Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), 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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.2 | ||
Root | \(1.65386 - 1.65386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.h.369.15 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 2.89996i | − | 1.67429i | −0.546980 | − | 0.837145i | \(-0.684223\pi\) | ||
0.546980 | − | 0.837145i | \(-0.315777\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50491 | + | 1.65386i | −0.673017 | + | 0.739627i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.580879i | 0.219552i | 0.993956 | + | 0.109776i | \(0.0350133\pi\) | ||||
−0.993956 | + | 0.109776i | \(0.964987\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.40975 | −1.80325 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0809094 | 0.0243951 | 0.0121975 | − | 0.999926i | \(-0.496117\pi\) | ||||
0.0121975 | + | 0.999926i | \(0.496117\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.02066i | 0.837779i | 0.908037 | + | 0.418890i | \(0.137581\pi\) | ||||
−0.908037 | + | 0.418890i | \(0.862419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.79611 | + | 4.36418i | 1.23835 | + | 1.12683i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.280529i | 0.0680384i | 0.999421 | + | 0.0340192i | \(0.0108307\pi\) | ||||
−0.999421 | + | 0.0340192i | \(0.989169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.72683 | 1.08441 | 0.542205 | − | 0.840246i | \(-0.317590\pi\) | ||||
0.542205 | + | 0.840246i | \(0.317590\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.68452 | 0.367593 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.470482 | − | 4.97782i | −0.0940965 | − | 0.995563i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.98817i | 1.34487i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.38057 | −0.256366 | −0.128183 | − | 0.991751i | \(-0.540914\pi\) | ||||
−0.128183 | + | 0.991751i | \(0.540914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.70770 | 1.02513 | 0.512567 | − | 0.858647i | \(-0.328695\pi\) | ||||
0.512567 | + | 0.858647i | \(0.328695\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.234634i | − | 0.0408445i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.960690 | − | 0.874171i | −0.162386 | − | 0.147762i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.61536i | 0.429962i | 0.976618 | + | 0.214981i | \(0.0689690\pi\) | ||||
−0.976618 | + | 0.214981i | \(0.931031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.75977 | 1.40269 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.31570 | 0.830172 | 0.415086 | − | 0.909782i | \(-0.363751\pi\) | ||||
0.415086 | + | 0.909782i | \(0.363751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.30240i | − | 1.11361i | −0.830645 | − | 0.556803i | \(-0.812028\pi\) | ||
0.830645 | − | 0.556803i | \(-0.187972\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.14119 | − | 8.94695i | 1.21362 | − | 1.33373i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2117i | 1.78125i | 0.454736 | + | 0.890626i | \(0.349734\pi\) | ||||
−0.454736 | + | 0.890626i | \(0.650266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.66258 | 0.951797 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.813523 | 0.113916 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.64032i | − | 0.912117i | −0.889950 | − | 0.456059i | \(-0.849261\pi\) | ||
0.889950 | − | 0.456059i | \(-0.150739\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.121761 | + | 0.133812i | −0.0164183 | + | 0.0180433i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 13.7076i | − | 1.81562i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.70211 | 0.481974 | 0.240987 | − | 0.970528i | \(-0.422529\pi\) | ||||
0.240987 | + | 0.970528i | \(0.422529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5113 | 1.47387 | 0.736936 | − | 0.675962i | \(-0.236272\pi\) | ||||
0.736936 | + | 0.675962i | \(0.236272\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.14241i | − | 0.395906i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.99573 | − | 4.54582i | −0.619644 | − | 0.563840i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.99193i | − | 0.732031i | −0.930609 | − | 0.366015i | \(-0.880722\pi\) | ||
0.930609 | − | 0.366015i | \(-0.119278\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.89996 | 0.349114 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8324 | 1.64160 | 0.820801 | − | 0.571214i | \(-0.193527\pi\) | ||||
0.820801 | + | 0.571214i | \(0.193527\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.14465i | 0.133971i | 0.997754 | + | 0.0669857i | \(0.0213382\pi\) | ||||
−0.997754 | + | 0.0669857i | \(0.978662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.4354 | + | 1.36438i | −1.66686 | + | 0.157545i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0469985i | 0.00535598i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.68167 | −0.189203 | −0.0946015 | − | 0.995515i | \(-0.530158\pi\) | ||||
−0.0946015 | + | 0.995515i | \(0.530158\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.03614 | 0.448460 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.86877i | − | 1.08324i | −0.840624 | − | 0.541619i | \(-0.817811\pi\) | ||
0.840624 | − | 0.541619i | \(-0.182189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.463955 | − | 0.422172i | −0.0503230 | − | 0.0457910i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00360i | 0.429231i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.69235 | −0.709388 | −0.354694 | − | 0.934982i | \(-0.615415\pi\) | ||||
−0.354694 | + | 0.934982i | \(0.615415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.75463 | −0.183936 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 16.5521i | − | 1.71637i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.11347 | + | 7.81751i | −0.729826 | + | 0.802059i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.8190i | 1.30158i | 0.759260 | + | 0.650788i | \(0.225561\pi\) | ||||
−0.759260 | + | 0.650788i | \(0.774439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.437699 | −0.0439904 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.01958 | −0.101452 | −0.0507262 | − | 0.998713i | \(-0.516154\pi\) | ||||
−0.0507262 | + | 0.998713i | \(0.516154\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.36255i | − | 0.232789i | −0.993203 | − | 0.116394i | \(-0.962866\pi\) | ||
0.993203 | − | 0.116394i | \(-0.0371336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.53506 | + | 2.78596i | −0.247396 | + | 0.271882i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.58207i | 0.539639i | 0.962911 | + | 0.269820i | \(0.0869641\pi\) | ||||
−0.962911 | + | 0.269820i | \(0.913036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.09973 | −0.584248 | −0.292124 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292124 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.58443 | 0.719882 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3938i | 1.63627i | 0.575023 | + | 0.818137i | \(0.304993\pi\) | ||||
