Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.96386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36221 | 1.67034 | 0.835168 | − | 0.549994i | \(-0.185370\pi\) | ||||
0.835168 | + | 0.549994i | \(0.185370\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.58005 | 1.79002 | ||||||||
\(5\) | 3.25906 | 1.45750 | 0.728748 | − | 0.684782i | \(-0.240103\pi\) | ||||
0.728748 | + | 0.684782i | \(0.240103\pi\) | |||||||
\(6\) | −2.36221 | −0.964369 | ||||||||
\(7\) | 3.14721 | 1.18953 | 0.594767 | − | 0.803898i | \(-0.297244\pi\) | ||||
0.594767 | + | 0.803898i | \(0.297244\pi\) | |||||||
\(8\) | 3.73241 | 1.31961 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.69859 | 2.43451 | ||||||||
\(11\) | 1.45931 | 0.439998 | 0.219999 | − | 0.975500i | \(-0.429395\pi\) | ||||
0.219999 | + | 0.975500i | \(0.429395\pi\) | |||||||
\(12\) | −3.58005 | −1.03347 | ||||||||
\(13\) | 1.99182 | 0.552433 | 0.276216 | − | 0.961095i | \(-0.410919\pi\) | ||||
0.276216 | + | 0.961095i | \(0.410919\pi\) | |||||||
\(14\) | 7.43438 | 1.98692 | ||||||||
\(15\) | −3.25906 | −0.841486 | ||||||||
\(16\) | 1.65665 | 0.414163 | ||||||||
\(17\) | −5.39964 | −1.30961 | −0.654803 | − | 0.755800i | \(-0.727248\pi\) | ||||
−0.654803 | + | 0.755800i | \(0.727248\pi\) | |||||||
\(18\) | 2.36221 | 0.556779 | ||||||||
\(19\) | 1.55174 | 0.355994 | 0.177997 | − | 0.984031i | \(-0.443038\pi\) | ||||
0.177997 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(20\) | 11.6676 | 2.60895 | ||||||||
\(21\) | −3.14721 | −0.686777 | ||||||||
\(22\) | 3.44720 | 0.734945 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −3.73241 | −0.761876 | ||||||||
\(25\) | 5.62147 | 1.12429 | ||||||||
\(26\) | 4.70511 | 0.922749 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 11.2672 | 2.12929 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −7.69859 | −1.40556 | ||||||||
\(31\) | −7.97707 | −1.43272 | −0.716362 | − | 0.697729i | \(-0.754194\pi\) | ||||
−0.716362 | + | 0.697729i | \(0.754194\pi\) | |||||||
\(32\) | −3.55146 | −0.627815 | ||||||||
\(33\) | −1.45931 | −0.254033 | ||||||||
\(34\) | −12.7551 | −2.18748 | ||||||||
\(35\) | 10.2569 | 1.73374 | ||||||||
\(36\) | 3.58005 | 0.596675 | ||||||||
\(37\) | −10.1874 | −1.67481 | −0.837403 | − | 0.546586i | \(-0.815927\pi\) | ||||
−0.837403 | + | 0.546586i | \(0.815927\pi\) | |||||||
\(38\) | 3.66555 | 0.594630 | ||||||||
\(39\) | −1.99182 | −0.318947 | ||||||||
\(40\) | 12.1642 | 1.92332 | ||||||||
\(41\) | −4.33929 | −0.677684 | −0.338842 | − | 0.940843i | \(-0.610035\pi\) | ||||
−0.338842 | + | 0.940843i | \(0.610035\pi\) | |||||||
\(42\) | −7.43438 | −1.14715 | ||||||||
\(43\) | −4.79243 | −0.730839 | −0.365420 | − | 0.930843i | \(-0.619075\pi\) | ||||
−0.365420 | + | 0.930843i | \(0.619075\pi\) | |||||||
\(44\) | 5.22439 | 0.787607 | ||||||||
\(45\) | 3.25906 | 0.485832 | ||||||||
\(46\) | −2.36221 | −0.348289 | ||||||||
\(47\) | −2.39075 | −0.348727 | −0.174363 | − | 0.984681i | \(-0.555787\pi\) | ||||
−0.174363 | + | 0.984681i | \(0.555787\pi\) | |||||||
\(48\) | −1.65665 | −0.239117 | ||||||||
\(49\) | 2.90493 | 0.414990 | ||||||||
\(50\) | 13.2791 | 1.87795 | ||||||||
\(51\) | 5.39964 | 0.756101 | ||||||||
\(52\) | 7.13083 | 0.988868 | ||||||||
\(53\) | 6.13279 | 0.842404 | 0.421202 | − | 0.906967i | \(-0.361608\pi\) | ||||
0.421202 | + | 0.906967i | \(0.361608\pi\) | |||||||
\(54\) | −2.36221 | −0.321456 | ||||||||
\(55\) | 4.75597 | 0.641295 | ||||||||
\(56\) | 11.7467 | 1.56972 | ||||||||
\(57\) | −1.55174 | −0.205533 | ||||||||
\(58\) | 2.36221 | 0.310174 | ||||||||
\(59\) | 5.55214 | 0.722827 | 0.361413 | − | 0.932406i | \(-0.382294\pi\) | ||||
0.361413 | + | 0.932406i | \(0.382294\pi\) | |||||||
\(60\) | −11.6676 | −1.50628 | ||||||||
\(61\) | 6.34330 | 0.812176 | 0.406088 | − | 0.913834i | \(-0.366893\pi\) | ||||
0.406088 | + | 0.913834i | \(0.366893\pi\) | |||||||
\(62\) | −18.8435 | −2.39313 | ||||||||
\(63\) | 3.14721 | 0.396511 | ||||||||
\(64\) | −11.7026 | −1.46283 | ||||||||
\(65\) | 6.49147 | 0.805168 | ||||||||
\(66\) | −3.44720 | −0.424320 | ||||||||
\(67\) | 8.62997 | 1.05432 | 0.527159 | − | 0.849767i | \(-0.323257\pi\) | ||||
0.527159 | + | 0.849767i | \(0.323257\pi\) | |||||||
\(68\) | −19.3310 | −2.34423 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 24.2291 | 2.89593 | ||||||||
\(71\) | 14.2522 | 1.69142 | 0.845710 | − | 0.533643i | \(-0.179177\pi\) | ||||
0.845710 | + | 0.533643i | \(0.179177\pi\) | |||||||
\(72\) | 3.73241 | 0.439869 | ||||||||
\(73\) | 0.308432 | 0.0360993 | 0.0180496 | − | 0.999837i | \(-0.494254\pi\) | ||||
0.0180496 | + | 0.999837i | \(0.494254\pi\) | |||||||
\(74\) | −24.0649 | −2.79749 | ||||||||
\(75\) | −5.62147 | −0.649111 | ||||||||
\(76\) | 5.55531 | 0.637238 | ||||||||
\(77\) | 4.59275 | 0.523392 | ||||||||
\(78\) | −4.70511 | −0.532749 | ||||||||
\(79\) | −2.60309 | −0.292871 | −0.146436 | − | 0.989220i | \(-0.546780\pi\) | ||||
−0.146436 | + | 0.989220i | \(0.546780\pi\) | |||||||
\(80\) | 5.39913 | 0.603641 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.2503 | −1.13196 | ||||||||
\(83\) | −17.7781 | −1.95140 | −0.975702 | − | 0.219102i | \(-0.929687\pi\) | ||||
−0.975702 | + | 0.219102i | \(0.929687\pi\) | |||||||
\(84\) | −11.2672 | −1.22935 | ||||||||
\(85\) | −17.5978 | −1.90874 | ||||||||
\(86\) | −11.3207 | −1.22075 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 5.44674 | 0.580624 | ||||||||
\(89\) | −0.673720 | −0.0714142 | −0.0357071 | − | 0.999362i | \(-0.511368\pi\) | ||||
−0.0357071 | + | 0.999362i | \(0.511368\pi\) | |||||||
\(90\) | 7.69859 | 0.811503 | ||||||||
\(91\) | 6.26869 | 0.657137 | ||||||||
\(92\) | −3.58005 | −0.373246 | ||||||||
\(93\) | 7.97707 | 0.827183 | ||||||||
\(94\) | −5.64746 | −0.582491 | ||||||||
\(95\) | 5.05722 | 0.518860 | ||||||||
\(96\) | 3.55146 | 0.362469 | ||||||||
\(97\) | 5.30656 | 0.538800 | 0.269400 | − | 0.963028i | \(-0.413175\pi\) | ||||
0.269400 | + | 0.963028i | \(0.413175\pi\) | |||||||
\(98\) | 6.86206 | 0.693173 | ||||||||
\(99\) | 1.45931 | 0.146666 | ||||||||
\(100\) | 20.1251 | 2.01251 | ||||||||
\(101\) | 7.47895 | 0.744184 | 0.372092 | − | 0.928196i | \(-0.378641\pi\) | ||||
0.372092 | + | 0.928196i | \(0.378641\pi\) | |||||||
\(102\) | 12.7551 | 1.26294 | ||||||||
\(103\) | −5.92379 | −0.583688 | −0.291844 | − | 0.956466i | \(-0.594269\pi\) | ||||
−0.291844 | + | 0.956466i | \(0.594269\pi\) | |||||||
\(104\) | 7.43431 | 0.728994 | ||||||||
\(105\) | −10.2569 | −1.00098 | ||||||||
\(106\) | 14.4870 | 1.40710 | ||||||||
\(107\) | 10.9806 | 1.06154 | 0.530768 | − | 0.847517i | \(-0.321904\pi\) | ||||
0.530768 | + | 0.847517i | \(0.321904\pi\) | |||||||
\(108\) | −3.58005 | −0.344490 | ||||||||
\(109\) | −12.4247 | −1.19007 | −0.595037 | − | 0.803698i | \(-0.702863\pi\) | ||||
−0.595037 | + | 0.803698i | \(0.702863\pi\) | |||||||
\(110\) | 11.2346 | 1.07118 | ||||||||
\(111\) | 10.1874 | 0.966949 | ||||||||
\(112\) | 5.21384 | 0.492661 | ||||||||
\(113\) | −6.26445 | −0.589310 | −0.294655 | − | 0.955604i | \(-0.595205\pi\) | ||||
−0.294655 | + | 0.955604i | \(0.595205\pi\) | |||||||
