Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,6,Mod(37,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.e (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: | \(10.1041806482\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-83})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.2 | ||
Root | \(-3.69493 - 2.71062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.46 |
Dual form | 63.6.e.c.37.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.19493 | + | 5.53379i | 0.564790 | + | 0.978245i | 0.997069 | + | 0.0765049i | \(0.0243761\pi\) |
−0.432279 | + | 0.901740i | \(0.642291\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.41520 | + | 7.64735i | −0.137975 | + | 0.238980i | ||||
\(5\) | 19.3645 | + | 33.5404i | 0.346403 | + | 0.599988i | 0.985608 | − | 0.169049i | \(-0.0540695\pi\) |
−0.639204 | + | 0.769037i | \(0.720736\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −87.5000 | + | 95.6596i | −0.674937 | + | 0.737876i | ||||
\(8\) | 148.051 | 0.817872 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −123.737 | + | 214.318i | −0.391290 | + | 0.677734i | ||||
\(11\) | −288.195 | + | 499.168i | −0.718133 | + | 1.24384i | 0.243606 | + | 0.969874i | \(0.421670\pi\) |
−0.961739 | + | 0.273968i | \(0.911664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 391.491 | 0.642486 | 0.321243 | − | 0.946997i | \(-0.395899\pi\) | ||||
0.321243 | + | 0.946997i | \(0.395899\pi\) | |||||||
\(14\) | −808.916 | − | 178.580i | −1.10302 | − | 0.243508i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 614.298 | + | 1064.00i | 0.599901 | + | 1.03906i | ||||
\(17\) | −664.850 | + | 1151.55i | −0.557958 | + | 0.966412i | 0.439709 | + | 0.898140i | \(0.355082\pi\) |
−0.997667 | + | 0.0682711i | \(0.978252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −471.237 | − | 816.206i | −0.299471 | − | 0.518699i | 0.676544 | − | 0.736402i | \(-0.263477\pi\) |
−0.976015 | + | 0.217703i | \(0.930144\pi\) | |||||||
\(20\) | −341.993 | −0.191180 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3683.05 | −1.62238 | ||||||||
\(23\) | −816.040 | − | 1413.42i | −0.321656 | − | 0.557124i | 0.659174 | − | 0.751991i | \(-0.270906\pi\) |
−0.980830 | + | 0.194866i | \(0.937573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 812.530 | − | 1407.34i | 0.260009 | − | 0.450350i | ||||
\(26\) | 1250.79 | + | 2166.43i | 0.362869 | + | 0.628508i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −345.212 | − | 1091.50i | −0.0832130 | − | 0.263105i | ||||
\(29\) | 1463.54 | 0.323155 | 0.161577 | − | 0.986860i | \(-0.448342\pi\) | ||||
0.161577 | + | 0.986860i | \(0.448342\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1956.21 | − | 3388.25i | 0.365604 | − | 0.633245i | −0.623269 | − | 0.782008i | \(-0.714196\pi\) |
0.988873 | + | 0.148763i | \(0.0475291\pi\) | |||||||
\(32\) | −1556.47 | + | 2695.89i | −0.268700 | + | 0.465401i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8496.61 | −1.26052 | ||||||||
\(35\) | −4902.85 | − | 1082.38i | −0.676517 | − | 0.149351i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8150.17 | + | 14116.5i | 0.978729 | + | 1.69521i | 0.667038 | + | 0.745024i | \(0.267562\pi\) |
0.311691 | + | 0.950184i | \(0.399105\pi\) | |||||||
\(38\) | 3011.14 | − | 5215.45i | 0.338277 | − | 0.585912i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2866.93 | + | 4965.67i | 0.283314 | + | 0.490714i | ||||
\(41\) | 13103.8 | 1.21741 | 0.608707 | − | 0.793395i | \(-0.291688\pi\) | ||||
0.608707 | + | 0.793395i | \(0.291688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14733.5 | 1.21516 | 0.607582 | − | 0.794257i | \(-0.292140\pi\) | ||||
0.607582 | + | 0.794257i | \(0.292140\pi\) | |||||||
\(44\) | −2544.88 | − | 4407.86i | −0.198169 | − | 0.343238i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5214.38 | − | 9031.58i | 0.363336 | − | 0.629316i | ||||
\(47\) | −3407.26 | − | 5901.55i | −0.224989 | − | 0.389692i | 0.731327 | − | 0.682027i | \(-0.238901\pi\) |
−0.956316 | + | 0.292335i | \(0.905568\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1494.50 | − | 16740.4i | −0.0889213 | − | 0.996039i | ||||
\(50\) | 10383.9 | 0.587403 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1728.51 | + | 2993.87i | −0.0886470 | + | 0.153541i | ||||
\(53\) | −1005.67 | + | 1741.87i | −0.0491775 | + | 0.0851779i | −0.889566 | − | 0.456806i | \(-0.848993\pi\) |
0.840389 | + | 0.541984i | \(0.182327\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22323.0 | −0.995054 | ||||||||
\(56\) | −12954.4 | + | 14162.5i | −0.552012 | + | 0.603488i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4675.93 | + | 8098.94i | 0.182515 | + | 0.316125i | ||||
\(59\) | 25726.6 | − | 44559.7i | 0.962170 | − | 1.66653i | 0.245135 | − | 0.969489i | \(-0.421168\pi\) |
0.717035 | − | 0.697037i | \(-0.245499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20548.9 | − | 35591.8i | −0.707073 | − | 1.22469i | −0.965938 | − | 0.258773i | \(-0.916682\pi\) |
0.258865 | − | 0.965913i | \(-0.416651\pi\) | |||||||
\(62\) | 24999.8 | 0.825958 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 19423.8 | 0.592766 | ||||||||
\(65\) | 7581.04 | + | 13130.8i | 0.222559 | + | 0.385484i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −25289.1 | + | 43802.0i | −0.688250 | + | 1.19208i | 0.284153 | + | 0.958779i | \(0.408288\pi\) |
−0.972404 | + | 0.233305i | \(0.925046\pi\) | |||||||
\(68\) | −5870.89 | − | 10168.7i | −0.153968 | − | 0.266681i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9674.63 | − | 30589.5i | −0.235988 | − | 0.746151i | ||||
\(71\) | −39970.6 | −0.941012 | −0.470506 | − | 0.882397i | \(-0.655929\pi\) | ||||
−0.470506 | + | 0.882397i | \(0.655929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 27843.3 | − | 48226.0i | 0.611524 | − | 1.05919i | −0.379459 | − | 0.925208i | \(-0.623890\pi\) |
0.990984 | − | 0.133983i | \(-0.0427767\pi\) | |||||||
\(74\) | −52078.5 | + | 90202.6i | −1.10555 | + | 1.91487i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8322.42 | 0.165278 | ||||||||
\(77\) | −22533.2 | − | 71245.8i | −0.433107 | − | 1.36941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31575.7 | + | 54690.7i | 0.569226 | + | 0.985929i | 0.996643 | + | 0.0818739i | \(0.0260905\pi\) |
−0.427416 | + | 0.904055i | \(0.640576\pi\) | |||||||
\(80\) | −23791.2 | + | 41207.6i | −0.415615 | + | 0.719867i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 41865.9 | + | 72513.8i | 0.687583 | + | 1.19093i | ||||
\(83\) | −45572.4 | −0.726116 | −0.363058 | − | 0.931766i | \(-0.618267\pi\) | ||||
−0.363058 | + | 0.931766i | \(0.618267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −51498.1 | −0.773114 | ||||||||
\(86\) | 47072.5 | + | 81532.0i | 0.686312 | + | 1.18873i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −42667.5 | + | 73902.2i | −0.587341 | + | 1.01730i | ||||
\(89\) | 7843.34 | + | 13585.1i | 0.104961 | + | 0.181797i | 0.913722 | − | 0.406340i | \(-0.133195\pi\) |
−0.808762 | + | 0.588137i | \(0.799862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −34255.5 | + | 37449.9i | −0.433637 | + | 0.474075i | ||||
\(92\) | 14411.9 | 0.177522 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 21771.9 | − | 37710.1i | 0.254143 | − | 0.440188i | ||||
\(95\) | 18250.6 | − | 31610.9i | 0.207476 | − | 0.359358i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3128.49 | 0.0337603 | 0.0168801 | − | 0.999858i | \(-0.494627\pi\) | ||||
0.0168801 | + | 0.999858i | \(0.494627\pi\) | |||||||
\(98\) | 87863.1 | − | 61754.8i | 0.924148 | − | 0.649539i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7174.96 | + | 12427.4i | 0.0717496 | + | 0.124274i | ||||
\(101\) | −84505.5 | + | 146368.i | −0.824292 | + | 1.42772i | 0.0781663 | + | 0.996940i | \(0.475093\pi\) |
−0.902459 | + | 0.430776i | \(0.858240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −56410.1 | − | 97705.1i | −0.523918 | − | 0.907453i | −0.999612 | − | 0.0278422i | \(-0.991136\pi\) |
0.475694 | − | 0.879611i | \(-0.342197\pi\) | |||||||
\(104\) | 57960.5 | 0.525471 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12852.2 | −0.111100 | ||||||||
\(107\) | −11154.7 | − | 19320.6i | −0.0941890 | − | 0.163140i | 0.815081 | − | 0.579347i | \(-0.196692\pi\) |
−0.909270 | + | 0.416207i | \(0.863359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 41909.8 | − | 72589.8i | 0.337869 | − | 0.585207i | −0.646162 | − | 0.763200i | \(-0.723627\pi\) |
0.984032 | + | 0.177993i | \(0.0569604\pi\) | |||||||
\(110\) | −71320.6 | − | 123531.i | −0.561996 | − | 0.973406i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −155532. | − | 34336.1i | −1.17159 | − | 0.258646i | ||||
