Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), 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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.34 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.13 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.58213i | 0.913446i | 0.889609 | + | 0.456723i | \(0.150977\pi\) | ||||
−0.889609 | + | 0.456723i | \(0.849023\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.58424i | 1.60292i | 0.598049 | + | 0.801459i | \(0.295943\pi\) | ||||
−0.598049 | + | 0.801459i | \(0.704057\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.89303i | 0.715497i | 0.933818 | + | 0.357748i | \(0.116455\pi\) | ||||
−0.933818 | + | 0.357748i | \(0.883545\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.496852 | 0.165617 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.56283i | − | 0.471210i | −0.971849 | − | 0.235605i | \(-0.924293\pi\) | ||
0.971849 | − | 0.235605i | \(-0.0757072\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.45085 | 1.23444 | 0.617221 | − | 0.786790i | \(-0.288258\pi\) | ||||
0.617221 | + | 0.786790i | \(0.288258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.67074 | −1.46418 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.09490 | − | 0.481483i | 0.993158 | − | 0.116777i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.20490 | −1.19409 | −0.597043 | − | 0.802209i | \(-0.703658\pi\) | ||||
−0.597043 | + | 0.802209i | \(0.703658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.99502 | −0.653567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.19080i | − | 0.665327i | −0.943046 | − | 0.332663i | \(-0.892053\pi\) | ||
0.943046 | − | 0.332663i | \(-0.107947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.84674 | −1.56935 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.53249i | 1.06473i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.05381i | 0.938469i | 0.883073 | + | 0.469235i | \(0.155470\pi\) | ||||
−0.883073 | + | 0.469235i | \(0.844530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.34568i | 0.600901i | 0.953797 | + | 0.300451i | \(0.0971371\pi\) | ||||
−0.953797 | + | 0.300451i | \(0.902863\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.47260 | 0.430425 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.78505 | −1.14688 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.4521i | 1.71832i | 0.511708 | + | 0.859159i | \(0.329013\pi\) | ||||
−0.511708 | + | 0.859159i | \(0.670987\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.04183i | 1.12760i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.35341i | − | 1.46076i | −0.683042 | − | 0.730379i | \(-0.739344\pi\) | ||
0.683042 | − | 0.730379i | \(-0.260656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.48993 | −1.14220 | −0.571102 | − | 0.820879i | \(-0.693484\pi\) | ||||
−0.571102 | + | 0.820879i | \(0.693484\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.78083i | 0.265471i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.79104 | −1.28230 | −0.641152 | − | 0.767413i | \(-0.721543\pi\) | ||||
−0.641152 | + | 0.767413i | \(0.721543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.41645 | 0.488064 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.761771 | + | 6.47867i | 0.106669 | + | 0.907196i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.62104 | −0.360027 | −0.180014 | − | 0.983664i | \(-0.557614\pi\) | ||||
−0.180014 | + | 0.983664i | \(0.557614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.60154 | 0.755312 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.23485i | − | 1.09073i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4686i | 1.59644i | 0.602365 | + | 0.798221i | \(0.294225\pi\) | ||||
−0.602365 | + | 0.798221i | \(0.705775\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.940554i | 0.118499i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.9529i | 1.97871i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.37777 | 0.168322 | 0.0841610 | − | 0.996452i | \(-0.473179\pi\) | ||||
0.0841610 | + | 0.996452i | \(0.473179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.04827 | 0.607740 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.38491i | 1.11378i | 0.830585 | + | 0.556892i | \(0.188006\pi\) | ||||
−0.830585 | + | 0.556892i | \(0.811994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.343768i | − | 0.0402350i | −0.999798 | − | 0.0201175i | \(-0.993596\pi\) | ||
0.999798 | − | 0.0201175i | \(-0.00640403\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 12.4146i | − | 1.43351i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.95847 | 0.337149 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0938078i | 0.0105542i | 0.999986 | + | 0.00527710i | \(0.00167976\pi\) | ||||
−0.999986 | + | 0.00527710i | \(0.998320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.26258 | −0.806954 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.61501 | −0.616327 | −0.308164 | − | 0.951333i | \(-0.599714\pi\) | ||||
−0.308164 | + | 0.951333i | \(0.599714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.72575 | + | 14.6771i | 0.187184 | + | 1.59195i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.99581 | −0.857241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.62341 | 0.808080 | 0.404040 | − | 0.914741i | \(-0.367606\pi\) | ||||
0.404040 | + | 0.914741i | \(0.367606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.42557i | 0.883240i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.29331 | −0.548891 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 18.6556i | − | 1.91402i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.3041i | − | 1.75696i | −0.477778 | − | 0.878481i | \(-0.658558\pi\) | ||
0.477778 | − | 0.878481i | \(-0.341442\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.776494i | − | 0.0780406i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.25828 | −0.622722 | −0.311361 | − | 0.950292i | \(-0.600785\pi\) | ||||
−0.311361 | + | 0.950292i | \(0.600785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.23906 | −0.516220 | −0.258110 | − | 0.966116i | \(-0.583100\pi\) | ||||
−0.258110 | + | 0.966116i | \(0.583100\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 10.7349i | − | 1.04762i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5877i | 1.50692i | 0.657493 | + | 0.753461i | \(0.271617\pi\) | ||||
−0.657493 | + | 0.753461i | \(0.728383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.3432i | − | 0.990702i | −0.868693 | − | 0.495351i | \(-0.835040\pi\) | ||
