Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1057,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.t (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.13 | ||
Character | \(\chi\) | \(=\) | 1380.1057 |
Dual form | 1380.2.t.a.1333.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.951596 | + | 2.02348i | −0.425567 | + | 0.904927i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.48236 | − | 3.48236i | 1.31621 | − | 1.31621i | 0.399454 | − | 0.916753i | \(-0.369200\pi\) |
0.916753 | − | 0.399454i | \(-0.130800\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.73277i | − | 0.823963i | −0.911192 | − | 0.411981i | \(-0.864837\pi\) | ||
0.911192 | − | 0.411981i | \(-0.135163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.367971 | + | 0.367971i | −0.102057 | + | 0.102057i | −0.756292 | − | 0.654235i | \(-0.772991\pi\) |
0.654235 | + | 0.756292i | \(0.272991\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.757935 | + | 2.10370i | 0.195698 | + | 0.543172i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.02066 | − | 5.02066i | 1.21769 | − | 1.21769i | 0.249251 | − | 0.968439i | \(-0.419816\pi\) |
0.968439 | − | 0.249251i | \(-0.0801843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.91117 | −1.35612 | −0.678058 | − | 0.735008i | \(-0.737178\pi\) | ||||
−0.678058 | + | 0.735008i | \(0.737178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.92480i | − | 1.07468i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82390 | + | 3.87629i | −0.588823 | + | 0.808262i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.18893 | − | 3.85107i | −0.637786 | − | 0.770214i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00084i | 0.371547i | 0.982593 | + | 0.185773i | \(0.0594790\pi\) | ||||
−0.982593 | + | 0.185773i | \(0.940521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.49808 | 0.448669 | 0.224334 | − | 0.974512i | \(-0.427979\pi\) | ||||
0.224334 | + | 0.974512i | \(0.427979\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.93236 | − | 1.93236i | −0.336381 | − | 0.336381i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.73268 | + | 10.3603i | 0.630938 | + | 1.75121i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.38531 | − | 6.38531i | 1.04974 | − | 1.04974i | 0.0510416 | − | 0.998697i | \(-0.483746\pi\) |
0.998697 | − | 0.0510416i | \(-0.0162541\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.520390i | 0.0833291i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.05805 | −0.946109 | −0.473054 | − | 0.881033i | \(-0.656849\pi\) | ||||
−0.473054 | + | 0.881033i | \(0.656849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.07971 | − | 2.07971i | −0.317153 | − | 0.317153i | 0.530520 | − | 0.847673i | \(-0.321997\pi\) |
−0.847673 | + | 0.530520i | \(0.821997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.02348 | + | 0.951596i | 0.301642 | + | 0.141856i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.01416 | + | 4.01416i | 0.585526 | + | 0.585526i | 0.936416 | − | 0.350891i | \(-0.114121\pi\) |
−0.350891 | + | 0.936416i | \(0.614121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 17.2536i | − | 2.46480i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 7.10029i | − | 0.994240i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.794878 | − | 0.794878i | −0.109185 | − | 0.109185i | 0.650404 | − | 0.759589i | \(-0.274600\pi\) |
−0.759589 | + | 0.650404i | \(0.774600\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.52971 | + | 2.60050i | 0.745626 | + | 0.350651i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.17983 | + | 4.17983i | −0.553632 | + | 0.553632i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00908i | 0.652127i | 0.945348 | + | 0.326063i | \(0.105722\pi\) | ||||
−0.945348 | + | 0.326063i | \(0.894278\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.72089i | − | 1.24463i | −0.782766 | − | 0.622316i | \(-0.786192\pi\) | ||
0.782766 | − | 0.622316i | \(-0.213808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.48236 | − | 3.48236i | −0.438736 | − | 0.438736i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.394422 | − | 1.09474i | −0.0489220 | − | 0.135786i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.09702 | − | 2.09702i | 0.256191 | − | 0.256191i | −0.567312 | − | 0.823503i | \(-0.692017\pi\) |
0.823503 | + | 0.567312i | \(0.192017\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.744154 | + | 4.73775i | 0.0895856 | + | 0.570358i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.35585 | 1.11034 | 0.555168 | − | 0.831738i | \(-0.312654\pi\) | ||||
0.555168 | + | 0.831738i | \(0.312654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.18100 | − | 8.18100i | 0.957513 | − | 0.957513i | −0.0416204 | − | 0.999133i | \(-0.513252\pi\) |
0.999133 | + | 0.0416204i | \(0.0132520\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.97803 | − | 0.468202i | −0.574813 | − | 0.0540634i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.51650 | − | 9.51650i | −1.08451 | − | 1.08451i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.90814 | −0.327192 | −0.163596 | − | 0.986527i | \(-0.552309\pi\) | ||||
−0.163596 | + | 0.986527i | \(0.552309\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.48074 | + | 7.48074i | 0.821118 | + | 0.821118i | 0.986268 | − | 0.165150i | \(-0.0528110\pi\) |
−0.165150 | + | 0.986268i | \(0.552811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.38156 | + | 14.9368i | 0.583712 | + | 1.62013i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.41481 | + | 1.41481i | 0.151683 | + | 0.151683i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.7859 | 1.24930 | 0.624650 | − | 0.780905i | \(-0.285242\pi\) | ||||
0.624650 | + | 0.780905i | \(0.285242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.56282i | 0.268656i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.76641 | − | 1.76641i | 0.183168 | − | 0.183168i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.62505 | − | 11.9611i | 0.577118 | − | 1.22719i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.793720 | − | 0.793720i | 0.0805901 | − | 0.0805901i | −0.665663 | − | 0.746253i | \(-0.731851\pi\) |
0.746253 | + | 0.665663i | \(0.231851\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.73277 | −0.274654 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.66129 | 0.264808 | 0.132404 | − | 0.991196i | \(-0.457730\pi\) | ||||
0.132404 | + | 0.991196i | \(0.457730\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.17934 | − | 3.17934i | −0.313269 | − | 0.313269i | 0.532906 | − | 0.846175i | \(-0.321100\pi\) |
−0.846175 | + | 0.532906i | \(0.821100\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.96522 | + | 4.68642i | 0.972506 | + | 0.457347i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5484 | + | 12.5484i | −1.21310 | + | 1.21310i | −0.243097 | + | 0.970002i | \(0.578163\pi\) |
−0.970002 | + | 0.243097i | \(0.921837\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.2093 | −0.977876 | −0.488938 | − | 0.872318i | \(-0.662616\pi\) | ||||
−0.488938 | + | 0.872318i | \(0.662616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.03019i | − | 0.857108i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.74744 | − | 2.74744i | −0.258458 | − | 0.258458i | 0.565969 | − | 0.824427i | \(-0.308502\pi\) |
