Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.44805 | 0.836032 | 0.418016 | − | 0.908440i | \(-0.362726\pi\) | ||||
0.418016 | + | 0.908440i | \(0.362726\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.26245 | 1.45901 | 0.729507 | − | 0.683974i | \(-0.239750\pi\) | ||||
0.729507 | + | 0.683974i | \(0.239750\pi\) | |||||||
\(6\) | 1.44805 | 0.591164 | ||||||||
\(7\) | −3.72778 | −1.40897 | −0.704485 | − | 0.709719i | \(-0.748822\pi\) | ||||
−0.704485 | + | 0.709719i | \(0.748822\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.903151 | −0.301050 | ||||||||
\(10\) | 3.26245 | 1.03168 | ||||||||
\(11\) | −4.09702 | −1.23530 | −0.617649 | − | 0.786454i | \(-0.711915\pi\) | ||||
−0.617649 | + | 0.786454i | \(0.711915\pi\) | |||||||
\(12\) | 1.44805 | 0.418016 | ||||||||
\(13\) | −2.98138 | −0.826886 | −0.413443 | − | 0.910530i | \(-0.635674\pi\) | ||||
−0.413443 | + | 0.910530i | \(0.635674\pi\) | |||||||
\(14\) | −3.72778 | −0.996292 | ||||||||
\(15\) | 4.72419 | 1.21978 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.49368 | −0.362272 | −0.181136 | − | 0.983458i | \(-0.557977\pi\) | ||||
−0.181136 | + | 0.983458i | \(0.557977\pi\) | |||||||
\(18\) | −0.903151 | −0.212875 | ||||||||
\(19\) | −1.05316 | −0.241611 | −0.120806 | − | 0.992676i | \(-0.538548\pi\) | ||||
−0.120806 | + | 0.992676i | \(0.538548\pi\) | |||||||
\(20\) | 3.26245 | 0.729507 | ||||||||
\(21\) | −5.39802 | −1.17794 | ||||||||
\(22\) | −4.09702 | −0.873488 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.44805 | 0.295582 | ||||||||
\(25\) | 5.64360 | 1.12872 | ||||||||
\(26\) | −2.98138 | −0.584697 | ||||||||
\(27\) | −5.65196 | −1.08772 | ||||||||
\(28\) | −3.72778 | −0.704485 | ||||||||
\(29\) | −4.90034 | −0.909971 | −0.454985 | − | 0.890499i | \(-0.650356\pi\) | ||||
−0.454985 | + | 0.890499i | \(0.650356\pi\) | |||||||
\(30\) | 4.72419 | 0.862516 | ||||||||
\(31\) | 6.60489 | 1.18627 | 0.593136 | − | 0.805102i | \(-0.297889\pi\) | ||||
0.593136 | + | 0.805102i | \(0.297889\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.93269 | −1.03275 | ||||||||
\(34\) | −1.49368 | −0.256165 | ||||||||
\(35\) | −12.1617 | −2.05571 | ||||||||
\(36\) | −0.903151 | −0.150525 | ||||||||
\(37\) | −8.08086 | −1.32849 | −0.664243 | − | 0.747517i | \(-0.731246\pi\) | ||||
−0.664243 | + | 0.747517i | \(0.731246\pi\) | |||||||
\(38\) | −1.05316 | −0.170845 | ||||||||
\(39\) | −4.31719 | −0.691304 | ||||||||
\(40\) | 3.26245 | 0.515839 | ||||||||
\(41\) | 2.30886 | 0.360583 | 0.180291 | − | 0.983613i | \(-0.442296\pi\) | ||||
0.180291 | + | 0.983613i | \(0.442296\pi\) | |||||||
\(42\) | −5.39802 | −0.832932 | ||||||||
\(43\) | −6.47442 | −0.987340 | −0.493670 | − | 0.869649i | \(-0.664345\pi\) | ||||
−0.493670 | + | 0.869649i | \(0.664345\pi\) | |||||||
\(44\) | −4.09702 | −0.617649 | ||||||||
\(45\) | −2.94649 | −0.439236 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −8.29223 | −1.20955 | −0.604773 | − | 0.796398i | \(-0.706736\pi\) | ||||
−0.604773 | + | 0.796398i | \(0.706736\pi\) | |||||||
\(48\) | 1.44805 | 0.209008 | ||||||||
\(49\) | 6.89637 | 0.985196 | ||||||||
\(50\) | 5.64360 | 0.798125 | ||||||||
\(51\) | −2.16293 | −0.302871 | ||||||||
\(52\) | −2.98138 | −0.413443 | ||||||||
\(53\) | 0.309487 | 0.0425113 | 0.0212557 | − | 0.999774i | \(-0.493234\pi\) | ||||
0.0212557 | + | 0.999774i | \(0.493234\pi\) | |||||||
\(54\) | −5.65196 | −0.769134 | ||||||||
\(55\) | −13.3663 | −1.80232 | ||||||||
\(56\) | −3.72778 | −0.498146 | ||||||||
\(57\) | −1.52503 | −0.201995 | ||||||||
\(58\) | −4.90034 | −0.643446 | ||||||||
\(59\) | 12.9613 | 1.68742 | 0.843712 | − | 0.536796i | \(-0.180366\pi\) | ||||
0.843712 | + | 0.536796i | \(0.180366\pi\) | |||||||
\(60\) | 4.72419 | 0.609891 | ||||||||
\(61\) | −13.5111 | −1.72991 | −0.864957 | − | 0.501847i | \(-0.832654\pi\) | ||||
−0.864957 | + | 0.501847i | \(0.832654\pi\) | |||||||
\(62\) | 6.60489 | 0.838822 | ||||||||
\(63\) | 3.36675 | 0.424171 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.72662 | −1.20644 | ||||||||
\(66\) | −5.93269 | −0.730264 | ||||||||
\(67\) | 13.0224 | 1.59094 | 0.795471 | − | 0.605992i | \(-0.207224\pi\) | ||||
0.795471 | + | 0.605992i | \(0.207224\pi\) | |||||||
\(68\) | −1.49368 | −0.181136 | ||||||||
\(69\) | −1.44805 | −0.174325 | ||||||||
\(70\) | −12.1617 | −1.45360 | ||||||||
\(71\) | 7.82972 | 0.929217 | 0.464609 | − | 0.885516i | \(-0.346195\pi\) | ||||
0.464609 | + | 0.885516i | \(0.346195\pi\) | |||||||
\(72\) | −0.903151 | −0.106437 | ||||||||
\(73\) | 4.03401 | 0.472146 | 0.236073 | − | 0.971735i | \(-0.424140\pi\) | ||||
0.236073 | + | 0.971735i | \(0.424140\pi\) | |||||||
\(74\) | −8.08086 | −0.939381 | ||||||||
\(75\) | 8.17221 | 0.943646 | ||||||||
\(76\) | −1.05316 | −0.120806 | ||||||||
\(77\) | 15.2728 | 1.74050 | ||||||||
\(78\) | −4.31719 | −0.488825 | ||||||||
\(79\) | −2.73118 | −0.307282 | −0.153641 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153641 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(80\) | 3.26245 | 0.364753 | ||||||||
\(81\) | −5.47486 | −0.608318 | ||||||||
\(82\) | 2.30886 | 0.254970 | ||||||||
\(83\) | −0.859840 | −0.0943797 | −0.0471898 | − | 0.998886i | \(-0.515027\pi\) | ||||
−0.0471898 | + | 0.998886i | \(0.515027\pi\) | |||||||
\(84\) | −5.39802 | −0.588972 | ||||||||
\(85\) | −4.87307 | −0.528559 | ||||||||
\(86\) | −6.47442 | −0.698155 | ||||||||
\(87\) | −7.09594 | −0.760765 | ||||||||
\(88\) | −4.09702 | −0.436744 | ||||||||
\(89\) | 13.3306 | 1.41304 | 0.706522 | − | 0.707691i | \(-0.250263\pi\) | ||||
0.706522 | + | 0.707691i | \(0.250263\pi\) | |||||||
\(90\) | −2.94649 | −0.310587 | ||||||||
\(91\) | 11.1139 | 1.16506 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 9.56421 | 0.991762 | ||||||||
\(94\) | −8.29223 | −0.855278 | ||||||||
\(95\) | −3.43588 | −0.352514 | ||||||||
\(96\) | 1.44805 | 0.147791 | ||||||||
\(97\) | 2.53866 | 0.257762 | 0.128881 | − | 0.991660i | \(-0.458861\pi\) | ||||
0.128881 | + | 0.991660i | \(0.458861\pi\) | |||||||
\(98\) | 6.89637 | 0.696639 | ||||||||
\(99\) | 3.70023 | 0.371887 | ||||||||
\(100\) | 5.64360 | 0.564360 | ||||||||
\(101\) | −17.8685 | −1.77798 | −0.888990 | − | 0.457928i | \(-0.848592\pi\) | ||||
−0.888990 | + | 0.457928i | \(0.848592\pi\) | |||||||
\(102\) | −2.16293 | −0.214162 | ||||||||
\(103\) | 0.452882 | 0.0446238 | 0.0223119 | − | 0.999751i | \(-0.492897\pi\) | ||||
0.0223119 | + | 0.999751i | \(0.492897\pi\) | |||||||
\(104\) | −2.98138 | −0.292348 | ||||||||
\(105\) | −17.6108 | −1.71864 | ||||||||
\(106\) | 0.309487 | 0.0300600 | ||||||||
\(107\) | −9.35237 | −0.904128 | −0.452064 | − | 0.891986i | \(-0.649312\pi\) | ||||
−0.452064 | + | 0.891986i | \(0.649312\pi\) | |||||||
\(108\) | −5.65196 | −0.543860 | ||||||||
\(109\) | −9.43508 | −0.903716 | −0.451858 | − | 0.892090i | \(-0.649239\pi\) | ||||
−0.451858 | + | 0.892090i | \(0.649239\pi\) | |||||||
\(110\) | −13.3663 | −1.27443 | ||||||||
\(111\) | −11.7015 | −1.11066 | ||||||||
\(112\) | −3.72778 | −0.352242 | ||||||||
\(113\) | −13.2693 | −1.24827 | −0.624135 | − | 0.781316i | \(-0.714549\pi\) | ||||
