Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.70716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70716 | −1.20714 | −0.603572 | − | 0.797309i | \(-0.706256\pi\) | ||||
−0.603572 | + | 0.797309i | \(0.706256\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.914391 | 0.457196 | ||||||||
\(5\) | −4.06637 | −1.81854 | −0.909268 | − | 0.416211i | \(-0.863358\pi\) | ||||
−0.909268 | + | 0.416211i | \(0.863358\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.85331 | 0.655243 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.94194 | 2.19523 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.27792 | −0.909132 | −0.454566 | − | 0.890713i | \(-0.650206\pi\) | ||||
−0.454566 | + | 0.890713i | \(0.650206\pi\) | |||||||
\(14\) | 1.70716 | 0.456257 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99267 | −1.24817 | ||||||||
\(17\) | −1.32088 | −0.320361 | −0.160180 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160180 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.16175 | −0.495939 | −0.247969 | − | 0.968768i | \(-0.579763\pi\) | ||||
−0.247969 | + | 0.968768i | \(0.579763\pi\) | |||||||
\(20\) | −3.71825 | −0.831427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.86611 | 0.389112 | 0.194556 | − | 0.980891i | \(-0.437673\pi\) | ||||
0.194556 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.5354 | 2.30707 | ||||||||
\(26\) | 5.59593 | 1.09745 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.914391 | −0.172804 | ||||||||
\(29\) | −0.244102 | −0.0453286 | −0.0226643 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226643 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.86988 | −1.23387 | −0.616933 | − | 0.787015i | \(-0.711625\pi\) | ||||
−0.616933 | + | 0.787015i | \(0.711625\pi\) | |||||||
\(32\) | 4.81667 | 0.851475 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.25495 | 0.386721 | ||||||||
\(35\) | 4.06637 | 0.687342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.255619 | 0.0420236 | 0.0210118 | − | 0.999779i | \(-0.493311\pi\) | ||||
0.0210118 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(38\) | 3.69045 | 0.598669 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.53623 | −1.19158 | ||||||||
\(41\) | −5.73233 | −0.895239 | −0.447620 | − | 0.894224i | \(-0.647728\pi\) | ||||
−0.447620 | + | 0.894224i | \(0.647728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.01781 | 1.22270 | 0.611352 | − | 0.791358i | \(-0.290626\pi\) | ||||
0.611352 | + | 0.791358i | \(0.290626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.18575 | −0.469714 | ||||||||
\(47\) | 4.06768 | 0.593332 | 0.296666 | − | 0.954981i | \(-0.404125\pi\) | ||||
0.296666 | + | 0.954981i | \(0.404125\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −19.6927 | −2.78497 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.99730 | −0.415651 | ||||||||
\(53\) | 5.00585 | 0.687607 | 0.343803 | − | 0.939042i | \(-0.388285\pi\) | ||||
0.343803 | + | 0.939042i | \(0.388285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.85331 | −0.247658 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.416720 | 0.0547181 | ||||||||
\(59\) | 0.983592 | 0.128053 | 0.0640264 | − | 0.997948i | \(-0.479606\pi\) | ||||
0.0640264 | + | 0.997948i | \(0.479606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.84671 | −0.236447 | −0.118223 | − | 0.992987i | \(-0.537720\pi\) | ||||
−0.118223 | + | 0.992987i | \(0.537720\pi\) | |||||||
\(62\) | 11.7280 | 1.48945 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.76252 | 0.220315 | ||||||||
\(65\) | 13.3292 | 1.65329 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00700 | −0.367364 | −0.183682 | − | 0.982986i | \(-0.558802\pi\) | ||||
−0.183682 | + | 0.982986i | \(0.558802\pi\) | |||||||
\(68\) | −1.20780 | −0.146468 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.94194 | −0.829720 | ||||||||
\(71\) | −6.47642 | −0.768609 | −0.384305 | − | 0.923206i | \(-0.625559\pi\) | ||||
−0.384305 | + | 0.923206i | \(0.625559\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.65164 | 1.12964 | 0.564820 | − | 0.825214i | \(-0.308946\pi\) | ||||
0.564820 | + | 0.825214i | \(0.308946\pi\) | |||||||
\(74\) | −0.436383 | −0.0507285 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.97668 | −0.226741 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.53450 | 0.622680 | 0.311340 | − | 0.950299i | \(-0.399222\pi\) | ||||
0.311340 | + | 0.950299i | \(0.399222\pi\) | |||||||
\(80\) | 20.3020 | 2.26984 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.78600 | 1.08068 | ||||||||
\(83\) | 2.07023 | 0.227237 | 0.113618 | − | 0.993524i | \(-0.463756\pi\) | ||||
0.113618 | + | 0.993524i | \(0.463756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.37119 | 0.582588 | ||||||||
\(86\) | −13.6877 | −1.47598 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.6306 | −1.76284 | −0.881421 | − | 0.472331i | \(-0.843413\pi\) | ||||
−0.881421 | + | 0.472331i | \(0.843413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.27792 | 0.343620 | ||||||||
\(92\) | 1.70636 | 0.177900 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.94417 | −0.716237 | ||||||||
\(95\) | 8.79046 | 0.901883 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.58559 | −0.262527 | −0.131264 | − | 0.991348i | \(-0.541903\pi\) | ||||
−0.131264 | + | 0.991348i | \(0.541903\pi\) | |||||||
\(98\) | −1.70716 | −0.172449 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.5478 | 1.05478 | ||||||||
\(101\) | 10.5686 | 1.05162 | 0.525808 | − | 0.850604i | \(-0.323763\pi\) | ||||
0.525808 | + | 0.850604i | \(0.323763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8489 | 1.36457 | 0.682286 | − | 0.731086i | \(-0.260986\pi\) | ||||
0.682286 | + | 0.731086i | \(0.260986\pi\) | |||||||
\(104\) | −6.07499 | −0.595702 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.54578 | −0.830040 | ||||||||
\(107\) | 12.4286 | 1.20152 | 0.600761 | − | 0.799428i | \(-0.294864\pi\) | ||||
0.600761 | + | 0.799428i | \(0.294864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.36748 | 0.705676 | 0.352838 | − | 0.935684i | \(-0.385217\pi\) | ||||
0.352838 | + | 0.935684i | \(0.385217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.99267 | 0.471763 | ||||||||
\(113\) | −11.4083 | −1.07320 | −0.536600 | − | 0.843837i | \(-0.680292\pi\) | ||||
−0.536600 | + | 0.843837i | \(0.680292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.58831 | −0.707614 | ||||||||
\(116\) | −0.223205 | −0.0207240 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.67915 | −0.154578 | ||||||||
