Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(21.5196833447\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1957.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.693822\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.74747 | −1.23565 | −0.617823 | − | 0.786317i | \(-0.711985\pi\) | ||||
−0.617823 | + | 0.786317i | \(0.711985\pi\) | |||||||
\(3\) | −2.44129 | −1.40948 | −0.704740 | − | 0.709466i | \(-0.748936\pi\) | ||||
−0.704740 | + | 0.709466i | \(0.748936\pi\) | |||||||
\(4\) | 1.05365 | 0.526823 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 4.26608 | 1.74162 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.65372 | 0.584680 | ||||||||
\(9\) | 2.95990 | 0.986634 | ||||||||
\(10\) | −1.74747 | −0.552598 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.57226 | −0.742546 | ||||||||
\(13\) | 1.88258 | 0.522134 | 0.261067 | − | 0.965321i | \(-0.415926\pi\) | ||||
0.261067 | + | 0.965321i | \(0.415926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.44129 | −0.630339 | ||||||||
\(16\) | −4.99712 | −1.24928 | ||||||||
\(17\) | −2.57226 | −0.623864 | −0.311932 | − | 0.950104i | \(-0.600976\pi\) | ||||
−0.311932 | + | 0.950104i | \(0.600976\pi\) | |||||||
\(18\) | −5.17233 | −1.21913 | ||||||||
\(19\) | 3.06719 | 0.703662 | 0.351831 | − | 0.936063i | \(-0.385559\pi\) | ||||
0.351831 | + | 0.936063i | \(0.385559\pi\) | |||||||
\(20\) | 1.05365 | 0.235602 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.74747 | −0.372562 | ||||||||
\(23\) | −5.83834 | −1.21738 | −0.608689 | − | 0.793409i | \(-0.708304\pi\) | ||||
−0.608689 | + | 0.793409i | \(0.708304\pi\) | |||||||
\(24\) | −4.03722 | −0.824094 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.28975 | −0.645174 | ||||||||
\(27\) | 0.0978926 | 0.0188394 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.56286 | −0.475911 | −0.237955 | − | 0.971276i | \(-0.576477\pi\) | ||||
−0.237955 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(30\) | 4.26608 | 0.778876 | ||||||||
\(31\) | 2.84846 | 0.511599 | 0.255799 | − | 0.966730i | \(-0.417661\pi\) | ||||
0.255799 | + | 0.966730i | \(0.417661\pi\) | |||||||
\(32\) | 5.42487 | 0.958990 | ||||||||
\(33\) | −2.44129 | −0.424974 | ||||||||
\(34\) | 4.49494 | 0.770875 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.11869 | 0.519781 | ||||||||
\(37\) | −4.98357 | −0.819295 | −0.409647 | − | 0.912244i | \(-0.634348\pi\) | ||||
−0.409647 | + | 0.912244i | \(0.634348\pi\) | |||||||
\(38\) | −5.35982 | −0.869478 | ||||||||
\(39\) | −4.59593 | −0.735938 | ||||||||
\(40\) | 1.65372 | 0.261477 | ||||||||
\(41\) | 1.57928 | 0.246642 | 0.123321 | − | 0.992367i | \(-0.460645\pi\) | ||||
0.123321 | + | 0.992367i | \(0.460645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7818 | −1.64421 | −0.822105 | − | 0.569335i | \(-0.807201\pi\) | ||||
−0.822105 | + | 0.569335i | \(0.807201\pi\) | |||||||
\(44\) | 1.05365 | 0.158843 | ||||||||
\(45\) | 2.95990 | 0.441236 | ||||||||
\(46\) | 10.2023 | 1.50425 | ||||||||
\(47\) | −4.87843 | −0.711593 | −0.355796 | − | 0.934564i | \(-0.615790\pi\) | ||||
−0.355796 | + | 0.934564i | \(0.615790\pi\) | |||||||
\(48\) | 12.1994 | 1.76084 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.74747 | −0.247129 | ||||||||
\(51\) | 6.27963 | 0.879324 | ||||||||
\(52\) | 1.98357 | 0.275072 | ||||||||
\(53\) | −1.90499 | −0.261670 | −0.130835 | − | 0.991404i | \(-0.541766\pi\) | ||||
−0.130835 | + | 0.991404i | \(0.541766\pi\) | |||||||
\(54\) | −0.171064 | −0.0232789 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.48791 | −0.991798 | ||||||||
\(58\) | 4.47851 | 0.588057 | ||||||||
\(59\) | 8.36812 | 1.08944 | 0.544718 | − | 0.838619i | \(-0.316637\pi\) | ||||
0.544718 | + | 0.838619i | \(0.316637\pi\) | |||||||
\(60\) | −2.57226 | −0.332077 | ||||||||
\(61\) | −6.89613 | −0.882959 | −0.441479 | − | 0.897271i | \(-0.645546\pi\) | ||||
−0.441479 | + | 0.897271i | \(0.645546\pi\) | |||||||
\(62\) | −4.97760 | −0.632155 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.514463 | 0.0643078 | ||||||||
\(65\) | 1.88258 | 0.233506 | ||||||||
\(66\) | 4.26608 | 0.525118 | ||||||||
\(67\) | 14.6142 | 1.78540 | 0.892702 | − | 0.450647i | \(-0.148807\pi\) | ||||
0.892702 | + | 0.450647i | \(0.148807\pi\) | |||||||
\(68\) | −2.71025 | −0.328666 | ||||||||
\(69\) | 14.2531 | 1.71587 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.51573 | 0.535919 | 0.267959 | − | 0.963430i | \(-0.413651\pi\) | ||||
0.267959 | + | 0.963430i | \(0.413651\pi\) | |||||||
\(72\) | 4.89486 | 0.576865 | ||||||||
\(73\) | 0.100993 | 0.0118203 | 0.00591017 | − | 0.999983i | \(-0.498119\pi\) | ||||
0.00591017 | + | 0.999983i | \(0.498119\pi\) | |||||||
\(74\) | 8.70864 | 1.01236 | ||||||||
\(75\) | −2.44129 | −0.281896 | ||||||||
\(76\) | 3.23174 | 0.370706 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.03124 | 0.909359 | ||||||||
\(79\) | 9.19528 | 1.03455 | 0.517275 | − | 0.855819i | \(-0.326946\pi\) | ||||
0.517275 | + | 0.855819i | \(0.326946\pi\) | |||||||
\(80\) | −4.99712 | −0.558695 | ||||||||
\(81\) | −9.11869 | −1.01319 | ||||||||
\(82\) | −2.75975 | −0.304763 | ||||||||
\(83\) | 7.62375 | 0.836815 | 0.418408 | − | 0.908259i | \(-0.362588\pi\) | ||||
0.418408 | + | 0.908259i | \(0.362588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.57226 | −0.279000 | ||||||||
\(86\) | 18.8409 | 2.03166 | ||||||||
\(87\) | 6.25668 | 0.670786 | ||||||||
\(88\) | 1.65372 | 0.176288 | ||||||||
\(89\) | 14.1911 | 1.50426 | 0.752129 | − | 0.659016i | \(-0.229027\pi\) | ||||
0.752129 | + | 0.659016i | \(0.229027\pi\) | |||||||
\(90\) | −5.17233 | −0.545212 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.15154 | −0.641342 | ||||||||
\(93\) | −6.95392 | −0.721088 | ||||||||
\(94\) | 8.52491 | 0.879277 | ||||||||
\(95\) | 3.06719 | 0.314687 | ||||||||
\(96\) | −13.2437 | −1.35168 | ||||||||
\(97\) | 1.79824 | 0.182583 | 0.0912916 | − | 0.995824i | \(-0.470900\pi\) | ||||
0.0912916 | + | 0.995824i | \(0.470900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.95990 | 0.297481 | ||||||||
\(100\) | 1.05365 | 0.105365 | ||||||||
\(101\) | −10.7664 | −1.07130 | −0.535650 | − | 0.844440i | \(-0.679933\pi\) | ||||
−0.535650 | + | 0.844440i | \(0.679933\pi\) | |||||||
\(102\) | −10.9734 | −1.08653 | ||||||||
\(103\) | 4.63635 | 0.456833 | 0.228417 | − | 0.973563i | \(-0.426645\pi\) | ||||
0.228417 | + | 0.973563i | \(0.426645\pi\) | |||||||
\(104\) | 3.11327 | 0.305281 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.32890 | 0.323332 | ||||||||
\(107\) | −1.63708 | −0.158262 | −0.0791311 | − | 0.996864i | \(-0.525215\pi\) | ||||
−0.0791311 | + | 0.996864i | \(0.525215\pi\) | |||||||
\(108\) | 0.103144 | 0.00992505 | ||||||||
\(109\) | −16.6501 | −1.59479 | −0.797396 | − | 0.603456i | \(-0.793790\pi\) | ||||
−0.797396 | + | 0.603456i | \(0.793790\pi\) | |||||||
\(110\) | −1.74747 | −0.166615 | ||||||||
