Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 729.16 | ||
Character | \(\chi\) | \(=\) | 1148.729 |
Dual form | 1148.2.k.b.337.16 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71130 | − | 1.71130i | 0.988022 | − | 0.988022i | −0.0119072 | − | 0.999929i | \(-0.503790\pi\) |
0.999929 | + | 0.0119072i | \(0.00379027\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.46933i | 1.10432i | 0.833738 | + | 0.552160i | \(0.186196\pi\) | ||||
−0.833738 | + | 0.552160i | \(0.813804\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.85712i | − | 0.952375i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.89109 | + | 3.89109i | −1.17321 | + | 1.17321i | −0.191768 | + | 0.981440i | \(0.561422\pi\) |
−0.981440 | + | 0.191768i | \(0.938578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.36139 | + | 2.36139i | −0.654932 | + | 0.654932i | −0.954176 | − | 0.299245i | \(-0.903265\pi\) |
0.299245 | + | 0.954176i | \(0.403265\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.22578 | + | 4.22578i | 1.09109 | + | 1.09109i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41870 | + | 1.41870i | 0.344085 | + | 0.344085i | 0.857901 | − | 0.513816i | \(-0.171769\pi\) |
−0.513816 | + | 0.857901i | \(0.671769\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.77167 | + | 2.77167i | 0.635864 | + | 0.635864i | 0.949533 | − | 0.313668i | \(-0.101558\pi\) |
−0.313668 | + | 0.949533i | \(0.601558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.42015i | 0.528120i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.33212 | −1.32034 | −0.660169 | − | 0.751117i | \(-0.729516\pi\) | ||||
−0.660169 | + | 0.751117i | \(0.729516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.09761 | −0.219522 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.244504 | + | 0.244504i | 0.0470549 | + | 0.0470549i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.38204 | + | 1.38204i | −0.256638 | + | 0.256638i | −0.823685 | − | 0.567047i | \(-0.808086\pi\) |
0.567047 | + | 0.823685i | \(0.308086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.75810 | 1.21379 | 0.606895 | − | 0.794782i | \(-0.292415\pi\) | ||||
0.606895 | + | 0.794782i | \(0.292415\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.3177i | 2.31831i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.74608 | − | 1.74608i | −0.295142 | − | 0.295142i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.731303 | 0.120225 | 0.0601127 | − | 0.998192i | \(-0.480854\pi\) | ||||
0.0601127 | + | 0.998192i | \(0.480854\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.08211i | 1.29417i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.55889 | − | 4.49628i | 0.711980 | − | 0.702200i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.12884i | 1.08714i | 0.839365 | + | 0.543569i | \(0.182927\pi\) | ||||
−0.839365 | + | 0.543569i | \(0.817073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.05519 | 1.05173 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.61063 | − | 5.61063i | −0.818395 | − | 0.818395i | 0.167480 | − | 0.985875i | \(-0.446437\pi\) |
−0.985875 | + | 0.167480i | \(0.946437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.85565 | 0.679927 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.60712 | − | 4.60712i | 0.632836 | − | 0.632836i | −0.315942 | − | 0.948778i | \(-0.602321\pi\) |
0.948778 | + | 0.315942i | \(0.102321\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.60841 | − | 9.60841i | −1.29560 | − | 1.29560i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.48634 | 1.25650 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.1934 | −1.32707 | −0.663533 | − | 0.748147i | \(-0.730944\pi\) | ||||
−0.663533 | + | 0.748147i | \(0.730944\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.57500i | 1.22595i | 0.790101 | + | 0.612976i | \(0.210028\pi\) | ||||
−0.790101 | + | 0.612976i | \(0.789972\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.02029 | + | 2.02029i | 0.254533 | + | 0.254533i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.83106 | − | 5.83106i | −0.723254 | − | 0.723254i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.13423 | − | 3.13423i | −0.382908 | − | 0.382908i | 0.489241 | − | 0.872149i | \(-0.337274\pi\) |
−0.872149 | + | 0.489241i | \(0.837274\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.8362 | + | 10.8362i | −1.30452 | + | 1.30452i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.44329 | + | 2.44329i | −0.289966 | + | 0.289966i | −0.837067 | − | 0.547101i | \(-0.815731\pi\) |
0.547101 | + | 0.837067i | \(0.315731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.6735i | − | 1.60036i | −0.599759 | − | 0.800181i | \(-0.704737\pi\) | ||
0.599759 | − | 0.800181i | \(-0.295263\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.87834 | + | 1.87834i | −0.216893 | + | 0.216893i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.50284i | − | 0.627106i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.22940 | + | 1.22940i | −0.138318 | + | 0.138318i | −0.772876 | − | 0.634558i | \(-0.781182\pi\) |
0.634558 | + | 0.772876i | \(0.281182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.40821 | 1.04536 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.98865 | 0.767104 | 0.383552 | − | 0.923519i | \(-0.374701\pi\) | ||||
0.383552 | + | 0.923519i | \(0.374701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.50324 | + | 3.50324i | −0.379980 | + | 0.379980i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.73018i | 0.507129i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.5345 | − | 11.5345i | 1.22266 | − | 1.22266i | 0.255975 | − | 0.966683i | \(-0.417603\pi\) |
0.966683 | − | 0.255975i | \(-0.0823965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.33951i | − | 0.350076i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.5652 | − | 11.5652i | 1.19925 | − | 1.19925i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.84417 | + | 6.84417i | −0.702197 | + | 0.702197i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0829 | + | 11.0829i | 1.12530 | + | 1.12530i | 0.990932 | + | 0.134365i | \(0.0428996\pi\) |
0.134365 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.1173 | + | 11.1173i | 1.11733 | + | 1.11733i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.96559 | − | 2.96559i | −0.295087 | − | 0.295087i | 0.543999 | − | 0.839086i | \(-0.316910\pi\) |
−0.839086 | + | 0.543999i | \(0.816910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0539i | 1.08918i | 0.838704 | + | 0.544588i | \(0.183314\pi\) | ||||
−0.838704 | + | 0.544588i | \(0.816686\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.97616 | −0.583213 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.31574 | −0.417218 | −0.208609 | − | 0.977999i | \(-0.566894\pi\) | ||||
−0.208609 | + | 0.977999i | \(0.566894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.24007 | + | 8.24007i | 0.789256 | + | 0.789256i | 0.981372 | − | 0.192116i | \(-0.0615350\pi\) |
−0.192116 | + | 0.981372i | \(0.561535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.25148 | − | 1.25148i | 0.118785 | − | 0.118785i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0370 | 1.32049 | 0.660246 | − | 0.751049i | \(-0.270452\pi\) | ||||
