Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(1701,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.1701");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 48 x^{18} + 878 x^{16} + 8102 x^{14} + 41081 x^{12} + 115688 x^{10} + 175041 x^{8} + 134990 x^{6} + 49782 x^{4} + 6932 x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1701.14 | ||
Root | \(-0.0120170i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.1701 |
Dual form | 1850.2.d.i.1701.4 |
$q$-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 \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.987983 | −0.570412 | −0.285206 | − | 0.958466i | \(-0.592062\pi\) | ||||
−0.285206 | + | 0.958466i | \(0.592062\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 0.987983i | − | 0.403342i | ||||||
\(7\) | −4.78937 | −1.81021 | −0.905106 | − | 0.425186i | \(-0.860209\pi\) | ||||
−0.905106 | + | 0.425186i | \(0.860209\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.02389 | −0.674630 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.98732 | −1.80525 | −0.902623 | − | 0.430432i | \(-0.858361\pi\) | ||||
−0.902623 | + | 0.430432i | \(0.858361\pi\) | |||||||
\(12\) | 0.987983 | 0.285206 | ||||||||
\(13\) | − | 3.49410i | − | 0.969088i | −0.874767 | − | 0.484544i | \(-0.838985\pi\) | ||
0.874767 | − | 0.484544i | \(-0.161015\pi\) | |||||||
\(14\) | − | 4.78937i | − | 1.28001i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.96343i | − | 1.20381i | −0.798568 | − | 0.601905i | \(-0.794409\pi\) | ||
0.798568 | − | 0.601905i | \(-0.205591\pi\) | |||||||
\(18\) | − | 2.02389i | − | 0.477035i | ||||||
\(19\) | 7.33092i | 1.68183i | 0.541168 | + | 0.840915i | \(0.317982\pi\) | ||||
−0.541168 | + | 0.840915i | \(0.682018\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.73182 | 1.03257 | ||||||||
\(22\) | − | 5.98732i | − | 1.27650i | ||||||
\(23\) | − | 1.74873i | − | 0.364635i | −0.983240 | − | 0.182318i | \(-0.941640\pi\) | ||
0.983240 | − | 0.182318i | \(-0.0583599\pi\) | |||||||
\(24\) | 0.987983i | 0.201671i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.49410 | 0.685249 | ||||||||
\(27\) | 4.96352 | 0.955229 | ||||||||
\(28\) | 4.78937 | 0.905106 | ||||||||
\(29\) | 7.85004i | 1.45772i | 0.684665 | + | 0.728858i | \(0.259949\pi\) | ||||
−0.684665 | + | 0.728858i | \(0.740051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.24097i | − | 0.582096i | −0.956708 | − | 0.291048i | \(-0.905996\pi\) | ||
0.956708 | − | 0.291048i | \(-0.0940039\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 5.91537 | 1.02973 | ||||||||
\(34\) | 4.96343 | 0.851222 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.02389 | 0.337315 | ||||||||
\(37\) | 4.61424 | + | 3.96343i | 0.758576 | + | 0.651584i | ||||
\(38\) | −7.33092 | −1.18923 | ||||||||
\(39\) | 3.45211i | 0.552780i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.530665 | −0.0828760 | −0.0414380 | − | 0.999141i | \(-0.513194\pi\) | ||||
−0.0414380 | + | 0.999141i | \(0.513194\pi\) | |||||||
\(42\) | 4.73182i | 0.730135i | ||||||||
\(43\) | 1.76838i | 0.269676i | 0.990868 | + | 0.134838i | \(0.0430514\pi\) | ||||
−0.990868 | + | 0.134838i | \(0.956949\pi\) | |||||||
\(44\) | 5.98732 | 0.902623 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.74873 | 0.257836 | ||||||||
\(47\) | −4.30638 | −0.628150 | −0.314075 | − | 0.949398i | \(-0.601694\pi\) | ||||
−0.314075 | + | 0.949398i | \(0.601694\pi\) | |||||||
\(48\) | −0.987983 | −0.142603 | ||||||||
\(49\) | 15.9381 | 2.27687 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.90379i | 0.686668i | ||||||||
\(52\) | 3.49410i | 0.484544i | ||||||||
\(53\) | 3.66238 | 0.503067 | 0.251534 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251534 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(54\) | 4.96352i | 0.675449i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.78937i | 0.640007i | ||||||||
\(57\) | − | 7.24283i | − | 0.959336i | ||||||
\(58\) | −7.85004 | −1.03076 | ||||||||
\(59\) | − | 2.15110i | − | 0.280049i | −0.990148 | − | 0.140025i | \(-0.955282\pi\) | ||
0.990148 | − | 0.140025i | \(-0.0447182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.06584i | 0.392541i | 0.980550 | + | 0.196270i | \(0.0628830\pi\) | ||||
−0.980550 | + | 0.196270i | \(0.937117\pi\) | |||||||
\(62\) | 3.24097 | 0.411604 | ||||||||
\(63\) | 9.69316 | 1.22122 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.91537i | 0.728132i | ||||||||
\(67\) | −3.79622 | −0.463782 | −0.231891 | − | 0.972742i | \(-0.574491\pi\) | ||||
−0.231891 | + | 0.972742i | \(0.574491\pi\) | |||||||
\(68\) | 4.96343i | 0.601905i | ||||||||
\(69\) | 1.72772i | 0.207992i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.47719 | −1.00606 | −0.503028 | − | 0.864270i | \(-0.667781\pi\) | ||||
−0.503028 | + | 0.864270i | \(0.667781\pi\) | |||||||
\(72\) | 2.02389i | 0.238518i | ||||||||
\(73\) | −9.05445 | −1.05974 | −0.529872 | − | 0.848078i | \(-0.677760\pi\) | ||||
−0.529872 | + | 0.848078i | \(0.677760\pi\) | |||||||
\(74\) | −3.96343 | + | 4.61424i | −0.460740 | + | 0.536394i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.33092i | − | 0.840915i | ||||||
\(77\) | 28.6755 | 3.26788 | ||||||||
\(78\) | −3.45211 | −0.390874 | ||||||||
\(79\) | − | 5.56622i | − | 0.626248i | −0.949712 | − | 0.313124i | \(-0.898624\pi\) | ||
0.949712 | − | 0.313124i | \(-0.101376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.16780 | 0.129755 | ||||||||
\(82\) | − | 0.530665i | − | 0.0586022i | ||||||
\(83\) | 3.77680 | 0.414558 | 0.207279 | − | 0.978282i | \(-0.433539\pi\) | ||||
0.207279 | + | 0.978282i | \(0.433539\pi\) | |||||||
\(84\) | −4.73182 | −0.516284 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.76838 | −0.190690 | ||||||||
\(87\) | − | 7.75571i | − | 0.831499i | ||||||
\(88\) | 5.98732i | 0.638251i | ||||||||
\(89\) | − | 8.45791i | − | 0.896537i | −0.893899 | − | 0.448268i | \(-0.852041\pi\) | ||
0.893899 | − | 0.448268i | \(-0.147959\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.7345i | 1.75426i | ||||||||
\(92\) | 1.74873i | 0.182318i | ||||||||
\(93\) | 3.20203i | 0.332035i | ||||||||
\(94\) | − | 4.30638i | − | 0.444169i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 0.987983i | − | 0.100836i | ||||||
\(97\) | − | 3.64747i | − | 0.370345i | −0.982706 | − | 0.185172i | \(-0.940716\pi\) | ||
0.982706 | − | 0.185172i | \(-0.0592843\pi\) | |||||||
\(98\) | 15.9381i | 1.60999i | ||||||||
\(99\) | 12.1177 | 1.21787 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.30416 | 0.229272 | 0.114636 | − | 0.993408i | \(-0.463430\pi\) | ||||
0.114636 | + | 0.993408i | \(0.463430\pi\) | |||||||
\(102\) | −4.90379 | −0.485547 | ||||||||
\(103\) | − | 11.1716i | − | 1.10077i | −0.834912 | − | 0.550383i | \(-0.814482\pi\) | ||
0.834912 | − | 0.550383i | \(-0.185518\pi\) | |||||||
\(104\) | −3.49410 | −0.342625 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.66238i | 0.355722i | ||||||||
\(107\) | 6.51807 | 0.630126 | 0.315063 | − | 0.949071i | \(-0.397974\pi\) | ||||
0.315063 | + | 0.949071i | \(0.397974\pi\) | |||||||
\(108\) | −4.96352 | −0.477615 | ||||||||
\(109\) | − | 1.33812i | − | 0.128169i | −0.997944 | − | 0.0640846i | \(-0.979587\pi\) | ||
