Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.867375 | 0.613327 | 0.306663 | − | 0.951818i | \(-0.400787\pi\) | ||||
0.306663 | + | 0.951818i | \(0.400787\pi\) | |||||||
\(3\) | 0.595469 | 0.343794 | 0.171897 | − | 0.985115i | \(-0.445010\pi\) | ||||
0.171897 | + | 0.985115i | \(0.445010\pi\) | |||||||
\(4\) | −1.24766 | −0.623830 | ||||||||
\(5\) | 3.84366 | 1.71894 | 0.859469 | − | 0.511188i | \(-0.170794\pi\) | ||||
0.859469 | + | 0.511188i | \(0.170794\pi\) | |||||||
\(6\) | 0.516495 | 0.210858 | ||||||||
\(7\) | 1.26797 | 0.479248 | 0.239624 | − | 0.970866i | \(-0.422976\pi\) | ||||
0.239624 | + | 0.970866i | \(0.422976\pi\) | |||||||
\(8\) | −2.81694 | −0.995938 | ||||||||
\(9\) | −2.64542 | −0.881805 | ||||||||
\(10\) | 3.33390 | 1.05427 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.742944 | −0.214469 | ||||||||
\(13\) | 5.03984 | 1.39780 | 0.698901 | − | 0.715219i | \(-0.253673\pi\) | ||||
0.698901 | + | 0.715219i | \(0.253673\pi\) | |||||||
\(14\) | 1.09981 | 0.293936 | ||||||||
\(15\) | 2.28878 | 0.590961 | ||||||||
\(16\) | 0.0519793 | 0.0129948 | ||||||||
\(17\) | −3.67254 | −0.890722 | −0.445361 | − | 0.895351i | \(-0.646925\pi\) | ||||
−0.445361 | + | 0.895351i | \(0.646925\pi\) | |||||||
\(18\) | −2.29457 | −0.540835 | ||||||||
\(19\) | 3.68668 | 0.845783 | 0.422891 | − | 0.906180i | \(-0.361015\pi\) | ||||
0.422891 | + | 0.906180i | \(0.361015\pi\) | |||||||
\(20\) | −4.79559 | −1.07233 | ||||||||
\(21\) | 0.755038 | 0.164763 | ||||||||
\(22\) | −0.867375 | −0.184925 | ||||||||
\(23\) | 5.90488 | 1.23125 | 0.615627 | − | 0.788038i | \(-0.288903\pi\) | ||||
0.615627 | + | 0.788038i | \(0.288903\pi\) | |||||||
\(24\) | −1.67740 | −0.342398 | ||||||||
\(25\) | 9.77374 | 1.95475 | ||||||||
\(26\) | 4.37143 | 0.857309 | ||||||||
\(27\) | −3.36167 | −0.646954 | ||||||||
\(28\) | −1.58200 | −0.298970 | ||||||||
\(29\) | 8.38794 | 1.55760 | 0.778800 | − | 0.627272i | \(-0.215829\pi\) | ||||
0.778800 | + | 0.627272i | \(0.215829\pi\) | |||||||
\(30\) | 1.98523 | 0.362452 | ||||||||
\(31\) | 4.86681 | 0.874105 | 0.437053 | − | 0.899436i | \(-0.356022\pi\) | ||||
0.437053 | + | 0.899436i | \(0.356022\pi\) | |||||||
\(32\) | 5.67896 | 1.00391 | ||||||||
\(33\) | −0.595469 | −0.103658 | ||||||||
\(34\) | −3.18547 | −0.546303 | ||||||||
\(35\) | 4.87366 | 0.823798 | ||||||||
\(36\) | 3.30058 | 0.550097 | ||||||||
\(37\) | −2.88281 | −0.473931 | −0.236965 | − | 0.971518i | \(-0.576153\pi\) | ||||
−0.236965 | + | 0.971518i | \(0.576153\pi\) | |||||||
\(38\) | 3.19773 | 0.518741 | ||||||||
\(39\) | 3.00107 | 0.480556 | ||||||||
\(40\) | −10.8274 | −1.71196 | ||||||||
\(41\) | −1.35972 | −0.212352 | −0.106176 | − | 0.994347i | \(-0.533861\pi\) | ||||
−0.106176 | + | 0.994347i | \(0.533861\pi\) | |||||||
\(42\) | 0.654901 | 0.101053 | ||||||||
\(43\) | −7.22890 | −1.10240 | −0.551198 | − | 0.834374i | \(-0.685829\pi\) | ||||
−0.551198 | + | 0.834374i | \(0.685829\pi\) | |||||||
\(44\) | 1.24766 | 0.188092 | ||||||||
\(45\) | −10.1681 | −1.51577 | ||||||||
\(46\) | 5.12175 | 0.755160 | ||||||||
\(47\) | −2.45880 | −0.358653 | −0.179327 | − | 0.983790i | \(-0.557392\pi\) | ||||
−0.179327 | + | 0.983790i | \(0.557392\pi\) | |||||||
\(48\) | 0.0309521 | 0.00446755 | ||||||||
\(49\) | −5.39225 | −0.770321 | ||||||||
\(50\) | 8.47750 | 1.19890 | ||||||||
\(51\) | −2.18688 | −0.306225 | ||||||||
\(52\) | −6.28802 | −0.871991 | ||||||||
\(53\) | 2.17735 | 0.299082 | 0.149541 | − | 0.988756i | \(-0.452220\pi\) | ||||
0.149541 | + | 0.988756i | \(0.452220\pi\) | |||||||
\(54\) | −2.91583 | −0.396794 | ||||||||
\(55\) | −3.84366 | −0.518279 | ||||||||
\(56\) | −3.57180 | −0.477302 | ||||||||
\(57\) | 2.19531 | 0.290775 | ||||||||
\(58\) | 7.27548 | 0.955318 | ||||||||
\(59\) | 9.50732 | 1.23775 | 0.618874 | − | 0.785490i | \(-0.287589\pi\) | ||||
0.618874 | + | 0.785490i | \(0.287589\pi\) | |||||||
\(60\) | −2.85562 | −0.368660 | ||||||||
\(61\) | −3.72670 | −0.477155 | −0.238577 | − | 0.971123i | \(-0.576681\pi\) | ||||
−0.238577 | + | 0.971123i | \(0.576681\pi\) | |||||||
\(62\) | 4.22135 | 0.536112 | ||||||||
\(63\) | −3.35431 | −0.422604 | ||||||||
\(64\) | 4.82183 | 0.602729 | ||||||||
\(65\) | 19.3715 | 2.40273 | ||||||||
\(66\) | −0.516495 | −0.0635761 | ||||||||
\(67\) | 4.48935 | 0.548462 | 0.274231 | − | 0.961664i | \(-0.411577\pi\) | ||||
0.274231 | + | 0.961664i | \(0.411577\pi\) | |||||||
\(68\) | 4.58208 | 0.555659 | ||||||||
\(69\) | 3.51618 | 0.423298 | ||||||||
\(70\) | 4.22729 | 0.505257 | ||||||||
\(71\) | −4.16560 | −0.494366 | −0.247183 | − | 0.968969i | \(-0.579505\pi\) | ||||
−0.247183 | + | 0.968969i | \(0.579505\pi\) | |||||||
\(72\) | 7.45198 | 0.878224 | ||||||||
\(73\) | −7.67820 | −0.898665 | −0.449333 | − | 0.893365i | \(-0.648338\pi\) | ||||
−0.449333 | + | 0.893365i | \(0.648338\pi\) | |||||||
\(74\) | −2.50047 | −0.290674 | ||||||||
\(75\) | 5.81996 | 0.672031 | ||||||||
\(76\) | −4.59973 | −0.527625 | ||||||||
\(77\) | −1.26797 | −0.144499 | ||||||||
\(78\) | 2.60305 | 0.294738 | ||||||||
\(79\) | 5.11376 | 0.575343 | 0.287672 | − | 0.957729i | \(-0.407119\pi\) | ||||
0.287672 | + | 0.957729i | \(0.407119\pi\) | |||||||
\(80\) | 0.199791 | 0.0223373 | ||||||||
\(81\) | 5.93448 | 0.659386 | ||||||||
\(82\) | −1.17939 | −0.130241 | ||||||||
\(83\) | −4.45753 | −0.489277 | −0.244639 | − | 0.969614i | \(-0.578669\pi\) | ||||
−0.244639 | + | 0.969614i | \(0.578669\pi\) | |||||||
\(84\) | −0.942032 | −0.102784 | ||||||||
\(85\) | −14.1160 | −1.53110 | ||||||||
\(86\) | −6.27016 | −0.676129 | ||||||||
\(87\) | 4.99476 | 0.535494 | ||||||||
\(88\) | 2.81694 | 0.300287 | ||||||||
\(89\) | −15.0346 | −1.59367 | −0.796833 | − | 0.604199i | \(-0.793493\pi\) | ||||
−0.796833 | + | 0.604199i | \(0.793493\pi\) | |||||||
\(90\) | −8.81954 | −0.929661 | ||||||||
\(91\) | 6.39038 | 0.669894 | ||||||||
\(92\) | −7.36729 | −0.768093 | ||||||||
\(93\) | 2.89804 | 0.300512 | ||||||||
\(94\) | −2.13271 | −0.219972 | ||||||||
\(95\) | 14.1704 | 1.45385 | ||||||||
\(96\) | 3.38165 | 0.345138 | ||||||||
\(97\) | −2.95569 | −0.300105 | −0.150052 | − | 0.988678i | \(-0.547944\pi\) | ||||
−0.150052 | + | 0.988678i | \(0.547944\pi\) | |||||||
\(98\) | −4.67710 | −0.472458 | ||||||||
\(99\) | 2.64542 | 0.265874 | ||||||||
\(100\) | −12.1943 | −1.21943 | ||||||||
\(101\) | 10.3820 | 1.03305 | 0.516524 | − | 0.856273i | \(-0.327226\pi\) | ||||
0.516524 | + | 0.856273i | \(0.327226\pi\) | |||||||
\(102\) | −1.89685 | −0.187816 | ||||||||
\(103\) | −1.30158 | −0.128249 | −0.0641243 | − | 0.997942i | \(-0.520425\pi\) | ||||
−0.0641243 | + | 0.997942i | \(0.520425\pi\) | |||||||
\(104\) | −14.1969 | −1.39212 | ||||||||
\(105\) | 2.90211 | 0.283217 | ||||||||
\(106\) | 1.88858 | 0.183435 | ||||||||
\(107\) | −5.63697 | −0.544947 | −0.272473 | − | 0.962163i | \(-0.587842\pi\) | ||||
−0.272473 | + | 0.962163i | \(0.587842\pi\) | |||||||
\(108\) | 4.19423 | 0.403590 | ||||||||
\(109\) | 2.62758 | 0.251676 | 0.125838 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125838 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(110\) | −3.33390 | −0.317875 | ||||||||
\(111\) | −1.71662 | −0.162935 | ||||||||
