Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(89,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bo (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(-1.27963 - 1.83372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.269 |
Dual form | 630.2.bo.b.89.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.27963 | − | 1.83372i | −0.572269 | − | 0.820066i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.732536 | + | 2.54232i | −0.276872 | + | 0.960907i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.948234 | − | 2.02506i | 0.299858 | − | 0.640379i | ||||
\(11\) | −2.07577 | − | 1.19845i | −0.625869 | − | 0.361346i | 0.153282 | − | 0.988183i | \(-0.451016\pi\) |
−0.779150 | + | 0.626837i | \(0.784349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.67714 | −1.57455 | −0.787277 | − | 0.616599i | \(-0.788510\pi\) | ||||
−0.787277 | + | 0.616599i | \(0.788510\pi\) | |||||||
\(14\) | −2.56798 | + | 0.636766i | −0.686322 | + | 0.170183i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.79434 | + | 1.03596i | 0.435191 | + | 0.251258i | 0.701556 | − | 0.712615i | \(-0.252489\pi\) |
−0.266365 | + | 0.963872i | \(0.585823\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.12164 | + | 2.95698i | −1.17499 | + | 0.678378i | −0.954849 | − | 0.297091i | \(-0.903984\pi\) |
−0.220136 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(20\) | 2.22787 | − | 0.191334i | 0.498166 | − | 0.0427835i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.39690i | − | 0.511020i | ||||||
\(23\) | 0.930877 | + | 1.61233i | 0.194101 | + | 0.336193i | 0.946606 | − | 0.322394i | \(-0.104488\pi\) |
−0.752504 | + | 0.658587i | \(0.771154\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.72508 | + | 4.69298i | −0.345016 | + | 0.938597i | ||||
\(26\) | −2.83857 | − | 4.91654i | −0.556689 | − | 0.964214i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.83545 | − | 1.90555i | −0.346867 | − | 0.360116i | ||||
\(29\) | − | 4.88913i | − | 0.907889i | −0.891030 | − | 0.453944i | \(-0.850016\pi\) | ||
0.891030 | − | 0.453944i | \(-0.149984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.92008 | − | 2.26326i | −0.704067 | − | 0.406493i | 0.104794 | − | 0.994494i | \(-0.466582\pi\) |
−0.808860 | + | 0.588001i | \(0.799915\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.07192i | 0.355332i | ||||||||
\(35\) | 5.59929 | − | 1.90997i | 0.946452 | − | 0.322844i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.57132 | − | 1.48455i | 0.422723 | − | 0.244059i | −0.273519 | − | 0.961867i | \(-0.588188\pi\) |
0.696242 | + | 0.717807i | \(0.254854\pi\) | |||||||
\(38\) | −5.12164 | − | 2.95698i | −0.830840 | − | 0.479686i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.27963 | + | 1.83372i | 0.202328 | + | 0.289937i | ||||
\(41\) | −7.04428 | −1.10013 | −0.550066 | − | 0.835121i | \(-0.685397\pi\) | ||||
−0.550066 | + | 0.835121i | \(0.685397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.55956i | 1.30532i | 0.757651 | + | 0.652660i | \(0.226347\pi\) | ||||
−0.757651 | + | 0.652660i | \(0.773653\pi\) | |||||||
\(44\) | 2.07577 | − | 1.19845i | 0.312934 | − | 0.180673i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.930877 | + | 1.61233i | −0.137250 | + | 0.237725i | ||||
\(47\) | −4.83140 | + | 2.78941i | −0.704732 | + | 0.406877i | −0.809107 | − | 0.587661i | \(-0.800049\pi\) |
0.104375 | + | 0.994538i | \(0.466716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92678 | − | 3.72468i | −0.846683 | − | 0.532097i | ||||
\(50\) | −4.92678 | + | 0.852531i | −0.696752 | + | 0.120566i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.83857 | − | 4.91654i | 0.393639 | − | 0.681802i | ||||
\(53\) | 2.09538 | − | 3.62931i | 0.287823 | − | 0.498524i | −0.685467 | − | 0.728104i | \(-0.740402\pi\) |
0.973290 | + | 0.229580i | \(0.0737352\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.458606 | + | 5.33996i | 0.0618385 | + | 0.720041i | ||||
\(56\) | 0.732536 | − | 2.54232i | 0.0978892 | − | 0.339732i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.23411 | − | 2.44457i | 0.555966 | − | 0.320987i | ||||
\(59\) | −1.00312 | + | 1.73746i | −0.130595 | + | 0.226198i | −0.923906 | − | 0.382619i | \(-0.875022\pi\) |
0.793311 | + | 0.608817i | \(0.208356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7862 | − | 6.22739i | 1.38103 | − | 0.797335i | 0.388744 | − | 0.921346i | \(-0.372909\pi\) |
0.992281 | + | 0.124011i | \(0.0395757\pi\) | |||||||
\(62\) | − | 4.52651i | − | 0.574868i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.26465 | + | 10.4103i | 0.901069 | + | 1.29124i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.60103 | + | 3.81111i | 0.806445 | + | 0.465601i | 0.845720 | − | 0.533627i | \(-0.179171\pi\) |
−0.0392750 | + | 0.999228i | \(0.512505\pi\) | |||||||
\(68\) | −1.79434 | + | 1.03596i | −0.217596 | + | 0.125629i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.45373 | + | 3.89414i | 0.532322 | + | 0.465439i | ||||
\(71\) | − | 9.14126i | − | 1.08487i | −0.840099 | − | 0.542434i | \(-0.817503\pi\) | ||
0.840099 | − | 0.542434i | \(-0.182497\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.541173 | − | 0.937339i | 0.0633395 | − | 0.109707i | −0.832617 | − | 0.553850i | \(-0.813158\pi\) |
0.895956 | + | 0.444142i | \(0.146492\pi\) | |||||||
\(74\) | 2.57132 | + | 1.48455i | 0.298910 | + | 0.172576i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.91397i | − | 0.678378i | ||||||
\(77\) | 4.56742 | − | 4.39937i | 0.520505 | − | 0.501355i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.38392 | + | 14.5214i | 0.943265 | + | 1.63378i | 0.759189 | + | 0.650870i | \(0.225596\pi\) |
0.184076 | + | 0.982912i | \(0.441071\pi\) | |||||||
\(80\) | −0.948234 | + | 2.02506i | −0.106016 | + | 0.226408i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.52214 | − | 6.10053i | −0.388955 | − | 0.673690i | ||||
\(83\) | − | 13.6122i | − | 1.49414i | −0.664747 | − | 0.747068i | \(-0.731461\pi\) | ||
0.664747 | − | 0.747068i | \(-0.268539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.396428 | − | 4.61597i | −0.0429987 | − | 0.500672i | ||||
\(86\) | −7.41279 | + | 4.27978i | −0.799342 | + | 0.461500i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.07577 | + | 1.19845i | 0.221278 | + | 0.127755i | ||||
\(89\) | 6.63129 | + | 11.4857i | 0.702916 | + | 1.21749i | 0.967438 | + | 0.253106i | \(0.0814523\pi\) |
−0.264523 | + | 0.964379i | \(0.585214\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.15870 | − | 14.4331i | 0.435951 | − | 1.51300i | ||||
\(92\) | −1.86175 | −0.194101 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.83140 | − | 2.78941i | −0.498321 | − | 0.287706i | ||||
\(95\) | 11.9761 | + | 5.60782i | 1.22872 | + | 0.575350i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8260 | −1.30229 | −0.651143 | − | 0.758955i | \(-0.725710\pi\) | ||||
−0.651143 | + | 0.758955i | \(0.725710\pi\) | |||||||
\(98\) | 0.262276 | − | 6.99508i | 0.0264939 | − | 0.706610i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.20171 | − | 3.84045i | −0.320171 | − | 0.384045i | ||||
\(101\) | −4.45573 | + | 7.71756i | −0.443362 | + | 0.767926i | −0.997937 | − | 0.0642084i | \(-0.979548\pi\) |
0.554574 | + | 0.832134i | \(0.312881\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.40989 | + | 9.37021i | 0.533053 | + | 0.923274i | 0.999255 | + | 0.0385960i | \(0.0122885\pi\) |
−0.466202 | + | 0.884678i | \(0.654378\pi\) | |||||||
\(104\) | 5.67714 | 0.556689 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.19077 | 0.407043 | ||||||||
\(107\) | 2.78854 | + | 4.82989i | 0.269578 | + | 0.466923i | 0.968753 | − | 0.248028i | \(-0.0797825\pi\) |
−0.699175 | + | 0.714951i | \(0.746449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | −4.39524 | + | 3.06715i | −0.419070 | + | 0.292441i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.56798 | − | 0.636766i | 0.242651 | − | 0.0601687i | ||||
\(113\) | −14.5030 | −1.36432 | −0.682161 | − | 0.731202i | \(-0.738960\pi\) | ||||
−0.682161 | + | 0.731202i | \(0.738960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.76538 | − | 3.77016i | 0.164622 | − | 0.351569i | ||||
\(116\) | 4.23411 | + | 2.44457i | 0.393127 | + | 0.226972i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00624 | −0.184690 | ||||||||
\(119\) | −3.94816 | + | 3.80290i | −0.361928 | + | 0.348612i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.62745 | − | 4.55087i | −0.238859 | − | 0.413715i | ||||
\(122\) | 10.7862 | + | 6.22739i | 0.976532 | + | 0.563801i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.92008 | − | 2.26326i | 0.352033 | − | 0.203247i | ||||
