Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.903670 | 0.638991 | 0.319496 | − | 0.947588i | \(-0.396486\pi\) | ||||
0.319496 | + | 0.947588i | \(0.396486\pi\) | |||||||
\(3\) | 2.25573 | 1.30235 | 0.651173 | − | 0.758930i | \(-0.274277\pi\) | ||||
0.651173 | + | 0.758930i | \(0.274277\pi\) | |||||||
\(4\) | −1.18338 | −0.591690 | ||||||||
\(5\) | 1.13079 | 0.505704 | 0.252852 | − | 0.967505i | \(-0.418632\pi\) | ||||
0.252852 | + | 0.967505i | \(0.418632\pi\) | |||||||
\(6\) | 2.03843 | 0.832188 | ||||||||
\(7\) | 2.22819 | 0.842175 | 0.421088 | − | 0.907020i | \(-0.361648\pi\) | ||||
0.421088 | + | 0.907020i | \(0.361648\pi\) | |||||||
\(8\) | −2.87673 | −1.01708 | ||||||||
\(9\) | 2.08831 | 0.696103 | ||||||||
\(10\) | 1.02186 | 0.323140 | ||||||||
\(11\) | 2.22736 | 0.671573 | 0.335787 | − | 0.941938i | \(-0.390998\pi\) | ||||
0.335787 | + | 0.941938i | \(0.390998\pi\) | |||||||
\(12\) | −2.66938 | −0.770585 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 2.01355 | 0.538143 | ||||||||
\(15\) | 2.55075 | 0.658601 | ||||||||
\(16\) | −0.232853 | −0.0582132 | ||||||||
\(17\) | 3.96482 | 0.961611 | 0.480806 | − | 0.876827i | \(-0.340344\pi\) | ||||
0.480806 | + | 0.876827i | \(0.340344\pi\) | |||||||
\(18\) | 1.88714 | 0.444804 | ||||||||
\(19\) | 4.47586 | 1.02683 | 0.513416 | − | 0.858140i | \(-0.328380\pi\) | ||||
0.513416 | + | 0.858140i | \(0.328380\pi\) | |||||||
\(20\) | −1.33815 | −0.299220 | ||||||||
\(21\) | 5.02618 | 1.09680 | ||||||||
\(22\) | 2.01280 | 0.429130 | ||||||||
\(23\) | 0.0963147 | 0.0200830 | 0.0100415 | − | 0.999950i | \(-0.496804\pi\) | ||||
0.0100415 | + | 0.999950i | \(0.496804\pi\) | |||||||
\(24\) | −6.48911 | −1.32458 | ||||||||
\(25\) | −3.72132 | −0.744264 | ||||||||
\(26\) | −0.903670 | −0.177224 | ||||||||
\(27\) | −2.05653 | −0.395779 | ||||||||
\(28\) | −2.63679 | −0.498307 | ||||||||
\(29\) | −3.60531 | −0.669490 | −0.334745 | − | 0.942309i | \(-0.608650\pi\) | ||||
−0.334745 | + | 0.942309i | \(0.608650\pi\) | |||||||
\(30\) | 2.30504 | 0.420840 | ||||||||
\(31\) | 7.04913 | 1.26606 | 0.633030 | − | 0.774127i | \(-0.281811\pi\) | ||||
0.633030 | + | 0.774127i | \(0.281811\pi\) | |||||||
\(32\) | 5.54303 | 0.979879 | ||||||||
\(33\) | 5.02431 | 0.874620 | ||||||||
\(34\) | 3.58289 | 0.614461 | ||||||||
\(35\) | 2.51961 | 0.425891 | ||||||||
\(36\) | −2.47126 | −0.411877 | ||||||||
\(37\) | −4.21245 | −0.692522 | −0.346261 | − | 0.938138i | \(-0.612549\pi\) | ||||
−0.346261 | + | 0.938138i | \(0.612549\pi\) | |||||||
\(38\) | 4.04470 | 0.656137 | ||||||||
\(39\) | −2.25573 | −0.361206 | ||||||||
\(40\) | −3.25297 | −0.514339 | ||||||||
\(41\) | 4.72050 | 0.737218 | 0.368609 | − | 0.929585i | \(-0.379834\pi\) | ||||
0.368609 | + | 0.929585i | \(0.379834\pi\) | |||||||
\(42\) | 4.54201 | 0.700848 | ||||||||
\(43\) | 6.32020 | 0.963821 | 0.481910 | − | 0.876220i | \(-0.339943\pi\) | ||||
0.481910 | + | 0.876220i | \(0.339943\pi\) | |||||||
\(44\) | −2.63581 | −0.397363 | ||||||||
\(45\) | 2.36143 | 0.352022 | ||||||||
\(46\) | 0.0870367 | 0.0128329 | ||||||||
\(47\) | 4.12572 | 0.601797 | 0.300899 | − | 0.953656i | \(-0.402713\pi\) | ||||
0.300899 | + | 0.953656i | \(0.402713\pi\) | |||||||
\(48\) | −0.525252 | −0.0758137 | ||||||||
\(49\) | −2.03519 | −0.290741 | ||||||||
\(50\) | −3.36285 | −0.475578 | ||||||||
\(51\) | 8.94357 | 1.25235 | ||||||||
\(52\) | 1.18338 | 0.164105 | ||||||||
\(53\) | −6.20318 | −0.852073 | −0.426036 | − | 0.904706i | \(-0.640090\pi\) | ||||
−0.426036 | + | 0.904706i | \(0.640090\pi\) | |||||||
\(54\) | −1.85842 | −0.252899 | ||||||||
\(55\) | 2.51867 | 0.339617 | ||||||||
\(56\) | −6.40988 | −0.856557 | ||||||||
\(57\) | 10.0963 | 1.33729 | ||||||||
\(58\) | −3.25802 | −0.427798 | ||||||||
\(59\) | −8.61233 | −1.12123 | −0.560615 | − | 0.828077i | \(-0.689435\pi\) | ||||
−0.560615 | + | 0.828077i | \(0.689435\pi\) | |||||||
\(60\) | −3.01851 | −0.389687 | ||||||||
\(61\) | 1.39069 | 0.178059 | 0.0890297 | − | 0.996029i | \(-0.471623\pi\) | ||||
0.0890297 | + | 0.996029i | \(0.471623\pi\) | |||||||
\(62\) | 6.37009 | 0.809002 | ||||||||
\(63\) | 4.65314 | 0.586241 | ||||||||
\(64\) | 5.47478 | 0.684347 | ||||||||
\(65\) | −1.13079 | −0.140257 | ||||||||
\(66\) | 4.54032 | 0.558875 | ||||||||
\(67\) | 1.77035 | 0.216283 | 0.108141 | − | 0.994136i | \(-0.465510\pi\) | ||||
0.108141 | + | 0.994136i | \(0.465510\pi\) | |||||||
\(68\) | −4.69189 | −0.568976 | ||||||||
\(69\) | 0.217260 | 0.0261550 | ||||||||
\(70\) | 2.27689 | 0.272141 | ||||||||
\(71\) | 8.33313 | 0.988961 | 0.494480 | − | 0.869189i | \(-0.335358\pi\) | ||||
0.494480 | + | 0.869189i | \(0.335358\pi\) | |||||||
\(72\) | −6.00749 | −0.707990 | ||||||||
\(73\) | −10.8259 | −1.26708 | −0.633540 | − | 0.773710i | \(-0.718399\pi\) | ||||
−0.633540 | + | 0.773710i | \(0.718399\pi\) | |||||||
\(74\) | −3.80667 | −0.442516 | ||||||||
\(75\) | −8.39429 | −0.969289 | ||||||||
\(76\) | −5.29664 | −0.607566 | ||||||||
\(77\) | 4.96297 | 0.565582 | ||||||||
\(78\) | −2.03843 | −0.230807 | ||||||||
\(79\) | −4.74504 | −0.533858 | −0.266929 | − | 0.963716i | \(-0.586009\pi\) | ||||
−0.266929 | + | 0.963716i | \(0.586009\pi\) | |||||||
\(80\) | −0.263307 | −0.0294386 | ||||||||
\(81\) | −10.9039 | −1.21154 | ||||||||
\(82\) | 4.26578 | 0.471076 | ||||||||
\(83\) | −10.3415 | −1.13513 | −0.567565 | − | 0.823329i | \(-0.692114\pi\) | ||||
−0.567565 | + | 0.823329i | \(0.692114\pi\) | |||||||
\(84\) | −5.94788 | −0.648967 | ||||||||
\(85\) | 4.48337 | 0.486290 | ||||||||
\(86\) | 5.71137 | 0.615873 | ||||||||
\(87\) | −8.13261 | −0.871907 | ||||||||
\(88\) | −6.40749 | −0.683041 | ||||||||
\(89\) | 1.80124 | 0.190931 | 0.0954655 | − | 0.995433i | \(-0.469566\pi\) | ||||
0.0954655 | + | 0.995433i | \(0.469566\pi\) | |||||||
\(90\) | 2.13396 | 0.224939 | ||||||||
\(91\) | −2.22819 | −0.233577 | ||||||||
\(92\) | −0.113977 | −0.0118829 | ||||||||
\(93\) | 15.9009 | 1.64885 | ||||||||
\(94\) | 3.72829 | 0.384543 | ||||||||
\(95\) | 5.06124 | 0.519273 | ||||||||
\(96\) | 12.5036 | 1.27614 | ||||||||
\(97\) | −10.1464 | −1.03021 | −0.515107 | − | 0.857126i | \(-0.672248\pi\) | ||||
−0.515107 | + | 0.857126i | \(0.672248\pi\) | |||||||
\(98\) | −1.83914 | −0.185781 | ||||||||
\(99\) | 4.65141 | 0.467484 | ||||||||
\(100\) | 4.40373 | 0.440373 | ||||||||
\(101\) | −1.09105 | −0.108564 | −0.0542818 | − | 0.998526i | \(-0.517287\pi\) | ||||
−0.0542818 | + | 0.998526i | \(0.517287\pi\) | |||||||
\(102\) | 8.08204 | 0.800241 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 2.87673 | 0.282086 | ||||||||
\(105\) | 5.68354 | 0.554657 | ||||||||
\(106\) | −5.60563 | −0.544467 | ||||||||
\(107\) | 5.80619 | 0.561305 | 0.280653 | − | 0.959809i | \(-0.409449\pi\) | ||||
0.280653 | + | 0.959809i | \(0.409449\pi\) | |||||||
\(108\) | 2.43365 | 0.234178 | ||||||||
\(109\) | 16.7131 | 1.60082 | 0.800412 | − | 0.599450i | \(-0.204614\pi\) | ||||
0.800412 | + | 0.599450i | \(0.204614\pi\) | |||||||
\(110\) | 2.27604 | 0.217012 | ||||||||
\(111\) | −9.50214 | −0.901903 | ||||||||
\(112\) | −0.518839 | −0.0490257 | ||||||||
\(113\) | −8.03065 | −0.755460 | −0.377730 | − | 0.925916i | \(-0.623295\pi\) | ||||
