Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32398 | −1.64330 | −0.821652 | − | 0.569990i | \(-0.806947\pi\) | ||||
−0.821652 | + | 0.569990i | \(0.806947\pi\) | |||||||
\(3\) | −3.12042 | −1.80158 | −0.900788 | − | 0.434259i | \(-0.857010\pi\) | ||||
−0.900788 | + | 0.434259i | \(0.857010\pi\) | |||||||
\(4\) | 3.40089 | 1.70045 | ||||||||
\(5\) | 3.91464 | 1.75068 | 0.875341 | − | 0.483507i | \(-0.160637\pi\) | ||||
0.875341 | + | 0.483507i | \(0.160637\pi\) | |||||||
\(6\) | 7.25180 | 2.96054 | ||||||||
\(7\) | −0.989043 | −0.373823 | −0.186912 | − | 0.982377i | \(-0.559848\pi\) | ||||
−0.186912 | + | 0.982377i | \(0.559848\pi\) | |||||||
\(8\) | −3.25564 | −1.15104 | ||||||||
\(9\) | 6.73703 | 2.24568 | ||||||||
\(10\) | −9.09756 | −2.87690 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −10.6122 | −3.06348 | ||||||||
\(13\) | −5.46513 | −1.51575 | −0.757877 | − | 0.652397i | \(-0.773763\pi\) | ||||
−0.757877 | + | 0.652397i | \(0.773763\pi\) | |||||||
\(14\) | 2.29852 | 0.614305 | ||||||||
\(15\) | −12.2153 | −3.15399 | ||||||||
\(16\) | 0.764273 | 0.191068 | ||||||||
\(17\) | 2.88434 | 0.699555 | 0.349777 | − | 0.936833i | \(-0.386257\pi\) | ||||
0.349777 | + | 0.936833i | \(0.386257\pi\) | |||||||
\(18\) | −15.6567 | −3.69033 | ||||||||
\(19\) | −4.30630 | −0.987932 | −0.493966 | − | 0.869481i | \(-0.664453\pi\) | ||||
−0.493966 | + | 0.869481i | \(0.664453\pi\) | |||||||
\(20\) | 13.3133 | 2.97694 | ||||||||
\(21\) | 3.08623 | 0.673471 | ||||||||
\(22\) | −2.32398 | −0.495475 | ||||||||
\(23\) | −7.74043 | −1.61399 | −0.806996 | − | 0.590557i | \(-0.798908\pi\) | ||||
−0.806996 | + | 0.590557i | \(0.798908\pi\) | |||||||
\(24\) | 10.1590 | 2.07369 | ||||||||
\(25\) | 10.3244 | 2.06489 | ||||||||
\(26\) | 12.7009 | 2.49084 | ||||||||
\(27\) | −11.6611 | −2.24418 | ||||||||
\(28\) | −3.36363 | −0.635666 | ||||||||
\(29\) | 0.271701 | 0.0504537 | 0.0252268 | − | 0.999682i | \(-0.491969\pi\) | ||||
0.0252268 | + | 0.999682i | \(0.491969\pi\) | |||||||
\(30\) | 28.3882 | 5.18295 | ||||||||
\(31\) | 10.4398 | 1.87505 | 0.937525 | − | 0.347918i | \(-0.113111\pi\) | ||||
0.937525 | + | 0.347918i | \(0.113111\pi\) | |||||||
\(32\) | 4.73513 | 0.837060 | ||||||||
\(33\) | −3.12042 | −0.543196 | ||||||||
\(34\) | −6.70315 | −1.14958 | ||||||||
\(35\) | −3.87175 | −0.654445 | ||||||||
\(36\) | 22.9119 | 3.81865 | ||||||||
\(37\) | 7.72811 | 1.27049 | 0.635247 | − | 0.772309i | \(-0.280898\pi\) | ||||
0.635247 | + | 0.772309i | \(0.280898\pi\) | |||||||
\(38\) | 10.0078 | 1.62347 | ||||||||
\(39\) | 17.0535 | 2.73075 | ||||||||
\(40\) | −12.7447 | −2.01511 | ||||||||
\(41\) | −0.0770176 | −0.0120281 | −0.00601406 | − | 0.999982i | \(-0.501914\pi\) | ||||
−0.00601406 | + | 0.999982i | \(0.501914\pi\) | |||||||
\(42\) | −7.17235 | −1.10672 | ||||||||
\(43\) | −0.563563 | −0.0859425 | −0.0429712 | − | 0.999076i | \(-0.513682\pi\) | ||||
−0.0429712 | + | 0.999076i | \(0.513682\pi\) | |||||||
\(44\) | 3.40089 | 0.512703 | ||||||||
\(45\) | 26.3731 | 3.93147 | ||||||||
\(46\) | 17.9886 | 2.65228 | ||||||||
\(47\) | −8.68749 | −1.26720 | −0.633601 | − | 0.773660i | \(-0.718424\pi\) | ||||
−0.633601 | + | 0.773660i | \(0.718424\pi\) | |||||||
\(48\) | −2.38486 | −0.344224 | ||||||||
\(49\) | −6.02179 | −0.860256 | ||||||||
\(50\) | −23.9938 | −3.39323 | ||||||||
\(51\) | −9.00035 | −1.26030 | ||||||||
\(52\) | −18.5863 | −2.57746 | ||||||||
\(53\) | 1.79037 | 0.245926 | 0.122963 | − | 0.992411i | \(-0.460760\pi\) | ||||
0.122963 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(54\) | 27.1002 | 3.68787 | ||||||||
\(55\) | 3.91464 | 0.527850 | ||||||||
\(56\) | 3.21997 | 0.430287 | ||||||||
\(57\) | 13.4375 | 1.77984 | ||||||||
\(58\) | −0.631429 | −0.0829107 | ||||||||
\(59\) | 1.90517 | 0.248032 | 0.124016 | − | 0.992280i | \(-0.460423\pi\) | ||||
0.124016 | + | 0.992280i | \(0.460423\pi\) | |||||||
\(60\) | −41.5430 | −5.36318 | ||||||||
\(61\) | −2.52628 | −0.323458 | −0.161729 | − | 0.986835i | \(-0.551707\pi\) | ||||
−0.161729 | + | 0.986835i | \(0.551707\pi\) | |||||||
\(62\) | −24.2620 | −3.08128 | ||||||||
\(63\) | −6.66322 | −0.839486 | ||||||||
\(64\) | −12.5329 | −1.56661 | ||||||||
\(65\) | −21.3940 | −2.65360 | ||||||||
\(66\) | 7.25180 | 0.892635 | ||||||||
\(67\) | 13.7996 | 1.68589 | 0.842945 | − | 0.538000i | \(-0.180820\pi\) | ||||
0.842945 | + | 0.538000i | \(0.180820\pi\) | |||||||
\(68\) | 9.80932 | 1.18955 | ||||||||
\(69\) | 24.1534 | 2.90773 | ||||||||
\(70\) | 8.99788 | 1.07545 | ||||||||
\(71\) | −4.88488 | −0.579729 | −0.289864 | − | 0.957068i | \(-0.593610\pi\) | ||||
−0.289864 | + | 0.957068i | \(0.593610\pi\) | |||||||
\(72\) | −21.9334 | −2.58487 | ||||||||
\(73\) | 2.95790 | 0.346196 | 0.173098 | − | 0.984905i | \(-0.444622\pi\) | ||||
0.173098 | + | 0.984905i | \(0.444622\pi\) | |||||||
\(74\) | −17.9600 | −2.08781 | ||||||||
\(75\) | −32.2166 | −3.72005 | ||||||||
\(76\) | −14.6452 | −1.67992 | ||||||||
\(77\) | −0.989043 | −0.112712 | ||||||||
\(78\) | −39.6320 | −4.48744 | ||||||||
\(79\) | 4.88730 | 0.549864 | 0.274932 | − | 0.961464i | \(-0.411345\pi\) | ||||
0.274932 | + | 0.961464i | \(0.411345\pi\) | |||||||
\(80\) | 2.99186 | 0.334500 | ||||||||
\(81\) | 16.1765 | 1.79739 | ||||||||
\(82\) | 0.178987 | 0.0197659 | ||||||||
\(83\) | −10.2679 | −1.12705 | −0.563525 | − | 0.826099i | \(-0.690555\pi\) | ||||
−0.563525 | + | 0.826099i | \(0.690555\pi\) | |||||||
\(84\) | 10.4959 | 1.14520 | ||||||||
\(85\) | 11.2912 | 1.22470 | ||||||||
\(86\) | 1.30971 | 0.141230 | ||||||||
\(87\) | −0.847823 | −0.0908962 | ||||||||
\(88\) | −3.25564 | −0.347053 | ||||||||
\(89\) | 3.31687 | 0.351587 | 0.175794 | − | 0.984427i | \(-0.443751\pi\) | ||||
0.175794 | + | 0.984427i | \(0.443751\pi\) | |||||||
\(90\) | −61.2905 | −6.46059 | ||||||||
\(91\) | 5.40525 | 0.566624 | ||||||||
\(92\) | −26.3244 | −2.74450 | ||||||||
\(93\) | −32.5767 | −3.37805 | ||||||||
\(94\) | 20.1896 | 2.08240 | ||||||||
\(95\) | −16.8576 | −1.72955 | ||||||||
\(96\) | −14.7756 | −1.50803 | ||||||||
\(97\) | −7.85906 | −0.797966 | −0.398983 | − | 0.916958i | \(-0.630637\pi\) | ||||
−0.398983 | + | 0.916958i | \(0.630637\pi\) | |||||||
\(98\) | 13.9945 | 1.41366 | ||||||||
\(99\) | 6.73703 | 0.677097 | ||||||||
\(100\) | 35.1122 | 3.51122 | ||||||||
\(101\) | −9.28820 | −0.924210 | −0.462105 | − | 0.886825i | \(-0.652906\pi\) | ||||
−0.462105 | + | 0.886825i | \(0.652906\pi\) | |||||||
\(102\) | 20.9167 | 2.07106 | ||||||||
\(103\) | −13.3614 | −1.31654 | −0.658270 | − | 0.752782i | \(-0.728711\pi\) | ||||
−0.658270 | + | 0.752782i | \(0.728711\pi\) | |||||||
\(104\) | 17.7925 | 1.74470 | ||||||||
\(105\) | 12.0815 | 1.17903 | ||||||||
\(106\) | −4.16078 | −0.404130 | ||||||||
\(107\) | −5.85554 | −0.566076 | −0.283038 | − | 0.959109i | \(-0.591342\pi\) | ||||
−0.283038 | + | 0.959109i | \(0.591342\pi\) | |||||||
\(108\) | −39.6582 | −3.81611 | ||||||||
\(109\) | 18.7078 | 1.79189 | 0.895943 | − | 0.444168i | \(-0.146501\pi\) | ||||
0.895943 | + | 0.444168i | \(0.146501\pi\) | |||||||
\(110\) | −9.09756 | −0.867418 | ||||||||
\(111\) | −24.1150 | −2.28889 | ||||||||
