Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7350,2,Mod(1,7350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7350.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7350.a (trivial) |
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: | yes |
Analytic conductor: | \(58.6900454856\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7350.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41421 | 1.02942 | 0.514712 | − | 0.857363i | \(-0.327899\pi\) | ||||
0.514712 | + | 0.857363i | \(0.327899\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.82843 | −1.41360 | −0.706801 | − | 0.707413i | \(-0.749862\pi\) | ||||
−0.706801 | + | 0.707413i | \(0.749862\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.41421 | 0.324443 | 0.162221 | − | 0.986754i | \(-0.448134\pi\) | ||||
0.162221 | + | 0.986754i | \(0.448134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.41421 | 0.727913 | ||||||||
\(23\) | 0.414214 | 0.0863695 | 0.0431847 | − | 0.999067i | \(-0.486250\pi\) | ||||
0.0431847 | + | 0.999067i | \(0.486250\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.41421 | −0.433606 | −0.216803 | − | 0.976215i | \(-0.569563\pi\) | ||||
−0.216803 | + | 0.976215i | \(0.569563\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.41421 | −0.594338 | ||||||||
\(34\) | −5.82843 | −0.999567 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.07107 | −1.16248 | −0.581238 | − | 0.813733i | \(-0.697432\pi\) | ||||
−0.581238 | + | 0.813733i | \(0.697432\pi\) | |||||||
\(38\) | 1.41421 | 0.229416 | ||||||||
\(39\) | 3.00000 | 0.480384 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.82843 | −0.910247 | −0.455124 | − | 0.890428i | \(-0.650405\pi\) | ||||
−0.455124 | + | 0.890428i | \(0.650405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.58579 | −0.241830 | −0.120915 | − | 0.992663i | \(-0.538583\pi\) | ||||
−0.120915 | + | 0.992663i | \(0.538583\pi\) | |||||||
\(44\) | 3.41421 | 0.514712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.414214 | 0.0610725 | ||||||||
\(47\) | 1.65685 | 0.241677 | 0.120839 | − | 0.992672i | \(-0.461442\pi\) | ||||
0.120839 | + | 0.992672i | \(0.461442\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.82843 | 0.816143 | ||||||||
\(52\) | −3.00000 | −0.416025 | ||||||||
\(53\) | −12.6569 | −1.73855 | −0.869276 | − | 0.494326i | \(-0.835415\pi\) | ||||
−0.869276 | + | 0.494326i | \(0.835415\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.41421 | −0.187317 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 7.24264 | 0.942912 | 0.471456 | − | 0.881890i | \(-0.343729\pi\) | ||||
0.471456 | + | 0.881890i | \(0.343729\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.171573 | −0.0219677 | −0.0109838 | − | 0.999940i | \(-0.503496\pi\) | ||||
−0.0109838 | + | 0.999940i | \(0.503496\pi\) | |||||||
\(62\) | −2.41421 | −0.306605 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.41421 | −0.420261 | ||||||||
\(67\) | 15.3137 | 1.87087 | 0.935434 | − | 0.353502i | \(-0.115009\pi\) | ||||
0.935434 | + | 0.353502i | \(0.115009\pi\) | |||||||
\(68\) | −5.82843 | −0.706801 | ||||||||
\(69\) | −0.414214 | −0.0498655 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.31371 | −1.10533 | −0.552667 | − | 0.833402i | \(-0.686390\pi\) | ||||
−0.552667 | + | 0.833402i | \(0.686390\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −15.0711 | −1.76394 | −0.881968 | − | 0.471310i | \(-0.843781\pi\) | ||||
−0.881968 | + | 0.471310i | \(0.843781\pi\) | |||||||
\(74\) | −7.07107 | −0.821995 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41421 | 0.162221 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | 1.07107 | 0.120505 | 0.0602523 | − | 0.998183i | \(-0.480809\pi\) | ||||
0.0602523 | + | 0.998183i | \(0.480809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.82843 | −0.643642 | ||||||||
\(83\) | 0.0710678 | 0.00780071 | 0.00390035 | − | 0.999992i | \(-0.498758\pi\) | ||||
0.00390035 | + | 0.999992i | \(0.498758\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.58579 | −0.171000 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 3.41421 | 0.363956 | ||||||||
\(89\) | 4.00000 | 0.423999 | 0.212000 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212000 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.414214 | 0.0431847 | ||||||||
\(93\) | 2.41421 | 0.250342 | ||||||||
\(94\) | 1.65685 | 0.170891 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.343146 | 0.0348412 | 0.0174206 | − | 0.999848i | \(-0.494455\pi\) | ||||
0.0174206 | + | 0.999848i | \(0.494455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.41421 | 0.343141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.65685 | 0.562878 | 0.281439 | − | 0.959579i | \(-0.409188\pi\) | ||||
0.281439 | + | 0.959579i | \(0.409188\pi\) | |||||||
\(102\) | 5.82843 | 0.577100 | ||||||||
\(103\) | 0.0710678 | 0.00700252 | 0.00350126 | − | 0.999994i | \(-0.498886\pi\) | ||||
0.00350126 | + | 0.999994i | \(0.498886\pi\) | |||||||
\(104\) | −3.00000 | −0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.6569 | −1.22934 | ||||||||
\(107\) | −6.48528 | −0.626956 | −0.313478 | − | 0.949595i | \(-0.601494\pi\) | ||||
−0.313478 | + | 0.949595i | \(0.601494\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −11.3137 | −1.08366 | −0.541828 | − | 0.840489i | \(-0.682268\pi\) | ||||
−0.541828 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.07107 | 0.671156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.58579 | −0.619539 | −0.309769 | − | 0.950812i | \(-0.600252\pi\) | ||||
−0.309769 | + | 0.950812i | \(0.600252\pi\) | |||||||
\(114\) | −1.41421 | −0.132453 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −3.00000 | −0.277350 | ||||||||
\(118\) | 7.24264 | 0.666739 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.656854 | 0.0597140 | ||||||||
\(122\) | −0.171573 | −0.0155335 | ||||||||
\(123\) | 5.82843 | 0.525532 | ||||||||
\(124\) | −2.41421 | −0.216803 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.17157 | 0.281432 | 0.140716 | − | 0.990050i | \(-0.455060\pi\) | ||||