−0.575023 | + | 0.818137i | \(0.695007\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.65386 | − | 1.50491i | −0.154223 | − | 0.140334i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 16.3410i | − | 1.51073i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.162954 | −0.0149379 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9935 | −0.999405 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 15.4153i | − | 1.38995i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.94063 | + | 6.71306i | 0.799674 | + | 0.600434i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.9365i | − | 1.05919i | −0.848250 | − | 0.529597i | \(-0.822343\pi\) | ||
0.848250 | − | 0.529597i | \(-0.177657\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.1767 | −1.86450 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.84214 | 0.859912 | 0.429956 | − | 0.902850i | \(-0.358529\pi\) | ||||
0.429956 | + | 0.902850i | \(0.358529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.74572i | 0.238084i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.5574 | − | 10.5166i | −0.994705 | − | 0.905123i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.93256i | 0.250545i | 0.992122 | + | 0.125273i | \(0.0399805\pi\) | ||||
−0.992122 | + | 0.125273i | \(0.960019\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.96075 | 0.420766 | 0.210383 | − | 0.977619i | \(-0.432529\pi\) | ||||
0.210383 | + | 0.977619i | \(0.432529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.4133 | 2.98233 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.244399i | 0.0204377i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.07764 | − | 2.28327i | 0.172539 | − | 0.189615i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 19.3212i | − | 1.59359i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0375 | −1.47769 | −0.738846 | − | 0.673874i | \(-0.764629\pi\) | ||||
−0.738846 | + | 0.673874i | \(0.764629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1026 | 1.47317 | 0.736585 | − | 0.676345i | \(-0.236437\pi\) | ||||
0.736585 | + | 0.676345i | \(0.236437\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.51759i | − | 0.122690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.58958 | + | 9.43972i | −0.689932 | + | 0.758216i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2698i | 1.21867i | 0.792915 | + | 0.609333i | \(0.208563\pi\) | ||||
−0.792915 | + | 0.609333i | \(0.791437\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.2566 | −1.52715 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.580879 | −0.0457797 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.1488i | − | 1.26487i | −0.774613 | − | 0.632435i | \(-0.782055\pi\) | ||
0.774613 | − | 0.632435i | \(-0.217945\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.388050 | + | 0.353103i | 0.0302097 | + | 0.0274890i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.77915i | − | 0.524586i | −0.964988 | − | 0.262293i | \(-0.915521\pi\) | ||
0.964988 | − | 0.262293i | \(-0.0844787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.87563 | 0.298126 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.5710 | −1.95546 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 21.9428i | − | 1.66828i | −0.551553 | − | 0.834140i | \(-0.685965\pi\) | ||
0.551553 | − | 0.834140i | \(-0.314035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.89151 | − | 0.273293i | 0.218577 | − | 0.0206590i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 10.7360i | − | 0.806964i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.76302 | 0.505492 | 0.252746 | − | 0.967533i | \(-0.418666\pi\) | ||||
0.252746 | + | 0.967533i | \(0.418666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1572 | 0.903641 | 0.451820 | − | 0.892109i | \(-0.350775\pi\) | ||||
0.451820 | + | 0.892109i | \(0.350775\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 33.3823i | − | 2.46769i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.32543 | − | 3.93589i | −0.318012 | − | 0.289372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0226975i | 0.00165980i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.05928 | −0.295269 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.87427 | −0.642119 | −0.321060 | − | 0.947059i | \(-0.604039\pi\) | ||||
−0.321060 | + | 0.947059i | \(0.604039\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7026i | 0.842374i | 0.906974 | + | 0.421187i | \(0.138386\pi\) | ||||
−0.906974 | + | 0.421187i | \(0.861614\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.1827 | + | 14.4874i | −0.944032 | + | 1.03746i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.330763i | − | 0.0235659i | −0.999931 | − | 0.0117829i | \(-0.996249\pi\) | ||
0.999931 | − | 0.0117829i | \(-0.00375071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.72600 | 0.689458 | 0.344729 | − | 0.938702i | \(-0.387971\pi\) | ||||
0.344729 | + | 0.938702i | \(0.387971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.3763 | −1.22563 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.801945i | − | 0.0562855i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.99965 | + | 8.79140i | −0.558720 | + | 0.614018i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.40975i | − | 0.376004i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.382445 | 0.0264543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.63709 | 0.456916 | 0.228458 | − | 0.973554i | \(-0.426632\pi\) | ||||
0.228458 | + | 0.973554i | \(0.426632\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 40.1133i | − | 2.74852i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0771 | + | 10.9895i | 0.823653 | + | 0.749476i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.31548i | 0.225070i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.31944 | 0.224307 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.847383 | −0.0570012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.4323i | 1.83700i | 0.395420 | + | 0.918500i | \(0.370599\pi\) | ||||
−0.395420 | + | 0.918500i | \(0.629401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.54519 | + | 26.9287i | 0.169679 | + | 1.79525i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 20.6195i | − | 1.36856i | −0.729218 | − | 0.684281i | \(-0.760116\pi\) | ||
0.729218 | − | 0.684281i | \(-0.239884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2949 | 1.47329 | 0.736644 | − | 0.676280i | \(-0.236409\pi\) | ||||
0.736644 | + | 0.676280i | \(0.236409\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.136294 | 0.00896747 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.5331i | 1.67273i | 0.548173 | + | 0.836365i | \(0.315324\pi\) | ||||