\(113\) | 40928.4 | 0.301529 | 0.150764 | − | 0.988570i | \(-0.451826\pi\) | ||||
0.150764 | + | 0.988570i | \(0.451826\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31604.4 | − | 54740.5i | 0.222845 | − | 0.385980i | ||||
\(116\) | −6461.84 | + | 11192.2i | −0.0445873 | + | 0.0772275i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 328779. | 2.17369 | ||||||||
\(119\) | −51982.8 | − | 164360.i | −0.336505 | − | 1.06397i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85587.1 | − | 148241.i | −0.531429 | − | 0.920462i | ||||
\(122\) | 131305. | − | 227427.i | 0.798695 | − | 1.38338i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17274.1 | + | 29919.6i | 0.100888 | + | 0.174744i | ||||
\(125\) | 183965. | 1.05308 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 83270.1 | 0.458120 | 0.229060 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229060 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(128\) | 111865. | + | 193756.i | 0.603488 | + | 1.04527i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −48441.9 | + | 83903.8i | −0.251398 | + | 0.435435i | ||||
\(131\) | −83437.4 | − | 144518.i | −0.424798 | − | 0.735772i | 0.571603 | − | 0.820530i | \(-0.306322\pi\) |
−0.996402 | + | 0.0847580i | \(0.972988\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 119311. | + | 26339.7i | 0.584860 | + | 0.129117i | ||||
\(134\) | −323188. | −1.55487 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −98431.5 | + | 170488.i | −0.456338 | + | 0.790401i | ||||
\(137\) | 19111.9 | − | 33102.9i | 0.0869969 | − | 0.150683i | −0.819244 | − | 0.573446i | \(-0.805606\pi\) |
0.906240 | + | 0.422763i | \(0.138940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 106263. | 0.466492 | 0.233246 | − | 0.972418i | \(-0.425065\pi\) | ||||
0.233246 | + | 0.972418i | \(0.425065\pi\) | |||||||
\(140\) | 29924.4 | − | 32714.9i | 0.129034 | − | 0.141067i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −127703. | − | 221189.i | −0.531474 | − | 0.920540i | ||||
\(143\) | −112826. | + | 195420.i | −0.461390 | + | 0.799151i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28340.8 | + | 49087.8i | 0.111942 | + | 0.193889i | ||||
\(146\) | 355830. | 1.38153 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −143938. | −0.540160 | ||||||||
\(149\) | 96277.8 | + | 166758.i | 0.355271 | + | 0.615348i | 0.987164 | − | 0.159708i | \(-0.0510551\pi\) |
−0.631893 | + | 0.775056i | \(0.717722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −70849.3 | + | 122715.i | −0.252868 | + | 0.437980i | −0.964314 | − | 0.264761i | \(-0.914707\pi\) |
0.711447 | + | 0.702740i | \(0.248040\pi\) | |||||||
\(152\) | −69766.9 | − | 120840.i | −0.244929 | − | 0.424230i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 322267. | − | 352319.i | 1.09500 | − | 1.19711i | ||||
\(155\) | 151524. | 0.506586 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −282885. | + | 489972.i | −0.915928 | + | 1.58643i | −0.110392 | + | 0.993888i | \(0.535211\pi\) |
−0.805536 | + | 0.592546i | \(0.798123\pi\) | |||||||
\(158\) | −201764. | + | 349466.i | −0.642986 | + | 1.11368i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −120562. | −0.372314 | ||||||||
\(161\) | 206611. | + | 45612.4i | 0.628186 | + | 0.138682i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 215101. | + | 372565.i | 0.634121 | + | 1.09833i | 0.986701 | + | 0.162549i | \(0.0519714\pi\) |
−0.352579 | + | 0.935782i | \(0.614695\pi\) | |||||||
\(164\) | −57856.0 | + | 100210.i | −0.167973 | + | 0.290937i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −145601. | − | 252188.i | −0.410103 | − | 0.710319i | ||||
\(167\) | 240265. | 0.666653 | 0.333327 | − | 0.942811i | \(-0.391829\pi\) | ||||
0.333327 | + | 0.942811i | \(0.391829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −218028. | −0.587212 | ||||||||
\(170\) | −164533. | − | 284979.i | −0.436647 | − | 0.756295i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −65051.3 | + | 112672.i | −0.167662 | + | 0.290399i | ||||
\(173\) | −89650.1 | − | 155279.i | −0.227738 | − | 0.394454i | 0.729399 | − | 0.684088i | \(-0.239800\pi\) |
−0.957137 | + | 0.289634i | \(0.906466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 63529.4 | + | 200869.i | 0.156812 | + | 0.495812i | ||||
\(176\) | −708151. | −1.72323 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −50117.9 | + | 86806.8i | −0.118561 | + | 0.205354i | ||||
\(179\) | −287780. | + | 498449.i | −0.671317 | + | 1.16275i | 0.306214 | + | 0.951963i | \(0.400938\pi\) |
−0.977531 | + | 0.210792i | \(0.932396\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 581006. | 1.31821 | 0.659105 | − | 0.752051i | \(-0.270935\pi\) | ||||
0.659105 | + | 0.752051i | \(0.270935\pi\) | |||||||
\(182\) | −316684. | − | 69912.7i | −0.708675 | − | 0.156451i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −120815. | − | 209258.i | −0.263073 | − | 0.455657i | ||||
\(185\) | −315648. | + | 546719.i | −0.678070 | + | 1.17445i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −383213. | − | 663744.i | −0.801376 | − | 1.38802i | ||||
\(188\) | 60174.9 | 0.124171 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 233237. | 0.468721 | ||||||||
\(191\) | −330280. | − | 572062.i | −0.655087 | − | 1.13464i | −0.981872 | − | 0.189545i | \(-0.939299\pi\) |
0.326785 | − | 0.945099i | \(-0.394035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 278655. | − | 482645.i | 0.538485 | − | 0.932684i | −0.460501 | − | 0.887659i | \(-0.652330\pi\) |
0.998986 | − | 0.0450243i | \(-0.0143365\pi\) | |||||||
\(194\) | 9995.33 | + | 17312.4i | 0.0190675 | + | 0.0330258i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 134618. | + | 62483.3i | 0.250302 | + | 0.116178i | ||||
\(197\) | 761400. | 1.39781 | 0.698904 | − | 0.715216i | \(-0.253672\pi\) | ||||
0.698904 | + | 0.715216i | \(0.253672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 67929.9 | − | 117658.i | 0.121598 | − | 0.210615i | −0.798800 | − | 0.601597i | \(-0.794531\pi\) |
0.920398 | + | 0.390982i | \(0.127865\pi\) | |||||||
\(200\) | 120296. | − | 208358.i | 0.212655 | − | 0.368328i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.07996e6 | −1.86221 | ||||||||
\(203\) | −128060. | + | 140002.i | −0.218109 | + | 0.238448i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 253750. | + | 439507.i | 0.421716 | + | 0.730434i | ||||
\(206\) | 360453. | − | 624323.i | 0.591807 | − | 1.02504i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 240492. | + | 416545.i | 0.385428 | + | 0.667581i | ||||
\(209\) | 543232. | 0.860240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −991157. | −1.53263 | −0.766313 | − | 0.642467i | \(-0.777911\pi\) | ||||
−0.766313 | + | 0.642467i | \(0.777911\pi\) | |||||||
\(212\) | −8880.48 | − | 15381.4i | −0.0135705 | − | 0.0235048i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 71277.3 | − | 123456.i | 0.106394 | − | 0.184280i | ||||
\(215\) | 285307. | + | 494167.i | 0.420937 | + | 0.729084i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 152951. | + | 483602.i | 0.220496 | + | 0.697170i | ||||
\(218\) | 535596. | 0.763301 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 98560.7 | − | 170712.i | 0.137293 | − | 0.237798i | ||||
\(221\) | −260283. | + | 450823.i | −0.358480 | + | 0.620906i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 543344. | 0.731666 | 0.365833 | − | 0.930681i | \(-0.380784\pi\) | ||||
0.365833 | + | 0.930681i | \(0.380784\pi\) | |||||||
\(224\) | −121696. | − | 384782.i | −0.162053 | − | 0.512383i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 130764. | + | 226489.i | 0.170300 | + | 0.294969i | ||||
\(227\) | 8.16704 | − | 14.1457i | 1.05196e−5 | − | 1.82205e-5i | −0.866020 | − | 0.500009i | \(-0.833330\pi\) |
0.866031 | + | 0.499991i | \(0.166663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 38689.5 | + | 67012.2i | 0.0487534 | + | 0.0844433i | 0.889372 | − | 0.457184i | \(-0.151142\pi\) |
−0.840619 | + | 0.541627i | \(0.817808\pi\) | |||||||
\(230\) | 403896. | 0.503443 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 216679. | 0.264299 | ||||||||
\(233\) | −51828.6 | − | 89769.9i | −0.0625432 | − | 0.108328i | 0.833058 | − | 0.553185i | \(-0.186588\pi\) |
−0.895602 | + | 0.444857i | \(0.853254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 131960. | − | 228561.i | 0.155874 | − | 0.269981i | ||||
\(236\) | 227176. | + | 393480.i | 0.265511 | + | 0.459878i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 743453. | − | 812782.i | 0.850768 | − | 0.930104i | ||||
\(239\) | −689109. | −0.780356 | −0.390178 | − | 0.920739i | \(-0.627587\pi\) | ||||
