Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [550,2,Mod(199,550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("550.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.39177211117\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 17x^{2} + 64 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 110) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(-2.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 550.199 |
Dual form | 550.2.b.f.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/550\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 3.37228i | − 1.94699i | −0.228714 | − | 0.973494i | \(-0.573452\pi\) | ||||
0.228714 | − | 0.973494i | \(-0.426548\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.37228 | 1.37673 | ||||||||
\(7\) | − 3.37228i | − 1.27460i | −0.770615 | − | 0.637301i | \(-0.780051\pi\) | ||||
0.770615 | − | 0.637301i | \(-0.219949\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −8.37228 | −2.79076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.37228i | 0.973494i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 3.37228 | 0.901280 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 1.37228i | − 0.332827i | −0.986056 | − | 0.166414i | \(-0.946781\pi\) | ||||
0.986056 | − | 0.166414i | \(-0.0532187\pi\) | |||||||
\(18\) | − 8.37228i | − 1.97337i | ||||||||
\(19\) | −0.627719 | −0.144009 | −0.0720043 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720043 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.3723 | −2.48164 | ||||||||
\(22\) | − 1.00000i | − 0.213201i | ||||||||
\(23\) | 2.74456i | 0.572281i | 0.958188 | + | 0.286140i | \(0.0923724\pi\) | ||||
−0.958188 | + | 0.286140i | \(0.907628\pi\) | |||||||
\(24\) | −3.37228 | −0.688364 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 18.1168i | 3.48659i | ||||||||
\(28\) | 3.37228i | 0.637301i | ||||||||
\(29\) | −1.37228 | −0.254826 | −0.127413 | − | 0.991850i | \(-0.540667\pi\) | ||||
−0.127413 | + | 0.991850i | \(0.540667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.37228 | 0.605680 | 0.302840 | − | 0.953041i | \(-0.402065\pi\) | ||||
0.302840 | + | 0.953041i | \(0.402065\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 3.37228i | 0.587039i | ||||||||
\(34\) | 1.37228 | 0.235344 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.37228 | 1.39538 | ||||||||
\(37\) | − 9.37228i | − 1.54079i | −0.637565 | − | 0.770397i | \(-0.720058\pi\) | ||||
0.637565 | − | 0.770397i | \(-0.279942\pi\) | |||||||
\(38\) | − 0.627719i | − 0.101829i | ||||||||
\(39\) | 6.74456 | 1.07999 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4891 | −1.79430 | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | − 11.3723i | − 1.75478i | ||||||||
\(43\) | − 4.00000i | − 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.74456 | −0.404664 | ||||||||
\(47\) | − 2.74456i | − 0.400336i | −0.979762 | − | 0.200168i | \(-0.935851\pi\) | ||||
0.979762 | − | 0.200168i | \(-0.0641487\pi\) | |||||||
\(48\) | − 3.37228i | − 0.486747i | ||||||||
\(49\) | −4.37228 | −0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.62772 | −0.648010 | ||||||||
\(52\) | − 2.00000i | − 0.277350i | ||||||||
\(53\) | − 4.11684i | − 0.565492i | −0.959195 | − | 0.282746i | \(-0.908755\pi\) | ||||
0.959195 | − | 0.282746i | \(-0.0912454\pi\) | |||||||
\(54\) | −18.1168 | −2.46539 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.37228 | −0.450640 | ||||||||
\(57\) | 2.11684i | 0.280383i | ||||||||
\(58\) | − 1.37228i | − 0.180189i | ||||||||
\(59\) | 2.74456 | 0.357312 | 0.178656 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178656 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.37228 | −0.687850 | −0.343925 | − | 0.938997i | \(-0.611757\pi\) | ||||
−0.343925 | + | 0.938997i | \(0.611757\pi\) | |||||||
\(62\) | 3.37228i | 0.428280i | ||||||||
\(63\) | 28.2337i | 3.55711i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.37228 | −0.415099 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 1.37228i | 0.166414i | ||||||||
\(69\) | 9.25544 | 1.11422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1168 | 1.20065 | 0.600324 | − | 0.799757i | \(-0.295038\pi\) | ||||
0.600324 | + | 0.799757i | \(0.295038\pi\) | |||||||
\(72\) | 8.37228i | 0.986683i | ||||||||
\(73\) | − 15.4891i | − 1.81286i | −0.422351 | − | 0.906432i | \(-0.638795\pi\) | ||||
0.422351 | − | 0.906432i | \(-0.361205\pi\) | |||||||
\(74\) | 9.37228 | 1.08951 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.627719 | 0.0720043 | ||||||||
\(77\) | 3.37228i | 0.384307i | ||||||||
\(78\) | 6.74456i | 0.763671i | ||||||||
\(79\) | 1.25544 | 0.141248 | 0.0706239 | − | 0.997503i | \(-0.477501\pi\) | ||||
0.0706239 | + | 0.997503i | \(0.477501\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | − 11.4891i | − 1.26876i | ||||||||
\(83\) | − 2.74456i | − 0.301255i | −0.988591 | − | 0.150627i | \(-0.951871\pi\) | ||||
0.988591 | − | 0.150627i | \(-0.0481294\pi\) | |||||||
\(84\) | 11.3723 | 1.24082 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 4.62772i | 0.496144i | ||||||||
\(88\) | 1.00000i | 0.106600i | ||||||||
\(89\) | 1.37228 | 0.145462 | 0.0727308 | − | 0.997352i | \(-0.476829\pi\) | ||||
0.0727308 | + | 0.997352i | \(0.476829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.74456 | 0.707022 | ||||||||
\(92\) | − 2.74456i | − 0.286140i | ||||||||
\(93\) | − 11.3723i | − 1.17925i | ||||||||
\(94\) | 2.74456 | 0.283080 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.37228 | 0.344182 | ||||||||
\(97\) | 12.7446i | 1.29401i | 0.762484 | + | 0.647007i | \(0.223980\pi\) | ||||
−0.762484 | + | 0.647007i | \(0.776020\pi\) | |||||||
\(98\) | − 4.37228i | − 0.441667i | ||||||||
\(99\) | 8.37228 | 0.841446 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | − 4.62772i | − 0.458212i | ||||||||
\(103\) | − 9.48913i | − 0.934991i | −0.883995 | − | 0.467496i | \(-0.845156\pi\) | ||||
0.883995 | − | 0.467496i | \(-0.154844\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.11684 | 0.399863 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | − 18.1168i | − 1.74329i | ||||||||
\(109\) | 15.4891 | 1.48359 | 0.741795 | − | 0.670627i | \(-0.233975\pi\) | ||||
0.741795 | + | 0.670627i | \(0.233975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −31.6060 | −2.99991 | ||||||||
\(112\) | − 3.37228i | − 0.318651i | ||||||||
\(113\) | 3.25544i | 0.306246i | 0.988207 | + | 0.153123i | \(0.0489330\pi\) | ||||
−0.988207 | + | 0.153123i | \(0.951067\pi\) | |||||||
\(114\) | −2.11684 | −0.198261 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.37228 | 0.127413 | ||||||||
\(117\) | − 16.7446i | − 1.54804i | ||||||||
\(118\) | 2.74456i | 0.252657i | ||||||||
