Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7225,2,Mod(1,7225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7225, 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("7225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7225 = 5^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7225.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: | \(57.6919154604\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 21 x^{8} - 232 x^{7} + 44 x^{6} + 424 x^{5} - 137 x^{4} + \cdots + 17 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 85) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.35190\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35190 | −1.66305 | −0.831523 | − | 0.555490i | \(-0.812531\pi\) | ||||
−0.831523 | + | 0.555490i | \(0.812531\pi\) | |||||||
\(3\) | 1.56935 | 0.906065 | 0.453032 | − | 0.891494i | \(-0.350342\pi\) | ||||
0.453032 | + | 0.891494i | \(0.350342\pi\) | |||||||
\(4\) | 3.53144 | 1.76572 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.69096 | −1.50683 | ||||||||
\(7\) | 3.58212 | 1.35392 | 0.676958 | − | 0.736022i | \(-0.263298\pi\) | ||||
0.676958 | + | 0.736022i | \(0.263298\pi\) | |||||||
\(8\) | −3.60181 | −1.27343 | ||||||||
\(9\) | −0.537139 | −0.179046 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.48259 | −0.748530 | −0.374265 | − | 0.927322i | \(-0.622105\pi\) | ||||
−0.374265 | + | 0.927322i | \(0.622105\pi\) | |||||||
\(12\) | 5.54207 | 1.59986 | ||||||||
\(13\) | 1.25948 | 0.349317 | 0.174659 | − | 0.984629i | \(-0.444118\pi\) | ||||
0.174659 | + | 0.984629i | \(0.444118\pi\) | |||||||
\(14\) | −8.42480 | −2.25162 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.40821 | 0.352052 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.26330 | 0.297762 | ||||||||
\(19\) | −3.63431 | −0.833768 | −0.416884 | − | 0.908960i | \(-0.636878\pi\) | ||||
−0.416884 | + | 0.908960i | \(0.636878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.62161 | 1.22674 | ||||||||
\(22\) | 5.83882 | 1.24484 | ||||||||
\(23\) | 8.83293 | 1.84179 | 0.920896 | − | 0.389808i | \(-0.127459\pi\) | ||||
0.920896 | + | 0.389808i | \(0.127459\pi\) | |||||||
\(24\) | −5.65249 | −1.15381 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.96218 | −0.580931 | ||||||||
\(27\) | −5.55101 | −1.06829 | ||||||||
\(28\) | 12.6501 | 2.39064 | ||||||||
\(29\) | 8.75919 | 1.62654 | 0.813271 | − | 0.581885i | \(-0.197685\pi\) | ||||
0.813271 | + | 0.581885i | \(0.197685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.44403 | −0.438961 | −0.219480 | − | 0.975617i | \(-0.570436\pi\) | ||||
−0.219480 | + | 0.975617i | \(0.570436\pi\) | |||||||
\(32\) | 3.89165 | 0.687953 | ||||||||
\(33\) | −3.89606 | −0.678217 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.89688 | −0.316146 | ||||||||
\(37\) | 4.60155 | 0.756490 | 0.378245 | − | 0.925705i | \(-0.376528\pi\) | ||||
0.378245 | + | 0.925705i | \(0.376528\pi\) | |||||||
\(38\) | 8.54755 | 1.38660 | ||||||||
\(39\) | 1.97657 | 0.316504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.32497 | 0.675447 | 0.337724 | − | 0.941245i | \(-0.390343\pi\) | ||||
0.337724 | + | 0.941245i | \(0.390343\pi\) | |||||||
\(42\) | −13.2215 | −2.04012 | ||||||||
\(43\) | −7.54720 | −1.15094 | −0.575469 | − | 0.817824i | \(-0.695180\pi\) | ||||
−0.575469 | + | 0.817824i | \(0.695180\pi\) | |||||||
\(44\) | −8.76714 | −1.32170 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.7742 | −3.06299 | ||||||||
\(47\) | 11.3322 | 1.65297 | 0.826484 | − | 0.562961i | \(-0.190338\pi\) | ||||
0.826484 | + | 0.562961i | \(0.190338\pi\) | |||||||
\(48\) | 2.20997 | 0.318982 | ||||||||
\(49\) | 5.83161 | 0.833087 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.44779 | 0.616797 | ||||||||
\(53\) | −5.69139 | −0.781772 | −0.390886 | − | 0.920439i | \(-0.627831\pi\) | ||||
−0.390886 | + | 0.920439i | \(0.627831\pi\) | |||||||
\(54\) | 13.0554 | 1.77662 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.9021 | −1.72412 | ||||||||
\(57\) | −5.70351 | −0.755448 | ||||||||
\(58\) | −20.6008 | −2.70501 | ||||||||
\(59\) | −4.47000 | −0.581945 | −0.290972 | − | 0.956731i | \(-0.593979\pi\) | ||||
−0.290972 | + | 0.956731i | \(0.593979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.242871 | 0.0310964 | 0.0155482 | − | 0.999879i | \(-0.495051\pi\) | ||||
0.0155482 | + | 0.999879i | \(0.495051\pi\) | |||||||
\(62\) | 5.74812 | 0.730012 | ||||||||
\(63\) | −1.92410 | −0.242414 | ||||||||
\(64\) | −11.9692 | −1.49615 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.16315 | 1.12791 | ||||||||
\(67\) | 7.23278 | 0.883625 | 0.441812 | − | 0.897108i | \(-0.354336\pi\) | ||||
0.441812 | + | 0.897108i | \(0.354336\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.8620 | 1.66878 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.83778 | −0.218105 | −0.109052 | − | 0.994036i | \(-0.534782\pi\) | ||||
−0.109052 | + | 0.994036i | \(0.534782\pi\) | |||||||
\(72\) | 1.93467 | 0.228003 | ||||||||
\(73\) | −5.47256 | −0.640515 | −0.320257 | − | 0.947331i | \(-0.603769\pi\) | ||||
−0.320257 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(74\) | −10.8224 | −1.25808 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.8344 | −1.47220 | ||||||||
\(77\) | −8.89296 | −1.01345 | ||||||||
\(78\) | −4.64870 | −0.526361 | ||||||||
\(79\) | 9.03570 | 1.01660 | 0.508298 | − | 0.861181i | \(-0.330275\pi\) | ||||
0.508298 | + | 0.861181i | \(0.330275\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.10006 | −0.788896 | ||||||||
\(82\) | −10.1719 | −1.12330 | ||||||||
\(83\) | −7.31575 | −0.803008 | −0.401504 | − | 0.915857i | \(-0.631512\pi\) | ||||
−0.401504 | + | 0.915857i | \(0.631512\pi\) | |||||||
\(84\) | 19.8524 | 2.16607 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 17.7503 | 1.91406 | ||||||||
\(87\) | 13.7462 | 1.47375 | ||||||||
\(88\) | 8.94182 | 0.953201 | ||||||||
\(89\) | −2.19350 | −0.232510 | −0.116255 | − | 0.993219i | \(-0.537089\pi\) | ||||
−0.116255 | + | 0.993219i | \(0.537089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.51162 | 0.472946 | ||||||||
\(92\) | 31.1930 | 3.25209 | ||||||||
\(93\) | −3.83554 | −0.397727 | ||||||||
\(94\) | −26.6522 | −2.74896 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.10736 | 0.623330 | ||||||||
\(97\) | 9.82039 | 0.997110 | 0.498555 | − | 0.866858i | \(-0.333864\pi\) | ||||
0.498555 | + | 0.866858i | \(0.333864\pi\) | |||||||
\(98\) | −13.7154 | −1.38546 | ||||||||
\(99\) | 1.33350 | 0.134022 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.46415 | −0.543704 | −0.271852 | − | 0.962339i | \(-0.587636\pi\) | ||||
−0.271852 | + | 0.962339i | \(0.587636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.16074 | −0.705568 | −0.352784 | − | 0.935705i | \(-0.614765\pi\) | ||||
−0.352784 | + | 0.935705i | \(0.614765\pi\) | |||||||
\(104\) | −4.53641 | −0.444832 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.3856 | 1.30012 | ||||||||
