Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(49,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.bb (of order \(12\), degree \(4\), not 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.529 |
Dual form | 576.2.bb.b.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.133975i | 0.223607 | + | 0.0599153i | 0.368883 | − | 0.929476i | \(-0.379740\pi\) |
−0.145276 | + | 0.989391i | \(0.546407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.13397 | + | 1.23205i | 0.806567 | + | 0.465671i | 0.845762 | − | 0.533560i | \(-0.179146\pi\) |
−0.0391956 | + | 0.999232i | \(0.512480\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.133975 | − | 0.500000i | −0.0403949 | − | 0.150756i | 0.942783 | − | 0.333408i | \(-0.108199\pi\) |
−0.983178 | + | 0.182652i | \(0.941532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23205 | + | 4.59808i | −0.341709 | + | 1.27528i | 0.554700 | + | 0.832050i | \(0.312833\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.232051 | + | 0.866025i | −0.0599153 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 3.00000i | 0.688247 | + | 0.688247i | 0.961844 | − | 0.273597i | \(-0.0882135\pi\) |
−0.273597 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.13397 | + | 3.69615i | −0.465671 | + | 0.806567i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.401924 | + | 0.232051i | −0.0838069 | + | 0.0483859i | −0.541318 | − | 0.840818i | \(-0.682074\pi\) |
0.457511 | + | 0.889204i | \(0.348741\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.09808 | − | 2.36603i | −0.819615 | − | 0.473205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.23205 | + | 0.866025i | −0.600177 | + | 0.160817i | −0.546100 | − | 0.837720i | \(-0.683888\pi\) |
−0.0540766 | + | 0.998537i | \(0.517222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.598076 | − | 1.03590i | −0.107418 | − | 0.186053i | 0.807306 | − | 0.590133i | \(-0.200925\pi\) |
−0.914723 | + | 0.404081i | \(0.867592\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.866025 | − | 0.232051i | 0.150756 | − | 0.0403949i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.901924 | + | 0.901924i | 0.152453 | + | 0.152453i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.73205 | + | 7.73205i | −1.27114 | + | 1.27114i | −0.325651 | + | 0.945490i | \(0.605584\pi\) |
−0.945490 | + | 0.325651i | \(0.894416\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.96410 | − | 2.13397i | −1.27528 | − | 0.341709i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.69615 | − | 5.59808i | 1.51428 | − | 0.874273i | 0.514425 | − | 0.857536i | \(-0.328006\pi\) |
0.999860 | − | 0.0167371i | \(-0.00532782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.33013 | + | 8.69615i | 0.355341 | + | 1.32615i | 0.880055 | + | 0.474872i | \(0.157506\pi\) |
−0.524714 | + | 0.851279i | \(0.675828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | − | 0.401924i | −0.223607 | − | 0.0599153i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.59808 | + | 7.96410i | −0.670698 | + | 1.16168i | 0.307008 | + | 0.951707i | \(0.400672\pi\) |
−0.977706 | + | 0.209977i | \(0.932661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.464102 | − | 0.803848i | −0.0663002 | − | 0.114835i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.92820i | 0.970143i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.26795 | − | 2.26795i | 0.311527 | − | 0.311527i | −0.533974 | − | 0.845501i | \(-0.679302\pi\) |
0.845501 | + | 0.533974i | \(0.179302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.267949i | − | 0.0361303i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.19615 | + | 5.19615i | −0.688247 | + | 0.688247i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.59808 | − | 1.50000i | −0.728807 | − | 0.195283i | −0.124709 | − | 0.992193i | \(-0.539800\pi\) |
−0.604098 | + | 0.796910i | \(0.706467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4282 | − | 3.86603i | 1.84734 | − | 0.494994i | 0.847957 | − | 0.530065i | \(-0.177832\pi\) |
0.999385 | + | 0.0350707i | \(0.0111656\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.40192 | − | 3.69615i | −0.806567 | − | 0.465671i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23205 | + | 2.13397i | −0.152817 | + | 0.264687i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.330127 | − | 1.23205i | 0.0403314 | − | 0.150519i | −0.942824 | − | 0.333292i | \(-0.891841\pi\) |
0.983155 | + | 0.182773i | \(0.0585073\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.401924 | − | 0.696152i | −0.0483859 | − | 0.0838069i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.9282i | − | 1.29694i | −0.761241 | − | 0.648470i | \(-0.775409\pi\) | ||
0.761241 | − | 0.648470i | \(-0.224591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.535898i | 0.0627222i | 0.999508 | + | 0.0313611i | \(0.00998418\pi\) | ||||
−0.999508 | + | 0.0313611i | \(0.990016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.09808 | − | 7.09808i | 0.473205 | − | 0.819615i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.330127 | − | 1.23205i | 0.0376215 | − | 0.140405i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.866025 | + | 1.50000i | −0.0974355 | + | 0.168763i | −0.910622 | − | 0.413239i | \(-0.864397\pi\) |
0.813187 | + | 0.582003i | \(0.197731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7942 | − | 3.16025i | 1.29458 | − | 0.346883i | 0.455185 | − | 0.890397i | \(-0.349573\pi\) |
0.839400 | + | 0.543514i | \(0.182907\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | + | 0.535898i | 0.216930 | + | 0.0581263i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | − | 5.59808i | −0.160817 | − | 0.600177i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 11.8564i | − | 1.25678i | −0.777900 | − | 0.628388i | \(-0.783715\pi\) | ||
0.777900 | − | 0.628388i | \(-0.216285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.29423 | + | 8.29423i | −0.869471 | + | 0.869471i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.79423 | − | 1.03590i | 0.186053 | − | 0.107418i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.09808 | + | 1.90192i | 0.112660 | + | 0.195133i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | + | 0.866025i | −0.0507673 | + | 0.0879316i | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.401924 | + | 1.50000i | 0.0403949 | + | 0.150756i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.500000 | + | 1.86603i | 0.0497519 | + | 0.185676i | 0.986330 | − | 0.164783i | \(-0.0526922\pi\) |
−0.936578 | + | 0.350459i | \(0.886026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.79423 | + | 1.03590i | −0.176791 | + | 0.102070i | −0.585784 | − | 0.810467i | \(-0.699213\pi\) |
0.408993 | + | 0.912537i | \(0.365880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.56218 | + | 1.56218i | −0.152453 | + | 0.152453i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3923 | − | 11.3923i | 1.10134 | − | 1.10134i | 0.107086 | − | 0.994250i | \(-0.465848\pi\) |
0.994250 | − | 0.107086i | \(-0.0341520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.73205 | + | 1.73205i | 0.165900 | + | 0.165900i | 0.785175 | − | 0.619274i | \(-0.212573\pi\) |
−0.619274 | + | 0.785175i | \(0.712573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.3923 | − | 13.3923i | −1.27114 | − | 1.27114i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.76795 | − | 4.79423i | −0.260387 | − | 0.451003i | 0.705958 | − | 0.708254i | \(-0.250517\pi\) |
−0.966345 | + | 0.257251i | \(0.917183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.232051 | + | 0.0621778i | −0.0216388 | + | 0.00579811i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.69615 | − | 13.7942i | 0.341709 | − | 1.27528i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.53590 | + | 4.92820i | 0.782485 | + | 0.451768i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.29423 | − | 5.36603i | 0.844930 | − | 0.487820i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.69615 | + | 16.7942i | 0.874273 | + | 1.51428i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.56218 | − | 3.56218i | −0.318611 | − | 0.318611i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3923 | 1.80952 | 0.904762 | − | 0.425917i | \(-0.140048\pi\) | ||||