\(111\) | 12.1664 | 1.15478 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0135 | −1.41236 | −0.706178 | − | 0.708034i | \(-0.749582\pi\) | ||||
−0.706178 | + | 0.708034i | \(0.749582\pi\) | |||||||
\(114\) | 13.0849 | 1.22551 | ||||||||
\(115\) | −5.83834 | −0.544428 | ||||||||
\(116\) | −2.70034 | −0.250721 | ||||||||
\(117\) | 5.57226 | 0.515155 | ||||||||
\(118\) | −14.6230 | −1.34616 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.03722 | −0.368546 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 12.0508 | 1.09103 | ||||||||
\(123\) | −3.85549 | −0.347638 | ||||||||
\(124\) | 3.00127 | 0.269522 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5179 | 0.933311 | 0.466656 | − | 0.884439i | \(-0.345459\pi\) | ||||
0.466656 | + | 0.884439i | \(0.345459\pi\) | |||||||
\(128\) | −11.7487 | −1.03845 | ||||||||
\(129\) | 26.3215 | 2.31748 | ||||||||
\(130\) | −3.28975 | −0.288530 | ||||||||
\(131\) | 20.6852 | 1.80727 | 0.903637 | − | 0.428300i | \(-0.140887\pi\) | ||||
0.903637 | + | 0.428300i | \(0.140887\pi\) | |||||||
\(132\) | −2.57226 | −0.223886 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −25.5378 | −2.20613 | ||||||||
\(135\) | 0.0978926 | 0.00842525 | ||||||||
\(136\) | −4.25380 | −0.364760 | ||||||||
\(137\) | −21.6149 | −1.84669 | −0.923343 | − | 0.383977i | \(-0.874554\pi\) | ||||
−0.923343 | + | 0.383977i | \(0.874554\pi\) | |||||||
\(138\) | −24.9068 | −2.12021 | ||||||||
\(139\) | −16.4798 | −1.39780 | −0.698898 | − | 0.715221i | \(-0.746326\pi\) | ||||
−0.698898 | + | 0.715221i | \(0.746326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.9097 | 1.00298 | ||||||||
\(142\) | −7.89110 | −0.662206 | ||||||||
\(143\) | 1.88258 | 0.157429 | ||||||||
\(144\) | −14.7910 | −1.23258 | ||||||||
\(145\) | −2.56286 | −0.212834 | ||||||||
\(146\) | −0.176482 | −0.0146058 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.25092 | −0.431623 | ||||||||
\(149\) | 8.94452 | 0.732764 | 0.366382 | − | 0.930465i | \(-0.380596\pi\) | ||||
0.366382 | + | 0.930465i | \(0.380596\pi\) | |||||||
\(150\) | 4.26608 | 0.348324 | ||||||||
\(151\) | 13.9427 | 1.13464 | 0.567322 | − | 0.823496i | \(-0.307979\pi\) | ||||
0.567322 | + | 0.823496i | \(0.307979\pi\) | |||||||
\(152\) | 5.07229 | 0.411417 | ||||||||
\(153\) | −7.61363 | −0.615525 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.84846 | 0.228794 | ||||||||
\(156\) | −4.84248 | −0.387709 | ||||||||
\(157\) | −3.00288 | −0.239656 | −0.119828 | − | 0.992795i | \(-0.538234\pi\) | ||||
−0.119828 | + | 0.992795i | \(0.538234\pi\) | |||||||
\(158\) | −16.0685 | −1.27834 | ||||||||
\(159\) | 4.65062 | 0.368818 | ||||||||
\(160\) | 5.42487 | 0.428873 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 15.9346 | 1.25194 | ||||||||
\(163\) | −22.2697 | −1.74430 | −0.872150 | − | 0.489239i | \(-0.837275\pi\) | ||||
−0.872150 | + | 0.489239i | \(0.837275\pi\) | |||||||
\(164\) | 1.66400 | 0.129937 | ||||||||
\(165\) | −2.44129 | −0.190054 | ||||||||
\(166\) | −13.3223 | −1.03401 | ||||||||
\(167\) | −7.35385 | −0.569058 | −0.284529 | − | 0.958667i | \(-0.591837\pi\) | ||||
−0.284529 | + | 0.958667i | \(0.591837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.45589 | −0.727376 | ||||||||
\(170\) | 4.49494 | 0.344746 | ||||||||
\(171\) | 9.07859 | 0.694257 | ||||||||
\(172\) | −11.3602 | −0.866208 | ||||||||
\(173\) | −23.2108 | −1.76469 | −0.882343 | − | 0.470607i | \(-0.844035\pi\) | ||||
−0.882343 | + | 0.470607i | \(0.844035\pi\) | |||||||
\(174\) | −10.9333 | −0.828855 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.99712 | −0.376672 | ||||||||
\(177\) | −20.4290 | −1.53554 | ||||||||
\(178\) | −24.7986 | −1.85873 | ||||||||
\(179\) | −18.9160 | −1.41385 | −0.706923 | − | 0.707290i | \(-0.749917\pi\) | ||||
−0.706923 | + | 0.707290i | \(0.749917\pi\) | |||||||
\(180\) | 3.11869 | 0.232453 | ||||||||
\(181\) | 21.8510 | 1.62417 | 0.812086 | − | 0.583538i | \(-0.198332\pi\) | ||||
0.812086 | + | 0.583538i | \(0.198332\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.8355 | 1.24451 | ||||||||
\(184\) | −9.65499 | −0.711776 | ||||||||
\(185\) | −4.98357 | −0.366400 | ||||||||
\(186\) | 12.1518 | 0.891010 | ||||||||
\(187\) | −2.57226 | −0.188102 | ||||||||
\(188\) | −5.14014 | −0.374883 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.35982 | −0.388842 | ||||||||
\(191\) | 3.14756 | 0.227749 | 0.113875 | − | 0.993495i | \(-0.463674\pi\) | ||||
0.113875 | + | 0.993495i | \(0.463674\pi\) | |||||||
\(192\) | −1.25595 | −0.0906406 | ||||||||
\(193\) | 21.2390 | 1.52882 | 0.764409 | − | 0.644731i | \(-0.223031\pi\) | ||||
0.764409 | + | 0.644731i | \(0.223031\pi\) | |||||||
\(194\) | −3.14236 | −0.225608 | ||||||||
\(195\) | −4.59593 | −0.329121 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.39202 | 0.597906 | 0.298953 | − | 0.954268i | \(-0.403363\pi\) | ||||
0.298953 | + | 0.954268i | \(0.403363\pi\) | |||||||
\(198\) | −5.17233 | −0.367582 | ||||||||
\(199\) | 23.4653 | 1.66341 | 0.831705 | − | 0.555218i | \(-0.187365\pi\) | ||||
0.831705 | + | 0.555218i | \(0.187365\pi\) | |||||||
\(200\) | 1.65372 | 0.116936 | ||||||||
\(201\) | −35.6774 | −2.51649 | ||||||||
\(202\) | 18.8140 | 1.32375 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.61650 | 0.463248 | ||||||||
\(205\) | 1.57928 | 0.110302 | ||||||||
\(206\) | −8.10187 | −0.564484 | ||||||||
\(207\) | −17.2809 | −1.20111 | ||||||||
\(208\) | −9.40749 | −0.652292 | ||||||||
\(209\) | 3.06719 | 0.212162 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.283774 | 0.0195358 | 0.00976791 | − | 0.999952i | \(-0.496891\pi\) | ||||
0.00976791 | + | 0.999952i | \(0.496891\pi\) | |||||||
\(212\) | −2.00718 | −0.137854 | ||||||||
\(213\) | −11.0242 | −0.755367 | ||||||||
\(214\) | 2.86074 | 0.195556 | ||||||||
\(215\) | −10.7818 | −0.735313 | ||||||||
\(216\) | 0.161887 | 0.0110150 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 29.0956 | 1.97060 | ||||||||
\(219\) | −0.246553 | −0.0166605 | ||||||||
\(220\) | 1.05365 | 0.0710368 | ||||||||
\(221\) | −4.84248 | −0.325741 | ||||||||
\(222\) | −21.2603 | −1.42690 | ||||||||
\(223\) | −27.4540 | −1.83845 | −0.919226 | − | 0.393729i | \(-0.871185\pi\) | ||||
−0.919226 | + | 0.393729i | \(0.871185\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.95990 | 0.197327 | ||||||||
\(226\) | 26.2357 | 1.74517 | ||||||||
\(227\) | 2.79586 | 0.185568 | 0.0927840 | − | 0.995686i | \(-0.470423\pi\) | ||||
0.0927840 | + | 0.995686i | \(0.470423\pi\) | |||||||
\(228\) | −7.88961 | −0.522502 | ||||||||
\(229\) | −12.8497 | −0.849134 | −0.424567 | − | 0.905396i | \(-0.639574\pi\) | ||||
−0.424567 | + | 0.905396i | \(0.639574\pi\) | |||||||
\(230\) | 10.2023 | 0.672720 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.23826 | −0.278255 | ||||||||
\(233\) | −18.4684 | −1.20990 | −0.604952 | − | 0.796262i | \(-0.706808\pi\) | ||||
−0.604952 | + | 0.796262i | \(0.706808\pi\) | |||||||
\(234\) | −9.73734 | −0.636550 | ||||||||
\(235\) | −4.87843 | −0.318234 | ||||||||
\(236\) | 8.81704 | 0.573940 | ||||||||