\(107\) | −0.623156 | −0.0602427 | −0.0301214 | − | 0.999546i | \(-0.509589\pi\) | ||||
−0.0301214 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(108\) | −19.6031 | −1.88631 | ||||||||
\(109\) | −6.18952 | −0.592848 | −0.296424 | − | 0.955056i | \(-0.595794\pi\) | ||||
−0.296424 | + | 0.955056i | \(0.595794\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.22144 | 0.685429 | ||||||||
\(112\) | 5.04437 | 0.476648 | ||||||||
\(113\) | 16.0596 | 1.51076 | 0.755380 | − | 0.655287i | \(-0.227452\pi\) | ||||
0.755380 | + | 0.655287i | \(0.227452\pi\) | |||||||
\(114\) | 13.4141 | 1.25635 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 30.9326 | 2.87202 | ||||||||
\(117\) | −0.676517 | −0.0625440 | ||||||||
\(118\) | 10.5130 | 0.967801 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.83672 | −0.439702 | ||||||||
\(122\) | −0.571208 | −0.0517147 | ||||||||
\(123\) | 6.78740 | 0.611999 | ||||||||
\(124\) | −8.63096 | −0.775083 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.52529 | 0.403145 | ||||||||
\(127\) | 5.91786 | 0.525125 | 0.262563 | − | 0.964915i | \(-0.415432\pi\) | ||||
0.262563 | + | 0.964915i | \(0.415432\pi\) | |||||||
\(128\) | 20.3671 | 1.80021 | ||||||||
\(129\) | −11.8442 | −1.04282 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.1207 | 1.40848 | 0.704238 | − | 0.709964i | \(-0.251289\pi\) | ||||
0.704238 | + | 0.709964i | \(0.251289\pi\) | |||||||
\(132\) | −13.7587 | −1.19754 | ||||||||
\(133\) | −13.0186 | −1.12885 | ||||||||
\(134\) | −17.0108 | −1.46951 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.1320 | 1.46369 | 0.731843 | − | 0.681473i | \(-0.238661\pi\) | ||||
0.731843 | + | 0.681473i | \(0.238661\pi\) | |||||||
\(138\) | −32.6020 | −2.77526 | ||||||||
\(139\) | 2.13307 | 0.180925 | 0.0904624 | − | 0.995900i | \(-0.471165\pi\) | ||||
0.0904624 | + | 0.995900i | \(0.471165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.7842 | 1.49770 | ||||||||
\(142\) | 4.32229 | 0.362718 | ||||||||
\(143\) | −3.12678 | −0.261475 | ||||||||
\(144\) | −0.756403 | −0.0630335 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.8709 | 1.06521 | ||||||||
\(147\) | 9.15184 | 0.754831 | ||||||||
\(148\) | 16.2501 | 1.33575 | ||||||||
\(149\) | 18.5384 | 1.51872 | 0.759362 | − | 0.650669i | \(-0.225511\pi\) | ||||
0.759362 | + | 0.650669i | \(0.225511\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.91261 | 0.725298 | 0.362649 | − | 0.931926i | \(-0.381872\pi\) | ||||
0.362649 | + | 0.931926i | \(0.381872\pi\) | |||||||
\(152\) | 13.0901 | 1.06175 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.9154 | 1.68541 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.98014 | 0.558859 | ||||||||
\(157\) | −18.2426 | −1.45592 | −0.727960 | − | 0.685620i | \(-0.759531\pi\) | ||||
−0.727960 | + | 0.685620i | \(0.759531\pi\) | |||||||
\(158\) | −21.2511 | −1.69064 | ||||||||
\(159\) | −8.93178 | −0.708337 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 31.6406 | 2.49363 | ||||||||
\(162\) | 16.6987 | 1.31197 | ||||||||
\(163\) | 9.36510 | 0.733531 | 0.366766 | − | 0.930313i | \(-0.380465\pi\) | ||||
0.366766 | + | 0.930313i | \(0.380465\pi\) | |||||||
\(164\) | 15.2734 | 1.19265 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.2059 | 1.33544 | ||||||||
\(167\) | −9.28133 | −0.718211 | −0.359106 | − | 0.933297i | \(-0.616918\pi\) | ||||
−0.359106 | + | 0.933297i | \(0.616918\pi\) | |||||||
\(168\) | −20.2479 | −1.56216 | ||||||||
\(169\) | −11.4137 | −0.877977 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.95213 | 0.149283 | ||||||||
\(172\) | −26.6525 | −2.03224 | ||||||||
\(173\) | 4.29978 | 0.326906 | 0.163453 | − | 0.986551i | \(-0.447737\pi\) | ||||
0.163453 | + | 0.986551i | \(0.447737\pi\) | |||||||
\(174\) | −32.3298 | −2.45092 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.49601 | −0.263521 | ||||||||
\(177\) | −7.01500 | −0.527280 | ||||||||
\(178\) | 5.15889 | 0.386675 | ||||||||
\(179\) | −0.117678 | −0.00879567 | −0.00439783 | − | 0.999990i | \(-0.501400\pi\) | ||||
−0.00439783 | + | 0.999990i | \(0.501400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.32364 | 0.172715 | 0.0863574 | − | 0.996264i | \(-0.472477\pi\) | ||||
0.0863574 | + | 0.996264i | \(0.472477\pi\) | |||||||
\(182\) | −10.6109 | −0.786531 | ||||||||
\(183\) | 0.381149 | 0.0281754 | ||||||||
\(184\) | −31.8145 | −2.34539 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.02082 | 0.661438 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 40.0189 | 2.91868 | ||||||||
\(189\) | −19.8844 | −1.44638 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6622 | −1.06092 | −0.530461 | − | 0.847710i | \(-0.677981\pi\) | ||||
−0.530461 | + | 0.847710i | \(0.677981\pi\) | |||||||
\(192\) | −18.7838 | −1.35561 | ||||||||
\(193\) | −8.39606 | −0.604362 | −0.302181 | − | 0.953251i | \(-0.597715\pi\) | ||||
−0.302181 | + | 0.953251i | \(0.597715\pi\) | |||||||
\(194\) | −23.0966 | −1.65824 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.5940 | 1.47100 | ||||||||
\(197\) | 6.68150 | 0.476037 | 0.238019 | − | 0.971261i | \(-0.423502\pi\) | ||||
0.238019 | + | 0.971261i | \(0.423502\pi\) | |||||||
\(198\) | −3.13626 | −0.222884 | ||||||||
\(199\) | 18.8718 | 1.33779 | 0.668893 | − | 0.743359i | \(-0.266768\pi\) | ||||
0.668893 | + | 0.743359i | \(0.266768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3508 | 0.800621 | ||||||||
\(202\) | 12.8512 | 0.904204 | ||||||||
\(203\) | 31.3765 | 2.20220 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.8414 | 1.17339 | ||||||||
\(207\) | −4.74451 | −0.329766 | ||||||||
\(208\) | 1.77361 | 0.122978 | ||||||||
\(209\) | 9.02252 | 0.624101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.61973 | −0.455721 | −0.227860 | − | 0.973694i | \(-0.573173\pi\) | ||||
−0.227860 | + | 0.973694i | \(0.573173\pi\) | |||||||
\(212\) | −20.0988 | −1.38039 | ||||||||
\(213\) | −2.88413 | −0.197617 | ||||||||
\(214\) | 1.46560 | 0.100186 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 19.9937 | 1.36040 | ||||||||
\(217\) | −8.75482 | −0.594316 | ||||||||
\(218\) | 14.5571 | 0.985934 | ||||||||
\(219\) | −8.58836 | −0.580348 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −16.9841 | −1.13990 | ||||||||
\(223\) | −2.94266 | −0.197055 | −0.0985275 | − | 0.995134i | \(-0.531413\pi\) | ||||
−0.0985275 | + | 0.995134i | \(0.531413\pi\) | |||||||
\(224\) | 13.9404 | 0.931429 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.7706 | −2.51246 | ||||||||
\(227\) | 21.5256 | 1.42871 | 0.714353 | − | 0.699786i | \(-0.246721\pi\) | ||||
0.714353 | + | 0.699786i | \(0.246721\pi\) | |||||||
\(228\) | −20.1416 | −1.33391 | ||||||||
\(229\) | −11.9409 | −0.789075 | −0.394537 | − | 0.918880i | \(-0.629095\pi\) | ||||
−0.394537 | + | 0.918880i | \(0.629095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.9562 | −0.918249 | ||||||||
\(232\) | −31.5489 | −2.07129 | ||||||||