−0.548173 | + | 0.836365i | \(0.684676\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.1963 | − | 18.3775i | −1.31746 | − | 1.19881i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.87678i | 0.316781i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.6017 | 1.39730 | 0.698649 | − | 0.715465i | \(-0.253785\pi\) | ||||
0.698649 | + | 0.715465i | \(0.253785\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.6850 | 1.39685 | 0.698426 | − | 0.715682i | \(-0.253884\pi\) | ||||
0.698426 | + | 0.715682i | \(0.253884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.25988i | 0.594021i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0266 | + | 11.0190i | −0.640576 | + | 0.703975i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2781i | 0.908496i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.6190 | −1.81366 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.5991 | −1.67892 | −0.839461 | − | 0.543420i | \(-0.817129\pi\) | ||||
−0.839461 | + | 0.543420i | \(0.817129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0809094i | 0.00508673i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.22428 | + | 1.34545i | −0.0766674 | + | 0.0842554i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 0.156392i | − | 0.00975548i | −0.999988 | − | 0.00487774i | \(-0.998447\pi\) | ||
0.999988 | − | 0.00487774i | \(-0.00155264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.51921 | −0.0943989 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.46855 | 0.462292 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.1557i | 1.48951i | 0.667340 | + | 0.744753i | \(0.267433\pi\) | ||||
−0.667340 | + | 0.744753i | \(0.732567\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.9821 | + | 9.99309i | 0.674627 | + | 0.613870i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.4075i | 1.18772i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.270387 | −0.0164858 | −0.00824289 | − | 0.999966i | \(-0.502624\pi\) | ||||
−0.00824289 | + | 0.999966i | \(0.502624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0041 | −0.607704 | −0.303852 | − | 0.952719i | \(-0.598273\pi\) | ||||
−0.303852 | + | 0.952719i | \(0.598273\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.08837i | 0.307962i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0380664 | − | 0.402752i | −0.00229549 | − | 0.0242869i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.0842i | − | 0.726070i | −0.931776 | − | 0.363035i | \(-0.881741\pi\) | ||
0.931776 | − | 0.363035i | \(-0.118259\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.8772 | −1.84857 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.2912 | 1.32978 | 0.664890 | − | 0.746941i | \(-0.268478\pi\) | ||||
0.664890 | + | 0.746941i | \(0.268478\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5506i | 0.627165i | 0.949561 | + | 0.313583i | \(0.101529\pi\) | ||||
−0.949561 | + | 0.313583i | \(0.898471\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 22.6704 | + | 20.6287i | 1.34288 | + | 1.22194i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.08777i | 0.182266i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9213 | 0.995371 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.1746 | 2.17922 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.49506i | 0.496287i | 0.968723 | + | 0.248143i | \(0.0798204\pi\) | ||||
−0.968723 | + | 0.248143i | \(0.920180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.57135 | + | 6.12276i | −0.324376 | + | 0.356481i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.565408i | 0.0328083i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.02066 | −0.174689 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.24181 | 0.244494 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.95675i | 0.169861i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.3235 | + | 19.0381i | −0.991941 | + | 1.09012i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.1607i | − | 0.922339i | −0.887312 | − | 0.461170i | \(-0.847430\pi\) | ||
0.887312 | − | 0.461170i | \(-0.152570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.85128 | −0.389756 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.3027 | −1.88842 | −0.944211 | − | 0.329340i | \(-0.893174\pi\) | ||||
−0.944211 | + | 0.329340i | \(0.893174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.59232i | − | 0.485666i | −0.970068 | − | 0.242833i | \(-0.921923\pi\) | ||
0.970068 | − | 0.242833i | \(-0.0780768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.19709 | + | 4.72905i | 0.292823 | + | 0.266452i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.9109i | 1.84846i | 0.381837 | + | 0.924230i | \(0.375291\pi\) | ||||
−0.381837 | + | 0.924230i | \(0.624709\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.111701 | −0.00625407 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.1878 | 0.903513 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.32602i | 0.0737815i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.0363 | − | 1.42117i | 0.834062 | − | 0.0788321i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.6889i | 0.978201i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.09349 | −0.391077 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.19245 | −0.450298 | −0.225149 | − | 0.974324i | \(-0.572287\pi\) | ||||
−0.225149 | + | 0.974324i | \(0.572287\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 14.1484i | − | 0.775330i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.90979 | + | 9.01733i | 0.541430 | + | 0.492669i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.7372i | 1.40199i | 0.713165 | + | 0.700996i | \(0.247261\pi\) | ||||
−0.713165 | + | 0.700996i | \(0.752739\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 50.4414 | 2.73960 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.461806 | 0.0250082 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.93630i | 0.428520i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.36418 | + | 4.79611i | −0.234959 | + | 0.258214i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.1539i | 0.652455i | 0.945291 | + | 0.326228i | \(0.105778\pi\) | ||||
−0.945291 | + | 0.326228i | \(0.894222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.51456 | −0.241659 | −0.120829 | − | 0.992673i | \(-0.538555\pi\) | ||||
−0.120829 | + | 0.992673i | \(0.538555\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.1089 | −1.12671 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.7767i | − | 1.58485i | −0.609968 | − | 0.792426i | \(-0.708818\pi\) | ||
0.609968 | − | 0.792426i | \(-0.291182\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.8165 | + | 22.8768i | −1.10483 | + | 1.21417i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.472558i | 0.0250104i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.22436 | −0.222953 | −0.111477 | − | 0.993767i | \(-0.535558\pi\) | ||||