0.904762 | + | 0.425917i | \(0.140048\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.0622 | + | 4.03590i | −1.32615 | + | 0.355341i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.13397 | − | 11.6962i | 0.273817 | − | 1.02190i | −0.682814 | − | 0.730593i | \(-0.739244\pi\) |
0.956630 | − | 0.291305i | \(-0.0940894\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.70577 | + | 10.0981i | 0.234620 | + | 0.875614i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.696152 | − | 2.59808i | 0.0599153 | − | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4282 | + | 8.33013i | 1.23268 | + | 0.711691i | 0.967589 | − | 0.252531i | \(-0.0812631\pi\) |
0.265096 | + | 0.964222i | \(0.414596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.33013 | − | 1.16025i | −0.367277 | − | 0.0984115i | 0.0704603 | − | 0.997515i | \(-0.477553\pi\) |
−0.437737 | + | 0.899103i | \(0.644220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.7942 | − | 7.96410i | −1.16168 | − | 0.670698i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.46410 | 0.206059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.73205 | −0.143839 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.39230 | − | 0.803848i | 0.114835 | − | 0.0663002i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.6962 | − | 3.93782i | −1.20396 | − | 0.322599i | −0.399568 | − | 0.916704i | \(-0.630840\pi\) |
−0.804388 | + | 0.594105i | \(0.797507\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.06218 | + | 3.50000i | 0.493333 | + | 0.284826i | 0.725956 | − | 0.687741i | \(-0.241398\pi\) |
−0.232623 | + | 0.972567i | \(0.574731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.160254 | − | 0.598076i | −0.0128719 | − | 0.0480386i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.232051 | + | 0.866025i | −0.0185197 | + | 0.0691164i | −0.974567 | − | 0.224095i | \(-0.928057\pi\) |
0.956048 | + | 0.293212i | \(0.0947240\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.92820 | + | 3.92820i | 0.311527 | + | 0.311527i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.14359 | −0.0901278 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.9282 | − | 11.9282i | −0.934289 | − | 0.934289i | 0.0636813 | − | 0.997970i | \(-0.479716\pi\) |
−0.997970 | + | 0.0636813i | \(0.979716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.464102 | 0.0361303 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.25833 | − | 4.76795i | 0.639049 | − | 0.368955i | −0.145199 | − | 0.989402i | \(-0.546382\pi\) |
0.784248 | + | 0.620447i | \(0.213049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.36603 | − | 4.83013i | −0.643540 | − | 0.371548i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.00000 | − | 9.00000i | −0.688247 | − | 0.688247i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.96410 | + | 2.40192i | −0.681528 | + | 0.182615i | −0.582942 | − | 0.812514i | \(-0.698099\pi\) |
−0.0985859 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.83013 | − | 10.0981i | −0.440716 | − | 0.763343i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.59808 | − | 9.69615i | 0.195283 | − | 0.728807i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.92820 | − | 7.92820i | −0.592582 | − | 0.592582i | 0.345746 | − | 0.938328i | \(-0.387626\pi\) |
−0.938328 | + | 0.345746i | \(0.887626\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.26795 | + | 4.26795i | −0.317234 | + | 0.317234i | −0.847704 | − | 0.530470i | \(-0.822016\pi\) |
0.530470 | + | 0.847704i | \(0.322016\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.69615 | + | 24.9904i | 0.494994 | + | 1.84734i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.90192 | + | 2.83013i | −0.360397 | + | 0.208075i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.535898 | − | 2.00000i | −0.0391888 | − | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.40192 | − | 11.0885i | 0.465671 | − | 0.806567i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.59808 | + | 11.4282i | −0.477420 | + | 0.826916i | −0.999665 | − | 0.0258797i | \(-0.991761\pi\) |
0.522245 | + | 0.852795i | \(0.325095\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.23205 | − | 2.13397i | −0.0886850 | − | 0.153607i | 0.818271 | − | 0.574833i | \(-0.194933\pi\) |
−0.906956 | + | 0.421226i | \(0.861600\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.69615 | − | 2.13397i | −0.264687 | − | 0.152817i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4641 | − | 10.4641i | 0.745536 | − | 0.745536i | −0.228101 | − | 0.973637i | \(-0.573252\pi\) |
0.973637 | + | 0.228101i | \(0.0732517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.85641i | − | 0.415150i | −0.978219 | − | 0.207575i | \(-0.933443\pi\) | ||
0.978219 | − | 0.207575i | \(-0.0665570\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.13397 | + | 0.571797i | 0.150519 | + | 0.0403314i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.96410 | − | 2.13397i | −0.558970 | − | 0.149776i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.59808 | − | 1.50000i | 0.390987 | − | 0.104765i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.20577 | − | 0.696152i | 0.0838069 | − | 0.0483859i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.09808 | − | 1.90192i | 0.0759555 | − | 0.131559i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.526279 | − | 1.96410i | 0.0362306 | − | 0.135214i | −0.945442 | − | 0.325791i | \(-0.894369\pi\) |
0.981672 | + | 0.190577i | \(0.0610359\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.9282 | 1.29694 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.66025i | 0.317827i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.94744i | − | 0.200085i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.928203 | −0.0627222 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.92820 | + | 18.3923i | −0.331507 | + | 1.23720i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.79423 | − | 13.5000i | 0.521940 | − | 0.904027i | −0.477734 | − | 0.878504i | \(-0.658542\pi\) |
0.999674 | − | 0.0255224i | \(-0.00812491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2942 | + | 7.09808i | 0.819615 | + | 0.473205i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.2583 | + | 4.62436i | −1.14548 | + | 0.306929i | −0.781151 | − | 0.624343i | \(-0.785367\pi\) |
−0.364325 | + | 0.931272i | \(0.618700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.42820 | + | 2.52628i | 0.623033 | + | 0.166941i | 0.556506 | − | 0.830843i | \(-0.312142\pi\) |
0.0665269 | + | 0.997785i | \(0.478808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.13397 | + | 0.571797i | 0.140405 | + | 0.0376215i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.9282i | 1.50208i | 0.660259 | + | 0.751038i | \(0.270447\pi\) | ||||
−0.660259 | + | 0.751038i | \(0.729553\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.36603 | + | 3.36603i | −0.219575 | + | 0.219575i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.59808 | − | 1.50000i | −0.168763 | − | 0.0974355i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.59808 | + | 9.69615i | 0.362109 | + | 0.627192i | 0.988308 | − | 0.152472i | \(-0.0487233\pi\) |
−0.626198 | + | 0.779664i | \(0.715390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.23205 | + | 10.7942i | −0.401442 | + | 0.695317i | −0.993900 | − | 0.110284i | \(-0.964824\pi\) |
0.592458 | + | 0.805601i | \(0.298157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.124356 | − | 0.464102i | −0.00794479 | − | 0.0296504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.4904 | + | 10.0981i | −1.11289 | + | 0.642525i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.47372 | + | 20.4282i | 0.346883 | + | 1.29458i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.39230 | + | 7.39230i | −0.466598 | + | 0.466598i | −0.900811 | − | 0.434212i | \(-0.857027\pi\) |