−0.824427 | + | 0.565969i | \(0.808502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.15638 | − | 9.40275i | −0.480835 | − | 0.876811i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.367971 | + | 0.367971i | 0.0340190 | + | 0.0340190i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 34.9675i | − | 3.20546i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.53194 | 0.321086 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.28369 | + | 4.28369i | −0.386247 | + | 0.386247i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8271 | − | 2.78807i | 0.968408 | − | 0.249373i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1908 | + | 11.1908i | 0.993026 | + | 0.993026i | 0.999976 | − | 0.00695004i | \(-0.00221228\pi\) |
−0.00695004 | + | 0.999976i | \(0.502212\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.94116 | −0.258954 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2761 | −1.24731 | −0.623656 | − | 0.781699i | \(-0.714353\pi\) | ||||
−0.623656 | + | 0.781699i | \(0.714353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.5848 | + | 20.5848i | −1.78493 | + | 1.78493i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.10370 | − | 0.757935i | 0.181057 | − | 0.0652327i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.74076 | − | 3.74076i | 0.319594 | − | 0.319594i | −0.529017 | − | 0.848611i | \(-0.677439\pi\) |
0.848611 | + | 0.529017i | \(0.177439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.82831i | − | 0.324713i | −0.986732 | − | 0.162356i | \(-0.948091\pi\) | ||
0.986732 | − | 0.162356i | \(-0.0519094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.67688 | 0.478080 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00558 | + | 1.00558i | 0.0840911 | + | 0.0840911i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.04866 | − | 1.90399i | −0.336223 | − | 0.158118i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.2002 | − | 12.2002i | −1.00625 | − | 1.00625i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.3447 | 1.66670 | 0.833351 | − | 0.552744i | \(-0.186419\pi\) | ||||
0.833351 | + | 0.552744i | \(0.186419\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.5132 | −1.42521 | −0.712604 | − | 0.701567i | \(-0.752484\pi\) | ||||
−0.712604 | + | 0.701567i | \(0.752484\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.02066 | − | 5.02066i | −0.405897 | − | 0.405897i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.37716 | + | 5.05481i | −0.190938 | + | 0.406012i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.633264 | + | 0.633264i | −0.0505400 | + | 0.0505400i | −0.731925 | − | 0.681385i | \(-0.761378\pi\) |
0.681385 | + | 0.731925i | \(0.261378\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.12413 | −0.0891491 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.66481 | + | 23.3324i | 0.288827 | + | 1.83885i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.58716 | + | 9.58716i | −0.750925 | + | 0.750925i | −0.974652 | − | 0.223727i | \(-0.928178\pi\) |
0.223727 | + | 0.974652i | \(0.428178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.74893 | − | 2.07127i | 0.447553 | − | 0.161248i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.73651 | − | 9.73651i | −0.753434 | − | 0.753434i | 0.221685 | − | 0.975118i | \(-0.428844\pi\) |
−0.975118 | + | 0.221685i | \(0.928844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7292i | 0.979169i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.91117i | 0.452039i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.66666 | + | 7.66666i | −0.582885 | + | 0.582885i | −0.935695 | − | 0.352810i | \(-0.885226\pi\) |
0.352810 | + | 0.935695i | \(0.385226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.5158 | − | 2.30580i | −1.85322 | − | 0.174302i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.54195 | + | 3.54195i | 0.266230 | + | 0.266230i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.25360i | 0.317929i | 0.987284 | + | 0.158964i | \(0.0508155\pi\) | ||||
−0.987284 | + | 0.158964i | \(0.949185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9651i | 1.11235i | 0.831065 | + | 0.556175i | \(0.187731\pi\) | ||||
−0.831065 | + | 0.556175i | \(0.812269\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.87371 | − | 6.87371i | −0.508119 | − | 0.508119i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.84430 | + | 18.9968i | 0.503203 | + | 1.39667i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7203 | − | 13.7203i | −1.00333 | − | 1.00333i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.92480 | −0.358226 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.68877i | − | 0.194552i | −0.995257 | − | 0.0972762i | \(-0.968987\pi\) | ||
0.995257 | − | 0.0972762i | \(-0.0310130\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.19205 | + | 2.19205i | −0.157787 | + | 0.157787i | −0.781585 | − | 0.623798i | \(-0.785589\pi\) |
0.623798 | + | 0.781585i | \(0.285589\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.05300 | − | 0.495201i | −0.0754068 | − | 0.0354621i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.29614 | + | 9.29614i | 0.662323 | + | 0.662323i | 0.955927 | − | 0.293604i | \(-0.0948548\pi\) |
−0.293604 | + | 0.955927i | \(0.594855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.6926 | 1.89219 | 0.946096 | − | 0.323887i | \(-0.104990\pi\) | ||||
0.946096 | + | 0.323887i | \(0.104990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.96563i | − | 0.209179i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.96764 | + | 6.96764i | 0.489033 | + | 0.489033i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.76482 | − | 12.2583i | 0.402632 | − | 0.856160i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.87629 | + | 2.82390i | 0.269421 | + | 0.196274i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.1539i | 1.11739i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7587 | 1.56677 | 0.783386 | − | 0.621536i | \(-0.213491\pi\) | ||||
0.783386 | + | 0.621536i | \(0.213491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.61559 | − | 6.61559i | 0.453293 | − | 0.453293i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.18730 | − | 2.22921i | 0.421970 | − | 0.152031i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.69921 | − | 8.69921i | 0.590541 | − | 0.590541i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 11.5697i | − | 0.781806i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.69492i | 0.248547i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5272 | + | 12.5272i | −0.838881 | + | 0.838881i | −0.988712 | − | 0.149831i | \(-0.952127\pi\) |
0.149831 | + | 0.988712i | \(0.452127\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.85107 | + | 3.18893i | −0.256738 | + | 0.212595i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.4018 | + | 12.4018i | −0.823138 | + | 0.823138i | −0.986557 | − | 0.163419i | \(-0.947748\pi\) |
0.163419 | + | 0.986557i | \(0.447748\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.2938 | −1.01065 | −0.505323 | − | 0.862930i | \(-0.668627\pi\) | ||||
−0.505323 | + | 0.862930i | \(0.668627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.4584 | −0.885495 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.2955 | − | 15.2955i | 1.00204 | − | 1.00204i | 0.00204482 | − | 0.999998i | \(-0.499349\pi\) |
0.999998 | − | 0.00204482i | \(-0.000650886\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9424 | + | 4.30271i | −0.779038 | + | 0.280678i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.05637 | + | 2.05637i | −0.133575 | + | 0.133575i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.28742i | 0.536068i | 0.963409 | + | 0.268034i | \(0.0863740\pi\) | ||||
