Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5929,2,Mod(1,5929)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5929, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5929.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5929 = 7^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5929.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: | \(47.3433033584\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 26x^{8} + 245x^{6} - 1038x^{4} + 1884x^{2} - 968 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 539) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.10267\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5929.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74816 | 1.94325 | 0.971623 | − | 0.236536i | \(-0.0760120\pi\) | ||||
0.971623 | + | 0.236536i | \(0.0760120\pi\) | |||||||
\(3\) | −2.10267 | −1.21398 | −0.606988 | − | 0.794711i | \(-0.707622\pi\) | ||||
−0.606988 | + | 0.794711i | \(0.707622\pi\) | |||||||
\(4\) | 5.55241 | 2.77620 | ||||||||
\(5\) | −2.44342 | −1.09273 | −0.546365 | − | 0.837547i | \(-0.683989\pi\) | ||||
−0.546365 | + | 0.837547i | \(0.683989\pi\) | |||||||
\(6\) | −5.77848 | −2.35905 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.76260 | 3.45160 | ||||||||
\(9\) | 1.42122 | 0.473738 | ||||||||
\(10\) | −6.71492 | −2.12344 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −11.6749 | −3.37025 | ||||||||
\(13\) | 1.89199 | 0.524743 | 0.262371 | − | 0.964967i | \(-0.415495\pi\) | ||||
0.262371 | + | 0.964967i | \(0.415495\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.13770 | 1.32655 | ||||||||
\(16\) | 15.7244 | 3.93110 | ||||||||
\(17\) | 3.95040 | 0.958113 | 0.479056 | − | 0.877784i | \(-0.340979\pi\) | ||||
0.479056 | + | 0.877784i | \(0.340979\pi\) | |||||||
\(18\) | 3.90573 | 0.920590 | ||||||||
\(19\) | 2.88614 | 0.662127 | 0.331063 | − | 0.943609i | \(-0.392593\pi\) | ||||
0.331063 | + | 0.943609i | \(0.392593\pi\) | |||||||
\(20\) | −13.5669 | −3.03364 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.59322 | −1.37478 | −0.687391 | − | 0.726288i | \(-0.741244\pi\) | ||||
−0.687391 | + | 0.726288i | \(0.741244\pi\) | |||||||
\(24\) | −20.5275 | −4.19016 | ||||||||
\(25\) | 0.970299 | 0.194060 | ||||||||
\(26\) | 5.19949 | 1.01970 | ||||||||
\(27\) | 3.31966 | 0.638869 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.675675 | 0.125470 | 0.0627348 | − | 0.998030i | \(-0.480018\pi\) | ||||
0.0627348 | + | 0.998030i | \(0.480018\pi\) | |||||||
\(30\) | 14.1192 | 2.57781 | ||||||||
\(31\) | −7.81724 | −1.40402 | −0.702009 | − | 0.712168i | \(-0.747713\pi\) | ||||
−0.702009 | + | 0.712168i | \(0.747713\pi\) | |||||||
\(32\) | 23.6881 | 4.18750 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.8563 | 1.86185 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.89117 | 1.31519 | ||||||||
\(37\) | 5.87673 | 0.966129 | 0.483064 | − | 0.875585i | \(-0.339524\pi\) | ||||
0.483064 | + | 0.875585i | \(0.339524\pi\) | |||||||
\(38\) | 7.93160 | 1.28667 | ||||||||
\(39\) | −3.97822 | −0.637026 | ||||||||
\(40\) | −23.8541 | −3.77167 | ||||||||
\(41\) | −3.26890 | −0.510516 | −0.255258 | − | 0.966873i | \(-0.582160\pi\) | ||||
−0.255258 | + | 0.966873i | \(0.582160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.06719 | 0.162745 | 0.0813724 | − | 0.996684i | \(-0.474070\pi\) | ||||
0.0813724 | + | 0.996684i | \(0.474070\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.47263 | −0.517668 | ||||||||
\(46\) | −18.1192 | −2.67154 | ||||||||
\(47\) | 9.70227 | 1.41522 | 0.707611 | − | 0.706602i | \(-0.249773\pi\) | ||||
0.707611 | + | 0.706602i | \(0.249773\pi\) | |||||||
\(48\) | −33.0632 | −4.77227 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.66654 | 0.377106 | ||||||||
\(51\) | −8.30638 | −1.16313 | ||||||||
\(52\) | 10.5051 | 1.45679 | ||||||||
\(53\) | 3.74286 | 0.514122 | 0.257061 | − | 0.966395i | \(-0.417246\pi\) | ||||
0.257061 | + | 0.966395i | \(0.417246\pi\) | |||||||
\(54\) | 9.12297 | 1.24148 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.06860 | −0.803806 | ||||||||
\(58\) | 1.85686 | 0.243818 | ||||||||
\(59\) | 6.48233 | 0.843928 | 0.421964 | − | 0.906613i | \(-0.361341\pi\) | ||||
0.421964 | + | 0.906613i | \(0.361341\pi\) | |||||||
\(60\) | 28.5266 | 3.68277 | ||||||||
\(61\) | −6.09732 | −0.780682 | −0.390341 | − | 0.920670i | \(-0.627643\pi\) | ||||
−0.390341 | + | 0.920670i | \(0.627643\pi\) | |||||||
\(62\) | −21.4831 | −2.72835 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 33.6499 | 4.20623 | ||||||||
\(65\) | −4.62292 | −0.573403 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.39944 | 0.537477 | 0.268738 | − | 0.963213i | \(-0.413393\pi\) | ||||
0.268738 | + | 0.963213i | \(0.413393\pi\) | |||||||
\(68\) | 21.9342 | 2.65992 | ||||||||
\(69\) | 13.8634 | 1.66895 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.39944 | 0.996830 | 0.498415 | − | 0.866939i | \(-0.333916\pi\) | ||||
0.498415 | + | 0.866939i | \(0.333916\pi\) | |||||||
\(72\) | 13.8748 | 1.63516 | ||||||||
\(73\) | 2.66200 | 0.311564 | 0.155782 | − | 0.987791i | \(-0.450210\pi\) | ||||
0.155782 | + | 0.987791i | \(0.450210\pi\) | |||||||
\(74\) | 16.1502 | 1.87743 | ||||||||
\(75\) | −2.04022 | −0.235584 | ||||||||
\(76\) | 16.0250 | 1.83820 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −10.9328 | −1.23790 | ||||||||
\(79\) | −2.09038 | −0.235186 | −0.117593 | − | 0.993062i | \(-0.537518\pi\) | ||||
−0.117593 | + | 0.993062i | \(0.537518\pi\) | |||||||
\(80\) | −38.4213 | −4.29564 | ||||||||
\(81\) | −11.2438 | −1.24931 | ||||||||
\(82\) | −8.98347 | −0.992058 | ||||||||
\(83\) | 3.78398 | 0.415345 | 0.207673 | − | 0.978198i | \(-0.433411\pi\) | ||||
0.207673 | + | 0.978198i | \(0.433411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.65248 | −1.04696 | ||||||||
\(86\) | 2.93281 | 0.316253 | ||||||||
\(87\) | −1.42072 | −0.152317 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.44342 | −0.259002 | −0.129501 | − | 0.991579i | \(-0.541338\pi\) | ||||
−0.129501 | + | 0.991579i | \(0.541338\pi\) | |||||||
\(90\) | −9.54335 | −1.00596 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −36.6082 | −3.81667 | ||||||||
\(93\) | 16.4371 | 1.70444 | ||||||||
\(94\) | 26.6634 | 2.75012 | ||||||||
\(95\) | −7.05206 | −0.723526 | ||||||||
\(96\) | −49.8082 | −5.08352 | ||||||||
\(97\) | 12.3633 | 1.25531 | 0.627653 | − | 0.778493i | \(-0.284016\pi\) | ||||
0.627653 | + | 0.778493i | \(0.284016\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.38750 | 0.538750 | ||||||||
\(101\) | 10.2187 | 1.01679 | 0.508397 | − | 0.861123i | \(-0.330238\pi\) | ||||
0.508397 | + | 0.861123i | \(0.330238\pi\) | |||||||
\(102\) | −22.8273 | −2.26024 | ||||||||
\(103\) | 5.36461 | 0.528591 | 0.264296 | − | 0.964442i | \(-0.414861\pi\) | ||||
0.264296 | + | 0.964442i | \(0.414861\pi\) | |||||||
\(104\) | 18.4707 | 1.81120 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.2860 | 0.999065 | ||||||||
