Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(1\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41856 | −1.71018 | −0.855091 | − | 0.518477i | \(-0.826499\pi\) | ||||
−0.855091 | + | 0.518477i | \(0.826499\pi\) | |||||||
\(3\) | 2.09832 | 1.21147 | 0.605734 | − | 0.795667i | \(-0.292880\pi\) | ||||
0.605734 | + | 0.795667i | \(0.292880\pi\) | |||||||
\(4\) | 3.84945 | 1.92473 | ||||||||
\(5\) | −1.02982 | −0.460550 | −0.230275 | − | 0.973126i | \(-0.573963\pi\) | ||||
−0.230275 | + | 0.973126i | \(0.573963\pi\) | |||||||
\(6\) | −5.07493 | −2.07183 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −4.47302 | −1.58145 | ||||||||
\(9\) | 1.40297 | 0.467655 | ||||||||
\(10\) | 2.49069 | 0.787626 | ||||||||
\(11\) | 1.48551 | 0.447899 | 0.223950 | − | 0.974601i | \(-0.428105\pi\) | ||||
0.223950 | + | 0.974601i | \(0.428105\pi\) | |||||||
\(12\) | 8.07740 | 2.33174 | ||||||||
\(13\) | 1.08201 | 0.300096 | 0.150048 | − | 0.988679i | \(-0.452057\pi\) | ||||
0.150048 | + | 0.988679i | \(0.452057\pi\) | |||||||
\(14\) | 2.41856 | 0.646388 | ||||||||
\(15\) | −2.16090 | −0.557942 | ||||||||
\(16\) | 3.11937 | 0.779844 | ||||||||
\(17\) | −3.39749 | −0.824013 | −0.412006 | − | 0.911181i | \(-0.635172\pi\) | ||||
−0.412006 | + | 0.911181i | \(0.635172\pi\) | |||||||
\(18\) | −3.39316 | −0.799776 | ||||||||
\(19\) | −1.89904 | −0.435669 | −0.217835 | − | 0.975986i | \(-0.569899\pi\) | ||||
−0.217835 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(20\) | −3.96425 | −0.886433 | ||||||||
\(21\) | −2.09832 | −0.457892 | ||||||||
\(22\) | −3.59281 | −0.765990 | ||||||||
\(23\) | −0.994082 | −0.207280 | −0.103640 | − | 0.994615i | \(-0.533049\pi\) | ||||
−0.103640 | + | 0.994615i | \(0.533049\pi\) | |||||||
\(24\) | −9.38584 | −1.91588 | ||||||||
\(25\) | −3.93947 | −0.787893 | ||||||||
\(26\) | −2.61691 | −0.513219 | ||||||||
\(27\) | −3.35110 | −0.644919 | ||||||||
\(28\) | −3.84945 | −0.727478 | ||||||||
\(29\) | 10.1257 | 1.88030 | 0.940149 | − | 0.340762i | \(-0.110685\pi\) | ||||
0.940149 | + | 0.340762i | \(0.110685\pi\) | |||||||
\(30\) | 5.22628 | 0.954183 | ||||||||
\(31\) | 5.73591 | 1.03020 | 0.515100 | − | 0.857130i | \(-0.327755\pi\) | ||||
0.515100 | + | 0.857130i | \(0.327755\pi\) | |||||||
\(32\) | 1.40163 | 0.247775 | ||||||||
\(33\) | 3.11709 | 0.542616 | ||||||||
\(34\) | 8.21705 | 1.40921 | ||||||||
\(35\) | 1.02982 | 0.174072 | ||||||||
\(36\) | 5.40065 | 0.900109 | ||||||||
\(37\) | 3.51074 | 0.577162 | 0.288581 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288581 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(38\) | 4.59294 | 0.745074 | ||||||||
\(39\) | 2.27041 | 0.363556 | ||||||||
\(40\) | 4.60641 | 0.728338 | ||||||||
\(41\) | −3.95945 | −0.618362 | −0.309181 | − | 0.951003i | \(-0.600055\pi\) | ||||
−0.309181 | + | 0.951003i | \(0.600055\pi\) | |||||||
\(42\) | 5.07493 | 0.783079 | ||||||||
\(43\) | −9.30767 | −1.41941 | −0.709703 | − | 0.704501i | \(-0.751171\pi\) | ||||
−0.709703 | + | 0.704501i | \(0.751171\pi\) | |||||||
\(44\) | 5.71841 | 0.862083 | ||||||||
\(45\) | −1.44481 | −0.215379 | ||||||||
\(46\) | 2.40425 | 0.354487 | ||||||||
\(47\) | −1.20677 | −0.176026 | −0.0880130 | − | 0.996119i | \(-0.528052\pi\) | ||||
−0.0880130 | + | 0.996119i | \(0.528052\pi\) | |||||||
\(48\) | 6.54546 | 0.944756 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 9.52785 | 1.34744 | ||||||||
\(51\) | −7.12904 | −0.998266 | ||||||||
\(52\) | 4.16515 | 0.577602 | ||||||||
\(53\) | 12.5017 | 1.71725 | 0.858623 | − | 0.512608i | \(-0.171321\pi\) | ||||
0.858623 | + | 0.512608i | \(0.171321\pi\) | |||||||
\(54\) | 8.10484 | 1.10293 | ||||||||
\(55\) | −1.52981 | −0.206280 | ||||||||
\(56\) | 4.47302 | 0.597732 | ||||||||
\(57\) | −3.98480 | −0.527799 | ||||||||
\(58\) | −24.4897 | −3.21566 | ||||||||
\(59\) | −5.80890 | −0.756255 | −0.378127 | − | 0.925754i | \(-0.623432\pi\) | ||||
−0.378127 | + | 0.925754i | \(0.623432\pi\) | |||||||
\(60\) | −8.31828 | −1.07389 | ||||||||
\(61\) | 6.88980 | 0.882148 | 0.441074 | − | 0.897471i | \(-0.354598\pi\) | ||||
0.441074 | + | 0.897471i | \(0.354598\pi\) | |||||||
\(62\) | −13.8727 | −1.76183 | ||||||||
\(63\) | −1.40297 | −0.176757 | ||||||||
\(64\) | −9.62867 | −1.20358 | ||||||||
\(65\) | −1.11428 | −0.138209 | ||||||||
\(66\) | −7.53888 | −0.927972 | ||||||||
\(67\) | 0.104871 | 0.0128120 | 0.00640602 | − | 0.999979i | \(-0.497961\pi\) | ||||
0.00640602 | + | 0.999979i | \(0.497961\pi\) | |||||||
\(68\) | −13.0785 | −1.58600 | ||||||||
\(69\) | −2.08591 | −0.251114 | ||||||||
\(70\) | −2.49069 | −0.297694 | ||||||||
\(71\) | −3.31842 | −0.393824 | −0.196912 | − | 0.980421i | \(-0.563091\pi\) | ||||
−0.196912 | + | 0.980421i | \(0.563091\pi\) | |||||||
\(72\) | −6.27549 | −0.739574 | ||||||||
\(73\) | 5.17255 | 0.605401 | 0.302701 | − | 0.953086i | \(-0.402112\pi\) | ||||
0.302701 | + | 0.953086i | \(0.402112\pi\) | |||||||
\(74\) | −8.49094 | −0.987052 | ||||||||
\(75\) | −8.26628 | −0.954508 | ||||||||
\(76\) | −7.31025 | −0.838544 | ||||||||
\(77\) | −1.48551 | −0.169290 | ||||||||
\(78\) | −5.49113 | −0.621748 | ||||||||
\(79\) | −12.0716 | −1.35816 | −0.679082 | − | 0.734063i | \(-0.737622\pi\) | ||||
−0.679082 | + | 0.734063i | \(0.737622\pi\) | |||||||
\(80\) | −3.21240 | −0.359157 | ||||||||
\(81\) | −11.2406 | −1.24895 | ||||||||
\(82\) | 9.57618 | 1.05751 | ||||||||
\(83\) | −0.715863 | −0.0785761 | −0.0392881 | − | 0.999228i | \(-0.512509\pi\) | ||||
−0.0392881 | + | 0.999228i | \(0.512509\pi\) | |||||||
\(84\) | −8.07740 | −0.881317 | ||||||||
\(85\) | 3.49881 | 0.379500 | ||||||||
\(86\) | 22.5112 | 2.42745 | ||||||||
\(87\) | 21.2470 | 2.27792 | ||||||||
\(88\) | −6.64473 | −0.708330 | ||||||||
\(89\) | −15.1763 | −1.60868 | −0.804341 | − | 0.594167i | \(-0.797482\pi\) | ||||
−0.804341 | + | 0.594167i | \(0.797482\pi\) | |||||||
\(90\) | 3.49436 | 0.368337 | ||||||||
\(91\) | −1.08201 | −0.113426 | ||||||||
\(92\) | −3.82667 | −0.398958 | ||||||||
\(93\) | 12.0358 | 1.24805 | ||||||||
\(94\) | 2.91866 | 0.301037 | ||||||||
\(95\) | 1.95567 | 0.200648 | ||||||||
\(96\) | 2.94107 | 0.300172 | ||||||||
\(97\) | −11.5352 | −1.17122 | −0.585611 | − | 0.810592i | \(-0.699145\pi\) | ||||
−0.585611 | + | 0.810592i | \(0.699145\pi\) | |||||||
\(98\) | −2.41856 | −0.244312 | ||||||||
\(99\) | 2.08413 | 0.209463 | ||||||||
\(100\) | −15.1648 | −1.51648 | ||||||||
\(101\) | 3.29800 | 0.328163 | 0.164081 | − | 0.986447i | \(-0.447534\pi\) | ||||
0.164081 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(102\) | 17.2420 | 1.70722 | ||||||||
\(103\) | 1.26235 | 0.124383 | 0.0621915 | − | 0.998064i | \(-0.480191\pi\) | ||||
0.0621915 | + | 0.998064i | \(0.480191\pi\) | |||||||
\(104\) | −4.83985 | −0.474586 | ||||||||
\(105\) | 2.16090 | 0.210882 | ||||||||
\(106\) | −30.2362 | −2.93680 | ||||||||
\(107\) | 5.46590 | 0.528409 | 0.264204 | − | 0.964467i | \(-0.414891\pi\) | ||||
0.264204 | + | 0.964467i | \(0.414891\pi\) | |||||||
\(108\) | −12.8999 | −1.24129 | ||||||||
\(109\) | 2.27962 | 0.218348 | 0.109174 | − | 0.994023i | \(-0.465179\pi\) | ||||
0.109174 | + | 0.994023i | \(0.465179\pi\) | |||||||
