Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Root | \(2.24123 + 3.88192i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.109 |
Dual form | 378.4.g.f.163.3 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 5.59791 | + | 9.69587i | 0.500693 | + | 0.867225i | 1.00000 | 0.000799938i | \(0.000254628\pi\) | |
−0.499307 | + | 0.866425i | \(0.666412\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.7643 | − | 7.87127i | −0.905189 | − | 0.425009i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −11.1958 | + | 19.3917i | −0.354043 | + | 0.613221i | ||||
\(11\) | −9.69889 | + | 16.7990i | −0.265848 | + | 0.460462i | −0.967785 | − | 0.251777i | \(-0.918985\pi\) |
0.701938 | + | 0.712238i | \(0.252319\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −39.5348 | −0.843460 | −0.421730 | − | 0.906721i | \(-0.638577\pi\) | ||||
−0.421730 | + | 0.906721i | \(0.638577\pi\) | |||||||
\(14\) | −3.13090 | − | 36.9080i | −0.0597692 | − | 0.704576i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 17.9246 | − | 31.0464i | 0.255727 | − | 0.442933i | −0.709366 | − | 0.704841i | \(-0.751018\pi\) |
0.965093 | + | 0.261908i | \(0.0843517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.0911 | − | 48.6552i | −0.339186 | − | 0.587487i | 0.645094 | − | 0.764103i | \(-0.276818\pi\) |
−0.984280 | + | 0.176616i | \(0.943485\pi\) | |||||||
\(20\) | −44.7833 | −0.500693 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −38.7956 | −0.375966 | ||||||||
\(23\) | −20.4926 | − | 35.4943i | −0.185783 | − | 0.321786i | 0.758057 | − | 0.652188i | \(-0.226149\pi\) |
−0.943840 | + | 0.330403i | \(0.892815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.173272 | + | 0.300115i | −0.00138617 | + | 0.00240092i | ||||
\(26\) | −39.5348 | − | 68.4763i | −0.298208 | − | 0.516512i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 60.7956 | − | 42.3308i | 0.410331 | − | 0.285706i | ||||
\(29\) | −179.308 | −1.14816 | −0.574082 | − | 0.818798i | \(-0.694641\pi\) | ||||
−0.574082 | + | 0.818798i | \(0.694641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −111.582 | + | 193.266i | −0.646474 | + | 1.11973i | 0.337484 | + | 0.941331i | \(0.390424\pi\) |
−0.983959 | + | 0.178395i | \(0.942909\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 71.6986 | 0.361653 | ||||||||
\(35\) | −17.5265 | − | 206.608i | −0.0846435 | − | 0.997801i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13.6130 | − | 23.5785i | −0.0604857 | − | 0.104764i | 0.834197 | − | 0.551467i | \(-0.185932\pi\) |
−0.894683 | + | 0.446702i | \(0.852598\pi\) | |||||||
\(38\) | 56.1821 | − | 97.3103i | 0.239841 | − | 0.415416i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −44.7833 | − | 77.5670i | −0.177022 | − | 0.306610i | ||||
\(41\) | 100.096 | 0.381277 | 0.190639 | − | 0.981660i | \(-0.438944\pi\) | ||||
0.190639 | + | 0.981660i | \(0.438944\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −61.7538 | −0.219009 | −0.109504 | − | 0.993986i | \(-0.534926\pi\) | ||||
−0.109504 | + | 0.993986i | \(0.534926\pi\) | |||||||
\(44\) | −38.7956 | − | 67.1959i | −0.132924 | − | 0.230231i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 40.9853 | − | 70.9886i | 0.131368 | − | 0.227537i | ||||
\(47\) | −231.260 | − | 400.554i | −0.717717 | − | 1.24312i | −0.961902 | − | 0.273394i | \(-0.911854\pi\) |
0.244185 | − | 0.969729i | \(-0.421479\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 219.086 | + | 263.913i | 0.638735 | + | 0.769427i | ||||
\(50\) | −0.693086 | −0.00196034 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 79.0696 | − | 136.953i | 0.210865 | − | 0.365229i | ||||
\(53\) | 174.811 | − | 302.782i | 0.453060 | − | 0.784723i | −0.545514 | − | 0.838102i | \(-0.683666\pi\) |
0.998574 | + | 0.0533783i | \(0.0169989\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −217.174 | −0.532432 | ||||||||
\(56\) | 134.115 | + | 62.9702i | 0.320033 | + | 0.150263i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −179.308 | − | 310.571i | −0.405937 | − | 0.703104i | ||||
\(59\) | 121.964 | − | 211.248i | 0.269125 | − | 0.466139i | −0.699511 | − | 0.714622i | \(-0.746599\pi\) |
0.968636 | + | 0.248483i | \(0.0799320\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32.5638 | − | 56.4022i | −0.0683503 | − | 0.118386i | 0.829825 | − | 0.558024i | \(-0.188440\pi\) |
−0.898175 | + | 0.439638i | \(0.855107\pi\) | |||||||
\(62\) | −446.328 | −0.914253 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −221.312 | − | 383.324i | −0.422314 | − | 0.731470i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −85.4760 | + | 148.049i | −0.155859 | + | 0.269956i | −0.933371 | − | 0.358912i | \(-0.883148\pi\) |
0.777513 | + | 0.628867i | \(0.216481\pi\) | |||||||
\(68\) | 71.6986 | + | 124.186i | 0.127864 | + | 0.221466i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 340.328 | − | 236.964i | 0.581100 | − | 0.404609i | ||||
\(71\) | −1009.91 | −1.68809 | −0.844045 | − | 0.536272i | \(-0.819832\pi\) | ||||
−0.844045 | + | 0.536272i | \(0.819832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −573.557 | + | 993.429i | −0.919585 | + | 1.59277i | −0.119539 | + | 0.992829i | \(0.538142\pi\) |
−0.800046 | + | 0.599939i | \(0.795192\pi\) | |||||||
\(74\) | 27.2261 | − | 47.1570i | 0.0427699 | − | 0.0740796i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 224.729 | 0.339186 | ||||||||
\(77\) | 294.825 | − | 205.281i | 0.436343 | − | 0.303818i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −340.780 | − | 590.248i | −0.485325 | − | 0.840608i | 0.514532 | − | 0.857471i | \(-0.327966\pi\) |
−0.999858 | + | 0.0168627i | \(0.994632\pi\) | |||||||
\(80\) | 89.5666 | − | 155.134i | 0.125173 | − | 0.216806i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 100.096 | + | 173.371i | 0.134802 | + | 0.233484i | ||||
\(83\) | −908.609 | −1.20160 | −0.600800 | − | 0.799400i | \(-0.705151\pi\) | ||||
−0.600800 | + | 0.799400i | \(0.705151\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 401.362 | 0.512163 | ||||||||
\(86\) | −61.7538 | − | 106.961i | −0.0774312 | − | 0.134115i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 77.5911 | − | 134.392i | 0.0939914 | − | 0.162798i | ||||
\(89\) | −315.344 | − | 546.192i | −0.375578 | − | 0.650520i | 0.614836 | − | 0.788655i | \(-0.289222\pi\) |
−0.990413 | + | 0.138136i | \(0.955889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 662.775 | + | 311.189i | 0.763491 | + | 0.358478i | ||||
\(92\) | 163.941 | 0.185783 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 462.519 | − | 801.107i | 0.507502 | − | 0.879020i | ||||
\(95\) | 314.503 | − | 544.735i | 0.339656 | − | 0.588301i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1330.32 | 1.39252 | 0.696258 | − | 0.717792i | \(-0.254847\pi\) | ||||
0.696258 | + | 0.717792i | \(0.254847\pi\) | |||||||
\(98\) | −238.025 | + | 643.382i | −0.245349 | + | 0.663177i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.693086 | − | 1.20046i | −0.000693086 | − | 0.00120046i | ||||
\(101\) | −252.164 | + | 436.762i | −0.248429 | + | 0.430291i | −0.963090 | − | 0.269180i | \(-0.913247\pi\) |
0.714661 | + | 0.699471i | \(0.246581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −80.1333 | − | 138.795i | −0.0766580 | − | 0.132775i | 0.825148 | − | 0.564916i | \(-0.191092\pi\) |
−0.901806 | + | 0.432141i | \(0.857758\pi\) | |||||||
\(104\) | 316.278 | 0.298208 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 699.246 | 0.640724 | ||||||||
\(107\) | 984.295 | + | 1704.85i | 0.889303 | + | 1.54032i | 0.840701 | + | 0.541500i | \(0.182143\pi\) |
0.0486022 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −577.764 | + | 1000.72i | −0.507704 | + | 0.879369i | 0.492256 | + | 0.870450i | \(0.336172\pi\) |
−0.999960 | + | 0.00891861i | \(0.997161\pi\) | |||||||
\(110\) | −217.174 | − | 376.157i | −0.188243 | − | 0.326047i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 25.0472 | + | 295.264i | 0.0211316 | + | 0.249105i | ||||
\(113\) | 1441.21 | 1.19980 | 0.599901 | − | 0.800074i | \(-0.295206\pi\) | ||||
0.599901 | + | 0.800074i | \(0.295206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 229.432 | − | 397.388i | 0.186040 | − | 0.322231i | ||||
\(116\) | 358.617 | − | 621.143i | 0.287041 | − | 0.497169i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 487.857 | 0.380601 | ||||||||
