Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0838915322\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.37228 | −1.94699 | −0.973494 | − | 0.228714i | \(-0.926548\pi\) | ||||
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.37228 | 1.50813 | 0.754065 | − | 0.656800i | \(-0.228090\pi\) | ||||
0.754065 | + | 0.656800i | \(0.228090\pi\) | |||||||
\(6\) | 3.37228 | 1.37673 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.37228 | 2.79076 | ||||||||
\(10\) | −3.37228 | −1.06641 | ||||||||
\(11\) | 1.37228 | 0.413758 | 0.206879 | − | 0.978366i | \(-0.433669\pi\) | ||||
0.206879 | + | 0.978366i | \(0.433669\pi\) | |||||||
\(12\) | −3.37228 | −0.973494 | ||||||||
\(13\) | −0.372281 | −0.103252 | −0.0516261 | − | 0.998666i | \(-0.516440\pi\) | ||||
−0.0516261 | + | 0.998666i | \(0.516440\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.3723 | −2.93631 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.74456 | 1.15073 | 0.575363 | − | 0.817898i | \(-0.304861\pi\) | ||||
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(18\) | −8.37228 | −1.97337 | ||||||||
\(19\) | 5.37228 | 1.23249 | 0.616243 | − | 0.787556i | \(-0.288654\pi\) | ||||
0.616243 | + | 0.787556i | \(0.288654\pi\) | |||||||
\(20\) | 3.37228 | 0.754065 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.37228 | −0.292571 | ||||||||
\(23\) | −8.74456 | −1.82337 | −0.911684 | − | 0.410893i | \(-0.865217\pi\) | ||||
−0.911684 | + | 0.410893i | \(0.865217\pi\) | |||||||
\(24\) | 3.37228 | 0.688364 | ||||||||
\(25\) | 6.37228 | 1.27446 | ||||||||
\(26\) | 0.372281 | 0.0730104 | ||||||||
\(27\) | −18.1168 | −3.48659 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.11684 | −1.32156 | −0.660782 | − | 0.750578i | \(-0.729775\pi\) | ||||
−0.660782 | + | 0.750578i | \(0.729775\pi\) | |||||||
\(30\) | 11.3723 | 2.07629 | ||||||||
\(31\) | −2.74456 | −0.492938 | −0.246469 | − | 0.969151i | \(-0.579270\pi\) | ||||
−0.246469 | + | 0.969151i | \(0.579270\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.62772 | −0.805582 | ||||||||
\(34\) | −4.74456 | −0.813686 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.37228 | 1.39538 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −5.37228 | −0.871499 | ||||||||
\(39\) | 1.25544 | 0.201031 | ||||||||
\(40\) | −3.37228 | −0.533204 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.37228 | −0.971764 | −0.485882 | − | 0.874024i | \(-0.661501\pi\) | ||||
−0.485882 | + | 0.874024i | \(0.661501\pi\) | |||||||
\(44\) | 1.37228 | 0.206879 | ||||||||
\(45\) | 28.2337 | 4.20883 | ||||||||
\(46\) | 8.74456 | 1.28932 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | −3.37228 | −0.486747 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.37228 | −0.901177 | ||||||||
\(51\) | −16.0000 | −2.24045 | ||||||||
\(52\) | −0.372281 | −0.0516261 | ||||||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | 18.1168 | 2.46539 | ||||||||
\(55\) | 4.62772 | 0.624001 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.1168 | −2.39963 | ||||||||
\(58\) | 7.11684 | 0.934487 | ||||||||
\(59\) | 0.372281 | 0.0484669 | 0.0242335 | − | 0.999706i | \(-0.492285\pi\) | ||||
0.0242335 | + | 0.999706i | \(0.492285\pi\) | |||||||
\(60\) | −11.3723 | −1.46816 | ||||||||
\(61\) | −2.62772 | −0.336445 | −0.168222 | − | 0.985749i | \(-0.553803\pi\) | ||||
−0.168222 | + | 0.985749i | \(0.553803\pi\) | |||||||
\(62\) | 2.74456 | 0.348560 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.25544 | −0.155718 | ||||||||
\(66\) | 4.62772 | 0.569633 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 4.74456 | 0.575363 | ||||||||
\(69\) | 29.4891 | 3.55007 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7446 | −1.39382 | −0.696912 | − | 0.717157i | \(-0.745443\pi\) | ||||
−0.696912 | + | 0.717157i | \(0.745443\pi\) | |||||||
\(72\) | −8.37228 | −0.986683 | ||||||||
\(73\) | −13.1168 | −1.53521 | −0.767605 | − | 0.640923i | \(-0.778552\pi\) | ||||
−0.767605 | + | 0.640923i | \(0.778552\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | −21.4891 | −2.48135 | ||||||||
\(76\) | 5.37228 | 0.616243 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.25544 | −0.142150 | ||||||||
\(79\) | −4.62772 | −0.520659 | −0.260330 | − | 0.965520i | \(-0.583831\pi\) | ||||
−0.260330 | + | 0.965520i | \(0.583831\pi\) | |||||||
\(80\) | 3.37228 | 0.377033 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | 0.372281 | 0.0408632 | 0.0204316 | − | 0.999791i | \(-0.493496\pi\) | ||||
0.0204316 | + | 0.999791i | \(0.493496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.0000 | 1.73544 | ||||||||
\(86\) | 6.37228 | 0.687141 | ||||||||
\(87\) | 24.0000 | 2.57307 | ||||||||
\(88\) | −1.37228 | −0.146286 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | −28.2337 | −2.97609 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.74456 | −0.911684 | ||||||||
\(93\) | 9.25544 | 0.959744 | ||||||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 18.1168 | 1.85875 | ||||||||
\(96\) | 3.37228 | 0.344182 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.4891 | 1.15470 | ||||||||
\(100\) | 6.37228 | 0.637228 | ||||||||
\(101\) | −3.25544 | −0.323928 | −0.161964 | − | 0.986797i | \(-0.551783\pi\) | ||||
−0.161964 | + | 0.986797i | \(0.551783\pi\) | |||||||
\(102\) | 16.0000 | 1.58424 | ||||||||
\(103\) | 10.7446 | 1.05869 | 0.529347 | − | 0.848406i | \(-0.322437\pi\) | ||||
0.529347 | + | 0.848406i | \(0.322437\pi\) | |||||||
\(104\) | 0.372281 | 0.0365052 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | 1.11684 | 0.107969 | 0.0539847 | − | 0.998542i | \(-0.482808\pi\) | ||||
0.0539847 | + | 0.998542i | \(0.482808\pi\) | |||||||
\(108\) | −18.1168 | −1.74329 | ||||||||
\(109\) | 5.62772 | 0.539038 | 0.269519 | − | 0.962995i | \(-0.413135\pi\) | ||||
0.269519 | + | 0.962995i | \(0.413135\pi\) | |||||||
\(110\) | −4.62772 | −0.441236 | ||||||||
\(111\) | 6.74456 | 0.640166 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.48913 | 0.610446 | 0.305223 | − | 0.952281i | \(-0.401269\pi\) | ||||
0.305223 | + | 0.952281i | \(0.401269\pi\) | |||||||
\(114\) | 18.1168 | 1.69680 | ||||||||
\(115\) | −29.4891 | −2.74988 | ||||||||
\(116\) | −7.11684 | −0.660782 | ||||||||
\(117\) | −3.11684 | −0.288152 | ||||||||
\(118\) | −0.372281 | −0.0342713 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 11.3723 | 1.03814 | ||||||||
\(121\) | −9.11684 | −0.828804 | ||||||||
\(122\) | 2.62772 | 0.237902 | ||||||||
\(123\) | −3.37228 | −0.304068 | ||||||||
\(124\) | −2.74456 | −0.246469 | ||||||||
\(125\) | 4.62772 | 0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00000 | −0.532414 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 21.4891 | 1.89201 | ||||||||