\(107\) | 16.0158 | 1.54831 | 0.774155 | − | 0.632996i | \(-0.218175\pi\) | ||||
0.774155 | + | 0.632996i | \(0.218175\pi\) | |||||||
\(108\) | 18.4321 | 1.77363 | ||||||||
\(109\) | −3.57086 | −0.342026 | −0.171013 | − | 0.985269i | \(-0.554704\pi\) | ||||
−0.171013 | + | 0.985269i | \(0.554704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.3568 | −1.17286 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7244 | 1.38516 | 0.692578 | − | 0.721343i | \(-0.256475\pi\) | ||||
0.692578 | + | 0.721343i | \(0.256475\pi\) | |||||||
\(114\) | −16.6775 | −1.56199 | ||||||||
\(115\) | 16.1100 | 1.50227 | ||||||||
\(116\) | 3.75162 | 0.348329 | ||||||||
\(117\) | 2.68892 | 0.248591 | ||||||||
\(118\) | 17.8145 | 1.63996 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 50.1573 | 4.57872 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.7565 | −1.51706 | ||||||||
\(123\) | 6.87341 | 0.619754 | ||||||||
\(124\) | −43.4045 | −3.89784 | ||||||||
\(125\) | 9.84625 | 0.880675 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1864 | 1.52505 | 0.762525 | − | 0.646959i | \(-0.223959\pi\) | ||||
0.762525 | + | 0.646959i | \(0.223959\pi\) | |||||||
\(128\) | 45.0993 | 3.98625 | ||||||||
\(129\) | −2.24394 | −0.197568 | ||||||||
\(130\) | −12.7045 | −1.11426 | ||||||||
\(131\) | −13.6154 | −1.18958 | −0.594790 | − | 0.803881i | \(-0.702765\pi\) | ||||
−0.594790 | + | 0.803881i | \(0.702765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.0904 | 1.04445 | ||||||||
\(135\) | −8.11132 | −0.698112 | ||||||||
\(136\) | 38.5662 | 3.30702 | ||||||||
\(137\) | 0.0111106 | 0.000949243 0 | 0.000474622 | − | 1.00000i | \(-0.499849\pi\) | ||||
0.000474622 | 1.00000i | \(0.499849\pi\) | ||||||||
\(138\) | 38.0988 | 3.24318 | ||||||||
\(139\) | 21.4191 | 1.81675 | 0.908374 | − | 0.418158i | \(-0.137324\pi\) | ||||
0.908374 | + | 0.418158i | \(0.137324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.4007 | −1.71805 | ||||||||
\(142\) | 23.0830 | 1.93709 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 22.3478 | 1.86231 | ||||||||
\(145\) | −1.65096 | −0.137104 | ||||||||
\(146\) | 7.31562 | 0.605445 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.6300 | 2.68217 | ||||||||
\(149\) | −21.9761 | −1.80035 | −0.900177 | − | 0.435525i | \(-0.856563\pi\) | ||||
−0.900177 | + | 0.435525i | \(0.856563\pi\) | |||||||
\(150\) | −5.60685 | −0.457798 | ||||||||
\(151\) | 0.224758 | 0.0182906 | 0.00914528 | − | 0.999958i | \(-0.497089\pi\) | ||||
0.00914528 | + | 0.999958i | \(0.497089\pi\) | |||||||
\(152\) | 28.1763 | 2.28540 | ||||||||
\(153\) | 5.61437 | 0.453895 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.1008 | 1.53421 | ||||||||
\(156\) | −22.0887 | −1.76851 | ||||||||
\(157\) | 23.3823 | 1.86611 | 0.933056 | − | 0.359732i | \(-0.117132\pi\) | ||||
0.933056 | + | 0.359732i | \(0.117132\pi\) | |||||||
\(158\) | −5.74471 | −0.457024 | ||||||||
\(159\) | −7.87000 | −0.624132 | ||||||||
\(160\) | −57.8799 | −4.57581 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −30.8998 | −2.42772 | ||||||||
\(163\) | −12.2642 | −0.960608 | −0.480304 | − | 0.877102i | \(-0.659474\pi\) | ||||
−0.480304 | + | 0.877102i | \(0.659474\pi\) | |||||||
\(164\) | −18.1503 | −1.41730 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.3990 | 0.807118 | ||||||||
\(167\) | 17.6352 | 1.36465 | 0.682325 | − | 0.731049i | \(-0.260969\pi\) | ||||
0.682325 | + | 0.731049i | \(0.260969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.42038 | −0.724645 | ||||||||
\(170\) | −26.5266 | −2.03450 | ||||||||
\(171\) | 4.10183 | 0.313675 | ||||||||
\(172\) | 5.92547 | 0.451813 | ||||||||
\(173\) | −20.5022 | −1.55875 | −0.779377 | − | 0.626555i | \(-0.784464\pi\) | ||||
−0.779377 | + | 0.626555i | \(0.784464\pi\) | |||||||
\(174\) | −3.90437 | −0.295990 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.6302 | −1.02451 | ||||||||
\(178\) | −6.71492 | −0.503304 | ||||||||
\(179\) | 6.44901 | 0.482021 | 0.241011 | − | 0.970522i | \(-0.422521\pi\) | ||||
0.241011 | + | 0.970522i | \(0.422521\pi\) | |||||||
\(180\) | −19.2814 | −1.43715 | ||||||||
\(181\) | −1.35627 | −0.100811 | −0.0504053 | − | 0.998729i | \(-0.516051\pi\) | ||||
−0.0504053 | + | 0.998729i | \(0.516051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8207 | 0.947730 | ||||||||
\(184\) | −64.3669 | −4.74519 | ||||||||
\(185\) | −14.3593 | −1.05572 | ||||||||
\(186\) | 45.1718 | 3.31215 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 53.8710 | 3.92894 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −19.3802 | −1.40599 | ||||||||
\(191\) | −8.47788 | −0.613438 | −0.306719 | − | 0.951800i | \(-0.599231\pi\) | ||||
−0.306719 | + | 0.951800i | \(0.599231\pi\) | |||||||
\(192\) | −70.7545 | −5.10627 | ||||||||
\(193\) | −18.2624 | −1.31456 | −0.657278 | − | 0.753649i | \(-0.728292\pi\) | ||||
−0.657278 | + | 0.753649i | \(0.728292\pi\) | |||||||
\(194\) | 33.9765 | 2.43937 | ||||||||
\(195\) | 9.72047 | 0.696097 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3802 | −1.23829 | −0.619145 | − | 0.785277i | \(-0.712521\pi\) | ||||
−0.619145 | + | 0.785277i | \(0.712521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.48005 | −0.388470 | −0.194235 | − | 0.980955i | \(-0.562222\pi\) | ||||
−0.194235 | + | 0.980955i | \(0.562222\pi\) | |||||||
\(200\) | 9.47264 | 0.669817 | ||||||||
\(201\) | −9.25056 | −0.652484 | ||||||||
\(202\) | 28.0825 | 1.97588 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −46.1204 | −3.22907 | ||||||||
\(205\) | 7.98729 | 0.557856 | ||||||||
\(206\) | 14.7428 | 1.02718 | ||||||||
\(207\) | −9.37038 | −0.651287 | ||||||||
\(208\) | 29.7504 | 2.06282 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.03239 | 0.484130 | 0.242065 | − | 0.970260i | \(-0.422175\pi\) | ||||
0.242065 | + | 0.970260i | \(0.422175\pi\) | |||||||
\(212\) | 20.7819 | 1.42731 | ||||||||
\(213\) | −17.6612 | −1.21013 | ||||||||
\(214\) | 44.0142 | 3.00875 | ||||||||
\(215\) | −2.60759 | −0.177836 | ||||||||
\(216\) | 32.4085 | 2.20512 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.81331 | −0.664641 | ||||||||
\(219\) | −5.59731 | −0.378231 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.47411 | 0.502763 | ||||||||
\(222\) | −33.9586 | −2.27915 | ||||||||
\(223\) | −0.419109 | −0.0280656 | −0.0140328 | − | 0.999902i | \(-0.504467\pi\) | ||||
−0.0140328 | + | 0.999902i | \(0.504467\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.37900 | 0.0919336 | ||||||||
\(226\) | 40.4651 | 2.69170 | ||||||||
\(227\) | −25.5405 | −1.69518 | −0.847591 | − | 0.530651i | \(-0.821948\pi\) | ||||
−0.847591 | + | 0.530651i | \(0.821948\pi\) | |||||||
\(228\) | −33.6954 | −2.23153 | ||||||||
\(229\) | 14.6118 | 0.965574 | 0.482787 | − | 0.875738i | \(-0.339625\pi\) | ||||
0.482787 | + | 0.875738i | \(0.339625\pi\) | |||||||
