Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), 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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.84779568.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 13x^{4} - 4x^{3} + 152x^{2} - 96x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.2 | ||
Root | \(-1.66402 - 2.88216i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.4.e.q.136.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.06306 | − | 1.84127i | −0.375848 | − | 0.650988i | 0.614605 | − | 0.788835i | \(-0.289315\pi\) |
−0.990454 | + | 0.137846i | \(0.955982\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73981 | − | 3.01344i | 0.217476 | − | 0.376679i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.3500 | − | 26.5870i | −0.828823 | − | 1.43556i | −0.898962 | − | 0.438027i | \(-0.855678\pi\) |
0.0701387 | − | 0.997537i | \(-0.477656\pi\) | |||||||
\(8\) | −24.4070 | −1.07865 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.6306 | 0.336169 | ||||||||
\(11\) | −25.0774 | − | 43.4353i | −0.687375 | − | 1.19057i | −0.972684 | − | 0.232132i | \(-0.925430\pi\) |
0.285310 | − | 0.958435i | \(-0.407904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.97962 | − | 13.8211i | 0.170242 | − | 0.294868i | −0.768262 | − | 0.640135i | \(-0.778878\pi\) |
0.938504 | + | 0.345267i | \(0.112212\pi\) | |||||||
\(14\) | −32.6360 | + | 56.5272i | −0.623024 | + | 1.07911i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.0277 | + | 20.8325i | 0.187932 | + | 0.325508i | ||||
\(17\) | 105.668 | 1.50755 | 0.753774 | − | 0.657134i | \(-0.228231\pi\) | ||||
0.753774 | + | 0.657134i | \(0.228231\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.3040 | −0.257235 | −0.128618 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128618 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(20\) | 8.69904 | + | 15.0672i | 0.0972582 | + | 0.168456i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −53.3175 | + | 92.3487i | −0.516697 | + | 0.894946i | ||||
\(23\) | −68.0684 | + | 117.898i | −0.617098 | + | 1.06884i | 0.372915 | + | 0.927866i | \(0.378358\pi\) |
−0.990013 | + | 0.140979i | \(0.954975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −33.9312 | −0.255941 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −106.824 | −0.720997 | ||||||||
\(29\) | 112.162 | + | 194.270i | 0.718203 | + | 1.24396i | 0.961711 | + | 0.274065i | \(0.0883685\pi\) |
−0.243508 | + | 0.969899i | \(0.578298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 112.991 | − | 195.706i | 0.654638 | − | 1.13387i | −0.327347 | − | 0.944904i | \(-0.606155\pi\) |
0.981985 | − | 0.188961i | \(-0.0605121\pi\) | |||||||
\(32\) | −72.0559 | + | 124.804i | −0.398056 | + | 0.689454i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −112.332 | − | 194.564i | −0.566609 | − | 0.981396i | ||||
\(35\) | 153.500 | 0.741322 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −416.386 | −1.85009 | −0.925046 | − | 0.379854i | \(-0.875974\pi\) | ||||
−0.925046 | + | 0.379854i | \(0.875974\pi\) | |||||||
\(38\) | 22.6474 | + | 39.2264i | 0.0966814 | + | 0.167457i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 61.0176 | − | 105.686i | 0.241193 | − | 0.417759i | ||||
\(41\) | −38.0706 | + | 65.9402i | −0.145015 | + | 0.251174i | −0.929379 | − | 0.369128i | \(-0.879656\pi\) |
0.784363 | + | 0.620302i | \(0.212990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15.8686 | − | 27.4852i | −0.0562777 | − | 0.0974758i | 0.836514 | − | 0.547945i | \(-0.184590\pi\) |
−0.892792 | + | 0.450470i | \(0.851257\pi\) | |||||||
\(44\) | −174.519 | −0.597950 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 289.443 | 0.927741 | ||||||||
\(47\) | −30.4013 | − | 52.6566i | −0.0943507 | − | 0.163420i | 0.814987 | − | 0.579480i | \(-0.196744\pi\) |
−0.909337 | + | 0.416059i | \(0.863411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −299.746 | + | 519.176i | −0.873896 | + | 1.51363i | ||||
\(50\) | −26.5765 | + | 46.0318i | −0.0751697 | + | 0.130198i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −27.7660 | − | 48.0921i | −0.0740471 | − | 0.128253i | ||||
\(53\) | −466.532 | −1.20911 | −0.604557 | − | 0.796562i | \(-0.706650\pi\) | ||||
−0.604557 | + | 0.796562i | \(0.706650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 250.774 | 0.614806 | ||||||||
\(56\) | 374.649 | + | 648.910i | 0.894009 | + | 1.54847i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 238.469 | − | 413.040i | 0.539871 | − | 0.935084i | ||||
\(59\) | −47.7119 | + | 82.6395i | −0.105281 | + | 0.182352i | −0.913853 | − | 0.406045i | \(-0.866907\pi\) |
0.808572 | + | 0.588397i | \(0.200241\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 178.587 | + | 309.322i | 0.374848 | + | 0.649256i | 0.990304 | − | 0.138915i | \(-0.0443616\pi\) |
−0.615456 | + | 0.788171i | \(0.711028\pi\) | |||||||
\(62\) | −480.464 | −0.984178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 498.842 | 0.974300 | ||||||||
\(65\) | 39.8981 | + | 69.1055i | 0.0761346 | + | 0.131869i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −43.9172 | + | 76.0668i | −0.0800797 | + | 0.138702i | −0.903284 | − | 0.429043i | \(-0.858851\pi\) |
0.823204 | + | 0.567745i | \(0.192184\pi\) | |||||||
\(68\) | 183.842 | − | 318.424i | 0.327855 | − | 0.567862i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −163.180 | − | 282.636i | −0.278625 | − | 0.482592i | ||||
\(71\) | 412.693 | 0.689826 | 0.344913 | − | 0.938635i | \(-0.387908\pi\) | ||||
0.344913 | + | 0.938635i | \(0.387908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −331.133 | −0.530906 | −0.265453 | − | 0.964124i | \(-0.585522\pi\) | ||||
−0.265453 | + | 0.964124i | \(0.585522\pi\) | |||||||
\(74\) | 442.643 | + | 766.680i | 0.695354 | + | 1.20439i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37.0648 | + | 64.1981i | −0.0559424 | + | 0.0968952i | ||||
\(77\) | −769.877 | + | 1333.47i | −1.13942 | + | 1.97354i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 124.062 | + | 214.881i | 0.176684 | + | 0.306025i | 0.940743 | − | 0.339121i | \(-0.110130\pi\) |
−0.764059 | + | 0.645146i | \(0.776796\pi\) | |||||||
\(80\) | −120.277 | −0.168092 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 161.885 | 0.218015 | ||||||||
\(83\) | 276.253 | + | 478.484i | 0.365333 | + | 0.632776i | 0.988830 | − | 0.149050i | \(-0.0476217\pi\) |
−0.623496 | + | 0.781826i | \(0.714288\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −264.171 | + | 457.557i | −0.337098 | + | 0.583871i | ||||
\(86\) | −33.7386 | + | 58.4369i | −0.0423038 | + | 0.0732723i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 612.065 | + | 1060.13i | 0.741436 | + | 1.28420i | ||||
\(89\) | −291.478 | −0.347153 | −0.173577 | − | 0.984820i | \(-0.555532\pi\) | ||||
−0.173577 | + | 0.984820i | \(0.555532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −489.949 | −0.564402 | ||||||||
\(92\) | 236.852 | + | 410.240i | 0.268408 | + | 0.464896i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −64.6368 | + | 111.954i | −0.0709231 | + | 0.122842i | ||||
\(95\) | 53.2599 | − | 92.2489i | 0.0575195 | − | 0.0996267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −99.3032 | − | 171.998i | −0.103946 | − | 0.180039i | 0.809361 | − | 0.587311i | \(-0.199813\pi\) |
−0.913307 | + | 0.407272i | \(0.866480\pi\) | |||||||
\(98\) | 1274.59 | 1.31381 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −86.9904 | −0.0869904 | ||||||||
\(101\) | −408.117 | − | 706.880i | −0.402071 | − | 0.696408i | 0.591904 | − | 0.806008i | \(-0.298376\pi\) |
−0.993976 | + | 0.109600i | \(0.965043\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 701.186 | − | 1214.49i | 0.670776 | − | 1.16182i | −0.306908 | − | 0.951739i | \(-0.599294\pi\) |
0.977684 | − | 0.210079i | \(-0.0673722\pi\) | |||||||
\(104\) | −194.759 | + | 337.332i | −0.183631 | + | 0.318059i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 495.951 | + | 859.013i | 0.454444 | + | 0.787120i | ||||
\(107\) | −978.996 | −0.884515 | −0.442258 | − | 0.896888i | \(-0.645822\pi\) | ||||
−0.442258 | + | 0.896888i | \(0.645822\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2122.96 | 1.86553 | 0.932766 | − | 0.360484i | \(-0.117388\pi\) | ||||
0.932766 | + | 0.360484i | \(0.117388\pi\) | |||||||
\(110\) | −266.588 | − | 461.743i | −0.231074 | − | 0.400232i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 369.250 | − | 639.560i | 0.311525 | − | 0.539578i | ||||