\(125\) | 10.8131 | − | 2.84199i | 0.967153 | − | 0.254195i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2462i | 1.70783i | 0.520416 | + | 0.853913i | \(0.325777\pi\) | ||||
−0.520416 | + | 0.853913i | \(0.674223\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.38325 | + | 11.4965i | −0.472142 | + | 1.00831i | ||||
\(131\) | 2.34970 | + | 4.06980i | 0.205294 | + | 0.355580i | 0.950226 | − | 0.311560i | \(-0.100851\pi\) |
−0.744932 | + | 0.667140i | \(0.767518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.76581 | − | 15.1870i | −0.326537 | − | 1.31688i | ||||
\(134\) | 7.62222i | 0.658459i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.79434 | − | 1.03596i | −0.153863 | − | 0.0888330i | ||||
\(137\) | −11.4422 | + | 19.8185i | −0.977577 | + | 1.69321i | −0.306421 | + | 0.951896i | \(0.599132\pi\) |
−0.671155 | + | 0.741317i | \(0.734202\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.13862i | − | 0.775127i | −0.921843 | − | 0.387564i | \(-0.873317\pi\) | ||
0.921843 | − | 0.387564i | \(-0.126683\pi\) | |||||||
\(140\) | −1.14556 | + | 5.80411i | −0.0968176 | + | 0.490537i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.91656 | − | 4.57063i | 0.664343 | − | 0.383559i | ||||
\(143\) | 11.7844 | + | 6.80375i | 0.985465 | + | 0.568958i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.96531 | + | 6.25629i | −0.744528 | + | 0.519557i | ||||
\(146\) | 1.08235 | 0.0895756 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.96911i | 0.244059i | ||||||||
\(149\) | 9.05052 | − | 5.22532i | 0.741448 | − | 0.428075i | −0.0811477 | − | 0.996702i | \(-0.525859\pi\) |
0.822596 | + | 0.568627i | \(0.192525\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.85937 | − | 15.3449i | 0.720965 | − | 1.24875i | −0.239648 | − | 0.970860i | \(-0.577032\pi\) |
0.960613 | − | 0.277888i | \(-0.0896346\pi\) | |||||||
\(152\) | 5.12164 | − | 2.95698i | 0.415420 | − | 0.239843i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.09368 | + | 1.75581i | 0.491042 | + | 0.141487i | ||||
\(155\) | 0.866074 | + | 10.0845i | 0.0695647 | + | 0.810004i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.04149 | + | 5.26801i | −0.242737 | + | 0.420433i | −0.961493 | − | 0.274830i | \(-0.911379\pi\) |
0.718756 | + | 0.695263i | \(0.244712\pi\) | |||||||
\(158\) | −8.38392 | + | 14.5214i | −0.666989 | + | 1.15526i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.22787 | + | 0.191334i | −0.176128 | + | 0.0151262i | ||||
\(161\) | −4.78095 | + | 1.18550i | −0.376792 | + | 0.0934305i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.811759 | + | 0.468670i | −0.0635819 | + | 0.0367090i | −0.531454 | − | 0.847087i | \(-0.678354\pi\) |
0.467872 | + | 0.883796i | \(0.345021\pi\) | |||||||
\(164\) | 3.52214 | − | 6.10053i | 0.275033 | − | 0.476371i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.7885 | − | 6.80611i | 0.914968 | − | 0.528257i | ||||
\(167\) | − | 17.2101i | − | 1.33176i | −0.746060 | − | 0.665879i | \(-0.768057\pi\) | ||
0.746060 | − | 0.665879i | \(-0.231943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.2299 | 1.47922 | ||||||||
\(170\) | 3.79933 | − | 2.65130i | 0.291396 | − | 0.203346i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.41279 | − | 4.27978i | −0.565220 | − | 0.326330i | ||||
\(173\) | 1.71146 | − | 0.988114i | 0.130120 | − | 0.0751249i | −0.433527 | − | 0.901141i | \(-0.642731\pi\) |
0.563647 | + | 0.826016i | \(0.309398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.6674 | − | 7.82348i | −0.806379 | − | 0.591399i | ||||
\(176\) | 2.39690i | 0.180673i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.63129 | + | 11.4857i | −0.497037 | + | 0.860893i | ||||
\(179\) | 0.768461 | + | 0.443671i | 0.0574375 | + | 0.0331615i | 0.528444 | − | 0.848968i | \(-0.322776\pi\) |
−0.471006 | + | 0.882130i | \(0.656109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.89973i | − | 0.364194i | −0.983281 | − | 0.182097i | \(-0.941712\pi\) | ||
0.983281 | − | 0.182097i | \(-0.0582885\pi\) | |||||||
\(182\) | 14.5788 | − | 3.61500i | 1.08065 | − | 0.267962i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.930877 | − | 1.61233i | −0.0686252 | − | 0.118862i | ||||
\(185\) | −6.01261 | − | 2.81541i | −0.442056 | − | 0.206993i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.48309 | − | 4.30084i | −0.181582 | − | 0.314509i | ||||
\(188\) | − | 5.57882i | − | 0.406877i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.13154 | + | 13.1755i | 0.0820905 | + | 0.955853i | ||||
\(191\) | 2.44949 | − | 1.41421i | 0.177239 | − | 0.102329i | −0.408756 | − | 0.912644i | \(-0.634037\pi\) |
0.585995 | + | 0.810315i | \(0.300704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8845 | − | 9.74828i | −1.21537 | − | 0.701697i | −0.251449 | − | 0.967871i | \(-0.580907\pi\) |
−0.963925 | + | 0.266174i | \(0.914240\pi\) | |||||||
\(194\) | −6.41301 | − | 11.1077i | −0.460428 | − | 0.797484i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.18906 | − | 3.27040i | 0.442076 | − | 0.233600i | ||||
\(197\) | −27.1576 | −1.93490 | −0.967448 | − | 0.253069i | \(-0.918560\pi\) | ||||
−0.967448 | + | 0.253069i | \(0.918560\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00000 | − | 1.73205i | −0.212664 | − | 0.122782i | 0.389885 | − | 0.920864i | \(-0.372515\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | 1.72508 | − | 4.69298i | 0.121981 | − | 0.331844i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.91147 | −0.627009 | ||||||||
\(203\) | 12.4297 | + | 3.58146i | 0.872396 | + | 0.251369i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.01409 | + | 12.9173i | 0.629572 | + | 0.902180i | ||||
\(206\) | −5.40989 | + | 9.37021i | −0.376925 | + | 0.652853i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.83857 | + | 4.91654i | 0.196819 | + | 0.340901i | ||||
\(209\) | 14.1752 | 0.980516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.06071 | −0.279551 | −0.139775 | − | 0.990183i | \(-0.544638\pi\) | ||||
−0.139775 | + | 0.990183i | \(0.544638\pi\) | |||||||
\(212\) | 2.09538 | + | 3.62931i | 0.143912 | + | 0.249262i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.78854 | + | 4.82989i | −0.190620 | + | 0.330164i | ||||
\(215\) | 15.6959 | − | 10.9531i | 1.07045 | − | 0.746995i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.62552 | − | 8.30817i | 0.585538 | − | 0.563996i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.85385 | − | 2.27282i | −0.327246 | − | 0.153233i | ||||
\(221\) | −10.1867 | − | 5.88130i | −0.685232 | − | 0.395619i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1486 | 1.08139 | 0.540696 | − | 0.841218i | \(-0.318161\pi\) | ||||
0.540696 | + | 0.841218i | \(0.318161\pi\) | |||||||
\(224\) | 1.83545 | + | 1.90555i | 0.122636 | + | 0.127320i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.25148 | − | 12.5599i | −0.482361 | − | 0.835474i | ||||
\(227\) | −1.45475 | − | 0.839901i | −0.0965552 | − | 0.0557462i | 0.450945 | − | 0.892552i | \(-0.351087\pi\) |
−0.547500 | + | 0.836806i | \(0.684420\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9143 | + | 6.30136i | −0.721236 | + | 0.416406i | −0.815207 | − | 0.579169i | \(-0.803377\pi\) |
0.0939717 | + | 0.995575i | \(0.470044\pi\) | |||||||
\(230\) | 4.14774 | − | 0.356216i | 0.273494 | − | 0.0234882i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.88913i | 0.320987i | ||||||||
\(233\) | 7.25818 | + | 12.5715i | 0.475499 | + | 0.823589i | 0.999606 | − | 0.0280635i | \(-0.00893407\pi\) |
−0.524107 | + | 0.851653i | \(0.675601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.2974 | + | 5.29003i | 0.736963 | + | 0.345083i | ||||
\(236\) | −1.00312 | − | 1.73746i | −0.0652977 | − | 0.113099i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.26749 | − | 1.51776i | −0.341441 | − | 0.0983816i | ||||
\(239\) | 0.207089i | 0.0133955i | 0.999978 | + | 0.00669774i | \(0.00213197\pi\) | ||||
−0.999978 | + | 0.00669774i | \(0.997868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.04172 | + | 5.22024i | 0.582428 | + | 0.336265i | 0.762098 | − | 0.647462i | \(-0.224169\pi\) |
−0.179669 | + | 0.983727i | \(0.557503\pi\) | |||||||
\(242\) | 2.62745 | − | 4.55087i | 0.168899 | − | 0.292541i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.4548i | 0.797335i | ||||||||
\(245\) | 0.754077 | + | 15.6343i | 0.0481762 | + | 0.998839i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.0763 | − | 16.7872i | 1.85008 | − | 1.06814i | ||||
\(248\) | 3.92008 | + | 2.26326i | 0.248925 | + | 0.143717i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.86778 | + | 7.94343i | 0.497602 | + | 0.502386i | ||||
\(251\) | −28.6464 | −1.80815 | −0.904074 | − | 0.427377i | \(-0.859438\pi\) | ||||