0.660246 | + | 0.751049i | \(0.270452\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 15.6361i | − | 1.45808i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.74678 | + | 6.74678i | 0.623740 | + | 0.623740i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00634 | −0.183921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 19.2812i | − | 1.75284i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.107159 | − | 15.4961i | 0.00966217 | − | 1.39724i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.63630i | 0.861897i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.91790 | −0.347657 | −0.173829 | − | 0.984776i | \(-0.555614\pi\) | ||||
−0.173829 | + | 0.984776i | \(0.555614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.1996 | + | 12.1996i | 1.07412 | + | 1.07412i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.98844i | − | 0.261102i | −0.991442 | − | 0.130551i | \(-0.958325\pi\) | ||
0.991442 | − | 0.130551i | \(-0.0416746\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.91973 | −0.339884 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.603763 | + | 0.603763i | −0.0519637 | + | 0.0519637i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.46592 | − | 6.46592i | −0.552421 | − | 0.552421i | 0.374718 | − | 0.927139i | \(-0.377740\pi\) |
−0.927139 | + | 0.374718i | \(0.877740\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.71747 | 0.824225 | 0.412113 | − | 0.911133i | \(-0.364791\pi\) | ||||
0.412113 | + | 0.911133i | \(0.364791\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.2030 | −1.61718 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 18.3768i | − | 1.53674i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.41272 | − | 3.41272i | −0.283411 | − | 0.283411i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.71130 | − | 1.71130i | −0.141146 | − | 0.141146i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.19072 | − | 3.19072i | −0.261394 | − | 0.261394i | 0.564226 | − | 0.825620i | \(-0.309175\pi\) |
−0.825620 | + | 0.564226i | \(0.809175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8972 | − | 14.8972i | 1.21232 | − | 1.21232i | 0.242054 | − | 0.970263i | \(-0.422179\pi\) |
0.970263 | − | 0.242054i | \(-0.0778212\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.05340 | − | 4.05340i | 0.327698 | − | 0.327698i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.6880i | 1.34041i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.35695 | + | 7.35695i | −0.587149 | + | 0.587149i | −0.936858 | − | 0.349710i | \(-0.886280\pi\) |
0.349710 | + | 0.936858i | \(0.386280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 15.7684i | − | 1.25051i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.47749 | − | 4.47749i | 0.352875 | − | 0.352875i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.828390 | 0.0648845 | 0.0324422 | − | 0.999474i | \(-0.489671\pi\) | ||||
0.0324422 | + | 0.999474i | \(0.489671\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −32.8858 | −2.56016 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3713 | + | 11.3713i | −0.879941 | + | 0.879941i | −0.993528 | − | 0.113587i | \(-0.963766\pi\) |
0.113587 | + | 0.993528i | \(0.463766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.84768i | 0.142129i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.91900 | − | 7.91900i | 0.605581 | − | 0.605581i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.39269i | 0.638085i | 0.947740 | + | 0.319042i | \(0.103361\pi\) | ||||
−0.947740 | + | 0.319042i | \(0.896639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.776127 | − | 0.776127i | 0.0586697 | − | 0.0586697i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.4440 | + | 17.4440i | −1.31117 | + | 1.31117i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.4721 | − | 11.4721i | −0.857467 | − | 0.857467i | 0.133572 | − | 0.991039i | \(-0.457355\pi\) |
−0.991039 | + | 0.133572i | \(0.957355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.07525 | + | 4.07525i | 0.302911 | + | 0.302911i | 0.842152 | − | 0.539241i | \(-0.181289\pi\) |
−0.539241 | + | 0.842152i | \(0.681289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.3857 | + | 16.3857i | 1.21127 | + | 1.21127i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.80583i | 0.132767i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0406 | −0.807366 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.345782 | −0.0251519 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.19834 | + | 9.19834i | 0.665568 | + | 0.665568i | 0.956687 | − | 0.291119i | \(-0.0940274\pi\) |
−0.291119 | + | 0.956687i | \(0.594027\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0353 | − | 10.0353i | 0.722359 | − | 0.722359i | −0.246727 | − | 0.969085i | \(-0.579355\pi\) |
0.969085 | + | 0.246727i | \(0.0793550\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.9574 | −1.42918 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.58657i | 0.469274i | 0.972083 | + | 0.234637i | \(0.0753901\pi\) | ||||
−0.972083 | + | 0.234637i | \(0.924610\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.494452 | + | 0.494452i | 0.0350508 | + | 0.0350508i | 0.724415 | − | 0.689364i | \(-0.242110\pi\) |
−0.689364 | + | 0.724415i | \(0.742110\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.7273 | −0.756642 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.95450i | − | 0.137179i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1028 | + | 11.2574i | 0.775454 | + | 0.786253i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.0917i | 1.25746i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.5696 | −1.49200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2804 | + | 17.2804i | 1.18963 | + | 1.18963i | 0.977169 | + | 0.212462i | \(0.0681482\pi\) |
0.212462 | + | 0.977169i | \(0.431852\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.36244i | 0.572985i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.6035 | −1.20055 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.77869 | + | 4.77869i | −0.324399 | + | 0.324399i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.3995 | − | 23.3995i | −1.58119 | − | 1.58119i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.70020 | −0.450704 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.6275 | −1.31436 | −0.657178 | − | 0.753736i | \(-0.728250\pi\) | ||||
−0.657178 | + | 0.753736i | \(0.728250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.13601i | 0.209067i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.16148 | + | 5.16148i | 0.342579 | + | 0.342579i | 0.857336 | − | 0.514757i | \(-0.172118\pi\) |
−0.514757 | + | 0.857336i | \(0.672118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8018 | − | 15.8018i | −1.04421 | − | 1.04421i | −0.998976 | − | 0.0452363i | \(-0.985596\pi\) |
−0.0452363 | − | 0.998976i | \(-0.514404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.41703 | − | 9.41703i | −0.619595 | − | 0.619595i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.81829 | + | 9.81829i | −0.643218 | + | 0.643218i | −0.951345 | − | 0.308128i | \(-0.900298\pi\) |
0.308128 | + | 0.951345i | \(0.400298\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8545 | − | 13.8545i | 0.903770 | − | 0.903770i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.20774i | 0.273322i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0642 | − | 14.0642i | 0.909736 | − | 0.909736i | −0.0865143 | − | 0.996251i | \(-0.527573\pi\) |
