Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(1,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, 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("349.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.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: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.09071\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 349.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09071 | −0.771252 | −0.385626 | − | 0.922655i | \(-0.626014\pi\) | ||||
−0.385626 | + | 0.922655i | \(0.626014\pi\) | |||||||
\(3\) | 2.75693 | 1.59171 | 0.795856 | − | 0.605486i | \(-0.207021\pi\) | ||||
0.795856 | + | 0.605486i | \(0.207021\pi\) | |||||||
\(4\) | −0.810342 | −0.405171 | ||||||||
\(5\) | 1.35282 | 0.605000 | 0.302500 | − | 0.953149i | \(-0.402179\pi\) | ||||
0.302500 | + | 0.953149i | \(0.402179\pi\) | |||||||
\(6\) | −3.00702 | −1.22761 | ||||||||
\(7\) | 0.0387215 | 0.0146354 | 0.00731768 | − | 0.999973i | \(-0.497671\pi\) | ||||
0.00731768 | + | 0.999973i | \(0.497671\pi\) | |||||||
\(8\) | 3.06528 | 1.08374 | ||||||||
\(9\) | 4.60064 | 1.53355 | ||||||||
\(10\) | −1.47554 | −0.466607 | ||||||||
\(11\) | −2.52544 | −0.761449 | −0.380724 | − | 0.924689i | \(-0.624325\pi\) | ||||
−0.380724 | + | 0.924689i | \(0.624325\pi\) | |||||||
\(12\) | −2.23405 | −0.644915 | ||||||||
\(13\) | 3.42579 | 0.950145 | 0.475072 | − | 0.879947i | \(-0.342422\pi\) | ||||
0.475072 | + | 0.879947i | \(0.342422\pi\) | |||||||
\(14\) | −0.0422341 | −0.0112875 | ||||||||
\(15\) | 3.72962 | 0.962985 | ||||||||
\(16\) | −1.72266 | −0.430666 | ||||||||
\(17\) | 0.349950 | 0.0848754 | 0.0424377 | − | 0.999099i | \(-0.486488\pi\) | ||||
0.0424377 | + | 0.999099i | \(0.486488\pi\) | |||||||
\(18\) | −5.01798 | −1.18275 | ||||||||
\(19\) | 0.797001 | 0.182845 | 0.0914223 | − | 0.995812i | \(-0.470859\pi\) | ||||
0.0914223 | + | 0.995812i | \(0.470859\pi\) | |||||||
\(20\) | −1.09625 | −0.245128 | ||||||||
\(21\) | 0.106752 | 0.0232953 | ||||||||
\(22\) | 2.75453 | 0.587269 | ||||||||
\(23\) | 7.33792 | 1.53006 | 0.765031 | − | 0.643993i | \(-0.222723\pi\) | ||||
0.765031 | + | 0.643993i | \(0.222723\pi\) | |||||||
\(24\) | 8.45075 | 1.72500 | ||||||||
\(25\) | −3.16988 | −0.633976 | ||||||||
\(26\) | −3.73656 | −0.732801 | ||||||||
\(27\) | 4.41285 | 0.849252 | ||||||||
\(28\) | −0.0313777 | −0.00592982 | ||||||||
\(29\) | −4.43160 | −0.822927 | −0.411463 | − | 0.911426i | \(-0.634982\pi\) | ||||
−0.411463 | + | 0.911426i | \(0.634982\pi\) | |||||||
\(30\) | −4.06796 | −0.742704 | ||||||||
\(31\) | −3.02716 | −0.543694 | −0.271847 | − | 0.962341i | \(-0.587634\pi\) | ||||
−0.271847 | + | 0.962341i | \(0.587634\pi\) | |||||||
\(32\) | −4.25163 | −0.751589 | ||||||||
\(33\) | −6.96245 | −1.21201 | ||||||||
\(34\) | −0.381696 | −0.0654603 | ||||||||
\(35\) | 0.0523833 | 0.00885439 | ||||||||
\(36\) | −3.72809 | −0.621349 | ||||||||
\(37\) | 2.34285 | 0.385162 | 0.192581 | − | 0.981281i | \(-0.438314\pi\) | ||||
0.192581 | + | 0.981281i | \(0.438314\pi\) | |||||||
\(38\) | −0.869300 | −0.141019 | ||||||||
\(39\) | 9.44466 | 1.51236 | ||||||||
\(40\) | 4.14677 | 0.655662 | ||||||||
\(41\) | 1.21384 | 0.189570 | 0.0947849 | − | 0.995498i | \(-0.469784\pi\) | ||||
0.0947849 | + | 0.995498i | \(0.469784\pi\) | |||||||
\(42\) | −0.116436 | −0.0179665 | ||||||||
\(43\) | 4.67252 | 0.712553 | 0.356277 | − | 0.934381i | \(-0.384046\pi\) | ||||
0.356277 | + | 0.934381i | \(0.384046\pi\) | |||||||
\(44\) | 2.04647 | 0.308517 | ||||||||
\(45\) | 6.22384 | 0.927795 | ||||||||
\(46\) | −8.00358 | −1.18006 | ||||||||
\(47\) | 6.08599 | 0.887733 | 0.443866 | − | 0.896093i | \(-0.353606\pi\) | ||||
0.443866 | + | 0.896093i | \(0.353606\pi\) | |||||||
\(48\) | −4.74925 | −0.685495 | ||||||||
\(49\) | −6.99850 | −0.999786 | ||||||||
\(50\) | 3.45743 | 0.488955 | ||||||||
\(51\) | 0.964787 | 0.135097 | ||||||||
\(52\) | −2.77607 | −0.384971 | ||||||||
\(53\) | 1.83205 | 0.251651 | 0.125826 | − | 0.992052i | \(-0.459842\pi\) | ||||
0.125826 | + | 0.992052i | \(0.459842\pi\) | |||||||
\(54\) | −4.81315 | −0.654987 | ||||||||
\(55\) | −3.41647 | −0.460676 | ||||||||
\(56\) | 0.118692 | 0.0158609 | ||||||||
\(57\) | 2.19727 | 0.291036 | ||||||||
\(58\) | 4.83361 | 0.634684 | ||||||||
\(59\) | 5.73115 | 0.746133 | 0.373066 | − | 0.927805i | \(-0.378306\pi\) | ||||
0.373066 | + | 0.927805i | \(0.378306\pi\) | |||||||
\(60\) | −3.02227 | −0.390174 | ||||||||
\(61\) | −14.1922 | −1.81712 | −0.908560 | − | 0.417755i | \(-0.862817\pi\) | ||||
−0.908560 | + | 0.417755i | \(0.862817\pi\) | |||||||
\(62\) | 3.30177 | 0.419325 | ||||||||
\(63\) | 0.178144 | 0.0224440 | ||||||||
\(64\) | 8.08264 | 1.01033 | ||||||||
\(65\) | 4.63448 | 0.574837 | ||||||||
\(66\) | 7.59405 | 0.934762 | ||||||||
\(67\) | −5.42047 | −0.662215 | −0.331108 | − | 0.943593i | \(-0.607422\pi\) | ||||
−0.331108 | + | 0.943593i | \(0.607422\pi\) | |||||||
\(68\) | −0.283579 | −0.0343890 | ||||||||
\(69\) | 20.2301 | 2.43542 | ||||||||
\(70\) | −0.0571352 | −0.00682896 | ||||||||
\(71\) | −9.26457 | −1.09950 | −0.549751 | − | 0.835328i | \(-0.685277\pi\) | ||||
−0.549751 | + | 0.835328i | \(0.685277\pi\) | |||||||
\(72\) | 14.1023 | 1.66197 | ||||||||
\(73\) | −1.57837 | −0.184734 | −0.0923672 | − | 0.995725i | \(-0.529443\pi\) | ||||
−0.0923672 | + | 0.995725i | \(0.529443\pi\) | |||||||
\(74\) | −2.55538 | −0.297057 | ||||||||
\(75\) | −8.73912 | −1.00911 | ||||||||
\(76\) | −0.645843 | −0.0740833 | ||||||||
\(77\) | −0.0977889 | −0.0111441 | ||||||||
\(78\) | −10.3014 | −1.16641 | ||||||||
\(79\) | −12.1896 | −1.37144 | −0.685718 | − | 0.727867i | \(-0.740512\pi\) | ||||
−0.685718 | + | 0.727867i | \(0.740512\pi\) | |||||||
\(80\) | −2.33045 | −0.260552 | ||||||||
\(81\) | −1.63603 | −0.181781 | ||||||||
\(82\) | −1.32395 | −0.146206 | ||||||||
\(83\) | −6.51564 | −0.715185 | −0.357592 | − | 0.933878i | \(-0.616402\pi\) | ||||
−0.357592 | + | 0.933878i | \(0.616402\pi\) | |||||||
\(84\) | −0.0865059 | −0.00943857 | ||||||||
\(85\) | 0.473420 | 0.0513496 | ||||||||
\(86\) | −5.09639 | −0.549558 | ||||||||
\(87\) | −12.2176 | −1.30986 | ||||||||
\(88\) | −7.74118 | −0.825213 | ||||||||
\(89\) | −0.0481816 | −0.00510724 | −0.00255362 | − | 0.999997i | \(-0.500813\pi\) | ||||
−0.00255362 | + | 0.999997i | \(0.500813\pi\) | |||||||
\(90\) | −6.78843 | −0.715563 | ||||||||
\(91\) | 0.132652 | 0.0139057 | ||||||||
\(92\) | −5.94623 | −0.619937 | ||||||||
\(93\) | −8.34565 | −0.865404 | ||||||||
\(94\) | −6.63808 | −0.684665 | ||||||||
\(95\) | 1.07820 | 0.110621 | ||||||||
\(96\) | −11.7214 | −1.19631 | ||||||||
\(97\) | −0.0462142 | −0.00469234 | −0.00234617 | − | 0.999997i | \(-0.500747\pi\) | ||||
−0.00234617 | + | 0.999997i | \(0.500747\pi\) | |||||||
\(98\) | 7.63337 | 0.771086 | ||||||||
\(99\) | −11.6186 | −1.16772 | ||||||||
\(100\) | 2.56868 | 0.256868 | ||||||||
\(101\) | −15.5165 | −1.54395 | −0.771973 | − | 0.635656i | \(-0.780730\pi\) | ||||
−0.771973 | + | 0.635656i | \(0.780730\pi\) | |||||||
\(102\) | −1.05231 | −0.104194 | ||||||||
\(103\) | −12.1548 | −1.19765 | −0.598824 | − | 0.800881i | \(-0.704365\pi\) | ||||
−0.598824 | + | 0.800881i | \(0.704365\pi\) | |||||||
\(104\) | 10.5010 | 1.02971 | ||||||||
\(105\) | 0.144417 | 0.0140936 | ||||||||
