Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2005,2,Mod(1,2005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2005, 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("2005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2005 = 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2005.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: | \(16.0100056053\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 2005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88267 | −1.33125 | −0.665623 | − | 0.746288i | \(-0.731834\pi\) | ||||
−0.665623 | + | 0.746288i | \(0.731834\pi\) | |||||||
\(3\) | 2.47026 | 1.42620 | 0.713101 | − | 0.701061i | \(-0.247290\pi\) | ||||
0.713101 | + | 0.701061i | \(0.247290\pi\) | |||||||
\(4\) | 1.54444 | 0.772218 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −4.65067 | −1.89863 | ||||||||
\(7\) | 0.359672 | 0.135943 | 0.0679715 | − | 0.997687i | \(-0.478347\pi\) | ||||
0.0679715 | + | 0.997687i | \(0.478347\pi\) | |||||||
\(8\) | 0.857674 | 0.303234 | ||||||||
\(9\) | 3.10216 | 1.03405 | ||||||||
\(10\) | −1.88267 | −0.595352 | ||||||||
\(11\) | 5.16983 | 1.55876 | 0.779381 | − | 0.626550i | \(-0.215534\pi\) | ||||
0.779381 | + | 0.626550i | \(0.215534\pi\) | |||||||
\(12\) | 3.81515 | 1.10134 | ||||||||
\(13\) | 3.84899 | 1.06752 | 0.533759 | − | 0.845636i | \(-0.320779\pi\) | ||||
0.533759 | + | 0.845636i | \(0.320779\pi\) | |||||||
\(14\) | −0.677142 | −0.180974 | ||||||||
\(15\) | 2.47026 | 0.637817 | ||||||||
\(16\) | −4.70359 | −1.17590 | ||||||||
\(17\) | 0.331790 | 0.0804710 | 0.0402355 | − | 0.999190i | \(-0.487189\pi\) | ||||
0.0402355 | + | 0.999190i | \(0.487189\pi\) | |||||||
\(18\) | −5.84034 | −1.37658 | ||||||||
\(19\) | 6.07013 | 1.39258 | 0.696292 | − | 0.717759i | \(-0.254832\pi\) | ||||
0.696292 | + | 0.717759i | \(0.254832\pi\) | |||||||
\(20\) | 1.54444 | 0.345347 | ||||||||
\(21\) | 0.888481 | 0.193882 | ||||||||
\(22\) | −9.73307 | −2.07510 | ||||||||
\(23\) | 4.55195 | 0.949148 | 0.474574 | − | 0.880216i | \(-0.342602\pi\) | ||||
0.474574 | + | 0.880216i | \(0.342602\pi\) | |||||||
\(24\) | 2.11867 | 0.432472 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −7.24638 | −1.42113 | ||||||||
\(27\) | 0.252368 | 0.0485683 | ||||||||
\(28\) | 0.555490 | 0.104978 | ||||||||
\(29\) | −8.88940 | −1.65072 | −0.825360 | − | 0.564607i | \(-0.809028\pi\) | ||||
−0.825360 | + | 0.564607i | \(0.809028\pi\) | |||||||
\(30\) | −4.65067 | −0.849092 | ||||||||
\(31\) | 3.86039 | 0.693347 | 0.346673 | − | 0.937986i | \(-0.387311\pi\) | ||||
0.346673 | + | 0.937986i | \(0.387311\pi\) | |||||||
\(32\) | 7.13995 | 1.26218 | ||||||||
\(33\) | 12.7708 | 2.22311 | ||||||||
\(34\) | −0.624651 | −0.107127 | ||||||||
\(35\) | 0.359672 | 0.0607956 | ||||||||
\(36\) | 4.79109 | 0.798516 | ||||||||
\(37\) | −0.0839175 | −0.0137959 | −0.00689797 | − | 0.999976i | \(-0.502196\pi\) | ||||
−0.00689797 | + | 0.999976i | \(0.502196\pi\) | |||||||
\(38\) | −11.4280 | −1.85387 | ||||||||
\(39\) | 9.50800 | 1.52250 | ||||||||
\(40\) | 0.857674 | 0.135610 | ||||||||
\(41\) | −3.28822 | −0.513534 | −0.256767 | − | 0.966473i | \(-0.582657\pi\) | ||||
−0.256767 | + | 0.966473i | \(0.582657\pi\) | |||||||
\(42\) | −1.67271 | −0.258105 | ||||||||
\(43\) | −12.0070 | −1.83105 | −0.915527 | − | 0.402256i | \(-0.868226\pi\) | ||||
−0.915527 | + | 0.402256i | \(0.868226\pi\) | |||||||
\(44\) | 7.98447 | 1.20370 | ||||||||
\(45\) | 3.10216 | 0.462443 | ||||||||
\(46\) | −8.56982 | −1.26355 | ||||||||
\(47\) | −9.56754 | −1.39557 | −0.697784 | − | 0.716308i | \(-0.745831\pi\) | ||||
−0.697784 | + | 0.716308i | \(0.745831\pi\) | |||||||
\(48\) | −11.6191 | −1.67707 | ||||||||
\(49\) | −6.87064 | −0.981519 | ||||||||
\(50\) | −1.88267 | −0.266249 | ||||||||
\(51\) | 0.819607 | 0.114768 | ||||||||
\(52\) | 5.94453 | 0.824358 | ||||||||
\(53\) | 3.98325 | 0.547142 | 0.273571 | − | 0.961852i | \(-0.411795\pi\) | ||||
0.273571 | + | 0.961852i | \(0.411795\pi\) | |||||||
\(54\) | −0.475125 | −0.0646563 | ||||||||
\(55\) | 5.16983 | 0.697100 | ||||||||
\(56\) | 0.308481 | 0.0412225 | ||||||||
\(57\) | 14.9948 | 1.98611 | ||||||||
\(58\) | 16.7358 | 2.19752 | ||||||||
\(59\) | 8.52046 | 1.10927 | 0.554635 | − | 0.832094i | \(-0.312858\pi\) | ||||
0.554635 | + | 0.832094i | \(0.312858\pi\) | |||||||
\(60\) | 3.81515 | 0.492534 | ||||||||
\(61\) | −2.90830 | −0.372370 | −0.186185 | − | 0.982515i | \(-0.559612\pi\) | ||||
−0.186185 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(62\) | −7.26783 | −0.923016 | ||||||||
\(63\) | 1.11576 | 0.140573 | ||||||||
\(64\) | −4.03497 | −0.504371 | ||||||||
\(65\) | 3.84899 | 0.477409 | ||||||||
\(66\) | −24.0432 | −2.95951 | ||||||||
\(67\) | −5.56751 | −0.680180 | −0.340090 | − | 0.940393i | \(-0.610458\pi\) | ||||
−0.340090 | + | 0.940393i | \(0.610458\pi\) | |||||||
\(68\) | 0.512429 | 0.0621412 | ||||||||
\(69\) | 11.2445 | 1.35368 | ||||||||
\(70\) | −0.677142 | −0.0809339 | ||||||||
\(71\) | −5.78381 | −0.686412 | −0.343206 | − | 0.939260i | \(-0.611513\pi\) | ||||
−0.343206 | + | 0.939260i | \(0.611513\pi\) | |||||||
\(72\) | 2.66064 | 0.313560 | ||||||||
\(73\) | 16.4780 | 1.92861 | 0.964303 | − | 0.264802i | \(-0.0853068\pi\) | ||||
0.964303 | + | 0.264802i | \(0.0853068\pi\) | |||||||
\(74\) | 0.157989 | 0.0183658 | ||||||||
\(75\) | 2.47026 | 0.285241 | ||||||||
\(76\) | 9.37493 | 1.07538 | ||||||||
\(77\) | 1.85944 | 0.211903 | ||||||||
\(78\) | −17.9004 | −2.02682 | ||||||||
\(79\) | −6.53012 | −0.734696 | −0.367348 | − | 0.930084i | \(-0.619734\pi\) | ||||
−0.367348 | + | 0.930084i | \(0.619734\pi\) | |||||||
\(80\) | −4.70359 | −0.525877 | ||||||||
\(81\) | −8.68307 | −0.964786 | ||||||||
\(82\) | 6.19063 | 0.683641 | ||||||||
\(83\) | 1.94202 | 0.213164 | 0.106582 | − | 0.994304i | \(-0.466009\pi\) | ||||
0.106582 | + | 0.994304i | \(0.466009\pi\) | |||||||
\(84\) | 1.37220 | 0.149720 | ||||||||
\(85\) | 0.331790 | 0.0359877 | ||||||||
\(86\) | 22.6052 | 2.43759 | ||||||||
\(87\) | −21.9591 | −2.35426 | ||||||||
\(88\) | 4.43403 | 0.472669 | ||||||||
\(89\) | 13.9230 | 1.47584 | 0.737918 | − | 0.674890i | \(-0.235809\pi\) | ||||
0.737918 | + | 0.674890i | \(0.235809\pi\) | |||||||
\(90\) | −5.84034 | −0.615626 | ||||||||
\(91\) | 1.38437 | 0.145122 | ||||||||
\(92\) | 7.03021 | 0.732950 | ||||||||
\(93\) | 9.53615 | 0.988853 | ||||||||
\(94\) | 18.0125 | 1.85785 | ||||||||
\(95\) | 6.07013 | 0.622782 | ||||||||
\(96\) | 17.6375 | 1.80012 | ||||||||
\(97\) | −0.131070 | −0.0133081 | −0.00665407 | − | 0.999978i | \(-0.502118\pi\) | ||||
−0.00665407 | + | 0.999978i | \(0.502118\pi\) | |||||||
\(98\) | 12.9351 | 1.30664 | ||||||||
\(99\) | 16.0376 | 1.61184 | ||||||||
\(100\) | 1.54444 | 0.154444 | ||||||||
\(101\) | −7.81189 | −0.777312 | −0.388656 | − | 0.921383i | \(-0.627061\pi\) | ||||
−0.388656 | + | 0.921383i | \(0.627061\pi\) | |||||||
\(102\) | −1.54305 | −0.152784 | ||||||||
\(103\) | −13.8492 | −1.36460 | −0.682302 | − | 0.731070i | \(-0.739021\pi\) | ||||
−0.682302 | + | 0.731070i | \(0.739021\pi\) | |||||||
\(104\) | 3.30118 | 0.323707 | ||||||||
\(105\) | 0.888481 | 0.0867068 | ||||||||
\(106\) | −7.49914 | −0.728381 | ||||||||
