Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(449,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.g (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.9 | ||
Root | \(0.271831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.449 |
Dual form | 2240.2.g.n.449.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.19794i | 1.26898i | 0.772931 | + | 0.634490i | \(0.218790\pi\) | ||||
−0.772931 | + | 0.634490i | \(0.781210\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.64514 | − | 1.51444i | −0.735728 | − | 0.677277i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.83094 | −0.610312 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.37460 | −0.414457 | −0.207228 | − | 0.978293i | \(-0.566444\pi\) | ||||
−0.207228 | + | 0.978293i | \(0.566444\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.74160i | 0.760383i | 0.924908 | + | 0.380192i | \(0.124142\pi\) | ||||
−0.924908 | + | 0.380192i | \(0.875858\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.32864 | − | 3.61591i | 0.859451 | − | 0.933625i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.94455i | 1.68430i | 0.539242 | + | 0.842151i | \(0.318711\pi\) | ||||
−0.539242 | + | 0.842151i | \(0.681289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.29028 | −0.296010 | −0.148005 | − | 0.988987i | \(-0.547285\pi\) | ||||
−0.148005 | + | 0.988987i | \(0.547285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.19794 | −0.479630 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.31915i | − | 1.73466i | −0.497731 | − | 0.867331i | \(-0.665833\pi\) | ||
0.497731 | − | 0.867331i | \(-0.334167\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.412961 | + | 4.98292i | 0.0825921 | + | 0.996583i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.56953i | 0.494507i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.40089 | −1.56001 | −0.780003 | − | 0.625775i | \(-0.784783\pi\) | ||||
−0.780003 | + | 0.625775i | \(0.784783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.49323 | 1.70503 | 0.852517 | − | 0.522699i | \(-0.175075\pi\) | ||||
0.852517 | + | 0.522699i | \(0.175075\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.02128i | − | 0.525937i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.51444 | − | 1.64514i | 0.255987 | − | 0.278079i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.73860i | − | 0.285824i | −0.989735 | − | 0.142912i | \(-0.954353\pi\) | ||
0.989735 | − | 0.142912i | \(-0.0456465\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.02587 | −0.964912 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.30855 | −0.829057 | −0.414528 | − | 0.910036i | \(-0.636053\pi\) | ||||
−0.414528 | + | 0.910036i | \(0.636053\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.83136i | − | 1.19427i | −0.802140 | − | 0.597136i | \(-0.796305\pi\) | ||
0.802140 | − | 0.597136i | \(-0.203695\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.01214 | + | 2.77284i | 0.449024 | + | 0.413350i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.48822i | − | 0.508809i | −0.967098 | − | 0.254404i | \(-0.918121\pi\) | ||
0.967098 | − | 0.254404i | \(-0.0818794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.2637 | −2.13735 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.13448i | 0.842635i | 0.906913 | + | 0.421317i | \(0.138432\pi\) | ||||
−0.906913 | + | 0.421317i | \(0.861568\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.26140 | + | 2.08174i | 0.304927 | + | 0.280702i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.83595i | − | 0.375631i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.26070 | −0.815074 | −0.407537 | − | 0.913189i | \(-0.633612\pi\) | ||||
−0.407537 | + | 0.913189i | \(0.633612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.59883 | −0.844894 | −0.422447 | − | 0.906388i | \(-0.638829\pi\) | ||||
−0.422447 | + | 0.906388i | \(0.638829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.83094i | − | 0.230676i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.15198 | − | 4.51031i | 0.514990 | − | 0.559435i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.66187i | 0.203030i | 0.994834 | + | 0.101515i | \(0.0323690\pi\) | ||||
−0.994834 | + | 0.101515i | \(0.967631\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.2850 | 2.20125 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.0236 | −1.90165 | −0.950825 | − | 0.309730i | \(-0.899761\pi\) | ||||
−0.950825 | + | 0.309730i | \(0.899761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.13448i | − | 0.249821i | −0.992168 | − | 0.124911i | \(-0.960136\pi\) | ||
0.992168 | − | 0.124911i | \(-0.0398644\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.9521 | + | 0.907662i | −1.26465 | + | 0.104808i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.37460i | − | 0.156650i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.45132 | −0.613322 | −0.306661 | − | 0.951819i | \(-0.599212\pi\) | ||||
−0.306661 | + | 0.951819i | \(0.599212\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1405 | −1.23783 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.54624i | − | 0.279486i | −0.990188 | − | 0.139743i | \(-0.955372\pi\) | ||
0.990188 | − | 0.139743i | \(-0.0446277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.5171 | − | 11.4248i | 1.14074 | − | 1.23919i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 18.4646i | − | 1.97962i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.43548 | −0.152161 | −0.0760804 | − | 0.997102i | \(-0.524241\pi\) | ||||
−0.0760804 | + | 0.997102i | \(0.524241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.74160 | −0.287398 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.8655i | 2.16366i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.12268 | + | 1.95404i | 0.217783 | + | 0.200481i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.69375i | − | 0.984251i | −0.870524 | − | 0.492125i | \(-0.836220\pi\) | ||
0.870524 | − | 0.492125i | \(-0.163780\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.51680 | 0.252948 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.25067 | −0.820973 | −0.410486 | − | 0.911867i | \(-0.634641\pi\) | ||||
−0.410486 | + | 0.911867i | \(0.634641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.1501i | − | 1.29572i | −0.761761 | − | 0.647858i | \(-0.775665\pi\) | ||
0.761761 | − | 0.647858i | \(-0.224335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.61591 | + | 3.32864i | 0.352877 | + | 0.324842i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.153454i | 0.0148349i | 0.999972 | + | 0.00741746i | \(0.00236107\pi\) | ||||
−0.999972 | + | 0.00741746i | \(0.997639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.23741 | −0.789001 | −0.394500 | − | 0.918896i | \(-0.629082\pi\) | ||||
−0.394500 | + | 0.918896i | \(0.629082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.82133 | 0.362705 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.0532i | − | 1.03979i | −0.854229 | − | 0.519897i | \(-0.825970\pi\) | ||