−0.111477 | + | 0.993767i | \(0.535558\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.34296 | 0.175945 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.8805i | 1.67329i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.89309 | − | 1.72260i | −0.0990889 | − | 0.0901650i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 31.9394i | − | 1.66722i | −0.552351 | − | 0.833611i | \(-0.686269\pi\) | ||
0.552351 | − | 0.833611i | \(-0.313731\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.7566 | −1.49701 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.85722 | 0.200257 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.3524i | − | 0.691361i | −0.938352 | − | 0.345681i | \(-0.887648\pi\) | ||
0.938352 | − | 0.345681i | \(-0.112352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.4676 | − | 25.9274i | 1.00530 | − | 1.33889i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.17024i | − | 0.214778i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0481 | 1.02980 | 0.514901 | − | 0.857250i | \(-0.327829\pi\) | ||||
0.514901 | + | 0.857250i | \(0.327829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.6153 | −1.77340 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.7850i | 0.653281i | 0.945149 | + | 0.326640i | \(0.105917\pi\) | ||||
−0.945149 | + | 0.326640i | \(0.894083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0777288 | − | 0.0707286i | −0.00396143 | − | 0.00360466i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 39.5042i | 2.00811i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.69492 | −0.288744 | −0.144372 | − | 0.989523i | \(-0.546116\pi\) | ||||
−0.144372 | + | 0.989523i | \(0.546116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.280529 | −0.0141870 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 28.5418i | − | 1.43974i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.53077 | − | 2.78125i | 0.127337 | − | 0.139940i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2231i | 0.563269i | 0.959522 | + | 0.281635i | \(0.0908766\pi\) | ||||
−0.959522 | + | 0.281635i | \(0.909123\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.96246 | 0.398622 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.1979 | −1.35820 | −0.679098 | − | 0.734047i | \(-0.737629\pi\) | ||||
−0.679098 | + | 0.734047i | \(0.737629\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2410i | 0.858836i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.07403 | + | 6.67519i | −0.301821 | + | 0.331693i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.211607i | 0.0104890i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2012 | 1.39446 | 0.697230 | − | 0.716848i | \(-0.254416\pi\) | ||||
0.697230 | + | 0.716848i | \(0.254416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.50428 | 0.419485 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.15048i | 0.105818i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.3215 | + | 14.8516i | 0.801192 | + | 0.729038i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 14.3860i | − | 0.704484i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.5731 | 0.907356 | 0.453678 | − | 0.891166i | \(-0.350112\pi\) | ||||
0.453678 | + | 0.891166i | \(0.350112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6531 | −0.811622 | −0.405811 | − | 0.913957i | \(-0.633011\pi\) | ||||
−0.405811 | + | 0.913957i | \(0.633011\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 66.0620i | − | 3.21204i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.39642 | − | 0.131984i | 0.0677365 | − | 0.00640217i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.68668i | 0.323591i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.708748 | 0.0342187 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.446399 | 0.0215023 | 0.0107511 | − | 0.999942i | \(-0.496578\pi\) | ||||
0.0107511 | + | 0.999942i | \(0.496578\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.87406i | 0.0900616i | 0.998986 | + | 0.0450308i | \(0.0143386\pi\) | ||||
−0.998986 | + | 0.0450308i | \(0.985661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.62138 | − | 6.02507i | −0.317471 | − | 0.288880i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.72683i | 0.226115i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6607 | −0.651991 | −0.325995 | − | 0.945371i | \(-0.605699\pi\) | ||||
−0.325995 | + | 0.945371i | \(0.605699\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.0429 | −1.71633 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.6380i | 1.02805i | 0.857774 | + | 0.514027i | \(0.171847\pi\) | ||||
−0.857774 | + | 0.514027i | \(0.828153\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0714 | − | 11.0682i | 0.477430 | − | 0.524683i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 52.3080i | 2.47409i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3547 | 1.05499 | 0.527493 | − | 0.849560i | \(-0.323132\pi\) | ||||
0.527493 | + | 0.849560i | \(0.323132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.430090 | 0.0202521 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 52.4968i | − | 2.46652i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.64057 | − | 2.90191i | 0.123792 | − | 0.136044i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8614i | 0.648408i | 0.945987 | + | 0.324204i | \(0.105096\pi\) | ||||
−0.945987 | + | 0.324204i | \(0.894904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.96039 | −0.0915030 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.4880 | −1.23367 | −0.616834 | − | 0.787093i | \(-0.711585\pi\) | ||||
−0.616834 | + | 0.787093i | \(0.711585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 31.3980i | − | 1.45919i | −0.683881 | − | 0.729594i | \(-0.739709\pi\) | ||
0.683881 | − | 0.729594i | \(-0.260291\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.3748 | + | 24.9094i | 1.26947 | + | 1.15515i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.27210i | 0.151415i | 0.997130 | + | 0.0757074i | \(0.0241215\pi\) | ||||
−0.997130 | + | 0.0757074i | \(0.975879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.48058 | 0.160718 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.2819 | 2.04040 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.590833i | − | 0.0271665i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.22389 | − | 23.5293i | −0.102039 | − | 1.07960i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 35.9224i | 1.64478i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.4865 | −1.39296 | −0.696482 | − | 0.717574i | \(-0.745253\pi\) | ||||
−0.696482 | + | 0.717574i | \(0.745253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.90010 | −0.360214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.68452i | 0.0766485i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.2008 | − | 19.2915i | −0.962680 | − | 0.875982i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.8997i | − | 0.584542i | −0.956336 | − | 0.292271i | \(-0.905589\pi\) | ||
0.956336 | − | 0.292271i | \(-0.0944109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.8308 | −2.11776 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.53828 | −0.0694217 | −0.0347109 | − | 0.999397i | \(-0.511051\pi\) | ||||
