Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(1\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37815 | −1.68161 | −0.840804 | − | 0.541340i | \(-0.817917\pi\) | ||||
−0.840804 | + | 0.541340i | \(0.817917\pi\) | |||||||
\(3\) | 2.24175 | 1.29428 | 0.647138 | − | 0.762373i | \(-0.275966\pi\) | ||||
0.647138 | + | 0.762373i | \(0.275966\pi\) | |||||||
\(4\) | 3.65561 | 1.82781 | ||||||||
\(5\) | 2.50193 | 1.11890 | 0.559449 | − | 0.828865i | \(-0.311013\pi\) | ||||
0.559449 | + | 0.828865i | \(0.311013\pi\) | |||||||
\(6\) | −5.33123 | −2.17647 | ||||||||
\(7\) | −3.50735 | −1.32566 | −0.662828 | − | 0.748772i | \(-0.730644\pi\) | ||||
−0.662828 | + | 0.748772i | \(0.730644\pi\) | |||||||
\(8\) | −3.93730 | −1.39205 | ||||||||
\(9\) | 2.02545 | 0.675150 | ||||||||
\(10\) | −5.94998 | −1.88155 | ||||||||
\(11\) | −4.72784 | −1.42550 | −0.712749 | − | 0.701419i | \(-0.752550\pi\) | ||||
−0.712749 | + | 0.701419i | \(0.752550\pi\) | |||||||
\(12\) | 8.19497 | 2.36569 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 8.34103 | 2.22923 | ||||||||
\(15\) | 5.60871 | 1.44816 | ||||||||
\(16\) | 2.05228 | 0.513069 | ||||||||
\(17\) | 0.105110 | 0.0254930 | 0.0127465 | − | 0.999919i | \(-0.495943\pi\) | ||||
0.0127465 | + | 0.999919i | \(0.495943\pi\) | |||||||
\(18\) | −4.81683 | −1.13534 | ||||||||
\(19\) | 2.87419 | 0.659386 | 0.329693 | − | 0.944088i | \(-0.393055\pi\) | ||||
0.329693 | + | 0.944088i | \(0.393055\pi\) | |||||||
\(20\) | 9.14610 | 2.04513 | ||||||||
\(21\) | −7.86262 | −1.71576 | ||||||||
\(22\) | 11.2435 | 2.39713 | ||||||||
\(23\) | −5.90670 | −1.23163 | −0.615816 | − | 0.787890i | \(-0.711173\pi\) | ||||
−0.615816 | + | 0.787890i | \(0.711173\pi\) | |||||||
\(24\) | −8.82645 | −1.80169 | ||||||||
\(25\) | 1.25967 | 0.251933 | ||||||||
\(26\) | −2.37815 | −0.466394 | ||||||||
\(27\) | −2.18470 | −0.420445 | ||||||||
\(28\) | −12.8215 | −2.42304 | ||||||||
\(29\) | 8.85260 | 1.64389 | 0.821943 | − | 0.569569i | \(-0.192890\pi\) | ||||
0.821943 | + | 0.569569i | \(0.192890\pi\) | |||||||
\(30\) | −13.3384 | −2.43524 | ||||||||
\(31\) | 5.66043 | 1.01664 | 0.508322 | − | 0.861167i | \(-0.330266\pi\) | ||||
0.508322 | + | 0.861167i | \(0.330266\pi\) | |||||||
\(32\) | 2.99397 | 0.529264 | ||||||||
\(33\) | −10.5986 | −1.84499 | ||||||||
\(34\) | −0.249968 | −0.0428692 | ||||||||
\(35\) | −8.77516 | −1.48327 | ||||||||
\(36\) | 7.40426 | 1.23404 | ||||||||
\(37\) | 6.18356 | 1.01657 | 0.508285 | − | 0.861189i | \(-0.330280\pi\) | ||||
0.508285 | + | 0.861189i | \(0.330280\pi\) | |||||||
\(38\) | −6.83528 | −1.10883 | ||||||||
\(39\) | 2.24175 | 0.358968 | ||||||||
\(40\) | −9.85086 | −1.55756 | ||||||||
\(41\) | 5.52352 | 0.862629 | 0.431315 | − | 0.902202i | \(-0.358050\pi\) | ||||
0.431315 | + | 0.902202i | \(0.358050\pi\) | |||||||
\(42\) | 18.6985 | 2.88524 | ||||||||
\(43\) | −7.13642 | −1.08829 | −0.544147 | − | 0.838990i | \(-0.683147\pi\) | ||||
−0.544147 | + | 0.838990i | \(0.683147\pi\) | |||||||
\(44\) | −17.2832 | −2.60553 | ||||||||
\(45\) | 5.06754 | 0.755424 | ||||||||
\(46\) | 14.0470 | 2.07112 | ||||||||
\(47\) | 3.13636 | 0.457485 | 0.228743 | − | 0.973487i | \(-0.426539\pi\) | ||||
0.228743 | + | 0.973487i | \(0.426539\pi\) | |||||||
\(48\) | 4.60069 | 0.664053 | ||||||||
\(49\) | 5.30154 | 0.757362 | ||||||||
\(50\) | −2.99568 | −0.423653 | ||||||||
\(51\) | 0.235631 | 0.0329949 | ||||||||
\(52\) | 3.65561 | 0.506942 | ||||||||
\(53\) | −4.15489 | −0.570717 | −0.285359 | − | 0.958421i | \(-0.592113\pi\) | ||||
−0.285359 | + | 0.958421i | \(0.592113\pi\) | |||||||
\(54\) | 5.19555 | 0.707024 | ||||||||
\(55\) | −11.8287 | −1.59499 | ||||||||
\(56\) | 13.8095 | 1.84537 | ||||||||
\(57\) | 6.44323 | 0.853427 | ||||||||
\(58\) | −21.0528 | −2.76437 | ||||||||
\(59\) | −6.63482 | −0.863780 | −0.431890 | − | 0.901926i | \(-0.642153\pi\) | ||||
−0.431890 | + | 0.901926i | \(0.642153\pi\) | |||||||
\(60\) | 20.5033 | 2.64696 | ||||||||
\(61\) | −10.7653 | −1.37835 | −0.689175 | − | 0.724595i | \(-0.742027\pi\) | ||||
−0.689175 | + | 0.724595i | \(0.742027\pi\) | |||||||
\(62\) | −13.4614 | −1.70960 | ||||||||
\(63\) | −7.10397 | −0.895017 | ||||||||
\(64\) | −11.2247 | −1.40308 | ||||||||
\(65\) | 2.50193 | 0.310327 | ||||||||
\(66\) | 25.2052 | 3.10255 | ||||||||
\(67\) | 3.63647 | 0.444265 | 0.222133 | − | 0.975016i | \(-0.428698\pi\) | ||||
0.222133 | + | 0.975016i | \(0.428698\pi\) | |||||||
\(68\) | 0.384242 | 0.0465962 | ||||||||
\(69\) | −13.2413 | −1.59407 | ||||||||
\(70\) | 20.8687 | 2.49428 | ||||||||
\(71\) | −0.128553 | −0.0152565 | −0.00762823 | − | 0.999971i | \(-0.502428\pi\) | ||||
−0.00762823 | + | 0.999971i | \(0.502428\pi\) | |||||||
\(72\) | −7.97481 | −0.939840 | ||||||||
\(73\) | −4.52614 | −0.529745 | −0.264873 | − | 0.964283i | \(-0.585330\pi\) | ||||
−0.264873 | + | 0.964283i | \(0.585330\pi\) | |||||||
\(74\) | −14.7054 | −1.70947 | ||||||||
\(75\) | 2.82386 | 0.326071 | ||||||||
\(76\) | 10.5069 | 1.20523 | ||||||||
\(77\) | 16.5822 | 1.88972 | ||||||||
\(78\) | −5.33123 | −0.603643 | ||||||||
\(79\) | −4.46982 | −0.502894 | −0.251447 | − | 0.967871i | \(-0.580906\pi\) | ||||
−0.251447 | + | 0.967871i | \(0.580906\pi\) | |||||||
\(80\) | 5.13466 | 0.574072 | ||||||||
\(81\) | −10.9739 | −1.21932 | ||||||||
\(82\) | −13.1358 | −1.45060 | ||||||||
\(83\) | 9.21052 | 1.01099 | 0.505493 | − | 0.862831i | \(-0.331311\pi\) | ||||
0.505493 | + | 0.862831i | \(0.331311\pi\) | |||||||
\(84\) | −28.7427 | −3.13608 | ||||||||
\(85\) | 0.262979 | 0.0285240 | ||||||||
\(86\) | 16.9715 | 1.83008 | ||||||||
\(87\) | 19.8453 | 2.12764 | ||||||||
\(88\) | 18.6149 | 1.98436 | ||||||||
\(89\) | −2.90807 | −0.308255 | −0.154127 | − | 0.988051i | \(-0.549257\pi\) | ||||
−0.154127 | + | 0.988051i | \(0.549257\pi\) | |||||||
\(90\) | −12.0514 | −1.27033 | ||||||||
\(91\) | −3.50735 | −0.367671 | ||||||||
\(92\) | −21.5926 | −2.25118 | ||||||||
\(93\) | 12.6893 | 1.31582 | ||||||||
\(94\) | −7.45875 | −0.769311 | ||||||||
\(95\) | 7.19104 | 0.737785 | ||||||||
\(96\) | 6.71174 | 0.685014 | ||||||||
\(97\) | 0.930007 | 0.0944279 | 0.0472140 | − | 0.998885i | \(-0.484966\pi\) | ||||
0.0472140 | + | 0.998885i | \(0.484966\pi\) | |||||||
\(98\) | −12.6079 | −1.27359 | ||||||||
\(99\) | −9.57601 | −0.962425 | ||||||||
\(100\) | 4.60485 | 0.460485 | ||||||||
\(101\) | −16.0190 | −1.59395 | −0.796974 | − | 0.604014i | \(-0.793567\pi\) | ||||
−0.796974 | + | 0.604014i | \(0.793567\pi\) | |||||||
\(102\) | −0.560366 | −0.0554845 | ||||||||
\(103\) | −19.0494 | −1.87700 | −0.938499 | − | 0.345283i | \(-0.887783\pi\) | ||||
−0.938499 | + | 0.345283i | \(0.887783\pi\) | |||||||
\(104\) | −3.93730 | −0.386084 | ||||||||
\(105\) | −19.6717 | −1.91977 | ||||||||
\(106\) | 9.88095 | 0.959723 | ||||||||
\(107\) | 17.8326 | 1.72394 | 0.861970 | − | 0.506960i | \(-0.169231\pi\) | ||||
0.861970 | + | 0.506960i | \(0.169231\pi\) | |||||||
\(108\) | −7.98641 | −0.768492 | ||||||||
\(109\) | 6.46069 | 0.618822 | 0.309411 | − | 0.950928i | \(-0.399868\pi\) | ||||
0.309411 | + | 0.950928i | \(0.399868\pi\) | |||||||
\(110\) | 28.1306 | 2.68214 | ||||||||