0.996251 | + | 0.0865143i | \(0.0275728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.6985i | 1.39773i | 0.715256 | + | 0.698863i | \(0.246310\pi\) | ||||
−0.715256 | + | 0.698863i | \(0.753690\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3668 | − | 15.3668i | 0.985781 | − | 0.985781i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.46933 | 0.157760 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.0900 | −0.832895 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.9597 | − | 11.9597i | 0.757916 | − | 0.757916i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 28.9086i | − | 1.82470i | −0.409416 | − | 0.912348i | \(-0.634267\pi\) | ||
0.409416 | − | 0.912348i | \(-0.365733\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6389 | − | 24.6389i | 1.54903 | − | 1.54903i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.9902i | 0.750856i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.7345 | + | 17.7345i | −1.10625 | + | 1.10625i | −0.112611 | + | 0.993639i | \(0.535921\pi\) |
−0.993639 | + | 0.112611i | \(0.964079\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.517109 | + | 0.517109i | −0.0321316 | + | 0.0321316i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.94866 | + | 3.94866i | 0.244416 | + | 0.244416i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.62764 | − | 5.62764i | −0.347015 | − | 0.347015i | 0.511981 | − | 0.858997i | \(-0.328912\pi\) |
−0.858997 | + | 0.511981i | \(0.828912\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.3765 | + | 11.3765i | 0.698853 | + | 0.698853i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 39.4782i | − | 2.41603i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.20242 | −0.561082 | −0.280541 | − | 0.959842i | \(-0.590514\pi\) | ||||
−0.280541 | + | 0.959842i | \(0.590514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.97809 | 0.302398 | 0.151199 | − | 0.988503i | \(-0.451687\pi\) | ||||
0.151199 | + | 0.988503i | \(0.451687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.71492 | − | 5.71492i | −0.345882 | − | 0.345882i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.27090 | − | 4.27090i | 0.257545 | − | 0.257545i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.8880 | 0.774366 | 0.387183 | − | 0.922003i | \(-0.373448\pi\) | ||||
0.387183 | + | 0.922003i | \(0.373448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 19.3087i | − | 1.15598i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.70012 | + | 7.70012i | 0.459351 | + | 0.459351i | 0.898442 | − | 0.439091i | \(-0.144700\pi\) |
−0.439091 | + | 0.898442i | \(0.644700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4347 | −0.739166 | −0.369583 | − | 0.929198i | \(-0.620499\pi\) | ||||
−0.369583 | + | 0.929198i | \(0.620499\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.4249i | 1.38757i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0442777 | + | 6.40297i | −0.00261363 | + | 0.377955i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 12.9746i | − | 0.763211i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.9324 | 2.22364 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.813768 | − | 0.813768i | −0.0475409 | − | 0.0475409i | 0.682937 | − | 0.730478i | \(-0.260702\pi\) |
−0.730478 | + | 0.682937i | \(0.760702\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 25.1709i | − | 1.46551i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.90278 | −0.110410 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.9526 | − | 14.9526i | 0.864732 | − | 0.864732i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.04085 | − | 5.04085i | −0.290550 | − | 0.290550i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1501 | −0.583105 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.6439 | −1.35384 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.9471i | − | 1.70917i | −0.519310 | − | 0.854586i | \(-0.673811\pi\) | ||
0.519310 | − | 0.854586i | \(-0.326189\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.9166 | + | 18.9166i | 1.07613 | + | 1.07613i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.623845 | + | 0.623845i | 0.0353750 | + | 0.0353750i | 0.724573 | − | 0.689198i | \(-0.242037\pi\) |
−0.689198 | + | 0.724573i | \(0.742037\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9142 | − | 16.9142i | −0.956046 | − | 0.956046i | 0.0430274 | − | 0.999074i | \(-0.486300\pi\) |
−0.999074 | + | 0.0430274i | \(0.986300\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.98877 | + | 4.98877i | −0.281086 | + | 0.281086i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.1934 | − | 13.1934i | 0.741016 | − | 0.741016i | −0.231757 | − | 0.972774i | \(-0.574448\pi\) |
0.972774 | + | 0.231757i | \(0.0744475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.7553i | − | 0.602181i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.38555 | + | 7.38555i | −0.412221 | + | 0.412221i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.86432i | 0.437582i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.59188 | − | 2.59188i | 0.143772 | − | 0.143772i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.2025 | 1.55960 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.93464 | 0.437451 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.16080 | + | 1.16080i | −0.0638035 | + | 0.0638035i | −0.738289 | − | 0.674485i | \(-0.764366\pi\) |
0.674485 | + | 0.738289i | \(0.264366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.08942i | − | 0.114500i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.73947 | − | 7.73947i | 0.422852 | − | 0.422852i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2758i | 0.668703i | 0.942448 | + | 0.334352i | \(0.108517\pi\) | ||||
−0.942448 | + | 0.334352i | \(0.891483\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.0216 | − | 24.0216i | 1.30468 | − | 1.30468i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.2964 | + | 26.2964i | −1.42403 | + | 1.42403i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.7582 | − | 26.7582i | −1.44061 | − | 1.44061i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.90649 | + | 4.90649i | 0.263394 | + | 0.263394i | 0.826432 | − | 0.563037i | \(-0.190367\pi\) |
−0.563037 | + | 0.826432i | \(0.690367\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.8998i | − | 0.797567i | −0.917045 | − | 0.398784i | \(-0.869432\pi\) | ||
0.917045 | − | 0.398784i | \(-0.130568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.15474 | −0.0616355 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.5527 | 1.73260 | 0.866302 | − | 0.499521i | \(-0.166491\pi\) | ||||
0.866302 | + | 0.499521i | \(0.166491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.03331 | − | 6.03331i | −0.320215 | − | 0.320215i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.43346 | + | 3.43346i | −0.181718 | + | 0.181718i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.4786 | −1.18638 | −0.593188 | − | 0.805064i | \(-0.702131\pi\) | ||||
−0.593188 | + | 0.805064i | \(0.702131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 3.63571i | − | 0.191353i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.9960 | − | 32.9960i | −1.73184 | − | 1.73184i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.7644 | 1.76731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.8441i | 1.08805i | 0.839068 | + | 0.544026i | \(0.183101\pi\) | ||||
