Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.4 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.z.1351.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | − 3.69202i | − 1.39545i | −0.716364 | − | 0.697726i | \(-0.754195\pi\) | ||||
0.716364 | − | 0.697726i | \(-0.245805\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.04892i | 0.919283i | 0.888105 | + | 0.459642i | \(0.152022\pi\) | ||||
−0.888105 | + | 0.459642i | \(0.847978\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.69202 | 0.986734 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.85086 | 1.66158 | 0.830788 | − | 0.556589i | \(-0.187890\pi\) | ||||
0.830788 | + | 0.556589i | \(0.187890\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0.911854i | 0.209194i | 0.994515 | + | 0.104597i | \(0.0333552\pi\) | ||||
−0.994515 | + | 0.104597i | \(0.966645\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | − 3.69202i | − 0.805665i | ||||||||
\(22\) | −3.04892 | −0.650031 | ||||||||
\(23\) | 0.356896 | 0.0744179 | 0.0372090 | − | 0.999308i | \(-0.488153\pi\) | ||||
0.0372090 | + | 0.999308i | \(0.488153\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.69202i | 0.697726i | ||||||||
\(29\) | 10.5036 | 1.95048 | 0.975239 | − | 0.221153i | \(-0.0709819\pi\) | ||||
0.975239 | + | 0.221153i | \(0.0709819\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 2.06100i | 0.370166i | 0.982723 | + | 0.185083i | \(0.0592555\pi\) | ||||
−0.982723 | + | 0.185083i | \(0.940745\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 3.04892i | 0.530748i | ||||||||
\(34\) | 6.85086i | 1.17491i | ||||||||
\(35\) | −3.69202 | −0.624066 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.899772i | 0.147922i | 0.997261 | + | 0.0739608i | \(0.0235640\pi\) | ||||
−0.997261 | + | 0.0739608i | \(0.976436\pi\) | |||||||
\(38\) | −0.911854 | −0.147922 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 10.2959i | 1.60795i | 0.594664 | + | 0.803974i | \(0.297285\pi\) | ||||
−0.594664 | + | 0.803974i | \(0.702715\pi\) | |||||||
\(42\) | 3.69202 | 0.569691 | ||||||||
\(43\) | −9.43296 | −1.43851 | −0.719256 | − | 0.694745i | \(-0.755517\pi\) | ||||
−0.719256 | + | 0.694745i | \(0.755517\pi\) | |||||||
\(44\) | − 3.04892i | − 0.459642i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | 0.356896i | 0.0526214i | ||||||||
\(47\) | − 11.5918i | − 1.69084i | −0.534105 | − | 0.845418i | \(-0.679351\pi\) | ||||
0.534105 | − | 0.845418i | \(-0.320649\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.63102 | −0.947289 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 6.85086 | 0.959312 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.40581 | −0.467824 | −0.233912 | − | 0.972258i | \(-0.575153\pi\) | ||||
−0.233912 | + | 0.972258i | \(0.575153\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 3.04892 | 0.411116 | ||||||||
\(56\) | −3.69202 | −0.493367 | ||||||||
\(57\) | 0.911854i | 0.120778i | ||||||||
\(58\) | 10.5036i | 1.37920i | ||||||||
\(59\) | − 8.54288i | − 1.11219i | −0.831119 | − | 0.556094i | \(-0.812299\pi\) | ||||
0.831119 | − | 0.556094i | \(-0.187701\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 1.55496 | 0.199092 | 0.0995460 | − | 0.995033i | \(-0.468261\pi\) | ||||
0.0995460 | + | 0.995033i | \(0.468261\pi\) | |||||||
\(62\) | −2.06100 | −0.261747 | ||||||||
\(63\) | − 3.69202i | − 0.465151i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.04892 | −0.375296 | ||||||||
\(67\) | 1.14914i | 0.140390i | 0.997533 | + | 0.0701952i | \(0.0223622\pi\) | ||||
−0.997533 | + | 0.0701952i | \(0.977638\pi\) | |||||||
\(68\) | −6.85086 | −0.830788 | ||||||||
\(69\) | 0.356896 | 0.0429652 | ||||||||
\(70\) | − 3.69202i | − 0.441281i | ||||||||
\(71\) | − 4.13706i | − 0.490979i | −0.969399 | − | 0.245490i | \(-0.921051\pi\) | ||||
0.969399 | − | 0.245490i | \(-0.0789487\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 11.1685i | − 1.30718i | −0.756850 | − | 0.653588i | \(-0.773263\pi\) | ||||
0.756850 | − | 0.653588i | \(-0.226737\pi\) | |||||||
\(74\) | −0.899772 | −0.104596 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | − 0.911854i | − 0.104597i | ||||||||
\(77\) | 11.2567 | 1.28282 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.62565 | 1.08297 | 0.541485 | − | 0.840710i | \(-0.317862\pi\) | ||||
0.541485 | + | 0.840710i | \(0.317862\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.2959 | −1.13699 | ||||||||
\(83\) | − 9.86054i | − 1.08234i | −0.840915 | − | 0.541168i | \(-0.817982\pi\) | ||||
0.840915 | − | 0.541168i | \(-0.182018\pi\) | |||||||
\(84\) | 3.69202i | 0.402833i | ||||||||
\(85\) | − 6.85086i | − 0.743080i | ||||||||
\(86\) | − 9.43296i | − 1.01718i | ||||||||
\(87\) | 10.5036 | 1.12611 | ||||||||
\(88\) | 3.04892 | 0.325016 | ||||||||
\(89\) | 6.41119i | 0.679585i | 0.940500 | + | 0.339792i | \(0.110357\pi\) | ||||
−0.940500 | + | 0.339792i | \(0.889643\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.356896 | −0.0372090 | ||||||||
\(93\) | 2.06100i | 0.213716i | ||||||||
\(94\) | 11.5918 | 1.19560 | ||||||||
\(95\) | 0.911854 | 0.0935542 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 6.97823i | 0.708532i | 0.935145 | + | 0.354266i | \(0.115269\pi\) | ||||
−0.935145 | + | 0.354266i | \(0.884731\pi\) | |||||||
\(98\) | − 6.63102i | − 0.669834i | ||||||||
\(99\) | 3.04892i | 0.306428i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.09783 | 0.407750 | 0.203875 | − | 0.978997i | \(-0.434646\pi\) | ||||
0.203875 | + | 0.978997i | \(0.434646\pi\) | |||||||
\(102\) | 6.85086i | 0.678336i | ||||||||
\(103\) | 16.9215 | 1.66733 | 0.833665 | − | 0.552271i | \(-0.186239\pi\) | ||||
0.833665 | + | 0.552271i | \(0.186239\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.69202 | −0.360304 | ||||||||
\(106\) | − 3.40581i | − 0.330802i | ||||||||
\(107\) | −12.7192 | −1.22961 | −0.614804 | − | 0.788680i | \(-0.710765\pi\) | ||||
−0.614804 | + | 0.788680i | \(0.710765\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 19.9922i | 1.91491i | 0.288585 | + | 0.957454i | \(0.406815\pi\) | ||||
−0.288585 | + | 0.957454i | \(0.593185\pi\) | |||||||
\(110\) | 3.04892i | 0.290703i | ||||||||
\(111\) | 0.899772i | 0.0854026i | ||||||||
\(112\) | − 3.69202i | − 0.348863i | ||||||||
\(113\) | −4.49934 | −0.423262 | −0.211631 | − | 0.977350i | \(-0.567877\pi\) | ||||
−0.211631 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(114\) | −0.911854 | −0.0854030 | ||||||||
\(115\) | − 0.356896i | − 0.0332807i | ||||||||
\(116\) | −10.5036 | −0.975239 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.54288 | 0.786436 | ||||||||
\(119\) | − 25.2935i | − 2.31865i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 1.70410 | 0.154918 | ||||||||
\(122\) | 1.55496i | 0.140779i | ||||||||
\(123\) | 10.2959i | 0.928350i | ||||||||
\(124\) | − 2.06100i | − 0.185083i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 3.69202 | 0.328911 | ||||||||
\(127\) | 7.08815 | 0.628971 | 0.314486 | − | 0.949262i | \(-0.398168\pi\) | ||||