0.868693 | − | 0.495351i | \(-0.164960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.5367 | −1.56959 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.39401i | − | 0.225209i | −0.993640 | − | 0.112605i | \(-0.964081\pi\) | ||
0.993640 | − | 0.112605i | \(-0.0359193\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4366 | 1.06646 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.21141 | 0.204445 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.911460 | + | 7.75175i | 0.0835534 | + | 0.710602i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.55757 | 0.777961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.7984 | 1.33432 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.2034i | − | 0.912619i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00038 | 0.443712 | 0.221856 | − | 0.975079i | \(-0.428789\pi\) | ||||
0.221856 | + | 0.975079i | \(0.428789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 11.8501i | − | 1.04334i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12.3002i | − | 1.07467i | −0.843368 | − | 0.537336i | \(-0.819431\pi\) | ||
0.843368 | − | 0.537336i | \(-0.180569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 9.85302i | − | 0.854365i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.8297 | −1.70667 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8131 | 0.923826 | 0.461913 | − | 0.886925i | \(-0.347163\pi\) | ||||
0.461913 | + | 0.886925i | \(0.347163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.0120i | − | 1.01884i | −0.860517 | − | 0.509422i | \(-0.829859\pi\) | ||
0.860517 | − | 0.509422i | \(-0.170141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 13.9086i | − | 1.17132i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.95590i | − | 0.581682i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.1141 | −1.50429 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.40528i | 0.445820i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.55621 | −0.455183 | −0.227591 | − | 0.973757i | \(-0.573085\pi\) | ||||
−0.227591 | + | 0.973757i | \(0.573085\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.65649 | 0.134803 | 0.0674017 | − | 0.997726i | \(-0.478529\pi\) | ||||
0.0674017 | + | 0.997726i | \(0.478529\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.03456 | − | 0.239226i | 0.164484 | − | 0.0193403i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.9917 | −0.963196 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.3905 | −1.86677 | −0.933384 | − | 0.358879i | \(-0.883159\pi\) | ||||
−0.933384 | + | 0.358879i | \(0.883159\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 4.14683i | − | 0.328865i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.04026 | 0.476039 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.0466i | − | 1.25687i | −0.777863 | − | 0.628434i | \(-0.783696\pi\) | ||
0.777863 | − | 0.628434i | \(-0.216304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.86239i | 0.689936i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.2908i | 1.18324i | 0.806218 | + | 0.591619i | \(0.201511\pi\) | ||||
−0.806218 | + | 0.591619i | \(0.798489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.81003 | 0.523848 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.58607 | −0.197761 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0988i | 1.37602i | 0.725699 | + | 0.688012i | \(0.241516\pi\) | ||||
−0.725699 | + | 0.688012i | \(0.758484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 14.8541i | − | 1.12286i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.58213i | 0.118920i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.81731 | −0.285319 | −0.142660 | − | 0.989772i | \(-0.545565\pi\) | ||||
−0.142660 | + | 0.989772i | \(0.545565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.6812i | 1.09125i | 0.838030 | + | 0.545623i | \(0.183707\pi\) | ||||
−0.838030 | + | 0.545623i | \(0.816293\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.7270 | −1.45826 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −37.4629 | −2.75433 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.752475 | − | 6.39961i | −0.0550264 | − | 0.467986i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.4731 | −0.761810 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0400 | 1.73947 | 0.869736 | − | 0.493516i | \(-0.164289\pi\) | ||||
0.869736 | + | 0.493516i | \(0.164289\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.17007i | 0.516113i | 0.966130 | + | 0.258056i | \(0.0830820\pi\) | ||||
−0.966130 | + | 0.258056i | \(0.916918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −25.2396 | −1.80744 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26.2724i | − | 1.87183i | −0.352223 | − | 0.935916i | \(-0.614574\pi\) | ||
0.352223 | − | 0.935916i | \(-0.385426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.6922i | − | 1.32505i | −0.749039 | − | 0.662526i | \(-0.769484\pi\) | ||
0.749039 | − | 0.662526i | \(-0.230516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.17982i | 0.153753i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.56700 | −0.671472 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.5248 | 2.34148 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.58535i | − | 0.110190i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.13436i | 0.562666i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.31656i | 0.228321i | 0.993462 | + | 0.114161i | \(0.0364179\pi\) | ||||
−0.993462 | + | 0.114161i | \(0.963582\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.8482 | −1.01738 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 26.8457i | − | 1.83086i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.33346 | −0.429943 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.543887 | 0.0367525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.2258 | − | 2.14301i | 1.22600 | − | 0.144154i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.9721 | 1.60529 | 0.802646 | − | 0.596455i | \(-0.203425\pi\) | ||||
0.802646 | + | 0.596455i | \(0.203425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.89867 | −0.259911 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.60333i | 0.371906i | 0.982559 | + | 0.185953i | \(0.0595373\pi\) | ||||
−0.982559 | + | 0.185953i | \(0.940463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.4728 | −1.48504 | −0.742522 | − | 0.669822i | \(-0.766371\pi\) | ||||
−0.742522 | + | 0.669822i | \(0.766371\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.68070i | 0.307968i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.42422i | 0.0933040i | 0.998911 | + | 0.0466520i | \(0.0148552\pi\) | ||||