\(112\) | 0.0659083 | 0.00622775 | ||||||||
\(113\) | 1.54047 | 0.144915 | 0.0724575 | − | 0.997371i | \(-0.476916\pi\) | ||||
0.0724575 | + | 0.997371i | \(0.476916\pi\) | |||||||
\(114\) | 1.90415 | 0.178340 | ||||||||
\(115\) | 22.6964 | 2.11645 | ||||||||
\(116\) | −10.4653 | −0.971679 | ||||||||
\(117\) | −13.3325 | −1.23259 | ||||||||
\(118\) | 8.24641 | 0.759144 | ||||||||
\(119\) | −4.65668 | −0.426877 | ||||||||
\(120\) | −6.44736 | −0.588561 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.23244 | −0.292652 | ||||||||
\(123\) | −0.809671 | −0.0730055 | ||||||||
\(124\) | −6.07213 | −0.545294 | ||||||||
\(125\) | 18.3486 | 1.64115 | ||||||||
\(126\) | −2.90945 | −0.259194 | ||||||||
\(127\) | −10.8282 | −0.960843 | −0.480422 | − | 0.877038i | \(-0.659516\pi\) | ||||
−0.480422 | + | 0.877038i | \(0.659516\pi\) | |||||||
\(128\) | −7.17559 | −0.634239 | ||||||||
\(129\) | −4.30459 | −0.378998 | ||||||||
\(130\) | 16.8023 | 1.47366 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 0.742944 | 0.0646649 | ||||||||
\(133\) | 4.67461 | 0.405340 | ||||||||
\(134\) | 3.89395 | 0.336386 | ||||||||
\(135\) | −12.9211 | −1.11207 | ||||||||
\(136\) | 10.3453 | 0.887104 | ||||||||
\(137\) | 1.62529 | 0.138858 | 0.0694289 | − | 0.997587i | \(-0.477882\pi\) | ||||
0.0694289 | + | 0.997587i | \(0.477882\pi\) | |||||||
\(138\) | 3.04984 | 0.259620 | ||||||||
\(139\) | 16.9885 | 1.44095 | 0.720473 | − | 0.693483i | \(-0.243925\pi\) | ||||
0.720473 | + | 0.693483i | \(0.243925\pi\) | |||||||
\(140\) | −6.08067 | −0.513910 | ||||||||
\(141\) | −1.46414 | −0.123303 | ||||||||
\(142\) | −3.61314 | −0.303208 | ||||||||
\(143\) | −5.03984 | −0.421453 | ||||||||
\(144\) | −0.137507 | −0.0114589 | ||||||||
\(145\) | 32.2404 | 2.67742 | ||||||||
\(146\) | −6.65988 | −0.551175 | ||||||||
\(147\) | −3.21092 | −0.264832 | ||||||||
\(148\) | 3.59677 | 0.295652 | ||||||||
\(149\) | 1.64713 | 0.134938 | 0.0674690 | − | 0.997721i | \(-0.478508\pi\) | ||||
0.0674690 | + | 0.997721i | \(0.478508\pi\) | |||||||
\(150\) | 5.04809 | 0.412175 | ||||||||
\(151\) | −13.9952 | −1.13892 | −0.569458 | − | 0.822021i | \(-0.692847\pi\) | ||||
−0.569458 | + | 0.822021i | \(0.692847\pi\) | |||||||
\(152\) | −10.3852 | −0.842347 | ||||||||
\(153\) | 9.71540 | 0.785443 | ||||||||
\(154\) | −1.09981 | −0.0886250 | ||||||||
\(155\) | 18.7064 | 1.50253 | ||||||||
\(156\) | −3.74432 | −0.299786 | ||||||||
\(157\) | −16.6427 | −1.32824 | −0.664118 | − | 0.747628i | \(-0.731193\pi\) | ||||
−0.664118 | + | 0.747628i | \(0.731193\pi\) | |||||||
\(158\) | 4.43555 | 0.352873 | ||||||||
\(159\) | 1.29654 | 0.102823 | ||||||||
\(160\) | 21.8280 | 1.72566 | ||||||||
\(161\) | 7.48723 | 0.590076 | ||||||||
\(162\) | 5.14742 | 0.404419 | ||||||||
\(163\) | 14.7990 | 1.15914 | 0.579572 | − | 0.814921i | \(-0.303220\pi\) | ||||
0.579572 | + | 0.814921i | \(0.303220\pi\) | |||||||
\(164\) | 1.69647 | 0.132472 | ||||||||
\(165\) | −2.28878 | −0.178181 | ||||||||
\(166\) | −3.86635 | −0.300087 | ||||||||
\(167\) | 2.68372 | 0.207672 | 0.103836 | − | 0.994594i | \(-0.466888\pi\) | ||||
0.103836 | + | 0.994594i | \(0.466888\pi\) | |||||||
\(168\) | −2.12690 | −0.164094 | ||||||||
\(169\) | 12.4000 | 0.953849 | ||||||||
\(170\) | −12.2439 | −0.939061 | ||||||||
\(171\) | −9.75281 | −0.745816 | ||||||||
\(172\) | 9.01921 | 0.687708 | ||||||||
\(173\) | −22.9315 | −1.74345 | −0.871724 | − | 0.489998i | \(-0.836997\pi\) | ||||
−0.871724 | + | 0.489998i | \(0.836997\pi\) | |||||||
\(174\) | 4.33233 | 0.328433 | ||||||||
\(175\) | 12.3928 | 0.936810 | ||||||||
\(176\) | −0.0519793 | −0.00391809 | ||||||||
\(177\) | 5.66132 | 0.425531 | ||||||||
\(178\) | −13.0407 | −0.977438 | ||||||||
\(179\) | −10.7008 | −0.799814 | −0.399907 | − | 0.916556i | \(-0.630958\pi\) | ||||
−0.399907 | + | 0.916556i | \(0.630958\pi\) | |||||||
\(180\) | 12.6863 | 0.945583 | ||||||||
\(181\) | −12.8845 | −0.957698 | −0.478849 | − | 0.877897i | \(-0.658946\pi\) | ||||
−0.478849 | + | 0.877897i | \(0.658946\pi\) | |||||||
\(182\) | 5.54286 | 0.410864 | ||||||||
\(183\) | −2.21913 | −0.164043 | ||||||||
\(184\) | −16.6337 | −1.22625 | ||||||||
\(185\) | −11.0805 | −0.814657 | ||||||||
\(186\) | 2.51368 | 0.184312 | ||||||||
\(187\) | 3.67254 | 0.268563 | ||||||||
\(188\) | 3.06775 | 0.223739 | ||||||||
\(189\) | −4.26251 | −0.310052 | ||||||||
\(190\) | 12.2910 | 0.891684 | ||||||||
\(191\) | 5.67609 | 0.410708 | 0.205354 | − | 0.978688i | \(-0.434165\pi\) | ||||
0.205354 | + | 0.978688i | \(0.434165\pi\) | |||||||
\(192\) | 2.87125 | 0.207215 | ||||||||
\(193\) | 6.16025 | 0.443424 | 0.221712 | − | 0.975112i | \(-0.428835\pi\) | ||||
0.221712 | + | 0.975112i | \(0.428835\pi\) | |||||||
\(194\) | −2.56369 | −0.184062 | ||||||||
\(195\) | 11.5351 | 0.826046 | ||||||||
\(196\) | 6.72770 | 0.480550 | ||||||||
\(197\) | −15.2154 | −1.08405 | −0.542026 | − | 0.840362i | \(-0.682342\pi\) | ||||
−0.542026 | + | 0.840362i | \(0.682342\pi\) | |||||||
\(198\) | 2.29457 | 0.163068 | ||||||||
\(199\) | −19.4965 | −1.38207 | −0.691036 | − | 0.722821i | \(-0.742845\pi\) | ||||
−0.691036 | + | 0.722821i | \(0.742845\pi\) | |||||||
\(200\) | −27.5320 | −1.94681 | ||||||||
\(201\) | 2.67327 | 0.188558 | ||||||||
\(202\) | 9.00509 | 0.633596 | ||||||||
\(203\) | 10.6357 | 0.746478 | ||||||||
\(204\) | 2.72849 | 0.191032 | ||||||||
\(205\) | −5.22630 | −0.365021 | ||||||||
\(206\) | −1.12896 | −0.0786583 | ||||||||
\(207\) | −15.6209 | −1.08573 | ||||||||
\(208\) | 0.261968 | 0.0181642 | ||||||||
\(209\) | −3.68668 | −0.255013 | ||||||||
\(210\) | 2.51722 | 0.173705 | ||||||||
\(211\) | −12.9329 | −0.890338 | −0.445169 | − | 0.895446i | \(-0.646856\pi\) | ||||
−0.445169 | + | 0.895446i | \(0.646856\pi\) | |||||||
\(212\) | −2.71659 | −0.186576 | ||||||||
\(213\) | −2.48049 | −0.169960 | ||||||||
\(214\) | −4.88937 | −0.334230 | ||||||||
\(215\) | −27.7854 | −1.89495 | ||||||||
\(216\) | 9.46963 | 0.644326 | ||||||||
\(217\) | 6.17098 | 0.418914 | ||||||||
\(218\) | 2.27909 | 0.154360 | ||||||||
\(219\) | −4.57213 | −0.308956 | ||||||||
\(220\) | 4.79559 | 0.323318 | ||||||||
\(221\) | −18.5090 | −1.24505 | ||||||||
\(222\) | −1.48896 | −0.0999321 | ||||||||
\(223\) | 23.7404 | 1.58977 | 0.794886 | − | 0.606759i | \(-0.207531\pi\) | ||||
0.794886 | + | 0.606759i | \(0.207531\pi\) | |||||||
\(224\) | 7.20077 | 0.481122 | ||||||||
\(225\) | −25.8556 | −1.72371 | ||||||||
\(226\) | 1.33616 | 0.0888802 | ||||||||
\(227\) | 1.00908 | 0.0669749 | 0.0334874 | − | 0.999439i | \(-0.489339\pi\) | ||||
0.0334874 | + | 0.999439i | \(0.489339\pi\) | |||||||
\(228\) | −2.73900 | −0.181394 | ||||||||
\(229\) | −4.62476 | −0.305613 | −0.152806 | − | 0.988256i | \(-0.548831\pi\) | ||||
−0.152806 | + | 0.988256i | \(0.548831\pi\) | |||||||
\(230\) | 19.6863 | 1.29807 | ||||||||
\(231\) | −0.755038 | −0.0496779 | ||||||||
\(232\) | −23.6283 | −1.55127 | ||||||||
\(233\) | −22.3623 | −1.46500 | −0.732501 | − | 0.680766i | \(-0.761647\pi\) | ||||
−0.732501 | + | 0.680766i | \(0.761647\pi\) | |||||||
\(234\) | −11.5643 | −0.755980 | ||||||||
\(235\) | −9.45081 | −0.616503 | ||||||||
\(236\) | −11.8619 | −0.772145 | ||||||||