0.314486 | + | 0.949262i | \(0.398168\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −9.43296 | −0.830526 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7506 | 1.72562 | 0.862810 | − | 0.505528i | \(-0.168702\pi\) | ||||
0.862810 | + | 0.505528i | \(0.168702\pi\) | |||||||
\(132\) | − 3.04892i | − 0.265374i | ||||||||
\(133\) | 3.36658 | 0.291920 | ||||||||
\(134\) | −1.14914 | −0.0992710 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | − 6.85086i | − 0.587456i | ||||||||
\(137\) | 7.94331i | 0.678643i | 0.940670 | + | 0.339322i | \(0.110197\pi\) | ||||
−0.940670 | + | 0.339322i | \(0.889803\pi\) | |||||||
\(138\) | 0.356896i | 0.0303810i | ||||||||
\(139\) | −1.71379 | −0.145362 | −0.0726810 | − | 0.997355i | \(-0.523155\pi\) | ||||
−0.0726810 | + | 0.997355i | \(0.523155\pi\) | |||||||
\(140\) | 3.69202 | 0.312033 | ||||||||
\(141\) | − 11.5918i | − 0.976205i | ||||||||
\(142\) | 4.13706 | 0.347175 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 10.5036i | − 0.872280i | ||||||||
\(146\) | 11.1685 | 0.924313 | ||||||||
\(147\) | −6.63102 | −0.546918 | ||||||||
\(148\) | − 0.899772i | − 0.0739608i | ||||||||
\(149\) | − 6.91185i | − 0.566241i | −0.959084 | − | 0.283121i | \(-0.908630\pi\) | ||||
0.959084 | − | 0.283121i | \(-0.0913697\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | − 5.43296i | − 0.442128i | −0.975259 | − | 0.221064i | \(-0.929047\pi\) | ||||
0.975259 | − | 0.221064i | \(-0.0709530\pi\) | |||||||
\(152\) | 0.911854 | 0.0739611 | ||||||||
\(153\) | 6.85086 | 0.553859 | ||||||||
\(154\) | 11.2567i | 0.907088i | ||||||||
\(155\) | 2.06100 | 0.165543 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.13706 | −0.729217 | −0.364609 | − | 0.931161i | \(-0.618797\pi\) | ||||
−0.364609 | + | 0.931161i | \(0.618797\pi\) | |||||||
\(158\) | 9.62565i | 0.765775i | ||||||||
\(159\) | −3.40581 | −0.270099 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | − 1.31767i | − 0.103847i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − 14.3773i | − 1.12612i | −0.826416 | − | 0.563060i | \(-0.809624\pi\) | ||||
0.826416 | − | 0.563060i | \(-0.190376\pi\) | |||||||
\(164\) | − 10.2959i | − 0.803974i | ||||||||
\(165\) | 3.04892 | 0.237358 | ||||||||
\(166\) | 9.86054 | 0.765327 | ||||||||
\(167\) | 3.00538i | 0.232563i | 0.993216 | + | 0.116282i | \(0.0370975\pi\) | ||||
−0.993216 | + | 0.116282i | \(0.962903\pi\) | |||||||
\(168\) | −3.69202 | −0.284846 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.85086 | 0.525437 | ||||||||
\(171\) | 0.911854i | 0.0697312i | ||||||||
\(172\) | 9.43296 | 0.719256 | ||||||||
\(173\) | −6.89546 | −0.524252 | −0.262126 | − | 0.965034i | \(-0.584424\pi\) | ||||
−0.262126 | + | 0.965034i | \(0.584424\pi\) | |||||||
\(174\) | 10.5036i | 0.796279i | ||||||||
\(175\) | 3.69202i | 0.279091i | ||||||||
\(176\) | 3.04892i | 0.229821i | ||||||||
\(177\) | − 8.54288i | − 0.642122i | ||||||||
\(178\) | −6.41119 | −0.480539 | ||||||||
\(179\) | 25.6461 | 1.91688 | 0.958439 | − | 0.285296i | \(-0.0920921\pi\) | ||||
0.958439 | + | 0.285296i | \(0.0920921\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 25.8092 | 1.91839 | 0.959193 | − | 0.282753i | \(-0.0912478\pi\) | ||||
0.959193 | + | 0.282753i | \(0.0912478\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.55496 | 0.114946 | ||||||||
\(184\) | − 0.356896i | − 0.0263107i | ||||||||
\(185\) | 0.899772 | 0.0661526 | ||||||||
\(186\) | −2.06100 | −0.151120 | ||||||||
\(187\) | 20.8877i | 1.52746i | ||||||||
\(188\) | 11.5918i | 0.845418i | ||||||||
\(189\) | − 3.69202i | − 0.268555i | ||||||||
\(190\) | 0.911854i | 0.0661528i | ||||||||
\(191\) | −14.5700 | −1.05425 | −0.527125 | − | 0.849788i | \(-0.676730\pi\) | ||||
−0.527125 | + | 0.849788i | \(0.676730\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − 8.32544i | − 0.599278i | −0.954053 | − | 0.299639i | \(-0.903134\pi\) | ||||
0.954053 | − | 0.299639i | \(-0.0968662\pi\) | |||||||
\(194\) | −6.97823 | −0.501008 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.63102 | 0.473644 | ||||||||
\(197\) | − 26.8810i | − 1.91519i | −0.288116 | − | 0.957595i | \(-0.593029\pi\) | ||||
0.288116 | − | 0.957595i | \(-0.406971\pi\) | |||||||
\(198\) | −3.04892 | −0.216677 | ||||||||
\(199\) | 18.7047 | 1.32594 | 0.662970 | − | 0.748646i | \(-0.269296\pi\) | ||||
0.662970 | + | 0.748646i | \(0.269296\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 1.14914i | 0.0810544i | ||||||||
\(202\) | 4.09783i | 0.288323i | ||||||||
\(203\) | − 38.7797i | − 2.72180i | ||||||||
\(204\) | −6.85086 | −0.479656 | ||||||||
\(205\) | 10.2959 | 0.719097 | ||||||||
\(206\) | 16.9215i | 1.17898i | ||||||||
\(207\) | 0.356896 | 0.0248060 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.78017 | −0.192308 | ||||||||
\(210\) | − 3.69202i | − 0.254774i | ||||||||
\(211\) | 2.93362 | 0.201959 | 0.100980 | − | 0.994889i | \(-0.467802\pi\) | ||||
0.100980 | + | 0.994889i | \(0.467802\pi\) | |||||||
\(212\) | 3.40581 | 0.233912 | ||||||||
\(213\) | − 4.13706i | − 0.283467i | ||||||||
\(214\) | − 12.7192i | − 0.869464i | ||||||||
\(215\) | 9.43296i | 0.643323i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 7.60925 | 0.516550 | ||||||||
\(218\) | −19.9922 | −1.35404 | ||||||||
\(219\) | − 11.1685i | − 0.754699i | ||||||||
\(220\) | −3.04892 | −0.205558 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.899772 | −0.0603888 | ||||||||
\(223\) | − 18.1444i | − 1.21504i | −0.794306 | − | 0.607518i | \(-0.792165\pi\) | ||||
0.794306 | − | 0.607518i | \(-0.207835\pi\) | |||||||
\(224\) | 3.69202 | 0.246684 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 4.49934i | − 0.299291i | ||||||||
\(227\) | 12.3056i | 0.816750i | 0.912814 | + | 0.408375i | \(0.133904\pi\) | ||||
−0.912814 | + | 0.408375i | \(0.866096\pi\) | |||||||
\(228\) | − 0.911854i | − 0.0603890i | ||||||||
\(229\) | − 4.64848i | − 0.307180i | −0.988135 | − | 0.153590i | \(-0.950916\pi\) | ||||
0.988135 | − | 0.153590i | \(-0.0490835\pi\) | |||||||
\(230\) | 0.356896 | 0.0235330 | ||||||||
\(231\) | 11.2567 | 0.740634 | ||||||||
\(232\) | − 10.5036i | − 0.689598i | ||||||||
\(233\) | −0.658170 | −0.0431181 | −0.0215591 | − | 0.999768i | \(-0.506863\pi\) | ||||
−0.0215591 | + | 0.999768i | \(0.506863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.5918 | −0.756165 | ||||||||
\(236\) | 8.54288i | 0.556094i | ||||||||
\(237\) | 9.62565 | 0.625253 | ||||||||
\(238\) | 25.2935 | 1.63953 | ||||||||
\(239\) | − 18.7748i | − 1.21444i | −0.794534 | − | 0.607220i | \(-0.792285\pi\) | ||||
0.794534 | − | 0.607220i | \(-0.207715\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | − 18.0271i | − 1.16123i | −0.814178 | − | 0.580615i | \(-0.802812\pi\) | ||||
0.814178 | − | 0.580615i | \(-0.197188\pi\) | |||||||
\(242\) | 1.70410i | 0.109544i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.55496 | −0.0995460 | ||||||||
\(245\) | 6.63102i | 0.423640i | ||||||||
\(246\) | −10.2959 | −0.656442 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.06100 | 0.130874 | ||||||||