−0.624135 | + | 0.781316i | \(0.714549\pi\) | |||||||
\(114\) | −1.52503 | −0.142832 | ||||||||
\(115\) | −3.26245 | −0.304225 | ||||||||
\(116\) | −4.90034 | −0.454985 | ||||||||
\(117\) | 2.69264 | 0.248934 | ||||||||
\(118\) | 12.9613 | 1.19319 | ||||||||
\(119\) | 5.56813 | 0.510430 | ||||||||
\(120\) | 4.72419 | 0.431258 | ||||||||
\(121\) | 5.78558 | 0.525962 | ||||||||
\(122\) | −13.5111 | −1.22323 | ||||||||
\(123\) | 3.34334 | 0.301459 | ||||||||
\(124\) | 6.60489 | 0.593136 | ||||||||
\(125\) | 2.09971 | 0.187804 | ||||||||
\(126\) | 3.36675 | 0.299934 | ||||||||
\(127\) | 2.35002 | 0.208531 | 0.104265 | − | 0.994550i | \(-0.466751\pi\) | ||||
0.104265 | + | 0.994550i | \(0.466751\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.37529 | −0.825448 | ||||||||
\(130\) | −9.72662 | −0.853081 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −5.93269 | −0.516374 | ||||||||
\(133\) | 3.92595 | 0.340423 | ||||||||
\(134\) | 13.0224 | 1.12497 | ||||||||
\(135\) | −18.4392 | −1.58700 | ||||||||
\(136\) | −1.49368 | −0.128082 | ||||||||
\(137\) | 4.91743 | 0.420125 | 0.210062 | − | 0.977688i | \(-0.432633\pi\) | ||||
0.210062 | + | 0.977688i | \(0.432633\pi\) | |||||||
\(138\) | −1.44805 | −0.123266 | ||||||||
\(139\) | −15.7808 | −1.33851 | −0.669255 | − | 0.743032i | \(-0.733387\pi\) | ||||
−0.669255 | + | 0.743032i | \(0.733387\pi\) | |||||||
\(140\) | −12.1617 | −1.02785 | ||||||||
\(141\) | −12.0076 | −1.01122 | ||||||||
\(142\) | 7.82972 | 0.657056 | ||||||||
\(143\) | 12.2148 | 1.02145 | ||||||||
\(144\) | −0.903151 | −0.0752626 | ||||||||
\(145\) | −15.9871 | −1.32766 | ||||||||
\(146\) | 4.03401 | 0.333857 | ||||||||
\(147\) | 9.98629 | 0.823656 | ||||||||
\(148\) | −8.08086 | −0.664243 | ||||||||
\(149\) | −18.4294 | −1.50979 | −0.754896 | − | 0.655845i | \(-0.772313\pi\) | ||||
−0.754896 | + | 0.655845i | \(0.772313\pi\) | |||||||
\(150\) | 8.17221 | 0.667258 | ||||||||
\(151\) | 1.03384 | 0.0841327 | 0.0420663 | − | 0.999115i | \(-0.486606\pi\) | ||||
0.0420663 | + | 0.999115i | \(0.486606\pi\) | |||||||
\(152\) | −1.05316 | −0.0854224 | ||||||||
\(153\) | 1.34902 | 0.109062 | ||||||||
\(154\) | 15.2728 | 1.23072 | ||||||||
\(155\) | 21.5481 | 1.73079 | ||||||||
\(156\) | −4.31719 | −0.345652 | ||||||||
\(157\) | 4.32678 | 0.345314 | 0.172657 | − | 0.984982i | \(-0.444765\pi\) | ||||
0.172657 | + | 0.984982i | \(0.444765\pi\) | |||||||
\(158\) | −2.73118 | −0.217281 | ||||||||
\(159\) | 0.448153 | 0.0355408 | ||||||||
\(160\) | 3.26245 | 0.257920 | ||||||||
\(161\) | 3.72778 | 0.293791 | ||||||||
\(162\) | −5.47486 | −0.430146 | ||||||||
\(163\) | −13.6321 | −1.06775 | −0.533876 | − | 0.845563i | \(-0.679265\pi\) | ||||
−0.533876 | + | 0.845563i | \(0.679265\pi\) | |||||||
\(164\) | 2.30886 | 0.180291 | ||||||||
\(165\) | −19.3551 | −1.50679 | ||||||||
\(166\) | −0.859840 | −0.0667365 | ||||||||
\(167\) | 1.13278 | 0.0876575 | 0.0438288 | − | 0.999039i | \(-0.486044\pi\) | ||||
0.0438288 | + | 0.999039i | \(0.486044\pi\) | |||||||
\(168\) | −5.39802 | −0.416466 | ||||||||
\(169\) | −4.11137 | −0.316259 | ||||||||
\(170\) | −4.87307 | −0.373748 | ||||||||
\(171\) | 0.951161 | 0.0727371 | ||||||||
\(172\) | −6.47442 | −0.493670 | ||||||||
\(173\) | −9.88200 | −0.751314 | −0.375657 | − | 0.926759i | \(-0.622583\pi\) | ||||
−0.375657 | + | 0.926759i | \(0.622583\pi\) | |||||||
\(174\) | −7.09594 | −0.537942 | ||||||||
\(175\) | −21.0381 | −1.59033 | ||||||||
\(176\) | −4.09702 | −0.308825 | ||||||||
\(177\) | 18.7687 | 1.41074 | ||||||||
\(178\) | 13.3306 | 0.999173 | ||||||||
\(179\) | 21.2799 | 1.59054 | 0.795269 | − | 0.606257i | \(-0.207330\pi\) | ||||
0.795269 | + | 0.606257i | \(0.207330\pi\) | |||||||
\(180\) | −2.94649 | −0.219618 | ||||||||
\(181\) | 22.6914 | 1.68664 | 0.843319 | − | 0.537413i | \(-0.180598\pi\) | ||||
0.843319 | + | 0.537413i | \(0.180598\pi\) | |||||||
\(182\) | 11.1139 | 0.823820 | ||||||||
\(183\) | −19.5647 | −1.44626 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −26.3634 | −1.93828 | ||||||||
\(186\) | 9.56421 | 0.701282 | ||||||||
\(187\) | 6.11965 | 0.447513 | ||||||||
\(188\) | −8.29223 | −0.604773 | ||||||||
\(189\) | 21.0693 | 1.53256 | ||||||||
\(190\) | −3.43588 | −0.249265 | ||||||||
\(191\) | 3.53360 | 0.255682 | 0.127841 | − | 0.991795i | \(-0.459195\pi\) | ||||
0.127841 | + | 0.991795i | \(0.459195\pi\) | |||||||
\(192\) | 1.44805 | 0.104504 | ||||||||
\(193\) | 11.5607 | 0.832157 | 0.416078 | − | 0.909329i | \(-0.363404\pi\) | ||||
0.416078 | + | 0.909329i | \(0.363404\pi\) | |||||||
\(194\) | 2.53866 | 0.182266 | ||||||||
\(195\) | −14.0846 | −1.00862 | ||||||||
\(196\) | 6.89637 | 0.492598 | ||||||||
\(197\) | 6.21116 | 0.442527 | 0.221263 | − | 0.975214i | \(-0.428982\pi\) | ||||
0.221263 | + | 0.975214i | \(0.428982\pi\) | |||||||
\(198\) | 3.70023 | 0.262964 | ||||||||
\(199\) | 1.35355 | 0.0959504 | 0.0479752 | − | 0.998849i | \(-0.484723\pi\) | ||||
0.0479752 | + | 0.998849i | \(0.484723\pi\) | |||||||
\(200\) | 5.64360 | 0.399063 | ||||||||
\(201\) | 18.8571 | 1.33008 | ||||||||
\(202\) | −17.8685 | −1.25722 | ||||||||
\(203\) | 18.2674 | 1.28212 | ||||||||
\(204\) | −2.16293 | −0.151435 | ||||||||
\(205\) | 7.53253 | 0.526095 | ||||||||
\(206\) | 0.452882 | 0.0315538 | ||||||||
\(207\) | 0.903151 | 0.0627733 | ||||||||
\(208\) | −2.98138 | −0.206722 | ||||||||
\(209\) | 4.31481 | 0.298462 | ||||||||
\(210\) | −17.6108 | −1.21526 | ||||||||
\(211\) | 5.48824 | 0.377826 | 0.188913 | − | 0.981994i | \(-0.439504\pi\) | ||||
0.188913 | + | 0.981994i | \(0.439504\pi\) | |||||||
\(212\) | 0.309487 | 0.0212557 | ||||||||
\(213\) | 11.3378 | 0.776855 | ||||||||
\(214\) | −9.35237 | −0.639315 | ||||||||
\(215\) | −21.1225 | −1.44054 | ||||||||
\(216\) | −5.65196 | −0.384567 | ||||||||
\(217\) | −24.6216 | −1.67142 | ||||||||
\(218\) | −9.43508 | −0.639024 | ||||||||
\(219\) | 5.84146 | 0.394729 | ||||||||
\(220\) | −13.3663 | −0.901158 | ||||||||
\(221\) | 4.45324 | 0.299557 | ||||||||
\(222\) | −11.7015 | −0.785353 | ||||||||
\(223\) | 10.7643 | 0.720832 | 0.360416 | − | 0.932792i | \(-0.382635\pi\) | ||||
0.360416 | + | 0.932792i | \(0.382635\pi\) | |||||||
\(224\) | −3.72778 | −0.249073 | ||||||||
\(225\) | −5.09702 | −0.339801 | ||||||||
\(226\) | −13.2693 | −0.882660 | ||||||||
\(227\) | 3.87295 | 0.257056 | 0.128528 | − | 0.991706i | \(-0.458975\pi\) | ||||
0.128528 | + | 0.991706i | \(0.458975\pi\) | |||||||
\(228\) | −1.52503 | −0.100997 | ||||||||
\(229\) | −4.62184 | −0.305420 | −0.152710 | − | 0.988271i | \(-0.548800\pi\) | ||||
−0.152710 | + | 0.988271i | \(0.548800\pi\) | |||||||
\(230\) | −3.26245 | −0.215120 | ||||||||
\(231\) | 22.1158 | 1.45511 | ||||||||
\(232\) | −4.90034 | −0.321723 | ||||||||
\(233\) | 11.5937 | 0.759527 | 0.379764 | − | 0.925084i | \(-0.376005\pi\) | ||||
0.379764 | + | 0.925084i | \(0.376005\pi\) | |||||||
\(234\) | 2.69264 | 0.176023 | ||||||||
\(235\) | −27.0530 | −1.76474 | ||||||||
\(236\) | 12.9613 | 0.843712 | ||||||||
\(237\) | −3.95488 | −0.256897 | ||||||||
\(238\) | 5.56813 | 0.360928 | ||||||||