0.854229 | − | 0.519897i | \(-0.174030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.5988 | + | 13.6862i | −1.17485 | + | 1.27624i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.01969i | − | 0.464071i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.94455 | −0.636606 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.11048 | −0.828226 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 11.6679i | − | 1.05206i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.86694 | − | 8.82299i | 0.614198 | − | 0.789152i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.74460i | 0.687222i | 0.939112 | + | 0.343611i | \(0.111650\pi\) | ||||
−0.939112 | + | 0.343611i | \(0.888350\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.2128 | 1.51551 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.75228 | −0.415209 | −0.207605 | − | 0.978213i | \(-0.566567\pi\) | ||||
−0.207605 | + | 0.978213i | \(0.566567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.29028i | − | 0.111881i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.89140 | − | 4.22724i | 0.334918 | − | 0.363823i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3002i | 1.56349i | 0.623599 | + | 0.781745i | \(0.285670\pi\) | ||||
−0.623599 | + | 0.781745i | \(0.714330\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9370 | 1.60621 | 0.803106 | − | 0.595836i | \(-0.203179\pi\) | ||||
0.803106 | + | 0.595836i | \(0.203179\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.66688 | 0.645668 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.76860i | − | 0.315146i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.8206 | + | 12.7226i | 1.14774 | + | 1.05656i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.19794i | − | 0.181283i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1155 | 0.828694 | 0.414347 | − | 0.910119i | \(-0.364010\pi\) | ||||
0.414347 | + | 0.910119i | \(0.364010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.567654 | 0.0461951 | 0.0230975 | − | 0.999733i | \(-0.492647\pi\) | ||||
0.0230975 | + | 0.999733i | \(0.492647\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 12.7150i | − | 1.02795i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.6177 | − | 14.3769i | −1.25444 | − | 1.15478i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.87542i | − | 0.229484i | −0.993395 | − | 0.114742i | \(-0.963396\pi\) | ||
0.993395 | − | 0.114742i | \(-0.0366041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.4832 | −1.06929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.31915 | 0.655641 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.2212i | − | 0.800589i | −0.916387 | − | 0.400294i | \(-0.868908\pi\) | ||
0.916387 | − | 0.400294i | \(-0.131092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.57554 | + | 4.97042i | −0.356205 | + | 0.386947i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.7672i | 1.52963i | 0.644249 | + | 0.764816i | \(0.277170\pi\) | ||||
−0.644249 | + | 0.764816i | \(0.722830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.48363 | 0.421817 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.36241 | 0.180658 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 21.7281i | − | 1.65195i | −0.563704 | − | 0.825977i | \(-0.690624\pi\) | ||
0.563704 | − | 0.825977i | \(-0.309376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.98292 | + | 0.412961i | −0.376673 | + | 0.0312169i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 13.7606i | − | 1.03431i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.1611 | 1.58166 | 0.790828 | − | 0.612039i | \(-0.209650\pi\) | ||||
0.790828 | + | 0.612039i | \(0.209650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8396 | −0.880031 | −0.440016 | − | 0.897990i | \(-0.645027\pi\) | ||||
−0.440016 | + | 0.897990i | \(0.645027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.5038i | − | 1.07215i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.63300 | + | 2.86023i | −0.193582 | + | 0.210289i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.54596i | − | 0.698070i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.56953 | −0.186906 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.82068 | −0.131739 | −0.0658697 | − | 0.997828i | \(-0.520982\pi\) | ||||
−0.0658697 | + | 0.997828i | \(0.520982\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.62770i | 0.261128i | 0.991440 | + | 0.130564i | \(0.0416788\pi\) | ||||
−0.991440 | + | 0.130564i | \(0.958321\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.91339 | + | 9.12580i | 0.709913 | + | 0.653512i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.49380i | 0.462664i | 0.972875 | + | 0.231332i | \(0.0743084\pi\) | ||||
−0.972875 | + | 0.231332i | \(0.925692\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.69145 | −0.332568 | −0.166284 | − | 0.986078i | \(-0.553177\pi\) | ||||
−0.166284 | + | 0.986078i | \(0.553177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.65269 | −0.257641 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 8.40089i | − | 0.589627i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.73331 | + | 8.03947i | 0.609961 | + | 0.561501i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.2318i | 1.05869i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.77361 | 0.122683 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0159 | 1.17142 | 0.585710 | − | 0.810521i | \(-0.300816\pi\) | ||||
0.585710 | + | 0.810521i | \(0.300816\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 35.2189i | − | 2.41316i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.8601 | + | 12.8837i | −0.808852 | + | 0.878659i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.49323i | 0.644442i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.69145 | 0.317019 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.0392 | −1.28071 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.39251i | 0.628969i | 0.949263 | + | 0.314485i | \(0.101832\pi\) | ||||
−0.949263 | + | 0.314485i | \(0.898168\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.756104 | − | 9.12340i | −0.0504069 | − | 0.608227i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.3134i | − | 0.950016i | −0.879981 | − | 0.475008i | \(-0.842445\pi\) | ||
0.879981 | − | 0.475008i | \(-0.157555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.78351 | −0.580430 | −0.290215 | − | 0.956961i | \(-0.593727\pi\) | ||||
−0.290215 | + | 0.956961i | \(0.593727\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.02128 | 0.198786 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7706i | 0.967652i | 0.875164 | + | 0.483826i | \(0.160753\pi\) | ||||
−0.875164 | + | 0.483826i | \(0.839247\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.28268 | + | 5.73860i | −0.344604 | + | 0.374345i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 11.9817i | − | 0.778294i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.0525 | −1.62051 | −0.810256 | − | 0.586076i | \(-0.800672\pi\) | ||||