\(237\) | −22.4484 | −1.45818 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0893 | −1.36415 | −0.682075 | − | 0.731282i | \(-0.738922\pi\) | ||||
−0.682075 | + | 0.731282i | \(0.738922\pi\) | |||||||
\(240\) | 12.1994 | 0.787470 | ||||||||
\(241\) | −9.37100 | −0.603639 | −0.301819 | − | 0.953365i | \(-0.597594\pi\) | ||||
−0.301819 | + | 0.953365i | \(0.597594\pi\) | |||||||
\(242\) | −1.74747 | −0.112332 | ||||||||
\(243\) | 21.9677 | 1.40923 | ||||||||
\(244\) | −7.26608 | −0.465163 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.73734 | 0.429557 | ||||||||
\(247\) | 5.77424 | 0.367406 | ||||||||
\(248\) | 4.71057 | 0.299121 | ||||||||
\(249\) | −18.6118 | −1.17947 | ||||||||
\(250\) | −1.74747 | −0.110520 | ||||||||
\(251\) | −14.4075 | −0.909393 | −0.454696 | − | 0.890647i | \(-0.650252\pi\) | ||||
−0.454696 | + | 0.890647i | \(0.650252\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.83834 | −0.367053 | ||||||||
\(254\) | −18.3797 | −1.15324 | ||||||||
\(255\) | 6.27963 | 0.393245 | ||||||||
\(256\) | 19.5016 | 1.21885 | ||||||||
\(257\) | 16.3074 | 1.01723 | 0.508615 | − | 0.860994i | \(-0.330158\pi\) | ||||
0.508615 | + | 0.860994i | \(0.330158\pi\) | |||||||
\(258\) | −45.9961 | −2.86359 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.98357 | 0.123016 | ||||||||
\(261\) | −7.58580 | −0.469549 | ||||||||
\(262\) | −36.1467 | −2.23315 | ||||||||
\(263\) | −26.3192 | −1.62291 | −0.811456 | − | 0.584413i | \(-0.801325\pi\) | ||||
−0.811456 | + | 0.584413i | \(0.801325\pi\) | |||||||
\(264\) | −4.03722 | −0.248474 | ||||||||
\(265\) | −1.90499 | −0.117022 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −34.6447 | −2.12022 | ||||||||
\(268\) | 15.3982 | 0.940592 | ||||||||
\(269\) | 0.470216 | 0.0286696 | 0.0143348 | − | 0.999897i | \(-0.495437\pi\) | ||||
0.0143348 | + | 0.999897i | \(0.495437\pi\) | |||||||
\(270\) | −0.171064 | −0.0104106 | ||||||||
\(271\) | 17.9883 | 1.09271 | 0.546355 | − | 0.837554i | \(-0.316015\pi\) | ||||
0.546355 | + | 0.837554i | \(0.316015\pi\) | |||||||
\(272\) | 12.8539 | 0.779381 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 37.7713 | 2.28185 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 15.0177 | 0.903959 | ||||||||
\(277\) | 24.9706 | 1.50034 | 0.750168 | − | 0.661247i | \(-0.229973\pi\) | ||||
0.750168 | + | 0.661247i | \(0.229973\pi\) | |||||||
\(278\) | 28.7979 | 1.72718 | ||||||||
\(279\) | 8.43116 | 0.504761 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4277 | −1.33793 | −0.668964 | − | 0.743295i | \(-0.733262\pi\) | ||||
−0.668964 | + | 0.743295i | \(0.733262\pi\) | |||||||
\(282\) | −20.8118 | −1.23932 | ||||||||
\(283\) | −21.2464 | −1.26297 | −0.631483 | − | 0.775390i | \(-0.717553\pi\) | ||||
−0.631483 | + | 0.775390i | \(0.717553\pi\) | |||||||
\(284\) | 4.75798 | 0.282334 | ||||||||
\(285\) | −7.48791 | −0.443546 | ||||||||
\(286\) | −3.28975 | −0.194527 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.0571 | 0.946172 | ||||||||
\(289\) | −10.3835 | −0.610794 | ||||||||
\(290\) | 4.47851 | 0.262987 | ||||||||
\(291\) | −4.39002 | −0.257347 | ||||||||
\(292\) | 0.106411 | 0.00622722 | ||||||||
\(293\) | −16.3043 | −0.952510 | −0.476255 | − | 0.879307i | \(-0.658006\pi\) | ||||
−0.476255 | + | 0.879307i | \(0.658006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.36812 | 0.487211 | ||||||||
\(296\) | −8.24146 | −0.479025 | ||||||||
\(297\) | 0.0978926 | 0.00568030 | ||||||||
\(298\) | −15.6303 | −0.905437 | ||||||||
\(299\) | −10.9911 | −0.635634 | ||||||||
\(300\) | −2.57226 | −0.148509 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −24.3645 | −1.40202 | ||||||||
\(303\) | 26.2840 | 1.50998 | ||||||||
\(304\) | −15.3271 | −0.879072 | ||||||||
\(305\) | −6.89613 | −0.394871 | ||||||||
\(306\) | 13.3046 | 0.760572 | ||||||||
\(307\) | 1.80820 | 0.103199 | 0.0515996 | − | 0.998668i | \(-0.483568\pi\) | ||||
0.0515996 | + | 0.998668i | \(0.483568\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3187 | −0.643897 | ||||||||
\(310\) | −4.97760 | −0.282708 | ||||||||
\(311\) | −30.3806 | −1.72273 | −0.861363 | − | 0.507990i | \(-0.830389\pi\) | ||||
−0.861363 | + | 0.507990i | \(0.830389\pi\) | |||||||
\(312\) | −7.60040 | −0.430288 | ||||||||
\(313\) | 17.7832 | 1.00517 | 0.502584 | − | 0.864528i | \(-0.332383\pi\) | ||||
0.502584 | + | 0.864528i | \(0.332383\pi\) | |||||||
\(314\) | 5.24743 | 0.296130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.68857 | 0.545025 | ||||||||
\(317\) | 5.71699 | 0.321098 | 0.160549 | − | 0.987028i | \(-0.448673\pi\) | ||||
0.160549 | + | 0.987028i | \(0.448673\pi\) | |||||||
\(318\) | −8.12682 | −0.455729 | ||||||||
\(319\) | −2.56286 | −0.143492 | ||||||||
\(320\) | 0.514463 | 0.0287593 | ||||||||
\(321\) | 3.99658 | 0.223067 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.88961 | −0.438990 | ||||||||
\(324\) | −9.60787 | −0.533771 | ||||||||
\(325\) | 1.88258 | 0.104427 | ||||||||
\(326\) | 38.9156 | 2.15534 | ||||||||
\(327\) | 40.6478 | 2.24783 | ||||||||
\(328\) | 2.61170 | 0.144207 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.26608 | 0.234840 | ||||||||
\(331\) | −8.09032 | −0.444684 | −0.222342 | − | 0.974969i | \(-0.571370\pi\) | ||||
−0.222342 | + | 0.974969i | \(0.571370\pi\) | |||||||
\(332\) | 8.03273 | 0.440854 | ||||||||
\(333\) | −14.7509 | −0.808344 | ||||||||
\(334\) | 12.8506 | 0.703154 | ||||||||
\(335\) | 14.6142 | 0.798457 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3367 | 0.617549 | 0.308775 | − | 0.951135i | \(-0.400081\pi\) | ||||
0.308775 | + | 0.951135i | \(0.400081\pi\) | |||||||
\(338\) | 16.5239 | 0.898780 | ||||||||
\(339\) | 36.6524 | 1.99069 | ||||||||
\(340\) | −2.71025 | −0.146984 | ||||||||
\(341\) | 2.84846 | 0.154253 | ||||||||
\(342\) | −15.8645 | −0.857857 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.8301 | −0.961337 | ||||||||
\(345\) | 14.2531 | 0.767360 | ||||||||
\(346\) | 40.5602 | 2.18053 | ||||||||
\(347\) | −0.406764 | −0.0218363 | −0.0109181 | − | 0.999940i | \(-0.503475\pi\) | ||||
−0.0109181 | + | 0.999940i | \(0.503475\pi\) | |||||||
\(348\) | 6.59233 | 0.353386 | ||||||||
\(349\) | 4.87916 | 0.261175 | 0.130588 | − | 0.991437i | \(-0.458314\pi\) | ||||
0.130588 | + | 0.991437i | \(0.458314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.184291 | 0.00983671 | ||||||||
\(352\) | 5.42487 | 0.289146 | ||||||||
\(353\) | 8.99734 | 0.478880 | 0.239440 | − | 0.970911i | \(-0.423036\pi\) | ||||
0.239440 | + | 0.970911i | \(0.423036\pi\) | |||||||
\(354\) | 35.6991 | 1.89738 | ||||||||
\(355\) | 4.51573 | 0.239670 | ||||||||
\(356\) | 14.9524 | 0.792477 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 33.0551 | 1.74701 | ||||||||
\(359\) | −4.69692 | −0.247894 | −0.123947 | − | 0.992289i | \(-0.539555\pi\) | ||||
−0.123947 | + | 0.992289i | \(0.539555\pi\) | |||||||
\(360\) | 4.89486 | 0.257982 | ||||||||
\(361\) | −9.59233 | −0.504859 | ||||||||
\(362\) | −38.1839 | −2.00690 | ||||||||