\(119\) | −4.62772 | −0.424222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 5.37228i | − 0.486383i | ||||||||
\(123\) | 38.7446i | 3.49348i | ||||||||
\(124\) | −3.37228 | −0.302840 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −28.2337 | −2.51526 | ||||||||
\(127\) | − 8.00000i | − 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −13.4891 | −1.18765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.1168 | 1.93236 | 0.966179 | − | 0.257873i | \(-0.0830216\pi\) | ||||
0.966179 | + | 0.257873i | \(0.0830216\pi\) | |||||||
\(132\) | − 3.37228i | − 0.293519i | ||||||||
\(133\) | 2.11684i | 0.183554i | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.37228 | −0.117672 | ||||||||
\(137\) | − 8.74456i | − 0.747098i | −0.927610 | − | 0.373549i | \(-0.878141\pi\) | ||||
0.927610 | − | 0.373549i | \(-0.121859\pi\) | |||||||
\(138\) | 9.25544i | 0.787875i | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.25544 | −0.779448 | ||||||||
\(142\) | 10.1168i | 0.848987i | ||||||||
\(143\) | − 2.00000i | − 0.167248i | ||||||||
\(144\) | −8.37228 | −0.697690 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 15.4891 | 1.28189 | ||||||||
\(147\) | 14.7446i | 1.21611i | ||||||||
\(148\) | 9.37228i | 0.770397i | ||||||||
\(149\) | −21.6060 | −1.77003 | −0.885015 | − | 0.465563i | \(-0.845852\pi\) | ||||
−0.885015 | + | 0.465563i | \(0.845852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2337 | −0.995563 | −0.497782 | − | 0.867302i | \(-0.665852\pi\) | ||||
−0.497782 | + | 0.867302i | \(0.665852\pi\) | |||||||
\(152\) | 0.627719i | 0.0509147i | ||||||||
\(153\) | 11.4891i | 0.928841i | ||||||||
\(154\) | −3.37228 | −0.271746 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.74456 | −0.539997 | ||||||||
\(157\) | − 9.37228i | − 0.747989i | −0.927431 | − | 0.373995i | \(-0.877988\pi\) | ||||
0.927431 | − | 0.373995i | \(-0.122012\pi\) | |||||||
\(158\) | 1.25544i | 0.0998772i | ||||||||
\(159\) | −13.8832 | −1.10101 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.25544 | 0.729431 | ||||||||
\(162\) | 35.9783i | 2.82672i | ||||||||
\(163\) | − 5.88316i | − 0.460804i | −0.973095 | − | 0.230402i | \(-0.925996\pi\) | ||||
0.973095 | − | 0.230402i | \(-0.0740042\pi\) | |||||||
\(164\) | 11.4891 | 0.897150 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.74456 | 0.213019 | ||||||||
\(167\) | 4.62772i | 0.358104i | 0.983840 | + | 0.179052i | \(0.0573030\pi\) | ||||
−0.983840 | + | 0.179052i | \(0.942697\pi\) | |||||||
\(168\) | 11.3723i | 0.877391i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.25544 | 0.401893 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | − 6.00000i | − 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | −4.62772 | −0.350826 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | − 9.25544i | − 0.695681i | ||||||||
\(178\) | 1.37228i | 0.102857i | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 6.74456i | 0.499940i | ||||||||
\(183\) | 18.1168i | 1.33924i | ||||||||
\(184\) | 2.74456 | 0.202332 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.3723 | 0.833856 | ||||||||
\(187\) | 1.37228i | 0.100351i | ||||||||
\(188\) | 2.74456i | 0.200168i | ||||||||
\(189\) | 61.0951 | 4.44401 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.48913 | −0.397179 | −0.198590 | − | 0.980083i | \(-0.563636\pi\) | ||||
−0.198590 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(192\) | 3.37228i | 0.243373i | ||||||||
\(193\) | 14.8614i | 1.06975i | 0.844932 | + | 0.534874i | \(0.179641\pi\) | ||||
−0.844932 | + | 0.534874i | \(0.820359\pi\) | |||||||
\(194\) | −12.7446 | −0.915006 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.37228 | 0.312306 | ||||||||
\(197\) | 20.7446i | 1.47799i | 0.673712 | + | 0.738994i | \(0.264699\pi\) | ||||
−0.673712 | + | 0.738994i | \(0.735301\pi\) | |||||||
\(198\) | 8.37228i | 0.594992i | ||||||||
\(199\) | −18.1168 | −1.28427 | −0.642135 | − | 0.766592i | \(-0.721951\pi\) | ||||
−0.642135 | + | 0.766592i | \(0.721951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.9783 | −1.90290 | ||||||||
\(202\) | 6.00000i | 0.422159i | ||||||||
\(203\) | 4.62772i | 0.324802i | ||||||||
\(204\) | 4.62772 | 0.324005 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.48913 | 0.661139 | ||||||||
\(207\) | − 22.9783i | − 1.59710i | ||||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | 0.627719 | 0.0434202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.11684 | 0.421101 | 0.210550 | − | 0.977583i | \(-0.432474\pi\) | ||||
0.210550 | + | 0.977583i | \(0.432474\pi\) | |||||||
\(212\) | 4.11684i | 0.282746i | ||||||||
\(213\) | − 34.1168i | − 2.33765i | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 18.1168 | 1.23270 | ||||||||
\(217\) | − 11.3723i | − 0.772001i | ||||||||
\(218\) | 15.4891i | 1.04906i | ||||||||
\(219\) | −52.2337 | −3.52963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.74456 | 0.184619 | ||||||||
\(222\) | − 31.6060i | − 2.12125i | ||||||||
\(223\) | − 18.7446i | − 1.25523i | −0.778524 | − | 0.627614i | \(-0.784031\pi\) | ||||
0.778524 | − | 0.627614i | \(-0.215969\pi\) | |||||||
\(224\) | 3.37228 | 0.225320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.25544 | −0.216548 | ||||||||
\(227\) | 2.74456i | 0.182163i | 0.995843 | + | 0.0910815i | \(0.0290324\pi\) | ||||
−0.995843 | + | 0.0910815i | \(0.970968\pi\) | |||||||
\(228\) | − 2.11684i | − 0.140191i | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3723 | 0.748241 | ||||||||
\(232\) | 1.37228i | 0.0900947i | ||||||||
\(233\) | 1.37228i | 0.0899011i | 0.998989 | + | 0.0449506i | \(0.0143130\pi\) | ||||
−0.998989 | + | 0.0449506i | \(0.985687\pi\) | |||||||
\(234\) | 16.7446 | 1.09463 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.74456 | −0.178656 | ||||||||
\(237\) | − 4.23369i | − 0.275008i | ||||||||
\(238\) | − 4.62772i | − 0.299970i | ||||||||
\(239\) | 14.7446 | 0.953746 | 0.476873 | − | 0.878972i | \(-0.341770\pi\) | ||||
0.476873 | + | 0.878972i | \(0.341770\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | − 66.9783i | − 4.29666i | ||||||||
\(244\) | 5.37228 | 0.343925 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −38.7446 | −2.47026 | ||||||||
\(247\) | − 1.25544i | − 0.0798816i | ||||||||
\(248\) | − 3.37228i | − 0.214140i | ||||||||
\(249\) | −9.25544 | −0.586540 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.74456 | 0.173235 | 0.0866176 | − | 0.996242i | \(-0.472394\pi\) | ||||
0.0866176 | + | 0.996242i | \(0.472394\pi\) | |||||||
\(252\) | − 28.2337i | − 1.77856i | ||||||||
\(253\) | − 2.74456i | − 0.172549i | ||||||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 18.0000i | − 1.12281i | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||||