\(111\) | 13.8620 | 1.31572 | ||||||||
\(112\) | −7.19806 | −0.680153 | ||||||||
\(113\) | 12.0549 | 1.13403 | 0.567016 | − | 0.823707i | \(-0.308098\pi\) | ||||
0.567016 | + | 0.823707i | \(0.308098\pi\) | |||||||
\(114\) | −15.3230 | −1.43513 | ||||||||
\(115\) | −14.7782 | −1.37807 | ||||||||
\(116\) | 32.3617 | 3.00471 | ||||||||
\(117\) | 2.02545 | 0.187253 | ||||||||
\(118\) | 15.7786 | 1.45254 | ||||||||
\(119\) | −0.368659 | −0.0337949 | ||||||||
\(120\) | −22.0832 | −2.01591 | ||||||||
\(121\) | 11.3525 | 1.03205 | ||||||||
\(122\) | 25.6014 | 2.31785 | ||||||||
\(123\) | 12.3824 | 1.11648 | ||||||||
\(124\) | 20.6924 | 1.85823 | ||||||||
\(125\) | −9.35806 | −0.837011 | ||||||||
\(126\) | 16.8943 | 1.50507 | ||||||||
\(127\) | 11.4918 | 1.01973 | 0.509866 | − | 0.860254i | \(-0.329695\pi\) | ||||
0.509866 | + | 0.860254i | \(0.329695\pi\) | |||||||
\(128\) | 20.7061 | 1.83017 | ||||||||
\(129\) | −15.9981 | −1.40855 | ||||||||
\(130\) | −5.94998 | −0.521848 | ||||||||
\(131\) | −14.1479 | −1.23611 | −0.618055 | − | 0.786135i | \(-0.712079\pi\) | ||||
−0.618055 | + | 0.786135i | \(0.712079\pi\) | |||||||
\(132\) | −38.7446 | −3.37228 | ||||||||
\(133\) | −10.0808 | −0.874118 | ||||||||
\(134\) | −8.64808 | −0.747080 | ||||||||
\(135\) | −5.46597 | −0.470435 | ||||||||
\(136\) | −0.413850 | −0.0354874 | ||||||||
\(137\) | −15.4742 | −1.32205 | −0.661024 | − | 0.750365i | \(-0.729878\pi\) | ||||
−0.661024 | + | 0.750365i | \(0.729878\pi\) | |||||||
\(138\) | 31.4899 | 2.68060 | ||||||||
\(139\) | 5.79097 | 0.491184 | 0.245592 | − | 0.969373i | \(-0.421018\pi\) | ||||
0.245592 | + | 0.969373i | \(0.421018\pi\) | |||||||
\(140\) | −32.0786 | −2.71114 | ||||||||
\(141\) | 7.03094 | 0.592112 | ||||||||
\(142\) | 0.305719 | 0.0256554 | ||||||||
\(143\) | −4.72784 | −0.395362 | ||||||||
\(144\) | 4.15678 | 0.346399 | ||||||||
\(145\) | 22.1486 | 1.83934 | ||||||||
\(146\) | 10.7639 | 0.890824 | ||||||||
\(147\) | 11.8847 | 0.980236 | ||||||||
\(148\) | 22.6047 | 1.85809 | ||||||||
\(149\) | 1.69713 | 0.139035 | 0.0695173 | − | 0.997581i | \(-0.477854\pi\) | ||||
0.0695173 | + | 0.997581i | \(0.477854\pi\) | |||||||
\(150\) | −6.71557 | −0.548324 | ||||||||
\(151\) | −0.191220 | −0.0155612 | −0.00778062 | − | 0.999970i | \(-0.502477\pi\) | ||||
−0.00778062 | + | 0.999970i | \(0.502477\pi\) | |||||||
\(152\) | −11.3166 | −0.917895 | ||||||||
\(153\) | 0.212895 | 0.0172116 | ||||||||
\(154\) | −39.4351 | −3.17777 | ||||||||
\(155\) | 14.1620 | 1.13752 | ||||||||
\(156\) | 8.19497 | 0.656123 | ||||||||
\(157\) | 15.1809 | 1.21157 | 0.605784 | − | 0.795629i | \(-0.292860\pi\) | ||||
0.605784 | + | 0.795629i | \(0.292860\pi\) | |||||||
\(158\) | 10.6299 | 0.845671 | ||||||||
\(159\) | −9.31422 | −0.738666 | ||||||||
\(160\) | 7.49071 | 0.592193 | ||||||||
\(161\) | 20.7169 | 1.63272 | ||||||||
\(162\) | 26.0976 | 2.05042 | ||||||||
\(163\) | −2.83971 | −0.222423 | −0.111211 | − | 0.993797i | \(-0.535473\pi\) | ||||
−0.111211 | + | 0.993797i | \(0.535473\pi\) | |||||||
\(164\) | 20.1919 | 1.57672 | ||||||||
\(165\) | −26.5171 | −2.06435 | ||||||||
\(166\) | −21.9040 | −1.70008 | ||||||||
\(167\) | −8.32604 | −0.644288 | −0.322144 | − | 0.946691i | \(-0.604404\pi\) | ||||
−0.322144 | + | 0.946691i | \(0.604404\pi\) | |||||||
\(168\) | 30.9575 | 2.38842 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.625403 | −0.0479662 | ||||||||
\(171\) | 5.82154 | 0.445184 | ||||||||
\(172\) | −26.0880 | −1.98919 | ||||||||
\(173\) | −15.9041 | −1.20917 | −0.604584 | − | 0.796541i | \(-0.706661\pi\) | ||||
−0.604584 | + | 0.796541i | \(0.706661\pi\) | |||||||
\(174\) | −47.1952 | −3.57786 | ||||||||
\(175\) | −4.41810 | −0.333977 | ||||||||
\(176\) | −9.70284 | −0.731379 | ||||||||
\(177\) | −14.8736 | −1.11797 | ||||||||
\(178\) | 6.91583 | 0.518364 | ||||||||
\(179\) | −20.6598 | −1.54419 | −0.772094 | − | 0.635508i | \(-0.780791\pi\) | ||||
−0.772094 | + | 0.635508i | \(0.780791\pi\) | |||||||
\(180\) | 18.5250 | 1.38077 | ||||||||
\(181\) | −10.9163 | −0.811399 | −0.405699 | − | 0.914007i | \(-0.632972\pi\) | ||||
−0.405699 | + | 0.914007i | \(0.632972\pi\) | |||||||
\(182\) | 8.34103 | 0.618278 | ||||||||
\(183\) | −24.1330 | −1.78397 | ||||||||
\(184\) | 23.2564 | 1.71449 | ||||||||
\(185\) | 15.4708 | 1.13744 | ||||||||
\(186\) | −30.1771 | −2.21269 | ||||||||
\(187\) | −0.496944 | −0.0363402 | ||||||||
\(188\) | 11.4653 | 0.836194 | ||||||||
\(189\) | 7.66251 | 0.557366 | ||||||||
\(190\) | −17.1014 | −1.24067 | ||||||||
\(191\) | −19.9101 | −1.44065 | −0.720323 | − | 0.693639i | \(-0.756006\pi\) | ||||
−0.720323 | + | 0.693639i | \(0.756006\pi\) | |||||||
\(192\) | −25.1629 | −1.81598 | ||||||||
\(193\) | −17.5021 | −1.25983 | −0.629916 | − | 0.776664i | \(-0.716911\pi\) | ||||
−0.629916 | + | 0.776664i | \(0.716911\pi\) | |||||||
\(194\) | −2.21170 | −0.158791 | ||||||||
\(195\) | 5.60871 | 0.401648 | ||||||||
\(196\) | 19.3804 | 1.38431 | ||||||||
\(197\) | 22.7279 | 1.61930 | 0.809648 | − | 0.586916i | \(-0.199658\pi\) | ||||
0.809648 | + | 0.586916i | \(0.199658\pi\) | |||||||
\(198\) | 22.7732 | 1.61842 | ||||||||
\(199\) | −17.6723 | −1.25276 | −0.626378 | − | 0.779519i | \(-0.715463\pi\) | ||||
−0.626378 | + | 0.779519i | \(0.715463\pi\) | |||||||
\(200\) | −4.95968 | −0.350703 | ||||||||
\(201\) | 8.15206 | 0.575002 | ||||||||
\(202\) | 38.0956 | 2.68039 | ||||||||
\(203\) | −31.0492 | −2.17923 | ||||||||
\(204\) | 0.861375 | 0.0603083 | ||||||||
\(205\) | 13.8195 | 0.965194 | ||||||||
\(206\) | 45.3025 | 3.15637 | ||||||||
\(207\) | −11.9637 | −0.831536 | ||||||||
\(208\) | 2.05228 | 0.142300 | ||||||||
\(209\) | −13.5887 | −0.939953 | ||||||||
\(210\) | 46.7824 | 3.22829 | ||||||||
\(211\) | −2.38955 | −0.164503 | −0.0822517 | − | 0.996612i | \(-0.526211\pi\) | ||||
−0.0822517 | + | 0.996612i | \(0.526211\pi\) | |||||||
\(212\) | −15.1887 | −1.04316 | ||||||||
\(213\) | −0.288184 | −0.0197461 | ||||||||
\(214\) | −42.4086 | −2.89899 | ||||||||
\(215\) | −17.8548 | −1.21769 | ||||||||
\(216\) | 8.60181 | 0.585279 | ||||||||
\(217\) | −19.8532 | −1.34772 | ||||||||
\(218\) | −15.3645 | −1.04062 | ||||||||
\(219\) | −10.1465 | −0.685636 | ||||||||
\(220\) | −43.2413 | −2.91533 | ||||||||
\(221\) | 0.105110 | 0.00707048 | ||||||||
\(222\) | −32.9660 | −2.21253 | ||||||||
\(223\) | 0.0900022 | 0.00602699 | 0.00301350 | − | 0.999995i | \(-0.499041\pi\) | ||||
0.00301350 | + | 0.999995i | \(0.499041\pi\) | |||||||
\(224\) | −10.5009 | −0.701622 | ||||||||
\(225\) | 2.55139 | 0.170093 | ||||||||
\(226\) | −28.6684 | −1.90700 | ||||||||
\(227\) | −22.1818 | −1.47226 | −0.736128 | − | 0.676842i | \(-0.763348\pi\) | ||||
−0.736128 | + | 0.676842i | \(0.763348\pi\) | |||||||
\(228\) | 23.5540 | 1.55990 | ||||||||
\(229\) | −24.9623 | −1.64955 | −0.824777 | − | 0.565458i | \(-0.808699\pi\) | ||||
−0.824777 | + | 0.565458i | \(0.808699\pi\) | |||||||
\(230\) | 35.1447 | 2.31737 | ||||||||
\(231\) | 37.1732 | 2.44582 | ||||||||
\(232\) | −34.8553 | −2.28837 | ||||||||
\(233\) | −6.55348 | −0.429333 | −0.214666 | − | 0.976687i | \(-0.568866\pi\) | ||||