0.997944 | − | 0.0640846i | \(-0.0204127\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.55879 | − | 3.91580i | −0.432701 | − | 0.371672i | ||||
\(112\) | −4.78937 | −0.452553 | ||||||||
\(113\) | − | 1.39109i | − | 0.130863i | −0.997857 | − | 0.0654315i | \(-0.979158\pi\) | ||
0.997857 | − | 0.0654315i | \(-0.0208424\pi\) | |||||||
\(114\) | 7.24283 | 0.678353 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.85004i | − | 0.728858i | ||||||
\(117\) | 7.07167i | 0.653776i | ||||||||
\(118\) | 2.15110 | 0.198025 | ||||||||
\(119\) | 23.7717i | 2.17915i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.8480 | 2.25891 | ||||||||
\(122\) | −3.06584 | −0.277568 | ||||||||
\(123\) | 0.524288 | 0.0472735 | ||||||||
\(124\) | 3.24097i | 0.291048i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.69316i | 0.863535i | ||||||||
\(127\) | −7.51024 | −0.666426 | −0.333213 | − | 0.942852i | \(-0.608133\pi\) | ||||
−0.333213 | + | 0.942852i | \(0.608133\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | − | 1.74713i | − | 0.153827i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.19975i | − | 0.541675i | −0.962625 | − | 0.270837i | \(-0.912699\pi\) | ||
0.962625 | − | 0.270837i | \(-0.0873006\pi\) | |||||||
\(132\) | −5.91537 | −0.514867 | ||||||||
\(133\) | − | 35.1105i | − | 3.04447i | ||||||
\(134\) | − | 3.79622i | − | 0.327943i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.96343 | −0.425611 | ||||||||
\(137\) | −8.97186 | −0.766518 | −0.383259 | − | 0.923641i | \(-0.625198\pi\) | ||||
−0.383259 | + | 0.923641i | \(0.625198\pi\) | |||||||
\(138\) | −1.72772 | −0.147073 | ||||||||
\(139\) | −5.04168 | −0.427629 | −0.213815 | − | 0.976874i | \(-0.568589\pi\) | ||||
−0.213815 | + | 0.976874i | \(0.568589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.25463 | 0.358305 | ||||||||
\(142\) | − | 8.47719i | − | 0.711390i | ||||||
\(143\) | 20.9203i | 1.74944i | ||||||||
\(144\) | −2.02389 | −0.168657 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 9.05445i | − | 0.749352i | ||||||
\(147\) | −15.7466 | −1.29875 | ||||||||
\(148\) | −4.61424 | − | 3.96343i | −0.379288 | − | 0.325792i | ||||
\(149\) | 21.6451 | 1.77324 | 0.886619 | − | 0.462500i | \(-0.153048\pi\) | ||||
0.886619 | + | 0.462500i | \(0.153048\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47544 | 0.526964 | 0.263482 | − | 0.964664i | \(-0.415129\pi\) | ||||
0.263482 | + | 0.964664i | \(0.415129\pi\) | |||||||
\(152\) | 7.33092 | 0.594616 | ||||||||
\(153\) | 10.0454i | 0.812126i | ||||||||
\(154\) | 28.6755i | 2.31074i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | − | 3.45211i | − | 0.276390i | ||||||
\(157\) | −13.1689 | −1.05099 | −0.525495 | − | 0.850797i | \(-0.676120\pi\) | ||||
−0.525495 | + | 0.850797i | \(0.676120\pi\) | |||||||
\(158\) | 5.56622 | 0.442825 | ||||||||
\(159\) | −3.61837 | −0.286956 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.37532i | 0.660067i | ||||||||
\(162\) | 1.16780i | 0.0917509i | ||||||||
\(163\) | 18.7651i | 1.46979i | 0.678180 | + | 0.734896i | \(0.262769\pi\) | ||||
−0.678180 | + | 0.734896i | \(0.737231\pi\) | |||||||
\(164\) | 0.530665 | 0.0414380 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.77680i | 0.293136i | ||||||||
\(167\) | − | 7.19692i | − | 0.556914i | −0.960449 | − | 0.278457i | \(-0.910177\pi\) | ||
0.960449 | − | 0.278457i | \(-0.0898230\pi\) | |||||||
\(168\) | − | 4.73182i | − | 0.365068i | ||||||
\(169\) | 0.791278 | 0.0608676 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 14.8370i | − | 1.13461i | ||||||
\(172\) | − | 1.76838i | − | 0.134838i | ||||||
\(173\) | 9.79406 | 0.744629 | 0.372314 | − | 0.928107i | \(-0.378564\pi\) | ||||
0.372314 | + | 0.928107i | \(0.378564\pi\) | |||||||
\(174\) | 7.75571 | 0.587959 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.98732 | −0.451311 | ||||||||
\(177\) | 2.12525i | 0.159743i | ||||||||
\(178\) | 8.45791 | 0.633947 | ||||||||
\(179\) | 11.2829i | 0.843320i | 0.906754 | + | 0.421660i | \(0.138552\pi\) | ||||
−0.906754 | + | 0.421660i | \(0.861448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.82697 | 0.135798 | 0.0678989 | − | 0.997692i | \(-0.478370\pi\) | ||||
0.0678989 | + | 0.997692i | \(0.478370\pi\) | |||||||
\(182\) | −16.7345 | −1.24045 | ||||||||
\(183\) | − | 3.02900i | − | 0.223910i | ||||||
\(184\) | −1.74873 | −0.128918 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.20203 | −0.234784 | ||||||||
\(187\) | 29.7177i | 2.17317i | ||||||||
\(188\) | 4.30638 | 0.314075 | ||||||||
\(189\) | −23.7721 | −1.72917 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.8204i | 1.72358i | 0.507264 | + | 0.861791i | \(0.330657\pi\) | ||||
−0.507264 | + | 0.861791i | \(0.669343\pi\) | |||||||
\(192\) | 0.987983 | 0.0713015 | ||||||||
\(193\) | 8.40405i | 0.604937i | 0.953159 | + | 0.302468i | \(0.0978107\pi\) | ||||
−0.953159 | + | 0.302468i | \(0.902189\pi\) | |||||||
\(194\) | 3.64747 | 0.261873 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.9381 | −1.13843 | ||||||||
\(197\) | 4.22797 | 0.301230 | 0.150615 | − | 0.988592i | \(-0.451875\pi\) | ||||
0.150615 | + | 0.988592i | \(0.451875\pi\) | |||||||
\(198\) | 12.1177i | 0.861166i | ||||||||
\(199\) | 17.7545i | 1.25858i | 0.777170 | + | 0.629290i | \(0.216654\pi\) | ||||
−0.777170 | + | 0.629290i | \(0.783346\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.75060 | 0.264547 | ||||||||
\(202\) | 2.30416i | 0.162120i | ||||||||
\(203\) | − | 37.5968i | − | 2.63878i | ||||||
\(204\) | − | 4.90379i | − | 0.343334i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.1716 | 0.778360 | ||||||||
\(207\) | 3.53924i | 0.245994i | ||||||||
\(208\) | − | 3.49410i | − | 0.242272i | ||||||
\(209\) | − | 43.8926i | − | 3.03611i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.57321 | 0.314833 | 0.157417 | − | 0.987532i | \(-0.449683\pi\) | ||||
0.157417 | + | 0.987532i | \(0.449683\pi\) | |||||||
\(212\) | −3.66238 | −0.251534 | ||||||||
\(213\) | 8.37532 | 0.573867 | ||||||||
\(214\) | 6.51807i | 0.445566i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 4.96352i | − | 0.337725i | ||||||
\(217\) | 15.5222i | 1.05372i | ||||||||
\(218\) | 1.33812 | 0.0906293 | ||||||||
\(219\) | 8.94565 | 0.604491 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.3427 | −1.16660 | ||||||||
\(222\) | 3.91580 | − | 4.55879i | 0.262812 | − | 0.305966i | ||||
\(223\) | 20.3205 | 1.36076 | 0.680380 | − | 0.732860i | \(-0.261815\pi\) | ||||
0.680380 | + | 0.732860i | \(0.261815\pi\) | |||||||
\(224\) | − | 4.78937i | − | 0.320003i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.39109 | 0.0925341 | ||||||||
\(227\) | 5.74303i | 0.381178i | 0.981670 | + | 0.190589i | \(0.0610398\pi\) | ||||
−0.981670 | + | 0.190589i | \(0.938960\pi\) | |||||||
\(228\) | 7.24283i | 0.479668i | ||||||||
\(229\) | −23.4383 | −1.54885 | −0.774423 | − | 0.632669i | \(-0.781960\pi\) | ||||
−0.774423 | + | 0.632669i | \(0.781960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.3309 | −1.86404 | ||||||||
\(232\) | 7.85004 | 0.515380 | ||||||||
\(233\) | −17.2961 | −1.13310 | −0.566551 | − | 0.824027i | \(-0.691723\pi\) | ||||
−0.566551 | + | 0.824027i | \(0.691723\pi\) | |||||||
\(234\) | −7.07167 | −0.462289 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.15110i | 0.140025i | ||||||||
