Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4650,2,Mod(3349,4650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4650, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4650.3349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4650.d (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: | \(37.1304369399\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 930) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3349.2 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4650.3349 |
Dual form | 4650.2.d.bd.3349.3 |
$q$-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 \(\left(\mathbb{Z}/4650\mathbb{Z}\right)^\times\).
\(n\) | \(1801\) | \(2977\) | \(3101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.56155i | 0.590211i | 0.955465 | + | 0.295106i | \(0.0953549\pi\) | ||||
−0.955465 | + | 0.295106i | \(0.904645\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.56155 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 1.56155 | 0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 5.12311i | − 1.24254i | −0.783598 | − | 0.621268i | \(-0.786618\pi\) | ||||
0.783598 | − | 0.621268i | \(-0.213382\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −4.68466 | −1.07473 | −0.537367 | − | 0.843348i | \(-0.680581\pi\) | ||||
−0.537367 | + | 0.843348i | \(0.680581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.56155 | 0.340759 | ||||||||
\(22\) | 1.56155i | 0.332924i | ||||||||
\(23\) | 5.56155i | 1.15966i | 0.814736 | + | 0.579832i | \(0.196882\pi\) | ||||
−0.814736 | + | 0.579832i | \(0.803118\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 1.56155i | − 0.295106i | ||||||||
\(29\) | 1.12311 | 0.208555 | 0.104278 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104278 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 1.56155i | 0.271831i | ||||||||
\(34\) | −5.12311 | −0.878605 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 5.12311i | − 0.842233i | −0.907006 | − | 0.421117i | \(-0.861638\pi\) | ||||
0.907006 | − | 0.421117i | \(-0.138362\pi\) | |||||||
\(38\) | 4.68466i | 0.759952i | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.12311 | −0.175400 | −0.0876998 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0876998 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(42\) | − 1.56155i | − 0.240953i | ||||||||
\(43\) | − 7.80776i | − 1.19067i | −0.803477 | − | 0.595336i | \(-0.797019\pi\) | ||||
0.803477 | − | 0.595336i | \(-0.202981\pi\) | |||||||
\(44\) | 1.56155 | 0.235413 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.56155 | 0.820006 | ||||||||
\(47\) | 3.12311i | 0.455552i | 0.973714 | + | 0.227776i | \(0.0731454\pi\) | ||||
−0.973714 | + | 0.227776i | \(0.926855\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 4.56155 | 0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.12311 | −0.717378 | ||||||||
\(52\) | − 2.00000i | − 0.277350i | ||||||||
\(53\) | 11.5616i | 1.58810i | 0.607852 | + | 0.794051i | \(0.292032\pi\) | ||||
−0.607852 | + | 0.794051i | \(0.707968\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.56155 | −0.208671 | ||||||||
\(57\) | 4.68466i | 0.620498i | ||||||||
\(58\) | − 1.12311i | − 0.147471i | ||||||||
\(59\) | 4.87689 | 0.634918 | 0.317459 | − | 0.948272i | \(-0.397170\pi\) | ||||
0.317459 | + | 0.948272i | \(0.397170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | − 1.00000i | − 0.127000i | ||||||||
\(63\) | − 1.56155i | − 0.196737i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.56155 | 0.192214 | ||||||||
\(67\) | − 9.36932i | − 1.14464i | −0.820029 | − | 0.572322i | \(-0.806043\pi\) | ||||
0.820029 | − | 0.572322i | \(-0.193957\pi\) | |||||||
\(68\) | 5.12311i | 0.621268i | ||||||||
\(69\) | 5.56155 | 0.669532 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.68466 | 0.555967 | 0.277983 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277983 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 9.80776i | 1.14791i | 0.818886 | + | 0.573956i | \(0.194592\pi\) | ||||
−0.818886 | + | 0.573956i | \(0.805408\pi\) | |||||||
\(74\) | −5.12311 | −0.595549 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.68466 | 0.537367 | ||||||||
\(77\) | − 2.43845i | − 0.277887i | ||||||||
\(78\) | − 2.00000i | − 0.226455i | ||||||||
\(79\) | 16.6847 | 1.87717 | 0.938585 | − | 0.345047i | \(-0.112137\pi\) | ||||
0.938585 | + | 0.345047i | \(0.112137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.12311i | 0.124026i | ||||||||
\(83\) | − 2.24621i | − 0.246554i | −0.992372 | − | 0.123277i | \(-0.960660\pi\) | ||||
0.992372 | − | 0.123277i | \(-0.0393403\pi\) | |||||||
\(84\) | −1.56155 | −0.170379 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.80776 | −0.841933 | ||||||||
\(87\) | − 1.12311i | − 0.120410i | ||||||||
\(88\) | − 1.56155i | − 0.166462i | ||||||||
\(89\) | 1.31534 | 0.139426 | 0.0697130 | − | 0.997567i | \(-0.477792\pi\) | ||||
0.0697130 | + | 0.997567i | \(0.477792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.12311 | −0.327390 | ||||||||
\(92\) | − 5.56155i | − 0.579832i | ||||||||
\(93\) | − 1.00000i | − 0.103695i | ||||||||
\(94\) | 3.12311 | 0.322124 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | − 4.56155i | − 0.460786i | ||||||||
\(99\) | 1.56155 | 0.156942 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.56155 | 0.354388 | 0.177194 | − | 0.984176i | \(-0.443298\pi\) | ||||
0.177194 | + | 0.984176i | \(0.443298\pi\) | |||||||
\(102\) | 5.12311i | 0.507263i | ||||||||
\(103\) | − 18.2462i | − 1.79785i | −0.438100 | − | 0.898926i | \(-0.644348\pi\) | ||||
0.438100 | − | 0.898926i | \(-0.355652\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.5616 | 1.12296 | ||||||||
\(107\) | − 1.56155i | − 0.150961i | −0.997147 | − | 0.0754805i | \(-0.975951\pi\) | ||||
0.997147 | − | 0.0754805i | \(-0.0240491\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | 19.3693 | 1.85524 | 0.927622 | − | 0.373520i | \(-0.121849\pi\) | ||||
0.927622 | + | 0.373520i | \(0.121849\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.12311 | −0.486264 | ||||||||
\(112\) | 1.56155i | 0.147553i | ||||||||
\(113\) | 10.6847i | 1.00513i | 0.864540 | + | 0.502564i | \(0.167610\pi\) | ||||
−0.864540 | + | 0.502564i | \(0.832390\pi\) | |||||||
\(114\) | 4.68466 | 0.438758 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.12311 | −0.104278 | ||||||||
\(117\) | − 2.00000i | − 0.184900i | ||||||||
\(118\) | − 4.87689i | − 0.448955i | ||||||||
\(119\) | 8.00000 | 0.733359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | − 6.00000i | − 0.543214i | ||||||||