\(106\) | −1.99824 | −0.194086 | ||||||||
\(107\) | 15.4919 | 1.49765 | 0.748827 | − | 0.662765i | \(-0.230617\pi\) | ||||
0.748827 | + | 0.662765i | \(0.230617\pi\) | |||||||
\(108\) | −3.57591 | −0.344092 | ||||||||
\(109\) | −9.41409 | −0.901707 | −0.450853 | − | 0.892598i | \(-0.648880\pi\) | ||||
−0.450853 | + | 0.892598i | \(0.648880\pi\) | |||||||
\(110\) | 3.72639 | 0.355297 | ||||||||
\(111\) | 6.45906 | 0.613067 | ||||||||
\(112\) | −0.0667041 | −0.00630295 | ||||||||
\(113\) | 14.1869 | 1.33459 | 0.667294 | − | 0.744794i | \(-0.267452\pi\) | ||||
0.667294 | + | 0.744794i | \(0.267452\pi\) | |||||||
\(114\) | −2.39660 | −0.224462 | ||||||||
\(115\) | 9.92689 | 0.925687 | ||||||||
\(116\) | 3.59111 | 0.333426 | ||||||||
\(117\) | 15.7608 | 1.45709 | ||||||||
\(118\) | −6.25105 | −0.575456 | ||||||||
\(119\) | 0.0135506 | 0.00124218 | ||||||||
\(120\) | 11.4323 | 1.04363 | ||||||||
\(121\) | −4.62215 | −0.420196 | ||||||||
\(122\) | 15.4796 | 1.40146 | ||||||||
\(123\) | 3.34646 | 0.301740 | ||||||||
\(124\) | 2.45303 | 0.220289 | ||||||||
\(125\) | −11.0524 | −0.988554 | ||||||||
\(126\) | −0.194304 | −0.0173100 | ||||||||
\(127\) | −18.0392 | −1.60072 | −0.800359 | − | 0.599521i | \(-0.795358\pi\) | ||||
−0.800359 | + | 0.599521i | \(0.795358\pi\) | |||||||
\(128\) | −0.312593 | −0.0276295 | ||||||||
\(129\) | 12.8818 | 1.13418 | ||||||||
\(130\) | −5.05490 | −0.443344 | ||||||||
\(131\) | 8.94960 | 0.781930 | 0.390965 | − | 0.920406i | \(-0.372141\pi\) | ||||
0.390965 | + | 0.920406i | \(0.372141\pi\) | |||||||
\(132\) | 5.64197 | 0.491070 | ||||||||
\(133\) | 0.0308611 | 0.00267600 | ||||||||
\(134\) | 5.91218 | 0.510735 | ||||||||
\(135\) | 5.96979 | 0.513797 | ||||||||
\(136\) | 1.07270 | 0.0919829 | ||||||||
\(137\) | 11.2254 | 0.959049 | 0.479524 | − | 0.877529i | \(-0.340809\pi\) | ||||
0.479524 | + | 0.877529i | \(0.340809\pi\) | |||||||
\(138\) | −22.0653 | −1.87832 | ||||||||
\(139\) | −6.64598 | −0.563705 | −0.281852 | − | 0.959458i | \(-0.590949\pi\) | ||||
−0.281852 | + | 0.959458i | \(0.590949\pi\) | |||||||
\(140\) | −0.0424483 | −0.00358754 | ||||||||
\(141\) | 16.7786 | 1.41302 | ||||||||
\(142\) | 10.1050 | 0.847993 | ||||||||
\(143\) | −8.65164 | −0.723486 | ||||||||
\(144\) | −7.92535 | −0.660446 | ||||||||
\(145\) | −5.99515 | −0.497870 | ||||||||
\(146\) | 1.72155 | 0.142477 | ||||||||
\(147\) | −19.2943 | −1.59137 | ||||||||
\(148\) | −1.89851 | −0.156056 | ||||||||
\(149\) | 5.65306 | 0.463116 | 0.231558 | − | 0.972821i | \(-0.425618\pi\) | ||||
0.231558 | + | 0.972821i | \(0.425618\pi\) | |||||||
\(150\) | 9.53188 | 0.778275 | ||||||||
\(151\) | 1.22246 | 0.0994824 | 0.0497412 | − | 0.998762i | \(-0.484160\pi\) | ||||
0.0497412 | + | 0.998762i | \(0.484160\pi\) | |||||||
\(152\) | 2.44303 | 0.198156 | ||||||||
\(153\) | 1.61000 | 0.130160 | ||||||||
\(154\) | 0.106660 | 0.00859489 | ||||||||
\(155\) | −4.09520 | −0.328934 | ||||||||
\(156\) | −7.65341 | −0.612763 | ||||||||
\(157\) | 2.61794 | 0.208934 | 0.104467 | − | 0.994528i | \(-0.466686\pi\) | ||||
0.104467 | + | 0.994528i | \(0.466686\pi\) | |||||||
\(158\) | 13.2954 | 1.05772 | ||||||||
\(159\) | 5.05082 | 0.400556 | ||||||||
\(160\) | −5.75169 | −0.454711 | ||||||||
\(161\) | 0.284136 | 0.0223930 | ||||||||
\(162\) | 1.78444 | 0.140199 | ||||||||
\(163\) | 17.7600 | 1.39107 | 0.695535 | − | 0.718492i | \(-0.255167\pi\) | ||||
0.695535 | + | 0.718492i | \(0.255167\pi\) | |||||||
\(164\) | −0.983624 | −0.0768081 | ||||||||
\(165\) | −9.41894 | −0.733264 | ||||||||
\(166\) | 7.10670 | 0.551587 | ||||||||
\(167\) | 12.0908 | 0.935610 | 0.467805 | − | 0.883832i | \(-0.345045\pi\) | ||||
0.467805 | + | 0.883832i | \(0.345045\pi\) | |||||||
\(168\) | 0.327226 | 0.0252460 | ||||||||
\(169\) | −1.26393 | −0.0972253 | ||||||||
\(170\) | −0.516366 | −0.0396034 | ||||||||
\(171\) | 3.66671 | 0.280401 | ||||||||
\(172\) | −3.78634 | −0.288706 | ||||||||
\(173\) | 2.62524 | 0.199593 | 0.0997966 | − | 0.995008i | \(-0.468181\pi\) | ||||
0.0997966 | + | 0.995008i | \(0.468181\pi\) | |||||||
\(174\) | 13.3259 | 1.01023 | ||||||||
\(175\) | −0.122743 | −0.00927846 | ||||||||
\(176\) | 4.35048 | 0.327930 | ||||||||
\(177\) | 15.8004 | 1.18763 | ||||||||
\(178\) | 0.0525524 | 0.00393897 | ||||||||
\(179\) | 10.4691 | 0.782501 | 0.391250 | − | 0.920284i | \(-0.372043\pi\) | ||||
0.391250 | + | 0.920284i | \(0.372043\pi\) | |||||||
\(180\) | −5.04344 | −0.375916 | ||||||||
\(181\) | 6.23267 | 0.463271 | 0.231635 | − | 0.972803i | \(-0.425592\pi\) | ||||
0.231635 | + | 0.972803i | \(0.425592\pi\) | |||||||
\(182\) | −0.144685 | −0.0107248 | ||||||||
\(183\) | −39.1267 | −2.89233 | ||||||||
\(184\) | 22.4928 | 1.65819 | ||||||||
\(185\) | 3.16945 | 0.233023 | ||||||||
\(186\) | 9.10272 | 0.667444 | ||||||||
\(187\) | −0.883778 | −0.0646283 | ||||||||
\(188\) | −4.93173 | −0.359684 | ||||||||
\(189\) | 0.170872 | 0.0124291 | ||||||||
\(190\) | −1.17601 | −0.0853165 | ||||||||
\(191\) | 19.6696 | 1.42324 | 0.711622 | − | 0.702563i | \(-0.247961\pi\) | ||||
0.711622 | + | 0.702563i | \(0.247961\pi\) | |||||||
\(192\) | 22.2832 | 1.60815 | ||||||||
\(193\) | 16.8057 | 1.20970 | 0.604851 | − | 0.796339i | \(-0.293233\pi\) | ||||
0.604851 | + | 0.796339i | \(0.293233\pi\) | |||||||
\(194\) | 0.0504065 | 0.00361897 | ||||||||
\(195\) | 12.7769 | 0.914975 | ||||||||
\(196\) | 5.67118 | 0.405084 | ||||||||
\(197\) | −23.2824 | −1.65880 | −0.829402 | − | 0.558652i | \(-0.811319\pi\) | ||||
−0.829402 | + | 0.558652i | \(0.811319\pi\) | |||||||
\(198\) | 12.6726 | 0.900604 | ||||||||
\(199\) | 7.74945 | 0.549344 | 0.274672 | − | 0.961538i | \(-0.411431\pi\) | ||||
0.274672 | + | 0.961538i | \(0.411431\pi\) | |||||||
\(200\) | −9.71657 | −0.687065 | ||||||||
\(201\) | −14.9438 | −1.05406 | ||||||||
\(202\) | 16.9240 | 1.19077 | ||||||||
\(203\) | −0.171598 | −0.0120438 | ||||||||
\(204\) | −0.781807 | −0.0547375 | ||||||||
\(205\) | 1.64211 | 0.114690 | ||||||||
\(206\) | 13.2574 | 0.923688 | ||||||||
\(207\) | 33.7591 | 2.34642 | ||||||||
\(208\) | −5.90149 | −0.409195 | ||||||||
\(209\) | −2.01278 | −0.139227 | ||||||||
\(210\) | −0.157517 | −0.0108697 | ||||||||
\(211\) | 11.9992 | 0.826059 | 0.413030 | − | 0.910718i | \(-0.364471\pi\) | ||||
0.413030 | + | 0.910718i | \(0.364471\pi\) | |||||||
\(212\) | −1.48459 | −0.101962 | ||||||||
\(213\) | −25.5417 | −1.75009 | ||||||||
\(214\) | −16.8972 | −1.15507 | ||||||||
\(215\) | 6.32108 | 0.431094 | ||||||||
\(216\) | 13.5266 | 0.920369 | ||||||||
\(217\) | −0.117216 | −0.00795715 | ||||||||
\(218\) | 10.2681 | 0.695443 | ||||||||
\(219\) | −4.35145 | −0.294044 | ||||||||
\(220\) | 2.76851 | 0.186653 | ||||||||
\(221\) | 1.19886 | 0.0806439 | ||||||||
\(222\) | −7.04499 | −0.472829 | ||||||||
\(223\) | 11.0373 | 0.739115 | 0.369557 | − | 0.929208i | \(-0.379509\pi\) | ||||
0.369557 | + | 0.929208i | \(0.379509\pi\) | |||||||
\(224\) | −0.164630 | −0.0109998 | ||||||||
\(225\) | −14.5835 | −0.972231 | ||||||||
\(226\) | −15.4738 | −1.02930 | ||||||||
\(227\) | 13.7433 | 0.912176 | 0.456088 | − | 0.889935i | \(-0.349250\pi\) | ||||
0.456088 | + | 0.889935i | \(0.349250\pi\) | |||||||
\(228\) | −1.78054 | −0.117919 | ||||||||
\(229\) | 6.07797 | 0.401643 | 0.200822 | − | 0.979628i | \(-0.435639\pi\) | ||||