\(110\) | 3.69996 | 0.352777 | ||||||||
\(111\) | 7.36667 | 0.699213 | ||||||||
\(112\) | −3.11937 | −0.294753 | ||||||||
\(113\) | 20.3751 | 1.91673 | 0.958364 | − | 0.285548i | \(-0.0921758\pi\) | ||||
0.958364 | + | 0.285548i | \(0.0921758\pi\) | |||||||
\(114\) | 9.63749 | 0.902633 | ||||||||
\(115\) | 1.02373 | 0.0954631 | ||||||||
\(116\) | 38.9785 | 3.61906 | ||||||||
\(117\) | 1.51802 | 0.140341 | ||||||||
\(118\) | 14.0492 | 1.29333 | ||||||||
\(119\) | 3.39749 | 0.311448 | ||||||||
\(120\) | 9.66575 | 0.882358 | ||||||||
\(121\) | −8.79325 | −0.799386 | ||||||||
\(122\) | −16.6634 | −1.50863 | ||||||||
\(123\) | −8.30821 | −0.749126 | ||||||||
\(124\) | 22.0801 | 1.98285 | ||||||||
\(125\) | 9.20606 | 0.823415 | ||||||||
\(126\) | 3.39316 | 0.302287 | ||||||||
\(127\) | −15.6781 | −1.39121 | −0.695605 | − | 0.718425i | \(-0.744863\pi\) | ||||
−0.695605 | + | 0.718425i | \(0.744863\pi\) | |||||||
\(128\) | 20.4843 | 1.81057 | ||||||||
\(129\) | −19.5305 | −1.71957 | ||||||||
\(130\) | 2.69495 | 0.236363 | ||||||||
\(131\) | −14.5064 | −1.26743 | −0.633713 | − | 0.773568i | \(-0.718470\pi\) | ||||
−0.633713 | + | 0.773568i | \(0.718470\pi\) | |||||||
\(132\) | 11.9991 | 1.04439 | ||||||||
\(133\) | 1.89904 | 0.164667 | ||||||||
\(134\) | −0.253637 | −0.0219109 | ||||||||
\(135\) | 3.45103 | 0.297018 | ||||||||
\(136\) | 15.1970 | 1.30314 | ||||||||
\(137\) | 9.16330 | 0.782873 | 0.391437 | − | 0.920205i | \(-0.371978\pi\) | ||||
0.391437 | + | 0.920205i | \(0.371978\pi\) | |||||||
\(138\) | 5.04490 | 0.429450 | ||||||||
\(139\) | −12.9502 | −1.09842 | −0.549212 | − | 0.835683i | \(-0.685072\pi\) | ||||
−0.549212 | + | 0.835683i | \(0.685072\pi\) | |||||||
\(140\) | 3.96425 | 0.335040 | ||||||||
\(141\) | −2.53220 | −0.213250 | ||||||||
\(142\) | 8.02582 | 0.673512 | ||||||||
\(143\) | 1.60734 | 0.134413 | ||||||||
\(144\) | 4.37638 | 0.364698 | ||||||||
\(145\) | −10.4277 | −0.865973 | ||||||||
\(146\) | −12.5101 | −1.03535 | ||||||||
\(147\) | 2.09832 | 0.173067 | ||||||||
\(148\) | 13.5144 | 1.11088 | ||||||||
\(149\) | 3.64635 | 0.298721 | 0.149360 | − | 0.988783i | \(-0.452279\pi\) | ||||
0.149360 | + | 0.988783i | \(0.452279\pi\) | |||||||
\(150\) | 19.9925 | 1.63238 | ||||||||
\(151\) | 14.0468 | 1.14311 | 0.571556 | − | 0.820563i | \(-0.306340\pi\) | ||||
0.571556 | + | 0.820563i | \(0.306340\pi\) | |||||||
\(152\) | 8.49443 | 0.688989 | ||||||||
\(153\) | −4.76657 | −0.385354 | ||||||||
\(154\) | 3.59281 | 0.289517 | ||||||||
\(155\) | −5.90696 | −0.474459 | ||||||||
\(156\) | 8.73983 | 0.699746 | ||||||||
\(157\) | 8.05538 | 0.642890 | 0.321445 | − | 0.946928i | \(-0.395832\pi\) | ||||
0.321445 | + | 0.946928i | \(0.395832\pi\) | |||||||
\(158\) | 29.1960 | 2.32271 | ||||||||
\(159\) | 26.2327 | 2.08039 | ||||||||
\(160\) | −1.44343 | −0.114113 | ||||||||
\(161\) | 0.994082 | 0.0783446 | ||||||||
\(162\) | 27.1861 | 2.13594 | ||||||||
\(163\) | −7.61628 | −0.596553 | −0.298276 | − | 0.954480i | \(-0.596412\pi\) | ||||
−0.298276 | + | 0.954480i | \(0.596412\pi\) | |||||||
\(164\) | −15.2417 | −1.19018 | ||||||||
\(165\) | −3.21005 | −0.249902 | ||||||||
\(166\) | 1.73136 | 0.134380 | ||||||||
\(167\) | −17.2568 | −1.33537 | −0.667687 | − | 0.744442i | \(-0.732715\pi\) | ||||
−0.667687 | + | 0.744442i | \(0.732715\pi\) | |||||||
\(168\) | 9.38584 | 0.724133 | ||||||||
\(169\) | −11.8293 | −0.909943 | ||||||||
\(170\) | −8.46210 | −0.649014 | ||||||||
\(171\) | −2.66429 | −0.203743 | ||||||||
\(172\) | −35.8294 | −2.73197 | ||||||||
\(173\) | 10.0334 | 0.762826 | 0.381413 | − | 0.924405i | \(-0.375438\pi\) | ||||
0.381413 | + | 0.924405i | \(0.375438\pi\) | |||||||
\(174\) | −51.3873 | −3.89566 | ||||||||
\(175\) | 3.93947 | 0.297796 | ||||||||
\(176\) | 4.63387 | 0.349291 | ||||||||
\(177\) | −12.1890 | −0.916178 | ||||||||
\(178\) | 36.7048 | 2.75114 | ||||||||
\(179\) | −20.2444 | −1.51314 | −0.756569 | − | 0.653913i | \(-0.773126\pi\) | ||||
−0.756569 | + | 0.653913i | \(0.773126\pi\) | |||||||
\(180\) | −5.56171 | −0.414545 | ||||||||
\(181\) | −19.0471 | −1.41576 | −0.707879 | − | 0.706334i | \(-0.750348\pi\) | ||||
−0.707879 | + | 0.706334i | \(0.750348\pi\) | |||||||
\(182\) | 2.61691 | 0.193978 | ||||||||
\(183\) | 14.4570 | 1.06869 | ||||||||
\(184\) | 4.44654 | 0.327804 | ||||||||
\(185\) | −3.61543 | −0.265812 | ||||||||
\(186\) | −29.1093 | −2.13440 | ||||||||
\(187\) | −5.04702 | −0.369075 | ||||||||
\(188\) | −4.64542 | −0.338802 | ||||||||
\(189\) | 3.35110 | 0.243756 | ||||||||
\(190\) | −4.72992 | −0.343144 | ||||||||
\(191\) | −23.6796 | −1.71340 | −0.856700 | − | 0.515816i | \(-0.827489\pi\) | ||||
−0.856700 | + | 0.515816i | \(0.827489\pi\) | |||||||
\(192\) | −20.2041 | −1.45810 | ||||||||
\(193\) | −4.19935 | −0.302276 | −0.151138 | − | 0.988513i | \(-0.548294\pi\) | ||||
−0.151138 | + | 0.988513i | \(0.548294\pi\) | |||||||
\(194\) | 27.8986 | 2.00300 | ||||||||
\(195\) | −2.33812 | −0.167436 | ||||||||
\(196\) | 3.84945 | 0.274961 | ||||||||
\(197\) | −5.81385 | −0.414220 | −0.207110 | − | 0.978318i | \(-0.566406\pi\) | ||||
−0.207110 | + | 0.978318i | \(0.566406\pi\) | |||||||
\(198\) | −5.04059 | −0.358219 | ||||||||
\(199\) | −11.0846 | −0.785769 | −0.392885 | − | 0.919588i | \(-0.628523\pi\) | ||||
−0.392885 | + | 0.919588i | \(0.628523\pi\) | |||||||
\(200\) | 17.6213 | 1.24601 | ||||||||
\(201\) | 0.220053 | 0.0155214 | ||||||||
\(202\) | −7.97641 | −0.561218 | ||||||||
\(203\) | −10.1257 | −0.710686 | ||||||||
\(204\) | −27.4429 | −1.92139 | ||||||||
\(205\) | 4.07753 | 0.284787 | ||||||||
\(206\) | −3.05308 | −0.212718 | ||||||||
\(207\) | −1.39466 | −0.0969358 | ||||||||
\(208\) | 3.37520 | 0.234028 | ||||||||
\(209\) | −2.82105 | −0.195136 | ||||||||
\(210\) | −5.22628 | −0.360647 | ||||||||
\(211\) | −1.57843 | −0.108663 | −0.0543317 | − | 0.998523i | \(-0.517303\pi\) | ||||
−0.0543317 | + | 0.998523i | \(0.517303\pi\) | |||||||
\(212\) | 48.1248 | 3.30523 | ||||||||
\(213\) | −6.96313 | −0.477106 | ||||||||
\(214\) | −13.2196 | −0.903676 | ||||||||
\(215\) | 9.58525 | 0.653708 | ||||||||
\(216\) | 14.9895 | 1.01991 | ||||||||
\(217\) | −5.73591 | −0.389379 | ||||||||
\(218\) | −5.51342 | −0.373416 | ||||||||
\(219\) | 10.8537 | 0.733424 | ||||||||
\(220\) | −5.88895 | −0.397033 | ||||||||
\(221\) | −3.67612 | −0.247283 | ||||||||
\(222\) | −17.8168 | −1.19578 | ||||||||
\(223\) | −15.9116 | −1.06552 | −0.532761 | − | 0.846266i | \(-0.678846\pi\) | ||||
−0.532761 | + | 0.846266i | \(0.678846\pi\) | |||||||
\(224\) | −1.40163 | −0.0936501 | ||||||||
\(225\) | −5.52694 | −0.368463 | ||||||||
\(226\) | −49.2785 | −3.27796 | ||||||||
\(227\) | −12.1747 | −0.808064 | −0.404032 | − | 0.914745i | \(-0.632391\pi\) | ||||
−0.404032 | + | 0.914745i | \(0.632391\pi\) | |||||||
\(228\) | −15.3393 | −1.01587 | ||||||||
\(229\) | −26.5406 | −1.75385 | −0.876927 | − | 0.480624i | \(-0.840410\pi\) | ||||
−0.876927 | + | 0.480624i | \(0.840410\pi\) | |||||||
\(230\) | −2.47595 | −0.163259 | ||||||||
\(231\) | −3.11709 | −0.205089 | ||||||||
\(232\) | −45.2925 | −2.97360 | ||||||||
\(233\) | 29.3076 | 1.92000 | 0.960001 | − | 0.279997i | \(-0.0903334\pi\) | ||||