−0.904074 | + | 0.427377i | \(0.859438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.46243i | − | 0.280551i | ||||||
\(254\) | −16.6677 | + | 9.62311i | −1.04583 | + | 0.603808i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −21.5805 | + | 12.4595i | −1.34615 | + | 0.777202i | −0.987702 | − | 0.156346i | \(-0.950029\pi\) |
−0.358452 | + | 0.933548i | \(0.616695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.89063 | + | 7.62462i | 0.117478 | + | 0.473771i | ||||
\(260\) | −12.6479 | + | 1.08623i | −0.784390 | + | 0.0673649i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.34970 | + | 4.06980i | −0.145165 | + | 0.251433i | ||||
\(263\) | −9.59538 | + | 16.6197i | −0.591677 | + | 1.02481i | 0.402330 | + | 0.915495i | \(0.368200\pi\) |
−0.994007 | + | 0.109319i | \(0.965133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.33647 | + | 0.801834i | −0.573535 | + | 0.0492563i | ||||
\(266\) | 11.2694 | − | 10.8548i | 0.690970 | − | 0.665548i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.60103 | + | 3.81111i | −0.403222 | + | 0.232801i | ||||
\(269\) | −2.42744 | + | 4.20446i | −0.148004 | + | 0.256350i | −0.930490 | − | 0.366318i | \(-0.880618\pi\) |
0.782486 | + | 0.622668i | \(0.213951\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8344 | + | 6.83257i | −0.718886 | + | 0.415049i | −0.814342 | − | 0.580385i | \(-0.802902\pi\) |
0.0954567 | + | 0.995434i | \(0.469569\pi\) | |||||||
\(272\) | − | 2.07192i | − | 0.125629i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.8845 | −1.38250 | ||||||||
\(275\) | 9.20517 | − | 7.67415i | 0.555092 | − | 0.462769i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.5047 | + | 6.06491i | 0.631168 | + | 0.364405i | 0.781204 | − | 0.624276i | \(-0.214606\pi\) |
−0.150036 | + | 0.988680i | \(0.547939\pi\) | |||||||
\(278\) | 7.91427 | − | 4.56931i | 0.474667 | − | 0.274049i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.59929 | + | 1.90997i | −0.334621 | + | 0.114143i | ||||
\(281\) | − | 32.6206i | − | 1.94598i | −0.230839 | − | 0.972992i | \(-0.574147\pi\) | ||
0.230839 | − | 0.972992i | \(-0.425853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.33045 | − | 10.9647i | 0.376306 | − | 0.651781i | −0.614216 | − | 0.789138i | \(-0.710527\pi\) |
0.990522 | + | 0.137357i | \(0.0438608\pi\) | |||||||
\(284\) | 7.91656 | + | 4.57063i | 0.469761 | + | 0.271217i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.6075i | 0.804628i | ||||||||
\(287\) | 5.16019 | − | 17.9088i | 0.304596 | − | 1.05712i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.35357 | − | 11.0047i | −0.373739 | − | 0.647335i | ||||
\(290\) | −9.90076 | − | 4.63604i | −0.581393 | − | 0.272238i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.541173 | + | 0.937339i | 0.0316698 | + | 0.0548536i | ||||
\(293\) | − | 25.1151i | − | 1.46724i | −0.679559 | − | 0.733621i | \(-0.737829\pi\) | ||
0.679559 | − | 0.733621i | \(-0.262171\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.46965 | − | 0.383862i | 0.260233 | − | 0.0223493i | ||||
\(296\) | −2.57132 | + | 1.48455i | −0.149455 | + | 0.0862880i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.05052 | + | 5.22532i | 0.524283 | + | 0.302695i | ||||
\(299\) | −5.28472 | − | 9.15340i | −0.305623 | − | 0.529355i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.7611 | − | 6.27018i | −1.25429 | − | 0.361407i | ||||
\(302\) | 17.7187 | 1.01960 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.12164 | + | 2.95698i | 0.293746 | + | 0.169595i | ||||
\(305\) | −25.2216 | − | 11.8100i | −1.44419 | − | 0.676241i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.5674 | −1.05970 | −0.529849 | − | 0.848092i | \(-0.677751\pi\) | ||||
−0.529849 | + | 0.848092i | \(0.677751\pi\) | |||||||
\(308\) | 1.52626 | + | 6.15518i | 0.0869668 | + | 0.350724i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.30037 | + | 5.79228i | −0.471429 | + | 0.328979i | ||||
\(311\) | 6.21831 | − | 10.7704i | 0.352608 | − | 0.610735i | −0.634098 | − | 0.773253i | \(-0.718628\pi\) |
0.986706 | + | 0.162518i | \(0.0519616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.20675 | − | 10.7504i | −0.350826 | − | 0.607649i | 0.635568 | − | 0.772045i | \(-0.280766\pi\) |
−0.986394 | + | 0.164396i | \(0.947433\pi\) | |||||||
\(314\) | −6.08297 | −0.343282 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7678 | −0.943265 | ||||||||
\(317\) | −12.3232 | − | 21.3444i | −0.692141 | − | 1.19882i | −0.971135 | − | 0.238530i | \(-0.923335\pi\) |
0.278995 | − | 0.960293i | \(-0.409999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.85937 | + | 10.1487i | −0.328062 | + | 0.568219i | ||||
\(320\) | −1.27963 | − | 1.83372i | −0.0715337 | − | 0.102508i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.41715 | − | 3.54767i | −0.190430 | − | 0.197704i | ||||
\(323\) | −12.2533 | −0.681791 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.79350 | − | 26.6427i | 0.543246 | − | 1.47787i | ||||
\(326\) | −0.811759 | − | 0.468670i | −0.0449592 | − | 0.0259572i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.04428 | 0.388955 | ||||||||
\(329\) | −3.55240 | − | 14.3263i | −0.195850 | − | 0.789835i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5788 | + | 21.7871i | 0.691392 | + | 1.19753i | 0.971382 | + | 0.237524i | \(0.0763357\pi\) |
−0.279989 | + | 0.960003i | \(0.590331\pi\) | |||||||
\(332\) | 11.7885 | + | 6.80611i | 0.646980 | + | 0.373534i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.9044 | − | 8.60505i | 0.815531 | − | 0.470847i | ||||
\(335\) | −1.45839 | − | 16.9813i | −0.0796801 | − | 0.927787i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4214i | 0.785584i | 0.919627 | + | 0.392792i | \(0.128491\pi\) | ||||
−0.919627 | + | 0.392792i | \(0.871509\pi\) | |||||||
\(338\) | 9.61494 | + | 16.6536i | 0.522984 | + | 0.905834i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.19576 | + | 1.96467i | 0.227547 | + | 0.106549i | ||||
\(341\) | 5.42479 | + | 9.39601i | 0.293769 | + | 0.508823i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8109 | − | 12.3393i | 0.745719 | − | 0.666261i | ||||
\(344\) | − | 8.55956i | − | 0.461500i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.71146 | + | 0.988114i | 0.0920088 | + | 0.0531213i | ||||
\(347\) | 7.24329 | − | 12.5457i | 0.388840 | − | 0.673491i | −0.603454 | − | 0.797398i | \(-0.706209\pi\) |
0.992294 | + | 0.123907i | \(0.0395425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.12483i | 0.113739i | 0.998382 | + | 0.0568697i | \(0.0181119\pi\) | ||||
−0.998382 | + | 0.0568697i | \(0.981888\pi\) | |||||||
\(350\) | 1.44164 | − | 13.1500i | 0.0770587 | − | 0.702895i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.07577 | + | 1.19845i | −0.110639 | + | 0.0638775i | ||||
\(353\) | 12.5805 | + | 7.26335i | 0.669592 | + | 0.386589i | 0.795922 | − | 0.605399i | \(-0.206987\pi\) |
−0.126330 | + | 0.991988i | \(0.540320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.7625 | + | 11.6975i | −0.889663 | + | 0.620836i | ||||
\(356\) | −13.2626 | −0.702916 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.887342i | 0.0468975i | ||||||||
\(359\) | −3.42054 | + | 1.97485i | −0.180529 | + | 0.104228i | −0.587541 | − | 0.809194i | \(-0.699904\pi\) |
0.407012 | + | 0.913423i | \(0.366571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.98749 | − | 13.8347i | 0.420394 | − | 0.728144i | ||||
\(362\) | 4.24329 | − | 2.44986i | 0.223022 | − | 0.128762i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.4201 | + | 10.8181i | 0.546160 | + | 0.567022i | ||||
\(365\) | −2.41132 | + | 0.207089i | −0.126214 | + | 0.0108395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8464 | + | 23.9826i | −0.722775 | + | 1.25188i | 0.237109 | + | 0.971483i | \(0.423800\pi\) |
−0.959883 | + | 0.280400i | \(0.909533\pi\) | |||||||
\(368\) | 0.930877 | − | 1.61233i | 0.0485253 | − | 0.0840483i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.568090 | − | 6.61478i | −0.0295336 | − | 0.343886i | ||||
\(371\) | 7.69193 | + | 7.98574i | 0.399345 | + | 0.414599i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5047 | − | 6.06491i | 0.543914 | − | 0.314029i | −0.202750 | − | 0.979231i | \(-0.564988\pi\) |
0.746664 | + | 0.665202i | \(0.231654\pi\) | |||||||
\(374\) | 2.48309 | − | 4.30084i | 0.128398 | − | 0.222391i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.83140 | − | 2.78941i | 0.249160 | − | 0.143853i | ||||
\(377\) | 27.7563i | 1.42952i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.6821 | −0.959636 | −0.479818 | − | 0.877368i | \(-0.659297\pi\) | ||||
−0.479818 | + | 0.877368i | \(0.659297\pi\) | |||||||