−0.963409 | + | 0.268034i | \(0.913626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.97259i | 0.642391i | 0.947013 | + | 0.321196i | \(0.104085\pi\) | ||||
−0.947013 | + | 0.321196i | \(0.895915\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 34.9123 | + | 16.4185i | 2.23047 | + | 1.04894i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.17514 | − | 2.17514i | 0.138401 | − | 0.138401i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.5794 | 0.670440 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.73360i | 0.235663i | 0.993034 | + | 0.117831i | \(0.0375943\pi\) | ||||
−0.993034 | + | 0.117831i | \(0.962406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5930 | + | 7.71707i | 0.665978 | + | 0.485168i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.3673 | + | 6.75661i | 0.899714 | + | 0.423115i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.9838 | − | 17.9838i | −1.12180 | − | 1.12180i | −0.991471 | − | 0.130325i | \(-0.958398\pi\) |
−0.130325 | − | 0.991471i | \(-0.541602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 44.4718i | − | 2.76335i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00084 | 0.123849 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.76385 | + | 9.76385i | 0.602065 | + | 0.602065i | 0.940860 | − | 0.338795i | \(-0.110019\pi\) |
−0.338795 | + | 0.940860i | \(0.610019\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.36482 | − | 0.852016i | 0.145270 | − | 0.0523389i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.33387 | − | 8.33387i | 0.510025 | − | 0.510025i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.86177i | 0.601283i | 0.953737 | + | 0.300641i | \(0.0972007\pi\) | ||||
−0.953737 | + | 0.300641i | \(0.902799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.9582 | 1.88058 | 0.940289 | − | 0.340378i | \(-0.110555\pi\) | ||||
0.940289 | + | 0.340378i | \(0.110555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.81218 | + | 1.81218i | 0.109678 | + | 0.109678i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.5241 | + | 8.71463i | −0.634627 | + | 0.525512i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.28631 | − | 5.28631i | −0.317624 | − | 0.317624i | 0.530230 | − | 0.847854i | \(-0.322106\pi\) |
−0.847854 | + | 0.530230i | \(0.822106\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.49808i | − | 0.149556i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.12633i | 0.484776i | 0.970179 | + | 0.242388i | \(0.0779307\pi\) | ||||
−0.970179 | + | 0.242388i | \(0.922069\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.11664 | + | 1.11664i | 0.0663772 | + | 0.0663772i | 0.739516 | − | 0.673139i | \(-0.235054\pi\) |
−0.673139 | + | 0.739516i | \(0.735054\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.48029 | − | 12.4353i | −0.265389 | − | 0.736604i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.0963 | + | 21.0963i | −1.24528 | + | 1.24528i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 33.4141i | − | 1.96554i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.12249i | − | 0.0658015i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.0252 | − | 11.0252i | −0.644097 | − | 0.644097i | 0.307463 | − | 0.951560i | \(-0.400520\pi\) |
−0.951560 | + | 0.307463i | \(0.900520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1358 | − | 4.76662i | −0.590127 | − | 0.277523i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.93236 | + | 1.93236i | −0.112127 | + | 0.112127i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.387250 | − | 2.46548i | −0.0223953 | − | 0.142582i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.4846 | −0.834878 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.88182 | − | 1.88182i | 0.108108 | − | 0.108108i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.6700 | + | 9.25036i | 1.12630 | + | 0.529674i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3268 | + | 22.3268i | 1.27426 | + | 1.27426i | 0.943833 | + | 0.330424i | \(0.107192\pi\) |
0.330424 | + | 0.943833i | \(0.392808\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.49626 | −0.255783 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.95458 | 0.224244 | 0.112122 | − | 0.993694i | \(-0.464235\pi\) | ||||
0.112122 | + | 0.993694i | \(0.464235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9975 | + | 22.9975i | 1.29990 | + | 1.29990i | 0.928457 | + | 0.371439i | \(0.121136\pi\) |
0.371439 | + | 0.928457i | \(0.378864\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.3603 | − | 3.73268i | 0.583735 | − | 0.210313i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0622 | − | 13.0622i | −0.733647 | − | 0.733647i | 0.237693 | − | 0.971340i | \(-0.423609\pi\) |
−0.971340 | + | 0.237693i | \(0.923609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.46785 | 0.306141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.7461i | 0.990491i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −29.6780 | + | 29.6780i | −1.65133 | + | 1.65133i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.59052 | + | 0.243648i | 0.143696 | + | 0.0135152i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.21908 | + | 7.21908i | −0.399216 | + | 0.399216i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.9575 | 1.54135 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.29715 | 0.126263 | 0.0631314 | − | 0.998005i | \(-0.479891\pi\) | ||||
0.0631314 | + | 0.998005i | \(0.479891\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.38531 | − | 6.38531i | −0.349913 | − | 0.349913i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.24776 | + | 6.23878i | 0.122808 | + | 0.340861i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8232 | + | 23.8232i | −1.29773 | + | 1.29773i | −0.367849 | + | 0.929885i | \(0.619906\pi\) |
−0.929885 | + | 0.367849i | \(0.880094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.88547 | −0.211030 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.82669i | − | 0.369686i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −35.7068 | − | 35.7068i | −1.92798 | − | 1.92798i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.2949 | − | 3.00264i | −0.554257 | − | 0.161657i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1228 | + | 15.1228i | 0.811836 | + | 0.811836i | 0.984909 | − | 0.173073i | \(-0.0553698\pi\) |
−0.173073 | + | 0.984909i | \(0.555370\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.85339i | 0.206267i | 0.994668 | + | 0.103133i | \(0.0328869\pi\) | ||||
−0.994668 | + | 0.103133i | \(0.967113\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.520390 | 0.0277764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.0525 | + | 17.0525i | −0.907611 | + | 0.907611i | −0.996079 | − | 0.0884682i | \(-0.971803\pi\) |
0.0884682 | + | 0.996079i | \(0.471803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.90299 | + | 18.9314i | −0.472522 | + | 1.00477i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.7257 | − | 24.7257i | −1.30863 | − | 1.30863i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.39323 | 0.337422 | 0.168711 | − | 0.985666i | \(-0.446040\pi\) | ||||
0.168711 | + | 0.985666i | \(0.446040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9420 | 0.839050 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.49746 | − | 2.49746i | 0.131083 | − | 0.131083i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.76906 | + | 24.3391i | 0.458994 | + | 1.27397i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.27685 | + | 1.27685i | −0.0666508 | + | 0.0666508i | −0.739646 | − | 0.672996i | \(-0.765007\pi\) |