\(237\) | 3.04509 | 0.197800 | ||||||||
\(238\) | −4.03908 | −0.261815 | ||||||||
\(239\) | 18.2618 | 1.18125 | 0.590627 | − | 0.806944i | \(-0.298880\pi\) | ||||
0.590627 | + | 0.806944i | \(0.298880\pi\) | |||||||
\(240\) | 0.118969 | 0.00767944 | ||||||||
\(241\) | −27.7795 | −1.78943 | −0.894717 | − | 0.446634i | \(-0.852623\pi\) | ||||
−0.894717 | + | 0.446634i | \(0.852623\pi\) | |||||||
\(242\) | 0.867375 | 0.0557570 | ||||||||
\(243\) | 13.6188 | 0.873647 | ||||||||
\(244\) | 4.64965 | 0.297664 | ||||||||
\(245\) | −20.7260 | −1.32413 | ||||||||
\(246\) | −0.702288 | −0.0447762 | ||||||||
\(247\) | 18.5803 | 1.18224 | ||||||||
\(248\) | −13.7095 | −0.870555 | ||||||||
\(249\) | −2.65432 | −0.168211 | ||||||||
\(250\) | 15.9152 | 1.00656 | ||||||||
\(251\) | −17.1272 | −1.08106 | −0.540529 | − | 0.841325i | \(-0.681776\pi\) | ||||
−0.540529 | + | 0.841325i | \(0.681776\pi\) | |||||||
\(252\) | 4.18505 | 0.263633 | ||||||||
\(253\) | −5.90488 | −0.371237 | ||||||||
\(254\) | −9.39207 | −0.589311 | ||||||||
\(255\) | −8.40564 | −0.526382 | ||||||||
\(256\) | −15.8676 | −0.991725 | ||||||||
\(257\) | 29.3116 | 1.82841 | 0.914203 | − | 0.405258i | \(-0.132818\pi\) | ||||
0.914203 | + | 0.405258i | \(0.132818\pi\) | |||||||
\(258\) | −3.73369 | −0.232449 | ||||||||
\(259\) | −3.65532 | −0.227130 | ||||||||
\(260\) | −24.1690 | −1.49890 | ||||||||
\(261\) | −22.1896 | −1.37350 | ||||||||
\(262\) | 0.867375 | 0.0535866 | ||||||||
\(263\) | 0.190663 | 0.0117568 | 0.00587839 | − | 0.999983i | \(-0.498129\pi\) | ||||
0.00587839 | + | 0.999983i | \(0.498129\pi\) | |||||||
\(264\) | 1.67740 | 0.103237 | ||||||||
\(265\) | 8.36900 | 0.514103 | ||||||||
\(266\) | 4.05464 | 0.248606 | ||||||||
\(267\) | −8.95265 | −0.547893 | ||||||||
\(268\) | −5.60119 | −0.342147 | ||||||||
\(269\) | 20.9533 | 1.27755 | 0.638774 | − | 0.769395i | \(-0.279442\pi\) | ||||
0.638774 | + | 0.769395i | \(0.279442\pi\) | |||||||
\(270\) | −11.2075 | −0.682065 | ||||||||
\(271\) | −30.2804 | −1.83940 | −0.919701 | − | 0.392619i | \(-0.871569\pi\) | ||||
−0.919701 | + | 0.392619i | \(0.871569\pi\) | |||||||
\(272\) | −0.190896 | −0.0115748 | ||||||||
\(273\) | 3.80528 | 0.230306 | ||||||||
\(274\) | 1.40973 | 0.0851652 | ||||||||
\(275\) | −9.77374 | −0.589379 | ||||||||
\(276\) | −4.38699 | −0.264066 | ||||||||
\(277\) | 9.93007 | 0.596640 | 0.298320 | − | 0.954466i | \(-0.403574\pi\) | ||||
0.298320 | + | 0.954466i | \(0.403574\pi\) | |||||||
\(278\) | 14.7354 | 0.883771 | ||||||||
\(279\) | −12.8747 | −0.770791 | ||||||||
\(280\) | −13.7288 | −0.820452 | ||||||||
\(281\) | −20.0093 | −1.19366 | −0.596829 | − | 0.802369i | \(-0.703573\pi\) | ||||
−0.596829 | + | 0.802369i | \(0.703573\pi\) | |||||||
\(282\) | −1.26996 | −0.0756250 | ||||||||
\(283\) | 29.5664 | 1.75754 | 0.878769 | − | 0.477248i | \(-0.158366\pi\) | ||||
0.878769 | + | 0.477248i | \(0.158366\pi\) | |||||||
\(284\) | 5.19726 | 0.308401 | ||||||||
\(285\) | 8.43801 | 0.499825 | ||||||||
\(286\) | −4.37143 | −0.258488 | ||||||||
\(287\) | −1.72409 | −0.101770 | ||||||||
\(288\) | −15.0232 | −0.885252 | ||||||||
\(289\) | −3.51246 | −0.206615 | ||||||||
\(290\) | 27.9645 | 1.64213 | ||||||||
\(291\) | −1.76002 | −0.103174 | ||||||||
\(292\) | 9.57979 | 0.560615 | ||||||||
\(293\) | 0.259296 | 0.0151482 | 0.00757412 | − | 0.999971i | \(-0.497589\pi\) | ||||
0.00757412 | + | 0.999971i | \(0.497589\pi\) | |||||||
\(294\) | −2.78507 | −0.162429 | ||||||||
\(295\) | 36.5429 | 2.12761 | ||||||||
\(296\) | 8.12069 | 0.472006 | ||||||||
\(297\) | 3.36167 | 0.195064 | ||||||||
\(298\) | 1.42868 | 0.0827611 | ||||||||
\(299\) | 29.7597 | 1.72105 | ||||||||
\(300\) | −7.26134 | −0.419234 | ||||||||
\(301\) | −9.16604 | −0.528322 | ||||||||
\(302\) | −12.1391 | −0.698527 | ||||||||
\(303\) | 6.18216 | 0.355156 | ||||||||
\(304\) | 0.191631 | 0.0109908 | ||||||||
\(305\) | −14.3242 | −0.820199 | ||||||||
\(306\) | 8.42689 | 0.481733 | ||||||||
\(307\) | −10.4703 | −0.597570 | −0.298785 | − | 0.954320i | \(-0.596581\pi\) | ||||
−0.298785 | + | 0.954320i | \(0.596581\pi\) | |||||||
\(308\) | 1.58200 | 0.0901428 | ||||||||
\(309\) | −0.775052 | −0.0440912 | ||||||||
\(310\) | 16.2254 | 0.921543 | ||||||||
\(311\) | 20.6984 | 1.17370 | 0.586849 | − | 0.809696i | \(-0.300368\pi\) | ||||
0.586849 | + | 0.809696i | \(0.300368\pi\) | |||||||
\(312\) | −8.45384 | −0.478604 | ||||||||
\(313\) | −32.4711 | −1.83537 | −0.917686 | − | 0.397306i | \(-0.869945\pi\) | ||||
−0.917686 | + | 0.397306i | \(0.869945\pi\) | |||||||
\(314\) | −14.4355 | −0.814642 | ||||||||
\(315\) | −12.8929 | −0.726430 | ||||||||
\(316\) | −6.38024 | −0.358917 | ||||||||
\(317\) | 7.29773 | 0.409882 | 0.204941 | − | 0.978774i | \(-0.434300\pi\) | ||||
0.204941 | + | 0.978774i | \(0.434300\pi\) | |||||||
\(318\) | 1.12459 | 0.0630639 | ||||||||
\(319\) | −8.38794 | −0.469634 | ||||||||
\(320\) | 18.5335 | 1.03605 | ||||||||
\(321\) | −3.35664 | −0.187350 | ||||||||
\(322\) | 6.49423 | 0.361909 | ||||||||
\(323\) | −13.5395 | −0.753357 | ||||||||
\(324\) | −7.40421 | −0.411345 | ||||||||
\(325\) | 49.2581 | 2.73235 | ||||||||
\(326\) | 12.8362 | 0.710934 | ||||||||
\(327\) | 1.56464 | 0.0865248 | ||||||||
\(328\) | 3.83024 | 0.211490 | ||||||||
\(329\) | −3.11770 | −0.171884 | ||||||||
\(330\) | −1.98523 | −0.109283 | ||||||||
\(331\) | 24.2183 | 1.33116 | 0.665580 | − | 0.746327i | \(-0.268184\pi\) | ||||
0.665580 | + | 0.746327i | \(0.268184\pi\) | |||||||
\(332\) | 5.56148 | 0.305226 | ||||||||
\(333\) | 7.62622 | 0.417915 | ||||||||
\(334\) | 2.32779 | 0.127371 | ||||||||
\(335\) | 17.2556 | 0.942772 | ||||||||
\(336\) | 0.0392464 | 0.00214107 | ||||||||
\(337\) | −33.0504 | −1.80037 | −0.900184 | − | 0.435510i | \(-0.856568\pi\) | ||||
−0.900184 | + | 0.435510i | \(0.856568\pi\) | |||||||
\(338\) | 10.7555 | 0.585021 | ||||||||
\(339\) | 0.917301 | 0.0498210 | ||||||||
\(340\) | 17.6120 | 0.955144 | ||||||||
\(341\) | −4.86681 | −0.263553 | ||||||||
\(342\) | −8.45934 | −0.457429 | ||||||||
\(343\) | −15.7130 | −0.848424 | ||||||||
\(344\) | 20.3634 | 1.09792 | ||||||||
\(345\) | 13.5150 | 0.727623 | ||||||||
\(346\) | −19.8902 | −1.06930 | ||||||||
\(347\) | −8.92109 | −0.478909 | −0.239454 | − | 0.970908i | \(-0.576969\pi\) | ||||
−0.239454 | + | 0.970908i | \(0.576969\pi\) | |||||||
\(348\) | −6.23176 | −0.334058 | ||||||||
\(349\) | 22.1550 | 1.18593 | 0.592965 | − | 0.805228i | \(-0.297957\pi\) | ||||
0.592965 | + | 0.805228i | \(0.297957\pi\) | |||||||
\(350\) | 10.7492 | 0.574570 | ||||||||
\(351\) | −16.9423 | −0.904313 | ||||||||
\(352\) | −5.67896 | −0.302690 | ||||||||
\(353\) | 26.3039 | 1.40002 | 0.700009 | − | 0.714134i | \(-0.253179\pi\) | ||||
0.700009 | + | 0.714134i | \(0.253179\pi\) | |||||||
\(354\) | 4.91049 | 0.260989 | ||||||||
\(355\) | −16.0112 | −0.849785 | ||||||||
\(356\) | 18.7581 | 0.994178 | ||||||||
\(357\) | −2.77291 | −0.146758 | ||||||||
\(358\) | −9.28158 | −0.490547 | ||||||||
\(359\) | −33.2141 | −1.75297 | −0.876487 | − | 0.481425i | \(-0.840119\pi\) | ||||
−0.876487 | + | 0.481425i | \(0.840119\pi\) | |||||||
\(360\) | 28.6429 | 1.50961 | ||||||||