\(230\) | 44.2729 | 2.91927 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.59634 | 0.433071 | ||||||||
\(233\) | 17.2716 | 1.13150 | 0.565749 | − | 0.824577i | \(-0.308587\pi\) | ||||
0.565749 | + | 0.824577i | \(0.308587\pi\) | |||||||
\(234\) | 7.38960 | 0.483073 | ||||||||
\(235\) | −23.7067 | −1.54646 | ||||||||
\(236\) | 35.9925 | 2.34292 | ||||||||
\(237\) | 4.39538 | 0.285510 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.8945 | 1.02813 | 0.514065 | − | 0.857752i | \(-0.328139\pi\) | ||||
0.514065 | + | 0.857752i | \(0.328139\pi\) | |||||||
\(240\) | 80.7873 | 5.21480 | ||||||||
\(241\) | −8.85565 | −0.570443 | −0.285221 | − | 0.958462i | \(-0.592067\pi\) | ||||
−0.285221 | + | 0.958462i | \(0.592067\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.6830 | 0.877764 | ||||||||
\(244\) | −33.8548 | −2.16733 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.8893 | 1.20434 | ||||||||
\(247\) | 5.46055 | 0.347446 | ||||||||
\(248\) | −76.3166 | −4.84611 | ||||||||
\(249\) | −7.95645 | −0.504219 | ||||||||
\(250\) | 27.0591 | 1.71137 | ||||||||
\(251\) | −11.1416 | −0.703254 | −0.351627 | − | 0.936140i | \(-0.614371\pi\) | ||||
−0.351627 | + | 0.936140i | \(0.614371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 47.2312 | 2.96355 | ||||||||
\(255\) | 20.2960 | 1.27098 | ||||||||
\(256\) | 56.6404 | 3.54003 | ||||||||
\(257\) | 13.7681 | 0.858831 | 0.429415 | − | 0.903107i | \(-0.358720\pi\) | ||||
0.429415 | + | 0.903107i | \(0.358720\pi\) | |||||||
\(258\) | −6.16673 | −0.383924 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −25.6683 | −1.59188 | ||||||||
\(261\) | 0.960279 | 0.0594398 | ||||||||
\(262\) | −37.4173 | −2.31165 | ||||||||
\(263\) | 5.80622 | 0.358027 | 0.179013 | − | 0.983847i | \(-0.442709\pi\) | ||||
0.179013 | + | 0.983847i | \(0.442709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.14539 | −0.561797 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.13770 | 0.314422 | ||||||||
\(268\) | 24.4275 | 1.49215 | ||||||||
\(269\) | 6.23095 | 0.379908 | 0.189954 | − | 0.981793i | \(-0.439166\pi\) | ||||
0.189954 | + | 0.981793i | \(0.439166\pi\) | |||||||
\(270\) | −22.2913 | −1.35660 | ||||||||
\(271\) | 10.5576 | 0.641329 | 0.320664 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320664 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(272\) | 62.1177 | 3.76644 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0305338 | 0.00184461 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 76.9750 | 4.63335 | ||||||||
\(277\) | 25.9920 | 1.56171 | 0.780853 | − | 0.624715i | \(-0.214785\pi\) | ||||
0.780853 | + | 0.624715i | \(0.214785\pi\) | |||||||
\(278\) | 58.8633 | 3.53039 | ||||||||
\(279\) | −11.1100 | −0.665137 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.8167 | 0.764580 | 0.382290 | − | 0.924042i | \(-0.375136\pi\) | ||||
0.382290 | + | 0.924042i | \(0.375136\pi\) | |||||||
\(282\) | −56.0644 | −3.33859 | ||||||||
\(283\) | −31.2813 | −1.85948 | −0.929741 | − | 0.368213i | \(-0.879970\pi\) | ||||
−0.929741 | + | 0.368213i | \(0.879970\pi\) | |||||||
\(284\) | 46.6371 | 2.76740 | ||||||||
\(285\) | 14.8281 | 0.878343 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 33.6658 | 1.98378 | ||||||||
\(289\) | −1.39434 | −0.0820202 | ||||||||
\(290\) | −4.53710 | −0.266428 | ||||||||
\(291\) | −25.9960 | −1.52391 | ||||||||
\(292\) | 14.7805 | 0.864965 | ||||||||
\(293\) | 12.2025 | 0.712875 | 0.356438 | − | 0.934319i | \(-0.383991\pi\) | ||||
0.356438 | + | 0.934319i | \(0.383991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.8391 | −0.922186 | ||||||||
\(296\) | 57.3722 | 3.33469 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −60.3940 | −3.49853 | ||||||||
\(299\) | −12.4743 | −0.721407 | ||||||||
\(300\) | −11.3281 | −0.654029 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.617673 | 0.0355431 | ||||||||
\(303\) | −21.4864 | −1.23436 | ||||||||
\(304\) | 45.3829 | 2.60289 | ||||||||
\(305\) | 14.8983 | 0.853075 | ||||||||
\(306\) | 15.4292 | 0.882029 | ||||||||
\(307\) | −21.5077 | −1.22751 | −0.613754 | − | 0.789498i | \(-0.710341\pi\) | ||||
−0.613754 | + | 0.789498i | \(0.710341\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2800 | −0.641697 | ||||||||
\(310\) | 52.4921 | 2.98135 | ||||||||
\(311\) | −0.407674 | −0.0231171 | −0.0115585 | − | 0.999933i | \(-0.503679\pi\) | ||||
−0.0115585 | + | 0.999933i | \(0.503679\pi\) | |||||||
\(312\) | −38.8378 | −2.19876 | ||||||||
\(313\) | −17.2967 | −0.977666 | −0.488833 | − | 0.872377i | \(-0.662577\pi\) | ||||
−0.488833 | + | 0.872377i | \(0.662577\pi\) | |||||||
\(314\) | 64.2584 | 3.62631 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.6066 | −0.652925 | ||||||||
\(317\) | 10.5834 | 0.594422 | 0.297211 | − | 0.954812i | \(-0.403943\pi\) | ||||
0.297211 | + | 0.954812i | \(0.403943\pi\) | |||||||
\(318\) | −21.6281 | −1.21284 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −82.2208 | −4.59628 | ||||||||
\(321\) | −33.6760 | −1.87961 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.4014 | 0.634392 | ||||||||
\(324\) | −62.4301 | −3.46834 | ||||||||
\(325\) | 1.83579 | 0.101832 | ||||||||
\(326\) | −33.7041 | −1.86670 | ||||||||
\(327\) | 7.50834 | 0.415212 | ||||||||
\(328\) | −31.9129 | −1.76210 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.19895 | −0.285760 | −0.142880 | − | 0.989740i | \(-0.545636\pi\) | ||||
−0.142880 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(332\) | 21.0102 | 1.15308 | ||||||||
\(333\) | 8.35210 | 0.457692 | ||||||||
\(334\) | 48.4644 | 2.65185 | ||||||||
\(335\) | −10.7497 | −0.587317 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4256 | −0.622393 | −0.311196 | − | 0.950346i | \(-0.600730\pi\) | ||||
−0.311196 | + | 0.950346i | \(0.600730\pi\) | |||||||
\(338\) | −25.8888 | −1.40816 | ||||||||
\(339\) | −30.9606 | −1.68155 | ||||||||
\(340\) | −53.5945 | −2.90657 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 11.2725 | 0.609547 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.4185 | 0.561730 | ||||||||
\(345\) | −33.8740 | −1.82371 | ||||||||
\(346\) | −56.3434 | −3.02904 | ||||||||
\(347\) | 25.9849 | 1.39494 | 0.697470 | − | 0.716614i | \(-0.254309\pi\) | ||||
0.697470 | + | 0.716614i | \(0.254309\pi\) | |||||||
\(348\) | −7.88842 | −0.422863 | ||||||||
\(349\) | −26.4416 | −1.41539 | −0.707694 | − | 0.706519i | \(-0.750264\pi\) | ||||
−0.707694 | + | 0.706519i | \(0.750264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.28076 | 0.335242 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −37.3344 | −1.98711 | −0.993555 | − | 0.113351i | \(-0.963842\pi\) | ||||
−0.993555 | + | 0.113351i | \(0.963842\pi\) | |||||||
\(354\) | −37.4580 | −1.99087 | ||||||||
\(355\) | −20.5234 | −1.08927 | ||||||||
\(356\) | −13.5669 | −0.719042 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.7229 | 0.936686 | ||||||||
\(359\) | −25.3873 | −1.33989 | −0.669945 | − | 0.742410i | \(-0.733683\pi\) | ||||
