Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70672 | −1.91394 | −0.956971 | − | 0.290184i | \(-0.906283\pi\) | ||||
−0.956971 | + | 0.290184i | \(0.906283\pi\) | |||||||
\(3\) | −0.0191468 | −0.0110544 | −0.00552720 | − | 0.999985i | \(-0.501759\pi\) | ||||
−0.00552720 | + | 0.999985i | \(0.501759\pi\) | |||||||
\(4\) | 5.32634 | 2.66317 | ||||||||
\(5\) | 0.870977 | 0.389513 | 0.194756 | − | 0.980852i | \(-0.437608\pi\) | ||||
0.194756 | + | 0.980852i | \(0.437608\pi\) | |||||||
\(6\) | 0.0518250 | 0.0211575 | ||||||||
\(7\) | −3.03945 | −1.14880 | −0.574401 | − | 0.818574i | \(-0.694765\pi\) | ||||
−0.574401 | + | 0.818574i | \(0.694765\pi\) | |||||||
\(8\) | −9.00349 | −3.18321 | ||||||||
\(9\) | −2.99963 | −0.999878 | ||||||||
\(10\) | −2.35749 | −0.745504 | ||||||||
\(11\) | −3.59310 | −1.08336 | −0.541681 | − | 0.840584i | \(-0.682212\pi\) | ||||
−0.541681 | + | 0.840584i | \(0.682212\pi\) | |||||||
\(12\) | −0.101982 | −0.0294398 | ||||||||
\(13\) | −5.77445 | −1.60154 | −0.800772 | − | 0.598970i | \(-0.795577\pi\) | ||||
−0.800772 | + | 0.598970i | \(0.795577\pi\) | |||||||
\(14\) | 8.22694 | 2.19874 | ||||||||
\(15\) | −0.0166764 | −0.00430583 | ||||||||
\(16\) | 13.7173 | 3.42931 | ||||||||
\(17\) | −3.74142 | −0.907429 | −0.453714 | − | 0.891147i | \(-0.649901\pi\) | ||||
−0.453714 | + | 0.891147i | \(0.649901\pi\) | |||||||
\(18\) | 8.11917 | 1.91371 | ||||||||
\(19\) | 6.69279 | 1.53543 | 0.767715 | − | 0.640791i | \(-0.221394\pi\) | ||||
0.767715 | + | 0.640791i | \(0.221394\pi\) | |||||||
\(20\) | 4.63912 | 1.03734 | ||||||||
\(21\) | 0.0581956 | 0.0126993 | ||||||||
\(22\) | 9.72554 | 2.07349 | ||||||||
\(23\) | 5.05288 | 1.05360 | 0.526799 | − | 0.849990i | \(-0.323392\pi\) | ||||
0.526799 | + | 0.849990i | \(0.323392\pi\) | |||||||
\(24\) | 0.172388 | 0.0351885 | ||||||||
\(25\) | −4.24140 | −0.848280 | ||||||||
\(26\) | 15.6298 | 3.06526 | ||||||||
\(27\) | 0.114874 | 0.0221074 | ||||||||
\(28\) | −16.1891 | −3.05946 | ||||||||
\(29\) | 5.40420 | 1.00353 | 0.501767 | − | 0.865003i | \(-0.332683\pi\) | ||||
0.501767 | + | 0.865003i | \(0.332683\pi\) | |||||||
\(30\) | 0.0451384 | 0.00824110 | ||||||||
\(31\) | 1.79712 | 0.322773 | 0.161386 | − | 0.986891i | \(-0.448403\pi\) | ||||
0.161386 | + | 0.986891i | \(0.448403\pi\) | |||||||
\(32\) | −19.1218 | −3.38029 | ||||||||
\(33\) | 0.0687964 | 0.0119759 | ||||||||
\(34\) | 10.1270 | 1.73677 | ||||||||
\(35\) | −2.64729 | −0.447473 | ||||||||
\(36\) | −15.9771 | −2.66285 | ||||||||
\(37\) | 5.63669 | 0.926666 | 0.463333 | − | 0.886184i | \(-0.346653\pi\) | ||||
0.463333 | + | 0.886184i | \(0.346653\pi\) | |||||||
\(38\) | −18.1155 | −2.93872 | ||||||||
\(39\) | 0.110562 | 0.0177041 | ||||||||
\(40\) | −7.84183 | −1.23990 | ||||||||
\(41\) | 2.08926 | 0.326288 | 0.163144 | − | 0.986602i | \(-0.447836\pi\) | ||||
0.163144 | + | 0.986602i | \(0.447836\pi\) | |||||||
\(42\) | −0.157519 | −0.0243057 | ||||||||
\(43\) | −3.83798 | −0.585286 | −0.292643 | − | 0.956222i | \(-0.594535\pi\) | ||||
−0.292643 | + | 0.956222i | \(0.594535\pi\) | |||||||
\(44\) | −19.1381 | −2.88518 | ||||||||
\(45\) | −2.61261 | −0.389465 | ||||||||
\(46\) | −13.6767 | −2.01653 | ||||||||
\(47\) | −2.15769 | −0.314731 | −0.157365 | − | 0.987540i | \(-0.550300\pi\) | ||||
−0.157365 | + | 0.987540i | \(0.550300\pi\) | |||||||
\(48\) | −0.262641 | −0.0379090 | ||||||||
\(49\) | 2.23823 | 0.319747 | ||||||||
\(50\) | 11.4803 | 1.62356 | ||||||||
\(51\) | 0.0716362 | 0.0100311 | ||||||||
\(52\) | −30.7567 | −4.26519 | ||||||||
\(53\) | 7.27647 | 0.999500 | 0.499750 | − | 0.866170i | \(-0.333425\pi\) | ||||
0.499750 | + | 0.866170i | \(0.333425\pi\) | |||||||
\(54\) | −0.310931 | −0.0423123 | ||||||||
\(55\) | −3.12951 | −0.421983 | ||||||||
\(56\) | 27.3656 | 3.65688 | ||||||||
\(57\) | −0.128145 | −0.0169732 | ||||||||
\(58\) | −14.6277 | −1.92071 | ||||||||
\(59\) | 2.34252 | 0.304971 | 0.152485 | − | 0.988306i | \(-0.451272\pi\) | ||||
0.152485 | + | 0.988306i | \(0.451272\pi\) | |||||||
\(60\) | −0.0888242 | −0.0114672 | ||||||||
\(61\) | 4.67760 | 0.598905 | 0.299453 | − | 0.954111i | \(-0.403196\pi\) | ||||
0.299453 | + | 0.954111i | \(0.403196\pi\) | |||||||
\(62\) | −4.86431 | −0.617769 | ||||||||
\(63\) | 9.11722 | 1.14866 | ||||||||
\(64\) | 24.3229 | 3.04037 | ||||||||
\(65\) | −5.02941 | −0.623821 | ||||||||
\(66\) | −0.186213 | −0.0229212 | ||||||||
\(67\) | 10.3912 | 1.26949 | 0.634744 | − | 0.772722i | \(-0.281105\pi\) | ||||
0.634744 | + | 0.772722i | \(0.281105\pi\) | |||||||
\(68\) | −19.9281 | −2.41664 | ||||||||
\(69\) | −0.0967464 | −0.0116469 | ||||||||
\(70\) | 7.16547 | 0.856437 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | 27.0072 | 3.18283 | ||||||||
\(73\) | 14.0439 | 1.64371 | 0.821857 | − | 0.569695i | \(-0.192938\pi\) | ||||
0.821857 | + | 0.569695i | \(0.192938\pi\) | |||||||
\(74\) | −15.2570 | −1.77358 | ||||||||
\(75\) | 0.0812091 | 0.00937722 | ||||||||
\(76\) | 35.6481 | 4.08912 | ||||||||
\(77\) | 10.9210 | 1.24457 | ||||||||
\(78\) | −0.299261 | −0.0338846 | ||||||||
\(79\) | −1.41032 | −0.158674 | −0.0793368 | − | 0.996848i | \(-0.525280\pi\) | ||||
−0.0793368 | + | 0.996848i | \(0.525280\pi\) | |||||||
\(80\) | 11.9474 | 1.33576 | ||||||||
\(81\) | 8.99670 | 0.999633 | ||||||||
\(82\) | −5.65506 | −0.624496 | ||||||||
\(83\) | −13.1146 | −1.43951 | −0.719756 | − | 0.694227i | \(-0.755746\pi\) | ||||
−0.719756 | + | 0.694227i | \(0.755746\pi\) | |||||||
\(84\) | 0.309970 | 0.0338205 | ||||||||
\(85\) | −3.25869 | −0.353455 | ||||||||
\(86\) | 10.3883 | 1.12020 | ||||||||
\(87\) | −0.103473 | −0.0110935 | ||||||||
\(88\) | 32.3505 | 3.44857 | ||||||||
\(89\) | 10.5583 | 1.11918 | 0.559591 | − | 0.828769i | \(-0.310958\pi\) | ||||
0.559591 | + | 0.828769i | \(0.310958\pi\) | |||||||
\(90\) | 7.07161 | 0.745413 | ||||||||
\(91\) | 17.5511 | 1.83986 | ||||||||
\(92\) | 26.9134 | 2.80591 | ||||||||
\(93\) | −0.0344091 | −0.00356806 | ||||||||
\(94\) | 5.84026 | 0.602376 | ||||||||
\(95\) | 5.82926 | 0.598069 | ||||||||
\(96\) | 0.366121 | 0.0373671 | ||||||||
\(97\) | 2.32124 | 0.235686 | 0.117843 | − | 0.993032i | \(-0.462402\pi\) | ||||
0.117843 | + | 0.993032i | \(0.462402\pi\) | |||||||
\(98\) | −6.05827 | −0.611978 | ||||||||
\(99\) | 10.7780 | 1.08323 | ||||||||
\(100\) | −22.5912 | −2.25912 | ||||||||
\(101\) | 9.13572 | 0.909038 | 0.454519 | − | 0.890737i | \(-0.349811\pi\) | ||||
0.454519 | + | 0.890737i | \(0.349811\pi\) | |||||||
\(102\) | −0.193899 | −0.0191989 | ||||||||
\(103\) | −7.50397 | −0.739388 | −0.369694 | − | 0.929154i | \(-0.620538\pi\) | ||||
−0.369694 | + | 0.929154i | \(0.620538\pi\) | |||||||
\(104\) | 51.9902 | 5.09806 | ||||||||
\(105\) | 0.0506870 | 0.00494654 | ||||||||
\(106\) | −19.6954 | −1.91299 | ||||||||
\(107\) | −1.76571 | −0.170698 | −0.0853489 | − | 0.996351i | \(-0.527200\pi\) | ||||
−0.0853489 | + | 0.996351i | \(0.527200\pi\) | |||||||
\(108\) | 0.611856 | 0.0588759 | ||||||||
\(109\) | 7.18422 | 0.688124 | 0.344062 | − | 0.938947i | \(-0.388197\pi\) | ||||
0.344062 | + | 0.938947i | \(0.388197\pi\) | |||||||
\(110\) | 8.47072 | 0.807651 | ||||||||
\(111\) | −0.107924 | −0.0102437 | ||||||||