\(233\) | 10.0687 | 0.659623 | 0.329812 | − | 0.944047i | \(-0.393015\pi\) | ||||
0.329812 | + | 0.944047i | \(0.393015\pi\) | |||||||
\(234\) | 1.59110 | 0.104014 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.7856 | −1.02755 | ||||||||
\(237\) | 14.1802 | 0.921101 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.6253 | −1.07540 | −0.537701 | − | 0.843135i | \(-0.680707\pi\) | ||||
−0.537701 | + | 0.843135i | \(0.680707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.92200 | 0.381470 | 0.190735 | − | 0.981642i | \(-0.438913\pi\) | ||||
0.190735 | + | 0.981642i | \(0.438913\pi\) | |||||||
\(242\) | 11.3755 | 0.731245 | ||||||||
\(243\) | 5.51054 | 0.353502 | ||||||||
\(244\) | 0.857684 | 0.0549076 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.9633 | −1.01778 | ||||||||
\(247\) | −4.57735 | −0.291250 | ||||||||
\(248\) | 8.80292 | 0.558986 | ||||||||
\(249\) | −11.4810 | −0.727577 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.77270 | 0.490608 | 0.245304 | − | 0.969446i | \(-0.421112\pi\) | ||||
0.245304 | + | 0.969446i | \(0.421112\pi\) | |||||||
\(252\) | −6.79484 | −0.428035 | ||||||||
\(253\) | −21.9286 | −1.37864 | ||||||||
\(254\) | −13.9182 | −0.873307 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −23.9630 | −1.49768 | ||||||||
\(257\) | 8.06588 | 0.503135 | 0.251568 | − | 0.967840i | \(-0.419054\pi\) | ||||
0.251568 | + | 0.967840i | \(0.419054\pi\) | |||||||
\(258\) | 27.8564 | 1.73426 | ||||||||
\(259\) | 16.4833 | 1.02422 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.70491 | −0.291226 | ||||||||
\(262\) | −37.9144 | −2.34236 | ||||||||
\(263\) | 21.3252 | 1.31497 | 0.657483 | − | 0.753469i | \(-0.271621\pi\) | ||||
0.657483 | + | 0.753469i | \(0.271621\pi\) | |||||||
\(264\) | 14.0329 | 0.863662 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 30.6184 | 1.87733 | ||||||||
\(267\) | −3.44237 | −0.210670 | ||||||||
\(268\) | 25.5422 | 1.56024 | ||||||||
\(269\) | −4.20185 | −0.256191 | −0.128096 | − | 0.991762i | \(-0.540886\pi\) | ||||
−0.128096 | + | 0.991762i | \(0.540886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.7136 | 1.50124 | 0.750621 | − | 0.660733i | \(-0.229755\pi\) | ||||
0.750621 | + | 0.660733i | \(0.229755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.08031 | 0.428520 | ||||||||
\(274\) | −40.2928 | −2.43418 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 48.9527 | 2.94661 | ||||||||
\(277\) | 20.0627 | 1.20545 | 0.602725 | − | 0.797949i | \(-0.294082\pi\) | ||||
0.602725 | + | 0.797949i | \(0.294082\pi\) | |||||||
\(278\) | −5.01678 | −0.300886 | ||||||||
\(279\) | 1.31278 | 0.0785943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.1805 | 1.50215 | 0.751073 | − | 0.660219i | \(-0.229537\pi\) | ||||
0.751073 | + | 0.660219i | \(0.229537\pi\) | |||||||
\(282\) | −41.8266 | −2.49074 | ||||||||
\(283\) | 8.48659 | 0.504476 | 0.252238 | − | 0.967665i | \(-0.418833\pi\) | ||||
0.252238 | + | 0.967665i | \(0.418833\pi\) | |||||||
\(284\) | −6.49003 | −0.385112 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.35389 | 0.434845 | ||||||||
\(287\) | 15.4926 | 0.914499 | ||||||||
\(288\) | −2.09036 | −0.123175 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.4116 | 0.903446 | ||||||||
\(292\) | −19.3260 | −1.13097 | ||||||||
\(293\) | −25.9873 | −1.51820 | −0.759098 | − | 0.650977i | \(-0.774360\pi\) | ||||
−0.759098 | + | 0.650977i | \(0.774360\pi\) | |||||||
\(294\) | −21.5242 | −1.25532 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16.5739 | −0.963338 | ||||||||
\(297\) | 13.7809 | 0.799649 | ||||||||
\(298\) | −43.6005 | −2.52571 | ||||||||
\(299\) | 11.1249 | 0.643370 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.0350 | −1.55827 | ||||||||
\(302\) | −20.9616 | −1.20620 | ||||||||
\(303\) | −8.57517 | −0.492631 | ||||||||
\(304\) | −5.11786 | −0.293529 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9475 | −0.967245 | −0.483622 | − | 0.875277i | \(-0.660679\pi\) | ||||
−0.483622 | + | 0.875277i | \(0.660679\pi\) | |||||||
\(308\) | −31.4050 | −1.78947 | ||||||||
\(309\) | −11.2377 | −0.639291 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.1905 | 0.974782 | 0.487391 | − | 0.873184i | \(-0.337949\pi\) | ||||
0.487391 | + | 0.873184i | \(0.337949\pi\) | |||||||
\(312\) | −7.11922 | −0.403046 | ||||||||
\(313\) | −5.91487 | −0.334328 | −0.167164 | − | 0.985929i | \(-0.553461\pi\) | ||||
−0.167164 | + | 0.985929i | \(0.553461\pi\) | |||||||
\(314\) | 42.9049 | 2.42126 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 31.9090 | 1.79502 | ||||||||
\(317\) | −0.640574 | −0.0359782 | −0.0179891 | − | 0.999838i | \(-0.505726\pi\) | ||||
−0.0179891 | + | 0.999838i | \(0.505726\pi\) | |||||||
\(318\) | 21.0067 | 1.17800 | ||||||||
\(319\) | −21.7455 | −1.21752 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.977950 | −0.0545838 | ||||||||
\(322\) | −74.4157 | −4.14702 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −25.0735 | −1.39297 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.0258 | −1.21990 | ||||||||
\(327\) | −9.71352 | −0.537159 | ||||||||
\(328\) | −15.5777 | −0.860135 | ||||||||
\(329\) | 40.5932 | 2.23798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6609 | 0.640939 | 0.320469 | − | 0.947259i | \(-0.396159\pi\) | ||||
0.320469 | + | 0.947259i | \(0.396159\pi\) | |||||||
\(332\) | −25.8352 | −1.41789 | ||||||||
\(333\) | −2.47167 | −0.135447 | ||||||||
\(334\) | 21.8288 | 1.19442 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.91638 | 0.431874 | ||||||||
\(337\) | 30.8806 | 1.68217 | 0.841087 | − | 0.540900i | \(-0.181916\pi\) | ||||
0.841087 | + | 0.540900i | \(0.181916\pi\) | |||||||
\(338\) | 26.8439 | 1.46012 | ||||||||
\(339\) | 25.2031 | 1.36885 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.06754 | 0.328576 | ||||||||
\(342\) | −4.59122 | −0.248265 | ||||||||
\(343\) | −4.18533 | −0.225986 | ||||||||
\(344\) | 27.1836 | 1.46564 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.1127 | −0.543660 | ||||||||
\(347\) | −0.0149992 | −0.000805197 0 | −0.000402598 | − | 1.00000i | \(-0.500128\pi\) | ||||
−0.000402598 | 1.00000i | \(0.500128\pi\) | ||||||||
\(348\) | 48.5441 | 2.60224 | ||||||||
\(349\) | −3.65491 | −0.195643 | −0.0978215 | − | 0.995204i | \(-0.531187\pi\) | ||||
−0.0978215 | + | 0.995204i | \(0.531187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.99140 | −0.373173 | ||||||||
\(352\) | −9.66138 | −0.514953 | ||||||||
\(353\) | −3.82333 | −0.203495 | −0.101748 | − | 0.994810i | \(-0.532443\pi\) | ||||
−0.101748 | + | 0.994810i | \(0.532443\pi\) | |||||||
\(354\) | 16.4986 | 0.876891 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.74622 | −0.410549 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.276767 | 0.0146276 | ||||||||
\(359\) | −6.69675 | −0.353441 | −0.176721 | − | 0.984261i | \(-0.556549\pi\) | ||||
−0.176721 | + | 0.984261i | \(0.556549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.79178 | −0.304830 | ||||||||
