Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(961,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1537.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1537 |
Dual form | 2352.2.q.be.961.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.292893 | − | 0.507306i | −0.130986 | − | 0.226874i | 0.793071 | − | 0.609129i | \(-0.208481\pi\) |
−0.924057 | + | 0.382255i | \(0.875148\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.414214 | + | 0.717439i | −0.124890 | + | 0.216316i | −0.921690 | − | 0.387927i | \(-0.873191\pi\) |
0.796800 | + | 0.604243i | \(0.206524\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.12132 | + | 1.94218i | −0.271960 | + | 0.471049i | −0.969364 | − | 0.245630i | \(-0.921005\pi\) |
0.697404 | + | 0.716679i | \(0.254339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.41421 | + | 5.91359i | 0.783274 | + | 1.35667i | 0.930025 | + | 0.367497i | \(0.119785\pi\) |
−0.146750 | + | 0.989174i | \(0.546881\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.41421 | + | 4.18154i | 0.503398 | + | 0.871911i | 0.999992 | + | 0.00392850i | \(0.00125049\pi\) |
−0.496594 | + | 0.867983i | \(0.665416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.32843 | − | 4.03295i | 0.465685 | − | 0.806591i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528 | 1.57568 | 0.787839 | − | 0.615882i | \(-0.211200\pi\) | ||||
0.787839 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.58579 | − | 4.47871i | 0.464421 | − | 0.804401i | −0.534754 | − | 0.845008i | \(-0.679596\pi\) |
0.999175 | + | 0.0406069i | \(0.0129291\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.414214 | + | 0.717439i | 0.0721053 | + | 0.124890i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.828427 | − | 1.43488i | −0.136193 | − | 0.235892i | 0.789860 | − | 0.613287i | \(-0.210153\pi\) |
−0.926052 | + | 0.377395i | \(0.876820\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.707107 | + | 1.22474i | −0.113228 | + | 0.196116i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.585786 | −0.0914845 | −0.0457422 | − | 0.998953i | \(-0.514565\pi\) | ||||
−0.0457422 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.292893 | + | 0.507306i | −0.0436619 | + | 0.0756247i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.41421 | + | 5.91359i | 0.498014 | + | 0.862586i | 0.999997 | − | 0.00229145i | \(-0.000729392\pi\) |
−0.501983 | + | 0.864877i | \(0.667396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.12132 | + | 1.94218i | 0.157016 | + | 0.271960i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.65685 | − | 11.5300i | 0.914389 | − | 1.58377i | 0.106596 | − | 0.994302i | \(-0.466005\pi\) |
0.807793 | − | 0.589466i | \(-0.200662\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.485281 | 0.0654353 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.82843 | 0.904447 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.58579 | − | 4.47871i | 0.336641 | − | 0.583079i | −0.647158 | − | 0.762356i | \(-0.724043\pi\) |
0.983799 | + | 0.179277i | \(0.0573759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.94975 | − | 12.0373i | −0.889824 | − | 1.54122i | −0.840083 | − | 0.542458i | \(-0.817494\pi\) |
−0.0497412 | − | 0.998762i | \(-0.515840\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.414214 | + | 0.717439i | 0.0513769 | + | 0.0889873i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.82843 | 0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.828427 | 0.0983162 | 0.0491581 | − | 0.998791i | \(-0.484346\pi\) | ||||
0.0491581 | + | 0.998791i | \(0.484346\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.53553 | − | 9.58783i | 0.647885 | − | 1.12217i | −0.335742 | − | 0.941954i | \(-0.608987\pi\) |
0.983627 | − | 0.180216i | \(-0.0576797\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.32843 | − | 4.03295i | −0.268864 | − | 0.465685i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.17157 | − | 2.02922i | −0.131812 | − | 0.228306i | 0.792563 | − | 0.609790i | \(-0.208746\pi\) |
−0.924375 | + | 0.381485i | \(0.875413\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.3137 | −1.68090 | −0.840449 | − | 0.541891i | \(-0.817709\pi\) | ||||
−0.840449 | + | 0.541891i | \(0.817709\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.31371 | 0.142492 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.24264 | − | 7.34847i | 0.454859 | − | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.36396 | + | 9.29065i | 0.568579 | + | 0.984807i | 0.996707 | + | 0.0810892i | \(0.0258399\pi\) |
−0.428128 | + | 0.903718i | \(0.640827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.58579 | − | 4.47871i | −0.268134 | − | 0.464421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | − | 3.46410i | 0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.75736 | −0.787641 | −0.393820 | − | 0.919187i | \(-0.628847\pi\) | ||||
−0.393820 | + | 0.919187i | \(0.628847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.828427 | 0.0832601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.70711 | + | 2.95680i | −0.169863 | + | 0.294212i | −0.938372 | − | 0.345628i | \(-0.887666\pi\) |
0.768508 | + | 0.639840i | \(0.220999\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.41421 | + | 9.37769i | 0.533478 | + | 0.924012i | 0.999235 | + | 0.0390989i | \(0.0124487\pi\) |
−0.465757 | + | 0.884913i | \(0.654218\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.24264 | + | 12.5446i | 0.700173 | + | 1.21273i | 0.968406 | + | 0.249380i | \(0.0802269\pi\) |
−0.268233 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.65685 | − | 9.79796i | 0.541828 | − | 0.938474i | −0.456971 | − | 0.889482i | \(-0.651066\pi\) |
0.998799 | − | 0.0489926i | \(-0.0156011\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.65685 | −0.157262 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.41421 | − | 2.44949i | 0.131876 | − | 0.228416i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.707107 | + | 1.22474i | 0.0653720 | + | 0.113228i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.15685 | + | 8.93193i | 0.468805 | + | 0.811994i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.292893 | + | 0.507306i | −0.0264093 | + | 0.0457422i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3137 | 1.35887 | 0.679436 | − | 0.733735i | \(-0.262225\pi\) | ||||
0.679436 | + | 0.733735i | \(0.262225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | − | 6.92820i | 0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.65685 | − | 6.33386i | −0.319501 | − | 0.553392i | 0.660883 | − | 0.750489i | \(-0.270182\pi\) |