0.140716 | + | 0.990050i | \(0.455060\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.58579 | 0.139621 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.8284 | −1.64505 | −0.822524 | − | 0.568731i | \(-0.807435\pi\) | ||||
−0.822524 | + | 0.568731i | \(0.807435\pi\) | |||||||
\(132\) | −3.41421 | −0.297169 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.3137 | 1.32290 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.82843 | −0.499784 | ||||||||
\(137\) | 23.2132 | 1.98324 | 0.991619 | − | 0.129197i | \(-0.0412401\pi\) | ||||
0.991619 | + | 0.129197i | \(0.0412401\pi\) | |||||||
\(138\) | −0.414214 | −0.0352602 | ||||||||
\(139\) | −15.5563 | −1.31947 | −0.659736 | − | 0.751497i | \(-0.729332\pi\) | ||||
−0.659736 | + | 0.751497i | \(0.729332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.65685 | −0.139532 | ||||||||
\(142\) | −9.31371 | −0.781589 | ||||||||
\(143\) | −10.2426 | −0.856533 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.0711 | −1.24729 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.07107 | −0.581238 | ||||||||
\(149\) | 4.65685 | 0.381504 | 0.190752 | − | 0.981638i | \(-0.438907\pi\) | ||||
0.190752 | + | 0.981638i | \(0.438907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.89949 | 0.642852 | 0.321426 | − | 0.946935i | \(-0.395838\pi\) | ||||
0.321426 | + | 0.946935i | \(0.395838\pi\) | |||||||
\(152\) | 1.41421 | 0.114708 | ||||||||
\(153\) | −5.82843 | −0.471200 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | 19.7990 | 1.58013 | 0.790066 | − | 0.613022i | \(-0.210046\pi\) | ||||
0.790066 | + | 0.613022i | \(0.210046\pi\) | |||||||
\(158\) | 1.07107 | 0.0852096 | ||||||||
\(159\) | 12.6569 | 1.00375 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −5.24264 | −0.410635 | −0.205318 | − | 0.978695i | \(-0.565823\pi\) | ||||
−0.205318 | + | 0.978695i | \(0.565823\pi\) | |||||||
\(164\) | −5.82843 | −0.455124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0710678 | 0.00551593 | ||||||||
\(167\) | 8.82843 | 0.683164 | 0.341582 | − | 0.939852i | \(-0.389037\pi\) | ||||
0.341582 | + | 0.939852i | \(0.389037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.41421 | 0.108148 | ||||||||
\(172\) | −1.58579 | −0.120915 | ||||||||
\(173\) | −14.2426 | −1.08285 | −0.541424 | − | 0.840750i | \(-0.682115\pi\) | ||||
−0.541424 | + | 0.840750i | \(0.682115\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41421 | 0.257356 | ||||||||
\(177\) | −7.24264 | −0.544390 | ||||||||
\(178\) | 4.00000 | 0.299813 | ||||||||
\(179\) | −5.07107 | −0.379029 | −0.189515 | − | 0.981878i | \(-0.560691\pi\) | ||||
−0.189515 | + | 0.981878i | \(0.560691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.3137 | −1.73289 | −0.866447 | − | 0.499269i | \(-0.833602\pi\) | ||||
−0.866447 | + | 0.499269i | \(0.833602\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.171573 | 0.0126830 | ||||||||
\(184\) | 0.414214 | 0.0305362 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.41421 | 0.177019 | ||||||||
\(187\) | −19.8995 | −1.45520 | ||||||||
\(188\) | 1.65685 | 0.120839 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0711 | 1.16286 | 0.581431 | − | 0.813596i | \(-0.302493\pi\) | ||||
0.581431 | + | 0.813596i | \(0.302493\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.82843 | 0.491521 | 0.245760 | − | 0.969331i | \(-0.420962\pi\) | ||||
0.245760 | + | 0.969331i | \(0.420962\pi\) | |||||||
\(194\) | 0.343146 | 0.0246364 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.1421 | −1.64881 | −0.824404 | − | 0.566001i | \(-0.808490\pi\) | ||||
−0.824404 | + | 0.566001i | \(0.808490\pi\) | |||||||
\(198\) | 3.41421 | 0.242638 | ||||||||
\(199\) | 19.6569 | 1.39344 | 0.696719 | − | 0.717344i | \(-0.254643\pi\) | ||||
0.696719 | + | 0.717344i | \(0.254643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.3137 | −1.08015 | ||||||||
\(202\) | 5.65685 | 0.398015 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.82843 | 0.408072 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.0710678 | 0.00495153 | ||||||||
\(207\) | 0.414214 | 0.0287898 | ||||||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | 4.82843 | 0.333989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.5563 | −1.82821 | −0.914107 | − | 0.405473i | \(-0.867107\pi\) | ||||
−0.914107 | + | 0.405473i | \(0.867107\pi\) | |||||||
\(212\) | −12.6569 | −0.869276 | ||||||||
\(213\) | 9.31371 | 0.638165 | ||||||||
\(214\) | −6.48528 | −0.443325 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.3137 | −0.766261 | ||||||||
\(219\) | 15.0711 | 1.01841 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.4853 | 1.17619 | ||||||||
\(222\) | 7.07107 | 0.474579 | ||||||||
\(223\) | −24.5563 | −1.64441 | −0.822207 | − | 0.569188i | \(-0.807258\pi\) | ||||
−0.822207 | + | 0.569188i | \(0.807258\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.58579 | −0.438080 | ||||||||
\(227\) | −25.3848 | −1.68485 | −0.842423 | − | 0.538816i | \(-0.818872\pi\) | ||||
−0.842423 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(228\) | −1.41421 | −0.0936586 | ||||||||
\(229\) | 29.3137 | 1.93710 | 0.968552 | − | 0.248810i | \(-0.0800396\pi\) | ||||
0.968552 | + | 0.248810i | \(0.0800396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −14.2426 | −0.933066 | −0.466533 | − | 0.884504i | \(-0.654497\pi\) | ||||
−0.466533 | + | 0.884504i | \(0.654497\pi\) | |||||||
\(234\) | −3.00000 | −0.196116 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.24264 | 0.471456 | ||||||||
\(237\) | −1.07107 | −0.0695733 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 0.656854 | 0.0422242 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.171573 | −0.0109838 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.82843 | 0.371607 | ||||||||
\(247\) | −4.24264 | −0.269953 | ||||||||
\(248\) | −2.41421 | −0.153303 | ||||||||
\(249\) | −0.0710678 | −0.00450374 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.92893 | −0.121753 | −0.0608766 | − | 0.998145i | \(-0.519390\pi\) | ||||
−0.0608766 | + | 0.998145i | \(0.519390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.41421 | 0.0889108 | ||||||||
\(254\) | 3.17157 | 0.199002 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.3431 | −0.832323 | −0.416161 | − | 0.909291i | \(-0.636625\pi\) | ||||