\(239\) | 11.6851 | 0.755844 | 0.377922 | − | 0.925837i | \(-0.376639\pi\) | ||||
0.377922 | + | 0.925837i | \(0.376639\pi\) | |||||||
\(240\) | 4.72419 | 0.304945 | ||||||||
\(241\) | −25.4567 | −1.63981 | −0.819904 | − | 0.572501i | \(-0.805973\pi\) | ||||
−0.819904 | + | 0.572501i | \(0.805973\pi\) | |||||||
\(242\) | 5.78558 | 0.371911 | ||||||||
\(243\) | 9.02800 | 0.579146 | ||||||||
\(244\) | −13.5111 | −0.864957 | ||||||||
\(245\) | 22.4991 | 1.43741 | ||||||||
\(246\) | 3.34334 | 0.213163 | ||||||||
\(247\) | 3.13987 | 0.199785 | ||||||||
\(248\) | 6.60489 | 0.419411 | ||||||||
\(249\) | −1.24509 | −0.0789044 | ||||||||
\(250\) | 2.09971 | 0.132797 | ||||||||
\(251\) | 7.69696 | 0.485828 | 0.242914 | − | 0.970048i | \(-0.421897\pi\) | ||||
0.242914 | + | 0.970048i | \(0.421897\pi\) | |||||||
\(252\) | 3.36675 | 0.212085 | ||||||||
\(253\) | 4.09702 | 0.257577 | ||||||||
\(254\) | 2.35002 | 0.147453 | ||||||||
\(255\) | −7.05645 | −0.441892 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.6785 | 0.728483 | 0.364241 | − | 0.931305i | \(-0.381328\pi\) | ||||
0.364241 | + | 0.931305i | \(0.381328\pi\) | |||||||
\(258\) | −9.37529 | −0.583680 | ||||||||
\(259\) | 30.1237 | 1.87180 | ||||||||
\(260\) | −9.72662 | −0.603219 | ||||||||
\(261\) | 4.42575 | 0.273947 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 6.70714 | 0.413580 | 0.206790 | − | 0.978385i | \(-0.433698\pi\) | ||||
0.206790 | + | 0.978385i | \(0.433698\pi\) | |||||||
\(264\) | −5.93269 | −0.365132 | ||||||||
\(265\) | 1.00969 | 0.0620246 | ||||||||
\(266\) | 3.92595 | 0.240715 | ||||||||
\(267\) | 19.3034 | 1.18135 | ||||||||
\(268\) | 13.0224 | 0.795471 | ||||||||
\(269\) | −10.4258 | −0.635674 | −0.317837 | − | 0.948145i | \(-0.602956\pi\) | ||||
−0.317837 | + | 0.948145i | \(0.602956\pi\) | |||||||
\(270\) | −18.4392 | −1.12218 | ||||||||
\(271\) | −6.60454 | −0.401197 | −0.200599 | − | 0.979674i | \(-0.564289\pi\) | ||||
−0.200599 | + | 0.979674i | \(0.564289\pi\) | |||||||
\(272\) | −1.49368 | −0.0905679 | ||||||||
\(273\) | 16.0935 | 0.974026 | ||||||||
\(274\) | 4.91743 | 0.297073 | ||||||||
\(275\) | −23.1219 | −1.39431 | ||||||||
\(276\) | −1.44805 | −0.0871624 | ||||||||
\(277\) | 31.1450 | 1.87132 | 0.935662 | − | 0.352898i | \(-0.114804\pi\) | ||||
0.935662 | + | 0.352898i | \(0.114804\pi\) | |||||||
\(278\) | −15.7808 | −0.946470 | ||||||||
\(279\) | −5.96521 | −0.357128 | ||||||||
\(280\) | −12.1617 | −0.726802 | ||||||||
\(281\) | −6.42679 | −0.383390 | −0.191695 | − | 0.981455i | \(-0.561398\pi\) | ||||
−0.191695 | + | 0.981455i | \(0.561398\pi\) | |||||||
\(282\) | −12.0076 | −0.715040 | ||||||||
\(283\) | 24.5134 | 1.45717 | 0.728585 | − | 0.684955i | \(-0.240178\pi\) | ||||
0.728585 | + | 0.684955i | \(0.240178\pi\) | |||||||
\(284\) | 7.82972 | 0.464609 | ||||||||
\(285\) | −4.97532 | −0.294713 | ||||||||
\(286\) | 12.2148 | 0.722275 | ||||||||
\(287\) | −8.60692 | −0.508050 | ||||||||
\(288\) | −0.903151 | −0.0532187 | ||||||||
\(289\) | −14.7689 | −0.868759 | ||||||||
\(290\) | −15.9871 | −0.938797 | ||||||||
\(291\) | 3.67611 | 0.215498 | ||||||||
\(292\) | 4.03401 | 0.236073 | ||||||||
\(293\) | 24.0566 | 1.40540 | 0.702701 | − | 0.711485i | \(-0.251977\pi\) | ||||
0.702701 | + | 0.711485i | \(0.251977\pi\) | |||||||
\(294\) | 9.98629 | 0.582413 | ||||||||
\(295\) | 42.2858 | 2.46197 | ||||||||
\(296\) | −8.08086 | −0.469691 | ||||||||
\(297\) | 23.1562 | 1.34366 | ||||||||
\(298\) | −18.4294 | −1.06758 | ||||||||
\(299\) | 2.98138 | 0.172418 | ||||||||
\(300\) | 8.17221 | 0.471823 | ||||||||
\(301\) | 24.1353 | 1.39113 | ||||||||
\(302\) | 1.03384 | 0.0594908 | ||||||||
\(303\) | −25.8744 | −1.48645 | ||||||||
\(304\) | −1.05316 | −0.0604028 | ||||||||
\(305\) | −44.0792 | −2.52397 | ||||||||
\(306\) | 1.34902 | 0.0771185 | ||||||||
\(307\) | 14.4246 | 0.823255 | 0.411628 | − | 0.911352i | \(-0.364960\pi\) | ||||
0.411628 | + | 0.911352i | \(0.364960\pi\) | |||||||
\(308\) | 15.2728 | 0.870249 | ||||||||
\(309\) | 0.655796 | 0.0373069 | ||||||||
\(310\) | 21.5481 | 1.22385 | ||||||||
\(311\) | −29.8190 | −1.69088 | −0.845441 | − | 0.534069i | \(-0.820662\pi\) | ||||
−0.845441 | + | 0.534069i | \(0.820662\pi\) | |||||||
\(312\) | −4.31719 | −0.244413 | ||||||||
\(313\) | −16.6481 | −0.941006 | −0.470503 | − | 0.882398i | \(-0.655928\pi\) | ||||
−0.470503 | + | 0.882398i | \(0.655928\pi\) | |||||||
\(314\) | 4.32678 | 0.244174 | ||||||||
\(315\) | 10.9839 | 0.618871 | ||||||||
\(316\) | −2.73118 | −0.153641 | ||||||||
\(317\) | 28.1380 | 1.58039 | 0.790195 | − | 0.612856i | \(-0.209979\pi\) | ||||
0.790195 | + | 0.612856i | \(0.209979\pi\) | |||||||
\(318\) | 0.448153 | 0.0251312 | ||||||||
\(319\) | 20.0768 | 1.12409 | ||||||||
\(320\) | 3.26245 | 0.182377 | ||||||||
\(321\) | −13.5427 | −0.755880 | ||||||||
\(322\) | 3.72778 | 0.207741 | ||||||||
\(323\) | 1.57309 | 0.0875288 | ||||||||
\(324\) | −5.47486 | −0.304159 | ||||||||
\(325\) | −16.8257 | −0.933323 | ||||||||
\(326\) | −13.6321 | −0.755014 | ||||||||
\(327\) | −13.6625 | −0.755536 | ||||||||
\(328\) | 2.30886 | 0.127485 | ||||||||
\(329\) | 30.9116 | 1.70421 | ||||||||
\(330\) | −19.3551 | −1.06546 | ||||||||
\(331\) | −30.9825 | −1.70295 | −0.851477 | − | 0.524392i | \(-0.824293\pi\) | ||||
−0.851477 | + | 0.524392i | \(0.824293\pi\) | |||||||
\(332\) | −0.859840 | −0.0471898 | ||||||||
\(333\) | 7.29824 | 0.399941 | ||||||||
\(334\) | 1.13278 | 0.0619832 | ||||||||
\(335\) | 42.4850 | 2.32121 | ||||||||
\(336\) | −5.39802 | −0.294486 | ||||||||
\(337\) | −20.9581 | −1.14166 | −0.570830 | − | 0.821068i | \(-0.693379\pi\) | ||||
−0.570830 | + | 0.821068i | \(0.693379\pi\) | |||||||
\(338\) | −4.11137 | −0.223629 | ||||||||
\(339\) | −19.2146 | −1.04359 | ||||||||
\(340\) | −4.87307 | −0.264279 | ||||||||
\(341\) | −27.0604 | −1.46540 | ||||||||
\(342\) | 0.951161 | 0.0514329 | ||||||||
\(343\) | 0.386296 | 0.0208580 | ||||||||
\(344\) | −6.47442 | −0.349078 | ||||||||
\(345\) | −4.72419 | −0.254342 | ||||||||
\(346\) | −9.88200 | −0.531260 | ||||||||
\(347\) | 10.7389 | 0.576493 | 0.288246 | − | 0.957556i | \(-0.406928\pi\) | ||||
0.288246 | + | 0.957556i | \(0.406928\pi\) | |||||||
\(348\) | −7.09594 | −0.380382 | ||||||||
\(349\) | −24.0172 | −1.28561 | −0.642805 | − | 0.766030i | \(-0.722230\pi\) | ||||
−0.642805 | + | 0.766030i | \(0.722230\pi\) | |||||||
\(350\) | −21.0381 | −1.12453 | ||||||||
\(351\) | 16.8506 | 0.899421 | ||||||||
\(352\) | −4.09702 | −0.218372 | ||||||||
\(353\) | −24.8423 | −1.32222 | −0.661112 | − | 0.750287i | \(-0.729915\pi\) | ||||
−0.661112 | + | 0.750287i | \(0.729915\pi\) | |||||||
\(354\) | 18.7687 | 0.997544 | ||||||||
\(355\) | 25.5441 | 1.35574 | ||||||||
\(356\) | 13.3306 | 0.706522 | ||||||||
\(357\) | 8.06293 | 0.426736 | ||||||||
\(358\) | 21.2799 | 1.12468 | ||||||||
\(359\) | −32.2827 | −1.70382 | −0.851908 | − | 0.523692i | \(-0.824554\pi\) | ||||
−0.851908 | + | 0.523692i | \(0.824554\pi\) | |||||||
\(360\) | −2.94649 | −0.155294 | ||||||||
\(361\) | −17.8909 | −0.941624 | ||||||||
\(362\) | 22.6914 | 1.19263 | ||||||||