−0.980384 | + | 0.197097i | \(0.936849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.292893 | + | 0.507306i | 0.0252082 | + | 0.0436619i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.24264 | + | 3.88437i | −0.191602 | + | 0.331864i | −0.945781 | − | 0.324804i | \(-0.894702\pi\) |
0.754179 | + | 0.656668i | \(0.228035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.65685 | 0.140533 | 0.0702663 | − | 0.997528i | \(-0.477615\pi\) | ||||
0.0702663 | + | 0.997528i | \(0.477615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.82843 | 0.575057 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.585786 | − | 1.01461i | 0.0489859 | − | 0.0848461i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.48528 | − | 4.30463i | −0.206391 | − | 0.357480i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.82843 | − | 8.36308i | 0.392932 | − | 0.680578i | −0.599903 | − | 0.800073i | \(-0.704794\pi\) |
0.992835 | + | 0.119495i | \(0.0381275\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.24264 | 0.181307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.02944 | −0.243330 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.94975 | − | 12.0373i | 0.554650 | − | 0.960682i | −0.443280 | − | 0.896383i | \(-0.646185\pi\) |
0.997931 | − | 0.0642994i | \(-0.0204813\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.65685 | − | 11.5300i | −0.527923 | − | 0.914389i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.82843 | − | 11.8272i | −0.534844 | − | 0.926376i | −0.999171 | − | 0.0407127i | \(-0.987037\pi\) |
0.464327 | − | 0.885664i | \(-0.346296\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.242641 | − | 0.420266i | 0.0188896 | − | 0.0327177i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.17157 | −0.0906590 | −0.0453295 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453295 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.41421 | − | 5.91359i | 0.261091 | − | 0.452224i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.70711 | + | 2.95680i | 0.129789 | + | 0.224801i | 0.923595 | − | 0.383370i | \(-0.125237\pi\) |
−0.793806 | + | 0.608171i | \(0.791903\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.58579 | − | 4.47871i | −0.194360 | − | 0.336641i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.89949 | − | 15.4144i | 0.665179 | − | 1.15212i | −0.314057 | − | 0.949404i | \(-0.601688\pi\) |
0.979237 | − | 0.202721i | \(-0.0649783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.89949 | −0.735824 | −0.367912 | − | 0.929861i | \(-0.619927\pi\) | ||||
−0.367912 | + | 0.929861i | \(0.619927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8995 | −1.02748 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.485281 | + | 0.840532i | −0.0356786 | + | 0.0617971i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.928932 | − | 1.60896i | −0.0679302 | − | 0.117659i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.58579 | + | 13.1390i | 0.548888 | + | 0.950702i | 0.998351 | + | 0.0574033i | \(0.0182821\pi\) |
−0.449463 | + | 0.893299i | \(0.648385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3137 | + | 21.3280i | −0.886360 | + | 1.53522i | −0.0422134 | + | 0.999109i | \(0.513441\pi\) |
−0.844147 | + | 0.536112i | \(0.819892\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.828427 | 0.0593249 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.82843 | − | 4.89898i | 0.200502 | − | 0.347279i | −0.748188 | − | 0.663486i | \(-0.769076\pi\) |
0.948690 | + | 0.316207i | \(0.102409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | + | 6.92820i | 0.282138 | + | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.171573 | + | 0.297173i | 0.0119832 | + | 0.0207555i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.41421 | − | 4.18154i | 0.167799 | − | 0.290637i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3431 | 0.987423 | 0.493711 | − | 0.869626i | \(-0.335640\pi\) | ||||
0.493711 | + | 0.869626i | \(0.335640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.414214 | − | 0.717439i | 0.0283814 | − | 0.0491581i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.34315 | − | 4.05845i | −0.159801 | − | 0.276784i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.53553 | − | 9.58783i | −0.374057 | − | 0.647885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.58579 | − | 2.74666i | 0.106672 | − | 0.184761i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6569 | 0.914531 | 0.457265 | − | 0.889330i | \(-0.348829\pi\) | ||||
0.457265 | + | 0.889330i | \(0.348829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.89949 | + | 17.1464i | −0.657053 | + | 1.13805i | 0.324322 | + | 0.945947i | \(0.394864\pi\) |
−0.981375 | + | 0.192102i | \(0.938470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.53553 | − | 13.0519i | −0.497962 | − | 0.862496i | 0.502035 | − | 0.864847i | \(-0.332585\pi\) |
−0.999997 | + | 0.00235157i | \(0.999251\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.2426 | + | 24.6690i | 0.933066 | + | 1.61612i | 0.778046 | + | 0.628207i | \(0.216211\pi\) |
0.155020 | + | 0.987911i | \(0.450456\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | − | 3.46410i | 0.130466 | − | 0.225973i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.34315 | −0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.17157 | 0.205152 | 0.102576 | − | 0.994725i | \(-0.467292\pi\) | ||||
0.102576 | + | 0.994725i | \(0.467292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9497 | − | 18.9655i | 0.705335 | − | 1.22168i | −0.261235 | − | 0.965275i | \(-0.584130\pi\) |
0.966570 | − | 0.256401i | \(-0.0825369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.82843 | − | 8.36308i | −0.307225 | − | 0.532130i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.65685 | + | 13.2621i | −0.485233 | + | 0.840449i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.48528 | −0.535586 | −0.267793 | − | 0.963476i | \(-0.586294\pi\) | ||||
−0.267793 | + | 0.963476i | \(0.586294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.656854 | − | 1.13770i | 0.0411338 | − | 0.0712458i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.1213 | + | 26.1909i | 0.943242 | + | 1.63374i | 0.759233 | + | 0.650819i | \(0.225574\pi\) |
0.184009 | + | 0.982925i | \(0.441093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24264 | − | 7.34847i | −0.262613 | − | 0.454859i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4142 | − | 21.5020i | 0.765493 | − | 1.32587i | −0.174492 | − | 0.984659i | \(-0.555828\pi\) |
0.939985 | − | 0.341215i | \(-0.110838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.79899 | −0.479088 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7279 | 0.656538 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0208 | + | 26.0168i | −0.915835 | + | 1.58627i | −0.110162 | + | 0.993914i | \(0.535137\pi\) |
