Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −0.945997 | −0.546172 | −0.273086 | − | 0.961990i | \(-0.588044\pi\) | ||||
−0.273086 | + | 0.961990i | \(0.588044\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.44770 | −1.09464 | −0.547322 | − | 0.836922i | \(-0.684353\pi\) | ||||
−0.547322 | + | 0.836922i | \(0.684353\pi\) | |||||||
\(6\) | −0.945997 | −0.386202 | ||||||||
\(7\) | 2.03235 | 0.768156 | 0.384078 | − | 0.923301i | \(-0.374519\pi\) | ||||
0.384078 | + | 0.923301i | \(0.374519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.10509 | −0.701697 | ||||||||
\(10\) | −2.44770 | −0.774030 | ||||||||
\(11\) | −2.80078 | −0.844466 | −0.422233 | − | 0.906487i | \(-0.638754\pi\) | ||||
−0.422233 | + | 0.906487i | \(0.638754\pi\) | |||||||
\(12\) | −0.945997 | −0.273086 | ||||||||
\(13\) | −1.99090 | −0.552177 | −0.276088 | − | 0.961132i | \(-0.589038\pi\) | ||||
−0.276088 | + | 0.961132i | \(0.589038\pi\) | |||||||
\(14\) | 2.03235 | 0.543169 | ||||||||
\(15\) | 2.31551 | 0.597863 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.52248 | 1.33940 | 0.669699 | − | 0.742632i | \(-0.266423\pi\) | ||||
0.669699 | + | 0.742632i | \(0.266423\pi\) | |||||||
\(18\) | −2.10509 | −0.496174 | ||||||||
\(19\) | 2.90068 | 0.665463 | 0.332731 | − | 0.943022i | \(-0.392030\pi\) | ||||
0.332731 | + | 0.943022i | \(0.392030\pi\) | |||||||
\(20\) | −2.44770 | −0.547322 | ||||||||
\(21\) | −1.92260 | −0.419545 | ||||||||
\(22\) | −2.80078 | −0.597128 | ||||||||
\(23\) | 6.12514 | 1.27718 | 0.638590 | − | 0.769547i | \(-0.279518\pi\) | ||||
0.638590 | + | 0.769547i | \(0.279518\pi\) | |||||||
\(24\) | −0.945997 | −0.193101 | ||||||||
\(25\) | 0.991226 | 0.198245 | ||||||||
\(26\) | −1.99090 | −0.390448 | ||||||||
\(27\) | 4.82940 | 0.929418 | ||||||||
\(28\) | 2.03235 | 0.384078 | ||||||||
\(29\) | −3.04955 | −0.566287 | −0.283144 | − | 0.959078i | \(-0.591377\pi\) | ||||
−0.283144 | + | 0.959078i | \(0.591377\pi\) | |||||||
\(30\) | 2.31551 | 0.422753 | ||||||||
\(31\) | −0.837606 | −0.150439 | −0.0752193 | − | 0.997167i | \(-0.523966\pi\) | ||||
−0.0752193 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.64953 | 0.461223 | ||||||||
\(34\) | 5.52248 | 0.947098 | ||||||||
\(35\) | −4.97458 | −0.840858 | ||||||||
\(36\) | −2.10509 | −0.350848 | ||||||||
\(37\) | 6.35990 | 1.04556 | 0.522781 | − | 0.852467i | \(-0.324895\pi\) | ||||
0.522781 | + | 0.852467i | \(0.324895\pi\) | |||||||
\(38\) | 2.90068 | 0.470553 | ||||||||
\(39\) | 1.88339 | 0.301583 | ||||||||
\(40\) | −2.44770 | −0.387015 | ||||||||
\(41\) | 3.39380 | 0.530023 | 0.265011 | − | 0.964245i | \(-0.414624\pi\) | ||||
0.265011 | + | 0.964245i | \(0.414624\pi\) | |||||||
\(42\) | −1.92260 | −0.296663 | ||||||||
\(43\) | −12.3524 | −1.88372 | −0.941859 | − | 0.336009i | \(-0.890923\pi\) | ||||
−0.941859 | + | 0.336009i | \(0.890923\pi\) | |||||||
\(44\) | −2.80078 | −0.422233 | ||||||||
\(45\) | 5.15262 | 0.768108 | ||||||||
\(46\) | 6.12514 | 0.903102 | ||||||||
\(47\) | −8.79264 | −1.28254 | −0.641269 | − | 0.767316i | \(-0.721592\pi\) | ||||
−0.641269 | + | 0.767316i | \(0.721592\pi\) | |||||||
\(48\) | −0.945997 | −0.136543 | ||||||||
\(49\) | −2.86955 | −0.409936 | ||||||||
\(50\) | 0.991226 | 0.140181 | ||||||||
\(51\) | −5.22425 | −0.731541 | ||||||||
\(52\) | −1.99090 | −0.276088 | ||||||||
\(53\) | −7.11992 | −0.977996 | −0.488998 | − | 0.872285i | \(-0.662638\pi\) | ||||
−0.488998 | + | 0.872285i | \(0.662638\pi\) | |||||||
\(54\) | 4.82940 | 0.657198 | ||||||||
\(55\) | 6.85545 | 0.924389 | ||||||||
\(56\) | 2.03235 | 0.271584 | ||||||||
\(57\) | −2.74404 | −0.363457 | ||||||||
\(58\) | −3.04955 | −0.400426 | ||||||||
\(59\) | 0.529488 | 0.0689335 | 0.0344667 | − | 0.999406i | \(-0.489027\pi\) | ||||
0.0344667 | + | 0.999406i | \(0.489027\pi\) | |||||||
\(60\) | 2.31551 | 0.298932 | ||||||||
\(61\) | −7.57201 | −0.969496 | −0.484748 | − | 0.874654i | \(-0.661089\pi\) | ||||
−0.484748 | + | 0.874654i | \(0.661089\pi\) | |||||||
\(62\) | −0.837606 | −0.106376 | ||||||||
\(63\) | −4.27828 | −0.539013 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.87312 | 0.604437 | ||||||||
\(66\) | 2.64953 | 0.326134 | ||||||||
\(67\) | −0.246931 | −0.0301674 | −0.0150837 | − | 0.999886i | \(-0.504801\pi\) | ||||
−0.0150837 | + | 0.999886i | \(0.504801\pi\) | |||||||
\(68\) | 5.52248 | 0.669699 | ||||||||
\(69\) | −5.79436 | −0.697559 | ||||||||
\(70\) | −4.97458 | −0.594576 | ||||||||
\(71\) | −1.27323 | −0.151105 | −0.0755525 | − | 0.997142i | \(-0.524072\pi\) | ||||
−0.0755525 | + | 0.997142i | \(0.524072\pi\) | |||||||
\(72\) | −2.10509 | −0.248087 | ||||||||
\(73\) | −7.08356 | −0.829068 | −0.414534 | − | 0.910034i | \(-0.636055\pi\) | ||||
−0.414534 | + | 0.910034i | \(0.636055\pi\) | |||||||
\(74\) | 6.35990 | 0.739324 | ||||||||
\(75\) | −0.937697 | −0.108276 | ||||||||
\(76\) | 2.90068 | 0.332731 | ||||||||
\(77\) | −5.69216 | −0.648682 | ||||||||
\(78\) | 1.88339 | 0.213252 | ||||||||
\(79\) | −8.73964 | −0.983286 | −0.491643 | − | 0.870797i | \(-0.663603\pi\) | ||||
−0.491643 | + | 0.870797i | \(0.663603\pi\) | |||||||
\(80\) | −2.44770 | −0.273661 | ||||||||
\(81\) | 1.74667 | 0.194075 | ||||||||
\(82\) | 3.39380 | 0.374783 | ||||||||
\(83\) | −15.0794 | −1.65518 | −0.827588 | − | 0.561336i | \(-0.810288\pi\) | ||||
−0.827588 | + | 0.561336i | \(0.810288\pi\) | |||||||
\(84\) | −1.92260 | −0.209773 | ||||||||
\(85\) | −13.5174 | −1.46616 | ||||||||
\(86\) | −12.3524 | −1.33199 | ||||||||
\(87\) | 2.88487 | 0.309290 | ||||||||
\(88\) | −2.80078 | −0.298564 | ||||||||
\(89\) | 10.3602 | 1.09818 | 0.549089 | − | 0.835764i | \(-0.314975\pi\) | ||||
0.549089 | + | 0.835764i | \(0.314975\pi\) | |||||||
\(90\) | 5.15262 | 0.543134 | ||||||||
\(91\) | −4.04621 | −0.424158 | ||||||||
\(92\) | 6.12514 | 0.638590 | ||||||||
\(93\) | 0.792373 | 0.0821653 | ||||||||
\(94\) | −8.79264 | −0.906892 | ||||||||
\(95\) | −7.10000 | −0.728445 | ||||||||
\(96\) | −0.945997 | −0.0965504 | ||||||||
\(97\) | 1.35477 | 0.137556 | 0.0687778 | − | 0.997632i | \(-0.478090\pi\) | ||||
0.0687778 | + | 0.997632i | \(0.478090\pi\) | |||||||
\(98\) | −2.86955 | −0.289868 | ||||||||
\(99\) | 5.89589 | 0.592559 | ||||||||
\(100\) | 0.991226 | 0.0991226 | ||||||||
\(101\) | −2.66728 | −0.265404 | −0.132702 | − | 0.991156i | \(-0.542365\pi\) | ||||
−0.132702 | + | 0.991156i | \(0.542365\pi\) | |||||||
\(102\) | −5.22425 | −0.517278 | ||||||||
\(103\) | −15.3143 | −1.50896 | −0.754480 | − | 0.656323i | \(-0.772111\pi\) | ||||
−0.754480 | + | 0.656323i | \(0.772111\pi\) | |||||||
\(104\) | −1.99090 | −0.195224 | ||||||||
\(105\) | 4.70594 | 0.459253 | ||||||||
\(106\) | −7.11992 | −0.691548 | ||||||||
\(107\) | 14.4192 | 1.39396 | 0.696980 | − | 0.717090i | \(-0.254526\pi\) | ||||
0.696980 | + | 0.717090i | \(0.254526\pi\) | |||||||
\(108\) | 4.82940 | 0.464709 | ||||||||
\(109\) | −2.62093 | −0.251039 | −0.125520 | − | 0.992091i | \(-0.540060\pi\) | ||||
−0.125520 | + | 0.992091i | \(0.540060\pi\) | |||||||
\(110\) | 6.85545 | 0.653642 | ||||||||
\(111\) | −6.01645 | −0.571056 | ||||||||
\(112\) | 2.03235 | 0.192039 | ||||||||