0.960001 | + | 0.279997i | \(0.0903334\pi\) | |||||||
\(234\) | −3.67144 | −0.240009 | ||||||||
\(235\) | 1.24276 | 0.0810689 | ||||||||
\(236\) | −22.3611 | −1.45558 | ||||||||
\(237\) | −25.3302 | −1.64537 | ||||||||
\(238\) | −8.21705 | −0.532632 | ||||||||
\(239\) | −8.32212 | −0.538313 | −0.269157 | − | 0.963096i | \(-0.586745\pi\) | ||||
−0.269157 | + | 0.963096i | \(0.586745\pi\) | |||||||
\(240\) | −6.74066 | −0.435108 | ||||||||
\(241\) | 9.98443 | 0.643154 | 0.321577 | − | 0.946884i | \(-0.395787\pi\) | ||||
0.321577 | + | 0.946884i | \(0.395787\pi\) | |||||||
\(242\) | 21.2670 | 1.36710 | ||||||||
\(243\) | −13.5331 | −0.868149 | ||||||||
\(244\) | 26.5219 | 1.69789 | ||||||||
\(245\) | −1.02982 | −0.0657929 | ||||||||
\(246\) | 20.0939 | 1.28114 | ||||||||
\(247\) | −2.05478 | −0.130742 | ||||||||
\(248\) | −25.6568 | −1.62921 | ||||||||
\(249\) | −1.50211 | −0.0951925 | ||||||||
\(250\) | −22.2654 | −1.40819 | ||||||||
\(251\) | 15.3489 | 0.968817 | 0.484408 | − | 0.874842i | \(-0.339035\pi\) | ||||
0.484408 | + | 0.874842i | \(0.339035\pi\) | |||||||
\(252\) | −5.40065 | −0.340209 | ||||||||
\(253\) | −1.47672 | −0.0928407 | ||||||||
\(254\) | 37.9186 | 2.37922 | ||||||||
\(255\) | 7.34164 | 0.459752 | ||||||||
\(256\) | −30.2853 | −1.89283 | ||||||||
\(257\) | 20.1594 | 1.25751 | 0.628754 | − | 0.777605i | \(-0.283565\pi\) | ||||
0.628754 | + | 0.777605i | \(0.283565\pi\) | |||||||
\(258\) | 47.2358 | 2.94077 | ||||||||
\(259\) | −3.51074 | −0.218147 | ||||||||
\(260\) | −4.28936 | −0.266015 | ||||||||
\(261\) | 14.2060 | 0.879332 | ||||||||
\(262\) | 35.0845 | 2.16753 | ||||||||
\(263\) | −13.1857 | −0.813064 | −0.406532 | − | 0.913637i | \(-0.633262\pi\) | ||||
−0.406532 | + | 0.913637i | \(0.633262\pi\) | |||||||
\(264\) | −13.9428 | −0.858120 | ||||||||
\(265\) | −12.8746 | −0.790878 | ||||||||
\(266\) | −4.59294 | −0.281611 | ||||||||
\(267\) | −31.8448 | −1.94887 | ||||||||
\(268\) | 0.403696 | 0.0246597 | ||||||||
\(269\) | −24.0545 | −1.46663 | −0.733315 | − | 0.679889i | \(-0.762028\pi\) | ||||
−0.733315 | + | 0.679889i | \(0.762028\pi\) | |||||||
\(270\) | −8.34654 | −0.507954 | ||||||||
\(271\) | 26.5726 | 1.61417 | 0.807084 | − | 0.590436i | \(-0.201044\pi\) | ||||
0.807084 | + | 0.590436i | \(0.201044\pi\) | |||||||
\(272\) | −10.5981 | −0.642601 | ||||||||
\(273\) | −2.27041 | −0.137411 | ||||||||
\(274\) | −22.1620 | −1.33886 | ||||||||
\(275\) | −5.85213 | −0.352897 | ||||||||
\(276\) | −8.02960 | −0.483325 | ||||||||
\(277\) | −6.02419 | −0.361958 | −0.180979 | − | 0.983487i | \(-0.557927\pi\) | ||||
−0.180979 | + | 0.983487i | \(0.557927\pi\) | |||||||
\(278\) | 31.3210 | 1.87851 | ||||||||
\(279\) | 8.04728 | 0.481778 | ||||||||
\(280\) | −4.60641 | −0.275286 | ||||||||
\(281\) | 22.9831 | 1.37106 | 0.685529 | − | 0.728045i | \(-0.259571\pi\) | ||||
0.685529 | + | 0.728045i | \(0.259571\pi\) | |||||||
\(282\) | 6.12429 | 0.364696 | ||||||||
\(283\) | −13.2858 | −0.789758 | −0.394879 | − | 0.918733i | \(-0.629214\pi\) | ||||
−0.394879 | + | 0.918733i | \(0.629214\pi\) | |||||||
\(284\) | −12.7741 | −0.758004 | ||||||||
\(285\) | 4.10363 | 0.243078 | ||||||||
\(286\) | −3.88746 | −0.229870 | ||||||||
\(287\) | 3.95945 | 0.233719 | ||||||||
\(288\) | 1.96644 | 0.115873 | ||||||||
\(289\) | −5.45705 | −0.321003 | ||||||||
\(290\) | 25.2200 | 1.48097 | ||||||||
\(291\) | −24.2046 | −1.41890 | ||||||||
\(292\) | 19.9115 | 1.16523 | ||||||||
\(293\) | 4.13869 | 0.241785 | 0.120893 | − | 0.992666i | \(-0.461424\pi\) | ||||
0.120893 | + | 0.992666i | \(0.461424\pi\) | |||||||
\(294\) | −5.07493 | −0.295976 | ||||||||
\(295\) | 5.98214 | 0.348293 | ||||||||
\(296\) | −15.7036 | −0.912752 | ||||||||
\(297\) | −4.97810 | −0.288859 | ||||||||
\(298\) | −8.81894 | −0.510867 | ||||||||
\(299\) | −1.07561 | −0.0622039 | ||||||||
\(300\) | −31.8206 | −1.83717 | ||||||||
\(301\) | 9.30767 | 0.536485 | ||||||||
\(302\) | −33.9731 | −1.95493 | ||||||||
\(303\) | 6.92027 | 0.397559 | ||||||||
\(304\) | −5.92381 | −0.339754 | ||||||||
\(305\) | −7.09526 | −0.406274 | ||||||||
\(306\) | 11.5282 | 0.659026 | ||||||||
\(307\) | −6.72084 | −0.383579 | −0.191789 | − | 0.981436i | \(-0.561429\pi\) | ||||
−0.191789 | + | 0.981436i | \(0.561429\pi\) | |||||||
\(308\) | −5.71841 | −0.325837 | ||||||||
\(309\) | 2.64882 | 0.150686 | ||||||||
\(310\) | 14.2864 | 0.811411 | ||||||||
\(311\) | 20.4775 | 1.16117 | 0.580587 | − | 0.814198i | \(-0.302823\pi\) | ||||
0.580587 | + | 0.814198i | \(0.302823\pi\) | |||||||
\(312\) | −10.1556 | −0.574946 | ||||||||
\(313\) | 3.04133 | 0.171906 | 0.0859531 | − | 0.996299i | \(-0.472606\pi\) | ||||
0.0859531 | + | 0.996299i | \(0.472606\pi\) | |||||||
\(314\) | −19.4825 | −1.09946 | ||||||||
\(315\) | 1.44481 | 0.0814056 | ||||||||
\(316\) | −46.4691 | −2.61409 | ||||||||
\(317\) | −24.2259 | −1.36066 | −0.680330 | − | 0.732906i | \(-0.738163\pi\) | ||||
−0.680330 | + | 0.732906i | \(0.738163\pi\) | |||||||
\(318\) | −63.4455 | −3.55784 | ||||||||
\(319\) | 15.0419 | 0.842184 | ||||||||
\(320\) | 9.91582 | 0.554311 | ||||||||
\(321\) | 11.4692 | 0.640151 | ||||||||
\(322\) | −2.40425 | −0.133984 | ||||||||
\(323\) | 6.45197 | 0.358997 | ||||||||
\(324\) | −43.2701 | −2.40389 | ||||||||
\(325\) | −4.26254 | −0.236443 | ||||||||
\(326\) | 18.4204 | 1.02021 | ||||||||
\(327\) | 4.78339 | 0.264522 | ||||||||
\(328\) | 17.7107 | 0.977909 | ||||||||
\(329\) | 1.20677 | 0.0665316 | ||||||||
\(330\) | 7.76371 | 0.427378 | ||||||||
\(331\) | 20.4554 | 1.12433 | 0.562165 | − | 0.827025i | \(-0.309969\pi\) | ||||
0.562165 | + | 0.827025i | \(0.309969\pi\) | |||||||
\(332\) | −2.75568 | −0.151238 | ||||||||
\(333\) | 4.92545 | 0.269913 | ||||||||
\(334\) | 41.7367 | 2.28373 | ||||||||
\(335\) | −0.107998 | −0.00590059 | ||||||||
\(336\) | −6.54546 | −0.357084 | ||||||||
\(337\) | 1.41685 | 0.0771805 | 0.0385903 | − | 0.999255i | \(-0.487713\pi\) | ||||
0.0385903 | + | 0.999255i | \(0.487713\pi\) | |||||||
\(338\) | 28.6098 | 1.55617 | ||||||||
\(339\) | 42.7536 | 2.32206 | ||||||||
\(340\) | 13.4685 | 0.730433 | ||||||||
\(341\) | 8.52077 | 0.461425 | ||||||||
\(342\) | 6.44375 | 0.348438 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 41.6334 | 2.24472 | ||||||||
\(345\) | 2.14811 | 0.115650 | ||||||||
\(346\) | −24.2664 | −1.30457 | ||||||||
\(347\) | 5.24673 | 0.281659 | 0.140830 | − | 0.990034i | \(-0.455023\pi\) | ||||
0.140830 | + | 0.990034i | \(0.455023\pi\) | |||||||
\(348\) | 81.7895 | 4.38438 | ||||||||
\(349\) | −32.1140 | −1.71902 | −0.859512 | − | 0.511115i | \(-0.829232\pi\) | ||||
−0.859512 | + | 0.511115i | \(0.829232\pi\) | |||||||
\(350\) | −9.52785 | −0.509285 | ||||||||
\(351\) | −3.62592 | −0.193537 | ||||||||
\(352\) | 2.08214 | 0.110978 | ||||||||
\(353\) | −24.1244 | −1.28401 | −0.642007 | − | 0.766699i | \(-0.721898\pi\) | ||||
−0.642007 | + | 0.766699i | \(0.721898\pi\) | |||||||
\(354\) | 29.4798 | 1.56683 | ||||||||
\(355\) | 3.41739 | 0.181376 | ||||||||
\(356\) | −58.4204 | −3.09627 | ||||||||
\(357\) | 7.12904 | 0.377309 | ||||||||
\(358\) | 48.9624 | 2.58774 | ||||||||