\(112\) | −0.755899 | −0.0714258 | ||||||||
\(113\) | 18.5240 | 1.74259 | 0.871295 | − | 0.490759i | \(-0.163281\pi\) | ||||
0.871295 | + | 0.490759i | \(0.163281\pi\) | |||||||
\(114\) | −31.2284 | −2.92481 | ||||||||
\(115\) | −30.3010 | −2.82559 | ||||||||
\(116\) | 0.924027 | 0.0857937 | ||||||||
\(117\) | −36.8187 | −3.40389 | ||||||||
\(118\) | −4.42759 | −0.407592 | ||||||||
\(119\) | −2.85274 | −0.261510 | ||||||||
\(120\) | 39.7688 | 3.63038 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.87104 | 0.531539 | ||||||||
\(123\) | 0.240327 | 0.0216696 | ||||||||
\(124\) | 35.5047 | 3.18842 | ||||||||
\(125\) | 20.8432 | 1.86427 | ||||||||
\(126\) | 15.4852 | 1.37953 | ||||||||
\(127\) | −12.5205 | −1.11101 | −0.555506 | − | 0.831512i | \(-0.687476\pi\) | ||||
−0.555506 | + | 0.831512i | \(0.687476\pi\) | |||||||
\(128\) | 19.6560 | 1.73736 | ||||||||
\(129\) | 1.75855 | 0.154832 | ||||||||
\(130\) | 49.7193 | 4.36067 | ||||||||
\(131\) | 16.4051 | 1.43332 | 0.716661 | − | 0.697422i | \(-0.245669\pi\) | ||||
0.716661 | + | 0.697422i | \(0.245669\pi\) | |||||||
\(132\) | −10.6122 | −0.923674 | ||||||||
\(133\) | 4.25911 | 0.369312 | ||||||||
\(134\) | −32.0700 | −2.77043 | ||||||||
\(135\) | −45.6491 | −3.92885 | ||||||||
\(136\) | −9.39037 | −0.805218 | ||||||||
\(137\) | 6.54882 | 0.559503 | 0.279752 | − | 0.960072i | \(-0.409748\pi\) | ||||
0.279752 | + | 0.960072i | \(0.409748\pi\) | |||||||
\(138\) | −56.1321 | −4.77828 | ||||||||
\(139\) | −14.7493 | −1.25102 | −0.625509 | − | 0.780217i | \(-0.715109\pi\) | ||||
−0.625509 | + | 0.780217i | \(0.715109\pi\) | |||||||
\(140\) | −13.1674 | −1.11285 | ||||||||
\(141\) | 27.1086 | 2.28296 | ||||||||
\(142\) | 11.3524 | 0.952670 | ||||||||
\(143\) | −5.46513 | −0.457017 | ||||||||
\(144\) | 5.14893 | 0.429078 | ||||||||
\(145\) | 1.06361 | 0.0883283 | ||||||||
\(146\) | −6.87411 | −0.568905 | ||||||||
\(147\) | 18.7905 | 1.54982 | ||||||||
\(148\) | 26.2825 | 2.16040 | ||||||||
\(149\) | −20.8605 | −1.70896 | −0.854478 | − | 0.519487i | \(-0.826123\pi\) | ||||
−0.854478 | + | 0.519487i | \(0.826123\pi\) | |||||||
\(150\) | 74.8707 | 6.11317 | ||||||||
\(151\) | 8.79515 | 0.715739 | 0.357870 | − | 0.933772i | \(-0.383503\pi\) | ||||
0.357870 | + | 0.933772i | \(0.383503\pi\) | |||||||
\(152\) | 14.0198 | 1.13715 | ||||||||
\(153\) | 19.4319 | 1.57097 | ||||||||
\(154\) | 2.29852 | 0.185220 | ||||||||
\(155\) | 40.8682 | 3.28261 | ||||||||
\(156\) | 57.9971 | 4.64348 | ||||||||
\(157\) | 0.853945 | 0.0681522 | 0.0340761 | − | 0.999419i | \(-0.489151\pi\) | ||||
0.0340761 | + | 0.999419i | \(0.489151\pi\) | |||||||
\(158\) | −11.3580 | −0.903594 | ||||||||
\(159\) | −5.58669 | −0.443054 | ||||||||
\(160\) | 18.5363 | 1.46543 | ||||||||
\(161\) | 7.65562 | 0.603348 | ||||||||
\(162\) | −37.5939 | −2.95365 | ||||||||
\(163\) | −16.8640 | −1.32089 | −0.660445 | − | 0.750875i | \(-0.729632\pi\) | ||||
−0.660445 | + | 0.750875i | \(0.729632\pi\) | |||||||
\(164\) | −0.261928 | −0.0204532 | ||||||||
\(165\) | −12.2153 | −0.950963 | ||||||||
\(166\) | 23.8624 | 1.85208 | ||||||||
\(167\) | −5.35048 | −0.414032 | −0.207016 | − | 0.978338i | \(-0.566375\pi\) | ||||
−0.207016 | + | 0.978338i | \(0.566375\pi\) | |||||||
\(168\) | −10.0477 | −0.775195 | ||||||||
\(169\) | 16.8676 | 1.29751 | ||||||||
\(170\) | −26.2404 | −2.01255 | ||||||||
\(171\) | −29.0117 | −2.21858 | ||||||||
\(172\) | −1.91661 | −0.146140 | ||||||||
\(173\) | −17.5815 | −1.33670 | −0.668350 | − | 0.743847i | \(-0.732999\pi\) | ||||
−0.668350 | + | 0.743847i | \(0.732999\pi\) | |||||||
\(174\) | 1.97033 | 0.149370 | ||||||||
\(175\) | −10.2113 | −0.771902 | ||||||||
\(176\) | 0.764273 | 0.0576093 | ||||||||
\(177\) | −5.94494 | −0.446849 | ||||||||
\(178\) | −7.70834 | −0.577764 | ||||||||
\(179\) | 8.33719 | 0.623151 | 0.311576 | − | 0.950221i | \(-0.399143\pi\) | ||||
0.311576 | + | 0.950221i | \(0.399143\pi\) | |||||||
\(180\) | 89.6919 | 6.68524 | ||||||||
\(181\) | −10.0813 | −0.749340 | −0.374670 | − | 0.927158i | \(-0.622244\pi\) | ||||
−0.374670 | + | 0.927158i | \(0.622244\pi\) | |||||||
\(182\) | −12.5617 | −0.931135 | ||||||||
\(183\) | 7.88307 | 0.582734 | ||||||||
\(184\) | 25.2001 | 1.85777 | ||||||||
\(185\) | 30.2528 | 2.22423 | ||||||||
\(186\) | 75.7076 | 5.55115 | ||||||||
\(187\) | 2.88434 | 0.210924 | ||||||||
\(188\) | −29.5452 | −2.15481 | ||||||||
\(189\) | 11.5333 | 0.838928 | ||||||||
\(190\) | 39.1768 | 2.84218 | ||||||||
\(191\) | 3.91318 | 0.283148 | 0.141574 | − | 0.989928i | \(-0.454784\pi\) | ||||
0.141574 | + | 0.989928i | \(0.454784\pi\) | |||||||
\(192\) | 39.1079 | 2.82237 | ||||||||
\(193\) | −13.2973 | −0.957162 | −0.478581 | − | 0.878043i | \(-0.658849\pi\) | ||||
−0.478581 | + | 0.878043i | \(0.658849\pi\) | |||||||
\(194\) | 18.2643 | 1.31130 | ||||||||
\(195\) | 66.7584 | 4.78067 | ||||||||
\(196\) | −20.4795 | −1.46282 | ||||||||
\(197\) | −8.35699 | −0.595411 | −0.297705 | − | 0.954658i | \(-0.596221\pi\) | ||||
−0.297705 | + | 0.954658i | \(0.596221\pi\) | |||||||
\(198\) | −15.6567 | −1.11268 | ||||||||
\(199\) | 18.0808 | 1.28171 | 0.640855 | − | 0.767662i | \(-0.278580\pi\) | ||||
0.640855 | + | 0.767662i | \(0.278580\pi\) | |||||||
\(200\) | −33.6126 | −2.37677 | ||||||||
\(201\) | −43.0606 | −3.03726 | ||||||||
\(202\) | 21.5856 | 1.51876 | ||||||||
\(203\) | −0.268725 | −0.0188608 | ||||||||
\(204\) | −30.6092 | −2.14307 | ||||||||
\(205\) | −0.301496 | −0.0210574 | ||||||||
\(206\) | 31.0517 | 2.16347 | ||||||||
\(207\) | −52.1475 | −3.62450 | ||||||||
\(208\) | −4.17685 | −0.289613 | ||||||||
\(209\) | −4.30630 | −0.297873 | ||||||||
\(210\) | −28.0772 | −1.93751 | ||||||||
\(211\) | 4.83386 | 0.332776 | 0.166388 | − | 0.986060i | \(-0.446790\pi\) | ||||
0.166388 | + | 0.986060i | \(0.446790\pi\) | |||||||
\(212\) | 6.08884 | 0.418183 | ||||||||
\(213\) | 15.2429 | 1.04443 | ||||||||
\(214\) | 13.6082 | 0.930235 | ||||||||
\(215\) | −2.20615 | −0.150458 | ||||||||
\(216\) | 37.9644 | 2.58315 | ||||||||
\(217\) | −10.3255 | −0.700937 | ||||||||
\(218\) | −43.4767 | −2.94461 | ||||||||
\(219\) | −9.22990 | −0.623699 | ||||||||
\(220\) | 13.3133 | 0.897580 | ||||||||
\(221\) | −15.7633 | −1.06035 | ||||||||
\(222\) | 56.0427 | 3.76134 | ||||||||
\(223\) | −3.64940 | −0.244382 | −0.122191 | − | 0.992507i | \(-0.538992\pi\) | ||||
−0.122191 | + | 0.992507i | \(0.538992\pi\) | |||||||
\(224\) | −4.68325 | −0.312913 | ||||||||
\(225\) | 69.5560 | 4.63707 | ||||||||
\(226\) | −43.0494 | −2.86360 | ||||||||
\(227\) | 11.3474 | 0.753156 | 0.376578 | − | 0.926385i | \(-0.377101\pi\) | ||||
0.376578 | + | 0.926385i | \(0.377101\pi\) | |||||||
\(228\) | 45.6993 | 3.02651 | ||||||||
\(229\) | 10.0950 | 0.667095 | 0.333548 | − | 0.942733i | \(-0.391754\pi\) | ||||
0.333548 | + | 0.942733i | \(0.391754\pi\) | |||||||
\(230\) | 70.4190 | 4.64329 | ||||||||
\(231\) | 3.08623 | 0.203059 | ||||||||
\(232\) | −0.884563 | −0.0580744 | ||||||||
\(233\) | 3.27832 | 0.214770 | 0.107385 | − | 0.994218i | \(-0.465752\pi\) | ||||
0.107385 | + | 0.994218i | \(0.465752\pi\) | |||||||