\(249\) | − 9.86054i | − 0.624887i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 2.18060 | 0.137638 | 0.0688192 | − | 0.997629i | \(-0.478077\pi\) | ||||
0.0688192 | + | 0.997629i | \(0.478077\pi\) | |||||||
\(252\) | 3.69202i | 0.232575i | ||||||||
\(253\) | 1.08815i | 0.0684112i | ||||||||
\(254\) | 7.08815i | 0.444750i | ||||||||
\(255\) | − 6.85086i | − 0.429017i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.58748 | 0.598051 | 0.299025 | − | 0.954245i | \(-0.403338\pi\) | ||||
0.299025 | + | 0.954245i | \(0.403338\pi\) | |||||||
\(258\) | − 9.43296i | − 0.587270i | ||||||||
\(259\) | 3.32198 | 0.206418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5036 | 0.650159 | ||||||||
\(262\) | 19.7506i | 1.22020i | ||||||||
\(263\) | −1.41789 | −0.0874311 | −0.0437156 | − | 0.999044i | \(-0.513920\pi\) | ||||
−0.0437156 | + | 0.999044i | \(0.513920\pi\) | |||||||
\(264\) | 3.04892 | 0.187648 | ||||||||
\(265\) | 3.40581i | 0.209217i | ||||||||
\(266\) | 3.36658i | 0.206419i | ||||||||
\(267\) | 6.41119i | 0.392358i | ||||||||
\(268\) | − 1.14914i | − 0.0701952i | ||||||||
\(269\) | −4.14675 | −0.252832 | −0.126416 | − | 0.991977i | \(-0.540347\pi\) | ||||
−0.126416 | + | 0.991977i | \(0.540347\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 6.40044i | − 0.388799i | −0.980922 | − | 0.194399i | \(-0.937724\pi\) | ||||
0.980922 | − | 0.194399i | \(-0.0622758\pi\) | |||||||
\(272\) | 6.85086 | 0.415394 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.94331 | −0.479873 | ||||||||
\(275\) | − 3.04892i | − 0.183857i | ||||||||
\(276\) | −0.356896 | −0.0214826 | ||||||||
\(277\) | −10.3394 | −0.621237 | −0.310618 | − | 0.950535i | \(-0.600536\pi\) | ||||
−0.310618 | + | 0.950535i | \(0.600536\pi\) | |||||||
\(278\) | − 1.71379i | − 0.102786i | ||||||||
\(279\) | 2.06100i | 0.123389i | ||||||||
\(280\) | 3.69202i | 0.220640i | ||||||||
\(281\) | − 5.08144i | − 0.303133i | −0.988447 | − | 0.151567i | \(-0.951568\pi\) | ||||
0.988447 | − | 0.151567i | \(-0.0484318\pi\) | |||||||
\(282\) | 11.5918 | 0.690281 | ||||||||
\(283\) | −24.5284 | −1.45806 | −0.729031 | − | 0.684481i | \(-0.760029\pi\) | ||||
−0.729031 | + | 0.684481i | \(0.760029\pi\) | |||||||
\(284\) | 4.13706i | 0.245490i | ||||||||
\(285\) | 0.911854 | 0.0540136 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.0127 | 2.24382 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 29.9342 | 1.76084 | ||||||||
\(290\) | 10.5036 | 0.616795 | ||||||||
\(291\) | 6.97823i | 0.409071i | ||||||||
\(292\) | 11.1685i | 0.653588i | ||||||||
\(293\) | − 15.8538i | − 0.926191i | −0.886308 | − | 0.463096i | \(-0.846739\pi\) | ||||
0.886308 | − | 0.463096i | \(-0.153261\pi\) | |||||||
\(294\) | − 6.63102i | − 0.386729i | ||||||||
\(295\) | −8.54288 | −0.497386 | ||||||||
\(296\) | 0.899772 | 0.0522982 | ||||||||
\(297\) | 3.04892i | 0.176916i | ||||||||
\(298\) | 6.91185 | 0.400393 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 34.8267i | 2.00738i | ||||||||
\(302\) | 5.43296 | 0.312632 | ||||||||
\(303\) | 4.09783 | 0.235414 | ||||||||
\(304\) | 0.911854i | 0.0522984i | ||||||||
\(305\) | − 1.55496i | − 0.0890366i | ||||||||
\(306\) | 6.85086i | 0.391637i | ||||||||
\(307\) | 14.2121i | 0.811125i | 0.914067 | + | 0.405563i | \(0.132924\pi\) | ||||
−0.914067 | + | 0.405563i | \(0.867076\pi\) | |||||||
\(308\) | −11.2567 | −0.641408 | ||||||||
\(309\) | 16.9215 | 0.962633 | ||||||||
\(310\) | 2.06100i | 0.117057i | ||||||||
\(311\) | −15.0127 | −0.851291 | −0.425645 | − | 0.904890i | \(-0.639953\pi\) | ||||
−0.425645 | + | 0.904890i | \(0.639953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4993 | −0.763028 | −0.381514 | − | 0.924363i | \(-0.624597\pi\) | ||||
−0.381514 | + | 0.924363i | \(0.624597\pi\) | |||||||
\(314\) | − 9.13706i | − 0.515634i | ||||||||
\(315\) | −3.69202 | −0.208022 | ||||||||
\(316\) | −9.62565 | −0.541485 | ||||||||
\(317\) | 33.9463i | 1.90661i | 0.302003 | + | 0.953307i | \(0.402345\pi\) | ||||
−0.302003 | + | 0.953307i | \(0.597655\pi\) | |||||||
\(318\) | − 3.40581i | − 0.190989i | ||||||||
\(319\) | 32.0248i | 1.79304i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −12.7192 | −0.709915 | ||||||||
\(322\) | 1.31767 | 0.0734307 | ||||||||
\(323\) | 6.24698i | 0.347591i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.3773 | 0.796287 | ||||||||
\(327\) | 19.9922i | 1.10557i | ||||||||
\(328\) | 10.2959 | 0.568496 | ||||||||
\(329\) | −42.7972 | −2.35948 | ||||||||
\(330\) | 3.04892i | 0.167837i | ||||||||
\(331\) | − 6.84415i | − 0.376189i | −0.982151 | − | 0.188094i | \(-0.939769\pi\) | ||||
0.982151 | − | 0.188094i | \(-0.0602310\pi\) | |||||||
\(332\) | 9.86054i | 0.541168i | ||||||||
\(333\) | 0.899772i | 0.0493072i | ||||||||
\(334\) | −3.00538 | −0.164447 | ||||||||
\(335\) | 1.14914 | 0.0627845 | ||||||||
\(336\) | − 3.69202i | − 0.201416i | ||||||||
\(337\) | −27.7332 | −1.51072 | −0.755361 | − | 0.655309i | \(-0.772538\pi\) | ||||
−0.755361 | + | 0.655309i | \(0.772538\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.49934 | −0.244370 | ||||||||
\(340\) | 6.85086i | 0.371540i | ||||||||
\(341\) | −6.28382 | −0.340288 | ||||||||
\(342\) | −0.911854 | −0.0493074 | ||||||||
\(343\) | − 1.36227i | − 0.0735558i | ||||||||
\(344\) | 9.43296i | 0.508591i | ||||||||
\(345\) | − 0.356896i | − 0.0192146i | ||||||||
\(346\) | − 6.89546i | − 0.370702i | ||||||||
\(347\) | −10.4862 | −0.562928 | −0.281464 | − | 0.959572i | \(-0.590820\pi\) | ||||
−0.281464 | + | 0.959572i | \(0.590820\pi\) | |||||||
\(348\) | −10.5036 | −0.563055 | ||||||||
\(349\) | 8.13467i | 0.435439i | 0.976011 | + | 0.217719i | \(0.0698618\pi\) | ||||
−0.976011 | + | 0.217719i | \(0.930138\pi\) | |||||||
\(350\) | −3.69202 | −0.197347 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.04892 | −0.162508 | ||||||||
\(353\) | − 25.8649i | − 1.37665i | −0.725404 | − | 0.688324i | \(-0.758347\pi\) | ||||
0.725404 | − | 0.688324i | \(-0.241653\pi\) | |||||||
\(354\) | 8.54288 | 0.454049 | ||||||||
\(355\) | −4.13706 | −0.219573 | ||||||||
\(356\) | − 6.41119i | − 0.339792i | ||||||||
\(357\) | − 25.2935i | − 1.33867i | ||||||||
\(358\) | 25.6461i | 1.35544i | ||||||||
\(359\) | 30.2959i | 1.59896i | 0.600695 | + | 0.799478i | \(0.294891\pi\) | ||||
−0.600695 | + | 0.799478i | \(0.705109\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 18.1685 | 0.956238 | ||||||||
\(362\) | 25.8092i | 1.35650i | ||||||||
\(363\) | 1.70410 | 0.0894422 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.1685 | −0.584587 | ||||||||
\(366\) | 1.55496i | 0.0812790i | ||||||||
\(367\) | −3.41013 | −0.178007 | −0.0890035 | − | 0.996031i | \(-0.528368\pi\) | ||||
−0.0890035 | + | 0.996031i | \(0.528368\pi\) | |||||||
\(368\) | 0.356896 | 0.0186045 | ||||||||
\(369\) | 10.2959i | 0.535983i | ||||||||
\(370\) | 0.899772i | 0.0467769i | ||||||||
\(371\) | 12.5743i | 0.652827i | ||||||||
\(372\) | − 2.06100i | − 0.106858i | ||||||||
\(373\) | 3.35988 | 0.173968 | 0.0869840 | − | 0.996210i | \(-0.472277\pi\) | ||||
0.0869840 | + | 0.996210i | \(0.472277\pi\) | |||||||
