Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, 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("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 760) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.4 | ||
Root | \(-1.75233 - 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.k.3649.3 |
$q$-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 \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.363328i | 0.209768i | 0.994484 | + | 0.104884i | \(0.0334471\pi\) | ||||
−0.994484 | + | 0.104884i | \(0.966553\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.14134i | − 0.431385i | −0.976461 | − | 0.215692i | \(-0.930799\pi\) | ||||
0.976461 | − | 0.215692i | \(-0.0692008\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.86799 | 0.955998 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72666 | −0.822118 | −0.411059 | − | 0.911609i | \(-0.634841\pi\) | ||||
−0.411059 | + | 0.911609i | \(0.634841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.64600i | − 1.28857i | −0.764786 | − | 0.644284i | \(-0.777155\pi\) | ||||
0.764786 | − | 0.644284i | \(-0.222845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.858664i | 0.208257i | 0.994564 | + | 0.104128i | \(0.0332053\pi\) | ||||
−0.994564 | + | 0.104128i | \(0.966795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.414680 | 0.0904905 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.41468i | − 0.920524i | −0.887783 | − | 0.460262i | \(-0.847755\pi\) | ||||
0.887783 | − | 0.460262i | \(-0.152245\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13201i | 0.410305i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.42401 | −1.74999 | −0.874997 | − | 0.484128i | \(-0.839137\pi\) | ||||
−0.874997 | + | 0.484128i | \(0.839137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2827 | −1.84682 | −0.923411 | − | 0.383812i | \(-0.874611\pi\) | ||||
−0.923411 | + | 0.383812i | \(0.874611\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 0.990671i | − 0.172454i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.77801i | − 1.11430i | −0.830413 | − | 0.557149i | \(-0.811895\pi\) | ||||
0.830413 | − | 0.557149i | \(-0.188105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.68802 | 0.270300 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.55602 | −1.18005 | −0.590026 | − | 0.807384i | \(-0.700882\pi\) | ||||
−0.590026 | + | 0.807384i | \(0.700882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.29200i | 1.41702i | 0.705702 | + | 0.708508i | \(0.250632\pi\) | ||||
−0.705702 | + | 0.708508i | \(0.749368\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00933i | 1.02242i | 0.859457 | + | 0.511208i | \(0.170802\pi\) | ||||
−0.859457 | + | 0.511208i | \(0.829198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.69735 | 0.813907 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.311977 | −0.0436855 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.64600i | − 1.18762i | −0.804605 | − | 0.593810i | \(-0.797623\pi\) | ||||
0.804605 | − | 0.593810i | \(-0.202377\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.363328i | 0.0481240i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.14134 | 0.669345 | 0.334672 | − | 0.942335i | \(-0.391374\pi\) | ||||
0.334672 | + | 0.942335i | \(0.391374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.45331 | 1.21037 | 0.605186 | − | 0.796084i | \(-0.293099\pi\) | ||||
0.605186 | + | 0.796084i | \(0.293099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.27334i | − 0.412403i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6553i | 1.66826i | 0.551565 | + | 0.834132i | \(0.314031\pi\) | ||||
−0.551565 | + | 0.834132i | \(0.685969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.60398 | 0.193096 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.45331 | −0.647189 | −0.323595 | − | 0.946196i | \(-0.604891\pi\) | ||||
−0.323595 | + | 0.946196i | \(0.604891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.87732i | 0.804930i | 0.915435 | + | 0.402465i | \(0.131846\pi\) | ||||
−0.915435 | + | 0.402465i | \(0.868154\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.11203i | 0.354649i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.2920 | −1.94550 | −0.972751 | − | 0.231852i | \(-0.925521\pi\) | ||||
−0.972751 | + | 0.231852i | \(0.925521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82936 | 0.869929 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 14.2827i | − 1.56773i | −0.620933 | − | 0.783863i | \(-0.713246\pi\) | ||||
0.620933 | − | 0.783863i | \(-0.286754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 3.42401i | − 0.367092i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.0093 | −1.37899 | −0.689493 | − | 0.724292i | \(-0.742167\pi\) | ||||
−0.689493 | + | 0.724292i | \(0.742167\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.30265 | −0.555869 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.73599i | − 0.387404i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.68463i | 0.983326i | 0.870786 | + | 0.491663i | \(0.163611\pi\) | ||||
−0.870786 | + | 0.491663i | \(0.836389\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.82003 | −0.785943 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.45331 | 0.144610 | 0.0723050 | − | 0.997383i | \(-0.476964\pi\) | ||||
0.0723050 | + | 0.997383i | \(0.476964\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.23132i | 0.219859i | 0.993939 | + | 0.109929i | \(0.0350624\pi\) | ||||
−0.993939 | + | 0.109929i | \(0.964938\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 13.6553i | − 1.32011i | −0.751217 | − | 0.660055i | \(-0.770533\pi\) | ||||