\(234\) | 85.5661 | 5.59363 | ||||||||
\(235\) | −34.0084 | −2.21847 | ||||||||
\(236\) | 6.47928 | 0.421765 | ||||||||
\(237\) | −15.2504 | −0.990623 | ||||||||
\(238\) | 6.62971 | 0.429740 | ||||||||
\(239\) | 30.5312 | 1.97490 | 0.987449 | − | 0.157940i | \(-0.0504852\pi\) | ||||
0.987449 | + | 0.157940i | \(0.0504852\pi\) | |||||||
\(240\) | −9.33585 | −0.602627 | ||||||||
\(241\) | −0.511349 | −0.0329389 | −0.0164694 | − | 0.999864i | \(-0.505243\pi\) | ||||
−0.0164694 | + | 0.999864i | \(0.505243\pi\) | |||||||
\(242\) | −2.32398 | −0.149391 | ||||||||
\(243\) | −15.4942 | −0.993951 | ||||||||
\(244\) | −8.59162 | −0.550022 | ||||||||
\(245\) | −23.5732 | −1.50603 | ||||||||
\(246\) | −0.558516 | −0.0356097 | ||||||||
\(247\) | 23.5345 | 1.49746 | ||||||||
\(248\) | −33.9884 | −2.15826 | ||||||||
\(249\) | 32.0402 | 2.03047 | ||||||||
\(250\) | −48.4393 | −3.06357 | ||||||||
\(251\) | −7.72835 | −0.487809 | −0.243905 | − | 0.969799i | \(-0.578428\pi\) | ||||
−0.243905 | + | 0.969799i | \(0.578428\pi\) | |||||||
\(252\) | −22.6609 | −1.42750 | ||||||||
\(253\) | −7.74043 | −0.486637 | ||||||||
\(254\) | 29.0974 | 1.82573 | ||||||||
\(255\) | −35.2332 | −2.20639 | ||||||||
\(256\) | −20.6143 | −1.28839 | ||||||||
\(257\) | −0.877666 | −0.0547473 | −0.0273737 | − | 0.999625i | \(-0.508714\pi\) | ||||
−0.0273737 | + | 0.999625i | \(0.508714\pi\) | |||||||
\(258\) | −4.08684 | −0.254436 | ||||||||
\(259\) | −7.64344 | −0.474940 | ||||||||
\(260\) | −72.7587 | −4.51231 | ||||||||
\(261\) | 1.83046 | 0.113303 | ||||||||
\(262\) | −38.1252 | −2.35538 | ||||||||
\(263\) | 0.120138 | 0.00740801 | 0.00370400 | − | 0.999993i | \(-0.498821\pi\) | ||||
0.00370400 | + | 0.999993i | \(0.498821\pi\) | |||||||
\(264\) | 10.1590 | 0.625242 | ||||||||
\(265\) | 7.00864 | 0.430537 | ||||||||
\(266\) | −9.89810 | −0.606892 | ||||||||
\(267\) | −10.3500 | −0.633411 | ||||||||
\(268\) | 46.9309 | 2.86676 | ||||||||
\(269\) | 10.7429 | 0.655005 | 0.327503 | − | 0.944850i | \(-0.393793\pi\) | ||||
0.327503 | + | 0.944850i | \(0.393793\pi\) | |||||||
\(270\) | 106.088 | 6.45629 | ||||||||
\(271\) | −21.3912 | −1.29942 | −0.649711 | − | 0.760182i | \(-0.725110\pi\) | ||||
−0.649711 | + | 0.760182i | \(0.725110\pi\) | |||||||
\(272\) | 2.20442 | 0.133663 | ||||||||
\(273\) | −16.8667 | −1.02082 | ||||||||
\(274\) | −15.2193 | −0.919434 | ||||||||
\(275\) | 10.3244 | 0.622586 | ||||||||
\(276\) | 82.1431 | 4.94443 | ||||||||
\(277\) | 31.0245 | 1.86408 | 0.932042 | − | 0.362351i | \(-0.118026\pi\) | ||||
0.932042 | + | 0.362351i | \(0.118026\pi\) | |||||||
\(278\) | 34.2771 | 2.05580 | ||||||||
\(279\) | 70.3335 | 4.21076 | ||||||||
\(280\) | 12.6050 | 0.753295 | ||||||||
\(281\) | −7.99646 | −0.477029 | −0.238514 | − | 0.971139i | \(-0.576660\pi\) | ||||
−0.238514 | + | 0.971139i | \(0.576660\pi\) | |||||||
\(282\) | −63.0000 | −3.75159 | ||||||||
\(283\) | −22.0007 | −1.30781 | −0.653903 | − | 0.756578i | \(-0.726870\pi\) | ||||
−0.653903 | + | 0.756578i | \(0.726870\pi\) | |||||||
\(284\) | −16.6129 | −0.985797 | ||||||||
\(285\) | 52.6029 | 3.11592 | ||||||||
\(286\) | 12.7009 | 0.751018 | ||||||||
\(287\) | 0.0761737 | 0.00449639 | ||||||||
\(288\) | 31.9007 | 1.87977 | ||||||||
\(289\) | −8.68059 | −0.510623 | ||||||||
\(290\) | −2.47182 | −0.145150 | ||||||||
\(291\) | 24.5236 | 1.43760 | ||||||||
\(292\) | 10.0595 | 0.588688 | ||||||||
\(293\) | −21.7929 | −1.27315 | −0.636577 | − | 0.771214i | \(-0.719650\pi\) | ||||
−0.636577 | + | 0.771214i | \(0.719650\pi\) | |||||||
\(294\) | −43.6689 | −2.54682 | ||||||||
\(295\) | 7.45807 | 0.434226 | ||||||||
\(296\) | −25.1600 | −1.46239 | ||||||||
\(297\) | −11.6611 | −0.676646 | ||||||||
\(298\) | 48.4794 | 2.80833 | ||||||||
\(299\) | 42.3025 | 2.44641 | ||||||||
\(300\) | −109.565 | −6.32574 | ||||||||
\(301\) | 0.557388 | 0.0321273 | ||||||||
\(302\) | −20.4398 | −1.17618 | ||||||||
\(303\) | 28.9831 | 1.66504 | ||||||||
\(304\) | −3.29119 | −0.188763 | ||||||||
\(305\) | −9.88950 | −0.566271 | ||||||||
\(306\) | −45.1593 | −2.58159 | ||||||||
\(307\) | 12.4051 | 0.707998 | 0.353999 | − | 0.935246i | \(-0.384822\pi\) | ||||
0.353999 | + | 0.935246i | \(0.384822\pi\) | |||||||
\(308\) | −3.36363 | −0.191660 | ||||||||
\(309\) | 41.6933 | 2.37185 | ||||||||
\(310\) | −94.9770 | −5.39433 | ||||||||
\(311\) | −24.0234 | −1.36224 | −0.681121 | − | 0.732171i | \(-0.738507\pi\) | ||||
−0.681121 | + | 0.732171i | \(0.738507\pi\) | |||||||
\(312\) | −55.5201 | −3.14321 | ||||||||
\(313\) | −34.6386 | −1.95789 | −0.978944 | − | 0.204129i | \(-0.934564\pi\) | ||||
−0.978944 | + | 0.204129i | \(0.934564\pi\) | |||||||
\(314\) | −1.98455 | −0.111995 | ||||||||
\(315\) | −26.0841 | −1.46967 | ||||||||
\(316\) | 16.6212 | 0.935014 | ||||||||
\(317\) | 26.3736 | 1.48129 | 0.740645 | − | 0.671897i | \(-0.234520\pi\) | ||||
0.740645 | + | 0.671897i | \(0.234520\pi\) | |||||||
\(318\) | 12.9834 | 0.728071 | ||||||||
\(319\) | 0.271701 | 0.0152124 | ||||||||
\(320\) | −49.0618 | −2.74264 | ||||||||
\(321\) | 18.2718 | 1.01983 | ||||||||
\(322\) | −17.7915 | −0.991483 | ||||||||
\(323\) | −12.4208 | −0.691113 | ||||||||
\(324\) | 55.0145 | 3.05636 | ||||||||
\(325\) | −56.4243 | −3.12986 | ||||||||
\(326\) | 39.1916 | 2.17062 | ||||||||
\(327\) | −58.3764 | −3.22822 | ||||||||
\(328\) | 0.250742 | 0.0138449 | ||||||||
\(329\) | 8.59231 | 0.473709 | ||||||||
\(330\) | 28.3882 | 1.56272 | ||||||||
\(331\) | 2.15727 | 0.118574 | 0.0592872 | − | 0.998241i | \(-0.481117\pi\) | ||||
0.0592872 | + | 0.998241i | \(0.481117\pi\) | |||||||
\(332\) | −34.9200 | −1.91649 | ||||||||
\(333\) | 52.0645 | 2.85312 | ||||||||
\(334\) | 12.4344 | 0.680381 | ||||||||
\(335\) | 54.0205 | 2.95146 | ||||||||
\(336\) | 2.35873 | 0.128679 | ||||||||
\(337\) | −30.3746 | −1.65461 | −0.827304 | − | 0.561755i | \(-0.810126\pi\) | ||||
−0.827304 | + | 0.561755i | \(0.810126\pi\) | |||||||
\(338\) | −39.2001 | −2.13220 | ||||||||
\(339\) | −57.8027 | −3.13941 | ||||||||
\(340\) | 38.4000 | 2.08253 | ||||||||
\(341\) | 10.4398 | 0.565349 | ||||||||
\(342\) | 67.4225 | 3.64579 | ||||||||
\(343\) | 12.8791 | 0.695407 | ||||||||
\(344\) | 1.83476 | 0.0989236 | ||||||||
\(345\) | 94.5520 | 5.09051 | ||||||||
\(346\) | 40.8592 | 2.19660 | ||||||||
\(347\) | −13.2719 | −0.712472 | −0.356236 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356236 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(348\) | −2.88335 | −0.154564 | ||||||||
\(349\) | 25.8817 | 1.38542 | 0.692708 | − | 0.721218i | \(-0.256417\pi\) | ||||
0.692708 | + | 0.721218i | \(0.256417\pi\) | |||||||
\(350\) | 23.7309 | 1.26847 | ||||||||
\(351\) | 63.7295 | 3.40163 | ||||||||
\(352\) | 4.73513 | 0.252383 | ||||||||
\(353\) | −7.14649 | −0.380369 | −0.190185 | − | 0.981748i | \(-0.560909\pi\) | ||||
−0.190185 | + | 0.981748i | \(0.560909\pi\) | |||||||
\(354\) | 13.8159 | 0.734309 | ||||||||
\(355\) | −19.1226 | −1.01492 | ||||||||
\(356\) | 11.2803 | 0.597855 | ||||||||
\(357\) | 8.90174 | 0.471130 | ||||||||
\(358\) | −19.3755 | −1.02403 | ||||||||
\(359\) | −22.8912 | −1.20815 | −0.604075 | − | 0.796928i | \(-0.706457\pi\) | ||||