−0.214666 | + | 0.976687i | \(0.568866\pi\) | |||||||
\(234\) | −4.81683 | −0.314886 | ||||||||
\(235\) | 7.84696 | 0.511879 | ||||||||
\(236\) | −24.2543 | −1.57882 | ||||||||
\(237\) | −10.0202 | −0.650884 | ||||||||
\(238\) | 0.876727 | 0.0568298 | ||||||||
\(239\) | −6.71661 | −0.434461 | −0.217231 | − | 0.976120i | \(-0.569702\pi\) | ||||
−0.217231 | + | 0.976120i | \(0.569702\pi\) | |||||||
\(240\) | 11.5106 | 0.743008 | ||||||||
\(241\) | −2.99824 | −0.193134 | −0.0965669 | − | 0.995326i | \(-0.530786\pi\) | ||||
−0.0965669 | + | 0.995326i | \(0.530786\pi\) | |||||||
\(242\) | −26.9980 | −1.73550 | ||||||||
\(243\) | −18.0467 | −1.15769 | ||||||||
\(244\) | −39.3536 | −2.51936 | ||||||||
\(245\) | 13.2641 | 0.847411 | ||||||||
\(246\) | −29.4472 | −1.87748 | ||||||||
\(247\) | 2.87419 | 0.182881 | ||||||||
\(248\) | −22.2868 | −1.41521 | ||||||||
\(249\) | 20.6477 | 1.30849 | ||||||||
\(250\) | 22.2549 | 1.40752 | ||||||||
\(251\) | −10.9778 | −0.692912 | −0.346456 | − | 0.938066i | \(-0.612615\pi\) | ||||
−0.346456 | + | 0.938066i | \(0.612615\pi\) | |||||||
\(252\) | −25.9694 | −1.63592 | ||||||||
\(253\) | 27.9259 | 1.75569 | ||||||||
\(254\) | −27.3293 | −1.71479 | ||||||||
\(255\) | 0.589533 | 0.0369180 | ||||||||
\(256\) | −26.7928 | −1.67455 | ||||||||
\(257\) | 8.21707 | 0.512567 | 0.256284 | − | 0.966602i | \(-0.417502\pi\) | ||||
0.256284 | + | 0.966602i | \(0.417502\pi\) | |||||||
\(258\) | 38.0459 | 2.36863 | ||||||||
\(259\) | −21.6879 | −1.34762 | ||||||||
\(260\) | 9.14610 | 0.567217 | ||||||||
\(261\) | 17.9305 | 1.10987 | ||||||||
\(262\) | 33.6460 | 2.07865 | ||||||||
\(263\) | −17.1376 | −1.05675 | −0.528376 | − | 0.849011i | \(-0.677199\pi\) | ||||
−0.528376 | + | 0.849011i | \(0.677199\pi\) | |||||||
\(264\) | 41.7301 | 2.56831 | ||||||||
\(265\) | −10.3952 | −0.638575 | ||||||||
\(266\) | 23.9737 | 1.46992 | ||||||||
\(267\) | −6.51917 | −0.398967 | ||||||||
\(268\) | 13.2935 | 0.812031 | ||||||||
\(269\) | −4.90970 | −0.299350 | −0.149675 | − | 0.988735i | \(-0.547823\pi\) | ||||
−0.149675 | + | 0.988735i | \(0.547823\pi\) | |||||||
\(270\) | 12.9989 | 0.791088 | ||||||||
\(271\) | −6.03044 | −0.366323 | −0.183162 | − | 0.983083i | \(-0.558633\pi\) | ||||
−0.183162 | + | 0.983083i | \(0.558633\pi\) | |||||||
\(272\) | 0.215715 | 0.0130797 | ||||||||
\(273\) | −7.86262 | −0.475867 | ||||||||
\(274\) | 36.7999 | 2.22317 | ||||||||
\(275\) | −5.95550 | −0.359130 | ||||||||
\(276\) | −48.4052 | −2.91365 | ||||||||
\(277\) | −30.6866 | −1.84378 | −0.921890 | − | 0.387452i | \(-0.873355\pi\) | ||||
−0.921890 | + | 0.387452i | \(0.873355\pi\) | |||||||
\(278\) | −13.7718 | −0.825979 | ||||||||
\(279\) | 11.4649 | 0.686387 | ||||||||
\(280\) | 34.5505 | 2.06478 | ||||||||
\(281\) | −5.60986 | −0.334656 | −0.167328 | − | 0.985901i | \(-0.553514\pi\) | ||||
−0.167328 | + | 0.985901i | \(0.553514\pi\) | |||||||
\(282\) | −16.7207 | −0.995701 | ||||||||
\(283\) | 15.7660 | 0.937190 | 0.468595 | − | 0.883413i | \(-0.344760\pi\) | ||||
0.468595 | + | 0.883413i | \(0.344760\pi\) | |||||||
\(284\) | −0.469941 | −0.0278859 | ||||||||
\(285\) | 16.1205 | 0.954898 | ||||||||
\(286\) | 11.2435 | 0.664844 | ||||||||
\(287\) | −19.3729 | −1.14355 | ||||||||
\(288\) | 6.06414 | 0.357333 | ||||||||
\(289\) | −16.9890 | −0.999350 | ||||||||
\(290\) | −52.6728 | −3.09305 | ||||||||
\(291\) | 2.08484 | 0.122216 | ||||||||
\(292\) | −16.5458 | −0.968271 | ||||||||
\(293\) | 33.2134 | 1.94035 | 0.970174 | − | 0.242411i | \(-0.0779383\pi\) | ||||
0.970174 | + | 0.242411i | \(0.0779383\pi\) | |||||||
\(294\) | −28.2637 | −1.64837 | ||||||||
\(295\) | −16.5999 | −0.966482 | ||||||||
\(296\) | −24.3465 | −1.41511 | ||||||||
\(297\) | 10.3289 | 0.599344 | ||||||||
\(298\) | −4.03604 | −0.233802 | ||||||||
\(299\) | −5.90670 | −0.341593 | ||||||||
\(300\) | 10.3229 | 0.595995 | ||||||||
\(301\) | 25.0300 | 1.44270 | ||||||||
\(302\) | 0.454750 | 0.0261679 | ||||||||
\(303\) | −35.9106 | −2.06301 | ||||||||
\(304\) | 5.89864 | 0.338310 | ||||||||
\(305\) | −26.9340 | −1.54223 | ||||||||
\(306\) | −0.506298 | −0.0289431 | ||||||||
\(307\) | −13.8893 | −0.792704 | −0.396352 | − | 0.918099i | \(-0.629724\pi\) | ||||
−0.396352 | + | 0.918099i | \(0.629724\pi\) | |||||||
\(308\) | 60.6182 | 3.45404 | ||||||||
\(309\) | −42.7041 | −2.42935 | ||||||||
\(310\) | −33.6795 | −1.91286 | ||||||||
\(311\) | 5.07844 | 0.287972 | 0.143986 | − | 0.989580i | \(-0.454008\pi\) | ||||
0.143986 | + | 0.989580i | \(0.454008\pi\) | |||||||
\(312\) | −8.82645 | −0.499699 | ||||||||
\(313\) | 2.75156 | 0.155528 | 0.0777638 | − | 0.996972i | \(-0.475222\pi\) | ||||
0.0777638 | + | 0.996972i | \(0.475222\pi\) | |||||||
\(314\) | −36.1025 | −2.03738 | ||||||||
\(315\) | −17.7737 | −1.00143 | ||||||||
\(316\) | −16.3399 | −0.919193 | ||||||||
\(317\) | −28.6464 | −1.60894 | −0.804471 | − | 0.593992i | \(-0.797551\pi\) | ||||
−0.804471 | + | 0.593992i | \(0.797551\pi\) | |||||||
\(318\) | 22.1506 | 1.24215 | ||||||||
\(319\) | −41.8537 | −2.34336 | ||||||||
\(320\) | −28.0834 | −1.56991 | ||||||||
\(321\) | 39.9762 | 2.23125 | ||||||||
\(322\) | −49.2679 | −2.74559 | ||||||||
\(323\) | 0.302107 | 0.0168097 | ||||||||
\(324\) | −40.1163 | −2.22868 | ||||||||
\(325\) | 1.25967 | 0.0698737 | ||||||||
\(326\) | 6.75325 | 0.374028 | ||||||||
\(327\) | 14.4833 | 0.800926 | ||||||||
\(328\) | −21.7478 | −1.20082 | ||||||||
\(329\) | −11.0003 | −0.606468 | ||||||||
\(330\) | 63.0617 | 3.47143 | ||||||||
\(331\) | −24.9743 | −1.37271 | −0.686356 | − | 0.727265i | \(-0.740791\pi\) | ||||
−0.686356 | + | 0.727265i | \(0.740791\pi\) | |||||||
\(332\) | 33.6701 | 1.84789 | ||||||||
\(333\) | 12.5245 | 0.686338 | ||||||||
\(334\) | 19.8006 | 1.08344 | ||||||||
\(335\) | 9.09820 | 0.497088 | ||||||||
\(336\) | −16.1363 | −0.880306 | ||||||||
\(337\) | 28.9325 | 1.57605 | 0.788026 | − | 0.615642i | \(-0.211103\pi\) | ||||
0.788026 | + | 0.615642i | \(0.211103\pi\) | |||||||
\(338\) | −2.37815 | −0.129354 | ||||||||
\(339\) | 27.0241 | 1.46775 | ||||||||
\(340\) | 0.961348 | 0.0521364 | ||||||||
\(341\) | −26.7616 | −1.44922 | ||||||||
\(342\) | −13.8445 | −0.748626 | ||||||||
\(343\) | 5.95712 | 0.321654 | ||||||||
\(344\) | 28.0982 | 1.51496 | ||||||||
\(345\) | −33.1289 | −1.78360 | ||||||||
\(346\) | 37.8225 | 2.03335 | ||||||||
\(347\) | 7.03820 | 0.377830 | 0.188915 | − | 0.981993i | \(-0.439503\pi\) | ||||
0.188915 | + | 0.981993i | \(0.439503\pi\) | |||||||
\(348\) | 72.5468 | 3.88892 | ||||||||
\(349\) | −7.05133 | −0.377449 | −0.188725 | − | 0.982030i | \(-0.560435\pi\) | ||||
−0.188725 | + | 0.982030i | \(0.560435\pi\) | |||||||
\(350\) | 10.5069 | 0.561618 | ||||||||
\(351\) | −2.18470 | −0.116611 | ||||||||
\(352\) | −14.1550 | −0.754465 | ||||||||
\(353\) | 27.9622 | 1.48828 | 0.744139 | − | 0.668025i | \(-0.232860\pi\) | ||||
0.744139 | + | 0.668025i | \(0.232860\pi\) | |||||||
\(354\) | 35.3718 | 1.87999 | ||||||||
\(355\) | −0.321631 | −0.0170704 | ||||||||
\(356\) | −10.6308 | −0.563430 | ||||||||
\(357\) | −0.826441 | −0.0437399 | ||||||||
\(358\) | 49.1322 | 2.59672 | ||||||||