\(380\) | −10.8446 | + | 7.56771i | −0.556315 | + | 0.388215i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.44949 | + | 1.41421i | 0.125327 | + | 0.0723575i | ||||
\(383\) | 9.55162 | − | 5.51463i | 0.488065 | − | 0.281784i | −0.235706 | − | 0.971824i | \(-0.575740\pi\) |
0.723771 | + | 0.690040i | \(0.242407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.9118 | − | 2.74579i | −0.709013 | − | 0.139938i | ||||
\(386\) | − | 19.4966i | − | 0.992349i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.41301 | − | 11.1077i | 0.325571 | − | 0.563906i | ||||
\(389\) | −29.7662 | − | 17.1855i | −1.50921 | − | 0.871341i | −0.999942 | − | 0.0107299i | \(-0.996584\pi\) |
−0.509264 | − | 0.860611i | \(-0.670082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.85741i | 0.195078i | ||||||||
\(392\) | 5.92678 | + | 3.72468i | 0.299348 | + | 0.188125i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.5788 | − | 23.5191i | −0.684089 | − | 1.18488i | ||||
\(395\) | 15.8998 | − | 33.9558i | 0.800007 | − | 1.70850i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5054 | − | 26.8561i | −0.778191 | − | 1.34787i | −0.932983 | − | 0.359920i | \(-0.882804\pi\) |
0.154792 | − | 0.987947i | \(-0.450529\pi\) | |||||||
\(398\) | − | 3.46410i | − | 0.173640i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.92678 | − | 0.852531i | 0.246339 | − | 0.0426266i | ||||
\(401\) | −8.20771 | + | 4.73872i | −0.409873 | + | 0.236641i | −0.690735 | − | 0.723108i | \(-0.742713\pi\) |
0.280862 | + | 0.959748i | \(0.409380\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.2548 | + | 12.8488i | 1.10859 | + | 0.640045i | ||||
\(404\) | −4.45573 | − | 7.71756i | −0.221681 | − | 0.383963i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.11323 | + | 12.5552i | 0.154507 | + | 0.623104i | ||||
\(407\) | −7.11665 | −0.352759 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.20805 | + | 4.73892i | 0.405862 | + | 0.234324i | 0.689010 | − | 0.724752i | \(-0.258046\pi\) |
−0.283148 | + | 0.959076i | \(0.591379\pi\) | |||||||
\(410\) | −6.67962 | + | 14.2651i | −0.329883 | + | 0.704501i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.8198 | −0.533053 | ||||||||
\(413\) | −3.68235 | − | 3.82301i | −0.181197 | − | 0.188118i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.9611 | + | 17.4187i | −1.22529 | + | 0.855048i | ||||
\(416\) | −2.83857 | + | 4.91654i | −0.139172 | + | 0.241053i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.08758 | + | 12.2760i | 0.346665 | + | 0.600441i | ||||
\(419\) | 2.54445 | 0.124305 | 0.0621523 | − | 0.998067i | \(-0.480204\pi\) | ||||
0.0621523 | + | 0.998067i | \(0.480204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.08573 | −0.247863 | −0.123932 | − | 0.992291i | \(-0.539550\pi\) | ||||
−0.123932 | + | 0.992291i | \(0.539550\pi\) | |||||||
\(422\) | −2.03035 | − | 3.51668i | −0.0988361 | − | 0.171189i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.09538 | + | 3.62931i | −0.101761 | + | 0.176255i | ||||
\(425\) | −7.95713 | + | 6.63369i | −0.385977 | + | 0.321781i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.93077 | + | 31.9836i | 0.383797 | + | 1.54780i | ||||
\(428\) | −5.57707 | −0.269578 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.3336 | + | 8.11646i | 0.835900 | + | 0.391411i | ||||
\(431\) | 11.5164 | + | 6.64902i | 0.554727 | + | 0.320272i | 0.751027 | − | 0.660272i | \(-0.229559\pi\) |
−0.196299 | + | 0.980544i | \(0.562892\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.7895 | −0.614626 | −0.307313 | − | 0.951608i | \(-0.599430\pi\) | ||||
−0.307313 | + | 0.951608i | \(0.599430\pi\) | |||||||
\(434\) | 11.5078 | + | 3.31583i | 0.552394 | + | 0.159165i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | −9.53524 | − | 5.50517i | −0.456132 | − | 0.263348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.323211 | − | 0.186606i | 0.0154260 | − | 0.00890623i | −0.492267 | − | 0.870444i | \(-0.663832\pi\) |
0.507693 | + | 0.861538i | \(0.330498\pi\) | |||||||
\(440\) | −0.458606 | − | 5.33996i | −0.0218632 | − | 0.254573i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 11.7626i | − | 0.559490i | ||||||
\(443\) | 12.3165 | + | 21.3328i | 0.585175 | + | 1.01355i | 0.994854 | + | 0.101323i | \(0.0323075\pi\) |
−0.409679 | + | 0.912230i | \(0.634359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.5760 | − | 26.8575i | 0.596161 | − | 1.27317i | ||||
\(446\) | 8.07432 | + | 13.9851i | 0.382330 | + | 0.662215i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.732536 | + | 2.54232i | −0.0346091 | + | 0.120113i | ||||
\(449\) | 40.6223i | 1.91708i | 0.284950 | + | 0.958542i | \(0.408023\pi\) | ||||
−0.284950 | + | 0.958542i | \(0.591977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6223 | + | 8.44220i | 0.688538 | + | 0.397528i | ||||
\(452\) | 7.25148 | − | 12.5599i | 0.341081 | − | 0.590769i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.67980i | − | 0.0788370i | ||||||
\(455\) | −31.7879 | + | 10.8432i | −1.49024 | + | 0.508335i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.857843 | + | 0.495276i | −0.0401282 | + | 0.0231680i | −0.519930 | − | 0.854209i | \(-0.674042\pi\) |
0.479802 | + | 0.877377i | \(0.340709\pi\) | |||||||
\(458\) | −10.9143 | − | 6.30136i | −0.509991 | − | 0.294443i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.38236 | + | 3.41394i | 0.111078 | + | 0.159176i | ||||
\(461\) | 20.7397 | 0.965945 | 0.482972 | − | 0.875636i | \(-0.339557\pi\) | ||||
0.482972 | + | 0.875636i | \(0.339557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.46421i | − | 0.0680476i | −0.999421 | − | 0.0340238i | \(-0.989168\pi\) | ||
0.999421 | − | 0.0340238i | \(-0.0108322\pi\) | |||||||
\(464\) | −4.23411 | + | 2.44457i | −0.196564 | + | 0.113486i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.25818 | + | 12.5715i | −0.336229 | + | 0.582365i | ||||
\(467\) | −31.4090 | + | 18.1340i | −1.45344 | + | 0.839142i | −0.998675 | − | 0.0514705i | \(-0.983609\pi\) |
−0.454762 | + | 0.890613i | \(0.650276\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.5246 | + | 13.9902i | −0.670682 | + | 0.646006i | ||||
\(470\) | 1.06742 | + | 12.4289i | 0.0492362 | + | 0.573301i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.00312 | − | 1.73746i | 0.0461724 | − | 0.0799730i | ||||
\(473\) | 10.2582 | − | 17.7677i | 0.471672 | − | 0.816959i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.04184 | − | 29.1368i | −0.231336 | − | 1.33689i | ||||
\(476\) | −1.31933 | − | 5.32066i | −0.0604714 | − | 0.243872i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.179344 | + | 0.103545i | −0.00820302 | + | 0.00473602i | ||||
\(479\) | 5.16288 | − | 8.94237i | 0.235898 | − | 0.408587i | −0.723635 | − | 0.690183i | \(-0.757530\pi\) |
0.959533 | + | 0.281595i | \(0.0908635\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.5978 | + | 8.42802i | −0.665600 | + | 0.384285i | ||||
\(482\) | 10.4405i | 0.475551i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.25489 | 0.238859 | ||||||||
\(485\) | 16.4126 | + | 23.5194i | 0.745258 | + | 1.06796i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.6055 | − | 10.1645i | −0.797781 | − | 0.460599i | 0.0449135 | − | 0.998991i | \(-0.485699\pi\) |
−0.842695 | + | 0.538392i | \(0.819032\pi\) | |||||||
\(488\) | −10.7862 | + | 6.22739i | −0.488266 | + | 0.281901i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.1627 | + | 8.47020i | −0.594629 | + | 0.382645i | ||||
\(491\) | 34.6034i | 1.56163i | 0.624764 | + | 0.780814i | \(0.285195\pi\) | ||||
−0.624764 | + | 0.780814i | \(0.714805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.06495 | − | 8.77276i | 0.228114 | − | 0.395105i | ||||
\(494\) | 29.0763 | + | 16.7872i | 1.30820 | + | 0.755292i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.52651i | 0.203247i | ||||||||
\(497\) | 23.2400 | + | 6.69630i | 1.04246 | + | 0.300370i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.47545 | − | 2.55555i | −0.0660501 | − | 0.114402i | 0.831109 | − | 0.556109i | \(-0.187706\pi\) |
−0.897159 | + | 0.441707i | \(0.854373\pi\) | |||||||
\(500\) | −2.94532 | + | 10.7854i | −0.131719 | + | 0.482338i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.3232 | − | 24.8085i | −0.639277 | − | 1.10726i | ||||
\(503\) | 31.8907i | 1.42193i | 0.703225 | + | 0.710967i | \(0.251742\pi\) | ||||
−0.703225 | + | 0.710967i | \(0.748258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.8536 | − | 1.70506i | 0.883472 | − | 0.0758743i | ||||
\(506\) | 3.86458 | − | 2.23121i | 0.171801 | − | 0.0991896i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.6677 | − | 9.62311i | −0.739510 | − | 0.426957i | ||||