0.200822 | + | 0.979628i | \(0.435639\pi\) | |||||||
\(230\) | −10.8274 | −0.713938 | ||||||||
\(231\) | −0.269597 | −0.0177382 | ||||||||
\(232\) | −13.5841 | −0.891839 | ||||||||
\(233\) | −1.92732 | −0.126263 | −0.0631314 | − | 0.998005i | \(-0.520109\pi\) | ||||
−0.0631314 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(234\) | −17.1906 | −1.12378 | ||||||||
\(235\) | 8.23325 | 0.537078 | ||||||||
\(236\) | −4.64419 | −0.302311 | ||||||||
\(237\) | −33.6058 | −2.18293 | ||||||||
\(238\) | −0.0147798 | −0.000958035 0 | ||||||||
\(239\) | −12.0785 | −0.781290 | −0.390645 | − | 0.920541i | \(-0.627748\pi\) | ||||
−0.390645 | + | 0.920541i | \(0.627748\pi\) | |||||||
\(240\) | −6.42488 | −0.414724 | ||||||||
\(241\) | 2.68122 | 0.172712 | 0.0863562 | − | 0.996264i | \(-0.472478\pi\) | ||||
0.0863562 | + | 0.996264i | \(0.472478\pi\) | |||||||
\(242\) | 5.04145 | 0.324077 | ||||||||
\(243\) | −17.7490 | −1.13860 | ||||||||
\(244\) | 11.5005 | 0.736244 | ||||||||
\(245\) | −9.46771 | −0.604870 | ||||||||
\(246\) | −3.65004 | −0.232718 | ||||||||
\(247\) | 2.73036 | 0.173729 | ||||||||
\(248\) | −9.27909 | −0.589223 | ||||||||
\(249\) | −17.9631 | −1.13837 | ||||||||
\(250\) | 12.0550 | 0.762424 | ||||||||
\(251\) | −15.8710 | −1.00177 | −0.500884 | − | 0.865515i | \(-0.666992\pi\) | ||||
−0.500884 | + | 0.865515i | \(0.666992\pi\) | |||||||
\(252\) | −0.144357 | −0.00909366 | ||||||||
\(253\) | −18.5315 | −1.16506 | ||||||||
\(254\) | 19.6756 | 1.23456 | ||||||||
\(255\) | 1.30518 | 0.0817337 | ||||||||
\(256\) | −15.8243 | −0.989020 | ||||||||
\(257\) | 18.8695 | 1.17705 | 0.588524 | − | 0.808480i | \(-0.299709\pi\) | ||||
0.588524 | + | 0.808480i | \(0.299709\pi\) | |||||||
\(258\) | −14.0504 | −0.874738 | ||||||||
\(259\) | 0.0907186 | 0.00563698 | ||||||||
\(260\) | −3.75552 | −0.232907 | ||||||||
\(261\) | −20.3882 | −1.26200 | ||||||||
\(262\) | −9.76146 | −0.603065 | ||||||||
\(263\) | −24.2982 | −1.49829 | −0.749145 | − | 0.662406i | \(-0.769535\pi\) | ||||
−0.749145 | + | 0.662406i | \(0.769535\pi\) | |||||||
\(264\) | −21.3419 | −1.31350 | ||||||||
\(265\) | 2.47843 | 0.152249 | ||||||||
\(266\) | −0.0336606 | −0.00206387 | ||||||||
\(267\) | −0.132833 | −0.00812926 | ||||||||
\(268\) | 4.39243 | 0.268310 | ||||||||
\(269\) | 11.0375 | 0.672970 | 0.336485 | − | 0.941689i | \(-0.390762\pi\) | ||||
0.336485 | + | 0.941689i | \(0.390762\pi\) | |||||||
\(270\) | −6.51133 | −0.396267 | ||||||||
\(271\) | 26.5146 | 1.61065 | 0.805325 | − | 0.592834i | \(-0.201991\pi\) | ||||
0.805325 | + | 0.592834i | \(0.201991\pi\) | |||||||
\(272\) | −0.602846 | −0.0365529 | ||||||||
\(273\) | 0.365712 | 0.0221339 | ||||||||
\(274\) | −12.2437 | −0.739668 | ||||||||
\(275\) | 8.00534 | 0.482740 | ||||||||
\(276\) | −16.3933 | −0.986761 | ||||||||
\(277\) | 25.0782 | 1.50680 | 0.753401 | − | 0.657562i | \(-0.228412\pi\) | ||||
0.753401 | + | 0.657562i | \(0.228412\pi\) | |||||||
\(278\) | 7.24887 | 0.434758 | ||||||||
\(279\) | −13.9269 | −0.833780 | ||||||||
\(280\) | 0.160569 | 0.00959586 | ||||||||
\(281\) | −9.33195 | −0.556697 | −0.278349 | − | 0.960480i | \(-0.589787\pi\) | ||||
−0.278349 | + | 0.960480i | \(0.589787\pi\) | |||||||
\(282\) | −18.3007 | −1.08979 | ||||||||
\(283\) | −10.6182 | −0.631185 | −0.315593 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315593 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(284\) | 7.50747 | 0.445486 | ||||||||
\(285\) | 2.97251 | 0.176076 | ||||||||
\(286\) | 9.43647 | 0.557990 | ||||||||
\(287\) | 0.0470017 | 0.00277442 | ||||||||
\(288\) | −19.5602 | −1.15260 | ||||||||
\(289\) | −16.8775 | −0.992796 | ||||||||
\(290\) | 6.53900 | 0.383983 | ||||||||
\(291\) | −0.127409 | −0.00746885 | ||||||||
\(292\) | 1.27902 | 0.0748490 | ||||||||
\(293\) | −31.1009 | −1.81693 | −0.908467 | − | 0.417956i | \(-0.862747\pi\) | ||||
−0.908467 | + | 0.417956i | \(0.862747\pi\) | |||||||
\(294\) | 21.0446 | 1.22735 | ||||||||
\(295\) | 7.75322 | 0.451410 | ||||||||
\(296\) | 7.18149 | 0.417415 | ||||||||
\(297\) | −11.1444 | −0.646662 | ||||||||
\(298\) | −6.16587 | −0.357179 | ||||||||
\(299\) | 25.1382 | 1.45378 | ||||||||
\(300\) | 7.08167 | 0.408861 | ||||||||
\(301\) | 0.180927 | 0.0104285 | ||||||||
\(302\) | −1.33335 | −0.0767259 | ||||||||
\(303\) | −42.7777 | −2.45752 | ||||||||
\(304\) | −1.37296 | −0.0787448 | ||||||||
\(305\) | −19.1994 | −1.09936 | ||||||||
\(306\) | −1.75605 | −0.100386 | ||||||||
\(307\) | 14.6154 | 0.834148 | 0.417074 | − | 0.908873i | \(-0.363056\pi\) | ||||
0.417074 | + | 0.908873i | \(0.363056\pi\) | |||||||
\(308\) | 0.0792424 | 0.00451526 | ||||||||
\(309\) | −33.5099 | −1.90631 | ||||||||
\(310\) | 4.46669 | 0.253691 | ||||||||
\(311\) | 24.0649 | 1.36459 | 0.682297 | − | 0.731075i | \(-0.260981\pi\) | ||||
0.682297 | + | 0.731075i | \(0.260981\pi\) | |||||||
\(312\) | 28.9505 | 1.63900 | ||||||||
\(313\) | 8.99735 | 0.508560 | 0.254280 | − | 0.967131i | \(-0.418161\pi\) | ||||
0.254280 | + | 0.967131i | \(0.418161\pi\) | |||||||
\(314\) | −2.85543 | −0.161141 | ||||||||
\(315\) | 0.240996 | 0.0135786 | ||||||||
\(316\) | 9.87774 | 0.555666 | ||||||||
\(317\) | −22.1657 | −1.24495 | −0.622475 | − | 0.782640i | \(-0.713873\pi\) | ||||
−0.622475 | + | 0.782640i | \(0.713873\pi\) | |||||||
\(318\) | −5.50900 | −0.308930 | ||||||||
\(319\) | 11.1917 | 0.626617 | ||||||||
\(320\) | 10.9344 | 0.611249 | ||||||||
\(321\) | 42.7099 | 2.38383 | ||||||||
\(322\) | −0.309911 | −0.0172707 | ||||||||
\(323\) | 0.278911 | 0.0155190 | ||||||||
\(324\) | 1.32575 | 0.0736526 | ||||||||
\(325\) | −10.8594 | −0.602368 | ||||||||
\(326\) | −19.3711 | −1.07287 | ||||||||
\(327\) | −25.9540 | −1.43526 | ||||||||
\(328\) | 3.72076 | 0.205444 | ||||||||
\(329\) | 0.235659 | 0.0129923 | ||||||||
\(330\) | 10.2734 | 0.565531 | ||||||||
\(331\) | 32.2705 | 1.77375 | 0.886875 | − | 0.462010i | \(-0.152872\pi\) | ||||
0.886875 | + | 0.462010i | \(0.152872\pi\) | |||||||
\(332\) | 5.27990 | 0.289772 | ||||||||
\(333\) | 10.7786 | 0.590664 | ||||||||
\(334\) | −13.1876 | −0.721591 | ||||||||
\(335\) | −7.33292 | −0.400640 | ||||||||
\(336\) | −0.183898 | −0.0100325 | ||||||||
\(337\) | −14.4513 | −0.787211 | −0.393605 | − | 0.919279i | \(-0.628772\pi\) | ||||
−0.393605 | + | 0.919279i | \(0.628772\pi\) | |||||||
\(338\) | 1.37859 | 0.0749852 | ||||||||
\(339\) | 39.1121 | 2.12428 | ||||||||
\(340\) | −0.383632 | −0.0208054 | ||||||||
\(341\) | 7.64491 | 0.413995 | ||||||||
\(342\) | −3.99934 | −0.216259 | ||||||||
\(343\) | −0.542043 | −0.0292676 | ||||||||
\(344\) | 14.3226 | 0.772223 | ||||||||
\(345\) | 27.3677 | 1.47343 | ||||||||
\(346\) | −2.86339 | −0.153937 | ||||||||
\(347\) | −26.4572 | −1.42030 | −0.710148 | − | 0.704052i | \(-0.751372\pi\) | ||||
−0.710148 | + | 0.704052i | \(0.751372\pi\) | |||||||
\(348\) | 9.90042 | 0.530718 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | 0.133877 | 0.00715603 | ||||||||
\(351\) | 15.1175 | 0.806913 | ||||||||
\(352\) | 10.7372 | 0.572296 | ||||||||
\(353\) | 13.8482 | 0.737067 | 0.368534 | − | 0.929614i | \(-0.379860\pi\) | ||||
0.368534 | + | 0.929614i | \(0.379860\pi\) | |||||||
\(354\) | −17.2337 | −0.915960 | ||||||||
\(355\) | −12.5333 | −0.665198 | ||||||||
\(356\) | 0.0390436 | 0.00206931 | ||||||||
\(357\) | 0.0373580 | 0.00197720 | ||||||||