−0.839068 | + | 0.544026i | \(0.816899\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.8464 | − | 13.0253i | −0.668758 | − | 0.678071i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.51545i | 0.338265i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.3888 | 1.62525 | 0.812626 | − | 0.582786i | \(-0.198037\pi\) | ||||
0.812626 | + | 0.582786i | \(0.198037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.4906 | + | 16.4906i | 0.851573 | + | 0.851573i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.52707i | − | 0.336161i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.34594 | 0.377335 | 0.188668 | − | 0.982041i | \(-0.439583\pi\) | ||||
0.188668 | + | 0.982041i | \(0.439583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.70471 | + | 6.70471i | −0.343493 | + | 0.343493i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.758270 | − | 0.758270i | −0.0387458 | − | 0.0387458i | 0.687468 | − | 0.726214i | \(-0.258722\pi\) |
−0.726214 | + | 0.687468i | \(0.758722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5883 | 0.692526 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.3680 | 1.03536 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.8495i | 1.96975i | 0.173274 | + | 0.984874i | \(0.444565\pi\) | ||||
−0.173274 | + | 0.984874i | \(0.555435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.98337 | − | 8.98337i | −0.454308 | − | 0.454308i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.11414 | − | 5.11414i | −0.257974 | − | 0.257974i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.03579 | − | 3.03579i | −0.152747 | − | 0.152747i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.931306 | + | 0.931306i | −0.0467409 | + | 0.0467409i | −0.730091 | − | 0.683350i | \(-0.760522\pi\) |
0.683350 | + | 0.730091i | \(0.260522\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.70785 | + | 6.70785i | −0.335813 | + | 0.335813i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.00028i | 0.249702i | 0.992175 | + | 0.124851i | \(0.0398453\pi\) | ||||
−0.992175 | + | 0.124851i | \(0.960155\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.9585 | + | 15.9585i | −0.794949 | + | 0.794949i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.2320i | 1.15441i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.84557 | + | 2.84557i | −0.141050 | + | 0.141050i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.2256 | 1.00009 | 0.500046 | − | 0.865999i | \(-0.333316\pi\) | ||||
0.500046 | + | 0.865999i | \(0.333316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.1303 | −1.09161 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.20782 | − | 7.20782i | 0.354673 | − | 0.354673i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2573i | 0.847128i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.6295 | − | 16.6295i | 0.814352 | − | 0.814352i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.6402i | − | 1.10605i | −0.833165 | − | 0.553024i | \(-0.813474\pi\) | ||
0.833165 | − | 0.553024i | \(-0.186526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.01713 | − | 1.01713i | 0.0495717 | − | 0.0495717i | −0.681886 | − | 0.731458i | \(-0.738840\pi\) |
0.731458 | + | 0.681886i | \(0.238840\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.0303 | + | 16.0303i | −0.779419 | + | 0.779419i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.55718 | − | 1.55718i | −0.0755342 | − | 0.0755342i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.77055 | − | 6.77055i | −0.327650 | − | 0.327650i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.4483 | − | 31.4483i | −1.51834 | − | 1.51834i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.1361i | 0.536408i | 0.963362 | + | 0.268204i | \(0.0864300\pi\) | ||||
−0.963362 | + | 0.268204i | \(0.913570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.4182 | 0.500668 | 0.250334 | − | 0.968160i | \(-0.419460\pi\) | ||||
0.250334 | + | 0.968160i | \(0.419460\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.6804 | −0.560032 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.5505 | − | 17.5505i | −0.839556 | − | 0.839556i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.3721 | − | 13.3721i | 0.638217 | − | 0.638217i | −0.311899 | − | 0.950115i | \(-0.600965\pi\) |
0.950115 | + | 0.311899i | \(0.100965\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.85712 | −0.136054 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.9456i | 1.89787i | 0.315467 | + | 0.948937i | \(0.397839\pi\) | ||||
−0.315467 | + | 0.948937i | \(0.602161\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.4826 | + | 28.4826i | 1.35021 | + | 1.35021i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.9206 | −0.516526 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 11.3177i | − | 0.534117i | −0.963680 | − | 0.267059i | \(-0.913948\pi\) | ||
0.963680 | − | 0.267059i | \(-0.0860517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.243653 | + | 35.2345i | −0.0114732 | + | 1.65913i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 50.9873i | − | 2.39559i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.24636 | 0.386596 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.162747 | + | 0.162747i | 0.00761300 | + | 0.00761300i | 0.710903 | − | 0.703290i | \(-0.248286\pi\) |
−0.703290 | + | 0.710903i | \(0.748286\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.693756i | 0.0323818i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.70236 | 0.265585 | 0.132793 | − | 0.991144i | \(-0.457606\pi\) | ||||
0.132793 | + | 0.991144i | \(0.457606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.84943 | − | 5.84943i | 0.271846 | − | 0.271846i | −0.557997 | − | 0.829843i | \(-0.688430\pi\) |
0.829843 | + | 0.557997i | \(0.188430\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28.5582 | + | 28.5582i | 1.32436 | + | 1.32436i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.2083 | 0.981402 | 0.490701 | − | 0.871328i | \(-0.336741\pi\) | ||||
0.490701 | + | 0.871328i | \(0.336741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.43248 | 0.204673 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.1800i | 1.16023i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.7390 | − | 27.7390i | −1.27544 | − | 1.27544i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.04221 | − | 3.04221i | −0.139586 | − | 0.139586i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.1631 | − | 13.1631i | −0.602697 | − | 0.602697i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.5963 | + | 29.5963i | −1.35229 | + | 1.35229i | −0.469196 | + | 0.883094i | \(0.655456\pi\) |
−0.883094 | + | 0.469196i | \(0.844544\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.72689 | + | 1.72689i | −0.0787395 | + | 0.0787395i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 15.3247i | − | 0.697297i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27.3674 | + | 27.3674i | −1.24269 | + | 1.24269i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.1422i | − | 0.550217i | −0.961413 | − | 0.275109i | \(-0.911286\pi\) | ||
0.961413 | − | 0.275109i | \(-0.0887138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.41763 | − | 1.41763i | 0.0641073 | − | 0.0641073i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.9160 | 1.12444 | 0.562222 | − | 0.826986i | \(-0.309947\pi\) | ||||