\(362\) | −5.46497 | −0.287232 | ||||||||
\(363\) | −7.59052 | −0.398399 | ||||||||
\(364\) | 15.9325 | 0.835092 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.896426 | −0.0468569 | ||||||||
\(367\) | 23.0276 | 1.20203 | 0.601015 | − | 0.799238i | \(-0.294763\pi\) | ||||
0.601015 | + | 0.799238i | \(0.294763\pi\) | |||||||
\(368\) | 12.4386 | 0.648406 | ||||||||
\(369\) | −2.32311 | −0.120936 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.3873 | −1.05845 | ||||||||
\(372\) | −13.5450 | −0.702275 | ||||||||
\(373\) | −23.7303 | −1.22871 | −0.614355 | − | 0.789030i | \(-0.710584\pi\) | ||||
−0.614355 | + | 0.789030i | \(0.710584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −40.8163 | −2.10494 | ||||||||
\(377\) | 11.0320 | 0.568179 | ||||||||
\(378\) | 46.7662 | 2.40539 | ||||||||
\(379\) | −2.97819 | −0.152979 | −0.0764897 | − | 0.997070i | \(-0.524371\pi\) | ||||
−0.0764897 | + | 0.997070i | \(0.524371\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.28720 | 0.475798 | ||||||||
\(382\) | 34.4841 | 1.76436 | ||||||||
\(383\) | 24.4222 | 1.24791 | 0.623957 | − | 0.781459i | \(-0.285524\pi\) | ||||
0.623957 | + | 0.781459i | \(0.285524\pi\) | |||||||
\(384\) | 31.9631 | 1.63111 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.7467 | 1.00508 | ||||||||
\(387\) | 4.05390 | 0.206071 | ||||||||
\(388\) | 34.6802 | 1.76062 | ||||||||
\(389\) | 1.68867 | 0.0856191 | 0.0428095 | − | 0.999083i | \(-0.486369\pi\) | ||||
0.0428095 | + | 0.999083i | \(0.486369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −21.0043 | −1.06088 | ||||||||
\(393\) | 25.2991 | 1.27617 | ||||||||
\(394\) | −15.7142 | −0.791671 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.70917 | 0.236645 | ||||||||
\(397\) | 31.5256 | 1.58222 | 0.791112 | − | 0.611671i | \(-0.209502\pi\) | ||||
0.791112 | + | 0.611671i | \(0.209502\pi\) | |||||||
\(398\) | −44.3846 | −2.22480 | ||||||||
\(399\) | −20.4307 | −1.02281 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.06607 | 0.252987 | 0.126494 | − | 0.991967i | \(-0.459628\pi\) | ||||
0.126494 | + | 0.991967i | \(0.459628\pi\) | |||||||
\(402\) | −26.6959 | −1.33147 | ||||||||
\(403\) | −3.07821 | −0.153337 | ||||||||
\(404\) | −19.2964 | −0.960029 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −73.7945 | −3.66236 | ||||||||
\(407\) | −11.4238 | −0.566256 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.1178 | −1.29144 | −0.645722 | − | 0.763573i | \(-0.723443\pi\) | ||||
−0.645722 | + | 0.763573i | \(0.723443\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.8861 | 1.32619 | ||||||||
\(412\) | −25.2877 | −1.24584 | ||||||||
\(413\) | −16.0121 | −0.787904 | ||||||||
\(414\) | 11.1586 | 0.548416 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.90146 | 0.240314 | ||||||||
\(417\) | 3.34754 | 0.163930 | ||||||||
\(418\) | −21.2201 | −1.03791 | ||||||||
\(419\) | −7.29855 | −0.356557 | −0.178279 | − | 0.983980i | \(-0.557053\pi\) | ||||
−0.178279 | + | 0.983980i | \(0.557053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.0644 | −1.02662 | −0.513309 | − | 0.858204i | \(-0.671580\pi\) | ||||
−0.513309 | + | 0.858204i | \(0.671580\pi\) | |||||||
\(422\) | 15.5690 | 0.757885 | ||||||||
\(423\) | −6.08695 | −0.295958 | ||||||||
\(424\) | 20.4993 | 0.995533 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.78319 | 0.328646 | ||||||||
\(427\) | 0.869993 | 0.0421019 | ||||||||
\(428\) | −2.20064 | −0.106372 | ||||||||
\(429\) | −4.90702 | −0.236913 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.0432 | −1.01362 | −0.506809 | − | 0.862059i | \(-0.669175\pi\) | ||||
−0.506809 | + | 0.862059i | \(0.669175\pi\) | |||||||
\(432\) | −7.81697 | −0.376094 | ||||||||
\(433\) | −37.1262 | −1.78417 | −0.892084 | − | 0.451869i | \(-0.850758\pi\) | ||||
−0.892084 | + | 0.451869i | \(0.850758\pi\) | |||||||
\(434\) | 20.5905 | 0.988375 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.8579 | −1.04680 | ||||||||
\(437\) | −32.1016 | −1.53563 | ||||||||
\(438\) | 20.1990 | 0.965145 | ||||||||
\(439\) | −0.471326 | −0.0224952 | −0.0112476 | − | 0.999937i | \(-0.503580\pi\) | ||||
−0.0112476 | + | 0.999937i | \(0.503580\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.13238 | −0.149161 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0249 | 0.523808 | 0.261904 | − | 0.965094i | \(-0.415650\pi\) | ||||
0.261904 | + | 0.965094i | \(0.415650\pi\) | |||||||
\(444\) | 25.5021 | 1.21028 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.92084 | 0.327711 | ||||||||
\(447\) | 29.0932 | 1.37606 | ||||||||
\(448\) | −42.8751 | −2.02566 | ||||||||
\(449\) | −17.2633 | −0.814703 | −0.407352 | − | 0.913271i | \(-0.633548\pi\) | ||||
−0.407352 | + | 0.913271i | \(0.633548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.7372 | −0.505593 | ||||||||
\(452\) | 56.7136 | 2.66758 | ||||||||
\(453\) | 13.9870 | 0.657167 | ||||||||
\(454\) | −50.6262 | −2.37600 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.5429 | 0.962011 | ||||||||
\(457\) | −11.2676 | −0.527078 | −0.263539 | − | 0.964649i | \(-0.584890\pi\) | ||||
−0.263539 | + | 0.964649i | \(0.584890\pi\) | |||||||
\(458\) | 28.0837 | 1.31227 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0075 | 1.39759 | 0.698794 | − | 0.715323i | \(-0.253720\pi\) | ||||
0.698794 | + | 0.715323i | \(0.253720\pi\) | |||||||
\(462\) | 32.8235 | 1.52709 | ||||||||
\(463\) | 17.1592 | 0.797457 | 0.398728 | − | 0.917069i | \(-0.369452\pi\) | ||||
0.398728 | + | 0.917069i | \(0.369452\pi\) | |||||||
\(464\) | 12.3348 | 0.572627 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.6806 | −1.09698 | ||||||||
\(467\) | 26.5914 | 1.23051 | 0.615253 | − | 0.788330i | \(-0.289054\pi\) | ||||
0.615253 | + | 0.788330i | \(0.289054\pi\) | |||||||
\(468\) | −2.38908 | −0.110435 | ||||||||
\(469\) | 25.9087 | 1.19635 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.6291 | −1.31916 | ||||||||
\(472\) | 16.1001 | 0.741066 | ||||||||
\(473\) | 18.7366 | 0.861512 | ||||||||
\(474\) | −33.3504 | −1.53183 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.05707 | 0.139974 | ||||||||
\(478\) | 39.1011 | 1.78844 | ||||||||
\(479\) | −22.9101 | −1.04679 | −0.523395 | − | 0.852090i | \(-0.675335\pi\) | ||||
−0.523395 | + | 0.852090i | \(0.675335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.79557 | 0.264255 | ||||||||
\(482\) | −13.9280 | −0.634402 | ||||||||
\(483\) | 49.6552 | 2.25939 | ||||||||
\(484\) | −17.0806 | −0.776392 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −12.9603 | −0.587889 | ||||||||
\(487\) | 15.7135 | 0.712048 | 0.356024 | − | 0.934477i | \(-0.384132\pi\) | ||||
0.356024 | + | 0.934477i | \(0.384132\pi\) | |||||||
\(488\) | −0.874773 | −0.0395991 | ||||||||
