Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(897,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.897");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.m (of order \(4\), 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: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2689.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.2689 |
Dual form | 3584.2.m.be.897.2 |
$q$-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 \(\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 1.73205 | + | 1.73205i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73205 | − | 2.73205i | 1.22181 | − | 1.22181i | 0.254822 | − | 0.966988i | \(-0.417983\pi\) |
0.966988 | − | 0.254822i | \(-0.0820170\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | + | 2.00000i | −0.603023 | + | 0.603023i | −0.941113 | − | 0.338091i | \(-0.890219\pi\) |
0.338091 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73205 | − | 4.73205i | −1.31243 | − | 1.31243i | −0.919616 | − | 0.392819i | \(-0.871500\pi\) |
−0.392819 | − | 0.919616i | \(-0.628500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.46410 | 2.44362 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205 | + | 1.73205i | 0.397360 | + | 0.397360i | 0.877301 | − | 0.479941i | \(-0.159342\pi\) |
−0.479941 | + | 0.877301i | \(0.659342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205 | − | 1.73205i | 0.377964 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 9.46410i | − | 1.97340i | −0.162547 | − | 0.986701i | \(-0.551971\pi\) | ||
0.162547 | − | 0.986701i | \(-0.448029\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 9.92820i | − | 1.98564i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.46410 | − | 2.46410i | −0.457572 | − | 0.457572i | 0.440286 | − | 0.897858i | \(-0.354877\pi\) |
−0.897858 | + | 0.440286i | \(0.854877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.46410 | −1.34059 | −0.670296 | − | 0.742094i | \(-0.733833\pi\) | ||||
−0.670296 | + | 0.742094i | \(0.733833\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.92820 | −1.20605 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.73205 | − | 2.73205i | −0.461801 | − | 0.461801i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.464102 | − | 0.464102i | 0.0762978 | − | 0.0762978i | −0.667928 | − | 0.744226i | \(-0.732819\pi\) |
0.744226 | + | 0.667928i | \(0.232819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 16.3923i | − | 2.62487i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.46410 | − | 7.46410i | 1.13826 | − | 1.13826i | 0.149504 | − | 0.988761i | \(-0.452232\pi\) |
0.988761 | − | 0.149504i | \(-0.0477676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.19615 | + | 8.19615i | 1.22181 | + | 1.22181i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4641 | 1.67221 | 0.836106 | − | 0.548569i | \(-0.184827\pi\) | ||||
0.836106 | + | 0.548569i | \(0.184827\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | − | 6.00000i | −0.840168 | − | 0.840168i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.9282i | 1.47356i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.26795 | − | 2.26795i | 0.295262 | − | 0.295262i | −0.543893 | − | 0.839155i | \(-0.683050\pi\) |
0.839155 | + | 0.543893i | \(0.183050\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.26795 | + | 5.26795i | 0.674492 | + | 0.674492i | 0.958748 | − | 0.284256i | \(-0.0917467\pi\) |
−0.284256 | + | 0.958748i | \(0.591747\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.00000 | 0.377964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −25.8564 | −3.20709 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.92820 | + | 2.92820i | 0.357737 | + | 0.357737i | 0.862978 | − | 0.505241i | \(-0.168596\pi\) |
−0.505241 | + | 0.862978i | \(0.668596\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.3923 | − | 16.3923i | 1.97340 | − | 1.97340i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000i | 0.474713i | 0.971423 | + | 0.237356i | \(0.0762809\pi\) | ||||
−0.971423 | + | 0.237356i | \(0.923719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.1962 | − | 17.1962i | 1.98564 | − | 1.98564i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | + | 2.00000i | 0.227921 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.26795 | + | 2.26795i | 0.248940 | + | 0.248940i | 0.820535 | − | 0.571596i | \(-0.193675\pi\) |
−0.571596 | + | 0.820535i | \(0.693675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.46410 | + | 9.46410i | −1.02653 | + | 1.02653i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.53590i | − | 0.915144i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.92820i | − | 0.946388i | −0.880958 | − | 0.473194i | \(-0.843101\pi\) | ||
0.880958 | − | 0.473194i | \(-0.156899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.73205 | + | 4.73205i | −0.496054 | + | 0.496054i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.9282 | − | 12.9282i | −1.34059 | − | 1.34059i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.46410 | 0.970996 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.39230 | −0.242902 | −0.121451 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121451 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | − | 6.00000i | −0.603023 | − | 0.603023i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.26795 | + | 1.26795i | −0.126166 | + | 0.126166i | −0.767370 | − | 0.641204i | \(-0.778435\pi\) |
0.641204 | + | 0.767370i | \(0.278435\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4641i | 1.52372i | 0.647740 | + | 0.761862i | \(0.275714\pi\) | ||||
−0.647740 | + | 0.761862i | \(0.724286\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 9.46410i | − | 0.923602i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.46410 | + | 1.46410i | −0.141540 | + | 0.141540i | −0.774326 | − | 0.632786i | \(-0.781911\pi\) |
0.632786 | + | 0.774326i | \(0.281911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.46410 | − | 8.46410i | −0.810714 | − | 0.810714i | 0.174027 | − | 0.984741i | \(-0.444322\pi\) |
−0.984741 | + | 0.174027i | \(0.944322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.60770 | 0.152596 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8564 | 1.30350 | 0.651751 | − | 0.758433i | \(-0.274035\pi\) | ||||
0.651751 | + | 0.758433i | \(0.274035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.8564 | − | 25.8564i | −2.41112 | − | 2.41112i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.1962 | − | 14.1962i | 1.31243 | − | 1.31243i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.46410i | 0.317554i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000i | 0.272727i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | + | 6.00000i | −0.541002 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.4641 | − | 13.4641i | −1.20427 | − | 1.20427i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.392305 | −0.0348114 | −0.0174057 | − | 0.999849i | \(-0.505541\pi\) | ||||