\(237\) | 5.49933i | 0.357220i | ||||||||
\(238\) | −23.7717 | −1.54089 | ||||||||
\(239\) | 3.68796i | 0.238554i | 0.992861 | + | 0.119277i | \(0.0380577\pi\) | ||||
−0.992861 | + | 0.119277i | \(0.961942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.3613i | − | 0.731844i | −0.930646 | − | 0.365922i | \(-0.880754\pi\) | ||
0.930646 | − | 0.365922i | \(-0.119246\pi\) | |||||||
\(242\) | 24.8480i | 1.59729i | ||||||||
\(243\) | −16.0443 | −1.02924 | ||||||||
\(244\) | − | 3.06584i | − | 0.196270i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.524288i | 0.0334274i | ||||||||
\(247\) | 25.6150 | 1.62984 | ||||||||
\(248\) | −3.24097 | −0.205802 | ||||||||
\(249\) | −3.73141 | −0.236469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.8260i | − | 0.809567i | −0.914412 | − | 0.404784i | \(-0.867347\pi\) | ||
0.914412 | − | 0.404784i | \(-0.132653\pi\) | |||||||
\(252\) | −9.69316 | −0.610612 | ||||||||
\(253\) | 10.4702i | 0.658256i | ||||||||
\(254\) | − | 7.51024i | − | 0.471234i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 14.0268i | − | 0.874965i | −0.899227 | − | 0.437483i | \(-0.855870\pi\) | ||
0.899227 | − | 0.437483i | \(-0.144130\pi\) | |||||||
\(258\) | 1.74713 | 0.108772 | ||||||||
\(259\) | −22.0993 | − | 18.9824i | −1.37318 | − | 1.17951i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 15.8876i | − | 0.983419i | ||||||
\(262\) | 6.19975 | 0.383022 | ||||||||
\(263\) | 3.57182 | 0.220248 | 0.110124 | − | 0.993918i | \(-0.464875\pi\) | ||||
0.110124 | + | 0.993918i | \(0.464875\pi\) | |||||||
\(264\) | − | 5.91537i | − | 0.364066i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 35.1105 | 2.15276 | ||||||||
\(267\) | 8.35627i | 0.511396i | ||||||||
\(268\) | 3.79622 | 0.231891 | ||||||||
\(269\) | 0.458895 | 0.0279793 | 0.0139897 | − | 0.999902i | \(-0.495547\pi\) | ||||
0.0139897 | + | 0.999902i | \(0.495547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.8897 | 1.75492 | 0.877462 | − | 0.479645i | \(-0.159235\pi\) | ||||
0.877462 | + | 0.479645i | \(0.159235\pi\) | |||||||
\(272\) | − | 4.96343i | − | 0.300952i | ||||||
\(273\) | − | 16.5334i | − | 1.00065i | ||||||
\(274\) | − | 8.97186i | − | 0.542010i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 1.72772i | − | 0.103996i | ||||||
\(277\) | − | 22.4482i | − | 1.34878i | −0.738374 | − | 0.674391i | \(-0.764406\pi\) | ||
0.738374 | − | 0.674391i | \(-0.235594\pi\) | |||||||
\(278\) | − | 5.04168i | − | 0.302380i | ||||||
\(279\) | 6.55937i | 0.392699i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.04908i | − | 0.360858i | −0.983588 | − | 0.180429i | \(-0.942251\pi\) | ||
0.983588 | − | 0.180429i | \(-0.0577486\pi\) | |||||||
\(282\) | 4.25463i | 0.253360i | ||||||||
\(283\) | 10.8317i | 0.643878i | 0.946760 | + | 0.321939i | \(0.104335\pi\) | ||||
−0.946760 | + | 0.321939i | \(0.895665\pi\) | |||||||
\(284\) | 8.47719 | 0.503028 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.9203 | −1.23704 | ||||||||
\(287\) | 2.54155 | 0.150023 | ||||||||
\(288\) | − | 2.02389i | − | 0.119259i | ||||||
\(289\) | −7.63567 | −0.449157 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.60364i | 0.211249i | ||||||||
\(292\) | 9.05445 | 0.529872 | ||||||||
\(293\) | 23.3144 | 1.36204 | 0.681021 | − | 0.732264i | \(-0.261536\pi\) | ||||
0.681021 | + | 0.732264i | \(0.261536\pi\) | |||||||
\(294\) | − | 15.7466i | − | 0.918357i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.96343 | − | 4.61424i | 0.230370 | − | 0.268197i | ||||
\(297\) | −29.7182 | −1.72442 | ||||||||
\(298\) | 21.6451i | 1.25387i | ||||||||
\(299\) | −6.11023 | −0.353364 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 8.46945i | − | 0.488171i | ||||||
\(302\) | 6.47544i | 0.372620i | ||||||||
\(303\) | −2.27647 | −0.130780 | ||||||||
\(304\) | 7.33092i | 0.420457i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.0454 | −0.574260 | ||||||||
\(307\) | −14.2651 | −0.814153 | −0.407077 | − | 0.913394i | \(-0.633452\pi\) | ||||
−0.407077 | + | 0.913394i | \(0.633452\pi\) | |||||||
\(308\) | −28.6755 | −1.63394 | ||||||||
\(309\) | 11.0373i | 0.627891i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 22.5322i | − | 1.27768i | −0.769339 | − | 0.638841i | \(-0.779414\pi\) | ||
0.769339 | − | 0.638841i | \(-0.220586\pi\) | |||||||
\(312\) | 3.45211 | 0.195437 | ||||||||
\(313\) | − | 10.0000i | − | 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | − | 13.1689i | − | 0.743162i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.56622i | 0.313124i | ||||||||
\(317\) | 12.3877 | 0.695764 | 0.347882 | − | 0.937538i | \(-0.386901\pi\) | ||||
0.347882 | + | 0.937538i | \(0.386901\pi\) | |||||||
\(318\) | − | 3.61837i | − | 0.202908i | ||||||
\(319\) | − | 47.0007i | − | 2.63154i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.43975 | −0.359432 | ||||||||
\(322\) | −8.37532 | −0.466738 | ||||||||
\(323\) | 36.3865 | 2.02460 | ||||||||
\(324\) | −1.16780 | −0.0648777 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.7651 | −1.03930 | ||||||||
\(327\) | 1.32204i | 0.0731092i | ||||||||
\(328\) | 0.530665i | 0.0293011i | ||||||||
\(329\) | 20.6249 | 1.13709 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0068i | 1.04471i | 0.852728 | + | 0.522355i | \(0.174946\pi\) | ||||
−0.852728 | + | 0.522355i | \(0.825054\pi\) | |||||||
\(332\) | −3.77680 | −0.207279 | ||||||||
\(333\) | −9.33871 | − | 8.02155i | −0.511758 | − | 0.439578i | ||||
\(334\) | 7.19692 | 0.393798 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.73182 | 0.258142 | ||||||||
\(337\) | 25.1046 | 1.36753 | 0.683766 | − | 0.729701i | \(-0.260341\pi\) | ||||
0.683766 | + | 0.729701i | \(0.260341\pi\) | |||||||
\(338\) | 0.791278i | 0.0430399i | ||||||||
\(339\) | 1.37438i | 0.0746459i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.4047i | 1.05083i | ||||||||
\(342\) | 14.8370 | 0.802292 | ||||||||
\(343\) | −42.8078 | −2.31140 | ||||||||
\(344\) | 1.76838 | 0.0953449 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.79406i | 0.526532i | ||||||||
\(347\) | − | 30.4282i | − | 1.63347i | −0.577011 | − | 0.816736i | \(-0.695781\pi\) | ||
0.577011 | − | 0.816736i | \(-0.304219\pi\) | |||||||
\(348\) | 7.75571i | 0.415750i | ||||||||
\(349\) | −15.1341 | −0.810111 | −0.405056 | − | 0.914292i | \(-0.632748\pi\) | ||||
−0.405056 | + | 0.914292i | \(0.632748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 17.3430i | − | 0.925702i | ||||||
\(352\) | − | 5.98732i | − | 0.319125i | ||||||
\(353\) | − | 10.1331i | − | 0.539332i | −0.962954 | − | 0.269666i | \(-0.913087\pi\) | ||
0.962954 | − | 0.269666i | \(-0.0869133\pi\) | |||||||
\(354\) | −2.12525 | −0.112956 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.45791i | 0.448268i | ||||||||
\(357\) | − | 23.4861i | − | 1.24301i | ||||||
\(358\) | −11.2829 | −0.596317 | ||||||||
\(359\) | 26.3685 | 1.39168 | 0.695838 | − | 0.718199i | \(-0.255033\pi\) | ||||
0.695838 | + | 0.718199i | \(0.255033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −34.7424 | −1.82855 | ||||||||
\(362\) | 1.82697i | 0.0960235i | ||||||||
\(363\) | −24.5494 | −1.28851 | ||||||||
\(364\) | − | 16.7345i | − | 0.877128i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.02900 | 0.158328 | ||||||||