−0.810256 | + | 0.586076i | \(0.800672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.32975 | 0.214488 | 0.107244 | − | 0.994233i | \(-0.465797\pi\) | ||||
0.107244 | + | 0.994233i | \(0.465797\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 16.7775i | − | 1.07628i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.64514 | + | 1.51444i | 0.105104 | + | 0.0967538i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.53742i | − | 0.225081i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.59648 | 0.354663 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.89135 | −0.624336 | −0.312168 | − | 0.950027i | \(-0.601055\pi\) | ||||
−0.312168 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.4355i | 0.718943i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.1109 | + | 23.1159i | 1.57251 | + | 1.44758i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.6117i | − | 0.849073i | −0.905411 | − | 0.424536i | \(-0.860437\pi\) | ||
0.905411 | − | 0.424536i | \(-0.139563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.73860 | 0.108031 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.3815 | 0.952090 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.11550i | 0.253772i | 0.991917 | + | 0.126886i | \(0.0404983\pi\) | ||||
−0.991917 | + | 0.126886i | \(0.959502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.29028 | − | 10.0921i | 0.570697 | − | 0.619950i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.15510i | − | 0.193089i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7409 | 0.654887 | 0.327443 | − | 0.944871i | \(-0.393813\pi\) | ||||
0.327443 | + | 0.944871i | \(0.393813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.7438 | 1.98904 | 0.994521 | − | 0.104535i | \(-0.0333355\pi\) | ||||
0.994521 | + | 0.104535i | \(0.0333355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.02587i | − | 0.364702i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.567654 | − | 6.84950i | −0.0342309 | − | 0.413041i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.92623i | 0.416157i | 0.978112 | + | 0.208078i | \(0.0667209\pi\) | ||||
−0.978112 | + | 0.208078i | \(0.933279\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.3815 | −1.04060 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.61209 | −0.155824 | −0.0779122 | − | 0.996960i | \(-0.524825\pi\) | ||||
−0.0779122 | + | 0.996960i | \(0.524825\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.99972i | 0.416090i | 0.978119 | + | 0.208045i | \(0.0667101\pi\) | ||||
−0.978119 | + | 0.208045i | \(0.933290\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.29487 | + | 4.66553i | −0.254406 | + | 0.276362i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.30855i | − | 0.313354i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.2268 | −1.83687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.3063 | 1.24900 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.7099i | 0.859362i | 0.902981 | + | 0.429681i | \(0.141374\pi\) | ||||
−0.902981 | + | 0.429681i | \(0.858626\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2997 | + | 9.48144i | 0.599673 | + | 0.552031i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.53207i | − | 0.204952i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.8078 | 1.31901 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.83136 | 0.451392 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 18.1345i | − | 1.04180i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.8560 | + | 9.99351i | 0.621612 | + | 0.572227i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.5567i | 1.85811i | 0.369942 | + | 0.929055i | \(0.379377\pi\) | ||||
−0.369942 | + | 0.929055i | \(0.620623\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.9031 | 1.64424 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.4065 | −1.83760 | −0.918802 | − | 0.394719i | \(-0.870842\pi\) | ||||
−0.918802 | + | 0.394719i | \(0.870842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2347i | 1.20026i | 0.799904 | + | 0.600128i | \(0.204884\pi\) | ||||
−0.799904 | + | 0.600128i | \(0.795116\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.77284 | + | 3.01214i | −0.156232 | + | 0.169715i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.1847i | 1.86384i | 0.362667 | + | 0.931919i | \(0.381866\pi\) | ||||
−0.362667 | + | 0.931919i | \(0.618134\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5478 | 0.646555 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.337282 | −0.0188252 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.96040i | − | 0.498570i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.6612 | + | 1.13217i | −0.757785 | + | 0.0628017i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 18.1053i | − | 1.00123i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.48822 | 0.192312 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.38585 | −0.460928 | −0.230464 | − | 0.973081i | \(-0.574024\pi\) | ||||
−0.230464 | + | 0.973081i | \(0.574024\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.18326i | 0.174442i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.51680 | − | 2.73401i | 0.137507 | − | 0.149375i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.59953i | 0.468446i | 0.972183 | + | 0.234223i | \(0.0752546\pi\) | ||||
−0.972183 | + | 0.234223i | \(0.924745\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.2942 | 1.31948 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.0494 | −0.706663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.0813 | − | 27.6915i | −1.61952 | − | 1.49086i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.37773i | 0.288692i | 0.989527 | + | 0.144346i | \(0.0461078\pi\) | ||||
−0.989527 | + | 0.144346i | \(0.953892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1582 | −0.597284 | −0.298642 | − | 0.954365i | \(-0.596534\pi\) | ||||
−0.298642 | + | 0.954365i | \(0.596534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.04463 | −0.376015 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.1040i | 1.33615i | 0.744093 | + | 0.668076i | \(0.232882\pi\) | ||||
−0.744093 | + | 0.668076i | \(0.767118\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.3610 | + | 24.2667i | 1.39910 | + | 1.28794i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 15.2637i | − | 0.807841i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4545 | −1.29066 | −0.645329 | − | 0.763905i | \(-0.723280\pi\) | ||||
−0.645329 | + | 0.763905i | \(0.723280\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3352 | −0.912378 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 20.0243i | − | 1.05100i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.23253 | + | 3.51151i | −0.169198 | + | 0.183801i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6016i | 1.17979i | 0.807478 | + | 0.589897i | \(0.200832\pi\) | ||||