−0.416161 | + | 0.909291i | \(0.636625\pi\) | |||||||
\(258\) | 1.58579 | 0.0987268 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −18.8284 | −1.16322 | ||||||||
\(263\) | 10.5563 | 0.650932 | 0.325466 | − | 0.945554i | \(-0.394479\pi\) | ||||
0.325466 | + | 0.945554i | \(0.394479\pi\) | |||||||
\(264\) | −3.41421 | −0.210130 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.00000 | −0.244796 | ||||||||
\(268\) | 15.3137 | 0.935434 | ||||||||
\(269\) | 0.443651 | 0.0270499 | 0.0135249 | − | 0.999909i | \(-0.495695\pi\) | ||||
0.0135249 | + | 0.999909i | \(0.495695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5147 | −0.699469 | −0.349735 | − | 0.936849i | \(-0.613728\pi\) | ||||
−0.349735 | + | 0.936849i | \(0.613728\pi\) | |||||||
\(272\) | −5.82843 | −0.353400 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.2132 | 1.40236 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.414214 | −0.0249327 | ||||||||
\(277\) | 24.0416 | 1.44452 | 0.722261 | − | 0.691621i | \(-0.243103\pi\) | ||||
0.722261 | + | 0.691621i | \(0.243103\pi\) | |||||||
\(278\) | −15.5563 | −0.933008 | ||||||||
\(279\) | −2.41421 | −0.144535 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000 | 1.19310 | 0.596550 | − | 0.802576i | \(-0.296538\pi\) | ||||
0.596550 | + | 0.802576i | \(0.296538\pi\) | |||||||
\(282\) | −1.65685 | −0.0986642 | ||||||||
\(283\) | 0.242641 | 0.0144235 | 0.00721175 | − | 0.999974i | \(-0.497704\pi\) | ||||
0.00721175 | + | 0.999974i | \(0.497704\pi\) | |||||||
\(284\) | −9.31371 | −0.552667 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.2426 | −0.605660 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 16.9706 | 0.998268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.343146 | −0.0201156 | ||||||||
\(292\) | −15.0711 | −0.881968 | ||||||||
\(293\) | 11.3137 | 0.660954 | 0.330477 | − | 0.943814i | \(-0.392790\pi\) | ||||
0.330477 | + | 0.943814i | \(0.392790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.07107 | −0.410997 | ||||||||
\(297\) | −3.41421 | −0.198113 | ||||||||
\(298\) | 4.65685 | 0.269764 | ||||||||
\(299\) | −1.24264 | −0.0718638 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.89949 | 0.454565 | ||||||||
\(303\) | −5.65685 | −0.324978 | ||||||||
\(304\) | 1.41421 | 0.0811107 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.82843 | −0.333189 | ||||||||
\(307\) | −8.58579 | −0.490017 | −0.245008 | − | 0.969521i | \(-0.578791\pi\) | ||||
−0.245008 | + | 0.969521i | \(0.578791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0710678 | −0.00404291 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4142 | −0.647241 | −0.323620 | − | 0.946187i | \(-0.604900\pi\) | ||||
−0.323620 | + | 0.946187i | \(0.604900\pi\) | |||||||
\(312\) | 3.00000 | 0.169842 | ||||||||
\(313\) | 16.0416 | 0.906727 | 0.453363 | − | 0.891326i | \(-0.350224\pi\) | ||||
0.453363 | + | 0.891326i | \(0.350224\pi\) | |||||||
\(314\) | 19.7990 | 1.11732 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.07107 | 0.0602523 | ||||||||
\(317\) | −19.9706 | −1.12166 | −0.560829 | − | 0.827931i | \(-0.689518\pi\) | ||||
−0.560829 | + | 0.827931i | \(0.689518\pi\) | |||||||
\(318\) | 12.6569 | 0.709761 | ||||||||
\(319\) | 3.41421 | 0.191159 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.48528 | 0.361973 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.24264 | −0.458633 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.24264 | −0.290363 | ||||||||
\(327\) | 11.3137 | 0.625650 | ||||||||
\(328\) | −5.82843 | −0.321821 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0711 | −1.32307 | −0.661533 | − | 0.749916i | \(-0.730094\pi\) | ||||
−0.661533 | + | 0.749916i | \(0.730094\pi\) | |||||||
\(332\) | 0.0710678 | 0.00390035 | ||||||||
\(333\) | −7.07107 | −0.387492 | ||||||||
\(334\) | 8.82843 | 0.483070 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.79899 | −0.261418 | −0.130709 | − | 0.991421i | \(-0.541725\pi\) | ||||
−0.130709 | + | 0.991421i | \(0.541725\pi\) | |||||||
\(338\) | −4.00000 | −0.217571 | ||||||||
\(339\) | 6.58579 | 0.357691 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.24264 | −0.446364 | ||||||||
\(342\) | 1.41421 | 0.0764719 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.58579 | −0.0854999 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.2426 | −0.765689 | ||||||||
\(347\) | 9.79899 | 0.526037 | 0.263019 | − | 0.964791i | \(-0.415282\pi\) | ||||
0.263019 | + | 0.964791i | \(0.415282\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | 24.6569 | 1.31985 | 0.659926 | − | 0.751331i | \(-0.270588\pi\) | ||||
0.659926 | + | 0.751331i | \(0.270588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.00000 | 0.160128 | ||||||||
\(352\) | 3.41421 | 0.181978 | ||||||||
\(353\) | −20.4853 | −1.09032 | −0.545161 | − | 0.838332i | \(-0.683531\pi\) | ||||
−0.545161 | + | 0.838332i | \(0.683531\pi\) | |||||||
\(354\) | −7.24264 | −0.384942 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.00000 | 0.212000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.07107 | −0.268014 | ||||||||
\(359\) | 33.8701 | 1.78759 | 0.893797 | − | 0.448472i | \(-0.148032\pi\) | ||||
0.893797 | + | 0.448472i | \(0.148032\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | −23.3137 | −1.22534 | ||||||||
\(363\) | −0.656854 | −0.0344759 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.171573 | 0.00896826 | ||||||||
\(367\) | −0.757359 | −0.0395338 | −0.0197669 | − | 0.999805i | \(-0.506292\pi\) | ||||
−0.0197669 | + | 0.999805i | \(0.506292\pi\) | |||||||
\(368\) | 0.414214 | 0.0215924 | ||||||||
\(369\) | −5.82843 | −0.303416 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.41421 | 0.125171 | ||||||||
\(373\) | −2.34315 | −0.121323 | −0.0606617 | − | 0.998158i | \(-0.519321\pi\) | ||||
−0.0606617 | + | 0.998158i | \(0.519321\pi\) | |||||||
\(374\) | −19.8995 | −1.02898 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.65685 | 0.0854457 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.2132 | −1.75741 | −0.878707 | − | 0.477361i | \(-0.841593\pi\) | ||||
−0.878707 | + | 0.477361i | \(0.841593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.17157 | −0.162485 | ||||||||