\(358\) | −11.4189 | −0.603505 | ||||||||
\(359\) | 25.4455 | 1.34296 | 0.671482 | − | 0.741021i | \(-0.265658\pi\) | ||||
0.671482 | + | 0.741021i | \(0.265658\pi\) | |||||||
\(360\) | 19.0778 | 1.00549 | ||||||||
\(361\) | −18.3648 | −0.966568 | ||||||||
\(362\) | −6.79807 | −0.357298 | ||||||||
\(363\) | −12.7429 | −0.668830 | ||||||||
\(364\) | −0.107493 | −0.00563419 | ||||||||
\(365\) | −2.13525 | −0.111764 | ||||||||
\(366\) | 42.6761 | 2.23071 | ||||||||
\(367\) | 27.6581 | 1.44374 | 0.721869 | − | 0.692029i | \(-0.243283\pi\) | ||||
0.721869 | + | 0.692029i | \(0.243283\pi\) | |||||||
\(368\) | −12.6408 | −0.658945 | ||||||||
\(369\) | 5.58443 | 0.290714 | ||||||||
\(370\) | −3.45697 | −0.179719 | ||||||||
\(371\) | 0.0709397 | 0.00368300 | ||||||||
\(372\) | 6.76283 | 0.350636 | ||||||||
\(373\) | −19.9861 | −1.03484 | −0.517419 | − | 0.855732i | \(-0.673107\pi\) | ||||
−0.517419 | + | 0.855732i | \(0.673107\pi\) | |||||||
\(374\) | 0.963950 | 0.0498447 | ||||||||
\(375\) | −30.4706 | −1.57349 | ||||||||
\(376\) | 18.6553 | 0.962072 | ||||||||
\(377\) | −15.1817 | −0.781899 | ||||||||
\(378\) | −0.186373 | −0.00958598 | ||||||||
\(379\) | 0.204570 | 0.0105080 | 0.00525402 | − | 0.999986i | \(-0.498328\pi\) | ||||
0.00525402 | + | 0.999986i | \(0.498328\pi\) | |||||||
\(380\) | −0.873709 | −0.0448203 | ||||||||
\(381\) | −49.7326 | −2.54788 | ||||||||
\(382\) | −21.4539 | −1.09768 | ||||||||
\(383\) | 35.0565 | 1.79131 | 0.895653 | − | 0.444754i | \(-0.146709\pi\) | ||||
0.895653 | + | 0.444754i | \(0.146709\pi\) | |||||||
\(384\) | −0.861794 | −0.0439783 | ||||||||
\(385\) | −0.132291 | −0.00674216 | ||||||||
\(386\) | −18.3302 | −0.932984 | ||||||||
\(387\) | 21.4966 | 1.09273 | ||||||||
\(388\) | 0.0374493 | 0.00190120 | ||||||||
\(389\) | 9.50268 | 0.481805 | 0.240902 | − | 0.970549i | \(-0.422557\pi\) | ||||
0.240902 | + | 0.970549i | \(0.422557\pi\) | |||||||
\(390\) | −13.9360 | −0.705676 | ||||||||
\(391\) | 2.56791 | 0.129865 | ||||||||
\(392\) | −21.4524 | −1.08351 | ||||||||
\(393\) | 24.6734 | 1.24461 | ||||||||
\(394\) | 25.3945 | 1.27936 | ||||||||
\(395\) | −16.4903 | −0.829718 | ||||||||
\(396\) | 9.41507 | 0.473125 | ||||||||
\(397\) | 16.3138 | 0.818767 | 0.409383 | − | 0.912362i | \(-0.365744\pi\) | ||||
0.409383 | + | 0.912362i | \(0.365744\pi\) | |||||||
\(398\) | −8.45243 | −0.423682 | ||||||||
\(399\) | 0.0850817 | 0.00425941 | ||||||||
\(400\) | 5.46063 | 0.273031 | ||||||||
\(401\) | 8.56261 | 0.427596 | 0.213798 | − | 0.976878i | \(-0.431417\pi\) | ||||
0.213798 | + | 0.976878i | \(0.431417\pi\) | |||||||
\(402\) | 16.2994 | 0.812943 | ||||||||
\(403\) | −10.3704 | −0.516588 | ||||||||
\(404\) | 12.5736 | 0.625562 | ||||||||
\(405\) | −2.21326 | −0.109978 | ||||||||
\(406\) | 0.187165 | 0.00928882 | ||||||||
\(407\) | −5.91672 | −0.293281 | ||||||||
\(408\) | 2.95734 | 0.146410 | ||||||||
\(409\) | 18.7315 | 0.926213 | 0.463107 | − | 0.886303i | \(-0.346735\pi\) | ||||
0.463107 | + | 0.886303i | \(0.346735\pi\) | |||||||
\(410\) | −1.79107 | −0.0884545 | ||||||||
\(411\) | 30.9475 | 1.52653 | ||||||||
\(412\) | 9.84954 | 0.485252 | ||||||||
\(413\) | 0.221919 | 0.0109199 | ||||||||
\(414\) | −36.8216 | −1.80968 | ||||||||
\(415\) | −8.81449 | −0.432686 | ||||||||
\(416\) | −14.5652 | −0.714118 | ||||||||
\(417\) | −18.3225 | −0.897256 | ||||||||
\(418\) | 2.19537 | 0.107379 | ||||||||
\(419\) | 25.6171 | 1.25148 | 0.625739 | − | 0.780032i | \(-0.284797\pi\) | ||||
0.625739 | + | 0.780032i | \(0.284797\pi\) | |||||||
\(420\) | −0.117027 | −0.00571033 | ||||||||
\(421\) | −29.1083 | −1.41865 | −0.709326 | − | 0.704881i | \(-0.751000\pi\) | ||||
−0.709326 | + | 0.704881i | \(0.751000\pi\) | |||||||
\(422\) | −13.0877 | −0.637100 | ||||||||
\(423\) | 27.9995 | 1.36138 | ||||||||
\(424\) | 5.61574 | 0.272724 | ||||||||
\(425\) | −1.10930 | −0.0538089 | ||||||||
\(426\) | 27.8587 | 1.34976 | ||||||||
\(427\) | −0.549542 | −0.0265942 | ||||||||
\(428\) | −12.5537 | −0.606806 | ||||||||
\(429\) | −23.8519 | −1.15158 | ||||||||
\(430\) | −6.89450 | −0.332482 | ||||||||
\(431\) | −22.8305 | −1.09970 | −0.549852 | − | 0.835262i | \(-0.685316\pi\) | ||||
−0.549852 | + | 0.835262i | \(0.685316\pi\) | |||||||
\(432\) | −7.60184 | −0.365744 | ||||||||
\(433\) | −36.5699 | −1.75744 | −0.878719 | − | 0.477340i | \(-0.841601\pi\) | ||||
−0.878719 | + | 0.477340i | \(0.841601\pi\) | |||||||
\(434\) | 0.127849 | 0.00613697 | ||||||||
\(435\) | −16.5282 | −0.792466 | ||||||||
\(436\) | 7.62863 | 0.365345 | ||||||||
\(437\) | 5.84833 | 0.279764 | ||||||||
\(438\) | 4.74619 | 0.226782 | ||||||||
\(439\) | −30.7581 | −1.46801 | −0.734003 | − | 0.679146i | \(-0.762350\pi\) | ||||
−0.734003 | + | 0.679146i | \(0.762350\pi\) | |||||||
\(440\) | −10.4724 | −0.499253 | ||||||||
\(441\) | −32.1976 | −1.53322 | ||||||||
\(442\) | −1.30761 | −0.0621967 | ||||||||
\(443\) | −25.0439 | −1.18987 | −0.594936 | − | 0.803773i | \(-0.702823\pi\) | ||||
−0.594936 | + | 0.803773i | \(0.702823\pi\) | |||||||
\(444\) | −5.23404 | −0.248397 | ||||||||
\(445\) | −0.0651811 | −0.00308988 | ||||||||
\(446\) | −12.0386 | −0.570044 | ||||||||
\(447\) | 15.5851 | 0.737148 | ||||||||
\(448\) | 0.312972 | 0.0147865 | ||||||||
\(449\) | 14.4519 | 0.682025 | 0.341012 | − | 0.940059i | \(-0.389230\pi\) | ||||
0.341012 | + | 0.940059i | \(0.389230\pi\) | |||||||
\(450\) | 15.9064 | 0.749835 | ||||||||
\(451\) | −3.06548 | −0.144348 | ||||||||
\(452\) | −11.4962 | −0.540736 | ||||||||
\(453\) | 3.37023 | 0.158347 | ||||||||
\(454\) | −14.9900 | −0.703517 | ||||||||
\(455\) | 0.179454 | 0.00841295 | ||||||||
\(456\) | 6.73525 | 0.315407 | ||||||||
\(457\) | 6.86842 | 0.321291 | 0.160646 | − | 0.987012i | \(-0.448642\pi\) | ||||
0.160646 | + | 0.987012i | \(0.448642\pi\) | |||||||
\(458\) | −6.62933 | −0.309768 | ||||||||
\(459\) | 1.54428 | 0.0720806 | ||||||||
\(460\) | −8.04418 | −0.375062 | ||||||||
\(461\) | 16.9413 | 0.789037 | 0.394519 | − | 0.918888i | \(-0.370911\pi\) | ||||
0.394519 | + | 0.918888i | \(0.370911\pi\) | |||||||
\(462\) | 0.294053 | 0.0136806 | ||||||||
\(463\) | 19.8411 | 0.922094 | 0.461047 | − | 0.887376i | \(-0.347474\pi\) | ||||
0.461047 | + | 0.887376i | \(0.347474\pi\) | |||||||
\(464\) | 7.63414 | 0.354406 | ||||||||
\(465\) | −11.2902 | −0.523569 | ||||||||
\(466\) | 2.10215 | 0.0973804 | ||||||||
\(467\) | −14.3809 | −0.665469 | −0.332735 | − | 0.943021i | \(-0.607971\pi\) | ||||
−0.332735 | + | 0.943021i | \(0.607971\pi\) | |||||||
\(468\) | −12.7717 | −0.590371 | ||||||||
\(469\) | −0.209889 | −0.00969176 | ||||||||
\(470\) | −8.98013 | −0.414222 | ||||||||
\(471\) | 7.21747 | 0.332563 | ||||||||
\(472\) | 17.5676 | 0.808614 | ||||||||
\(473\) | −11.8002 | −0.542573 | ||||||||
\(474\) | 36.6543 | 1.68359 | ||||||||
\(475\) | −2.52639 | −0.115919 | ||||||||
\(476\) | −0.0109806 | −0.000503296 0 | ||||||||
\(477\) | 8.42859 | 0.385919 | ||||||||
\(478\) | 13.1741 | 0.602572 | ||||||||
\(479\) | −15.3411 | −0.700951 | −0.350476 | − | 0.936572i | \(-0.613980\pi\) | ||||
−0.350476 | + | 0.936572i | \(0.613980\pi\) | |||||||
\(480\) | −15.8570 | −0.723769 | ||||||||
\(481\) | 8.02612 | 0.365959 | ||||||||
\(482\) | −2.92444 | −0.133205 | ||||||||
\(483\) | 0.783341 | 0.0356432 | ||||||||
\(484\) | 3.74552 | 0.170251 | ||||||||