\(107\) | 5.38180 | 0.520278 | 0.260139 | − | 0.965571i | \(-0.416232\pi\) | ||||
0.260139 | + | 0.965571i | \(0.416232\pi\) | |||||||
\(108\) | 0.389767 | 0.0375053 | ||||||||
\(109\) | 5.90613 | 0.565705 | 0.282852 | − | 0.959163i | \(-0.408719\pi\) | ||||
0.282852 | + | 0.959163i | \(0.408719\pi\) | |||||||
\(110\) | −9.73307 | −0.928012 | ||||||||
\(111\) | −0.207298 | −0.0196758 | ||||||||
\(112\) | −1.69175 | −0.159855 | ||||||||
\(113\) | 3.00127 | 0.282335 | 0.141168 | − | 0.989986i | \(-0.454914\pi\) | ||||
0.141168 | + | 0.989986i | \(0.454914\pi\) | |||||||
\(114\) | −28.2302 | −2.64400 | ||||||||
\(115\) | 4.55195 | 0.424472 | ||||||||
\(116\) | −13.7291 | −1.27472 | ||||||||
\(117\) | 11.9402 | 1.10387 | ||||||||
\(118\) | −16.0412 | −1.47671 | ||||||||
\(119\) | 0.119336 | 0.0109395 | ||||||||
\(120\) | 2.11867 | 0.193408 | ||||||||
\(121\) | 15.7271 | 1.42974 | ||||||||
\(122\) | 5.47537 | 0.495717 | ||||||||
\(123\) | −8.12276 | −0.732404 | ||||||||
\(124\) | 5.96213 | 0.535415 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.10060 | −0.187137 | ||||||||
\(127\) | −5.65507 | −0.501806 | −0.250903 | − | 0.968012i | \(-0.580728\pi\) | ||||
−0.250903 | + | 0.968012i | \(0.580728\pi\) | |||||||
\(128\) | −6.68339 | −0.590734 | ||||||||
\(129\) | −29.6604 | −2.61146 | ||||||||
\(130\) | −7.24638 | −0.635549 | ||||||||
\(131\) | −1.04380 | −0.0911974 | −0.0455987 | − | 0.998960i | \(-0.514520\pi\) | ||||
−0.0455987 | + | 0.998960i | \(0.514520\pi\) | |||||||
\(132\) | 19.7237 | 1.71673 | ||||||||
\(133\) | 2.18325 | 0.189312 | ||||||||
\(134\) | 10.4818 | 0.905488 | ||||||||
\(135\) | 0.252368 | 0.0217204 | ||||||||
\(136\) | 0.284568 | 0.0244015 | ||||||||
\(137\) | −20.1434 | −1.72097 | −0.860484 | − | 0.509477i | \(-0.829839\pi\) | ||||
−0.860484 | + | 0.509477i | \(0.829839\pi\) | |||||||
\(138\) | −21.1696 | −1.80208 | ||||||||
\(139\) | −20.2698 | −1.71926 | −0.859632 | − | 0.510913i | \(-0.829307\pi\) | ||||
−0.859632 | + | 0.510913i | \(0.829307\pi\) | |||||||
\(140\) | 0.555490 | 0.0469475 | ||||||||
\(141\) | −23.6343 | −1.99036 | ||||||||
\(142\) | 10.8890 | 0.913784 | ||||||||
\(143\) | 19.8986 | 1.66401 | ||||||||
\(144\) | −14.5913 | −1.21594 | ||||||||
\(145\) | −8.88940 | −0.738224 | ||||||||
\(146\) | −31.0226 | −2.56745 | ||||||||
\(147\) | −16.9722 | −1.39985 | ||||||||
\(148\) | −0.129605 | −0.0106535 | ||||||||
\(149\) | 2.66820 | 0.218587 | 0.109294 | − | 0.994010i | \(-0.465141\pi\) | ||||
0.109294 | + | 0.994010i | \(0.465141\pi\) | |||||||
\(150\) | −4.65067 | −0.379726 | ||||||||
\(151\) | 0.152848 | 0.0124386 | 0.00621929 | − | 0.999981i | \(-0.498020\pi\) | ||||
0.00621929 | + | 0.999981i | \(0.498020\pi\) | |||||||
\(152\) | 5.20619 | 0.422278 | ||||||||
\(153\) | 1.02927 | 0.0832114 | ||||||||
\(154\) | −3.50071 | −0.282095 | ||||||||
\(155\) | 3.86039 | 0.310074 | ||||||||
\(156\) | 14.6845 | 1.17570 | ||||||||
\(157\) | 12.4116 | 0.990557 | 0.495278 | − | 0.868734i | \(-0.335066\pi\) | ||||
0.495278 | + | 0.868734i | \(0.335066\pi\) | |||||||
\(158\) | 12.2940 | 0.978062 | ||||||||
\(159\) | 9.83966 | 0.780336 | ||||||||
\(160\) | 7.13995 | 0.564462 | ||||||||
\(161\) | 1.63721 | 0.129030 | ||||||||
\(162\) | 16.3473 | 1.28437 | ||||||||
\(163\) | 5.45902 | 0.427583 | 0.213792 | − | 0.976879i | \(-0.431419\pi\) | ||||
0.213792 | + | 0.976879i | \(0.431419\pi\) | |||||||
\(164\) | −5.07846 | −0.396561 | ||||||||
\(165\) | 12.7708 | 0.994205 | ||||||||
\(166\) | −3.65617 | −0.283774 | ||||||||
\(167\) | 8.71943 | 0.674730 | 0.337365 | − | 0.941374i | \(-0.390464\pi\) | ||||
0.337365 | + | 0.941374i | \(0.390464\pi\) | |||||||
\(168\) | 0.762027 | 0.0587916 | ||||||||
\(169\) | 1.81475 | 0.139596 | ||||||||
\(170\) | −0.624651 | −0.0479086 | ||||||||
\(171\) | 18.8305 | 1.44001 | ||||||||
\(172\) | −18.5441 | −1.41397 | ||||||||
\(173\) | 25.9281 | 1.97128 | 0.985638 | − | 0.168872i | \(-0.0540125\pi\) | ||||
0.985638 | + | 0.168872i | \(0.0540125\pi\) | |||||||
\(174\) | 41.3417 | 3.13410 | ||||||||
\(175\) | 0.359672 | 0.0271886 | ||||||||
\(176\) | −24.3167 | −1.83294 | ||||||||
\(177\) | 21.0477 | 1.58204 | ||||||||
\(178\) | −26.2124 | −1.96470 | ||||||||
\(179\) | 7.47024 | 0.558352 | 0.279176 | − | 0.960240i | \(-0.409939\pi\) | ||||
0.279176 | + | 0.960240i | \(0.409939\pi\) | |||||||
\(180\) | 4.79109 | 0.357107 | ||||||||
\(181\) | −17.2665 | −1.28341 | −0.641705 | − | 0.766952i | \(-0.721773\pi\) | ||||
−0.641705 | + | 0.766952i | \(0.721773\pi\) | |||||||
\(182\) | −2.60632 | −0.193193 | ||||||||
\(183\) | −7.18425 | −0.531075 | ||||||||
\(184\) | 3.90409 | 0.287813 | ||||||||
\(185\) | −0.0839175 | −0.00616974 | ||||||||
\(186\) | −17.9534 | −1.31641 | ||||||||
\(187\) | 1.71530 | 0.125435 | ||||||||
\(188\) | −14.7765 | −1.07768 | ||||||||
\(189\) | 0.0907696 | 0.00660252 | ||||||||
\(190\) | −11.4280 | −0.829077 | ||||||||
\(191\) | −18.5808 | −1.34446 | −0.672228 | − | 0.740344i | \(-0.734663\pi\) | ||||
−0.672228 | + | 0.740344i | \(0.734663\pi\) | |||||||
\(192\) | −9.96740 | −0.719335 | ||||||||
\(193\) | −7.18286 | −0.517034 | −0.258517 | − | 0.966007i | \(-0.583234\pi\) | ||||
−0.258517 | + | 0.966007i | \(0.583234\pi\) | |||||||
\(194\) | 0.246761 | 0.0177164 | ||||||||
\(195\) | 9.50800 | 0.680882 | ||||||||
\(196\) | −10.6113 | −0.757947 | ||||||||
\(197\) | 15.2620 | 1.08737 | 0.543685 | − | 0.839290i | \(-0.317029\pi\) | ||||
0.543685 | + | 0.839290i | \(0.317029\pi\) | |||||||
\(198\) | −30.1936 | −2.14576 | ||||||||
\(199\) | −3.03183 | −0.214921 | −0.107460 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107460 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(200\) | 0.857674 | 0.0606467 | ||||||||
\(201\) | −13.7532 | −0.970075 | ||||||||
\(202\) | 14.7072 | 1.03479 | ||||||||
\(203\) | −3.19726 | −0.224404 | ||||||||
\(204\) | 1.26583 | 0.0886259 | ||||||||
\(205\) | −3.28822 | −0.229660 | ||||||||
\(206\) | 26.0735 | 1.81663 | ||||||||
\(207\) | 14.1209 | 0.981471 | ||||||||
\(208\) | −18.1041 | −1.25529 | ||||||||
\(209\) | 31.3815 | 2.17071 | ||||||||
\(210\) | −1.67271 | −0.115428 | ||||||||
\(211\) | −8.63615 | −0.594537 | −0.297269 | − | 0.954794i | \(-0.596076\pi\) | ||||
−0.297269 | + | 0.954794i | \(0.596076\pi\) | |||||||
\(212\) | 6.15189 | 0.422513 | ||||||||
\(213\) | −14.2875 | −0.978963 | ||||||||
\(214\) | −10.1321 | −0.692618 | ||||||||
\(215\) | −12.0070 | −0.818873 | ||||||||
\(216\) | 0.216449 | 0.0147275 | ||||||||
\(217\) | 1.38847 | 0.0942557 | ||||||||
\(218\) | −11.1193 | −0.753093 | ||||||||
\(219\) | 40.7049 | 2.75058 | ||||||||
\(220\) | 7.98447 | 0.538313 | ||||||||
\(221\) | 1.27706 | 0.0859043 | ||||||||
\(222\) | 0.390273 | 0.0261934 | ||||||||
\(223\) | 10.1783 | 0.681589 | 0.340794 | − | 0.940138i | \(-0.389304\pi\) | ||||
0.340794 | + | 0.940138i | \(0.389304\pi\) | |||||||
\(224\) | 2.56804 | 0.171584 | ||||||||
\(225\) | 3.10216 | 0.206811 | ||||||||
\(226\) | −5.65039 | −0.375858 | ||||||||
\(227\) | 25.3332 | 1.68143 | 0.840713 | − | 0.541481i | \(-0.182136\pi\) | ||||
0.840713 | + | 0.541481i | \(0.182136\pi\) | |||||||
\(228\) | 23.1585 | 1.53371 | ||||||||
\(229\) | −20.1348 | −1.33055 | −0.665273 | − | 0.746601i | \(-0.731685\pi\) | ||||