\(112\) | −41.6929 | −3.93961 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | 0.346854 | 0.0324858 | ||||||||
\(115\) | 4.40094 | 0.410390 | ||||||||
\(116\) | 28.7846 | 2.67258 | ||||||||
\(117\) | 17.3212 | 1.60135 | ||||||||
\(118\) | −6.34056 | −0.583696 | ||||||||
\(119\) | 11.3719 | 1.04246 | ||||||||
\(120\) | 0.150146 | 0.0137064 | ||||||||
\(121\) | 1.91040 | 0.173673 | ||||||||
\(122\) | −12.6610 | −1.14627 | ||||||||
\(123\) | −0.0400026 | −0.00360692 | ||||||||
\(124\) | 9.57210 | 0.859600 | ||||||||
\(125\) | −8.04904 | −0.719928 | ||||||||
\(126\) | −24.6778 | −2.19847 | ||||||||
\(127\) | 1.86070 | 0.165111 | 0.0825554 | − | 0.996586i | \(-0.473692\pi\) | ||||
0.0825554 | + | 0.996586i | \(0.473692\pi\) | |||||||
\(128\) | −27.5918 | −2.43879 | ||||||||
\(129\) | 0.0734849 | 0.00646998 | ||||||||
\(130\) | 13.6132 | 1.19396 | ||||||||
\(131\) | −15.5210 | −1.35607 | −0.678037 | − | 0.735028i | \(-0.737169\pi\) | ||||
−0.678037 | + | 0.735028i | \(0.737169\pi\) | |||||||
\(132\) | 0.366433 | 0.0318939 | ||||||||
\(133\) | −20.3424 | −1.76391 | ||||||||
\(134\) | −28.1261 | −2.42973 | ||||||||
\(135\) | 0.100052 | 0.00861113 | ||||||||
\(136\) | 33.6859 | 2.88854 | ||||||||
\(137\) | −21.4363 | −1.83142 | −0.915712 | − | 0.401836i | \(-0.868372\pi\) | ||||
−0.915712 | + | 0.401836i | \(0.868372\pi\) | |||||||
\(138\) | 0.261866 | 0.0222915 | ||||||||
\(139\) | 6.68471 | 0.566990 | 0.283495 | − | 0.958974i | \(-0.408506\pi\) | ||||
0.283495 | + | 0.958974i | \(0.408506\pi\) | |||||||
\(140\) | −14.1004 | −1.19170 | ||||||||
\(141\) | 0.0413127 | 0.00347916 | ||||||||
\(142\) | 2.70672 | 0.227143 | ||||||||
\(143\) | 20.7482 | 1.73505 | ||||||||
\(144\) | −41.1467 | −3.42890 | ||||||||
\(145\) | 4.70693 | 0.390889 | ||||||||
\(146\) | −38.0129 | −3.14597 | ||||||||
\(147\) | −0.0428549 | −0.00353461 | ||||||||
\(148\) | 30.0230 | 2.46787 | ||||||||
\(149\) | −15.0295 | −1.23126 | −0.615630 | − | 0.788035i | \(-0.711099\pi\) | ||||
−0.615630 | + | 0.788035i | \(0.711099\pi\) | |||||||
\(150\) | −0.219810 | −0.0179474 | ||||||||
\(151\) | 21.4359 | 1.74443 | 0.872213 | − | 0.489126i | \(-0.162684\pi\) | ||||
0.872213 | + | 0.489126i | \(0.162684\pi\) | |||||||
\(152\) | −60.2584 | −4.88760 | ||||||||
\(153\) | 11.2229 | 0.907318 | ||||||||
\(154\) | −29.5602 | −2.38203 | ||||||||
\(155\) | 1.56525 | 0.125724 | ||||||||
\(156\) | 0.588891 | 0.0471490 | ||||||||
\(157\) | −24.1743 | −1.92932 | −0.964659 | − | 0.263500i | \(-0.915123\pi\) | ||||
−0.964659 | + | 0.263500i | \(0.915123\pi\) | |||||||
\(158\) | 3.81735 | 0.303692 | ||||||||
\(159\) | −0.139321 | −0.0110489 | ||||||||
\(160\) | −16.6547 | −1.31667 | ||||||||
\(161\) | −15.3580 | −1.21038 | ||||||||
\(162\) | −24.3516 | −1.91324 | ||||||||
\(163\) | 22.4650 | 1.75960 | 0.879799 | − | 0.475346i | \(-0.157677\pi\) | ||||
0.879799 | + | 0.475346i | \(0.157677\pi\) | |||||||
\(164\) | 11.1281 | 0.868962 | ||||||||
\(165\) | 0.0599200 | 0.00466477 | ||||||||
\(166\) | 35.4975 | 2.75514 | ||||||||
\(167\) | −22.1461 | −1.71372 | −0.856860 | − | 0.515550i | \(-0.827588\pi\) | ||||
−0.856860 | + | 0.515550i | \(0.827588\pi\) | |||||||
\(168\) | −0.523963 | −0.0404246 | ||||||||
\(169\) | 20.3442 | 1.56494 | ||||||||
\(170\) | 8.82038 | 0.676492 | ||||||||
\(171\) | −20.0759 | −1.53524 | ||||||||
\(172\) | −20.4424 | −1.55872 | ||||||||
\(173\) | 17.4539 | 1.32699 | 0.663497 | − | 0.748179i | \(-0.269071\pi\) | ||||
0.663497 | + | 0.748179i | \(0.269071\pi\) | |||||||
\(174\) | 0.280072 | 0.0212322 | ||||||||
\(175\) | 12.8915 | 0.974506 | ||||||||
\(176\) | −49.2875 | −3.71519 | ||||||||
\(177\) | −0.0448518 | −0.00337126 | ||||||||
\(178\) | −28.5785 | −2.14205 | ||||||||
\(179\) | 9.11157 | 0.681031 | 0.340515 | − | 0.940239i | \(-0.389398\pi\) | ||||
0.340515 | + | 0.940239i | \(0.389398\pi\) | |||||||
\(180\) | −13.9157 | −1.03721 | ||||||||
\(181\) | −3.03403 | −0.225518 | −0.112759 | − | 0.993622i | \(-0.535969\pi\) | ||||
−0.112759 | + | 0.993622i | \(0.535969\pi\) | |||||||
\(182\) | −47.5060 | −3.52138 | ||||||||
\(183\) | −0.0895609 | −0.00662053 | ||||||||
\(184\) | −45.4936 | −3.35383 | ||||||||
\(185\) | 4.90943 | 0.360948 | ||||||||
\(186\) | 0.0931359 | 0.00682906 | ||||||||
\(187\) | 13.4433 | 0.983074 | ||||||||
\(188\) | −11.4926 | −0.838182 | ||||||||
\(189\) | −0.349152 | −0.0253971 | ||||||||
\(190\) | −15.7782 | −1.14467 | ||||||||
\(191\) | −9.51203 | −0.688266 | −0.344133 | − | 0.938921i | \(-0.611827\pi\) | ||||
−0.344133 | + | 0.938921i | \(0.611827\pi\) | |||||||
\(192\) | −0.465706 | −0.0336094 | ||||||||
\(193\) | 9.10434 | 0.655345 | 0.327672 | − | 0.944791i | \(-0.393736\pi\) | ||||
0.327672 | + | 0.944791i | \(0.393736\pi\) | |||||||
\(194\) | −6.28294 | −0.451089 | ||||||||
\(195\) | 0.0962969 | 0.00689597 | ||||||||
\(196\) | 11.9216 | 0.851542 | ||||||||
\(197\) | 9.99320 | 0.711986 | 0.355993 | − | 0.934489i | \(-0.384143\pi\) | ||||
0.355993 | + | 0.934489i | \(0.384143\pi\) | |||||||
\(198\) | −29.1730 | −2.07324 | ||||||||
\(199\) | 10.7795 | 0.764136 | 0.382068 | − | 0.924134i | \(-0.375212\pi\) | ||||
0.382068 | + | 0.924134i | \(0.375212\pi\) | |||||||
\(200\) | 38.1874 | 2.70026 | ||||||||
\(201\) | −0.198958 | −0.0140334 | ||||||||
\(202\) | −24.7278 | −1.73985 | ||||||||
\(203\) | −16.4258 | −1.15286 | ||||||||
\(204\) | 0.381559 | 0.0267145 | ||||||||
\(205\) | 1.81970 | 0.127093 | ||||||||
\(206\) | 20.3112 | 1.41515 | ||||||||
\(207\) | −15.1568 | −1.05347 | ||||||||
\(208\) | −79.2096 | −5.49219 | ||||||||
\(209\) | −24.0479 | −1.66343 | ||||||||
\(210\) | −0.137196 | −0.00946740 | ||||||||
\(211\) | −17.0183 | −1.17159 | −0.585795 | − | 0.810459i | \(-0.699218\pi\) | ||||
−0.585795 | + | 0.810459i | \(0.699218\pi\) | |||||||
\(212\) | 38.7570 | 2.66184 | ||||||||
\(213\) | 0.0191468 | 0.00131192 | ||||||||
\(214\) | 4.77929 | 0.326706 | ||||||||
\(215\) | −3.34279 | −0.227976 | ||||||||
\(216\) | −1.03426 | −0.0703727 | ||||||||
\(217\) | −5.46226 | −0.370802 | ||||||||
\(218\) | −19.4457 | −1.31703 | ||||||||
\(219\) | −0.268895 | −0.0181703 | ||||||||
\(220\) | −16.6689 | −1.12381 | ||||||||
\(221\) | 21.6047 | 1.45329 | ||||||||
\(222\) | 0.292121 | 0.0196059 | ||||||||
\(223\) | −10.1801 | −0.681708 | −0.340854 | − | 0.940116i | \(-0.610716\pi\) | ||||
−0.340854 | + | 0.940116i | \(0.610716\pi\) | |||||||
\(224\) | 58.1197 | 3.88329 | ||||||||
\(225\) | 12.7226 | 0.848176 | ||||||||
\(226\) | 2.70672 | 0.180048 | ||||||||
\(227\) | −3.70955 | −0.246211 | −0.123106 | − | 0.992394i | \(-0.539285\pi\) | ||||
−0.123106 | + | 0.992394i | \(0.539285\pi\) | |||||||
\(228\) | −0.682546 | −0.0452027 | ||||||||
\(229\) | 2.73934 | 0.181020 | 0.0905102 | − | 0.995896i | \(-0.471150\pi\) | ||||
0.0905102 | + | 0.995896i | \(0.471150\pi\) | |||||||
\(230\) | −11.9121 | −0.785462 | ||||||||
\(231\) | −0.209103 | −0.0137580 | ||||||||
\(232\) | −48.6566 | −3.19446 | ||||||||
\(233\) | −17.8643 | −1.17033 | −0.585165 | − | 0.810915i | \(-0.698970\pi\) | ||||
−0.585165 | + | 0.810915i | \(0.698970\pi\) | |||||||
\(234\) | −46.8837 | −3.06489 | ||||||||
\(235\) | −1.87929 | −0.122592 | ||||||||
\(236\) | 12.4771 | 0.812189 | ||||||||