0.434212 | + | 0.900811i | \(0.357027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.169873 | + | 0.169873i | 0.0106798 | + | 0.0106798i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.928203 | + | 3.46410i | −0.0581263 | + | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.16025 | − | 8.93782i | −0.321888 | − | 0.557526i | 0.658990 | − | 0.752152i | \(-0.270984\pi\) |
−0.980878 | + | 0.194626i | \(0.937651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.0263 | + | 6.97372i | −1.61719 | + | 0.433326i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.69615 | − | 2.59808i | 0.600177 | − | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.40192 | − | 1.96410i | −0.209772 | − | 0.121112i | 0.391434 | − | 0.920206i | \(-0.371979\pi\) |
−0.601205 | + | 0.799095i | \(0.705313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.43782 | − | 0.830127i | 0.0883247 | − | 0.0509943i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.5359 | 1.25678 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.73205 | + | 7.73205i | 0.471431 | + | 0.471431i | 0.902378 | − | 0.430946i | \(-0.141820\pi\) |
−0.430946 | + | 0.902378i | \(0.641820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9282 | 0.906824 | 0.453412 | − | 0.891301i | \(-0.350207\pi\) | ||||
0.453412 | + | 0.891301i | \(0.350207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.3660 | − | 14.3660i | −0.869471 | − | 0.869471i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.633975 | + | 2.36603i | −0.0382301 | + | 0.142677i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.69615 | − | 13.7942i | −0.222080 | − | 0.828815i | −0.983553 | − | 0.180618i | \(-0.942190\pi\) |
0.761473 | − | 0.648197i | \(-0.224477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.79423 | + | 3.10770i | 0.107418 | + | 0.186053i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9641 | + | 9.79423i | 1.01199 | + | 0.584275i | 0.911775 | − | 0.410691i | \(-0.134712\pi\) |
0.100219 | + | 0.994965i | \(0.468046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5263 | + | 4.16025i | 0.922942 | + | 0.247301i | 0.688842 | − | 0.724911i | \(-0.258119\pi\) |
0.234099 | + | 0.972213i | \(0.424786\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.29423 | + | 1.90192i | −0.195133 | + | 0.112660i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.5885 | 1.62850 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50000 | − | 0.866025i | −0.0879316 | − | 0.0507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.4282 | − | 3.86603i | −0.842905 | − | 0.225856i | −0.188569 | − | 0.982060i | \(-0.560385\pi\) |
−0.654336 | + | 0.756204i | \(0.727052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.59808 | − | 1.50000i | −0.151266 | − | 0.0873334i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.59808 | + | 0.696152i | −0.150756 | + | 0.0403949i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.571797 | − | 2.13397i | −0.0330679 | − | 0.123411i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.74167 | + | 21.4282i | −0.330944 | + | 1.23510i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.23205 | + | 0.866025i | −0.185676 | + | 0.0497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.73205 | 0.442736 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.92820 | + | 5.92820i | 0.338340 | + | 0.338340i | 0.855742 | − | 0.517402i | \(-0.173101\pi\) |
−0.517402 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.79423 | − | 3.10770i | −0.102070 | − | 0.176791i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.1865 | + | 15.6962i | −1.54161 | + | 0.890047i | −0.542869 | + | 0.839817i | \(0.682662\pi\) |
−0.998738 | + | 0.0502299i | \(0.984005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.83975 | − | 4.52628i | −0.443129 | − | 0.255840i | 0.261795 | − | 0.965123i | \(-0.415686\pi\) |
−0.704924 | + | 0.709283i | \(0.749019\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.70577 | − | 2.70577i | −0.152453 | − | 0.152453i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.03590 | − | 0.545517i | 0.114347 | − | 0.0306393i | −0.201192 | − | 0.979552i | \(-0.564481\pi\) |
0.315539 | + | 0.948913i | \(0.397815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.866025 | + | 1.50000i | 0.0484881 | + | 0.0839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.7321 | + | 19.7321i | 1.10134 | + | 1.10134i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | + | 12.0000i | 0.667698 | + | 0.667698i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.9282 | − | 15.9282i | 0.883538 | − | 0.883538i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.00000 | + | 3.00000i | −0.165900 | + | 0.165900i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.6244 | + | 11.3301i | −1.08193 | + | 0.624650i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.06218 | − | 26.3564i | −0.388172 | − | 1.44868i | −0.833105 | − | 0.553115i | \(-0.813439\pi\) |
0.444933 | − | 0.895564i | \(-0.353228\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.1962 | − | 23.1962i | 1.27114 | − | 1.27114i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.330127 | − | 0.571797i | 0.0180368 | − | 0.0312406i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.696152 | + | 1.20577i | 0.0379218 | + | 0.0656826i | 0.884363 | − | 0.466799i | \(-0.154593\pi\) |
−0.846442 | + | 0.532482i | \(0.821260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.30385 | − | 4.79423i | 0.451003 | − | 0.260387i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.437822 | + | 0.437822i | −0.0237094 | + | 0.0237094i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5359i | − | 1.05484i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.107695 | − | 0.401924i | −0.00579811 | − | 0.0216388i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.5263 | − | 5.23205i | −1.04823 | − | 0.280871i | −0.306707 | − | 0.951804i | \(-0.599227\pi\) |
−0.741518 | + | 0.670933i | \(0.765894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.96410 | − | 2.13397i | 0.426309 | − | 0.114229i | −0.0392843 | − | 0.999228i | \(-0.512508\pi\) |
0.465593 | + | 0.884999i | \(0.345841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.8923 | + | 6.40192i | 1.27528 | + | 0.341709i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.2321 | + | 26.3827i | −0.810720 | + | 1.40421i | 0.101640 | + | 0.994821i | \(0.467591\pi\) |
−0.912361 | + | 0.409387i | \(0.865742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.46410 | − | 5.46410i | 0.0777064 | − | 0.290004i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.53590 | + | 14.7846i | −0.451768 | + | 0.782485i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0718i | 0.795459i | 0.917503 | + | 0.397730i | \(0.130202\pi\) | ||||
−0.917503 | + | 0.397730i | \(0.869798\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.29423 | + | 16.0981i | 0.487820 | + | 0.844930i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0717968 | + | 0.267949i | −0.00375801 | + | 0.0140251i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.4545 | + | 26.7679i | −0.806717 | + | 1.39728i | 0.108408 | + | 0.994106i | \(0.465425\pi\) |
−0.915125 | + | 0.403169i | \(0.867909\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29.0885 | + | 16.7942i | −1.51428 | + | 0.874273i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.63397 | − | 2.04552i | 0.396336 | − | 0.106198i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.4282 | − | 3.59808i | −0.695286 | − | 0.186301i | −0.106168 | − | 0.994348i | \(-0.533858\pi\) |
−0.589118 | + | 0.808047i | \(0.700525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.16987 | − | 6.16987i | 0.318611 | − | 0.318611i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.9282i | − | 0.820344i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5885 | + | 15.5885i | −0.800725 | + | 0.800725i | −0.983209 | − | 0.182484i | \(-0.941586\pi\) |