\(114\) | −3.66555 | −0.343310 | ||||||||
\(115\) | −3.25906 | −0.303909 | ||||||||
\(116\) | 3.58005 | 0.332399 | ||||||||
\(117\) | 1.99182 | 0.184144 | ||||||||
\(118\) | 13.1153 | 1.20736 | ||||||||
\(119\) | −16.9938 | −1.55782 | ||||||||
\(120\) | −12.1642 | −1.11043 | ||||||||
\(121\) | −8.87042 | −0.806402 | ||||||||
\(122\) | 14.9842 | 1.35661 | ||||||||
\(123\) | 4.33929 | 0.391261 | ||||||||
\(124\) | −28.5583 | −2.56461 | ||||||||
\(125\) | 2.02540 | 0.181157 | ||||||||
\(126\) | 7.43438 | 0.662307 | ||||||||
\(127\) | −5.48635 | −0.486835 | −0.243418 | − | 0.969922i | \(-0.578269\pi\) | ||||
−0.243418 | + | 0.969922i | \(0.578269\pi\) | |||||||
\(128\) | −20.5411 | −1.81560 | ||||||||
\(129\) | 4.79243 | 0.421950 | ||||||||
\(130\) | 15.3342 | 1.34490 | ||||||||
\(131\) | 4.33605 | 0.378843 | 0.189421 | − | 0.981896i | \(-0.439339\pi\) | ||||
0.189421 | + | 0.981896i | \(0.439339\pi\) | |||||||
\(132\) | −5.22439 | −0.454725 | ||||||||
\(133\) | 4.88366 | 0.423467 | ||||||||
\(134\) | 20.3858 | 1.76107 | ||||||||
\(135\) | −3.25906 | −0.280495 | ||||||||
\(136\) | −20.1537 | −1.72816 | ||||||||
\(137\) | −10.2133 | −0.872579 | −0.436289 | − | 0.899806i | \(-0.643708\pi\) | ||||
−0.436289 | + | 0.899806i | \(0.643708\pi\) | |||||||
\(138\) | 2.36221 | 0.201085 | ||||||||
\(139\) | 18.4979 | 1.56897 | 0.784484 | − | 0.620150i | \(-0.212928\pi\) | ||||
0.784484 | + | 0.620150i | \(0.212928\pi\) | |||||||
\(140\) | 36.7204 | 3.10344 | ||||||||
\(141\) | 2.39075 | 0.201338 | ||||||||
\(142\) | 33.6666 | 2.82524 | ||||||||
\(143\) | 2.90668 | 0.243069 | ||||||||
\(144\) | 1.65665 | 0.138054 | ||||||||
\(145\) | 3.25906 | 0.270650 | ||||||||
\(146\) | 0.728583 | 0.0602979 | ||||||||
\(147\) | −2.90493 | −0.239594 | ||||||||
\(148\) | −36.4716 | −2.99794 | ||||||||
\(149\) | 23.4402 | 1.92030 | 0.960148 | − | 0.279491i | \(-0.0901658\pi\) | ||||
0.960148 | + | 0.279491i | \(0.0901658\pi\) | |||||||
\(150\) | −13.2791 | −1.08423 | ||||||||
\(151\) | 24.1988 | 1.96927 | 0.984637 | − | 0.174616i | \(-0.0558684\pi\) | ||||
0.984637 | + | 0.174616i | \(0.0558684\pi\) | |||||||
\(152\) | 5.79174 | 0.469772 | ||||||||
\(153\) | −5.39964 | −0.436535 | ||||||||
\(154\) | 10.8490 | 0.874241 | ||||||||
\(155\) | −25.9977 | −2.08819 | ||||||||
\(156\) | −7.13083 | −0.570923 | ||||||||
\(157\) | 6.75085 | 0.538777 | 0.269388 | − | 0.963032i | \(-0.413178\pi\) | ||||
0.269388 | + | 0.963032i | \(0.413178\pi\) | |||||||
\(158\) | −6.14906 | −0.489193 | ||||||||
\(159\) | −6.13279 | −0.486362 | ||||||||
\(160\) | −11.5744 | −0.915037 | ||||||||
\(161\) | −3.14721 | −0.248035 | ||||||||
\(162\) | 2.36221 | 0.185593 | ||||||||
\(163\) | 12.5645 | 0.984130 | 0.492065 | − | 0.870558i | \(-0.336242\pi\) | ||||
0.492065 | + | 0.870558i | \(0.336242\pi\) | |||||||
\(164\) | −15.5349 | −1.21307 | ||||||||
\(165\) | −4.75597 | −0.370252 | ||||||||
\(166\) | −41.9957 | −3.25950 | ||||||||
\(167\) | 6.12109 | 0.473664 | 0.236832 | − | 0.971551i | \(-0.423891\pi\) | ||||
0.236832 | + | 0.971551i | \(0.423891\pi\) | |||||||
\(168\) | −11.7467 | −0.906276 | ||||||||
\(169\) | −9.03264 | −0.694818 | ||||||||
\(170\) | −41.5696 | −3.18825 | ||||||||
\(171\) | 1.55174 | 0.118665 | ||||||||
\(172\) | −17.1571 | −1.30822 | ||||||||
\(173\) | 10.1985 | 0.775381 | 0.387690 | − | 0.921790i | \(-0.373273\pi\) | ||||
0.387690 | + | 0.921790i | \(0.373273\pi\) | |||||||
\(174\) | −2.36221 | −0.179079 | ||||||||
\(175\) | 17.6919 | 1.33738 | ||||||||
\(176\) | 2.41757 | 0.182231 | ||||||||
\(177\) | −5.55214 | −0.417324 | ||||||||
\(178\) | −1.59147 | −0.119286 | ||||||||
\(179\) | −20.4498 | −1.52849 | −0.764244 | − | 0.644927i | \(-0.776888\pi\) | ||||
−0.764244 | + | 0.644927i | \(0.776888\pi\) | |||||||
\(180\) | 11.6676 | 0.869651 | ||||||||
\(181\) | 1.56194 | 0.116098 | 0.0580492 | − | 0.998314i | \(-0.481512\pi\) | ||||
0.0580492 | + | 0.998314i | \(0.481512\pi\) | |||||||
\(182\) | 14.8080 | 1.09764 | ||||||||
\(183\) | −6.34330 | −0.468910 | ||||||||
\(184\) | −3.73241 | −0.275157 | ||||||||
\(185\) | −33.2015 | −2.44102 | ||||||||
\(186\) | 18.8435 | 1.38167 | ||||||||
\(187\) | −7.87974 | −0.576224 | ||||||||
\(188\) | −8.55900 | −0.624230 | ||||||||
\(189\) | −3.14721 | −0.228926 | ||||||||
\(190\) | 11.9462 | 0.866671 | ||||||||
\(191\) | 17.5488 | 1.26979 | 0.634895 | − | 0.772598i | \(-0.281043\pi\) | ||||
0.634895 | + | 0.772598i | \(0.281043\pi\) | |||||||
\(192\) | 11.7026 | 0.844563 | ||||||||
\(193\) | 5.23453 | 0.376790 | 0.188395 | − | 0.982093i | \(-0.439672\pi\) | ||||
0.188395 | + | 0.982093i | \(0.439672\pi\) | |||||||
\(194\) | 12.5352 | 0.899977 | ||||||||
\(195\) | −6.49147 | −0.464864 | ||||||||
\(196\) | 10.3998 | 0.742842 | ||||||||
\(197\) | −2.58232 | −0.183983 | −0.0919913 | − | 0.995760i | \(-0.529323\pi\) | ||||
−0.0919913 | + | 0.995760i | \(0.529323\pi\) | |||||||
\(198\) | 3.44720 | 0.244982 | ||||||||
\(199\) | −16.8047 | −1.19126 | −0.595628 | − | 0.803260i | \(-0.703097\pi\) | ||||
−0.595628 | + | 0.803260i | \(0.703097\pi\) | |||||||
\(200\) | 20.9816 | 1.48363 | ||||||||
\(201\) | −8.62997 | −0.608711 | ||||||||
\(202\) | 17.6669 | 1.24304 | ||||||||
\(203\) | 3.14721 | 0.220891 | ||||||||
\(204\) | 19.3310 | 1.35344 | ||||||||
\(205\) | −14.1420 | −0.987721 | ||||||||
\(206\) | −13.9932 | −0.974955 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 3.29976 | 0.228797 | ||||||||
\(209\) | 2.26447 | 0.156637 | ||||||||
\(210\) | −24.2291 | −1.67197 | ||||||||
\(211\) | 8.97860 | 0.618112 | 0.309056 | − | 0.951044i | \(-0.399987\pi\) | ||||
0.309056 | + | 0.951044i | \(0.399987\pi\) | |||||||
\(212\) | 21.9557 | 1.50792 | ||||||||
\(213\) | −14.2522 | −0.976542 | ||||||||
\(214\) | 25.9386 | 1.77312 | ||||||||
\(215\) | −15.6188 | −1.06520 | ||||||||
\(216\) | −3.73241 | −0.253959 | ||||||||
\(217\) | −25.1055 | −1.70427 | ||||||||
\(218\) | −29.3499 | −1.98783 | ||||||||
\(219\) | −0.308432 | −0.0208419 | ||||||||
\(220\) | 17.0266 | 1.14793 | ||||||||
\(221\) | −10.7551 | −0.723469 | ||||||||
\(222\) | 24.0649 | 1.61513 | ||||||||
\(223\) | 7.08920 | 0.474728 | 0.237364 | − | 0.971421i | \(-0.423717\pi\) | ||||
0.237364 | + | 0.971421i | \(0.423717\pi\) | |||||||
\(224\) | −11.1772 | −0.746806 | ||||||||
\(225\) | 5.62147 | 0.374765 | ||||||||
\(226\) | −14.7980 | −0.984346 | ||||||||
\(227\) | 6.89075 | 0.457355 | 0.228678 | − | 0.973502i | \(-0.426560\pi\) | ||||
0.228678 | + | 0.973502i | \(0.426560\pi\) | |||||||
\(228\) | −5.55531 | −0.367910 | ||||||||
\(229\) | −14.4803 | −0.956883 | −0.478442 | − | 0.878119i | \(-0.658798\pi\) | ||||
−0.478442 | + | 0.878119i | \(0.658798\pi\) | |||||||
\(230\) | −7.69859 | −0.507630 | ||||||||
\(231\) | −4.59275 | −0.302181 | ||||||||
\(232\) | 3.73241 | 0.245045 | ||||||||
\(233\) | 6.05994 | 0.397000 | 0.198500 | − | 0.980101i | \(-0.436393\pi\) | ||||
0.198500 | + | 0.980101i | \(0.436393\pi\) | |||||||
\(234\) | 4.70511 | 0.307583 | ||||||||
\(235\) | −7.79160 | −0.508268 | ||||||||
\(236\) | 19.8769 | 1.29388 | ||||||||
\(237\) | 2.60309 | 0.169089 | ||||||||
\(238\) | −40.1430 | −2.60208 | ||||||||
