Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.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: | \(4.01647522167\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.95007\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.392284 | −0.277386 | −0.138693 | − | 0.990335i | \(-0.544290\pi\) | ||||
−0.138693 | + | 0.990335i | \(0.544290\pi\) | |||||||
\(3\) | 0.950069 | 0.548523 | 0.274261 | − | 0.961655i | \(-0.411567\pi\) | ||||
0.274261 | + | 0.961655i | \(0.411567\pi\) | |||||||
\(4\) | −1.84611 | −0.923057 | ||||||||
\(5\) | −2.28693 | −1.02275 | −0.511374 | − | 0.859358i | \(-0.670863\pi\) | ||||
−0.511374 | + | 0.859358i | \(0.670863\pi\) | |||||||
\(6\) | −0.372697 | −0.152153 | ||||||||
\(7\) | 2.71022 | 1.02437 | 0.512184 | − | 0.858876i | \(-0.328837\pi\) | ||||
0.512184 | + | 0.858876i | \(0.328837\pi\) | |||||||
\(8\) | 1.50877 | 0.533430 | ||||||||
\(9\) | −2.09737 | −0.699123 | ||||||||
\(10\) | 0.897127 | 0.283697 | ||||||||
\(11\) | 1.36880 | 0.412710 | 0.206355 | − | 0.978477i | \(-0.433840\pi\) | ||||
0.206355 | + | 0.978477i | \(0.433840\pi\) | |||||||
\(12\) | −1.75393 | −0.506317 | ||||||||
\(13\) | −2.93079 | −0.812856 | −0.406428 | − | 0.913683i | \(-0.633226\pi\) | ||||
−0.406428 | + | 0.913683i | \(0.633226\pi\) | |||||||
\(14\) | −1.06318 | −0.284146 | ||||||||
\(15\) | −2.17275 | −0.561001 | ||||||||
\(16\) | 3.10036 | 0.775091 | ||||||||
\(17\) | −2.61287 | −0.633715 | −0.316857 | − | 0.948473i | \(-0.602628\pi\) | ||||
−0.316857 | + | 0.948473i | \(0.602628\pi\) | |||||||
\(18\) | 0.822764 | 0.193927 | ||||||||
\(19\) | −7.79104 | −1.78739 | −0.893694 | − | 0.448677i | \(-0.851895\pi\) | ||||
−0.893694 | + | 0.448677i | \(0.851895\pi\) | |||||||
\(20\) | 4.22194 | 0.944055 | ||||||||
\(21\) | 2.57490 | 0.561888 | ||||||||
\(22\) | −0.536960 | −0.114480 | ||||||||
\(23\) | −2.61064 | −0.544356 | −0.272178 | − | 0.962247i | \(-0.587744\pi\) | ||||
−0.272178 | + | 0.962247i | \(0.587744\pi\) | |||||||
\(24\) | 1.43343 | 0.292598 | ||||||||
\(25\) | 0.230071 | 0.0460143 | ||||||||
\(26\) | 1.14970 | 0.225475 | ||||||||
\(27\) | −4.84285 | −0.932007 | ||||||||
\(28\) | −5.00337 | −0.945549 | ||||||||
\(29\) | −0.314480 | −0.0583974 | −0.0291987 | − | 0.999574i | \(-0.509296\pi\) | ||||
−0.0291987 | + | 0.999574i | \(0.509296\pi\) | |||||||
\(30\) | 0.852333 | 0.155614 | ||||||||
\(31\) | −7.95126 | −1.42809 | −0.714044 | − | 0.700101i | \(-0.753138\pi\) | ||||
−0.714044 | + | 0.700101i | \(0.753138\pi\) | |||||||
\(32\) | −4.23376 | −0.748430 | ||||||||
\(33\) | 1.30046 | 0.226381 | ||||||||
\(34\) | 1.02499 | 0.175784 | ||||||||
\(35\) | −6.19810 | −1.04767 | ||||||||
\(36\) | 3.87198 | 0.645330 | ||||||||
\(37\) | −4.17299 | −0.686035 | −0.343017 | − | 0.939329i | \(-0.611449\pi\) | ||||
−0.343017 | + | 0.939329i | \(0.611449\pi\) | |||||||
\(38\) | 3.05630 | 0.495797 | ||||||||
\(39\) | −2.78446 | −0.445870 | ||||||||
\(40\) | −3.45045 | −0.545565 | ||||||||
\(41\) | 6.16482 | 0.962783 | 0.481391 | − | 0.876506i | \(-0.340132\pi\) | ||||
0.481391 | + | 0.876506i | \(0.340132\pi\) | |||||||
\(42\) | −1.01009 | −0.155860 | ||||||||
\(43\) | 0.457851 | 0.0698216 | 0.0349108 | − | 0.999390i | \(-0.488885\pi\) | ||||
0.0349108 | + | 0.999390i | \(0.488885\pi\) | |||||||
\(44\) | −2.52697 | −0.380955 | ||||||||
\(45\) | 4.79655 | 0.715027 | ||||||||
\(46\) | 1.02411 | 0.150997 | ||||||||
\(47\) | 7.67118 | 1.11896 | 0.559478 | − | 0.828845i | \(-0.311002\pi\) | ||||
0.559478 | + | 0.828845i | \(0.311002\pi\) | |||||||
\(48\) | 2.94556 | 0.425155 | ||||||||
\(49\) | 0.345296 | 0.0493279 | ||||||||
\(50\) | −0.0902533 | −0.0127637 | ||||||||
\(51\) | −2.48241 | −0.347607 | ||||||||
\(52\) | 5.41058 | 0.750312 | ||||||||
\(53\) | 7.26306 | 0.997658 | 0.498829 | − | 0.866700i | \(-0.333763\pi\) | ||||
0.498829 | + | 0.866700i | \(0.333763\pi\) | |||||||
\(54\) | 1.89977 | 0.258526 | ||||||||
\(55\) | −3.13037 | −0.422099 | ||||||||
\(56\) | 4.08909 | 0.546428 | ||||||||
\(57\) | −7.40203 | −0.980423 | ||||||||
\(58\) | 0.123365 | 0.0161987 | ||||||||
\(59\) | 0.217166 | 0.0282726 | 0.0141363 | − | 0.999900i | \(-0.495500\pi\) | ||||
0.0141363 | + | 0.999900i | \(0.495500\pi\) | |||||||
\(60\) | 4.01114 | 0.517835 | ||||||||
\(61\) | 7.26694 | 0.930436 | 0.465218 | − | 0.885196i | \(-0.345976\pi\) | ||||
0.465218 | + | 0.885196i | \(0.345976\pi\) | |||||||
\(62\) | 3.11915 | 0.396132 | ||||||||
\(63\) | −5.68433 | −0.716159 | ||||||||
\(64\) | −4.53989 | −0.567486 | ||||||||
\(65\) | 6.70253 | 0.831347 | ||||||||
\(66\) | −0.510149 | −0.0627950 | ||||||||
\(67\) | 10.1022 | 1.23418 | 0.617091 | − | 0.786892i | \(-0.288311\pi\) | ||||
0.617091 | + | 0.786892i | \(0.288311\pi\) | |||||||
\(68\) | 4.82366 | 0.584955 | ||||||||
\(69\) | −2.48029 | −0.298592 | ||||||||
\(70\) | 2.43141 | 0.290609 | ||||||||
\(71\) | −16.5088 | −1.95924 | −0.979619 | − | 0.200863i | \(-0.935625\pi\) | ||||
−0.979619 | + | 0.200863i | \(0.935625\pi\) | |||||||
\(72\) | −3.16444 | −0.372933 | ||||||||
\(73\) | 2.86838 | 0.335718 | 0.167859 | − | 0.985811i | \(-0.446315\pi\) | ||||
0.167859 | + | 0.985811i | \(0.446315\pi\) | |||||||
\(74\) | 1.63699 | 0.190297 | ||||||||
\(75\) | 0.218584 | 0.0252399 | ||||||||
\(76\) | 14.3831 | 1.64986 | ||||||||
\(77\) | 3.70976 | 0.422767 | ||||||||
\(78\) | 1.09230 | 0.123678 | ||||||||
\(79\) | −16.0222 | −1.80264 | −0.901320 | − | 0.433153i | \(-0.857401\pi\) | ||||
−0.901320 | + | 0.433153i | \(0.857401\pi\) | |||||||
\(80\) | −7.09033 | −0.792723 | ||||||||
\(81\) | 1.69106 | 0.187896 | ||||||||
\(82\) | −2.41836 | −0.267063 | ||||||||
\(83\) | 12.5312 | 1.37548 | 0.687741 | − | 0.725956i | \(-0.258602\pi\) | ||||
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(84\) | −4.75355 | −0.518655 | ||||||||
\(85\) | 5.97547 | 0.648131 | ||||||||
\(86\) | −0.179608 | −0.0193676 | ||||||||
\(87\) | −0.298777 | −0.0320323 | ||||||||
\(88\) | 2.06521 | 0.220152 | ||||||||
\(89\) | −0.0952234 | −0.0100937 | −0.00504683 | − | 0.999987i | \(-0.501606\pi\) | ||||
−0.00504683 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(90\) | −1.88161 | −0.198339 | ||||||||
\(91\) | −7.94310 | −0.832663 | ||||||||
\(92\) | 4.81954 | 0.502472 | ||||||||
\(93\) | −7.55424 | −0.783339 | ||||||||
\(94\) | −3.00928 | −0.310383 | ||||||||
\(95\) | 17.8176 | 1.82805 | ||||||||
\(96\) | −4.02236 | −0.410530 | ||||||||
\(97\) | −9.27640 | −0.941875 | −0.470938 | − | 0.882167i | \(-0.656084\pi\) | ||||
−0.470938 | + | 0.882167i | \(0.656084\pi\) | |||||||
\(98\) | −0.135454 | −0.0136829 | ||||||||
\(99\) | −2.87089 | −0.288535 | ||||||||
\(100\) | −0.424738 | −0.0424738 | ||||||||
\(101\) | 8.77727 | 0.873371 | 0.436686 | − | 0.899614i | \(-0.356152\pi\) | ||||
0.436686 | + | 0.899614i | \(0.356152\pi\) | |||||||
\(102\) | 0.973809 | 0.0964214 | ||||||||
\(103\) | 1.52475 | 0.150238 | 0.0751189 | − | 0.997175i | \(-0.476066\pi\) | ||||
0.0751189 | + | 0.997175i | \(0.476066\pi\) | |||||||
\(104\) | −4.42189 | −0.433602 | ||||||||
\(105\) | −5.88862 | −0.574670 | ||||||||
\(106\) | −2.84918 | −0.276737 | ||||||||
\(107\) | −17.6358 | −1.70492 | −0.852460 | − | 0.522792i | \(-0.824890\pi\) | ||||
−0.852460 | + | 0.522792i | \(0.824890\pi\) | |||||||