−0.998911 | + | 0.0466520i | \(0.985145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 31.5092i | − | 2.05543i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.148416 | −0.00964068 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.15838 | 0.139614 | 0.0698069 | − | 0.997561i | \(-0.477762\pi\) | ||||
0.0698069 | + | 0.997561i | \(0.477762\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.58435i | − | 0.230888i | −0.993314 | − | 0.115444i | \(-0.963171\pi\) | ||
0.993314 | − | 0.115444i | \(-0.0368292\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.10709i | 0.327620i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2454i | 0.782327i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.1662 | −1.47403 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 8.88369i | − | 0.562981i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.1042 | 1.71080 | 0.855402 | − | 0.517965i | \(-0.173310\pi\) | ||||
0.855402 | + | 0.517965i | \(0.173310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.98666 | −0.313509 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.2211 | + | 2.73037i | −1.45416 | + | 0.170982i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.0133424 | 0.000832275 | 0.000416138 | − | 1.00000i | \(-0.499868\pi\) | ||||
0.000416138 | 1.00000i | \(0.499868\pi\) | ||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.7862 | −1.22945 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.51100i | 0.155427i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.6287 | 1.51867 | 0.759336 | − | 0.650699i | \(-0.225524\pi\) | ||||
0.759336 | + | 0.650699i | \(0.225524\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.39441i | − | 0.577094i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0613i | 0.738137i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 20.8960i | − | 1.27405i | −0.770842 | − | 0.637026i | \(-0.780164\pi\) | ||
0.770842 | − | 0.637026i | \(-0.219836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.90014 | 0.297662 | 0.148831 | − | 0.988863i | \(-0.452449\pi\) | ||||
0.148831 | + | 0.988863i | \(0.452449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.3304 | −0.806791 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2631i | 0.739493i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6.82078i | − | 0.409821i | −0.978781 | − | 0.204911i | \(-0.934310\pi\) | ||
0.978781 | − | 0.204911i | \(-0.0656904\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.66231i | 0.0995196i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6085 | 0.811813 | 0.405907 | − | 0.913915i | \(-0.366956\pi\) | ||||
0.405907 | + | 0.913915i | \(0.366956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.0157633i | − | 0.000937032i | −1.00000 | 0.000468516i | \(-0.999851\pi\) | |||
1.00000 | 0.000468516i | \(-0.000149133\pi\) | ||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29.5157 | 1.74836 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.7063 | 1.04517 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5363 | − | 3.94325i | 0.972726 | − | 0.231956i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.3774 | 1.60489 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.9213 | 1.16382 | 0.581909 | − | 0.813254i | \(-0.302306\pi\) | ||||
0.581909 | + | 0.813254i | \(0.302306\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58424i | 0.208682i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.64632 | 0.501711 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 14.2017i | − | 0.821308i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 14.1786i | − | 0.817244i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.90143i | − | 0.568822i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −44.6904 | −2.55897 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.9494 | −1.53808 | −0.769041 | − | 0.639200i | \(-0.779266\pi\) | ||||
−0.769041 | + | 0.639200i | \(0.779266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 8.28890i | − | 0.471539i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.3066i | 1.49171i | 0.666107 | + | 0.745856i | \(0.267959\pi\) | ||||
−0.666107 | + | 0.745856i | \(0.732041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.40205i | 0.248819i | 0.992231 | + | 0.124409i | \(0.0397036\pi\) | ||||
−0.992231 | + | 0.124409i | \(0.960296\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.37117 | −0.189944 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.6804i | 1.77935i | 0.456596 | + | 0.889674i | \(0.349069\pi\) | ||||
−0.456596 | + | 0.889674i | \(0.650931\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.89824 | 0.442216 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.6619 | −1.37649 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.3135 | + | 2.50607i | −1.18592 | + | 0.139442i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −34.9246 | −1.93727 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.3644 | 0.904952 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 16.6417i | − | 0.917485i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.43983 | 0.134105 | 0.0670526 | − | 0.997749i | \(-0.478640\pi\) | ||||
0.0670526 | + | 0.997749i | \(0.478640\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.19316i | 0.284583i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.93827i | 0.269806i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.74925i | − | 0.367655i | −0.982959 | − | 0.183827i | \(-0.941151\pi\) | ||
0.982959 | − | 0.183827i | \(-0.0588488\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.78764 | 0.205716 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.22871 | 0.283151 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7186i | 1.06471i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.0942i | 0.974158i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.92260i | 0.532673i | 0.963880 | + | 0.266336i | \(0.0858132\pi\) | ||||
−0.963880 | + | 0.266336i | \(0.914187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.02529 | 0.268997 | 0.134499 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134499 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.6243i | 1.31435i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5183 | 0.932404 | 0.466202 | − | 0.884678i | \(-0.345622\pi\) | ||||
0.466202 | + | 0.884678i | \(0.345622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.6377 | −1.78531 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.2643 | + | 1.44205i | −0.649096 | + | 0.0763215i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.3101 | 1.12471 | 0.562353 | − | 0.826897i | \(-0.309896\pi\) | ||||
