
−0.793967 | + | 0.607961i | \(0.791988\pi\) | |||||||
\(600\) | 1.53177 | + | 0.884367i | 0.0625342 | + | 0.0361041i | ||||
\(601\) | −23.5566 | −0.960893 | −0.480447 | − | 0.877024i | \(-0.659525\pi\) | ||||
−0.480447 | + | 0.877024i | \(0.659525\pi\) | |||||||
\(602\) | −0.464862 | − | 6.15795i | −0.0189464 | − | 0.250979i | ||||
\(603\) | 11.7408i | 0.478123i | ||||||||
\(604\) | 17.3278 | + | 10.0042i | 0.705057 | + | 0.407065i | ||||
\(605\) | 4.44336 | − | 2.56538i | 0.180648 | − | 0.104297i | ||||
\(606\) | −3.08771 | + | 1.78269i | −0.125429 | + | 0.0724168i | ||||
\(607\) | −8.01932 | + | 13.8899i | −0.325494 | + | 0.563772i | −0.981612 | − | 0.190886i | \(-0.938864\pi\) |
0.656118 | + | 0.754658i | \(0.272197\pi\) | |||||||
\(608\) | 1.33411 | 0.0541053 | ||||||||
\(609\) | −10.2878 | + | 21.3928i | −0.416883 | + | 0.866878i | ||||
\(610\) | −10.5012 | −0.425180 | ||||||||
\(611\) | −31.1967 | − | 16.1324i | −1.26208 | − | 0.652648i | ||||
\(612\) | −1.41647 | − | 2.45340i | −0.0572575 | − | 0.0991729i | ||||
\(613\) | −7.37710 | + | 4.25917i | −0.297958 | + | 0.172026i | −0.641525 | − | 0.767102i | \(-0.721698\pi\) |
0.343567 | + | 0.939128i | \(0.388365\pi\) | |||||||
\(614\) | −11.6391 | + | 20.1596i | −0.469718 | + | 0.813575i | ||||
\(615\) | −7.89949 | −0.318538 | ||||||||
\(616\) | 4.12985 | − | 8.58773i | 0.166396 | − | 0.346009i | ||||
\(617\) | 1.40905i | 0.0567261i | 0.999598 | + | 0.0283631i | \(0.00902945\pi\) | ||||
−0.999598 | + | 0.0283631i | \(0.990971\pi\) | |||||||
\(618\) | 16.5194 | + | 9.53747i | 0.664507 | + | 0.383653i | ||||
\(619\) | −39.3641 | + | 22.7269i | −1.58218 | + | 0.913470i | −0.587635 | + | 0.809126i | \(0.699941\pi\) |
−0.994541 | + | 0.104344i | \(0.966726\pi\) | |||||||
\(620\) | −5.20336 | − | 9.01248i | −0.208972 | − | 0.361950i | ||||
\(621\) | −1.46789 | + | 2.54247i | −0.0589046 | + | 0.102026i | ||||
\(622\) | − | 16.5459i | − | 0.663429i | ||||||
\(623\) | 1.62655 | + | 21.5467i | 0.0651665 | + | 0.863250i | ||||
\(624\) | 3.60168 | − | 0.167055i | 0.144183 | − | 0.00668756i | ||||
\(625\) | 15.3576 | − | 26.6002i | 0.614305 | − | 1.06401i | ||||
\(626\) | 8.68442 | − | 5.01395i | 0.347099 | − | 0.200398i | ||||
\(627\) | 2.40252 | + | 4.16128i | 0.0959474 | + | 0.166186i | ||||
\(628\) | 10.6724 | − | 18.4852i | 0.425876 | − | 0.737639i | ||||
\(629\) | − | 0.473258i | − | 0.0188700i | ||||||
\(630\) | 3.88067 | + | 5.68521i | 0.154609 | + | 0.226504i | ||||
\(631\) | 35.2313i | 1.40253i | 0.712898 | + | 0.701267i | \(0.247382\pi\) | ||||
−0.712898 | + | 0.701267i | \(0.752618\pi\) | |||||||
\(632\) | −5.83773 | − | 3.37041i | −0.232212 | − | 0.134068i | ||||
\(633\) | −11.3371 | − | 19.6365i | −0.450611 | − | 0.780481i | ||||
\(634\) | 10.7045 | + | 18.5408i | 0.425131 | + | 0.736348i | ||||
\(635\) | −22.6182 | − | 13.0587i | −0.897578 | − | 0.518217i | ||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | −8.09619 | + | 23.9051i | −0.320783 | + | 0.947153i | ||||
\(638\) | 32.3146 | 1.27935 | ||||||||
\(639\) | 4.99587 | + | 2.88437i | 0.197634 | + | 0.114104i | ||||
\(640\) | −1.30084 | − | 2.25312i | −0.0514202 | − | 0.0890624i | ||||
\(641\) | −11.1168 | − | 19.2549i | −0.439087 | − | 0.760521i | 0.558532 | − | 0.829483i | \(-0.311365\pi\) |
−0.997619 | + | 0.0689616i | \(0.978031\pi\) | |||||||
\(642\) | −6.99108 | − | 4.03630i | −0.275916 | − | 0.159300i | ||||
\(643\) | − | 3.64031i | − | 0.143560i | −0.997420 | − | 0.0717800i | \(-0.977132\pi\) | ||
0.997420 | − | 0.0717800i | \(-0.0228679\pi\) | |||||||
\(644\) | 4.37902 | + | 6.41531i | 0.172558 | + | 0.252799i | ||||
\(645\) | − | 6.07261i | − | 0.239109i | ||||||
\(646\) | 1.88973 | − | 3.27311i | 0.0743505 | − | 0.128779i | ||||
\(647\) | −7.02791 | − | 12.1727i | −0.276296 | − | 0.478558i | 0.694166 | − | 0.719815i | \(-0.255774\pi\) |
−0.970461 | + | 0.241257i | \(0.922440\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −20.8425 | + | 36.1003i | −0.818140 | + | 1.41706i | ||||
