Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4368,2,Mod(337,4368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4368.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4368.h (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: | \(34.8786556029\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 15x^{6} + 67x^{4} + 77x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(2.54814i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4368.337 |
Dual form | 4368.2.h.q.337.7 |
$q$-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 \(\left(\mathbb{Z}/4368\mathbb{Z}\right)^\times\).
\(n\) | \(1093\) | \(1249\) | \(1457\) | \(2017\) | \(3823\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.49301i | − | 1.56212i | −0.624454 | − | 0.781061i | \(-0.714679\pi\) | ||
0.624454 | − | 0.781061i | \(-0.285321\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.708126i | − | 0.213508i | −0.994285 | − | 0.106754i | \(-0.965954\pi\) | ||
0.994285 | − | 0.106754i | \(-0.0340458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.25627 | + | 1.54814i | −0.903126 | + | 0.429377i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.49301i | − | 0.901892i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.09628 | 1.72110 | 0.860550 | − | 0.509366i | \(-0.170120\pi\) | ||||
0.860550 | + | 0.509366i | \(0.170120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.311392i | − | 0.0714382i | −0.999362 | − | 0.0357191i | \(-0.988628\pi\) | ||
0.999362 | − | 0.0357191i | \(-0.0113722\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.88116 | 1.64334 | 0.821668 | − | 0.569966i | \(-0.193044\pi\) | ||||
0.821668 | + | 0.569966i | \(0.193044\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.20114 | −1.44023 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29742 | 0.983706 | 0.491853 | − | 0.870678i | \(-0.336320\pi\) | ||||
0.491853 | + | 0.870678i | \(0.336320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.29742i | 1.31065i | 0.755345 | + | 0.655327i | \(0.227469\pi\) | ||||
−0.755345 | + | 0.655327i | \(0.772531\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.708126i | − | 0.123269i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.49301 | 0.590427 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.41625i | − | 0.232831i | −0.993201 | − | 0.116415i | \(-0.962860\pi\) | ||
0.993201 | − | 0.116415i | \(-0.0371403\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.25627 | + | 1.54814i | −0.521420 | + | 0.247901i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.8044i | − | 1.84354i | −0.387739 | − | 0.921769i | \(-0.626744\pi\) | ||
0.387739 | − | 0.921769i | \(-0.373256\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.29742 | 0.502851 | 0.251426 | − | 0.967877i | \(-0.419101\pi\) | ||||
0.251426 | + | 0.967877i | \(0.419101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 3.49301i | − | 0.520708i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.11580i | 0.892081i | 0.895013 | + | 0.446040i | \(0.147166\pi\) | ||||
−0.895013 | + | 0.446040i | \(0.852834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.09628 | 0.993678 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.72764 | −0.512031 | −0.256016 | − | 0.966673i | \(-0.582410\pi\) | ||||
−0.256016 | + | 0.966673i | \(0.582410\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.47349 | −0.333526 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.311392i | − | 0.0412448i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.19560i | − | 0.285842i | −0.989734 | − | 0.142921i | \(-0.954350\pi\) | ||
0.989734 | − | 0.142921i | \(-0.0456495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.51253 | 0.321697 | 0.160848 | − | 0.986979i | \(-0.448577\pi\) | ||||
0.160848 | + | 0.986979i | \(0.448577\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.40767 | + | 11.3742i | 0.670739 | + | 1.41079i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.17858i | − | 1.12134i | −0.828039 | − | 0.560671i | \(-0.810543\pi\) | ||
0.828039 | − | 0.560671i | \(-0.189457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.88116 | 0.948781 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.708126i | 0.0840391i | 0.999117 | + | 0.0420196i | \(0.0133792\pi\) | ||||
−0.999117 | + | 0.0420196i | \(0.986621\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.21511i | − | 0.610383i | −0.952291 | − | 0.305191i | \(-0.901280\pi\) | ||
0.952291 | − | 0.305191i | \(-0.0987205\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.20114 | −0.831516 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.708126 | 0.0806985 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.78489 | 0.313324 | 0.156662 | − | 0.987652i | \(-0.449927\pi\) | ||||
0.156662 | + | 0.987652i | \(0.449927\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.11580i | − | 0.671296i | −0.941988 | − | 0.335648i | \(-0.891045\pi\) | ||
0.941988 | − | 0.335648i | \(-0.108955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 24.7874i | − | 2.68857i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.29742 | 0.567943 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 11.1018i | − | 1.17679i | −0.808573 | − | 0.588395i | \(-0.799760\pi\) | ||
0.808573 | − | 0.588395i | \(-0.200240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.54814 | − | 3.25627i | −0.162289 | − | 0.341349i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.29742i | 0.756707i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.08770 | −0.111595 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.79886i | 0.791854i | 0.918282 | + | 0.395927i | \(0.129577\pi\) | ||||
−0.918282 | + | 0.395927i | \(0.870423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.708126i | − | 0.0711694i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.6911 | 1.76033 | 0.880166 | − | 0.474666i | \(-0.157431\pi\) | ||||
0.880166 | + | 0.474666i | \(0.157431\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.52651 | −0.544543 | −0.272271 | − | 0.962221i | \(-0.587775\pi\) | ||||
−0.272271 | + | 0.962221i | \(0.587775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.49301 | 0.340883 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.1786 | −1.85406 | −0.927032 | − | 0.374983i | \(-0.877649\pi\) | ||||
−0.927032 | + | 0.374983i | \(0.877649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.20653i | − | 0.307130i | −0.988139 | − | 0.153565i | \(-0.950925\pi\) | ||
0.988139 | − | 0.153565i | \(-0.0490754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.41625i | − | 0.134425i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.29742 | −0.498339 | −0.249170 | − | 0.968460i | \(-0.580158\pi\) | ||||