−0.377730 | + | 0.925916i | \(0.623295\pi\) | |||||||
\(114\) | 9.12374 | 0.854517 | ||||||||
\(115\) | 0.108911 | 0.0101560 | ||||||||
\(116\) | 4.26646 | 0.396130 | ||||||||
\(117\) | −2.08831 | −0.193064 | ||||||||
\(118\) | −7.78271 | −0.716456 | ||||||||
\(119\) | 8.83437 | 0.809845 | ||||||||
\(120\) | −7.33781 | −0.669847 | ||||||||
\(121\) | −6.03888 | −0.548989 | ||||||||
\(122\) | 1.25672 | 0.113778 | ||||||||
\(123\) | 10.6482 | 0.960113 | ||||||||
\(124\) | −8.34179 | −0.749115 | ||||||||
\(125\) | −9.86196 | −0.882080 | ||||||||
\(126\) | 4.20491 | 0.374603 | ||||||||
\(127\) | −12.8089 | −1.13660 | −0.568301 | − | 0.822820i | \(-0.692399\pi\) | ||||
−0.568301 | + | 0.822820i | \(0.692399\pi\) | |||||||
\(128\) | −6.13867 | −0.542587 | ||||||||
\(129\) | 14.2566 | 1.25523 | ||||||||
\(130\) | −1.02186 | −0.0896230 | ||||||||
\(131\) | 10.2802 | 0.898184 | 0.449092 | − | 0.893486i | \(-0.351748\pi\) | ||||
0.449092 | + | 0.893486i | \(0.351748\pi\) | |||||||
\(132\) | −5.94567 | −0.517504 | ||||||||
\(133\) | 9.97304 | 0.864772 | ||||||||
\(134\) | 1.59981 | 0.138203 | ||||||||
\(135\) | −2.32549 | −0.200147 | ||||||||
\(136\) | −11.4057 | −0.978032 | ||||||||
\(137\) | −10.2616 | −0.876704 | −0.438352 | − | 0.898803i | \(-0.644438\pi\) | ||||
−0.438352 | + | 0.898803i | \(0.644438\pi\) | |||||||
\(138\) | 0.196331 | 0.0167128 | ||||||||
\(139\) | 3.75566 | 0.318551 | 0.159275 | − | 0.987234i | \(-0.449084\pi\) | ||||
0.159275 | + | 0.987234i | \(0.449084\pi\) | |||||||
\(140\) | −2.98165 | −0.251995 | ||||||||
\(141\) | 9.30649 | 0.783748 | ||||||||
\(142\) | 7.53041 | 0.631938 | ||||||||
\(143\) | −2.22736 | −0.186261 | ||||||||
\(144\) | −0.486269 | −0.0405224 | ||||||||
\(145\) | −4.07684 | −0.338563 | ||||||||
\(146\) | −9.78308 | −0.809654 | ||||||||
\(147\) | −4.59082 | −0.378645 | ||||||||
\(148\) | 4.98493 | 0.409758 | ||||||||
\(149\) | −11.1166 | −0.910707 | −0.455353 | − | 0.890311i | \(-0.650487\pi\) | ||||
−0.455353 | + | 0.890311i | \(0.650487\pi\) | |||||||
\(150\) | −7.58567 | −0.619367 | ||||||||
\(151\) | −3.13721 | −0.255303 | −0.127651 | − | 0.991819i | \(-0.540744\pi\) | ||||
−0.127651 | + | 0.991819i | \(0.540744\pi\) | |||||||
\(152\) | −12.8758 | −1.04437 | ||||||||
\(153\) | 8.27978 | 0.669381 | ||||||||
\(154\) | 4.48488 | 0.361402 | ||||||||
\(155\) | 7.97106 | 0.640251 | ||||||||
\(156\) | 2.66938 | 0.213722 | ||||||||
\(157\) | −4.44102 | −0.354432 | −0.177216 | − | 0.984172i | \(-0.556709\pi\) | ||||
−0.177216 | + | 0.984172i | \(0.556709\pi\) | |||||||
\(158\) | −4.28795 | −0.341131 | ||||||||
\(159\) | −13.9927 | −1.10969 | ||||||||
\(160\) | 6.26799 | 0.495528 | ||||||||
\(161\) | 0.214607 | 0.0169134 | ||||||||
\(162\) | −9.85352 | −0.774166 | ||||||||
\(163\) | −18.9769 | −1.48639 | −0.743193 | − | 0.669077i | \(-0.766689\pi\) | ||||
−0.743193 | + | 0.669077i | \(0.766689\pi\) | |||||||
\(164\) | −5.58614 | −0.436205 | ||||||||
\(165\) | 5.68143 | 0.442299 | ||||||||
\(166\) | −9.34532 | −0.725338 | ||||||||
\(167\) | 6.23721 | 0.482649 | 0.241325 | − | 0.970444i | \(-0.422418\pi\) | ||||
0.241325 | + | 0.970444i | \(0.422418\pi\) | |||||||
\(168\) | −14.4590 | −1.11553 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.05149 | 0.310735 | ||||||||
\(171\) | 9.34697 | 0.714781 | ||||||||
\(172\) | −7.47919 | −0.570283 | ||||||||
\(173\) | −6.83448 | −0.519616 | −0.259808 | − | 0.965660i | \(-0.583659\pi\) | ||||
−0.259808 | + | 0.965660i | \(0.583659\pi\) | |||||||
\(174\) | −7.34920 | −0.557141 | ||||||||
\(175\) | −8.29179 | −0.626801 | ||||||||
\(176\) | −0.518646 | −0.0390944 | ||||||||
\(177\) | −19.4271 | −1.46023 | ||||||||
\(178\) | 1.62773 | 0.122003 | ||||||||
\(179\) | 5.66656 | 0.423539 | 0.211769 | − | 0.977320i | \(-0.432077\pi\) | ||||
0.211769 | + | 0.977320i | \(0.432077\pi\) | |||||||
\(180\) | −2.79447 | −0.208288 | ||||||||
\(181\) | −2.76231 | −0.205321 | −0.102661 | − | 0.994716i | \(-0.532736\pi\) | ||||
−0.102661 | + | 0.994716i | \(0.532736\pi\) | |||||||
\(182\) | −2.01355 | −0.149254 | ||||||||
\(183\) | 3.13701 | 0.231895 | ||||||||
\(184\) | −0.277071 | −0.0204259 | ||||||||
\(185\) | −4.76338 | −0.350211 | ||||||||
\(186\) | 14.3692 | 1.05360 | ||||||||
\(187\) | 8.83108 | 0.645792 | ||||||||
\(188\) | −4.88229 | −0.356077 | ||||||||
\(189\) | −4.58232 | −0.333315 | ||||||||
\(190\) | 4.57369 | 0.331811 | ||||||||
\(191\) | −5.53593 | −0.400566 | −0.200283 | − | 0.979738i | \(-0.564186\pi\) | ||||
−0.200283 | + | 0.979738i | \(0.564186\pi\) | |||||||
\(192\) | 12.3496 | 0.891256 | ||||||||
\(193\) | 12.8074 | 0.921899 | 0.460950 | − | 0.887426i | \(-0.347509\pi\) | ||||
0.460950 | + | 0.887426i | \(0.347509\pi\) | |||||||
\(194\) | −9.16904 | −0.658299 | ||||||||
\(195\) | −2.55075 | −0.182663 | ||||||||
\(196\) | 2.40840 | 0.172028 | ||||||||
\(197\) | 0.250974 | 0.0178812 | 0.00894058 | − | 0.999960i | \(-0.497154\pi\) | ||||
0.00894058 | + | 0.999960i | \(0.497154\pi\) | |||||||
\(198\) | 4.20334 | 0.298718 | ||||||||
\(199\) | 6.22262 | 0.441110 | 0.220555 | − | 0.975375i | \(-0.429213\pi\) | ||||
0.220555 | + | 0.975375i | \(0.429213\pi\) | |||||||
\(200\) | 10.7052 | 0.756973 | ||||||||
\(201\) | 3.99343 | 0.281675 | ||||||||
\(202\) | −0.985950 | −0.0693712 | ||||||||
\(203\) | −8.03331 | −0.563828 | ||||||||
\(204\) | −10.5836 | −0.741003 | ||||||||
\(205\) | 5.33788 | 0.372814 | ||||||||
\(206\) | 0.903670 | 0.0629617 | ||||||||
\(207\) | 0.201135 | 0.0139798 | ||||||||
\(208\) | 0.232853 | 0.0161454 | ||||||||
\(209\) | 9.96933 | 0.689593 | ||||||||
\(210\) | 5.13605 | 0.354421 | ||||||||
\(211\) | 4.89217 | 0.336791 | 0.168395 | − | 0.985720i | \(-0.446141\pi\) | ||||
0.168395 | + | 0.985720i | \(0.446141\pi\) | |||||||
\(212\) | 7.34072 | 0.504163 | ||||||||
\(213\) | 18.7973 | 1.28797 | ||||||||
\(214\) | 5.24688 | 0.358669 | ||||||||
\(215\) | 7.14680 | 0.487408 | ||||||||
\(216\) | 5.91606 | 0.402537 | ||||||||
\(217\) | 15.7068 | 1.06624 | ||||||||
\(218\) | 15.1031 | 1.02291 | ||||||||
\(219\) | −24.4204 | −1.65018 | ||||||||
\(220\) | −2.98054 | −0.200948 | ||||||||
\(221\) | −3.96482 | −0.266703 | ||||||||
\(222\) | −8.58680 | −0.576308 | ||||||||
\(223\) | 1.67018 | 0.111843 | 0.0559216 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559216 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(224\) | 12.3509 | 0.825230 | ||||||||
\(225\) | −7.77127 | −0.518084 | ||||||||
\(226\) | −7.25706 | −0.482733 | ||||||||
\(227\) | −8.25340 | −0.547798 | −0.273899 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273899 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(228\) | −11.9478 | −0.791261 | ||||||||
\(229\) | 3.90549 | 0.258082 | 0.129041 | − | 0.991639i | \(-0.458810\pi\) | ||||
0.129041 | + | 0.991639i | \(0.458810\pi\) | |||||||
\(230\) | 0.0984201 | 0.00648963 | ||||||||
\(231\) | 11.1951 | 0.736584 | ||||||||
\(232\) | 10.3715 | 0.680922 | ||||||||
\(233\) | −26.3188 | −1.72420 | −0.862100 | − | 0.506738i | \(-0.830851\pi\) | ||||
−0.862100 | + | 0.506738i | \(0.830851\pi\) | |||||||
\(234\) | −1.88714 | −0.123366 | ||||||||
\(235\) | 4.66531 | 0.304331 | ||||||||
\(236\) | 10.1917 | 0.663420 | ||||||||