\(489\) | 14.6971 | 0.664627 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.859183 | −0.0387744 | −0.0193872 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193872 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(492\) | 23.9693 | 1.08062 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 10.7655 | 0.484362 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.44170 | −0.154537 | ||||||||
\(497\) | −6.58317 | −0.295296 | ||||||||
\(498\) | 27.0021 | 1.20999 | ||||||||
\(499\) | −22.6396 | −1.01349 | −0.506744 | − | 0.862097i | \(-0.669151\pi\) | ||||
−0.506744 | + | 0.862097i | \(0.669151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.5657 | −0.650746 | ||||||||
\(502\) | −18.2806 | −0.815904 | ||||||||
\(503\) | −17.1150 | −0.763121 | −0.381560 | − | 0.924344i | \(-0.624613\pi\) | ||||
−0.381560 | + | 0.924344i | \(0.624613\pi\) | |||||||
\(504\) | 6.93023 | 0.308697 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 51.5739 | 2.29274 | ||||||||
\(507\) | −17.9121 | −0.795504 | ||||||||
\(508\) | 20.8986 | 0.927225 | ||||||||
\(509\) | −29.7081 | −1.31679 | −0.658393 | − | 0.752674i | \(-0.728764\pi\) | ||||
−0.658393 | + | 0.752674i | \(0.728764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.6034 | −0.867203 | ||||||||
\(512\) | 15.6244 | 0.690508 | ||||||||
\(513\) | 20.1741 | 0.890709 | ||||||||
\(514\) | −18.9701 | −0.836737 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −41.8271 | −1.84134 | ||||||||
\(517\) | −28.1332 | −1.23730 | ||||||||
\(518\) | −38.7672 | −1.70333 | ||||||||
\(519\) | 6.74786 | 0.296198 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.6564 | 1.69357 | 0.846784 | − | 0.531936i | \(-0.178535\pi\) | ||||
0.846784 | + | 0.531936i | \(0.178535\pi\) | |||||||
\(522\) | 11.0655 | 0.484323 | ||||||||
\(523\) | −0.599508 | −0.0262147 | −0.0131073 | − | 0.999914i | \(-0.504172\pi\) | ||||
−0.0131073 | + | 0.999914i | \(0.504172\pi\) | |||||||
\(524\) | 56.9295 | 2.48698 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −50.1547 | −2.18685 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −5.48646 | −0.238767 | ||||||||
\(529\) | 55.0206 | 2.39220 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.40101 | 0.104195 | ||||||||
\(532\) | −45.9743 | −1.99324 | ||||||||
\(533\) | 5.44723 | 0.235946 | ||||||||
\(534\) | 8.09611 | 0.350353 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26.0511 | −1.12523 | ||||||||
\(537\) | −0.184678 | −0.00796945 | ||||||||
\(538\) | 9.88234 | 0.426058 | ||||||||
\(539\) | −14.4775 | −0.623591 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.7072 | −1.70715 | −0.853573 | − | 0.520973i | \(-0.825569\pi\) | ||||
−0.853573 | + | 0.520973i | \(0.825569\pi\) | |||||||
\(542\) | −58.1239 | −2.49663 | ||||||||
\(543\) | 3.64660 | 0.156491 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.6522 | −0.712649 | ||||||||
\(547\) | 4.03770 | 0.172639 | 0.0863197 | − | 0.996267i | \(-0.472489\pi\) | ||||
0.0863197 | + | 0.996267i | \(0.472489\pi\) | |||||||
\(548\) | 60.5007 | 2.58446 | ||||||||
\(549\) | −0.130455 | −0.00556770 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.8336 | −1.35616 | ||||||||
\(552\) | −49.9281 | −2.12508 | ||||||||
\(553\) | 32.3670 | 1.37638 | ||||||||
\(554\) | −47.1854 | −2.00472 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.53283 | 0.319463 | ||||||||
\(557\) | −5.42781 | −0.229984 | −0.114992 | − | 0.993366i | \(-0.536684\pi\) | ||||
−0.114992 | + | 0.993366i | \(0.536684\pi\) | |||||||
\(558\) | −3.08754 | −0.130706 | ||||||||
\(559\) | −9.50557 | −0.402043 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −59.2222 | −2.49814 | ||||||||
\(563\) | 5.18858 | 0.218673 | 0.109336 | − | 0.994005i | \(-0.465127\pi\) | ||||
0.109336 | + | 0.994005i | \(0.465127\pi\) | |||||||
\(564\) | 62.8037 | 2.64451 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.9596 | −0.838966 | ||||||||
\(567\) | −25.4333 | −1.06810 | ||||||||
\(568\) | 6.61934 | 0.277741 | ||||||||
\(569\) | −11.9963 | −0.502911 | −0.251455 | − | 0.967869i | \(-0.580909\pi\) | ||||
−0.251455 | + | 0.967869i | \(0.580909\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.5118 | −1.82091 | −0.910456 | − | 0.413606i | \(-0.864269\pi\) | ||||
−0.910456 | + | 0.413606i | \(0.864269\pi\) | |||||||
\(572\) | −11.0421 | −0.461692 | ||||||||
\(573\) | −23.0102 | −0.961263 | ||||||||
\(574\) | −36.4371 | −1.52085 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.42912 | 0.267880 | ||||||||
\(577\) | 27.7097 | 1.15357 | 0.576784 | − | 0.816897i | \(-0.304307\pi\) | ||||
0.576784 | + | 0.816897i | \(0.304307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.1764 | −0.547591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.2059 | −1.08720 | ||||||||
\(582\) | −36.2467 | −1.50247 | ||||||||
\(583\) | 14.1294 | 0.585180 | ||||||||
\(584\) | 19.7111 | 0.815651 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 61.1196 | 2.52483 | ||||||||
\(587\) | −4.37916 | −0.180747 | −0.0903736 | − | 0.995908i | \(-0.528806\pi\) | ||||
−0.0903736 | + | 0.995908i | \(0.528806\pi\) | |||||||
\(588\) | 32.3192 | 1.33282 | ||||||||
\(589\) | 8.88237 | 0.365992 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.4856 | 0.431320 | ||||||||
\(592\) | 6.47993 | 0.266324 | ||||||||
\(593\) | 35.8783 | 1.47335 | 0.736673 | − | 0.676250i | \(-0.236396\pi\) | ||||
0.736673 | + | 0.676250i | \(0.236396\pi\) | |||||||
\(594\) | −32.4114 | −1.32985 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 65.4673 | 2.68164 | ||||||||
\(597\) | 29.6165 | 1.21212 | ||||||||
\(598\) | −26.1647 | −1.06995 | ||||||||
\(599\) | 11.1415 | 0.455230 | 0.227615 | − | 0.973751i | \(-0.426907\pi\) | ||||
0.227615 | + | 0.973751i | \(0.426907\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4505 | 0.834193 | 0.417096 | − | 0.908862i | \(-0.363048\pi\) | ||||
0.417096 | + | 0.908862i | \(0.363048\pi\) | |||||||
\(602\) | 63.5837 | 2.59148 | ||||||||
\(603\) | −3.88501 | −0.158210 | ||||||||
\(604\) | 31.4744 | 1.28067 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.1680 | 0.819268 | ||||||||
\(607\) | −1.57554 | −0.0639492 | −0.0319746 | − | 0.999489i | \(-0.510180\pi\) | ||||
−0.0319746 | + | 0.999489i | \(0.510180\pi\) | |||||||
\(608\) | −14.1435 | −0.573593 | ||||||||
\(609\) | 49.2407 | 1.99534 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.2727 | 0.577410 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4800 | 0.907959 | 0.453980 | − | 0.891012i | \(-0.350004\pi\) | ||||
0.453980 | + | 0.891012i | \(0.350004\pi\) | |||||||
\(614\) | 39.8589 | 1.60857 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 32.0307 | 1.29055 | ||||||||
\(617\) | 27.1976 | 1.09493 | 0.547467 | − | 0.836827i | \(-0.315592\pi\) | ||||
0.547467 | + | 0.836827i | \(0.315592\pi\) | |||||||
\(618\) | 26.4300 | 1.06317 | ||||||||
\(619\) | −14.3702 | −0.577588 | −0.288794 | − | 0.957391i | \(-0.593254\pi\) | ||||
−0.288794 | + | 0.957391i | \(0.593254\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.0317 | −1.96757 | ||||||||
\(622\) | −40.4303 | −1.62111 | ||||||||