−0.669945 | + | 0.742410i | \(0.733683\pi\) | |||||||
\(360\) | −33.9018 | −1.78678 | ||||||||
\(361\) | −10.6702 | −0.561588 | ||||||||
\(362\) | −3.72725 | −0.195900 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.50439 | −0.340455 | ||||||||
\(366\) | 35.2333 | 1.84167 | ||||||||
\(367\) | 10.2663 | 0.535897 | 0.267948 | − | 0.963433i | \(-0.413654\pi\) | ||||
0.267948 | + | 0.963433i | \(0.413654\pi\) | |||||||
\(368\) | −103.674 | −5.40441 | ||||||||
\(369\) | −4.64581 | −0.241851 | ||||||||
\(370\) | −39.4618 | −2.05152 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 91.2653 | 4.73188 | ||||||||
\(373\) | −36.7010 | −1.90031 | −0.950154 | − | 0.311782i | \(-0.899074\pi\) | ||||
−0.950154 | + | 0.311782i | \(0.899074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.7034 | −1.06912 | ||||||||
\(376\) | 94.7194 | 4.88478 | ||||||||
\(377\) | 1.27837 | 0.0658393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.26506 | 0.116348 | 0.0581742 | − | 0.998306i | \(-0.481472\pi\) | ||||
0.0581742 | + | 0.998306i | \(0.481472\pi\) | |||||||
\(380\) | −39.1559 | −2.00866 | ||||||||
\(381\) | −36.1374 | −1.85137 | ||||||||
\(382\) | −23.2986 | −1.19206 | ||||||||
\(383\) | −11.4550 | −0.585322 | −0.292661 | − | 0.956216i | \(-0.594541\pi\) | ||||
−0.292661 | + | 0.956216i | \(0.594541\pi\) | |||||||
\(384\) | −94.8288 | −4.83921 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −50.1880 | −2.55450 | ||||||||
\(387\) | 1.51671 | 0.0770985 | ||||||||
\(388\) | 68.6462 | 3.48498 | ||||||||
\(389\) | 14.1205 | 0.715939 | 0.357970 | − | 0.933733i | \(-0.383469\pi\) | ||||
0.357970 | + | 0.933733i | \(0.383469\pi\) | |||||||
\(390\) | 26.7134 | 1.35269 | ||||||||
\(391\) | −26.0458 | −1.31720 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.6286 | 1.44412 | ||||||||
\(394\) | −47.7637 | −2.40630 | ||||||||
\(395\) | 5.10768 | 0.256995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.4119 | −0.974258 | −0.487129 | − | 0.873330i | \(-0.661956\pi\) | ||||
−0.487129 | + | 0.873330i | \(0.661956\pi\) | |||||||
\(398\) | −15.0601 | −0.754893 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.2574 | 0.762869 | ||||||||
\(401\) | 3.95645 | 0.197576 | 0.0987878 | − | 0.995109i | \(-0.468504\pi\) | ||||
0.0987878 | + | 0.995109i | \(0.468504\pi\) | |||||||
\(402\) | −25.4221 | −1.26794 | ||||||||
\(403\) | −14.7901 | −0.736748 | ||||||||
\(404\) | 56.7381 | 2.82283 | ||||||||
\(405\) | 27.4733 | 1.36516 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −81.0919 | −4.01465 | ||||||||
\(409\) | −4.18623 | −0.206996 | −0.103498 | − | 0.994630i | \(-0.533003\pi\) | ||||
−0.103498 | + | 0.994630i | \(0.533003\pi\) | |||||||
\(410\) | 21.9504 | 1.08405 | ||||||||
\(411\) | −0.0233619 | −0.00115236 | ||||||||
\(412\) | 29.7865 | 1.46748 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −25.7514 | −1.26561 | ||||||||
\(415\) | −9.24584 | −0.453860 | ||||||||
\(416\) | 44.8175 | 2.19736 | ||||||||
\(417\) | −45.0374 | −2.20549 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.3050 | 1.04082 | 0.520409 | − | 0.853917i | \(-0.325779\pi\) | ||||
0.520409 | + | 0.853917i | \(0.325779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.4277 | 0.849375 | 0.424688 | − | 0.905340i | \(-0.360384\pi\) | ||||
0.424688 | + | 0.905340i | \(0.360384\pi\) | |||||||
\(422\) | 19.3262 | 0.940783 | ||||||||
\(423\) | 13.7890 | 0.670445 | ||||||||
\(424\) | 36.5401 | 1.77454 | ||||||||
\(425\) | 3.83307 | 0.185931 | ||||||||
\(426\) | −48.5360 | −2.35158 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 88.9265 | 4.29843 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.16609 | −0.345579 | ||||||||
\(431\) | 3.81498 | 0.183761 | 0.0918805 | − | 0.995770i | \(-0.470712\pi\) | ||||
0.0918805 | + | 0.995770i | \(0.470712\pi\) | |||||||
\(432\) | 52.1997 | 2.51146 | ||||||||
\(433\) | −22.6851 | −1.09018 | −0.545088 | − | 0.838379i | \(-0.683504\pi\) | ||||
−0.545088 | + | 0.838379i | \(0.683504\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.47141 | 0.166442 | ||||||||
\(436\) | −19.8269 | −0.949535 | ||||||||
\(437\) | −19.0290 | −0.910279 | ||||||||
\(438\) | −15.3823 | −0.734996 | ||||||||
\(439\) | 5.51513 | 0.263223 | 0.131611 | − | 0.991301i | \(-0.457985\pi\) | ||||
0.131611 | + | 0.991301i | \(0.457985\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.5401 | 0.976992 | ||||||||
\(443\) | −18.7968 | −0.893064 | −0.446532 | − | 0.894768i | \(-0.647341\pi\) | ||||
−0.446532 | + | 0.894768i | \(0.647341\pi\) | |||||||
\(444\) | −68.6101 | −3.25609 | ||||||||
\(445\) | 5.97030 | 0.283019 | ||||||||
\(446\) | −1.15178 | −0.0545384 | ||||||||
\(447\) | 46.2085 | 2.18559 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.4269 | 0.539268 | 0.269634 | − | 0.962963i | \(-0.413097\pi\) | ||||
0.269634 | + | 0.962963i | \(0.413097\pi\) | |||||||
\(450\) | 3.78973 | 0.178650 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 81.7559 | 3.84548 | ||||||||
\(453\) | −0.472592 | −0.0222043 | ||||||||
\(454\) | −70.1894 | −3.29415 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −59.2453 | −2.77442 | ||||||||
\(457\) | 12.3374 | 0.577117 | 0.288559 | − | 0.957462i | \(-0.406824\pi\) | ||||
0.288559 | + | 0.957462i | \(0.406824\pi\) | |||||||
\(458\) | 40.1556 | 1.87635 | ||||||||
\(459\) | 13.1140 | 0.612108 | ||||||||
\(460\) | 89.4493 | 4.17059 | ||||||||
\(461\) | −10.4788 | −0.488046 | −0.244023 | − | 0.969769i | \(-0.578467\pi\) | ||||
−0.244023 | + | 0.969769i | \(0.578467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.05543 | −0.188472 | −0.0942360 | − | 0.995550i | \(-0.530041\pi\) | ||||
−0.0942360 | + | 0.995550i | \(0.530041\pi\) | |||||||
\(464\) | 10.6246 | 0.493234 | ||||||||
\(465\) | −40.1626 | −1.86250 | ||||||||
\(466\) | 47.4651 | 2.19878 | ||||||||
\(467\) | 13.5049 | 0.624932 | 0.312466 | − | 0.949929i | \(-0.398845\pi\) | ||||
0.312466 | + | 0.949929i | \(0.398845\pi\) | |||||||
\(468\) | 14.9300 | 0.690139 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −65.1500 | −3.00514 | ||||||||
\(471\) | −49.1653 | −2.26542 | ||||||||
\(472\) | 63.2844 | 2.91290 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.0792 | 0.554817 | ||||||||
\(475\) | 2.80042 | 0.128492 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.31942 | 0.243559 | ||||||||
\(478\) | 43.6807 | 1.99791 | ||||||||
\(479\) | −6.40998 | −0.292879 | −0.146440 | − | 0.989220i | \(-0.546781\pi\) | ||||
−0.146440 | + | 0.989220i | \(0.546781\pi\) | |||||||
\(480\) | 121.702 | 5.55492 | ||||||||
\(481\) | 11.1187 | 0.506969 | ||||||||
\(482\) | −24.3368 | −1.10851 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.2088 | −1.37171 | ||||||||
\(486\) | 37.6031 | 1.70571 | ||||||||
\(487\) | 7.67581 | 0.347824 | 0.173912 | − | 0.984761i | \(-0.444359\pi\) | ||||
0.173912 | + | 0.984761i | \(0.444359\pi\) | |||||||
\(488\) | −59.5257 | −2.69460 | ||||||||