\(123\) | 1.12311i | 0.101267i | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.56155 | −0.139114 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −7.80776 | −0.687435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.36932 | 0.818601 | 0.409301 | − | 0.912400i | \(-0.365773\pi\) | ||||
0.409301 | + | 0.912400i | \(0.365773\pi\) | |||||||
\(132\) | − 1.56155i | − 0.135916i | ||||||||
\(133\) | − 7.31534i | − 0.634321i | ||||||||
\(134\) | −9.36932 | −0.809386 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.12311 | 0.439303 | ||||||||
\(137\) | − 3.75379i | − 0.320708i | −0.987060 | − | 0.160354i | \(-0.948736\pi\) | ||||
0.987060 | − | 0.160354i | \(-0.0512635\pi\) | |||||||
\(138\) | − 5.56155i | − 0.473431i | ||||||||
\(139\) | 8.87689 | 0.752928 | 0.376464 | − | 0.926431i | \(-0.377140\pi\) | ||||
0.376464 | + | 0.926431i | \(0.377140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.12311 | 0.263013 | ||||||||
\(142\) | − 4.68466i | − 0.393128i | ||||||||
\(143\) | − 3.12311i | − 0.261167i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.80776 | 0.811696 | ||||||||
\(147\) | − 4.56155i | − 0.376231i | ||||||||
\(148\) | 5.12311i | 0.421117i | ||||||||
\(149\) | 20.0540 | 1.64289 | 0.821443 | − | 0.570291i | \(-0.193170\pi\) | ||||
0.821443 | + | 0.570291i | \(0.193170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | − 4.68466i | − 0.379976i | ||||||||
\(153\) | 5.12311i | 0.414179i | ||||||||
\(154\) | −2.43845 | −0.196496 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 20.0540i | 1.60048i | 0.599679 | + | 0.800241i | \(0.295295\pi\) | ||||
−0.599679 | + | 0.800241i | \(0.704705\pi\) | |||||||
\(158\) | − 16.6847i | − 1.32736i | ||||||||
\(159\) | 11.5616 | 0.916891 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.68466 | −0.684447 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 9.36932i | 0.733862i | 0.930248 | + | 0.366931i | \(0.119591\pi\) | ||||
−0.930248 | + | 0.366931i | \(0.880409\pi\) | |||||||
\(164\) | 1.12311 | 0.0876998 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.24621 | −0.174340 | ||||||||
\(167\) | 2.43845i | 0.188693i | 0.995539 | + | 0.0943464i | \(0.0300761\pi\) | ||||
−0.995539 | + | 0.0943464i | \(0.969924\pi\) | |||||||
\(168\) | 1.56155i | 0.120476i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.68466 | 0.358245 | ||||||||
\(172\) | 7.80776i | 0.595336i | ||||||||
\(173\) | − 8.24621i | − 0.626948i | −0.949597 | − | 0.313474i | \(-0.898507\pi\) | ||||
0.949597 | − | 0.313474i | \(-0.101493\pi\) | |||||||
\(174\) | −1.12311 | −0.0851424 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.56155 | −0.117706 | ||||||||
\(177\) | − 4.87689i | − 0.366570i | ||||||||
\(178\) | − 1.31534i | − 0.0985890i | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.0540 | 1.78792 | 0.893959 | − | 0.448149i | \(-0.147917\pi\) | ||||
0.893959 | + | 0.448149i | \(0.147917\pi\) | |||||||
\(182\) | 3.12311i | 0.231500i | ||||||||
\(183\) | − 6.00000i | − 0.443533i | ||||||||
\(184\) | −5.56155 | −0.410003 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.00000 | −0.0733236 | ||||||||
\(187\) | 8.00000i | 0.585018i | ||||||||
\(188\) | − 3.12311i | − 0.227776i | ||||||||
\(189\) | −1.56155 | −0.113586 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.24621 | 0.162530 | 0.0812651 | − | 0.996693i | \(-0.474104\pi\) | ||||
0.0812651 | + | 0.996693i | \(0.474104\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − 18.4924i | − 1.33111i | −0.746347 | − | 0.665557i | \(-0.768194\pi\) | ||||
0.746347 | − | 0.665557i | \(-0.231806\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.56155 | −0.325825 | ||||||||
\(197\) | − 6.00000i | − 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | − 1.56155i | − 0.110975i | ||||||||
\(199\) | −3.80776 | −0.269925 | −0.134963 | − | 0.990851i | \(-0.543091\pi\) | ||||
−0.134963 | + | 0.990851i | \(0.543091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.36932 | −0.660861 | ||||||||
\(202\) | − 3.56155i | − 0.250590i | ||||||||
\(203\) | 1.75379i | 0.123092i | ||||||||
\(204\) | 5.12311 | 0.358689 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −18.2462 | −1.27127 | ||||||||
\(207\) | − 5.56155i | − 0.386555i | ||||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | 7.31534 | 0.506013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3153 | −0.778980 | −0.389490 | − | 0.921031i | \(-0.627349\pi\) | ||||
−0.389490 | + | 0.921031i | \(0.627349\pi\) | |||||||
\(212\) | − 11.5616i | − 0.794051i | ||||||||
\(213\) | − 4.68466i | − 0.320988i | ||||||||
\(214\) | −1.56155 | −0.106746 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 1.56155i | 0.106005i | ||||||||
\(218\) | − 19.3693i | − 1.31186i | ||||||||
\(219\) | 9.80776 | 0.662747 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.2462 | 0.689235 | ||||||||
\(222\) | 5.12311i | 0.343840i | ||||||||
\(223\) | − 12.8769i | − 0.862301i | −0.902280 | − | 0.431150i | \(-0.858108\pi\) | ||||
0.902280 | − | 0.431150i | \(-0.141892\pi\) | |||||||
\(224\) | 1.56155 | 0.104336 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.6847 | 0.710733 | ||||||||
\(227\) | 4.68466i | 0.310932i | 0.987841 | + | 0.155466i | \(0.0496879\pi\) | ||||
−0.987841 | + | 0.155466i | \(0.950312\pi\) | |||||||
\(228\) | − 4.68466i | − 0.310249i | ||||||||
\(229\) | 12.4384 | 0.821956 | 0.410978 | − | 0.911645i | \(-0.365187\pi\) | ||||
0.410978 | + | 0.911645i | \(0.365187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.43845 | −0.160438 | ||||||||
\(232\) | 1.12311i | 0.0737355i | ||||||||
\(233\) | 20.0540i | 1.31378i | 0.753987 | + | 0.656890i | \(0.228128\pi\) | ||||
−0.753987 | + | 0.656890i | \(0.771872\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.87689 | −0.317459 | ||||||||
\(237\) | − 16.6847i | − 1.08379i | ||||||||
\(238\) | − 8.00000i | − 0.518563i | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.24621 | −0.273523 | −0.136761 | − | 0.990604i | \(-0.543669\pi\) | ||||
−0.136761 | + | 0.990604i | \(0.543669\pi\) | |||||||
\(242\) | 8.56155i | 0.550357i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.12311 | 0.0716066 | ||||||||
\(247\) | − 9.36932i | − 0.596155i | ||||||||
\(248\) | 1.00000i | 0.0635001i | ||||||||
\(249\) | −2.24621 | −0.142348 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4924 | −1.04099 | −0.520496 | − | 0.853864i | \(-0.674253\pi\) | ||||
−0.520496 | + | 0.853864i | \(0.674253\pi\) | |||||||