\(623\) | −7.85738 | −0.314799 | ||||||||
\(624\) | 2.78342 | 0.111426 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.9112 | 0.556003 | ||||||||
\(627\) | 14.1595 | 0.565476 | ||||||||
\(628\) | −64.4228 | −2.57075 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2691 | −0.926330 | −0.463165 | − | 0.886272i | \(-0.653286\pi\) | ||||
−0.463165 | + | 0.886272i | \(0.653286\pi\) | |||||||
\(632\) | −32.5448 | −1.29456 | ||||||||
\(633\) | −10.3887 | −0.412913 | ||||||||
\(634\) | 1.50657 | 0.0598334 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −31.5421 | −1.25073 | ||||||||
\(637\) | 7.34480 | 0.291012 | ||||||||
\(638\) | 51.1434 | 2.02478 | ||||||||
\(639\) | 0.987146 | 0.0390509 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.38403 | −0.212656 | −0.106328 | − | 0.994331i | \(-0.533909\pi\) | ||||
−0.106328 | + | 0.994331i | \(0.533909\pi\) | |||||||
\(642\) | 2.30004 | 0.0907754 | ||||||||
\(643\) | 16.1891 | 0.638438 | 0.319219 | − | 0.947681i | \(-0.396580\pi\) | ||||
0.319219 | + | 0.947681i | \(0.396580\pi\) | |||||||
\(644\) | 111.737 | 4.40306 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.8383 | 1.01581 | 0.507904 | − | 0.861413i | \(-0.330420\pi\) | ||||
0.507904 | + | 0.861413i | \(0.330420\pi\) | |||||||
\(648\) | 25.5730 | 1.00460 | ||||||||
\(649\) | 11.0972 | 0.435604 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.7394 | −0.538489 | ||||||||
\(652\) | 33.0723 | 1.29521 | ||||||||
\(653\) | −12.4784 | −0.488319 | −0.244159 | − | 0.969735i | \(-0.578512\pi\) | ||||
−0.244159 | + | 0.969735i | \(0.578512\pi\) | |||||||
\(654\) | 22.8452 | 0.893320 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.09045 | 0.237792 | ||||||||
\(657\) | 2.93953 | 0.114682 | ||||||||
\(658\) | −95.4713 | −3.72186 | ||||||||
\(659\) | 41.7109 | 1.62483 | 0.812413 | − | 0.583082i | \(-0.198153\pi\) | ||||
0.812413 | + | 0.583082i | \(0.198153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.1720 | 0.706808 | 0.353404 | − | 0.935471i | \(-0.385024\pi\) | ||||
0.353404 | + | 0.935471i | \(0.385024\pi\) | |||||||
\(662\) | −27.4252 | −1.06591 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.3499 | 1.02257 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.81313 | 0.225254 | ||||||||
\(667\) | 77.3693 | 2.99575 | ||||||||
\(668\) | −32.7765 | −1.26816 | ||||||||
\(669\) | −4.61806 | −0.178545 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.602949 | −0.0232766 | ||||||||
\(672\) | 21.8773 | 0.843936 | ||||||||
\(673\) | −6.39677 | −0.246577 | −0.123289 | − | 0.992371i | \(-0.539344\pi\) | ||||
−0.123289 | + | 0.992371i | \(0.539344\pi\) | |||||||
\(674\) | −72.6282 | −2.79753 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −40.3069 | −1.55026 | ||||||||
\(677\) | −41.8887 | −1.60991 | −0.804957 | − | 0.593334i | \(-0.797811\pi\) | ||||
−0.804957 | + | 0.593334i | \(0.797811\pi\) | |||||||
\(678\) | −59.2753 | −2.27645 | ||||||||
\(679\) | 35.1779 | 1.35000 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.7812 | 1.29450 | ||||||||
\(682\) | −14.2703 | −0.546436 | ||||||||
\(683\) | −30.3064 | −1.15964 | −0.579820 | − | 0.814744i | \(-0.696877\pi\) | ||||
−0.579820 | + | 0.814744i | \(0.696877\pi\) | |||||||
\(684\) | 6.89384 | 0.263593 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.84348 | 0.375826 | ||||||||
\(687\) | −18.7394 | −0.714953 | ||||||||
\(688\) | −10.6280 | −0.405189 | ||||||||
\(689\) | −7.16820 | −0.273087 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.79281 | −0.220369 | −0.110184 | − | 0.993911i | \(-0.535144\pi\) | ||||
−0.110184 | + | 0.993911i | \(0.535144\pi\) | |||||||
\(692\) | 15.1844 | 0.577225 | ||||||||
\(693\) | 4.77676 | 0.181454 | ||||||||
\(694\) | 0.0352765 | 0.00133908 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −49.5113 | −1.87672 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 8.59600 | 0.325363 | ||||||||
\(699\) | 15.8013 | 0.597662 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.24783 | 0.198208 | 0.0991039 | − | 0.995077i | \(-0.468402\pi\) | ||||
0.0991039 | + | 0.995077i | \(0.468402\pi\) | |||||||
\(702\) | 16.4431 | 0.620604 | ||||||||
\(703\) | −16.7235 | −0.630738 | ||||||||
\(704\) | 29.7146 | 1.11991 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.99209 | 0.338422 | ||||||||
\(707\) | −19.5733 | −0.736129 | ||||||||
\(708\) | −24.7731 | −0.931030 | ||||||||
\(709\) | 41.7572 | 1.56823 | 0.784113 | − | 0.620618i | \(-0.213118\pi\) | ||||
0.784113 | + | 0.620618i | \(0.213118\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.85343 | −0.182018 | ||||||||
\(712\) | 7.90055 | 0.296086 | ||||||||
\(713\) | −21.5879 | −0.808475 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.415573 | −0.0155307 | ||||||||
\(717\) | −26.0910 | −0.974385 | ||||||||
\(718\) | 15.7501 | 0.587789 | ||||||||
\(719\) | −10.1819 | −0.379719 | −0.189860 | − | 0.981811i | \(-0.560803\pi\) | ||||
−0.189860 | + | 0.981811i | \(0.560803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.6506 | −0.955280 | ||||||||
\(722\) | 13.6217 | 0.506947 | ||||||||
\(723\) | 9.29370 | 0.345636 | ||||||||
\(724\) | 8.20580 | 0.304966 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.8521 | 0.662555 | ||||||||
\(727\) | −46.0182 | −1.70672 | −0.853361 | − | 0.521321i | \(-0.825439\pi\) | ||||
−0.853361 | + | 0.521321i | \(0.825439\pi\) | |||||||
\(728\) | −16.2500 | −0.602264 | ||||||||
\(729\) | 29.9482 | 1.10919 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.34601 | 0.0497498 | ||||||||
\(733\) | 2.55919 | 0.0945257 | 0.0472629 | − | 0.998882i | \(-0.484950\pi\) | ||||
0.0472629 | + | 0.998882i | \(0.484950\pi\) | |||||||
\(734\) | −54.1586 | −1.99903 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.3746 | 1.26707 | ||||||||
\(737\) | −17.9561 | −0.661420 | ||||||||
\(738\) | 5.46373 | 0.201123 | ||||||||
\(739\) | −2.47667 | −0.0911057 | −0.0455528 | − | 0.998962i | \(-0.514505\pi\) | ||||
−0.0455528 | + | 0.998962i | \(0.514505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.18347 | −0.263891 | ||||||||
\(742\) | 47.9488 | 1.76026 | ||||||||
\(743\) | −1.59477 | −0.0585064 | −0.0292532 | − | 0.999572i | \(-0.509313\pi\) | ||||
−0.0292532 | + | 0.999572i | \(0.509313\pi\) | |||||||
\(744\) | 13.8149 | 0.506478 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 55.8114 | 2.04340 | ||||||||
\(747\) | 3.92957 | 0.143776 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.23222 | −0.0815636 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7441 | 0.465041 | 0.232520 | − | 0.972592i | \(-0.425303\pi\) | ||||
0.232520 | + | 0.972592i | \(0.425303\pi\) | |||||||
\(752\) | 15.9580 | 0.581930 | ||||||||
\(753\) | 12.1981 | 0.444523 | ||||||||
\(754\) | −25.9463 | −0.944908 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −70.2207 | −2.55390 | ||||||||
\(757\) | 46.0573 | 1.67398 | 0.836991 | − | 0.547217i | \(-0.184313\pi\) | ||||
0.836991 | + | 0.547217i | \(0.184313\pi\) | |||||||
