Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(413,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.413");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.8869743.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{3} + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 413.2 | ||
Root | \(-1.07255 + 0.921756i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.413 |
Dual form | 552.2.b.a.413.1 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07255 | + | 0.921756i | −0.758408 | + | 0.651780i | ||||
\(3\) | −1.37328 | − | 1.05550i | −0.792866 | − | 0.609396i | ||||
\(4\) | 0.300733 | − | 1.97726i | 0.150366 | − | 0.988630i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | 2.44584 | − | 0.133749i | 0.998508 | − | 0.0546029i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 1.50000 | + | 2.39792i | 0.530330 | + | 0.847791i | ||||
\(9\) | 0.771819 | + | 2.89902i | 0.257273 | + | 0.966339i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | −2.50000 | + | 2.39792i | −0.721688 | + | 0.692219i | ||||
\(13\) | 1.57601i | 0.437107i | 0.975825 | + | 0.218554i | \(0.0701339\pi\) | ||||
−0.975825 | + | 0.218554i | \(0.929866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.81912 | − | 1.18925i | −0.954780 | − | 0.297314i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −3.50000 | − | 2.39792i | −0.824958 | − | 0.565194i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.79583i | − | 1.00000i | ||||||
\(24\) | 0.471086 | − | 4.87628i | 0.0961600 | − | 0.995366i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −1.45270 | − | 1.69035i | −0.284898 | − | 0.331506i | ||||
\(27\) | 2.00000 | − | 4.79583i | 0.384900 | − | 0.922958i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.94950 | 0.733404 | 0.366702 | − | 0.930339i | \(-0.380487\pi\) | ||||
0.366702 | + | 0.930339i | \(0.380487\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.83384 | 1.04779 | 0.523895 | − | 0.851783i | \(-0.324479\pi\) | ||||
0.523895 | + | 0.851783i | \(0.324479\pi\) | |||||||
\(32\) | 5.19240 | − | 2.24476i | 0.917896 | − | 0.396821i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.96422 | − | 0.654257i | 0.994037 | − | 0.109043i | ||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.66349 | − | 2.16431i | 0.266372 | − | 0.346568i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.64601i | 0.413237i | 0.978422 | + | 0.206618i | \(0.0662459\pi\) | ||||
−0.978422 | + | 0.206618i | \(0.933754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.42059 | + | 5.14378i | 0.651780 | + | 0.758408i | ||||
\(47\) | − | 13.7071i | − | 1.99938i | −0.0248485 | − | 0.999691i | \(-0.507910\pi\) | ||
0.0248485 | − | 0.999691i | \(-0.492090\pi\) | |||||||
\(48\) | 3.98947 | + | 5.66428i | 0.575831 | + | 0.817569i | ||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −5.36276 | + | 4.60878i | −0.758408 | + | 0.651780i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.11619 | + | 0.473959i | 0.432138 | + | 0.0657263i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 2.27548 | + | 6.98729i | 0.309654 | + | 0.950849i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.23604 | + | 3.64047i | −0.556219 | + | 0.478018i | ||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −6.25710 | + | 5.37738i | −0.794652 | + | 0.682928i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.50000 | + | 7.19375i | −0.437500 | + | 0.899218i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.06202 | + | 6.58604i | −0.609396 | + | 0.792866i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.04102i | − | 0.123546i | −0.998090 | − | 0.0617729i | \(-0.980325\pi\) | ||
0.998090 | − | 0.0617729i | \(-0.0196755\pi\) | |||||||
\(72\) | −5.79387 | + | 6.19928i | −0.682814 | + | 0.730592i | ||||
\(73\) | 9.44264 | 1.10518 | 0.552588 | − | 0.833454i | \(-0.313640\pi\) | ||||
0.552588 | + | 0.833454i | \(0.313640\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.86642 | − | 5.27752i | −0.792866 | − | 0.609396i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.210791 | + | 3.85467i | 0.0238673 | + | 0.436455i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.80859 | + | 4.47503i | −0.867621 | + | 0.497225i | ||||
\(82\) | −2.43897 | − | 2.83798i | −0.269339 | − | 0.313402i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.42378 | − | 4.16872i | −0.581491 | − | 0.446933i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.48261 | − | 1.44226i | −0.988630 | − | 0.150366i | ||||
\(93\) | −8.01152 | − | 6.15765i | −0.830756 | − | 0.638519i | ||||