\(252\) | 1.56155i | 0.0983686i | ||||||||
\(253\) | − 8.68466i | − 0.546000i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 10.6847i | − 0.666491i | −0.942840 | − | 0.333245i | \(-0.891856\pi\) | ||||
0.942840 | − | 0.333245i | \(-0.108144\pi\) | |||||||
\(258\) | 7.80776i | 0.486090i | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.12311 | −0.0695185 | ||||||||
\(262\) | − 9.36932i | − 0.578838i | ||||||||
\(263\) | 12.4924i | 0.770316i | 0.922851 | + | 0.385158i | \(0.125853\pi\) | ||||
−0.922851 | + | 0.385158i | \(0.874147\pi\) | |||||||
\(264\) | −1.56155 | −0.0961069 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.31534 | −0.448532 | ||||||||
\(267\) | − 1.31534i | − 0.0804976i | ||||||||
\(268\) | 9.36932i | 0.572322i | ||||||||
\(269\) | −16.2462 | −0.990549 | −0.495274 | − | 0.868737i | \(-0.664933\pi\) | ||||
−0.495274 | + | 0.868737i | \(0.664933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0540 | −0.610736 | −0.305368 | − | 0.952234i | \(-0.598779\pi\) | ||||
−0.305368 | + | 0.952234i | \(0.598779\pi\) | |||||||
\(272\) | − 5.12311i | − 0.310634i | ||||||||
\(273\) | 3.12311i | 0.189019i | ||||||||
\(274\) | −3.75379 | −0.226775 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.56155 | −0.334766 | ||||||||
\(277\) | − 19.3693i | − 1.16379i | −0.813264 | − | 0.581895i | \(-0.802312\pi\) | ||||
0.813264 | − | 0.581895i | \(-0.197688\pi\) | |||||||
\(278\) | − 8.87689i | − 0.532401i | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.1231 | 0.782859 | 0.391429 | − | 0.920208i | \(-0.371981\pi\) | ||||
0.391429 | + | 0.920208i | \(0.371981\pi\) | |||||||
\(282\) | − 3.12311i | − 0.185978i | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | −4.68466 | −0.277983 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.12311 | −0.184673 | ||||||||
\(287\) | − 1.75379i | − 0.103523i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −9.24621 | −0.543895 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | 0.351726 | ||||||||
\(292\) | − 9.80776i | − 0.573956i | ||||||||
\(293\) | − 6.49242i | − 0.379291i | −0.981853 | − | 0.189646i | \(-0.939266\pi\) | ||||
0.981853 | − | 0.189646i | \(-0.0607339\pi\) | |||||||
\(294\) | −4.56155 | −0.266035 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.12311 | 0.297774 | ||||||||
\(297\) | − 1.56155i | − 0.0906105i | ||||||||
\(298\) | − 20.0540i | − 1.16170i | ||||||||
\(299\) | −11.1231 | −0.643266 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1922 | 0.702749 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 3.56155i | − 0.204606i | ||||||||
\(304\) | −4.68466 | −0.268684 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.12311 | 0.292868 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 2.43845i | 0.138943i | ||||||||
\(309\) | −18.2462 | −1.03799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.2462 | −1.03465 | −0.517324 | − | 0.855790i | \(-0.673072\pi\) | ||||
−0.517324 | + | 0.855790i | \(0.673072\pi\) | |||||||
\(312\) | 2.00000i | 0.113228i | ||||||||
\(313\) | − 10.0000i | − 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | 20.0540 | 1.13171 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.6847 | −0.938585 | ||||||||
\(317\) | − 25.1231i | − 1.41105i | −0.708683 | − | 0.705527i | \(-0.750710\pi\) | ||||
0.708683 | − | 0.705527i | \(-0.249290\pi\) | |||||||
\(318\) | − 11.5616i | − 0.648340i | ||||||||
\(319\) | −1.75379 | −0.0981933 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.56155 | −0.0871574 | ||||||||
\(322\) | 8.68466i | 0.483977i | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.36932 | 0.518918 | ||||||||
\(327\) | − 19.3693i | − 1.07113i | ||||||||
\(328\) | − 1.12311i | − 0.0620131i | ||||||||
\(329\) | −4.87689 | −0.268872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2462 | 0.563183 | 0.281591 | − | 0.959534i | \(-0.409138\pi\) | ||||
0.281591 | + | 0.959534i | \(0.409138\pi\) | |||||||
\(332\) | 2.24621i | 0.123277i | ||||||||
\(333\) | 5.12311i | 0.280744i | ||||||||
\(334\) | 2.43845 | 0.133426 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.56155 | 0.0851897 | ||||||||
\(337\) | 10.0000i | 0.544735i | 0.962193 | + | 0.272367i | \(0.0878066\pi\) | ||||
−0.962193 | + | 0.272367i | \(0.912193\pi\) | |||||||
\(338\) | − 9.00000i | − 0.489535i | ||||||||
\(339\) | 10.6847 | 0.580311 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.56155 | −0.0845628 | ||||||||
\(342\) | − 4.68466i | − 0.253317i | ||||||||
\(343\) | 18.0540i | 0.974823i | ||||||||
\(344\) | 7.80776 | 0.420966 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.24621 | −0.443319 | ||||||||
\(347\) | 2.24621i | 0.120583i | 0.998181 | + | 0.0602915i | \(0.0192030\pi\) | ||||
−0.998181 | + | 0.0602915i | \(0.980797\pi\) | |||||||
\(348\) | 1.12311i | 0.0602048i | ||||||||
\(349\) | 19.3693 | 1.03682 | 0.518408 | − | 0.855133i | \(-0.326525\pi\) | ||||
0.518408 | + | 0.855133i | \(0.326525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 1.56155i | 0.0832310i | ||||||||
\(353\) | 16.2462i | 0.864699i | 0.901706 | + | 0.432349i | \(0.142315\pi\) | ||||
−0.901706 | + | 0.432349i | \(0.857685\pi\) | |||||||
\(354\) | −4.87689 | −0.259204 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.31534 | −0.0697130 | ||||||||
\(357\) | − 8.00000i | − 0.423405i | ||||||||
\(358\) | − 12.0000i | − 0.634220i | ||||||||
\(359\) | 19.3153 | 1.01942 | 0.509712 | − | 0.860345i | \(-0.329752\pi\) | ||||
0.509712 | + | 0.860345i | \(0.329752\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.94602 | 0.155054 | ||||||||
\(362\) | − 24.0540i | − 1.26425i | ||||||||
\(363\) | 8.56155i | 0.449365i | ||||||||
\(364\) | 3.12311 | 0.163695 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | 9.36932i | 0.489074i | 0.969640 | + | 0.244537i | \(0.0786360\pi\) | ||||
−0.969640 | + | 0.244537i | \(0.921364\pi\) | |||||||
\(368\) | 5.56155i | 0.289916i | ||||||||
\(369\) | 1.12311 | 0.0584665 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0540 | −0.937316 | ||||||||
\(372\) | 1.00000i | 0.0518476i | ||||||||
\(373\) | 6.68466i | 0.346118i | 0.984911 | + | 0.173059i | \(0.0553652\pi\) | ||||
−0.984911 | + | 0.173059i | \(0.944635\pi\) | |||||||
\(374\) | 8.00000 | 0.413670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.12311 | −0.161062 | ||||||||
\(377\) | 2.24621i | 0.115686i | ||||||||
\(378\) | 1.56155i | 0.0803176i | ||||||||
\(379\) | −30.0540 | −1.54377 | −0.771885 | − | 0.635763i | \(-0.780686\pi\) | ||||