\(485\) | −0.0625195 | −0.00283886 | ||||||||
\(486\) | 19.3590 | 0.878144 | ||||||||
\(487\) | −37.8081 | −1.71325 | −0.856625 | − | 0.515939i | \(-0.827443\pi\) | ||||
−0.856625 | + | 0.515939i | \(0.827443\pi\) | |||||||
\(488\) | −43.5029 | −1.96929 | ||||||||
\(489\) | 48.9630 | 2.21418 | ||||||||
\(490\) | 10.3266 | 0.466507 | ||||||||
\(491\) | 5.26778 | 0.237731 | 0.118866 | − | 0.992910i | \(-0.462074\pi\) | ||||
0.118866 | + | 0.992910i | \(0.462074\pi\) | |||||||
\(492\) | −2.71178 | −0.122256 | ||||||||
\(493\) | −1.55084 | −0.0698462 | ||||||||
\(494\) | −2.97804 | −0.133989 | ||||||||
\(495\) | −15.7179 | −0.706468 | ||||||||
\(496\) | 5.21477 | 0.234150 | ||||||||
\(497\) | −0.358738 | −0.0160916 | ||||||||
\(498\) | 19.5927 | 0.877968 | ||||||||
\(499\) | 26.9094 | 1.20463 | 0.602316 | − | 0.798258i | \(-0.294245\pi\) | ||||
0.602316 | + | 0.798258i | \(0.294245\pi\) | |||||||
\(500\) | 8.95620 | 0.400534 | ||||||||
\(501\) | 33.3333 | 1.48922 | ||||||||
\(502\) | 17.3107 | 0.772614 | ||||||||
\(503\) | 31.1411 | 1.38851 | 0.694257 | − | 0.719727i | \(-0.255733\pi\) | ||||
0.694257 | + | 0.719727i | \(0.255733\pi\) | |||||||
\(504\) | 0.546061 | 0.0243235 | ||||||||
\(505\) | −20.9910 | −0.934086 | ||||||||
\(506\) | 20.2126 | 0.898558 | ||||||||
\(507\) | −3.48456 | −0.154755 | ||||||||
\(508\) | 14.6179 | 0.648564 | ||||||||
\(509\) | −25.1512 | −1.11481 | −0.557404 | − | 0.830242i | \(-0.688202\pi\) | ||||
−0.557404 | + | 0.830242i | \(0.688202\pi\) | |||||||
\(510\) | −1.42358 | −0.0630373 | ||||||||
\(511\) | −0.0611169 | −0.00270365 | ||||||||
\(512\) | 17.8850 | 0.790413 | ||||||||
\(513\) | 3.51704 | 0.155281 | ||||||||
\(514\) | −20.5813 | −0.907800 | ||||||||
\(515\) | −16.4433 | −0.724576 | ||||||||
\(516\) | −10.4387 | −0.459537 | ||||||||
\(517\) | −15.3698 | −0.675963 | ||||||||
\(518\) | −0.0989481 | −0.00434753 | ||||||||
\(519\) | 7.23759 | 0.317695 | ||||||||
\(520\) | 14.2060 | 0.622974 | ||||||||
\(521\) | −1.30073 | −0.0569862 | −0.0284931 | − | 0.999594i | \(-0.509071\pi\) | ||||
−0.0284931 | + | 0.999594i | \(0.509071\pi\) | |||||||
\(522\) | 22.2377 | 0.973317 | ||||||||
\(523\) | −7.02745 | −0.307289 | −0.153644 | − | 0.988126i | \(-0.549101\pi\) | ||||
−0.153644 | + | 0.988126i | \(0.549101\pi\) | |||||||
\(524\) | −7.25224 | −0.316815 | ||||||||
\(525\) | −0.338392 | −0.0147686 | ||||||||
\(526\) | 26.5024 | 1.15556 | ||||||||
\(527\) | −1.05935 | −0.0461462 | ||||||||
\(528\) | 11.9940 | 0.521970 | ||||||||
\(529\) | 30.8451 | 1.34109 | ||||||||
\(530\) | −2.70326 | −0.117422 | ||||||||
\(531\) | 26.3670 | 1.14423 | ||||||||
\(532\) | −0.0250080 | −0.00108424 | ||||||||
\(533\) | 4.15836 | 0.180119 | ||||||||
\(534\) | 0.144883 | 0.00626970 | ||||||||
\(535\) | 20.9577 | 0.906080 | ||||||||
\(536\) | −16.6153 | −0.717670 | ||||||||
\(537\) | 28.8627 | 1.24552 | ||||||||
\(538\) | −12.0388 | −0.519029 | ||||||||
\(539\) | 17.6743 | 0.761286 | ||||||||
\(540\) | −4.83757 | −0.208176 | ||||||||
\(541\) | −28.5841 | −1.22893 | −0.614464 | − | 0.788945i | \(-0.710627\pi\) | ||||
−0.614464 | + | 0.788945i | \(0.710627\pi\) | |||||||
\(542\) | −28.9199 | −1.24222 | ||||||||
\(543\) | 17.1830 | 0.737394 | ||||||||
\(544\) | −1.48786 | −0.0637914 | ||||||||
\(545\) | −12.7356 | −0.545532 | ||||||||
\(546\) | −0.398887 | −0.0170708 | ||||||||
\(547\) | 4.04299 | 0.172866 | 0.0864330 | − | 0.996258i | \(-0.472453\pi\) | ||||
0.0864330 | + | 0.996258i | \(0.472453\pi\) | |||||||
\(548\) | −9.09639 | −0.388579 | ||||||||
\(549\) | −65.2930 | −2.78664 | ||||||||
\(550\) | −8.73154 | −0.372314 | ||||||||
\(551\) | −3.53199 | −0.150468 | ||||||||
\(552\) | 62.0110 | 2.63936 | ||||||||
\(553\) | −0.472000 | −0.0200715 | ||||||||
\(554\) | −27.3531 | −1.16212 | ||||||||
\(555\) | 8.73794 | 0.370905 | ||||||||
\(556\) | 5.38552 | 0.228397 | ||||||||
\(557\) | −19.3600 | −0.820308 | −0.410154 | − | 0.912016i | \(-0.634525\pi\) | ||||
−0.410154 | + | 0.912016i | \(0.634525\pi\) | |||||||
\(558\) | 15.1902 | 0.643054 | ||||||||
\(559\) | 16.0071 | 0.677029 | ||||||||
\(560\) | −0.0902387 | −0.00381328 | ||||||||
\(561\) | −2.43651 | −0.102870 | ||||||||
\(562\) | 10.1785 | 0.429354 | ||||||||
\(563\) | 26.2875 | 1.10789 | 0.553944 | − | 0.832554i | \(-0.313122\pi\) | ||||
0.553944 | + | 0.832554i | \(0.313122\pi\) | |||||||
\(564\) | −13.5964 | −0.572513 | ||||||||
\(565\) | 19.1923 | 0.807425 | ||||||||
\(566\) | 11.5814 | 0.486803 | ||||||||
\(567\) | −0.0633497 | −0.00266044 | ||||||||
\(568\) | −28.3985 | −1.19158 | ||||||||
\(569\) | 31.9316 | 1.33864 | 0.669322 | − | 0.742973i | \(-0.266585\pi\) | ||||
0.669322 | + | 0.742973i | \(0.266585\pi\) | |||||||
\(570\) | −3.24216 | −0.135799 | ||||||||
\(571\) | 3.81070 | 0.159473 | 0.0797363 | − | 0.996816i | \(-0.474592\pi\) | ||||
0.0797363 | + | 0.996816i | \(0.474592\pi\) | |||||||
\(572\) | 7.01079 | 0.293136 | ||||||||
\(573\) | 54.2277 | 2.26539 | ||||||||
\(574\) | −0.0512654 | −0.00213978 | ||||||||
\(575\) | −23.2603 | −0.970023 | ||||||||
\(576\) | 37.1853 | 1.54939 | ||||||||
\(577\) | −22.8247 | −0.950203 | −0.475102 | − | 0.879931i | \(-0.657589\pi\) | ||||
−0.475102 | + | 0.879931i | \(0.657589\pi\) | |||||||
\(578\) | 18.4086 | 0.765696 | ||||||||
\(579\) | 46.3321 | 1.92550 | ||||||||
\(580\) | 4.85812 | 0.201723 | ||||||||
\(581\) | −0.252296 | −0.0104670 | ||||||||
\(582\) | 0.138967 | 0.00576036 | ||||||||
\(583\) | −4.62673 | −0.191619 | ||||||||
\(584\) | −4.83815 | −0.200204 | ||||||||
\(585\) | 21.3216 | 0.881539 | ||||||||
\(586\) | 33.9222 | 1.40131 | ||||||||
\(587\) | −14.9870 | −0.618580 | −0.309290 | − | 0.950968i | \(-0.600091\pi\) | ||||
−0.309290 | + | 0.950968i | \(0.600091\pi\) | |||||||
\(588\) | 15.6350 | 0.644777 | ||||||||
\(589\) | −2.41265 | −0.0994114 | ||||||||
\(590\) | −8.45655 | −0.348151 | ||||||||
\(591\) | −64.1880 | −2.64034 | ||||||||
\(592\) | −4.03594 | −0.165876 | ||||||||
\(593\) | 18.0250 | 0.740200 | 0.370100 | − | 0.928992i | \(-0.379323\pi\) | ||||
0.370100 | + | 0.928992i | \(0.379323\pi\) | |||||||
\(594\) | 12.1553 | 0.498739 | ||||||||
\(595\) | 0.0183315 | 0.000751520 0 | ||||||||
\(596\) | −4.58091 | −0.187641 | ||||||||
\(597\) | 21.3647 | 0.874397 | ||||||||
\(598\) | −27.4186 | −1.12123 | ||||||||
\(599\) | −17.3166 | −0.707537 | −0.353769 | − | 0.935333i | \(-0.615100\pi\) | ||||
−0.353769 | + | 0.935333i | \(0.615100\pi\) | |||||||
\(600\) | −26.7878 | −1.09361 | ||||||||
\(601\) | −38.0096 | −1.55045 | −0.775223 | − | 0.631688i | \(-0.782362\pi\) | ||||
−0.775223 | + | 0.631688i | \(0.782362\pi\) | |||||||
\(602\) | −0.197340 | −0.00804298 | ||||||||
\(603\) | −24.9376 | −1.01554 | ||||||||
\(604\) | −0.990611 | −0.0403074 | ||||||||
\(605\) | −6.25294 | −0.254218 | ||||||||
\(606\) | 46.6583 | 1.89536 | ||||||||
\(607\) | −16.3355 | −0.663039 | −0.331519 | − | 0.943448i | \(-0.607561\pi\) | ||||
−0.331519 | + | 0.943448i | \(0.607561\pi\) | |||||||
\(608\) | −3.38855 | −0.137424 | ||||||||
\(609\) | −0.473083 | −0.0191703 | ||||||||
\(610\) | 20.9411 | 0.847880 | ||||||||
\(611\) | 20.8494 | 0.843475 | ||||||||
\(612\) | −1.30465 | −0.0527372 | ||||||||
\(613\) | −14.0167 | −0.566130 | −0.283065 | − | 0.959101i | \(-0.591351\pi\) | ||||
−0.283065 | + | 0.959101i | \(0.591351\pi\) | |||||||