\(237\) | 0.0270031 | 0.00175404 | ||||||||
\(238\) | −30.7805 | −1.99520 | ||||||||
\(239\) | −13.1300 | −0.849310 | −0.424655 | − | 0.905355i | \(-0.639605\pi\) | ||||
−0.424655 | + | 0.905355i | \(0.639605\pi\) | |||||||
\(240\) | −0.228754 | −0.0147660 | ||||||||
\(241\) | −7.96526 | −0.513088 | −0.256544 | − | 0.966533i | \(-0.582584\pi\) | ||||
−0.256544 | + | 0.966533i | \(0.582584\pi\) | |||||||
\(242\) | −5.17093 | −0.332400 | ||||||||
\(243\) | −0.516879 | −0.0331578 | ||||||||
\(244\) | 24.9145 | 1.59499 | ||||||||
\(245\) | 1.94945 | 0.124546 | ||||||||
\(246\) | 0.108276 | 0.00690343 | ||||||||
\(247\) | −38.6471 | −2.45906 | ||||||||
\(248\) | −16.1804 | −1.02746 | ||||||||
\(249\) | 0.251102 | 0.0159129 | ||||||||
\(250\) | 21.7865 | 1.37790 | ||||||||
\(251\) | −5.49554 | −0.346875 | −0.173438 | − | 0.984845i | \(-0.555488\pi\) | ||||
−0.173438 | + | 0.984845i | \(0.555488\pi\) | |||||||
\(252\) | 48.5615 | 3.05909 | ||||||||
\(253\) | −18.1555 | −1.14143 | ||||||||
\(254\) | −5.03641 | −0.316012 | ||||||||
\(255\) | 0.0623935 | 0.00390723 | ||||||||
\(256\) | 26.0375 | 1.62734 | ||||||||
\(257\) | −10.6605 | −0.664983 | −0.332491 | − | 0.943106i | \(-0.607889\pi\) | ||||
−0.332491 | + | 0.943106i | \(0.607889\pi\) | |||||||
\(258\) | −0.198903 | −0.0123832 | ||||||||
\(259\) | −17.1324 | −1.06456 | ||||||||
\(260\) | −26.7884 | −1.66134 | ||||||||
\(261\) | −16.2106 | −1.00341 | ||||||||
\(262\) | 42.0110 | 2.59545 | ||||||||
\(263\) | 15.3488 | 0.946445 | 0.473222 | − | 0.880943i | \(-0.343091\pi\) | ||||
0.473222 | + | 0.880943i | \(0.343091\pi\) | |||||||
\(264\) | −0.619407 | −0.0381219 | ||||||||
\(265\) | 6.33764 | 0.389318 | ||||||||
\(266\) | 55.0611 | 3.37601 | ||||||||
\(267\) | −0.202158 | −0.0123719 | ||||||||
\(268\) | 55.3472 | 3.38087 | ||||||||
\(269\) | −9.48596 | −0.578369 | −0.289185 | − | 0.957273i | \(-0.593384\pi\) | ||||
−0.289185 | + | 0.957273i | \(0.593384\pi\) | |||||||
\(270\) | −0.270814 | −0.0164812 | ||||||||
\(271\) | −15.6593 | −0.951234 | −0.475617 | − | 0.879653i | \(-0.657775\pi\) | ||||
−0.475617 | + | 0.879653i | \(0.657775\pi\) | |||||||
\(272\) | −51.3221 | −3.11186 | ||||||||
\(273\) | −0.336047 | −0.0203385 | ||||||||
\(274\) | 58.0220 | 3.50524 | ||||||||
\(275\) | 15.2398 | 0.918994 | ||||||||
\(276\) | −0.515304 | −0.0310177 | ||||||||
\(277\) | −26.7052 | −1.60456 | −0.802281 | − | 0.596946i | \(-0.796381\pi\) | ||||
−0.802281 | + | 0.596946i | \(0.796381\pi\) | |||||||
\(278\) | −18.0936 | −1.08518 | ||||||||
\(279\) | −5.39071 | −0.322733 | ||||||||
\(280\) | 23.8348 | 1.42440 | ||||||||
\(281\) | 1.82146 | 0.108659 | 0.0543297 | − | 0.998523i | \(-0.482698\pi\) | ||||
0.0543297 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(282\) | −0.111822 | −0.00665890 | ||||||||
\(283\) | −3.03336 | −0.180314 | −0.0901571 | − | 0.995928i | \(-0.528737\pi\) | ||||
−0.0901571 | + | 0.995928i | \(0.528737\pi\) | |||||||
\(284\) | −5.32634 | −0.316060 | ||||||||
\(285\) | −0.111612 | −0.00661130 | ||||||||
\(286\) | −56.1596 | −3.32079 | ||||||||
\(287\) | −6.35020 | −0.374841 | ||||||||
\(288\) | 57.3585 | 3.37988 | ||||||||
\(289\) | −3.00175 | −0.176573 | ||||||||
\(290\) | −12.7403 | −0.748139 | ||||||||
\(291\) | −0.0444442 | −0.00260536 | ||||||||
\(292\) | 74.8026 | 4.37749 | ||||||||
\(293\) | −27.5871 | −1.61166 | −0.805828 | − | 0.592150i | \(-0.798279\pi\) | ||||
−0.805828 | + | 0.592150i | \(0.798279\pi\) | |||||||
\(294\) | 0.115996 | 0.00676504 | ||||||||
\(295\) | 2.04028 | 0.118790 | ||||||||
\(296\) | −50.7499 | −2.94978 | ||||||||
\(297\) | −0.412753 | −0.0239504 | ||||||||
\(298\) | 40.6806 | 2.35656 | ||||||||
\(299\) | −29.1776 | −1.68738 | ||||||||
\(300\) | 0.432548 | 0.0249732 | ||||||||
\(301\) | 11.6653 | 0.672378 | ||||||||
\(302\) | −58.0209 | −3.33873 | ||||||||
\(303\) | −0.174919 | −0.0100489 | ||||||||
\(304\) | 91.8067 | 5.26547 | ||||||||
\(305\) | 4.07408 | 0.233281 | ||||||||
\(306\) | −30.3773 | −1.73655 | ||||||||
\(307\) | −8.28799 | −0.473021 | −0.236510 | − | 0.971629i | \(-0.576004\pi\) | ||||
−0.236510 | + | 0.971629i | \(0.576004\pi\) | |||||||
\(308\) | 58.1693 | 3.31450 | ||||||||
\(309\) | 0.143677 | 0.00817349 | ||||||||
\(310\) | −4.23670 | −0.240629 | ||||||||
\(311\) | 20.7945 | 1.17915 | 0.589575 | − | 0.807714i | \(-0.299295\pi\) | ||||
0.589575 | + | 0.807714i | \(0.299295\pi\) | |||||||
\(312\) | −0.995444 | −0.0563559 | ||||||||
\(313\) | 1.21920 | 0.0689135 | 0.0344568 | − | 0.999406i | \(-0.489030\pi\) | ||||
0.0344568 | + | 0.999406i | \(0.489030\pi\) | |||||||
\(314\) | 65.4331 | 3.69260 | ||||||||
\(315\) | 7.94089 | 0.447418 | ||||||||
\(316\) | −7.51186 | −0.422575 | ||||||||
\(317\) | −11.2070 | −0.629450 | −0.314725 | − | 0.949183i | \(-0.601912\pi\) | ||||
−0.314725 | + | 0.949183i | \(0.601912\pi\) | |||||||
\(318\) | 0.377103 | 0.0211469 | ||||||||
\(319\) | −19.4178 | −1.08719 | ||||||||
\(320\) | 21.1847 | 1.18426 | ||||||||
\(321\) | 0.0338077 | 0.00188696 | ||||||||
\(322\) | 41.5697 | 2.31659 | ||||||||
\(323\) | −25.0405 | −1.39329 | ||||||||
\(324\) | 47.9195 | 2.66220 | ||||||||
\(325\) | 24.4917 | 1.35856 | ||||||||
\(326\) | −60.8066 | −3.36777 | ||||||||
\(327\) | −0.137555 | −0.00760679 | ||||||||
\(328\) | −18.8107 | −1.03865 | ||||||||
\(329\) | 6.55817 | 0.361564 | ||||||||
\(330\) | −0.162187 | −0.00892809 | ||||||||
\(331\) | 33.6414 | 1.84910 | 0.924549 | − | 0.381064i | \(-0.124442\pi\) | ||||
0.924549 | + | 0.381064i | \(0.124442\pi\) | |||||||
\(332\) | −69.8528 | −3.83367 | ||||||||
\(333\) | −16.9080 | −0.926553 | ||||||||
\(334\) | 59.9434 | 3.27996 | ||||||||
\(335\) | 9.05050 | 0.494482 | ||||||||
\(336\) | 0.798284 | 0.0435499 | ||||||||
\(337\) | 26.0447 | 1.41874 | 0.709371 | − | 0.704835i | \(-0.248979\pi\) | ||||
0.709371 | + | 0.704835i | \(0.248979\pi\) | |||||||
\(338\) | −55.0662 | −2.99520 | ||||||||
\(339\) | 0.0191468 | 0.00103991 | ||||||||
\(340\) | −17.3569 | −0.941311 | ||||||||
\(341\) | −6.45725 | −0.349680 | ||||||||
\(342\) | 54.3399 | 2.93836 | ||||||||
\(343\) | 14.4731 | 0.781476 | ||||||||
\(344\) | 34.5552 | 1.86309 | ||||||||
\(345\) | −0.0842638 | −0.00453661 | ||||||||
\(346\) | −47.2428 | −2.53979 | ||||||||
\(347\) | 12.9155 | 0.693342 | 0.346671 | − | 0.937987i | \(-0.387312\pi\) | ||||
0.346671 | + | 0.937987i | \(0.387312\pi\) | |||||||
\(348\) | −0.551132 | −0.0295438 | ||||||||
\(349\) | −1.80159 | −0.0964369 | −0.0482184 | − | 0.998837i | \(-0.515354\pi\) | ||||
−0.0482184 | + | 0.998837i | \(0.515354\pi\) | |||||||
\(350\) | −34.8937 | −1.86515 | ||||||||
\(351\) | −0.663331 | −0.0354060 | ||||||||
\(352\) | 68.7067 | 3.66208 | ||||||||
\(353\) | 22.1581 | 1.17936 | 0.589679 | − | 0.807637i | \(-0.299254\pi\) | ||||
0.589679 | + | 0.807637i | \(0.299254\pi\) | |||||||
\(354\) | 0.121401 | 0.00645240 | ||||||||
\(355\) | −0.870977 | −0.0462266 | ||||||||
\(356\) | 56.2374 | 2.98058 | ||||||||
\(357\) | −0.217734 | −0.0115237 | ||||||||
\(358\) | −24.6625 | −1.30345 | ||||||||
\(359\) | −19.8543 | −1.04787 | −0.523934 | − | 0.851759i | \(-0.675536\pi\) | ||||
−0.523934 | + | 0.851759i | \(0.675536\pi\) | |||||||
\(360\) | 23.5226 | 1.23975 | ||||||||