\(130\) | 1.25544 | 0.110109 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | −4.62772 | −0.402791 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | −61.0951 | −5.25823 | ||||||||
\(136\) | −4.74456 | −0.406843 | ||||||||
\(137\) | 2.74456 | 0.234484 | 0.117242 | − | 0.993103i | \(-0.462595\pi\) | ||||
0.117242 | + | 0.993103i | \(0.462595\pi\) | |||||||
\(138\) | −29.4891 | −2.51028 | ||||||||
\(139\) | −5.25544 | −0.445760 | −0.222880 | − | 0.974846i | \(-0.571546\pi\) | ||||
−0.222880 | + | 0.974846i | \(0.571546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.9783 | 2.27198 | ||||||||
\(142\) | 11.7446 | 0.985582 | ||||||||
\(143\) | −0.510875 | −0.0427215 | ||||||||
\(144\) | 8.37228 | 0.697690 | ||||||||
\(145\) | −24.0000 | −1.99309 | ||||||||
\(146\) | 13.1168 | 1.08556 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 2.88316 | 0.236197 | 0.118099 | − | 0.993002i | \(-0.462320\pi\) | ||||
0.118099 | + | 0.993002i | \(0.462320\pi\) | |||||||
\(150\) | 21.4891 | 1.75458 | ||||||||
\(151\) | −0.883156 | −0.0718702 | −0.0359351 | − | 0.999354i | \(-0.511441\pi\) | ||||
−0.0359351 | + | 0.999354i | \(0.511441\pi\) | |||||||
\(152\) | −5.37228 | −0.435750 | ||||||||
\(153\) | 39.7228 | 3.21140 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.25544 | −0.743415 | ||||||||
\(156\) | 1.25544 | 0.100515 | ||||||||
\(157\) | 15.8614 | 1.26588 | 0.632939 | − | 0.774202i | \(-0.281848\pi\) | ||||
0.632939 | + | 0.774202i | \(0.281848\pi\) | |||||||
\(158\) | 4.62772 | 0.368162 | ||||||||
\(159\) | 33.7228 | 2.67439 | ||||||||
\(160\) | −3.37228 | −0.266602 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −35.9783 | −2.82672 | ||||||||
\(163\) | 13.1168 | 1.02739 | 0.513695 | − | 0.857973i | \(-0.328276\pi\) | ||||
0.513695 | + | 0.857973i | \(0.328276\pi\) | |||||||
\(164\) | 1.00000 | 0.0780869 | ||||||||
\(165\) | −15.6060 | −1.21492 | ||||||||
\(166\) | −0.372281 | −0.0288946 | ||||||||
\(167\) | 13.6277 | 1.05454 | 0.527272 | − | 0.849696i | \(-0.323215\pi\) | ||||
0.527272 | + | 0.849696i | \(0.323215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8614 | −0.989339 | ||||||||
\(170\) | −16.0000 | −1.22714 | ||||||||
\(171\) | 44.9783 | 3.43957 | ||||||||
\(172\) | −6.37228 | −0.485882 | ||||||||
\(173\) | 10.1168 | 0.769169 | 0.384585 | − | 0.923090i | \(-0.374345\pi\) | ||||
0.384585 | + | 0.923090i | \(0.374345\pi\) | |||||||
\(174\) | −24.0000 | −1.81944 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.37228 | 0.103440 | ||||||||
\(177\) | −1.25544 | −0.0943645 | ||||||||
\(178\) | −2.00000 | −0.149906 | ||||||||
\(179\) | 13.3723 | 0.999491 | 0.499746 | − | 0.866172i | \(-0.333427\pi\) | ||||
0.499746 | + | 0.866172i | \(0.333427\pi\) | |||||||
\(180\) | 28.2337 | 2.10441 | ||||||||
\(181\) | −23.4891 | −1.74593 | −0.872966 | − | 0.487780i | \(-0.837807\pi\) | ||||
−0.872966 | + | 0.487780i | \(0.837807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.86141 | 0.655054 | ||||||||
\(184\) | 8.74456 | 0.644658 | ||||||||
\(185\) | −6.74456 | −0.495870 | ||||||||
\(186\) | −9.25544 | −0.678642 | ||||||||
\(187\) | 6.51087 | 0.476122 | ||||||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.1168 | −1.31433 | ||||||||
\(191\) | −13.6277 | −0.986067 | −0.493034 | − | 0.870010i | \(-0.664112\pi\) | ||||
−0.493034 | + | 0.870010i | \(0.664112\pi\) | |||||||
\(192\) | −3.37228 | −0.243373 | ||||||||
\(193\) | 1.25544 | 0.0903684 | 0.0451842 | − | 0.998979i | \(-0.485613\pi\) | ||||
0.0451842 | + | 0.998979i | \(0.485613\pi\) | |||||||
\(194\) | 8.00000 | 0.574367 | ||||||||
\(195\) | 4.23369 | 0.303181 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.37228 | 0.525253 | 0.262627 | − | 0.964898i | \(-0.415411\pi\) | ||||
0.262627 | + | 0.964898i | \(0.415411\pi\) | |||||||
\(198\) | −11.4891 | −0.816497 | ||||||||
\(199\) | −2.37228 | −0.168167 | −0.0840833 | − | 0.996459i | \(-0.526796\pi\) | ||||
−0.0840833 | + | 0.996459i | \(0.526796\pi\) | |||||||
\(200\) | −6.37228 | −0.450588 | ||||||||
\(201\) | 26.9783 | 1.90290 | ||||||||
\(202\) | 3.25544 | 0.229052 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.0000 | −1.12022 | ||||||||
\(205\) | 3.37228 | 0.235530 | ||||||||
\(206\) | −10.7446 | −0.748609 | ||||||||
\(207\) | −73.2119 | −5.08858 | ||||||||
\(208\) | −0.372281 | −0.0258131 | ||||||||
\(209\) | 7.37228 | 0.509951 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.11684 | −0.558787 | −0.279393 | − | 0.960177i | \(-0.590133\pi\) | ||||
−0.279393 | + | 0.960177i | \(0.590133\pi\) | |||||||
\(212\) | −10.0000 | −0.686803 | ||||||||
\(213\) | 39.6060 | 2.71376 | ||||||||
\(214\) | −1.11684 | −0.0763459 | ||||||||
\(215\) | −21.4891 | −1.46555 | ||||||||
\(216\) | 18.1168 | 1.23270 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.62772 | −0.381157 | ||||||||
\(219\) | 44.2337 | 2.98904 | ||||||||
\(220\) | 4.62772 | 0.312001 | ||||||||
\(221\) | −1.76631 | −0.118815 | ||||||||
\(222\) | −6.74456 | −0.452665 | ||||||||
\(223\) | −3.25544 | −0.218000 | −0.109000 | − | 0.994042i | \(-0.534765\pi\) | ||||
−0.109000 | + | 0.994042i | \(0.534765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 53.3505 | 3.55670 | ||||||||
\(226\) | −6.48913 | −0.431650 | ||||||||
\(227\) | −11.3723 | −0.754805 | −0.377402 | − | 0.926049i | \(-0.623183\pi\) | ||||
−0.377402 | + | 0.926049i | \(0.623183\pi\) | |||||||
\(228\) | −18.1168 | −1.19982 | ||||||||
\(229\) | 5.62772 | 0.371890 | 0.185945 | − | 0.982560i | \(-0.440465\pi\) | ||||
0.185945 | + | 0.982560i | \(0.440465\pi\) | |||||||
\(230\) | 29.4891 | 1.94446 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.11684 | 0.467244 | ||||||||
\(233\) | −23.4891 | −1.53882 | −0.769412 | − | 0.638753i | \(-0.779451\pi\) | ||||
−0.769412 | + | 0.638753i | \(0.779451\pi\) | |||||||
\(234\) | 3.11684 | 0.203754 | ||||||||
\(235\) | −26.9783 | −1.75987 | ||||||||
\(236\) | 0.372281 | 0.0242335 | ||||||||
\(237\) | 15.6060 | 1.01372 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3723 | −1.25309 | −0.626544 | − | 0.779386i | \(-0.715531\pi\) | ||||
−0.626544 | + | 0.779386i | \(0.715531\pi\) | |||||||
\(240\) | −11.3723 | −0.734078 | ||||||||
\(241\) | 6.88316 | 0.443383 | 0.221692 | − | 0.975117i | \(-0.428842\pi\) | ||||
0.221692 | + | 0.975117i | \(0.428842\pi\) | |||||||
\(242\) | 9.11684 | 0.586053 | ||||||||
\(243\) | −66.9783 | −4.29666 | ||||||||
\(244\) | −2.62772 | −0.168222 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.37228 | 0.215009 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 2.74456 | 0.174280 | ||||||||