\(509\) | −0.421199 | − | 0.729538i | −0.0186693 | − | 0.0323362i | 0.856540 | − | 0.516081i | \(-0.172610\pi\) |
−0.875209 | + | 0.483745i | \(0.839276\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.98659 | + | 2.06247i | 0.0878815 | + | 0.0912383i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.5805 | − | 12.4595i | −0.951875 | − | 0.549565i | ||||
\(515\) | 10.2597 | − | 21.9107i | 0.452096 | − | 0.965500i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3718 | 0.588093 | ||||||||
\(518\) | −5.65780 | + | 5.44964i | −0.248589 | + | 0.239443i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.26465 | − | 10.4103i | −0.318576 | − | 0.456522i | ||||
\(521\) | 2.81499 | − | 4.87571i | 0.123327 | − | 0.213609i | −0.797751 | − | 0.602987i | \(-0.793977\pi\) |
0.921078 | + | 0.389379i | \(0.127310\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.91899 | + | 15.4482i | 0.390000 | + | 0.675500i | 0.992449 | − | 0.122657i | \(-0.0391415\pi\) |
−0.602449 | + | 0.798158i | \(0.705808\pi\) | |||||||
\(524\) | −4.69940 | −0.205294 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1908 | −0.836757 | ||||||||
\(527\) | −4.68930 | − | 8.12210i | −0.204269 | − | 0.353804i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.76694 | − | 16.9168i | 0.424649 | − | 0.735514i | ||||
\(530\) | −5.36264 | − | 7.68470i | −0.232938 | − | 0.333802i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.0352 | + | 4.33219i | 0.651858 | + | 0.187824i | ||||
\(533\) | 39.9913 | 1.73222 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.28837 | − | 11.2939i | 0.228636 | − | 0.488277i | ||||
\(536\) | −6.60103 | − | 3.81111i | −0.285121 | − | 0.164615i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.85489 | −0.209309 | ||||||||
\(539\) | 7.83882 | + | 14.8345i | 0.337642 | + | 0.638968i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7120 | + | 22.0179i | 0.546533 | + | 0.946623i | 0.998509 | + | 0.0545925i | \(0.0173860\pi\) |
−0.451976 | + | 0.892030i | \(0.649281\pi\) | |||||||
\(542\) | −11.8344 | − | 6.83257i | −0.508329 | − | 0.293484i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.79434 | − | 1.03596i | 0.0769316 | − | 0.0444165i | ||||
\(545\) | 4.45573 | − | 0.382667i | 0.190863 | − | 0.0163917i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.1182i | − | 0.518138i | −0.965859 | − | 0.259069i | \(-0.916584\pi\) | ||
0.965859 | − | 0.259069i | \(-0.0834158\pi\) | |||||||
\(548\) | −11.4422 | − | 19.8185i | −0.488788 | − | 0.846606i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.2486 | + | 4.13483i | 0.479642 | + | 0.176310i | ||||
\(551\) | 14.4571 | + | 25.0404i | 0.615892 | + | 1.06676i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.0595 | + | 10.6772i | −1.83108 | + | 0.454040i | ||||
\(554\) | 12.1298i | 0.515346i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.91427 | + | 4.56931i | 0.335640 | + | 0.193782i | ||||
\(557\) | −0.769786 | + | 1.33331i | −0.0326169 | + | 0.0564941i | −0.881873 | − | 0.471487i | \(-0.843717\pi\) |
0.849256 | + | 0.527981i | \(0.177051\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 48.5938i | − | 2.05530i | ||||||
\(560\) | −4.45373 | − | 3.89414i | −0.188204 | − | 0.164557i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.2503 | − | 16.3103i | 1.19167 | − | 0.688009i | ||||
\(563\) | −19.4548 | − | 11.2322i | −0.819920 | − | 0.473381i | 0.0304689 | − | 0.999536i | \(-0.490300\pi\) |
−0.850389 | + | 0.526155i | \(0.823633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.5585 | + | 26.5944i | 0.780760 | + | 1.11883i | ||||
\(566\) | 12.6609 | 0.532177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.14126i | 0.383559i | ||||||||
\(569\) | 9.35810 | − | 5.40290i | 0.392312 | − | 0.226501i | −0.290849 | − | 0.956769i | \(-0.593938\pi\) |
0.683161 | + | 0.730267i | \(0.260605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.98169 | − | 6.89649i | 0.166629 | − | 0.288609i | −0.770604 | − | 0.637314i | \(-0.780045\pi\) |
0.937232 | + | 0.348705i | \(0.113379\pi\) | |||||||
\(572\) | −11.7844 | + | 6.80375i | −0.492732 | + | 0.284479i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.0896 | − | 4.48555i | 0.755045 | − | 0.187223i | ||||
\(575\) | −9.17246 | + | 1.58720i | −0.382518 | + | 0.0661910i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.2964 | + | 21.2980i | −0.511906 | + | 0.886648i | 0.487998 | + | 0.872845i | \(0.337727\pi\) |
−0.999905 | + | 0.0138033i | \(0.995606\pi\) | |||||||
\(578\) | 6.35357 | − | 11.0047i | 0.264274 | − | 0.457735i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.935455 | − | 10.8923i | −0.0388426 | − | 0.452280i | ||||
\(581\) | 34.6066 | + | 9.97144i | 1.43573 | + | 0.413685i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.69908 | + | 5.02242i | −0.360279 | + | 0.208007i | ||||
\(584\) | −0.541173 | + | 0.937339i | −0.0223939 | + | 0.0387874i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.7503 | − | 12.5576i | 0.898498 | − | 0.518748i | ||||
\(587\) | 12.8469i | 0.530248i | 0.964214 | + | 0.265124i | \(0.0854129\pi\) | ||||
−0.964214 | + | 0.265124i | \(0.914587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.7696 | 1.10302 | ||||||||
\(590\) | 2.56726 | + | 3.67890i | 0.105692 | + | 0.151458i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.57132 | − | 1.48455i | −0.105681 | − | 0.0610148i | ||||
\(593\) | 14.8637 | − | 8.58155i | 0.610379 | − | 0.352402i | −0.162735 | − | 0.986670i | \(-0.552032\pi\) |
0.773114 | + | 0.634268i | \(0.218698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0257 | + | 2.37352i | 0.493005 | + | 0.0973046i | ||||
\(596\) | 10.4506i | 0.428075i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.28472 | − | 9.15340i | 0.216108 | − | 0.374310i | ||||
\(599\) | −16.9813 | − | 9.80416i | −0.693837 | − | 0.400587i | 0.111211 | − | 0.993797i | \(-0.464527\pi\) |
−0.805048 | + | 0.593210i | \(0.797860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.2340i | 1.15169i | 0.817560 | + | 0.575844i | \(0.195326\pi\) | ||||
−0.817560 | + | 0.575844i | \(0.804674\pi\) | |||||||
\(602\) | −5.45043 | − | 21.9808i | −0.222143 | − | 0.895870i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.85937 | + | 15.3449i | 0.360483 | + | 0.624374i | ||||
\(605\) | −4.98287 | + | 10.6415i | −0.202582 | + | 0.432637i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.82657 | + | 8.35987i | 0.195904 | + | 0.339316i | 0.947197 | − | 0.320653i | \(-0.103902\pi\) |
−0.751292 | + | 0.659970i | \(0.770569\pi\) | |||||||
\(608\) | 5.91397i | 0.239843i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.38302 | − | 27.7476i | −0.0964855 | − | 1.12347i | ||||
\(611\) | 27.4285 | − | 15.8359i | 1.10964 | − | 0.640650i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.84262 | + | 4.52794i | 0.316761 | + | 0.182882i | 0.649948 | − | 0.759979i | \(-0.274791\pi\) |
−0.333187 | + | 0.942861i | \(0.608124\pi\) | |||||||
\(614\) | −9.28370 | − | 16.0798i | −0.374660 | − | 0.648930i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.56742 | + | 4.39937i | −0.184026 | + | 0.177256i | ||||
\(617\) | 25.3122 | 1.01903 | 0.509515 | − | 0.860462i | \(-0.329825\pi\) | ||||
0.509515 | + | 0.860462i | \(0.329825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.6634 | + | 19.4356i | 1.35304 | + | 0.781181i | 0.988675 | − | 0.150073i | \(-0.0479510\pi\) |
0.364370 | + | 0.931254i | \(0.381284\pi\) | |||||||
\(620\) | −9.16645 | − | 4.29219i | −0.368133 | − | 0.172379i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.4366 | 0.498663 | ||||||||
\(623\) | −34.0581 | + | 8.44516i | −1.36451 | + | 0.338348i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0482 | − | 16.1915i | −0.761929 | − | 0.647661i | ||||
\(626\) | 6.20675 | − | 10.7504i | 0.248072 | − | 0.429673i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.04149 | − | 5.26801i | −0.121369 | − | 0.210216i | ||||
\(629\) | 6.15177 | 0.245287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8670 | −0.950129 | −0.475065 | − | 0.879951i | \(-0.657575\pi\) | ||||
−0.475065 | + | 0.879951i | \(0.657575\pi\) | |||||||
\(632\) | −8.38392 | − | 14.5214i | −0.333494 | − | 0.577629i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.3232 | − | 21.3444i | 0.489417 | − | 0.847696i | ||||
\(635\) | 35.2922 | − | 24.6281i | 1.40053 | − | 0.977337i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.6472 | + | 21.1455i | 1.33315 | + | 0.837816i | ||||
\(638\) | −11.7187 | −0.463949 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.948234 | − | 2.02506i | 0.0374822 | − | 0.0800474i | ||||
\(641\) | 30.2066 | + | 17.4398i | 1.19309 | + | 0.688830i | 0.959006 | − | 0.283386i | \(-0.0914578\pi\) |
