Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 11x^{7} + 51x^{6} + 25x^{5} - 180x^{4} + 29x^{3} + 119x^{2} - 8x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.362196\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.82978 | 1.71273 | 0.856366 | − | 0.516370i | \(-0.172717\pi\) | ||||
0.856366 | + | 0.516370i | \(0.172717\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.790105 | −0.298632 | −0.149316 | − | 0.988790i | \(-0.547707\pi\) | ||||
−0.149316 | + | 0.988790i | \(0.547707\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.82978 | −1.21108 | ||||||||
\(11\) | 0.446910 | 0.134748 | 0.0673741 | − | 0.997728i | \(-0.478538\pi\) | ||||
0.0673741 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.193805 | 0.0537517 | 0.0268759 | − | 0.999639i | \(-0.491444\pi\) | ||||
0.0268759 | + | 0.999639i | \(0.491444\pi\) | |||||||
\(14\) | 0.790105 | 0.211164 | ||||||||
\(15\) | −3.82978 | −0.988846 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.41306 | −1.07032 | −0.535162 | − | 0.844749i | \(-0.679750\pi\) | ||||
−0.535162 | + | 0.844749i | \(0.679750\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.82978 | 0.856366 | ||||||||
\(21\) | 0.790105 | 0.172415 | ||||||||
\(22\) | −0.446910 | −0.0952814 | ||||||||
\(23\) | 4.46341 | 0.930685 | 0.465343 | − | 0.885131i | \(-0.345931\pi\) | ||||
0.465343 | + | 0.885131i | \(0.345931\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 9.66725 | 1.93345 | ||||||||
\(26\) | −0.193805 | −0.0380082 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.790105 | −0.149316 | ||||||||
\(29\) | −3.07194 | −0.570446 | −0.285223 | − | 0.958461i | \(-0.592068\pi\) | ||||
−0.285223 | + | 0.958461i | \(0.592068\pi\) | |||||||
\(30\) | 3.82978 | 0.699220 | ||||||||
\(31\) | 2.03661 | 0.365786 | 0.182893 | − | 0.983133i | \(-0.441454\pi\) | ||||
0.182893 | + | 0.983133i | \(0.441454\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.446910 | −0.0777970 | ||||||||
\(34\) | 4.41306 | 0.756834 | ||||||||
\(35\) | −3.02593 | −0.511476 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.71886 | −1.10457 | −0.552287 | − | 0.833654i | \(-0.686245\pi\) | ||||
−0.552287 | + | 0.833654i | \(0.686245\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −0.193805 | −0.0310336 | ||||||||
\(40\) | −3.82978 | −0.605542 | ||||||||
\(41\) | −0.0299034 | −0.00467013 | −0.00233507 | − | 0.999997i | \(-0.500743\pi\) | ||||
−0.00233507 | + | 0.999997i | \(0.500743\pi\) | |||||||
\(42\) | −0.790105 | −0.121916 | ||||||||
\(43\) | 0.658880 | 0.100478 | 0.0502392 | − | 0.998737i | \(-0.484002\pi\) | ||||
0.0502392 | + | 0.998737i | \(0.484002\pi\) | |||||||
\(44\) | 0.446910 | 0.0673741 | ||||||||
\(45\) | 3.82978 | 0.570911 | ||||||||
\(46\) | −4.46341 | −0.658094 | ||||||||
\(47\) | 6.54823 | 0.955158 | 0.477579 | − | 0.878589i | \(-0.341515\pi\) | ||||
0.477579 | + | 0.878589i | \(0.341515\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.37573 | −0.910819 | ||||||||
\(50\) | −9.66725 | −1.36716 | ||||||||
\(51\) | 4.41306 | 0.617952 | ||||||||
\(52\) | 0.193805 | 0.0268759 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.71157 | 0.230788 | ||||||||
\(56\) | 0.790105 | 0.105582 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 3.07194 | 0.403366 | ||||||||
\(59\) | −4.62022 | −0.601501 | −0.300751 | − | 0.953703i | \(-0.597237\pi\) | ||||
−0.300751 | + | 0.953703i | \(0.597237\pi\) | |||||||
\(60\) | −3.82978 | −0.494423 | ||||||||
\(61\) | 8.27631 | 1.05967 | 0.529837 | − | 0.848100i | \(-0.322253\pi\) | ||||
0.529837 | + | 0.848100i | \(0.322253\pi\) | |||||||
\(62\) | −2.03661 | −0.258650 | ||||||||
\(63\) | −0.790105 | −0.0995439 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.742230 | 0.0920623 | ||||||||
\(66\) | 0.446910 | 0.0550108 | ||||||||
\(67\) | 5.32352 | 0.650372 | 0.325186 | − | 0.945650i | \(-0.394573\pi\) | ||||
0.325186 | + | 0.945650i | \(0.394573\pi\) | |||||||
\(68\) | −4.41306 | −0.535162 | ||||||||
\(69\) | −4.46341 | −0.537331 | ||||||||
\(70\) | 3.02593 | 0.361668 | ||||||||
\(71\) | 6.92682 | 0.822062 | 0.411031 | − | 0.911621i | \(-0.365169\pi\) | ||||
0.411031 | + | 0.911621i | \(0.365169\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 8.46217 | 0.990423 | 0.495211 | − | 0.868773i | \(-0.335091\pi\) | ||||
0.495211 | + | 0.868773i | \(0.335091\pi\) | |||||||
\(74\) | 6.71886 | 0.781052 | ||||||||
\(75\) | −9.66725 | −1.11628 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −0.353105 | −0.0402401 | ||||||||
\(78\) | 0.193805 | 0.0219441 | ||||||||
\(79\) | 11.7730 | 1.32456 | 0.662280 | − | 0.749256i | \(-0.269589\pi\) | ||||
0.662280 | + | 0.749256i | \(0.269589\pi\) | |||||||
\(80\) | 3.82978 | 0.428183 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.0299034 | 0.00330228 | ||||||||
\(83\) | 10.0300 | 1.10094 | 0.550468 | − | 0.834856i | \(-0.314449\pi\) | ||||
0.550468 | + | 0.834856i | \(0.314449\pi\) | |||||||
\(84\) | 0.790105 | 0.0862075 | ||||||||
\(85\) | −16.9011 | −1.83318 | ||||||||
\(86\) | −0.658880 | −0.0710489 | ||||||||
\(87\) | 3.07194 | 0.329347 | ||||||||
\(88\) | −0.446910 | −0.0476407 | ||||||||
\(89\) | −14.3347 | −1.51947 | −0.759737 | − | 0.650231i | \(-0.774672\pi\) | ||||
−0.759737 | + | 0.650231i | \(0.774672\pi\) | |||||||
\(90\) | −3.82978 | −0.403695 | ||||||||
\(91\) | −0.153126 | −0.0160520 | ||||||||
\(92\) | 4.46341 | 0.465343 | ||||||||
\(93\) | −2.03661 | −0.211187 | ||||||||
\(94\) | −6.54823 | −0.675398 | ||||||||
\(95\) | −3.82978 | −0.392928 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 13.3255 | 1.35300 | 0.676502 | − | 0.736441i | \(-0.263495\pi\) | ||||
0.676502 | + | 0.736441i | \(0.263495\pi\) | |||||||
\(98\) | 6.37573 | 0.644046 | ||||||||
\(99\) | 0.446910 | 0.0449161 | ||||||||
\(100\) | 9.66725 | 0.966725 | ||||||||
\(101\) | 5.76906 | 0.574043 | 0.287021 | − | 0.957924i | \(-0.407335\pi\) | ||||
0.287021 | + | 0.957924i | \(0.407335\pi\) | |||||||
\(102\) | −4.41306 | −0.436958 | ||||||||
\(103\) | −4.31765 | −0.425431 | −0.212715 | − | 0.977114i | \(-0.568231\pi\) | ||||
−0.212715 | + | 0.977114i | \(0.568231\pi\) | |||||||
\(104\) | −0.193805 | −0.0190041 | ||||||||
\(105\) | 3.02593 | 0.295301 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | 14.0342 | 1.35674 | 0.678368 | − | 0.734722i | \(-0.262688\pi\) | ||||
0.678368 | + | 0.734722i | \(0.262688\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 11.7618 | 1.12658 | 0.563289 | − | 0.826260i | \(-0.309536\pi\) | ||||
0.563289 | + | 0.826260i | \(0.309536\pi\) | |||||||
\(110\) | −1.71157 | −0.163192 | ||||||||
\(111\) | 6.71886 | 0.637726 | ||||||||
\(112\) | −0.790105 | −0.0746579 | ||||||||
\(113\) | −5.70150 | −0.536352 | −0.268176 | − | 0.963370i | \(-0.586421\pi\) | ||||
−0.268176 | + | 0.963370i | \(0.586421\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 17.0939 | 1.59401 | ||||||||
\(116\) | −3.07194 | −0.285223 | ||||||||
\(117\) | 0.193805 | 0.0179172 | ||||||||
\(118\) | 4.62022 | 0.425325 | ||||||||
\(119\) | 3.48678 | 0.319633 | ||||||||
\(120\) | 3.82978 | 0.349610 | ||||||||