\(363\) | −2.44129 | −0.128135 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.100993 | 0.00528621 | ||||||||
\(366\) | −29.4194 | −1.53778 | ||||||||
\(367\) | 4.59173 | 0.239686 | 0.119843 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119843 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(368\) | 29.1749 | 1.52085 | ||||||||
\(369\) | 4.67452 | 0.243346 | ||||||||
\(370\) | 8.70864 | 0.452741 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.32697 | −0.379886 | ||||||||
\(373\) | −13.0675 | −0.676610 | −0.338305 | − | 0.941036i | \(-0.609854\pi\) | ||||
−0.338305 | + | 0.941036i | \(0.609854\pi\) | |||||||
\(374\) | 4.49494 | 0.232428 | ||||||||
\(375\) | −2.44129 | −0.126068 | ||||||||
\(376\) | −8.06758 | −0.416054 | ||||||||
\(377\) | −4.82479 | −0.248489 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.4099 | −0.534719 | −0.267359 | − | 0.963597i | \(-0.586151\pi\) | ||||
−0.267359 | + | 0.963597i | \(0.586151\pi\) | |||||||
\(380\) | 3.23174 | 0.165785 | ||||||||
\(381\) | −25.6772 | −1.31548 | ||||||||
\(382\) | −5.50026 | −0.281418 | ||||||||
\(383\) | −22.9451 | −1.17244 | −0.586221 | − | 0.810152i | \(-0.699385\pi\) | ||||
−0.586221 | + | 0.810152i | \(0.699385\pi\) | |||||||
\(384\) | 28.6821 | 1.46368 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −37.1145 | −1.88908 | ||||||||
\(387\) | −31.9131 | −1.62223 | ||||||||
\(388\) | 1.89470 | 0.0961891 | ||||||||
\(389\) | 11.6665 | 0.591517 | 0.295759 | − | 0.955263i | \(-0.404428\pi\) | ||||
0.295759 | + | 0.955263i | \(0.404428\pi\) | |||||||
\(390\) | 8.03124 | 0.406678 | ||||||||
\(391\) | 15.0177 | 0.759477 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −50.4986 | −2.54732 | ||||||||
\(394\) | −14.6648 | −0.738801 | ||||||||
\(395\) | 9.19528 | 0.462665 | ||||||||
\(396\) | 3.11869 | 0.156720 | ||||||||
\(397\) | −2.41496 | −0.121203 | −0.0606017 | − | 0.998162i | \(-0.519302\pi\) | ||||
−0.0606017 | + | 0.998162i | \(0.519302\pi\) | |||||||
\(398\) | −41.0048 | −2.05539 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.99712 | −0.249856 | ||||||||
\(401\) | −33.8495 | −1.69037 | −0.845183 | − | 0.534477i | \(-0.820509\pi\) | ||||
−0.845183 | + | 0.534477i | \(0.820509\pi\) | |||||||
\(402\) | 62.3452 | 3.10950 | ||||||||
\(403\) | 5.36246 | 0.267123 | ||||||||
\(404\) | −11.3440 | −0.564386 | ||||||||
\(405\) | −9.11869 | −0.453111 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.98357 | −0.247027 | ||||||||
\(408\) | 10.3848 | 0.514123 | ||||||||
\(409\) | −9.17056 | −0.453455 | −0.226728 | − | 0.973958i | \(-0.572803\pi\) | ||||
−0.226728 | + | 0.973958i | \(0.572803\pi\) | |||||||
\(410\) | −2.75975 | −0.136294 | ||||||||
\(411\) | 52.7682 | 2.60287 | ||||||||
\(412\) | 4.88507 | 0.240670 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 30.1978 | 1.48414 | ||||||||
\(415\) | 7.62375 | 0.374235 | ||||||||
\(416\) | 10.2128 | 0.500721 | ||||||||
\(417\) | 40.2319 | 1.97017 | ||||||||
\(418\) | −5.35982 | −0.262158 | ||||||||
\(419\) | −9.98307 | −0.487705 | −0.243852 | − | 0.969812i | \(-0.578411\pi\) | ||||
−0.243852 | + | 0.969812i | \(0.578411\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.5141 | −0.804846 | −0.402423 | − | 0.915454i | \(-0.631832\pi\) | ||||
−0.402423 | + | 0.915454i | \(0.631832\pi\) | |||||||
\(422\) | −0.495886 | −0.0241394 | ||||||||
\(423\) | −14.4397 | −0.702081 | ||||||||
\(424\) | −3.15032 | −0.152993 | ||||||||
\(425\) | −2.57226 | −0.124773 | ||||||||
\(426\) | 19.2645 | 0.933367 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.72490 | −0.0833761 | ||||||||
\(429\) | −4.59593 | −0.221894 | ||||||||
\(430\) | 18.8409 | 0.908588 | ||||||||
\(431\) | −16.4554 | −0.792628 | −0.396314 | − | 0.918115i | \(-0.629711\pi\) | ||||
−0.396314 | + | 0.918115i | \(0.629711\pi\) | |||||||
\(432\) | −0.489181 | −0.0235357 | ||||||||
\(433\) | −17.9836 | −0.864235 | −0.432118 | − | 0.901817i | \(-0.642234\pi\) | ||||
−0.432118 | + | 0.901817i | \(0.642234\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.25668 | 0.299985 | ||||||||
\(436\) | −17.5433 | −0.840173 | ||||||||
\(437\) | −17.9073 | −0.856622 | ||||||||
\(438\) | 0.430844 | 0.0205865 | ||||||||
\(439\) | 23.0726 | 1.10120 | 0.550598 | − | 0.834771i | \(-0.314400\pi\) | ||||
0.550598 | + | 0.834771i | \(0.314400\pi\) | |||||||
\(440\) | 1.65372 | 0.0788382 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.46209 | 0.402500 | ||||||||
\(443\) | 9.63027 | 0.457548 | 0.228774 | − | 0.973480i | \(-0.426528\pi\) | ||||
0.228774 | + | 0.973480i | \(0.426528\pi\) | |||||||
\(444\) | 12.8190 | 0.608364 | ||||||||
\(445\) | 14.1911 | 0.672724 | ||||||||
\(446\) | 47.9749 | 2.27168 | ||||||||
\(447\) | −21.8362 | −1.03282 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.45196 | −0.257294 | −0.128647 | − | 0.991690i | \(-0.541063\pi\) | ||||
−0.128647 | + | 0.991690i | \(0.541063\pi\) | |||||||
\(450\) | −5.17233 | −0.243826 | ||||||||
\(451\) | 1.57928 | 0.0743655 | ||||||||
\(452\) | −15.8190 | −0.744061 | ||||||||
\(453\) | −34.0383 | −1.59926 | ||||||||
\(454\) | −4.88568 | −0.229296 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.3829 | −0.579884 | ||||||||
\(457\) | 26.3853 | 1.23425 | 0.617125 | − | 0.786865i | \(-0.288297\pi\) | ||||
0.617125 | + | 0.786865i | \(0.288297\pi\) | |||||||
\(458\) | 22.4545 | 1.04923 | ||||||||
\(459\) | −0.251805 | −0.0117532 | ||||||||
\(460\) | −6.15154 | −0.286817 | ||||||||
\(461\) | 14.6685 | 0.683182 | 0.341591 | − | 0.939849i | \(-0.389034\pi\) | ||||
0.341591 | + | 0.939849i | \(0.389034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.7719 | 1.38362 | 0.691809 | − | 0.722081i | \(-0.256814\pi\) | ||||
0.691809 | + | 0.722081i | \(0.256814\pi\) | |||||||
\(464\) | 12.8069 | 0.594546 | ||||||||
\(465\) | −6.95392 | −0.322480 | ||||||||
\(466\) | 32.2729 | 1.49501 | ||||||||
\(467\) | 7.01013 | 0.324390 | 0.162195 | − | 0.986759i | \(-0.448143\pi\) | ||||
0.162195 | + | 0.986759i | \(0.448143\pi\) | |||||||
\(468\) | 5.87119 | 0.271396 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.52491 | 0.393225 | ||||||||
\(471\) | 7.33090 | 0.337790 | ||||||||
\(472\) | 13.8386 | 0.636971 | ||||||||
\(473\) | −10.7818 | −0.495748 | ||||||||
\(474\) | 39.2278 | 1.80179 | ||||||||
\(475\) | 3.06719 | 0.140732 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.63857 | −0.258172 | ||||||||
\(478\) | 36.8528 | 1.68561 | ||||||||
\(479\) | 13.9532 | 0.637538 | 0.318769 | − | 0.947832i | \(-0.396731\pi\) | ||||
0.318769 | + | 0.947832i | \(0.396731\pi\) | |||||||
\(480\) | −13.2437 | −0.604488 | ||||||||
\(481\) | −9.38199 | −0.427782 | ||||||||
\(482\) | 16.3755 | 0.745885 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.05365 | 0.0478930 | ||||||||
\(485\) | 1.79824 | 0.0816537 | ||||||||
\(486\) | −38.3879 | −1.74131 | ||||||||
\(487\) | 6.72132 | 0.304572 | 0.152286 | − | 0.988336i | \(-0.451336\pi\) | ||||
0.152286 | + | 0.988336i | \(0.451336\pi\) | |||||||