\(249\) | −1.25544 | −0.0795601 | ||||||||
\(250\) | −4.62772 | −0.292683 | ||||||||
\(251\) | −13.8614 | −0.874924 | −0.437462 | − | 0.899237i | \(-0.644123\pi\) | ||||
−0.437462 | + | 0.899237i | \(0.644123\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 6.00000 | 0.376473 | ||||||||
\(255\) | −53.9565 | −3.37889 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | −21.4891 | −1.33785 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.25544 | −0.0778589 | ||||||||
\(261\) | −59.5842 | −3.68817 | ||||||||
\(262\) | −12.0000 | −0.741362 | ||||||||
\(263\) | −13.6277 | −0.840321 | −0.420161 | − | 0.907450i | \(-0.638026\pi\) | ||||
−0.420161 | + | 0.907450i | \(0.638026\pi\) | |||||||
\(264\) | 4.62772 | 0.284816 | ||||||||
\(265\) | −33.7228 | −2.07158 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.74456 | −0.412761 | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | −28.3505 | −1.72856 | −0.864281 | − | 0.503009i | \(-0.832226\pi\) | ||||
−0.864281 | + | 0.503009i | \(0.832226\pi\) | |||||||
\(270\) | 61.0951 | 3.71813 | ||||||||
\(271\) | 28.7446 | 1.74611 | 0.873054 | − | 0.487624i | \(-0.162136\pi\) | ||||
0.873054 | + | 0.487624i | \(0.162136\pi\) | |||||||
\(272\) | 4.74456 | 0.287681 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.74456 | −0.165805 | ||||||||
\(275\) | 8.74456 | 0.527317 | ||||||||
\(276\) | 29.4891 | 1.77504 | ||||||||
\(277\) | 17.6060 | 1.05784 | 0.528920 | − | 0.848672i | \(-0.322597\pi\) | ||||
0.528920 | + | 0.848672i | \(0.322597\pi\) | |||||||
\(278\) | 5.25544 | 0.315200 | ||||||||
\(279\) | −22.9783 | −1.37567 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.25544 | −0.432823 | −0.216412 | − | 0.976302i | \(-0.569435\pi\) | ||||
−0.216412 | + | 0.976302i | \(0.569435\pi\) | |||||||
\(282\) | −26.9783 | −1.60653 | ||||||||
\(283\) | 19.6277 | 1.16675 | 0.583373 | − | 0.812204i | \(-0.301732\pi\) | ||||
0.583373 | + | 0.812204i | \(0.301732\pi\) | |||||||
\(284\) | −11.7446 | −0.696912 | ||||||||
\(285\) | −61.0951 | −3.61896 | ||||||||
\(286\) | 0.510875 | 0.0302087 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8.37228 | −0.493341 | ||||||||
\(289\) | 5.51087 | 0.324169 | ||||||||
\(290\) | 24.0000 | 1.40933 | ||||||||
\(291\) | 26.9783 | 1.58149 | ||||||||
\(292\) | −13.1168 | −0.767605 | ||||||||
\(293\) | 1.62772 | 0.0950923 | 0.0475462 | − | 0.998869i | \(-0.484860\pi\) | ||||
0.0475462 | + | 0.998869i | \(0.484860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.25544 | 0.0730944 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | −24.8614 | −1.44261 | ||||||||
\(298\) | −2.88316 | −0.167017 | ||||||||
\(299\) | 3.25544 | 0.188267 | ||||||||
\(300\) | −21.4891 | −1.24068 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.883156 | 0.0508199 | ||||||||
\(303\) | 10.9783 | 0.630684 | ||||||||
\(304\) | 5.37228 | 0.308121 | ||||||||
\(305\) | −8.86141 | −0.507403 | ||||||||
\(306\) | −39.7228 | −2.27080 | ||||||||
\(307\) | −23.8614 | −1.36184 | −0.680921 | − | 0.732357i | \(-0.738420\pi\) | ||||
−0.680921 | + | 0.732357i | \(0.738420\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.2337 | −2.06126 | ||||||||
\(310\) | 9.25544 | 0.525674 | ||||||||
\(311\) | −10.3723 | −0.588158 | −0.294079 | − | 0.955781i | \(-0.595013\pi\) | ||||
−0.294079 | + | 0.955781i | \(0.595013\pi\) | |||||||
\(312\) | −1.25544 | −0.0710751 | ||||||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | −15.8614 | −0.895111 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.62772 | −0.260330 | ||||||||
\(317\) | −24.7446 | −1.38979 | −0.694897 | − | 0.719110i | \(-0.744550\pi\) | ||||
−0.694897 | + | 0.719110i | \(0.744550\pi\) | |||||||
\(318\) | −33.7228 | −1.89108 | ||||||||
\(319\) | −9.76631 | −0.546808 | ||||||||
\(320\) | 3.37228 | 0.188516 | ||||||||
\(321\) | −3.76631 | −0.210215 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4891 | 1.41825 | ||||||||
\(324\) | 35.9783 | 1.99879 | ||||||||
\(325\) | −2.37228 | −0.131590 | ||||||||
\(326\) | −13.1168 | −0.726475 | ||||||||
\(327\) | −18.9783 | −1.04950 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 15.6060 | 0.859080 | ||||||||
\(331\) | −0.744563 | −0.0409249 | −0.0204624 | − | 0.999791i | \(-0.506514\pi\) | ||||
−0.0204624 | + | 0.999791i | \(0.506514\pi\) | |||||||
\(332\) | 0.372281 | 0.0204316 | ||||||||
\(333\) | −16.7446 | −0.917596 | ||||||||
\(334\) | −13.6277 | −0.745676 | ||||||||
\(335\) | −26.9783 | −1.47398 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 12.8614 | 0.699568 | ||||||||
\(339\) | −21.8832 | −1.18853 | ||||||||
\(340\) | 16.0000 | 0.867722 | ||||||||
\(341\) | −3.76631 | −0.203957 | ||||||||
\(342\) | −44.9783 | −2.43215 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.37228 | 0.343570 | ||||||||
\(345\) | 99.4456 | 5.35397 | ||||||||
\(346\) | −10.1168 | −0.543885 | ||||||||
\(347\) | −15.6060 | −0.837772 | −0.418886 | − | 0.908039i | \(-0.637579\pi\) | ||||
−0.418886 | + | 0.908039i | \(0.637579\pi\) | |||||||
\(348\) | 24.0000 | 1.28654 | ||||||||
\(349\) | −22.7446 | −1.21749 | −0.608744 | − | 0.793367i | \(-0.708326\pi\) | ||||
−0.608744 | + | 0.793367i | \(0.708326\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.74456 | 0.359998 | ||||||||
\(352\) | −1.37228 | −0.0731428 | ||||||||
\(353\) | 35.0000 | 1.86286 | 0.931431 | − | 0.363918i | \(-0.118561\pi\) | ||||
0.931431 | + | 0.363918i | \(0.118561\pi\) | |||||||
\(354\) | 1.25544 | 0.0667257 | ||||||||
\(355\) | −39.6060 | −2.10207 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.3723 | −0.706747 | ||||||||
\(359\) | 35.4891 | 1.87304 | 0.936522 | − | 0.350608i | \(-0.114025\pi\) | ||||
0.936522 | + | 0.350608i | \(0.114025\pi\) | |||||||
\(360\) | −28.2337 | −1.48805 | ||||||||
\(361\) | 9.86141 | 0.519021 | ||||||||
\(362\) | 23.4891 | 1.23456 | ||||||||
\(363\) | 30.7446 | 1.61367 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −44.2337 | −2.31530 | ||||||||
\(366\) | −8.86141 | −0.463193 | ||||||||
\(367\) | 10.0000 | 0.521996 | 0.260998 | − | 0.965339i | \(-0.415948\pi\) | ||||
0.260998 | + | 0.965339i | \(0.415948\pi\) | |||||||
\(368\) | −8.74456 | −0.455842 | ||||||||
\(369\) | 8.37228 | 0.435844 | ||||||||
\(370\) | 6.74456 | 0.350633 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.25544 | 0.479872 | ||||||||
\(373\) | −14.6277 | −0.757395 | −0.378697 | − | 0.925521i | \(-0.623628\pi\) | ||||
−0.378697 | + | 0.925521i | \(0.623628\pi\) | |||||||
\(374\) | −6.51087 | −0.336669 | ||||||||