0.562222 | + | 0.826986i | \(0.309947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.92139 | −0.176611 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.4524 | + | 27.4524i | −1.23389 | + | 1.23389i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.45534i | − | 0.154993i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5105 | − | 17.5105i | 0.783877 | − | 0.783877i | −0.196606 | − | 0.980483i | \(-0.562992\pi\) |
0.980483 | + | 0.196606i | \(0.0629920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.9197i | 1.73880i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.02603 | − | 9.02603i | 0.402451 | − | 0.402451i | −0.476645 | − | 0.879096i | \(-0.658147\pi\) |
0.879096 | + | 0.476645i | \(0.158147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.32303 | − | 7.32303i | 0.325871 | − | 0.325871i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.16194 | + | 3.16194i | 0.140426 | + | 0.140426i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.1880 | − | 10.1880i | −0.451575 | − | 0.451575i | 0.444302 | − | 0.895877i | \(-0.353452\pi\) |
−0.895877 | + | 0.444302i | \(0.853452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.66862 | + | 9.66862i | 0.427715 | + | 0.427715i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.35537i | 0.0598411i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.2958 | −1.20280 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.6630 | 1.92030 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.3624 | + | 14.3624i | 0.630442 | + | 0.630442i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.30470 | + | 1.30470i | −0.0571600 | + | 0.0571600i | −0.735109 | − | 0.677949i | \(-0.762869\pi\) |
0.677949 | + | 0.735109i | \(0.262869\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.85916 | 0.343657 | 0.171828 | − | 0.985127i | \(-0.445033\pi\) | ||||
0.171828 | + | 0.985127i | \(0.445033\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.65638i | − | 0.115934i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.58769 | + | 9.58769i | 0.417647 | + | 0.417647i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0958 | 0.743295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.1238i | 1.26386i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.147866 | + | 21.3828i | −0.00640478 | + | 0.926191i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 10.6570i | − | 0.460743i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −39.2646 | −1.69439 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.89109 | + | 3.89109i | 0.167601 | + | 0.167601i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.0287i | − | 0.646134i | −0.946376 | − | 0.323067i | \(-0.895286\pi\) | ||
0.946376 | − | 0.323067i | \(-0.104714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.9480 | 0.598565 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.3475 | + | 20.3475i | −0.871591 | + | 0.871591i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9351 | − | 27.9351i | −1.19442 | − | 1.19442i | −0.975813 | − | 0.218608i | \(-0.929848\pi\) |
−0.218608 | − | 0.975813i | \(-0.570152\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.3570 | 1.16757 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.66111 | −0.326374 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.73863i | − | 0.0739340i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.09033 | + | 3.09033i | 0.131177 | + | 0.131177i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.05263 | + | 9.05263i | 0.383572 | + | 0.383572i | 0.872387 | − | 0.488815i | \(-0.162571\pi\) |
−0.488815 | + | 0.872387i | \(0.662571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.8340 | − | 16.8340i | −0.712001 | − | 0.712001i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.8938 | + | 18.8938i | −0.797696 | + | 0.797696i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.5537 | + | 23.5537i | −0.992671 | + | 0.992671i | −0.999973 | − | 0.00730207i | \(-0.997676\pi\) |
0.00730207 | + | 0.999973i | \(0.497676\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.6621i | 1.45825i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.65261 | + | 6.65261i | −0.279383 | + | 0.279383i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.9470i | 0.458924i | 0.973318 | + | 0.229462i | \(0.0736967\pi\) | ||||
−0.973318 | + | 0.229462i | \(0.926303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.3870 | + | 10.3870i | −0.434683 | + | 0.434683i | −0.890218 | − | 0.455535i | \(-0.849448\pi\) |
0.455535 | + | 0.890218i | \(0.349448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.4823 | 1.31519 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.95020 | 0.289843 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.6991 | + | 23.6991i | −0.986608 | + | 0.986608i | −0.999912 | − | 0.0133038i | \(-0.995765\pi\) |
0.0133038 | + | 0.999912i | \(0.495765\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 34.3470i | − | 1.42741i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.94172 | + | 4.94172i | −0.205017 | + | 0.205017i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.8534i | 1.48490i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.6601 | + | 16.6601i | −0.688809 | + | 0.688809i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.4013 | + | 31.4013i | −1.29607 | + | 1.29607i | −0.365106 | + | 0.930966i | \(0.618967\pi\) |
−0.930966 | + | 0.365106i | \(0.881033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.7312 | + | 18.7312i | 0.771806 | + | 0.771806i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.2716 | + | 11.2716i | 0.463653 | + | 0.463653i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.3528 | − | 30.3528i | −1.24644 | − | 1.24644i | −0.957280 | − | 0.289162i | \(-0.906623\pi\) |
−0.289162 | − | 0.957280i | \(-0.593377\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 4.95433i | − | 0.203108i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.69231 | 0.0692618 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.4104 | 1.40597 | 0.702985 | − | 0.711204i | \(-0.251850\pi\) | ||||
0.702985 | + | 0.711204i | \(0.251850\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0421 | + | 21.0421i | 0.858324 | + | 0.858324i | 0.991141 | − | 0.132816i | \(-0.0424021\pi\) |
−0.132816 | + | 0.991141i | \(0.542402\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.95489 | + | 8.95489i | −0.364671 | + | 0.364671i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 47.6117 | 1.93569 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.5145i | 0.832656i | 0.909214 | + | 0.416328i | \(0.136683\pi\) | ||||
−0.909214 | + | 0.416328i | \(0.863317\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.34474 | − | 3.34474i | −0.135536 | − | 0.135536i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.4978 | 1.07199 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.1384i | 0.974941i | 0.873140 | + | 0.487470i | \(0.162080\pi\) | ||||
−0.873140 | + | 0.487470i | \(0.837920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.2652 | + | 0.264611i | 1.54300 | + | 0.0106701i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.57610i | − | 0.385519i | −0.981246 | − | 0.192760i | \(-0.938256\pi\) | ||
