Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(601,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.601");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.bg (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 601.2 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.601 |
Dual form | 1560.2.bg.f.841.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.219224 | + | 0.379706i | −0.0828587 | + | 0.143516i | −0.904477 | − | 0.426523i | \(-0.859738\pi\) |
0.821618 | + | 0.570038i | \(0.193072\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.28078 | − | 3.95042i | −0.687680 | − | 1.19110i | −0.972587 | − | 0.232541i | \(-0.925296\pi\) |
0.284907 | − | 0.958555i | \(-0.408037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.34233 | − | 1.35234i | 0.926995 | − | 0.375073i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.500000 | + | 0.866025i | 0.129099 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.56155 | − | 4.43674i | 0.587661 | − | 1.01786i | −0.406877 | − | 0.913483i | \(-0.633382\pi\) |
0.994538 | − | 0.104375i | \(-0.0332843\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.438447 | −0.0956770 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.28078 | − | 3.95042i | −0.475575 | − | 0.823720i | 0.524034 | − | 0.851697i | \(-0.324427\pi\) |
−0.999609 | + | 0.0279778i | \(0.991093\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.84233 | + | 3.19101i | 0.342112 | + | 0.592555i | 0.984825 | − | 0.173552i | \(-0.0555245\pi\) |
−0.642713 | + | 0.766107i | \(0.722191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.12311 | 0.740532 | 0.370266 | − | 0.928926i | \(-0.379267\pi\) | ||||
0.370266 | + | 0.928926i | \(0.379267\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.28078 | − | 3.95042i | 0.397032 | − | 0.687680i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.219224 | + | 0.379706i | −0.0370556 | + | 0.0641821i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.28078 | − | 3.95042i | −0.374957 | − | 0.649445i | 0.615363 | − | 0.788244i | \(-0.289009\pi\) |
−0.990321 | + | 0.138798i | \(0.955676\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.84233 | + | 2.21837i | 0.455137 | + | 0.355223i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | + | 1.73205i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.06155 | − | 5.30277i | 0.466882 | − | 0.808664i | −0.532402 | − | 0.846492i | \(-0.678710\pi\) |
0.999284 | + | 0.0378277i | \(0.0120438\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.56155 | 0.957101 | 0.478550 | − | 0.878060i | \(-0.341162\pi\) | ||||
0.478550 | + | 0.878060i | \(0.341162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.40388 | + | 5.89570i | 0.486269 | + | 0.842242i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.12311 | 0.154270 | 0.0771352 | − | 0.997021i | \(-0.475423\pi\) | ||||
0.0771352 | + | 0.997021i | \(0.475423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.28078 | − | 3.95042i | −0.307540 | − | 0.532675i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.12311 | 0.678572 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.84233 | − | 3.19101i | 0.239851 | − | 0.415434i | −0.720820 | − | 0.693122i | \(-0.756235\pi\) |
0.960671 | + | 0.277688i | \(0.0895681\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34233 | + | 9.25319i | −0.684015 | + | 1.18475i | 0.289730 | + | 0.957108i | \(0.406434\pi\) |
−0.973745 | + | 0.227641i | \(0.926899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.219224 | − | 0.379706i | −0.0276196 | − | 0.0478385i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.34233 | − | 1.35234i | 0.414565 | − | 0.167738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.21922 | + | 2.11176i | 0.148952 | + | 0.257992i | 0.930840 | − | 0.365426i | \(-0.119077\pi\) |
−0.781888 | + | 0.623418i | \(0.785743\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.28078 | − | 3.95042i | 0.274573 | − | 0.475575i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.43845 | 0.519481 | 0.259740 | − | 0.965678i | \(-0.416363\pi\) | ||||
0.259740 | + | 0.965678i | \(0.416363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.753789 | −0.0848079 | −0.0424039 | − | 0.999101i | \(-0.513502\pi\) | ||||
−0.0424039 | + | 0.999101i | \(0.513502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3693 | −1.24794 | −0.623972 | − | 0.781446i | \(-0.714482\pi\) | ||||
−0.623972 | + | 0.781446i | \(0.714482\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.84233 | + | 3.19101i | −0.197518 | + | 0.342112i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.00000 | − | 1.73205i | −0.106000 | − | 0.183597i | 0.808146 | − | 0.588982i | \(-0.200471\pi\) |
−0.914146 | + | 0.405385i | \(0.867138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.219224 | + | 1.56557i | −0.0229809 | + | 0.164116i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.06155 | + | 3.57071i | 0.213773 | + | 0.370266i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.56155 | − | 4.43674i | 0.262810 | − | 0.455200i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.21922 | + | 7.30791i | −0.428397 | + | 0.742006i | −0.996731 | − | 0.0807924i | \(-0.974255\pi\) |
0.568334 | + | 0.822798i | \(0.307588\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.56155 | 0.458453 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.12311 | − | 7.14143i | −0.410264 | − | 0.710599i | 0.584654 | − | 0.811283i | \(-0.301230\pi\) |
−0.994918 | + | 0.100684i | \(0.967897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.56155 | −0.350930 | −0.175465 | − | 0.984486i | \(-0.556143\pi\) | ||||
−0.175465 | + | 0.984486i | \(0.556143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.438447 | −0.0427881 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.43845 | + | 2.49146i | 0.139060 | + | 0.240859i | 0.927141 | − | 0.374713i | \(-0.122259\pi\) |
−0.788081 | + | 0.615571i | \(0.788925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8078 | 1.70567 | 0.852837 | − | 0.522177i | \(-0.174880\pi\) | ||||
0.852837 | + | 0.522177i | \(0.174880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.28078 | − | 3.95042i | 0.216482 | − | 0.374957i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.15767 | + | 5.46925i | −0.297049 | + | 0.514503i | −0.975459 | − | 0.220179i | \(-0.929336\pi\) |
0.678411 | + | 0.734683i | \(0.262669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.28078 | − | 3.95042i | −0.212683 | − | 0.368379i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | + | 3.57071i | −0.0462250 | + | 0.330113i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.438447 | + | 0.759413i | 0.0401924 | + | 0.0696153i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.90388 | + | 8.49377i | −0.445807 | + | 0.772161i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.34233 | − | 2.32498i | −0.119112 | − | 0.206309i | 0.800304 | − | 0.599595i | \(-0.204672\pi\) |
−0.919416 | + | 0.393286i | \(0.871338\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.12311 | 0.539109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.56155 | −0.223804 | −0.111902 | − | 0.993719i | \(-0.535694\pi\) | ||||