\(119\) | 1.32088 | 0.121085 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.15263 | 0.285425 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.28176 | −0.564119 | ||||||||
\(125\) | −26.5752 | −2.37696 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.74845 | 0.776300 | 0.388150 | − | 0.921596i | \(-0.373114\pi\) | ||||
0.388150 | + | 0.921596i | \(0.373114\pi\) | |||||||
\(128\) | −12.6422 | −1.11743 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22.7551 | −1.99576 | ||||||||
\(131\) | −12.5516 | −1.09664 | −0.548319 | − | 0.836269i | \(-0.684732\pi\) | ||||
−0.548319 | + | 0.836269i | \(0.684732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.16175 | 0.187447 | ||||||||
\(134\) | 5.13343 | 0.443461 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.44800 | −0.209914 | ||||||||
\(137\) | 6.32819 | 0.540654 | 0.270327 | − | 0.962769i | \(-0.412868\pi\) | ||||
0.270327 | + | 0.962769i | \(0.412868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.4429 | −1.22503 | −0.612517 | − | 0.790457i | \(-0.709843\pi\) | ||||
−0.612517 | + | 0.790457i | \(0.709843\pi\) | |||||||
\(140\) | 3.71825 | 0.314250 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.0563 | 0.927822 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.992608 | 0.0824316 | ||||||||
\(146\) | −16.4769 | −1.36364 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.233736 | 0.0192130 | ||||||||
\(149\) | 24.0592 | 1.97101 | 0.985504 | − | 0.169653i | \(-0.0542648\pi\) | ||||
0.985504 | + | 0.169653i | \(0.0542648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.32418 | 0.107760 | 0.0538802 | − | 0.998547i | \(-0.482841\pi\) | ||||
0.0538802 | + | 0.998547i | \(0.482841\pi\) | |||||||
\(152\) | −4.00638 | −0.324960 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.9355 | 2.24383 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6141 | 1.16633 | 0.583165 | − | 0.812354i | \(-0.301814\pi\) | ||||
0.583165 | + | 0.812354i | \(0.301814\pi\) | |||||||
\(158\) | −9.44827 | −0.751664 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −19.5864 | −1.54844 | ||||||||
\(161\) | −1.86611 | −0.147070 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.9215 | −1.63870 | −0.819349 | − | 0.573296i | \(-0.805665\pi\) | ||||
−0.819349 | + | 0.573296i | \(0.805665\pi\) | |||||||
\(164\) | −5.24159 | −0.409300 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.53421 | −0.274308 | ||||||||
\(167\) | 4.91335 | 0.380206 | 0.190103 | − | 0.981764i | \(-0.439118\pi\) | ||||
0.190103 | + | 0.981764i | \(0.439118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.25523 | −0.173479 | ||||||||
\(170\) | −9.16948 | −0.703267 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.33142 | 0.559015 | ||||||||
\(173\) | 19.6578 | 1.49456 | 0.747279 | − | 0.664511i | \(-0.231360\pi\) | ||||
0.747279 | + | 0.664511i | \(0.231360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.5354 | −0.871992 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 28.3911 | 2.12800 | ||||||||
\(179\) | 25.3588 | 1.89541 | 0.947705 | − | 0.319149i | \(-0.103397\pi\) | ||||
0.947705 | + | 0.319149i | \(0.103397\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.97569 | −0.146852 | −0.0734258 | − | 0.997301i | \(-0.523393\pi\) | ||||
−0.0734258 | + | 0.997301i | \(0.523393\pi\) | |||||||
\(182\) | −5.59593 | −0.414798 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.45848 | 0.254963 | ||||||||
\(185\) | −1.03944 | −0.0764214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.71945 | 0.271269 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.0067 | −1.08870 | ||||||||
\(191\) | −0.972995 | −0.0704035 | −0.0352017 | − | 0.999380i | \(-0.511207\pi\) | ||||
−0.0352017 | + | 0.999380i | \(0.511207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.1326 | 1.66512 | 0.832562 | − | 0.553932i | \(-0.186873\pi\) | ||||
0.832562 | + | 0.553932i | \(0.186873\pi\) | |||||||
\(194\) | 4.41402 | 0.316908 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.914391 | 0.0653137 | ||||||||
\(197\) | −9.91237 | −0.706227 | −0.353114 | − | 0.935580i | \(-0.614877\pi\) | ||||
−0.353114 | + | 0.935580i | \(0.614877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3847 | 0.736154 | 0.368077 | − | 0.929795i | \(-0.380016\pi\) | ||||
0.368077 | + | 0.929795i | \(0.380016\pi\) | |||||||
\(200\) | 21.3786 | 1.51169 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.0423 | −1.26945 | ||||||||
\(203\) | 0.244102 | 0.0171326 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.3098 | 1.62803 | ||||||||
\(206\) | −23.6422 | −1.64723 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.3656 | 1.13475 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9916 | 0.894378 | 0.447189 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447189 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(212\) | 4.57731 | 0.314371 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −21.2177 | −1.45041 | ||||||||
\(215\) | −32.6034 | −2.22353 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.86988 | 0.466358 | ||||||||
\(218\) | −12.5775 | −0.851853 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.32975 | 0.291250 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.3527 | −0.961127 | −0.480563 | − | 0.876960i | \(-0.659568\pi\) | ||||
−0.480563 | + | 0.876960i | \(0.659568\pi\) | |||||||
\(224\) | −4.81667 | −0.321827 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.4757 | 1.29551 | ||||||||
\(227\) | 6.37479 | 0.423110 | 0.211555 | − | 0.977366i | \(-0.432147\pi\) | ||||
0.211555 | + | 0.977366i | \(0.432147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00237 | −0.528812 | −0.264406 | − | 0.964412i | \(-0.585176\pi\) | ||||
−0.264406 | + | 0.964412i | \(0.585176\pi\) | |||||||
\(230\) | 12.9545 | 0.854191 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.452395 | −0.0297012 | ||||||||
\(233\) | −10.8022 | −0.707675 | −0.353837 | − | 0.935307i | \(-0.615123\pi\) | ||||
−0.353837 | + | 0.935307i | \(0.615123\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.5407 | −1.07900 | ||||||||
\(236\) | 0.899388 | 0.0585452 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.25495 | −0.146167 | ||||||||
\(239\) | 25.1583 | 1.62735 | 0.813676 | − | 0.581318i | \(-0.197463\pi\) | ||||
0.813676 | + | 0.581318i | \(0.197463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2462 | 1.17534 | 0.587669 | − | 0.809101i | \(-0.300046\pi\) | ||||
0.587669 | + | 0.809101i | \(0.300046\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.68862 | −0.108103 | ||||||||
\(245\) | −4.06637 | −0.259791 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.08604 | 0.450874 | ||||||||