\(361\) | 25.7934 | 1.35755 | ||||||||
\(362\) | 8.21229 | 0.431628 | ||||||||
\(363\) | −0.0365780 | −0.00191985 | ||||||||
\(364\) | 93.4833 | 4.89986 | ||||||||
\(365\) | 12.2319 | 0.640247 | ||||||||
\(366\) | 0.242416 | 0.0126713 | ||||||||
\(367\) | 6.45293 | 0.336840 | 0.168420 | − | 0.985715i | \(-0.446133\pi\) | ||||
0.168420 | + | 0.985715i | \(0.446133\pi\) | |||||||
\(368\) | 69.3117 | 3.61312 | ||||||||
\(369\) | −6.26702 | −0.326248 | ||||||||
\(370\) | −13.2885 | −0.690834 | ||||||||
\(371\) | −22.1164 | −1.14823 | ||||||||
\(372\) | −0.183275 | −0.00950236 | ||||||||
\(373\) | −6.53623 | −0.338433 | −0.169217 | − | 0.985579i | \(-0.554124\pi\) | ||||
−0.169217 | + | 0.985579i | \(0.554124\pi\) | |||||||
\(374\) | −36.3874 | −1.88155 | ||||||||
\(375\) | 0.154113 | 0.00795837 | ||||||||
\(376\) | 19.4267 | 1.00186 | ||||||||
\(377\) | −31.2062 | −1.60720 | ||||||||
\(378\) | 0.945058 | 0.0486085 | ||||||||
\(379\) | −14.6164 | −0.750792 | −0.375396 | − | 0.926865i | \(-0.622493\pi\) | ||||
−0.375396 | + | 0.926865i | \(0.622493\pi\) | |||||||
\(380\) | 31.0486 | 1.59276 | ||||||||
\(381\) | −0.0356265 | −0.00182520 | ||||||||
\(382\) | 25.7464 | 1.31730 | ||||||||
\(383\) | −15.7867 | −0.806665 | −0.403332 | − | 0.915054i | \(-0.632148\pi\) | ||||
−0.403332 | + | 0.915054i | \(0.632148\pi\) | |||||||
\(384\) | 0.528294 | 0.0269594 | ||||||||
\(385\) | 9.51198 | 0.484775 | ||||||||
\(386\) | −24.6429 | −1.25429 | ||||||||
\(387\) | 11.5125 | 0.585215 | ||||||||
\(388\) | 12.3637 | 0.627672 | ||||||||
\(389\) | 8.20744 | 0.416133 | 0.208067 | − | 0.978115i | \(-0.433283\pi\) | ||||
0.208067 | + | 0.978115i | \(0.433283\pi\) | |||||||
\(390\) | −0.260649 | −0.0131985 | ||||||||
\(391\) | −18.9050 | −0.956066 | ||||||||
\(392\) | −20.1519 | −1.01782 | ||||||||
\(393\) | 0.297177 | 0.0149906 | ||||||||
\(394\) | −27.0488 | −1.36270 | ||||||||
\(395\) | −1.22836 | −0.0618053 | ||||||||
\(396\) | 57.4073 | 2.88483 | ||||||||
\(397\) | −8.43733 | −0.423457 | −0.211729 | − | 0.977328i | \(-0.567909\pi\) | ||||
−0.211729 | + | 0.977328i | \(0.567909\pi\) | |||||||
\(398\) | −29.1770 | −1.46251 | ||||||||
\(399\) | 0.389490 | 0.0194989 | ||||||||
\(400\) | −58.1804 | −2.90902 | ||||||||
\(401\) | −5.60049 | −0.279675 | −0.139838 | − | 0.990174i | \(-0.544658\pi\) | ||||
−0.139838 | + | 0.990174i | \(0.544658\pi\) | |||||||
\(402\) | 0.538524 | 0.0268592 | ||||||||
\(403\) | −10.3774 | −0.516935 | ||||||||
\(404\) | 48.6600 | 2.42092 | ||||||||
\(405\) | 7.83592 | 0.389370 | ||||||||
\(406\) | 44.4600 | 2.20651 | ||||||||
\(407\) | −20.2532 | −1.00391 | ||||||||
\(408\) | −0.644976 | −0.0319311 | ||||||||
\(409\) | −14.2337 | −0.703811 | −0.351905 | − | 0.936036i | \(-0.614466\pi\) | ||||
−0.351905 | + | 0.936036i | \(0.614466\pi\) | |||||||
\(410\) | −4.92542 | −0.243249 | ||||||||
\(411\) | 0.410435 | 0.0202453 | ||||||||
\(412\) | −39.9687 | −1.96912 | ||||||||
\(413\) | −7.11997 | −0.350351 | ||||||||
\(414\) | 41.0252 | 2.01628 | ||||||||
\(415\) | −11.4225 | −0.560708 | ||||||||
\(416\) | 110.418 | 5.41368 | ||||||||
\(417\) | −0.127991 | −0.00626773 | ||||||||
\(418\) | 65.0909 | 3.18370 | ||||||||
\(419\) | 2.75702 | 0.134689 | 0.0673447 | − | 0.997730i | \(-0.478547\pi\) | ||||
0.0673447 | + | 0.997730i | \(0.478547\pi\) | |||||||
\(420\) | 0.269976 | 0.0131735 | ||||||||
\(421\) | 28.2291 | 1.37580 | 0.687900 | − | 0.725805i | \(-0.258533\pi\) | ||||
0.687900 | + | 0.725805i | \(0.258533\pi\) | |||||||
\(422\) | 46.0639 | 2.24236 | ||||||||
\(423\) | 6.47227 | 0.314692 | ||||||||
\(424\) | −65.5136 | −3.18162 | ||||||||
\(425\) | 15.8689 | 0.769753 | ||||||||
\(426\) | −0.0518250 | −0.00251093 | ||||||||
\(427\) | −14.2173 | −0.688024 | ||||||||
\(428\) | −9.40479 | −0.454598 | ||||||||
\(429\) | −0.397261 | −0.0191799 | ||||||||
\(430\) | 9.04800 | 0.436334 | ||||||||
\(431\) | −18.3722 | −0.884959 | −0.442480 | − | 0.896779i | \(-0.645901\pi\) | ||||
−0.442480 | + | 0.896779i | \(0.645901\pi\) | |||||||
\(432\) | 1.57575 | 0.0758133 | ||||||||
\(433\) | 25.1084 | 1.20663 | 0.603317 | − | 0.797501i | \(-0.293845\pi\) | ||||
0.603317 | + | 0.797501i | \(0.293845\pi\) | |||||||
\(434\) | 14.7848 | 0.709694 | ||||||||
\(435\) | −0.0901225 | −0.00432104 | ||||||||
\(436\) | 38.2657 | 1.83259 | ||||||||
\(437\) | 33.8179 | 1.61773 | ||||||||
\(438\) | 0.727824 | 0.0347768 | ||||||||
\(439\) | 5.85340 | 0.279367 | 0.139684 | − | 0.990196i | \(-0.455391\pi\) | ||||
0.139684 | + | 0.990196i | \(0.455391\pi\) | |||||||
\(440\) | 28.1765 | 1.34326 | ||||||||
\(441\) | −6.71387 | −0.319708 | ||||||||
\(442\) | −58.4778 | −2.78150 | ||||||||
\(443\) | 1.64491 | 0.0781519 | 0.0390760 | − | 0.999236i | \(-0.487559\pi\) | ||||
0.0390760 | + | 0.999236i | \(0.487559\pi\) | |||||||
\(444\) | −0.574843 | −0.0272808 | ||||||||
\(445\) | 9.19608 | 0.435936 | ||||||||
\(446\) | 27.5546 | 1.30475 | ||||||||
\(447\) | 0.287766 | 0.0136108 | ||||||||
\(448\) | −73.9283 | −3.49278 | ||||||||
\(449\) | 12.3635 | 0.583471 | 0.291735 | − | 0.956499i | \(-0.405767\pi\) | ||||
0.291735 | + | 0.956499i | \(0.405767\pi\) | |||||||
\(450\) | −34.4367 | −1.62336 | ||||||||
\(451\) | −7.50694 | −0.353488 | ||||||||
\(452\) | −5.32634 | −0.250530 | ||||||||
\(453\) | −0.410428 | −0.0192836 | ||||||||
\(454\) | 10.0407 | 0.471234 | ||||||||
\(455\) | 15.2866 | 0.716647 | ||||||||
\(456\) | 1.15375 | 0.0540295 | ||||||||
\(457\) | −25.4522 | −1.19060 | −0.595302 | − | 0.803502i | \(-0.702968\pi\) | ||||
−0.595302 | + | 0.803502i | \(0.702968\pi\) | |||||||
\(458\) | −7.41462 | −0.346462 | ||||||||
\(459\) | −0.429791 | −0.0200609 | ||||||||
\(460\) | 23.4409 | 1.09294 | ||||||||
\(461\) | −39.1010 | −1.82112 | −0.910559 | − | 0.413380i | \(-0.864348\pi\) | ||||
−0.910559 | + | 0.413380i | \(0.864348\pi\) | |||||||
\(462\) | 0.565983 | 0.0263319 | ||||||||
\(463\) | 10.6904 | 0.496827 | 0.248414 | − | 0.968654i | \(-0.420091\pi\) | ||||
0.248414 | + | 0.968654i | \(0.420091\pi\) | |||||||
\(464\) | 74.1307 | 3.44143 | ||||||||
\(465\) | −0.0299695 | −0.00138980 | ||||||||
\(466\) | 48.3537 | 2.23994 | ||||||||
\(467\) | −5.67525 | −0.262619 | −0.131310 | − | 0.991341i | \(-0.541918\pi\) | ||||
−0.131310 | + | 0.991341i | \(0.541918\pi\) | |||||||
\(468\) | 92.2588 | 4.26466 | ||||||||
\(469\) | −31.5835 | −1.45839 | ||||||||
\(470\) | 5.08673 | 0.234633 | ||||||||
\(471\) | 0.462860 | 0.0213274 | ||||||||
\(472\) | −21.0909 | −0.970787 | ||||||||
\(473\) | 13.7903 | 0.634077 | ||||||||
\(474\) | −0.0730899 | −0.00335713 | ||||||||
\(475\) | −28.3868 | −1.30247 | ||||||||
\(476\) | 60.5704 | 2.77624 | ||||||||
\(477\) | −21.8267 | −0.999378 | ||||||||
\(478\) | 35.5393 | 1.62553 | ||||||||
\(479\) | −29.7070 | −1.35735 | −0.678674 | − | 0.734440i | \(-0.737445\pi\) | ||||
−0.678674 | + | 0.734440i | \(0.737445\pi\) | |||||||
\(480\) | 0.318883 | 0.0145550 | ||||||||
\(481\) | −32.5488 | −1.48410 | ||||||||
\(482\) | 21.5598 | 0.982020 | ||||||||
\(483\) | 0.294055 | 0.0133800 | ||||||||
\(484\) | 10.1755 | 0.462521 | ||||||||
\(485\) | 2.02174 | 0.0918026 | ||||||||
\(486\) | 1.39905 | 0.0634620 | ||||||||
