Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 6 x^{14} + 68 x^{13} - 126 x^{12} - 148 x^{11} + 1006 x^{10} - 1516 x^{9} + \cdots + 5956 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.11 | ||
Root | \(-1.65334 + 0.722492i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.g.1791.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.44498 | 0.834261 | 0.417131 | − | 0.908846i | \(-0.363036\pi\) | ||||
0.417131 | + | 0.908846i | \(0.363036\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.48080 | + | 0.919594i | −0.937653 | + | 0.347574i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.912023 | −0.304008 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.66807i | 1.70899i | 0.519461 | + | 0.854494i | \(0.326133\pi\) | ||||
−0.519461 | + | 0.854494i | \(0.673867\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.14588i | − | 1.42721i | −0.700549 | − | 0.713605i | \(-0.747061\pi\) | ||
0.700549 | − | 0.713605i | \(-0.252939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.44498i | − | 0.373093i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.65490i | − | 0.401373i | −0.979656 | − | 0.200687i | \(-0.935683\pi\) | ||
0.979656 | − | 0.200687i | \(-0.0643173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.33951 | −0.307304 | −0.153652 | − | 0.988125i | \(-0.549103\pi\) | ||||
−0.153652 | + | 0.988125i | \(0.549103\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.58471 | + | 1.32880i | −0.782247 | + | 0.289968i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.62209i | − | 0.755257i | −0.925957 | − | 0.377628i | \(-0.876740\pi\) | ||
0.925957 | − | 0.377628i | \(-0.123260\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65281 | −1.08788 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0482240 | 0.00895496 | 0.00447748 | − | 0.999990i | \(-0.498575\pi\) | ||||
0.00447748 | + | 0.999990i | \(0.498575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.08555 | 0.554181 | 0.277090 | − | 0.960844i | \(-0.410630\pi\) | ||||
0.277090 | + | 0.960844i | \(0.410630\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.19027i | 1.42574i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.919594 | + | 2.48080i | 0.155440 | + | 0.419331i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.2462 | −1.84887 | −0.924434 | − | 0.381343i | \(-0.875462\pi\) | ||||
−0.924434 | + | 0.381343i | \(0.875462\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 7.43570i | − | 1.19067i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.37889i | − | 0.371520i | −0.982595 | − | 0.185760i | \(-0.940525\pi\) | ||
0.982595 | − | 0.185760i | \(-0.0594747\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.18334i | − | 0.942950i | −0.881879 | − | 0.471475i | \(-0.843722\pi\) | ||
0.881879 | − | 0.471475i | \(-0.156278\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.912023i | 0.135956i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.75943 | −1.13183 | −0.565915 | − | 0.824464i | \(-0.691477\pi\) | ||||
−0.565915 | + | 0.824464i | \(0.691477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.30869 | − | 4.56265i | 0.758385 | − | 0.651807i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.39131i | − | 0.334850i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5028 | −1.44267 | −0.721333 | − | 0.692588i | \(-0.756470\pi\) | ||||
−0.721333 | + | 0.692588i | \(0.756470\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.66807 | 0.764283 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.93556 | −0.256372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.32378 | −0.693097 | −0.346549 | − | 0.938032i | \(-0.612646\pi\) | ||||
−0.346549 | + | 0.938032i | \(0.612646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.30924i | 0.295668i | 0.989012 | + | 0.147834i | \(0.0472301\pi\) | ||||
−0.989012 | + | 0.147834i | \(0.952770\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.26254 | − | 0.838692i | 0.285054 | − | 0.105665i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.14588 | −0.638267 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.207825i | 0.0253899i | 0.999919 | + | 0.0126949i | \(0.00404103\pi\) | ||||
−0.999919 | + | 0.0126949i | \(0.995959\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 5.23385i | − | 0.630082i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.67465i | − | 0.792135i | −0.918221 | − | 0.396068i | \(-0.870375\pi\) | ||
0.918221 | − | 0.396068i | \(-0.129625\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.42442i | − | 0.400798i | −0.979714 | − | 0.200399i | \(-0.935776\pi\) | ||
0.979714 | − | 0.200399i | \(-0.0642238\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.44498 | −0.166852 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.21233 | − | 14.0613i | −0.594000 | − | 1.60244i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.73371i | − | 0.195058i | −0.995233 | − | 0.0975289i | \(-0.968906\pi\) | ||
0.995233 | − | 0.0975289i | \(-0.0310938\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.43214 | −0.603572 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2384 | −1.34333 | −0.671667 | − | 0.740853i | \(-0.734421\pi\) | ||||
−0.671667 | + | 0.740853i | \(0.734421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.65490 | −0.179500 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0696828 | 0.00747078 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.28261i | 0.453956i | 0.973900 | + | 0.226978i | \(0.0728845\pi\) | ||||
−0.973900 | + | 0.226978i | \(0.927115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.73212 | + | 12.7659i | 0.496061 | + | 1.33823i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.45856 | 0.462331 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.33951i | 0.137430i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.1226i | − | 1.23086i | −0.788190 | − | 0.615432i | \(-0.788981\pi\) | ||
0.788190 | − | 0.615432i | \(-0.211019\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.16942i | − | 0.519546i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4565i | 1.23947i | 0.784812 | + | 0.619734i | \(0.212760\pi\) | ||||
−0.784812 | + | 0.619734i | \(0.787240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.57029 | 0.844455 | 0.422228 | − | 0.906490i | \(-0.361248\pi\) | ||||
0.422228 | + | 0.906490i | \(0.361248\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.32880 | + | 3.58471i | 0.129677 | + | 0.349832i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.1310i | 1.75279i | 0.481592 | + | 0.876395i | \(0.340059\pi\) | ||||
−0.481592 | + | 0.876395i | \(0.659941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.9272 | −1.33398 | −0.666991 | − | 0.745066i | \(-0.732418\pi\) | ||||