\(121\) | −10.8003 | −0.981843 | ||||||||
\(122\) | −8.27631 | −0.749302 | ||||||||
\(123\) | 0.0299034 | 0.00269630 | ||||||||
\(124\) | 2.03661 | 0.182893 | ||||||||
\(125\) | 17.8746 | 1.59875 | ||||||||
\(126\) | 0.790105 | 0.0703881 | ||||||||
\(127\) | 1.60126 | 0.142089 | 0.0710444 | − | 0.997473i | \(-0.477367\pi\) | ||||
0.0710444 | + | 0.997473i | \(0.477367\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.658880 | −0.0580112 | ||||||||
\(130\) | −0.742230 | −0.0650979 | ||||||||
\(131\) | 12.8066 | 1.11892 | 0.559459 | − | 0.828858i | \(-0.311009\pi\) | ||||
0.559459 | + | 0.828858i | \(0.311009\pi\) | |||||||
\(132\) | −0.446910 | −0.0388985 | ||||||||
\(133\) | 0.790105 | 0.0685108 | ||||||||
\(134\) | −5.32352 | −0.459883 | ||||||||
\(135\) | −3.82978 | −0.329615 | ||||||||
\(136\) | 4.41306 | 0.378417 | ||||||||
\(137\) | 6.61702 | 0.565330 | 0.282665 | − | 0.959219i | \(-0.408782\pi\) | ||||
0.282665 | + | 0.959219i | \(0.408782\pi\) | |||||||
\(138\) | 4.46341 | 0.379951 | ||||||||
\(139\) | 0.642811 | 0.0545225 | 0.0272613 | − | 0.999628i | \(-0.491321\pi\) | ||||
0.0272613 | + | 0.999628i | \(0.491321\pi\) | |||||||
\(140\) | −3.02593 | −0.255738 | ||||||||
\(141\) | −6.54823 | −0.551460 | ||||||||
\(142\) | −6.92682 | −0.581286 | ||||||||
\(143\) | 0.0866131 | 0.00724295 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −11.7649 | −0.977020 | ||||||||
\(146\) | −8.46217 | −0.700335 | ||||||||
\(147\) | 6.37573 | 0.525862 | ||||||||
\(148\) | −6.71886 | −0.552287 | ||||||||
\(149\) | 0.421009 | 0.0344904 | 0.0172452 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172452 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(150\) | 9.66725 | 0.789328 | ||||||||
\(151\) | 13.0626 | 1.06302 | 0.531511 | − | 0.847052i | \(-0.321625\pi\) | ||||
0.531511 | + | 0.847052i | \(0.321625\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −4.41306 | −0.356775 | ||||||||
\(154\) | 0.353105 | 0.0284540 | ||||||||
\(155\) | 7.79978 | 0.626493 | ||||||||
\(156\) | −0.193805 | −0.0155168 | ||||||||
\(157\) | 14.4289 | 1.15155 | 0.575775 | − | 0.817608i | \(-0.304700\pi\) | ||||
0.575775 | + | 0.817608i | \(0.304700\pi\) | |||||||
\(158\) | −11.7730 | −0.936606 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | −3.82978 | −0.302771 | ||||||||
\(161\) | −3.52656 | −0.277932 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 18.1071 | 1.41825 | 0.709127 | − | 0.705081i | \(-0.249089\pi\) | ||||
0.709127 | + | 0.705081i | \(0.249089\pi\) | |||||||
\(164\) | −0.0299034 | −0.00233507 | ||||||||
\(165\) | −1.71157 | −0.133245 | ||||||||
\(166\) | −10.0300 | −0.778479 | ||||||||
\(167\) | 21.5543 | 1.66792 | 0.833960 | − | 0.551825i | \(-0.186068\pi\) | ||||
0.833960 | + | 0.551825i | \(0.186068\pi\) | |||||||
\(168\) | −0.790105 | −0.0609579 | ||||||||
\(169\) | −12.9624 | −0.997111 | ||||||||
\(170\) | 16.9011 | 1.29625 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0.658880 | 0.0502392 | ||||||||
\(173\) | −1.64948 | −0.125408 | −0.0627039 | − | 0.998032i | \(-0.519972\pi\) | ||||
−0.0627039 | + | 0.998032i | \(0.519972\pi\) | |||||||
\(174\) | −3.07194 | −0.232883 | ||||||||
\(175\) | −7.63814 | −0.577389 | ||||||||
\(176\) | 0.446910 | 0.0336871 | ||||||||
\(177\) | 4.62022 | 0.347277 | ||||||||
\(178\) | 14.3347 | 1.07443 | ||||||||
\(179\) | −24.5074 | −1.83177 | −0.915885 | − | 0.401440i | \(-0.868510\pi\) | ||||
−0.915885 | + | 0.401440i | \(0.868510\pi\) | |||||||
\(180\) | 3.82978 | 0.285455 | ||||||||
\(181\) | −8.78529 | −0.653006 | −0.326503 | − | 0.945196i | \(-0.605870\pi\) | ||||
−0.326503 | + | 0.945196i | \(0.605870\pi\) | |||||||
\(182\) | 0.153126 | 0.0113505 | ||||||||
\(183\) | −8.27631 | −0.611803 | ||||||||
\(184\) | −4.46341 | −0.329047 | ||||||||
\(185\) | −25.7318 | −1.89184 | ||||||||
\(186\) | 2.03661 | 0.149332 | ||||||||
\(187\) | −1.97224 | −0.144224 | ||||||||
\(188\) | 6.54823 | 0.477579 | ||||||||
\(189\) | 0.790105 | 0.0574717 | ||||||||
\(190\) | 3.82978 | 0.277842 | ||||||||
\(191\) | −7.06173 | −0.510969 | −0.255485 | − | 0.966813i | \(-0.582235\pi\) | ||||
−0.255485 | + | 0.966813i | \(0.582235\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.35398 | 0.601333 | 0.300666 | − | 0.953729i | \(-0.402791\pi\) | ||||
0.300666 | + | 0.953729i | \(0.402791\pi\) | |||||||
\(194\) | −13.3255 | −0.956718 | ||||||||
\(195\) | −0.742230 | −0.0531522 | ||||||||
\(196\) | −6.37573 | −0.455410 | ||||||||
\(197\) | 10.5400 | 0.750942 | 0.375471 | − | 0.926834i | \(-0.377481\pi\) | ||||
0.375471 | + | 0.926834i | \(0.377481\pi\) | |||||||
\(198\) | −0.446910 | −0.0317605 | ||||||||
\(199\) | −14.2303 | −1.00876 | −0.504381 | − | 0.863481i | \(-0.668279\pi\) | ||||
−0.504381 | + | 0.863481i | \(0.668279\pi\) | |||||||
\(200\) | −9.66725 | −0.683578 | ||||||||
\(201\) | −5.32352 | −0.375492 | ||||||||
\(202\) | −5.76906 | −0.405910 | ||||||||
\(203\) | 2.42716 | 0.170353 | ||||||||
\(204\) | 4.41306 | 0.308976 | ||||||||
\(205\) | −0.114524 | −0.00799868 | ||||||||
\(206\) | 4.31765 | 0.300825 | ||||||||
\(207\) | 4.46341 | 0.310228 | ||||||||
\(208\) | 0.193805 | 0.0134379 | ||||||||
\(209\) | −0.446910 | −0.0309134 | ||||||||
\(210\) | −3.02593 | −0.208809 | ||||||||
\(211\) | −22.3210 | −1.53664 | −0.768319 | − | 0.640067i | \(-0.778907\pi\) | ||||
−0.768319 | + | 0.640067i | \(0.778907\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | −6.92682 | −0.474618 | ||||||||
\(214\) | −14.0342 | −0.959357 | ||||||||
\(215\) | 2.52337 | 0.172092 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.60914 | −0.109235 | ||||||||
\(218\) | −11.7618 | −0.796612 | ||||||||
\(219\) | −8.46217 | −0.571821 | ||||||||
\(220\) | 1.71157 | 0.115394 | ||||||||
\(221\) | −0.855272 | −0.0575318 | ||||||||
\(222\) | −6.71886 | −0.450941 | ||||||||
\(223\) | −12.9146 | −0.864828 | −0.432414 | − | 0.901675i | \(-0.642338\pi\) | ||||
−0.432414 | + | 0.901675i | \(0.642338\pi\) | |||||||
\(224\) | 0.790105 | 0.0527911 | ||||||||
\(225\) | 9.66725 | 0.644483 | ||||||||
\(226\) | 5.70150 | 0.379258 | ||||||||
\(227\) | −7.82435 | −0.519320 | −0.259660 | − | 0.965700i | \(-0.583611\pi\) | ||||
−0.259660 | + | 0.965700i | \(0.583611\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −9.42402 | −0.622757 | −0.311378 | − | 0.950286i | \(-0.600791\pi\) | ||||
−0.311378 | + | 0.950286i | \(0.600791\pi\) | |||||||
\(230\) | −17.0939 | −1.12714 | ||||||||
\(231\) | 0.353105 | 0.0232326 | ||||||||
\(232\) | 3.07194 | 0.201683 | ||||||||
\(233\) | −1.78897 | −0.117199 | −0.0585996 | − | 0.998282i | \(-0.518664\pi\) | ||||
−0.0585996 | + | 0.998282i | \(0.518664\pi\) | |||||||
\(234\) | −0.193805 | −0.0126694 | ||||||||
\(235\) | 25.0783 | 1.63593 | ||||||||
\(236\) | −4.62022 | −0.300751 | ||||||||
\(237\) | −11.7730 | −0.764736 | ||||||||
\(238\) | −3.48678 | −0.226015 | ||||||||
\(239\) | 16.7328 | 1.08236 | 0.541178 | − | 0.840908i | \(-0.317979\pi\) | ||||
0.541178 | + | 0.840908i | \(0.317979\pi\) | |||||||
\(240\) | −3.82978 | −0.247212 | ||||||||
\(241\) | −10.9047 | −0.702434 | −0.351217 | − | 0.936294i | \(-0.614232\pi\) | ||||
