Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2667,2,Mod(1,2667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, 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("2667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2667 = 3 \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2667.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: | \(21.2961022191\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.118870813.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.52532\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.246202 | 0.174091 | 0.0870455 | − | 0.996204i | \(-0.472257\pi\) | ||||
0.0870455 | + | 0.996204i | \(0.472257\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.93938 | −0.969692 | ||||||||
\(5\) | −0.318209 | −0.142307 | −0.0711537 | − | 0.997465i | \(-0.522668\pi\) | ||||
−0.0711537 | + | 0.997465i | \(0.522668\pi\) | |||||||
\(6\) | 0.246202 | 0.100511 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.969884 | −0.342906 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.0783436 | −0.0247744 | ||||||||
\(11\) | 2.79943 | 0.844061 | 0.422031 | − | 0.906582i | \(-0.361317\pi\) | ||||
0.422031 | + | 0.906582i | \(0.361317\pi\) | |||||||
\(12\) | −1.93938 | −0.559852 | ||||||||
\(13\) | −6.49995 | −1.80276 | −0.901381 | − | 0.433027i | \(-0.857445\pi\) | ||||
−0.901381 | + | 0.433027i | \(0.857445\pi\) | |||||||
\(14\) | 0.246202 | 0.0658002 | ||||||||
\(15\) | −0.318209 | −0.0821612 | ||||||||
\(16\) | 3.63998 | 0.909996 | ||||||||
\(17\) | −1.33136 | −0.322901 | −0.161451 | − | 0.986881i | \(-0.551617\pi\) | ||||
−0.161451 | + | 0.986881i | \(0.551617\pi\) | |||||||
\(18\) | 0.246202 | 0.0580303 | ||||||||
\(19\) | 4.36328 | 1.00101 | 0.500503 | − | 0.865735i | \(-0.333149\pi\) | ||||
0.500503 | + | 0.865735i | \(0.333149\pi\) | |||||||
\(20\) | 0.617130 | 0.137994 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.689226 | 0.146943 | ||||||||
\(23\) | −5.29356 | −1.10378 | −0.551892 | − | 0.833915i | \(-0.686094\pi\) | ||||
−0.551892 | + | 0.833915i | \(0.686094\pi\) | |||||||
\(24\) | −0.969884 | −0.197977 | ||||||||
\(25\) | −4.89874 | −0.979749 | ||||||||
\(26\) | −1.60030 | −0.313845 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.93938 | −0.366509 | ||||||||
\(29\) | −2.35110 | −0.436589 | −0.218295 | − | 0.975883i | \(-0.570049\pi\) | ||||
−0.218295 | + | 0.975883i | \(0.570049\pi\) | |||||||
\(30\) | −0.0783436 | −0.0143035 | ||||||||
\(31\) | −4.76449 | −0.855729 | −0.427864 | − | 0.903843i | \(-0.640734\pi\) | ||||
−0.427864 | + | 0.903843i | \(0.640734\pi\) | |||||||
\(32\) | 2.83594 | 0.501328 | ||||||||
\(33\) | 2.79943 | 0.487319 | ||||||||
\(34\) | −0.327782 | −0.0562142 | ||||||||
\(35\) | −0.318209 | −0.0537871 | ||||||||
\(36\) | −1.93938 | −0.323231 | ||||||||
\(37\) | 1.06889 | 0.175725 | 0.0878624 | − | 0.996133i | \(-0.471996\pi\) | ||||
0.0878624 | + | 0.996133i | \(0.471996\pi\) | |||||||
\(38\) | 1.07425 | 0.174266 | ||||||||
\(39\) | −6.49995 | −1.04082 | ||||||||
\(40\) | 0.308626 | 0.0487980 | ||||||||
\(41\) | −1.46345 | −0.228553 | −0.114277 | − | 0.993449i | \(-0.536455\pi\) | ||||
−0.114277 | + | 0.993449i | \(0.536455\pi\) | |||||||
\(42\) | 0.246202 | 0.0379898 | ||||||||
\(43\) | 8.04774 | 1.22727 | 0.613635 | − | 0.789590i | \(-0.289707\pi\) | ||||
0.613635 | + | 0.789590i | \(0.289707\pi\) | |||||||
\(44\) | −5.42918 | −0.818480 | ||||||||
\(45\) | −0.318209 | −0.0474358 | ||||||||
\(46\) | −1.30329 | −0.192159 | ||||||||
\(47\) | −7.16642 | −1.04533 | −0.522665 | − | 0.852538i | \(-0.675062\pi\) | ||||
−0.522665 | + | 0.852538i | \(0.675062\pi\) | |||||||
\(48\) | 3.63998 | 0.525386 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.20608 | −0.170565 | ||||||||
\(51\) | −1.33136 | −0.186427 | ||||||||
\(52\) | 12.6059 | 1.74812 | ||||||||
\(53\) | 9.12591 | 1.25354 | 0.626770 | − | 0.779204i | \(-0.284377\pi\) | ||||
0.626770 | + | 0.779204i | \(0.284377\pi\) | |||||||
\(54\) | 0.246202 | 0.0335038 | ||||||||
\(55\) | −0.890805 | −0.120116 | ||||||||
\(56\) | −0.969884 | −0.129606 | ||||||||
\(57\) | 4.36328 | 0.577931 | ||||||||
\(58\) | −0.578846 | −0.0760063 | ||||||||
\(59\) | −5.02542 | −0.654255 | −0.327127 | − | 0.944980i | \(-0.606081\pi\) | ||||
−0.327127 | + | 0.944980i | \(0.606081\pi\) | |||||||
\(60\) | 0.617130 | 0.0796711 | ||||||||
\(61\) | −2.48901 | −0.318685 | −0.159343 | − | 0.987223i | \(-0.550937\pi\) | ||||
−0.159343 | + | 0.987223i | \(0.550937\pi\) | |||||||
\(62\) | −1.17303 | −0.148975 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −6.58175 | −0.822719 | ||||||||
\(65\) | 2.06834 | 0.256546 | ||||||||
\(66\) | 0.689226 | 0.0848378 | ||||||||
\(67\) | 0.549822 | 0.0671714 | 0.0335857 | − | 0.999436i | \(-0.489307\pi\) | ||||
0.0335857 | + | 0.999436i | \(0.489307\pi\) | |||||||
\(68\) | 2.58201 | 0.313115 | ||||||||
\(69\) | −5.29356 | −0.637270 | ||||||||
\(70\) | −0.0783436 | −0.00936386 | ||||||||
\(71\) | −11.9210 | −1.41476 | −0.707380 | − | 0.706833i | \(-0.750123\pi\) | ||||
−0.707380 | + | 0.706833i | \(0.750123\pi\) | |||||||
\(72\) | −0.969884 | −0.114302 | ||||||||
\(73\) | −13.8588 | −1.62205 | −0.811027 | − | 0.585008i | \(-0.801091\pi\) | ||||
−0.811027 | + | 0.585008i | \(0.801091\pi\) | |||||||
\(74\) | 0.263163 | 0.0305921 | ||||||||
\(75\) | −4.89874 | −0.565658 | ||||||||
\(76\) | −8.46208 | −0.970667 | ||||||||
\(77\) | 2.79943 | 0.319025 | ||||||||
\(78\) | −1.60030 | −0.181198 | ||||||||
\(79\) | −1.49518 | −0.168221 | −0.0841106 | − | 0.996456i | \(-0.526805\pi\) | ||||
−0.0841106 | + | 0.996456i | \(0.526805\pi\) | |||||||
\(80\) | −1.15827 | −0.129499 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.360305 | −0.0397891 | ||||||||
\(83\) | −17.1283 | −1.88008 | −0.940039 | − | 0.341067i | \(-0.889212\pi\) | ||||
−0.940039 | + | 0.341067i | \(0.889212\pi\) | |||||||
\(84\) | −1.93938 | −0.211604 | ||||||||
\(85\) | 0.423650 | 0.0459512 | ||||||||
\(86\) | 1.98137 | 0.213657 | ||||||||
\(87\) | −2.35110 | −0.252065 | ||||||||
\(88\) | −2.71513 | −0.289433 | ||||||||
\(89\) | 12.8927 | 1.36662 | 0.683309 | − | 0.730129i | \(-0.260540\pi\) | ||||
0.683309 | + | 0.730129i | \(0.260540\pi\) | |||||||
\(90\) | −0.0783436 | −0.00825814 | ||||||||
\(91\) | −6.49995 | −0.681380 | ||||||||
\(92\) | 10.2663 | 1.07033 | ||||||||
\(93\) | −4.76449 | −0.494055 | ||||||||
\(94\) | −1.76439 | −0.181983 | ||||||||
\(95\) | −1.38844 | −0.142450 | ||||||||
\(96\) | 2.83594 | 0.289442 | ||||||||
\(97\) | −7.20075 | −0.731125 | −0.365563 | − | 0.930787i | \(-0.619123\pi\) | ||||
−0.365563 | + | 0.930787i | \(0.619123\pi\) | |||||||
\(98\) | 0.246202 | 0.0248701 | ||||||||
\(99\) | 2.79943 | 0.281354 | ||||||||
\(100\) | 9.50055 | 0.950055 | ||||||||
\(101\) | −0.894063 | −0.0889625 | −0.0444813 | − | 0.999010i | \(-0.514164\pi\) | ||||
−0.0444813 | + | 0.999010i | \(0.514164\pi\) | |||||||
\(102\) | −0.327782 | −0.0324553 | ||||||||
\(103\) | 10.2130 | 1.00631 | 0.503157 | − | 0.864195i | \(-0.332172\pi\) | ||||
0.503157 | + | 0.864195i | \(0.332172\pi\) | |||||||
\(104\) | 6.30420 | 0.618177 | ||||||||
\(105\) | −0.318209 | −0.0310540 | ||||||||
\(106\) | 2.24682 | 0.218230 | ||||||||
\(107\) | 1.98724 | 0.192114 | 0.0960569 | − | 0.995376i | \(-0.469377\pi\) | ||||