0.182484 | + | 0.983209i | \(0.441586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.3205i | 1.80952i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.3301 | − | 21.3564i | −0.630040 | − | 1.09126i | −0.987543 | − | 0.157349i | \(-0.949705\pi\) |
0.357503 | − | 0.933912i | \(-0.383628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.330127 | − | 0.571797i | 0.0168248 | − | 0.0291415i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.99038 | − | 26.0885i | −0.355341 | − | 1.32615i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.03590 | − | 7.59808i | −0.103224 | − | 0.385238i | 0.894914 | − | 0.446240i | \(-0.147237\pi\) |
−0.998138 | + | 0.0610019i | \(0.980570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.60770 | + | 0.928203i | −0.0813046 | + | 0.0469413i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.2583 | + | 5.42820i | 1.02190 | + | 0.273817i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.633975 | + | 0.633975i | −0.0318987 | + | 0.0318987i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0526 | − | 21.0526i | −1.05660 | − | 1.05660i | −0.998299 | − | 0.0582984i | \(-0.981433\pi\) |
−0.0582984 | − | 0.998299i | \(-0.518567\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.4904 | + | 4.68653i | −0.875614 | + | 0.234620i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.16025 | + | 2.00962i | 0.0579403 | + | 0.100356i | 0.893541 | − | 0.448982i | \(-0.148213\pi\) |
−0.835600 | + | 0.549338i | \(0.814880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.50000 | − | 1.47372i | 0.273975 | − | 0.0734112i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.50000 | + | 1.20577i | 0.223607 | + | 0.0599153i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.90192 | + | 2.83013i | 0.242979 | + | 0.140284i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.62436 | + | 2.66987i | −0.228660 | + | 0.132017i | −0.609954 | − | 0.792437i | \(-0.708812\pi\) |
0.381294 | + | 0.924454i | \(0.375479\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4282 | + | 24.9904i | −0.711691 | + | 1.23268i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.0981 | − | 10.0981i | −0.496894 | − | 0.496894i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.32051 | 0.310262 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.00962 | − | 7.50000i | 0.0984115 | − | 0.367277i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.526279 | − | 1.96410i | 0.0257104 | − | 0.0959526i | −0.951878 | − | 0.306476i | \(-0.900850\pi\) |
0.977589 | + | 0.210523i | \(0.0675168\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.89230 | − | 10.7942i | −0.140962 | − | 0.526079i | −0.999902 | − | 0.0140017i | \(-0.995543\pi\) |
0.858940 | − | 0.512077i | \(-0.171124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.7942 | − | 23.8923i | 0.670698 | − | 1.16168i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.3923 | − | 9.46410i | −0.795144 | − | 0.459076i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.5526 | + | 9.52628i | 1.72051 | + | 0.461009i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.26795i | 0.206059i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.3205 | −1.50866 | −0.754328 | − | 0.656498i | \(-0.772037\pi\) | ||||
−0.754328 | + | 0.656498i | \(0.772037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3923 | 1.17222 | 0.586110 | − | 0.810232i | \(-0.300659\pi\) | ||||
0.586110 | + | 0.810232i | \(0.300659\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.00000i | − | 0.143839i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.90192 | − | 0.509619i | −0.0909814 | − | 0.0243784i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0622 | + | 10.4282i | 0.862061 | + | 0.497711i | 0.864702 | − | 0.502286i | \(-0.167507\pi\) |
−0.00264111 | + | 0.999997i | \(0.500841\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.39230 | + | 2.41154i | 0.0663002 | + | 0.114835i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.33013 | + | 16.1603i | 0.205731 | + | 0.767797i | 0.989226 | + | 0.146399i | \(0.0467683\pi\) |
−0.783495 | + | 0.621398i | \(0.786565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.58846 | − | 5.92820i | 0.0753001 | − | 0.281024i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.82051 | − | 25.4545i | 0.322599 | − | 1.20396i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.679492 | 0.0320672 | 0.0160336 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160336 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.09808 | − | 4.09808i | −0.192971 | − | 0.192971i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.06218 | + | 10.5000i | −0.284826 | + | 0.493333i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.25833 | + | 3.03590i | −0.246514 | + | 0.142325i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0359 | − | 10.9904i | −0.890462 | − | 0.514108i | −0.0163683 | − | 0.999866i | \(-0.505210\pi\) |
−0.874094 | + | 0.485758i | \(0.838544\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 20.7846i | − | 0.970143i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.23205 | − | 0.598076i | 0.103957 | − | 0.0278552i | −0.206466 | − | 0.978454i | \(-0.566196\pi\) |
0.310423 | + | 0.950599i | \(0.399529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.33013 | − | 5.76795i | −0.154764 | − | 0.268059i | 0.778209 | − | 0.628005i | \(-0.216128\pi\) |
−0.932973 | + | 0.359946i | \(0.882795\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.03590 | − | 0.277568i | 0.0480386 | − | 0.0128719i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.7846 | + | 19.7846i | 0.915523 | + | 0.915523i | 0.996700 | − | 0.0811771i | \(-0.0258679\pi\) |
−0.0811771 | + | 0.996700i | \(0.525868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.22243 | − | 2.22243i | 0.102622 | − | 0.102622i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.50000 | − | 0.401924i | −0.0691164 | − | 0.0185197i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.03590 | − | 2.33013i | 0.185571 | − | 0.107139i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.19615 | − | 19.3923i | −0.238416 | − | 0.889780i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.80385 | + | 6.80385i | −0.311527 | + | 0.311527i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.669873 | + | 1.16025i | −0.0306073 | + | 0.0530134i | −0.880923 | − | 0.473259i | \(-0.843077\pi\) |
0.850316 | + | 0.526272i | \(0.176411\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.0263 | − | 45.0788i | −1.18670 | − | 2.05542i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.98076i | − | 0.0901278i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.366025 | + | 0.366025i | −0.0166204 | + | 0.0166204i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.7846i | − | 1.57624i | −0.615521 | − | 0.788121i | \(-0.711054\pi\) | ||
0.615521 | − | 0.788121i | \(-0.288946\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.6603 | − | 20.6603i | 0.934289 | − | 0.934289i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.86603 | + | 0.500000i | 0.0842125 | + | 0.0225647i | 0.300679 | − | 0.953725i | \(-0.402787\pi\) |
−0.216467 | + | 0.976290i | \(0.569453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.9282 | + | 3.46410i | −0.582257 | + | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.803848i | 0.0361303i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.4641 | − | 23.3205i | 0.603947 | − | 1.04607i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.669873 | + | 2.50000i | −0.0299876 | + | 0.111915i | −0.979297 | − | 0.202427i | \(-0.935117\pi\) |
0.949310 | + | 0.314342i | \(0.101784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.25833 | + | 14.3038i | 0.368955 | + | 0.639049i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8564i | 0.617827i | 0.951090 | + | 0.308913i | \(0.0999653\pi\) | ||||