0.562353 | + | 0.826897i | \(0.309896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.09101 | 0.425843 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.5392i | 0.710625i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.23215 | 0.0644934 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.3182i | − | 0.590808i | −0.955372 | − | 0.295404i | \(-0.904546\pi\) | ||
0.955372 | − | 0.295404i | \(-0.0954542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.64726i | − | 0.241927i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.96169i | − | 0.257598i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.2356 | −1.41021 | −0.705104 | − | 0.709104i | \(-0.749100\pi\) | ||||
−0.705104 | + | 0.709104i | \(0.749100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.1431 | 0.833628 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.4937i | 1.15849i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.8756i | − | 0.815473i | −0.913100 | − | 0.407737i | \(-0.866318\pi\) | ||
0.913100 | − | 0.407737i | \(-0.133682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.91127i | 0.405307i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.5223 | −1.61072 | −0.805358 | − | 0.592788i | \(-0.798027\pi\) | ||||
−0.805358 | + | 0.592788i | \(0.798027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.6039i | 0.540423i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.72139 | −0.189169 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.593284 | 0.0300807 | 0.0150403 | − | 0.999887i | \(-0.495212\pi\) | ||||
0.0150403 | + | 0.999887i | \(0.495212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53631 | − | 13.0660i | −0.0776947 | − | 0.660775i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.4605 | 0.981654 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.336229 | −0.0169175 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.0032i | 1.15450i | 0.816568 | + | 0.577249i | \(0.195874\pi\) | ||||
−0.816568 | + | 0.577249i | \(0.804126\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.5888 | 0.780416 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.7157i | − | 0.585052i | −0.956258 | − | 0.292526i | \(-0.905504\pi\) | ||
0.956258 | − | 0.292526i | \(-0.0944959\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.8911i | 0.741778i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 26.0308i | − | 1.29348i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.3349 | 0.809689 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8877 | 0.983383 | 0.491692 | − | 0.870769i | \(-0.336379\pi\) | ||||
0.491692 | + | 0.870769i | \(0.336379\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.1078i | 0.843865i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.89303i | 0.0931498i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.1255i | − | 0.987922i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.0046 | 0.930658 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.1372i | 0.641796i | 0.947114 | + | 0.320898i | \(0.103985\pi\) | ||||
−0.947114 | + | 0.320898i | \(0.896015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9753 | −0.827326 | −0.413663 | − | 0.910430i | \(-0.635751\pi\) | ||||
−0.413663 | + | 0.910430i | \(0.635751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.36785 | −0.212372 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −32.1316 | + | 3.77807i | −1.55861 | + | 0.183263i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.6034 | −1.14225 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.0052 | 0.531335 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 25.5419i | − | 1.23031i | −0.788407 | − | 0.615155i | \(-0.789094\pi\) | ||
0.788407 | − | 0.615155i | \(-0.210906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.83130 | −0.472462 | −0.236231 | − | 0.971697i | \(-0.575912\pi\) | ||||
−0.236231 | + | 0.971697i | \(0.575912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 28.6589i | − | 1.37409i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.6078i | 0.794458i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.76931i | 0.132172i | 0.997814 | + | 0.0660859i | \(0.0210511\pi\) | ||||
−0.997814 | + | 0.0660859i | \(0.978949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.69747 | 0.0808319 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.6505 | 0.601046 | 0.300523 | − | 0.953775i | \(-0.402839\pi\) | ||||
0.300523 | + | 0.953775i | \(0.402839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.3241i | 1.29529i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 8.79067i | − | 0.415784i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.6353i | 1.30419i | 0.758136 | + | 0.652096i | \(0.226110\pi\) | ||||
−0.758136 | + | 0.652096i | \(0.773890\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.6178 | −0.688324 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.62079i | 0.123136i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.1992 | −1.41576 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.73621 | 0.315106 | 0.157553 | − | 0.987510i | \(-0.449639\pi\) | ||||
0.157553 | + | 0.987510i | \(0.449639\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.66380 | + | 22.6550i | 0.124335 | + | 1.05744i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.4289 | 1.65009 | 0.825044 | − | 0.565068i | \(-0.191150\pi\) | ||||
0.825044 | + | 0.565068i | \(0.191150\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.8991 | −1.43600 | −0.718001 | − | 0.696042i | \(-0.754943\pi\) | ||||
−0.718001 | + | 0.696042i | \(0.754943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 18.9725i | − | 0.879827i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −42.9151 | −1.98588 | −0.992938 | − | 0.118635i | \(-0.962148\pi\) | ||||
−0.992938 | + | 0.118635i | \(0.962148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.60816i | 0.120434i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 37.0070i | − | 1.70519i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7055i | 0.538218i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.8415 | 1.87394 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.30227 | −0.0596267 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.0325i | 0.869619i | 0.900522 | + | 0.434810i | \(0.143184\pi\) | ||||
−0.900522 | + | 0.434810i | \(0.856816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 46.5208i | 2.12117i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.55650i | 0.434836i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 62.0218 | 2.81627 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8292i | 0.581346i | 0.956823 | + | 0.290673i | \(0.0938791\pi\) | ||||