−0.111902 | + | 0.993719i | \(0.535694\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.12311 | + | 1.94528i | 0.0973856 | + | 0.168677i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.28078 | − | 3.95042i | 0.194860 | − | 0.337507i | −0.751995 | − | 0.659169i | \(-0.770908\pi\) |
0.946855 | + | 0.321662i | \(0.104241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.90388 | − | 15.4220i | 0.755217 | − | 1.30807i | −0.190049 | − | 0.981775i | \(-0.560865\pi\) |
0.945266 | − | 0.326300i | \(-0.105802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.28078 | + | 5.68247i | 0.276291 | + | 0.478550i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.9654 | − | 10.1192i | −1.08422 | − | 0.846211i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.84233 | + | 3.19101i | 0.152997 | + | 0.264999i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.40388 | + | 5.89570i | −0.280747 | + | 0.486269i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.96543 | − | 12.0645i | 0.570631 | − | 0.988361i | −0.425871 | − | 0.904784i | \(-0.640032\pi\) |
0.996501 | − | 0.0835772i | \(-0.0266345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.00000 | + | 1.73205i | 0.0808452 | + | 0.140028i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.12311 | 0.331176 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2462 | 0.897545 | 0.448773 | − | 0.893646i | \(-0.351861\pi\) | ||||
0.448773 | + | 0.893646i | \(0.351861\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.561553 | + | 0.972638i | 0.0445340 | + | 0.0771352i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0616 | + | 17.4271i | −0.788082 | + | 1.36500i | 0.139059 | + | 0.990284i | \(0.455592\pi\) |
−0.927141 | + | 0.374713i | \(0.877741\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.28078 | − | 3.95042i | 0.177558 | − | 0.307540i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7192 | − | 18.5662i | −0.829478 | − | 1.43670i | −0.898448 | − | 0.439080i | \(-0.855304\pi\) |
0.0689695 | − | 0.997619i | \(-0.478029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.34233 | − | 9.03996i | 0.718641 | − | 0.695382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.56155 | + | 4.43674i | 0.195887 | + | 0.339286i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | − | 3.46410i | 0.152057 | − | 0.263371i | −0.779926 | − | 0.625871i | \(-0.784744\pi\) |
0.931984 | + | 0.362500i | \(0.118077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.219224 | + | 0.379706i | −0.0165717 | + | 0.0287031i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.68466 | 0.276956 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.40388 | − | 9.35980i | −0.403905 | − | 0.699584i | 0.590288 | − | 0.807193i | \(-0.299014\pi\) |
−0.994193 | + | 0.107608i | \(0.965681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.12311 | −0.232139 | −0.116069 | − | 0.993241i | \(-0.537029\pi\) | ||||
−0.116069 | + | 0.993241i | \(0.537029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.6847 | −0.789833 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.28078 | − | 3.95042i | −0.167686 | − | 0.290441i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.12311 | −0.667148 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.219224 | − | 0.379706i | 0.0159462 | − | 0.0276196i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0000 | + | 17.3205i | −0.723575 | + | 1.25327i | 0.235983 | + | 0.971757i | \(0.424169\pi\) |
−0.959558 | + | 0.281511i | \(0.909164\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.02699 | + | 15.6352i | 0.649777 | + | 1.12545i | 0.983176 | + | 0.182661i | \(0.0584710\pi\) |
−0.333399 | + | 0.942786i | \(0.608196\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.84233 | + | 2.21837i | 0.203543 | + | 0.158861i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | + | 6.92820i | 0.284988 | + | 0.493614i | 0.972606 | − | 0.232458i | \(-0.0746770\pi\) |
−0.687618 | + | 0.726073i | \(0.741344\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.78078 | + | 11.7446i | −0.480676 | + | 0.832556i | −0.999754 | − | 0.0221709i | \(-0.992942\pi\) |
0.519078 | + | 0.854727i | \(0.326276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.21922 | + | 2.11176i | −0.0859974 | + | 0.148952i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.61553 | −0.113388 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00000 | + | 1.73205i | 0.0698430 | + | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.56155 | 0.317050 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.3693 | −1.61649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.02699 | + | 12.1711i | 0.483758 | + | 0.837893i | 0.999826 | − | 0.0186544i | \(-0.00593824\pi\) |
−0.516068 | + | 0.856547i | \(0.672605\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.06155 | − | 5.30277i | 0.208796 | − | 0.361646i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.903882 | + | 1.56557i | −0.0613595 | + | 0.106278i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.21922 | + | 3.84381i | 0.149961 | + | 0.259740i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00000 | − | 7.14143i | 0.0672673 | − | 0.480384i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.80776 | − | 15.2555i | −0.589812 | − | 1.02158i | −0.994257 | − | 0.107021i | \(-0.965869\pi\) |
0.404445 | − | 0.914562i | \(-0.367465\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6847 | + | 21.9705i | −0.841910 | + | 1.45823i | 0.0463672 | + | 0.998924i | \(0.485236\pi\) |
−0.888278 | + | 0.459307i | \(0.848098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.7386 | 1.37045 | 0.685224 | − | 0.728333i | \(-0.259704\pi\) | ||||
0.685224 | + | 0.728333i | \(0.259704\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | + | 1.73205i | 0.0657952 | + | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.0540 | −1.37929 | −0.689646 | − | 0.724147i | \(-0.742234\pi\) | ||||
−0.689646 | + | 0.724147i | \(0.742234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.56155 | 0.428029 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.376894 | − | 0.652800i | −0.0244819 | − | 0.0424039i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0345652 | − | 0.0598686i | 0.00222654 | − | 0.00385648i | −0.864910 | − | 0.501927i | \(-0.832625\pi\) |
0.867137 | + | 0.498071i | \(0.165958\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.40388 | + | 5.89570i | 0.217466 | + | 0.376662i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.56155 | − | 18.2931i | 0.162988 | − | 1.16397i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.68466 | − | 9.84612i | −0.360251 | − | 0.623972i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.28078 | + | 9.14657i | −0.333320 | + | 0.577327i | −0.983161 | − | 0.182744i | \(-0.941502\pi\) |
0.649841 | + | 0.760070i | \(0.274835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.4039 | + | 18.0201i | −0.654086 | + | 1.13291i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.28078 | − | 14.3427i | −0.516541 | − | 0.894675i | −0.999816 | − | 0.0192060i | \(-0.993886\pi\) |