\(113\) | −897.399 | + | 1554.34i | −0.747082 | + | 1.29398i | 0.202134 | + | 0.979358i | \(0.435212\pi\) |
−0.949216 | + | 0.314626i | \(0.898121\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −340.342 | − | 589.490i | −0.275975 | − | 0.478002i | ||||
\(116\) | 780.559 | 0.624768 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 202.883 | 0.158278 | ||||||||
\(119\) | −1622.01 | − | 2809.40i | −1.24949 | − | 2.16418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −592.252 | + | 1025.81i | −0.444968 | + | 0.770706i | ||||
\(122\) | 379.697 | − | 657.655i | 0.281772 | − | 0.488043i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −393.165 | − | 680.982i | −0.284736 | − | 0.493177i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −748.894 | −0.523257 | −0.261628 | − | 0.965169i | \(-0.584259\pi\) | ||||
−0.261628 | + | 0.965169i | \(0.584259\pi\) | |||||||
\(128\) | 46.1486 | + | 79.9317i | 0.0318672 | + | 0.0551955i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 84.8281 | − | 146.927i | 0.0572301 | − | 0.0991255i | ||||
\(131\) | 1198.05 | − | 2075.09i | 0.799042 | − | 1.38398i | −0.121198 | − | 0.992628i | \(-0.538674\pi\) |
0.920240 | − | 0.391353i | \(-0.127993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 327.016 | + | 566.409i | 0.213202 | + | 0.369277i | ||||
\(134\) | 186.746 | 0.120391 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2579.05 | −1.62611 | ||||||||
\(137\) | −502.238 | − | 869.901i | −0.313205 | − | 0.542486i | 0.665850 | − | 0.746086i | \(-0.268069\pi\) |
−0.979054 | + | 0.203600i | \(0.934736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1201.51 | + | 2081.08i | −0.733172 | + | 1.26989i | 0.222348 | + | 0.974967i | \(0.428628\pi\) |
−0.955521 | + | 0.294924i | \(0.904706\pi\) | |||||||
\(140\) | 267.061 | − | 462.563i | 0.161220 | − | 0.279241i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −438.717 | − | 759.881i | −0.259270 | − | 0.449069i | ||||
\(143\) | −800.432 | −0.468080 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1121.62 | −0.642380 | ||||||||
\(146\) | 352.014 | + | 609.706i | 0.199540 | + | 0.345614i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −724.432 | + | 1254.75i | −0.402351 | + | 0.696892i | ||||
\(149\) | −254.824 | + | 441.368i | −0.140107 | + | 0.242673i | −0.927537 | − | 0.373732i | \(-0.878078\pi\) |
0.787429 | + | 0.616405i | \(0.211411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −721.648 | − | 1249.93i | −0.388920 | − | 0.673629i | 0.603385 | − | 0.797450i | \(-0.293818\pi\) |
−0.992305 | + | 0.123821i | \(0.960485\pi\) | |||||||
\(152\) | 519.967 | 0.277466 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3273.70 | 1.71300 | ||||||||
\(155\) | 564.955 | + | 978.530i | 0.292763 | + | 0.507080i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1077.82 | − | 1866.84i | 0.547895 | − | 0.948981i | −0.450524 | − | 0.892764i | \(-0.648763\pi\) |
0.998419 | − | 0.0562170i | \(-0.0179039\pi\) | |||||||
\(158\) | 263.770 | − | 456.863i | 0.132813 | − | 0.230038i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −360.279 | − | 624.022i | −0.178016 | − | 0.308333i | ||||
\(161\) | 4179.41 | 2.04586 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −529.909 | −0.254636 | −0.127318 | − | 0.991862i | \(-0.540637\pi\) | ||||
−0.127318 | + | 0.991862i | \(0.540637\pi\) | |||||||
\(164\) | 132.471 | + | 229.446i | 0.0630747 | + | 0.109249i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 587.346 | − | 1017.31i | 0.274620 | − | 0.475656i | ||||
\(167\) | 1489.64 | − | 2580.13i | 0.690250 | − | 1.19555i | −0.281506 | − | 0.959559i | \(-0.590834\pi\) |
0.971756 | − | 0.235988i | \(-0.0758327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 971.151 | + | 1682.08i | 0.442035 | + | 0.765628i | ||||
\(170\) | 1123.32 | 0.506791 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −110.433 | −0.0489562 | ||||||||
\(173\) | −889.939 | − | 1541.42i | −0.391103 | − | 0.677410i | 0.601493 | − | 0.798878i | \(-0.294573\pi\) |
−0.992595 | + | 0.121469i | \(0.961240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −383.751 | + | 664.675i | −0.165765 | + | 0.287113i | ||||
\(176\) | 603.246 | − | 1044.85i | 0.258360 | − | 0.447492i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 309.859 | + | 536.692i | 0.130477 | + | 0.225993i | ||||
\(179\) | −2836.26 | −1.18431 | −0.592157 | − | 0.805823i | \(-0.701724\pi\) | ||||
−0.592157 | + | 0.805823i | \(0.701724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 811.890 | 0.333410 | 0.166705 | − | 0.986007i | \(-0.446687\pi\) | ||||
0.166705 | + | 0.986007i | \(0.446687\pi\) | |||||||
\(182\) | 520.845 | + | 902.130i | 0.212130 | + | 0.367419i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1661.35 | − | 2877.54i | 0.665632 | − | 1.15291i | ||||
\(185\) | 1040.96 | − | 1803.00i | 0.413693 | − | 0.716538i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2649.88 | − | 4589.73i | −1.03625 | − | 1.79484i | ||||
\(188\) | −211.570 | −0.0820761 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −226.474 | −0.0864745 | ||||||||
\(191\) | −574.231 | − | 994.597i | −0.217539 | − | 0.376788i | 0.736516 | − | 0.676420i | \(-0.236469\pi\) |
−0.954055 | + | 0.299632i | \(0.903136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1075.47 | − | 1862.76i | 0.401107 | − | 0.694739i | −0.592752 | − | 0.805385i | \(-0.701959\pi\) |
0.993860 | + | 0.110646i | \(0.0352921\pi\) | |||||||
\(194\) | −211.131 | + | 365.689i | −0.0781355 | + | 0.135335i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1043.00 | + | 1806.53i | 0.380103 | + | 0.658357i | ||||
\(197\) | −5057.51 | −1.82910 | −0.914551 | − | 0.404471i | \(-0.867456\pi\) | ||||
−0.914551 | + | 0.404471i | \(0.867456\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3554.12 | −1.26605 | −0.633027 | − | 0.774130i | \(-0.718188\pi\) | ||||
−0.633027 | + | 0.774130i | \(0.718188\pi\) | |||||||
\(200\) | 305.088 | + | 528.428i | 0.107865 | + | 0.186827i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −867.707 | + | 1502.91i | −0.302236 | + | 0.523488i | ||||
\(203\) | 3443.37 | − | 5964.09i | 1.19053 | − | 2.06205i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −190.353 | − | 329.701i | −0.0648528 | − | 0.112328i | ||||
\(206\) | −2981.61 | −1.00844 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 383.905 | 0.127976 | ||||||||
\(209\) | 534.248 | + | 925.345i | 0.176817 | + | 0.306256i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 53.9547 | − | 93.4523i | 0.0176038 | − | 0.0304906i | −0.857089 | − | 0.515168i | \(-0.827730\pi\) |
0.874693 | + | 0.484677i | \(0.161063\pi\) | |||||||
\(212\) | −811.676 | + | 1405.86i | −0.262953 | + | 0.455449i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1040.73 | + | 1802.60i | 0.332444 | + | 0.575809i | ||||
\(215\) | 158.686 | 0.0503363 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6937.65 | −2.17032 | ||||||||
\(218\) | −2256.84 | − | 3908.95i | −0.701157 | − | 1.21444i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 436.299 | − | 755.691i | 0.133706 | − | 0.231585i | ||||
\(221\) | 843.192 | − | 1460.45i | 0.256648 | − | 0.444528i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 971.013 | + | 1681.84i | 0.291587 | + | 0.505043i | 0.974185 | − | 0.225751i | \(-0.0724834\pi\) |
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(224\) | 4424.24 | 1.31967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3815.96 | 1.12316 | ||||||||
\(227\) | −1721.99 | − | 2982.58i | −0.503492 | − | 0.872074i | −0.999992 | − | 0.00403708i | \(-0.998715\pi\) |
0.496500 | − | 0.868037i | \(-0.334618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1034.70 | + | 1792.15i | −0.298579 | + | 0.517155i | −0.975811 | − | 0.218615i | \(-0.929846\pi\) |
0.677232 | + | 0.735770i | \(0.263179\pi\) | |||||||
\(230\) | −723.608 | + | 1253.33i | −0.207449 | + | 0.359313i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2737.53 | − | 4741.55i | −0.774689 | − | 1.34180i | ||||
\(233\) | −2769.24 | −0.778622 | −0.389311 | − | 0.921106i | \(-0.627287\pi\) | ||||
−0.389311 | + | 0.921106i | \(0.627287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 304.013 | 0.0843898 | ||||||||
\(236\) | 166.019 | + | 287.554i | 0.0457921 | + | 0.0793142i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3448.59 | + | 5973.13i | −0.939238 | + | 1.62681i | ||||