\(361\) | −5.40838 | −0.284652 | ||||||||
\(362\) | −11.1757 | −0.587382 | ||||||||
\(363\) | 0.595469 | 0.0312540 | ||||||||
\(364\) | −7.97303 | −0.417900 | ||||||||
\(365\) | −29.5124 | −1.54475 | ||||||||
\(366\) | −1.92482 | −0.100612 | ||||||||
\(367\) | −18.6855 | −0.975377 | −0.487689 | − | 0.873018i | \(-0.662160\pi\) | ||||
−0.487689 | + | 0.873018i | \(0.662160\pi\) | |||||||
\(368\) | 0.306932 | 0.0159999 | ||||||||
\(369\) | 3.59702 | 0.187253 | ||||||||
\(370\) | −9.61098 | −0.499651 | ||||||||
\(371\) | 2.76082 | 0.143335 | ||||||||
\(372\) | −3.61577 | −0.187469 | ||||||||
\(373\) | −28.8666 | −1.49465 | −0.747327 | − | 0.664457i | \(-0.768663\pi\) | ||||
−0.747327 | + | 0.664457i | \(0.768663\pi\) | |||||||
\(374\) | 3.18547 | 0.164717 | ||||||||
\(375\) | 10.9261 | 0.564219 | ||||||||
\(376\) | 6.92630 | 0.357197 | ||||||||
\(377\) | 42.2739 | 2.17722 | ||||||||
\(378\) | −3.69719 | −0.190163 | ||||||||
\(379\) | 16.2912 | 0.836824 | 0.418412 | − | 0.908257i | \(-0.362587\pi\) | ||||
0.418412 | + | 0.908257i | \(0.362587\pi\) | |||||||
\(380\) | −17.6798 | −0.906955 | ||||||||
\(381\) | −6.44783 | −0.330333 | ||||||||
\(382\) | 4.92330 | 0.251898 | ||||||||
\(383\) | −6.93561 | −0.354393 | −0.177197 | − | 0.984175i | \(-0.556703\pi\) | ||||
−0.177197 | + | 0.984175i | \(0.556703\pi\) | |||||||
\(384\) | −4.27284 | −0.218048 | ||||||||
\(385\) | −4.87366 | −0.248385 | ||||||||
\(386\) | 5.34324 | 0.271964 | ||||||||
\(387\) | 19.1234 | 0.972099 | ||||||||
\(388\) | 3.68770 | 0.187214 | ||||||||
\(389\) | −6.63758 | −0.336539 | −0.168269 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168269 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(390\) | 10.0053 | 0.506636 | ||||||||
\(391\) | −21.6859 | −1.09670 | ||||||||
\(392\) | 15.1896 | 0.767192 | ||||||||
\(393\) | 0.595469 | 0.0300374 | ||||||||
\(394\) | −13.1974 | −0.664877 | ||||||||
\(395\) | 19.6556 | 0.988979 | ||||||||
\(396\) | −3.30058 | −0.165861 | ||||||||
\(397\) | 38.5529 | 1.93491 | 0.967457 | − | 0.253034i | \(-0.0814283\pi\) | ||||
0.967457 | + | 0.253034i | \(0.0814283\pi\) | |||||||
\(398\) | −16.9108 | −0.847661 | ||||||||
\(399\) | 2.78359 | 0.139354 | ||||||||
\(400\) | 0.508032 | 0.0254016 | ||||||||
\(401\) | −29.5892 | −1.47762 | −0.738808 | − | 0.673916i | \(-0.764611\pi\) | ||||
−0.738808 | + | 0.673916i | \(0.764611\pi\) | |||||||
\(402\) | 2.31873 | 0.115648 | ||||||||
\(403\) | 24.5280 | 1.22183 | ||||||||
\(404\) | −12.9532 | −0.644447 | ||||||||
\(405\) | 22.8101 | 1.13344 | ||||||||
\(406\) | 9.22511 | 0.457835 | ||||||||
\(407\) | 2.88281 | 0.142895 | ||||||||
\(408\) | 6.16032 | 0.304981 | ||||||||
\(409\) | 28.4586 | 1.40719 | 0.703594 | − | 0.710602i | \(-0.251577\pi\) | ||||
0.703594 | + | 0.710602i | \(0.251577\pi\) | |||||||
\(410\) | −4.53316 | −0.223877 | ||||||||
\(411\) | 0.967810 | 0.0477385 | ||||||||
\(412\) | 1.62393 | 0.0800054 | ||||||||
\(413\) | 12.0550 | 0.593189 | ||||||||
\(414\) | −13.5492 | −0.665904 | ||||||||
\(415\) | −17.1332 | −0.841037 | ||||||||
\(416\) | 28.6211 | 1.40326 | ||||||||
\(417\) | 10.1161 | 0.495389 | ||||||||
\(418\) | −3.19773 | −0.156406 | ||||||||
\(419\) | 26.4337 | 1.29137 | 0.645685 | − | 0.763604i | \(-0.276572\pi\) | ||||
0.645685 | + | 0.763604i | \(0.276572\pi\) | |||||||
\(420\) | −3.62085 | −0.176680 | ||||||||
\(421\) | 2.61960 | 0.127672 | 0.0638358 | − | 0.997960i | \(-0.479667\pi\) | ||||
0.0638358 | + | 0.997960i | \(0.479667\pi\) | |||||||
\(422\) | −11.2177 | −0.546068 | ||||||||
\(423\) | 6.50456 | 0.316263 | ||||||||
\(424\) | −6.13346 | −0.297867 | ||||||||
\(425\) | −35.8944 | −1.74114 | ||||||||
\(426\) | −2.15151 | −0.104241 | ||||||||
\(427\) | −4.72535 | −0.228676 | ||||||||
\(428\) | 7.03303 | 0.339954 | ||||||||
\(429\) | −3.00107 | −0.144893 | ||||||||
\(430\) | −24.1004 | −1.16222 | ||||||||
\(431\) | −12.5844 | −0.606169 | −0.303084 | − | 0.952964i | \(-0.598016\pi\) | ||||
−0.303084 | + | 0.952964i | \(0.598016\pi\) | |||||||
\(432\) | −0.174737 | −0.00840706 | ||||||||
\(433\) | −1.91400 | −0.0919811 | −0.0459906 | − | 0.998942i | \(-0.514644\pi\) | ||||
−0.0459906 | + | 0.998942i | \(0.514644\pi\) | |||||||
\(434\) | 5.35256 | 0.256931 | ||||||||
\(435\) | 19.1982 | 0.920481 | ||||||||
\(436\) | −3.27832 | −0.157003 | ||||||||
\(437\) | 21.7694 | 1.04137 | ||||||||
\(438\) | −3.96575 | −0.189491 | ||||||||
\(439\) | −15.4552 | −0.737634 | −0.368817 | − | 0.929502i | \(-0.620237\pi\) | ||||
−0.368817 | + | 0.929502i | \(0.620237\pi\) | |||||||
\(440\) | 10.8274 | 0.516174 | ||||||||
\(441\) | 14.2647 | 0.679273 | ||||||||
\(442\) | −16.0543 | −0.763624 | ||||||||
\(443\) | 23.3994 | 1.11174 | 0.555870 | − | 0.831269i | \(-0.312385\pi\) | ||||
0.555870 | + | 0.831269i | \(0.312385\pi\) | |||||||
\(444\) | 2.14176 | 0.101644 | ||||||||
\(445\) | −57.7880 | −2.73941 | ||||||||
\(446\) | 20.5918 | 0.975049 | ||||||||
\(447\) | 0.980815 | 0.0463909 | ||||||||
\(448\) | 6.11395 | 0.288857 | ||||||||
\(449\) | 7.91672 | 0.373613 | 0.186807 | − | 0.982397i | \(-0.440186\pi\) | ||||
0.186807 | + | 0.982397i | \(0.440186\pi\) | |||||||
\(450\) | −22.4265 | −1.05720 | ||||||||
\(451\) | 1.35972 | 0.0640266 | ||||||||
\(452\) | −1.92198 | −0.0904024 | ||||||||
\(453\) | −8.33373 | −0.391553 | ||||||||
\(454\) | 0.875249 | 0.0410775 | ||||||||
\(455\) | 24.5625 | 1.15151 | ||||||||
\(456\) | −6.18404 | −0.289594 | ||||||||
\(457\) | −5.17072 | −0.241876 | −0.120938 | − | 0.992660i | \(-0.538590\pi\) | ||||
−0.120938 | + | 0.992660i | \(0.538590\pi\) | |||||||
\(458\) | −4.01140 | −0.187440 | ||||||||
\(459\) | 12.3459 | 0.576256 | ||||||||
\(460\) | −28.3174 | −1.32030 | ||||||||
\(461\) | −23.3908 | −1.08942 | −0.544708 | − | 0.838626i | \(-0.683360\pi\) | ||||
−0.544708 | + | 0.838626i | \(0.683360\pi\) | |||||||
\(462\) | −0.654901 | −0.0304688 | ||||||||
\(463\) | 23.3101 | 1.08331 | 0.541656 | − | 0.840600i | \(-0.317797\pi\) | ||||
0.541656 | + | 0.840600i | \(0.317797\pi\) | |||||||
\(464\) | 0.435999 | 0.0202408 | ||||||||
\(465\) | 11.1391 | 0.516562 | ||||||||
\(466\) | −19.3965 | −0.898525 | ||||||||
\(467\) | 1.40125 | 0.0648420 | 0.0324210 | − | 0.999474i | \(-0.489678\pi\) | ||||
0.0324210 | + | 0.999474i | \(0.489678\pi\) | |||||||
\(468\) | 16.6344 | 0.768926 | ||||||||
\(469\) | 5.69238 | 0.262849 | ||||||||
\(470\) | −8.19740 | −0.378118 | ||||||||
\(471\) | −9.91024 | −0.456640 | ||||||||
\(472\) | −26.7816 | −1.23272 | ||||||||
\(473\) | 7.22890 | 0.332385 | ||||||||
\(474\) | 2.64123 | 0.121316 | ||||||||
\(475\) | 36.0327 | 1.65329 | ||||||||
\(476\) | 5.80995 | 0.266299 | ||||||||
\(477\) | −5.76000 | −0.263732 | ||||||||
\(478\) | 15.8398 | 0.724495 | ||||||||
\(479\) | 7.91235 | 0.361524 | 0.180762 | − | 0.983527i | \(-0.442144\pi\) | ||||
0.180762 | + | 0.983527i | \(0.442144\pi\) | |||||||
\(480\) | 12.9979 | 0.593271 | ||||||||
\(481\) | −14.5289 | −0.662461 | ||||||||
\(482\) | −24.0952 | −1.09751 | ||||||||
\(483\) | 4.45841 | 0.202865 | ||||||||
\(484\) | −1.24766 | −0.0567119 | ||||||||
\(485\) | −11.3607 | −0.515861 | ||||||||
\(486\) | 11.8126 | 0.535831 | ||||||||