−0.666991 | + | 0.745066i | \(0.732418\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.2506 | −1.54244 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.13757 | −0.483302 | −0.241651 | − | 0.970363i | \(-0.577689\pi\) | ||||
−0.241651 | + | 0.970363i | \(0.577689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.62209 | −0.337761 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.69316i | 0.433883i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.52184 | + | 4.10548i | 0.139507 | + | 0.376349i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.1271 | −1.92064 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.43745i | − | 0.309945i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1695i | 1.52355i | 0.647841 | + | 0.761775i | \(0.275672\pi\) | ||||
−0.647841 | + | 0.761775i | \(0.724328\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.93482i | − | 0.786667i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.37209 | 0.818843 | 0.409422 | − | 0.912345i | \(-0.365731\pi\) | ||||
0.409422 | + | 0.912345i | \(0.365731\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.32304 | − | 1.23180i | 0.288144 | − | 0.106811i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65281i | 0.486516i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.3631 | 1.73973 | 0.869867 | − | 0.493287i | \(-0.164205\pi\) | ||||
0.869867 | + | 0.493287i | \(0.164205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.6541 | 1.75186 | 0.875930 | − | 0.482438i | \(-0.160248\pi\) | ||||
0.875930 | + | 0.482438i | \(0.160248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.2123 | −0.944242 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.1672 | 2.43908 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.0482240i | − | 0.00400478i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.67097 | − | 6.59295i | 0.632691 | − | 0.543778i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4375 | −0.855076 | −0.427538 | − | 0.903997i | \(-0.640619\pi\) | ||||
−0.427538 | + | 0.903997i | \(0.640619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.01484i | − | 0.408102i | −0.978960 | − | 0.204051i | \(-0.934589\pi\) | ||
0.978960 | − | 0.204051i | \(-0.0654108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.50931i | 0.122021i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.08555i | − | 0.247837i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.287851i | − | 0.0229730i | −0.999934 | − | 0.0114865i | \(-0.996344\pi\) | ||
0.999934 | − | 0.0114865i | \(-0.00365635\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.1763 | −1.20356 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.33085 | + | 8.98565i | 0.262508 | + | 0.708169i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.02740i | − | 0.628755i | −0.949298 | − | 0.314377i | \(-0.898204\pi\) | ||
0.949298 | − | 0.314377i | \(-0.101796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.19027 | 0.637612 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.74986 | 0.135408 | 0.0677040 | − | 0.997705i | \(-0.478433\pi\) | ||||
0.0677040 | + | 0.997705i | \(0.478433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.4800 | −1.03693 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.22166 | 0.0934227 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 19.0563i | − | 1.44882i | −0.689368 | − | 0.724412i | \(-0.742112\pi\) | ||
0.689368 | − | 0.724412i | \(-0.257888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.48080 | − | 0.919594i | 0.187531 | − | 0.0695148i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.69277 | −0.578224 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.22119i | − | 0.614480i | −0.951632 | − | 0.307240i | \(-0.900594\pi\) | ||
0.951632 | − | 0.307240i | \(-0.0994055\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.7060i | 1.91071i | 0.295461 | + | 0.955355i | \(0.404527\pi\) | ||||
−0.295461 | + | 0.955355i | \(0.595473\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.33681i | 0.246664i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.2462i | 0.826839i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.38012 | 0.685942 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.0235 | − | 5.19829i | 1.02006 | − | 0.378120i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4549i | 0.756489i | 0.925706 | + | 0.378244i | \(0.123472\pi\) | ||||
−0.925706 | + | 0.378244i | \(0.876528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1128 | −1.51973 | −0.759867 | − | 0.650079i | \(-0.774736\pi\) | ||||
−0.759867 | + | 0.650079i | \(0.774736\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.43570 | −0.532482 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.9221 | 1.98937 | 0.994683 | − | 0.102988i | \(-0.0328403\pi\) | ||||
0.994683 | + | 0.102988i | \(0.0328403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.4173 | 1.51823 | 0.759117 | − | 0.650955i | \(-0.225631\pi\) | ||||
0.759117 | + | 0.650955i | \(0.225631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.300304i | 0.0211818i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.119634 | + | 0.0443465i | −0.00839664 | + | 0.00311251i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.37889 | −0.166149 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.30343i | 0.229604i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7.59242i | − | 0.525179i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.56333i | − | 0.107624i | −0.998551 | − | 0.0538122i | \(-0.982863\pi\) | ||
0.998551 | − | 0.0538122i | \(-0.0171372\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 9.64476i | − | 0.660848i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.18334 | −0.421700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.65461 | + | 2.83745i | −0.519629 | + | 0.192619i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 4.94823i | − | 0.334370i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.51593 | −0.572843 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2856 | −1.09057 | −0.545283 | − | 0.838252i | \(-0.683578\pi\) | ||||
−0.545283 | + | 0.838252i | \(0.683578\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.912023 | 0.0608016 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2890 | 1.14751 | 0.573757 | − | 0.819025i | \(-0.305485\pi\) | ||||
0.573757 | + | 0.819025i | \(0.305485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.9786i | − | 1.71671i | −0.513055 | − | 0.858356i | \(-0.671486\pi\) | ||
0.513055 | − | 0.858356i | \(-0.328514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.53173 | − | 20.3184i | −0.495551 | − | 1.33685i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.47013 | −0.554896 | −0.277448 | − | 0.960741i | \(-0.589489\pi\) | ||||
−0.277448 | + | 0.960741i | \(0.589489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.75943i | 0.506170i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2.50518i | − | 0.162729i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.72523i | 0.435019i | 0.976058 | + | 0.217510i | \(0.0697933\pi\) | ||||