0.751217 | − | 0.660055i | \(-0.229467\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.1693 | −1.93187 | −0.965935 | − | 0.258784i | \(-0.916678\pi\) | ||||
−0.965935 | + | 0.258784i | \(0.916678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.46264 | 0.233744 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 10.0514i | − 0.945552i | −0.881183 | − | 0.472776i | \(-0.843252\pi\) | ||||
0.881183 | − | 0.472776i | \(-0.156748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 13.3247i | − 1.23187i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.980024 | 0.0898387 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.56534 | −0.324122 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.74531i | − 0.247537i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0700i | 1.24851i | 0.781220 | + | 0.624256i | \(0.214598\pi\) | ||||
−0.781220 | + | 0.624256i | \(0.785402\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.37605 | −0.297244 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.14134i | − 0.0989664i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.85866i | 0.415104i | 0.978224 | + | 0.207552i | \(0.0665496\pi\) | ||||
−0.978224 | + | 0.207552i | \(0.933450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.17997 | 0.354540 | 0.177270 | − | 0.984162i | \(-0.443273\pi\) | ||||
0.177270 | + | 0.984162i | \(0.443273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.54669 | −0.214470 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.6680i | 1.05936i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.07001i | 0.170731i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.45331 | −0.119060 | −0.0595300 | − | 0.998227i | \(-0.518960\pi\) | ||||
−0.0595300 | + | 0.998227i | \(0.518960\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.27334 | 0.591896 | 0.295948 | − | 0.955204i | \(-0.404364\pi\) | ||||
0.295948 | + | 0.955204i | \(0.404364\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.46264i | 0.199093i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 17.0093i | − 1.35749i | −0.734373 | − | 0.678746i | \(-0.762524\pi\) | ||||
0.734373 | − | 0.678746i | \(-0.237476\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.14134 | 0.249124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.03863 | −0.397100 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 10.1800i | − 0.797357i | −0.917091 | − | 0.398678i | \(-0.869469\pi\) | ||||
0.917091 | − | 0.398678i | \(-0.130531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 6.07001i | − 0.469711i | −0.972030 | − | 0.234856i | \(-0.924538\pi\) | ||||
0.972030 | − | 0.234856i | \(-0.0754618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.58532 | −0.660409 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.86799 | 0.219321 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.22199i | − 0.397021i | −0.980099 | − | 0.198510i | \(-0.936390\pi\) | ||||
0.980099 | − | 0.198510i | \(-0.0636103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.86799i | 0.140407i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.55602 | 0.116302 | 0.0581510 | − | 0.998308i | \(-0.481480\pi\) | ||||
0.0581510 | + | 0.998308i | \(0.481480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.43466i | 0.253897i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.34128i | − 0.171211i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.43334 | 0.176999 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.03863 | −0.364583 | −0.182291 | − | 0.983245i | \(-0.558351\pi\) | ||||
−0.182291 | + | 0.983245i | \(0.558351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 9.68463i | − 0.697115i | −0.937287 | − | 0.348558i | \(-0.886672\pi\) | ||||
0.937287 | − | 0.348558i | \(-0.113328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.8867 | −1.40973 | −0.704864 | − | 0.709343i | \(-0.748992\pi\) | ||||
−0.704864 | + | 0.709343i | \(0.748992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.96137 | −0.349948 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7560i | 0.754920i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 12.6613i | − 0.880019i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.72666 | −0.188607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.31198 | 0.296849 | 0.148424 | − | 0.988924i | \(-0.452580\pi\) | ||||
0.148424 | + | 0.988924i | \(0.452580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.98134i | − 0.135759i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.7360i | 0.796691i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.49873 | −0.168848 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.98935 | 0.268353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 18.5327i | − 1.24104i | −0.784191 | − | 0.620519i | \(-0.786922\pi\) | ||||
0.784191 | − | 0.620519i | \(-0.213078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4.82597i | − 0.320311i | −0.987092 | − | 0.160155i | \(-0.948800\pi\) | ||||
0.987092 | − | 0.160155i | \(-0.0511995\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7360 | −1.56852 | −0.784259 | − | 0.620434i | \(-0.786957\pi\) | ||||
−0.784259 | + | 0.620434i | \(0.786957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.13069 | −0.0743939 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.5653i | − 0.954207i | −0.878847 | − | 0.477104i | \(-0.841687\pi\) | ||||
0.878847 | − | 0.477104i | \(-0.158313\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 6.28267i | − 0.408103i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.43334 | −0.157399 | −0.0786997 | − | 0.996898i | \(-0.525077\pi\) | ||||