−0.351217 | + | 0.936294i | \(0.614232\pi\) | |||||||
\(242\) | 10.8003 | 0.694268 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.27631 | 0.529837 | ||||||||
\(245\) | −24.4177 | −1.55999 | ||||||||
\(246\) | −0.0299034 | −0.00190657 | ||||||||
\(247\) | −0.193805 | −0.0123315 | ||||||||
\(248\) | −2.03661 | −0.129325 | ||||||||
\(249\) | −10.0300 | −0.635626 | ||||||||
\(250\) | −17.8746 | −1.13049 | ||||||||
\(251\) | 28.9380 | 1.82655 | 0.913277 | − | 0.407340i | \(-0.133543\pi\) | ||||
0.913277 | + | 0.407340i | \(0.133543\pi\) | |||||||
\(252\) | −0.790105 | −0.0497719 | ||||||||
\(253\) | 1.99474 | 0.125408 | ||||||||
\(254\) | −1.60126 | −0.100472 | ||||||||
\(255\) | 16.9011 | 1.05839 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.68567 | −0.167528 | −0.0837639 | − | 0.996486i | \(-0.526694\pi\) | ||||
−0.0837639 | + | 0.996486i | \(0.526694\pi\) | |||||||
\(258\) | 0.658880 | 0.0410201 | ||||||||
\(259\) | 5.30861 | 0.329861 | ||||||||
\(260\) | 0.742230 | 0.0460311 | ||||||||
\(261\) | −3.07194 | −0.190149 | ||||||||
\(262\) | −12.8066 | −0.791195 | ||||||||
\(263\) | 4.59887 | 0.283579 | 0.141789 | − | 0.989897i | \(-0.454714\pi\) | ||||
0.141789 | + | 0.989897i | \(0.454714\pi\) | |||||||
\(264\) | 0.446910 | 0.0275054 | ||||||||
\(265\) | 3.82978 | 0.235262 | ||||||||
\(266\) | −0.790105 | −0.0484444 | ||||||||
\(267\) | 14.3347 | 0.877268 | ||||||||
\(268\) | 5.32352 | 0.325186 | ||||||||
\(269\) | −10.6225 | −0.647668 | −0.323834 | − | 0.946114i | \(-0.604972\pi\) | ||||
−0.323834 | + | 0.946114i | \(0.604972\pi\) | |||||||
\(270\) | 3.82978 | 0.233073 | ||||||||
\(271\) | −2.73151 | −0.165927 | −0.0829637 | − | 0.996553i | \(-0.526439\pi\) | ||||
−0.0829637 | + | 0.996553i | \(0.526439\pi\) | |||||||
\(272\) | −4.41306 | −0.267581 | ||||||||
\(273\) | 0.153126 | 0.00926761 | ||||||||
\(274\) | −6.61702 | −0.399749 | ||||||||
\(275\) | 4.32039 | 0.260529 | ||||||||
\(276\) | −4.46341 | −0.268666 | ||||||||
\(277\) | 13.3642 | 0.802980 | 0.401490 | − | 0.915864i | \(-0.368493\pi\) | ||||
0.401490 | + | 0.915864i | \(0.368493\pi\) | |||||||
\(278\) | −0.642811 | −0.0385532 | ||||||||
\(279\) | 2.03661 | 0.121929 | ||||||||
\(280\) | 3.02593 | 0.180834 | ||||||||
\(281\) | 3.02842 | 0.180660 | 0.0903302 | − | 0.995912i | \(-0.471208\pi\) | ||||
0.0903302 | + | 0.995912i | \(0.471208\pi\) | |||||||
\(282\) | 6.54823 | 0.389941 | ||||||||
\(283\) | −17.0084 | −1.01104 | −0.505521 | − | 0.862814i | \(-0.668700\pi\) | ||||
−0.505521 | + | 0.862814i | \(0.668700\pi\) | |||||||
\(284\) | 6.92682 | 0.411031 | ||||||||
\(285\) | 3.82978 | 0.226857 | ||||||||
\(286\) | −0.0866131 | −0.00512154 | ||||||||
\(287\) | 0.0236268 | 0.00139465 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 2.47512 | 0.145595 | ||||||||
\(290\) | 11.7649 | 0.690858 | ||||||||
\(291\) | −13.3255 | −0.781157 | ||||||||
\(292\) | 8.46217 | 0.495211 | ||||||||
\(293\) | −1.69944 | −0.0992826 | −0.0496413 | − | 0.998767i | \(-0.515808\pi\) | ||||
−0.0496413 | + | 0.998767i | \(0.515808\pi\) | |||||||
\(294\) | −6.37573 | −0.371840 | ||||||||
\(295\) | −17.6944 | −1.03021 | ||||||||
\(296\) | 6.71886 | 0.390526 | ||||||||
\(297\) | −0.446910 | −0.0259323 | ||||||||
\(298\) | −0.421009 | −0.0243884 | ||||||||
\(299\) | 0.865029 | 0.0500259 | ||||||||
\(300\) | −9.66725 | −0.558139 | ||||||||
\(301\) | −0.520585 | −0.0300060 | ||||||||
\(302\) | −13.0626 | −0.751670 | ||||||||
\(303\) | −5.76906 | −0.331424 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 31.6965 | 1.81494 | ||||||||
\(306\) | 4.41306 | 0.252278 | ||||||||
\(307\) | 10.9862 | 0.627016 | 0.313508 | − | 0.949585i | \(-0.398496\pi\) | ||||
0.313508 | + | 0.949585i | \(0.398496\pi\) | |||||||
\(308\) | −0.353105 | −0.0201200 | ||||||||
\(309\) | 4.31765 | 0.245622 | ||||||||
\(310\) | −7.79978 | −0.442998 | ||||||||
\(311\) | 12.7816 | 0.724779 | 0.362389 | − | 0.932027i | \(-0.381961\pi\) | ||||
0.362389 | + | 0.932027i | \(0.381961\pi\) | |||||||
\(312\) | 0.193805 | 0.0109720 | ||||||||
\(313\) | −9.87055 | −0.557916 | −0.278958 | − | 0.960303i | \(-0.589989\pi\) | ||||
−0.278958 | + | 0.960303i | \(0.589989\pi\) | |||||||
\(314\) | −14.4289 | −0.814269 | ||||||||
\(315\) | −3.02593 | −0.170492 | ||||||||
\(316\) | 11.7730 | 0.662280 | ||||||||
\(317\) | 6.53804 | 0.367213 | 0.183607 | − | 0.983000i | \(-0.441223\pi\) | ||||
0.183607 | + | 0.983000i | \(0.441223\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | −1.37288 | −0.0768666 | ||||||||
\(320\) | 3.82978 | 0.214091 | ||||||||
\(321\) | −14.0342 | −0.783312 | ||||||||
\(322\) | 3.52656 | 0.196528 | ||||||||
\(323\) | 4.41306 | 0.245549 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.87356 | 0.103926 | ||||||||
\(326\) | −18.1071 | −1.00286 | ||||||||
\(327\) | −11.7618 | −0.650431 | ||||||||
\(328\) | 0.0299034 | 0.00165114 | ||||||||
\(329\) | −5.17379 | −0.285240 | ||||||||
\(330\) | 1.71157 | 0.0942187 | ||||||||
\(331\) | −1.85852 | −0.102154 | −0.0510768 | − | 0.998695i | \(-0.516265\pi\) | ||||
−0.0510768 | + | 0.998695i | \(0.516265\pi\) | |||||||
\(332\) | 10.0300 | 0.550468 | ||||||||
\(333\) | −6.71886 | −0.368192 | ||||||||
\(334\) | −21.5543 | −1.17940 | ||||||||
\(335\) | 20.3880 | 1.11391 | ||||||||
\(336\) | 0.790105 | 0.0431038 | ||||||||
\(337\) | −5.34743 | −0.291293 | −0.145647 | − | 0.989337i | \(-0.546526\pi\) | ||||
−0.145647 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(338\) | 12.9624 | 0.705064 | ||||||||
\(339\) | 5.70150 | 0.309663 | ||||||||
\(340\) | −16.9011 | −0.916590 | ||||||||
\(341\) | 0.910181 | 0.0492891 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 10.5682 | 0.570631 | ||||||||
\(344\) | −0.658880 | −0.0355245 | ||||||||
\(345\) | −17.0939 | −0.920304 | ||||||||
\(346\) | 1.64948 | 0.0886767 | ||||||||
\(347\) | 23.5161 | 1.26241 | 0.631205 | − | 0.775616i | \(-0.282560\pi\) | ||||
0.631205 | + | 0.775616i | \(0.282560\pi\) | |||||||
\(348\) | 3.07194 | 0.164673 | ||||||||
\(349\) | −18.1502 | −0.971556 | −0.485778 | − | 0.874082i | \(-0.661464\pi\) | ||||
−0.485778 | + | 0.874082i | \(0.661464\pi\) | |||||||
\(350\) | 7.63814 | 0.408276 | ||||||||
\(351\) | −0.193805 | −0.0103445 | ||||||||
\(352\) | −0.446910 | −0.0238204 | ||||||||
\(353\) | −9.08780 | −0.483695 | −0.241847 | − | 0.970314i | \(-0.577753\pi\) | ||||
−0.241847 | + | 0.970314i | \(0.577753\pi\) | |||||||
\(354\) | −4.62022 | −0.245562 | ||||||||
\(355\) | 26.5282 | 1.40797 | ||||||||
\(356\) | −14.3347 | −0.759737 | ||||||||
\(357\) | −3.48678 | −0.184540 | ||||||||
\(358\) | 24.5074 | 1.29526 | ||||||||
\(359\) | 12.8542 | 0.678421 | 0.339210 | − | 0.940711i | \(-0.389840\pi\) | ||||
0.339210 | + | 0.940711i | \(0.389840\pi\) | |||||||
\(360\) | −3.82978 | −0.201847 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 8.78529 | 0.461745 | ||||||||
\(363\) | 10.8003 | 0.566867 | ||||||||
\(364\) | −0.153126 | −0.00802598 | ||||||||
\(365\) | 32.4083 | 1.69633 | ||||||||
\(366\) | 8.27631 | 0.432610 | ||||||||
\(367\) | 2.90067 | 0.151414 | 0.0757068 | − | 0.997130i | \(-0.475879\pi\) | ||||