\(374\) | −20.8877 | −1.08008 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −11.5918 | −0.597801 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.69202 | 0.189897 | ||||||||
\(379\) | − 31.4916i | − 1.61761i | −0.588075 | − | 0.808807i | \(-0.700114\pi\) | ||||
0.588075 | − | 0.808807i | \(-0.299886\pi\) | |||||||
\(380\) | −0.911854 | −0.0467771 | ||||||||
\(381\) | 7.08815 | 0.363137 | ||||||||
\(382\) | − 14.5700i | − 0.745467i | ||||||||
\(383\) | 21.8485i | 1.11640i | 0.829705 | + | 0.558202i | \(0.188509\pi\) | ||||
−0.829705 | + | 0.558202i | \(0.811491\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | − 11.2567i | − 0.573693i | ||||||||
\(386\) | 8.32544 | 0.423754 | ||||||||
\(387\) | −9.43296 | −0.479504 | ||||||||
\(388\) | − 6.97823i | − 0.354266i | ||||||||
\(389\) | 11.3787 | 0.576921 | 0.288461 | − | 0.957492i | \(-0.406857\pi\) | ||||
0.288461 | + | 0.957492i | \(0.406857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.44504 | 0.123651 | ||||||||
\(392\) | 6.63102i | 0.334917i | ||||||||
\(393\) | 19.7506 | 0.996287 | ||||||||
\(394\) | 26.8810 | 1.35424 | ||||||||
\(395\) | − 9.62565i | − 0.484319i | ||||||||
\(396\) | − 3.04892i | − 0.153214i | ||||||||
\(397\) | − 22.0476i | − 1.10654i | −0.833003 | − | 0.553268i | \(-0.813380\pi\) | ||||
0.833003 | − | 0.553268i | \(-0.186620\pi\) | |||||||
\(398\) | 18.7047i | 0.937582i | ||||||||
\(399\) | 3.36658 | 0.168540 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 10.2459i | − 0.511657i | −0.966722 | − | 0.255828i | \(-0.917652\pi\) | ||||
0.966722 | − | 0.255828i | \(-0.0823482\pi\) | |||||||
\(402\) | −1.14914 | −0.0573141 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.09783 | −0.203875 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 38.7797 | 1.92460 | ||||||||
\(407\) | −2.74333 | −0.135982 | ||||||||
\(408\) | − 6.85086i | − 0.339168i | ||||||||
\(409\) | 22.8189i | 1.12832i | 0.825664 | + | 0.564162i | \(0.190800\pi\) | ||||
−0.825664 | + | 0.564162i | \(0.809200\pi\) | |||||||
\(410\) | 10.2959i | 0.508478i | ||||||||
\(411\) | 7.94331i | 0.391815i | ||||||||
\(412\) | −16.9215 | −0.833665 | ||||||||
\(413\) | −31.5405 | −1.55201 | ||||||||
\(414\) | 0.356896i | 0.0175405i | ||||||||
\(415\) | −9.86054 | −0.484035 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.71379 | −0.0839247 | ||||||||
\(418\) | − 2.78017i | − 0.135982i | ||||||||
\(419\) | −28.5773 | −1.39609 | −0.698047 | − | 0.716052i | \(-0.745947\pi\) | ||||
−0.698047 | + | 0.716052i | \(0.745947\pi\) | |||||||
\(420\) | 3.69202 | 0.180152 | ||||||||
\(421\) | 32.3937i | 1.57877i | 0.613896 | + | 0.789387i | \(0.289601\pi\) | ||||
−0.613896 | + | 0.789387i | \(0.710399\pi\) | |||||||
\(422\) | 2.93362i | 0.142807i | ||||||||
\(423\) | − 11.5918i | − 0.563612i | ||||||||
\(424\) | 3.40581i | 0.165401i | ||||||||
\(425\) | −6.85086 | −0.332315 | ||||||||
\(426\) | 4.13706 | 0.200441 | ||||||||
\(427\) | − 5.74094i | − 0.277824i | ||||||||
\(428\) | 12.7192 | 0.614804 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.43296 | −0.454898 | ||||||||
\(431\) | − 14.6455i | − 0.705449i | −0.935727 | − | 0.352724i | \(-0.885255\pi\) | ||||
0.935727 | − | 0.352724i | \(-0.114745\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 35.8485 | 1.72277 | 0.861384 | − | 0.507955i | \(-0.169598\pi\) | ||||
0.861384 | + | 0.507955i | \(0.169598\pi\) | |||||||
\(434\) | 7.60925i | 0.365256i | ||||||||
\(435\) | − 10.5036i | − 0.503611i | ||||||||
\(436\) | − 19.9922i | − 0.957454i | ||||||||
\(437\) | 0.325437i | 0.0155678i | ||||||||
\(438\) | 11.1685 | 0.533653 | ||||||||
\(439\) | −2.55927 | −0.122147 | −0.0610736 | − | 0.998133i | \(-0.519452\pi\) | ||||
−0.0610736 | + | 0.998133i | \(0.519452\pi\) | |||||||
\(440\) | − 3.04892i | − 0.145351i | ||||||||
\(441\) | −6.63102 | −0.315763 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.2857 | 1.10634 | 0.553169 | − | 0.833069i | \(-0.313418\pi\) | ||||
0.553169 | + | 0.833069i | \(0.313418\pi\) | |||||||
\(444\) | − 0.899772i | − 0.0427013i | ||||||||
\(445\) | 6.41119 | 0.303920 | ||||||||
\(446\) | 18.1444 | 0.859160 | ||||||||
\(447\) | − 6.91185i | − 0.326919i | ||||||||
\(448\) | 3.69202i | 0.174432i | ||||||||
\(449\) | 27.3327i | 1.28991i | 0.764220 | + | 0.644956i | \(0.223124\pi\) | ||||
−0.764220 | + | 0.644956i | \(0.776876\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | −31.3913 | −1.47816 | ||||||||
\(452\) | 4.49934 | 0.211631 | ||||||||
\(453\) | − 5.43296i | − 0.255263i | ||||||||
\(454\) | −12.3056 | −0.577530 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.911854 | 0.0427015 | ||||||||
\(457\) | − 7.74094i | − 0.362106i | −0.983473 | − | 0.181053i | \(-0.942049\pi\) | ||||
0.983473 | − | 0.181053i | \(-0.0579505\pi\) | |||||||
\(458\) | 4.64848 | 0.217209 | ||||||||
\(459\) | 6.85086 | 0.319771 | ||||||||
\(460\) | 0.356896i | 0.0166404i | ||||||||
\(461\) | 17.1511i | 0.798805i | 0.916776 | + | 0.399402i | \(0.130782\pi\) | ||||
−0.916776 | + | 0.399402i | \(0.869218\pi\) | |||||||
\(462\) | 11.2567i | 0.523708i | ||||||||
\(463\) | 34.2747i | 1.59288i | 0.604717 | + | 0.796441i | \(0.293286\pi\) | ||||
−0.604717 | + | 0.796441i | \(0.706714\pi\) | |||||||
\(464\) | 10.5036 | 0.487620 | ||||||||
\(465\) | 2.06100 | 0.0955765 | ||||||||
\(466\) | − 0.658170i | − 0.0304891i | ||||||||
\(467\) | −20.9474 | −0.969328 | −0.484664 | − | 0.874700i | \(-0.661058\pi\) | ||||
−0.484664 | + | 0.874700i | \(0.661058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.24267 | 0.195908 | ||||||||
\(470\) | − 11.5918i | − 0.534690i | ||||||||
\(471\) | −9.13706 | −0.421014 | ||||||||
\(472\) | −8.54288 | −0.393218 | ||||||||
\(473\) | − 28.7603i | − 1.32240i | ||||||||
\(474\) | 9.62565i | 0.442121i | ||||||||
\(475\) | − 0.911854i | − 0.0418387i | ||||||||
\(476\) | 25.2935i | 1.15933i | ||||||||
\(477\) | −3.40581 | −0.155941 | ||||||||
\(478\) | 18.7748 | 0.858739 | ||||||||
\(479\) | − 15.8310i | − 0.723337i | −0.932307 | − | 0.361669i | \(-0.882207\pi\) | ||||
0.932307 | − | 0.361669i | \(-0.117793\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.0271 | 0.821114 | ||||||||
\(483\) | − 1.31767i | − 0.0599559i | ||||||||
\(484\) | −1.70410 | −0.0774592 | ||||||||
\(485\) | 6.97823 | 0.316865 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 33.7060i | 1.52737i | 0.645592 | + | 0.763683i | \(0.276611\pi\) | ||||
−0.645592 | + | 0.763683i | \(0.723389\pi\) | |||||||
\(488\) | − 1.55496i | − 0.0703896i | ||||||||
\(489\) | − 14.3773i | − 0.650166i | ||||||||
\(490\) | −6.63102 | −0.299559 | ||||||||
\(491\) | −3.98925 | −0.180032 | −0.0900161 | − | 0.995940i | \(-0.528692\pi\) | ||||
−0.0900161 | + | 0.995940i | \(0.528692\pi\) | |||||||
\(492\) | − 10.2959i | − 0.464175i | ||||||||
\(493\) | 71.9590 | 3.24087 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.04892 | 0.137039 | ||||||||
\(496\) | 2.06100i | 0.0925416i | ||||||||
\(497\) | −15.2741 | −0.685138 | ||||||||
\(498\) | 9.86054 | 0.441862 | ||||||||
\(499\) | 20.4698i | 0.916354i | 0.888861 | + | 0.458177i | \(0.151497\pi\) | ||||