0.981246 | − | 0.192760i | \(-0.0617438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.76769 | −0.111243 | −0.0556215 | − | 0.998452i | \(-0.517714\pi\) | ||||
−0.0556215 | + | 0.998452i | \(0.517714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.54823 | − | 1.54823i | −0.0621284 | − | 0.0621284i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.3123i | 0.653538i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.2833 | −1.17133 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −36.9122 | + | 36.9122i | −1.47413 | + | 1.47413i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.03750 | + | 1.03750i | 0.0413677 | + | 0.0413677i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.64602 | 0.344193 | 0.172096 | − | 0.985080i | \(-0.444946\pi\) | ||||
0.172096 | + | 0.985080i | \(0.444946\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 59.1440 | 2.35076 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 9.67460i | − | 0.383925i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.36139 | + | 2.36139i | 0.0935617 | + | 0.0935617i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.98079 | + | 6.98079i | 0.276156 | + | 0.276156i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.20348 | + | 2.20348i | 0.0870323 | + | 0.0870323i | 0.749283 | − | 0.662250i | \(-0.230398\pi\) |
−0.662250 | + | 0.749283i | \(0.730398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.6065 | + | 10.6065i | −0.418278 | + | 0.418278i | −0.884610 | − | 0.466332i | \(-0.845575\pi\) |
0.466332 | + | 0.884610i | \(0.345575\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.1249 | + | 30.1249i | −1.18617 | + | 1.18617i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 40.9173i | − | 1.60863i | −0.594206 | − | 0.804313i | \(-0.702534\pi\) | ||
0.594206 | − | 0.804313i | \(-0.297466\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.6634 | − | 39.6634i | 1.55693 | − | 1.55693i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.3556i | 0.641027i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.7064 | + | 22.7064i | −0.888569 | + | 0.888569i | −0.994386 | − | 0.105816i | \(-0.966254\pi\) |
0.105816 | + | 0.994386i | \(0.466254\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.37947 | 0.288340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.0669 | −1.52414 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.10062 | − | 4.10062i | 0.159737 | − | 0.159737i | −0.622713 | − | 0.782450i | \(-0.713970\pi\) |
0.782450 | + | 0.622713i | \(0.213970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5.07644i | − | 0.197451i | −0.995115 | − | 0.0987254i | \(-0.968523\pi\) | ||
0.995115 | − | 0.0987254i | \(-0.0314765\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.4661 | + | 11.4661i | −0.445305 | + | 0.445305i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.67912i | − | 0.375340i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.75125 | − | 8.75125i | 0.338850 | − | 0.338850i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.5886 | + | 33.5886i | −1.29861 | + | 1.29861i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.2572 | − | 37.2572i | −1.43830 | − | 1.43830i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.53374 | − | 1.53374i | −0.0591213 | − | 0.0591213i | 0.676928 | − | 0.736049i | \(-0.263311\pi\) |
−0.736049 | + | 0.676928i | \(0.763311\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.268371 | − | 0.268371i | −0.0103296 | − | 0.0103296i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.1845i | − | 0.622019i | −0.950407 | − | 0.311010i | \(-0.899333\pi\) | ||
0.950407 | − | 0.311010i | \(-0.100667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.6736 | −0.601497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6657 | 0.676952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.3842 | + | 29.3842i | 1.12435 | + | 1.12435i | 0.991079 | + | 0.133275i | \(0.0425495\pi\) |
0.133275 | + | 0.991079i | \(0.457451\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.9665 | − | 15.9665i | 0.610049 | − | 0.610049i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −54.0834 | −2.06341 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.7584i | 0.828929i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.78735 | − | 5.78735i | −0.220161 | − | 0.220161i | 0.588405 | − | 0.808566i | \(-0.299756\pi\) |
−0.808566 | + | 0.588405i | \(0.799756\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.7223 | −0.597240 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.9957i | 0.910208i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8465 | + | 0.0888362i | 0.486598 | + | 0.00336491i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.6042i | 1.27103i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.6444 | 1.76173 | 0.880867 | − | 0.473364i | \(-0.156960\pi\) | ||||
0.880867 | + | 0.473364i | \(0.156960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.02693 | + | 2.02693i | 0.0764471 | + | 0.0764471i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 47.4186i | − | 1.78589i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.19398 | 0.157731 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.9441 | − | 29.9441i | 1.12457 | − | 1.12457i | 0.133528 | − | 0.991045i | \(-0.457369\pi\) |
0.991045 | − | 0.133528i | \(-0.0426305\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.51254 | + | 3.51254i | 0.131730 | + | 0.131730i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.7931 | −1.60261 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.3784 | 1.69706 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 48.1362i | − | 1.79768i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.6174 | − | 14.6174i | −0.545135 | − | 0.545135i | 0.379895 | − | 0.925030i | \(-0.375960\pi\) |
−0.925030 | + | 0.379895i | \(0.875960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.81631 | − | 7.81631i | −0.291094 | − | 0.291094i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.1328 | + | 37.1328i | 1.38098 | + | 1.38098i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.51694 | − | 1.51694i | 0.0563378 | − | 0.0563378i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.8827 | + | 21.8827i | −0.811585 | + | 0.811585i | −0.984871 | − | 0.173287i | \(-0.944561\pi\) |
0.173287 | + | 0.984871i | \(0.444561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 24.3699i | − | 0.902589i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.1137 | + | 10.1137i | −0.374067 | + | 0.374067i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 47.8460i | − | 1.76723i | −0.468211 | − | 0.883617i | \(-0.655101\pi\) | ||
0.468211 | − | 0.883617i | \(-0.344899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.22578 | − | 4.22578i | 0.155870 | − | 0.155870i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.3912 | 0.898461 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.7356 | 1.02027 | 0.510135 | − | 0.860094i | \(-0.329595\pi\) | ||||
0.510135 | + | 0.860094i | \(0.329595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.4009 | + | 22.4009i | −0.822919 | + | 0.822919i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.35243i | 0.269734i | 0.990864 | + | 0.134867i | \(0.0430608\pi\) | ||||