\(237\) | −10.7035 | −0.695268 | ||||||||
\(238\) | 7.98336 | 0.517484 | ||||||||
\(239\) | 17.1497 | 1.10932 | 0.554660 | − | 0.832077i | \(-0.312849\pi\) | ||||
0.554660 | + | 0.832077i | \(0.312849\pi\) | |||||||
\(240\) | −0.593949 | −0.0383392 | ||||||||
\(241\) | −15.7608 | −1.01524 | −0.507622 | − | 0.861580i | \(-0.669475\pi\) | ||||
−0.507622 | + | 0.861580i | \(0.669475\pi\) | |||||||
\(242\) | −5.45716 | −0.350800 | ||||||||
\(243\) | −18.4266 | −1.18207 | ||||||||
\(244\) | −1.64571 | −0.105356 | ||||||||
\(245\) | −2.30136 | −0.147029 | ||||||||
\(246\) | 9.62243 | 0.613504 | ||||||||
\(247\) | −4.47586 | −0.284792 | ||||||||
\(248\) | −20.2784 | −1.28768 | ||||||||
\(249\) | −23.3277 | −1.47833 | ||||||||
\(250\) | −8.91196 | −0.563642 | ||||||||
\(251\) | 26.6394 | 1.68146 | 0.840732 | − | 0.541452i | \(-0.182125\pi\) | ||||
0.840732 | + | 0.541452i | \(0.182125\pi\) | |||||||
\(252\) | −5.50644 | −0.346873 | ||||||||
\(253\) | 0.214527 | 0.0134872 | ||||||||
\(254\) | −11.5750 | −0.726280 | ||||||||
\(255\) | 10.1133 | 0.633318 | ||||||||
\(256\) | −16.4969 | −1.03106 | ||||||||
\(257\) | −26.6341 | −1.66139 | −0.830695 | − | 0.556728i | \(-0.812056\pi\) | ||||
−0.830695 | + | 0.556728i | \(0.812056\pi\) | |||||||
\(258\) | 12.8833 | 0.802080 | ||||||||
\(259\) | −9.38612 | −0.583225 | ||||||||
\(260\) | 1.33815 | 0.0829886 | ||||||||
\(261\) | −7.52901 | −0.466034 | ||||||||
\(262\) | 9.28990 | 0.573932 | ||||||||
\(263\) | 18.4550 | 1.13799 | 0.568993 | − | 0.822342i | \(-0.307333\pi\) | ||||
0.568993 | + | 0.822342i | \(0.307333\pi\) | |||||||
\(264\) | −14.4536 | −0.889555 | ||||||||
\(265\) | −7.01448 | −0.430896 | ||||||||
\(266\) | 9.01234 | 0.552582 | ||||||||
\(267\) | 4.06311 | 0.248658 | ||||||||
\(268\) | −2.09500 | −0.127972 | ||||||||
\(269\) | −9.81711 | −0.598560 | −0.299280 | − | 0.954165i | \(-0.596746\pi\) | ||||
−0.299280 | + | 0.954165i | \(0.596746\pi\) | |||||||
\(270\) | −2.10148 | −0.127892 | ||||||||
\(271\) | −11.4232 | −0.693907 | −0.346954 | − | 0.937882i | \(-0.612784\pi\) | ||||
−0.346954 | + | 0.937882i | \(0.612784\pi\) | |||||||
\(272\) | −0.923220 | −0.0559784 | ||||||||
\(273\) | −5.02618 | −0.304198 | ||||||||
\(274\) | −9.27306 | −0.560206 | ||||||||
\(275\) | −8.28871 | −0.499828 | ||||||||
\(276\) | −0.257101 | −0.0154757 | ||||||||
\(277\) | 23.8560 | 1.43337 | 0.716683 | − | 0.697399i | \(-0.245659\pi\) | ||||
0.716683 | + | 0.697399i | \(0.245659\pi\) | |||||||
\(278\) | 3.39388 | 0.203551 | ||||||||
\(279\) | 14.7208 | 0.881309 | ||||||||
\(280\) | −7.24821 | −0.433164 | ||||||||
\(281\) | 17.9354 | 1.06994 | 0.534968 | − | 0.844872i | \(-0.320323\pi\) | ||||
0.534968 | + | 0.844872i | \(0.320323\pi\) | |||||||
\(282\) | 8.41000 | 0.500808 | ||||||||
\(283\) | −11.0837 | −0.658856 | −0.329428 | − | 0.944181i | \(-0.606856\pi\) | ||||
−0.329428 | + | 0.944181i | \(0.606856\pi\) | |||||||
\(284\) | −9.86126 | −0.585158 | ||||||||
\(285\) | 11.4168 | 0.676272 | ||||||||
\(286\) | −2.01280 | −0.119019 | ||||||||
\(287\) | 10.5182 | 0.620867 | ||||||||
\(288\) | 11.5756 | 0.682097 | ||||||||
\(289\) | −1.28017 | −0.0753040 | ||||||||
\(290\) | −3.68412 | −0.216339 | ||||||||
\(291\) | −22.8876 | −1.34170 | ||||||||
\(292\) | 12.8112 | 0.749719 | ||||||||
\(293\) | 11.2580 | 0.657699 | 0.328849 | − | 0.944382i | \(-0.393339\pi\) | ||||
0.328849 | + | 0.944382i | \(0.393339\pi\) | |||||||
\(294\) | −4.14859 | −0.241951 | ||||||||
\(295\) | −9.73871 | −0.567010 | ||||||||
\(296\) | 12.1181 | 0.704348 | ||||||||
\(297\) | −4.58062 | −0.265794 | ||||||||
\(298\) | −10.0457 | −0.581934 | ||||||||
\(299\) | −0.0963147 | −0.00557002 | ||||||||
\(300\) | 9.93363 | 0.573518 | ||||||||
\(301\) | 14.0826 | 0.811706 | ||||||||
\(302\) | −2.83501 | −0.163136 | ||||||||
\(303\) | −2.46111 | −0.141387 | ||||||||
\(304\) | −1.04222 | −0.0597751 | ||||||||
\(305\) | 1.57257 | 0.0900452 | ||||||||
\(306\) | 7.48219 | 0.427728 | ||||||||
\(307\) | 2.03265 | 0.116009 | 0.0580047 | − | 0.998316i | \(-0.481526\pi\) | ||||
0.0580047 | + | 0.998316i | \(0.481526\pi\) | |||||||
\(308\) | −5.87307 | −0.334649 | ||||||||
\(309\) | 2.25573 | 0.128324 | ||||||||
\(310\) | 7.20321 | 0.409115 | ||||||||
\(311\) | −9.81849 | −0.556755 | −0.278378 | − | 0.960472i | \(-0.589797\pi\) | ||||
−0.278378 | + | 0.960472i | \(0.589797\pi\) | |||||||
\(312\) | 6.48911 | 0.367374 | ||||||||
\(313\) | 11.5664 | 0.653773 | 0.326887 | − | 0.945064i | \(-0.394000\pi\) | ||||
0.326887 | + | 0.945064i | \(0.394000\pi\) | |||||||
\(314\) | −4.01322 | −0.226479 | ||||||||
\(315\) | 5.26172 | 0.296464 | ||||||||
\(316\) | 5.61518 | 0.315879 | ||||||||
\(317\) | −3.10943 | −0.174643 | −0.0873215 | − | 0.996180i | \(-0.527831\pi\) | ||||
−0.0873215 | + | 0.996180i | \(0.527831\pi\) | |||||||
\(318\) | −12.6448 | −0.709084 | ||||||||
\(319\) | −8.03032 | −0.449612 | ||||||||
\(320\) | 6.19081 | 0.346077 | ||||||||
\(321\) | 13.0972 | 0.731013 | ||||||||
\(322\) | 0.193934 | 0.0108075 | ||||||||
\(323\) | 17.7460 | 0.987413 | ||||||||
\(324\) | 12.9034 | 0.716858 | ||||||||
\(325\) | 3.72132 | 0.206422 | ||||||||
\(326\) | −17.1489 | −0.949788 | ||||||||
\(327\) | 37.7002 | 2.08483 | ||||||||
\(328\) | −13.5796 | −0.749807 | ||||||||
\(329\) | 9.19286 | 0.506819 | ||||||||
\(330\) | 5.13414 | 0.282625 | ||||||||
\(331\) | −0.0569490 | −0.00313020 | −0.00156510 | − | 0.999999i | \(-0.500498\pi\) | ||||
−0.00156510 | + | 0.999999i | \(0.500498\pi\) | |||||||
\(332\) | 12.2379 | 0.671644 | ||||||||
\(333\) | −8.79690 | −0.482067 | ||||||||
\(334\) | 5.63638 | 0.308409 | ||||||||
\(335\) | 2.00189 | 0.109375 | ||||||||
\(336\) | −1.17036 | −0.0638484 | ||||||||
\(337\) | −1.80926 | −0.0985565 | −0.0492783 | − | 0.998785i | \(-0.515692\pi\) | ||||
−0.0492783 | + | 0.998785i | \(0.515692\pi\) | |||||||
\(338\) | 0.903670 | 0.0491532 | ||||||||
\(339\) | −18.1150 | −0.983870 | ||||||||
\(340\) | −5.30553 | −0.287733 | ||||||||
\(341\) | 15.7009 | 0.850252 | ||||||||
\(342\) | 8.44658 | 0.456739 | ||||||||
\(343\) | −20.1321 | −1.08703 | ||||||||
\(344\) | −18.1815 | −0.980279 | ||||||||
\(345\) | 0.245675 | 0.0132267 | ||||||||
\(346\) | −6.17612 | −0.332030 | ||||||||
\(347\) | −12.2642 | −0.658377 | −0.329188 | − | 0.944264i | \(-0.606775\pi\) | ||||
−0.329188 | + | 0.944264i | \(0.606775\pi\) | |||||||
\(348\) | 9.62396 | 0.515899 | ||||||||
\(349\) | −18.1887 | −0.973618 | −0.486809 | − | 0.873508i | \(-0.661839\pi\) | ||||
−0.486809 | + | 0.873508i | \(0.661839\pi\) | |||||||
\(350\) | −7.49305 | −0.400520 | ||||||||
\(351\) | 2.05653 | 0.109769 | ||||||||
\(352\) | 12.3463 | 0.658060 | ||||||||
\(353\) | 6.08261 | 0.323744 | 0.161872 | − | 0.986812i | \(-0.448247\pi\) | ||||
0.161872 | + | 0.986812i | \(0.448247\pi\) | |||||||
\(354\) | −17.5557 | −0.933073 | ||||||||
\(355\) | 9.42300 | 0.500121 | ||||||||
\(356\) | −2.13155 | −0.112972 | ||||||||
\(357\) | 19.9279 | 1.05470 | ||||||||
\(358\) | 5.12071 | 0.270638 | ||||||||
\(359\) | −1.98443 | −0.104734 | −0.0523670 | − | 0.998628i | \(-0.516677\pi\) | ||||
−0.0523670 | + | 0.998628i | \(0.516677\pi\) | |||||||
\(360\) | −6.79320 | −0.358033 | ||||||||