−0.604075 | + | 0.796928i | \(0.706457\pi\) | |||||||
\(360\) | −85.8613 | −4.52529 | ||||||||
\(361\) | −0.455812 | −0.0239901 | ||||||||
\(362\) | 23.4289 | 1.23139 | ||||||||
\(363\) | −3.12042 | −0.163780 | ||||||||
\(364\) | 18.3827 | 0.963513 | ||||||||
\(365\) | 11.5791 | 0.606079 | ||||||||
\(366\) | −18.3201 | −0.957608 | ||||||||
\(367\) | −31.5802 | −1.64847 | −0.824236 | − | 0.566246i | \(-0.808395\pi\) | ||||
−0.824236 | + | 0.566246i | \(0.808395\pi\) | |||||||
\(368\) | −5.91581 | −0.308383 | ||||||||
\(369\) | −0.518870 | −0.0270113 | ||||||||
\(370\) | −70.3069 | −3.65508 | ||||||||
\(371\) | −1.77075 | −0.0919327 | ||||||||
\(372\) | −110.790 | −5.74418 | ||||||||
\(373\) | 8.13353 | 0.421138 | 0.210569 | − | 0.977579i | \(-0.432468\pi\) | ||||
0.210569 | + | 0.977579i | \(0.432468\pi\) | |||||||
\(374\) | −6.70315 | −0.346612 | ||||||||
\(375\) | −65.0396 | −3.35863 | ||||||||
\(376\) | 28.2834 | 1.45860 | ||||||||
\(377\) | −1.48488 | −0.0764754 | ||||||||
\(378\) | −26.8033 | −1.37861 | ||||||||
\(379\) | 9.60766 | 0.493512 | 0.246756 | − | 0.969078i | \(-0.420635\pi\) | ||||
0.246756 | + | 0.969078i | \(0.420635\pi\) | |||||||
\(380\) | −57.3309 | −2.94101 | ||||||||
\(381\) | 39.0692 | 2.00157 | ||||||||
\(382\) | −9.09416 | −0.465298 | ||||||||
\(383\) | 26.9494 | 1.37705 | 0.688525 | − | 0.725212i | \(-0.258258\pi\) | ||||
0.688525 | + | 0.725212i | \(0.258258\pi\) | |||||||
\(384\) | −61.3349 | −3.12998 | ||||||||
\(385\) | −3.87175 | −0.197323 | ||||||||
\(386\) | 30.9027 | 1.57291 | ||||||||
\(387\) | −3.79674 | −0.192999 | ||||||||
\(388\) | −26.7278 | −1.35690 | ||||||||
\(389\) | 1.85321 | 0.0939616 | 0.0469808 | − | 0.998896i | \(-0.485040\pi\) | ||||
0.0469808 | + | 0.998896i | \(0.485040\pi\) | |||||||
\(390\) | −155.145 | −7.85609 | ||||||||
\(391\) | −22.3260 | −1.12908 | ||||||||
\(392\) | 19.6048 | 0.990192 | ||||||||
\(393\) | −51.1909 | −2.58224 | ||||||||
\(394\) | 19.4215 | 0.978441 | ||||||||
\(395\) | 19.1320 | 0.962637 | ||||||||
\(396\) | 22.9119 | 1.15137 | ||||||||
\(397\) | 29.8357 | 1.49741 | 0.748706 | − | 0.662902i | \(-0.230675\pi\) | ||||
0.748706 | + | 0.662902i | \(0.230675\pi\) | |||||||
\(398\) | −42.0193 | −2.10624 | ||||||||
\(399\) | −13.2902 | −0.665344 | ||||||||
\(400\) | 7.89068 | 0.394534 | ||||||||
\(401\) | 7.20686 | 0.359894 | 0.179947 | − | 0.983676i | \(-0.442407\pi\) | ||||
0.179947 | + | 0.983676i | \(0.442407\pi\) | |||||||
\(402\) | 100.072 | 4.99114 | ||||||||
\(403\) | −57.0551 | −2.84211 | ||||||||
\(404\) | −31.5881 | −1.57157 | ||||||||
\(405\) | 63.3252 | 3.14666 | ||||||||
\(406\) | 0.624511 | 0.0309940 | ||||||||
\(407\) | 7.72811 | 0.383068 | ||||||||
\(408\) | 29.3019 | 1.45066 | ||||||||
\(409\) | −29.8441 | −1.47569 | −0.737847 | − | 0.674968i | \(-0.764157\pi\) | ||||
−0.737847 | + | 0.674968i | \(0.764157\pi\) | |||||||
\(410\) | 0.700672 | 0.0346037 | ||||||||
\(411\) | −20.4351 | −1.00799 | ||||||||
\(412\) | −45.4407 | −2.23870 | ||||||||
\(413\) | −1.88430 | −0.0927203 | ||||||||
\(414\) | 121.190 | 5.95616 | ||||||||
\(415\) | −40.1952 | −1.97311 | ||||||||
\(416\) | −25.8781 | −1.26878 | ||||||||
\(417\) | 46.0240 | 2.25380 | ||||||||
\(418\) | 10.0078 | 0.489495 | ||||||||
\(419\) | −27.4342 | −1.34025 | −0.670125 | − | 0.742248i | \(-0.733760\pi\) | ||||
−0.670125 | + | 0.742248i | \(0.733760\pi\) | |||||||
\(420\) | 41.0878 | 2.00488 | ||||||||
\(421\) | −19.1594 | −0.933770 | −0.466885 | − | 0.884318i | \(-0.654624\pi\) | ||||
−0.466885 | + | 0.884318i | \(0.654624\pi\) | |||||||
\(422\) | −11.2338 | −0.546853 | ||||||||
\(423\) | −58.5279 | −2.84572 | ||||||||
\(424\) | −5.82879 | −0.283071 | ||||||||
\(425\) | 29.7791 | 1.44450 | ||||||||
\(426\) | −35.4242 | −1.71631 | ||||||||
\(427\) | 2.49861 | 0.120916 | ||||||||
\(428\) | −19.9140 | −0.962582 | ||||||||
\(429\) | 17.0535 | 0.823351 | ||||||||
\(430\) | 5.12704 | 0.247248 | ||||||||
\(431\) | 5.18554 | 0.249779 | 0.124889 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124889 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(432\) | −8.91228 | −0.428792 | ||||||||
\(433\) | −9.97758 | −0.479492 | −0.239746 | − | 0.970836i | \(-0.577064\pi\) | ||||
−0.239746 | + | 0.970836i | \(0.577064\pi\) | |||||||
\(434\) | 23.9962 | 1.15185 | ||||||||
\(435\) | −3.31892 | −0.159130 | ||||||||
\(436\) | 63.6233 | 3.04700 | ||||||||
\(437\) | 33.3326 | 1.59451 | ||||||||
\(438\) | 21.4501 | 1.02493 | ||||||||
\(439\) | −6.52581 | −0.311460 | −0.155730 | − | 0.987800i | \(-0.549773\pi\) | ||||
−0.155730 | + | 0.987800i | \(0.549773\pi\) | |||||||
\(440\) | −12.7447 | −0.607579 | ||||||||
\(441\) | −40.5690 | −1.93186 | ||||||||
\(442\) | 36.6336 | 1.74248 | ||||||||
\(443\) | 2.91342 | 0.138421 | 0.0692104 | − | 0.997602i | \(-0.477952\pi\) | ||||
0.0692104 | + | 0.997602i | \(0.477952\pi\) | |||||||
\(444\) | −82.0123 | −3.89213 | ||||||||
\(445\) | 12.9843 | 0.615517 | ||||||||
\(446\) | 8.48113 | 0.401593 | ||||||||
\(447\) | 65.0935 | 3.07882 | ||||||||
\(448\) | 12.3956 | 0.585636 | ||||||||
\(449\) | 39.0106 | 1.84102 | 0.920512 | − | 0.390715i | \(-0.127772\pi\) | ||||
0.920512 | + | 0.390715i | \(0.127772\pi\) | |||||||
\(450\) | −161.647 | −7.62010 | ||||||||
\(451\) | −0.0770176 | −0.00362662 | ||||||||
\(452\) | 62.9981 | 2.96318 | ||||||||
\(453\) | −27.4446 | −1.28946 | ||||||||
\(454\) | −26.3712 | −1.23766 | ||||||||
\(455\) | 21.1596 | 0.991978 | ||||||||
\(456\) | −43.7476 | −2.04867 | ||||||||
\(457\) | −12.5891 | −0.588891 | −0.294446 | − | 0.955668i | \(-0.595135\pi\) | ||||
−0.294446 | + | 0.955668i | \(0.595135\pi\) | |||||||
\(458\) | −23.4606 | −1.09624 | ||||||||
\(459\) | −33.6346 | −1.56993 | ||||||||
\(460\) | −103.050 | −4.80475 | ||||||||
\(461\) | 6.64598 | 0.309534 | 0.154767 | − | 0.987951i | \(-0.450537\pi\) | ||||
0.154767 | + | 0.987951i | \(0.450537\pi\) | |||||||
\(462\) | −7.17235 | −0.333688 | ||||||||
\(463\) | −13.7760 | −0.640225 | −0.320113 | − | 0.947379i | \(-0.603721\pi\) | ||||
−0.320113 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(464\) | 0.207654 | 0.00964010 | ||||||||
\(465\) | −127.526 | −5.91388 | ||||||||
\(466\) | −7.61876 | −0.352932 | ||||||||
\(467\) | 29.5667 | 1.36818 | 0.684092 | − | 0.729396i | \(-0.260199\pi\) | ||||
0.684092 | + | 0.729396i | \(0.260199\pi\) | |||||||
\(468\) | −125.217 | −5.78814 | ||||||||
\(469\) | −13.6484 | −0.630225 | ||||||||
\(470\) | 79.0350 | 3.64561 | ||||||||
\(471\) | −2.66467 | −0.122781 | ||||||||
\(472\) | −6.20256 | −0.285496 | ||||||||
\(473\) | −0.563563 | −0.0259126 | ||||||||
\(474\) | 35.4417 | 1.62789 | ||||||||
\(475\) | −44.4600 | −2.03997 | ||||||||
\(476\) | −9.70184 | −0.444683 | ||||||||
\(477\) | 12.0617 | 0.552269 | ||||||||
\(478\) | −70.9539 | −3.24536 | ||||||||
\(479\) | −17.0721 | −0.780046 | −0.390023 | − | 0.920805i | \(-0.627533\pi\) | ||||
−0.390023 | + | 0.920805i | \(0.627533\pi\) | |||||||
\(480\) | −57.8412 | −2.64008 | ||||||||
\(481\) | −42.2351 | −1.92576 | ||||||||
\(482\) | 1.18836 | 0.0541285 | ||||||||
\(483\) | −23.8888 | −1.08698 | ||||||||