\(375\) | −15.6060 | −0.805889 | ||||||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 2.64947 | 0.136455 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.8614 | 1.73934 | 0.869672 | − | 0.493630i | \(-0.164330\pi\) | ||||
0.869672 | + | 0.493630i | \(0.164330\pi\) | |||||||
\(380\) | 18.1168 | 0.929374 | ||||||||
\(381\) | 20.2337 | 1.03660 | ||||||||
\(382\) | 13.6277 | 0.697255 | ||||||||
\(383\) | −35.4674 | −1.81230 | −0.906149 | − | 0.422958i | \(-0.860992\pi\) | ||||
−0.906149 | + | 0.422958i | \(0.860992\pi\) | |||||||
\(384\) | 3.37228 | 0.172091 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.25544 | −0.0639001 | ||||||||
\(387\) | −53.3505 | −2.71196 | ||||||||
\(388\) | −8.00000 | −0.406138 | ||||||||
\(389\) | −2.11684 | −0.107328 | −0.0536641 | − | 0.998559i | \(-0.517090\pi\) | ||||
−0.0536641 | + | 0.998559i | \(0.517090\pi\) | |||||||
\(390\) | −4.23369 | −0.214381 | ||||||||
\(391\) | −41.4891 | −2.09820 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −40.4674 | −2.04131 | ||||||||
\(394\) | −7.37228 | −0.371410 | ||||||||
\(395\) | −15.6060 | −0.785222 | ||||||||
\(396\) | 11.4891 | 0.577350 | ||||||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | 2.37228 | 0.118912 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.37228 | 0.318614 | ||||||||
\(401\) | −13.7446 | −0.686371 | −0.343185 | − | 0.939268i | \(-0.611506\pi\) | ||||
−0.343185 | + | 0.939268i | \(0.611506\pi\) | |||||||
\(402\) | −26.9783 | −1.34555 | ||||||||
\(403\) | 1.02175 | 0.0508970 | ||||||||
\(404\) | −3.25544 | −0.161964 | ||||||||
\(405\) | 121.329 | 6.02888 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.74456 | −0.136043 | ||||||||
\(408\) | 16.0000 | 0.792118 | ||||||||
\(409\) | 15.7446 | 0.778519 | 0.389259 | − | 0.921128i | \(-0.372731\pi\) | ||||
0.389259 | + | 0.921128i | \(0.372731\pi\) | |||||||
\(410\) | −3.37228 | −0.166545 | ||||||||
\(411\) | −9.25544 | −0.456537 | ||||||||
\(412\) | 10.7446 | 0.529347 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 73.2119 | 3.59817 | ||||||||
\(415\) | 1.25544 | 0.0616270 | ||||||||
\(416\) | 0.372281 | 0.0182526 | ||||||||
\(417\) | 17.7228 | 0.867890 | ||||||||
\(418\) | −7.37228 | −0.360590 | ||||||||
\(419\) | −0.138593 | −0.00677073 | −0.00338536 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338536 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 8.11684 | 0.395122 | ||||||||
\(423\) | −66.9783 | −3.25659 | ||||||||
\(424\) | 10.0000 | 0.485643 | ||||||||
\(425\) | 30.2337 | 1.46655 | ||||||||
\(426\) | −39.6060 | −1.91892 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.11684 | 0.0539847 | ||||||||
\(429\) | 1.72281 | 0.0831782 | ||||||||
\(430\) | 21.4891 | 1.03630 | ||||||||
\(431\) | −9.48913 | −0.457075 | −0.228538 | − | 0.973535i | \(-0.573394\pi\) | ||||
−0.228538 | + | 0.973535i | \(0.573394\pi\) | |||||||
\(432\) | −18.1168 | −0.871647 | ||||||||
\(433\) | 10.6277 | 0.510736 | 0.255368 | − | 0.966844i | \(-0.417803\pi\) | ||||
0.255368 | + | 0.966844i | \(0.417803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 80.9348 | 3.88052 | ||||||||
\(436\) | 5.62772 | 0.269519 | ||||||||
\(437\) | −46.9783 | −2.24727 | ||||||||
\(438\) | −44.2337 | −2.11357 | ||||||||
\(439\) | 3.74456 | 0.178718 | 0.0893591 | − | 0.995999i | \(-0.471518\pi\) | ||||
0.0893591 | + | 0.995999i | \(0.471518\pi\) | |||||||
\(440\) | −4.62772 | −0.220618 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.76631 | 0.0840149 | ||||||||
\(443\) | 33.3505 | 1.58453 | 0.792266 | − | 0.610176i | \(-0.208901\pi\) | ||||
0.792266 | + | 0.610176i | \(0.208901\pi\) | |||||||
\(444\) | 6.74456 | 0.320083 | ||||||||
\(445\) | 6.74456 | 0.319723 | ||||||||
\(446\) | 3.25544 | 0.154149 | ||||||||
\(447\) | −9.72281 | −0.459873 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2337 | 1.09647 | 0.548233 | − | 0.836326i | \(-0.315301\pi\) | ||||
0.548233 | + | 0.836326i | \(0.315301\pi\) | |||||||
\(450\) | −53.3505 | −2.51497 | ||||||||
\(451\) | 1.37228 | 0.0646182 | ||||||||
\(452\) | 6.48913 | 0.305223 | ||||||||
\(453\) | 2.97825 | 0.139930 | ||||||||
\(454\) | 11.3723 | 0.533728 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.1168 | 0.848399 | ||||||||
\(457\) | 26.2337 | 1.22716 | 0.613580 | − | 0.789632i | \(-0.289729\pi\) | ||||
0.613580 | + | 0.789632i | \(0.289729\pi\) | |||||||
\(458\) | −5.62772 | −0.262966 | ||||||||
\(459\) | −85.9565 | −4.01211 | ||||||||
\(460\) | −29.4891 | −1.37494 | ||||||||
\(461\) | 3.60597 | 0.167947 | 0.0839734 | − | 0.996468i | \(-0.473239\pi\) | ||||
0.0839734 | + | 0.996468i | \(0.473239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7446 | 0.824660 | 0.412330 | − | 0.911035i | \(-0.364715\pi\) | ||||
0.412330 | + | 0.911035i | \(0.364715\pi\) | |||||||
\(464\) | −7.11684 | −0.330391 | ||||||||
\(465\) | 31.2119 | 1.44742 | ||||||||
\(466\) | 23.4891 | 1.08811 | ||||||||
\(467\) | 10.5109 | 0.486385 | 0.243193 | − | 0.969978i | \(-0.421805\pi\) | ||||
0.243193 | + | 0.969978i | \(0.421805\pi\) | |||||||
\(468\) | −3.11684 | −0.144076 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 26.9783 | 1.24441 | ||||||||
\(471\) | −53.4891 | −2.46465 | ||||||||
\(472\) | −0.372281 | −0.0171356 | ||||||||
\(473\) | −8.74456 | −0.402075 | ||||||||
\(474\) | −15.6060 | −0.716806 | ||||||||
\(475\) | 34.2337 | 1.57075 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −83.7228 | −3.83340 | ||||||||
\(478\) | 19.3723 | 0.886068 | ||||||||
\(479\) | −24.4891 | −1.11894 | −0.559468 | − | 0.828852i | \(-0.688995\pi\) | ||||
−0.559468 | + | 0.828852i | \(0.688995\pi\) | |||||||
\(480\) | 11.3723 | 0.519071 | ||||||||
\(481\) | 0.744563 | 0.0339491 | ||||||||
\(482\) | −6.88316 | −0.313519 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.11684 | −0.414402 | ||||||||
\(485\) | −26.9783 | −1.22502 | ||||||||
\(486\) | 66.9783 | 3.03820 | ||||||||
\(487\) | −13.2554 | −0.600661 | −0.300331 | − | 0.953835i | \(-0.597097\pi\) | ||||
−0.300331 | + | 0.953835i | \(0.597097\pi\) | |||||||
\(488\) | 2.62772 | 0.118951 | ||||||||
\(489\) | −44.2337 | −2.00032 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.1168 | −0.772472 | −0.386236 | − | 0.922400i | \(-0.626225\pi\) | ||||
−0.386236 | + | 0.922400i | \(0.626225\pi\) | |||||||
\(492\) | −3.37228 | −0.152034 | ||||||||
\(493\) | −33.7663 | −1.52076 | ||||||||
\(494\) | 2.00000 | 0.0899843 | ||||||||
\(495\) | 38.7446 | 1.74144 | ||||||||
\(496\) | −2.74456 | −0.123235 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.25544 | 0.0562575 | ||||||||
\(499\) | −4.74456 | −0.212396 | −0.106198 | − | 0.994345i | \(-0.533868\pi\) | ||||
−0.106198 | + | 0.994345i | \(0.533868\pi\) | |||||||
\(500\) | 4.62772 | 0.206958 | ||||||||