−0.976058 | + | 0.217510i | \(0.930207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 24.8505i | − | 1.60076i | −0.599492 | − | 0.800381i | \(-0.704631\pi\) | ||
0.599492 | − | 0.800381i | \(-0.295369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.10907 | 0.584347 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.56265 | − | 5.30869i | −0.291497 | − | 0.339160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.89293i | 0.438587i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.6842 | −1.12069 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3141 | −0.840379 | −0.420189 | − | 0.907436i | \(-0.638036\pi\) | ||||
−0.420189 | + | 0.907436i | \(0.638036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.5302 | 1.29073 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.39131 | −0.149750 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 24.8989i | − | 1.55315i | −0.630023 | − | 0.776577i | \(-0.716955\pi\) | ||
0.630023 | − | 0.776577i | \(-0.283045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.8996 | − | 10.3420i | 1.73360 | − | 0.642618i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0439814 | −0.00272238 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.70131i | − | 0.166570i | −0.996526 | − | 0.0832850i | \(-0.973459\pi\) | ||
0.996526 | − | 0.0832850i | \(-0.0265412\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5028i | 0.645180i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.18830i | 0.378718i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.0495i | 1.52730i | 0.645632 | + | 0.763648i | \(0.276594\pi\) | ||||
−0.645632 | + | 0.763648i | \(0.723406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9628 | −0.848177 | −0.424088 | − | 0.905621i | \(-0.639405\pi\) | ||||
−0.424088 | + | 0.905621i | \(0.639405\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.83783 | + | 18.4465i | 0.413844 | + | 1.11643i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.66807i | − | 0.341798i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6112 | 0.817816 | 0.408908 | − | 0.912576i | \(-0.365910\pi\) | ||||
0.408908 | + | 0.912576i | \(0.365910\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.81409 | −0.168475 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1166 | 1.43868 | 0.719338 | − | 0.694660i | \(-0.244445\pi\) | ||||
0.719338 | + | 0.694660i | \(0.244445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.3390 | −1.38736 | −0.693680 | − | 0.720283i | \(-0.744012\pi\) | ||||
−0.693680 | + | 0.720283i | \(0.744012\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.93556i | 0.114653i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.18761 | + | 5.90153i | 0.129131 | + | 0.348357i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2613 | 0.838900 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 17.5170i | − | 1.02686i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.56273i | − | 0.441820i | −0.975294 | − | 0.220910i | \(-0.929097\pi\) | ||
0.975294 | − | 0.220910i | \(-0.0709026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.32378i | 0.309962i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 32.0405i | − | 1.85918i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.6388 | −1.07791 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.68616 | + | 15.3396i | 0.327745 | + | 0.884160i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.9994i | 1.03404i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.30924 | 0.132227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.3775 | −1.44837 | −0.724184 | − | 0.689607i | \(-0.757783\pi\) | ||||
−0.724184 | + | 0.689607i | \(0.757783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.3839 | 0.704497 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.939191 | −0.0532566 | −0.0266283 | − | 0.999645i | \(-0.508477\pi\) | ||||
−0.0266283 | + | 0.999645i | \(0.508477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0637i | 1.13407i | 0.823694 | + | 0.567035i | \(0.191910\pi\) | ||||
−0.823694 | + | 0.567035i | \(0.808090\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.838692 | − | 2.26254i | −0.0472549 | − | 0.127480i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.9990 | −0.786260 | −0.393130 | − | 0.919483i | \(-0.628608\pi\) | ||||
−0.393130 | + | 0.919483i | \(0.628608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.273337i | 0.0153039i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.1990i | 1.46229i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.21675i | 0.123343i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.14588i | 0.285442i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.1245 | −1.11289 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.2496 | − | 7.13553i | 1.06126 | − | 0.393395i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.0893i | − | 0.939312i | −0.882850 | − | 0.469656i | \(-0.844378\pi\) | ||
0.882850 | − | 0.469656i | \(-0.155622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2568 | 0.562070 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.207825 | 0.0113547 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.384299 | 0.0209341 | 0.0104670 | − | 0.999945i | \(-0.496668\pi\) | ||||
0.0104670 | + | 0.999945i | \(0.496668\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.42371 | −0.403201 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.4891i | 0.947088i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.97399 | + | 16.2008i | −0.484550 | + | 0.874764i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.23385 | −0.281781 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.51811i | 0.242545i | 0.992619 | + | 0.121273i | \(0.0386975\pi\) | ||||
−0.992619 | + | 0.121273i | \(0.961303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.7108i | 1.05510i | 0.849525 | + | 0.527549i | \(0.176889\pi\) | ||||
−0.849525 | + | 0.527549i | \(0.823111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.0887i | 1.55264i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.79118i | − | 0.467907i | −0.972248 | − | 0.233954i | \(-0.924834\pi\) | ||
0.972248 | − | 0.233954i | \(-0.0751664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.67465 | −0.354254 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.19903 | + | 5.93235i | 0.116385 | + | 0.313973i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.3042i | − | 1.38828i | −0.719839 | − | 0.694141i | \(-0.755784\pi\) | ||
0.719839 | − | 0.694141i | \(-0.244216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2057 | −0.905564 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.5283 | −1.60232 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.42442 | −0.179242 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.1194 | 0.841428 | 0.420714 | − | 0.907193i | \(-0.361780\pi\) | ||||