−0.665273 | + | 0.746601i | \(0.731685\pi\) | |||||||
\(230\) | −8.56982 | −0.565077 | ||||||||
\(231\) | 4.59329 | 0.302216 | ||||||||
\(232\) | −7.62421 | −0.500554 | ||||||||
\(233\) | −4.71918 | −0.309164 | −0.154582 | − | 0.987980i | \(-0.549403\pi\) | ||||
−0.154582 | + | 0.987980i | \(0.549403\pi\) | |||||||
\(234\) | −22.4794 | −1.46953 | ||||||||
\(235\) | −9.56754 | −0.624117 | ||||||||
\(236\) | 13.1593 | 0.856599 | ||||||||
\(237\) | −16.1311 | −1.04783 | ||||||||
\(238\) | −0.224669 | −0.0145631 | ||||||||
\(239\) | 4.76557 | 0.308259 | 0.154129 | − | 0.988051i | \(-0.450743\pi\) | ||||
0.154129 | + | 0.988051i | \(0.450743\pi\) | |||||||
\(240\) | −11.6191 | −0.750007 | ||||||||
\(241\) | 7.37790 | 0.475253 | 0.237626 | − | 0.971357i | \(-0.423631\pi\) | ||||
0.237626 | + | 0.971357i | \(0.423631\pi\) | |||||||
\(242\) | −29.6090 | −1.90334 | ||||||||
\(243\) | −22.2065 | −1.42455 | ||||||||
\(244\) | −4.49169 | −0.287551 | ||||||||
\(245\) | −6.87064 | −0.438949 | ||||||||
\(246\) | 15.2924 | 0.975011 | ||||||||
\(247\) | 23.3639 | 1.48661 | ||||||||
\(248\) | 3.31096 | 0.210246 | ||||||||
\(249\) | 4.79728 | 0.304015 | ||||||||
\(250\) | −1.88267 | −0.119070 | ||||||||
\(251\) | 29.2656 | 1.84723 | 0.923616 | − | 0.383320i | \(-0.125219\pi\) | ||||
0.923616 | + | 0.383320i | \(0.125219\pi\) | |||||||
\(252\) | 1.72322 | 0.108553 | ||||||||
\(253\) | 23.5328 | 1.47950 | ||||||||
\(254\) | 10.6466 | 0.668028 | ||||||||
\(255\) | 0.819607 | 0.0513258 | ||||||||
\(256\) | 20.6525 | 1.29078 | ||||||||
\(257\) | −2.09085 | −0.130424 | −0.0652118 | − | 0.997871i | \(-0.520772\pi\) | ||||
−0.0652118 | + | 0.997871i | \(0.520772\pi\) | |||||||
\(258\) | 55.8407 | 3.47649 | ||||||||
\(259\) | −0.0301827 | −0.00187546 | ||||||||
\(260\) | 5.94453 | 0.368664 | ||||||||
\(261\) | −27.5764 | −1.70693 | ||||||||
\(262\) | 1.96513 | 0.121406 | ||||||||
\(263\) | −9.51589 | −0.586775 | −0.293387 | − | 0.955994i | \(-0.594783\pi\) | ||||
−0.293387 | + | 0.955994i | \(0.594783\pi\) | |||||||
\(264\) | 10.9532 | 0.674122 | ||||||||
\(265\) | 3.98325 | 0.244689 | ||||||||
\(266\) | −4.11034 | −0.252021 | ||||||||
\(267\) | 34.3934 | 2.10484 | ||||||||
\(268\) | −8.59867 | −0.525248 | ||||||||
\(269\) | 15.0493 | 0.917574 | 0.458787 | − | 0.888546i | \(-0.348284\pi\) | ||||
0.458787 | + | 0.888546i | \(0.348284\pi\) | |||||||
\(270\) | −0.475125 | −0.0289152 | ||||||||
\(271\) | −13.1023 | −0.795907 | −0.397954 | − | 0.917405i | \(-0.630280\pi\) | ||||
−0.397954 | + | 0.917405i | \(0.630280\pi\) | |||||||
\(272\) | −1.56061 | −0.0946256 | ||||||||
\(273\) | 3.41976 | 0.206973 | ||||||||
\(274\) | 37.9234 | 2.29103 | ||||||||
\(275\) | 5.16983 | 0.311752 | ||||||||
\(276\) | 17.3664 | 1.04533 | ||||||||
\(277\) | −3.73137 | −0.224196 | −0.112098 | − | 0.993697i | \(-0.535757\pi\) | ||||
−0.112098 | + | 0.993697i | \(0.535757\pi\) | |||||||
\(278\) | 38.1614 | 2.28877 | ||||||||
\(279\) | 11.9756 | 0.716958 | ||||||||
\(280\) | 0.308481 | 0.0184353 | ||||||||
\(281\) | −6.95712 | −0.415027 | −0.207513 | − | 0.978232i | \(-0.566537\pi\) | ||||
−0.207513 | + | 0.978232i | \(0.566537\pi\) | |||||||
\(282\) | 44.4955 | 2.64967 | ||||||||
\(283\) | 12.6825 | 0.753899 | 0.376950 | − | 0.926234i | \(-0.376973\pi\) | ||||
0.376950 | + | 0.926234i | \(0.376973\pi\) | |||||||
\(284\) | −8.93274 | −0.530060 | ||||||||
\(285\) | 14.9948 | 0.888214 | ||||||||
\(286\) | −37.4625 | −2.21521 | ||||||||
\(287\) | −1.18268 | −0.0698114 | ||||||||
\(288\) | 22.1493 | 1.30516 | ||||||||
\(289\) | −16.8899 | −0.993524 | ||||||||
\(290\) | 16.7358 | 0.982759 | ||||||||
\(291\) | −0.323776 | −0.0189801 | ||||||||
\(292\) | 25.4492 | 1.48930 | ||||||||
\(293\) | −10.2431 | −0.598410 | −0.299205 | − | 0.954189i | \(-0.596721\pi\) | ||||
−0.299205 | + | 0.954189i | \(0.596721\pi\) | |||||||
\(294\) | 31.9531 | 1.86354 | ||||||||
\(295\) | 8.52046 | 0.496081 | ||||||||
\(296\) | −0.0719738 | −0.00418339 | ||||||||
\(297\) | 1.30470 | 0.0757064 | ||||||||
\(298\) | −5.02333 | −0.290994 | ||||||||
\(299\) | 17.5204 | 1.01323 | ||||||||
\(300\) | 3.81515 | 0.220268 | ||||||||
\(301\) | −4.31859 | −0.248919 | ||||||||
\(302\) | −0.287762 | −0.0165588 | ||||||||
\(303\) | −19.2974 | −1.10860 | ||||||||
\(304\) | −28.5514 | −1.63753 | ||||||||
\(305\) | −2.90830 | −0.166529 | ||||||||
\(306\) | −1.93777 | −0.110775 | ||||||||
\(307\) | 13.7117 | 0.782567 | 0.391284 | − | 0.920270i | \(-0.372031\pi\) | ||||
0.391284 | + | 0.920270i | \(0.372031\pi\) | |||||||
\(308\) | 2.87179 | 0.163635 | ||||||||
\(309\) | −34.2111 | −1.94620 | ||||||||
\(310\) | −7.26783 | −0.412785 | ||||||||
\(311\) | 2.48910 | 0.141144 | 0.0705721 | − | 0.997507i | \(-0.477518\pi\) | ||||
0.0705721 | + | 0.997507i | \(0.477518\pi\) | |||||||
\(312\) | 8.15476 | 0.461672 | ||||||||
\(313\) | 18.9284 | 1.06989 | 0.534947 | − | 0.844885i | \(-0.320332\pi\) | ||||
0.534947 | + | 0.844885i | \(0.320332\pi\) | |||||||
\(314\) | −23.3670 | −1.31868 | ||||||||
\(315\) | 1.11576 | 0.0628659 | ||||||||
\(316\) | −10.0854 | −0.567346 | ||||||||
\(317\) | 21.3008 | 1.19637 | 0.598187 | − | 0.801357i | \(-0.295888\pi\) | ||||
0.598187 | + | 0.801357i | \(0.295888\pi\) | |||||||
\(318\) | −18.5248 | −1.03882 | ||||||||
\(319\) | −45.9567 | −2.57308 | ||||||||
\(320\) | −4.03497 | −0.225561 | ||||||||
\(321\) | 13.2944 | 0.742022 | ||||||||
\(322\) | −3.08232 | −0.171771 | ||||||||
\(323\) | 2.01401 | 0.112063 | ||||||||
\(324\) | −13.4105 | −0.745026 | ||||||||
\(325\) | 3.84899 | 0.213504 | ||||||||
\(326\) | −10.2775 | −0.569219 | ||||||||
\(327\) | 14.5897 | 0.806810 | ||||||||
\(328\) | −2.82022 | −0.155721 | ||||||||
\(329\) | −3.44117 | −0.189718 | ||||||||
\(330\) | −24.0432 | −1.32353 | ||||||||
\(331\) | −22.7554 | −1.25075 | −0.625374 | − | 0.780325i | \(-0.715053\pi\) | ||||
−0.625374 | + | 0.780325i | \(0.715053\pi\) | |||||||
\(332\) | 2.99932 | 0.164609 | ||||||||
\(333\) | −0.260326 | −0.0142658 | ||||||||
\(334\) | −16.4158 | −0.898232 | ||||||||
\(335\) | −5.56751 | −0.304186 | ||||||||
\(336\) | −4.17905 | −0.227986 | ||||||||
\(337\) | 14.5814 | 0.794298 | 0.397149 | − | 0.917754i | \(-0.370000\pi\) | ||||
0.397149 | + | 0.917754i | \(0.370000\pi\) | |||||||
\(338\) | −3.41657 | −0.185837 | ||||||||
\(339\) | 7.41390 | 0.402668 | ||||||||
\(340\) | 0.512429 | 0.0277904 | ||||||||
\(341\) | 19.9576 | 1.08076 | ||||||||
\(342\) | −35.4516 | −1.91700 | ||||||||
\(343\) | −4.98887 | −0.269374 | ||||||||
\(344\) | −10.2981 | −0.555237 | ||||||||
\(345\) | 11.2445 | 0.605383 | ||||||||
\(346\) | −48.8140 | −2.62426 | ||||||||
\(347\) | 10.2104 | 0.548121 | 0.274060 | − | 0.961712i | \(-0.411633\pi\) | ||||
0.274060 | + | 0.961712i | \(0.411633\pi\) | |||||||
\(348\) | −33.9144 | −1.81800 | ||||||||
\(349\) | −4.69795 | −0.251475 | −0.125738 | − | 0.992064i | \(-0.540130\pi\) | ||||
−0.125738 | + | 0.992064i | \(0.540130\pi\) | |||||||
\(350\) | −0.677142 | −0.0361948 | ||||||||
\(351\) | 0.971363 | 0.0518475 | ||||||||
\(352\) | 36.9123 | 1.96743 | ||||||||
\(353\) | 33.2339 | 1.76886 | 0.884432 | − | 0.466669i | \(-0.154546\pi\) | ||||
0.884432 | + | 0.466669i | \(0.154546\pi\) | |||||||