\(359\) | −16.7082 | −0.881827 | −0.440913 | − | 0.897550i | \(-0.645345\pi\) | ||||
−0.440913 | + | 0.897550i | \(0.645345\pi\) | |||||||
\(360\) | 6.46264 | 0.340611 | ||||||||
\(361\) | −15.3937 | −0.810192 | ||||||||
\(362\) | 46.0666 | 2.42120 | ||||||||
\(363\) | −18.4511 | −0.968431 | ||||||||
\(364\) | −4.16515 | −0.218313 | ||||||||
\(365\) | −5.32681 | −0.278818 | ||||||||
\(366\) | −34.9652 | −1.82766 | ||||||||
\(367\) | −27.4628 | −1.43354 | −0.716772 | − | 0.697307i | \(-0.754381\pi\) | ||||
−0.716772 | + | 0.697307i | \(0.754381\pi\) | |||||||
\(368\) | −3.10091 | −0.161646 | ||||||||
\(369\) | −5.55497 | −0.289180 | ||||||||
\(370\) | 8.74416 | 0.454587 | ||||||||
\(371\) | −12.5017 | −0.649058 | ||||||||
\(372\) | 46.3312 | 2.40216 | ||||||||
\(373\) | 8.86703 | 0.459117 | 0.229559 | − | 0.973295i | \(-0.426272\pi\) | ||||
0.229559 | + | 0.973295i | \(0.426272\pi\) | |||||||
\(374\) | 12.2065 | 0.631185 | ||||||||
\(375\) | 19.3173 | 0.997541 | ||||||||
\(376\) | 5.39792 | 0.278376 | ||||||||
\(377\) | 10.9561 | 0.564270 | ||||||||
\(378\) | −8.10484 | −0.416868 | ||||||||
\(379\) | −19.3655 | −0.994740 | −0.497370 | − | 0.867539i | \(-0.665701\pi\) | ||||
−0.497370 | + | 0.867539i | \(0.665701\pi\) | |||||||
\(380\) | 7.52826 | 0.386192 | ||||||||
\(381\) | −32.8978 | −1.68541 | ||||||||
\(382\) | 57.2707 | 2.93023 | ||||||||
\(383\) | 28.5629 | 1.45949 | 0.729747 | − | 0.683717i | \(-0.239638\pi\) | ||||
0.729747 | + | 0.683717i | \(0.239638\pi\) | |||||||
\(384\) | 42.9827 | 2.19345 | ||||||||
\(385\) | 1.52981 | 0.0779666 | ||||||||
\(386\) | 10.1564 | 0.516947 | ||||||||
\(387\) | −13.0584 | −0.663793 | ||||||||
\(388\) | −44.4042 | −2.25428 | ||||||||
\(389\) | 10.7195 | 0.543500 | 0.271750 | − | 0.962368i | \(-0.412398\pi\) | ||||
0.271750 | + | 0.962368i | \(0.412398\pi\) | |||||||
\(390\) | 5.65489 | 0.286346 | ||||||||
\(391\) | 3.37739 | 0.170802 | ||||||||
\(392\) | −4.47302 | −0.225921 | ||||||||
\(393\) | −30.4390 | −1.53545 | ||||||||
\(394\) | 14.0612 | 0.708392 | ||||||||
\(395\) | 12.4316 | 0.625503 | ||||||||
\(396\) | 8.02274 | 0.403158 | ||||||||
\(397\) | 16.2121 | 0.813660 | 0.406830 | − | 0.913504i | \(-0.366634\pi\) | ||||
0.406830 | + | 0.913504i | \(0.366634\pi\) | |||||||
\(398\) | 26.8089 | 1.34381 | ||||||||
\(399\) | 3.98480 | 0.199489 | ||||||||
\(400\) | −12.2887 | −0.614434 | ||||||||
\(401\) | −15.6289 | −0.780469 | −0.390234 | − | 0.920716i | \(-0.627606\pi\) | ||||
−0.390234 | + | 0.920716i | \(0.627606\pi\) | |||||||
\(402\) | −0.532213 | −0.0265444 | ||||||||
\(403\) | 6.20631 | 0.309158 | ||||||||
\(404\) | 12.6955 | 0.631623 | ||||||||
\(405\) | 11.5758 | 0.575206 | ||||||||
\(406\) | 24.4897 | 1.21540 | ||||||||
\(407\) | 5.21525 | 0.258510 | ||||||||
\(408\) | 31.8883 | 1.57871 | ||||||||
\(409\) | −23.4653 | −1.16028 | −0.580141 | − | 0.814516i | \(-0.697003\pi\) | ||||
−0.580141 | + | 0.814516i | \(0.697003\pi\) | |||||||
\(410\) | −9.86176 | −0.487038 | ||||||||
\(411\) | 19.2276 | 0.948426 | ||||||||
\(412\) | 4.85936 | 0.239403 | ||||||||
\(413\) | 5.80890 | 0.285837 | ||||||||
\(414\) | 3.37308 | 0.165778 | ||||||||
\(415\) | 0.737211 | 0.0361883 | ||||||||
\(416\) | 1.51657 | 0.0743562 | ||||||||
\(417\) | −27.1738 | −1.33071 | ||||||||
\(418\) | 6.82288 | 0.333718 | ||||||||
\(419\) | −0.0876217 | −0.00428060 | −0.00214030 | − | 0.999998i | \(-0.500681\pi\) | ||||
−0.00214030 | + | 0.999998i | \(0.500681\pi\) | |||||||
\(420\) | 8.31828 | 0.405891 | ||||||||
\(421\) | 7.89977 | 0.385011 | 0.192506 | − | 0.981296i | \(-0.438339\pi\) | ||||
0.192506 | + | 0.981296i | \(0.438339\pi\) | |||||||
\(422\) | 3.81753 | 0.185834 | ||||||||
\(423\) | −1.69306 | −0.0823195 | ||||||||
\(424\) | −55.9205 | −2.71574 | ||||||||
\(425\) | 13.3843 | 0.649234 | ||||||||
\(426\) | 16.8408 | 0.815938 | ||||||||
\(427\) | −6.88980 | −0.333421 | ||||||||
\(428\) | 21.0407 | 1.01704 | ||||||||
\(429\) | 3.37272 | 0.162837 | ||||||||
\(430\) | −23.1825 | −1.11796 | ||||||||
\(431\) | 18.8740 | 0.909130 | 0.454565 | − | 0.890714i | \(-0.349795\pi\) | ||||
0.454565 | + | 0.890714i | \(0.349795\pi\) | |||||||
\(432\) | −10.4533 | −0.502936 | ||||||||
\(433\) | −7.88200 | −0.378785 | −0.189392 | − | 0.981901i | \(-0.560652\pi\) | ||||
−0.189392 | + | 0.981901i | \(0.560652\pi\) | |||||||
\(434\) | 13.8727 | 0.665909 | ||||||||
\(435\) | −21.8807 | −1.04910 | ||||||||
\(436\) | 8.77530 | 0.420261 | ||||||||
\(437\) | 1.88780 | 0.0903057 | ||||||||
\(438\) | −26.2503 | −1.25429 | ||||||||
\(439\) | 32.7339 | 1.56231 | 0.781153 | − | 0.624340i | \(-0.214632\pi\) | ||||
0.781153 | + | 0.624340i | \(0.214632\pi\) | |||||||
\(440\) | 6.84289 | 0.326222 | ||||||||
\(441\) | 1.40297 | 0.0668079 | ||||||||
\(442\) | 8.89094 | 0.422899 | ||||||||
\(443\) | 27.0414 | 1.28478 | 0.642389 | − | 0.766379i | \(-0.277943\pi\) | ||||
0.642389 | + | 0.766379i | \(0.277943\pi\) | |||||||
\(444\) | 28.3576 | 1.34579 | ||||||||
\(445\) | 15.6289 | 0.740880 | ||||||||
\(446\) | 38.4833 | 1.82224 | ||||||||
\(447\) | 7.65123 | 0.361891 | ||||||||
\(448\) | 9.62867 | 0.454912 | ||||||||
\(449\) | 23.5207 | 1.11001 | 0.555005 | − | 0.831847i | \(-0.312716\pi\) | ||||
0.555005 | + | 0.831847i | \(0.312716\pi\) | |||||||
\(450\) | 13.3673 | 0.630138 | ||||||||
\(451\) | −5.88181 | −0.276964 | ||||||||
\(452\) | 78.4330 | 3.68918 | ||||||||
\(453\) | 29.4748 | 1.38484 | ||||||||
\(454\) | 29.4453 | 1.38194 | ||||||||
\(455\) | 1.11428 | 0.0522382 | ||||||||
\(456\) | 17.8241 | 0.834688 | ||||||||
\(457\) | 16.0734 | 0.751884 | 0.375942 | − | 0.926643i | \(-0.377319\pi\) | ||||
0.375942 | + | 0.926643i | \(0.377319\pi\) | |||||||
\(458\) | 64.1902 | 2.99941 | ||||||||
\(459\) | 11.3853 | 0.531421 | ||||||||
\(460\) | 3.94079 | 0.183740 | ||||||||
\(461\) | −10.6683 | −0.496874 | −0.248437 | − | 0.968648i | \(-0.579917\pi\) | ||||
−0.248437 | + | 0.968648i | \(0.579917\pi\) | |||||||
\(462\) | 7.53888 | 0.350741 | ||||||||
\(463\) | 5.19512 | 0.241438 | 0.120719 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120719 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(464\) | 31.5859 | 1.46634 | ||||||||
\(465\) | −12.3947 | −0.574792 | ||||||||
\(466\) | −70.8822 | −3.28355 | ||||||||
\(467\) | 1.15133 | 0.0532770 | 0.0266385 | − | 0.999645i | \(-0.491520\pi\) | ||||
0.0266385 | + | 0.999645i | \(0.491520\pi\) | |||||||
\(468\) | 5.84356 | 0.270119 | ||||||||
\(469\) | −0.104871 | −0.00484249 | ||||||||
\(470\) | −3.00570 | −0.138643 | ||||||||
\(471\) | 16.9028 | 0.778840 | ||||||||
\(472\) | 25.9833 | 1.19598 | ||||||||
\(473\) | −13.8267 | −0.635751 | ||||||||
\(474\) | 61.2627 | 2.81389 | ||||||||
\(475\) | 7.48119 | 0.343261 | ||||||||
\(476\) | 13.0785 | 0.599451 | ||||||||
\(477\) | 17.5395 | 0.803079 | ||||||||
\(478\) | 20.1276 | 0.920614 | ||||||||
\(479\) | 22.7050 | 1.03742 | 0.518708 | − | 0.854951i | \(-0.326413\pi\) | ||||
0.518708 | + | 0.854951i | \(0.326413\pi\) | |||||||
\(480\) | −3.02878 | −0.138244 | ||||||||
\(481\) | 3.79865 | 0.173204 | ||||||||
\(482\) | −24.1480 | −1.09991 | ||||||||
\(483\) | 2.08591 | 0.0949120 | ||||||||
\(484\) | −33.8492 | −1.53860 | ||||||||