−0.807478 | + | 0.589897i | \(0.799168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.71962 | 0.505983 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.13448 | −0.318486 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.4377i | 0.592221i | 0.955154 | + | 0.296111i | \(0.0956897\pi\) | ||||
−0.955154 | + | 0.296111i | \(0.904310\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.3924 | + | 15.0931i | 1.00142 | + | 0.779405i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 23.0319i | − | 1.18620i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5122 | −1.15638 | −0.578188 | − | 0.815904i | \(-0.696240\pi\) | ||||
−0.578188 | + | 0.815904i | \(0.696240\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.0222 | −0.872072 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.0106i | 1.02249i | 0.859434 | + | 0.511247i | \(0.170816\pi\) | ||||
−0.859434 | + | 0.511247i | \(0.829184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.08174 | + | 2.26140i | −0.106095 | + | 0.115252i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.3387i | 0.728878i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5476 | −1.14321 | −0.571605 | − | 0.820529i | \(-0.693679\pi\) | ||||
−0.571605 | + | 0.820529i | \(0.693679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.7728 | 2.92170 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.4452i | − | 0.526892i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.96818 | + | 8.25569i | 0.451238 | + | 0.415389i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.35871i | 0.469700i | 0.972032 | + | 0.234850i | \(0.0754599\pi\) | ||||
−0.972032 | + | 0.234850i | \(0.924540\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.83595 | 0.141975 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.2475 | −1.56042 | −0.780212 | − | 0.625516i | \(-0.784889\pi\) | ||||
−0.780212 | + | 0.625516i | \(0.784889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.0266i | 1.29648i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.3276 | + | 16.8716i | 0.910707 | + | 0.838355i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.38987i | 0.118462i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.0098 | 1.38499 | 0.692497 | − | 0.721421i | \(-0.256511\pi\) | ||||
0.692497 | + | 0.721421i | \(0.256511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −40.2227 | −1.98404 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.26070i | − | 0.308069i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.85612 | + | 4.18892i | −0.189290 | + | 0.205626i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41.6223i | 2.03825i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8212 | 0.821769 | 0.410885 | − | 0.911687i | \(-0.365220\pi\) | ||||
0.410885 | + | 0.911687i | \(0.365220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.354309 | 0.0172680 | 0.00863398 | − | 0.999963i | \(-0.497252\pi\) | ||||
0.00863398 | + | 0.999963i | \(0.497252\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.38670i | 0.310532i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.6041 | + | 2.86783i | −1.67855 | + | 0.139110i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.59883i | − | 0.319340i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.28315 | 0.399914 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8578 | −0.715675 | −0.357837 | − | 0.933784i | \(-0.616486\pi\) | ||||
−0.357837 | + | 0.933784i | \(0.616486\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6602i | 0.656469i | 0.944596 | + | 0.328235i | \(0.106454\pi\) | ||||
−0.944596 | + | 0.328235i | \(0.893546\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27.9635 | + | 30.3769i | −1.34075 | + | 1.45646i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.7340i | 0.513477i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.3663 | −1.21067 | −0.605334 | − | 0.795972i | \(-0.706960\pi\) | ||||
−0.605334 | + | 0.795972i | \(0.706960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.83094 | 0.0871874 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 32.8555i | − | 1.56101i | −0.625148 | − | 0.780506i | \(-0.714961\pi\) | ||
0.625148 | − | 0.780506i | \(-0.285039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.36157 | + | 2.17395i | 0.111949 | + | 0.103055i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.2332i | 1.05160i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.2268 | −1.61526 | −0.807632 | − | 0.589687i | \(-0.799251\pi\) | ||||
−0.807632 | + | 0.589687i | \(0.799251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.29712 | 0.343608 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.24767i | 0.0586206i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.51031 | + | 4.15198i | 0.211447 | + | 0.194648i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.8661i | − | 1.02285i | −0.859327 | − | 0.511427i | \(-0.829117\pi\) | ||
0.859327 | − | 0.511427i | \(-0.170883\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.8443 | −0.832899 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.8358 | 1.52932 | 0.764659 | − | 0.644436i | \(-0.222908\pi\) | ||||
0.764659 | + | 0.644436i | \(0.222908\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.9970i | − | 0.975811i | −0.872896 | − | 0.487906i | \(-0.837761\pi\) | ||
0.872896 | − | 0.487906i | \(-0.162239\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.5995 | − | 34.3267i | 1.46539 | − | 1.59186i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 9.88718i | − | 0.457524i | −0.973482 | − | 0.228762i | \(-0.926532\pi\) | ||
0.973482 | − | 0.228762i | \(-0.0734678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.66187 | −0.0767381 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.32000 | 0.291210 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.7650i | 0.494974i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.532833 | − | 6.42934i | −0.0244481 | − | 0.294998i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 11.2318i | − | 0.514270i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.1115 | 0.827534 | 0.413767 | − | 0.910383i | \(-0.364213\pi\) | ||||
0.413767 | + | 0.910383i | \(0.364213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.76654 | 0.217336 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.2850i | 0.831996i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.6806 | + | 15.9476i | −0.666610 | + | 0.724141i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.4907i | − | 1.06447i | −0.846597 | − | 0.532234i | \(-0.821353\pi\) | ||
0.846597 | − | 0.532234i | \(-0.178647\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.4656 | 1.01593 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1693 | 1.13588 | 0.567938 | − | 0.823072i | \(-0.307742\pi\) | ||||