−0.805674 | + | 0.592360i | \(0.798197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.58579 | − | 11.4069i | −0.400058 | − | 0.692921i | 0.593674 | − | 0.804705i | \(-0.297677\pi\) |
−0.993732 | + | 0.111784i | \(0.964343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.92893 | + | 3.34101i | 0.116319 | + | 0.201470i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00000 | − | 5.19615i | 0.180253 | − | 0.312207i | −0.761714 | − | 0.647913i | \(-0.775642\pi\) |
0.941966 | + | 0.335707i | \(0.108975\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.17157 | −0.309614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4853 | −0.744809 | −0.372405 | − | 0.928070i | \(-0.621467\pi\) | ||||
−0.372405 | + | 0.928070i | \(0.621467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.41421 | + | 12.8418i | −0.440729 | + | 0.763365i | −0.997744 | − | 0.0671373i | \(-0.978613\pi\) |
0.557014 | + | 0.830503i | \(0.311947\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.00000 | − | 3.46410i | −0.118470 | − | 0.205196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.98528 | + | 10.3668i | 0.352075 | + | 0.609812i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.87868 | + | 6.71807i | −0.227372 | + | 0.393820i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.07107 | 0.0625724 | 0.0312862 | − | 0.999510i | \(-0.490040\pi\) | ||||
0.0312862 | + | 0.999510i | \(0.490040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.02944 | −0.176381 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.414214 | − | 0.717439i | 0.0240351 | − | 0.0416300i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.41421 | − | 5.91359i | −0.197449 | − | 0.341992i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.70711 | + | 2.95680i | 0.0980707 | + | 0.169863i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.07107 | + | 7.05130i | −0.233109 | + | 0.403756i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5147 | 0.657180 | 0.328590 | − | 0.944473i | \(-0.393427\pi\) | ||||
0.328590 | + | 0.944473i | \(0.393427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8284 | 0.616008 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0711 | + | 22.6398i | −0.741192 | + | 1.28378i | 0.210761 | + | 0.977538i | \(0.432406\pi\) |
−0.951953 | + | 0.306245i | \(0.900927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.70711 | + | 15.0812i | 0.492155 | + | 0.852437i | 0.999959 | − | 0.00903532i | \(-0.00287607\pi\) |
−0.507804 | + | 0.861472i | \(0.669543\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6569 | − | 18.4582i | −0.598549 | − | 1.03672i | −0.993036 | − | 0.117815i | \(-0.962411\pi\) |
0.394487 | − | 0.918902i | \(-0.370922\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.51472 | + | 6.08767i | −0.196786 | + | 0.340844i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.4853 | 0.808490 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3137 | −0.852078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.29289 | + | 5.70346i | −0.182657 | + | 0.316371i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.65685 | − | 9.79796i | −0.312825 | − | 0.541828i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.34315 | − | 7.52255i | −0.238721 | − | 0.413477i | 0.721627 | − | 0.692282i | \(-0.243395\pi\) |
−0.960348 | + | 0.278806i | \(0.910061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.828427 | + | 1.43488i | −0.0453975 | + | 0.0786308i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.68629 | 0.256039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.9706 | −0.924445 | −0.462223 | − | 0.886764i | \(-0.652948\pi\) | ||||
−0.462223 | + | 0.886764i | \(0.652948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.14214 | + | 3.71029i | 0.116003 | + | 0.200923i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.41421 | − | 2.44949i | −0.0761387 | − | 0.131876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.07107 | + | 3.58719i | −0.111181 | + | 0.192571i | −0.916247 | − | 0.400615i | \(-0.868797\pi\) |
0.805066 | + | 0.593185i | \(0.202130\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3848 | 1.62646 | 0.813230 | − | 0.581943i | \(-0.197707\pi\) | ||||
0.813230 | + | 0.581943i | \(0.197707\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41421 | 0.0754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.94975 | − | 13.7694i | 0.423122 | − | 0.732869i | −0.573121 | − | 0.819471i | \(-0.694267\pi\) |
0.996243 | + | 0.0866016i | \(0.0276007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.242641 | − | 0.420266i | −0.0128780 | − | 0.0223054i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.7279 | − | 30.7057i | −0.935644 | − | 1.62058i | −0.773482 | − | 0.633819i | \(-0.781487\pi\) |
−0.162162 | − | 0.986764i | \(-0.551847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.8137 | + | 23.9260i | −0.727037 | + | 1.25927i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.3137 | 0.541329 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.48528 | −0.339455 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.292893 | + | 0.507306i | 0.0152474 | + | 0.0264093i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.34315 | − | 12.7187i | −0.380214 | − | 0.658549i | 0.610879 | − | 0.791724i | \(-0.290816\pi\) |
−0.991093 | + | 0.133175i | \(0.957483\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.82843 | + | 4.89898i | −0.146059 | + | 0.252982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.686292 | 0.0352524 | 0.0176262 | − | 0.999845i | \(-0.494389\pi\) | ||||
0.0176262 | + | 0.999845i | \(0.494389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.65685 | − | 13.2621i | 0.392273 | − | 0.679436i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4853 | + | 21.6251i | 0.637968 | + | 1.10499i | 0.985878 | + | 0.167465i | \(0.0535582\pi\) |
−0.347910 | + | 0.937528i | \(0.613108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.07107 | − | 12.2474i | 0.358517 | − | 0.620970i | −0.629196 | − | 0.777247i | \(-0.716616\pi\) |
0.987713 | + | 0.156276i | \(0.0499491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8284 | −0.547617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.31371 | −0.368928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.686292 | + | 1.18869i | −0.0345311 | + | 0.0598096i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.63604 | − | 6.29780i | −0.182488 | − | 0.316078i | 0.760239 | − | 0.649643i | \(-0.225082\pi\) |