\(248\) | −12.7320 | −0.808482 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 45.3681 | 2.86933 | ||||||||
\(251\) | −15.3284 | −0.967520 | −0.483760 | − | 0.875201i | \(-0.660729\pi\) | ||||
−0.483760 | + | 0.875201i | \(0.660729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −14.9350 | −0.937105 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.0573 | 1.12858 | ||||||||
\(257\) | −2.67980 | −0.167161 | −0.0835805 | − | 0.996501i | \(-0.526636\pi\) | ||||
−0.0835805 | + | 0.996501i | \(0.526636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.255619 | −0.0158834 | ||||||||
\(260\) | 12.1881 | 0.755877 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.4276 | 1.32380 | ||||||||
\(263\) | −9.97733 | −0.615229 | −0.307614 | − | 0.951511i | \(-0.599531\pi\) | ||||
−0.307614 | + | 0.951511i | \(0.599531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.3556 | −1.25044 | ||||||||
\(266\) | −3.69045 | −0.226276 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.74958 | −0.167957 | ||||||||
\(269\) | 21.5774 | 1.31560 | 0.657798 | − | 0.753194i | \(-0.271488\pi\) | ||||
0.657798 | + | 0.753194i | \(0.271488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9862 | 0.910349 | 0.455175 | − | 0.890402i | \(-0.349577\pi\) | ||||
0.455175 | + | 0.890402i | \(0.349577\pi\) | |||||||
\(272\) | 6.59473 | 0.399864 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8032 | −0.652647 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.20640 | −0.312822 | −0.156411 | − | 0.987692i | \(-0.549992\pi\) | ||||
−0.156411 | + | 0.987692i | \(0.549992\pi\) | |||||||
\(278\) | 24.6564 | 1.47879 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.53623 | 0.450376 | ||||||||
\(281\) | 15.1601 | 0.904374 | 0.452187 | − | 0.891923i | \(-0.350644\pi\) | ||||
0.452187 | + | 0.891923i | \(0.350644\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.66559 | 0.336784 | 0.168392 | − | 0.985720i | \(-0.446143\pi\) | ||||
0.168392 | + | 0.985720i | \(0.446143\pi\) | |||||||
\(284\) | −5.92198 | −0.351405 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.73233 | 0.338369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2553 | −0.897369 | ||||||||
\(290\) | −1.69454 | −0.0995068 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.82538 | 0.516466 | ||||||||
\(293\) | −26.9403 | −1.57387 | −0.786935 | − | 0.617035i | \(-0.788334\pi\) | ||||
−0.786935 | + | 0.617035i | \(0.788334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.99965 | −0.232869 | ||||||||
\(296\) | 0.473741 | 0.0275356 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −41.0729 | −2.37929 | ||||||||
\(299\) | −6.11698 | −0.353754 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.01781 | −0.462139 | ||||||||
\(302\) | −2.26059 | −0.130082 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.7929 | 0.619015 | ||||||||
\(305\) | 7.50941 | 0.429987 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.6157 | −1.40489 | −0.702447 | − | 0.711736i | \(-0.747909\pi\) | ||||
−0.702447 | + | 0.711736i | \(0.747909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −47.6903 | −2.70863 | ||||||||
\(311\) | 10.2131 | 0.579132 | 0.289566 | − | 0.957158i | \(-0.406489\pi\) | ||||
0.289566 | + | 0.957158i | \(0.406489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.4003 | 1.26614 | 0.633069 | − | 0.774096i | \(-0.281795\pi\) | ||||
0.633069 | + | 0.774096i | \(0.281795\pi\) | |||||||
\(314\) | −24.9485 | −1.40793 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.06070 | 0.284687 | ||||||||
\(317\) | −23.3595 | −1.31200 | −0.656000 | − | 0.754761i | \(-0.727753\pi\) | ||||
−0.656000 | + | 0.754761i | \(0.727753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −7.16707 | −0.400651 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.18575 | 0.177535 | ||||||||
\(323\) | 2.85541 | 0.158879 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.8120 | −2.09743 | ||||||||
\(326\) | 35.7163 | 1.97814 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6238 | −0.586599 | ||||||||
\(329\) | −4.06768 | −0.224258 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.6444 | 0.859892 | 0.429946 | − | 0.902855i | \(-0.358533\pi\) | ||||
0.429946 | + | 0.902855i | \(0.358533\pi\) | |||||||
\(332\) | 1.89300 | 0.103892 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.38787 | −0.458964 | ||||||||
\(335\) | 12.2276 | 0.668064 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.5910 | −1.77534 | −0.887672 | − | 0.460477i | \(-0.847678\pi\) | ||||
−0.887672 | + | 0.460477i | \(0.847678\pi\) | |||||||
\(338\) | 3.85004 | 0.209414 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.91137 | 0.266356 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 14.8595 | 0.801169 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.5590 | −1.80415 | ||||||||
\(347\) | 5.75284 | 0.308829 | 0.154414 | − | 0.988006i | \(-0.450651\pi\) | ||||
0.154414 | + | 0.988006i | \(0.450651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.183939 | 0.00984606 | 0.00492303 | − | 0.999988i | \(-0.498433\pi\) | ||||
0.00492303 | + | 0.999988i | \(0.498433\pi\) | |||||||
\(350\) | 19.6927 | 1.05262 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.0211 | −1.01239 | −0.506195 | − | 0.862419i | \(-0.668948\pi\) | ||||
−0.506195 | + | 0.862419i | \(0.668948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.3355 | 1.39774 | ||||||||
\(356\) | −15.2069 | −0.805964 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −43.2916 | −2.28803 | ||||||||
\(359\) | −0.718928 | −0.0379435 | −0.0189718 | − | 0.999820i | \(-0.506039\pi\) | ||||
−0.0189718 | + | 0.999820i | \(0.506039\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3268 | −0.754045 | ||||||||
\(362\) | 3.37281 | 0.177271 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.99730 | 0.157101 | ||||||||
\(365\) | −39.2471 | −2.05429 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.89295 | −0.412009 | −0.206004 | − | 0.978551i | \(-0.566046\pi\) | ||||
−0.206004 | + | 0.978551i | \(0.566046\pi\) | |||||||
\(368\) | −9.31689 | −0.485677 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.77449 | 0.0922516 | ||||||||
\(371\) | −5.00585 | −0.259891 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6686 | −0.811292 | −0.405646 | − | 0.914030i | \(-0.632953\pi\) | ||||
−0.405646 | + | 0.914030i | \(0.632953\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.53865 | 0.388776 | ||||||||
\(377\) | 0.800146 | 0.0412096 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.3144 | −0.683914 | −0.341957 | − | 0.939716i | \(-0.611090\pi\) | ||||
