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: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.4.e.i.136.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.176777 | + | 0.306186i | 0.940775 | − | 0.339032i | \(-0.110100\pi\) |
−0.763998 | + | 0.645219i | \(0.776766\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.50000 | − | 6.06218i | 0.437500 | − | 0.757772i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0000 | + | 20.7846i | 0.647939 | + | 1.12226i | 0.983614 | + | 0.180286i | \(0.0577022\pi\) |
−0.335675 | + | 0.941978i | \(0.608964\pi\) | |||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | 0.158114 | ||||||||
\(11\) | 26.0000 | + | 45.0333i | 0.712663 | + | 1.23437i | 0.963854 | + | 0.266431i | \(0.0858445\pi\) |
−0.251191 | + | 0.967938i | \(0.580822\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.0000 | + | 19.0526i | −0.234681 | + | 0.406479i | −0.959180 | − | 0.282797i | \(-0.908738\pi\) |
0.724499 | + | 0.689276i | \(0.242071\pi\) | |||||||
\(14\) | −12.0000 | + | 20.7846i | −0.229081 | + | 0.396780i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20.5000 | − | 35.5070i | −0.320312 | − | 0.554798i | ||||
\(17\) | 14.0000 | 0.199735 | 0.0998676 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998676 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.0000 | −0.241490 | −0.120745 | − | 0.992684i | \(-0.538528\pi\) | ||||
−0.120745 | + | 0.992684i | \(0.538528\pi\) | |||||||
\(20\) | −17.5000 | − | 30.3109i | −0.195656 | − | 0.338886i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −26.0000 | + | 45.0333i | −0.251964 | + | 0.436415i | ||||
\(23\) | −84.0000 | + | 145.492i | −0.761531 | + | 1.31901i | 0.180530 | + | 0.983569i | \(0.442219\pi\) |
−0.942061 | + | 0.335441i | \(0.891115\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −22.0000 | −0.165944 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 168.000 | 1.13389 | ||||||||
\(29\) | 115.000 | + | 199.186i | 0.736378 | + | 1.27544i | 0.954116 | + | 0.299437i | \(0.0967988\pi\) |
−0.217738 | + | 0.976007i | \(0.569868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 144.000 | − | 249.415i | 0.834296 | − | 1.44504i | −0.0603071 | − | 0.998180i | \(-0.519208\pi\) |
0.894603 | − | 0.446862i | \(-0.147459\pi\) | |||||||
\(32\) | 80.5000 | − | 139.430i | 0.444704 | − | 0.770250i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.00000 | + | 12.1244i | 0.0353085 | + | 0.0611562i | ||||
\(35\) | 120.000 | 0.579534 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.0000 | −0.151069 | −0.0755347 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755347 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(38\) | −10.0000 | − | 17.3205i | −0.0426898 | − | 0.0739410i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 37.5000 | − | 64.9519i | 0.148232 | − | 0.256745i | ||||
\(41\) | 61.0000 | − | 105.655i | 0.232356 | − | 0.402453i | −0.726145 | − | 0.687542i | \(-0.758690\pi\) |
0.958501 | + | 0.285089i | \(0.0920232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 94.0000 | + | 162.813i | 0.333369 | + | 0.577412i | 0.983170 | − | 0.182692i | \(-0.0584812\pi\) |
−0.649801 | + | 0.760104i | \(0.725148\pi\) | |||||||
\(44\) | 364.000 | 1.24716 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −168.000 | −0.538484 | ||||||||
\(47\) | 128.000 | + | 221.703i | 0.397249 | + | 0.688056i | 0.993385 | − | 0.114827i | \(-0.0366315\pi\) |
−0.596136 | + | 0.802883i | \(0.703298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −116.500 | + | 201.784i | −0.339650 | + | 0.588291i | ||||
\(50\) | 12.5000 | − | 21.6506i | 0.0353553 | − | 0.0612372i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 77.0000 | + | 133.368i | 0.205346 | + | 0.355669i | ||||
\(53\) | 338.000 | 0.875998 | 0.437999 | − | 0.898976i | \(-0.355687\pi\) | ||||
0.437999 | + | 0.898976i | \(0.355687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 260.000 | 0.637425 | ||||||||
\(56\) | 180.000 | + | 311.769i | 0.429527 | + | 0.743963i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −115.000 | + | 199.186i | −0.260349 | + | 0.450938i | ||||
\(59\) | 50.0000 | − | 86.6025i | 0.110330 | − | 0.191096i | −0.805574 | − | 0.592496i | \(-0.798143\pi\) |
0.915903 | + | 0.401399i | \(0.131476\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −371.000 | − | 642.591i | −0.778716 | − | 1.34878i | −0.932682 | − | 0.360700i | \(-0.882538\pi\) |
0.153966 | − | 0.988076i | \(-0.450795\pi\) | |||||||
\(62\) | 288.000 | 0.589936 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 55.0000 | + | 95.2628i | 0.104952 | + | 0.181783i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42.0000 | − | 72.7461i | 0.0765838 | − | 0.132647i | −0.825190 | − | 0.564855i | \(-0.808932\pi\) |
0.901774 | + | 0.432208i | \(0.142265\pi\) | |||||||
\(68\) | 49.0000 | − | 84.8705i | 0.0873842 | − | 0.151354i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 60.0000 | + | 103.923i | 0.102448 | + | 0.177445i | ||||
\(71\) | 328.000 | 0.548260 | 0.274130 | − | 0.961693i | \(-0.411610\pi\) | ||||
0.274130 | + | 0.961693i | \(0.411610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −38.0000 | −0.0609255 | −0.0304628 | − | 0.999536i | \(-0.509698\pi\) | ||||
−0.0304628 | + | 0.999536i | \(0.509698\pi\) | |||||||
\(74\) | −17.0000 | − | 29.4449i | −0.0267055 | − | 0.0462553i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −70.0000 | + | 121.244i | −0.105652 | + | 0.182995i | ||||
\(77\) | −624.000 | + | 1080.80i | −0.923525 | + | 1.59959i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 120.000 | + | 207.846i | 0.170899 | + | 0.296006i | 0.938735 | − | 0.344641i | \(-0.111999\pi\) |
−0.767835 | + | 0.640647i | \(0.778666\pi\) | |||||||
\(80\) | −205.000 | −0.286496 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 122.000 | 0.164301 | ||||||||
\(83\) | 606.000 | + | 1049.62i | 0.801411 | + | 1.38809i | 0.918687 | + | 0.394986i | \(0.129250\pi\) |
−0.117276 | + | 0.993099i | \(0.537416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.0000 | − | 60.6218i | 0.0446622 | − | 0.0773571i | ||||
\(86\) | −94.0000 | + | 162.813i | −0.117864 | + | 0.204146i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 390.000 | + | 675.500i | 0.472433 | + | 0.818279i | ||||
\(89\) | −330.000 | −0.393033 | −0.196516 | − | 0.980501i | \(-0.562963\pi\) | ||||
−0.196516 | + | 0.980501i | \(0.562963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −528.000 | −0.608236 | ||||||||
\(92\) | 588.000 | + | 1018.45i | 0.666340 | + | 1.15413i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −128.000 | + | 221.703i | −0.140449 | + | 0.243265i | ||||
\(95\) | −50.0000 | + | 86.6025i | −0.0539989 | + | 0.0935288i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −433.000 | − | 749.978i | −0.453242 | − | 0.785038i | 0.545343 | − | 0.838213i | \(-0.316399\pi\) |
−0.998585 | + | 0.0531745i | \(0.983066\pi\) | |||||||
\(98\) | −233.000 | −0.240169 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −175.000 | −0.175000 | ||||||||
\(101\) | −609.000 | − | 1054.82i | −0.599978 | − | 1.03919i | −0.992824 | − | 0.119588i | \(-0.961843\pi\) |
0.392846 | − | 0.919604i | \(-0.371491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 44.0000 | − | 76.2102i | 0.0420917 | − | 0.0729050i | −0.844212 | − | 0.536009i | \(-0.819931\pi\) |
0.886304 | + | 0.463104i | \(0.153264\pi\) | |||||||
\(104\) | −165.000 | + | 285.788i | −0.155573 | + | 0.269460i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 169.000 | + | 292.717i | 0.154856 | + | 0.268218i | ||||
\(107\) | −36.0000 | −0.0325257 | −0.0162629 | − | 0.999868i | \(-0.505177\pi\) | ||||
−0.0162629 | + | 0.999868i | \(0.505177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −970.000 | −0.852378 | −0.426189 | − | 0.904634i | \(-0.640144\pi\) | ||||
−0.426189 | + | 0.904634i | \(0.640144\pi\) | |||||||
\(110\) | 130.000 | + | 225.167i | 0.112682 | + | 0.195171i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 492.000 | − | 852.169i | 0.415086 | − | 0.718950i | ||||
\(113\) | 521.000 | − | 902.398i | 0.433731 | − | 0.751243i | −0.563460 | − | 0.826143i | \(-0.690530\pi\) |
0.997191 | + | 0.0748996i | \(0.0238636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 420.000 | + | 727.461i | 0.340567 | + | 0.589879i | ||||
\(116\) | 1610.00 | 1.28866 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 100.000 | 0.0780148 | ||||||||