0.827541 | − | 0.561405i | \(-0.189739\pi\) | |||||||
\(258\) | − 13.4891i | − 0.839796i | ||||||||
\(259\) | −31.6060 | −1.96390 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4891 | 0.711159 | ||||||||
\(262\) | 22.1168i | 1.36638i | ||||||||
\(263\) | − 24.8614i | − 1.53302i | −0.642232 | − | 0.766510i | \(-0.721992\pi\) | ||||
0.642232 | − | 0.766510i | \(-0.278008\pi\) | |||||||
\(264\) | 3.37228 | 0.207550 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.11684 | −0.129792 | ||||||||
\(267\) | − 4.62772i | − 0.283212i | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 8.74456 | 0.533165 | 0.266583 | − | 0.963812i | \(-0.414105\pi\) | ||||
0.266583 | + | 0.963812i | \(0.414105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | − 1.37228i | − 0.0832068i | ||||||||
\(273\) | − 22.7446i | − 1.37656i | ||||||||
\(274\) | 8.74456 | 0.528278 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.25544 | −0.557112 | ||||||||
\(277\) | 12.7446i | 0.765747i | 0.923801 | + | 0.382873i | \(0.125065\pi\) | ||||
−0.923801 | + | 0.382873i | \(0.874935\pi\) | |||||||
\(278\) | 4.00000i | 0.239904i | ||||||||
\(279\) | −28.2337 | −1.69031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | − 9.25544i | − 0.551153i | ||||||||
\(283\) | 5.25544i | 0.312403i | 0.987725 | + | 0.156202i | \(0.0499250\pi\) | ||||
−0.987725 | + | 0.156202i | \(0.950075\pi\) | |||||||
\(284\) | −10.1168 | −0.600324 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 38.7446i | 2.28702i | ||||||||
\(288\) | − 8.37228i | − 0.493341i | ||||||||
\(289\) | 15.1168 | 0.889226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 42.9783 | 2.51943 | ||||||||
\(292\) | 15.4891i | 0.906432i | ||||||||
\(293\) | 23.4891i | 1.37225i | 0.727484 | + | 0.686125i | \(0.240690\pi\) | ||||
−0.727484 | + | 0.686125i | \(0.759310\pi\) | |||||||
\(294\) | −14.7446 | −0.859920 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.37228 | −0.544753 | ||||||||
\(297\) | − 18.1168i | − 1.05125i | ||||||||
\(298\) | − 21.6060i | − 1.25160i | ||||||||
\(299\) | −5.48913 | −0.317444 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4891 | −0.777500 | ||||||||
\(302\) | − 12.2337i | − 0.703970i | ||||||||
\(303\) | − 20.2337i | − 1.16240i | ||||||||
\(304\) | −0.627719 | −0.0360021 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.4891 | −0.656790 | ||||||||
\(307\) | − 5.25544i | − 0.299944i | −0.988690 | − | 0.149972i | \(-0.952082\pi\) | ||||
0.988690 | − | 0.149972i | \(-0.0479183\pi\) | |||||||
\(308\) | − 3.37228i | − 0.192154i | ||||||||
\(309\) | −32.0000 | −1.82042 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3723 | 1.09850 | 0.549251 | − | 0.835658i | \(-0.314913\pi\) | ||||
0.549251 | + | 0.835658i | \(0.314913\pi\) | |||||||
\(312\) | − 6.74456i | − 0.381836i | ||||||||
\(313\) | − 22.0000i | − 1.24351i | −0.783210 | − | 0.621757i | \(-0.786419\pi\) | ||||
0.783210 | − | 0.621757i | \(-0.213581\pi\) | |||||||
\(314\) | 9.37228 | 0.528908 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.25544 | −0.0706239 | ||||||||
\(317\) | 24.3505i | 1.36766i | 0.729640 | + | 0.683831i | \(0.239687\pi\) | ||||
−0.729640 | + | 0.683831i | \(0.760313\pi\) | |||||||
\(318\) | − 13.8832i | − 0.778529i | ||||||||
\(319\) | 1.37228 | 0.0768330 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.4674 | 2.25867 | ||||||||
\(322\) | 9.25544i | 0.515785i | ||||||||
\(323\) | 0.861407i | 0.0479299i | ||||||||
\(324\) | −35.9783 | −1.99879 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.88316 | 0.325838 | ||||||||
\(327\) | − 52.2337i | − 2.88853i | ||||||||
\(328\) | 11.4891i | 0.634381i | ||||||||
\(329\) | −9.25544 | −0.510269 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.9783 | 1.70272 | 0.851359 | − | 0.524583i | \(-0.175779\pi\) | ||||
0.851359 | + | 0.524583i | \(0.175779\pi\) | |||||||
\(332\) | 2.74456i | 0.150627i | ||||||||
\(333\) | 78.4674i | 4.29999i | ||||||||
\(334\) | −4.62772 | −0.253217 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −11.3723 | −0.620409 | ||||||||
\(337\) | − 24.1168i | − 1.31373i | −0.754009 | − | 0.656864i | \(-0.771883\pi\) | ||||
0.754009 | − | 0.656864i | \(-0.228117\pi\) | |||||||
\(338\) | 9.00000i | 0.489535i | ||||||||
\(339\) | 10.9783 | 0.596257 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.37228 | −0.182619 | ||||||||
\(342\) | 5.25544i | 0.284182i | ||||||||
\(343\) | − 8.86141i | − 0.478471i | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | 32.2337i | 1.73040i | 0.501431 | + | 0.865198i | \(0.332807\pi\) | ||||
−0.501431 | + | 0.865198i | \(0.667193\pi\) | |||||||
\(348\) | − 4.62772i | − 0.248072i | ||||||||
\(349\) | −19.4891 | −1.04323 | −0.521614 | − | 0.853181i | \(-0.674670\pi\) | ||||
−0.521614 | + | 0.853181i | \(0.674670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.2337 | −1.93401 | ||||||||
\(352\) | − 1.00000i | − 0.0533002i | ||||||||
\(353\) | − 0.510875i | − 0.0271911i | −0.999908 | − | 0.0135956i | \(-0.995672\pi\) | ||||
0.999908 | − | 0.0135956i | \(-0.00432773\pi\) | |||||||
\(354\) | 9.25544 | 0.491921 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.37228 | −0.0727308 | ||||||||
\(357\) | 15.6060i | 0.825955i | ||||||||
\(358\) | 12.0000i | 0.634220i | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | − 10.0000i | − 0.525588i | ||||||||
\(363\) | − 3.37228i | − 0.176999i | ||||||||
\(364\) | −6.74456 | −0.353511 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −18.1168 | −0.946983 | ||||||||
\(367\) | 4.00000i | 0.208798i | 0.994535 | + | 0.104399i | \(0.0332919\pi\) | ||||
−0.994535 | + | 0.104399i | \(0.966708\pi\) | |||||||
\(368\) | 2.74456i | 0.143070i | ||||||||
\(369\) | 96.1902 | 5.00746 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8832 | −0.720778 | ||||||||
\(372\) | 11.3723i | 0.589625i | ||||||||
\(373\) | 31.4891i | 1.63045i | 0.579148 | + | 0.815223i | \(0.303385\pi\) | ||||
−0.579148 | + | 0.815223i | \(0.696615\pi\) | |||||||
\(374\) | −1.37228 | −0.0709590 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.74456 | −0.141540 | ||||||||
\(377\) | − 2.74456i | − 0.141352i | ||||||||
\(378\) | 61.0951i | 3.14239i | ||||||||
\(379\) | 0.233688 | 0.0120037 | 0.00600187 | − | 0.999982i | \(-0.498090\pi\) | ||||
0.00600187 | + | 0.999982i | \(0.498090\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.9783 | −1.38214 | ||||||||
\(382\) | − 5.48913i | − 0.280848i | ||||||||
\(383\) | 32.2337i | 1.64706i | 0.567269 | + | 0.823532i | \(0.308000\pi\) | ||||
−0.567269 | + | 0.823532i | \(0.692000\pi\) | |||||||
\(384\) | −3.37228 | −0.172091 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.8614 | −0.756426 | ||||||||
\(387\) | 33.4891i | 1.70235i | ||||||||