−0.942727 | + | 0.333565i | \(0.891748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.24264 | + | 10.8126i | 0.311743 | + | 0.539954i | 0.978740 | − | 0.205106i | \(-0.0657540\pi\) |
−0.666997 | + | 0.745060i | \(0.732421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.65685 | + | 6.33386i | −0.182161 | + | 0.315512i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.585786 | 0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.37258 | 0.0680364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.12132 | + | 14.0665i | −0.401573 | + | 0.695546i | −0.993916 | − | 0.110141i | \(-0.964870\pi\) |
0.592343 | + | 0.805686i | \(0.298203\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.24264 | + | 3.88437i | 0.110621 | + | 0.191602i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.48528 | + | 7.76874i | 0.220174 | + | 0.381352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.828427 | − | 1.43488i | 0.0405683 | − | 0.0702663i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.8284 | −0.529003 | −0.264502 | − | 0.964385i | \(-0.585207\pi\) | ||||
−0.264502 | + | 0.964385i | \(0.585207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.68629 | 0.325870 | 0.162935 | − | 0.986637i | \(-0.447904\pi\) | ||||
0.162935 | + | 0.986637i | \(0.447904\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.41421 | − | 5.91359i | 0.166005 | − | 0.287529i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.22183 | + | 9.04447i | 0.253296 | + | 0.438721i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.585786 | − | 1.01461i | −0.0282820 | − | 0.0489859i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.2426 | + | 26.4010i | −0.734212 | + | 1.27169i | 0.220856 | + | 0.975306i | \(0.429115\pi\) |
−0.955068 | + | 0.296386i | \(0.904218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3848 | 1.26797 | 0.633986 | − | 0.773345i | \(-0.281418\pi\) | ||||
0.633986 | + | 0.773345i | \(0.281418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.97056 | −0.238320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.4853 | + | 28.5533i | −0.788598 | + | 1.36589i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.65685 | − | 2.86976i | −0.0790773 | − | 0.136966i | 0.823775 | − | 0.566917i | \(-0.191864\pi\) |
−0.902852 | + | 0.429951i | \(0.858531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.2426 | + | 33.3292i | 0.914245 | + | 1.58352i | 0.808002 | + | 0.589179i | \(0.200549\pi\) |
0.106243 | + | 0.994340i | \(0.466118\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.14214 | − | 5.44234i | 0.148952 | − | 0.257992i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.242641 | − | 0.420266i | 0.0114255 | − | 0.0197896i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.82843 | − | 8.36308i | −0.226859 | − | 0.392932i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3137 | − | 17.8639i | −0.482455 | − | 0.835636i | 0.517342 | − | 0.855779i | \(-0.326921\pi\) |
−0.999797 | + | 0.0201422i | \(0.993588\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.12132 | − | 1.94218i | 0.0523388 | − | 0.0906534i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.2426 | 0.849644 | 0.424822 | − | 0.905277i | \(-0.360337\pi\) | ||||
0.424822 | + | 0.905277i | \(0.360337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9706 | −0.974585 | −0.487292 | − | 0.873239i | \(-0.662015\pi\) | ||||
−0.487292 | + | 0.873239i | \(0.662015\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.51472 | + | 2.62357i | −0.0702434 | + | 0.121665i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.41421 | − | 9.37769i | −0.250540 | − | 0.433948i | 0.713135 | − | 0.701027i | \(-0.247275\pi\) |
−0.963675 | + | 0.267079i | \(0.913941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.94975 | − | 12.0373i | −0.320227 | − | 0.554650i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.31371 | + | 5.73951i | −0.152364 | + | 0.263903i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.7990 | 1.45904 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.3137 | −0.609593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.5563 | + | 37.3367i | −0.984935 | + | 1.70596i | −0.342709 | + | 0.939442i | \(0.611344\pi\) |
−0.642226 | + | 0.766515i | \(0.721989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.17157 | + | 2.02922i | 0.0534191 | + | 0.0925246i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.27208 | + | 3.93535i | 0.103170 | + | 0.178695i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4853 | + | 18.1610i | −0.475133 | + | 0.822955i | −0.999594 | − | 0.0284792i | \(-0.990934\pi\) |
0.524461 | + | 0.851435i | \(0.324267\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.6569 | −0.617584 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.1421 | −1.08952 | −0.544760 | − | 0.838592i | \(-0.683379\pi\) | ||||
−0.544760 | + | 0.838592i | \(0.683379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.51472 | + | 16.4800i | −0.428521 | + | 0.742221i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.242641 | − | 0.420266i | −0.0109059 | − | 0.0188896i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.1421 | − | 24.4949i | −0.633089 | − | 1.09654i | −0.986917 | − | 0.161232i | \(-0.948453\pi\) |
0.353828 | − | 0.935311i | \(-0.384880\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.585786 | + | 1.01461i | −0.0261710 | + | 0.0453295i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6274 | 0.652204 | 0.326102 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326102 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.50000 | + | 9.52628i | −0.244264 | + | 0.423077i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5355 | − | 32.1045i | −0.821573 | − | 1.42301i | −0.904510 | − | 0.426452i | \(-0.859763\pi\) |
0.0829373 | − | 0.996555i | \(-0.473570\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.41421 | − | 5.91359i | −0.150741 | − | 0.261091i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.17157 | − | 5.49333i | 0.139756 | − | 0.242065i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.41421 | 0.149867 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3640 | + | 26.6112i | −0.673107 | + | 1.16586i | 0.303911 | + | 0.952700i | \(0.401707\pi\) |
−0.977018 | + | 0.213156i | \(0.931626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.82843 | + | 8.36308i | 0.211132 | + | 0.365692i | 0.952069 | − | 0.305883i | \(-0.0989516\pi\) |