\(650\) | 0.295476 | + | 6.37041i | 0.0115895 | + | 0.249868i | ||||
\(651\) | −0.796642 | − | 10.5530i | −0.0312229 | − | 0.413604i | ||||
\(652\) | − | 1.02791i | − | 0.0402560i | ||||||
\(653\) | 8.62403 | − | 14.9373i | 0.337484 | − | 0.584540i | −0.646475 | − | 0.762936i | \(-0.723757\pi\) |
0.983959 | + | 0.178396i | \(0.0570907\pi\) | |||||||
\(654\) | 6.43462 | + | 11.1451i | 0.251614 | + | 0.435808i | ||||
\(655\) | −18.2756 | + | 10.5514i | −0.714087 | + | 0.412278i | ||||
\(656\) | 2.62952 | + | 1.51815i | 0.102665 | + | 0.0592739i | ||||
\(657\) | − | 11.4709i | − | 0.447523i | ||||||
\(658\) | −11.1693 | + | 23.2257i | −0.435423 | + | 0.905432i | ||||
\(659\) | −21.6999 | −0.845307 | −0.422653 | − | 0.906291i | \(-0.638901\pi\) | ||||
−0.422653 | + | 0.906291i | \(0.638901\pi\) | |||||||
\(660\) | 4.68521 | − | 8.11502i | 0.182371 | − | 0.315877i | ||||
\(661\) | 20.0758 | − | 11.5908i | 0.780857 | − | 0.450828i | −0.0558767 | − | 0.998438i | \(-0.517795\pi\) |
0.836734 | + | 0.547609i | \(0.184462\pi\) | |||||||
\(662\) | −17.9302 | − | 31.0561i | −0.696878 | − | 1.20703i | ||||
\(663\) | 4.69183 | − | 9.07300i | 0.182215 | − | 0.352366i | ||||
\(664\) | 8.10051 | 0.314361 | ||||||||
\(665\) | −3.97992 | + | 8.27596i | −0.154335 | + | 0.320928i | ||||
\(666\) | 0.167055 | 0.00647326 | ||||||||
\(667\) | −13.1701 | + | 22.8113i | −0.509948 | + | 0.883256i | ||||
\(668\) | 5.16997 | − | 2.98488i | 0.200032 | − | 0.115489i | ||||
\(669\) | 7.96307 | − | 4.59748i | 0.307870 | − | 0.177749i | ||||
\(670\) | 26.4535 | + | 15.2729i | 1.02199 | + | 0.590045i | ||||
\(671\) | 14.5375i | 0.561213i | ||||||||
\(672\) | −0.199160 | − | 2.63824i | −0.00768278 | − | 0.101772i | ||||
\(673\) | 7.56538 | 0.291624 | 0.145812 | − | 0.989312i | \(-0.453421\pi\) | ||||
0.145812 | + | 0.989312i | \(0.453421\pi\) | |||||||
\(674\) | 5.83571 | + | 3.36925i | 0.224783 | + | 0.129779i | ||||
\(675\) | 0.884367 | + | 1.53177i | 0.0340393 | + | 0.0589578i | ||||
\(676\) | 7.51423 | + | 10.6083i | 0.289009 | + | 0.408012i | ||||
\(677\) | 10.4581 | − | 18.1140i | 0.401939 | − | 0.696179i | −0.592021 | − | 0.805923i | \(-0.701670\pi\) |
0.993960 | + | 0.109744i | \(0.0350031\pi\) | |||||||
\(678\) | 19.8800i | 0.763486i | ||||||||
\(679\) | 0.304067 | − | 0.207553i | 0.0116690 | − | 0.00796515i | ||||
\(680\) | −7.37041 | −0.282642 | ||||||||
\(681\) | 11.7238 | + | 6.76873i | 0.449257 | + | 0.259378i | ||||
\(682\) | −12.4766 | + | 7.20336i | −0.477753 | + | 0.275831i | ||||
\(683\) | −17.0981 | + | 9.87158i | −0.654240 | + | 0.377725i | −0.790079 | − | 0.613005i | \(-0.789960\pi\) |
0.135839 | + | 0.990731i | \(0.456627\pi\) | |||||||
\(684\) | 1.15537 | + | 0.667055i | 0.0441768 | + | 0.0255055i | ||||
\(685\) | 12.0447 | 0.460204 | ||||||||
\(686\) | 17.7064 | + | 5.42989i | 0.676033 | + | 0.207314i | ||||
\(687\) | − | 18.4067i | − | 0.702260i | ||||||
\(688\) | −1.16706 | + | 2.02140i | −0.0444936 | + | 0.0770651i | ||||
\(689\) | −5.83654 | − | 9.10685i | −0.222354 | − | 0.346944i | ||||
\(690\) | 3.81899 | + | 6.61469i | 0.145387 | + | 0.251817i | ||||
\(691\) | −23.4013 | − | 13.5107i | −0.890226 | − | 0.513972i | −0.0162096 | − | 0.999869i | \(-0.505160\pi\) |
−0.874016 | + | 0.485896i | \(0.838493\pi\) | |||||||
\(692\) | 16.5822 | 0.630359 | ||||||||
\(693\) | 7.87041 | − | 5.37227i | 0.298972 | − | 0.204076i | ||||
\(694\) | − | 34.5738i | − | 1.31240i | ||||||
\(695\) | −2.10845 | − | 1.21731i | −0.0799779 | − | 0.0461753i | ||||
\(696\) | 7.77006 | − | 4.48605i | 0.294523 | − | 0.170043i | ||||
\(697\) | 7.44927 | − | 4.30084i | 0.282161 | − | 0.162906i | ||||
\(698\) | −10.8886 | + | 18.8595i | −0.412138 | + | 0.713844i | ||||
\(699\) | −11.7301 | −0.443673 | ||||||||
\(700\) | 4.66635 | − | 0.352262i | 0.176372 | − | 0.0133142i | ||||
\(701\) | 46.3956 | 1.75234 | 0.876169 | − | 0.482004i | \(-0.160091\pi\) | ||||
0.876169 | + | 0.482004i | \(0.160091\pi\) | |||||||