0.567938 | + | 0.823072i | \(0.307742\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 58.3404i | − | 2.62752i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.14048 | − | 3.81153i | −0.186101 | − | 0.171316i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 16.0236i | − | 0.718756i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5266 | 0.784601 | 0.392300 | − | 0.919837i | \(-0.371679\pi\) | ||||
0.392300 | + | 0.919837i | \(0.371679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −43.4471 | −1.94107 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 33.0352i | − | 1.47297i | −0.676456 | − | 0.736483i | \(-0.736485\pi\) | ||
0.676456 | − | 0.736483i | \(-0.263515\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5735 | + | 12.4951i | 0.604013 | + | 0.556026i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0527i | 0.535278i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.4535 | −0.950909 | −0.475455 | − | 0.879740i | \(-0.657716\pi\) | ||||
−0.475455 | + | 0.879740i | \(0.657716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.13448 | 0.0944236 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.31541i | − | 0.146379i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.9150 | + | 21.6337i | −0.877559 | + | 0.953295i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.79489i | 0.210879i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 47.7569 | 2.09630 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4249 | 1.02626 | 0.513132 | − | 0.858310i | \(-0.328485\pi\) | ||||
0.513132 | + | 0.858310i | \(0.328485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4736i | 0.676611i | 0.941036 | + | 0.338306i | \(0.109854\pi\) | ||||
−0.941036 | + | 0.338306i | \(0.890146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.907662 | − | 10.9521i | −0.0396136 | − | 0.477991i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 65.9262i | 2.87179i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −46.2083 | −2.00906 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4629 | 0.497449 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 14.5539i | − | 0.630401i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.232396 | − | 0.252452i | 0.0100473 | − | 0.0109145i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 46.5108i | 2.00709i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.37460 | 0.0592081 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.24274 | 0.268396 | 0.134198 | − | 0.990955i | \(-0.457154\pi\) | ||||
0.134198 | + | 0.990955i | \(0.457154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 26.0227i | − | 1.11674i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.5517 | + | 12.4750i | 0.580490 | + | 0.534372i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.8997i | 1.44945i | 0.689040 | + | 0.724724i | \(0.258033\pi\) | ||||
−0.689040 | + | 0.724724i | \(0.741967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0820 | 0.515649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8395 | 0.461777 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.45132i | − | 0.231814i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.28662 | − | 5.78717i | −0.266852 | − | 0.245651i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.161941i | − | 0.00686165i | −0.999994 | − | 0.00343083i | \(-0.998908\pi\) | ||
0.999994 | − | 0.00343083i | \(-0.00109207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.4705 | 0.908104 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9814 | 0.885837 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 38.6514i | − | 1.62896i | −0.580189 | − | 0.814482i | \(-0.697021\pi\) | ||
0.580189 | − | 0.814482i | \(-0.302979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.7393 | + | 18.1840i | −0.704228 | + | 0.765006i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 11.1405i | − | 0.467856i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.9523 | 1.12990 | 0.564949 | − | 0.825126i | \(-0.308896\pi\) | ||||
0.564949 | + | 0.825126i | \(0.308896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.2525 | −1.01493 | −0.507467 | − | 0.861671i | \(-0.669418\pi\) | ||||
−0.507467 | + | 0.861671i | \(0.669418\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 4.00173i | − | 0.167175i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41.4536 | − | 3.43548i | 1.72874 | − | 0.143269i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.2848i | − | 0.594684i | −0.954771 | − | 0.297342i | \(-0.903900\pi\) | ||
0.954771 | − | 0.297342i | \(-0.0961001\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.97347 | −0.331366 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.54624 | 0.105636 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.43243i | − | 0.349236i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.60201 | + | 8.25809i | −0.314304 | + | 0.341430i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.6314i | 1.26429i | 0.774849 | + | 0.632146i | \(0.217826\pi\) | ||||
−0.774849 | + | 0.632146i | \(0.782174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.2489 | −0.504707 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.2730 | −0.587112 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4568i | 1.53817i | 0.639149 | + | 0.769083i | \(0.279287\pi\) | ||||
−0.639149 | + | 0.769083i | \(0.720713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4248 | + | 10.5171i | 0.468369 | + | 0.431159i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 10.3115i | − | 0.422022i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.9394 | 0.773843 | 0.386921 | − | 0.922113i | \(-0.373538\pi\) | ||||
0.386921 | + | 0.922113i | \(0.373538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.49158 | −0.346379 | −0.173189 | − | 0.984889i | \(-0.555407\pi\) | ||||
−0.173189 | + | 0.984889i | \(0.555407\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 3.04278i | − | 0.123911i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.9880 | + | 13.7973i | 0.609349 | + | 0.560938i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.4717i | 0.952688i | 0.879259 | + | 0.476344i | \(0.158038\pi\) | ||||
−0.879259 | + | 0.476344i | \(0.841962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.4646 | 0.748225 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.56329 | 0.386889 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.9078i | 1.36952i | 0.728767 | + | 0.684762i | \(0.240094\pi\) | ||||
−0.728767 | + | 0.684762i | \(0.759906\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.6703 | + | 19.1953i | −0.712534 | + | 0.774028i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23.7015i | − | 0.954186i | −0.878853 | − | 0.477093i | \(-0.841690\pi\) | ||
0.878853 | − | 0.477093i | \(-0.158310\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5275 | 0.704491 | 0.352246 | − | 0.935908i | \(-0.385418\pi\) | ||||