0.483275 | − | 0.875469i | \(-0.339447\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.68466 | −0.228075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.96543 | − | 3.40423i | −0.121194 | − | 0.209914i | 0.799045 | − | 0.601271i | \(-0.205339\pi\) |
−0.920239 | + | 0.391357i | \(0.872006\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.12311 | 0.0689918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.00000 | − | 1.73205i | 0.0611990 | − | 0.106000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.12311 | − | 7.14143i | 0.251390 | − | 0.435421i | −0.712519 | − | 0.701653i | \(-0.752446\pi\) |
0.963909 | + | 0.266233i | \(0.0857789\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8693 | − | 22.2903i | −0.781755 | − | 1.35404i | −0.930918 | − | 0.365227i | \(-0.880991\pi\) |
0.149163 | − | 0.988813i | \(-0.452342\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.46543 | + | 0.592932i | −0.0886922 | + | 0.0358859i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.28078 | − | 3.95042i | −0.137536 | − | 0.238219i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.71922 | + | 9.90599i | −0.343635 | + | 0.595193i | −0.985105 | − | 0.171955i | \(-0.944992\pi\) |
0.641470 | + | 0.767148i | \(0.278325\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.06155 | + | 3.57071i | −0.123422 | + | 0.213773i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.8617 | −1.90071 | −0.950356 | − | 0.311165i | \(-0.899281\pi\) | ||||
−0.950356 | + | 0.311165i | \(0.899281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.50000 | − | 2.59808i | −0.0891657 | − | 0.154440i | 0.817993 | − | 0.575228i | \(-0.195087\pi\) |
−0.907159 | + | 0.420789i | \(0.861753\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.12311 | 0.303467 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.876894 | −0.0517614 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.43845 | −0.494671 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.56155 | − | 11.3649i | 0.383330 | − | 0.663947i | −0.608206 | − | 0.793779i | \(-0.708111\pi\) |
0.991536 | + | 0.129832i | \(0.0414439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.84233 | − | 3.19101i | 0.107265 | − | 0.185788i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.28078 | + | 3.95042i | 0.132344 | + | 0.229227i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.9654 | − | 10.1192i | −0.749810 | − | 0.585209i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.34233 | + | 2.32498i | 0.0773706 | + | 0.134010i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.12311 | − | 7.14143i | 0.236866 | − | 0.410264i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.34233 | + | 9.25319i | −0.305901 | + | 0.529836i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9309 | −0.852150 | −0.426075 | − | 0.904688i | \(-0.640104\pi\) | ||||
−0.426075 | + | 0.904688i | \(0.640104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.78078 | − | 3.08440i | −0.101305 | − | 0.175465i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.36932 | −0.304466 | −0.152233 | − | 0.988345i | \(-0.548646\pi\) | ||||
−0.152233 | + | 0.988345i | \(0.548646\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0540 | −0.794378 | −0.397189 | − | 0.917737i | \(-0.630014\pi\) | ||||
−0.397189 | + | 0.917737i | \(0.630014\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.219224 | − | 0.379706i | −0.0123519 | − | 0.0213940i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.75379 | 0.0985026 | 0.0492513 | − | 0.998786i | \(-0.484316\pi\) | ||||
0.0492513 | + | 0.998786i | \(0.484316\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.40388 | − | 14.5560i | 0.470527 | − | 0.814977i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.43845 | + | 2.49146i | −0.0802863 | + | 0.139060i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.12311 | − | 8.87348i | −0.285057 | − | 0.493734i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.34233 | − | 1.35234i | 0.185399 | − | 0.0750146i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.90388 | + | 15.4220i | 0.492386 | + | 0.852837i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.43845 | + | 2.49146i | −0.0793042 | + | 0.137359i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.78078 | + | 8.28055i | −0.262775 | + | 0.455140i | −0.966978 | − | 0.254859i | \(-0.917971\pi\) |
0.704203 | + | 0.709999i | \(0.251304\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.56155 | 0.249972 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.21922 | + | 2.11176i | 0.0666133 | + | 0.115378i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.8078 | −1.18794 | −0.593972 | − | 0.804485i | \(-0.702441\pi\) | ||||
−0.593972 | + | 0.804485i | \(0.702441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.31534 | −0.343002 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.40388 | − | 16.2880i | −0.509249 | − | 0.882045i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.05398 | −0.326884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.28078 | − | 3.95042i | 0.122793 | − | 0.212683i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.68466 | + | 9.84612i | −0.305168 | + | 0.528567i | −0.977299 | − | 0.211866i | \(-0.932046\pi\) |
0.672130 | + | 0.740433i | \(0.265379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3423 | + | 17.9134i | 0.553612 | + | 0.958884i | 0.998010 | + | 0.0630549i | \(0.0200843\pi\) |
−0.444398 | + | 0.895830i | \(0.646582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.34233 | + | 1.35234i | −0.178400 | + | 0.0721828i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.87689 | + | 10.1791i | 0.312796 | + | 0.541778i | 0.978966 | − | 0.204021i | \(-0.0654012\pi\) |
−0.666171 | + | 0.745799i | \(0.732068\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.438447 | + | 0.759413i | −0.0232051 | + | 0.0401924i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.8769 | 0.890728 | 0.445364 | − | 0.895349i | \(-0.353074\pi\) | ||||
0.445364 | + | 0.895349i | \(0.353074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.62311 | − | 6.27540i | −0.190690 | − | 0.330284i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.80776 | −0.514774 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.43845 | 0.232319 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.5885 | − | 18.3399i | −0.552717 | − | 0.957334i | −0.998077 | − | 0.0619828i | \(-0.980258\pi\) |
0.445360 | − | 0.895352i | \(-0.353076\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.246211 | + | 0.426450i | −0.0127827 | + | 0.0221402i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.62311 | + | 6.27540i | −0.187597 | + | 0.324928i | −0.944449 | − | 0.328659i | \(-0.893403\pi\) |
0.756851 | + | 0.653587i | \(0.226737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4730 | + | 8.17394i | 0.539388 | + | 0.420979i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.5885 | + | 20.0719i | 0.595263 | + | 1.03103i | 0.993510 | + | 0.113748i | \(0.0362856\pi\) |
−0.398246 | + | 0.917279i | \(0.630381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.34233 | − | 2.32498i | 0.0687696 | − | 0.119112i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.52699 | + | 14.7692i | −0.435709 | + | 0.754670i | −0.997353 | − | 0.0727090i | \(-0.976836\pi\) |