−0.951090 | + | 0.308913i | \(0.900035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00000i | 0.0444994i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.36603 | − | 14.4904i | 0.371548 | − | 0.643540i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.69615 | − | 21.2583i | 0.252478 | − | 0.942259i | −0.716999 | − | 0.697074i | \(-0.754485\pi\) |
0.969476 | − | 0.245185i | \(-0.0788486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.660254 | + | 1.14359i | −0.0292079 | + | 0.0505896i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.5885 | − | 15.5885i | 0.688247 | − | 0.688247i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.03590 | + | 0.277568i | −0.0456471 | + | 0.0122311i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.59808 | + | 1.23205i | 0.202223 | + | 0.0541855i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.16025 | − | 15.5263i | −0.182615 | − | 0.681528i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14.1436i | − | 0.619642i | −0.950795 | − | 0.309821i | \(-0.899731\pi\) | ||
0.950795 | − | 0.309821i | \(-0.100269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.12436 | − | 2.12436i | 0.0928916 | − | 0.0928916i | −0.659134 | − | 0.752026i | \(-0.729077\pi\) |
0.752026 | + | 0.659134i | \(0.229077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.4904 | − | 10.0981i | 0.763343 | − | 0.440716i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.39230 | − | 4.14359i | −0.104210 | − | 0.180498i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3923 | + | 19.7321i | −0.495318 | + | 0.857915i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.7942 | + | 4.50000i | 0.728807 | + | 0.195283i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.7942 | + | 51.4808i | 0.597494 | + | 2.22988i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.22243 | − | 4.16987i | 0.312253 | − | 0.180279i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.7321 | − | 13.7321i | 0.592582 | − | 0.592582i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.339746 | + | 0.339746i | −0.0146339 | + | 0.0146339i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | − | 15.0000i | −0.644900 | − | 0.644900i | 0.306856 | − | 0.951756i | \(-0.400723\pi\) |
−0.951756 | + | 0.306856i | \(0.900723\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.39230 | − | 7.39230i | −0.317234 | − | 0.317234i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.633975 | + | 1.09808i | 0.0271565 | + | 0.0470364i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2583 | − | 7.57180i | 1.20824 | − | 0.323747i | 0.402168 | − | 0.915566i | \(-0.368257\pi\) |
0.806071 | + | 0.591819i | \(0.201590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −43.2846 | + | 11.5981i | −1.84734 | + | 0.494994i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.2942 | − | 7.09808i | −0.523752 | − | 0.302388i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.69615 | + | 2.13397i | −0.157176 | + | 0.0907458i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.90192 | − | 8.49038i | −0.208075 | − | 0.360397i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.9808 | + | 27.9808i | 1.18558 | + | 1.18558i | 0.978276 | + | 0.207307i | \(0.0664699\pi\) |
0.207307 | + | 0.978276i | \(0.433530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.8564 | −1.81263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.46410 | − | 0.928203i | 0.146254 | − | 0.0391888i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.86603 | + | 29.3564i | −0.331513 | + | 1.23723i | 0.576086 | + | 0.817389i | \(0.304579\pi\) |
−0.907600 | + | 0.419836i | \(0.862088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.741670 | − | 2.76795i | −0.0312023 | − | 0.116448i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.2058 | + | 11.0885i | 0.806567 | + | 0.465671i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.4808 | − | 14.1340i | −1.02629 | − | 0.592527i | −0.110368 | − | 0.993891i | \(-0.535203\pi\) |
−0.915919 | + | 0.401364i | \(0.868536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.40192 | + | 1.44744i | 0.226063 | + | 0.0605735i | 0.370073 | − | 0.929003i | \(-0.379333\pi\) |
−0.144009 | + | 0.989576i | \(0.545999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.7942 | − | 11.4282i | −0.826916 | − | 0.477420i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.19615 | 0.0915859 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.1769 | 1.54770 | 0.773848 | − | 0.633372i | \(-0.218330\pi\) | ||||
0.773848 | + | 0.633372i | \(0.218330\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.69615 | − | 2.13397i | 0.153607 | − | 0.0886850i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.0622 | + | 7.78719i | 1.20570 | + | 0.323067i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.43782 | − | 0.830127i | −0.0595485 | − | 0.0343803i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.69615 | − | 6.40192i | 0.152817 | − | 0.264687i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.794229 | − | 2.96410i | −0.0327813 | − | 0.122342i | 0.947596 | − | 0.319470i | \(-0.103505\pi\) |
−0.980378 | + | 0.197129i | \(0.936838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31347 | − | 4.90192i | 0.0541204 | − | 0.201980i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.1244 | + | 18.1244i | 0.745536 | + | 0.745536i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.46410 | 0.0601234 | 0.0300617 | − | 0.999548i | \(-0.490430\pi\) | ||||
0.0300617 | + | 0.999548i | \(0.490430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.60770 | + | 3.60770i | 0.147901 | + | 0.147901i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.1436 | 0.415150 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.3109 | − | 17.5000i | 1.23847 | − | 0.715031i | 0.269688 | − | 0.962948i | \(-0.413079\pi\) |
0.968781 | + | 0.247917i | \(0.0797461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2321 | + | 17.4545i | 1.23319 | + | 0.711983i | 0.967694 | − | 0.252128i | \(-0.0811305\pi\) |
0.265497 | + | 0.964112i | \(0.414464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.990381 | + | 3.69615i | −0.0403314 | + | 0.150519i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.36603 | − | 1.43782i | 0.218160 | − | 0.0584558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.59808 | + | 7.96410i | 0.186630 | + | 0.323253i | 0.944125 | − | 0.329589i | \(-0.106910\pi\) |
−0.757494 | + | 0.652842i | \(0.773577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.69615 | − | 13.7942i | 0.149776 | − | 0.558970i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.9545 | − | 30.9545i | −1.25228 | − | 1.25228i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.58846 | + | 7.58846i | −0.306495 | + | 0.306495i | −0.843548 | − | 0.537053i | \(-0.819537\pi\) |
0.537053 | + | 0.843548i | \(0.319537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.59808 | + | 9.69615i | 0.104765 | + | 0.390987i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.08846 | − | 4.66987i | 0.325629 | − | 0.188002i | −0.328270 | − | 0.944584i | \(-0.606466\pi\) |
0.653899 | + | 0.756582i | \(0.273132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.86603 | − | 33.0885i | −0.356356 | − | 1.32994i | −0.878770 | − | 0.477246i | \(-0.841635\pi\) |
0.522414 | − | 0.852692i | \(-0.325031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.20577 | + | 2.08846i | 0.0483859 | + | 0.0838069i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.6077 | − | 25.3013i | 0.585245 | − | 1.01367i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.5263 | + | 18.2321i | 0.421051 | + | 0.729282i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.29423 | + | 1.90192i | 0.131559 | + | 0.0759555i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.9282 | + | 30.9282i | −1.23319 | + | 1.23319i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2487i | 1.28380i | 0.766788 | + | 0.641900i | \(0.221854\pi\) | ||||