\(382\) | 16.0711 | 0.822267 | ||||||||
\(383\) | −27.5563 | −1.40806 | −0.704032 | − | 0.710168i | \(-0.748619\pi\) | ||||
−0.704032 | + | 0.710168i | \(0.748619\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.82843 | 0.347558 | ||||||||
\(387\) | −1.58579 | −0.0806101 | ||||||||
\(388\) | 0.343146 | 0.0174206 | ||||||||
\(389\) | −10.3431 | −0.524418 | −0.262209 | − | 0.965011i | \(-0.584451\pi\) | ||||
−0.262209 | + | 0.965011i | \(0.584451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.41421 | −0.122092 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.8284 | 0.949769 | ||||||||
\(394\) | −23.1421 | −1.16588 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.41421 | 0.171571 | ||||||||
\(397\) | −30.3137 | −1.52140 | −0.760701 | − | 0.649103i | \(-0.775144\pi\) | ||||
−0.760701 | + | 0.649103i | \(0.775144\pi\) | |||||||
\(398\) | 19.6569 | 0.985309 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.1005 | 0.604270 | 0.302135 | − | 0.953265i | \(-0.402301\pi\) | ||||
0.302135 | + | 0.953265i | \(0.402301\pi\) | |||||||
\(402\) | −15.3137 | −0.763778 | ||||||||
\(403\) | 7.24264 | 0.360782 | ||||||||
\(404\) | 5.65685 | 0.281439 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.1421 | −1.19668 | ||||||||
\(408\) | 5.82843 | 0.288550 | ||||||||
\(409\) | 22.5858 | 1.11680 | 0.558398 | − | 0.829573i | \(-0.311416\pi\) | ||||
0.558398 | + | 0.829573i | \(0.311416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.2132 | −1.14502 | ||||||||
\(412\) | 0.0710678 | 0.00350126 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.414214 | 0.0203575 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.00000 | −0.147087 | ||||||||
\(417\) | 15.5563 | 0.761798 | ||||||||
\(418\) | 4.82843 | 0.236166 | ||||||||
\(419\) | 24.5563 | 1.19966 | 0.599828 | − | 0.800129i | \(-0.295236\pi\) | ||||
0.599828 | + | 0.800129i | \(0.295236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.6569 | −1.73781 | −0.868904 | − | 0.494980i | \(-0.835175\pi\) | ||||
−0.868904 | + | 0.494980i | \(0.835175\pi\) | |||||||
\(422\) | −26.5563 | −1.29274 | ||||||||
\(423\) | 1.65685 | 0.0805590 | ||||||||
\(424\) | −12.6569 | −0.614671 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.31371 | 0.451251 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.48528 | −0.313478 | ||||||||
\(429\) | 10.2426 | 0.494519 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.0416 | 1.59156 | 0.795780 | − | 0.605586i | \(-0.207061\pi\) | ||||
0.795780 | + | 0.605586i | \(0.207061\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −28.6274 | −1.37575 | −0.687873 | − | 0.725831i | \(-0.741455\pi\) | ||||
−0.687873 | + | 0.725831i | \(0.741455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.3137 | −0.541828 | ||||||||
\(437\) | 0.585786 | 0.0280220 | ||||||||
\(438\) | 15.0711 | 0.720123 | ||||||||
\(439\) | 1.58579 | 0.0756855 | 0.0378427 | − | 0.999284i | \(-0.487951\pi\) | ||||
0.0378427 | + | 0.999284i | \(0.487951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.4853 | 0.831690 | ||||||||
\(443\) | 14.3431 | 0.681463 | 0.340732 | − | 0.940161i | \(-0.389325\pi\) | ||||
0.340732 | + | 0.940161i | \(0.389325\pi\) | |||||||
\(444\) | 7.07107 | 0.335578 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.5563 | −1.16278 | ||||||||
\(447\) | −4.65685 | −0.220262 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.0711 | −1.18318 | −0.591588 | − | 0.806240i | \(-0.701499\pi\) | ||||
−0.591588 | + | 0.806240i | \(0.701499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.8995 | −0.937031 | ||||||||
\(452\) | −6.58579 | −0.309769 | ||||||||
\(453\) | −7.89949 | −0.371151 | ||||||||
\(454\) | −25.3848 | −1.19137 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.41421 | −0.0662266 | ||||||||
\(457\) | 3.82843 | 0.179086 | 0.0895431 | − | 0.995983i | \(-0.471459\pi\) | ||||
0.0895431 | + | 0.995983i | \(0.471459\pi\) | |||||||
\(458\) | 29.3137 | 1.36974 | ||||||||
\(459\) | 5.82843 | 0.272048 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0000 | 0.931493 | 0.465746 | − | 0.884918i | \(-0.345786\pi\) | ||||
0.465746 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.8995 | −1.38955 | −0.694774 | − | 0.719228i | \(-0.744495\pi\) | ||||
−0.694774 | + | 0.719228i | \(0.744495\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.2426 | −0.659778 | ||||||||
\(467\) | 1.24264 | 0.0575026 | 0.0287513 | − | 0.999587i | \(-0.490847\pi\) | ||||
0.0287513 | + | 0.999587i | \(0.490847\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.7990 | −0.912289 | ||||||||
\(472\) | 7.24264 | 0.333370 | ||||||||
\(473\) | −5.41421 | −0.248946 | ||||||||
\(474\) | −1.07107 | −0.0491958 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.6569 | −0.579518 | ||||||||
\(478\) | −11.3137 | −0.517477 | ||||||||
\(479\) | 20.2426 | 0.924910 | 0.462455 | − | 0.886643i | \(-0.346969\pi\) | ||||
0.462455 | + | 0.886643i | \(0.346969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.2132 | 0.967239 | ||||||||
\(482\) | −6.00000 | −0.273293 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.656854 | 0.0298570 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −5.51472 | −0.249896 | −0.124948 | − | 0.992163i | \(-0.539876\pi\) | ||||
−0.124948 | + | 0.992163i | \(0.539876\pi\) | |||||||
\(488\) | −0.171573 | −0.00776674 | ||||||||
\(489\) | 5.24264 | 0.237080 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.142136 | −0.00641449 | −0.00320725 | − | 0.999995i | \(-0.501021\pi\) | ||||
−0.00320725 | + | 0.999995i | \(0.501021\pi\) | |||||||
\(492\) | 5.82843 | 0.262766 | ||||||||
\(493\) | −5.82843 | −0.262499 | ||||||||
\(494\) | −4.24264 | −0.190885 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.41421 | −0.108401 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0710678 | −0.00318462 | ||||||||
\(499\) | −26.0711 | −1.16710 | −0.583551 | − | 0.812077i | \(-0.698337\pi\) | ||||
−0.583551 | + | 0.812077i | \(0.698337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.82843 | −0.394425 | ||||||||
\(502\) | −1.92893 | −0.0860925 | ||||||||
\(503\) | 24.8701 | 1.10890 | 0.554451 | − | 0.832217i | \(-0.312928\pi\) | ||||