\(363\) | 8.37781 | 0.439721 | ||||||||
\(364\) | 11.1139 | 0.582529 | ||||||||
\(365\) | 13.1608 | 0.688867 | ||||||||
\(366\) | −19.5647 | −1.02266 | ||||||||
\(367\) | 24.4870 | 1.27821 | 0.639106 | − | 0.769119i | \(-0.279305\pi\) | ||||
0.639106 | + | 0.769119i | \(0.279305\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −2.08525 | −0.108554 | ||||||||
\(370\) | −26.3634 | −1.37057 | ||||||||
\(371\) | −1.15370 | −0.0598972 | ||||||||
\(372\) | 9.56421 | 0.495881 | ||||||||
\(373\) | 12.3106 | 0.637417 | 0.318709 | − | 0.947853i | \(-0.396751\pi\) | ||||
0.318709 | + | 0.947853i | \(0.396751\pi\) | |||||||
\(374\) | 6.11965 | 0.316440 | ||||||||
\(375\) | 3.04048 | 0.157010 | ||||||||
\(376\) | −8.29223 | −0.427639 | ||||||||
\(377\) | 14.6098 | 0.752442 | ||||||||
\(378\) | 21.0693 | 1.08369 | ||||||||
\(379\) | 19.3124 | 0.992012 | 0.496006 | − | 0.868319i | \(-0.334799\pi\) | ||||
0.496006 | + | 0.868319i | \(0.334799\pi\) | |||||||
\(380\) | −3.43588 | −0.176257 | ||||||||
\(381\) | 3.40295 | 0.174338 | ||||||||
\(382\) | 3.53360 | 0.180795 | ||||||||
\(383\) | −26.5607 | −1.35719 | −0.678594 | − | 0.734514i | \(-0.737410\pi\) | ||||
−0.678594 | + | 0.734514i | \(0.737410\pi\) | |||||||
\(384\) | 1.44805 | 0.0738955 | ||||||||
\(385\) | 49.8268 | 2.53941 | ||||||||
\(386\) | 11.5607 | 0.588424 | ||||||||
\(387\) | 5.84738 | 0.297239 | ||||||||
\(388\) | 2.53866 | 0.128881 | ||||||||
\(389\) | −9.58462 | −0.485960 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(390\) | −14.0846 | −0.713203 | ||||||||
\(391\) | 1.49368 | 0.0755388 | ||||||||
\(392\) | 6.89637 | 0.348319 | ||||||||
\(393\) | 1.44805 | 0.0730445 | ||||||||
\(394\) | 6.21116 | 0.312914 | ||||||||
\(395\) | −8.91034 | −0.448328 | ||||||||
\(396\) | 3.70023 | 0.185943 | ||||||||
\(397\) | 5.00689 | 0.251289 | 0.125644 | − | 0.992075i | \(-0.459900\pi\) | ||||
0.125644 | + | 0.992075i | \(0.459900\pi\) | |||||||
\(398\) | 1.35355 | 0.0678472 | ||||||||
\(399\) | 5.68497 | 0.284604 | ||||||||
\(400\) | 5.64360 | 0.282180 | ||||||||
\(401\) | −14.9221 | −0.745175 | −0.372587 | − | 0.927997i | \(-0.621529\pi\) | ||||
−0.372587 | + | 0.927997i | \(0.621529\pi\) | |||||||
\(402\) | 18.8571 | 0.940507 | ||||||||
\(403\) | −19.6917 | −0.980913 | ||||||||
\(404\) | −17.8685 | −0.888990 | ||||||||
\(405\) | −17.8615 | −0.887544 | ||||||||
\(406\) | 18.2674 | 0.906597 | ||||||||
\(407\) | 33.1075 | 1.64108 | ||||||||
\(408\) | −2.16293 | −0.107081 | ||||||||
\(409\) | 30.3856 | 1.50247 | 0.751235 | − | 0.660034i | \(-0.229458\pi\) | ||||
0.751235 | + | 0.660034i | \(0.229458\pi\) | |||||||
\(410\) | 7.53253 | 0.372005 | ||||||||
\(411\) | 7.12069 | 0.351238 | ||||||||
\(412\) | 0.452882 | 0.0223119 | ||||||||
\(413\) | −48.3171 | −2.37753 | ||||||||
\(414\) | 0.903151 | 0.0443875 | ||||||||
\(415\) | −2.80519 | −0.137701 | ||||||||
\(416\) | −2.98138 | −0.146174 | ||||||||
\(417\) | −22.8514 | −1.11904 | ||||||||
\(418\) | 4.31481 | 0.211044 | ||||||||
\(419\) | −5.78674 | −0.282701 | −0.141350 | − | 0.989960i | \(-0.545144\pi\) | ||||
−0.141350 | + | 0.989960i | \(0.545144\pi\) | |||||||
\(420\) | −17.6108 | −0.859318 | ||||||||
\(421\) | −9.77900 | −0.476599 | −0.238300 | − | 0.971192i | \(-0.576590\pi\) | ||||
−0.238300 | + | 0.971192i | \(0.576590\pi\) | |||||||
\(422\) | 5.48824 | 0.267164 | ||||||||
\(423\) | 7.48914 | 0.364134 | ||||||||
\(424\) | 0.309487 | 0.0150300 | ||||||||
\(425\) | −8.42975 | −0.408903 | ||||||||
\(426\) | 11.3378 | 0.549320 | ||||||||
\(427\) | 50.3663 | 2.43740 | ||||||||
\(428\) | −9.35237 | −0.452064 | ||||||||
\(429\) | 17.6876 | 0.853966 | ||||||||
\(430\) | −21.1225 | −1.01862 | ||||||||
\(431\) | 16.1958 | 0.780125 | 0.390063 | − | 0.920788i | \(-0.372453\pi\) | ||||
0.390063 | + | 0.920788i | \(0.372453\pi\) | |||||||
\(432\) | −5.65196 | −0.271930 | ||||||||
\(433\) | 28.6150 | 1.37515 | 0.687575 | − | 0.726113i | \(-0.258675\pi\) | ||||
0.687575 | + | 0.726113i | \(0.258675\pi\) | |||||||
\(434\) | −24.6216 | −1.18187 | ||||||||
\(435\) | −23.1502 | −1.10997 | ||||||||
\(436\) | −9.43508 | −0.451858 | ||||||||
\(437\) | 1.05316 | 0.0503794 | ||||||||
\(438\) | 5.84146 | 0.279116 | ||||||||
\(439\) | 7.14980 | 0.341241 | 0.170621 | − | 0.985337i | \(-0.445423\pi\) | ||||
0.170621 | + | 0.985337i | \(0.445423\pi\) | |||||||
\(440\) | −13.3663 | −0.637215 | ||||||||
\(441\) | −6.22847 | −0.296594 | ||||||||
\(442\) | 4.45324 | 0.211819 | ||||||||
\(443\) | −41.1251 | −1.95391 | −0.976956 | − | 0.213440i | \(-0.931533\pi\) | ||||
−0.976956 | + | 0.213440i | \(0.931533\pi\) | |||||||
\(444\) | −11.7015 | −0.555328 | ||||||||
\(445\) | 43.4906 | 2.06165 | ||||||||
\(446\) | 10.7643 | 0.509705 | ||||||||
\(447\) | −26.6866 | −1.26223 | ||||||||
\(448\) | −3.72778 | −0.176121 | ||||||||
\(449\) | −10.1368 | −0.478385 | −0.239192 | − | 0.970972i | \(-0.576883\pi\) | ||||
−0.239192 | + | 0.970972i | \(0.576883\pi\) | |||||||
\(450\) | −5.09702 | −0.240276 | ||||||||
\(451\) | −9.45943 | −0.445427 | ||||||||
\(452\) | −13.2693 | −0.624135 | ||||||||
\(453\) | 1.49705 | 0.0703376 | ||||||||
\(454\) | 3.87295 | 0.181766 | ||||||||
\(455\) | 36.2587 | 1.69984 | ||||||||
\(456\) | −1.52503 | −0.0714159 | ||||||||
\(457\) | −27.1345 | −1.26930 | −0.634650 | − | 0.772800i | \(-0.718856\pi\) | ||||
−0.634650 | + | 0.772800i | \(0.718856\pi\) | |||||||
\(458\) | −4.62184 | −0.215965 | ||||||||
\(459\) | 8.44224 | 0.394050 | ||||||||
\(460\) | −3.26245 | −0.152113 | ||||||||
\(461\) | 23.7116 | 1.10436 | 0.552180 | − | 0.833725i | \(-0.313796\pi\) | ||||
0.552180 | + | 0.833725i | \(0.313796\pi\) | |||||||
\(462\) | 22.1158 | 1.02892 | ||||||||
\(463\) | 9.48950 | 0.441015 | 0.220507 | − | 0.975385i | \(-0.429229\pi\) | ||||
0.220507 | + | 0.975385i | \(0.429229\pi\) | |||||||
\(464\) | −4.90034 | −0.227493 | ||||||||
\(465\) | 31.2028 | 1.44699 | ||||||||
\(466\) | 11.5937 | 0.537067 | ||||||||
\(467\) | −4.43197 | −0.205087 | −0.102544 | − | 0.994729i | \(-0.532698\pi\) | ||||
−0.102544 | + | 0.994729i | \(0.532698\pi\) | |||||||
\(468\) | 2.69264 | 0.124467 | ||||||||
\(469\) | −48.5448 | −2.24159 | ||||||||
\(470\) | −27.0530 | −1.24786 | ||||||||
\(471\) | 6.26539 | 0.288694 | ||||||||
\(472\) | 12.9613 | 0.596594 | ||||||||
\(473\) | 26.5259 | 1.21966 | ||||||||
\(474\) | −3.95488 | −0.181654 | ||||||||
\(475\) | −5.94360 | −0.272711 | ||||||||
\(476\) | 5.56813 | 0.255215 | ||||||||
\(477\) | −0.279514 | −0.0127980 | ||||||||
\(478\) | 11.6851 | 0.534462 | ||||||||
\(479\) | 11.3773 | 0.519844 | 0.259922 | − | 0.965630i | \(-0.416303\pi\) | ||||
0.259922 | + | 0.965630i | \(0.416303\pi\) | |||||||
\(480\) | 4.72419 | 0.215629 | ||||||||
\(481\) | 24.0921 | 1.09851 | ||||||||
\(482\) | −25.4567 | −1.15952 | ||||||||
\(483\) | 5.39802 | 0.245618 | ||||||||
\(484\) | 5.78558 | 0.262981 | ||||||||
\(485\) | 8.28227 | 0.376079 | ||||||||
\(486\) | 9.02800 | 0.409518 | ||||||||
\(487\) | 29.6295 | 1.34264 | 0.671320 | − | 0.741168i | \(-0.265728\pi\) | ||||
0.671320 | + | 0.741168i | \(0.265728\pi\) | |||||||