\(501\) | −45.9565 | −2.05319 | ||||||||
\(502\) | 13.8614 | 0.618665 | ||||||||
\(503\) | 35.3723 | 1.57717 | 0.788586 | − | 0.614924i | \(-0.210814\pi\) | ||||
0.788586 | + | 0.614924i | \(0.210814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9783 | −0.488526 | ||||||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | 43.3723 | 1.92623 | ||||||||
\(508\) | −6.00000 | −0.266207 | ||||||||
\(509\) | 30.0951 | 1.33394 | 0.666971 | − | 0.745084i | \(-0.267591\pi\) | ||||
0.666971 | + | 0.745084i | \(0.267591\pi\) | |||||||
\(510\) | 53.9565 | 2.38923 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −97.3288 | −4.29717 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 36.2337 | 1.59665 | ||||||||
\(516\) | 21.4891 | 0.946006 | ||||||||
\(517\) | −10.9783 | −0.482823 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34.1168 | −1.49756 | ||||||||
\(520\) | 1.25544 | 0.0550546 | ||||||||
\(521\) | 1.25544 | 0.0550017 | 0.0275009 | − | 0.999622i | \(-0.491245\pi\) | ||||
0.0275009 | + | 0.999622i | \(0.491245\pi\) | |||||||
\(522\) | 59.5842 | 2.60793 | ||||||||
\(523\) | 28.4674 | 1.24479 | 0.622396 | − | 0.782703i | \(-0.286159\pi\) | ||||
0.622396 | + | 0.782703i | \(0.286159\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.6277 | 0.594197 | ||||||||
\(527\) | −13.0217 | −0.567236 | ||||||||
\(528\) | −4.62772 | −0.201396 | ||||||||
\(529\) | 53.4674 | 2.32467 | ||||||||
\(530\) | 33.7228 | 1.46483 | ||||||||
\(531\) | 3.11684 | 0.135260 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.372281 | −0.0161253 | ||||||||
\(534\) | 6.74456 | 0.291866 | ||||||||
\(535\) | 3.76631 | 0.162832 | ||||||||
\(536\) | 8.00000 | 0.345547 | ||||||||
\(537\) | −45.0951 | −1.94600 | ||||||||
\(538\) | 28.3505 | 1.22228 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −61.0951 | −2.62911 | ||||||||
\(541\) | 28.9783 | 1.24587 | 0.622936 | − | 0.782273i | \(-0.285940\pi\) | ||||
0.622936 | + | 0.782273i | \(0.285940\pi\) | |||||||
\(542\) | −28.7446 | −1.23468 | ||||||||
\(543\) | 79.2119 | 3.39931 | ||||||||
\(544\) | −4.74456 | −0.203421 | ||||||||
\(545\) | 18.9783 | 0.812939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.48913 | 0.234698 | 0.117349 | − | 0.993091i | \(-0.462560\pi\) | ||||
0.117349 | + | 0.993091i | \(0.462560\pi\) | |||||||
\(548\) | 2.74456 | 0.117242 | ||||||||
\(549\) | −22.0000 | −0.938937 | ||||||||
\(550\) | −8.74456 | −0.372869 | ||||||||
\(551\) | −38.2337 | −1.62881 | ||||||||
\(552\) | −29.4891 | −1.25514 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −17.6060 | −0.748006 | ||||||||
\(555\) | 22.7446 | 0.965453 | ||||||||
\(556\) | −5.25544 | −0.222880 | ||||||||
\(557\) | −35.3505 | −1.49785 | −0.748925 | − | 0.662655i | \(-0.769430\pi\) | ||||
−0.748925 | + | 0.662655i | \(0.769430\pi\) | |||||||
\(558\) | 22.9783 | 0.972747 | ||||||||
\(559\) | 2.37228 | 0.100337 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.9565 | −0.927004 | ||||||||
\(562\) | 7.25544 | 0.306052 | ||||||||
\(563\) | 17.3723 | 0.732154 | 0.366077 | − | 0.930584i | \(-0.380701\pi\) | ||||
0.366077 | + | 0.930584i | \(0.380701\pi\) | |||||||
\(564\) | 26.9783 | 1.13599 | ||||||||
\(565\) | 21.8832 | 0.920631 | ||||||||
\(566\) | −19.6277 | −0.825015 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.7446 | 0.492791 | ||||||||
\(569\) | 44.8397 | 1.87978 | 0.939888 | − | 0.341483i | \(-0.110929\pi\) | ||||
0.939888 | + | 0.341483i | \(0.110929\pi\) | |||||||
\(570\) | 61.0951 | 2.55899 | ||||||||
\(571\) | 25.6060 | 1.07158 | 0.535788 | − | 0.844352i | \(-0.320015\pi\) | ||||
0.535788 | + | 0.844352i | \(0.320015\pi\) | |||||||
\(572\) | −0.510875 | −0.0213607 | ||||||||
\(573\) | 45.9565 | 1.91986 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −55.7228 | −2.32380 | ||||||||
\(576\) | 8.37228 | 0.348845 | ||||||||
\(577\) | −21.2554 | −0.884875 | −0.442438 | − | 0.896799i | \(-0.645886\pi\) | ||||
−0.442438 | + | 0.896799i | \(0.645886\pi\) | |||||||
\(578\) | −5.51087 | −0.229222 | ||||||||
\(579\) | −4.23369 | −0.175946 | ||||||||
\(580\) | −24.0000 | −0.996546 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −26.9783 | −1.11828 | ||||||||
\(583\) | −13.7228 | −0.568341 | ||||||||
\(584\) | 13.1168 | 0.542779 | ||||||||
\(585\) | −10.5109 | −0.434571 | ||||||||
\(586\) | −1.62772 | −0.0672404 | ||||||||
\(587\) | −37.3723 | −1.54252 | −0.771260 | − | 0.636521i | \(-0.780373\pi\) | ||||
−0.771260 | + | 0.636521i | \(0.780373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.7446 | −0.607539 | ||||||||
\(590\) | −1.25544 | −0.0516855 | ||||||||
\(591\) | −24.8614 | −1.02266 | ||||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | −26.2337 | −1.07729 | −0.538644 | − | 0.842533i | \(-0.681063\pi\) | ||||
−0.538644 | + | 0.842533i | \(0.681063\pi\) | |||||||
\(594\) | 24.8614 | 1.02008 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.88316 | 0.118099 | ||||||||
\(597\) | 8.00000 | 0.327418 | ||||||||
\(598\) | −3.25544 | −0.133125 | ||||||||
\(599\) | 6.51087 | 0.266027 | 0.133014 | − | 0.991114i | \(-0.457535\pi\) | ||||
0.133014 | + | 0.991114i | \(0.457535\pi\) | |||||||
\(600\) | 21.4891 | 0.877290 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −66.9783 | −2.72757 | ||||||||
\(604\) | −0.883156 | −0.0359351 | ||||||||
\(605\) | −30.7446 | −1.24994 | ||||||||
\(606\) | −10.9783 | −0.445961 | ||||||||
\(607\) | 11.4891 | 0.466329 | 0.233165 | − | 0.972437i | \(-0.425092\pi\) | ||||
0.233165 | + | 0.972437i | \(0.425092\pi\) | |||||||
\(608\) | −5.37228 | −0.217875 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.86141 | 0.358788 | ||||||||
\(611\) | 2.97825 | 0.120487 | ||||||||
\(612\) | 39.7228 | 1.60570 | ||||||||
\(613\) | −27.3723 | −1.10556 | −0.552778 | − | 0.833329i | \(-0.686432\pi\) | ||||
−0.552778 | + | 0.833329i | \(0.686432\pi\) | |||||||
\(614\) | 23.8614 | 0.962968 | ||||||||
\(615\) | −11.3723 | −0.458575 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.5109 | 0.785478 | 0.392739 | − | 0.919650i | \(-0.371528\pi\) | ||||
0.392739 | + | 0.919650i | \(0.371528\pi\) | |||||||
\(618\) | 36.2337 | 1.45753 | ||||||||
\(619\) | 46.6060 | 1.87325 | 0.936626 | − | 0.350331i | \(-0.113931\pi\) | ||||
0.936626 | + | 0.350331i | \(0.113931\pi\) | |||||||
\(620\) | −9.25544 | −0.371707 | ||||||||
\(621\) | 158.424 | 6.35733 | ||||||||
\(622\) | 10.3723 | 0.415891 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.25544 | 0.0502577 | ||||||||
\(625\) | −16.2554 | −0.650217 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.8614 | −0.992869 | ||||||||
\(628\) | 15.8614 | 0.632939 | ||||||||