0.554451 | + | 0.832217i | \(0.312928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.41421 | 0.0628695 | ||||||||
\(507\) | 4.00000 | 0.177646 | ||||||||
\(508\) | 3.17157 | 0.140716 | ||||||||
\(509\) | −6.04163 | −0.267791 | −0.133895 | − | 0.990995i | \(-0.542749\pi\) | ||||
−0.133895 | + | 0.990995i | \(0.542749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.41421 | −0.0624391 | ||||||||
\(514\) | −13.3431 | −0.588541 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.58579 | 0.0698104 | ||||||||
\(517\) | 5.65685 | 0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.2426 | 0.625183 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.6569 | −0.466885 | −0.233443 | − | 0.972371i | \(-0.574999\pi\) | ||||
−0.233443 | + | 0.972371i | \(0.574999\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 24.2843 | 1.06188 | 0.530939 | − | 0.847410i | \(-0.321840\pi\) | ||||
0.530939 | + | 0.847410i | \(0.321840\pi\) | |||||||
\(524\) | −18.8284 | −0.822524 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.5563 | 0.460279 | ||||||||
\(527\) | 14.0711 | 0.612945 | ||||||||
\(528\) | −3.41421 | −0.148585 | ||||||||
\(529\) | −22.8284 | −0.992540 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.24264 | 0.314304 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.4853 | 0.757372 | ||||||||
\(534\) | −4.00000 | −0.173097 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.3137 | 0.661451 | ||||||||
\(537\) | 5.07107 | 0.218833 | ||||||||
\(538\) | 0.443651 | 0.0191271 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.2426 | −1.47221 | −0.736103 | − | 0.676869i | \(-0.763336\pi\) | ||||
−0.736103 | + | 0.676869i | \(0.763336\pi\) | |||||||
\(542\) | −11.5147 | −0.494600 | ||||||||
\(543\) | 23.3137 | 1.00049 | ||||||||
\(544\) | −5.82843 | −0.249892 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.8701 | −1.44818 | −0.724090 | − | 0.689706i | \(-0.757740\pi\) | ||||
−0.724090 | + | 0.689706i | \(0.757740\pi\) | |||||||
\(548\) | 23.2132 | 0.991619 | ||||||||
\(549\) | −0.171573 | −0.00732255 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.41421 | 0.0602475 | ||||||||
\(552\) | −0.414214 | −0.0176301 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.0416 | 1.02143 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.5563 | −0.659736 | ||||||||
\(557\) | 19.3137 | 0.818348 | 0.409174 | − | 0.912456i | \(-0.365817\pi\) | ||||
0.409174 | + | 0.912456i | \(0.365817\pi\) | |||||||
\(558\) | −2.41421 | −0.102202 | ||||||||
\(559\) | 4.75736 | 0.201215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.8995 | 0.840157 | ||||||||
\(562\) | 20.0000 | 0.843649 | ||||||||
\(563\) | −27.3848 | −1.15413 | −0.577065 | − | 0.816698i | \(-0.695802\pi\) | ||||
−0.577065 | + | 0.816698i | \(0.695802\pi\) | |||||||
\(564\) | −1.65685 | −0.0697661 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.242641 | 0.0101989 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.31371 | −0.390795 | ||||||||
\(569\) | −28.2426 | −1.18399 | −0.591997 | − | 0.805941i | \(-0.701660\pi\) | ||||
−0.591997 | + | 0.805941i | \(0.701660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0122 | 1.50706 | 0.753532 | − | 0.657412i | \(-0.228349\pi\) | ||||
0.753532 | + | 0.657412i | \(0.228349\pi\) | |||||||
\(572\) | −10.2426 | −0.428266 | ||||||||
\(573\) | −16.0711 | −0.671378 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −19.6569 | −0.818326 | −0.409163 | − | 0.912461i | \(-0.634179\pi\) | ||||
−0.409163 | + | 0.912461i | \(0.634179\pi\) | |||||||
\(578\) | 16.9706 | 0.705882 | ||||||||
\(579\) | −6.82843 | −0.283780 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.343146 | −0.0142238 | ||||||||
\(583\) | −43.2132 | −1.78971 | ||||||||
\(584\) | −15.0711 | −0.623645 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.3137 | 0.467365 | ||||||||
\(587\) | 41.5269 | 1.71400 | 0.857000 | − | 0.515317i | \(-0.172326\pi\) | ||||
0.857000 | + | 0.515317i | \(0.172326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.41421 | −0.140680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.1421 | 0.951940 | ||||||||
\(592\) | −7.07107 | −0.290619 | ||||||||
\(593\) | 26.0000 | 1.06769 | 0.533846 | − | 0.845582i | \(-0.320746\pi\) | ||||
0.533846 | + | 0.845582i | \(0.320746\pi\) | |||||||
\(594\) | −3.41421 | −0.140087 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.65685 | 0.190752 | ||||||||
\(597\) | −19.6569 | −0.804501 | ||||||||
\(598\) | −1.24264 | −0.0508154 | ||||||||
\(599\) | −30.4142 | −1.24269 | −0.621346 | − | 0.783537i | \(-0.713414\pi\) | ||||
−0.621346 | + | 0.783537i | \(0.713414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.27208 | 0.0518891 | 0.0259446 | − | 0.999663i | \(-0.491741\pi\) | ||||
0.0259446 | + | 0.999663i | \(0.491741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.3137 | 0.623622 | ||||||||
\(604\) | 7.89949 | 0.321426 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.65685 | −0.229794 | ||||||||
\(607\) | −39.9411 | −1.62116 | −0.810580 | − | 0.585628i | \(-0.800848\pi\) | ||||
−0.810580 | + | 0.585628i | \(0.800848\pi\) | |||||||
\(608\) | 1.41421 | 0.0573539 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.97056 | −0.201087 | ||||||||
\(612\) | −5.82843 | −0.235600 | ||||||||
\(613\) | 22.0000 | 0.888572 | 0.444286 | − | 0.895885i | \(-0.353457\pi\) | ||||
0.444286 | + | 0.895885i | \(0.353457\pi\) | |||||||
\(614\) | −8.58579 | −0.346494 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.3848 | −0.901177 | −0.450589 | − | 0.892732i | \(-0.648786\pi\) | ||||
−0.450589 | + | 0.892732i | \(0.648786\pi\) | |||||||
\(618\) | −0.0710678 | −0.00285877 | ||||||||
\(619\) | −12.1421 | −0.488034 | −0.244017 | − | 0.969771i | \(-0.578465\pi\) | ||||
−0.244017 | + | 0.969771i | \(0.578465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.414214 | −0.0166218 | ||||||||
\(622\) | −11.4142 | −0.457668 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.00000 | 0.120096 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.0416 | 0.641153 | ||||||||
\(627\) | −4.82843 | −0.192829 | ||||||||
\(628\) | 19.7990 | 0.790066 | ||||||||