0.234083 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.25944 | −0.246848 | −0.123424 | − | 0.992354i | \(-0.539388\pi\) | ||||
−0.123424 | + | 0.992354i | \(0.539388\pi\) | |||||||
\(644\) | 1.36380 | − | 4.73317i | 0.0537413 | − | 0.186513i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.12664 | − | 10.6117i | −0.241050 | − | 0.417510i | ||||
\(647\) | 32.4778 | + | 18.7511i | 1.27683 | + | 0.737181i | 0.976265 | − | 0.216579i | \(-0.0694898\pi\) |
0.300570 | + | 0.953760i | \(0.402823\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.16451 | − | 2.40438i | 0.163471 | − | 0.0943801i | ||||
\(650\) | 27.9700 | − | 4.83994i | 1.09707 | − | 0.189838i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 0.937339i | − | 0.0367090i | ||||||
\(653\) | −13.2258 | − | 22.9077i | −0.517565 | − | 0.896449i | −0.999792 | − | 0.0204023i | \(-0.993505\pi\) |
0.482227 | − | 0.876046i | \(-0.339828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.45613 | − | 9.51656i | 0.174116 | − | 0.371843i | ||||
\(656\) | 3.52214 | + | 6.10053i | 0.137516 | + | 0.238186i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.6307 | − | 10.2396i | 0.414430 | − | 0.399182i | ||||
\(659\) | − | 19.9524i | − | 0.777234i | −0.921399 | − | 0.388617i | \(-0.872953\pi\) | ||
0.921399 | − | 0.388617i | \(-0.127047\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.71203 | + | 2.72049i | 0.183277 | + | 0.105815i | 0.588831 | − | 0.808256i | \(-0.299588\pi\) |
−0.405555 | + | 0.914071i | \(0.632922\pi\) | |||||||
\(662\) | −12.5788 | + | 21.7871i | −0.488888 | + | 0.846779i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6122i | 0.528257i | ||||||||
\(665\) | −23.0298 | + | 26.3392i | −0.893058 | + | 1.02139i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.88287 | − | 4.55118i | 0.305226 | − | 0.176222i | ||||
\(668\) | 14.9044 | + | 8.60505i | 0.576668 | + | 0.332939i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.9770 | − | 9.75364i | 0.539980 | − | 0.376816i | ||||
\(671\) | −29.8528 | −1.15245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.50635i | − | 0.327896i | −0.986469 | − | 0.163948i | \(-0.947577\pi\) | ||
0.986469 | − | 0.163948i | \(-0.0524228\pi\) | |||||||
\(674\) | −12.4893 | + | 7.21070i | −0.481070 | + | 0.277746i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.61494 | + | 16.6536i | −0.369805 | + | 0.640522i | ||||
\(677\) | 4.40495 | − | 2.54320i | 0.169296 | − | 0.0977430i | −0.412958 | − | 0.910750i | \(-0.635504\pi\) |
0.582254 | + | 0.813007i | \(0.302171\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.39552 | − | 32.6079i | 0.360567 | − | 1.25138i | ||||
\(680\) | 0.396428 | + | 4.61597i | 0.0152023 | + | 0.177014i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.42479 | + | 9.39601i | −0.207726 | + | 0.359792i | ||||
\(683\) | −10.5073 | + | 18.1991i | −0.402050 | + | 0.696370i | −0.993973 | − | 0.109624i | \(-0.965035\pi\) |
0.591924 | + | 0.805994i | \(0.298369\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.9836 | − | 4.37857i | 1.94798 | − | 0.167297i | ||||
\(686\) | 17.5916 | + | 5.79094i | 0.671651 | + | 0.221099i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.41279 | − | 4.27978i | 0.282610 | − | 0.163165i | ||||
\(689\) | −11.8958 | + | 20.6041i | −0.453193 | + | 0.784953i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5723 | + | 12.4548i | −0.820649 | + | 0.473802i | −0.850640 | − | 0.525748i | \(-0.823785\pi\) |
0.0299912 | + | 0.999550i | \(0.490452\pi\) | |||||||
\(692\) | 1.97623i | 0.0751249i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.4866 | 0.549903 | ||||||||
\(695\) | −16.7577 | + | 11.6941i | −0.635655 | + | 0.443582i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.6398 | − | 7.29761i | −0.478767 | − | 0.276417i | ||||
\(698\) | −1.84015 | + | 1.06241i | −0.0696508 | + | 0.0402129i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.1090 | − | 5.32649i | 0.457678 | − | 0.201322i | ||||
\(701\) | − | 22.5321i | − | 0.851025i | −0.904953 | − | 0.425512i | \(-0.860094\pi\) | ||
0.904953 | − | 0.425512i | \(-0.139906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.77961 | + | 15.2067i | −0.331129 | + | 0.573532i | ||||
\(704\) | −2.07577 | − | 1.19845i | −0.0782336 | − | 0.0451682i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5267i | 0.546719i | ||||||||
\(707\) | −16.3565 | − | 16.9813i | −0.615150 | − | 0.638647i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4504 | − | 21.5648i | −0.467586 | − | 0.809882i | 0.531728 | − | 0.846915i | \(-0.321543\pi\) |
−0.999314 | + | 0.0370327i | \(0.988209\pi\) | |||||||
\(710\) | −18.5116 | − | 8.66805i | −0.694726 | − | 0.325306i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.63129 | − | 11.4857i | −0.248518 | − | 0.430446i | ||||
\(713\) | − | 8.42726i | − | 0.315603i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.60357 | − | 30.3157i | −0.0973681 | − | 1.13374i | ||||
\(716\) | −0.768461 | + | 0.443671i | −0.0287187 | + | 0.0165808i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.42054 | − | 1.97485i | −0.127653 | − | 0.0737007i | ||||
\(719\) | 19.9241 | + | 34.5096i | 0.743045 | + | 1.28699i | 0.951103 | + | 0.308875i | \(0.0999526\pi\) |
−0.208057 | + | 0.978117i | \(0.566714\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.7850 | + | 6.88967i | −1.03477 | + | 0.256585i | ||||
\(722\) | 15.9750 | 0.594527 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.24329 | + | 2.44986i | 0.157701 | + | 0.0910485i | ||||
\(725\) | 22.9446 | + | 8.43413i | 0.852142 | + | 0.313236i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.124004 | 0.00459906 | 0.00229953 | − | 0.999997i | \(-0.499268\pi\) | ||||
0.00229953 | + | 0.999997i | \(0.499268\pi\) | |||||||
\(728\) | −4.15870 | + | 14.4331i | −0.154132 | + | 0.534926i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.38501 | − | 1.98472i | −0.0512614 | − | 0.0734579i | ||||
\(731\) | −8.86738 | + | 15.3587i | −0.327972 | + | 0.568064i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.2739 | + | 24.7231i | 0.527218 | + | 0.913168i | 0.999497 | + | 0.0317189i | \(0.0100981\pi\) |
−0.472279 | + | 0.881449i | \(0.656569\pi\) | |||||||
\(734\) | −27.6927 | −1.02216 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.86175 | 0.0686252 | ||||||||
\(737\) | −9.13483 | − | 15.8220i | −0.336486 | − | 0.582811i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.51807 | − | 16.4858i | 0.350128 | − | 0.606439i | −0.636144 | − | 0.771571i | \(-0.719471\pi\) |
0.986272 | + | 0.165131i | \(0.0528048\pi\) | |||||||
\(740\) | 5.44452 | − | 3.79937i | 0.200145 | − | 0.139668i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.06989 | + | 10.6543i | −0.112699 | + | 0.391131i | ||||
\(743\) | 17.0800 | 0.626605 | 0.313303 | − | 0.949653i | \(-0.398565\pi\) | ||||
0.313303 | + | 0.949653i | \(0.398565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.1631 | − | 9.90966i | −0.775358 | − | 0.363062i | ||||
\(746\) | 10.5047 | + | 6.06491i | 0.384605 | + | 0.222052i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.96618 | 0.181582 | ||||||||
\(749\) | −14.3218 | + | 3.55129i | −0.523308 | + | 0.129761i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.44463 | + | 14.6265i | 0.308149 | + | 0.533730i | 0.977957 | − | 0.208804i | \(-0.0669572\pi\) |
−0.669809 | + | 0.742534i | \(0.733624\pi\) | |||||||
\(752\) | 4.83140 | + | 2.78941i | 0.176183 | + | 0.101719i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.0376 | + | 13.8781i | −0.875399 | + | 0.505412i | ||||
\(755\) | −39.4750 | + | 3.39019i | −1.43664 | + | 0.123382i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.4057i | 1.21415i | 0.794644 | + | 0.607076i | \(0.207658\pi\) | ||||
−0.794644 | + | 0.607076i | \(0.792342\pi\) | |||||||
\(758\) | −9.34106 | − | 16.1792i | −0.339282 | − | 0.587655i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.9761 | − | 5.60782i | −0.434419 | − | 0.203417i | ||||
\(761\) | 16.3074 | + | 28.2453i | 0.591143 | + | 1.02389i | 0.994079 | + | 0.108662i | \(0.0346566\pi\) |
−0.402935 | + | 0.915228i | \(0.632010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.67089 | − | 3.81111i | −0.132895 | − | 0.137971i | ||||
\(764\) | 2.82843i | 0.102329i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.55162 | + | 5.51463i | 0.345114 | + | 0.199252i | ||||
\(767\) | 5.69486 | − | 9.86379i | 0.205630 | − | 0.356161i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4396i | 0.809192i | 0.914495 | + | 0.404596i | \(0.132588\pi\) | ||||
−0.914495 | + | 0.404596i | \(0.867412\pi\) | |||||||