\(702\) | 3.20267 | + | 1.65617i | 0.120877 | + | 0.0625079i | ||||
\(703\) | 0.111435 | + | 0.193011i | 0.00420285 | + | 0.00727955i | ||||
\(704\) | −3.11915 | + | 1.80084i | −0.117557 | + | 0.0678717i | ||||
\(705\) | −12.6713 | + | 21.9473i | −0.477227 | + | 0.826581i | ||||
\(706\) | 20.3509 | 0.765916 | ||||||||
\(707\) | −4.08822 | + | 8.50117i | −0.153753 | + | 0.319719i | ||||
\(708\) | 11.5738i | 0.434969i | ||||||||
\(709\) | −35.7795 | − | 20.6573i | −1.34373 | − | 0.775801i | −0.356375 | − | 0.934343i | \(-0.615987\pi\) |
−0.987352 | + | 0.158542i | \(0.949321\pi\) | |||||||
\(710\) | 12.9977 | − | 7.50420i | 0.487793 | − | 0.281628i | ||||
\(711\) | −3.37041 | − | 5.83773i | −0.126400 | − | 0.218932i | ||||
\(712\) | 4.08353 | − | 7.07288i | 0.153037 | − | 0.265067i | ||||
\(713\) | − | 11.7432i | − | 0.439785i | ||||||
\(714\) | −6.75478 | − | 3.24838i | −0.252791 | − | 0.121568i | ||||
\(715\) | 33.7492 | − | 1.56538i | 1.26215 | − | 0.0585417i | ||||
\(716\) | −9.37041 | + | 16.2300i | −0.350189 | + | 0.606545i | ||||
\(717\) | 9.67621 | − | 5.58656i | 0.361365 | − | 0.208634i | ||||
\(718\) | 0.716146 | + | 1.24040i | 0.0267263 | + | 0.0462914i | ||||
\(719\) | 14.9721 | − | 25.9324i | 0.558365 | − | 0.967116i | −0.439268 | − | 0.898356i | \(-0.644762\pi\) |
0.997633 | − | 0.0687604i | \(-0.0219044\pi\) | |||||||
\(720\) | − | 2.60168i | − | 0.0969589i | ||||||
\(721\) | 50.3244 | − | 3.79897i | 1.87418 | − | 0.141481i | ||||
\(722\) | − | 17.2201i | − | 0.640868i | ||||||
\(723\) | 12.7659 | + | 7.37041i | 0.474770 | + | 0.274109i | ||||
\(724\) | −0.213114 | − | 0.369125i | −0.00792032 | − | 0.0137184i | ||||
\(725\) | 7.93462 | + | 13.7432i | 0.294685 | + | 0.510409i | ||||
\(726\) | −1.70788 | − | 0.986046i | −0.0633855 | − | 0.0365956i | ||||
\(727\) | 22.8860 | 0.848796 | 0.424398 | − | 0.905476i | \(-0.360486\pi\) | ||||
0.424398 | + | 0.905476i | \(0.360486\pi\) | |||||||
\(728\) | 7.62123 | − | 5.73732i | 0.282462 | − | 0.212639i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −25.8454 | − | 14.9218i | −0.956580 | − | 0.552282i | ||||
\(731\) | 3.30620 | + | 5.72651i | 0.122284 | + | 0.211803i | ||||
\(732\) | 2.01815 | + | 3.49554i | 0.0745930 | + | 0.129199i | ||||
\(733\) | 33.8210 | + | 19.5265i | 1.24921 | + | 0.721229i | 0.970951 | − | 0.239278i | \(-0.0769107\pi\) |
0.278255 | + | 0.960507i | \(0.410244\pi\) | |||||||
\(734\) | − | 24.3509i | − | 0.898808i | ||||||
\(735\) | 16.9601 | + | 6.63495i | 0.625583 | + | 0.244734i | ||||
\(736\) | − | 2.93579i | − | 0.108215i | ||||||
\(737\) | 21.1433 | − | 36.6213i | 0.778825 | − | 1.34896i | ||||
\(738\) | 1.51815 | + | 2.62952i | 0.0558839 | + | 0.0967938i | ||||
\(739\) | 42.8282 | − | 24.7269i | 1.57546 | − | 0.909593i | 0.579980 | − | 0.814631i | \(-0.303060\pi\) |
0.995481 | − | 0.0949620i | \(-0.0302729\pi\) | |||||||
\(740\) | 0.217312 | − | 0.376395i | 0.00798855 | − | 0.0138366i | ||||
\(741\) | 0.222870 | + | 4.80504i | 0.00818734 | + | 0.176517i | ||||
\(742\) | −6.55562 | + | 4.47480i | −0.240664 | + | 0.164275i | ||||
\(743\) | 0.203358i | 0.00746049i | 0.999993 | + | 0.00373025i | \(0.00118738\pi\) | ||||
−0.999993 | + | 0.00373025i | \(0.998813\pi\) | |||||||
\(744\) | −2.00000 | + | 3.46410i | −0.0733236 | + | 0.127000i | ||||
\(745\) | 10.5877 | + | 18.3385i | 0.387904 | + | 0.671870i | ||||
\(746\) | −27.6717 | + | 15.9763i | −1.01313 | + | 0.584934i | ||||
\(747\) | 7.01525 | + | 4.05026i | 0.256675 | + | 0.148191i | ||||
\(748\) | 10.2034i | 0.373072i | ||||||||
\(749\) | −21.2975 | + | 1.60774i | −0.778194 | + | 0.0587457i | ||||
\(750\) | −8.40672 | −0.306970 | ||||||||
\(751\) | 21.4733 | − | 37.1928i | 0.783570 | − | 1.35718i | −0.146279 | − | 0.989243i | \(-0.546730\pi\) |
0.929849 | − | 0.367940i | \(-0.119937\pi\) | |||||||
\(752\) | 8.43580 | − | 4.87041i | 0.307622 | − | 0.177606i | ||||
\(753\) | −11.4733 | − | 19.8723i | −0.418109 | − | 0.724186i | ||||