\(239\) | 1471.92 | − | 2549.44i | 0.398371 | − | 0.689999i | −0.595154 | − | 0.803612i | \(-0.702909\pi\) |
0.993525 | + | 0.113613i | \(0.0362423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2237.27 | − | 3875.06i | −0.597988 | − | 1.03575i | −0.993118 | − | 0.117120i | \(-0.962634\pi\) |
0.395130 | − | 0.918625i | \(-0.370700\pi\) | |||||||
\(242\) | 2518.40 | 0.668961 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1242.83 | 0.326082 | ||||||||
\(245\) | −1498.73 | − | 2595.88i | −0.390818 | − | 0.676917i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −169.997 | + | 294.444i | −0.0437922 | + | 0.0758504i | ||||
\(248\) | −2757.77 | + | 4776.60i | −0.706124 | + | 1.22304i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −132.882 | − | 230.159i | −0.0336169 | − | 0.0582262i | ||||
\(251\) | −2121.41 | −0.533474 | −0.266737 | − | 0.963769i | \(-0.585945\pi\) | ||||
−0.266737 | + | 0.963769i | \(0.585945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6827.92 | 1.69671 | ||||||||
\(254\) | 796.119 | + | 1378.92i | 0.196665 | + | 0.340634i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2093.48 | − | 3626.02i | 0.511104 | − | 0.885259i | ||||
\(257\) | −2274.12 | + | 3938.89i | −0.551967 | + | 0.956035i | 0.446165 | + | 0.894951i | \(0.352789\pi\) |
−0.998133 | + | 0.0610849i | \(0.980544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6391.53 | + | 11070.5i | 1.53340 | + | 2.65593i | ||||
\(260\) | 277.660 | 0.0662298 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5094.42 | −1.20127 | ||||||||
\(263\) | 1749.92 | + | 3030.95i | 0.410284 | + | 0.710632i | 0.994921 | − | 0.100663i | \(-0.0320964\pi\) |
−0.584637 | + | 0.811295i | \(0.698763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1166.33 | − | 2020.14i | 0.270366 | − | 0.468288i | ||||
\(266\) | 695.276 | − | 1204.25i | 0.160264 | − | 0.277585i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 152.815 | + | 264.683i | 0.0348308 | + | 0.0603287i | ||||
\(269\) | 2594.25 | 0.588008 | 0.294004 | − | 0.955804i | \(-0.405012\pi\) | ||||
0.294004 | + | 0.955804i | \(0.405012\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8518.20 | 1.90939 | 0.954693 | − | 0.297593i | \(-0.0961838\pi\) | ||||
0.954693 | + | 0.297593i | \(0.0961838\pi\) | |||||||
\(272\) | 1270.94 | + | 2201.34i | 0.283317 | + | 0.490720i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1067.82 | + | 1849.51i | −0.235435 | + | 0.407785i | ||||
\(275\) | −626.935 | + | 1085.88i | −0.137475 | + | 0.238114i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 945.248 | + | 1637.22i | 0.205034 | + | 0.355130i | 0.950144 | − | 0.311813i | \(-0.100936\pi\) |
−0.745109 | + | 0.666942i | \(0.767603\pi\) | |||||||
\(278\) | 5109.12 | 1.10225 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3746.49 | −0.799626 | ||||||||
\(281\) | −1569.34 | − | 2718.18i | −0.333164 | − | 0.577057i | 0.649967 | − | 0.759963i | \(-0.274783\pi\) |
−0.983130 | + | 0.182906i | \(0.941450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2034.55 | + | 3523.94i | −0.427354 | + | 0.740199i | −0.996637 | − | 0.0819429i | \(-0.973888\pi\) |
0.569283 | + | 0.822142i | \(0.307221\pi\) | |||||||
\(284\) | 718.007 | − | 1243.62i | 0.150021 | − | 0.259843i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 850.907 | + | 1473.81i | 0.175927 | + | 0.304715i | ||||
\(287\) | 2337.54 | 0.480768 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6252.77 | 1.27270 | ||||||||
\(290\) | 1192.35 | + | 2065.20i | 0.241438 | + | 0.418182i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −576.108 | + | 997.848i | −0.115459 | + | 0.199982i | ||||
\(293\) | −1818.97 | + | 3150.56i | −0.362681 | + | 0.628182i | −0.988401 | − | 0.151865i | \(-0.951472\pi\) |
0.625720 | + | 0.780048i | \(0.284805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −238.560 | − | 413.197i | −0.0470830 | − | 0.0815501i | ||||
\(296\) | 10162.7 | 1.99560 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1083.57 | 0.210637 | ||||||||
\(299\) | 1086.32 | + | 1881.56i | 0.210112 | + | 0.363925i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −487.167 | + | 843.798i | −0.0932885 | + | 0.161580i | ||||
\(302\) | −1534.31 | + | 2657.50i | −0.292350 | + | 0.506365i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −256.237 | − | 443.816i | −0.0483428 | − | 0.0837322i | ||||
\(305\) | −1785.87 | −0.335274 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6829.07 | −1.26956 | −0.634781 | − | 0.772692i | \(-0.718910\pi\) | ||||
−0.634781 | + | 0.772692i | \(0.718910\pi\) | |||||||
\(308\) | 2678.88 | + | 4639.95i | 0.495595 | + | 0.858395i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1201.16 | − | 2080.47i | 0.220069 | − | 0.381171i | ||||
\(311\) | −3300.51 | + | 5716.66i | −0.601785 | + | 1.04232i | 0.390766 | + | 0.920490i | \(0.372210\pi\) |
−0.992551 | + | 0.121831i | \(0.961123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1383.30 | − | 2395.94i | −0.249803 | − | 0.432672i | 0.713668 | − | 0.700484i | \(-0.247033\pi\) |
−0.963471 | + | 0.267812i | \(0.913699\pi\) | |||||||
\(314\) | −4583.15 | −0.823701 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 863.373 | 0.153698 | ||||||||
\(317\) | −2282.21 | − | 3952.90i | −0.404358 | − | 0.700368i | 0.589889 | − | 0.807485i | \(-0.299172\pi\) |
−0.994247 | + | 0.107116i | \(0.965838\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5625.44 | − | 9743.55i | 0.987349 | − | 1.71014i | ||||
\(320\) | −1247.10 | + | 2160.05i | −0.217860 | + | 0.377345i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4442.96 | − | 7695.43i | −0.768933 | − | 1.33183i | ||||
\(323\) | −2251.15 | −0.387794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −398.981 | −0.0680968 | ||||||||
\(326\) | 563.325 | + | 975.707i | 0.0957045 | + | 0.165765i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 929.190 | − | 1609.40i | 0.156421 | − | 0.270928i | ||||
\(329\) | −933.321 | + | 1616.56i | −0.156400 | + | 0.270893i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2332.81 | + | 4040.54i | 0.387380 | + | 0.670962i | 0.992096 | − | 0.125479i | \(-0.0400468\pi\) |
−0.604716 | + | 0.796441i | \(0.706713\pi\) | |||||||
\(332\) | 1922.51 | 0.317805 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6334.30 | −1.03772 | ||||||||
\(335\) | −219.586 | − | 380.334i | −0.0358127 | − | 0.0620295i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1903.53 | − | 3297.01i | 0.307691 | − | 0.532937i | −0.670166 | − | 0.742212i | \(-0.733777\pi\) |
0.977857 | + | 0.209275i | \(0.0671103\pi\) | |||||||
\(338\) | 2064.78 | − | 3576.31i | 0.332276 | − | 0.575520i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 919.212 | + | 1592.12i | 0.146621 | + | 0.253956i | ||||
\(341\) | −11334.1 | −1.79993 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7874.33 | 1.23957 | ||||||||
\(344\) | 387.306 | + | 670.833i | 0.0607039 | + | 0.105142i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1892.12 | + | 3277.24i | −0.293991 | + | 0.509207i | ||||
\(347\) | −1155.63 | + | 2001.61i | −0.178783 | + | 0.309660i | −0.941464 | − | 0.337114i | \(-0.890549\pi\) |
0.762681 | + | 0.646775i | \(0.223883\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5436.61 | + | 9416.49i | 0.833854 | + | 1.44428i | 0.894960 | + | 0.446147i | \(0.147204\pi\) |
−0.0611053 | + | 0.998131i | \(0.519463\pi\) | |||||||
\(350\) | 1631.80 | 0.249209 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7227.89 | 1.09445 | ||||||||
\(353\) | 1446.87 | + | 2506.05i | 0.218156 | + | 0.377857i | 0.954244 | − | 0.299029i | \(-0.0966626\pi\) |
−0.736088 | + | 0.676885i | \(0.763329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1031.73 | + | 1787.01i | −0.154250 | + | 0.267168i | ||||
\(356\) | −507.117 | + | 878.352i | −0.0754975 | + | 0.130766i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3015.12 | + | 5222.34i | 0.445123 | + | 0.770975i | ||||
\(359\) | −9875.47 | −1.45183 | −0.725915 | − | 0.687784i | \(-0.758584\pi\) | ||||
−0.725915 | + | 0.687784i | \(0.758584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6405.14 | −0.933830 | ||||||||
\(362\) | −863.087 | − | 1494.91i | −0.125312 | − | 0.217046i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −852.417 | + | 1476.43i | −0.122744 | + | 0.212599i | ||||
\(365\) | 827.832 | − | 1433.85i | 0.118714 | − | 0.205619i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5361.08 | − | 9285.66i | −0.762523 | − | 1.32073i | −0.941546 | − | 0.336884i | \(-0.890627\pi\) |