\(354\) | −39.6259 | −2.10609 | ||||||||
\(355\) | −5.78381 | −0.306973 | ||||||||
\(356\) | 21.5032 | 1.13967 | ||||||||
\(357\) | 0.294789 | 0.0156019 | ||||||||
\(358\) | −14.0640 | −0.743304 | ||||||||
\(359\) | 19.1315 | 1.00972 | 0.504861 | − | 0.863201i | \(-0.331544\pi\) | ||||
0.504861 | + | 0.863201i | \(0.331544\pi\) | |||||||
\(360\) | 2.66064 | 0.140228 | ||||||||
\(361\) | 17.8465 | 0.939288 | ||||||||
\(362\) | 32.5071 | 1.70853 | ||||||||
\(363\) | 38.8500 | 2.03910 | ||||||||
\(364\) | 2.13808 | 0.112066 | ||||||||
\(365\) | 16.4780 | 0.862499 | ||||||||
\(366\) | 13.5256 | 0.706992 | ||||||||
\(367\) | −17.6567 | −0.921672 | −0.460836 | − | 0.887485i | \(-0.652450\pi\) | ||||
−0.460836 | + | 0.887485i | \(0.652450\pi\) | |||||||
\(368\) | −21.4105 | −1.11610 | ||||||||
\(369\) | −10.2006 | −0.531022 | ||||||||
\(370\) | 0.157989 | 0.00821344 | ||||||||
\(371\) | 1.43266 | 0.0743802 | ||||||||
\(372\) | 14.7280 | 0.763611 | ||||||||
\(373\) | −23.8902 | −1.23699 | −0.618493 | − | 0.785790i | \(-0.712256\pi\) | ||||
−0.618493 | + | 0.785790i | \(0.712256\pi\) | |||||||
\(374\) | −3.22934 | −0.166985 | ||||||||
\(375\) | 2.47026 | 0.127563 | ||||||||
\(376\) | −8.20583 | −0.423183 | ||||||||
\(377\) | −34.2152 | −1.76217 | ||||||||
\(378\) | −0.170889 | −0.00878958 | ||||||||
\(379\) | −21.4359 | −1.10109 | −0.550544 | − | 0.834806i | \(-0.685580\pi\) | ||||
−0.550544 | + | 0.834806i | \(0.685580\pi\) | |||||||
\(380\) | 9.37493 | 0.480924 | ||||||||
\(381\) | −13.9695 | −0.715677 | ||||||||
\(382\) | 34.9814 | 1.78980 | ||||||||
\(383\) | 37.9957 | 1.94149 | 0.970744 | − | 0.240118i | \(-0.0771860\pi\) | ||||
0.970744 | + | 0.240118i | \(0.0771860\pi\) | |||||||
\(384\) | −16.5097 | −0.842506 | ||||||||
\(385\) | 1.85944 | 0.0947659 | ||||||||
\(386\) | 13.5229 | 0.688300 | ||||||||
\(387\) | −37.2478 | −1.89341 | ||||||||
\(388\) | −0.202429 | −0.0102768 | ||||||||
\(389\) | −19.1324 | −0.970054 | −0.485027 | − | 0.874499i | \(-0.661190\pi\) | ||||
−0.485027 | + | 0.874499i | \(0.661190\pi\) | |||||||
\(390\) | −17.9004 | −0.906422 | ||||||||
\(391\) | 1.51029 | 0.0763789 | ||||||||
\(392\) | −5.89277 | −0.297630 | ||||||||
\(393\) | −2.57846 | −0.130066 | ||||||||
\(394\) | −28.7332 | −1.44756 | ||||||||
\(395\) | −6.53012 | −0.328566 | ||||||||
\(396\) | 24.7691 | 1.24470 | ||||||||
\(397\) | 23.5575 | 1.18232 | 0.591158 | − | 0.806556i | \(-0.298671\pi\) | ||||
0.591158 | + | 0.806556i | \(0.298671\pi\) | |||||||
\(398\) | 5.70793 | 0.286113 | ||||||||
\(399\) | 5.39319 | 0.269997 | ||||||||
\(400\) | −4.70359 | −0.235179 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 25.8927 | 1.29141 | ||||||||
\(403\) | 14.8586 | 0.740161 | ||||||||
\(404\) | −12.0650 | −0.600255 | ||||||||
\(405\) | −8.68307 | −0.431465 | ||||||||
\(406\) | 6.01938 | 0.298737 | ||||||||
\(407\) | −0.433839 | −0.0215046 | ||||||||
\(408\) | 0.702956 | 0.0348015 | ||||||||
\(409\) | −14.9218 | −0.737836 | −0.368918 | − | 0.929462i | \(-0.620272\pi\) | ||||
−0.368918 | + | 0.929462i | \(0.620272\pi\) | |||||||
\(410\) | 6.19063 | 0.305734 | ||||||||
\(411\) | −49.7594 | −2.45445 | ||||||||
\(412\) | −21.3892 | −1.05377 | ||||||||
\(413\) | 3.06457 | 0.150798 | ||||||||
\(414\) | −26.5850 | −1.30658 | ||||||||
\(415\) | 1.94202 | 0.0953299 | ||||||||
\(416\) | 27.4816 | 1.34740 | ||||||||
\(417\) | −50.0717 | −2.45202 | ||||||||
\(418\) | −59.0810 | −2.88975 | ||||||||
\(419\) | −39.2555 | −1.91775 | −0.958877 | − | 0.283822i | \(-0.908398\pi\) | ||||
−0.958877 | + | 0.283822i | \(0.908398\pi\) | |||||||
\(420\) | 1.37220 | 0.0669566 | ||||||||
\(421\) | 1.33621 | 0.0651229 | 0.0325614 | − | 0.999470i | \(-0.489634\pi\) | ||||
0.0325614 | + | 0.999470i | \(0.489634\pi\) | |||||||
\(422\) | 16.2590 | 0.791476 | ||||||||
\(423\) | −29.6801 | −1.44309 | ||||||||
\(424\) | 3.41633 | 0.165912 | ||||||||
\(425\) | 0.331790 | 0.0160942 | ||||||||
\(426\) | 26.8986 | 1.30324 | ||||||||
\(427\) | −1.04603 | −0.0506211 | ||||||||
\(428\) | 8.31184 | 0.401768 | ||||||||
\(429\) | 49.1547 | 2.37321 | ||||||||
\(430\) | 22.6052 | 1.09012 | ||||||||
\(431\) | 4.64440 | 0.223713 | 0.111856 | − | 0.993724i | \(-0.464320\pi\) | ||||
0.111856 | + | 0.993724i | \(0.464320\pi\) | |||||||
\(432\) | −1.18704 | −0.0571113 | ||||||||
\(433\) | −33.0190 | −1.58679 | −0.793397 | − | 0.608704i | \(-0.791690\pi\) | ||||
−0.793397 | + | 0.608704i | \(0.791690\pi\) | |||||||
\(434\) | −2.61403 | −0.125478 | ||||||||
\(435\) | −21.9591 | −1.05286 | ||||||||
\(436\) | 9.12165 | 0.436848 | ||||||||
\(437\) | 27.6309 | 1.32177 | ||||||||
\(438\) | −76.6338 | −3.66170 | ||||||||
\(439\) | 0.233804 | 0.0111589 | 0.00557944 | − | 0.999984i | \(-0.498224\pi\) | ||||
0.00557944 | + | 0.999984i | \(0.498224\pi\) | |||||||
\(440\) | 4.43403 | 0.211384 | ||||||||
\(441\) | −21.3138 | −1.01494 | ||||||||
\(442\) | −2.40428 | −0.114360 | ||||||||
\(443\) | −39.3825 | −1.87112 | −0.935559 | − | 0.353170i | \(-0.885104\pi\) | ||||
−0.935559 | + | 0.353170i | \(0.885104\pi\) | |||||||
\(444\) | −0.320158 | −0.0151940 | ||||||||
\(445\) | 13.9230 | 0.660014 | ||||||||
\(446\) | −19.1623 | −0.907363 | ||||||||
\(447\) | 6.59113 | 0.311750 | ||||||||
\(448\) | −1.45126 | −0.0685657 | ||||||||
\(449\) | −22.5649 | −1.06490 | −0.532451 | − | 0.846461i | \(-0.678729\pi\) | ||||
−0.532451 | + | 0.846461i | \(0.678729\pi\) | |||||||
\(450\) | −5.84034 | −0.275316 | ||||||||
\(451\) | −16.9996 | −0.800478 | ||||||||
\(452\) | 4.63527 | 0.218025 | ||||||||
\(453\) | 0.377573 | 0.0177399 | ||||||||
\(454\) | −47.6941 | −2.23839 | ||||||||
\(455\) | 1.38437 | 0.0649004 | ||||||||
\(456\) | 12.8606 | 0.602254 | ||||||||
\(457\) | 14.7318 | 0.689124 | 0.344562 | − | 0.938764i | \(-0.388027\pi\) | ||||
0.344562 | + | 0.938764i | \(0.388027\pi\) | |||||||
\(458\) | 37.9071 | 1.77128 | ||||||||
\(459\) | 0.0837333 | 0.00390834 | ||||||||
\(460\) | 7.03021 | 0.327785 | ||||||||
\(461\) | −26.5125 | −1.23481 | −0.617404 | − | 0.786646i | \(-0.711816\pi\) | ||||
−0.617404 | + | 0.786646i | \(0.711816\pi\) | |||||||
\(462\) | −8.64764 | −0.402325 | ||||||||
\(463\) | −24.6790 | −1.14693 | −0.573466 | − | 0.819230i | \(-0.694401\pi\) | ||||
−0.573466 | + | 0.819230i | \(0.694401\pi\) | |||||||
\(464\) | 41.8121 | 1.94108 | ||||||||
\(465\) | 9.53615 | 0.442229 | ||||||||
\(466\) | 8.88466 | 0.411574 | ||||||||
\(467\) | 5.32908 | 0.246600 | 0.123300 | − | 0.992369i | \(-0.460652\pi\) | ||||
0.123300 | + | 0.992369i | \(0.460652\pi\) | |||||||
\(468\) | 18.4409 | 0.852431 | ||||||||
\(469\) | −2.00248 | −0.0924658 | ||||||||
\(470\) | 18.0125 | 0.830854 | ||||||||
\(471\) | 30.6599 | 1.41273 | ||||||||
\(472\) | 7.30778 | 0.336368 | ||||||||
\(473\) | −62.0743 | −2.85418 | ||||||||
\(474\) | 30.3694 | 1.39491 | ||||||||
\(475\) | 6.07013 | 0.278517 | ||||||||
\(476\) | 0.184306 | 0.00844766 | ||||||||
\(477\) | 12.3567 | 0.565775 | ||||||||
\(478\) | −8.97197 | −0.410369 | ||||||||
\(479\) | 27.1255 | 1.23940 | 0.619698 | − | 0.784841i | \(-0.287255\pi\) | ||||
0.619698 | + | 0.784841i | \(0.287255\pi\) | |||||||
\(480\) | 17.6375 | 0.805038 | ||||||||
\(481\) | −0.322998 | −0.0147274 | ||||||||
\(482\) | −13.8901 | −0.632679 | ||||||||