\(488\) | −11.4043 | −0.516248 | ||||||||
\(489\) | 54.3669 | 2.45855 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9471 | −1.17098 | −0.585489 | − | 0.810681i | \(-0.699097\pi\) | ||||
−0.585489 | + | 0.810681i | \(0.699097\pi\) | |||||||
\(492\) | −4.06232 | −0.183143 | ||||||||
\(493\) | 6.59233 | 0.296903 | ||||||||
\(494\) | −10.0903 | −0.453984 | ||||||||
\(495\) | 2.95990 | 0.133038 | ||||||||
\(496\) | −14.2341 | −0.639130 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 32.5235 | 1.45741 | ||||||||
\(499\) | 20.8050 | 0.931359 | 0.465679 | − | 0.884953i | \(-0.345810\pi\) | ||||
0.465679 | + | 0.884953i | \(0.345810\pi\) | |||||||
\(500\) | 1.05365 | 0.0471205 | ||||||||
\(501\) | 17.9529 | 0.802075 | ||||||||
\(502\) | 25.1766 | 1.12369 | ||||||||
\(503\) | 30.1238 | 1.34315 | 0.671576 | − | 0.740936i | \(-0.265618\pi\) | ||||
0.671576 | + | 0.740936i | \(0.265618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7664 | −0.479100 | ||||||||
\(506\) | 10.2023 | 0.453548 | ||||||||
\(507\) | 23.0846 | 1.02522 | ||||||||
\(508\) | 11.0821 | 0.491690 | ||||||||
\(509\) | −10.5596 | −0.468045 | −0.234022 | − | 0.972231i | \(-0.575189\pi\) | ||||
−0.234022 | + | 0.972231i | \(0.575189\pi\) | |||||||
\(510\) | −10.9734 | −0.485912 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.5810 | −0.467618 | ||||||||
\(513\) | 0.300255 | 0.0132566 | ||||||||
\(514\) | −28.4968 | −1.25694 | ||||||||
\(515\) | 4.63635 | 0.204302 | ||||||||
\(516\) | 27.7336 | 1.22090 | ||||||||
\(517\) | −4.87843 | −0.214553 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.6644 | 2.48729 | ||||||||
\(520\) | 3.11327 | 0.136526 | ||||||||
\(521\) | −14.9118 | −0.653299 | −0.326650 | − | 0.945146i | \(-0.605920\pi\) | ||||
−0.326650 | + | 0.945146i | \(0.605920\pi\) | |||||||
\(522\) | 13.2560 | 0.580197 | ||||||||
\(523\) | 6.86179 | 0.300045 | 0.150022 | − | 0.988683i | \(-0.452065\pi\) | ||||
0.150022 | + | 0.988683i | \(0.452065\pi\) | |||||||
\(524\) | 21.7949 | 0.952113 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.9920 | 2.00535 | ||||||||
\(527\) | −7.32697 | −0.319168 | ||||||||
\(528\) | 12.1994 | 0.530912 | ||||||||
\(529\) | 11.0862 | 0.482007 | ||||||||
\(530\) | 3.32890 | 0.144598 | ||||||||
\(531\) | 24.7688 | 1.07487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.97313 | 0.128780 | ||||||||
\(534\) | 60.5405 | 2.61984 | ||||||||
\(535\) | −1.63708 | −0.0707770 | ||||||||
\(536\) | 24.1678 | 1.04389 | ||||||||
\(537\) | 46.1794 | 1.99279 | ||||||||
\(538\) | −0.821688 | −0.0354255 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.103144 | 0.00443862 | ||||||||
\(541\) | −13.7677 | −0.591920 | −0.295960 | − | 0.955200i | \(-0.595639\pi\) | ||||
−0.295960 | + | 0.955200i | \(0.595639\pi\) | |||||||
\(542\) | −31.4339 | −1.35020 | ||||||||
\(543\) | −53.3447 | −2.28924 | ||||||||
\(544\) | −13.9541 | −0.598279 | ||||||||
\(545\) | −16.6501 | −0.713213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.87135 | −0.379312 | −0.189656 | − | 0.981851i | \(-0.560737\pi\) | ||||
−0.189656 | + | 0.981851i | \(0.560737\pi\) | |||||||
\(548\) | −22.7744 | −0.972876 | ||||||||
\(549\) | −20.4119 | −0.871157 | ||||||||
\(550\) | −1.74747 | −0.0745123 | ||||||||
\(551\) | −7.86078 | −0.334880 | ||||||||
\(552\) | 23.5706 | 1.00323 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −43.6353 | −1.85389 | ||||||||
\(555\) | 12.1664 | 0.516433 | ||||||||
\(556\) | −17.3639 | −0.736392 | ||||||||
\(557\) | 12.5634 | 0.532328 | 0.266164 | − | 0.963928i | \(-0.414244\pi\) | ||||
0.266164 | + | 0.963928i | \(0.414244\pi\) | |||||||
\(558\) | −14.7332 | −0.623706 | ||||||||
\(559\) | −20.2976 | −0.858499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.27963 | 0.265126 | ||||||||
\(562\) | 39.1918 | 1.65321 | ||||||||
\(563\) | −14.4847 | −0.610455 | −0.305228 | − | 0.952279i | \(-0.598733\pi\) | ||||
−0.305228 | + | 0.952279i | \(0.598733\pi\) | |||||||
\(564\) | 12.5486 | 0.528391 | ||||||||
\(565\) | −15.0135 | −0.631625 | ||||||||
\(566\) | 37.1274 | 1.56058 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.46777 | 0.313341 | ||||||||
\(569\) | −34.4444 | −1.44399 | −0.721993 | − | 0.691901i | \(-0.756774\pi\) | ||||
−0.721993 | + | 0.691901i | \(0.756774\pi\) | |||||||
\(570\) | 13.0849 | 0.548066 | ||||||||
\(571\) | 45.9789 | 1.92416 | 0.962078 | − | 0.272775i | \(-0.0879415\pi\) | ||||
0.962078 | + | 0.272775i | \(0.0879415\pi\) | |||||||
\(572\) | 1.98357 | 0.0829374 | ||||||||
\(573\) | −7.68410 | −0.321008 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.83834 | −0.243475 | ||||||||
\(576\) | 1.52276 | 0.0634483 | ||||||||
\(577\) | −40.3967 | −1.68174 | −0.840868 | − | 0.541240i | \(-0.817955\pi\) | ||||
−0.840868 | + | 0.541240i | \(0.817955\pi\) | |||||||
\(578\) | 18.1448 | 0.754726 | ||||||||
\(579\) | −51.8506 | −2.15484 | ||||||||
\(580\) | −2.70034 | −0.112126 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.67142 | 0.317991 | ||||||||
\(583\) | −1.90499 | −0.0788964 | ||||||||
\(584\) | 0.167014 | 0.00691111 | ||||||||
\(585\) | 5.57226 | 0.230384 | ||||||||
\(586\) | 28.4913 | 1.17697 | ||||||||
\(587\) | −21.4627 | −0.885860 | −0.442930 | − | 0.896556i | \(-0.646061\pi\) | ||||
−0.442930 | + | 0.896556i | \(0.646061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.73678 | 0.359993 | ||||||||
\(590\) | −14.6230 | −0.602020 | ||||||||
\(591\) | −20.4874 | −0.842737 | ||||||||
\(592\) | 24.9035 | 1.02353 | ||||||||
\(593\) | −11.6017 | −0.476424 | −0.238212 | − | 0.971213i | \(-0.576561\pi\) | ||||
−0.238212 | + | 0.971213i | \(0.576561\pi\) | |||||||
\(594\) | −0.171064 | −0.00701885 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.42436 | 0.386037 | ||||||||
\(597\) | −57.2856 | −2.34454 | ||||||||
\(598\) | 19.2067 | 0.785419 | ||||||||
\(599\) | −13.7763 | −0.562886 | −0.281443 | − | 0.959578i | \(-0.590813\pi\) | ||||
−0.281443 | + | 0.959578i | \(0.590813\pi\) | |||||||
\(600\) | −4.03722 | −0.164819 | ||||||||
\(601\) | −28.9935 | −1.18267 | −0.591335 | − | 0.806426i | \(-0.701399\pi\) | ||||
−0.591335 | + | 0.806426i | \(0.701399\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 43.2565 | 1.76154 | ||||||||
\(604\) | 14.6907 | 0.597757 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −45.9305 | −1.86580 | ||||||||
\(607\) | 41.4893 | 1.68400 | 0.842000 | − | 0.539478i | \(-0.181378\pi\) | ||||
0.842000 | + | 0.539478i | \(0.181378\pi\) | |||||||
\(608\) | 16.6391 | 0.674805 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0508 | 0.487921 | ||||||||
\(611\) | −9.18405 | −0.371547 | ||||||||
\(612\) | −8.02207 | −0.324273 | ||||||||
\(613\) | 34.2229 | 1.38225 | 0.691124 | − | 0.722736i | \(-0.257116\pi\) | ||||
0.691124 | + | 0.722736i | \(0.257116\pi\) | |||||||
\(614\) | −3.15977 | −0.127518 | ||||||||
\(615\) | −3.85549 | −0.155468 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.4992 | 1.22785 | 0.613926 | − | 0.789363i | \(-0.289589\pi\) | ||||