−0.390178 | + | 0.920739i | \(0.627587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −110148. | + | 190782.i | −0.122161 | + | 0.211590i | −0.920620 | − | 0.390460i | \(-0.872316\pi\) |
0.798458 | + | 0.602050i | \(0.205649\pi\) | |||||||
\(242\) | 546890. | − | 947242.i | 0.600291 | − | 1.03973i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 362910. | 0.390234 | ||||||||
\(245\) | 532539. | − | 374297.i | 0.566809 | − | 0.398383i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −184485. | − | 319537.i | −0.192406 | − | 0.333257i | ||||
\(248\) | 289618. | − | 501633.i | 0.299017 | − | 0.517913i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 587757. | + | 1.01803e6i | 0.594768 | + | 1.03017i | ||||
\(251\) | −1.43641e6 | −1.43912 | −0.719558 | − | 0.694433i | \(-0.755655\pi\) | ||||
−0.719558 | + | 0.694433i | \(0.755655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 940714. | 0.923966 | ||||||||
\(254\) | 266042. | + | 460799.i | 0.258742 | + | 0.448154i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −404021. | + | 699785.i | −0.385305 | + | 0.667367i | ||||
\(257\) | −454598. | − | 787388.i | −0.429334 | − | 0.743628i | 0.567480 | − | 0.823387i | \(-0.307918\pi\) |
−0.996814 | + | 0.0797589i | \(0.974585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.06352e6 | − | 455553.i | −1.91143 | − | 0.421977i | ||||
\(260\) | −133887. | −0.122830 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 533154. | − | 923450.i | 0.479843 | − | 0.831113i | ||||
\(263\) | 374528. | − | 648702.i | 0.333884 | − | 0.578304i | −0.649386 | − | 0.760459i | \(-0.724974\pi\) |
0.983270 | + | 0.182155i | \(0.0583073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −77897.4 | −0.0681410 | ||||||||
\(266\) | 235433. | + | 744396.i | 0.204015 | + | 0.645060i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −223313. | − | 386789.i | −0.189923 | − | 0.328956i | ||||
\(269\) | 334972. | − | 580189.i | 0.282246 | − | 0.488865i | −0.689691 | − | 0.724104i | \(-0.742254\pi\) |
0.971938 | + | 0.235238i | \(0.0755871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −270330. | − | 468225.i | −0.223599 | − | 0.387285i | 0.732299 | − | 0.680983i | \(-0.238447\pi\) |
−0.955898 | + | 0.293698i | \(0.905114\pi\) | |||||||
\(272\) | −1.63367e6 | −1.33888 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 244246. | 0.196540 | ||||||||
\(275\) | 468334. | + | 811178.i | 0.373443 | + | 0.646821i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 200955. | − | 348064.i | 0.157362 | − | 0.272558i | −0.776555 | − | 0.630050i | \(-0.783035\pi\) |
0.933916 | + | 0.357491i | \(0.116368\pi\) | |||||||
\(278\) | 339502. | + | 588035.i | 0.263470 | + | 0.456343i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −725871. | − | 160247.i | −0.553304 | − | 0.122150i | ||||
\(281\) | 429139. | 0.324214 | 0.162107 | − | 0.986773i | \(-0.448171\pi\) | ||||
0.162107 | + | 0.986773i | \(0.448171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 170463. | − | 295251.i | 0.126522 | − | 0.219142i | −0.795805 | − | 0.605553i | \(-0.792952\pi\) |
0.922327 | + | 0.386411i | \(0.126285\pi\) | |||||||
\(284\) | 176478. | − | 305669.i | 0.129836 | − | 0.224883i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.44188e6 | −1.04235 | ||||||||
\(287\) | −1.14658e6 | + | 1.25351e6i | −0.821678 | + | 0.898301i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −174123. | − | 301590.i | −0.122634 | − | 0.212409i | ||||
\(290\) | −181094. | + | 313664.i | −0.126447 | + | 0.219013i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 245868. | + | 425855.i | 0.168750 | + | 0.292284i | ||||
\(293\) | 388847. | 0.264612 | 0.132306 | − | 0.991209i | \(-0.457762\pi\) | ||||
0.132306 | + | 0.991209i | \(0.457762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.99273e6 | 1.33319 | ||||||||
\(296\) | 1.20664e6 | + | 2.08996e6i | 0.800475 | + | 1.38646i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −615202. | + | 1.06556e6i | −0.401307 | + | 0.695085i | ||||
\(299\) | −319472. | − | 553342.i | −0.206659 | − | 0.357945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.28918e6 | + | 1.40940e6i | −0.820158 | + | 0.896640i | ||||
\(302\) | −905435. | −0.571268 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 578960. | − | 1.00279e6i | 0.359306 | − | 0.622336i | ||||
\(305\) | 795840. | − | 1.37844e6i | 0.489865 | − | 0.848471i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.35747e6 | −1.42758 | −0.713789 | − | 0.700361i | \(-0.753022\pi\) | ||||
−0.713789 | + | 0.700361i | \(0.753022\pi\) | |||||||
\(308\) | 644330. | + | 142246.i | 0.387018 | + | 0.0854402i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 484110. | + | 838503.i | 0.286114 | + | 0.495565i | ||||
\(311\) | −718314. | + | 1.24416e6i | −0.421127 | + | 0.729414i | −0.996050 | − | 0.0887939i | \(-0.971699\pi\) |
0.574923 | + | 0.818208i | \(0.305032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 411400. | + | 712566.i | 0.237358 | + | 0.411116i | 0.959955 | − | 0.280153i | \(-0.0903853\pi\) |
−0.722598 | + | 0.691269i | \(0.757052\pi\) | |||||||
\(314\) | −3.61520e6 | −2.06923 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −557652. | −0.314156 | ||||||||
\(317\) | −883467. | − | 1.53021e6i | −0.493790 | − | 0.855269i | 0.506184 | − | 0.862425i | \(-0.331056\pi\) |
−0.999974 | + | 0.00715584i | \(0.997722\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −421786. | + | 730555.i | −0.232068 | + | 0.401954i | ||||
\(320\) | 376132. | + | 651480.i | 0.205336 | + | 0.355653i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 407698. | + | 1.28907e6i | 0.219129 | + | 0.692845i | ||||
\(323\) | 1.25321e6 | 0.668370 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 318098. | − | 550962.i | 0.167052 | − | 0.289343i | ||||
\(326\) | −1.37446e6 | + | 2.38064e6i | −0.716291 | + | 1.24065i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.94003e6 | 0.995689 | ||||||||
\(329\) | 862675. | + | 190448.i | 0.439397 | + | 0.0970036i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1526.14 | + | 2643.35i | 0.000765638 | + | 0.00132612i | 0.866408 | − | 0.499337i | \(-0.166423\pi\) |
−0.865642 | + | 0.500663i | \(0.833090\pi\) | |||||||
\(332\) | 201211. | − | 348508.i | 0.100186 | − | 0.173527i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 767632. | + | 1.32958e6i | 0.376519 | + | 0.652150i | ||||
\(335\) | −1.95885e6 | −0.953649 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.02939e6 | 0.973398 | 0.486699 | − | 0.873570i | \(-0.338201\pi\) | ||||
0.486699 | + | 0.873570i | \(0.338201\pi\) | |||||||
\(338\) | −696584. | − | 1.20652e6i | −0.331651 | − | 0.574437i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 227374. | − | 393824.i | 0.106670 | − | 0.184759i | ||||
\(341\) | 1.12754e6 | + | 1.95295e6i | 0.525104 | + | 0.909507i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.73215e6 | + | 1.32182e6i | 0.794969 | + | 0.606650i | ||||
\(344\) | 2.18130e6 | 0.993848 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 572852. | − | 992209.i | 0.257248 | − | 0.445567i | ||||
\(347\) | 1.89109e6 | − | 3.27547e6i | 0.843119 | − | 1.46033i | −0.0441252 | − | 0.999026i | \(-0.514050\pi\) |
0.887245 | − | 0.461299i | \(-0.152617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 291147. | 0.127953 | 0.0639763 | − | 0.997951i | \(-0.479622\pi\) | ||||
0.0639763 | + | 0.997951i | \(0.479622\pi\) | |||||||
\(350\) | −908592. | + | 993320.i | −0.396460 | + | 0.433430i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −897136. | − | 1.55389e6i | −0.385924 | − | 0.668440i | ||||
\(353\) | 192538. | − | 333486.i | 0.0822394 | − | 0.142443i | −0.821972 | − | 0.569528i | \(-0.807126\pi\) |
0.904212 | + | 0.427085i | \(0.140459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −774013. | − | 1.34063e6i | −0.325970 | − | 0.564596i | ||||
\(356\) | −138520. | −0.0579277 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.67775e6 | −1.51661 | ||||||||
\(359\) | −1.61507e6 | − | 2.79738e6i | −0.661385 | − | 1.14555i | −0.980252 | − | 0.197753i | \(-0.936635\pi\) |
0.318866 | − | 0.947800i | \(-0.396698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 793921. | − | 1.37511e6i | 0.320634 | − | 0.555354i | ||||
\(362\) | 1.85628e6 | + | 3.21517e6i | 0.744511 | + | 1.28953i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −135148. | − | 427312.i | −0.0534632 | − | 0.169041i | ||||
\(365\) | 2.15669e6 | 0.847336 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 239779. | − | 415310.i | 0.0929280 | − | 0.160956i | −0.815814 | − | 0.578314i | \(-0.803711\pi\) |
0.908742 | + | 0.417358i | \(0.137044\pi\) | |||||||
\(368\) | 1.00258e6 | − | 1.73653e6i | 0.385923 | − | 0.668439i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.03390e6 | −1.53187 | ||||||||