\(113\) | −11.3017 | −1.06318 | −0.531589 | − | 0.847003i | \(-0.678405\pi\) | ||||
−0.531589 | + | 0.847003i | \(0.678405\pi\) | |||||||
\(114\) | −2.74404 | −0.257003 | ||||||||
\(115\) | −14.9925 | −1.39806 | ||||||||
\(116\) | −3.04955 | −0.283144 | ||||||||
\(117\) | 4.19103 | 0.387460 | ||||||||
\(118\) | 0.529488 | 0.0487433 | ||||||||
\(119\) | 11.2236 | 1.02887 | ||||||||
\(120\) | 2.31551 | 0.211377 | ||||||||
\(121\) | −3.15565 | −0.286877 | ||||||||
\(122\) | −7.57201 | −0.685537 | ||||||||
\(123\) | −3.21053 | −0.289483 | ||||||||
\(124\) | −0.837606 | −0.0752193 | ||||||||
\(125\) | 9.81227 | 0.877636 | ||||||||
\(126\) | −4.27828 | −0.381140 | ||||||||
\(127\) | −1.86707 | −0.165676 | −0.0828380 | − | 0.996563i | \(-0.526398\pi\) | ||||
−0.0828380 | + | 0.996563i | \(0.526398\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 11.6853 | 1.02883 | ||||||||
\(130\) | 4.87312 | 0.427401 | ||||||||
\(131\) | −4.97772 | −0.434905 | −0.217453 | − | 0.976071i | \(-0.569775\pi\) | ||||
−0.217453 | + | 0.976071i | \(0.569775\pi\) | |||||||
\(132\) | 2.64953 | 0.230612 | ||||||||
\(133\) | 5.89521 | 0.511179 | ||||||||
\(134\) | −0.246931 | −0.0213315 | ||||||||
\(135\) | −11.8209 | −1.01738 | ||||||||
\(136\) | 5.52248 | 0.473549 | ||||||||
\(137\) | −16.0530 | −1.37150 | −0.685751 | − | 0.727836i | \(-0.740526\pi\) | ||||
−0.685751 | + | 0.727836i | \(0.740526\pi\) | |||||||
\(138\) | −5.79436 | −0.493249 | ||||||||
\(139\) | −16.7441 | −1.42022 | −0.710110 | − | 0.704091i | \(-0.751355\pi\) | ||||
−0.710110 | + | 0.704091i | \(0.751355\pi\) | |||||||
\(140\) | −4.97458 | −0.420429 | ||||||||
\(141\) | 8.31781 | 0.700486 | ||||||||
\(142\) | −1.27323 | −0.106847 | ||||||||
\(143\) | 5.57607 | 0.466294 | ||||||||
\(144\) | −2.10509 | −0.175424 | ||||||||
\(145\) | 7.46438 | 0.619883 | ||||||||
\(146\) | −7.08356 | −0.586240 | ||||||||
\(147\) | 2.71459 | 0.223895 | ||||||||
\(148\) | 6.35990 | 0.522781 | ||||||||
\(149\) | −9.63045 | −0.788957 | −0.394479 | − | 0.918905i | \(-0.629075\pi\) | ||||
−0.394479 | + | 0.918905i | \(0.629075\pi\) | |||||||
\(150\) | −0.937697 | −0.0765626 | ||||||||
\(151\) | 11.0569 | 0.899798 | 0.449899 | − | 0.893080i | \(-0.351460\pi\) | ||||
0.449899 | + | 0.893080i | \(0.351460\pi\) | |||||||
\(152\) | 2.90068 | 0.235277 | ||||||||
\(153\) | −11.6253 | −0.939851 | ||||||||
\(154\) | −5.69216 | −0.458687 | ||||||||
\(155\) | 2.05021 | 0.164677 | ||||||||
\(156\) | 1.88339 | 0.150792 | ||||||||
\(157\) | 23.6561 | 1.88796 | 0.943982 | − | 0.329997i | \(-0.107048\pi\) | ||||
0.943982 | + | 0.329997i | \(0.107048\pi\) | |||||||
\(158\) | −8.73964 | −0.695288 | ||||||||
\(159\) | 6.73542 | 0.534154 | ||||||||
\(160\) | −2.44770 | −0.193508 | ||||||||
\(161\) | 12.4484 | 0.981073 | ||||||||
\(162\) | 1.74667 | 0.137231 | ||||||||
\(163\) | 1.48955 | 0.116671 | 0.0583354 | − | 0.998297i | \(-0.481421\pi\) | ||||
0.0583354 | + | 0.998297i | \(0.481421\pi\) | |||||||
\(164\) | 3.39380 | 0.265011 | ||||||||
\(165\) | −6.48524 | −0.504875 | ||||||||
\(166\) | −15.0794 | −1.17039 | ||||||||
\(167\) | 10.1098 | 0.782321 | 0.391160 | − | 0.920323i | \(-0.372074\pi\) | ||||
0.391160 | + | 0.920323i | \(0.372074\pi\) | |||||||
\(168\) | −1.92260 | −0.148332 | ||||||||
\(169\) | −9.03631 | −0.695101 | ||||||||
\(170\) | −13.5174 | −1.03673 | ||||||||
\(171\) | −6.10620 | −0.466953 | ||||||||
\(172\) | −12.3524 | −0.941859 | ||||||||
\(173\) | −7.11640 | −0.541050 | −0.270525 | − | 0.962713i | \(-0.587197\pi\) | ||||
−0.270525 | + | 0.962713i | \(0.587197\pi\) | |||||||
\(174\) | 2.88487 | 0.218701 | ||||||||
\(175\) | 2.01452 | 0.152283 | ||||||||
\(176\) | −2.80078 | −0.211116 | ||||||||
\(177\) | −0.500894 | −0.0376495 | ||||||||
\(178\) | 10.3602 | 0.776530 | ||||||||
\(179\) | −24.0359 | −1.79653 | −0.898263 | − | 0.439458i | \(-0.855170\pi\) | ||||
−0.898263 | + | 0.439458i | \(0.855170\pi\) | |||||||
\(180\) | 5.15262 | 0.384054 | ||||||||
\(181\) | −10.7648 | −0.800145 | −0.400072 | − | 0.916484i | \(-0.631015\pi\) | ||||
−0.400072 | + | 0.916484i | \(0.631015\pi\) | |||||||
\(182\) | −4.04621 | −0.299925 | ||||||||
\(183\) | 7.16310 | 0.529511 | ||||||||
\(184\) | 6.12514 | 0.451551 | ||||||||
\(185\) | −15.5671 | −1.14452 | ||||||||
\(186\) | 0.792373 | 0.0580996 | ||||||||
\(187\) | −15.4672 | −1.13108 | ||||||||
\(188\) | −8.79264 | −0.641269 | ||||||||
\(189\) | 9.81503 | 0.713939 | ||||||||
\(190\) | −7.10000 | −0.515088 | ||||||||
\(191\) | 21.1184 | 1.52807 | 0.764037 | − | 0.645173i | \(-0.223215\pi\) | ||||
0.764037 | + | 0.645173i | \(0.223215\pi\) | |||||||
\(192\) | −0.945997 | −0.0682715 | ||||||||
\(193\) | 16.5811 | 1.19354 | 0.596768 | − | 0.802414i | \(-0.296451\pi\) | ||||
0.596768 | + | 0.802414i | \(0.296451\pi\) | |||||||
\(194\) | 1.35477 | 0.0972665 | ||||||||
\(195\) | −4.60996 | −0.330126 | ||||||||
\(196\) | −2.86955 | −0.204968 | ||||||||
\(197\) | 17.8425 | 1.27122 | 0.635612 | − | 0.772008i | \(-0.280748\pi\) | ||||
0.635612 | + | 0.772008i | \(0.280748\pi\) | |||||||
\(198\) | 5.89589 | 0.419002 | ||||||||
\(199\) | −2.34031 | −0.165901 | −0.0829503 | − | 0.996554i | \(-0.526434\pi\) | ||||
−0.0829503 | + | 0.996554i | \(0.526434\pi\) | |||||||
\(200\) | 0.991226 | 0.0700903 | ||||||||
\(201\) | 0.233596 | 0.0164766 | ||||||||
\(202\) | −2.66728 | −0.187669 | ||||||||
\(203\) | −6.19775 | −0.434997 | ||||||||
\(204\) | −5.22425 | −0.365771 | ||||||||
\(205\) | −8.30700 | −0.580186 | ||||||||
\(206\) | −15.3143 | −1.06700 | ||||||||
\(207\) | −12.8940 | −0.896192 | ||||||||
\(208\) | −1.99090 | −0.138044 | ||||||||
\(209\) | −8.12417 | −0.561960 | ||||||||
\(210\) | 4.70594 | 0.324741 | ||||||||
\(211\) | 17.8337 | 1.22772 | 0.613861 | − | 0.789414i | \(-0.289615\pi\) | ||||
0.613861 | + | 0.789414i | \(0.289615\pi\) | |||||||
\(212\) | −7.11992 | −0.488998 | ||||||||
\(213\) | 1.20448 | 0.0825293 | ||||||||
\(214\) | 14.4192 | 0.985679 | ||||||||
\(215\) | 30.2349 | 2.06200 | ||||||||
\(216\) | 4.82940 | 0.328599 | ||||||||
\(217\) | −1.70231 | −0.115560 | ||||||||
\(218\) | −2.62093 | −0.177512 | ||||||||
\(219\) | 6.70103 | 0.452813 | ||||||||
\(220\) | 6.85545 | 0.462195 | ||||||||
\(221\) | −10.9947 | −0.739585 | ||||||||
\(222\) | −6.01645 | −0.403798 | ||||||||
\(223\) | −3.72901 | −0.249713 | −0.124856 | − | 0.992175i | \(-0.539847\pi\) | ||||
−0.124856 | + | 0.992175i | \(0.539847\pi\) | |||||||
\(224\) | 2.03235 | 0.135792 | ||||||||
\(225\) | −2.08662 | −0.139108 | ||||||||
\(226\) | −11.3017 | −0.751780 | ||||||||
\(227\) | −27.0598 | −1.79602 | −0.898010 | − | 0.439975i | \(-0.854987\pi\) | ||||
−0.898010 | + | 0.439975i | \(0.854987\pi\) | |||||||
\(228\) | −2.74404 | −0.181728 | ||||||||
\(229\) | −13.4293 | −0.887430 | −0.443715 | − | 0.896168i | \(-0.646340\pi\) | ||||
−0.443715 | + | 0.896168i | \(0.646340\pi\) | |||||||
\(230\) | −14.9925 | −0.988575 | ||||||||
\(231\) | 5.38477 | 0.354292 | ||||||||
\(232\) | −3.04955 | −0.200213 | ||||||||
\(233\) | 25.4347 | 1.66629 | 0.833143 | − | 0.553058i | \(-0.186539\pi\) | ||||
0.833143 | + | 0.553058i | \(0.186539\pi\) | |||||||
\(234\) | 4.19103 | 0.273976 | ||||||||
\(235\) | 21.5217 | 1.40392 | ||||||||