−0.0786997 | + | 0.996898i | \(0.525077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1986 | 1.17228 | 0.586138 | − | 0.810211i | \(-0.300648\pi\) | ||||
0.586138 | + | 0.810211i | \(0.300648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.24065i | 0.592788i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.64600i | − 0.295618i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.18930 | 0.328858 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.1120 | −0.953863 | −0.476931 | − | 0.878940i | \(-0.658251\pi\) | ||||
−0.476931 | + | 0.878940i | \(0.658251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0373i | 0.756779i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 12.2313i | − 0.762969i | −0.924375 | − | 0.381484i | \(-0.875413\pi\) | ||||
0.924375 | − | 0.381484i | \(-0.124587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.73599 | −0.480691 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.0280 | −1.67299 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.5840i | 1.39259i | 0.717756 | + | 0.696295i | \(0.245169\pi\) | ||||
−0.717756 | + | 0.696295i | \(0.754831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 4.72666i | − 0.289267i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1120 | 0.799455 | 0.399727 | − | 0.916634i | \(-0.369105\pi\) | ||||
0.399727 | + | 0.916634i | \(0.369105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8960 | −1.26934 | −0.634670 | − | 0.772783i | \(-0.718864\pi\) | ||||
−0.634670 | + | 0.772783i | \(0.718864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1.92660i | − 0.116603i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1800i | 1.21250i | 0.795275 | + | 0.606248i | \(0.207326\pi\) | ||||
−0.795275 | + | 0.606248i | \(0.792674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.4906 | −1.76556 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4626 | −1.34001 | −0.670004 | − | 0.742357i | \(-0.733708\pi\) | ||||
−0.670004 | + | 0.742357i | \(0.733708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 0.829359i | − 0.0493003i | −0.999696 | − | 0.0246501i | \(-0.992153\pi\) | ||||
0.999696 | − | 0.0246501i | \(-0.00784718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.62395i | 0.509056i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2627 | 0.956629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.51870 | −0.206270 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 31.2886i | − 1.82790i | −0.405827 | − | 0.913950i | \(-0.633016\pi\) | ||||
0.405827 | − | 0.913950i | \(-0.366984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5.81325i | − 0.337319i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.5106 | −1.18616 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.6053 | 0.611279 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.528030i | 0.0303345i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.11929i | 0.178027i | 0.996030 | + | 0.0890136i | \(0.0283715\pi\) | ||||
−0.996030 | + | 0.0890136i | \(0.971629\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.810702 | −0.0461192 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.4240 | −1.21484 | −0.607422 | − | 0.794379i | \(-0.707796\pi\) | ||||
−0.607422 | + | 0.794379i | \(0.707796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 12.1320i | − 0.685742i | −0.939383 | − | 0.342871i | \(-0.888601\pi\) | ||||
0.939383 | − | 0.342871i | \(-0.111399\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 16.7487i | − 0.940701i | −0.882480 | − | 0.470350i | \(-0.844128\pi\) | ||||
0.882480 | − | 0.470350i | \(-0.155872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.6960 | 1.43870 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.96137 | 0.276916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.858664i | 0.0477773i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 7.32808i | − 0.405244i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.97070 | −0.328179 | −0.164090 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164090 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 19.4393i | − 1.06527i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3340i | 1.10766i | 0.832628 | + | 0.553832i | \(0.186835\pi\) | ||||
−0.832628 | + | 0.553832i | \(0.813165\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.65194 | 0.198346 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.0373 | 1.51831 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 14.4919i | − 0.782492i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 20.8294i | − 1.11818i | −0.829107 | − | 0.559089i | \(-0.811151\pi\) | ||||
0.829107 | − | 0.559089i | \(-0.188849\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0187 | 1.07157 | 0.535787 | − | 0.844353i | \(-0.320015\pi\) | ||||
0.535787 | + | 0.844353i | \(0.320015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.90531 | 0.528706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 27.1413i | − 1.44459i | −0.691586 | − | 0.722294i | \(-0.743088\pi\) | ||||
0.691586 | − | 0.722294i | \(-0.256912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.356070i | 0.0188452i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.59465 | 0.242496 | 0.121248 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121248 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.29539i | − 0.0679904i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.1214i | 1.78112i | 0.454865 | + | 0.890560i | \(0.349687\pi\) | ||||