0.672996 | + | 0.739646i | \(0.265007\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.05805i | 0.315370i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.53610 | −0.287420 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0669 | + | 11.0669i | 0.573021 | + | 0.573021i | 0.932971 | − | 0.359951i | \(-0.117206\pi\) |
−0.359951 | + | 0.932971i | \(0.617206\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.68447 | − | 9.62740i | 0.293545 | − | 0.497157i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.736252 | − | 0.736252i | −0.0379189 | − | 0.0379189i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.2350 | 0.628467 | 0.314234 | − | 0.949346i | \(-0.398252\pi\) | ||||
0.314234 | + | 0.949346i | \(0.398252\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.8262 | 0.810802 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9126 | − | 11.9126i | −0.608708 | − | 0.608708i | 0.333901 | − | 0.942608i | \(-0.391635\pi\) |
−0.942608 | + | 0.333901i | \(0.891635\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.3123 | − | 10.2006i | 1.44293 | − | 0.519869i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.07971 | + | 2.07971i | −0.105718 | + | 0.105718i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.06586 | −0.307551 | −0.153776 | − | 0.988106i | \(-0.549143\pi\) | ||||
−0.153776 | + | 0.988106i | \(0.549143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.28371 | + | 33.6394i | 0.267209 | + | 1.70122i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.0947 | + | 10.0947i | −0.509213 | + | 0.509213i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.76738 | − | 5.88456i | 0.139242 | − | 0.296085i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.17259 | − | 5.17259i | −0.259605 | − | 0.259605i | 0.565288 | − | 0.824893i | \(-0.308765\pi\) |
−0.824893 | + | 0.565288i | \(0.808765\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 29.1113i | 1.45739i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.5270i | 1.52445i | 0.647314 | + | 0.762223i | \(0.275892\pi\) | ||||
−0.647314 | + | 0.762223i | \(0.724108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.919222 | + | 0.919222i | −0.0457897 | + | 0.0457897i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.951596 | − | 2.02348i | 0.0472852 | − | 0.100547i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.4496 | − | 17.4496i | −0.864945 | − | 0.864945i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7162i | 0.727668i | 0.931464 | + | 0.363834i | \(0.118532\pi\) | ||||
−0.931464 | + | 0.363834i | \(0.881468\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.29023i | − | 0.260948i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.4434 | + | 17.4434i | 0.858334 | + | 0.858334i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.2558 | + | 8.01847i | −1.09249 | + | 0.393611i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.70702 | − | 2.70702i | −0.132563 | − | 0.132563i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.7417 | −1.59954 | −0.799769 | − | 0.600308i | \(-0.795045\pi\) | ||||
−0.799769 | + | 0.600308i | \(0.795045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.8474i | − | 0.869828i | −0.900472 | − | 0.434914i | \(-0.856779\pi\) | ||
0.900472 | − | 0.434914i | \(-0.143221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.01416 | − | 4.01416i | 0.195175 | − | 0.195175i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35.3455 | − | 3.32437i | −1.71451 | − | 0.161256i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.8516 | − | 33.8516i | −1.63819 | − | 1.63819i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.42211 | 0.0686601 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.2783i | − | 0.591424i | −0.955277 | − | 0.295712i | \(-0.904443\pi\) | ||
0.955277 | − | 0.295712i | \(-0.0955569\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.1039 | − | 23.1039i | −1.11030 | − | 1.11030i | −0.993109 | − | 0.117192i | \(-0.962611\pi\) |
−0.117192 | − | 0.993109i | \(-0.537389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.20916 | + | 1.51651i | −0.201814 | + | 0.0727110i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.6925 | − | 22.9134i | 0.798512 | − | 1.09610i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.3865i | − | 0.782084i | −0.920373 | − | 0.391042i | \(-0.872115\pi\) | ||
0.920373 | − | 0.391042i | \(-0.127885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.2536 | −0.821601 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.9738 | + | 17.9738i | −0.853959 | + | 0.853959i | −0.990618 | − | 0.136659i | \(-0.956364\pi\) |
0.136659 | + | 0.990618i | \(0.456364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.2154 | + | 23.8485i | −0.531661 | + | 1.13053i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.3859 | − | 14.3859i | 0.680429 | − | 0.680429i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.07546i | − | 0.0979471i | −0.998800 | − | 0.0489736i | \(-0.984405\pi\) | ||
0.998800 | − | 0.0489736i | \(-0.0155950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.5553i | 0.779558i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.3837 | + | 12.3837i | −0.581838 | + | 0.581838i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.18580 | − | 2.43876i | −0.243114 | − | 0.114331i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.7693 | + | 17.7693i | −0.831215 | + | 0.831215i | −0.987683 | − | 0.156468i | \(-0.949989\pi\) |
0.156468 | + | 0.987683i | \(0.449989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.10029 | −0.331413 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.62611 | 0.401758 | 0.200879 | − | 0.979616i | \(-0.435620\pi\) | ||||
0.200879 | + | 0.979616i | \(0.435620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.70757 | + | 8.70757i | −0.404675 | + | 0.404675i | −0.879877 | − | 0.475202i | \(-0.842375\pi\) |
0.475202 | + | 0.879877i | \(0.342375\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.89338 | + | 5.25520i | 0.0878036 | + | 0.243704i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.96286 | + | 2.96286i | −0.137105 | + | 0.137105i | −0.772328 | − | 0.635224i | \(-0.780908\pi\) |
0.635224 | + | 0.772328i | \(0.280908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14.6051i | − | 0.674402i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.895570i | 0.0412657i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.68338 | + | 5.68338i | −0.261322 | + | 0.261322i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.8503 | + | 22.7643i | 0.864912 | + | 1.04450i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.794878 | + | 0.794878i | −0.0363950 | + | 0.0363950i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.4955 | −1.07354 | −0.536768 | − | 0.843730i | \(-0.680355\pi\) | ||||
−0.536768 | + | 0.843730i | \(0.680355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.69922i | 0.214266i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.0899 | + | 13.9071i | 0.868622 | + | 0.632796i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.850775 | + | 2.36138i | 0.0386317 | + | 0.107225i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5628 | + | 16.5628i | 0.750532 | + | 0.750532i | 0.974578 | − | 0.224047i | \(-0.0719269\pi\) |
−0.224047 | + | 0.974578i | \(0.571927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.5583i | 0.613127i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.39587 | 0.108124 | 0.0540620 | − | 0.998538i | \(-0.482783\pi\) | ||||