\(239\) | −11.5519 | −0.747233 | −0.373616 | − | 0.927583i | \(-0.621882\pi\) | ||||
−0.373616 | + | 0.927583i | \(0.621882\pi\) | |||||||
\(240\) | −5.39913 | −0.348513 | ||||||||
\(241\) | −10.0097 | −0.644780 | −0.322390 | − | 0.946607i | \(-0.604486\pi\) | ||||
−0.322390 | + | 0.946607i | \(0.604486\pi\) | |||||||
\(242\) | −20.9538 | −1.34696 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 22.7093 | 1.45381 | ||||||||
\(245\) | 9.46733 | 0.604846 | ||||||||
\(246\) | 10.2503 | 0.653537 | ||||||||
\(247\) | 3.09080 | 0.196663 | ||||||||
\(248\) | −29.7737 | −1.89063 | ||||||||
\(249\) | 17.7781 | 1.12664 | ||||||||
\(250\) | 4.78443 | 0.302594 | ||||||||
\(251\) | 5.01221 | 0.316368 | 0.158184 | − | 0.987410i | \(-0.449436\pi\) | ||||
0.158184 | + | 0.987410i | \(0.449436\pi\) | |||||||
\(252\) | 11.2672 | 0.709765 | ||||||||
\(253\) | −1.45931 | −0.0917459 | ||||||||
\(254\) | −12.9599 | −0.813179 | ||||||||
\(255\) | 17.5978 | 1.10201 | ||||||||
\(256\) | −25.1173 | −1.56983 | ||||||||
\(257\) | −7.41284 | −0.462400 | −0.231200 | − | 0.972906i | \(-0.574265\pi\) | ||||
−0.231200 | + | 0.972906i | \(0.574265\pi\) | |||||||
\(258\) | 11.3207 | 0.704799 | ||||||||
\(259\) | −32.0620 | −1.99224 | ||||||||
\(260\) | 23.2398 | 1.44127 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 10.2427 | 0.632795 | ||||||||
\(263\) | 9.73785 | 0.600462 | 0.300231 | − | 0.953867i | \(-0.402936\pi\) | ||||
0.300231 | + | 0.953867i | \(0.402936\pi\) | |||||||
\(264\) | −5.44674 | −0.335224 | ||||||||
\(265\) | 19.9871 | 1.22780 | ||||||||
\(266\) | 11.5362 | 0.707332 | ||||||||
\(267\) | 0.673720 | 0.0412310 | ||||||||
\(268\) | 30.8957 | 1.88726 | ||||||||
\(269\) | 0.499903 | 0.0304796 | 0.0152398 | − | 0.999884i | \(-0.495149\pi\) | ||||
0.0152398 | + | 0.999884i | \(0.495149\pi\) | |||||||
\(270\) | −7.69859 | −0.468521 | ||||||||
\(271\) | −9.54186 | −0.579626 | −0.289813 | − | 0.957083i | \(-0.593593\pi\) | ||||
−0.289813 | + | 0.957083i | \(0.593593\pi\) | |||||||
\(272\) | −8.94534 | −0.542391 | ||||||||
\(273\) | −6.26869 | −0.379398 | ||||||||
\(274\) | −24.1259 | −1.45750 | ||||||||
\(275\) | 8.20345 | 0.494687 | ||||||||
\(276\) | 3.58005 | 0.215494 | ||||||||
\(277\) | −19.7349 | −1.18576 | −0.592878 | − | 0.805292i | \(-0.702008\pi\) | ||||
−0.592878 | + | 0.805292i | \(0.702008\pi\) | |||||||
\(278\) | 43.6959 | 2.62070 | ||||||||
\(279\) | −7.97707 | −0.477574 | ||||||||
\(280\) | 38.2831 | 2.28786 | ||||||||
\(281\) | −23.4853 | −1.40102 | −0.700509 | − | 0.713644i | \(-0.747043\pi\) | ||||
−0.700509 | + | 0.713644i | \(0.747043\pi\) | |||||||
\(282\) | 5.64746 | 0.336301 | ||||||||
\(283\) | −16.2076 | −0.963440 | −0.481720 | − | 0.876325i | \(-0.659988\pi\) | ||||
−0.481720 | + | 0.876325i | \(0.659988\pi\) | |||||||
\(284\) | 51.0234 | 3.02768 | ||||||||
\(285\) | −5.05722 | −0.299564 | ||||||||
\(286\) | 6.86621 | 0.406007 | ||||||||
\(287\) | −13.6567 | −0.806128 | ||||||||
\(288\) | −3.55146 | −0.209272 | ||||||||
\(289\) | 12.1561 | 0.715067 | ||||||||
\(290\) | 7.69859 | 0.452077 | ||||||||
\(291\) | −5.30656 | −0.311076 | ||||||||
\(292\) | 1.10420 | 0.0646186 | ||||||||
\(293\) | −18.5400 | −1.08312 | −0.541559 | − | 0.840662i | \(-0.682166\pi\) | ||||
−0.541559 | + | 0.840662i | \(0.682166\pi\) | |||||||
\(294\) | −6.86206 | −0.400203 | ||||||||
\(295\) | 18.0948 | 1.05352 | ||||||||
\(296\) | −38.0237 | −2.21009 | ||||||||
\(297\) | −1.45931 | −0.0846776 | ||||||||
\(298\) | 55.3708 | 3.20754 | ||||||||
\(299\) | −1.99182 | −0.115190 | ||||||||
\(300\) | −20.1251 | −1.16193 | ||||||||
\(301\) | −15.0828 | −0.869358 | ||||||||
\(302\) | 57.1628 | 3.28935 | ||||||||
\(303\) | −7.47895 | −0.429655 | ||||||||
\(304\) | 2.57070 | 0.147440 | ||||||||
\(305\) | 20.6732 | 1.18374 | ||||||||
\(306\) | −12.7551 | −0.729161 | ||||||||
\(307\) | −12.5888 | −0.718482 | −0.359241 | − | 0.933245i | \(-0.616964\pi\) | ||||
−0.359241 | + | 0.933245i | \(0.616964\pi\) | |||||||
\(308\) | 16.4423 | 0.936885 | ||||||||
\(309\) | 5.92379 | 0.336992 | ||||||||
\(310\) | −61.4122 | −3.48798 | ||||||||
\(311\) | −16.3135 | −0.925053 | −0.462527 | − | 0.886605i | \(-0.653057\pi\) | ||||
−0.462527 | + | 0.886605i | \(0.653057\pi\) | |||||||
\(312\) | −7.43431 | −0.420885 | ||||||||
\(313\) | 12.7002 | 0.717858 | 0.358929 | − | 0.933365i | \(-0.383142\pi\) | ||||
0.358929 | + | 0.933365i | \(0.383142\pi\) | |||||||
\(314\) | 15.9469 | 0.899938 | ||||||||
\(315\) | 10.2569 | 0.577913 | ||||||||
\(316\) | −9.31921 | −0.524246 | ||||||||
\(317\) | −15.8264 | −0.888900 | −0.444450 | − | 0.895804i | \(-0.646601\pi\) | ||||
−0.444450 | + | 0.895804i | \(0.646601\pi\) | |||||||
\(318\) | −14.4870 | −0.812388 | ||||||||
\(319\) | 1.45931 | 0.0817056 | ||||||||
\(320\) | −38.1395 | −2.13206 | ||||||||
\(321\) | −10.9806 | −0.612878 | ||||||||
\(322\) | −7.43438 | −0.414302 | ||||||||
\(323\) | −8.37885 | −0.466212 | ||||||||
\(324\) | 3.58005 | 0.198892 | ||||||||
\(325\) | 11.1970 | 0.621097 | ||||||||
\(326\) | 29.6801 | 1.64383 | ||||||||
\(327\) | 12.4247 | 0.687090 | ||||||||
\(328\) | −16.1960 | −0.894276 | ||||||||
\(329\) | −7.52419 | −0.414822 | ||||||||
\(330\) | −11.2346 | −0.618445 | ||||||||
\(331\) | 7.32656 | 0.402704 | 0.201352 | − | 0.979519i | \(-0.435466\pi\) | ||||
0.201352 | + | 0.979519i | \(0.435466\pi\) | |||||||
\(332\) | −63.6466 | −3.49306 | ||||||||
\(333\) | −10.1874 | −0.558268 | ||||||||
\(334\) | 14.4593 | 0.791179 | ||||||||
\(335\) | 28.1256 | 1.53666 | ||||||||
\(336\) | −5.21384 | −0.284438 | ||||||||
\(337\) | −0.348221 | −0.0189688 | −0.00948441 | − | 0.999955i | \(-0.503019\pi\) | ||||
−0.00948441 | + | 0.999955i | \(0.503019\pi\) | |||||||
\(338\) | −21.3370 | −1.16058 | ||||||||
\(339\) | 6.26445 | 0.340238 | ||||||||
\(340\) | −63.0008 | −3.41670 | ||||||||
\(341\) | −11.6410 | −0.630395 | ||||||||
\(342\) | 3.66555 | 0.198210 | ||||||||
\(343\) | −12.8880 | −0.695889 | ||||||||
\(344\) | −17.8873 | −0.964421 | ||||||||
\(345\) | 3.25906 | 0.175462 | ||||||||
\(346\) | 24.0911 | 1.29515 | ||||||||
\(347\) | 23.0544 | 1.23763 | 0.618814 | − | 0.785538i | \(-0.287614\pi\) | ||||
0.618814 | + | 0.785538i | \(0.287614\pi\) | |||||||
\(348\) | −3.58005 | −0.191911 | ||||||||
\(349\) | 2.29304 | 0.122744 | 0.0613719 | − | 0.998115i | \(-0.480452\pi\) | ||||
0.0613719 | + | 0.998115i | \(0.480452\pi\) | |||||||
\(350\) | 41.7921 | 2.23388 | ||||||||
\(351\) | −1.99182 | −0.106316 | ||||||||
\(352\) | −5.18267 | −0.276237 | ||||||||
\(353\) | −29.5910 | −1.57497 | −0.787486 | − | 0.616333i | \(-0.788618\pi\) | ||||
−0.787486 | + | 0.616333i | \(0.788618\pi\) | |||||||
\(354\) | −13.1153 | −0.697072 | ||||||||
\(355\) | 46.4486 | 2.46524 | ||||||||
\(356\) | −2.41195 | −0.127833 | ||||||||
\(357\) | 16.9938 | 0.899408 | ||||||||
\(358\) | −48.3067 | −2.55309 | ||||||||
\(359\) | 26.7858 | 1.41370 | 0.706850 | − | 0.707363i | \(-0.250116\pi\) | ||||
0.706850 | + | 0.707363i | \(0.250116\pi\) | |||||||
\(360\) | 12.1642 | 0.641107 | ||||||||
\(361\) | −16.5921 | −0.873268 | ||||||||
\(362\) | 3.68964 | 0.193923 | ||||||||