\(236\) | 0.529488 | 0.0344667 | ||||||||
\(237\) | 8.26767 | 0.537043 | ||||||||
\(238\) | 11.2236 | 0.727519 | ||||||||
\(239\) | −15.9974 | −1.03478 | −0.517391 | − | 0.855749i | \(-0.673097\pi\) | ||||
−0.517391 | + | 0.855749i | \(0.673097\pi\) | |||||||
\(240\) | 2.31551 | 0.149466 | ||||||||
\(241\) | 29.8860 | 1.92512 | 0.962562 | − | 0.271061i | \(-0.0873745\pi\) | ||||
0.962562 | + | 0.271061i | \(0.0873745\pi\) | |||||||
\(242\) | −3.15565 | −0.202853 | ||||||||
\(243\) | −16.1405 | −1.03542 | ||||||||
\(244\) | −7.57201 | −0.484748 | ||||||||
\(245\) | 7.02379 | 0.448734 | ||||||||
\(246\) | −3.21053 | −0.204696 | ||||||||
\(247\) | −5.77498 | −0.367453 | ||||||||
\(248\) | −0.837606 | −0.0531881 | ||||||||
\(249\) | 14.2650 | 0.904010 | ||||||||
\(250\) | 9.81227 | 0.620582 | ||||||||
\(251\) | 22.8719 | 1.44366 | 0.721831 | − | 0.692070i | \(-0.243301\pi\) | ||||
0.721831 | + | 0.692070i | \(0.243301\pi\) | |||||||
\(252\) | −4.27828 | −0.269506 | ||||||||
\(253\) | −17.1551 | −1.07853 | ||||||||
\(254\) | −1.86707 | −0.117151 | ||||||||
\(255\) | 12.7874 | 0.800777 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.6713 | 1.35182 | 0.675909 | − | 0.736985i | \(-0.263751\pi\) | ||||
0.675909 | + | 0.736985i | \(0.263751\pi\) | |||||||
\(258\) | 11.6853 | 0.727495 | ||||||||
\(259\) | 12.9256 | 0.803155 | ||||||||
\(260\) | 4.87312 | 0.302218 | ||||||||
\(261\) | 6.41958 | 0.397362 | ||||||||
\(262\) | −4.97772 | −0.307524 | ||||||||
\(263\) | −1.96752 | −0.121323 | −0.0606613 | − | 0.998158i | \(-0.519321\pi\) | ||||
−0.0606613 | + | 0.998158i | \(0.519321\pi\) | |||||||
\(264\) | 2.64953 | 0.163067 | ||||||||
\(265\) | 17.4274 | 1.07056 | ||||||||
\(266\) | 5.89521 | 0.361458 | ||||||||
\(267\) | −9.80071 | −0.599794 | ||||||||
\(268\) | −0.246931 | −0.0150837 | ||||||||
\(269\) | −7.94985 | −0.484711 | −0.242355 | − | 0.970188i | \(-0.577920\pi\) | ||||
−0.242355 | + | 0.970188i | \(0.577920\pi\) | |||||||
\(270\) | −11.8209 | −0.719398 | ||||||||
\(271\) | −23.2965 | −1.41516 | −0.707582 | − | 0.706631i | \(-0.750214\pi\) | ||||
−0.707582 | + | 0.706631i | \(0.750214\pi\) | |||||||
\(272\) | 5.52248 | 0.334850 | ||||||||
\(273\) | 3.82770 | 0.231663 | ||||||||
\(274\) | −16.0530 | −0.969799 | ||||||||
\(275\) | −2.77620 | −0.167411 | ||||||||
\(276\) | −5.79436 | −0.348780 | ||||||||
\(277\) | −27.0992 | −1.62823 | −0.814116 | − | 0.580702i | \(-0.802778\pi\) | ||||
−0.814116 | + | 0.580702i | \(0.802778\pi\) | |||||||
\(278\) | −16.7441 | −1.00425 | ||||||||
\(279\) | 1.76324 | 0.105562 | ||||||||
\(280\) | −4.97458 | −0.297288 | ||||||||
\(281\) | −10.1699 | −0.606687 | −0.303343 | − | 0.952881i | \(-0.598103\pi\) | ||||
−0.303343 | + | 0.952881i | \(0.598103\pi\) | |||||||
\(282\) | 8.31781 | 0.495319 | ||||||||
\(283\) | −19.4096 | −1.15378 | −0.576890 | − | 0.816822i | \(-0.695734\pi\) | ||||
−0.576890 | + | 0.816822i | \(0.695734\pi\) | |||||||
\(284\) | −1.27323 | −0.0755525 | ||||||||
\(285\) | 6.71658 | 0.397856 | ||||||||
\(286\) | 5.57607 | 0.329720 | ||||||||
\(287\) | 6.89739 | 0.407140 | ||||||||
\(288\) | −2.10509 | −0.124044 | ||||||||
\(289\) | 13.4978 | 0.793989 | ||||||||
\(290\) | 7.46438 | 0.438323 | ||||||||
\(291\) | −1.28160 | −0.0751290 | ||||||||
\(292\) | −7.08356 | −0.414534 | ||||||||
\(293\) | −4.93456 | −0.288280 | −0.144140 | − | 0.989557i | \(-0.546042\pi\) | ||||
−0.144140 | + | 0.989557i | \(0.546042\pi\) | |||||||
\(294\) | 2.71459 | 0.158318 | ||||||||
\(295\) | −1.29603 | −0.0754576 | ||||||||
\(296\) | 6.35990 | 0.369662 | ||||||||
\(297\) | −13.5261 | −0.784862 | ||||||||
\(298\) | −9.63045 | −0.557877 | ||||||||
\(299\) | −12.1945 | −0.705229 | ||||||||
\(300\) | −0.937697 | −0.0541379 | ||||||||
\(301\) | −25.1043 | −1.44699 | ||||||||
\(302\) | 11.0569 | 0.636253 | ||||||||
\(303\) | 2.52324 | 0.144956 | ||||||||
\(304\) | 2.90068 | 0.166366 | ||||||||
\(305\) | 18.5340 | 1.06125 | ||||||||
\(306\) | −11.6253 | −0.664575 | ||||||||
\(307\) | −15.2499 | −0.870360 | −0.435180 | − | 0.900343i | \(-0.643315\pi\) | ||||
−0.435180 | + | 0.900343i | \(0.643315\pi\) | |||||||
\(308\) | −5.69216 | −0.324341 | ||||||||
\(309\) | 14.4873 | 0.824152 | ||||||||
\(310\) | 2.05021 | 0.116444 | ||||||||
\(311\) | 21.6782 | 1.22926 | 0.614630 | − | 0.788815i | \(-0.289305\pi\) | ||||
0.614630 | + | 0.788815i | \(0.289305\pi\) | |||||||
\(312\) | 1.88339 | 0.106626 | ||||||||
\(313\) | −15.4715 | −0.874499 | −0.437249 | − | 0.899340i | \(-0.644047\pi\) | ||||
−0.437249 | + | 0.899340i | \(0.644047\pi\) | |||||||
\(314\) | 23.6561 | 1.33499 | ||||||||
\(315\) | 10.4719 | 0.590027 | ||||||||
\(316\) | −8.73964 | −0.491643 | ||||||||
\(317\) | −1.67493 | −0.0940733 | −0.0470367 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470367 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(318\) | 6.73542 | 0.377704 | ||||||||
\(319\) | 8.54111 | 0.478210 | ||||||||
\(320\) | −2.44770 | −0.136830 | ||||||||
\(321\) | −13.6406 | −0.761342 | ||||||||
\(322\) | 12.4484 | 0.693724 | ||||||||
\(323\) | 16.0190 | 0.891320 | ||||||||
\(324\) | 1.74667 | 0.0970373 | ||||||||
\(325\) | −1.97343 | −0.109466 | ||||||||
\(326\) | 1.48955 | 0.0824987 | ||||||||
\(327\) | 2.47939 | 0.137111 | ||||||||
\(328\) | 3.39380 | 0.187391 | ||||||||
\(329\) | −17.8697 | −0.985190 | ||||||||
\(330\) | −6.48524 | −0.357001 | ||||||||
\(331\) | 15.1393 | 0.832131 | 0.416066 | − | 0.909335i | \(-0.363409\pi\) | ||||
0.416066 | + | 0.909335i | \(0.363409\pi\) | |||||||
\(332\) | −15.0794 | −0.827588 | ||||||||
\(333\) | −13.3882 | −0.733667 | ||||||||
\(334\) | 10.1098 | 0.553184 | ||||||||
\(335\) | 0.604411 | 0.0330225 | ||||||||
\(336\) | −1.92260 | −0.104886 | ||||||||
\(337\) | −14.3131 | −0.779687 | −0.389843 | − | 0.920881i | \(-0.627471\pi\) | ||||
−0.389843 | + | 0.920881i | \(0.627471\pi\) | |||||||
\(338\) | −9.03631 | −0.491511 | ||||||||
\(339\) | 10.6914 | 0.580677 | ||||||||
\(340\) | −13.5174 | −0.733082 | ||||||||
\(341\) | 2.34595 | 0.127040 | ||||||||
\(342\) | −6.10620 | −0.330186 | ||||||||
\(343\) | −20.0584 | −1.08305 | ||||||||
\(344\) | −12.3524 | −0.665995 | ||||||||
\(345\) | 14.1828 | 0.763579 | ||||||||
\(346\) | −7.11640 | −0.382580 | ||||||||
\(347\) | −29.7433 | −1.59670 | −0.798351 | − | 0.602192i | \(-0.794294\pi\) | ||||
−0.798351 | + | 0.602192i | \(0.794294\pi\) | |||||||
\(348\) | 2.88487 | 0.154645 | ||||||||
\(349\) | −18.8272 | −1.00780 | −0.503898 | − | 0.863763i | \(-0.668101\pi\) | ||||
−0.503898 | + | 0.863763i | \(0.668101\pi\) | |||||||
\(350\) | 2.01452 | 0.107681 | ||||||||
\(351\) | −9.61486 | −0.513203 | ||||||||
\(352\) | −2.80078 | −0.149282 | ||||||||
\(353\) | −14.7578 | −0.785477 | −0.392738 | − | 0.919650i | \(-0.628472\pi\) | ||||
−0.392738 | + | 0.919650i | \(0.628472\pi\) | |||||||
\(354\) | −0.500894 | −0.0266222 | ||||||||
\(355\) | 3.11649 | 0.165406 | ||||||||
\(356\) | 10.3602 | 0.549089 | ||||||||
\(357\) | −10.6175 | −0.561938 | ||||||||
\(358\) | −24.0359 | −1.27034 | ||||||||
\(359\) | 22.4878 | 1.18686 | 0.593431 | − | 0.804885i | \(-0.297773\pi\) | ||||
0.593431 | + | 0.804885i | \(0.297773\pi\) | |||||||