0.0540620 | + | 0.998538i | \(0.482783\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0455 | + | 10.0455i | 0.452429 | + | 0.452429i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.60050 | − | 5.52971i | 0.116884 | − | 0.248542i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.5804 | − | 32.5804i | 1.46143 | − | 1.46143i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.30108i | − | 0.103010i | −0.998673 | − | 0.0515052i | \(-0.983598\pi\) | ||
0.998673 | − | 0.0515052i | \(-0.0164019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.7695 | −0.615176 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.59225 | + | 5.59225i | 0.249346 | + | 0.249346i | 0.820702 | − | 0.571356i | \(-0.193582\pi\) |
−0.571356 | + | 0.820702i | \(0.693582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.53247 | + | 5.38506i | −0.112694 | + | 0.239632i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00090 | + | 9.00090i | 0.399744 | + | 0.399744i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.88491i | − | 0.172195i | −0.996287 | − | 0.0860977i | \(-0.972560\pi\) | ||
0.996287 | − | 0.0860977i | \(-0.0274397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 56.9783i | − | 2.52057i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.17983 | + | 4.17983i | 0.184544 | + | 0.184544i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.45876 | − | 3.40787i | 0.416803 | − | 0.150169i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.9698 | − | 10.9698i | 0.482451 | − | 0.482451i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.8423i | 0.475924i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 15.4956i | − | 0.678876i | −0.940628 | − | 0.339438i | \(-0.889763\pi\) | ||
0.940628 | − | 0.339438i | \(-0.110237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.3365 | − | 20.3365i | −0.889254 | − | 0.889254i | 0.105197 | − | 0.994451i | \(-0.466453\pi\) |
−0.994451 | + | 0.105197i | \(0.966453\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.9657 | + | 15.7048i | −0.827732 | + | 0.685415i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.5420 | − | 12.5420i | 0.546339 | − | 0.546339i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.05123 | − | 21.8925i | −0.306575 | − | 0.951846i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.00908 | 0.217376 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.22919 | − | 2.22919i | 0.0965569 | − | 0.0965569i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.4504 | − | 37.3324i | −0.581512 | − | 1.61402i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.00775 | + | 3.00775i | 0.129794 | + | 0.129794i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −47.1503 | −2.03091 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.7381 | 1.45051 | 0.725257 | − | 0.688478i | \(-0.241721\pi\) | ||||
0.725257 | + | 0.688478i | \(0.241721\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5819 | + | 10.5819i | 0.454115 | + | 0.454115i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.71515 | − | 20.6584i | 0.416152 | − | 0.884907i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.0432 | + | 31.0432i | 1.32731 | + | 1.32731i | 0.907706 | + | 0.419606i | \(0.137832\pi\) |
0.419606 | + | 0.907706i | \(0.362168\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.72089 | −0.414877 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.8273i | − | 0.503861i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.1272 | + | 10.1272i | −0.430652 | + | 0.430652i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.2724 | + | 8.59309i | 0.775620 | + | 0.364756i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.3749 | − | 16.3749i | 0.693827 | − | 0.693827i | −0.269245 | − | 0.963072i | \(-0.586774\pi\) |
0.963072 | + | 0.269245i | \(0.0867741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.53055 | 0.0647353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.4035 | −0.819216 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.8732 | + | 23.8732i | 1.00613 | + | 1.00613i | 0.999981 | + | 0.00615292i | \(0.00195855\pi\) |
0.00615292 | + | 0.999981i | \(0.498041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.17384 | − | 2.94493i | 0.343876 | − | 0.123894i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.48236 | + | 3.48236i | −0.146245 | + | 0.146245i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.7218 | −1.03639 | −0.518195 | − | 0.855262i | \(-0.673396\pi\) | ||||
−0.518195 | + | 0.855262i | \(0.673396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 18.4534i | − | 0.772249i | −0.922447 | − | 0.386124i | \(-0.873814\pi\) | ||
0.922447 | − | 0.386124i | \(-0.126186\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.90125 | − | 1.90125i | −0.0794257 | − | 0.0794257i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.9331 | − | 1.48620i | 0.998077 | − | 0.0619787i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.1580 | − | 27.1580i | −1.13060 | − | 1.13060i | −0.990077 | − | 0.140525i | \(-0.955121\pi\) |
−0.140525 | − | 0.990077i | \(-0.544879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.10002i | 0.128833i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.1012 | 2.16152 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.17222 | + | 2.17222i | −0.0899643 | + | 0.0899643i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.09474 | + | 0.394422i | −0.0452620 | + | 0.0163073i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.91964 | − | 7.91964i | −0.326878 | − | 0.326878i | 0.524520 | − | 0.851398i | \(-0.324245\pi\) |
−0.851398 | + | 0.524520i | \(0.824245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.7666 | −0.608447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.1467 | 0.540784 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.1679 | − | 21.1679i | 0.869263 | − | 0.869263i | −0.123128 | − | 0.992391i | \(-0.539292\pi\) |
0.992391 | + | 0.123128i | \(0.0392925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 70.7560 | + | 33.2749i | 2.90071 | + | 1.36414i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.8745 | − | 18.8745i | 0.772484 | − | 0.772484i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 11.8908i | − | 0.485843i | −0.970046 | − | 0.242922i | \(-0.921894\pi\) | ||
0.970046 | − | 0.242922i | \(-0.0781058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.3702 | 1.32041 | 0.660203 | − | 0.751087i | \(-0.270470\pi\) | ||||
0.660203 | + | 0.751087i | \(0.270470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.09702 | − | 2.09702i | −0.0853971 | − | 0.0853971i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.36098 | + | 7.14681i | −0.136643 | + | 0.290559i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.1596 | + | 28.1596i | 1.14296 | + | 1.14296i | 0.987906 | + | 0.155057i | \(0.0495561\pi\) |
0.155057 | + | 0.987906i | \(0.450444\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.85373 | 0.399293 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.95419 | −0.119514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4800 | + | 13.4800i | 0.544450 | + | 0.544450i | 0.924830 | − | 0.380380i | \(-0.124207\pi\) |
−0.380380 | + | 0.924830i | \(0.624207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.59161 | − | 12.7443i | −0.185152 | − | 0.513900i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.1443 | − | 14.1443i | 0.569430 | − | 0.569430i | −0.362539 | − | 0.931969i | \(-0.618090\pi\) |
0.931969 | + | 0.362539i | \(0.118090\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.83694 | 0.234607 | 0.117303 | − | 0.993096i | \(-0.462575\pi\) | ||||