0.179023 | − | 0.983845i | \(-0.442706\pi\) | |||||||
\(368\) | −3274.82 | −0.463891 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4426.43 | −0.621944 | ||||||||
\(371\) | 7161.27 | + | 12403.7i | 1.00214 | + | 1.73576i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2087.95 | + | 3616.44i | −0.289839 | + | 0.502016i | −0.973771 | − | 0.227530i | \(-0.926935\pi\) |
0.683932 | + | 0.729546i | \(0.260268\pi\) | |||||||
\(374\) | −5633.97 | + | 9758.32i | −0.778946 | + | 1.34917i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 742.005 | + | 1285.19i | 0.101771 | + | 0.176273i | ||||
\(377\) | 3580.03 | 0.489074 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1715.14 | 0.232457 | 0.116228 | − | 0.993223i | \(-0.462920\pi\) | ||||
0.116228 | + | 0.993223i | \(0.462920\pi\) | |||||||
\(380\) | −185.324 | − | 320.991i | −0.0250182 | − | 0.0433328i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1220.88 | + | 2114.63i | −0.163523 | + | 0.283230i | ||||
\(383\) | −2569.53 | + | 4450.56i | −0.342812 | + | 0.593768i | −0.984954 | − | 0.172818i | \(-0.944713\pi\) |
0.642142 | + | 0.766586i | \(0.278046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3849.39 | − | 6667.33i | −0.509566 | − | 0.882594i | ||||
\(386\) | −4573.14 | −0.603022 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −691.074 | −0.0904226 | ||||||||
\(389\) | −4498.27 | − | 7791.23i | −0.586301 | − | 1.01550i | −0.994712 | − | 0.102705i | \(-0.967250\pi\) |
0.408411 | − | 0.912798i | \(-0.366083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7192.67 | + | 12458.1i | −0.930304 | + | 1.61133i | ||||
\(392\) | 7315.92 | − | 12671.5i | 0.942627 | − | 1.63268i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5376.44 | + | 9312.27i | 0.687465 | + | 1.19072i | ||||
\(395\) | −1240.62 | −0.158031 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −105.823 | −0.0133781 | −0.00668905 | − | 0.999978i | \(-0.502129\pi\) | ||||
−0.00668905 | + | 0.999978i | \(0.502129\pi\) | |||||||
\(398\) | 3778.24 | + | 6544.10i | 0.475844 | + | 0.824186i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 300.692 | − | 520.814i | 0.0375865 | − | 0.0651017i | ||||
\(401\) | −7240.91 | + | 12541.6i | −0.901730 | + | 1.56184i | −0.0764824 | + | 0.997071i | \(0.524369\pi\) |
−0.825248 | + | 0.564771i | \(0.808964\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1803.25 | − | 3123.32i | −0.222894 | − | 0.386063i | ||||
\(404\) | −2840.18 | −0.349763 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14642.0 | −1.78983 | ||||||||
\(407\) | 10441.9 | + | 18085.9i | 1.27171 | + | 2.20266i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 430.532 | − | 745.704i | 0.0520500 | − | 0.0901533i | −0.838826 | − | 0.544399i | \(-0.816758\pi\) |
0.890876 | + | 0.454246i | \(0.150091\pi\) | |||||||
\(410\) | −404.713 | + | 700.983i | −0.0487496 | + | 0.0844368i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2439.86 | − | 4225.96i | −0.291755 | − | 0.505335i | ||||
\(413\) | 2929.52 | 0.349037 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2762.53 | −0.326764 | ||||||||
\(416\) | 1149.96 | + | 1991.78i | 0.135532 | + | 0.234748i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1135.88 | − | 1967.39i | 0.132913 | − | 0.230211i | ||||
\(419\) | 6508.87 | − | 11273.7i | 0.758900 | − | 1.31445i | −0.184512 | − | 0.982830i | \(-0.559070\pi\) |
0.943412 | − | 0.331623i | \(-0.107596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7273.28 | − | 12597.7i | −0.841991 | − | 1.45837i | −0.888209 | − | 0.459439i | \(-0.848050\pi\) |
0.0462188 | − | 0.998931i | \(-0.485283\pi\) | |||||||
\(422\) | −229.428 | −0.0264654 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11386.7 | 1.30421 | ||||||||
\(425\) | −1320.85 | − | 2287.78i | −0.150755 | − | 0.261115i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5482.63 | − | 9496.19i | 0.621365 | − | 1.07624i | ||||
\(428\) | −1703.27 | + | 2950.14i | −0.192361 | + | 0.333179i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −168.693 | − | 292.185i | −0.0189188 | − | 0.0327683i | ||||
\(431\) | −3539.94 | −0.395622 | −0.197811 | − | 0.980240i | \(-0.563383\pi\) | ||||
−0.197811 | + | 0.980240i | \(0.563383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 669.471 | 0.0743019 | 0.0371509 | − | 0.999310i | \(-0.488172\pi\) | ||||
0.0371509 | + | 0.999310i | \(0.488172\pi\) | |||||||
\(434\) | 7375.14 | + | 12774.1i | 0.815710 | + | 1.41285i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3693.55 | − | 6397.41i | 0.405708 | − | 0.702707i | ||||
\(437\) | 1450.13 | − | 2511.70i | 0.158739 | − | 0.274944i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6284.27 | − | 10884.7i | −0.683216 | − | 1.18337i | −0.973994 | − | 0.226575i | \(-0.927247\pi\) |
0.290777 | − | 0.956791i | \(-0.406086\pi\) | |||||||
\(440\) | −6120.65 | −0.663160 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3585.45 | −0.385843 | ||||||||
\(443\) | −5530.17 | − | 9578.53i | −0.593106 | − | 1.02729i | −0.993811 | − | 0.111083i | \(-0.964568\pi\) |
0.400705 | − | 0.916207i | \(-0.368765\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 728.696 | − | 1262.14i | 0.0776259 | − | 0.134452i | ||||
\(446\) | 2064.49 | − | 3575.80i | 0.219185 | − | 0.379639i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7657.23 | − | 13262.7i | −0.807522 | − | 1.39867i | ||||
\(449\) | 18553.9 | 1.95014 | 0.975072 | − | 0.221891i | \(-0.0712228\pi\) | ||||
0.975072 | + | 0.221891i | \(0.0712228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3818.84 | 0.398719 | ||||||||
\(452\) | 3122.60 | + | 5408.51i | 0.324945 | + | 0.562821i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3661.16 | + | 6341.32i | −0.378473 | + | 0.655535i | ||||
\(455\) | 1224.87 | − | 2121.54i | 0.126204 | − | 0.218592i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3401.13 | + | 5890.93i | 0.348136 | + | 0.602989i | 0.985918 | − | 0.167228i | \(-0.0534814\pi\) |
−0.637782 | + | 0.770217i | \(0.720148\pi\) | |||||||
\(458\) | 4399.78 | 0.448882 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2368.52 | −0.240071 | ||||||||
\(461\) | −7447.19 | − | 12898.9i | −0.752386 | − | 1.30317i | −0.946663 | − | 0.322224i | \(-0.895569\pi\) |
0.194277 | − | 0.980947i | \(-0.437764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7144.33 | − | 12374.3i | 0.717117 | − | 1.24208i | −0.245020 | − | 0.969518i | \(-0.578794\pi\) |
0.962137 | − | 0.272566i | \(-0.0878722\pi\) | |||||||
\(464\) | −2698.09 | + | 4673.22i | −0.269947 | + | 0.467562i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2943.87 | + | 5098.93i | 0.292644 | + | 0.506874i | ||||
\(467\) | 13115.1 | 1.29956 | 0.649780 | − | 0.760122i | \(-0.274861\pi\) | ||||
0.649780 | + | 0.760122i | \(0.274861\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2696.52 | 0.265488 | ||||||||
\(470\) | −323.184 | − | 559.771i | −0.0317178 | − | 0.0549368i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1164.51 | − | 2016.99i | 0.113561 | − | 0.196693i | ||||
\(473\) | −795.887 | + | 1378.52i | −0.0773677 | + | 0.134005i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 266.300 | + | 461.244i | 0.0257235 | + | 0.0445544i | ||||
\(476\) | −11287.9 | −1.08694 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6258.96 | −0.598908 | ||||||||
\(479\) | −3959.89 | − | 6858.74i | −0.377729 | − | 0.654246i | 0.613002 | − | 0.790081i | \(-0.289962\pi\) |
−0.990731 | + | 0.135835i | \(0.956628\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3322.60 | + | 5754.91i | −0.314964 | + | 0.545533i | ||||
\(482\) | −4756.70 | + | 8238.85i | −0.449506 | + | 0.778567i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2060.81 | + | 3569.43i | 0.193540 | + | 0.335220i | ||||
\(485\) | 993.032 | 0.0929717 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17003.1 | −1.58210 | −0.791051 | − | 0.611751i | \(-0.790466\pi\) | ||||
−0.791051 | + | 0.611751i | \(0.790466\pi\) | |||||||
\(488\) | −4358.78 | − | 7549.63i | −0.404329 | − | 0.700319i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3186.48 | + | 5519.15i | −0.293777 | + | 0.508836i | ||||
\(491\) | −3195.87 | + | 5535.41i | −0.293743 | + | 0.508777i | −0.974692 | − | 0.223554i | \(-0.928234\pi\) |
0.680949 | + | 0.732331i | \(0.261568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11851.9 | + | 20528.1i | 1.08273 | + | 1.87534i | ||||