0.0757068 | + | 0.997130i | \(0.475879\pi\) | |||||||
\(368\) | 4.46341 | 0.232671 | ||||||||
\(369\) | −0.0299034 | −0.00155671 | ||||||||
\(370\) | 25.7318 | 1.33773 | ||||||||
\(371\) | −0.790105 | −0.0410202 | ||||||||
\(372\) | −2.03661 | −0.105593 | ||||||||
\(373\) | −21.8174 | −1.12966 | −0.564832 | − | 0.825206i | \(-0.691059\pi\) | ||||
−0.564832 | + | 0.825206i | \(0.691059\pi\) | |||||||
\(374\) | 1.97224 | 0.101982 | ||||||||
\(375\) | −17.8746 | −0.923038 | ||||||||
\(376\) | −6.54823 | −0.337699 | ||||||||
\(377\) | −0.595357 | −0.0306624 | ||||||||
\(378\) | −0.790105 | −0.0406386 | ||||||||
\(379\) | −21.1583 | −1.08683 | −0.543415 | − | 0.839464i | \(-0.682869\pi\) | ||||
−0.543415 | + | 0.839464i | \(0.682869\pi\) | |||||||
\(380\) | −3.82978 | −0.196464 | ||||||||
\(381\) | −1.60126 | −0.0820350 | ||||||||
\(382\) | 7.06173 | 0.361310 | ||||||||
\(383\) | 8.88087 | 0.453791 | 0.226896 | − | 0.973919i | \(-0.427142\pi\) | ||||
0.226896 | + | 0.973919i | \(0.427142\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.35232 | −0.0689205 | ||||||||
\(386\) | −8.35398 | −0.425206 | ||||||||
\(387\) | 0.658880 | 0.0334928 | ||||||||
\(388\) | 13.3255 | 0.676502 | ||||||||
\(389\) | 25.4647 | 1.29111 | 0.645556 | − | 0.763713i | \(-0.276626\pi\) | ||||
0.645556 | + | 0.763713i | \(0.276626\pi\) | |||||||
\(390\) | 0.742230 | 0.0375843 | ||||||||
\(391\) | −19.6973 | −0.996135 | ||||||||
\(392\) | 6.37573 | 0.322023 | ||||||||
\(393\) | −12.8066 | −0.646008 | ||||||||
\(394\) | −10.5400 | −0.530996 | ||||||||
\(395\) | 45.0879 | 2.26862 | ||||||||
\(396\) | 0.446910 | 0.0224580 | ||||||||
\(397\) | −0.921126 | −0.0462300 | −0.0231150 | − | 0.999733i | \(-0.507358\pi\) | ||||
−0.0231150 | + | 0.999733i | \(0.507358\pi\) | |||||||
\(398\) | 14.2303 | 0.713302 | ||||||||
\(399\) | −0.790105 | −0.0395547 | ||||||||
\(400\) | 9.66725 | 0.483362 | ||||||||
\(401\) | 26.0639 | 1.30157 | 0.650785 | − | 0.759262i | \(-0.274440\pi\) | ||||
0.650785 | + | 0.759262i | \(0.274440\pi\) | |||||||
\(402\) | 5.32352 | 0.265513 | ||||||||
\(403\) | 0.394705 | 0.0196616 | ||||||||
\(404\) | 5.76906 | 0.287021 | ||||||||
\(405\) | 3.82978 | 0.190304 | ||||||||
\(406\) | −2.42716 | −0.120458 | ||||||||
\(407\) | −3.00272 | −0.148840 | ||||||||
\(408\) | −4.41306 | −0.218479 | ||||||||
\(409\) | 26.3759 | 1.30420 | 0.652102 | − | 0.758131i | \(-0.273887\pi\) | ||||
0.652102 | + | 0.758131i | \(0.273887\pi\) | |||||||
\(410\) | 0.114524 | 0.00565592 | ||||||||
\(411\) | −6.61702 | −0.326393 | ||||||||
\(412\) | −4.31765 | −0.212715 | ||||||||
\(413\) | 3.65046 | 0.179627 | ||||||||
\(414\) | −4.46341 | −0.219365 | ||||||||
\(415\) | 38.4127 | 1.88561 | ||||||||
\(416\) | −0.193805 | −0.00950205 | ||||||||
\(417\) | −0.642811 | −0.0314786 | ||||||||
\(418\) | 0.446910 | 0.0218591 | ||||||||
\(419\) | 15.8308 | 0.773383 | 0.386692 | − | 0.922209i | \(-0.373618\pi\) | ||||
0.386692 | + | 0.922209i | \(0.373618\pi\) | |||||||
\(420\) | 3.02593 | 0.147650 | ||||||||
\(421\) | 18.9690 | 0.924490 | 0.462245 | − | 0.886752i | \(-0.347044\pi\) | ||||
0.462245 | + | 0.886752i | \(0.347044\pi\) | |||||||
\(422\) | 22.3210 | 1.08657 | ||||||||
\(423\) | 6.54823 | 0.318386 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | −42.6622 | −2.06942 | ||||||||
\(426\) | 6.92682 | 0.335605 | ||||||||
\(427\) | −6.53915 | −0.316452 | ||||||||
\(428\) | 14.0342 | 0.678368 | ||||||||
\(429\) | −0.0866131 | −0.00418172 | ||||||||
\(430\) | −2.52337 | −0.121688 | ||||||||
\(431\) | 15.9307 | 0.767357 | 0.383678 | − | 0.923467i | \(-0.374657\pi\) | ||||
0.383678 | + | 0.923467i | \(0.374657\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.6597 | −0.752555 | −0.376277 | − | 0.926507i | \(-0.622796\pi\) | ||||
−0.376277 | + | 0.926507i | \(0.622796\pi\) | |||||||
\(434\) | 1.60914 | 0.0772410 | ||||||||
\(435\) | 11.7649 | 0.564083 | ||||||||
\(436\) | 11.7618 | 0.563289 | ||||||||
\(437\) | −4.46341 | −0.213514 | ||||||||
\(438\) | 8.46217 | 0.404338 | ||||||||
\(439\) | −16.6208 | −0.793268 | −0.396634 | − | 0.917977i | \(-0.629822\pi\) | ||||
−0.396634 | + | 0.917977i | \(0.629822\pi\) | |||||||
\(440\) | −1.71157 | −0.0815958 | ||||||||
\(441\) | −6.37573 | −0.303606 | ||||||||
\(442\) | 0.855272 | 0.0406811 | ||||||||
\(443\) | −12.9754 | −0.616481 | −0.308240 | − | 0.951308i | \(-0.599740\pi\) | ||||
−0.308240 | + | 0.951308i | \(0.599740\pi\) | |||||||
\(444\) | 6.71886 | 0.318863 | ||||||||
\(445\) | −54.8987 | −2.60245 | ||||||||
\(446\) | 12.9146 | 0.611526 | ||||||||
\(447\) | −0.421009 | −0.0199131 | ||||||||
\(448\) | −0.790105 | −0.0373289 | ||||||||
\(449\) | −1.70560 | −0.0804921 | −0.0402460 | − | 0.999190i | \(-0.512814\pi\) | ||||
−0.0402460 | + | 0.999190i | \(0.512814\pi\) | |||||||
\(450\) | −9.66725 | −0.455718 | ||||||||
\(451\) | −0.0133641 | −0.000629292 0 | ||||||||
\(452\) | −5.70150 | −0.268176 | ||||||||
\(453\) | −13.0626 | −0.613736 | ||||||||
\(454\) | 7.82435 | 0.367215 | ||||||||
\(455\) | −0.586439 | −0.0274927 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −15.7323 | −0.735928 | −0.367964 | − | 0.929840i | \(-0.619945\pi\) | ||||
−0.367964 | + | 0.929840i | \(0.619945\pi\) | |||||||
\(458\) | 9.42402 | 0.440355 | ||||||||
\(459\) | 4.41306 | 0.205984 | ||||||||
\(460\) | 17.0939 | 0.797007 | ||||||||
\(461\) | 30.5681 | 1.42370 | 0.711850 | − | 0.702331i | \(-0.247857\pi\) | ||||
0.711850 | + | 0.702331i | \(0.247857\pi\) | |||||||
\(462\) | −0.353105 | −0.0164280 | ||||||||
\(463\) | −4.71049 | −0.218915 | −0.109457 | − | 0.993991i | \(-0.534911\pi\) | ||||
−0.109457 | + | 0.993991i | \(0.534911\pi\) | |||||||
\(464\) | −3.07194 | −0.142611 | ||||||||
\(465\) | −7.79978 | −0.361706 | ||||||||
\(466\) | 1.78897 | 0.0828723 | ||||||||
\(467\) | 35.6878 | 1.65143 | 0.825716 | − | 0.564086i | \(-0.190771\pi\) | ||||
0.825716 | + | 0.564086i | \(0.190771\pi\) | |||||||
\(468\) | 0.193805 | 0.00895862 | ||||||||
\(469\) | −4.20614 | −0.194222 | ||||||||
\(470\) | −25.0783 | −1.15678 | ||||||||
\(471\) | −14.4289 | −0.664848 | ||||||||
\(472\) | 4.62022 | 0.212663 | ||||||||
\(473\) | 0.294460 | 0.0135393 | ||||||||
\(474\) | 11.7730 | 0.540750 | ||||||||
\(475\) | −9.66725 | −0.443564 | ||||||||
\(476\) | 3.48678 | 0.159816 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | −16.7328 | −0.765341 | ||||||||
\(479\) | 26.4955 | 1.21061 | 0.605306 | − | 0.795993i | \(-0.293051\pi\) | ||||
0.605306 | + | 0.795993i | \(0.293051\pi\) | |||||||
\(480\) | 3.82978 | 0.174805 | ||||||||
\(481\) | −1.30215 | −0.0593728 | ||||||||
\(482\) | 10.9047 | 0.496696 | ||||||||
\(483\) | 3.52656 | 0.160464 | ||||||||
\(484\) | −10.8003 | −0.490921 | ||||||||
\(485\) | 51.0339 | 2.31733 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −6.22402 | −0.282037 | −0.141019 | − | 0.990007i | \(-0.545038\pi\) | ||||
−0.141019 | + | 0.990007i | \(0.545038\pi\) | |||||||
\(488\) | −8.27631 | −0.374651 | ||||||||
\(489\) | −18.1071 | −0.818830 | ||||||||
\(490\) | 24.4177 | 1.10308 | ||||||||