\(388\) | − 12.7446i | − 0.647007i | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.76631 | 0.190471 | ||||||||
\(392\) | 4.37228i | 0.220834i | ||||||||
\(393\) | − 74.5842i | − 3.76228i | ||||||||
\(394\) | −20.7446 | −1.04510 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.37228 | −0.420723 | ||||||||
\(397\) | − 24.9783i | − 1.25362i | −0.779171 | − | 0.626811i | \(-0.784360\pi\) | ||||
0.779171 | − | 0.626811i | \(-0.215640\pi\) | |||||||
\(398\) | − 18.1168i | − 0.908115i | ||||||||
\(399\) | 7.13859 | 0.357377 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3723 | 0.667780 | 0.333890 | − | 0.942612i | \(-0.391639\pi\) | ||||
0.333890 | + | 0.942612i | \(0.391639\pi\) | |||||||
\(402\) | − 26.9783i | − 1.34555i | ||||||||
\(403\) | 6.74456i | 0.335971i | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.62772 | −0.229670 | ||||||||
\(407\) | 9.37228i | 0.464567i | ||||||||
\(408\) | 4.62772i | 0.229106i | ||||||||
\(409\) | 1.76631 | 0.0873385 | 0.0436693 | − | 0.999046i | \(-0.486095\pi\) | ||||
0.0436693 | + | 0.999046i | \(0.486095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.4891 | −1.45459 | ||||||||
\(412\) | 9.48913i | 0.467496i | ||||||||
\(413\) | − 9.25544i | − 0.455430i | ||||||||
\(414\) | 22.9783 | 1.12932 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | − 13.4891i | − 0.660565i | ||||||||
\(418\) | 0.627719i | 0.0307027i | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2337 | 0.498759 | 0.249380 | − | 0.968406i | \(-0.419773\pi\) | ||||
0.249380 | + | 0.968406i | \(0.419773\pi\) | |||||||
\(422\) | 6.11684i | 0.297763i | ||||||||
\(423\) | 22.9783i | 1.11724i | ||||||||
\(424\) | −4.11684 | −0.199932 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 34.1168 | 1.65297 | ||||||||
\(427\) | 18.1168i | 0.876736i | ||||||||
\(428\) | − 12.0000i | − 0.580042i | ||||||||
\(429\) | −6.74456 | −0.325631 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.9783 | −1.68484 | −0.842422 | − | 0.538819i | \(-0.818871\pi\) | ||||
−0.842422 | + | 0.538819i | \(0.818871\pi\) | |||||||
\(432\) | 18.1168i | 0.871647i | ||||||||
\(433\) | 27.7228i | 1.33227i | 0.745830 | + | 0.666137i | \(0.232053\pi\) | ||||
−0.745830 | + | 0.666137i | \(0.767947\pi\) | |||||||
\(434\) | 11.3723 | 0.545887 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.4891 | −0.741795 | ||||||||
\(437\) | − 1.72281i | − 0.0824133i | ||||||||
\(438\) | − 52.2337i | − 2.49582i | ||||||||
\(439\) | −18.9783 | −0.905782 | −0.452891 | − | 0.891566i | \(-0.649607\pi\) | ||||
−0.452891 | + | 0.891566i | \(0.649607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 36.6060 | 1.74314 | ||||||||
\(442\) | 2.74456i | 0.130546i | ||||||||
\(443\) | 29.4891i | 1.40107i | 0.713618 | + | 0.700535i | \(0.247055\pi\) | ||||
−0.713618 | + | 0.700535i | \(0.752945\pi\) | |||||||
\(444\) | 31.6060 | 1.49995 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18.7446 | 0.887581 | ||||||||
\(447\) | 72.8614i | 3.44623i | ||||||||
\(448\) | 3.37228i | 0.159325i | ||||||||
\(449\) | −28.9783 | −1.36757 | −0.683784 | − | 0.729684i | \(-0.739667\pi\) | ||||
−0.683784 | + | 0.729684i | \(0.739667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.4891 | 0.541002 | ||||||||
\(452\) | − 3.25544i | − 0.153123i | ||||||||
\(453\) | 41.2554i | 1.93835i | ||||||||
\(454\) | −2.74456 | −0.128809 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.11684 | 0.0991303 | ||||||||
\(457\) | 16.3505i | 0.764846i | 0.923987 | + | 0.382423i | \(0.124910\pi\) | ||||
−0.923987 | + | 0.382423i | \(0.875090\pi\) | |||||||
\(458\) | 10.0000i | 0.467269i | ||||||||
\(459\) | 24.8614 | 1.16043 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1168 | 0.750636 | 0.375318 | − | 0.926896i | \(-0.377533\pi\) | ||||
0.375318 | + | 0.926896i | \(0.377533\pi\) | |||||||
\(462\) | 11.3723i | 0.529086i | ||||||||
\(463\) | − 0.233688i | − 0.0108604i | −0.999985 | − | 0.00543020i | \(-0.998272\pi\) | ||||
0.999985 | − | 0.00543020i | \(-0.00172849\pi\) | |||||||
\(464\) | −1.37228 | −0.0637066 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.37228 | −0.0635697 | ||||||||
\(467\) | 19.3723i | 0.896442i | 0.893923 | + | 0.448221i | \(0.147942\pi\) | ||||
−0.893923 | + | 0.448221i | \(0.852058\pi\) | |||||||
\(468\) | 16.7446i | 0.774018i | ||||||||
\(469\) | −26.9783 | −1.24574 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.6060 | −1.45633 | ||||||||
\(472\) | − 2.74456i | − 0.126329i | ||||||||
\(473\) | 4.00000i | 0.183920i | ||||||||
\(474\) | 4.23369 | 0.194460 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.62772 | 0.212111 | ||||||||
\(477\) | 34.4674i | 1.57815i | ||||||||
\(478\) | 14.7446i | 0.674401i | ||||||||
\(479\) | −5.48913 | −0.250805 | −0.125402 | − | 0.992106i | \(-0.540022\pi\) | ||||
−0.125402 | + | 0.992106i | \(0.540022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.7446 | 0.854678 | ||||||||
\(482\) | − 22.0000i | − 1.00207i | ||||||||
\(483\) | − 31.2119i | − 1.42019i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 66.9783 | 3.03820 | ||||||||
\(487\) | − 20.0000i | − 0.906287i | −0.891438 | − | 0.453143i | \(-0.850303\pi\) | ||||
0.891438 | − | 0.453143i | \(-0.149697\pi\) | |||||||
\(488\) | 5.37228i | 0.243192i | ||||||||
\(489\) | −19.8397 | −0.897180 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.37228 | −0.332706 | −0.166353 | − | 0.986066i | \(-0.553199\pi\) | ||||
−0.166353 | + | 0.986066i | \(0.553199\pi\) | |||||||
\(492\) | − 38.7446i | − 1.74674i | ||||||||
\(493\) | 1.88316i | 0.0848131i | ||||||||
\(494\) | 1.25544 | 0.0564848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.37228 | 0.151420 | ||||||||
\(497\) | − 34.1168i | − 1.53035i | ||||||||
\(498\) | − 9.25544i | − 0.414746i | ||||||||
\(499\) | 33.4891 | 1.49918 | 0.749590 | − | 0.661903i | \(-0.230251\pi\) | ||||
0.749590 | + | 0.661903i | \(0.230251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.6060 | 0.697223 | ||||||||
\(502\) | 2.74456i | 0.122496i | ||||||||
\(503\) | − 34.9783i | − 1.55960i | −0.626027 | − | 0.779802i | \(-0.715320\pi\) | ||||
0.626027 | − | 0.779802i | \(-0.284680\pi\) | |||||||
\(504\) | 28.2337 | 1.25763 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.74456 | 0.122011 | ||||||||
\(507\) | − 30.3505i | − 1.34791i | ||||||||
\(508\) | 8.00000i | 0.354943i | ||||||||
\(509\) | −9.76631 | −0.432884 | −0.216442 | − | 0.976295i | \(-0.569445\pi\) | ||||
−0.216442 | + | 0.976295i | \(0.569445\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −52.2337 | −2.31068 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 11.3723i | − 0.502098i | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 13.4891 | 0.593826 | ||||||||