\(119\) | −544.869 | + | 379.383i | −0.419732 | + | 0.292252i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 477.363 | + | 826.817i | 0.358650 | + | 0.621200i | ||||
\(122\) | 65.1276 | − | 112.804i | 0.0483310 | − | 0.0837117i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −446.328 | − | 773.062i | −0.323237 | − | 0.559863i | ||||
\(125\) | 1395.60 | 0.998609 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −989.467 | −0.691346 | −0.345673 | − | 0.938355i | \(-0.612349\pi\) | ||||
−0.345673 | + | 0.938355i | \(0.612349\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 442.625 | − | 766.649i | 0.298621 | − | 0.517227i | ||||
\(131\) | 77.8773 | + | 134.887i | 0.0519402 | + | 0.0899631i | 0.890827 | − | 0.454344i | \(-0.150126\pi\) |
−0.838886 | + | 0.544307i | \(0.816793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 87.9504 | + | 1036.78i | 0.0573403 | + | 0.675944i | ||||
\(134\) | −341.904 | −0.220418 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −143.397 | + | 248.371i | −0.0904133 | + | 0.156600i | ||||
\(137\) | −491.335 | + | 851.017i | −0.306406 | + | 0.530710i | −0.977573 | − | 0.210596i | \(-0.932460\pi\) |
0.671168 | + | 0.741306i | \(0.265793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2232.74 | −1.36243 | −0.681216 | − | 0.732082i | \(-0.738549\pi\) | ||||
−0.681216 | + | 0.732082i | \(0.738549\pi\) | |||||||
\(140\) | 750.763 | + | 352.501i | 0.453222 | + | 0.212799i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1009.91 | − | 1749.22i | −0.596830 | − | 1.03374i | ||||
\(143\) | 383.444 | − | 664.144i | 0.224232 | − | 0.388381i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1003.75 | − | 1738.55i | −0.574877 | − | 0.995716i | ||||
\(146\) | −2294.23 | −1.30049 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 108.904 | 0.0604857 | ||||||||
\(149\) | 1535.08 | + | 2658.84i | 0.844019 | + | 1.46188i | 0.886470 | + | 0.462786i | \(0.153150\pi\) |
−0.0424511 | + | 0.999099i | \(0.513517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1362.59 | + | 2360.07i | −0.734343 | + | 1.27192i | 0.220668 | + | 0.975349i | \(0.429176\pi\) |
−0.955011 | + | 0.296571i | \(0.904157\pi\) | |||||||
\(152\) | 224.729 | + | 389.241i | 0.119920 | + | 0.207708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 650.382 | + | 305.370i | 0.340320 | + | 0.159789i | ||||
\(155\) | −2498.50 | −1.29474 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −636.491 | + | 1102.43i | −0.323551 | + | 0.560407i | −0.981218 | − | 0.192902i | \(-0.938210\pi\) |
0.657667 | + | 0.753309i | \(0.271543\pi\) | |||||||
\(158\) | 681.559 | − | 1180.50i | 0.343177 | − | 0.594400i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 358.266 | 0.177022 | ||||||||
\(161\) | 64.1604 | + | 756.341i | 0.0314071 | + | 0.370236i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 141.011 | + | 244.238i | 0.0677597 | + | 0.117363i | 0.897915 | − | 0.440169i | \(-0.145082\pi\) |
−0.830155 | + | 0.557532i | \(0.811748\pi\) | |||||||
\(164\) | −200.192 | + | 346.743i | −0.0953193 | + | 0.165098i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −908.609 | − | 1573.76i | −0.424830 | − | 0.735827i | ||||
\(167\) | 4159.02 | 1.92715 | 0.963576 | − | 0.267435i | \(-0.0861761\pi\) | ||||
0.963576 | + | 0.267435i | \(0.0861761\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −633.999 | −0.288575 | ||||||||
\(170\) | 401.362 | + | 695.180i | 0.181077 | + | 0.313635i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 123.508 | − | 213.922i | 0.0547522 | − | 0.0948335i | ||||
\(173\) | −118.262 | − | 204.835i | −0.0519727 | − | 0.0900194i | 0.838869 | − | 0.544334i | \(-0.183218\pi\) |
−0.890841 | + | 0.454315i | \(0.849884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.26707 | − | 3.66737i | 0.00227516 | − | 0.00158415i | ||||
\(176\) | 310.364 | 0.132924 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 630.688 | − | 1092.38i | 0.265574 | − | 0.459987i | ||||
\(179\) | −1580.82 | + | 2738.06i | −0.660088 | + | 1.14331i | 0.320504 | + | 0.947247i | \(0.396148\pi\) |
−0.980592 | + | 0.196059i | \(0.937185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3304.47 | −1.35701 | −0.678506 | − | 0.734595i | \(-0.737372\pi\) | ||||
−0.678506 | + | 0.734595i | \(0.737372\pi\) | |||||||
\(182\) | 123.780 | + | 1459.15i | 0.0504129 | + | 0.594282i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 163.941 | + | 283.954i | 0.0656842 | + | 0.113768i | ||||
\(185\) | 152.409 | − | 263.981i | 0.0605695 | − | 0.104909i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 347.698 | + | 602.231i | 0.135969 | + | 0.235505i | ||||
\(188\) | 1850.08 | 0.717717 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1258.01 | 0.480346 | ||||||||
\(191\) | 1038.38 | + | 1798.53i | 0.393374 | + | 0.681344i | 0.992892 | − | 0.119017i | \(-0.0379744\pi\) |
−0.599518 | + | 0.800361i | \(0.704641\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1306.12 | + | 2262.27i | −0.487133 | + | 0.843739i | −0.999891 | − | 0.0147947i | \(-0.995291\pi\) |
0.512758 | + | 0.858533i | \(0.328624\pi\) | |||||||
\(194\) | 1330.32 | + | 2304.19i | 0.492329 | + | 0.852738i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1352.39 | + | 231.110i | −0.492855 | + | 0.0842239i | ||||
\(197\) | −3418.62 | −1.23638 | −0.618189 | − | 0.786029i | \(-0.712134\pi\) | ||||
−0.618189 | + | 0.786029i | \(0.712134\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1812.08 | − | 3138.61i | 0.645501 | − | 1.11804i | −0.338684 | − | 0.940900i | \(-0.609982\pi\) |
0.984185 | − | 0.177141i | \(-0.0566849\pi\) | |||||||
\(200\) | 1.38617 | − | 2.40092i | 0.000490086 | − | 0.000848854i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1008.66 | −0.351331 | ||||||||
\(203\) | 3005.99 | + | 1411.39i | 1.03931 | + | 0.487979i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 560.329 | + | 970.517i | 0.190903 | + | 0.330653i | ||||
\(206\) | 160.267 | − | 277.590i | 0.0542054 | − | 0.0938864i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 316.278 | + | 547.810i | 0.105433 | + | 0.182614i | ||||
\(209\) | 1089.81 | 0.360687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4087.38 | 1.33359 | 0.666794 | − | 0.745242i | \(-0.267666\pi\) | ||||
0.666794 | + | 0.745242i | \(0.267666\pi\) | |||||||
\(212\) | 699.246 | + | 1211.13i | 0.226530 | + | 0.392362i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1968.59 | + | 3409.70i | −0.628832 | + | 1.08917i | ||||
\(215\) | −345.693 | − | 598.757i | −0.109656 | − | 0.189930i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3391.84 | − | 2361.68i | 1.06108 | − | 0.738807i | ||||
\(218\) | −2311.05 | −0.718002 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 434.348 | − | 752.313i | 0.133108 | − | 0.230550i | ||||
\(221\) | −708.647 | + | 1227.41i | −0.215696 | + | 0.373596i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3393.50 | −1.01904 | −0.509520 | − | 0.860459i | \(-0.670177\pi\) | ||||
−0.509520 | + | 0.860459i | \(0.670177\pi\) | |||||||
\(224\) | −486.364 | + | 338.647i | −0.145074 | + | 0.101012i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1441.21 | + | 2496.25i | 0.424194 | + | 0.734726i | ||||
\(227\) | 1276.99 | − | 2211.80i | 0.373377 | − | 0.646707i | −0.616706 | − | 0.787194i | \(-0.711533\pi\) |
0.990083 | + | 0.140486i | \(0.0448666\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 351.347 | + | 608.550i | 0.101387 | + | 0.175608i | 0.912256 | − | 0.409620i | \(-0.134339\pi\) |
−0.810869 | + | 0.585227i | \(0.801005\pi\) | |||||||
\(230\) | 917.728 | 0.263101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1434.47 | 0.405937 | ||||||||
\(233\) | −205.573 | − | 356.063i | −0.0578006 | − | 0.100114i | 0.835677 | − | 0.549221i | \(-0.185075\pi\) |
−0.893478 | + | 0.449107i | \(0.851742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2589.14 | − | 4484.53i | 0.718711 | − | 1.24484i | ||||
\(236\) | 487.857 | + | 844.994i | 0.134563 | + | 0.233070i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1201.98 | − | 564.359i | −0.327364 | − | 0.153706i | ||||
\(239\) | −178.567 | −0.0483286 | −0.0241643 | − | 0.999708i | \(-0.507692\pi\) | ||||
−0.0241643 | + | 0.999708i | \(0.507692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2030.95 | − | 3517.71i | 0.542843 | − | 0.940232i | −0.455896 | − | 0.890033i | \(-0.650681\pi\) |
0.998739 | − | 0.0501987i | \(-0.0159854\pi\) | |||||||