\(629\) | −9.48913 | −0.378356 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 4.62772 | 0.184081 | ||||||||
\(633\) | 27.3723 | 1.08795 | ||||||||
\(634\) | 24.7446 | 0.982732 | ||||||||
\(635\) | −20.2337 | −0.802949 | ||||||||
\(636\) | 33.7228 | 1.33720 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.76631 | 0.386652 | ||||||||
\(639\) | −98.3288 | −3.88983 | ||||||||
\(640\) | −3.37228 | −0.133301 | ||||||||
\(641\) | −38.4674 | −1.51937 | −0.759685 | − | 0.650291i | \(-0.774647\pi\) | ||||
−0.759685 | + | 0.650291i | \(0.774647\pi\) | |||||||
\(642\) | 3.76631 | 0.148644 | ||||||||
\(643\) | −31.0951 | −1.22627 | −0.613135 | − | 0.789978i | \(-0.710092\pi\) | ||||
−0.613135 | + | 0.789978i | \(0.710092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 72.4674 | 2.85340 | ||||||||
\(646\) | −25.4891 | −1.00286 | ||||||||
\(647\) | −8.23369 | −0.323700 | −0.161850 | − | 0.986815i | \(-0.551746\pi\) | ||||
−0.161850 | + | 0.986815i | \(0.551746\pi\) | |||||||
\(648\) | −35.9783 | −1.41336 | ||||||||
\(649\) | 0.510875 | 0.0200536 | ||||||||
\(650\) | 2.37228 | 0.0930485 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.1168 | 0.513695 | ||||||||
\(653\) | 3.86141 | 0.151109 | 0.0755543 | − | 0.997142i | \(-0.475927\pi\) | ||||
0.0755543 | + | 0.997142i | \(0.475927\pi\) | |||||||
\(654\) | 18.9783 | 0.742108 | ||||||||
\(655\) | 40.4674 | 1.58119 | ||||||||
\(656\) | 1.00000 | 0.0390434 | ||||||||
\(657\) | −109.818 | −4.28440 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.48913 | 0.213826 | 0.106913 | − | 0.994268i | \(-0.465903\pi\) | ||||
0.106913 | + | 0.994268i | \(0.465903\pi\) | |||||||
\(660\) | −15.6060 | −0.607462 | ||||||||
\(661\) | −29.3723 | −1.14245 | −0.571225 | − | 0.820794i | \(-0.693531\pi\) | ||||
−0.571225 | + | 0.820794i | \(0.693531\pi\) | |||||||
\(662\) | 0.744563 | 0.0289382 | ||||||||
\(663\) | 5.95650 | 0.231331 | ||||||||
\(664\) | −0.372281 | −0.0144473 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.7446 | 0.648839 | ||||||||
\(667\) | 62.2337 | 2.40970 | ||||||||
\(668\) | 13.6277 | 0.527272 | ||||||||
\(669\) | 10.9783 | 0.424444 | ||||||||
\(670\) | 26.9783 | 1.04226 | ||||||||
\(671\) | −3.60597 | −0.139207 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.51087 | −0.328070 | −0.164035 | − | 0.986455i | \(-0.552451\pi\) | ||||
−0.164035 | + | 0.986455i | \(0.552451\pi\) | |||||||
\(674\) | 5.00000 | 0.192593 | ||||||||
\(675\) | −115.446 | −4.44350 | ||||||||
\(676\) | −12.8614 | −0.494669 | ||||||||
\(677\) | 13.8832 | 0.533573 | 0.266787 | − | 0.963756i | \(-0.414038\pi\) | ||||
0.266787 | + | 0.963756i | \(0.414038\pi\) | |||||||
\(678\) | 21.8832 | 0.840418 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.0000 | −0.613572 | ||||||||
\(681\) | 38.3505 | 1.46960 | ||||||||
\(682\) | 3.76631 | 0.144220 | ||||||||
\(683\) | −20.7446 | −0.793769 | −0.396884 | − | 0.917869i | \(-0.629909\pi\) | ||||
−0.396884 | + | 0.917869i | \(0.629909\pi\) | |||||||
\(684\) | 44.9783 | 1.71979 | ||||||||
\(685\) | 9.25544 | 0.353632 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.9783 | −0.724065 | ||||||||
\(688\) | −6.37228 | −0.242941 | ||||||||
\(689\) | 3.72281 | 0.141828 | ||||||||
\(690\) | −99.4456 | −3.78583 | ||||||||
\(691\) | −0.627719 | −0.0238795 | −0.0119398 | − | 0.999929i | \(-0.503801\pi\) | ||||
−0.0119398 | + | 0.999929i | \(0.503801\pi\) | |||||||
\(692\) | 10.1168 | 0.384585 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.6060 | 0.592394 | ||||||||
\(695\) | −17.7228 | −0.672265 | ||||||||
\(696\) | −24.0000 | −0.909718 | ||||||||
\(697\) | 4.74456 | 0.179713 | ||||||||
\(698\) | 22.7446 | 0.860894 | ||||||||
\(699\) | 79.2119 | 2.99607 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.11684 | 0.155491 | 0.0777455 | − | 0.996973i | \(-0.475228\pi\) | ||||
0.0777455 | + | 0.996973i | \(0.475228\pi\) | |||||||
\(702\) | −6.74456 | −0.254557 | ||||||||
\(703\) | −10.7446 | −0.405239 | ||||||||
\(704\) | 1.37228 | 0.0517198 | ||||||||
\(705\) | 90.9783 | 3.42644 | ||||||||
\(706\) | −35.0000 | −1.31724 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.25544 | −0.0471822 | ||||||||
\(709\) | 42.3723 | 1.59132 | 0.795662 | − | 0.605741i | \(-0.207123\pi\) | ||||
0.795662 | + | 0.605741i | \(0.207123\pi\) | |||||||
\(710\) | 39.6060 | 1.48639 | ||||||||
\(711\) | −38.7446 | −1.45303 | ||||||||
\(712\) | −2.00000 | −0.0749532 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.72281 | −0.0644296 | ||||||||
\(716\) | 13.3723 | 0.499746 | ||||||||
\(717\) | 65.3288 | 2.43975 | ||||||||
\(718\) | −35.4891 | −1.32444 | ||||||||
\(719\) | −11.2337 | −0.418946 | −0.209473 | − | 0.977814i | \(-0.567175\pi\) | ||||
−0.209473 | + | 0.977814i | \(0.567175\pi\) | |||||||
\(720\) | 28.2337 | 1.05221 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.86141 | −0.367004 | ||||||||
\(723\) | −23.2119 | −0.863261 | ||||||||
\(724\) | −23.4891 | −0.872966 | ||||||||
\(725\) | −45.3505 | −1.68428 | ||||||||
\(726\) | −30.7446 | −1.14104 | ||||||||
\(727\) | −37.3505 | −1.38525 | −0.692627 | − | 0.721296i | \(-0.743547\pi\) | ||||
−0.692627 | + | 0.721296i | \(0.743547\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 117.935 | 4.36795 | ||||||||
\(730\) | 44.2337 | 1.63716 | ||||||||
\(731\) | −30.2337 | −1.11823 | ||||||||
\(732\) | 8.86141 | 0.327527 | ||||||||
\(733\) | 29.2554 | 1.08057 | 0.540287 | − | 0.841481i | \(-0.318316\pi\) | ||||
0.540287 | + | 0.841481i | \(0.318316\pi\) | |||||||
\(734\) | −10.0000 | −0.369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.74456 | 0.322329 | ||||||||
\(737\) | −10.9783 | −0.404389 | ||||||||
\(738\) | −8.37228 | −0.308188 | ||||||||
\(739\) | 11.6277 | 0.427733 | 0.213866 | − | 0.976863i | \(-0.431394\pi\) | ||||
0.213866 | + | 0.976863i | \(0.431394\pi\) | |||||||
\(740\) | −6.74456 | −0.247935 | ||||||||
\(741\) | 6.74456 | 0.247768 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7228 | −0.870306 | −0.435153 | − | 0.900357i | \(-0.643306\pi\) | ||||
−0.435153 | + | 0.900357i | \(0.643306\pi\) | |||||||
\(744\) | −9.25544 | −0.339321 | ||||||||
\(745\) | 9.72281 | 0.356216 | ||||||||
\(746\) | 14.6277 | 0.535559 | ||||||||
\(747\) | 3.11684 | 0.114039 | ||||||||
\(748\) | 6.51087 | 0.238061 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15.6060 | 0.569849 | ||||||||
\(751\) | 40.9565 | 1.49452 | 0.747262 | − | 0.664530i | \(-0.231368\pi\) | ||||
0.747262 | + | 0.664530i | \(0.231368\pi\) | |||||||
\(752\) | −8.00000 | −0.291730 | ||||||||
\(753\) | 46.7446 | 1.70347 | ||||||||
\(754\) | −2.64947 | −0.0964879 | ||||||||