\(629\) | 41.2132 | 1.64328 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.8284 | −1.62535 | −0.812677 | − | 0.582714i | \(-0.801991\pi\) | ||||
−0.812677 | + | 0.582714i | \(0.801991\pi\) | |||||||
\(632\) | 1.07107 | 0.0426048 | ||||||||
\(633\) | 26.5563 | 1.05552 | ||||||||
\(634\) | −19.9706 | −0.793132 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.6569 | 0.501877 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.41421 | 0.135170 | ||||||||
\(639\) | −9.31371 | −0.368445 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.7574 | 1.25434 | 0.627170 | − | 0.778882i | \(-0.284213\pi\) | ||||
0.627170 | + | 0.778882i | \(0.284213\pi\) | |||||||
\(642\) | 6.48528 | 0.255954 | ||||||||
\(643\) | 13.7574 | 0.542537 | 0.271269 | − | 0.962504i | \(-0.412557\pi\) | ||||
0.271269 | + | 0.962504i | \(0.412557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.24264 | −0.324302 | ||||||||
\(647\) | −4.87006 | −0.191462 | −0.0957309 | − | 0.995407i | \(-0.530519\pi\) | ||||
−0.0957309 | + | 0.995407i | \(0.530519\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 24.7279 | 0.970656 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.24264 | −0.205318 | ||||||||
\(653\) | 12.6863 | 0.496453 | 0.248226 | − | 0.968702i | \(-0.420152\pi\) | ||||
0.248226 | + | 0.968702i | \(0.420152\pi\) | |||||||
\(654\) | 11.3137 | 0.442401 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.82843 | −0.227562 | ||||||||
\(657\) | −15.0711 | −0.587978 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.17157 | 0.123547 | 0.0617735 | − | 0.998090i | \(-0.480324\pi\) | ||||
0.0617735 | + | 0.998090i | \(0.480324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.3431 | 1.33579 | 0.667897 | − | 0.744254i | \(-0.267195\pi\) | ||||
0.667897 | + | 0.744254i | \(0.267195\pi\) | |||||||
\(662\) | −24.0711 | −0.935549 | ||||||||
\(663\) | −17.4853 | −0.679072 | ||||||||
\(664\) | 0.0710678 | 0.00275797 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.07107 | −0.273998 | ||||||||
\(667\) | 0.414214 | 0.0160384 | ||||||||
\(668\) | 8.82843 | 0.341582 | ||||||||
\(669\) | 24.5563 | 0.949403 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.585786 | −0.0226140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.798990 | 0.0307988 | 0.0153994 | − | 0.999881i | \(-0.495098\pi\) | ||||
0.0153994 | + | 0.999881i | \(0.495098\pi\) | |||||||
\(674\) | −4.79899 | −0.184850 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 4.38478 | 0.168521 | 0.0842603 | − | 0.996444i | \(-0.473147\pi\) | ||||
0.0842603 | + | 0.996444i | \(0.473147\pi\) | |||||||
\(678\) | 6.58579 | 0.252926 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.3848 | 0.972747 | ||||||||
\(682\) | −8.24264 | −0.315627 | ||||||||
\(683\) | −25.0711 | −0.959318 | −0.479659 | − | 0.877455i | \(-0.659240\pi\) | ||||
−0.479659 | + | 0.877455i | \(0.659240\pi\) | |||||||
\(684\) | 1.41421 | 0.0540738 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.3137 | −1.11839 | ||||||||
\(688\) | −1.58579 | −0.0604575 | ||||||||
\(689\) | 37.9706 | 1.44656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.1127 | 1.25967 | 0.629833 | − | 0.776730i | \(-0.283123\pi\) | ||||
0.629833 | + | 0.776730i | \(0.283123\pi\) | |||||||
\(692\) | −14.2426 | −0.541424 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.79899 | 0.371965 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | 33.9706 | 1.28673 | ||||||||
\(698\) | 24.6569 | 0.933276 | ||||||||
\(699\) | 14.2426 | 0.538706 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.3137 | 1.37155 | 0.685775 | − | 0.727814i | \(-0.259463\pi\) | ||||
0.685775 | + | 0.727814i | \(0.259463\pi\) | |||||||
\(702\) | 3.00000 | 0.113228 | ||||||||
\(703\) | −10.0000 | −0.377157 | ||||||||
\(704\) | 3.41421 | 0.128678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.4853 | −0.770974 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.24264 | −0.272195 | ||||||||
\(709\) | 19.8995 | 0.747341 | 0.373671 | − | 0.927561i | \(-0.378099\pi\) | ||||
0.373671 | + | 0.927561i | \(0.378099\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.07107 | 0.0401682 | ||||||||
\(712\) | 4.00000 | 0.149906 | ||||||||
\(713\) | −1.00000 | −0.0374503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.07107 | −0.189515 | ||||||||
\(717\) | 11.3137 | 0.422518 | ||||||||
\(718\) | 33.8701 | 1.26402 | ||||||||
\(719\) | 18.9289 | 0.705930 | 0.352965 | − | 0.935637i | \(-0.385173\pi\) | ||||
0.352965 | + | 0.935637i | \(0.385173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | 6.00000 | 0.223142 | ||||||||
\(724\) | −23.3137 | −0.866447 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.656854 | −0.0243781 | ||||||||
\(727\) | 37.8701 | 1.40452 | 0.702261 | − | 0.711919i | \(-0.252174\pi\) | ||||
0.702261 | + | 0.711919i | \(0.252174\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.24264 | 0.341851 | ||||||||
\(732\) | 0.171573 | 0.00634152 | ||||||||
\(733\) | 0.514719 | 0.0190116 | 0.00950578 | − | 0.999955i | \(-0.496974\pi\) | ||||
0.00950578 | + | 0.999955i | \(0.496974\pi\) | |||||||
\(734\) | −0.757359 | −0.0279546 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.414214 | 0.0152681 | ||||||||
\(737\) | 52.2843 | 1.92592 | ||||||||
\(738\) | −5.82843 | −0.214547 | ||||||||
\(739\) | 53.8701 | 1.98164 | 0.990821 | − | 0.135180i | \(-0.0431613\pi\) | ||||
0.990821 | + | 0.135180i | \(0.0431613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.24264 | 0.155857 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.5563 | 1.34112 | 0.670561 | − | 0.741854i | \(-0.266053\pi\) | ||||
0.670561 | + | 0.741854i | \(0.266053\pi\) | |||||||
\(744\) | 2.41421 | 0.0885094 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.34315 | −0.0857887 | ||||||||
\(747\) | 0.0710678 | 0.00260024 | ||||||||
\(748\) | −19.8995 | −0.727598 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9706 | −0.473303 | −0.236651 | − | 0.971595i | \(-0.576050\pi\) | ||||
−0.236651 | + | 0.971595i | \(0.576050\pi\) | |||||||
\(752\) | 1.65685 | 0.0604193 | ||||||||
\(753\) | 1.92893 | 0.0702942 | ||||||||
\(754\) | −3.00000 | −0.109254 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.2426 | 1.60803 | 0.804013 | − | 0.594612i | \(-0.202694\pi\) | ||||