−0.249170 | + | 0.968460i | \(0.580158\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 27.5290i | − | 2.56709i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.25627 | + | 1.54814i | −0.301042 | + | 0.143126i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.09628i | 0.650515i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4986 | 0.954414 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 11.8044i | − | 1.06437i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.68861i | 0.687690i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3028 | 1.26917 | 0.634585 | − | 0.772853i | \(-0.281171\pi\) | ||||
0.634585 | + | 0.772853i | \(0.281171\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.29742 | 0.290321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4023 | −1.08359 | −0.541796 | − | 0.840510i | \(-0.682255\pi\) | ||||
−0.541796 | + | 0.840510i | \(0.682255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.311392 | 0.0270011 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.49301i | − | 0.300631i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.58390i | − | 0.477065i | −0.971135 | − | 0.238532i | \(-0.923334\pi\) | ||
0.971135 | − | 0.238532i | \(-0.0766663\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.52651 | 0.129476 | 0.0647382 | − | 0.997902i | \(-0.479379\pi\) | ||||
0.0647382 | + | 0.997902i | \(0.479379\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.11580i | 0.515043i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.09628 | + | 2.30585i | 0.0916754 | + | 0.192825i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 18.5039i | − | 1.53667i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.7765i | 1.29246i | 0.763144 | + | 0.646229i | \(0.223655\pi\) | ||||
−0.763144 | + | 0.646229i | \(0.776345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.83251i | − | 0.556021i | −0.960578 | − | 0.278011i | \(-0.910325\pi\) | ||
0.960578 | − | 0.278011i | \(-0.0896751\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.09628 | 0.573700 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.4900 | 2.04740 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1926 | −0.973072 | −0.486536 | − | 0.873661i | \(-0.661740\pi\) | ||||
−0.486536 | + | 0.873661i | \(0.661740\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.72764 | −0.295621 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.88116i | 0.621123i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.0390i | − | 0.786318i | −0.919470 | − | 0.393159i | \(-0.871382\pi\) | ||
0.919470 | − | 0.393159i | \(-0.128618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.47349 | −0.192561 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.7106i | 1.91217i | 0.293096 | + | 0.956083i | \(0.405314\pi\) | ||||
−0.293096 | + | 0.956083i | \(0.594686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.20653 | − | 10.0823i | 0.631272 | − | 0.775562i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 0.311392i | − | 0.0238127i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.4735 | 0.796285 | 0.398143 | − | 0.917324i | \(-0.369655\pi\) | ||||
0.398143 | + | 0.917324i | \(0.369655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.20114i | − | 0.544355i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.19560i | − | 0.165031i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.2584 | −0.841491 | −0.420745 | − | 0.907179i | \(-0.638231\pi\) | ||||
−0.420745 | + | 0.907179i | \(0.638231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.59484 | −0.638849 | −0.319425 | − | 0.947612i | \(-0.603490\pi\) | ||||
−0.319425 | + | 0.947612i | \(0.603490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.51253 | 0.185732 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.94699 | −0.363710 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.02506i | − | 0.367469i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.98603 | −0.360776 | −0.180388 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180388 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.98603i | − | 0.502865i | −0.967875 | − | 0.251433i | \(-0.919098\pi\) | ||
0.967875 | − | 0.251433i | \(-0.0809017\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.40767 | + | 11.3742i | 0.387251 | + | 0.814522i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.8044i | − | 1.55350i | −0.629809 | − | 0.776750i | \(-0.716867\pi\) | ||
0.629809 | − | 0.776750i | \(-0.283133\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.622783 | −0.0441479 | −0.0220740 | − | 0.999756i | \(-0.507027\pi\) | ||||
−0.0220740 | + | 0.999756i | \(0.507027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 9.17858i | − | 0.647407i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.29742i | 0.371806i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −41.2329 | −2.87983 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.88116 | 0.547779 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.220505 | −0.0152526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3547 | −1.12590 | −0.562951 | − | 0.826491i | \(-0.690334\pi\) | ||||
−0.562951 | + | 0.826491i | \(0.690334\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.708126i | 0.0485200i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 11.5179i | − | 0.785516i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.29742 | −0.495381 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 5.21511i | − | 0.352405i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.1074 | + | 10.9860i | −1.55437 | + | 0.739000i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.71367i | − | 0.583511i | −0.956493 | − | 0.291755i | \(-0.905761\pi\) | ||
0.956493 | − | 0.291755i | \(-0.0942393\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.20114 | −0.480076 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 12.9440i | − | 0.859120i | −0.903038 | − | 0.429560i | \(-0.858669\pi\) | ||
0.903038 | − | 0.429560i | \(-0.141331\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6521i | 1.29865i | 0.760513 | + | 0.649323i | \(0.224948\pi\) | ||||
−0.760513 | + | 0.649323i | \(0.775052\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.708126 | 0.0465913 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.72764 | 0.244206 | 0.122103 | − | 0.992517i | \(-0.461036\pi\) | ||||
0.122103 | + | 0.992517i | \(0.461036\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.3626 | 1.39354 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.78489 | 0.180898 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.86165i | − | 0.573212i | −0.958048 | − | 0.286606i | \(-0.907473\pi\) | ||