0.561644 | + | 0.827379i | \(0.310169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.06155 | + | 5.30277i | 0.155627 | + | 0.269555i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.3002 | 1.48558 | 0.742789 | − | 0.669525i | \(-0.233502\pi\) | ||||
0.742789 | + | 0.669525i | \(0.233502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.12311 | −0.461375 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.28078 | − | 2.21837i | −0.0646066 | − | 0.111902i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.753789 | −0.0379272 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.06155 | − | 10.4989i | 0.304221 | − | 0.526926i | −0.672867 | − | 0.739764i | \(-0.734937\pi\) |
0.977087 | + | 0.212838i | \(0.0682707\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.12311 | + | 1.94528i | −0.0562256 | + | 0.0973856i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.87689 | + | 4.98293i | 0.143665 | + | 0.248836i | 0.928874 | − | 0.370395i | \(-0.120778\pi\) |
−0.785209 | + | 0.619231i | \(0.787444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.7808 | − | 5.57586i | 0.686469 | − | 0.277753i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.500000 | − | 0.866025i | −0.0248452 | − | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4039 | + | 18.0201i | −0.515701 | + | 0.893221i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.9039 | + | 29.2784i | −0.835843 | + | 1.44772i | 0.0574989 | + | 0.998346i | \(0.481687\pi\) |
−0.893342 | + | 0.449377i | \(0.851646\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.56155 | 0.225005 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.807764 | + | 1.39909i | 0.0397475 | + | 0.0688446i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.3693 | −0.558098 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.8078 | 0.872050 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.56155 | − | 13.0970i | −0.369406 | − | 0.639830i | 0.620067 | − | 0.784549i | \(-0.287106\pi\) |
−0.989473 | + | 0.144719i | \(0.953772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.8078 | −1.74516 | −0.872582 | − | 0.488468i | \(-0.837556\pi\) | ||||
−0.872582 | + | 0.488468i | \(0.837556\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.28078 | + | 5.68247i | −0.159517 | + | 0.276291i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.34233 | − | 4.05703i | −0.113353 | − | 0.196334i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.28078 | − | 16.2880i | 0.110117 | − | 0.786392i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.24621 | + | 10.8188i | 0.300869 | + | 0.521121i | 0.976333 | − | 0.216272i | \(-0.0693898\pi\) |
−0.675464 | + | 0.737393i | \(0.736057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.7116 | + | 27.2134i | −0.755054 | + | 1.30779i | 0.190294 | + | 0.981727i | \(0.439056\pi\) |
−0.945348 | + | 0.326064i | \(0.894278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.84233 | + | 3.19101i | −0.0883329 | + | 0.152997i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.3693 | −1.11791 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1501 | + | 24.5087i | 0.675347 | + | 1.16974i | 0.976367 | + | 0.216118i | \(0.0693395\pi\) |
−0.301020 | + | 0.953618i | \(0.597327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.80776 | −0.324179 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.3693 | −1.39538 | −0.697689 | − | 0.716401i | \(-0.745788\pi\) | ||||
−0.697689 | + | 0.716401i | \(0.745788\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | − | 1.73205i | −0.0474045 | − | 0.0821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.9309 | 0.658908 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6847 | − | 18.5064i | 0.504240 | − | 0.873370i | −0.495748 | − | 0.868467i | \(-0.665106\pi\) |
0.999988 | − | 0.00490311i | \(-0.00156071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.56155 | − | 7.90084i | 0.214795 | − | 0.372036i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | + | 13.8564i | 0.375873 | + | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.219224 | + | 1.56557i | −0.0102774 | + | 0.0733950i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.46543 | − | 4.27026i | −0.115328 | − | 0.199754i | 0.802583 | − | 0.596541i | \(-0.203459\pi\) |
−0.917911 | + | 0.396787i | \(0.870125\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4039 | − | 23.2162i | 0.624281 | − | 1.08129i | −0.364398 | − | 0.931243i | \(-0.618725\pi\) |
0.988679 | − | 0.150043i | \(-0.0479413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.80776 | 0.0840139 | 0.0420070 | − | 0.999117i | \(-0.486625\pi\) | ||||
0.0420070 | + | 0.999117i | \(0.486625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.06155 | + | 3.57071i | 0.0956022 | + | 0.165588i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.6155 | 1.00025 | 0.500124 | − | 0.865954i | \(-0.333288\pi\) | ||||
0.500124 | + | 0.865954i | \(0.333288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.06913 | −0.0493679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.62311 | + | 9.73950i | 0.259099 | + | 0.448773i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.9309 | −1.28426 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.56155 | − | 4.43674i | 0.117532 | − | 0.203572i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.561553 | + | 0.972638i | −0.0257117 | + | 0.0445340i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.9309 | + | 18.9328i | 0.499444 | + | 0.865063i | 1.00000 | 0.000641682i | \(-0.000204254\pi\) | |
−0.500556 | + | 0.865704i | \(0.666871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.9654 | − | 10.1192i | −0.591173 | − | 0.461396i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | + | 1.73205i | 0.0455016 | + | 0.0788110i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.21922 | + | 7.30791i | −0.191585 | + | 0.331835i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.6847 | + | 23.7025i | −0.620111 | + | 1.07406i | 0.369354 | + | 0.929289i | \(0.379579\pi\) |
−0.989465 | + | 0.144775i | \(0.953754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.1231 | −0.909998 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.24621 | + | 3.89055i | 0.101370 | + | 0.175578i | 0.912249 | − | 0.409635i | \(-0.134344\pi\) |
−0.810879 | + | 0.585213i | \(0.801011\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.36932 | 0.331897 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.56155 | 0.205027 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4924 | 0.738302 | 0.369151 | − | 0.929369i | \(-0.379648\pi\) | ||||
0.369151 | + | 0.929369i | \(0.379648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7192 | − | 18.5662i | 0.478900 | − | 0.829478i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.6847 | + | 28.8987i | −0.743932 | + | 1.28853i | 0.206760 | + | 0.978392i | \(0.433708\pi\) |
−0.950692 | + | 0.310137i | \(0.899625\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.12311 | − | 7.14143i | −0.183476 | − | 0.317789i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5000 | + | 3.57071i | 0.555144 | + | 0.158581i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.15767 | + | 15.8616i | 0.405907 | + | 0.703051i | 0.994427 | − | 0.105432i | \(-0.0336225\pi\) |