0.420714 | + | 0.907193i | \(0.361780\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.16960i | 0.112945i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.0552 | − | 9.65829i | 1.35272 | − | 0.501434i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.18477 | −0.423791 | −0.211896 | − | 0.977292i | \(-0.567964\pi\) | ||||
−0.211896 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.44498i | 0.0746186i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.248154i | − | 0.0127806i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.5932i | 1.10917i | 0.832128 | + | 0.554583i | \(0.187122\pi\) | ||||
−0.832128 | + | 0.554583i | \(0.812878\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.8097i | 1.27104i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.5100 | 0.741424 | 0.370712 | − | 0.928748i | \(-0.379114\pi\) | ||||
0.370712 | + | 0.928748i | \(0.379114\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.0613 | + | 5.21233i | −0.716632 | + | 0.265645i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.63935i | 0.286664i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.86183 | 0.347909 | 0.173954 | − | 0.984754i | \(-0.444345\pi\) | ||||
0.173954 | + | 0.984754i | \(0.444345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.99420 | −0.303140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5425 | 0.683129 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.73371 | −0.0872325 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.5352i | − | 0.829877i | −0.909849 | − | 0.414939i | \(-0.863803\pi\) | ||
0.909849 | − | 0.414939i | \(-0.136197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.80174 | − | 1.77993i | 0.240387 | − | 0.0891081i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.9269 | 1.39460 | 0.697300 | − | 0.716779i | \(-0.254384\pi\) | ||||
0.697300 | + | 0.716779i | \(0.254384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 15.8778i | − | 0.790932i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.43214i | 0.269925i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 63.7444i | − | 3.15969i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.782697i | − | 0.0387019i | −0.999813 | − | 0.0193509i | \(-0.993840\pi\) | ||
0.999813 | − | 0.0193509i | \(-0.00615998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.4243 | 1.45139 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.2072 | − | 4.89572i | 0.649884 | − | 0.240903i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.2384i | 0.600757i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.8449 | 1.46151 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.5686 | −1.73764 | −0.868820 | − | 0.495129i | \(-0.835121\pi\) | ||||
−0.868820 | + | 0.495129i | \(0.835121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.1499 | −0.884571 | −0.442286 | − | 0.896874i | \(-0.645832\pi\) | ||||
−0.442286 | + | 0.896874i | \(0.645832\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.07679 | 0.344085 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.65490i | 0.0802746i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.12357 | − | 5.72875i | −0.102767 | − | 0.277234i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 42.1461 | 2.03483 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 25.2831i | − | 1.21784i | −0.793230 | − | 0.608922i | \(-0.791602\pi\) | ||
0.793230 | − | 0.608922i | \(-0.208398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.25385i | − | 0.252484i | −0.991999 | − | 0.126242i | \(-0.959708\pi\) | ||
0.991999 | − | 0.126242i | \(-0.0402916\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.0696828i | − | 0.00334103i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.85180i | 0.232093i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.80378 | −0.133817 | −0.0669086 | − | 0.997759i | \(-0.521314\pi\) | ||||
−0.0669086 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.84165 | + | 4.16124i | −0.230555 | + | 0.198154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0548i | 0.572739i | 0.958119 | + | 0.286369i | \(0.0924484\pi\) | ||||
−0.958119 | + | 0.286369i | \(0.907552\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.28261 | 0.203015 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0821 | −0.713357 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.59847 | 0.358594 | 0.179297 | − | 0.983795i | \(-0.442618\pi\) | ||||
0.179297 | + | 0.983795i | \(0.442618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.4837 | 0.634923 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7.24636i | − | 0.340464i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.7659 | − | 4.73212i | 0.598473 | − | 0.221845i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.4671 | −0.629966 | −0.314983 | − | 0.949097i | \(-0.601999\pi\) | ||||
−0.314983 | + | 0.949097i | \(0.601999\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.35485i | 0.436647i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3606i | 0.529117i | 0.964370 | + | 0.264558i | \(0.0852262\pi\) | ||||
−0.964370 | + | 0.264558i | \(0.914774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.25805i | − | 0.104940i | −0.998622 | − | 0.0524702i | \(-0.983291\pi\) | ||
0.998622 | − | 0.0524702i | \(-0.0167095\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 4.45856i | − | 0.206761i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.9266 | 1.33856 | 0.669282 | − | 0.743009i | \(-0.266602\pi\) | ||||
0.669282 | + | 0.743009i | \(0.266602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.191115 | − | 0.515571i | −0.00882486 | − | 0.0238069i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 0.415940i | − | 0.0191655i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.0476 | 1.61149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.33951 | 0.0614607 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.57877 | 0.438582 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.476369 | −0.0217659 | −0.0108829 | − | 0.999941i | \(-0.503464\pi\) | ||||
−0.0108829 | + | 0.999941i | \(0.503464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 57.8717i | 2.63872i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.81302 | + | 12.9841i | 0.219000 | + | 0.590798i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.1226 | −0.550459 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.2827i | 0.556582i | 0.960497 | + | 0.278291i | \(0.0897679\pi\) | ||||
−0.960497 | + | 0.278291i | \(0.910232\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 11.5995i | − | 0.524546i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.06404i | 0.0480195i | 0.999712 | + | 0.0240098i | \(0.00764328\pi\) | ||||