\(119\) | 168.000 | + | 290.985i | 0.129416 | + | 0.224156i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −686.500 | + | 1189.05i | −0.515778 | + | 0.893353i | ||||
\(122\) | 371.000 | − | 642.591i | 0.275318 | − | 0.476864i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1008.00 | − | 1745.91i | −0.730009 | − | 1.26441i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1936.00 | 1.35269 | 0.676347 | − | 0.736583i | \(-0.263562\pi\) | ||||
0.676347 | + | 0.736583i | \(0.263562\pi\) | |||||||
\(128\) | −727.500 | − | 1260.07i | −0.502363 | − | 0.870119i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −55.0000 | + | 95.2628i | −0.0371063 | + | 0.0642700i | ||||
\(131\) | 366.000 | − | 633.931i | 0.244104 | − | 0.422800i | −0.717776 | − | 0.696274i | \(-0.754840\pi\) |
0.961879 | + | 0.273475i | \(0.0881730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −240.000 | − | 415.692i | −0.156471 | − | 0.271016i | ||||
\(134\) | 84.0000 | 0.0541529 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 210.000 | 0.132407 | ||||||||
\(137\) | −1107.00 | − | 1917.38i | −0.690346 | − | 1.19571i | −0.971725 | − | 0.236117i | \(-0.924125\pi\) |
0.281379 | − | 0.959597i | \(-0.409208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | + | 17.3205i | −0.00610208 | + | 0.0105691i | −0.869060 | − | 0.494706i | \(-0.835276\pi\) |
0.862958 | + | 0.505275i | \(0.168609\pi\) | |||||||
\(140\) | 420.000 | − | 727.461i | 0.253546 | − | 0.439155i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 164.000 | + | 284.056i | 0.0969195 | + | 0.167870i | ||||
\(143\) | −1144.00 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1150.00 | 0.658637 | ||||||||
\(146\) | −19.0000 | − | 32.9090i | −0.0107702 | − | 0.0186546i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −119.000 | + | 206.114i | −0.0660928 | + | 0.114476i | ||||
\(149\) | −665.000 | + | 1151.81i | −0.365630 | + | 0.633290i | −0.988877 | − | 0.148735i | \(-0.952480\pi\) |
0.623247 | + | 0.782025i | \(0.285813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 604.000 | + | 1046.16i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | −300.000 | −0.160087 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1248.00 | −0.653031 | ||||||||
\(155\) | −720.000 | − | 1247.08i | −0.373108 | − | 0.646243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1757.00 | − | 3043.21i | 0.893146 | − | 1.54697i | 0.0570627 | − | 0.998371i | \(-0.481827\pi\) |
0.836083 | − | 0.548603i | \(-0.184840\pi\) | |||||||
\(158\) | −120.000 | + | 207.846i | −0.0604221 | + | 0.104654i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −402.500 | − | 697.150i | −0.198878 | − | 0.344466i | ||||
\(161\) | −4032.00 | −1.97370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2068.00 | −0.993732 | −0.496866 | − | 0.867827i | \(-0.665516\pi\) | ||||
−0.496866 | + | 0.867827i | \(0.665516\pi\) | |||||||
\(164\) | −427.000 | − | 739.586i | −0.203312 | − | 0.352146i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −606.000 | + | 1049.62i | −0.283342 | + | 0.490762i | ||||
\(167\) | −12.0000 | + | 20.7846i | −0.00556041 | + | 0.00963091i | −0.868792 | − | 0.495177i | \(-0.835103\pi\) |
0.863232 | + | 0.504808i | \(0.168437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 856.500 | + | 1483.50i | 0.389850 | + | 0.675240i | ||||
\(170\) | 70.0000 | 0.0315809 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1316.00 | 0.583396 | ||||||||
\(173\) | −309.000 | − | 535.204i | −0.135797 | − | 0.235207i | 0.790105 | − | 0.612972i | \(-0.210026\pi\) |
−0.925902 | + | 0.377765i | \(0.876693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 300.000 | − | 519.615i | 0.129588 | − | 0.224453i | ||||
\(176\) | 1066.00 | − | 1846.37i | 0.456550 | − | 0.790768i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −165.000 | − | 285.788i | −0.0694791 | − | 0.120341i | ||||
\(179\) | −3340.00 | −1.39466 | −0.697328 | − | 0.716752i | \(-0.745628\pi\) | ||||
−0.697328 | + | 0.716752i | \(0.745628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −178.000 | −0.0730974 | −0.0365487 | − | 0.999332i | \(-0.511636\pi\) | ||||
−0.0365487 | + | 0.999332i | \(0.511636\pi\) | |||||||
\(182\) | −264.000 | − | 457.261i | −0.107522 | − | 0.186233i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1260.00 | + | 2182.38i | −0.504828 | + | 0.874389i | ||||
\(185\) | −85.0000 | + | 147.224i | −0.0337801 | + | 0.0585089i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 364.000 | + | 630.466i | 0.142344 | + | 0.246547i | ||||
\(188\) | 1792.00 | 0.695186 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −100.000 | −0.0381830 | ||||||||
\(191\) | −944.000 | − | 1635.06i | −0.357620 | − | 0.619416i | 0.629943 | − | 0.776642i | \(-0.283078\pi\) |
−0.987563 | + | 0.157225i | \(0.949745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −961.000 | + | 1664.50i | −0.358416 | + | 0.620795i | −0.987696 | − | 0.156384i | \(-0.950016\pi\) |
0.629280 | + | 0.777178i | \(0.283350\pi\) | |||||||
\(194\) | 433.000 | − | 749.978i | 0.160245 | − | 0.277553i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 815.500 | + | 1412.49i | 0.297194 | + | 0.514755i | ||||
\(197\) | −2526.00 | −0.913554 | −0.456777 | − | 0.889581i | \(-0.650996\pi\) | ||||
−0.456777 | + | 0.889581i | \(0.650996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1160.00 | −0.413217 | −0.206609 | − | 0.978424i | \(-0.566243\pi\) | ||||
−0.206609 | + | 0.978424i | \(0.566243\pi\) | |||||||
\(200\) | −187.500 | − | 324.760i | −0.0662913 | − | 0.114820i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 609.000 | − | 1054.82i | 0.212124 | − | 0.367410i | ||||
\(203\) | −2760.00 | + | 4780.46i | −0.954256 | + | 1.65282i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −305.000 | − | 528.275i | −0.103913 | − | 0.179982i | ||||
\(206\) | 88.0000 | 0.0297634 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 902.000 | 0.300685 | ||||||||
\(209\) | −520.000 | − | 900.666i | −0.172101 | − | 0.298088i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2234.00 | − | 3869.40i | 0.728886 | − | 1.26247i | −0.228469 | − | 0.973551i | \(-0.573372\pi\) |
0.957354 | − | 0.288916i | \(-0.0932948\pi\) | |||||||
\(212\) | 1183.00 | − | 2049.02i | 0.383249 | − | 0.663807i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0000 | − | 31.1769i | −0.00574979 | − | 0.00995893i | ||||
\(215\) | 940.000 | 0.298174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6912.00 | 2.16229 | ||||||||
\(218\) | −485.000 | − | 840.045i | −0.150680 | − | 0.260986i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 910.000 | − | 1576.17i | 0.278874 | − | 0.483023i | ||||
\(221\) | −154.000 | + | 266.736i | −0.0468740 | + | 0.0811882i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3016.00 | − | 5223.87i | −0.905678 | − | 1.56868i | −0.820004 | − | 0.572358i | \(-0.806029\pi\) |
−0.0856746 | − | 0.996323i | \(-0.527305\pi\) | |||||||
\(224\) | 3864.00 | 1.15256 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1042.00 | 0.306694 | ||||||||
\(227\) | 1318.00 | + | 2282.84i | 0.385369 | + | 0.667478i | 0.991820 | − | 0.127642i | \(-0.0407409\pi\) |
−0.606451 | + | 0.795121i | \(0.707408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2415.00 | + | 4182.90i | −0.696889 | + | 1.20705i | 0.272650 | + | 0.962113i | \(0.412100\pi\) |
−0.969540 | + | 0.244935i | \(0.921233\pi\) | |||||||
\(230\) | −420.000 | + | 727.461i | −0.120409 | + | 0.208554i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1725.00 | + | 2987.79i | 0.488154 | + | 0.845508i | ||||
\(233\) | −2682.00 | −0.754093 | −0.377046 | − | 0.926194i | \(-0.623060\pi\) | ||||
−0.377046 | + | 0.926194i | \(0.623060\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1280.00 | 0.355311 | ||||||||
\(236\) | −350.000 | − | 606.218i | −0.0965384 | − | 0.167209i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −168.000 | + | 290.985i | −0.0457556 | + | 0.0792509i | ||||
\(239\) | 1160.00 | − | 2009.18i | 0.313950 | − | 0.543778i | −0.665263 | − | 0.746609i | \(-0.731681\pi\) |
0.979214 | + | 0.202831i | \(0.0650141\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1001.00 | − | 1733.78i | −0.267552 | − | 0.463414i | 0.700677 | − | 0.713479i | \(-0.252881\pi\) |
−0.968229 | + | 0.250065i | \(0.919548\pi\) | |||||||
\(242\) | −1373.00 | −0.364710 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5194.00 | −1.36275 | ||||||||
\(245\) | 582.500 | + | 1008.92i | 0.151896 | + | 0.263092i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 220.000 | − | 381.051i | 0.0566731 | − | 0.0981608i | ||||