−0.588520 | + | 0.808483i | \(0.700289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.973012 | + | 1.68531i | −0.0430435 | + | 0.0745536i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.56155 | + | 4.43674i | −0.113095 | + | 0.195887i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.56155 | −0.156941 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.9654 | − | 25.9209i | −0.658179 | − | 1.14000i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.00000 | 0.175581 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7386 | −1.08382 | −0.541910 | − | 0.840437i | \(-0.682298\pi\) | ||||
−0.541910 | + | 0.840437i | \(0.682298\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2808 | − | 19.5389i | −0.493274 | − | 0.854375i | 0.506696 | − | 0.862125i | \(-0.330867\pi\) |
−0.999970 | + | 0.00774928i | \(0.997533\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.438447 | −0.0191354 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.12311 | − | 7.14143i | 0.179605 | − | 0.311086i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.09612 | − | 1.89853i | 0.0476573 | − | 0.0825449i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.84233 | + | 3.19101i | 0.0799503 | + | 0.138478i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.68466 | + | 4.43674i | 0.246230 | + | 0.192177i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.43845 | + | 2.49146i | 0.0621895 | + | 0.107715i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.40388 | − | 9.35980i | 0.233195 | − | 0.403905i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5270 | − | 26.8935i | 0.668795 | − | 1.15839i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.94602 | 0.255640 | 0.127820 | − | 0.991797i | \(-0.459202\pi\) | ||||
0.127820 | + | 0.991797i | \(0.459202\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.56155 | − | 2.70469i | −0.0670126 | − | 0.116069i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.8078 | 0.762801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6847 | 1.22647 | 0.613234 | − | 0.789902i | \(-0.289868\pi\) | ||||
0.613234 | + | 0.789902i | \(0.289868\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.34233 | − | 9.25319i | −0.228005 | − | 0.394916i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.8769 | 0.804183 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.165248 | − | 0.286218i | 0.00702707 | − | 0.0121712i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.28078 | − | 3.95042i | 0.0968136 | − | 0.167686i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.6847 | − | 30.6307i | −0.749323 | − | 1.29787i | −0.948148 | − | 0.317830i | \(-0.897046\pi\) |
0.198825 | − | 0.980035i | \(-0.436288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.06155 | − | 21.8639i | 0.129490 | − | 0.924743i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.56155 | − | 7.90084i | −0.192589 | − | 0.333574i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.80776 | + | 16.9875i | −0.413348 | + | 0.715940i | −0.995253 | − | 0.0973167i | \(-0.968974\pi\) |
0.581905 | + | 0.813256i | \(0.302307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.15767 | + | 5.46925i | −0.132844 | + | 0.230093i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.438447 | 0.0184131 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.5616 | − | 32.1496i | −0.778141 | − | 1.34778i | −0.933012 | − | 0.359845i | \(-0.882830\pi\) |
0.154871 | − | 0.987935i | \(-0.450504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.2311 | 1.64177 | 0.820884 | − | 0.571095i | \(-0.193481\pi\) | ||||
0.820884 | + | 0.571095i | \(0.193481\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0000 | −0.835512 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.28078 | − | 3.95042i | −0.0951150 | − | 0.164744i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.9848 | −1.62296 | −0.811480 | − | 0.584380i | \(-0.801338\pi\) | ||||
−0.811480 | + | 0.584380i | \(0.801338\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.02699 | + | 15.6352i | −0.375149 | + | 0.649777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.49242 | − | 4.31700i | 0.103403 | − | 0.179099i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.56155 | − | 4.43674i | −0.106089 | − | 0.183751i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | + | 3.57071i | −0.0206725 | + | 0.147631i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.31534 | + | 14.4026i | 0.343211 | + | 0.594459i | 0.985027 | − | 0.172400i | \(-0.0551521\pi\) |
−0.641816 | + | 0.766859i | \(0.721819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5616 | − | 18.2931i | 0.435181 | − | 0.753756i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.00000 | + | 6.92820i | −0.164538 | + | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.3002 | 1.77813 | 0.889063 | − | 0.457785i | \(-0.151357\pi\) | ||||
0.889063 | + | 0.457785i | \(0.151357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.438447 | + | 0.759413i | 0.0179746 | + | 0.0311329i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.5616 | −0.555037 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.36932 | 0.137667 | 0.0688333 | − | 0.997628i | \(-0.478072\pi\) | ||||
0.0688333 | + | 0.997628i | \(0.478072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0346 | + | 17.3804i | 0.409318 | + | 0.708960i | 0.994814 | − | 0.101716i | \(-0.0324332\pi\) |
−0.585495 | + | 0.810676i | \(0.699100\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.43845 | −0.0993012 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.90388 | + | 8.49377i | −0.199371 | + | 0.345321i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.6847 | − | 27.1666i | 0.636621 | − | 1.10266i | −0.349549 | − | 0.936918i | \(-0.613665\pi\) |
0.986169 | − | 0.165741i | \(-0.0530016\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.807764 | − | 1.39909i | −0.0327323 | − | 0.0566939i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.9309 | − | 8.87348i | 0.887228 | − | 0.358983i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.3078 | + | 35.1741i | 0.820223 | + | 1.42067i | 0.905516 | + | 0.424312i | \(0.139484\pi\) |
−0.0852933 | + | 0.996356i | \(0.527183\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.00000 | + | 1.73205i | −0.0403239 | + | 0.0698430i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.71922 | + | 13.3701i | −0.310764 | + | 0.538259i | −0.978528 | − | 0.206114i | \(-0.933918\pi\) |
0.667764 | + | 0.744373i | \(0.267252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.4233 | 1.34340 | 0.671698 | − | 0.740825i | \(-0.265565\pi\) | ||||
0.671698 | + | 0.740825i | \(0.265565\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.28078 | + | 3.95042i | 0.0915244 | + | 0.158525i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.876894 | 0.0351320 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.6847 | − | 20.2384i | −0.466640 | − | 0.808245i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.12311 | −0.363762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.21922 | + | 2.11176i | −0.0485365 | + | 0.0840677i | −0.889273 | − | 0.457377i | \(-0.848789\pi\) |