0.958048 | − | 0.286606i | \(-0.0925271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0025i | 0.644318i | 0.946686 | + | 0.322159i | \(0.104409\pi\) | ||||
−0.946686 | + | 0.322159i | \(0.895591\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.49301i | 0.223160i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.482078 | + | 1.01397i | 0.0306739 | + | 0.0645176i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.11580i | − | 0.387573i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.24557 | −0.583575 | −0.291788 | − | 0.956483i | \(-0.594250\pi\) | ||||
−0.291788 | + | 0.956483i | \(0.594250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.58086i | − | 0.350866i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 24.7874i | − | 1.55225i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.5516 | −0.907702 | −0.453851 | − | 0.891078i | \(-0.649950\pi\) | ||||
−0.453851 | + | 0.891078i | \(0.649950\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.41625 | 0.0880017 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.29742 | 0.327902 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.7137 | 0.907284 | 0.453642 | − | 0.891184i | \(-0.350125\pi\) | ||||
0.453642 | + | 0.891184i | \(0.350125\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0207i | 0.799856i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 11.1018i | − | 0.679420i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0433 | −0.734291 | −0.367145 | − | 0.930164i | \(-0.619665\pi\) | ||||
−0.367145 | + | 0.930164i | \(0.619665\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.38830i | 0.448808i | 0.974496 | + | 0.224404i | \(0.0720434\pi\) | ||||
−0.974496 | + | 0.224404i | \(0.927957\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.54814 | − | 3.25627i | −0.0936976 | − | 0.197078i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.09932i | 0.307500i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6997 | 0.823135 | 0.411567 | − | 0.911379i | \(-0.364981\pi\) | ||||
0.411567 | + | 0.911379i | \(0.364981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.29742i | 0.436885i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.62582i | 0.275953i | 0.990435 | + | 0.137977i | \(0.0440599\pi\) | ||||
−0.990435 | + | 0.137977i | \(0.955940\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.9721 | −1.06833 | −0.534164 | − | 0.845381i | \(-0.679373\pi\) | ||||
−0.534164 | + | 0.845381i | \(0.679373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.08770 | −0.0644295 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.8044 | 0.696792 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.3572 | 1.96219 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.79886i | 0.457177i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.87023i | − | 0.401363i | −0.979657 | − | 0.200682i | \(-0.935684\pi\) | ||
0.979657 | − | 0.200682i | \(-0.0643156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.66924 | −0.446521 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.708126i | − | 0.0410897i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.6632 | + | 12.2011i | −1.48414 | + | 0.705610i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.29742i | 0.190060i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.6911 | 1.01633 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.77630i | − | 0.502530i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.9202i | − | 0.680322i | −0.940367 | − | 0.340161i | \(-0.889518\pi\) | ||
0.940367 | − | 0.340161i | \(-0.110482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.52651 | −0.314392 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.7874 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.73304 | −0.380574 | −0.190287 | − | 0.981729i | \(-0.560942\pi\) | ||||
−0.190287 | + | 0.981729i | \(0.560942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.49301 | 0.196809 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.1537i | − | 1.07578i | −0.843016 | − | 0.537889i | \(-0.819222\pi\) | ||
0.843016 | − | 0.537889i | \(-0.180778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.75124i | − | 0.210029i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.1786 | −1.07044 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.20972i | − | 0.122952i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.4488 | − | 11.1484i | 1.30071 | − | 0.618400i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.20653i | − | 0.177322i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.11580 | −0.337175 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.5247i | 1.29303i | 0.762900 | + | 0.646516i | \(0.223775\pi\) | ||||
−0.762900 | + | 0.646516i | \(0.776225\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.41625i | − | 0.0776102i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −32.0609 | −1.75167 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.7258 | 1.61927 | 0.809634 | − | 0.586935i | \(-0.199666\pi\) | ||||
0.809634 | + | 0.586935i | \(0.199666\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.29742 | −0.287716 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.16749 | 0.279836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 27.5290i | − | 1.48211i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.2036 | 1.72878 | 0.864391 | − | 0.502820i | \(-0.167704\pi\) | ||||
0.864391 | + | 0.502820i | \(0.167704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.5752i | − | 0.673133i | −0.941660 | − | 0.336567i | \(-0.890734\pi\) | ||
0.941660 | − | 0.336567i | \(-0.109266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.25627 | + | 1.54814i | −0.173807 | + | 0.0826336i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.4132i | 0.820363i | 0.912004 | + | 0.410181i | \(0.134535\pi\) | ||||
−0.912004 | + | 0.410181i | \(0.865465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.47349 | 0.131279 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.09628i | 0.375575i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.6910i | − | 1.30314i | −0.758589 | − | 0.651570i | \(-0.774111\pi\) | ||
0.758589 | − | 0.651570i | \(-0.225889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9030 | 0.994897 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4986 | 0.551031 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.2165 | −0.953493 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8758 | −0.567711 | −0.283855 | − | 0.958867i | \(-0.591614\pi\) | ||||