0.0960569 | + | 0.995376i | \(0.469377\pi\) | |||||||
\(108\) | −1.93938 | −0.186617 | ||||||||
\(109\) | −18.2252 | −1.74566 | −0.872831 | − | 0.488022i | \(-0.837718\pi\) | ||||
−0.872831 | + | 0.488022i | \(0.837718\pi\) | |||||||
\(110\) | −0.219318 | −0.0209111 | ||||||||
\(111\) | 1.06889 | 0.101455 | ||||||||
\(112\) | 3.63998 | 0.343946 | ||||||||
\(113\) | −6.23590 | −0.586624 | −0.293312 | − | 0.956017i | \(-0.594757\pi\) | ||||
−0.293312 | + | 0.956017i | \(0.594757\pi\) | |||||||
\(114\) | 1.07425 | 0.100613 | ||||||||
\(115\) | 1.68446 | 0.157077 | ||||||||
\(116\) | 4.55970 | 0.423357 | ||||||||
\(117\) | −6.49995 | −0.600921 | ||||||||
\(118\) | −1.23727 | −0.113900 | ||||||||
\(119\) | −1.33136 | −0.122045 | ||||||||
\(120\) | 0.308626 | 0.0281735 | ||||||||
\(121\) | −3.16317 | −0.287561 | ||||||||
\(122\) | −0.612799 | −0.0554802 | ||||||||
\(123\) | −1.46345 | −0.131955 | ||||||||
\(124\) | 9.24019 | 0.829793 | ||||||||
\(125\) | 3.14987 | 0.281733 | ||||||||
\(126\) | 0.246202 | 0.0219334 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −7.29232 | −0.644556 | ||||||||
\(129\) | 8.04774 | 0.708564 | ||||||||
\(130\) | 0.509230 | 0.0446624 | ||||||||
\(131\) | −18.7890 | −1.64160 | −0.820800 | − | 0.571215i | \(-0.806472\pi\) | ||||
−0.820800 | + | 0.571215i | \(0.806472\pi\) | |||||||
\(132\) | −5.42918 | −0.472549 | ||||||||
\(133\) | 4.36328 | 0.378344 | ||||||||
\(134\) | 0.135367 | 0.0116939 | ||||||||
\(135\) | −0.318209 | −0.0273871 | ||||||||
\(136\) | 1.29126 | 0.110725 | ||||||||
\(137\) | 20.9329 | 1.78842 | 0.894209 | − | 0.447649i | \(-0.147739\pi\) | ||||
0.894209 | + | 0.447649i | \(0.147739\pi\) | |||||||
\(138\) | −1.30329 | −0.110943 | ||||||||
\(139\) | −5.77630 | −0.489940 | −0.244970 | − | 0.969531i | \(-0.578778\pi\) | ||||
−0.244970 | + | 0.969531i | \(0.578778\pi\) | |||||||
\(140\) | 0.617130 | 0.0521570 | ||||||||
\(141\) | −7.16642 | −0.603522 | ||||||||
\(142\) | −2.93497 | −0.246297 | ||||||||
\(143\) | −18.1962 | −1.52164 | ||||||||
\(144\) | 3.63998 | 0.303332 | ||||||||
\(145\) | 0.748143 | 0.0621299 | ||||||||
\(146\) | −3.41207 | −0.282385 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −2.07299 | −0.170399 | ||||||||
\(149\) | −5.65638 | −0.463389 | −0.231694 | − | 0.972789i | \(-0.574427\pi\) | ||||
−0.231694 | + | 0.972789i | \(0.574427\pi\) | |||||||
\(150\) | −1.20608 | −0.0984760 | ||||||||
\(151\) | −2.50255 | −0.203655 | −0.101827 | − | 0.994802i | \(-0.532469\pi\) | ||||
−0.101827 | + | 0.994802i | \(0.532469\pi\) | |||||||
\(152\) | −4.23188 | −0.343250 | ||||||||
\(153\) | −1.33136 | −0.107634 | ||||||||
\(154\) | 0.689226 | 0.0555394 | ||||||||
\(155\) | 1.51610 | 0.121776 | ||||||||
\(156\) | 12.6059 | 1.00928 | ||||||||
\(157\) | −14.3393 | −1.14440 | −0.572201 | − | 0.820113i | \(-0.693910\pi\) | ||||
−0.572201 | + | 0.820113i | \(0.693910\pi\) | |||||||
\(158\) | −0.368117 | −0.0292858 | ||||||||
\(159\) | 9.12591 | 0.723731 | ||||||||
\(160\) | −0.902421 | −0.0713426 | ||||||||
\(161\) | −5.29356 | −0.417191 | ||||||||
\(162\) | 0.246202 | 0.0193434 | ||||||||
\(163\) | −16.7787 | −1.31421 | −0.657105 | − | 0.753799i | \(-0.728219\pi\) | ||||
−0.657105 | + | 0.753799i | \(0.728219\pi\) | |||||||
\(164\) | 2.83820 | 0.221626 | ||||||||
\(165\) | −0.890805 | −0.0693491 | ||||||||
\(166\) | −4.21703 | −0.327305 | ||||||||
\(167\) | −10.9980 | −0.851048 | −0.425524 | − | 0.904947i | \(-0.639910\pi\) | ||||
−0.425524 | + | 0.904947i | \(0.639910\pi\) | |||||||
\(168\) | −0.969884 | −0.0748282 | ||||||||
\(169\) | 29.2493 | 2.24995 | ||||||||
\(170\) | 0.104303 | 0.00799970 | ||||||||
\(171\) | 4.36328 | 0.333668 | ||||||||
\(172\) | −15.6077 | −1.19007 | ||||||||
\(173\) | 14.9307 | 1.13516 | 0.567579 | − | 0.823319i | \(-0.307880\pi\) | ||||
0.567579 | + | 0.823319i | \(0.307880\pi\) | |||||||
\(174\) | −0.578846 | −0.0438822 | ||||||||
\(175\) | −4.89874 | −0.370310 | ||||||||
\(176\) | 10.1899 | 0.768092 | ||||||||
\(177\) | −5.02542 | −0.377734 | ||||||||
\(178\) | 3.17419 | 0.237916 | ||||||||
\(179\) | 10.5989 | 0.792200 | 0.396100 | − | 0.918207i | \(-0.370363\pi\) | ||||
0.396100 | + | 0.918207i | \(0.370363\pi\) | |||||||
\(180\) | 0.617130 | 0.0459981 | ||||||||
\(181\) | 14.6508 | 1.08898 | 0.544491 | − | 0.838766i | \(-0.316723\pi\) | ||||
0.544491 | + | 0.838766i | \(0.316723\pi\) | |||||||
\(182\) | −1.60030 | −0.118622 | ||||||||
\(183\) | −2.48901 | −0.183993 | ||||||||
\(184\) | 5.13414 | 0.378494 | ||||||||
\(185\) | −0.340131 | −0.0250069 | ||||||||
\(186\) | −1.17303 | −0.0860105 | ||||||||
\(187\) | −3.72704 | −0.272548 | ||||||||
\(188\) | 13.8985 | 1.01365 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −0.341835 | −0.0247993 | ||||||||
\(191\) | −17.6738 | −1.27883 | −0.639415 | − | 0.768862i | \(-0.720823\pi\) | ||||
−0.639415 | + | 0.768862i | \(0.720823\pi\) | |||||||
\(192\) | −6.58175 | −0.474997 | ||||||||
\(193\) | −13.3112 | −0.958158 | −0.479079 | − | 0.877772i | \(-0.659029\pi\) | ||||
−0.479079 | + | 0.877772i | \(0.659029\pi\) | |||||||
\(194\) | −1.77284 | −0.127282 | ||||||||
\(195\) | 2.06834 | 0.148117 | ||||||||
\(196\) | −1.93938 | −0.138527 | ||||||||
\(197\) | 3.10847 | 0.221469 | 0.110735 | − | 0.993850i | \(-0.464680\pi\) | ||||
0.110735 | + | 0.993850i | \(0.464680\pi\) | |||||||
\(198\) | 0.689226 | 0.0489812 | ||||||||
\(199\) | −21.0921 | −1.49518 | −0.747590 | − | 0.664160i | \(-0.768789\pi\) | ||||
−0.747590 | + | 0.664160i | \(0.768789\pi\) | |||||||
\(200\) | 4.75121 | 0.335961 | ||||||||
\(201\) | 0.549822 | 0.0387814 | ||||||||
\(202\) | −0.220120 | −0.0154876 | ||||||||
\(203\) | −2.35110 | −0.165015 | ||||||||
\(204\) | 2.58201 | 0.180777 | ||||||||
\(205\) | 0.465684 | 0.0325248 | ||||||||
\(206\) | 2.51445 | 0.175190 | ||||||||
\(207\) | −5.29356 | −0.367928 | ||||||||
\(208\) | −23.6597 | −1.64051 | ||||||||
\(209\) | 12.2147 | 0.844910 | ||||||||
\(210\) | −0.0783436 | −0.00540622 | ||||||||
\(211\) | 3.11651 | 0.214549 | 0.107275 | − | 0.994229i | \(-0.465788\pi\) | ||||
0.107275 | + | 0.994229i | \(0.465788\pi\) | |||||||
\(212\) | −17.6986 | −1.21555 | ||||||||
\(213\) | −11.9210 | −0.816812 | ||||||||
\(214\) | 0.489262 | 0.0334453 | ||||||||
\(215\) | −2.56086 | −0.174649 | ||||||||
\(216\) | −0.969884 | −0.0659922 | ||||||||
\(217\) | −4.76449 | −0.323435 | ||||||||
\(218\) | −4.48709 | −0.303904 | ||||||||
\(219\) | −13.8588 | −0.936494 | ||||||||
\(220\) | 1.72761 | 0.116476 | ||||||||
\(221\) | 8.65375 | 0.582114 | ||||||||
\(222\) | 0.263163 | 0.0176624 | ||||||||
\(223\) | −14.2513 | −0.954337 | −0.477169 | − | 0.878812i | \(-0.658337\pi\) | ||||
−0.477169 | + | 0.878812i | \(0.658337\pi\) | |||||||
\(224\) | 2.83594 | 0.189484 | ||||||||
\(225\) | −4.89874 | −0.326583 | ||||||||
\(226\) | −1.53529 | −0.102126 | ||||||||
\(227\) | 14.3103 | 0.949808 | 0.474904 | − | 0.880038i | \(-0.342483\pi\) | ||||
0.474904 | + | 0.880038i | \(0.342483\pi\) | |||||||
\(228\) | −8.46208 | −0.560415 | ||||||||
\(229\) | 19.1899 | 1.26810 | 0.634051 | − | 0.773291i | \(-0.281391\pi\) | ||||
0.634051 | + | 0.773291i | \(0.281391\pi\) | |||||||
\(230\) | 0.414717 | 0.0273456 | ||||||||
\(231\) | 2.79943 | 0.184189 | ||||||||