0.840736 | + | 0.541445i | \(0.182122\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.02699 | + | 12.1711i | −0.279298 | + | 0.483758i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.34233 | − | 2.32498i | −0.0532687 | − | 0.0922641i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.3499 | + | 15.1021i | 0.766671 | + | 0.598369i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0000 | + | 29.4449i | −0.671460 | + | 1.16300i | 0.306031 | + | 0.952022i | \(0.400999\pi\) |
−0.977490 | + | 0.210981i | \(0.932334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.41146 | + | 2.44472i | −0.0556625 | + | 0.0964103i | −0.892514 | − | 0.451020i | \(-0.851060\pi\) |
0.836851 | + | 0.547430i | \(0.184394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.12311 | 0.241097 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0540 | + | 31.2704i | 0.709775 | + | 1.22937i | 0.964940 | + | 0.262469i | \(0.0845367\pi\) |
−0.255165 | + | 0.966897i | \(0.582130\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.8078 | −0.659762 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.80776 | −0.0708519 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.87689 | + | 6.71498i | 0.151715 | + | 0.262777i | 0.931858 | − | 0.362823i | \(-0.118187\pi\) |
−0.780143 | + | 0.625601i | \(0.784854\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.56155 | −0.100088 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.21922 | + | 3.84381i | −0.0865802 | + | 0.149961i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0885 | − | 27.8662i | 0.626721 | − | 1.08551i | −0.361485 | − | 0.932378i | \(-0.617730\pi\) |
0.988205 | − | 0.153134i | \(-0.0489366\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.21922 | + | 9.03996i | 0.203004 | + | 0.351614i | 0.949495 | − | 0.313782i | \(-0.101596\pi\) |
−0.746491 | + | 0.665396i | \(0.768263\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.68466 | − | 2.70469i | 0.259611 | − | 0.105041i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.12311 | + | 1.94528i | 0.0435522 | + | 0.0754346i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.40388 | − | 14.5560i | 0.325400 | − | 0.563609i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.80776 | − | 15.2555i | 0.340528 | − | 0.589812i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.7386 | 1.88153 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3423 | − | 28.3057i | −0.629950 | − | 1.09111i | −0.987561 | − | 0.157235i | \(-0.949742\pi\) |
0.357611 | − | 0.933871i | \(-0.383592\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.2462 | 0.393794 | 0.196897 | − | 0.980424i | \(-0.436914\pi\) | ||||
0.196897 | + | 0.980424i | \(0.436914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.84991 | − | 3.20413i | −0.0709929 | − | 0.122963i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.3693 | −0.972154 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.1231 | + | 22.7299i | −0.502142 | + | 0.869735i | 0.497855 | + | 0.867260i | \(0.334121\pi\) |
−0.999997 | + | 0.00247477i | \(0.999212\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.28078 | − | 3.95042i | 0.0871440 | − | 0.150938i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.3693 | + | 17.9602i | 0.395614 | + | 0.685224i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.75379 | − | 1.51883i | 0.143008 | − | 0.0578626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.1501 | + | 19.3125i | 0.424170 | + | 0.734683i | 0.996342 | − | 0.0854498i | \(-0.0272327\pi\) |
−0.572173 | + | 0.820133i | \(0.693899\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | + | 1.73205i | −0.0379869 | + | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.90388 | − | 15.4220i | 0.337743 | − | 0.584989i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.5270 | − | 18.2333i | −0.398167 | − | 0.689646i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.6847 | −1.34779 | −0.673895 | − | 0.738827i | \(-0.735380\pi\) | ||||
−0.673895 | + | 0.738827i | \(0.735380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.3693 | −0.881390 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.28078 | + | 5.68247i | 0.123561 | + | 0.214014i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.61553 | 0.135976 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.9039 | − | 37.9386i | 0.822618 | − | 1.42482i | −0.0811090 | − | 0.996705i | \(-0.525846\pi\) |
0.903727 | − | 0.428110i | \(-0.140820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.376894 | − | 0.652800i | 0.0141346 | − | 0.0244819i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.40388 | − | 16.2880i | −0.352178 | − | 0.609990i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.9654 | − | 10.1192i | −0.484880 | − | 0.378437i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.00000 | + | 3.46410i | 0.0746914 | + | 0.129369i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.75379 | + | 16.8941i | −0.363755 | + | 0.630042i | −0.988576 | − | 0.150726i | \(-0.951839\pi\) |
0.624821 | + | 0.780768i | \(0.285172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.780776 | − | 1.35234i | 0.0290776 | − | 0.0503639i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0691303 | 0.00257098 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.84233 | + | 3.19101i | 0.0684224 | + | 0.118511i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6847 | −0.915503 | −0.457752 | − | 0.889080i | \(-0.651345\pi\) | ||||
−0.457752 | + | 0.889080i | \(0.651345\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.12311 | − | 10.6055i | −0.226471 | − | 0.392260i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.4233 | 0.643544 | 0.321772 | − | 0.946817i | \(-0.395722\pi\) | ||||
0.321772 | + | 0.946817i | \(0.395722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.40388 | + | 5.89570i | −0.125554 | + | 0.217466i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.56155 | − | 9.63289i | 0.204862 | − | 0.354832i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.2462 | + | 41.9957i | 0.891911 | + | 1.54484i | 0.837581 | + | 0.546313i | \(0.183969\pi\) |
0.0543300 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.1231 | − | 6.92820i | 0.629033 | − | 0.254514i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.4039 | + | 21.4842i | 0.455054 | + | 0.788177i | 0.998691 | − | 0.0511433i | \(-0.0162865\pi\) |
−0.543637 | + | 0.839320i | \(0.682953\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.96543 | − | 12.0645i | 0.255194 | − | 0.442009i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.68466 | − | 9.84612i | 0.207991 | − | 0.360251i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.26137 | −0.0460893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5270 | − | 19.9653i | −0.420626 | − | 0.728545i | 0.575375 | − | 0.817890i | \(-0.304856\pi\) |
−0.996001 | + | 0.0893445i | \(0.971523\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.5616 | −0.384884 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.4924 | − | 30.2978i | −0.635773 | − | 1.10119i | −0.986351 | − | 0.164657i | \(-0.947348\pi\) |