−0.766788 | + | 0.641900i | \(0.778146\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.40192 | + | 0.911543i | 0.135214 | + | 0.0362306i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.1962 | + | 2.73205i | 0.404622 | + | 0.108418i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.26795 | − | 1.14359i | 0.169102 | − | 0.0453108i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.7846i | 1.29694i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.76795 | − | 9.99038i | 0.227820 | − | 0.394596i | −0.729342 | − | 0.684150i | \(-0.760173\pi\) |
0.957162 | + | 0.289553i | \(0.0935068\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.277568 | − | 1.03590i | 0.0109462 | − | 0.0408518i | −0.960237 | − | 0.279187i | \(-0.909935\pi\) |
0.971183 | + | 0.238335i | \(0.0766017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.07180 | −0.317827 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.3923i | − | 1.82387i | −0.410335 | − | 0.911935i | \(-0.634588\pi\) | ||
0.410335 | − | 0.911935i | \(-0.365412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000i | 0.117760i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.10512 | 0.200085 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.71539 | − | 21.3301i | 0.223661 | − | 0.834712i | −0.759276 | − | 0.650768i | \(-0.774447\pi\) |
0.982937 | − | 0.183944i | \(-0.0588865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.13397 | − | 5.42820i | 0.122455 | − | 0.212097i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.60770i | − | 0.0627222i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.33013 | + | 2.23205i | −0.324496 | + | 0.0869484i | −0.417390 | − | 0.908728i | \(-0.637055\pi\) |
0.0928939 | + | 0.995676i | \(0.470388\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6962 | − | 4.20577i | −0.610510 | − | 0.163586i | −0.0596998 | − | 0.998216i | \(-0.519014\pi\) |
−0.550810 | + | 0.834631i | \(0.685681\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.8564 | − | 8.53590i | −1.23720 | − | 0.331507i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.41154i | 0.209851i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.09808 | − | 1.09808i | 0.0425177 | − | 0.0425177i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.3827 | + | 13.5000i | 0.904027 | + | 0.521940i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.86603 | − | 6.69615i | −0.149246 | − | 0.258502i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.83975 | − | 6.65064i | 0.148011 | − | 0.256363i | −0.782481 | − | 0.622674i | \(-0.786046\pi\) |
0.930492 | + | 0.366311i | \(0.119379\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.2942 | + | 21.2942i | −0.473205 | + | 0.819615i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.2321 | − | 45.6506i | −0.470116 | − | 1.75450i | −0.639345 | − | 0.768920i | \(-0.720795\pi\) |
0.169229 | − | 0.985577i | \(-0.445872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.13397 | + | 1.23205i | −0.0818944 | + | 0.0472818i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.00962 | − | 29.8923i | −0.306929 | − | 1.14548i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.39230 | − | 5.39230i | 0.206331 | − | 0.206331i | −0.596375 | − | 0.802706i | \(-0.703393\pi\) |
0.802706 | + | 0.596375i | \(0.203393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.09808 | + | 6.09808i | 0.232996 | + | 0.232996i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.37564 | + | 16.3301i | −0.166941 | + | 0.623033i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.63397 | + | 13.2224i | 0.290831 | + | 0.503735i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5263 | − | 4.96410i | 0.704773 | − | 0.188843i | 0.111405 | − | 0.993775i | \(-0.464465\pi\) |
0.593367 | + | 0.804932i | \(0.297798\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.990381 | + | 3.69615i | −0.0376215 | + | 0.140405i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.00962 | − | 1.16025i | −0.0762292 | − | 0.0440109i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.7846 | − | 22.3923i | 1.46907 | − | 0.848169i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.7128 | −1.50208 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.0526 | − | 21.0526i | −0.795144 | − | 0.795144i | 0.187181 | − | 0.982325i | \(-0.440065\pi\) |
−0.982325 | + | 0.187181i | \(0.940065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.3923 | −1.74972 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.83013 | − | 5.83013i | −0.219575 | − | 0.219575i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.23205 | + | 4.59808i | −0.0463360 | + | 0.172928i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7487 | + | 40.1147i | 0.403676 | + | 1.50654i | 0.806484 | + | 0.591256i | \(0.201368\pi\) |
−0.402808 | + | 0.915285i | \(0.631966\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.59808 | − | 4.50000i | 0.0974355 | − | 0.168763i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.480762 | + | 0.277568i | 0.0180047 | + | 0.0103950i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.23205 | + | 0.330127i | 0.0460761 | + | 0.0123461i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.7942 | + | 9.69615i | −0.627192 | + | 0.362109i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.3205 | −0.869708 | −0.434854 | − | 0.900501i | \(-0.643200\pi\) | ||||
−0.434854 | + | 0.900501i | \(0.643200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.10512 | −0.190125 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.6962 | − | 10.7942i | −0.695317 | − | 0.401442i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.2942 | + | 4.09808i | 0.568013 | + | 0.152199i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.06218 | − | 5.23205i | −0.336098 | − | 0.194046i | 0.322447 | − | 0.946587i | \(-0.395494\pi\) |
−0.658545 | + | 0.752541i | \(0.728828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.32051 | + | 34.7846i | 0.344731 | + | 1.28656i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.37564 | + | 27.5263i | −0.272426 | + | 1.01671i | 0.685121 | + | 0.728429i | \(0.259749\pi\) |
−0.957547 | + | 0.288277i | \(0.906917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.803848 | − | 0.215390i | 0.0296504 | − | 0.00794479i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.660254 | −0.0243208 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7321 | + | 29.7321i | 1.09371 | + | 1.09371i | 0.995129 | + | 0.0985823i | \(0.0314308\pi\) |
0.0985823 | + | 0.995129i | \(0.468569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.4904 | − | 30.2942i | −0.642525 | − | 1.11289i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1147 | + | 14.5000i | −0.921370 | + | 0.531953i | −0.884072 | − | 0.467351i | \(-0.845209\pi\) |
−0.0372984 | + | 0.999304i | \(0.511875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.82051 | − | 3.93782i | −0.249884 | − | 0.144271i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.3827 | + | 9.48076i | −1.29458 | + | 0.346883i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.3468 | − | 10.2750i | 1.40116 | − | 0.375440i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.72243 | − | 8.17949i | −0.172324 | − | 0.298474i | 0.766908 | − | 0.641757i | \(-0.221794\pi\) |
−0.939232 | + | 0.343283i | \(0.888461\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.8038 | − | 12.8038i | −0.466598 | − | 0.466598i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.56218 | + | 2.56218i | 0.0932472 | + | 0.0932472i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.46410 | − | 8.46410i | 0.307633 | − | 0.307633i | −0.536358 | − | 0.843991i | \(-0.680200\pi\) |
0.843991 | + | 0.536358i | \(0.180200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.294229 | + | 0.294229i | −0.0106798 | + | 0.0106798i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.2846 | + | 14.5981i | −0.916566 | + | 0.529180i | −0.882538 | − | 0.470241i | \(-0.844167\pi\) |