\(487\) | −38.7460 | −1.75575 | −0.877874 | − | 0.478892i | \(-0.841038\pi\) | ||||
−0.877874 | + | 0.478892i | \(0.841038\pi\) | |||||||
\(488\) | 10.4979 | 0.475217 | ||||||||
\(489\) | 8.81233 | 0.398507 | ||||||||
\(490\) | −17.9772 | −0.812127 | ||||||||
\(491\) | 28.8886 | 1.30372 | 0.651861 | − | 0.758338i | \(-0.273989\pi\) | ||||
0.651861 | + | 0.758338i | \(0.273989\pi\) | |||||||
\(492\) | 1.01019 | 0.0455431 | ||||||||
\(493\) | −30.8050 | −1.38739 | ||||||||
\(494\) | 16.1161 | 0.725097 | ||||||||
\(495\) | 10.1681 | 0.457022 | ||||||||
\(496\) | 0.252974 | 0.0113589 | ||||||||
\(497\) | −5.28187 | −0.236924 | ||||||||
\(498\) | −2.30229 | −0.103168 | ||||||||
\(499\) | 36.1054 | 1.61630 | 0.808149 | − | 0.588978i | \(-0.200469\pi\) | ||||
0.808149 | + | 0.588978i | \(0.200469\pi\) | |||||||
\(500\) | −22.8929 | −1.02380 | ||||||||
\(501\) | 1.59807 | 0.0713966 | ||||||||
\(502\) | −14.8557 | −0.663042 | ||||||||
\(503\) | 5.13330 | 0.228882 | 0.114441 | − | 0.993430i | \(-0.463492\pi\) | ||||
0.114441 | + | 0.993430i | \(0.463492\pi\) | |||||||
\(504\) | 9.44890 | 0.420887 | ||||||||
\(505\) | 39.9049 | 1.77575 | ||||||||
\(506\) | −5.12175 | −0.227689 | ||||||||
\(507\) | 7.38384 | 0.327928 | ||||||||
\(508\) | 13.5099 | 0.599403 | ||||||||
\(509\) | 12.0429 | 0.533793 | 0.266896 | − | 0.963725i | \(-0.414002\pi\) | ||||
0.266896 | + | 0.963725i | \(0.414002\pi\) | |||||||
\(510\) | −7.29084 | −0.322844 | ||||||||
\(511\) | −9.73574 | −0.430684 | ||||||||
\(512\) | 0.588034 | 0.0259877 | ||||||||
\(513\) | −12.3934 | −0.547182 | ||||||||
\(514\) | 25.4241 | 1.12141 | ||||||||
\(515\) | −5.00284 | −0.220451 | ||||||||
\(516\) | 5.37066 | 0.236430 | ||||||||
\(517\) | 2.45880 | 0.108138 | ||||||||
\(518\) | −3.17053 | −0.139305 | ||||||||
\(519\) | −13.6550 | −0.599387 | ||||||||
\(520\) | −54.5682 | −2.39298 | ||||||||
\(521\) | −25.0171 | −1.09602 | −0.548009 | − | 0.836473i | \(-0.684614\pi\) | ||||
−0.548009 | + | 0.836473i | \(0.684614\pi\) | |||||||
\(522\) | −19.2467 | −0.842405 | ||||||||
\(523\) | 32.1032 | 1.40378 | 0.701888 | − | 0.712287i | \(-0.252341\pi\) | ||||
0.701888 | + | 0.712287i | \(0.252341\pi\) | |||||||
\(524\) | −1.24766 | −0.0545043 | ||||||||
\(525\) | 7.37955 | 0.322070 | ||||||||
\(526\) | 0.165376 | 0.00721075 | ||||||||
\(527\) | −17.8736 | −0.778584 | ||||||||
\(528\) | −0.0309521 | −0.00134702 | ||||||||
\(529\) | 11.8676 | 0.515984 | ||||||||
\(530\) | 7.25906 | 0.315313 | ||||||||
\(531\) | −25.1508 | −1.09145 | ||||||||
\(532\) | −5.83233 | −0.252863 | ||||||||
\(533\) | −6.85277 | −0.296826 | ||||||||
\(534\) | −7.76531 | −0.336038 | ||||||||
\(535\) | −21.6666 | −0.936730 | ||||||||
\(536\) | −12.6462 | −0.546234 | ||||||||
\(537\) | −6.37198 | −0.274971 | ||||||||
\(538\) | 18.1744 | 0.783554 | ||||||||
\(539\) | 5.39225 | 0.232261 | ||||||||
\(540\) | 16.1212 | 0.693746 | ||||||||
\(541\) | 1.16455 | 0.0500678 | 0.0250339 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250339 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(542\) | −26.2644 | −1.12815 | ||||||||
\(543\) | −7.67233 | −0.329251 | ||||||||
\(544\) | −20.8562 | −0.894203 | ||||||||
\(545\) | 10.0995 | 0.432616 | ||||||||
\(546\) | 3.30060 | 0.141253 | ||||||||
\(547\) | −15.6353 | −0.668518 | −0.334259 | − | 0.942481i | \(-0.608486\pi\) | ||||
−0.334259 | + | 0.942481i | \(0.608486\pi\) | |||||||
\(548\) | −2.02781 | −0.0866237 | ||||||||
\(549\) | 9.85867 | 0.420758 | ||||||||
\(550\) | −8.47750 | −0.361482 | ||||||||
\(551\) | 30.9236 | 1.31739 | ||||||||
\(552\) | −9.90485 | −0.421579 | ||||||||
\(553\) | 6.48411 | 0.275732 | ||||||||
\(554\) | 8.61309 | 0.365935 | ||||||||
\(555\) | −6.59812 | −0.280075 | ||||||||
\(556\) | −21.1959 | −0.898906 | ||||||||
\(557\) | −15.3129 | −0.648828 | −0.324414 | − | 0.945915i | \(-0.605167\pi\) | ||||
−0.324414 | + | 0.945915i | \(0.605167\pi\) | |||||||
\(558\) | −11.1672 | −0.472747 | ||||||||
\(559\) | −36.4325 | −1.54093 | ||||||||
\(560\) | 0.253329 | 0.0107051 | ||||||||
\(561\) | 2.18688 | 0.0923303 | ||||||||
\(562\) | −17.3556 | −0.732102 | ||||||||
\(563\) | 33.3451 | 1.40533 | 0.702664 | − | 0.711522i | \(-0.251994\pi\) | ||||
0.702664 | + | 0.711522i | \(0.251994\pi\) | |||||||
\(564\) | 1.82675 | 0.0769202 | ||||||||
\(565\) | 5.92104 | 0.249100 | ||||||||
\(566\) | 25.6451 | 1.07794 | ||||||||
\(567\) | 7.52475 | 0.316010 | ||||||||
\(568\) | 11.7343 | 0.492358 | ||||||||
\(569\) | −15.0210 | −0.629714 | −0.314857 | − | 0.949139i | \(-0.601957\pi\) | ||||
−0.314857 | + | 0.949139i | \(0.601957\pi\) | |||||||
\(570\) | 7.31892 | 0.306556 | ||||||||
\(571\) | 9.46964 | 0.396292 | 0.198146 | − | 0.980173i | \(-0.436508\pi\) | ||||
0.198146 | + | 0.980173i | \(0.436508\pi\) | |||||||
\(572\) | 6.28802 | 0.262915 | ||||||||
\(573\) | 3.37994 | 0.141199 | ||||||||
\(574\) | −1.49543 | −0.0624180 | ||||||||
\(575\) | 57.7128 | 2.40679 | ||||||||
\(576\) | −12.7558 | −0.531490 | ||||||||
\(577\) | −30.5253 | −1.27079 | −0.635393 | − | 0.772189i | \(-0.719162\pi\) | ||||
−0.635393 | + | 0.772189i | \(0.719162\pi\) | |||||||
\(578\) | −3.04662 | −0.126723 | ||||||||
\(579\) | 3.66824 | 0.152447 | ||||||||
\(580\) | −40.2251 | −1.67026 | ||||||||
\(581\) | −5.65202 | −0.234485 | ||||||||
\(582\) | −1.52660 | −0.0632795 | ||||||||
\(583\) | −2.17735 | −0.0901766 | ||||||||
\(584\) | 21.6290 | 0.895015 | ||||||||
\(585\) | −51.2456 | −2.11874 | ||||||||
\(586\) | 0.224907 | 0.00929082 | ||||||||
\(587\) | 3.21876 | 0.132853 | 0.0664263 | − | 0.997791i | \(-0.478840\pi\) | ||||
0.0664263 | + | 0.997791i | \(0.478840\pi\) | |||||||
\(588\) | 4.00614 | 0.165210 | ||||||||
\(589\) | 17.9424 | 0.739303 | ||||||||
\(590\) | 31.6964 | 1.30492 | ||||||||
\(591\) | −9.06029 | −0.372691 | ||||||||
\(592\) | −0.149846 | −0.00615865 | ||||||||
\(593\) | −42.3987 | −1.74111 | −0.870553 | − | 0.492075i | \(-0.836239\pi\) | ||||
−0.870553 | + | 0.492075i | \(0.836239\pi\) | |||||||
\(594\) | 2.91583 | 0.119638 | ||||||||
\(595\) | −17.8987 | −0.733775 | ||||||||
\(596\) | −2.05506 | −0.0841785 | ||||||||
\(597\) | −11.6096 | −0.475148 | ||||||||
\(598\) | 25.8128 | 1.05556 | ||||||||
\(599\) | 12.7398 | 0.520532 | 0.260266 | − | 0.965537i | \(-0.416190\pi\) | ||||
0.260266 | + | 0.965537i | \(0.416190\pi\) | |||||||
\(600\) | −16.3945 | −0.669302 | ||||||||
\(601\) | 9.94914 | 0.405834 | 0.202917 | − | 0.979196i | \(-0.434958\pi\) | ||||
0.202917 | + | 0.979196i | \(0.434958\pi\) | |||||||
\(602\) | −7.95039 | −0.324034 | ||||||||
\(603\) | −11.8762 | −0.483637 | ||||||||
\(604\) | 17.4613 | 0.710490 | ||||||||
\(605\) | 3.84366 | 0.156267 | ||||||||
\(606\) | 5.36225 | 0.217827 | ||||||||
\(607\) | 28.2258 | 1.14565 | 0.572825 | − | 0.819678i | \(-0.305847\pi\) | ||||
0.572825 | + | 0.819678i | \(0.305847\pi\) | |||||||
\(608\) | 20.9365 | 0.849088 | ||||||||
\(609\) | 6.33321 | 0.256635 | ||||||||
\(610\) | −12.4244 | −0.503050 | ||||||||
\(611\) | −12.3920 | −0.501326 | ||||||||
\(612\) | −12.1215 | −0.489983 | ||||||||
\(613\) | 15.4348 | 0.623407 | 0.311704 | − | 0.950179i | \(-0.399100\pi\) | ||||
0.311704 | + | 0.950179i | \(0.399100\pi\) | |||||||