0.804013 | + | 0.594612i | \(0.202694\pi\) | |||||||
\(758\) | −34.2132 | −1.24268 | ||||||||
\(759\) | −1.41421 | −0.0513327 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0294 | 0.544817 | 0.272408 | − | 0.962182i | \(-0.412180\pi\) | ||||
0.272408 | + | 0.962182i | \(0.412180\pi\) | |||||||
\(762\) | −3.17157 | −0.114894 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.0711 | 0.581431 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.5563 | −0.995651 | ||||||||
\(767\) | −21.7279 | −0.784550 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −15.3137 | −0.552226 | −0.276113 | − | 0.961125i | \(-0.589046\pi\) | ||||
−0.276113 | + | 0.961125i | \(0.589046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.3431 | 0.480542 | ||||||||
\(772\) | 6.82843 | 0.245760 | ||||||||
\(773\) | 19.3137 | 0.694666 | 0.347333 | − | 0.937742i | \(-0.387087\pi\) | ||||
0.347333 | + | 0.937742i | \(0.387087\pi\) | |||||||
\(774\) | −1.58579 | −0.0569999 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.343146 | 0.0123182 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.3431 | −0.370820 | ||||||||
\(779\) | −8.24264 | −0.295323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.7990 | −1.13786 | ||||||||
\(782\) | −2.41421 | −0.0863321 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.8284 | 0.671588 | ||||||||
\(787\) | 43.4558 | 1.54903 | 0.774517 | − | 0.632553i | \(-0.217993\pi\) | ||||
0.774517 | + | 0.632553i | \(0.217993\pi\) | |||||||
\(788\) | −23.1421 | −0.824404 | ||||||||
\(789\) | −10.5563 | −0.375816 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.41421 | 0.121319 | ||||||||
\(793\) | 0.514719 | 0.0182782 | ||||||||
\(794\) | −30.3137 | −1.07579 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.6569 | 0.696719 | ||||||||
\(797\) | −16.2426 | −0.575344 | −0.287672 | − | 0.957729i | \(-0.592881\pi\) | ||||
−0.287672 | + | 0.957729i | \(0.592881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.65685 | −0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.00000 | 0.141333 | ||||||||
\(802\) | 12.1005 | 0.427284 | ||||||||
\(803\) | −51.4558 | −1.81584 | ||||||||
\(804\) | −15.3137 | −0.540073 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.24264 | 0.255111 | ||||||||
\(807\) | −0.443651 | −0.0156172 | ||||||||
\(808\) | 5.65685 | 0.199007 | ||||||||
\(809\) | −34.6274 | −1.21744 | −0.608718 | − | 0.793387i | \(-0.708316\pi\) | ||||
−0.608718 | + | 0.793387i | \(0.708316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.7574 | 1.18538 | 0.592691 | − | 0.805430i | \(-0.298066\pi\) | ||||
0.592691 | + | 0.805430i | \(0.298066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.5147 | 0.403839 | ||||||||
\(814\) | −24.1421 | −0.846181 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.82843 | 0.204036 | ||||||||
\(817\) | −2.24264 | −0.0784601 | ||||||||
\(818\) | 22.5858 | 0.789694 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.1716 | 0.459691 | 0.229846 | − | 0.973227i | \(-0.426178\pi\) | ||||
0.229846 | + | 0.973227i | \(0.426178\pi\) | |||||||
\(822\) | −23.2132 | −0.809653 | ||||||||
\(823\) | −28.5858 | −0.996438 | −0.498219 | − | 0.867051i | \(-0.666012\pi\) | ||||
−0.498219 | + | 0.867051i | \(0.666012\pi\) | |||||||
\(824\) | 0.0710678 | 0.00247576 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.8995 | 0.413786 | 0.206893 | − | 0.978364i | \(-0.433665\pi\) | ||||
0.206893 | + | 0.978364i | \(0.433665\pi\) | |||||||
\(828\) | 0.414214 | 0.0143949 | ||||||||
\(829\) | −0.798990 | −0.0277501 | −0.0138750 | − | 0.999904i | \(-0.504417\pi\) | ||||
−0.0138750 | + | 0.999904i | \(0.504417\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.0416 | −0.833995 | ||||||||
\(832\) | −3.00000 | −0.104006 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.5563 | 0.538672 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.82843 | 0.166995 | ||||||||
\(837\) | 2.41421 | 0.0834474 | ||||||||
\(838\) | 24.5563 | 0.848285 | ||||||||
\(839\) | 17.4142 | 0.601205 | 0.300603 | − | 0.953749i | \(-0.402812\pi\) | ||||
0.300603 | + | 0.953749i | \(0.402812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −35.6569 | −1.22882 | ||||||||
\(843\) | −20.0000 | −0.688837 | ||||||||
\(844\) | −26.5563 | −0.914107 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.65685 | 0.0569638 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.6569 | −0.434638 | ||||||||
\(849\) | −0.242641 | −0.00832741 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.92893 | −0.100403 | ||||||||
\(852\) | 9.31371 | 0.319082 | ||||||||
\(853\) | −14.3137 | −0.490092 | −0.245046 | − | 0.969511i | \(-0.578803\pi\) | ||||
−0.245046 | + | 0.969511i | \(0.578803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.48528 | −0.221662 | ||||||||
\(857\) | −29.4558 | −1.00619 | −0.503096 | − | 0.864230i | \(-0.667806\pi\) | ||||
−0.503096 | + | 0.864230i | \(0.667806\pi\) | |||||||
\(858\) | 10.2426 | 0.349678 | ||||||||
\(859\) | 21.9411 | 0.748622 | 0.374311 | − | 0.927303i | \(-0.377879\pi\) | ||||
0.374311 | + | 0.927303i | \(0.377879\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.0416 | 1.12540 | ||||||||
\(863\) | −24.9706 | −0.850008 | −0.425004 | − | 0.905192i | \(-0.639727\pi\) | ||||
−0.425004 | + | 0.905192i | \(0.639727\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.6274 | −0.972799 | ||||||||
\(867\) | −16.9706 | −0.576351 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.65685 | 0.124050 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.9411 | −1.55666 | ||||||||
\(872\) | −11.3137 | −0.383131 | ||||||||
\(873\) | 0.343146 | 0.0116137 | ||||||||
\(874\) | 0.585786 | 0.0198145 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.0711 | 0.509204 | ||||||||
\(877\) | 26.3431 | 0.889545 | 0.444772 | − | 0.895644i | \(-0.353285\pi\) | ||||
0.444772 | + | 0.895644i | \(0.353285\pi\) | |||||||
\(878\) | 1.58579 | 0.0535177 | ||||||||
\(879\) | −11.3137 | −0.381602 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.6274 | 1.40246 | 0.701232 | − | 0.712933i | \(-0.252634\pi\) | ||||