\(363\) | 8.87042 | 0.465576 | ||||||||
\(364\) | 22.4422 | 1.17629 | ||||||||
\(365\) | 1.00520 | 0.0526145 | ||||||||
\(366\) | −14.9842 | −0.783237 | ||||||||
\(367\) | 5.84694 | 0.305208 | 0.152604 | − | 0.988287i | \(-0.451234\pi\) | ||||
0.152604 | + | 0.988287i | \(0.451234\pi\) | |||||||
\(368\) | −1.65665 | −0.0863591 | ||||||||
\(369\) | −4.33929 | −0.225895 | ||||||||
\(370\) | −78.4290 | −4.07733 | ||||||||
\(371\) | 19.3012 | 1.00207 | ||||||||
\(372\) | 28.5583 | 1.48068 | ||||||||
\(373\) | 2.69778 | 0.139686 | 0.0698430 | − | 0.997558i | \(-0.477750\pi\) | ||||
0.0698430 | + | 0.997558i | \(0.477750\pi\) | |||||||
\(374\) | −18.6136 | −0.962487 | ||||||||
\(375\) | −2.02540 | −0.104591 | ||||||||
\(376\) | −8.92327 | −0.460182 | ||||||||
\(377\) | 1.99182 | 0.102584 | ||||||||
\(378\) | −7.43438 | −0.382383 | ||||||||
\(379\) | 17.2760 | 0.887409 | 0.443704 | − | 0.896173i | \(-0.353664\pi\) | ||||
0.443704 | + | 0.896173i | \(0.353664\pi\) | |||||||
\(380\) | 18.1051 | 0.928772 | ||||||||
\(381\) | 5.48635 | 0.281074 | ||||||||
\(382\) | 41.4541 | 2.12098 | ||||||||
\(383\) | 20.4954 | 1.04726 | 0.523632 | − | 0.851945i | \(-0.324577\pi\) | ||||
0.523632 | + | 0.851945i | \(0.324577\pi\) | |||||||
\(384\) | 20.5411 | 1.04823 | ||||||||
\(385\) | 14.9680 | 0.762842 | ||||||||
\(386\) | 12.3651 | 0.629365 | ||||||||
\(387\) | −4.79243 | −0.243613 | ||||||||
\(388\) | 18.9977 | 0.964464 | ||||||||
\(389\) | 38.8139 | 1.96794 | 0.983972 | − | 0.178321i | \(-0.0570664\pi\) | ||||
0.983972 | + | 0.178321i | \(0.0570664\pi\) | |||||||
\(390\) | −15.3342 | −0.776480 | ||||||||
\(391\) | 5.39964 | 0.273072 | ||||||||
\(392\) | 10.8424 | 0.547623 | ||||||||
\(393\) | −4.33605 | −0.218725 | ||||||||
\(394\) | −6.09999 | −0.307313 | ||||||||
\(395\) | −8.48364 | −0.426858 | ||||||||
\(396\) | 5.22439 | 0.262536 | ||||||||
\(397\) | −36.1654 | −1.81509 | −0.907544 | − | 0.419957i | \(-0.862045\pi\) | ||||
−0.907544 | + | 0.419957i | \(0.862045\pi\) | |||||||
\(398\) | −39.6964 | −1.98980 | ||||||||
\(399\) | −4.88366 | −0.244489 | ||||||||
\(400\) | 9.31283 | 0.465641 | ||||||||
\(401\) | 31.4018 | 1.56813 | 0.784066 | − | 0.620677i | \(-0.213142\pi\) | ||||
0.784066 | + | 0.620677i | \(0.213142\pi\) | |||||||
\(402\) | −20.3858 | −1.01675 | ||||||||
\(403\) | −15.8889 | −0.791483 | ||||||||
\(404\) | 26.7750 | 1.33211 | ||||||||
\(405\) | 3.25906 | 0.161944 | ||||||||
\(406\) | 7.43438 | 0.368962 | ||||||||
\(407\) | −14.8666 | −0.736911 | ||||||||
\(408\) | 20.1537 | 0.997756 | ||||||||
\(409\) | 9.87827 | 0.488449 | 0.244224 | − | 0.969719i | \(-0.421467\pi\) | ||||
0.244224 | + | 0.969719i | \(0.421467\pi\) | |||||||
\(410\) | −33.4064 | −1.64983 | ||||||||
\(411\) | 10.2133 | 0.503784 | ||||||||
\(412\) | −21.2074 | −1.04482 | ||||||||
\(413\) | 17.4737 | 0.859827 | ||||||||
\(414\) | −2.36221 | −0.116096 | ||||||||
\(415\) | −57.9400 | −2.84416 | ||||||||
\(416\) | −7.07388 | −0.346825 | ||||||||
\(417\) | −18.4979 | −0.905844 | ||||||||
\(418\) | 5.34916 | 0.261636 | ||||||||
\(419\) | 12.3077 | 0.601273 | 0.300636 | − | 0.953739i | \(-0.402801\pi\) | ||||
0.300636 | + | 0.953739i | \(0.402801\pi\) | |||||||
\(420\) | −36.7204 | −1.79177 | ||||||||
\(421\) | 26.2999 | 1.28178 | 0.640890 | − | 0.767633i | \(-0.278566\pi\) | ||||
0.640890 | + | 0.767633i | \(0.278566\pi\) | |||||||
\(422\) | 21.2094 | 1.03246 | ||||||||
\(423\) | −2.39075 | −0.116242 | ||||||||
\(424\) | 22.8901 | 1.11164 | ||||||||
\(425\) | −30.3539 | −1.47238 | ||||||||
\(426\) | −33.6666 | −1.63115 | ||||||||
\(427\) | 19.9637 | 0.966110 | ||||||||
\(428\) | 39.3111 | 1.90018 | ||||||||
\(429\) | −2.90668 | −0.140336 | ||||||||
\(430\) | −36.8950 | −1.77923 | ||||||||
\(431\) | −30.2923 | −1.45913 | −0.729564 | − | 0.683913i | \(-0.760277\pi\) | ||||
−0.729564 | + | 0.683913i | \(0.760277\pi\) | |||||||
\(432\) | −1.65665 | −0.0797058 | ||||||||
\(433\) | −18.9515 | −0.910750 | −0.455375 | − | 0.890300i | \(-0.650495\pi\) | ||||
−0.455375 | + | 0.890300i | \(0.650495\pi\) | |||||||
\(434\) | −59.3045 | −2.84671 | ||||||||
\(435\) | −3.25906 | −0.156260 | ||||||||
\(436\) | −44.4812 | −2.13026 | ||||||||
\(437\) | −1.55174 | −0.0742299 | ||||||||
\(438\) | −0.728583 | −0.0348130 | ||||||||
\(439\) | 6.83911 | 0.326413 | 0.163206 | − | 0.986592i | \(-0.447816\pi\) | ||||
0.163206 | + | 0.986592i | \(0.447816\pi\) | |||||||
\(440\) | 17.7512 | 0.846257 | ||||||||
\(441\) | 2.90493 | 0.138330 | ||||||||
\(442\) | −25.4059 | −1.20844 | ||||||||
\(443\) | −0.0392883 | −0.00186664 | −0.000933321 | − | 1.00000i | \(-0.500297\pi\) | ||||
−0.000933321 | 1.00000i | \(0.500297\pi\) | ||||||||
\(444\) | 36.4716 | 1.73086 | ||||||||
\(445\) | −2.19569 | −0.104086 | ||||||||
\(446\) | 16.7462 | 0.792955 | ||||||||
\(447\) | −23.4402 | −1.10868 | ||||||||
\(448\) | −36.8305 | −1.74008 | ||||||||
\(449\) | −25.4521 | −1.20116 | −0.600580 | − | 0.799564i | \(-0.705064\pi\) | ||||
−0.600580 | + | 0.799564i | \(0.705064\pi\) | |||||||
\(450\) | 13.2791 | 0.625983 | ||||||||
\(451\) | −6.33237 | −0.298179 | ||||||||
\(452\) | −22.4270 | −1.05488 | ||||||||
\(453\) | −24.1988 | −1.13696 | ||||||||
\(454\) | 16.2774 | 0.763937 | ||||||||
\(455\) | 20.4300 | 0.957775 | ||||||||
\(456\) | −5.79174 | −0.271223 | ||||||||
\(457\) | 11.6847 | 0.546588 | 0.273294 | − | 0.961931i | \(-0.411887\pi\) | ||||
0.273294 | + | 0.961931i | \(0.411887\pi\) | |||||||
\(458\) | −34.2055 | −1.59832 | ||||||||
\(459\) | 5.39964 | 0.252034 | ||||||||
\(460\) | −11.6676 | −0.544004 | ||||||||
\(461\) | −1.88294 | −0.0876973 | −0.0438486 | − | 0.999038i | \(-0.513962\pi\) | ||||
−0.0438486 | + | 0.999038i | \(0.513962\pi\) | |||||||
\(462\) | −10.8490 | −0.504743 | ||||||||
\(463\) | −11.5245 | −0.535588 | −0.267794 | − | 0.963476i | \(-0.586295\pi\) | ||||
−0.267794 | + | 0.963476i | \(0.586295\pi\) | |||||||
\(464\) | 1.65665 | 0.0769082 | ||||||||
\(465\) | 25.9977 | 1.20562 | ||||||||
\(466\) | 14.3149 | 0.663124 | ||||||||
\(467\) | 18.6749 | 0.864169 | 0.432085 | − | 0.901833i | \(-0.357778\pi\) | ||||
0.432085 | + | 0.901833i | \(0.357778\pi\) | |||||||
\(468\) | 7.13083 | 0.329623 | ||||||||
\(469\) | 27.1603 | 1.25415 | ||||||||
\(470\) | −18.4054 | −0.848978 | ||||||||
\(471\) | −6.75085 | −0.311063 | ||||||||
\(472\) | 20.7229 | 0.953848 | ||||||||
\(473\) | −6.99364 | −0.321568 | ||||||||
\(474\) | 6.14906 | 0.282436 | ||||||||
\(475\) | 8.72307 | 0.400242 | ||||||||
\(476\) | −60.8387 | −2.78854 | ||||||||
\(477\) | 6.13279 | 0.280801 | ||||||||
\(478\) | −27.2881 | −1.24813 | ||||||||
\(479\) | −26.1025 | −1.19265 | −0.596327 | − | 0.802742i | \(-0.703374\pi\) | ||||
−0.596327 | + | 0.802742i | \(0.703374\pi\) | |||||||
\(480\) | 11.5744 | 0.528297 | ||||||||
\(481\) | −20.2916 | −0.925217 | ||||||||
\(482\) | −23.6450 | −1.07700 | ||||||||
\(483\) | 3.14721 | 0.143203 | ||||||||
\(484\) | −31.7565 | −1.44348 | ||||||||
\(485\) | 17.2944 | 0.785298 | ||||||||
\(486\) | −2.36221 | −0.107152 | ||||||||
\(487\) | 15.2270 | 0.690000 | 0.345000 | − | 0.938603i | \(-0.387879\pi\) | ||||