\(485\) | 11.8792 | 0.539407 | ||||||||
\(486\) | 32.7307 | 1.48469 | ||||||||
\(487\) | 9.30730 | 0.421754 | 0.210877 | − | 0.977513i | \(-0.432368\pi\) | ||||
0.210877 | + | 0.977513i | \(0.432368\pi\) | |||||||
\(488\) | −30.8182 | −1.39507 | ||||||||
\(489\) | −15.9814 | −0.722705 | ||||||||
\(490\) | 2.49069 | 0.112518 | ||||||||
\(491\) | 31.2996 | 1.41253 | 0.706265 | − | 0.707947i | \(-0.250379\pi\) | ||||
0.706265 | + | 0.707947i | \(0.250379\pi\) | |||||||
\(492\) | −31.9820 | −1.44186 | ||||||||
\(493\) | −34.4021 | −1.54939 | ||||||||
\(494\) | 4.96961 | 0.223593 | ||||||||
\(495\) | −2.14628 | −0.0964681 | ||||||||
\(496\) | 17.8924 | 0.803394 | ||||||||
\(497\) | 3.31842 | 0.148852 | ||||||||
\(498\) | 3.63295 | 0.162797 | ||||||||
\(499\) | −43.2064 | −1.93418 | −0.967091 | − | 0.254431i | \(-0.918112\pi\) | ||||
−0.967091 | + | 0.254431i | \(0.918112\pi\) | |||||||
\(500\) | 35.4383 | 1.58485 | ||||||||
\(501\) | −36.2104 | −1.61776 | ||||||||
\(502\) | −37.1224 | −1.65685 | ||||||||
\(503\) | −35.9591 | −1.60334 | −0.801668 | − | 0.597769i | \(-0.796054\pi\) | ||||
−0.801668 | + | 0.597769i | \(0.796054\pi\) | |||||||
\(504\) | 6.27549 | 0.279533 | ||||||||
\(505\) | −3.39635 | −0.151136 | ||||||||
\(506\) | 3.57155 | 0.158775 | ||||||||
\(507\) | −24.8216 | −1.10237 | ||||||||
\(508\) | −60.3522 | −2.67770 | ||||||||
\(509\) | 24.2796 | 1.07617 | 0.538087 | − | 0.842889i | \(-0.319147\pi\) | ||||
0.538087 | + | 0.842889i | \(0.319147\pi\) | |||||||
\(510\) | −17.7562 | −0.786259 | ||||||||
\(511\) | −5.17255 | −0.228820 | ||||||||
\(512\) | 32.2782 | 1.42651 | ||||||||
\(513\) | 6.36386 | 0.280971 | ||||||||
\(514\) | −48.7567 | −2.15057 | ||||||||
\(515\) | −1.30000 | −0.0572847 | ||||||||
\(516\) | −75.1818 | −3.30969 | ||||||||
\(517\) | −1.79268 | −0.0788419 | ||||||||
\(518\) | 8.49094 | 0.373071 | ||||||||
\(519\) | 21.0533 | 0.924139 | ||||||||
\(520\) | 4.98419 | 0.218571 | ||||||||
\(521\) | −4.53090 | −0.198502 | −0.0992511 | − | 0.995062i | \(-0.531645\pi\) | ||||
−0.0992511 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(522\) | −34.3582 | −1.50382 | ||||||||
\(523\) | −39.9600 | −1.74733 | −0.873665 | − | 0.486528i | \(-0.838263\pi\) | ||||
−0.873665 | + | 0.486528i | \(0.838263\pi\) | |||||||
\(524\) | −55.8415 | −2.43945 | ||||||||
\(525\) | 8.26628 | 0.360770 | ||||||||
\(526\) | 31.8904 | 1.39049 | ||||||||
\(527\) | −19.4877 | −0.848897 | ||||||||
\(528\) | 9.72337 | 0.423155 | ||||||||
\(529\) | −22.0118 | −0.957035 | ||||||||
\(530\) | 31.1380 | 1.35255 | ||||||||
\(531\) | −8.14969 | −0.353667 | ||||||||
\(532\) | 7.31025 | 0.316940 | ||||||||
\(533\) | −4.28416 | −0.185568 | ||||||||
\(534\) | 77.0186 | 3.33292 | ||||||||
\(535\) | −5.62891 | −0.243359 | ||||||||
\(536\) | −0.469090 | −0.0202616 | ||||||||
\(537\) | −42.4794 | −1.83312 | ||||||||
\(538\) | 58.1774 | 2.50821 | ||||||||
\(539\) | 1.48551 | 0.0639856 | ||||||||
\(540\) | 13.2846 | 0.571677 | ||||||||
\(541\) | 5.93881 | 0.255330 | 0.127665 | − | 0.991817i | \(-0.459252\pi\) | ||||
0.127665 | + | 0.991817i | \(0.459252\pi\) | |||||||
\(542\) | −64.2674 | −2.76052 | ||||||||
\(543\) | −39.9669 | −1.71515 | ||||||||
\(544\) | −4.76202 | −0.204170 | ||||||||
\(545\) | −2.34761 | −0.100560 | ||||||||
\(546\) | 5.49113 | 0.234999 | ||||||||
\(547\) | −17.7257 | −0.757898 | −0.378949 | − | 0.925418i | \(-0.623714\pi\) | ||||
−0.378949 | + | 0.925418i | \(0.623714\pi\) | |||||||
\(548\) | 35.2737 | 1.50682 | ||||||||
\(549\) | 9.66615 | 0.412541 | ||||||||
\(550\) | 14.1538 | 0.603518 | ||||||||
\(551\) | −19.2291 | −0.819188 | ||||||||
\(552\) | 9.33029 | 0.397124 | ||||||||
\(553\) | 12.0716 | 0.513338 | ||||||||
\(554\) | 14.5699 | 0.619015 | ||||||||
\(555\) | −7.58636 | −0.322023 | ||||||||
\(556\) | −49.8513 | −2.11417 | ||||||||
\(557\) | −31.7621 | −1.34580 | −0.672901 | − | 0.739732i | \(-0.734952\pi\) | ||||
−0.672901 | + | 0.739732i | \(0.734952\pi\) | |||||||
\(558\) | −19.4629 | −0.823929 | ||||||||
\(559\) | −10.0710 | −0.425958 | ||||||||
\(560\) | 3.21240 | 0.135749 | ||||||||
\(561\) | −10.5903 | −0.447122 | ||||||||
\(562\) | −55.5862 | −2.34476 | ||||||||
\(563\) | −28.6635 | −1.20802 | −0.604011 | − | 0.796976i | \(-0.706432\pi\) | ||||
−0.604011 | + | 0.796976i | \(0.706432\pi\) | |||||||
\(564\) | −9.74759 | −0.410448 | ||||||||
\(565\) | −20.9827 | −0.882750 | ||||||||
\(566\) | 32.1325 | 1.35063 | ||||||||
\(567\) | 11.2406 | 0.472060 | ||||||||
\(568\) | 14.8434 | 0.622814 | ||||||||
\(569\) | −13.0571 | −0.547384 | −0.273692 | − | 0.961817i | \(-0.588245\pi\) | ||||
−0.273692 | + | 0.961817i | \(0.588245\pi\) | |||||||
\(570\) | −9.92490 | −0.415708 | ||||||||
\(571\) | 11.8830 | 0.497288 | 0.248644 | − | 0.968595i | \(-0.420015\pi\) | ||||
0.248644 | + | 0.968595i | \(0.420015\pi\) | |||||||
\(572\) | 6.18738 | 0.258707 | ||||||||
\(573\) | −49.6876 | −2.07573 | ||||||||
\(574\) | −9.57618 | −0.399702 | ||||||||
\(575\) | 3.91615 | 0.163315 | ||||||||
\(576\) | −13.5087 | −0.562863 | ||||||||
\(577\) | 25.3055 | 1.05348 | 0.526741 | − | 0.850026i | \(-0.323414\pi\) | ||||
0.526741 | + | 0.850026i | \(0.323414\pi\) | |||||||
\(578\) | 13.1982 | 0.548973 | ||||||||
\(579\) | −8.81160 | −0.366198 | ||||||||
\(580\) | −40.1409 | −1.66676 | ||||||||
\(581\) | 0.715863 | 0.0296990 | ||||||||
\(582\) | 58.5403 | 2.42657 | ||||||||
\(583\) | 18.5715 | 0.769153 | ||||||||
\(584\) | −23.1369 | −0.957412 | ||||||||
\(585\) | −1.56329 | −0.0646343 | ||||||||
\(586\) | −10.0097 | −0.413497 | ||||||||
\(587\) | −8.79091 | −0.362840 | −0.181420 | − | 0.983406i | \(-0.558069\pi\) | ||||
−0.181420 | + | 0.983406i | \(0.558069\pi\) | |||||||
\(588\) | 8.07740 | 0.333106 | ||||||||
\(589\) | −10.8927 | −0.448826 | ||||||||
\(590\) | −14.4682 | −0.595645 | ||||||||
\(591\) | −12.1993 | −0.501814 | ||||||||
\(592\) | 10.9513 | 0.450096 | ||||||||
\(593\) | 17.6922 | 0.726531 | 0.363265 | − | 0.931686i | \(-0.381662\pi\) | ||||
0.363265 | + | 0.931686i | \(0.381662\pi\) | |||||||
\(594\) | 12.0398 | 0.494001 | ||||||||
\(595\) | −3.49881 | −0.143437 | ||||||||
\(596\) | 14.0365 | 0.574956 | ||||||||
\(597\) | −23.2592 | −0.951935 | ||||||||
\(598\) | 2.60142 | 0.106380 | ||||||||
\(599\) | −19.2824 | −0.787858 | −0.393929 | − | 0.919141i | \(-0.628884\pi\) | ||||
−0.393929 | + | 0.919141i | \(0.628884\pi\) | |||||||
\(600\) | 36.9752 | 1.50951 | ||||||||
\(601\) | −20.0154 | −0.816444 | −0.408222 | − | 0.912883i | \(-0.633851\pi\) | ||||
−0.408222 | + | 0.912883i | \(0.633851\pi\) | |||||||
\(602\) | −22.5112 | −0.917488 | ||||||||
\(603\) | 0.147131 | 0.00599162 | ||||||||
\(604\) | 54.0725 | 2.20018 | ||||||||
\(605\) | 9.05548 | 0.368158 | ||||||||
\(606\) | −16.7371 | −0.679898 | ||||||||
\(607\) | 27.4368 | 1.11362 | 0.556812 | − | 0.830638i | \(-0.312024\pi\) | ||||
0.556812 | + | 0.830638i | \(0.312024\pi\) | |||||||
\(608\) | −2.66174 | −0.107948 | ||||||||
\(609\) | −21.2470 | −0.860974 | ||||||||
\(610\) | 17.1603 | 0.694802 | ||||||||
\(611\) | −1.30574 | −0.0528246 | ||||||||
\(612\) | −18.3487 | −0.741701 | ||||||||
\(613\) | 8.68507 | 0.350787 | 0.175393 | − | 0.984498i | \(-0.443880\pi\) | ||||
