Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, 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("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 | ||||||||
\(3\) | −2.32940 | −1.34488 | −0.672440 | − | 0.740151i | \(-0.734754\pi\) | ||||
−0.672440 | + | 0.740151i | \(0.734754\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.43485 | −1.08890 | −0.544448 | − | 0.838794i | \(-0.683261\pi\) | ||||
−0.544448 | + | 0.838794i | \(0.683261\pi\) | |||||||
\(6\) | −2.32940 | −0.950974 | ||||||||
\(7\) | 0.839554 | 0.317322 | 0.158661 | − | 0.987333i | \(-0.449282\pi\) | ||||
0.158661 | + | 0.987333i | \(0.449282\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.42611 | 0.808705 | ||||||||
\(10\) | −2.43485 | −0.769966 | ||||||||
\(11\) | −5.28397 | −1.59318 | −0.796588 | − | 0.604522i | \(-0.793364\pi\) | ||||
−0.796588 | + | 0.604522i | \(0.793364\pi\) | |||||||
\(12\) | −2.32940 | −0.672440 | ||||||||
\(13\) | −0.826967 | −0.229359 | −0.114680 | − | 0.993403i | \(-0.536584\pi\) | ||||
−0.114680 | + | 0.993403i | \(0.536584\pi\) | |||||||
\(14\) | 0.839554 | 0.224380 | ||||||||
\(15\) | 5.67174 | 1.46444 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.19444 | 0.289695 | 0.144847 | − | 0.989454i | \(-0.453731\pi\) | ||||
0.144847 | + | 0.989454i | \(0.453731\pi\) | |||||||
\(18\) | 2.42611 | 0.571841 | ||||||||
\(19\) | 3.71172 | 0.851526 | 0.425763 | − | 0.904835i | \(-0.360006\pi\) | ||||
0.425763 | + | 0.904835i | \(0.360006\pi\) | |||||||
\(20\) | −2.43485 | −0.544448 | ||||||||
\(21\) | −1.95566 | −0.426760 | ||||||||
\(22\) | −5.28397 | −1.12655 | ||||||||
\(23\) | −1.07783 | −0.224743 | −0.112371 | − | 0.993666i | \(-0.535845\pi\) | ||||
−0.112371 | + | 0.993666i | \(0.535845\pi\) | |||||||
\(24\) | −2.32940 | −0.475487 | ||||||||
\(25\) | 0.928478 | 0.185696 | ||||||||
\(26\) | −0.826967 | −0.162182 | ||||||||
\(27\) | 1.33681 | 0.257269 | ||||||||
\(28\) | 0.839554 | 0.158661 | ||||||||
\(29\) | 8.71254 | 1.61788 | 0.808939 | − | 0.587893i | \(-0.200042\pi\) | ||||
0.808939 | + | 0.587893i | \(0.200042\pi\) | |||||||
\(30\) | 5.67174 | 1.03551 | ||||||||
\(31\) | −1.57356 | −0.282620 | −0.141310 | − | 0.989965i | \(-0.545131\pi\) | ||||
−0.141310 | + | 0.989965i | \(0.545131\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 12.3085 | 2.14263 | ||||||||
\(34\) | 1.19444 | 0.204845 | ||||||||
\(35\) | −2.04418 | −0.345530 | ||||||||
\(36\) | 2.42611 | 0.404352 | ||||||||
\(37\) | −1.49810 | −0.246286 | −0.123143 | − | 0.992389i | \(-0.539297\pi\) | ||||
−0.123143 | + | 0.992389i | \(0.539297\pi\) | |||||||
\(38\) | 3.71172 | 0.602120 | ||||||||
\(39\) | 1.92634 | 0.308461 | ||||||||
\(40\) | −2.43485 | −0.384983 | ||||||||
\(41\) | −0.609475 | −0.0951839 | −0.0475920 | − | 0.998867i | \(-0.515155\pi\) | ||||
−0.0475920 | + | 0.998867i | \(0.515155\pi\) | |||||||
\(42\) | −1.95566 | −0.301765 | ||||||||
\(43\) | −2.45587 | −0.374516 | −0.187258 | − | 0.982311i | \(-0.559960\pi\) | ||||
−0.187258 | + | 0.982311i | \(0.559960\pi\) | |||||||
\(44\) | −5.28397 | −0.796588 | ||||||||
\(45\) | −5.90722 | −0.880596 | ||||||||
\(46\) | −1.07783 | −0.158917 | ||||||||
\(47\) | 4.85052 | 0.707520 | 0.353760 | − | 0.935336i | \(-0.384903\pi\) | ||||
0.353760 | + | 0.935336i | \(0.384903\pi\) | |||||||
\(48\) | −2.32940 | −0.336220 | ||||||||
\(49\) | −6.29515 | −0.899307 | ||||||||