−0.0174057 | + | 0.999849i | \(0.505541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.8564 | 2.27653 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.26795 | − | 6.26795i | −0.547633 | − | 0.547633i | 0.378122 | − | 0.925756i | \(-0.376570\pi\) |
−0.925756 | + | 0.378122i | \(0.876570\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.73205 | − | 1.73205i | 0.150188 | − | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.07180i | − | 0.0915698i | −0.998951 | − | 0.0457849i | \(-0.985421\pi\) | ||
0.998951 | − | 0.0457849i | \(-0.0145789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.19615 | + | 1.19615i | −0.101456 | + | 0.101456i | −0.756013 | − | 0.654557i | \(-0.772855\pi\) |
0.654557 | + | 0.756013i | \(0.272855\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.8564 | + | 19.8564i | 1.67221 | + | 1.67221i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.9282 | 1.58286 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.4641 | −1.11813 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.73205 | − | 1.73205i | −0.142857 | − | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.92820 | + | 9.92820i | −0.813350 | + | 0.813350i | −0.985135 | − | 0.171784i | \(-0.945047\pi\) |
0.171784 | + | 0.985135i | \(0.445047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.39230i | − | 0.682956i | −0.939890 | − | 0.341478i | \(-0.889073\pi\) | ||
0.939890 | − | 0.341478i | \(-0.110927\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 10.3923i | − | 0.840168i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.3923 | + | 20.3923i | −1.63795 | + | 1.63795i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.73205 | − | 4.73205i | −0.377659 | − | 0.377659i | 0.492598 | − | 0.870257i | \(-0.336047\pi\) |
−0.870257 | + | 0.492598i | \(0.836047\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.46410 | 0.274721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.46410 | −0.745876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | − | 6.00000i | −0.469956 | − | 0.469956i | 0.431944 | − | 0.901900i | \(-0.357828\pi\) |
−0.901900 | + | 0.431944i | \(0.857828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.9282 | + | 18.9282i | −1.47356 | + | 1.47356i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.32051i | 0.721243i | 0.932712 | + | 0.360621i | \(0.117435\pi\) | ||||
−0.932712 | + | 0.360621i | \(0.882565\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.7846i | 2.44497i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.19615 | + | 5.19615i | −0.397360 | + | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.73205 | − | 4.73205i | −0.359771 | − | 0.359771i | 0.503957 | − | 0.863729i | \(-0.331877\pi\) |
−0.863729 | + | 0.503957i | \(0.831877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.92820 | −0.750502 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.85641 | 0.590524 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8564 | + | 13.8564i | 1.03568 | + | 1.03568i | 0.999340 | + | 0.0363368i | \(0.0115689\pi\) |
0.0363368 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.6603 | + | 11.6603i | −0.866700 | + | 0.866700i | −0.992106 | − | 0.125406i | \(-0.959977\pi\) |
0.125406 | + | 0.992106i | \(0.459977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.2487i | 1.34898i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.53590i | − | 0.186443i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.92820 | − | 6.92820i | 0.506640 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.92820 | 0.501307 | 0.250654 | − | 0.968077i | \(-0.419354\pi\) | ||||
0.250654 | + | 0.968077i | \(0.419354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −44.7846 | − | 44.7846i | −3.20709 | − | 3.20709i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8564 | + | 10.8564i | −0.773487 | + | 0.773487i | −0.978714 | − | 0.205227i | \(-0.934207\pi\) |
0.205227 | + | 0.978714i | \(0.434207\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3923i | 1.02024i | 0.860102 | + | 0.510122i | \(0.170400\pi\) | ||||
−0.860102 | + | 0.510122i | \(0.829600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.1436i | 0.715474i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.46410 | + | 2.46410i | −0.172946 | + | 0.172946i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.46410 | + | 9.46410i | 0.661002 | + | 0.661002i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 28.3923 | 1.97340 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.92820 | −0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.85641 | − | 9.85641i | −0.678543 | − | 0.678543i | 0.281127 | − | 0.959670i | \(-0.409292\pi\) |
−0.959670 | + | 0.281127i | \(0.909292\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.92820 | + | 6.92820i | −0.474713 | + | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 40.7846i | − | 2.78149i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.46410i | 0.506696i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3923 | − | 10.3923i | 0.702247 | − | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3923 | + | 16.3923i | 1.10267 | + | 1.10267i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9282 | 0.731807 | 0.365903 | − | 0.930653i | \(-0.380760\pi\) | ||||
0.365903 | + | 0.930653i | \(0.380760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 29.7846 | 1.98564 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.1962 | − | 13.1962i | −0.875859 | − | 0.875859i | 0.117244 | − | 0.993103i | \(-0.462594\pi\) |
−0.993103 | + | 0.117244i | \(0.962594\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7321 | − | 16.7321i | 1.10569 | − | 1.10569i | 0.111974 | − | 0.993711i | \(-0.464283\pi\) |
0.993711 | − | 0.111974i | \(-0.0357173\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.92820i | 0.455842i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.85641i | 0.514690i | 0.966320 | + | 0.257345i | \(0.0828477\pi\) | ||||
−0.966320 | + | 0.257345i | \(0.917152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.3205 | − | 31.3205i | 2.04312 | − | 2.04312i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.92820 | + | 6.92820i | 0.450035 | + | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.46410 | −0.612182 | −0.306091 | − | 0.952002i | \(-0.599021\pi\) | ||||
−0.306091 | + | 0.952002i | \(0.599021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3205 | 0.858049 | 0.429025 | − | 0.903293i | \(-0.358857\pi\) | ||||
0.429025 | + | 0.903293i | \(0.358857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | + | 15.5885i | 1.00000 | + | 1.00000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.73205 | + | 2.73205i | −0.174544 | + | 0.174544i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 16.3923i | − | 1.04302i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.85641i | 0.497880i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.73205 | + | 5.73205i | −0.361804 | + | 0.361804i | −0.864477 | − | 0.502673i | \(-0.832350\pi\) |