−0.956823 | + | 0.290673i | \(0.906121\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.3879 | 1.14808 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.6194 | 1.87826 | 0.939128 | − | 0.343568i | \(-0.111636\pi\) | ||||
0.939128 | + | 0.343568i | \(0.111636\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.43332 | + | 20.6948i | 0.109591 | + | 0.932049i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.78314 | 0.125093 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.7659 | −0.796909 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.1730i | − | 0.589704i | −0.955543 | − | 0.294852i | \(-0.904730\pi\) | ||
0.955543 | − | 0.294852i | \(-0.0952703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.1921 | −1.08082 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.1004i | 0.851645i | 0.904807 | + | 0.425822i | \(0.140015\pi\) | ||||
−0.904807 | + | 0.425822i | \(0.859985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 22.4311i | − | 0.998172i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.7744i | 0.478507i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.61049 | 0.337329 | 0.168665 | − | 0.985674i | \(-0.446055\pi\) | ||||
0.168665 | + | 0.985674i | \(0.446055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.650762 | 0.0287880 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 28.7961i | − | 1.27138i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 18.7780i | − | 0.827459i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.7389i | 0.604235i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.6347 | −1.25692 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.2618i | − | 0.537200i | −0.963252 | − | 0.268600i | \(-0.913439\pi\) | ||
0.963252 | − | 0.268600i | \(-0.0865609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8885 | 0.563576 | 0.281788 | − | 0.959477i | \(-0.409073\pi\) | ||||
0.281788 | + | 0.959477i | \(0.409073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 23.5012 | 1.02567 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.61089 | + | 13.7002i | 0.0701713 | + | 0.596790i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.8188 | 0.557340 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.496852 | 0.0215615 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 41.6306i | − | 1.80322i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.8700 | −2.41547 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 6.03949i | − | 0.260623i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.33932i | − | 0.229981i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.06145i | − | 0.131622i | −0.997832 | − | 0.0658110i | \(-0.979037\pi\) | ||
0.997832 | − | 0.0658110i | \(-0.0209634\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.2277 | −0.996795 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.0726 | 1.58801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.3138i | − | 0.483742i | −0.970308 | − | 0.241871i | \(-0.922239\pi\) | ||
0.970308 | − | 0.241871i | \(-0.0777611\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.19505i | 0.264398i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 26.3046i | − | 1.12061i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.177581 | −0.00755150 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 59.2713i | − | 2.51593i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.2845 | 0.689997 | 0.344998 | − | 0.938603i | \(-0.387879\pi\) | ||||
0.344998 | + | 0.938603i | \(0.387879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.3365 | −1.40999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1250 | − | 1.19052i | 0.427480 | − | 0.0502636i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8913 | 0.459015 | 0.229507 | − | 0.973307i | \(-0.426288\pi\) | ||||
0.229507 | + | 0.973307i | \(0.426288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.58068 | 0.360992 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 13.7483i | − | 0.577373i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.94516 | −0.249234 | −0.124617 | − | 0.992205i | \(-0.539770\pi\) | ||||
−0.124617 | + | 0.992205i | \(0.539770\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 33.2531i | − | 1.39160i | −0.718236 | − | 0.695800i | \(-0.755050\pi\) | ||
0.718236 | − | 0.695800i | \(-0.244950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.0345i | 1.58891i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.0373i | 1.04413i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.8801 | 1.41045 | 0.705223 | − | 0.708986i | \(-0.250847\pi\) | ||||
0.705223 | + | 0.708986i | \(0.250847\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3440 | −0.471441 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 10.6294i | − | 0.440980i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.09623i | 0.169648i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.92622i | 0.327709i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.40852 | −0.347057 | −0.173528 | − | 0.984829i | \(-0.555517\pi\) | ||||
−0.173528 | + | 0.984829i | \(0.555517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 17.4139i | − | 0.717528i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.5665 | 1.70982 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.05925 | 0.330954 | 0.165477 | − | 0.986214i | \(-0.447084\pi\) | ||||
0.165477 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.7841 | + | 3.26689i | −1.13904 | + | 0.133929i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.5735 | 1.21036 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7884 | −0.522521 | −0.261261 | − | 0.965268i | \(-0.584138\pi\) | ||||
−0.261261 | + | 0.965268i | \(0.584138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.7382i | 1.13147i | 0.824588 | + | 0.565733i | \(0.191407\pi\) | ||||
−0.824588 | + | 0.565733i | \(0.808593\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.684550 | 0.0278770 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.6723i | 1.24701i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.8395i | − | 0.886437i | −0.896414 | − | 0.443218i | \(-0.853837\pi\) | ||
0.896414 | − | 0.443218i | \(-0.146163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 15.1363i | − | 0.613353i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.1276 | −1.58293 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.60258 | −0.185896 | −0.0929482 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929482 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 53.0408i | 2.13881i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 20.2849i | − | 0.816638i | −0.912839 | − | 0.408319i | \(-0.866115\pi\) | ||