\(248\) | 2160.00 | − | 3741.23i | 0.553065 | − | 0.957937i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −62.5000 | − | 108.253i | −0.0158114 | − | 0.0273861i | ||||
\(251\) | −132.000 | −0.0331943 | −0.0165971 | − | 0.999862i | \(-0.505283\pi\) | ||||
−0.0165971 | + | 0.999862i | \(0.505283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8736.00 | −2.17086 | ||||||||
\(254\) | 968.000 | + | 1676.63i | 0.239125 | + | 0.414176i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 59.5000 | − | 103.057i | 0.0145264 | − | 0.0251604i | ||||
\(257\) | −3807.00 | + | 6593.92i | −0.924024 | + | 1.60046i | −0.130900 | + | 0.991396i | \(0.541787\pi\) |
−0.793124 | + | 0.609061i | \(0.791547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −408.000 | − | 706.677i | −0.0978837 | − | 0.169540i | ||||
\(260\) | 770.000 | 0.183667 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 732.000 | 0.172607 | ||||||||
\(263\) | −2444.00 | − | 4233.13i | −0.573017 | − | 0.992495i | −0.996254 | − | 0.0864757i | \(-0.972440\pi\) |
0.423237 | − | 0.906019i | \(-0.360894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 845.000 | − | 1463.58i | 0.195879 | − | 0.339272i | ||||
\(266\) | 240.000 | − | 415.692i | 0.0553208 | − | 0.0958185i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −294.000 | − | 509.223i | −0.0670109 | − | 0.116066i | ||||
\(269\) | −1270.00 | −0.287856 | −0.143928 | − | 0.989588i | \(-0.545973\pi\) | ||||
−0.143928 | + | 0.989588i | \(0.545973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1072.00 | 0.240293 | 0.120146 | − | 0.992756i | \(-0.461664\pi\) | ||||
0.120146 | + | 0.992756i | \(0.461664\pi\) | |||||||
\(272\) | −287.000 | − | 497.099i | −0.0639777 | − | 0.110813i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1107.00 | − | 1917.38i | 0.244074 | − | 0.422749i | ||||
\(275\) | 650.000 | − | 1125.83i | 0.142533 | − | 0.246874i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2697.00 | + | 4671.34i | 0.585007 | + | 1.01326i | 0.994875 | + | 0.101117i | \(0.0322417\pi\) |
−0.409867 | + | 0.912145i | \(0.634425\pi\) | |||||||
\(278\) | −20.0000 | −0.00431482 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1800.00 | 0.384181 | ||||||||
\(281\) | 1221.00 | + | 2114.83i | 0.259213 | + | 0.448969i | 0.966031 | − | 0.258425i | \(-0.0832036\pi\) |
−0.706819 | + | 0.707395i | \(0.749870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1386.00 | + | 2400.62i | −0.291128 | + | 0.504248i | −0.974077 | − | 0.226218i | \(-0.927364\pi\) |
0.682949 | + | 0.730466i | \(0.260697\pi\) | |||||||
\(284\) | 1148.00 | − | 1988.39i | 0.239864 | − | 0.415456i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −572.000 | − | 990.733i | −0.118262 | − | 0.204837i | ||||
\(287\) | 2928.00 | 0.602210 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 575.000 | + | 995.929i | 0.116432 | + | 0.201665i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −133.000 | + | 230.363i | −0.0266549 | + | 0.0461677i | ||||
\(293\) | 2271.00 | − | 3933.49i | 0.452810 | − | 0.784289i | −0.545750 | − | 0.837948i | \(-0.683755\pi\) |
0.998559 | + | 0.0536589i | \(0.0170884\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −250.000 | − | 433.013i | −0.0493409 | − | 0.0854609i | ||||
\(296\) | −510.000 | −0.100146 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1330.00 | −0.258540 | ||||||||
\(299\) | −1848.00 | − | 3200.83i | −0.357433 | − | 0.619093i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2256.00 | + | 3907.51i | −0.432006 | + | 0.748256i | ||||
\(302\) | −604.000 | + | 1046.16i | −0.115087 | + | 0.199337i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 410.000 | + | 710.141i | 0.0773523 | + | 0.133978i | ||||
\(305\) | −3710.00 | −0.696505 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5116.00 | 0.951093 | 0.475546 | − | 0.879691i | \(-0.342250\pi\) | ||||
0.475546 | + | 0.879691i | \(0.342250\pi\) | |||||||
\(308\) | 4368.00 | + | 7565.60i | 0.808084 | + | 1.39964i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 720.000 | − | 1247.08i | 0.131914 | − | 0.228481i | ||||
\(311\) | −1404.00 | + | 2431.80i | −0.255992 | + | 0.443391i | −0.965165 | − | 0.261644i | \(-0.915735\pi\) |
0.709172 | + | 0.705035i | \(0.249069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3659.00 | + | 6337.57i | 0.660763 | + | 1.14448i | 0.980415 | + | 0.196941i | \(0.0631006\pi\) |
−0.319652 | + | 0.947535i | \(0.603566\pi\) | |||||||
\(314\) | 3514.00 | 0.631549 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1680.00 | 0.299074 | ||||||||
\(317\) | 1123.00 | + | 1945.09i | 0.198971 | + | 0.344629i | 0.948195 | − | 0.317688i | \(-0.102907\pi\) |
−0.749224 | + | 0.662317i | \(0.769573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5980.00 | + | 10357.7i | −1.04958 | + | 1.81792i | ||||
\(320\) | −417.500 | + | 723.131i | −0.0729342 | + | 0.126326i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2016.00 | − | 3491.81i | −0.348905 | − | 0.604321i | ||||
\(323\) | −280.000 | −0.0482341 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 550.000 | 0.0938723 | ||||||||
\(326\) | −1034.00 | − | 1790.94i | −0.175669 | − | 0.304267i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 915.000 | − | 1584.83i | 0.154032 | − | 0.266791i | ||||
\(329\) | −3072.00 | + | 5320.86i | −0.514787 | + | 0.891637i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −666.000 | − | 1153.55i | −0.110594 | − | 0.191555i | 0.805416 | − | 0.592710i | \(-0.201942\pi\) |
−0.916010 | + | 0.401155i | \(0.868609\pi\) | |||||||
\(332\) | 8484.00 | 1.40247 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.0000 | −0.00393180 | ||||||||
\(335\) | −210.000 | − | 363.731i | −0.0342493 | − | 0.0593216i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5767.00 | − | 9988.74i | 0.932191 | − | 1.61460i | 0.152624 | − | 0.988284i | \(-0.451228\pi\) |
0.779567 | − | 0.626319i | \(-0.215439\pi\) | |||||||
\(338\) | −856.500 | + | 1483.50i | −0.137833 | + | 0.238733i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −245.000 | − | 424.352i | −0.0390794 | − | 0.0676875i | ||||
\(341\) | 14976.0 | 2.37829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2640.00 | 0.415588 | ||||||||
\(344\) | 1410.00 | + | 2442.19i | 0.220994 | + | 0.382774i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 309.000 | − | 535.204i | 0.0480114 | − | 0.0831582i | ||||
\(347\) | 5978.00 | − | 10354.2i | 0.924830 | − | 1.60185i | 0.132994 | − | 0.991117i | \(-0.457541\pi\) |
0.791835 | − | 0.610735i | \(-0.209126\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2435.00 | − | 4217.54i | −0.373474 | − | 0.646877i | 0.616623 | − | 0.787259i | \(-0.288500\pi\) |
−0.990097 | + | 0.140382i | \(0.955167\pi\) | |||||||
\(350\) | 600.000 | 0.0916324 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8372.00 | 1.26770 | ||||||||
\(353\) | 5361.00 | + | 9285.52i | 0.808321 | + | 1.40005i | 0.914026 | + | 0.405655i | \(0.132957\pi\) |
−0.105705 | + | 0.994397i | \(0.533710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 820.000 | − | 1420.28i | 0.122595 | − | 0.212340i | ||||
\(356\) | −1155.00 | + | 2000.52i | −0.171952 | + | 0.297829i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1670.00 | − | 2892.52i | −0.246543 | − | 0.427024i | ||||
\(359\) | −120.000 | −0.0176417 | −0.00882083 | − | 0.999961i | \(-0.502808\pi\) | ||||
−0.00882083 | + | 0.999961i | \(0.502808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6459.00 | −0.941682 | ||||||||
\(362\) | −89.0000 | − | 154.153i | −0.0129219 | − | 0.0223814i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1848.00 | + | 3200.83i | −0.266103 | + | 0.460904i | ||||
\(365\) | −95.0000 | + | 164.545i | −0.0136234 | + | 0.0235964i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1968.00 | − | 3408.68i | −0.279915 | − | 0.484827i | 0.691448 | − | 0.722426i | \(-0.256973\pi\) |
−0.971363 | + | 0.237599i | \(0.923640\pi\) | |||||||
\(368\) | 6888.00 | 0.975711 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −170.000 | −0.0238862 | ||||||||
\(371\) | 4056.00 | + | 7025.20i | 0.567593 | + | 0.983100i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1511.00 | + | 2617.13i | −0.209750 | + | 0.363297i | −0.951636 | − | 0.307229i | \(-0.900598\pi\) |
0.741886 | + | 0.670526i | \(0.233932\pi\) | |||||||