0.502673 | + | 0.864477i | \(0.332350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.9282 | + | 18.9282i | 1.19001 | + | 1.19001i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −32.7846 | −2.05305 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.9282 | 1.30547 | 0.652733 | − | 0.757588i | \(-0.273622\pi\) | ||||
0.652733 | + | 0.757588i | \(0.273622\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.464102 | − | 0.464102i | −0.0288379 | − | 0.0288379i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.39230 | − | 7.39230i | 0.457572 | − | 0.457572i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.7846i | − | 0.788333i | −0.919039 | − | 0.394166i | \(-0.871033\pi\) | ||
0.919039 | − | 0.394166i | \(-0.128967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.46410i | − | 0.335657i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.4641 | − | 15.4641i | 0.946388 | − | 0.946388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.1244 | − | 13.1244i | −0.800206 | − | 0.800206i | 0.182921 | − | 0.983128i | \(-0.441445\pi\) |
−0.983128 | + | 0.182921i | \(0.941445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.92820 | −0.177876 | −0.0889378 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889378 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.3923 | −0.992107 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.8564 | + | 19.8564i | 1.19739 | + | 1.19739i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00000 | − | 3.00000i | 0.180253 | − | 0.180253i | −0.611213 | − | 0.791466i | \(-0.709318\pi\) |
0.791466 | + | 0.611213i | \(0.209318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 22.3923i | − | 1.34059i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0000i | 0.596550i | 0.954480 | + | 0.298275i | \(0.0964112\pi\) | ||||
−0.954480 | + | 0.298275i | \(0.903589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.26795 | − | 6.26795i | 0.372591 | − | 0.372591i | −0.495829 | − | 0.868420i | \(-0.665136\pi\) |
0.868420 | + | 0.495829i | \(0.165136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.3923 | + | 16.3923i | 0.970996 | + | 0.970996i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.46410 | 0.204479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.14359 | − | 4.14359i | −0.242902 | − | 0.242902i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2679 | − | 17.2679i | 1.00880 | − | 1.00880i | 0.00884347 | − | 0.999961i | \(-0.497185\pi\) |
0.999961 | − | 0.00884347i | \(-0.00281500\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 12.3923i | − | 0.721508i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −44.7846 | + | 44.7846i | −2.58996 | + | 2.58996i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.46410 | − | 7.46410i | −0.430224 | − | 0.430224i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.39230 | −0.252331 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.7846 | 1.64820 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.73205 | − | 1.73205i | −0.0988534 | − | 0.0988534i | 0.655951 | − | 0.754804i | \(-0.272268\pi\) |
−0.754804 | + | 0.655951i | \(0.772268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.7846 | + | 26.7846i | −1.52372 | + | 1.52372i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.7128i | 1.57145i | 0.618576 | + | 0.785725i | \(0.287710\pi\) | ||||
−0.618576 | + | 0.785725i | \(0.712290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.2487i | 1.82280i | 0.411516 | + | 0.911402i | \(0.364999\pi\) | ||||
−0.411516 | + | 0.911402i | \(0.635001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.19615 | − | 8.19615i | 0.461801 | − | 0.461801i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.9282 | − | 11.9282i | −0.669955 | − | 0.669955i | 0.287751 | − | 0.957705i | \(-0.407093\pi\) |
−0.957705 | + | 0.287751i | \(0.907093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.85641 | 0.551853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.07180 | −0.283080 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | − | 6.00000i | −0.333849 | − | 0.333849i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −46.9808 | + | 46.9808i | −2.60602 | + | 2.60602i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 29.3205i | − | 1.62143i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 11.4641i | − | 0.632036i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.53590 | − | 8.53590i | 0.469175 | − | 0.469175i | −0.432472 | − | 0.901647i | \(-0.642359\pi\) |
0.901647 | + | 0.432472i | \(0.142359\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.39230 | + | 1.39230i | 0.0762978 | + | 0.0762978i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.0000 | 0.874173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.0000 | + | 24.0000i | 1.30350 | + | 1.30350i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.9282 | − | 14.9282i | 0.808408 | − | 0.808408i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 89.5692i | − | 4.82224i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.3923 | − | 22.3923i | 1.20208 | − | 1.20208i | 0.228550 | − | 0.973532i | \(-0.426602\pi\) |
0.973532 | − | 0.228550i | \(-0.0733983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.33975 | + | 4.33975i | 0.232301 | + | 0.232301i | 0.813653 | − | 0.581351i | \(-0.197476\pi\) |
−0.581351 | + | 0.813653i | \(0.697476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9282 | 0.688099 | 0.344049 | − | 0.938952i | \(-0.388201\pi\) | ||||
0.344049 | + | 0.938952i | \(0.388201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.9282 | + | 10.9282i | 0.580009 | + | 0.580009i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | + | 6.00000i | −0.317554 | + | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.4641i | 1.55506i | 0.628848 | + | 0.777528i | \(0.283527\pi\) | ||||
−0.628848 | + | 0.777528i | \(0.716473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.0000i | − | 0.684211i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.19615 | + | 5.19615i | −0.272727 | + | 0.272727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3923 | − | 16.3923i | −0.858012 | − | 0.858012i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0718 | 1.09994 | 0.549969 | − | 0.835185i | \(-0.314639\pi\) | ||||
0.549969 | + | 0.835185i | \(0.314639\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.3923 | −0.541002 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.00000 | − | 1.00000i | −0.0519174 | − | 0.0519174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.92820 | − | 9.92820i | 0.514063 | − | 0.514063i | −0.401706 | − | 0.915769i | \(-0.631583\pi\) |
0.915769 | + | 0.401706i | \(0.131583\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 46.6410i | − | 2.40853i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.3205i | 1.20107i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3923 | + | 10.3923i | −0.533817 | + | 0.533817i | −0.921706 | − | 0.387889i | \(-0.873204\pi\) |