\(359\) | 21.1097 | 1.11413 | 0.557064 | − | 0.830470i | \(-0.311928\pi\) | ||||
0.557064 | + | 0.830470i | \(0.311928\pi\) | |||||||
\(360\) | −19.9524 | −1.05159 | ||||||||
\(361\) | −10.7390 | −0.565211 | ||||||||
\(362\) | 25.9605 | 1.36445 | ||||||||
\(363\) | 25.4495 | 1.33575 | ||||||||
\(364\) | −12.8215 | −0.672031 | ||||||||
\(365\) | −11.3241 | −0.592731 | ||||||||
\(366\) | 57.3921 | 2.99993 | ||||||||
\(367\) | 14.7325 | 0.769031 | 0.384516 | − | 0.923118i | \(-0.374368\pi\) | ||||
0.384516 | + | 0.923118i | \(0.374368\pi\) | |||||||
\(368\) | −12.1222 | −0.631912 | ||||||||
\(369\) | 11.1876 | 0.582404 | ||||||||
\(370\) | −36.7920 | −1.91273 | ||||||||
\(371\) | 14.5727 | 0.756575 | ||||||||
\(372\) | 46.3871 | 2.40506 | ||||||||
\(373\) | 1.07397 | 0.0556080 | 0.0278040 | − | 0.999613i | \(-0.491149\pi\) | ||||
0.0278040 | + | 0.999613i | \(0.491149\pi\) | |||||||
\(374\) | 1.18181 | 0.0611099 | ||||||||
\(375\) | −20.9785 | −1.08332 | ||||||||
\(376\) | −12.3488 | −0.636840 | ||||||||
\(377\) | 8.85260 | 0.455932 | ||||||||
\(378\) | −18.2226 | −0.937271 | ||||||||
\(379\) | −0.256521 | −0.0131766 | −0.00658831 | − | 0.999978i | \(-0.502097\pi\) | ||||
−0.00658831 | + | 0.999978i | \(0.502097\pi\) | |||||||
\(380\) | 26.2877 | 1.34853 | ||||||||
\(381\) | 25.7618 | 1.31982 | ||||||||
\(382\) | 47.3493 | 2.42260 | ||||||||
\(383\) | −29.2418 | −1.49419 | −0.747094 | − | 0.664719i | \(-0.768551\pi\) | ||||
−0.747094 | + | 0.664719i | \(0.768551\pi\) | |||||||
\(384\) | 46.4178 | 2.36875 | ||||||||
\(385\) | 41.4876 | 2.11440 | ||||||||
\(386\) | 41.6228 | 2.11854 | ||||||||
\(387\) | −14.4545 | −0.734762 | ||||||||
\(388\) | 3.39975 | 0.172596 | ||||||||
\(389\) | −12.5029 | −0.633922 | −0.316961 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316961 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(390\) | −13.3384 | −0.675415 | ||||||||
\(391\) | −0.620854 | −0.0313979 | ||||||||
\(392\) | −20.8737 | −1.05428 | ||||||||
\(393\) | −31.7162 | −1.59987 | ||||||||
\(394\) | −54.0504 | −2.72302 | ||||||||
\(395\) | −11.1832 | −0.562687 | ||||||||
\(396\) | −35.0062 | −1.75913 | ||||||||
\(397\) | 5.52599 | 0.277341 | 0.138671 | − | 0.990339i | \(-0.455717\pi\) | ||||
0.138671 | + | 0.990339i | \(0.455717\pi\) | |||||||
\(398\) | 42.0274 | 2.10665 | ||||||||
\(399\) | −22.5987 | −1.13135 | ||||||||
\(400\) | 2.58518 | 0.129259 | ||||||||
\(401\) | 24.6712 | 1.23202 | 0.616010 | − | 0.787738i | \(-0.288748\pi\) | ||||
0.616010 | + | 0.787738i | \(0.288748\pi\) | |||||||
\(402\) | −19.3868 | −0.966928 | ||||||||
\(403\) | 5.66043 | 0.281966 | ||||||||
\(404\) | −58.5591 | −2.91343 | ||||||||
\(405\) | −27.4560 | −1.36430 | ||||||||
\(406\) | 73.8398 | 3.66461 | ||||||||
\(407\) | −29.2349 | −1.44912 | ||||||||
\(408\) | −0.927749 | −0.0459304 | ||||||||
\(409\) | 2.85516 | 0.141178 | 0.0705892 | − | 0.997505i | \(-0.477512\pi\) | ||||
0.0705892 | + | 0.997505i | \(0.477512\pi\) | |||||||
\(410\) | −32.8648 | −1.62308 | ||||||||
\(411\) | −34.6892 | −1.71109 | ||||||||
\(412\) | −69.6374 | −3.43079 | ||||||||
\(413\) | 23.2707 | 1.14508 | ||||||||
\(414\) | 28.4516 | 1.39832 | ||||||||
\(415\) | 23.0441 | 1.13119 | ||||||||
\(416\) | 2.99397 | 0.146792 | ||||||||
\(417\) | 12.9819 | 0.635727 | ||||||||
\(418\) | 32.3161 | 1.58063 | ||||||||
\(419\) | 38.7933 | 1.89518 | 0.947589 | − | 0.319491i | \(-0.103512\pi\) | ||||
0.947589 | + | 0.319491i | \(0.103512\pi\) | |||||||
\(420\) | −71.9123 | −3.50896 | ||||||||
\(421\) | −18.6868 | −0.910739 | −0.455370 | − | 0.890302i | \(-0.650493\pi\) | ||||
−0.455370 | + | 0.890302i | \(0.650493\pi\) | |||||||
\(422\) | 5.68272 | 0.276630 | ||||||||
\(423\) | 6.35254 | 0.308871 | ||||||||
\(424\) | 16.3590 | 0.794465 | ||||||||
\(425\) | 0.132404 | 0.00642252 | ||||||||
\(426\) | 0.685347 | 0.0332052 | ||||||||
\(427\) | 37.7576 | 1.82722 | ||||||||
\(428\) | 65.1889 | 3.15103 | ||||||||
\(429\) | −10.5986 | −0.511708 | ||||||||
\(430\) | 42.4616 | 2.04768 | ||||||||
\(431\) | 18.9446 | 0.912531 | 0.456266 | − | 0.889844i | \(-0.349187\pi\) | ||||
0.456266 | + | 0.889844i | \(0.349187\pi\) | |||||||
\(432\) | −4.48360 | −0.215718 | ||||||||
\(433\) | −35.5309 | −1.70750 | −0.853752 | − | 0.520679i | \(-0.825679\pi\) | ||||
−0.853752 | + | 0.520679i | \(0.825679\pi\) | |||||||
\(434\) | 47.2138 | 2.26634 | ||||||||
\(435\) | 49.6517 | 2.38062 | ||||||||
\(436\) | 23.6178 | 1.13109 | ||||||||
\(437\) | −16.9770 | −0.812120 | ||||||||
\(438\) | 24.1299 | 1.15297 | ||||||||
\(439\) | 36.3646 | 1.73559 | 0.867793 | − | 0.496926i | \(-0.165538\pi\) | ||||
0.867793 | + | 0.496926i | \(0.165538\pi\) | |||||||
\(440\) | 46.5733 | 2.22030 | ||||||||
\(441\) | 10.7380 | 0.511333 | ||||||||
\(442\) | −0.249968 | −0.0118898 | ||||||||
\(443\) | 5.76070 | 0.273699 | 0.136849 | − | 0.990592i | \(-0.456302\pi\) | ||||
0.136849 | + | 0.990592i | \(0.456302\pi\) | |||||||
\(444\) | 50.6741 | 2.40489 | ||||||||
\(445\) | −7.27579 | −0.344906 | ||||||||
\(446\) | −0.214039 | −0.0101350 | ||||||||
\(447\) | 3.80455 | 0.179949 | ||||||||
\(448\) | 39.3689 | 1.86001 | ||||||||
\(449\) | 31.1123 | 1.46828 | 0.734139 | − | 0.678999i | \(-0.237586\pi\) | ||||
0.734139 | + | 0.678999i | \(0.237586\pi\) | |||||||
\(450\) | −6.06760 | −0.286029 | ||||||||
\(451\) | −26.1143 | −1.22968 | ||||||||
\(452\) | 44.0681 | 2.07279 | ||||||||
\(453\) | −0.428667 | −0.0201405 | ||||||||
\(454\) | 52.7517 | 2.47576 | ||||||||
\(455\) | −8.77516 | −0.411386 | ||||||||
\(456\) | −25.3689 | −1.18801 | ||||||||
\(457\) | 1.76591 | 0.0826057 | 0.0413028 | − | 0.999147i | \(-0.486849\pi\) | ||||
0.0413028 | + | 0.999147i | \(0.486849\pi\) | |||||||
\(458\) | 59.3641 | 2.77390 | ||||||||
\(459\) | −0.229634 | −0.0107184 | ||||||||
\(460\) | −54.0232 | −2.51884 | ||||||||
\(461\) | −18.7198 | −0.871870 | −0.435935 | − | 0.899978i | \(-0.643582\pi\) | ||||
−0.435935 | + | 0.899978i | \(0.643582\pi\) | |||||||
\(462\) | −88.4036 | −4.11291 | ||||||||
\(463\) | −21.2147 | −0.985931 | −0.492966 | − | 0.870049i | \(-0.664087\pi\) | ||||
−0.492966 | + | 0.870049i | \(0.664087\pi\) | |||||||
\(464\) | 18.1680 | 0.843427 | ||||||||
\(465\) | 31.7477 | 1.47227 | ||||||||
\(466\) | 15.5852 | 0.721970 | ||||||||
\(467\) | −7.66006 | −0.354465 | −0.177233 | − | 0.984169i | \(-0.556715\pi\) | ||||
−0.177233 | + | 0.984169i | \(0.556715\pi\) | |||||||
\(468\) | 7.40426 | 0.342262 | ||||||||
\(469\) | −12.7544 | −0.588943 | ||||||||
\(470\) | −18.6613 | −0.860781 | ||||||||
\(471\) | 34.0318 | 1.56810 | ||||||||
\(472\) | 26.1233 | 1.20242 | ||||||||
\(473\) | 33.7399 | 1.55136 | ||||||||
\(474\) | 23.8296 | 1.09453 | ||||||||
\(475\) | 3.62053 | 0.166121 | ||||||||
\(476\) | −1.34767 | −0.0617705 | ||||||||
\(477\) | −8.41552 | −0.385320 | ||||||||
\(478\) | 15.9731 | 0.730593 | ||||||||
\(479\) | −4.83577 | −0.220952 | −0.110476 | − | 0.993879i | \(-0.535238\pi\) | ||||
−0.110476 | + | 0.993879i | \(0.535238\pi\) | |||||||
\(480\) | 16.7923 | 0.766461 | ||||||||
\(481\) | 6.18356 | 0.281946 | ||||||||
\(482\) | 7.13028 | 0.324775 | ||||||||
\(483\) | 46.4421 | 2.11319 | ||||||||
\(484\) | 41.5003 | 1.88638 | ||||||||