\(371\) | −78630.6 | − | 248616.i | −0.0296590 | − | 0.0937766i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −436333. | − | 755751.i | −0.162385 | − | 0.281259i | 0.773339 | − | 0.633993i | \(-0.218585\pi\) |
−0.935724 | + | 0.352734i | \(0.885252\pi\) | |||||||
\(374\) | 2.44868e6 | − | 4.24124e6i | 0.905217 | − | 1.56788i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −504447. | − | 873728.i | −0.184012 | − | 0.318718i | ||||
\(377\) | 572965. | 0.207622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.43493e6 | −0.870742 | −0.435371 | − | 0.900251i | \(-0.643383\pi\) | ||||
−0.435371 | + | 0.900251i | \(0.643383\pi\) | |||||||
\(380\) | 161160. | + | 279137.i | 0.0572529 | + | 0.0991650i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.11044e6 | − | 3.65540e6i | 0.739973 | − | 1.28167i | ||||
\(383\) | −1.80584e6 | − | 3.12781e6i | −0.629047 | − | 1.08954i | −0.987743 | − | 0.156087i | \(-0.950112\pi\) |
0.358696 | − | 0.933454i | \(-0.383222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.95327e6 | − | 2.13541e6i | 0.671598 | − | 0.734226i | ||||
\(386\) | 3.56114e6 | 1.21652 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13812.9 | + | 23924.7i | −0.00465807 | + | 0.00806802i | ||||
\(389\) | −87616.2 | + | 151756.i | −0.0293569 | + | 0.0508477i | −0.880331 | − | 0.474361i | \(-0.842679\pi\) |
0.850974 | + | 0.525208i | \(0.176013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.17018e6 | 0.717882 | ||||||||
\(392\) | −221262. | − | 2.47843e6i | −0.0727262 | − | 0.814632i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.43262e6 | + | 4.21343e6i | 0.789467 | + | 1.36740i | ||||
\(395\) | −1.22290e6 | + | 2.11812e6i | −0.394364 | + | 0.683058i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −942577. | − | 1.63259e6i | −0.300152 | − | 0.519878i | 0.676019 | − | 0.736885i | \(-0.263704\pi\) |
−0.976170 | + | 0.217007i | \(0.930371\pi\) | |||||||
\(398\) | 868126. | 0.274710 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.99654e6 | 0.623920 | ||||||||
\(401\) | 669915. | + | 1.16033e6i | 0.208046 | + | 0.360346i | 0.951099 | − | 0.308887i | \(-0.0999564\pi\) |
−0.743053 | + | 0.669232i | \(0.766623\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 765839. | − | 1.32647e6i | 0.234895 | − | 0.406851i | ||||
\(404\) | −746217. | − | 1.29249e6i | −0.227463 | − | 0.393978i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.18388e6 | − | 261360.i | −0.356446 | − | 0.0786909i | ||||
\(407\) | −9.39535e6 | −2.81143 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.29314e6 | + | 5.70388e6i | −0.973423 | + | 1.68602i | −0.288381 | + | 0.957516i | \(0.593117\pi\) |
−0.685043 | + | 0.728503i | \(0.740217\pi\) | |||||||
\(410\) | −1.62143e6 | + | 2.80839e6i | −0.476362 | + | 0.825084i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 996247. | 0.289150 | ||||||||
\(413\) | 2.01149e6 | + | 6.35996e6i | 0.580286 | + | 1.83476i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −882487. | − | 1.52851e6i | −0.251529 | − | 0.435661i | ||||
\(416\) | −609346. | + | 1.05542e6i | −0.172636 | + | 0.299014i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.73559e6 | + | 3.00613e6i | 0.485855 | + | 0.841525i | ||||
\(419\) | 6.96869e6 | 1.93917 | 0.969585 | − | 0.244754i | \(-0.0787071\pi\) | ||||
0.969585 | + | 0.244754i | \(0.0787071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.84041e6 | 1.05602 | 0.528010 | − | 0.849238i | \(-0.322938\pi\) | ||||
0.528010 | + | 0.849238i | \(0.322938\pi\) | |||||||
\(422\) | −3.16668e6 | − | 5.48485e6i | −0.865612 | − | 1.49928i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −148890. | + | 257886.i | −0.0402209 | + | 0.0696647i | ||||
\(425\) | 1.08042e6 | + | 1.87134e6i | 0.290149 | + | 0.502552i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.20272e6 | + | 1.14858e6i | 1.38090 | + | 0.304854i | ||||
\(428\) | 197002. | 0.0519829 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.82308e6 | + | 3.15766e6i | −0.475481 | + | 0.823558i | ||||
\(431\) | 1.51818e6 | − | 2.62957e6i | 0.393668 | − | 0.681854i | −0.599262 | − | 0.800553i | \(-0.704539\pi\) |
0.992930 | + | 0.118699i | \(0.0378725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −941529. | −0.241332 | −0.120666 | − | 0.992693i | \(-0.538503\pi\) | ||||
−0.120666 | + | 0.992693i | \(0.538503\pi\) | |||||||
\(434\) | −2.18749e6 | + | 2.39147e6i | −0.557469 | + | 0.609454i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 370080. | + | 640997.i | 0.0932351 | + | 0.161488i | ||||
\(437\) | −769096. | + | 1.33211e6i | −0.192653 | + | 0.333686i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −670546. | − | 1.16142e6i | −0.166061 | − | 0.287626i | 0.770971 | − | 0.636871i | \(-0.219771\pi\) |
−0.937031 | + | 0.349245i | \(0.886438\pi\) | |||||||
\(440\) | −3.30494e6 | −0.813827 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.32635e6 | −0.809864 | ||||||||
\(443\) | −386171. | − | 668867.i | −0.0934910 | − | 0.161931i | 0.815487 | − | 0.578776i | \(-0.196469\pi\) |
−0.908978 | + | 0.416844i | \(0.863136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −303765. | + | 526137.i | −0.0727174 | + | 0.125950i | ||||
\(446\) | 1.73595e6 | + | 3.00675e6i | 0.413238 | + | 0.715748i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.69958e6 | + | 1.85807e6i | −0.400080 | + | 0.437388i | ||||
\(449\) | −2.25684e6 | −0.528304 | −0.264152 | − | 0.964481i | \(-0.585092\pi\) | ||||
−0.264152 | + | 0.964481i | \(0.585092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.77646e6 | + | 6.54101e6i | −0.874265 | + | 1.51427i | ||||
\(452\) | −180707. | + | 312994.i | −0.0416034 | + | 0.0720593i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 104.373 | 2.37655e−5 | ||||||||
\(455\) | −1.91942e6 | − | 423742.i | −0.434653 | − | 0.0959561i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.14235e6 | − | 3.71066e6i | −0.479844 | − | 0.831114i | 0.519889 | − | 0.854234i | \(-0.325973\pi\) |
−0.999733 | + | 0.0231196i | \(0.992640\pi\) | |||||||
\(458\) | −247221. | + | 428199.i | −0.0550708 | + | 0.0953854i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 279080. | + | 483381.i | 0.0614942 | + | 0.106511i | ||||
\(461\) | 3.10462e6 | 0.680387 | 0.340193 | − | 0.940355i | \(-0.389507\pi\) | ||||
0.340193 | + | 0.940355i | \(0.389507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.53386e6 | −0.766121 | −0.383060 | − | 0.923723i | \(-0.625130\pi\) | ||||
−0.383060 | + | 0.923723i | \(0.625130\pi\) | |||||||
\(464\) | 899053. | + | 1.55721e6i | 0.193861 | + | 0.335777i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 331178. | − | 573617.i | 0.0706475 | − | 0.122365i | ||||
\(467\) | 1.36230e6 | + | 2.35957e6i | 0.289054 | + | 0.500657i | 0.973584 | − | 0.228328i | \(-0.0733258\pi\) |
−0.684530 | + | 0.728985i | \(0.739993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.97728e6 | − | 6.25182e6i | −0.415085 | − | 1.31242i | ||||
\(470\) | 1.68641e6 | 0.352143 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.80883e6 | − | 6.59709e6i | 0.786932 | − | 1.36301i | ||||
\(473\) | −4.24612e6 | + | 7.35449e6i | −0.872649 | + | 1.51147i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.53158e6 | −0.311461 | ||||||||
\(476\) | 1.48643e6 | + | 328153.i | 0.300697 | + | 0.0663833i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.20166e6 | − | 3.81338e6i | −0.440737 | − | 0.763379i | ||||
\(479\) | 489342. | − | 847566.i | 0.0974482 | − | 0.168785i | −0.813180 | − | 0.582013i | \(-0.802265\pi\) |
0.910628 | + | 0.413228i | \(0.135599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.19072e6 | + | 5.52649e6i | 0.628819 | + | 1.08915i | ||||
\(482\) | −1.40766e6 | −0.275982 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.51154e6 | 0.293296 | ||||||||
\(485\) | 60581.8 | + | 104931.i | 0.0116947 | + | 0.0202558i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.96372e6 | + | 3.40126e6i | −0.375195 | + | 0.649857i | −0.990356 | − | 0.138544i | \(-0.955758\pi\) |
0.615161 | + | 0.788401i | \(0.289091\pi\) | |||||||
\(488\) | −3.04228e6 | − | 5.26938e6i | −0.578295 | − | 1.00164i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.77271e6 | + | 1.75111e6i | 0.709844 | + | 0.329475i | ||||
\(491\) | −2.63241e6 | −0.492777 | −0.246388 | − | 0.969171i | \(-0.579244\pi\) | ||||
−0.246388 | + | 0.969171i | \(0.579244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −973037. | + | 1.68535e6i | −0.180307 | + | 0.312301i | ||||
\(494\) | 1.17883e6 | − | 2.04180e6i | 0.217338 | − | 0.376440i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.80678e6 | 0.877305 | ||||||||