0.352246 | + | 0.935908i | \(0.385418\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.3763 | 0.857803 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.43548i | − | 0.0575113i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.6589 | + | 4.11550i | −0.986357 | + | 0.164620i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.89829i | 0.155683i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0738 | 0.481413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9892 | −0.556902 | −0.278451 | − | 0.960450i | \(-0.589821\pi\) | ||||
−0.278451 | + | 0.960450i | \(0.589821\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.3998i | 1.48651i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.7287 | − | 12.7409i | 0.465440 | − | 0.505609i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.74160i | − | 0.108626i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.3381 | 1.16060 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.7939 | 1.53227 | 0.766133 | − | 0.642682i | \(-0.222178\pi\) | ||||
0.766133 | + | 0.642682i | \(0.222178\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.9729i | 1.61581i | 0.589310 | + | 0.807907i | \(0.299400\pi\) | ||||
−0.589310 | + | 0.807907i | \(0.700600\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.3175 | − | 26.0678i | −1.11500 | − | 1.02642i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.17647i | − | 0.282136i | −0.990000 | − | 0.141068i | \(-0.954946\pi\) | ||
0.990000 | − | 0.141068i | \(-0.0450536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.60594 | 0.337813 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.8655 | −0.817785 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 21.6869i | − | 0.848672i | −0.905505 | − | 0.424336i | \(-0.860508\pi\) | ||
0.905505 | − | 0.424336i | \(-0.139492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.81817 | + | 7.19704i | 0.305481 | + | 0.281211i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.90809i | 0.152469i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.56012 | 0.216592 | 0.108296 | − | 0.994119i | \(-0.465461\pi\) | ||||
0.108296 | + | 0.994119i | \(0.465461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.4543 | 1.37901 | 0.689507 | − | 0.724279i | \(-0.257827\pi\) | ||||
0.689507 | + | 0.724279i | \(0.257827\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 41.8470i | − | 1.62520i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.95404 | + | 2.12268i | −0.0757745 | + | 0.0823141i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 69.8883i | 2.70609i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.6442 | −0.798149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.07073 | 0.350172 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.8018i | − | 1.11023i | −0.831775 | − | 0.555114i | \(-0.812675\pi\) | ||
0.831775 | − | 0.555114i | \(-0.187325\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.8038 | + | 1.06112i | −0.492817 | + | 0.0408424i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.41481i | 0.169675i | 0.996395 | + | 0.0848375i | \(0.0270371\pi\) | ||||
−0.996395 | + | 0.0848375i | \(0.972963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.69375 | 0.372012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.4601 | 1.20555 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 29.9092i | − | 1.14444i | −0.820099 | − | 0.572221i | \(-0.806082\pi\) | ||
0.820099 | − | 0.572221i | \(-0.193918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.7145 | − | 30.1063i | 1.05892 | − | 1.15030i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 19.3056i | − | 0.736555i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.8183 | −0.640726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.79869 | 0.106467 | 0.0532337 | − | 0.998582i | \(-0.483047\pi\) | ||||
0.0532337 | + | 0.998582i | \(0.483047\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.51680i | 0.0956053i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.1539 | − | 28.6788i | −1.18174 | − | 1.08785i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 36.8655i | − | 1.39638i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.4648 | −1.22793 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.3081 | 1.71126 | 0.855632 | − | 0.517584i | \(-0.173168\pi\) | ||||
0.855632 | + | 0.517584i | \(0.173168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.24327i | 0.0846066i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.6131 | − | 11.6110i | −0.475036 | − | 0.437296i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 8.25067i | − | 0.310298i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2038 | 0.420768 | 0.210384 | − | 0.977619i | \(-0.432529\pi\) | ||||
0.210384 | + | 0.977619i | \(0.432529\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.98102 | 0.374318 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 78.9756i | − | 2.95766i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.70730 | + | 6.19986i | −0.213441 | + | 0.231862i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 55.0639i | − | 2.05640i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.1695 | 0.826782 | 0.413391 | − | 0.910554i | \(-0.364344\pi\) | ||||
0.413391 | + | 0.910554i | \(0.364344\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1501 | 0.489735 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.31858i | 0.272181i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.46924 | − | 41.8609i | −0.128844 | − | 1.55468i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 17.4515i | − | 0.647241i | −0.946187 | − | 0.323620i | \(-0.895100\pi\) | ||
0.946187 | − | 0.323620i | \(-0.104900\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.45447 | 0.127943 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.3853 | 2.01151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0171i | 0.960962i | 0.877005 | + | 0.480481i | \(0.159538\pi\) | ||||
−0.877005 | + | 0.480481i | \(0.840462\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.32864 | + | 3.61591i | −0.122779 | + | 0.133375i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.28440i | − | 0.0841471i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.81093 | −0.103402 | −0.0517008 | − | 0.998663i | \(-0.516464\pi\) | ||||
−0.0517008 | + | 0.998663i | \(0.516464\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.77504 | 0.285623 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.8466i | 0.838159i | 0.907950 | + | 0.419080i | \(0.137647\pi\) | ||||
−0.907950 | + | 0.419080i | \(0.862353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.6414 | − | 15.3193i | −0.609693 | − | 0.561255i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.66200i | 0.170574i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.153454 | −0.00560707 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.7651 | 1.88893 | 0.944467 | − | 0.328607i | \(-0.106579\pi\) | ||||
0.944467 | + | 0.328607i | \(0.106579\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.7406i | − | 0.792271i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.933870 | − | 0.859677i | −0.0339870 | − | 0.0312868i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.13016i | 0.295496i | 0.989025 | + | 0.147748i | \(0.0472024\pi\) | ||||