\(614\) | −15.9413 | −0.643338 | ||||||||
\(615\) | 4.52716 | 0.182553 | ||||||||
\(616\) | −0.299750 | −0.0120773 | ||||||||
\(617\) | 3.46481 | 0.139488 | 0.0697439 | − | 0.997565i | \(-0.477782\pi\) | ||||
0.0697439 | + | 0.997565i | \(0.477782\pi\) | |||||||
\(618\) | 36.5497 | 1.47025 | ||||||||
\(619\) | −37.6697 | −1.51407 | −0.757037 | − | 0.653372i | \(-0.773354\pi\) | ||||
−0.757037 | + | 0.653372i | \(0.773354\pi\) | |||||||
\(620\) | 3.31851 | 0.133275 | ||||||||
\(621\) | 32.3811 | 1.29941 | ||||||||
\(622\) | −26.2479 | −1.05245 | ||||||||
\(623\) | −0.00186567 | −7.47463e−5 0 | ||||||||
\(624\) | −16.2700 | −0.651320 | ||||||||
\(625\) | 0.897516 | 0.0359006 | ||||||||
\(626\) | −9.81354 | −0.392228 | ||||||||
\(627\) | −5.54908 | −0.221609 | ||||||||
\(628\) | −2.12143 | −0.0846541 | ||||||||
\(629\) | 0.819880 | 0.0326908 | ||||||||
\(630\) | −0.262858 | −0.0104725 | ||||||||
\(631\) | 27.4376 | 1.09227 | 0.546137 | − | 0.837696i | \(-0.316098\pi\) | ||||
0.546137 | + | 0.837696i | \(0.316098\pi\) | |||||||
\(632\) | −37.3645 | −1.48628 | ||||||||
\(633\) | 33.0809 | 1.31485 | ||||||||
\(634\) | 24.1764 | 0.960169 | ||||||||
\(635\) | −24.4037 | −0.968433 | ||||||||
\(636\) | −4.09289 | −0.162294 | ||||||||
\(637\) | −23.9754 | −0.949941 | ||||||||
\(638\) | −12.2070 | −0.483279 | ||||||||
\(639\) | −42.6230 | −1.68614 | ||||||||
\(640\) | −0.422881 | −0.0167159 | ||||||||
\(641\) | −31.1942 | −1.23210 | −0.616048 | − | 0.787709i | \(-0.711267\pi\) | ||||
−0.616048 | + | 0.787709i | \(0.711267\pi\) | |||||||
\(642\) | −46.5843 | −1.83854 | ||||||||
\(643\) | 47.1640 | 1.85997 | 0.929984 | − | 0.367601i | \(-0.119821\pi\) | ||||
0.929984 | + | 0.367601i | \(0.119821\pi\) | |||||||
\(644\) | −0.230247 | −0.00907300 | ||||||||
\(645\) | 17.4268 | 0.686178 | ||||||||
\(646\) | −0.304212 | −0.0119691 | ||||||||
\(647\) | −0.314143 | −0.0123502 | −0.00617512 | − | 0.999981i | \(-0.501966\pi\) | ||||
−0.00617512 | + | 0.999981i | \(0.501966\pi\) | |||||||
\(648\) | −5.01490 | −0.197004 | ||||||||
\(649\) | −14.4737 | −0.568142 | ||||||||
\(650\) | 11.8445 | 0.464578 | ||||||||
\(651\) | −0.323156 | −0.0126655 | ||||||||
\(652\) | −14.3917 | −0.563621 | ||||||||
\(653\) | −42.4013 | −1.65929 | −0.829645 | − | 0.558292i | \(-0.811457\pi\) | ||||
−0.829645 | + | 0.558292i | \(0.811457\pi\) | |||||||
\(654\) | 28.3084 | 1.10694 | ||||||||
\(655\) | 12.1072 | 0.473067 | ||||||||
\(656\) | −2.09103 | −0.0816411 | ||||||||
\(657\) | −7.26152 | −0.283299 | ||||||||
\(658\) | −0.257037 | −0.0100203 | ||||||||
\(659\) | 22.2905 | 0.868316 | 0.434158 | − | 0.900837i | \(-0.357046\pi\) | ||||
0.434158 | + | 0.900837i | \(0.357046\pi\) | |||||||
\(660\) | 7.63256 | 0.297097 | ||||||||
\(661\) | 47.8018 | 1.85927 | 0.929637 | − | 0.368477i | \(-0.120121\pi\) | ||||
0.929637 | + | 0.368477i | \(0.120121\pi\) | |||||||
\(662\) | −35.1980 | −1.36801 | ||||||||
\(663\) | 3.30516 | 0.128362 | ||||||||
\(664\) | −19.9723 | −0.775074 | ||||||||
\(665\) | 0.0417495 | 0.00161898 | ||||||||
\(666\) | −11.7564 | −0.455550 | ||||||||
\(667\) | −32.5187 | −1.25913 | ||||||||
\(668\) | −9.79764 | −0.379082 | ||||||||
\(669\) | 30.4291 | 1.17646 | ||||||||
\(670\) | 7.99812 | 0.308994 | ||||||||
\(671\) | 35.8414 | 1.38364 | ||||||||
\(672\) | −0.453871 | −0.0175085 | ||||||||
\(673\) | 10.4837 | 0.404118 | 0.202059 | − | 0.979373i | \(-0.435237\pi\) | ||||
0.202059 | + | 0.979373i | \(0.435237\pi\) | |||||||
\(674\) | 15.7622 | 0.607138 | ||||||||
\(675\) | −13.9882 | −0.538405 | ||||||||
\(676\) | 1.02421 | 0.0393929 | ||||||||
\(677\) | 6.69615 | 0.257354 | 0.128677 | − | 0.991687i | \(-0.458927\pi\) | ||||
0.128677 | + | 0.991687i | \(0.458927\pi\) | |||||||
\(678\) | −42.6602 | −1.63835 | ||||||||
\(679\) | −0.00178948 | −6.86741e−5 0 | ||||||||
\(680\) | 1.45116 | 0.0556496 | ||||||||
\(681\) | 37.8893 | 1.45192 | ||||||||
\(682\) | −8.33841 | −0.319294 | ||||||||
\(683\) | 27.5839 | 1.05547 | 0.527734 | − | 0.849410i | \(-0.323042\pi\) | ||||
0.527734 | + | 0.849410i | \(0.323042\pi\) | |||||||
\(684\) | −2.97129 | −0.113610 | ||||||||
\(685\) | 15.1859 | 0.580224 | ||||||||
\(686\) | 0.591214 | 0.0225727 | ||||||||
\(687\) | 16.7565 | 0.639301 | ||||||||
\(688\) | −8.04918 | −0.306872 | ||||||||
\(689\) | 6.27622 | 0.239105 | ||||||||
\(690\) | −29.8503 | −1.13638 | ||||||||
\(691\) | 41.6672 | 1.58510 | 0.792548 | − | 0.609809i | \(-0.208754\pi\) | ||||
0.792548 | + | 0.609809i | \(0.208754\pi\) | |||||||
\(692\) | −2.12734 | −0.0808693 | ||||||||
\(693\) | −0.449891 | −0.0170900 | ||||||||
\(694\) | 28.8572 | 1.09541 | ||||||||
\(695\) | −8.99082 | −0.341041 | ||||||||
\(696\) | −37.4503 | −1.41955 | ||||||||
\(697\) | 0.424783 | 0.0160898 | ||||||||
\(698\) | −1.09071 | −0.0412842 | ||||||||
\(699\) | −5.31347 | −0.200974 | ||||||||
\(700\) | 0.0994634 | 0.00375936 | ||||||||
\(701\) | −5.03648 | −0.190225 | −0.0951125 | − | 0.995467i | \(-0.530321\pi\) | ||||
−0.0951125 | + | 0.995467i | \(0.530321\pi\) | |||||||
\(702\) | −16.4889 | −0.622333 | ||||||||
\(703\) | 1.86725 | 0.0704247 | ||||||||
\(704\) | −20.4122 | −0.769314 | ||||||||
\(705\) | 22.6985 | 0.854873 | ||||||||
\(706\) | −15.1045 | −0.568464 | ||||||||
\(707\) | −0.600821 | −0.0225962 | ||||||||
\(708\) | −12.8037 | −0.481192 | ||||||||
\(709\) | 13.7487 | 0.516342 | 0.258171 | − | 0.966099i | \(-0.416880\pi\) | ||||
0.258171 | + | 0.966099i | \(0.416880\pi\) | |||||||
\(710\) | 13.6702 | 0.513035 | ||||||||
\(711\) | −56.0799 | −2.10316 | ||||||||
\(712\) | −0.147690 | −0.00553492 | ||||||||
\(713\) | −22.2131 | −0.831886 | ||||||||
\(714\) | −0.0407469 | −0.00152492 | ||||||||
\(715\) | −11.7041 | −0.437709 | ||||||||
\(716\) | −8.48359 | −0.317047 | ||||||||
\(717\) | −33.2994 | −1.24359 | ||||||||
\(718\) | −27.7538 | −1.03576 | ||||||||
\(719\) | 29.3766 | 1.09556 | 0.547781 | − | 0.836622i | \(-0.315473\pi\) | ||||
0.547781 | + | 0.836622i | \(0.315473\pi\) | |||||||
\(720\) | −10.7216 | −0.399569 | ||||||||
\(721\) | −0.470652 | −0.0175280 | ||||||||
\(722\) | 20.0307 | 0.745467 | ||||||||
\(723\) | 7.39191 | 0.274908 | ||||||||
\(724\) | −5.05060 | −0.187704 | ||||||||
\(725\) | 14.0476 | 0.521715 | ||||||||
\(726\) | 13.8989 | 0.515837 | ||||||||
\(727\) | −16.2108 | −0.601227 | −0.300613 | − | 0.953746i | \(-0.597191\pi\) | ||||
−0.300613 | + | 0.953746i | \(0.597191\pi\) | |||||||
\(728\) | 0.406616 | 0.0150702 | ||||||||
\(729\) | −44.0245 | −1.63054 | ||||||||
\(730\) | 2.32895 | 0.0861983 | ||||||||
\(731\) | 1.63515 | 0.0604782 | ||||||||
\(732\) | 31.7060 | 1.17189 | ||||||||
\(733\) | 40.4449 | 1.49387 | 0.746933 | − | 0.664899i | \(-0.231526\pi\) | ||||
0.746933 | + | 0.664899i | \(0.231526\pi\) | |||||||
\(734\) | −30.1670 | −1.11349 | ||||||||
\(735\) | −26.1018 | −0.962779 | ||||||||
\(736\) | −31.1981 | −1.14998 | ||||||||
\(737\) | 13.6891 | 0.504243 | ||||||||
\(738\) | −6.09102 | −0.224214 | ||||||||
\(739\) | −21.9408 | −0.807106 | −0.403553 | − | 0.914956i | \(-0.632225\pi\) | ||||
−0.403553 | + | 0.914956i | \(0.632225\pi\) | |||||||
\(740\) | −2.56834 | −0.0944140 | ||||||||
\(741\) | 7.52740 | 0.276526 | ||||||||
\(742\) | −0.0773749 | −0.00284052 | ||||||||
\(743\) | 47.1912 | 1.73128 | 0.865639 | − | 0.500668i | \(-0.166912\pi\) | ||||