−0.0340283 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.56218 | + | 5.83013i | 0.0565546 | + | 0.211065i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | − | 1.60770i | −0.216930 | − | 0.0581263i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.7942 | − | 23.8923i | 0.498081 | − | 0.862701i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.50000 | − | 6.06218i | −0.126213 | − | 0.218608i | 0.795993 | − | 0.605305i | \(-0.206949\pi\) |
−0.922207 | + | 0.386698i | \(0.873616\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4808 | − | 8.93782i | 0.557526 | − | 0.321888i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.58846 | − | 7.58846i | 0.272938 | − | 0.272938i | −0.557344 | − | 0.830282i | \(-0.688179\pi\) |
0.830282 | + | 0.557344i | \(0.188179\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.66025i | 0.203322i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.0788 | − | 45.0788i | −0.433326 | − | 1.61719i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45.8827 | + | 12.2942i | 1.64392 | + | 0.440486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.46410 | + | 1.46410i | −0.195521 | + | 0.0523897i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.50000 | + | 16.7942i | 0.160817 | + | 0.600177i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.232051 | + | 0.401924i | −0.00828225 | + | 0.0143453i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.06218 | + | 33.8205i | −0.323032 | + | 1.20557i | 0.593244 | + | 0.805023i | \(0.297847\pi\) |
−0.916276 | + | 0.400548i | \(0.868820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.40192 | − | 5.89230i | 0.121112 | − | 0.209772i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 13.6410i | − | 0.485019i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 71.1051i | 2.52502i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.43782 | + | 2.49038i | 0.0509943 | + | 0.0883247i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.284610 | − | 1.06218i | 0.0100814 | − | 0.0376243i | −0.960702 | − | 0.277582i | \(-0.910467\pi\) |
0.970783 | + | 0.239958i | \(0.0771336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.3923 | + | 31.8564i | −0.650673 | + | 1.12700i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.5692i | 1.25678i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.267949 | − | 0.0717968i | 0.00945572 | − | 0.00253365i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.571797 | − | 0.153212i | −0.0201532 | − | 0.00540003i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.3923 | + | 13.3923i | −0.471431 | + | 0.471431i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.6410i | 1.14760i | 0.818997 | + | 0.573799i | \(0.194531\pi\) | ||||
−0.818997 | + | 0.573799i | \(0.805469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5359 | − | 11.5359i | 0.405080 | − | 0.405080i | −0.474939 | − | 0.880019i | \(-0.657530\pi\) |
0.880019 | + | 0.474939i | \(0.157530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.8564i | 0.906824i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.36603 | − | 7.56218i | −0.152935 | − | 0.264892i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.0981 | + | 33.0788i | −0.668157 | + | 1.15728i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.8827 | − | 24.8827i | 0.869471 | − | 0.869471i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.01666 | + | 18.7224i | 0.175083 | + | 0.653417i | 0.996538 | + | 0.0831439i | \(0.0264961\pi\) |
−0.821455 | + | 0.570273i | \(0.806837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.65064 | + | 3.83975i | −0.231827 | + | 0.133845i | −0.611414 | − | 0.791311i | \(-0.709399\pi\) |
0.379588 | + | 0.925156i | \(0.376066\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.09808 | − | 1.09808i | −0.142677 | − | 0.0382301i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6077 | − | 10.6077i | 0.368866 | − | 0.368866i | −0.498198 | − | 0.867063i | \(-0.666005\pi\) |
0.867063 | + | 0.498198i | \(0.166005\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7321 | − | 17.7321i | −0.615860 | − | 0.615860i | 0.328607 | − | 0.944467i | \(-0.393421\pi\) |
−0.944467 | + | 0.328607i | \(0.893421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.8923 | − | 6.40192i | 0.828815 | − | 0.222080i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.85641 | − | 3.21539i | −0.0643207 | − | 0.111407i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.76795 | − | 1.27757i | 0.165002 | − | 0.0442121i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.38269 | + | 3.10770i | −0.186053 | + | 0.107418i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.2583 | + | 16.8923i | 1.01011 | + | 0.583187i | 0.911224 | − | 0.411912i | \(-0.135139\pi\) |
0.0988859 | + | 0.995099i | \(0.468472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.4186 | + | 8.90192i | −0.531675 | + | 0.306963i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.9641 | + | 29.3827i | −0.584275 | + | 1.01199i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.53590 | − | 3.53590i | −0.121639 | − | 0.121639i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.4449 | 0.908656 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.20577 | + | 26.8923i | −0.247301 | + | 0.922942i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.31347 | − | 4.90192i | 0.0450251 | − | 0.168036i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.69615 | − | 10.0622i | −0.0923145 | − | 0.344522i | 0.904284 | − | 0.426931i | \(-0.140405\pi\) |
−0.996599 | + | 0.0824088i | \(0.973739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.29423 | − | 5.70577i | −0.112660 | − | 0.195133i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.3564 | − | 24.4545i | −1.44687 | − | 0.835349i | −0.448574 | − | 0.893746i | \(-0.648068\pi\) |
−0.998293 | + | 0.0583966i | \(0.981401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7942 | − | 4.50000i | −0.573012 | − | 0.153538i | −0.0393342 | − | 0.999226i | \(-0.512524\pi\) |
−0.533677 | + | 0.845688i | \(0.679190\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 47.7846i | 1.62850i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.4641 | 1.13913 | 0.569566 | − | 0.821946i | \(-0.307111\pi\) | ||||
0.569566 | + | 0.821946i | \(0.307111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.80385 | −0.163336 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.73205i | − | 0.0588235i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.866025 | + | 0.232051i | 0.0293779 | + | 0.00787178i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.25833 | + | 3.03590i | 0.178172 | + | 0.102867i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.50000 | − | 2.59808i | 0.0507673 | − | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.21281 | − | 11.9904i | −0.108613 | − | 0.405349i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.94486 | + | 33.3827i | −0.302047 | + | 1.12725i | 0.633411 | + | 0.773815i | \(0.281654\pi\) |
−0.935458 | + | 0.353438i | \(0.885013\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.69615 | − | 24.9904i | 0.225856 | − | 0.842905i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.32051 | −0.111871 | −0.0559354 | − | 0.998434i | \(-0.517814\pi\) | ||||
−0.0559354 | + | 0.998434i | \(0.517814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.00000 | + | 3.00000i | 0.100958 | + | 0.100958i | 0.755782 | − | 0.654824i | \(-0.227257\pi\) |
−0.654824 | + | 0.755782i | \(0.727257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.59808 | − | 4.50000i | 0.0873334 | − | 0.151266i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0622 | − | 12.1603i | 0.707199 | − | 0.408301i | −0.102824 | − | 0.994700i | \(-0.532788\pi\) |