\(242\) | −954.726 | + | 1653.63i | −0.253604 | + | 0.439255i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 260.510 | 0.0683503 | ||||||||
\(245\) | −1332.44 | + | 3601.60i | −0.347456 | + | 0.939173i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1110.57 | + | 1923.57i | 0.286090 | + | 0.495522i | ||||
\(248\) | 892.655 | − | 1546.12i | 0.228563 | − | 0.395883i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1395.60 | + | 2417.25i | 0.353062 | + | 0.611521i | ||||
\(251\) | −2040.70 | −0.513178 | −0.256589 | − | 0.966521i | \(-0.582599\pi\) | ||||
−0.256589 | + | 0.966521i | \(0.582599\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 795.023 | 0.197560 | ||||||||
\(254\) | −989.467 | − | 1713.81i | −0.244428 | − | 0.423361i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2283.44 | − | 3955.04i | −0.554231 | − | 0.959956i | −0.997963 | − | 0.0637964i | \(-0.979679\pi\) |
0.443732 | − | 0.896159i | \(-0.353654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 42.6211 | + | 502.430i | 0.0102253 | + | 0.120539i | ||||
\(260\) | 1770.50 | 0.422314 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −155.755 | + | 269.775i | −0.0367273 | + | 0.0636135i | ||||
\(263\) | 2668.42 | − | 4621.83i | 0.625634 | − | 1.08363i | −0.362784 | − | 0.931873i | \(-0.618174\pi\) |
0.988418 | − | 0.151756i | \(-0.0484928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3914.32 | 0.907376 | ||||||||
\(266\) | −1707.81 | + | 1189.12i | −0.393657 | + | 0.274096i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −341.904 | − | 592.195i | −0.0779295 | − | 0.134978i | ||||
\(269\) | 3209.62 | − | 5559.22i | 0.727486 | − | 1.26004i | −0.230456 | − | 0.973083i | \(-0.574022\pi\) |
0.957942 | − | 0.286960i | \(-0.0926448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3540.34 | − | 6132.05i | −0.793580 | − | 1.37452i | −0.923737 | − | 0.383028i | \(-0.874881\pi\) |
0.130157 | − | 0.991493i | \(-0.458452\pi\) | |||||||
\(272\) | −573.589 | −0.127864 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1965.34 | −0.433323 | ||||||||
\(275\) | −3.36108 | − | 5.82157i | −0.000737022 | − | 0.00127656i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2333.66 | + | 4042.02i | −0.506195 | + | 0.876756i | 0.493779 | + | 0.869588i | \(0.335615\pi\) |
−0.999974 | + | 0.00716871i | \(0.997718\pi\) | |||||||
\(278\) | −2232.74 | − | 3867.21i | −0.481693 | − | 0.834316i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 140.212 | + | 1652.86i | 0.0299260 | + | 0.352776i | ||||
\(281\) | −8234.13 | −1.74807 | −0.874034 | − | 0.485865i | \(-0.838505\pi\) | ||||
−0.874034 | + | 0.485865i | \(0.838505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −101.417 | + | 175.660i | −0.0213026 | + | 0.0368971i | −0.876480 | − | 0.481438i | \(-0.840115\pi\) |
0.855178 | + | 0.518335i | \(0.173448\pi\) | |||||||
\(284\) | 2019.82 | − | 3498.43i | 0.422023 | − | 0.730964i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1533.77 | 0.317112 | ||||||||
\(287\) | −1678.04 | − | 787.882i | −0.345128 | − | 0.162046i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1813.91 | + | 3141.79i | 0.369207 | + | 0.639485i | ||||
\(290\) | 2007.51 | − | 3477.10i | 0.406499 | − | 0.704078i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2294.23 | − | 3973.72i | −0.459793 | − | 0.796384i | ||||
\(293\) | 3612.05 | 0.720199 | 0.360100 | − | 0.932914i | \(-0.382743\pi\) | ||||
0.360100 | + | 0.932914i | \(0.382743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2730.98 | 0.538997 | ||||||||
\(296\) | 108.904 | + | 188.628i | 0.0213849 | + | 0.0370398i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3070.16 | + | 5317.68i | −0.596812 | + | 1.03371i | ||||
\(299\) | 810.172 | + | 1403.26i | 0.156701 | + | 0.271413i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1035.26 | + | 486.081i | 0.198244 | + | 0.0930806i | ||||
\(302\) | −5450.35 | −1.03852 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −449.457 | + | 778.483i | −0.0847965 | + | 0.146872i | ||||
\(305\) | 364.579 | − | 631.469i | 0.0684450 | − | 0.118550i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4684.69 | −0.870910 | −0.435455 | − | 0.900210i | \(-0.643413\pi\) | ||||
−0.435455 | + | 0.900210i | \(0.643413\pi\) | |||||||
\(308\) | 121.465 | + | 1431.86i | 0.0224712 | + | 0.264896i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2498.50 | − | 4327.54i | −0.457760 | − | 0.792863i | ||||
\(311\) | 3810.20 | − | 6599.46i | 0.694716 | − | 1.20328i | −0.275560 | − | 0.961284i | \(-0.588863\pi\) |
0.970276 | − | 0.242000i | \(-0.0778033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2901.80 | + | 5026.07i | 0.524024 | + | 0.907636i | 0.999609 | + | 0.0279665i | \(0.00890316\pi\) |
−0.475585 | + | 0.879670i | \(0.657764\pi\) | |||||||
\(314\) | −2545.96 | −0.457570 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2726.24 | 0.485325 | ||||||||
\(317\) | −2131.98 | − | 3692.69i | −0.377740 | − | 0.654266i | 0.612993 | − | 0.790089i | \(-0.289966\pi\) |
−0.990733 | + | 0.135823i | \(0.956632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1739.09 | − | 3012.20i | 0.305237 | − | 0.528685i | ||||
\(320\) | 358.266 | + | 620.536i | 0.0625866 | + | 0.108403i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1245.86 | + | 867.470i | −0.215618 | + | 0.150131i | ||||
\(323\) | −2014.09 | −0.346956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.85026 | − | 11.8650i | 0.00116918 | − | 0.00202508i | ||||
\(326\) | −282.022 | + | 488.476i | −0.0479133 | + | 0.0829883i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −800.768 | −0.134802 | ||||||||
\(329\) | 724.051 | + | 8535.32i | 0.121332 | + | 1.43030i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4174.62 | − | 7230.66i | −0.693226 | − | 1.20070i | −0.970775 | − | 0.239992i | \(-0.922855\pi\) |
0.277549 | − | 0.960712i | \(-0.410478\pi\) | |||||||
\(332\) | 1817.22 | − | 3147.51i | 0.300400 | − | 0.520308i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4159.02 | + | 7203.63i | 0.681351 | + | 1.18013i | ||||
\(335\) | −1913.95 | −0.312150 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9133.23 | 1.47632 | 0.738158 | − | 0.674628i | \(-0.235696\pi\) | ||||
0.738158 | + | 0.674628i | \(0.235696\pi\) | |||||||
\(338\) | −633.999 | − | 1098.12i | −0.102027 | − | 0.176715i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −802.725 | + | 1390.36i | −0.128041 | + | 0.221773i | ||||
\(341\) | −2164.44 | − | 3748.92i | −0.343728 | − | 0.595354i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1595.50 | − | 6148.82i | −0.251164 | − | 0.967945i | ||||
\(344\) | 494.031 | 0.0774312 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 236.524 | − | 409.671i | 0.0367502 | − | 0.0636533i | ||||
\(347\) | −425.840 | + | 737.577i | −0.0658798 | + | 0.114107i | −0.897084 | − | 0.441860i | \(-0.854319\pi\) |
0.831204 | + | 0.555967i | \(0.187652\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2348.88 | 0.360266 | 0.180133 | − | 0.983642i | \(-0.442347\pi\) | ||||
0.180133 | + | 0.983642i | \(0.442347\pi\) | |||||||
\(350\) | 11.6191 | + | 5.45547i | 0.00177448 | + | 0.000833163i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 310.364 | + | 537.567i | 0.0469957 | + | 0.0813989i | ||||
\(353\) | 393.157 | − | 680.969i | 0.0592795 | − | 0.102675i | −0.834863 | − | 0.550458i | \(-0.814453\pi\) |
0.894142 | + | 0.447783i | \(0.147786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5653.40 | − | 9791.97i | −0.845214 | − | 1.46395i | ||||
\(356\) | 2522.75 | 0.375578 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6323.27 | −0.933506 | ||||||||
\(359\) | 3690.81 | + | 6392.67i | 0.542601 | + | 0.939812i | 0.998754 | + | 0.0499105i | \(0.0158936\pi\) |
−0.456153 | + | 0.889901i | \(0.650773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1851.28 | − | 3206.52i | 0.269906 | − | 0.467491i | ||||
\(362\) | −3304.47 | − | 5723.50i | −0.479776 | − | 0.830996i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2403.54 | + | 1673.54i | −0.346098 | + | 0.240982i | ||||
\(365\) | −12842.9 | −1.84172 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1220.46 | − | 2113.90i | 0.173590 | − | 0.300667i | −0.766082 | − | 0.642742i | \(-0.777797\pi\) |
0.939672 | + | 0.342075i | \(0.111130\pi\) | |||||||