\(517\) | 2.74456i | 0.120706i | ||||||||
\(518\) | − 31.6060i | − 1.38869i | ||||||||
\(519\) | −20.2337 | −0.888160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5109 | 0.548111 | 0.274056 | − | 0.961714i | \(-0.411635\pi\) | ||||
0.274056 | + | 0.961714i | \(0.411635\pi\) | |||||||
\(522\) | 11.4891i | 0.502865i | ||||||||
\(523\) | 30.9783i | 1.35458i | 0.735714 | + | 0.677292i | \(0.236847\pi\) | ||||
−0.735714 | + | 0.677292i | \(0.763153\pi\) | |||||||
\(524\) | −22.1168 | −0.966179 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.8614 | 1.08401 | ||||||||
\(527\) | − 4.62772i | − 0.201587i | ||||||||
\(528\) | 3.37228i | 0.146760i | ||||||||
\(529\) | 15.4674 | 0.672495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.9783 | −0.997171 | ||||||||
\(532\) | − 2.11684i | − 0.0917768i | ||||||||
\(533\) | − 22.9783i | − 0.995299i | ||||||||
\(534\) | 4.62772 | 0.200261 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | − 40.4674i | − 1.74630i | ||||||||
\(538\) | 8.74456i | 0.377005i | ||||||||
\(539\) | 4.37228 | 0.188327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.1168 | −0.864891 | −0.432445 | − | 0.901660i | \(-0.642349\pi\) | ||||
−0.432445 | + | 0.901660i | \(0.642349\pi\) | |||||||
\(542\) | − 16.0000i | − 0.687259i | ||||||||
\(543\) | 33.7228i | 1.44718i | ||||||||
\(544\) | 1.37228 | 0.0588361 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 22.7446 | 0.973377 | ||||||||
\(547\) | − 20.0000i | − 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | 8.74456i | 0.373549i | ||||||||
\(549\) | 44.9783 | 1.91962 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.861407 | 0.0366972 | ||||||||
\(552\) | − 9.25544i | − 0.393938i | ||||||||
\(553\) | − 4.23369i | − 0.180035i | ||||||||
\(554\) | −12.7446 | −0.541465 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | − 4.97825i | − 0.210935i | −0.994423 | − | 0.105468i | \(-0.966366\pi\) | ||||
0.994423 | − | 0.105468i | \(-0.0336339\pi\) | |||||||
\(558\) | − 28.2337i | − 1.19523i | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.62772 | 0.195382 | ||||||||
\(562\) | 18.0000i | 0.759284i | ||||||||
\(563\) | − 8.23369i | − 0.347009i | −0.984833 | − | 0.173504i | \(-0.944491\pi\) | ||||
0.984833 | − | 0.173504i | \(-0.0555090\pi\) | |||||||
\(564\) | 9.25544 | 0.389724 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.25544 | −0.220903 | ||||||||
\(567\) | − 121.329i | − 5.09533i | ||||||||
\(568\) | − 10.1168i | − 0.424493i | ||||||||
\(569\) | 15.2554 | 0.639541 | 0.319771 | − | 0.947495i | \(-0.396394\pi\) | ||||
0.319771 | + | 0.947495i | \(0.396394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3723 | 0.643310 | 0.321655 | − | 0.946857i | \(-0.395761\pi\) | ||||
0.321655 | + | 0.946857i | \(0.395761\pi\) | |||||||
\(572\) | 2.00000i | 0.0836242i | ||||||||
\(573\) | 18.5109i | 0.773303i | ||||||||
\(574\) | −38.7446 | −1.61717 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.37228 | 0.348845 | ||||||||
\(577\) | − 36.9783i | − 1.53942i | −0.638391 | − | 0.769712i | \(-0.720400\pi\) | ||||
0.638391 | − | 0.769712i | \(-0.279600\pi\) | |||||||
\(578\) | 15.1168i | 0.628778i | ||||||||
\(579\) | 50.1168 | 2.08278 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.25544 | −0.383980 | ||||||||
\(582\) | 42.9783i | 1.78151i | ||||||||
\(583\) | 4.11684i | 0.170502i | ||||||||
\(584\) | −15.4891 | −0.640945 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.4891 | −0.970327 | ||||||||
\(587\) | − 24.8614i | − 1.02614i | −0.858347 | − | 0.513070i | \(-0.828508\pi\) | ||||
0.858347 | − | 0.513070i | \(-0.171492\pi\) | |||||||
\(588\) | − 14.7446i | − 0.608056i | ||||||||
\(589\) | −2.11684 | −0.0872230 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 69.9565 | 2.87763 | ||||||||
\(592\) | − 9.37228i | − 0.385198i | ||||||||
\(593\) | − 12.5109i | − 0.513760i | −0.966443 | − | 0.256880i | \(-0.917305\pi\) | ||||
0.966443 | − | 0.256880i | \(-0.0826945\pi\) | |||||||
\(594\) | 18.1168 | 0.743343 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.6060 | 0.885015 | ||||||||
\(597\) | 61.0951i | 2.50046i | ||||||||
\(598\) | − 5.48913i | − 0.224467i | ||||||||
\(599\) | 39.6060 | 1.61826 | 0.809128 | − | 0.587632i | \(-0.199940\pi\) | ||||
0.809128 | + | 0.587632i | \(0.199940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5109 | −0.673493 | −0.336746 | − | 0.941595i | \(-0.609326\pi\) | ||||
−0.336746 | + | 0.941595i | \(0.609326\pi\) | |||||||
\(602\) | − 13.4891i | − 0.549776i | ||||||||
\(603\) | 66.9783i | 2.72757i | ||||||||
\(604\) | 12.2337 | 0.497782 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.2337 | 0.821937 | ||||||||
\(607\) | 5.88316i | 0.238790i | 0.992847 | + | 0.119395i | \(0.0380955\pi\) | ||||
−0.992847 | + | 0.119395i | \(0.961905\pi\) | |||||||
\(608\) | − 0.627719i | − 0.0254574i | ||||||||
\(609\) | 15.6060 | 0.632386 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.48913 | 0.222066 | ||||||||
\(612\) | − 11.4891i | − 0.464420i | ||||||||
\(613\) | 20.5109i | 0.828426i | 0.910180 | + | 0.414213i | \(0.135943\pi\) | ||||
−0.910180 | + | 0.414213i | \(0.864057\pi\) | |||||||
\(614\) | 5.25544 | 0.212092 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.37228 | 0.135873 | ||||||||
\(617\) | 2.23369i | 0.0899249i | 0.998989 | + | 0.0449624i | \(0.0143168\pi\) | ||||
−0.998989 | + | 0.0449624i | \(0.985683\pi\) | |||||||
\(618\) | − 32.0000i | − 1.28723i | ||||||||
\(619\) | 44.4674 | 1.78729 | 0.893647 | − | 0.448770i | \(-0.148138\pi\) | ||||
0.893647 | + | 0.448770i | \(0.148138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.7228 | −1.99531 | ||||||||
\(622\) | 19.3723i | 0.776758i | ||||||||
\(623\) | − 4.62772i | − 0.185406i | ||||||||
\(624\) | 6.74456 | 0.269999 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.0000 | 0.879297 | ||||||||
\(627\) | − 2.11684i | − 0.0845386i | ||||||||
\(628\) | 9.37228i | 0.373995i | ||||||||
\(629\) | −12.8614 | −0.512818 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1168 | 1.67665 | 0.838323 | − | 0.545175i | \(-0.183537\pi\) | ||||
0.838323 | + | 0.545175i | \(0.183537\pi\) | |||||||
\(632\) | − 1.25544i | − 0.0499386i | ||||||||
\(633\) | − 20.6277i | − 0.819878i | ||||||||
\(634\) | −24.3505 | −0.967083 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.8832 | 0.550503 | ||||||||
\(637\) | − 8.74456i | − 0.346472i | ||||||||
\(638\) | 1.37228i | 0.0543291i | ||||||||
\(639\) | −84.7011 | −3.35072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.0951 | −1.07019 | −0.535096 | − | 0.844791i | \(-0.679725\pi\) | ||||
−0.535096 | + | 0.844791i | \(0.679725\pi\) | |||||||
\(642\) | 40.4674i | 1.59712i | ||||||||