−0.771885 | + | 0.635763i | \(0.780686\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 2.24621i | − 0.114926i | ||||||||
\(383\) | 6.24621i | 0.319166i | 0.987184 | + | 0.159583i | \(0.0510150\pi\) | ||||
−0.987184 | + | 0.159583i | \(0.948985\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.4924 | −0.941240 | ||||||||
\(387\) | 7.80776i | 0.396891i | ||||||||
\(388\) | − 6.00000i | − 0.304604i | ||||||||
\(389\) | −24.2462 | −1.22933 | −0.614666 | − | 0.788788i | \(-0.710709\pi\) | ||||
−0.614666 | + | 0.788788i | \(0.710709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.4924 | 1.44092 | ||||||||
\(392\) | 4.56155i | 0.230393i | ||||||||
\(393\) | − 9.36932i | − 0.472620i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.56155 | −0.0784710 | ||||||||
\(397\) | 28.0540i | 1.40799i | 0.710206 | + | 0.703994i | \(0.248602\pi\) | ||||
−0.710206 | + | 0.703994i | \(0.751398\pi\) | |||||||
\(398\) | 3.80776i | 0.190866i | ||||||||
\(399\) | −7.31534 | −0.366225 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.31534 | −0.0656850 | −0.0328425 | − | 0.999461i | \(-0.510456\pi\) | ||||
−0.0328425 | + | 0.999461i | \(0.510456\pi\) | |||||||
\(402\) | 9.36932i | 0.467299i | ||||||||
\(403\) | 2.00000i | 0.0996271i | ||||||||
\(404\) | −3.56155 | −0.177194 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.75379 | 0.0870391 | ||||||||
\(407\) | 8.00000i | 0.396545i | ||||||||
\(408\) | − 5.12311i | − 0.253632i | ||||||||
\(409\) | 12.6307 | 0.624547 | 0.312274 | − | 0.949992i | \(-0.398909\pi\) | ||||
0.312274 | + | 0.949992i | \(0.398909\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.75379 | −0.185161 | ||||||||
\(412\) | 18.2462i | 0.898926i | ||||||||
\(413\) | 7.61553i | 0.374736i | ||||||||
\(414\) | −5.56155 | −0.273335 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | − 8.87689i | − 0.434703i | ||||||||
\(418\) | − 7.31534i | − 0.357805i | ||||||||
\(419\) | −22.2462 | −1.08680 | −0.543399 | − | 0.839474i | \(-0.682863\pi\) | ||||
−0.543399 | + | 0.839474i | \(0.682863\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4924 | 0.901266 | 0.450633 | − | 0.892709i | \(-0.351198\pi\) | ||||
0.450633 | + | 0.892709i | \(0.351198\pi\) | |||||||
\(422\) | 11.3153i | 0.550822i | ||||||||
\(423\) | − 3.12311i | − 0.151851i | ||||||||
\(424\) | −11.5616 | −0.561479 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.68466 | −0.226972 | ||||||||
\(427\) | 9.36932i | 0.453413i | ||||||||
\(428\) | 1.56155i | 0.0754805i | ||||||||
\(429\) | −3.12311 | −0.150785 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.7538 | −0.662497 | −0.331248 | − | 0.943544i | \(-0.607470\pi\) | ||||
−0.331248 | + | 0.943544i | \(0.607470\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − 18.3002i | − 0.879451i | −0.898132 | − | 0.439725i | \(-0.855076\pi\) | ||||
0.898132 | − | 0.439725i | \(-0.144924\pi\) | |||||||
\(434\) | 1.56155 | 0.0749569 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.3693 | −0.927622 | ||||||||
\(437\) | − 26.0540i | − 1.24633i | ||||||||
\(438\) | − 9.80776i | − 0.468633i | ||||||||
\(439\) | 31.6155 | 1.50893 | 0.754463 | − | 0.656342i | \(-0.227897\pi\) | ||||
0.754463 | + | 0.656342i | \(0.227897\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.56155 | −0.217217 | ||||||||
\(442\) | − 10.2462i | − 0.487363i | ||||||||
\(443\) | − 14.0540i | − 0.667725i | −0.942622 | − | 0.333862i | \(-0.891648\pi\) | ||||
0.942622 | − | 0.333862i | \(-0.108352\pi\) | |||||||
\(444\) | 5.12311 | 0.243132 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.8769 | −0.609739 | ||||||||
\(447\) | − 20.0540i | − 0.948520i | ||||||||
\(448\) | − 1.56155i | − 0.0737764i | ||||||||
\(449\) | 22.4924 | 1.06148 | 0.530742 | − | 0.847534i | \(-0.321913\pi\) | ||||
0.530742 | + | 0.847534i | \(0.321913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75379 | 0.0825827 | ||||||||
\(452\) | − 10.6847i | − 0.502564i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.68466 | 0.219862 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.68466 | −0.219379 | ||||||||
\(457\) | − 24.7386i | − 1.15722i | −0.815603 | − | 0.578612i | \(-0.803594\pi\) | ||||
0.815603 | − | 0.578612i | \(-0.196406\pi\) | |||||||
\(458\) | − 12.4384i | − 0.581210i | ||||||||
\(459\) | 5.12311 | 0.239126 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3693 | −0.715820 | −0.357910 | − | 0.933756i | \(-0.616511\pi\) | ||||
−0.357910 | + | 0.933756i | \(0.616511\pi\) | |||||||
\(462\) | 2.43845i | 0.113447i | ||||||||
\(463\) | − 18.7386i | − 0.870858i | −0.900223 | − | 0.435429i | \(-0.856597\pi\) | ||||
0.900223 | − | 0.435429i | \(-0.143403\pi\) | |||||||
\(464\) | 1.12311 | 0.0521389 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.0540 | 0.928982 | ||||||||
\(467\) | 26.2462i | 1.21453i | 0.794499 | + | 0.607265i | \(0.207733\pi\) | ||||
−0.794499 | + | 0.607265i | \(0.792267\pi\) | |||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | 14.6307 | 0.675582 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0540 | 0.924038 | ||||||||
\(472\) | 4.87689i | 0.224477i | ||||||||
\(473\) | 12.1922i | 0.560600i | ||||||||
\(474\) | −16.6847 | −0.766352 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | − 11.5616i | − 0.529367i | ||||||||
\(478\) | 24.0000i | 1.09773i | ||||||||
\(479\) | −6.43845 | −0.294180 | −0.147090 | − | 0.989123i | \(-0.546991\pi\) | ||||
−0.147090 | + | 0.989123i | \(0.546991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.2462 | 0.467187 | ||||||||
\(482\) | 4.24621i | 0.193410i | ||||||||
\(483\) | 8.68466i | 0.395166i | ||||||||
\(484\) | 8.56155 | 0.389161 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − 24.0000i | − 1.08754i | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||||
0.839233 | − | 0.543772i | \(-0.183004\pi\) | |||||||
\(488\) | 6.00000i | 0.271607i | ||||||||
\(489\) | 9.36932 | 0.423695 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.93087 | 0.132268 | 0.0661341 | − | 0.997811i | \(-0.478933\pi\) | ||||
0.0661341 | + | 0.997811i | \(0.478933\pi\) | |||||||
\(492\) | − 1.12311i | − 0.0506335i | ||||||||
\(493\) | − 5.75379i | − 0.259138i | ||||||||
\(494\) | −9.36932 | −0.421545 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 7.31534i | 0.328138i | ||||||||
\(498\) | 2.24621i | 0.100655i | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.43845 | 0.108942 | ||||||||
\(502\) | 16.4924i | 0.736093i | ||||||||
\(503\) | 9.75379i | 0.434900i | 0.976071 | + | 0.217450i | \(0.0697739\pi\) | ||||