−0.341957 | + | 0.939716i | \(0.611090\pi\) | |||||||
\(380\) | 8.03792 | 0.412337 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.66106 | 0.0849871 | ||||||||
\(383\) | −11.8484 | −0.605426 | −0.302713 | − | 0.953082i | \(-0.597892\pi\) | ||||
−0.302713 | + | 0.953082i | \(0.597892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −39.4911 | −2.01004 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.36424 | −0.120026 | ||||||||
\(389\) | 6.04972 | 0.306733 | 0.153366 | − | 0.988169i | \(-0.450989\pi\) | ||||
0.153366 | + | 0.988169i | \(0.450989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.46491 | −0.124656 | ||||||||
\(392\) | 1.85331 | 0.0936061 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.9220 | 0.852518 | ||||||||
\(395\) | −22.5053 | −1.13237 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5763 | −0.580996 | −0.290498 | − | 0.956876i | \(-0.593821\pi\) | ||||
−0.290498 | + | 0.956876i | \(0.593821\pi\) | |||||||
\(398\) | −17.7284 | −0.888643 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −57.5923 | −2.87961 | ||||||||
\(401\) | −33.7924 | −1.68751 | −0.843755 | − | 0.536728i | \(-0.819660\pi\) | ||||
−0.843755 | + | 0.536728i | \(0.819660\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.5189 | 1.12175 | ||||||||
\(404\) | 9.66384 | 0.480794 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.416720 | −0.0206815 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0520 | −0.892613 | −0.446306 | − | 0.894880i | \(-0.647261\pi\) | ||||
−0.446306 | + | 0.894880i | \(0.647261\pi\) | |||||||
\(410\) | −39.7935 | −1.96526 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.6633 | 0.623876 | ||||||||
\(413\) | −0.983592 | −0.0483994 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.41831 | −0.413239 | ||||||||
\(416\) | −15.7887 | −0.774103 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.58559 | −0.126314 | −0.0631571 | − | 0.998004i | \(-0.520117\pi\) | ||||
−0.0631571 | + | 0.998004i | \(0.520117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9948 | 0.682064 | 0.341032 | − | 0.940052i | \(-0.389224\pi\) | ||||
0.341032 | + | 0.940052i | \(0.389224\pi\) | |||||||
\(422\) | −22.1787 | −1.07964 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.27738 | 0.450549 | ||||||||
\(425\) | −15.2368 | −0.739096 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.84671 | 0.0893686 | ||||||||
\(428\) | 11.3646 | 0.549331 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 55.6592 | 2.68412 | ||||||||
\(431\) | −33.6682 | −1.62174 | −0.810870 | − | 0.585227i | \(-0.801005\pi\) | ||||
−0.810870 | + | 0.585227i | \(0.801005\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.52292 | 0.361529 | 0.180764 | − | 0.983526i | \(-0.442143\pi\) | ||||
0.180764 | + | 0.983526i | \(0.442143\pi\) | |||||||
\(434\) | −11.7280 | −0.562961 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.73676 | 0.322632 | ||||||||
\(437\) | −4.03407 | −0.192976 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.0123 | 1.05059 | 0.525294 | − | 0.850921i | \(-0.323955\pi\) | ||||
0.525294 | + | 0.850921i | \(0.323955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.39156 | −0.351581 | ||||||||
\(443\) | −23.6893 | −1.12551 | −0.562756 | − | 0.826623i | \(-0.690259\pi\) | ||||
−0.562756 | + | 0.826623i | \(0.690259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 67.6263 | 3.20579 | ||||||||
\(446\) | 24.5023 | 1.16022 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.76252 | −0.0832713 | ||||||||
\(449\) | −2.27513 | −0.107370 | −0.0536851 | − | 0.998558i | \(-0.517097\pi\) | ||||
−0.0536851 | + | 0.998558i | \(0.517097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −10.4316 | −0.490663 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.8828 | −0.510754 | ||||||||
\(455\) | −13.3292 | −0.624885 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.3134 | 1.27767 | 0.638833 | − | 0.769345i | \(-0.279417\pi\) | ||||
0.638833 | + | 0.769345i | \(0.279417\pi\) | |||||||
\(458\) | 13.6613 | 0.638351 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.93868 | −0.323518 | ||||||||
\(461\) | −8.21908 | −0.382801 | −0.191400 | − | 0.981512i | \(-0.561303\pi\) | ||||
−0.191400 | + | 0.981512i | \(0.561303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.9839 | −1.30052 | −0.650261 | − | 0.759711i | \(-0.725340\pi\) | ||||
−0.650261 | + | 0.759711i | \(0.725340\pi\) | |||||||
\(464\) | 1.21872 | 0.0565776 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.4411 | 0.854265 | ||||||||
\(467\) | −26.6745 | −1.23435 | −0.617175 | − | 0.786826i | \(-0.711723\pi\) | ||||
−0.617175 | + | 0.786826i | \(0.711723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.00700 | 0.138850 | ||||||||
\(470\) | 28.2376 | 1.30250 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.82290 | 0.0839057 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.9365 | −1.14417 | ||||||||
\(476\) | 1.20780 | 0.0553595 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −42.9491 | −1.96445 | ||||||||
\(479\) | −23.2240 | −1.06113 | −0.530566 | − | 0.847644i | \(-0.678020\pi\) | ||||
−0.530566 | + | 0.847644i | \(0.678020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.837900 | −0.0382050 | ||||||||
\(482\) | −31.1491 | −1.41880 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5140 | 0.477415 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.7920 | −0.851548 | −0.425774 | − | 0.904830i | \(-0.639998\pi\) | ||||
−0.425774 | + | 0.904830i | \(0.639998\pi\) | |||||||
\(488\) | −3.42252 | −0.154930 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.94194 | 0.313605 | ||||||||
\(491\) | 7.40573 | 0.334216 | 0.167108 | − | 0.985939i | \(-0.446557\pi\) | ||||
0.167108 | + | 0.985939i | \(0.446557\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.322429 | 0.0145215 | ||||||||
\(494\) | −12.0970 | −0.544269 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.2991 | 1.54007 | ||||||||
\(497\) | 6.47642 | 0.290507 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.6703 | 1.05963 | 0.529815 | − | 0.848113i | \(-0.322261\pi\) | ||||
0.529815 | + | 0.848113i | \(0.322261\pi\) | |||||||
\(500\) | −24.3001 | −1.08674 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.1680 | 1.16794 | ||||||||
\(503\) | −8.39731 | −0.374418 | −0.187209 | − | 0.982320i | \(-0.559944\pi\) | ||||
−0.187209 | + | 0.982320i | \(0.559944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.9758 | −1.91240 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.99951 | 0.354921 | ||||||||