\(491\) | −3.70736 | −0.167311 | −0.0836555 | − | 0.996495i | \(-0.526660\pi\) | ||||
−0.0836555 | + | 0.996495i | \(0.526660\pi\) | |||||||
\(492\) | 0.0299034 | 0.00134815 | ||||||||
\(493\) | 13.5567 | 0.610562 | ||||||||
\(494\) | 0.193805 | 0.00871968 | ||||||||
\(495\) | 1.71157 | 0.0769292 | ||||||||
\(496\) | 2.03661 | 0.0914465 | ||||||||
\(497\) | −5.47291 | −0.245494 | ||||||||
\(498\) | 10.0300 | 0.449455 | ||||||||
\(499\) | −26.8514 | −1.20203 | −0.601016 | − | 0.799237i | \(-0.705237\pi\) | ||||
−0.601016 | + | 0.799237i | \(0.705237\pi\) | |||||||
\(500\) | 17.8746 | 0.799374 | ||||||||
\(501\) | −21.5543 | −0.962974 | ||||||||
\(502\) | −28.9380 | −1.29157 | ||||||||
\(503\) | −14.8535 | −0.662287 | −0.331143 | − | 0.943580i | \(-0.607434\pi\) | ||||
−0.331143 | + | 0.943580i | \(0.607434\pi\) | |||||||
\(504\) | 0.790105 | 0.0351941 | ||||||||
\(505\) | 22.0943 | 0.983182 | ||||||||
\(506\) | −1.99474 | −0.0886770 | ||||||||
\(507\) | 12.9624 | 0.575682 | ||||||||
\(508\) | 1.60126 | 0.0710444 | ||||||||
\(509\) | 16.0631 | 0.711984 | 0.355992 | − | 0.934489i | \(-0.384143\pi\) | ||||
0.355992 | + | 0.934489i | \(0.384143\pi\) | |||||||
\(510\) | −16.9011 | −0.748392 | ||||||||
\(511\) | −6.68601 | −0.295771 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 2.68567 | 0.118460 | ||||||||
\(515\) | −16.5357 | −0.728648 | ||||||||
\(516\) | −0.658880 | −0.0290056 | ||||||||
\(517\) | 2.92647 | 0.128706 | ||||||||
\(518\) | −5.30861 | −0.233247 | ||||||||
\(519\) | 1.64948 | 0.0724043 | ||||||||
\(520\) | −0.742230 | −0.0325489 | ||||||||
\(521\) | −38.4530 | −1.68466 | −0.842328 | − | 0.538966i | \(-0.818815\pi\) | ||||
−0.842328 | + | 0.538966i | \(0.818815\pi\) | |||||||
\(522\) | 3.07194 | 0.134455 | ||||||||
\(523\) | 4.20178 | 0.183731 | 0.0918656 | − | 0.995771i | \(-0.470717\pi\) | ||||
0.0918656 | + | 0.995771i | \(0.470717\pi\) | |||||||
\(524\) | 12.8066 | 0.559459 | ||||||||
\(525\) | 7.63814 | 0.333356 | ||||||||
\(526\) | −4.59887 | −0.200520 | ||||||||
\(527\) | −8.98769 | −0.391510 | ||||||||
\(528\) | −0.446910 | −0.0194492 | ||||||||
\(529\) | −3.07798 | −0.133825 | ||||||||
\(530\) | −3.82978 | −0.166355 | ||||||||
\(531\) | −4.62022 | −0.200500 | ||||||||
\(532\) | 0.790105 | 0.0342554 | ||||||||
\(533\) | −0.00579542 | −0.000251028 0 | ||||||||
\(534\) | −14.3347 | −0.620322 | ||||||||
\(535\) | 53.7479 | 2.32372 | ||||||||
\(536\) | −5.32352 | −0.229941 | ||||||||
\(537\) | 24.5074 | 1.05757 | ||||||||
\(538\) | 10.6225 | 0.457970 | ||||||||
\(539\) | −2.84938 | −0.122731 | ||||||||
\(540\) | −3.82978 | −0.164808 | ||||||||
\(541\) | −42.0824 | −1.80926 | −0.904631 | − | 0.426196i | \(-0.859853\pi\) | ||||
−0.904631 | + | 0.426196i | \(0.859853\pi\) | |||||||
\(542\) | 2.73151 | 0.117328 | ||||||||
\(543\) | 8.78529 | 0.377013 | ||||||||
\(544\) | 4.41306 | 0.189209 | ||||||||
\(545\) | 45.0453 | 1.92953 | ||||||||
\(546\) | −0.153126 | −0.00655319 | ||||||||
\(547\) | 7.95114 | 0.339966 | 0.169983 | − | 0.985447i | \(-0.445629\pi\) | ||||
0.169983 | + | 0.985447i | \(0.445629\pi\) | |||||||
\(548\) | 6.61702 | 0.282665 | ||||||||
\(549\) | 8.27631 | 0.353224 | ||||||||
\(550\) | −4.32039 | −0.184222 | ||||||||
\(551\) | 3.07194 | 0.130869 | ||||||||
\(552\) | 4.46341 | 0.189975 | ||||||||
\(553\) | −9.30187 | −0.395556 | ||||||||
\(554\) | −13.3642 | −0.567792 | ||||||||
\(555\) | 25.7318 | 1.09225 | ||||||||
\(556\) | 0.642811 | 0.0272613 | ||||||||
\(557\) | 9.35756 | 0.396493 | 0.198246 | − | 0.980152i | \(-0.436475\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436475\pi\) | |||||||
\(558\) | −2.03661 | −0.0862166 | ||||||||
\(559\) | 0.127694 | 0.00540088 | ||||||||
\(560\) | −3.02593 | −0.127869 | ||||||||
\(561\) | 1.97224 | 0.0832680 | ||||||||
\(562\) | −3.02842 | −0.127746 | ||||||||
\(563\) | 20.1890 | 0.850864 | 0.425432 | − | 0.904990i | \(-0.360122\pi\) | ||||
0.425432 | + | 0.904990i | \(0.360122\pi\) | |||||||
\(564\) | −6.54823 | −0.275730 | ||||||||
\(565\) | −21.8355 | −0.918628 | ||||||||
\(566\) | 17.0084 | 0.714915 | ||||||||
\(567\) | −0.790105 | −0.0331813 | ||||||||
\(568\) | −6.92682 | −0.290643 | ||||||||
\(569\) | 5.00784 | 0.209939 | 0.104970 | − | 0.994475i | \(-0.466525\pi\) | ||||
0.104970 | + | 0.994475i | \(0.466525\pi\) | |||||||
\(570\) | −3.82978 | −0.160412 | ||||||||
\(571\) | −9.85105 | −0.412254 | −0.206127 | − | 0.978525i | \(-0.566086\pi\) | ||||
−0.206127 | + | 0.978525i | \(0.566086\pi\) | |||||||
\(572\) | 0.0866131 | 0.00362148 | ||||||||
\(573\) | 7.06173 | 0.295008 | ||||||||
\(574\) | −0.0236268 | −0.000986166 0 | ||||||||
\(575\) | 43.1489 | 1.79943 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 45.6607 | 1.90088 | 0.950439 | − | 0.310911i | \(-0.100634\pi\) | ||||
0.950439 | + | 0.310911i | \(0.100634\pi\) | |||||||
\(578\) | −2.47512 | −0.102952 | ||||||||
\(579\) | −8.35398 | −0.347179 | ||||||||
\(580\) | −11.7649 | −0.488510 | ||||||||
\(581\) | −7.92475 | −0.328774 | ||||||||
\(582\) | 13.3255 | 0.552361 | ||||||||
\(583\) | 0.446910 | 0.0185091 | ||||||||
\(584\) | −8.46217 | −0.350167 | ||||||||
\(585\) | 0.742230 | 0.0306874 | ||||||||
\(586\) | 1.69944 | 0.0702034 | ||||||||
\(587\) | −30.1982 | −1.24641 | −0.623207 | − | 0.782057i | \(-0.714171\pi\) | ||||
−0.623207 | + | 0.782057i | \(0.714171\pi\) | |||||||
\(588\) | 6.37573 | 0.262931 | ||||||||
\(589\) | −2.03661 | −0.0839171 | ||||||||
\(590\) | 17.6944 | 0.728468 | ||||||||
\(591\) | −10.5400 | −0.433556 | ||||||||
\(592\) | −6.71886 | −0.276144 | ||||||||
\(593\) | 13.9809 | 0.574128 | 0.287064 | − | 0.957911i | \(-0.407321\pi\) | ||||
0.287064 | + | 0.957911i | \(0.407321\pi\) | |||||||
\(594\) | 0.446910 | 0.0183369 | ||||||||
\(595\) | 13.3536 | 0.547445 | ||||||||
\(596\) | 0.421009 | 0.0172452 | ||||||||
\(597\) | 14.2303 | 0.582409 | ||||||||
\(598\) | −0.865029 | −0.0353737 | ||||||||
\(599\) | −31.0504 | −1.26868 | −0.634342 | − | 0.773053i | \(-0.718729\pi\) | ||||
−0.634342 | + | 0.773053i | \(0.718729\pi\) | |||||||
\(600\) | 9.66725 | 0.394664 | ||||||||
\(601\) | 36.1523 | 1.47468 | 0.737342 | − | 0.675519i | \(-0.236080\pi\) | ||||
0.737342 | + | 0.675519i | \(0.236080\pi\) | |||||||
\(602\) | 0.520585 | 0.0212174 | ||||||||
\(603\) | 5.32352 | 0.216791 | ||||||||
\(604\) | 13.0626 | 0.531511 | ||||||||
\(605\) | −41.3627 | −1.68163 | ||||||||
\(606\) | 5.76906 | 0.234352 | ||||||||
\(607\) | 12.7071 | 0.515763 | 0.257882 | − | 0.966176i | \(-0.416976\pi\) | ||||
0.257882 | + | 0.966176i | \(0.416976\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −2.42716 | −0.0983534 | ||||||||
\(610\) | −31.6965 | −1.28335 | ||||||||
\(611\) | 1.26908 | 0.0513414 | ||||||||
\(612\) | −4.41306 | −0.178387 | ||||||||
\(613\) | −10.8643 | −0.438803 | −0.219402 | − | 0.975635i | \(-0.570411\pi\) | ||||
−0.219402 | + | 0.975635i | \(0.570411\pi\) | |||||||
\(614\) | −10.9862 | −0.443368 | ||||||||
\(615\) | 0.114524 | 0.00461804 | ||||||||
\(616\) | 0.353105 | 0.0142270 | ||||||||
\(617\) | −32.6827 | −1.31576 | −0.657878 | − | 0.753125i | \(-0.728546\pi\) | ||||