−0.976071 | + | 0.217450i | \(0.930226\pi\) | |||||||
\(504\) | 1.56155 | 0.0695571 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.68466 | −0.386080 | ||||||||
\(507\) | − 9.00000i | − 0.399704i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.6155 | 0.958091 | 0.479046 | − | 0.877790i | \(-0.340983\pi\) | ||||
0.479046 | + | 0.877790i | \(0.340983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.3153 | −0.677511 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 4.68466i | − 0.206833i | ||||||||
\(514\) | −10.6847 | −0.471280 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.80776 | 0.343718 | ||||||||
\(517\) | − 4.87689i | − 0.214486i | ||||||||
\(518\) | − 8.00000i | − 0.351500i | ||||||||
\(519\) | −8.24621 | −0.361968 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.7538 | −0.690186 | −0.345093 | − | 0.938568i | \(-0.612153\pi\) | ||||
−0.345093 | + | 0.938568i | \(0.612153\pi\) | |||||||
\(522\) | 1.12311i | 0.0491570i | ||||||||
\(523\) | 39.4233i | 1.72386i | 0.507027 | + | 0.861930i | \(0.330744\pi\) | ||||
−0.507027 | + | 0.861930i | \(0.669256\pi\) | |||||||
\(524\) | −9.36932 | −0.409301 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.4924 | 0.544696 | ||||||||
\(527\) | − 5.12311i | − 0.223166i | ||||||||
\(528\) | 1.56155i | 0.0679579i | ||||||||
\(529\) | −7.93087 | −0.344820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.87689 | −0.211639 | ||||||||
\(532\) | 7.31534i | 0.317160i | ||||||||
\(533\) | − 2.24621i | − 0.0972942i | ||||||||
\(534\) | −1.31534 | −0.0569204 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.36932 | 0.404693 | ||||||||
\(537\) | − 12.0000i | − 0.517838i | ||||||||
\(538\) | 16.2462i | 0.700424i | ||||||||
\(539\) | −7.12311 | −0.306814 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.2462 | 1.55835 | 0.779173 | − | 0.626809i | \(-0.215639\pi\) | ||||
0.779173 | + | 0.626809i | \(0.215639\pi\) | |||||||
\(542\) | 10.0540i | 0.431855i | ||||||||
\(543\) | − 24.0540i | − 1.03225i | ||||||||
\(544\) | −5.12311 | −0.219651 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.12311 | 0.133657 | ||||||||
\(547\) | − 35.1231i | − 1.50176i | −0.660441 | − | 0.750878i | \(-0.729631\pi\) | ||||
0.660441 | − | 0.750878i | \(-0.270369\pi\) | |||||||
\(548\) | 3.75379i | 0.160354i | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.26137 | −0.224142 | ||||||||
\(552\) | 5.56155i | 0.236715i | ||||||||
\(553\) | 26.0540i | 1.10793i | ||||||||
\(554\) | −19.3693 | −0.822923 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.87689 | −0.376464 | ||||||||
\(557\) | 6.19224i | 0.262373i | 0.991358 | + | 0.131187i | \(0.0418787\pi\) | ||||
−0.991358 | + | 0.131187i | \(0.958121\pi\) | |||||||
\(558\) | 1.00000i | 0.0423334i | ||||||||
\(559\) | 15.6155 | 0.660466 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | − 13.1231i | − 0.553565i | ||||||||
\(563\) | − 16.4924i | − 0.695073i | −0.937667 | − | 0.347536i | \(-0.887018\pi\) | ||||
0.937667 | − | 0.347536i | \(-0.112982\pi\) | |||||||
\(564\) | −3.12311 | −0.131506 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.56155i | 0.0655791i | ||||||||
\(568\) | 4.68466i | 0.196564i | ||||||||
\(569\) | −10.1922 | −0.427281 | −0.213640 | − | 0.976912i | \(-0.568532\pi\) | ||||
−0.213640 | + | 0.976912i | \(0.568532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.8769 | 1.37586 | 0.687928 | − | 0.725779i | \(-0.258521\pi\) | ||||
0.687928 | + | 0.725779i | \(0.258521\pi\) | |||||||
\(572\) | 3.12311i | 0.130584i | ||||||||
\(573\) | − 2.24621i | − 0.0938368i | ||||||||
\(574\) | −1.75379 | −0.0732017 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 6.87689i | − 0.286289i | −0.989702 | − | 0.143144i | \(-0.954279\pi\) | ||||
0.989702 | − | 0.143144i | \(-0.0457213\pi\) | |||||||
\(578\) | 9.24621i | 0.384592i | ||||||||
\(579\) | −18.4924 | −0.768519 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.50758 | 0.145519 | ||||||||
\(582\) | − 6.00000i | − 0.248708i | ||||||||
\(583\) | − 18.0540i | − 0.747719i | ||||||||
\(584\) | −9.80776 | −0.405848 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.49242 | −0.268200 | ||||||||
\(587\) | − 32.4924i | − 1.34111i | −0.741862 | − | 0.670553i | \(-0.766057\pi\) | ||||
0.741862 | − | 0.670553i | \(-0.233943\pi\) | |||||||
\(588\) | 4.56155i | 0.188115i | ||||||||
\(589\) | −4.68466 | −0.193028 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | − 5.12311i | − 0.210558i | ||||||||
\(593\) | − 30.0000i | − 1.23195i | −0.787765 | − | 0.615976i | \(-0.788762\pi\) | ||||
0.787765 | − | 0.615976i | \(-0.211238\pi\) | |||||||
\(594\) | −1.56155 | −0.0640713 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.0540 | −0.821443 | ||||||||
\(597\) | 3.80776i | 0.155841i | ||||||||
\(598\) | 11.1231i | 0.454858i | ||||||||
\(599\) | 23.4233 | 0.957050 | 0.478525 | − | 0.878074i | \(-0.341172\pi\) | ||||
0.478525 | + | 0.878074i | \(0.341172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | − 12.1922i | − 0.496918i | ||||||||
\(603\) | 9.36932i | 0.381548i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.56155 | −0.144678 | ||||||||
\(607\) | 30.0540i | 1.21985i | 0.792458 | + | 0.609927i | \(0.208801\pi\) | ||||
−0.792458 | + | 0.609927i | \(0.791199\pi\) | |||||||
\(608\) | 4.68466i | 0.189988i | ||||||||
\(609\) | 1.75379 | 0.0710671 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.24621 | −0.252695 | ||||||||
\(612\) | − 5.12311i | − 0.207089i | ||||||||
\(613\) | 2.00000i | 0.0807792i | 0.999184 | + | 0.0403896i | \(0.0128599\pi\) | ||||
−0.999184 | + | 0.0403896i | \(0.987140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.43845 | 0.0982478 | ||||||||
\(617\) | 19.5616i | 0.787518i | 0.919214 | + | 0.393759i | \(0.128826\pi\) | ||||
−0.919214 | + | 0.393759i | \(0.871174\pi\) | |||||||
\(618\) | 18.2462i | 0.733970i | ||||||||
\(619\) | 13.3693 | 0.537358 | 0.268679 | − | 0.963230i | \(-0.413413\pi\) | ||||
0.268679 | + | 0.963230i | \(0.413413\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.56155 | −0.223177 | ||||||||
\(622\) | 18.2462i | 0.731606i | ||||||||
\(623\) | 2.05398i | 0.0822908i | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | − 7.31534i | − 0.292147i | ||||||||
\(628\) | − 20.0540i | − 0.800241i | ||||||||
\(629\) | −26.2462 | −1.04650 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.3002 | −0.967375 | −0.483688 | − | 0.875241i | \(-0.660703\pi\) | ||||
−0.483688 | + | 0.875241i | \(0.660703\pi\) | |||||||
\(632\) | 16.6847i | 0.663680i | ||||||||