\(108\) | 8.94045 | 0.860296 | ||||||||
\(109\) | −4.91427 | −0.470702 | −0.235351 | − | 0.971910i | \(-0.575624\pi\) | ||||
−0.235351 | + | 0.971910i | \(0.575624\pi\) | |||||||
\(110\) | 1.22799 | 0.117084 | ||||||||
\(111\) | −3.96462 | −0.376305 | ||||||||
\(112\) | 8.40266 | 0.793977 | ||||||||
\(113\) | 0.102880 | 0.00967811 | 0.00483905 | − | 0.999988i | \(-0.498460\pi\) | ||||
0.00483905 | + | 0.999988i | \(0.498460\pi\) | |||||||
\(114\) | 2.90369 | 0.271956 | ||||||||
\(115\) | 5.97037 | 0.556740 | ||||||||
\(116\) | 0.580565 | 0.0539041 | ||||||||
\(117\) | 6.14696 | 0.568286 | ||||||||
\(118\) | −0.0851906 | −0.00784243 | ||||||||
\(119\) | −7.08146 | −0.649157 | ||||||||
\(120\) | −3.27817 | −0.299254 | ||||||||
\(121\) | −9.12637 | −0.829670 | ||||||||
\(122\) | −2.85070 | −0.258090 | ||||||||
\(123\) | 5.85700 | 0.528108 | ||||||||
\(124\) | 14.6789 | 1.31821 | ||||||||
\(125\) | 10.9085 | 0.975687 | ||||||||
\(126\) | 2.22987 | 0.198653 | ||||||||
\(127\) | 14.7682 | 1.31046 | 0.655232 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655232 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(128\) | 10.2484 | 0.905843 | ||||||||
\(129\) | 0.434990 | 0.0382987 | ||||||||
\(130\) | −2.62929 | −0.230604 | ||||||||
\(131\) | 3.01646 | 0.263549 | 0.131775 | − | 0.991280i | \(-0.457932\pi\) | ||||
0.131775 | + | 0.991280i | \(0.457932\pi\) | |||||||
\(132\) | −2.40079 | −0.208962 | ||||||||
\(133\) | −21.1154 | −1.83094 | ||||||||
\(134\) | −3.96293 | −0.342345 | ||||||||
\(135\) | 11.0753 | 0.953209 | ||||||||
\(136\) | −3.94222 | −0.338042 | ||||||||
\(137\) | 0.370190 | 0.0316275 | 0.0158137 | − | 0.999875i | \(-0.494966\pi\) | ||||
0.0158137 | + | 0.999875i | \(0.494966\pi\) | |||||||
\(138\) | 0.972977 | 0.0828253 | ||||||||
\(139\) | 13.0944 | 1.11065 | 0.555324 | − | 0.831634i | \(-0.312594\pi\) | ||||
0.555324 | + | 0.831634i | \(0.312594\pi\) | |||||||
\(140\) | 11.4424 | 0.967059 | ||||||||
\(141\) | 7.28815 | 0.613773 | ||||||||
\(142\) | 6.47615 | 0.543466 | ||||||||
\(143\) | −4.01168 | −0.335474 | ||||||||
\(144\) | −6.50260 | −0.541884 | ||||||||
\(145\) | 0.719195 | 0.0597259 | ||||||||
\(146\) | −1.12522 | −0.0931237 | ||||||||
\(147\) | 0.328055 | 0.0270575 | ||||||||
\(148\) | 7.70381 | 0.633249 | ||||||||
\(149\) | −5.61923 | −0.460345 | −0.230173 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230173 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(150\) | −0.0857468 | −0.00700120 | ||||||||
\(151\) | −6.99662 | −0.569377 | −0.284689 | − | 0.958620i | \(-0.591890\pi\) | ||||
−0.284689 | + | 0.958620i | \(0.591890\pi\) | |||||||
\(152\) | −11.7549 | −0.953446 | ||||||||
\(153\) | 5.48016 | 0.443045 | ||||||||
\(154\) | −1.45528 | −0.117270 | ||||||||
\(155\) | 18.1840 | 1.46058 | ||||||||
\(156\) | 5.14042 | 0.411563 | ||||||||
\(157\) | 10.5849 | 0.844764 | 0.422382 | − | 0.906418i | \(-0.361194\pi\) | ||||
0.422382 | + | 0.906418i | \(0.361194\pi\) | |||||||
\(158\) | 6.28526 | 0.500028 | ||||||||
\(159\) | 6.90041 | 0.547238 | ||||||||
\(160\) | 9.68233 | 0.765455 | ||||||||
\(161\) | −7.07541 | −0.557621 | ||||||||
\(162\) | −0.663377 | −0.0521198 | ||||||||
\(163\) | −4.74396 | −0.371576 | −0.185788 | − | 0.982590i | \(-0.559484\pi\) | ||||
−0.185788 | + | 0.982590i | \(0.559484\pi\) | |||||||
\(164\) | −11.3810 | −0.888703 | ||||||||
\(165\) | −2.97406 | −0.231531 | ||||||||
\(166\) | −4.91580 | −0.381540 | ||||||||
\(167\) | 15.4650 | 1.19672 | 0.598360 | − | 0.801227i | \(-0.295819\pi\) | ||||
0.598360 | + | 0.801227i | \(0.295819\pi\) | |||||||
\(168\) | 3.88492 | 0.299728 | ||||||||
\(169\) | −4.41045 | −0.339265 | ||||||||
\(170\) | −2.34408 | −0.179783 | ||||||||
\(171\) | 16.3407 | 1.24960 | ||||||||
\(172\) | −0.845245 | −0.0644493 | ||||||||
\(173\) | −18.0030 | −1.36874 | −0.684372 | − | 0.729133i | \(-0.739924\pi\) | ||||
−0.684372 | + | 0.729133i | \(0.739924\pi\) | |||||||
\(174\) | 0.117206 | 0.00888533 | ||||||||
\(175\) | 0.623544 | 0.0471355 | ||||||||
\(176\) | 4.24379 | 0.319888 | ||||||||
\(177\) | 0.206322 | 0.0155081 | ||||||||
\(178\) | 0.0373546 | 0.00279985 | ||||||||
\(179\) | 22.6390 | 1.69212 | 0.846058 | − | 0.533092i | \(-0.178970\pi\) | ||||
0.846058 | + | 0.533092i | \(0.178970\pi\) | |||||||
\(180\) | −8.85497 | −0.660010 | ||||||||
\(181\) | 2.97984 | 0.221490 | 0.110745 | − | 0.993849i | \(-0.464676\pi\) | ||||
0.110745 | + | 0.993849i | \(0.464676\pi\) | |||||||
\(182\) | 3.11595 | 0.230969 | ||||||||
\(183\) | 6.90409 | 0.510365 | ||||||||
\(184\) | −3.93885 | −0.290376 | ||||||||
\(185\) | 9.54335 | 0.701641 | ||||||||
\(186\) | 2.96341 | 0.217288 | ||||||||
\(187\) | −3.57651 | −0.261541 | ||||||||
\(188\) | −14.1619 | −1.03286 | ||||||||
\(189\) | −13.1252 | −0.954718 | ||||||||
\(190\) | −6.98956 | −0.507076 | ||||||||
\(191\) | 4.09564 | 0.296350 | 0.148175 | − | 0.988961i | \(-0.452660\pi\) | ||||
0.148175 | + | 0.988961i | \(0.452660\pi\) | |||||||
\(192\) | −4.31321 | −0.311279 | ||||||||
\(193\) | −21.1708 | −1.52391 | −0.761955 | − | 0.647630i | \(-0.775760\pi\) | ||||
−0.761955 | + | 0.647630i | \(0.775760\pi\) | |||||||
\(194\) | 3.63898 | 0.261263 | ||||||||
\(195\) | 6.36787 | 0.456013 | ||||||||
\(196\) | −0.637455 | −0.0455325 | ||||||||
\(197\) | 18.5139 | 1.31906 | 0.659531 | − | 0.751677i | \(-0.270755\pi\) | ||||
0.659531 | + | 0.751677i | \(0.270755\pi\) | |||||||
\(198\) | 1.12620 | 0.0800358 | ||||||||
\(199\) | −1.56711 | −0.111089 | −0.0555447 | − | 0.998456i | \(-0.517690\pi\) | ||||
−0.0555447 | + | 0.998456i | \(0.517690\pi\) | |||||||
\(200\) | 0.347124 | 0.0245454 | ||||||||
\(201\) | 9.59779 | 0.676976 | ||||||||
\(202\) | −3.44318 | −0.242261 | ||||||||
\(203\) | −0.852309 | −0.0598204 | ||||||||
\(204\) | 4.58281 | 0.320861 | ||||||||
\(205\) | −14.0985 | −0.984685 | ||||||||
\(206\) | −0.598133 | −0.0416739 | ||||||||
\(207\) | 5.47548 | 0.380572 | ||||||||
\(208\) | −9.08652 | −0.630037 | ||||||||
\(209\) | −10.6644 | −0.737673 | ||||||||
\(210\) | 2.31001 | 0.159406 | ||||||||
\(211\) | −22.8488 | −1.57298 | −0.786489 | − | 0.617604i | \(-0.788103\pi\) | ||||
−0.786489 | + | 0.617604i | \(0.788103\pi\) | |||||||
\(212\) | −13.4084 | −0.920895 | ||||||||
\(213\) | −15.6845 | −1.07469 | ||||||||
\(214\) | 6.91825 | 0.472922 | ||||||||
\(215\) | −1.04708 | −0.0714100 | ||||||||
\(216\) | −7.30674 | −0.497161 | ||||||||
\(217\) | −21.5497 | −1.46289 | ||||||||
\(218\) | 1.92779 | 0.130566 | ||||||||
\(219\) | 2.72516 | 0.184149 | ||||||||
\(220\) | 5.77901 | 0.389621 | ||||||||
\(221\) | 7.65779 | 0.515119 | ||||||||
\(222\) | 1.55526 | 0.104382 | ||||||||
\(223\) | 4.75557 | 0.318457 | 0.159228 | − | 0.987242i | \(-0.449099\pi\) | ||||
0.159228 | + | 0.987242i | \(0.449099\pi\) | |||||||
\(224\) | −11.4744 | −0.766667 | ||||||||
\(225\) | −0.482545 | −0.0321696 | ||||||||
\(226\) | −0.0403580 | −0.00268458 | ||||||||
\(227\) | −27.4709 | −1.82331 | −0.911655 | − | 0.410956i | \(-0.865195\pi\) | ||||
−0.911655 | + | 0.410956i | \(0.865195\pi\) | |||||||
\(228\) | 13.6650 | 0.904986 | ||||||||
\(229\) | −4.52436 | −0.298978 | −0.149489 | − | 0.988763i | \(-0.547763\pi\) | ||||
−0.149489 | + | 0.988763i | \(0.547763\pi\) | |||||||
\(230\) | −2.34208 | −0.154432 | ||||||||