\(368\) | −327.882 | + | 567.908i | −0.0464457 | + | 0.0804464i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 609.637 | 0.0856582 | ||||||||
\(371\) | −5313.88 | + | 3699.96i | −0.743619 | + | 0.517769i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5938.04 | + | 10285.0i | 0.824290 | + | 1.42771i | 0.902461 | + | 0.430772i | \(0.141759\pi\) |
−0.0781707 | + | 0.996940i | \(0.524908\pi\) | |||||||
\(374\) | −695.397 | + | 1204.46i | −0.0961446 | + | 0.166527i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1850.08 | + | 3204.43i | 0.253751 | + | 0.439510i | ||||
\(377\) | 7088.92 | 0.968430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4202.37 | −0.569554 | −0.284777 | − | 0.958594i | \(-0.591920\pi\) | ||||
−0.284777 | + | 0.958594i | \(0.591920\pi\) | |||||||
\(380\) | 1258.01 | + | 2178.94i | 0.169828 | + | 0.294151i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2076.76 | + | 3597.05i | −0.278158 | + | 0.481783i | ||||
\(383\) | −7048.40 | − | 12208.2i | −0.940357 | − | 1.62875i | −0.764791 | − | 0.644278i | \(-0.777158\pi\) |
−0.175565 | − | 0.984468i | \(-0.556175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3640.78 | + | 1709.44i | 0.481952 | + | 0.226288i | ||||
\(386\) | −5224.48 | −0.688910 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2660.65 | + | 4608.38i | −0.348129 | + | 0.602977i | ||||
\(389\) | 5668.66 | − | 9818.40i | 0.738849 | − | 1.27972i | −0.214165 | − | 0.976798i | \(-0.568703\pi\) |
0.953014 | − | 0.302927i | \(-0.0979637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1469.29 | −0.190039 | ||||||||
\(392\) | −1752.69 | − | 2111.31i | −0.225827 | − | 0.272033i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3418.62 | − | 5921.22i | −0.437126 | − | 0.757124i | ||||
\(395\) | 3815.31 | − | 6608.31i | 0.485998 | − | 0.841773i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −493.685 | − | 855.088i | −0.0624115 | − | 0.108100i | 0.833131 | − | 0.553075i | \(-0.186546\pi\) |
−0.895543 | + | 0.444975i | \(0.853212\pi\) | |||||||
\(398\) | 7248.31 | 0.912877 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.54469 | 0.000693086 | ||||||||
\(401\) | −4246.79 | − | 7355.66i | −0.528864 | − | 0.916020i | −0.999433 | − | 0.0336569i | \(-0.989285\pi\) |
0.470569 | − | 0.882363i | \(-0.344049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4411.37 | − | 7640.72i | 0.545275 | − | 0.944445i | ||||
\(404\) | −1008.66 | − | 1747.05i | −0.124214 | − | 0.215146i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 561.397 | + | 6617.91i | 0.0686248 | + | 0.808969i | ||||
\(407\) | 528.126 | 0.0643200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4632.80 | + | 8024.25i | −0.560091 | + | 0.970107i | 0.437396 | + | 0.899269i | \(0.355901\pi\) |
−0.997488 | + | 0.0708381i | \(0.977433\pi\) | |||||||
\(410\) | −1120.66 | + | 1941.03i | −0.134989 | + | 0.233807i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 641.066 | 0.0766580 | ||||||||
\(413\) | −3707.44 | + | 2581.43i | −0.441723 | + | 0.307563i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5086.31 | − | 8809.75i | −0.601632 | − | 1.04206i | ||||
\(416\) | −632.557 | + | 1095.62i | −0.0745521 | + | 0.129128i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1089.81 | + | 1887.60i | 0.127522 | + | 0.220875i | ||||
\(419\) | −4398.11 | −0.512797 | −0.256398 | − | 0.966571i | \(-0.582536\pi\) | ||||
−0.256398 | + | 0.966571i | \(0.582536\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9335.15 | −1.08068 | −0.540341 | − | 0.841446i | \(-0.681705\pi\) | ||||
−0.540341 | + | 0.841446i | \(0.681705\pi\) | |||||||
\(422\) | 4087.38 | + | 7079.56i | 0.471495 | + | 0.816653i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1398.49 | + | 2422.26i | −0.160181 | + | 0.277442i | ||||
\(425\) | 6.21166 | + | 10.7589i | 0.000708964 | + | 0.00122796i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 101.954 | + | 1201.86i | 0.0115548 | + | 0.136211i | ||||
\(428\) | −7874.36 | −0.889303 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 691.385 | − | 1197.51i | 0.0775385 | − | 0.134301i | ||||
\(431\) | 138.876 | − | 240.540i | 0.0155207 | − | 0.0268827i | −0.858161 | − | 0.513381i | \(-0.828393\pi\) |
0.873681 | + | 0.486498i | \(0.161726\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 706.915 | 0.0784577 | 0.0392289 | − | 0.999230i | \(-0.487510\pi\) | ||||
0.0392289 | + | 0.999230i | \(0.487510\pi\) | |||||||
\(434\) | 7482.39 | + | 3513.17i | 0.827572 | + | 0.388565i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2311.05 | − | 4002.86i | −0.253852 | − | 0.439684i | ||||
\(437\) | −1151.32 | + | 1994.14i | −0.126030 | + | 0.218290i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −710.440 | − | 1230.52i | −0.0772379 | − | 0.133780i | 0.824819 | − | 0.565396i | \(-0.191277\pi\) |
−0.902057 | + | 0.431616i | \(0.857943\pi\) | |||||||
\(440\) | 1737.39 | 0.188243 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2834.59 | −0.305040 | ||||||||
\(443\) | 6029.64 | + | 10443.6i | 0.646674 | + | 1.12007i | 0.983912 | + | 0.178653i | \(0.0571741\pi\) |
−0.337238 | + | 0.941420i | \(0.609493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3530.54 | − | 6115.07i | 0.376098 | − | 0.651421i | ||||
\(446\) | −3393.50 | − | 5877.72i | −0.360285 | − | 0.624032i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1072.92 | − | 503.761i | −0.113149 | − | 0.0531261i | ||||
\(449\) | 1519.39 | 0.159698 | 0.0798491 | − | 0.996807i | \(-0.474556\pi\) | ||||
0.0798491 | + | 0.996807i | \(0.474556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −970.820 | + | 1681.51i | −0.101362 | + | 0.175564i | ||||
\(452\) | −2882.42 | + | 4992.50i | −0.299951 | + | 0.519530i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5107.94 | 0.528034 | ||||||||
\(455\) | 692.907 | + | 8168.19i | 0.0713934 | + | 0.841606i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2724.80 | + | 4719.49i | 0.278908 | + | 0.483082i | 0.971114 | − | 0.238618i | \(-0.0766944\pi\) |
−0.692206 | + | 0.721700i | \(0.743361\pi\) | |||||||
\(458\) | −702.694 | + | 1217.10i | −0.0716915 | + | 0.124173i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 917.728 | + | 1589.55i | 0.0930202 | + | 0.161116i | ||||
\(461\) | 9435.17 | 0.953232 | 0.476616 | − | 0.879112i | \(-0.341863\pi\) | ||||
0.476616 | + | 0.879112i | \(0.341863\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17319.2 | −1.73843 | −0.869214 | − | 0.494436i | \(-0.835375\pi\) | ||||
−0.869214 | + | 0.494436i | \(0.835375\pi\) | |||||||
\(464\) | 1434.47 | + | 2484.57i | 0.143520 | + | 0.248585i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 411.146 | − | 712.126i | 0.0408712 | − | 0.0707910i | ||||
\(467\) | 3336.47 | + | 5778.93i | 0.330606 | + | 0.572627i | 0.982631 | − | 0.185571i | \(-0.0594134\pi\) |
−0.652024 | + | 0.758198i | \(0.726080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2598.28 | − | 1809.13i | 0.255815 | − | 0.178120i | ||||
\(470\) | 10356.6 | 1.01641 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −975.715 | + | 1689.99i | −0.0951502 | + | 0.164805i | ||||
\(473\) | 598.944 | − | 1037.40i | 0.0582230 | − | 0.100845i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.4695 | 0.00188068 | ||||||||
\(476\) | −224.481 | − | 2646.25i | −0.0216157 | − | 0.254812i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −178.567 | − | 309.287i | −0.0170868 | − | 0.0295951i | ||||
\(479\) | 7748.69 | − | 13421.1i | 0.739138 | − | 1.28022i | −0.213747 | − | 0.976889i | \(-0.568567\pi\) |
0.952884 | − | 0.303335i | \(-0.0981000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 538.189 | + | 932.171i | 0.0510173 | + | 0.0883645i | ||||
\(482\) | 8123.81 | 0.767696 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3818.90 | −0.358650 | ||||||||
\(485\) | 7447.04 | + | 12898.7i | 0.697222 | + | 1.20762i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1862.88 | − | 3226.60i | 0.173337 | − | 0.300229i | −0.766247 | − | 0.642546i | \(-0.777878\pi\) |
0.939585 | + | 0.342317i | \(0.111212\pi\) | |||||||
\(488\) | 260.510 | + | 451.217i | 0.0241655 | + | 0.0418558i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7570.59 | + | 1293.74i | −0.697968 | + | 0.119276i | ||||
\(491\) | −18496.7 | −1.70009 | −0.850045 | − | 0.526711i | \(-0.823425\pi\) | ||||
−0.850045 | + | 0.526711i | \(0.823425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3214.04 | + | 5566.88i | −0.293617 | + | 0.508559i | ||||