\(488\) | −13.5111 | −0.611617 | ||||||||
\(489\) | −19.7400 | −0.892675 | ||||||||
\(490\) | 22.4991 | 1.01641 | ||||||||
\(491\) | 24.8058 | 1.11947 | 0.559735 | − | 0.828671i | \(-0.310903\pi\) | ||||
0.559735 | + | 0.828671i | \(0.310903\pi\) | |||||||
\(492\) | 3.34334 | 0.150729 | ||||||||
\(493\) | 7.31956 | 0.329656 | ||||||||
\(494\) | 3.13987 | 0.141269 | ||||||||
\(495\) | 12.0718 | 0.542588 | ||||||||
\(496\) | 6.60489 | 0.296568 | ||||||||
\(497\) | −29.1875 | −1.30924 | ||||||||
\(498\) | −1.24509 | −0.0557939 | ||||||||
\(499\) | 9.82637 | 0.439889 | 0.219944 | − | 0.975512i | \(-0.429412\pi\) | ||||
0.219944 | + | 0.975512i | \(0.429412\pi\) | |||||||
\(500\) | 2.09971 | 0.0939019 | ||||||||
\(501\) | 1.64033 | 0.0732845 | ||||||||
\(502\) | 7.69696 | 0.343532 | ||||||||
\(503\) | −28.3634 | −1.26466 | −0.632330 | − | 0.774699i | \(-0.717901\pi\) | ||||
−0.632330 | + | 0.774699i | \(0.717901\pi\) | |||||||
\(504\) | 3.36675 | 0.149967 | ||||||||
\(505\) | −58.2950 | −2.59410 | ||||||||
\(506\) | 4.09702 | 0.182135 | ||||||||
\(507\) | −5.95346 | −0.264403 | ||||||||
\(508\) | 2.35002 | 0.104265 | ||||||||
\(509\) | −16.1797 | −0.717154 | −0.358577 | − | 0.933500i | \(-0.616738\pi\) | ||||
−0.358577 | + | 0.933500i | \(0.616738\pi\) | |||||||
\(510\) | −7.05645 | −0.312465 | ||||||||
\(511\) | −15.0379 | −0.665239 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.95241 | 0.262805 | ||||||||
\(514\) | 11.6785 | 0.515115 | ||||||||
\(515\) | 1.47751 | 0.0651067 | ||||||||
\(516\) | −9.37529 | −0.412724 | ||||||||
\(517\) | 33.9734 | 1.49415 | ||||||||
\(518\) | 30.1237 | 1.32356 | ||||||||
\(519\) | −14.3096 | −0.628123 | ||||||||
\(520\) | −9.72662 | −0.426540 | ||||||||
\(521\) | −38.6356 | −1.69265 | −0.846327 | − | 0.532663i | \(-0.821191\pi\) | ||||
−0.846327 | + | 0.532663i | \(0.821191\pi\) | |||||||
\(522\) | 4.42575 | 0.193710 | ||||||||
\(523\) | 3.34181 | 0.146127 | 0.0730636 | − | 0.997327i | \(-0.476722\pi\) | ||||
0.0730636 | + | 0.997327i | \(0.476722\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | −30.4642 | −1.32957 | ||||||||
\(526\) | 6.70714 | 0.292445 | ||||||||
\(527\) | −9.86561 | −0.429753 | ||||||||
\(528\) | −5.93269 | −0.258187 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 1.00969 | 0.0438580 | ||||||||
\(531\) | −11.7061 | −0.507999 | ||||||||
\(532\) | 3.92595 | 0.170211 | ||||||||
\(533\) | −6.88358 | −0.298161 | ||||||||
\(534\) | 19.3034 | 0.835341 | ||||||||
\(535\) | −30.5117 | −1.31913 | ||||||||
\(536\) | 13.0224 | 0.562483 | ||||||||
\(537\) | 30.8144 | 1.32974 | ||||||||
\(538\) | −10.4258 | −0.449489 | ||||||||
\(539\) | −28.2546 | −1.21701 | ||||||||
\(540\) | −18.4392 | −0.793499 | ||||||||
\(541\) | −8.49344 | −0.365162 | −0.182581 | − | 0.983191i | \(-0.558445\pi\) | ||||
−0.182581 | + | 0.983191i | \(0.558445\pi\) | |||||||
\(542\) | −6.60454 | −0.283689 | ||||||||
\(543\) | 32.8583 | 1.41008 | ||||||||
\(544\) | −1.49368 | −0.0640412 | ||||||||
\(545\) | −30.7815 | −1.31853 | ||||||||
\(546\) | 16.0935 | 0.688740 | ||||||||
\(547\) | 16.8274 | 0.719489 | 0.359745 | − | 0.933051i | \(-0.382864\pi\) | ||||
0.359745 | + | 0.933051i | \(0.382864\pi\) | |||||||
\(548\) | 4.91743 | 0.210062 | ||||||||
\(549\) | 12.2025 | 0.520791 | ||||||||
\(550\) | −23.1219 | −0.985923 | ||||||||
\(551\) | 5.16084 | 0.219859 | ||||||||
\(552\) | −1.44805 | −0.0616331 | ||||||||
\(553\) | 10.1812 | 0.432951 | ||||||||
\(554\) | 31.1450 | 1.32323 | ||||||||
\(555\) | −38.1756 | −1.62046 | ||||||||
\(556\) | −15.7808 | −0.669255 | ||||||||
\(557\) | −6.60948 | −0.280053 | −0.140026 | − | 0.990148i | \(-0.544719\pi\) | ||||
−0.140026 | + | 0.990148i | \(0.544719\pi\) | |||||||
\(558\) | −5.96521 | −0.252528 | ||||||||
\(559\) | 19.3027 | 0.816418 | ||||||||
\(560\) | −12.1617 | −0.513926 | ||||||||
\(561\) | 8.86156 | 0.374135 | ||||||||
\(562\) | −6.42679 | −0.271098 | ||||||||
\(563\) | 3.80207 | 0.160238 | 0.0801191 | − | 0.996785i | \(-0.474470\pi\) | ||||
0.0801191 | + | 0.996785i | \(0.474470\pi\) | |||||||
\(564\) | −12.0076 | −0.505610 | ||||||||
\(565\) | −43.2904 | −1.82124 | ||||||||
\(566\) | 24.5134 | 1.03038 | ||||||||
\(567\) | 20.4091 | 0.857102 | ||||||||
\(568\) | 7.82972 | 0.328528 | ||||||||
\(569\) | 1.92744 | 0.0808026 | 0.0404013 | − | 0.999184i | \(-0.487136\pi\) | ||||
0.0404013 | + | 0.999184i | \(0.487136\pi\) | |||||||
\(570\) | −4.97532 | −0.208393 | ||||||||
\(571\) | 4.28832 | 0.179461 | 0.0897303 | − | 0.995966i | \(-0.471399\pi\) | ||||
0.0897303 | + | 0.995966i | \(0.471399\pi\) | |||||||
\(572\) | 12.2148 | 0.510726 | ||||||||
\(573\) | 5.11682 | 0.213758 | ||||||||
\(574\) | −8.60692 | −0.359246 | ||||||||
\(575\) | −5.64360 | −0.235354 | ||||||||
\(576\) | −0.903151 | −0.0376313 | ||||||||
\(577\) | −30.6857 | −1.27746 | −0.638732 | − | 0.769429i | \(-0.720541\pi\) | ||||
−0.638732 | + | 0.769429i | \(0.720541\pi\) | |||||||
\(578\) | −14.7689 | −0.614306 | ||||||||
\(579\) | 16.7405 | 0.695710 | ||||||||
\(580\) | −15.9871 | −0.663830 | ||||||||
\(581\) | 3.20530 | 0.132978 | ||||||||
\(582\) | 3.67611 | 0.152380 | ||||||||
\(583\) | −1.26797 | −0.0525141 | ||||||||
\(584\) | 4.03401 | 0.166929 | ||||||||
\(585\) | 8.78460 | 0.363199 | ||||||||
\(586\) | 24.0566 | 0.993769 | ||||||||
\(587\) | 40.7625 | 1.68245 | 0.841224 | − | 0.540687i | \(-0.181835\pi\) | ||||
0.841224 | + | 0.540687i | \(0.181835\pi\) | |||||||
\(588\) | 9.98629 | 0.411828 | ||||||||
\(589\) | −6.95599 | −0.286617 | ||||||||
\(590\) | 42.2858 | 1.74088 | ||||||||
\(591\) | 8.99407 | 0.369966 | ||||||||
\(592\) | −8.08086 | −0.332121 | ||||||||
\(593\) | −34.7883 | −1.42858 | −0.714291 | − | 0.699848i | \(-0.753251\pi\) | ||||
−0.714291 | + | 0.699848i | \(0.753251\pi\) | |||||||
\(594\) | 23.1562 | 0.950110 | ||||||||
\(595\) | 18.1658 | 0.744724 | ||||||||
\(596\) | −18.4294 | −0.754896 | ||||||||
\(597\) | 1.96000 | 0.0802176 | ||||||||
\(598\) | 2.98138 | 0.121918 | ||||||||
\(599\) | −37.6513 | −1.53839 | −0.769195 | − | 0.639014i | \(-0.779342\pi\) | ||||
−0.769195 | + | 0.639014i | \(0.779342\pi\) | |||||||
\(600\) | 8.17221 | 0.333629 | ||||||||
\(601\) | −42.4996 | −1.73360 | −0.866798 | − | 0.498660i | \(-0.833826\pi\) | ||||
−0.866798 | + | 0.498660i | \(0.833826\pi\) | |||||||
\(602\) | 24.1353 | 0.983680 | ||||||||
\(603\) | −11.7612 | −0.478954 | ||||||||
\(604\) | 1.03384 | 0.0420663 | ||||||||
\(605\) | 18.8752 | 0.767385 | ||||||||
\(606\) | −25.8744 | −1.05108 | ||||||||
\(607\) | −7.17688 | −0.291301 | −0.145650 | − | 0.989336i | \(-0.546527\pi\) | ||||
−0.145650 | + | 0.989336i | \(0.546527\pi\) | |||||||
\(608\) | −1.05316 | −0.0427112 | ||||||||
\(609\) | 26.4521 | 1.07189 | ||||||||
\(610\) | −44.0792 | −1.78471 | ||||||||
\(611\) | 24.7223 | 1.00016 | ||||||||
\(612\) | 1.34902 | 0.0545310 | ||||||||
\(613\) | 40.2014 | 1.62372 | 0.811860 | − | 0.583852i | \(-0.198455\pi\) | ||||
0.811860 | + | 0.583852i | \(0.198455\pi\) | |||||||
\(614\) | 14.4246 | 0.582129 | ||||||||
\(615\) | 10.9075 | 0.439832 | ||||||||
\(616\) | 15.2728 | 0.615359 | ||||||||