−0.740937 | + | 0.671575i | \(0.765618\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.79899 | + | 10.0441i | 0.252608 | + | 0.437530i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.156854 | + | 0.271680i | −0.00681975 | + | 0.0118122i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.17157 | −0.224427 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.828427 | 0.0358832 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.24264 | − | 7.34847i | 0.183425 | − | 0.317702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.89949 | − | 15.4144i | −0.384042 | − | 0.665179i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.3137 | − | 31.7203i | −0.787368 | − | 1.36376i | −0.927574 | − | 0.373639i | \(-0.878110\pi\) |
0.140206 | − | 0.990122i | \(-0.455223\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.94975 | + | 8.57321i | −0.212414 | + | 0.367912i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.62742 | −0.283887 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9706 | −1.23869 | −0.619346 | − | 0.785118i | \(-0.712602\pi\) | ||||
−0.619346 | + | 0.785118i | \(0.712602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.94975 | + | 12.0373i | −0.296608 | + | 0.513740i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.9706 | + | 50.1785i | 1.23419 | + | 2.13768i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.485281 | + | 0.840532i | 0.0205990 | + | 0.0356786i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.9706 | − | 20.7336i | 0.507209 | − | 0.878512i | −0.492756 | − | 0.870167i | \(-0.664011\pi\) |
0.999965 | − | 0.00834436i | \(-0.00265612\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.3137 | −0.478519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.85786 | −0.0784391 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5858 | − | 18.3351i | 0.446138 | − | 0.772733i | −0.551993 | − | 0.833849i | \(-0.686132\pi\) |
0.998131 | + | 0.0611156i | \(0.0194658\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.75736 | − | 3.04384i | −0.0739327 | − | 0.128055i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.585786 | − | 1.01461i | −0.0245574 | − | 0.0425347i | 0.853486 | − | 0.521117i | \(-0.174484\pi\) |
−0.878043 | + | 0.478582i | \(0.841151\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.14214 | + | 14.1026i | −0.340738 | + | 0.590175i | −0.984570 | − | 0.174992i | \(-0.944010\pi\) |
0.643832 | + | 0.765167i | \(0.277343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.1716 | 0.633802 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.4853 | 0.937701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.29289 | − | 5.70346i | 0.137085 | − | 0.237438i | −0.789307 | − | 0.613999i | \(-0.789560\pi\) |
0.926392 | + | 0.376561i | \(0.122893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.3137 | + | 21.3280i | 0.511740 | + | 0.886360i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.51472 | + | 9.55177i | 0.228396 | + | 0.395594i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.414214 | − | 0.717439i | 0.0171256 | − | 0.0296624i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1716 | 0.873844 | 0.436922 | − | 0.899499i | \(-0.356069\pi\) | ||||
0.436922 | + | 0.899499i | \(0.356069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.3137 | 1.45508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.00000 | − | 1.73205i | 0.0411345 | − | 0.0712470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.46447 | − | 12.9288i | −0.306529 | − | 0.530924i | 0.671072 | − | 0.741392i | \(-0.265834\pi\) |
−0.977601 | + | 0.210469i | \(0.932501\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.82843 | − | 4.89898i | −0.115760 | − | 0.200502i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.07107 | + | 10.5154i | −0.248057 | + | 0.429648i | −0.962987 | − | 0.269549i | \(-0.913125\pi\) |
0.714930 | + | 0.699196i | \(0.246459\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.75736 | −0.153266 | −0.0766329 | − | 0.997059i | \(-0.524417\pi\) | ||||
−0.0766329 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.02082 | − | 5.23221i | 0.122814 | − | 0.212719i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.7990 | − | 41.2211i | −0.965971 | − | 1.67311i | −0.706983 | − | 0.707231i | \(-0.749944\pi\) |
−0.258988 | − | 0.965880i | \(-0.583389\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.82843 | − | 8.36308i | −0.195337 | − | 0.338334i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.82843 | − | 11.8272i | 0.275798 | − | 0.477695i | −0.694538 | − | 0.719456i | \(-0.744391\pi\) |
0.970336 | + | 0.241760i | \(0.0777247\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.343146 | 0.0138370 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.4558 | −1.18585 | −0.592924 | − | 0.805259i | \(-0.702026\pi\) | ||||
−0.592924 | + | 0.805259i | \(0.702026\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.14214 | − | 14.1026i | 0.327260 | − | 0.566831i | −0.654707 | − | 0.755883i | \(-0.727208\pi\) |
0.981967 | + | 0.189052i | \(0.0605414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.41421 | − | 4.18154i | −0.0968791 | − | 0.167799i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.98528 | − | 17.2950i | −0.399411 | − | 0.691801i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.82843 | + | 4.89898i | −0.112956 | + | 0.195646i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.71573 | 0.148156 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.2843 | −1.92217 | −0.961083 | − | 0.276259i | \(-0.910905\pi\) | ||||
−0.961083 | + | 0.276259i | \(0.910905\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.17157 | − | 12.4215i | 0.285044 | − | 0.493711i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.48528 | − | 7.76874i | −0.177993 | − | 0.308293i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.414214 | − | 0.717439i | −0.0163860 | − | 0.0283814i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.4142 | + | 26.6982i | −0.608825 | + | 1.05452i | 0.382610 | + | 0.923910i | \(0.375025\pi\) |
−0.991434 | + | 0.130605i | \(0.958308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.4853 | −1.43884 | −0.719420 | − | 0.694576i | \(-0.755592\pi\) | ||||
−0.719420 | + | 0.694576i | \(0.755592\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.68629 | −0.184523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.58579 | − | 7.94282i | 0.180286 | − | 0.312264i | −0.761692 | − | 0.647939i | \(-0.775631\pi\) |
0.941978 | + | 0.335675i | \(0.108964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.14214 | + | 3.71029i | 0.0840862 | + | 0.145642i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.41421 | + | 2.44949i | 0.0553425 | + | 0.0958559i | 0.892369 | − | 0.451306i | \(-0.149042\pi\) |