0.345000 | + | 0.938603i | \(0.387879\pi\) | |||||||
\(488\) | 23.6758 | 1.07175 | ||||||||
\(489\) | −12.5645 | −0.568188 | ||||||||
\(490\) | 22.3639 | 1.01030 | ||||||||
\(491\) | 34.5319 | 1.55840 | 0.779201 | − | 0.626774i | \(-0.215625\pi\) | ||||
0.779201 | + | 0.626774i | \(0.215625\pi\) | |||||||
\(492\) | 15.5349 | 0.700367 | ||||||||
\(493\) | −5.39964 | −0.243188 | ||||||||
\(494\) | 7.30112 | 0.328493 | ||||||||
\(495\) | 4.75597 | 0.213765 | ||||||||
\(496\) | −13.2152 | −0.593382 | ||||||||
\(497\) | 44.8545 | 2.01200 | ||||||||
\(498\) | 41.9957 | 1.88187 | ||||||||
\(499\) | −29.8743 | −1.33736 | −0.668678 | − | 0.743552i | \(-0.733140\pi\) | ||||
−0.668678 | + | 0.743552i | \(0.733140\pi\) | |||||||
\(500\) | 7.25104 | 0.324276 | ||||||||
\(501\) | −6.12109 | −0.273470 | ||||||||
\(502\) | 11.8399 | 0.528441 | ||||||||
\(503\) | −18.6093 | −0.829748 | −0.414874 | − | 0.909879i | \(-0.636174\pi\) | ||||
−0.414874 | + | 0.909879i | \(0.636174\pi\) | |||||||
\(504\) | 11.7467 | 0.523239 | ||||||||
\(505\) | 24.3744 | 1.08464 | ||||||||
\(506\) | −3.44720 | −0.153247 | ||||||||
\(507\) | 9.03264 | 0.401153 | ||||||||
\(508\) | −19.6414 | −0.871447 | ||||||||
\(509\) | −25.5195 | −1.13113 | −0.565567 | − | 0.824702i | \(-0.691343\pi\) | ||||
−0.565567 | + | 0.824702i | \(0.691343\pi\) | |||||||
\(510\) | 41.5696 | 1.84073 | ||||||||
\(511\) | 0.970701 | 0.0429413 | ||||||||
\(512\) | −18.2502 | −0.806551 | ||||||||
\(513\) | −1.55174 | −0.0685111 | ||||||||
\(514\) | −17.5107 | −0.772364 | ||||||||
\(515\) | −19.3060 | −0.850723 | ||||||||
\(516\) | 17.1571 | 0.755301 | ||||||||
\(517\) | −3.48884 | −0.153439 | ||||||||
\(518\) | −75.7373 | −3.32771 | ||||||||
\(519\) | −10.1985 | −0.447666 | ||||||||
\(520\) | 24.2289 | 1.06251 | ||||||||
\(521\) | −21.9999 | −0.963833 | −0.481917 | − | 0.876217i | \(-0.660059\pi\) | ||||
−0.481917 | + | 0.876217i | \(0.660059\pi\) | |||||||
\(522\) | 2.36221 | 0.103391 | ||||||||
\(523\) | 21.1377 | 0.924286 | 0.462143 | − | 0.886805i | \(-0.347081\pi\) | ||||
0.462143 | + | 0.886805i | \(0.347081\pi\) | |||||||
\(524\) | 15.5233 | 0.678138 | ||||||||
\(525\) | −17.6919 | −0.772139 | ||||||||
\(526\) | 23.0029 | 1.00297 | ||||||||
\(527\) | 43.0733 | 1.87630 | ||||||||
\(528\) | −2.41757 | −0.105211 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 47.2139 | 2.05084 | ||||||||
\(531\) | 5.55214 | 0.240942 | ||||||||
\(532\) | 17.4837 | 0.758016 | ||||||||
\(533\) | −8.64311 | −0.374375 | ||||||||
\(534\) | 1.59147 | 0.0688697 | ||||||||
\(535\) | 35.7865 | 1.54718 | ||||||||
\(536\) | 32.2106 | 1.39129 | ||||||||
\(537\) | 20.4498 | 0.882473 | ||||||||
\(538\) | 1.18088 | 0.0509113 | ||||||||
\(539\) | 4.23918 | 0.182595 | ||||||||
\(540\) | −11.6676 | −0.502093 | ||||||||
\(541\) | −10.5851 | −0.455087 | −0.227544 | − | 0.973768i | \(-0.573069\pi\) | ||||
−0.227544 | + | 0.973768i | \(0.573069\pi\) | |||||||
\(542\) | −22.5399 | −0.968171 | ||||||||
\(543\) | −1.56194 | −0.0670294 | ||||||||
\(544\) | 19.1766 | 0.822189 | ||||||||
\(545\) | −40.4930 | −1.73453 | ||||||||
\(546\) | −14.8080 | −0.633723 | ||||||||
\(547\) | −0.756387 | −0.0323408 | −0.0161704 | − | 0.999869i | \(-0.505147\pi\) | ||||
−0.0161704 | + | 0.999869i | \(0.505147\pi\) | |||||||
\(548\) | −36.5640 | −1.56194 | ||||||||
\(549\) | 6.34330 | 0.270725 | ||||||||
\(550\) | 19.3783 | 0.826293 | ||||||||
\(551\) | 1.55174 | 0.0661064 | ||||||||
\(552\) | 3.73241 | 0.158862 | ||||||||
\(553\) | −8.19248 | −0.348380 | ||||||||
\(554\) | −46.6181 | −1.98061 | ||||||||
\(555\) | 33.2015 | 1.40932 | ||||||||
\(556\) | 66.2232 | 2.80849 | ||||||||
\(557\) | 43.0236 | 1.82297 | 0.911483 | − | 0.411337i | \(-0.134938\pi\) | ||||
0.911483 | + | 0.411337i | \(0.134938\pi\) | |||||||
\(558\) | −18.8435 | −0.797710 | ||||||||
\(559\) | −9.54569 | −0.403740 | ||||||||
\(560\) | 16.9922 | 0.718052 | ||||||||
\(561\) | 7.87974 | 0.332683 | ||||||||
\(562\) | −55.4773 | −2.34017 | ||||||||
\(563\) | 39.1328 | 1.64925 | 0.824626 | − | 0.565678i | \(-0.191386\pi\) | ||||
0.824626 | + | 0.565678i | \(0.191386\pi\) | |||||||
\(564\) | 8.55900 | 0.360399 | ||||||||
\(565\) | −20.4162 | −0.858917 | ||||||||
\(566\) | −38.2857 | −1.60927 | ||||||||
\(567\) | 3.14721 | 0.132170 | ||||||||
\(568\) | 53.1949 | 2.23201 | ||||||||
\(569\) | 17.9418 | 0.752158 | 0.376079 | − | 0.926588i | \(-0.377272\pi\) | ||||
0.376079 | + | 0.926588i | \(0.377272\pi\) | |||||||
\(570\) | −11.9462 | −0.500373 | ||||||||
\(571\) | 16.5548 | 0.692797 | 0.346399 | − | 0.938087i | \(-0.387404\pi\) | ||||
0.346399 | + | 0.938087i | \(0.387404\pi\) | |||||||
\(572\) | 10.4061 | 0.435100 | ||||||||
\(573\) | −17.5488 | −0.733114 | ||||||||
\(574\) | −32.2600 | −1.34650 | ||||||||
\(575\) | −5.62147 | −0.234431 | ||||||||
\(576\) | −11.7026 | −0.487608 | ||||||||
\(577\) | 23.6425 | 0.984251 | 0.492125 | − | 0.870524i | \(-0.336220\pi\) | ||||
0.492125 | + | 0.870524i | \(0.336220\pi\) | |||||||
\(578\) | 28.7154 | 1.19440 | ||||||||
\(579\) | −5.23453 | −0.217540 | ||||||||
\(580\) | 11.6676 | 0.484470 | ||||||||
\(581\) | −55.9515 | −2.32126 | ||||||||
\(582\) | −12.5352 | −0.519602 | ||||||||
\(583\) | 8.94963 | 0.370656 | ||||||||
\(584\) | 1.15120 | 0.0476368 | ||||||||
\(585\) | 6.49147 | 0.268389 | ||||||||
\(586\) | −43.7954 | −1.80917 | ||||||||
\(587\) | 40.7585 | 1.68228 | 0.841142 | − | 0.540814i | \(-0.181884\pi\) | ||||
0.841142 | + | 0.540814i | \(0.181884\pi\) | |||||||
\(588\) | −10.3998 | −0.428880 | ||||||||
\(589\) | −12.3784 | −0.510041 | ||||||||
\(590\) | 42.7437 | 1.75973 | ||||||||
\(591\) | 2.58232 | 0.106222 | ||||||||
\(592\) | −16.8771 | −0.693643 | ||||||||
\(593\) | 9.13372 | 0.375077 | 0.187539 | − | 0.982257i | \(-0.439949\pi\) | ||||
0.187539 | + | 0.982257i | \(0.439949\pi\) | |||||||
\(594\) | −3.44720 | −0.141440 | ||||||||
\(595\) | −55.3838 | −2.27052 | ||||||||
\(596\) | 83.9171 | 3.43738 | ||||||||
\(597\) | 16.8047 | 0.687772 | ||||||||
\(598\) | −4.70511 | −0.192406 | ||||||||
\(599\) | 43.6351 | 1.78288 | 0.891442 | − | 0.453136i | \(-0.149695\pi\) | ||||
0.891442 | + | 0.453136i | \(0.149695\pi\) | |||||||
\(600\) | −20.9816 | −0.856572 | ||||||||
\(601\) | 4.90324 | 0.200007 | 0.100004 | − | 0.994987i | \(-0.468115\pi\) | ||||
0.100004 | + | 0.994987i | \(0.468115\pi\) | |||||||
\(602\) | −35.6288 | −1.45212 | ||||||||
\(603\) | 8.62997 | 0.351439 | ||||||||
\(604\) | 86.6330 | 3.52505 | ||||||||
\(605\) | −28.9092 | −1.17533 | ||||||||
\(606\) | −17.6669 | −0.717668 | ||||||||
\(607\) | −2.74891 | −0.111575 | −0.0557875 | − | 0.998443i | \(-0.517767\pi\) | ||||
−0.0557875 | + | 0.998443i | \(0.517767\pi\) | |||||||
\(608\) | −5.51094 | −0.223498 | ||||||||
\(609\) | −3.14721 | −0.127531 | ||||||||
\(610\) | 48.8344 | 1.97725 | ||||||||
\(611\) | −4.76196 | −0.192648 | ||||||||
\(612\) | −19.3310 | −0.781409 | ||||||||
\(613\) | −43.8181 | −1.76980 | −0.884899 | − | 0.465783i | \(-0.845773\pi\) | ||||
−0.884899 | + | 0.465783i | \(0.845773\pi\) | |||||||
\(614\) | −29.7375 | −1.20011 | ||||||||
\(615\) | 14.1420 | 0.570261 | ||||||||