0.350578 | − | 0.936534i | \(-0.385985\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.8078 | −0.755274 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8769 | − | 18.8393i | 0.394287 | − | 0.682925i | −0.598723 | − | 0.800956i | \(-0.704325\pi\) |
0.993010 | + | 0.118031i | \(0.0376582\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.90388 | + | 6.76172i | −0.141330 | + | 0.244791i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.00000 | + | 1.73205i | 0.0361551 | + | 0.0626224i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.84233 | − | 13.1569i | 0.0665227 | − | 0.475067i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.596118 | + | 1.03251i | 0.0214966 | + | 0.0372331i | 0.876574 | − | 0.481268i | \(-0.159824\pi\) |
−0.855077 | + | 0.518501i | \(0.826490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.28078 | − | 14.3427i | 0.298225 | − | 0.516541i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.4384 | − | 31.9363i | 0.663185 | − | 1.14867i | −0.316589 | − | 0.948563i | \(-0.602538\pi\) |
0.979774 | − | 0.200107i | \(-0.0641290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.12311 | 0.148106 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.00000 | + | 1.73205i | 0.0358748 | + | 0.0621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.2462 | 0.367109 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.84233 | − | 3.19101i | −0.0658395 | − | 0.114037i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.2462 | 0.401394 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.8153 | + | 20.4648i | −0.421171 | + | 0.729490i | −0.996054 | − | 0.0887454i | \(-0.971714\pi\) |
0.574883 | + | 0.818236i | \(0.305048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.96543 | − | 3.40423i | 0.0699713 | − | 0.121194i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.38447 | − | 2.39798i | −0.0492262 | − | 0.0852622i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.34233 | + | 38.1519i | −0.189712 | + | 1.35481i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.561553 | + | 0.972638i | 0.0199162 | + | 0.0344959i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.3153 | + | 23.0628i | −0.471654 | + | 0.816928i | −0.999474 | − | 0.0324280i | \(-0.989676\pi\) |
0.527820 | + | 0.849356i | \(0.323009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.56155 | − | 11.3649i | 0.232131 | − | 0.402063i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.1231 | − | 17.5337i | −0.357237 | − | 0.618752i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.24621 | 0.290280 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.4384 | + | 37.1325i | 0.753736 | + | 1.30551i | 0.946000 | + | 0.324165i | \(0.105083\pi\) |
−0.192265 | + | 0.981343i | \(0.561583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1922 | −0.568586 | −0.284293 | − | 0.958737i | \(-0.591759\pi\) | ||||
−0.284293 | + | 0.958737i | \(0.591759\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.8693 | − | 22.2903i | 0.451347 | − | 0.781755i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0616 | + | 17.4271i | −0.352441 | + | 0.610445i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.6847 | − | 27.1666i | −0.548737 | − | 0.950440i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.24621 | − | 0.972638i | −0.0435461 | − | 0.0339867i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.84233 | − | 4.92306i | −0.0991980 | − | 0.171816i | 0.812155 | − | 0.583442i | \(-0.198294\pi\) |
−0.911353 | + | 0.411626i | \(0.864961\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.9309 | − | 20.6649i | 0.415884 | − | 0.720332i | −0.579637 | − | 0.814875i | \(-0.696806\pi\) |
0.995521 | + | 0.0945428i | \(0.0301389\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.28078 | − | 3.95042i | 0.0794064 | − | 0.137536i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 56.7386 | 1.97300 | 0.986498 | − | 0.163774i | \(-0.0523669\pi\) | ||||
0.986498 | + | 0.163774i | \(0.0523669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.6577 | − | 32.3160i | −0.648008 | − | 1.12238i | −0.983598 | − | 0.180374i | \(-0.942269\pi\) |
0.335590 | − | 0.942008i | \(-0.391064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.4384 | −0.396795 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.6155 | 0.471750 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.7192 | − | 18.5662i | −0.370954 | − | 0.642511i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.12311 | −0.142515 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1231 | − | 24.4619i | 0.487584 | − | 0.844520i | −0.512314 | − | 0.858798i | \(-0.671212\pi\) |
0.999898 | + | 0.0142782i | \(0.00454504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.71165 | − | 13.3570i | 0.265919 | − | 0.460585i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.9309 | − | 27.5931i | −0.548688 | − | 0.950356i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.34233 | − | 9.03996i | 0.321386 | − | 0.310984i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.15009 | − | 3.72407i | −0.0738781 | − | 0.127961i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.50000 | − | 2.59808i | 0.0514799 | − | 0.0891657i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.4039 | + | 18.0201i | −0.356640 | + | 0.617719i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.6155 | 1.73304 | 0.866521 | − | 0.499140i | \(-0.166351\pi\) | ||||
0.866521 | + | 0.499140i | \(0.166351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.56155 | + | 4.43674i | 0.0876033 | + | 0.151733i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 54.4233 | 1.85906 | 0.929532 | − | 0.368741i | \(-0.120211\pi\) | ||||
0.929532 | + | 0.368741i | \(0.120211\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.80776 | 0.0616801 | 0.0308401 | − | 0.999524i | \(-0.490182\pi\) | ||||
0.0308401 | + | 0.999524i | \(0.490182\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.438447 | − | 0.759413i | −0.0149422 | − | 0.0258807i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.3002 | 1.88244 | 0.941220 | − | 0.337794i | \(-0.109681\pi\) | ||||
0.941220 | + | 0.337794i | \(0.109681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | − | 3.46410i | 0.0680020 | − | 0.117783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.50000 | + | 11.2583i | −0.220752 | + | 0.382353i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.71922 | + | 2.97778i | 0.0583207 | + | 0.101014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.93087 | + | 5.40938i | 0.234844 | + | 0.183290i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.21922 | − | 7.30791i | −0.142799 | − | 0.247335i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.219224 | + | 0.379706i | −0.00741111 | + | 0.0128364i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.15767 | − | 12.3974i | 0.241697 | − | 0.418632i | −0.719501 | − | 0.694492i | \(-0.755629\pi\) |
0.961198 | + | 0.275860i | \(0.0889625\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.1231 | 0.442631 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.5616 | − | 42.5419i | −0.827500 | − | 1.43327i | −0.899994 | − | 0.435903i | \(-0.856429\pi\) |