\(489\) | 25.7876 | 1.16616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9051 | −0.853175 | −0.426588 | − | 0.904446i | \(-0.640284\pi\) | ||||
−0.426588 | + | 0.904446i | \(0.640284\pi\) | |||||||
\(492\) | 38.1640 | 1.72056 | ||||||||
\(493\) | 2.66918 | 0.120214 | ||||||||
\(494\) | 15.0065 | 0.675174 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −122.921 | −5.51934 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −21.8656 | −0.979822 | ||||||||
\(499\) | −16.5765 | −0.742068 | −0.371034 | − | 0.928619i | \(-0.620997\pi\) | ||||
−0.371034 | + | 0.928619i | \(0.620997\pi\) | |||||||
\(500\) | 54.6704 | 2.44493 | ||||||||
\(501\) | −37.0809 | −1.65665 | ||||||||
\(502\) | −30.6190 | −1.36659 | ||||||||
\(503\) | 1.21118 | 0.0540039 | 0.0270020 | − | 0.999635i | \(-0.491404\pi\) | ||||
0.0270020 | + | 0.999635i | \(0.491404\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.9685 | −1.11108 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.8079 | 0.879702 | ||||||||
\(508\) | 95.4261 | 4.23385 | ||||||||
\(509\) | −10.7702 | −0.477380 | −0.238690 | − | 0.971096i | \(-0.576718\pi\) | ||||
−0.238690 | + | 0.971096i | \(0.576718\pi\) | |||||||
\(510\) | 55.7767 | 2.46983 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 65.4587 | 2.89289 | ||||||||
\(513\) | 9.58102 | 0.423012 | ||||||||
\(514\) | 37.8370 | 1.66892 | ||||||||
\(515\) | −13.1080 | −0.577608 | ||||||||
\(516\) | −12.4593 | −0.548490 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.1094 | 1.89229 | ||||||||
\(520\) | −45.1317 | −1.97916 | ||||||||
\(521\) | −38.1463 | −1.67122 | −0.835611 | − | 0.549322i | \(-0.814886\pi\) | ||||
−0.835611 | + | 0.549322i | \(0.814886\pi\) | |||||||
\(522\) | 2.63901 | 0.115506 | ||||||||
\(523\) | −5.58225 | −0.244095 | −0.122047 | − | 0.992524i | \(-0.538946\pi\) | ||||
−0.122047 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(524\) | −75.5981 | −3.30252 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.9564 | 0.695734 | ||||||||
\(527\) | −30.8812 | −1.34521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.4705 | 0.890023 | ||||||||
\(530\) | −25.1330 | −1.09171 | ||||||||
\(531\) | 9.21279 | 0.399801 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.18471 | −0.267890 | ||||||||
\(534\) | 14.1192 | 0.611000 | ||||||||
\(535\) | −39.1334 | −1.69189 | ||||||||
\(536\) | 42.9500 | 1.85516 | ||||||||
\(537\) | −13.5601 | −0.585163 | ||||||||
\(538\) | 17.1237 | 0.738254 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −45.0374 | −1.93810 | ||||||||
\(541\) | 20.0012 | 0.859917 | 0.429959 | − | 0.902849i | \(-0.358528\pi\) | ||||
0.429959 | + | 0.902849i | \(0.358528\pi\) | |||||||
\(542\) | 29.0140 | 1.24626 | ||||||||
\(543\) | 2.85178 | 0.122382 | ||||||||
\(544\) | 93.5773 | 4.01209 | ||||||||
\(545\) | 8.72511 | 0.373743 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.04355 | 0.172890 | 0.0864449 | − | 0.996257i | \(-0.472449\pi\) | ||||
0.0864449 | + | 0.996257i | \(0.472449\pi\) | |||||||
\(548\) | 0.0616906 | 0.00263529 | ||||||||
\(549\) | −8.66561 | −0.369839 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.95009 | 0.0830768 | ||||||||
\(552\) | 135.342 | 5.76055 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 71.4302 | 3.03478 | ||||||||
\(555\) | 30.1929 | 1.28162 | ||||||||
\(556\) | 118.928 | 5.04366 | ||||||||
\(557\) | −17.9326 | −0.759827 | −0.379913 | − | 0.925022i | \(-0.624046\pi\) | ||||
−0.379913 | + | 0.925022i | \(0.624046\pi\) | |||||||
\(558\) | −30.5321 | −1.29252 | ||||||||
\(559\) | 2.01911 | 0.0853992 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 35.2224 | 1.48577 | ||||||||
\(563\) | 14.9267 | 0.629085 | 0.314542 | − | 0.949243i | \(-0.398149\pi\) | ||||
0.314542 | + | 0.949243i | \(0.398149\pi\) | |||||||
\(564\) | −113.273 | −4.76965 | ||||||||
\(565\) | −35.9779 | −1.51360 | ||||||||
\(566\) | −85.9663 | −3.61343 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 82.0003 | 3.44066 | ||||||||
\(569\) | −35.2133 | −1.47622 | −0.738110 | − | 0.674681i | \(-0.764281\pi\) | ||||
−0.738110 | + | 0.674681i | \(0.764281\pi\) | |||||||
\(570\) | 40.7502 | 1.70684 | ||||||||
\(571\) | 6.78432 | 0.283915 | 0.141958 | − | 0.989873i | \(-0.454660\pi\) | ||||
0.141958 | + | 0.989873i | \(0.454660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.8262 | 0.744699 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.39739 | −0.266790 | ||||||||
\(576\) | 47.8237 | 1.99266 | ||||||||
\(577\) | 35.4345 | 1.47516 | 0.737579 | − | 0.675261i | \(-0.235969\pi\) | ||||
0.737579 | + | 0.675261i | \(0.235969\pi\) | |||||||
\(578\) | −3.83188 | −0.159385 | ||||||||
\(579\) | 38.3997 | 1.59584 | ||||||||
\(580\) | −9.16678 | −0.380630 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −71.4412 | −2.96133 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 25.9881 | 1.07539 | ||||||||
\(585\) | −6.57016 | −0.271643 | ||||||||
\(586\) | 33.5344 | 1.38529 | ||||||||
\(587\) | 24.5453 | 1.01309 | 0.506547 | − | 0.862212i | \(-0.330922\pi\) | ||||
0.506547 | + | 0.862212i | \(0.330922\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.5617 | −0.929638 | ||||||||
\(590\) | −43.5283 | −1.79203 | ||||||||
\(591\) | 36.5448 | 1.50325 | ||||||||
\(592\) | 92.4082 | 3.79795 | ||||||||
\(593\) | 19.5710 | 0.803683 | 0.401842 | − | 0.915709i | \(-0.368370\pi\) | ||||
0.401842 | + | 0.915709i | \(0.368370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −122.020 | −4.99815 | ||||||||
\(597\) | 11.5227 | 0.471594 | ||||||||
\(598\) | −34.2814 | −1.40187 | ||||||||
\(599\) | 36.4275 | 1.48839 | 0.744193 | − | 0.667965i | \(-0.232834\pi\) | ||||
0.744193 | + | 0.667965i | \(0.232834\pi\) | |||||||
\(600\) | −19.9178 | −0.813142 | ||||||||
\(601\) | 15.5885 | 0.635866 | 0.317933 | − | 0.948113i | \(-0.397011\pi\) | ||||
0.317933 | + | 0.948113i | \(0.397011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.25255 | 0.254624 | ||||||||
\(604\) | 1.24795 | 0.0507783 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −59.0483 | −2.39867 | ||||||||
\(607\) | −10.4999 | −0.426177 | −0.213089 | − | 0.977033i | \(-0.568352\pi\) | ||||
−0.213089 | + | 0.977033i | \(0.568352\pi\) | |||||||
\(608\) | 68.3672 | 2.77265 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 40.9430 | 1.65774 | ||||||||
\(611\) | 18.3566 | 0.742628 | ||||||||
\(612\) | 31.1733 | 1.26010 | ||||||||
\(613\) | −10.3208 | −0.416853 | −0.208427 | − | 0.978038i | \(-0.566834\pi\) | ||||
−0.208427 | + | 0.978038i | \(0.566834\pi\) | |||||||
\(614\) | −59.1066 | −2.38535 | ||||||||
\(615\) | −16.7946 | −0.677225 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8079 | 0.757179 | 0.378590 | − | 0.925565i | \(-0.376409\pi\) | ||||
0.378590 | + | 0.925565i | \(0.376409\pi\) | |||||||
\(618\) | −30.9993 | −1.24697 | ||||||||
\(619\) | −16.1480 | −0.649043 | −0.324521 | − | 0.945878i | \(-0.605203\pi\) | ||||