0.912839 | − | 0.408319i | \(-0.133885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1774i | 0.529643i | 0.964297 | + | 0.264822i | \(0.0853131\pi\) | ||||
−0.964297 | + | 0.264822i | \(0.914687\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.6530 | 0.708392 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.4313i | 0.578179i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.66235 | −0.106494 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.8697 | −0.513964 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.03252 | + | 42.8004i | 0.200660 | + | 1.70656i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.2829 | −1.16573 | −0.582867 | − | 0.812567i | \(-0.698069\pi\) | ||||
−0.582867 | + | 0.812567i | \(0.698069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.24724 | −0.208559 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.9225i | 0.711234i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.2061 | 0.602487 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.66291i | 0.184462i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.14950i | − | 0.163895i | −0.996637 | − | 0.0819477i | \(-0.973886\pi\) | ||
0.996637 | − | 0.0819477i | \(-0.0261141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.693712i | 0.0273573i | 0.999906 | + | 0.0136787i | \(0.00435419\pi\) | ||||
−0.999906 | + | 0.0136787i | \(0.995646\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42.4735 | 1.67239 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.9107 | −1.68699 | −0.843497 | − | 0.537133i | \(-0.819507\pi\) | ||||
−0.843497 | + | 0.537133i | \(0.819507\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.56283i | − | 0.0613463i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 10.0204i | − | 0.392729i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 44.3141i | − | 1.73415i | −0.498182 | − | 0.867073i | \(-0.665999\pi\) | ||
0.498182 | − | 0.867073i | \(-0.334001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.0867 | 1.72261 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.170802i | − | 0.00666361i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.3683 | −0.988208 | −0.494104 | − | 0.869403i | \(-0.664504\pi\) | ||||
−0.494104 | + | 0.869403i | \(0.664504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.6011 | 1.03466 | 0.517331 | − | 0.855785i | \(-0.326926\pi\) | ||||
0.517331 | + | 0.855785i | \(0.326926\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.39052 | + | 28.8356i | 0.131677 | + | 1.11988i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.3155 | 1.36948 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.1257 | 0.624389 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.9271i | 1.46635i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.4863 | 0.752260 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3769i | 0.901114i | 0.892748 | + | 0.450557i | \(0.148775\pi\) | ||||
−0.892748 | + | 0.450557i | \(0.851225\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 43.4120i | − | 1.67093i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.91913i | − | 0.227491i | −0.993510 | − | 0.113745i | \(-0.963715\pi\) | ||
0.993510 | − | 0.113745i | \(-0.0362848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.7571 | 1.25710 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.86522 | −0.339716 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.2331i | 1.50121i | 0.660749 | + | 0.750607i | \(0.270239\pi\) | ||||
−0.660749 | + | 0.750607i | \(0.729761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.7567i | 1.48082i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 35.5550i | − | 1.35651i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.6658 | −0.444433 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 0.796860i | − | 0.0303140i | −0.999885 | − | 0.0151570i | \(-0.995175\pi\) | ||
0.999885 | − | 0.0151570i | \(-0.00482481\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.46992 | 0.0558378 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.0538 | 1.63312 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.50351 | − | 38.3013i | −0.170583 | − | 1.45076i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.25331 | −0.0852281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.4629 | −1.94373 | −0.971863 | − | 0.235547i | \(-0.924312\pi\) | ||||
−0.971863 | + | 0.235547i | \(0.924312\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 54.4023i | − | 2.05182i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 49.8517 | 1.87752 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 11.8471i | − | 0.445555i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.03296i | 0.339240i | 0.985510 | + | 0.169620i | \(0.0542540\pi\) | ||||
−0.985510 | + | 0.169620i | \(0.945746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0466086i | 0.00174796i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.6754 | 0.399796 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.9316 | 0.932389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.41484i | 0.127530i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.4318i | 1.20950i | 0.796414 | + | 0.604751i | \(0.206727\pi\) | ||||
−0.796414 | + | 0.604751i | \(0.793273\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 9.91768i | − | 0.369354i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.67093 | 0.210904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 39.6560i | − | 1.47279i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.10920 | −0.0782260 | −0.0391130 | − | 0.999235i | \(-0.512453\pi\) | ||||
−0.0391130 | + | 0.999235i | \(0.512453\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.8678 | −1.10622 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.6705 | + | 3.60628i | −1.13439 | + | 0.133383i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.0998 | 1.59193 | 0.795965 | − | 0.605343i | \(-0.206964\pi\) | ||||
0.795965 | + | 0.605343i | \(0.206964\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.3738 | −0.714613 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.15322i | − | 0.0793150i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3126 | 0.747213 | 0.373606 | − | 0.927587i | \(-0.378121\pi\) | ||||
0.373606 | + | 0.927587i | \(0.378121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 36.6521i | − | 1.34645i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.0484i | 0.625444i | 0.949845 | + | 0.312722i | \(0.101241\pi\) | ||||