\(232\) | 2.28030 | 0.149709 | ||||||||
\(233\) | −11.6209 | −0.761310 | −0.380655 | − | 0.924717i | \(-0.624301\pi\) | ||||
−0.380655 | + | 0.924717i | \(0.624301\pi\) | |||||||
\(234\) | −1.60030 | −0.104615 | ||||||||
\(235\) | 2.28042 | 0.148758 | ||||||||
\(236\) | 9.74623 | 0.634426 | ||||||||
\(237\) | −1.49518 | −0.0971226 | ||||||||
\(238\) | −0.327782 | −0.0212470 | ||||||||
\(239\) | 0.298510 | 0.0193090 | 0.00965449 | − | 0.999953i | \(-0.496927\pi\) | ||||
0.00965449 | + | 0.999953i | \(0.496927\pi\) | |||||||
\(240\) | −1.15827 | −0.0747663 | ||||||||
\(241\) | 18.4344 | 1.18747 | 0.593734 | − | 0.804662i | \(-0.297653\pi\) | ||||
0.593734 | + | 0.804662i | \(0.297653\pi\) | |||||||
\(242\) | −0.778778 | −0.0500617 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.82715 | 0.309027 | ||||||||
\(245\) | −0.318209 | −0.0203296 | ||||||||
\(246\) | −0.360305 | −0.0229722 | ||||||||
\(247\) | −28.3611 | −1.80457 | ||||||||
\(248\) | 4.62101 | 0.293434 | ||||||||
\(249\) | −17.1283 | −1.08546 | ||||||||
\(250\) | 0.775504 | 0.0490472 | ||||||||
\(251\) | 27.6399 | 1.74462 | 0.872308 | − | 0.488956i | \(-0.162622\pi\) | ||||
0.872308 | + | 0.488956i | \(0.162622\pi\) | |||||||
\(252\) | −1.93938 | −0.122170 | ||||||||
\(253\) | −14.8190 | −0.931662 | ||||||||
\(254\) | −0.246202 | −0.0154481 | ||||||||
\(255\) | 0.423650 | 0.0265300 | ||||||||
\(256\) | 11.3681 | 0.710508 | ||||||||
\(257\) | 2.39616 | 0.149469 | 0.0747343 | − | 0.997203i | \(-0.476189\pi\) | ||||
0.0747343 | + | 0.997203i | \(0.476189\pi\) | |||||||
\(258\) | 1.98137 | 0.123355 | ||||||||
\(259\) | 1.06889 | 0.0664177 | ||||||||
\(260\) | −4.01131 | −0.248771 | ||||||||
\(261\) | −2.35110 | −0.145530 | ||||||||
\(262\) | −4.62588 | −0.285788 | ||||||||
\(263\) | 19.2268 | 1.18558 | 0.592789 | − | 0.805358i | \(-0.298027\pi\) | ||||
0.592789 | + | 0.805358i | \(0.298027\pi\) | |||||||
\(264\) | −2.71513 | −0.167104 | ||||||||
\(265\) | −2.90395 | −0.178388 | ||||||||
\(266\) | 1.07425 | 0.0658664 | ||||||||
\(267\) | 12.8927 | 0.789017 | ||||||||
\(268\) | −1.06632 | −0.0651356 | ||||||||
\(269\) | 16.0800 | 0.980414 | 0.490207 | − | 0.871606i | \(-0.336921\pi\) | ||||
0.490207 | + | 0.871606i | \(0.336921\pi\) | |||||||
\(270\) | −0.0783436 | −0.00476784 | ||||||||
\(271\) | −24.7242 | −1.50189 | −0.750945 | − | 0.660365i | \(-0.770402\pi\) | ||||
−0.750945 | + | 0.660365i | \(0.770402\pi\) | |||||||
\(272\) | −4.84611 | −0.293839 | ||||||||
\(273\) | −6.49995 | −0.393395 | ||||||||
\(274\) | 5.15372 | 0.311348 | ||||||||
\(275\) | −13.7137 | −0.826968 | ||||||||
\(276\) | 10.2663 | 0.617956 | ||||||||
\(277\) | 27.1986 | 1.63421 | 0.817103 | − | 0.576492i | \(-0.195579\pi\) | ||||
0.817103 | + | 0.576492i | \(0.195579\pi\) | |||||||
\(278\) | −1.42214 | −0.0852941 | ||||||||
\(279\) | −4.76449 | −0.285243 | ||||||||
\(280\) | 0.308626 | 0.0184439 | ||||||||
\(281\) | 21.1941 | 1.26433 | 0.632167 | − | 0.774832i | \(-0.282166\pi\) | ||||
0.632167 | + | 0.774832i | \(0.282166\pi\) | |||||||
\(282\) | −1.76439 | −0.105068 | ||||||||
\(283\) | 31.0745 | 1.84719 | 0.923593 | − | 0.383374i | \(-0.125238\pi\) | ||||
0.923593 | + | 0.383374i | \(0.125238\pi\) | |||||||
\(284\) | 23.1194 | 1.37188 | ||||||||
\(285\) | −1.38844 | −0.0822438 | ||||||||
\(286\) | −4.47993 | −0.264904 | ||||||||
\(287\) | −1.46345 | −0.0863850 | ||||||||
\(288\) | 2.83594 | 0.167109 | ||||||||
\(289\) | −15.2275 | −0.895735 | ||||||||
\(290\) | 0.184194 | 0.0108163 | ||||||||
\(291\) | −7.20075 | −0.422115 | ||||||||
\(292\) | 26.8776 | 1.57289 | ||||||||
\(293\) | −18.9325 | −1.10605 | −0.553024 | − | 0.833165i | \(-0.686526\pi\) | ||||
−0.553024 | + | 0.833165i | \(0.686526\pi\) | |||||||
\(294\) | 0.246202 | 0.0143588 | ||||||||
\(295\) | 1.59914 | 0.0931052 | ||||||||
\(296\) | −1.03670 | −0.0602570 | ||||||||
\(297\) | 2.79943 | 0.162440 | ||||||||
\(298\) | −1.39261 | −0.0806718 | ||||||||
\(299\) | 34.4079 | 1.98986 | ||||||||
\(300\) | 9.50055 | 0.548514 | ||||||||
\(301\) | 8.04774 | 0.463864 | ||||||||
\(302\) | −0.616133 | −0.0354545 | ||||||||
\(303\) | −0.894063 | −0.0513626 | ||||||||
\(304\) | 15.8823 | 0.910910 | ||||||||
\(305\) | 0.792026 | 0.0453513 | ||||||||
\(306\) | −0.327782 | −0.0187381 | ||||||||
\(307\) | −4.25979 | −0.243119 | −0.121559 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121559 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(308\) | −5.42918 | −0.309356 | ||||||||
\(309\) | 10.2130 | 0.580996 | ||||||||
\(310\) | 0.373268 | 0.0212002 | ||||||||
\(311\) | 21.6483 | 1.22757 | 0.613783 | − | 0.789475i | \(-0.289647\pi\) | ||||
0.613783 | + | 0.789475i | \(0.289647\pi\) | |||||||
\(312\) | 6.30420 | 0.356905 | ||||||||
\(313\) | −0.443304 | −0.0250570 | −0.0125285 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125285 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(314\) | −3.53037 | −0.199230 | ||||||||
\(315\) | −0.318209 | −0.0179290 | ||||||||
\(316\) | 2.89974 | 0.163123 | ||||||||
\(317\) | 9.20138 | 0.516801 | 0.258401 | − | 0.966038i | \(-0.416805\pi\) | ||||
0.258401 | + | 0.966038i | \(0.416805\pi\) | |||||||
\(318\) | 2.24682 | 0.125995 | ||||||||
\(319\) | −6.58176 | −0.368508 | ||||||||
\(320\) | 2.09437 | 0.117079 | ||||||||
\(321\) | 1.98724 | 0.110917 | ||||||||
\(322\) | −1.30329 | −0.0726293 | ||||||||
\(323\) | −5.80908 | −0.323226 | ||||||||
\(324\) | −1.93938 | −0.107744 | ||||||||
\(325\) | 31.8416 | 1.76625 | ||||||||
\(326\) | −4.13095 | −0.228792 | ||||||||
\(327\) | −18.2252 | −1.00786 | ||||||||
\(328\) | 1.41938 | 0.0783722 | ||||||||
\(329\) | −7.16642 | −0.395098 | ||||||||
\(330\) | −0.219318 | −0.0120731 | ||||||||
\(331\) | 20.2676 | 1.11401 | 0.557005 | − | 0.830509i | \(-0.311951\pi\) | ||||
0.557005 | + | 0.830509i | \(0.311951\pi\) | |||||||
\(332\) | 33.2184 | 1.82310 | ||||||||
\(333\) | 1.06889 | 0.0585749 | ||||||||
\(334\) | −2.70772 | −0.148160 | ||||||||
\(335\) | −0.174958 | −0.00955899 | ||||||||
\(336\) | 3.63998 | 0.198577 | ||||||||
\(337\) | 4.22202 | 0.229988 | 0.114994 | − | 0.993366i | \(-0.463315\pi\) | ||||
0.114994 | + | 0.993366i | \(0.463315\pi\) | |||||||
\(338\) | 7.20124 | 0.391696 | ||||||||
\(339\) | −6.23590 | −0.338687 | ||||||||
\(340\) | −0.821619 | −0.0445586 | ||||||||
\(341\) | −13.3379 | −0.722287 | ||||||||
\(342\) | 1.07425 | 0.0580887 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.80538 | −0.420838 | ||||||||
\(345\) | 1.68446 | 0.0906883 | ||||||||
\(346\) | 3.67596 | 0.197621 | ||||||||
\(347\) | 23.1846 | 1.24462 | 0.622308 | − | 0.782773i | \(-0.286195\pi\) | ||||
0.622308 | + | 0.782773i | \(0.286195\pi\) | |||||||
\(348\) | 4.55970 | 0.244425 | ||||||||
\(349\) | 10.0741 | 0.539255 | 0.269628 | − | 0.962965i | \(-0.413099\pi\) | ||||
0.269628 | + | 0.962965i | \(0.413099\pi\) | |||||||
\(350\) | −1.20608 | −0.0644677 | ||||||||
\(351\) | −6.49995 | −0.346942 | ||||||||
\(352\) | 7.93902 | 0.423151 | ||||||||
\(353\) | −26.1314 | −1.39084 | −0.695418 | − | 0.718606i | \(-0.744781\pi\) | ||||
−0.695418 | + | 0.718606i | \(0.744781\pi\) | |||||||
\(354\) | −1.23727 | −0.0657601 | ||||||||
\(355\) | 3.79336 | 0.201331 | ||||||||
\(356\) | −25.0038 | −1.32520 | ||||||||
\(357\) | −1.33136 | −0.0704629 | ||||||||