\(483\) | 4.04432 | 0.184023 | ||||||||
\(484\) | 24.2896 | 1.10407 | ||||||||
\(485\) | −0.131070 | −0.00595158 | ||||||||
\(486\) | 41.8075 | 1.89643 | ||||||||
\(487\) | −8.85228 | −0.401135 | −0.200568 | − | 0.979680i | \(-0.564279\pi\) | ||||
−0.200568 | + | 0.979680i | \(0.564279\pi\) | |||||||
\(488\) | −2.49438 | −0.112915 | ||||||||
\(489\) | 13.4852 | 0.609820 | ||||||||
\(490\) | 12.9351 | 0.584349 | ||||||||
\(491\) | 5.50856 | 0.248598 | 0.124299 | − | 0.992245i | \(-0.460332\pi\) | ||||
0.124299 | + | 0.992245i | \(0.460332\pi\) | |||||||
\(492\) | −12.5451 | −0.565576 | ||||||||
\(493\) | −2.94942 | −0.132835 | ||||||||
\(494\) | −43.9864 | −1.97904 | ||||||||
\(495\) | 16.0376 | 0.720839 | ||||||||
\(496\) | −18.1577 | −0.815305 | ||||||||
\(497\) | −2.08027 | −0.0933130 | ||||||||
\(498\) | −9.03168 | −0.404719 | ||||||||
\(499\) | −29.3998 | −1.31611 | −0.658057 | − | 0.752968i | \(-0.728622\pi\) | ||||
−0.658057 | + | 0.752968i | \(0.728622\pi\) | |||||||
\(500\) | 1.54444 | 0.0690693 | ||||||||
\(501\) | 21.5392 | 0.962301 | ||||||||
\(502\) | −55.0975 | −2.45912 | ||||||||
\(503\) | 30.0406 | 1.33945 | 0.669723 | − | 0.742611i | \(-0.266413\pi\) | ||||
0.669723 | + | 0.742611i | \(0.266413\pi\) | |||||||
\(504\) | 0.956958 | 0.0426263 | ||||||||
\(505\) | −7.81189 | −0.347624 | ||||||||
\(506\) | −44.3045 | −1.96957 | ||||||||
\(507\) | 4.48290 | 0.199093 | ||||||||
\(508\) | −8.73389 | −0.387504 | ||||||||
\(509\) | −22.8233 | −1.01162 | −0.505812 | − | 0.862644i | \(-0.668807\pi\) | ||||
−0.505812 | + | 0.862644i | \(0.668807\pi\) | |||||||
\(510\) | −1.54305 | −0.0683273 | ||||||||
\(511\) | 5.92667 | 0.262181 | ||||||||
\(512\) | −25.5151 | −1.12762 | ||||||||
\(513\) | 1.53191 | 0.0676353 | ||||||||
\(514\) | 3.93637 | 0.173626 | ||||||||
\(515\) | −13.8492 | −0.610270 | ||||||||
\(516\) | −45.8087 | −2.01661 | ||||||||
\(517\) | −49.4625 | −2.17536 | ||||||||
\(518\) | 0.0568240 | 0.00249671 | ||||||||
\(519\) | 64.0490 | 2.81144 | ||||||||
\(520\) | 3.30118 | 0.144766 | ||||||||
\(521\) | 22.2596 | 0.975211 | 0.487605 | − | 0.873064i | \(-0.337871\pi\) | ||||
0.487605 | + | 0.873064i | \(0.337871\pi\) | |||||||
\(522\) | 51.9171 | 2.27235 | ||||||||
\(523\) | 11.5568 | 0.505344 | 0.252672 | − | 0.967552i | \(-0.418691\pi\) | ||||
0.252672 | + | 0.967552i | \(0.418691\pi\) | |||||||
\(524\) | −1.61209 | −0.0704243 | ||||||||
\(525\) | 0.888481 | 0.0387765 | ||||||||
\(526\) | 17.9153 | 0.781142 | ||||||||
\(527\) | 1.28084 | 0.0557943 | ||||||||
\(528\) | −60.0686 | −2.61415 | ||||||||
\(529\) | −2.27971 | −0.0991180 | ||||||||
\(530\) | −7.49914 | −0.325742 | ||||||||
\(531\) | 26.4319 | 1.14705 | ||||||||
\(532\) | 3.37190 | 0.146190 | ||||||||
\(533\) | −12.6564 | −0.548208 | ||||||||
\(534\) | −64.7514 | −2.80207 | ||||||||
\(535\) | 5.38180 | 0.232675 | ||||||||
\(536\) | −4.77511 | −0.206253 | ||||||||
\(537\) | 18.4534 | 0.796323 | ||||||||
\(538\) | −28.3329 | −1.22152 | ||||||||
\(539\) | −35.5200 | −1.52996 | ||||||||
\(540\) | 0.389767 | 0.0167729 | ||||||||
\(541\) | −41.4991 | −1.78418 | −0.892092 | − | 0.451853i | \(-0.850763\pi\) | ||||
−0.892092 | + | 0.451853i | \(0.850763\pi\) | |||||||
\(542\) | 24.6673 | 1.05955 | ||||||||
\(543\) | −42.6527 | −1.83040 | ||||||||
\(544\) | 2.36897 | 0.101569 | ||||||||
\(545\) | 5.90613 | 0.252991 | ||||||||
\(546\) | −6.43826 | −0.275532 | ||||||||
\(547\) | −2.73715 | −0.117032 | −0.0585160 | − | 0.998286i | \(-0.518637\pi\) | ||||
−0.0585160 | + | 0.998286i | \(0.518637\pi\) | |||||||
\(548\) | −31.1102 | −1.32896 | ||||||||
\(549\) | −9.02203 | −0.385051 | ||||||||
\(550\) | −9.73307 | −0.415019 | ||||||||
\(551\) | −53.9598 | −2.29876 | ||||||||
\(552\) | 9.64411 | 0.410480 | ||||||||
\(553\) | −2.34870 | −0.0998768 | ||||||||
\(554\) | 7.02493 | 0.298461 | ||||||||
\(555\) | −0.207298 | −0.00879929 | ||||||||
\(556\) | −31.3055 | −1.32765 | ||||||||
\(557\) | −43.1801 | −1.82960 | −0.914801 | − | 0.403905i | \(-0.867652\pi\) | ||||
−0.914801 | + | 0.403905i | \(0.867652\pi\) | |||||||
\(558\) | −22.5460 | −0.954449 | ||||||||
\(559\) | −46.2150 | −1.95469 | ||||||||
\(560\) | −1.69175 | −0.0714894 | ||||||||
\(561\) | 4.23723 | 0.178896 | ||||||||
\(562\) | 13.0979 | 0.552503 | ||||||||
\(563\) | −9.14382 | −0.385366 | −0.192683 | − | 0.981261i | \(-0.561719\pi\) | ||||
−0.192683 | + | 0.981261i | \(0.561719\pi\) | |||||||
\(564\) | −36.5016 | −1.53700 | ||||||||
\(565\) | 3.00127 | 0.126264 | ||||||||
\(566\) | −23.8770 | −1.00363 | ||||||||
\(567\) | −3.12305 | −0.131156 | ||||||||
\(568\) | −4.96063 | −0.208143 | ||||||||
\(569\) | 9.36512 | 0.392606 | 0.196303 | − | 0.980543i | \(-0.437106\pi\) | ||||
0.196303 | + | 0.980543i | \(0.437106\pi\) | |||||||
\(570\) | −28.2302 | −1.18243 | ||||||||
\(571\) | 21.7699 | 0.911041 | 0.455520 | − | 0.890225i | \(-0.349453\pi\) | ||||
0.455520 | + | 0.890225i | \(0.349453\pi\) | |||||||
\(572\) | 30.7322 | 1.28498 | ||||||||
\(573\) | −45.8992 | −1.91747 | ||||||||
\(574\) | 2.22659 | 0.0929363 | ||||||||
\(575\) | 4.55195 | 0.189830 | ||||||||
\(576\) | −12.5171 | −0.521547 | ||||||||
\(577\) | 38.2125 | 1.59081 | 0.795404 | − | 0.606080i | \(-0.207259\pi\) | ||||
0.795404 | + | 0.606080i | \(0.207259\pi\) | |||||||
\(578\) | 31.7981 | 1.32263 | ||||||||
\(579\) | −17.7435 | −0.737395 | ||||||||
\(580\) | −13.7291 | −0.570070 | ||||||||
\(581\) | 0.698488 | 0.0289782 | ||||||||
\(582\) | 0.609563 | 0.0252672 | ||||||||
\(583\) | 20.5927 | 0.852864 | ||||||||
\(584\) | 14.1328 | 0.584818 | ||||||||
\(585\) | 11.9402 | 0.493667 | ||||||||
\(586\) | 19.2844 | 0.796632 | ||||||||
\(587\) | −8.61476 | −0.355569 | −0.177785 | − | 0.984069i | \(-0.556893\pi\) | ||||
−0.177785 | + | 0.984069i | \(0.556893\pi\) | |||||||
\(588\) | −26.2125 | −1.08099 | ||||||||
\(589\) | 23.4331 | 0.965543 | ||||||||
\(590\) | −16.0412 | −0.660406 | ||||||||
\(591\) | 37.7009 | 1.55081 | ||||||||
\(592\) | 0.394713 | 0.0162226 | ||||||||
\(593\) | 34.9986 | 1.43722 | 0.718611 | − | 0.695413i | \(-0.244778\pi\) | ||||
0.718611 | + | 0.695413i | \(0.244778\pi\) | |||||||
\(594\) | −2.45632 | −0.100784 | ||||||||
\(595\) | 0.119336 | 0.00489228 | ||||||||
\(596\) | 4.12086 | 0.168797 | ||||||||
\(597\) | −7.48940 | −0.306521 | ||||||||
\(598\) | −32.9852 | −1.34886 | ||||||||
\(599\) | −44.8538 | −1.83268 | −0.916339 | − | 0.400404i | \(-0.868870\pi\) | ||||
−0.916339 | + | 0.400404i | \(0.868870\pi\) | |||||||
\(600\) | 2.11867 | 0.0864945 | ||||||||
\(601\) | 34.1735 | 1.39396 | 0.696982 | − | 0.717088i | \(-0.254526\pi\) | ||||
0.696982 | + | 0.717088i | \(0.254526\pi\) | |||||||
\(602\) | 8.13046 | 0.331373 | ||||||||
\(603\) | −17.2713 | −0.703343 | ||||||||
\(604\) | 0.236064 | 0.00960530 | ||||||||
\(605\) | 15.7271 | 0.639399 | ||||||||
\(606\) | 36.3305 | 1.47583 | ||||||||
\(607\) | −8.06230 | −0.327239 | −0.163619 | − | 0.986524i | \(-0.552317\pi\) | ||||
−0.163619 | + | 0.986524i | \(0.552317\pi\) | |||||||
\(608\) | 43.3404 | 1.75768 | ||||||||
\(609\) | −7.89806 | −0.320046 | ||||||||
\(610\) | 5.47537 | 0.221691 | ||||||||
\(611\) | −36.8254 | −1.48980 | ||||||||
\(612\) | 1.58964 | 0.0642574 | ||||||||