−0.888861 | + | 0.458177i | \(0.848503\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | 3.00538i | 0.134270i | ||||||||
\(502\) | 2.18060i | 0.0973251i | ||||||||
\(503\) | 22.5351 | 1.00479 | 0.502395 | − | 0.864638i | \(-0.332452\pi\) | ||||
0.502395 | + | 0.864638i | \(0.332452\pi\) | |||||||
\(504\) | −3.69202 | −0.164456 | ||||||||
\(505\) | − 4.09783i | − 0.182351i | ||||||||
\(506\) | −1.08815 | −0.0483740 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.08815 | −0.314486 | ||||||||
\(509\) | − 10.9718i | − 0.486316i | −0.969987 | − | 0.243158i | \(-0.921817\pi\) | ||||
0.969987 | − | 0.243158i | \(-0.0781833\pi\) | |||||||
\(510\) | 6.85086 | 0.303361 | ||||||||
\(511\) | −41.2344 | −1.82410 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.911854i | 0.0402593i | ||||||||
\(514\) | 9.58748i | 0.422886i | ||||||||
\(515\) | − 16.9215i | − 0.745652i | ||||||||
\(516\) | 9.43296 | 0.415263 | ||||||||
\(517\) | 35.3424 | 1.55436 | ||||||||
\(518\) | 3.32198i | 0.145959i | ||||||||
\(519\) | −6.89546 | −0.302677 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9691 | 0.699620 | 0.349810 | − | 0.936821i | \(-0.386246\pi\) | ||||
0.349810 | + | 0.936821i | \(0.386246\pi\) | |||||||
\(522\) | 10.5036i | 0.459732i | ||||||||
\(523\) | −24.7681 | −1.08303 | −0.541516 | − | 0.840690i | \(-0.682150\pi\) | ||||
−0.541516 | + | 0.840690i | \(0.682150\pi\) | |||||||
\(524\) | −19.7506 | −0.862810 | ||||||||
\(525\) | 3.69202i | 0.161133i | ||||||||
\(526\) | − 1.41789i | − 0.0618232i | ||||||||
\(527\) | 14.1196i | 0.615060i | ||||||||
\(528\) | 3.04892i | 0.132687i | ||||||||
\(529\) | −22.8726 | −0.994462 | ||||||||
\(530\) | −3.40581 | −0.147939 | ||||||||
\(531\) | − 8.54288i | − 0.370729i | ||||||||
\(532\) | −3.36658 | −0.145960 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.41119 | −0.277439 | ||||||||
\(535\) | 12.7192i | 0.549898i | ||||||||
\(536\) | 1.14914 | 0.0496355 | ||||||||
\(537\) | 25.6461 | 1.10671 | ||||||||
\(538\) | − 4.14675i | − 0.178779i | ||||||||
\(539\) | − 20.2174i | − 0.870827i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | − 0.460107i | − 0.0197816i | −0.999951 | − | 0.00989078i | \(-0.996852\pi\) | ||||
0.999951 | − | 0.00989078i | \(-0.00314838\pi\) | |||||||
\(542\) | 6.40044 | 0.274922 | ||||||||
\(543\) | 25.8092 | 1.10758 | ||||||||
\(544\) | 6.85086i | 0.293728i | ||||||||
\(545\) | 19.9922 | 0.856373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.70410 | −0.372161 | −0.186080 | − | 0.982535i | \(-0.559578\pi\) | ||||
−0.186080 | + | 0.982535i | \(0.559578\pi\) | |||||||
\(548\) | − 7.94331i | − 0.339322i | ||||||||
\(549\) | 1.55496 | 0.0663640 | ||||||||
\(550\) | 3.04892 | 0.130006 | ||||||||
\(551\) | 9.57779i | 0.408028i | ||||||||
\(552\) | − 0.356896i | − 0.0151905i | ||||||||
\(553\) | − 35.5381i | − 1.51123i | ||||||||
\(554\) | − 10.3394i | − 0.439281i | ||||||||
\(555\) | 0.899772 | 0.0381932 | ||||||||
\(556\) | 1.71379 | 0.0726810 | ||||||||
\(557\) | 36.7415i | 1.55679i | 0.627776 | + | 0.778394i | \(0.283966\pi\) | ||||
−0.627776 | + | 0.778394i | \(0.716034\pi\) | |||||||
\(558\) | −2.06100 | −0.0872490 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.69202 | −0.156016 | ||||||||
\(561\) | 20.8877i | 0.881879i | ||||||||
\(562\) | 5.08144 | 0.214348 | ||||||||
\(563\) | 27.7713 | 1.17042 | 0.585211 | − | 0.810881i | \(-0.301012\pi\) | ||||
0.585211 | + | 0.810881i | \(0.301012\pi\) | |||||||
\(564\) | 11.5918i | 0.488103i | ||||||||
\(565\) | 4.49934i | 0.189288i | ||||||||
\(566\) | − 24.5284i | − 1.03101i | ||||||||
\(567\) | − 3.69202i | − 0.155050i | ||||||||
\(568\) | −4.13706 | −0.173587 | ||||||||
\(569\) | −38.4379 | −1.61140 | −0.805700 | − | 0.592324i | \(-0.798210\pi\) | ||||
−0.805700 | + | 0.592324i | \(0.798210\pi\) | |||||||
\(570\) | 0.911854i | 0.0381934i | ||||||||
\(571\) | −10.8086 | −0.452328 | −0.226164 | − | 0.974089i | \(-0.572618\pi\) | ||||
−0.226164 | + | 0.974089i | \(0.572618\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.5700 | −0.608671 | ||||||||
\(574\) | 38.0127i | 1.58662i | ||||||||
\(575\) | −0.356896 | −0.0148836 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 35.5991i | 1.48201i | 0.671500 | + | 0.741005i | \(0.265650\pi\) | ||||
−0.671500 | + | 0.741005i | \(0.734350\pi\) | |||||||
\(578\) | 29.9342i | 1.24510i | ||||||||
\(579\) | − 8.32544i | − 0.345993i | ||||||||
\(580\) | 10.5036i | 0.436140i | ||||||||
\(581\) | −36.4053 | −1.51035 | ||||||||
\(582\) | −6.97823 | −0.289257 | ||||||||
\(583\) | − 10.3840i | − 0.430063i | ||||||||
\(584\) | −11.1685 | −0.462157 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.8538 | 0.654916 | ||||||||
\(587\) | 11.4741i | 0.473587i | 0.971560 | + | 0.236794i | \(0.0760965\pi\) | ||||
−0.971560 | + | 0.236794i | \(0.923903\pi\) | |||||||
\(588\) | 6.63102 | 0.273459 | ||||||||
\(589\) | −1.87933 | −0.0774364 | ||||||||
\(590\) | − 8.54288i | − 0.351705i | ||||||||
\(591\) | − 26.8810i | − 1.10574i | ||||||||
\(592\) | 0.899772i | 0.0369804i | ||||||||
\(593\) | − 15.5147i | − 0.637111i | −0.947904 | − | 0.318555i | \(-0.896802\pi\) | ||||
0.947904 | − | 0.318555i | \(-0.103198\pi\) | |||||||
\(594\) | −3.04892 | −0.125099 | ||||||||
\(595\) | −25.2935 | −1.03693 | ||||||||
\(596\) | 6.91185i | 0.283121i | ||||||||
\(597\) | 18.7047 | 0.765532 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.2034 | −0.580337 | −0.290168 | − | 0.956976i | \(-0.593711\pi\) | ||||
−0.290168 | + | 0.956976i | \(0.593711\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −39.5579 | −1.61360 | −0.806801 | − | 0.590823i | \(-0.798803\pi\) | ||||
−0.806801 | + | 0.590823i | \(0.798803\pi\) | |||||||
\(602\) | −34.8267 | −1.41943 | ||||||||
\(603\) | 1.14914i | 0.0467968i | ||||||||
\(604\) | 5.43296i | 0.221064i | ||||||||
\(605\) | − 1.70410i | − 0.0692816i | ||||||||
\(606\) | 4.09783i | 0.166463i | ||||||||
\(607\) | 4.77346 | 0.193749 | 0.0968744 | − | 0.995297i | \(-0.469115\pi\) | ||||
0.0968744 | + | 0.995297i | \(0.469115\pi\) | |||||||
\(608\) | −0.911854 | −0.0369806 | ||||||||
\(609\) | − 38.7797i | − 1.57143i | ||||||||
\(610\) | 1.55496 | 0.0629584 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.85086 | −0.276929 | ||||||||
\(613\) | 5.43429i | 0.219489i | 0.993960 | + | 0.109744i | \(0.0350032\pi\) | ||||
−0.993960 | + | 0.109744i | \(0.964997\pi\) | |||||||
\(614\) | −14.2121 | −0.573552 | ||||||||
\(615\) | 10.2959 | 0.415171 | ||||||||
\(616\) | − 11.2567i | − 0.453544i | ||||||||
\(617\) | − 20.6692i | − 0.832110i | −0.909339 | − | 0.416055i | \(-0.863412\pi\) | ||||
0.909339 | − | 0.416055i | \(-0.136588\pi\) | |||||||
\(618\) | 16.9215i | 0.680684i | ||||||||
\(619\) | − 24.4077i | − 0.981030i | −0.871433 | − | 0.490515i | \(-0.836809\pi\) | ||||
0.871433 | − | 0.490515i | \(-0.163191\pi\) | |||||||
\(620\) | −2.06100 | −0.0827717 | ||||||||
\(621\) | 0.356896 | 0.0143217 | ||||||||
\(622\) | − 15.0127i | − 0.601953i | ||||||||