\(358\) | 2.60947 | 0.137915 | ||||||||
\(359\) | 12.9795 | 0.685033 | 0.342517 | − | 0.939512i | \(-0.388721\pi\) | ||||
0.342517 | + | 0.939512i | \(0.388721\pi\) | |||||||
\(360\) | 0.308626 | 0.0162660 | ||||||||
\(361\) | 0.0382221 | 0.00201169 | ||||||||
\(362\) | 3.60704 | 0.189582 | ||||||||
\(363\) | −3.16317 | −0.166023 | ||||||||
\(364\) | 12.6059 | 0.660729 | ||||||||
\(365\) | 4.41001 | 0.230830 | ||||||||
\(366\) | −0.612799 | −0.0320315 | ||||||||
\(367\) | −10.0344 | −0.523792 | −0.261896 | − | 0.965096i | \(-0.584348\pi\) | ||||
−0.261896 | + | 0.965096i | \(0.584348\pi\) | |||||||
\(368\) | −19.2685 | −1.00444 | ||||||||
\(369\) | −1.46345 | −0.0761844 | ||||||||
\(370\) | −0.0837409 | −0.00435348 | ||||||||
\(371\) | 9.12591 | 0.473793 | ||||||||
\(372\) | 9.24019 | 0.479081 | ||||||||
\(373\) | −35.1339 | −1.81916 | −0.909581 | − | 0.415527i | \(-0.863597\pi\) | ||||
−0.909581 | + | 0.415527i | \(0.863597\pi\) | |||||||
\(374\) | −0.917605 | −0.0474482 | ||||||||
\(375\) | 3.14987 | 0.162659 | ||||||||
\(376\) | 6.95060 | 0.358450 | ||||||||
\(377\) | 15.2821 | 0.787066 | ||||||||
\(378\) | 0.246202 | 0.0126633 | ||||||||
\(379\) | 13.4078 | 0.688710 | 0.344355 | − | 0.938840i | \(-0.388098\pi\) | ||||
0.344355 | + | 0.938840i | \(0.388098\pi\) | |||||||
\(380\) | 2.69271 | 0.138133 | ||||||||
\(381\) | −1.00000 | −0.0512316 | ||||||||
\(382\) | −4.35132 | −0.222633 | ||||||||
\(383\) | −30.0733 | −1.53667 | −0.768337 | − | 0.640046i | \(-0.778915\pi\) | ||||
−0.768337 | + | 0.640046i | \(0.778915\pi\) | |||||||
\(384\) | −7.29232 | −0.372134 | ||||||||
\(385\) | −0.890805 | −0.0453996 | ||||||||
\(386\) | −3.27723 | −0.166807 | ||||||||
\(387\) | 8.04774 | 0.409090 | ||||||||
\(388\) | 13.9650 | 0.708967 | ||||||||
\(389\) | −16.7975 | −0.851667 | −0.425833 | − | 0.904802i | \(-0.640019\pi\) | ||||
−0.425833 | + | 0.904802i | \(0.640019\pi\) | |||||||
\(390\) | 0.509230 | 0.0257858 | ||||||||
\(391\) | 7.04762 | 0.356414 | ||||||||
\(392\) | −0.969884 | −0.0489865 | ||||||||
\(393\) | −18.7890 | −0.947778 | ||||||||
\(394\) | 0.765310 | 0.0385558 | ||||||||
\(395\) | 0.475781 | 0.0239391 | ||||||||
\(396\) | −5.42918 | −0.272827 | ||||||||
\(397\) | −21.2921 | −1.06862 | −0.534309 | − | 0.845289i | \(-0.679428\pi\) | ||||
−0.534309 | + | 0.845289i | \(0.679428\pi\) | |||||||
\(398\) | −5.19292 | −0.260297 | ||||||||
\(399\) | 4.36328 | 0.218437 | ||||||||
\(400\) | −17.8313 | −0.891567 | ||||||||
\(401\) | −6.43709 | −0.321453 | −0.160727 | − | 0.986999i | \(-0.551384\pi\) | ||||
−0.160727 | + | 0.986999i | \(0.551384\pi\) | |||||||
\(402\) | 0.135367 | 0.00675150 | ||||||||
\(403\) | 30.9690 | 1.54267 | ||||||||
\(404\) | 1.73393 | 0.0862663 | ||||||||
\(405\) | −0.318209 | −0.0158119 | ||||||||
\(406\) | −0.578846 | −0.0287277 | ||||||||
\(407\) | 2.99229 | 0.148322 | ||||||||
\(408\) | 1.29126 | 0.0639269 | ||||||||
\(409\) | 8.28563 | 0.409698 | 0.204849 | − | 0.978794i | \(-0.434330\pi\) | ||||
0.204849 | + | 0.978794i | \(0.434330\pi\) | |||||||
\(410\) | 0.114652 | 0.00566228 | ||||||||
\(411\) | 20.9329 | 1.03254 | ||||||||
\(412\) | −19.8069 | −0.975816 | ||||||||
\(413\) | −5.02542 | −0.247285 | ||||||||
\(414\) | −1.30329 | −0.0640530 | ||||||||
\(415\) | 5.45039 | 0.267549 | ||||||||
\(416\) | −18.4335 | −0.903774 | ||||||||
\(417\) | −5.77630 | −0.282867 | ||||||||
\(418\) | 3.00729 | 0.147091 | ||||||||
\(419\) | 27.2585 | 1.33167 | 0.665833 | − | 0.746101i | \(-0.268076\pi\) | ||||
0.665833 | + | 0.746101i | \(0.268076\pi\) | |||||||
\(420\) | 0.617130 | 0.0301128 | ||||||||
\(421\) | −21.3651 | −1.04127 | −0.520635 | − | 0.853780i | \(-0.674305\pi\) | ||||
−0.520635 | + | 0.853780i | \(0.674305\pi\) | |||||||
\(422\) | 0.767290 | 0.0373511 | ||||||||
\(423\) | −7.16642 | −0.348443 | ||||||||
\(424\) | −8.85107 | −0.429846 | ||||||||
\(425\) | 6.52197 | 0.316362 | ||||||||
\(426\) | −2.93497 | −0.142200 | ||||||||
\(427\) | −2.48901 | −0.120452 | ||||||||
\(428\) | −3.85402 | −0.186291 | ||||||||
\(429\) | −18.1962 | −0.878520 | ||||||||
\(430\) | −0.630490 | −0.0304049 | ||||||||
\(431\) | −11.7546 | −0.566197 | −0.283099 | − | 0.959091i | \(-0.591362\pi\) | ||||
−0.283099 | + | 0.959091i | \(0.591362\pi\) | |||||||
\(432\) | 3.63998 | 0.175129 | ||||||||
\(433\) | 5.70487 | 0.274159 | 0.137079 | − | 0.990560i | \(-0.456228\pi\) | ||||
0.137079 | + | 0.990560i | \(0.456228\pi\) | |||||||
\(434\) | −1.17303 | −0.0563071 | ||||||||
\(435\) | 0.748143 | 0.0358707 | ||||||||
\(436\) | 35.3458 | 1.69276 | ||||||||
\(437\) | −23.0973 | −1.10489 | ||||||||
\(438\) | −3.41207 | −0.163035 | ||||||||
\(439\) | 2.94845 | 0.140722 | 0.0703609 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703609 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(440\) | 0.863977 | 0.0411885 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.13057 | 0.101341 | ||||||||
\(443\) | −4.63594 | −0.220260 | −0.110130 | − | 0.993917i | \(-0.535127\pi\) | ||||
−0.110130 | + | 0.993917i | \(0.535127\pi\) | |||||||
\(444\) | −2.07299 | −0.0983799 | ||||||||
\(445\) | −4.10256 | −0.194480 | ||||||||
\(446\) | −3.50869 | −0.166141 | ||||||||
\(447\) | −5.65638 | −0.267538 | ||||||||
\(448\) | −6.58175 | −0.310959 | ||||||||
\(449\) | 39.5232 | 1.86522 | 0.932608 | − | 0.360890i | \(-0.117527\pi\) | ||||
0.932608 | + | 0.360890i | \(0.117527\pi\) | |||||||
\(450\) | −1.20608 | −0.0568551 | ||||||||
\(451\) | −4.09685 | −0.192913 | ||||||||
\(452\) | 12.0938 | 0.568845 | ||||||||
\(453\) | −2.50255 | −0.117580 | ||||||||
\(454\) | 3.52322 | 0.165353 | ||||||||
\(455\) | 2.06834 | 0.0969654 | ||||||||
\(456\) | −4.23188 | −0.198176 | ||||||||
\(457\) | −28.2011 | −1.31919 | −0.659597 | − | 0.751620i | \(-0.729273\pi\) | ||||
−0.659597 | + | 0.751620i | \(0.729273\pi\) | |||||||
\(458\) | 4.72458 | 0.220765 | ||||||||
\(459\) | −1.33136 | −0.0621424 | ||||||||
\(460\) | −3.26682 | −0.152316 | ||||||||
\(461\) | 25.8036 | 1.20179 | 0.600897 | − | 0.799327i | \(-0.294810\pi\) | ||||
0.600897 | + | 0.799327i | \(0.294810\pi\) | |||||||
\(462\) | 0.689226 | 0.0320657 | ||||||||
\(463\) | −11.7873 | −0.547801 | −0.273900 | − | 0.961758i | \(-0.588314\pi\) | ||||
−0.273900 | + | 0.961758i | \(0.588314\pi\) | |||||||
\(464\) | −8.55798 | −0.397294 | ||||||||
\(465\) | 1.51610 | 0.0703077 | ||||||||
\(466\) | −2.86108 | −0.132537 | ||||||||
\(467\) | −21.0242 | −0.972884 | −0.486442 | − | 0.873713i | \(-0.661706\pi\) | ||||
−0.486442 | + | 0.873713i | \(0.661706\pi\) | |||||||
\(468\) | 12.6059 | 0.582708 | ||||||||
\(469\) | 0.549822 | 0.0253884 | ||||||||
\(470\) | 0.561444 | 0.0258975 | ||||||||
\(471\) | −14.3393 | −0.660721 | ||||||||
\(472\) | 4.87408 | 0.224348 | ||||||||
\(473\) | 22.5291 | 1.03589 | ||||||||
\(474\) | −0.368117 | −0.0169082 | ||||||||
\(475\) | −21.3746 | −0.980734 | ||||||||
\(476\) | 2.58201 | 0.118346 | ||||||||
\(477\) | 9.12591 | 0.417847 | ||||||||
\(478\) | 0.0734936 | 0.00336152 | ||||||||
\(479\) | 29.9975 | 1.37062 | 0.685311 | − | 0.728251i | \(-0.259666\pi\) | ||||
0.685311 | + | 0.728251i | \(0.259666\pi\) | |||||||
\(480\) | −0.902421 | −0.0411897 | ||||||||
\(481\) | −6.94774 | −0.316790 | ||||||||
\(482\) | 4.53860 | 0.206727 | ||||||||