−0.0347109 | + | 0.999397i | \(0.511051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.387291i | − | 0.0174427i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.658699 | − | 0.723892i | 0.0296063 | − | 0.0325365i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.03494i | 0.360416i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0529 | 0.808160 | 0.404080 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404080 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.6592 | −0.878310 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.35252i | − | 0.327832i | −0.986474 | − | 0.163916i | \(-0.947587\pi\) | ||
0.986474 | − | 0.163916i | \(-0.0524127\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.53439 | − | 1.68625i | 0.0682792 | − | 0.0750370i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.2392i | − | 0.499149i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.3564 | 1.30120 | 0.650600 | − | 0.759421i | \(-0.274517\pi\) | ||||
0.650600 | + | 0.759421i | \(0.274517\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.664904 | −0.0294136 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.0319i | 1.45839i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.90731 | + | 3.55542i | 0.172177 | + | 0.156671i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.988037i | 0.0434538i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −63.6331 | −2.79318 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.1800 | −1.67270 | −0.836349 | − | 0.548198i | \(-0.815314\pi\) | ||||
−0.836349 | + | 0.548198i | \(0.815314\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 37.7527i | − | 1.65081i | −0.564540 | − | 0.825405i | \(-0.690947\pi\) | ||
0.564540 | − | 0.825405i | \(-0.309053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.792538 | − | 8.38524i | −0.0345892 | − | 0.365962i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.60118i | 0.0697484i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.0275 | −0.869119 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.0569i | 0.695501i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.23194 | − | 8.40052i | −0.399132 | − | 0.363186i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 19.6125i | − | 0.846341i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.539065 | 0.0232192 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.30694 | −0.271157 | −0.135578 | − | 0.990767i | \(-0.543289\pi\) | ||||
−0.135578 | + | 0.990767i | \(0.543289\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 35.2555i | − | 1.51296i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.17955 | − | 10.0881i | 0.393209 | − | 0.432126i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.9574i | 1.75121i | 0.483027 | + | 0.875606i | \(0.339537\pi\) | ||||
−0.483027 | + | 0.875606i | \(0.660463\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −62.2733 | −2.65776 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.52574 | −0.278006 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.976848i | − | 0.0415398i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.4139 | + | 12.5436i | −0.484493 | + | 0.532444i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.6143i | 1.29717i | 0.761142 | + | 0.648586i | \(0.224639\pi\) | ||||
−0.761142 | + | 0.648586i | \(0.775361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.0581 | 0.932956 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0658217 | 0.00277899 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.8221i | 0.835400i | 0.908585 | + | 0.417700i | \(0.137164\pi\) | ||||
−0.908585 | + | 0.417700i | \(0.862836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.7669 | − | 26.1762i | −1.21023 | − | 1.10124i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.34451i | 0.0984600i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.8830 | −1.46237 | −0.731185 | − | 0.682179i | \(-0.761032\pi\) | ||||
−0.731185 | + | 0.682179i | \(0.761032\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5730 | −0.442466 | −0.221233 | − | 0.975221i | \(-0.571008\pi\) | ||||
−0.221233 | + | 0.975221i | \(0.571008\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.7350i | 1.07509i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.97782 | − | 0.470482i | 0.207589 | − | 0.0196205i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 12.7839i | − | 0.532201i | −0.963945 | − | 0.266101i | \(-0.914265\pi\) | ||
0.963945 | − | 0.266101i | \(-0.0857354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.9371 | 1.41038 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.73256 | 0.237827 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.537264i | − | 0.0222512i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.0257 | + | 24.5918i | 1.11737 | + | 1.01674i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.4015i | 0.429317i | 0.976689 | + | 0.214658i | \(0.0688638\pi\) | ||||
−0.976689 | + | 0.214658i | \(0.931136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.9794 | 1.11166 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.959198 | −0.0394561 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.7468i | − | 1.05729i | −0.848842 | − | 0.528647i | \(-0.822700\pi\) | ||
0.848842 | − | 0.528647i | \(-0.177300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.245231 | − | 0.269502i | 0.0100535 | − | 0.0110485i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 28.2050i | − | 1.15435i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.2360 | 0.867680 | 0.433840 | − | 0.900990i | \(-0.357158\pi\) | ||||
0.433840 | + | 0.900990i | \(0.357158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9088 | −0.444980 | −0.222490 | − | 0.974935i | \(-0.571418\pi\) | ||||
−0.222490 | + | 0.974935i | \(0.571418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.4148i | 1.32003i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.5442 | − | 18.1816i | 0.672616 | − | 0.739187i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.15713i | 0.249910i | 0.992162 | + | 0.124955i | \(0.0398787\pi\) | ||||
−0.992162 | + | 0.124955i | \(0.960121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.32561 | −0.0942383 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.8872 | −1.49230 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.3588i | − | 0.822283i | −0.911572 | − | 0.411142i | \(-0.865130\pi\) | ||
0.911572 | − | 0.411142i | \(-0.134870\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 25.4947 | + | 23.1986i | 1.02804 | + | 0.935460i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.9290i | − | 0.560759i | −0.959889 | − | 0.280380i | \(-0.909540\pi\) | ||
0.959889 | − | 0.280380i | \(-0.0904604\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.4617 | −1.82726 | −0.913629 | − | 0.406548i | \(-0.866732\pi\) | ||||