\(367\) | −2.21157 | −0.115443 | −0.0577215 | − | 0.998333i | \(-0.518384\pi\) | ||||
−0.0577215 | + | 0.998333i | \(0.518384\pi\) | |||||||
\(368\) | − | 1.74873i | − | 0.0911588i | ||||||
\(369\) | 1.07401 | 0.0559106 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.5405 | −0.910658 | ||||||||
\(372\) | − | 3.20203i | − | 0.166017i | ||||||
\(373\) | 6.08275 | 0.314953 | 0.157476 | − | 0.987523i | \(-0.449664\pi\) | ||||
0.157476 | + | 0.987523i | \(0.449664\pi\) | |||||||
\(374\) | −29.7177 | −1.53666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.30638i | 0.222085i | ||||||||
\(377\) | 27.4288 | 1.41266 | ||||||||
\(378\) | − | 23.7721i | − | 1.22271i | ||||||
\(379\) | 20.0919 | 1.03205 | 0.516025 | − | 0.856574i | \(-0.327411\pi\) | ||||
0.516025 | + | 0.856574i | \(0.327411\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.41999 | 0.380138 | ||||||||
\(382\) | −23.8204 | −1.21876 | ||||||||
\(383\) | 11.5368i | 0.589501i | 0.955574 | + | 0.294751i | \(0.0952366\pi\) | ||||
−0.955574 | + | 0.294751i | \(0.904763\pi\) | |||||||
\(384\) | 0.987983i | 0.0504178i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.40405 | −0.427755 | ||||||||
\(387\) | − | 3.57901i | − | 0.181932i | ||||||
\(388\) | 3.64747i | 0.185172i | ||||||||
\(389\) | 8.55057i | 0.433531i | 0.976224 | + | 0.216766i | \(0.0695507\pi\) | ||||
−0.976224 | + | 0.216766i | \(0.930449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.67970 | −0.438951 | ||||||||
\(392\) | − | 15.9381i | − | 0.804995i | ||||||
\(393\) | 6.12525i | 0.308978i | ||||||||
\(394\) | 4.22797i | 0.213002i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.1177 | −0.608936 | ||||||||
\(397\) | −9.84444 | −0.494078 | −0.247039 | − | 0.969006i | \(-0.579458\pi\) | ||||
−0.247039 | + | 0.969006i | \(0.579458\pi\) | |||||||
\(398\) | −17.7545 | −0.889951 | ||||||||
\(399\) | 34.6886i | 1.73660i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.0959i | 1.55285i | 0.630207 | + | 0.776427i | \(0.282970\pi\) | ||||
−0.630207 | + | 0.776427i | \(0.717030\pi\) | |||||||
\(402\) | 3.75060i | 0.187063i | ||||||||
\(403\) | −11.3243 | −0.564102 | ||||||||
\(404\) | −2.30416 | −0.114636 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 37.5968 | 1.86590 | ||||||||
\(407\) | −27.6269 | − | 23.7304i | −1.36942 | − | 1.17627i | ||||
\(408\) | 4.90379 | 0.242774 | ||||||||
\(409\) | 38.3150i | 1.89455i | 0.320417 | + | 0.947277i | \(0.396177\pi\) | ||||
−0.320417 | + | 0.947277i | \(0.603823\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.86404 | 0.437231 | ||||||||
\(412\) | 11.1716i | 0.550383i | ||||||||
\(413\) | 10.3024i | 0.506948i | ||||||||
\(414\) | −3.53924 | −0.173944 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.49410 | 0.171312 | ||||||||
\(417\) | 4.98109 | 0.243925 | ||||||||
\(418\) | 43.8926 | 2.14686 | ||||||||
\(419\) | −29.0183 | −1.41764 | −0.708819 | − | 0.705391i | \(-0.750772\pi\) | ||||
−0.708819 | + | 0.705391i | \(0.750772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.6443i | 1.15235i | 0.817326 | + | 0.576175i | \(0.195455\pi\) | ||||
−0.817326 | + | 0.576175i | \(0.804545\pi\) | |||||||
\(422\) | 4.57321i | 0.222621i | ||||||||
\(423\) | 8.71564 | 0.423769 | ||||||||
\(424\) | − | 3.66238i | − | 0.177861i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.37532i | 0.405785i | ||||||||
\(427\) | − | 14.6834i | − | 0.710582i | ||||||
\(428\) | −6.51807 | −0.315063 | ||||||||
\(429\) | − | 20.6689i | − | 0.997904i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.1126i | − | 1.54681i | −0.633912 | − | 0.773406i | \(-0.718552\pi\) | ||
0.633912 | − | 0.773406i | \(-0.281448\pi\) | |||||||
\(432\) | 4.96352 | 0.238807 | ||||||||
\(433\) | 13.0575 | 0.627504 | 0.313752 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313752 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(434\) | −15.5222 | −0.745091 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.33812i | 0.0640846i | ||||||||
\(437\) | 12.8198 | 0.613254 | ||||||||
\(438\) | 8.94565i | 0.427440i | ||||||||
\(439\) | − | 28.0499i | − | 1.33875i | −0.742924 | − | 0.669375i | \(-0.766562\pi\) | ||
0.742924 | − | 0.669375i | \(-0.233438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.2569 | −1.53604 | ||||||||
\(442\) | − | 17.3427i | − | 0.824909i | ||||||
\(443\) | −6.79629 | −0.322902 | −0.161451 | − | 0.986881i | \(-0.551617\pi\) | ||||
−0.161451 | + | 0.986881i | \(0.551617\pi\) | |||||||
\(444\) | 4.55879 | + | 3.91580i | 0.216351 | + | 0.185836i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.3205i | 0.962203i | ||||||||
\(447\) | −21.3850 | −1.01148 | ||||||||
\(448\) | 4.78937 | 0.226277 | ||||||||
\(449\) | − | 17.3278i | − | 0.817747i | −0.912591 | − | 0.408874i | \(-0.865922\pi\) | ||
0.912591 | − | 0.408874i | \(-0.134078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.17726 | 0.149611 | ||||||||
\(452\) | 1.39109i | 0.0654315i | ||||||||
\(453\) | −6.39762 | −0.300587 | ||||||||
\(454\) | −5.74303 | −0.269534 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.24283 | −0.339176 | ||||||||
\(457\) | − | 3.20960i | − | 0.150139i | −0.997178 | − | 0.0750693i | \(-0.976082\pi\) | ||
0.997178 | − | 0.0750693i | \(-0.0239178\pi\) | |||||||
\(458\) | − | 23.4383i | − | 1.09520i | ||||||
\(459\) | − | 24.6361i | − | 1.14991i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 34.0347i | − | 1.58515i | −0.609773 | − | 0.792576i | \(-0.708739\pi\) | ||
0.609773 | − | 0.792576i | \(-0.291261\pi\) | |||||||
\(462\) | − | 28.3309i | − | 1.31807i | ||||||
\(463\) | 26.0543i | 1.21085i | 0.795904 | + | 0.605423i | \(0.206996\pi\) | ||||
−0.795904 | + | 0.605423i | \(0.793004\pi\) | |||||||
\(464\) | 7.85004i | 0.364429i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 17.2961i | − | 0.801224i | ||||||
\(467\) | 20.3289i | 0.940710i | 0.882477 | + | 0.470355i | \(0.155874\pi\) | ||||
−0.882477 | + | 0.470355i | \(0.844126\pi\) | |||||||
\(468\) | − | 7.07167i | − | 0.326888i | ||||||
\(469\) | 18.1815 | 0.839544 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.0106 | 0.599498 | ||||||||
\(472\) | −2.15110 | −0.0990123 | ||||||||
\(473\) | − | 10.5879i | − | 0.486832i | ||||||
\(474\) | −5.49933 | −0.252593 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 23.7717i | − | 1.08958i | ||||||
\(477\) | −7.41226 | −0.339384 | ||||||||
\(478\) | −3.68796 | −0.168683 | ||||||||
\(479\) | − | 6.22972i | − | 0.284643i | −0.989820 | − | 0.142322i | \(-0.954543\pi\) | ||
0.989820 | − | 0.142322i | \(-0.0454567\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.8486 | − | 16.1226i | 0.631443 | − | 0.735127i | ||||
\(482\) | 11.3613 | 0.517492 | ||||||||
\(483\) | − | 8.27467i | − | 0.376511i | ||||||
\(484\) | −24.8480 | −1.12946 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 16.0443i | − | 0.727785i | ||||||
\(487\) | 30.5352i | 1.38368i | 0.722050 | + | 0.691841i | \(0.243200\pi\) | ||||
−0.722050 | + | 0.691841i | \(0.756800\pi\) | |||||||
\(488\) | 3.06584 | 0.138784 | ||||||||
\(489\) | − | 18.5396i | − | 0.838387i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.5944 | 1.10993 | 0.554965 | − | 0.831874i | \(-0.312732\pi\) | ||||
0.554965 | + | 0.831874i | \(0.312732\pi\) | |||||||
\(492\) | −0.524288 | −0.0236367 | ||||||||