\(483\) | −5.29356 | −0.240866 | ||||||||
\(484\) | 6.13460 | 0.278845 | ||||||||
\(485\) | 2.29134 | 0.104045 | ||||||||
\(486\) | 0.246202 | 0.0111679 | ||||||||
\(487\) | 12.1673 | 0.551354 | 0.275677 | − | 0.961250i | \(-0.411098\pi\) | ||||
0.275677 | + | 0.961250i | \(0.411098\pi\) | |||||||
\(488\) | 2.41405 | 0.109279 | ||||||||
\(489\) | −16.7787 | −0.758760 | ||||||||
\(490\) | −0.0783436 | −0.00353920 | ||||||||
\(491\) | 16.0438 | 0.724048 | 0.362024 | − | 0.932169i | \(-0.382086\pi\) | ||||
0.362024 | + | 0.932169i | \(0.382086\pi\) | |||||||
\(492\) | 2.83820 | 0.127956 | ||||||||
\(493\) | 3.13016 | 0.140975 | ||||||||
\(494\) | −6.98256 | −0.314160 | ||||||||
\(495\) | −0.890805 | −0.0400387 | ||||||||
\(496\) | −17.3427 | −0.778709 | ||||||||
\(497\) | −11.9210 | −0.534729 | ||||||||
\(498\) | −4.21703 | −0.188969 | ||||||||
\(499\) | −26.3857 | −1.18119 | −0.590593 | − | 0.806970i | \(-0.701106\pi\) | ||||
−0.590593 | + | 0.806970i | \(0.701106\pi\) | |||||||
\(500\) | −6.10881 | −0.273194 | ||||||||
\(501\) | −10.9980 | −0.491353 | ||||||||
\(502\) | 6.80500 | 0.303722 | ||||||||
\(503\) | 18.3203 | 0.816862 | 0.408431 | − | 0.912789i | \(-0.366076\pi\) | ||||
0.408431 | + | 0.912789i | \(0.366076\pi\) | |||||||
\(504\) | −0.969884 | −0.0432021 | ||||||||
\(505\) | 0.284499 | 0.0126600 | ||||||||
\(506\) | −3.64846 | −0.162194 | ||||||||
\(507\) | 29.2493 | 1.29901 | ||||||||
\(508\) | 1.93938 | 0.0860463 | ||||||||
\(509\) | 36.9703 | 1.63868 | 0.819339 | − | 0.573309i | \(-0.194340\pi\) | ||||
0.819339 | + | 0.573309i | \(0.194340\pi\) | |||||||
\(510\) | 0.104303 | 0.00461863 | ||||||||
\(511\) | −13.8588 | −0.613079 | ||||||||
\(512\) | 17.3835 | 0.768249 | ||||||||
\(513\) | 4.36328 | 0.192644 | ||||||||
\(514\) | 0.589940 | 0.0260211 | ||||||||
\(515\) | −3.24986 | −0.143206 | ||||||||
\(516\) | −15.6077 | −0.687089 | ||||||||
\(517\) | −20.0619 | −0.882323 | ||||||||
\(518\) | 0.263163 | 0.0115627 | ||||||||
\(519\) | 14.9307 | 0.655384 | ||||||||
\(520\) | −2.00605 | −0.0879712 | ||||||||
\(521\) | −2.13160 | −0.0933871 | −0.0466936 | − | 0.998909i | \(-0.514868\pi\) | ||||
−0.0466936 | + | 0.998909i | \(0.514868\pi\) | |||||||
\(522\) | −0.578846 | −0.0253354 | ||||||||
\(523\) | −24.4693 | −1.06997 | −0.534983 | − | 0.844863i | \(-0.679682\pi\) | ||||
−0.534983 | + | 0.844863i | \(0.679682\pi\) | |||||||
\(524\) | 36.4390 | 1.59185 | ||||||||
\(525\) | −4.89874 | −0.213799 | ||||||||
\(526\) | 4.73368 | 0.206398 | ||||||||
\(527\) | 6.34324 | 0.276316 | ||||||||
\(528\) | 10.1899 | 0.443458 | ||||||||
\(529\) | 5.02182 | 0.218340 | ||||||||
\(530\) | −0.714957 | −0.0310557 | ||||||||
\(531\) | −5.02542 | −0.218085 | ||||||||
\(532\) | −8.46208 | −0.366878 | ||||||||
\(533\) | 9.51238 | 0.412027 | ||||||||
\(534\) | 3.17419 | 0.137361 | ||||||||
\(535\) | −0.632358 | −0.0273392 | ||||||||
\(536\) | −0.533263 | −0.0230335 | ||||||||
\(537\) | 10.5989 | 0.457377 | ||||||||
\(538\) | 3.95892 | 0.170681 | ||||||||
\(539\) | 2.79943 | 0.120580 | ||||||||
\(540\) | 0.617130 | 0.0265570 | ||||||||
\(541\) | −3.07605 | −0.132250 | −0.0661250 | − | 0.997811i | \(-0.521064\pi\) | ||||
−0.0661250 | + | 0.997811i | \(0.521064\pi\) | |||||||
\(542\) | −6.08715 | −0.261466 | ||||||||
\(543\) | 14.6508 | 0.628724 | ||||||||
\(544\) | −3.77564 | −0.161879 | ||||||||
\(545\) | 5.79944 | 0.248421 | ||||||||
\(546\) | −1.60030 | −0.0684865 | ||||||||
\(547\) | 38.7810 | 1.65816 | 0.829078 | − | 0.559133i | \(-0.188866\pi\) | ||||
0.829078 | + | 0.559133i | \(0.188866\pi\) | |||||||
\(548\) | −40.5969 | −1.73422 | ||||||||
\(549\) | −2.48901 | −0.106228 | ||||||||
\(550\) | −3.37634 | −0.143968 | ||||||||
\(551\) | −10.2585 | −0.437028 | ||||||||
\(552\) | 5.13414 | 0.218524 | ||||||||
\(553\) | −1.49518 | −0.0635817 | ||||||||
\(554\) | 6.69635 | 0.284500 | ||||||||
\(555\) | −0.340131 | −0.0144378 | ||||||||
\(556\) | 11.2025 | 0.475091 | ||||||||
\(557\) | 15.3795 | 0.651651 | 0.325825 | − | 0.945430i | \(-0.394358\pi\) | ||||
0.325825 | + | 0.945430i | \(0.394358\pi\) | |||||||
\(558\) | −1.17303 | −0.0496582 | ||||||||
\(559\) | −52.3099 | −2.21247 | ||||||||
\(560\) | −1.15827 | −0.0489461 | ||||||||
\(561\) | −3.72704 | −0.157356 | ||||||||
\(562\) | 5.21803 | 0.220109 | ||||||||
\(563\) | 17.9471 | 0.756380 | 0.378190 | − | 0.925728i | \(-0.376547\pi\) | ||||
0.378190 | + | 0.925728i | \(0.376547\pi\) | |||||||
\(564\) | 13.8985 | 0.585230 | ||||||||
\(565\) | 1.98432 | 0.0834809 | ||||||||
\(566\) | 7.65060 | 0.321579 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 11.5620 | 0.485129 | ||||||||
\(569\) | 10.7314 | 0.449884 | 0.224942 | − | 0.974372i | \(-0.427781\pi\) | ||||
0.224942 | + | 0.974372i | \(0.427781\pi\) | |||||||
\(570\) | −0.341835 | −0.0143179 | ||||||||
\(571\) | −18.4705 | −0.772966 | −0.386483 | − | 0.922296i | \(-0.626310\pi\) | ||||
−0.386483 | + | 0.922296i | \(0.626310\pi\) | |||||||
\(572\) | 35.2894 | 1.47552 | ||||||||
\(573\) | −17.6738 | −0.738333 | ||||||||
\(574\) | −0.360305 | −0.0150389 | ||||||||
\(575\) | 25.9318 | 1.08143 | ||||||||
\(576\) | −6.58175 | −0.274240 | ||||||||
\(577\) | −0.892310 | −0.0371473 | −0.0185737 | − | 0.999827i | \(-0.505913\pi\) | ||||
−0.0185737 | + | 0.999827i | \(0.505913\pi\) | |||||||
\(578\) | −3.74904 | −0.155939 | ||||||||
\(579\) | −13.3112 | −0.553193 | ||||||||
\(580\) | −1.45094 | −0.0602469 | ||||||||
\(581\) | −17.1283 | −0.710603 | ||||||||
\(582\) | −1.77284 | −0.0734865 | ||||||||
\(583\) | 25.5474 | 1.05806 | ||||||||
\(584\) | 13.4415 | 0.556212 | ||||||||
\(585\) | 2.06834 | 0.0855154 | ||||||||
\(586\) | −4.66121 | −0.192553 | ||||||||
\(587\) | −30.5797 | −1.26216 | −0.631080 | − | 0.775718i | \(-0.717388\pi\) | ||||
−0.631080 | + | 0.775718i | \(0.717388\pi\) | |||||||
\(588\) | −1.93938 | −0.0799789 | ||||||||
\(589\) | −20.7888 | −0.856589 | ||||||||
\(590\) | 0.393710 | 0.0162088 | ||||||||
\(591\) | 3.10847 | 0.127865 | ||||||||
\(592\) | 3.89075 | 0.159909 | ||||||||
\(593\) | 33.7801 | 1.38718 | 0.693590 | − | 0.720370i | \(-0.256028\pi\) | ||||
0.693590 | + | 0.720370i | \(0.256028\pi\) | |||||||
\(594\) | 0.689226 | 0.0282793 | ||||||||
\(595\) | 0.423650 | 0.0173679 | ||||||||
\(596\) | 10.9699 | 0.449344 | ||||||||
\(597\) | −21.0921 | −0.863243 | ||||||||
\(598\) | 8.47129 | 0.346417 | ||||||||
\(599\) | −8.67399 | −0.354410 | −0.177205 | − | 0.984174i | \(-0.556706\pi\) | ||||
−0.177205 | + | 0.984174i | \(0.556706\pi\) | |||||||
\(600\) | 4.75121 | 0.193967 | ||||||||
\(601\) | −19.4904 | −0.795031 | −0.397516 | − | 0.917595i | \(-0.630128\pi\) | ||||
−0.397516 | + | 0.917595i | \(0.630128\pi\) | |||||||
\(602\) | 1.98137 | 0.0807546 | ||||||||
\(603\) | 0.549822 | 0.0223905 | ||||||||
\(604\) | 4.85341 | 0.197483 | ||||||||
\(605\) | 1.00655 | 0.0409220 | ||||||||
\(606\) | −0.220120 | −0.00894176 | ||||||||
\(607\) | −32.4809 | −1.31836 | −0.659179 | − | 0.751986i | \(-0.729096\pi\) | ||||
−0.659179 | + | 0.751986i | \(0.729096\pi\) | |||||||
\(608\) | 12.3740 | 0.501832 | ||||||||
\(609\) | −2.35110 | −0.0952716 | ||||||||
\(610\) | 0.194998 | 0.00789524 | ||||||||
\(611\) | 46.5814 | 1.88448 | ||||||||
\(612\) | 2.58201 | 0.104372 | ||||||||