\(231\) | 3.52453 | 0.231897 | ||||||||
\(232\) | −0.474477 | −0.0311509 | ||||||||
\(233\) | −10.5567 | −0.691594 | −0.345797 | − | 0.938309i | \(-0.612391\pi\) | ||||
−0.345797 | + | 0.938309i | \(0.612391\pi\) | |||||||
\(234\) | −2.41135 | −0.157635 | ||||||||
\(235\) | −17.5435 | −1.14441 | ||||||||
\(236\) | −0.400913 | −0.0260972 | ||||||||
\(237\) | −15.2222 | −0.988789 | ||||||||
\(238\) | 2.77794 | 0.180067 | ||||||||
\(239\) | −28.3072 | −1.83104 | −0.915522 | − | 0.402269i | \(-0.868222\pi\) | ||||
−0.915522 | + | 0.402269i | \(0.868222\pi\) | |||||||
\(240\) | −6.73630 | −0.434826 | ||||||||
\(241\) | −10.6922 | −0.688748 | −0.344374 | − | 0.938833i | \(-0.611909\pi\) | ||||
−0.344374 | + | 0.938833i | \(0.611909\pi\) | |||||||
\(242\) | 3.58013 | 0.230139 | ||||||||
\(243\) | 16.1352 | 1.03507 | ||||||||
\(244\) | −13.4156 | −0.858846 | ||||||||
\(245\) | −0.789669 | −0.0504501 | ||||||||
\(246\) | −2.29761 | −0.146490 | ||||||||
\(247\) | 22.8339 | 1.45289 | ||||||||
\(248\) | −11.9966 | −0.761785 | ||||||||
\(249\) | 11.9055 | 0.754483 | ||||||||
\(250\) | −4.27923 | −0.270642 | ||||||||
\(251\) | −3.42359 | −0.216095 | −0.108048 | − | 0.994146i | \(-0.534460\pi\) | ||||
−0.108048 | + | 0.994146i | \(0.534460\pi\) | |||||||
\(252\) | 10.4939 | 0.661055 | ||||||||
\(253\) | −3.57346 | −0.224661 | ||||||||
\(254\) | −5.79331 | −0.363505 | ||||||||
\(255\) | 5.67711 | 0.355514 | ||||||||
\(256\) | 5.05948 | 0.316218 | ||||||||
\(257\) | −11.2524 | −0.701906 | −0.350953 | − | 0.936393i | \(-0.614142\pi\) | ||||
−0.350953 | + | 0.936393i | \(0.614142\pi\) | |||||||
\(258\) | −0.170640 | −0.0106236 | ||||||||
\(259\) | −11.3097 | −0.702751 | ||||||||
\(260\) | −12.3736 | −0.767381 | ||||||||
\(261\) | 0.659580 | 0.0408270 | ||||||||
\(262\) | −1.18331 | −0.0731050 | ||||||||
\(263\) | 0.429180 | 0.0264643 | 0.0132322 | − | 0.999912i | \(-0.495788\pi\) | ||||
0.0132322 | + | 0.999912i | \(0.495788\pi\) | |||||||
\(264\) | 1.96209 | 0.120758 | ||||||||
\(265\) | −16.6102 | −1.02035 | ||||||||
\(266\) | 8.28325 | 0.507878 | ||||||||
\(267\) | −0.0904688 | −0.00553660 | ||||||||
\(268\) | −18.6498 | −1.13922 | ||||||||
\(269\) | 15.2320 | 0.928712 | 0.464356 | − | 0.885649i | \(-0.346286\pi\) | ||||
0.464356 | + | 0.885649i | \(0.346286\pi\) | |||||||
\(270\) | −4.34465 | −0.264407 | ||||||||
\(271\) | 17.7850 | 1.08036 | 0.540182 | − | 0.841548i | \(-0.318355\pi\) | ||||
0.540182 | + | 0.841548i | \(0.318355\pi\) | |||||||
\(272\) | −8.10085 | −0.491186 | ||||||||
\(273\) | −7.54649 | −0.456734 | ||||||||
\(274\) | −0.145219 | −0.00877303 | ||||||||
\(275\) | 0.314923 | 0.0189906 | ||||||||
\(276\) | 4.57889 | 0.275617 | ||||||||
\(277\) | 15.1882 | 0.912570 | 0.456285 | − | 0.889834i | \(-0.349180\pi\) | ||||
0.456285 | + | 0.889834i | \(0.349180\pi\) | |||||||
\(278\) | −5.13670 | −0.308079 | ||||||||
\(279\) | 16.6767 | 0.998409 | ||||||||
\(280\) | −9.35149 | −0.558858 | ||||||||
\(281\) | 20.0885 | 1.19838 | 0.599191 | − | 0.800606i | \(-0.295489\pi\) | ||||
0.599191 | + | 0.800606i | \(0.295489\pi\) | |||||||
\(282\) | −2.85902 | −0.170252 | ||||||||
\(283\) | −1.63497 | −0.0971889 | −0.0485945 | − | 0.998819i | \(-0.515474\pi\) | ||||
−0.0485945 | + | 0.998819i | \(0.515474\pi\) | |||||||
\(284\) | 30.4772 | 1.80849 | ||||||||
\(285\) | 16.9280 | 1.00273 | ||||||||
\(286\) | 1.57372 | 0.0930559 | ||||||||
\(287\) | 16.7080 | 0.986243 | ||||||||
\(288\) | 8.87975 | 0.523244 | ||||||||
\(289\) | −10.1729 | −0.598405 | ||||||||
\(290\) | −0.282128 | −0.0165671 | ||||||||
\(291\) | −8.81321 | −0.516640 | ||||||||
\(292\) | −5.29535 | −0.309887 | ||||||||
\(293\) | −10.1892 | −0.595262 | −0.297631 | − | 0.954681i | \(-0.596196\pi\) | ||||
−0.297631 | + | 0.954681i | \(0.596196\pi\) | |||||||
\(294\) | −0.128690 | −0.00750538 | ||||||||
\(295\) | −0.496644 | −0.0289157 | ||||||||
\(296\) | −6.29607 | −0.365951 | ||||||||
\(297\) | −6.62892 | −0.384649 | ||||||||
\(298\) | 2.20433 | 0.127694 | ||||||||
\(299\) | 7.65125 | 0.442483 | ||||||||
\(300\) | −0.403530 | −0.0232978 | ||||||||
\(301\) | 1.24088 | 0.0715230 | ||||||||
\(302\) | 2.74466 | 0.157938 | ||||||||
\(303\) | 8.33901 | 0.479064 | ||||||||
\(304\) | −24.1551 | −1.38539 | ||||||||
\(305\) | −16.6190 | −0.951602 | ||||||||
\(306\) | −2.14978 | −0.122895 | ||||||||
\(307\) | −16.3682 | −0.934184 | −0.467092 | − | 0.884209i | \(-0.654698\pi\) | ||||
−0.467092 | + | 0.884209i | \(0.654698\pi\) | |||||||
\(308\) | −6.84864 | −0.390238 | ||||||||
\(309\) | 1.44861 | 0.0824088 | ||||||||
\(310\) | −7.13329 | −0.405144 | ||||||||
\(311\) | 6.98922 | 0.396322 | 0.198161 | − | 0.980169i | \(-0.436503\pi\) | ||||
0.198161 | + | 0.980169i | \(0.436503\pi\) | |||||||
\(312\) | −4.20110 | −0.237840 | ||||||||
\(313\) | 2.22444 | 0.125733 | 0.0628665 | − | 0.998022i | \(-0.479976\pi\) | ||||
0.0628665 | + | 0.998022i | \(0.479976\pi\) | |||||||
\(314\) | −4.15227 | −0.234326 | ||||||||
\(315\) | 12.9997 | 0.732450 | ||||||||
\(316\) | 29.5788 | 1.66394 | ||||||||
\(317\) | 3.49687 | 0.196404 | 0.0982019 | − | 0.995167i | \(-0.468691\pi\) | ||||
0.0982019 | + | 0.995167i | \(0.468691\pi\) | |||||||
\(318\) | −2.70692 | −0.151796 | ||||||||
\(319\) | −0.430461 | −0.0241012 | ||||||||
\(320\) | 10.3824 | 0.580396 | ||||||||
\(321\) | −16.7553 | −0.935187 | ||||||||
\(322\) | 2.77557 | 0.154676 | ||||||||
\(323\) | 20.3570 | 1.13269 | ||||||||
\(324\) | −3.12190 | −0.173439 | ||||||||
\(325\) | −0.674292 | −0.0374030 | ||||||||
\(326\) | 1.86098 | 0.103070 | ||||||||
\(327\) | −4.66889 | −0.258190 | ||||||||
\(328\) | 9.30128 | 0.513577 | ||||||||
\(329\) | 20.7906 | 1.14622 | ||||||||
\(330\) | 1.16668 | 0.0642235 | ||||||||
\(331\) | −13.8654 | −0.762112 | −0.381056 | − | 0.924552i | \(-0.624439\pi\) | ||||
−0.381056 | + | 0.924552i | \(0.624439\pi\) | |||||||
\(332\) | −23.1341 | −1.26965 | ||||||||
\(333\) | 8.75229 | 0.479623 | ||||||||
\(334\) | −6.06668 | −0.331954 | ||||||||
\(335\) | −23.1031 | −1.26226 | ||||||||
\(336\) | 7.98311 | 0.435514 | ||||||||
\(337\) | −33.0259 | −1.79903 | −0.899517 | − | 0.436885i | \(-0.856082\pi\) | ||||
−0.899517 | + | 0.436885i | \(0.856082\pi\) | |||||||
\(338\) | 1.73015 | 0.0941076 | ||||||||
\(339\) | 0.0977428 | 0.00530866 | ||||||||
\(340\) | −11.0314 | −0.598262 | ||||||||
\(341\) | −10.8837 | −0.589387 | ||||||||
\(342\) | −6.41019 | −0.346623 | ||||||||
\(343\) | −18.0357 | −0.973837 | ||||||||
\(344\) | 0.690791 | 0.0372450 | ||||||||
\(345\) | 5.67226 | 0.305384 | ||||||||
\(346\) | 7.06229 | 0.379671 | ||||||||
\(347\) | −0.417829 | −0.0224302 | −0.0112151 | − | 0.999937i | \(-0.503570\pi\) | ||||
−0.0112151 | + | 0.999937i | \(0.503570\pi\) | |||||||
\(348\) | 0.551577 | 0.0295676 | ||||||||
\(349\) | −8.68607 | −0.464955 | −0.232477 | − | 0.972602i | \(-0.574683\pi\) | ||||
−0.232477 | + | 0.972602i | \(0.574683\pi\) | |||||||
\(350\) | −0.244606 | −0.0130748 | ||||||||
\(351\) | 14.1934 | 0.757588 | ||||||||
\(352\) | −5.79519 | −0.308884 | ||||||||
\(353\) | −9.09582 | −0.484122 | −0.242061 | − | 0.970261i | \(-0.577823\pi\) | ||||
−0.242061 | + | 0.970261i | \(0.577823\pi\) | |||||||
\(354\) | −0.0809369 | −0.00430175 | ||||||||
\(355\) | 37.7546 | 2.00381 | ||||||||