\(94\) | 12.6346 | + | 14.7015i | 1.30316 | + | 1.51635i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.50000 | − | 2.39792i | −0.969590 | − | 0.244736i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | −7.50786 | + | 6.45229i | −0.758408 | + | 0.651780i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.50366 | − | 9.88630i | 0.150366 | − | 0.988630i | ||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | −3.77915 | + | 2.36402i | −0.370576 | + | 0.231811i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | −8.88114 | − | 5.39679i | −0.854588 | − | 0.519306i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.18774 | − | 7.80919i | 0.110279 | − | 0.725065i | ||||
\(117\) | −4.56889 | + | 1.21640i | −0.422394 | + | 0.112456i | ||||
\(118\) | −12.8706 | + | 11.0611i | −1.18484 | + | 1.01825i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.79287 | − | 3.63372i | 0.251825 | − | 0.327641i | ||||
\(124\) | 1.75443 | − | 11.5350i | 0.157552 | − | 1.03588i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.3133 | −1.97998 | −0.989990 | − | 0.141134i | \(-0.954925\pi\) | ||||
−0.989990 | + | 0.141134i | \(0.954925\pi\) | |||||||
\(128\) | −2.87695 | − | 10.9418i | −0.254289 | − | 0.967128i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.92112 | 0.779442 | 0.389721 | − | 0.920933i | \(-0.372572\pi\) | ||||
0.389721 | + | 0.920933i | \(0.372572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −0.641439 | − | 11.7298i | −0.0546029 | − | 0.998508i | ||||
\(139\) | − | 12.6371i | − | 1.07186i | −0.844261 | − | 0.535932i | \(-0.819960\pi\) | ||
0.844261 | − | 0.535932i | \(-0.180040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.4679 | + | 18.8237i | −1.21842 | + | 1.58524i | ||||
\(142\) | 0.959562 | + | 1.11654i | 0.0805247 | + | 0.0936982i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | − | 11.9896i | 0.0416667 | − | 0.999132i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.1277 | + | 8.70380i | −0.838175 | + | 0.720332i | ||||
\(147\) | −9.61299 | − | 7.38853i | −0.792866 | − | 0.609396i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 12.2292 | − | 0.668746i | 0.998508 | − | 0.0546029i | ||||
\(151\) | −10.6456 | −0.866324 | −0.433162 | − | 0.901316i | \(-0.642602\pi\) | ||||
−0.433162 | + | 0.901316i | \(0.642602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.77915 | − | 3.94003i | −0.302574 | − | 0.315455i | ||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.25023 | − | 11.9973i | 0.333930 | − | 0.942598i | ||||
\(163\) | 25.3031i | 1.98189i | 0.134250 | + | 0.990947i | \(0.457137\pi\) | ||||
−0.134250 | + | 0.990947i | \(0.542863\pi\) | |||||||
\(164\) | 5.23185 | + | 0.795741i | 0.408538 | + | 0.0621369i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.59166i | 0.742225i | 0.928588 | + | 0.371113i | \(0.121024\pi\) | ||||
−0.928588 | + | 0.371113i | \(0.878976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5162 | 0.808937 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 9.65983 | − | 0.528243i | 0.732309 | − | 0.0400460i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.4794 | − | 12.6661i | −1.23867 | − | 0.952039i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.4005 | 1.89852 | 0.949262 | − | 0.314486i | \(-0.101832\pi\) | ||||
0.949262 | + | 0.314486i | \(0.101832\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.5000 | − | 7.19375i | 0.847791 | − | 0.530330i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.2686 | − | 0.780272i | 1.04623 | − | 0.0572123i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −27.1025 | − | 4.12217i | −1.97665 | − | 0.300640i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 12.3995 | − | 6.18479i | 0.894859 | − | 0.446349i | ||||
\(193\) | −18.7045 | −1.34638 | −0.673188 | − | 0.739471i | \(-0.735076\pi\) | ||||
−0.673188 | + | 0.739471i | \(0.735076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.10513 | − | 13.8408i | 0.150366 | − | 0.988630i | ||||
\(197\) | 13.2113 | 0.941268 | 0.470634 | − | 0.882329i | \(-0.344025\pi\) | ||||
0.470634 | + | 0.882329i | \(0.344025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 7.50000 | + | 11.9896i | 0.530330 | + | 0.847791i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.43531 | − | 5.53053i | 0.452787 | − | 0.389127i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.9032 | − | 3.70151i | 0.966339 | − | 0.257273i | ||||
\(208\) | 1.87428 | − | 6.01898i | 0.129958 | − | 0.417341i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.7750i | 1.98095i | 0.137686 | + | 0.990476i | \(0.456034\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.09880 | + | 1.42961i | −0.0752884 | + | 0.0979553i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.5000 | − | 2.39792i | 0.986600 | − | 0.163158i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.9674 | − | 9.96675i | −0.876257 | − | 0.673490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.85909 | + | 14.4951i | 0.257273 | + | 0.966339i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.92425 | + | 9.47057i | 0.388946 | + | 0.621773i | ||||