\(361\) | 1.03329 | 0.0543836 | ||||||||
\(362\) | −2.49622 | −0.131198 | ||||||||
\(363\) | −13.6221 | −0.714974 | ||||||||
\(364\) | 2.63679 | 0.138205 | ||||||||
\(365\) | −12.2418 | −0.640767 | ||||||||
\(366\) | 2.83483 | 0.148179 | ||||||||
\(367\) | 24.7346 | 1.29113 | 0.645567 | − | 0.763704i | \(-0.276621\pi\) | ||||
0.645567 | + | 0.763704i | \(0.276621\pi\) | |||||||
\(368\) | −0.0224271 | −0.00116910 | ||||||||
\(369\) | 9.85786 | 0.513180 | ||||||||
\(370\) | −4.30453 | −0.223782 | ||||||||
\(371\) | −13.8219 | −0.717595 | ||||||||
\(372\) | −18.8168 | −0.975607 | ||||||||
\(373\) | 6.09102 | 0.315381 | 0.157691 | − | 0.987489i | \(-0.449595\pi\) | ||||
0.157691 | + | 0.987489i | \(0.449595\pi\) | |||||||
\(374\) | 7.98038 | 0.412656 | ||||||||
\(375\) | −22.2459 | −1.14877 | ||||||||
\(376\) | −11.8686 | −0.612074 | ||||||||
\(377\) | 3.60531 | 0.185683 | ||||||||
\(378\) | −4.14091 | −0.212985 | ||||||||
\(379\) | 4.59817 | 0.236192 | 0.118096 | − | 0.993002i | \(-0.462321\pi\) | ||||
0.118096 | + | 0.993002i | \(0.462321\pi\) | |||||||
\(380\) | −5.98937 | −0.307248 | ||||||||
\(381\) | −28.8933 | −1.48025 | ||||||||
\(382\) | −5.00265 | −0.255958 | ||||||||
\(383\) | −1.09401 | −0.0559012 | −0.0279506 | − | 0.999609i | \(-0.508898\pi\) | ||||
−0.0279506 | + | 0.999609i | \(0.508898\pi\) | |||||||
\(384\) | −13.8472 | −0.706635 | ||||||||
\(385\) | 5.61206 | 0.286017 | ||||||||
\(386\) | 11.5737 | 0.589086 | ||||||||
\(387\) | 13.1985 | 0.670919 | ||||||||
\(388\) | 12.0071 | 0.609568 | ||||||||
\(389\) | 26.9512 | 1.36648 | 0.683240 | − | 0.730193i | \(-0.260570\pi\) | ||||
0.683240 | + | 0.730193i | \(0.260570\pi\) | |||||||
\(390\) | −2.30504 | −0.116720 | ||||||||
\(391\) | 0.381871 | 0.0193120 | ||||||||
\(392\) | 5.85467 | 0.295706 | ||||||||
\(393\) | 23.1893 | 1.16975 | ||||||||
\(394\) | 0.226798 | 0.0114259 | ||||||||
\(395\) | −5.36563 | −0.269974 | ||||||||
\(396\) | −5.50438 | −0.276606 | ||||||||
\(397\) | −35.0178 | −1.75749 | −0.878747 | − | 0.477288i | \(-0.841620\pi\) | ||||
−0.878747 | + | 0.477288i | \(0.841620\pi\) | |||||||
\(398\) | 5.62319 | 0.281865 | ||||||||
\(399\) | 22.4965 | 1.12623 | ||||||||
\(400\) | 0.866519 | 0.0433260 | ||||||||
\(401\) | −11.8182 | −0.590173 | −0.295087 | − | 0.955471i | \(-0.595348\pi\) | ||||
−0.295087 | + | 0.955471i | \(0.595348\pi\) | |||||||
\(402\) | 3.60874 | 0.179988 | ||||||||
\(403\) | −7.04913 | −0.351142 | ||||||||
\(404\) | 1.29113 | 0.0642360 | ||||||||
\(405\) | −12.3300 | −0.612682 | ||||||||
\(406\) | −7.25947 | −0.360281 | ||||||||
\(407\) | −9.38262 | −0.465079 | ||||||||
\(408\) | −25.7282 | −1.27374 | ||||||||
\(409\) | −2.64552 | −0.130813 | −0.0654063 | − | 0.997859i | \(-0.520834\pi\) | ||||
−0.0654063 | + | 0.997859i | \(0.520834\pi\) | |||||||
\(410\) | 4.82369 | 0.238225 | ||||||||
\(411\) | −23.1473 | −1.14177 | ||||||||
\(412\) | −1.18338 | −0.0583009 | ||||||||
\(413\) | −19.1899 | −0.944272 | ||||||||
\(414\) | 0.181760 | 0.00893300 | ||||||||
\(415\) | −11.6941 | −0.574039 | ||||||||
\(416\) | −5.54303 | −0.271769 | ||||||||
\(417\) | 8.47175 | 0.414863 | ||||||||
\(418\) | 9.00899 | 0.440644 | ||||||||
\(419\) | 17.6740 | 0.863430 | 0.431715 | − | 0.902010i | \(-0.357909\pi\) | ||||
0.431715 | + | 0.902010i | \(0.357909\pi\) | |||||||
\(420\) | −6.72579 | −0.328185 | ||||||||
\(421\) | 27.6691 | 1.34851 | 0.674254 | − | 0.738499i | \(-0.264465\pi\) | ||||
0.674254 | + | 0.738499i | \(0.264465\pi\) | |||||||
\(422\) | 4.42091 | 0.215207 | ||||||||
\(423\) | 8.61577 | 0.418913 | ||||||||
\(424\) | 17.8449 | 0.866623 | ||||||||
\(425\) | −14.7544 | −0.715692 | ||||||||
\(426\) | 16.9865 | 0.823001 | ||||||||
\(427\) | 3.09871 | 0.149957 | ||||||||
\(428\) | −6.87092 | −0.332119 | ||||||||
\(429\) | −5.02431 | −0.242576 | ||||||||
\(430\) | 6.45835 | 0.311449 | ||||||||
\(431\) | 34.0927 | 1.64219 | 0.821095 | − | 0.570792i | \(-0.193364\pi\) | ||||
0.821095 | + | 0.570792i | \(0.193364\pi\) | |||||||
\(432\) | 0.478868 | 0.0230395 | ||||||||
\(433\) | 16.1001 | 0.773721 | 0.386860 | − | 0.922138i | \(-0.373560\pi\) | ||||
0.386860 | + | 0.922138i | \(0.373560\pi\) | |||||||
\(434\) | 14.1937 | 0.681321 | ||||||||
\(435\) | −9.19625 | −0.440926 | ||||||||
\(436\) | −19.7779 | −0.947191 | ||||||||
\(437\) | 0.431091 | 0.0206219 | ||||||||
\(438\) | −22.0680 | −1.05445 | ||||||||
\(439\) | 12.3597 | 0.589897 | 0.294948 | − | 0.955513i | \(-0.404698\pi\) | ||||
0.294948 | + | 0.955513i | \(0.404698\pi\) | |||||||
\(440\) | −7.24551 | −0.345416 | ||||||||
\(441\) | −4.25010 | −0.202386 | ||||||||
\(442\) | −3.58289 | −0.170421 | ||||||||
\(443\) | −14.9741 | −0.711440 | −0.355720 | − | 0.934593i | \(-0.615764\pi\) | ||||
−0.355720 | + | 0.934593i | \(0.615764\pi\) | |||||||
\(444\) | 11.2446 | 0.533647 | ||||||||
\(445\) | 2.03682 | 0.0965545 | ||||||||
\(446\) | 1.50929 | 0.0714669 | ||||||||
\(447\) | −25.0760 | −1.18605 | ||||||||
\(448\) | 12.1988 | 0.576340 | ||||||||
\(449\) | −9.90349 | −0.467375 | −0.233687 | − | 0.972312i | \(-0.575079\pi\) | ||||
−0.233687 | + | 0.972312i | \(0.575079\pi\) | |||||||
\(450\) | −7.02266 | −0.331052 | ||||||||
\(451\) | 10.5142 | 0.495096 | ||||||||
\(452\) | 9.50331 | 0.446998 | ||||||||
\(453\) | −7.07670 | −0.332492 | ||||||||
\(454\) | −7.45836 | −0.350038 | ||||||||
\(455\) | −2.51961 | −0.118121 | ||||||||
\(456\) | −29.0443 | −1.36013 | ||||||||
\(457\) | 34.1375 | 1.59689 | 0.798443 | − | 0.602071i | \(-0.205658\pi\) | ||||
0.798443 | + | 0.602071i | \(0.205658\pi\) | |||||||
\(458\) | 3.52927 | 0.164912 | ||||||||
\(459\) | −8.15376 | −0.380585 | ||||||||
\(460\) | −0.128884 | −0.00600923 | ||||||||
\(461\) | −19.8327 | −0.923700 | −0.461850 | − | 0.886958i | \(-0.652814\pi\) | ||||
−0.461850 | + | 0.886958i | \(0.652814\pi\) | |||||||
\(462\) | 10.1167 | 0.470671 | ||||||||
\(463\) | 5.86990 | 0.272797 | 0.136399 | − | 0.990654i | \(-0.456447\pi\) | ||||
0.136399 | + | 0.990654i | \(0.456447\pi\) | |||||||
\(464\) | 0.839507 | 0.0389731 | ||||||||
\(465\) | 17.9806 | 0.833828 | ||||||||
\(466\) | −23.7835 | −1.10175 | ||||||||
\(467\) | 29.6514 | 1.37210 | 0.686051 | − | 0.727554i | \(-0.259343\pi\) | ||||
0.686051 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(468\) | 2.47126 | 0.114234 | ||||||||
\(469\) | 3.94467 | 0.182148 | ||||||||
\(470\) | 4.21590 | 0.194465 | ||||||||
\(471\) | −10.0177 | −0.461593 | ||||||||
\(472\) | 24.7753 | 1.14038 | ||||||||
\(473\) | 14.0773 | 0.647276 | ||||||||
\(474\) | −9.67245 | −0.444270 | ||||||||
\(475\) | −16.6561 | −0.764234 | ||||||||
\(476\) | −10.4544 | −0.479177 | ||||||||
\(477\) | −12.9542 | −0.593131 | ||||||||
\(478\) | 15.4976 | 0.708845 | ||||||||
\(479\) | −0.439562 | −0.0200841 | −0.0100421 | − | 0.999950i | \(-0.503197\pi\) | ||||
−0.0100421 | + | 0.999950i | \(0.503197\pi\) | |||||||
\(480\) | 14.1389 | 0.645349 | ||||||||
\(481\) | 4.21245 | 0.192071 | ||||||||
\(482\) | −14.2426 | −0.648732 | ||||||||
\(483\) | 0.484095 | 0.0220271 | ||||||||
\(484\) | 7.14629 | 0.324831 | ||||||||
\(485\) | −11.4735 | −0.520983 | ||||||||
\(486\) | −16.6516 | −0.755332 | ||||||||