\(633\) | 11.3153i | 0.449744i | ||||||||
\(634\) | −25.1231 | −0.997766 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.5616 | −0.458445 | ||||||||
\(637\) | 9.12311i | 0.361471i | ||||||||
\(638\) | 1.75379i | 0.0694332i | ||||||||
\(639\) | −4.68466 | −0.185322 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.4924 | −1.52036 | −0.760180 | − | 0.649713i | \(-0.774889\pi\) | ||||
−0.760180 | + | 0.649713i | \(0.774889\pi\) | |||||||
\(642\) | 1.56155i | 0.0616296i | ||||||||
\(643\) | 30.0540i | 1.18521i | 0.805492 | + | 0.592607i | \(0.201901\pi\) | ||||
−0.805492 | + | 0.592607i | \(0.798099\pi\) | |||||||
\(644\) | 8.68466 | 0.342223 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | 17.0691i | 0.671057i | 0.942030 | + | 0.335528i | \(0.108915\pi\) | ||||
−0.942030 | + | 0.335528i | \(0.891085\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −7.61553 | −0.298936 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.56155 | 0.0612021 | ||||||||
\(652\) | − 9.36932i | − 0.366931i | ||||||||
\(653\) | 23.7538i | 0.929558i | 0.885427 | + | 0.464779i | \(0.153866\pi\) | ||||
−0.885427 | + | 0.464779i | \(0.846134\pi\) | |||||||
\(654\) | −19.3693 | −0.757400 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.12311 | −0.0438499 | ||||||||
\(657\) | − 9.80776i | − 0.382637i | ||||||||
\(658\) | 4.87689i | 0.190121i | ||||||||
\(659\) | −18.7386 | −0.729954 | −0.364977 | − | 0.931017i | \(-0.618923\pi\) | ||||
−0.364977 | + | 0.931017i | \(0.618923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.49242 | −0.252526 | −0.126263 | − | 0.991997i | \(-0.540298\pi\) | ||||
−0.126263 | + | 0.991997i | \(0.540298\pi\) | |||||||
\(662\) | − 10.2462i | − 0.398230i | ||||||||
\(663\) | − 10.2462i | − 0.397930i | ||||||||
\(664\) | 2.24621 | 0.0871699 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.12311 | 0.198516 | ||||||||
\(667\) | 6.24621i | 0.241854i | ||||||||
\(668\) | − 2.43845i | − 0.0943464i | ||||||||
\(669\) | −12.8769 | −0.497849 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.36932 | −0.361698 | ||||||||
\(672\) | − 1.56155i | − 0.0602382i | ||||||||
\(673\) | 28.2462i | 1.08881i | 0.838822 | + | 0.544406i | \(0.183245\pi\) | ||||
−0.838822 | + | 0.544406i | \(0.816755\pi\) | |||||||
\(674\) | 10.0000 | 0.385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 29.4233i | 1.13083i | 0.824807 | + | 0.565414i | \(0.191284\pi\) | ||||
−0.824807 | + | 0.565414i | \(0.808716\pi\) | |||||||
\(678\) | − 10.6847i | − 0.410342i | ||||||||
\(679\) | −9.36932 | −0.359561 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.68466 | 0.179517 | ||||||||
\(682\) | 1.56155i | 0.0597949i | ||||||||
\(683\) | 19.3153i | 0.739081i | 0.929215 | + | 0.369541i | \(0.120485\pi\) | ||||
−0.929215 | + | 0.369541i | \(0.879515\pi\) | |||||||
\(684\) | −4.68466 | −0.179122 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.0540 | 0.689304 | ||||||||
\(687\) | − 12.4384i | − 0.474556i | ||||||||
\(688\) | − 7.80776i | − 0.297668i | ||||||||
\(689\) | −23.1231 | −0.880920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0540 | −0.838973 | −0.419486 | − | 0.907762i | \(-0.637790\pi\) | ||||
−0.419486 | + | 0.907762i | \(0.637790\pi\) | |||||||
\(692\) | 8.24621i | 0.313474i | ||||||||
\(693\) | 2.43845i | 0.0926289i | ||||||||
\(694\) | 2.24621 | 0.0852650 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.12311 | 0.0425712 | ||||||||
\(697\) | 5.75379i | 0.217940i | ||||||||
\(698\) | − 19.3693i | − 0.733139i | ||||||||
\(699\) | 20.0540 | 0.758511 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.8078 | 0.974746 | 0.487373 | − | 0.873194i | \(-0.337955\pi\) | ||||
0.487373 | + | 0.873194i | \(0.337955\pi\) | |||||||
\(702\) | 2.00000i | 0.0754851i | ||||||||
\(703\) | 24.0000i | 0.905177i | ||||||||
\(704\) | 1.56155 | 0.0588532 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.2462 | 0.611434 | ||||||||
\(707\) | 5.56155i | 0.209164i | ||||||||
\(708\) | 4.87689i | 0.183285i | ||||||||
\(709\) | 20.0540 | 0.753143 | 0.376571 | − | 0.926388i | \(-0.377103\pi\) | ||||
0.376571 | + | 0.926388i | \(0.377103\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.6847 | −0.625724 | ||||||||
\(712\) | 1.31534i | 0.0492945i | ||||||||
\(713\) | 5.56155i | 0.208282i | ||||||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 24.0000i | 0.896296i | ||||||||
\(718\) | − 19.3153i | − 0.720842i | ||||||||
\(719\) | 43.1231 | 1.60822 | 0.804110 | − | 0.594480i | \(-0.202642\pi\) | ||||
0.804110 | + | 0.594480i | \(0.202642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.4924 | 1.06111 | ||||||||
\(722\) | − 2.94602i | − 0.109640i | ||||||||
\(723\) | 4.24621i | 0.157918i | ||||||||
\(724\) | −24.0540 | −0.893959 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.56155 | 0.317749 | ||||||||
\(727\) | 14.0540i | 0.521233i | 0.965442 | + | 0.260617i | \(0.0839258\pi\) | ||||
−0.965442 | + | 0.260617i | \(0.916074\pi\) | |||||||
\(728\) | − 3.12311i | − 0.115750i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.0000 | −1.47945 | ||||||||
\(732\) | 6.00000i | 0.221766i | ||||||||
\(733\) | 26.4924i | 0.978520i | 0.872138 | + | 0.489260i | \(0.162733\pi\) | ||||
−0.872138 | + | 0.489260i | \(0.837267\pi\) | |||||||
\(734\) | 9.36932 | 0.345828 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.56155 | 0.205002 | ||||||||
\(737\) | 14.6307i | 0.538928i | ||||||||
\(738\) | − 1.12311i | − 0.0413421i | ||||||||
\(739\) | 12.9848 | 0.477655 | 0.238828 | − | 0.971062i | \(-0.423237\pi\) | ||||
0.238828 | + | 0.971062i | \(0.423237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.36932 | −0.344190 | ||||||||
\(742\) | 18.0540i | 0.662782i | ||||||||
\(743\) | 11.4233i | 0.419080i | 0.977800 | + | 0.209540i | \(0.0671966\pi\) | ||||
−0.977800 | + | 0.209540i | \(0.932803\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.68466 | 0.244743 | ||||||||
\(747\) | 2.24621i | 0.0821846i | ||||||||
\(748\) | − 8.00000i | − 0.292509i | ||||||||
\(749\) | 2.43845 | 0.0890989 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.8769 | 1.34566 | 0.672828 | − | 0.739798i | \(-0.265079\pi\) | ||||
0.672828 | + | 0.739798i | \(0.265079\pi\) | |||||||
\(752\) | 3.12311i | 0.113888i | ||||||||
\(753\) | 16.4924i | 0.601017i | ||||||||
\(754\) | 2.24621 | 0.0818022 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.56155 | 0.0567931 | ||||||||
\(757\) | − 10.0000i | − 0.363456i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||||