\(493\) | 38.9632 | 1.75481 | ||||||||
\(494\) | 25.6150i | 1.15247i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.24097i | − | 0.145524i | ||||||
\(497\) | 40.6004 | 1.82118 | ||||||||
\(498\) | − | 3.73141i | − | 0.167209i | ||||||
\(499\) | − | 33.5739i | − | 1.50297i | −0.659747 | − | 0.751487i | \(-0.729337\pi\) | ||
0.659747 | − | 0.751487i | \(-0.270663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.11043i | 0.317671i | ||||||||
\(502\) | 12.8260 | 0.572451 | ||||||||
\(503\) | − | 1.77931i | − | 0.0793357i | −0.999213 | − | 0.0396679i | \(-0.987370\pi\) | ||
0.999213 | − | 0.0396679i | \(-0.0126300\pi\) | |||||||
\(504\) | − | 9.69316i | − | 0.431768i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.4702 | −0.465458 | ||||||||
\(507\) | −0.781770 | −0.0347196 | ||||||||
\(508\) | 7.51024 | 0.333213 | ||||||||
\(509\) | −29.5114 | −1.30807 | −0.654035 | − | 0.756464i | \(-0.726925\pi\) | ||||
−0.654035 | + | 0.756464i | \(0.726925\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.3651 | 1.91836 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 36.3872i | 1.60653i | ||||||||
\(514\) | 14.0268 | 0.618694 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.74713i | 0.0769133i | ||||||||
\(517\) | 25.7837 | 1.13397 | ||||||||
\(518\) | 18.9824 | − | 22.0993i | 0.834037 | − | 0.970988i | ||||
\(519\) | −9.67637 | −0.424745 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.2841 | 1.28296 | 0.641481 | − | 0.767139i | \(-0.278320\pi\) | ||||
0.641481 | + | 0.767139i | \(0.278320\pi\) | |||||||
\(522\) | 15.8876 | 0.695382 | ||||||||
\(523\) | − | 29.9729i | − | 1.31062i | −0.755359 | − | 0.655312i | \(-0.772537\pi\) | ||
0.755359 | − | 0.655312i | \(-0.227463\pi\) | |||||||
\(524\) | 6.19975i | 0.270837i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.57182i | 0.155739i | ||||||||
\(527\) | −16.0864 | −0.700732 | ||||||||
\(528\) | 5.91537 | 0.257434 | ||||||||
\(529\) | 19.9419 | 0.867041 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.35359i | 0.188930i | ||||||||
\(532\) | 35.1105i | 1.52223i | ||||||||
\(533\) | 1.85420i | 0.0803141i | ||||||||
\(534\) | −8.35627 | −0.361611 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.79622i | 0.163972i | ||||||||
\(537\) | − | 11.1473i | − | 0.481040i | ||||||
\(538\) | 0.458895i | 0.0197844i | ||||||||
\(539\) | −95.4264 | −4.11031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7155i | 0.804644i | 0.915498 | + | 0.402322i | \(0.131797\pi\) | ||||
−0.915498 | + | 0.402322i | \(0.868203\pi\) | |||||||
\(542\) | 28.8897i | 1.24092i | ||||||||
\(543\) | −1.80502 | −0.0774607 | ||||||||
\(544\) | 4.96343 | 0.212805 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.5334 | 0.707566 | ||||||||
\(547\) | 32.4792i | 1.38871i | 0.719633 | + | 0.694355i | \(0.244310\pi\) | ||||
−0.719633 | + | 0.694355i | \(0.755690\pi\) | |||||||
\(548\) | 8.97186 | 0.383259 | ||||||||
\(549\) | − | 6.20492i | − | 0.264820i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −57.5480 | −2.45163 | ||||||||
\(552\) | 1.72772 | 0.0735364 | ||||||||
\(553\) | 26.6587i | 1.13364i | ||||||||
\(554\) | 22.4482 | 0.953733 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.04168 | 0.213815 | ||||||||
\(557\) | 16.0158i | 0.678612i | 0.940676 | + | 0.339306i | \(0.110192\pi\) | ||||
−0.940676 | + | 0.339306i | \(0.889808\pi\) | |||||||
\(558\) | −6.55937 | −0.277680 | ||||||||
\(559\) | 6.17891 | 0.261340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 29.3606i | − | 1.23960i | ||||||
\(562\) | 6.04908 | 0.255165 | ||||||||
\(563\) | − | 15.3069i | − | 0.645109i | −0.946551 | − | 0.322554i | \(-0.895458\pi\) | ||
0.946551 | − | 0.322554i | \(-0.104542\pi\) | |||||||
\(564\) | −4.25463 | −0.179152 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.8317 | −0.455291 | ||||||||
\(567\) | −5.59302 | −0.234885 | ||||||||
\(568\) | 8.47719i | 0.355695i | ||||||||
\(569\) | 26.6494i | 1.11720i | 0.829437 | + | 0.558601i | \(0.188662\pi\) | ||||
−0.829437 | + | 0.558601i | \(0.811338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1683 | 0.969564 | 0.484782 | − | 0.874635i | \(-0.338899\pi\) | ||||
0.484782 | + | 0.874635i | \(0.338899\pi\) | |||||||
\(572\) | − | 20.9203i | − | 0.874721i | ||||||
\(573\) | − | 23.5341i | − | 0.983152i | ||||||
\(574\) | 2.54155i | 0.106082i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.02389 | 0.0843287 | ||||||||
\(577\) | 3.54110i | 0.147418i | 0.997280 | + | 0.0737091i | \(0.0234836\pi\) | ||||
−0.997280 | + | 0.0737091i | \(0.976516\pi\) | |||||||
\(578\) | − | 7.63567i | − | 0.317602i | ||||||
\(579\) | − | 8.30306i | − | 0.345063i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0885 | −0.750437 | ||||||||
\(582\) | −3.60364 | −0.149376 | ||||||||
\(583\) | −21.9279 | −0.908160 | ||||||||
\(584\) | 9.05445i | 0.374676i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.3144i | 0.963109i | ||||||||
\(587\) | − | 12.0976i | − | 0.499320i | −0.968334 | − | 0.249660i | \(-0.919681\pi\) | ||
0.968334 | − | 0.249660i | \(-0.0803188\pi\) | |||||||
\(588\) | 15.7466 | 0.649377 | ||||||||
\(589\) | 23.7593 | 0.978986 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.17716 | −0.171825 | ||||||||
\(592\) | 4.61424 | + | 3.96343i | 0.189644 | + | 0.162896i | ||||
\(593\) | 17.2007 | 0.706348 | 0.353174 | − | 0.935558i | \(-0.385102\pi\) | ||||
0.353174 | + | 0.935558i | \(0.385102\pi\) | |||||||
\(594\) | − | 29.7182i | − | 1.21935i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.6451 | −0.886619 | ||||||||
\(597\) | − | 17.5411i | − | 0.717910i | ||||||
\(598\) | − | 6.11023i | − | 0.249866i | ||||||
\(599\) | −2.41919 | −0.0988454 | −0.0494227 | − | 0.998778i | \(-0.515738\pi\) | ||||
−0.0494227 | + | 0.998778i | \(0.515738\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.0483 | −1.59281 | −0.796407 | − | 0.604761i | \(-0.793269\pi\) | ||||
−0.796407 | + | 0.604761i | \(0.793269\pi\) | |||||||
\(602\) | 8.46945 | 0.345189 | ||||||||
\(603\) | 7.68313 | 0.312881 | ||||||||
\(604\) | −6.47544 | −0.263482 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 2.27647i | − | 0.0924752i | ||||||
\(607\) | 38.0508i | 1.54443i | 0.635359 | + | 0.772217i | \(0.280852\pi\) | ||||
−0.635359 | + | 0.772217i | \(0.719148\pi\) | |||||||
\(608\) | −7.33092 | −0.297308 | ||||||||
\(609\) | 37.1450i | 1.50519i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0469i | 0.608733i | ||||||||
\(612\) | − | 10.0454i | − | 0.406063i | ||||||
\(613\) | 7.12176 | 0.287645 | 0.143823 | − | 0.989603i | \(-0.454061\pi\) | ||||
0.143823 | + | 0.989603i | \(0.454061\pi\) | |||||||
\(614\) | − | 14.2651i | − | 0.575693i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 28.6755i | − | 1.15537i | ||||||
\(617\) | −42.6678 | −1.71774 | −0.858871 | − | 0.512192i | \(-0.828834\pi\) | ||||
−0.858871 | + | 0.512192i | \(0.828834\pi\) | |||||||
\(618\) | −11.0373 | −0.443986 | ||||||||
\(619\) | 6.30429 | 0.253391 | 0.126695 | − | 0.991942i | \(-0.459563\pi\) | ||||
0.126695 | + | 0.991942i | \(0.459563\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 8.67985i | − | 0.348310i | ||||||
\(622\) | 22.5322 | 0.903458 | ||||||||
\(623\) | 40.5081i | 1.62292i | ||||||||