\(616\) | 17.1420 | 0.690672 | ||||||||
\(617\) | 10.9918 | 0.442511 | 0.221256 | − | 0.975216i | \(-0.428984\pi\) | ||||
0.221256 | + | 0.975216i | \(0.428984\pi\) | |||||||
\(618\) | 13.9932 | 0.562891 | ||||||||
\(619\) | 22.9060 | 0.920670 | 0.460335 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460335 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(620\) | −93.0732 | −3.73791 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −38.5359 | −1.54515 | ||||||||
\(623\) | −2.12034 | −0.0849496 | ||||||||
\(624\) | −3.29976 | −0.132096 | ||||||||
\(625\) | −21.5064 | −0.860257 | ||||||||
\(626\) | 30.0006 | 1.19906 | ||||||||
\(627\) | −2.26447 | −0.0904342 | ||||||||
\(628\) | 24.1684 | 0.964423 | ||||||||
\(629\) | 55.0086 | 2.19333 | ||||||||
\(630\) | 24.2291 | 0.965310 | ||||||||
\(631\) | −23.3247 | −0.928540 | −0.464270 | − | 0.885694i | \(-0.653683\pi\) | ||||
−0.464270 | + | 0.885694i | \(0.653683\pi\) | |||||||
\(632\) | −9.71582 | −0.386475 | ||||||||
\(633\) | −8.97860 | −0.356867 | ||||||||
\(634\) | −37.3854 | −1.48476 | ||||||||
\(635\) | −17.8804 | −0.709560 | ||||||||
\(636\) | −21.9557 | −0.870600 | ||||||||
\(637\) | 5.78611 | 0.229254 | ||||||||
\(638\) | 3.44720 | 0.136476 | ||||||||
\(639\) | 14.2522 | 0.563807 | ||||||||
\(640\) | −66.9447 | −2.64622 | ||||||||
\(641\) | 47.3515 | 1.87027 | 0.935136 | − | 0.354290i | \(-0.115278\pi\) | ||||
0.935136 | + | 0.354290i | \(0.115278\pi\) | |||||||
\(642\) | −25.9386 | −1.02371 | ||||||||
\(643\) | −8.49217 | −0.334898 | −0.167449 | − | 0.985881i | \(-0.553553\pi\) | ||||
−0.167449 | + | 0.985881i | \(0.553553\pi\) | |||||||
\(644\) | −11.2672 | −0.443989 | ||||||||
\(645\) | 15.6188 | 0.614991 | ||||||||
\(646\) | −19.7926 | −0.778731 | ||||||||
\(647\) | 29.7442 | 1.16936 | 0.584682 | − | 0.811263i | \(-0.301219\pi\) | ||||
0.584682 | + | 0.811263i | \(0.301219\pi\) | |||||||
\(648\) | 3.73241 | 0.146623 | ||||||||
\(649\) | 8.10228 | 0.318042 | ||||||||
\(650\) | 26.4496 | 1.03744 | ||||||||
\(651\) | 25.1055 | 0.983962 | ||||||||
\(652\) | 44.9816 | 1.76162 | ||||||||
\(653\) | 27.5308 | 1.07736 | 0.538681 | − | 0.842510i | \(-0.318923\pi\) | ||||
0.538681 | + | 0.842510i | \(0.318923\pi\) | |||||||
\(654\) | 29.3499 | 1.14767 | ||||||||
\(655\) | 14.1315 | 0.552162 | ||||||||
\(656\) | −7.18871 | −0.280672 | ||||||||
\(657\) | 0.308432 | 0.0120331 | ||||||||
\(658\) | −17.7737 | −0.692893 | ||||||||
\(659\) | 46.5492 | 1.81330 | 0.906651 | − | 0.421882i | \(-0.138630\pi\) | ||||
0.906651 | + | 0.421882i | \(0.138630\pi\) | |||||||
\(660\) | −17.0266 | −0.662760 | ||||||||
\(661\) | 39.8206 | 1.54884 | 0.774421 | − | 0.632671i | \(-0.218041\pi\) | ||||
0.774421 | + | 0.632671i | \(0.218041\pi\) | |||||||
\(662\) | 17.3069 | 0.672651 | ||||||||
\(663\) | 10.7551 | 0.417695 | ||||||||
\(664\) | −66.3553 | −2.57509 | ||||||||
\(665\) | 15.9161 | 0.617201 | ||||||||
\(666\) | −24.0649 | −0.932496 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 21.9138 | 0.847871 | ||||||||
\(669\) | −7.08920 | −0.274084 | ||||||||
\(670\) | 66.4386 | 2.56675 | ||||||||
\(671\) | 9.25682 | 0.357356 | ||||||||
\(672\) | 11.1772 | 0.431169 | ||||||||
\(673\) | −26.3989 | −1.01760 | −0.508801 | − | 0.860884i | \(-0.669911\pi\) | ||||
−0.508801 | + | 0.860884i | \(0.669911\pi\) | |||||||
\(674\) | −0.822573 | −0.0316843 | ||||||||
\(675\) | −5.62147 | −0.216370 | ||||||||
\(676\) | −32.3373 | −1.24374 | ||||||||
\(677\) | 17.7173 | 0.680933 | 0.340466 | − | 0.940257i | \(-0.389415\pi\) | ||||
0.340466 | + | 0.940257i | \(0.389415\pi\) | |||||||
\(678\) | 14.7980 | 0.568313 | ||||||||
\(679\) | 16.7009 | 0.640920 | ||||||||
\(680\) | −65.6821 | −2.51879 | ||||||||
\(681\) | −6.89075 | −0.264054 | ||||||||
\(682\) | −27.4985 | −1.05297 | ||||||||
\(683\) | 26.2424 | 1.00414 | 0.502068 | − | 0.864828i | \(-0.332573\pi\) | ||||
0.502068 | + | 0.864828i | \(0.332573\pi\) | |||||||
\(684\) | 5.55531 | 0.212413 | ||||||||
\(685\) | −33.2857 | −1.27178 | ||||||||
\(686\) | −30.4443 | −1.16237 | ||||||||
\(687\) | 14.4803 | 0.552457 | ||||||||
\(688\) | −7.93940 | −0.302687 | ||||||||
\(689\) | 12.2154 | 0.465371 | ||||||||
\(690\) | 7.69859 | 0.293080 | ||||||||
\(691\) | −48.7391 | −1.85412 | −0.927061 | − | 0.374910i | \(-0.877674\pi\) | ||||
−0.927061 | + | 0.374910i | \(0.877674\pi\) | |||||||
\(692\) | 36.5113 | 1.38795 | ||||||||
\(693\) | 4.59275 | 0.174464 | ||||||||
\(694\) | 54.4595 | 2.06725 | ||||||||
\(695\) | 60.2856 | 2.28676 | ||||||||
\(696\) | −3.73241 | −0.141477 | ||||||||
\(697\) | 23.4306 | 0.887498 | ||||||||
\(698\) | 5.41666 | 0.205024 | ||||||||
\(699\) | −6.05994 | −0.229208 | ||||||||
\(700\) | 63.3380 | 2.39395 | ||||||||
\(701\) | −1.46943 | −0.0554995 | −0.0277497 | − | 0.999615i | \(-0.508834\pi\) | ||||
−0.0277497 | + | 0.999615i | \(0.508834\pi\) | |||||||
\(702\) | −4.70511 | −0.177583 | ||||||||
\(703\) | −15.8083 | −0.596221 | ||||||||
\(704\) | −17.0777 | −0.643640 | ||||||||
\(705\) | 7.79160 | 0.293449 | ||||||||
\(706\) | −69.9003 | −2.63073 | ||||||||
\(707\) | 23.5378 | 0.885232 | ||||||||
\(708\) | −19.8769 | −0.747021 | ||||||||
\(709\) | 14.1235 | 0.530418 | 0.265209 | − | 0.964191i | \(-0.414559\pi\) | ||||
0.265209 | + | 0.964191i | \(0.414559\pi\) | |||||||
\(710\) | 109.722 | 4.11778 | ||||||||
\(711\) | −2.60309 | −0.0976237 | ||||||||
\(712\) | −2.51460 | −0.0942387 | ||||||||
\(713\) | 7.97707 | 0.298743 | ||||||||
\(714\) | 40.1430 | 1.50231 | ||||||||
\(715\) | 9.47306 | 0.354272 | ||||||||
\(716\) | −73.2112 | −2.73603 | ||||||||
\(717\) | 11.5519 | 0.431415 | ||||||||
\(718\) | 63.2737 | 2.36136 | ||||||||
\(719\) | 11.4231 | 0.426011 | 0.213005 | − | 0.977051i | \(-0.431675\pi\) | ||||
0.213005 | + | 0.977051i | \(0.431675\pi\) | |||||||
\(720\) | 5.39913 | 0.201214 | ||||||||
\(721\) | −18.6434 | −0.694316 | ||||||||
\(722\) | −39.1941 | −1.45865 | ||||||||
\(723\) | 10.0097 | 0.372264 | ||||||||
\(724\) | 5.59184 | 0.207819 | ||||||||
\(725\) | 5.62147 | 0.208776 | ||||||||
\(726\) | 20.9538 | 0.777669 | ||||||||
\(727\) | 15.9489 | 0.591513 | 0.295757 | − | 0.955263i | \(-0.404428\pi\) | ||||
0.295757 | + | 0.955263i | \(0.404428\pi\) | |||||||
\(728\) | 23.3973 | 0.867163 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.37449 | 0.0878840 | ||||||||
\(731\) | 25.8774 | 0.957111 | ||||||||
\(732\) | −22.7093 | −0.839360 | ||||||||
\(733\) | −28.1439 | −1.03952 | −0.519760 | − | 0.854312i | \(-0.673979\pi\) | ||||
−0.519760 | + | 0.854312i | \(0.673979\pi\) | |||||||
\(734\) | 13.8117 | 0.509800 | ||||||||
\(735\) | −9.46733 | −0.349208 | ||||||||
\(736\) | 3.55146 | 0.130908 | ||||||||
\(737\) | 12.5938 | 0.463898 | ||||||||
\(738\) | −10.2503 | −0.377320 | ||||||||
\(739\) | −45.8284 | −1.68582 | −0.842912 | − | 0.538051i | \(-0.819161\pi\) | ||||
−0.842912 | + | 0.538051i | \(0.819161\pi\) | |||||||
\(740\) | −118.863 | −4.36949 | ||||||||
\(741\) | −3.09080 | −0.113543 | ||||||||
\(742\) | 45.5935 | 1.67379 | ||||||||
\(743\) | 15.6780 | 0.575172 | 0.287586 | − | 0.957755i | \(-0.407147\pi\) | ||||