\(613\) | −7.74253 | −0.312718 | −0.156359 | − | 0.987700i | \(-0.549976\pi\) | ||||
−0.156359 | + | 0.987700i | \(0.549976\pi\) | |||||||
\(614\) | −1.04877 | −0.0423248 | ||||||||
\(615\) | 0.465684 | 0.0187782 | ||||||||
\(616\) | −2.71513 | −0.109396 | ||||||||
\(617\) | 36.9258 | 1.48658 | 0.743288 | − | 0.668971i | \(-0.233265\pi\) | ||||
0.743288 | + | 0.668971i | \(0.233265\pi\) | |||||||
\(618\) | 2.51445 | 0.101146 | ||||||||
\(619\) | 5.50391 | 0.221221 | 0.110610 | − | 0.993864i | \(-0.464719\pi\) | ||||
0.110610 | + | 0.993864i | \(0.464719\pi\) | |||||||
\(620\) | −2.94031 | −0.118086 | ||||||||
\(621\) | −5.29356 | −0.212423 | ||||||||
\(622\) | 5.32986 | 0.213708 | ||||||||
\(623\) | 12.8927 | 0.516533 | ||||||||
\(624\) | −23.6597 | −0.947146 | ||||||||
\(625\) | 23.4914 | 0.939656 | ||||||||
\(626\) | −0.109142 | −0.00436221 | ||||||||
\(627\) | 12.2147 | 0.487809 | ||||||||
\(628\) | 27.8095 | 1.10972 | ||||||||
\(629\) | −1.42308 | −0.0567417 | ||||||||
\(630\) | −0.0783436 | −0.00312129 | ||||||||
\(631\) | 30.7518 | 1.22421 | 0.612105 | − | 0.790777i | \(-0.290323\pi\) | ||||
0.612105 | + | 0.790777i | \(0.290323\pi\) | |||||||
\(632\) | 1.45015 | 0.0576840 | ||||||||
\(633\) | 3.11651 | 0.123870 | ||||||||
\(634\) | 2.26540 | 0.0899704 | ||||||||
\(635\) | 0.318209 | 0.0126277 | ||||||||
\(636\) | −17.6986 | −0.701797 | ||||||||
\(637\) | −6.49995 | −0.257537 | ||||||||
\(638\) | −1.62044 | −0.0641539 | ||||||||
\(639\) | −11.9210 | −0.471587 | ||||||||
\(640\) | 2.32048 | 0.0917250 | ||||||||
\(641\) | 11.7811 | 0.465324 | 0.232662 | − | 0.972558i | \(-0.425256\pi\) | ||||
0.232662 | + | 0.972558i | \(0.425256\pi\) | |||||||
\(642\) | 0.489262 | 0.0193096 | ||||||||
\(643\) | −34.3871 | −1.35609 | −0.678047 | − | 0.735019i | \(-0.737173\pi\) | ||||
−0.678047 | + | 0.735019i | \(0.737173\pi\) | |||||||
\(644\) | 10.2663 | 0.404547 | ||||||||
\(645\) | −2.56086 | −0.100834 | ||||||||
\(646\) | −1.43021 | −0.0562707 | ||||||||
\(647\) | −6.03048 | −0.237083 | −0.118541 | − | 0.992949i | \(-0.537822\pi\) | ||||
−0.118541 | + | 0.992949i | \(0.537822\pi\) | |||||||
\(648\) | −0.969884 | −0.0381006 | ||||||||
\(649\) | −14.0683 | −0.552231 | ||||||||
\(650\) | 7.83946 | 0.307489 | ||||||||
\(651\) | −4.76449 | −0.186735 | ||||||||
\(652\) | 32.5404 | 1.27438 | ||||||||
\(653\) | 6.35698 | 0.248768 | 0.124384 | − | 0.992234i | \(-0.460305\pi\) | ||||
0.124384 | + | 0.992234i | \(0.460305\pi\) | |||||||
\(654\) | −4.48709 | −0.175459 | ||||||||
\(655\) | 5.97882 | 0.233612 | ||||||||
\(656\) | −5.32695 | −0.207982 | ||||||||
\(657\) | −13.8588 | −0.540685 | ||||||||
\(658\) | −1.76439 | −0.0687830 | ||||||||
\(659\) | 22.5576 | 0.878720 | 0.439360 | − | 0.898311i | \(-0.355205\pi\) | ||||
0.439360 | + | 0.898311i | \(0.355205\pi\) | |||||||
\(660\) | 1.72761 | 0.0672473 | ||||||||
\(661\) | −44.8294 | −1.74366 | −0.871830 | − | 0.489809i | \(-0.837067\pi\) | ||||
−0.871830 | + | 0.489809i | \(0.837067\pi\) | |||||||
\(662\) | 4.98993 | 0.193939 | ||||||||
\(663\) | 8.65375 | 0.336084 | ||||||||
\(664\) | 16.6125 | 0.644690 | ||||||||
\(665\) | −1.38844 | −0.0538412 | ||||||||
\(666\) | 0.263163 | 0.0101974 | ||||||||
\(667\) | 12.4457 | 0.481900 | ||||||||
\(668\) | 21.3293 | 0.825255 | ||||||||
\(669\) | −14.2513 | −0.550987 | ||||||||
\(670\) | −0.0430750 | −0.00166413 | ||||||||
\(671\) | −6.96782 | −0.268990 | ||||||||
\(672\) | 2.83594 | 0.109399 | ||||||||
\(673\) | 25.0877 | 0.967059 | 0.483529 | − | 0.875328i | \(-0.339355\pi\) | ||||
0.483529 | + | 0.875328i | \(0.339355\pi\) | |||||||
\(674\) | 1.03947 | 0.0400388 | ||||||||
\(675\) | −4.89874 | −0.188553 | ||||||||
\(676\) | −56.7257 | −2.18176 | ||||||||
\(677\) | −34.4793 | −1.32515 | −0.662573 | − | 0.748997i | \(-0.730536\pi\) | ||||
−0.662573 | + | 0.748997i | \(0.730536\pi\) | |||||||
\(678\) | −1.53529 | −0.0589624 | ||||||||
\(679\) | −7.20075 | −0.276339 | ||||||||
\(680\) | −0.410891 | −0.0157569 | ||||||||
\(681\) | 14.3103 | 0.548372 | ||||||||
\(682\) | −3.28381 | −0.125744 | ||||||||
\(683\) | 12.6147 | 0.482690 | 0.241345 | − | 0.970439i | \(-0.422411\pi\) | ||||
0.241345 | + | 0.970439i | \(0.422411\pi\) | |||||||
\(684\) | −8.46208 | −0.323556 | ||||||||
\(685\) | −6.66104 | −0.254505 | ||||||||
\(686\) | 0.246202 | 0.00940003 | ||||||||
\(687\) | 19.1899 | 0.732139 | ||||||||
\(688\) | 29.2936 | 1.11681 | ||||||||
\(689\) | −59.3179 | −2.25983 | ||||||||
\(690\) | 0.414717 | 0.0157880 | ||||||||
\(691\) | −41.2619 | −1.56968 | −0.784839 | − | 0.619700i | \(-0.787254\pi\) | ||||
−0.784839 | + | 0.619700i | \(0.787254\pi\) | |||||||
\(692\) | −28.9563 | −1.10075 | ||||||||
\(693\) | 2.79943 | 0.106342 | ||||||||
\(694\) | 5.70810 | 0.216676 | ||||||||
\(695\) | 1.83807 | 0.0697220 | ||||||||
\(696\) | 2.28030 | 0.0864345 | ||||||||
\(697\) | 1.94838 | 0.0738002 | ||||||||
\(698\) | 2.48027 | 0.0938795 | ||||||||
\(699\) | −11.6209 | −0.439542 | ||||||||
\(700\) | 9.50055 | 0.359087 | ||||||||
\(701\) | −34.9290 | −1.31925 | −0.659624 | − | 0.751595i | \(-0.729285\pi\) | ||||
−0.659624 | + | 0.751595i | \(0.729285\pi\) | |||||||
\(702\) | −1.60030 | −0.0603994 | ||||||||
\(703\) | 4.66387 | 0.175901 | ||||||||
\(704\) | −18.4252 | −0.694425 | ||||||||
\(705\) | 2.28042 | 0.0858856 | ||||||||
\(706\) | −6.43361 | −0.242132 | ||||||||
\(707\) | −0.894063 | −0.0336247 | ||||||||
\(708\) | 9.74623 | 0.366286 | ||||||||
\(709\) | 26.8327 | 1.00772 | 0.503861 | − | 0.863785i | \(-0.331912\pi\) | ||||
0.503861 | + | 0.863785i | \(0.331912\pi\) | |||||||
\(710\) | 0.933933 | 0.0350499 | ||||||||
\(711\) | −1.49518 | −0.0560738 | ||||||||
\(712\) | −12.5044 | −0.468621 | ||||||||
\(713\) | 25.2212 | 0.944540 | ||||||||
\(714\) | −0.327782 | −0.0122669 | ||||||||
\(715\) | 5.79019 | 0.216541 | ||||||||
\(716\) | −20.5554 | −0.768191 | ||||||||
\(717\) | 0.298510 | 0.0111480 | ||||||||
\(718\) | 3.19558 | 0.119258 | ||||||||
\(719\) | 20.7889 | 0.775296 | 0.387648 | − | 0.921808i | \(-0.373288\pi\) | ||||
0.387648 | + | 0.921808i | \(0.373288\pi\) | |||||||
\(720\) | −1.15827 | −0.0431664 | ||||||||
\(721\) | 10.2130 | 0.380351 | ||||||||
\(722\) | 0.00941036 | 0.000350217 0 | ||||||||
\(723\) | 18.4344 | 0.685585 | ||||||||
\(724\) | −28.4135 | −1.05598 | ||||||||
\(725\) | 11.5175 | 0.427748 | ||||||||
\(726\) | −0.778778 | −0.0289032 | ||||||||
\(727\) | 22.0538 | 0.817928 | 0.408964 | − | 0.912550i | \(-0.365890\pi\) | ||||
0.408964 | + | 0.912550i | \(0.365890\pi\) | |||||||
\(728\) | 6.30420 | 0.233649 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.08575 | 0.0401855 | ||||||||
\(731\) | −10.7144 | −0.396287 | ||||||||
\(732\) | 4.82715 | 0.178417 | ||||||||
\(733\) | −31.0700 | −1.14760 | −0.573798 | − | 0.818997i | \(-0.694531\pi\) | ||||
−0.573798 | + | 0.818997i | \(0.694531\pi\) | |||||||
\(734\) | −2.47049 | −0.0911875 | ||||||||
\(735\) | −0.318209 | −0.0117373 | ||||||||
\(736\) | −15.0122 | −0.553358 | ||||||||
\(737\) | 1.53919 | 0.0566968 | ||||||||
\(738\) | −0.360305 | −0.0132630 | ||||||||
\(739\) | 47.8405 | 1.75984 | 0.879921 | − | 0.475120i | \(-0.157595\pi\) | ||||
0.879921 | + | 0.475120i | \(0.157595\pi\) | |||||||
\(740\) | 0.659645 | 0.0242490 | ||||||||
\(741\) | −28.3611 | −1.04187 | ||||||||