\(485\) | 2.32681 | 0.105655 | ||||||||
\(486\) | 42.9177 | 1.94679 | ||||||||
\(487\) | −37.3725 | −1.69351 | −0.846754 | − | 0.531985i | \(-0.821446\pi\) | ||||
−0.846754 | + | 0.531985i | \(0.821446\pi\) | |||||||
\(488\) | 42.3861 | 1.91873 | ||||||||
\(489\) | −6.36591 | −0.287877 | ||||||||
\(490\) | −31.5440 | −1.42501 | ||||||||
\(491\) | −20.4687 | −0.923739 | −0.461870 | − | 0.886948i | \(-0.652821\pi\) | ||||
−0.461870 | + | 0.886948i | \(0.652821\pi\) | |||||||
\(492\) | 45.2651 | 2.04071 | ||||||||
\(493\) | 0.930498 | 0.0419075 | ||||||||
\(494\) | −6.83528 | −0.307534 | ||||||||
\(495\) | −23.9585 | −1.07686 | ||||||||
\(496\) | 11.6168 | 0.521609 | ||||||||
\(497\) | 0.450882 | 0.0202248 | ||||||||
\(498\) | −49.1034 | −2.20037 | ||||||||
\(499\) | −22.5475 | −1.00936 | −0.504682 | − | 0.863305i | \(-0.668390\pi\) | ||||
−0.504682 | + | 0.863305i | \(0.668390\pi\) | |||||||
\(500\) | −34.2094 | −1.52989 | ||||||||
\(501\) | −18.6649 | −0.833887 | ||||||||
\(502\) | 26.1068 | 1.16521 | ||||||||
\(503\) | −1.06285 | −0.0473904 | −0.0236952 | − | 0.999719i | \(-0.507543\pi\) | ||||
−0.0236952 | + | 0.999719i | \(0.507543\pi\) | |||||||
\(504\) | 27.9705 | 1.24590 | ||||||||
\(505\) | −40.0784 | −1.78346 | ||||||||
\(506\) | −66.4121 | −2.95238 | ||||||||
\(507\) | 2.24175 | 0.0995597 | ||||||||
\(508\) | 42.0096 | 1.86387 | ||||||||
\(509\) | 26.6956 | 1.18326 | 0.591630 | − | 0.806209i | \(-0.298484\pi\) | ||||
0.591630 | + | 0.806209i | \(0.298484\pi\) | |||||||
\(510\) | −1.40200 | −0.0620816 | ||||||||
\(511\) | 15.8748 | 0.702260 | ||||||||
\(512\) | 22.3053 | 0.985765 | ||||||||
\(513\) | −6.27925 | −0.277236 | ||||||||
\(514\) | −19.5415 | −0.861937 | ||||||||
\(515\) | −47.6604 | −2.10017 | ||||||||
\(516\) | −58.4828 | −2.57456 | ||||||||
\(517\) | −14.8282 | −0.652144 | ||||||||
\(518\) | 51.5772 | 2.26617 | ||||||||
\(519\) | −35.6531 | −1.56500 | ||||||||
\(520\) | −9.85086 | −0.431989 | ||||||||
\(521\) | −6.61042 | −0.289608 | −0.144804 | − | 0.989460i | \(-0.546255\pi\) | ||||
−0.144804 | + | 0.989460i | \(0.546255\pi\) | |||||||
\(522\) | −42.6415 | −1.86637 | ||||||||
\(523\) | −1.11548 | −0.0487766 | −0.0243883 | − | 0.999703i | \(-0.507764\pi\) | ||||
−0.0243883 | + | 0.999703i | \(0.507764\pi\) | |||||||
\(524\) | −51.7194 | −2.25937 | ||||||||
\(525\) | −9.90427 | −0.432258 | ||||||||
\(526\) | 40.7559 | 1.77704 | ||||||||
\(527\) | 0.594969 | 0.0259173 | ||||||||
\(528\) | −21.7514 | −0.946606 | ||||||||
\(529\) | 11.8890 | 0.516915 | ||||||||
\(530\) | 24.7215 | 1.07383 | ||||||||
\(531\) | −13.4385 | −0.583181 | ||||||||
\(532\) | −36.8516 | −1.59772 | ||||||||
\(533\) | 5.52352 | 0.239250 | ||||||||
\(534\) | 15.5036 | 0.670906 | ||||||||
\(535\) | 44.6159 | 1.92891 | ||||||||
\(536\) | −14.3179 | −0.618438 | ||||||||
\(537\) | −46.3142 | −1.99861 | ||||||||
\(538\) | 11.6760 | 0.503389 | ||||||||
\(539\) | −25.0648 | −1.07962 | ||||||||
\(540\) | −19.9815 | −0.859865 | ||||||||
\(541\) | 22.7322 | 0.977334 | 0.488667 | − | 0.872470i | \(-0.337483\pi\) | ||||
0.488667 | + | 0.872470i | \(0.337483\pi\) | |||||||
\(542\) | 14.3413 | 0.616012 | ||||||||
\(543\) | −24.4715 | −1.05017 | ||||||||
\(544\) | 0.314697 | 0.0134925 | ||||||||
\(545\) | 16.1642 | 0.692398 | ||||||||
\(546\) | 18.6985 | 0.800222 | ||||||||
\(547\) | 30.8568 | 1.31934 | 0.659671 | − | 0.751554i | \(-0.270696\pi\) | ||||
0.659671 | + | 0.751554i | \(0.270696\pi\) | |||||||
\(548\) | −56.5675 | −2.41645 | ||||||||
\(549\) | −21.8045 | −0.930594 | ||||||||
\(550\) | 14.1631 | 0.603917 | ||||||||
\(551\) | 25.4441 | 1.08396 | ||||||||
\(552\) | 52.1351 | 2.21902 | ||||||||
\(553\) | 15.6772 | 0.666664 | ||||||||
\(554\) | 72.9775 | 3.10052 | ||||||||
\(555\) | 34.6818 | 1.47216 | ||||||||
\(556\) | 21.1695 | 0.897789 | ||||||||
\(557\) | −1.53405 | −0.0649998 | −0.0324999 | − | 0.999472i | \(-0.510347\pi\) | ||||
−0.0324999 | + | 0.999472i | \(0.510347\pi\) | |||||||
\(558\) | −27.2654 | −1.15423 | ||||||||
\(559\) | −7.13642 | −0.301838 | ||||||||
\(560\) | −18.0091 | −0.761022 | ||||||||
\(561\) | −1.11403 | −0.0470342 | ||||||||
\(562\) | 13.3411 | 0.562761 | ||||||||
\(563\) | −1.48277 | −0.0624913 | −0.0312457 | − | 0.999512i | \(-0.509947\pi\) | ||||
−0.0312457 | + | 0.999512i | \(0.509947\pi\) | |||||||
\(564\) | 25.7024 | 1.08227 | ||||||||
\(565\) | 30.1606 | 1.26887 | ||||||||
\(566\) | −37.4939 | −1.57599 | ||||||||
\(567\) | 38.4894 | 1.61640 | ||||||||
\(568\) | 0.506153 | 0.0212377 | ||||||||
\(569\) | −25.5034 | −1.06916 | −0.534579 | − | 0.845118i | \(-0.679530\pi\) | ||||
−0.534579 | + | 0.845118i | \(0.679530\pi\) | |||||||
\(570\) | −38.3371 | −1.60576 | ||||||||
\(571\) | −8.53230 | −0.357066 | −0.178533 | − | 0.983934i | \(-0.557135\pi\) | ||||
−0.178533 | + | 0.983934i | \(0.557135\pi\) | |||||||
\(572\) | −17.2832 | −0.722645 | ||||||||
\(573\) | −44.6335 | −1.86459 | ||||||||
\(574\) | 46.0718 | 1.92300 | ||||||||
\(575\) | −7.44046 | −0.310289 | ||||||||
\(576\) | −22.7350 | −0.947293 | ||||||||
\(577\) | −19.3591 | −0.805931 | −0.402965 | − | 0.915215i | \(-0.632021\pi\) | ||||
−0.402965 | + | 0.915215i | \(0.632021\pi\) | |||||||
\(578\) | 40.4023 | 1.68052 | ||||||||
\(579\) | −39.2354 | −1.63057 | ||||||||
\(580\) | 80.9667 | 3.36196 | ||||||||
\(581\) | −32.3045 | −1.34022 | ||||||||
\(582\) | −4.95808 | −0.205519 | ||||||||
\(583\) | 19.6436 | 0.813557 | ||||||||
\(584\) | 17.8208 | 0.737429 | ||||||||
\(585\) | 5.06754 | 0.209517 | ||||||||
\(586\) | −78.9865 | −3.26290 | ||||||||
\(587\) | −40.7167 | −1.68056 | −0.840278 | − | 0.542156i | \(-0.817608\pi\) | ||||
−0.840278 | + | 0.542156i | \(0.817608\pi\) | |||||||
\(588\) | 43.4460 | 1.79168 | ||||||||
\(589\) | 16.2692 | 0.670360 | ||||||||
\(590\) | 39.4771 | 1.62524 | ||||||||
\(591\) | 50.9503 | 2.09582 | ||||||||
\(592\) | 12.6904 | 0.521571 | ||||||||
\(593\) | 15.7761 | 0.647847 | 0.323923 | − | 0.946083i | \(-0.394998\pi\) | ||||
0.323923 | + | 0.946083i | \(0.394998\pi\) | |||||||
\(594\) | −24.5637 | −1.00786 | ||||||||
\(595\) | −0.922359 | −0.0378130 | ||||||||
\(596\) | 6.20406 | 0.254128 | ||||||||
\(597\) | −39.6169 | −1.62141 | ||||||||
\(598\) | 14.0470 | 0.574426 | ||||||||
\(599\) | 24.3147 | 0.993470 | 0.496735 | − | 0.867902i | \(-0.334532\pi\) | ||||
0.496735 | + | 0.867902i | \(0.334532\pi\) | |||||||
\(600\) | −11.1184 | −0.453906 | ||||||||
\(601\) | 9.68715 | 0.395147 | 0.197573 | − | 0.980288i | \(-0.436694\pi\) | ||||
0.197573 | + | 0.980288i | \(0.436694\pi\) | |||||||
\(602\) | −59.5251 | −2.42606 | ||||||||
\(603\) | 7.36549 | 0.299946 | ||||||||
\(604\) | −0.699025 | −0.0284429 | ||||||||
\(605\) | 28.4032 | 1.15475 | ||||||||
\(606\) | 85.4008 | 3.46917 | ||||||||
\(607\) | −11.6975 | −0.474788 | −0.237394 | − | 0.971413i | \(-0.576293\pi\) | ||||
−0.237394 | + | 0.971413i | \(0.576293\pi\) | |||||||
\(608\) | 8.60526 | 0.348989 | ||||||||
\(609\) | −69.6046 | −2.82052 | ||||||||
\(610\) | 64.0531 | 2.59343 | ||||||||
\(611\) | 3.13636 | 0.126884 | ||||||||
\(612\) | 0.778263 | 0.0314594 | ||||||||