−0.949845 | + | 0.312722i | \(0.898759\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 19.9148i | − | 0.729621i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.78983 | −0.102074 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.5080 | −1.07820 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4080i | 0.452774i | 0.974037 | + | 0.226387i | \(0.0726914\pi\) | ||||
−0.974037 | + | 0.226387i | \(0.927309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42.8825i | 1.56273i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.93726i | 0.216079i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.1856 | 1.60595 | 0.802977 | − | 0.596010i | \(-0.203248\pi\) | ||||
0.802977 | + | 0.596010i | \(0.203248\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 7.88957i | − | 0.286373i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.6006 | −1.58052 | −0.790260 | − | 0.612771i | \(-0.790055\pi\) | ||||
−0.790260 | + | 0.612771i | \(0.790055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.5800 | 0.708844 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.857441 | + | 7.29233i | 0.0310009 | + | 0.263655i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.45085 | 0.160711 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.3200 | −1.23761 | −0.618805 | − | 0.785545i | \(-0.712383\pi\) | ||||
−0.618805 | + | 0.785545i | \(0.712383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0211094i | 0.000760238i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.7230 | 0.637453 | 0.318727 | − | 0.947847i | \(-0.396745\pi\) | ||||
0.318727 | + | 0.947847i | \(0.396745\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 26.2527i | − | 0.943023i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 31.3043i | − | 1.12304i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48.6836i | 1.74427i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6670 | 0.524826 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.9602 | −0.999215 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 83.8372i | − | 2.99228i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.9869i | 0.427286i | 0.976912 | + | 0.213643i | \(0.0685330\pi\) | ||||
−0.976912 | + | 0.213643i | \(0.931467\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.9659i | 1.38722i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.53192 | 0.161137 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.4959i | 1.97072i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.8632 | 0.527144 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.8688 | 0.526679 | 0.263340 | − | 0.964703i | \(-0.415176\pi\) | ||||
0.263340 | + | 0.964703i | \(0.415176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.9984 | + | 4.23274i | −1.27353 | + | 0.149743i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.78771 | 0.133832 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.537250 | −0.0189591 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.6497i | 0.763052i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.0603 | 1.16378 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.78859i | 0.238674i | 0.992854 | + | 0.119337i | \(0.0380769\pi\) | ||||
−0.992854 | + | 0.119337i | \(0.961923\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 48.3778i | − | 1.69877i | −0.527771 | − | 0.849387i | \(-0.676972\pi\) | ||
0.527771 | − | 0.849387i | \(-0.323028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.75268i | 0.271898i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 57.5148 | 2.01466 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.9844 | 1.36389 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.18626i | 0.146280i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.2609i | 1.26552i | 0.774350 | + | 0.632758i | \(0.218077\pi\) | ||||
−0.774350 | + | 0.632758i | \(0.781923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 42.0596i | − | 1.46611i | −0.680171 | − | 0.733053i | \(-0.738095\pi\) | ||
0.680171 | − | 0.733053i | \(-0.261905\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.4019 | −0.675486 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.6803i | 1.58846i | 0.607618 | + | 0.794229i | \(0.292125\pi\) | ||||
−0.607618 | + | 0.794229i | \(0.707875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.7905 | 1.17359 | 0.586797 | − | 0.809734i | \(-0.300389\pi\) | ||||
0.586797 | + | 0.809734i | \(0.300389\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7914 | 0.374349 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.9900 | − | 1.64496i | 0.484725 | − | 0.0569946i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.8059 | −1.89664 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.5099 | −0.639796 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 22.5082i | − | 0.777070i | −0.921434 | − | 0.388535i | \(-0.872981\pi\) | ||
0.921434 | − | 0.388535i | \(-0.127019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.45898 | 0.119275 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.5304i | 0.741547i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.4087i | 0.839686i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.1997i | 0.556629i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0249397 | 0.000855928 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.3506 | 1.14324 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8377i | 1.02162i | 0.859693 | + | 0.510812i | \(0.170655\pi\) | ||||
−0.859693 | + | 0.510812i | \(0.829345\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 9.26907i | − | 0.316995i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.5786i | 1.42030i | 0.704051 | + | 0.710149i | \(0.251372\pi\) | ||||
−0.704051 | + | 0.710149i | \(0.748628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.8165 | 1.52912 | 0.764559 | − | 0.644553i | \(-0.222957\pi\) | ||||
0.764559 | + | 0.644553i | \(0.222957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.0137i | 0.954704i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.6589 | 1.69041 | 0.845204 | − | 0.534445i | \(-0.179479\pi\) | ||||
0.845204 | + | 0.534445i | \(0.179479\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −64.8702 | −2.20565 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.23874 | + | 26.1627i | 0.211879 | + | 0.888533i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.146605 | 0.00497324 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.13226 | 0.207784 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.59756i | − | 0.290983i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.3153 | 0.652976 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 33.2814i | − | 1.12383i | −0.827194 | − | 0.561917i | \(-0.810064\pi\) | ||