0.387889 | + | 0.921706i | \(0.373204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.679492 | − | 0.679492i | −0.0348114 | − | 0.0348114i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.2487 | 0.830270 | 0.415135 | − | 0.909760i | \(-0.363734\pi\) | ||||
0.415135 | + | 0.909760i | \(0.363734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.9282 | 0.556953 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.3923 | + | 22.3923i | 1.13826 | + | 1.13826i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4641 | + | 18.4641i | −0.936167 | + | 0.936167i | −0.998081 | − | 0.0619144i | \(-0.980279\pi\) |
0.0619144 | + | 0.998081i | \(0.480279\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.7846i | 1.65799i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 21.7128i | − | 1.09527i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9282 | − | 10.9282i | 0.549858 | − | 0.549858i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.5167 | − | 25.5167i | −1.28064 | − | 1.28064i | −0.940301 | − | 0.340343i | \(-0.889457\pi\) |
−0.340343 | − | 0.940301i | \(-0.610543\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.00000 | 0.300376 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0718 | 0.552899 | 0.276450 | − | 0.961028i | \(-0.410842\pi\) | ||||
0.276450 | + | 0.961028i | \(0.410842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.3205 | + | 35.3205i | 1.75944 | + | 1.75944i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.5885 | − | 24.5885i | 1.22181 | − | 1.22181i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85641i | 0.0920187i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3205i | 1.64759i | 0.566886 | + | 0.823797i | \(0.308148\pi\) | ||||
−0.566886 | + | 0.823797i | \(0.691852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.85641 | − | 1.85641i | 0.0915698 | − | 0.0915698i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.26795 | − | 2.26795i | −0.111598 | − | 0.111598i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.3923 | 0.608314 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.14359 | −0.202913 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.8038 | + | 10.8038i | 0.527802 | + | 0.527802i | 0.919917 | − | 0.392114i | \(-0.128256\pi\) |
−0.392114 | + | 0.919917i | \(0.628256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0000 | − | 13.0000i | 0.633581 | − | 0.633581i | −0.315383 | − | 0.948964i | \(-0.602133\pi\) |
0.948964 | + | 0.315383i | \(0.102133\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.3923i | 1.67221i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.3923i | 1.66827i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.26795 | − | 5.26795i | 0.254934 | − | 0.254934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.7846 | + | 32.7846i | 1.58286 | + | 1.58286i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.2487 | 0.879009 | 0.439505 | − | 0.898240i | \(-0.355154\pi\) | ||||
0.439505 | + | 0.898240i | \(0.355154\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3923 | 0.691650 | 0.345825 | − | 0.938299i | \(-0.387599\pi\) | ||||
0.345825 | + | 0.938299i | \(0.387599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.3205 | − | 23.3205i | −1.11813 | − | 1.11813i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3923 | − | 16.3923i | 0.784150 | − | 0.784150i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 38.6410i | − | 1.84424i | −0.386910 | − | 0.922118i | \(-0.626458\pi\) | ||
0.386910 | − | 0.922118i | \(-0.373542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.00000i | − | 0.142857i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.07180 | + | 1.07180i | −0.0509226 | + | 0.0509226i | −0.732110 | − | 0.681187i | \(-0.761464\pi\) |
0.681187 | + | 0.732110i | \(0.261464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.3923 | − | 24.3923i | −1.15631 | − | 1.15631i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.3923 | −1.62670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.92820 | − | 6.92820i | −0.326236 | − | 0.326236i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.5359 | − | 14.5359i | 0.682956 | − | 0.682956i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.8564i | 1.21217i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.85641i | 0.180395i | 0.995924 | + | 0.0901975i | \(0.0287498\pi\) | ||||
−0.995924 | + | 0.0901975i | \(0.971250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.1962 | + | 18.1962i | 0.847479 | + | 0.847479i | 0.989818 | − | 0.142339i | \(-0.0454622\pi\) |
−0.142339 | + | 0.989818i | \(0.545462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8564 | 0.643962 | 0.321981 | − | 0.946746i | \(-0.395651\pi\) | ||||
0.321981 | + | 0.946746i | \(0.395651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −70.6410 | −3.27590 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.80385 | − | 6.80385i | −0.314845 | − | 0.314845i | 0.531938 | − | 0.846783i | \(-0.321464\pi\) |
−0.846783 | + | 0.531938i | \(0.821464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.92820 | − | 2.92820i | 0.135212 | − | 0.135212i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 16.3923i | − | 0.755318i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.8564i | 1.37280i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.1962 | − | 17.1962i | 0.789014 | − | 0.789014i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | + | 3.00000i | 0.137361 | + | 0.137361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.3923 | 1.38866 | 0.694330 | − | 0.719657i | \(-0.255701\pi\) | ||||
0.694330 | + | 0.719657i | \(0.255701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.39230 | −0.200272 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.3923 | − | 16.3923i | −0.745876 | − | 0.745876i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.53590 | + | 6.53590i | −0.296780 | + | 0.296780i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.2487i | − | 0.464413i | −0.972666 | − | 0.232207i | \(-0.925405\pi\) | ||
0.972666 | − | 0.232207i | \(-0.0745946\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 20.7846i | − | 0.939913i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.0718 | + | 13.0718i | −0.589922 | + | 0.589922i | −0.937610 | − | 0.347688i | \(-0.886967\pi\) |
0.347688 | + | 0.937610i | \(0.386967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.53590 | + | 8.53590i | 0.384438 | + | 0.384438i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32.7846 | −1.47356 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | 0.179425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.46410 | + | 5.46410i | 0.244607 | + | 0.244607i | 0.818753 | − | 0.574146i | \(-0.194666\pi\) |
−0.574146 | + | 0.818753i | \(0.694666\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.1436 | + | 16.1436i | −0.721243 | + | 0.721243i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.78461i | 0.391686i | 0.980635 | + | 0.195843i | \(0.0627444\pi\) | ||||