0.701232 | + | 0.712933i | \(0.252634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.5269 | 1.06097 | 0.530483 | − | 0.847696i | \(-0.322011\pi\) | ||||
0.530483 | + | 0.847696i | \(0.322011\pi\) | |||||||
\(884\) | 17.4853 | 0.588094 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.3431 | 0.481867 | ||||||||
\(887\) | 25.7574 | 0.864847 | 0.432424 | − | 0.901671i | \(-0.357658\pi\) | ||||
0.432424 | + | 0.901671i | \(0.357658\pi\) | |||||||
\(888\) | 7.07107 | 0.237289 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.41421 | 0.114380 | ||||||||
\(892\) | −24.5563 | −0.822207 | ||||||||
\(893\) | 2.34315 | 0.0784104 | ||||||||
\(894\) | −4.65685 | −0.155749 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.24264 | 0.0414906 | ||||||||
\(898\) | −25.0711 | −0.836632 | ||||||||
\(899\) | −2.41421 | −0.0805185 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73.7696 | 2.45762 | ||||||||
\(902\) | −19.8995 | −0.662581 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.58579 | −0.219040 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.89949 | −0.262443 | ||||||||
\(907\) | −40.6985 | −1.35137 | −0.675686 | − | 0.737190i | \(-0.736152\pi\) | ||||
−0.675686 | + | 0.737190i | \(0.736152\pi\) | |||||||
\(908\) | −25.3848 | −0.842423 | ||||||||
\(909\) | 5.65685 | 0.187626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0711 | 0.731247 | 0.365624 | − | 0.930763i | \(-0.380856\pi\) | ||||
0.365624 | + | 0.930763i | \(0.380856\pi\) | |||||||
\(912\) | −1.41421 | −0.0468293 | ||||||||
\(913\) | 0.242641 | 0.00803023 | ||||||||
\(914\) | 3.82843 | 0.126633 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.3137 | 0.968552 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.82843 | 0.192367 | ||||||||
\(919\) | 4.44365 | 0.146583 | 0.0732913 | − | 0.997311i | \(-0.476650\pi\) | ||||
0.0732913 | + | 0.997311i | \(0.476650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.58579 | 0.282911 | ||||||||
\(922\) | 20.0000 | 0.658665 | ||||||||
\(923\) | 27.9411 | 0.919693 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29.8995 | −0.982558 | ||||||||
\(927\) | 0.0710678 | 0.00233417 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −8.65685 | −0.284022 | −0.142011 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142011 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.2426 | −0.466533 | ||||||||
\(933\) | 11.4142 | 0.373685 | ||||||||
\(934\) | 1.24264 | 0.0406604 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.00000 | −0.0980581 | ||||||||
\(937\) | −0.242641 | −0.00792673 | −0.00396336 | − | 0.999992i | \(-0.501262\pi\) | ||||
−0.00396336 | + | 0.999992i | \(0.501262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0416 | −0.523499 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.3137 | 1.67278 | 0.836390 | − | 0.548136i | \(-0.184662\pi\) | ||||
0.836390 | + | 0.548136i | \(0.184662\pi\) | |||||||
\(942\) | −19.7990 | −0.645086 | ||||||||
\(943\) | −2.41421 | −0.0786176 | ||||||||
\(944\) | 7.24264 | 0.235728 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.41421 | −0.176031 | ||||||||
\(947\) | 25.2132 | 0.819319 | 0.409660 | − | 0.912239i | \(-0.365648\pi\) | ||||
0.409660 | + | 0.912239i | \(0.365648\pi\) | |||||||
\(948\) | −1.07107 | −0.0347867 | ||||||||
\(949\) | 45.2132 | 1.46768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9706 | 0.647590 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.5980 | 1.02356 | 0.511779 | − | 0.859117i | \(-0.328986\pi\) | ||||
0.511779 | + | 0.859117i | \(0.328986\pi\) | |||||||
\(954\) | −12.6569 | −0.409781 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.3137 | −0.365911 | ||||||||
\(957\) | −3.41421 | −0.110366 | ||||||||
\(958\) | 20.2426 | 0.654010 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.1716 | −0.811986 | ||||||||
\(962\) | 21.2132 | 0.683941 | ||||||||
\(963\) | −6.48528 | −0.208985 | ||||||||
\(964\) | −6.00000 | −0.193247 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0416 | 1.41628 | 0.708142 | − | 0.706070i | \(-0.249534\pi\) | ||||
0.708142 | + | 0.706070i | \(0.249534\pi\) | |||||||
\(968\) | 0.656854 | 0.0211121 | ||||||||
\(969\) | 8.24264 | 0.264792 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.9706 | −1.44317 | −0.721587 | − | 0.692324i | \(-0.756587\pi\) | ||||
−0.721587 | + | 0.692324i | \(0.756587\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.51472 | −0.176703 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.171573 | −0.00549191 | ||||||||
\(977\) | 8.44365 | 0.270136 | 0.135068 | − | 0.990836i | \(-0.456875\pi\) | ||||
0.135068 | + | 0.990836i | \(0.456875\pi\) | |||||||
\(978\) | 5.24264 | 0.167641 | ||||||||
\(979\) | 13.6569 | 0.436475 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3137 | −0.361219 | ||||||||
\(982\) | −0.142136 | −0.00453573 | ||||||||
\(983\) | −28.6863 | −0.914951 | −0.457475 | − | 0.889222i | \(-0.651246\pi\) | ||||
−0.457475 | + | 0.889222i | \(0.651246\pi\) | |||||||
\(984\) | 5.82843 | 0.185803 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.82843 | −0.185615 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.24264 | −0.134976 | ||||||||
\(989\) | −0.656854 | −0.0208867 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3431 | −0.582689 | −0.291345 | − | 0.956618i | \(-0.594103\pi\) | ||||
−0.291345 | + | 0.956618i | \(0.594103\pi\) | |||||||
\(992\) | −2.41421 | −0.0766514 | ||||||||
\(993\) | 24.0711 | 0.763872 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0710678 | −0.00225187 | ||||||||
\(997\) | 25.3137 | 0.801693 | 0.400847 | − | 0.916145i | \(-0.368716\pi\) | ||||
0.400847 | + | 0.916145i | \(0.368716\pi\) | |||||||
\(998\) | −26.0711 | −0.825265 | ||||||||
\(999\) | 7.07107 | 0.223719 |
(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 | 7350.2.a.dj.1.2 | yes | 2 | |
5.4 | even | 2 | 7350.2.a.dg.1.2 | yes | 2 | ||
7.6 | odd | 2 | 7350.2.a.dm.1.2 | yes | 2 | ||
35.34 | odd | 2 | 7350.2.a.dc.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7350.2.a.dc.1.2 | ✓ | 2 | 35.34 | odd | 2 | ||
7350.2.a.dg.1.2 | yes | 2 | 5.4 | even | 2 | ||
7350.2.a.dj.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
7350.2.a.dm.1.2 | yes | 2 | 7.6 | odd | 2 |