\(494\) | 722.870 | 0.0658370 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5436.07 | 0.492111 | ||||||||
\(497\) | −6334.85 | − | 10972.3i | −0.571744 | − | 0.990289i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1337.06 | − | 2315.85i | 0.119950 | − | 0.207759i | −0.799798 | − | 0.600270i | \(-0.795060\pi\) |
0.919748 | + | 0.392510i | \(0.128393\pi\) | |||||||
\(500\) | 217.476 | − | 376.679i | 0.0194516 | − | 0.0336912i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2255.18 | + | 3906.09i | 0.200505 | + | 0.347285i | ||||
\(503\) | 1263.13 | 0.111969 | 0.0559843 | − | 0.998432i | \(-0.482170\pi\) | ||||
0.0559843 | + | 0.998432i | \(0.482170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4081.17 | 0.359624 | ||||||||
\(506\) | −7258.48 | − | 12572.1i | −0.637706 | − | 1.10454i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1302.93 | + | 2256.74i | −0.113796 | + | 0.197100i | ||||
\(509\) | −690.421 | + | 1195.84i | −0.0601226 | + | 0.104135i | −0.894520 | − | 0.447028i | \(-0.852482\pi\) |
0.834397 | + | 0.551163i | \(0.185816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5082.90 | + | 8803.84i | 0.440028 | + | 0.762150i | ||||
\(512\) | −8163.62 | −0.704657 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9670.09 | 0.829824 | ||||||||
\(515\) | 3505.93 | + | 6072.45i | 0.299980 | + | 0.519581i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1524.77 | + | 2640.98i | −0.129709 | + | 0.224662i | ||||
\(518\) | 13589.2 | − | 23537.1i | 1.15265 | − | 1.99645i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −973.794 | − | 1686.66i | −0.0821225 | − | 0.142240i | ||||
\(521\) | 2689.80 | 0.226185 | 0.113092 | − | 0.993584i | \(-0.463924\pi\) | ||||
0.113092 | + | 0.993584i | \(0.463924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7144.18 | 0.597310 | 0.298655 | − | 0.954361i | \(-0.403462\pi\) | ||||
0.298655 | + | 0.954361i | \(0.403462\pi\) | |||||||
\(524\) | −4168.77 | − | 7220.52i | −0.347545 | − | 0.601966i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3720.54 | − | 6444.16i | 0.308409 | − | 0.534180i | ||||
\(527\) | 11939.6 | − | 20679.9i | 0.986897 | − | 1.70936i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3183.13 | − | 5513.34i | −0.261620 | − | 0.453138i | ||||
\(530\) | −4959.51 | −0.406467 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2275.78 | 0.185466 | ||||||||
\(533\) | 607.577 | + | 1052.35i | 0.0493754 | + | 0.0855207i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2447.49 | − | 4239.18i | 0.197784 | − | 0.342571i | ||||
\(536\) | 1071.89 | − | 1856.57i | 0.0863779 | − | 0.149611i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2757.84 | − | 4776.72i | −0.221002 | − | 0.382786i | ||||
\(539\) | 30067.4 | 2.40278 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3310.57 | −0.263091 | −0.131546 | − | 0.991310i | \(-0.541994\pi\) | ||||
−0.131546 | + | 0.991310i | \(0.541994\pi\) | |||||||
\(542\) | −9055.35 | − | 15684.3i | −0.717640 | − | 1.24299i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7614.02 | + | 13187.9i | −0.600089 | + | 1.03938i | ||||
\(545\) | −5307.41 | + | 9192.70i | −0.417145 | + | 0.722517i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1143.26 | − | 1980.18i | −0.0893643 | − | 0.154784i | 0.817878 | − | 0.575391i | \(-0.195150\pi\) |
−0.907243 | + | 0.420608i | \(0.861817\pi\) | |||||||
\(548\) | −3495.19 | −0.272458 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2665.88 | 0.206679 | ||||||||
\(551\) | −2389.49 | − | 4138.71i | −0.184747 | − | 0.319991i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3808.70 | − | 6596.85i | 0.292879 | − | 0.507282i | ||||
\(554\) | 2009.71 | − | 3480.92i | 0.154124 | − | 0.266950i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4180.80 | + | 7241.36i | 0.318895 | + | 0.552342i | ||||
\(557\) | −13846.6 | −1.05332 | −0.526658 | − | 0.850077i | \(-0.676555\pi\) | ||||
−0.526658 | + | 0.850077i | \(0.676555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −506.502 | −0.0383233 | ||||||||
\(560\) | 1846.25 | + | 3197.80i | 0.139318 | + | 0.241307i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3336.61 | + | 5779.17i | −0.250438 | + | 0.433772i | ||||
\(563\) | −8082.21 | + | 13998.8i | −0.605017 | + | 1.04792i | 0.387032 | + | 0.922066i | \(0.373500\pi\) |
−0.992049 | + | 0.125853i | \(0.959833\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4487.00 | − | 7771.71i | −0.334105 | − | 0.578687i | ||||
\(566\) | 8651.37 | 0.642481 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10072.6 | −0.744080 | ||||||||
\(569\) | 248.167 | + | 429.838i | 0.0182842 | + | 0.0316691i | 0.875023 | − | 0.484082i | \(-0.160846\pi\) |
−0.856739 | + | 0.515751i | \(0.827513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2985.59 | + | 5171.20i | −0.218815 | + | 0.378998i | −0.954446 | − | 0.298384i | \(-0.903552\pi\) |
0.735631 | + | 0.677382i | \(0.236886\pi\) | |||||||
\(572\) | −1392.60 | + | 2412.05i | −0.101796 | + | 0.176316i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2484.94 | − | 4304.04i | −0.180696 | − | 0.312974i | ||||
\(575\) | 3403.42 | 0.246839 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9571.82 | 0.690607 | 0.345304 | − | 0.938491i | \(-0.387776\pi\) | ||||
0.345304 | + | 0.938491i | \(0.387776\pi\) | |||||||
\(578\) | −6647.07 | − | 11513.1i | −0.478342 | − | 0.828513i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1951.40 | + | 3379.92i | −0.139702 | + | 0.241971i | ||||
\(581\) | 8480.97 | − | 14689.5i | 0.605594 | − | 1.04892i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11699.4 | + | 20264.0i | 0.831115 | + | 1.43953i | ||||
\(584\) | 8081.97 | 0.572662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7734.71 | 0.545253 | ||||||||
\(587\) | 2661.09 | + | 4609.14i | 0.187112 | + | 0.324088i | 0.944286 | − | 0.329125i | \(-0.106754\pi\) |
−0.757174 | + | 0.653213i | \(0.773420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2407.16 | + | 4169.31i | −0.168396 | + | 0.291670i | ||||
\(590\) | −507.206 | + | 878.507i | −0.0353921 | + | 0.0613010i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5008.15 | − | 8674.38i | −0.347692 | − | 0.602221i | ||||
\(593\) | 11066.5 | 0.766354 | 0.383177 | − | 0.923675i | \(-0.374830\pi\) | ||||
0.383177 | + | 0.923675i | \(0.374830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16220.1 | 1.11758 | ||||||||
\(596\) | 886.690 | + | 1535.79i | 0.0609400 | + | 0.105551i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2309.65 | − | 4000.42i | 0.157941 | − | 0.273561i | ||||
\(599\) | 9192.50 | − | 15921.9i | 0.627037 | − | 1.08606i | −0.361106 | − | 0.932525i | \(-0.617601\pi\) |
0.988143 | − | 0.153536i | \(-0.0490660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 308.915 | + | 535.057i | 0.0209666 | + | 0.0363152i | 0.876318 | − | 0.481733i | \(-0.159992\pi\) |
−0.855352 | + | 0.518048i | \(0.826659\pi\) | |||||||
\(602\) | 2071.55 | 0.140249 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5022.12 | −0.338323 | ||||||||
\(605\) | −2961.26 | − | 5129.05i | −0.198996 | − | 0.344670i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6919.89 | + | 11985.6i | −0.462718 | + | 0.801451i | −0.999095 | − | 0.0425272i | \(-0.986459\pi\) |
0.536377 | + | 0.843978i | \(0.319792\pi\) | |||||||
\(608\) | 1535.08 | − | 2658.83i | 0.102394 | − | 0.177352i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1898.49 | + | 3288.28i | 0.126012 | + | 0.218260i | ||||
\(611\) | −970.362 | −0.0642498 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25655.4 | −1.69039 | −0.845196 | − | 0.534457i | \(-0.820516\pi\) | ||||
−0.845196 | + | 0.534457i | \(0.820516\pi\) | |||||||
\(614\) | 7259.71 | + | 12574.2i | 0.477163 | + | 0.826470i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18790.4 | − | 32546.0i | 1.22904 | − | 2.12876i | ||||
\(617\) | 2109.13 | − | 3653.12i | 0.137618 | − | 0.238361i | −0.788977 | − | 0.614423i | \(-0.789389\pi\) |
0.926594 | + | 0.376062i | \(0.122722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6091.28 | − | 10550.4i | −0.395524 | − | 0.685067i | 0.597644 | − | 0.801761i | \(-0.296104\pi\) |
−0.993168 | + | 0.116694i | \(0.962770\pi\) | |||||||
\(620\) | 3931.65 | 0.254676 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14034.6 | 0.904719 | ||||||||