\(374\) | −364.000 | + | 630.466i | −0.0503262 | + | 0.0871675i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1920.00 | + | 3325.54i | 0.263342 | + | 0.456121i | ||||
\(377\) | −5060.00 | −0.691255 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13340.0 | −1.80799 | −0.903997 | − | 0.427539i | \(-0.859381\pi\) | ||||
−0.903997 | + | 0.427539i | \(0.859381\pi\) | |||||||
\(380\) | 350.000 | + | 606.218i | 0.0472490 | + | 0.0818377i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 944.000 | − | 1635.06i | 0.126438 | − | 0.218997i | ||||
\(383\) | −504.000 | + | 872.954i | −0.0672407 | + | 0.116464i | −0.897686 | − | 0.440636i | \(-0.854753\pi\) |
0.830445 | + | 0.557101i | \(0.188086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3120.00 | + | 5404.00i | 0.413013 | + | 0.715359i | ||||
\(386\) | −1922.00 | −0.253438 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6062.00 | −0.793174 | ||||||||
\(389\) | 4815.00 | + | 8339.82i | 0.627584 | + | 1.08701i | 0.988035 | + | 0.154229i | \(0.0492895\pi\) |
−0.360451 | + | 0.932778i | \(0.617377\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1176.00 | + | 2036.89i | −0.152105 | + | 0.263453i | ||||
\(392\) | −1747.50 | + | 3026.76i | −0.225158 | + | 0.389986i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1263.00 | − | 2187.58i | −0.161495 | − | 0.279718i | ||||
\(395\) | 1200.00 | 0.152857 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7126.00 | 0.900866 | 0.450433 | − | 0.892810i | \(-0.351270\pi\) | ||||
0.450433 | + | 0.892810i | \(0.351270\pi\) | |||||||
\(398\) | −580.000 | − | 1004.59i | −0.0730472 | − | 0.126521i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −512.500 | + | 887.676i | −0.0640625 | + | 0.110960i | ||||
\(401\) | −4359.00 | + | 7550.01i | −0.542838 | + | 0.940223i | 0.455901 | + | 0.890030i | \(0.349317\pi\) |
−0.998740 | + | 0.0501929i | \(0.984016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3168.00 | + | 5487.14i | 0.391586 | + | 0.678248i | ||||
\(404\) | −8526.00 | −1.04996 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5520.00 | −0.674761 | ||||||||
\(407\) | −884.000 | − | 1531.13i | −0.107662 | − | 0.186475i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5435.00 | − | 9413.70i | 0.657074 | − | 1.13809i | −0.324295 | − | 0.945956i | \(-0.605127\pi\) |
0.981369 | − | 0.192130i | \(-0.0615396\pi\) | |||||||
\(410\) | 305.000 | − | 528.275i | 0.0367387 | − | 0.0636333i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −308.000 | − | 533.472i | −0.0368303 | − | 0.0637919i | ||||
\(413\) | 2400.00 | 0.285947 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6060.00 | 0.716804 | ||||||||
\(416\) | 1771.00 | + | 3067.46i | 0.208727 | + | 0.361526i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 520.000 | − | 900.666i | 0.0608470 | − | 0.105390i | ||||
\(419\) | −4850.00 | + | 8400.45i | −0.565484 | + | 0.979448i | 0.431520 | + | 0.902103i | \(0.357977\pi\) |
−0.997004 | + | 0.0773445i | \(0.975356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −431.000 | − | 746.514i | −0.0498947 | − | 0.0864201i | 0.839999 | − | 0.542587i | \(-0.182555\pi\) |
−0.889894 | + | 0.456167i | \(0.849222\pi\) | |||||||
\(422\) | 4468.00 | 0.515400 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5070.00 | 0.580710 | ||||||||
\(425\) | −175.000 | − | 303.109i | −0.0199735 | − | 0.0345952i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8904.00 | − | 15422.2i | 1.00912 | − | 1.74785i | ||||
\(428\) | −126.000 | + | 218.238i | −0.0142300 | + | 0.0246471i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 470.000 | + | 814.064i | 0.0527103 | + | 0.0912969i | ||||
\(431\) | −15792.0 | −1.76490 | −0.882452 | − | 0.470402i | \(-0.844109\pi\) | ||||
−0.882452 | + | 0.470402i | \(0.844109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11602.0 | 1.28766 | 0.643830 | − | 0.765169i | \(-0.277345\pi\) | ||||
0.643830 | + | 0.765169i | \(0.277345\pi\) | |||||||
\(434\) | 3456.00 | + | 5985.97i | 0.382243 | + | 0.662064i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3395.00 | + | 5880.31i | −0.372915 | + | 0.645908i | ||||
\(437\) | 1680.00 | − | 2909.85i | 0.183902 | − | 0.318528i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 220.000 | + | 381.051i | 0.0239181 | + | 0.0414273i | 0.877737 | − | 0.479143i | \(-0.159053\pi\) |
−0.853819 | + | 0.520571i | \(0.825719\pi\) | |||||||
\(440\) | 3900.00 | 0.422557 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −308.000 | −0.0331449 | ||||||||
\(443\) | −5094.00 | − | 8823.07i | −0.546328 | − | 0.946268i | −0.998522 | − | 0.0543481i | \(-0.982692\pi\) |
0.452194 | − | 0.891920i | \(-0.350641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −825.000 | + | 1428.94i | −0.0878848 | + | 0.152221i | ||||
\(446\) | 3016.00 | − | 5223.87i | 0.320206 | − | 0.554613i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2004.00 | − | 3471.03i | −0.211340 | − | 0.366051i | ||||
\(449\) | 13310.0 | 1.39897 | 0.699485 | − | 0.714647i | \(-0.253413\pi\) | ||||
0.699485 | + | 0.714647i | \(0.253413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6344.00 | 0.662367 | ||||||||
\(452\) | −3647.00 | − | 6316.79i | −0.379514 | − | 0.657338i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1318.00 | + | 2282.84i | −0.136248 | + | 0.235989i | ||||
\(455\) | −1320.00 | + | 2286.31i | −0.136006 | + | 0.235569i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1613.00 | − | 2793.80i | −0.165105 | − | 0.285970i | 0.771588 | − | 0.636123i | \(-0.219463\pi\) |
−0.936693 | + | 0.350153i | \(0.886130\pi\) | |||||||
\(458\) | −4830.00 | −0.492775 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5880.00 | 0.595992 | ||||||||
\(461\) | 3291.00 | + | 5700.18i | 0.332488 | + | 0.575887i | 0.982999 | − | 0.183610i | \(-0.0587784\pi\) |
−0.650511 | + | 0.759497i | \(0.725445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7536.00 | + | 13052.7i | −0.756431 | + | 1.31018i | 0.188229 | + | 0.982125i | \(0.439725\pi\) |
−0.944660 | + | 0.328052i | \(0.893608\pi\) | |||||||
\(464\) | 4715.00 | − | 8166.62i | 0.471742 | − | 0.817081i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1341.00 | − | 2322.68i | −0.133306 | − | 0.230893i | ||||
\(467\) | −476.000 | −0.0471663 | −0.0235831 | − | 0.999722i | \(-0.507507\pi\) | ||||
−0.0235831 | + | 0.999722i | \(0.507507\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2016.00 | 0.198487 | ||||||||
\(470\) | 640.000 | + | 1108.51i | 0.0628106 | + | 0.108791i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 750.000 | − | 1299.04i | 0.0731389 | − | 0.126680i | ||||
\(473\) | −4888.00 | + | 8466.26i | −0.475160 | + | 0.823001i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 250.000 | + | 433.013i | 0.0241490 | + | 0.0418273i | ||||
\(476\) | 2352.00 | 0.226478 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2320.00 | 0.221997 | ||||||||
\(479\) | −9840.00 | − | 17043.4i | −0.938624 | − | 1.62575i | −0.768040 | − | 0.640402i | \(-0.778768\pi\) |
−0.170585 | − | 0.985343i | \(-0.554566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 374.000 | − | 647.787i | 0.0354531 | − | 0.0614065i | ||||
\(482\) | 1001.00 | − | 1733.78i | 0.0945940 | − | 0.163842i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4805.50 | + | 8323.37i | 0.451305 | + | 0.781684i | ||||
\(485\) | −4330.00 | −0.405392 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5944.00 | −0.553077 | −0.276538 | − | 0.961003i | \(-0.589187\pi\) | ||||
−0.276538 | + | 0.961003i | \(0.589187\pi\) | |||||||
\(488\) | −5565.00 | − | 9638.86i | −0.516221 | − | 0.894121i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −582.500 | + | 1008.92i | −0.0537034 | + | 0.0930170i | ||||
\(491\) | 5386.00 | − | 9328.83i | 0.495044 | − | 0.857442i | −0.504939 | − | 0.863155i | \(-0.668485\pi\) |
0.999984 | + | 0.00571287i | \(0.00181847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1610.00 | + | 2788.60i | 0.147081 | + | 0.254751i | ||||
\(494\) | 440.000 | 0.0400740 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11808.0 | −1.06894 | ||||||||
\(497\) | 3936.00 | + | 6817.35i | 0.355239 | + | 0.615292i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4070.00 | + | 7049.45i | −0.365127 | + | 0.632418i | −0.988796 | − | 0.149270i | \(-0.952308\pi\) |
0.623670 | + | 0.781688i | \(0.285641\pi\) | |||||||
\(500\) | −437.500 | + | 757.772i | −0.0391312 | + | 0.0677772i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −66.0000 | − | 114.315i | −0.00586798 | − | 0.0101636i | ||||