−0.980635 | + | 0.195843i | \(0.937256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.92820i | 0.308301i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −55.0526 | + | 55.0526i | −2.44497 | + | 2.44497i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.73205 | + | 8.73205i | 0.387041 | + | 0.387041i | 0.873631 | − | 0.486589i | \(-0.161759\pi\) |
−0.486589 | + | 0.873631i | \(0.661759\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.2487 | + | 42.2487i | 1.86170 | + | 1.86170i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.9282 | + | 22.9282i | −1.00838 | + | 1.00838i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 16.3923i | − | 0.719542i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.1769i | − | 1.54113i | −0.637362 | − | 0.770564i | \(-0.719975\pi\) | ||
0.637362 | − | 0.770564i | \(-0.280025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.7321 | − | 25.7321i | 1.12518 | − | 1.12518i | 0.134234 | − | 0.990950i | \(-0.457142\pi\) |
0.990950 | − | 0.134234i | \(-0.0428575\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.1962 | − | 17.1962i | −0.750502 | − | 0.750502i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.8564 | 1.12632 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −66.5692 | −2.89431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.80385 | + | 6.80385i | 0.295262 | + | 0.295262i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.3923 | − | 16.3923i | 0.710030 | − | 0.710030i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000i | 0.345870i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 48.0000i | 2.07135i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | − | 2.00000i | 0.0861461 | − | 0.0861461i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.856406 | + | 0.856406i | 0.0368198 | + | 0.0368198i | 0.725277 | − | 0.688457i | \(-0.241712\pi\) |
−0.688457 | + | 0.725277i | \(0.741712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.3923 | −1.73340 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −46.2487 | −1.98108 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8564 | + | 19.8564i | 0.848999 | + | 0.848999i | 0.990008 | − | 0.141010i | \(-0.0450348\pi\) |
−0.141010 | + | 0.990008i | \(0.545035\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.8038 | + | 15.8038i | −0.674492 | + | 0.674492i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.53590i | − | 0.363641i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.00000i | − | 0.170097i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.39230 | − | 4.39230i | 0.186443 | − | 0.186443i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.7128 | − | 26.7128i | −1.13186 | − | 1.13186i | −0.989868 | − | 0.141990i | \(-0.954650\pi\) |
−0.141990 | − | 0.989868i | \(-0.545350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −70.6410 | −2.98780 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.5885 | − | 11.5885i | −0.488395 | − | 0.488395i | 0.419404 | − | 0.907800i | \(-0.362239\pi\) |
−0.907800 | + | 0.419404i | \(0.862239\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.8564 | − | 37.8564i | 1.59263 | − | 1.59263i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 9.00000i | − | 0.377964i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.7846i | 0.619803i | 0.950769 | + | 0.309902i | \(0.100296\pi\) | ||||
−0.950769 | + | 0.309902i | \(0.899704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4641 | + | 19.4641i | −0.814547 | + | 0.814547i | −0.985312 | − | 0.170765i | \(-0.945376\pi\) |
0.170765 | + | 0.985312i | \(0.445376\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | + | 12.0000i | 0.501307 | + | 0.501307i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −93.9615 | −3.91847 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.7846 | −0.948536 | −0.474268 | − | 0.880381i | \(-0.657287\pi\) | ||||
−0.474268 | + | 0.880381i | \(0.657287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.3205 | − | 17.3205i | −0.719816 | − | 0.719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.26795 | − | 2.26795i | 0.0940904 | − | 0.0940904i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 77.5692i | − | 3.20709i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.5167 | + | 26.5167i | −1.09446 | + | 1.09446i | −0.0994135 | + | 0.995046i | \(0.531697\pi\) |
−0.995046 | + | 0.0994135i | \(0.968303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.9282 | − | 12.9282i | −0.532697 | − | 0.532697i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.6077 | −1.54697 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.6410 | −1.17615 | −0.588073 | − | 0.808808i | \(-0.700113\pi\) | ||||
−0.588073 | + | 0.808808i | \(0.700113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.46410 | + | 9.46410i | 0.387990 | + | 0.387990i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.9282 | + | 24.9282i | −1.02024 | + | 1.02024i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.7846i | 0.685801i | 0.939372 | + | 0.342900i | \(0.111409\pi\) | ||||
−0.939372 | + | 0.342900i | \(0.888591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.6410i | − | 1.49462i | −0.664477 | − | 0.747309i | \(-0.731345\pi\) | ||
0.664477 | − | 0.747309i | \(-0.268655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.78461 | + | 8.78461i | −0.357737 | + | 0.357737i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.19615 | + | 8.19615i | 0.333221 | + | 0.333221i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.8564 | 0.887124 | 0.443562 | − | 0.896244i | \(-0.353715\pi\) | ||||
0.443562 | + | 0.896244i | \(0.353715\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.53590 | −0.345892 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54.2487 | − | 54.2487i | −2.19467 | − | 2.19467i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4641 | − | 12.4641i | 0.503420 | − | 0.503420i | −0.409079 | − | 0.912499i | \(-0.634150\pi\) |
0.912499 | + | 0.409079i | \(0.134150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.7846i | 1.32200i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.85641i | 0.396804i | 0.980121 | + | 0.198402i | \(0.0635752\pi\) | ||||
−0.980121 | + | 0.198402i | \(0.936425\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.0526 | − | 27.0526i | 1.08733 | − | 1.08733i | 0.0915320 | − | 0.995802i | \(-0.470824\pi\) |
0.995802 | − | 0.0915320i | \(-0.0291764\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.92820 | −0.357701 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9282 | −0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.0000 | − | 12.0000i | −0.479234 | − | 0.479234i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.60770 | + | 1.60770i | −0.0641030 | + | 0.0641030i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.7128i | 1.26247i | 0.775593 | + | 0.631234i | \(0.217451\pi\) | ||||