0.865639 | + | 0.500668i | \(0.166912\pi\) | |||||||
\(744\) | −25.5818 | −0.937873 | ||||||||
\(745\) | 7.64757 | 0.280185 | ||||||||
\(746\) | 21.7991 | 0.798121 | ||||||||
\(747\) | −29.9761 | −1.09677 | ||||||||
\(748\) | 0.716163 | 0.0261855 | ||||||||
\(749\) | 0.599868 | 0.0219187 | ||||||||
\(750\) | 33.2347 | 1.21356 | ||||||||
\(751\) | −4.98219 | −0.181803 | −0.0909013 | − | 0.995860i | \(-0.528975\pi\) | ||||
−0.0909013 | + | 0.995860i | \(0.528975\pi\) | |||||||
\(752\) | −10.4841 | −0.382316 | ||||||||
\(753\) | −43.7551 | −1.59452 | ||||||||
\(754\) | 16.5589 | 0.603041 | ||||||||
\(755\) | 1.65377 | 0.0601868 | ||||||||
\(756\) | −0.138465 | −0.00503592 | ||||||||
\(757\) | 43.8266 | 1.59290 | 0.796452 | − | 0.604702i | \(-0.206708\pi\) | ||||
0.796452 | + | 0.604702i | \(0.206708\pi\) | |||||||
\(758\) | −0.223127 | −0.00810434 | ||||||||
\(759\) | −51.0899 | −1.85445 | ||||||||
\(760\) | 3.30498 | 0.119884 | ||||||||
\(761\) | 52.8508 | 1.91584 | 0.957920 | − | 0.287035i | \(-0.0926695\pi\) | ||||
0.957920 | + | 0.287035i | \(0.0926695\pi\) | |||||||
\(762\) | 54.2441 | 1.96506 | ||||||||
\(763\) | −0.364528 | −0.0131968 | ||||||||
\(764\) | −15.9391 | −0.576657 | ||||||||
\(765\) | 2.17803 | 0.0787470 | ||||||||
\(766\) | −38.2367 | −1.38155 | ||||||||
\(767\) | 19.6338 | 0.708934 | ||||||||
\(768\) | −43.6265 | −1.57424 | ||||||||
\(769\) | 6.83975 | 0.246648 | 0.123324 | − | 0.992366i | \(-0.460645\pi\) | ||||
0.123324 | + | 0.992366i | \(0.460645\pi\) | |||||||
\(770\) | 0.144291 | 0.00519990 | ||||||||
\(771\) | 52.0219 | 1.87352 | ||||||||
\(772\) | −13.6184 | −0.490136 | ||||||||
\(773\) | 27.0532 | 0.973034 | 0.486517 | − | 0.873671i | \(-0.338267\pi\) | ||||
0.486517 | + | 0.873671i | \(0.338267\pi\) | |||||||
\(774\) | −23.4467 | −0.842772 | ||||||||
\(775\) | 9.59572 | 0.344689 | ||||||||
\(776\) | −0.141659 | −0.00508528 | ||||||||
\(777\) | 0.250105 | 0.00897245 | ||||||||
\(778\) | −10.3647 | −0.371593 | ||||||||
\(779\) | 0.967430 | 0.0346618 | ||||||||
\(780\) | −10.3537 | −0.370721 | ||||||||
\(781\) | 23.3971 | 0.837215 | ||||||||
\(782\) | −2.80086 | −0.100158 | ||||||||
\(783\) | −19.5559 | −0.698873 | ||||||||
\(784\) | 12.0561 | 0.430573 | ||||||||
\(785\) | 3.54160 | 0.126405 | ||||||||
\(786\) | −26.9116 | −0.959906 | ||||||||
\(787\) | −46.4839 | −1.65697 | −0.828486 | − | 0.560010i | \(-0.810797\pi\) | ||||
−0.828486 | + | 0.560010i | \(0.810797\pi\) | |||||||
\(788\) | 18.8667 | 0.672100 | ||||||||
\(789\) | −66.9883 | −2.38485 | ||||||||
\(790\) | 17.9862 | 0.639922 | ||||||||
\(791\) | 0.549337 | 0.0195322 | ||||||||
\(792\) | −35.6144 | −1.26550 | ||||||||
\(793\) | −48.6194 | −1.72653 | ||||||||
\(794\) | −17.7937 | −0.631475 | ||||||||
\(795\) | 6.83285 | 0.242336 | ||||||||
\(796\) | −6.27970 | −0.222578 | ||||||||
\(797\) | 0.951060 | 0.0336883 | 0.0168441 | − | 0.999858i | \(-0.494638\pi\) | ||||
0.0168441 | + | 0.999858i | \(0.494638\pi\) | |||||||
\(798\) | −0.0927999 | −0.00328508 | ||||||||
\(799\) | 2.12979 | 0.0753467 | ||||||||
\(800\) | 13.4771 | 0.476489 | ||||||||
\(801\) | −0.221666 | −0.00783219 | ||||||||
\(802\) | −9.33936 | −0.329784 | ||||||||
\(803\) | 3.98608 | 0.140666 | ||||||||
\(804\) | 12.1096 | 0.427073 | ||||||||
\(805\) | 0.384384 | 0.0135478 | ||||||||
\(806\) | 11.3112 | 0.398419 | ||||||||
\(807\) | 30.4297 | 1.07117 | ||||||||
\(808\) | −47.5623 | −1.67324 | ||||||||
\(809\) | −54.2923 | −1.90881 | −0.954407 | − | 0.298507i | \(-0.903511\pi\) | ||||
−0.954407 | + | 0.298507i | \(0.903511\pi\) | |||||||
\(810\) | 2.41403 | 0.0848205 | ||||||||
\(811\) | −39.6326 | −1.39169 | −0.695844 | − | 0.718193i | \(-0.744970\pi\) | ||||
−0.695844 | + | 0.718193i | \(0.744970\pi\) | |||||||
\(812\) | 0.139053 | 0.00487981 | ||||||||
\(813\) | 73.0989 | 2.56369 | ||||||||
\(814\) | 6.45345 | 0.226193 | ||||||||
\(815\) | 24.0261 | 0.841597 | ||||||||
\(816\) | −1.66200 | −0.0581817 | ||||||||
\(817\) | 3.72400 | 0.130286 | ||||||||
\(818\) | −20.4307 | −0.714344 | ||||||||
\(819\) | 0.610284 | 0.0213251 | ||||||||
\(820\) | −1.33067 | −0.0464689 | ||||||||
\(821\) | −20.6885 | −0.722032 | −0.361016 | − | 0.932560i | \(-0.617570\pi\) | ||||
−0.361016 | + | 0.932560i | \(0.617570\pi\) | |||||||
\(822\) | −33.7549 | −1.17734 | ||||||||
\(823\) | −25.9870 | −0.905850 | −0.452925 | − | 0.891549i | \(-0.649620\pi\) | ||||
−0.452925 | + | 0.891549i | \(0.649620\pi\) | |||||||
\(824\) | −37.2579 | −1.29794 | ||||||||
\(825\) | 22.0701 | 0.768383 | ||||||||
\(826\) | −0.242050 | −0.00842200 | ||||||||
\(827\) | 20.9851 | 0.729725 | 0.364862 | − | 0.931062i | \(-0.381116\pi\) | ||||
0.364862 | + | 0.931062i | \(0.381116\pi\) | |||||||
\(828\) | −27.3565 | −0.950702 | ||||||||
\(829\) | −36.0721 | −1.25284 | −0.626418 | − | 0.779487i | \(-0.715480\pi\) | ||||
−0.626418 | + | 0.779487i | \(0.715480\pi\) | |||||||
\(830\) | 9.61409 | 0.333710 | ||||||||
\(831\) | 69.1387 | 2.39839 | ||||||||
\(832\) | 27.6895 | 0.959959 | ||||||||
\(833\) | −2.44913 | −0.0848572 | ||||||||
\(834\) | 19.9846 | 0.692010 | ||||||||
\(835\) | 16.3566 | 0.566044 | ||||||||
\(836\) | 1.63104 | 0.0564106 | ||||||||
\(837\) | −13.3584 | −0.461733 | ||||||||
\(838\) | −27.9410 | −0.965205 | ||||||||
\(839\) | −2.77402 | −0.0957698 | −0.0478849 | − | 0.998853i | \(-0.515248\pi\) | ||||
−0.0478849 | + | 0.998853i | \(0.515248\pi\) | |||||||
\(840\) | 0.442678 | 0.0152738 | ||||||||
\(841\) | −9.36096 | −0.322792 | ||||||||
\(842\) | 31.7488 | 1.09414 | ||||||||
\(843\) | −25.7275 | −0.886102 | ||||||||
\(844\) | −9.72346 | −0.334695 | ||||||||
\(845\) | −1.70987 | −0.0588213 | ||||||||
\(846\) | −30.5394 | −1.04997 | ||||||||
\(847\) | −0.178977 | −0.00614971 | ||||||||
\(848\) | −3.15600 | −0.108377 | ||||||||
\(849\) | −29.2735 | −1.00467 | ||||||||
\(850\) | 1.20993 | 0.0415002 | ||||||||
\(851\) | 17.1916 | 0.589322 | ||||||||
\(852\) | 20.6975 | 0.709086 | ||||||||
\(853\) | −11.2688 | −0.385838 | −0.192919 | − | 0.981215i | \(-0.561795\pi\) | ||||
−0.192919 | + | 0.981215i | \(0.561795\pi\) | |||||||
\(854\) | 0.599393 | 0.0205108 | ||||||||
\(855\) | 4.96040 | 0.169642 | ||||||||
\(856\) | 47.4869 | 1.62307 | ||||||||
\(857\) | −14.2951 | −0.488311 | −0.244156 | − | 0.969736i | \(-0.578511\pi\) | ||||
−0.244156 | + | 0.969736i | \(0.578511\pi\) | |||||||
\(858\) | 26.0156 | 0.888159 | ||||||||
\(859\) | 10.4946 | 0.358070 | 0.179035 | − | 0.983843i | \(-0.442702\pi\) | ||||
0.179035 | + | 0.983843i | \(0.442702\pi\) | |||||||
\(860\) | −5.12224 | −0.174667 | ||||||||
\(861\) | 0.129580 | 0.00441608 | ||||||||
\(862\) | 24.9015 | 0.848149 | ||||||||
\(863\) | 41.4464 | 1.41085 | 0.705426 | − | 0.708783i | \(-0.250756\pi\) | ||||
0.705426 | + | 0.708783i | \(0.250756\pi\) | |||||||
\(864\) | −18.7618 | −0.638289 | ||||||||
\(865\) | 3.55147 | 0.120754 | ||||||||
\(866\) | 39.8873 | 1.35543 | ||||||||
\(867\) | −46.5301 | −1.58025 | ||||||||
\(868\) | 0.0949852 | 0.00322401 | ||||||||
\(869\) | 30.7841 | 1.04428 | ||||||||
\(870\) | 18.0275 | 0.611191 | ||||||||
\(871\) | −18.5694 | −0.629200 | ||||||||
\(872\) | −28.8568 | −0.977216 | ||||||||
\(873\) | −0.212615 | −0.00719592 | ||||||||
\(874\) | −6.37886 | −0.215768 | ||||||||
\(875\) | −0.427965 | −0.0144679 | ||||||||