\(643\) | − 5.88316i | − 0.232009i | −0.993249 | − | 0.116005i | \(-0.962991\pi\) | ||||
0.993249 | − | 0.116005i | \(-0.0370087\pi\) | |||||||
\(644\) | −9.25544 | −0.364715 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.861407 | −0.0338916 | ||||||||
\(647\) | 37.7228i | 1.48304i | 0.670933 | + | 0.741518i | \(0.265894\pi\) | ||||
−0.670933 | + | 0.741518i | \(0.734106\pi\) | |||||||
\(648\) | − 35.9783i | − 1.41336i | ||||||||
\(649\) | −2.74456 | −0.107734 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.3505 | −1.50308 | ||||||||
\(652\) | 5.88316i | 0.230402i | ||||||||
\(653\) | 10.6277i | 0.415895i | 0.978140 | + | 0.207947i | \(0.0666783\pi\) | ||||
−0.978140 | + | 0.207947i | \(0.933322\pi\) | |||||||
\(654\) | 52.2337 | 2.04250 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.4891 | −0.448575 | ||||||||
\(657\) | 129.679i | 5.05927i | ||||||||
\(658\) | − 9.25544i | − 0.360815i | ||||||||
\(659\) | −12.8614 | −0.501009 | −0.250505 | − | 0.968115i | \(-0.580597\pi\) | ||||
−0.250505 | + | 0.968115i | \(0.580597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.51087 | 0.331035 | 0.165517 | − | 0.986207i | \(-0.447071\pi\) | ||||
0.165517 | + | 0.986207i | \(0.447071\pi\) | |||||||
\(662\) | 30.9783i | 1.20400i | ||||||||
\(663\) | − 9.25544i | − 0.359451i | ||||||||
\(664\) | −2.74456 | −0.106510 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −78.4674 | −3.04055 | ||||||||
\(667\) | − 3.76631i | − 0.145832i | ||||||||
\(668\) | − 4.62772i | − 0.179052i | ||||||||
\(669\) | −63.2119 | −2.44391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.37228 | 0.207395 | ||||||||
\(672\) | − 11.3723i | − 0.438695i | ||||||||
\(673\) | 14.8614i | 0.572865i | 0.958100 | + | 0.286433i | \(0.0924694\pi\) | ||||
−0.958100 | + | 0.286433i | \(0.907531\pi\) | |||||||
\(674\) | 24.1168 | 0.928946 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | − 3.25544i | − 0.125117i | −0.998041 | − | 0.0625583i | \(-0.980074\pi\) | ||||
0.998041 | − | 0.0625583i | \(-0.0199259\pi\) | |||||||
\(678\) | 10.9783i | 0.421617i | ||||||||
\(679\) | 42.9783 | 1.64935 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.25544 | 0.354669 | ||||||||
\(682\) | − 3.37228i | − 0.129131i | ||||||||
\(683\) | − 28.6277i | − 1.09541i | −0.836672 | − | 0.547705i | \(-0.815502\pi\) | ||||
0.836672 | − | 0.547705i | \(-0.184498\pi\) | |||||||
\(684\) | −5.25544 | −0.200947 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.86141 | 0.338330 | ||||||||
\(687\) | − 33.7228i | − 1.28661i | ||||||||
\(688\) | − 4.00000i | − 0.152499i | ||||||||
\(689\) | 8.23369 | 0.313679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.2337 | 1.53056 | 0.765281 | − | 0.643697i | \(-0.222600\pi\) | ||||
0.765281 | + | 0.643697i | \(0.222600\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | − 28.2337i | − 1.07251i | ||||||||
\(694\) | −32.2337 | −1.22357 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.62772 | 0.175413 | ||||||||
\(697\) | 15.7663i | 0.597192i | ||||||||
\(698\) | − 19.4891i | − 0.737674i | ||||||||
\(699\) | 4.62772 | 0.175036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.3723 | −1.41153 | −0.705766 | − | 0.708445i | \(-0.749397\pi\) | ||||
−0.705766 | + | 0.708445i | \(0.749397\pi\) | |||||||
\(702\) | − 36.2337i | − 1.36755i | ||||||||
\(703\) | 5.88316i | 0.221887i | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.510875 | 0.0192270 | ||||||||
\(707\) | − 20.2337i | − 0.760966i | ||||||||
\(708\) | 9.25544i | 0.347841i | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5109 | −0.394189 | ||||||||
\(712\) | − 1.37228i | − 0.0514284i | ||||||||
\(713\) | 9.25544i | 0.346619i | ||||||||
\(714\) | −15.6060 | −0.584039 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | − 49.7228i | − 1.85693i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.8832 | −0.517754 | −0.258877 | − | 0.965910i | \(-0.583352\pi\) | ||||
−0.258877 | + | 0.965910i | \(0.583352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.0000 | −1.19174 | ||||||||
\(722\) | − 18.6060i | − 0.692442i | ||||||||
\(723\) | 74.1902i | 2.75916i | ||||||||
\(724\) | 10.0000 | 0.371647 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.37228 | 0.125157 | ||||||||
\(727\) | 24.2337i | 0.898778i | 0.893336 | + | 0.449389i | \(0.148358\pi\) | ||||
−0.893336 | + | 0.449389i | \(0.851642\pi\) | |||||||
\(728\) | − 6.74456i | − 0.249970i | ||||||||
\(729\) | −117.935 | −4.36795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.48913 | −0.203023 | ||||||||
\(732\) | − 18.1168i | − 0.669618i | ||||||||
\(733\) | 46.2337i | 1.70768i | 0.520535 | + | 0.853840i | \(0.325732\pi\) | ||||
−0.520535 | + | 0.853840i | \(0.674268\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.74456 | −0.101166 | ||||||||
\(737\) | 8.00000i | 0.294684i | ||||||||
\(738\) | 96.1902i | 3.54081i | ||||||||
\(739\) | 20.4674 | 0.752905 | 0.376452 | − | 0.926436i | \(-0.377144\pi\) | ||||
0.376452 | + | 0.926436i | \(0.377144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.23369 | −0.155528 | ||||||||
\(742\) | − 13.8832i | − 0.509667i | ||||||||
\(743\) | − 4.62772i | − 0.169775i | −0.996391 | − | 0.0848873i | \(-0.972947\pi\) | ||||
0.996391 | − | 0.0848873i | \(-0.0270530\pi\) | |||||||
\(744\) | −11.3723 | −0.416928 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31.4891 | −1.15290 | ||||||||
\(747\) | 22.9783i | 0.840730i | ||||||||
\(748\) | − 1.37228i | − 0.0501756i | ||||||||
\(749\) | 40.4674 | 1.47865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.86141 | 0.323357 | 0.161679 | − | 0.986843i | \(-0.448309\pi\) | ||||
0.161679 | + | 0.986843i | \(0.448309\pi\) | |||||||
\(752\) | − 2.74456i | − 0.100084i | ||||||||
\(753\) | − 9.25544i | − 0.337287i | ||||||||
\(754\) | 2.74456 | 0.0999511 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −61.0951 | −2.22201 | ||||||||
\(757\) | 20.9783i | 0.762467i | 0.924479 | + | 0.381234i | \(0.124501\pi\) | ||||
−0.924479 | + | 0.381234i | \(0.875499\pi\) | |||||||
\(758\) | 0.233688i | 0.00848793i | ||||||||
\(759\) | −9.25544 | −0.335951 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.97825 | 0.180461 | 0.0902307 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902307 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(762\) | − 26.9783i | − 0.977319i | ||||||||
\(763\) | − 52.2337i | − 1.89099i | ||||||||
\(764\) | 5.48913 | 0.198590 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.2337 | −1.16465 | ||||||||
\(767\) | 5.48913i | 0.198201i | ||||||||
\(768\) | − 3.37228i | − 0.121687i | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −60.7011 | −2.18610 | ||||||||
\(772\) | − 14.8614i | − 0.534874i | ||||||||