−0.913629 | + | 0.406548i | \(0.866732\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.98817 | −0.280426 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.88745i | − | 0.155747i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.5573 | + | 4.68395i | −0.982292 | + | 0.187358i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.10907i | − | 0.0442922i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.733685 | −0.0292540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.7205 | −1.58125 | −0.790624 | − | 0.612303i | \(-0.790243\pi\) | ||||
−0.790624 | + | 0.612303i | \(0.790243\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 19.2473i | − | 0.765011i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.7413 | + | 17.9634i | 0.783408 | + | 0.712855i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.1254i | 0.797396i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −74.8297 | −2.96022 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.4730 | 0.769137 | 0.384568 | − | 0.923096i | \(-0.374350\pi\) | ||||
0.384568 | + | 0.923096i | \(0.374350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.3269i | − | 1.43259i | −0.697795 | − | 0.716297i | \(-0.745836\pi\) | ||
0.697795 | − | 0.716297i | \(-0.254164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.8690 | − | 35.0231i | 1.25484 | − | 1.37904i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 4.18108i | − | 0.164375i | −0.996617 | − | 0.0821875i | \(-0.973809\pi\) | ||
0.996617 | − | 0.0821875i | \(-0.0261906\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.299535 | 0.0117578 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.61475 | 0.376832 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 30.5378i | − | 1.19504i | −0.801855 | − | 0.597519i | \(-0.796153\pi\) | ||
0.801855 | − | 0.597519i | \(-0.203847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.8116 | + | 16.2775i | −0.578735 | + | 0.636014i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.19228i | − | 0.241584i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.7062 | −1.54673 | −0.773366 | − | 0.633960i | \(-0.781429\pi\) | ||||
−0.773366 | + | 0.633960i | \(0.781429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.53963 | 0.176571 | 0.0882857 | − | 0.996095i | \(-0.471861\pi\) | ||||
0.0882857 | + | 0.996095i | \(0.471861\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.45737i | 0.0954365i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.54102 | − | 4.13206i | −0.176093 | − | 0.160234i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.38057i | − | 0.0534560i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 79.5524 | 3.07567 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.931373 | 0.0359553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.2447i | − | 1.08875i | −0.838841 | − | 0.544377i | \(-0.816766\pi\) | ||
0.838841 | − | 0.544377i | \(-0.183234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 34.7858 | − | 3.28781i | 1.33891 | − | 0.126548i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 10.0502i | − | 0.386260i | −0.981173 | − | 0.193130i | \(-0.938136\pi\) | ||
0.981173 | − | 0.193130i | \(-0.0618639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.44630 | −0.285763 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −59.7956 | −2.29137 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 13.1814i | − | 0.504372i | −0.967679 | − | 0.252186i | \(-0.918851\pi\) | ||
0.967679 | − | 0.252186i | \(-0.0811495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85003 | − | 4.41324i | −0.185310 | − | 0.168621i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 64.6542i | − | 2.46671i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.0581 | 0.764153 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.3908 | −1.84087 | −0.920436 | − | 0.390894i | \(-0.872166\pi\) | ||||
−0.920436 | + | 0.390894i | \(0.872166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 0.254250i | − | 0.00965817i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.46550 | + | 8.20437i | −0.283182 | + | 0.311210i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.49121i | 0.0564836i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 74.0449 | 2.80064 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.4310 | 1.30044 | 0.650220 | − | 0.759746i | \(-0.274677\pi\) | ||||
0.650220 | + | 0.759746i | \(0.274677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3624i | 0.466256i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −53.2938 | + | 58.5685i | −2.00716 | + | 2.20582i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 0.592255i | − | 0.0222740i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.7221 | −0.515346 | −0.257673 | − | 0.966232i | \(-0.582956\pi\) | ||||
−0.257673 | + | 0.966232i | \(0.582956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.09743 | 0.341180 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.70770i | 0.213755i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.404202 | − | 0.367799i | −0.0151163 | − | 0.0137549i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 62.6440i | − | 2.33948i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.7900 | −1.29745 | −0.648724 | − | 0.761024i | \(-0.724697\pi\) | ||||
−0.648724 | + | 0.761024i | \(0.724697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.37235 | 0.0511091 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 62.8855i | − | 2.33874i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.649535 | + | 6.87224i | 0.0241231 | + | 0.255228i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.35114i | 0.124287i | 0.998067 | + | 0.0621435i | \(0.0197937\pi\) | ||||
−0.998067 | + | 0.0621435i | \(0.980206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.9617 | 1.44302 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.04854 | 0.0757680 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.20440i | − | 0.118357i | −0.998247 | − | 0.0591786i | \(-0.981152\pi\) | ||
0.998247 | − | 0.0591786i | \(-0.0188482\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.9545 | + | 29.0767i | 1.17866 | + | 1.07251i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.484803i | − | 0.0178580i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.3376 | 1.41027 | 0.705136 | − | 0.709072i | \(-0.250886\pi\) | ||||
0.705136 | + | 0.709072i | \(0.250886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 41.4060 | 1.52109 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5137i | 0.789261i | 0.918840 | + | 0.394631i | \(0.129127\pi\) | ||||
−0.918840 | + | 0.394631i | \(0.870873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.1449 | − | 29.8315i | 0.994512 | − | 1.09294i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 53.3876i | 1.95335i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.24251 | −0.118479 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.9353 | 1.09236 | 0.546178 | − | 0.837669i | \(-0.316082\pi\) | ||||