−0.283855 | + | 0.958867i | \(0.591614\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 11.8044i | − | 0.614513i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.72764i | − | 0.193530i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.71906 | −0.0890096 | −0.0445048 | − | 0.999009i | \(-0.514171\pi\) | ||||
−0.0445048 | + | 0.999009i | \(0.514171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.68861i | 0.397038i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.2498 | + | 8.20114i | −0.888410 | + | 0.422380i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.3028 | 0.732755 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.5528i | 1.86776i | 0.357588 | + | 0.933879i | \(0.383599\pi\) | ||||
−0.357588 | + | 0.933879i | \(0.616401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 2.47349i | − | 0.126061i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.29742 | 0.167617 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.1367 | 1.83220 | 0.916101 | − | 0.400948i | \(-0.131319\pi\) | ||||
0.916101 | + | 0.400948i | \(0.131319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 55.9269 | 2.82835 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.4023 | −0.625612 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 9.72764i | − | 0.489451i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.3657i | 1.22288i | 0.791290 | + | 0.611441i | \(0.209410\pi\) | ||||
−0.791290 | + | 0.611441i | \(0.790590\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.311392 | 0.0155891 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.76537i | − | 0.188034i | −0.995571 | − | 0.0940168i | \(-0.970029\pi\) | ||
0.995571 | − | 0.0940168i | \(-0.0299707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.2974 | − | 23.7623i | −0.562764 | − | 1.18369i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 3.49301i | − | 0.173569i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.00289 | −0.0497112 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3235i | 1.54885i | 0.632667 | + | 0.774424i | \(0.281960\pi\) | ||||
−0.632667 | + | 0.774424i | \(0.718040\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.58390i | − | 0.275433i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.19560 | 0.108038 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.3626 | −1.04865 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.52651 | 0.0747533 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3572 | 1.28763 | 0.643816 | − | 0.765180i | \(-0.277350\pi\) | ||||
0.643816 | + | 0.765180i | \(0.277350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.5168i | − | 1.09740i | −0.836019 | − | 0.548700i | \(-0.815123\pi\) | ||
0.836019 | − | 0.548700i | \(-0.184877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.11580i | 0.297360i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −51.1013 | −2.47878 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.51253i | 0.121590i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.09628 | + | 2.30585i | 0.0529288 | + | 0.111327i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5374i | 0.796580i | 0.917259 | + | 0.398290i | \(0.130396\pi\) | ||||
−0.917259 | + | 0.398290i | \(0.869604\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2720 | 1.21449 | 0.607247 | − | 0.794513i | \(-0.292274\pi\) | ||||
0.607247 | + | 0.794513i | \(0.292274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 18.5039i | − | 0.887196i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.45413i | − | 0.117397i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.52651 | −0.263766 | −0.131883 | − | 0.991265i | \(-0.542102\pi\) | ||||
−0.131883 | + | 0.991265i | \(0.542102\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.25838 | 0.344856 | 0.172428 | − | 0.985022i | \(-0.444839\pi\) | ||||
0.172428 | + | 0.985022i | \(0.444839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.7788 | −1.83829 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.7765i | 0.746201i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.1787i | 1.14107i | 0.821275 | + | 0.570533i | \(0.193263\pi\) | ||||
−0.821275 | + | 0.570533i | \(0.806737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.35901 | −0.393610 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 6.83251i | − | 0.321019i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3742 | + | 5.40767i | −0.533230 | + | 0.253515i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.3991i | 1.56234i | 0.624316 | + | 0.781172i | \(0.285378\pi\) | ||||
−0.624316 | + | 0.781172i | \(0.714622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.09628 | 0.331226 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 10.3882i | − | 0.483824i | −0.970298 | − | 0.241912i | \(-0.922225\pi\) | ||
0.970298 | − | 0.241912i | \(-0.0777746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.9330i | − | 1.11226i | −0.831095 | − | 0.556131i | \(-0.812285\pi\) | ||
0.831095 | − | 0.556131i | \(-0.187715\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.4900 | 1.18207 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.84329 | −0.409219 | −0.204609 | − | 0.978844i | \(-0.565592\pi\) | ||||
−0.204609 | + | 0.978844i | \(0.565592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.17858 | 0.423828 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.1926 | −0.561803 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.33499i | − | 0.107363i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.24238i | 0.102887i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.72764 | −0.170677 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.9623i | 0.637953i | 0.947763 | + | 0.318976i | \(0.103339\pi\) | ||||
−0.947763 | + | 0.318976i | \(0.896661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.19256 | + | 4.61170i | 0.0999720 | + | 0.210275i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.88116i | 0.358605i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.2415 | 1.23697 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.41306i | 0.109346i | 0.998504 | + | 0.0546731i | \(0.0174117\pi\) | ||||
−0.998504 | + | 0.0546731i | \(0.982588\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 10.0390i | − | 0.453981i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.15063 | −0.412962 | −0.206481 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206481 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.5919 | 1.69306 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.47349 | −0.111175 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.708126 | −0.0317638 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.34927i | − | 0.239466i | −0.992806 | − | 0.119733i | \(-0.961796\pi\) | ||