\(497\) | 3.49743e6 | − | 3.82357e6i | 0.635123 | − | 0.694350i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.06272e6 | − | 1.84069e6i | −0.191059 | − | 0.330924i | 0.754542 | − | 0.656251i | \(-0.227859\pi\) |
−0.945601 | + | 0.325327i | \(0.894526\pi\) | |||||||
\(500\) | −812244. | + | 1.40685e6i | −0.145299 | + | 0.251665i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.58925e6 | − | 7.94881e6i | −0.812798 | − | 1.40781i | ||||
\(503\) | −2.60929e6 | −0.459835 | −0.229917 | − | 0.973210i | \(-0.573846\pi\) | ||||
−0.229917 | + | 0.973210i | \(0.573846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.54564e6 | −1.14215 | ||||||||
\(506\) | 3.00552e6 | + | 5.20571e6i | 0.521847 | + | 0.903865i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −367654. | + | 636795.i | −0.0632092 | + | 0.109481i | ||||
\(509\) | −5.00911e6 | − | 8.67603e6i | −0.856970 | − | 1.48432i | −0.874805 | − | 0.484475i | \(-0.839011\pi\) |
0.0178348 | − | 0.999841i | \(-0.494323\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.17699e6 | + | 6.88326e6i | 0.368811 | + | 1.16612i | ||||
\(512\) | 1.99607e6 | 0.336512 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.90482e6 | − | 5.03130e6i | 0.484967 | − | 0.839987i | ||||
\(515\) | 2.18471e6 | − | 3.78403e6i | 0.362974 | − | 0.628689i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.92782e6 | 0.646287 | ||||||||
\(518\) | −4.07187e6 | − | 1.28745e7i | −0.666760 | − | 2.10818i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.12238e6 | + | 1.94402e6i | 0.182025 | + | 0.315277i | ||||
\(521\) | −2.08970e6 | + | 3.61947e6i | −0.337280 | + | 0.584186i | −0.983920 | − | 0.178609i | \(-0.942840\pi\) |
0.646640 | + | 0.762795i | \(0.276174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.80263e6 | − | 3.12224e6i | −0.288172 | − | 0.499128i | 0.685202 | − | 0.728353i | \(-0.259714\pi\) |
−0.973373 | + | 0.229225i | \(0.926381\pi\) | |||||||
\(524\) | 1.47357e6 | 0.234446 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.78637e6 | 0.754297 | ||||||||
\(527\) | 2.60117e6 | + | 4.50536e6i | 0.407983 | + | 0.706648i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.88633e6 | − | 3.26722e6i | 0.293075 | − | 0.507621i | ||||
\(530\) | −248877. | − | 431068.i | −0.0384853 | − | 0.0666586i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −728212. | + | 796119.i | −0.111552 | + | 0.121955i | ||||
\(533\) | 5.13003e6 | 0.782172 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 432013. | − | 748268.i | 0.0652547 | − | 0.113025i | ||||
\(536\) | −3.74407e6 | + | 6.48492e6i | −0.562901 | + | 0.974972i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.28086e6 | 0.637640 | ||||||||
\(539\) | 8.78699e6 | + | 4.07850e6i | 1.30277 | + | 0.604684i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.34083e6 | + | 5.78648e6i | 0.490751 | + | 0.850005i | 0.999943 | − | 0.0106475i | \(-0.00338926\pi\) |
−0.509193 | + | 0.860653i | \(0.670056\pi\) | |||||||
\(542\) | 1.72737e6 | − | 2.99189e6i | 0.252573 | − | 0.437470i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.06964e6 | − | 3.58473e6i | −0.299846 | − | 0.519349i | ||||
\(545\) | 3.24625e6 | 0.468156 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.69076e6 | 1.24191 | 0.620954 | − | 0.783847i | \(-0.286745\pi\) | ||||
0.620954 | + | 0.783847i | \(0.286745\pi\) | |||||||
\(548\) | 168766. | + | 292312.i | 0.0240068 | + | 0.0415810i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.99259e6 | + | 5.18332e6i | −0.421833 | + | 0.730636i | ||||
\(551\) | −689676. | − | 1.19455e6i | −0.0967756 | − | 0.167620i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.99456e6 | − | 1.76492e6i | −1.11168 | − | 0.245421i | ||||
\(554\) | 2.56815e6 | 0.355505 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −469171. | + | 812628.i | −0.0643642 | + | 0.111482i | ||||
\(557\) | 3.12371e6 | − | 5.41042e6i | 0.426612 | − | 0.738913i | −0.569958 | − | 0.821674i | \(-0.693040\pi\) |
0.996569 | + | 0.0827611i | \(0.0263738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.76803e6 | 0.780725 | ||||||||
\(560\) | −1.86017e6 | − | 5.88152e6i | −0.250658 | − | 0.792537i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.37107e6 | + | 2.37476e6i | 0.183113 | + | 0.317161i | ||||
\(563\) | −5.95223e6 | + | 1.03096e7i | −0.791423 | + | 1.37078i | 0.133663 | + | 0.991027i | \(0.457326\pi\) |
−0.925086 | + | 0.379758i | \(0.876007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 792560. | + | 1.37275e6i | 0.104451 | + | 0.180914i | ||||
\(566\) | 2.17848e6 | 0.285833 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.91768e6 | −0.769627 | ||||||||
\(569\) | 10707.2 | + | 18545.4i | 0.00138642 | + | 0.00240135i | 0.866718 | − | 0.498799i | \(-0.166225\pi\) |
−0.865331 | + | 0.501200i | \(0.832892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.55823e6 | + | 6.16304e6i | −0.456714 | + | 0.791051i | −0.998785 | − | 0.0492811i | \(-0.984307\pi\) |
0.542071 | + | 0.840333i | \(0.317640\pi\) | |||||||
\(572\) | −996297. | − | 1.72564e6i | −0.127321 | − | 0.220526i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.05999e7 | − | 2.34009e6i | −1.34283 | − | 0.296451i | ||||
\(575\) | −2.65223e6 | −0.334534 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.33259e6 | − | 9.23632e6i | 0.666805 | − | 1.15494i | −0.311988 | − | 0.950086i | \(-0.600995\pi\) |
0.978793 | − | 0.204854i | \(-0.0656719\pi\) | |||||||
\(578\) | 1.11262e6 | − | 1.92712e6i | 0.138525 | − | 0.239932i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −500522. | −0.0617808 | ||||||||
\(581\) | 3.98758e6 | − | 4.35943e6i | 0.490083 | − | 0.535784i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −579659. | − | 1.00400e6i | −0.0706319 | − | 0.122338i | ||||
\(584\) | 4.12222e6 | − | 7.13990e6i | 0.500149 | − | 0.866283i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.24234e6 | + | 2.15180e6i | 0.149450 | + | 0.258856i | ||||
\(587\) | 1.30101e7 | 1.55843 | 0.779213 | − | 0.626759i | \(-0.215619\pi\) | ||||
0.779213 | + | 0.626759i | \(0.215619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.68735e6 | −0.437952 | ||||||||
\(590\) | 6.36664e6 | + | 1.10273e7i | 0.752975 | + | 1.30419i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00133e7 | + | 1.73435e7i | −1.17428 | + | 2.03391i | ||||
\(593\) | 2.13043e6 | + | 3.69002e6i | 0.248789 | + | 0.430915i | 0.963190 | − | 0.268821i | \(-0.0866342\pi\) |
−0.714401 | + | 0.699736i | \(0.753301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.50608e6 | − | 4.92628e6i | 0.521803 | − | 0.570462i | ||||
\(596\) | −1.70034e6 | −0.196074 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.04139e6 | − | 3.53578e6i | 0.233438 | − | 0.404327i | ||||
\(599\) | −6.89790e6 | + | 1.19475e7i | −0.785507 | + | 1.36054i | 0.143189 | + | 0.989695i | \(0.454264\pi\) |
−0.928696 | + | 0.370842i | \(0.879069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.99695e6 | 0.564311 | 0.282155 | − | 0.959369i | \(-0.408951\pi\) | ||||
0.282155 | + | 0.959369i | \(0.408951\pi\) | |||||||
\(602\) | −1.19182e7 | − | 2.63111e6i | −1.34035 | − | 0.295902i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −625628. | − | 1.08362e6i | −0.0697788 | − | 0.120860i | ||||
\(605\) | 3.31471e6 | − | 5.74125e6i | 0.368177 | − | 0.637702i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.52473e6 | + | 2.64091e6i | 0.167966 | + | 0.290926i | 0.937705 | − | 0.347434i | \(-0.112947\pi\) |
−0.769739 | + | 0.638359i | \(0.779613\pi\) | |||||||
\(608\) | 2.93387e6 | 0.321871 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.01706e7 | 1.10668 | ||||||||
\(611\) | −1.33391e6 | − | 2.31040e6i | −0.144552 | − | 0.250372i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.51813e6 | − | 6.09357e6i | 0.378147 | − | 0.654969i | −0.612646 | − | 0.790357i | \(-0.709895\pi\) |
0.990793 | + | 0.135388i | \(0.0432282\pi\) | |||||||
\(614\) | −7.53195e6 | − | 1.30457e7i | −0.806281 | − | 1.39652i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.33605e6 | − | 1.05480e7i | −0.354226 | − | 1.12000i | ||||
\(617\) | −1.00066e7 | −1.05822 | −0.529108 | − | 0.848554i | \(-0.677473\pi\) | ||||
−0.529108 | + | 0.848554i | \(0.677473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.27533e6 | − | 5.67304e6i | 0.343581 | − | 0.595099i | −0.641514 | − | 0.767111i | \(-0.721693\pi\) |
0.985095 | + | 0.172012i | \(0.0550268\pi\) | |||||||
\(620\) | −669010. | + | 1.15876e6i | −0.0698962 | + | 0.121064i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.17986e6 | −0.951393 | ||||||||
\(623\) | −1.98583e6 | − | 438403.i | −0.204985 | − | 0.0452536i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.02325e6 | + | 1.77232e6i | 0.104781 | + | 0.181485i | ||||