\(233\) | 22.6861i | 1.48622i | 0.669171 | + | 0.743108i | \(0.266649\pi\) | ||||
−0.669171 | + | 0.743108i | \(0.733351\pi\) | |||||||
\(234\) | 3.77915 | − | 5.51605i | 0.247051 | − | 0.360595i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.60879 | − | 23.7271i | 0.234912 | − | 1.54450i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.3731i | 1.70594i | 0.521963 | + | 0.852968i | \(0.325200\pi\) | ||||
−0.521963 | + | 0.852968i | \(0.674800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −11.7981 | + | 10.1393i | −0.758408 | + | 0.651780i | ||||
\(243\) | 15.4468 | + | 2.09652i | 0.990915 | + | 0.134492i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.353901 | + | 6.47170i | 0.0225639 | + | 0.412620i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.75076 | + | 13.9891i | 0.555674 | + | 0.888306i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 23.9321 | − | 20.5674i | 1.50163 | − | 1.29051i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.1713 | + | 9.08381i | 0.823209 | + | 0.567738i | ||||
\(257\) | 12.1021i | 0.754907i | 0.926028 | + | 0.377454i | \(0.123200\pi\) | ||||
−0.926028 | + | 0.377454i | \(0.876800\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.04830 | + | 11.4497i | 0.188685 | + | 0.708716i | ||||
\(262\) | −9.56836 | + | 8.22309i | −0.591135 | + | 0.508024i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.0093 | 1.76873 | 0.884365 | − | 0.466797i | \(-0.154592\pi\) | ||||
0.884365 | + | 0.466797i | \(0.154592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.5000 | + | 11.9896i | 0.692219 | + | 0.721688i | ||||
\(277\) | − | 33.2122i | − | 1.99553i | −0.0668451 | − | 0.997763i | \(-0.521293\pi\) | ||
0.0668451 | − | 0.997763i | \(-0.478707\pi\) | |||||||
\(278\) | 11.6483 | + | 13.5539i | 0.698619 | + | 0.812910i | ||||
\(279\) | 4.50267 | + | 16.9124i | 0.269568 | + | 1.01252i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −1.83331 | − | 33.5253i | −0.109172 | − | 1.99640i | ||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −2.05836 | − | 0.313068i | −0.122141 | − | 0.0185771i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 10.5152 | + | 13.3203i | 0.619613 | + | 0.784907i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.83971 | − | 18.6706i | 0.166181 | − | 1.09261i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 17.1208 | − | 0.936245i | 0.998508 | − | 0.0546029i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.55829 | 0.437107 | ||||||||
\(300\) | −12.5000 | + | 11.9896i | −0.721688 | + | 0.692219i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.4179 | − | 9.81261i | 0.657027 | − | 0.564652i | ||||
\(303\) | 8.23970 | + | 6.33303i | 0.473359 | + | 0.363823i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.7750i | − | 1.64228i | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||
0.570730 | − | 0.821138i | \(-0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.6250i | − | 0.659196i | −0.944121 | − | 0.329598i | \(-0.893087\pi\) | ||
0.944121 | − | 0.329598i | \(-0.106913\pi\) | |||||||
\(312\) | 7.68508 | + | 0.742437i | 0.435082 | + | 0.0420322i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.0000 | 1.68497 | 0.842484 | − | 0.538721i | \(-0.181092\pi\) | ||||
0.842484 | + | 0.538721i | \(0.181092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 6.50000 | + | 16.7854i | 0.361111 | + | 0.932523i | ||||
\(325\) | 7.88006i | 0.437107i | ||||||||
\(326\) | −23.3233 | − | 27.1389i | −1.29176 | − | 1.50309i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.34490 | + | 3.96901i | −0.350339 | + | 0.219152i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0289779i | 0.00159277i | 1.00000 | 0.000796384i | \(0.000253497\pi\) | |||||
−1.00000 | 0.000796384i | \(0.999747\pi\) | ||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.84117 | − | 10.2876i | −0.483767 | − | 0.562910i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | −11.2791 | + | 9.69335i | −0.613505 | + | 0.527249i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.3059 | − | 16.5916i | 1.03789 | − | 0.891970i | ||||
\(347\) | −36.0000 | −1.93258 | −0.966291 | − | 0.257454i | \(-0.917117\pi\) | ||||
−0.966291 | + | 0.257454i | \(0.917117\pi\) | |||||||
\(348\) | −9.87375 | + | 9.47057i | −0.529288 | + | 0.507676i | ||||
\(349\) | − | 26.9081i | − | 1.44036i | −0.693788 | − | 0.720180i | \(-0.744059\pi\) | ||
0.693788 | − | 0.720180i | \(-0.255941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.55829 | + | 3.15203i | 0.403432 | + | 0.168243i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 37.4342i | − | 1.99242i | −0.0869714 | − | 0.996211i | \(-0.527719\pi\) | ||