\(356\) | 0.175793 | 0.00931703 | ||||||||
\(357\) | −6.72788 | −0.356077 | ||||||||
\(358\) | −8.88089 | −0.469370 | ||||||||
\(359\) | 5.51998 | 0.291333 | 0.145667 | − | 0.989334i | \(-0.453467\pi\) | ||||
0.145667 | + | 0.989334i | \(0.453467\pi\) | |||||||
\(360\) | 7.23687 | 0.381417 | ||||||||
\(361\) | 41.7004 | 2.19476 | ||||||||
\(362\) | −1.16894 | −0.0614383 | ||||||||
\(363\) | −8.67068 | −0.455093 | ||||||||
\(364\) | 14.6639 | 0.768595 | ||||||||
\(365\) | −6.55979 | −0.343355 | ||||||||
\(366\) | −2.70836 | −0.141568 | ||||||||
\(367\) | 16.3639 | 0.854188 | 0.427094 | − | 0.904207i | \(-0.359537\pi\) | ||||
0.427094 | + | 0.904207i | \(0.359537\pi\) | |||||||
\(368\) | −8.09393 | −0.421925 | ||||||||
\(369\) | −12.9299 | −0.673104 | ||||||||
\(370\) | −3.74370 | −0.194626 | ||||||||
\(371\) | 19.6845 | 1.02197 | ||||||||
\(372\) | 13.9460 | 0.723066 | ||||||||
\(373\) | −23.5721 | −1.22051 | −0.610257 | − | 0.792203i | \(-0.708934\pi\) | ||||
−0.610257 | + | 0.792203i | \(0.708934\pi\) | |||||||
\(374\) | 1.40301 | 0.0725478 | ||||||||
\(375\) | 10.3638 | 0.535186 | ||||||||
\(376\) | 11.5740 | 0.596885 | ||||||||
\(377\) | 0.921675 | 0.0474687 | ||||||||
\(378\) | 5.14880 | 0.264826 | ||||||||
\(379\) | −22.8307 | −1.17273 | −0.586367 | − | 0.810045i | \(-0.699442\pi\) | ||||
−0.586367 | + | 0.810045i | \(0.699442\pi\) | |||||||
\(380\) | −32.8933 | −1.68739 | ||||||||
\(381\) | 14.0308 | 0.718819 | ||||||||
\(382\) | −1.60665 | −0.0822034 | ||||||||
\(383\) | 21.8257 | 1.11524 | 0.557622 | − | 0.830095i | \(-0.311714\pi\) | ||||
0.557622 | + | 0.830095i | \(0.311714\pi\) | |||||||
\(384\) | 9.73672 | 0.496875 | ||||||||
\(385\) | −8.48399 | −0.432384 | ||||||||
\(386\) | 8.30497 | 0.422712 | ||||||||
\(387\) | −0.960283 | −0.0488139 | ||||||||
\(388\) | 17.1253 | 0.869404 | ||||||||
\(389\) | 29.7462 | 1.50819 | 0.754097 | − | 0.656763i | \(-0.228075\pi\) | ||||
0.754097 | + | 0.656763i | \(0.228075\pi\) | |||||||
\(390\) | −2.49801 | −0.126492 | ||||||||
\(391\) | 6.82127 | 0.344967 | ||||||||
\(392\) | 0.520971 | 0.0263130 | ||||||||
\(393\) | 2.86584 | 0.144563 | ||||||||
\(394\) | −7.26271 | −0.365890 | ||||||||
\(395\) | 36.6418 | 1.84365 | ||||||||
\(396\) | 5.29999 | 0.266334 | ||||||||
\(397\) | 28.5561 | 1.43319 | 0.716595 | − | 0.697489i | \(-0.245700\pi\) | ||||
0.716595 | + | 0.697489i | \(0.245700\pi\) | |||||||
\(398\) | 0.614751 | 0.0308147 | ||||||||
\(399\) | −20.0611 | −1.00431 | ||||||||
\(400\) | 0.713305 | 0.0356652 | ||||||||
\(401\) | 13.9970 | 0.698975 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(402\) | −3.76506 | −0.187784 | ||||||||
\(403\) | 23.3035 | 1.16083 | ||||||||
\(404\) | −16.2038 | −0.806171 | ||||||||
\(405\) | −3.86735 | −0.192170 | ||||||||
\(406\) | 0.334347 | 0.0165934 | ||||||||
\(407\) | −5.71200 | −0.283133 | ||||||||
\(408\) | −3.74538 | −0.185424 | ||||||||
\(409\) | −18.2429 | −0.902055 | −0.451028 | − | 0.892510i | \(-0.648942\pi\) | ||||
−0.451028 | + | 0.892510i | \(0.648942\pi\) | |||||||
\(410\) | 5.53063 | 0.273138 | ||||||||
\(411\) | 0.351706 | 0.0173484 | ||||||||
\(412\) | −2.81486 | −0.138678 | ||||||||
\(413\) | 0.588567 | 0.0289615 | ||||||||
\(414\) | −2.14794 | −0.105566 | ||||||||
\(415\) | −28.6581 | −1.40677 | ||||||||
\(416\) | 12.4083 | 0.608365 | ||||||||
\(417\) | 12.4405 | 0.609216 | ||||||||
\(418\) | 4.18348 | 0.204621 | ||||||||
\(419\) | 9.78645 | 0.478099 | 0.239050 | − | 0.971007i | \(-0.423164\pi\) | ||||
0.239050 | + | 0.971007i | \(0.423164\pi\) | |||||||
\(420\) | 10.8711 | 0.530453 | ||||||||
\(421\) | 2.26639 | 0.110457 | 0.0552286 | − | 0.998474i | \(-0.482411\pi\) | ||||
0.0552286 | + | 0.998474i | \(0.482411\pi\) | |||||||
\(422\) | 8.96322 | 0.436323 | ||||||||
\(423\) | −16.0893 | −0.782288 | ||||||||
\(424\) | 10.9583 | 0.532181 | ||||||||
\(425\) | −0.601147 | −0.0291599 | ||||||||
\(426\) | 6.15279 | 0.298104 | ||||||||
\(427\) | 19.6950 | 0.953109 | ||||||||
\(428\) | 32.5578 | 1.57374 | ||||||||
\(429\) | −3.81138 | −0.184015 | ||||||||
\(430\) | 0.410751 | 0.0198082 | ||||||||
\(431\) | 4.29790 | 0.207023 | 0.103511 | − | 0.994628i | \(-0.466992\pi\) | ||||
0.103511 | + | 0.994628i | \(0.466992\pi\) | |||||||
\(432\) | −15.0146 | −0.722390 | ||||||||
\(433\) | −16.6114 | −0.798292 | −0.399146 | − | 0.916887i | \(-0.630693\pi\) | ||||
−0.399146 | + | 0.916887i | \(0.630693\pi\) | |||||||
\(434\) | 8.45358 | 0.405785 | ||||||||
\(435\) | 0.683284 | 0.0327610 | ||||||||
\(436\) | 9.07230 | 0.434484 | ||||||||
\(437\) | 20.3396 | 0.972976 | ||||||||
\(438\) | −1.06903 | −0.0510805 | ||||||||
\(439\) | −21.4863 | −1.02548 | −0.512742 | − | 0.858542i | \(-0.671370\pi\) | ||||
−0.512742 | + | 0.858542i | \(0.671370\pi\) | |||||||
\(440\) | −4.72300 | −0.225160 | ||||||||
\(441\) | −0.724212 | −0.0344863 | ||||||||
\(442\) | −3.00403 | −0.142887 | ||||||||
\(443\) | −19.6047 | −0.931447 | −0.465724 | − | 0.884930i | \(-0.654206\pi\) | ||||
−0.465724 | + | 0.884930i | \(0.654206\pi\) | |||||||
\(444\) | 7.31915 | 0.347351 | ||||||||
\(445\) | 0.217770 | 0.0103233 | ||||||||
\(446\) | −1.86553 | −0.0883356 | ||||||||
\(447\) | −5.33866 | −0.252510 | ||||||||
\(448\) | −12.3041 | −0.581314 | ||||||||
\(449\) | −35.1455 | −1.65862 | −0.829310 | − | 0.558789i | \(-0.811266\pi\) | ||||
−0.829310 | + | 0.558789i | \(0.811266\pi\) | |||||||
\(450\) | 0.189294 | 0.00892342 | ||||||||
\(451\) | 8.43843 | 0.397350 | ||||||||
\(452\) | −0.189928 | −0.00893344 | ||||||||
\(453\) | −6.64728 | −0.312316 | ||||||||
\(454\) | 10.7764 | 0.505762 | ||||||||
\(455\) | 18.1653 | 0.851605 | ||||||||
\(456\) | −11.1679 | −0.522987 | ||||||||
\(457\) | −11.8432 | −0.554002 | −0.277001 | − | 0.960870i | \(-0.589341\pi\) | ||||
−0.277001 | + | 0.960870i | \(0.589341\pi\) | |||||||
\(458\) | 1.77483 | 0.0829325 | ||||||||
\(459\) | 12.6538 | 0.590627 | ||||||||
\(460\) | −11.0220 | −0.513902 | ||||||||
\(461\) | 17.1286 | 0.797756 | 0.398878 | − | 0.917004i | \(-0.369400\pi\) | ||||
0.398878 | + | 0.917004i | \(0.369400\pi\) | |||||||
\(462\) | −1.38262 | −0.0643251 | ||||||||
\(463\) | −6.92218 | −0.321701 | −0.160850 | − | 0.986979i | \(-0.551424\pi\) | ||||
−0.160850 | + | 0.986979i | \(0.551424\pi\) | |||||||
\(464\) | −0.975001 | −0.0452633 | ||||||||
\(465\) | 17.2761 | 0.801158 | ||||||||
\(466\) | 4.14123 | 0.191839 | ||||||||
\(467\) | −32.6395 | −1.51038 | −0.755188 | − | 0.655508i | \(-0.772455\pi\) | ||||
−0.755188 | + | 0.655508i | \(0.772455\pi\) | |||||||
\(468\) | −11.3480 | −0.524560 | ||||||||
\(469\) | 27.3792 | 1.26425 | ||||||||
\(470\) | 6.88202 | 0.317444 | ||||||||
\(471\) | 10.0563 | 0.463372 | ||||||||
\(472\) | 0.327653 | 0.0150814 | ||||||||
\(473\) | 0.626709 | 0.0288161 | ||||||||
\(474\) | 5.97143 | 0.274277 | ||||||||
\(475\) | −1.79250 | −0.0822454 | ||||||||
\(476\) | 13.0732 | 0.599208 | ||||||||
\(477\) | −15.2333 | −0.697486 | ||||||||
\(478\) | 11.1045 | 0.507907 | ||||||||
\(479\) | 8.78005 | 0.401171 | 0.200585 | − | 0.979676i | \(-0.435716\pi\) | ||||
0.200585 | + | 0.979676i | \(0.435716\pi\) | |||||||
\(480\) | 9.19888 | 0.419869 | ||||||||
\(481\) | 12.2302 | 0.557647 | ||||||||
\(482\) | 4.19439 | 0.191049 | ||||||||