\(503\) | 13768.0 | 1.22045 | 0.610223 | − | 0.792229i | \(-0.291080\pi\) | ||||
0.610223 | + | 0.792229i | \(0.291080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6090.00 | −0.536637 | ||||||||
\(506\) | −4368.00 | − | 7565.60i | −0.383757 | − | 0.664687i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6776.00 | − | 11736.4i | 0.591804 | − | 1.02503i | ||||
\(509\) | 11075.0 | − | 19182.5i | 0.964422 | − | 1.67043i | 0.253262 | − | 0.967398i | \(-0.418497\pi\) |
0.711160 | − | 0.703030i | \(-0.248170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −456.000 | − | 789.815i | −0.0394760 | − | 0.0683745i | ||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7614.00 | −0.653384 | ||||||||
\(515\) | −220.000 | − | 381.051i | −0.0188240 | − | 0.0326041i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6656.00 | + | 11528.5i | −0.566210 | + | 0.980704i | ||||
\(518\) | 408.000 | − | 706.677i | 0.0346071 | − | 0.0599413i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 825.000 | + | 1428.94i | 0.0695743 | + | 0.120506i | ||||
\(521\) | −1562.00 | −0.131348 | −0.0656741 | − | 0.997841i | \(-0.520920\pi\) | ||||
−0.0656741 | + | 0.997841i | \(0.520920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −668.000 | −0.0558501 | −0.0279250 | − | 0.999610i | \(-0.508890\pi\) | ||||
−0.0279250 | + | 0.999610i | \(0.508890\pi\) | |||||||
\(524\) | −2562.00 | − | 4437.51i | −0.213591 | − | 0.369950i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2444.00 | − | 4233.13i | 0.202592 | − | 0.350900i | ||||
\(527\) | 2016.00 | − | 3491.81i | 0.166638 | − | 0.288626i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8028.50 | − | 13905.8i | −0.659859 | − | 1.14291i | ||||
\(530\) | 1690.00 | 0.138507 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3360.00 | −0.273824 | ||||||||
\(533\) | 1342.00 | + | 2324.41i | 0.109059 | + | 0.188896i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −90.0000 | + | 155.885i | −0.00727297 | + | 0.0125972i | ||||
\(536\) | 630.000 | − | 1091.19i | 0.0507684 | − | 0.0879334i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −635.000 | − | 1099.85i | −0.0508862 | − | 0.0881375i | ||||
\(539\) | −12116.0 | −0.968225 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6138.00 | −0.487788 | −0.243894 | − | 0.969802i | \(-0.578425\pi\) | ||||
−0.243894 | + | 0.969802i | \(0.578425\pi\) | |||||||
\(542\) | 536.000 | + | 928.379i | 0.0424782 | + | 0.0735744i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1127.00 | − | 1952.02i | 0.0888230 | − | 0.153846i | ||||
\(545\) | −2425.00 | + | 4200.22i | −0.190597 | + | 0.330124i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5242.00 | + | 9079.41i | 0.409747 | + | 0.709703i | 0.994861 | − | 0.101248i | \(-0.0322836\pi\) |
−0.585114 | + | 0.810951i | \(0.698950\pi\) | |||||||
\(548\) | −15498.0 | −1.20811 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1300.00 | 0.100786 | ||||||||
\(551\) | −2300.00 | − | 3983.72i | −0.177828 | − | 0.308007i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2880.00 | + | 4988.31i | −0.221465 | + | 0.383588i | ||||
\(554\) | −2697.00 | + | 4671.34i | −0.206831 | + | 0.358242i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 70.0000 | + | 121.244i | 0.00533932 | + | 0.00924797i | ||||
\(557\) | −3606.00 | −0.274311 | −0.137155 | − | 0.990550i | \(-0.543796\pi\) | ||||
−0.137155 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4136.00 | −0.312941 | ||||||||
\(560\) | −2460.00 | − | 4260.84i | −0.185632 | − | 0.321524i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1221.00 | + | 2114.83i | −0.0916455 | + | 0.158735i | ||||
\(563\) | 6126.00 | − | 10610.5i | 0.458579 | − | 0.794283i | −0.540307 | − | 0.841468i | \(-0.681692\pi\) |
0.998886 | + | 0.0471855i | \(0.0150252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2605.00 | − | 4511.99i | −0.193970 | − | 0.335966i | ||||
\(566\) | −2772.00 | −0.205858 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4920.00 | 0.363448 | ||||||||
\(569\) | −7275.00 | − | 12600.7i | −0.536000 | − | 0.928379i | −0.999114 | − | 0.0420803i | \(-0.986601\pi\) |
0.463114 | − | 0.886298i | \(-0.346732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12734.0 | − | 22055.9i | 0.933277 | − | 1.61648i | 0.155600 | − | 0.987820i | \(-0.450269\pi\) |
0.777677 | − | 0.628663i | \(-0.216398\pi\) | |||||||
\(572\) | −4004.00 | + | 6935.13i | −0.292685 | + | 0.506945i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1464.00 | + | 2535.72i | 0.106457 | + | 0.184389i | ||||
\(575\) | 4200.00 | 0.304612 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12866.0 | 0.928282 | 0.464141 | − | 0.885761i | \(-0.346363\pi\) | ||||
0.464141 | + | 0.885761i | \(0.346363\pi\) | |||||||
\(578\) | −2358.50 | − | 4085.04i | −0.169724 | − | 0.293971i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4025.00 | − | 6971.50i | 0.288153 | − | 0.499096i | ||||
\(581\) | −14544.0 | + | 25190.9i | −1.03853 | + | 1.79879i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8788.00 | + | 15221.3i | 0.624291 | + | 1.08130i | ||||
\(584\) | −570.000 | −0.0403883 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4542.00 | 0.320185 | ||||||||
\(587\) | −7422.00 | − | 12855.3i | −0.521872 | − | 0.903908i | −0.999676 | − | 0.0254422i | \(-0.991901\pi\) |
0.477805 | − | 0.878466i | \(-0.341433\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2880.00 | + | 4988.31i | −0.201474 | + | 0.348964i | ||||
\(590\) | 250.000 | − | 433.013i | 0.0174446 | − | 0.0302150i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 697.000 | + | 1207.24i | 0.0483894 | + | 0.0838129i | ||||
\(593\) | −20402.0 | −1.41283 | −0.706416 | − | 0.707797i | \(-0.749689\pi\) | ||||
−0.706416 | + | 0.707797i | \(0.749689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1680.00 | 0.115753 | ||||||||
\(596\) | 4655.00 | + | 8062.70i | 0.319927 | + | 0.554129i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1848.00 | − | 3200.83i | 0.126372 | − | 0.218882i | ||||
\(599\) | 5380.00 | − | 9318.43i | 0.366980 | − | 0.635627i | −0.622112 | − | 0.782928i | \(-0.713725\pi\) |
0.989092 | + | 0.147301i | \(0.0470585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7141.00 | − | 12368.6i | −0.484671 | − | 0.839475i | 0.515174 | − | 0.857086i | \(-0.327727\pi\) |
−0.999845 | + | 0.0176105i | \(0.994394\pi\) | |||||||
\(602\) | −4512.00 | −0.305474 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8456.00 | 0.569652 | ||||||||
\(605\) | 3432.50 | + | 5945.26i | 0.230663 | + | 0.399520i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5528.00 | + | 9574.78i | −0.369645 | + | 0.640244i | −0.989510 | − | 0.144464i | \(-0.953854\pi\) |
0.619865 | + | 0.784709i | \(0.287187\pi\) | |||||||
\(608\) | −1610.00 | + | 2788.60i | −0.107392 | + | 0.186008i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1855.00 | − | 3212.95i | −0.123126 | − | 0.213260i | ||||
\(611\) | −5632.00 | −0.372907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16418.0 | −1.08176 | −0.540878 | − | 0.841101i | \(-0.681908\pi\) | ||||
−0.540878 | + | 0.841101i | \(0.681908\pi\) | |||||||
\(614\) | 2558.00 | + | 4430.59i | 0.168131 | + | 0.291212i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9360.00 | + | 16212.0i | −0.612216 | + | 1.06039i | ||||
\(617\) | −5187.00 | + | 8984.15i | −0.338445 | + | 0.586204i | −0.984140 | − | 0.177391i | \(-0.943234\pi\) |
0.645695 | + | 0.763595i | \(0.276568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2630.00 | + | 4555.29i | 0.170773 | + | 0.295788i | 0.938690 | − | 0.344761i | \(-0.112040\pi\) |
−0.767917 | + | 0.640549i | \(0.778707\pi\) | |||||||
\(620\) | −10080.0 | −0.652940 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2808.00 | −0.181014 | ||||||||
\(623\) | −3960.00 | − | 6858.92i | −0.254661 | − | 0.441086i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −3659.00 | + | 6337.57i | −0.233615 | + | 0.404633i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12299.0 | − | 21302.5i | −0.781502 | − | 1.35360i | ||||
\(629\) | −476.000 | −0.0301739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21352.0 | 1.34708 | 0.673542 | − | 0.739149i | \(-0.264772\pi\) | ||||
0.673542 | + | 0.739149i | \(0.264772\pi\) | |||||||
\(632\) | 1800.00 | + | 3117.69i | 0.113291 | + | 0.196226i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1123.00 | + | 1945.09i | −0.0703470 | + | 0.121845i | ||||