−0.990864 | + | 0.134867i | \(0.956939\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.87896 | − | 7.87896i | 0.288663 | − | 0.288663i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.9674i | − | 0.730571i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.05169 | − | 3.05169i | 0.111506 | − | 0.111506i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.9471 | − | 19.9471i | 0.727881 | − | 0.727881i | −0.242316 | − | 0.970197i | \(-0.577907\pi\) |
0.970197 | + | 0.242316i | \(0.0779072\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −49.4714 | − | 49.4714i | −1.80284 | − | 1.80284i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.7862 | + | 36.7862i | 1.33879 | + | 1.33879i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.3190 | + | 33.3190i | 1.21100 | + | 1.21100i | 0.970699 | + | 0.240301i | \(0.0772460\pi\) |
0.240301 | + | 0.970699i | \(0.422754\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 84.3292i | − | 3.06096i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.1208 | 1.27313 | 0.636565 | − | 0.771223i | \(-0.280355\pi\) | ||||
0.636565 | + | 0.771223i | \(0.280355\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6532 | −0.421875 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.0092 | + | 10.0092i | 0.361883 | + | 0.361883i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0706 | − | 24.0706i | 0.869138 | − | 0.869138i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.8614 | 1.87017 | 0.935085 | − | 0.354423i | \(-0.115323\pi\) | ||||
0.935085 | + | 0.354423i | \(0.115323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.6984i | 2.18600i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.18747 | + | 7.18747i | 0.258515 | + | 0.258515i | 0.824450 | − | 0.565935i | \(-0.191485\pi\) |
−0.565935 | + | 0.824450i | \(0.691485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.41775 | −0.266454 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.76986i | 0.0634935i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.0979 | + | 0.173557i | 0.899226 | + | 0.00621831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 19.0142i | − | 0.680380i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.675830 | −0.0241522 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.1668 | − | 18.1668i | −0.648400 | − | 0.648400i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.0153i | − | 0.856052i | −0.903767 | − | 0.428026i | \(-0.859209\pi\) | ||
0.903767 | − | 0.428026i | \(-0.140791\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.2612 | −0.685718 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.92568 | + | 9.92568i | −0.352916 | + | 0.352916i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.6103 | − | 22.6103i | −0.802915 | − | 0.802915i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 38.9373 | 1.38097 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.2773 | −0.682836 | −0.341418 | − | 0.939911i | \(-0.610907\pi\) | ||||
−0.341418 | + | 0.939911i | \(0.610907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.9196i | − | 0.563195i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.9556 | − | 32.9556i | −1.16443 | − | 1.16443i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 53.2048 | + | 53.2048i | 1.87756 | + | 1.87756i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0564 | + | 11.0564i | 0.389687 | + | 0.389687i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.7481 | + | 15.7481i | −0.554361 | + | 0.554361i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.5212 | − | 11.5212i | 0.405064 | − | 0.405064i | −0.474949 | − | 0.880013i | \(-0.657534\pi\) |
0.880013 | + | 0.474949i | \(0.157534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.99712i | − | 0.105243i | −0.998615 | − | 0.0526216i | \(-0.983242\pi\) | ||
0.998615 | − | 0.0526216i | \(-0.0167577\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.51903 | − | 8.51903i | 0.298776 | − | 0.298776i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.04557i | 0.0716532i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.7588 | + | 19.7588i | −0.691272 | + | 0.691272i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.54139 | −0.333403 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.9692 | −0.662030 | −0.331015 | − | 0.943626i | \(-0.607391\pi\) | ||||
−0.331015 | + | 0.943626i | \(0.607391\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6015 | − | 23.6015i | 0.822696 | − | 0.822696i | −0.163798 | − | 0.986494i | \(-0.552375\pi\) |
0.986494 | + | 0.163798i | \(0.0523746\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 14.6176i | − | 0.508920i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.5498 | − | 14.5498i | 0.505945 | − | 0.505945i | −0.407334 | − | 0.913279i | \(-0.633542\pi\) |
0.913279 | + | 0.407334i | \(0.133542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.8322i | 1.10558i | 0.833321 | + | 0.552790i | \(0.186437\pi\) | ||||
−0.833321 | + | 0.552790i | \(0.813563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0553 | − | 22.0553i | 0.765091 | − | 0.765091i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.41870 | − | 1.41870i | 0.0491550 | − | 0.0491550i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.0797 | − | 28.0797i | −0.971737 | − | 0.971737i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.65238 | + | 1.65238i | 0.0571148 | + | 0.0571148i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.5998 | − | 18.5998i | −0.642136 | − | 0.642136i | 0.308944 | − | 0.951080i | \(-0.400024\pi\) |
−0.951080 | + | 0.308944i | \(0.900024\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.1799i | 0.868273i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.3545 | 0.907697 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.56253 | −0.156956 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.6339 | + | 13.6339i | 0.468465 | + | 0.468465i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.2795 | + | 21.2795i | −0.730312 | + | 0.730312i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.63070 | −0.158738 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.2260i | − | 0.932200i | −0.884732 | − | 0.466100i | \(-0.845659\pi\) | ||
0.884732 | − | 0.466100i | \(-0.154341\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.5547 | + | 19.5547i | 0.668755 | + | 0.668755i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.3110 | −0.488856 | −0.244428 | − | 0.969667i | \(-0.578600\pi\) | ||||
−0.244428 | + | 0.969667i | \(0.578600\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.6603i | 1.31907i | 0.751673 | + | 0.659536i | \(0.229247\pi\) | ||||
−0.751673 | + | 0.659536i | \(0.770753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.8817 | + | 11.0332i | 0.370846 | + | 0.376011i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.3830i | − | 0.830008i | −0.909820 | − | 0.415004i | \(-0.863780\pi\) | ||
0.909820 | − | 0.415004i | \(-0.136220\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.7244 | −0.704649 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.2035 | − | 22.2035i | −0.754070 | − | 0.754070i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.56739i | − | 0.324552i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.8023 | 0.501557 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.6652 | − | 31.6652i | 1.07170 | − | 1.07170i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.81390 | − | 6.81390i | −0.230352 | − | 0.230352i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.5877 | −1.37055 | −0.685274 | − | 0.728285i | \(-0.740318\pi\) | ||||