0.827194 | − | 0.561917i | \(-0.189936\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.5182i | 1.06308i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.2188i | − | 1.42239i | −0.702995 | − | 0.711194i | \(-0.748155\pi\) | ||
0.702995 | − | 0.711194i | \(-0.251845\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.4815 | 0.722908 | 0.361454 | − | 0.932390i | \(-0.382280\pi\) | ||||
0.361454 | + | 0.932390i | \(0.382280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.67074 | −0.190620 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.65510i | 0.290610i | 0.989387 | + | 0.145305i | \(0.0464163\pi\) | ||||
−0.989387 | + | 0.145305i | \(0.953584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.46585i | 0.317475i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.3502i | 0.380245i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.7565 | 1.53118 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13.6821i | − | 0.457343i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.4691 | 0.750220 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.9084 | −0.563927 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7329 | + | 1.26198i | −0.357564 | + | 0.0420428i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.4325 | 0.746508 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −52.6210 | −1.74918 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 20.3331i | − | 0.675148i | −0.941299 | − | 0.337574i | \(-0.890394\pi\) | ||
0.941299 | − | 0.337574i | \(-0.109606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.10944 | −0.103133 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22.1710i | − | 0.734557i | −0.930111 | − | 0.367278i | \(-0.880290\pi\) | ||
0.930111 | − | 0.367278i | \(-0.119710\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.77529i | 0.290420i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 70.7062i | − | 2.33748i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.2846 | 0.768924 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.4400 | 0.344382 | 0.172191 | − | 0.985064i | \(-0.444915\pi\) | ||||
0.172191 | + | 0.985064i | \(0.444915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 42.6375i | − | 1.40495i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.7708i | 1.37490i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 82.0151i | − | 2.69664i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.60304 | −0.0854950 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 32.0755i | − | 1.05236i | −0.850372 | − | 0.526181i | \(-0.823623\pi\) | ||
0.850372 | − | 0.526181i | \(-0.176377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.7823 | −0.582791 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −41.6206 | −1.36260 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.9377 | − | 2.69705i | 0.750144 | − | 0.0882028i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.5251 | −1.45457 | −0.727286 | − | 0.686334i | \(-0.759219\pi\) | ||||
−0.727286 | + | 0.686334i | \(0.759219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.96463 | −0.227282 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.50560i | 0.179477i | 0.995965 | + | 0.0897387i | \(0.0286032\pi\) | ||||
−0.995965 | + | 0.0897387i | \(0.971397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.8448 | −0.971881 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 37.5382i | − | 1.22112i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.9363i | − | 0.485365i | −0.970106 | − | 0.242682i | \(-0.921973\pi\) | ||
0.970106 | − | 0.242682i | \(-0.0780273\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.53006i | − | 0.0496678i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −50.1226 | −1.62534 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.0150 | 1.65254 | 0.826269 | − | 0.563275i | \(-0.190459\pi\) | ||||
0.826269 | + | 0.563275i | \(0.190459\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 86.1650i | 2.78823i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.4961i | 0.403940i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.4695i | 0.660995i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.8064 | 0.638918 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.74479i | 0.249572i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.6992 | −0.827287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6627 | 0.953888 | 0.476944 | − | 0.878934i | \(-0.341745\pi\) | ||||
0.476944 | + | 0.878934i | \(0.341745\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.96494 | − | 33.7209i | −0.127372 | − | 1.08327i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.6626 | 1.01610 | 0.508051 | − | 0.861327i | \(-0.330366\pi\) | ||||
0.508051 | + | 0.861327i | \(0.330366\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.7390 | 0.728979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 55.2555i | − | 1.76959i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.0522 | −1.37736 | −0.688682 | − | 0.725064i | \(-0.741810\pi\) | ||||
−0.688682 | + | 0.725064i | \(0.741810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.9141i | − | 0.380776i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 5.13905i | − | 0.164077i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 40.7923i | − | 1.30107i | −0.759475 | − | 0.650536i | \(-0.774544\pi\) | ||
0.759475 | − | 0.650536i | \(-0.225456\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 94.1665 | 3.00040 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.3294 | 0.838073 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.8988i | 0.759939i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6.81018i | − | 0.216332i | −0.994133 | − | 0.108166i | \(-0.965502\pi\) | ||
0.994133 | − | 0.108166i | \(-0.0344979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.86014i | 0.122498i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 66.9971 | 2.12395 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.8118i | 1.26085i | 0.776249 | + | 0.630427i | \(0.217120\pi\) | ||||
−0.776249 | + | 0.630427i | \(0.782880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −57.8263 | −1.82954 |
(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 | 4012.2.b.b.237.34 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.13 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.13 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.34 | yes | 46 | 1.1 | even | 1 | trivial |