0.287586 | + | 0.957755i | \(0.407147\pi\) | |||||||
\(744\) | 29.7737 | 1.09156 | ||||||||
\(745\) | 76.3930 | 2.79882 | ||||||||
\(746\) | 6.37274 | 0.233323 | ||||||||
\(747\) | −17.7781 | −0.650468 | ||||||||
\(748\) | −28.2099 | −1.03145 | ||||||||
\(749\) | 34.5583 | 1.26273 | ||||||||
\(750\) | −4.78443 | −0.174703 | ||||||||
\(751\) | 48.5188 | 1.77047 | 0.885237 | − | 0.465140i | \(-0.153996\pi\) | ||||
0.885237 | + | 0.465140i | \(0.153996\pi\) | |||||||
\(752\) | −3.96065 | −0.144430 | ||||||||
\(753\) | −5.01221 | −0.182655 | ||||||||
\(754\) | 4.70511 | 0.171350 | ||||||||
\(755\) | 78.8654 | 2.87021 | ||||||||
\(756\) | −11.2672 | −0.409783 | ||||||||
\(757\) | −29.3527 | −1.06684 | −0.533421 | − | 0.845850i | \(-0.679094\pi\) | ||||
−0.533421 | + | 0.845850i | \(0.679094\pi\) | |||||||
\(758\) | 40.8096 | 1.48227 | ||||||||
\(759\) | 1.45931 | 0.0529695 | ||||||||
\(760\) | 18.8756 | 0.684691 | ||||||||
\(761\) | −42.6826 | −1.54724 | −0.773621 | − | 0.633648i | \(-0.781557\pi\) | ||||
−0.773621 | + | 0.633648i | \(0.781557\pi\) | |||||||
\(762\) | 12.9599 | 0.469489 | ||||||||
\(763\) | −39.1033 | −1.41563 | ||||||||
\(764\) | 62.8257 | 2.27296 | ||||||||
\(765\) | −17.5978 | −0.636248 | ||||||||
\(766\) | 48.4144 | 1.74928 | ||||||||
\(767\) | 11.0589 | 0.399313 | ||||||||
\(768\) | 25.1173 | 0.906343 | ||||||||
\(769\) | −6.84739 | −0.246923 | −0.123462 | − | 0.992349i | \(-0.539400\pi\) | ||||
−0.123462 | + | 0.992349i | \(0.539400\pi\) | |||||||
\(770\) | 35.3577 | 1.27420 | ||||||||
\(771\) | 7.41284 | 0.266967 | ||||||||
\(772\) | 18.7399 | 0.674463 | ||||||||
\(773\) | −21.5447 | −0.774909 | −0.387454 | − | 0.921889i | \(-0.626646\pi\) | ||||
−0.387454 | + | 0.921889i | \(0.626646\pi\) | |||||||
\(774\) | −11.3207 | −0.406916 | ||||||||
\(775\) | −44.8428 | −1.61080 | ||||||||
\(776\) | 19.8063 | 0.711004 | ||||||||
\(777\) | 32.0620 | 1.15022 | ||||||||
\(778\) | 91.6868 | 3.28713 | ||||||||
\(779\) | −6.73347 | −0.241251 | ||||||||
\(780\) | −23.2398 | −0.832118 | ||||||||
\(781\) | 20.7983 | 0.744221 | ||||||||
\(782\) | 12.7551 | 0.456122 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 4.81246 | 0.171874 | ||||||||
\(785\) | 22.0014 | 0.785265 | ||||||||
\(786\) | −10.2427 | −0.365344 | ||||||||
\(787\) | −30.5152 | −1.08775 | −0.543875 | − | 0.839166i | \(-0.683043\pi\) | ||||
−0.543875 | + | 0.839166i | \(0.683043\pi\) | |||||||
\(788\) | −9.24483 | −0.329333 | ||||||||
\(789\) | −9.73785 | −0.346677 | ||||||||
\(790\) | −20.0402 | −0.712997 | ||||||||
\(791\) | −19.7155 | −0.701004 | ||||||||
\(792\) | 5.44674 | 0.193541 | ||||||||
\(793\) | 12.6347 | 0.448672 | ||||||||
\(794\) | −85.4303 | −3.03181 | ||||||||
\(795\) | −19.9871 | −0.708871 | ||||||||
\(796\) | −60.1618 | −2.13238 | ||||||||
\(797\) | −33.2045 | −1.17616 | −0.588082 | − | 0.808801i | \(-0.700117\pi\) | ||||
−0.588082 | + | 0.808801i | \(0.700117\pi\) | |||||||
\(798\) | −11.5362 | −0.408378 | ||||||||
\(799\) | 12.9092 | 0.456695 | ||||||||
\(800\) | −19.9644 | −0.705848 | ||||||||
\(801\) | −0.673720 | −0.0238047 | ||||||||
\(802\) | 74.1778 | 2.61931 | ||||||||
\(803\) | 0.450098 | 0.0158836 | ||||||||
\(804\) | −30.8957 | −1.08961 | ||||||||
\(805\) | −10.2569 | −0.361510 | ||||||||
\(806\) | −37.5330 | −1.32204 | ||||||||
\(807\) | −0.499903 | −0.0175974 | ||||||||
\(808\) | 27.9145 | 0.982030 | ||||||||
\(809\) | 25.3486 | 0.891210 | 0.445605 | − | 0.895230i | \(-0.352989\pi\) | ||||
0.445605 | + | 0.895230i | \(0.352989\pi\) | |||||||
\(810\) | 7.69859 | 0.270501 | ||||||||
\(811\) | −29.7398 | −1.04431 | −0.522153 | − | 0.852852i | \(-0.674871\pi\) | ||||
−0.522153 | + | 0.852852i | \(0.674871\pi\) | |||||||
\(812\) | 11.2672 | 0.395400 | ||||||||
\(813\) | 9.54186 | 0.334647 | ||||||||
\(814\) | −35.1181 | −1.23089 | ||||||||
\(815\) | 40.9486 | 1.43437 | ||||||||
\(816\) | 8.94534 | 0.313149 | ||||||||
\(817\) | −7.43662 | −0.260174 | ||||||||
\(818\) | 23.3346 | 0.815874 | ||||||||
\(819\) | 6.26869 | 0.219046 | ||||||||
\(820\) | −50.6291 | −1.76805 | ||||||||
\(821\) | 8.37546 | 0.292306 | 0.146153 | − | 0.989262i | \(-0.453311\pi\) | ||||
0.146153 | + | 0.989262i | \(0.453311\pi\) | |||||||
\(822\) | 24.1259 | 0.841488 | ||||||||
\(823\) | 42.0013 | 1.46407 | 0.732037 | − | 0.681265i | \(-0.238570\pi\) | ||||
0.732037 | + | 0.681265i | \(0.238570\pi\) | |||||||
\(824\) | −22.1100 | −0.770239 | ||||||||
\(825\) | −8.20345 | −0.285608 | ||||||||
\(826\) | 41.2767 | 1.43620 | ||||||||
\(827\) | 12.4090 | 0.431504 | 0.215752 | − | 0.976448i | \(-0.430780\pi\) | ||||
0.215752 | + | 0.976448i | \(0.430780\pi\) | |||||||
\(828\) | −3.58005 | −0.124415 | ||||||||
\(829\) | −48.7584 | −1.69345 | −0.846725 | − | 0.532031i | \(-0.821429\pi\) | ||||
−0.846725 | + | 0.532031i | \(0.821429\pi\) | |||||||
\(830\) | −136.867 | −4.75071 | ||||||||
\(831\) | 19.7349 | 0.684597 | ||||||||
\(832\) | −23.3095 | −0.808113 | ||||||||
\(833\) | −15.6856 | −0.543473 | ||||||||
\(834\) | −43.6959 | −1.51306 | ||||||||
\(835\) | 19.9490 | 0.690364 | ||||||||
\(836\) | 8.10691 | 0.280383 | ||||||||
\(837\) | 7.97707 | 0.275728 | ||||||||
\(838\) | 29.0735 | 1.00433 | ||||||||
\(839\) | −23.4433 | −0.809352 | −0.404676 | − | 0.914460i | \(-0.632616\pi\) | ||||
−0.404676 | + | 0.914460i | \(0.632616\pi\) | |||||||
\(840\) | −38.2831 | −1.32089 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 62.1260 | 2.14100 | ||||||||
\(843\) | 23.4853 | 0.808878 | ||||||||
\(844\) | 32.1438 | 1.10644 | ||||||||
\(845\) | −29.4379 | −1.01269 | ||||||||
\(846\) | −5.64746 | −0.194164 | ||||||||
\(847\) | −27.9171 | −0.959242 | ||||||||
\(848\) | 10.1599 | 0.348893 | ||||||||
\(849\) | 16.2076 | 0.556242 | ||||||||
\(850\) | −71.7024 | −2.45937 | ||||||||
\(851\) | 10.1874 | 0.349221 | ||||||||
\(852\) | −51.0234 | −1.74803 | ||||||||
\(853\) | 8.35330 | 0.286011 | 0.143006 | − | 0.989722i | \(-0.454323\pi\) | ||||
0.143006 | + | 0.989722i | \(0.454323\pi\) | |||||||
\(854\) | 47.1585 | 1.61373 | ||||||||
\(855\) | 5.05722 | 0.172953 | ||||||||
\(856\) | 40.9842 | 1.40081 | ||||||||
\(857\) | 18.4877 | 0.631528 | 0.315764 | − | 0.948838i | \(-0.397739\pi\) | ||||
0.315764 | + | 0.948838i | \(0.397739\pi\) | |||||||
\(858\) | −6.86621 | −0.234408 | ||||||||
\(859\) | 31.3092 | 1.06826 | 0.534128 | − | 0.845404i | \(-0.320640\pi\) | ||||
0.534128 | + | 0.845404i | \(0.320640\pi\) | |||||||
\(860\) | −55.9162 | −1.90673 | ||||||||
\(861\) | 13.6567 | 0.465418 | ||||||||
\(862\) | −71.5568 | −2.43723 | ||||||||
\(863\) | −33.8041 | −1.15070 | −0.575352 | − | 0.817906i | \(-0.695135\pi\) | ||||
−0.575352 | + | 0.817906i | \(0.695135\pi\) | |||||||
\(864\) | 3.55146 | 0.120823 | ||||||||
\(865\) | 33.2377 | 1.13011 | ||||||||
\(866\) | −44.7674 | −1.52126 | ||||||||
\(867\) | −12.1561 | −0.412844 | ||||||||
\(868\) | −89.8789 | −3.05069 | ||||||||
\(869\) | −3.79872 | −0.128863 | ||||||||
\(870\) | −7.69859 | −0.261007 | ||||||||
\(871\) | 17.1894 | 0.582440 | ||||||||
\(872\) | −46.3743 | −1.57043 | ||||||||
\(873\) | 5.30656 | 0.179600 | ||||||||
\(874\) | −3.66555 | −0.123989 | ||||||||