\(487\) | −26.9021 | −1.21905 | −0.609525 | − | 0.792767i | \(-0.708640\pi\) | ||||
−0.609525 | + | 0.792767i | \(0.708640\pi\) | |||||||
\(488\) | −4.00063 | −0.181100 | ||||||||
\(489\) | −42.8067 | −1.93579 | ||||||||
\(490\) | −2.07967 | −0.0939500 | ||||||||
\(491\) | −14.8866 | −0.671821 | −0.335911 | − | 0.941894i | \(-0.609044\pi\) | ||||
−0.335911 | + | 0.941894i | \(0.609044\pi\) | |||||||
\(492\) | −12.6008 | −0.568089 | ||||||||
\(493\) | −14.2944 | −0.643789 | ||||||||
\(494\) | −4.04470 | −0.181980 | ||||||||
\(495\) | 5.25976 | 0.236408 | ||||||||
\(496\) | −1.64141 | −0.0737014 | ||||||||
\(497\) | 18.5678 | 0.832878 | ||||||||
\(498\) | −21.0805 | −0.944640 | ||||||||
\(499\) | −16.8021 | −0.752166 | −0.376083 | − | 0.926586i | \(-0.622729\pi\) | ||||
−0.376083 | + | 0.926586i | \(0.622729\pi\) | |||||||
\(500\) | 11.6704 | 0.521918 | ||||||||
\(501\) | 14.0694 | 0.628576 | ||||||||
\(502\) | 24.0732 | 1.07444 | ||||||||
\(503\) | −38.4444 | −1.71415 | −0.857075 | − | 0.515191i | \(-0.827721\pi\) | ||||
−0.857075 | + | 0.515191i | \(0.827721\pi\) | |||||||
\(504\) | −13.3858 | −0.596252 | ||||||||
\(505\) | −1.23375 | −0.0549010 | ||||||||
\(506\) | 0.193862 | 0.00861821 | ||||||||
\(507\) | 2.25573 | 0.100180 | ||||||||
\(508\) | 15.1578 | 0.672516 | ||||||||
\(509\) | −35.7475 | −1.58448 | −0.792240 | − | 0.610210i | \(-0.791085\pi\) | ||||
−0.792240 | + | 0.610210i | \(0.791085\pi\) | |||||||
\(510\) | 9.13907 | 0.404685 | ||||||||
\(511\) | −24.1222 | −1.06710 | ||||||||
\(512\) | −2.63042 | −0.116249 | ||||||||
\(513\) | −9.20471 | −0.406398 | ||||||||
\(514\) | −24.0684 | −1.06161 | ||||||||
\(515\) | 1.13079 | 0.0498285 | ||||||||
\(516\) | −16.8710 | −0.742706 | ||||||||
\(517\) | 9.18944 | 0.404151 | ||||||||
\(518\) | −8.48196 | −0.372676 | ||||||||
\(519\) | −15.4167 | −0.676720 | ||||||||
\(520\) | 3.25297 | 0.142652 | ||||||||
\(521\) | 27.9008 | 1.22236 | 0.611179 | − | 0.791492i | \(-0.290696\pi\) | ||||
0.611179 | + | 0.791492i | \(0.290696\pi\) | |||||||
\(522\) | −6.80374 | −0.297792 | ||||||||
\(523\) | 15.9778 | 0.698662 | 0.349331 | − | 0.936999i | \(-0.386409\pi\) | ||||
0.349331 | + | 0.936999i | \(0.386409\pi\) | |||||||
\(524\) | −12.1654 | −0.531446 | ||||||||
\(525\) | −18.7040 | −0.816311 | ||||||||
\(526\) | 16.6773 | 0.727163 | ||||||||
\(527\) | 27.9485 | 1.21746 | ||||||||
\(528\) | −1.16992 | −0.0509144 | ||||||||
\(529\) | −22.9907 | −0.999597 | ||||||||
\(530\) | −6.33878 | −0.275339 | ||||||||
\(531\) | −17.9852 | −0.780491 | ||||||||
\(532\) | −11.8019 | −0.511677 | ||||||||
\(533\) | −4.72050 | −0.204468 | ||||||||
\(534\) | 3.67171 | 0.158890 | ||||||||
\(535\) | 6.56556 | 0.283854 | ||||||||
\(536\) | −5.09281 | −0.219976 | ||||||||
\(537\) | 12.7822 | 0.551594 | ||||||||
\(538\) | −8.87143 | −0.382475 | ||||||||
\(539\) | −4.53308 | −0.195254 | ||||||||
\(540\) | 2.75194 | 0.118425 | ||||||||
\(541\) | 32.4710 | 1.39604 | 0.698018 | − | 0.716080i | \(-0.254065\pi\) | ||||
0.698018 | + | 0.716080i | \(0.254065\pi\) | |||||||
\(542\) | −10.3228 | −0.443401 | ||||||||
\(543\) | −6.23103 | −0.267399 | ||||||||
\(544\) | 21.9771 | 0.942262 | ||||||||
\(545\) | 18.8990 | 0.809542 | ||||||||
\(546\) | −4.54201 | −0.194380 | ||||||||
\(547\) | 26.7174 | 1.14235 | 0.571176 | − | 0.820827i | \(-0.306487\pi\) | ||||
0.571176 | + | 0.820827i | \(0.306487\pi\) | |||||||
\(548\) | 12.1433 | 0.518737 | ||||||||
\(549\) | 2.90419 | 0.123948 | ||||||||
\(550\) | −7.49026 | −0.319386 | ||||||||
\(551\) | −16.1369 | −0.687454 | ||||||||
\(552\) | −0.624997 | −0.0266016 | ||||||||
\(553\) | −10.5728 | −0.449602 | ||||||||
\(554\) | 21.5579 | 0.915909 | ||||||||
\(555\) | −10.7449 | −0.456096 | ||||||||
\(556\) | −4.44437 | −0.188483 | ||||||||
\(557\) | 31.4267 | 1.33159 | 0.665795 | − | 0.746135i | \(-0.268092\pi\) | ||||
0.665795 | + | 0.746135i | \(0.268092\pi\) | |||||||
\(558\) | 13.3027 | 0.563149 | ||||||||
\(559\) | −6.32020 | −0.267316 | ||||||||
\(560\) | −0.586697 | −0.0247925 | ||||||||
\(561\) | 19.9205 | 0.841045 | ||||||||
\(562\) | 16.2077 | 0.683681 | ||||||||
\(563\) | 9.77243 | 0.411859 | 0.205929 | − | 0.978567i | \(-0.433978\pi\) | ||||
0.205929 | + | 0.978567i | \(0.433978\pi\) | |||||||
\(564\) | −11.0131 | −0.463736 | ||||||||
\(565\) | −9.08096 | −0.382039 | ||||||||
\(566\) | −10.0160 | −0.421003 | ||||||||
\(567\) | −24.2959 | −1.02033 | ||||||||
\(568\) | −23.9721 | −1.00585 | ||||||||
\(569\) | 31.6223 | 1.32568 | 0.662839 | − | 0.748762i | \(-0.269352\pi\) | ||||
0.662839 | + | 0.748762i | \(0.269352\pi\) | |||||||
\(570\) | 10.3170 | 0.432132 | ||||||||
\(571\) | 11.6719 | 0.488455 | 0.244227 | − | 0.969718i | \(-0.421466\pi\) | ||||
0.244227 | + | 0.969718i | \(0.421466\pi\) | |||||||
\(572\) | 2.63581 | 0.110209 | ||||||||
\(573\) | −12.4875 | −0.521675 | ||||||||
\(574\) | 9.50494 | 0.396729 | ||||||||
\(575\) | −0.358418 | −0.0149471 | ||||||||
\(576\) | 11.4330 | 0.476376 | ||||||||
\(577\) | −37.4894 | −1.56070 | −0.780352 | − | 0.625341i | \(-0.784960\pi\) | ||||
−0.780352 | + | 0.625341i | \(0.784960\pi\) | |||||||
\(578\) | −1.15685 | −0.0481186 | ||||||||
\(579\) | 28.8901 | 1.20063 | ||||||||
\(580\) | 4.82445 | 0.200325 | ||||||||
\(581\) | −23.0428 | −0.955978 | ||||||||
\(582\) | −20.6829 | −0.857332 | ||||||||
\(583\) | −13.8167 | −0.572229 | ||||||||
\(584\) | 31.1433 | 1.28872 | ||||||||
\(585\) | −2.36143 | −0.0976333 | ||||||||
\(586\) | 10.1735 | 0.420264 | ||||||||
\(587\) | 35.1772 | 1.45192 | 0.725960 | − | 0.687737i | \(-0.241396\pi\) | ||||
0.725960 | + | 0.687737i | \(0.241396\pi\) | |||||||
\(588\) | 5.43269 | 0.224040 | ||||||||
\(589\) | 31.5509 | 1.30003 | ||||||||
\(590\) | −8.80059 | −0.362314 | ||||||||
\(591\) | 0.566129 | 0.0232874 | ||||||||
\(592\) | 0.980880 | 0.0403139 | ||||||||
\(593\) | 34.4406 | 1.41431 | 0.707154 | − | 0.707060i | \(-0.249979\pi\) | ||||
0.707154 | + | 0.707060i | \(0.249979\pi\) | |||||||
\(594\) | −4.13937 | −0.169840 | ||||||||
\(595\) | 9.98979 | 0.409542 | ||||||||
\(596\) | 13.1551 | 0.538856 | ||||||||
\(597\) | 14.0365 | 0.574477 | ||||||||
\(598\) | −0.0870367 | −0.00355920 | ||||||||
\(599\) | 12.8653 | 0.525660 | 0.262830 | − | 0.964842i | \(-0.415344\pi\) | ||||
0.262830 | + | 0.964842i | \(0.415344\pi\) | |||||||
\(600\) | 24.1481 | 0.985840 | ||||||||
\(601\) | −35.2591 | −1.43825 | −0.719125 | − | 0.694881i | \(-0.755457\pi\) | ||||
−0.719125 | + | 0.694881i | \(0.755457\pi\) | |||||||
\(602\) | 12.7260 | 0.518673 | ||||||||
\(603\) | 3.69704 | 0.150555 | ||||||||
\(604\) | 3.71251 | 0.151060 | ||||||||
\(605\) | −6.82869 | −0.277626 | ||||||||
\(606\) | −2.22403 | −0.0903452 | ||||||||
\(607\) | 22.7548 | 0.923587 | 0.461794 | − | 0.886987i | \(-0.347206\pi\) | ||||
0.461794 | + | 0.886987i | \(0.347206\pi\) | |||||||
\(608\) | 24.8098 | 1.00617 | ||||||||
\(609\) | −18.1210 | −0.734299 | ||||||||
\(610\) | 1.42109 | 0.0575381 | ||||||||
\(611\) | −4.12572 | −0.166909 | ||||||||
\(612\) | −9.79813 | −0.396066 | ||||||||
\(613\) | −41.4744 | −1.67514 | −0.837568 | − | 0.546333i | \(-0.816023\pi\) | ||||
−0.837568 | + | 0.546333i | \(0.816023\pi\) | |||||||
\(614\) | 1.83684 | 0.0741290 | ||||||||