−0.324521 | + | 0.945878i | \(0.605203\pi\) | |||||||
\(620\) | 106.055 | 4.25929 | ||||||||
\(621\) | −21.8872 | −0.878305 | ||||||||
\(622\) | −1.12035 | −0.0449221 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −62.5552 | −2.50421 | ||||||||
\(625\) | −28.9100 | −1.15640 | ||||||||
\(626\) | −47.5341 | −1.89985 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 129.828 | 5.18071 | ||||||||
\(629\) | 23.2154 | 0.925660 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.5398 | −0.817678 | −0.408839 | − | 0.912607i | \(-0.634066\pi\) | ||||
−0.408839 | + | 0.912607i | \(0.634066\pi\) | |||||||
\(632\) | −20.4075 | −0.811768 | ||||||||
\(633\) | −14.7868 | −0.587722 | ||||||||
\(634\) | 29.0849 | 1.15511 | ||||||||
\(635\) | −41.9937 | −1.66647 | ||||||||
\(636\) | −43.6975 | −1.73272 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.9374 | 0.472237 | ||||||||
\(640\) | −110.196 | −4.35590 | ||||||||
\(641\) | 33.6667 | 1.32976 | 0.664878 | − | 0.746952i | \(-0.268484\pi\) | ||||
0.664878 | + | 0.746952i | \(0.268484\pi\) | |||||||
\(642\) | −92.5472 | −3.65255 | ||||||||
\(643\) | −22.3937 | −0.883123 | −0.441562 | − | 0.897231i | \(-0.645575\pi\) | ||||
−0.441562 | + | 0.897231i | \(0.645575\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.48290 | 0.215889 | ||||||||
\(646\) | 31.3330 | 1.23278 | ||||||||
\(647\) | −25.1811 | −0.989970 | −0.494985 | − | 0.868902i | \(-0.664826\pi\) | ||||
−0.494985 | + | 0.868902i | \(0.664826\pi\) | |||||||
\(648\) | −109.769 | −4.31212 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.04506 | 0.197884 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −68.0960 | −2.66684 | ||||||||
\(653\) | −7.68403 | −0.300699 | −0.150350 | − | 0.988633i | \(-0.548040\pi\) | ||||
−0.150350 | + | 0.988633i | \(0.548040\pi\) | |||||||
\(654\) | 20.6341 | 0.806859 | ||||||||
\(655\) | 33.2681 | 1.29989 | ||||||||
\(656\) | −51.4015 | −2.00689 | ||||||||
\(657\) | 3.78328 | 0.147600 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.4280 | 1.02949 | 0.514745 | − | 0.857344i | \(-0.327887\pi\) | ||||
0.514745 | + | 0.857344i | \(0.327887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.6085 | −1.22943 | −0.614715 | − | 0.788749i | \(-0.710729\pi\) | ||||
−0.614715 | + | 0.788749i | \(0.710729\pi\) | |||||||
\(662\) | −14.2876 | −0.555302 | ||||||||
\(663\) | −15.7156 | −0.610342 | ||||||||
\(664\) | 36.9414 | 1.43361 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 22.9530 | 0.889409 | ||||||||
\(667\) | −4.45487 | −0.172493 | ||||||||
\(668\) | 97.9177 | 3.78855 | ||||||||
\(669\) | 0.881247 | 0.0340710 | ||||||||
\(670\) | −29.5419 | −1.14130 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.6584 | −0.873418 | −0.436709 | − | 0.899603i | \(-0.643856\pi\) | ||||
−0.436709 | + | 0.899603i | \(0.643856\pi\) | |||||||
\(674\) | −31.3995 | −1.20946 | ||||||||
\(675\) | 3.22106 | 0.123979 | ||||||||
\(676\) | −52.3058 | −2.01176 | ||||||||
\(677\) | 26.9107 | 1.03426 | 0.517130 | − | 0.855907i | \(-0.327000\pi\) | ||||
0.517130 | + | 0.855907i | \(0.327000\pi\) | |||||||
\(678\) | −85.0847 | −3.26766 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −94.2333 | −3.61368 | ||||||||
\(681\) | 53.7032 | 2.05791 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1197 | −0.463747 | −0.231874 | − | 0.972746i | \(-0.574486\pi\) | ||||
−0.231874 | + | 0.972746i | \(0.574486\pi\) | |||||||
\(684\) | 22.7750 | 0.870825 | ||||||||
\(685\) | −0.0271479 | −0.00103727 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.7237 | −1.17218 | ||||||||
\(688\) | 16.7809 | 0.639767 | ||||||||
\(689\) | 7.08145 | 0.269782 | ||||||||
\(690\) | −93.0913 | −3.54392 | ||||||||
\(691\) | 10.0908 | 0.383872 | 0.191936 | − | 0.981407i | \(-0.438523\pi\) | ||||
0.191936 | + | 0.981407i | \(0.438523\pi\) | |||||||
\(692\) | −113.837 | −4.32742 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 71.4107 | 2.71071 | ||||||||
\(695\) | −52.3360 | −1.98522 | ||||||||
\(696\) | −13.8699 | −0.525738 | ||||||||
\(697\) | −12.9135 | −0.489132 | ||||||||
\(698\) | −72.6659 | −2.75045 | ||||||||
\(699\) | −36.3164 | −1.37361 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0714 | 0.871395 | 0.435698 | − | 0.900093i | \(-0.356502\pi\) | ||||
0.435698 | + | 0.900093i | \(0.356502\pi\) | |||||||
\(702\) | 17.2606 | 0.651458 | ||||||||
\(703\) | 16.9611 | 0.639700 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 49.8474 | 1.87736 | ||||||||
\(706\) | −102.601 | −3.86144 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −75.6804 | −2.84424 | ||||||||
\(709\) | 42.1958 | 1.58470 | 0.792348 | − | 0.610070i | \(-0.208859\pi\) | ||||
0.792348 | + | 0.610070i | \(0.208859\pi\) | |||||||
\(710\) | −56.4015 | −2.11671 | ||||||||
\(711\) | −2.97088 | −0.111417 | ||||||||
\(712\) | −23.8541 | −0.893971 | ||||||||
\(713\) | 51.5408 | 1.93022 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 35.8075 | 1.33819 | ||||||||
\(717\) | −33.4208 | −1.24812 | ||||||||
\(718\) | −69.7685 | −2.60374 | ||||||||
\(719\) | 51.2748 | 1.91223 | 0.956114 | − | 0.292995i | \(-0.0946519\pi\) | ||||
0.956114 | + | 0.292995i | \(0.0946519\pi\) | |||||||
\(720\) | −54.6050 | −2.03501 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −29.3234 | −1.09130 | ||||||||
\(723\) | 18.6205 | 0.692504 | ||||||||
\(724\) | −7.53056 | −0.279871 | ||||||||
\(725\) | 0.655606 | 0.0243486 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.742649 | −0.0275433 | −0.0137717 | − | 0.999905i | \(-0.504384\pi\) | ||||
−0.0137717 | + | 0.999905i | \(0.504384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.96059 | 0.183725 | ||||||||
\(730\) | −17.8751 | −0.661588 | ||||||||
\(731\) | 4.21582 | 0.155928 | ||||||||
\(732\) | 71.1855 | 2.63109 | ||||||||
\(733\) | 8.53582 | 0.315278 | 0.157639 | − | 0.987497i | \(-0.449612\pi\) | ||||
0.157639 | + | 0.987497i | \(0.449612\pi\) | |||||||
\(734\) | 28.2135 | 1.04138 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −156.181 | −5.75689 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.7674 | −0.469976 | ||||||||
\(739\) | −10.7081 | −0.393902 | −0.196951 | − | 0.980413i | \(-0.563104\pi\) | ||||
−0.196951 | + | 0.980413i | \(0.563104\pi\) | |||||||
\(740\) | −79.7288 | −2.93089 | ||||||||
\(741\) | −11.4817 | −0.421792 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.7623 | −1.75223 | −0.876114 | − | 0.482103i | \(-0.839873\pi\) | ||||
−0.876114 | + | 0.482103i | \(0.839873\pi\) | |||||||
\(744\) | 160.468 | 5.88306 | ||||||||
\(745\) | 53.6969 | 1.96730 | ||||||||
\(746\) | −100.860 | −3.69276 | ||||||||
\(747\) | 5.37784 | 0.196765 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −56.8963 | −2.07756 | ||||||||
\(751\) | 11.0243 | 0.402284 | 0.201142 | − | 0.979562i | \(-0.435535\pi\) | ||||
0.201142 | + | 0.979562i | \(0.435535\pi\) | |||||||
\(752\) | 152.563 | 5.56338 | ||||||||
\(753\) | 23.4272 | 0.853733 | ||||||||