\(617\) | 12.0681 | 0.485843 | 0.242922 | − | 0.970046i | \(-0.421894\pi\) | ||||
0.242922 | + | 0.970046i | \(0.421894\pi\) | |||||||
\(618\) | 0.655796 | 0.0263800 | ||||||||
\(619\) | 44.9348 | 1.80608 | 0.903041 | − | 0.429554i | \(-0.141329\pi\) | ||||
0.903041 | + | 0.429554i | \(0.141329\pi\) | |||||||
\(620\) | 21.5481 | 0.865394 | ||||||||
\(621\) | 5.65196 | 0.226805 | ||||||||
\(622\) | −29.8190 | −1.19563 | ||||||||
\(623\) | −49.6937 | −1.99094 | ||||||||
\(624\) | −4.31719 | −0.172826 | ||||||||
\(625\) | −21.3678 | −0.854712 | ||||||||
\(626\) | −16.6481 | −0.665392 | ||||||||
\(627\) | 6.24806 | 0.249524 | ||||||||
\(628\) | 4.32678 | 0.172657 | ||||||||
\(629\) | 12.0703 | 0.481273 | ||||||||
\(630\) | 10.9839 | 0.437608 | ||||||||
\(631\) | 10.8493 | 0.431904 | 0.215952 | − | 0.976404i | \(-0.430715\pi\) | ||||
0.215952 | + | 0.976404i | \(0.430715\pi\) | |||||||
\(632\) | −2.73118 | −0.108640 | ||||||||
\(633\) | 7.94725 | 0.315875 | ||||||||
\(634\) | 28.1380 | 1.11750 | ||||||||
\(635\) | 7.66684 | 0.304249 | ||||||||
\(636\) | 0.448153 | 0.0177704 | ||||||||
\(637\) | −20.5607 | −0.814645 | ||||||||
\(638\) | 20.0768 | 0.794848 | ||||||||
\(639\) | −7.07142 | −0.279741 | ||||||||
\(640\) | 3.26245 | 0.128960 | ||||||||
\(641\) | −34.3263 | −1.35581 | −0.677903 | − | 0.735151i | \(-0.737111\pi\) | ||||
−0.677903 | + | 0.735151i | \(0.737111\pi\) | |||||||
\(642\) | −13.5427 | −0.534488 | ||||||||
\(643\) | −0.468965 | −0.0184942 | −0.00924710 | − | 0.999957i | \(-0.502943\pi\) | ||||
−0.00924710 | + | 0.999957i | \(0.502943\pi\) | |||||||
\(644\) | 3.72778 | 0.146895 | ||||||||
\(645\) | −30.5864 | −1.20434 | ||||||||
\(646\) | 1.57309 | 0.0618922 | ||||||||
\(647\) | −49.1637 | −1.93283 | −0.966413 | − | 0.256995i | \(-0.917267\pi\) | ||||
−0.966413 | + | 0.256995i | \(0.917267\pi\) | |||||||
\(648\) | −5.47486 | −0.215073 | ||||||||
\(649\) | −53.1029 | −2.08447 | ||||||||
\(650\) | −16.8257 | −0.659959 | ||||||||
\(651\) | −35.6533 | −1.39736 | ||||||||
\(652\) | −13.6321 | −0.533876 | ||||||||
\(653\) | 15.8344 | 0.619647 | 0.309823 | − | 0.950794i | \(-0.399730\pi\) | ||||
0.309823 | + | 0.950794i | \(0.399730\pi\) | |||||||
\(654\) | −13.6625 | −0.534245 | ||||||||
\(655\) | 3.26245 | 0.127475 | ||||||||
\(656\) | 2.30886 | 0.0901457 | ||||||||
\(657\) | −3.64332 | −0.142140 | ||||||||
\(658\) | 30.9116 | 1.20506 | ||||||||
\(659\) | −46.1821 | −1.79900 | −0.899499 | − | 0.436922i | \(-0.856069\pi\) | ||||
−0.899499 | + | 0.436922i | \(0.856069\pi\) | |||||||
\(660\) | −19.3551 | −0.753397 | ||||||||
\(661\) | −10.7136 | −0.416712 | −0.208356 | − | 0.978053i | \(-0.566811\pi\) | ||||
−0.208356 | + | 0.978053i | \(0.566811\pi\) | |||||||
\(662\) | −30.9825 | −1.20417 | ||||||||
\(663\) | 6.44852 | 0.250440 | ||||||||
\(664\) | −0.859840 | −0.0333683 | ||||||||
\(665\) | 12.8082 | 0.496681 | ||||||||
\(666\) | 7.29824 | 0.282801 | ||||||||
\(667\) | 4.90034 | 0.189742 | ||||||||
\(668\) | 1.13278 | 0.0438288 | ||||||||
\(669\) | 15.5873 | 0.602638 | ||||||||
\(670\) | 42.4850 | 1.64134 | ||||||||
\(671\) | 55.3551 | 2.13696 | ||||||||
\(672\) | −5.39802 | −0.208233 | ||||||||
\(673\) | −31.5207 | −1.21503 | −0.607517 | − | 0.794306i | \(-0.707834\pi\) | ||||
−0.607517 | + | 0.794306i | \(0.707834\pi\) | |||||||
\(674\) | −20.9581 | −0.807276 | ||||||||
\(675\) | −31.8974 | −1.22773 | ||||||||
\(676\) | −4.11137 | −0.158129 | ||||||||
\(677\) | −22.0298 | −0.846672 | −0.423336 | − | 0.905973i | \(-0.639141\pi\) | ||||
−0.423336 | + | 0.905973i | \(0.639141\pi\) | |||||||
\(678\) | −19.2146 | −0.737932 | ||||||||
\(679\) | −9.46359 | −0.363179 | ||||||||
\(680\) | −4.87307 | −0.186874 | ||||||||
\(681\) | 5.60822 | 0.214907 | ||||||||
\(682\) | −27.0604 | −1.03619 | ||||||||
\(683\) | 19.4924 | 0.745855 | 0.372927 | − | 0.927861i | \(-0.378354\pi\) | ||||
0.372927 | + | 0.927861i | \(0.378354\pi\) | |||||||
\(684\) | 0.951161 | 0.0363685 | ||||||||
\(685\) | 16.0429 | 0.612967 | ||||||||
\(686\) | 0.386296 | 0.0147489 | ||||||||
\(687\) | −6.69266 | −0.255341 | ||||||||
\(688\) | −6.47442 | −0.246835 | ||||||||
\(689\) | −0.922699 | −0.0351520 | ||||||||
\(690\) | −4.72419 | −0.179847 | ||||||||
\(691\) | 27.8578 | 1.05976 | 0.529880 | − | 0.848073i | \(-0.322237\pi\) | ||||
0.529880 | + | 0.848073i | \(0.322237\pi\) | |||||||
\(692\) | −9.88200 | −0.375657 | ||||||||
\(693\) | −13.7937 | −0.523978 | ||||||||
\(694\) | 10.7389 | 0.407642 | ||||||||
\(695\) | −51.4842 | −1.95291 | ||||||||
\(696\) | −7.09594 | −0.268971 | ||||||||
\(697\) | −3.44870 | −0.130629 | ||||||||
\(698\) | −24.0172 | −0.909064 | ||||||||
\(699\) | 16.7882 | 0.634989 | ||||||||
\(700\) | −21.0381 | −0.795166 | ||||||||
\(701\) | −0.0618821 | −0.00233726 | −0.00116863 | − | 0.999999i | \(-0.500372\pi\) | ||||
−0.00116863 | + | 0.999999i | \(0.500372\pi\) | |||||||
\(702\) | 16.8506 | 0.635986 | ||||||||
\(703\) | 8.51043 | 0.320977 | ||||||||
\(704\) | −4.09702 | −0.154412 | ||||||||
\(705\) | −39.1741 | −1.47538 | ||||||||
\(706\) | −24.8423 | −0.934953 | ||||||||
\(707\) | 66.6098 | 2.50512 | ||||||||
\(708\) | 18.7687 | 0.705370 | ||||||||
\(709\) | 10.5171 | 0.394977 | 0.197488 | − | 0.980305i | \(-0.436722\pi\) | ||||
0.197488 | + | 0.980305i | \(0.436722\pi\) | |||||||
\(710\) | 25.5441 | 0.958653 | ||||||||
\(711\) | 2.46667 | 0.0925073 | ||||||||
\(712\) | 13.3306 | 0.499587 | ||||||||
\(713\) | −6.60489 | −0.247355 | ||||||||
\(714\) | 8.06293 | 0.301748 | ||||||||
\(715\) | 39.8501 | 1.49031 | ||||||||
\(716\) | 21.2799 | 0.795269 | ||||||||
\(717\) | 16.9206 | 0.631910 | ||||||||
\(718\) | −32.2827 | −1.20478 | ||||||||
\(719\) | 23.5496 | 0.878252 | 0.439126 | − | 0.898425i | \(-0.355288\pi\) | ||||
0.439126 | + | 0.898425i | \(0.355288\pi\) | |||||||
\(720\) | −2.94649 | −0.109809 | ||||||||
\(721\) | −1.68825 | −0.0628736 | ||||||||
\(722\) | −17.8909 | −0.665829 | ||||||||
\(723\) | −36.8625 | −1.37093 | ||||||||
\(724\) | 22.6914 | 0.843319 | ||||||||
\(725\) | −27.6556 | −1.02710 | ||||||||
\(726\) | 8.37781 | 0.310930 | ||||||||
\(727\) | −27.8291 | −1.03213 | −0.516063 | − | 0.856551i | \(-0.672603\pi\) | ||||
−0.516063 | + | 0.856551i | \(0.672603\pi\) | |||||||
\(728\) | 11.1139 | 0.411910 | ||||||||
\(729\) | 29.4976 | 1.09250 | ||||||||
\(730\) | 13.1608 | 0.487102 | ||||||||
\(731\) | 9.67074 | 0.357685 | ||||||||
\(732\) | −19.5647 | −0.723131 | ||||||||
\(733\) | −24.0836 | −0.889549 | −0.444774 | − | 0.895643i | \(-0.646716\pi\) | ||||
−0.444774 | + | 0.895643i | \(0.646716\pi\) | |||||||
\(734\) | 24.4870 | 0.903832 | ||||||||
\(735\) | 32.5798 | 1.20172 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −53.3531 | −1.96529 | ||||||||
\(738\) | −2.08525 | −0.0767590 | ||||||||
\(739\) | 1.37489 | 0.0505762 | 0.0252881 | − | 0.999680i | \(-0.491950\pi\) | ||||
0.0252881 | + | 0.999680i | \(0.491950\pi\) | |||||||
\(740\) | −26.3634 | −0.969139 | ||||||||
\(741\) | 4.54668 | 0.167027 | ||||||||
\(742\) | −1.15370 | −0.0423537 | ||||||||
\(743\) | 12.7805 | 0.468870 | 0.234435 | − | 0.972132i | \(-0.424676\pi\) | ||||