\(494\) | −2221.15 | + | 3847.14i | −0.202296 | + | 0.350387i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3570.62 | 0.323237 | ||||||||
\(497\) | 16930.5 | + | 7949.28i | 1.52804 | + | 0.717453i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1851.59 | + | 3207.04i | 0.166109 | + | 0.287709i | 0.937049 | − | 0.349199i | \(-0.113546\pi\) |
−0.770940 | + | 0.636908i | \(0.780213\pi\) | |||||||
\(500\) | −2791.20 | + | 4834.50i | −0.249652 | + | 0.432410i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2040.70 | − | 3534.59i | −0.181436 | − | 0.314256i | ||||
\(503\) | −6872.91 | −0.609240 | −0.304620 | − | 0.952474i | \(-0.598529\pi\) | ||||
−0.304620 | + | 0.952474i | \(0.598529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5646.38 | −0.497546 | ||||||||
\(506\) | 795.023 | + | 1377.02i | 0.0698480 | + | 0.120980i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1978.93 | − | 3427.61i | 0.172837 | − | 0.299362i | ||||
\(509\) | 4973.42 | + | 8614.22i | 0.433091 | + | 0.750135i | 0.997138 | − | 0.0756076i | \(-0.0240896\pi\) |
−0.564047 | + | 0.825743i | \(0.690756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17434.8 | − | 12139.6i | 1.50934 | − | 1.05093i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4566.89 | − | 7910.08i | 0.391900 | − | 0.678791i | ||||
\(515\) | 897.159 | − | 1553.92i | 0.0767641 | − | 0.132959i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8971.85 | 0.763214 | ||||||||
\(518\) | −827.613 | + | 576.252i | −0.0701993 | + | 0.0488785i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1770.50 | + | 3066.59i | 0.149311 | + | 0.258614i | ||||
\(521\) | 4227.85 | − | 7322.84i | 0.355519 | − | 0.615777i | −0.631688 | − | 0.775223i | \(-0.717638\pi\) |
0.987207 | + | 0.159446i | \(0.0509709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3554.65 | + | 6156.84i | 0.297197 | + | 0.514761i | 0.975494 | − | 0.220028i | \(-0.0706148\pi\) |
−0.678296 | + | 0.734788i | \(0.737281\pi\) | |||||||
\(524\) | −623.018 | −0.0519402 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10673.7 | 0.884780 | ||||||||
\(527\) | 4000.13 | + | 6928.43i | 0.330642 | + | 0.572689i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5243.60 | − | 9082.19i | 0.430969 | − | 0.746461i | ||||
\(530\) | 3914.32 | + | 6779.80i | 0.320806 | + | 0.555652i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3767.43 | − | 1768.90i | −0.307028 | − | 0.144157i | ||||
\(533\) | −3957.27 | −0.321592 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11020.0 | + | 19087.2i | −0.890535 | + | 1.54245i | ||||
\(536\) | 683.808 | − | 1184.39i | 0.0551045 | − | 0.0954437i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12838.5 | 1.02882 | ||||||||
\(539\) | −6558.36 | + | 1120.76i | −0.524098 | + | 0.0895629i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6264.28 | + | 10850.1i | 0.497823 | + | 0.862256i | 0.999997 | − | 0.00251141i | \(-0.000799407\pi\) |
−0.502173 | + | 0.864767i | \(0.667466\pi\) | |||||||
\(542\) | 7080.68 | − | 12264.1i | 0.561146 | − | 0.971933i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −573.589 | − | 993.484i | −0.0452066 | − | 0.0783002i | ||||
\(545\) | −12937.1 | −1.01681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4698.99 | 0.367302 | 0.183651 | − | 0.982991i | \(-0.441208\pi\) | ||||
0.183651 | + | 0.982991i | \(0.441208\pi\) | |||||||
\(548\) | −1965.34 | − | 3404.07i | −0.153203 | − | 0.265355i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.72217 | − | 11.6431i | 0.000521153 | − | 0.000902664i | ||||
\(551\) | 5036.97 | + | 8724.28i | 0.389441 | + | 0.674532i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1066.95 | + | 12577.5i | 0.0820456 | + | 0.967177i | ||||
\(554\) | −9334.65 | −0.715868 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4465.47 | − | 7734.42i | 0.340608 | − | 0.589951i | ||||
\(557\) | 73.3775 | − | 127.094i | 0.00558188 | − | 0.00966809i | −0.863221 | − | 0.504826i | \(-0.831557\pi\) |
0.868803 | + | 0.495158i | \(0.164890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2441.43 | 0.184725 | ||||||||
\(560\) | −2722.63 | + | 1895.72i | −0.205450 | + | 0.143051i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8234.13 | − | 14261.9i | −0.618035 | − | 1.07047i | ||||
\(563\) | −7340.75 | + | 12714.5i | −0.549513 | + | 0.951784i | 0.448795 | + | 0.893635i | \(0.351853\pi\) |
−0.998308 | + | 0.0581491i | \(0.981480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8067.77 | + | 13973.8i | 0.600732 | + | 1.04050i | ||||
\(566\) | −405.669 | −0.0301264 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8079.29 | 0.596830 | ||||||||
\(569\) | 10220.1 | + | 17701.8i | 0.752987 | + | 1.30421i | 0.946369 | + | 0.323088i | \(0.104721\pi\) |
−0.193382 | + | 0.981123i | \(0.561946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9365.03 | − | 16220.7i | 0.686364 | − | 1.18882i | −0.286641 | − | 0.958038i | \(-0.592539\pi\) |
0.973006 | − | 0.230780i | \(-0.0741278\pi\) | |||||||
\(572\) | 1533.77 | + | 2656.58i | 0.112116 | + | 0.194191i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −313.391 | − | 3694.34i | −0.0227886 | − | 0.268639i | ||||
\(575\) | 14.2032 | 0.00103011 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3087.66 | + | 5347.98i | −0.222774 | + | 0.385856i | −0.955649 | − | 0.294507i | \(-0.904845\pi\) |
0.732875 | + | 0.680363i | \(0.238178\pi\) | |||||||
\(578\) | −3627.83 | + | 6283.58i | −0.261069 | + | 0.452184i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8030.03 | 0.574877 | ||||||||
\(581\) | 15232.2 | + | 7151.90i | 1.08768 | + | 0.510690i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3390.95 | + | 5873.30i | 0.240890 | + | 0.417234i | ||||
\(584\) | 4588.45 | − | 7947.43i | 0.325122 | − | 0.563129i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3612.05 | + | 6256.26i | 0.254629 | + | 0.441030i | ||||
\(587\) | 6964.63 | 0.489712 | 0.244856 | − | 0.969559i | \(-0.421259\pi\) | ||||
0.244856 | + | 0.969559i | \(0.421259\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12537.8 | 0.877100 | ||||||||
\(590\) | 2730.98 | + | 4730.20i | 0.190564 | + | 0.330067i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −217.809 | + | 377.256i | −0.0151214 | + | 0.0261911i | ||||
\(593\) | 2472.15 | + | 4281.89i | 0.171196 | + | 0.296520i | 0.938838 | − | 0.344359i | \(-0.111904\pi\) |
−0.767642 | + | 0.640878i | \(0.778570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6728.58 | − | 3159.23i | −0.463605 | − | 0.217674i | ||||
\(596\) | −12280.7 | −0.844019 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1620.34 | + | 2806.52i | −0.110804 | + | 0.191918i | ||||
\(599\) | −3158.77 | + | 5471.16i | −0.215466 | + | 0.373198i | −0.953417 | − | 0.301657i | \(-0.902460\pi\) |
0.737951 | + | 0.674855i | \(0.235794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22912.5 | −1.55511 | −0.777555 | − | 0.628816i | \(-0.783540\pi\) | ||||
−0.777555 | + | 0.628816i | \(0.783540\pi\) | |||||||
\(602\) | 193.345 | + | 2279.21i | 0.0130900 | + | 0.154308i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5450.35 | − | 9440.29i | −0.367172 | − | 0.635960i | ||||
\(605\) | −5344.47 | + | 9256.90i | −0.359147 | + | 0.622060i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1850.95 | − | 3205.93i | −0.123769 | − | 0.214374i | 0.797482 | − | 0.603342i | \(-0.206165\pi\) |
−0.921251 | + | 0.388969i | \(0.872831\pi\) | |||||||
\(608\) | −1797.83 | −0.119920 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1458.32 | 0.0967958 | ||||||||
\(611\) | 9142.81 | + | 15835.8i | 0.605366 | + | 1.04852i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3816.69 | + | 6610.70i | −0.251476 | + | 0.435569i | −0.963932 | − | 0.266148i | \(-0.914249\pi\) |
0.712457 | + | 0.701716i | \(0.247582\pi\) | |||||||
\(614\) | −4684.69 | − | 8114.12i | −0.307913 | − | 0.533322i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2358.60 | + | 1642.25i | −0.154270 | + | 0.107416i | ||||
\(617\) | 4657.33 | 0.303885 | 0.151942 | − | 0.988389i | \(-0.451447\pi\) | ||||
0.151942 | + | 0.988389i | \(0.451447\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3276.14 | − | 5674.44i | 0.212729 | − | 0.368457i | −0.739839 | − | 0.672784i | \(-0.765098\pi\) |
0.952568 | + | 0.304327i | \(0.0984316\pi\) | |||||||