0.992806 | − | 0.119733i | \(-0.0382039\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.7106i | 1.10399i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.1617 | −1.56778 | −0.783892 | − | 0.620897i | \(-0.786768\pi\) | ||||
−0.783892 | + | 0.620897i | \(0.786768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 61.7953i | − | 2.74985i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.20653 | − | 10.0823i | 0.364465 | − | 0.447771i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.4790i | 0.819069i | 0.912295 | + | 0.409534i | \(0.134309\pi\) | ||||
−0.912295 | + | 0.409534i | \(0.865691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.21511 | 0.230703 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.311392i | − | 0.0137483i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.3042i | 0.850643i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.33076 | 0.190466 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.4735 | 0.459735 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.1385 | 0.531798 | 0.265899 | − | 0.964001i | \(-0.414331\pi\) | ||||
0.265899 | + | 0.964001i | \(0.414331\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.4205 | 0.499383 | 0.249691 | − | 0.968325i | \(-0.419671\pi\) | ||||
0.249691 | + | 0.968325i | \(0.419671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 7.20114i | − | 0.314283i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.7845i | 2.25577i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.1128 | 1.70055 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.19560i | − | 0.0952807i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.2749 | + | 38.4383i | 0.791572 | + | 1.66495i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 66.9910i | 2.89628i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.2584 | −0.485835 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.708126i | 0.0305012i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3851i | 0.704451i | 0.935915 | + | 0.352226i | \(0.114575\pi\) | ||||
−0.935915 | + | 0.352226i | \(0.885425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.59484 | −0.368840 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.2005 | −0.479775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4620 | 0.832136 | 0.416068 | − | 0.909333i | \(-0.363408\pi\) | ||||
0.416068 | + | 0.909333i | \(0.363408\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.51253 | 0.107232 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.64957i | − | 0.0702741i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.78489i | 0.118425i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.94699 | −0.209988 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.5248i | 1.63235i | 0.577806 | + | 0.816174i | \(0.303909\pi\) | ||||
−0.577806 | + | 0.816174i | \(0.696091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.7373 | + | 5.10486i | −0.454138 | + | 0.215913i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5.02506i | − | 0.212158i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.7903 | 0.581191 | 0.290595 | − | 0.956846i | \(-0.406147\pi\) | ||||
0.290595 | + | 0.956846i | \(0.406147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.5039i | 0.778467i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.29742 | −0.222079 | −0.111040 | − | 0.993816i | \(-0.535418\pi\) | ||||
−0.111040 | + | 0.993816i | \(0.535418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7928 | 1.16309 | 0.581546 | − | 0.813514i | \(-0.302448\pi\) | ||||
0.581546 | + | 0.813514i | \(0.302448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.98603 | −0.208294 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −56.7534 | −2.36678 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18.7333i | − | 0.779879i | −0.920840 | − | 0.389940i | \(-0.872496\pi\) | ||
0.920840 | − | 0.389940i | \(-0.127504\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 6.98603i | − | 0.290329i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.11580 | 0.253726 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.63964i | 0.109323i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.40767 | + | 11.3742i | 0.223580 | + | 0.470264i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.93721i | 0.368878i | 0.982844 | + | 0.184439i | \(0.0590469\pi\) | ||||
−0.982844 | + | 0.184439i | \(0.940953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.27236 | 0.0936308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 21.8044i | − | 0.896913i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9655i | 0.450298i | 0.974324 | + | 0.225149i | \(0.0722869\pi\) | ||||
−0.974324 | + | 0.225149i | \(0.927713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.7874 | 1.01618 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.622783 | −0.0254888 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.2663 | −1.31836 | −0.659182 | − | 0.751983i | \(-0.729097\pi\) | ||||
−0.659182 | + | 0.751983i | \(0.729097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2999 | −0.787260 | −0.393630 | − | 0.919269i | \(-0.628781\pi\) | ||||
−0.393630 | + | 0.919269i | \(0.628781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 9.17858i | − | 0.373781i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 36.6716i | − | 1.49091i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.6632 | −1.28517 | −0.642584 | − | 0.766215i | \(-0.722138\pi\) | ||||
−0.642584 | + | 0.766215i | \(0.722138\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.29742i | 0.214662i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.46810 | − | 19.9147i | −0.383038 | − | 0.805661i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.23478i | − | 0.130652i | −0.997864 | − | 0.0653259i | \(-0.979191\pi\) | ||
0.997864 | − | 0.0653259i | \(-0.0208087\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.2329 | −1.66267 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1365i | 0.448339i | 0.974550 | + | 0.224169i | \(0.0719669\pi\) | ||||
−0.974550 | + | 0.224169i | \(0.928033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.82643i | 0.274377i | 0.990545 | + | 0.137189i | \(0.0438067\pi\) | ||||
−0.990545 | + | 0.137189i | \(0.956193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.88116 | 0.316260 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.1018 | 0.444785 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.14929 | −0.365972 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.220505 | −0.00880611 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 10.0501i | − | 0.400725i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.9689i | − | 0.755138i | −0.925981 | − | 0.377569i | \(-0.876760\pi\) | ||