−0.657878 | + | 0.753125i | \(0.728546\pi\) | |||||||
\(618\) | −4.31765 | −0.173681 | ||||||||
\(619\) | 8.72781 | 0.350800 | 0.175400 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175400 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(620\) | 7.79978 | 0.313247 | ||||||||
\(621\) | −4.46341 | −0.179110 | ||||||||
\(622\) | −12.7816 | −0.512496 | ||||||||
\(623\) | 11.3259 | 0.453763 | ||||||||
\(624\) | −0.193805 | −0.00775839 | ||||||||
\(625\) | 20.1195 | 0.804778 | ||||||||
\(626\) | 9.87055 | 0.394506 | ||||||||
\(627\) | 0.446910 | 0.0178478 | ||||||||
\(628\) | 14.4289 | 0.575775 | ||||||||
\(629\) | 29.6508 | 1.18225 | ||||||||
\(630\) | 3.02593 | 0.120556 | ||||||||
\(631\) | 27.2592 | 1.08517 | 0.542586 | − | 0.840000i | \(-0.317445\pi\) | ||||
0.542586 | + | 0.840000i | \(0.317445\pi\) | |||||||
\(632\) | −11.7730 | −0.468303 | ||||||||
\(633\) | 22.3210 | 0.887179 | ||||||||
\(634\) | −6.53804 | −0.259659 | ||||||||
\(635\) | 6.13248 | 0.243360 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −1.23565 | −0.0489581 | ||||||||
\(638\) | 1.37288 | 0.0543529 | ||||||||
\(639\) | 6.92682 | 0.274021 | ||||||||
\(640\) | −3.82978 | −0.151386 | ||||||||
\(641\) | −13.8963 | −0.548870 | −0.274435 | − | 0.961606i | \(-0.588491\pi\) | ||||
−0.274435 | + | 0.961606i | \(0.588491\pi\) | |||||||
\(642\) | 14.0342 | 0.553885 | ||||||||
\(643\) | 3.63156 | 0.143215 | 0.0716073 | − | 0.997433i | \(-0.477187\pi\) | ||||
0.0716073 | + | 0.997433i | \(0.477187\pi\) | |||||||
\(644\) | −3.52656 | −0.138966 | ||||||||
\(645\) | −2.52337 | −0.0993576 | ||||||||
\(646\) | −4.41306 | −0.173630 | ||||||||
\(647\) | 39.8219 | 1.56556 | 0.782780 | − | 0.622299i | \(-0.213801\pi\) | ||||
0.782780 | + | 0.622299i | \(0.213801\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −2.06482 | −0.0810512 | ||||||||
\(650\) | −1.87356 | −0.0734870 | ||||||||
\(651\) | 1.60914 | 0.0630670 | ||||||||
\(652\) | 18.1071 | 0.709127 | ||||||||
\(653\) | −3.81742 | −0.149387 | −0.0746937 | − | 0.997207i | \(-0.523798\pi\) | ||||
−0.0746937 | + | 0.997207i | \(0.523798\pi\) | |||||||
\(654\) | 11.7618 | 0.459924 | ||||||||
\(655\) | 49.0465 | 1.91641 | ||||||||
\(656\) | −0.0299034 | −0.00116753 | ||||||||
\(657\) | 8.46217 | 0.330141 | ||||||||
\(658\) | 5.17379 | 0.201695 | ||||||||
\(659\) | 29.3038 | 1.14151 | 0.570757 | − | 0.821119i | \(-0.306650\pi\) | ||||
0.570757 | + | 0.821119i | \(0.306650\pi\) | |||||||
\(660\) | −1.71157 | −0.0666227 | ||||||||
\(661\) | −2.97186 | −0.115592 | −0.0577959 | − | 0.998328i | \(-0.518407\pi\) | ||||
−0.0577959 | + | 0.998328i | \(0.518407\pi\) | |||||||
\(662\) | 1.85852 | 0.0722334 | ||||||||
\(663\) | 0.855272 | 0.0332160 | ||||||||
\(664\) | −10.0300 | −0.389240 | ||||||||
\(665\) | 3.02593 | 0.117341 | ||||||||
\(666\) | 6.71886 | 0.260351 | ||||||||
\(667\) | −13.7113 | −0.530905 | ||||||||
\(668\) | 21.5543 | 0.833960 | ||||||||
\(669\) | 12.9146 | 0.499309 | ||||||||
\(670\) | −20.3880 | −0.787655 | ||||||||
\(671\) | 3.69876 | 0.142789 | ||||||||
\(672\) | −0.790105 | −0.0304790 | ||||||||
\(673\) | 25.1267 | 0.968564 | 0.484282 | − | 0.874912i | \(-0.339081\pi\) | ||||
0.484282 | + | 0.874912i | \(0.339081\pi\) | |||||||
\(674\) | 5.34743 | 0.205975 | ||||||||
\(675\) | −9.66725 | −0.372093 | ||||||||
\(676\) | −12.9624 | −0.498555 | ||||||||
\(677\) | −11.5563 | −0.444143 | −0.222072 | − | 0.975030i | \(-0.571282\pi\) | ||||
−0.222072 | + | 0.975030i | \(0.571282\pi\) | |||||||
\(678\) | −5.70150 | −0.218965 | ||||||||
\(679\) | −10.5286 | −0.404050 | ||||||||
\(680\) | 16.9011 | 0.648127 | ||||||||
\(681\) | 7.82435 | 0.299830 | ||||||||
\(682\) | −0.910181 | −0.0348526 | ||||||||
\(683\) | −48.6571 | −1.86181 | −0.930907 | − | 0.365258i | \(-0.880981\pi\) | ||||
−0.930907 | + | 0.365258i | \(0.880981\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 25.3418 | 0.968259 | ||||||||
\(686\) | −10.5682 | −0.403497 | ||||||||
\(687\) | 9.42402 | 0.359549 | ||||||||
\(688\) | 0.658880 | 0.0251196 | ||||||||
\(689\) | 0.193805 | 0.00738337 | ||||||||
\(690\) | 17.0939 | 0.650753 | ||||||||
\(691\) | −10.2327 | −0.389272 | −0.194636 | − | 0.980876i | \(-0.562353\pi\) | ||||
−0.194636 | + | 0.980876i | \(0.562353\pi\) | |||||||
\(692\) | −1.64948 | −0.0627039 | ||||||||
\(693\) | −0.353105 | −0.0134134 | ||||||||
\(694\) | −23.5161 | −0.892659 | ||||||||
\(695\) | 2.46183 | 0.0933824 | ||||||||
\(696\) | −3.07194 | −0.116442 | ||||||||
\(697\) | 0.131966 | 0.00499856 | ||||||||
\(698\) | 18.1502 | 0.686994 | ||||||||
\(699\) | 1.78897 | 0.0676650 | ||||||||
\(700\) | −7.63814 | −0.288695 | ||||||||
\(701\) | 21.7552 | 0.821681 | 0.410841 | − | 0.911707i | \(-0.365235\pi\) | ||||
0.410841 | + | 0.911707i | \(0.365235\pi\) | |||||||
\(702\) | 0.193805 | 0.00731468 | ||||||||
\(703\) | 6.71886 | 0.253407 | ||||||||
\(704\) | 0.446910 | 0.0168435 | ||||||||
\(705\) | −25.0783 | −0.944504 | ||||||||
\(706\) | 9.08780 | 0.342024 | ||||||||
\(707\) | −4.55816 | −0.171427 | ||||||||
\(708\) | 4.62022 | 0.173638 | ||||||||
\(709\) | −3.93319 | −0.147714 | −0.0738571 | − | 0.997269i | \(-0.523531\pi\) | ||||
−0.0738571 | + | 0.997269i | \(0.523531\pi\) | |||||||
\(710\) | −26.5282 | −0.995586 | ||||||||
\(711\) | 11.7730 | 0.441520 | ||||||||
\(712\) | 14.3347 | 0.537215 | ||||||||
\(713\) | 9.09023 | 0.340432 | ||||||||
\(714\) | 3.48678 | 0.130490 | ||||||||
\(715\) | 0.331710 | 0.0124052 | ||||||||
\(716\) | −24.5074 | −0.915885 | ||||||||
\(717\) | −16.7328 | −0.624898 | ||||||||
\(718\) | −12.8542 | −0.479716 | ||||||||
\(719\) | 25.9932 | 0.969382 | 0.484691 | − | 0.874685i | \(-0.338932\pi\) | ||||
0.484691 | + | 0.874685i | \(0.338932\pi\) | |||||||
\(720\) | 3.82978 | 0.142728 | ||||||||
\(721\) | 3.41140 | 0.127047 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 10.9047 | 0.405550 | ||||||||
\(724\) | −8.78529 | −0.326503 | ||||||||
\(725\) | −29.6972 | −1.10293 | ||||||||
\(726\) | −10.8003 | −0.400836 | ||||||||
\(727\) | 14.5643 | 0.540159 | 0.270079 | − | 0.962838i | \(-0.412950\pi\) | ||||
0.270079 | + | 0.962838i | \(0.412950\pi\) | |||||||
\(728\) | 0.153126 | 0.00567523 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −32.4083 | −1.19949 | ||||||||
\(731\) | −2.90768 | −0.107544 | ||||||||
\(732\) | −8.27631 | −0.305901 | ||||||||
\(733\) | −27.1835 | −1.00405 | −0.502023 | − | 0.864854i | \(-0.667411\pi\) | ||||
−0.502023 | + | 0.864854i | \(0.667411\pi\) | |||||||
\(734\) | −2.90067 | −0.107066 | ||||||||
\(735\) | 24.4177 | 0.900660 | ||||||||
\(736\) | −4.46341 | −0.164523 | ||||||||
\(737\) | 2.37913 | 0.0876365 | ||||||||
\(738\) | 0.0299034 | 0.00110076 | ||||||||
\(739\) | 3.08182 | 0.113367 | 0.0566833 | − | 0.998392i | \(-0.481947\pi\) | ||||
0.0566833 | + | 0.998392i | \(0.481947\pi\) | |||||||
\(740\) | −25.7318 | −0.945920 | ||||||||
\(741\) | 0.193805 | 0.00711959 | ||||||||
\(742\) | 0.790105 | 0.0290057 | ||||||||
\(743\) | 40.4728 | 1.48480 | 0.742401 | − | 0.669956i | \(-0.233687\pi\) | ||||
0.742401 | + | 0.669956i | \(0.233687\pi\) | |||||||