\(509\) | −14.3065 | −0.634123 | −0.317061 | − | 0.948405i | \(-0.602696\pi\) | ||||
−0.317061 | + | 0.948405i | \(0.602696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.65164 | −0.426963 | ||||||||
\(512\) | −5.54215 | −0.244931 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.57484 | 0.201787 | ||||||||
\(515\) | −56.3147 | −2.48152 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.436383 | 0.0191736 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.7032 | 1.08331 | ||||||||
\(521\) | 33.3684 | 1.46189 | 0.730947 | − | 0.682434i | \(-0.239079\pi\) | ||||
0.730947 | + | 0.682434i | \(0.239079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.3817 | −0.585143 | −0.292571 | − | 0.956244i | \(-0.594511\pi\) | ||||
−0.292571 | + | 0.956244i | \(0.594511\pi\) | |||||||
\(524\) | −11.4771 | −0.501378 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.0329 | 0.742669 | ||||||||
\(527\) | 9.07430 | 0.395283 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5176 | −0.848592 | ||||||||
\(530\) | 34.7503 | 1.50946 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.97668 | 0.0857001 | ||||||||
\(533\) | 18.7901 | 0.813891 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −50.5395 | −2.18501 | ||||||||
\(536\) | −5.57289 | −0.240712 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.8360 | −1.58811 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0639 | 1.46452 | 0.732262 | − | 0.681023i | \(-0.238465\pi\) | ||||
0.732262 | + | 0.681023i | \(0.238465\pi\) | |||||||
\(542\) | −25.5839 | −1.09892 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.36225 | −0.272779 | ||||||||
\(545\) | −29.9589 | −1.28330 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7614 | 0.673909 | 0.336954 | − | 0.941521i | \(-0.390603\pi\) | ||||
0.336954 | + | 0.941521i | \(0.390603\pi\) | |||||||
\(548\) | 5.78644 | 0.247185 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.527686 | 0.0224802 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.53450 | −0.235351 | ||||||||
\(554\) | 8.88815 | 0.377621 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.2065 | −0.560080 | ||||||||
\(557\) | 16.1024 | 0.682282 | 0.341141 | − | 0.940012i | \(-0.389187\pi\) | ||||
0.341141 | + | 0.940012i | \(0.389187\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.2818 | −1.11160 | ||||||||
\(560\) | −20.3020 | −0.857918 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.8806 | −1.09171 | ||||||||
\(563\) | −17.2305 | −0.726177 | −0.363089 | − | 0.931755i | \(-0.618278\pi\) | ||||
−0.363089 | + | 0.931755i | \(0.618278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46.3903 | 1.95165 | ||||||||
\(566\) | −9.67206 | −0.406547 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0028 | −0.503626 | ||||||||
\(569\) | −35.6143 | −1.49303 | −0.746514 | − | 0.665370i | \(-0.768274\pi\) | ||||
−0.746514 | + | 0.665370i | \(0.768274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.6026 | −1.11329 | −0.556643 | − | 0.830752i | \(-0.687911\pi\) | ||||
−0.556643 | + | 0.830752i | \(0.687911\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.78600 | −0.408460 | ||||||||
\(575\) | 21.5263 | 0.897709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.8725 | 1.20198 | 0.600989 | − | 0.799257i | \(-0.294773\pi\) | ||||
0.600989 | + | 0.799257i | \(0.294773\pi\) | |||||||
\(578\) | 26.0432 | 1.08325 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.907632 | 0.0376874 | ||||||||
\(581\) | −2.07023 | −0.0858875 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 17.8874 | 0.740188 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45.9914 | 1.89989 | ||||||||
\(587\) | −2.43414 | −0.100468 | −0.0502339 | − | 0.998737i | \(-0.515997\pi\) | ||||
−0.0502339 | + | 0.998737i | \(0.515997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8509 | 0.611922 | ||||||||
\(590\) | 6.82804 | 0.281106 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.27622 | −0.0524525 | ||||||||
\(593\) | 15.6870 | 0.644187 | 0.322093 | − | 0.946708i | \(-0.395613\pi\) | ||||
0.322093 | + | 0.946708i | \(0.395613\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.37119 | −0.220197 | ||||||||
\(596\) | 21.9995 | 0.901136 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.4426 | 0.427032 | ||||||||
\(599\) | 13.2218 | 0.540229 | 0.270115 | − | 0.962828i | \(-0.412938\pi\) | ||||
0.270115 | + | 0.962828i | \(0.412938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2303 | 0.458093 | 0.229047 | − | 0.973415i | \(-0.426439\pi\) | ||||
0.229047 | + | 0.973415i | \(0.426439\pi\) | |||||||
\(602\) | 13.6877 | 0.557868 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.21082 | 0.0492676 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.3477 | −0.785298 | −0.392649 | − | 0.919688i | \(-0.628441\pi\) | ||||
−0.392649 | + | 0.919688i | \(0.628441\pi\) | |||||||
\(608\) | −10.4124 | −0.422279 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.8197 | −0.519056 | ||||||||
\(611\) | −13.3335 | −0.539417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0549 | −0.850398 | −0.425199 | − | 0.905100i | \(-0.639796\pi\) | ||||
−0.425199 | + | 0.905100i | \(0.639796\pi\) | |||||||
\(614\) | 42.0230 | 1.69591 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.1496 | 0.972228 | 0.486114 | − | 0.873895i | \(-0.338414\pi\) | ||||
0.486114 | + | 0.873895i | \(0.338414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.62475 | 0.105497 | 0.0527487 | − | 0.998608i | \(-0.483202\pi\) | ||||
0.0527487 | + | 0.998608i | \(0.483202\pi\) | |||||||
\(620\) | 25.5440 | 1.02587 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.4354 | −0.699095 | ||||||||
\(623\) | 16.6306 | 0.666292 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 50.3878 | 2.01551 | ||||||||
\(626\) | −38.2408 | −1.52841 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.3630 | 0.533241 | ||||||||
\(629\) | −0.337643 | −0.0134627 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.1176 | −0.999914 | −0.499957 | − | 0.866050i | \(-0.666651\pi\) | ||||
−0.499957 | + | 0.866050i | \(0.666651\pi\) | |||||||
\(632\) | 10.2571 | 0.408006 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39.8784 | 1.58377 | ||||||||
\(635\) | −35.5744 | −1.41173 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.27792 | −0.129876 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 51.4080 | 2.03208 | ||||||||
\(641\) | −20.6584 | −0.815958 | −0.407979 | − | 0.912991i | \(-0.633766\pi\) | ||||
−0.407979 | + | 0.912991i | \(0.633766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.4632 | 0.649246 | 0.324623 | − | 0.945844i | \(-0.394763\pi\) | ||||