\(620\) | 4997.01 | − | 8655.07i | 0.323685 | − | 0.560639i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15240.8 | 0.982477 | ||||||||
\(623\) | 987.312 | + | 11638.7i | 0.0634925 | + | 0.748467i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7834.10 | + | 13569.1i | 0.501382 | + | 0.868420i | ||||
\(626\) | −5803.60 | + | 10052.1i | −0.370541 | + | 0.641796i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2545.96 | − | 4409.74i | −0.161775 | − | 0.280203i | ||||
\(629\) | −976.036 | −0.0618714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17505.8 | −1.10443 | −0.552215 | − | 0.833702i | \(-0.686217\pi\) | ||||
−0.552215 | + | 0.833702i | \(0.686217\pi\) | |||||||
\(632\) | 2726.24 | + | 4721.98i | 0.171588 | + | 0.297200i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4263.95 | − | 7385.38i | 0.267103 | − | 0.462636i | ||||
\(635\) | −5538.95 | − | 9593.74i | −0.346152 | − | 0.599553i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8661.53 | − | 10433.8i | −0.538748 | − | 0.648981i | ||||
\(638\) | 6956.37 | 0.431670 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −716.533 | + | 1241.07i | −0.0442554 | + | 0.0766526i | ||||
\(641\) | 5989.15 | − | 10373.5i | 0.369044 | − | 0.639203i | −0.620373 | − | 0.784307i | \(-0.713019\pi\) |
0.989416 | + | 0.145105i | \(0.0463519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14582.6 | −0.894370 | −0.447185 | − | 0.894441i | \(-0.647573\pi\) | ||||
−0.447185 | + | 0.894441i | \(0.647573\pi\) | |||||||
\(644\) | −2748.36 | − | 1290.42i | −0.168169 | − | 0.0789594i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2014.09 | − | 3488.51i | −0.122668 | − | 0.212467i | ||||
\(647\) | 13631.5 | − | 23610.5i | 0.828300 | − | 1.43466i | −0.0710702 | − | 0.997471i | \(-0.522641\pi\) |
0.899371 | − | 0.437187i | \(-0.144025\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2365.84 | + | 4097.75i | 0.143093 | + | 0.247844i | ||||
\(650\) | 27.4010 | 0.00165347 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1128.09 | −0.0677597 | ||||||||
\(653\) | −13800.8 | − | 23903.6i | −0.827053 | − | 1.43250i | −0.900340 | − | 0.435187i | \(-0.856682\pi\) |
0.0732872 | − | 0.997311i | \(-0.476651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −871.900 | + | 1510.18i | −0.0520122 | + | 0.0900877i | ||||
\(656\) | −800.768 | − | 1386.97i | −0.0476596 | − | 0.0825489i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14059.6 | + | 9789.42i | −0.832977 | + | 0.579987i | ||||
\(659\) | 10780.5 | 0.637254 | 0.318627 | − | 0.947880i | \(-0.396778\pi\) | ||||
0.318627 | + | 0.947880i | \(0.396778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5517.83 | − | 9557.17i | 0.324688 | − | 0.562376i | −0.656761 | − | 0.754099i | \(-0.728074\pi\) |
0.981449 | + | 0.191722i | \(0.0614073\pi\) | |||||||
\(662\) | 8349.24 | − | 14461.3i | 0.490185 | − | 0.849025i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7268.87 | 0.424830 | ||||||||
\(665\) | −9560.19 | + | 6656.58i | −0.557486 | + | 0.388167i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3674.50 | + | 6364.42i | 0.213309 | + | 0.369462i | ||||
\(668\) | −8318.03 | + | 14407.3i | −0.481788 | + | 0.834481i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1913.95 | − | 3315.06i | −0.110362 | − | 0.191152i | ||||
\(671\) | 1263.33 | 0.0726831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28007.8 | −1.60419 | −0.802097 | − | 0.597193i | \(-0.796283\pi\) | ||||
−0.802097 | + | 0.597193i | \(0.796283\pi\) | |||||||
\(674\) | 9133.23 | + | 15819.2i | 0.521957 | + | 0.904055i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1268.00 | − | 2196.24i | 0.0721437 | − | 0.124957i | ||||
\(677\) | 2.53680 | + | 4.39387i | 0.000144014 | + | 0.000249439i | 0.866097 | − | 0.499875i | \(-0.166621\pi\) |
−0.865953 | + | 0.500125i | \(0.833287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22302.0 | − | 10471.3i | −1.26049 | − | 0.591831i | ||||
\(680\) | −3210.90 | −0.181077 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4328.88 | − | 7497.85i | 0.243052 | − | 0.420979i | ||||
\(683\) | 4976.40 | − | 8619.37i | 0.278794 | − | 0.482886i | −0.692291 | − | 0.721618i | \(-0.743399\pi\) |
0.971085 | + | 0.238732i | \(0.0767319\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11001.8 | −0.613660 | ||||||||
\(686\) | 9054.56 | − | 8912.31i | 0.503943 | − | 0.496026i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 494.031 | + | 855.686i | 0.0273761 | + | 0.0474168i | ||||
\(689\) | −6911.14 | + | 11970.4i | −0.382138 | + | 0.661883i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6159.06 | + | 10667.8i | 0.339076 | + | 0.587298i | 0.984259 | − | 0.176731i | \(-0.0565521\pi\) |
−0.645183 | + | 0.764028i | \(0.723219\pi\) | |||||||
\(692\) | 946.094 | 0.0519727 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1703.36 | −0.0931681 | ||||||||
\(695\) | −12498.7 | − | 21648.3i | −0.682160 | − | 1.18154i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1794.18 | − | 3107.62i | 0.0975030 | − | 0.168880i | ||||
\(698\) | 2348.88 | + | 4068.38i | 0.127373 | + | 0.220617i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.16999 | + | 25.5804i | 0.000117168 | + | 0.00138121i | ||||
\(701\) | −15992.8 | −0.861685 | −0.430843 | − | 0.902427i | \(-0.641784\pi\) | ||||
−0.430843 | + | 0.902427i | \(0.641784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −764.810 | + | 1324.69i | −0.0410318 | + | 0.0710692i | ||||
\(704\) | −620.729 | + | 1075.13i | −0.0332310 | + | 0.0575577i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1572.63 | 0.0838338 | ||||||||
\(707\) | 7665.24 | − | 5337.17i | 0.407752 | − | 0.283911i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9594.98 | + | 16619.0i | 0.508247 | + | 0.880310i | 0.999954 | + | 0.00954922i | \(0.00303966\pi\) |
−0.491707 | + | 0.870761i | \(0.663627\pi\) | |||||||
\(710\) | 11306.8 | − | 19583.9i | 0.597657 | − | 1.03517i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2522.75 | + | 4369.54i | 0.132787 | + | 0.229993i | ||||
\(713\) | 9146.43 | 0.480416 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8585.94 | 0.449085 | ||||||||
\(716\) | −6323.27 | − | 10952.2i | −0.330044 | − | 0.571653i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7381.62 | + | 12785.3i | −0.383677 | + | 0.664547i | ||||
\(719\) | −5469.47 | − | 9473.40i | −0.283695 | − | 0.491375i | 0.688597 | − | 0.725145i | \(-0.258227\pi\) |
−0.972292 | + | 0.233770i | \(0.924894\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 250.889 | + | 2957.56i | 0.0129592 | + | 0.152767i | ||||
\(722\) | 7405.13 | 0.381704 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6608.93 | − | 11447.0i | 0.339253 | − | 0.587603i | ||||
\(725\) | 31.0691 | − | 53.8132i | 0.00159155 | − | 0.00275665i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24352.3 | −1.24233 | −0.621166 | − | 0.783679i | \(-0.713341\pi\) | ||||
−0.621166 | + | 0.783679i | \(0.713341\pi\) | |||||||
\(728\) | −5302.20 | − | 2489.51i | −0.269935 | − | 0.126741i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12842.9 | − | 22244.5i | −0.651146 | − | 1.12782i | ||||
\(731\) | −1106.92 | + | 1917.23i | −0.0560065 | + | 0.0970061i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 993.651 | + | 1721.05i | 0.0500700 | + | 0.0867239i | 0.889974 | − | 0.456011i | \(-0.150722\pi\) |
−0.839904 | + | 0.542735i | \(0.817389\pi\) | |||||||
\(734\) | 4881.85 | 0.245494 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1311.53 | −0.0656842 | ||||||||
\(737\) | −1658.04 | − | 2871.82i | −0.0828695 | − | 0.143534i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6181.23 | + | 10706.2i | −0.307687 | + | 0.532929i | −0.977856 | − | 0.209280i | \(-0.932888\pi\) |
0.670169 | + | 0.742208i | \(0.266221\pi\) | |||||||
\(740\) | 609.637 | + | 1055.92i | 0.0302848 | + | 0.0524547i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11722.4 | − | 5503.95i | −0.579976 | − | 0.272313i | ||||
\(743\) | −7775.46 | −0.383922 | −0.191961 | − | 0.981403i | \(-0.561485\pi\) | ||||
−0.191961 | + | 0.981403i | \(0.561485\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17186.5 | + | 29767.9i | −0.845188 | + | 1.46391i | ||||
\(746\) | −11876.1 | + | 20570.0i | −0.582861 | + | 1.00954i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2781.59 | −0.135969 | ||||||||