−0.999712 | + | 0.0240098i | \(0.992357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.0798060i | − | 0.00359428i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.16942 | −0.232348 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.13797 | + | 16.5584i | 0.275326 | + | 0.742748i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.3062i | − | 0.729968i | −0.931014 | − | 0.364984i | \(-0.881074\pi\) | ||
0.931014 | − | 0.364984i | \(-0.118926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.52851 | 0.112966 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.483813 | 0.0215721 | 0.0107861 | − | 0.999942i | \(-0.496567\pi\) | ||||
0.0107861 | + | 0.999942i | \(0.496567\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4565 | 0.554307 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.4784 | −0.865068 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 38.0294i | − | 1.68562i | −0.538209 | − | 0.842811i | \(-0.680899\pi\) | ||
0.538209 | − | 0.842811i | \(-0.319101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.14908 | + | 8.49528i | 0.139307 | + | 0.375809i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.57197 | 0.334311 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 8.57029i | − | 0.377652i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 43.9811i | − | 1.93428i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 27.5360i | − | 1.20870i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.2374i | 1.71902i | 0.511119 | + | 0.859510i | \(0.329231\pi\) | ||||
−0.511119 | + | 0.859510i | \(0.670769\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.4346 | −1.11218 | −0.556088 | − | 0.831123i | \(-0.687698\pi\) | ||||
−0.556088 | + | 0.831123i | \(0.687698\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.58471 | − | 1.32880i | 0.156449 | − | 0.0579935i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5.10628i | − | 0.222433i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.88050 | 0.429587 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.85541 | 0.210707 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.2415 | −0.530237 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.1310 | 0.783872 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 11.8795i | − | 0.512637i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.8614 | + | 30.0901i | 1.11393 | + | 1.29607i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.2141 | −1.85792 | −0.928960 | − | 0.370181i | \(-0.879296\pi\) | ||||
−0.928960 | + | 0.370181i | \(0.879296\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.1447i | 1.59403i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.9272i | 0.596575i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.50599i | 0.363690i | 0.983327 | + | 0.181845i | \(0.0582069\pi\) | ||||
−0.983327 | + | 0.181845i | \(0.941793\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 2.10608i | − | 0.0898854i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0645963 | −0.00275189 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.59431 | + | 4.30098i | 0.0677970 | + | 0.182896i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.2506i | 0.689800i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.9999 | 0.720309 | 0.360155 | − | 0.932893i | \(-0.382724\pi\) | ||||
0.360155 | + | 0.932893i | \(0.382724\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.8187 | −1.34579 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5541 | 0.572255 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.94755 | 0.377094 | 0.188547 | − | 0.982064i | \(-0.439622\pi\) | ||||
0.188547 | + | 0.982064i | \(0.439622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.13757i | 0.216139i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.4760 | − | 4.99537i | 0.565940 | − | 0.209786i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.8378 | 0.831644 | 0.415822 | − | 0.909446i | \(-0.363494\pi\) | ||||
0.415822 | + | 0.909446i | \(0.363494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.9383i | 1.33657i | 0.743903 | + | 0.668287i | \(0.232972\pi\) | ||||
−0.743903 | + | 0.668287i | \(0.767028\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.1071i | 0.631109i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.62209i | 0.151051i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 31.1339i | − | 1.29612i | −0.761589 | − | 0.648061i | \(-0.775580\pi\) | ||
0.761589 | − | 0.648061i | \(-0.224420\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.5077 | −1.26786 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.3609 | − | 11.2543i | 1.25958 | − | 0.466908i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 59.5305i | − | 2.46550i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.69316 | 0.194038 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.4665 | −0.638371 | −0.319186 | − | 0.947692i | \(-0.603409\pi\) | ||||
−0.319186 | + | 0.947692i | \(0.603409\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.13311 | −0.170302 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.3469 | 1.65965 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3740i | 0.549204i | 0.961558 | + | 0.274602i | \(0.0885461\pi\) | ||||
−0.961558 | + | 0.274602i | \(0.911454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.10548 | − | 1.52184i | 0.168308 | − | 0.0623894i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.9477 | 1.26660 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.1853i | 1.31506i | 0.753430 | + | 0.657528i | \(0.228398\pi\) | ||||
−0.753430 | + | 0.657528i | \(0.771602\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.3375i | − | 1.11512i | −0.830136 | − | 0.557561i | \(-0.811737\pi\) | ||
0.830136 | − | 0.557561i | \(-0.188263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 0.189541i | − | 0.00771872i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.1271i | 0.858937i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.3275 | −1.23095 | −0.615477 | − | 0.788155i | \(-0.711037\pi\) | ||||
−0.615477 | + | 0.788155i | \(0.711037\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.172869 | + | 0.0640799i | −0.00700500 | + | 0.00259665i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.9291i | 1.61536i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.89751 | −0.117029 | −0.0585146 | − | 0.998287i | \(-0.518636\pi\) | ||||
−0.0585146 | + | 0.998287i | \(0.518636\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.43745 | −0.138612 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1763 | 0.852526 | 0.426263 | − | 0.904599i | \(-0.359830\pi\) | ||||
0.426263 | + | 0.904599i | \(0.359830\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.4589 | 1.26444 | 0.632220 | − | 0.774789i | \(-0.282144\pi\) | ||||