0.0724940 | − | 0.997369i | \(-0.476904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8769 | 0.399689 | 0.199845 | − | 0.979828i | \(-0.435956\pi\) | ||||
0.199845 | + | 0.979828i | \(0.435956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.68466 | 0.123858 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8963 | + | 36.1935i | 0.701629 | + | 1.21526i | 0.967894 | + | 0.251358i | \(0.0808770\pi\) |
−0.266265 | + | 0.963900i | \(0.585790\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.17708 | 0.0394780 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.28078 | + | 3.95042i | −0.0764089 | + | 0.132344i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.8078 | − | 29.1119i | 0.562450 | − | 0.974193i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.40388 | − | 9.35980i | −0.180632 | − | 0.312864i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.28078 | − | 16.2880i | 0.0761529 | − | 0.543841i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.59612 | + | 13.1569i | 0.253345 | + | 0.438806i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12311 | − | 1.94528i | 0.0374161 | − | 0.0648065i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.34233 | + | 2.32498i | −0.0446699 | + | 0.0773706i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.12311 | −0.103816 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.7192 | − | 32.4226i | −0.621562 | − | 1.07658i | −0.989195 | − | 0.146606i | \(-0.953165\pi\) |
0.367633 | − | 0.929971i | \(-0.380168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.24621 | 0.273510 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.6155 | 1.24626 | 0.623129 | − | 0.782119i | \(-0.285861\pi\) | ||||
0.623129 | + | 0.782119i | \(0.285861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.9309 | + | 44.9136i | 0.858187 | + | 1.48642i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.6847 | −0.353224 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.561553 | − | 0.972638i | 0.0185441 | − | 0.0321193i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.4924 | + | 28.5657i | −0.544035 | + | 0.942296i | 0.454632 | + | 0.890679i | \(0.349771\pi\) |
−0.998667 | + | 0.0516167i | \(0.983563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.46543 | − | 12.9305i | −0.245994 | − | 0.426075i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.28078 | − | 3.95042i | −0.0749915 | − | 0.129889i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.78078 | − | 3.08440i | 0.0584884 | − | 0.101305i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.6155 | + | 27.0469i | −0.512329 | + | 0.887380i | 0.487569 | + | 0.873084i | \(0.337884\pi\) |
−0.999898 | + | 0.0142951i | \(0.995450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.8769 | 1.14304 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.68466 | − | 4.64996i | −0.0878918 | − | 0.152233i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.12311 | −0.298357 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.2462 | −0.792089 | −0.396045 | − | 0.918231i | \(-0.629617\pi\) | ||||
−0.396045 | + | 0.918231i | \(0.629617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.02699 | − | 12.1711i | −0.229317 | − | 0.397189i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.3542 | 1.83709 | 0.918547 | − | 0.395313i | \(-0.129364\pi\) | ||||
0.918547 | + | 0.395313i | \(0.129364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.56155 | − | 7.90084i | 0.148545 | − | 0.257287i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.219224 | − | 0.379706i | 0.00713134 | − | 0.0123519i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.3153 | − | 26.5269i | −0.497682 | − | 0.862010i | 0.502315 | − | 0.864685i | \(-0.332482\pi\) |
−0.999996 | + | 0.00267484i | \(0.999149\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.8348 | − | 6.00231i | 0.481556 | − | 0.194843i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.876894 | + | 1.51883i | 0.0284352 | + | 0.0492513i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.5961 | + | 18.3530i | −0.343242 | + | 0.594512i | −0.985033 | − | 0.172367i | \(-0.944858\pi\) |
0.641791 | + | 0.766880i | \(0.278192\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0000 | + | 17.3205i | −0.323592 | + | 0.560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.8078 | 0.543318 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.00000 | + | 1.73205i | 0.0322917 | + | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | −0.451613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.87689 | −0.0927066 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.02699 | + | 15.6352i | 0.290589 | + | 0.503315i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2462 | 0.329496 | 0.164748 | − | 0.986336i | \(-0.447319\pi\) | ||||
0.164748 | + | 0.986336i | \(0.447319\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.12311 | − | 8.87348i | 0.164578 | − | 0.285057i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.2462 | + | 31.6034i | −0.585549 | + | 1.01420i | 0.409258 | + | 0.912419i | \(0.365788\pi\) |
−0.994807 | + | 0.101782i | \(0.967546\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.90388 | + | 6.76172i | 0.125153 | + | 0.216771i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.84233 | + | 2.21837i | 0.0910274 | + | 0.0710447i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.650093 | + | 1.12599i | 0.0207983 | + | 0.0360238i | 0.876237 | − | 0.481880i | \(-0.160046\pi\) |
−0.855439 | + | 0.517904i | \(0.826713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.56155 | + | 7.90084i | −0.145788 | + | 0.252512i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.90388 | + | 15.4220i | −0.284279 | + | 0.492386i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.19224 | 0.0380264 | 0.0190132 | − | 0.999819i | \(-0.493948\pi\) | ||||
0.0190132 | + | 0.999819i | \(0.493948\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00000 | + | 6.92820i | 0.127451 | + | 0.220751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.87689 | −0.0915726 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.9309 | −0.888150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.8423 | − | 30.9038i | −0.566780 | − | 0.981692i | −0.996882 | − | 0.0789116i | \(-0.974856\pi\) |
0.430101 | − | 0.902781i | \(-0.358478\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.56155 | −0.303427 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.78078 | + | 11.7446i | −0.214965 | + | 0.372330i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.2732 | + | 31.6501i | −0.578718 | + | 1.00237i | 0.416909 | + | 0.908948i | \(0.363113\pi\) |
−0.995627 | + | 0.0934206i | \(0.970220\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.28078 | + | 3.95042i | 0.0721606 | + | 0.124986i |
(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 | 1560.2.bg.f.601.2 | ✓ | 4 | |
13.9 | even | 3 | inner | 1560.2.bg.f.841.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.bg.f.601.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1560.2.bg.f.841.2 | yes | 4 | 13.9 | even | 3 | inner |