0.324623 | + | 0.945844i | \(0.394763\pi\) | |||||||
\(644\) | −1.70636 | −0.0672399 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.87464 | −0.191790 | ||||||||
\(647\) | 34.9584 | 1.37435 | 0.687177 | − | 0.726490i | \(-0.258850\pi\) | ||||
0.687177 | + | 0.726490i | \(0.258850\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 64.5511 | 2.53190 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.1304 | −0.749205 | ||||||||
\(653\) | −2.41649 | −0.0945645 | −0.0472823 | − | 0.998882i | \(-0.515056\pi\) | ||||
−0.0472823 | + | 0.998882i | \(0.515056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51.0395 | 1.99428 | ||||||||
\(656\) | 28.6196 | 1.11741 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.94417 | 0.270712 | ||||||||
\(659\) | 16.9733 | 0.661186 | 0.330593 | − | 0.943773i | \(-0.392751\pi\) | ||||
0.330593 | + | 0.943773i | \(0.392751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.96946 | 0.309976 | 0.154988 | − | 0.987916i | \(-0.450466\pi\) | ||||
0.154988 | + | 0.987916i | \(0.450466\pi\) | |||||||
\(662\) | −26.7074 | −1.03801 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.83677 | 0.148895 | ||||||||
\(665\) | −8.79046 | −0.340880 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.455522 | −0.0176379 | ||||||||
\(668\) | 4.49272 | 0.173829 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.8744 | −0.806449 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0250 | −0.617717 | −0.308859 | − | 0.951108i | \(-0.599947\pi\) | ||||
−0.308859 | + | 0.951108i | \(0.599947\pi\) | |||||||
\(674\) | 55.6380 | 2.14309 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.06216 | −0.0793140 | ||||||||
\(677\) | 15.2366 | 0.585589 | 0.292794 | − | 0.956175i | \(-0.405415\pi\) | ||||
0.292794 | + | 0.956175i | \(0.405415\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.58559 | 0.0992259 | ||||||||
\(680\) | 9.95446 | 0.381736 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.3742 | −0.550013 | −0.275007 | − | 0.961442i | \(-0.588680\pi\) | ||||
−0.275007 | + | 0.961442i | \(0.588680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.7328 | −0.983198 | ||||||||
\(686\) | 1.70716 | 0.0651796 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −40.0303 | −1.52614 | ||||||||
\(689\) | −16.4088 | −0.625125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.7978 | −1.70419 | −0.852095 | − | 0.523387i | \(-0.824668\pi\) | ||||
−0.852095 | + | 0.523387i | \(0.824668\pi\) | |||||||
\(692\) | 17.9750 | 0.683305 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.82101 | −0.372800 | ||||||||
\(695\) | 58.7303 | 2.22777 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.57173 | 0.286800 | ||||||||
\(698\) | −0.314014 | −0.0118856 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.5478 | −0.398671 | ||||||||
\(701\) | −0.240330 | −0.00907713 | −0.00453857 | − | 0.999990i | \(-0.501445\pi\) | ||||
−0.00453857 | + | 0.999990i | \(0.501445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.552584 | −0.0208411 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.4720 | 1.22210 | ||||||||
\(707\) | −10.5686 | −0.397473 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7534 | 0.403852 | 0.201926 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201926 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(710\) | −44.9589 | −1.68728 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −30.8216 | −1.15509 | ||||||||
\(713\) | −12.8200 | −0.480112 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.1879 | 0.866573 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.22732 | 0.0458033 | ||||||||
\(719\) | 25.7748 | 0.961239 | 0.480620 | − | 0.876929i | \(-0.340412\pi\) | ||||
0.480620 | + | 0.876929i | \(0.340412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8489 | −0.515759 | ||||||||
\(722\) | 24.4582 | 0.910240 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.80655 | −0.0671399 | ||||||||
\(725\) | −2.81580 | −0.104576 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.47160 | −0.202930 | −0.101465 | − | 0.994839i | \(-0.532353\pi\) | ||||
−0.101465 | + | 0.994839i | \(0.532353\pi\) | |||||||
\(728\) | 6.07499 | 0.225154 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 67.0011 | 2.47982 | ||||||||
\(731\) | −10.5906 | −0.391707 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.8563 | 0.733411 | 0.366705 | − | 0.930337i | \(-0.380486\pi\) | ||||
0.366705 | + | 0.930337i | \(0.380486\pi\) | |||||||
\(734\) | 13.4745 | 0.497354 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.98845 | 0.331319 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.80077 | −0.0662423 | −0.0331212 | − | 0.999451i | \(-0.510545\pi\) | ||||
−0.0331212 | + | 0.999451i | \(0.510545\pi\) | |||||||
\(740\) | −0.950458 | −0.0349395 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.54578 | 0.313726 | ||||||||
\(743\) | 48.0579 | 1.76307 | 0.881537 | − | 0.472115i | \(-0.156509\pi\) | ||||
0.881537 | + | 0.472115i | \(0.156509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −97.8337 | −3.58435 | ||||||||
\(746\) | 26.7489 | 0.979346 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.4286 | −0.454133 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0465 | −0.913961 | −0.456980 | − | 0.889477i | \(-0.651069\pi\) | ||||
−0.456980 | + | 0.889477i | \(0.651069\pi\) | |||||||
\(752\) | −20.3086 | −0.740578 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.36598 | −0.0497459 | ||||||||
\(755\) | −5.38461 | −0.195966 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.6487 | 0.387032 | 0.193516 | − | 0.981097i | \(-0.438011\pi\) | ||||
0.193516 | + | 0.981097i | \(0.438011\pi\) | |||||||
\(758\) | 22.7298 | 0.825583 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.2914 | 0.590952 | ||||||||
\(761\) | −29.8160 | −1.08083 | −0.540414 | − | 0.841399i | \(-0.681732\pi\) | ||||
−0.540414 | + | 0.841399i | \(0.681732\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.36748 | −0.266721 | ||||||||
\(764\) | −0.889698 | −0.0321882 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.2271 | 0.730836 | ||||||||
\(767\) | −3.22414 | −0.116417 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.3115 | 1.02094 | 0.510470 | − | 0.859896i | \(-0.329471\pi\) | ||||
0.510470 | + | 0.859896i | \(0.329471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.1523 | 0.761287 | ||||||||
\(773\) | −13.2564 | −0.476800 | −0.238400 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238400 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −79.2466 | −2.84662 | ||||||||