0.234435 | + | 0.972132i | \(0.424676\pi\) | |||||||
\(744\) | 9.56421 | 0.350641 | ||||||||
\(745\) | −60.1249 | −2.20281 | ||||||||
\(746\) | 12.3106 | 0.450722 | ||||||||
\(747\) | 0.776565 | 0.0284130 | ||||||||
\(748\) | 6.11965 | 0.223757 | ||||||||
\(749\) | 34.8636 | 1.27389 | ||||||||
\(750\) | 3.04048 | 0.111023 | ||||||||
\(751\) | 21.2704 | 0.776168 | 0.388084 | − | 0.921624i | \(-0.373137\pi\) | ||||
0.388084 | + | 0.921624i | \(0.373137\pi\) | |||||||
\(752\) | −8.29223 | −0.302387 | ||||||||
\(753\) | 11.1456 | 0.406168 | ||||||||
\(754\) | 14.6098 | 0.532057 | ||||||||
\(755\) | 3.37285 | 0.122751 | ||||||||
\(756\) | 21.0693 | 0.766282 | ||||||||
\(757\) | 50.6899 | 1.84236 | 0.921178 | − | 0.389141i | \(-0.127228\pi\) | ||||
0.921178 | + | 0.389141i | \(0.127228\pi\) | |||||||
\(758\) | 19.3124 | 0.701459 | ||||||||
\(759\) | 5.93269 | 0.215343 | ||||||||
\(760\) | −3.43588 | −0.124632 | ||||||||
\(761\) | 23.0128 | 0.834214 | 0.417107 | − | 0.908857i | \(-0.363044\pi\) | ||||
0.417107 | + | 0.908857i | \(0.363044\pi\) | |||||||
\(762\) | 3.40295 | 0.123276 | ||||||||
\(763\) | 35.1719 | 1.27331 | ||||||||
\(764\) | 3.53360 | 0.127841 | ||||||||
\(765\) | 4.40112 | 0.159123 | ||||||||
\(766\) | −26.5607 | −0.959677 | ||||||||
\(767\) | −38.6427 | −1.39531 | ||||||||
\(768\) | 1.44805 | 0.0522520 | ||||||||
\(769\) | 19.8921 | 0.717327 | 0.358663 | − | 0.933467i | \(-0.383233\pi\) | ||||
0.358663 | + | 0.933467i | \(0.383233\pi\) | |||||||
\(770\) | 49.8268 | 1.79563 | ||||||||
\(771\) | 16.9110 | 0.609035 | ||||||||
\(772\) | 11.5607 | 0.416078 | ||||||||
\(773\) | −28.2713 | −1.01685 | −0.508423 | − | 0.861107i | \(-0.669771\pi\) | ||||
−0.508423 | + | 0.861107i | \(0.669771\pi\) | |||||||
\(774\) | 5.84738 | 0.210180 | ||||||||
\(775\) | 37.2753 | 1.33897 | ||||||||
\(776\) | 2.53866 | 0.0911328 | ||||||||
\(777\) | 43.6206 | 1.56488 | ||||||||
\(778\) | −9.58462 | −0.343625 | ||||||||
\(779\) | −2.43159 | −0.0871208 | ||||||||
\(780\) | −14.0846 | −0.504311 | ||||||||
\(781\) | −32.0785 | −1.14786 | ||||||||
\(782\) | 1.49368 | 0.0534140 | ||||||||
\(783\) | 27.6965 | 0.989793 | ||||||||
\(784\) | 6.89637 | 0.246299 | ||||||||
\(785\) | 14.1159 | 0.503818 | ||||||||
\(786\) | 1.44805 | 0.0516502 | ||||||||
\(787\) | −36.8594 | −1.31389 | −0.656947 | − | 0.753937i | \(-0.728153\pi\) | ||||
−0.656947 | + | 0.753937i | \(0.728153\pi\) | |||||||
\(788\) | 6.21116 | 0.221263 | ||||||||
\(789\) | 9.71227 | 0.345766 | ||||||||
\(790\) | −8.91034 | −0.317016 | ||||||||
\(791\) | 49.4651 | 1.75878 | ||||||||
\(792\) | 3.70023 | 0.131482 | ||||||||
\(793\) | 40.2816 | 1.43044 | ||||||||
\(794\) | 5.00689 | 0.177688 | ||||||||
\(795\) | 1.46208 | 0.0518545 | ||||||||
\(796\) | 1.35355 | 0.0479752 | ||||||||
\(797\) | 2.54217 | 0.0900483 | 0.0450242 | − | 0.998986i | \(-0.485664\pi\) | ||||
0.0450242 | + | 0.998986i | \(0.485664\pi\) | |||||||
\(798\) | 5.68497 | 0.201246 | ||||||||
\(799\) | 12.3860 | 0.438184 | ||||||||
\(800\) | 5.64360 | 0.199531 | ||||||||
\(801\) | −12.0396 | −0.425398 | ||||||||
\(802\) | −14.9221 | −0.526918 | ||||||||
\(803\) | −16.5274 | −0.583241 | ||||||||
\(804\) | 18.8571 | 0.665039 | ||||||||
\(805\) | 12.1617 | 0.428644 | ||||||||
\(806\) | −19.6917 | −0.693610 | ||||||||
\(807\) | −15.0971 | −0.531443 | ||||||||
\(808\) | −17.8685 | −0.628611 | ||||||||
\(809\) | 29.3048 | 1.03030 | 0.515151 | − | 0.857099i | \(-0.327736\pi\) | ||||
0.515151 | + | 0.857099i | \(0.327736\pi\) | |||||||
\(810\) | −17.8615 | −0.627589 | ||||||||
\(811\) | 40.2923 | 1.41485 | 0.707427 | − | 0.706786i | \(-0.249856\pi\) | ||||
0.707427 | + | 0.706786i | \(0.249856\pi\) | |||||||
\(812\) | 18.2674 | 0.641061 | ||||||||
\(813\) | −9.56370 | −0.335414 | ||||||||
\(814\) | 33.1075 | 1.16042 | ||||||||
\(815\) | −44.4742 | −1.55786 | ||||||||
\(816\) | −2.16293 | −0.0757176 | ||||||||
\(817\) | 6.81859 | 0.238552 | ||||||||
\(818\) | 30.3856 | 1.06241 | ||||||||
\(819\) | −10.0376 | −0.350741 | ||||||||
\(820\) | 7.53253 | 0.263047 | ||||||||
\(821\) | 2.95497 | 0.103129 | 0.0515646 | − | 0.998670i | \(-0.483579\pi\) | ||||
0.0515646 | + | 0.998670i | \(0.483579\pi\) | |||||||
\(822\) | 7.12069 | 0.248363 | ||||||||
\(823\) | 24.2496 | 0.845288 | 0.422644 | − | 0.906296i | \(-0.361102\pi\) | ||||
0.422644 | + | 0.906296i | \(0.361102\pi\) | |||||||
\(824\) | 0.452882 | 0.0157769 | ||||||||
\(825\) | −33.4817 | −1.16568 | ||||||||
\(826\) | −48.3171 | −1.68117 | ||||||||
\(827\) | 7.73882 | 0.269105 | 0.134553 | − | 0.990906i | \(-0.457040\pi\) | ||||
0.134553 | + | 0.990906i | \(0.457040\pi\) | |||||||
\(828\) | 0.903151 | 0.0313867 | ||||||||
\(829\) | −38.8842 | −1.35050 | −0.675252 | − | 0.737587i | \(-0.735965\pi\) | ||||
−0.675252 | + | 0.737587i | \(0.735965\pi\) | |||||||
\(830\) | −2.80519 | −0.0973694 | ||||||||
\(831\) | 45.0996 | 1.56449 | ||||||||
\(832\) | −2.98138 | −0.103361 | ||||||||
\(833\) | −10.3010 | −0.356909 | ||||||||
\(834\) | −22.8514 | −0.791279 | ||||||||
\(835\) | 3.69566 | 0.127893 | ||||||||
\(836\) | 4.31481 | 0.149231 | ||||||||
\(837\) | −37.3305 | −1.29033 | ||||||||
\(838\) | −5.78674 | −0.199900 | ||||||||
\(839\) | −18.4640 | −0.637447 | −0.318723 | − | 0.947848i | \(-0.603254\pi\) | ||||
−0.318723 | + | 0.947848i | \(0.603254\pi\) | |||||||
\(840\) | −17.6108 | −0.607630 | ||||||||
\(841\) | −4.98664 | −0.171953 | ||||||||
\(842\) | −9.77900 | −0.337007 | ||||||||
\(843\) | −9.30632 | −0.320527 | ||||||||
\(844\) | 5.48824 | 0.188913 | ||||||||
\(845\) | −13.4131 | −0.461426 | ||||||||
\(846\) | 7.48914 | 0.257482 | ||||||||
\(847\) | −21.5674 | −0.741064 | ||||||||
\(848\) | 0.309487 | 0.0106278 | ||||||||
\(849\) | 35.4966 | 1.21824 | ||||||||
\(850\) | −8.42975 | −0.289138 | ||||||||
\(851\) | 8.08086 | 0.277008 | ||||||||
\(852\) | 11.3378 | 0.388428 | ||||||||
\(853\) | −46.8286 | −1.60338 | −0.801690 | − | 0.597740i | \(-0.796066\pi\) | ||||
−0.801690 | + | 0.597740i | \(0.796066\pi\) | |||||||
\(854\) | 50.3663 | 1.72350 | ||||||||
\(855\) | 3.10312 | 0.106124 | ||||||||
\(856\) | −9.35237 | −0.319657 | ||||||||
\(857\) | 9.28335 | 0.317113 | 0.158557 | − | 0.987350i | \(-0.449316\pi\) | ||||
0.158557 | + | 0.987350i | \(0.449316\pi\) | |||||||
\(858\) | 17.6876 | 0.603845 | ||||||||
\(859\) | −16.0116 | −0.546310 | −0.273155 | − | 0.961970i | \(-0.588067\pi\) | ||||
−0.273155 | + | 0.961970i | \(0.588067\pi\) | |||||||
\(860\) | −21.1225 | −0.720271 | ||||||||
\(861\) | −12.4632 | −0.424746 | ||||||||
\(862\) | 16.1958 | 0.551632 | ||||||||
\(863\) | −29.3940 | −1.00058 | −0.500291 | − | 0.865857i | \(-0.666774\pi\) | ||||
−0.500291 | + | 0.865857i | \(0.666774\pi\) | |||||||
\(864\) | −5.65196 | −0.192284 | ||||||||
\(865\) | −32.2396 | −1.09618 | ||||||||
\(866\) | 28.6150 | 0.972378 | ||||||||
\(867\) | −21.3861 | −0.726311 | ||||||||
\(868\) | −24.6216 | −0.835711 | ||||||||
\(869\) | 11.1897 | 0.379584 | ||||||||
\(870\) | −23.1502 | −0.784864 | ||||||||
\(871\) | −38.8248 | −1.31553 | ||||||||
\(872\) | −9.43508 | −0.319512 | ||||||||