0.546178 | + | 0.837669i | \(0.316082\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 77.1363i | 2.81100i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.2429 | + | 29.9391i | −0.991469 | + | 1.08960i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.2518i | 0.845102i | 0.906339 | + | 0.422551i | \(0.138865\pi\) | ||||
−0.906339 | + | 0.422551i | \(0.861135\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.234634 | 0.00851666 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.7791 | 1.47824 | 0.739120 | − | 0.673574i | \(-0.235242\pi\) | ||||
0.739120 | + | 0.673574i | \(0.235242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.54320i | − | 0.128272i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.50988 | + | 2.28384i | 0.0907450 | + | 0.0825726i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1828i | 0.403788i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.08570 | 0.0391515 | 0.0195757 | − | 0.999808i | \(-0.493768\pi\) | ||||
0.0195757 | + | 0.999808i | \(0.493768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.453531 | −0.0163335 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.7659i | 1.35835i | 0.733978 | + | 0.679173i | \(0.237662\pi\) | ||||
−0.733978 | + | 0.679173i | \(0.762338\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.68537 | − | 28.4119i | −0.0964614 | − | 1.02058i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.40563i | 0.158051i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.1264 | 0.900247 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.11917 | 0.0400470 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.64767i | − | 0.344780i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.2541 | − | 22.9798i | −0.901358 | − | 0.820183i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.0489i | − | 1.35630i | −0.734925 | − | 0.678149i | \(-0.762782\pi\) | ||
0.734925 | − | 0.678149i | \(-0.237218\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 70.0506 | 2.49387 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.1037 | −0.359246 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.7717i | 1.23478i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.9795 | − | 31.8477i | 1.02780 | − | 1.12952i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.8798i | − | 0.456227i | −0.973634 | − | 0.228114i | \(-0.926744\pi\) | ||
0.973634 | − | 0.228114i | \(-0.0732558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.42573 | −0.121194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.2040 | 1.27920 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0926131i | 0.00326825i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.874171 | − | 0.960690i | 0.0308105 | − | 0.0338599i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.784110i | 0.0276020i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.0775700 | 0.00272722 | 0.00136361 | − | 0.999999i | \(-0.499566\pi\) | ||||
0.00136361 | + | 0.999999i | \(0.499566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0163427 | 0.000573869 | 0.000286934 | − | 1.00000i | \(-0.499909\pi\) | ||||
0.000286934 | 1.00000i | \(0.499909\pi\) | ||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.0114i | 1.01747i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.7078 | + | 24.3025i | 0.935533 | + | 0.851279i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 34.5173i | − | 1.20761i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.49214 | 0.331682 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.85832 | 0.239357 | 0.119678 | − | 0.992813i | \(-0.461814\pi\) | ||||
0.119678 | + | 0.992813i | \(0.461814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24.4740i | − | 0.853109i | −0.904462 | − | 0.426554i | \(-0.859727\pi\) | ||
0.904462 | − | 0.426554i | \(-0.140273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.16796 | + | 0.110391i | −0.0406633 | + | 0.00384332i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.5556i | − | 0.401828i | −0.979609 | − | 0.200914i | \(-0.935609\pi\) | ||
0.979609 | − | 0.200914i | \(-0.0643912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.7496 | 1.48475 | 0.742377 | − | 0.669983i | \(-0.233698\pi\) | ||||
0.742377 | + | 0.669983i | \(0.233698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.0437 | −1.21565 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.86905i | 0.0647587i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.2117 | + | 10.2020i | 0.387998 | + | 0.353055i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.8864i | 1.37867i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.4396 | 1.81042 | 0.905209 | − | 0.424968i | \(-0.139714\pi\) | ||||
0.905209 | + | 0.424968i | \(0.139714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0940 | −0.934277 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 64.6434i | − | 2.22644i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.83249 | + | 6.40974i | −0.200644 | + | 0.220502i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.38586i | − | 0.219421i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.5961 | 1.05006 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.61536 | −0.0896534 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.6690i | − | 0.810410i | −0.914226 | − | 0.405205i | \(-0.867200\pi\) | ||
0.914226 | − | 0.405205i | \(-0.132800\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 38.4821 | − | 42.2907i | 1.31606 | − | 1.44631i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.1587i | 0.791088i | 0.918447 | + | 0.395544i | \(0.129444\pi\) | ||||
−0.918447 | + | 0.395544i | \(0.870556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.6044 | −0.395939 | −0.197969 | − | 0.980208i | \(-0.563435\pi\) | ||||
−0.197969 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.95441 | 0.305166 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.71131i | − | 0.0922940i | −0.998935 | − | 0.0461470i | \(-0.985306\pi\) | ||
0.998935 | − | 0.0461470i | \(-0.0146943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.2902 | + | 33.0220i | 1.23390 | + | 1.12278i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 49.0710i | − | 1.66654i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.136063 | −0.00461562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.0996 | 0.613280 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 69.3477i | − | 2.34706i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.89947 | + | 5.19342i | −0.131826 | + | 0.175570i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 48.0862i | − | 1.62375i | −0.583828 | − | 0.811877i | \(-0.698446\pi\) | ||
0.583828 | − | 0.811877i | \(-0.301554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.6353 | 0.830928 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.70507 | 0.0911361 | 0.0455680 | − | 0.998961i | \(-0.485490\pi\) | ||||