\(360\) | 5.15262 | 0.271567 | ||||||||
\(361\) | −10.5860 | −0.557160 | ||||||||
\(362\) | −10.7648 | −0.565788 | ||||||||
\(363\) | 2.98524 | 0.156684 | ||||||||
\(364\) | −4.04621 | −0.212079 | ||||||||
\(365\) | 17.3384 | 0.907534 | ||||||||
\(366\) | 7.16310 | 0.374421 | ||||||||
\(367\) | 37.2009 | 1.94187 | 0.970936 | − | 0.239341i | \(-0.0769314\pi\) | ||||
0.970936 | + | 0.239341i | \(0.0769314\pi\) | |||||||
\(368\) | 6.12514 | 0.319295 | ||||||||
\(369\) | −7.14426 | −0.371915 | ||||||||
\(370\) | −15.5671 | −0.809296 | ||||||||
\(371\) | −14.4702 | −0.751254 | ||||||||
\(372\) | 0.792373 | 0.0410826 | ||||||||
\(373\) | −23.6565 | −1.22489 | −0.612444 | − | 0.790514i | \(-0.709813\pi\) | ||||
−0.612444 | + | 0.790514i | \(0.709813\pi\) | |||||||
\(374\) | −15.4672 | −0.799792 | ||||||||
\(375\) | −9.28238 | −0.479340 | ||||||||
\(376\) | −8.79264 | −0.453446 | ||||||||
\(377\) | 6.07135 | 0.312691 | ||||||||
\(378\) | 9.81503 | 0.504831 | ||||||||
\(379\) | 11.7923 | 0.605732 | 0.302866 | − | 0.953033i | \(-0.402057\pi\) | ||||
0.302866 | + | 0.953033i | \(0.402057\pi\) | |||||||
\(380\) | −7.10000 | −0.364222 | ||||||||
\(381\) | 1.76625 | 0.0904875 | ||||||||
\(382\) | 21.1184 | 1.08051 | ||||||||
\(383\) | −36.7542 | −1.87805 | −0.939025 | − | 0.343848i | \(-0.888269\pi\) | ||||
−0.939025 | + | 0.343848i | \(0.888269\pi\) | |||||||
\(384\) | −0.945997 | −0.0482752 | ||||||||
\(385\) | 13.9327 | 0.710075 | ||||||||
\(386\) | 16.5811 | 0.843958 | ||||||||
\(387\) | 26.0028 | 1.32180 | ||||||||
\(388\) | 1.35477 | 0.0687778 | ||||||||
\(389\) | 28.9807 | 1.46938 | 0.734690 | − | 0.678403i | \(-0.237328\pi\) | ||||
0.734690 | + | 0.678403i | \(0.237328\pi\) | |||||||
\(390\) | −4.60996 | −0.233434 | ||||||||
\(391\) | 33.8260 | 1.71065 | ||||||||
\(392\) | −2.86955 | −0.144934 | ||||||||
\(393\) | 4.70891 | 0.237533 | ||||||||
\(394\) | 17.8425 | 0.898891 | ||||||||
\(395\) | 21.3920 | 1.07635 | ||||||||
\(396\) | 5.89589 | 0.296279 | ||||||||
\(397\) | −34.8860 | −1.75088 | −0.875439 | − | 0.483329i | \(-0.839428\pi\) | ||||
−0.875439 | + | 0.483329i | \(0.839428\pi\) | |||||||
\(398\) | −2.34031 | −0.117309 | ||||||||
\(399\) | −5.57685 | −0.279192 | ||||||||
\(400\) | 0.991226 | 0.0495613 | ||||||||
\(401\) | 0.263485 | 0.0131578 | 0.00657891 | − | 0.999978i | \(-0.497906\pi\) | ||||
0.00657891 | + | 0.999978i | \(0.497906\pi\) | |||||||
\(402\) | 0.233596 | 0.0116507 | ||||||||
\(403\) | 1.66759 | 0.0830686 | ||||||||
\(404\) | −2.66728 | −0.132702 | ||||||||
\(405\) | −4.27533 | −0.212443 | ||||||||
\(406\) | −6.19775 | −0.307589 | ||||||||
\(407\) | −17.8127 | −0.882941 | ||||||||
\(408\) | −5.22425 | −0.258639 | ||||||||
\(409\) | −6.03471 | −0.298397 | −0.149199 | − | 0.988807i | \(-0.547669\pi\) | ||||
−0.149199 | + | 0.988807i | \(0.547669\pi\) | |||||||
\(410\) | −8.30700 | −0.410254 | ||||||||
\(411\) | 15.1861 | 0.749076 | ||||||||
\(412\) | −15.3143 | −0.754480 | ||||||||
\(413\) | 1.07611 | 0.0529517 | ||||||||
\(414\) | −12.8940 | −0.633704 | ||||||||
\(415\) | 36.9097 | 1.81183 | ||||||||
\(416\) | −1.99090 | −0.0976120 | ||||||||
\(417\) | 15.8399 | 0.775683 | ||||||||
\(418\) | −8.12417 | −0.397366 | ||||||||
\(419\) | 17.2897 | 0.844658 | 0.422329 | − | 0.906443i | \(-0.361213\pi\) | ||||
0.422329 | + | 0.906443i | \(0.361213\pi\) | |||||||
\(420\) | 4.70594 | 0.229626 | ||||||||
\(421\) | −21.0468 | −1.02576 | −0.512879 | − | 0.858461i | \(-0.671421\pi\) | ||||
−0.512879 | + | 0.858461i | \(0.671421\pi\) | |||||||
\(422\) | 17.8337 | 0.868131 | ||||||||
\(423\) | 18.5093 | 0.899953 | ||||||||
\(424\) | −7.11992 | −0.345774 | ||||||||
\(425\) | 5.47403 | 0.265529 | ||||||||
\(426\) | 1.20448 | 0.0583570 | ||||||||
\(427\) | −15.3890 | −0.744725 | ||||||||
\(428\) | 14.4192 | 0.696980 | ||||||||
\(429\) | −5.27494 | −0.254677 | ||||||||
\(430\) | 30.2349 | 1.45805 | ||||||||
\(431\) | −37.9200 | −1.82654 | −0.913272 | − | 0.407350i | \(-0.866453\pi\) | ||||
−0.913272 | + | 0.407350i | \(0.866453\pi\) | |||||||
\(432\) | 4.82940 | 0.232355 | ||||||||
\(433\) | −31.0593 | −1.49262 | −0.746308 | − | 0.665601i | \(-0.768175\pi\) | ||||
−0.746308 | + | 0.665601i | \(0.768175\pi\) | |||||||
\(434\) | −1.70231 | −0.0817135 | ||||||||
\(435\) | −7.06128 | −0.338562 | ||||||||
\(436\) | −2.62093 | −0.125520 | ||||||||
\(437\) | 17.7671 | 0.849915 | ||||||||
\(438\) | 6.70103 | 0.320187 | ||||||||
\(439\) | 14.5169 | 0.692854 | 0.346427 | − | 0.938077i | \(-0.387395\pi\) | ||||
0.346427 | + | 0.938077i | \(0.387395\pi\) | |||||||
\(440\) | 6.85545 | 0.326821 | ||||||||
\(441\) | 6.04066 | 0.287651 | ||||||||
\(442\) | −10.9947 | −0.522965 | ||||||||
\(443\) | 2.05491 | 0.0976315 | 0.0488157 | − | 0.998808i | \(-0.484455\pi\) | ||||
0.0488157 | + | 0.998808i | \(0.484455\pi\) | |||||||
\(444\) | −6.01645 | −0.285528 | ||||||||
\(445\) | −25.3586 | −1.20211 | ||||||||
\(446\) | −3.72901 | −0.176574 | ||||||||
\(447\) | 9.11038 | 0.430906 | ||||||||
\(448\) | 2.03235 | 0.0960195 | ||||||||
\(449\) | 14.0686 | 0.663937 | 0.331969 | − | 0.943290i | \(-0.392287\pi\) | ||||
0.331969 | + | 0.943290i | \(0.392287\pi\) | |||||||
\(450\) | −2.08662 | −0.0983642 | ||||||||
\(451\) | −9.50528 | −0.447586 | ||||||||
\(452\) | −11.3017 | −0.531589 | ||||||||
\(453\) | −10.4598 | −0.491444 | ||||||||
\(454\) | −27.0598 | −1.26998 | ||||||||
\(455\) | 9.90390 | 0.464302 | ||||||||
\(456\) | −2.74404 | −0.128501 | ||||||||
\(457\) | 2.31968 | 0.108510 | 0.0542550 | − | 0.998527i | \(-0.482722\pi\) | ||||
0.0542550 | + | 0.998527i | \(0.482722\pi\) | |||||||
\(458\) | −13.4293 | −0.627508 | ||||||||
\(459\) | 26.6703 | 1.24486 | ||||||||
\(460\) | −14.9925 | −0.699028 | ||||||||
\(461\) | −5.12438 | −0.238666 | −0.119333 | − | 0.992854i | \(-0.538076\pi\) | ||||
−0.119333 | + | 0.992854i | \(0.538076\pi\) | |||||||
\(462\) | 5.38477 | 0.250522 | ||||||||
\(463\) | 14.2523 | 0.662360 | 0.331180 | − | 0.943568i | \(-0.392553\pi\) | ||||
0.331180 | + | 0.943568i | \(0.392553\pi\) | |||||||
\(464\) | −3.04955 | −0.141572 | ||||||||
\(465\) | −1.93949 | −0.0899417 | ||||||||
\(466\) | 25.4347 | 1.17824 | ||||||||
\(467\) | 13.4011 | 0.620128 | 0.310064 | − | 0.950716i | \(-0.399650\pi\) | ||||
0.310064 | + | 0.950716i | \(0.399650\pi\) | |||||||
\(468\) | 4.19103 | 0.193730 | ||||||||
\(469\) | −0.501849 | −0.0231733 | ||||||||
\(470\) | 21.5217 | 0.992724 | ||||||||
\(471\) | −22.3786 | −1.03115 | ||||||||
\(472\) | 0.529488 | 0.0243717 | ||||||||
\(473\) | 34.5962 | 1.59074 | ||||||||
\(474\) | 8.26767 | 0.379747 | ||||||||
\(475\) | 2.87523 | 0.131925 | ||||||||
\(476\) | 11.2236 | 0.514434 | ||||||||
\(477\) | 14.9881 | 0.686257 | ||||||||
\(478\) | −15.9974 | −0.731702 | ||||||||
\(479\) | 34.5704 | 1.57956 | 0.789780 | − | 0.613390i | \(-0.210195\pi\) | ||||
0.789780 | + | 0.613390i | \(0.210195\pi\) | |||||||
\(480\) | 2.31551 | 0.105688 | ||||||||
\(481\) | −12.6619 | −0.577335 | ||||||||
\(482\) | 29.8860 | 1.36127 | ||||||||
\(483\) | −11.7762 | −0.535834 | ||||||||
\(484\) | −3.15565 | −0.143439 | ||||||||
\(485\) | −3.31606 | −0.150574 | ||||||||