\(876\) | 3.52616 | 0.119138 | ||||||||
\(877\) | 43.0640 | 1.45417 | 0.727084 | − | 0.686549i | \(-0.240875\pi\) | ||||
0.727084 | + | 0.686549i | \(0.240875\pi\) | |||||||
\(878\) | 33.5484 | 1.13220 | ||||||||
\(879\) | −85.7429 | −2.89204 | ||||||||
\(880\) | 5.88542 | 0.198397 | ||||||||
\(881\) | −31.3397 | −1.05586 | −0.527931 | − | 0.849287i | \(-0.677032\pi\) | ||||
−0.527931 | + | 0.849287i | \(0.677032\pi\) | |||||||
\(882\) | 35.1184 | 1.18250 | ||||||||
\(883\) | 5.78397 | 0.194646 | 0.0973230 | − | 0.995253i | \(-0.468972\pi\) | ||||
0.0973230 | + | 0.995253i | \(0.468972\pi\) | |||||||
\(884\) | −0.971485 | −0.0326746 | ||||||||
\(885\) | 21.3750 | 0.718514 | ||||||||
\(886\) | 27.3158 | 0.917691 | ||||||||
\(887\) | −23.3160 | −0.782873 | −0.391437 | − | 0.920205i | \(-0.628022\pi\) | ||||
−0.391437 | + | 0.920205i | \(0.628022\pi\) | |||||||
\(888\) | 19.7988 | 0.664405 | ||||||||
\(889\) | −0.698504 | −0.0234271 | ||||||||
\(890\) | 0.0710939 | 0.00238307 | ||||||||
\(891\) | 4.13170 | 0.138417 | ||||||||
\(892\) | −8.94402 | −0.299468 | ||||||||
\(893\) | 4.85054 | 0.162317 | ||||||||
\(894\) | −16.9988 | −0.568526 | ||||||||
\(895\) | 14.1629 | 0.473413 | ||||||||
\(896\) | −0.0121041 | −0.000404368 0 | ||||||||
\(897\) | 69.3042 | 2.31400 | ||||||||
\(898\) | −15.7628 | −0.526013 | ||||||||
\(899\) | 13.4151 | 0.447420 | ||||||||
\(900\) | 11.8176 | 0.393920 | ||||||||
\(901\) | 0.641126 | 0.0213590 | ||||||||
\(902\) | 3.34356 | 0.111328 | ||||||||
\(903\) | 0.498803 | 0.0165991 | ||||||||
\(904\) | 43.4867 | 1.44635 | ||||||||
\(905\) | 8.43168 | 0.280279 | ||||||||
\(906\) | −3.67596 | −0.122126 | ||||||||
\(907\) | 38.2886 | 1.27135 | 0.635676 | − | 0.771956i | \(-0.280722\pi\) | ||||
0.635676 | + | 0.771956i | \(0.280722\pi\) | |||||||
\(908\) | −11.1368 | −0.369587 | ||||||||
\(909\) | −71.3856 | −2.36771 | ||||||||
\(910\) | −0.195733 | −0.00648850 | ||||||||
\(911\) | −14.7550 | −0.488853 | −0.244427 | − | 0.969668i | \(-0.578600\pi\) | ||||
−0.244427 | + | 0.969668i | \(0.578600\pi\) | |||||||
\(912\) | −3.78516 | −0.125339 | ||||||||
\(913\) | 16.4549 | 0.544576 | ||||||||
\(914\) | −7.49149 | −0.247796 | ||||||||
\(915\) | −52.9314 | −1.74986 | ||||||||
\(916\) | −4.92523 | −0.162734 | ||||||||
\(917\) | 0.346542 | 0.0114438 | ||||||||
\(918\) | −1.68436 | −0.0555923 | ||||||||
\(919\) | 0.848311 | 0.0279832 | 0.0139916 | − | 0.999902i | \(-0.495546\pi\) | ||||
0.0139916 | + | 0.999902i | \(0.495546\pi\) | |||||||
\(920\) | 30.4287 | 1.00320 | ||||||||
\(921\) | 40.2937 | 1.32772 | ||||||||
\(922\) | −18.4782 | −0.608546 | ||||||||
\(923\) | −31.7385 | −1.04469 | ||||||||
\(924\) | 0.218466 | 0.00718699 | ||||||||
\(925\) | −7.42654 | −0.244183 | ||||||||
\(926\) | −21.6410 | −0.711166 | ||||||||
\(927\) | −55.9199 | −1.83665 | ||||||||
\(928\) | 18.8415 | 0.618503 | ||||||||
\(929\) | −22.4040 | −0.735052 | −0.367526 | − | 0.930013i | \(-0.619795\pi\) | ||||
−0.367526 | + | 0.930013i | \(0.619795\pi\) | |||||||
\(930\) | 12.3143 | 0.403803 | ||||||||
\(931\) | −5.57781 | −0.182805 | ||||||||
\(932\) | 1.56179 | 0.0511580 | ||||||||
\(933\) | 66.3451 | 2.17204 | ||||||||
\(934\) | 15.6855 | 0.513244 | ||||||||
\(935\) | −1.19559 | −0.0391001 | ||||||||
\(936\) | 48.3114 | 1.57911 | ||||||||
\(937\) | 48.2000 | 1.57462 | 0.787312 | − | 0.616554i | \(-0.211472\pi\) | ||||
0.787312 | + | 0.616554i | \(0.211472\pi\) | |||||||
\(938\) | 0.228929 | 0.00747479 | ||||||||
\(939\) | 24.8050 | 0.809481 | ||||||||
\(940\) | −6.67175 | −0.217608 | ||||||||
\(941\) | −43.0919 | −1.40476 | −0.702379 | − | 0.711803i | \(-0.747879\pi\) | ||||
−0.702379 | + | 0.711803i | \(0.747879\pi\) | |||||||
\(942\) | −7.87220 | −0.256490 | ||||||||
\(943\) | 8.90705 | 0.290054 | ||||||||
\(944\) | −9.87284 | −0.321334 | ||||||||
\(945\) | 0.231159 | 0.00751961 | ||||||||
\(946\) | 12.8706 | 0.418460 | ||||||||
\(947\) | −35.8037 | −1.16346 | −0.581732 | − | 0.813381i | \(-0.697625\pi\) | ||||
−0.581732 | + | 0.813381i | \(0.697625\pi\) | |||||||
\(948\) | 27.2322 | 0.884460 | ||||||||
\(949\) | −5.40718 | −0.175524 | ||||||||
\(950\) | 2.75558 | 0.0894027 | ||||||||
\(951\) | −61.1092 | −1.98160 | ||||||||
\(952\) | 0.0415364 | 0.00134620 | ||||||||
\(953\) | −11.1213 | −0.360256 | −0.180128 | − | 0.983643i | \(-0.557651\pi\) | ||||
−0.180128 | + | 0.983643i | \(0.557651\pi\) | |||||||
\(954\) | −9.19319 | −0.297640 | ||||||||
\(955\) | 26.6094 | 0.861061 | ||||||||
\(956\) | 9.78768 | 0.316556 | ||||||||
\(957\) | 30.8548 | 0.997393 | ||||||||
\(958\) | 16.7327 | 0.540610 | ||||||||
\(959\) | 0.434664 | 0.0140360 | ||||||||
\(960\) | 30.1452 | 0.972932 | ||||||||
\(961\) | −21.8363 | −0.704397 | ||||||||
\(962\) | −8.75420 | −0.282247 | ||||||||
\(963\) | 71.2725 | 2.29672 | ||||||||
\(964\) | −2.17270 | −0.0699780 | ||||||||
\(965\) | 22.7351 | 0.731869 | ||||||||
\(966\) | −0.854401 | −0.0274899 | ||||||||
\(967\) | −38.3634 | −1.23368 | −0.616842 | − | 0.787087i | \(-0.711588\pi\) | ||||
−0.616842 | + | 0.787087i | \(0.711588\pi\) | |||||||
\(968\) | −14.1682 | −0.455383 | ||||||||
\(969\) | 0.768936 | 0.0247018 | ||||||||
\(970\) | 0.0681909 | 0.00218948 | ||||||||
\(971\) | −32.4519 | −1.04143 | −0.520715 | − | 0.853730i | \(-0.674335\pi\) | ||||
−0.520715 | + | 0.853730i | \(0.674335\pi\) | |||||||
\(972\) | 14.3827 | 0.461326 | ||||||||
\(973\) | −0.257343 | −0.00825002 | ||||||||
\(974\) | 41.2379 | 1.32135 | ||||||||
\(975\) | −29.9384 | −0.958797 | ||||||||
\(976\) | 24.4483 | 0.782571 | ||||||||
\(977\) | −4.09532 | −0.131021 | −0.0655104 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655104 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(978\) | −53.4046 | −1.70769 | ||||||||
\(979\) | 0.121680 | 0.00388890 | ||||||||
\(980\) | 7.67208 | 0.245076 | ||||||||
\(981\) | −43.3109 | −1.38281 | ||||||||
\(982\) | −5.74564 | −0.183351 | ||||||||
\(983\) | −47.8897 | −1.52744 | −0.763722 | − | 0.645546i | \(-0.776630\pi\) | ||||
−0.763722 | + | 0.645546i | \(0.776630\pi\) | |||||||
\(984\) | 10.2578 | 0.327008 | ||||||||
\(985\) | −31.4969 | −1.00358 | ||||||||
\(986\) | 1.69152 | 0.0538690 | ||||||||
\(987\) | 0.649694 | 0.0206800 | ||||||||
\(988\) | −2.21253 | −0.0703898 | ||||||||
\(989\) | 34.2866 | 1.09025 | ||||||||
\(990\) | 17.1438 | 0.544865 | ||||||||
\(991\) | 0.564451 | 0.0179304 | 0.00896519 | − | 0.999960i | \(-0.497146\pi\) | ||||
0.00896519 | + | 0.999960i | \(0.497146\pi\) | |||||||
\(992\) | 12.8704 | 0.408634 | ||||||||
\(993\) | 88.9675 | 2.82330 | ||||||||
\(994\) | 0.391281 | 0.0124107 | ||||||||
\(995\) | 10.4836 | 0.332353 | ||||||||
\(996\) | 14.5563 | 0.461234 | ||||||||
\(997\) | 16.0474 | 0.508225 | 0.254112 | − | 0.967175i | \(-0.418217\pi\) | ||||
0.254112 | + | 0.967175i | \(0.418217\pi\) | |||||||
\(998\) | −29.3505 | −0.929074 | ||||||||
\(999\) | 10.3386 | 0.327100 |
(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 | 349.2.a.b.1.5 | ✓ | 17 | |
3.2 | odd | 2 | 3141.2.a.e.1.13 | 17 | |||
4.3 | odd | 2 | 5584.2.a.m.1.3 | 17 | |||
5.4 | even | 2 | 8725.2.a.m.1.13 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.a.b.1.5 | ✓ | 17 | 1.1 | even | 1 | trivial | |
3141.2.a.e.1.13 | 17 | 3.2 | odd | 2 | |||
5584.2.a.m.1.3 | 17 | 4.3 | odd | 2 | |||
8725.2.a.m.1.13 | 17 | 5.4 | even | 2 |