0.925981 | − | 0.377569i | \(-0.123240\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.3547 | −0.650039 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 49.9599i | − | 1.98260i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.25627 | − | 1.54814i | 0.129018 | − | 0.0613395i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.708126i | 0.0280130i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.45413 | −0.333918 | −0.166959 | − | 0.985964i | \(-0.553395\pi\) | ||||
−0.166959 | + | 0.985964i | \(0.553395\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 37.4102i | − | 1.47531i | −0.675176 | − | 0.737657i | \(-0.735932\pi\) | ||
0.675176 | − | 0.737657i | \(-0.264068\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 11.5179i | − | 0.453518i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2627 | 0.678668 | 0.339334 | − | 0.940666i | \(-0.389798\pi\) | ||||
0.339334 | + | 0.940666i | \(0.389798\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.55476 | −0.0610296 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.29742 | −0.286008 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.2456 | 1.06620 | 0.533101 | − | 0.846052i | \(-0.321027\pi\) | ||||
0.533101 | + | 0.846052i | \(0.321027\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.3213i | 1.69270i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.21511i | − | 0.203461i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0458 | 1.40414 | 0.702072 | − | 0.712106i | \(-0.252258\pi\) | ||||
0.702072 | + | 0.712106i | \(0.252258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.3626i | 0.986489i | 0.869891 | + | 0.493245i | \(0.164189\pi\) | ||||
−0.869891 | + | 0.493245i | \(0.835811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.1074 | + | 10.9860i | −0.897416 | + | 0.426662i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.08770i | − | 0.0421790i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.7498 | 1.61656 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 8.71367i | − | 0.336890i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.77919i | − | 0.0686849i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.7355 | −1.57024 | −0.785120 | − | 0.619344i | \(-0.787399\pi\) | ||||
−0.785120 | + | 0.619344i | \(0.787399\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.20114 | −0.277172 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.7333 | −1.48864 | −0.744322 | − | 0.667821i | \(-0.767227\pi\) | ||||
−0.744322 | + | 0.667821i | \(0.767227\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.79886 | −0.299293 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.9440i | − | 0.496013i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 32.0682i | − | 1.22705i | −0.789673 | − | 0.613527i | \(-0.789750\pi\) | ||
0.789673 | − | 0.613527i | \(-0.210250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5046 | −0.745234 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.6521i | 0.749774i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.1382 | − | 5.77091i | 0.462429 | − | 0.219854i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.4259i | 0.548786i | 0.961618 | + | 0.274393i | \(0.0884769\pi\) | ||||
−0.961618 | + | 0.274393i | \(0.911523\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.708126 | 0.0268995 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.33210i | − | 0.202258i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 83.7673i | − | 3.17291i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.72764 | 0.140992 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.0490 | 0.417314 | 0.208657 | − | 0.977989i | \(-0.433091\pi\) | ||||
0.208657 | + | 0.977989i | \(0.433091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.441009 | −0.0166330 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.3626 | 0.804560 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.6911i | 0.665343i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 19.8293i | − | 0.744706i | −0.928091 | − | 0.372353i | \(-0.878551\pi\) | ||
0.928091 | − | 0.372353i | \(-0.121449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.78489 | 0.104441 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 57.5122i | 2.15385i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.05436 | − | 3.82931i | 0.301216 | − | 0.143208i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.86165i | − | 0.330944i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.21261 | 0.119810 | 0.0599050 | − | 0.998204i | \(-0.480920\pi\) | ||||
0.0599050 | + | 0.998204i | \(0.480920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 5.52651i | − | 0.205818i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0025i | 0.371997i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −38.1474 | −1.41676 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.3493 | 0.495097 | 0.247548 | − | 0.968876i | \(-0.420375\pi\) | ||||
0.247548 | + | 0.968876i | \(0.420375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.3994 | 0.865458 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17.4185i | − | 0.643365i | −0.946848 | − | 0.321683i | \(-0.895752\pi\) | ||
0.946848 | − | 0.321683i | \(-0.104248\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.49301i | 0.128842i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.49960 | −0.239416 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.80137i | 0.0662643i | 0.999451 | + | 0.0331322i | \(0.0105482\pi\) | ||||
−0.999451 | + | 0.0331322i | \(0.989452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.482078 | + | 1.01397i | 0.0177096 | + | 0.0372493i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.86484i | 0.141787i | 0.997484 | + | 0.0708936i | \(0.0225851\pi\) | ||||
−0.997484 | + | 0.0708936i | \(0.977415\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.1074 | 2.01898 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.11580i | − | 0.223765i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.1786i | − | 0.700770i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.8923 | −1.09078 | −0.545392 | − | 0.838181i | \(-0.683619\pi\) | ||||
−0.545392 | + | 0.838181i | \(0.683619\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.24557 | −0.336927 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.8660 | −0.868574 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.8933 | −1.41360 | −0.706800 | − | 0.707413i | \(-0.749862\pi\) | ||||