\(742\) | 2.24682 | 0.0824832 | ||||||||
\(743\) | 17.0228 | 0.624507 | 0.312254 | − | 0.949999i | \(-0.398916\pi\) | ||||
0.312254 | + | 0.949999i | \(0.398916\pi\) | |||||||
\(744\) | 4.62101 | 0.169414 | ||||||||
\(745\) | 1.79991 | 0.0659436 | ||||||||
\(746\) | −8.65002 | −0.316700 | ||||||||
\(747\) | −17.1283 | −0.626693 | ||||||||
\(748\) | 7.22817 | 0.264288 | ||||||||
\(749\) | 1.98724 | 0.0726122 | ||||||||
\(750\) | 0.775504 | 0.0283174 | ||||||||
\(751\) | −24.1639 | −0.881754 | −0.440877 | − | 0.897568i | \(-0.645332\pi\) | ||||
−0.440877 | + | 0.897568i | \(0.645332\pi\) | |||||||
\(752\) | −26.0857 | −0.951246 | ||||||||
\(753\) | 27.6399 | 1.00725 | ||||||||
\(754\) | 3.76247 | 0.137021 | ||||||||
\(755\) | 0.796335 | 0.0289816 | ||||||||
\(756\) | −1.93938 | −0.0705347 | ||||||||
\(757\) | −35.9690 | −1.30732 | −0.653658 | − | 0.756790i | \(-0.726767\pi\) | ||||
−0.653658 | + | 0.756790i | \(0.726767\pi\) | |||||||
\(758\) | 3.30101 | 0.119898 | ||||||||
\(759\) | −14.8190 | −0.537895 | ||||||||
\(760\) | 1.34662 | 0.0488471 | ||||||||
\(761\) | −28.0258 | −1.01593 | −0.507967 | − | 0.861376i | \(-0.669603\pi\) | ||||
−0.507967 | + | 0.861376i | \(0.669603\pi\) | |||||||
\(762\) | −0.246202 | −0.00891895 | ||||||||
\(763\) | −18.2252 | −0.659798 | ||||||||
\(764\) | 34.2763 | 1.24007 | ||||||||
\(765\) | 0.423650 | 0.0153171 | ||||||||
\(766\) | −7.40410 | −0.267521 | ||||||||
\(767\) | 32.6650 | 1.17946 | ||||||||
\(768\) | 11.3681 | 0.410212 | ||||||||
\(769\) | −15.0578 | −0.542997 | −0.271498 | − | 0.962439i | \(-0.587519\pi\) | ||||
−0.271498 | + | 0.962439i | \(0.587519\pi\) | |||||||
\(770\) | −0.219318 | −0.00790367 | ||||||||
\(771\) | 2.39616 | 0.0862957 | ||||||||
\(772\) | 25.8155 | 0.929119 | ||||||||
\(773\) | 29.8191 | 1.07252 | 0.536260 | − | 0.844053i | \(-0.319837\pi\) | ||||
0.536260 | + | 0.844053i | \(0.319837\pi\) | |||||||
\(774\) | 1.98137 | 0.0712189 | ||||||||
\(775\) | 23.3400 | 0.838399 | ||||||||
\(776\) | 6.98389 | 0.250707 | ||||||||
\(777\) | 1.06889 | 0.0383463 | ||||||||
\(778\) | −4.13557 | −0.148268 | ||||||||
\(779\) | −6.38546 | −0.228783 | ||||||||
\(780\) | −4.01131 | −0.143628 | ||||||||
\(781\) | −33.3720 | −1.19414 | ||||||||
\(782\) | 1.73514 | 0.0620484 | ||||||||
\(783\) | −2.35110 | −0.0840216 | ||||||||
\(784\) | 3.63998 | 0.129999 | ||||||||
\(785\) | 4.56290 | 0.162857 | ||||||||
\(786\) | −4.62588 | −0.165000 | ||||||||
\(787\) | 22.2169 | 0.791947 | 0.395974 | − | 0.918262i | \(-0.370407\pi\) | ||||
0.395974 | + | 0.918262i | \(0.370407\pi\) | |||||||
\(788\) | −6.02851 | −0.214757 | ||||||||
\(789\) | 19.2268 | 0.684494 | ||||||||
\(790\) | 0.117138 | 0.00416759 | ||||||||
\(791\) | −6.23590 | −0.221723 | ||||||||
\(792\) | −2.71513 | −0.0964778 | ||||||||
\(793\) | 16.1784 | 0.574513 | ||||||||
\(794\) | −5.24215 | −0.186037 | ||||||||
\(795\) | −2.90395 | −0.102992 | ||||||||
\(796\) | 40.9057 | 1.44987 | ||||||||
\(797\) | 10.9848 | 0.389102 | 0.194551 | − | 0.980892i | \(-0.437675\pi\) | ||||
0.194551 | + | 0.980892i | \(0.437675\pi\) | |||||||
\(798\) | 1.07425 | 0.0380280 | ||||||||
\(799\) | 9.54106 | 0.337539 | ||||||||
\(800\) | −13.8925 | −0.491175 | ||||||||
\(801\) | 12.8927 | 0.455539 | ||||||||
\(802\) | −1.58482 | −0.0559621 | ||||||||
\(803\) | −38.7969 | −1.36911 | ||||||||
\(804\) | −1.06632 | −0.0376061 | ||||||||
\(805\) | 1.68446 | 0.0593694 | ||||||||
\(806\) | 7.62462 | 0.268566 | ||||||||
\(807\) | 16.0800 | 0.566042 | ||||||||
\(808\) | 0.867137 | 0.0305058 | ||||||||
\(809\) | 15.6198 | 0.549162 | 0.274581 | − | 0.961564i | \(-0.411461\pi\) | ||||
0.274581 | + | 0.961564i | \(0.411461\pi\) | |||||||
\(810\) | −0.0783436 | −0.00275271 | ||||||||
\(811\) | −33.9143 | −1.19089 | −0.595447 | − | 0.803395i | \(-0.703025\pi\) | ||||
−0.595447 | + | 0.803395i | \(0.703025\pi\) | |||||||
\(812\) | 4.55970 | 0.160014 | ||||||||
\(813\) | −24.7242 | −0.867117 | ||||||||
\(814\) | 0.736708 | 0.0258216 | ||||||||
\(815\) | 5.33914 | 0.187022 | ||||||||
\(816\) | −4.84611 | −0.169648 | ||||||||
\(817\) | 35.1146 | 1.22850 | ||||||||
\(818\) | 2.03994 | 0.0713247 | ||||||||
\(819\) | −6.49995 | −0.227127 | ||||||||
\(820\) | −0.903141 | −0.0315391 | ||||||||
\(821\) | 15.7908 | 0.551102 | 0.275551 | − | 0.961286i | \(-0.411140\pi\) | ||||
0.275551 | + | 0.961286i | \(0.411140\pi\) | |||||||
\(822\) | 5.15372 | 0.179757 | ||||||||
\(823\) | 21.7601 | 0.758509 | 0.379254 | − | 0.925292i | \(-0.376181\pi\) | ||||
0.379254 | + | 0.925292i | \(0.376181\pi\) | |||||||
\(824\) | −9.90540 | −0.345071 | ||||||||
\(825\) | −13.7137 | −0.477450 | ||||||||
\(826\) | −1.23727 | −0.0430501 | ||||||||
\(827\) | −35.0663 | −1.21937 | −0.609687 | − | 0.792642i | \(-0.708705\pi\) | ||||
−0.609687 | + | 0.792642i | \(0.708705\pi\) | |||||||
\(828\) | 10.2663 | 0.356777 | ||||||||
\(829\) | 9.47354 | 0.329030 | 0.164515 | − | 0.986375i | \(-0.447394\pi\) | ||||
0.164515 | + | 0.986375i | \(0.447394\pi\) | |||||||
\(830\) | 1.34190 | 0.0465779 | ||||||||
\(831\) | 27.1986 | 0.943509 | ||||||||
\(832\) | 42.7811 | 1.48317 | ||||||||
\(833\) | −1.33136 | −0.0461288 | ||||||||
\(834\) | −1.42214 | −0.0492446 | ||||||||
\(835\) | 3.49965 | 0.121110 | ||||||||
\(836\) | −23.6890 | −0.819302 | ||||||||
\(837\) | −4.76449 | −0.164685 | ||||||||
\(838\) | 6.71109 | 0.231831 | ||||||||
\(839\) | 0.187162 | 0.00646157 | 0.00323078 | − | 0.999995i | \(-0.498972\pi\) | ||||
0.00323078 | + | 0.999995i | \(0.498972\pi\) | |||||||
\(840\) | 0.308626 | 0.0106486 | ||||||||
\(841\) | −23.4723 | −0.809390 | ||||||||
\(842\) | −5.26012 | −0.181276 | ||||||||
\(843\) | 21.1941 | 0.729963 | ||||||||
\(844\) | −6.04411 | −0.208047 | ||||||||
\(845\) | −9.30740 | −0.320184 | ||||||||
\(846\) | −1.76439 | −0.0606609 | ||||||||
\(847\) | −3.16317 | −0.108688 | ||||||||
\(848\) | 33.2181 | 1.14072 | ||||||||
\(849\) | 31.0745 | 1.06647 | ||||||||
\(850\) | 1.60572 | 0.0550758 | ||||||||
\(851\) | −5.65825 | −0.193962 | ||||||||
\(852\) | 23.1194 | 0.792056 | ||||||||
\(853\) | −17.7583 | −0.608034 | −0.304017 | − | 0.952667i | \(-0.598328\pi\) | ||||
−0.304017 | + | 0.952667i | \(0.598328\pi\) | |||||||
\(854\) | −0.612799 | −0.0209696 | ||||||||
\(855\) | −1.38844 | −0.0474835 | ||||||||
\(856\) | −1.92739 | −0.0658769 | ||||||||
\(857\) | −24.4576 | −0.835455 | −0.417727 | − | 0.908572i | \(-0.637173\pi\) | ||||
−0.417727 | + | 0.908572i | \(0.637173\pi\) | |||||||
\(858\) | −4.47993 | −0.152942 | ||||||||
\(859\) | 6.32700 | 0.215874 | 0.107937 | − | 0.994158i | \(-0.465575\pi\) | ||||
0.107937 | + | 0.994158i | \(0.465575\pi\) | |||||||
\(860\) | 4.96650 | 0.169356 | ||||||||
\(861\) | −1.46345 | −0.0498744 | ||||||||
\(862\) | −2.89399 | −0.0985698 | ||||||||
\(863\) | −0.857036 | −0.0291738 | −0.0145869 | − | 0.999894i | \(-0.504643\pi\) | ||||
−0.0145869 | + | 0.999894i | \(0.504643\pi\) | |||||||
\(864\) | 2.83594 | 0.0964806 | ||||||||
\(865\) | −4.75108 | −0.161541 | ||||||||
\(866\) | 1.40455 | 0.0477286 | ||||||||
\(867\) | −15.2275 | −0.517153 | ||||||||
\(868\) | 9.24019 | 0.313632 | ||||||||
\(869\) | −4.18567 | −0.141989 | ||||||||
\(870\) | 0.184194 | 0.00624477 | ||||||||
\(871\) | −3.57381 | −0.121094 | ||||||||
\(872\) | 17.6764 | 0.598598 | ||||||||