\(635\) | 4840.00 | − | 8383.13i | 0.302472 | − | 0.523896i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2563.00 | − | 4439.25i | −0.159419 | − | 0.276121i | ||||
\(638\) | −11960.0 | −0.742164 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7275.00 | −0.449328 | ||||||||
\(641\) | −14559.0 | − | 25216.9i | −0.897108 | − | 1.55384i | −0.831174 | − | 0.556012i | \(-0.812331\pi\) |
−0.0659331 | − | 0.997824i | \(-0.521002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2886.00 | + | 4998.70i | −0.177003 | + | 0.306578i | −0.940853 | − | 0.338816i | \(-0.889973\pi\) |
0.763850 | + | 0.645394i | \(0.223307\pi\) | |||||||
\(644\) | −14112.0 | + | 24442.7i | −0.863495 | + | 1.49562i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −140.000 | − | 242.487i | −0.00852667 | − | 0.0147686i | ||||
\(647\) | 14264.0 | 0.866732 | 0.433366 | − | 0.901218i | \(-0.357326\pi\) | ||||
0.433366 | + | 0.901218i | \(0.357326\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5200.00 | 0.314511 | ||||||||
\(650\) | 275.000 | + | 476.314i | 0.0165944 | + | 0.0287424i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7238.00 | + | 12536.6i | −0.434758 | + | 0.753022i | ||||
\(653\) | 3451.00 | − | 5977.31i | 0.206812 | − | 0.358208i | −0.743897 | − | 0.668295i | \(-0.767025\pi\) |
0.950708 | + | 0.310086i | \(0.100358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1830.00 | − | 3169.65i | −0.109166 | − | 0.189082i | ||||
\(656\) | −5002.00 | −0.297706 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6144.00 | −0.364009 | ||||||||
\(659\) | 10070.0 | + | 17441.8i | 0.595253 | + | 1.03101i | 0.993511 | + | 0.113735i | \(0.0362814\pi\) |
−0.398258 | + | 0.917273i | \(0.630385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1609.00 | − | 2786.87i | 0.0946790 | − | 0.163989i | −0.814796 | − | 0.579748i | \(-0.803151\pi\) |
0.909475 | + | 0.415759i | \(0.136484\pi\) | |||||||
\(662\) | 666.000 | − | 1153.55i | 0.0391009 | − | 0.0677248i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9090.00 | + | 15744.3i | 0.531266 | + | 0.920179i | ||||
\(665\) | −2400.00 | −0.139952 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38640.0 | −2.24310 | ||||||||
\(668\) | 84.0000 | + | 145.492i | 0.00486536 | + | 0.00842704i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 210.000 | − | 363.731i | 0.0121090 | − | 0.0209733i | ||||
\(671\) | 19292.0 | − | 33414.7i | 1.10992 | − | 1.92245i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3759.00 | + | 6510.78i | 0.215303 | + | 0.372915i | 0.953366 | − | 0.301816i | \(-0.0975928\pi\) |
−0.738063 | + | 0.674731i | \(0.764259\pi\) | |||||||
\(674\) | 11534.0 | 0.659159 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11991.0 | 0.682237 | ||||||||
\(677\) | −9057.00 | − | 15687.2i | −0.514164 | − | 0.890558i | −0.999865 | − | 0.0164327i | \(-0.994769\pi\) |
0.485701 | − | 0.874125i | \(-0.338564\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10392.0 | − | 17999.5i | 0.587347 | − | 1.01731i | ||||
\(680\) | 525.000 | − | 909.327i | 0.0296071 | − | 0.0512810i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7488.00 | + | 12969.6i | 0.420426 | + | 0.728199i | ||||
\(683\) | 23868.0 | 1.33716 | 0.668582 | − | 0.743638i | \(-0.266901\pi\) | ||||
0.668582 | + | 0.743638i | \(0.266901\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11070.0 | −0.617464 | ||||||||
\(686\) | 1320.00 | + | 2286.31i | 0.0734662 | + | 0.127247i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3854.00 | − | 6675.32i | 0.213564 | − | 0.369905i | ||||
\(689\) | −3718.00 | + | 6439.76i | −0.205580 | + | 0.356075i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −86.0000 | − | 148.956i | −0.00473458 | − | 0.00820053i | 0.863648 | − | 0.504095i | \(-0.168174\pi\) |
−0.868383 | + | 0.495894i | \(0.834840\pi\) | |||||||
\(692\) | −4326.00 | −0.237644 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11956.0 | 0.653953 | ||||||||
\(695\) | 50.0000 | + | 86.6025i | 0.00272893 | + | 0.00472665i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 854.000 | − | 1479.17i | 0.0464097 | − | 0.0803839i | ||||
\(698\) | 2435.00 | − | 4217.54i | 0.132043 | − | 0.228705i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2100.00 | − | 3637.31i | −0.113389 | − | 0.196396i | ||||
\(701\) | 22138.0 | 1.19278 | 0.596391 | − | 0.802694i | \(-0.296601\pi\) | ||||
0.596391 | + | 0.802694i | \(0.296601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 680.000 | 0.0364818 | ||||||||
\(704\) | −4342.00 | − | 7520.56i | −0.232451 | − | 0.402616i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5361.00 | + | 9285.52i | −0.285785 | + | 0.494993i | ||||
\(707\) | 14616.0 | − | 25315.7i | 0.777498 | − | 1.34667i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1535.00 | − | 2658.70i | −0.0813091 | − | 0.140831i | 0.822503 | − | 0.568760i | \(-0.192577\pi\) |
−0.903812 | + | 0.427929i | \(0.859243\pi\) | |||||||
\(710\) | 1640.00 | 0.0866875 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4950.00 | −0.260546 | ||||||||
\(713\) | 24192.0 | + | 41901.8i | 1.27068 | + | 2.20089i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2860.00 | + | 4953.67i | −0.149592 | + | 0.259100i | ||||
\(716\) | −11690.0 | + | 20247.7i | −0.610162 | + | 1.05683i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −60.0000 | − | 103.923i | −0.00311864 | − | 0.00540163i | ||||
\(719\) | −15600.0 | −0.809154 | −0.404577 | − | 0.914504i | \(-0.632581\pi\) | ||||
−0.404577 | + | 0.914504i | \(0.632581\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2112.00 | 0.109092 | ||||||||
\(722\) | −3229.50 | − | 5593.66i | −0.166468 | − | 0.288330i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −623.000 | + | 1079.07i | −0.0319801 | + | 0.0553912i | ||||
\(725\) | 2875.00 | − | 4979.65i | 0.147276 | − | 0.255089i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10348.0 | − | 17923.3i | −0.527904 | − | 0.914356i | −0.999471 | − | 0.0325260i | \(-0.989645\pi\) |
0.471567 | − | 0.881830i | \(-0.343689\pi\) | |||||||
\(728\) | −7920.00 | −0.403207 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −190.000 | −0.00963317 | ||||||||
\(731\) | 1316.00 | + | 2279.38i | 0.0665855 | + | 0.115330i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15389.0 | − | 26654.5i | 0.775451 | − | 1.34312i | −0.159089 | − | 0.987264i | \(-0.550856\pi\) |
0.934541 | − | 0.355857i | \(-0.115811\pi\) | |||||||
\(734\) | 1968.00 | − | 3408.68i | 0.0989649 | − | 0.171412i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13524.0 | + | 23424.3i | 0.677311 | + | 1.17314i | ||||
\(737\) | 4368.00 | 0.218314 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11740.0 | 0.584388 | 0.292194 | − | 0.956359i | \(-0.405615\pi\) | ||||
0.292194 | + | 0.956359i | \(0.405615\pi\) | |||||||
\(740\) | 595.000 | + | 1030.57i | 0.0295576 | + | 0.0511953i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4056.00 | + | 7025.20i | −0.200674 | + | 0.347578i | ||||
\(743\) | 1316.00 | − | 2279.38i | 0.0649789 | − | 0.112547i | −0.831706 | − | 0.555217i | \(-0.812635\pi\) |
0.896685 | + | 0.442670i | \(0.145969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3325.00 | + | 5759.07i | 0.163515 | + | 0.283216i | ||||
\(746\) | −3022.00 | −0.148315 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5096.00 | 0.249102 | ||||||||
\(749\) | −432.000 | − | 748.246i | −0.0210747 | − | 0.0365024i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10264.0 | − | 17777.8i | 0.498720 | − | 0.863808i | −0.501279 | − | 0.865286i | \(-0.667137\pi\) |
0.999999 | + | 0.00147745i | \(0.000470287\pi\) | |||||||
\(752\) | 5248.00 | − | 9089.80i | 0.254488 | − | 0.440786i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2530.00 | − | 4382.09i | −0.122198 | − | 0.211653i | ||||
\(755\) | 6040.00 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21646.0 | 1.03928 | 0.519642 | − | 0.854384i | \(-0.326066\pi\) | ||||
0.519642 | + | 0.854384i | \(0.326066\pi\) | |||||||
\(758\) | −6670.00 | − | 11552.8i | −0.319611 | − | 0.553583i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −750.000 | + | 1299.04i | −0.0357965 | + | 0.0620014i | ||||
\(761\) | 9141.00 | − | 15832.7i | 0.435428 | − | 0.754184i | −0.561902 | − | 0.827204i | \(-0.689930\pi\) |
0.997331 | + | 0.0730197i | \(0.0232636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11640.0 | − | 20161.1i | −0.552289 | − | 0.956592i | ||||
\(764\) | −13216.0 | −0.625835 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1008.00 | −0.0475464 | ||||||||