\(614\) | −9.08165 | −0.366506 | ||||||||
\(615\) | −3.11210 | −0.125492 | ||||||||
\(616\) | 3.57180 | 0.143912 | ||||||||
\(617\) | 37.2977 | 1.50155 | 0.750774 | − | 0.660559i | \(-0.229681\pi\) | ||||
0.750774 | + | 0.660559i | \(0.229681\pi\) | |||||||
\(618\) | −0.672260 | −0.0270423 | ||||||||
\(619\) | 34.9963 | 1.40662 | 0.703311 | − | 0.710883i | \(-0.251704\pi\) | ||||
0.703311 | + | 0.710883i | \(0.251704\pi\) | |||||||
\(620\) | −23.3392 | −0.937326 | ||||||||
\(621\) | −19.8503 | −0.796564 | ||||||||
\(622\) | 17.9533 | 0.719860 | ||||||||
\(623\) | −19.0635 | −0.763762 | ||||||||
\(624\) | 0.155994 | 0.00624475 | ||||||||
\(625\) | 21.6573 | 0.866292 | ||||||||
\(626\) | −28.1646 | −1.12568 | ||||||||
\(627\) | −2.19531 | −0.0876720 | ||||||||
\(628\) | 20.7645 | 0.828594 | ||||||||
\(629\) | 10.5872 | 0.422140 | ||||||||
\(630\) | −11.1829 | −0.445539 | ||||||||
\(631\) | −30.5790 | −1.21733 | −0.608665 | − | 0.793427i | \(-0.708295\pi\) | ||||
−0.608665 | + | 0.793427i | \(0.708295\pi\) | |||||||
\(632\) | −14.4052 | −0.573006 | ||||||||
\(633\) | −7.70115 | −0.306093 | ||||||||
\(634\) | 6.32987 | 0.251391 | ||||||||
\(635\) | −41.6198 | −1.65163 | ||||||||
\(636\) | −1.61765 | −0.0641439 | ||||||||
\(637\) | −27.1761 | −1.07676 | ||||||||
\(638\) | −7.27548 | −0.288039 | ||||||||
\(639\) | 11.0198 | 0.435935 | ||||||||
\(640\) | −27.5806 | −1.09022 | ||||||||
\(641\) | −1.66285 | −0.0656785 | −0.0328392 | − | 0.999461i | \(-0.510455\pi\) | ||||
−0.0328392 | + | 0.999461i | \(0.510455\pi\) | |||||||
\(642\) | −2.91147 | −0.114907 | ||||||||
\(643\) | −16.9066 | −0.666730 | −0.333365 | − | 0.942798i | \(-0.608184\pi\) | ||||
−0.333365 | + | 0.942798i | \(0.608184\pi\) | |||||||
\(644\) | −9.34152 | −0.368107 | ||||||||
\(645\) | −16.5454 | −0.651473 | ||||||||
\(646\) | −11.7438 | −0.462054 | ||||||||
\(647\) | 47.7281 | 1.87639 | 0.938193 | − | 0.346112i | \(-0.112498\pi\) | ||||
0.938193 | + | 0.346112i | \(0.112498\pi\) | |||||||
\(648\) | −16.7171 | −0.656708 | ||||||||
\(649\) | −9.50732 | −0.373195 | ||||||||
\(650\) | 42.7253 | 1.67582 | ||||||||
\(651\) | 3.67463 | 0.144020 | ||||||||
\(652\) | −18.4641 | −0.723109 | ||||||||
\(653\) | 7.82868 | 0.306360 | 0.153180 | − | 0.988198i | \(-0.451049\pi\) | ||||
0.153180 | + | 0.988198i | \(0.451049\pi\) | |||||||
\(654\) | 1.35713 | 0.0530680 | ||||||||
\(655\) | 3.84366 | 0.150184 | ||||||||
\(656\) | −0.0706772 | −0.00275948 | ||||||||
\(657\) | 20.3120 | 0.792448 | ||||||||
\(658\) | −2.70421 | −0.105421 | ||||||||
\(659\) | 27.2725 | 1.06238 | 0.531192 | − | 0.847251i | \(-0.321744\pi\) | ||||
0.531192 | + | 0.847251i | \(0.321744\pi\) | |||||||
\(660\) | 2.85562 | 0.111155 | ||||||||
\(661\) | 31.7462 | 1.23478 | 0.617392 | − | 0.786656i | \(-0.288189\pi\) | ||||
0.617392 | + | 0.786656i | \(0.288189\pi\) | |||||||
\(662\) | 21.0064 | 0.816436 | ||||||||
\(663\) | −11.0216 | −0.428042 | ||||||||
\(664\) | 12.5566 | 0.487290 | ||||||||
\(665\) | 17.9676 | 0.696754 | ||||||||
\(666\) | 6.61480 | 0.256318 | ||||||||
\(667\) | 49.5298 | 1.91780 | ||||||||
\(668\) | −3.34837 | −0.129552 | ||||||||
\(669\) | 14.1366 | 0.546554 | ||||||||
\(670\) | 14.9670 | 0.578227 | ||||||||
\(671\) | 3.72670 | 0.143868 | ||||||||
\(672\) | 4.28784 | 0.165407 | ||||||||
\(673\) | 21.8473 | 0.842153 | 0.421077 | − | 0.907025i | \(-0.361652\pi\) | ||||
0.421077 | + | 0.907025i | \(0.361652\pi\) | |||||||
\(674\) | −28.6670 | −1.10421 | ||||||||
\(675\) | −32.8561 | −1.26463 | ||||||||
\(676\) | −15.4710 | −0.595040 | ||||||||
\(677\) | −23.9730 | −0.921356 | −0.460678 | − | 0.887567i | \(-0.652394\pi\) | ||||
−0.460678 | + | 0.887567i | \(0.652394\pi\) | |||||||
\(678\) | 0.795644 | 0.0305565 | ||||||||
\(679\) | −3.74773 | −0.143825 | ||||||||
\(680\) | 39.7639 | 1.52488 | ||||||||
\(681\) | 0.600875 | 0.0230256 | ||||||||
\(682\) | −4.22135 | −0.161644 | ||||||||
\(683\) | 3.72529 | 0.142544 | 0.0712722 | − | 0.997457i | \(-0.477294\pi\) | ||||
0.0712722 | + | 0.997457i | \(0.477294\pi\) | |||||||
\(684\) | 12.1682 | 0.465263 | ||||||||
\(685\) | 6.24706 | 0.238688 | ||||||||
\(686\) | −13.6291 | −0.520361 | ||||||||
\(687\) | −2.75390 | −0.105068 | ||||||||
\(688\) | −0.375753 | −0.0143255 | ||||||||
\(689\) | 10.9735 | 0.418057 | ||||||||
\(690\) | 11.7226 | 0.446270 | ||||||||
\(691\) | −27.1674 | −1.03350 | −0.516748 | − | 0.856138i | \(-0.672857\pi\) | ||||
−0.516748 | + | 0.856138i | \(0.672857\pi\) | |||||||
\(692\) | 28.6107 | 1.08762 | ||||||||
\(693\) | 3.35431 | 0.127420 | ||||||||
\(694\) | −7.73793 | −0.293728 | ||||||||
\(695\) | 65.2981 | 2.47690 | ||||||||
\(696\) | −14.0699 | −0.533319 | ||||||||
\(697\) | 4.99362 | 0.189147 | ||||||||
\(698\) | 19.2167 | 0.727363 | ||||||||
\(699\) | −13.3161 | −0.503659 | ||||||||
\(700\) | −15.4620 | −0.584411 | ||||||||
\(701\) | 27.5977 | 1.04235 | 0.521176 | − | 0.853450i | \(-0.325494\pi\) | ||||
0.521176 | + | 0.853450i | \(0.325494\pi\) | |||||||
\(702\) | −14.6953 | −0.554639 | ||||||||
\(703\) | −10.6280 | −0.400842 | ||||||||
\(704\) | −4.82183 | −0.181730 | ||||||||
\(705\) | −5.62767 | −0.211950 | ||||||||
\(706\) | 22.8154 | 0.858668 | ||||||||
\(707\) | 13.1641 | 0.495087 | ||||||||
\(708\) | −7.06341 | −0.265459 | ||||||||
\(709\) | 5.35679 | 0.201178 | 0.100589 | − | 0.994928i | \(-0.467927\pi\) | ||||
0.100589 | + | 0.994928i | \(0.467927\pi\) | |||||||
\(710\) | −13.8877 | −0.521196 | ||||||||
\(711\) | −13.5280 | −0.507341 | ||||||||
\(712\) | 42.3516 | 1.58719 | ||||||||
\(713\) | 28.7380 | 1.07624 | ||||||||
\(714\) | −2.40515 | −0.0900105 | ||||||||
\(715\) | −19.3715 | −0.724452 | ||||||||
\(716\) | 13.3509 | 0.498948 | ||||||||
\(717\) | 10.8743 | 0.406109 | ||||||||
\(718\) | −28.8091 | −1.07515 | ||||||||
\(719\) | −36.4342 | −1.35877 | −0.679383 | − | 0.733783i | \(-0.737753\pi\) | ||||
−0.679383 | + | 0.733783i | \(0.737753\pi\) | |||||||
\(720\) | −0.528530 | −0.0196972 | ||||||||
\(721\) | −1.65037 | −0.0614630 | ||||||||
\(722\) | −4.69110 | −0.174585 | ||||||||
\(723\) | −16.5418 | −0.615197 | ||||||||
\(724\) | 16.0755 | 0.597441 | ||||||||
\(725\) | 81.9815 | 3.04472 | ||||||||
\(726\) | 0.516495 | 0.0191689 | ||||||||
\(727\) | −13.4891 | −0.500282 | −0.250141 | − | 0.968209i | \(-0.580477\pi\) | ||||
−0.250141 | + | 0.968209i | \(0.580477\pi\) | |||||||
\(728\) | −18.0013 | −0.667173 | ||||||||
\(729\) | −9.69385 | −0.359031 | ||||||||
\(730\) | −25.5983 | −0.947436 | ||||||||
\(731\) | 26.5484 | 0.981928 | ||||||||
\(732\) | 2.76873 | 0.102335 | ||||||||
\(733\) | −41.1742 | −1.52080 | −0.760402 | − | 0.649452i | \(-0.774998\pi\) | ||||
−0.760402 | + | 0.649452i | \(0.774998\pi\) | |||||||
\(734\) | −16.2074 | −0.598225 | ||||||||
\(735\) | −12.3417 | −0.455230 | ||||||||
\(736\) | 33.5336 | 1.23607 | ||||||||
\(737\) | −4.48935 | −0.165367 | ||||||||
\(738\) | 3.11997 | 0.114848 | ||||||||
\(739\) | 0.159177 | 0.00585542 | 0.00292771 | − | 0.999996i | \(-0.499068\pi\) | ||||
0.00292771 | + | 0.999996i | \(0.499068\pi\) | |||||||
\(740\) | 13.8248 | 0.508208 | ||||||||
\(741\) | 11.0640 | 0.406446 | ||||||||
\(742\) | 2.39466 | 0.0879109 | ||||||||