\(486\) | −16.1405 | −0.732150 | ||||||||
\(487\) | 21.3436 | 0.967170 | 0.483585 | − | 0.875297i | \(-0.339334\pi\) | ||||
0.483585 | + | 0.875297i | \(0.339334\pi\) | |||||||
\(488\) | −7.57201 | −0.342769 | ||||||||
\(489\) | −1.40911 | −0.0637223 | ||||||||
\(490\) | 7.02379 | 0.317303 | ||||||||
\(491\) | 38.9925 | 1.75971 | 0.879854 | − | 0.475245i | \(-0.157640\pi\) | ||||
0.879854 | + | 0.475245i | \(0.157640\pi\) | |||||||
\(492\) | −3.21053 | −0.144742 | ||||||||
\(493\) | −16.8411 | −0.758484 | ||||||||
\(494\) | −5.77498 | −0.259828 | ||||||||
\(495\) | −14.4313 | −0.648641 | ||||||||
\(496\) | −0.837606 | −0.0376096 | ||||||||
\(497\) | −2.58766 | −0.116072 | ||||||||
\(498\) | 14.2650 | 0.639232 | ||||||||
\(499\) | −34.5883 | −1.54838 | −0.774191 | − | 0.632952i | \(-0.781843\pi\) | ||||
−0.774191 | + | 0.632952i | \(0.781843\pi\) | |||||||
\(500\) | 9.81227 | 0.438818 | ||||||||
\(501\) | −9.56385 | −0.427281 | ||||||||
\(502\) | 22.8719 | 1.02082 | ||||||||
\(503\) | 0.0152657 | 0.000680664 0 | 0.000340332 | − | 1.00000i | \(-0.499892\pi\) | ||||
0.000340332 | 1.00000i | \(0.499892\pi\) | ||||||||
\(504\) | −4.27828 | −0.190570 | ||||||||
\(505\) | 6.52870 | 0.290523 | ||||||||
\(506\) | −17.1551 | −0.762639 | ||||||||
\(507\) | 8.54832 | 0.379644 | ||||||||
\(508\) | −1.86707 | −0.0828380 | ||||||||
\(509\) | 33.0886 | 1.46663 | 0.733313 | − | 0.679891i | \(-0.237973\pi\) | ||||
0.733313 | + | 0.679891i | \(0.237973\pi\) | |||||||
\(510\) | 12.7874 | 0.566235 | ||||||||
\(511\) | −14.3963 | −0.636854 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 14.0086 | 0.618493 | ||||||||
\(514\) | 21.6713 | 0.955879 | ||||||||
\(515\) | 37.4847 | 1.65177 | ||||||||
\(516\) | 11.6853 | 0.514417 | ||||||||
\(517\) | 24.6262 | 1.08306 | ||||||||
\(518\) | 12.9256 | 0.567916 | ||||||||
\(519\) | 6.73209 | 0.295506 | ||||||||
\(520\) | 4.87312 | 0.213701 | ||||||||
\(521\) | 2.38215 | 0.104364 | 0.0521820 | − | 0.998638i | \(-0.483382\pi\) | ||||
0.0521820 | + | 0.998638i | \(0.483382\pi\) | |||||||
\(522\) | 6.41958 | 0.280977 | ||||||||
\(523\) | −2.31364 | −0.101169 | −0.0505843 | − | 0.998720i | \(-0.516108\pi\) | ||||
−0.0505843 | + | 0.998720i | \(0.516108\pi\) | |||||||
\(524\) | −4.97772 | −0.217453 | ||||||||
\(525\) | −1.90573 | −0.0831728 | ||||||||
\(526\) | −1.96752 | −0.0857880 | ||||||||
\(527\) | −4.62567 | −0.201497 | ||||||||
\(528\) | 2.64953 | 0.115306 | ||||||||
\(529\) | 14.5173 | 0.631187 | ||||||||
\(530\) | 17.4274 | 0.756999 | ||||||||
\(531\) | −1.11462 | −0.0483704 | ||||||||
\(532\) | 5.89521 | 0.255590 | ||||||||
\(533\) | −6.75672 | −0.292666 | ||||||||
\(534\) | −9.80071 | −0.424118 | ||||||||
\(535\) | −35.2940 | −1.52589 | ||||||||
\(536\) | −0.246931 | −0.0106658 | ||||||||
\(537\) | 22.7379 | 0.981212 | ||||||||
\(538\) | −7.94985 | −0.342742 | ||||||||
\(539\) | 8.03697 | 0.346177 | ||||||||
\(540\) | −11.8209 | −0.508691 | ||||||||
\(541\) | 34.4381 | 1.48061 | 0.740306 | − | 0.672270i | \(-0.234681\pi\) | ||||
0.740306 | + | 0.672270i | \(0.234681\pi\) | |||||||
\(542\) | −23.2965 | −1.00067 | ||||||||
\(543\) | 10.1835 | 0.437016 | ||||||||
\(544\) | 5.52248 | 0.236774 | ||||||||
\(545\) | 6.41524 | 0.274799 | ||||||||
\(546\) | 3.82770 | 0.163810 | ||||||||
\(547\) | 40.0425 | 1.71209 | 0.856046 | − | 0.516900i | \(-0.172914\pi\) | ||||
0.856046 | + | 0.516900i | \(0.172914\pi\) | |||||||
\(548\) | −16.0530 | −0.685751 | ||||||||
\(549\) | 15.9398 | 0.680292 | ||||||||
\(550\) | −2.77620 | −0.118378 | ||||||||
\(551\) | −8.84578 | −0.376843 | ||||||||
\(552\) | −5.79436 | −0.246624 | ||||||||
\(553\) | −17.7620 | −0.755317 | ||||||||
\(554\) | −27.0992 | −1.15133 | ||||||||
\(555\) | 14.7265 | 0.625103 | ||||||||
\(556\) | −16.7441 | −0.710110 | ||||||||
\(557\) | −24.8877 | −1.05453 | −0.527263 | − | 0.849702i | \(-0.676782\pi\) | ||||
−0.527263 | + | 0.849702i | \(0.676782\pi\) | |||||||
\(558\) | 1.76324 | 0.0746438 | ||||||||
\(559\) | 24.5923 | 1.04014 | ||||||||
\(560\) | −4.97458 | −0.210214 | ||||||||
\(561\) | 14.6320 | 0.617762 | ||||||||
\(562\) | −10.1699 | −0.428992 | ||||||||
\(563\) | −5.50949 | −0.232197 | −0.116099 | − | 0.993238i | \(-0.537039\pi\) | ||||
−0.116099 | + | 0.993238i | \(0.537039\pi\) | |||||||
\(564\) | 8.31781 | 0.350243 | ||||||||
\(565\) | 27.6632 | 1.16380 | ||||||||
\(566\) | −19.4096 | −0.815845 | ||||||||
\(567\) | 3.54985 | 0.149080 | ||||||||
\(568\) | −1.27323 | −0.0534237 | ||||||||
\(569\) | 32.9404 | 1.38093 | 0.690467 | − | 0.723364i | \(-0.257405\pi\) | ||||
0.690467 | + | 0.723364i | \(0.257405\pi\) | |||||||
\(570\) | 6.71658 | 0.281326 | ||||||||
\(571\) | 42.1235 | 1.76281 | 0.881407 | − | 0.472358i | \(-0.156597\pi\) | ||||
0.881407 | + | 0.472358i | \(0.156597\pi\) | |||||||
\(572\) | 5.57607 | 0.233147 | ||||||||
\(573\) | −19.9779 | −0.834590 | ||||||||
\(574\) | 6.89739 | 0.287892 | ||||||||
\(575\) | 6.07139 | 0.253195 | ||||||||
\(576\) | −2.10509 | −0.0877121 | ||||||||
\(577\) | −24.5786 | −1.02322 | −0.511611 | − | 0.859217i | \(-0.670951\pi\) | ||||
−0.511611 | + | 0.859217i | \(0.670951\pi\) | |||||||
\(578\) | 13.4978 | 0.561435 | ||||||||
\(579\) | −15.6857 | −0.651876 | ||||||||
\(580\) | 7.46438 | 0.309941 | ||||||||
\(581\) | −30.6466 | −1.27143 | ||||||||
\(582\) | −1.28160 | −0.0531242 | ||||||||
\(583\) | 19.9413 | 0.825885 | ||||||||
\(584\) | −7.08356 | −0.293120 | ||||||||
\(585\) | −10.2584 | −0.424131 | ||||||||
\(586\) | −4.93456 | −0.203845 | ||||||||
\(587\) | 25.2733 | 1.04314 | 0.521570 | − | 0.853209i | \(-0.325347\pi\) | ||||
0.521570 | + | 0.853209i | \(0.325347\pi\) | |||||||
\(588\) | 2.71459 | 0.111948 | ||||||||
\(589\) | −2.42963 | −0.100111 | ||||||||
\(590\) | −1.29603 | −0.0533566 | ||||||||
\(591\) | −16.8789 | −0.694307 | ||||||||
\(592\) | 6.35990 | 0.261390 | ||||||||
\(593\) | 10.3757 | 0.426079 | 0.213040 | − | 0.977044i | \(-0.431664\pi\) | ||||
0.213040 | + | 0.977044i | \(0.431664\pi\) | |||||||
\(594\) | −13.5261 | −0.554981 | ||||||||
\(595\) | −27.4720 | −1.12624 | ||||||||
\(596\) | −9.63045 | −0.394479 | ||||||||
\(597\) | 2.21393 | 0.0906102 | ||||||||
\(598\) | −12.1945 | −0.498672 | ||||||||
\(599\) | 14.9728 | 0.611771 | 0.305885 | − | 0.952068i | \(-0.401048\pi\) | ||||
0.305885 | + | 0.952068i | \(0.401048\pi\) | |||||||
\(600\) | −0.937697 | −0.0382813 | ||||||||
\(601\) | 25.0716 | 1.02269 | 0.511347 | − | 0.859375i | \(-0.329147\pi\) | ||||
0.511347 | + | 0.859375i | \(0.329147\pi\) | |||||||
\(602\) | −25.1043 | −1.02318 | ||||||||
\(603\) | 0.519811 | 0.0211683 | ||||||||
\(604\) | 11.0569 | 0.449899 | ||||||||
\(605\) | 7.72408 | 0.314029 | ||||||||
\(606\) | 2.52324 | 0.102500 | ||||||||
\(607\) | 5.27851 | 0.214248 | 0.107124 | − | 0.994246i | \(-0.465836\pi\) | ||||
0.107124 | + | 0.994246i | \(0.465836\pi\) | |||||||
\(608\) | 2.90068 | 0.117638 | ||||||||
\(609\) | 5.86306 | 0.237583 | ||||||||
\(610\) | 18.5340 | 0.750419 | ||||||||
\(611\) | 17.5053 | 0.708188 | ||||||||
\(612\) | −11.6253 | −0.469926 | ||||||||
\(613\) | 35.5060 | 1.43407 | 0.717037 | − | 0.697036i | \(-0.245498\pi\) | ||||
0.717037 | + | 0.697036i | \(0.245498\pi\) | |||||||