\(484\) | 3.40089 | 0.154586 | ||||||||
\(485\) | −30.7654 | −1.39698 | ||||||||
\(486\) | 36.0081 | 1.63336 | ||||||||
\(487\) | 31.4032 | 1.42301 | 0.711507 | − | 0.702679i | \(-0.248013\pi\) | ||||
0.711507 | + | 0.702679i | \(0.248013\pi\) | |||||||
\(488\) | 8.22468 | 0.372314 | ||||||||
\(489\) | 52.6227 | 2.37968 | ||||||||
\(490\) | 54.7836 | 2.47487 | ||||||||
\(491\) | −27.5209 | −1.24200 | −0.621000 | − | 0.783810i | \(-0.713273\pi\) | ||||
−0.621000 | + | 0.783810i | \(0.713273\pi\) | |||||||
\(492\) | 0.817327 | 0.0368479 | ||||||||
\(493\) | 0.783679 | 0.0352951 | ||||||||
\(494\) | −54.6937 | −2.46078 | ||||||||
\(495\) | 26.3731 | 1.18538 | ||||||||
\(496\) | 7.97889 | 0.358263 | ||||||||
\(497\) | 4.83136 | 0.216716 | ||||||||
\(498\) | −74.4609 | −3.33667 | ||||||||
\(499\) | 5.11144 | 0.228819 | 0.114410 | − | 0.993434i | \(-0.463502\pi\) | ||||
0.114410 | + | 0.993434i | \(0.463502\pi\) | |||||||
\(500\) | 70.8855 | 3.17010 | ||||||||
\(501\) | 16.6957 | 0.745911 | ||||||||
\(502\) | 17.9606 | 0.801619 | ||||||||
\(503\) | −4.40334 | −0.196335 | −0.0981676 | − | 0.995170i | \(-0.531298\pi\) | ||||
−0.0981676 | + | 0.995170i | \(0.531298\pi\) | |||||||
\(504\) | 21.6931 | 0.966285 | ||||||||
\(505\) | −36.3600 | −1.61800 | ||||||||
\(506\) | 17.9886 | 0.799692 | ||||||||
\(507\) | −52.6341 | −2.33756 | ||||||||
\(508\) | −42.5808 | −1.88922 | ||||||||
\(509\) | −5.18003 | −0.229601 | −0.114800 | − | 0.993389i | \(-0.536623\pi\) | ||||
−0.114800 | + | 0.993389i | \(0.536623\pi\) | |||||||
\(510\) | 81.8812 | 3.62576 | ||||||||
\(511\) | −2.92549 | −0.129416 | ||||||||
\(512\) | 8.59533 | 0.379864 | ||||||||
\(513\) | 50.2162 | 2.21710 | ||||||||
\(514\) | 2.03968 | 0.0899665 | ||||||||
\(515\) | −52.3052 | −2.30484 | ||||||||
\(516\) | 5.98065 | 0.263283 | ||||||||
\(517\) | −8.68749 | −0.382076 | ||||||||
\(518\) | 17.7632 | 0.780471 | ||||||||
\(519\) | 54.8618 | 2.40817 | ||||||||
\(520\) | 69.6513 | 3.05441 | ||||||||
\(521\) | 37.4812 | 1.64208 | 0.821041 | − | 0.570869i | \(-0.193394\pi\) | ||||
0.821041 | + | 0.570869i | \(0.193394\pi\) | |||||||
\(522\) | −4.25396 | −0.186191 | ||||||||
\(523\) | 15.4728 | 0.676578 | 0.338289 | − | 0.941042i | \(-0.390152\pi\) | ||||
0.338289 | + | 0.941042i | \(0.390152\pi\) | |||||||
\(524\) | 55.7920 | 2.43729 | ||||||||
\(525\) | 31.8636 | 1.39064 | ||||||||
\(526\) | −0.279198 | −0.0121736 | ||||||||
\(527\) | 30.1120 | 1.31170 | ||||||||
\(528\) | −2.38486 | −0.103787 | ||||||||
\(529\) | 36.9143 | 1.60497 | ||||||||
\(530\) | −16.2879 | −0.707503 | ||||||||
\(531\) | 12.8352 | 0.557001 | ||||||||
\(532\) | 14.4848 | 0.627995 | ||||||||
\(533\) | 0.420911 | 0.0182317 | ||||||||
\(534\) | 24.0533 | 1.04089 | ||||||||
\(535\) | −22.9223 | −0.991019 | ||||||||
\(536\) | −44.9266 | −1.94053 | ||||||||
\(537\) | −26.0156 | −1.12265 | ||||||||
\(538\) | −24.9663 | −1.07637 | ||||||||
\(539\) | −6.02179 | −0.259377 | ||||||||
\(540\) | −155.248 | −6.68079 | ||||||||
\(541\) | −33.1585 | −1.42560 | −0.712799 | − | 0.701369i | \(-0.752573\pi\) | ||||
−0.712799 | + | 0.701369i | \(0.752573\pi\) | |||||||
\(542\) | 49.7127 | 2.13534 | ||||||||
\(543\) | 31.4580 | 1.34999 | ||||||||
\(544\) | 13.6577 | 0.585570 | ||||||||
\(545\) | 73.2345 | 3.13702 | ||||||||
\(546\) | 39.1978 | 1.67751 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 22.2718 | 0.951405 | ||||||||
\(549\) | −17.0197 | −0.726381 | ||||||||
\(550\) | −23.9938 | −1.02310 | ||||||||
\(551\) | −1.17003 | −0.0498448 | ||||||||
\(552\) | −78.6349 | −3.34692 | ||||||||
\(553\) | −4.83375 | −0.205552 | ||||||||
\(554\) | −72.1004 | −3.06325 | ||||||||
\(555\) | −94.4015 | −4.00712 | ||||||||
\(556\) | −50.1607 | −2.12729 | ||||||||
\(557\) | 10.1001 | 0.427954 | 0.213977 | − | 0.976839i | \(-0.431358\pi\) | ||||
0.213977 | + | 0.976839i | \(0.431358\pi\) | |||||||
\(558\) | −163.454 | −6.91955 | ||||||||
\(559\) | 3.07994 | 0.130268 | ||||||||
\(560\) | −2.95908 | −0.125044 | ||||||||
\(561\) | −9.00035 | −0.379995 | ||||||||
\(562\) | 18.5836 | 0.783903 | ||||||||
\(563\) | 13.2203 | 0.557168 | 0.278584 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278584 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(564\) | 92.1935 | 3.88205 | ||||||||
\(565\) | 72.5148 | 3.05072 | ||||||||
\(566\) | 51.1293 | 2.14912 | ||||||||
\(567\) | −15.9993 | −0.671906 | ||||||||
\(568\) | 15.9034 | 0.667293 | ||||||||
\(569\) | −33.1591 | −1.39010 | −0.695050 | − | 0.718961i | \(-0.744618\pi\) | ||||
−0.695050 | + | 0.718961i | \(0.744618\pi\) | |||||||
\(570\) | −122.248 | −5.12041 | ||||||||
\(571\) | −4.12183 | −0.172493 | −0.0862466 | − | 0.996274i | \(-0.527487\pi\) | ||||
−0.0862466 | + | 0.996274i | \(0.527487\pi\) | |||||||
\(572\) | −18.5863 | −0.777132 | ||||||||
\(573\) | −12.2108 | −0.510112 | ||||||||
\(574\) | −0.177026 | −0.00738894 | ||||||||
\(575\) | −79.9155 | −3.33271 | ||||||||
\(576\) | −84.4345 | −3.51811 | ||||||||
\(577\) | 12.9288 | 0.538232 | 0.269116 | − | 0.963108i | \(-0.413268\pi\) | ||||
0.269116 | + | 0.963108i | \(0.413268\pi\) | |||||||
\(578\) | 20.1735 | 0.839109 | ||||||||
\(579\) | 41.4932 | 1.72440 | ||||||||
\(580\) | 3.61723 | 0.150197 | ||||||||
\(581\) | 10.1554 | 0.421317 | ||||||||
\(582\) | −56.9923 | −2.36241 | ||||||||
\(583\) | 1.79037 | 0.0741493 | ||||||||
\(584\) | −9.62987 | −0.398487 | ||||||||
\(585\) | −144.132 | −5.95913 | ||||||||
\(586\) | 50.6462 | 2.09218 | ||||||||
\(587\) | 2.70196 | 0.111522 | 0.0557609 | − | 0.998444i | \(-0.482242\pi\) | ||||
0.0557609 | + | 0.998444i | \(0.482242\pi\) | |||||||
\(588\) | 63.9045 | 2.63538 | ||||||||
\(589\) | −44.9570 | −1.85242 | ||||||||
\(590\) | −17.3324 | −0.713564 | ||||||||
\(591\) | 26.0773 | 1.07268 | ||||||||
\(592\) | 5.90639 | 0.242751 | ||||||||
\(593\) | 2.24776 | 0.0923043 | 0.0461521 | − | 0.998934i | \(-0.485304\pi\) | ||||
0.0461521 | + | 0.998934i | \(0.485304\pi\) | |||||||
\(594\) | 27.1002 | 1.11194 | ||||||||
\(595\) | −11.1674 | −0.457820 | ||||||||
\(596\) | −70.9442 | −2.90599 | ||||||||
\(597\) | −56.4196 | −2.30910 | ||||||||
\(598\) | −98.3101 | −4.02020 | ||||||||
\(599\) | −39.3969 | −1.60971 | −0.804856 | − | 0.593470i | \(-0.797758\pi\) | ||||
−0.804856 | + | 0.593470i | \(0.797758\pi\) | |||||||
\(600\) | 104.886 | 4.28194 | ||||||||
\(601\) | −46.1784 | −1.88366 | −0.941828 | − | 0.336095i | \(-0.890894\pi\) | ||||
−0.941828 | + | 0.336095i | \(0.890894\pi\) | |||||||
\(602\) | −1.29536 | −0.0527949 | ||||||||
\(603\) | 92.9684 | 3.78596 | ||||||||
\(604\) | 29.9113 | 1.21708 | ||||||||
\(605\) | 3.91464 | 0.159153 | ||||||||
\(606\) | −67.3562 | −2.73616 | ||||||||
\(607\) | −35.5472 | −1.44282 | −0.721408 | − | 0.692510i | \(-0.756505\pi\) | ||||
−0.721408 | + | 0.692510i | \(0.756505\pi\) | |||||||
\(608\) | −20.3909 | −0.826959 | ||||||||
\(609\) | 0.838534 | 0.0339791 | ||||||||
\(610\) | 22.9830 | 0.930555 | ||||||||
\(611\) | 47.4783 | 1.92077 | ||||||||
\(612\) | 66.0857 | 2.67136 | ||||||||
\(613\) | 29.3972 | 1.18734 | 0.593672 | − | 0.804707i | \(-0.297678\pi\) | ||||
0.593672 | + | 0.804707i | \(0.297678\pi\) | |||||||