\(487\) | 3.48301 | 0.157830 | 0.0789151 | − | 0.996881i | \(-0.474854\pi\) | ||||
0.0789151 | + | 0.996881i | \(0.474854\pi\) | |||||||
\(488\) | −42.1147 | −1.90644 | ||||||||
\(489\) | −0.430133 | −0.0194513 | ||||||||
\(490\) | −5.27661 | −0.238373 | ||||||||
\(491\) | −1.50232 | −0.0677987 | −0.0338993 | − | 0.999425i | \(-0.510793\pi\) | ||||
−0.0338993 | + | 0.999425i | \(0.510793\pi\) | |||||||
\(492\) | −0.213068 | −0.00960584 | ||||||||
\(493\) | −20.2194 | −0.910635 | ||||||||
\(494\) | 104.607 | 4.70649 | ||||||||
\(495\) | 9.38738 | 0.421932 | ||||||||
\(496\) | 24.6516 | 1.10689 | ||||||||
\(497\) | 3.03945 | 0.136338 | ||||||||
\(498\) | −0.679663 | −0.0304564 | ||||||||
\(499\) | 7.63426 | 0.341756 | 0.170878 | − | 0.985292i | \(-0.445340\pi\) | ||||
0.170878 | + | 0.985292i | \(0.445340\pi\) | |||||||
\(500\) | −42.8720 | −1.91729 | ||||||||
\(501\) | 0.424027 | 0.0189441 | ||||||||
\(502\) | 14.8749 | 0.663899 | ||||||||
\(503\) | −14.7350 | −0.657003 | −0.328502 | − | 0.944503i | \(-0.606544\pi\) | ||||
−0.328502 | + | 0.944503i | \(0.606544\pi\) | |||||||
\(504\) | −82.0868 | −3.65644 | ||||||||
\(505\) | 7.95700 | 0.354082 | ||||||||
\(506\) | 49.1420 | 2.18463 | ||||||||
\(507\) | −0.389526 | −0.0172995 | ||||||||
\(508\) | 9.91075 | 0.439719 | ||||||||
\(509\) | 22.9002 | 1.01503 | 0.507516 | − | 0.861642i | \(-0.330564\pi\) | ||||
0.507516 | + | 0.861642i | \(0.330564\pi\) | |||||||
\(510\) | −0.168882 | −0.00747821 | ||||||||
\(511\) | −42.6856 | −1.88830 | ||||||||
\(512\) | −15.2926 | −0.675843 | ||||||||
\(513\) | 0.768824 | 0.0339444 | ||||||||
\(514\) | 28.8550 | 1.27274 | ||||||||
\(515\) | −6.53578 | −0.288001 | ||||||||
\(516\) | 0.391406 | 0.0172307 | ||||||||
\(517\) | 7.75279 | 0.340967 | ||||||||
\(518\) | 46.3727 | 2.03750 | ||||||||
\(519\) | −0.334186 | −0.0146691 | ||||||||
\(520\) | 45.2822 | 1.98576 | ||||||||
\(521\) | 18.5688 | 0.813514 | 0.406757 | − | 0.913536i | \(-0.366660\pi\) | ||||
0.406757 | + | 0.913536i | \(0.366660\pi\) | |||||||
\(522\) | 43.8776 | 1.92047 | ||||||||
\(523\) | 29.5702 | 1.29301 | 0.646507 | − | 0.762908i | \(-0.276229\pi\) | ||||
0.646507 | + | 0.762908i | \(0.276229\pi\) | |||||||
\(524\) | −82.6701 | −3.61146 | ||||||||
\(525\) | −0.246831 | −0.0107726 | ||||||||
\(526\) | −41.5448 | −1.81144 | ||||||||
\(527\) | −6.72380 | −0.292893 | ||||||||
\(528\) | 0.943697 | 0.0410692 | ||||||||
\(529\) | 2.53161 | 0.110070 | ||||||||
\(530\) | −17.1542 | −0.745132 | ||||||||
\(531\) | −7.02671 | −0.304933 | ||||||||
\(532\) | −108.350 | −4.69759 | ||||||||
\(533\) | −12.0643 | −0.522565 | ||||||||
\(534\) | 0.547186 | 0.0236791 | ||||||||
\(535\) | −1.53789 | −0.0664889 | ||||||||
\(536\) | −93.5572 | −4.04105 | ||||||||
\(537\) | −0.174457 | −0.00752838 | ||||||||
\(538\) | 25.6759 | 1.10696 | ||||||||
\(539\) | −8.04220 | −0.346402 | ||||||||
\(540\) | 0.532913 | 0.0229329 | ||||||||
\(541\) | 3.51792 | 0.151247 | 0.0756236 | − | 0.997136i | \(-0.475905\pi\) | ||||
0.0756236 | + | 0.997136i | \(0.475905\pi\) | |||||||
\(542\) | 42.3853 | 1.82061 | ||||||||
\(543\) | 0.0580919 | 0.00249296 | ||||||||
\(544\) | 71.5429 | 3.06737 | ||||||||
\(545\) | 6.25729 | 0.268033 | ||||||||
\(546\) | 0.909586 | 0.0389267 | ||||||||
\(547\) | −38.3009 | −1.63763 | −0.818814 | − | 0.574059i | \(-0.805368\pi\) | ||||
−0.818814 | + | 0.574059i | \(0.805368\pi\) | |||||||
\(548\) | −114.177 | −4.87740 | ||||||||
\(549\) | −14.0311 | −0.598832 | ||||||||
\(550\) | −41.2499 | −1.75890 | ||||||||
\(551\) | 36.1691 | 1.54086 | ||||||||
\(552\) | 0.871055 | 0.0370746 | ||||||||
\(553\) | 4.28659 | 0.182285 | ||||||||
\(554\) | 72.2837 | 3.07104 | ||||||||
\(555\) | −0.0939996 | −0.00399006 | ||||||||
\(556\) | 35.6051 | 1.50999 | ||||||||
\(557\) | 19.5749 | 0.829414 | 0.414707 | − | 0.909955i | \(-0.363884\pi\) | ||||
0.414707 | + | 0.909955i | \(0.363884\pi\) | |||||||
\(558\) | 14.5912 | 0.617693 | ||||||||
\(559\) | 22.1622 | 0.937361 | ||||||||
\(560\) | −36.3135 | −1.53453 | ||||||||
\(561\) | −0.257396 | −0.0108673 | ||||||||
\(562\) | −4.93019 | −0.207968 | ||||||||
\(563\) | 10.0518 | 0.423634 | 0.211817 | − | 0.977309i | \(-0.432062\pi\) | ||||
0.211817 | + | 0.977309i | \(0.432062\pi\) | |||||||
\(564\) | 0.220046 | 0.00926560 | ||||||||
\(565\) | −0.870977 | −0.0366423 | ||||||||
\(566\) | 8.21045 | 0.345111 | ||||||||
\(567\) | −27.3450 | −1.14838 | ||||||||
\(568\) | 9.00349 | 0.377778 | ||||||||
\(569\) | 33.7209 | 1.41366 | 0.706828 | − | 0.707386i | \(-0.250126\pi\) | ||||
0.706828 | + | 0.707386i | \(0.250126\pi\) | |||||||
\(570\) | 0.302101 | 0.0126536 | ||||||||
\(571\) | 11.0748 | 0.463465 | 0.231732 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231732 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(572\) | 110.512 | 4.62074 | ||||||||
\(573\) | 0.182125 | 0.00760837 | ||||||||
\(574\) | 17.1882 | 0.717423 | ||||||||
\(575\) | −21.4313 | −0.893747 | ||||||||
\(576\) | −72.9599 | −3.04000 | ||||||||
\(577\) | −16.8628 | −0.702008 | −0.351004 | − | 0.936374i | \(-0.614160\pi\) | ||||
−0.351004 | + | 0.936374i | \(0.614160\pi\) | |||||||
\(578\) | 8.12489 | 0.337951 | ||||||||
\(579\) | −0.174319 | −0.00724444 | ||||||||
\(580\) | 25.0707 | 1.04101 | ||||||||
\(581\) | 39.8611 | 1.65372 | ||||||||
\(582\) | 0.120298 | 0.00498652 | ||||||||
\(583\) | −26.1451 | −1.08282 | ||||||||
\(584\) | −126.444 | −5.23229 | ||||||||
\(585\) | 15.0864 | 0.623745 | ||||||||
\(586\) | 74.6706 | 3.08461 | ||||||||
\(587\) | −25.7797 | −1.06404 | −0.532021 | − | 0.846731i | \(-0.678567\pi\) | ||||
−0.532021 | + | 0.846731i | \(0.678567\pi\) | |||||||
\(588\) | −0.228260 | −0.00941328 | ||||||||
\(589\) | 12.0278 | 0.495595 | ||||||||
\(590\) | −5.52248 | −0.227357 | ||||||||
\(591\) | −0.191337 | −0.00787057 | ||||||||
\(592\) | 77.3199 | 3.17783 | ||||||||
\(593\) | 32.2514 | 1.32441 | 0.662203 | − | 0.749324i | \(-0.269621\pi\) | ||||
0.662203 | + | 0.749324i | \(0.269621\pi\) | |||||||
\(594\) | 1.11721 | 0.0458396 | ||||||||
\(595\) | 9.90462 | 0.406050 | ||||||||
\(596\) | −80.0521 | −3.27906 | ||||||||
\(597\) | −0.206392 | −0.00844706 | ||||||||
\(598\) | 78.9756 | 3.22955 | ||||||||
\(599\) | 17.2427 | 0.704519 | 0.352260 | − | 0.935902i | \(-0.385413\pi\) | ||||
0.352260 | + | 0.935902i | \(0.385413\pi\) | |||||||
\(600\) | −0.731165 | −0.0298497 | ||||||||
\(601\) | 5.11099 | 0.208481 | 0.104241 | − | 0.994552i | \(-0.466759\pi\) | ||||
0.104241 | + | 0.994552i | \(0.466759\pi\) | |||||||
\(602\) | −31.5748 | −1.28689 | ||||||||
\(603\) | −31.1698 | −1.26933 | ||||||||
\(604\) | 114.175 | 4.64571 | ||||||||
\(605\) | 1.66392 | 0.0676478 | ||||||||
\(606\) | 0.473458 | 0.0192329 | ||||||||
\(607\) | 12.1784 | 0.494306 | 0.247153 | − | 0.968977i | \(-0.420505\pi\) | ||||
0.247153 | + | 0.968977i | \(0.420505\pi\) | |||||||
\(608\) | −127.978 | −5.19020 | ||||||||
\(609\) | 0.314500 | 0.0127442 | ||||||||
\(610\) | −11.0274 | −0.446486 | ||||||||
\(611\) | 12.4594 | 0.504055 | ||||||||
\(612\) | 59.7770 | 2.41634 | ||||||||
\(613\) | −46.0533 | −1.86007 | −0.930037 | − | 0.367467i | \(-0.880225\pi\) | ||||
−0.930037 | + | 0.367467i | \(0.880225\pi\) | |||||||
\(614\) | 22.4333 | 0.905334 | ||||||||