−0.454865 | + | 0.890560i | \(0.650313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.6706 | −1.12813 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.86799 | −0.512321 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 7.81664i | − 0.404730i | −0.979310 | − | 0.202365i | \(-0.935137\pi\) | ||||
0.979310 | − | 0.202365i | \(-0.0648628\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.7839i | 2.25499i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0573 | 1.18437 | 0.592187 | − | 0.805801i | \(-0.298265\pi\) | ||||
0.592187 | + | 0.805801i | \(0.298265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.11203 | −0.261897 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.8807i | 0.862564i | 0.902217 | + | 0.431282i | \(0.141939\pi\) | ||||
−0.902217 | + | 0.431282i | \(0.858061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.6494i | 1.35466i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3013 | 0.927914 | 0.463957 | − | 0.885858i | \(-0.346429\pi\) | ||||
0.463957 | + | 0.885858i | \(0.346429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.79073 | 0.191705 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.45331i | − 0.0733099i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12.1800i | − 0.611295i | −0.952145 | − | 0.305648i | \(-0.901127\pi\) | ||||
0.952145 | − | 0.305648i | \(-0.0988729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.414680 | 0.0207599 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5840 | 0.828166 | 0.414083 | − | 0.910239i | \(-0.364102\pi\) | ||||
0.414083 | + | 0.910239i | \(0.364102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47.7733i | 2.37976i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.4813i | 0.916084i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.5653 | −0.917997 | −0.458999 | − | 0.888437i | \(-0.651792\pi\) | ||||
−0.458999 | + | 0.888437i | \(0.651792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.76529 | −0.0870753 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.86799i | − 0.288745i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.51870i | 0.0743711i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.84802 | −0.139135 | −0.0695674 | − | 0.997577i | \(-0.522162\pi\) | ||||
−0.0695674 | + | 0.997577i | \(0.522162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.5360 | 1.19581 | 0.597907 | − | 0.801566i | \(-0.295999\pi\) | ||||
0.597907 | + | 0.801566i | \(0.295999\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.1027i | 0.977427i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10.7894i | − 0.522136i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.60266 | −0.222218 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.53736 | −0.363062 | −0.181531 | − | 0.983385i | \(-0.558105\pi\) | ||||
−0.181531 | + | 0.983385i | \(0.558105\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 0.392633i | − 0.0188687i | −0.999955 | − | 0.00943437i | \(-0.996997\pi\) | ||||
0.999955 | − | 0.00943437i | \(-0.00300310\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.41468i | − 0.211183i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.29200 | −0.252573 | −0.126287 | − | 0.991994i | \(-0.540306\pi\) | ||||
−0.126287 | + | 0.991994i | \(0.540306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3400 | 0.778093 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 22.0187i | − 1.04614i | −0.852290 | − | 0.523069i | \(-0.824787\pi\) | ||||
0.852290 | − | 0.523069i | \(-0.175213\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 0.528030i | − 0.0249749i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.90663 | 0.231558 | 0.115779 | − | 0.993275i | \(-0.463064\pi\) | ||||
0.115779 | + | 0.993275i | \(0.463064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6027 | 0.970141 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.64261i | 0.124161i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 26.9800i | − 1.26207i | −0.775753 | − | 0.631036i | \(-0.782630\pi\) | ||||
0.775753 | − | 0.631036i | \(-0.217370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.83068 | −0.0854487 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.1307 | −1.26360 | −0.631801 | − | 0.775131i | \(-0.717684\pi\) | ||||
−0.631801 | + | 0.775131i | \(0.717684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 16.9253i | − 0.786585i | −0.919413 | − | 0.393292i | \(-0.871336\pi\) | ||||
0.919413 | − | 0.393292i | \(-0.128664\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 42.6213i | 1.97228i | 0.165917 | + | 0.986140i | \(0.446942\pi\) | ||||
−0.165917 | + | 0.986140i | \(0.553058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.5853 | 0.719663 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.17997 | 0.284758 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 25.3361i | − 1.16495i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 24.7967i | − 1.13536i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.3107 | 1.15647 | 0.578237 | − | 0.815869i | \(-0.303741\pi\) | ||||
0.578237 | + | 0.815869i | \(0.303741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.4906 | −1.43585 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.83068i | − 0.0832987i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 25.4020i | − 1.15107i | −0.817776 | − | 0.575536i | \(-0.804793\pi\) | ||||
0.817776 | − | 0.575536i | \(-0.195207\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.69867 | 0.167260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.6240 | 0.930746 | 0.465373 | − | 0.885115i | \(-0.345920\pi\) | ||||