−0.837027 | + | 0.547162i | \(0.815708\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.14214 | + | 3.71029i | −0.0837002 | + | 0.144973i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.0711 | −0.431923 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.4853 | −1.65499 | −0.827496 | − | 0.561472i | \(-0.810235\pi\) | ||||
−0.827496 | + | 0.561472i | \(0.810235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6777 | + | 41.0109i | −0.920955 | + | 1.59514i | −0.123013 | + | 0.992405i | \(0.539256\pi\) |
−0.797941 | + | 0.602735i | \(0.794078\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.58579 | − | 2.74666i | −0.0615868 | − | 0.106672i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.4853 | + | 35.4815i | 0.793193 | + | 1.37385i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.82843 | − | 11.8272i | 0.264002 | − | 0.457265i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5147 | 0.444521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.31371 | −0.281923 | −0.140961 | − | 0.990015i | \(-0.545019\pi\) | ||||
−0.140961 | + | 0.990015i | \(0.545019\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.32843 | + | 4.03295i | −0.0896212 | + | 0.155228i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.7782 | − | 25.5965i | −0.567971 | − | 0.983755i | −0.996766 | − | 0.0803535i | \(-0.974395\pi\) |
0.428795 | − | 0.903402i | \(-0.358938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.89949 | + | 17.1464i | 0.379349 | + | 0.657053i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.07107 | + | 13.9795i | −0.308831 | + | 0.534911i | −0.978107 | − | 0.208103i | \(-0.933271\pi\) |
0.669276 | + | 0.743014i | \(0.266604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.62742 | 0.100388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.0711 | −0.574997 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.41421 | + | 16.3059i | −0.358653 | + | 0.621205i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0000 | + | 24.2487i | 0.532585 | + | 0.922464i | 0.999276 | + | 0.0380440i | \(0.0121127\pi\) |
−0.466691 | + | 0.884420i | \(0.654554\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.485281 | − | 0.840532i | −0.0184078 | − | 0.0318832i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.656854 | − | 1.13770i | 0.0248801 | − | 0.0430936i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.4853 | 1.07741 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.17157 | −0.195328 | −0.0976638 | − | 0.995219i | \(-0.531137\pi\) | ||||
−0.0976638 | + | 0.995219i | \(0.531137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.65685 | − | 9.79796i | 0.213352 | − | 0.369537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.00000 | − | 3.46410i | −0.0753244 | − | 0.130466i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | + | 6.92820i | 0.150223 | + | 0.260194i | 0.931309 | − | 0.364229i | \(-0.118667\pi\) |
−0.781086 | + | 0.624423i | \(0.785334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.17157 | + | 2.02922i | −0.0439374 | + | 0.0761018i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.9706 | 0.935155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.686292 | −0.0256658 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.58579 | − | 2.74666i | 0.0592223 | − | 0.102576i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.34315 | − | 4.05845i | −0.0873846 | − | 0.151355i | 0.819020 | − | 0.573765i | \(-0.194518\pi\) |
−0.906405 | + | 0.422410i | \(0.861184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.9497 | − | 18.9655i | −0.407225 | − | 0.705335i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.7574 | − | 34.2208i | 0.733770 | − | 1.27093i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4558 | −0.944105 | −0.472052 | − | 0.881570i | \(-0.656487\pi\) | ||||
−0.472052 | + | 0.881570i | \(0.656487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.97056 | + | 15.5375i | −0.331788 | + | 0.574674i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.87868 | − | 10.1822i | −0.217134 | − | 0.376087i | 0.736797 | − | 0.676114i | \(-0.236338\pi\) |
−0.953931 | + | 0.300027i | \(0.903004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.31371 | − | 5.73951i | −0.122062 | − | 0.211418i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.1421 | − | 17.5667i | 0.373084 | − | 0.646201i | −0.616954 | − | 0.786999i | \(-0.711633\pi\) |
0.990038 | + | 0.140798i | \(0.0449668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.65685 | −0.354753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.1716 | 0.409845 | 0.204923 | − | 0.978778i | \(-0.434306\pi\) | ||||
0.204923 | + | 0.978778i | \(0.434306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.92893 | − | 5.07306i | 0.107308 | − | 0.185863i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.65685 | + | 13.2621i | 0.280150 | + | 0.485233i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.8284 | + | 25.6836i | 0.541097 | + | 0.937207i | 0.998841 | + | 0.0481236i | \(0.0153242\pi\) |
−0.457744 | + | 0.889084i | \(0.651343\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.24264 | + | 7.34847i | −0.154610 | + | 0.267793i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | −0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3137 | −0.411204 | −0.205602 | − | 0.978636i | \(-0.565915\pi\) | ||||
−0.205602 | + | 0.978636i | \(0.565915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.00000 | + | 3.46410i | −0.0725954 | + | 0.125739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.87868 | + | 8.45012i | 0.176852 | + | 0.306317i | 0.940801 | − | 0.338960i | \(-0.110075\pi\) |
−0.763949 | + | 0.645277i | \(0.776742\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.656854 | − | 1.13770i | −0.0237486 | − | 0.0411338i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.65685 | + | 6.33386i | −0.132041 | + | 0.228702i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0711 | 0.543477 | 0.271738 | − | 0.962371i | \(-0.412401\pi\) | ||||
0.271738 | + | 0.962371i | \(0.412401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.2426 | 1.08916 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.70711 | − | 2.95680i | 0.0614004 | − | 0.106349i | −0.833691 | − | 0.552231i | \(-0.813777\pi\) |
0.895092 | + | 0.445882i | \(0.147110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.0416 | − | 20.8567i | −0.432548 | − | 0.749195i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.00000 | − | 3.46410i | −0.0716574 | − | 0.124114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.343146 | + | 0.594346i | −0.0122787 | + | 0.0212674i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.48528 | −0.303239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.14214 | −0.290605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.31371 | + | 9.20361i | −0.189413 | + | 0.328073i | −0.945055 | − | 0.326912i | \(-0.893992\pi\) |