0.175393 | + | 0.984498i | \(0.443880\pi\) | |||||||
\(614\) | 16.2548 | 0.655990 | ||||||||
\(615\) | 8.55598 | 0.345010 | ||||||||
\(616\) | 6.64473 | 0.267724 | ||||||||
\(617\) | −16.4522 | −0.662341 | −0.331170 | − | 0.943571i | \(-0.607444\pi\) | ||||
−0.331170 | + | 0.943571i | \(0.607444\pi\) | |||||||
\(618\) | −6.40634 | −0.257701 | ||||||||
\(619\) | −27.2271 | −1.09435 | −0.547175 | − | 0.837018i | \(-0.684297\pi\) | ||||
−0.547175 | + | 0.837018i | \(0.684297\pi\) | |||||||
\(620\) | −22.7386 | −0.913203 | ||||||||
\(621\) | 3.33126 | 0.133679 | ||||||||
\(622\) | −49.5262 | −1.98582 | ||||||||
\(623\) | 15.1763 | 0.608025 | ||||||||
\(624\) | 7.08226 | 0.283517 | ||||||||
\(625\) | 10.2167 | 0.408669 | ||||||||
\(626\) | −7.35565 | −0.293991 | ||||||||
\(627\) | −5.91947 | −0.236401 | ||||||||
\(628\) | 31.0088 | 1.23739 | ||||||||
\(629\) | −11.9277 | −0.475589 | ||||||||
\(630\) | −3.49436 | −0.139218 | ||||||||
\(631\) | −41.3731 | −1.64704 | −0.823518 | − | 0.567289i | \(-0.807992\pi\) | ||||
−0.823518 | + | 0.567289i | \(0.807992\pi\) | |||||||
\(632\) | 53.9966 | 2.14787 | ||||||||
\(633\) | −3.31205 | −0.131642 | ||||||||
\(634\) | 58.5918 | 2.32698 | ||||||||
\(635\) | 16.1457 | 0.640722 | ||||||||
\(636\) | 100.982 | 4.00418 | ||||||||
\(637\) | 1.08201 | 0.0428708 | ||||||||
\(638\) | −36.3798 | −1.44029 | ||||||||
\(639\) | −4.65564 | −0.184174 | ||||||||
\(640\) | −21.0952 | −0.833861 | ||||||||
\(641\) | 45.3067 | 1.78951 | 0.894754 | − | 0.446560i | \(-0.147351\pi\) | ||||
0.894754 | + | 0.446560i | \(0.147351\pi\) | |||||||
\(642\) | −27.7391 | −1.09477 | ||||||||
\(643\) | 5.71604 | 0.225418 | 0.112709 | − | 0.993628i | \(-0.464047\pi\) | ||||
0.112709 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(644\) | 3.82667 | 0.150792 | ||||||||
\(645\) | 20.1130 | 0.791947 | ||||||||
\(646\) | −15.6045 | −0.613951 | ||||||||
\(647\) | −7.42167 | −0.291776 | −0.145888 | − | 0.989301i | \(-0.546604\pi\) | ||||
−0.145888 | + | 0.989301i | \(0.546604\pi\) | |||||||
\(648\) | 50.2793 | 1.97516 | ||||||||
\(649\) | −8.62920 | −0.338726 | ||||||||
\(650\) | 10.3092 | 0.404361 | ||||||||
\(651\) | −12.0358 | −0.471720 | ||||||||
\(652\) | −29.3185 | −1.14820 | ||||||||
\(653\) | −43.2905 | −1.69409 | −0.847044 | − | 0.531523i | \(-0.821620\pi\) | ||||
−0.847044 | + | 0.531523i | \(0.821620\pi\) | |||||||
\(654\) | −11.5689 | −0.452381 | ||||||||
\(655\) | 14.9390 | 0.583713 | ||||||||
\(656\) | −12.3510 | −0.482226 | ||||||||
\(657\) | 7.25691 | 0.283119 | ||||||||
\(658\) | −2.91866 | −0.113781 | ||||||||
\(659\) | −3.31724 | −0.129221 | −0.0646107 | − | 0.997911i | \(-0.520581\pi\) | ||||
−0.0646107 | + | 0.997911i | \(0.520581\pi\) | |||||||
\(660\) | −12.3569 | −0.480993 | ||||||||
\(661\) | 35.2547 | 1.37125 | 0.685625 | − | 0.727955i | \(-0.259529\pi\) | ||||
0.685625 | + | 0.727955i | \(0.259529\pi\) | |||||||
\(662\) | −49.4727 | −1.92281 | ||||||||
\(663\) | −7.71370 | −0.299575 | ||||||||
\(664\) | 3.20207 | 0.124264 | ||||||||
\(665\) | −1.95567 | −0.0758377 | ||||||||
\(666\) | −11.9125 | −0.461600 | ||||||||
\(667\) | −10.0658 | −0.389749 | ||||||||
\(668\) | −66.4293 | −2.57023 | ||||||||
\(669\) | −33.3878 | −1.29085 | ||||||||
\(670\) | 0.261201 | 0.0100911 | ||||||||
\(671\) | 10.2349 | 0.395113 | ||||||||
\(672\) | −2.94107 | −0.113454 | ||||||||
\(673\) | 12.7403 | 0.491103 | 0.245552 | − | 0.969384i | \(-0.421031\pi\) | ||||
0.245552 | + | 0.969384i | \(0.421031\pi\) | |||||||
\(674\) | −3.42673 | −0.131993 | ||||||||
\(675\) | 13.2015 | 0.508127 | ||||||||
\(676\) | −45.5361 | −1.75139 | ||||||||
\(677\) | −41.8809 | −1.60961 | −0.804806 | − | 0.593538i | \(-0.797731\pi\) | ||||
−0.804806 | + | 0.593538i | \(0.797731\pi\) | |||||||
\(678\) | −103.402 | −3.97114 | ||||||||
\(679\) | 11.5352 | 0.442680 | ||||||||
\(680\) | −15.6502 | −0.600160 | ||||||||
\(681\) | −25.5465 | −0.978943 | ||||||||
\(682\) | −20.6080 | −0.789122 | ||||||||
\(683\) | 23.1358 | 0.885268 | 0.442634 | − | 0.896702i | \(-0.354044\pi\) | ||||
0.442634 | + | 0.896702i | \(0.354044\pi\) | |||||||
\(684\) | −10.2560 | −0.392149 | ||||||||
\(685\) | −9.43657 | −0.360553 | ||||||||
\(686\) | 2.41856 | 0.0923412 | ||||||||
\(687\) | −55.6908 | −2.12474 | ||||||||
\(688\) | −29.0341 | −1.10692 | ||||||||
\(689\) | 13.5270 | 0.515338 | ||||||||
\(690\) | −5.19535 | −0.197783 | ||||||||
\(691\) | −33.2244 | −1.26392 | −0.631959 | − | 0.775002i | \(-0.717749\pi\) | ||||
−0.631959 | + | 0.775002i | \(0.717749\pi\) | |||||||
\(692\) | 38.6231 | 1.46823 | ||||||||
\(693\) | −2.08413 | −0.0791694 | ||||||||
\(694\) | −12.6896 | −0.481689 | ||||||||
\(695\) | 13.3364 | 0.505880 | ||||||||
\(696\) | −95.0384 | −3.60242 | ||||||||
\(697\) | 13.4522 | 0.509538 | ||||||||
\(698\) | 77.6698 | 2.93985 | ||||||||
\(699\) | 61.4968 | 2.32602 | ||||||||
\(700\) | 15.1648 | 0.573175 | ||||||||
\(701\) | −24.2115 | −0.914455 | −0.457227 | − | 0.889350i | \(-0.651157\pi\) | ||||
−0.457227 | + | 0.889350i | \(0.651157\pi\) | |||||||
\(702\) | 8.76952 | 0.330984 | ||||||||
\(703\) | −6.66702 | −0.251451 | ||||||||
\(704\) | −14.3035 | −0.539084 | ||||||||
\(705\) | 2.60772 | 0.0982123 | ||||||||
\(706\) | 58.3465 | 2.19590 | ||||||||
\(707\) | −3.29800 | −0.124034 | ||||||||
\(708\) | −46.9208 | −1.76339 | ||||||||
\(709\) | −1.17792 | −0.0442378 | −0.0221189 | − | 0.999755i | \(-0.507041\pi\) | ||||
−0.0221189 | + | 0.999755i | \(0.507041\pi\) | |||||||
\(710\) | −8.26516 | −0.310186 | ||||||||
\(711\) | −16.9361 | −0.635153 | ||||||||
\(712\) | 67.8838 | 2.54405 | ||||||||
\(713\) | −5.70196 | −0.213540 | ||||||||
\(714\) | −17.2420 | −0.645267 | ||||||||
\(715\) | −1.65528 | −0.0619038 | ||||||||
\(716\) | −77.9299 | −2.91238 | ||||||||
\(717\) | −17.4625 | −0.652149 | ||||||||
\(718\) | 40.4099 | 1.50808 | ||||||||
\(719\) | −25.2437 | −0.941430 | −0.470715 | − | 0.882285i | \(-0.656004\pi\) | ||||
−0.470715 | + | 0.882285i | \(0.656004\pi\) | |||||||
\(720\) | −4.50689 | −0.167962 | ||||||||
\(721\) | −1.26235 | −0.0470124 | ||||||||
\(722\) | 37.2305 | 1.38558 | ||||||||
\(723\) | 20.9506 | 0.779160 | ||||||||
\(724\) | −73.3208 | −2.72494 | ||||||||
\(725\) | −39.8899 | −1.48147 | ||||||||
\(726\) | 44.6251 | 1.65619 | ||||||||
\(727\) | −31.3492 | −1.16268 | −0.581339 | − | 0.813662i | \(-0.697471\pi\) | ||||
−0.581339 | + | 0.813662i | \(0.697471\pi\) | |||||||
\(728\) | 4.83985 | 0.179377 | ||||||||
\(729\) | 5.32489 | 0.197218 | ||||||||
\(730\) | 12.8832 | 0.476829 | ||||||||
\(731\) | 31.6227 | 1.16961 | ||||||||
\(732\) | 55.6516 | 2.05694 | ||||||||
\(733\) | −23.6872 | −0.874907 | −0.437454 | − | 0.899241i | \(-0.644120\pi\) | ||||
−0.437454 | + | 0.899241i | \(0.644120\pi\) | |||||||
\(734\) | 66.4205 | 2.45162 | ||||||||
\(735\) | −2.16090 | −0.0797060 | ||||||||
\(736\) | −1.39333 | −0.0513589 | ||||||||
\(737\) | 0.155787 | 0.00573850 | ||||||||
\(738\) | 13.4351 | 0.494551 | ||||||||
\(739\) | 53.7040 | 1.97553 | 0.987767 | − | 0.155940i | \(-0.0498406\pi\) | ||||
0.987767 | + | 0.155940i | \(0.0498406\pi\) | |||||||
\(740\) | −13.9174 | −0.511615 | ||||||||