0.983349 | − | 0.181728i | \(-0.0581691\pi\) | |||||||
\(758\) | 30.0540i | 1.09161i | ||||||||
\(759\) | −8.68466 | −0.315233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.4233 | 1.50159 | 0.750797 | − | 0.660533i | \(-0.229670\pi\) | ||||
0.750797 | + | 0.660533i | \(0.229670\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.2462i | 1.09499i | ||||||||
\(764\) | −2.24621 | −0.0812651 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.24621 | 0.225685 | ||||||||
\(767\) | 9.75379i | 0.352189i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | 16.4384 | 0.592786 | 0.296393 | − | 0.955066i | \(-0.404216\pi\) | ||||
0.296393 | + | 0.955066i | \(0.404216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.6847 | −0.384799 | ||||||||
\(772\) | 18.4924i | 0.665557i | ||||||||
\(773\) | − 15.5616i | − 0.559710i | −0.960042 | − | 0.279855i | \(-0.909714\pi\) | ||||
0.960042 | − | 0.279855i | \(-0.0902864\pi\) | |||||||
\(774\) | 7.80776 | 0.280644 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | − 8.00000i | − 0.286998i | ||||||||
\(778\) | 24.2462i | 0.869269i | ||||||||
\(779\) | 5.26137 | 0.188508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.31534 | −0.261764 | ||||||||
\(782\) | − 28.4924i | − 1.01889i | ||||||||
\(783\) | 1.12311i | 0.0401365i | ||||||||
\(784\) | 4.56155 | 0.162913 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.36932 | −0.334192 | ||||||||
\(787\) | − 10.9309i | − 0.389643i | −0.980839 | − | 0.194822i | \(-0.937587\pi\) | ||||
0.980839 | − | 0.194822i | \(-0.0624128\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | 12.4924 | 0.444742 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.6847 | −0.593238 | ||||||||
\(792\) | 1.56155i | 0.0554874i | ||||||||
\(793\) | 12.0000i | 0.426132i | ||||||||
\(794\) | 28.0540 | 0.995598 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.80776 | 0.134963 | ||||||||
\(797\) | − 38.9848i | − 1.38091i | −0.723373 | − | 0.690457i | \(-0.757409\pi\) | ||||
0.723373 | − | 0.690457i | \(-0.242591\pi\) | |||||||
\(798\) | 7.31534i | 0.258960i | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.31534 | −0.0464753 | ||||||||
\(802\) | 1.31534i | 0.0464463i | ||||||||
\(803\) | − 15.3153i | − 0.540467i | ||||||||
\(804\) | 9.36932 | 0.330430 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | 16.2462i | 0.571894i | ||||||||
\(808\) | 3.56155i | 0.125295i | ||||||||
\(809\) | 25.3153 | 0.890040 | 0.445020 | − | 0.895521i | \(-0.353197\pi\) | ||||
0.445020 | + | 0.895521i | \(0.353197\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.6695 | 1.88459 | 0.942296 | − | 0.334782i | \(-0.108663\pi\) | ||||
0.942296 | + | 0.334782i | \(0.108663\pi\) | |||||||
\(812\) | − 1.75379i | − 0.0615459i | ||||||||
\(813\) | 10.0540i | 0.352608i | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.12311 | −0.179345 | ||||||||
\(817\) | 36.5767i | 1.27966i | ||||||||
\(818\) | − 12.6307i | − 0.441621i | ||||||||
\(819\) | 3.12311 | 0.109130 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.6155 | −0.754387 | −0.377194 | − | 0.926134i | \(-0.623111\pi\) | ||||
−0.377194 | + | 0.926134i | \(0.623111\pi\) | |||||||
\(822\) | 3.75379i | 0.130928i | ||||||||
\(823\) | 15.6155i | 0.544323i | 0.962252 | + | 0.272162i | \(0.0877385\pi\) | ||||
−0.962252 | + | 0.272162i | \(0.912261\pi\) | |||||||
\(824\) | 18.2462 | 0.635637 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.61553 | 0.264978 | ||||||||
\(827\) | − 18.2462i | − 0.634483i | −0.948345 | − | 0.317241i | \(-0.897243\pi\) | ||||
0.948345 | − | 0.317241i | \(-0.102757\pi\) | |||||||
\(828\) | 5.56155i | 0.193277i | ||||||||
\(829\) | 37.4233 | 1.29976 | 0.649882 | − | 0.760035i | \(-0.274818\pi\) | ||||
0.649882 | + | 0.760035i | \(0.274818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.3693 | −0.671914 | ||||||||
\(832\) | − 2.00000i | − 0.0693375i | ||||||||
\(833\) | − 23.3693i | − 0.809699i | ||||||||
\(834\) | −8.87689 | −0.307382 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.31534 | −0.253006 | ||||||||
\(837\) | 1.00000i | 0.0345651i | ||||||||
\(838\) | 22.2462i | 0.768483i | ||||||||
\(839\) | −34.9309 | −1.20595 | −0.602974 | − | 0.797761i | \(-0.706018\pi\) | ||||
−0.602974 | + | 0.797761i | \(0.706018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7386 | −0.956505 | ||||||||
\(842\) | − 18.4924i | − 0.637291i | ||||||||
\(843\) | − 13.1231i | − 0.451984i | ||||||||
\(844\) | 11.3153 | 0.389490 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.12311 | −0.107375 | ||||||||
\(847\) | − 13.3693i | − 0.459375i | ||||||||
\(848\) | 11.5616i | 0.397025i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.4924 | 0.976708 | ||||||||
\(852\) | 4.68466i | 0.160494i | ||||||||
\(853\) | − 38.7926i | − 1.32823i | −0.747629 | − | 0.664117i | \(-0.768808\pi\) | ||||
0.747629 | − | 0.664117i | \(-0.231192\pi\) | |||||||
\(854\) | 9.36932 | 0.320611 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.56155 | 0.0533728 | ||||||||
\(857\) | 53.2311i | 1.81834i | 0.416427 | + | 0.909169i | \(0.363282\pi\) | ||||
−0.416427 | + | 0.909169i | \(0.636718\pi\) | |||||||
\(858\) | 3.12311i | 0.106621i | ||||||||
\(859\) | 22.7386 | 0.775832 | 0.387916 | − | 0.921695i | \(-0.373195\pi\) | ||||
0.387916 | + | 0.921695i | \(0.373195\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.75379 | −0.0597690 | ||||||||
\(862\) | 13.7538i | 0.468456i | ||||||||
\(863\) | − 30.5464i | − 1.03981i | −0.854224 | − | 0.519906i | \(-0.825967\pi\) | ||||
0.854224 | − | 0.519906i | \(-0.174033\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.3002 | −0.621866 | ||||||||
\(867\) | 9.24621i | 0.314018i | ||||||||
\(868\) | − 1.56155i | − 0.0530026i | ||||||||
\(869\) | −26.0540 | −0.883821 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7386 | 0.634934 | ||||||||
\(872\) | 19.3693i | 0.655928i | ||||||||
\(873\) | − 6.00000i | − 0.203069i | ||||||||
\(874\) | −26.0540 | −0.881289 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.80776 | −0.331374 | ||||||||
\(877\) | 50.0000i | 1.68838i | 0.536044 | + | 0.844190i | \(0.319918\pi\) | ||||
−0.536044 | + | 0.844190i | \(0.680082\pi\) | |||||||
\(878\) | − 31.6155i | − 1.06697i | ||||||||
\(879\) | −6.49242 | −0.218984 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.4924 | 1.43161 | 0.715803 | − | 0.698302i | \(-0.246061\pi\) | ||||
0.715803 | + | 0.698302i | \(0.246061\pi\) | |||||||
\(882\) | 4.56155i | 0.153595i | ||||||||