\(770\) | −4.57800 | − | 13.4209i | −0.164980 | − | 0.483656i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.8845 | − | 9.74828i | 0.607687 | − | 0.350848i | ||||
\(773\) | −34.4965 | − | 19.9165i | −1.24075 | − | 0.716348i | −0.271505 | − | 0.962437i | \(-0.587521\pi\) |
−0.969247 | + | 0.246089i | \(0.920855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3839 | − | 14.4926i | 0.624447 | − | 0.520588i | ||||
\(776\) | 12.8260 | 0.460428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 34.3710i | − | 1.23226i | ||||||
\(779\) | 36.0783 | − | 20.8298i | 1.29264 | − | 0.746306i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9553 | + | 18.9752i | −0.392012 | + | 0.678985i | ||||
\(782\) | −3.34062 | + | 1.92871i | −0.119460 | + | 0.0689704i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.262276 | + | 6.99508i | −0.00936701 | + | 0.249824i | ||||
\(785\) | 13.5521 | − | 1.16388i | 0.483694 | − | 0.0415405i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.36649 | + | 14.4912i | −0.298233 | + | 0.516555i | −0.975732 | − | 0.218969i | \(-0.929731\pi\) |
0.677499 | + | 0.735524i | \(0.263064\pi\) | |||||||
\(788\) | 13.5788 | − | 23.5191i | 0.483724 | − | 0.837835i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 37.3565 | − | 3.20825i | 1.32909 | − | 0.114144i | ||||
\(791\) | 10.6239 | − | 36.8711i | 0.377743 | − | 1.31099i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.2344 | + | 35.3537i | −2.17450 | + | 1.25545i | ||||
\(794\) | 15.5054 | − | 26.8561i | 0.550264 | − | 0.953086i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | − | 1.73205i | 0.106332 | − | 0.0613909i | ||||
\(797\) | 2.68812i | 0.0952182i | 0.998866 | + | 0.0476091i | \(0.0151602\pi\) | ||||
−0.998866 | + | 0.0476091i | \(0.984840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5589 | −0.408924 | ||||||||
\(800\) | 3.20171 | + | 3.84045i | 0.113197 | + | 0.135781i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.20771 | − | 4.73872i | −0.289824 | − | 0.167330i | ||||
\(803\) | −2.24670 | + | 1.29714i | −0.0792845 | + | 0.0457749i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.29174 | + | 7.24993i | 0.292245 | + | 0.255526i | ||||
\(806\) | 25.6976i | 0.905161i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.45573 | − | 7.71756i | 0.156752 | − | 0.271503i | ||||
\(809\) | −27.2213 | − | 15.7162i | −0.957051 | − | 0.552554i | −0.0617867 | − | 0.998089i | \(-0.519680\pi\) |
−0.895264 | + | 0.445536i | \(0.853013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.3830i | 1.73407i | 0.498246 | + | 0.867036i | \(0.333978\pi\) | ||||
−0.498246 | + | 0.867036i | \(0.666022\pi\) | |||||||
\(812\) | −9.31651 | + | 8.97374i | −0.326945 | + | 0.314916i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.55832 | − | 6.16320i | −0.124719 | − | 0.216020i | ||||
\(815\) | 1.89816 | + | 0.888817i | 0.0664898 | + | 0.0311339i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.3105 | − | 43.8390i | −0.885501 | − | 1.53373i | ||||
\(818\) | 9.47784i | 0.331385i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.6937 | + | 1.34781i | −0.548048 | + | 0.0470675i | ||||
\(821\) | −38.7342 | + | 22.3632i | −1.35183 | + | 0.780480i | −0.988506 | − | 0.151182i | \(-0.951692\pi\) |
−0.363325 | + | 0.931662i | \(0.618359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.3808 | − | 6.57071i | −0.396710 | − | 0.229041i | 0.288353 | − | 0.957524i | \(-0.406892\pi\) |
−0.685063 | + | 0.728483i | \(0.740226\pi\) | |||||||
\(824\) | −5.40989 | − | 9.37021i | −0.188463 | − | 0.326427i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.46965 | − | 5.10052i | 0.0511355 | − | 0.177470i | ||||
\(827\) | 47.4125 | 1.64869 | 0.824346 | − | 0.566086i | \(-0.191543\pi\) | ||||
0.824346 | + | 0.566086i | \(0.191543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.11516 | + | 4.10794i | 0.247120 | + | 0.142675i | 0.618445 | − | 0.785828i | \(-0.287763\pi\) |
−0.371325 | + | 0.928503i | \(0.621096\pi\) | |||||||
\(830\) | −27.5655 | − | 12.9076i | −0.956814 | − | 0.448029i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.67714 | −0.196819 | ||||||||
\(833\) | −6.77603 | − | 12.8233i | −0.234775 | − | 0.444300i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.5585 | + | 22.0226i | −1.09213 | + | 0.762124i | ||||
\(836\) | −7.08758 | + | 12.2760i | −0.245129 | + | 0.424576i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.27223 | + | 2.20356i | 0.0439483 | + | 0.0761208i | ||||
\(839\) | 17.6943 | 0.610875 | 0.305437 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305437 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.09640 | 0.175738 | ||||||||
\(842\) | −2.54286 | − | 4.40437i | −0.0876328 | − | 0.151785i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.03035 | − | 3.51668i | 0.0698877 | − | 0.121049i | ||||
\(845\) | −24.6072 | − | 35.2623i | −0.846513 | − | 1.21306i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.4945 | − | 3.34613i | 0.463675 | − | 0.114975i | ||||
\(848\) | −4.19077 | −0.143912 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.72351 | − | 3.57423i | −0.333514 | − | 0.122595i | ||||
\(851\) | 4.78717 | + | 2.76388i | 0.164102 | + | 0.0947444i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.1129 | 1.37344 | 0.686720 | − | 0.726922i | \(-0.259050\pi\) | ||||
0.686720 | + | 0.726922i | \(0.259050\pi\) | |||||||
\(854\) | −23.7333 | + | 22.8601i | −0.812135 | + | 0.782255i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.78854 | − | 4.82989i | −0.0953102 | − | 0.165082i | ||||
\(857\) | 38.2184 | + | 22.0654i | 1.30552 | + | 0.753740i | 0.981344 | − | 0.192259i | \(-0.0615813\pi\) |
0.324171 | + | 0.945998i | \(0.394915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.4339 | + | 7.17873i | −0.424240 | + | 0.244935i | −0.696890 | − | 0.717178i | \(-0.745433\pi\) |
0.272650 | + | 0.962113i | \(0.412100\pi\) | |||||||
\(860\) | 1.63773 | + | 19.0696i | 0.0558461 | + | 0.650266i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.2980i | 0.452933i | ||||||||
\(863\) | −6.40143 | − | 11.0876i | −0.217907 | − | 0.377426i | 0.736261 | − | 0.676698i | \(-0.236590\pi\) |
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00197 | − | 1.87393i | −0.136071 | − | 0.0637154i | ||||
\(866\) | −6.39477 | − | 11.0761i | −0.217303 | − | 0.376380i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.88233 | + | 11.6240i | 0.0978326 | + | 0.394544i | ||||
\(869\) | − | 40.1908i | − | 1.36338i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.4750 | − | 21.6362i | −1.26979 | − | 0.733114i | ||||
\(872\) | 1.00000 | − | 1.73205i | 0.0338643 | − | 0.0586546i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.0103i | − | 0.372431i | ||||||
\(875\) | −0.695745 | + | 29.5722i | −0.0235205 | + | 0.999723i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.4650 | − | 29.1360i | 1.70408 | − | 0.983853i | 0.762551 | − | 0.646928i | \(-0.223947\pi\) |
0.941532 | − | 0.336925i | \(-0.109387\pi\) | |||||||
\(878\) | 0.323211 | + | 0.186606i | 0.0109079 | + | 0.00629765i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.39524 | − | 3.06715i | 0.148164 | − | 0.103394i | ||||
\(881\) | −1.80667 | −0.0608682 | −0.0304341 | − | 0.999537i | \(-0.509689\pi\) | ||||
−0.0304341 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.8997i | − | 0.467761i | −0.972265 | − | 0.233881i | \(-0.924858\pi\) | ||
0.972265 | − | 0.233881i | \(-0.0751425\pi\) | |||||||
\(884\) | 10.1867 | − | 5.88130i | 0.342616 | − | 0.197809i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.3165 | + | 21.3328i | −0.413781 | + | 0.716690i | ||||
\(887\) | −22.9426 | + | 13.2459i | −0.770337 | + | 0.444754i | −0.832995 | − | 0.553281i | \(-0.813376\pi\) |
0.0626581 | + | 0.998035i | \(0.480042\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.9301 | − | 14.0985i | −1.64106 | − | 0.472850i | ||||
\(890\) | 29.5473 | − | 2.53758i | 0.990427 | − | 0.0850598i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.07432 | + | 13.9851i | −0.270348 | + | 0.468257i | ||||
\(893\) | 16.4965 | − | 28.5727i | 0.552033 | − | 0.956150i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.169778 | − | 1.97688i | −0.00567506 | − | 0.0660798i | ||||
\(896\) | −2.56798 | + | 0.636766i | −0.0857902 | + | 0.0212728i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.1799 | + | 20.3111i | −1.17397 | + | 0.677792i | ||||
\(899\) | −11.0654 | + | 19.1658i | −0.369050 | + | 0.639214i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.51966 | − | 4.34148i | 0.250516 | − | 0.144636i | ||||
\(902\) | 16.8844i | 0.562189i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.5030 | 0.482361 | ||||||||