\(613\) | −34.7708 | −1.40438 | −0.702190 | − | 0.711989i | \(-0.747794\pi\) | ||||
−0.702190 | + | 0.711989i | \(0.747794\pi\) | |||||||
\(614\) | −25.8145 | −1.04179 | ||||||||
\(615\) | −8.12276 | −0.327541 | ||||||||
\(616\) | 1.59479 | 0.0642561 | ||||||||
\(617\) | 9.44795 | 0.380360 | 0.190180 | − | 0.981749i | \(-0.439093\pi\) | ||||
0.190180 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(618\) | 64.4082 | 2.59088 | ||||||||
\(619\) | 25.7746 | 1.03597 | 0.517984 | − | 0.855390i | \(-0.326683\pi\) | ||||
0.517984 | + | 0.855390i | \(0.326683\pi\) | |||||||
\(620\) | 5.96213 | 0.239445 | ||||||||
\(621\) | 1.14877 | 0.0460985 | ||||||||
\(622\) | −4.68615 | −0.187898 | ||||||||
\(623\) | 5.00771 | 0.200630 | ||||||||
\(624\) | −44.7217 | −1.79030 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −35.6358 | −1.42429 | ||||||||
\(627\) | 77.5204 | 3.09587 | ||||||||
\(628\) | 19.1690 | 0.764926 | ||||||||
\(629\) | −0.0278430 | −0.00111017 | ||||||||
\(630\) | −2.10060 | −0.0836901 | ||||||||
\(631\) | 20.0942 | 0.799937 | 0.399969 | − | 0.916529i | \(-0.369021\pi\) | ||||
0.399969 | + | 0.916529i | \(0.369021\pi\) | |||||||
\(632\) | −5.60071 | −0.222784 | ||||||||
\(633\) | −21.3335 | −0.847930 | ||||||||
\(634\) | −40.1024 | −1.59267 | ||||||||
\(635\) | −5.65507 | −0.224414 | ||||||||
\(636\) | 15.1967 | 0.602590 | ||||||||
\(637\) | −26.4450 | −1.04779 | ||||||||
\(638\) | 86.5211 | 3.42540 | ||||||||
\(639\) | −17.9423 | −0.709788 | ||||||||
\(640\) | −6.68339 | −0.264184 | ||||||||
\(641\) | −4.91683 | −0.194203 | −0.0971015 | − | 0.995274i | \(-0.530957\pi\) | ||||
−0.0971015 | + | 0.995274i | \(0.530957\pi\) | |||||||
\(642\) | −25.0290 | −0.987814 | ||||||||
\(643\) | 43.2595 | 1.70599 | 0.852994 | − | 0.521922i | \(-0.174785\pi\) | ||||
0.852994 | + | 0.521922i | \(0.174785\pi\) | |||||||
\(644\) | 2.52857 | 0.0996394 | ||||||||
\(645\) | −29.6604 | −1.16788 | ||||||||
\(646\) | −3.79171 | −0.149183 | ||||||||
\(647\) | −35.4758 | −1.39470 | −0.697348 | − | 0.716732i | \(-0.745637\pi\) | ||||
−0.697348 | + | 0.716732i | \(0.745637\pi\) | |||||||
\(648\) | −7.44725 | −0.292555 | ||||||||
\(649\) | 44.0493 | 1.72909 | ||||||||
\(650\) | −7.24638 | −0.284226 | ||||||||
\(651\) | 3.42988 | 0.134428 | ||||||||
\(652\) | 8.43111 | 0.330188 | ||||||||
\(653\) | −18.8927 | −0.739330 | −0.369665 | − | 0.929165i | \(-0.620528\pi\) | ||||
−0.369665 | + | 0.929165i | \(0.620528\pi\) | |||||||
\(654\) | −27.4675 | −1.07406 | ||||||||
\(655\) | −1.04380 | −0.0407847 | ||||||||
\(656\) | 15.4665 | 0.603864 | ||||||||
\(657\) | 51.1175 | 1.99428 | ||||||||
\(658\) | 6.47858 | 0.252561 | ||||||||
\(659\) | 15.4408 | 0.601489 | 0.300744 | − | 0.953705i | \(-0.402765\pi\) | ||||
0.300744 | + | 0.953705i | \(0.402765\pi\) | |||||||
\(660\) | 19.7237 | 0.767744 | ||||||||
\(661\) | −46.9182 | −1.82491 | −0.912454 | − | 0.409179i | \(-0.865815\pi\) | ||||
−0.912454 | + | 0.409179i | \(0.865815\pi\) | |||||||
\(662\) | 42.8408 | 1.66505 | ||||||||
\(663\) | 3.15466 | 0.122517 | ||||||||
\(664\) | 1.66562 | 0.0646385 | ||||||||
\(665\) | 2.18325 | 0.0846629 | ||||||||
\(666\) | 0.490107 | 0.0189912 | ||||||||
\(667\) | −40.4641 | −1.56678 | ||||||||
\(668\) | 13.4666 | 0.521039 | ||||||||
\(669\) | 25.1430 | 0.972084 | ||||||||
\(670\) | 10.4818 | 0.404946 | ||||||||
\(671\) | −15.0354 | −0.580436 | ||||||||
\(672\) | 6.34370 | 0.244714 | ||||||||
\(673\) | 35.9705 | 1.38656 | 0.693281 | − | 0.720668i | \(-0.256165\pi\) | ||||
0.693281 | + | 0.720668i | \(0.256165\pi\) | |||||||
\(674\) | −27.4519 | −1.05741 | ||||||||
\(675\) | 0.252368 | 0.00971365 | ||||||||
\(676\) | 2.80277 | 0.107799 | ||||||||
\(677\) | −35.8881 | −1.37929 | −0.689646 | − | 0.724146i | \(-0.742234\pi\) | ||||
−0.689646 | + | 0.724146i | \(0.742234\pi\) | |||||||
\(678\) | −13.9579 | −0.536050 | ||||||||
\(679\) | −0.0471422 | −0.00180915 | ||||||||
\(680\) | 0.284568 | 0.0109127 | ||||||||
\(681\) | 62.5796 | 2.39805 | ||||||||
\(682\) | −37.5735 | −1.43876 | ||||||||
\(683\) | 8.62788 | 0.330137 | 0.165068 | − | 0.986282i | \(-0.447216\pi\) | ||||
0.165068 | + | 0.986282i | \(0.447216\pi\) | |||||||
\(684\) | 29.0826 | 1.11200 | ||||||||
\(685\) | −20.1434 | −0.769641 | ||||||||
\(686\) | 9.39239 | 0.358603 | ||||||||
\(687\) | −49.7381 | −1.89763 | ||||||||
\(688\) | 56.4761 | 2.15313 | ||||||||
\(689\) | 15.3315 | 0.584084 | ||||||||
\(690\) | −21.1696 | −0.805914 | ||||||||
\(691\) | −9.07301 | −0.345154 | −0.172577 | − | 0.984996i | \(-0.555209\pi\) | ||||
−0.172577 | + | 0.984996i | \(0.555209\pi\) | |||||||
\(692\) | 40.0443 | 1.52226 | ||||||||
\(693\) | 5.76829 | 0.219119 | ||||||||
\(694\) | −19.2227 | −0.729684 | ||||||||
\(695\) | −20.2698 | −0.768879 | ||||||||
\(696\) | −18.8337 | −0.713891 | ||||||||
\(697\) | −1.09100 | −0.0413246 | ||||||||
\(698\) | 8.84467 | 0.334776 | ||||||||
\(699\) | −11.6576 | −0.440931 | ||||||||
\(700\) | 0.555490 | 0.0209955 | ||||||||
\(701\) | 27.3340 | 1.03239 | 0.516195 | − | 0.856471i | \(-0.327348\pi\) | ||||
0.516195 | + | 0.856471i | \(0.327348\pi\) | |||||||
\(702\) | −1.82875 | −0.0690219 | ||||||||
\(703\) | −0.509390 | −0.0192120 | ||||||||
\(704\) | −20.8601 | −0.786194 | ||||||||
\(705\) | −23.6343 | −0.890118 | ||||||||
\(706\) | −62.5685 | −2.35480 | ||||||||
\(707\) | −2.80971 | −0.105670 | ||||||||
\(708\) | 32.5069 | 1.22168 | ||||||||
\(709\) | 29.4217 | 1.10495 | 0.552477 | − | 0.833528i | \(-0.313683\pi\) | ||||
0.552477 | + | 0.833528i | \(0.313683\pi\) | |||||||
\(710\) | 10.8890 | 0.408657 | ||||||||
\(711\) | −20.2575 | −0.759715 | ||||||||
\(712\) | 11.9414 | 0.447523 | ||||||||
\(713\) | 17.5723 | 0.658089 | ||||||||
\(714\) | −0.554990 | −0.0207700 | ||||||||
\(715\) | 19.8986 | 0.744167 | ||||||||
\(716\) | 11.5373 | 0.431170 | ||||||||
\(717\) | 11.7722 | 0.439640 | ||||||||
\(718\) | −36.0183 | −1.34419 | ||||||||
\(719\) | −37.3915 | −1.39447 | −0.697234 | − | 0.716844i | \(-0.745586\pi\) | ||||
−0.697234 | + | 0.716844i | \(0.745586\pi\) | |||||||
\(720\) | −14.5913 | −0.543786 | ||||||||
\(721\) | −4.98117 | −0.185509 | ||||||||
\(722\) | −33.5990 | −1.25042 | ||||||||
\(723\) | 18.2253 | 0.677807 | ||||||||
\(724\) | −26.6670 | −0.991072 | ||||||||
\(725\) | −8.88940 | −0.330144 | ||||||||
\(726\) | −73.1417 | −2.71454 | ||||||||
\(727\) | −10.8008 | −0.400579 | −0.200289 | − | 0.979737i | \(-0.564188\pi\) | ||||
−0.200289 | + | 0.979737i | \(0.564188\pi\) | |||||||
\(728\) | 1.18734 | 0.0440058 | ||||||||
\(729\) | −28.8066 | −1.06691 | ||||||||
\(730\) | −31.0226 | −1.14820 | ||||||||
\(731\) | −3.98382 | −0.147347 | ||||||||
\(732\) | −11.0956 | −0.410106 | ||||||||
\(733\) | −9.70111 | −0.358319 | −0.179159 | − | 0.983820i | \(-0.557338\pi\) | ||||
−0.179159 | + | 0.983820i | \(0.557338\pi\) | |||||||
\(734\) | 33.2417 | 1.22697 | ||||||||
\(735\) | −16.9722 | −0.626030 | ||||||||
\(736\) | 32.5007 | 1.19799 | ||||||||
\(737\) | −28.7831 | −1.06024 | ||||||||
\(738\) | 19.2044 | 0.706922 | ||||||||
\(739\) | 14.9881 | 0.551347 | 0.275673 | − | 0.961251i | \(-0.411099\pi\) | ||||
0.275673 | + | 0.961251i | \(0.411099\pi\) | |||||||
\(740\) | −0.129605 | −0.00476438 | ||||||||