0.465373 | + | 0.885115i | \(0.345920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.09206i | − 0.364448i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.22406i | 0.279187i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3693 | −0.777555 | −0.388778 | − | 0.921332i | \(-0.627103\pi\) | ||||
−0.388778 | + | 0.921332i | \(0.627103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.20541 | 0.0985303 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 14.9987i | − 0.668758i | −0.942439 | − | 0.334379i | \(-0.891473\pi\) | ||||
0.942439 | − | 0.334379i | \(-0.108527\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 3.11929i | − 0.138533i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.9160 | 0.882759 | 0.441380 | − | 0.897320i | \(-0.354489\pi\) | ||||
0.441380 | + | 0.897320i | \(0.354489\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.84934 | 0.347234 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.13201i | 0.0941304i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 19.1120i | − 0.840546i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.89730 | 0.0832821 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8294 | −0.649686 | −0.324843 | − | 0.945768i | \(-0.605311\pi\) | ||||
−0.324843 | + | 0.945768i | \(0.605311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9966i | 0.524575i | 0.964990 | + | 0.262288i | \(0.0844769\pi\) | ||||
−0.964990 | + | 0.262288i | \(0.915523\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.82936i | − 0.384613i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.51060 | 0.152635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.7453 | 0.639892 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.1053i | 1.52058i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.565344i | 0.0243964i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.5347 | −0.669128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.01866 | −0.0867889 | −0.0433944 | − | 0.999058i | \(-0.513817\pi\) | ||||
−0.0433944 | + | 0.999058i | \(0.513817\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.99322i | 0.343022i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6940i | 0.799296i | 0.916669 | + | 0.399648i | \(0.130868\pi\) | ||||
−0.916669 | + | 0.399648i | \(0.869132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.1120 | 1.15711 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.42401 | −0.401476 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.7360i | 0.839259i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11.0866i | − 0.469754i | −0.972025 | − | 0.234877i | \(-0.924531\pi\) | ||||
0.972025 | − | 0.234877i | \(-0.0754688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.1706 | 1.82592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.850654 | 0.0359146 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.69396i | 0.113537i | 0.998387 | + | 0.0567685i | \(0.0180797\pi\) | ||||
−0.998387 | + | 0.0567685i | \(0.981920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 8.93593i | − 0.375274i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.4134 | −1.23307 | −0.616536 | − | 0.787327i | \(-0.711465\pi\) | ||||
−0.616536 | + | 0.787327i | \(0.711465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.0466 | −1.38296 | −0.691479 | − | 0.722396i | \(-0.743041\pi\) | ||||
−0.691479 | + | 0.722396i | \(0.743041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.83068i | − 0.0764777i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.396022i | 0.0164866i | 0.999966 | + | 0.00824331i | \(0.00262396\pi\) | ||||
−0.999966 | + | 0.00824331i | \(0.997376\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.51870 | 0.146232 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.3013 | −0.676293 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.5747i | 0.976363i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0773i | 0.581031i | 0.956870 | + | 0.290515i | \(0.0938268\pi\) | ||||
−0.956870 | + | 0.290515i | \(0.906173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.2827 | −0.423690 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.726656 | −0.0298907 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.43466i | 0.223175i | 0.993755 | + | 0.111587i | \(0.0355935\pi\) | ||||
−0.993755 | + | 0.111587i | \(0.964407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 7.22538i | − 0.295715i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.6333 | −0.475323 | −0.237662 | − | 0.971348i | \(-0.576381\pi\) | ||||
−0.237662 | + | 0.971348i | \(0.576381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.12136 | 0.331277 | 0.165639 | − | 0.986187i | \(-0.447031\pi\) | ||||
0.165639 | + | 0.986187i | \(0.447031\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 39.1634i | 1.59486i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 10.5327i | − 0.427507i | −0.976888 | − | 0.213754i | \(-0.931431\pi\) | ||||
0.976888 | − | 0.213754i | \(-0.0685689\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.90794 | −0.158358 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.5653 | 1.31745 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.3293i | 1.91161i | 0.293996 | + | 0.955807i | \(0.405015\pi\) | ||||
−0.293996 | + | 0.955807i | \(0.594985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.3693i | 1.34340i | 0.740825 | + | 0.671698i | \(0.234435\pi\) | ||||
−0.740825 | + | 0.671698i | \(0.765565\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.8760 | 1.36159 | 0.680796 | − | 0.732473i | \(-0.261634\pi\) | ||||