\(624\) | 3.45211i | 0.138195i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | 43.3651i | 1.73184i | ||||||||
\(628\) | 13.1689 | 0.525495 | ||||||||
\(629\) | 19.6722 | − | 22.9025i | 0.784383 | − | 0.913181i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.6385i | 1.29932i | 0.760225 | + | 0.649660i | \(0.225089\pi\) | ||||
−0.760225 | + | 0.649660i | \(0.774911\pi\) | |||||||
\(632\) | −5.56622 | −0.221412 | ||||||||
\(633\) | −4.51826 | −0.179585 | ||||||||
\(634\) | 12.3877i | 0.491979i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.61837 | 0.143478 | ||||||||
\(637\) | − | 55.6892i | − | 2.20649i | ||||||
\(638\) | 47.0007 | 1.86078 | ||||||||
\(639\) | 17.1569 | 0.678716 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1721 | −0.480767 | −0.240384 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240384 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(642\) | − | 6.43975i | − | 0.254156i | ||||||
\(643\) | 10.0853i | 0.397727i | 0.980027 | + | 0.198864i | \(0.0637251\pi\) | ||||
−0.980027 | + | 0.198864i | \(0.936275\pi\) | |||||||
\(644\) | − | 8.37532i | − | 0.330034i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.3865i | 1.43161i | ||||||||
\(647\) | 38.5061i | 1.51383i | 0.653512 | + | 0.756916i | \(0.273295\pi\) | ||||
−0.653512 | + | 0.756916i | \(0.726705\pi\) | |||||||
\(648\) | − | 1.16780i | − | 0.0458754i | ||||||
\(649\) | 12.8793i | 0.505558i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 15.3357i | − | 0.601053i | ||||||
\(652\) | − | 18.7651i | − | 0.734896i | ||||||
\(653\) | − | 2.20349i | − | 0.0862293i | −0.999070 | − | 0.0431146i | \(-0.986272\pi\) | ||
0.999070 | − | 0.0431146i | \(-0.0137281\pi\) | |||||||
\(654\) | −1.32204 | −0.0516960 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.530665 | −0.0207190 | ||||||||
\(657\) | 18.3252 | 0.714935 | ||||||||
\(658\) | 20.6249i | 0.804041i | ||||||||
\(659\) | 20.4048 | 0.794859 | 0.397430 | − | 0.917633i | \(-0.369902\pi\) | ||||
0.397430 | + | 0.917633i | \(0.369902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0306i | 1.05137i | 0.850680 | + | 0.525684i | \(0.176191\pi\) | ||||
−0.850680 | + | 0.525684i | \(0.823809\pi\) | |||||||
\(662\) | −19.0068 | −0.738721 | ||||||||
\(663\) | 17.1343 | 0.665442 | ||||||||
\(664\) | − | 3.77680i | − | 0.146568i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.02155 | − | 9.33871i | 0.310829 | − | 0.361868i | ||||
\(667\) | 13.7276 | 0.531535 | ||||||||
\(668\) | 7.19692i | 0.278457i | ||||||||
\(669\) | −20.0763 | −0.776194 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18.3562i | − | 0.708632i | ||||||
\(672\) | 4.73182i | 0.182534i | ||||||||
\(673\) | 11.6776 | 0.450139 | 0.225070 | − | 0.974343i | \(-0.427739\pi\) | ||||
0.225070 | + | 0.974343i | \(0.427739\pi\) | |||||||
\(674\) | 25.1046i | 0.966991i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.791278 | −0.0304338 | ||||||||
\(677\) | −37.2578 | −1.43193 | −0.715966 | − | 0.698135i | \(-0.754014\pi\) | ||||
−0.715966 | + | 0.698135i | \(0.754014\pi\) | |||||||
\(678\) | −1.37438 | −0.0527826 | ||||||||
\(679\) | 17.4691i | 0.670402i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 5.67402i | − | 0.217429i | ||||||
\(682\) | −19.4047 | −0.743046 | ||||||||
\(683\) | − | 46.3018i | − | 1.77169i | −0.463981 | − | 0.885845i | \(-0.653580\pi\) | ||
0.463981 | − | 0.885845i | \(-0.346420\pi\) | |||||||
\(684\) | 14.8370i | 0.567306i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 42.8078i | − | 1.63441i | ||||||
\(687\) | 23.1566 | 0.883480 | ||||||||
\(688\) | 1.76838i | 0.0674190i | ||||||||
\(689\) | − | 12.7967i | − | 0.487516i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.7037 | 1.12998 | 0.564991 | − | 0.825097i | \(-0.308879\pi\) | ||||
0.564991 | + | 0.825097i | \(0.308879\pi\) | |||||||
\(692\) | −9.79406 | −0.372314 | ||||||||
\(693\) | −58.0361 | −2.20461 | ||||||||
\(694\) | 30.4282 | 1.15504 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.75571 | −0.293979 | ||||||||
\(697\) | 2.63392i | 0.0997669i | ||||||||
\(698\) | − | 15.1341i | − | 0.572835i | ||||||
\(699\) | 17.0882 | 0.646336 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 45.9214i | − | 1.73443i | −0.497936 | − | 0.867214i | \(-0.665909\pi\) | ||
0.497936 | − | 0.867214i | \(-0.334091\pi\) | |||||||
\(702\) | 17.3430 | 0.654570 | ||||||||
\(703\) | −29.0556 | + | 33.8266i | −1.09585 | + | 1.27580i | ||||
\(704\) | 5.98732 | 0.225656 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.1331 | 0.381365 | ||||||||
\(707\) | −11.0355 | −0.415031 | ||||||||
\(708\) | − | 2.12525i | − | 0.0798717i | ||||||
\(709\) | 52.6575i | 1.97759i | 0.149266 | + | 0.988797i | \(0.452309\pi\) | ||||
−0.149266 | + | 0.988797i | \(0.547691\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.2654i | 0.422486i | ||||||||
\(712\) | −8.45791 | −0.316974 | ||||||||
\(713\) | −5.66759 | −0.212253 | ||||||||
\(714\) | 23.4861 | 0.878944 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 11.2829i | − | 0.421660i | ||||||
\(717\) | − | 3.64364i | − | 0.136074i | ||||||
\(718\) | 26.3685i | 0.984063i | ||||||||
\(719\) | 13.3494 | 0.497850 | 0.248925 | − | 0.968523i | \(-0.419923\pi\) | ||||
0.248925 | + | 0.968523i | \(0.419923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.5048i | 1.99262i | ||||||||
\(722\) | − | 34.7424i | − | 1.29298i | ||||||
\(723\) | 11.2247i | 0.417453i | ||||||||
\(724\) | −1.82697 | −0.0678989 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 24.5494i | − | 0.911115i | ||||||
\(727\) | − | 13.1733i | − | 0.488571i | −0.969703 | − | 0.244286i | \(-0.921447\pi\) | ||
0.969703 | − | 0.244286i | \(-0.0785534\pi\) | |||||||
\(728\) | 16.7345 | 0.620223 | ||||||||
\(729\) | 12.3481 | 0.457338 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.77726 | 0.324639 | ||||||||
\(732\) | 3.02900i | 0.111955i | ||||||||
\(733\) | −32.3264 | −1.19400 | −0.597001 | − | 0.802241i | \(-0.703641\pi\) | ||||
−0.597001 | + | 0.802241i | \(0.703641\pi\) | |||||||
\(734\) | − | 2.21157i | − | 0.0816305i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.74873 | 0.0644590 | ||||||||
\(737\) | 22.7292 | 0.837240 | ||||||||
\(738\) | 1.07401i | 0.0395348i | ||||||||
\(739\) | −6.94169 | −0.255354 | −0.127677 | − | 0.991816i | \(-0.540752\pi\) | ||||
−0.127677 | + | 0.991816i | \(0.540752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.3072 | −0.929681 | ||||||||
\(742\) | − | 17.5405i | − | 0.643933i | ||||||
\(743\) | −36.0784 | −1.32359 | −0.661795 | − | 0.749685i | \(-0.730205\pi\) | ||||
−0.661795 | + | 0.749685i | \(0.730205\pi\) | |||||||
\(744\) | 3.20203 | 0.117392 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.08275i | 0.222705i | ||||||||
\(747\) | −7.64382 | −0.279673 | ||||||||
\(748\) | − | 29.7177i | − | 1.08659i | ||||||
\(749\) | −31.2175 | −1.14066 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.9052 | −1.09126 | −0.545629 | − | 0.838027i | \(-0.683709\pi\) | ||||
−0.545629 | + | 0.838027i | \(0.683709\pi\) | |||||||
\(752\) | −4.30638 | −0.157038 | ||||||||
\(753\) | 12.6718i | 0.461787i | ||||||||
\(754\) | 27.4288i | 0.998898i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 23.7721 | 0.864584 | ||||||||
\(757\) | − | 24.9464i | − | 0.906693i | −0.891334 | − | 0.453347i | \(-0.850230\pi\) | ||