0.632220 | + | 0.774789i | \(0.282144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.4750i | 0.821632i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.93826 | − | 10.6243i | −0.157783 | − | 0.425653i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 10.9709i | − | 0.438136i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.6114i | 0.742086i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.3798i | 0.970545i | 0.874363 | + | 0.485273i | \(0.161280\pi\) | ||||
−0.874363 | + | 0.485273i | \(0.838720\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.25899i | − | 0.0897868i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.1695 | 0.681353 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.4788 | − | 27.3179i | −0.930265 | − | 1.08237i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.08744i | 0.240815i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.42059 | −0.253598 | −0.126799 | − | 0.991928i | \(-0.540470\pi\) | ||||
−0.126799 | + | 0.991928i | \(0.540470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.3031 | 0.840111 | 0.420056 | − | 0.907498i | \(-0.362011\pi\) | ||||
0.420056 | + | 0.907498i | \(0.362011\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.93482 | −0.351808 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.0503 | 1.26003 | 0.630014 | − | 0.776584i | \(-0.283049\pi\) | ||||
0.630014 | + | 0.776584i | \(0.283049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.1756i | − | 1.18450i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.0608 | + | 4.10007i | −0.433506 | + | 0.160694i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.8031 | 0.814088 | 0.407044 | − | 0.913408i | \(-0.366560\pi\) | ||||
0.407044 | + | 0.913408i | \(0.366560\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 9.37209i | − | 0.366198i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.12315i | 0.121846i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0443i | 0.936634i | 0.883561 | + | 0.468317i | \(0.155139\pi\) | ||||
−0.883561 | + | 0.468317i | \(0.844861\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.26973i | 0.127178i | 0.997976 | + | 0.0635888i | \(0.0202546\pi\) | ||||
−0.997976 | + | 0.0635888i | \(0.979745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.3054 | −0.477901 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.23180 | − | 3.32304i | −0.0477672 | − | 0.128862i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 0.174671i | − | 0.00676330i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.5324 | −0.909817 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0889 | −0.505293 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.99925 | −0.154160 | −0.0770798 | − | 0.997025i | \(-0.524560\pi\) | ||||
−0.0770798 | + | 0.997025i | \(0.524560\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.65281 | 0.217577 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.79714i | 0.376535i | 0.982118 | + | 0.188267i | \(0.0602871\pi\) | ||||
−0.982118 | + | 0.188267i | \(0.939713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.1479 | + | 30.0737i | 0.427816 | + | 1.15412i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.9824 | 0.957327 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.4747i | 1.58698i | 0.608580 | + | 0.793492i | \(0.291739\pi\) | ||||
−0.608580 | + | 0.793492i | \(0.708261\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 20.3631i | − | 0.778032i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 37.5386i | − | 1.43219i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.0460i | 2.05899i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.2780 | −1.07574 | −0.537872 | − | 0.843026i | \(-0.680772\pi\) | ||||
−0.537872 | + | 0.843026i | \(0.680772\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.75377 | + | 12.8243i | 0.180581 | + | 0.487153i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 20.6541i | − | 0.783456i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.93683 | −0.149118 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.2392 | −0.462929 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.3111 | −1.22037 | −0.610186 | − | 0.792258i | \(-0.708905\pi\) | ||||
−0.610186 | + | 0.792258i | \(0.708905\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.0644 | 0.568164 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.2123i | 0.422278i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.4549 | − | 30.9020i | −0.430807 | − | 1.16219i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.463813 | 0.0174189 | 0.00870943 | − | 0.999962i | \(-0.497228\pi\) | ||||
0.00870943 | + | 0.999962i | \(0.497228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.58118i | 0.0592991i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 11.1761i | − | 0.418549i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 29.1672i | − | 1.09079i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.71785i | 0.362920i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.133597 | 0.00498231 | 0.00249116 | − | 0.999997i | \(-0.499207\pi\) | ||||
0.00249116 | + | 0.999997i | \(0.499207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.2611 | + | 7.88119i | −0.791806 | + | 0.293511i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 35.9085i | − | 1.33545i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0482240 | −0.00179099 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.1815 | −0.414700 | −0.207350 | − | 0.978267i | \(-0.566484\pi\) | ||||
−0.207350 | + | 0.978267i | \(0.566484\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.4589 | 1.09107 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.2328 | −0.378475 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.9801i | 1.47670i | 0.674418 | + | 0.738350i | \(0.264395\pi\) | ||||
−0.674418 | + | 0.738350i | \(0.735605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.59295 | − | 7.67097i | −0.243185 | − | 0.282948i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.17797 | −0.0433910 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.7898i | − | 0.617622i | −0.951123 | − | 0.308811i | \(-0.900069\pi\) | ||
0.951123 | − | 0.308811i | \(-0.0999311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.96017i | 0.365896i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.1106i | − | 0.884534i | −0.896883 | − | 0.442267i | \(-0.854174\pi\) | ||
0.896883 | − | 0.442267i | \(-0.145826\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.4375i | 0.382402i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.1617 | 0.408384 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.6732 | − | 44.9793i | −0.609224 | − | 1.64351i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 38.0487i | − | 1.38842i | −0.719774 | − | 0.694208i | \(-0.755755\pi\) | ||