\(754\) | 28.7347 | + | 14.8593i | 1.04646 | + | 0.541143i | ||||
\(755\) | 52.0554 | 1.89449 | ||||||||
\(756\) | 1.14664 | − | 2.38437i | 0.0417031 | − | 0.0867186i | ||||
\(757\) | −19.5180 | −0.709392 | −0.354696 | − | 0.934982i | \(-0.615416\pi\) | ||||
−0.354696 | + | 0.934982i | \(0.615416\pi\) | |||||||
\(758\) | 1.39832 | − | 2.42196i | 0.0507893 | − | 0.0879696i | ||||
\(759\) | 9.15715 | − | 5.28689i | 0.332384 | − | 0.191902i | ||||
\(760\) | 3.00591 | − | 1.73546i | 0.109036 | − | 0.0629519i | ||||
\(761\) | −36.3876 | − | 21.0084i | −1.31905 | − | 0.761554i | −0.335474 | − | 0.942049i | \(-0.608896\pi\) |
−0.983576 | + | 0.180496i | \(0.942230\pi\) | |||||||
\(762\) | 10.0386i | 0.363661i | ||||||||
\(763\) | 30.6850 | + | 14.7565i | 1.11087 | + | 0.534219i | ||||
\(764\) | 8.86925 | 0.320878 | ||||||||
\(765\) | −6.38297 | − | 3.68521i | −0.230777 | − | 0.133239i | ||||
\(766\) | 4.92184 | + | 8.52487i | 0.177833 | + | 0.308016i | ||||
\(767\) | −35.1336 | + | 22.5169i | −1.26860 | + | 0.813039i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 51.9502i | 1.87337i | 0.350168 | + | 0.936687i | \(0.386125\pi\) | ||||
−0.350168 | + | 0.936687i | \(0.613875\pi\) | |||||||
\(770\) | −1.86622 | − | 24.7214i | −0.0672537 | − | 0.890899i | ||||
\(771\) | −0.740827 | −0.0266802 | ||||||||
\(772\) | −6.06945 | − | 3.50420i | −0.218444 | − | 0.126119i | ||||
\(773\) | 36.4022 | − | 21.0168i | 1.30929 | − | 0.755921i | 0.327316 | − | 0.944915i | \(-0.393856\pi\) |
0.981978 | + | 0.188993i | \(0.0605225\pi\) | |||||||
\(774\) | −2.02140 | + | 1.16706i | −0.0726577 | + | 0.0419489i | ||||
\(775\) | −6.12708 | − | 3.53747i | −0.220091 | − | 0.127070i | ||||
\(776\) | −0.139148 | −0.00499511 | ||||||||
\(777\) | 0.365050 | − | 0.249180i | 0.0130961 | − | 0.00893927i | ||||
\(778\) | − | 16.3811i | − | 0.587292i | ||||||
\(779\) | −2.02538 | + | 3.50806i | −0.0725668 | + | 0.125689i | ||||
\(780\) | 7.89770 | − | 5.06160i | 0.282783 | − | 0.181234i | ||||
\(781\) | −10.3886 | − | 17.9935i | −0.371732 | − | 0.643859i | ||||
\(782\) | −7.20267 | − | 4.15846i | −0.257567 | − | 0.148706i | ||||
\(783\) | 8.97209 | 0.320636 | ||||||||
\(784\) | −4.37041 | − | 5.46804i | −0.156086 | − | 0.195287i | ||||
\(785\) | − | 55.5324i | − | 1.98204i | ||||||
\(786\) | 7.02454 | + | 4.05562i | 0.250557 | + | 0.144659i | ||||
\(787\) | −7.61610 | + | 4.39716i | −0.271485 | + | 0.156742i | −0.629562 | − | 0.776950i | \(-0.716766\pi\) |
0.358078 | + | 0.933692i | \(0.383432\pi\) | |||||||
\(788\) | −15.4196 | + | 8.90252i | −0.549301 | + | 0.317139i | ||||
\(789\) | 10.5042 | − | 18.1938i | 0.373959 | − | 0.647717i | ||||
\(790\) | −17.5375 | −0.623955 | ||||||||
\(791\) | 29.6530 | + | 43.4419i | 1.05434 | + | 1.54461i | ||||
\(792\) | −3.60168 | −0.127980 | ||||||||
\(793\) | −6.68479 | + | 12.9270i | −0.237384 | + | 0.459050i | ||||
\(794\) | −2.72151 | − | 4.71379i | −0.0965828 | − | 0.167286i | ||||
\(795\) | −6.75936 | + | 3.90252i | −0.239730 | + | 0.138408i | ||||
\(796\) | −13.5545 | + | 23.4770i | −0.480425 | + | 0.832120i | ||||
\(797\) | −6.25039 | −0.221400 | −0.110700 | − | 0.993854i | \(-0.535309\pi\) | ||||
−0.110700 | + | 0.993854i | \(0.535309\pi\) | |||||||
\(798\) | 3.51971 | − | 0.265702i | 0.124596 | − | 0.00940575i | ||||
\(799\) | − | 27.5952i | − | 0.976249i | ||||||
\(800\) | −1.53177 | − | 0.884367i | −0.0541562 | − | 0.0312671i | ||||
\(801\) | 7.07288 | − | 4.08353i | 0.249908 | − | 0.144284i | ||||
\(802\) | 8.78805 | + | 15.2214i | 0.310317 | + | 0.537485i | ||||
\(803\) | −20.6573 | + | 35.7795i | −0.728980 | + | 1.26263i | ||||
\(804\) | − | 11.7408i | − | 0.414067i | ||||||
\(805\) | 18.2118 | + | 8.75805i | 0.641880 | + | 0.308681i | ||||
\(806\) | −14.4067 | + | 0.668221i | −0.507455 | + | 0.0235371i | ||||
\(807\) | 15.5587 | − | 26.9484i | 0.547691 | − | 0.948628i | ||||
\(808\) | 3.08771 | − | 1.78269i | 0.108625 | − | 0.0627147i | ||||