\(626\) | −2.62879e6 | + | 4.55320e6i | −0.268114 | + | 0.464388i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.49799e6 | − | 4.32665e6i | −0.252750 | − | 0.437777i | ||||
\(629\) | −2.16746e7 | −2.18436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.22672e6 | 0.222635 | 0.111317 | − | 0.993785i | \(-0.464493\pi\) | ||||
0.111317 | + | 0.993785i | \(0.464493\pi\) | |||||||
\(632\) | 4.67480e6 | + | 8.09699e6i | 0.465554 | + | 0.806364i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.64524e6 | − | 9.77784e6i | 0.557775 | − | 0.966095i | ||||
\(635\) | 1.61249e6 | + | 2.79291e6i | 0.158694 | + | 0.274867i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −585084. | − | 6.55373e6i | −0.0571307 | − | 0.639941i | ||||
\(638\) | −5.39031e6 | −0.524279 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.33242e6 | + | 7.50397e6i | −0.418101 | + | 0.724171i | ||||
\(641\) | −7.96698e6 | + | 1.37992e7i | −0.765859 | + | 1.32651i | 0.173932 | + | 0.984758i | \(0.444353\pi\) |
−0.939791 | + | 0.341749i | \(0.888981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.49933e7 | −1.43011 | −0.715056 | − | 0.699067i | \(-0.753599\pi\) | ||||
−0.715056 | + | 0.699067i | \(0.753599\pi\) | |||||||
\(644\) | −1.26104e6 | + | 1.37864e6i | −0.119816 | + | 0.130989i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.00391e6 | + | 6.93498e6i | 0.377488 | + | 0.653829i | ||||
\(647\) | 6.49027e6 | − | 1.12415e7i | 0.609540 | − | 1.05575i | −0.381776 | − | 0.924255i | \(-0.624687\pi\) |
0.991316 | − | 0.131500i | \(-0.0419792\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.48285e7 | + | 2.56838e7i | 1.38193 | + | 2.39357i | ||||
\(650\) | 4.06521e6 | 0.377398 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.79885e6 | −0.349972 | ||||||||
\(653\) | −8.27460e6 | − | 1.43320e7i | −0.759389 | − | 1.31530i | −0.943163 | − | 0.332332i | \(-0.892165\pi\) |
0.183774 | − | 0.982969i | \(-0.441169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.23145e6 | − | 5.59704e6i | 0.294303 | − | 0.509748i | ||||
\(656\) | 8.04966e6 | + | 1.39424e7i | 0.730328 | + | 1.26497i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.70229e6 | + | 5.38233e6i | 0.153274 | + | 0.484625i | ||||
\(659\) | −5.86879e6 | −0.526423 | −0.263212 | − | 0.964738i | \(-0.584782\pi\) | ||||
−0.263212 | + | 0.964738i | \(0.584782\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.63843e6 | + | 6.30195e6i | −0.323900 | + | 0.561011i | −0.981289 | − | 0.192540i | \(-0.938327\pi\) |
0.657389 | + | 0.753551i | \(0.271661\pi\) | |||||||
\(662\) | −9751.81 | + | 16890.6i | −0.000864849 | + | 0.00149796i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.74702e6 | −0.593870 | ||||||||
\(665\) | 1.42696e6 | + | 4.51179e6i | 0.125129 | + | 0.395635i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.19431e6 | − | 2.06861e6i | −0.103945 | − | 0.180038i | ||||
\(668\) | −1.06082e6 | + | 1.83739e6i | −0.0919815 | + | 0.159317i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.25838e6 | − | 1.08398e7i | −0.538611 | − | 0.932902i | ||||
\(671\) | 2.36884e7 | 2.03109 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.82417e7 | −1.55248 | −0.776241 | − | 0.630437i | \(-0.782876\pi\) | ||||
−0.776241 | + | 0.630437i | \(0.782876\pi\) | |||||||
\(674\) | 6.48376e6 | + | 1.12302e7i | 0.549765 | + | 0.952222i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 962636. | − | 1.66733e6i | 0.0810205 | − | 0.140332i | ||||
\(677\) | −3.88203e6 | − | 6.72387e6i | −0.325527 | − | 0.563829i | 0.656092 | − | 0.754681i | \(-0.272208\pi\) |
−0.981619 | + | 0.190852i | \(0.938875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −273743. | + | 299270.i | −0.0227860 | + | 0.0249109i | ||||
\(680\) | −7.62432e6 | −0.632308 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.20482e6 | + | 1.24791e7i | −0.593147 | + | 1.02736i | ||||
\(683\) | 4.28162e6 | − | 7.41598e6i | 0.351201 | − | 0.608299i | −0.635259 | − | 0.772299i | \(-0.719107\pi\) |
0.986460 | + | 0.164001i | \(0.0524399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.48038e6 | 0.120544 | ||||||||
\(686\) | −1.78059e6 | + | 1.38085e7i | −0.144462 | + | 1.12030i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.05076e6 | + | 1.56764e7i | 0.728978 | + | 1.26263i | ||||
\(689\) | −393712. | + | 681928.i | −0.0315959 | + | 0.0547256i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.22547e6 | − | 1.42469e7i | −0.655338 | − | 1.13508i | −0.981809 | − | 0.189872i | \(-0.939193\pi\) |
0.326471 | − | 0.945207i | \(-0.394140\pi\) | |||||||
\(692\) | 1.58329e6 | 0.125689 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.41677e7 | 1.90474 | ||||||||
\(695\) | 2.05773e6 | + | 3.56409e6i | 0.161594 | + | 0.279890i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.71208e6 | + | 1.50898e7i | −0.679266 | + | 1.17652i | ||||
\(698\) | 930197. | + | 1.61115e6i | 0.0722664 | + | 0.125169i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.81661e6 | − | 401044.i | −0.140125 | − | 0.0309347i | ||||
\(701\) | 1.66928e7 | 1.28302 | 0.641512 | − | 0.767113i | \(-0.278307\pi\) | ||||
0.641512 | + | 0.767113i | \(0.278307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.68132e6 | − | 1.33044e7i | 0.586202 | − | 1.01533i | ||||
\(704\) | −5.59783e6 | + | 9.69573e6i | −0.425685 | + | 0.737308i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.46059e6 | 0.185792 | ||||||||
\(707\) | −6.60725e6 | − | 2.08909e7i | −0.497132 | − | 1.57184i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.80890e6 | − | 4.86515e6i | −0.209855 | − | 0.363480i | 0.741813 | − | 0.670606i | \(-0.233966\pi\) |
−0.951669 | + | 0.307126i | \(0.900633\pi\) | |||||||
\(710\) | 4.94584e6 | − | 8.56644e6i | 0.368209 | − | 0.637756i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.16121e6 | + | 2.01128e6i | 0.0858443 | + | 0.148687i | ||||
\(713\) | −6.38537e6 | −0.470395 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.73927e6 | −0.639308 | ||||||||
\(716\) | −2.54121e6 | − | 4.40150e6i | −0.185250 | − | 0.320862i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.03201e7 | − | 1.78749e7i | 0.747087 | − | 1.29399i | ||||
\(719\) | 5.18592e6 | + | 8.98227e6i | 0.374113 | + | 0.647983i | 0.990194 | − | 0.139700i | \(-0.0446138\pi\) |
−0.616081 | + | 0.787683i | \(0.711280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42823e7 | + | 3.15303e6i | 1.02320 | + | 0.225887i | ||||
\(722\) | 1.01461e7 | 0.724363 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.56526e6 | + | 4.44316e6i | −0.181880 | + | 0.315025i | ||||
\(725\) | 1.18917e6 | − | 2.05971e6i | 0.0840233 | − | 0.145533i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.15369e7 | 0.809565 | 0.404783 | − | 0.914413i | \(-0.367347\pi\) | ||||
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(728\) | −5.07155e6 | + | 5.54448e6i | −0.354660 | + | 0.387733i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.89049e6 | + | 1.19347e7i | 0.478567 | + | 0.828902i | ||||
\(731\) | −9.79557e6 | + | 1.69664e7i | −0.678010 | + | 1.17435i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.47349e6 | − | 1.29445e7i | −0.513764 | − | 0.889865i | −0.999873 | − | 0.0159667i | \(-0.994917\pi\) |
0.486109 | − | 0.873898i | \(-0.338416\pi\) | |||||||
\(734\) | 3.06432e6 | 0.209939 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.08058e6 | 0.345715 | ||||||||
\(737\) | −1.45764e7 | − | 2.52470e7i | −0.988510 | − | 1.71215i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.50682e6 | + | 7.80604e6i | −0.303570 | + | 0.525799i | −0.976942 | − | 0.213505i | \(-0.931512\pi\) |
0.673372 | + | 0.739304i | \(0.264845\pi\) | |||||||
\(740\) | −2.78730e6 | − | 4.82775e6i | −0.187113 | − | 0.324090i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.12457e6 | − | 1.22944e6i | 0.0749853 | − | 0.0819779i | ||||
\(743\) | 2.10239e7 | 1.39714 | 0.698571 | − | 0.715541i | \(-0.253820\pi\) | ||||
0.698571 | + | 0.715541i | \(0.253820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.72875e6 | + | 6.45838e6i | −0.246134 | + | 0.426317i | ||||
\(746\) | 2.78811e6 | − | 4.82915e6i | 0.183427 | − | 0.317705i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.76785e6 | 0.442279 | ||||||||
\(749\) | 2.82424e6 | + | 623493.i | 0.183949 | + | 0.0406094i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.02110e6 | − | 3.50064e6i | −0.130764 | − | 0.226489i | 0.793207 | − | 0.608952i | \(-0.208410\pi\) |
−0.923971 | + | 0.382462i | \(0.875076\pi\) | |||||||
\(752\) | 4.18615e6 | − | 7.25062e6i | 0.269942 | − | 0.467553i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.83058e6 | + | 3.17066e6i | 0.117263 | + | 0.203106i | ||||