\(623\) | 4474.20 | + | 7749.54i | 0.287729 | + | 0.498361i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −2941.05 | + | 5094.05i | −0.187776 | + | 0.325238i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3750.40 | − | 6495.89i | −0.238308 | − | 0.412761i | ||||
\(629\) | −43998.8 | −2.78910 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16673.2 | 1.05190 | 0.525951 | − | 0.850515i | \(-0.323709\pi\) | ||||
0.525951 | + | 0.850515i | \(0.323709\pi\) | |||||||
\(632\) | −3027.98 | − | 5244.61i | −0.190580 | − | 0.330094i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4852.24 | + | 8404.33i | −0.303954 | + | 0.526465i | ||||
\(635\) | 1872.23 | − | 3242.81i | 0.117004 | − | 0.202656i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4783.72 | + | 8285.65i | 0.297548 | + | 0.515368i | ||||
\(638\) | −23920.7 | −1.48437 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −461.486 | −0.0285028 | ||||||||
\(641\) | 13135.4 | + | 22751.2i | 0.809388 | + | 1.40190i | 0.913289 | + | 0.407313i | \(0.133534\pi\) |
−0.103901 | + | 0.994588i | \(0.533133\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5778.17 | + | 10008.1i | −0.354384 | + | 0.613810i | −0.987012 | − | 0.160645i | \(-0.948643\pi\) |
0.632629 | + | 0.774455i | \(0.281976\pi\) | |||||||
\(644\) | 7271.37 | − | 12594.4i | 0.444925 | − | 0.770634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2393.11 | + | 4144.99i | 0.145752 | + | 0.252449i | ||||
\(647\) | 25395.2 | 1.54310 | 0.771552 | − | 0.636166i | \(-0.219481\pi\) | ||||
0.771552 | + | 0.636166i | \(0.219481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4785.96 | 0.289469 | ||||||||
\(650\) | 424.140 | + | 734.633i | 0.0255941 | + | 0.0443303i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −921.939 | + | 1596.85i | −0.0553772 | + | 0.0959161i | ||||
\(653\) | −3091.42 | + | 5354.50i | −0.185263 | + | 0.320885i | −0.943665 | − | 0.330902i | \(-0.892647\pi\) |
0.758402 | + | 0.651787i | \(0.225980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5990.27 | + | 10375.5i | 0.357343 | + | 0.618935i | ||||
\(656\) | −1831.60 | −0.109012 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3968.70 | 0.235131 | ||||||||
\(659\) | −4442.66 | − | 7694.91i | −0.262612 | − | 0.454858i | 0.704323 | − | 0.709880i | \(-0.251251\pi\) |
−0.966935 | + | 0.255022i | \(0.917917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3585.80 | − | 6210.79i | 0.211001 | − | 0.365464i | −0.741027 | − | 0.671475i | \(-0.765661\pi\) |
0.952028 | + | 0.306011i | \(0.0989944\pi\) | |||||||
\(662\) | 4959.83 | − | 8590.68i | 0.291192 | − | 0.504360i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6742.51 | − | 11678.4i | −0.394066 | − | 0.682543i | ||||
\(665\) | −3270.16 | −0.190694 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30538.7 | −1.77281 | ||||||||
\(668\) | −5183.37 | − | 8977.86i | −0.300226 | − | 0.520006i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −466.866 | + | 808.636i | −0.0269203 | + | 0.0466273i | ||||
\(671\) | 8957.00 | − | 15514.0i | 0.515322 | − | 0.892564i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2125.26 | + | 3681.06i | 0.121728 | + | 0.210839i | 0.920449 | − | 0.390862i | \(-0.127823\pi\) |
−0.798721 | + | 0.601701i | \(0.794490\pi\) | |||||||
\(674\) | −8094.27 | −0.462581 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6758.47 | 0.384528 | ||||||||
\(677\) | 1116.83 | + | 1934.40i | 0.0634019 | + | 0.109815i | 0.895984 | − | 0.444086i | \(-0.146472\pi\) |
−0.832582 | + | 0.553902i | \(0.813138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3048.61 | + | 5280.35i | −0.172305 | + | 0.298441i | ||||
\(680\) | 6447.62 | − | 11167.6i | 0.363610 | − | 0.629791i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12048.8 | + | 20869.1i | 0.676499 | + | 1.17173i | ||||
\(683\) | 6071.62 | 0.340153 | 0.170076 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170076 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5022.38 | 0.280139 | ||||||||
\(686\) | −8370.89 | − | 14498.8i | −0.465892 | − | 0.806949i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 381.725 | − | 661.167i | 0.0211528 | − | 0.0366377i | ||||
\(689\) | −3722.74 | + | 6447.98i | −0.205842 | + | 0.356529i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 382.892 | + | 663.188i | 0.0210794 | + | 0.0365107i | 0.876373 | − | 0.481634i | \(-0.159956\pi\) |
−0.855293 | + | 0.518144i | \(0.826623\pi\) | |||||||
\(692\) | −6193.29 | −0.340222 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4914.02 | 0.268780 | ||||||||
\(695\) | −6007.56 | − | 10405.4i | −0.327885 | − | 0.567913i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4022.85 | + | 6967.78i | −0.218617 | + | 0.378656i | ||||
\(698\) | 11558.9 | − | 20020.6i | 0.626806 | − | 1.08566i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1335.30 | + | 2312.82i | 0.0720997 | + | 0.124880i | ||||
\(701\) | −23564.3 | −1.26963 | −0.634814 | − | 0.772665i | \(-0.718923\pi\) | ||||
−0.634814 | + | 0.772665i | \(0.718923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8870.67 | 0.475909 | ||||||||
\(704\) | −12509.6 | − | 21667.3i | −0.669709 | − | 1.15997i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3076.21 | − | 5328.16i | 0.163987 | − | 0.284034i | ||||
\(707\) | −12529.2 | + | 21701.3i | −0.666492 | + | 1.15440i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12086.1 | − | 20933.8i | −0.640204 | − | 1.10887i | −0.985387 | − | 0.170331i | \(-0.945516\pi\) |
0.345183 | − | 0.938535i | \(-0.387817\pi\) | |||||||
\(710\) | 4387.17 | 0.231898 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7114.13 | 0.374457 | ||||||||
\(713\) | 15382.2 | + | 26642.8i | 0.807951 | + | 1.39941i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2001.08 | − | 3465.97i | 0.104666 | − | 0.181287i | ||||
\(716\) | −4934.55 | + | 8546.90i | −0.257560 | + | 0.446107i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10498.2 | + | 18183.4i | 0.545668 | + | 0.945125i | ||||
\(719\) | −12829.0 | −0.665424 | −0.332712 | − | 0.943028i | \(-0.607964\pi\) | ||||
−0.332712 | + | 0.943028i | \(0.607964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43052.9 | −2.22382 | ||||||||
\(722\) | 6809.05 | + | 11793.6i | 0.350979 | + | 0.607913i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1412.53 | − | 2446.58i | 0.0725088 | − | 0.125589i | ||||
\(725\) | 2804.04 | − | 4856.74i | 0.143641 | − | 0.248793i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12362.4 | + | 21412.2i | 0.630666 | + | 1.09235i | 0.987416 | + | 0.158146i | \(0.0505517\pi\) |
−0.356749 | + | 0.934200i | \(0.616115\pi\) | |||||||
\(728\) | 11958.2 | 0.608792 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3520.14 | −0.178474 | ||||||||
\(731\) | −1676.81 | − | 2904.32i | −0.0848413 | − | 0.146949i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10086.1 | − | 17469.7i | 0.508239 | − | 0.880296i | −0.491715 | − | 0.870756i | \(-0.663630\pi\) |
0.999954 | − | 0.00954010i | \(-0.00303675\pi\) | |||||||
\(734\) | −11398.3 | + | 19742.4i | −0.573186 | + | 0.992788i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9809.46 | − | 16990.5i | −0.491279 | − | 0.850921i | ||||
\(737\) | 4405.32 | 0.220179 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16452.8 | −0.818979 | −0.409489 | − | 0.912315i | \(-0.634293\pi\) | ||||
−0.409489 | + | 0.912315i | \(0.634293\pi\) | |||||||
\(740\) | −3622.16 | − | 6273.76i | −0.179937 | − | 0.311660i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15225.7 | − | 26371.7i | 0.753307 | − | 1.30477i | ||||
\(743\) | 10432.3 | − | 18069.3i | 0.515107 | − | 0.892191i | −0.484739 | − | 0.874659i | \(-0.661086\pi\) |
0.999846 | − | 0.0175328i | \(-0.00558115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1274.12 | − | 2206.84i | −0.0626579 | − | 0.108527i | ||||
\(746\) | 8878.47 | 0.435742 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18441.2 | −0.901438 | ||||||||
\(749\) | 15027.6 | + | 26028.6i | 0.733107 | + | 1.26978i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7762.84 | + | 13445.6i | −0.377191 | + | 0.653313i | −0.990652 | − | 0.136411i | \(-0.956443\pi\) |
0.613462 | + | 0.789725i | \(0.289777\pi\) | |||||||
\(752\) | 731.313 | − | 1266.67i | 0.0354631 | − | 0.0614239i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3805.78 | − | 6591.81i | −0.183818 | − | 0.318381i | ||||