\(613\) | −37.2724 | −1.50542 | −0.752709 | − | 0.658353i | \(-0.771253\pi\) | ||||
−0.752709 | + | 0.658353i | \(0.771253\pi\) | |||||||
\(614\) | 33.0309 | 1.33302 | ||||||||
\(615\) | 30.9798 | 1.24923 | ||||||||
\(616\) | −65.2892 | −2.63058 | ||||||||
\(617\) | 1.00000 | 0.0402585 | ||||||||
\(618\) | 101.557 | 4.08522 | ||||||||
\(619\) | 12.3610 | 0.496829 | 0.248415 | − | 0.968654i | \(-0.420090\pi\) | ||||
0.248415 | + | 0.968654i | \(0.420090\pi\) | |||||||
\(620\) | 51.7709 | 2.07917 | ||||||||
\(621\) | 12.9043 | 0.517833 | ||||||||
\(622\) | −12.0773 | −0.484256 | ||||||||
\(623\) | 10.1996 | 0.408640 | ||||||||
\(624\) | 4.60069 | 0.184175 | ||||||||
\(625\) | −29.7116 | −1.18846 | ||||||||
\(626\) | −6.54364 | −0.261537 | ||||||||
\(627\) | −30.4626 | −1.21656 | ||||||||
\(628\) | 55.4955 | 2.21451 | ||||||||
\(629\) | 0.649955 | 0.0259154 | ||||||||
\(630\) | 42.2685 | 1.68402 | ||||||||
\(631\) | −43.1706 | −1.71859 | −0.859297 | − | 0.511478i | \(-0.829098\pi\) | ||||
−0.859297 | + | 0.511478i | \(0.829098\pi\) | |||||||
\(632\) | 17.5990 | 0.700052 | ||||||||
\(633\) | −5.35678 | −0.212913 | ||||||||
\(634\) | 68.1255 | 2.70561 | ||||||||
\(635\) | 28.7517 | 1.14098 | ||||||||
\(636\) | −34.0492 | −1.35014 | ||||||||
\(637\) | 5.30154 | 0.210055 | ||||||||
\(638\) | 99.5345 | 3.94061 | ||||||||
\(639\) | −0.260378 | −0.0103004 | ||||||||
\(640\) | 51.8051 | 2.04778 | ||||||||
\(641\) | 38.9831 | 1.53974 | 0.769870 | − | 0.638201i | \(-0.220321\pi\) | ||||
0.769870 | + | 0.638201i | \(0.220321\pi\) | |||||||
\(642\) | −95.0695 | −3.75209 | ||||||||
\(643\) | −38.9950 | −1.53781 | −0.768906 | − | 0.639362i | \(-0.779199\pi\) | ||||
−0.768906 | + | 0.639362i | \(0.779199\pi\) | |||||||
\(644\) | 75.7329 | 2.98429 | ||||||||
\(645\) | −40.0261 | −1.57603 | ||||||||
\(646\) | −0.718457 | −0.0282673 | ||||||||
\(647\) | 7.78946 | 0.306235 | 0.153118 | − | 0.988208i | \(-0.451069\pi\) | ||||
0.153118 | + | 0.988208i | \(0.451069\pi\) | |||||||
\(648\) | 43.2075 | 1.69735 | ||||||||
\(649\) | 31.3684 | 1.23132 | ||||||||
\(650\) | −2.99568 | −0.117500 | ||||||||
\(651\) | −44.5058 | −1.74432 | ||||||||
\(652\) | −10.3809 | −0.406546 | ||||||||
\(653\) | 9.09892 | 0.356068 | 0.178034 | − | 0.984024i | \(-0.443026\pi\) | ||||
0.178034 | + | 0.984024i | \(0.443026\pi\) | |||||||
\(654\) | −34.4434 | −1.34684 | ||||||||
\(655\) | −35.3972 | −1.38308 | ||||||||
\(656\) | 11.3358 | 0.442588 | ||||||||
\(657\) | −9.16748 | −0.357658 | ||||||||
\(658\) | 26.1605 | 1.01984 | ||||||||
\(659\) | 37.7491 | 1.47050 | 0.735248 | − | 0.677798i | \(-0.237066\pi\) | ||||
0.735248 | + | 0.677798i | \(0.237066\pi\) | |||||||
\(660\) | −96.9363 | −3.77324 | ||||||||
\(661\) | 2.59922 | 0.101098 | 0.0505491 | − | 0.998722i | \(-0.483903\pi\) | ||||
0.0505491 | + | 0.998722i | \(0.483903\pi\) | |||||||
\(662\) | 59.3927 | 2.30836 | ||||||||
\(663\) | 0.235631 | 0.00915115 | ||||||||
\(664\) | −36.2646 | −1.40734 | ||||||||
\(665\) | −25.2215 | −0.978049 | ||||||||
\(666\) | −29.7852 | −1.15415 | ||||||||
\(667\) | −52.2896 | −2.02466 | ||||||||
\(668\) | −30.4368 | −1.17763 | ||||||||
\(669\) | 0.201763 | 0.00780059 | ||||||||
\(670\) | −21.6369 | −0.835907 | ||||||||
\(671\) | 50.8965 | 1.96484 | ||||||||
\(672\) | −23.5405 | −0.908093 | ||||||||
\(673\) | −8.52553 | −0.328635 | −0.164318 | − | 0.986407i | \(-0.552542\pi\) | ||||
−0.164318 | + | 0.986407i | \(0.552542\pi\) | |||||||
\(674\) | −68.8059 | −2.65030 | ||||||||
\(675\) | −2.75199 | −0.105924 | ||||||||
\(676\) | 3.65561 | 0.140600 | ||||||||
\(677\) | 42.2460 | 1.62365 | 0.811823 | − | 0.583904i | \(-0.198475\pi\) | ||||
0.811823 | + | 0.583904i | \(0.198475\pi\) | |||||||
\(678\) | −64.2675 | −2.46818 | ||||||||
\(679\) | −3.26186 | −0.125179 | ||||||||
\(680\) | −1.03543 | −0.0397068 | ||||||||
\(681\) | −49.7260 | −1.90551 | ||||||||
\(682\) | 63.6433 | 2.43703 | ||||||||
\(683\) | 33.8343 | 1.29463 | 0.647316 | − | 0.762222i | \(-0.275891\pi\) | ||||
0.647316 | + | 0.762222i | \(0.275891\pi\) | |||||||
\(684\) | 21.2813 | 0.813711 | ||||||||
\(685\) | −38.7153 | −1.47924 | ||||||||
\(686\) | −14.1669 | −0.540896 | ||||||||
\(687\) | −55.9592 | −2.13498 | ||||||||
\(688\) | −14.6459 | −0.558370 | ||||||||
\(689\) | −4.15489 | −0.158289 | ||||||||
\(690\) | 78.7857 | 2.99932 | ||||||||
\(691\) | −23.4453 | −0.891903 | −0.445952 | − | 0.895057i | \(-0.647135\pi\) | ||||
−0.445952 | + | 0.895057i | \(0.647135\pi\) | |||||||
\(692\) | −58.1393 | −2.21013 | ||||||||
\(693\) | 33.5865 | 1.27584 | ||||||||
\(694\) | −16.7379 | −0.635362 | ||||||||
\(695\) | 14.4886 | 0.549585 | ||||||||
\(696\) | −78.1370 | −2.96178 | ||||||||
\(697\) | 0.580578 | 0.0219910 | ||||||||
\(698\) | 16.7691 | 0.634722 | ||||||||
\(699\) | −14.6913 | −0.555675 | ||||||||
\(700\) | −16.1508 | −0.610445 | ||||||||
\(701\) | 0.196821 | 0.00743381 | 0.00371691 | − | 0.999993i | \(-0.498817\pi\) | ||||
0.00371691 | + | 0.999993i | \(0.498817\pi\) | |||||||
\(702\) | 5.19555 | 0.196093 | ||||||||
\(703\) | 17.7728 | 0.670312 | ||||||||
\(704\) | 53.0685 | 2.00009 | ||||||||
\(705\) | 17.5909 | 0.662513 | ||||||||
\(706\) | −66.4984 | −2.50270 | ||||||||
\(707\) | 56.1842 | 2.11302 | ||||||||
\(708\) | −54.3722 | −2.04343 | ||||||||
\(709\) | 21.6522 | 0.813165 | 0.406583 | − | 0.913614i | \(-0.366720\pi\) | ||||
0.406583 | + | 0.913614i | \(0.366720\pi\) | |||||||
\(710\) | 0.764889 | 0.0287058 | ||||||||
\(711\) | −9.05340 | −0.339529 | ||||||||
\(712\) | 11.4499 | 0.429105 | ||||||||
\(713\) | −33.4345 | −1.25213 | ||||||||
\(714\) | 1.96540 | 0.0735534 | ||||||||
\(715\) | −11.8287 | −0.442370 | ||||||||
\(716\) | −75.5243 | −2.82248 | ||||||||
\(717\) | −15.0570 | −0.562313 | ||||||||
\(718\) | −50.2021 | −1.87353 | ||||||||
\(719\) | 34.4191 | 1.28362 | 0.641808 | − | 0.766866i | \(-0.278185\pi\) | ||||
0.641808 | + | 0.766866i | \(0.278185\pi\) | |||||||
\(720\) | 10.4000 | 0.387585 | ||||||||
\(721\) | 66.8131 | 2.48825 | ||||||||
\(722\) | 25.5390 | 0.950463 | ||||||||
\(723\) | −6.72131 | −0.249968 | ||||||||
\(724\) | −39.9056 | −1.48308 | ||||||||
\(725\) | 11.1513 | 0.414150 | ||||||||
\(726\) | −60.5228 | −2.24621 | ||||||||
\(727\) | −45.8045 | −1.69880 | −0.849398 | − | 0.527753i | \(-0.823035\pi\) | ||||
−0.849398 | + | 0.527753i | \(0.823035\pi\) | |||||||
\(728\) | 13.8095 | 0.511814 | ||||||||
\(729\) | −7.53445 | −0.279054 | ||||||||
\(730\) | 26.9305 | 0.996741 | ||||||||
\(731\) | −0.750111 | −0.0277438 | ||||||||
\(732\) | −88.2211 | −3.26074 | ||||||||
\(733\) | −2.80654 | −0.103662 | −0.0518310 | − | 0.998656i | \(-0.516506\pi\) | ||||
−0.0518310 | + | 0.998656i | \(0.516506\pi\) | |||||||
\(734\) | −35.0362 | −1.29321 | ||||||||
\(735\) | 29.7348 | 1.09678 | ||||||||
\(736\) | −17.6845 | −0.651858 | ||||||||
\(737\) | −17.1927 | −0.633299 | ||||||||
\(738\) | −26.6059 | −0.979376 | ||||||||
\(739\) | −50.0863 | −1.84245 | −0.921227 | − | 0.389025i | \(-0.872812\pi\) | ||||
−0.921227 | + | 0.389025i | \(0.872812\pi\) | |||||||
\(740\) | 56.5554 | 2.07902 | ||||||||
\(741\) | 6.44323 | 0.236698 | ||||||||
\(742\) | −34.6560 | −1.27226 | ||||||||