\(754\) | 3.51317 | 0.127942 | ||||||||
\(755\) | −0.549179 | −0.0199867 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.6362 | 1.14984 | 0.574919 | − | 0.818210i | \(-0.305034\pi\) | ||||
0.574919 | + | 0.818210i | \(0.305034\pi\) | |||||||
\(758\) | 6.22476 | 0.226093 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −68.8464 | −2.49732 | ||||||||
\(761\) | −24.6478 | −0.893484 | −0.446742 | − | 0.894663i | \(-0.647416\pi\) | ||||
−0.446742 | + | 0.894663i | \(0.647416\pi\) | |||||||
\(762\) | −99.3115 | −3.59767 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −47.0726 | −1.70303 | ||||||||
\(765\) | −13.7183 | −0.495985 | ||||||||
\(766\) | −31.4802 | −1.13743 | ||||||||
\(767\) | 12.2645 | 0.442845 | ||||||||
\(768\) | −119.096 | −4.29751 | ||||||||
\(769\) | −24.1344 | −0.870307 | −0.435154 | − | 0.900356i | \(-0.643306\pi\) | ||||
−0.435154 | + | 0.900356i | \(0.643306\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.9498 | −1.04260 | ||||||||
\(772\) | −101.400 | −3.64947 | ||||||||
\(773\) | −15.7682 | −0.567142 | −0.283571 | − | 0.958951i | \(-0.591519\pi\) | ||||
−0.283571 | + | 0.958951i | \(0.591519\pi\) | |||||||
\(774\) | 4.16816 | 0.149821 | ||||||||
\(775\) | −7.58506 | −0.272463 | ||||||||
\(776\) | 120.698 | 4.33281 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.8055 | 1.39125 | ||||||||
\(779\) | −9.43451 | −0.338026 | ||||||||
\(780\) | 53.9720 | 1.93251 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −71.5783 | −2.55963 | ||||||||
\(783\) | 2.24301 | 0.0801587 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −57.1328 | −2.03916 | ||||||||
\(786\) | 78.6761 | 2.80628 | ||||||||
\(787\) | −55.5828 | −1.98131 | −0.990656 | − | 0.136387i | \(-0.956451\pi\) | ||||
−0.990656 | + | 0.136387i | \(0.956451\pi\) | |||||||
\(788\) | −96.5020 | −3.43774 | ||||||||
\(789\) | −12.2086 | −0.434636 | ||||||||
\(790\) | 14.0367 | 0.499405 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5361 | −0.409658 | ||||||||
\(794\) | −53.3472 | −1.89322 | ||||||||
\(795\) | 19.2297 | 0.682008 | ||||||||
\(796\) | −30.4274 | −1.07847 | ||||||||
\(797\) | −32.2398 | −1.14199 | −0.570997 | − | 0.820952i | \(-0.693443\pi\) | ||||
−0.570997 | + | 0.820952i | \(0.693443\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.3279 | 1.35594 | ||||||||
\(800\) | 22.9845 | 0.812625 | ||||||||
\(801\) | −3.47263 | −0.122699 | ||||||||
\(802\) | 10.8730 | 0.383938 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −51.3629 | −1.81143 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −40.6457 | −1.43168 | ||||||||
\(807\) | −13.1016 | −0.461199 | ||||||||
\(808\) | 99.7606 | 3.50957 | ||||||||
\(809\) | 49.4935 | 1.74010 | 0.870050 | − | 0.492963i | \(-0.164086\pi\) | ||||
0.870050 | + | 0.492963i | \(0.164086\pi\) | |||||||
\(810\) | 75.5012 | 2.65284 | ||||||||
\(811\) | −13.7840 | −0.484022 | −0.242011 | − | 0.970273i | \(-0.577807\pi\) | ||||
−0.242011 | + | 0.970273i | \(0.577807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.1991 | −0.778558 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.9667 | 1.04969 | ||||||||
\(816\) | −130.613 | −4.57237 | ||||||||
\(817\) | 3.08006 | 0.107758 | ||||||||
\(818\) | −11.5044 | −0.402243 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 44.3487 | 1.54872 | ||||||||
\(821\) | 2.18076 | 0.0761091 | 0.0380545 | − | 0.999276i | \(-0.487884\pi\) | ||||
0.0380545 | + | 0.999276i | \(0.487884\pi\) | |||||||
\(822\) | −0.0642024 | −0.00223932 | ||||||||
\(823\) | 46.2602 | 1.61253 | 0.806265 | − | 0.591555i | \(-0.201486\pi\) | ||||
0.806265 | + | 0.591555i | \(0.201486\pi\) | |||||||
\(824\) | 52.3726 | 1.82448 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.27184 | −0.183320 | −0.0916599 | − | 0.995790i | \(-0.529217\pi\) | ||||
−0.0916599 | + | 0.995790i | \(0.529217\pi\) | |||||||
\(828\) | −52.0282 | −1.80810 | ||||||||
\(829\) | −13.9453 | −0.484339 | −0.242170 | − | 0.970234i | \(-0.577859\pi\) | ||||
−0.242170 | + | 0.970234i | \(0.577859\pi\) | |||||||
\(830\) | −25.4091 | −0.881962 | ||||||||
\(831\) | −54.6525 | −1.89587 | ||||||||
\(832\) | 63.6652 | 2.20719 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −123.770 | −4.28581 | ||||||||
\(835\) | −43.0901 | −1.49120 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.9506 | −0.896983 | ||||||||
\(838\) | 58.5497 | 2.02257 | ||||||||
\(839\) | 22.6533 | 0.782077 | 0.391039 | − | 0.920374i | \(-0.372116\pi\) | ||||
0.391039 | + | 0.920374i | \(0.372116\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5435 | −0.984257 | ||||||||
\(842\) | 47.8943 | 1.65054 | ||||||||
\(843\) | −26.9493 | −0.928182 | ||||||||
\(844\) | 39.0467 | 1.34404 | ||||||||
\(845\) | 23.0179 | 0.791841 | ||||||||
\(846\) | 37.8945 | 1.30284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 58.8543 | 2.02107 | ||||||||
\(849\) | 65.7743 | 2.25737 | ||||||||
\(850\) | 10.5339 | 0.361310 | ||||||||
\(851\) | −38.7466 | −1.32822 | ||||||||
\(852\) | −98.0624 | −3.35956 | ||||||||
\(853\) | 19.7192 | 0.675172 | 0.337586 | − | 0.941295i | \(-0.390390\pi\) | ||||
0.337586 | + | 0.941295i | \(0.390390\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.0225 | −0.342762 | ||||||||
\(856\) | 156.356 | 5.34415 | ||||||||
\(857\) | −13.6176 | −0.465168 | −0.232584 | − | 0.972576i | \(-0.574718\pi\) | ||||
−0.232584 | + | 0.972576i | \(0.574718\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.2078 | −0.723600 | −0.361800 | − | 0.932256i | \(-0.617838\pi\) | ||||
−0.361800 | + | 0.932256i | \(0.617838\pi\) | |||||||
\(860\) | −14.4784 | −0.493710 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.4842 | 0.357093 | ||||||||
\(863\) | −9.69536 | −0.330034 | −0.165017 | − | 0.986291i | \(-0.552768\pi\) | ||||
−0.165017 | + | 0.986291i | \(0.552768\pi\) | |||||||
\(864\) | 78.6363 | 2.67526 | ||||||||
\(865\) | 50.0955 | 1.70330 | ||||||||
\(866\) | −62.3424 | −2.11848 | ||||||||
\(867\) | 2.93184 | 0.0995705 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 9.54002 | 0.323437 | ||||||||
\(871\) | 8.32368 | 0.282037 | ||||||||
\(872\) | −34.8609 | −1.18054 | ||||||||
\(873\) | 17.5710 | 0.594687 | ||||||||
\(874\) | −52.2947 | −1.76890 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.0785 | −1.05005 | ||||||||
\(877\) | −28.9184 | −0.976505 | −0.488252 | − | 0.872702i | \(-0.662365\pi\) | ||||
−0.488252 | + | 0.872702i | \(0.662365\pi\) | |||||||
\(878\) | 15.1565 | 0.511507 | ||||||||
\(879\) | −25.6577 | −0.865414 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.7222 | −1.00137 | −0.500683 | − | 0.865631i | \(-0.666918\pi\) | ||||
−0.500683 | + | 0.865631i | \(0.666918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.4560 | −0.890316 | −0.445158 | − | 0.895452i | \(-0.646853\pi\) | ||||
−0.445158 | + | 0.895452i | \(0.646853\pi\) | |||||||
\(884\) | 41.4993 | 1.39577 | ||||||||
\(885\) | 33.3043 | 1.11951 | ||||||||
\(886\) | −51.6568 | −1.73544 | ||||||||