\(883\) | − 31.4233i | − 1.05748i | −0.848784 | − | 0.528739i | \(-0.822665\pi\) | ||||
0.848784 | − | 0.528739i | \(-0.177335\pi\) | |||||||
\(884\) | −10.2462 | −0.344617 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.0540 | −0.472153 | ||||||||
\(887\) | 57.3693i | 1.92627i | 0.269013 | + | 0.963137i | \(0.413303\pi\) | ||||
−0.269013 | + | 0.963137i | \(0.586697\pi\) | |||||||
\(888\) | − 5.12311i | − 0.171920i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.56155 | −0.0523140 | ||||||||
\(892\) | 12.8769i | 0.431150i | ||||||||
\(893\) | − 14.6307i | − 0.489597i | ||||||||
\(894\) | −20.0540 | −0.670705 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.56155 | −0.0521678 | ||||||||
\(897\) | 11.1231i | 0.371390i | ||||||||
\(898\) | − 22.4924i | − 0.750582i | ||||||||
\(899\) | 1.12311 | 0.0374577 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.2311 | 1.97327 | ||||||||
\(902\) | − 1.75379i | − 0.0583948i | ||||||||
\(903\) | − 12.1922i | − 0.405732i | ||||||||
\(904\) | −10.6847 | −0.355366 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 24.0000i | − 0.796907i | −0.917189 | − | 0.398453i | \(-0.869547\pi\) | ||||
0.917189 | − | 0.398453i | \(-0.130453\pi\) | |||||||
\(908\) | − 4.68466i | − 0.155466i | ||||||||
\(909\) | −3.56155 | −0.118129 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.4924 | −1.47410 | −0.737050 | − | 0.675838i | \(-0.763782\pi\) | ||||
−0.737050 | + | 0.675838i | \(0.763782\pi\) | |||||||
\(912\) | 4.68466i | 0.155125i | ||||||||
\(913\) | 3.50758i | 0.116084i | ||||||||
\(914\) | −24.7386 | −0.818281 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.4384 | −0.410978 | ||||||||
\(917\) | 14.6307i | 0.483148i | ||||||||
\(918\) | − 5.12311i | − 0.169088i | ||||||||
\(919\) | −39.6155 | −1.30680 | −0.653398 | − | 0.757015i | \(-0.726657\pi\) | ||||
−0.653398 | + | 0.757015i | \(0.726657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.3693i | 0.506161i | ||||||||
\(923\) | 9.36932i | 0.308395i | ||||||||
\(924\) | 2.43845 | 0.0802190 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.7386 | −0.615790 | ||||||||
\(927\) | 18.2462i | 0.599284i | ||||||||
\(928\) | − 1.12311i | − 0.0368677i | ||||||||
\(929\) | −11.5616 | −0.379322 | −0.189661 | − | 0.981850i | \(-0.560739\pi\) | ||||
−0.189661 | + | 0.981850i | \(0.560739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.3693 | −0.700351 | ||||||||
\(932\) | − 20.0540i | − 0.656890i | ||||||||
\(933\) | 18.2462i | 0.597354i | ||||||||
\(934\) | 26.2462 | 0.858802 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | − 16.6307i | − 0.543301i | −0.962396 | − | 0.271650i | \(-0.912431\pi\) | ||||
0.962396 | − | 0.271650i | \(-0.0875694\pi\) | |||||||
\(938\) | − 14.6307i | − 0.477709i | ||||||||
\(939\) | −10.0000 | −0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.3693 | 0.892214 | 0.446107 | − | 0.894980i | \(-0.352810\pi\) | ||||
0.446107 | + | 0.894980i | \(0.352810\pi\) | |||||||
\(942\) | − 20.0540i | − 0.653394i | ||||||||
\(943\) | − 6.24621i | − 0.203405i | ||||||||
\(944\) | 4.87689 | 0.158729 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.1922 | 0.396404 | ||||||||
\(947\) | 0.876894i | 0.0284952i | 0.999898 | + | 0.0142476i | \(0.00453531\pi\) | ||||
−0.999898 | + | 0.0142476i | \(0.995465\pi\) | |||||||
\(948\) | 16.6847i | 0.541893i | ||||||||
\(949\) | −19.6155 | −0.636747 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.1231 | −0.814673 | ||||||||
\(952\) | 8.00000i | 0.259281i | ||||||||
\(953\) | − 58.1080i | − 1.88230i | −0.337988 | − | 0.941151i | \(-0.609746\pi\) | ||||
0.337988 | − | 0.941151i | \(-0.390254\pi\) | |||||||
\(954\) | −11.5616 | −0.374319 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | 1.75379i | 0.0566919i | ||||||||
\(958\) | 6.43845i | 0.208017i | ||||||||
\(959\) | 5.86174 | 0.189285 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | − 10.2462i | − 0.330351i | ||||||||
\(963\) | 1.56155i | 0.0503203i | ||||||||
\(964\) | 4.24621 | 0.136761 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.68466 | 0.279424 | ||||||||
\(967\) | 25.7538i | 0.828186i | 0.910235 | + | 0.414093i | \(0.135901\pi\) | ||||
−0.910235 | + | 0.414093i | \(0.864099\pi\) | |||||||
\(968\) | − 8.56155i | − 0.275179i | ||||||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.8769 | −0.926704 | −0.463352 | − | 0.886174i | \(-0.653353\pi\) | ||||
−0.463352 | + | 0.886174i | \(0.653353\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 13.8617i | 0.444387i | ||||||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 22.9848i | 0.735350i | 0.929954 | + | 0.367675i | \(0.119846\pi\) | ||||
−0.929954 | + | 0.367675i | \(0.880154\pi\) | |||||||
\(978\) | − 9.36932i | − 0.299598i | ||||||||
\(979\) | −2.05398 | −0.0656453 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.3693 | −0.618415 | ||||||||
\(982\) | − 2.93087i | − 0.0935278i | ||||||||
\(983\) | − 24.9848i | − 0.796893i | −0.917192 | − | 0.398446i | \(-0.869549\pi\) | ||||
0.917192 | − | 0.398446i | \(-0.130451\pi\) | |||||||
\(984\) | −1.12311 | −0.0358033 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.75379 | −0.183238 | ||||||||
\(987\) | 4.87689i | 0.155233i | ||||||||
\(988\) | 9.36932i | 0.298078i | ||||||||
\(989\) | 43.4233 | 1.38078 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.3153 | 0.740636 | 0.370318 | − | 0.928905i | \(-0.379249\pi\) | ||||
0.370318 | + | 0.928905i | \(0.379249\pi\) | |||||||
\(992\) | − 1.00000i | − 0.0317500i | ||||||||
\(993\) | − 10.2462i | − 0.325154i | ||||||||
\(994\) | 7.31534 | 0.232029 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.24621 | 0.0711739 | ||||||||
\(997\) | 62.4924i | 1.97915i | 0.144002 | + | 0.989577i | \(0.454003\pi\) | ||||
−0.144002 | + | 0.989577i | \(0.545997\pi\) | |||||||
\(998\) | 20.0000i | 0.633089i | ||||||||
\(999\) | 5.12311 | 0.162088 |
(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 | 4650.2.d.bd.3349.2 | 4 | ||
5.2 | odd | 4 | 930.2.a.p.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 4650.2.a.ce.1.2 | 2 | |||
5.4 | even | 2 | inner | 4650.2.d.bd.3349.3 | 4 | ||
15.2 | even | 4 | 2790.2.a.be.1.1 | 2 | |||
20.7 | even | 4 | 7440.2.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.p.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
2790.2.a.be.1.1 | 2 | 15.2 | even | 4 | |||
4650.2.a.ce.1.2 | 2 | 5.3 | odd | 4 | |||
4650.2.d.bd.3349.2 | 4 | 1.1 | even | 1 | trivial | ||
4650.2.d.bd.3349.3 | 4 | 5.4 | even | 2 | inner | ||
7440.2.a.bl.1.2 | 2 | 20.7 | even | 4 |