\(741\) | 57.7148 | 2.12021 | ||||||||
\(742\) | −2.69723 | −0.0990184 | ||||||||
\(743\) | 45.6383 | 1.67431 | 0.837153 | − | 0.546969i | \(-0.184218\pi\) | ||||
0.837153 | + | 0.546969i | \(0.184218\pi\) | |||||||
\(744\) | 8.17891 | 0.299853 | ||||||||
\(745\) | 2.66820 | 0.0977552 | ||||||||
\(746\) | 44.9772 | 1.64673 | ||||||||
\(747\) | 6.02445 | 0.220423 | ||||||||
\(748\) | 2.64917 | 0.0968633 | ||||||||
\(749\) | 1.93568 | 0.0707282 | ||||||||
\(750\) | −4.65067 | −0.169818 | ||||||||
\(751\) | 44.6761 | 1.63026 | 0.815128 | − | 0.579281i | \(-0.196667\pi\) | ||||
0.815128 | + | 0.579281i | \(0.196667\pi\) | |||||||
\(752\) | 45.0018 | 1.64105 | ||||||||
\(753\) | 72.2936 | 2.63453 | ||||||||
\(754\) | 64.4159 | 2.34589 | ||||||||
\(755\) | 0.152848 | 0.00556270 | ||||||||
\(756\) | 0.140188 | 0.00509859 | ||||||||
\(757\) | −30.1368 | −1.09534 | −0.547670 | − | 0.836695i | \(-0.684485\pi\) | ||||
−0.547670 | + | 0.836695i | \(0.684485\pi\) | |||||||
\(758\) | 40.3566 | 1.46582 | ||||||||
\(759\) | 58.1321 | 2.11006 | ||||||||
\(760\) | 5.20619 | 0.188848 | ||||||||
\(761\) | −48.6214 | −1.76253 | −0.881263 | − | 0.472627i | \(-0.843306\pi\) | ||||
−0.881263 | + | 0.472627i | \(0.843306\pi\) | |||||||
\(762\) | 26.2998 | 0.952743 | ||||||||
\(763\) | 2.12427 | 0.0769036 | ||||||||
\(764\) | −28.6968 | −1.03821 | ||||||||
\(765\) | 1.02927 | 0.0372133 | ||||||||
\(766\) | −71.5332 | −2.58460 | ||||||||
\(767\) | 32.7952 | 1.18417 | ||||||||
\(768\) | 51.0170 | 1.84092 | ||||||||
\(769\) | −7.22344 | −0.260484 | −0.130242 | − | 0.991482i | \(-0.541575\pi\) | ||||
−0.130242 | + | 0.991482i | \(0.541575\pi\) | |||||||
\(770\) | −3.50071 | −0.126157 | ||||||||
\(771\) | −5.16493 | −0.186010 | ||||||||
\(772\) | −11.0935 | −0.399263 | ||||||||
\(773\) | 17.2166 | 0.619238 | 0.309619 | − | 0.950861i | \(-0.399798\pi\) | ||||
0.309619 | + | 0.950861i | \(0.399798\pi\) | |||||||
\(774\) | 70.1251 | 2.52060 | ||||||||
\(775\) | 3.86039 | 0.138669 | ||||||||
\(776\) | −0.112415 | −0.00403548 | ||||||||
\(777\) | −0.0745591 | −0.00267479 | ||||||||
\(778\) | 36.0200 | 1.29138 | ||||||||
\(779\) | −19.9599 | −0.715139 | ||||||||
\(780\) | 14.6845 | 0.525790 | ||||||||
\(781\) | −29.9013 | −1.06995 | ||||||||
\(782\) | −2.84338 | −0.101679 | ||||||||
\(783\) | −2.24340 | −0.0801726 | ||||||||
\(784\) | 32.3166 | 1.15417 | ||||||||
\(785\) | 12.4116 | 0.442990 | ||||||||
\(786\) | 4.85438 | 0.173150 | ||||||||
\(787\) | −44.7451 | −1.59499 | −0.797495 | − | 0.603325i | \(-0.793842\pi\) | ||||
−0.797495 | + | 0.603325i | \(0.793842\pi\) | |||||||
\(788\) | 23.5711 | 0.839687 | ||||||||
\(789\) | −23.5067 | −0.836860 | ||||||||
\(790\) | 12.2940 | 0.437402 | ||||||||
\(791\) | 1.07947 | 0.0383815 | ||||||||
\(792\) | 13.7551 | 0.488765 | ||||||||
\(793\) | −11.1940 | −0.397512 | ||||||||
\(794\) | −44.3509 | −1.57395 | ||||||||
\(795\) | 9.83966 | 0.348977 | ||||||||
\(796\) | −4.68247 | −0.165966 | ||||||||
\(797\) | 5.42828 | 0.192280 | 0.0961399 | − | 0.995368i | \(-0.469350\pi\) | ||||
0.0961399 | + | 0.995368i | \(0.469350\pi\) | |||||||
\(798\) | −10.1536 | −0.359433 | ||||||||
\(799\) | −3.17442 | −0.112303 | ||||||||
\(800\) | 7.13995 | 0.252435 | ||||||||
\(801\) | 43.1915 | 1.52610 | ||||||||
\(802\) | 1.88267 | 0.0664793 | ||||||||
\(803\) | 85.1885 | 3.00624 | ||||||||
\(804\) | −21.2409 | −0.749110 | ||||||||
\(805\) | 1.63721 | 0.0577040 | ||||||||
\(806\) | −27.9738 | −0.985337 | ||||||||
\(807\) | 37.1757 | 1.30865 | ||||||||
\(808\) | −6.70005 | −0.235707 | ||||||||
\(809\) | 23.0741 | 0.811243 | 0.405621 | − | 0.914041i | \(-0.367055\pi\) | ||||
0.405621 | + | 0.914041i | \(0.367055\pi\) | |||||||
\(810\) | 16.3473 | 0.574387 | ||||||||
\(811\) | 5.36379 | 0.188348 | 0.0941741 | − | 0.995556i | \(-0.469979\pi\) | ||||
0.0941741 | + | 0.995556i | \(0.469979\pi\) | |||||||
\(812\) | −4.93797 | −0.173289 | ||||||||
\(813\) | −32.3660 | −1.13513 | ||||||||
\(814\) | 0.816775 | 0.0286279 | ||||||||
\(815\) | 5.45902 | 0.191221 | ||||||||
\(816\) | −3.85509 | −0.134955 | ||||||||
\(817\) | −72.8842 | −2.54990 | ||||||||
\(818\) | 28.0928 | 0.982242 | ||||||||
\(819\) | 4.29455 | 0.150064 | ||||||||
\(820\) | −5.07846 | −0.177347 | ||||||||
\(821\) | 16.0163 | 0.558974 | 0.279487 | − | 0.960150i | \(-0.409836\pi\) | ||||
0.279487 | + | 0.960150i | \(0.409836\pi\) | |||||||
\(822\) | 93.6804 | 3.26748 | ||||||||
\(823\) | −8.92417 | −0.311077 | −0.155538 | − | 0.987830i | \(-0.549711\pi\) | ||||
−0.155538 | + | 0.987830i | \(0.549711\pi\) | |||||||
\(824\) | −11.8781 | −0.413794 | ||||||||
\(825\) | 12.7708 | 0.444622 | ||||||||
\(826\) | −5.76956 | −0.200749 | ||||||||
\(827\) | −30.6036 | −1.06419 | −0.532096 | − | 0.846684i | \(-0.678596\pi\) | ||||
−0.532096 | + | 0.846684i | \(0.678596\pi\) | |||||||
\(828\) | 21.8088 | 0.757910 | ||||||||
\(829\) | −2.52311 | −0.0876314 | −0.0438157 | − | 0.999040i | \(-0.513951\pi\) | ||||
−0.0438157 | + | 0.999040i | \(0.513951\pi\) | |||||||
\(830\) | −3.65617 | −0.126908 | ||||||||
\(831\) | −9.21744 | −0.319749 | ||||||||
\(832\) | −15.5306 | −0.538425 | ||||||||
\(833\) | −2.27961 | −0.0789839 | ||||||||
\(834\) | 94.2683 | 3.26424 | ||||||||
\(835\) | 8.71943 | 0.301748 | ||||||||
\(836\) | 48.4668 | 1.67626 | ||||||||
\(837\) | 0.974240 | 0.0336746 | ||||||||
\(838\) | 73.9050 | 2.55300 | ||||||||
\(839\) | −12.9948 | −0.448631 | −0.224315 | − | 0.974517i | \(-0.572015\pi\) | ||||
−0.224315 | + | 0.974517i | \(0.572015\pi\) | |||||||
\(840\) | 0.762027 | 0.0262924 | ||||||||
\(841\) | 50.0214 | 1.72488 | ||||||||
\(842\) | −2.51564 | −0.0866946 | ||||||||
\(843\) | −17.1859 | −0.591912 | ||||||||
\(844\) | −13.3380 | −0.459112 | ||||||||
\(845\) | 1.81475 | 0.0624293 | ||||||||
\(846\) | 55.8777 | 1.92111 | ||||||||
\(847\) | 5.65660 | 0.194363 | ||||||||
\(848\) | −18.7356 | −0.643383 | ||||||||
\(849\) | 31.3291 | 1.07521 | ||||||||
\(850\) | −0.624651 | −0.0214254 | ||||||||
\(851\) | −0.381989 | −0.0130944 | ||||||||
\(852\) | −22.0661 | −0.755973 | ||||||||
\(853\) | −38.7716 | −1.32751 | −0.663757 | − | 0.747948i | \(-0.731039\pi\) | ||||
−0.663757 | + | 0.747948i | \(0.731039\pi\) | |||||||
\(854\) | 1.96933 | 0.0673892 | ||||||||
\(855\) | 18.8305 | 0.643990 | ||||||||
\(856\) | 4.61583 | 0.157766 | ||||||||
\(857\) | −5.83115 | −0.199188 | −0.0995941 | − | 0.995028i | \(-0.531754\pi\) | ||||
−0.0995941 | + | 0.995028i | \(0.531754\pi\) | |||||||
\(858\) | −92.5420 | −3.15933 | ||||||||
\(859\) | −9.47873 | −0.323410 | −0.161705 | − | 0.986839i | \(-0.551699\pi\) | ||||
−0.161705 | + | 0.986839i | \(0.551699\pi\) | |||||||
\(860\) | −18.5441 | −0.632348 | ||||||||
\(861\) | −2.92152 | −0.0995653 | ||||||||
\(862\) | −8.74385 | −0.297817 | ||||||||
\(863\) | −23.6659 | −0.805597 | −0.402799 | − | 0.915289i | \(-0.631963\pi\) | ||||
−0.402799 | + | 0.915289i | \(0.631963\pi\) | |||||||
\(864\) | 1.80189 | 0.0613017 | ||||||||
\(865\) | 25.9281 | 0.881581 | ||||||||
\(866\) | 62.1639 | 2.11241 | ||||||||
\(867\) | −41.7224 | −1.41697 | ||||||||
\(868\) | 2.14441 | 0.0727860 | ||||||||
\(869\) | −33.7596 | −1.14522 | ||||||||
\(870\) | 41.3417 | 1.40161 | ||||||||