\(615\) | 12.0408 | 0.485532 | ||||||||
\(616\) | −14.2771 | −0.575240 | ||||||||
\(617\) | 31.4984 | 1.26808 | 0.634038 | − | 0.773302i | \(-0.281396\pi\) | ||||
0.634038 | + | 0.773302i | \(0.281396\pi\) | |||||||
\(618\) | 2.03843 | 0.0819979 | ||||||||
\(619\) | −45.2965 | −1.82062 | −0.910310 | − | 0.413926i | \(-0.864157\pi\) | ||||
−0.910310 | + | 0.413926i | \(0.864157\pi\) | |||||||
\(620\) | −9.43280 | −0.378830 | ||||||||
\(621\) | −0.198074 | −0.00794842 | ||||||||
\(622\) | −8.87268 | −0.355762 | ||||||||
\(623\) | 4.01350 | 0.160797 | ||||||||
\(624\) | 0.525252 | 0.0210269 | ||||||||
\(625\) | 7.45482 | 0.298193 | ||||||||
\(626\) | 10.4522 | 0.417756 | ||||||||
\(627\) | 22.4881 | 0.898088 | ||||||||
\(628\) | 5.25542 | 0.209714 | ||||||||
\(629\) | −16.7016 | −0.665937 | ||||||||
\(630\) | 4.75486 | 0.189438 | ||||||||
\(631\) | −9.56661 | −0.380841 | −0.190420 | − | 0.981703i | \(-0.560985\pi\) | ||||
−0.190420 | + | 0.981703i | \(0.560985\pi\) | |||||||
\(632\) | 13.6502 | 0.542975 | ||||||||
\(633\) | 11.0354 | 0.438618 | ||||||||
\(634\) | −2.80990 | −0.111595 | ||||||||
\(635\) | −14.4841 | −0.574784 | ||||||||
\(636\) | 16.5587 | 0.656594 | ||||||||
\(637\) | 2.03519 | 0.0806370 | ||||||||
\(638\) | −7.25676 | −0.287298 | ||||||||
\(639\) | 17.4022 | 0.688419 | ||||||||
\(640\) | −6.94153 | −0.274388 | ||||||||
\(641\) | 32.6148 | 1.28821 | 0.644103 | − | 0.764939i | \(-0.277231\pi\) | ||||
0.644103 | + | 0.764939i | \(0.277231\pi\) | |||||||
\(642\) | 11.8355 | 0.467111 | ||||||||
\(643\) | −38.8264 | −1.53116 | −0.765582 | − | 0.643338i | \(-0.777549\pi\) | ||||
−0.765582 | + | 0.643338i | \(0.777549\pi\) | |||||||
\(644\) | −0.253962 | −0.0100075 | ||||||||
\(645\) | 16.1212 | 0.634773 | ||||||||
\(646\) | 16.0365 | 0.630948 | ||||||||
\(647\) | 2.11253 | 0.0830521 | 0.0415260 | − | 0.999137i | \(-0.486778\pi\) | ||||
0.0415260 | + | 0.999137i | \(0.486778\pi\) | |||||||
\(648\) | 31.3675 | 1.23223 | ||||||||
\(649\) | −19.1827 | −0.752988 | ||||||||
\(650\) | 3.36285 | 0.131902 | ||||||||
\(651\) | 35.4302 | 1.38862 | ||||||||
\(652\) | 22.4569 | 0.879479 | ||||||||
\(653\) | 18.1623 | 0.710746 | 0.355373 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355373 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(654\) | 34.0685 | 1.33219 | ||||||||
\(655\) | 11.6247 | 0.454215 | ||||||||
\(656\) | −1.09918 | −0.0429158 | ||||||||
\(657\) | −22.6079 | −0.882019 | ||||||||
\(658\) | 8.30732 | 0.323853 | ||||||||
\(659\) | 26.4829 | 1.03163 | 0.515813 | − | 0.856701i | \(-0.327490\pi\) | ||||
0.515813 | + | 0.856701i | \(0.327490\pi\) | |||||||
\(660\) | −6.72329 | −0.261704 | ||||||||
\(661\) | 7.52159 | 0.292556 | 0.146278 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146278 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(662\) | −0.0514631 | −0.00200017 | ||||||||
\(663\) | −8.94357 | −0.347339 | ||||||||
\(664\) | 29.7497 | 1.15451 | ||||||||
\(665\) | 11.2774 | 0.437318 | ||||||||
\(666\) | −7.94950 | −0.308037 | ||||||||
\(667\) | −0.347245 | −0.0134454 | ||||||||
\(668\) | −7.38098 | −0.285579 | ||||||||
\(669\) | 3.76746 | 0.145659 | ||||||||
\(670\) | 1.80905 | 0.0698896 | ||||||||
\(671\) | 3.09756 | 0.119580 | ||||||||
\(672\) | 27.8603 | 1.07473 | ||||||||
\(673\) | −32.7473 | −1.26231 | −0.631157 | − | 0.775655i | \(-0.717420\pi\) | ||||
−0.631157 | + | 0.775655i | \(0.717420\pi\) | |||||||
\(674\) | −1.63497 | −0.0629768 | ||||||||
\(675\) | 7.65299 | 0.294564 | ||||||||
\(676\) | −1.18338 | −0.0455146 | ||||||||
\(677\) | 45.9277 | 1.76514 | 0.882572 | − | 0.470177i | \(-0.155810\pi\) | ||||
0.882572 | + | 0.470177i | \(0.155810\pi\) | |||||||
\(678\) | −16.3700 | −0.628685 | ||||||||
\(679\) | −22.6082 | −0.867621 | ||||||||
\(680\) | −12.8974 | −0.494594 | ||||||||
\(681\) | −18.6174 | −0.713422 | ||||||||
\(682\) | 14.1885 | 0.543304 | ||||||||
\(683\) | 47.3508 | 1.81183 | 0.905914 | − | 0.423461i | \(-0.139185\pi\) | ||||
0.905914 | + | 0.423461i | \(0.139185\pi\) | |||||||
\(684\) | −11.0610 | −0.422929 | ||||||||
\(685\) | −11.6036 | −0.443352 | ||||||||
\(686\) | −18.1928 | −0.694603 | ||||||||
\(687\) | 8.80972 | 0.336112 | ||||||||
\(688\) | −1.47167 | −0.0561071 | ||||||||
\(689\) | 6.20318 | 0.236323 | ||||||||
\(690\) | 0.222009 | 0.00845173 | ||||||||
\(691\) | 26.9497 | 1.02521 | 0.512607 | − | 0.858623i | \(-0.328680\pi\) | ||||
0.512607 | + | 0.858623i | \(0.328680\pi\) | |||||||
\(692\) | 8.08779 | 0.307452 | ||||||||
\(693\) | 10.3642 | 0.393704 | ||||||||
\(694\) | −11.0828 | −0.420697 | ||||||||
\(695\) | 4.24685 | 0.161092 | ||||||||
\(696\) | 23.3953 | 0.886796 | ||||||||
\(697\) | 18.7160 | 0.708917 | ||||||||
\(698\) | −16.4366 | −0.622134 | ||||||||
\(699\) | −59.3680 | −2.24550 | ||||||||
\(700\) | 9.81234 | 0.370872 | ||||||||
\(701\) | 42.6310 | 1.61015 | 0.805076 | − | 0.593171i | \(-0.202124\pi\) | ||||
0.805076 | + | 0.593171i | \(0.202124\pi\) | |||||||
\(702\) | 1.85842 | 0.0701416 | ||||||||
\(703\) | −18.8543 | −0.711104 | ||||||||
\(704\) | 12.1943 | 0.459589 | ||||||||
\(705\) | 10.5237 | 0.396344 | ||||||||
\(706\) | 5.49667 | 0.206870 | ||||||||
\(707\) | −2.43106 | −0.0914296 | ||||||||
\(708\) | 22.9896 | 0.864002 | ||||||||
\(709\) | 19.3382 | 0.726260 | 0.363130 | − | 0.931738i | \(-0.381708\pi\) | ||||
0.363130 | + | 0.931738i | \(0.381708\pi\) | |||||||
\(710\) | 8.51529 | 0.319573 | ||||||||
\(711\) | −9.90910 | −0.371620 | ||||||||
\(712\) | −5.18167 | −0.194191 | ||||||||
\(713\) | 0.678934 | 0.0254263 | ||||||||
\(714\) | 18.0083 | 0.673943 | ||||||||
\(715\) | −2.51867 | −0.0941928 | ||||||||
\(716\) | −6.70570 | −0.250604 | ||||||||
\(717\) | 38.6850 | 1.44472 | ||||||||
\(718\) | −1.79327 | −0.0669241 | ||||||||
\(719\) | −0.129535 | −0.00483084 | −0.00241542 | − | 0.999997i | \(-0.500769\pi\) | ||||
−0.00241542 | + | 0.999997i | \(0.500769\pi\) | |||||||
\(720\) | −0.549866 | −0.0204923 | ||||||||
\(721\) | 2.22819 | 0.0829820 | ||||||||
\(722\) | 0.933753 | 0.0347507 | ||||||||
\(723\) | −35.5521 | −1.32220 | ||||||||
\(724\) | 3.26887 | 0.121486 | ||||||||
\(725\) | 13.4165 | 0.498277 | ||||||||
\(726\) | −12.3099 | −0.456862 | ||||||||
\(727\) | 34.8868 | 1.29388 | 0.646939 | − | 0.762541i | \(-0.276049\pi\) | ||||
0.646939 | + | 0.762541i | \(0.276049\pi\) | |||||||
\(728\) | 6.40988 | 0.237566 | ||||||||
\(729\) | −8.85381 | −0.327919 | ||||||||
\(730\) | −11.0626 | −0.409445 | ||||||||
\(731\) | 25.0585 | 0.926821 | ||||||||
\(732\) | −3.71228 | −0.137210 | ||||||||
\(733\) | 24.4474 | 0.902986 | 0.451493 | − | 0.892275i | \(-0.350892\pi\) | ||||
0.451493 | + | 0.892275i | \(0.350892\pi\) | |||||||
\(734\) | 22.3519 | 0.825024 | ||||||||
\(735\) | −5.19125 | −0.191482 | ||||||||
\(736\) | 0.533875 | 0.0196789 | ||||||||
\(737\) | 3.94320 | 0.145250 | ||||||||
\(738\) | 8.90826 | 0.327918 | ||||||||
\(739\) | −12.6222 | −0.464315 | −0.232158 | − | 0.972678i | \(-0.574579\pi\) | ||||
−0.232158 | + | 0.972678i | \(0.574579\pi\) | |||||||
\(740\) | 5.63689 | 0.207216 | ||||||||
\(741\) | −10.0963 | −0.370897 | ||||||||
\(742\) | −12.4904 | −0.458537 | ||||||||
\(743\) | 10.9176 | 0.400528 | 0.200264 | − | 0.979742i | \(-0.435820\pi\) | ||||