\(614\) | −28.8293 | −1.16346 | ||||||||
\(615\) | 0.940796 | 0.0379365 | ||||||||
\(616\) | 3.21997 | 0.129736 | ||||||||
\(617\) | −26.7220 | −1.07579 | −0.537894 | − | 0.843012i | \(-0.680780\pi\) | ||||
−0.537894 | + | 0.843012i | \(0.680780\pi\) | |||||||
\(618\) | −96.8944 | −3.89766 | ||||||||
\(619\) | −37.3098 | −1.49961 | −0.749803 | − | 0.661661i | \(-0.769852\pi\) | ||||
−0.749803 | + | 0.661661i | \(0.769852\pi\) | |||||||
\(620\) | 138.988 | 5.58191 | ||||||||
\(621\) | 90.2621 | 3.62209 | ||||||||
\(622\) | 55.8300 | 2.23858 | ||||||||
\(623\) | −3.28052 | −0.131431 | ||||||||
\(624\) | 13.0335 | 0.521759 | ||||||||
\(625\) | 29.9716 | 1.19887 | ||||||||
\(626\) | 80.4994 | 3.21740 | ||||||||
\(627\) | 13.4375 | 0.536640 | ||||||||
\(628\) | 2.90417 | 0.115889 | ||||||||
\(629\) | 22.2905 | 0.888780 | ||||||||
\(630\) | 60.6190 | 2.41512 | ||||||||
\(631\) | 17.8482 | 0.710526 | 0.355263 | − | 0.934766i | \(-0.384391\pi\) | ||||
0.355263 | + | 0.934766i | \(0.384391\pi\) | |||||||
\(632\) | −15.9113 | −0.632918 | ||||||||
\(633\) | −15.0837 | −0.599522 | ||||||||
\(634\) | −61.2918 | −2.43421 | ||||||||
\(635\) | −49.0132 | −1.94503 | ||||||||
\(636\) | −18.9997 | −0.753388 | ||||||||
\(637\) | 32.9099 | 1.30394 | ||||||||
\(638\) | −0.631429 | −0.0249985 | ||||||||
\(639\) | −32.9096 | −1.30188 | ||||||||
\(640\) | 76.9461 | 3.04156 | ||||||||
\(641\) | −1.39722 | −0.0551867 | −0.0275934 | − | 0.999619i | \(-0.508784\pi\) | ||||
−0.0275934 | + | 0.999619i | \(0.508784\pi\) | |||||||
\(642\) | −42.4632 | −1.67589 | ||||||||
\(643\) | 20.7995 | 0.820251 | 0.410126 | − | 0.912029i | \(-0.365485\pi\) | ||||
0.410126 | + | 0.912029i | \(0.365485\pi\) | |||||||
\(644\) | 26.0359 | 1.02596 | ||||||||
\(645\) | 6.88411 | 0.271061 | ||||||||
\(646\) | 28.8657 | 1.13571 | ||||||||
\(647\) | −22.4543 | −0.882770 | −0.441385 | − | 0.897318i | \(-0.645513\pi\) | ||||
−0.441385 | + | 0.897318i | \(0.645513\pi\) | |||||||
\(648\) | −52.6649 | −2.06887 | ||||||||
\(649\) | 1.90517 | 0.0747846 | ||||||||
\(650\) | 131.129 | 5.14331 | ||||||||
\(651\) | 32.2198 | 1.26279 | ||||||||
\(652\) | −57.3526 | −2.24610 | ||||||||
\(653\) | 16.1770 | 0.633056 | 0.316528 | − | 0.948583i | \(-0.397483\pi\) | ||||
0.316528 | + | 0.948583i | \(0.397483\pi\) | |||||||
\(654\) | 135.666 | 5.30494 | ||||||||
\(655\) | 64.2202 | 2.50929 | ||||||||
\(656\) | −0.0588625 | −0.00229819 | ||||||||
\(657\) | 19.9275 | 0.777445 | ||||||||
\(658\) | −19.9684 | −0.778448 | ||||||||
\(659\) | −18.0432 | −0.702862 | −0.351431 | − | 0.936214i | \(-0.614305\pi\) | ||||
−0.351431 | + | 0.936214i | \(0.614305\pi\) | |||||||
\(660\) | −41.5430 | −1.61706 | ||||||||
\(661\) | −24.3431 | −0.946839 | −0.473419 | − | 0.880837i | \(-0.656980\pi\) | ||||
−0.473419 | + | 0.880837i | \(0.656980\pi\) | |||||||
\(662\) | −5.01346 | −0.194854 | ||||||||
\(663\) | 49.1881 | 1.91031 | ||||||||
\(664\) | 33.4287 | 1.29728 | ||||||||
\(665\) | 16.6729 | 0.646548 | ||||||||
\(666\) | −120.997 | −4.68854 | ||||||||
\(667\) | −2.10309 | −0.0814318 | ||||||||
\(668\) | −18.1964 | −0.704039 | ||||||||
\(669\) | 11.3877 | 0.440272 | ||||||||
\(670\) | −125.543 | −4.85014 | ||||||||
\(671\) | −2.52628 | −0.0975261 | ||||||||
\(672\) | 14.6137 | 0.563736 | ||||||||
\(673\) | −23.5376 | −0.907307 | −0.453653 | − | 0.891178i | \(-0.649880\pi\) | ||||
−0.453653 | + | 0.891178i | \(0.649880\pi\) | |||||||
\(674\) | 70.5899 | 2.71902 | ||||||||
\(675\) | −120.394 | −4.63398 | ||||||||
\(676\) | 57.3650 | 2.20635 | ||||||||
\(677\) | 23.1229 | 0.888687 | 0.444343 | − | 0.895857i | \(-0.353437\pi\) | ||||
0.444343 | + | 0.895857i | \(0.353437\pi\) | |||||||
\(678\) | 134.332 | 5.15900 | ||||||||
\(679\) | 7.77295 | 0.298298 | ||||||||
\(680\) | −36.7600 | −1.40968 | ||||||||
\(681\) | −35.4088 | −1.35687 | ||||||||
\(682\) | −24.2620 | −0.929039 | ||||||||
\(683\) | −20.5893 | −0.787828 | −0.393914 | − | 0.919147i | \(-0.628879\pi\) | ||||
−0.393914 | + | 0.919147i | \(0.628879\pi\) | |||||||
\(684\) | −98.6654 | −3.77257 | ||||||||
\(685\) | 25.6363 | 0.979512 | ||||||||
\(686\) | −29.9308 | −1.14276 | ||||||||
\(687\) | −31.5006 | −1.20182 | ||||||||
\(688\) | −0.430716 | −0.0164209 | ||||||||
\(689\) | −9.78458 | −0.372763 | ||||||||
\(690\) | −219.737 | −8.36525 | ||||||||
\(691\) | 18.2539 | 0.694412 | 0.347206 | − | 0.937789i | \(-0.387130\pi\) | ||||
0.347206 | + | 0.937789i | \(0.387130\pi\) | |||||||
\(692\) | −59.7929 | −2.27299 | ||||||||
\(693\) | −6.66322 | −0.253115 | ||||||||
\(694\) | 30.8436 | 1.17081 | ||||||||
\(695\) | −57.7382 | −2.19013 | ||||||||
\(696\) | 2.76021 | 0.104625 | ||||||||
\(697\) | −0.222145 | −0.00841433 | ||||||||
\(698\) | −60.1486 | −2.27666 | ||||||||
\(699\) | −10.2298 | −0.386925 | ||||||||
\(700\) | −34.7275 | −1.31258 | ||||||||
\(701\) | 10.1841 | 0.384650 | 0.192325 | − | 0.981331i | \(-0.438397\pi\) | ||||
0.192325 | + | 0.981331i | \(0.438397\pi\) | |||||||
\(702\) | −148.106 | −5.58991 | ||||||||
\(703\) | −33.2795 | −1.25516 | ||||||||
\(704\) | −12.5329 | −0.472351 | ||||||||
\(705\) | 106.121 | 3.99673 | ||||||||
\(706\) | 16.6083 | 0.625062 | ||||||||
\(707\) | 9.18643 | 0.345491 | ||||||||
\(708\) | −20.2181 | −0.759843 | ||||||||
\(709\) | −36.9445 | −1.38748 | −0.693739 | − | 0.720226i | \(-0.744038\pi\) | ||||
−0.693739 | + | 0.720226i | \(0.744038\pi\) | |||||||
\(710\) | 44.4405 | 1.66782 | ||||||||
\(711\) | 32.9259 | 1.23482 | ||||||||
\(712\) | −10.7985 | −0.404692 | ||||||||
\(713\) | −80.8089 | −3.02632 | ||||||||
\(714\) | −20.6875 | −0.774209 | ||||||||
\(715\) | −21.3940 | −0.800091 | ||||||||
\(716\) | 28.3539 | 1.05963 | ||||||||
\(717\) | −95.2701 | −3.55793 | ||||||||
\(718\) | 53.1986 | 1.98536 | ||||||||
\(719\) | −13.1988 | −0.492232 | −0.246116 | − | 0.969240i | \(-0.579154\pi\) | ||||
−0.246116 | + | 0.969240i | \(0.579154\pi\) | |||||||
\(720\) | 20.1562 | 0.751178 | ||||||||
\(721\) | 13.2150 | 0.492153 | ||||||||
\(722\) | 1.05930 | 0.0394230 | ||||||||
\(723\) | 1.59562 | 0.0593419 | ||||||||
\(724\) | −34.2855 | −1.27421 | ||||||||
\(725\) | 2.80516 | 0.104181 | ||||||||
\(726\) | 7.25180 | 0.269140 | ||||||||
\(727\) | −3.14236 | −0.116544 | −0.0582718 | − | 0.998301i | \(-0.518559\pi\) | ||||
−0.0582718 | + | 0.998301i | \(0.518559\pi\) | |||||||
\(728\) | −17.5976 | −0.652209 | ||||||||
\(729\) | −0.181194 | −0.00671090 | ||||||||
\(730\) | −26.9097 | −0.995972 | ||||||||
\(731\) | −1.62551 | −0.0601215 | ||||||||
\(732\) | 26.8095 | 0.990906 | ||||||||
\(733\) | −9.07674 | −0.335257 | −0.167628 | − | 0.985850i | \(-0.553611\pi\) | ||||
−0.167628 | + | 0.985850i | \(0.553611\pi\) | |||||||
\(734\) | 73.3918 | 2.70894 | ||||||||
\(735\) | 73.5582 | 2.71324 | ||||||||
\(736\) | −36.6519 | −1.35101 | ||||||||
\(737\) | 13.7996 | 0.508315 | ||||||||
\(738\) | 1.20584 | 0.0443877 | ||||||||
\(739\) | 35.5021 | 1.30597 | 0.652983 | − | 0.757373i | \(-0.273517\pi\) | ||||
0.652983 | + | 0.757373i | \(0.273517\pi\) | |||||||
\(740\) | 102.886 | 3.78218 | ||||||||
\(741\) | −73.4375 | −2.69779 | ||||||||