\(623\) | 23.6703 | 0.948329 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 13.4993i | − 0.539542i | ||||||||
\(627\) | −2.78017 | −0.111029 | ||||||||
\(628\) | 9.13706 | 0.364609 | ||||||||
\(629\) | 6.16421i | 0.245783i | ||||||||
\(630\) | − 3.69202i | − 0.147094i | ||||||||
\(631\) | 32.0538i | 1.27604i | 0.770019 | + | 0.638021i | \(0.220247\pi\) | ||||
−0.770019 | + | 0.638021i | \(0.779753\pi\) | |||||||
\(632\) | − 9.62565i | − 0.382888i | ||||||||
\(633\) | 2.93362 | 0.116601 | ||||||||
\(634\) | −33.9463 | −1.34818 | ||||||||
\(635\) | − 7.08815i | − 0.281284i | ||||||||
\(636\) | 3.40581 | 0.135049 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.0248 | −1.26787 | ||||||||
\(639\) | − 4.13706i | − 0.163660i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −18.5327 | −0.731998 | −0.365999 | − | 0.930615i | \(-0.619273\pi\) | ||||
−0.365999 | + | 0.930615i | \(0.619273\pi\) | |||||||
\(642\) | − 12.7192i | − 0.501986i | ||||||||
\(643\) | − 22.3454i | − 0.881217i | −0.897699 | − | 0.440608i | \(-0.854763\pi\) | ||||
0.897699 | − | 0.440608i | \(-0.145237\pi\) | |||||||
\(644\) | 1.31767i | 0.0519234i | ||||||||
\(645\) | 9.43296i | 0.371422i | ||||||||
\(646\) | −6.24698 | −0.245784 | ||||||||
\(647\) | −7.86964 | −0.309388 | −0.154694 | − | 0.987962i | \(-0.549439\pi\) | ||||
−0.154694 | + | 0.987962i | \(0.549439\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 26.0465 | 1.02242 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.60925 | 0.298230 | ||||||||
\(652\) | 14.3773i | 0.563060i | ||||||||
\(653\) | −47.2271 | −1.84814 | −0.924070 | − | 0.382223i | \(-0.875159\pi\) | ||||
−0.924070 | + | 0.382223i | \(0.875159\pi\) | |||||||
\(654\) | −19.9922 | −0.781758 | ||||||||
\(655\) | − 19.7506i | − 0.771721i | ||||||||
\(656\) | 10.2959i | 0.401987i | ||||||||
\(657\) | − 11.1685i | − 0.435726i | ||||||||
\(658\) | − 42.7972i | − 1.66841i | ||||||||
\(659\) | −46.6276 | −1.81635 | −0.908176 | − | 0.418588i | \(-0.862525\pi\) | ||||
−0.908176 | + | 0.418588i | \(0.862525\pi\) | |||||||
\(660\) | −3.04892 | −0.118679 | ||||||||
\(661\) | 39.9415i | 1.55354i | 0.629781 | + | 0.776772i | \(0.283144\pi\) | ||||
−0.629781 | + | 0.776772i | \(0.716856\pi\) | |||||||
\(662\) | 6.84415 | 0.266005 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.86054 | −0.382663 | ||||||||
\(665\) | − 3.36658i | − 0.130551i | ||||||||
\(666\) | −0.899772 | −0.0348655 | ||||||||
\(667\) | 3.74871 | 0.145151 | ||||||||
\(668\) | − 3.00538i | − 0.116282i | ||||||||
\(669\) | − 18.1444i | − 0.701501i | ||||||||
\(670\) | 1.14914i | 0.0443953i | ||||||||
\(671\) | 4.74094i | 0.183022i | ||||||||
\(672\) | 3.69202 | 0.142423 | ||||||||
\(673\) | 35.3612 | 1.36307 | 0.681537 | − | 0.731783i | \(-0.261312\pi\) | ||||
0.681537 | + | 0.731783i | \(0.261312\pi\) | |||||||
\(674\) | − 27.7332i | − 1.06824i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.1715 | 0.736821 | 0.368410 | − | 0.929663i | \(-0.379902\pi\) | ||||
0.368410 | + | 0.929663i | \(0.379902\pi\) | |||||||
\(678\) | − 4.49934i | − 0.172796i | ||||||||
\(679\) | 25.7638 | 0.988723 | ||||||||
\(680\) | −6.85086 | −0.262718 | ||||||||
\(681\) | 12.3056i | 0.471551i | ||||||||
\(682\) | − 6.28382i | − 0.240620i | ||||||||
\(683\) | 1.13946i | 0.0436001i | 0.999762 | + | 0.0218000i | \(0.00693972\pi\) | ||||
−0.999762 | + | 0.0218000i | \(0.993060\pi\) | |||||||
\(684\) | − 0.911854i | − 0.0348656i | ||||||||
\(685\) | 7.94331 | 0.303498 | ||||||||
\(686\) | 1.36227 | 0.0520118 | ||||||||
\(687\) | − 4.64848i | − 0.177351i | ||||||||
\(688\) | −9.43296 | −0.359628 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.356896 | 0.0135868 | ||||||||
\(691\) | 11.9071i | 0.452966i | 0.974015 | + | 0.226483i | \(0.0727228\pi\) | ||||
−0.974015 | + | 0.226483i | \(0.927277\pi\) | |||||||
\(692\) | 6.89546 | 0.262126 | ||||||||
\(693\) | 11.2567 | 0.427605 | ||||||||
\(694\) | − 10.4862i | − 0.398050i | ||||||||
\(695\) | 1.71379i | 0.0650078i | ||||||||
\(696\) | − 10.5036i | − 0.398140i | ||||||||
\(697\) | 70.5357i | 2.67173i | ||||||||
\(698\) | −8.13467 | −0.307902 | ||||||||
\(699\) | −0.658170 | −0.0248943 | ||||||||
\(700\) | − 3.69202i | − 0.139545i | ||||||||
\(701\) | −38.0575 | −1.43741 | −0.718707 | − | 0.695313i | \(-0.755266\pi\) | ||||
−0.718707 | + | 0.695313i | \(0.755266\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.820461 | −0.0309443 | ||||||||
\(704\) | − 3.04892i | − 0.114910i | ||||||||
\(705\) | −11.5918 | −0.436572 | ||||||||
\(706\) | 25.8649 | 0.973437 | ||||||||
\(707\) | − 15.1293i | − 0.568996i | ||||||||
\(708\) | 8.54288i | 0.321061i | ||||||||
\(709\) | 26.1215i | 0.981014i | 0.871437 | + | 0.490507i | \(0.163188\pi\) | ||||
−0.871437 | + | 0.490507i | \(0.836812\pi\) | |||||||
\(710\) | − 4.13706i | − 0.155261i | ||||||||
\(711\) | 9.62565 | 0.360990 | ||||||||
\(712\) | 6.41119 | 0.240270 | ||||||||
\(713\) | 0.735562i | 0.0275470i | ||||||||
\(714\) | 25.2935 | 0.946586 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.6461 | −0.958439 | ||||||||
\(717\) | − 18.7748i | − 0.701157i | ||||||||
\(718\) | −30.2959 | −1.13063 | ||||||||
\(719\) | −21.3739 | −0.797111 | −0.398556 | − | 0.917144i | \(-0.630488\pi\) | ||||
−0.398556 | + | 0.917144i | \(0.630488\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | − 62.4747i | − 2.32668i | ||||||||
\(722\) | 18.1685i | 0.676162i | ||||||||
\(723\) | − 18.0271i | − 0.670437i | ||||||||
\(724\) | −25.8092 | −0.959193 | ||||||||
\(725\) | −10.5036 | −0.390096 | ||||||||
\(726\) | 1.70410i | 0.0632452i | ||||||||
\(727\) | 17.9124 | 0.664336 | 0.332168 | − | 0.943220i | \(-0.392220\pi\) | ||||
0.332168 | + | 0.943220i | \(0.392220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 11.1685i | − 0.413366i | ||||||||
\(731\) | −64.6238 | −2.39020 | ||||||||
\(732\) | −1.55496 | −0.0574729 | ||||||||
\(733\) | − 27.5386i | − 1.01716i | −0.861015 | − | 0.508580i | \(-0.830171\pi\) | ||||
0.861015 | − | 0.508580i | \(-0.169829\pi\) | |||||||
\(734\) | − 3.41013i | − 0.125870i | ||||||||
\(735\) | 6.63102i | 0.244589i | ||||||||
\(736\) | 0.356896i | 0.0131554i | ||||||||
\(737\) | −3.50365 | −0.129059 | ||||||||
\(738\) | −10.2959 | −0.378997 | ||||||||
\(739\) | − 7.99090i | − 0.293950i | −0.989140 | − | 0.146975i | \(-0.953046\pi\) | ||||
0.989140 | − | 0.146975i | \(-0.0469537\pi\) | |||||||
\(740\) | −0.899772 | −0.0330763 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.5743 | −0.461618 | ||||||||
\(743\) | − 19.8398i | − 0.727853i | −0.931428 | − | 0.363927i | \(-0.881436\pi\) | ||||
0.931428 | − | 0.363927i | \(-0.118564\pi\) | |||||||
\(744\) | 2.06100 | 0.0755599 | ||||||||
\(745\) | −6.91185 | −0.253231 | ||||||||
\(746\) | 3.35988i | 0.123014i | ||||||||
\(747\) | − 9.86054i | − 0.360778i | ||||||||
\(748\) | − 20.8877i | − 0.763730i | ||||||||
\(749\) | 46.9594i | 1.71586i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 25.7525 | 0.939724 | 0.469862 | − | 0.882740i | \(-0.344304\pi\) | ||||
0.469862 | + | 0.882740i | \(0.344304\pi\) | |||||||