−0.775593 | + | 0.631234i | \(0.782549\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 34.1436i | − | 1.35709i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.07180 | + | 1.07180i | −0.0425330 | + | 0.0425330i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.73205 | + | 4.73205i | 0.187491 | + | 0.187491i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.92820 | 0.352643 | 0.176321 | − | 0.984333i | \(-0.443580\pi\) | ||||
0.176321 | + | 0.984333i | \(0.443580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.8038 | + | 10.8038i | 0.426062 | + | 0.426062i | 0.887285 | − | 0.461222i | \(-0.152589\pi\) |
−0.461222 | + | 0.887285i | \(0.652589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 70.6410 | − | 70.6410i | 2.78149 | − | 2.78149i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 45.3205i | − | 1.78173i | −0.454265 | − | 0.890867i | \(-0.650098\pi\) | ||
0.454265 | − | 0.890867i | \(-0.349902\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.07180i | 0.356099i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.9282 | + | 12.9282i | −0.506696 | + | 0.506696i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.3205 | − | 28.3205i | −1.10827 | − | 1.10827i | −0.993378 | − | 0.114889i | \(-0.963349\pi\) |
−0.114889 | − | 0.993378i | \(-0.536651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.2487 | −1.33821 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.0000 | 0.702247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.7846 | − | 18.7846i | −0.731745 | − | 0.731745i | 0.239221 | − | 0.970965i | \(-0.423108\pi\) |
−0.970965 | + | 0.239221i | \(0.923108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0526 | − | 18.0526i | 0.702163 | − | 0.702163i | −0.262711 | − | 0.964874i | \(-0.584617\pi\) |
0.964874 | + | 0.262711i | \(0.0846167\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.7846i | 2.20533i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.46410i | − | 0.367002i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.3205 | + | 23.3205i | −0.902974 | + | 0.902974i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.9282 | + | 18.9282i | 0.731807 | + | 0.731807i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0718 | −0.813468 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.07180 | 0.349692 | 0.174846 | − | 0.984596i | \(-0.444057\pi\) | ||||
0.174846 | + | 0.984596i | \(0.444057\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.0526 | + | 12.0526i | −0.463217 | + | 0.463217i | −0.899709 | − | 0.436491i | \(-0.856221\pi\) |
0.436491 | + | 0.899709i | \(0.356221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.39230i | 0.0918082i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 45.7128i | − | 1.75172i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.53590 | + | 6.53590i | −0.250089 | + | 0.250089i | −0.821007 | − | 0.570918i | \(-0.806587\pi\) |
0.570918 | + | 0.821007i | \(0.306587\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.92820 | − | 2.92820i | −0.111881 | − | 0.111881i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 57.9615 | 2.21137 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.46410 | −0.360554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1244 | + | 36.1244i | 1.37424 | + | 1.37424i | 0.854059 | + | 0.520176i | \(0.174134\pi\) |
0.520176 | + | 0.854059i | \(0.325866\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.00000 | + | 6.00000i | −0.227921 | + | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.53590i | 0.247921i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.6077 | + | 13.6077i | −0.514690 | + | 0.514690i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.53590 | + | 3.53590i | 0.133549 | + | 0.133549i | 0.770721 | − | 0.637172i | \(-0.219896\pi\) |
−0.637172 | + | 0.770721i | \(0.719896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.60770 | 0.0606354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 108.497 | 4.08625 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.26795 | + | 1.26795i | 0.0476861 | + | 0.0476861i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.4641 | − | 16.4641i | 0.618322 | − | 0.618322i | −0.326779 | − | 0.945101i | \(-0.605963\pi\) |
0.945101 | + | 0.326779i | \(0.105963\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000i | 0.450035i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 70.6410i | 2.64553i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 51.7128 | − | 51.7128i | 1.93395 | − | 1.93395i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.3923 | − | 16.3923i | −0.612182 | − | 0.612182i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.4641 | −0.427539 | −0.213769 | − | 0.976884i | \(-0.568574\pi\) | ||||
−0.213769 | + | 0.976884i | \(0.568574\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4641 | 0.575913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.0718 | + | 23.0718i | 0.858049 | + | 0.858049i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.4641 | + | 24.4641i | −0.908574 | + | 0.908574i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.4641i | 1.61199i | 0.591919 | + | 0.805997i | \(0.298370\pi\) | ||||
−0.591919 | + | 0.805997i | \(0.701630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8564 | + | 25.8564i | −0.956334 | + | 0.956334i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.1962 | − | 16.1962i | −0.598219 | − | 0.598219i | 0.341620 | − | 0.939838i | \(-0.389025\pi\) |
−0.939838 | + | 0.341620i | \(0.889025\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.46410 | −0.349089 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.7128 | −0.431447 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9282 | + | 16.9282i | 0.622714 | + | 0.622714i | 0.946225 | − | 0.323511i | \(-0.104863\pi\) |
−0.323511 | + | 0.946225i | \(0.604863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.3923 | − | 28.3923i | 1.04302 | − | 1.04302i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.67949i | 0.171674i | 0.996309 | + | 0.0858370i | \(0.0273564\pi\) | ||||
−0.996309 | + | 0.0858370i | \(0.972644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.2487i | 1.98752i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.80385 | + | 6.80385i | −0.248940 | + | 0.248940i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.46410 | + | 1.46410i | 0.0534971 | + | 0.0534971i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.3923 | 0.452202 | 0.226101 | − | 0.974104i | \(-0.427402\pi\) | ||||
0.226101 | + | 0.974104i | \(0.427402\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.8564 | −0.723608 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.9282 | − | 22.9282i | −0.834443 | − | 0.834443i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.3205 | − | 34.3205i | 1.24740 | − | 1.24740i | 0.290536 | − | 0.956864i | \(-0.406166\pi\) |
0.956864 | − | 0.290536i | \(-0.0938336\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 65.5692i | 2.38001i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.1769i | − | 0.695163i | −0.937650 | − | 0.347581i | \(-0.887003\pi\) | ||