\(755\) | −2.97825 | −0.108390 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.35053 | 0.339851 | 0.169925 | − | 0.985457i | \(-0.445647\pi\) | ||||
0.169925 | + | 0.985457i | \(0.445647\pi\) | |||||||
\(758\) | −33.8614 | −1.22990 | ||||||||
\(759\) | 40.4674 | 1.46887 | ||||||||
\(760\) | −18.1168 | −0.657167 | ||||||||
\(761\) | 48.9783 | 1.77546 | 0.887730 | − | 0.460364i | \(-0.152281\pi\) | ||||
0.887730 | + | 0.460364i | \(0.152281\pi\) | |||||||
\(762\) | −20.2337 | −0.732989 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.6277 | −0.493034 | ||||||||
\(765\) | 133.957 | 4.84321 | ||||||||
\(766\) | 35.4674 | 1.28149 | ||||||||
\(767\) | −0.138593 | −0.00500432 | ||||||||
\(768\) | −3.37228 | −0.121687 | ||||||||
\(769\) | 10.6277 | 0.383245 | 0.191623 | − | 0.981469i | \(-0.438625\pi\) | ||||
0.191623 | + | 0.981469i | \(0.438625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.25544 | 0.0451842 | ||||||||
\(773\) | −4.51087 | −0.162245 | −0.0811224 | − | 0.996704i | \(-0.525850\pi\) | ||||
−0.0811224 | + | 0.996704i | \(0.525850\pi\) | |||||||
\(774\) | 53.3505 | 1.91765 | ||||||||
\(775\) | −17.4891 | −0.628228 | ||||||||
\(776\) | 8.00000 | 0.287183 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.11684 | 0.0758925 | ||||||||
\(779\) | 5.37228 | 0.192482 | ||||||||
\(780\) | 4.23369 | 0.151590 | ||||||||
\(781\) | −16.1168 | −0.576706 | ||||||||
\(782\) | 41.4891 | 1.48365 | ||||||||
\(783\) | 128.935 | 4.60775 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.4891 | 1.90911 | ||||||||
\(786\) | 40.4674 | 1.44342 | ||||||||
\(787\) | −20.0000 | −0.712923 | −0.356462 | − | 0.934310i | \(-0.616017\pi\) | ||||
−0.356462 | + | 0.934310i | \(0.616017\pi\) | |||||||
\(788\) | 7.37228 | 0.262627 | ||||||||
\(789\) | 45.9565 | 1.63609 | ||||||||
\(790\) | 15.6060 | 0.555235 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −11.4891 | −0.408248 | ||||||||
\(793\) | 0.978251 | 0.0347387 | ||||||||
\(794\) | −14.0000 | −0.496841 | ||||||||
\(795\) | 113.723 | 4.03333 | ||||||||
\(796\) | −2.37228 | −0.0840833 | ||||||||
\(797\) | 41.2554 | 1.46134 | 0.730671 | − | 0.682729i | \(-0.239207\pi\) | ||||
0.730671 | + | 0.682729i | \(0.239207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.9565 | −1.34280 | ||||||||
\(800\) | −6.37228 | −0.225294 | ||||||||
\(801\) | 16.7446 | 0.591640 | ||||||||
\(802\) | 13.7446 | 0.485337 | ||||||||
\(803\) | −18.0000 | −0.635206 | ||||||||
\(804\) | 26.9783 | 0.951450 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.02175 | −0.0359896 | ||||||||
\(807\) | 95.6060 | 3.36549 | ||||||||
\(808\) | 3.25544 | 0.114526 | ||||||||
\(809\) | 1.48913 | 0.0523549 | 0.0261774 | − | 0.999657i | \(-0.491667\pi\) | ||||
0.0261774 | + | 0.999657i | \(0.491667\pi\) | |||||||
\(810\) | −121.329 | −4.26306 | ||||||||
\(811\) | 32.8397 | 1.15316 | 0.576578 | − | 0.817042i | \(-0.304388\pi\) | ||||
0.576578 | + | 0.817042i | \(0.304388\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −96.9348 | −3.39965 | ||||||||
\(814\) | 2.74456 | 0.0961969 | ||||||||
\(815\) | 44.2337 | 1.54944 | ||||||||
\(816\) | −16.0000 | −0.560112 | ||||||||
\(817\) | −34.2337 | −1.19769 | ||||||||
\(818\) | −15.7446 | −0.550496 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.37228 | 0.117765 | ||||||||
\(821\) | 37.6060 | 1.31246 | 0.656229 | − | 0.754562i | \(-0.272151\pi\) | ||||
0.656229 | + | 0.754562i | \(0.272151\pi\) | |||||||
\(822\) | 9.25544 | 0.322820 | ||||||||
\(823\) | 18.1168 | 0.631513 | 0.315757 | − | 0.948840i | \(-0.397742\pi\) | ||||
0.315757 | + | 0.948840i | \(0.397742\pi\) | |||||||
\(824\) | −10.7446 | −0.374305 | ||||||||
\(825\) | −29.4891 | −1.02668 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.9783 | 1.21631 | 0.608156 | − | 0.793817i | \(-0.291909\pi\) | ||||
0.608156 | + | 0.793817i | \(0.291909\pi\) | |||||||
\(828\) | −73.2119 | −2.54429 | ||||||||
\(829\) | −17.7228 | −0.615539 | −0.307769 | − | 0.951461i | \(-0.599583\pi\) | ||||
−0.307769 | + | 0.951461i | \(0.599583\pi\) | |||||||
\(830\) | −1.25544 | −0.0435769 | ||||||||
\(831\) | −59.3723 | −2.05960 | ||||||||
\(832\) | −0.372281 | −0.0129065 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.7228 | −0.613691 | ||||||||
\(835\) | 45.9565 | 1.59039 | ||||||||
\(836\) | 7.37228 | 0.254976 | ||||||||
\(837\) | 49.7228 | 1.71867 | ||||||||
\(838\) | 0.138593 | 0.00478763 | ||||||||
\(839\) | −20.7663 | −0.716933 | −0.358466 | − | 0.933543i | \(-0.616700\pi\) | ||||
−0.358466 | + | 0.933543i | \(0.616700\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.6495 | 0.746533 | ||||||||
\(842\) | −2.00000 | −0.0689246 | ||||||||
\(843\) | 24.4674 | 0.842701 | ||||||||
\(844\) | −8.11684 | −0.279393 | ||||||||
\(845\) | −43.3723 | −1.49205 | ||||||||
\(846\) | 66.9783 | 2.30276 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.0000 | −0.343401 | ||||||||
\(849\) | −66.1902 | −2.27164 | ||||||||
\(850\) | −30.2337 | −1.03701 | ||||||||
\(851\) | 17.4891 | 0.599519 | ||||||||
\(852\) | 39.6060 | 1.35688 | ||||||||
\(853\) | −17.6060 | −0.602817 | −0.301408 | − | 0.953495i | \(-0.597457\pi\) | ||||
−0.301408 | + | 0.953495i | \(0.597457\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 151.679 | 5.18732 | ||||||||
\(856\) | −1.11684 | −0.0381729 | ||||||||
\(857\) | −35.2337 | −1.20356 | −0.601780 | − | 0.798662i | \(-0.705542\pi\) | ||||
−0.601780 | + | 0.798662i | \(0.705542\pi\) | |||||||
\(858\) | −1.72281 | −0.0588159 | ||||||||
\(859\) | −19.3505 | −0.660232 | −0.330116 | − | 0.943940i | \(-0.607088\pi\) | ||||
−0.330116 | + | 0.943940i | \(0.607088\pi\) | |||||||
\(860\) | −21.4891 | −0.732773 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.48913 | 0.323201 | ||||||||
\(863\) | −51.4891 | −1.75271 | −0.876355 | − | 0.481666i | \(-0.840032\pi\) | ||||
−0.876355 | + | 0.481666i | \(0.840032\pi\) | |||||||
\(864\) | 18.1168 | 0.616348 | ||||||||
\(865\) | 34.1168 | 1.16001 | ||||||||
\(866\) | −10.6277 | −0.361145 | ||||||||
\(867\) | −18.5842 | −0.631153 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.35053 | −0.215427 | ||||||||
\(870\) | −80.9348 | −2.74395 | ||||||||
\(871\) | 2.97825 | 0.100914 | ||||||||
\(872\) | −5.62772 | −0.190579 | ||||||||
\(873\) | −66.9783 | −2.26687 | ||||||||
\(874\) | 46.9783 | 1.58906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.2337 | 1.49452 | ||||||||
\(877\) | 10.1168 | 0.341622 | 0.170811 | − | 0.985304i | \(-0.445361\pi\) | ||||
0.170811 | + | 0.985304i | \(0.445361\pi\) | |||||||
\(878\) | −3.74456 | −0.126373 | ||||||||
\(879\) | −5.48913 | −0.185144 | ||||||||
\(880\) | 4.62772 | 0.156000 | ||||||||