\(871\) | −21.4293 | −0.726105 | ||||||||
\(872\) | 5.06553 | 0.171541 | ||||||||
\(873\) | −0.406601 | −0.0137613 | ||||||||
\(874\) | −52.0199 | −1.75960 | ||||||||
\(875\) | 0.359672 | 0.0121591 | ||||||||
\(876\) | 62.8661 | 2.12405 | ||||||||
\(877\) | 29.9042 | 1.00979 | 0.504897 | − | 0.863179i | \(-0.331530\pi\) | ||||
0.504897 | + | 0.863179i | \(0.331530\pi\) | |||||||
\(878\) | −0.440176 | −0.0148552 | ||||||||
\(879\) | −25.3032 | −0.853454 | ||||||||
\(880\) | −24.3167 | −0.819717 | ||||||||
\(881\) | 16.5853 | 0.558774 | 0.279387 | − | 0.960179i | \(-0.409869\pi\) | ||||
0.279387 | + | 0.960179i | \(0.409869\pi\) | |||||||
\(882\) | 40.1269 | 1.35114 | ||||||||
\(883\) | 17.0913 | 0.575169 | 0.287584 | − | 0.957755i | \(-0.407148\pi\) | ||||
0.287584 | + | 0.957755i | \(0.407148\pi\) | |||||||
\(884\) | 1.97234 | 0.0663369 | ||||||||
\(885\) | 21.0477 | 0.707512 | ||||||||
\(886\) | 74.1441 | 2.49092 | ||||||||
\(887\) | 45.7489 | 1.53610 | 0.768049 | − | 0.640391i | \(-0.221227\pi\) | ||||
0.768049 | + | 0.640391i | \(0.221227\pi\) | |||||||
\(888\) | −0.177794 | −0.00596637 | ||||||||
\(889\) | −2.03397 | −0.0682170 | ||||||||
\(890\) | −26.2124 | −0.878642 | ||||||||
\(891\) | −44.8900 | −1.50387 | ||||||||
\(892\) | 15.7197 | 0.526335 | ||||||||
\(893\) | −58.0762 | −1.94345 | ||||||||
\(894\) | −12.4089 | −0.415016 | ||||||||
\(895\) | 7.47024 | 0.249703 | ||||||||
\(896\) | −2.40383 | −0.0803062 | ||||||||
\(897\) | 43.2800 | 1.44508 | ||||||||
\(898\) | 42.4822 | 1.41765 | ||||||||
\(899\) | −34.3166 | −1.14452 | ||||||||
\(900\) | 4.79109 | 0.159703 | ||||||||
\(901\) | 1.32161 | 0.0440291 | ||||||||
\(902\) | 32.0045 | 1.06563 | ||||||||
\(903\) | −10.6680 | −0.355009 | ||||||||
\(904\) | 2.57411 | 0.0856136 | ||||||||
\(905\) | −17.2665 | −0.573958 | ||||||||
\(906\) | −0.710844 | −0.0236162 | ||||||||
\(907\) | −52.0051 | −1.72680 | −0.863400 | − | 0.504520i | \(-0.831670\pi\) | ||||
−0.863400 | + | 0.504520i | \(0.831670\pi\) | |||||||
\(908\) | 39.1256 | 1.29843 | ||||||||
\(909\) | −24.2337 | −0.803783 | ||||||||
\(910\) | −2.60632 | −0.0863985 | ||||||||
\(911\) | 18.5204 | 0.613608 | 0.306804 | − | 0.951773i | \(-0.400740\pi\) | ||||
0.306804 | + | 0.951773i | \(0.400740\pi\) | |||||||
\(912\) | −70.5292 | −2.33546 | ||||||||
\(913\) | 10.0399 | 0.332272 | ||||||||
\(914\) | −27.7351 | −0.917394 | ||||||||
\(915\) | −7.18425 | −0.237504 | ||||||||
\(916\) | −31.0969 | −1.02747 | ||||||||
\(917\) | −0.375426 | −0.0123977 | ||||||||
\(918\) | −0.157642 | −0.00520296 | ||||||||
\(919\) | 41.1033 | 1.35587 | 0.677937 | − | 0.735120i | \(-0.262874\pi\) | ||||
0.677937 | + | 0.735120i | \(0.262874\pi\) | |||||||
\(920\) | 3.90409 | 0.128714 | ||||||||
\(921\) | 33.8714 | 1.11610 | ||||||||
\(922\) | 49.9142 | 1.64384 | ||||||||
\(923\) | −22.2619 | −0.732758 | ||||||||
\(924\) | 7.09405 | 0.233377 | ||||||||
\(925\) | −0.0839175 | −0.00275919 | ||||||||
\(926\) | 46.4624 | 1.52685 | ||||||||
\(927\) | −42.9625 | −1.41107 | ||||||||
\(928\) | −63.4698 | −2.08350 | ||||||||
\(929\) | 39.6944 | 1.30233 | 0.651166 | − | 0.758935i | \(-0.274280\pi\) | ||||
0.651166 | + | 0.758935i | \(0.274280\pi\) | |||||||
\(930\) | −17.9534 | −0.588715 | ||||||||
\(931\) | −41.7056 | −1.36685 | ||||||||
\(932\) | −7.28848 | −0.238742 | ||||||||
\(933\) | 6.14872 | 0.201300 | ||||||||
\(934\) | −10.0329 | −0.328286 | ||||||||
\(935\) | 1.71530 | 0.0560963 | ||||||||
\(936\) | 10.2408 | 0.334731 | ||||||||
\(937\) | 9.73210 | 0.317934 | 0.158967 | − | 0.987284i | \(-0.449184\pi\) | ||||
0.158967 | + | 0.987284i | \(0.449184\pi\) | |||||||
\(938\) | 3.77000 | 0.123095 | ||||||||
\(939\) | 46.7579 | 1.52589 | ||||||||
\(940\) | −14.7765 | −0.481955 | ||||||||
\(941\) | 42.3982 | 1.38214 | 0.691071 | − | 0.722787i | \(-0.257139\pi\) | ||||
0.691071 | + | 0.722787i | \(0.257139\pi\) | |||||||
\(942\) | −57.7224 | −1.88070 | ||||||||
\(943\) | −14.9678 | −0.487420 | ||||||||
\(944\) | −40.0768 | −1.30439 | ||||||||
\(945\) | 0.0907696 | 0.00295274 | ||||||||
\(946\) | 116.865 | 3.79962 | ||||||||
\(947\) | 36.3265 | 1.18045 | 0.590227 | − | 0.807237i | \(-0.299038\pi\) | ||||
0.590227 | + | 0.807237i | \(0.299038\pi\) | |||||||
\(948\) | −24.9134 | −0.809150 | ||||||||
\(949\) | 63.4238 | 2.05882 | ||||||||
\(950\) | −11.4280 | −0.370774 | ||||||||
\(951\) | 52.6185 | 1.70627 | ||||||||
\(952\) | 0.102351 | 0.00331722 | ||||||||
\(953\) | −44.4553 | −1.44005 | −0.720025 | − | 0.693948i | \(-0.755870\pi\) | ||||
−0.720025 | + | 0.693948i | \(0.755870\pi\) | |||||||
\(954\) | −23.2636 | −0.753186 | ||||||||
\(955\) | −18.5808 | −0.601259 | ||||||||
\(956\) | 7.36011 | 0.238043 | ||||||||
\(957\) | −113.525 | −3.66973 | ||||||||
\(958\) | −51.0683 | −1.64994 | ||||||||
\(959\) | −7.24502 | −0.233954 | ||||||||
\(960\) | −9.96740 | −0.321696 | ||||||||
\(961\) | −16.0974 | −0.519270 | ||||||||
\(962\) | 0.608098 | 0.0196059 | ||||||||
\(963\) | 16.6952 | 0.537995 | ||||||||
\(964\) | 11.3947 | 0.366999 | ||||||||
\(965\) | −7.18286 | −0.231225 | ||||||||
\(966\) | −7.61412 | −0.244980 | ||||||||
\(967\) | −37.5166 | −1.20645 | −0.603226 | − | 0.797571i | \(-0.706118\pi\) | ||||
−0.603226 | + | 0.797571i | \(0.706118\pi\) | |||||||
\(968\) | 13.4887 | 0.433545 | ||||||||
\(969\) | 4.97512 | 0.159824 | ||||||||
\(970\) | 0.246761 | 0.00792303 | ||||||||
\(971\) | 29.2648 | 0.939153 | 0.469576 | − | 0.882892i | \(-0.344407\pi\) | ||||
0.469576 | + | 0.882892i | \(0.344407\pi\) | |||||||
\(972\) | −34.2966 | −1.10006 | ||||||||
\(973\) | −7.29048 | −0.233722 | ||||||||
\(974\) | 16.6659 | 0.534010 | ||||||||
\(975\) | 9.50800 | 0.304500 | ||||||||
\(976\) | 13.6795 | 0.437869 | ||||||||
\(977\) | −48.6799 | −1.55741 | −0.778703 | − | 0.627392i | \(-0.784122\pi\) | ||||
−0.778703 | + | 0.627392i | \(0.784122\pi\) | |||||||
\(978\) | −25.3881 | −0.811821 | ||||||||
\(979\) | 71.9796 | 2.30048 | ||||||||
\(980\) | −10.6113 | −0.338964 | ||||||||
\(981\) | 18.3218 | 0.584969 | ||||||||
\(982\) | −10.3708 | −0.330945 | ||||||||
\(983\) | −12.9095 | −0.411750 | −0.205875 | − | 0.978578i | \(-0.566004\pi\) | ||||
−0.205875 | + | 0.978578i | \(0.566004\pi\) | |||||||
\(984\) | −6.96668 | −0.222089 | ||||||||
\(985\) | 15.2620 | 0.486286 | ||||||||
\(986\) | 5.55277 | 0.176836 | ||||||||
\(987\) | −8.50057 | −0.270576 | ||||||||
\(988\) | 36.0840 | 1.14799 | ||||||||
\(989\) | −54.6554 | −1.73794 | ||||||||
\(990\) | −30.1936 | −0.959614 | ||||||||
\(991\) | −28.6531 | −0.910194 | −0.455097 | − | 0.890442i | \(-0.650395\pi\) | ||||
−0.455097 | + | 0.890442i | \(0.650395\pi\) | |||||||
\(992\) | 27.5630 | 0.875126 | ||||||||
\(993\) | −56.2115 | −1.78382 | ||||||||
\(994\) | 3.91646 | 0.124223 | ||||||||
\(995\) | −3.03183 | −0.0961155 | ||||||||
\(996\) | 7.40909 | 0.234766 | ||||||||
\(997\) | −24.0393 | −0.761332 | −0.380666 | − | 0.924713i | \(-0.624305\pi\) | ||||
−0.380666 | + | 0.924713i | \(0.624305\pi\) | |||||||
\(998\) | 55.3500 | 1.75207 | ||||||||
\(999\) | −0.0211781 | −0.000670045 0 |
(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 | 2005.2.a.g.1.7 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2005.2.a.g.1.7 | ✓ | 37 | 1.1 | even | 1 | trivial |