0.680796 | + | 0.732473i | \(0.261634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.41213 | 0.377696 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.8480i | 0.594873i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.990671i | − 0.0395636i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.82003 | 0.232060 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.8573 | 1.10898 | 0.554492 | − | 0.832189i | \(-0.312913\pi\) | ||||
0.554492 | + | 0.832189i | \(0.312913\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.56666i | 0.0622693i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 26.4699i | − 1.04878i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.6401 | −0.618711 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.74531 | −0.187429 | −0.0937143 | − | 0.995599i | \(-0.529874\pi\) | ||||
−0.0937143 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.28267i | − 0.247764i | −0.992297 | − | 0.123882i | \(-0.960466\pi\) | ||||
0.992297 | − | 0.123882i | \(-0.0395345\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 16.1507i | − 0.634948i | −0.948267 | − | 0.317474i | \(-0.897165\pi\) | ||||
0.948267 | − | 0.317474i | \(-0.102835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.0187 | −0.550280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.26401 | −0.167120 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.8760i | 1.16914i | 0.811344 | + | 0.584569i | \(0.198736\pi\) | ||||
−0.811344 | + | 0.584569i | \(0.801264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.7241i | 0.769511i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4427 | 0.679470 | 0.339735 | − | 0.940521i | \(-0.389663\pi\) | ||||
0.339735 | + | 0.940521i | \(0.389663\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.87732 | −0.111915 | −0.0559574 | − | 0.998433i | \(-0.517821\pi\) | ||||
−0.0559574 | + | 0.998433i | \(0.517821\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.44944i | 0.0562918i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.6040i | 1.61091i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.73344 | 0.260330 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.7759 | −0.995069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9393i | 0.421680i | 0.977521 | + | 0.210840i | \(0.0676199\pi\) | ||||
−0.977521 | + | 0.210840i | \(0.932380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 19.0900i | − 0.733688i | −0.930283 | − | 0.366844i | \(-0.880438\pi\) | ||||
0.930283 | − | 0.366844i | \(-0.119562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.0534 | 0.424191 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.75341 | 0.0671909 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7687i | 0.986011i | 0.870026 | + | 0.493006i | \(0.164102\pi\) | ||||
−0.870026 | + | 0.493006i | \(0.835898\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 8.62395i | − 0.329024i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.1693 | −1.53033 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.2334 | −1.03601 | −0.518004 | − | 0.855378i | \(-0.673325\pi\) | ||||
−0.518004 | + | 0.855378i | \(0.673325\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.92528i | 0.339043i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 6.48808i | − 0.245753i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.29200 | 0.200162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.6960 | 1.87699 | 0.938497 | − | 0.345288i | \(-0.112219\pi\) | ||||
0.938497 | + | 0.345288i | \(0.112219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.77801i | − 0.255637i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.65872i | − 0.0623825i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.64006 | −0.211817 | −0.105908 | − | 0.994376i | \(-0.533775\pi\) | ||||
−0.105908 | + | 0.994376i | \(0.533775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −49.5933 | −1.85990 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.3947i | 1.70005i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 0.884100i | − 0.0330173i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.4240 | 1.24651 | 0.623253 | − | 0.782021i | \(-0.285811\pi\) | ||||
0.623253 | + | 0.782021i | \(0.285811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54669 | 0.0948436 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.61208i | 0.245906i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3306i | 0.531494i | 0.964043 | + | 0.265747i | \(0.0856185\pi\) | ||||
−0.964043 | + | 0.265747i | \(0.914381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1307 | 0.745581 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.97871 | −0.295103 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 40.8853i | − 1.51013i | −0.655648 | − | 0.755067i | \(-0.727604\pi\) | ||||
0.655648 | − | 0.755067i | \(-0.272396\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 37.2334i | − 1.37151i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8294 | 1.06051 | 0.530253 | − | 0.847840i | \(-0.322097\pi\) | ||||
0.530253 | + | 0.847840i | \(0.322097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.68802 | 0.0620111 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 8.05135i | − 0.295375i | −0.989034 | − | 0.147688i | \(-0.952817\pi\) | ||||
0.989034 | − | 0.147688i | \(-0.0471831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 40.9626i | − 1.49874i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.5853 | −0.569475 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.3107 | 1.72639 | 0.863195 | − | 0.504870i | \(-0.168460\pi\) | ||||
0.863195 | + | 0.504870i | \(0.168460\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 5.49063i | − 0.200090i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 6.20541i | − 0.225539i | −0.993621 | − | 0.112770i | \(-0.964028\pi\) | ||||