0.937650 | − | 0.347581i | \(-0.112997\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.46410 | + | 8.46410i | −0.306421 | + | 0.306421i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −28.3923 | − | 28.3923i | −1.02653 | − | 1.02653i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.4641 | −0.775024 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.535898 | −0.0193250 | −0.00966250 | − | 0.999953i | \(-0.503076\pi\) | ||||
−0.00966250 | + | 0.999953i | \(0.503076\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.2487 | + | 36.2487i | 1.30547 | + | 1.30547i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.0526 | − | 10.0526i | 0.361565 | − | 0.361565i | −0.502824 | − | 0.864389i | \(-0.667705\pi\) |
0.864389 | + | 0.502824i | \(0.167705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 74.1051i | 2.66193i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.60770i | − | 0.0576757i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | + | 6.00000i | −0.214972 | + | 0.214972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | − | 8.00000i | −0.286263 | − | 0.286263i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.8564 | −0.922855 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.58846 | − | 7.58846i | −0.270499 | − | 0.270499i | 0.558802 | − | 0.829301i | \(-0.311261\pi\) |
−0.829301 | + | 0.558802i | \(0.811261\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.1436 | − | 22.1436i | 0.788333 | − | 0.788333i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 13.8564i | − | 0.492677i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 49.8564i | − | 1.77045i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.46410 | − | 9.46410i | 0.335657 | − | 0.335657i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.2679 | + | 15.2679i | 0.540819 | + | 0.540819i | 0.923769 | − | 0.382950i | \(-0.125092\pi\) |
−0.382950 | + | 0.923769i | \(0.625092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.7128 | −1.40494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.7846 | 0.946388 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.0000 | + | 12.0000i | 0.423471 | + | 0.423471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.8564 | + | 25.8564i | −0.911319 | + | 0.911319i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 45.4641i | − | 1.60041i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 30.0000i | − | 1.05474i | −0.849635 | − | 0.527372i | \(-0.823177\pi\) | ||
0.849635 | − | 0.527372i | \(-0.176823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.5885 | + | 23.5885i | −0.828303 | + | 0.828303i | −0.987282 | − | 0.158979i | \(-0.949180\pi\) |
0.158979 | + | 0.987282i | \(0.449180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.07180 | − | 5.07180i | −0.177876 | − | 0.177876i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.7846 | −1.14839 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.8564 | 0.904601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.1962 | − | 14.1962i | −0.496054 | − | 0.496054i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.7846 | + | 37.7846i | −1.31869 | + | 1.31869i | −0.403880 | + | 0.914812i | \(0.632339\pi\) |
−0.914812 | + | 0.403880i | \(0.867661\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.6410i | − | 0.789216i | −0.918850 | − | 0.394608i | \(-0.870880\pi\) | ||
0.918850 | − | 0.394608i | \(-0.129120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 68.7846i | 2.39477i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.46410 | − | 5.46410i | 0.190005 | − | 0.190005i | −0.605693 | − | 0.795698i | \(-0.707104\pi\) |
0.795698 | + | 0.605693i | \(0.207104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.66025 | − | 5.66025i | −0.196589 | − | 0.196589i | 0.601947 | − | 0.798536i | \(-0.294392\pi\) |
−0.798536 | + | 0.601947i | \(0.794392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.3923 | 0.360505 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.4641 | + | 25.4641i | 0.881222 | + | 0.881222i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 22.3923i | − | 0.773068i | −0.922275 | − | 0.386534i | \(-0.873672\pi\) | ||
0.922275 | − | 0.386534i | \(-0.126328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 16.8564i | − | 0.581255i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.3205 | + | 17.3205i | −0.596550 | + | 0.596550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 86.8372 | + | 86.8372i | 2.98729 | + | 2.98729i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | 0.103081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.7128 | 0.745182 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.39230 | − | 4.39230i | −0.150566 | − | 0.150566i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5885 | + | 10.5885i | −0.362542 | + | 0.362542i | −0.864748 | − | 0.502206i | \(-0.832522\pi\) |
0.502206 | + | 0.864748i | \(0.332522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.3923i | 0.970996i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 47.4641i | − | 1.62134i | −0.585501 | − | 0.810671i | \(-0.699102\pi\) | ||
0.585501 | − | 0.810671i | \(-0.300898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.8038 | − | 22.8038i | 0.778057 | − | 0.778057i | −0.201443 | − | 0.979500i | \(-0.564563\pi\) |
0.979500 | + | 0.201443i | \(0.0645631\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | + | 6.00000i | 0.204479 | + | 0.204479i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.8564 | −1.15249 | −0.576243 | − | 0.817279i | \(-0.695482\pi\) | ||||
−0.576243 | + | 0.817279i | \(0.695482\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.8564 | −0.879144 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.66025 | − | 8.66025i | −0.294118 | − | 0.294118i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00000 | + | 8.00000i | −0.271381 | + | 0.271381i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 27.7128i | − | 0.939013i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7.17691i | − | 0.242902i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.4641 | + | 13.4641i | −0.455170 | + | 0.455170i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.39230 | − | 7.39230i | −0.249620 | − | 0.249620i | 0.571194 | − | 0.820815i | \(-0.306480\pi\) |
−0.820815 | + | 0.571194i | \(0.806480\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 59.8179 | 2.01761 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.07180 | −0.103491 | −0.0517457 | − | 0.998660i | \(-0.516479\pi\) | ||||
−0.0517457 | + | 0.998660i | \(0.516479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.60770 | + | 7.60770i | 0.256019 | + | 0.256019i | 0.823433 | − | 0.567414i | \(-0.192056\pi\) |
−0.567414 | + | 0.823433i | \(0.692056\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.4641 | − | 21.4641i | 0.721508 | − | 0.721508i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.6077i | 0.456902i | 0.973555 | + | 0.228451i | \(0.0733660\pi\) | ||||