0.117303 | + | 0.993096i | \(0.462575\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.73775 | − | 0.744154i | 0.190119 | − | 0.0298619i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41.0426 | − | 41.0426i | 1.64434 | − | 1.64434i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.66145 | + | 24.5616i | −0.186458 | + | 0.982463i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.4225 | + | 11.4225i | 0.456172 | + | 0.456172i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 64.1170i | − | 2.55651i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.84121i | 0.351963i | 0.984393 | + | 0.175982i | \(0.0563099\pi\) | ||||
−0.984393 | + | 0.175982i | \(0.943690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0928 | − | 16.0928i | 0.639632 | − | 0.639632i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.2936 | + | 11.9953i | −1.32121 | + | 0.476017i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.34884 | + | 6.34884i | 0.251550 | + | 0.251550i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 9.35585i | − | 0.370112i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 31.0727i | − | 1.22730i | −0.789579 | − | 0.613649i | \(-0.789701\pi\) | ||
0.789579 | − | 0.613649i | \(-0.210299\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.4613 | − | 25.4613i | −1.00410 | − | 1.00410i | −0.999992 | − | 0.00410535i | \(-0.998693\pi\) |
−0.00410535 | − | 0.999992i | \(-0.501307\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.79879 | − | 5.95137i | 0.110202 | − | 0.234335i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.6871 | − | 10.6871i | −0.420155 | − | 0.420155i | 0.465102 | − | 0.885257i | \(-0.346018\pi\) |
−0.885257 | + | 0.465102i | \(0.846018\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6887 | 0.537328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 12.3025i | − | 0.482175i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.982888 | − | 0.982888i | 0.0384634 | − | 0.0384634i | −0.687614 | − | 0.726077i | \(-0.741342\pi\) |
0.726077 | + | 0.687614i | \(0.241342\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5851 | − | 28.8874i | 0.530814 | − | 1.12873i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.18100 | − | 8.18100i | −0.319171 | − | 0.319171i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.2495 | 0.555084 | 0.277542 | − | 0.960714i | \(-0.410480\pi\) | ||||
0.277542 | + | 0.960714i | \(0.410480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 27.1286i | − | 1.05518i | −0.849499 | − | 0.527591i | \(-0.823095\pi\) | ||
0.849499 | − | 0.527591i | \(-0.176905\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.61270 | + | 2.61270i | 0.101469 | + | 0.101469i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.0645 | − | 61.2413i | −0.855625 | − | 2.37484i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.75584 | − | 5.65017i | −0.300307 | − | 0.218775i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.7161i | 0.684943i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.5650 | −1.02553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3225 | + | 10.3225i | −0.397902 | + | 0.397902i | −0.877493 | − | 0.479590i | \(-0.840785\pi\) |
0.479590 | + | 0.877493i | \(0.340785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.468202 | + | 4.97803i | −0.0180211 | + | 0.191604i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.1421 | − | 27.1421i | 1.04316 | − | 1.04316i | 0.0441292 | − | 0.999026i | \(-0.485949\pi\) |
0.999026 | − | 0.0441292i | \(-0.0140513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.52804i | − | 0.212147i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.5388i | 0.672089i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.74055 | + | 6.74055i | −0.257920 | + | 0.257920i | −0.824208 | − | 0.566288i | \(-0.808379\pi\) |
0.566288 | + | 0.824208i | \(0.308379\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00965 | + | 11.1290i | 0.153201 | + | 0.425218i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.8144 | + | 10.8144i | −0.412594 | + | 0.412594i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.584985 | 0.0222861 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.7074 | 1.32033 | 0.660166 | − | 0.751120i | \(-0.270486\pi\) | ||||
0.660166 | + | 0.751120i | \(0.270486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.51650 | + | 9.51650i | −0.361502 | + | 0.361502i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.74650 | + | 3.64300i | 0.293841 | + | 0.138187i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.4154 | + | 30.4154i | −1.15207 | + | 1.15207i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 21.6311i | − | 0.818164i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 38.3373i | − | 1.44798i | −0.689811 | − | 0.723990i | \(-0.742306\pi\) | ||
0.689811 | − | 0.723990i | \(-0.257694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.7447 | + | 37.7447i | −1.42357 | + | 1.42357i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.40210 | + | 11.4871i | −0.203455 | + | 0.432627i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.26756 | − | 9.26756i | 0.348543 | − | 0.348543i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.7671 | −0.629700 | −0.314850 | − | 0.949141i | \(-0.601954\pi\) | ||||
−0.314850 | + | 0.949141i | \(0.601954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.90814i | 0.109064i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.05432 | + | 9.68328i | −0.264186 | + | 0.362642i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.99168 | + | 1.07787i | −0.111883 | + | 0.0403099i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.86009 | + | 5.86009i | 0.218849 | + | 0.218849i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.0730i | 0.711302i | 0.934619 | + | 0.355651i | \(0.115741\pi\) | ||||
−0.934619 | + | 0.355651i | \(0.884259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.1432 | −0.824655 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.05169 | + | 7.05169i | 0.262255 | + | 0.262255i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.70537 | − | 6.38054i | 0.286170 | − | 0.236967i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.0514 | − | 33.0514i | 1.22581 | − | 1.22581i | 0.260273 | − | 0.965535i | \(-0.416187\pi\) |
0.965535 | − | 0.260273i | \(-0.0838126\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.8831 | −0.772388 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.13550 | − | 9.13550i | −0.337427 | − | 0.337427i | 0.517971 | − | 0.855398i | \(-0.326688\pi\) |
−0.855398 | + | 0.517971i | \(0.826688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.2964 | − | 13.0771i | 1.33881 | − | 0.482357i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.73067 | − | 5.73067i | −0.211092 | − | 0.211092i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8701i | 1.06200i | 0.847370 | + | 0.531002i | \(0.178184\pi\) | ||||
−0.847370 | + | 0.531002i | \(0.821816\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.07612i | − | 0.113004i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.7107 | − | 35.7107i | −1.31010 | − | 1.31010i | −0.921341 | − | 0.388756i | \(-0.872905\pi\) |
−0.388756 | − | 0.921341i | \(-0.627095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.3599 | + | 41.1671i | −0.709293 | + | 1.50824i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.48074 | − | 7.48074i | 0.273706 | − | 0.273706i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 87.3960i | 3.19338i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 18.1412i | − | 0.661982i | −0.943634 | − | 0.330991i | \(-0.892617\pi\) | ||