\(743\) | −17.2495 | −0.632823 | −0.316412 | − | 0.948622i | \(-0.602478\pi\) | ||||
−0.316412 | + | 0.948622i | \(0.602478\pi\) | |||||||
\(744\) | −49.9615 | −1.83168 | ||||||||
\(745\) | 4.24611 | 0.155566 | ||||||||
\(746\) | −2.55406 | −0.0935108 | ||||||||
\(747\) | 18.6554 | 0.682567 | ||||||||
\(748\) | −1.81664 | −0.0664228 | ||||||||
\(749\) | −62.5451 | −2.28535 | ||||||||
\(750\) | 49.8900 | 1.82172 | ||||||||
\(751\) | 16.2520 | 0.593044 | 0.296522 | − | 0.955026i | \(-0.404173\pi\) | ||||
0.296522 | + | 0.955026i | \(0.404173\pi\) | |||||||
\(752\) | 6.43668 | 0.234722 | ||||||||
\(753\) | −24.6095 | −0.896819 | ||||||||
\(754\) | −21.0528 | −0.766699 | ||||||||
\(755\) | −0.478419 | −0.0174114 | ||||||||
\(756\) | 28.0112 | 1.01876 | ||||||||
\(757\) | 27.1765 | 0.987748 | 0.493874 | − | 0.869533i | \(-0.335580\pi\) | ||||
0.493874 | + | 0.869533i | \(0.335580\pi\) | |||||||
\(758\) | 0.610047 | 0.0221579 | ||||||||
\(759\) | 62.6030 | 2.27234 | ||||||||
\(760\) | −28.3133 | −1.02703 | ||||||||
\(761\) | 13.7248 | 0.497525 | 0.248763 | − | 0.968565i | \(-0.419976\pi\) | ||||
0.248763 | + | 0.968565i | \(0.419976\pi\) | |||||||
\(762\) | −61.2654 | −2.21941 | ||||||||
\(763\) | −22.6599 | −0.820344 | ||||||||
\(764\) | −72.7837 | −2.63322 | ||||||||
\(765\) | 0.532650 | 0.0192580 | ||||||||
\(766\) | 69.5415 | 2.51264 | ||||||||
\(767\) | −6.63482 | −0.239570 | ||||||||
\(768\) | −60.0628 | −2.16733 | ||||||||
\(769\) | 38.3615 | 1.38335 | 0.691676 | − | 0.722208i | \(-0.256872\pi\) | ||||
0.691676 | + | 0.722208i | \(0.256872\pi\) | |||||||
\(770\) | −98.6639 | −3.55560 | ||||||||
\(771\) | 18.4206 | 0.663403 | ||||||||
\(772\) | −63.9810 | −2.30273 | ||||||||
\(773\) | 28.2532 | 1.01620 | 0.508099 | − | 0.861299i | \(-0.330348\pi\) | ||||
0.508099 | + | 0.861299i | \(0.330348\pi\) | |||||||
\(774\) | 34.3749 | 1.23558 | ||||||||
\(775\) | 7.13026 | 0.256126 | ||||||||
\(776\) | −3.66172 | −0.131448 | ||||||||
\(777\) | −48.6190 | −1.74420 | ||||||||
\(778\) | 29.7338 | 1.06601 | ||||||||
\(779\) | 15.8757 | 0.568805 | ||||||||
\(780\) | 20.5033 | 0.734135 | ||||||||
\(781\) | 0.607779 | 0.0217481 | ||||||||
\(782\) | 1.47649 | 0.0527990 | ||||||||
\(783\) | −19.3403 | −0.691164 | ||||||||
\(784\) | 10.8802 | 0.388579 | ||||||||
\(785\) | 37.9816 | 1.35562 | ||||||||
\(786\) | 75.4259 | 2.69035 | ||||||||
\(787\) | 39.7752 | 1.41783 | 0.708917 | − | 0.705292i | \(-0.249184\pi\) | ||||
0.708917 | + | 0.705292i | \(0.249184\pi\) | |||||||
\(788\) | 83.0844 | 2.95976 | ||||||||
\(789\) | −38.4183 | −1.36773 | ||||||||
\(790\) | 26.5953 | 0.946220 | ||||||||
\(791\) | −42.2809 | −1.50333 | ||||||||
\(792\) | 37.7036 | 1.33974 | ||||||||
\(793\) | −10.7653 | −0.382286 | ||||||||
\(794\) | −13.1416 | −0.466379 | ||||||||
\(795\) | −23.3036 | −0.826492 | ||||||||
\(796\) | −64.6031 | −2.28980 | ||||||||
\(797\) | 44.9581 | 1.59250 | 0.796249 | − | 0.604969i | \(-0.206814\pi\) | ||||
0.796249 | + | 0.604969i | \(0.206814\pi\) | |||||||
\(798\) | 53.7432 | 1.90249 | ||||||||
\(799\) | 0.329663 | 0.0116627 | ||||||||
\(800\) | 3.77140 | 0.133339 | ||||||||
\(801\) | −5.89015 | −0.208118 | ||||||||
\(802\) | −58.6718 | −2.07177 | ||||||||
\(803\) | 21.3989 | 0.755151 | ||||||||
\(804\) | 29.8008 | 1.05099 | ||||||||
\(805\) | 51.8322 | 1.82685 | ||||||||
\(806\) | −13.4614 | −0.474157 | ||||||||
\(807\) | −11.0063 | −0.387441 | ||||||||
\(808\) | 63.0715 | 2.21885 | ||||||||
\(809\) | 19.0268 | 0.668948 | 0.334474 | − | 0.942405i | \(-0.391441\pi\) | ||||
0.334474 | + | 0.942405i | \(0.391441\pi\) | |||||||
\(810\) | 65.2945 | 2.29421 | ||||||||
\(811\) | −2.91892 | −0.102497 | −0.0512486 | − | 0.998686i | \(-0.516320\pi\) | ||||
−0.0512486 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(812\) | −113.504 | −3.98320 | ||||||||
\(813\) | −13.5187 | −0.474123 | ||||||||
\(814\) | 69.5250 | 2.43685 | ||||||||
\(815\) | −7.10475 | −0.248869 | ||||||||
\(816\) | 0.483580 | 0.0169287 | ||||||||
\(817\) | −20.5115 | −0.717605 | ||||||||
\(818\) | −6.79000 | −0.237407 | ||||||||
\(819\) | −7.10397 | −0.248233 | ||||||||
\(820\) | 50.5186 | 1.76419 | ||||||||
\(821\) | 8.39898 | 0.293126 | 0.146563 | − | 0.989201i | \(-0.453179\pi\) | ||||
0.146563 | + | 0.989201i | \(0.453179\pi\) | |||||||
\(822\) | 82.4963 | 2.87739 | ||||||||
\(823\) | −4.44310 | −0.154877 | −0.0774384 | − | 0.996997i | \(-0.524674\pi\) | ||||
−0.0774384 | + | 0.996997i | \(0.524674\pi\) | |||||||
\(824\) | 75.0034 | 2.61287 | ||||||||
\(825\) | −13.3508 | −0.464814 | ||||||||
\(826\) | −55.3412 | −1.92557 | ||||||||
\(827\) | 10.3147 | 0.358678 | 0.179339 | − | 0.983787i | \(-0.442604\pi\) | ||||
0.179339 | + | 0.983787i | \(0.442604\pi\) | |||||||
\(828\) | −43.7347 | −1.51989 | ||||||||
\(829\) | −1.40088 | −0.0486546 | −0.0243273 | − | 0.999704i | \(-0.507744\pi\) | ||||
−0.0243273 | + | 0.999704i | \(0.507744\pi\) | |||||||
\(830\) | −54.8024 | −1.90222 | ||||||||
\(831\) | −68.7918 | −2.38636 | ||||||||
\(832\) | −11.2247 | −0.389146 | ||||||||
\(833\) | 0.557245 | 0.0193074 | ||||||||
\(834\) | −30.8730 | −1.06904 | ||||||||
\(835\) | −20.8312 | −0.720893 | ||||||||
\(836\) | −49.6752 | −1.71805 | ||||||||
\(837\) | −12.3663 | −0.427443 | ||||||||
\(838\) | −92.2565 | −3.18695 | ||||||||
\(839\) | −15.2350 | −0.525969 | −0.262985 | − | 0.964800i | \(-0.584707\pi\) | ||||
−0.262985 | + | 0.964800i | \(0.584707\pi\) | |||||||
\(840\) | 77.4535 | 2.67240 | ||||||||
\(841\) | 49.3685 | 1.70236 | ||||||||
\(842\) | 44.4401 | 1.53151 | ||||||||
\(843\) | −12.5759 | −0.433137 | ||||||||
\(844\) | −8.73527 | −0.300680 | ||||||||
\(845\) | 2.50193 | 0.0860691 | ||||||||
\(846\) | −15.1073 | −0.519400 | ||||||||
\(847\) | −39.8172 | −1.36814 | ||||||||
\(848\) | −8.52697 | −0.292818 | ||||||||
\(849\) | 35.3434 | 1.21298 | ||||||||
\(850\) | −0.314876 | −0.0108002 | ||||||||
\(851\) | −36.5244 | −1.25204 | ||||||||
\(852\) | −1.05349 | −0.0360920 | ||||||||
\(853\) | 26.7644 | 0.916395 | 0.458197 | − | 0.888850i | \(-0.348495\pi\) | ||||
0.458197 | + | 0.888850i | \(0.348495\pi\) | |||||||
\(854\) | −89.7933 | −3.07266 | ||||||||
\(855\) | 14.5651 | 0.498116 | ||||||||
\(856\) | −70.2122 | −2.39980 | ||||||||
\(857\) | 21.5674 | 0.736730 | 0.368365 | − | 0.929681i | \(-0.379918\pi\) | ||||
0.368365 | + | 0.929681i | \(0.379918\pi\) | |||||||
\(858\) | 25.2052 | 0.860492 | ||||||||
\(859\) | 49.1853 | 1.67818 | 0.839091 | − | 0.543991i | \(-0.183088\pi\) | ||||
0.839091 | + | 0.543991i | \(0.183088\pi\) | |||||||
\(860\) | −65.2704 | −2.22570 | ||||||||
\(861\) | −43.4293 | −1.48007 | ||||||||
\(862\) | −45.0532 | −1.53452 | ||||||||
\(863\) | 13.4745 | 0.458677 | 0.229338 | − | 0.973347i | \(-0.426344\pi\) | ||||
0.229338 | + | 0.973347i | \(0.426344\pi\) | |||||||
\(864\) | −6.54092 | −0.222527 | ||||||||
\(865\) | −39.7911 | −1.35294 | ||||||||
\(866\) | 84.4979 | 2.87135 | ||||||||
\(867\) | −38.0850 | −1.29343 | ||||||||
\(868\) | −72.5754 | −2.46337 | ||||||||
\(869\) | 21.1326 | 0.716875 | ||||||||
\(870\) | −118.079 | −4.00326 | ||||||||
\(871\) | 3.63647 | 0.123217 | ||||||||