\(741\) | −4.31159 | −0.158390 | ||||||||
\(742\) | 30.2362 | 1.11001 | ||||||||
\(743\) | −6.56075 | −0.240690 | −0.120345 | − | 0.992732i | \(-0.538400\pi\) | ||||
−0.120345 | + | 0.992732i | \(0.538400\pi\) | |||||||
\(744\) | −53.8363 | −1.97373 | ||||||||
\(745\) | −3.75510 | −0.137576 | ||||||||
\(746\) | −21.4455 | −0.785175 | ||||||||
\(747\) | −1.00433 | −0.0367466 | ||||||||
\(748\) | −19.4283 | −0.710368 | ||||||||
\(749\) | −5.46590 | −0.199720 | ||||||||
\(750\) | −46.7201 | −1.70598 | ||||||||
\(751\) | −20.3400 | −0.742216 | −0.371108 | − | 0.928590i | \(-0.621022\pi\) | ||||
−0.371108 | + | 0.928590i | \(0.621022\pi\) | |||||||
\(752\) | −3.76438 | −0.137273 | ||||||||
\(753\) | 32.2071 | 1.17369 | ||||||||
\(754\) | −26.4981 | −0.965004 | ||||||||
\(755\) | −14.4657 | −0.526461 | ||||||||
\(756\) | 12.8999 | 0.469164 | ||||||||
\(757\) | 45.4955 | 1.65356 | 0.826781 | − | 0.562525i | \(-0.190170\pi\) | ||||
0.826781 | + | 0.562525i | \(0.190170\pi\) | |||||||
\(758\) | 46.8367 | 1.70119 | ||||||||
\(759\) | −3.09864 | −0.112474 | ||||||||
\(760\) | −8.74775 | −0.317314 | ||||||||
\(761\) | 44.8309 | 1.62512 | 0.812560 | − | 0.582878i | \(-0.198074\pi\) | ||||
0.812560 | + | 0.582878i | \(0.198074\pi\) | |||||||
\(762\) | 79.5655 | 2.88235 | ||||||||
\(763\) | −2.27962 | −0.0825279 | ||||||||
\(764\) | −91.1537 | −3.29782 | ||||||||
\(765\) | 4.90872 | 0.177475 | ||||||||
\(766\) | −69.0811 | −2.49600 | ||||||||
\(767\) | −6.28529 | −0.226949 | ||||||||
\(768\) | −63.5483 | −2.29310 | ||||||||
\(769\) | 43.3073 | 1.56170 | 0.780851 | − | 0.624717i | \(-0.214786\pi\) | ||||
0.780851 | + | 0.624717i | \(0.214786\pi\) | |||||||
\(770\) | −3.69996 | −0.133337 | ||||||||
\(771\) | 42.3009 | 1.52343 | ||||||||
\(772\) | −16.1652 | −0.581798 | ||||||||
\(773\) | 13.2332 | 0.475964 | 0.237982 | − | 0.971270i | \(-0.423514\pi\) | ||||
0.237982 | + | 0.971270i | \(0.423514\pi\) | |||||||
\(774\) | 31.5825 | 1.13521 | ||||||||
\(775\) | −22.5964 | −0.811687 | ||||||||
\(776\) | 51.5971 | 1.85223 | ||||||||
\(777\) | −7.36667 | −0.264278 | ||||||||
\(778\) | −25.9258 | −0.929484 | ||||||||
\(779\) | 7.51914 | 0.269401 | ||||||||
\(780\) | −9.00047 | −0.322269 | ||||||||
\(781\) | −4.92956 | −0.176394 | ||||||||
\(782\) | −8.16842 | −0.292102 | ||||||||
\(783\) | −33.9322 | −1.21264 | ||||||||
\(784\) | 3.11937 | 0.111406 | ||||||||
\(785\) | −8.29561 | −0.296083 | ||||||||
\(786\) | 73.6187 | 2.62589 | ||||||||
\(787\) | 20.9538 | 0.746924 | 0.373462 | − | 0.927646i | \(-0.378171\pi\) | ||||
0.373462 | + | 0.927646i | \(0.378171\pi\) | |||||||
\(788\) | −22.3801 | −0.797259 | ||||||||
\(789\) | −27.6678 | −0.985001 | ||||||||
\(790\) | −30.0667 | −1.06972 | ||||||||
\(791\) | −20.3751 | −0.724455 | ||||||||
\(792\) | −9.32233 | −0.331255 | ||||||||
\(793\) | 7.45483 | 0.264729 | ||||||||
\(794\) | −39.2099 | −1.39151 | ||||||||
\(795\) | −27.0150 | −0.958124 | ||||||||
\(796\) | −42.6698 | −1.51239 | ||||||||
\(797\) | −38.8134 | −1.37484 | −0.687420 | − | 0.726260i | \(-0.741257\pi\) | ||||
−0.687420 | + | 0.726260i | \(0.741257\pi\) | |||||||
\(798\) | −9.63749 | −0.341163 | ||||||||
\(799\) | 4.10000 | 0.145048 | ||||||||
\(800\) | −5.52166 | −0.195220 | ||||||||
\(801\) | −21.2918 | −0.752309 | ||||||||
\(802\) | 37.7994 | 1.33474 | ||||||||
\(803\) | 7.68389 | 0.271159 | ||||||||
\(804\) | 0.847085 | 0.0298744 | ||||||||
\(805\) | −1.02373 | −0.0360817 | ||||||||
\(806\) | −15.0104 | −0.528717 | ||||||||
\(807\) | −50.4742 | −1.77678 | ||||||||
\(808\) | −14.7520 | −0.518973 | ||||||||
\(809\) | −43.5265 | −1.53031 | −0.765156 | − | 0.643845i | \(-0.777338\pi\) | ||||
−0.765156 | + | 0.643845i | \(0.777338\pi\) | |||||||
\(810\) | −27.9968 | −0.983708 | ||||||||
\(811\) | −19.7701 | −0.694222 | −0.347111 | − | 0.937824i | \(-0.612837\pi\) | ||||
−0.347111 | + | 0.937824i | \(0.612837\pi\) | |||||||
\(812\) | −38.9785 | −1.36788 | ||||||||
\(813\) | 55.7579 | 1.95551 | ||||||||
\(814\) | −12.6134 | −0.442100 | ||||||||
\(815\) | 7.84341 | 0.274743 | ||||||||
\(816\) | −22.2382 | −0.778491 | ||||||||
\(817\) | 17.6756 | 0.618392 | ||||||||
\(818\) | 56.7523 | 1.98430 | ||||||||
\(819\) | −1.51802 | −0.0530441 | ||||||||
\(820\) | 15.6962 | 0.548137 | ||||||||
\(821\) | 8.08980 | 0.282336 | 0.141168 | − | 0.989986i | \(-0.454914\pi\) | ||||
0.141168 | + | 0.989986i | \(0.454914\pi\) | |||||||
\(822\) | −46.5031 | −1.62198 | ||||||||
\(823\) | −3.15390 | −0.109938 | −0.0549691 | − | 0.998488i | \(-0.517506\pi\) | ||||
−0.0549691 | + | 0.998488i | \(0.517506\pi\) | |||||||
\(824\) | −5.64652 | −0.196706 | ||||||||
\(825\) | −12.2797 | −0.427523 | ||||||||
\(826\) | −14.0492 | −0.488834 | ||||||||
\(827\) | 21.4195 | 0.744829 | 0.372415 | − | 0.928066i | \(-0.378530\pi\) | ||||
0.372415 | + | 0.928066i | \(0.378530\pi\) | |||||||
\(828\) | −5.36869 | −0.186575 | ||||||||
\(829\) | −48.7102 | −1.69178 | −0.845888 | − | 0.533360i | \(-0.820929\pi\) | ||||
−0.845888 | + | 0.533360i | \(0.820929\pi\) | |||||||
\(830\) | −1.78299 | −0.0618886 | ||||||||
\(831\) | −12.6407 | −0.438501 | ||||||||
\(832\) | −10.4183 | −0.361190 | ||||||||
\(833\) | −3.39749 | −0.117716 | ||||||||
\(834\) | 65.7215 | 2.27575 | ||||||||
\(835\) | 17.7715 | 0.615007 | ||||||||
\(836\) | −10.8595 | −0.375583 | ||||||||
\(837\) | −19.2216 | −0.664395 | ||||||||
\(838\) | 0.211919 | 0.00732061 | ||||||||
\(839\) | 4.02063 | 0.138808 | 0.0694038 | − | 0.997589i | \(-0.477890\pi\) | ||||
0.0694038 | + | 0.997589i | \(0.477890\pi\) | |||||||
\(840\) | −9.66575 | −0.333500 | ||||||||
\(841\) | 73.5302 | 2.53552 | ||||||||
\(842\) | −19.1061 | −0.658440 | ||||||||
\(843\) | 48.2261 | 1.66099 | ||||||||
\(844\) | −6.07608 | −0.209147 | ||||||||
\(845\) | 12.1820 | 0.419074 | ||||||||
\(846\) | 4.09478 | 0.140781 | ||||||||
\(847\) | 8.79325 | 0.302140 | ||||||||
\(848\) | 38.9976 | 1.33918 | ||||||||
\(849\) | −27.8779 | −0.956767 | ||||||||
\(850\) | −32.3708 | −1.11031 | ||||||||
\(851\) | −3.48996 | −0.119634 | ||||||||
\(852\) | −26.8042 | −0.918298 | ||||||||
\(853\) | 34.4443 | 1.17935 | 0.589675 | − | 0.807641i | \(-0.299256\pi\) | ||||
0.589675 | + | 0.807641i | \(0.299256\pi\) | |||||||
\(854\) | 16.6634 | 0.570210 | ||||||||
\(855\) | 2.74374 | 0.0938340 | ||||||||
\(856\) | −24.4491 | −0.835652 | ||||||||
\(857\) | −53.3128 | −1.82113 | −0.910565 | − | 0.413367i | \(-0.864353\pi\) | ||||
−0.910565 | + | 0.413367i | \(0.864353\pi\) | |||||||
\(858\) | −8.15715 | −0.278480 | ||||||||
\(859\) | 19.6093 | 0.669062 | 0.334531 | − | 0.942385i | \(-0.391422\pi\) | ||||
0.334531 | + | 0.942385i | \(0.391422\pi\) | |||||||
\(860\) | 36.8979 | 1.25821 | ||||||||
\(861\) | 8.30821 | 0.283143 | ||||||||
\(862\) | −45.6480 | −1.55478 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −4.69699 | −0.159795 | ||||||||
\(865\) | −10.3326 | −0.351320 | ||||||||
\(866\) | 19.0631 | 0.647791 | ||||||||
\(867\) | −11.4507 | −0.388885 | ||||||||
\(868\) | −22.0801 | −0.749447 | ||||||||
\(869\) | −17.9326 | −0.608320 | ||||||||
\(870\) | 52.9198 | 1.79415 | ||||||||
\(871\) | 0.113472 | 0.00384484 | ||||||||