\(752\) | − 11.5918i | − 0.422709i | ||||||||
\(753\) | 2.18060 | 0.0794656 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.43296 | −0.197726 | ||||||||
\(756\) | 3.69202i | 0.134278i | ||||||||
\(757\) | −51.5096 | −1.87215 | −0.936074 | − | 0.351802i | \(-0.885569\pi\) | ||||
−0.936074 | + | 0.351802i | \(0.885569\pi\) | |||||||
\(758\) | 31.4916 | 1.14383 | ||||||||
\(759\) | 1.08815i | 0.0394972i | ||||||||
\(760\) | − 0.911854i | − 0.0330764i | ||||||||
\(761\) | − 31.4765i | − 1.14102i | −0.821290 | − | 0.570511i | \(-0.806745\pi\) | ||||
0.821290 | − | 0.570511i | \(-0.193255\pi\) | |||||||
\(762\) | 7.08815i | 0.256776i | ||||||||
\(763\) | 73.8117 | 2.67216 | ||||||||
\(764\) | 14.5700 | 0.527125 | ||||||||
\(765\) | − 6.85086i | − 0.247693i | ||||||||
\(766\) | −21.8485 | −0.789417 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 47.1584i | 1.70057i | 0.526319 | + | 0.850287i | \(0.323572\pi\) | ||||
−0.526319 | + | 0.850287i | \(0.676428\pi\) | |||||||
\(770\) | 11.2567 | 0.405662 | ||||||||
\(771\) | 9.58748 | 0.345285 | ||||||||
\(772\) | 8.32544i | 0.299639i | ||||||||
\(773\) | 3.71917i | 0.133769i | 0.997761 | + | 0.0668846i | \(0.0213059\pi\) | ||||
−0.997761 | + | 0.0668846i | \(0.978694\pi\) | |||||||
\(774\) | − 9.43296i | − 0.339061i | ||||||||
\(775\) | − 2.06100i | − 0.0740333i | ||||||||
\(776\) | 6.97823 | 0.250504 | ||||||||
\(777\) | 3.32198 | 0.119175 | ||||||||
\(778\) | 11.3787i | 0.407945i | ||||||||
\(779\) | −9.38835 | −0.336373 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6136 | 0.451349 | ||||||||
\(782\) | 2.44504i | 0.0874345i | ||||||||
\(783\) | 10.5036 | 0.375370 | ||||||||
\(784\) | −6.63102 | −0.236822 | ||||||||
\(785\) | 9.13706i | 0.326116i | ||||||||
\(786\) | 19.7506i | 0.704482i | ||||||||
\(787\) | 47.2282i | 1.68350i | 0.539865 | + | 0.841752i | \(0.318475\pi\) | ||||
−0.539865 | + | 0.841752i | \(0.681525\pi\) | |||||||
\(788\) | 26.8810i | 0.957595i | ||||||||
\(789\) | −1.41789 | −0.0504784 | ||||||||
\(790\) | 9.62565 | 0.342465 | ||||||||
\(791\) | 16.6116i | 0.590642i | ||||||||
\(792\) | 3.04892 | 0.108339 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 22.0476 | 0.782440 | ||||||||
\(795\) | 3.40581i | 0.120792i | ||||||||
\(796\) | −18.7047 | −0.662970 | ||||||||
\(797\) | −34.4359 | −1.21978 | −0.609892 | − | 0.792485i | \(-0.708787\pi\) | ||||
−0.609892 | + | 0.792485i | \(0.708787\pi\) | |||||||
\(798\) | 3.36658i | 0.119176i | ||||||||
\(799\) | − 79.4137i | − 2.80945i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 6.41119i | 0.226528i | ||||||||
\(802\) | 10.2459 | 0.361796 | ||||||||
\(803\) | 34.0519 | 1.20167 | ||||||||
\(804\) | − 1.14914i | − 0.0405272i | ||||||||
\(805\) | −1.31767 | −0.0464417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.14675 | −0.145973 | ||||||||
\(808\) | − 4.09783i | − 0.144161i | ||||||||
\(809\) | −32.3846 | −1.13858 | −0.569292 | − | 0.822136i | \(-0.692782\pi\) | ||||
−0.569292 | + | 0.822136i | \(0.692782\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 37.8297i | 1.32838i | 0.747564 | + | 0.664190i | \(0.231223\pi\) | ||||
−0.747564 | + | 0.664190i | \(0.768777\pi\) | |||||||
\(812\) | 38.7797i | 1.36090i | ||||||||
\(813\) | − 6.40044i | − 0.224473i | ||||||||
\(814\) | − 2.74333i | − 0.0961537i | ||||||||
\(815\) | −14.3773 | −0.503616 | ||||||||
\(816\) | 6.85086 | 0.239828 | ||||||||
\(817\) | − 8.60148i | − 0.300928i | ||||||||
\(818\) | −22.8189 | −0.797845 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.2959 | −0.359548 | ||||||||
\(821\) | 43.2820i | 1.51055i | 0.655406 | + | 0.755276i | \(0.272497\pi\) | ||||
−0.655406 | + | 0.755276i | \(0.727503\pi\) | |||||||
\(822\) | −7.94331 | −0.277055 | ||||||||
\(823\) | 26.7399 | 0.932093 | 0.466047 | − | 0.884760i | \(-0.345678\pi\) | ||||
0.466047 | + | 0.884760i | \(0.345678\pi\) | |||||||
\(824\) | − 16.9215i | − 0.589490i | ||||||||
\(825\) | − 3.04892i | − 0.106150i | ||||||||
\(826\) | − 31.5405i | − 1.09743i | ||||||||
\(827\) | − 21.4437i | − 0.745671i | −0.927897 | − | 0.372835i | \(-0.878386\pi\) | ||||
0.927897 | − | 0.372835i | \(-0.121614\pi\) | |||||||
\(828\) | −0.356896 | −0.0124030 | ||||||||
\(829\) | −22.4547 | −0.779885 | −0.389943 | − | 0.920839i | \(-0.627505\pi\) | ||||
−0.389943 | + | 0.920839i | \(0.627505\pi\) | |||||||
\(830\) | − 9.86054i | − 0.342264i | ||||||||
\(831\) | −10.3394 | −0.358671 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −45.4282 | −1.57399 | ||||||||
\(834\) | − 1.71379i | − 0.0593438i | ||||||||
\(835\) | 3.00538 | 0.104005 | ||||||||
\(836\) | 2.78017 | 0.0961541 | ||||||||
\(837\) | 2.06100i | 0.0712385i | ||||||||
\(838\) | − 28.5773i | − 0.987187i | ||||||||
\(839\) | − 24.4034i | − 0.842500i | −0.906945 | − | 0.421250i | \(-0.861592\pi\) | ||||
0.906945 | − | 0.421250i | \(-0.138408\pi\) | |||||||
\(840\) | 3.69202i | 0.127387i | ||||||||
\(841\) | 81.3266 | 2.80437 | ||||||||
\(842\) | −32.3937 | −1.11636 | ||||||||
\(843\) | − 5.08144i | − 0.175014i | ||||||||
\(844\) | −2.93362 | −0.100980 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.5918 | 0.398534 | ||||||||
\(847\) | − 6.29159i | − 0.216181i | ||||||||
\(848\) | −3.40581 | −0.116956 | ||||||||
\(849\) | −24.5284 | −0.841813 | ||||||||
\(850\) | − 6.85086i | − 0.234982i | ||||||||
\(851\) | 0.321125i | 0.0110080i | ||||||||
\(852\) | 4.13706i | 0.141733i | ||||||||
\(853\) | 7.96184i | 0.272608i | 0.990667 | + | 0.136304i | \(0.0435224\pi\) | ||||
−0.990667 | + | 0.136304i | \(0.956478\pi\) | |||||||
\(854\) | 5.74094 | 0.196451 | ||||||||
\(855\) | 0.911854 | 0.0311847 | ||||||||
\(856\) | 12.7192i | 0.434732i | ||||||||
\(857\) | 8.12737 | 0.277626 | 0.138813 | − | 0.990319i | \(-0.455671\pi\) | ||||
0.138813 | + | 0.990319i | \(0.455671\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.1666 | 0.585717 | 0.292858 | − | 0.956156i | \(-0.405394\pi\) | ||||
0.292858 | + | 0.956156i | \(0.405394\pi\) | |||||||
\(860\) | − 9.43296i | − 0.321661i | ||||||||
\(861\) | 38.0127 | 1.29547 | ||||||||
\(862\) | 14.6455 | 0.498828 | ||||||||
\(863\) | − 46.2857i | − 1.57558i | −0.615941 | − | 0.787792i | \(-0.711224\pi\) | ||||
0.615941 | − | 0.787792i | \(-0.288776\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 6.89546i | 0.234453i | ||||||||
\(866\) | 35.8485i | 1.21818i | ||||||||
\(867\) | 29.9342 | 1.01662 | ||||||||
\(868\) | −7.60925 | −0.258275 | ||||||||
\(869\) | 29.3478i | 0.995556i | ||||||||
\(870\) | 10.5036 | 0.356107 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19.9922 | 0.677022 | ||||||||
\(873\) | 6.97823i | 0.236177i | ||||||||
\(874\) | −0.325437 | −0.0110081 | ||||||||
\(875\) | 3.69202 | 0.124813 | ||||||||
\(876\) | 11.1685i | 0.377349i | ||||||||
\(877\) | 2.72156i | 0.0919006i | 0.998944 | + | 0.0459503i | \(0.0146316\pi\) | ||||
−0.998944 | + | 0.0459503i | \(0.985368\pi\) | |||||||
\(878\) | − 2.55927i | − 0.0863712i | ||||||||
\(879\) | − 15.8538i | − 0.534737i | ||||||||
\(880\) | 3.04892 | 0.102779 | ||||||||