0.0869714 | − | 0.996211i | \(-0.472281\pi\) | |||||||
\(354\) | 29.3500 | − | 1.60499i | 1.55994 | − | 0.0853043i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −27.2434 | + | 23.4131i | −1.43986 | + | 1.23742i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.1061 | − | 11.6106i | −0.792866 | − | 0.609396i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | −5.70346 | + | 18.3159i | −0.297314 | + | 0.954780i | ||||
\(369\) | −7.67082 | + | 2.04224i | −0.399327 | + | 0.106315i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −14.5846 | + | 13.9891i | −0.756177 | + | 0.725299i | ||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.8684 | − | 20.5606i | 1.69506 | − | 1.06033i | ||||
\(377\) | 6.22446i | 0.320576i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.6424 | + | 23.5517i | 1.56986 | + | 1.20659i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −7.59827 | + | 18.0628i | −0.387747 | + | 0.921766i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0615 | − | 17.2409i | 1.02110 | − | 0.877541i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 10.5000 | + | 16.7854i | 0.530330 | + | 0.847791i | ||||
\(393\) | −12.2512 | − | 9.41628i | −0.617993 | − | 0.474989i | ||||
\(394\) | −14.1698 | + | 12.1776i | −0.713865 | + | 0.613499i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 36.3642i | − | 1.82507i | −0.409002 | − | 0.912534i | \(-0.634123\pi\) | ||
0.409002 | − | 0.912534i | \(-0.365877\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.0956 | − | 5.94627i | −0.954780 | − | 0.297314i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.19421i | 0.457996i | ||||||||
\(404\) | −1.80440 | + | 11.8636i | −0.0897721 | + | 0.590234i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.7780 | 1.62077 | 0.810384 | − | 0.585899i | \(-0.199258\pi\) | ||||
0.810384 | + | 0.585899i | \(0.199258\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.5000 | + | 16.7854i | −0.565194 | + | 0.824958i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.53777 | + | 8.18330i | 0.173453 | + | 0.401219i | ||||
\(417\) | −13.3385 | + | 17.3543i | −0.653189 | + | 0.849844i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | −26.5235 | − | 30.8627i | −1.29114 | − | 1.50237i | ||||
\(423\) | 39.7370 | − | 10.5794i | 1.93208 | − | 0.514387i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.139235 | − | 2.54615i | −0.00674596 | − | 0.123362i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −13.3417 | + | 15.9373i | −0.641903 | + | 0.766786i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 23.0951 | − | 1.26295i | 1.10353 | − | 0.0603459i | ||||
\(439\) | −38.7927 | −1.85147 | −0.925736 | − | 0.378170i | \(-0.876554\pi\) | ||||
−0.925736 | + | 0.378170i | \(0.876554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.40273 | + | 20.2931i | 0.257273 | + | 0.966339i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41.8799 | −1.98978 | −0.994888 | − | 0.100985i | \(-0.967800\pi\) | ||||
−0.994888 | + | 0.100985i | \(0.967800\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.58041 | − | 7.37405i | 0.406294 | − | 0.349171i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 38.3667i | − | 1.81063i | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||
0.424736 | − | 0.905317i | \(-0.360367\pi\) | |||||||
\(450\) | −17.5000 | − | 11.9896i | −0.824958 | − | 0.565194i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.6194 | + | 11.2364i | 0.686879 | + | 0.527934i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.2711 | −1.78246 | −0.891232 | − | 0.453547i | \(-0.850158\pi\) | ||||
−0.891232 | + | 0.453547i | \(0.850158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | −15.0836 | − | 4.69696i | −0.700239 | − | 0.218051i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.9111 | − | 24.3320i | −0.968686 | − | 1.12716i | ||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 1.03112 | + | 9.39969i | 0.0476634 | + | 0.434501i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.0000 | + | 28.7750i | 0.828517 | + | 1.32448i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.3096 | − | 28.2865i | −1.11189 | − | 1.29380i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.30806 | − | 21.7499i | 0.150366 | − | 0.988630i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.5000 | + | 11.9896i | −0.839177 | + | 0.543858i | ||||
\(487\) | 27.1250 | 1.22915 | 0.614575 | − | 0.788858i | \(-0.289328\pi\) | ||||
0.614575 | + | 0.788858i | \(0.289328\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.7076 | − | 34.7484i | 1.20776 | − | 1.57138i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.0819 | −1.17706 | −0.588531 | − | 0.808475i | \(-0.700293\pi\) | ||||