\(809\) | 22.9260 | + | 39.7091i | 0.806036 | + | 1.39610i | 0.915589 | + | 0.402115i | \(0.131725\pi\) |
−0.109553 | + | 0.993981i | \(0.534942\pi\) | |||||||
\(810\) | 1.30084 | − | 2.25312i | 0.0457068 | − | 0.0791666i | ||||
\(811\) | 29.5096i | 1.03622i | 0.855314 | + | 0.518110i | \(0.173364\pi\) | ||||
−0.855314 | + | 0.518110i | \(0.826636\pi\) | |||||||
\(812\) | 10.2878 | − | 21.3928i | 0.361031 | − | 0.750739i | ||||
\(813\) | − | 2.00840i | − | 0.0704375i | ||||||
\(814\) | −0.521069 | − | 0.300840i | −0.0182635 | − | 0.0105444i | ||||
\(815\) | −1.33714 | − | 2.31600i | −0.0468381 | − | 0.0811259i | ||||
\(816\) | 1.41647 | + | 2.45340i | 0.0495865 | + | 0.0858863i | ||||
\(817\) | −2.69677 | − | 1.55698i | −0.0943480 | − | 0.0544718i | ||||
\(818\) | −19.0084 | −0.664613 | ||||||||
\(819\) | 9.46884 | − | 1.15804i | 0.330868 | − | 0.0404653i | ||||
\(820\) | 7.89949 | 0.275862 | ||||||||
\(821\) | 20.9197 | + | 12.0780i | 0.730101 | + | 0.421524i | 0.818459 | − | 0.574565i | \(-0.194829\pi\) |
−0.0883581 | + | 0.996089i | \(0.528162\pi\) | |||||||
\(822\) | −2.31479 | − | 4.00934i | −0.0807377 | − | 0.139842i | ||||
\(823\) | 15.3511 | + | 26.5889i | 0.535106 | + | 0.926830i | 0.999158 | + | 0.0410224i | \(0.0130615\pi\) |
−0.464053 | + | 0.885808i | \(0.653605\pi\) | |||||||
\(824\) | −16.5194 | − | 9.53747i | −0.575480 | − | 0.332253i | ||||
\(825\) | − | 6.37041i | − | 0.221789i | ||||||
\(826\) | 17.2634 | + | 25.2911i | 0.600672 | + | 0.879989i | ||||
\(827\) | − | 3.32338i | − | 0.115565i | −0.998329 | − | 0.0577827i | \(-0.981597\pi\) | ||
0.998329 | − | 0.0577827i | \(-0.0184031\pi\) | |||||||
\(828\) | 1.46789 | − | 2.54247i | 0.0510129 | − | 0.0883569i | ||||
\(829\) | 14.8232 | + | 25.6745i | 0.514831 | + | 0.891713i | 0.999852 | + | 0.0172105i | \(0.00547853\pi\) |
−0.485021 | + | 0.874502i | \(0.661188\pi\) | |||||||
\(830\) | 18.2514 | − | 10.5375i | 0.633516 | − | 0.365761i | ||||
\(831\) | −7.68404 | + | 13.3091i | −0.266556 | + | 0.461689i | ||||
\(832\) | −3.60168 | + | 0.167055i | −0.124866 | + | 0.00579160i | ||||
\(833\) | −19.6059 | + | 2.97705i | −0.679303 | + | 0.103149i | ||||
\(834\) | 0.935789i | 0.0324037i | ||||||||
\(835\) | 7.76570 | − | 13.4506i | 0.268743 | − | 0.465477i | ||||
\(836\) | −2.40252 | − | 4.16128i | −0.0830928 | − | 0.143921i | ||||
\(837\) | −3.46410 | + | 2.00000i | −0.119737 | + | 0.0691301i | ||||
\(838\) | 4.74725 | + | 2.74083i | 0.163991 | + | 0.0946803i | ||||
\(839\) | 5.51189i | 0.190292i | 0.995463 | + | 0.0951458i | \(0.0303317\pi\) | ||||
−0.995463 | + | 0.0951458i | \(0.969668\pi\) | |||||||
\(840\) | −3.88067 | − | 5.68521i | −0.133896 | − | 0.196158i | ||||
\(841\) | 51.4984 | 1.77581 | ||||||||
\(842\) | 1.58236 | − | 2.74073i | 0.0545318 | − | 0.0944518i | ||||
\(843\) | −14.4351 | + | 8.33411i | −0.497171 | + | 0.287042i | ||||
\(844\) | 11.3371 | + | 19.6365i | 0.390241 | + | 0.675916i | ||||
\(845\) | 30.7302 | + | 14.1270i | 1.05715 | + | 0.485983i | ||||
\(846\) | 9.74083 | 0.334897 | ||||||||
\(847\) | −5.20286 | + | 0.392763i | −0.178772 | + | 0.0134955i | ||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | −8.90252 | + | 15.4196i | −0.305534 | + | 0.529200i | ||||
\(850\) | −4.33942 | + | 2.50536i | −0.148841 | + | 0.0859333i | ||||
\(851\) | 0.424732 | − | 0.245219i | 0.0145596 | − | 0.00840601i | ||||
\(852\) | −4.99587 | − | 2.88437i | −0.171156 | − | 0.0988168i | ||||
\(853\) | − | 34.2611i | − | 1.17308i | −0.809921 | − | 0.586539i | \(-0.800490\pi\) | ||
0.809921 | − | 0.586539i | \(-0.199510\pi\) | |||||||
\(854\) | 9.62403 | + | 4.62820i | 0.329327 | + | 0.158374i | ||||
\(855\) | 3.47093 | 0.118703 | ||||||||
\(856\) | 6.99108 | + | 4.03630i | 0.238950 | + | 0.137958i | ||||
\(857\) | −18.2299 | − | 31.5751i | −0.622722 | − | 1.07859i | −0.988977 | − | 0.148071i | \(-0.952694\pi\) |
0.366255 | − | 0.930515i | \(-0.380640\pi\) | |||||||
\(858\) | −7.00712 | − | 10.9333i | −0.239219 | − | 0.373257i | ||||