0.891334 | − | 0.453347i | \(-0.149770\pi\) | |||||||
\(758\) | 20.0919i | 0.729769i | ||||||||
\(759\) | − | 10.3444i | − | 0.375477i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7647 | 0.426469 | 0.213235 | − | 0.977001i | \(-0.431600\pi\) | ||||
0.213235 | + | 0.977001i | \(0.431600\pi\) | |||||||
\(762\) | 7.41999i | 0.268798i | ||||||||
\(763\) | 6.40878i | 0.232013i | ||||||||
\(764\) | − | 23.8204i | − | 0.861791i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.5368 | −0.416840 | ||||||||
\(767\) | −7.51615 | −0.271392 | ||||||||
\(768\) | −0.987983 | −0.0356508 | ||||||||
\(769\) | − | 26.7939i | − | 0.966214i | −0.875561 | − | 0.483107i | \(-0.839508\pi\) | ||
0.875561 | − | 0.483107i | \(-0.160492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.8582i | 0.499091i | ||||||||
\(772\) | − | 8.40405i | − | 0.302468i | ||||||
\(773\) | 2.77358 | 0.0997589 | 0.0498794 | − | 0.998755i | \(-0.484116\pi\) | ||||
0.0498794 | + | 0.998755i | \(0.484116\pi\) | |||||||
\(774\) | 3.57901 | 0.128645 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.64747 | −0.130937 | ||||||||
\(777\) | 21.8337 | + | 18.7542i | 0.783281 | + | 0.672805i | ||||
\(778\) | −8.55057 | −0.306553 | ||||||||
\(779\) | − | 3.89026i | − | 0.139383i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.7556 | 1.81618 | ||||||||
\(782\) | − | 8.67970i | − | 0.310386i | ||||||
\(783\) | 38.9638i | 1.39245i | ||||||||
\(784\) | 15.9381 | 0.569217 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.12525 | −0.218480 | ||||||||
\(787\) | 28.0910 | 1.00134 | 0.500669 | − | 0.865639i | \(-0.333088\pi\) | ||||
0.500669 | + | 0.865639i | \(0.333088\pi\) | |||||||
\(788\) | −4.22797 | −0.150615 | ||||||||
\(789\) | −3.52890 | −0.125632 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.66246i | 0.236890i | ||||||||
\(792\) | − | 12.1177i | − | 0.430583i | ||||||
\(793\) | 10.7123 | 0.380407 | ||||||||
\(794\) | − | 9.84444i | − | 0.349366i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 17.7545i | − | 0.629290i | ||||||
\(797\) | − | 1.36472i | − | 0.0483407i | −0.999708 | − | 0.0241704i | \(-0.992306\pi\) | ||
0.999708 | − | 0.0241704i | \(-0.00769441\pi\) | |||||||
\(798\) | −34.6886 | −1.22796 | ||||||||
\(799\) | 21.3744i | 0.756173i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.1179i | 0.604831i | ||||||||
\(802\) | −31.0959 | −1.09803 | ||||||||
\(803\) | 54.2119 | 1.91310 | ||||||||
\(804\) | −3.75060 | −0.132273 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 11.3243i | − | 0.398881i | ||||||
\(807\) | −0.453381 | −0.0159598 | ||||||||
\(808\) | − | 2.30416i | − | 0.0810600i | ||||||
\(809\) | − | 0.636644i | − | 0.0223832i | −0.999937 | − | 0.0111916i | \(-0.996438\pi\) | ||
0.999937 | − | 0.0111916i | \(-0.00356247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3776 | 0.399521 | 0.199760 | − | 0.979845i | \(-0.435984\pi\) | ||||
0.199760 | + | 0.979845i | \(0.435984\pi\) | |||||||
\(812\) | 37.5968i | 1.31939i | ||||||||
\(813\) | −28.5425 | −1.00103 | ||||||||
\(814\) | 23.7304 | − | 27.6269i | 0.831748 | − | 0.968324i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.90379i | 0.171667i | ||||||||
\(817\) | −12.9639 | −0.453549 | ||||||||
\(818\) | −38.3150 | −1.33965 | ||||||||
\(819\) | − | 33.8688i | − | 1.18347i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.1807 | −0.913711 | −0.456856 | − | 0.889541i | \(-0.651024\pi\) | ||||
−0.456856 | + | 0.889541i | \(0.651024\pi\) | |||||||
\(822\) | 8.86404i | 0.309169i | ||||||||
\(823\) | −21.7020 | −0.756485 | −0.378242 | − | 0.925707i | \(-0.623471\pi\) | ||||
−0.378242 | + | 0.925707i | \(0.623471\pi\) | |||||||
\(824\) | −11.1716 | −0.389180 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.3024 | −0.358467 | ||||||||
\(827\) | − | 7.90798i | − | 0.274988i | −0.990503 | − | 0.137494i | \(-0.956095\pi\) | ||
0.990503 | − | 0.137494i | \(-0.0439047\pi\) | |||||||
\(828\) | − | 3.53924i | − | 0.122997i | ||||||
\(829\) | 21.7391i | 0.755030i | 0.926003 | + | 0.377515i | \(0.123221\pi\) | ||||
−0.926003 | + | 0.377515i | \(0.876779\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.1785i | 0.769362i | ||||||||
\(832\) | 3.49410i | 0.121136i | ||||||||
\(833\) | − | 79.1076i | − | 2.74092i | ||||||
\(834\) | 4.98109i | 0.172481i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 43.8926i | 1.51806i | ||||||||
\(837\) | − | 16.0866i | − | 0.556035i | ||||||
\(838\) | − | 29.0183i | − | 1.00242i | ||||||
\(839\) | −11.3258 | −0.391011 | −0.195506 | − | 0.980703i | \(-0.562635\pi\) | ||||
−0.195506 | + | 0.980703i | \(0.562635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32.6231 | −1.12494 | ||||||||
\(842\) | −23.6443 | −0.814835 | ||||||||
\(843\) | 5.97639i | 0.205838i | ||||||||
\(844\) | −4.57321 | −0.157417 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.71564i | 0.299650i | ||||||||
\(847\) | −119.006 | −4.08911 | ||||||||
\(848\) | 3.66238 | 0.125767 | ||||||||
\(849\) | − | 10.7015i | − | 0.367276i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.93097 | − | 8.06906i | 0.237591 | − | 0.276604i | ||||
\(852\) | −8.37532 | −0.286934 | ||||||||
\(853\) | 48.1277i | 1.64786i | 0.566691 | + | 0.823930i | \(0.308223\pi\) | ||||
−0.566691 | + | 0.823930i | \(0.691777\pi\) | |||||||
\(854\) | 14.6834 | 0.502457 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 6.51807i | − | 0.222783i | ||||||
\(857\) | − | 40.0486i | − | 1.36803i | −0.729466 | − | 0.684017i | \(-0.760231\pi\) | ||
0.729466 | − | 0.684017i | \(-0.239769\pi\) | |||||||
\(858\) | 20.6689 | 0.705624 | ||||||||
\(859\) | 7.66509i | 0.261530i | 0.991413 | + | 0.130765i | \(0.0417433\pi\) | ||||
−0.991413 | + | 0.130765i | \(0.958257\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.51101 | −0.0855750 | ||||||||
\(862\) | 32.1126 | 1.09376 | ||||||||
\(863\) | −50.9196 | −1.73332 | −0.866662 | − | 0.498896i | \(-0.833739\pi\) | ||||
−0.866662 | + | 0.498896i | \(0.833739\pi\) | |||||||
\(864\) | 4.96352i | 0.168862i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.0575i | 0.443712i | ||||||||
\(867\) | 7.54391 | 0.256205 | ||||||||
\(868\) | − | 15.5222i | − | 0.526859i | ||||||
\(869\) | 33.3267i | 1.13053i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.2644i | 0.449446i | ||||||||
\(872\) | −1.33812 | −0.0453146 | ||||||||
\(873\) | 7.38208i | 0.249846i | ||||||||
\(874\) | 12.8198i | 0.433636i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.94565 | −0.302245 | ||||||||
\(877\) | 2.50813 | 0.0846937 | 0.0423468 | − | 0.999103i | \(-0.486517\pi\) | ||||
0.0423468 | + | 0.999103i | \(0.486517\pi\) | |||||||
\(878\) | 28.0499 | 0.946640 | ||||||||
\(879\) | −23.0342 | −0.776925 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.0074 | 0.808829 | 0.404414 | − | 0.914576i | \(-0.367475\pi\) | ||||
0.404414 | + | 0.914576i | \(0.367475\pi\) | |||||||
\(882\) | − | 32.2569i | − | 1.08615i | ||||||
\(883\) | − | 34.7959i | − | 1.17098i | −0.810681 | − | 0.585488i | \(-0.800903\pi\) | ||
0.810681 | − | 0.585488i | \(-0.199097\pi\) | |||||||
\(884\) | 17.3427 | 0.583299 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 6.79629i | − | 0.228326i | ||||||
\(887\) | −0.672248 | −0.0225719 | −0.0112859 | − | 0.999936i | \(-0.503592\pi\) | ||||