0.613926 | + | 0.789363i | \(0.289589\pi\) | |||||||
\(618\) | 19.7790 | 0.795629 | ||||||||
\(619\) | 38.5147 | 1.54804 | 0.774018 | − | 0.633164i | \(-0.218244\pi\) | ||||
0.774018 | + | 0.633164i | \(0.218244\pi\) | |||||||
\(620\) | 3.00127 | 0.120534 | ||||||||
\(621\) | −0.571530 | −0.0229347 | ||||||||
\(622\) | 53.0891 | 2.12868 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 22.9664 | 0.919393 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −31.0756 | −1.24203 | ||||||||
\(627\) | −7.48791 | −0.299038 | ||||||||
\(628\) | −3.16397 | −0.126256 | ||||||||
\(629\) | 12.8190 | 0.511128 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.18173 | 0.0868534 | 0.0434267 | − | 0.999057i | \(-0.486172\pi\) | ||||
0.0434267 | + | 0.999057i | \(0.486172\pi\) | |||||||
\(632\) | 15.2065 | 0.604880 | ||||||||
\(633\) | −0.692775 | −0.0275353 | ||||||||
\(634\) | −9.99026 | −0.396764 | ||||||||
\(635\) | 10.5179 | 0.417389 | ||||||||
\(636\) | 4.90011 | 0.194302 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.47851 | 0.177306 | ||||||||
\(639\) | 13.3661 | 0.528756 | ||||||||
\(640\) | −11.7487 | −0.464410 | ||||||||
\(641\) | −41.0820 | −1.62264 | −0.811321 | − | 0.584601i | \(-0.801251\pi\) | ||||
−0.811321 | + | 0.584601i | \(0.801251\pi\) | |||||||
\(642\) | −6.98390 | −0.275632 | ||||||||
\(643\) | −36.7462 | −1.44913 | −0.724565 | − | 0.689206i | \(-0.757959\pi\) | ||||
−0.724565 | + | 0.689206i | \(0.757959\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26.3215 | 1.03641 | ||||||||
\(646\) | 13.7868 | 0.542436 | ||||||||
\(647\) | −38.3584 | −1.50802 | −0.754012 | − | 0.656861i | \(-0.771884\pi\) | ||||
−0.754012 | + | 0.656861i | \(0.771884\pi\) | |||||||
\(648\) | −15.0798 | −0.592390 | ||||||||
\(649\) | 8.36812 | 0.328477 | ||||||||
\(650\) | −3.28975 | −0.129035 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.4644 | −0.918937 | ||||||||
\(653\) | −14.4251 | −0.564497 | −0.282249 | − | 0.959341i | \(-0.591080\pi\) | ||||
−0.282249 | + | 0.959341i | \(0.591080\pi\) | |||||||
\(654\) | −71.0307 | −2.77752 | ||||||||
\(655\) | 20.6852 | 0.808237 | ||||||||
\(656\) | −7.89187 | −0.308126 | ||||||||
\(657\) | 0.298929 | 0.0116623 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.0717 | 0.820835 | 0.410418 | − | 0.911898i | \(-0.365383\pi\) | ||||
0.410418 | + | 0.911898i | \(0.365383\pi\) | |||||||
\(660\) | −2.57226 | −0.100125 | ||||||||
\(661\) | −22.0164 | −0.856340 | −0.428170 | − | 0.903698i | \(-0.640841\pi\) | ||||
−0.428170 | + | 0.903698i | \(0.640841\pi\) | |||||||
\(662\) | 14.1376 | 0.549473 | ||||||||
\(663\) | 11.8219 | 0.459125 | ||||||||
\(664\) | 12.6076 | 0.489269 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25.7767 | 0.998827 | ||||||||
\(667\) | 14.9628 | 0.579363 | ||||||||
\(668\) | −7.74835 | −0.299793 | ||||||||
\(669\) | 67.0231 | 2.59126 | ||||||||
\(670\) | −25.5378 | −0.986611 | ||||||||
\(671\) | −6.89613 | −0.266222 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.4552 | 1.13542 | 0.567708 | − | 0.823230i | \(-0.307830\pi\) | ||||
0.567708 | + | 0.823230i | \(0.307830\pi\) | |||||||
\(674\) | −19.8105 | −0.763072 | ||||||||
\(675\) | 0.0978926 | 0.00376789 | ||||||||
\(676\) | −9.96316 | −0.383198 | ||||||||
\(677\) | −25.5337 | −0.981342 | −0.490671 | − | 0.871345i | \(-0.663248\pi\) | ||||
−0.490671 | + | 0.871345i | \(0.663248\pi\) | |||||||
\(678\) | −64.0490 | −2.45979 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.25380 | −0.163126 | ||||||||
\(681\) | −6.82551 | −0.261554 | ||||||||
\(682\) | −4.97760 | −0.190602 | ||||||||
\(683\) | 17.0369 | 0.651898 | 0.325949 | − | 0.945387i | \(-0.394316\pi\) | ||||
0.325949 | + | 0.945387i | \(0.394316\pi\) | |||||||
\(684\) | 9.56562 | 0.365751 | ||||||||
\(685\) | −21.6149 | −0.825863 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.3699 | 1.19684 | ||||||||
\(688\) | 53.8780 | 2.05408 | ||||||||
\(689\) | −3.58629 | −0.136627 | ||||||||
\(690\) | −24.9068 | −0.948186 | ||||||||
\(691\) | −43.4197 | −1.65176 | −0.825881 | − | 0.563845i | \(-0.809322\pi\) | ||||
−0.825881 | + | 0.563845i | \(0.809322\pi\) | |||||||
\(692\) | −24.4560 | −0.929677 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.710808 | 0.0269819 | ||||||||
\(695\) | −16.4798 | −0.625114 | ||||||||
\(696\) | 10.3468 | 0.392195 | ||||||||
\(697\) | −4.06232 | −0.153871 | ||||||||
\(698\) | −8.52618 | −0.322721 | ||||||||
\(699\) | 45.0867 | 1.70534 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0563 | −0.719746 | −0.359873 | − | 0.933001i | \(-0.617180\pi\) | ||||
−0.359873 | + | 0.933001i | \(0.617180\pi\) | |||||||
\(702\) | −0.322042 | −0.0121547 | ||||||||
\(703\) | −15.2856 | −0.576507 | ||||||||
\(704\) | 0.514463 | 0.0193895 | ||||||||
\(705\) | 11.9097 | 0.448544 | ||||||||
\(706\) | −15.7226 | −0.591727 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −21.5249 | −0.808957 | ||||||||
\(709\) | 18.9528 | 0.711788 | 0.355894 | − | 0.934526i | \(-0.384176\pi\) | ||||
0.355894 | + | 0.934526i | \(0.384176\pi\) | |||||||
\(710\) | −7.89110 | −0.296148 | ||||||||
\(711\) | 27.2171 | 1.02072 | ||||||||
\(712\) | 23.4682 | 0.879509 | ||||||||
\(713\) | −16.6303 | −0.622809 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.88258 | 0.0704046 | ||||||||
\(716\) | −19.9307 | −0.744847 | ||||||||
\(717\) | 51.4850 | 1.92274 | ||||||||
\(718\) | 8.20772 | 0.306310 | ||||||||
\(719\) | −33.2346 | −1.23944 | −0.619721 | − | 0.784822i | \(-0.712754\pi\) | ||||
−0.619721 | + | 0.784822i | \(0.712754\pi\) | |||||||
\(720\) | −14.7910 | −0.551228 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.7623 | 0.623828 | ||||||||
\(723\) | 22.8773 | 0.850817 | ||||||||
\(724\) | 23.0232 | 0.855651 | ||||||||
\(725\) | −2.56286 | −0.0951821 | ||||||||
\(726\) | 4.26608 | 0.158329 | ||||||||
\(727\) | 9.83280 | 0.364678 | 0.182339 | − | 0.983236i | \(-0.441633\pi\) | ||||
0.182339 | + | 0.983236i | \(0.441633\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.2735 | −0.973091 | ||||||||
\(730\) | −0.176482 | −0.00653189 | ||||||||
\(731\) | 27.7336 | 1.02576 | ||||||||
\(732\) | 17.7386 | 0.655638 | ||||||||
\(733\) | −16.7024 | −0.616919 | −0.308459 | − | 0.951238i | \(-0.599813\pi\) | ||||
−0.308459 | + | 0.951238i | \(0.599813\pi\) | |||||||
\(734\) | −8.02390 | −0.296167 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.6722 | −1.16745 | ||||||||
\(737\) | 14.6142 | 0.538320 | ||||||||
\(738\) | −8.16858 | −0.300689 | ||||||||
\(739\) | −27.7647 | −1.02134 | −0.510670 | − | 0.859777i | \(-0.670603\pi\) | ||||
−0.510670 | + | 0.859777i | \(0.670603\pi\) | |||||||
\(740\) | −5.25092 | −0.193028 | ||||||||
\(741\) | −14.0966 | −0.517852 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.1302 | 0.591759 | 0.295880 | − | 0.955225i | \(-0.404387\pi\) | ||||
0.295880 | + | 0.955225i | \(0.404387\pi\) | |||||||
\(744\) | −11.4999 | −0.421606 | ||||||||