0.755642 | + | 0.654985i | \(0.227325\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.4142 | − | 21.5020i | −0.441958 | − | 0.765493i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.82843 | + | 17.0233i | 0.349018 | + | 0.604516i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.89949 | + | 6.75412i | −0.138301 | + | 0.239544i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.2132 | −1.53069 | −0.765345 | − | 0.643620i | \(-0.777432\pi\) | ||||
−0.765345 | + | 0.643620i | \(0.777432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.3137 | −0.541760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.36396 | − | 9.29065i | 0.189526 | − | 0.328269i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.58579 | + | 7.94282i | 0.161829 | + | 0.280296i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0208 | + | 26.0168i | 0.528758 | + | 0.915835i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0000 | − | 25.9808i | 0.527372 | − | 0.913435i | −0.472119 | − | 0.881535i | \(-0.656511\pi\) |
0.999491 | − | 0.0319002i | \(-0.0101559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9706 | 0.736376 | 0.368188 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368188 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.1716 | −0.461947 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | + | 6.92820i | −0.140114 | + | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3137 | + | 47.3087i | 0.955586 | + | 1.65512i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00000 | − | 8.66025i | −0.174501 | − | 0.302245i | 0.765487 | − | 0.643451i | \(-0.222498\pi\) |
−0.939989 | + | 0.341206i | \(0.889165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.17157 | + | 2.02922i | −0.0408385 | + | 0.0707343i | −0.885722 | − | 0.464216i | \(-0.846336\pi\) |
0.844884 | + | 0.534950i | \(0.179670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.85786 | 0.134314 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4558 | 0.676546 | 0.338273 | − | 0.941048i | \(-0.390157\pi\) | ||||
0.338273 | + | 0.941048i | \(0.390157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.63604 | + | 2.83370i | −0.0568220 | + | 0.0984186i | −0.893037 | − | 0.449983i | \(-0.851430\pi\) |
0.836215 | + | 0.548401i | \(0.184763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.00000 | − | 5.19615i | −0.104069 | − | 0.180253i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.343146 | + | 0.594346i | 0.0118750 | + | 0.0205682i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.58579 | + | 4.47871i | −0.0893779 | + | 0.154807i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.1716 | −1.69759 | −0.848796 | − | 0.528721i | \(-0.822672\pi\) | ||||
−0.848796 | + | 0.528721i | \(0.822672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.24264 | + | 10.8126i | −0.215008 | + | 0.372405i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.22183 | + | 5.58037i | 0.110834 | + | 0.191970i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.41421 | + | 12.8418i | 0.254455 | + | 0.440729i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | − | 6.92820i | 0.137118 | − | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.0416 | 1.23404 | 0.617021 | − | 0.786947i | \(-0.288339\pi\) | ||||
0.617021 | + | 0.786947i | \(0.288339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.8492 | − | 37.8440i | 0.746356 | − | 1.29273i | −0.203203 | − | 0.979137i | \(-0.565135\pi\) |
0.949559 | − | 0.313590i | \(-0.101532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.4142 | − | 33.6264i | −0.662404 | − | 1.14732i | −0.979982 | − | 0.199086i | \(-0.936203\pi\) |
0.317578 | − | 0.948232i | \(-0.397131\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.7574 | − | 25.5605i | −0.502346 | − | 0.870089i | −0.999996 | − | 0.00271146i | \(-0.999137\pi\) |
0.497650 | − | 0.867378i | \(-0.334196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | − | 1.73205i | 0.0340010 | − | 0.0588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9706 | 0.406542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.94113 | 0.0658482 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65685 | − | 9.79796i | 0.191675 | − | 0.331991i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.87868 | + | 6.71807i | 0.131273 | + | 0.227372i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.1421 | − | 17.5667i | −0.342476 | − | 0.593185i | 0.642416 | − | 0.766356i | \(-0.277932\pi\) |
−0.984892 | + | 0.173171i | \(0.944599\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.535534 | − | 0.927572i | 0.0180631 | − | 0.0312862i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0711 | −0.844666 | −0.422333 | − | 0.906441i | \(-0.638789\pi\) | ||||
−0.422333 | + | 0.906441i | \(0.638789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.3431 | −0.617296 | −0.308648 | − | 0.951176i | \(-0.599877\pi\) | ||||
−0.308648 | + | 0.951176i | \(0.599877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.51472 | + | 2.62357i | −0.0509167 | + | 0.0881903i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.7279 | + | 18.5813i | 0.360208 | + | 0.623899i | 0.987995 | − | 0.154486i | \(-0.0493723\pi\) |
−0.627787 | + | 0.778386i | \(0.716039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.414214 | − | 0.717439i | −0.0138767 | − | 0.0240351i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.3137 | + | 40.3805i | −0.780164 | + | 1.35128i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.4264 | −0.348516 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.82843 | −0.227995 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.9411 | − | 38.0031i | 0.731778 | − | 1.26748i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.9289 | + | 25.8577i | 0.497355 | + | 0.861444i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.89949 | + | 5.02207i | 0.0963825 | + | 0.166939i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.51472 | + | 6.08767i | −0.116704 | + | 0.202138i | −0.918460 | − | 0.395514i | \(-0.870566\pi\) |
0.801755 | + | 0.597652i | \(0.203900\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.41421 | 0.113242 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.4853 | 1.80518 | 0.902589 | − | 0.430503i | \(-0.141664\pi\) | ||||
0.902589 | + | 0.430503i | \(0.141664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.34315 | − | 10.9867i | 0.209927 | − | 0.363605i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.07107 | + | 7.05130i | 0.134585 | + | 0.233109i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.6274 | − | 42.6559i | −0.812384 | − | 1.40709i | −0.911192 | − | 0.411983i | \(-0.864836\pi\) |