\(755\) | 7216.48 | 0.347861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30105.7 | 1.44546 | 0.722729 | − | 0.691132i | \(-0.242888\pi\) | ||||
0.722729 | + | 0.691132i | \(0.242888\pi\) | |||||||
\(758\) | −1823.30 | − | 3158.05i | −0.0873684 | − | 0.151327i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1299.92 | + | 2251.52i | −0.0620433 | + | 0.107462i | ||||
\(761\) | −10869.9 | + | 18827.3i | −0.517786 | + | 0.896831i | 0.482001 | + | 0.876171i | \(0.339910\pi\) |
−0.999787 | + | 0.0206605i | \(0.993423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32587.5 | − | 56443.2i | −1.54620 | − | 2.67809i | ||||
\(764\) | −3996.21 | −0.189238 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10926.3 | 0.515381 | ||||||||
\(767\) | 761.446 | + | 1318.86i | 0.0358464 | + | 0.0620878i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −971.112 | + | 1682.02i | −0.0455386 | + | 0.0788752i | −0.887896 | − | 0.460044i | \(-0.847834\pi\) |
0.842358 | + | 0.538919i | \(0.181167\pi\) | |||||||
\(770\) | −8184.25 | + | 14175.5i | −0.383039 | + | 0.663443i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3742.21 | − | 6481.70i | −0.174462 | − | 0.302178i | ||||
\(773\) | −7921.02 | −0.368563 | −0.184282 | − | 0.982873i | \(-0.558996\pi\) | ||||
−0.184282 | + | 0.982873i | \(0.558996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5649.55 | −0.261855 | ||||||||
\(776\) | 2423.70 | + | 4197.97i | 0.112121 | + | 0.194199i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9563.85 | + | 16565.1i | −0.440721 | + | 0.763351i | ||||
\(779\) | 811.054 | − | 1404.79i | 0.0373030 | − | 0.0646107i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10349.3 | − | 17925.5i | −0.474169 | − | 0.821285i | ||||
\(782\) | 30585.0 | 1.39861 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14421.0 | −0.656933 | ||||||||
\(785\) | 5389.10 | + | 9334.20i | 0.245026 | + | 0.424397i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 680.702 | − | 1179.01i | 0.0308315 | − | 0.0534017i | −0.850198 | − | 0.526463i | \(-0.823518\pi\) |
0.881029 | + | 0.473061i | \(0.156851\pi\) | |||||||
\(788\) | −8799.10 | + | 15240.5i | −0.397786 | + | 0.688985i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1318.85 | + | 2284.31i | 0.0593956 | + | 0.102876i | ||||
\(791\) | 55100.4 | 2.47679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5700.22 | 0.255260 | ||||||||
\(794\) | 112.496 | + | 194.849i | 0.00502814 | + | 0.00870899i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6183.48 | + | 10710.1i | −0.275336 | + | 0.476896i | ||||
\(797\) | −13958.7 | + | 24177.2i | −0.620381 | + | 1.07453i | 0.369033 | + | 0.929416i | \(0.379689\pi\) |
−0.989415 | + | 0.145116i | \(0.953645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3212.45 | − | 5564.13i | −0.142238 | − | 0.246364i | ||||
\(800\) | 3602.79 | 0.159222 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30790.1 | 1.35565 | ||||||||
\(803\) | 8303.95 | + | 14382.9i | 0.364932 | + | 0.632080i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10448.5 | + | 18097.4i | −0.457468 | + | 0.792358i | ||||
\(806\) | −3833.92 | + | 6640.55i | −0.167549 | + | 0.290203i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9960.94 | + | 17252.9i | 0.433694 | + | 0.751180i | ||||
\(809\) | 5275.87 | 0.229283 | 0.114641 | − | 0.993407i | \(-0.463428\pi\) | ||||
0.114641 | + | 0.993407i | \(0.463428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23769.1 | −1.02916 | −0.514579 | − | 0.857443i | \(-0.672052\pi\) | ||||
−0.514579 | + | 0.857443i | \(0.672052\pi\) | |||||||
\(812\) | −11981.6 | − | 20752.7i | −0.517822 | − | 0.896894i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22200.7 | − | 38452.7i | 0.955938 | − | 1.65573i | ||||
\(815\) | 1324.77 | − | 2294.57i | 0.0569383 | − | 0.0986201i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 338.064 | + | 585.545i | 0.0144766 | + | 0.0250742i | ||||
\(818\) | −1830.73 | −0.0782516 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1324.71 | −0.0564157 | ||||||||
\(821\) | 17104.6 | + | 29626.1i | 0.727108 | + | 1.25939i | 0.958100 | + | 0.286432i | \(0.0924694\pi\) |
−0.230992 | + | 0.972956i | \(0.574197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −620.065 | + | 1073.98i | −0.0262626 | + | 0.0454882i | −0.878858 | − | 0.477083i | \(-0.841694\pi\) |
0.852595 | + | 0.522572i | \(0.175027\pi\) | |||||||
\(824\) | −17113.9 | + | 29642.1i | −0.723532 | + | 1.25319i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3114.25 | − | 5394.04i | −0.131185 | − | 0.227219i | ||||
\(827\) | −26971.0 | −1.13407 | −0.567034 | − | 0.823694i | \(-0.691909\pi\) | ||||
−0.567034 | + | 0.823694i | \(0.691909\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26743.1 | −1.12042 | −0.560208 | − | 0.828352i | \(-0.689279\pi\) | ||||
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(830\) | 2936.73 | + | 5086.57i | 0.122814 | + | 0.212720i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3980.56 | − | 6894.54i | 0.165867 | − | 0.287290i | ||||
\(833\) | −31673.7 | + | 54860.4i | −1.31744 | + | 2.28187i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7448.19 | + | 12900.7i | 0.308689 | + | 0.534665i | ||||
\(836\) | 3717.96 | 0.153814 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27677.3 | −1.14093 | ||||||||
\(839\) | 2636.57 | + | 4566.67i | 0.108492 | + | 0.187913i | 0.915159 | − | 0.403092i | \(-0.132065\pi\) |
−0.806668 | + | 0.591005i | \(0.798731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12966.0 | + | 22457.7i | −0.531631 | + | 0.920813i | ||||
\(842\) | −15463.9 | + | 26784.2i | −0.632922 | + | 1.09625i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −187.742 | − | 325.178i | −0.00765679 | − | 0.0132620i | ||||
\(845\) | −9711.51 | −0.395368 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36364.3 | 1.47520 | ||||||||
\(848\) | −5611.29 | − | 9719.04i | −0.227232 | − | 0.393577i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2808.29 | + | 4864.10i | −0.113322 | + | 0.196279i | ||||
\(851\) | 28342.7 | − | 49091.1i | 1.14169 | − | 1.97746i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2521.73 | − | 4367.76i | −0.101222 | − | 0.175322i | 0.810966 | − | 0.585093i | \(-0.198942\pi\) |
−0.912188 | + | 0.409771i | \(0.865609\pi\) | |||||||
\(854\) | −23313.5 | −0.934157 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23894.4 | 0.954081 | ||||||||
\(857\) | 7239.27 | + | 12538.8i | 0.288552 | + | 0.499786i | 0.973464 | − | 0.228839i | \(-0.0734930\pi\) |
−0.684913 | + | 0.728625i | \(0.740160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3936.94 | − | 6818.98i | 0.156376 | − | 0.270850i | −0.777183 | − | 0.629274i | \(-0.783352\pi\) |
0.933559 | + | 0.358424i | \(0.116686\pi\) | |||||||
\(860\) | 276.083 | − | 478.190i | 0.0109469 | − | 0.0189606i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3763.17 | + | 6518.01i | 0.148694 | + | 0.257545i | ||||
\(863\) | 24166.0 | 0.953209 | 0.476604 | − | 0.879118i | \(-0.341867\pi\) | ||||
0.476604 | + | 0.879118i | \(0.341867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8899.39 | 0.349813 | ||||||||
\(866\) | −711.688 | − | 1232.68i | −0.0279262 | − | 0.0483697i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12070.2 | + | 20906.2i | −0.471992 | + | 0.817513i | ||||
\(869\) | 6222.28 | − | 10777.3i | 0.242896 | − | 0.420708i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 700.885 | + | 1213.97i | 0.0272659 | + | 0.0472259i | ||||
\(872\) | −51815.2 | −2.01225 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6166.29 | −0.238647 | ||||||||
\(875\) | −1918.75 | − | 3323.38i | −0.0741322 | − | 0.128401i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3205.91 | + | 5552.80i | −0.123439 | + | 0.213802i | −0.921122 | − | 0.389275i | \(-0.872726\pi\) |
0.797683 | + | 0.603077i | \(0.206059\pi\) | |||||||
\(878\) | −13361.1 | + | 23142.1i | −0.513572 | + | 0.889532i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3016.23 | + | 5224.26i | 0.115542 | + | 0.200125i | ||||
\(881\) | 22908.5 | 0.876059 | 0.438029 | − | 0.898961i | \(-0.355677\pi\) | ||||
0.438029 | + | 0.898961i | \(0.355677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39198.4 | 1.49392 | 0.746960 | − | 0.664869i | \(-0.231513\pi\) | ||||
0.746960 | + | 0.664869i | \(0.231513\pi\) | |||||||
\(884\) | −2933.98 | − | 5081.81i | −0.111630 | − | 0.193348i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11757.8 | + | 20365.1i | −0.445836 | + | 0.772211i | ||||