\(881\) | 16.7241 | 0.563448 | 0.281724 | − | 0.959495i | \(-0.409094\pi\) | ||||
0.281724 | + | 0.959495i | \(0.409094\pi\) | |||||||
\(882\) | − 6.63102i | − 0.223278i | ||||||||
\(883\) | 2.88364 | 0.0970423 | 0.0485211 | − | 0.998822i | \(-0.484549\pi\) | ||||
0.0485211 | + | 0.998822i | \(0.484549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.54288 | −0.287166 | ||||||||
\(886\) | 23.2857i | 0.782300i | ||||||||
\(887\) | 55.8866 | 1.87649 | 0.938245 | − | 0.345973i | \(-0.112451\pi\) | ||||
0.938245 | + | 0.345973i | \(0.112451\pi\) | |||||||
\(888\) | 0.899772 | 0.0301944 | ||||||||
\(889\) | − 26.1696i | − 0.877700i | ||||||||
\(890\) | 6.41119i | 0.214904i | ||||||||
\(891\) | 3.04892i | 0.102143i | ||||||||
\(892\) | 18.1444i | 0.607518i | ||||||||
\(893\) | 10.5700 | 0.353712 | ||||||||
\(894\) | 6.91185 | 0.231167 | ||||||||
\(895\) | − 25.6461i | − 0.857254i | ||||||||
\(896\) | −3.69202 | −0.123342 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.3327 | −0.912105 | ||||||||
\(899\) | 21.6480i | 0.722001i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −23.3327 | −0.777326 | ||||||||
\(902\) | − 31.3913i | − 1.04522i | ||||||||
\(903\) | 34.8267i | 1.15896i | ||||||||
\(904\) | 4.49934i | 0.149646i | ||||||||
\(905\) | − 25.8092i | − 0.857928i | ||||||||
\(906\) | 5.43296 | 0.180498 | ||||||||
\(907\) | −49.5381 | −1.64489 | −0.822443 | − | 0.568848i | \(-0.807389\pi\) | ||||
−0.822443 | + | 0.568848i | \(0.807389\pi\) | |||||||
\(908\) | − 12.3056i | − 0.408375i | ||||||||
\(909\) | 4.09783 | 0.135917 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.0603 | 1.22786 | 0.613931 | − | 0.789360i | \(-0.289587\pi\) | ||||
0.613931 | + | 0.789360i | \(0.289587\pi\) | |||||||
\(912\) | 0.911854i | 0.0301945i | ||||||||
\(913\) | 30.0640 | 0.994973 | ||||||||
\(914\) | 7.74094 | 0.256047 | ||||||||
\(915\) | − 1.55496i | − 0.0514053i | ||||||||
\(916\) | 4.64848i | 0.153590i | ||||||||
\(917\) | − 72.9197i | − 2.40802i | ||||||||
\(918\) | 6.85086i | 0.226112i | ||||||||
\(919\) | 53.6228 | 1.76885 | 0.884426 | − | 0.466680i | \(-0.154550\pi\) | ||||
0.884426 | + | 0.466680i | \(0.154550\pi\) | |||||||
\(920\) | −0.356896 | −0.0117665 | ||||||||
\(921\) | 14.2121i | 0.468303i | ||||||||
\(922\) | −17.1511 | −0.564840 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −11.2567 | −0.370317 | ||||||||
\(925\) | − 0.899772i | − 0.0295843i | ||||||||
\(926\) | −34.2747 | −1.12634 | ||||||||
\(927\) | 16.9215 | 0.555776 | ||||||||
\(928\) | 10.5036i | 0.344799i | ||||||||
\(929\) | − 10.6726i | − 0.350158i | −0.984554 | − | 0.175079i | \(-0.943982\pi\) | ||||
0.984554 | − | 0.175079i | \(-0.0560181\pi\) | |||||||
\(930\) | 2.06100i | 0.0675828i | ||||||||
\(931\) | − 6.04652i | − 0.198167i | ||||||||
\(932\) | 0.658170 | 0.0215591 | ||||||||
\(933\) | −15.0127 | −0.491493 | ||||||||
\(934\) | − 20.9474i | − 0.685419i | ||||||||
\(935\) | 20.8877 | 0.683101 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0538 | 0.557124 | 0.278562 | − | 0.960418i | \(-0.410142\pi\) | ||||
0.278562 | + | 0.960418i | \(0.410142\pi\) | |||||||
\(938\) | 4.24267i | 0.138528i | ||||||||
\(939\) | −13.4993 | −0.440534 | ||||||||
\(940\) | 11.5918 | 0.378083 | ||||||||
\(941\) | − 46.7706i | − 1.52468i | −0.647178 | − | 0.762339i | \(-0.724051\pi\) | ||||
0.647178 | − | 0.762339i | \(-0.275949\pi\) | |||||||
\(942\) | − 9.13706i | − 0.297702i | ||||||||
\(943\) | 3.67456i | 0.119660i | ||||||||
\(944\) | − 8.54288i | − 0.278047i | ||||||||
\(945\) | −3.69202 | −0.120101 | ||||||||
\(946\) | 28.7603 | 0.935079 | ||||||||
\(947\) | 30.0398i | 0.976163i | 0.872798 | + | 0.488081i | \(0.162303\pi\) | ||||
−0.872798 | + | 0.488081i | \(0.837697\pi\) | |||||||
\(948\) | −9.62565 | −0.312626 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.911854 | 0.0295845 | ||||||||
\(951\) | 33.9463i | 1.10078i | ||||||||
\(952\) | −25.2935 | −0.819767 | ||||||||
\(953\) | 29.4252 | 0.953175 | 0.476588 | − | 0.879127i | \(-0.341873\pi\) | ||||
0.476588 | + | 0.879127i | \(0.341873\pi\) | |||||||
\(954\) | − 3.40581i | − 0.110267i | ||||||||
\(955\) | 14.5700i | 0.471475i | ||||||||
\(956\) | 18.7748i | 0.607220i | ||||||||
\(957\) | 32.0248i | 1.03521i | ||||||||
\(958\) | 15.8310 | 0.511477 | ||||||||
\(959\) | 29.3269 | 0.947014 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 26.7523 | 0.862977 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.7192 | −0.409869 | ||||||||
\(964\) | 18.0271i | 0.580615i | ||||||||
\(965\) | −8.32544 | −0.268005 | ||||||||
\(966\) | 1.31767 | 0.0423952 | ||||||||
\(967\) | 12.7023i | 0.408478i | 0.978921 | + | 0.204239i | \(0.0654720\pi\) | ||||
−0.978921 | + | 0.204239i | \(0.934528\pi\) | |||||||
\(968\) | − 1.70410i | − 0.0547719i | ||||||||
\(969\) | 6.24698i | 0.200682i | ||||||||
\(970\) | 6.97823i | 0.224057i | ||||||||
\(971\) | 22.9105 | 0.735234 | 0.367617 | − | 0.929977i | \(-0.380174\pi\) | ||||
0.367617 | + | 0.929977i | \(0.380174\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 6.32736i | 0.202846i | ||||||||
\(974\) | −33.7060 | −1.08001 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.55496 | 0.0497730 | ||||||||
\(977\) | − 25.1390i | − 0.804267i | −0.915581 | − | 0.402134i | \(-0.868269\pi\) | ||||
0.915581 | − | 0.402134i | \(-0.131731\pi\) | |||||||
\(978\) | 14.3773 | 0.459737 | ||||||||
\(979\) | −19.5472 | −0.624731 | ||||||||
\(980\) | − 6.63102i | − 0.211820i | ||||||||
\(981\) | 19.9922i | 0.638303i | ||||||||
\(982\) | − 3.98925i | − 0.127302i | ||||||||
\(983\) | 50.3895i | 1.60718i | 0.595186 | + | 0.803588i | \(0.297079\pi\) | ||||
−0.595186 | + | 0.803588i | \(0.702921\pi\) | |||||||
\(984\) | 10.2959 | 0.328221 | ||||||||
\(985\) | −26.8810 | −0.856499 | ||||||||
\(986\) | 71.9590i | 2.29164i | ||||||||
\(987\) | −42.7972 | −1.36225 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.36658 | −0.107051 | ||||||||
\(990\) | 3.04892i | 0.0969010i | ||||||||
\(991\) | 23.3375 | 0.741341 | 0.370670 | − | 0.928764i | \(-0.379128\pi\) | ||||
0.370670 | + | 0.928764i | \(0.379128\pi\) | |||||||
\(992\) | −2.06100 | −0.0654368 | ||||||||
\(993\) | − 6.84415i | − 0.217193i | ||||||||
\(994\) | − 15.2741i | − 0.484466i | ||||||||
\(995\) | − 18.7047i | − 0.592979i | ||||||||
\(996\) | 9.86054i | 0.312443i | ||||||||
\(997\) | 22.8127 | 0.722485 | 0.361243 | − | 0.932472i | \(-0.382353\pi\) | ||||
0.361243 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(998\) | −20.4698 | −0.647960 | ||||||||
\(999\) | 0.899772i | 0.0284675i |
(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 | 5070.2.b.z.1351.4 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bw.1.3 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bp.1.1 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.z.1351.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bp.1.1 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bw.1.3 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.z.1351.3 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.z.1351.4 | 6 | 1.1 | even | 1 | trivial |