\(755\) | −5.48786e6 | −0.350377 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.82059e7 | −1.15471 | −0.577353 | − | 0.816495i | \(-0.695914\pi\) | ||||
−0.577353 | + | 0.816495i | \(0.695914\pi\) | |||||||
\(758\) | −7.77945e6 | − | 1.34744e7i | −0.491786 | − | 0.851798i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.70201e6 | − | 4.68001e6i | 0.169689 | − | 0.293909i | ||||
\(761\) | −9.45999e6 | − | 1.63852e7i | −0.592146 | − | 1.02563i | −0.993943 | − | 0.109898i | \(-0.964947\pi\) |
0.401797 | − | 0.915729i | \(-0.368386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.27681e6 | + | 1.03607e7i | 0.203770 | + | 0.644283i | ||||
\(764\) | 5.83301e6 | 0.361542 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.15391e7 | − | 1.99863e7i | 0.710559 | − | 1.23072i | ||||
\(767\) | 1.00717e7 | − | 1.74447e7i | 0.618180 | − | 1.07072i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.12831e7 | −0.688037 | −0.344019 | − | 0.938963i | \(-0.611788\pi\) | ||||
−0.344019 | + | 0.938963i | \(0.611788\pi\) | |||||||
\(770\) | 1.80575e7 | + | 3.98646e6i | 1.09756 | + | 0.242304i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.46064e6 | + | 4.26195e6i | 0.148595 | + | 0.257374i | ||||
\(773\) | −1.84282e6 | + | 3.19186e6i | −0.110926 | + | 0.192130i | −0.916144 | − | 0.400849i | \(-0.868715\pi\) |
0.805218 | + | 0.592979i | \(0.202048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.17896e6 | − | 5.50611e6i | −0.190121 | − | 0.329299i | ||||
\(776\) | 463176. | 0.0276116 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.11971e6 | −0.0663219 | ||||||||
\(779\) | −6.17501e6 | − | 1.06954e7i | −0.364581 | − | 0.631472i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.15193e7 | − | 1.99521e7i | 0.675771 | − | 1.17047i | ||||
\(782\) | 6.93357e6 | + | 1.20093e7i | 0.405452 | + | 0.702264i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.68937e7 | − | 1.18738e7i | 0.981599 | − | 0.689919i | ||||
\(785\) | −2.19118e7 | −1.26912 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.03741e6 | − | 1.21891e7i | 0.405019 | − | 0.701514i | −0.589304 | − | 0.807911i | \(-0.700598\pi\) |
0.994324 | + | 0.106397i | \(0.0339314\pi\) | |||||||
\(788\) | −3.36173e6 | + | 5.82269e6i | −0.192862 | + | 0.334048i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.56283e7 | −0.890930 | ||||||||
\(791\) | −3.58124e6 | + | 3.91519e6i | −0.203513 | + | 0.222491i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.04472e6 | − | 1.39339e7i | −0.454284 | − | 0.786844i | ||||
\(794\) | 6.02294e6 | − | 1.04320e7i | 0.339045 | − | 0.587243i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 599848. | + | 1.03897e6i | 0.0335551 | + | 0.0581191i | ||||
\(797\) | 1.75191e7 | 0.976937 | 0.488469 | − | 0.872582i | \(-0.337556\pi\) | ||||
0.488469 | + | 0.872582i | \(0.337556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.06127e6 | 0.502137 | ||||||||
\(800\) | 2.52936e6 | + | 4.38099e6i | 0.139729 | + | 0.242018i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.28067e6 | + | 7.41433e6i | −0.235004 | + | 0.407039i | ||||
\(803\) | 1.60486e7 | + | 2.77970e7i | 0.878311 | + | 1.52128i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.47106e6 | + | 7.81306e6i | 0.134398 | + | 0.424944i | ||||
\(806\) | 9.78721e6 | 0.530666 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.25111e7 | + | 2.16698e7i | −0.674166 | + | 1.16769i | ||||
\(809\) | 407261. | − | 705396.i | 0.0218777 | − | 0.0378932i | −0.854879 | − | 0.518827i | \(-0.826369\pi\) |
0.876757 | + | 0.480934i | \(0.159702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.26533e7 | 0.675540 | 0.337770 | − | 0.941229i | \(-0.390327\pi\) | ||||
0.337770 | + | 0.941229i | \(0.390327\pi\) | |||||||
\(812\) | −505233. | − | 1.59746e6i | −0.0268907 | − | 0.0850235i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.00175e7 | − | 5.19919e7i | −1.58787 | − | 2.75026i | ||||
\(815\) | −8.33064e6 | + | 1.44291e7i | −0.439324 | + | 0.760931i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.94297e6 | − | 1.20256e7i | −0.363907 | − | 0.630305i | ||||
\(818\) | −4.20854e7 | −2.19912 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.48142e6 | −0.232745 | ||||||||
\(821\) | 2.13697e6 | + | 3.70133e6i | 0.110647 | + | 0.191646i | 0.916031 | − | 0.401107i | \(-0.131374\pi\) |
−0.805384 | + | 0.592753i | \(0.798041\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.52317e6 | + | 1.47626e7i | −0.438633 | + | 0.759735i | −0.997584 | − | 0.0694656i | \(-0.977871\pi\) |
0.558951 | + | 0.829201i | \(0.311204\pi\) | |||||||
\(824\) | −8.35155e6 | − | 1.44653e7i | −0.428498 | − | 0.742180i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.87681e7 | + | 3.14508e7i | −1.46711 | + | 1.60392i | ||||
\(827\) | −2.60828e6 | −0.132614 | −0.0663071 | − | 0.997799i | \(-0.521122\pi\) | ||||
−0.0663071 | + | 0.997799i | \(0.521122\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.06932e7 | + | 1.85212e7i | −0.540409 | + | 0.936016i | 0.458471 | + | 0.888709i | \(0.348397\pi\) |
−0.998880 | + | 0.0473066i | \(0.984936\pi\) | |||||||
\(830\) | 5.63898e6 | − | 9.76700e6i | 0.284122 | − | 0.492114i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.60423e6 | 0.380844 | ||||||||
\(833\) | 2.02711e7 | + | 9.40887e6i | 1.01220 | + | 0.469813i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.65263e6 | + | 8.05859e6i | 0.230931 | + | 0.399984i | ||||
\(836\) | −2.39848e6 | + | 4.15429e6i | −0.118692 | + | 0.205580i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.22645e7 | + | 3.85632e7i | 1.09522 | + | 1.89698i | ||||
\(839\) | −771393. | −0.0378330 | −0.0189165 | − | 0.999821i | \(-0.506022\pi\) | ||||
−0.0189165 | + | 0.999821i | \(0.506022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.83692e7 | −0.895571 | ||||||||
\(842\) | 1.22699e7 | + | 2.12520e7i | 0.596430 | + | 1.03305i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.37616e6 | − | 7.57973e6i | 0.211464 | − | 0.366267i | ||||
\(845\) | −4.22200e6 | − | 7.31272e6i | −0.203412 | − | 0.352320i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.16696e7 | + | 4.78388e6i | 1.03787 | + | 0.229125i | ||||
\(848\) | −2.47113e6 | −0.118006 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.90375e6 | + | 1.19576e7i | −0.327746 | + | 0.567673i | ||||
\(851\) | 1.33017e7 | − | 2.30393e7i | 0.629628 | − | 1.09055i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.94032e7 | 1.38364 | 0.691818 | − | 0.722072i | \(-0.256810\pi\) | ||||
0.691818 | + | 0.722072i | \(0.256810\pi\) | |||||||
\(854\) | 1.02664e7 | + | 3.24604e7i | 0.481694 | + | 1.52303i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.65147e6 | − | 2.86042e6i | −0.0770345 | − | 0.133428i | ||||
\(857\) | −1.32505e7 | + | 2.29505e7i | −0.616283 | + | 1.06743i | 0.373875 | + | 0.927479i | \(0.378029\pi\) |
−0.990158 | + | 0.139954i | \(0.955304\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.83759e7 | + | 3.18281e7i | 0.849702 | + | 1.47173i | 0.881475 | + | 0.472232i | \(0.156551\pi\) |
−0.0317727 | + | 0.999495i | \(0.510115\pi\) | |||||||
\(860\) | −5.03876e6 | −0.232315 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.94020e7 | 0.889360 | ||||||||
\(863\) | 5.90946e6 | + | 1.02355e7i | 0.270098 | + | 0.467823i | 0.968887 | − | 0.247505i | \(-0.0796106\pi\) |
−0.698789 | + | 0.715328i | \(0.746277\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.47207e6 | − | 6.01379e6i | 0.157778 | − | 0.273280i | ||||
\(866\) | −3.00812e6 | − | 5.21022e6i | −0.136302 | − | 0.236081i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.37358e6 | − | 965534.i | −0.197033 | − | 0.0434979i | ||||
\(869\) | −3.63998e7 | −1.63512 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.90046e6 | + | 1.71481e7i | −0.442191 | + | 0.765897i | ||||
\(872\) | 6.20477e6 | − | 1.07470e7i | 0.276334 | − | 0.478625i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.82884e6 | −0.435235 | ||||||||
\(875\) | −1.60970e7 | + | 1.75980e7i | −0.710762 | + | 0.777042i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.96754e6 | − | 6.87199e6i | −0.174190 | − | 0.301706i | 0.765691 | − | 0.643209i | \(-0.222397\pi\) |
−0.939881 | + | 0.341503i | \(0.889064\pi\) | |||||||
\(878\) | 4.28470e6 | − | 7.42131e6i | 0.187579 | − | 0.324896i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.37130e7 | − | 2.37516e7i | −0.596934 | − | 1.03392i | ||||
\(881\) | −4.20152e7 | −1.82375 | −0.911877 | − | 0.410464i | \(-0.865367\pi\) | ||||
−0.911877 | + | 0.410464i | \(0.865367\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.12461e7 | 0.917016 | 0.458508 | − | 0.888690i | \(-0.348384\pi\) | ||||
0.458508 | + | 0.888690i | \(0.348384\pi\) | |||||||