\(749\) | −3081.73 | − | 36328.3i | −0.150339 | − | 1.77224i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2550.98 | − | 4418.42i | −0.123950 | − | 0.214688i | 0.797372 | − | 0.603488i | \(-0.206223\pi\) |
−0.921322 | + | 0.388800i | \(0.872890\pi\) | |||||||
\(752\) | −3700.16 | + | 6408.86i | −0.179429 | + | 0.310781i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7088.92 | + | 12278.4i | 0.342392 | + | 0.593040i | ||||
\(755\) | −30510.6 | −1.47072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10003.6 | 0.480302 | 0.240151 | − | 0.970736i | \(-0.422803\pi\) | ||||
0.240151 | + | 0.970736i | \(0.422803\pi\) | |||||||
\(758\) | −4202.37 | − | 7278.71i | −0.201368 | − | 0.348779i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2516.02 | + | 4357.88i | −0.120086 | + | 0.207996i | ||||
\(761\) | −18874.3 | − | 32691.2i | −0.899070 | − | 1.55724i | −0.828685 | − | 0.559715i | \(-0.810911\pi\) |
−0.0703850 | − | 0.997520i | \(-0.522423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17562.7 | − | 12228.6i | 0.833307 | − | 0.580217i | ||||
\(764\) | −8307.03 | −0.393374 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14096.8 | − | 24416.4i | 0.664933 | − | 1.15170i | ||||
\(767\) | −4821.84 | + | 8351.67i | −0.226997 | + | 0.393170i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4279.68 | 0.200688 | 0.100344 | − | 0.994953i | \(-0.468006\pi\) | ||||
0.100344 | + | 0.994953i | \(0.468006\pi\) | |||||||
\(770\) | 679.951 | + | 8015.46i | 0.0318230 | + | 0.375139i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5224.48 | − | 9049.07i | −0.243566 | − | 0.421869i | ||||
\(773\) | 4215.77 | − | 7301.93i | 0.196159 | − | 0.339757i | −0.751121 | − | 0.660165i | \(-0.770487\pi\) |
0.947280 | + | 0.320408i | \(0.103820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.6680 | − | 66.9749i | −0.00179225 | − | 0.00310427i | ||||
\(776\) | −10642.6 | −0.492329 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22674.6 | 1.04489 | ||||||||
\(779\) | −2811.80 | − | 4870.18i | −0.129324 | − | 0.223995i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9795.02 | − | 16965.5i | 0.448775 | − | 0.777301i | ||||
\(782\) | −1469.29 | − | 2544.89i | −0.0671890 | − | 0.116375i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1904.20 | − | 5147.05i | 0.0867438 | − | 0.234469i | ||||
\(785\) | −14252.1 | −0.647998 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5126.16 | + | 8878.78i | −0.232183 | + | 0.402153i | −0.958450 | − | 0.285260i | \(-0.907920\pi\) |
0.726267 | + | 0.687412i | \(0.241253\pi\) | |||||||
\(788\) | 6837.24 | − | 11842.4i | 0.309095 | − | 0.535368i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15261.2 | 0.687304 | ||||||||
\(791\) | −24160.9 | − | 11344.2i | −1.08605 | − | 0.509927i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1287.40 | + | 2229.85i | 0.0576508 | + | 0.0998540i | ||||
\(794\) | 987.371 | − | 1710.18i | 0.0441316 | − | 0.0764381i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7248.31 | + | 12554.4i | 0.322751 | + | 0.559021i | ||||
\(797\) | 28639.0 | 1.27283 | 0.636415 | − | 0.771347i | \(-0.280417\pi\) | ||||
0.636415 | + | 0.771347i | \(0.280417\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16581.0 | −0.734159 | ||||||||
\(800\) | 5.54469 | + | 9.60369i | 0.000245043 | + | 0.000424427i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8493.58 | − | 14711.3i | 0.373964 | − | 0.647724i | ||||
\(803\) | −11125.7 | − | 19270.3i | −0.488939 | − | 0.846868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6974.22 | + | 4856.02i | −0.305353 | + | 0.212612i | ||||
\(806\) | 17645.5 | 0.771136 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2017.32 | − | 3494.09i | 0.0878328 | − | 0.152131i | ||||
\(809\) | −8194.17 | + | 14192.7i | −0.356108 | + | 0.616797i | −0.987307 | − | 0.158824i | \(-0.949230\pi\) |
0.631199 | + | 0.775621i | \(0.282563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31757.9 | 1.37506 | 0.687529 | − | 0.726157i | \(-0.258695\pi\) | ||||
0.687529 | + | 0.726157i | \(0.258695\pi\) | |||||||
\(812\) | −10901.2 | + | 7590.28i | −0.471128 | + | 0.328038i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 528.126 | + | 914.741i | 0.0227405 | + | 0.0393878i | ||||
\(815\) | −1578.73 | + | 2734.45i | −0.0678535 | + | 0.117526i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1734.73 | + | 3004.64i | 0.0742846 | + | 0.128665i | ||||
\(818\) | −18531.2 | −0.792089 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4482.63 | −0.190903 | ||||||||
\(821\) | −6783.08 | − | 11748.6i | −0.288345 | − | 0.499428i | 0.685070 | − | 0.728477i | \(-0.259772\pi\) |
−0.973415 | + | 0.229049i | \(0.926438\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10783.6 | + | 18677.7i | −0.456734 | + | 0.791086i | −0.998786 | − | 0.0492588i | \(-0.984314\pi\) |
0.542052 | + | 0.840345i | \(0.317647\pi\) | |||||||
\(824\) | 641.066 | + | 1110.36i | 0.0271027 | + | 0.0469432i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8178.61 | − | 3840.06i | −0.344516 | − | 0.161759i | ||||
\(827\) | 45594.6 | 1.91715 | 0.958574 | − | 0.284845i | \(-0.0919421\pi\) | ||||
0.958574 | + | 0.284845i | \(0.0919421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7067.31 | − | 12240.9i | 0.296089 | − | 0.512841i | −0.679149 | − | 0.734001i | \(-0.737651\pi\) |
0.975238 | + | 0.221160i | \(0.0709842\pi\) | |||||||
\(830\) | 10172.6 | − | 17619.5i | 0.425418 | − | 0.736846i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2530.23 | −0.105433 | ||||||||
\(833\) | 12120.6 | − | 2071.29i | 0.504146 | − | 0.0861534i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23281.8 | + | 40325.3i | 0.964911 | + | 1.67127i | ||||
\(836\) | −2179.62 | + | 3775.21i | −0.0901718 | + | 0.156182i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4398.11 | − | 7617.75i | −0.181301 | − | 0.314023i | ||||
\(839\) | 21256.2 | 0.874666 | 0.437333 | − | 0.899300i | \(-0.355923\pi\) | ||||
0.437333 | + | 0.899300i | \(0.355923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7762.52 | 0.318280 | ||||||||
\(842\) | −9335.15 | − | 16169.0i | −0.382079 | − | 0.661780i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8174.77 | + | 14159.1i | −0.333397 | + | 0.577461i | ||||
\(845\) | −3549.07 | − | 6147.17i | −0.144487 | − | 0.250259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1494.58 | − | 17618.5i | −0.0606308 | − | 0.714733i | ||||
\(848\) | −5593.97 | −0.226530 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.4233 | + | 21.5178i | −0.000501314 | + | 0.000868301i | ||||
\(851\) | −557.934 | + | 966.371i | −0.0224744 | + | 0.0389269i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42560.6 | −1.70838 | −0.854189 | − | 0.519962i | \(-0.825946\pi\) | ||||
−0.854189 | + | 0.519962i | \(0.825946\pi\) | |||||||
\(854\) | −1979.74 | + | 1378.45i | −0.0793269 | + | 0.0552338i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7874.36 | − | 13638.8i | −0.314416 | − | 0.544585i | ||||
\(857\) | −10487.2 | + | 18164.4i | −0.418013 | + | 0.724019i | −0.995740 | − | 0.0922108i | \(-0.970607\pi\) |
0.577727 | + | 0.816230i | \(0.303940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21779.9 | − | 37723.9i | −0.865099 | − | 1.49840i | −0.866948 | − | 0.498398i | \(-0.833922\pi\) |
0.00184898 | − | 0.999998i | \(-0.499411\pi\) | |||||||
\(860\) | 2765.54 | 0.109656 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 555.504 | 0.0219496 | ||||||||
\(863\) | 18441.1 | + | 31941.0i | 0.727397 | + | 1.25989i | 0.957980 | + | 0.286836i | \(0.0926036\pi\) |
−0.230582 | + | 0.973053i | \(0.574063\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1324.04 | − | 2293.30i | 0.0520447 | − | 0.0901440i | ||||
\(866\) | 706.915 | + | 1224.41i | 0.0277390 | + | 0.0480453i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1397.41 | + | 16473.0i | 0.0546441 | + | 0.644161i | ||||
\(869\) | 13220.7 | 0.516091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3379.28 | − | 5853.08i | 0.131461 | − | 0.227697i | ||||
\(872\) | 4622.11 | − | 8005.73i | 0.179500 | − | 0.310904i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4605.28 | −0.178233 | ||||||||
\(875\) | −23396.3 | − | 10985.1i | −0.903930 | − | 0.424417i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13395.6 | + | 23201.9i | 0.515778 | + | 0.893354i | 0.999832 | + | 0.0183162i | \(0.00583056\pi\) |