\(742\) | 4.11519 | 0.151073 | ||||||||
\(743\) | −25.9303 | −0.951290 | −0.475645 | − | 0.879637i | \(-0.657785\pi\) | ||||
−0.475645 | + | 0.879637i | \(0.657785\pi\) | |||||||
\(744\) | 106.058 | 3.88828 | ||||||||
\(745\) | −81.6613 | −2.99184 | ||||||||
\(746\) | −18.9022 | −0.692058 | ||||||||
\(747\) | −69.1753 | −2.53099 | ||||||||
\(748\) | 9.80932 | 0.358664 | ||||||||
\(749\) | 5.79138 | 0.211613 | ||||||||
\(750\) | 151.151 | 5.51925 | ||||||||
\(751\) | −0.803820 | −0.0293318 | −0.0146659 | − | 0.999892i | \(-0.504668\pi\) | ||||
−0.0146659 | + | 0.999892i | \(0.504668\pi\) | |||||||
\(752\) | −6.63962 | −0.242122 | ||||||||
\(753\) | 24.1157 | 0.878826 | ||||||||
\(754\) | 3.45084 | 0.125672 | ||||||||
\(755\) | 34.4299 | 1.25303 | ||||||||
\(756\) | 39.2237 | 1.42655 | ||||||||
\(757\) | −20.6466 | −0.750414 | −0.375207 | − | 0.926941i | \(-0.622428\pi\) | ||||
−0.375207 | + | 0.926941i | \(0.622428\pi\) | |||||||
\(758\) | −22.3280 | −0.810990 | ||||||||
\(759\) | 24.1534 | 0.876713 | ||||||||
\(760\) | 54.8824 | 1.99079 | ||||||||
\(761\) | 50.6273 | 1.83524 | 0.917618 | − | 0.397462i | \(-0.130109\pi\) | ||||
0.917618 | + | 0.397462i | \(0.130109\pi\) | |||||||
\(762\) | −90.7960 | −3.28919 | ||||||||
\(763\) | −18.5029 | −0.669849 | ||||||||
\(764\) | 13.3083 | 0.481477 | ||||||||
\(765\) | 76.0689 | 2.75028 | ||||||||
\(766\) | −62.6299 | −2.26291 | ||||||||
\(767\) | −10.4120 | −0.375956 | ||||||||
\(768\) | 64.3253 | 2.32114 | ||||||||
\(769\) | 18.1721 | 0.655303 | 0.327651 | − | 0.944799i | \(-0.393743\pi\) | ||||
0.327651 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(770\) | 8.99788 | 0.324261 | ||||||||
\(771\) | 2.73869 | 0.0986315 | ||||||||
\(772\) | −45.2227 | −1.62760 | ||||||||
\(773\) | 34.1281 | 1.22750 | 0.613750 | − | 0.789500i | \(-0.289660\pi\) | ||||
0.613750 | + | 0.789500i | \(0.289660\pi\) | |||||||
\(774\) | 8.82355 | 0.317156 | ||||||||
\(775\) | 107.785 | 3.87176 | ||||||||
\(776\) | 25.5863 | 0.918494 | ||||||||
\(777\) | 23.8507 | 0.855641 | ||||||||
\(778\) | −4.30683 | −0.154407 | ||||||||
\(779\) | 0.331661 | 0.0118830 | ||||||||
\(780\) | 227.038 | 8.12926 | ||||||||
\(781\) | −4.88488 | −0.174795 | ||||||||
\(782\) | 51.8853 | 1.85541 | ||||||||
\(783\) | −3.16834 | −0.113227 | ||||||||
\(784\) | −4.60230 | −0.164368 | ||||||||
\(785\) | 3.34289 | 0.119313 | ||||||||
\(786\) | 118.967 | 4.24340 | ||||||||
\(787\) | 36.8236 | 1.31262 | 0.656309 | − | 0.754492i | \(-0.272117\pi\) | ||||
0.656309 | + | 0.754492i | \(0.272117\pi\) | |||||||
\(788\) | −28.4212 | −1.01246 | ||||||||
\(789\) | −0.374880 | −0.0133461 | ||||||||
\(790\) | −44.4625 | −1.58191 | ||||||||
\(791\) | −18.3210 | −0.651421 | ||||||||
\(792\) | −21.9334 | −0.779368 | ||||||||
\(793\) | 13.8065 | 0.490282 | ||||||||
\(794\) | −69.3377 | −2.46070 | ||||||||
\(795\) | −21.8699 | −0.775646 | ||||||||
\(796\) | 61.4906 | 2.17948 | ||||||||
\(797\) | −45.3960 | −1.60801 | −0.804005 | − | 0.594622i | \(-0.797302\pi\) | ||||
−0.804005 | + | 0.594622i | \(0.797302\pi\) | |||||||
\(798\) | 30.8863 | 1.09336 | ||||||||
\(799\) | −25.0577 | −0.886477 | ||||||||
\(800\) | 48.8875 | 1.72843 | ||||||||
\(801\) | 22.3458 | 0.789551 | ||||||||
\(802\) | −16.7486 | −0.591414 | ||||||||
\(803\) | 2.95790 | 0.104382 | ||||||||
\(804\) | −146.444 | −5.16469 | ||||||||
\(805\) | 29.9690 | 1.05627 | ||||||||
\(806\) | 132.595 | 4.67046 | ||||||||
\(807\) | −33.5223 | −1.18004 | ||||||||
\(808\) | 30.2391 | 1.06381 | ||||||||
\(809\) | −34.4760 | −1.21211 | −0.606055 | − | 0.795423i | \(-0.707249\pi\) | ||||
−0.606055 | + | 0.795423i | \(0.707249\pi\) | |||||||
\(810\) | −147.167 | −5.17091 | ||||||||
\(811\) | 19.1727 | 0.673246 | 0.336623 | − | 0.941640i | \(-0.390715\pi\) | ||||
0.336623 | + | 0.941640i | \(0.390715\pi\) | |||||||
\(812\) | −0.913903 | −0.0320717 | ||||||||
\(813\) | 66.7495 | 2.34101 | ||||||||
\(814\) | −17.9600 | −0.629497 | ||||||||
\(815\) | −66.0165 | −2.31246 | ||||||||
\(816\) | −6.87873 | −0.240804 | ||||||||
\(817\) | 2.42687 | 0.0849054 | ||||||||
\(818\) | 69.3571 | 2.42501 | ||||||||
\(819\) | 36.4153 | 1.27245 | ||||||||
\(820\) | −1.02536 | −0.0358070 | ||||||||
\(821\) | −35.3962 | −1.23534 | −0.617668 | − | 0.786439i | \(-0.711922\pi\) | ||||
−0.617668 | + | 0.786439i | \(0.711922\pi\) | |||||||
\(822\) | 47.4907 | 1.65643 | ||||||||
\(823\) | 14.9994 | 0.522846 | 0.261423 | − | 0.965224i | \(-0.415808\pi\) | ||||
0.261423 | + | 0.965224i | \(0.415808\pi\) | |||||||
\(824\) | 43.5000 | 1.51539 | ||||||||
\(825\) | −32.2166 | −1.12164 | ||||||||
\(826\) | 4.37907 | 0.152367 | ||||||||
\(827\) | 17.1114 | 0.595023 | 0.297511 | − | 0.954718i | \(-0.403843\pi\) | ||||
0.297511 | + | 0.954718i | \(0.403843\pi\) | |||||||
\(828\) | −177.348 | −6.16327 | ||||||||
\(829\) | −32.2151 | −1.11888 | −0.559438 | − | 0.828872i | \(-0.688983\pi\) | ||||
−0.559438 | + | 0.828872i | \(0.688983\pi\) | |||||||
\(830\) | 93.4129 | 3.24241 | ||||||||
\(831\) | −96.8096 | −3.35829 | ||||||||
\(832\) | 68.4939 | 2.37460 | ||||||||
\(833\) | −17.3689 | −0.601796 | ||||||||
\(834\) | −106.959 | −3.70368 | ||||||||
\(835\) | −20.9452 | −0.724839 | ||||||||
\(836\) | −14.6452 | −0.506516 | ||||||||
\(837\) | −121.740 | −4.20795 | ||||||||
\(838\) | 63.7567 | 2.20244 | ||||||||
\(839\) | −57.2147 | −1.97527 | −0.987635 | − | 0.156773i | \(-0.949891\pi\) | ||||
−0.987635 | + | 0.156773i | \(0.949891\pi\) | |||||||
\(840\) | −39.3330 | −1.35712 | ||||||||
\(841\) | −28.9262 | −0.997454 | ||||||||
\(842\) | 44.5260 | 1.53447 | ||||||||
\(843\) | 24.9523 | 0.859404 | ||||||||
\(844\) | 16.4394 | 0.565868 | ||||||||
\(845\) | 66.0308 | 2.27153 | ||||||||
\(846\) | 136.018 | 4.67639 | ||||||||
\(847\) | −0.989043 | −0.0339839 | ||||||||
\(848\) | 1.36833 | 0.0469886 | ||||||||
\(849\) | 68.6515 | 2.35611 | ||||||||
\(850\) | −69.2062 | −2.37375 | ||||||||
\(851\) | −59.8189 | −2.05057 | ||||||||
\(852\) | 51.8394 | 1.77599 | ||||||||
\(853\) | 26.3255 | 0.901370 | 0.450685 | − | 0.892683i | \(-0.351180\pi\) | ||||
0.450685 | + | 0.892683i | \(0.351180\pi\) | |||||||
\(854\) | −5.80671 | −0.198702 | ||||||||
\(855\) | −113.570 | −3.88402 | ||||||||
\(856\) | 19.0635 | 0.651579 | ||||||||
\(857\) | −9.70733 | −0.331596 | −0.165798 | − | 0.986160i | \(-0.553020\pi\) | ||||
−0.165798 | + | 0.986160i | \(0.553020\pi\) | |||||||
\(858\) | −39.6320 | −1.35302 | ||||||||
\(859\) | −22.4855 | −0.767197 | −0.383598 | − | 0.923500i | \(-0.625315\pi\) | ||||
−0.383598 | + | 0.923500i | \(0.625315\pi\) | |||||||
\(860\) | −7.50286 | −0.255845 | ||||||||
\(861\) | −0.237694 | −0.00810060 | ||||||||
\(862\) | −12.0511 | −0.410462 | ||||||||
\(863\) | −40.7277 | −1.38639 | −0.693193 | − | 0.720752i | \(-0.743797\pi\) | ||||
−0.693193 | + | 0.720752i | \(0.743797\pi\) | |||||||
\(864\) | −55.2169 | −1.87852 | ||||||||
\(865\) | −68.8255 | −2.34014 | ||||||||
\(866\) | 23.1877 | 0.787951 | ||||||||
\(867\) | 27.0871 | 0.919927 | ||||||||
\(868\) | −35.1157 | −1.19191 | ||||||||
\(869\) | 4.88730 | 0.165790 | ||||||||
\(870\) | 7.71312 | 0.261499 | ||||||||