\(614\) | −15.2499 | −0.615438 | ||||||||
\(615\) | 7.85840 | 0.316881 | ||||||||
\(616\) | −5.69216 | −0.229344 | ||||||||
\(617\) | −16.3935 | −0.659976 | −0.329988 | − | 0.943985i | \(-0.607045\pi\) | ||||
−0.329988 | + | 0.943985i | \(0.607045\pi\) | |||||||
\(618\) | 14.4873 | 0.582763 | ||||||||
\(619\) | −35.3362 | −1.42028 | −0.710141 | − | 0.704059i | \(-0.751369\pi\) | ||||
−0.710141 | + | 0.704059i | \(0.751369\pi\) | |||||||
\(620\) | 2.05021 | 0.0823383 | ||||||||
\(621\) | 29.5807 | 1.18703 | ||||||||
\(622\) | 21.6782 | 0.869218 | ||||||||
\(623\) | 21.0556 | 0.843573 | ||||||||
\(624\) | 1.88339 | 0.0753958 | ||||||||
\(625\) | −28.9736 | −1.15894 | ||||||||
\(626\) | −15.4715 | −0.618364 | ||||||||
\(627\) | 7.68544 | 0.306927 | ||||||||
\(628\) | 23.6561 | 0.943982 | ||||||||
\(629\) | 35.1225 | 1.40042 | ||||||||
\(630\) | 10.4719 | 0.417212 | ||||||||
\(631\) | 8.66161 | 0.344813 | 0.172407 | − | 0.985026i | \(-0.444846\pi\) | ||||
0.172407 | + | 0.985026i | \(0.444846\pi\) | |||||||
\(632\) | −8.73964 | −0.347644 | ||||||||
\(633\) | −16.8706 | −0.670547 | ||||||||
\(634\) | −1.67493 | −0.0665199 | ||||||||
\(635\) | 4.57003 | 0.181356 | ||||||||
\(636\) | 6.73542 | 0.267077 | ||||||||
\(637\) | 5.71299 | 0.226357 | ||||||||
\(638\) | 8.54111 | 0.338146 | ||||||||
\(639\) | 2.68027 | 0.106030 | ||||||||
\(640\) | −2.44770 | −0.0967538 | ||||||||
\(641\) | 29.1668 | 1.15202 | 0.576010 | − | 0.817442i | \(-0.304609\pi\) | ||||
0.576010 | + | 0.817442i | \(0.304609\pi\) | |||||||
\(642\) | −13.6406 | −0.538350 | ||||||||
\(643\) | −26.7037 | −1.05309 | −0.526546 | − | 0.850146i | \(-0.676513\pi\) | ||||
−0.526546 | + | 0.850146i | \(0.676513\pi\) | |||||||
\(644\) | 12.4484 | 0.490537 | ||||||||
\(645\) | −28.6021 | −1.12621 | ||||||||
\(646\) | 16.0190 | 0.630258 | ||||||||
\(647\) | 29.4245 | 1.15680 | 0.578398 | − | 0.815755i | \(-0.303678\pi\) | ||||
0.578398 | + | 0.815755i | \(0.303678\pi\) | |||||||
\(648\) | 1.74667 | 0.0686157 | ||||||||
\(649\) | −1.48298 | −0.0582120 | ||||||||
\(650\) | −1.97343 | −0.0774044 | ||||||||
\(651\) | 1.61038 | 0.0631158 | ||||||||
\(652\) | 1.48955 | 0.0583354 | ||||||||
\(653\) | −12.0244 | −0.470552 | −0.235276 | − | 0.971929i | \(-0.575599\pi\) | ||||
−0.235276 | + | 0.971929i | \(0.575599\pi\) | |||||||
\(654\) | 2.47939 | 0.0969518 | ||||||||
\(655\) | 12.1839 | 0.476066 | ||||||||
\(656\) | 3.39380 | 0.132506 | ||||||||
\(657\) | 14.9115 | 0.581754 | ||||||||
\(658\) | −17.8697 | −0.696635 | ||||||||
\(659\) | 47.0705 | 1.83361 | 0.916803 | − | 0.399340i | \(-0.130761\pi\) | ||||
0.916803 | + | 0.399340i | \(0.130761\pi\) | |||||||
\(660\) | −6.48524 | −0.252438 | ||||||||
\(661\) | −13.1809 | −0.512677 | −0.256338 | − | 0.966587i | \(-0.582516\pi\) | ||||
−0.256338 | + | 0.966587i | \(0.582516\pi\) | |||||||
\(662\) | 15.1393 | 0.588406 | ||||||||
\(663\) | 10.4010 | 0.403940 | ||||||||
\(664\) | −15.0794 | −0.585193 | ||||||||
\(665\) | −14.4297 | −0.559559 | ||||||||
\(666\) | −13.3882 | −0.518781 | ||||||||
\(667\) | −18.6789 | −0.723250 | ||||||||
\(668\) | 10.1098 | 0.391160 | ||||||||
\(669\) | 3.52763 | 0.136386 | ||||||||
\(670\) | 0.604411 | 0.0233504 | ||||||||
\(671\) | 21.2075 | 0.818706 | ||||||||
\(672\) | −1.92260 | −0.0741658 | ||||||||
\(673\) | −21.3885 | −0.824465 | −0.412232 | − | 0.911079i | \(-0.635251\pi\) | ||||
−0.412232 | + | 0.911079i | \(0.635251\pi\) | |||||||
\(674\) | −14.3131 | −0.551322 | ||||||||
\(675\) | 4.78703 | 0.184253 | ||||||||
\(676\) | −9.03631 | −0.347551 | ||||||||
\(677\) | 4.15572 | 0.159717 | 0.0798587 | − | 0.996806i | \(-0.474553\pi\) | ||||
0.0798587 | + | 0.996806i | \(0.474553\pi\) | |||||||
\(678\) | 10.6914 | 0.410601 | ||||||||
\(679\) | 2.75336 | 0.105664 | ||||||||
\(680\) | −13.5174 | −0.518367 | ||||||||
\(681\) | 25.5985 | 0.980935 | ||||||||
\(682\) | 2.34595 | 0.0898310 | ||||||||
\(683\) | −24.6042 | −0.941452 | −0.470726 | − | 0.882279i | \(-0.656008\pi\) | ||||
−0.470726 | + | 0.882279i | \(0.656008\pi\) | |||||||
\(684\) | −6.10620 | −0.233476 | ||||||||
\(685\) | 39.2930 | 1.50131 | ||||||||
\(686\) | −20.0584 | −0.765833 | ||||||||
\(687\) | 12.7040 | 0.484689 | ||||||||
\(688\) | −12.3524 | −0.470929 | ||||||||
\(689\) | 14.1751 | 0.540027 | ||||||||
\(690\) | 14.1828 | 0.539932 | ||||||||
\(691\) | −34.8010 | −1.32389 | −0.661947 | − | 0.749551i | \(-0.730270\pi\) | ||||
−0.661947 | + | 0.749551i | \(0.730270\pi\) | |||||||
\(692\) | −7.11640 | −0.270525 | ||||||||
\(693\) | 11.9825 | 0.455178 | ||||||||
\(694\) | −29.7433 | −1.12904 | ||||||||
\(695\) | 40.9846 | 1.55463 | ||||||||
\(696\) | 2.88487 | 0.109351 | ||||||||
\(697\) | 18.7422 | 0.709912 | ||||||||
\(698\) | −18.8272 | −0.712619 | ||||||||
\(699\) | −24.0612 | −0.910078 | ||||||||
\(700\) | 2.01452 | 0.0761416 | ||||||||
\(701\) | 33.1897 | 1.25356 | 0.626778 | − | 0.779198i | \(-0.284373\pi\) | ||||
0.626778 | + | 0.779198i | \(0.284373\pi\) | |||||||
\(702\) | −9.61486 | −0.362889 | ||||||||
\(703\) | 18.4481 | 0.695782 | ||||||||
\(704\) | −2.80078 | −0.105558 | ||||||||
\(705\) | −20.3595 | −0.766783 | ||||||||
\(706\) | −14.7578 | −0.555416 | ||||||||
\(707\) | −5.42085 | −0.203872 | ||||||||
\(708\) | −0.500894 | −0.0188247 | ||||||||
\(709\) | −33.6642 | −1.26429 | −0.632143 | − | 0.774852i | \(-0.717825\pi\) | ||||
−0.632143 | + | 0.774852i | \(0.717825\pi\) | |||||||
\(710\) | 3.11649 | 0.116960 | ||||||||
\(711\) | 18.3977 | 0.689968 | ||||||||
\(712\) | 10.3602 | 0.388265 | ||||||||
\(713\) | −5.13045 | −0.192137 | ||||||||
\(714\) | −10.6175 | −0.397350 | ||||||||
\(715\) | −13.6485 | −0.510426 | ||||||||
\(716\) | −24.0359 | −0.898263 | ||||||||
\(717\) | 15.1335 | 0.565169 | ||||||||
\(718\) | 22.4878 | 0.839238 | ||||||||
\(719\) | −35.4095 | −1.32055 | −0.660276 | − | 0.751023i | \(-0.729561\pi\) | ||||
−0.660276 | + | 0.751023i | \(0.729561\pi\) | |||||||
\(720\) | 5.15262 | 0.192027 | ||||||||
\(721\) | −31.1240 | −1.15912 | ||||||||
\(722\) | −10.5860 | −0.393971 | ||||||||
\(723\) | −28.2720 | −1.05145 | ||||||||
\(724\) | −10.7648 | −0.400072 | ||||||||
\(725\) | −3.02279 | −0.112264 | ||||||||
\(726\) | 2.98524 | 0.110793 | ||||||||
\(727\) | −47.5717 | −1.76434 | −0.882168 | − | 0.470934i | \(-0.843917\pi\) | ||||
−0.882168 | + | 0.470934i | \(0.843917\pi\) | |||||||
\(728\) | −4.04621 | −0.149962 | ||||||||
\(729\) | 10.0289 | 0.371440 | ||||||||
\(730\) | 17.3384 | 0.641724 | ||||||||
\(731\) | −68.2157 | −2.52305 | ||||||||
\(732\) | 7.16310 | 0.264756 | ||||||||
\(733\) | −6.24495 | −0.230662 | −0.115331 | − | 0.993327i | \(-0.536793\pi\) | ||||
−0.115331 | + | 0.993327i | \(0.536793\pi\) | |||||||
\(734\) | 37.2009 | 1.37311 | ||||||||
\(735\) | −6.64449 | −0.245086 | ||||||||
\(736\) | 6.12514 | 0.225776 | ||||||||
\(737\) | 0.691597 | 0.0254753 | ||||||||
\(738\) | −7.14426 | −0.262984 | ||||||||
\(739\) | −21.8883 | −0.805174 | −0.402587 | − | 0.915382i | \(-0.631889\pi\) | ||||
−0.402587 | + | 0.915382i | \(0.631889\pi\) | |||||||
\(740\) | −15.5671 | −0.572259 | ||||||||
\(741\) | 5.46311 | 0.200692 | ||||||||
\(742\) | −14.4702 | −0.531217 | ||||||||