\(875\) | 6.37436 | 0.215493 | ||||||||
\(876\) | −1.10420 | −0.0373075 | ||||||||
\(877\) | −4.54543 | −0.153488 | −0.0767441 | − | 0.997051i | \(-0.524452\pi\) | ||||
−0.0767441 | + | 0.997051i | \(0.524452\pi\) | |||||||
\(878\) | 16.1554 | 0.545219 | ||||||||
\(879\) | 18.5400 | 0.625339 | ||||||||
\(880\) | 7.87900 | 0.265601 | ||||||||
\(881\) | −14.0971 | −0.474944 | −0.237472 | − | 0.971394i | \(-0.576319\pi\) | ||||
−0.237472 | + | 0.971394i | \(0.576319\pi\) | |||||||
\(882\) | 6.86206 | 0.231058 | ||||||||
\(883\) | −38.9958 | −1.31231 | −0.656156 | − | 0.754625i | \(-0.727819\pi\) | ||||
−0.656156 | + | 0.754625i | \(0.727819\pi\) | |||||||
\(884\) | −38.5039 | −1.29503 | ||||||||
\(885\) | −18.0948 | −0.608248 | ||||||||
\(886\) | −0.0928072 | −0.00311792 | ||||||||
\(887\) | −30.6389 | −1.02875 | −0.514377 | − | 0.857564i | \(-0.671977\pi\) | ||||
−0.514377 | + | 0.857564i | \(0.671977\pi\) | |||||||
\(888\) | 38.0237 | 1.27599 | ||||||||
\(889\) | −17.2667 | −0.579107 | ||||||||
\(890\) | −5.18670 | −0.173858 | ||||||||
\(891\) | 1.45931 | 0.0488887 | ||||||||
\(892\) | 25.3797 | 0.849775 | ||||||||
\(893\) | −3.70983 | −0.124145 | ||||||||
\(894\) | −55.3708 | −1.85187 | ||||||||
\(895\) | −66.6470 | −2.22776 | ||||||||
\(896\) | −64.6472 | −2.15971 | ||||||||
\(897\) | 1.99182 | 0.0665051 | ||||||||
\(898\) | −60.1234 | −2.00634 | ||||||||
\(899\) | −7.97707 | −0.266050 | ||||||||
\(900\) | 20.1251 | 0.670838 | ||||||||
\(901\) | −33.1149 | −1.10322 | ||||||||
\(902\) | −14.9584 | −0.498060 | ||||||||
\(903\) | 15.0828 | 0.501924 | ||||||||
\(904\) | −23.3815 | −0.777658 | ||||||||
\(905\) | 5.09047 | 0.169213 | ||||||||
\(906\) | −57.1628 | −1.89911 | ||||||||
\(907\) | 34.1387 | 1.13356 | 0.566779 | − | 0.823870i | \(-0.308189\pi\) | ||||
0.566779 | + | 0.823870i | \(0.308189\pi\) | |||||||
\(908\) | 24.6692 | 0.818677 | ||||||||
\(909\) | 7.47895 | 0.248061 | ||||||||
\(910\) | 48.2601 | 1.59981 | ||||||||
\(911\) | 22.4448 | 0.743630 | 0.371815 | − | 0.928307i | \(-0.378736\pi\) | ||||
0.371815 | + | 0.928307i | \(0.378736\pi\) | |||||||
\(912\) | −2.57070 | −0.0851244 | ||||||||
\(913\) | −25.9438 | −0.858613 | ||||||||
\(914\) | 27.6018 | 0.912985 | ||||||||
\(915\) | −20.6732 | −0.683434 | ||||||||
\(916\) | −51.8401 | −1.71284 | ||||||||
\(917\) | 13.6465 | 0.450646 | ||||||||
\(918\) | 12.7551 | 0.420981 | ||||||||
\(919\) | −22.5490 | −0.743824 | −0.371912 | − | 0.928268i | \(-0.621298\pi\) | ||||
−0.371912 | + | 0.928268i | \(0.621298\pi\) | |||||||
\(920\) | −12.1642 | −0.401040 | ||||||||
\(921\) | 12.5888 | 0.414816 | ||||||||
\(922\) | −4.44790 | −0.146484 | ||||||||
\(923\) | 28.3878 | 0.934396 | ||||||||
\(924\) | −16.4423 | −0.540911 | ||||||||
\(925\) | −57.2684 | −1.88297 | ||||||||
\(926\) | −27.2233 | −0.894612 | ||||||||
\(927\) | −5.92379 | −0.194563 | ||||||||
\(928\) | −3.55146 | −0.116582 | ||||||||
\(929\) | −50.6080 | −1.66039 | −0.830197 | − | 0.557470i | \(-0.811772\pi\) | ||||
−0.830197 | + | 0.557470i | \(0.811772\pi\) | |||||||
\(930\) | 61.4122 | 2.01378 | ||||||||
\(931\) | 4.50770 | 0.147734 | ||||||||
\(932\) | 21.6949 | 0.710640 | ||||||||
\(933\) | 16.3135 | 0.534080 | ||||||||
\(934\) | 44.1140 | 1.44345 | ||||||||
\(935\) | −25.6805 | −0.839843 | ||||||||
\(936\) | 7.43431 | 0.242998 | ||||||||
\(937\) | −3.29556 | −0.107661 | −0.0538306 | − | 0.998550i | \(-0.517143\pi\) | ||||
−0.0538306 | + | 0.998550i | \(0.517143\pi\) | |||||||
\(938\) | 64.1585 | 2.09485 | ||||||||
\(939\) | −12.7002 | −0.414455 | ||||||||
\(940\) | −27.8943 | −0.909812 | ||||||||
\(941\) | −30.5639 | −0.996353 | −0.498177 | − | 0.867076i | \(-0.665997\pi\) | ||||
−0.498177 | + | 0.867076i | \(0.665997\pi\) | |||||||
\(942\) | −15.9469 | −0.519580 | ||||||||
\(943\) | 4.33929 | 0.141307 | ||||||||
\(944\) | 9.19797 | 0.299369 | ||||||||
\(945\) | −10.2569 | −0.333658 | ||||||||
\(946\) | −16.5205 | −0.537126 | ||||||||
\(947\) | 12.8774 | 0.418458 | 0.209229 | − | 0.977867i | \(-0.432905\pi\) | ||||
0.209229 | + | 0.977867i | \(0.432905\pi\) | |||||||
\(948\) | 9.31921 | 0.302674 | ||||||||
\(949\) | 0.614343 | 0.0199424 | ||||||||
\(950\) | 20.6057 | 0.668539 | ||||||||
\(951\) | 15.8264 | 0.513207 | ||||||||
\(952\) | −63.4279 | −2.05571 | ||||||||
\(953\) | 20.7913 | 0.673496 | 0.336748 | − | 0.941595i | \(-0.390673\pi\) | ||||
0.336748 | + | 0.941595i | \(0.390673\pi\) | |||||||
\(954\) | 14.4870 | 0.469033 | ||||||||
\(955\) | 57.1927 | 1.85071 | ||||||||
\(956\) | −41.3565 | −1.33757 | ||||||||
\(957\) | −1.45931 | −0.0471727 | ||||||||
\(958\) | −61.6597 | −1.99213 | ||||||||
\(959\) | −32.1433 | −1.03796 | ||||||||
\(960\) | 38.1395 | 1.23095 | ||||||||
\(961\) | 32.6336 | 1.05270 | ||||||||
\(962\) | −47.9331 | −1.54542 | ||||||||
\(963\) | 10.9806 | 0.353845 | ||||||||
\(964\) | −35.8351 | −1.15417 | ||||||||
\(965\) | 17.0596 | 0.549169 | ||||||||
\(966\) | 7.43438 | 0.239197 | ||||||||
\(967\) | −49.7242 | −1.59902 | −0.799511 | − | 0.600652i | \(-0.794908\pi\) | ||||
−0.799511 | + | 0.600652i | \(0.794908\pi\) | |||||||
\(968\) | −33.1081 | −1.06413 | ||||||||
\(969\) | 8.37885 | 0.269168 | ||||||||
\(970\) | 40.8530 | 1.31171 | ||||||||
\(971\) | 36.5618 | 1.17333 | 0.586663 | − | 0.809831i | \(-0.300441\pi\) | ||||
0.586663 | + | 0.809831i | \(0.300441\pi\) | |||||||
\(972\) | −3.58005 | −0.114830 | ||||||||
\(973\) | 58.2166 | 1.86634 | ||||||||
\(974\) | 35.9694 | 1.15253 | ||||||||
\(975\) | −11.1970 | −0.358590 | ||||||||
\(976\) | 10.5086 | 0.336374 | ||||||||
\(977\) | 30.8588 | 0.987260 | 0.493630 | − | 0.869672i | \(-0.335670\pi\) | ||||
0.493630 | + | 0.869672i | \(0.335670\pi\) | |||||||
\(978\) | −29.6801 | −0.949065 | ||||||||
\(979\) | −0.983165 | −0.0314221 | ||||||||
\(980\) | 33.8935 | 1.08269 | ||||||||
\(981\) | −12.4247 | −0.396692 | ||||||||
\(982\) | 81.5716 | 2.60306 | ||||||||
\(983\) | −31.4282 | −1.00240 | −0.501202 | − | 0.865330i | \(-0.667109\pi\) | ||||
−0.501202 | + | 0.865330i | \(0.667109\pi\) | |||||||
\(984\) | 16.1960 | 0.516311 | ||||||||
\(985\) | −8.41593 | −0.268154 | ||||||||
\(986\) | −12.7551 | −0.406205 | ||||||||
\(987\) | 7.52419 | 0.239498 | ||||||||
\(988\) | 11.0652 | 0.352031 | ||||||||
\(989\) | 4.79243 | 0.152391 | ||||||||
\(990\) | 11.2346 | 0.357060 | ||||||||
\(991\) | −10.6121 | −0.337106 | −0.168553 | − | 0.985693i | \(-0.553909\pi\) | ||||
−0.168553 | + | 0.985693i | \(0.553909\pi\) | |||||||
\(992\) | 28.3302 | 0.899485 | ||||||||
\(993\) | −7.32656 | −0.232501 | ||||||||
\(994\) | 105.956 | 3.36072 | ||||||||
\(995\) | −54.7676 | −1.73625 | ||||||||
\(996\) | 63.6466 | 2.01672 | ||||||||
\(997\) | 3.37475 | 0.106879 | 0.0534397 | − | 0.998571i | \(-0.482982\pi\) | ||||
0.0534397 | + | 0.998571i | \(0.482982\pi\) | |||||||
\(998\) | −70.5694 | −2.23384 | ||||||||
\(999\) | 10.1874 | 0.322316 |
(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 | 2001.2.a.k.1.9 | ✓ | 10 | |
3.2 | odd | 2 | 6003.2.a.k.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.k.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6003.2.a.k.1.2 | 10 | 3.2 | odd | 2 |