0.0455680 | + | 0.998961i | \(0.485490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.5827i | − | 0.457094i | −0.973533 | − | 0.228547i | \(-0.926602\pi\) | ||
0.973533 | − | 0.228547i | \(-0.0733975\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.7557 | + | 16.1567i | 0.596853 | + | 0.543101i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.42335i | − | 0.114945i | −0.998347 | − | 0.0574724i | \(-0.981696\pi\) | ||
0.998347 | − | 0.0574724i | \(-0.0183041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.93366 | 0.232547 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.326561 | 0.0109402 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.7225i | 1.93161i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.1778 | + | 11.1851i | −0.340205 | + | 0.373876i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.75977i | 0.292480i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.87990 | −0.262809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.86280 | 0.0620590 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 12.3011i | − | 0.409354i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.2956 | + | 20.1063i | −0.608165 | + | 0.668357i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.90426i | 0.328865i | 0.986388 | + | 0.164433i | \(0.0525793\pi\) | ||||
−0.986388 | + | 0.164433i | \(0.947421\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.51570 | 0.182944 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.95943 | 0.0649187 | 0.0324593 | − | 0.999473i | \(-0.489666\pi\) | ||||
0.0324593 | + | 0.999473i | \(0.489666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 0.798476i | − | 0.0264257i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 55.2096 | + | 50.2374i | 1.82517 | + | 1.66080i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.71709i | 0.188795i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.8522 | −1.84239 | −0.921197 | − | 0.389096i | \(-0.872787\pi\) | ||||
−0.921197 | + | 0.389096i | \(0.872787\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.8653 | −1.54426 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.7829i | 1.37530i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.0188 | − | 1.23048i | 0.428055 | − | 0.0404580i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.7808i | 0.419776i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.0522 | −0.559464 | −0.279732 | − | 0.960078i | \(-0.590246\pi\) | ||||
−0.279732 | + | 0.960078i | \(0.590246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.4929 | 1.03214 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 96.5764i | 3.16177i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0375383 | − | 0.0341577i | −0.00122764 | − | 0.00111708i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.9074i | 1.00970i | 0.863207 | + | 0.504850i | \(0.168452\pi\) | ||||
−0.863207 | + | 0.504850i | \(0.831548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.9173 | −0.813147 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.4508 | −1.35126 | −0.675629 | − | 0.737242i | \(-0.736128\pi\) | ||||
−0.675629 | + | 0.737242i | \(0.736128\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.31570i | 0.173103i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.10885 | − | 6.71346i | 0.198721 | − | 0.218389i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 34.4896i | − | 1.12076i | −0.828236 | − | 0.560380i | \(-0.810655\pi\) | ||
0.828236 | − | 0.560380i | \(-0.189345\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.45760 | −0.112239 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 95.4401 | 3.09486 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 28.8622i | − | 0.934939i | −0.884009 | − | 0.467470i | \(-0.845166\pi\) | ||
0.884009 | − | 0.467470i | \(-0.154834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3550 | − | 14.6768i | 0.432157 | − | 0.474929i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.323929i | 0.0104711i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.70346 | −0.0550076 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.57784 | 0.0508982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 30.1976i | − | 0.973104i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.3545 | − | 17.6114i | −0.623042 | − | 0.566932i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.47559i | − | 0.208241i | −0.994565 | − | 0.104121i | \(-0.966797\pi\) | ||
0.994565 | − | 0.104121i | \(-0.0332028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.84539 | 0.123532 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.9296 | −1.08885 | −0.544426 | − | 0.838809i | \(-0.683253\pi\) | ||||
−0.544426 | + | 0.838809i | \(0.683253\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.88160i | 0.0923797i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.12132 | − | 43.6045i | −0.131988 | − | 1.39646i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.90638i | 0.0929832i | 0.998919 | + | 0.0464916i | \(0.0148041\pi\) | ||||
−0.998919 | + | 0.0464916i | \(0.985196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.541474 | −0.0173056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.9980 | 1.05354 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 8.66470i | − | 0.276361i | −0.990407 | − | 0.138180i | \(-0.955875\pi\) | ||
0.990407 | − | 0.138180i | \(-0.0441254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.547034 | + | 0.497769i | 0.0174300 | + | 0.0158602i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.5708i | 0.654776i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.30240 | 0.232203 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.4587 | 1.03108 | 0.515542 | − | 0.856864i | \(-0.327590\pi\) | ||||
0.515542 | + | 0.856864i | \(0.327590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.7577i | 0.753929i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.6368 | + | 16.0854i | −0.464017 | + | 0.509942i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.7623i | 1.95603i | 0.208534 | + | 0.978015i | \(0.433131\pi\) | ||||
−0.208534 | + | 0.978015i | \(0.566869\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.2766 | −0.578245 |
(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 | 1840.2.e.h.369.2 | 16 | ||
4.3 | odd | 2 | 920.2.e.c.369.15 | yes | 16 | ||
5.2 | odd | 4 | 9200.2.a.dd.1.2 | 8 | |||
5.3 | odd | 4 | 9200.2.a.de.1.7 | 8 | |||
5.4 | even | 2 | inner | 1840.2.e.h.369.15 | 16 | ||
20.3 | even | 4 | 4600.2.a.bj.1.2 | 8 | |||
20.7 | even | 4 | 4600.2.a.bk.1.7 | 8 | |||
20.19 | odd | 2 | 920.2.e.c.369.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.c.369.2 | ✓ | 16 | 20.19 | odd | 2 | ||
920.2.e.c.369.15 | yes | 16 | 4.3 | odd | 2 | ||
1840.2.e.h.369.2 | 16 | 1.1 | even | 1 | trivial | ||
1840.2.e.h.369.15 | 16 | 5.4 | even | 2 | inner | ||
4600.2.a.bj.1.2 | 8 | 20.3 | even | 4 | |||
4600.2.a.bk.1.7 | 8 | 20.7 | even | 4 | |||
9200.2.a.dd.1.2 | 8 | 5.2 | odd | 4 | |||
9200.2.a.de.1.7 | 8 | 5.3 | odd | 4 |