\(743\) | 41.8899 | 1.53679 | 0.768396 | − | 0.639974i | \(-0.221055\pi\) | ||||
0.768396 | + | 0.639974i | \(0.221055\pi\) | |||||||
\(744\) | 0.792373 | 0.0290498 | ||||||||
\(745\) | 23.5724 | 0.863627 | ||||||||
\(746\) | −23.6565 | −0.866126 | ||||||||
\(747\) | 31.7434 | 1.16143 | ||||||||
\(748\) | −15.4672 | −0.565538 | ||||||||
\(749\) | 29.3050 | 1.07078 | ||||||||
\(750\) | −9.28238 | −0.338944 | ||||||||
\(751\) | 14.7118 | 0.536843 | 0.268421 | − | 0.963302i | \(-0.413498\pi\) | ||||
0.268421 | + | 0.963302i | \(0.413498\pi\) | |||||||
\(752\) | −8.79264 | −0.320635 | ||||||||
\(753\) | −21.6367 | −0.788487 | ||||||||
\(754\) | 6.07135 | 0.221106 | ||||||||
\(755\) | −27.0639 | −0.984958 | ||||||||
\(756\) | 9.81503 | 0.356969 | ||||||||
\(757\) | −43.7693 | −1.59082 | −0.795411 | − | 0.606070i | \(-0.792745\pi\) | ||||
−0.795411 | + | 0.606070i | \(0.792745\pi\) | |||||||
\(758\) | 11.7923 | 0.428317 | ||||||||
\(759\) | 16.2287 | 0.589065 | ||||||||
\(760\) | −7.10000 | −0.257544 | ||||||||
\(761\) | −33.5741 | −1.21706 | −0.608531 | − | 0.793530i | \(-0.708241\pi\) | ||||
−0.608531 | + | 0.793530i | \(0.708241\pi\) | |||||||
\(762\) | 1.76625 | 0.0639843 | ||||||||
\(763\) | −5.32665 | −0.192838 | ||||||||
\(764\) | 21.1184 | 0.764037 | ||||||||
\(765\) | 28.4553 | 1.02880 | ||||||||
\(766\) | −36.7542 | −1.32798 | ||||||||
\(767\) | −1.05416 | −0.0380634 | ||||||||
\(768\) | −0.945997 | −0.0341357 | ||||||||
\(769\) | 47.2920 | 1.70539 | 0.852697 | − | 0.522406i | \(-0.174966\pi\) | ||||
0.852697 | + | 0.522406i | \(0.174966\pi\) | |||||||
\(770\) | 13.9327 | 0.502099 | ||||||||
\(771\) | −20.5010 | −0.738324 | ||||||||
\(772\) | 16.5811 | 0.596768 | ||||||||
\(773\) | 15.0744 | 0.542190 | 0.271095 | − | 0.962553i | \(-0.412614\pi\) | ||||
0.271095 | + | 0.962553i | \(0.412614\pi\) | |||||||
\(774\) | 26.0028 | 0.934653 | ||||||||
\(775\) | −0.830257 | −0.0298237 | ||||||||
\(776\) | 1.35477 | 0.0486332 | ||||||||
\(777\) | −12.2275 | −0.438660 | ||||||||
\(778\) | 28.9807 | 1.03901 | ||||||||
\(779\) | 9.84435 | 0.352710 | ||||||||
\(780\) | −4.60996 | −0.165063 | ||||||||
\(781\) | 3.56604 | 0.127603 | ||||||||
\(782\) | 33.8260 | 1.20961 | ||||||||
\(783\) | −14.7275 | −0.526318 | ||||||||
\(784\) | −2.86955 | −0.102484 | ||||||||
\(785\) | −57.9030 | −2.06665 | ||||||||
\(786\) | 4.70891 | 0.167961 | ||||||||
\(787\) | −28.4058 | −1.01256 | −0.506279 | − | 0.862370i | \(-0.668979\pi\) | ||||
−0.506279 | + | 0.862370i | \(0.668979\pi\) | |||||||
\(788\) | 17.8425 | 0.635612 | ||||||||
\(789\) | 1.86127 | 0.0662629 | ||||||||
\(790\) | 21.3920 | 0.761093 | ||||||||
\(791\) | −22.9691 | −0.816686 | ||||||||
\(792\) | 5.89589 | 0.209501 | ||||||||
\(793\) | 15.0751 | 0.535333 | ||||||||
\(794\) | −34.8860 | −1.23806 | ||||||||
\(795\) | −16.4863 | −0.584708 | ||||||||
\(796\) | −2.34031 | −0.0829503 | ||||||||
\(797\) | 10.1299 | 0.358819 | 0.179409 | − | 0.983775i | \(-0.442581\pi\) | ||||
0.179409 | + | 0.983775i | \(0.442581\pi\) | |||||||
\(798\) | −5.57685 | −0.197418 | ||||||||
\(799\) | −48.5572 | −1.71783 | ||||||||
\(800\) | 0.991226 | 0.0350451 | ||||||||
\(801\) | −21.8091 | −0.770588 | ||||||||
\(802\) | 0.263485 | 0.00930398 | ||||||||
\(803\) | 19.8395 | 0.700120 | ||||||||
\(804\) | 0.233596 | 0.00823828 | ||||||||
\(805\) | −30.4700 | −1.07393 | ||||||||
\(806\) | 1.66759 | 0.0587384 | ||||||||
\(807\) | 7.52053 | 0.264735 | ||||||||
\(808\) | −2.66728 | −0.0938346 | ||||||||
\(809\) | −19.6349 | −0.690327 | −0.345164 | − | 0.938543i | \(-0.612177\pi\) | ||||
−0.345164 | + | 0.938543i | \(0.612177\pi\) | |||||||
\(810\) | −4.27533 | −0.150220 | ||||||||
\(811\) | 32.6240 | 1.14558 | 0.572791 | − | 0.819701i | \(-0.305861\pi\) | ||||
0.572791 | + | 0.819701i | \(0.305861\pi\) | |||||||
\(812\) | −6.19775 | −0.217499 | ||||||||
\(813\) | 22.0385 | 0.772922 | ||||||||
\(814\) | −17.8127 | −0.624334 | ||||||||
\(815\) | −3.64598 | −0.127713 | ||||||||
\(816\) | −5.22425 | −0.182885 | ||||||||
\(817\) | −35.8303 | −1.25354 | ||||||||
\(818\) | −6.03471 | −0.210999 | ||||||||
\(819\) | 8.51763 | 0.297630 | ||||||||
\(820\) | −8.30700 | −0.290093 | ||||||||
\(821\) | −50.2708 | −1.75446 | −0.877232 | − | 0.480066i | \(-0.840613\pi\) | ||||
−0.877232 | + | 0.480066i | \(0.840613\pi\) | |||||||
\(822\) | 15.1861 | 0.529677 | ||||||||
\(823\) | 24.3559 | 0.848992 | 0.424496 | − | 0.905430i | \(-0.360451\pi\) | ||||
0.424496 | + | 0.905430i | \(0.360451\pi\) | |||||||
\(824\) | −15.3143 | −0.533498 | ||||||||
\(825\) | 2.62628 | 0.0914353 | ||||||||
\(826\) | 1.07611 | 0.0374425 | ||||||||
\(827\) | −36.9365 | −1.28441 | −0.642204 | − | 0.766533i | \(-0.721980\pi\) | ||||
−0.642204 | + | 0.766533i | \(0.721980\pi\) | |||||||
\(828\) | −12.8940 | −0.448096 | ||||||||
\(829\) | −35.1963 | −1.22242 | −0.611209 | − | 0.791470i | \(-0.709316\pi\) | ||||
−0.611209 | + | 0.791470i | \(0.709316\pi\) | |||||||
\(830\) | 36.9097 | 1.28116 | ||||||||
\(831\) | 25.6358 | 0.889294 | ||||||||
\(832\) | −1.99090 | −0.0690221 | ||||||||
\(833\) | −15.8470 | −0.549068 | ||||||||
\(834\) | 15.8399 | 0.548491 | ||||||||
\(835\) | −24.7458 | −0.856362 | ||||||||
\(836\) | −8.12417 | −0.280980 | ||||||||
\(837\) | −4.04514 | −0.139820 | ||||||||
\(838\) | 17.2897 | 0.597263 | ||||||||
\(839\) | −45.7810 | −1.58053 | −0.790267 | − | 0.612762i | \(-0.790058\pi\) | ||||
−0.790267 | + | 0.612762i | \(0.790058\pi\) | |||||||
\(840\) | 4.70594 | 0.162370 | ||||||||
\(841\) | −19.7002 | −0.679319 | ||||||||
\(842\) | −21.0468 | −0.725320 | ||||||||
\(843\) | 9.62072 | 0.331355 | ||||||||
\(844\) | 17.8337 | 0.613861 | ||||||||
\(845\) | 22.1182 | 0.760888 | ||||||||
\(846\) | 18.5093 | 0.636363 | ||||||||
\(847\) | −6.41339 | −0.220367 | ||||||||
\(848\) | −7.11992 | −0.244499 | ||||||||
\(849\) | 18.3614 | 0.630162 | ||||||||
\(850\) | 5.47403 | 0.187758 | ||||||||
\(851\) | 38.9553 | 1.33537 | ||||||||
\(852\) | 1.20448 | 0.0412647 | ||||||||
\(853\) | 16.9231 | 0.579435 | 0.289718 | − | 0.957112i | \(-0.406439\pi\) | ||||
0.289718 | + | 0.957112i | \(0.406439\pi\) | |||||||
\(854\) | −15.3890 | −0.526600 | ||||||||
\(855\) | 14.9461 | 0.511147 | ||||||||
\(856\) | 14.4192 | 0.492840 | ||||||||
\(857\) | −1.71618 | −0.0586234 | −0.0293117 | − | 0.999570i | \(-0.509332\pi\) | ||||
−0.0293117 | + | 0.999570i | \(0.509332\pi\) | |||||||
\(858\) | −5.27494 | −0.180084 | ||||||||
\(859\) | −49.5674 | −1.69122 | −0.845609 | − | 0.533803i | \(-0.820762\pi\) | ||||
−0.845609 | + | 0.533803i | \(0.820762\pi\) | |||||||
\(860\) | 30.2349 | 1.03100 | ||||||||
\(861\) | −6.52491 | −0.222368 | ||||||||
\(862\) | −37.9200 | −1.29156 | ||||||||
\(863\) | 5.09731 | 0.173514 | 0.0867572 | − | 0.996229i | \(-0.472350\pi\) | ||||
0.0867572 | + | 0.996229i | \(0.472350\pi\) | |||||||
\(864\) | 4.82940 | 0.164300 | ||||||||
\(865\) | 17.4188 | 0.592257 | ||||||||
\(866\) | −31.0593 | −1.05544 | ||||||||
\(867\) | −12.7689 | −0.433654 | ||||||||
\(868\) | −1.70231 | −0.0577802 | ||||||||
\(869\) | 24.4778 | 0.830351 | ||||||||
\(870\) | −7.06128 | −0.239400 | ||||||||
\(871\) | 0.491614 | 0.0166577 | ||||||||