0.810023 | + | 0.586398i | \(0.199455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.5167 | + | 25.1244i | 1.45950 | + | 0.842644i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.20577 | − | 4.50000i | −0.0403949 | − | 0.150756i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −37.6865 | + | 10.0981i | −1.26113 | + | 0.337919i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.90192 | − | 5.02628i | −0.0970006 | − | 0.168010i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.69615 | − | 0.990381i | 0.123411 | − | 0.0330679i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.83013 | + | 2.83013i | 0.0943900 | + | 0.0943900i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.07180 | − | 9.07180i | 0.302225 | − | 0.302225i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −37.1147 | − | 9.94486i | −1.23510 | − | 0.330944i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.70577 | + | 1.56218i | −0.0899429 | + | 0.0519285i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.06218 | + | 11.4282i | 0.101678 | + | 0.379467i | 0.997947 | − | 0.0640432i | \(-0.0203996\pi\) |
−0.896269 | + | 0.443510i | \(0.853733\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.50000 | − | 5.59808i | −0.0497519 | − | 0.185676i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.86603 | − | 10.1603i | 0.194350 | − | 0.336624i | −0.752337 | − | 0.658778i | \(-0.771074\pi\) |
0.946687 | + | 0.322154i | \(0.104407\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.16025 | − | 5.47372i | −0.104589 | − | 0.181154i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.3923i | 0.442736i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.0981 | − | 21.0981i | 0.696720 | − | 0.696720i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.4641i | 1.43375i | 0.697203 | + | 0.716874i | \(0.254428\pi\) | ||||
−0.697203 | + | 0.716874i | \(0.745572\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.2679 | + | 10.2679i | −0.338340 | + | 0.338340i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.2487 | + | 13.4641i | 1.65396 | + | 0.443176i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.9808 | − | 13.3923i | 1.64336 | − | 0.440336i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.38269 | − | 3.10770i | 0.176791 | − | 0.102070i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.3564 | + | 31.7942i | −0.602254 | + | 1.04313i | 0.390225 | + | 0.920720i | \(0.372397\pi\) |
−0.992479 | + | 0.122415i | \(0.960936\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.01924 | − | 3.80385i | 0.0334042 | − | 0.124666i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.1865 | − | 47.0885i | −0.890047 | − | 1.54161i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.07180i | − | 0.0350515i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9282i | 1.07572i | 0.843035 | + | 0.537859i | \(0.180767\pi\) | ||||
−0.843035 | + | 0.537859i | \(0.819233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.83975 | − | 13.5788i | 0.255840 | − | 0.443129i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.91154 | + | 10.8660i | −0.0949136 | + | 0.354222i | −0.997006 | − | 0.0773199i | \(-0.975364\pi\) |
0.902093 | + | 0.431542i | \(0.142030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.59808 | + | 4.50000i | −0.0846050 | + | 0.146540i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.68653 | − | 4.68653i | 0.152453 | − | 0.152453i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.9904 | − | 4.01666i | 0.487122 | − | 0.130524i | −0.00689497 | − | 0.999976i | \(-0.502195\pi\) |
0.494017 | + | 0.869452i | \(0.335528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.46410 | − | 0.660254i | −0.0799881 | − | 0.0214328i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.944864 | + | 3.52628i | 0.0306393 | + | 0.114347i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 39.4641i | − | 1.27837i | −0.769054 | − | 0.639184i | \(-0.779272\pi\) | ||
0.769054 | − | 0.639184i | \(-0.220728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.83013 | + | 4.83013i | −0.156299 | + | 0.156299i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.59808 | + | 1.50000i | −0.0839839 | + | 0.0484881i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.5263 | + | 35.5526i | 0.662828 | + | 1.14805i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7846 | − | 25.6077i | 0.476923 | − | 0.826055i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.1769 | + | 34.1769i | −1.10134 | + | 1.10134i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.330127 | − | 1.23205i | −0.0106272 | − | 0.0396611i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9378 | + | 8.62436i | −0.480368 | + | 0.277341i | −0.720570 | − | 0.693382i | \(-0.756120\pi\) |
0.240202 | + | 0.970723i | \(0.422786\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.7846 | + | 20.7846i | −0.667698 | + | 0.667698i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9808 | + | 27.9808i | −0.897945 | + | 0.897945i | −0.995254 | − | 0.0973088i | \(-0.968977\pi\) |
0.0973088 | + | 0.995254i | \(0.468977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.81089 | − | 7.81089i | −0.250406 | − | 0.250406i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.5885 | + | 27.5885i | 0.883538 | + | 0.883538i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.2846 | + | 29.9378i | 0.552984 | + | 0.957796i | 0.998057 | + | 0.0623018i | \(0.0198441\pi\) |
−0.445074 | + | 0.895494i | \(0.646823\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.92820 | + | 1.58846i | −0.189466 | + | 0.0507673i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.19615 | − | 5.19615i | −0.165900 | − | 0.165900i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.9186 | − | 23.6244i | −1.30510 | − | 0.753500i | −0.323826 | − | 0.946117i | \(-0.604969\pi\) |
−0.981274 | + | 0.192617i | \(0.938303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.63397 | − | 3.83013i | 0.211376 | − | 0.122038i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.6244 | − | 33.9904i | −0.624650 | − | 1.08193i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.95448 | − | 2.95448i | −0.0939471 | − | 0.0939471i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6077 | 0.749923 | 0.374962 | − | 0.927040i | \(-0.377656\pi\) | ||||
0.374962 | + | 0.927040i | \(0.377656\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.6506 | − | 12.2321i | 1.44868 | − | 0.388172i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.784610 | − | 2.92820i | 0.0248738 | − | 0.0928303i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.96410 | − | 11.0622i | −0.0938740 | − | 0.350343i | 0.902972 | − | 0.429699i | \(-0.141380\pi\) |
−0.996846 | + | 0.0793561i | \(0.974714\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.1769 | + | 40.1769i | 1.27114 | + | 1.27114i |
(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 | 576.2.bb.b.529.1 | 4 | ||
3.2 | odd | 2 | 1728.2.bc.b.721.1 | 4 | |||
4.3 | odd | 2 | 144.2.x.d.61.1 | yes | 4 | ||
9.4 | even | 3 | 576.2.bb.a.337.1 | 4 | |||
9.5 | odd | 6 | 1728.2.bc.c.145.1 | 4 | |||
12.11 | even | 2 | 432.2.y.a.397.1 | 4 | |||
16.5 | even | 4 | 576.2.bb.a.241.1 | 4 | |||
16.11 | odd | 4 | 144.2.x.a.133.1 | yes | 4 | ||
36.23 | even | 6 | 432.2.y.d.253.1 | 4 | |||
36.31 | odd | 6 | 144.2.x.a.13.1 | ✓ | 4 | ||
48.5 | odd | 4 | 1728.2.bc.c.1585.1 | 4 | |||
48.11 | even | 4 | 432.2.y.d.181.1 | 4 | |||
144.5 | odd | 12 | 1728.2.bc.b.1009.1 | 4 | |||
144.59 | even | 12 | 432.2.y.a.37.1 | 4 | |||
144.85 | even | 12 | inner | 576.2.bb.b.49.1 | 4 | ||
144.139 | odd | 12 | 144.2.x.d.85.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.a.13.1 | ✓ | 4 | 36.31 | odd | 6 | ||
144.2.x.a.133.1 | yes | 4 | 16.11 | odd | 4 | ||
144.2.x.d.61.1 | yes | 4 | 4.3 | odd | 2 | ||
144.2.x.d.85.1 | yes | 4 | 144.139 | odd | 12 | ||
432.2.y.a.37.1 | 4 | 144.59 | even | 12 | |||
432.2.y.a.397.1 | 4 | 12.11 | even | 2 | |||
432.2.y.d.181.1 | 4 | 48.11 | even | 4 | |||
432.2.y.d.253.1 | 4 | 36.23 | even | 6 | |||
576.2.bb.a.241.1 | 4 | 16.5 | even | 4 | |||
576.2.bb.a.337.1 | 4 | 9.4 | even | 3 | |||
576.2.bb.b.49.1 | 4 | 144.85 | even | 12 | inner | ||
576.2.bb.b.529.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.bc.b.721.1 | 4 | 3.2 | odd | 2 | |||
1728.2.bc.b.1009.1 | 4 | 144.5 | odd | 12 | |||
1728.2.bc.c.145.1 | 4 | 9.5 | odd | 6 | |||
1728.2.bc.c.1585.1 | 4 | 48.5 | odd | 4 |