\(767\) | 1100.00 | + | 1905.26i | 0.0517845 | + | 0.0896934i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12095.0 | − | 20949.2i | 0.567174 | − | 0.982374i | −0.429670 | − | 0.902986i | \(-0.641370\pi\) |
0.996844 | − | 0.0793882i | \(-0.0252967\pi\) | |||||||
\(770\) | −3120.00 | + | 5404.00i | −0.146022 | + | 0.252918i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6727.00 | + | 11651.5i | 0.313614 | + | 0.543195i | ||||
\(773\) | 25698.0 | 1.19572 | 0.597861 | − | 0.801600i | \(-0.296018\pi\) | ||||
0.597861 | + | 0.801600i | \(0.296018\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7200.00 | −0.333718 | ||||||||
\(776\) | −6495.00 | − | 11249.7i | −0.300460 | − | 0.520412i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4815.00 | + | 8339.82i | −0.221884 | + | 0.384315i | ||||
\(779\) | −1220.00 | + | 2113.10i | −0.0561117 | + | 0.0971884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8528.00 | + | 14770.9i | 0.390724 | + | 0.676755i | ||||
\(782\) | −2352.00 | −0.107554 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9553.00 | 0.435177 | ||||||||
\(785\) | −8785.00 | − | 15216.1i | −0.399427 | − | 0.691828i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16718.0 | + | 28956.4i | −0.757220 | + | 1.31154i | 0.187043 | + | 0.982352i | \(0.440110\pi\) |
−0.944263 | + | 0.329192i | \(0.893224\pi\) | |||||||
\(788\) | −8841.00 | + | 15313.1i | −0.399680 | + | 0.692266i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 600.000 | + | 1039.23i | 0.0270216 | + | 0.0468027i | ||||
\(791\) | 25008.0 | 1.12412 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16324.0 | 0.730999 | ||||||||
\(794\) | 3563.00 | + | 6171.30i | 0.159252 | + | 0.275833i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4060.00 | + | 7032.13i | −0.180783 | + | 0.313125i | ||||
\(797\) | −18797.0 | + | 32557.4i | −0.835413 | + | 1.44698i | 0.0582813 | + | 0.998300i | \(0.481438\pi\) |
−0.893694 | + | 0.448677i | \(0.851895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1792.00 | + | 3103.84i | 0.0793447 | + | 0.137429i | ||||
\(800\) | −4025.00 | −0.177882 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8718.00 | −0.383844 | ||||||||
\(803\) | −988.000 | − | 1711.27i | −0.0434194 | − | 0.0752046i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10080.0 | + | 17459.1i | −0.441333 | + | 0.764412i | ||||
\(806\) | −3168.00 | + | 5487.14i | −0.138447 | + | 0.239797i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9135.00 | − | 15822.3i | −0.397733 | − | 0.688894i | ||||
\(809\) | −4730.00 | −0.205560 | −0.102780 | − | 0.994704i | \(-0.532774\pi\) | ||||
−0.102780 | + | 0.994704i | \(0.532774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8748.00 | −0.378772 | −0.189386 | − | 0.981903i | \(-0.560650\pi\) | ||||
−0.189386 | + | 0.981903i | \(0.560650\pi\) | |||||||
\(812\) | 19320.0 | + | 33463.2i | 0.834974 | + | 1.44622i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 884.000 | − | 1531.13i | 0.0380641 | − | 0.0659290i | ||||
\(815\) | −5170.00 | + | 8954.70i | −0.222205 | + | 0.384871i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1880.00 | − | 3256.26i | −0.0805054 | − | 0.139439i | ||||
\(818\) | 10870.0 | 0.464622 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4270.00 | −0.181847 | ||||||||
\(821\) | 22071.0 | + | 38228.1i | 0.938226 | + | 1.62505i | 0.768779 | + | 0.639515i | \(0.220865\pi\) |
0.169447 | + | 0.985539i | \(0.445802\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1996.00 | + | 3457.17i | −0.0845397 | + | 0.146427i | −0.905195 | − | 0.424997i | \(-0.860275\pi\) |
0.820655 | + | 0.571424i | \(0.193609\pi\) | |||||||
\(824\) | 660.000 | − | 1143.15i | 0.0279031 | − | 0.0483297i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1200.00 | + | 2078.46i | 0.0505488 | + | 0.0875532i | ||||
\(827\) | 14444.0 | 0.607336 | 0.303668 | − | 0.952778i | \(-0.401789\pi\) | ||||
0.303668 | + | 0.952778i | \(0.401789\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42150.0 | 1.76590 | 0.882949 | − | 0.469468i | \(-0.155554\pi\) | ||||
0.882949 | + | 0.469468i | \(0.155554\pi\) | |||||||
\(830\) | 3030.00 | + | 5248.11i | 0.126714 | + | 0.219476i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1837.00 | − | 3181.78i | 0.0765463 | − | 0.132582i | ||||
\(833\) | −1631.00 | + | 2824.97i | −0.0678401 | + | 0.117502i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 60.0000 | + | 103.923i | 0.00248669 | + | 0.00430707i | ||||
\(836\) | −7280.00 | −0.301177 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9700.00 | −0.399858 | ||||||||
\(839\) | 6700.00 | + | 11604.7i | 0.275697 | + | 0.477521i | 0.970311 | − | 0.241862i | \(-0.0777581\pi\) |
−0.694614 | + | 0.719383i | \(0.744425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14255.5 | + | 24691.3i | −0.584505 | + | 1.01239i | ||||
\(842\) | 431.000 | − | 746.514i | 0.0176404 | − | 0.0305541i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15638.0 | − | 27085.8i | −0.637775 | − | 1.10466i | ||||
\(845\) | 8565.00 | 0.348692 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32952.0 | −1.33677 | ||||||||
\(848\) | −6929.00 | − | 12001.4i | −0.280593 | − | 0.486001i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 175.000 | − | 303.109i | 0.00706171 | − | 0.0122312i | ||||
\(851\) | 2856.00 | − | 4946.74i | 0.115044 | − | 0.199262i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4329.00 | + | 7498.05i | 0.173766 | + | 0.300971i | 0.939733 | − | 0.341908i | \(-0.111073\pi\) |
−0.765968 | + | 0.642879i | \(0.777740\pi\) | |||||||
\(854\) | 17808.0 | 0.713556 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −540.000 | −0.0215617 | ||||||||
\(857\) | 21413.0 | + | 37088.4i | 0.853505 | + | 1.47831i | 0.878025 | + | 0.478615i | \(0.158861\pi\) |
−0.0245192 | + | 0.999699i | \(0.507805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17950.0 | − | 31090.3i | 0.712976 | − | 1.23491i | −0.250759 | − | 0.968049i | \(-0.580680\pi\) |
0.963735 | − | 0.266861i | \(-0.0859863\pi\) | |||||||
\(860\) | 3290.00 | − | 5698.45i | 0.130451 | − | 0.225948i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7896.00 | − | 13676.3i | −0.311994 | − | 0.540389i | ||||
\(863\) | 3088.00 | 0.121804 | 0.0609019 | − | 0.998144i | \(-0.480602\pi\) | ||||
0.0609019 | + | 0.998144i | \(0.480602\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3090.00 | −0.121460 | ||||||||
\(866\) | 5801.00 | + | 10047.6i | 0.227628 | + | 0.394264i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24192.0 | − | 41901.8i | 0.946002 | − | 1.63852i | ||||
\(869\) | −6240.00 | + | 10808.0i | −0.243587 | + | 0.421906i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 924.000 | + | 1600.41i | 0.0359455 | + | 0.0622595i | ||||
\(872\) | −14550.0 | −0.565052 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3360.00 | 0.130039 | ||||||||
\(875\) | −1500.00 | − | 2598.08i | −0.0579534 | − | 0.100378i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17637.0 | − | 30548.2i | 0.679087 | − | 1.17621i | −0.296169 | − | 0.955135i | \(-0.595709\pi\) |
0.975256 | − | 0.221078i | \(-0.0709574\pi\) | |||||||
\(878\) | −220.000 | + | 381.051i | −0.00845631 | + | 0.0146468i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5330.00 | − | 9231.83i | −0.204175 | − | 0.353642i | ||||
\(881\) | −25042.0 | −0.957646 | −0.478823 | − | 0.877911i | \(-0.658936\pi\) | ||||
−0.478823 | + | 0.877911i | \(0.658936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12572.0 | 0.479141 | 0.239570 | − | 0.970879i | \(-0.422993\pi\) | ||||
0.239570 | + | 0.970879i | \(0.422993\pi\) | |||||||
\(884\) | 1078.00 | + | 1867.15i | 0.0410148 | + | 0.0710397i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5094.00 | − | 8823.07i | 0.193156 | − | 0.334556i | ||||
\(887\) | −10932.0 | + | 18934.8i | −0.413823 | + | 0.716762i | −0.995304 | − | 0.0967979i | \(-0.969140\pi\) |
0.581481 | + | 0.813560i | \(0.302473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23232.0 | + | 40239.0i | 0.876464 | + | 1.51808i | ||||
\(890\) | −1650.00 | −0.0621440 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −42224.0 | −1.58494 | ||||||||
\(893\) | −2560.00 | − | 4434.05i | −0.0959318 | − | 0.166159i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8350.00 | + | 14462.6i | −0.311854 | + | 0.540148i | ||||