\(872\) | −2.62093 | −0.0887558 | ||||||||
\(873\) | −2.85190 | −0.0965223 | ||||||||
\(874\) | 17.7671 | 0.600981 | ||||||||
\(875\) | 19.9420 | 0.674162 | ||||||||
\(876\) | 6.70103 | 0.226407 | ||||||||
\(877\) | 37.3296 | 1.26053 | 0.630265 | − | 0.776380i | \(-0.282946\pi\) | ||||
0.630265 | + | 0.776380i | \(0.282946\pi\) | |||||||
\(878\) | 14.5169 | 0.489922 | ||||||||
\(879\) | 4.66808 | 0.157450 | ||||||||
\(880\) | 6.85545 | 0.231097 | ||||||||
\(881\) | −29.5385 | −0.995179 | −0.497589 | − | 0.867413i | \(-0.665781\pi\) | ||||
−0.497589 | + | 0.867413i | \(0.665781\pi\) | |||||||
\(882\) | 6.04066 | 0.203400 | ||||||||
\(883\) | −5.47182 | −0.184141 | −0.0920707 | − | 0.995752i | \(-0.529349\pi\) | ||||
−0.0920707 | + | 0.995752i | \(0.529349\pi\) | |||||||
\(884\) | −10.9947 | −0.369792 | ||||||||
\(885\) | 1.22604 | 0.0412128 | ||||||||
\(886\) | 2.05491 | 0.0690359 | ||||||||
\(887\) | −1.83418 | −0.0615859 | −0.0307929 | − | 0.999526i | \(-0.509803\pi\) | ||||
−0.0307929 | + | 0.999526i | \(0.509803\pi\) | |||||||
\(888\) | −6.01645 | −0.201899 | ||||||||
\(889\) | −3.79455 | −0.127265 | ||||||||
\(890\) | −25.3586 | −0.850023 | ||||||||
\(891\) | −4.89204 | −0.163889 | ||||||||
\(892\) | −3.72901 | −0.124856 | ||||||||
\(893\) | −25.5047 | −0.853482 | ||||||||
\(894\) | 9.11038 | 0.304697 | ||||||||
\(895\) | 58.8326 | 1.96656 | ||||||||
\(896\) | 2.03235 | 0.0678961 | ||||||||
\(897\) | 11.5360 | 0.385176 | ||||||||
\(898\) | 14.0686 | 0.469475 | ||||||||
\(899\) | 2.55432 | 0.0851914 | ||||||||
\(900\) | −2.08662 | −0.0695540 | ||||||||
\(901\) | −39.3196 | −1.30993 | ||||||||
\(902\) | −9.50528 | −0.316491 | ||||||||
\(903\) | 23.7486 | 0.790305 | ||||||||
\(904\) | −11.3017 | −0.375890 | ||||||||
\(905\) | 26.3491 | 0.875874 | ||||||||
\(906\) | −10.4598 | −0.347503 | ||||||||
\(907\) | 49.8121 | 1.65398 | 0.826991 | − | 0.562215i | \(-0.190050\pi\) | ||||
0.826991 | + | 0.562215i | \(0.190050\pi\) | |||||||
\(908\) | −27.0598 | −0.898010 | ||||||||
\(909\) | 5.61486 | 0.186233 | ||||||||
\(910\) | 9.90390 | 0.328311 | ||||||||
\(911\) | 44.7340 | 1.48210 | 0.741052 | − | 0.671448i | \(-0.234327\pi\) | ||||
0.741052 | + | 0.671448i | \(0.234327\pi\) | |||||||
\(912\) | −2.74404 | −0.0908642 | ||||||||
\(913\) | 42.2339 | 1.39774 | ||||||||
\(914\) | 2.31968 | 0.0767282 | ||||||||
\(915\) | −17.5331 | −0.579626 | ||||||||
\(916\) | −13.4293 | −0.443715 | ||||||||
\(917\) | −10.1165 | −0.334075 | ||||||||
\(918\) | 26.6703 | 0.880250 | ||||||||
\(919\) | −12.9339 | −0.426650 | −0.213325 | − | 0.976981i | \(-0.568429\pi\) | ||||
−0.213325 | + | 0.976981i | \(0.568429\pi\) | |||||||
\(920\) | −14.9925 | −0.494288 | ||||||||
\(921\) | 14.4264 | 0.475366 | ||||||||
\(922\) | −5.12438 | −0.168762 | ||||||||
\(923\) | 2.53488 | 0.0834367 | ||||||||
\(924\) | 5.38477 | 0.177146 | ||||||||
\(925\) | 6.30410 | 0.207278 | ||||||||
\(926\) | 14.2523 | 0.468359 | ||||||||
\(927\) | 32.2379 | 1.05883 | ||||||||
\(928\) | −3.04955 | −0.100106 | ||||||||
\(929\) | 22.8592 | 0.749987 | 0.374994 | − | 0.927027i | \(-0.377645\pi\) | ||||
0.374994 | + | 0.927027i | \(0.377645\pi\) | |||||||
\(930\) | −1.93949 | −0.0635984 | ||||||||
\(931\) | −8.32366 | −0.272797 | ||||||||
\(932\) | 25.4347 | 0.833143 | ||||||||
\(933\) | −20.5076 | −0.671387 | ||||||||
\(934\) | 13.4011 | 0.438496 | ||||||||
\(935\) | 37.8591 | 1.23813 | ||||||||
\(936\) | 4.19103 | 0.136988 | ||||||||
\(937\) | 12.5428 | 0.409755 | 0.204877 | − | 0.978788i | \(-0.434320\pi\) | ||||
0.204877 | + | 0.978788i | \(0.434320\pi\) | |||||||
\(938\) | −0.501849 | −0.0163860 | ||||||||
\(939\) | 14.6360 | 0.477626 | ||||||||
\(940\) | 21.5217 | 0.701962 | ||||||||
\(941\) | −45.9702 | −1.49859 | −0.749294 | − | 0.662238i | \(-0.769607\pi\) | ||||
−0.749294 | + | 0.662238i | \(0.769607\pi\) | |||||||
\(942\) | −22.3786 | −0.729135 | ||||||||
\(943\) | 20.7875 | 0.676934 | ||||||||
\(944\) | 0.529488 | 0.0172334 | ||||||||
\(945\) | −24.0242 | −0.781508 | ||||||||
\(946\) | 34.5962 | 1.12482 | ||||||||
\(947\) | −26.8961 | −0.874006 | −0.437003 | − | 0.899460i | \(-0.643960\pi\) | ||||
−0.437003 | + | 0.899460i | \(0.643960\pi\) | |||||||
\(948\) | 8.26767 | 0.268521 | ||||||||
\(949\) | 14.1027 | 0.457792 | ||||||||
\(950\) | 2.87523 | 0.0932849 | ||||||||
\(951\) | 1.58448 | 0.0513802 | ||||||||
\(952\) | 11.2236 | 0.363760 | ||||||||
\(953\) | 38.8508 | 1.25850 | 0.629250 | − | 0.777203i | \(-0.283362\pi\) | ||||
0.629250 | + | 0.777203i | \(0.283362\pi\) | |||||||
\(954\) | 14.9881 | 0.485257 | ||||||||
\(955\) | −51.6914 | −1.67270 | ||||||||
\(956\) | −15.9974 | −0.517391 | ||||||||
\(957\) | −8.07986 | −0.261185 | ||||||||
\(958\) | 34.5704 | 1.11692 | ||||||||
\(959\) | −32.6254 | −1.05353 | ||||||||
\(960\) | 2.31551 | 0.0747329 | ||||||||
\(961\) | −30.2984 | −0.977368 | ||||||||
\(962\) | −12.6619 | −0.408237 | ||||||||
\(963\) | −30.3538 | −0.978138 | ||||||||
\(964\) | 29.8860 | 0.962562 | ||||||||
\(965\) | −40.5856 | −1.30650 | ||||||||
\(966\) | −11.7762 | −0.378892 | ||||||||
\(967\) | 7.68393 | 0.247098 | 0.123549 | − | 0.992338i | \(-0.460572\pi\) | ||||
0.123549 | + | 0.992338i | \(0.460572\pi\) | |||||||
\(968\) | −3.15565 | −0.101427 | ||||||||
\(969\) | −15.1539 | −0.486813 | ||||||||
\(970\) | −3.31606 | −0.106472 | ||||||||
\(971\) | 61.5889 | 1.97648 | 0.988241 | − | 0.152901i | \(-0.0488616\pi\) | ||||
0.988241 | + | 0.152901i | \(0.0488616\pi\) | |||||||
\(972\) | −16.1405 | −0.517708 | ||||||||
\(973\) | −34.0300 | −1.09095 | ||||||||
\(974\) | 21.3436 | 0.683893 | ||||||||
\(975\) | 1.86686 | 0.0597874 | ||||||||
\(976\) | −7.57201 | −0.242374 | ||||||||
\(977\) | 55.7670 | 1.78414 | 0.892072 | − | 0.451893i | \(-0.149251\pi\) | ||||
0.892072 | + | 0.451893i | \(0.149251\pi\) | |||||||
\(978\) | −1.40911 | −0.0450585 | ||||||||
\(979\) | −29.0166 | −0.927374 | ||||||||
\(980\) | 7.02379 | 0.224367 | ||||||||
\(981\) | 5.51729 | 0.176154 | ||||||||
\(982\) | 38.9925 | 1.24430 | ||||||||
\(983\) | 23.8112 | 0.759459 | 0.379730 | − | 0.925098i | \(-0.376017\pi\) | ||||
0.379730 | + | 0.925098i | \(0.376017\pi\) | |||||||
\(984\) | −3.21053 | −0.102348 | ||||||||
\(985\) | −43.6730 | −1.39154 | ||||||||
\(986\) | −16.8411 | −0.536329 | ||||||||
\(987\) | 16.9047 | 0.538083 | ||||||||
\(988\) | −5.77498 | −0.183726 | ||||||||
\(989\) | −75.6599 | −2.40585 | ||||||||
\(990\) | −14.4313 | −0.458658 | ||||||||
\(991\) | 23.4798 | 0.745862 | 0.372931 | − | 0.927859i | \(-0.378353\pi\) | ||||
0.372931 | + | 0.927859i | \(0.378353\pi\) | |||||||
\(992\) | −0.837606 | −0.0265940 | ||||||||
\(993\) | −14.3217 | −0.454486 | ||||||||
\(994\) | −2.58766 | −0.0820755 | ||||||||
\(995\) | 5.72838 | 0.181602 | ||||||||
\(996\) | 14.2650 | 0.452005 | ||||||||
\(997\) | 54.6426 | 1.73055 | 0.865275 | − | 0.501298i | \(-0.167144\pi\) | ||||
0.865275 | + | 0.501298i | \(0.167144\pi\) | |||||||
\(998\) | −34.5883 | −1.09487 | ||||||||
\(999\) | 30.7145 | 0.971764 |
(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 | 4034.2.a.a.1.14 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.a.1.14 | ✓ | 33 | 1.1 | even | 1 | trivial |