\(887\) | 2.52809 | 0.0848850 | 0.0424425 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424425 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(888\) | −120.635 | −4.04823 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.4074 | 0.549976 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.32706 | −0.0779158 | ||||||||
\(893\) | 28.0022 | 0.937056 | ||||||||
\(894\) | 126.989 | 4.24713 | ||||||||
\(895\) | −15.7576 | −0.526719 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.2293 | 0.875771 | ||||||||
\(898\) | 31.4030 | 1.04793 | ||||||||
\(899\) | −5.28191 | −0.176162 | ||||||||
\(900\) | 7.65679 | 0.255226 | ||||||||
\(901\) | 14.7858 | 0.492587 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 143.749 | 4.78100 | ||||||||
\(905\) | 3.31393 | 0.110159 | ||||||||
\(906\) | −1.29876 | −0.0431484 | ||||||||
\(907\) | 38.4844 | 1.27785 | 0.638926 | − | 0.769268i | \(-0.279379\pi\) | ||||
0.638926 | + | 0.769268i | \(0.279379\pi\) | |||||||
\(908\) | −141.811 | −4.70617 | ||||||||
\(909\) | 14.5229 | 0.481695 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.0724 | 1.02948 | 0.514738 | − | 0.857348i | \(-0.327889\pi\) | ||||
0.514738 | + | 0.857348i | \(0.327889\pi\) | |||||||
\(912\) | −95.4252 | −3.15984 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 33.9051 | 1.12148 | ||||||||
\(915\) | −31.3262 | −1.03561 | ||||||||
\(916\) | 81.1305 | 2.68063 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 36.0394 | 1.18948 | ||||||||
\(919\) | 25.3894 | 0.837520 | 0.418760 | − | 0.908097i | \(-0.362465\pi\) | ||||
0.418760 | + | 0.908097i | \(0.362465\pi\) | |||||||
\(920\) | 157.275 | 5.18522 | ||||||||
\(921\) | 45.2235 | 1.49016 | ||||||||
\(922\) | −28.7975 | −0.948394 | ||||||||
\(923\) | 15.8916 | 0.523080 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.70219 | 0.187487 | ||||||||
\(926\) | −11.1450 | −0.366247 | ||||||||
\(927\) | 7.62427 | 0.250414 | ||||||||
\(928\) | 16.0054 | 0.525404 | ||||||||
\(929\) | 13.2344 | 0.434206 | 0.217103 | − | 0.976149i | \(-0.430339\pi\) | ||||
0.217103 | + | 0.976149i | \(0.430339\pi\) | |||||||
\(930\) | −110.374 | −3.61929 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 95.8988 | 3.14127 | ||||||||
\(933\) | 0.857203 | 0.0280636 | ||||||||
\(934\) | 37.1137 | 1.21440 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 26.2509 | 0.858036 | ||||||||
\(937\) | 12.3994 | 0.405069 | 0.202535 | − | 0.979275i | \(-0.435082\pi\) | ||||
0.202535 | + | 0.979275i | \(0.435082\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.3692 | 1.18686 | ||||||||
\(940\) | −131.629 | −4.29328 | ||||||||
\(941\) | 29.5103 | 0.962009 | 0.481004 | − | 0.876718i | \(-0.340272\pi\) | ||||
0.481004 | + | 0.876718i | \(0.340272\pi\) | |||||||
\(942\) | −135.114 | −4.40226 | ||||||||
\(943\) | 21.5526 | 0.701848 | ||||||||
\(944\) | 101.931 | 3.31757 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.423958 | 0.0137768 | 0.00688838 | − | 0.999976i | \(-0.497807\pi\) | ||||
0.00688838 | + | 0.999976i | \(0.497807\pi\) | |||||||
\(948\) | 24.4049 | 0.792635 | ||||||||
\(949\) | 5.03648 | 0.163491 | ||||||||
\(950\) | 7.69602 | 0.249692 | ||||||||
\(951\) | −22.2534 | −0.721614 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −57.5354 | −1.86376 | −0.931878 | − | 0.362773i | \(-0.881830\pi\) | ||||
−0.931878 | + | 0.362773i | \(0.881830\pi\) | |||||||
\(954\) | 14.6186 | 0.473296 | ||||||||
\(955\) | 20.7150 | 0.670322 | ||||||||
\(956\) | 88.2527 | 2.85430 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.6157 | −0.569137 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 172.883 | 5.57978 | ||||||||
\(961\) | 30.1092 | 0.971265 | ||||||||
\(962\) | 30.5560 | 0.985166 | ||||||||
\(963\) | 22.7620 | 0.733494 | ||||||||
\(964\) | −49.1702 | −1.58366 | ||||||||
\(965\) | 44.6227 | 1.43645 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.79491 | 0.122036 | 0.0610180 | − | 0.998137i | \(-0.480565\pi\) | ||||
0.0610180 | + | 0.998137i | \(0.480565\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.9734 | −0.770137 | ||||||||
\(970\) | −83.0187 | −2.66557 | ||||||||
\(971\) | 1.02111 | 0.0327690 | 0.0163845 | − | 0.999866i | \(-0.494784\pi\) | ||||
0.0163845 | + | 0.999866i | \(0.494784\pi\) | |||||||
\(972\) | 75.9735 | 2.43685 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.0944 | 0.675908 | ||||||||
\(975\) | −3.86007 | −0.123621 | ||||||||
\(976\) | −95.8768 | −3.06894 | ||||||||
\(977\) | −46.4645 | −1.48653 | −0.743266 | − | 0.668996i | \(-0.766724\pi\) | ||||
−0.743266 | + | 0.668996i | \(0.766724\pi\) | |||||||
\(978\) | 70.8686 | 2.26613 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.07496 | −0.162031 | ||||||||
\(982\) | −51.9543 | −1.65793 | ||||||||
\(983\) | −2.77930 | −0.0886459 | −0.0443229 | − | 0.999017i | \(-0.514113\pi\) | ||||
−0.0443229 | + | 0.999017i | \(0.514113\pi\) | |||||||
\(984\) | 67.1023 | 2.13914 | ||||||||
\(985\) | 42.4672 | 1.35312 | ||||||||
\(986\) | 7.33536 | 0.233605 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30.3192 | 0.964582 | ||||||||
\(989\) | −7.03621 | −0.223738 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.66335 | 0.0528381 | 0.0264190 | − | 0.999651i | \(-0.491590\pi\) | ||||
0.0264190 | + | 0.999651i | \(0.491590\pi\) | |||||||
\(992\) | −185.175 | −5.87932 | ||||||||
\(993\) | 10.9317 | 0.346906 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.3901 | 0.424493 | ||||||||
\(996\) | −44.1774 | −1.39982 | ||||||||
\(997\) | −33.6708 | −1.06637 | −0.533183 | − | 0.846000i | \(-0.679004\pi\) | ||||
−0.533183 | + | 0.846000i | \(0.679004\pi\) | |||||||
\(998\) | −45.5550 | −1.44202 | ||||||||
\(999\) | 19.5088 | 0.617230 |
(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 | 5929.2.a.bv.1.9 | 10 | ||
7.6 | odd | 2 | inner | 5929.2.a.bv.1.10 | 10 | ||
11.10 | odd | 2 | 539.2.a.l.1.1 | ✓ | 10 | ||
33.32 | even | 2 | 4851.2.a.cg.1.10 | 10 | |||
44.43 | even | 2 | 8624.2.a.df.1.7 | 10 | |||
77.10 | even | 6 | 539.2.e.o.177.9 | 20 | |||
77.32 | odd | 6 | 539.2.e.o.177.10 | 20 | |||
77.54 | even | 6 | 539.2.e.o.67.9 | 20 | |||
77.65 | odd | 6 | 539.2.e.o.67.10 | 20 | |||
77.76 | even | 2 | 539.2.a.l.1.2 | yes | 10 | ||
231.230 | odd | 2 | 4851.2.a.cg.1.9 | 10 | |||
308.307 | odd | 2 | 8624.2.a.df.1.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
539.2.a.l.1.1 | ✓ | 10 | 11.10 | odd | 2 | ||
539.2.a.l.1.2 | yes | 10 | 77.76 | even | 2 | ||
539.2.e.o.67.9 | 20 | 77.54 | even | 6 | |||
539.2.e.o.67.10 | 20 | 77.65 | odd | 6 | |||
539.2.e.o.177.9 | 20 | 77.10 | even | 6 | |||
539.2.e.o.177.10 | 20 | 77.32 | odd | 6 | |||
4851.2.a.cg.1.9 | 10 | 231.230 | odd | 2 | |||
4851.2.a.cg.1.10 | 10 | 33.32 | even | 2 | |||
5929.2.a.bv.1.9 | 10 | 1.1 | even | 1 | trivial | ||
5929.2.a.bv.1.10 | 10 | 7.6 | odd | 2 | inner | ||
8624.2.a.df.1.4 | 10 | 308.307 | odd | 2 | |||
8624.2.a.df.1.7 | 10 | 44.43 | even | 2 |