\(776\) | −4.79189 | −0.172019 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.3278 | −0.370271 | ||||||||
\(779\) | 12.3918 | 0.443984 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.20800 | 0.150478 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.99267 | −0.178310 | ||||||||
\(785\) | −59.4262 | −2.12101 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.6771 | −1.87774 | −0.938868 | − | 0.344279i | \(-0.888124\pi\) | ||||
−0.938868 | + | 0.344279i | \(0.888124\pi\) | |||||||
\(788\) | −9.06379 | −0.322884 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 38.4202 | 1.36693 | ||||||||
\(791\) | 11.4083 | 0.405632 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.05337 | 0.214961 | ||||||||
\(794\) | 19.7625 | 0.701346 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.49570 | 0.336566 | ||||||||
\(797\) | 7.33480 | 0.259812 | 0.129906 | − | 0.991526i | \(-0.458532\pi\) | ||||
0.129906 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.37292 | −0.190080 | ||||||||
\(800\) | 55.5620 | 1.96442 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 57.6890 | 2.03707 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.58831 | 0.267453 | ||||||||
\(806\) | −38.4434 | −1.35411 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.5869 | 0.689063 | ||||||||
\(809\) | 8.66809 | 0.304754 | 0.152377 | − | 0.988322i | \(-0.451307\pi\) | ||||
0.152377 | + | 0.988322i | \(0.451307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.9487 | −0.700494 | −0.350247 | − | 0.936657i | \(-0.613902\pi\) | ||||
−0.350247 | + | 0.936657i | \(0.613902\pi\) | |||||||
\(812\) | 0.223205 | 0.00783294 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 85.0745 | 2.98003 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.3325 | −0.606387 | ||||||||
\(818\) | 30.8176 | 1.07751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.3143 | 0.744326 | ||||||||
\(821\) | 53.5648 | 1.86943 | 0.934713 | − | 0.355404i | \(-0.115657\pi\) | ||||
0.934713 | + | 0.355404i | \(0.115657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.44842 | −0.294493 | −0.147247 | − | 0.989100i | \(-0.547041\pi\) | ||||
−0.147247 | + | 0.989100i | \(0.547041\pi\) | |||||||
\(824\) | 25.6662 | 0.894125 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.67915 | 0.0584250 | ||||||||
\(827\) | −3.18260 | −0.110670 | −0.0553349 | − | 0.998468i | \(-0.517623\pi\) | ||||
−0.0553349 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 57.5089 | 1.99737 | 0.998684 | − | 0.0512831i | \(-0.0163311\pi\) | ||||
0.998684 | + | 0.0512831i | \(0.0163311\pi\) | |||||||
\(830\) | 14.3714 | 0.498838 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.77741 | −0.200296 | ||||||||
\(833\) | −1.32088 | −0.0457658 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.9795 | −0.691419 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.41401 | 0.152479 | ||||||||
\(839\) | −12.5594 | −0.433600 | −0.216800 | − | 0.976216i | \(-0.569562\pi\) | ||||
−0.216800 | + | 0.976216i | \(0.569562\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9404 | −0.997945 | ||||||||
\(842\) | −23.8913 | −0.823349 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.8794 | 0.408906 | ||||||||
\(845\) | 9.17060 | 0.315478 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.9926 | −0.858248 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.0117 | 0.892195 | ||||||||
\(851\) | 0.477015 | 0.0163519 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.3315 | −1.14125 | −0.570625 | − | 0.821211i | \(-0.693299\pi\) | ||||
−0.570625 | + | 0.821211i | \(0.693299\pi\) | |||||||
\(854\) | −3.15263 | −0.107881 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.0341 | 0.787289 | ||||||||
\(857\) | 54.0291 | 1.84560 | 0.922800 | − | 0.385279i | \(-0.125895\pi\) | ||||
0.922800 | + | 0.385279i | \(0.125895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.8624 | −0.438860 | −0.219430 | − | 0.975628i | \(-0.570420\pi\) | ||||
−0.219430 | + | 0.975628i | \(0.570420\pi\) | |||||||
\(860\) | −29.8123 | −1.01659 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 57.4769 | 1.95767 | ||||||||
\(863\) | 33.2271 | 1.13106 | 0.565531 | − | 0.824727i | \(-0.308671\pi\) | ||||
0.565531 | + | 0.824727i | \(0.308671\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −79.9360 | −2.71791 | ||||||||
\(866\) | −12.8428 | −0.436417 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.28176 | 0.213217 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.85671 | 0.333982 | ||||||||
\(872\) | 13.6542 | 0.462389 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.88679 | 0.232949 | ||||||||
\(875\) | 26.5752 | 0.898406 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.6709 | −0.934379 | −0.467189 | − | 0.884157i | \(-0.654733\pi\) | ||||
−0.467189 | + | 0.884157i | \(0.654733\pi\) | |||||||
\(878\) | −37.5784 | −1.26821 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.9636 | −1.64963 | −0.824813 | − | 0.565406i | \(-0.808720\pi\) | ||||
−0.824813 | + | 0.565406i | \(0.808720\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3223 | 0.717554 | 0.358777 | − | 0.933423i | \(-0.383194\pi\) | ||||
0.358777 | + | 0.933423i | \(0.383194\pi\) | |||||||
\(884\) | 3.95908 | 0.133158 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.4414 | 1.35865 | ||||||||
\(887\) | −45.2483 | −1.51929 | −0.759645 | − | 0.650338i | \(-0.774627\pi\) | ||||
−0.759645 | + | 0.650338i | \(0.774627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.74845 | −0.293414 | ||||||||
\(890\) | −115.449 | −3.86985 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.1240 | −0.439423 | ||||||||
\(893\) | −8.79329 | −0.294256 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −103.118 | −3.44687 | ||||||||
\(896\) | 12.6422 | 0.422348 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.88401 | 0.129611 | ||||||||
\(899\) | 1.67695 | 0.0559294 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.61213 | −0.220282 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.1430 | −0.703207 | ||||||||
\(905\) | 8.03388 | 0.267055 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.0665 | −1.49641 | −0.748205 | − | 0.663468i | \(-0.769084\pi\) | ||||
−0.748205 | + | 0.663468i | \(0.769084\pi\) | |||||||
\(908\) | 5.82906 | 0.193444 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.7551 | 0.754325 | ||||||||
\(911\) | 9.21469 | 0.305296 | 0.152648 | − | 0.988281i | \(-0.451220\pi\) | ||||
0.152648 | + | 0.988281i | \(0.451220\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −46.6283 | −1.54233 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.31730 | −0.241770 | ||||||||