\(872\) | −25.4377 | −0.861428 | ||||||||
\(873\) | 1.88368 | 0.0637530 | ||||||||
\(874\) | 40.3739 | 1.36567 | ||||||||
\(875\) | 32.8220 | 1.10959 | ||||||||
\(876\) | −37.0916 | −1.25321 | ||||||||
\(877\) | 39.2319 | 1.32477 | 0.662383 | − | 0.749165i | \(-0.269545\pi\) | ||||
0.662383 | + | 0.749165i | \(0.269545\pi\) | |||||||
\(878\) | −86.4805 | −2.91857 | ||||||||
\(879\) | 74.4562 | 2.51134 | ||||||||
\(880\) | −24.2759 | −0.818339 | ||||||||
\(881\) | 50.6525 | 1.70653 | 0.853263 | − | 0.521480i | \(-0.174620\pi\) | ||||
0.853263 | + | 0.521480i | \(0.174620\pi\) | |||||||
\(882\) | −25.5366 | −0.859862 | ||||||||
\(883\) | 12.4245 | 0.418118 | 0.209059 | − | 0.977903i | \(-0.432960\pi\) | ||||
0.209059 | + | 0.977903i | \(0.432960\pi\) | |||||||
\(884\) | 0.384242 | 0.0129235 | ||||||||
\(885\) | −37.2128 | −1.25089 | ||||||||
\(886\) | −13.6998 | −0.460254 | ||||||||
\(887\) | 17.6650 | 0.593132 | 0.296566 | − | 0.955012i | \(-0.404158\pi\) | ||||
0.296566 | + | 0.955012i | \(0.404158\pi\) | |||||||
\(888\) | −54.5789 | −1.83155 | ||||||||
\(889\) | −40.3058 | −1.35181 | ||||||||
\(890\) | 17.3030 | 0.579996 | ||||||||
\(891\) | 51.8829 | 1.73814 | ||||||||
\(892\) | 0.329013 | 0.0110162 | ||||||||
\(893\) | 9.01451 | 0.301659 | ||||||||
\(894\) | −9.04780 | −0.302604 | ||||||||
\(895\) | −51.6895 | −1.72779 | ||||||||
\(896\) | −72.6235 | −2.42618 | ||||||||
\(897\) | −13.2413 | −0.442116 | ||||||||
\(898\) | −73.9897 | −2.46907 | ||||||||
\(899\) | 50.1096 | 1.67125 | ||||||||
\(900\) | 9.32690 | 0.310897 | ||||||||
\(901\) | −0.436721 | −0.0145493 | ||||||||
\(902\) | 62.1039 | 2.06783 | ||||||||
\(903\) | 56.1110 | 1.86726 | ||||||||
\(904\) | −47.4638 | −1.57862 | ||||||||
\(905\) | −27.3117 | −0.907873 | ||||||||
\(906\) | 1.01944 | 0.0338685 | ||||||||
\(907\) | 13.6245 | 0.452396 | 0.226198 | − | 0.974081i | \(-0.427370\pi\) | ||||
0.226198 | + | 0.974081i | \(0.427370\pi\) | |||||||
\(908\) | −81.0880 | −2.69100 | ||||||||
\(909\) | −32.4456 | −1.07615 | ||||||||
\(910\) | 20.8687 | 0.691790 | ||||||||
\(911\) | −3.06188 | −0.101444 | −0.0507222 | − | 0.998713i | \(-0.516152\pi\) | ||||
−0.0507222 | + | 0.998713i | \(0.516152\pi\) | |||||||
\(912\) | 13.2233 | 0.437867 | ||||||||
\(913\) | −43.5459 | −1.44116 | ||||||||
\(914\) | −4.19960 | −0.138910 | ||||||||
\(915\) | −60.3792 | −1.99608 | ||||||||
\(916\) | −91.2524 | −3.01506 | ||||||||
\(917\) | 49.6218 | 1.63866 | ||||||||
\(918\) | 0.546105 | 0.0180241 | ||||||||
\(919\) | −46.5436 | −1.53533 | −0.767666 | − | 0.640850i | \(-0.778582\pi\) | ||||
−0.767666 | + | 0.640850i | \(0.778582\pi\) | |||||||
\(920\) | 58.1860 | 1.91834 | ||||||||
\(921\) | −31.1364 | −1.02598 | ||||||||
\(922\) | 44.5186 | 1.46614 | ||||||||
\(923\) | −0.128553 | −0.00423138 | ||||||||
\(924\) | 135.891 | 4.47048 | ||||||||
\(925\) | 7.78922 | 0.256108 | ||||||||
\(926\) | 50.4518 | 1.65795 | ||||||||
\(927\) | −38.5837 | −1.26726 | ||||||||
\(928\) | 26.5044 | 0.870050 | ||||||||
\(929\) | 52.3846 | 1.71868 | 0.859341 | − | 0.511403i | \(-0.170874\pi\) | ||||
0.859341 | + | 0.511403i | \(0.170874\pi\) | |||||||
\(930\) | −75.5010 | −2.47578 | ||||||||
\(931\) | 15.2376 | 0.499394 | ||||||||
\(932\) | −23.9570 | −0.784737 | ||||||||
\(933\) | 11.3846 | 0.372715 | ||||||||
\(934\) | 18.2168 | 0.596072 | ||||||||
\(935\) | −1.24332 | −0.0406610 | ||||||||
\(936\) | −7.97481 | −0.260665 | ||||||||
\(937\) | −1.92038 | −0.0627360 | −0.0313680 | − | 0.999508i | \(-0.509986\pi\) | ||||
−0.0313680 | + | 0.999508i | \(0.509986\pi\) | |||||||
\(938\) | 30.3319 | 0.990371 | ||||||||
\(939\) | 6.16833 | 0.201296 | ||||||||
\(940\) | 28.6855 | 0.935616 | ||||||||
\(941\) | 24.0292 | 0.783329 | 0.391665 | − | 0.920108i | \(-0.371899\pi\) | ||||
0.391665 | + | 0.920108i | \(0.371899\pi\) | |||||||
\(942\) | −80.9328 | −2.63693 | ||||||||
\(943\) | −32.6258 | −1.06244 | ||||||||
\(944\) | −13.6165 | −0.443179 | ||||||||
\(945\) | 19.1711 | 0.623635 | ||||||||
\(946\) | −80.2386 | −2.60878 | ||||||||
\(947\) | −12.1843 | −0.395937 | −0.197969 | − | 0.980208i | \(-0.563434\pi\) | ||||
−0.197969 | + | 0.980208i | \(0.563434\pi\) | |||||||
\(948\) | −36.6301 | −1.18969 | ||||||||
\(949\) | −4.52614 | −0.146925 | ||||||||
\(950\) | −8.61017 | −0.279351 | ||||||||
\(951\) | −64.2181 | −2.08242 | ||||||||
\(952\) | 1.45152 | 0.0470440 | ||||||||
\(953\) | −42.0618 | −1.36252 | −0.681258 | − | 0.732043i | \(-0.738567\pi\) | ||||
−0.681258 | + | 0.732043i | \(0.738567\pi\) | |||||||
\(954\) | 20.0134 | 0.647957 | ||||||||
\(955\) | −49.8138 | −1.61194 | ||||||||
\(956\) | −24.5533 | −0.794111 | ||||||||
\(957\) | −93.8256 | −3.03295 | ||||||||
\(958\) | 11.5002 | 0.371555 | ||||||||
\(959\) | 54.2734 | 1.75258 | ||||||||
\(960\) | −62.9560 | −2.03189 | ||||||||
\(961\) | 1.04052 | 0.0335651 | ||||||||
\(962\) | −14.7054 | −0.474123 | ||||||||
\(963\) | 36.1190 | 1.16392 | ||||||||
\(964\) | −10.9604 | −0.353011 | ||||||||
\(965\) | −43.7892 | −1.40962 | ||||||||
\(966\) | −110.446 | −3.55355 | ||||||||
\(967\) | −16.3981 | −0.527326 | −0.263663 | − | 0.964615i | \(-0.584931\pi\) | ||||
−0.263663 | + | 0.964615i | \(0.584931\pi\) | |||||||
\(968\) | −44.6982 | −1.43665 | ||||||||
\(969\) | 0.677249 | 0.0217564 | ||||||||
\(970\) | −5.53352 | −0.177671 | ||||||||
\(971\) | −50.5242 | −1.62140 | −0.810700 | − | 0.585462i | \(-0.800913\pi\) | ||||
−0.810700 | + | 0.585462i | \(0.800913\pi\) | |||||||
\(972\) | −65.9716 | −2.11604 | ||||||||
\(973\) | −20.3110 | −0.651141 | ||||||||
\(974\) | 88.8774 | 2.84782 | ||||||||
\(975\) | 2.82386 | 0.0904359 | ||||||||
\(976\) | −22.0933 | −0.707189 | ||||||||
\(977\) | −23.4779 | −0.751124 | −0.375562 | − | 0.926797i | \(-0.622550\pi\) | ||||
−0.375562 | + | 0.926797i | \(0.622550\pi\) | |||||||
\(978\) | 15.1391 | 0.484096 | ||||||||
\(979\) | 13.7489 | 0.439417 | ||||||||
\(980\) | 48.4884 | 1.54890 | ||||||||
\(981\) | 13.0858 | 0.417798 | ||||||||
\(982\) | 48.6777 | 1.55337 | ||||||||
\(983\) | 8.70841 | 0.277755 | 0.138878 | − | 0.990310i | \(-0.455651\pi\) | ||||
0.138878 | + | 0.990310i | \(0.455651\pi\) | |||||||
\(984\) | −48.7531 | −1.55419 | ||||||||
\(985\) | 56.8637 | 1.81183 | ||||||||
\(986\) | −2.21287 | −0.0704721 | ||||||||
\(987\) | −24.6600 | −0.784937 | ||||||||
\(988\) | 10.5069 | 0.334270 | ||||||||
\(989\) | 42.1527 | 1.34038 | ||||||||
\(990\) | 56.9771 | 1.81085 | ||||||||
\(991\) | −23.9640 | −0.761241 | −0.380620 | − | 0.924731i | \(-0.624290\pi\) | ||||
−0.380620 | + | 0.924731i | \(0.624290\pi\) | |||||||
\(992\) | 16.9472 | 0.538073 | ||||||||
\(993\) | −55.9862 | −1.77667 | ||||||||
\(994\) | −1.07227 | −0.0340102 | ||||||||
\(995\) | −44.2149 | −1.40171 | ||||||||
\(996\) | 75.4799 | 2.39167 | ||||||||
\(997\) | −44.3697 | −1.40520 | −0.702602 | − | 0.711583i | \(-0.747978\pi\) | ||||
−0.702602 | + | 0.711583i | \(0.747978\pi\) | |||||||
\(998\) | 53.6214 | 1.69735 | ||||||||
\(999\) | −13.5092 | −0.427412 |
(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 | 8021.2.a.a.1.12 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.a.1.12 | ✓ | 134 | 1.1 | even | 1 | trivial |