−0.685274 | + | 0.728285i | \(0.740318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.78521 | −0.0939428 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.38861i | 0.147856i | 0.997264 | + | 0.0739281i | \(0.0235535\pi\) | ||||
−0.997264 | + | 0.0739281i | \(0.976446\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.3411 | − | 25.3411i | −0.852795 | − | 0.852795i | 0.137682 | − | 0.990477i | \(-0.456035\pi\) |
−0.990477 | + | 0.137682i | \(0.956035\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −43.0750 | − | 43.0750i | −1.44795 | − | 1.44795i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.8091 | + | 13.8091i | 0.463663 | + | 0.463663i | 0.899854 | − | 0.436191i | \(-0.143673\pi\) |
−0.436191 | + | 0.899854i | \(0.643673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.77037 | − | 2.77037i | 0.0929153 | − | 0.0929153i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −36.6082 | + | 36.6082i | −1.22642 | + | 1.22642i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 31.1016i | − | 1.04078i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.3285 | − | 28.3285i | 0.946918 | − | 0.946918i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 51.1769i | − | 1.70875i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.33996 | + | 9.33996i | −0.311505 | + | 0.311505i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.0722 | 0.435499 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.2528 | −0.574139 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0632 | + | 10.0632i | −0.334511 | + | 0.334511i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.4661i | 1.04482i | 0.852696 | + | 0.522408i | \(0.174966\pi\) | ||||
−0.852696 | + | 0.522408i | \(0.825034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.47306 | + | 8.47306i | −0.281034 | + | 0.281034i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21.7610i | − | 0.720973i | −0.932764 | − | 0.360486i | \(-0.882611\pi\) | ||
0.932764 | − | 0.360486i | \(-0.117389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.1935 | + | 27.1935i | −0.899973 | + | 0.899973i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −40.4618 | + | 40.4618i | −1.33763 | + | 1.33763i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.11315 | + | 2.11315i | 0.0697823 | + | 0.0697823i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.08435 | − | 6.08435i | −0.200704 | − | 0.200704i | 0.599597 | − | 0.800302i | \(-0.295327\pi\) |
−0.800302 | + | 0.599597i | \(0.795327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.2486 | − | 51.2486i | −1.68870 | − | 1.68870i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 11.5391i | − | 0.379815i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.802685 | −0.0263921 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.5824 | 1.03730 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.1311 | − | 28.1311i | −0.922952 | − | 0.922952i | 0.0742849 | − | 0.997237i | \(-0.476333\pi\) |
−0.997237 | + | 0.0742849i | \(0.976333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.77167 | − | 2.77167i | 0.0908378 | − | 0.0908378i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.13518 | 0.0699026 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 27.2629i | − | 0.891591i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.1404 | − | 23.1404i | −0.755964 | − | 0.755964i | 0.219621 | − | 0.975585i | \(-0.429518\pi\) |
−0.975585 | + | 0.219621i | \(0.929518\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.8906 | −1.88919 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.1328i | 0.362919i | 0.983398 | + | 0.181460i | \(0.0580822\pi\) | ||||
−0.983398 | + | 0.181460i | \(0.941918\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.8675 | + | 28.4710i | −0.940054 | + | 0.927142i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 0.853850i | − | 0.0277757i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.4304 | 1.50878 | 0.754392 | − | 0.656424i | \(-0.227932\pi\) | ||||
0.754392 | + | 0.656424i | \(0.227932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.2885 | + | 32.2885i | 1.04813 | + | 1.04813i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 45.1559i | − | 1.46428i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.04537 | −0.260615 | −0.130308 | − | 0.991474i | \(-0.541596\pi\) | ||||
−0.130308 | + | 0.991474i | \(0.541596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.7138 | + | 22.7138i | −0.735000 | + | 0.735000i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.4056 | − | 18.4056i | −0.594968 | − | 0.594968i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.14420 | 0.295281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.6719 | 0.473285 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.3306i | 0.397348i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.7806 | + | 24.7806i | 0.797715 | + | 0.797715i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.7657 | − | 11.7657i | −0.378360 | − | 0.378360i | 0.492150 | − | 0.870510i | \(-0.336211\pi\) |
−0.870510 | + | 0.492150i | \(0.836211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.4582 | + | 13.4582i | 0.432341 | + | 0.432341i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5066 | + | 15.5066i | −0.497631 | + | 0.497631i | −0.910700 | − | 0.413069i | \(-0.864457\pi\) |
0.413069 | + | 0.910700i | \(0.364457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.87129 | + | 6.87129i | −0.220283 | + | 0.220283i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 8.87101i | − | 0.284100i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.88164 | − | 6.88164i | 0.220163 | − | 0.220163i | −0.588404 | − | 0.808567i | \(-0.700243\pi\) |
0.808567 | + | 0.588404i | \(0.200243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 89.7639i | 2.86887i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.5429 | − | 23.5429i | 0.751667 | − | 0.751667i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.46548 | −0.142427 | −0.0712134 | − | 0.997461i | \(-0.522687\pi\) | ||||
−0.0712134 | + | 0.997461i | \(0.522687\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.2644 | −0.518228 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.5786 | − | 13.5786i | 0.432211 | − | 0.432211i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 45.1407i | − | 1.43539i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.7804 | + | 38.7804i | −1.23190 | + | 1.23190i | −0.268665 | + | 0.963234i | \(0.586582\pi\) |
−0.963234 | + | 0.268665i | \(0.913418\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.97297i | 0.126078i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.22097 | + | 1.22097i | −0.0387072 | + | 0.0387072i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.9295 | − | 22.9295i | 0.726183 | − | 0.726183i | −0.243674 | − | 0.969857i | \(-0.578353\pi\) |
0.969857 | + | 0.243674i | \(0.0783526\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.178807 | + | 0.178807i | 0.00565720 | + | 0.00565720i |
(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 | 1148.2.k.b.729.16 | yes | 36 | |
41.9 | even | 4 | inner | 1148.2.k.b.337.16 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.b.337.16 | ✓ | 36 | 41.9 | even | 4 | inner | |
1148.2.k.b.729.16 | yes | 36 | 1.1 | even | 1 | trivial |