\(483\) | −6.72213 | −0.305868 | ||||||||
\(484\) | 16.8483 | 0.765833 | ||||||||
\(485\) | 21.2145 | 0.963301 | ||||||||
\(486\) | −6.32957 | −0.287115 | ||||||||
\(487\) | −23.1617 | −1.04956 | −0.524779 | − | 0.851238i | \(-0.675852\pi\) | ||||
−0.524779 | + | 0.851238i | \(0.675852\pi\) | |||||||
\(488\) | 10.9641 | 0.496323 | ||||||||
\(489\) | −4.50709 | −0.203818 | ||||||||
\(490\) | 0.309774 | 0.0139942 | ||||||||
\(491\) | 8.15363 | 0.367968 | 0.183984 | − | 0.982929i | \(-0.441100\pi\) | ||||
0.183984 | + | 0.982929i | \(0.441100\pi\) | |||||||
\(492\) | −10.8127 | −0.487474 | ||||||||
\(493\) | 0.821696 | 0.0370073 | ||||||||
\(494\) | −8.95738 | −0.403012 | ||||||||
\(495\) | 6.56554 | 0.295099 | ||||||||
\(496\) | −24.6518 | −1.10690 | ||||||||
\(497\) | −44.7426 | −2.00698 | ||||||||
\(498\) | −4.67035 | −0.209283 | ||||||||
\(499\) | 30.6993 | 1.37429 | 0.687144 | − | 0.726521i | \(-0.258864\pi\) | ||||
0.687144 | + | 0.726521i | \(0.258864\pi\) | |||||||
\(500\) | −20.1384 | −0.900615 | ||||||||
\(501\) | 14.6929 | 0.656428 | ||||||||
\(502\) | 1.34302 | 0.0599419 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | −8.57634 | −0.382020 | ||||||||
\(505\) | −20.0731 | −0.893239 | ||||||||
\(506\) | 1.40181 | 0.0623180 | ||||||||
\(507\) | −4.19023 | −0.186095 | ||||||||
\(508\) | −27.2637 | −1.20963 | ||||||||
\(509\) | −6.39080 | −0.283267 | −0.141634 | − | 0.989919i | \(-0.545235\pi\) | ||||
−0.141634 | + | 0.989919i | \(0.545235\pi\) | |||||||
\(510\) | −2.22704 | −0.0986149 | ||||||||
\(511\) | 7.77394 | 0.343899 | ||||||||
\(512\) | −22.4816 | −0.993557 | ||||||||
\(513\) | 37.7309 | 1.66586 | ||||||||
\(514\) | 4.41414 | 0.194699 | ||||||||
\(515\) | −3.48700 | −0.153655 | ||||||||
\(516\) | −0.803041 | −0.0353519 | ||||||||
\(517\) | 10.5003 | 0.461805 | ||||||||
\(518\) | 4.43662 | 0.194934 | ||||||||
\(519\) | −17.1041 | −0.750787 | ||||||||
\(520\) | 10.1126 | 0.443465 | ||||||||
\(521\) | −11.2745 | −0.493944 | −0.246972 | − | 0.969023i | \(-0.579436\pi\) | ||||
−0.246972 | + | 0.969023i | \(0.579436\pi\) | |||||||
\(522\) | −0.258743 | −0.0113249 | ||||||||
\(523\) | 18.6154 | 0.813993 | 0.406996 | − | 0.913430i | \(-0.366576\pi\) | ||||
0.406996 | + | 0.913430i | \(0.366576\pi\) | |||||||
\(524\) | −5.56872 | −0.243271 | ||||||||
\(525\) | 0.592410 | 0.0258549 | ||||||||
\(526\) | −0.168360 | −0.00734085 | ||||||||
\(527\) | 20.7756 | 0.905001 | ||||||||
\(528\) | 4.03189 | 0.175466 | ||||||||
\(529\) | −16.1846 | −0.703676 | ||||||||
\(530\) | 6.51589 | 0.283032 | ||||||||
\(531\) | −0.455477 | −0.0197660 | ||||||||
\(532\) | 38.9815 | 1.69006 | ||||||||
\(533\) | −18.0678 | −0.782604 | ||||||||
\(534\) | 0.0354894 | 0.00153578 | ||||||||
\(535\) | 40.3320 | 1.74370 | ||||||||
\(536\) | 15.2419 | 0.658349 | ||||||||
\(537\) | 21.5086 | 0.928163 | ||||||||
\(538\) | −5.97527 | −0.257612 | ||||||||
\(539\) | 0.472642 | 0.0203581 | ||||||||
\(540\) | −20.4462 | −0.879866 | ||||||||
\(541\) | −36.6446 | −1.57547 | −0.787736 | − | 0.616013i | \(-0.788747\pi\) | ||||
−0.787736 | + | 0.616013i | \(0.788747\pi\) | |||||||
\(542\) | −6.97678 | −0.299678 | ||||||||
\(543\) | 2.83105 | 0.121492 | ||||||||
\(544\) | 11.0623 | 0.474291 | ||||||||
\(545\) | 11.2386 | 0.481409 | ||||||||
\(546\) | 2.96036 | 0.126692 | ||||||||
\(547\) | 19.4186 | 0.830280 | 0.415140 | − | 0.909758i | \(-0.363733\pi\) | ||||
0.415140 | + | 0.909758i | \(0.363733\pi\) | |||||||
\(548\) | −0.683413 | −0.0291939 | ||||||||
\(549\) | −15.2415 | −0.650490 | ||||||||
\(550\) | −0.123539 | −0.00526772 | ||||||||
\(551\) | 2.45013 | 0.104379 | ||||||||
\(552\) | −3.74218 | −0.159278 | ||||||||
\(553\) | −43.4238 | −1.84657 | ||||||||
\(554\) | −5.95808 | −0.253135 | ||||||||
\(555\) | 9.06684 | 0.384866 | ||||||||
\(556\) | −24.1737 | −1.02519 | ||||||||
\(557\) | −35.6561 | −1.51080 | −0.755398 | − | 0.655266i | \(-0.772556\pi\) | ||||
−0.755398 | + | 0.655266i | \(0.772556\pi\) | |||||||
\(558\) | −6.54201 | −0.276945 | ||||||||
\(559\) | −1.34187 | −0.0567549 | ||||||||
\(560\) | −19.2163 | −0.812039 | ||||||||
\(561\) | −3.39793 | −0.143461 | ||||||||
\(562\) | −7.88041 | −0.332415 | ||||||||
\(563\) | −34.0879 | −1.43663 | −0.718316 | − | 0.695717i | \(-0.755087\pi\) | ||||
−0.718316 | + | 0.695717i | \(0.755087\pi\) | |||||||
\(564\) | −13.4547 | −0.566547 | ||||||||
\(565\) | −0.235279 | −0.00989827 | ||||||||
\(566\) | 0.641373 | 0.0269589 | ||||||||
\(567\) | 4.58316 | 0.192475 | ||||||||
\(568\) | −24.9080 | −1.04512 | ||||||||
\(569\) | 13.0323 | 0.546342 | 0.273171 | − | 0.961965i | \(-0.411927\pi\) | ||||
0.273171 | + | 0.961965i | \(0.411927\pi\) | |||||||
\(570\) | −6.64056 | −0.278143 | ||||||||
\(571\) | 28.5710 | 1.19566 | 0.597829 | − | 0.801624i | \(-0.296030\pi\) | ||||
0.597829 | + | 0.801624i | \(0.296030\pi\) | |||||||
\(572\) | 7.40602 | 0.309661 | ||||||||
\(573\) | 3.89114 | 0.162555 | ||||||||
\(574\) | −6.55428 | −0.273570 | ||||||||
\(575\) | −0.600634 | −0.0250482 | ||||||||
\(576\) | 9.52183 | 0.396743 | ||||||||
\(577\) | 40.1508 | 1.67150 | 0.835750 | − | 0.549110i | \(-0.185033\pi\) | ||||
0.835750 | + | 0.549110i | \(0.185033\pi\) | |||||||
\(578\) | 3.99066 | 0.165990 | ||||||||
\(579\) | −20.1137 | −0.835899 | ||||||||
\(580\) | −1.32771 | −0.0551304 | ||||||||
\(581\) | 33.9624 | 1.40900 | ||||||||
\(582\) | 3.45728 | 0.143309 | ||||||||
\(583\) | 9.94172 | 0.411744 | ||||||||
\(584\) | 4.32772 | 0.179082 | ||||||||
\(585\) | −14.0577 | −0.581214 | ||||||||
\(586\) | 3.99707 | 0.165118 | ||||||||
\(587\) | −1.26390 | −0.0521666 | −0.0260833 | − | 0.999660i | \(-0.508304\pi\) | ||||
−0.0260833 | + | 0.999660i | \(0.508304\pi\) | |||||||
\(588\) | −0.605626 | −0.0249756 | ||||||||
\(589\) | 61.9486 | 2.55255 | ||||||||
\(590\) | 0.194825 | 0.00802083 | ||||||||
\(591\) | 17.5895 | 0.723535 | ||||||||
\(592\) | −12.9378 | −0.531739 | ||||||||
\(593\) | 0.473003 | 0.0194239 | 0.00971196 | − | 0.999953i | \(-0.496909\pi\) | ||||
0.00971196 | + | 0.999953i | \(0.496909\pi\) | |||||||
\(594\) | 2.60042 | 0.106696 | ||||||||
\(595\) | 16.1948 | 0.663924 | ||||||||
\(596\) | 10.3737 | 0.424925 | ||||||||
\(597\) | −1.48886 | −0.0609350 | ||||||||
\(598\) | −3.00146 | −0.122739 | ||||||||
\(599\) | 28.8689 | 1.17955 | 0.589775 | − | 0.807568i | \(-0.299217\pi\) | ||||
0.589775 | + | 0.807568i | \(0.299217\pi\) | |||||||
\(600\) | 0.329792 | 0.0134637 | ||||||||
\(601\) | 8.88531 | 0.362439 | 0.181220 | − | 0.983443i | \(-0.441996\pi\) | ||||
0.181220 | + | 0.983443i | \(0.441996\pi\) | |||||||
\(602\) | −0.486776 | −0.0198395 | ||||||||
\(603\) | −21.1881 | −0.862845 | ||||||||
\(604\) | 12.9166 | 0.525568 | ||||||||
\(605\) | 20.8714 | 0.848544 | ||||||||
\(606\) | −3.27126 | −0.132886 | ||||||||
\(607\) | 28.6612 | 1.16332 | 0.581662 | − | 0.813431i | \(-0.302403\pi\) | ||||
0.581662 | + | 0.813431i | \(0.302403\pi\) | |||||||
\(608\) | 32.9854 | 1.33773 | ||||||||
\(609\) | −0.809753 | −0.0328128 | ||||||||
\(610\) | 6.51937 | 0.263962 | ||||||||
\(611\) | −22.4826 | −0.909550 | ||||||||
\(612\) | −10.1170 | −0.408955 | ||||||||
\(613\) | 46.9961 | 1.89815 | 0.949077 | − | 0.315043i | \(-0.102019\pi\) | ||||
0.949077 | + | 0.315043i | \(0.102019\pi\) | |||||||