\(872\) | −10.1968 | −0.345307 | ||||||||
\(873\) | −16.1835 | −0.547728 | ||||||||
\(874\) | −4.56576 | −0.154439 | ||||||||
\(875\) | −9.20606 | −0.311222 | ||||||||
\(876\) | 41.7807 | 1.41164 | ||||||||
\(877\) | 33.6985 | 1.13792 | 0.568960 | − | 0.822365i | \(-0.307346\pi\) | ||||
0.568960 | + | 0.822365i | \(0.307346\pi\) | |||||||
\(878\) | −79.1691 | −2.67183 | ||||||||
\(879\) | 8.68433 | 0.292915 | ||||||||
\(880\) | −4.77207 | −0.160866 | ||||||||
\(881\) | 42.2511 | 1.42348 | 0.711738 | − | 0.702445i | \(-0.247908\pi\) | ||||
0.711738 | + | 0.702445i | \(0.247908\pi\) | |||||||
\(882\) | −3.39316 | −0.114254 | ||||||||
\(883\) | −47.5207 | −1.59920 | −0.799600 | − | 0.600533i | \(-0.794955\pi\) | ||||
−0.799600 | + | 0.600533i | \(0.794955\pi\) | |||||||
\(884\) | −14.1511 | −0.475951 | ||||||||
\(885\) | 12.5525 | 0.421946 | ||||||||
\(886\) | −65.4015 | −2.19720 | ||||||||
\(887\) | 16.8097 | 0.564414 | 0.282207 | − | 0.959354i | \(-0.408934\pi\) | ||||
0.282207 | + | 0.959354i | \(0.408934\pi\) | |||||||
\(888\) | −32.9512 | −1.10577 | ||||||||
\(889\) | 15.6781 | 0.525828 | ||||||||
\(890\) | −37.7994 | −1.26704 | ||||||||
\(891\) | −16.6980 | −0.559405 | ||||||||
\(892\) | −61.2511 | −2.05084 | ||||||||
\(893\) | 2.29171 | 0.0766891 | ||||||||
\(894\) | −18.5050 | −0.618900 | ||||||||
\(895\) | 20.8481 | 0.696877 | ||||||||
\(896\) | −20.4843 | −0.684333 | ||||||||
\(897\) | −2.25697 | −0.0753581 | ||||||||
\(898\) | −56.8863 | −1.89832 | ||||||||
\(899\) | 58.0802 | 1.93708 | ||||||||
\(900\) | −21.2757 | −0.709189 | ||||||||
\(901\) | −42.4745 | −1.41503 | ||||||||
\(902\) | 14.2255 | 0.473659 | ||||||||
\(903\) | 19.5305 | 0.649935 | ||||||||
\(904\) | −91.1382 | −3.03121 | ||||||||
\(905\) | 19.6151 | 0.652028 | ||||||||
\(906\) | −71.2866 | −2.36834 | ||||||||
\(907\) | 53.3866 | 1.77267 | 0.886336 | − | 0.463042i | \(-0.153242\pi\) | ||||
0.886336 | + | 0.463042i | \(0.153242\pi\) | |||||||
\(908\) | −46.8659 | −1.55530 | ||||||||
\(909\) | 4.62698 | 0.153467 | ||||||||
\(910\) | −2.69495 | −0.0893368 | ||||||||
\(911\) | −10.8268 | −0.358707 | −0.179353 | − | 0.983785i | \(-0.557401\pi\) | ||||
−0.179353 | + | 0.983785i | \(0.557401\pi\) | |||||||
\(912\) | −12.4301 | −0.411601 | ||||||||
\(913\) | −1.06342 | −0.0351942 | ||||||||
\(914\) | −38.8746 | −1.28586 | ||||||||
\(915\) | −14.8882 | −0.492188 | ||||||||
\(916\) | −102.167 | −3.37569 | ||||||||
\(917\) | 14.5064 | 0.479042 | ||||||||
\(918\) | −27.5361 | −0.908827 | ||||||||
\(919\) | −53.8490 | −1.77631 | −0.888157 | − | 0.459541i | \(-0.848014\pi\) | ||||
−0.888157 | + | 0.459541i | \(0.848014\pi\) | |||||||
\(920\) | −4.57915 | −0.150970 | ||||||||
\(921\) | −14.1025 | −0.464694 | ||||||||
\(922\) | 25.8020 | 0.849745 | ||||||||
\(923\) | −3.59057 | −0.118185 | ||||||||
\(924\) | −11.9991 | −0.394741 | ||||||||
\(925\) | −13.8304 | −0.454742 | ||||||||
\(926\) | −12.5647 | −0.412903 | ||||||||
\(927\) | 1.77104 | 0.0581684 | ||||||||
\(928\) | 14.1925 | 0.465891 | ||||||||
\(929\) | −56.5111 | −1.85407 | −0.927035 | − | 0.374974i | \(-0.877651\pi\) | ||||
−0.927035 | + | 0.374974i | \(0.877651\pi\) | |||||||
\(930\) | 29.9774 | 0.982999 | ||||||||
\(931\) | −1.89904 | −0.0622384 | ||||||||
\(932\) | 112.818 | 3.69548 | ||||||||
\(933\) | 42.9685 | 1.40672 | ||||||||
\(934\) | −2.78456 | −0.0911135 | ||||||||
\(935\) | 5.19753 | 0.169978 | ||||||||
\(936\) | −6.79015 | −0.221943 | ||||||||
\(937\) | −26.7929 | −0.875287 | −0.437643 | − | 0.899149i | \(-0.644187\pi\) | ||||
−0.437643 | + | 0.899149i | \(0.644187\pi\) | |||||||
\(938\) | 0.253637 | 0.00828155 | ||||||||
\(939\) | 6.38170 | 0.208259 | ||||||||
\(940\) | 4.78395 | 0.156035 | ||||||||
\(941\) | 16.3860 | 0.534169 | 0.267084 | − | 0.963673i | \(-0.413940\pi\) | ||||
0.267084 | + | 0.963673i | \(0.413940\pi\) | |||||||
\(942\) | −40.8805 | −1.33196 | ||||||||
\(943\) | 3.93602 | 0.128174 | ||||||||
\(944\) | −18.1201 | −0.589760 | ||||||||
\(945\) | −3.45103 | −0.112262 | ||||||||
\(946\) | 33.4407 | 1.08725 | ||||||||
\(947\) | 11.2918 | 0.366935 | 0.183467 | − | 0.983026i | \(-0.441268\pi\) | ||||
0.183467 | + | 0.983026i | \(0.441268\pi\) | |||||||
\(948\) | −97.5073 | −3.16689 | ||||||||
\(949\) | 5.59675 | 0.181678 | ||||||||
\(950\) | −18.0937 | −0.587039 | ||||||||
\(951\) | −50.8337 | −1.64840 | ||||||||
\(952\) | −15.1970 | −0.492539 | ||||||||
\(953\) | 49.5611 | 1.60544 | 0.802721 | − | 0.596355i | \(-0.203385\pi\) | ||||
0.802721 | + | 0.596355i | \(0.203385\pi\) | |||||||
\(954\) | −42.4204 | −1.37341 | ||||||||
\(955\) | 24.3858 | 0.789107 | ||||||||
\(956\) | −32.0356 | −1.03611 | ||||||||
\(957\) | 31.5628 | 1.02028 | ||||||||
\(958\) | −54.9134 | −1.77417 | ||||||||
\(959\) | −9.16330 | −0.295898 | ||||||||
\(960\) | 20.8066 | 0.671531 | ||||||||
\(961\) | 1.90062 | 0.0613103 | ||||||||
\(962\) | −9.18729 | −0.296210 | ||||||||
\(963\) | 7.66848 | 0.247113 | ||||||||
\(964\) | 38.4346 | 1.23789 | ||||||||
\(965\) | 4.32459 | 0.139213 | ||||||||
\(966\) | −5.04490 | −0.162317 | ||||||||
\(967\) | 2.95115 | 0.0949024 | 0.0474512 | − | 0.998874i | \(-0.484890\pi\) | ||||
0.0474512 | + | 0.998874i | \(0.484890\pi\) | |||||||
\(968\) | 39.3324 | 1.26419 | ||||||||
\(969\) | 13.5383 | 0.434913 | ||||||||
\(970\) | −28.7306 | −0.922484 | ||||||||
\(971\) | −46.4932 | −1.49204 | −0.746019 | − | 0.665925i | \(-0.768037\pi\) | ||||
−0.746019 | + | 0.665925i | \(0.768037\pi\) | |||||||
\(972\) | −52.0951 | −1.67095 | ||||||||
\(973\) | 12.9502 | 0.415165 | ||||||||
\(974\) | −22.5103 | −0.721277 | ||||||||
\(975\) | −8.94420 | −0.286444 | ||||||||
\(976\) | 21.4919 | 0.687937 | ||||||||
\(977\) | −24.2919 | −0.777168 | −0.388584 | − | 0.921413i | \(-0.627036\pi\) | ||||
−0.388584 | + | 0.921413i | \(0.627036\pi\) | |||||||
\(978\) | 38.6521 | 1.23596 | ||||||||
\(979\) | −22.5446 | −0.720528 | ||||||||
\(980\) | −3.96425 | −0.126633 | ||||||||
\(981\) | 3.19824 | 0.102112 | ||||||||
\(982\) | −75.7001 | −2.41569 | ||||||||
\(983\) | 17.3581 | 0.553638 | 0.276819 | − | 0.960922i | \(-0.410720\pi\) | ||||
0.276819 | + | 0.960922i | \(0.410720\pi\) | |||||||
\(984\) | 37.1628 | 1.18471 | ||||||||
\(985\) | 5.98723 | 0.190769 | ||||||||
\(986\) | 83.2036 | 2.64974 | ||||||||
\(987\) | 2.53220 | 0.0806009 | ||||||||
\(988\) | −7.90977 | −0.251643 | ||||||||
\(989\) | 9.25259 | 0.294215 | ||||||||
\(990\) | 5.19091 | 0.164978 | ||||||||
\(991\) | −2.14789 | −0.0682300 | −0.0341150 | − | 0.999418i | \(-0.510861\pi\) | ||||
−0.0341150 | + | 0.999418i | \(0.510861\pi\) | |||||||
\(992\) | 8.03960 | 0.255258 | ||||||||
\(993\) | 42.9220 | 1.36209 | ||||||||
\(994\) | −8.02582 | −0.254563 | ||||||||
\(995\) | 11.4152 | 0.361886 | ||||||||
\(996\) | −5.78231 | −0.183219 | ||||||||
\(997\) | 28.3117 | 0.896641 | 0.448321 | − | 0.893873i | \(-0.352022\pi\) | ||||
0.448321 | + | 0.893873i | \(0.352022\pi\) | |||||||
\(998\) | 104.497 | 3.30781 | ||||||||
\(999\) | −11.7648 | −0.372222 |
(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 | 6041.2.a.d.1.7 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.d.1.7 | ✓ | 101 | 1.1 | even | 1 | trivial |