\(615\) | −0.0348414 | −0.00140494 | ||||||||
\(616\) | −98.3275 | −3.96173 | ||||||||
\(617\) | −29.9243 | −1.20471 | −0.602354 | − | 0.798229i | \(-0.705770\pi\) | ||||
−0.602354 | + | 0.798229i | \(0.705770\pi\) | |||||||
\(618\) | −0.388893 | −0.0156436 | ||||||||
\(619\) | −13.5477 | −0.544527 | −0.272263 | − | 0.962223i | \(-0.587772\pi\) | ||||
−0.272263 | + | 0.962223i | \(0.587772\pi\) | |||||||
\(620\) | 8.33708 | 0.334825 | ||||||||
\(621\) | 0.580443 | 0.0232924 | ||||||||
\(622\) | −56.2850 | −2.25682 | ||||||||
\(623\) | −32.0915 | −1.28572 | ||||||||
\(624\) | 1.51661 | 0.0607129 | ||||||||
\(625\) | 14.1965 | 0.567859 | ||||||||
\(626\) | −3.30005 | −0.131896 | ||||||||
\(627\) | 0.460439 | 0.0183882 | ||||||||
\(628\) | −128.761 | −5.13811 | ||||||||
\(629\) | −21.0892 | −0.840883 | ||||||||
\(630\) | −21.4938 | −0.856333 | ||||||||
\(631\) | 25.5043 | 1.01531 | 0.507656 | − | 0.861560i | \(-0.330512\pi\) | ||||
0.507656 | + | 0.861560i | \(0.330512\pi\) | |||||||
\(632\) | 12.6978 | 0.505092 | ||||||||
\(633\) | 0.325846 | 0.0129512 | ||||||||
\(634\) | 30.3344 | 1.20473 | ||||||||
\(635\) | 1.62063 | 0.0643128 | ||||||||
\(636\) | −0.742071 | −0.0294250 | ||||||||
\(637\) | −12.9245 | −0.512089 | ||||||||
\(638\) | 52.5587 | 2.08082 | ||||||||
\(639\) | 2.99963 | 0.118664 | ||||||||
\(640\) | −24.0318 | −0.949941 | ||||||||
\(641\) | 28.3366 | 1.11923 | 0.559615 | − | 0.828753i | \(-0.310949\pi\) | ||||
0.559615 | + | 0.828753i | \(0.310949\pi\) | |||||||
\(642\) | −0.0915080 | −0.00361153 | ||||||||
\(643\) | 0.987473 | 0.0389421 | 0.0194711 | − | 0.999810i | \(-0.493802\pi\) | ||||
0.0194711 | + | 0.999810i | \(0.493802\pi\) | |||||||
\(644\) | −81.8018 | −3.22344 | ||||||||
\(645\) | 0.0640036 | 0.00252014 | ||||||||
\(646\) | 67.7778 | 2.66668 | ||||||||
\(647\) | 6.72189 | 0.264265 | 0.132132 | − | 0.991232i | \(-0.457818\pi\) | ||||
0.132132 | + | 0.991232i | \(0.457818\pi\) | |||||||
\(648\) | −81.0017 | −3.18205 | ||||||||
\(649\) | −8.41693 | −0.330393 | ||||||||
\(650\) | −66.2923 | −2.60020 | ||||||||
\(651\) | 0.104585 | 0.00409899 | ||||||||
\(652\) | 119.657 | 4.68611 | ||||||||
\(653\) | 10.3910 | 0.406630 | 0.203315 | − | 0.979113i | \(-0.434828\pi\) | ||||
0.203315 | + | 0.979113i | \(0.434828\pi\) | |||||||
\(654\) | 0.372322 | 0.0145590 | ||||||||
\(655\) | −13.5184 | −0.528208 | ||||||||
\(656\) | 28.6590 | 1.11894 | ||||||||
\(657\) | −42.1265 | −1.64351 | ||||||||
\(658\) | −17.7511 | −0.692011 | ||||||||
\(659\) | −8.51494 | −0.331695 | −0.165847 | − | 0.986151i | \(-0.553036\pi\) | ||||
−0.165847 | + | 0.986151i | \(0.553036\pi\) | |||||||
\(660\) | 0.319155 | 0.0124231 | ||||||||
\(661\) | 10.9715 | 0.426743 | 0.213371 | − | 0.976971i | \(-0.431556\pi\) | ||||
0.213371 | + | 0.976971i | \(0.431556\pi\) | |||||||
\(662\) | −91.0579 | −3.53906 | ||||||||
\(663\) | −0.413659 | −0.0160652 | ||||||||
\(664\) | 118.077 | 4.58228 | ||||||||
\(665\) | −17.7177 | −0.687064 | ||||||||
\(666\) | 45.7653 | 1.77337 | ||||||||
\(667\) | 27.3068 | 1.05732 | ||||||||
\(668\) | −117.958 | −4.56393 | ||||||||
\(669\) | 0.194915 | 0.00753586 | ||||||||
\(670\) | −24.4972 | −0.946409 | ||||||||
\(671\) | −16.8071 | −0.648831 | ||||||||
\(672\) | −1.11281 | −0.0429274 | ||||||||
\(673\) | 38.8310 | 1.49682 | 0.748412 | − | 0.663234i | \(-0.230817\pi\) | ||||
0.748412 | + | 0.663234i | \(0.230817\pi\) | |||||||
\(674\) | −70.4956 | −2.71539 | ||||||||
\(675\) | −0.487225 | −0.0187533 | ||||||||
\(676\) | 108.360 | 4.16771 | ||||||||
\(677\) | 16.0646 | 0.617411 | 0.308706 | − | 0.951158i | \(-0.400104\pi\) | ||||
0.308706 | + | 0.951158i | \(0.400104\pi\) | |||||||
\(678\) | −0.0518250 | −0.00199033 | ||||||||
\(679\) | −7.05527 | −0.270757 | ||||||||
\(680\) | 29.3396 | 1.12512 | ||||||||
\(681\) | 0.0710259 | 0.00272172 | ||||||||
\(682\) | 17.4780 | 0.669267 | ||||||||
\(683\) | −30.3031 | −1.15952 | −0.579758 | − | 0.814789i | \(-0.696853\pi\) | ||||
−0.579758 | + | 0.814789i | \(0.696853\pi\) | |||||||
\(684\) | −106.931 | −4.08862 | ||||||||
\(685\) | −18.6705 | −0.713362 | ||||||||
\(686\) | −39.1748 | −1.49570 | ||||||||
\(687\) | −0.0524494 | −0.00200107 | ||||||||
\(688\) | −52.6465 | −2.00713 | ||||||||
\(689\) | −42.0176 | −1.60074 | ||||||||
\(690\) | 0.228079 | 0.00868281 | ||||||||
\(691\) | −2.01000 | −0.0764641 | −0.0382320 | − | 0.999269i | \(-0.512173\pi\) | ||||
−0.0382320 | + | 0.999269i | \(0.512173\pi\) | |||||||
\(692\) | 92.9654 | 3.53401 | ||||||||
\(693\) | −32.7591 | −1.24442 | ||||||||
\(694\) | −34.9588 | −1.32702 | ||||||||
\(695\) | 5.82223 | 0.220850 | ||||||||
\(696\) | 0.931617 | 0.0353129 | ||||||||
\(697\) | −7.81682 | −0.296083 | ||||||||
\(698\) | 4.87640 | 0.184575 | ||||||||
\(699\) | 0.342044 | 0.0129373 | ||||||||
\(700\) | 68.6646 | 2.59528 | ||||||||
\(701\) | −33.1146 | −1.25072 | −0.625360 | − | 0.780336i | \(-0.715048\pi\) | ||||
−0.625360 | + | 0.780336i | \(0.715048\pi\) | |||||||
\(702\) | 1.79545 | 0.0677650 | ||||||||
\(703\) | 37.7252 | 1.42283 | ||||||||
\(704\) | −87.3949 | −3.29382 | ||||||||
\(705\) | 0.0359824 | 0.00135518 | ||||||||
\(706\) | −59.9759 | −2.25722 | ||||||||
\(707\) | −27.7675 | −1.04430 | ||||||||
\(708\) | −0.238896 | −0.00897826 | ||||||||
\(709\) | −13.9956 | −0.525614 | −0.262807 | − | 0.964848i | \(-0.584648\pi\) | ||||
−0.262807 | + | 0.964848i | \(0.584648\pi\) | |||||||
\(710\) | 2.35749 | 0.0884751 | ||||||||
\(711\) | 4.23045 | 0.158654 | ||||||||
\(712\) | −95.0620 | −3.56260 | ||||||||
\(713\) | 9.08065 | 0.340073 | ||||||||
\(714\) | 0.589346 | 0.0220557 | ||||||||
\(715\) | 18.0712 | 0.675824 | ||||||||
\(716\) | 48.5314 | 1.81370 | ||||||||
\(717\) | 0.251397 | 0.00938861 | ||||||||
\(718\) | 53.7400 | 2.00556 | ||||||||
\(719\) | 3.72624 | 0.138965 | 0.0694827 | − | 0.997583i | \(-0.477865\pi\) | ||||
0.0694827 | + | 0.997583i | \(0.477865\pi\) | |||||||
\(720\) | −35.8379 | −1.33560 | ||||||||
\(721\) | 22.8079 | 0.849411 | ||||||||
\(722\) | −69.8155 | −2.59826 | ||||||||
\(723\) | 0.152509 | 0.00567187 | ||||||||
\(724\) | −16.1603 | −0.600593 | ||||||||
\(725\) | −22.9214 | −0.851278 | ||||||||
\(726\) | 0.0990066 | 0.00367448 | ||||||||
\(727\) | 44.3658 | 1.64544 | 0.822718 | − | 0.568450i | \(-0.192457\pi\) | ||||
0.822718 | + | 0.568450i | \(0.192457\pi\) | |||||||
\(728\) | −158.021 | −5.85666 | ||||||||
\(729\) | −26.9802 | −0.999267 | ||||||||
\(730\) | −33.1084 | −1.22540 | ||||||||
\(731\) | 14.3595 | 0.531106 | ||||||||
\(732\) | −0.477032 | −0.0176316 | ||||||||
\(733\) | −14.6686 | −0.541798 | −0.270899 | − | 0.962608i | \(-0.587321\pi\) | ||||
−0.270899 | + | 0.962608i | \(0.587321\pi\) | |||||||
\(734\) | −17.4663 | −0.644693 | ||||||||
\(735\) | −0.0373256 | −0.00137678 | ||||||||
\(736\) | −96.6203 | −3.56147 | ||||||||
\(737\) | −37.3367 | −1.37532 | ||||||||
\(738\) | 16.9631 | 0.624420 | ||||||||
\(739\) | −35.7985 | −1.31687 | −0.658435 | − | 0.752638i | \(-0.728781\pi\) | ||||
−0.658435 | + | 0.752638i | \(0.728781\pi\) | |||||||
\(740\) | 26.1493 | 0.961267 | ||||||||
\(741\) | 0.739968 | 0.0271834 | ||||||||
\(742\) | 59.8631 | 2.19764 | ||||||||