\(743\) | 4.13854 | 0.151828 | 0.0759142 | − | 0.997114i | \(-0.475812\pi\) | ||||
0.0759142 | + | 0.997114i | \(0.475812\pi\) | |||||||
\(744\) | −8.16359 | −0.299292 | ||||||||
\(745\) | 6.33101 | 0.231950 | ||||||||
\(746\) | −25.0381 | −0.916711 | ||||||||
\(747\) | 11.7920 | 0.431447 | ||||||||
\(748\) | −4.58208 | −0.167538 | ||||||||
\(749\) | −7.14753 | −0.261165 | ||||||||
\(750\) | 9.47698 | 0.346051 | ||||||||
\(751\) | −7.06567 | −0.257830 | −0.128915 | − | 0.991656i | \(-0.541149\pi\) | ||||
−0.128915 | + | 0.991656i | \(0.541149\pi\) | |||||||
\(752\) | −0.127807 | −0.00466064 | ||||||||
\(753\) | −10.1987 | −0.371662 | ||||||||
\(754\) | 36.6673 | 1.33534 | ||||||||
\(755\) | −53.7929 | −1.95772 | ||||||||
\(756\) | 5.31816 | 0.193420 | ||||||||
\(757\) | 1.70590 | 0.0620021 | 0.0310010 | − | 0.999519i | \(-0.490130\pi\) | ||||
0.0310010 | + | 0.999519i | \(0.490130\pi\) | |||||||
\(758\) | 14.1306 | 0.513246 | ||||||||
\(759\) | −3.51618 | −0.127629 | ||||||||
\(760\) | −39.9170 | −1.44794 | ||||||||
\(761\) | 35.5762 | 1.28964 | 0.644819 | − | 0.764336i | \(-0.276933\pi\) | ||||
0.644819 | + | 0.764336i | \(0.276933\pi\) | |||||||
\(762\) | −5.59269 | −0.202602 | ||||||||
\(763\) | 3.33169 | 0.120615 | ||||||||
\(764\) | −7.08184 | −0.256212 | ||||||||
\(765\) | 37.3427 | 1.35013 | ||||||||
\(766\) | −6.01578 | −0.217359 | ||||||||
\(767\) | 47.9154 | 1.73013 | ||||||||
\(768\) | −9.44866 | −0.340949 | ||||||||
\(769\) | 18.6049 | 0.670908 | 0.335454 | − | 0.942057i | \(-0.391110\pi\) | ||||
0.335454 | + | 0.942057i | \(0.391110\pi\) | |||||||
\(770\) | −4.22729 | −0.152341 | ||||||||
\(771\) | 17.4541 | 0.628595 | ||||||||
\(772\) | −7.68590 | −0.276621 | ||||||||
\(773\) | 29.5051 | 1.06122 | 0.530612 | − | 0.847615i | \(-0.321962\pi\) | ||||
0.530612 | + | 0.847615i | \(0.321962\pi\) | |||||||
\(774\) | 16.5872 | 0.596214 | ||||||||
\(775\) | 47.5670 | 1.70866 | ||||||||
\(776\) | 8.32599 | 0.298886 | ||||||||
\(777\) | −2.17663 | −0.0780862 | ||||||||
\(778\) | −5.75727 | −0.206408 | ||||||||
\(779\) | −5.01285 | −0.179604 | ||||||||
\(780\) | −14.3919 | −0.515313 | ||||||||
\(781\) | 4.16560 | 0.149057 | ||||||||
\(782\) | −18.8098 | −0.672638 | ||||||||
\(783\) | −28.1975 | −1.00770 | ||||||||
\(784\) | −0.280285 | −0.0100102 | ||||||||
\(785\) | −63.9691 | −2.28315 | ||||||||
\(786\) | 0.516495 | 0.0184228 | ||||||||
\(787\) | −40.5428 | −1.44520 | −0.722598 | − | 0.691269i | \(-0.757052\pi\) | ||||
−0.722598 | + | 0.691269i | \(0.757052\pi\) | |||||||
\(788\) | 18.9836 | 0.676264 | ||||||||
\(789\) | 0.113534 | 0.00404191 | ||||||||
\(790\) | 17.0487 | 0.606567 | ||||||||
\(791\) | 1.95327 | 0.0694503 | ||||||||
\(792\) | −7.45198 | −0.264794 | ||||||||
\(793\) | −18.7820 | −0.666968 | ||||||||
\(794\) | 33.4398 | 1.18673 | ||||||||
\(795\) | 4.98348 | 0.176746 | ||||||||
\(796\) | 24.3250 | 0.862178 | ||||||||
\(797\) | 49.5865 | 1.75644 | 0.878221 | − | 0.478255i | \(-0.158730\pi\) | ||||
0.878221 | + | 0.478255i | \(0.158730\pi\) | |||||||
\(798\) | 2.41441 | 0.0854693 | ||||||||
\(799\) | 9.03006 | 0.319460 | ||||||||
\(800\) | 55.5047 | 1.96239 | ||||||||
\(801\) | 39.7728 | 1.40530 | ||||||||
\(802\) | −25.6650 | −0.906261 | ||||||||
\(803\) | 7.67820 | 0.270958 | ||||||||
\(804\) | −3.33534 | −0.117628 | ||||||||
\(805\) | 28.7784 | 1.01430 | ||||||||
\(806\) | 21.2750 | 0.749378 | ||||||||
\(807\) | 12.4771 | 0.439214 | ||||||||
\(808\) | −29.2455 | −1.02885 | ||||||||
\(809\) | −12.6206 | −0.443718 | −0.221859 | − | 0.975079i | \(-0.571212\pi\) | ||||
−0.221859 | + | 0.975079i | \(0.571212\pi\) | |||||||
\(810\) | 19.7849 | 0.695172 | ||||||||
\(811\) | 17.1042 | 0.600609 | 0.300305 | − | 0.953843i | \(-0.402912\pi\) | ||||
0.300305 | + | 0.953843i | \(0.402912\pi\) | |||||||
\(812\) | −13.2697 | −0.465675 | ||||||||
\(813\) | −18.0310 | −0.632376 | ||||||||
\(814\) | 2.50047 | 0.0876416 | ||||||||
\(815\) | 56.8822 | 1.99250 | ||||||||
\(816\) | −0.113673 | −0.00397934 | ||||||||
\(817\) | −26.6506 | −0.932388 | ||||||||
\(818\) | 24.6843 | 0.863066 | ||||||||
\(819\) | −16.9052 | −0.590716 | ||||||||
\(820\) | 6.52065 | 0.227711 | ||||||||
\(821\) | −20.7235 | −0.723255 | −0.361628 | − | 0.932323i | \(-0.617779\pi\) | ||||
−0.361628 | + | 0.932323i | \(0.617779\pi\) | |||||||
\(822\) | 0.839454 | 0.0292793 | ||||||||
\(823\) | −6.01068 | −0.209519 | −0.104760 | − | 0.994498i | \(-0.533407\pi\) | ||||
−0.104760 | + | 0.994498i | \(0.533407\pi\) | |||||||
\(824\) | 3.66648 | 0.127728 | ||||||||
\(825\) | −5.81996 | −0.202625 | ||||||||
\(826\) | 10.4562 | 0.363818 | ||||||||
\(827\) | −5.08408 | −0.176791 | −0.0883954 | − | 0.996085i | \(-0.528174\pi\) | ||||
−0.0883954 | + | 0.996085i | \(0.528174\pi\) | |||||||
\(828\) | 19.4896 | 0.677309 | ||||||||
\(829\) | −13.4710 | −0.467866 | −0.233933 | − | 0.972253i | \(-0.575160\pi\) | ||||
−0.233933 | + | 0.972253i | \(0.575160\pi\) | |||||||
\(830\) | −14.8609 | −0.515831 | ||||||||
\(831\) | 5.91305 | 0.205122 | ||||||||
\(832\) | 24.3013 | 0.842496 | ||||||||
\(833\) | 19.8032 | 0.686142 | ||||||||
\(834\) | 8.77448 | 0.303835 | ||||||||
\(835\) | 10.3153 | 0.356976 | ||||||||
\(836\) | 4.59973 | 0.159085 | ||||||||
\(837\) | −16.3606 | −0.565506 | ||||||||
\(838\) | 22.9279 | 0.792032 | ||||||||
\(839\) | −30.1935 | −1.04240 | −0.521198 | − | 0.853436i | \(-0.674515\pi\) | ||||
−0.521198 | + | 0.853436i | \(0.674515\pi\) | |||||||
\(840\) | −8.17508 | −0.282067 | ||||||||
\(841\) | 41.3575 | 1.42612 | ||||||||
\(842\) | 2.27218 | 0.0783044 | ||||||||
\(843\) | −11.9149 | −0.410373 | ||||||||
\(844\) | 16.1359 | 0.555420 | ||||||||
\(845\) | 47.6616 | 1.63961 | ||||||||
\(846\) | 5.64189 | 0.193972 | ||||||||
\(847\) | 1.26797 | 0.0435680 | ||||||||
\(848\) | 0.113177 | 0.00388652 | ||||||||
\(849\) | 17.6059 | 0.604231 | ||||||||
\(850\) | −31.1339 | −1.06789 | ||||||||
\(851\) | −17.0226 | −0.583528 | ||||||||
\(852\) | 3.09481 | 0.106026 | ||||||||
\(853\) | 8.80353 | 0.301427 | 0.150714 | − | 0.988577i | \(-0.451843\pi\) | ||||
0.150714 | + | 0.988577i | \(0.451843\pi\) | |||||||
\(854\) | −4.09865 | −0.140253 | ||||||||
\(855\) | −37.4865 | −1.28201 | ||||||||
\(856\) | 15.8790 | 0.542733 | ||||||||
\(857\) | 20.4733 | 0.699354 | 0.349677 | − | 0.936870i | \(-0.386291\pi\) | ||||
0.349677 | + | 0.936870i | \(0.386291\pi\) | |||||||
\(858\) | −2.60305 | −0.0888668 | ||||||||
\(859\) | −33.7758 | −1.15241 | −0.576207 | − | 0.817304i | \(-0.695468\pi\) | ||||
−0.576207 | + | 0.817304i | \(0.695468\pi\) | |||||||
\(860\) | 34.6668 | 1.18213 | ||||||||
\(861\) | −1.02664 | −0.0349878 | ||||||||
\(862\) | −10.9154 | −0.371779 | ||||||||
\(863\) | 47.5170 | 1.61750 | 0.808748 | − | 0.588155i | \(-0.200146\pi\) | ||||
0.808748 | + | 0.588155i | \(0.200146\pi\) | |||||||
\(864\) | −19.0908 | −0.649483 | ||||||||
\(865\) | −88.1408 | −2.99688 | ||||||||
\(866\) | −1.66016 | −0.0564145 | ||||||||
\(867\) | −2.09156 | −0.0710331 | ||||||||
\(868\) | −7.69929 | −0.261331 | ||||||||
\(869\) | −5.11376 | −0.173472 | ||||||||
\(870\) | 16.6520 | 0.564556 | ||||||||
\(871\) | 22.6256 | 0.766641 | ||||||||