\(873\) | −2.29280 | −0.0775995 | ||||||||
\(874\) | 1.05316 | 0.0356236 | ||||||||
\(875\) | −7.82726 | −0.264610 | ||||||||
\(876\) | 5.84146 | 0.197364 | ||||||||
\(877\) | −43.1526 | −1.45716 | −0.728579 | − | 0.684962i | \(-0.759819\pi\) | ||||
−0.728579 | + | 0.684962i | \(0.759819\pi\) | |||||||
\(878\) | 7.14980 | 0.241294 | ||||||||
\(879\) | 34.8352 | 1.17496 | ||||||||
\(880\) | −13.3663 | −0.450579 | ||||||||
\(881\) | −23.2901 | −0.784662 | −0.392331 | − | 0.919824i | \(-0.628331\pi\) | ||||
−0.392331 | + | 0.919824i | \(0.628331\pi\) | |||||||
\(882\) | −6.22847 | −0.209723 | ||||||||
\(883\) | −41.1780 | −1.38575 | −0.692875 | − | 0.721058i | \(-0.743656\pi\) | ||||
−0.692875 | + | 0.721058i | \(0.743656\pi\) | |||||||
\(884\) | 4.45324 | 0.149779 | ||||||||
\(885\) | 61.2319 | 2.05829 | ||||||||
\(886\) | −41.1251 | −1.38162 | ||||||||
\(887\) | 1.71701 | 0.0576514 | 0.0288257 | − | 0.999584i | \(-0.490823\pi\) | ||||
0.0288257 | + | 0.999584i | \(0.490823\pi\) | |||||||
\(888\) | −11.7015 | −0.392676 | ||||||||
\(889\) | −8.76037 | −0.293814 | ||||||||
\(890\) | 43.4906 | 1.45781 | ||||||||
\(891\) | 22.4306 | 0.751455 | ||||||||
\(892\) | 10.7643 | 0.360416 | ||||||||
\(893\) | 8.73303 | 0.292240 | ||||||||
\(894\) | −26.6866 | −0.892534 | ||||||||
\(895\) | 69.4248 | 2.32062 | ||||||||
\(896\) | −3.72778 | −0.124537 | ||||||||
\(897\) | 4.31719 | 0.144147 | ||||||||
\(898\) | −10.1368 | −0.338269 | ||||||||
\(899\) | −32.3662 | −1.07947 | ||||||||
\(900\) | −5.09702 | −0.169901 | ||||||||
\(901\) | −0.462276 | −0.0154006 | ||||||||
\(902\) | −9.45943 | −0.314965 | ||||||||
\(903\) | 34.9491 | 1.16303 | ||||||||
\(904\) | −13.2693 | −0.441330 | ||||||||
\(905\) | 74.0296 | 2.46083 | ||||||||
\(906\) | 1.49705 | 0.0497362 | ||||||||
\(907\) | −45.4391 | −1.50878 | −0.754390 | − | 0.656426i | \(-0.772067\pi\) | ||||
−0.754390 | + | 0.656426i | \(0.772067\pi\) | |||||||
\(908\) | 3.87295 | 0.128528 | ||||||||
\(909\) | 16.1379 | 0.535261 | ||||||||
\(910\) | 36.2587 | 1.20196 | ||||||||
\(911\) | −10.0124 | −0.331725 | −0.165862 | − | 0.986149i | \(-0.553041\pi\) | ||||
−0.165862 | + | 0.986149i | \(0.553041\pi\) | |||||||
\(912\) | −1.52503 | −0.0504986 | ||||||||
\(913\) | 3.52278 | 0.116587 | ||||||||
\(914\) | −27.1345 | −0.897531 | ||||||||
\(915\) | −63.8289 | −2.11012 | ||||||||
\(916\) | −4.62184 | −0.152710 | ||||||||
\(917\) | −3.72778 | −0.123102 | ||||||||
\(918\) | 8.44224 | 0.278635 | ||||||||
\(919\) | −41.9809 | −1.38482 | −0.692412 | − | 0.721503i | \(-0.743452\pi\) | ||||
−0.692412 | + | 0.721503i | \(0.743452\pi\) | |||||||
\(920\) | −3.26245 | −0.107560 | ||||||||
\(921\) | 20.8875 | 0.688268 | ||||||||
\(922\) | 23.7116 | 0.780901 | ||||||||
\(923\) | −23.3434 | −0.768357 | ||||||||
\(924\) | 22.1158 | 0.727556 | ||||||||
\(925\) | −45.6051 | −1.49949 | ||||||||
\(926\) | 9.48950 | 0.311844 | ||||||||
\(927\) | −0.409021 | −0.0134340 | ||||||||
\(928\) | −4.90034 | −0.160862 | ||||||||
\(929\) | 28.0164 | 0.919188 | 0.459594 | − | 0.888129i | \(-0.347995\pi\) | ||||
0.459594 | + | 0.888129i | \(0.347995\pi\) | |||||||
\(930\) | 31.2028 | 1.02318 | ||||||||
\(931\) | −7.26297 | −0.238034 | ||||||||
\(932\) | 11.5937 | 0.379764 | ||||||||
\(933\) | −43.1794 | −1.41363 | ||||||||
\(934\) | −4.43197 | −0.145019 | ||||||||
\(935\) | 19.9651 | 0.652928 | ||||||||
\(936\) | 2.69264 | 0.0880116 | ||||||||
\(937\) | 13.1822 | 0.430643 | 0.215321 | − | 0.976543i | \(-0.430920\pi\) | ||||
0.215321 | + | 0.976543i | \(0.430920\pi\) | |||||||
\(938\) | −48.5448 | −1.58504 | ||||||||
\(939\) | −24.1073 | −0.786711 | ||||||||
\(940\) | −27.0530 | −0.882372 | ||||||||
\(941\) | −48.6416 | −1.58567 | −0.792835 | − | 0.609436i | \(-0.791396\pi\) | ||||
−0.792835 | + | 0.609436i | \(0.791396\pi\) | |||||||
\(942\) | 6.26539 | 0.204137 | ||||||||
\(943\) | −2.30886 | −0.0751867 | ||||||||
\(944\) | 12.9613 | 0.421856 | ||||||||
\(945\) | 68.7375 | 2.23603 | ||||||||
\(946\) | 26.5259 | 0.862430 | ||||||||
\(947\) | 26.8422 | 0.872254 | 0.436127 | − | 0.899885i | \(-0.356350\pi\) | ||||
0.436127 | + | 0.899885i | \(0.356350\pi\) | |||||||
\(948\) | −3.95488 | −0.128449 | ||||||||
\(949\) | −12.0269 | −0.390411 | ||||||||
\(950\) | −5.94360 | −0.192836 | ||||||||
\(951\) | 40.7453 | 1.32126 | ||||||||
\(952\) | 5.56813 | 0.180464 | ||||||||
\(953\) | −48.1239 | −1.55889 | −0.779443 | − | 0.626473i | \(-0.784498\pi\) | ||||
−0.779443 | + | 0.626473i | \(0.784498\pi\) | |||||||
\(954\) | −0.279514 | −0.00904958 | ||||||||
\(955\) | 11.5282 | 0.373044 | ||||||||
\(956\) | 11.6851 | 0.377922 | ||||||||
\(957\) | 29.0722 | 0.939771 | ||||||||
\(958\) | 11.3773 | 0.367585 | ||||||||
\(959\) | −18.3311 | −0.591943 | ||||||||
\(960\) | 4.72419 | 0.152473 | ||||||||
\(961\) | 12.6245 | 0.407243 | ||||||||
\(962\) | 24.0921 | 0.776762 | ||||||||
\(963\) | 8.44660 | 0.272188 | ||||||||
\(964\) | −25.4567 | −0.819904 | ||||||||
\(965\) | 37.7162 | 1.21413 | ||||||||
\(966\) | 5.39802 | 0.173678 | ||||||||
\(967\) | 33.4321 | 1.07510 | 0.537552 | − | 0.843231i | \(-0.319349\pi\) | ||||
0.537552 | + | 0.843231i | \(0.319349\pi\) | |||||||
\(968\) | 5.78558 | 0.185956 | ||||||||
\(969\) | 2.27791 | 0.0731769 | ||||||||
\(970\) | 8.28227 | 0.265928 | ||||||||
\(971\) | −51.5788 | −1.65524 | −0.827622 | − | 0.561286i | \(-0.810307\pi\) | ||||
−0.827622 | + | 0.561286i | \(0.810307\pi\) | |||||||
\(972\) | 9.02800 | 0.289573 | ||||||||
\(973\) | 58.8275 | 1.88592 | ||||||||
\(974\) | 29.6295 | 0.949389 | ||||||||
\(975\) | −24.3645 | −0.780288 | ||||||||
\(976\) | −13.5111 | −0.432478 | ||||||||
\(977\) | 33.1159 | 1.05947 | 0.529735 | − | 0.848163i | \(-0.322291\pi\) | ||||
0.529735 | + | 0.848163i | \(0.322291\pi\) | |||||||
\(978\) | −19.7400 | −0.631216 | ||||||||
\(979\) | −54.6159 | −1.74553 | ||||||||
\(980\) | 22.4991 | 0.718707 | ||||||||
\(981\) | 8.52130 | 0.272064 | ||||||||
\(982\) | 24.8058 | 0.791585 | ||||||||
\(983\) | −35.9782 | −1.14753 | −0.573763 | − | 0.819022i | \(-0.694517\pi\) | ||||
−0.573763 | + | 0.819022i | \(0.694517\pi\) | |||||||
\(984\) | 3.34334 | 0.106582 | ||||||||
\(985\) | 20.2636 | 0.645652 | ||||||||
\(986\) | 7.31956 | 0.233102 | ||||||||
\(987\) | 44.7616 | 1.42478 | ||||||||
\(988\) | 3.13987 | 0.0998924 | ||||||||
\(989\) | 6.47442 | 0.205875 | ||||||||
\(990\) | 12.0718 | 0.383668 | ||||||||
\(991\) | −12.6716 | −0.402526 | −0.201263 | − | 0.979537i | \(-0.564505\pi\) | ||||
−0.201263 | + | 0.979537i | \(0.564505\pi\) | |||||||
\(992\) | 6.60489 | 0.209705 | ||||||||
\(993\) | −44.8643 | −1.42372 | ||||||||
\(994\) | −29.1875 | −0.925772 | ||||||||
\(995\) | 4.41588 | 0.139993 | ||||||||
\(996\) | −1.24509 | −0.0394522 | ||||||||
\(997\) | 24.3353 | 0.770706 | 0.385353 | − | 0.922769i | \(-0.374080\pi\) | ||||
0.385353 | + | 0.922769i | \(0.374080\pi\) | |||||||
\(998\) | 9.82637 | 0.311048 | ||||||||
\(999\) | 45.6727 | 1.44502 |
(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 | 6026.2.a.g.1.17 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.g.1.17 | ✓ | 21 | 1.1 | even | 1 | trivial |