−0.706800 | + | 0.707413i | \(0.749862\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.58086i | − | 0.202572i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.33630i | − | 0.302191i | −0.988519 | − | 0.151095i | \(-0.951720\pi\) | ||
0.988519 | − | 0.151095i | \(-0.0482800\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.20653 | 0.116084 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 24.7874i | − | 0.896190i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.39909 | + | 7.14944i | 0.122734 | + | 0.258151i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.0811i | − | 0.615962i | −0.951393 | − | 0.307981i | \(-0.900347\pi\) | ||
0.951393 | − | 0.307981i | \(-0.0996533\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.5516 | −0.524062 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.0532i | 0.577392i | 0.957421 | + | 0.288696i | \(0.0932217\pi\) | ||||
−0.957421 | + | 0.288696i | \(0.906778\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 52.5497i | − | 1.88764i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.41625 | 0.0508078 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.67579 | −0.131699 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.501443 | 0.0179430 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.29742 | 0.189314 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.5888i | 1.52006i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5654i | 0.626140i | 0.949730 | + | 0.313070i | \(0.101357\pi\) | ||||
−0.949730 | + | 0.313070i | \(0.898643\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.7137 | 0.523821 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.29742i | − | 0.188354i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.18147 | + | 3.88975i | −0.290532 | + | 0.138129i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.0207i | 0.461797i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.0934 | −0.924275 | −0.462138 | − | 0.886808i | \(-0.652917\pi\) | ||||
−0.462138 | + | 0.886808i | \(0.652917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.3994i | 1.53536i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 11.1018i | − | 0.392264i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.69296 | −0.130322 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.5290 | 0.970270 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0433 | −0.423943 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.30030 | −0.221507 | −0.110753 | − | 0.993848i | \(-0.535326\pi\) | ||||
−0.110753 | + | 0.993848i | \(0.535326\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.16749i | 0.0409963i | 0.999790 | + | 0.0204981i | \(0.00652522\pi\) | ||||
−0.999790 | + | 0.0204981i | \(0.993475\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.38830i | 0.259119i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.0665 | −1.22833 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.02679i | − | 0.0359228i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.54814 | − | 3.25627i | −0.0540964 | − | 0.113783i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.9518i | 0.626524i | 0.949667 | + | 0.313262i | \(0.101422\pi\) | ||||
−0.949667 | + | 0.313262i | \(0.898578\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.66501 | 0.197470 | 0.0987349 | − | 0.995114i | \(-0.468520\pi\) | ||||
0.0987349 | + | 0.995114i | \(0.468520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.09932i | 0.177535i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.6942i | 0.406646i | 0.979112 | + | 0.203323i | \(0.0651741\pi\) | ||||
−0.979112 | + | 0.203323i | \(0.934826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.8024 | −1.06981 | −0.534906 | − | 0.844912i | \(-0.679653\pi\) | ||||
−0.534906 | + | 0.844912i | \(0.679653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.6997 | 0.475237 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.09628 | −0.245871 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 86.3146 | 2.98704 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.29742i | 0.252236i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 8.80760i | − | 0.304072i | −0.988375 | − | 0.152036i | \(-0.951417\pi\) | ||
0.988375 | − | 0.152036i | \(-0.0485830\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.937367 | −0.0323230 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.62582i | 0.159322i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.2176 | − | 28.6655i | −1.21152 | − | 0.986124i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.4986i | 0.360735i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.9721 | −0.616799 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 11.1617i | − | 0.382619i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.4109i | 0.493419i | 0.969090 | + | 0.246709i | \(0.0793493\pi\) | ||||
−0.969090 | + | 0.246709i | \(0.920651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.08770 | −0.0371984 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.9646 | −0.989413 | −0.494706 | − | 0.869060i | \(-0.664724\pi\) | ||||
−0.494706 | + | 0.869060i | \(0.664724\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.67291 | −0.227677 | −0.113838 | − | 0.993499i | \(-0.536315\pi\) | ||||
−0.113838 | + | 0.993499i | \(0.536315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.8044 | 0.402293 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.7300i | 0.637577i | 0.947826 | + | 0.318788i | \(0.103276\pi\) | ||||
−0.947826 | + | 0.318788i | \(0.896724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 36.5841i | − | 1.24390i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.3572 | 1.13287 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.97205i | − | 0.0668973i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.2097 | + | 29.8879i | 0.481478 | + | 1.01271i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.79886i | 0.263951i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.68861 | −0.259922 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.3743i | 1.56595i | 0.622053 | + | 0.782975i | \(0.286299\pi\) | ||||
−0.622053 | + | 0.782975i | \(0.713701\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 6.87023i | − | 0.231727i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0963 | 1.04766 | 0.523830 | − | 0.851823i | \(-0.324503\pi\) | ||||
0.523830 | + | 0.851823i | \(0.324503\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.9119 | −1.07392 | −0.536961 | − | 0.843607i | \(-0.680428\pi\) | ||||
−0.536961 | + | 0.843607i | \(0.680428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.66924 | −0.257799 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.43023 | −0.215906 | −0.107953 | − | 0.994156i | \(-0.534430\pi\) | ||||