0.943634 | − | 0.330991i | \(-0.107383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.64006 | + | 2.64006i | 0.0962090 | + | 0.0962090i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6655 | − | 35.4377i | 0.606521 | − | 1.28971i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.5361 | + | 18.5361i | −0.673707 | + | 0.673707i | −0.958569 | − | 0.284861i | \(-0.908052\pi\) |
0.284861 | + | 0.958569i | \(0.408052\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.9472 | − | 2.03361i | 0.469953 | − | 0.0738152i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.5294 | −1.61419 | −0.807094 | − | 0.590422i | \(-0.798961\pi\) | ||||
−0.807094 | + | 0.590422i | \(0.798961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.5525 | + | 35.5525i | −1.28709 | + | 1.28709i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.9368 | − | 5.38156i | 0.540043 | − | 0.194571i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.84320 | − | 1.84320i | −0.0665540 | − | 0.0665540i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4202 | 0.808494 | 0.404247 | − | 0.914650i | \(-0.367534\pi\) | ||||
0.404247 | + | 0.914650i | \(0.367534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.4329 | −0.915943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.2172 | + | 36.2172i | 1.30264 | + | 1.30264i | 0.926603 | + | 0.376040i | \(0.122715\pi\) |
0.376040 | + | 0.926603i | \(0.377285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.96621 | − | 9.62028i | −0.286155 | − | 0.345571i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.4463 | − | 31.4463i | −1.12813 | − | 1.12813i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.8102 | 1.28303 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 25.5674i | − | 0.914875i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.41481 | − | 1.41481i | 0.0505611 | − | 0.0505611i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.678784 | − | 1.88401i | −0.0242269 | − | 0.0672431i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.9021 | + | 35.9021i | −1.27977 | + | 1.27977i | −0.338979 | + | 0.940794i | \(0.610082\pi\) |
−0.940794 | + | 0.338979i | \(0.889918\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.8082 | 0.491584 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.1351 | −0.680367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.57701 | + | 3.57701i | 0.127023 | + | 0.127023i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.06971 | − | 2.27465i | 0.0379389 | − | 0.0806734i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.4445 | + | 20.4445i | −0.724181 | + | 0.724181i | −0.969454 | − | 0.245273i | \(-0.921122\pi\) |
0.245273 | + | 0.969454i | \(0.421122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.3075 | 1.42598 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 11.7859i | − | 0.416433i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.3568 | − | 22.3568i | −0.788955 | − | 0.788955i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.7001 | − | 14.7874i | −1.78694 | − | 0.521187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.97332 | + | 6.97332i | 0.245473 | + | 0.245473i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.7899i | 1.60989i | 0.593352 | + | 0.804943i | \(0.297804\pi\) | ||||
−0.593352 | + | 0.804943i | \(0.702196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.9944 | −1.43951 | −0.719755 | − | 0.694228i | \(-0.755746\pi\) | ||||
−0.719755 | + | 0.694228i | \(0.755746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.8908 | − | 21.8908i | 0.767742 | − | 0.767742i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.2763 | − | 28.5225i | −0.359964 | − | 0.999101i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.2935 | + | 12.2935i | 0.430096 | + | 0.430096i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.56282 | 0.0895520 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.5043 | 1.34381 | 0.671905 | − | 0.740637i | \(-0.265476\pi\) | ||||
0.671905 | + | 0.740637i | \(0.265476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6433 | − | 14.6433i | 0.510433 | − | 0.510433i | −0.404226 | − | 0.914659i | \(-0.632459\pi\) |
0.914659 | + | 0.404226i | \(0.132459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.27949 | + | 13.6038i | −0.0445462 | + | 0.473625i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.37209 | + | 9.37209i | −0.325900 | + | 0.325900i | −0.851025 | − | 0.525125i | \(-0.824018\pi\) |
0.525125 | + | 0.851025i | \(0.324018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 32.6312i | − | 1.13333i | −0.823949 | − | 0.566664i | \(-0.808234\pi\) | ||
0.823949 | − | 0.566664i | \(-0.191766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.47597 | −0.259339 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −86.6246 | − | 86.6246i | −3.00137 | − | 3.00137i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.9668 | − | 10.4364i | 1.00244 | − | 0.361166i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.76641 | − | 1.76641i | −0.0610561 | − | 0.0610561i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.2817 | −0.838298 | −0.419149 | − | 0.907918i | \(-0.637671\pi\) | ||||
−0.419149 | + | 0.907918i | \(0.637671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.9966 | 0.861953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.74618 | + | 5.74618i | 0.197909 | + | 0.197909i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.7572 | − | 12.1131i | −0.886076 | − | 0.416702i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2995 | − | 12.2995i | 0.422615 | − | 0.422615i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.57916 | 0.0541968 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.71985 | + | 42.7827i | 0.230354 | + | 1.46657i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.7179 | − | 39.7179i | 1.35992 | − | 1.35992i | 0.485903 | − | 0.874013i | \(-0.338491\pi\) |
0.874013 | − | 0.485903i | \(-0.161509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.9611 | − | 5.62505i | −0.409062 | − | 0.192373i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.7395 | + | 22.7395i | 0.776767 | + | 0.776767i | 0.979280 | − | 0.202512i | \(-0.0649106\pi\) |
−0.202512 | + | 0.979280i | \(0.564911\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 49.0394i | − | 1.67320i | −0.547813 | − | 0.836601i | \(-0.684540\pi\) | ||
0.547813 | − | 0.836601i | \(-0.315460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.8347i | 1.01676i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.6158 | + | 19.6158i | −0.667730 | + | 0.667730i | −0.957190 | − | 0.289460i | \(-0.906524\pi\) |
0.289460 | + | 0.957190i | \(0.406524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.21775 | − | 22.8089i | −0.279412 | − | 0.775525i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.6274 | − | 23.6274i | −0.802427 | − | 0.802427i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.94730i | 0.269594i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.54328i | 0.0522922i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.793720 | − | 0.793720i | −0.0268634 | − | 0.0268634i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.9949 | − | 47.4130i | 0.946399 | − | 1.60285i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.7427 | + | 29.7427i | 1.00434 | + | 1.00434i | 0.999991 | + | 0.00434836i | \(0.00138413\pi\) |