−0.588531 | + | 0.808475i | \(0.700293\pi\) | |||||||
\(492\) | −6.34490 | − | 6.61502i | −0.286050 | − | 0.298228i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.2801 | − | 6.93792i | −1.00041 | − | 0.311522i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.6072i | 1.41493i | 0.706747 | + | 0.707466i | \(0.250162\pi\) | ||||
−0.706747 | + | 0.707466i | \(0.749838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1240 | − | 13.1721i | 0.452309 | − | 0.588485i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.4417 | − | 11.0999i | −0.641379 | − | 0.492963i | ||||
\(508\) | −6.71033 | + | 44.1191i | −0.297723 | + | 1.95747i | ||||
\(509\) | 5.31232 | 0.235465 | 0.117732 | − | 0.993045i | \(-0.462438\pi\) | ||||
0.117732 | + | 0.993045i | \(0.462438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.5000 | + | 2.39792i | −0.994369 | + | 0.105974i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.1552 | − | 12.9801i | −0.492033 | − | 0.572528i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.7191 | + | 18.9991i | 1.08505 | + | 0.833967i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | −13.8232 | − | 9.47057i | −0.605027 | − | 0.414515i | ||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 2.68287 | − | 17.6394i | 0.117202 | − | 0.770580i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.26182 | + | 34.7882i | 0.401929 | + | 1.50968i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.17014 | −0.180629 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.8821 | − | 26.8104i | −1.50528 | − | 1.15695i | ||||
\(538\) | −31.1140 | + | 26.7395i | −1.34142 | + | 1.15282i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.7561i | 1.02135i | 0.859772 | + | 0.510677i | \(0.170605\pi\) | ||||
−0.859772 | + | 0.510677i | \(0.829395\pi\) | |||||||
\(542\) | 17.1608 | − | 14.7481i | 0.737120 | − | 0.633485i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.2733i | 1.89299i | 0.322722 | + | 0.946494i | \(0.395402\pi\) | ||||
−0.322722 | + | 0.946494i | \(0.604598\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −23.3858 | − | 2.25925i | −0.995366 | − | 0.0961600i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.6135 | + | 35.6218i | 1.30064 | + | 1.51342i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.9868 | − | 3.80038i | −1.05968 | − | 0.161172i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | −20.4184 | − | 13.9891i | −0.864382 | − | 0.592204i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(564\) | 32.8684 | + | 34.2677i | 1.38401 | + | 1.44293i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.49627 | − | 1.56152i | 0.104741 | − | 0.0655201i | ||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 23.9792i | − | 1.00000i | ||||||
\(576\) | −23.5562 | − | 4.59429i | −0.981507 | − | 0.191429i | ||||
\(577\) | −14.2544 | −0.593417 | −0.296708 | − | 0.954968i | \(-0.595889\pi\) | ||||
−0.296708 | + | 0.954968i | \(0.595889\pi\) | |||||||
\(578\) | 18.2334 | − | 15.6698i | 0.758408 | − | 0.651780i | ||||
\(579\) | 25.6865 | + | 19.7426i | 1.06750 | + | 0.820476i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.1640 | + | 22.6426i | 0.586109 | + | 0.936959i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −42.5613 | −1.75669 | −0.878347 | − | 0.478023i | \(-0.841354\pi\) | ||||
−0.878347 | + | 0.478023i | \(0.841354\pi\) | |||||||
\(588\) | −17.5000 | + | 16.7854i | −0.721688 | + | 0.692219i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.1429 | − | 13.9446i | −0.746299 | − | 0.573605i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 38.3667i | − | 1.57553i | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||
0.615976 | − | 0.787765i | \(-0.288762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.10666 | + | 6.96690i | −0.331506 | + | 0.284898i | ||||
\(599\) | − | 9.59166i | − | 0.391905i | −0.980613 | − | 0.195952i | \(-0.937220\pi\) | ||
0.980613 | − | 0.195952i | \(-0.0627798\pi\) | |||||||
\(600\) | 2.35543 | − | 24.3814i | 0.0961600 | − | 0.995366i | ||||
\(601\) | 0.180813 | 0.00737552 | 0.00368776 | − | 0.999993i | \(-0.498826\pi\) | ||||
0.00368776 | + | 0.999993i | \(0.498826\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.20147 | + | 21.0491i | −0.130266 | + | 0.856474i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.6750 | + | 0.802495i | −0.596132 | + | 0.0325991i | ||||
\(607\) | 40.0000 | 1.62355 | 0.811775 | − | 0.583970i | \(-0.198502\pi\) | ||||
0.811775 | + | 0.583970i | \(0.198502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.6025 | 0.873945 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(614\) | 26.5235 | + | 30.8627i | 1.07040 | + | 1.24552i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.0000 | − | 9.59166i | −0.922958 | − | 0.384900i | ||||