−0.0112859 | + | 0.999936i | \(0.503592\pi\) | |||||||
\(888\) | −3.91580 | + | 4.55879i | −0.131406 | + | 0.152983i | ||||
\(889\) | 35.9693 | 1.20637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.99198 | −0.234240 | ||||||||
\(892\) | −20.3205 | −0.680380 | ||||||||
\(893\) | − | 31.5698i | − | 1.05644i | ||||||
\(894\) | − | 21.3850i | − | 0.715222i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.78937i | 0.160002i | ||||||||
\(897\) | 6.03681 | 0.201563 | ||||||||
\(898\) | 17.3278 | 0.578235 | ||||||||
\(899\) | 25.4418 | 0.848531 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 18.1780i | − | 0.605597i | ||||||
\(902\) | 3.17726i | 0.105791i | ||||||||
\(903\) | 8.36767i | 0.278459i | ||||||||
\(904\) | −1.39109 | −0.0462671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 6.39762i | − | 0.212547i | ||||||
\(907\) | 36.6618i | 1.21734i | 0.793425 | + | 0.608668i | \(0.208296\pi\) | ||||
−0.793425 | + | 0.608668i | \(0.791704\pi\) | |||||||
\(908\) | − | 5.74303i | − | 0.190589i | ||||||
\(909\) | −4.66336 | −0.154674 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 20.5358i | − | 0.680381i | −0.940356 | − | 0.340191i | \(-0.889508\pi\) | ||
0.940356 | − | 0.340191i | \(-0.110492\pi\) | |||||||
\(912\) | − | 7.24283i | − | 0.239834i | ||||||
\(913\) | −22.6129 | −0.748378 | ||||||||
\(914\) | 3.20960 | 0.106164 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.4383 | 0.774423 | ||||||||
\(917\) | 29.6929i | 0.980546i | ||||||||
\(918\) | 24.6361 | 0.813112 | ||||||||
\(919\) | 42.3926i | 1.39840i | 0.714925 | + | 0.699202i | \(0.246461\pi\) | ||||
−0.714925 | + | 0.699202i | \(0.753539\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0937 | 0.464403 | ||||||||
\(922\) | 34.0347 | 1.12087 | ||||||||
\(923\) | 29.6201i | 0.974958i | ||||||||
\(924\) | 28.3309 | 0.932019 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26.0543 | −0.856197 | ||||||||
\(927\) | 22.6100i | 0.742610i | ||||||||
\(928\) | −7.85004 | −0.257690 | ||||||||
\(929\) | −1.22700 | −0.0402565 | −0.0201282 | − | 0.999797i | \(-0.506407\pi\) | ||||
−0.0201282 | + | 0.999797i | \(0.506407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 116.841i | 3.82930i | ||||||||
\(932\) | 17.2961 | 0.566551 | ||||||||
\(933\) | 22.2614i | 0.728806i | ||||||||
\(934\) | −20.3289 | −0.665183 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.07167 | 0.231145 | ||||||||
\(937\) | 31.9456 | 1.04362 | 0.521808 | − | 0.853063i | \(-0.325258\pi\) | ||||
0.521808 | + | 0.853063i | \(0.325258\pi\) | |||||||
\(938\) | 18.1815i | 0.593647i | ||||||||
\(939\) | 9.87983i | 0.322416i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.72808 | 0.219329 | 0.109665 | − | 0.993969i | \(-0.465022\pi\) | ||||
0.109665 | + | 0.993969i | \(0.465022\pi\) | |||||||
\(942\) | 13.0106i | 0.423909i | ||||||||
\(943\) | 0.927990i | 0.0302195i | ||||||||
\(944\) | − | 2.15110i | − | 0.0700123i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.5879 | 0.344242 | ||||||||
\(947\) | 3.77013i | 0.122513i | 0.998122 | + | 0.0612564i | \(0.0195107\pi\) | ||||
−0.998122 | + | 0.0612564i | \(0.980489\pi\) | |||||||
\(948\) | − | 5.49933i | − | 0.178610i | ||||||
\(949\) | 31.6372i | 1.02699i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.2389 | −0.396872 | ||||||||
\(952\) | 23.7717 | 0.770446 | ||||||||
\(953\) | 13.7237 | 0.444553 | 0.222276 | − | 0.974984i | \(-0.428651\pi\) | ||||
0.222276 | + | 0.974984i | \(0.428651\pi\) | |||||||
\(954\) | − | 7.41226i | − | 0.239981i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 3.68796i | − | 0.119277i | ||||||
\(957\) | 46.4359i | 1.50106i | ||||||||
\(958\) | 6.22972 | 0.201273 | ||||||||
\(959\) | 42.9696 | 1.38756 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.4961 | 0.661164 | ||||||||
\(962\) | 16.1226 | + | 13.8486i | 0.519814 | + | 0.446498i | ||||
\(963\) | −13.1919 | −0.425102 | ||||||||
\(964\) | 11.3613i | 0.365922i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.27467 | 0.266233 | ||||||||
\(967\) | − | 43.7304i | − | 1.40627i | −0.711055 | − | 0.703137i | \(-0.751782\pi\) | ||
0.711055 | − | 0.703137i | \(-0.248218\pi\) | |||||||
\(968\) | − | 24.8480i | − | 0.798646i | ||||||
\(969\) | −35.9493 | −1.15486 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.2807 | 1.16430 | 0.582151 | − | 0.813081i | \(-0.302211\pi\) | ||||
0.582151 | + | 0.813081i | \(0.302211\pi\) | |||||||
\(972\) | 16.0443 | 0.514622 | ||||||||
\(973\) | 24.1465 | 0.774100 | ||||||||
\(974\) | −30.5352 | −0.978410 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.06584i | 0.0981351i | ||||||||
\(977\) | − | 29.6513i | − | 0.948628i | −0.880356 | − | 0.474314i | \(-0.842696\pi\) | ||
0.880356 | − | 0.474314i | \(-0.157304\pi\) | |||||||
\(978\) | 18.5396 | 0.592829 | ||||||||
\(979\) | 50.6402i | 1.61847i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.70822i | 0.0864667i | ||||||||
\(982\) | 24.5944i | 0.784839i | ||||||||
\(983\) | 42.0082 | 1.33985 | 0.669927 | − | 0.742427i | \(-0.266325\pi\) | ||||
0.669927 | + | 0.742427i | \(0.266325\pi\) | |||||||
\(984\) | − | 0.524288i | − | 0.0167137i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 38.9632i | 1.24084i | ||||||||
\(987\) | −20.3770 | −0.648607 | ||||||||
\(988\) | −25.6150 | −0.814921 | ||||||||
\(989\) | 3.09243 | 0.0983334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 20.7399i | − | 0.658824i | −0.944186 | − | 0.329412i | \(-0.893149\pi\) | ||
0.944186 | − | 0.329412i | \(-0.106851\pi\) | |||||||
\(992\) | 3.24097 | 0.102901 | ||||||||
\(993\) | − | 18.7784i | − | 0.595915i | ||||||
\(994\) | 40.6004i | 1.28777i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.73141 | 0.118234 | ||||||||
\(997\) | − | 16.0224i | − | 0.507435i | −0.967278 | − | 0.253718i | \(-0.918347\pi\) | ||
0.967278 | − | 0.253718i | \(-0.0816534\pi\) | |||||||
\(998\) | 33.5739 | 1.06276 | ||||||||
\(999\) | 22.9029 | + | 19.6726i | 0.724614 | + | 0.622413i |
(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 | 1850.2.d.i.1701.14 | 20 | ||
5.2 | odd | 4 | 370.2.c.a.369.7 | yes | 10 | ||
5.3 | odd | 4 | 370.2.c.b.369.4 | yes | 10 | ||
5.4 | even | 2 | inner | 1850.2.d.i.1701.7 | 20 | ||
15.2 | even | 4 | 3330.2.e.d.739.9 | 10 | |||
15.8 | even | 4 | 3330.2.e.c.739.1 | 10 | |||
37.36 | even | 2 | inner | 1850.2.d.i.1701.4 | 20 | ||
185.73 | odd | 4 | 370.2.c.a.369.4 | ✓ | 10 | ||
185.147 | odd | 4 | 370.2.c.b.369.7 | yes | 10 | ||
185.184 | even | 2 | inner | 1850.2.d.i.1701.17 | 20 | ||
555.332 | even | 4 | 3330.2.e.c.739.2 | 10 | |||
555.443 | even | 4 | 3330.2.e.d.739.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.c.a.369.4 | ✓ | 10 | 185.73 | odd | 4 | ||
370.2.c.a.369.7 | yes | 10 | 5.2 | odd | 4 | ||
370.2.c.b.369.4 | yes | 10 | 5.3 | odd | 4 | ||
370.2.c.b.369.7 | yes | 10 | 185.147 | odd | 4 | ||
1850.2.d.i.1701.4 | 20 | 37.36 | even | 2 | inner | ||
1850.2.d.i.1701.7 | 20 | 5.4 | even | 2 | inner | ||
1850.2.d.i.1701.14 | 20 | 1.1 | even | 1 | trivial | ||
1850.2.d.i.1701.17 | 20 | 185.184 | even | 2 | inner | ||
3330.2.e.c.739.1 | 10 | 15.8 | even | 4 | |||
3330.2.e.c.739.2 | 10 | 555.332 | even | 4 | |||
3330.2.e.d.739.9 | 10 | 15.2 | even | 4 | |||
3330.2.e.d.739.10 | 10 | 555.443 | even | 4 |