\(917\) | 12.5516 | 0.414491 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.7144 | −1.63993 | −0.819963 | − | 0.572417i | \(-0.806006\pi\) | ||||
−0.819963 | + | 0.572417i | \(0.806006\pi\) | |||||||
\(920\) | −14.0635 | −0.463659 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.0313 | 0.462095 | ||||||||
\(923\) | 21.2292 | 0.698767 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.94866 | 0.0969514 | ||||||||
\(926\) | 47.7729 | 1.56992 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.17576 | −0.0385961 | ||||||||
\(929\) | −49.5105 | −1.62439 | −0.812193 | − | 0.583389i | \(-0.801726\pi\) | ||||
−0.812193 | + | 0.583389i | \(0.801726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.16175 | −0.0708484 | ||||||||
\(932\) | −9.87743 | −0.323546 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.5377 | 1.49004 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.98790 | −0.228285 | −0.114142 | − | 0.993464i | \(-0.536412\pi\) | ||||
−0.114142 | + | 0.993464i | \(0.536412\pi\) | |||||||
\(938\) | −5.13343 | −0.167612 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.1247 | −0.493312 | ||||||||
\(941\) | 46.8241 | 1.52642 | 0.763211 | − | 0.646150i | \(-0.223622\pi\) | ||||
0.763211 | + | 0.646150i | \(0.223622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.6972 | −0.348348 | ||||||||
\(944\) | −4.91075 | −0.159831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.1286 | −0.491614 | −0.245807 | − | 0.969319i | \(-0.579053\pi\) | ||||
−0.245807 | + | 0.969319i | \(0.579053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.6373 | −1.02699 | ||||||||
\(950\) | 42.5706 | 1.38117 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.44800 | 0.0793401 | ||||||||
\(953\) | −56.2273 | −1.82138 | −0.910690 | − | 0.413090i | \(-0.864450\pi\) | ||||
−0.910690 | + | 0.413090i | \(0.864450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.95656 | 0.128031 | ||||||||
\(956\) | 23.0045 | 0.744019 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.6470 | 1.28094 | ||||||||
\(959\) | −6.32819 | −0.204348 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1952 | 0.522427 | ||||||||
\(962\) | 1.43043 | 0.0461189 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.6841 | 0.537359 | ||||||||
\(965\) | −94.0658 | −3.02809 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.3761 | −1.49136 | −0.745678 | − | 0.666307i | \(-0.767874\pi\) | ||||
−0.745678 | + | 0.666307i | \(0.767874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.9490 | −0.576308 | ||||||||
\(971\) | −15.5400 | −0.498701 | −0.249351 | − | 0.968413i | \(-0.580217\pi\) | ||||
−0.249351 | + | 0.968413i | \(0.580217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.4429 | 0.463019 | ||||||||
\(974\) | 32.0810 | 1.02794 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.22002 | 0.295125 | ||||||||
\(977\) | −32.8287 | −1.05028 | −0.525141 | − | 0.851015i | \(-0.675988\pi\) | ||||
−0.525141 | + | 0.851015i | \(0.675988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.71825 | −0.118775 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.6428 | −0.403447 | ||||||||
\(983\) | −24.3184 | −0.775635 | −0.387817 | − | 0.921736i | \(-0.626771\pi\) | ||||
−0.387817 | + | 0.921736i | \(0.626771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.3074 | 1.28430 | ||||||||
\(986\) | −0.550438 | −0.0175295 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.47941 | 0.206138 | ||||||||
\(989\) | 14.9622 | 0.475769 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.7104 | −1.51557 | −0.757786 | − | 0.652503i | \(-0.773719\pi\) | ||||
−0.757786 | + | 0.652503i | \(0.773719\pi\) | |||||||
\(992\) | −33.0899 | −1.05061 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.0563 | −0.350684 | ||||||||
\(995\) | −42.2281 | −1.33872 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.8449 | −0.628494 | −0.314247 | − | 0.949341i | \(-0.601752\pi\) | ||||
−0.314247 | + | 0.949341i | \(0.601752\pi\) | |||||||
\(998\) | −40.4090 | −1.27913 | ||||||||
\(999\) | 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 | 7623.2.a.cw.1.2 | 8 | ||
3.2 | odd | 2 | 847.2.a.o.1.7 | 8 | |||
11.2 | odd | 10 | 693.2.m.i.631.1 | 16 | |||
11.6 | odd | 10 | 693.2.m.i.190.1 | 16 | |||
11.10 | odd | 2 | 7623.2.a.ct.1.7 | 8 | |||
21.20 | even | 2 | 5929.2.a.bs.1.7 | 8 | |||
33.2 | even | 10 | 77.2.f.b.15.4 | ✓ | 16 | ||
33.5 | odd | 10 | 847.2.f.x.729.1 | 16 | |||
33.8 | even | 10 | 847.2.f.w.372.1 | 16 | |||
33.14 | odd | 10 | 847.2.f.v.372.4 | 16 | |||
33.17 | even | 10 | 77.2.f.b.36.4 | yes | 16 | ||
33.20 | odd | 10 | 847.2.f.x.323.1 | 16 | |||
33.26 | odd | 10 | 847.2.f.v.148.4 | 16 | |||
33.29 | even | 10 | 847.2.f.w.148.1 | 16 | |||
33.32 | even | 2 | 847.2.a.p.1.2 | 8 | |||
231.2 | even | 30 | 539.2.q.g.312.4 | 32 | |||
231.17 | odd | 30 | 539.2.q.f.520.4 | 32 | |||
231.68 | odd | 30 | 539.2.q.f.312.4 | 32 | |||
231.83 | odd | 10 | 539.2.f.e.344.4 | 16 | |||
231.101 | odd | 30 | 539.2.q.f.422.1 | 32 | |||
231.116 | even | 30 | 539.2.q.g.520.4 | 32 | |||
231.149 | even | 30 | 539.2.q.g.410.1 | 32 | |||
231.167 | odd | 10 | 539.2.f.e.246.4 | 16 | |||
231.200 | even | 30 | 539.2.q.g.422.1 | 32 | |||
231.215 | odd | 30 | 539.2.q.f.410.1 | 32 | |||
231.230 | odd | 2 | 5929.2.a.bt.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.4 | ✓ | 16 | 33.2 | even | 10 | ||
77.2.f.b.36.4 | yes | 16 | 33.17 | even | 10 | ||
539.2.f.e.246.4 | 16 | 231.167 | odd | 10 | |||
539.2.f.e.344.4 | 16 | 231.83 | odd | 10 | |||
539.2.q.f.312.4 | 32 | 231.68 | odd | 30 | |||
539.2.q.f.410.1 | 32 | 231.215 | odd | 30 | |||
539.2.q.f.422.1 | 32 | 231.101 | odd | 30 | |||
539.2.q.f.520.4 | 32 | 231.17 | odd | 30 | |||
539.2.q.g.312.4 | 32 | 231.2 | even | 30 | |||
539.2.q.g.410.1 | 32 | 231.149 | even | 30 | |||
539.2.q.g.422.1 | 32 | 231.200 | even | 30 | |||
539.2.q.g.520.4 | 32 | 231.116 | even | 30 | |||
693.2.m.i.190.1 | 16 | 11.6 | odd | 10 | |||
693.2.m.i.631.1 | 16 | 11.2 | odd | 10 | |||
847.2.a.o.1.7 | 8 | 3.2 | odd | 2 | |||
847.2.a.p.1.2 | 8 | 33.32 | even | 2 | |||
847.2.f.v.148.4 | 16 | 33.26 | odd | 10 | |||
847.2.f.v.372.4 | 16 | 33.14 | odd | 10 | |||
847.2.f.w.148.1 | 16 | 33.29 | even | 10 | |||
847.2.f.w.372.1 | 16 | 33.8 | even | 10 | |||
847.2.f.x.323.1 | 16 | 33.20 | odd | 10 | |||
847.2.f.x.729.1 | 16 | 33.5 | odd | 10 | |||
5929.2.a.bs.1.7 | 8 | 21.20 | even | 2 | |||
5929.2.a.bt.1.2 | 8 | 231.230 | odd | 2 | |||
7623.2.a.ct.1.7 | 8 | 11.10 | odd | 2 | |||
7623.2.a.cw.1.2 | 8 | 1.1 | even | 1 | trivial |