\(905\) | −8.98474 | + | 6.26985i | −0.298663 | + | 0.208417i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.8091 | − | 18.3650i | −1.05620 | − | 0.609800i | −0.131824 | − | 0.991273i | \(-0.542083\pi\) |
−0.924380 | + | 0.381474i | \(0.875417\pi\) | |||||||
\(908\) | 1.45475 | − | 0.839901i | 0.0482776 | − | 0.0278731i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −25.2844 | − | 22.1076i | −0.838170 | − | 0.732859i | ||||
\(911\) | − | 39.8018i | − | 1.31869i | −0.751839 | − | 0.659347i | \(-0.770833\pi\) | ||
0.751839 | − | 0.659347i | \(-0.229167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.3135 | + | 28.2559i | −0.539900 | + | 0.935134i | ||||
\(914\) | −0.857843 | − | 0.495276i | −0.0283749 | − | 0.0163823i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 12.6027i | − | 0.416406i | ||||||
\(917\) | −12.0680 | + | 2.99242i | −0.398520 | + | 0.0988184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.1692 | + | 52.2545i | 0.995189 | + | 1.72372i | 0.582442 | + | 0.812872i | \(0.302097\pi\) |
0.412747 | + | 0.910846i | \(0.364570\pi\) | |||||||
\(920\) | −1.76538 | + | 3.77016i | −0.0582028 | + | 0.124298i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.3699 | + | 17.9611i | 0.341513 | + | 0.591518i | ||||
\(923\) | 51.8962i | 1.70818i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53126 | + | 14.6282i | 0.0832273 | + | 0.480971i | ||||
\(926\) | 1.26804 | − | 0.732105i | 0.0416705 | − | 0.0240585i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.23411 | − | 2.44457i | −0.138992 | − | 0.0802468i | ||||
\(929\) | −22.1749 | − | 38.4080i | −0.727533 | − | 1.26012i | −0.957923 | − | 0.287026i | \(-0.907333\pi\) |
0.230389 | − | 0.973099i | \(-0.426000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.3687 | + | 1.55109i | 1.35580 | + | 0.0508350i | ||||
\(932\) | −14.5164 | −0.475499 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.4090 | − | 18.1340i | −1.02774 | − | 0.593363i | ||||
\(935\) | −4.70910 | + | 10.0568i | −0.154004 | + | 0.328893i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.54073 | −0.0830021 | −0.0415010 | − | 0.999138i | \(-0.513214\pi\) | ||||
−0.0415010 | + | 0.999138i | \(0.513214\pi\) | |||||||
\(938\) | −19.3781 | − | 5.58355i | −0.632718 | − | 0.182309i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.2300 | + | 7.13884i | −0.333666 | + | 0.232843i | ||||
\(941\) | 16.9488 | − | 29.3563i | 0.552516 | − | 0.956987i | −0.445576 | − | 0.895244i | \(-0.647001\pi\) |
0.998092 | − | 0.0617423i | \(-0.0196657\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.55736 | − | 11.3577i | −0.213537 | − | 0.369857i | ||||
\(944\) | 2.00624 | 0.0652977 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.5164 | 0.667045 | ||||||||
\(947\) | −24.7544 | − | 42.8759i | −0.804411 | − | 1.39328i | −0.916688 | − | 0.399604i | \(-0.869148\pi\) |
0.112277 | − | 0.993677i | \(-0.464186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.07231 | + | 5.32140i | −0.0997315 | + | 0.172740i | ||||
\(950\) | 22.7123 | − | 18.9348i | 0.736885 | − | 0.614325i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.94816 | − | 3.80290i | 0.127961 | − | 0.123253i | ||||
\(953\) | 17.0625 | 0.552709 | 0.276355 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276355 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.72772 | − | 2.68201i | −0.185345 | − | 0.0867878i | ||||
\(956\) | −0.179344 | − | 0.103545i | −0.00580041 | − | 0.00334887i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.3258 | 0.333610 | ||||||||
\(959\) | −42.0032 | − | 43.6076i | −1.35636 | − | 1.40816i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.25533 | − | 9.10250i | −0.169527 | − | 0.293629i | ||||
\(962\) | −14.5978 | − | 8.42802i | −0.470651 | − | 0.271730i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.04172 | + | 5.22024i | −0.291214 | + | 0.168133i | ||||
\(965\) | 3.73035 | + | 43.4357i | 0.120084 | + | 1.39825i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 49.6639i | − | 1.59708i | −0.601940 | − | 0.798541i | \(-0.705606\pi\) | ||
0.601940 | − | 0.798541i | \(-0.294394\pi\) | |||||||
\(968\) | 2.62745 | + | 4.55087i | 0.0844493 | + | 0.146270i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.1621 | + | 25.9734i | −0.390501 | + | 0.833957i | ||||
\(971\) | −14.2930 | − | 24.7561i | −0.458683 | − | 0.794462i | 0.540209 | − | 0.841531i | \(-0.318345\pi\) |
−0.998892 | + | 0.0470689i | \(0.985012\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.2333 | + | 6.69436i | 0.744825 | + | 0.214611i | ||||
\(974\) | − | 20.3291i | − | 0.651386i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.7862 | − | 6.22739i | −0.345256 | − | 0.199334i | ||||
\(977\) | −13.8603 | + | 24.0067i | −0.443429 | + | 0.768042i | −0.997941 | − | 0.0641335i | \(-0.979572\pi\) |
0.554512 | + | 0.832176i | \(0.312905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.7890i | − | 1.01598i | ||||||
\(980\) | −13.9167 | − | 7.16410i | −0.444554 | − | 0.228849i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −29.9674 | + | 17.3017i | −0.956298 | + | 0.552119i | ||||
\(983\) | −37.0891 | − | 21.4134i | −1.18296 | − | 0.682982i | −0.226262 | − | 0.974067i | \(-0.572650\pi\) |
−0.956697 | + | 0.291085i | \(0.905984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.7517 | + | 49.7994i | 1.10728 | + | 1.58674i | ||||
\(986\) | 10.1299 | 0.322602 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.5744i | 1.06814i | ||||||||
\(989\) | −13.8008 | + | 7.96789i | −0.438840 | + | 0.253364i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3723 | + | 37.0179i | −0.678914 | + | 1.17591i | 0.296394 | + | 0.955066i | \(0.404216\pi\) |
−0.975308 | + | 0.220848i | \(0.929118\pi\) | |||||||
\(992\) | −3.92008 | + | 2.26326i | −0.124463 | + | 0.0718585i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.82084 | + | 23.4746i | 0.184626 | + | 0.744568i | ||||
\(995\) | 0.662799 | + | 7.71756i | 0.0210121 | + | 0.244663i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4359 | + | 28.4679i | −0.520531 | + | 0.901587i | 0.479184 | + | 0.877715i | \(0.340933\pi\) |
−0.999715 | + | 0.0238722i | \(0.992401\pi\) | |||||||
\(998\) | 1.47545 | − | 2.55555i | 0.0467045 | − | 0.0808945i | ||||
\(999\) | 0 | 0 |
(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 | 630.2.bo.b.269.2 | yes | 16 | |
3.2 | odd | 2 | 630.2.bo.a.269.7 | yes | 16 | ||
5.2 | odd | 4 | 3150.2.bf.f.1151.1 | 32 | |||
5.3 | odd | 4 | 3150.2.bf.f.1151.12 | 32 | |||
5.4 | even | 2 | 630.2.bo.a.269.4 | yes | 16 | ||
7.3 | odd | 6 | 4410.2.d.a.4409.2 | 16 | |||
7.4 | even | 3 | 4410.2.d.a.4409.15 | 16 | |||
7.5 | odd | 6 | inner | 630.2.bo.b.89.5 | yes | 16 | |
15.2 | even | 4 | 3150.2.bf.f.1151.11 | 32 | |||
15.8 | even | 4 | 3150.2.bf.f.1151.2 | 32 | |||
15.14 | odd | 2 | inner | 630.2.bo.b.269.5 | yes | 16 | |
21.5 | even | 6 | 630.2.bo.a.89.4 | ✓ | 16 | ||
21.11 | odd | 6 | 4410.2.d.b.4409.2 | 16 | |||
21.17 | even | 6 | 4410.2.d.b.4409.15 | 16 | |||
35.4 | even | 6 | 4410.2.d.b.4409.16 | 16 | |||
35.12 | even | 12 | 3150.2.bf.f.1601.11 | 32 | |||
35.19 | odd | 6 | 630.2.bo.a.89.7 | yes | 16 | ||
35.24 | odd | 6 | 4410.2.d.b.4409.1 | 16 | |||
35.33 | even | 12 | 3150.2.bf.f.1601.2 | 32 | |||
105.47 | odd | 12 | 3150.2.bf.f.1601.1 | 32 | |||
105.59 | even | 6 | 4410.2.d.a.4409.16 | 16 | |||
105.68 | odd | 12 | 3150.2.bf.f.1601.12 | 32 | |||
105.74 | odd | 6 | 4410.2.d.a.4409.1 | 16 | |||
105.89 | even | 6 | inner | 630.2.bo.b.89.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.4 | ✓ | 16 | 21.5 | even | 6 | ||
630.2.bo.a.89.7 | yes | 16 | 35.19 | odd | 6 | ||
630.2.bo.a.269.4 | yes | 16 | 5.4 | even | 2 | ||
630.2.bo.a.269.7 | yes | 16 | 3.2 | odd | 2 | ||
630.2.bo.b.89.2 | yes | 16 | 105.89 | even | 6 | inner | |
630.2.bo.b.89.5 | yes | 16 | 7.5 | odd | 6 | inner | |
630.2.bo.b.269.2 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.bo.b.269.5 | yes | 16 | 15.14 | odd | 2 | inner | |
3150.2.bf.f.1151.1 | 32 | 5.2 | odd | 4 | |||
3150.2.bf.f.1151.2 | 32 | 15.8 | even | 4 | |||
3150.2.bf.f.1151.11 | 32 | 15.2 | even | 4 | |||
3150.2.bf.f.1151.12 | 32 | 5.3 | odd | 4 | |||
3150.2.bf.f.1601.1 | 32 | 105.47 | odd | 12 | |||
3150.2.bf.f.1601.2 | 32 | 35.33 | even | 12 | |||
3150.2.bf.f.1601.11 | 32 | 35.12 | even | 12 | |||
3150.2.bf.f.1601.12 | 32 | 105.68 | odd | 12 | |||
4410.2.d.a.4409.1 | 16 | 105.74 | odd | 6 | |||
4410.2.d.a.4409.2 | 16 | 7.3 | odd | 6 | |||
4410.2.d.a.4409.15 | 16 | 7.4 | even | 3 | |||
4410.2.d.a.4409.16 | 16 | 105.59 | even | 6 | |||
4410.2.d.b.4409.1 | 16 | 35.24 | odd | 6 | |||
4410.2.d.b.4409.2 | 16 | 21.11 | odd | 6 | |||
4410.2.d.b.4409.15 | 16 | 21.17 | even | 6 | |||
4410.2.d.b.4409.16 | 16 | 35.4 | even | 6 |