\(614\) | 6.42099 | 0.259130 | ||||||||
\(615\) | −13.3946 | −0.540122 | ||||||||
\(616\) | 5.59717 | 0.225516 | ||||||||
\(617\) | −24.3030 | −0.978401 | −0.489201 | − | 0.872171i | \(-0.662711\pi\) | ||||
−0.489201 | + | 0.872171i | \(0.662711\pi\) | |||||||
\(618\) | −0.568268 | −0.0228591 | ||||||||
\(619\) | 39.4552 | 1.58584 | 0.792920 | − | 0.609326i | \(-0.208560\pi\) | ||||
0.792920 | + | 0.609326i | \(0.208560\pi\) | |||||||
\(620\) | −33.5698 | −1.34819 | ||||||||
\(621\) | 12.6429 | 0.507344 | ||||||||
\(622\) | −2.74176 | −0.109934 | ||||||||
\(623\) | −0.258077 | −0.0103396 | ||||||||
\(624\) | −8.63282 | −0.345589 | ||||||||
\(625\) | −26.0974 | −1.04390 | ||||||||
\(626\) | −0.872613 | −0.0348766 | ||||||||
\(627\) | −10.1319 | −0.404630 | ||||||||
\(628\) | −19.5408 | −0.779765 | ||||||||
\(629\) | 10.9035 | 0.434750 | ||||||||
\(630\) | −5.09957 | −0.203172 | ||||||||
\(631\) | 34.7457 | 1.38320 | 0.691602 | − | 0.722279i | \(-0.256905\pi\) | ||||
0.691602 | + | 0.722279i | \(0.256905\pi\) | |||||||
\(632\) | −24.1738 | −0.961583 | ||||||||
\(633\) | −21.7080 | −0.862814 | ||||||||
\(634\) | −1.37177 | −0.0544798 | ||||||||
\(635\) | −33.7738 | −1.34027 | ||||||||
\(636\) | −12.7389 | −0.505132 | ||||||||
\(637\) | −1.01199 | −0.0400965 | ||||||||
\(638\) | 0.168863 | 0.00668535 | ||||||||
\(639\) | 34.6251 | 1.36975 | ||||||||
\(640\) | −23.4375 | −0.926449 | ||||||||
\(641\) | −42.3173 | −1.67143 | −0.835716 | − | 0.549163i | \(-0.814947\pi\) | ||||
−0.835716 | + | 0.549163i | \(0.814947\pi\) | |||||||
\(642\) | 6.57282 | 0.259408 | ||||||||
\(643\) | −31.5672 | −1.24489 | −0.622444 | − | 0.782664i | \(-0.713860\pi\) | ||||
−0.622444 | + | 0.782664i | \(0.713860\pi\) | |||||||
\(644\) | 13.0620 | 0.514716 | ||||||||
\(645\) | −0.994794 | −0.0391700 | ||||||||
\(646\) | −7.98572 | −0.314194 | ||||||||
\(647\) | −45.6664 | −1.79533 | −0.897667 | − | 0.440675i | \(-0.854739\pi\) | ||||
−0.897667 | + | 0.440675i | \(0.854739\pi\) | |||||||
\(648\) | 2.55142 | 0.100229 | ||||||||
\(649\) | 0.297258 | 0.0116684 | ||||||||
\(650\) | 0.264514 | 0.0103751 | ||||||||
\(651\) | −20.4737 | −0.802426 | ||||||||
\(652\) | 8.75790 | 0.342986 | ||||||||
\(653\) | 7.15705 | 0.280077 | 0.140039 | − | 0.990146i | \(-0.455277\pi\) | ||||
0.140039 | + | 0.990146i | \(0.455277\pi\) | |||||||
\(654\) | 1.83153 | 0.0716185 | ||||||||
\(655\) | −6.89844 | −0.269545 | ||||||||
\(656\) | 19.1132 | 0.746244 | ||||||||
\(657\) | −6.01605 | −0.234708 | ||||||||
\(658\) | −8.15581 | −0.317946 | ||||||||
\(659\) | 12.1603 | 0.473696 | 0.236848 | − | 0.971547i | \(-0.423886\pi\) | ||||
0.236848 | + | 0.971547i | \(0.423886\pi\) | |||||||
\(660\) | 5.49046 | 0.213716 | ||||||||
\(661\) | −15.2194 | −0.591968 | −0.295984 | − | 0.955193i | \(-0.595647\pi\) | ||||
−0.295984 | + | 0.955193i | \(0.595647\pi\) | |||||||
\(662\) | 5.43917 | 0.211400 | ||||||||
\(663\) | 7.27543 | 0.282554 | ||||||||
\(664\) | 18.9067 | 0.733724 | ||||||||
\(665\) | 48.2896 | 1.87259 | ||||||||
\(666\) | −3.43338 | −0.133041 | ||||||||
\(667\) | 0.820994 | 0.0317890 | ||||||||
\(668\) | −28.5502 | −1.10464 | ||||||||
\(669\) | 4.51812 | 0.174681 | ||||||||
\(670\) | 9.06297 | 0.350133 | ||||||||
\(671\) | 9.94702 | 0.384001 | ||||||||
\(672\) | −10.9015 | −0.420534 | ||||||||
\(673\) | 34.9359 | 1.34668 | 0.673340 | − | 0.739333i | \(-0.264859\pi\) | ||||
0.673340 | + | 0.739333i | \(0.264859\pi\) | |||||||
\(674\) | 12.9555 | 0.499028 | ||||||||
\(675\) | −1.11420 | −0.0428856 | ||||||||
\(676\) | 8.14219 | 0.313161 | ||||||||
\(677\) | −17.6078 | −0.676721 | −0.338361 | − | 0.941016i | \(-0.609872\pi\) | ||||
−0.338361 | + | 0.941016i | \(0.609872\pi\) | |||||||
\(678\) | −0.0383429 | −0.00147255 | ||||||||
\(679\) | −25.1411 | −0.964826 | ||||||||
\(680\) | 9.01560 | 0.345732 | ||||||||
\(681\) | −26.0993 | −1.00013 | ||||||||
\(682\) | 4.26951 | 0.163488 | ||||||||
\(683\) | −43.5075 | −1.66477 | −0.832385 | − | 0.554198i | \(-0.813025\pi\) | ||||
−0.832385 | + | 0.554198i | \(0.813025\pi\) | |||||||
\(684\) | −30.1668 | −1.15346 | ||||||||
\(685\) | −0.846600 | −0.0323469 | ||||||||
\(686\) | 7.07512 | 0.270129 | ||||||||
\(687\) | −4.29846 | −0.163996 | ||||||||
\(688\) | 1.41950 | 0.0541181 | ||||||||
\(689\) | −21.2865 | −0.810953 | ||||||||
\(690\) | −2.22513 | −0.0847094 | ||||||||
\(691\) | −2.05256 | −0.0780829 | −0.0390415 | − | 0.999238i | \(-0.512430\pi\) | ||||
−0.0390415 | + | 0.999238i | \(0.512430\pi\) | |||||||
\(692\) | 33.2356 | 1.26343 | ||||||||
\(693\) | −7.78074 | −0.295566 | ||||||||
\(694\) | 0.163907 | 0.00622184 | ||||||||
\(695\) | −29.9459 | −1.13591 | ||||||||
\(696\) | −0.450786 | −0.0170870 | ||||||||
\(697\) | −16.1079 | −0.610130 | ||||||||
\(698\) | 3.40741 | 0.128972 | ||||||||
\(699\) | −10.0296 | −0.379355 | ||||||||
\(700\) | −1.15113 | −0.0435088 | ||||||||
\(701\) | −9.44349 | −0.356676 | −0.178338 | − | 0.983969i | \(-0.557072\pi\) | ||||
−0.178338 | + | 0.983969i | \(0.557072\pi\) | |||||||
\(702\) | −5.56784 | −0.210145 | ||||||||
\(703\) | 32.5119 | 1.22621 | ||||||||
\(704\) | −6.21422 | −0.234207 | ||||||||
\(705\) | −16.6675 | −0.627735 | ||||||||
\(706\) | 3.56814 | 0.134289 | ||||||||
\(707\) | 23.7883 | 0.894653 | ||||||||
\(708\) | −0.380895 | −0.0143149 | ||||||||
\(709\) | 15.9123 | 0.597598 | 0.298799 | − | 0.954316i | \(-0.403414\pi\) | ||||
0.298799 | + | 0.954316i | \(0.403414\pi\) | |||||||
\(710\) | −14.8105 | −0.555829 | ||||||||
\(711\) | 33.6045 | 1.26027 | ||||||||
\(712\) | −0.143670 | −0.00538426 | ||||||||
\(713\) | 20.7579 | 0.777389 | ||||||||
\(714\) | 2.63924 | 0.0987710 | ||||||||
\(715\) | 9.17446 | 0.343105 | ||||||||
\(716\) | −41.7941 | −1.56192 | ||||||||
\(717\) | −26.8938 | −1.00437 | ||||||||
\(718\) | −2.16540 | −0.0808119 | ||||||||
\(719\) | 24.9061 | 0.928842 | 0.464421 | − | 0.885615i | \(-0.346263\pi\) | ||||
0.464421 | + | 0.885615i | \(0.346263\pi\) | |||||||
\(720\) | 14.8710 | 0.554211 | ||||||||
\(721\) | 4.13240 | 0.153899 | ||||||||
\(722\) | −16.3584 | −0.608795 | ||||||||
\(723\) | −10.1584 | −0.377794 | ||||||||
\(724\) | −5.50112 | −0.204448 | ||||||||
\(725\) | −0.0723528 | −0.00268712 | ||||||||
\(726\) | 3.40137 | 0.126237 | ||||||||
\(727\) | 11.5573 | 0.428636 | 0.214318 | − | 0.976764i | \(-0.431247\pi\) | ||||
0.214318 | + | 0.976764i | \(0.431247\pi\) | |||||||
\(728\) | −11.9843 | −0.444167 | ||||||||
\(729\) | 10.2563 | 0.379865 | ||||||||
\(730\) | 2.57330 | 0.0952421 | ||||||||
\(731\) | −1.19631 | −0.0442470 | ||||||||
\(732\) | −12.7457 | −0.471096 | ||||||||
\(733\) | 11.9918 | 0.442926 | 0.221463 | − | 0.975169i | \(-0.428917\pi\) | ||||
0.221463 | + | 0.975169i | \(0.428917\pi\) | |||||||
\(734\) | −6.41928 | −0.236940 | ||||||||
\(735\) | −0.750240 | −0.0276730 | ||||||||
\(736\) | 11.0528 | 0.407412 | ||||||||
\(737\) | 13.8280 | 0.509359 | ||||||||
\(738\) | 5.07219 | 0.186710 | ||||||||
\(739\) | 48.3255 | 1.77768 | 0.888840 | − | 0.458217i | \(-0.151512\pi\) | ||||
0.888840 | + | 0.458217i | \(0.151512\pi\) | |||||||
\(740\) | −17.6181 | −0.647654 | ||||||||
\(741\) | 21.6938 | 0.796942 | ||||||||
\(742\) | −7.72191 | −0.283480 | ||||||||
\(743\) | 40.3146 | 1.47900 | 0.739499 | − | 0.673158i | \(-0.235063\pi\) | ||||