\(884\) | −2.29840e6 | − | 3.98095e6i | −0.0989226 | − | 0.171339i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.46758e6 | − | 4.27397e6i | 0.105606 | − | 0.182914i | ||||
\(887\) | 9.42452e6 | + | 1.63238e7i | 0.402208 | + | 0.696644i | 0.993992 | − | 0.109452i | \(-0.0349097\pi\) |
−0.591784 | + | 0.806096i | \(0.701576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.28613e6 | + | 7.96558e6i | −0.309202 | + | 0.338036i | ||||
\(890\) | −3.88204e6 | −0.164280 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.39897e6 | + | 4.15514e6i | −0.100952 | + | 0.174853i | ||||
\(893\) | −3.21125e6 | + | 5.56205e6i | −0.134755 | + | 0.233403i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.22909e7 | −0.930186 | ||||||||
\(896\) | −2.83227e7 | − | 6.25267e6i | −1.17860 | − | 0.260193i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.21044e6 | − | 1.24889e7i | −0.298381 | − | 0.516811i | ||||
\(899\) | 2.86300e6 | − | 4.95886e6i | 0.118147 | − | 0.204636i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.33724e6 | − | 2.31617e6i | −0.0548780 | − | 0.0950514i | ||||
\(902\) | −4.82621e7 | −1.97510 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.05948e6 | 0.246612 | ||||||||
\(905\) | 1.12509e7 | + | 1.94872e7i | 0.456632 | + | 0.790910i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.09723e6 | − | 5.36456e6i | 0.125013 | − | 0.216529i | −0.796725 | − | 0.604342i | \(-0.793436\pi\) |
0.921738 | + | 0.387813i | \(0.126769\pi\) | |||||||
\(908\) | 72.1183 | + | 124.912i | 2.90289e−6 | + | 5.02795e-6i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.78753e6 | − | 1.19755e7i | −0.151619 | − | 0.479392i | ||||
\(911\) | 2.50171e7 | 0.998712 | 0.499356 | − | 0.866397i | \(-0.333570\pi\) | ||||
0.499356 | + | 0.866397i | \(0.333570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.31337e7 | − | 2.27483e7i | 0.521448 | − | 0.903174i | ||||
\(914\) | 1.36893e7 | − | 2.37106e7i | 0.542022 | − | 0.938810i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −683288. | −0.0269070 | ||||||||
\(917\) | 2.11253e7 | + | 4.66373e6i | 0.829620 | + | 0.183151i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.74961e6 | − | 1.34227e7i | −0.302685 | − | 0.524266i | 0.674058 | − | 0.738678i | \(-0.264550\pi\) |
−0.976743 | + | 0.214412i | \(0.931216\pi\) | |||||||
\(920\) | 4.67906e6 | − | 8.10437e6i | 0.182259 | − | 0.315682i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.91905e6 | + | 1.71803e7i | 0.384276 | + | 0.665585i | ||||
\(923\) | −1.56481e7 | −0.604587 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.64890e7 | 1.01791 | ||||||||
\(926\) | −1.12905e7 | − | 1.95556e7i | −0.432697 | − | 0.749453i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.27797e6 | + | 3.94556e6i | −0.0868316 | + | 0.150397i | ||||
\(929\) | 1.87643e7 | + | 3.25007e7i | 0.713333 | + | 1.23553i | 0.963599 | + | 0.267352i | \(0.0861485\pi\) |
−0.250266 | + | 0.968177i | \(0.580518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.29594e7 | + | 9.10852e6i | −0.490015 | + | 0.344408i | ||||
\(932\) | 915335. | 0.0345176 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.70489e6 | + | 1.50773e7i | −0.326510 | + | 0.565532i | ||||
\(935\) | 1.48415e7 | − | 2.57062e7i | 0.555198 | − | 0.961632i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.08298e7 | −0.402969 | −0.201485 | − | 0.979492i | \(-0.564577\pi\) | ||||
−0.201485 | + | 0.979492i | \(0.564577\pi\) | |||||||
\(938\) | 2.82789e7 | − | 3.09160e7i | 1.04944 | − | 1.14730i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.16526e6 | + | 2.01829e6i | 0.0430133 | + | 0.0745013i | ||||
\(941\) | 1.62295e7 | − | 2.81104e7i | 0.597492 | − | 1.03489i | −0.395699 | − | 0.918380i | \(-0.629497\pi\) |
0.993190 | − | 0.116505i | \(-0.0371692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.06932e7 | − | 1.85212e7i | −0.391589 | − | 0.678251i | ||||
\(944\) | 6.32151e7 | 2.30883 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.42643e7 | −1.97145 | ||||||||
\(947\) | 3.76939e6 | + | 6.52877e6i | 0.136583 | + | 0.236568i | 0.926201 | − | 0.377030i | \(-0.123055\pi\) |
−0.789618 | + | 0.613598i | \(0.789721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.09004e7 | − | 1.88801e7i | 0.392896 | − | 0.680516i | ||||
\(950\) | −4.89328e6 | − | 8.47541e6i | −0.175910 | − | 0.304686i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.69608e6 | − | 2.43336e7i | −0.275218 | − | 0.870191i | ||||
\(953\) | 3.01356e7 | 1.07485 | 0.537424 | − | 0.843312i | \(-0.319398\pi\) | ||||
0.537424 | + | 0.843312i | \(0.319398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.27914e7 | − | 2.21554e7i | 0.453848 | − | 0.786089i | ||||
\(956\) | 3.04255e6 | − | 5.26986e6i | 0.107670 | − | 0.186489i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.25366e6 | 0.220151 | ||||||||
\(959\) | 1.49431e6 | + | 4.72474e6i | 0.0524680 | + | 0.165894i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.66107e6 | + | 1.15373e7i | 0.232667 | + | 0.402992i | ||||
\(962\) | −2.03883e7 | + | 3.53135e7i | −0.710301 | + | 1.23028i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −972650. | − | 1.68468e6i | −0.0337104 | − | 0.0583882i | ||||
\(965\) | 2.15841e7 | 0.746132 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.88021e6 | 0.0990509 | 0.0495255 | − | 0.998773i | \(-0.484229\pi\) | ||||
0.0495255 | + | 0.998773i | \(0.484229\pi\) | |||||||
\(968\) | −1.26712e7 | − | 2.19472e7i | −0.434641 | − | 0.752820i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −387110. | + | 670494.i | −0.0132101 | + | 0.0228805i | ||||
\(971\) | −1.37245e7 | − | 2.37715e7i | −0.467142 | − | 0.809113i | 0.532154 | − | 0.846648i | \(-0.321383\pi\) |
−0.999295 | + | 0.0375347i | \(0.988050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.29799e6 | + | 1.01650e7i | −0.314852 | + | 0.344213i | ||||
\(974\) | −2.50958e7 | −0.847626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.52463e7 | − | 4.37279e7i | 0.848347 | − | 1.46938i | ||||
\(977\) | −2.94262e7 | + | 5.09676e7i | −0.986274 | + | 1.70828i | −0.350141 | + | 0.936697i | \(0.613866\pi\) |
−0.636133 | + | 0.771579i | \(0.719467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.04164e6 | −0.301502 | ||||||||
\(980\) | 511109. | + | 5.72511e6i | 0.0170000 | + | 0.190423i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.41039e6 | − | 1.45672e7i | −0.278315 | − | 0.482056i | ||||
\(983\) | 9.30384e6 | − | 1.61147e7i | 0.307099 | − | 0.531911i | −0.670627 | − | 0.741794i | \(-0.733975\pi\) |
0.977726 | + | 0.209883i | \(0.0673084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.47442e7 | + | 2.55376e7i | 0.484205 | + | 0.838668i | ||||
\(986\) | −1.24352e7 | −0.407342 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.25815e6 | 0.106189 | ||||||||
\(989\) | −1.20231e7 | − | 2.08246e7i | −0.390865 | − | 0.676997i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.23577e7 | + | 2.14041e7i | −0.399718 | + | 0.692331i | −0.993691 | − | 0.112154i | \(-0.964225\pi\) |
0.593973 | + | 0.804485i | \(0.297558\pi\) | |||||||
\(992\) | 6.08958e6 | + | 1.05475e7i | 0.196475 | + | 0.340305i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.23329e7 | + | 7.13797e6i | 1.03796 | + | 0.229144i | ||||
\(995\) | 5.26172e6 | 0.168488 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.97906e6 | − | 1.55522e7i | 0.286084 | − | 0.495511i | −0.686788 | − | 0.726858i | \(-0.740980\pi\) |
0.972871 | + | 0.231347i | \(0.0743131\pi\) | |||||||
\(998\) | 6.79064e6 | − | 1.17617e7i | 0.215816 | − | 0.373805i | ||||
\(999\) | 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 | 63.6.e.c.46.2 | 4 | ||
3.2 | odd | 2 | 21.6.e.b.4.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 63.6.e.c.37.2 | 4 | ||
7.3 | odd | 6 | 441.6.a.s.1.1 | 2 | |||
7.4 | even | 3 | 441.6.a.t.1.1 | 2 | |||
12.11 | even | 2 | 336.6.q.e.193.1 | 4 | |||
21.2 | odd | 6 | 21.6.e.b.16.1 | yes | 4 | ||
21.5 | even | 6 | 147.6.e.l.79.1 | 4 | |||
21.11 | odd | 6 | 147.6.a.i.1.2 | 2 | |||
21.17 | even | 6 | 147.6.a.k.1.2 | 2 | |||
21.20 | even | 2 | 147.6.e.l.67.1 | 4 | |||
84.23 | even | 6 | 336.6.q.e.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.b.4.1 | ✓ | 4 | 3.2 | odd | 2 | ||
21.6.e.b.16.1 | yes | 4 | 21.2 | odd | 6 | ||
63.6.e.c.37.2 | 4 | 7.2 | even | 3 | inner | ||
63.6.e.c.46.2 | 4 | 1.1 | even | 1 | trivial | ||
147.6.a.i.1.2 | 2 | 21.11 | odd | 6 | |||
147.6.a.k.1.2 | 2 | 21.17 | even | 6 | |||
147.6.e.l.67.1 | 4 | 21.20 | even | 2 | |||
147.6.e.l.79.1 | 4 | 21.5 | even | 6 | |||
336.6.q.e.193.1 | 4 | 12.11 | even | 2 | |||
336.6.q.e.289.1 | 4 | 84.23 | even | 6 | |||
441.6.a.s.1.1 | 2 | 7.3 | odd | 6 | |||
441.6.a.t.1.1 | 2 | 7.4 | even | 3 |