0.0988080 | − | 0.995107i | \(-0.468497\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.75736 | − | 9.97204i | 0.189711 | − | 0.328590i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.17157 | −0.0385628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.71573 | −0.253692 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.41421 | − | 9.37769i | 0.177826 | − | 0.308004i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.4350 | − | 52.7150i | −0.998541 | − | 1.72952i | −0.546036 | − | 0.837762i | \(-0.683864\pi\) |
−0.452505 | − | 0.891762i | \(-0.649469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.0711 | + | 22.6398i | 0.427928 | + | 0.741192i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.544156 | + | 0.942506i | −0.0177958 | + | 0.0308232i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.10051 | −0.199295 | −0.0996474 | − | 0.995023i | \(-0.531771\pi\) | ||||
−0.0996474 | + | 0.995023i | \(0.531771\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.4142 | 0.568291 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.9497 | − | 38.0181i | 0.715541 | − | 1.23935i | −0.247209 | − | 0.968962i | \(-0.579513\pi\) |
0.962750 | − | 0.270392i | \(-0.0871532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.41421 | − | 2.44949i | −0.0460531 | − | 0.0797664i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.0711 | + | 17.4436i | 0.327266 | + | 0.566841i | 0.981968 | − | 0.189046i | \(-0.0605394\pi\) |
−0.654703 | + | 0.755887i | \(0.727206\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.82843 | + | 13.5592i | −0.254121 | + | 0.440151i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.3137 | −0.691144 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.37258 | −0.238821 | −0.119411 | − | 0.992845i | \(-0.538101\pi\) | ||||
−0.119411 | + | 0.992845i | \(0.538101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.44365 | − | 7.69663i | 0.143793 | − | 0.249057i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.51472 | + | 6.08767i | 0.113615 | + | 0.196786i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.12742 | + | 3.68479i | 0.0686264 | + | 0.118864i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.24264 | − | 12.5446i | 0.233391 | − | 0.404245i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.4264 | 0.464402 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.6274 | 1.11354 | 0.556771 | − | 0.830666i | \(-0.312040\pi\) | ||||
0.556771 | + | 0.830666i | \(0.312040\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.65685 | + | 13.2621i | −0.245974 | + | 0.426039i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.6274 | − | 49.5841i | −0.918698 | − | 1.59123i | −0.801396 | − | 0.598134i | \(-0.795909\pi\) |
−0.117302 | − | 0.993096i | \(-0.537424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.29289 | + | 5.70346i | 0.105457 | + | 0.182657i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.9289 | + | 18.9295i | −0.349648 | + | 0.605607i | −0.986187 | − | 0.165637i | \(-0.947032\pi\) |
0.636539 | + | 0.771244i | \(0.280365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.88730 | −0.284039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3137 | −0.361219 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.31371 | + | 12.6677i | −0.233271 | + | 0.404037i | −0.958769 | − | 0.284187i | \(-0.908276\pi\) |
0.725498 | + | 0.688225i | \(0.241610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.585786 | − | 1.01461i | −0.0186647 | − | 0.0323282i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.3137 | + | 33.4523i | 0.614140 | + | 1.06372i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.6569 | − | 20.1903i | 0.370292 | − | 0.641365i | −0.619318 | − | 0.785140i | \(-0.712591\pi\) |
0.989610 | + | 0.143775i | \(0.0459242\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.68629 | −0.275651 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.31371 | −0.105052 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.2929 | − | 29.9522i | 0.547671 | − | 0.948595i | −0.450762 | − | 0.892644i | \(-0.648848\pi\) |
0.998434 | − | 0.0559506i | \(-0.0178189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.828427 | + | 1.43488i | 0.0262103 | + | 0.0453975i |
(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 | 2352.2.q.be.1537.2 | 4 | ||
4.3 | odd | 2 | 1176.2.q.k.361.2 | 4 | |||
7.2 | even | 3 | inner | 2352.2.q.be.961.2 | 4 | ||
7.3 | odd | 6 | 2352.2.a.bd.1.2 | 2 | |||
7.4 | even | 3 | 2352.2.a.bb.1.1 | 2 | |||
7.5 | odd | 6 | 2352.2.q.bc.961.1 | 4 | |||
7.6 | odd | 2 | 2352.2.q.bc.1537.1 | 4 | |||
12.11 | even | 2 | 3528.2.s.bm.361.1 | 4 | |||
21.11 | odd | 6 | 7056.2.a.cg.1.2 | 2 | |||
21.17 | even | 6 | 7056.2.a.cx.1.1 | 2 | |||
28.3 | even | 6 | 1176.2.a.j.1.2 | ✓ | 2 | ||
28.11 | odd | 6 | 1176.2.a.o.1.1 | yes | 2 | ||
28.19 | even | 6 | 1176.2.q.o.961.1 | 4 | |||
28.23 | odd | 6 | 1176.2.q.k.961.2 | 4 | |||
28.27 | even | 2 | 1176.2.q.o.361.1 | 4 | |||
56.3 | even | 6 | 9408.2.a.ee.1.1 | 2 | |||
56.11 | odd | 6 | 9408.2.a.dg.1.2 | 2 | |||
56.45 | odd | 6 | 9408.2.a.ds.1.1 | 2 | |||
56.53 | even | 6 | 9408.2.a.du.1.2 | 2 | |||
84.11 | even | 6 | 3528.2.a.bb.1.2 | 2 | |||
84.23 | even | 6 | 3528.2.s.bm.3313.1 | 4 | |||
84.47 | odd | 6 | 3528.2.s.bd.3313.2 | 4 | |||
84.59 | odd | 6 | 3528.2.a.bl.1.1 | 2 | |||
84.83 | odd | 2 | 3528.2.s.bd.361.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.j.1.2 | ✓ | 2 | 28.3 | even | 6 | ||
1176.2.a.o.1.1 | yes | 2 | 28.11 | odd | 6 | ||
1176.2.q.k.361.2 | 4 | 4.3 | odd | 2 | |||
1176.2.q.k.961.2 | 4 | 28.23 | odd | 6 | |||
1176.2.q.o.361.1 | 4 | 28.27 | even | 2 | |||
1176.2.q.o.961.1 | 4 | 28.19 | even | 6 | |||
2352.2.a.bb.1.1 | 2 | 7.4 | even | 3 | |||
2352.2.a.bd.1.2 | 2 | 7.3 | odd | 6 | |||
2352.2.q.bc.961.1 | 4 | 7.5 | odd | 6 | |||
2352.2.q.bc.1537.1 | 4 | 7.6 | odd | 2 | |||
2352.2.q.be.961.2 | 4 | 7.2 | even | 3 | inner | ||
2352.2.q.be.1537.2 | 4 | 1.1 | even | 1 | trivial | ||
3528.2.a.bb.1.2 | 2 | 84.11 | even | 6 | |||
3528.2.a.bl.1.1 | 2 | 84.59 | odd | 6 | |||
3528.2.s.bd.361.2 | 4 | 84.83 | odd | 2 | |||
3528.2.s.bd.3313.2 | 4 | 84.47 | odd | 6 | |||
3528.2.s.bm.361.1 | 4 | 12.11 | even | 2 | |||
3528.2.s.bm.3313.1 | 4 | 84.23 | even | 6 | |||
7056.2.a.cg.1.2 | 2 | 21.11 | odd | 6 | |||
7056.2.a.cx.1.1 | 2 | 21.17 | even | 6 | |||
9408.2.a.dg.1.2 | 2 | 56.11 | odd | 6 | |||
9408.2.a.ds.1.1 | 2 | 56.45 | odd | 6 | |||
9408.2.a.du.1.2 | 2 | 56.53 | even | 6 | |||
9408.2.a.ee.1.1 | 2 | 56.3 | even | 6 |