−0.484054 | + | 0.875038i | \(0.660836\pi\) | |||||||
\(878\) | 1420.88 | − | 2461.04i | 0.0546154 | − | 0.0945967i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1737.39 | + | 3009.25i | 0.0665540 | + | 0.115275i | ||||
\(881\) | −39675.6 | −1.51726 | −0.758630 | − | 0.651522i | \(-0.774131\pi\) | ||||
−0.758630 | + | 0.651522i | \(0.774131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33838.4 | 1.28964 | 0.644820 | − | 0.764335i | \(-0.276932\pi\) | ||||
0.644820 | + | 0.764335i | \(0.276932\pi\) | |||||||
\(884\) | −2834.59 | − | 4909.65i | −0.107848 | − | 0.186798i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12059.3 | + | 20887.3i | −0.457268 | + | 0.792011i | ||||
\(887\) | 19071.6 | + | 33033.0i | 0.721942 | + | 1.25044i | 0.960220 | + | 0.279243i | \(0.0900836\pi\) |
−0.238278 | + | 0.971197i | \(0.576583\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16587.8 | + | 7788.36i | 0.625799 | + | 0.293828i | ||||
\(890\) | 14122.2 | 0.531883 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6787.01 | − | 11755.4i | 0.254760 | − | 0.441257i | ||||
\(893\) | −12992.7 | + | 22504.0i | −0.486879 | + | 0.843299i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35397.1 | −1.32201 | ||||||||
\(896\) | −200.378 | − | 2362.11i | −0.00747115 | − | 0.0880720i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1519.39 | + | 2631.66i | 0.0564618 | + | 0.0977947i | ||||
\(899\) | 20007.6 | − | 34654.2i | 0.742258 | − | 1.28563i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6266.86 | − | 10854.5i | −0.231720 | − | 0.401350i | ||||
\(902\) | −3883.28 | −0.143347 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11529.7 | −0.424194 | ||||||||
\(905\) | −18498.1 | − | 32039.7i | −0.679446 | − | 1.17683i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13008.0 | − | 22530.5i | 0.476212 | − | 0.824823i | −0.523417 | − | 0.852077i | \(-0.675343\pi\) |
0.999629 | + | 0.0272538i | \(0.00867624\pi\) | |||||||
\(908\) | 5107.94 | + | 8847.21i | 0.186688 | + | 0.323354i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13454.8 | + | 9368.34i | −0.490135 | + | 0.341272i | ||||
\(911\) | −37680.4 | −1.37037 | −0.685185 | − | 0.728369i | \(-0.740279\pi\) | ||||
−0.685185 | + | 0.728369i | \(0.740279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8812.50 | − | 15263.7i | 0.319443 | − | 0.553291i | ||||
\(914\) | −5449.60 | + | 9438.98i | −0.197217 | + | 0.341591i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2810.77 | −0.101387 | ||||||||
\(917\) | −243.826 | − | 2874.29i | −0.00878064 | − | 0.103509i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5999.92 | + | 10392.2i | 0.215364 | + | 0.373021i | 0.953385 | − | 0.301757i | \(-0.0975730\pi\) |
−0.738021 | + | 0.674777i | \(0.764240\pi\) | |||||||
\(920\) | −1835.46 | + | 3179.10i | −0.0657752 | + | 0.113926i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9435.17 | + | 16342.2i | 0.337018 | + | 0.583733i | ||||
\(923\) | 39926.6 | 1.42384 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.43502 | 0.000335375 | ||||||||
\(926\) | −17319.2 | − | 29997.8i | −0.614627 | − | 1.06457i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2868.94 | + | 4969.14i | −0.101484 | + | 0.175776i | ||||
\(929\) | −5321.14 | − | 9216.49i | −0.187924 | − | 0.325493i | 0.756634 | − | 0.653838i | \(-0.226842\pi\) |
−0.944558 | + | 0.328345i | \(0.893509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6686.38 | − | 18073.3i | 0.235378 | − | 0.636228i | ||||
\(932\) | 1644.59 | 0.0578006 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6672.93 | + | 11557.9i | −0.233774 | + | 0.404909i | ||||
\(935\) | −3892.77 | + | 6742.47i | −0.136157 | + | 0.235832i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29565.1 | 1.03079 | 0.515395 | − | 0.856952i | \(-0.327645\pi\) | ||||
0.515395 | + | 0.856952i | \(0.327645\pi\) | |||||||
\(938\) | 5731.79 | + | 2691.22i | 0.199520 | + | 0.0936795i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10356.6 | + | 17938.1i | 0.359356 | + | 0.622422i | ||||
\(941\) | −20553.3 | + | 35599.3i | −0.712028 | + | 1.23327i | 0.252067 | + | 0.967710i | \(0.418890\pi\) |
−0.964095 | + | 0.265558i | \(0.914444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2051.23 | − | 3552.83i | −0.0708348 | − | 0.122689i | ||||
\(944\) | −3902.86 | −0.134563 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2395.77 | 0.0823397 | ||||||||
\(947\) | −10606.7 | − | 18371.4i | −0.363962 | − | 0.630401i | 0.624647 | − | 0.780907i | \(-0.285243\pi\) |
−0.988609 | + | 0.150507i | \(0.951910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22675.4 | − | 39275.0i | 0.775634 | − | 1.34344i | ||||
\(950\) | 19.4695 | + | 33.7222i | 0.000664921 | + | 0.00115168i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4358.95 | − | 3035.06i | 0.148398 | − | 0.103327i | ||||
\(953\) | 36533.1 | 1.24179 | 0.620894 | − | 0.783894i | \(-0.286770\pi\) | ||||
0.620894 | + | 0.783894i | \(0.286770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11625.5 | + | 20136.0i | −0.393919 | + | 0.682288i | ||||
\(956\) | 357.134 | − | 618.574i | 0.0120822 | − | 0.0209269i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30994.8 | 1.04530 | ||||||||
\(959\) | 14935.5 | − | 10399.3i | 0.502911 | − | 0.350168i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10005.6 | − | 17330.1i | −0.335858 | − | 0.581724i | ||||
\(962\) | −1076.38 | + | 1864.34i | −0.0360747 | + | 0.0624832i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8123.81 | + | 14070.9i | 0.271421 | + | 0.470116i | ||||
\(965\) | −29246.2 | −0.975615 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2657.34 | −0.0883706 | −0.0441853 | − | 0.999023i | \(-0.514069\pi\) | ||||
−0.0441853 | + | 0.999023i | \(0.514069\pi\) | |||||||
\(968\) | −3818.90 | − | 6614.54i | −0.126802 | − | 0.219627i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14894.1 | + | 25797.3i | −0.493011 | + | 0.853919i | ||||
\(971\) | 17188.4 | + | 29771.2i | 0.568076 | + | 0.983937i | 0.996756 | + | 0.0804803i | \(0.0256454\pi\) |
−0.428680 | + | 0.903456i | \(0.641021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37430.3 | + | 17574.5i | 1.23326 | + | 0.579046i | ||||
\(974\) | 7451.52 | 0.245136 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −521.021 | + | 902.435i | −0.0170876 | + | 0.0295966i | ||||
\(977\) | 26246.5 | − | 45460.2i | 0.859466 | − | 1.48864i | −0.0129729 | − | 0.999916i | \(-0.504130\pi\) |
0.872439 | − | 0.488723i | \(-0.162537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12234.0 | 0.399386 | ||||||||
\(980\) | −9811.41 | − | 11818.9i | −0.319810 | − | 0.385246i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18496.7 | − | 32037.2i | −0.601072 | − | 1.04109i | ||||
\(983\) | −14154.9 | + | 24517.0i | −0.459279 | + | 0.795495i | −0.998923 | − | 0.0463988i | \(-0.985226\pi\) |
0.539644 | + | 0.841893i | \(0.318559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19137.1 | − | 33146.5i | −0.619046 | − | 1.07222i | ||||
\(986\) | −12856.2 | −0.415237 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8884.60 | −0.286090 | ||||||||
\(989\) | 1265.50 | + | 2191.91i | 0.0406881 | + | 0.0704738i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8153.36 | − | 14122.0i | 0.261352 | − | 0.452675i | −0.705249 | − | 0.708959i | \(-0.749165\pi\) |
0.966601 | + | 0.256284i | \(0.0824983\pi\) | |||||||
\(992\) | 3570.62 | + | 6184.50i | 0.114282 | + | 0.197942i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3161.93 | + | 37273.8i | 0.100896 | + | 1.18939i | ||||
\(995\) | 40575.4 | 1.29279 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20310.9 | − | 35179.6i | 0.645190 | − | 1.11750i | −0.339068 | − | 0.940762i | \(-0.610112\pi\) |
0.984258 | − | 0.176739i | \(-0.0565550\pi\) | |||||||
\(998\) | −3703.17 | + | 6414.08i | −0.117457 | + | 0.203441i | ||||
\(999\) | 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 | 378.4.g.f.109.3 | yes | 8 | |
3.2 | odd | 2 | 378.4.g.c.109.2 | ✓ | 8 | ||
7.2 | even | 3 | inner | 378.4.g.f.163.3 | yes | 8 | |
21.2 | odd | 6 | 378.4.g.c.163.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.g.c.109.2 | ✓ | 8 | 3.2 | odd | 2 | ||
378.4.g.c.163.2 | yes | 8 | 21.2 | odd | 6 | ||
378.4.g.f.109.3 | yes | 8 | 1.1 | even | 1 | trivial | |
378.4.g.f.163.3 | yes | 8 | 7.2 | even | 3 | inner |