\(872\) | −7.40172 | −0.250654 | ||||||||
\(873\) | 7.81902 | 0.264634 | ||||||||
\(874\) | 18.8822 | 0.638701 | ||||||||
\(875\) | 23.2656 | 0.786520 | ||||||||
\(876\) | 5.70447 | 0.192736 | ||||||||
\(877\) | −52.2233 | −1.76346 | −0.881728 | − | 0.471759i | \(-0.843619\pi\) | ||||
−0.881728 | + | 0.471759i | \(0.843619\pi\) | |||||||
\(878\) | −13.4054 | −0.452411 | ||||||||
\(879\) | 0.154403 | 0.00520788 | ||||||||
\(880\) | −0.199791 | −0.00673495 | ||||||||
\(881\) | −38.5855 | −1.29998 | −0.649990 | − | 0.759943i | \(-0.725227\pi\) | ||||
−0.649990 | + | 0.759943i | \(0.725227\pi\) | |||||||
\(882\) | 12.3729 | 0.416616 | ||||||||
\(883\) | 44.7200 | 1.50495 | 0.752474 | − | 0.658622i | \(-0.228860\pi\) | ||||
0.752474 | + | 0.658622i | \(0.228860\pi\) | |||||||
\(884\) | 23.0930 | 0.776701 | ||||||||
\(885\) | 21.7602 | 0.731461 | ||||||||
\(886\) | 20.2961 | 0.681859 | ||||||||
\(887\) | −15.2555 | −0.512229 | −0.256114 | − | 0.966646i | \(-0.582442\pi\) | ||||
−0.256114 | + | 0.966646i | \(0.582442\pi\) | |||||||
\(888\) | 4.83562 | 0.162273 | ||||||||
\(889\) | −13.7298 | −0.460483 | ||||||||
\(890\) | −50.1239 | −1.68016 | ||||||||
\(891\) | −5.93448 | −0.198812 | ||||||||
\(892\) | −29.6199 | −0.991748 | ||||||||
\(893\) | −9.06483 | −0.303343 | ||||||||
\(894\) | 0.850734 | 0.0284528 | ||||||||
\(895\) | −41.1302 | −1.37483 | ||||||||
\(896\) | −9.09845 | −0.303958 | ||||||||
\(897\) | 17.7210 | 0.591686 | ||||||||
\(898\) | 6.86676 | 0.229147 | ||||||||
\(899\) | 40.8225 | 1.36151 | ||||||||
\(900\) | 32.2590 | 1.07530 | ||||||||
\(901\) | −7.99640 | −0.266399 | ||||||||
\(902\) | 1.17939 | 0.0392692 | ||||||||
\(903\) | −5.45809 | −0.181634 | ||||||||
\(904\) | −4.33940 | −0.144326 | ||||||||
\(905\) | −49.5237 | −1.64622 | ||||||||
\(906\) | −7.22846 | −0.240150 | ||||||||
\(907\) | −29.7506 | −0.987853 | −0.493927 | − | 0.869504i | \(-0.664439\pi\) | ||||
−0.493927 | + | 0.869504i | \(0.664439\pi\) | |||||||
\(908\) | −1.25899 | −0.0417810 | ||||||||
\(909\) | −27.4647 | −0.910947 | ||||||||
\(910\) | 21.3049 | 0.706250 | ||||||||
\(911\) | −36.9951 | −1.22570 | −0.612851 | − | 0.790199i | \(-0.709977\pi\) | ||||
−0.612851 | + | 0.790199i | \(0.709977\pi\) | |||||||
\(912\) | 0.114110 | 0.00377858 | ||||||||
\(913\) | 4.45753 | 0.147523 | ||||||||
\(914\) | −4.48496 | −0.148349 | ||||||||
\(915\) | −8.52960 | −0.281980 | ||||||||
\(916\) | 5.77013 | 0.190651 | ||||||||
\(917\) | 1.26797 | 0.0418721 | ||||||||
\(918\) | 10.7085 | 0.353433 | ||||||||
\(919\) | −36.0714 | −1.18989 | −0.594943 | − | 0.803768i | \(-0.702825\pi\) | ||||
−0.594943 | + | 0.803768i | \(0.702825\pi\) | |||||||
\(920\) | −63.9343 | −2.10785 | ||||||||
\(921\) | −6.23473 | −0.205441 | ||||||||
\(922\) | −20.2886 | −0.668168 | ||||||||
\(923\) | −20.9940 | −0.691026 | ||||||||
\(924\) | 0.942032 | 0.0309906 | ||||||||
\(925\) | −28.1758 | −0.926415 | ||||||||
\(926\) | 20.2186 | 0.664424 | ||||||||
\(927\) | 3.44323 | 0.113090 | ||||||||
\(928\) | 47.6348 | 1.56369 | ||||||||
\(929\) | 46.8108 | 1.53581 | 0.767906 | − | 0.640563i | \(-0.221299\pi\) | ||||
0.767906 | + | 0.640563i | \(0.221299\pi\) | |||||||
\(930\) | 9.66175 | 0.316821 | ||||||||
\(931\) | −19.8795 | −0.651524 | ||||||||
\(932\) | 27.9005 | 0.913913 | ||||||||
\(933\) | 12.3253 | 0.403511 | ||||||||
\(934\) | 1.21541 | 0.0397693 | ||||||||
\(935\) | 14.1160 | 0.461643 | ||||||||
\(936\) | 37.5568 | 1.22758 | ||||||||
\(937\) | −11.8377 | −0.386720 | −0.193360 | − | 0.981128i | \(-0.561938\pi\) | ||||
−0.193360 | + | 0.981128i | \(0.561938\pi\) | |||||||
\(938\) | 4.93742 | 0.161213 | ||||||||
\(939\) | −19.3355 | −0.630991 | ||||||||
\(940\) | 11.7914 | 0.384593 | ||||||||
\(941\) | −5.97152 | −0.194666 | −0.0973330 | − | 0.995252i | \(-0.531031\pi\) | ||||
−0.0973330 | + | 0.995252i | \(0.531031\pi\) | |||||||
\(942\) | −8.59589 | −0.280069 | ||||||||
\(943\) | −8.02898 | −0.261459 | ||||||||
\(944\) | 0.494184 | 0.0160843 | ||||||||
\(945\) | −16.3836 | −0.532960 | ||||||||
\(946\) | 6.27016 | 0.203861 | ||||||||
\(947\) | 34.7025 | 1.12768 | 0.563840 | − | 0.825884i | \(-0.309323\pi\) | ||||
0.563840 | + | 0.825884i | \(0.309323\pi\) | |||||||
\(948\) | −3.79924 | −0.123393 | ||||||||
\(949\) | −38.6969 | −1.25616 | ||||||||
\(950\) | 31.2538 | 1.01401 | ||||||||
\(951\) | 4.34558 | 0.140915 | ||||||||
\(952\) | 13.1176 | 0.425143 | ||||||||
\(953\) | −26.9293 | −0.872325 | −0.436162 | − | 0.899868i | \(-0.643663\pi\) | ||||
−0.436162 | + | 0.899868i | \(0.643663\pi\) | |||||||
\(954\) | −4.99608 | −0.161754 | ||||||||
\(955\) | 21.8170 | 0.705981 | ||||||||
\(956\) | −22.7845 | −0.736903 | ||||||||
\(957\) | −4.99476 | −0.161458 | ||||||||
\(958\) | 6.86297 | 0.221733 | ||||||||
\(959\) | 2.06082 | 0.0665474 | ||||||||
\(960\) | 11.0361 | 0.356189 | ||||||||
\(961\) | −7.31414 | −0.235940 | ||||||||
\(962\) | −12.6020 | −0.406305 | ||||||||
\(963\) | 14.9121 | 0.480537 | ||||||||
\(964\) | 34.6594 | 1.11630 | ||||||||
\(965\) | 23.6779 | 0.762219 | ||||||||
\(966\) | 3.86712 | 0.124422 | ||||||||
\(967\) | −16.8814 | −0.542868 | −0.271434 | − | 0.962457i | \(-0.587498\pi\) | ||||
−0.271434 | + | 0.962457i | \(0.587498\pi\) | |||||||
\(968\) | −2.81694 | −0.0905399 | ||||||||
\(969\) | −8.06234 | −0.259000 | ||||||||
\(970\) | −9.85395 | −0.316391 | ||||||||
\(971\) | −42.9313 | −1.37773 | −0.688865 | − | 0.724889i | \(-0.741891\pi\) | ||||
−0.688865 | + | 0.724889i | \(0.741891\pi\) | |||||||
\(972\) | −16.9917 | −0.545008 | ||||||||
\(973\) | 21.5410 | 0.690571 | ||||||||
\(974\) | −33.6073 | −1.07685 | ||||||||
\(975\) | 29.3317 | 0.939366 | ||||||||
\(976\) | −0.193711 | −0.00620054 | ||||||||
\(977\) | 27.0054 | 0.863979 | 0.431990 | − | 0.901879i | \(-0.357812\pi\) | ||||
0.431990 | + | 0.901879i | \(0.357812\pi\) | |||||||
\(978\) | 7.64359 | 0.244415 | ||||||||
\(979\) | 15.0346 | 0.480509 | ||||||||
\(980\) | 25.8590 | 0.826035 | ||||||||
\(981\) | −6.95103 | −0.221929 | ||||||||
\(982\) | 25.0572 | 0.799607 | ||||||||
\(983\) | −44.2278 | −1.41065 | −0.705324 | − | 0.708885i | \(-0.749198\pi\) | ||||
−0.705324 | + | 0.708885i | \(0.749198\pi\) | |||||||
\(984\) | 2.28079 | 0.0727090 | ||||||||
\(985\) | −58.4828 | −1.86342 | ||||||||
\(986\) | −26.7195 | −0.850922 | ||||||||
\(987\) | −1.85649 | −0.0590928 | ||||||||
\(988\) | −23.1819 | −0.737515 | ||||||||
\(989\) | −42.6858 | −1.35733 | ||||||||
\(990\) | 8.81954 | 0.280303 | ||||||||
\(991\) | 42.8353 | 1.36071 | 0.680355 | − | 0.732883i | \(-0.261826\pi\) | ||||
0.680355 | + | 0.732883i | \(0.261826\pi\) | |||||||
\(992\) | 27.6385 | 0.877522 | ||||||||
\(993\) | 14.4213 | 0.457645 | ||||||||
\(994\) | −4.58136 | −0.145312 | ||||||||
\(995\) | −74.9380 | −2.37570 | ||||||||
\(996\) | 3.31169 | 0.104935 | ||||||||
\(997\) | 44.7819 | 1.41826 | 0.709128 | − | 0.705080i | \(-0.249089\pi\) | ||||
0.709128 | + | 0.705080i | \(0.249089\pi\) | |||||||
\(998\) | 31.3169 | 0.991319 | ||||||||
\(999\) | 9.69105 | 0.306611 |
(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 | 1441.2.a.f.1.19 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.f.1.19 | ✓ | 31 | 1.1 | even | 1 | trivial |