\(622\) | 10.7155 | + | 12.4685i | 0.429650 | + | 0.499940i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.92698 | + | 6.28746i | −0.357365 | + | 0.251700i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.3721 | − | 39.5162i | 1.20718 | − | 1.57063i | ||||
\(634\) | −32.1765 | + | 27.6527i | −1.27789 | + | 1.09823i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0321i | 0.437107i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.01792 | − | 0.803476i | 0.119387 | − | 0.0317850i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.0392i | 1.53479i | 0.641175 | + | 0.767395i | \(0.278447\pi\) | ||||
−0.641175 | + | 0.767395i | \(0.721553\pi\) | |||||||
\(648\) | −22.4436 | − | 12.0118i | −0.881669 | − | 0.471868i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.26349 | − | 8.45177i | −0.284898 | − | 0.331506i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 50.0309 | + | 7.60948i | 1.95936 | + | 0.298010i | ||||
\(653\) | −36.9083 | −1.44433 | −0.722167 | − | 0.691719i | \(-0.756854\pi\) | ||||
−0.722167 | + | 0.691719i | \(0.756854\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.14677 | − | 10.1054i | 0.122861 | − | 0.394550i | ||||
\(657\) | 7.28800 | + | 27.3744i | 0.284332 | + | 1.06798i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | −0.0267105 | − | 0.0310802i | −0.00103813 | − | 0.00120797i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.9411i | − | 0.733404i | ||||||
\(668\) | 18.9652 | + | 2.88453i | 0.733786 | + | 0.111606i | ||||
\(669\) | 10.9863 | + | 8.44404i | 0.424754 | + | 0.326465i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.6633 | 1.99147 | 0.995737 | − | 0.0922433i | \(-0.0294037\pi\) | ||||
0.995737 | + | 0.0922433i | \(0.0294037\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | − | 23.9792i | 0.384900 | − | 0.922958i | ||||
\(676\) | 3.16256 | − | 20.7932i | 0.121637 | − | 0.799740i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0377 | 0.919777 | 0.459889 | − | 0.887977i | \(-0.347889\pi\) | ||||
0.459889 | + | 0.887977i | \(0.347889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.7750i | 1.09465i | 0.836919 | + | 0.547326i | \(0.184354\pi\) | ||||
−0.836919 | + | 0.547326i | \(0.815646\pi\) | |||||||
\(692\) | −5.41319 | + | 35.5907i | −0.205779 | + | 1.35296i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.6118 | − | 33.1832i | 1.46569 | − | 1.25962i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.86055 | − | 19.2589i | 0.0705241 | − | 0.730005i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 24.8027 | + | 28.8604i | 0.938797 | + | 1.09238i | ||||
\(699\) | 23.9453 | − | 31.1545i | 0.905695 | − | 1.17837i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | −11.0121 | + | 3.58619i | −0.415623 | + | 0.135352i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.5052 | + | 40.1501i | 1.29862 | + | 1.51107i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −30.0000 | + | 28.7750i | −1.12747 | + | 1.08143i | ||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.9781i | − | 1.04779i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.63877 | − | 50.2235i | 0.285474 | − | 1.87694i | ||||
\(717\) | 27.8370 | − | 36.2178i | 1.03959 | − | 1.35258i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.9583i | 1.78854i | 0.447524 | + | 0.894272i | \(0.352306\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.3785 | − | 17.5134i | 0.758408 | − | 0.651780i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.7475 | 0.733404 | ||||||||
\(726\) | 26.9042 | − | 1.47124i | 0.998508 | − | 0.0546029i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.0000 | − | 19.1833i | −0.703704 | − | 0.710494i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.7655 | − | 24.9019i | −0.396821 | − | 0.917896i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 6.34490 | − | 9.26102i | 0.233559 | − | 0.340903i | ||||
\(739\) | − | 12.6950i | − | 0.466994i | −0.972357 | − | 0.233497i | \(-0.924983\pi\) | ||
0.972357 | − | 0.233497i | \(-0.0750170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 2.74824 | − | 28.4474i | 0.100755 | − | 1.04293i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | −16.3012 | + | 52.3490i | −0.594443 | + | 1.90897i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.73743 | − | 6.67606i | −0.208945 | − | 0.243128i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.81007i | 0.246865i | 0.992353 | + | 0.123432i | \(0.0393902\pi\) | ||||
−0.992353 | + | 0.123432i | \(0.960610\pi\) | |||||||
\(762\) | −54.5745 | + | 2.98438i | −1.97703 | + | 0.108113i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.9122i | 0.682878i | ||||||||