\(743\) | −20.6388 | −0.757166 | −0.378583 | − | 0.925567i | \(-0.623589\pi\) | ||||
−0.378583 | + | 0.925567i | \(0.623589\pi\) | |||||||
\(744\) | 0.309802 | 0.0113579 | ||||||||
\(745\) | −13.0903 | −0.479592 | ||||||||
\(746\) | 17.6918 | 0.647742 | ||||||||
\(747\) | 39.3389 | 1.43934 | ||||||||
\(748\) | 71.6038 | 2.61809 | ||||||||
\(749\) | 5.36678 | 0.196098 | ||||||||
\(750\) | −0.417142 | −0.0152319 | ||||||||
\(751\) | 50.0216 | 1.82531 | 0.912657 | − | 0.408727i | \(-0.134027\pi\) | ||||
0.912657 | + | 0.408727i | \(0.134027\pi\) | |||||||
\(752\) | −29.5975 | −1.07931 | ||||||||
\(753\) | 0.105222 | 0.00383450 | ||||||||
\(754\) | 84.4666 | 3.07609 | ||||||||
\(755\) | 18.6701 | 0.679476 | ||||||||
\(756\) | −1.85970 | −0.0676368 | ||||||||
\(757\) | 40.8599 | 1.48508 | 0.742540 | − | 0.669802i | \(-0.233621\pi\) | ||||
0.742540 | + | 0.669802i | \(0.233621\pi\) | |||||||
\(758\) | 39.5624 | 1.43697 | ||||||||
\(759\) | 0.347620 | 0.0126178 | ||||||||
\(760\) | −52.4837 | −1.90378 | ||||||||
\(761\) | −50.2049 | −1.81993 | −0.909963 | − | 0.414690i | \(-0.863890\pi\) | ||||
−0.909963 | + | 0.414690i | \(0.863890\pi\) | |||||||
\(762\) | 0.0964310 | 0.00349333 | ||||||||
\(763\) | −21.8361 | −0.790518 | ||||||||
\(764\) | −50.6643 | −1.83297 | ||||||||
\(765\) | 9.77489 | 0.353412 | ||||||||
\(766\) | 42.7303 | 1.54391 | ||||||||
\(767\) | −13.5268 | −0.488423 | ||||||||
\(768\) | −0.498534 | −0.0179893 | ||||||||
\(769\) | −19.5198 | −0.703901 | −0.351950 | − | 0.936019i | \(-0.614481\pi\) | ||||
−0.351950 | + | 0.936019i | \(0.614481\pi\) | |||||||
\(770\) | −25.7463 | −0.927832 | ||||||||
\(771\) | 0.204114 | 0.00735098 | ||||||||
\(772\) | 48.4928 | 1.74530 | ||||||||
\(773\) | 5.00052 | 0.179856 | 0.0899281 | − | 0.995948i | \(-0.471336\pi\) | ||||
0.0899281 | + | 0.995948i | \(0.471336\pi\) | |||||||
\(774\) | −31.1612 | −1.12007 | ||||||||
\(775\) | −7.62232 | −0.273802 | ||||||||
\(776\) | −20.8992 | −0.750239 | ||||||||
\(777\) | 0.328030 | 0.0117680 | ||||||||
\(778\) | −22.2152 | −0.796455 | ||||||||
\(779\) | 13.9830 | 0.500993 | ||||||||
\(780\) | 0.512911 | 0.0183651 | ||||||||
\(781\) | 3.59310 | 0.128571 | ||||||||
\(782\) | 51.1705 | 1.82985 | ||||||||
\(783\) | 0.620799 | 0.0221856 | ||||||||
\(784\) | 30.7024 | 1.09651 | ||||||||
\(785\) | −21.0552 | −0.751494 | ||||||||
\(786\) | −0.804374 | −0.0286911 | ||||||||
\(787\) | 41.8463 | 1.49166 | 0.745830 | − | 0.666137i | \(-0.232053\pi\) | ||||
0.745830 | + | 0.666137i | \(0.232053\pi\) | |||||||
\(788\) | 53.2272 | 1.89614 | ||||||||
\(789\) | −0.293879 | −0.0104624 | ||||||||
\(790\) | 3.32482 | 0.118292 | ||||||||
\(791\) | 3.03945 | 0.108070 | ||||||||
\(792\) | −97.0396 | −3.44815 | ||||||||
\(793\) | −27.0105 | −0.959172 | ||||||||
\(794\) | 22.8375 | 0.810472 | ||||||||
\(795\) | −0.121345 | −0.00430367 | ||||||||
\(796\) | 57.4151 | 2.03502 | ||||||||
\(797\) | −21.0571 | −0.745882 | −0.372941 | − | 0.927855i | \(-0.621651\pi\) | ||||
−0.372941 | + | 0.927855i | \(0.621651\pi\) | |||||||
\(798\) | −1.05424 | −0.0373198 | ||||||||
\(799\) | 8.07282 | 0.285596 | ||||||||
\(800\) | 81.1033 | 2.86743 | ||||||||
\(801\) | −31.6712 | −1.11905 | ||||||||
\(802\) | 15.1590 | 0.535282 | ||||||||
\(803\) | −50.4612 | −1.78074 | ||||||||
\(804\) | −1.05972 | −0.0373734 | ||||||||
\(805\) | −13.3764 | −0.471457 | ||||||||
\(806\) | 28.0887 | 0.989383 | ||||||||
\(807\) | 0.181625 | 0.00639352 | ||||||||
\(808\) | −82.2533 | −2.89366 | ||||||||
\(809\) | 34.8418 | 1.22497 | 0.612487 | − | 0.790481i | \(-0.290169\pi\) | ||||
0.612487 | + | 0.790481i | \(0.290169\pi\) | |||||||
\(810\) | −21.2096 | −0.745231 | ||||||||
\(811\) | −14.9088 | −0.523520 | −0.261760 | − | 0.965133i | \(-0.584303\pi\) | ||||
−0.261760 | + | 0.965133i | \(0.584303\pi\) | |||||||
\(812\) | −87.4893 | −3.07027 | ||||||||
\(813\) | 0.299825 | 0.0105153 | ||||||||
\(814\) | 54.8198 | 1.92143 | ||||||||
\(815\) | 19.5665 | 0.685386 | ||||||||
\(816\) | 0.982652 | 0.0343997 | ||||||||
\(817\) | −25.6868 | −0.898666 | ||||||||
\(818\) | 38.5266 | 1.34705 | ||||||||
\(819\) | −52.6469 | −1.83963 | ||||||||
\(820\) | 9.69235 | 0.338471 | ||||||||
\(821\) | −14.5154 | −0.506592 | −0.253296 | − | 0.967389i | \(-0.581515\pi\) | ||||
−0.253296 | + | 0.967389i | \(0.581515\pi\) | |||||||
\(822\) | −1.11093 | −0.0387483 | ||||||||
\(823\) | −25.5346 | −0.890081 | −0.445040 | − | 0.895510i | \(-0.646811\pi\) | ||||
−0.445040 | + | 0.895510i | \(0.646811\pi\) | |||||||
\(824\) | 67.5619 | 2.35363 | ||||||||
\(825\) | −0.291793 | −0.0101589 | ||||||||
\(826\) | 19.2718 | 0.670551 | ||||||||
\(827\) | 25.1087 | 0.873115 | 0.436558 | − | 0.899676i | \(-0.356197\pi\) | ||||
0.436558 | + | 0.899676i | \(0.356197\pi\) | |||||||
\(828\) | −80.7303 | −2.80557 | ||||||||
\(829\) | 14.9955 | 0.520814 | 0.260407 | − | 0.965499i | \(-0.416143\pi\) | ||||
0.260407 | + | 0.965499i | \(0.416143\pi\) | |||||||
\(830\) | 30.9175 | 1.07316 | ||||||||
\(831\) | 0.511319 | 0.0177375 | ||||||||
\(832\) | −140.452 | −4.86928 | ||||||||
\(833\) | −8.37417 | −0.290148 | ||||||||
\(834\) | 0.346435 | 0.0119961 | ||||||||
\(835\) | −19.2888 | −0.667515 | ||||||||
\(836\) | −128.087 | −4.42999 | ||||||||
\(837\) | 0.206442 | 0.00713568 | ||||||||
\(838\) | −7.46250 | −0.257788 | ||||||||
\(839\) | −2.13871 | −0.0738366 | −0.0369183 | − | 0.999318i | \(-0.511754\pi\) | ||||
−0.0369183 | + | 0.999318i | \(0.511754\pi\) | |||||||
\(840\) | −0.456360 | −0.0157459 | ||||||||
\(841\) | 0.205332 | 0.00708042 | ||||||||
\(842\) | −76.4083 | −2.63320 | ||||||||
\(843\) | −0.0348751 | −0.00120116 | ||||||||
\(844\) | −90.6455 | −3.12015 | ||||||||
\(845\) | 17.7193 | 0.609564 | ||||||||
\(846\) | −17.5186 | −0.602303 | ||||||||
\(847\) | −5.80656 | −0.199516 | ||||||||
\(848\) | 99.8132 | 3.42760 | ||||||||
\(849\) | 0.0580790 | 0.00199326 | ||||||||
\(850\) | −42.9526 | −1.47326 | ||||||||
\(851\) | 28.4815 | 0.976334 | ||||||||
\(852\) | 0.101982 | 0.00349386 | ||||||||
\(853\) | −3.08877 | −0.105758 | −0.0528788 | − | 0.998601i | \(-0.516840\pi\) | ||||
−0.0528788 | + | 0.998601i | \(0.516840\pi\) | |||||||
\(854\) | 38.4823 | 1.31684 | ||||||||
\(855\) | −17.4856 | −0.597996 | ||||||||
\(856\) | 15.8976 | 0.543368 | ||||||||
\(857\) | −34.0894 | −1.16447 | −0.582236 | − | 0.813020i | \(-0.697822\pi\) | ||||
−0.582236 | + | 0.813020i | \(0.697822\pi\) | |||||||
\(858\) | 1.07527 | 0.0367093 | ||||||||
\(859\) | 36.6353 | 1.24998 | 0.624991 | − | 0.780632i | \(-0.285103\pi\) | ||||
0.624991 | + | 0.780632i | \(0.285103\pi\) | |||||||
\(860\) | −17.8049 | −0.607140 | ||||||||
\(861\) | 0.121586 | 0.00414364 | ||||||||
\(862\) | 49.7285 | 1.69376 | ||||||||
\(863\) | −29.2272 | −0.994905 | −0.497452 | − | 0.867491i | \(-0.665731\pi\) | ||||
−0.497452 | + | 0.867491i | \(0.665731\pi\) | |||||||
\(864\) | −2.19659 | −0.0747296 | ||||||||
\(865\) | 15.2019 | 0.516881 | ||||||||
\(866\) | −67.9615 | −2.30943 | ||||||||
\(867\) | 0.0574737 | 0.00195191 | ||||||||
\(868\) | −29.0939 | −0.987511 | ||||||||
\(869\) | 5.06743 | 0.171901 | ||||||||
\(870\) | 0.243937 | 0.00827022 | ||||||||
\(871\) | −60.0035 | −2.03314 | ||||||||
\(872\) | −64.6831 | −2.19045 | ||||||||