\(758\) | 7.00441 | 0.254412 | ||||||||
\(759\) | −34.4136 | −1.24914 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.7003 | −1.07664 | −0.538318 | − | 0.842742i | \(-0.680940\pi\) | ||||
−0.538318 | + | 0.842742i | \(0.680940\pi\) | |||||||
\(762\) | −21.8426 | −0.791273 | ||||||||
\(763\) | −22.1716 | −0.802666 | ||||||||
\(764\) | −51.7788 | −1.87329 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −57.4385 | −2.07534 | ||||||||
\(767\) | −5.62989 | −0.203284 | ||||||||
\(768\) | −37.6063 | −1.35700 | ||||||||
\(769\) | 43.8299 | 1.58055 | 0.790273 | − | 0.612755i | \(-0.209939\pi\) | ||||
0.790273 | + | 0.612755i | \(0.209939\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.6582 | 0.455873 | ||||||||
\(772\) | −29.6502 | −1.06713 | ||||||||
\(773\) | 27.9122 | 1.00393 | 0.501966 | − | 0.864887i | \(-0.332610\pi\) | ||||
0.501966 | + | 0.864887i | \(0.332610\pi\) | |||||||
\(774\) | −9.53437 | −0.342706 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −35.3711 | −1.26975 | ||||||||
\(777\) | 25.8681 | 0.928013 | ||||||||
\(778\) | −3.97159 | −0.142388 | ||||||||
\(779\) | −15.7183 | −0.563167 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.56247 | 0.163258 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.6224 | −1.73762 | ||||||||
\(784\) | 8.21211 | 0.293289 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −59.5010 | −2.12233 | ||||||||
\(787\) | 30.0226 | 1.07019 | 0.535096 | − | 0.844792i | \(-0.320276\pi\) | ||||
0.535096 | + | 0.844792i | \(0.320276\pi\) | |||||||
\(788\) | 23.5953 | 0.840549 | ||||||||
\(789\) | 33.4667 | 1.19144 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.5275 | 2.04544 | ||||||||
\(792\) | −4.80300 | −0.170667 | ||||||||
\(793\) | 0.305891 | 0.0108625 | ||||||||
\(794\) | −74.1451 | −2.63131 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 66.6447 | 2.36216 | ||||||||
\(797\) | 5.16206 | 0.182850 | 0.0914249 | − | 0.995812i | \(-0.470858\pi\) | ||||
0.0914249 | + | 0.995812i | \(0.470858\pi\) | |||||||
\(798\) | 48.0509 | 1.70099 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.17821 | 0.0416301 | ||||||||
\(802\) | −11.9149 | −0.420730 | ||||||||
\(803\) | 13.5861 | 0.479445 | ||||||||
\(804\) | 40.0846 | 1.41367 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.23966 | 0.255006 | ||||||||
\(807\) | −6.59417 | −0.232126 | ||||||||
\(808\) | 19.6808 | 0.692369 | ||||||||
\(809\) | 22.2343 | 0.781717 | 0.390859 | − | 0.920451i | \(-0.372178\pi\) | ||||
0.390859 | + | 0.920451i | \(0.372178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6644 | −0.550051 | −0.275026 | − | 0.961437i | \(-0.588686\pi\) | ||||
−0.275026 | + | 0.961437i | \(0.588686\pi\) | |||||||
\(812\) | 110.804 | 3.88847 | ||||||||
\(813\) | 38.7842 | 1.36022 | ||||||||
\(814\) | 26.8676 | 0.941710 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.4289 | 0.959615 | ||||||||
\(818\) | 61.4266 | 2.14773 | ||||||||
\(819\) | −2.42337 | −0.0846793 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.9393 | −1.21939 | −0.609694 | − | 0.792637i | \(-0.708708\pi\) | ||||
−0.609694 | + | 0.792637i | \(0.708708\pi\) | |||||||
\(822\) | −63.2335 | −2.20552 | ||||||||
\(823\) | 2.44416 | 0.0851980 | 0.0425990 | − | 0.999092i | \(-0.486436\pi\) | ||||
0.0425990 | + | 0.999092i | \(0.486436\pi\) | |||||||
\(824\) | 25.7916 | 0.898492 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.6589 | 1.31032 | ||||||||
\(827\) | −50.8219 | −1.76725 | −0.883626 | − | 0.468194i | \(-0.844905\pi\) | ||||
−0.883626 | + | 0.468194i | \(0.844905\pi\) | |||||||
\(828\) | −16.7550 | −0.582275 | ||||||||
\(829\) | 41.5846 | 1.44429 | 0.722147 | − | 0.691740i | \(-0.243156\pi\) | ||||
0.722147 | + | 0.691740i | \(0.243156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.4854 | 1.09222 | ||||||||
\(832\) | −15.0750 | −0.522631 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.87308 | −0.272623 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 31.8625 | 1.10199 | ||||||||
\(837\) | 13.5668 | 0.468939 | ||||||||
\(838\) | 17.1655 | 0.592971 | ||||||||
\(839\) | 4.44768 | 0.153551 | 0.0767755 | − | 0.997048i | \(-0.475538\pi\) | ||||
0.0767755 | + | 0.997048i | \(0.475538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.7235 | 1.64564 | ||||||||
\(842\) | 49.5415 | 1.70731 | ||||||||
\(843\) | 39.5171 | 1.36104 | ||||||||
\(844\) | −23.3772 | −0.804676 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.3159 | 0.492191 | ||||||||
\(847\) | −17.3257 | −0.595320 | ||||||||
\(848\) | −8.01465 | −0.275224 | ||||||||
\(849\) | 13.3184 | 0.457088 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.6451 | 1.39330 | ||||||||
\(852\) | −10.1851 | −0.348937 | ||||||||
\(853\) | −17.8866 | −0.612426 | −0.306213 | − | 0.951963i | \(-0.599062\pi\) | ||||
−0.306213 | + | 0.951963i | \(0.599062\pi\) | |||||||
\(854\) | −2.04614 | −0.0700174 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.24449 | 0.0767150 | ||||||||
\(857\) | 38.5585 | 1.31713 | 0.658566 | − | 0.752523i | \(-0.271163\pi\) | ||||
0.658566 | + | 0.752523i | \(0.271163\pi\) | |||||||
\(858\) | 11.5408 | 0.393997 | ||||||||
\(859\) | 3.50985 | 0.119755 | 0.0598773 | − | 0.998206i | \(-0.480929\pi\) | ||||
0.0598773 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.3133 | 0.828595 | ||||||||
\(862\) | 49.4916 | 1.68569 | ||||||||
\(863\) | 21.9552 | 0.747365 | 0.373683 | − | 0.927557i | \(-0.378095\pi\) | ||||
0.373683 | + | 0.927557i | \(0.378095\pi\) | |||||||
\(864\) | −21.6026 | −0.734935 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 87.3171 | 2.96715 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −30.9171 | −1.04940 | ||||||||
\(869\) | −22.4320 | −0.760952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.10956 | 0.308666 | ||||||||
\(872\) | 22.2934 | 0.754951 | ||||||||
\(873\) | −5.27492 | −0.178529 | ||||||||
\(874\) | 75.4998 | 2.55382 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −30.3293 | −1.02473 | ||||||||
\(877\) | −5.65595 | −0.190988 | −0.0954939 | − | 0.995430i | \(-0.530443\pi\) | ||||
−0.0954939 | + | 0.995430i | \(0.530443\pi\) | |||||||
\(878\) | 1.10851 | 0.0374105 | ||||||||
\(879\) | −40.7832 | −1.37558 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3915 | −1.15868 | −0.579340 | − | 0.815086i | \(-0.696689\pi\) | ||||
−0.579340 | + | 0.815086i | \(0.696689\pi\) | |||||||
\(882\) | 7.36706 | 0.248062 | ||||||||
\(883\) | −58.3115 | −1.96234 | −0.981170 | − | 0.193148i | \(-0.938130\pi\) | ||||
−0.981170 | + | 0.193148i | \(0.938130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.9295 | −0.871117 | ||||||||
\(887\) | −44.5012 | −1.49420 | −0.747102 | − | 0.664710i | \(-0.768555\pi\) | ||||
−0.747102 | + | 0.664710i | \(0.768555\pi\) | |||||||
\(888\) | −26.0102 | −0.872846 | ||||||||
\(889\) | 21.1985 | 0.710975 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.6266 | 0.590513 | ||||||||