\(768\) | −8.50000 | − | 26.3771i | −0.306717 | − | 0.951801i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.7738 | − | 16.6196i | 0.460038 | − | 0.598540i | ||||
\(772\) | −5.62504 | + | 36.9836i | −0.202450 | + | 1.33107i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.1692 | 1.04779 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.89900 | − | 18.9411i | 0.282287 | − | 0.676901i | ||||
\(784\) | −26.7338 | − | 8.32478i | −0.954780 | − | 0.297314i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.8196 | − | 1.19319i | 0.778279 | − | 0.0425598i | ||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 3.97308 | − | 26.1222i | 0.141535 | − | 0.930566i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 33.5189 | + | 39.0025i | 1.18954 | + | 1.38415i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 25.9620 | − | 11.2238i | 0.917896 | − | 0.396821i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.47482 | − | 9.86126i | −0.298513 | − | 0.347348i | ||||
\(807\) | −39.8380 | − | 30.6195i | −1.40237 | − | 1.07786i | ||||
\(808\) | −9.00000 | − | 14.3875i | −0.316619 | − | 0.506150i | ||||
\(809\) | 38.3667i | 1.34890i | 0.738321 | + | 0.674450i | \(0.235619\pi\) | ||||
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 56.9393i | − | 1.99941i | −0.0242949 | − | 0.999705i | \(-0.507734\pi\) | ||
0.0242949 | − | 0.999705i | \(-0.492266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9725 | + | 16.8881i | 0.770611 | + | 0.592291i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −35.1561 | + | 30.2133i | −1.22920 | + | 1.05638i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.0000 | −1.88461 | −0.942306 | − | 0.334751i | \(-0.891348\pi\) | ||||
−0.942306 | + | 0.334751i | \(0.891348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.6486 | −1.59121 | −0.795605 | − | 0.605815i | \(-0.792847\pi\) | ||||
−0.795605 | + | 0.605815i | \(0.792847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | −3.13771 | − | 28.6034i | −0.109043 | − | 0.994037i | ||||
\(829\) | − | 57.5500i | − | 1.99879i | −0.0347314 | − | 0.999397i | \(-0.511058\pi\) | ||
0.0347314 | − | 0.999397i | \(-0.488942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.0556 | + | 45.6098i | −1.21607 | + | 1.58219i | ||||
\(832\) | −11.3374 | − | 5.51605i | −0.393055 | − | 0.191234i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.69020 | − | 30.9082i | −0.0585268 | − | 1.07026i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.6677 | − | 27.9781i | 0.403294 | − | 0.967066i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4015 | −0.462119 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 56.8957 | + | 8.65358i | 1.95843 | + | 0.297869i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −32.8684 | + | 47.9748i | −1.13004 | + | 1.64941i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 2.49627 | + | 2.60254i | 0.0855208 | + | 0.0891616i | ||||
\(853\) | − | 57.5500i | − | 1.97047i | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||
0.171197 | − | 0.985237i | \(-0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.4743i | 1.96328i | 0.190730 | + | 0.981642i | \(0.438914\pi\) | ||||
−0.190730 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 50.6353i | − | 1.72765i | −0.503790 | − | 0.863826i | \(-0.668061\pi\) | ||
0.503790 | − | 0.863826i | \(-0.331939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 55.8693i | − | 1.90181i | −0.309477 | − | 0.950907i | \(-0.600154\pi\) | ||
0.309477 | − | 0.950907i | \(-0.399846\pi\) | |||||||
\(864\) | −0.380679 | − | 29.3914i | −0.0129510 | − | 0.999916i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.3458 | + | 17.9436i | 0.792866 | + | 0.609396i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −23.6066 | + | 22.6426i | −0.797593 | + | 0.765024i | ||||
\(877\) | 57.5500i | 1.94332i | 0.236373 | + | 0.971662i | \(0.424041\pi\) | ||||
−0.236373 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(878\) | 41.6071 | − | 35.7574i | 1.40417 | − | 1.20675i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −24.5000 | − | 16.7854i | −0.824958 | − | 0.565194i | ||||
\(883\) | 28.7750i | 0.968355i | 0.874970 | + | 0.484178i | \(0.160881\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 44.9184 | − | 38.6031i | 1.50906 | − | 1.29690i | ||||
\(887\) | 30.5372i | 1.02534i | 0.858586 | + | 0.512669i | \(0.171343\pi\) | ||||
−0.858586 | + | 0.512669i | \(0.828657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.40586 | + | 15.8181i | −0.0805542 | + | 0.529629i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.3797 | − | 7.97782i | −0.346568 | − | 0.266372i | ||||
\(898\) | 35.3647 | + | 41.1502i | 1.18013 | + | 1.37320i | ||||
\(899\) | 23.0408 | 0.768452 | ||||||||