0.00434836 | + | 0.999991i | \(0.498616\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.5919 | −0.525903 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.36193i | 0.214339i | 0.994241 | + | 0.107169i | \(0.0341787\pi\) | ||||
−0.994241 | + | 0.107169i | \(0.965821\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.69497 | − | 4.69497i | 0.157998 | − | 0.157998i | −0.623681 | − | 0.781679i | \(-0.714363\pi\) |
0.781679 | + | 0.623681i | \(0.214363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.5376 | + | 3.79656i | −0.354217 | + | 0.127620i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.0726 | + | 31.0726i | 1.04331 | + | 1.04331i | 0.999018 | + | 0.0442963i | \(0.0141046\pi\) |
0.0442963 | + | 0.999018i | \(0.485895\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 77.9409 | 2.61406 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.73277i | 0.0915514i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.7284 | − | 23.7284i | −0.794041 | − | 0.794041i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.60706 | − | 4.04770i | −0.287702 | − | 0.135300i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.01718 | − | 1.46953i | −0.0673517 | − | 0.0490661i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.99826i | 0.166701i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.98163 | −0.265907 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.2422 | + | 10.2422i | −0.340838 | + | 0.340838i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.2816 | − | 14.2408i | −1.00660 | − | 0.473379i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.22151 | − | 6.22151i | 0.206582 | − | 0.206582i | −0.596231 | − | 0.802813i | \(-0.703336\pi\) |
0.802813 | + | 0.596231i | \(0.203336\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.66129i | − | 0.0882694i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.14528i | 0.203602i | 0.994805 | + | 0.101801i | \(0.0324605\pi\) | ||||
−0.994805 | + | 0.101801i | \(0.967539\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.4432 | − | 20.4432i | 0.676570 | − | 0.676570i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.4498 | − | 7.36780i | 0.676049 | − | 0.243572i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.7146 | + | 49.7146i | −1.64172 | + | 1.64172i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.86802 | 0.292529 | 0.146265 | − | 0.989246i | \(-0.453275\pi\) | ||||
0.146265 | + | 0.989246i | \(0.453275\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.5748 | 1.04043 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.44269 | + | 3.44269i | −0.113317 | + | 0.113317i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.9526 | − | 4.22796i | −1.47803 | − | 0.139014i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.17934 | + | 3.17934i | −0.104423 | + | 0.104423i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.3528i | 1.25831i | 0.777278 | + | 0.629157i | \(0.216600\pi\) | ||||
−0.777278 | + | 0.629157i | \(0.783400\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 101.989i | 3.34256i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.79631 | − | 2.79631i | 0.0915470 | − | 0.0915470i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.8190 | − | 14.7066i | 1.33493 | − | 0.480957i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.6795 | − | 15.6795i | 0.512226 | − | 0.512226i | −0.402982 | − | 0.915208i | \(-0.632026\pi\) |
0.915208 | + | 0.402982i | \(0.132026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.5234 | 1.06136 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 47.2322i | − | 1.53973i | −0.638209 | − | 0.769863i | \(-0.720324\pi\) | ||
0.638209 | − | 0.769863i | \(-0.279676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.1073 | − | 23.4828i | 0.557091 | − | 0.764704i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.68642 | − | 9.96522i | 0.152449 | − | 0.324169i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.60447 | + | 7.60447i | 0.247112 | + | 0.247112i | 0.819784 | − | 0.572672i | \(-0.194093\pi\) |
−0.572672 | + | 0.819784i | \(0.694093\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.02074i | 0.195442i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.4728 | −0.599020 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.6487 | + | 27.6487i | 0.895628 | + | 0.895628i | 0.995046 | − | 0.0994175i | \(-0.0316979\pi\) |
−0.0994175 | + | 0.995046i | \(0.531698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.44066 | + | 2.55862i | 0.176056 | + | 0.0827950i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.86635 | − | 3.86635i | 0.124981 | − | 0.124981i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 26.0533i | − | 0.841305i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7596 | −0.798696 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.5484 | + | 12.5484i | 0.404366 | + | 0.404366i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.34962 | − | 6.52151i | −0.0756369 | − | 0.209935i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.16686 | − | 9.16686i | −0.294786 | − | 0.294786i | 0.544181 | − | 0.838968i | \(-0.316840\pi\) |
−0.838968 | + | 0.544181i | \(0.816840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.9710i | 1.34830i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3130i | 0.459327i | 0.973270 | + | 0.229663i | \(0.0737626\pi\) | ||||
−0.973270 | + | 0.229663i | \(0.926237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.3315 | − | 13.3315i | −0.427389 | − | 0.427389i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00406 | − | 1.65949i | 0.0641812 | − | 0.0531461i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.39164 | − | 3.39164i | 0.108508 | − | 0.108508i | −0.650768 | − | 0.759276i | \(-0.725553\pi\) |
0.759276 | + | 0.650768i | \(0.225553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 32.2081i | − | 1.02938i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.2093i | 0.325959i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.3572 | − | 28.3572i | −0.904454 | − | 0.904454i | 0.0913638 | − | 0.995818i | \(-0.470877\pi\) |
−0.995818 | + | 0.0913638i | \(0.970877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.6567 | + | 9.96437i | −0.881216 | + | 0.317491i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.7689 | − | 19.7689i | 0.629252 | − | 0.629252i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.9345 | − | 2.18867i | 0.443090 | − | 0.0695958i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.98666 | −0.190172 | −0.0950862 | − | 0.995469i | \(-0.530313\pi\) | ||||
−0.0950862 | + | 0.995469i | \(0.530313\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.62433 | − | 1.62433i | 0.0515466 | − | 0.0515466i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.4006 | + | 54.0120i | −0.805254 | + | 1.71230i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.598100 | + | 0.598100i | 0.0189420 | + | 0.0189420i | 0.716514 | − | 0.697572i | \(-0.245736\pi\) |
−0.697572 | + | 0.716514i | \(0.745736\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.03019 | −0.285703 |
(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 | 1380.2.t.a.1057.13 | ✓ | 48 | |
5.3 | odd | 4 | inner | 1380.2.t.a.1333.14 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.t.a.1057.14 | yes | 48 | |
115.68 | even | 4 | inner | 1380.2.t.a.1333.13 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.t.a.1057.13 | ✓ | 48 | 1.1 | even | 1 | trivial | |
1380.2.t.a.1057.14 | yes | 48 | 23.22 | odd | 2 | inner | |
1380.2.t.a.1333.13 | yes | 48 | 115.68 | even | 4 | inner | |
1380.2.t.a.1333.14 | yes | 48 | 5.3 | odd | 4 | inner |