−0.973555 | + | 0.228451i | \(0.926634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.392305i | 0.0131575i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | + | 18.0000i | −0.603023 | + | 0.603023i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.8564 | + | 19.8564i | 0.664469 | + | 0.664469i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 75.7128 | 2.53080 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −155.138 | −5.17992 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.3923 | + | 18.3923i | 0.613418 | + | 0.613418i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.46410 | + | 3.46410i | −0.115406 | + | 0.115406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 25.8564i | − | 0.860447i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 63.7128i | 2.11789i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.80385 | − | 3.80385i | −0.126166 | − | 0.126166i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.2487 | 1.53229 | 0.766144 | − | 0.642669i | \(-0.222173\pi\) | ||||
0.766144 | + | 0.642669i | \(0.222173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.07180 | −0.300233 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 49.8564 | + | 49.8564i | 1.64820 | + | 1.64820i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.26795 | + | 6.26795i | −0.206986 | + | 0.206986i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.8564i | 1.24877i | 0.781118 | + | 0.624384i | \(0.214650\pi\) | ||||
−0.781118 | + | 0.624384i | \(0.785350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.00000i | − | 0.197707i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.9282 | − | 18.9282i | 0.623029 | − | 0.623029i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.60770 | − | 4.60770i | −0.151500 | − | 0.151500i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −46.3923 | −1.52372 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.46410 | −0.244889 | −0.122445 | − | 0.992475i | \(-0.539073\pi\) | ||||
−0.122445 | + | 0.992475i | \(0.539073\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.73205 | − | 1.73205i | −0.0567657 | − | 0.0567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.0000 | + | 48.0000i | −1.57145 | + | 1.57145i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 37.8564i | − | 1.23804i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6410i | 1.06634i | 0.846010 | + | 0.533168i | \(0.178999\pi\) | ||||
−0.846010 | + | 0.533168i | \(0.821001\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −55.8564 | + | 55.8564i | −1.82280 | + | 1.82280i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.19615 | + | 4.19615i | 0.136791 | + | 0.136791i | 0.772187 | − | 0.635396i | \(-0.219163\pi\) |
−0.635396 | + | 0.772187i | \(0.719163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.7846 | 1.06761 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.78461 | + | 6.78461i | 0.220470 | + | 0.220470i | 0.808696 | − | 0.588226i | \(-0.200174\pi\) |
−0.588226 | + | 0.808696i | \(0.700174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.3923 | + | 28.3923i | −0.921653 | + | 0.921653i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 41.3205i | − | 1.33991i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.1436i | 0.846874i | 0.905926 | + | 0.423437i | \(0.139177\pi\) | ||||
−0.905926 | + | 0.423437i | \(0.860823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.9282 | − | 18.9282i | 0.612502 | − | 0.612502i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.0718 | + | 17.0718i | 0.551853 | + | 0.551853i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.07180 | −0.0346101 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.7128 | 0.797188 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.39230 | − | 4.39230i | −0.141540 | − | 0.141540i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.3205 | + | 27.3205i | −0.879478 | + | 0.879478i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.5359i | 1.49649i | 0.663420 | + | 0.748247i | \(0.269104\pi\) | ||||
−0.663420 | + | 0.748247i | \(0.730896\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 20.7846i | − | 0.667698i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.7321 | − | 21.7321i | 0.697415 | − | 0.697415i | −0.266437 | − | 0.963852i | \(-0.585847\pi\) |
0.963852 | + | 0.266437i | \(0.0858466\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.19615 | + | 1.19615i | 0.0383469 | + | 0.0383469i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −162.746 | −5.21205 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.07180 | −0.290232 | −0.145116 | − | 0.989415i | \(-0.546356\pi\) | ||||
−0.145116 | + | 0.989415i | \(0.546356\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.8564 | + | 17.8564i | 0.570693 | + | 0.570693i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.3923 | − | 25.3923i | 0.810714 | − | 0.810714i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 29.3205i | − | 0.935179i | −0.883946 | − | 0.467589i | \(-0.845123\pi\) | ||
0.883946 | − | 0.467589i | \(-0.154877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.3205i | 1.89011i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.8564 | − | 19.8564i | 0.632036 | − | 0.632036i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −70.6410 | − | 70.6410i | −2.24625 | − | 2.24625i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.7128 | −0.372070 | −0.186035 | − | 0.982543i | \(-0.559564\pi\) | ||||
−0.186035 | + | 0.982543i | \(0.559564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.5692 | 0.938351 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.3205 | + | 39.3205i | 1.24654 | + | 1.24654i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.6603 | + | 25.6603i | −0.812668 | + | 0.812668i | −0.985033 | − | 0.172365i | \(-0.944859\pi\) |
0.172365 | + | 0.985033i | \(0.444859\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3584.2.m.be.2689.2 | yes | 4 | |
4.3 | odd | 2 | 3584.2.m.bf.2689.1 | yes | 4 | ||
8.3 | odd | 2 | 3584.2.m.bc.2689.2 | yes | 4 | ||
8.5 | even | 2 | 3584.2.m.bd.2689.1 | yes | 4 | ||
16.3 | odd | 4 | 3584.2.m.bc.897.2 | ✓ | 4 | ||
16.5 | even | 4 | inner | 3584.2.m.be.897.2 | yes | 4 | |
16.11 | odd | 4 | 3584.2.m.bf.897.1 | yes | 4 | ||
16.13 | even | 4 | 3584.2.m.bd.897.1 | yes | 4 | ||
32.5 | even | 8 | 7168.2.a.v.1.2 | 4 | |||
32.11 | odd | 8 | 7168.2.a.u.1.1 | 4 | |||
32.21 | even | 8 | 7168.2.a.v.1.3 | 4 | |||
32.27 | odd | 8 | 7168.2.a.u.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.m.bc.897.2 | ✓ | 4 | 16.3 | odd | 4 | ||
3584.2.m.bc.2689.2 | yes | 4 | 8.3 | odd | 2 | ||
3584.2.m.bd.897.1 | yes | 4 | 16.13 | even | 4 | ||
3584.2.m.bd.2689.1 | yes | 4 | 8.5 | even | 2 | ||
3584.2.m.be.897.2 | yes | 4 | 16.5 | even | 4 | inner | |
3584.2.m.be.2689.2 | yes | 4 | 1.1 | even | 1 | trivial | |
3584.2.m.bf.897.1 | yes | 4 | 16.11 | odd | 4 | ||
3584.2.m.bf.2689.1 | yes | 4 | 4.3 | odd | 2 | ||
7168.2.a.u.1.1 | 4 | 32.11 | odd | 8 | |||
7168.2.a.u.1.4 | 4 | 32.27 | odd | 8 | |||
7168.2.a.v.1.2 | 4 | 32.5 | even | 8 | |||
7168.2.a.v.1.3 | 4 | 32.21 | even | 8 |