−0.989025 | + | 0.147748i | \(0.952798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.1345 | −0.912324 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.2494 | 1.13279 | 0.566395 | − | 0.824134i | \(-0.308338\pi\) | ||||
0.566395 | + | 0.824134i | \(0.308338\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.23741i | − | 0.298214i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.2561 | + | 20.9180i | −0.696206 | + | 0.756291i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 17.1643i | − | 0.619769i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7711 | −1.03751 | −0.518757 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518757 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.9176 | 1.07746 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.7175i | 0.565318i | 0.959220 | + | 0.282659i | \(0.0912165\pi\) | ||||
−0.959220 | + | 0.282659i | \(0.908783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.92033 | + | 47.3040i | 0.140822 | + | 1.69921i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.82133i | 0.137089i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.84950 | 0.245409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.0260 | 0.788151 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 21.5864i | − | 0.771434i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.35464 | + | 4.73046i | −0.155424 | + | 0.168838i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.8516i | − | 1.02845i | −0.857656 | − | 0.514224i | \(-0.828080\pi\) | ||
0.857656 | − | 0.514224i | \(-0.171920\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.04561 | −0.322032 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0532 | 0.393005 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.0914i | − | 0.642443i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.1817 | + | 20.4195i | 0.786705 | + | 0.724204i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.81776i | − | 0.206076i | −0.994677 | − | 0.103038i | \(-0.967144\pi\) | ||
0.994677 | − | 0.103038i | \(-0.0328563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.2241 | 0.856987 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.62827 | 0.0928655 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.93404i | 0.103540i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.6862 | − | 12.5988i | −0.482374 | − | 0.444050i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.6079i | 0.831039i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.5157 | −0.932242 | −0.466121 | − | 0.884721i | \(-0.654349\pi\) | ||||
−0.466121 | + | 0.884721i | \(0.654349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.5069 | −1.94911 | −0.974556 | − | 0.224144i | \(-0.928041\pi\) | ||||
−0.974556 | + | 0.224144i | \(0.928041\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.9688i | 2.52406i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.4794 | + | 16.8153i | −0.542220 | + | 0.589016i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.1046i | 0.353516i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.01969 | 0.175402 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.1325 | 1.54024 | 0.770118 | − | 0.637902i | \(-0.220197\pi\) | ||||
0.770118 | + | 0.637902i | \(0.220197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.1816i | 0.668629i | 0.942461 | + | 0.334315i | \(0.108505\pi\) | ||||
−0.942461 | + | 0.334315i | \(0.891495\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.0548 | − | 1.24767i | 0.524141 | − | 0.0434383i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.36085i | 0.0473214i | 0.999720 | + | 0.0236607i | \(0.00753214\pi\) | ||||
−0.999720 | + | 0.0236607i | \(0.992468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.04654 | 0.244737 | 0.122368 | − | 0.992485i | \(-0.460951\pi\) | ||||
0.122368 | + | 0.992485i | \(0.460951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.2234 | −0.528095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.94455i | − | 0.240615i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.9362 | − | 32.5198i | 1.03598 | − | 1.12539i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.3932i | 0.843151i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.4808 | −0.499934 | −0.249967 | − | 0.968254i | \(-0.580420\pi\) | ||||
−0.249967 | + | 0.968254i | \(0.580420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.5750 | 1.43362 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.74122i | − | 0.197738i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.02132 | − | 8.30461i | −0.310343 | − | 0.285687i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.11048i | − | 0.313040i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.3850 | −0.528011 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.4637 | −0.495808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.3025i | − | 0.455470i | −0.973723 | − | 0.227735i | \(-0.926868\pi\) | ||
0.973723 | − | 0.227735i | \(-0.0731319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.88650 | − | 3.57773i | −0.132915 | − | 0.122356i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 36.0508i | − | 1.23147i | −0.787953 | − | 0.615736i | \(-0.788859\pi\) | ||
0.787953 | − | 0.615736i | \(-0.211141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.42934 | 0.219366 | 0.109683 | − | 0.993967i | \(-0.465016\pi\) | ||||
0.109683 | + | 0.993967i | \(0.465016\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6679 | 0.397640 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.28639i | − | 0.0778295i | −0.999243 | − | 0.0389148i | \(-0.987610\pi\) | ||
0.999243 | − | 0.0389148i | \(-0.0123901\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.9058 | + | 35.7457i | −1.11883 | + | 1.21539i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 68.6347i | − | 2.33096i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.49337 | 0.254195 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.55619 | −0.154380 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.7486i | 0.600700i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.82299 | + | 6.86694i | 0.298272 | + | 0.232145i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.7188i | 0.969764i | 0.874579 | + | 0.484882i | \(0.161138\pi\) | ||||
−0.874579 | + | 0.484882i | \(0.838862\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.3315 | −1.09051 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.4536 | −1.22815 | −0.614077 | − | 0.789246i | \(-0.710472\pi\) | ||||
−0.614077 | + | 0.789246i | \(0.710472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.6608i | − | 0.762597i | −0.924452 | − | 0.381298i | \(-0.875477\pi\) | ||
0.924452 | − | 0.381298i | \(-0.124523\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.8396 | + | 22.6382i | −0.700516 | + | 0.760973i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 13.7308i | − | 0.461035i | −0.973068 | − | 0.230517i | \(-0.925958\pi\) | ||