\(900\) | 29.8211 | − | 3.27129i | 0.994037 | − | 0.109043i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −26.0373 | + | 1.42384i | −0.865032 | + | 0.0473038i | ||||
\(907\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.63091 | − | 17.3941i | −0.153598 | − | 0.576926i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.3721 | + | 39.5162i | −1.00080 | + | 1.30210i | ||||
\(922\) | 41.0478 | − | 35.2766i | 1.35184 | − | 1.16177i | ||||
\(923\) | 1.64065 | 0.0540028 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34.3216 | + | 29.4962i | −1.12788 | + | 0.969305i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.5074 | − | 8.86567i | 0.673188 | − | 0.291030i | ||||
\(929\) | 46.8903i | 1.53842i | 0.638996 | + | 0.769210i | \(0.279350\pi\) | ||||
−0.638996 | + | 0.769210i | \(0.720650\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 44.8564 | + | 6.82246i | 1.46932 | + | 0.223477i | ||||
\(933\) | −12.2703 | + | 15.9645i | −0.401711 | + | 0.522654i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.77015 | − | 9.13121i | −0.319347 | − | 0.298463i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6898 | 0.413237 | ||||||||
\(944\) | −45.8294 | − | 14.2711i | −1.49162 | − | 0.464483i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.87688 | −0.223469 | −0.111734 | − | 0.993738i | \(-0.535641\pi\) | ||||
−0.111734 | + | 0.993738i | \(0.535641\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.8817i | 0.483081i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.1985 | − | 31.6651i | −1.33595 | − | 1.02681i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 52.1466 | + | 7.93127i | 1.68654 | + | 0.256515i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.03372 | 0.0978619 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.2721 | 1.77743 | 0.888715 | − | 0.458460i | \(-0.151599\pi\) | ||||
0.888715 | + | 0.458460i | \(0.151599\pi\) | |||||||
\(968\) | 16.5000 | + | 26.3771i | 0.530330 | + | 0.847791i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 8.79074 | − | 29.9119i | 0.281963 | − | 0.959425i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.0929 | + | 25.0026i | −0.932198 | + | 0.801135i | ||||
\(975\) | 8.31745 | − | 10.8216i | 0.266372 | − | 0.346568i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 3.38428 | + | 61.8873i | 0.108217 | + | 1.97894i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27.9742 | − | 24.0412i | 0.892693 | − | 0.767185i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 12.9027 | + | 1.24650i | 0.411322 | + | 0.0397368i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.0000 | −1.77890 | −0.889449 | − | 0.457034i | \(-0.848912\pi\) | ||||
−0.889449 | + | 0.457034i | \(0.848912\pi\) | |||||||
\(992\) | 30.2917 | − | 13.0956i | 0.961761 | − | 0.415785i | ||||
\(993\) | 0.0305863 | − | 0.0397948i | 0.000970626 | − | 0.00126285i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.5500i | 1.82263i | 0.411714 | + | 0.911313i | \(0.364930\pi\) | ||||
−0.411714 | + | 0.911313i | \(0.635070\pi\) | |||||||
\(998\) | −29.1341 | − | 33.9003i | −0.922224 | − | 1.07310i | ||||
\(999\) | 0 | 0 |
(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 | 552.2.b.a.413.2 | yes | 6 | |
3.2 | odd | 2 | 552.2.b.b.413.5 | yes | 6 | ||
4.3 | odd | 2 | 2208.2.b.a.689.6 | 6 | |||
8.3 | odd | 2 | 2208.2.b.b.689.1 | 6 | |||
8.5 | even | 2 | 552.2.b.b.413.6 | yes | 6 | ||
12.11 | even | 2 | 2208.2.b.b.689.2 | 6 | |||
23.22 | odd | 2 | CM | 552.2.b.a.413.2 | yes | 6 | |
24.5 | odd | 2 | inner | 552.2.b.a.413.1 | ✓ | 6 | |
24.11 | even | 2 | 2208.2.b.a.689.5 | 6 | |||
69.68 | even | 2 | 552.2.b.b.413.5 | yes | 6 | ||
92.91 | even | 2 | 2208.2.b.a.689.6 | 6 | |||
184.45 | odd | 2 | 552.2.b.b.413.6 | yes | 6 | ||
184.91 | even | 2 | 2208.2.b.b.689.1 | 6 | |||
276.275 | odd | 2 | 2208.2.b.b.689.2 | 6 | |||
552.275 | odd | 2 | 2208.2.b.a.689.5 | 6 | |||
552.413 | even | 2 | inner | 552.2.b.a.413.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.b.a.413.1 | ✓ | 6 | 24.5 | odd | 2 | inner | |
552.2.b.a.413.1 | ✓ | 6 | 552.413 | even | 2 | inner | |
552.2.b.a.413.2 | yes | 6 | 1.1 | even | 1 | trivial | |
552.2.b.a.413.2 | yes | 6 | 23.22 | odd | 2 | CM | |
552.2.b.b.413.5 | yes | 6 | 3.2 | odd | 2 | ||
552.2.b.b.413.5 | yes | 6 | 69.68 | even | 2 | ||
552.2.b.b.413.6 | yes | 6 | 8.5 | even | 2 | ||
552.2.b.b.413.6 | yes | 6 | 184.45 | odd | 2 | ||
2208.2.b.a.689.5 | 6 | 24.11 | even | 2 | |||
2208.2.b.a.689.5 | 6 | 552.275 | odd | 2 | |||
2208.2.b.a.689.6 | 6 | 4.3 | odd | 2 | |||
2208.2.b.a.689.6 | 6 | 92.91 | even | 2 | |||
2208.2.b.b.689.1 | 6 | 8.3 | odd | 2 | |||
2208.2.b.b.689.1 | 6 | 184.91 | even | 2 | |||
2208.2.b.b.689.2 | 6 | 12.11 | even | 2 | |||
2208.2.b.b.689.2 | 6 | 276.275 | odd | 2 |