0.200264 | + | 0.979742i | \(0.435820\pi\) | |||||||
\(744\) | −45.7426 | −1.67700 | ||||||||
\(745\) | −12.5705 | −0.460548 | ||||||||
\(746\) | 5.50428 | 0.201526 | ||||||||
\(747\) | −21.5963 | −0.790167 | ||||||||
\(748\) | −10.4505 | −0.382109 | ||||||||
\(749\) | 12.9373 | 0.472717 | ||||||||
\(750\) | −20.1030 | −0.734056 | ||||||||
\(751\) | 19.2343 | 0.701869 | 0.350934 | − | 0.936400i | \(-0.385864\pi\) | ||||
0.350934 | + | 0.936400i | \(0.385864\pi\) | |||||||
\(752\) | −0.960684 | −0.0350325 | ||||||||
\(753\) | 60.0912 | 2.18985 | ||||||||
\(754\) | 3.25802 | 0.118650 | ||||||||
\(755\) | −3.54752 | −0.129108 | ||||||||
\(756\) | 5.42263 | 0.197219 | ||||||||
\(757\) | 40.5213 | 1.47277 | 0.736386 | − | 0.676562i | \(-0.236531\pi\) | ||||
0.736386 | + | 0.676562i | \(0.236531\pi\) | |||||||
\(758\) | 4.15523 | 0.150925 | ||||||||
\(759\) | 0.483915 | 0.0175650 | ||||||||
\(760\) | −14.5598 | −0.528140 | ||||||||
\(761\) | −23.5856 | −0.854977 | −0.427489 | − | 0.904021i | \(-0.640602\pi\) | ||||
−0.427489 | + | 0.904021i | \(0.640602\pi\) | |||||||
\(762\) | −26.1100 | −0.945867 | ||||||||
\(763\) | 37.2399 | 1.34817 | ||||||||
\(764\) | 6.55110 | 0.237011 | ||||||||
\(765\) | 9.36267 | 0.338508 | ||||||||
\(766\) | −0.988623 | −0.0357204 | ||||||||
\(767\) | 8.61233 | 0.310973 | ||||||||
\(768\) | −37.2125 | −1.34279 | ||||||||
\(769\) | −36.8906 | −1.33031 | −0.665154 | − | 0.746706i | \(-0.731634\pi\) | ||||
−0.665154 | + | 0.746706i | \(0.731634\pi\) | |||||||
\(770\) | 5.07145 | 0.182762 | ||||||||
\(771\) | −60.0793 | −2.16370 | ||||||||
\(772\) | −15.1561 | −0.545479 | ||||||||
\(773\) | −9.44627 | −0.339759 | −0.169879 | − | 0.985465i | \(-0.554338\pi\) | ||||
−0.169879 | + | 0.985465i | \(0.554338\pi\) | |||||||
\(774\) | 11.9271 | 0.428711 | ||||||||
\(775\) | −26.2321 | −0.942283 | ||||||||
\(776\) | 29.1885 | 1.04781 | ||||||||
\(777\) | −21.1725 | −0.759561 | ||||||||
\(778\) | 24.3550 | 0.873170 | ||||||||
\(779\) | 21.1283 | 0.756999 | ||||||||
\(780\) | 3.01851 | 0.108080 | ||||||||
\(781\) | 18.5609 | 0.664160 | ||||||||
\(782\) | 0.345085 | 0.0123402 | ||||||||
\(783\) | 7.41442 | 0.264970 | ||||||||
\(784\) | 0.473898 | 0.0169249 | ||||||||
\(785\) | −5.02185 | −0.179238 | ||||||||
\(786\) | 20.9555 | 0.747458 | ||||||||
\(787\) | −17.1347 | −0.610786 | −0.305393 | − | 0.952226i | \(-0.598788\pi\) | ||||
−0.305393 | + | 0.952226i | \(0.598788\pi\) | |||||||
\(788\) | −0.296997 | −0.0105801 | ||||||||
\(789\) | 41.6295 | 1.48205 | ||||||||
\(790\) | −4.84876 | −0.172511 | ||||||||
\(791\) | −17.8938 | −0.636230 | ||||||||
\(792\) | −13.3808 | −0.475467 | ||||||||
\(793\) | −1.39069 | −0.0493848 | ||||||||
\(794\) | −31.6446 | −1.12302 | ||||||||
\(795\) | −15.8228 | −0.561176 | ||||||||
\(796\) | −7.36372 | −0.261000 | ||||||||
\(797\) | 0.489636 | 0.0173438 | 0.00867190 | − | 0.999962i | \(-0.497240\pi\) | ||||
0.00867190 | + | 0.999962i | \(0.497240\pi\) | |||||||
\(798\) | 20.3294 | 0.719653 | ||||||||
\(799\) | 16.3577 | 0.578695 | ||||||||
\(800\) | −20.6274 | −0.729288 | ||||||||
\(801\) | 3.76155 | 0.132908 | ||||||||
\(802\) | −10.6798 | −0.377116 | ||||||||
\(803\) | −24.1132 | −0.850937 | ||||||||
\(804\) | −4.72574 | −0.166664 | ||||||||
\(805\) | 0.242675 | 0.00855317 | ||||||||
\(806\) | −6.37009 | −0.224377 | ||||||||
\(807\) | −22.1447 | −0.779531 | ||||||||
\(808\) | 3.13865 | 0.110417 | ||||||||
\(809\) | 17.5604 | 0.617390 | 0.308695 | − | 0.951161i | \(-0.400108\pi\) | ||||
0.308695 | + | 0.951161i | \(0.400108\pi\) | |||||||
\(810\) | −11.1422 | −0.391498 | ||||||||
\(811\) | −31.6346 | −1.11084 | −0.555421 | − | 0.831569i | \(-0.687443\pi\) | ||||
−0.555421 | + | 0.831569i | \(0.687443\pi\) | |||||||
\(812\) | 9.50646 | 0.333611 | ||||||||
\(813\) | −25.7675 | −0.903707 | ||||||||
\(814\) | −8.47880 | −0.297182 | ||||||||
\(815\) | −21.4588 | −0.751670 | ||||||||
\(816\) | −2.08253 | −0.0729033 | ||||||||
\(817\) | 28.2883 | 0.989682 | ||||||||
\(818\) | −2.39068 | −0.0835881 | ||||||||
\(819\) | −4.65314 | −0.162594 | ||||||||
\(820\) | −6.31674 | −0.220590 | ||||||||
\(821\) | 16.9989 | 0.593267 | 0.296633 | − | 0.954991i | \(-0.404136\pi\) | ||||
0.296633 | + | 0.954991i | \(0.404136\pi\) | |||||||
\(822\) | −20.9175 | −0.729582 | ||||||||
\(823\) | −16.0717 | −0.560225 | −0.280113 | − | 0.959967i | \(-0.590372\pi\) | ||||
−0.280113 | + | 0.959967i | \(0.590372\pi\) | |||||||
\(824\) | −2.87673 | −0.100216 | ||||||||
\(825\) | −18.6971 | −0.650948 | ||||||||
\(826\) | −17.3413 | −0.603382 | ||||||||
\(827\) | 25.5240 | 0.887555 | 0.443778 | − | 0.896137i | \(-0.353638\pi\) | ||||
0.443778 | + | 0.896137i | \(0.353638\pi\) | |||||||
\(828\) | −0.238019 | −0.00827173 | ||||||||
\(829\) | −9.24249 | −0.321005 | −0.160503 | − | 0.987035i | \(-0.551311\pi\) | ||||
−0.160503 | + | 0.987035i | \(0.551311\pi\) | |||||||
\(830\) | −10.5676 | −0.366806 | ||||||||
\(831\) | 53.8126 | 1.86674 | ||||||||
\(832\) | −5.47478 | −0.189804 | ||||||||
\(833\) | −8.06915 | −0.279580 | ||||||||
\(834\) | 7.65567 | 0.265094 | ||||||||
\(835\) | 7.05295 | 0.244078 | ||||||||
\(836\) | −11.7975 | −0.408025 | ||||||||
\(837\) | −14.4967 | −0.501080 | ||||||||
\(838\) | 15.9714 | 0.551724 | ||||||||
\(839\) | 40.6143 | 1.40216 | 0.701081 | − | 0.713081i | \(-0.252701\pi\) | ||||
0.701081 | + | 0.713081i | \(0.252701\pi\) | |||||||
\(840\) | −16.3500 | −0.564129 | ||||||||
\(841\) | −16.0017 | −0.551783 | ||||||||
\(842\) | 25.0037 | 0.861686 | ||||||||
\(843\) | 40.4574 | 1.39343 | ||||||||
\(844\) | −5.78930 | −0.199276 | ||||||||
\(845\) | 1.13079 | 0.0389003 | ||||||||
\(846\) | 7.78582 | 0.267682 | ||||||||
\(847\) | −13.4558 | −0.462345 | ||||||||
\(848\) | 1.44443 | 0.0496019 | ||||||||
\(849\) | −25.0018 | −0.858058 | ||||||||
\(850\) | −13.3331 | −0.457321 | ||||||||
\(851\) | −0.405721 | −0.0139079 | ||||||||
\(852\) | −22.2443 | −0.762078 | ||||||||
\(853\) | −39.7341 | −1.36047 | −0.680235 | − | 0.732994i | \(-0.738122\pi\) | ||||
−0.680235 | + | 0.732994i | \(0.738122\pi\) | |||||||
\(854\) | 2.80021 | 0.0958214 | ||||||||
\(855\) | 10.5694 | 0.361467 | ||||||||
\(856\) | −16.7028 | −0.570890 | ||||||||
\(857\) | 20.5365 | 0.701512 | 0.350756 | − | 0.936467i | \(-0.385925\pi\) | ||||
0.350756 | + | 0.936467i | \(0.385925\pi\) | |||||||
\(858\) | −4.54032 | −0.155004 | ||||||||
\(859\) | −15.2790 | −0.521312 | −0.260656 | − | 0.965432i | \(-0.583939\pi\) | ||||
−0.260656 | + | 0.965432i | \(0.583939\pi\) | |||||||
\(860\) | −8.45738 | −0.288394 | ||||||||
\(861\) | 23.7261 | 0.808583 | ||||||||
\(862\) | 30.8086 | 1.04934 | ||||||||
\(863\) | 20.3166 | 0.691584 | 0.345792 | − | 0.938311i | \(-0.387610\pi\) | ||||
0.345792 | + | 0.938311i | \(0.387610\pi\) | |||||||
\(864\) | −11.3994 | −0.387815 | ||||||||
\(865\) | −7.72835 | −0.262772 | ||||||||
\(866\) | 14.5492 | 0.494401 | ||||||||
\(867\) | −2.88771 | −0.0980718 | ||||||||
\(868\) | −18.5871 | −0.630886 | ||||||||
\(869\) | −10.5689 | −0.358525 | ||||||||
\(870\) | −8.31038 | −0.281748 | ||||||||
\(871\) | −1.77035 | −0.0599860 | ||||||||
\(872\) | −48.0790 | −1.62816 | ||||||||