\(744\) | 2.03661 | 0.0746658 | ||||||||
\(745\) | 1.61238 | 0.0590729 | ||||||||
\(746\) | 21.8174 | 0.798793 | ||||||||
\(747\) | 10.0300 | 0.366979 | ||||||||
\(748\) | −1.97224 | −0.0721122 | ||||||||
\(749\) | −11.0885 | −0.405164 | ||||||||
\(750\) | 17.8746 | 0.652686 | ||||||||
\(751\) | 19.7039 | 0.719006 | 0.359503 | − | 0.933144i | \(-0.382946\pi\) | ||||
0.359503 | + | 0.933144i | \(0.382946\pi\) | |||||||
\(752\) | 6.54823 | 0.238789 | ||||||||
\(753\) | −28.9380 | −1.05456 | ||||||||
\(754\) | 0.595357 | 0.0216816 | ||||||||
\(755\) | 50.0270 | 1.82067 | ||||||||
\(756\) | 0.790105 | 0.0287358 | ||||||||
\(757\) | 7.27408 | 0.264381 | 0.132190 | − | 0.991224i | \(-0.457799\pi\) | ||||
0.132190 | + | 0.991224i | \(0.457799\pi\) | |||||||
\(758\) | 21.1583 | 0.768504 | ||||||||
\(759\) | −1.99474 | −0.0724045 | ||||||||
\(760\) | 3.82978 | 0.138921 | ||||||||
\(761\) | −16.4669 | −0.596924 | −0.298462 | − | 0.954421i | \(-0.596474\pi\) | ||||
−0.298462 | + | 0.954421i | \(0.596474\pi\) | |||||||
\(762\) | 1.60126 | 0.0580075 | ||||||||
\(763\) | −9.29308 | −0.336432 | ||||||||
\(764\) | −7.06173 | −0.255485 | ||||||||
\(765\) | −16.9011 | −0.611060 | ||||||||
\(766\) | −8.88087 | −0.320879 | ||||||||
\(767\) | −0.895419 | −0.0323317 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 29.1904 | 1.05263 | 0.526316 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526316 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(770\) | 1.35232 | 0.0487341 | ||||||||
\(771\) | 2.68567 | 0.0967222 | ||||||||
\(772\) | 8.35398 | 0.300666 | ||||||||
\(773\) | 37.0093 | 1.33113 | 0.665566 | − | 0.746339i | \(-0.268190\pi\) | ||||
0.665566 | + | 0.746339i | \(0.268190\pi\) | |||||||
\(774\) | −0.658880 | −0.0236830 | ||||||||
\(775\) | 19.6884 | 0.707229 | ||||||||
\(776\) | −13.3255 | −0.478359 | ||||||||
\(777\) | −5.30861 | −0.190445 | ||||||||
\(778\) | −25.4647 | −0.912954 | ||||||||
\(779\) | 0.0299034 | 0.00107140 | ||||||||
\(780\) | −0.742230 | −0.0265761 | ||||||||
\(781\) | 3.09566 | 0.110771 | ||||||||
\(782\) | 19.6973 | 0.704374 | ||||||||
\(783\) | 3.07194 | 0.109782 | ||||||||
\(784\) | −6.37573 | −0.227705 | ||||||||
\(785\) | 55.2595 | 1.97230 | ||||||||
\(786\) | 12.8066 | 0.456796 | ||||||||
\(787\) | 14.3131 | 0.510205 | 0.255103 | − | 0.966914i | \(-0.417891\pi\) | ||||
0.255103 | + | 0.966914i | \(0.417891\pi\) | |||||||
\(788\) | 10.5400 | 0.375471 | ||||||||
\(789\) | −4.59887 | −0.163724 | ||||||||
\(790\) | −45.0879 | −1.60415 | ||||||||
\(791\) | 4.50479 | 0.160172 | ||||||||
\(792\) | −0.446910 | −0.0158802 | ||||||||
\(793\) | 1.60399 | 0.0569593 | ||||||||
\(794\) | 0.921126 | 0.0326895 | ||||||||
\(795\) | −3.82978 | −0.135828 | ||||||||
\(796\) | −14.2303 | −0.504381 | ||||||||
\(797\) | 40.3661 | 1.42984 | 0.714921 | − | 0.699205i | \(-0.246463\pi\) | ||||
0.714921 | + | 0.699205i | \(0.246463\pi\) | |||||||
\(798\) | 0.790105 | 0.0279694 | ||||||||
\(799\) | −28.8978 | −1.02233 | ||||||||
\(800\) | −9.66725 | −0.341789 | ||||||||
\(801\) | −14.3347 | −0.506491 | ||||||||
\(802\) | −26.0639 | −0.920349 | ||||||||
\(803\) | 3.78183 | 0.133458 | ||||||||
\(804\) | −5.32352 | −0.187746 | ||||||||
\(805\) | −13.5060 | −0.476023 | ||||||||
\(806\) | −0.394705 | −0.0139029 | ||||||||
\(807\) | 10.6225 | 0.373931 | ||||||||
\(808\) | −5.76906 | −0.202955 | ||||||||
\(809\) | 3.57253 | 0.125603 | 0.0628017 | − | 0.998026i | \(-0.479996\pi\) | ||||
0.0628017 | + | 0.998026i | \(0.479996\pi\) | |||||||
\(810\) | −3.82978 | −0.134565 | ||||||||
\(811\) | −48.6333 | −1.70775 | −0.853874 | − | 0.520480i | \(-0.825753\pi\) | ||||
−0.853874 | + | 0.520480i | \(0.825753\pi\) | |||||||
\(812\) | 2.42716 | 0.0851765 | ||||||||
\(813\) | 2.73151 | 0.0957983 | ||||||||
\(814\) | 3.00272 | 0.105245 | ||||||||
\(815\) | 69.3461 | 2.42909 | ||||||||
\(816\) | 4.41306 | 0.154488 | ||||||||
\(817\) | −0.658880 | −0.0230513 | ||||||||
\(818\) | −26.3759 | −0.922212 | ||||||||
\(819\) | −0.153126 | −0.00535065 | ||||||||
\(820\) | −0.114524 | −0.00399934 | ||||||||
\(821\) | 21.1794 | 0.739167 | 0.369583 | − | 0.929198i | \(-0.379500\pi\) | ||||
0.369583 | + | 0.929198i | \(0.379500\pi\) | |||||||
\(822\) | 6.61702 | 0.230795 | ||||||||
\(823\) | 48.0999 | 1.67666 | 0.838328 | − | 0.545166i | \(-0.183533\pi\) | ||||
0.838328 | + | 0.545166i | \(0.183533\pi\) | |||||||
\(824\) | 4.31765 | 0.150412 | ||||||||
\(825\) | −4.32039 | −0.150417 | ||||||||
\(826\) | −3.65046 | −0.127016 | ||||||||
\(827\) | 39.7274 | 1.38146 | 0.690729 | − | 0.723113i | \(-0.257290\pi\) | ||||
0.690729 | + | 0.723113i | \(0.257290\pi\) | |||||||
\(828\) | 4.46341 | 0.155114 | ||||||||
\(829\) | −29.2919 | −1.01735 | −0.508675 | − | 0.860959i | \(-0.669864\pi\) | ||||
−0.508675 | + | 0.860959i | \(0.669864\pi\) | |||||||
\(830\) | −38.4127 | −1.33333 | ||||||||
\(831\) | −13.3642 | −0.463600 | ||||||||
\(832\) | 0.193805 | 0.00671897 | ||||||||
\(833\) | 28.1365 | 0.974872 | ||||||||
\(834\) | 0.642811 | 0.0222587 | ||||||||
\(835\) | 82.5482 | 2.85670 | ||||||||
\(836\) | −0.446910 | −0.0154567 | ||||||||
\(837\) | −2.03661 | −0.0703956 | ||||||||
\(838\) | −15.8308 | −0.546865 | ||||||||
\(839\) | −10.4066 | −0.359277 | −0.179639 | − | 0.983733i | \(-0.557493\pi\) | ||||
−0.179639 | + | 0.983733i | \(0.557493\pi\) | |||||||
\(840\) | −3.02593 | −0.104405 | ||||||||
\(841\) | −19.5632 | −0.674592 | ||||||||
\(842\) | −18.9690 | −0.653713 | ||||||||
\(843\) | −3.02842 | −0.104304 | ||||||||
\(844\) | −22.3210 | −0.768319 | ||||||||
\(845\) | −49.6433 | −1.70778 | ||||||||
\(846\) | −6.54823 | −0.225133 | ||||||||
\(847\) | 8.53335 | 0.293209 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | 17.0084 | 0.583726 | ||||||||
\(850\) | 42.6622 | 1.46330 | ||||||||
\(851\) | −29.9890 | −1.02801 | ||||||||
\(852\) | −6.92682 | −0.237309 | ||||||||
\(853\) | 48.3345 | 1.65494 | 0.827470 | − | 0.561510i | \(-0.189779\pi\) | ||||
0.827470 | + | 0.561510i | \(0.189779\pi\) | |||||||
\(854\) | 6.53915 | 0.223765 | ||||||||
\(855\) | −3.82978 | −0.130976 | ||||||||
\(856\) | −14.0342 | −0.479679 | ||||||||
\(857\) | 47.7651 | 1.63162 | 0.815812 | − | 0.578318i | \(-0.196291\pi\) | ||||
0.815812 | + | 0.578318i | \(0.196291\pi\) | |||||||
\(858\) | 0.0866131 | 0.00295692 | ||||||||
\(859\) | −15.5166 | −0.529420 | −0.264710 | − | 0.964328i | \(-0.585276\pi\) | ||||
−0.264710 | + | 0.964328i | \(0.585276\pi\) | |||||||
\(860\) | 2.52337 | 0.0860462 | ||||||||
\(861\) | −0.0236268 | −0.000805201 0 | ||||||||
\(862\) | −15.9307 | −0.542603 | ||||||||
\(863\) | −4.16698 | −0.141846 | −0.0709229 | − | 0.997482i | \(-0.522594\pi\) | ||||
−0.0709229 | + | 0.997482i | \(0.522594\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −6.31716 | −0.214790 | ||||||||
\(866\) | 15.6597 | 0.532137 | ||||||||
\(867\) | −2.47512 | −0.0840596 | ||||||||
\(868\) | −1.60914 | −0.0546176 | ||||||||
\(869\) | 5.26145 | 0.178482 | ||||||||
\(870\) | −11.7649 | −0.398867 | ||||||||
\(871\) | 1.03172 | 0.0349586 | ||||||||
\(872\) | −11.7618 | −0.398306 | ||||||||
\(873\) | 13.3255 | 0.451001 | ||||||||