\(859\) | −21.6743 | + | 37.5410i | −0.739517 | + | 1.28088i | 0.213196 | + | 0.977009i | \(0.431613\pi\) |
−0.952713 | + | 0.303872i | \(0.901721\pi\) | |||||||
\(860\) | 6.07261i | 0.207074i | ||||||||
\(861\) | 7.23966 | + | 3.48156i | 0.246727 | + | 0.118651i | ||||
\(862\) | −15.4370 | −0.525785 | ||||||||
\(863\) | −11.7907 | − | 6.80737i | −0.401360 | − | 0.231726i | 0.285710 | − | 0.958316i | \(-0.407770\pi\) |
−0.687071 | + | 0.726590i | \(0.741104\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 37.3616 | − | 21.5707i | 1.27033 | − | 0.733427i | ||||
\(866\) | 12.0740 | + | 6.97093i | 0.410291 | + | 0.236882i | ||||
\(867\) | −8.97442 | −0.304787 | ||||||||
\(868\) | 0.796642 | + | 10.5530i | 0.0270398 | + | 0.358191i | ||||
\(869\) | 24.2783i | 0.823585i | ||||||||
\(870\) | 11.6713 | − | 20.2152i | 0.395693 | − | 0.685360i | ||||
\(871\) | 35.6407 | − | 22.8419i | 1.20764 | − | 0.773970i | ||||
\(872\) | −6.43462 | − | 11.1451i | −0.217904 | − | 0.377421i | ||||
\(873\) | −0.120505 | − | 0.0695739i | −0.00407849 | − | 0.00235472i | ||||
\(874\) | 3.91667 | 0.132483 | ||||||||
\(875\) | −18.3704 | + | 12.5395i | −0.621033 | + | 0.423911i | ||||
\(876\) | 11.4709i | 0.387567i | ||||||||
\(877\) | −23.8292 | − | 13.7578i | −0.804656 | − | 0.464568i | 0.0404407 | − | 0.999182i | \(-0.487124\pi\) |
−0.845097 | + | 0.534614i | \(0.820457\pi\) | |||||||
\(878\) | 23.7180 | − | 13.6936i | 0.800444 | − | 0.462137i | ||||
\(879\) | −22.9265 | + | 13.2366i | −0.773292 | + | 0.446460i | ||||
\(880\) | −4.68521 | + | 8.11502i | −0.157938 | + | 0.273557i | ||||
\(881\) | −22.3341 | −0.752455 | −0.376228 | − | 0.926527i | \(-0.622779\pi\) | ||||
−0.376228 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(882\) | −1.05087 | − | 6.92067i | −0.0353846 | − | 0.233031i | ||||
\(883\) | 9.28669 | 0.312522 | 0.156261 | − | 0.987716i | \(-0.450056\pi\) | ||||
0.156261 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(884\) | −4.69183 | + | 9.07300i | −0.157803 | + | 0.305158i | ||||
\(885\) | 15.0556 | + | 26.0771i | 0.506089 | + | 0.876572i | ||||
\(886\) | −20.8809 | + | 12.0556i | −0.701509 | + | 0.405016i | ||||
\(887\) | 6.97209 | − | 12.0760i | 0.234100 | − | 0.405473i | −0.724911 | − | 0.688843i | \(-0.758119\pi\) |
0.959011 | + | 0.283370i | \(0.0914524\pi\) | |||||||
\(888\) | −0.167055 | −0.00560600 | ||||||||
\(889\) | 14.9736 | + | 21.9365i | 0.502199 | + | 0.735726i | ||||
\(890\) | − | 21.2481i | − | 0.712236i | ||||||
\(891\) | −3.11915 | − | 1.80084i | −0.104495 | − | 0.0603304i | ||||
\(892\) | −7.96307 | + | 4.59748i | −0.266623 | + | 0.153935i | ||||
\(893\) | 6.49767 | + | 11.2543i | 0.217436 | + | 0.376611i | ||||
\(894\) | 4.06957 | − | 7.04871i | 0.136107 | − | 0.235744i | ||||
\(895\) | 48.7576i | 1.62979i | ||||||||
\(896\) | 0.199160 | + | 2.63824i | 0.00665348 | + | 0.0881376i | ||||
\(897\) | 10.5738 | − | 0.490439i | 0.353048 | − | 0.0163753i | ||||
\(898\) | −1.29548 | + | 2.24383i | −0.0432306 | + | 0.0748776i | ||||
\(899\) | −31.0802 | + | 17.9442i | −1.03658 | + | 0.598472i | ||||
\(900\) | −0.884367 | − | 1.53177i | −0.0294789 | − | 0.0510590i | ||||
\(901\) | 4.24942 | − | 7.36021i | 0.141569 | − | 0.245204i | ||||
\(902\) | − | 10.9358i | − | 0.364122i | ||||||
\(903\) | −2.67639 | + | 5.56538i | −0.0890648 | + | 0.185204i | ||||
\(904\) | − | 19.8800i | − | 0.661198i | ||||||
\(905\) | −0.960344 | − | 0.554455i | −0.0319229 | − | 0.0184307i | ||||
\(906\) | −10.0042 | − | 17.3278i | −0.332367 | − | 0.575677i | ||||
\(907\) | −2.06957 | − | 3.58461i | −0.0687191 | − | 0.119025i | 0.829619 | − | 0.558330i | \(-0.188558\pi\) |
−0.898338 | + | 0.439306i | \(0.855225\pi\) | |||||||
\(908\) | −11.7238 | − | 6.76873i | −0.389068 | − | 0.224628i | ||||
\(909\) | 3.56538 | 0.118256 | ||||||||
\(910\) | 9.70823 | − | 22.8409i | 0.321825 | − | 0.757167i | ||||
\(911\) | 18.5566 | 0.614807 | 0.307404 | − | 0.951579i | \(-0.400540\pi\) | ||||