0.993621 | − | 0.112770i | \(-0.0359722\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.37350 | −0.158748 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.8280 | 1.58877 | 0.794383 | − | 0.607418i | \(-0.207795\pi\) | ||||
0.794383 | + | 0.607418i | \(0.207795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.0200i | 0.833379i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 23.8867i | − 0.862497i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.22538 | 0.116310 | 0.0581551 | − | 0.998308i | \(-0.481478\pi\) | ||||
0.0581551 | + | 0.998308i | \(0.481478\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.44398 | 0.160046 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.16470i | 0.221729i | 0.993836 | + | 0.110864i | \(0.0353619\pi\) | ||||
−0.993836 | + | 0.110864i | \(0.964638\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 2.81070i | − 0.100833i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.55602 | −0.270722 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.8693 | 0.532066 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 20.0921i | − 0.718031i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 35.1527i | − 1.25306i | −0.779397 | − | 0.626530i | \(-0.784475\pi\) | ||||
0.779397 | − | 0.626530i | \(-0.215525\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.20541 | −0.292120 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.4720 | −0.407896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 43.9201i | − 1.55965i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.3420i | 1.07477i | 0.843337 | + | 0.537385i | \(0.180588\pi\) | ||||
−0.843337 | + | 0.537385i | \(0.819412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.01866 | −0.212925 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.3107 | −1.31831 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 18.7521i | − 0.661747i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.76397i | 0.167700i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.96137 | 0.174432 | 0.0872162 | − | 0.996189i | \(-0.472203\pi\) | ||||
0.0872162 | + | 0.996189i | \(0.472203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.8094 | 1.04675 | 0.523375 | − | 0.852103i | \(-0.324673\pi\) | ||||
0.523375 | + | 0.852103i | \(0.324673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.59210i | − 0.266267i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.29200i | 0.325086i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.2080 | −0.531409 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.1520 | −0.389207 | −0.194603 | − | 0.980882i | \(-0.562342\pi\) | ||||
−0.194603 | + | 0.980882i | \(0.562342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 17.1413i | − 0.597509i | −0.954330 | − | 0.298755i | \(-0.903429\pi\) | ||||
0.954330 | − | 0.298755i | \(-0.0965712\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 24.8633i | − 0.864581i | −0.901734 | − | 0.432291i | \(-0.857705\pi\) | ||||
0.901734 | − | 0.432291i | \(-0.142295\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.7746 | 0.652069 | 0.326035 | − | 0.945358i | \(-0.394287\pi\) | ||||
0.326035 | + | 0.945358i | \(0.394287\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.33195 | −0.254343 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.89211i | 0.169502i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 21.9227i | − 0.757761i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.0280 | −1.00216 | −0.501079 | − | 0.865402i | \(-0.667063\pi\) | ||||
−0.501079 | + | 0.865402i | \(0.667063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.8119 | 2.06248 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 8.16131i | − 0.281091i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.06926i | 0.139821i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.301330 | 0.0103416 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.9227 | −1.02574 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.7894i | 1.39660i | 0.715804 | + | 0.698301i | \(0.246060\pi\) | ||||
−0.715804 | + | 0.698301i | \(0.753940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.6354i | 1.11480i | 0.830243 | + | 0.557401i | \(0.188201\pi\) | ||||
−0.830243 | + | 0.557401i | \(0.811799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.4906 | −1.14269 | −0.571343 | − | 0.820712i | \(-0.693577\pi\) | ||||
−0.571343 | + | 0.820712i | \(0.693577\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.13333 | −0.106783 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.13795i | 0.174898i | 0.996169 | + | 0.0874489i | \(0.0278714\pi\) | ||||
−0.996169 | + | 0.0874489i | \(0.972129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.90870i | 0.200670i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.1493 | 1.59943 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.4427 | 2.14967 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.7755i | 0.940057i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0220i | 0.541026i | 0.962716 | + | 0.270513i | \(0.0871933\pi\) | ||||
−0.962716 | + | 0.270513i | \(0.912807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.3680 | 0.383434 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.5306 | 0.388475 | 0.194238 | − | 0.980955i | \(-0.437777\pi\) | ||||
0.194238 | + | 0.980955i | \(0.437777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 39.5161i | − 1.32982i | −0.746923 | − | 0.664911i | \(-0.768470\pi\) | ||||