\(745\) | 8.94452 | 0.327702 | ||||||||
\(746\) | 22.8351 | 0.836051 | ||||||||
\(747\) | 22.5656 | 0.825630 | ||||||||
\(748\) | −2.71025 | −0.0990965 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.26608 | 0.155775 | ||||||||
\(751\) | −30.1891 | −1.10162 | −0.550809 | − | 0.834631i | \(-0.685681\pi\) | ||||
−0.550809 | + | 0.834631i | \(0.685681\pi\) | |||||||
\(752\) | 24.3781 | 0.888979 | ||||||||
\(753\) | 35.1729 | 1.28177 | ||||||||
\(754\) | 8.43116 | 0.307045 | ||||||||
\(755\) | 13.9427 | 0.507429 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3060 | 0.483615 | 0.241807 | − | 0.970324i | \(-0.422260\pi\) | ||||
0.241807 | + | 0.970324i | \(0.422260\pi\) | |||||||
\(758\) | 18.1909 | 0.660724 | ||||||||
\(759\) | 14.2531 | 0.517354 | ||||||||
\(760\) | 5.07229 | 0.183991 | ||||||||
\(761\) | 8.17689 | 0.296412 | 0.148206 | − | 0.988957i | \(-0.452650\pi\) | ||||
0.148206 | + | 0.988957i | \(0.452650\pi\) | |||||||
\(762\) | 44.8701 | 1.62547 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.31641 | 0.119984 | ||||||||
\(765\) | −7.61363 | −0.275271 | ||||||||
\(766\) | 40.0959 | 1.44872 | ||||||||
\(767\) | 15.7537 | 0.568832 | ||||||||
\(768\) | −47.6091 | −1.71795 | ||||||||
\(769\) | −54.6122 | −1.96936 | −0.984682 | − | 0.174358i | \(-0.944215\pi\) | ||||
−0.984682 | + | 0.174358i | \(0.944215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.8112 | −1.43377 | ||||||||
\(772\) | 22.3784 | 0.805417 | ||||||||
\(773\) | −39.6980 | −1.42784 | −0.713918 | − | 0.700229i | \(-0.753081\pi\) | ||||
−0.713918 | + | 0.700229i | \(0.753081\pi\) | |||||||
\(774\) | 55.7671 | 2.00451 | ||||||||
\(775\) | 2.84846 | 0.102320 | ||||||||
\(776\) | 2.97379 | 0.106753 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.3869 | −0.730906 | ||||||||
\(779\) | 4.84396 | 0.173553 | ||||||||
\(780\) | −4.84248 | −0.173389 | ||||||||
\(781\) | 4.51573 | 0.161586 | ||||||||
\(782\) | −26.2429 | −0.938446 | ||||||||
\(783\) | −0.250885 | −0.00896589 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.00288 | −0.107177 | ||||||||
\(786\) | 88.2446 | 3.14758 | ||||||||
\(787\) | 22.9272 | 0.817266 | 0.408633 | − | 0.912699i | \(-0.366006\pi\) | ||||
0.408633 | + | 0.912699i | \(0.366006\pi\) | |||||||
\(788\) | 8.84221 | 0.314991 | ||||||||
\(789\) | 64.2529 | 2.28746 | ||||||||
\(790\) | −16.0685 | −0.571690 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.89486 | 0.173931 | ||||||||
\(793\) | −12.9825 | −0.461023 | ||||||||
\(794\) | 4.22007 | 0.149765 | ||||||||
\(795\) | 4.65062 | 0.164941 | ||||||||
\(796\) | 24.7241 | 0.876323 | ||||||||
\(797\) | 26.4654 | 0.937451 | 0.468725 | − | 0.883344i | \(-0.344713\pi\) | ||||
0.468725 | + | 0.883344i | \(0.344713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5486 | 0.443937 | ||||||||
\(800\) | 5.42487 | 0.191798 | ||||||||
\(801\) | 42.0044 | 1.48415 | ||||||||
\(802\) | 59.1510 | 2.08870 | ||||||||
\(803\) | 0.100993 | 0.00356396 | ||||||||
\(804\) | −37.5914 | −1.32575 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.37073 | −0.330070 | ||||||||
\(807\) | −1.14793 | −0.0404092 | ||||||||
\(808\) | −17.8047 | −0.626367 | ||||||||
\(809\) | −24.6624 | −0.867084 | −0.433542 | − | 0.901133i | \(-0.642736\pi\) | ||||
−0.433542 | + | 0.901133i | \(0.642736\pi\) | |||||||
\(810\) | 15.9346 | 0.559885 | ||||||||
\(811\) | −36.8401 | −1.29363 | −0.646815 | − | 0.762647i | \(-0.723900\pi\) | ||||
−0.646815 | + | 0.762647i | \(0.723900\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.9146 | −1.54015 | ||||||||
\(814\) | 8.70864 | 0.305238 | ||||||||
\(815\) | −22.2697 | −0.780074 | ||||||||
\(816\) | −31.3801 | −1.09852 | ||||||||
\(817\) | −33.0699 | −1.15697 | ||||||||
\(818\) | 16.0253 | 0.560310 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.66400 | 0.0581096 | ||||||||
\(821\) | −8.38656 | −0.292693 | −0.146346 | − | 0.989233i | \(-0.546751\pi\) | ||||
−0.146346 | + | 0.989233i | \(0.546751\pi\) | |||||||
\(822\) | −92.2108 | −3.21622 | ||||||||
\(823\) | −50.8692 | −1.77319 | −0.886594 | − | 0.462548i | \(-0.846935\pi\) | ||||
−0.886594 | + | 0.462548i | \(0.846935\pi\) | |||||||
\(824\) | 7.66724 | 0.267101 | ||||||||
\(825\) | −2.44129 | −0.0849948 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.3029 | 1.33192 | 0.665961 | − | 0.745987i | \(-0.268022\pi\) | ||||
0.665961 | + | 0.745987i | \(0.268022\pi\) | |||||||
\(828\) | −18.2079 | −0.632770 | ||||||||
\(829\) | −3.97040 | −0.137898 | −0.0689489 | − | 0.997620i | \(-0.521965\pi\) | ||||
−0.0689489 | + | 0.997620i | \(0.521965\pi\) | |||||||
\(830\) | −13.3223 | −0.462423 | ||||||||
\(831\) | −60.9604 | −2.11469 | ||||||||
\(832\) | 0.968518 | 0.0335773 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −70.3040 | −2.43443 | ||||||||
\(835\) | −7.35385 | −0.254490 | ||||||||
\(836\) | 3.23174 | 0.111772 | ||||||||
\(837\) | 0.278843 | 0.00963823 | ||||||||
\(838\) | 17.4451 | 0.602631 | ||||||||
\(839\) | −34.3262 | −1.18507 | −0.592537 | − | 0.805543i | \(-0.701874\pi\) | ||||
−0.592537 | + | 0.805543i | \(0.701874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4318 | −0.773509 | ||||||||
\(842\) | 28.8578 | 0.994505 | ||||||||
\(843\) | 54.7526 | 1.88578 | ||||||||
\(844\) | 0.298997 | 0.0102919 | ||||||||
\(845\) | −9.45589 | −0.325292 | ||||||||
\(846\) | 25.2329 | 0.867525 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.51944 | 0.326899 | ||||||||
\(849\) | 51.8686 | 1.78012 | ||||||||
\(850\) | 4.49494 | 0.154175 | ||||||||
\(851\) | 29.0958 | 0.997391 | ||||||||
\(852\) | −11.6156 | −0.397945 | ||||||||
\(853\) | 11.6335 | 0.398322 | 0.199161 | − | 0.979967i | \(-0.436178\pi\) | ||||
0.199161 | + | 0.979967i | \(0.436178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.07859 | 0.310481 | ||||||||
\(856\) | −2.70727 | −0.0925326 | ||||||||
\(857\) | −48.2990 | −1.64986 | −0.824932 | − | 0.565232i | \(-0.808787\pi\) | ||||
−0.824932 | + | 0.565232i | \(0.808787\pi\) | |||||||
\(858\) | 8.03124 | 0.274182 | ||||||||
\(859\) | 4.26640 | 0.145568 | 0.0727838 | − | 0.997348i | \(-0.476812\pi\) | ||||
0.0727838 | + | 0.997348i | \(0.476812\pi\) | |||||||
\(860\) | −11.3602 | −0.387380 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.7553 | 0.979408 | ||||||||
\(863\) | −25.2236 | −0.858621 | −0.429310 | − | 0.903157i | \(-0.641243\pi\) | ||||
−0.429310 | + | 0.903157i | \(0.641243\pi\) | |||||||
\(864\) | 0.531054 | 0.0180668 | ||||||||
\(865\) | −23.2108 | −0.789192 | ||||||||
\(866\) | 31.4257 | 1.06789 | ||||||||
\(867\) | 25.3491 | 0.860902 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.19528 | 0.311929 | ||||||||
\(870\) | −10.9333 | −0.370675 | ||||||||
\(871\) | 27.5124 | 0.932221 | ||||||||
\(872\) | −27.5347 | −0.932443 | ||||||||
\(873\) | 5.32260 | 0.180143 | ||||||||
\(874\) | 31.2924 | 1.05848 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.259780 | −0.00877715 | ||||||||
\(877\) | 1.12831 | 0.0381003 | 0.0190502 | − | 0.999819i | \(-0.493936\pi\) | ||||