−0.107953 | + | 0.994156i | \(0.534430\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3028i | 0.479701i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 0.708126i | − | 0.0237231i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.90441 | 0.0637286 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.3257i | 1.31451i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.6632 | + | 12.2011i | −0.856868 | + | 0.407384i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.6575i | 1.28930i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.4524 | −0.881257 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.29742i | 0.109731i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.0219i | 0.997961i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.7541 | −1.32001 | −0.660006 | − | 0.751260i | \(-0.729446\pi\) | ||||
−0.660006 | + | 0.751260i | \(0.729446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.6911 | 0.586777 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.4652 | 0.678043 | 0.339021 | − | 0.940779i | \(-0.389904\pi\) | ||||
0.339021 | + | 0.940779i | \(0.389904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.33076 | −0.143327 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 8.77630i | − | 0.290136i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 12.4023i | − | 0.409559i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.2749 | −1.32855 | −0.664273 | − | 0.747490i | \(-0.731259\pi\) | ||||
−0.664273 | + | 0.747490i | \(0.731259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 11.9202i | − | 0.392784i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.09628 | − | 2.30585i | −0.0360844 | − | 0.0758979i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1986i | 0.335329i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.52651 | −0.181514 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 4.19124i | − | 0.137510i | −0.997634 | − | 0.0687551i | \(-0.978097\pi\) | ||
0.997634 | − | 0.0687551i | \(-0.0219027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.311392i | 0.0102055i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.7874 | 0.811503 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.5526 | −0.574032 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8446 | 0.778970 | 0.389485 | − | 0.921033i | \(-0.372653\pi\) | ||||
0.389485 | + | 0.921033i | \(0.372653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.73304 | −0.219724 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.24456i | 0.170968i | 0.996340 | + | 0.0854839i | \(0.0272436\pi\) | ||||
−0.996340 | + | 0.0854839i | \(0.972756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 93.0325i | − | 3.02955i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.49301 | 0.113628 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 10.4486i | − | 0.339533i | −0.985484 | − | 0.169767i | \(-0.945699\pi\) | ||
0.985484 | − | 0.169767i | \(-0.0543014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.07372 | + | 16.9818i | 0.262084 | + | 0.551252i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 19.1537i | − | 0.621100i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.4169 | −1.27684 | −0.638420 | − | 0.769689i | \(-0.720411\pi\) | ||||
−0.638420 | + | 0.769689i | \(0.720411\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.4163i | 0.563577i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.75124i | − | 0.121260i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.58390 | 0.180314 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2523 | −0.717816 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.1786 | −0.618021 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.4023 | −0.785537 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 20.5558i | − | 0.661030i | −0.943801 | − | 0.330515i | \(-0.892778\pi\) | ||
0.943801 | − | 0.330515i | \(-0.107222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 2.20972i | − | 0.0709865i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.8325 | −0.732730 | −0.366365 | − | 0.930471i | \(-0.619398\pi\) | ||||
−0.366365 | + | 0.930471i | \(0.619398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52651i | 0.0489375i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.4488 | − | 11.1484i | 0.750963 | − | 0.357033i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.49417i | 0.0797957i | 0.999204 | + | 0.0398978i | \(0.0127032\pi\) | ||||
−0.999204 | + | 0.0398978i | \(0.987297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.86149 | −0.251254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3.20653i | − | 0.102377i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 9.95119i | − | 0.317394i | −0.987327 | − | 0.158697i | \(-0.949271\pi\) | ||
0.987327 | − | 0.158697i | \(-0.0507292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.1631 | −2.42676 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.11580 | −0.194668 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.9875 | 0.826354 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.08096 | 0.0343378 | 0.0171689 | − | 0.999853i | \(-0.494535\pi\) | ||||
0.0171689 | + | 0.999853i | \(0.494535\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.5247i | 0.746532i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.17539i | 0.0689645i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.3129 | −0.801666 | −0.400833 | − | 0.916151i | \(-0.631279\pi\) | ||||
−0.400833 | + | 0.916151i | \(0.631279\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.41625i | − | 0.0448083i |
(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 | 4368.2.h.q.337.2 | 8 | ||
4.3 | odd | 2 | 273.2.c.c.64.2 | ✓ | 8 | ||
12.11 | even | 2 | 819.2.c.d.64.7 | 8 | |||
13.12 | even | 2 | inner | 4368.2.h.q.337.7 | 8 | ||
28.27 | even | 2 | 1911.2.c.l.883.2 | 8 | |||
52.31 | even | 4 | 3549.2.a.v.1.1 | 4 | |||
52.47 | even | 4 | 3549.2.a.x.1.4 | 4 | |||
52.51 | odd | 2 | 273.2.c.c.64.7 | yes | 8 | ||
156.155 | even | 2 | 819.2.c.d.64.2 | 8 | |||
364.363 | even | 2 | 1911.2.c.l.883.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.c.c.64.2 | ✓ | 8 | 4.3 | odd | 2 | ||
273.2.c.c.64.7 | yes | 8 | 52.51 | odd | 2 | ||
819.2.c.d.64.2 | 8 | 156.155 | even | 2 | |||
819.2.c.d.64.7 | 8 | 12.11 | even | 2 | |||
1911.2.c.l.883.2 | 8 | 28.27 | even | 2 | |||
1911.2.c.l.883.7 | 8 | 364.363 | even | 2 | |||
3549.2.a.v.1.1 | 4 | 52.31 | even | 4 | |||
3549.2.a.x.1.4 | 4 | 52.47 | even | 4 | |||
4368.2.h.q.337.2 | 8 | 1.1 | even | 1 | trivial | ||
4368.2.h.q.337.7 | 8 | 13.12 | even | 2 | inner |