0.973068 | − | 0.230517i | \(-0.0740418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.74460 | −0.259746 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.3137 | 0.513027 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.50076i | 0.150612i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.8129 | − | 32.0472i | −1.16367 | − | 1.07122i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50.1301i | 1.67380i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −79.7516 | −2.65986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.6012 | −1.41925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.2128i | 0.572808i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.4778 | + | 17.9303i | 0.647464 | + | 0.596025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 48.7472i | − | 1.61863i | −0.587378 | − | 0.809313i | \(-0.699840\pi\) | ||
0.587378 | − | 0.809313i | \(-0.300160\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1064 | 0.501049 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.1839 | −1.79519 | −0.897596 | − | 0.440820i | \(-0.854688\pi\) | ||||
−0.897596 | + | 0.440820i | \(0.854688\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.50006i | 0.115835i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.9651 | + | 23.8608i | −0.726145 | + | 0.788814i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.75228i | − | 0.156934i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.3450 | −0.968003 | −0.484002 | − | 0.875067i | \(-0.660817\pi\) | ||||
−0.484002 | + | 0.875067i | \(0.660817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −71.5577 | −2.35790 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 43.9303i | − | 1.44598i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.66329 | − | 0.717972i | 0.284847 | − | 0.0236068i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.0770i | 0.790791i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.9346 | −1.21179 | −0.605893 | − | 0.795546i | \(-0.707184\pi\) | ||||
−0.605893 | + | 0.795546i | \(0.707184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.29028 | 0.0422871 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 71.2275i | − | 2.33188i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.4568 | + | 15.7044i | −0.472787 | + | 0.513590i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.3625i | 0.632544i | 0.948668 | + | 0.316272i | \(0.102431\pi\) | ||||
−0.948668 | + | 0.316272i | \(0.897569\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.6726 | −1.52310 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.6807 | 0.445979 | 0.222990 | − | 0.974821i | \(-0.428418\pi\) | ||||
0.222990 | + | 0.974821i | \(0.428418\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.1627i | 1.43813i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.22724 | + | 3.89140i | 0.137512 | + | 0.126587i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0479i | 0.391504i | 0.980653 | + | 0.195752i | \(0.0627147\pi\) | ||||
−0.980653 | + | 0.195752i | \(0.937285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.85188 | 0.189960 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.9379 | −2.36517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 34.6708i | − | 1.12310i | −0.827443 | − | 0.561549i | \(-0.810206\pi\) | ||
0.827443 | − | 0.561549i | \(-0.189794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.99526 | + | 2.75730i | 0.0969244 | + | 0.0892241i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.3815i | 0.820466i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.3002 | −0.590943 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.1214 | 1.90714 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 0.280964i | − | 0.00905393i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.49393 | − | 5.96808i | 0.176856 | − | 0.192119i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6483i | 0.889111i | 0.895751 | + | 0.444555i | \(0.146638\pi\) | ||||
−0.895751 | + | 0.444555i | \(0.853362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.6944 | 0.632675 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.6217 | 1.62453 | 0.812264 | − | 0.583290i | \(-0.198235\pi\) | ||||
0.812264 | + | 0.583290i | \(0.198235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.9370i | 0.607091i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.48845 | − | 30.0264i | −0.0796941 | − | 0.961615i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.3458i | 0.874869i | 0.899250 | + | 0.437435i | \(0.144113\pi\) | ||||
−0.899250 | + | 0.437435i | \(0.855887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.97321 | 0.0630640 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.0822 | 0.481536 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 32.6694i | − | 1.04199i | −0.853559 | − | 0.520996i | \(-0.825561\pi\) | ||
0.853559 | − | 0.520996i | \(-0.174439\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.83445 | − | 10.6832i | 0.313352 | − | 0.340395i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.66688i | 0.244040i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −65.1503 | −2.07166 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.85330 | −0.154170 | −0.0770850 | − | 0.997025i | \(-0.524561\pi\) | ||||
−0.0770850 | + | 0.997025i | \(0.524561\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 18.4316i | − | 0.584909i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.71808 | + | 7.10490i | 0.244680 | + | 0.225240i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.2053i | 1.30498i | 0.757796 | + | 0.652492i | \(0.226276\pi\) | ||||
−0.757796 | + | 0.652492i | \(0.773724\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.46738 | 0.141342 |
(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 | 2240.2.g.n.449.9 | 10 | ||
4.3 | odd | 2 | 2240.2.g.o.449.2 | 10 | |||
5.4 | even | 2 | inner | 2240.2.g.n.449.2 | 10 | ||
8.3 | odd | 2 | 1120.2.g.b.449.9 | yes | 10 | ||
8.5 | even | 2 | 1120.2.g.c.449.2 | yes | 10 | ||
20.19 | odd | 2 | 2240.2.g.o.449.9 | 10 | |||
40.3 | even | 4 | 5600.2.a.bw.1.1 | 5 | |||
40.13 | odd | 4 | 5600.2.a.bv.1.5 | 5 | |||
40.19 | odd | 2 | 1120.2.g.b.449.2 | ✓ | 10 | ||
40.27 | even | 4 | 5600.2.a.bu.1.5 | 5 | |||
40.29 | even | 2 | 1120.2.g.c.449.9 | yes | 10 | ||
40.37 | odd | 4 | 5600.2.a.bx.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.b.449.2 | ✓ | 10 | 40.19 | odd | 2 | ||
1120.2.g.b.449.9 | yes | 10 | 8.3 | odd | 2 | ||
1120.2.g.c.449.2 | yes | 10 | 8.5 | even | 2 | ||
1120.2.g.c.449.9 | yes | 10 | 40.29 | even | 2 | ||
2240.2.g.n.449.2 | 10 | 5.4 | even | 2 | inner | ||
2240.2.g.n.449.9 | 10 | 1.1 | even | 1 | trivial | ||
2240.2.g.o.449.2 | 10 | 4.3 | odd | 2 | |||
2240.2.g.o.449.9 | 10 | 20.19 | odd | 2 | |||
5600.2.a.bu.1.5 | 5 | 40.27 | even | 4 | |||
5600.2.a.bv.1.5 | 5 | 40.13 | odd | 4 | |||
5600.2.a.bw.1.1 | 5 | 40.3 | even | 4 | |||
5600.2.a.bx.1.1 | 5 | 40.37 | odd | 4 |