\(873\) | −7.20075 | −0.243708 | ||||||||
\(874\) | −5.68660 | −0.192352 | ||||||||
\(875\) | 3.14987 | 0.106485 | ||||||||
\(876\) | 26.8776 | 0.908111 | ||||||||
\(877\) | 6.88110 | 0.232358 | 0.116179 | − | 0.993228i | \(-0.462935\pi\) | ||||
0.116179 | + | 0.993228i | \(0.462935\pi\) | |||||||
\(878\) | 0.725913 | 0.0244984 | ||||||||
\(879\) | −18.9325 | −0.638577 | ||||||||
\(880\) | −3.24251 | −0.109305 | ||||||||
\(881\) | −51.7694 | −1.74416 | −0.872078 | − | 0.489367i | \(-0.837228\pi\) | ||||
−0.872078 | + | 0.489367i | \(0.837228\pi\) | |||||||
\(882\) | 0.246202 | 0.00829005 | ||||||||
\(883\) | −18.4022 | −0.619283 | −0.309641 | − | 0.950853i | \(-0.600209\pi\) | ||||
−0.309641 | + | 0.950853i | \(0.600209\pi\) | |||||||
\(884\) | −16.7829 | −0.564472 | ||||||||
\(885\) | 1.59914 | 0.0537543 | ||||||||
\(886\) | −1.14138 | −0.0383453 | ||||||||
\(887\) | −54.6988 | −1.83661 | −0.918303 | − | 0.395878i | \(-0.870440\pi\) | ||||
−0.918303 | + | 0.395878i | \(0.870440\pi\) | |||||||
\(888\) | −1.03670 | −0.0347894 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −1.01006 | −0.0338572 | ||||||||
\(891\) | 2.79943 | 0.0937846 | ||||||||
\(892\) | 27.6387 | 0.925413 | ||||||||
\(893\) | −31.2691 | −1.04638 | ||||||||
\(894\) | −1.39261 | −0.0465759 | ||||||||
\(895\) | −3.37267 | −0.112736 | ||||||||
\(896\) | −7.29232 | −0.243619 | ||||||||
\(897\) | 34.4079 | 1.14885 | ||||||||
\(898\) | 9.73069 | 0.324717 | ||||||||
\(899\) | 11.2018 | 0.373602 | ||||||||
\(900\) | 9.50055 | 0.316685 | ||||||||
\(901\) | −12.1498 | −0.404770 | ||||||||
\(902\) | −1.00865 | −0.0335844 | ||||||||
\(903\) | 8.04774 | 0.267812 | ||||||||
\(904\) | 6.04810 | 0.201157 | ||||||||
\(905\) | −4.66200 | −0.154970 | ||||||||
\(906\) | −0.616133 | −0.0204696 | ||||||||
\(907\) | 39.2425 | 1.30303 | 0.651514 | − | 0.758637i | \(-0.274134\pi\) | ||||
0.651514 | + | 0.758637i | \(0.274134\pi\) | |||||||
\(908\) | −27.7532 | −0.921021 | ||||||||
\(909\) | −0.894063 | −0.0296542 | ||||||||
\(910\) | 0.509230 | 0.0168808 | ||||||||
\(911\) | 7.34578 | 0.243377 | 0.121688 | − | 0.992568i | \(-0.461169\pi\) | ||||
0.121688 | + | 0.992568i | \(0.461169\pi\) | |||||||
\(912\) | 15.8823 | 0.525914 | ||||||||
\(913\) | −47.9496 | −1.58690 | ||||||||
\(914\) | −6.94317 | −0.229660 | ||||||||
\(915\) | 0.792026 | 0.0261836 | ||||||||
\(916\) | −37.2165 | −1.22967 | ||||||||
\(917\) | −18.7890 | −0.620467 | ||||||||
\(918\) | −0.327782 | −0.0108184 | ||||||||
\(919\) | 58.3954 | 1.92629 | 0.963144 | − | 0.268986i | \(-0.0866887\pi\) | ||||
0.963144 | + | 0.268986i | \(0.0866887\pi\) | |||||||
\(920\) | −1.63373 | −0.0538625 | ||||||||
\(921\) | −4.25979 | −0.140365 | ||||||||
\(922\) | 6.35289 | 0.209221 | ||||||||
\(923\) | 77.4858 | 2.55048 | ||||||||
\(924\) | −5.42918 | −0.178607 | ||||||||
\(925\) | −5.23623 | −0.172166 | ||||||||
\(926\) | −2.90205 | −0.0953672 | ||||||||
\(927\) | 10.2130 | 0.335438 | ||||||||
\(928\) | −6.66759 | −0.218874 | ||||||||
\(929\) | −43.5784 | −1.42976 | −0.714880 | − | 0.699247i | \(-0.753519\pi\) | ||||
−0.714880 | + | 0.699247i | \(0.753519\pi\) | |||||||
\(930\) | 0.373268 | 0.0122399 | ||||||||
\(931\) | 4.36328 | 0.143001 | ||||||||
\(932\) | 22.5374 | 0.738236 | ||||||||
\(933\) | 21.6483 | 0.708735 | ||||||||
\(934\) | −5.17620 | −0.169370 | ||||||||
\(935\) | 1.18598 | 0.0387857 | ||||||||
\(936\) | 6.30420 | 0.206059 | ||||||||
\(937\) | 19.8795 | 0.649435 | 0.324718 | − | 0.945811i | \(-0.394731\pi\) | ||||
0.324718 | + | 0.945811i | \(0.394731\pi\) | |||||||
\(938\) | 0.135367 | 0.00441989 | ||||||||
\(939\) | −0.443304 | −0.0144667 | ||||||||
\(940\) | −4.42261 | −0.144250 | ||||||||
\(941\) | 8.08530 | 0.263573 | 0.131787 | − | 0.991278i | \(-0.457929\pi\) | ||||
0.131787 | + | 0.991278i | \(0.457929\pi\) | |||||||
\(942\) | −3.53037 | −0.115026 | ||||||||
\(943\) | 7.74689 | 0.252274 | ||||||||
\(944\) | −18.2925 | −0.595369 | ||||||||
\(945\) | −0.318209 | −0.0103513 | ||||||||
\(946\) | 5.54671 | 0.180339 | ||||||||
\(947\) | 40.1421 | 1.30444 | 0.652221 | − | 0.758028i | \(-0.273837\pi\) | ||||
0.652221 | + | 0.758028i | \(0.273837\pi\) | |||||||
\(948\) | 2.89974 | 0.0941790 | ||||||||
\(949\) | 90.0818 | 2.92418 | ||||||||
\(950\) | −5.26246 | −0.170737 | ||||||||
\(951\) | 9.20138 | 0.298375 | ||||||||
\(952\) | 1.29126 | 0.0418500 | ||||||||
\(953\) | 29.1867 | 0.945449 | 0.472725 | − | 0.881210i | \(-0.343271\pi\) | ||||
0.472725 | + | 0.881210i | \(0.343271\pi\) | |||||||
\(954\) | 2.24682 | 0.0727433 | ||||||||
\(955\) | 5.62396 | 0.181987 | ||||||||
\(956\) | −0.578925 | −0.0187238 | ||||||||
\(957\) | −6.58176 | −0.212758 | ||||||||
\(958\) | 7.38544 | 0.238613 | ||||||||
\(959\) | 20.9329 | 0.675959 | ||||||||
\(960\) | 2.09437 | 0.0675956 | ||||||||
\(961\) | −8.29959 | −0.267729 | ||||||||
\(962\) | −1.71055 | −0.0551502 | ||||||||
\(963\) | 1.98724 | 0.0640379 | ||||||||
\(964\) | −35.7515 | −1.15148 | ||||||||
\(965\) | 4.23573 | 0.136353 | ||||||||
\(966\) | −1.30329 | −0.0419325 | ||||||||
\(967\) | −15.3154 | −0.492511 | −0.246256 | − | 0.969205i | \(-0.579200\pi\) | ||||
−0.246256 | + | 0.969205i | \(0.579200\pi\) | |||||||
\(968\) | 3.06791 | 0.0986062 | ||||||||
\(969\) | −5.80908 | −0.186615 | ||||||||
\(970\) | 0.564133 | 0.0181132 | ||||||||
\(971\) | −50.0150 | −1.60506 | −0.802529 | − | 0.596613i | \(-0.796513\pi\) | ||||
−0.802529 | + | 0.596613i | \(0.796513\pi\) | |||||||
\(972\) | −1.93938 | −0.0622058 | ||||||||
\(973\) | −5.77630 | −0.185180 | ||||||||
\(974\) | 2.99562 | 0.0959858 | ||||||||
\(975\) | 31.8416 | 1.01975 | ||||||||
\(976\) | −9.05995 | −0.290002 | ||||||||
\(977\) | 11.7653 | 0.376406 | 0.188203 | − | 0.982130i | \(-0.439734\pi\) | ||||
0.188203 | + | 0.982130i | \(0.439734\pi\) | |||||||
\(978\) | −4.13095 | −0.132093 | ||||||||
\(979\) | 36.0921 | 1.15351 | ||||||||
\(980\) | 0.617130 | 0.0197135 | ||||||||
\(981\) | −18.2252 | −0.581887 | ||||||||
\(982\) | 3.95002 | 0.126050 | ||||||||
\(983\) | −10.5544 | −0.336633 | −0.168316 | − | 0.985733i | \(-0.553833\pi\) | ||||
−0.168316 | + | 0.985733i | \(0.553833\pi\) | |||||||
\(984\) | 1.41938 | 0.0452482 | ||||||||
\(985\) | −0.989142 | −0.0315167 | ||||||||
\(986\) | 0.770651 | 0.0245425 | ||||||||
\(987\) | −7.16642 | −0.228110 | ||||||||
\(988\) | 55.0031 | 1.74988 | ||||||||
\(989\) | −42.6013 | −1.35464 | ||||||||
\(990\) | −0.219318 | −0.00697038 | ||||||||
\(991\) | 2.89587 | 0.0919905 | 0.0459952 | − | 0.998942i | \(-0.485354\pi\) | ||||
0.0459952 | + | 0.998942i | \(0.485354\pi\) | |||||||
\(992\) | −13.5118 | −0.429000 | ||||||||
\(993\) | 20.2676 | 0.643174 | ||||||||
\(994\) | −2.93497 | −0.0930915 | ||||||||
\(995\) | 6.71170 | 0.212775 | ||||||||
\(996\) | 33.2184 | 1.05257 | ||||||||
\(997\) | −13.5622 | −0.429518 | −0.214759 | − | 0.976667i | \(-0.568897\pi\) | ||||
−0.214759 | + | 0.976667i | \(0.568897\pi\) | |||||||
\(998\) | −6.49621 | −0.205634 | ||||||||
\(999\) | 1.06889 | 0.0338182 |
(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 | 2667.2.a.j.1.4 | ✓ | 7 | |
3.2 | odd | 2 | 8001.2.a.l.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.j.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
8001.2.a.l.1.4 | 7 | 3.2 | odd | 2 |