\(773\) | − 33.6060i | − 1.20872i | −0.796710 | − | 0.604361i | \(-0.793428\pi\) | ||||
0.796710 | − | 0.604361i | \(-0.206572\pi\) | |||||||
\(774\) | −33.4891 | −1.20374 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.7446 | 0.457503 | ||||||||
\(777\) | 106.584i | 3.82369i | ||||||||
\(778\) | − 6.00000i | − 0.215110i | ||||||||
\(779\) | 7.21194 | 0.258395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1168 | −0.362009 | ||||||||
\(782\) | 3.76631i | 0.134683i | ||||||||
\(783\) | − 24.8614i | − 0.888474i | ||||||||
\(784\) | −4.37228 | −0.156153 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 74.5842 | 2.66033 | ||||||||
\(787\) | 44.4674i | 1.58509i | 0.609813 | + | 0.792545i | \(0.291245\pi\) | ||||
−0.609813 | + | 0.792545i | \(0.708755\pi\) | |||||||
\(788\) | − 20.7446i | − 0.738994i | ||||||||
\(789\) | −83.8397 | −2.98477 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.9783 | 0.390342 | ||||||||
\(792\) | − 8.37228i | − 0.297496i | ||||||||
\(793\) | − 10.7446i | − 0.381551i | ||||||||
\(794\) | 24.9783 | 0.886445 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.1168 | 0.642135 | ||||||||
\(797\) | − 11.4891i | − 0.406966i | −0.979079 | − | 0.203483i | \(-0.934774\pi\) | ||||
0.979079 | − | 0.203483i | \(-0.0652261\pi\) | |||||||
\(798\) | 7.13859i | 0.252703i | ||||||||
\(799\) | −3.76631 | −0.133243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4891 | −0.405948 | ||||||||
\(802\) | 13.3723i | 0.472192i | ||||||||
\(803\) | 15.4891i | 0.546599i | ||||||||
\(804\) | 26.9783 | 0.951450 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.74456 | −0.237567 | ||||||||
\(807\) | − 29.4891i | − 1.03807i | ||||||||
\(808\) | − 6.00000i | − 0.211079i | ||||||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.8614 | 1.57530 | 0.787649 | − | 0.616125i | \(-0.211298\pi\) | ||||
0.787649 | + | 0.616125i | \(0.211298\pi\) | |||||||
\(812\) | − 4.62772i | − 0.162401i | ||||||||
\(813\) | 53.9565i | 1.89234i | ||||||||
\(814\) | −9.37228 | −0.328498 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.62772 | −0.162003 | ||||||||
\(817\) | 2.51087i | 0.0878444i | ||||||||
\(818\) | 1.76631i | 0.0617577i | ||||||||
\(819\) | −56.4674 | −1.97313 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4891 | 0.400973 | 0.200487 | − | 0.979696i | \(-0.435748\pi\) | ||||
0.200487 | + | 0.979696i | \(0.435748\pi\) | |||||||
\(822\) | − 29.4891i | − 1.02855i | ||||||||
\(823\) | − 28.0000i | − 0.976019i | −0.872838 | − | 0.488009i | \(-0.837723\pi\) | ||||
0.872838 | − | 0.488009i | \(-0.162277\pi\) | |||||||
\(824\) | −9.48913 | −0.330569 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.25544 | 0.322038 | ||||||||
\(827\) | − 46.9783i | − 1.63359i | −0.576925 | − | 0.816797i | \(-0.695748\pi\) | ||||
0.576925 | − | 0.816797i | \(-0.304252\pi\) | |||||||
\(828\) | 22.9783i | 0.798549i | ||||||||
\(829\) | 24.7446 | 0.859414 | 0.429707 | − | 0.902968i | \(-0.358617\pi\) | ||||
0.429707 | + | 0.902968i | \(0.358617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.9783 | 1.49090 | ||||||||
\(832\) | − 2.00000i | − 0.0693375i | ||||||||
\(833\) | 6.00000i | 0.207888i | ||||||||
\(834\) | 13.4891 | 0.467090 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.627719 | −0.0217101 | ||||||||
\(837\) | 61.0951i | 2.11176i | ||||||||
\(838\) | 12.0000i | 0.414533i | ||||||||
\(839\) | 10.9783 | 0.379011 | 0.189506 | − | 0.981880i | \(-0.439311\pi\) | ||||
0.189506 | + | 0.981880i | \(0.439311\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1168 | −0.935064 | ||||||||
\(842\) | 10.2337i | 0.352676i | ||||||||
\(843\) | − 60.7011i | − 2.09066i | ||||||||
\(844\) | −6.11684 | −0.210550 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −22.9783 | −0.790009 | ||||||||
\(847\) | − 3.37228i | − 0.115873i | ||||||||
\(848\) | − 4.11684i | − 0.141373i | ||||||||
\(849\) | 17.7228 | 0.608245 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.7228 | 0.881767 | ||||||||
\(852\) | 34.1168i | 1.16882i | ||||||||
\(853\) | − 38.4674i | − 1.31710i | −0.752538 | − | 0.658549i | \(-0.771171\pi\) | ||||
0.752538 | − | 0.658549i | \(-0.228829\pi\) | |||||||
\(854\) | −18.1168 | −0.619946 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | − 36.3505i | − 1.24171i | −0.783925 | − | 0.620855i | \(-0.786785\pi\) | ||||
0.783925 | − | 0.620855i | \(-0.213215\pi\) | |||||||
\(858\) | − 6.74456i | − 0.230256i | ||||||||
\(859\) | 42.7446 | 1.45843 | 0.729213 | − | 0.684287i | \(-0.239886\pi\) | ||||
0.729213 | + | 0.684287i | \(0.239886\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 130.658 | 4.45280 | ||||||||
\(862\) | − 34.9783i | − 1.19136i | ||||||||
\(863\) | 21.2554i | 0.723544i | 0.932267 | + | 0.361772i | \(0.117828\pi\) | ||||
−0.932267 | + | 0.361772i | \(0.882172\pi\) | |||||||
\(864\) | −18.1168 | −0.616348 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27.7228 | −0.942060 | ||||||||
\(867\) | − 50.9783i | − 1.73131i | ||||||||
\(868\) | 11.3723i | 0.386000i | ||||||||
\(869\) | −1.25544 | −0.0425878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | − 15.4891i | − 0.524528i | ||||||||
\(873\) | − 106.701i | − 3.61128i | ||||||||
\(874\) | 1.72281 | 0.0582750 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 52.2337 | 1.76481 | ||||||||
\(877\) | − 36.9783i | − 1.24867i | −0.781158 | − | 0.624333i | \(-0.785371\pi\) | ||||
0.781158 | − | 0.624333i | \(-0.214629\pi\) | |||||||
\(878\) | − 18.9783i | − 0.640485i | ||||||||
\(879\) | 79.2119 | 2.67175 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 36.6060i | 1.23259i | ||||||||
\(883\) | 3.37228i | 0.113486i | 0.998389 | + | 0.0567432i | \(0.0180716\pi\) | ||||
−0.998389 | + | 0.0567432i | \(0.981928\pi\) | |||||||
\(884\) | −2.74456 | −0.0923096 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.4891 | −0.990707 | ||||||||
\(887\) | 10.9783i | 0.368614i | 0.982869 | + | 0.184307i | \(0.0590040\pi\) | ||||
−0.982869 | + | 0.184307i | \(0.940996\pi\) | |||||||
\(888\) | 31.6060i | 1.06063i | ||||||||
\(889\) | −26.9783 | −0.904821 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.9783 | −1.20532 | ||||||||
\(892\) | 18.7446i | 0.627614i | ||||||||
\(893\) | 1.72281i | 0.0576517i | ||||||||
\(894\) | −72.8614 | −2.43685 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.37228 | −0.112660 | ||||||||
\(897\) | 18.5109i | 0.618060i | ||||||||
\(898\) | − 28.9783i | − 0.967017i | ||||||||
\(899\) | −4.62772 | −0.154343 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64947 | −0.188211 | ||||||||
\(902\) | 11.4891i | 0.382546i | ||||||||
\(903\) | 45.4891i | 1.51378i | ||||||||
\(904\) | 3.25544 | 0.108274 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −41.2554 | −1.37062 | ||||||||