0.719774 | − | 0.694208i | \(-0.244245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.2387 | −0.701096 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.01484 | −0.182509 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.19151 | 0.0433060 | 0.0216530 | − | 0.999766i | \(-0.493107\pi\) | ||||
0.0216530 | + | 0.999766i | \(0.493107\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.6659 | 1.07680 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0562i | 0.364538i | 0.983249 | + | 0.182269i | \(0.0583441\pi\) | ||||
−0.983249 | + | 0.182269i | \(0.941656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.5505 | − | 12.8074i | 1.25081 | − | 0.463658i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.50931 | 0.0545692 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.3955i | 0.989195i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.1778i | − | 1.12430i | −0.827035 | − | 0.562150i | \(-0.809974\pi\) | ||
0.827035 | − | 0.562150i | \(-0.190026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 35.9785i | − | 1.29574i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 40.4974i | − | 1.45659i | −0.685264 | − | 0.728294i | \(-0.740313\pi\) | ||
0.685264 | − | 0.728294i | \(-0.259687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.08555 | −0.110836 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 40.3144 | − | 14.9440i | 1.44627 | − | 0.536112i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.18653i | 0.114169i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.8324 | 1.35375 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.272601 | −0.00974196 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.287851 | −0.0102738 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.24513 | −0.329553 | −0.164777 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164777 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3.90335i | − | 0.138963i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.7453 | − | 4.72448i | 0.453170 | − | 0.167983i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.8831 | 0.421980 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.1763i | 0.538249i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.51772i | 0.124604i | 0.998057 | + | 0.0623020i | \(0.0198442\pi\) | ||||
−0.998057 | + | 0.0623020i | \(0.980156\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.8411i | 0.454286i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.90584i | − | 0.138006i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.4099 | 0.684959 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.98565 | − | 3.33085i | 0.316703 | − | 0.117397i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.1961i | 1.27416i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.36429 | −0.0831240 | −0.0415620 | − | 0.999136i | \(-0.513233\pi\) | ||||
−0.0415620 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.3645 | −1.34716 | −0.673580 | − | 0.739114i | \(-0.735244\pi\) | ||||
−0.673580 | + | 0.739114i | \(0.735244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.1759 | −0.707601 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.02740 | −0.281188 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.28262i | 0.289772i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.31580 | − | 11.6428i | −0.150806 | − | 0.406831i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.57030 | 0.229305 | 0.114652 | − | 0.993406i | \(-0.463425\pi\) | ||||
0.114652 | + | 0.993406i | \(0.463425\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 21.8232i | − | 0.760708i | −0.924841 | − | 0.380354i | \(-0.875802\pi\) | ||
0.924841 | − | 0.380354i | \(-0.124198\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 8.19027i | − | 0.285149i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.11783i | − | 0.177965i | −0.996033 | − | 0.0889823i | \(-0.971639\pi\) | ||
0.996033 | − | 0.0889823i | \(-0.0283614\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.88700i | 0.135001i | 0.997719 | + | 0.0675006i | \(0.0215025\pi\) | ||||
−0.997719 | + | 0.0675006i | \(0.978498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.6679 | 0.682272 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.55075 | − | 8.78537i | −0.261618 | − | 0.304395i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.74986i | − | 0.0605563i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.4420 | −0.602884 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.4205 | −0.497851 | −0.248925 | − | 0.968523i | \(-0.580077\pi\) | ||||
−0.248925 | + | 0.968523i | \(0.580077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9977 | −0.999920 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.8481 | 1.20023 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.4800i | 0.463727i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52.4119 | − | 19.4283i | 1.80090 | − | 0.667565i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33.7245 | −1.15742 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.7348i | 1.39637i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 15.0531i | − | 0.515408i | −0.966224 | − | 0.257704i | \(-0.917034\pi\) | ||
0.966224 | − | 0.257704i | \(-0.0829659\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.22166i | − | 0.0417799i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 12.0124i | − | 0.410335i | −0.978727 | − | 0.205167i | \(-0.934226\pi\) | ||
0.978727 | − | 0.205167i | \(-0.0657739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1209 | 0.822995 | 0.411498 | − | 0.911411i | \(-0.365006\pi\) | ||||
0.411498 | + | 0.911411i | \(0.365006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.16106 | + | 8.52762i | 0.107729 | + | 0.290620i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.3179i | 1.50860i | 0.656530 | + | 0.754300i | \(0.272024\pi\) | ||||
−0.656530 | + | 0.754300i | \(0.727976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.0563 | −0.647933 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.6073 | 0.699862 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.82680 | 0.333351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.06944 | 0.0362367 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.0561i | 0.374192i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.919594 | − | 2.48080i | −0.0310880 | − | 0.0838662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.6049 | 0.999685 | 0.499843 | − | 0.866116i | \(-0.333391\pi\) | ||||
0.499843 | + | 0.866116i | \(0.333391\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 10.9280i | − | 0.368593i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.62314i | − | 0.0883758i | −0.999023 | − | 0.0441879i | \(-0.985930\pi\) | ||
0.999023 | − | 0.0441879i | \(-0.0140700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.4982i | 1.83401i | 0.398875 | + | 0.917005i | \(0.369401\pi\) | ||||