\(892\) | −10.3918 | −0.347944 | ||||||||
\(893\) | −41.1847 | −1.37819 | ||||||||
\(894\) | −68.4244 | −2.28845 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 72.9573 | 2.43733 | ||||||||
\(897\) | 17.4589 | 0.582935 | ||||||||
\(898\) | 40.6015 | 1.35489 | ||||||||
\(899\) | −21.4077 | −0.713988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 25.2527 | 0.840824 | ||||||||
\(903\) | −42.4274 | −1.41190 | ||||||||
\(904\) | −57.8436 | −1.92385 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −32.8961 | −1.09290 | ||||||||
\(907\) | 35.3726 | 1.17453 | 0.587264 | − | 0.809396i | \(-0.300205\pi\) | ||||
0.587264 | + | 0.809396i | \(0.300205\pi\) | |||||||
\(908\) | 76.0165 | 2.52270 | ||||||||
\(909\) | 2.93501 | 0.0973482 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.1810 | −1.62944 | −0.814719 | − | 0.579856i | \(-0.803109\pi\) | ||||
−0.814719 | + | 0.579856i | \(0.803109\pi\) | |||||||
\(912\) | −8.03172 | −0.265957 | ||||||||
\(913\) | 18.1620 | 0.601076 | ||||||||
\(914\) | 26.5004 | 0.876554 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −42.1685 | −1.39329 | ||||||||
\(917\) | 57.7465 | 1.90696 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.6635 | 1.63825 | 0.819123 | − | 0.573618i | \(-0.194460\pi\) | ||||
0.819123 | + | 0.573618i | \(0.194460\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.5966 | −0.876387 | ||||||||
\(922\) | −70.5747 | −2.32425 | ||||||||
\(923\) | −2.31466 | −0.0761878 | ||||||||
\(924\) | −49.2854 | −1.62137 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −40.3568 | −1.32621 | ||||||||
\(927\) | 3.84631 | 0.126329 | ||||||||
\(928\) | 34.0877 | 1.11898 | ||||||||
\(929\) | 34.1165 | 1.11933 | 0.559664 | − | 0.828720i | \(-0.310930\pi\) | ||||
0.559664 | + | 0.828720i | \(0.310930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.1939 | −0.694601 | ||||||||
\(932\) | 35.5571 | 1.16471 | ||||||||
\(933\) | 26.9779 | 0.883216 | ||||||||
\(934\) | −62.5405 | −2.04639 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.43668 | 0.0796455 | ||||||||
\(937\) | 38.5275 | 1.25864 | 0.629319 | − | 0.777147i | \(-0.283334\pi\) | ||||
0.629319 | + | 0.777147i | \(0.283334\pi\) | |||||||
\(938\) | −60.9347 | −1.98959 | ||||||||
\(939\) | −9.28250 | −0.302923 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.1363 | 1.21061 | 0.605305 | − | 0.795994i | \(-0.293051\pi\) | ||||
0.605305 | + | 0.795994i | \(0.293051\pi\) | |||||||
\(942\) | 67.3328 | 2.19382 | ||||||||
\(943\) | 38.2022 | 1.24403 | ||||||||
\(944\) | −6.29469 | −0.204875 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.0667 | −1.43273 | ||||||||
\(947\) | 2.23113 | 0.0725021 | 0.0362510 | − | 0.999343i | \(-0.488458\pi\) | ||||
0.0362510 | + | 0.999343i | \(0.488458\pi\) | |||||||
\(948\) | 50.0765 | 1.62641 | ||||||||
\(949\) | −6.89259 | −0.223743 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.00528 | −0.0325986 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.8280 | −0.836651 | −0.418326 | − | 0.908297i | \(-0.637383\pi\) | ||||
−0.418326 | + | 0.908297i | \(0.637383\pi\) | |||||||
\(954\) | −7.18992 | −0.232782 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −58.7114 | −1.89886 | ||||||||
\(957\) | −34.1264 | −1.10315 | ||||||||
\(958\) | 53.8823 | 1.74086 | ||||||||
\(959\) | 61.3689 | 1.98171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0267 | −0.807313 | ||||||||
\(962\) | −13.6306 | −0.439469 | ||||||||
\(963\) | 0.334721 | 0.0107862 | ||||||||
\(964\) | 20.9132 | 0.673569 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −116.784 | −3.75747 | ||||||||
\(967\) | 31.4013 | 1.00980 | 0.504899 | − | 0.863178i | \(-0.331530\pi\) | ||||
0.504899 | + | 0.863178i | \(0.331530\pi\) | |||||||
\(968\) | 17.4209 | 0.559930 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.1265 | 1.31981 | 0.659906 | − | 0.751348i | \(-0.270596\pi\) | ||||
0.659906 | + | 0.751348i | \(0.270596\pi\) | |||||||
\(972\) | 19.4602 | 0.624185 | ||||||||
\(973\) | 7.64093 | 0.244957 | ||||||||
\(974\) | −36.9567 | −1.18417 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.342012 | 0.0109475 | ||||||||
\(977\) | −27.8890 | −0.892250 | −0.446125 | − | 0.894971i | \(-0.647196\pi\) | ||||
−0.446125 | + | 0.894971i | \(0.647196\pi\) | |||||||
\(978\) | −34.5662 | −1.10530 | ||||||||
\(979\) | 5.44557 | 0.174041 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.32463 | 0.106147 | ||||||||
\(982\) | 2.02071 | 0.0644836 | ||||||||
\(983\) | −56.6933 | −1.80824 | −0.904118 | − | 0.427283i | \(-0.859471\pi\) | ||||
−0.904118 | + | 0.427283i | \(0.859471\pi\) | |||||||
\(984\) | −24.4469 | −0.779338 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 63.7050 | 2.02775 | ||||||||
\(988\) | −16.1647 | −0.514266 | ||||||||
\(989\) | −66.6639 | −2.11979 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.8868 | 1.13998 | 0.569991 | − | 0.821651i | \(-0.306947\pi\) | ||||
0.569991 | + | 0.821651i | \(0.306947\pi\) | |||||||
\(992\) | −9.51130 | −0.301984 | ||||||||
\(993\) | 18.3000 | 0.580732 | ||||||||
\(994\) | 15.4830 | 0.491090 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −40.5444 | −1.28470 | ||||||||
\(997\) | 32.9550 | 1.04370 | 0.521848 | − | 0.853038i | \(-0.325243\pi\) | ||||
0.521848 | + | 0.853038i | \(0.325243\pi\) | |||||||
\(998\) | 53.2461 | 1.68548 | ||||||||
\(999\) | −25.5433 | −0.808153 |
(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 | 7225.2.a.bs.1.1 | 12 | ||
5.4 | even | 2 | 1445.2.a.p.1.12 | 12 | |||
17.3 | odd | 16 | 425.2.m.b.26.1 | 24 | |||
17.6 | odd | 16 | 425.2.m.b.376.1 | 24 | |||
17.16 | even | 2 | 7225.2.a.bq.1.1 | 12 | |||
85.3 | even | 16 | 425.2.n.f.349.6 | 24 | |||
85.4 | even | 4 | 1445.2.d.j.866.1 | 24 | |||
85.23 | even | 16 | 425.2.n.c.274.1 | 24 | |||
85.37 | even | 16 | 425.2.n.c.349.1 | 24 | |||
85.54 | odd | 16 | 85.2.l.a.26.6 | ✓ | 24 | ||
85.57 | even | 16 | 425.2.n.f.274.6 | 24 | |||
85.64 | even | 4 | 1445.2.d.j.866.2 | 24 | |||
85.74 | odd | 16 | 85.2.l.a.36.6 | yes | 24 | ||
85.84 | even | 2 | 1445.2.a.q.1.12 | 12 | |||
255.74 | even | 16 | 765.2.be.b.631.1 | 24 | |||
255.224 | even | 16 | 765.2.be.b.451.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
85.2.l.a.26.6 | ✓ | 24 | 85.54 | odd | 16 | ||
85.2.l.a.36.6 | yes | 24 | 85.74 | odd | 16 | ||
425.2.m.b.26.1 | 24 | 17.3 | odd | 16 | |||
425.2.m.b.376.1 | 24 | 17.6 | odd | 16 | |||
425.2.n.c.274.1 | 24 | 85.23 | even | 16 | |||
425.2.n.c.349.1 | 24 | 85.37 | even | 16 | |||
425.2.n.f.274.6 | 24 | 85.57 | even | 16 | |||
425.2.n.f.349.6 | 24 | 85.3 | even | 16 | |||
765.2.be.b.451.1 | 24 | 255.224 | even | 16 | |||
765.2.be.b.631.1 | 24 | 255.74 | even | 16 | |||
1445.2.a.p.1.12 | 12 | 5.4 | even | 2 | |||
1445.2.a.q.1.12 | 12 | 85.84 | even | 2 | |||
1445.2.d.j.866.1 | 24 | 85.4 | even | 4 | |||
1445.2.d.j.866.2 | 24 | 85.64 | even | 4 | |||
7225.2.a.bq.1.1 | 12 | 17.16 | even | 2 | |||
7225.2.a.bs.1.1 | 12 | 1.1 | even | 1 | trivial |