\(873\) | −21.1889 | −0.717136 | ||||||||
\(874\) | 0.389564 | 0.0131772 | ||||||||
\(875\) | −21.9743 | −0.742866 | ||||||||
\(876\) | 28.8986 | 0.976393 | ||||||||
\(877\) | 12.5880 | 0.425065 | 0.212533 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212533 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(878\) | 11.1691 | 0.376939 | ||||||||
\(879\) | 25.3950 | 0.856551 | ||||||||
\(880\) | −0.586478 | −0.0197702 | ||||||||
\(881\) | 52.9080 | 1.78252 | 0.891259 | − | 0.453496i | \(-0.149823\pi\) | ||||
0.891259 | + | 0.453496i | \(0.149823\pi\) | |||||||
\(882\) | −3.84069 | −0.129323 | ||||||||
\(883\) | 31.2592 | 1.05196 | 0.525978 | − | 0.850498i | \(-0.323699\pi\) | ||||
0.525978 | + | 0.850498i | \(0.323699\pi\) | |||||||
\(884\) | 4.69189 | 0.157805 | ||||||||
\(885\) | −21.9679 | −0.738443 | ||||||||
\(886\) | −13.5316 | −0.454604 | ||||||||
\(887\) | 34.5533 | 1.16018 | 0.580092 | − | 0.814551i | \(-0.303016\pi\) | ||||
0.580092 | + | 0.814551i | \(0.303016\pi\) | |||||||
\(888\) | 27.3351 | 0.917304 | ||||||||
\(889\) | −28.5405 | −0.957219 | ||||||||
\(890\) | 1.84061 | 0.0616975 | ||||||||
\(891\) | −24.2869 | −0.813640 | ||||||||
\(892\) | −1.97645 | −0.0661765 | ||||||||
\(893\) | 18.4661 | 0.617945 | ||||||||
\(894\) | −22.6604 | −0.757879 | ||||||||
\(895\) | 6.40768 | 0.214185 | ||||||||
\(896\) | −13.6781 | −0.456953 | ||||||||
\(897\) | −0.217260 | −0.00725409 | ||||||||
\(898\) | −8.94949 | −0.298648 | ||||||||
\(899\) | −25.4143 | −0.847615 | ||||||||
\(900\) | 9.19636 | 0.306545 | ||||||||
\(901\) | −24.5945 | −0.819363 | ||||||||
\(902\) | 9.50140 | 0.316362 | ||||||||
\(903\) | 31.7665 | 1.05712 | ||||||||
\(904\) | 23.1020 | 0.768361 | ||||||||
\(905\) | −3.12359 | −0.103832 | ||||||||
\(906\) | −6.39500 | −0.212460 | ||||||||
\(907\) | −15.4038 | −0.511475 | −0.255737 | − | 0.966746i | \(-0.582318\pi\) | ||||
−0.255737 | + | 0.966746i | \(0.582318\pi\) | |||||||
\(908\) | 9.76691 | 0.324126 | ||||||||
\(909\) | −2.27845 | −0.0755714 | ||||||||
\(910\) | −2.27689 | −0.0754783 | ||||||||
\(911\) | 1.83754 | 0.0608805 | 0.0304403 | − | 0.999537i | \(-0.490309\pi\) | ||||
0.0304403 | + | 0.999537i | \(0.490309\pi\) | |||||||
\(912\) | −2.35095 | −0.0778479 | ||||||||
\(913\) | −23.0342 | −0.762322 | ||||||||
\(914\) | 30.8491 | 1.02040 | ||||||||
\(915\) | 3.54730 | 0.117270 | ||||||||
\(916\) | −4.62167 | −0.152704 | ||||||||
\(917\) | 22.9062 | 0.756428 | ||||||||
\(918\) | −7.36832 | −0.243191 | ||||||||
\(919\) | −17.2624 | −0.569435 | −0.284717 | − | 0.958611i | \(-0.591900\pi\) | ||||
−0.284717 | + | 0.958611i | \(0.591900\pi\) | |||||||
\(920\) | −0.313308 | −0.0103295 | ||||||||
\(921\) | 4.58510 | 0.151084 | ||||||||
\(922\) | −17.9222 | −0.590237 | ||||||||
\(923\) | −8.33313 | −0.274288 | ||||||||
\(924\) | −13.2481 | −0.435829 | ||||||||
\(925\) | 15.6759 | 0.515419 | ||||||||
\(926\) | 5.30446 | 0.174315 | ||||||||
\(927\) | 2.08831 | 0.0685891 | ||||||||
\(928\) | −19.9844 | −0.656019 | ||||||||
\(929\) | −59.9685 | −1.96750 | −0.983751 | − | 0.179538i | \(-0.942540\pi\) | ||||
−0.983751 | + | 0.179538i | \(0.942540\pi\) | |||||||
\(930\) | 16.2485 | 0.532809 | ||||||||
\(931\) | −9.10920 | −0.298542 | ||||||||
\(932\) | 31.1451 | 1.02019 | ||||||||
\(933\) | −22.1478 | −0.725088 | ||||||||
\(934\) | 26.7951 | 0.876761 | ||||||||
\(935\) | 9.98607 | 0.326579 | ||||||||
\(936\) | 6.00749 | 0.196361 | ||||||||
\(937\) | 1.88797 | 0.0616772 | 0.0308386 | − | 0.999524i | \(-0.490182\pi\) | ||||
0.0308386 | + | 0.999524i | \(0.490182\pi\) | |||||||
\(938\) | 3.56468 | 0.116391 | ||||||||
\(939\) | 26.0907 | 0.851439 | ||||||||
\(940\) | −5.52083 | −0.180070 | ||||||||
\(941\) | −25.2206 | −0.822168 | −0.411084 | − | 0.911598i | \(-0.634850\pi\) | ||||
−0.411084 | + | 0.911598i | \(0.634850\pi\) | |||||||
\(942\) | −9.05273 | −0.294954 | ||||||||
\(943\) | 0.454653 | 0.0148056 | ||||||||
\(944\) | 2.00540 | 0.0652703 | ||||||||
\(945\) | −5.18163 | −0.168559 | ||||||||
\(946\) | 12.7213 | 0.413604 | ||||||||
\(947\) | 27.2763 | 0.886361 | 0.443181 | − | 0.896432i | \(-0.353850\pi\) | ||||
0.443181 | + | 0.896432i | \(0.353850\pi\) | |||||||
\(948\) | 12.6663 | 0.411383 | ||||||||
\(949\) | 10.8259 | 0.351425 | ||||||||
\(950\) | −15.0516 | −0.488339 | ||||||||
\(951\) | −7.01403 | −0.227445 | ||||||||
\(952\) | −25.4141 | −0.823674 | ||||||||
\(953\) | 4.84988 | 0.157103 | 0.0785515 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785515 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(954\) | −11.7063 | −0.379005 | ||||||||
\(955\) | −6.25996 | −0.202567 | ||||||||
\(956\) | −20.2946 | −0.656373 | ||||||||
\(957\) | −18.1142 | −0.585549 | ||||||||
\(958\) | −0.397220 | −0.0128336 | ||||||||
\(959\) | −22.8647 | −0.738338 | ||||||||
\(960\) | 13.9648 | 0.450712 | ||||||||
\(961\) | 18.6902 | 0.602909 | ||||||||
\(962\) | 3.80667 | 0.122732 | ||||||||
\(963\) | 12.1251 | 0.390726 | ||||||||
\(964\) | 18.6510 | 0.600710 | ||||||||
\(965\) | 14.4825 | 0.466208 | ||||||||
\(966\) | 0.437463 | 0.0140751 | ||||||||
\(967\) | 10.0776 | 0.324074 | 0.162037 | − | 0.986785i | \(-0.448194\pi\) | ||||
0.162037 | + | 0.986785i | \(0.448194\pi\) | |||||||
\(968\) | 17.3722 | 0.558364 | ||||||||
\(969\) | 40.0301 | 1.28595 | ||||||||
\(970\) | −10.3682 | −0.332904 | ||||||||
\(971\) | −36.6814 | −1.17716 | −0.588581 | − | 0.808438i | \(-0.700313\pi\) | ||||
−0.588581 | + | 0.808438i | \(0.700313\pi\) | |||||||
\(972\) | 21.8057 | 0.699419 | ||||||||
\(973\) | 8.36831 | 0.268276 | ||||||||
\(974\) | −24.3106 | −0.778963 | ||||||||
\(975\) | 8.39429 | 0.268832 | ||||||||
\(976\) | −0.323825 | −0.0103654 | ||||||||
\(977\) | −50.2932 | −1.60902 | −0.804511 | − | 0.593937i | \(-0.797573\pi\) | ||||
−0.804511 | + | 0.593937i | \(0.797573\pi\) | |||||||
\(978\) | −38.6832 | −1.23695 | ||||||||
\(979\) | 4.01200 | 0.128224 | ||||||||
\(980\) | 2.72339 | 0.0869954 | ||||||||
\(981\) | 34.9021 | 1.11434 | ||||||||
\(982\) | −13.4525 | −0.429288 | ||||||||
\(983\) | −17.5930 | −0.561128 | −0.280564 | − | 0.959835i | \(-0.590522\pi\) | ||||
−0.280564 | + | 0.959835i | \(0.590522\pi\) | |||||||
\(984\) | −30.6319 | −0.976508 | ||||||||
\(985\) | 0.283798 | 0.00904256 | ||||||||
\(986\) | −12.9175 | −0.411376 | ||||||||
\(987\) | 20.7366 | 0.660053 | ||||||||
\(988\) | 5.29664 | 0.168508 | ||||||||
\(989\) | 0.608728 | 0.0193564 | ||||||||
\(990\) | 4.75309 | 0.151063 | ||||||||
\(991\) | −10.3839 | −0.329856 | −0.164928 | − | 0.986306i | \(-0.552739\pi\) | ||||
−0.164928 | + | 0.986306i | \(0.552739\pi\) | |||||||
\(992\) | 39.0735 | 1.24059 | ||||||||
\(993\) | −0.128462 | −0.00407660 | ||||||||
\(994\) | 16.7791 | 0.532202 | ||||||||
\(995\) | 7.03646 | 0.223071 | ||||||||
\(996\) | 27.6055 | 0.874713 | ||||||||
\(997\) | 43.8380 | 1.38836 | 0.694182 | − | 0.719799i | \(-0.255766\pi\) | ||||
0.694182 | + | 0.719799i | \(0.255766\pi\) | |||||||
\(998\) | −15.1836 | −0.480628 | ||||||||
\(999\) | 8.66301 | 0.274086 |
(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 | 1339.2.a.g.1.19 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.g.1.19 | ✓ | 30 | 1.1 | even | 1 | trivial |