\(887\) | −2711.10 | + | 4695.75i | −0.102626 | + | 0.177754i | −0.912766 | − | 0.408483i | \(-0.866058\pi\) |
0.810140 | + | 0.586237i | \(0.199391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11495.5 | + | 19910.9i | 0.433687 | + | 0.751168i | ||||
\(890\) | −3098.59 | −0.116702 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6757.51 | 0.253653 | ||||||||
\(893\) | 647.668 | + | 1121.79i | 0.0242703 | + | 0.0420374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7090.66 | − | 12281.4i | 0.264821 | − | 0.458683i | ||||
\(896\) | 1416.76 | − | 2453.91i | 0.0528245 | − | 0.0914947i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19723.9 | − | 34162.9i | −0.732958 | − | 1.26952i | ||||
\(899\) | 50693.0 | 1.88065 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49297.6 | −1.82280 | ||||||||
\(902\) | −4059.66 | − | 7031.54i | −0.149858 | − | 0.259562i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21902.9 | − | 37936.9i | 0.805839 | − | 1.39575i | ||||
\(905\) | −2029.72 | + | 3515.59i | −0.0745528 | + | 0.129129i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15363.5 | + | 26610.3i | 0.562444 | + | 0.974181i | 0.997282 | + | 0.0736727i | \(0.0234720\pi\) |
−0.434839 | + | 0.900508i | \(0.643195\pi\) | |||||||
\(908\) | −11983.8 | −0.437990 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5208.45 | −0.189735 | ||||||||
\(911\) | −2050.67 | − | 3551.86i | −0.0745793 | − | 0.129175i | 0.826324 | − | 0.563195i | \(-0.190428\pi\) |
−0.900903 | + | 0.434020i | \(0.857095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13855.4 | − | 23998.2i | 0.502242 | − | 0.869908i | ||||
\(914\) | 7231.21 | − | 12524.8i | 0.261693 | − | 0.453265i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3600.35 | + | 6235.98i | 0.129868 | + | 0.224937i | ||||
\(917\) | −73560.7 | −2.64906 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50926.3 | −1.82797 | −0.913984 | − | 0.405750i | \(-0.867010\pi\) | ||||
−0.913984 | + | 0.405750i | \(0.867010\pi\) | |||||||
\(920\) | 8306.74 | + | 14387.7i | 0.297680 | + | 0.515596i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15833.6 | + | 27424.6i | −0.565566 | + | 0.979589i | ||||
\(923\) | 3293.13 | − | 5703.87i | 0.117437 | − | 0.203408i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5204.82 | + | 9015.02i | 0.185009 | + | 0.320445i | ||||
\(926\) | −30379.4 | −1.07811 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32327.6 | −1.14354 | ||||||||
\(929\) | −11020.4 | − | 19087.9i | −0.389201 | − | 0.674116i | 0.603141 | − | 0.797634i | \(-0.293915\pi\) |
−0.992342 | + | 0.123519i | \(0.960582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6385.79 | − | 11060.5i | 0.224797 | − | 0.389359i | ||||
\(932\) | −4817.95 | + | 8344.93i | −0.169332 | + | 0.293291i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13942.1 | − | 24148.5i | −0.488438 | − | 0.845999i | ||||
\(935\) | 26498.8 | 0.926850 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28111.2 | 0.980097 | 0.490049 | − | 0.871695i | \(-0.336979\pi\) | ||||
0.490049 | + | 0.871695i | \(0.336979\pi\) | |||||||
\(938\) | −2866.56 | − | 4965.03i | −0.0997831 | − | 0.172829i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 528.924 | − | 916.123i | 0.0183528 | − | 0.0317879i | ||||
\(941\) | −26405.6 | + | 45735.9i | −0.914770 | + | 1.58443i | −0.107533 | + | 0.994201i | \(0.534295\pi\) |
−0.807237 | + | 0.590227i | \(0.799038\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5182.81 | − | 8976.89i | −0.178977 | − | 0.309998i | ||||
\(944\) | −2295.45 | −0.0791427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3384.30 | 0.116314 | ||||||||
\(947\) | 913.114 | + | 1581.56i | 0.0313329 | + | 0.0542701i | 0.881267 | − | 0.472619i | \(-0.156691\pi\) |
−0.849934 | + | 0.526890i | \(0.823358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2642.31 | + | 4576.62i | −0.0903826 | + | 0.156547i | ||||
\(950\) | 566.185 | − | 980.661i | 0.0193363 | − | 0.0334914i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 39588.4 | + | 68569.2i | 1.34776 | + | 2.33439i | ||||
\(953\) | −41164.2 | −1.39920 | −0.699601 | − | 0.714534i | \(-0.746639\pi\) | ||||
−0.699601 | + | 0.714534i | \(0.746639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5742.31 | 0.194573 | ||||||||
\(956\) | −5121.72 | − | 8871.08i | −0.173272 | − | 0.300116i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8419.21 | + | 14582.5i | −0.283938 | + | 0.491795i | ||||
\(959\) | −15418.7 | + | 26706.0i | −0.519183 | + | 0.899251i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10638.4 | − | 18426.2i | −0.357101 | − | 0.618517i | ||||
\(962\) | 14128.5 | 0.473514 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15569.7 | −0.520192 | ||||||||
\(965\) | 5377.33 | + | 9313.81i | 0.179381 | + | 0.310697i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3544.39 | − | 6139.06i | 0.117870 | − | 0.204156i | −0.801054 | − | 0.598593i | \(-0.795727\pi\) |
0.918923 | + | 0.394436i | \(0.129060\pi\) | |||||||
\(968\) | 14455.1 | − | 25037.0i | 0.479964 | − | 0.831321i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1055.65 | − | 1828.44i | −0.0349433 | − | 0.0605235i | ||||
\(971\) | 2355.90 | 0.0778625 | 0.0389312 | − | 0.999242i | \(-0.487605\pi\) | ||||
0.0389312 | + | 0.999242i | \(0.487605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 73773.0 | 2.43068 | ||||||||
\(974\) | 18075.3 | + | 31307.3i | 0.594630 | + | 1.02993i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4295.97 | + | 7440.84i | −0.140892 | + | 0.244032i | ||||
\(977\) | 8397.55 | − | 14545.0i | 0.274986 | − | 0.476290i | −0.695146 | − | 0.718869i | \(-0.744660\pi\) |
0.970132 | + | 0.242579i | \(0.0779934\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7309.52 | + | 12660.5i | 0.238624 | + | 0.413310i | ||||
\(980\) | −10430.0 | −0.339974 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13589.6 | 0.441611 | ||||||||
\(983\) | 7366.92 | + | 12759.9i | 0.239032 | + | 0.414015i | 0.960437 | − | 0.278498i | \(-0.0898367\pi\) |
−0.721405 | + | 0.692513i | \(0.756503\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12643.8 | − | 21899.7i | 0.409000 | − | 0.708408i | ||||
\(986\) | 25198.6 | − | 43645.3i | 0.813881 | − | 1.40968i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 591.526 | + | 1024.55i | 0.0190475 | + | 0.0329913i | ||||
\(989\) | 4320.61 | 0.138915 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36809.2 | 1.17990 | 0.589950 | − | 0.807440i | \(-0.299147\pi\) | ||||
0.589950 | + | 0.807440i | \(0.299147\pi\) | |||||||
\(992\) | 16283.3 | + | 28203.5i | 0.521165 | + | 0.902685i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13468.6 | + | 23328.4i | −0.429778 | + | 0.744397i | ||||
\(995\) | 8885.29 | − | 15389.8i | 0.283098 | − | 0.490340i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10605.0 | + | 18368.4i | 0.336875 | + | 0.583484i | 0.983843 | − | 0.179033i | \(-0.0572968\pi\) |
−0.646969 | + | 0.762517i | \(0.723964\pi\) | |||||||
\(998\) | −5685.49 | −0.180332 | ||||||||
\(999\) | 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 | 405.4.e.q.271.2 | 6 | ||
3.2 | odd | 2 | 405.4.e.v.271.2 | 6 | |||
9.2 | odd | 6 | 405.4.e.v.136.2 | 6 | |||
9.4 | even | 3 | 135.4.a.h.1.2 | yes | 3 | ||
9.5 | odd | 6 | 135.4.a.e.1.2 | ✓ | 3 | ||
9.7 | even | 3 | inner | 405.4.e.q.136.2 | 6 | ||
36.23 | even | 6 | 2160.4.a.bi.1.1 | 3 | |||
36.31 | odd | 6 | 2160.4.a.bq.1.1 | 3 | |||
45.4 | even | 6 | 675.4.a.p.1.2 | 3 | |||
45.13 | odd | 12 | 675.4.b.n.649.3 | 6 | |||
45.14 | odd | 6 | 675.4.a.s.1.2 | 3 | |||
45.22 | odd | 12 | 675.4.b.n.649.4 | 6 | |||
45.23 | even | 12 | 675.4.b.m.649.4 | 6 | |||
45.32 | even | 12 | 675.4.b.m.649.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.e.1.2 | ✓ | 3 | 9.5 | odd | 6 | ||
135.4.a.h.1.2 | yes | 3 | 9.4 | even | 3 | ||
405.4.e.q.136.2 | 6 | 9.7 | even | 3 | inner | ||
405.4.e.q.271.2 | 6 | 1.1 | even | 1 | trivial | ||
405.4.e.v.136.2 | 6 | 9.2 | odd | 6 | |||
405.4.e.v.271.2 | 6 | 3.2 | odd | 2 | |||
675.4.a.p.1.2 | 3 | 45.4 | even | 6 | |||
675.4.a.s.1.2 | 3 | 45.14 | odd | 6 | |||
675.4.b.m.649.3 | 6 | 45.32 | even | 12 | |||
675.4.b.m.649.4 | 6 | 45.23 | even | 12 | |||
675.4.b.n.649.3 | 6 | 45.13 | odd | 12 | |||
675.4.b.n.649.4 | 6 | 45.22 | odd | 12 | |||
2160.4.a.bi.1.1 | 3 | 36.23 | even | 6 | |||
2160.4.a.bq.1.1 | 3 | 36.31 | odd | 6 |