\(874\) | 4.46341 | 0.150977 | ||||||||
\(875\) | −14.1228 | −0.477437 | ||||||||
\(876\) | −8.46217 | −0.285910 | ||||||||
\(877\) | −13.5310 | −0.456911 | −0.228455 | − | 0.973554i | \(-0.573367\pi\) | ||||
−0.228455 | + | 0.973554i | \(0.573367\pi\) | |||||||
\(878\) | 16.6208 | 0.560925 | ||||||||
\(879\) | 1.69944 | 0.0573208 | ||||||||
\(880\) | 1.71157 | 0.0576969 | ||||||||
\(881\) | −13.4714 | −0.453862 | −0.226931 | − | 0.973911i | \(-0.572869\pi\) | ||||
−0.226931 | + | 0.973911i | \(0.572869\pi\) | |||||||
\(882\) | 6.37573 | 0.214682 | ||||||||
\(883\) | −20.1862 | −0.679321 | −0.339661 | − | 0.940548i | \(-0.610312\pi\) | ||||
−0.339661 | + | 0.940548i | \(0.610312\pi\) | |||||||
\(884\) | −0.855272 | −0.0287659 | ||||||||
\(885\) | 17.6944 | 0.594792 | ||||||||
\(886\) | 12.9754 | 0.435918 | ||||||||
\(887\) | −31.2512 | −1.04931 | −0.524657 | − | 0.851314i | \(-0.675806\pi\) | ||||
−0.524657 | + | 0.851314i | \(0.675806\pi\) | |||||||
\(888\) | −6.71886 | −0.225470 | ||||||||
\(889\) | −1.26516 | −0.0424322 | ||||||||
\(890\) | 54.8987 | 1.84021 | ||||||||
\(891\) | 0.446910 | 0.0149720 | ||||||||
\(892\) | −12.9146 | −0.432414 | ||||||||
\(893\) | −6.54823 | −0.219128 | ||||||||
\(894\) | 0.421009 | 0.0140807 | ||||||||
\(895\) | −93.8582 | −3.13733 | ||||||||
\(896\) | 0.790105 | 0.0263956 | ||||||||
\(897\) | −0.865029 | −0.0288825 | ||||||||
\(898\) | 1.70560 | 0.0569165 | ||||||||
\(899\) | −6.25635 | −0.208661 | ||||||||
\(900\) | 9.66725 | 0.322242 | ||||||||
\(901\) | −4.41306 | −0.147020 | ||||||||
\(902\) | 0.0133641 | 0.000444977 0 | ||||||||
\(903\) | 0.520585 | 0.0173240 | ||||||||
\(904\) | 5.70150 | 0.189629 | ||||||||
\(905\) | −33.6458 | −1.11842 | ||||||||
\(906\) | 13.0626 | 0.433977 | ||||||||
\(907\) | −20.5963 | −0.683887 | −0.341944 | − | 0.939720i | \(-0.611085\pi\) | ||||
−0.341944 | + | 0.939720i | \(0.611085\pi\) | |||||||
\(908\) | −7.82435 | −0.259660 | ||||||||
\(909\) | 5.76906 | 0.191348 | ||||||||
\(910\) | 0.586439 | 0.0194403 | ||||||||
\(911\) | 8.68508 | 0.287750 | 0.143875 | − | 0.989596i | \(-0.454044\pi\) | ||||
0.143875 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 4.48250 | 0.148349 | ||||||||
\(914\) | 15.7323 | 0.520379 | ||||||||
\(915\) | −31.6965 | −1.04785 | ||||||||
\(916\) | −9.42402 | −0.311378 | ||||||||
\(917\) | −10.1186 | −0.334144 | ||||||||
\(918\) | −4.41306 | −0.145653 | ||||||||
\(919\) | −23.4638 | −0.774000 | −0.387000 | − | 0.922080i | \(-0.626489\pi\) | ||||
−0.387000 | + | 0.922080i | \(0.626489\pi\) | |||||||
\(920\) | −17.0939 | −0.563569 | ||||||||
\(921\) | −10.9862 | −0.362008 | ||||||||
\(922\) | −30.5681 | −1.00671 | ||||||||
\(923\) | 1.34245 | 0.0441873 | ||||||||
\(924\) | 0.353105 | 0.0116163 | ||||||||
\(925\) | −64.9529 | −2.13564 | ||||||||
\(926\) | 4.71049 | 0.154796 | ||||||||
\(927\) | −4.31765 | −0.141810 | ||||||||
\(928\) | 3.07194 | 0.100841 | ||||||||
\(929\) | −50.8711 | −1.66903 | −0.834513 | − | 0.550988i | \(-0.814251\pi\) | ||||
−0.834513 | + | 0.550988i | \(0.814251\pi\) | |||||||
\(930\) | 7.79978 | 0.255765 | ||||||||
\(931\) | 6.37573 | 0.208956 | ||||||||
\(932\) | −1.78897 | −0.0585996 | ||||||||
\(933\) | −12.7816 | −0.418451 | ||||||||
\(934\) | −35.6878 | −1.16774 | ||||||||
\(935\) | −7.55325 | −0.247018 | ||||||||
\(936\) | −0.193805 | −0.00633470 | ||||||||
\(937\) | 7.18033 | 0.234571 | 0.117286 | − | 0.993098i | \(-0.462581\pi\) | ||||
0.117286 | + | 0.993098i | \(0.462581\pi\) | |||||||
\(938\) | 4.20614 | 0.137335 | ||||||||
\(939\) | 9.87055 | 0.322113 | ||||||||
\(940\) | 25.0783 | 0.817964 | ||||||||
\(941\) | −55.7667 | −1.81794 | −0.908972 | − | 0.416858i | \(-0.863131\pi\) | ||||
−0.908972 | + | 0.416858i | \(0.863131\pi\) | |||||||
\(942\) | 14.4289 | 0.470119 | ||||||||
\(943\) | −0.133471 | −0.00434642 | ||||||||
\(944\) | −4.62022 | −0.150375 | ||||||||
\(945\) | 3.02593 | 0.0984336 | ||||||||
\(946\) | −0.294460 | −0.00957372 | ||||||||
\(947\) | −52.8254 | −1.71660 | −0.858298 | − | 0.513151i | \(-0.828478\pi\) | ||||
−0.858298 | + | 0.513151i | \(0.828478\pi\) | |||||||
\(948\) | −11.7730 | −0.382368 | ||||||||
\(949\) | 1.64001 | 0.0532369 | ||||||||
\(950\) | 9.66725 | 0.313647 | ||||||||
\(951\) | −6.53804 | −0.212011 | ||||||||
\(952\) | −3.48678 | −0.113007 | ||||||||
\(953\) | −24.3972 | −0.790302 | −0.395151 | − | 0.918616i | \(-0.629308\pi\) | ||||
−0.395151 | + | 0.918616i | \(0.629308\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | −27.0449 | −0.875153 | ||||||||
\(956\) | 16.7328 | 0.541178 | ||||||||
\(957\) | 1.37288 | 0.0443789 | ||||||||
\(958\) | −26.4955 | −0.856031 | ||||||||
\(959\) | −5.22814 | −0.168825 | ||||||||
\(960\) | −3.82978 | −0.123606 | ||||||||
\(961\) | −26.8522 | −0.866201 | ||||||||
\(962\) | 1.30215 | 0.0419829 | ||||||||
\(963\) | 14.0342 | 0.452245 | ||||||||
\(964\) | −10.9047 | −0.351217 | ||||||||
\(965\) | 31.9939 | 1.02992 | ||||||||
\(966\) | −3.52656 | −0.113465 | ||||||||
\(967\) | −18.3483 | −0.590042 | −0.295021 | − | 0.955491i | \(-0.595327\pi\) | ||||
−0.295021 | + | 0.955491i | \(0.595327\pi\) | |||||||
\(968\) | 10.8003 | 0.347134 | ||||||||
\(969\) | −4.41306 | −0.141768 | ||||||||
\(970\) | −51.0339 | −1.63860 | ||||||||
\(971\) | 34.7578 | 1.11543 | 0.557716 | − | 0.830032i | \(-0.311678\pi\) | ||||
0.557716 | + | 0.830032i | \(0.311678\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −0.507888 | −0.0162821 | ||||||||
\(974\) | 6.22402 | 0.199430 | ||||||||
\(975\) | −1.87356 | −0.0600019 | ||||||||
\(976\) | 8.27631 | 0.264918 | ||||||||
\(977\) | 56.8459 | 1.81866 | 0.909331 | − | 0.416074i | \(-0.136594\pi\) | ||||
0.909331 | + | 0.416074i | \(0.136594\pi\) | |||||||
\(978\) | 18.1071 | 0.579000 | ||||||||
\(979\) | −6.40631 | −0.204746 | ||||||||
\(980\) | −24.4177 | −0.779994 | ||||||||
\(981\) | 11.7618 | 0.375526 | ||||||||
\(982\) | 3.70736 | 0.118307 | ||||||||
\(983\) | −21.4247 | −0.683342 | −0.341671 | − | 0.939820i | \(-0.610993\pi\) | ||||
−0.341671 | + | 0.939820i | \(0.610993\pi\) | |||||||
\(984\) | −0.0299034 | −0.000953287 0 | ||||||||
\(985\) | 40.3658 | 1.28616 | ||||||||
\(986\) | −13.5567 | −0.431733 | ||||||||
\(987\) | 5.17379 | 0.164684 | ||||||||
\(988\) | −0.193805 | −0.00616575 | ||||||||
\(989\) | 2.94085 | 0.0935137 | ||||||||
\(990\) | −1.71157 | −0.0543972 | ||||||||
\(991\) | −32.3546 | −1.02778 | −0.513889 | − | 0.857857i | \(-0.671796\pi\) | ||||
−0.513889 | + | 0.857857i | \(0.671796\pi\) | |||||||
\(992\) | −2.03661 | −0.0646625 | ||||||||
\(993\) | 1.85852 | 0.0589784 | ||||||||
\(994\) | 5.47291 | 0.173590 | ||||||||
\(995\) | −54.4991 | −1.72774 | ||||||||
\(996\) | −10.0300 | −0.317813 | ||||||||
\(997\) | −41.5468 | −1.31580 | −0.657900 | − | 0.753105i | \(-0.728555\pi\) | ||||
−0.657900 | + | 0.753105i | \(0.728555\pi\) | |||||||
\(998\) | 26.8514 | 0.849965 | ||||||||
\(999\) | 6.71886 | 0.212575 |
(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 | 6042.2.a.z.1.9 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.z.1.9 | ✓ | 9 | 1.1 | even | 1 | trivial |