\(873\) | −6.96286 | −0.235657 | ||||||||
\(874\) | −91.5355 | −3.09624 | ||||||||
\(875\) | 24.4646 | 0.827056 | ||||||||
\(876\) | −1.43223 | −0.0483905 | ||||||||
\(877\) | −20.0518 | −0.677100 | −0.338550 | − | 0.940948i | \(-0.609936\pi\) | ||||
−0.338550 | + | 0.940948i | \(0.609936\pi\) | |||||||
\(878\) | −15.8435 | −0.534693 | ||||||||
\(879\) | 0.528204 | 0.0178159 | ||||||||
\(880\) | −42.9283 | −1.44711 | ||||||||
\(881\) | 17.0122 | 0.573155 | 0.286578 | − | 0.958057i | \(-0.407482\pi\) | ||||
0.286578 | + | 0.958057i | \(0.407482\pi\) | |||||||
\(882\) | 18.1726 | 0.611903 | ||||||||
\(883\) | 40.1020 | 1.34954 | 0.674770 | − | 0.738028i | \(-0.264243\pi\) | ||||
0.674770 | + | 0.738028i | \(0.264243\pi\) | |||||||
\(884\) | 115.074 | 3.87035 | ||||||||
\(885\) | −0.0390648 | −0.00131315 | ||||||||
\(886\) | −4.45231 | −0.149578 | ||||||||
\(887\) | −49.1718 | −1.65103 | −0.825513 | − | 0.564383i | \(-0.809114\pi\) | ||||
−0.825513 | + | 0.564383i | \(0.809114\pi\) | |||||||
\(888\) | 0.971696 | 0.0326080 | ||||||||
\(889\) | −5.65551 | −0.189680 | ||||||||
\(890\) | −24.8912 | −0.834356 | ||||||||
\(891\) | −32.3261 | −1.08296 | ||||||||
\(892\) | −54.2225 | −1.81550 | ||||||||
\(893\) | −14.4409 | −0.483247 | ||||||||
\(894\) | −0.778901 | −0.0260504 | ||||||||
\(895\) | 7.93597 | 0.265270 | ||||||||
\(896\) | 83.8638 | 2.80169 | ||||||||
\(897\) | 0.558657 | 0.0186530 | ||||||||
\(898\) | −33.4646 | −1.11673 | ||||||||
\(899\) | 9.71201 | 0.323914 | ||||||||
\(900\) | 67.7652 | 2.25884 | ||||||||
\(901\) | −27.2244 | −0.906975 | ||||||||
\(902\) | 20.3192 | 0.676556 | ||||||||
\(903\) | −0.223353 | −0.00743273 | ||||||||
\(904\) | 9.00349 | 0.299452 | ||||||||
\(905\) | −2.64257 | −0.0878421 | ||||||||
\(906\) | 1.11091 | 0.0369076 | ||||||||
\(907\) | 47.3010 | 1.57060 | 0.785302 | − | 0.619113i | \(-0.212508\pi\) | ||||
0.785302 | + | 0.619113i | \(0.212508\pi\) | |||||||
\(908\) | −19.7583 | −0.655703 | ||||||||
\(909\) | −27.4038 | −0.908927 | ||||||||
\(910\) | −41.3766 | −1.37162 | ||||||||
\(911\) | 9.15601 | 0.303352 | 0.151676 | − | 0.988430i | \(-0.451533\pi\) | ||||
0.151676 | + | 0.988430i | \(0.451533\pi\) | |||||||
\(912\) | −1.75780 | −0.0582066 | ||||||||
\(913\) | 47.1221 | 1.55951 | ||||||||
\(914\) | 68.8921 | 2.27875 | ||||||||
\(915\) | −0.0780054 | −0.00257878 | ||||||||
\(916\) | 14.5906 | 0.482088 | ||||||||
\(917\) | 47.1752 | 1.55786 | ||||||||
\(918\) | 1.16332 | 0.0383954 | ||||||||
\(919\) | 39.0468 | 1.28804 | 0.644018 | − | 0.765011i | \(-0.277266\pi\) | ||||
0.644018 | + | 0.765011i | \(0.277266\pi\) | |||||||
\(920\) | −39.6238 | −1.30636 | ||||||||
\(921\) | 0.158688 | 0.00522896 | ||||||||
\(922\) | 105.836 | 3.48551 | ||||||||
\(923\) | 5.77445 | 0.190068 | ||||||||
\(924\) | −1.11375 | −0.0366398 | ||||||||
\(925\) | −23.9075 | −0.786072 | ||||||||
\(926\) | −28.9361 | −0.950898 | ||||||||
\(927\) | 22.5092 | 0.739298 | ||||||||
\(928\) | −103.338 | −3.39224 | ||||||||
\(929\) | 11.0530 | 0.362636 | 0.181318 | − | 0.983425i | \(-0.441964\pi\) | ||||
0.181318 | + | 0.983425i | \(0.441964\pi\) | |||||||
\(930\) | 0.0811192 | 0.00266000 | ||||||||
\(931\) | 14.9800 | 0.490950 | ||||||||
\(932\) | −95.1514 | −3.11679 | ||||||||
\(933\) | −0.398148 | −0.0130348 | ||||||||
\(934\) | 15.3613 | 0.502638 | ||||||||
\(935\) | 11.7088 | 0.382920 | ||||||||
\(936\) | −155.951 | −5.09743 | ||||||||
\(937\) | −2.28724 | −0.0747209 | −0.0373605 | − | 0.999302i | \(-0.511895\pi\) | ||||
−0.0373605 | + | 0.999302i | \(0.511895\pi\) | |||||||
\(938\) | 85.4878 | 2.79128 | ||||||||
\(939\) | −0.0233438 | −0.000761797 0 | ||||||||
\(940\) | −10.0098 | −0.326483 | ||||||||
\(941\) | −39.7887 | −1.29708 | −0.648538 | − | 0.761183i | \(-0.724619\pi\) | ||||
−0.648538 | + | 0.761183i | \(0.724619\pi\) | |||||||
\(942\) | −1.25283 | −0.0408195 | ||||||||
\(943\) | 10.5568 | 0.343777 | ||||||||
\(944\) | 32.1330 | 1.04584 | ||||||||
\(945\) | −0.304103 | −0.00989248 | ||||||||
\(946\) | −37.3264 | −1.21359 | ||||||||
\(947\) | 2.27351 | 0.0738792 | 0.0369396 | − | 0.999317i | \(-0.488239\pi\) | ||||
0.0369396 | + | 0.999317i | \(0.488239\pi\) | |||||||
\(948\) | 0.143828 | 0.00467131 | ||||||||
\(949\) | −81.0957 | −2.63248 | ||||||||
\(950\) | 76.8351 | 2.49286 | ||||||||
\(951\) | 0.214579 | 0.00695819 | ||||||||
\(952\) | −102.386 | −3.31836 | ||||||||
\(953\) | 41.8786 | 1.35658 | 0.678291 | − | 0.734794i | \(-0.262721\pi\) | ||||
0.678291 | + | 0.734794i | \(0.262721\pi\) | |||||||
\(954\) | 59.0789 | 1.91275 | ||||||||
\(955\) | −8.28476 | −0.268088 | ||||||||
\(956\) | −69.9350 | −2.26186 | ||||||||
\(957\) | 0.371789 | 0.0120182 | ||||||||
\(958\) | 80.4086 | 2.59788 | ||||||||
\(959\) | 65.1543 | 2.10394 | ||||||||
\(960\) | −0.405619 | −0.0130913 | ||||||||
\(961\) | −27.7703 | −0.895818 | ||||||||
\(962\) | 88.1005 | 2.84047 | ||||||||
\(963\) | 5.29649 | 0.170677 | ||||||||
\(964\) | −42.4257 | −1.36644 | ||||||||
\(965\) | 7.92967 | 0.255265 | ||||||||
\(966\) | −0.795926 | −0.0256085 | ||||||||
\(967\) | −8.74919 | −0.281355 | −0.140677 | − | 0.990055i | \(-0.544928\pi\) | ||||
−0.140677 | + | 0.990055i | \(0.544928\pi\) | |||||||
\(968\) | −17.2003 | −0.552838 | ||||||||
\(969\) | 0.479446 | 0.0154020 | ||||||||
\(970\) | −5.47230 | −0.175705 | ||||||||
\(971\) | −13.0245 | −0.417975 | −0.208987 | − | 0.977918i | \(-0.567017\pi\) | ||||
−0.208987 | + | 0.977918i | \(0.567017\pi\) | |||||||
\(972\) | −2.75307 | −0.0883049 | ||||||||
\(973\) | −20.3178 | −0.651359 | ||||||||
\(974\) | −9.42754 | −0.302078 | ||||||||
\(975\) | −0.468938 | −0.0150180 | ||||||||
\(976\) | 64.1638 | 2.05383 | ||||||||
\(977\) | −19.6210 | −0.627732 | −0.313866 | − | 0.949467i | \(-0.601624\pi\) | ||||
−0.313866 | + | 0.949467i | \(0.601624\pi\) | |||||||
\(978\) | 1.16425 | 0.0372286 | ||||||||
\(979\) | −37.9373 | −1.21248 | ||||||||
\(980\) | 10.3834 | 0.331686 | ||||||||
\(981\) | −21.5500 | −0.688040 | ||||||||
\(982\) | 4.06636 | 0.129763 | ||||||||
\(983\) | −24.0656 | −0.767573 | −0.383787 | − | 0.923422i | \(-0.625380\pi\) | ||||
−0.383787 | + | 0.923422i | \(0.625380\pi\) | |||||||
\(984\) | 0.360163 | 0.0114816 | ||||||||
\(985\) | 8.70384 | 0.277327 | ||||||||
\(986\) | 54.7283 | 1.74290 | ||||||||
\(987\) | −0.125568 | −0.00399687 | ||||||||
\(988\) | −205.848 | −6.54889 | ||||||||
\(989\) | −19.3929 | −0.616657 | ||||||||
\(990\) | −25.4090 | −0.807552 | ||||||||
\(991\) | −35.1652 | −1.11706 | −0.558529 | − | 0.829485i | \(-0.688634\pi\) | ||||
−0.558529 | + | 0.829485i | \(0.688634\pi\) | |||||||
\(992\) | −34.3643 | −1.09107 | ||||||||
\(993\) | −0.644124 | −0.0204406 | ||||||||
\(994\) | −8.22694 | −0.260943 | ||||||||
\(995\) | 9.38866 | 0.297640 | ||||||||
\(996\) | 1.33746 | 0.0423789 | ||||||||
\(997\) | −52.0092 | −1.64715 | −0.823574 | − | 0.567209i | \(-0.808023\pi\) | ||||
−0.823574 | + | 0.567209i | \(0.808023\pi\) | |||||||
\(998\) | −20.6638 | −0.654102 | ||||||||
\(999\) | 0.647507 | 0.0204862 |
(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 | 8023.2.a.c.1.8 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.8 | ✓ | 158 | 1.1 | even | 1 | trivial |