0.739499 | + | 0.673158i | \(0.235063\pi\) | |||||||
\(744\) | −11.3976 | −0.417856 | ||||||||
\(745\) | 12.8508 | 0.470817 | ||||||||
\(746\) | 9.24693 | 0.338554 | ||||||||
\(747\) | −26.2826 | −0.961632 | ||||||||
\(748\) | 6.60265 | 0.241417 | ||||||||
\(749\) | −47.7970 | −1.74646 | ||||||||
\(750\) | −4.06557 | −0.148453 | ||||||||
\(751\) | −48.6091 | −1.77377 | −0.886885 | − | 0.461990i | \(-0.847136\pi\) | ||||
−0.886885 | + | 0.461990i | \(0.847136\pi\) | |||||||
\(752\) | 23.7834 | 0.867292 | ||||||||
\(753\) | −3.25265 | −0.118533 | ||||||||
\(754\) | −0.361558 | −0.0131672 | ||||||||
\(755\) | 16.0008 | 0.582330 | ||||||||
\(756\) | 24.2306 | 0.881258 | ||||||||
\(757\) | −44.8319 | −1.62944 | −0.814721 | − | 0.579853i | \(-0.803110\pi\) | ||||
−0.814721 | + | 0.579853i | \(0.803110\pi\) | |||||||
\(758\) | 8.95611 | 0.325301 | ||||||||
\(759\) | −3.39503 | −0.123232 | ||||||||
\(760\) | 26.8826 | 0.975136 | ||||||||
\(761\) | −31.4812 | −1.14119 | −0.570596 | − | 0.821231i | \(-0.693288\pi\) | ||||
−0.570596 | + | 0.821231i | \(0.693288\pi\) | |||||||
\(762\) | −5.50405 | −0.199391 | ||||||||
\(763\) | −13.3188 | −0.482171 | ||||||||
\(764\) | −7.56101 | −0.273548 | ||||||||
\(765\) | −12.5328 | −0.453123 | ||||||||
\(766\) | −8.56189 | −0.309353 | ||||||||
\(767\) | −0.636468 | −0.0229815 | ||||||||
\(768\) | 4.80686 | 0.173453 | ||||||||
\(769\) | 30.6134 | 1.10395 | 0.551974 | − | 0.833861i | \(-0.313875\pi\) | ||||
0.551974 | + | 0.833861i | \(0.313875\pi\) | |||||||
\(770\) | 3.32813 | 0.119937 | ||||||||
\(771\) | −10.6906 | −0.385011 | ||||||||
\(772\) | 39.0837 | 1.40665 | ||||||||
\(773\) | 25.8605 | 0.930136 | 0.465068 | − | 0.885275i | \(-0.346030\pi\) | ||||
0.465068 | + | 0.885275i | \(0.346030\pi\) | |||||||
\(774\) | 0.376703 | 0.0135403 | ||||||||
\(775\) | −1.82936 | −0.0657125 | ||||||||
\(776\) | −13.9959 | −0.502424 | ||||||||
\(777\) | −10.7450 | −0.385475 | ||||||||
\(778\) | −11.6690 | −0.418352 | ||||||||
\(779\) | −48.0304 | −1.72087 | ||||||||
\(780\) | −11.7558 | −0.420925 | ||||||||
\(781\) | −22.5974 | −0.808598 | ||||||||
\(782\) | −2.67588 | −0.0956891 | ||||||||
\(783\) | 1.52298 | 0.0544268 | ||||||||
\(784\) | 1.07054 | 0.0382336 | ||||||||
\(785\) | −24.2069 | −0.863981 | ||||||||
\(786\) | −1.12422 | −0.0400997 | ||||||||
\(787\) | 31.7233 | 1.13081 | 0.565406 | − | 0.824813i | \(-0.308719\pi\) | ||||
0.565406 | + | 0.824813i | \(0.308719\pi\) | |||||||
\(788\) | −34.1788 | −1.21757 | ||||||||
\(789\) | 0.407750 | 0.0145163 | ||||||||
\(790\) | −14.3740 | −0.511403 | ||||||||
\(791\) | 0.278827 | 0.00991394 | ||||||||
\(792\) | −4.33150 | −0.153913 | ||||||||
\(793\) | −21.2979 | −0.756311 | ||||||||
\(794\) | −11.2021 | −0.397548 | ||||||||
\(795\) | −15.7808 | −0.559687 | ||||||||
\(796\) | 2.89306 | 0.102542 | ||||||||
\(797\) | −55.1753 | −1.95441 | −0.977205 | − | 0.212296i | \(-0.931906\pi\) | ||||
−0.977205 | + | 0.212296i | \(0.931906\pi\) | |||||||
\(798\) | 7.86965 | 0.278583 | ||||||||
\(799\) | −20.0438 | −0.709099 | ||||||||
\(800\) | −0.974066 | −0.0344384 | ||||||||
\(801\) | 0.199719 | 0.00705671 | ||||||||
\(802\) | −5.49078 | −0.193886 | ||||||||
\(803\) | 3.92625 | 0.138554 | ||||||||
\(804\) | −17.7186 | −0.624887 | ||||||||
\(805\) | 16.1810 | 0.570306 | ||||||||
\(806\) | −9.14158 | −0.321999 | ||||||||
\(807\) | 14.4715 | 0.509420 | ||||||||
\(808\) | 13.2429 | 0.465882 | ||||||||
\(809\) | −6.04923 | −0.212680 | −0.106340 | − | 0.994330i | \(-0.533913\pi\) | ||||
−0.106340 | + | 0.994330i | \(0.533913\pi\) | |||||||
\(810\) | 1.51710 | 0.0533055 | ||||||||
\(811\) | −3.97693 | −0.139649 | −0.0698244 | − | 0.997559i | \(-0.522244\pi\) | ||||
−0.0698244 | + | 0.997559i | \(0.522244\pi\) | |||||||
\(812\) | 1.57346 | 0.0552176 | ||||||||
\(813\) | 16.8970 | 0.592604 | ||||||||
\(814\) | 2.24073 | 0.0785374 | ||||||||
\(815\) | 10.8491 | 0.380029 | ||||||||
\(816\) | −7.69637 | −0.269427 | ||||||||
\(817\) | −3.56714 | −0.124798 | ||||||||
\(818\) | 7.15641 | 0.250218 | ||||||||
\(819\) | 16.6596 | 0.582134 | ||||||||
\(820\) | 26.0275 | 0.908920 | ||||||||
\(821\) | 16.5562 | 0.577815 | 0.288907 | − | 0.957357i | \(-0.406708\pi\) | ||||
0.288907 | + | 0.957357i | \(0.406708\pi\) | |||||||
\(822\) | −0.137968 | −0.00481220 | ||||||||
\(823\) | −29.9588 | −1.04430 | −0.522150 | − | 0.852854i | \(-0.674870\pi\) | ||||
−0.522150 | + | 0.852854i | \(0.674870\pi\) | |||||||
\(824\) | 2.30049 | 0.0801413 | ||||||||
\(825\) | 0.299198 | 0.0104168 | ||||||||
\(826\) | −0.230885 | −0.00803353 | ||||||||
\(827\) | −39.4061 | −1.37029 | −0.685143 | − | 0.728409i | \(-0.740260\pi\) | ||||
−0.685143 | + | 0.728409i | \(0.740260\pi\) | |||||||
\(828\) | −10.1084 | −0.351290 | ||||||||
\(829\) | 6.63817 | 0.230553 | 0.115277 | − | 0.993333i | \(-0.463225\pi\) | ||||
0.115277 | + | 0.993333i | \(0.463225\pi\) | |||||||
\(830\) | 11.2421 | 0.390220 | ||||||||
\(831\) | 14.4298 | 0.500565 | ||||||||
\(832\) | 13.3055 | 0.461285 | ||||||||
\(833\) | −0.902214 | −0.0312599 | ||||||||
\(834\) | −4.88022 | −0.168988 | ||||||||
\(835\) | −35.3675 | −1.22394 | ||||||||
\(836\) | 19.6877 | 0.680914 | ||||||||
\(837\) | 38.5068 | 1.33099 | ||||||||
\(838\) | −3.83906 | −0.132618 | ||||||||
\(839\) | −55.4839 | −1.91552 | −0.957759 | − | 0.287574i | \(-0.907151\pi\) | ||||
−0.957759 | + | 0.287574i | \(0.907151\pi\) | |||||||
\(840\) | −8.88456 | −0.306546 | ||||||||
\(841\) | −28.9011 | −0.996590 | ||||||||
\(842\) | −0.889068 | −0.0306393 | ||||||||
\(843\) | 19.0855 | 0.657340 | ||||||||
\(844\) | 42.1815 | 1.45195 | ||||||||
\(845\) | 10.0864 | 0.346983 | ||||||||
\(846\) | 6.31157 | 0.216996 | ||||||||
\(847\) | −24.7345 | −0.849887 | ||||||||
\(848\) | 22.5181 | 0.773276 | ||||||||
\(849\) | −1.55334 | −0.0533103 | ||||||||
\(850\) | 0.235820 | 0.00808857 | ||||||||
\(851\) | 10.8942 | 0.373447 | ||||||||
\(852\) | 28.9554 | 0.991997 | ||||||||
\(853\) | −23.3264 | −0.798680 | −0.399340 | − | 0.916803i | \(-0.630761\pi\) | ||||
−0.399340 | + | 0.916803i | \(0.630761\pi\) | |||||||
\(854\) | −7.72603 | −0.264379 | ||||||||
\(855\) | −37.3701 | −1.27803 | ||||||||
\(856\) | −26.6084 | −0.909456 | ||||||||
\(857\) | 20.5822 | 0.703075 | 0.351537 | − | 0.936174i | \(-0.385659\pi\) | ||||
0.351537 | + | 0.936174i | \(0.385659\pi\) | |||||||
\(858\) | 1.49514 | 0.0510433 | ||||||||
\(859\) | −45.7526 | −1.56106 | −0.780529 | − | 0.625120i | \(-0.785050\pi\) | ||||
−0.780529 | + | 0.625120i | \(0.785050\pi\) | |||||||
\(860\) | 1.93302 | 0.0659155 | ||||||||
\(861\) | 15.8738 | 0.540977 | ||||||||
\(862\) | −1.68600 | −0.0574253 | ||||||||
\(863\) | 10.0848 | 0.343290 | 0.171645 | − | 0.985159i | \(-0.445092\pi\) | ||||
0.171645 | + | 0.985159i | \(0.445092\pi\) | |||||||
\(864\) | 20.5035 | 0.697542 | ||||||||
\(865\) | 41.1717 | 1.39988 | ||||||||
\(866\) | 6.51638 | 0.221435 | ||||||||
\(867\) | −9.66495 | −0.328239 | ||||||||
\(868\) | 39.7831 | 1.35033 | ||||||||
\(869\) | −21.9313 | −0.743968 | ||||||||
\(870\) | −0.268041 | −0.00908745 | ||||||||
\(871\) | −29.6075 | −1.00321 | ||||||||
\(872\) | −7.41449 | −0.251086 | ||||||||
\(873\) | 19.4560 | 0.658487 | ||||||||
\(874\) | −7.97890 | −0.269890 | ||||||||