0.307404 | + | 0.951579i | \(0.400540\pi\) | |||||||
\(912\) | −1.15537 | − | 0.667055i | −0.0382582 | − | 0.0220884i | ||||
\(913\) | −14.5877 | − | 25.2667i | −0.482783 | − | 0.836205i | ||||
\(914\) | −5.23430 | − | 9.06607i | −0.173135 | − | 0.299879i | ||||
\(915\) | 9.09428 | + | 5.25058i | 0.300647 | + | 0.173579i | ||||
\(916\) | 18.4067i | 0.608175i | ||||||||
\(917\) | 21.3994 | − | 1.61544i | 0.706672 | − | 0.0533465i | ||||
\(918\) | 2.83294i | 0.0935011i | ||||||||
\(919\) | −25.6743 | + | 44.4692i | −0.846917 | + | 1.46690i | 0.0370298 | + | 0.999314i | \(0.488210\pi\) |
−0.883946 | + | 0.467588i | \(0.845123\pi\) | |||||||
\(920\) | −3.81899 | − | 6.61469i | −0.125908 | − | 0.218080i | ||||
\(921\) | 20.1596 | − | 11.6391i | 0.664281 | − | 0.383523i | ||||
\(922\) | −15.0084 | + | 25.9953i | −0.494275 | + | 0.856110i | ||||
\(923\) | −0.963697 | − | 20.7771i | −0.0317205 | − | 0.683888i | ||||
\(924\) | −7.87041 | + | 5.37227i | −0.258918 | + | 0.176735i | ||||
\(925\) | − | 0.295476i | − | 0.00971520i | ||||||
\(926\) | 9.73243 | − | 16.8571i | 0.319828 | − | 0.553958i | ||||
\(927\) | −9.53747 | − | 16.5194i | −0.313252 | − | 0.542568i | ||||
\(928\) | −7.77006 | + | 4.48605i | −0.255065 | + | 0.147262i | ||||
\(929\) | 6.01182 | + | 3.47093i | 0.197241 | + | 0.113877i | 0.595368 | − | 0.803453i | \(-0.297006\pi\) |
−0.398127 | + | 0.917330i | \(0.630340\pi\) | |||||||
\(930\) | 10.4067i | 0.341250i | ||||||||
\(931\) | 7.29497 | − | 5.83061i | 0.239083 | − | 0.191091i | ||||
\(932\) | 11.7301 | 0.384232 | ||||||||
\(933\) | −8.27293 | + | 14.3291i | −0.270844 | + | 0.469115i | ||||
\(934\) | 0.259927 | − | 0.150069i | 0.00850508 | − | 0.00491041i | ||||
\(935\) | 13.2729 | + | 22.9894i | 0.434071 | + | 0.751834i | ||||
\(936\) | −3.20267 | − | 1.65617i | −0.104683 | − | 0.0541335i | ||||
\(937\) | 37.1005 | 1.21202 | 0.606010 | − | 0.795457i | \(-0.292769\pi\) | ||||
0.606010 | + | 0.795457i | \(0.292769\pi\) | |||||||
\(938\) | −17.5126 | − | 25.6561i | −0.571807 | − | 0.837702i | ||||
\(939\) | −10.0279 | −0.327248 | ||||||||
\(940\) | 12.6713 | − | 21.9473i | 0.413291 | − | 0.715840i | ||||
\(941\) | 7.28447 | − | 4.20569i | 0.237467 | − | 0.137102i | −0.376545 | − | 0.926398i | \(-0.622888\pi\) |
0.614012 | + | 0.789297i | \(0.289555\pi\) | |||||||
\(942\) | −18.4852 | + | 10.6724i | −0.602279 | + | 0.347726i | ||||
\(943\) | 7.71970 | + | 4.45697i | 0.251388 | + | 0.145139i | ||||
\(944\) | − | 11.5738i | − | 0.376694i | ||||||
\(945\) | −0.518152 | − | 6.86387i | −0.0168555 | − | 0.223282i | ||||
\(946\) | 8.40672 | 0.273326 | ||||||||
\(947\) | 21.7953 | + | 12.5835i | 0.708252 | + | 0.408910i | 0.810414 | − | 0.585858i | \(-0.199242\pi\) |
−0.102161 | + | 0.994768i | \(0.532576\pi\) | |||||||
\(948\) | 3.37041 | + | 5.83773i | 0.109466 | + | 0.189601i | ||||
\(949\) | −34.8214 | + | 22.3168i | −1.13035 | + | 0.724435i | ||||
\(950\) | 1.17984 | − | 2.04355i | 0.0382792 | − | 0.0663015i | ||||
\(951\) | − | 21.4090i | − | 0.694236i | ||||||
\(952\) | 6.75478 | + | 3.24838i | 0.218924 | + | 0.105281i | ||||
\(953\) | 35.3681 | 1.14568 | 0.572842 | − | 0.819666i | \(-0.305841\pi\) | ||||
0.572842 | + | 0.819666i | \(0.305841\pi\) | |||||||
\(954\) | 2.59808 | + | 1.50000i | 0.0841158 | + | 0.0485643i | ||||
\(955\) | 19.9835 | − | 11.5375i | 0.646650 | − | 0.373344i | ||||
\(956\) | −9.67621 | + | 5.58656i | −0.312951 | + | 0.180682i | ||||
\(957\) | −27.9853 | − | 16.1573i | −0.904635 | − | 0.522291i | ||||
\(958\) | 23.5845 | 0.761981 | ||||||||
\(959\) | −11.0386 | − | 5.30849i | −0.356456 | − | 0.171420i | ||||
\(960\) | 2.60168i | 0.0839688i | ||||||||
\(961\) | −7.50000 | + | 12.9904i | −0.241935 | + | 0.419045i | ||||
\(962\) | −0.325008 | − | 0.507116i | −0.0104787 | − | 0.0163501i | ||||
\(963\) | 4.03630 | + | 6.99108i | 0.130068 | + | 0.225284i | ||||
\(964\) | −12.7659 | − | 7.37041i | −0.411163 | − | 0.237385i | ||||