−0.398875 | + | 0.917005i | \(0.630599\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.69277i | 0.258590i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.43247 | 0.316712 | 0.158356 | − | 0.987382i | \(-0.449381\pi\) | ||||
0.158356 | + | 0.987382i | \(0.449381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.7890 | − | 42.5941i | −0.529547 | − | 1.42856i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 30.7898i | − | 1.03150i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.3938 | 0.347815 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.22119 | −0.274804 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.9328 | −0.899259 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.148797 | 0.00496267 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.3811i | 0.579048i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.21641 | + | 22.1655i | 0.273425 | + | 0.737620i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.7060 | 0.854495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.3317i | − | 1.27278i | −0.771367 | − | 0.636391i | \(-0.780426\pi\) | ||
0.771367 | − | 0.636391i | \(-0.219574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 11.3606i | − | 0.376808i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.7714i | 1.74840i | 0.485570 | + | 0.874198i | \(0.338612\pi\) | ||||
−0.485570 | + | 0.874198i | \(0.661388\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 69.3679i | − | 2.29574i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.33681 | 0.110312 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.2502 | + | 8.61852i | −0.767790 | + | 0.284609i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.1019i | 0.597126i | 0.954390 | + | 0.298563i | \(0.0965073\pi\) | ||||
−0.954390 | + | 0.298563i | \(0.903493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.6700 | −1.20832 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.3469 | −1.13054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.2462 | 0.369773 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.81630 | −0.256721 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.0129i | 0.951884i | 0.879477 | + | 0.475942i | \(0.157893\pi\) | ||||
−0.879477 | + | 0.475942i | \(0.842107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.11102 | + | 6.11170i | −0.233054 | + | 0.200303i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.35711 | −0.0444299 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.38012i | − | 0.306763i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.2033i | 1.54207i | 0.636795 | + | 0.771033i | \(0.280260\pi\) | ||||
−0.636795 | + | 0.771033i | \(0.719740\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.9918i | 0.946111i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.79631i | 0.319350i | 0.987170 | + | 0.159675i | \(0.0510447\pi\) | ||||
−0.987170 | + | 0.159675i | \(0.948955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.61654 | −0.280593 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.19829 | − | 14.0235i | −0.169100 | − | 0.456183i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.3789i | 0.532243i | 0.963939 | + | 0.266122i | \(0.0857423\pi\) | ||||
−0.963939 | + | 0.266122i | \(0.914258\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.6216 | −0.572022 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.2283 | −0.655946 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.2951 | −0.851780 | −0.425890 | − | 0.904775i | \(-0.640039\pi\) | ||||
−0.425890 | + | 0.904775i | \(0.640039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.4549 | 0.338312 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.394967i | 0.0127675i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −50.5166 | + | 18.7258i | −1.63127 | + | 0.604686i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.4794 | −0.692884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 16.5359i | − | 0.532862i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.1128i | 0.679645i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.9593i | − | 0.416742i | −0.978050 | − | 0.208371i | \(-0.933184\pi\) | ||
0.978050 | − | 0.208371i | \(-0.0668161\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.20317i | 0.102901i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58.7681 | −1.88596 | −0.942979 | − | 0.332853i | \(-0.891989\pi\) | ||||
−0.942979 | + | 0.332853i | \(0.891989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.2387 | + | 18.9934i | −1.64264 | + | 0.608901i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.43570i | 0.238133i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.6628 | 0.821026 | 0.410513 | − | 0.911855i | \(-0.365350\pi\) | ||||
0.410513 | + | 0.911855i | \(0.365350\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.2742 | −0.775805 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7019 | 0.405541 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.8771 | −0.889142 | −0.444571 | − | 0.895744i | \(-0.646644\pi\) | ||||
−0.444571 | + | 0.895744i | \(0.646644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 27.9221i | − | 0.889671i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.8153 | − | 10.3107i | 0.885371 | − | 0.328194i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.3966 | −0.712170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 13.0915i | − | 0.415865i | −0.978143 | − | 0.207933i | \(-0.933327\pi\) | ||
0.978143 | − | 0.207933i | \(-0.0666735\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 24.6937i | − | 0.783632i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 21.4173i | − | 0.678974i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 45.8336i | − | 1.45157i | −0.687924 | − | 0.725783i | \(-0.741478\pi\) | ||
0.687924 | − | 0.725783i | \(-0.258522\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 63.5727 | 2.01135 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2240.2.k.g.1791.11 | 16 | ||
4.3 | odd | 2 | 2240.2.k.f.1791.5 | 16 | |||
7.6 | odd | 2 | 2240.2.k.f.1791.6 | 16 | |||
8.3 | odd | 2 | 1120.2.k.a.671.12 | yes | 16 | ||
8.5 | even | 2 | 1120.2.k.b.671.6 | yes | 16 | ||
28.27 | even | 2 | inner | 2240.2.k.g.1791.12 | 16 | ||
56.13 | odd | 2 | 1120.2.k.a.671.11 | ✓ | 16 | ||
56.27 | even | 2 | 1120.2.k.b.671.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.k.a.671.11 | ✓ | 16 | 56.13 | odd | 2 | ||
1120.2.k.a.671.12 | yes | 16 | 8.3 | odd | 2 | ||
1120.2.k.b.671.5 | yes | 16 | 56.27 | even | 2 | ||
1120.2.k.b.671.6 | yes | 16 | 8.5 | even | 2 | ||
2240.2.k.f.1791.5 | 16 | 4.3 | odd | 2 | |||
2240.2.k.f.1791.6 | 16 | 7.6 | odd | 2 | |||
2240.2.k.g.1791.11 | 16 | 1.1 | even | 1 | trivial | ||
2240.2.k.g.1791.12 | 16 | 28.27 | even | 2 | inner |