\(875\) | 29.5645 | 0.999462 | ||||||||
\(876\) | −5.03095 | −0.169980 | ||||||||
\(877\) | 3.30564 | 0.111624 | 0.0558118 | − | 0.998441i | \(-0.482225\pi\) | ||||
0.0558118 | + | 0.998441i | \(0.482225\pi\) | |||||||
\(878\) | 8.42872 | 0.284456 | ||||||||
\(879\) | −9.68048 | −0.326515 | ||||||||
\(880\) | −9.70527 | −0.327165 | ||||||||
\(881\) | 8.30907 | 0.279940 | 0.139970 | − | 0.990156i | \(-0.455299\pi\) | ||||
0.139970 | + | 0.990156i | \(0.455299\pi\) | |||||||
\(882\) | 0.284097 | 0.00956603 | ||||||||
\(883\) | 2.65895 | 0.0894807 | 0.0447403 | − | 0.998999i | \(-0.485754\pi\) | ||||
0.0447403 | + | 0.998999i | \(0.485754\pi\) | |||||||
\(884\) | −14.1372 | −0.475484 | ||||||||
\(885\) | −0.471846 | −0.0158609 | ||||||||
\(886\) | 7.69060 | 0.258371 | ||||||||
\(887\) | −21.5846 | −0.724740 | −0.362370 | − | 0.932034i | \(-0.618032\pi\) | ||||
−0.362370 | + | 0.932034i | \(0.618032\pi\) | |||||||
\(888\) | −5.98170 | −0.200733 | ||||||||
\(889\) | 40.0250 | 1.34240 | ||||||||
\(890\) | −0.0854276 | −0.00286354 | ||||||||
\(891\) | 2.31474 | 0.0775466 | ||||||||
\(892\) | −8.77932 | −0.293954 | ||||||||
\(893\) | −59.7665 | −2.00001 | ||||||||
\(894\) | 2.09427 | 0.0700428 | ||||||||
\(895\) | −51.7738 | −1.73061 | ||||||||
\(896\) | 27.7755 | 0.927915 | ||||||||
\(897\) | 7.26921 | 0.242712 | ||||||||
\(898\) | 13.7870 | 0.460079 | ||||||||
\(899\) | 2.50051 | 0.0833967 | ||||||||
\(900\) | 0.890832 | 0.0296944 | ||||||||
\(901\) | −18.9775 | −0.632231 | ||||||||
\(902\) | −3.31026 | −0.110220 | ||||||||
\(903\) | 1.17892 | 0.0392320 | ||||||||
\(904\) | 0.155222 | 0.00516259 | ||||||||
\(905\) | −6.81470 | −0.226528 | ||||||||
\(906\) | 2.60762 | 0.0866323 | ||||||||
\(907\) | −5.95616 | −0.197771 | −0.0988855 | − | 0.995099i | \(-0.531528\pi\) | ||||
−0.0988855 | + | 0.995099i | \(0.531528\pi\) | |||||||
\(908\) | 50.7145 | 1.68302 | ||||||||
\(909\) | −18.4092 | −0.610594 | ||||||||
\(910\) | −7.12597 | −0.236224 | ||||||||
\(911\) | 14.9730 | 0.496079 | 0.248040 | − | 0.968750i | \(-0.420214\pi\) | ||||
0.248040 | + | 0.968750i | \(0.420214\pi\) | |||||||
\(912\) | −22.9490 | −0.759916 | ||||||||
\(913\) | 17.1528 | 0.567676 | ||||||||
\(914\) | 4.64590 | 0.153673 | ||||||||
\(915\) | −15.7892 | −0.521975 | ||||||||
\(916\) | 8.35249 | 0.275974 | ||||||||
\(917\) | 8.17527 | 0.269971 | ||||||||
\(918\) | −4.96386 | −0.163832 | ||||||||
\(919\) | −21.4164 | −0.706463 | −0.353232 | − | 0.935536i | \(-0.614917\pi\) | ||||
−0.353232 | + | 0.935536i | \(0.614917\pi\) | |||||||
\(920\) | 9.00790 | 0.296982 | ||||||||
\(921\) | −15.5509 | −0.512421 | ||||||||
\(922\) | −6.71925 | −0.221287 | ||||||||
\(923\) | 48.3840 | 1.59258 | ||||||||
\(924\) | −6.50668 | −0.214054 | ||||||||
\(925\) | −0.960085 | −0.0315674 | ||||||||
\(926\) | 2.71546 | 0.0892354 | ||||||||
\(927\) | −3.19796 | −0.105035 | ||||||||
\(928\) | 1.33143 | 0.0437064 | ||||||||
\(929\) | −51.4153 | −1.68688 | −0.843441 | − | 0.537221i | \(-0.819474\pi\) | ||||
−0.843441 | + | 0.537221i | \(0.819474\pi\) | |||||||
\(930\) | −6.77712 | −0.222230 | ||||||||
\(931\) | −2.69021 | −0.0881682 | ||||||||
\(932\) | 19.4889 | 0.638381 | ||||||||
\(933\) | 6.64024 | 0.217392 | ||||||||
\(934\) | 12.8039 | 0.418958 | ||||||||
\(935\) | 8.17925 | 0.267490 | ||||||||
\(936\) | 9.27433 | 0.303141 | ||||||||
\(937\) | −41.9350 | −1.36996 | −0.684979 | − | 0.728563i | \(-0.740188\pi\) | ||||
−0.684979 | + | 0.728563i | \(0.740188\pi\) | |||||||
\(938\) | −10.7404 | −0.350687 | ||||||||
\(939\) | 2.11337 | 0.0689674 | ||||||||
\(940\) | 32.3873 | 1.05636 | ||||||||
\(941\) | −36.8467 | −1.20117 | −0.600585 | − | 0.799561i | \(-0.705065\pi\) | ||||
−0.600585 | + | 0.799561i | \(0.705065\pi\) | |||||||
\(942\) | −3.94494 | −0.128533 | ||||||||
\(943\) | −16.0941 | −0.524097 | ||||||||
\(944\) | 0.673293 | 0.0219138 | ||||||||
\(945\) | 30.0165 | 0.976436 | ||||||||
\(946\) | −0.245848 | −0.00799320 | ||||||||
\(947\) | 2.12177 | 0.0689481 | 0.0344741 | − | 0.999406i | \(-0.489024\pi\) | ||||
0.0344741 | + | 0.999406i | \(0.489024\pi\) | |||||||
\(948\) | 28.1019 | 0.912708 | ||||||||
\(949\) | −8.40663 | −0.272891 | ||||||||
\(950\) | 0.703167 | 0.0228138 | ||||||||
\(951\) | 3.32227 | 0.107732 | ||||||||
\(952\) | −10.6843 | −0.346280 | ||||||||
\(953\) | 13.5643 | 0.439391 | 0.219695 | − | 0.975569i | \(-0.429494\pi\) | ||||
0.219695 | + | 0.975569i | \(0.429494\pi\) | |||||||
\(954\) | 5.97579 | 0.193473 | ||||||||
\(955\) | −9.36645 | −0.303091 | ||||||||
\(956\) | 52.2584 | 1.69016 | ||||||||
\(957\) | −0.408968 | −0.0132201 | ||||||||
\(958\) | −3.44427 | −0.111279 | ||||||||
\(959\) | 1.00330 | 0.0323981 | ||||||||
\(960\) | 9.86403 | 0.318360 | ||||||||
\(961\) | 32.2225 | 1.03944 | ||||||||
\(962\) | −4.79769 | −0.154684 | ||||||||
\(963\) | 36.9889 | 1.19195 | ||||||||
\(964\) | 19.7391 | 0.635754 | ||||||||
\(965\) | 48.4163 | 1.55858 | ||||||||
\(966\) | 2.63698 | 0.0848435 | ||||||||
\(967\) | 5.95719 | 0.191570 | 0.0957851 | − | 0.995402i | \(-0.469464\pi\) | ||||
0.0957851 | + | 0.995402i | \(0.469464\pi\) | |||||||
\(968\) | −13.7696 | −0.442571 | ||||||||
\(969\) | 19.3406 | 0.621308 | ||||||||
\(970\) | −8.32211 | −0.267207 | ||||||||
\(971\) | 12.1772 | 0.390785 | 0.195392 | − | 0.980725i | \(-0.437402\pi\) | ||||
0.195392 | + | 0.980725i | \(0.437402\pi\) | |||||||
\(972\) | −29.7874 | −0.955431 | ||||||||
\(973\) | 35.4886 | 1.13771 | ||||||||
\(974\) | 9.08597 | 0.291133 | ||||||||
\(975\) | −0.640624 | −0.0205164 | ||||||||
\(976\) | 22.5301 | 0.721172 | ||||||||
\(977\) | 7.69439 | 0.246165 | 0.123083 | − | 0.992396i | \(-0.460722\pi\) | ||||
0.123083 | + | 0.992396i | \(0.460722\pi\) | |||||||
\(978\) | 1.76806 | 0.0565363 | ||||||||
\(979\) | −0.130342 | −0.00416576 | ||||||||
\(980\) | 1.45782 | 0.0465683 | ||||||||
\(981\) | 10.3070 | 0.329078 | ||||||||
\(982\) | −3.19854 | −0.102069 | ||||||||
\(983\) | −12.2144 | −0.389578 | −0.194789 | − | 0.980845i | \(-0.562402\pi\) | ||||
−0.194789 | + | 0.980845i | \(0.562402\pi\) | |||||||
\(984\) | 8.83686 | 0.281709 | ||||||||
\(985\) | −42.3401 | −1.34907 | ||||||||
\(986\) | −0.322338 | −0.0102653 | ||||||||
\(987\) | 19.7525 | 0.628729 | ||||||||
\(988\) | −42.1540 | −1.34110 | ||||||||
\(989\) | −1.19529 | −0.0380079 | ||||||||
\(990\) | −2.57555 | −0.0818564 | ||||||||
\(991\) | 2.35228 | 0.0747227 | 0.0373613 | − | 0.999302i | \(-0.488105\pi\) | ||||
0.0373613 | + | 0.999302i | \(0.488105\pi\) | |||||||
\(992\) | 33.6637 | 1.06882 | ||||||||
\(993\) | −13.1731 | −0.418036 | ||||||||
\(994\) | 17.5518 | 0.556709 | ||||||||
\(995\) | 3.58387 | 0.113616 | ||||||||
\(996\) | −21.9790 | −0.696431 | ||||||||
\(997\) | 19.2415 | 0.609384 | 0.304692 | − | 0.952451i | \(-0.401446\pi\) | ||||
0.304692 | + | 0.952451i | \(0.401446\pi\) | |||||||
\(998\) | −12.0428 | −0.381209 | ||||||||
\(999\) | 20.2092 | 0.639389 |
(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 | 503.2.a.e.1.6 | ✓ | 10 | |
3.2 | odd | 2 | 4527.2.a.k.1.5 | 10 | |||
4.3 | odd | 2 | 8048.2.a.p.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.6 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4527.2.a.k.1.5 | 10 | 3.2 | odd | 2 | |||
8048.2.a.p.1.2 | 10 | 4.3 | odd | 2 |