\(965\) | −18.2336 | −0.586960 | ||||||||
\(966\) | −0.584693 | − | 7.74533i | −0.0188122 | − | 0.249202i | ||||
\(967\) | 17.3123i | 0.556725i | 0.960476 | + | 0.278362i | \(0.0897917\pi\) | ||||
−0.960476 | + | 0.278362i | \(0.910208\pi\) | |||||||
\(968\) | 1.70788 | + | 0.986046i | 0.0548934 | + | 0.0316927i | ||||
\(969\) | −3.27311 | + | 1.88973i | −0.105147 | + | 0.0607069i | ||||
\(970\) | −0.313517 | + | 0.181009i | −0.0100664 | + | 0.00581185i | ||||
\(971\) | 26.6959 | − | 46.2387i | 0.856713 | − | 1.48387i | −0.0183332 | − | 0.999832i | \(-0.505836\pi\) |
0.875046 | − | 0.484039i | \(-0.160831\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 1.39582 | + | 2.04489i | 0.0447481 | + | 0.0655563i | ||||
\(974\) | 34.2420 | 1.09718 | ||||||||
\(975\) | 2.92932 | − | 5.66468i | 0.0938132 | − | 0.181415i | ||||
\(976\) | −2.01815 | − | 3.49554i | −0.0645995 | − | 0.111890i | ||||
\(977\) | −28.4656 | + | 16.4346i | −0.910695 | + | 0.525790i | −0.880655 | − | 0.473758i | \(-0.842897\pi\) |
−0.0300405 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(978\) | −0.513954 | + | 0.890194i | −0.0164344 | + | 0.0284653i | ||||
\(979\) | −29.4151 | −0.940111 | ||||||||
\(980\) | −16.9601 | − | 6.63495i | −0.541771 | − | 0.211946i | ||||
\(981\) | − | 12.8692i | − | 0.410883i | ||||||
\(982\) | −34.4291 | − | 19.8776i | −1.09868 | − | 0.634321i | ||||
\(983\) | 8.42126 | − | 4.86202i | 0.268597 | − | 0.155074i | −0.359653 | − | 0.933086i | \(-0.617105\pi\) |
0.628250 | + | 0.778012i | \(0.283772\pi\) | |||||||
\(984\) | −1.51815 | − | 2.62952i | −0.0483969 | − | 0.0838259i | ||||
\(985\) | −23.1615 | + | 40.1169i | −0.737987 | + | 1.27823i | ||||
\(986\) | 25.4174i | 0.809456i | ||||||||
\(987\) | 21.2857 | − | 14.5294i | 0.677532 | − | 0.462477i | ||||
\(988\) | −0.222870 | − | 4.80504i | −0.00709044 | − | 0.152869i | ||||
\(989\) | −3.42623 | + | 5.93440i | −0.108948 | + | 0.188703i | ||||
\(990\) | −8.11502 | + | 4.68521i | −0.257912 | + | 0.148906i | ||||
\(991\) | −16.2057 | − | 28.0691i | −0.514791 | − | 0.891644i | −0.999853 | − | 0.0171639i | \(-0.994536\pi\) |
0.485062 | − | 0.874480i | \(-0.338797\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | 35.8605i | 1.13800i | ||||||||
\(994\) | −15.2193 | + | 1.14890i | −0.482728 | + | 0.0364410i | ||||
\(995\) | 70.5287i | 2.23591i | ||||||||
\(996\) | −7.01525 | − | 4.05026i | −0.222287 | − | 0.128337i | ||||
\(997\) | 22.8395 | + | 39.5591i | 0.723333 | + | 1.25285i | 0.959656 | + | 0.281176i | \(0.0907243\pi\) |
−0.236323 | + | 0.971675i | \(0.575942\pi\) | |||||||
\(998\) | 6.12519 | + | 10.6091i | 0.193890 | + | 0.335827i | ||||
\(999\) | −0.144674 | − | 0.0835276i | −0.00457728 | − | 0.00264270i |
(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.bk.b.415.6 | yes | 12 | |
3.2 | odd | 2 | 1638.2.dm.c.415.1 | 12 | |||
7.2 | even | 3 | 3822.2.c.k.883.1 | 6 | |||
7.4 | even | 3 | inner | 546.2.bk.b.25.1 | ✓ | 12 | |
7.5 | odd | 6 | 3822.2.c.j.883.3 | 6 | |||
13.12 | even | 2 | inner | 546.2.bk.b.415.1 | yes | 12 | |
21.11 | odd | 6 | 1638.2.dm.c.1117.6 | 12 | |||
39.38 | odd | 2 | 1638.2.dm.c.415.6 | 12 | |||
91.12 | odd | 6 | 3822.2.c.j.883.4 | 6 | |||
91.25 | even | 6 | inner | 546.2.bk.b.25.6 | yes | 12 | |
91.51 | even | 6 | 3822.2.c.k.883.6 | 6 | |||
273.116 | odd | 6 | 1638.2.dm.c.1117.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bk.b.25.1 | ✓ | 12 | 7.4 | even | 3 | inner | |
546.2.bk.b.25.6 | yes | 12 | 91.25 | even | 6 | inner | |
546.2.bk.b.415.1 | yes | 12 | 13.12 | even | 2 | inner | |
546.2.bk.b.415.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1638.2.dm.c.415.1 | 12 | 3.2 | odd | 2 | |||
1638.2.dm.c.415.6 | 12 | 39.38 | odd | 2 | |||
1638.2.dm.c.1117.1 | 12 | 273.116 | odd | 6 | |||
1638.2.dm.c.1117.6 | 12 | 21.11 | odd | 6 | |||
3822.2.c.j.883.3 | 6 | 7.5 | odd | 6 | |||
3822.2.c.j.883.4 | 6 | 91.12 | odd | 6 | |||
3822.2.c.k.883.1 | 6 | 7.2 | even | 3 | |||
3822.2.c.k.883.6 | 6 | 91.51 | even | 6 |