0.0190502 | + | 0.999819i | \(0.493936\pi\) | |||||||
\(878\) | −40.3187 | −1.36069 | ||||||||
\(879\) | 39.8037 | 1.34254 | ||||||||
\(880\) | −4.99712 | −0.168453 | ||||||||
\(881\) | 28.1086 | 0.947003 | 0.473501 | − | 0.880793i | \(-0.342990\pi\) | ||||
0.473501 | + | 0.880793i | \(0.342990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.9702 | 0.604745 | 0.302372 | − | 0.953190i | \(-0.402221\pi\) | ||||
0.302372 | + | 0.953190i | \(0.402221\pi\) | |||||||
\(884\) | −5.10226 | −0.171608 | ||||||||
\(885\) | −20.4290 | −0.686714 | ||||||||
\(886\) | −16.8286 | −0.565368 | ||||||||
\(887\) | −5.94398 | −0.199579 | −0.0997897 | − | 0.995009i | \(-0.531817\pi\) | ||||
−0.0997897 | + | 0.995009i | \(0.531817\pi\) | |||||||
\(888\) | 20.1198 | 0.675176 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24.7986 | −0.831250 | ||||||||
\(891\) | −9.11869 | −0.305488 | ||||||||
\(892\) | −28.9268 | −0.968539 | ||||||||
\(893\) | −14.9631 | −0.500721 | ||||||||
\(894\) | 38.1580 | 1.27620 | ||||||||
\(895\) | −18.9160 | −0.632291 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.8326 | 0.895914 | ||||||||
\(898\) | 9.52713 | 0.317924 | ||||||||
\(899\) | −7.30020 | −0.243475 | ||||||||
\(900\) | 3.11869 | 0.103956 | ||||||||
\(901\) | 4.90011 | 0.163246 | ||||||||
\(902\) | −2.75975 | −0.0918895 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.8283 | −0.825776 | ||||||||
\(905\) | 21.8510 | 0.726352 | ||||||||
\(906\) | 59.4809 | 1.97612 | ||||||||
\(907\) | −8.97383 | −0.297971 | −0.148985 | − | 0.988839i | \(-0.547601\pi\) | ||||
−0.148985 | + | 0.988839i | \(0.547601\pi\) | |||||||
\(908\) | 2.94585 | 0.0977615 | ||||||||
\(909\) | −31.8676 | −1.05698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.2124 | 1.59735 | 0.798673 | − | 0.601765i | \(-0.205536\pi\) | ||||
0.798673 | + | 0.601765i | \(0.205536\pi\) | |||||||
\(912\) | 37.4180 | 1.23903 | ||||||||
\(913\) | 7.62375 | 0.252309 | ||||||||
\(914\) | −46.1074 | −1.52510 | ||||||||
\(915\) | 16.8355 | 0.556563 | ||||||||
\(916\) | −13.5391 | −0.447343 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.440021 | 0.0145229 | ||||||||
\(919\) | −12.0349 | −0.396996 | −0.198498 | − | 0.980101i | \(-0.563606\pi\) | ||||
−0.198498 | + | 0.980101i | \(0.563606\pi\) | |||||||
\(920\) | −9.65499 | −0.318316 | ||||||||
\(921\) | −4.41433 | −0.145457 | ||||||||
\(922\) | −25.6328 | −0.844172 | ||||||||
\(923\) | 8.50124 | 0.279822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.98357 | −0.163859 | ||||||||
\(926\) | −52.0255 | −1.70966 | ||||||||
\(927\) | 13.7231 | 0.450727 | ||||||||
\(928\) | −13.9032 | −0.456393 | ||||||||
\(929\) | −42.5633 | −1.39646 | −0.698229 | − | 0.715875i | \(-0.746028\pi\) | ||||
−0.698229 | + | 0.715875i | \(0.746028\pi\) | |||||||
\(930\) | 12.1518 | 0.398472 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −19.4591 | −0.637405 | ||||||||
\(933\) | 74.1679 | 2.42815 | ||||||||
\(934\) | −12.2500 | −0.400831 | ||||||||
\(935\) | −2.57226 | −0.0841218 | ||||||||
\(936\) | 9.21497 | 0.301201 | ||||||||
\(937\) | −17.7793 | −0.580824 | −0.290412 | − | 0.956902i | \(-0.593792\pi\) | ||||
−0.290412 | + | 0.956902i | \(0.593792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.4141 | −1.41676 | ||||||||
\(940\) | −5.14014 | −0.167653 | ||||||||
\(941\) | 23.1985 | 0.756250 | 0.378125 | − | 0.925755i | \(-0.376569\pi\) | ||||
0.378125 | + | 0.925755i | \(0.376569\pi\) | |||||||
\(942\) | −12.8105 | −0.417389 | ||||||||
\(943\) | −9.22038 | −0.300257 | ||||||||
\(944\) | −41.8165 | −1.36101 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.8409 | 0.612570 | ||||||||
\(947\) | −53.0306 | −1.72326 | −0.861632 | − | 0.507534i | \(-0.830557\pi\) | ||||
−0.861632 | + | 0.507534i | \(0.830557\pi\) | |||||||
\(948\) | −23.6526 | −0.768201 | ||||||||
\(949\) | 0.190128 | 0.00617180 | ||||||||
\(950\) | −5.35982 | −0.173896 | ||||||||
\(951\) | −13.9568 | −0.452582 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.6025 | −1.34764 | −0.673818 | − | 0.738898i | \(-0.735347\pi\) | ||||
−0.673818 | + | 0.738898i | \(0.735347\pi\) | |||||||
\(954\) | 9.85322 | 0.319010 | ||||||||
\(955\) | 3.14756 | 0.101853 | ||||||||
\(956\) | −22.2206 | −0.718666 | ||||||||
\(957\) | 6.25668 | 0.202250 | ||||||||
\(958\) | −24.3828 | −0.787772 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.25595 | −0.0405357 | ||||||||
\(961\) | −22.8863 | −0.738267 | ||||||||
\(962\) | 16.3947 | 0.528587 | ||||||||
\(963\) | −4.84558 | −0.156147 | ||||||||
\(964\) | −9.87371 | −0.318011 | ||||||||
\(965\) | 21.2390 | 0.683708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.1656 | 0.744955 | 0.372478 | − | 0.928041i | \(-0.378508\pi\) | ||||
0.372478 | + | 0.928041i | \(0.378508\pi\) | |||||||
\(968\) | 1.65372 | 0.0531527 | ||||||||
\(969\) | 19.2608 | 0.618747 | ||||||||
\(970\) | −3.14236 | −0.100895 | ||||||||
\(971\) | 29.2515 | 0.938724 | 0.469362 | − | 0.883006i | \(-0.344484\pi\) | ||||
0.469362 | + | 0.883006i | \(0.344484\pi\) | |||||||
\(972\) | 23.1462 | 0.742414 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.7453 | −0.376344 | ||||||||
\(975\) | −4.59593 | −0.147188 | ||||||||
\(976\) | 34.4608 | 1.10306 | ||||||||
\(977\) | −7.08584 | −0.226696 | −0.113348 | − | 0.993555i | \(-0.536158\pi\) | ||||
−0.113348 | + | 0.993555i | \(0.536158\pi\) | |||||||
\(978\) | −95.0044 | −3.03791 | ||||||||
\(979\) | 14.1911 | 0.453551 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −49.2827 | −1.57348 | ||||||||
\(982\) | 45.3418 | 1.44691 | ||||||||
\(983\) | 19.8510 | 0.633148 | 0.316574 | − | 0.948568i | \(-0.397467\pi\) | ||||
0.316574 | + | 0.948568i | \(0.397467\pi\) | |||||||
\(984\) | −6.37591 | −0.203257 | ||||||||
\(985\) | 8.39202 | 0.267392 | ||||||||
\(986\) | −11.5199 | −0.366868 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.08401 | 0.193558 | ||||||||
\(989\) | 62.9478 | 2.00162 | ||||||||
\(990\) | −5.17233 | −0.164388 | ||||||||
\(991\) | −16.0795 | −0.510782 | −0.255391 | − | 0.966838i | \(-0.582204\pi\) | ||||
−0.255391 | + | 0.966838i | \(0.582204\pi\) | |||||||
\(992\) | 15.4525 | 0.490618 | ||||||||
\(993\) | 19.7508 | 0.626774 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.4653 | 0.743900 | ||||||||
\(996\) | −19.6102 | −0.621374 | ||||||||
\(997\) | 22.8184 | 0.722665 | 0.361332 | − | 0.932437i | \(-0.382322\pi\) | ||||
0.361332 | + | 0.932437i | \(0.382322\pi\) | |||||||
\(998\) | −36.3560 | −1.15083 | ||||||||
\(999\) | −0.487855 | −0.0154350 |
(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 | 2695.2.a.j.1.2 | 4 | ||
7.2 | even | 3 | 385.2.i.a.221.3 | ✓ | 8 | ||
7.4 | even | 3 | 385.2.i.a.331.3 | yes | 8 | ||
7.6 | odd | 2 | 2695.2.a.k.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.i.a.221.3 | ✓ | 8 | 7.2 | even | 3 | ||
385.2.i.a.331.3 | yes | 8 | 7.4 | even | 3 | ||
2695.2.a.j.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2695.2.a.k.1.2 | 4 | 7.6 | odd | 2 |