0.746923 | − | 0.664911i | \(-0.231530\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8153i | 0.698910i | 0.936953 | + | 0.349455i | \(0.113633\pi\) | ||||
−0.936953 | + | 0.349455i | \(0.886367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0586 | 0.538588 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.3480 | −0.715184 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.00933i | 0.234558i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 7.45208i | − 0.248818i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 96.9040 | 3.23193 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.42401 | 0.247330 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.85320i | 0.128227i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 32.0339i | − 1.06367i | −0.846848 | − | 0.531835i | \(-0.821503\pi\) | ||||
0.846848 | − | 0.531835i | \(-0.178497\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.16809 | 0.138247 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.12136 | −0.0702838 | −0.0351419 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351419 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.9439i | 1.28886i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.56534i | 0.150761i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4333 | 0.871955 | 0.435978 | − | 0.899957i | \(-0.356403\pi\) | ||||
0.435978 | + | 0.899957i | \(0.356403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13333 | −0.0373444 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.3361i | 0.833948i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.39941i | 0.210184i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7907 | −0.583695 | −0.291847 | − | 0.956465i | \(-0.594270\pi\) | ||||
−0.291847 | + | 0.956465i | \(0.594270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.69735 | 0.186723 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 7.78395i | − 0.254835i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.46396i | 0.243837i | 0.992540 | + | 0.121918i | \(0.0389046\pi\) | ||||
−0.992540 | + | 0.121918i | \(0.961095\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.40790 | 0.143846 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.67869 | −0.0873229 | −0.0436615 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436615 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.3574i | 1.08627i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 42.5840i | − 1.38379i | −0.721996 | − | 0.691897i | \(-0.756775\pi\) | ||||
0.721996 | − | 0.691897i | \(-0.243225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.9520 | 1.03721 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.08528 | 0.197329 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.0046i | 1.94374i | 0.235517 | + | 0.971870i | \(0.424322\pi\) | ||||
−0.235517 | + | 0.971870i | \(0.575678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.33609i | 0.301793i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.54537 | 0.179069 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 74.7333 | 2.41075 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 39.1634i | − 1.26202i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61.1307i | 1.96583i | 0.184059 | + | 0.982915i | \(0.441076\pi\) | ||||
−0.184059 | + | 0.982915i | \(0.558924\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.311977 | −0.0100221 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.6213 | 1.75288 | 0.876441 | − | 0.481510i | \(-0.159911\pi\) | ||||
0.876441 | + | 0.481510i | \(0.159911\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.77075i | − 0.152943i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.3060i | 0.617655i | 0.951118 | + | 0.308827i | \(0.0999366\pi\) | ||||
−0.951118 | + | 0.308827i | \(0.900063\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.4720 | 1.13369 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −57.8455 | −1.84686 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.1820i | 0.803182i | 0.915819 | + | 0.401591i | \(0.131543\pi\) | ||||
−0.915819 | + | 0.401591i | \(0.868457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.90663i | 0.0925189i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.0212 | 1.30440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.82003 | −0.184879 | −0.0924397 | − | 0.995718i | \(-0.529467\pi\) | ||||
−0.0924397 | + | 0.995718i | \(0.529467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 2.16932i | − 0.0688414i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 8.97201i | − 0.284147i | −0.989856 | − | 0.142073i | \(-0.954623\pi\) | ||||
0.989856 | − | 0.142073i | \(-0.0453769\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.4508 | 0.457202 |
(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 | 3800.2.d.k.3649.4 | 6 | ||
5.2 | odd | 4 | 760.2.a.h.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 3800.2.a.y.1.2 | 3 | |||
5.4 | even | 2 | inner | 3800.2.d.k.3649.3 | 6 | ||
15.2 | even | 4 | 6840.2.a.bj.1.3 | 3 | |||
20.3 | even | 4 | 7600.2.a.bo.1.2 | 3 | |||
20.7 | even | 4 | 1520.2.a.r.1.2 | 3 | |||
40.27 | even | 4 | 6080.2.a.bs.1.2 | 3 | |||
40.37 | odd | 4 | 6080.2.a.bw.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.h.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
1520.2.a.r.1.2 | 3 | 20.7 | even | 4 | |||
3800.2.a.y.1.2 | 3 | 5.3 | odd | 4 | |||
3800.2.d.k.3649.3 | 6 | 5.4 | even | 2 | inner | ||
3800.2.d.k.3649.4 | 6 | 1.1 | even | 1 | trivial | ||
6080.2.a.bs.1.2 | 3 | 40.27 | even | 4 | |||
6080.2.a.bw.1.2 | 3 | 40.37 | odd | 4 | |||
6840.2.a.bj.1.3 | 3 | 15.2 | even | 4 | |||
7600.2.a.bo.1.2 | 3 | 20.3 | even | 4 |