\(907\) | 0.394031i | 0.0130836i | 0.999979 | + | 0.00654179i | \(0.00208233\pi\) | ||||
−0.999979 | + | 0.00654179i | \(0.997918\pi\) | |||||||
\(908\) | − 2.74456i | − 0.0910815i | ||||||||
\(909\) | −50.2337 | −1.66615 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.39403 | −0.278107 | −0.139053 | − | 0.990285i | \(-0.544406\pi\) | ||||
−0.139053 | + | 0.990285i | \(0.544406\pi\) | |||||||
\(912\) | 2.11684i | 0.0700957i | ||||||||
\(913\) | 2.74456i | 0.0908318i | ||||||||
\(914\) | −16.3505 | −0.540828 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | − 74.5842i | − 2.46299i | ||||||||
\(918\) | 24.8614i | 0.820549i | ||||||||
\(919\) | −18.9783 | −0.626035 | −0.313017 | − | 0.949747i | \(-0.601340\pi\) | ||||
−0.313017 | + | 0.949747i | \(0.601340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7228 | −0.583987 | ||||||||
\(922\) | 16.1168i | 0.530780i | ||||||||
\(923\) | 20.2337i | 0.666000i | ||||||||
\(924\) | −11.3723 | −0.374121 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.233688 | 0.00767946 | ||||||||
\(927\) | 79.4456i | 2.60934i | ||||||||
\(928\) | − 1.37228i | − 0.0450473i | ||||||||
\(929\) | −24.3505 | −0.798915 | −0.399458 | − | 0.916752i | \(-0.630801\pi\) | ||||
−0.399458 | + | 0.916752i | \(0.630801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.74456 | 0.0899494 | ||||||||
\(932\) | − 1.37228i | − 0.0449506i | ||||||||
\(933\) | − 65.3288i | − 2.13877i | ||||||||
\(934\) | −19.3723 | −0.633880 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.7446 | −0.547313 | ||||||||
\(937\) | 28.5109i | 0.931410i | 0.884940 | + | 0.465705i | \(0.154199\pi\) | ||||
−0.884940 | + | 0.465705i | \(0.845801\pi\) | |||||||
\(938\) | − 26.9783i | − 0.880871i | ||||||||
\(939\) | −74.1902 | −2.42111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.0951 | −0.492086 | −0.246043 | − | 0.969259i | \(-0.579130\pi\) | ||||
−0.246043 | + | 0.969259i | \(0.579130\pi\) | |||||||
\(942\) | − 31.6060i | − 1.02978i | ||||||||
\(943\) | − 31.5326i | − 1.02684i | ||||||||
\(944\) | 2.74456 | 0.0893279 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | − 48.8614i | − 1.58778i | −0.608060 | − | 0.793891i | \(-0.708052\pi\) | ||||
0.608060 | − | 0.793891i | \(-0.291948\pi\) | |||||||
\(948\) | 4.23369i | 0.137504i | ||||||||
\(949\) | 30.9783 | 1.00560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 82.1168 | 2.66282 | ||||||||
\(952\) | 4.62772i | 0.149985i | ||||||||
\(953\) | 40.1168i | 1.29951i | 0.760143 | + | 0.649756i | \(0.225129\pi\) | ||||
−0.760143 | + | 0.649756i | \(0.774871\pi\) | |||||||
\(954\) | −34.4674 | −1.11592 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.7446 | −0.476873 | ||||||||
\(957\) | − 4.62772i | − 0.149593i | ||||||||
\(958\) | − 5.48913i | − 0.177346i | ||||||||
\(959\) | −29.4891 | −0.952254 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.6277 | −0.633152 | ||||||||
\(962\) | 18.7446i | 0.604349i | ||||||||
\(963\) | − 100.467i | − 3.23752i | ||||||||
\(964\) | 22.0000 | 0.708572 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 31.2119 | 1.00423 | ||||||||
\(967\) | − 47.6060i | − 1.53090i | −0.643493 | − | 0.765452i | \(-0.722515\pi\) | ||||
0.643493 | − | 0.765452i | \(-0.277485\pi\) | |||||||
\(968\) | − 1.00000i | − 0.0321412i | ||||||||
\(969\) | 2.90491 | 0.0933190 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.02175 | −0.0327895 | −0.0163947 | − | 0.999866i | \(-0.505219\pi\) | ||||
−0.0163947 | + | 0.999866i | \(0.505219\pi\) | |||||||
\(972\) | 66.9783i | 2.14833i | ||||||||
\(973\) | − 13.4891i | − 0.432442i | ||||||||
\(974\) | 20.0000 | 0.640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.37228 | −0.171963 | ||||||||
\(977\) | − 14.2337i | − 0.455376i | −0.973734 | − | 0.227688i | \(-0.926883\pi\) | ||||
0.973734 | − | 0.227688i | \(-0.0731166\pi\) | |||||||
\(978\) | − 19.8397i | − 0.634402i | ||||||||
\(979\) | −1.37228 | −0.0438583 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −129.679 | −4.14034 | ||||||||
\(982\) | − 7.37228i | − 0.235259i | ||||||||
\(983\) | − 13.7228i | − 0.437690i | −0.975760 | − | 0.218845i | \(-0.929771\pi\) | ||||
0.975760 | − | 0.218845i | \(-0.0702289\pi\) | |||||||
\(984\) | 38.7446 | 1.23513 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.88316 | −0.0599719 | ||||||||
\(987\) | 31.2119i | 0.993487i | ||||||||
\(988\) | 1.25544i | 0.0399408i | ||||||||
\(989\) | 10.9783 | 0.349088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | 3.37228i | 0.107070i | ||||||||
\(993\) | − 104.467i | − 3.31517i | ||||||||
\(994\) | 34.1168 | 1.08212 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.25544 | 0.293270 | ||||||||
\(997\) | − 22.2337i | − 0.704148i | −0.935972 | − | 0.352074i | \(-0.885477\pi\) | ||||
0.935972 | − | 0.352074i | \(-0.114523\pi\) | |||||||
\(998\) | 33.4891i | 1.06008i | ||||||||
\(999\) | 169.796 | 5.37211 |
(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 | 550.2.b.f.199.3 | 4 | ||
3.2 | odd | 2 | 4950.2.c.bc.199.1 | 4 | |||
4.3 | odd | 2 | 4400.2.b.p.4049.4 | 4 | |||
5.2 | odd | 4 | 110.2.a.d.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 550.2.a.n.1.2 | 2 | |||
5.4 | even | 2 | inner | 550.2.b.f.199.2 | 4 | ||
15.2 | even | 4 | 990.2.a.m.1.2 | 2 | |||
15.8 | even | 4 | 4950.2.a.bw.1.1 | 2 | |||
15.14 | odd | 2 | 4950.2.c.bc.199.4 | 4 | |||
20.3 | even | 4 | 4400.2.a.bl.1.1 | 2 | |||
20.7 | even | 4 | 880.2.a.n.1.2 | 2 | |||
20.19 | odd | 2 | 4400.2.b.p.4049.1 | 4 | |||
35.27 | even | 4 | 5390.2.a.bp.1.2 | 2 | |||
40.27 | even | 4 | 3520.2.a.bj.1.1 | 2 | |||
40.37 | odd | 4 | 3520.2.a.bq.1.2 | 2 | |||
55.32 | even | 4 | 1210.2.a.r.1.1 | 2 | |||
55.43 | even | 4 | 6050.2.a.cb.1.2 | 2 | |||
60.47 | odd | 4 | 7920.2.a.bq.1.1 | 2 | |||
220.87 | odd | 4 | 9680.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
110.2.a.d.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
550.2.a.n.1.2 | 2 | 5.3 | odd | 4 | |||
550.2.b.f.199.2 | 4 | 5.4 | even | 2 | inner | ||
550.2.b.f.199.3 | 4 | 1.1 | even | 1 | trivial | ||
880.2.a.n.1.2 | 2 | 20.7 | even | 4 | |||
990.2.a.m.1.2 | 2 | 15.2 | even | 4 | |||
1210.2.a.r.1.1 | 2 | 55.32 | even | 4 | |||
3520.2.a.bj.1.1 | 2 | 40.27 | even | 4 | |||
3520.2.a.bq.1.2 | 2 | 40.37 | odd | 4 | |||
4400.2.a.bl.1.1 | 2 | 20.3 | even | 4 | |||
4400.2.b.p.4049.1 | 4 | 20.19 | odd | 2 | |||
4400.2.b.p.4049.4 | 4 | 4.3 | odd | 2 | |||
4950.2.a.bw.1.1 | 2 | 15.8 | even | 4 | |||
4950.2.c.bc.199.1 | 4 | 3.2 | odd | 2 | |||
4950.2.c.bc.199.4 | 4 | 15.14 | odd | 2 | |||
5390.2.a.bp.1.2 | 2 | 35.27 | even | 4 | |||
6050.2.a.cb.1.2 | 2 | 55.43 | even | 4 | |||
7920.2.a.bq.1.1 | 2 | 60.47 | odd | 4 | |||
9680.2.a.bt.1.2 | 2 | 220.87 | odd | 4 |