\(871\) | −75.4166 | −2.55539 | ||||||||
\(872\) | −60.9061 | −2.06254 | ||||||||
\(873\) | −52.9467 | −1.79197 | ||||||||
\(874\) | −77.4643 | −2.62027 | ||||||||
\(875\) | −20.6149 | −0.696909 | ||||||||
\(876\) | −31.3899 | −1.06057 | ||||||||
\(877\) | −34.6196 | −1.16902 | −0.584510 | − | 0.811387i | \(-0.698713\pi\) | ||||
−0.584510 | + | 0.811387i | \(0.698713\pi\) | |||||||
\(878\) | 15.1659 | 0.511823 | ||||||||
\(879\) | 68.0029 | 2.29368 | ||||||||
\(880\) | 2.99186 | 0.100855 | ||||||||
\(881\) | 4.22540 | 0.142357 | 0.0711787 | − | 0.997464i | \(-0.477324\pi\) | ||||
0.0711787 | + | 0.997464i | \(0.477324\pi\) | |||||||
\(882\) | 94.2816 | 3.17463 | ||||||||
\(883\) | 12.4434 | 0.418755 | 0.209378 | − | 0.977835i | \(-0.432856\pi\) | ||||
0.209378 | + | 0.977835i | \(0.432856\pi\) | |||||||
\(884\) | −53.6092 | −1.80307 | ||||||||
\(885\) | −23.2723 | −0.782291 | ||||||||
\(886\) | −6.77074 | −0.227467 | ||||||||
\(887\) | 48.0810 | 1.61440 | 0.807201 | − | 0.590276i | \(-0.200981\pi\) | ||||
0.807201 | + | 0.590276i | \(0.200981\pi\) | |||||||
\(888\) | 78.5097 | 2.63461 | ||||||||
\(889\) | 12.3833 | 0.415322 | ||||||||
\(890\) | −30.1754 | −1.01148 | ||||||||
\(891\) | 16.1765 | 0.541933 | ||||||||
\(892\) | −12.4112 | −0.415558 | ||||||||
\(893\) | 37.4109 | 1.25191 | ||||||||
\(894\) | −151.276 | −5.05943 | ||||||||
\(895\) | 32.6371 | 1.09094 | ||||||||
\(896\) | −19.4406 | −0.649465 | ||||||||
\(897\) | −132.002 | −4.40740 | ||||||||
\(898\) | −90.6599 | −3.02536 | ||||||||
\(899\) | 2.83652 | 0.0946032 | ||||||||
\(900\) | 236.552 | 7.88507 | ||||||||
\(901\) | 5.16402 | 0.172038 | ||||||||
\(902\) | 0.178987 | 0.00595963 | ||||||||
\(903\) | −1.73929 | −0.0578798 | ||||||||
\(904\) | −60.3075 | −2.00580 | ||||||||
\(905\) | −39.4648 | −1.31186 | ||||||||
\(906\) | 63.7807 | 2.11897 | ||||||||
\(907\) | −29.8929 | −0.992578 | −0.496289 | − | 0.868157i | \(-0.665304\pi\) | ||||
−0.496289 | + | 0.868157i | \(0.665304\pi\) | |||||||
\(908\) | 38.5914 | 1.28070 | ||||||||
\(909\) | −62.5749 | −2.07548 | ||||||||
\(910\) | −49.1746 | −1.63012 | ||||||||
\(911\) | 22.9212 | 0.759413 | 0.379707 | − | 0.925107i | \(-0.376025\pi\) | ||||
0.379707 | + | 0.925107i | \(0.376025\pi\) | |||||||
\(912\) | 10.2699 | 0.340070 | ||||||||
\(913\) | −10.2679 | −0.339818 | ||||||||
\(914\) | 29.2567 | 0.967727 | ||||||||
\(915\) | 30.8594 | 1.02018 | ||||||||
\(916\) | 34.3319 | 1.13436 | ||||||||
\(917\) | −16.2254 | −0.535809 | ||||||||
\(918\) | 78.1662 | 2.57987 | ||||||||
\(919\) | 51.0750 | 1.68481 | 0.842404 | − | 0.538847i | \(-0.181140\pi\) | ||||
0.842404 | + | 0.538847i | \(0.181140\pi\) | |||||||
\(920\) | 98.6493 | 3.25237 | ||||||||
\(921\) | −38.7092 | −1.27551 | ||||||||
\(922\) | −15.4451 | −0.508659 | ||||||||
\(923\) | 26.6965 | 0.878726 | ||||||||
\(924\) | 10.4959 | 0.345291 | ||||||||
\(925\) | 79.7883 | 2.62342 | ||||||||
\(926\) | 32.0152 | 1.05208 | ||||||||
\(927\) | −90.0163 | −2.95652 | ||||||||
\(928\) | 1.28654 | 0.0422328 | ||||||||
\(929\) | 47.8929 | 1.57132 | 0.785658 | − | 0.618661i | \(-0.212325\pi\) | ||||
0.785658 | + | 0.618661i | \(0.212325\pi\) | |||||||
\(930\) | 296.368 | 9.71830 | ||||||||
\(931\) | 25.9316 | 0.849875 | ||||||||
\(932\) | 11.1492 | 0.365205 | ||||||||
\(933\) | 74.9632 | 2.45418 | ||||||||
\(934\) | −68.7124 | −2.24834 | ||||||||
\(935\) | 11.2912 | 0.369260 | ||||||||
\(936\) | 119.869 | 3.91803 | ||||||||
\(937\) | 32.8592 | 1.07346 | 0.536731 | − | 0.843754i | \(-0.319659\pi\) | ||||
0.536731 | + | 0.843754i | \(0.319659\pi\) | |||||||
\(938\) | 31.7187 | 1.03565 | ||||||||
\(939\) | 108.087 | 3.52728 | ||||||||
\(940\) | −115.659 | −3.77238 | ||||||||
\(941\) | −32.8230 | −1.07000 | −0.535000 | − | 0.844852i | \(-0.679689\pi\) | ||||
−0.535000 | + | 0.844852i | \(0.679689\pi\) | |||||||
\(942\) | 6.19264 | 0.201767 | ||||||||
\(943\) | 0.596149 | 0.0194133 | ||||||||
\(944\) | 1.45607 | 0.0473911 | ||||||||
\(945\) | 45.1489 | 1.46869 | ||||||||
\(946\) | 1.30971 | 0.0425823 | ||||||||
\(947\) | −4.42335 | −0.143740 | −0.0718698 | − | 0.997414i | \(-0.522897\pi\) | ||||
−0.0718698 | + | 0.997414i | \(0.522897\pi\) | |||||||
\(948\) | −51.8651 | −1.68450 | ||||||||
\(949\) | −16.1653 | −0.524748 | ||||||||
\(950\) | 103.324 | 3.35228 | ||||||||
\(951\) | −82.2968 | −2.66866 | ||||||||
\(952\) | 9.28749 | 0.301009 | ||||||||
\(953\) | −32.7593 | −1.06118 | −0.530589 | − | 0.847629i | \(-0.678029\pi\) | ||||
−0.530589 | + | 0.847629i | \(0.678029\pi\) | |||||||
\(954\) | −28.0313 | −0.907546 | ||||||||
\(955\) | 15.3187 | 0.495702 | ||||||||
\(956\) | 103.833 | 3.35820 | ||||||||
\(957\) | −0.847823 | −0.0274062 | ||||||||
\(958\) | 39.6753 | 1.28185 | ||||||||
\(959\) | −6.47707 | −0.209155 | ||||||||
\(960\) | 153.094 | 4.94107 | ||||||||
\(961\) | 77.9902 | 2.51581 | ||||||||
\(962\) | 98.1536 | 3.16460 | ||||||||
\(963\) | −39.4490 | −1.27123 | ||||||||
\(964\) | −1.73904 | −0.0560107 | ||||||||
\(965\) | −52.0542 | −1.67569 | ||||||||
\(966\) | 55.5171 | 1.78623 | ||||||||
\(967\) | 34.9707 | 1.12458 | 0.562290 | − | 0.826940i | \(-0.309920\pi\) | ||||
0.562290 | + | 0.826940i | \(0.309920\pi\) | |||||||
\(968\) | −3.25564 | −0.104640 | ||||||||
\(969\) | 38.7582 | 1.24509 | ||||||||
\(970\) | 71.4982 | 2.29567 | ||||||||
\(971\) | 27.1071 | 0.869908 | 0.434954 | − | 0.900453i | \(-0.356765\pi\) | ||||
0.434954 | + | 0.900453i | \(0.356765\pi\) | |||||||
\(972\) | −52.6939 | −1.69016 | ||||||||
\(973\) | 14.5877 | 0.467660 | ||||||||
\(974\) | −72.9804 | −2.33844 | ||||||||
\(975\) | 176.068 | 5.63868 | ||||||||
\(976\) | −1.93077 | −0.0618025 | ||||||||
\(977\) | 55.0874 | 1.76240 | 0.881200 | − | 0.472743i | \(-0.156736\pi\) | ||||
0.881200 | + | 0.472743i | \(0.156736\pi\) | |||||||
\(978\) | −122.294 | −3.91054 | ||||||||
\(979\) | 3.31687 | 0.106008 | ||||||||
\(980\) | −80.1697 | −2.56093 | ||||||||
\(981\) | 126.035 | 4.02400 | ||||||||
\(982\) | 63.9580 | 2.04098 | ||||||||
\(983\) | 10.5168 | 0.335433 | 0.167716 | − | 0.985835i | \(-0.446361\pi\) | ||||
0.167716 | + | 0.985835i | \(0.446361\pi\) | |||||||
\(984\) | −0.782420 | −0.0249426 | ||||||||
\(985\) | −32.7146 | −1.04237 | ||||||||
\(986\) | −1.82126 | −0.0580006 | ||||||||
\(987\) | −26.8116 | −0.853423 | ||||||||
\(988\) | 80.0381 | 2.54635 | ||||||||
\(989\) | 4.36222 | 0.138710 | ||||||||
\(990\) | −61.2905 | −1.94794 | ||||||||
\(991\) | −37.3445 | −1.18629 | −0.593143 | − | 0.805097i | \(-0.702113\pi\) | ||||
−0.593143 | + | 0.805097i | \(0.702113\pi\) | |||||||
\(992\) | 49.4340 | 1.56953 | ||||||||
\(993\) | −6.73160 | −0.213621 | ||||||||
\(994\) | −11.2280 | −0.356130 | ||||||||
\(995\) | 70.7797 | 2.24387 | ||||||||
\(996\) | 108.965 | 3.45270 | ||||||||
\(997\) | −33.7762 | −1.06970 | −0.534852 | − | 0.844946i | \(-0.679633\pi\) | ||||
−0.534852 | + | 0.844946i | \(0.679633\pi\) | |||||||
\(998\) | −11.8789 | −0.376020 | ||||||||
\(999\) | −90.1184 | −2.85122 |
(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 | 6017.2.a.c.1.15 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.15 | ✓ | 106 | 1.1 | even | 1 | trivial |