\(896\) | 17460.0 | − | 30241.6i | 0.651002 | − | 1.12757i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6655.00 | + | 11526.8i | 0.247305 | + | 0.428345i | ||||
\(899\) | 66240.0 | 2.45743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4732.00 | 0.174968 | ||||||||
\(902\) | 3172.00 | + | 5494.07i | 0.117091 | + | 0.202807i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7815.00 | − | 13536.0i | 0.287525 | − | 0.498009i | ||||
\(905\) | −445.000 | + | 770.763i | −0.0163451 | + | 0.0283105i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15618.0 | − | 27051.2i | −0.571761 | − | 0.990319i | −0.996385 | − | 0.0849494i | \(-0.972927\pi\) |
0.424624 | − | 0.905370i | \(-0.360406\pi\) | |||||||
\(908\) | 18452.0 | 0.674396 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2640.00 | −0.0961705 | ||||||||
\(911\) | 4136.00 | + | 7163.76i | 0.150419 | + | 0.260534i | 0.931382 | − | 0.364044i | \(-0.118604\pi\) |
−0.780962 | + | 0.624578i | \(0.785271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31512.0 | + | 54580.4i | −1.14227 | + | 1.97847i | ||||
\(914\) | 1613.00 | − | 2793.80i | 0.0583734 | − | 0.101106i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16905.0 | + | 29280.3i | 0.609778 | + | 1.05617i | ||||
\(917\) | 17568.0 | 0.632657 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20200.0 | 0.725067 | 0.362533 | − | 0.931971i | \(-0.381912\pi\) | ||||
0.362533 | + | 0.931971i | \(0.381912\pi\) | |||||||
\(920\) | 6300.00 | + | 10911.9i | 0.225766 | + | 0.391038i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3291.00 | + | 5700.18i | −0.117552 | + | 0.203607i | ||||
\(923\) | −3608.00 | + | 6249.24i | −0.128666 | + | 0.222856i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 425.000 | + | 736.122i | 0.0151069 | + | 0.0261660i | ||||
\(926\) | −15072.0 | −0.534878 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 37030.0 | 1.30988 | ||||||||
\(929\) | 15505.0 | + | 26855.4i | 0.547581 | + | 0.948438i | 0.998440 | + | 0.0558425i | \(0.0177845\pi\) |
−0.450859 | + | 0.892595i | \(0.648882\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2330.00 | − | 4035.68i | 0.0820222 | − | 0.142067i | ||||
\(932\) | −9387.00 | + | 16258.8i | −0.329916 | + | 0.571431i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −238.000 | − | 412.228i | −0.00833790 | − | 0.0144417i | ||||
\(935\) | 3640.00 | 0.127316 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39174.0 | −1.36580 | −0.682902 | − | 0.730510i | \(-0.739283\pi\) | ||||
−0.682902 | + | 0.730510i | \(0.739283\pi\) | |||||||
\(938\) | 1008.00 | + | 1745.91i | 0.0350878 | + | 0.0607739i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4480.00 | − | 7759.59i | 0.155448 | − | 0.269245i | ||||
\(941\) | −2069.00 | + | 3583.61i | −0.0716764 | + | 0.124147i | −0.899636 | − | 0.436640i | \(-0.856168\pi\) |
0.827960 | + | 0.560788i | \(0.189502\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10248.0 | + | 17750.1i | 0.353893 | + | 0.612960i | ||||
\(944\) | −4100.00 | −0.141360 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9776.00 | −0.335989 | ||||||||
\(947\) | 11838.0 | + | 20504.0i | 0.406213 | + | 0.703581i | 0.994462 | − | 0.105099i | \(-0.0335159\pi\) |
−0.588249 | + | 0.808680i | \(0.700183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 418.000 | − | 723.997i | 0.0142981 | − | 0.0247650i | ||||
\(950\) | −250.000 | + | 433.013i | −0.00853797 | + | 0.0147882i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2520.00 | + | 4364.77i | 0.0857917 | + | 0.148596i | ||||
\(953\) | −18922.0 | −0.643173 | −0.321586 | − | 0.946880i | \(-0.604216\pi\) | ||||
−0.321586 | + | 0.946880i | \(0.604216\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9440.00 | −0.319865 | ||||||||
\(956\) | −8120.00 | − | 14064.3i | −0.274707 | − | 0.475806i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9840.00 | − | 17043.4i | 0.331854 | − | 0.574788i | ||||
\(959\) | 26568.0 | − | 46017.1i | 0.894604 | − | 1.54950i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26576.5 | − | 46031.8i | −0.892098 | − | 1.54516i | ||||
\(962\) | 748.000 | 0.0250691 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14014.0 | −0.468216 | ||||||||
\(965\) | 4805.00 | + | 8322.50i | 0.160289 | + | 0.277628i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19828.0 | + | 34343.1i | −0.659385 | + | 1.14209i | 0.321390 | + | 0.946947i | \(0.395850\pi\) |
−0.980775 | + | 0.195142i | \(0.937483\pi\) | |||||||
\(968\) | −10297.5 | + | 17835.8i | −0.341915 | + | 0.592215i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2165.00 | − | 3749.89i | −0.0716639 | − | 0.124125i | ||||
\(971\) | 33228.0 | 1.09818 | 0.549092 | − | 0.835762i | \(-0.314974\pi\) | ||||
0.549092 | + | 0.835762i | \(0.314974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −480.000 | −0.0158151 | ||||||||
\(974\) | −2972.00 | − | 5147.66i | −0.0977711 | − | 0.169344i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15211.0 | + | 26346.2i | −0.498865 | + | 0.864060i | ||||
\(977\) | −487.000 | + | 843.509i | −0.0159473 | + | 0.0276215i | −0.873889 | − | 0.486126i | \(-0.838410\pi\) |
0.857942 | + | 0.513747i | \(0.171743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8580.00 | − | 14861.0i | −0.280100 | − | 0.485148i | ||||
\(980\) | 8155.00 | 0.265818 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10772.0 | 0.350049 | ||||||||
\(983\) | −6804.00 | − | 11784.9i | −0.220767 | − | 0.382380i | 0.734274 | − | 0.678853i | \(-0.237523\pi\) |
−0.955041 | + | 0.296474i | \(0.904189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6315.00 | + | 10937.9i | −0.204277 | + | 0.353818i | ||||
\(986\) | −1610.00 | + | 2788.60i | −0.0520009 | + | 0.0900681i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1540.00 | − | 2667.36i | −0.0495890 | − | 0.0858907i | ||||
\(989\) | −31584.0 | −1.01548 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13472.0 | 0.431839 | 0.215919 | − | 0.976411i | \(-0.430725\pi\) | ||||
0.215919 | + | 0.976411i | \(0.430725\pi\) | |||||||
\(992\) | −23184.0 | − | 40155.9i | −0.742029 | − | 1.28523i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3936.00 | + | 6817.35i | −0.125596 | + | 0.217539i | ||||
\(995\) | −2900.00 | + | 5022.95i | −0.0923982 | + | 0.160038i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1617.00 | + | 2800.73i | 0.0513650 | + | 0.0889668i | 0.890565 | − | 0.454857i | \(-0.150309\pi\) |
−0.839200 | + | 0.543823i | \(0.816976\pi\) | |||||||
\(998\) | −8140.00 | −0.258184 | ||||||||
\(999\) | 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.i.271.1 | 2 | ||
3.2 | odd | 2 | 405.4.e.g.271.1 | 2 | |||
9.2 | odd | 6 | 405.4.e.g.136.1 | 2 | |||
9.4 | even | 3 | 45.4.a.c.1.1 | 1 | |||
9.5 | odd | 6 | 15.4.a.a.1.1 | ✓ | 1 | ||
9.7 | even | 3 | inner | 405.4.e.i.136.1 | 2 | ||
36.23 | even | 6 | 240.4.a.e.1.1 | 1 | |||
36.31 | odd | 6 | 720.4.a.n.1.1 | 1 | |||
45.4 | even | 6 | 225.4.a.f.1.1 | 1 | |||
45.13 | odd | 12 | 225.4.b.e.199.2 | 2 | |||
45.14 | odd | 6 | 75.4.a.b.1.1 | 1 | |||
45.22 | odd | 12 | 225.4.b.e.199.1 | 2 | |||
45.23 | even | 12 | 75.4.b.b.49.1 | 2 | |||
45.32 | even | 12 | 75.4.b.b.49.2 | 2 | |||
63.13 | odd | 6 | 2205.4.a.l.1.1 | 1 | |||
63.41 | even | 6 | 735.4.a.e.1.1 | 1 | |||
72.5 | odd | 6 | 960.4.a.b.1.1 | 1 | |||
72.59 | even | 6 | 960.4.a.ba.1.1 | 1 | |||
99.32 | even | 6 | 1815.4.a.e.1.1 | 1 | |||
180.23 | odd | 12 | 1200.4.f.b.49.1 | 2 | |||
180.59 | even | 6 | 1200.4.a.t.1.1 | 1 | |||
180.167 | odd | 12 | 1200.4.f.b.49.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.a.a.1.1 | ✓ | 1 | 9.5 | odd | 6 | ||
45.4.a.c.1.1 | 1 | 9.4 | even | 3 | |||
75.4.a.b.1.1 | 1 | 45.14 | odd | 6 | |||
75.4.b.b.49.1 | 2 | 45.23 | even | 12 | |||
75.4.b.b.49.2 | 2 | 45.32 | even | 12 | |||
225.4.a.f.1.1 | 1 | 45.4 | even | 6 | |||
225.4.b.e.199.1 | 2 | 45.22 | odd | 12 | |||
225.4.b.e.199.2 | 2 | 45.13 | odd | 12 | |||
240.4.a.e.1.1 | 1 | 36.23 | even | 6 | |||
405.4.e.g.136.1 | 2 | 9.2 | odd | 6 | |||
405.4.e.g.271.1 | 2 | 3.2 | odd | 2 | |||
405.4.e.i.136.1 | 2 | 9.7 | even | 3 | inner | ||
405.4.e.i.271.1 | 2 | 1.1 | even | 1 | trivial | ||
720.4.a.n.1.1 | 1 | 36.31 | odd | 6 | |||
735.4.a.e.1.1 | 1 | 63.41 | even | 6 | |||
960.4.a.b.1.1 | 1 | 72.5 | odd | 6 | |||
960.4.a.ba.1.1 | 1 | 72.59 | even | 6 | |||
1200.4.a.t.1.1 | 1 | 180.59 | even | 6 | |||
1200.4.f.b.49.1 | 2 | 180.23 | odd | 12 | |||
1200.4.f.b.49.2 | 2 | 180.167 | odd | 12 | |||
1815.4.a.e.1.1 | 1 | 99.32 | even | 6 | |||
2205.4.a.l.1.1 | 1 | 63.13 | odd | 6 |