\(881\) | −35.9783 | −1.21214 | −0.606069 | − | 0.795412i | \(-0.707254\pi\) | ||||
−0.606069 | + | 0.795412i | \(0.707254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.2337 | 0.882834 | 0.441417 | − | 0.897302i | \(-0.354476\pi\) | ||||
0.441417 | + | 0.897302i | \(0.354476\pi\) | |||||||
\(884\) | −1.76631 | −0.0594075 | ||||||||
\(885\) | −4.23369 | −0.142314 | ||||||||
\(886\) | −33.3505 | −1.12043 | ||||||||
\(887\) | −31.2337 | −1.04872 | −0.524362 | − | 0.851495i | \(-0.675696\pi\) | ||||
−0.524362 | + | 0.851495i | \(0.675696\pi\) | |||||||
\(888\) | −6.74456 | −0.226333 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.74456 | −0.226078 | ||||||||
\(891\) | 49.3723 | 1.65403 | ||||||||
\(892\) | −3.25544 | −0.109000 | ||||||||
\(893\) | −42.9783 | −1.43821 | ||||||||
\(894\) | 9.72281 | 0.325180 | ||||||||
\(895\) | 45.0951 | 1.50736 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.9783 | −0.366553 | ||||||||
\(898\) | −23.2337 | −0.775318 | ||||||||
\(899\) | 19.5326 | 0.651449 | ||||||||
\(900\) | 53.3505 | 1.77835 | ||||||||
\(901\) | −47.4456 | −1.58064 | ||||||||
\(902\) | −1.37228 | −0.0456920 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.48913 | −0.215825 | ||||||||
\(905\) | −79.2119 | −2.63309 | ||||||||
\(906\) | −2.97825 | −0.0989457 | ||||||||
\(907\) | 5.86141 | 0.194625 | 0.0973124 | − | 0.995254i | \(-0.468975\pi\) | ||||
0.0973124 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(908\) | −11.3723 | −0.377402 | ||||||||
\(909\) | −27.2554 | −0.904006 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.7446 | −1.88003 | −0.940016 | − | 0.341131i | \(-0.889190\pi\) | ||||
−0.940016 | + | 0.341131i | \(0.889190\pi\) | |||||||
\(912\) | −18.1168 | −0.599909 | ||||||||
\(913\) | 0.510875 | 0.0169075 | ||||||||
\(914\) | −26.2337 | −0.867733 | ||||||||
\(915\) | 29.8832 | 0.987907 | ||||||||
\(916\) | 5.62772 | 0.185945 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 85.9565 | 2.83699 | ||||||||
\(919\) | 33.0000 | 1.08857 | 0.544285 | − | 0.838901i | \(-0.316801\pi\) | ||||
0.544285 | + | 0.838901i | \(0.316801\pi\) | |||||||
\(920\) | 29.4891 | 0.972228 | ||||||||
\(921\) | 80.4674 | 2.65149 | ||||||||
\(922\) | −3.60597 | −0.118756 | ||||||||
\(923\) | 4.37228 | 0.143915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.7446 | −0.419039 | ||||||||
\(926\) | −17.7446 | −0.583123 | ||||||||
\(927\) | 89.9565 | 2.95456 | ||||||||
\(928\) | 7.11684 | 0.233622 | ||||||||
\(929\) | −34.0000 | −1.11550 | −0.557752 | − | 0.830008i | \(-0.688336\pi\) | ||||
−0.557752 | + | 0.830008i | \(0.688336\pi\) | |||||||
\(930\) | −31.2119 | −1.02348 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −23.4891 | −0.769412 | ||||||||
\(933\) | 34.9783 | 1.14514 | ||||||||
\(934\) | −10.5109 | −0.343926 | ||||||||
\(935\) | 21.9565 | 0.718054 | ||||||||
\(936\) | 3.11684 | 0.101877 | ||||||||
\(937\) | 40.4674 | 1.32201 | 0.661006 | − | 0.750381i | \(-0.270130\pi\) | ||||
0.661006 | + | 0.750381i | \(0.270130\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26.9783 | −0.879934 | ||||||||
\(941\) | −0.394031 | −0.0128450 | −0.00642252 | − | 0.999979i | \(-0.502044\pi\) | ||||
−0.00642252 | + | 0.999979i | \(0.502044\pi\) | |||||||
\(942\) | 53.4891 | 1.74277 | ||||||||
\(943\) | −8.74456 | −0.284762 | ||||||||
\(944\) | 0.372281 | 0.0121167 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.74456 | 0.284310 | ||||||||
\(947\) | −18.0951 | −0.588012 | −0.294006 | − | 0.955804i | \(-0.594988\pi\) | ||||
−0.294006 | + | 0.955804i | \(0.594988\pi\) | |||||||
\(948\) | 15.6060 | 0.506858 | ||||||||
\(949\) | 4.88316 | 0.158514 | ||||||||
\(950\) | −34.2337 | −1.11069 | ||||||||
\(951\) | 83.4456 | 2.70591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.8614 | −1.35602 | −0.678012 | − | 0.735051i | \(-0.737158\pi\) | ||||
−0.678012 | + | 0.735051i | \(0.737158\pi\) | |||||||
\(954\) | 83.7228 | 2.71063 | ||||||||
\(955\) | −45.9565 | −1.48712 | ||||||||
\(956\) | −19.3723 | −0.626544 | ||||||||
\(957\) | 32.9348 | 1.06463 | ||||||||
\(958\) | 24.4891 | 0.791208 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −11.3723 | −0.367039 | ||||||||
\(961\) | −23.4674 | −0.757012 | ||||||||
\(962\) | −0.744563 | −0.0240057 | ||||||||
\(963\) | 9.35053 | 0.301317 | ||||||||
\(964\) | 6.88316 | 0.221692 | ||||||||
\(965\) | 4.23369 | 0.136287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5109 | 0.498796 | 0.249398 | − | 0.968401i | \(-0.419767\pi\) | ||||
0.249398 | + | 0.968401i | \(0.419767\pi\) | |||||||
\(968\) | 9.11684 | 0.293026 | ||||||||
\(969\) | −85.9565 | −2.76132 | ||||||||
\(970\) | 26.9783 | 0.866219 | ||||||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | −66.9783 | −2.14833 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13.2554 | 0.424732 | ||||||||
\(975\) | 8.00000 | 0.256205 | ||||||||
\(976\) | −2.62772 | −0.0841112 | ||||||||
\(977\) | 14.7446 | 0.471720 | 0.235860 | − | 0.971787i | \(-0.424209\pi\) | ||||
0.235860 | + | 0.971787i | \(0.424209\pi\) | |||||||
\(978\) | 44.2337 | 1.41444 | ||||||||
\(979\) | 2.74456 | 0.0877166 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.1168 | 1.50433 | ||||||||
\(982\) | 17.1168 | 0.546220 | ||||||||
\(983\) | −12.0000 | −0.382741 | −0.191370 | − | 0.981518i | \(-0.561293\pi\) | ||||
−0.191370 | + | 0.981518i | \(0.561293\pi\) | |||||||
\(984\) | 3.37228 | 0.107504 | ||||||||
\(985\) | 24.8614 | 0.792150 | ||||||||
\(986\) | 33.7663 | 1.07534 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.00000 | −0.0636285 | ||||||||
\(989\) | 55.7228 | 1.77188 | ||||||||
\(990\) | −38.7446 | −1.23138 | ||||||||
\(991\) | −23.9783 | −0.761694 | −0.380847 | − | 0.924638i | \(-0.624368\pi\) | ||||
−0.380847 | + | 0.924638i | \(0.624368\pi\) | |||||||
\(992\) | 2.74456 | 0.0871400 | ||||||||
\(993\) | 2.51087 | 0.0796802 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | −0.253617 | ||||||||
\(996\) | −1.25544 | −0.0397801 | ||||||||
\(997\) | −31.3505 | −0.992881 | −0.496441 | − | 0.868071i | \(-0.665360\pi\) | ||||
−0.496441 | + | 0.868071i | \(0.665360\pi\) | |||||||
\(998\) | 4.74456 | 0.150187 | ||||||||
\(999\) | 36.2337 | 1.14638 |
(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 | 4018.2.a.u.1.1 | 2 | ||
7.3 | odd | 6 | 574.2.e.d.247.1 | yes | 4 | ||
7.5 | odd | 6 | 574.2.e.d.165.1 | ✓ | 4 | ||
7.6 | odd | 2 | 4018.2.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.e.d.165.1 | ✓ | 4 | 7.5 | odd | 6 | ||
574.2.e.d.247.1 | yes | 4 | 7.3 | odd | 6 | ||
4018.2.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4018.2.a.v.1.2 | 2 | 7.6 | odd | 2 |