\(50\) | 0.928478 | 0.131307 | ||||||||
\(51\) | −2.78234 | −0.389605 | ||||||||
\(52\) | −0.826967 | −0.114680 | ||||||||
\(53\) | 3.68255 | 0.505838 | 0.252919 | − | 0.967488i | \(-0.418609\pi\) | ||||
0.252919 | + | 0.967488i | \(0.418609\pi\) | |||||||
\(54\) | 1.33681 | 0.181917 | ||||||||
\(55\) | 12.8657 | 1.73480 | ||||||||
\(56\) | 0.839554 | 0.112190 | ||||||||
\(57\) | −8.64608 | −1.14520 | ||||||||
\(58\) | 8.71254 | 1.14401 | ||||||||
\(59\) | 2.81044 | 0.365888 | 0.182944 | − | 0.983123i | \(-0.441437\pi\) | ||||
0.182944 | + | 0.983123i | \(0.441437\pi\) | |||||||
\(60\) | 5.67174 | 0.732218 | ||||||||
\(61\) | 14.9799 | 1.91798 | 0.958992 | − | 0.283432i | \(-0.0914730\pi\) | ||||
0.958992 | + | 0.283432i | \(0.0914730\pi\) | |||||||
\(62\) | −1.57356 | −0.199843 | ||||||||
\(63\) | 2.03685 | 0.256619 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.01354 | 0.249749 | ||||||||
\(66\) | 12.3085 | 1.51507 | ||||||||
\(67\) | −6.07332 | −0.741974 | −0.370987 | − | 0.928638i | \(-0.620981\pi\) | ||||
−0.370987 | + | 0.928638i | \(0.620981\pi\) | |||||||
\(68\) | 1.19444 | 0.144847 | ||||||||
\(69\) | 2.51070 | 0.302252 | ||||||||
\(70\) | −2.04418 | −0.244327 | ||||||||
\(71\) | 10.5814 | 1.25578 | 0.627891 | − | 0.778301i | \(-0.283918\pi\) | ||||
0.627891 | + | 0.778301i | \(0.283918\pi\) | |||||||
\(72\) | 2.42611 | 0.285920 | ||||||||
\(73\) | −12.0486 | −1.41018 | −0.705090 | − | 0.709118i | \(-0.749093\pi\) | ||||
−0.705090 | + | 0.709118i | \(0.749093\pi\) | |||||||
\(74\) | −1.49810 | −0.174151 | ||||||||
\(75\) | −2.16280 | −0.249739 | ||||||||
\(76\) | 3.71172 | 0.425763 | ||||||||
\(77\) | −4.43618 | −0.505549 | ||||||||
\(78\) | 1.92634 | 0.218115 | ||||||||
\(79\) | 11.2960 | 1.27089 | 0.635447 | − | 0.772145i | \(-0.280816\pi\) | ||||
0.635447 | + | 0.772145i | \(0.280816\pi\) | |||||||
\(80\) | −2.43485 | −0.272224 | ||||||||
\(81\) | −10.3923 | −1.15470 | ||||||||
\(82\) | −0.609475 | −0.0673052 | ||||||||
\(83\) | −1.64570 | −0.180639 | −0.0903195 | − | 0.995913i | \(-0.528789\pi\) | ||||
−0.0903195 | + | 0.995913i | \(0.528789\pi\) | |||||||
\(84\) | −1.95566 | −0.213380 | ||||||||
\(85\) | −2.90828 | −0.315448 | ||||||||
\(86\) | −2.45587 | −0.264823 | ||||||||
\(87\) | −20.2950 | −2.17585 | ||||||||
\(88\) | −5.28397 | −0.563273 | ||||||||
\(89\) | 3.88182 | 0.411472 | 0.205736 | − | 0.978608i | \(-0.434041\pi\) | ||||
0.205736 | + | 0.978608i | \(0.434041\pi\) | |||||||
\(90\) | −5.90722 | −0.622675 | ||||||||
\(91\) | −0.694283 | −0.0727806 | ||||||||
\(92\) | −1.07783 | −0.112371 | ||||||||
\(93\) | 3.66546 | 0.380090 | ||||||||
\(94\) | 4.85052 | 0.500292 | ||||||||
\(95\) | −9.03746 | −0.927224 | ||||||||
\(96\) | −2.32940 | −0.237744 | ||||||||
\(97\) | −8.04003 | −0.816342 | −0.408171 | − | 0.912906i | \(-0.633833\pi\) | ||||
−0.408171 | + | 0.912906i | \(0.633833\pi\) | |||||||
\(98\) | −6.29515 | −0.635906 | ||||||||
\(99\) | −12.8195 | −1.28841 | ||||||||
\(100\) | 0.928478 | 0.0928478 | ||||||||
\(101\) | −12.2146 | −1.21540 | −0.607699 | − | 0.794167i | \(-0.707907\pi\) | ||||
−0.607699 | + | 0.794167i | \(0.707907\pi\) | |||||||
\(102\) | −2.78234 | −0.275492 | ||||||||
\(103\) | −1.71547 | −0.169030 | −0.0845150 | − | 0.996422i | \(-0.526934\pi\) | ||||
−0.0845150 | + | 0.996422i | \(0.526934\pi\) | |||||||
\(104\) | −0.826967 | −0.0810908 | ||||||||
\(105\) | 4.76173 | 0.464697 | ||||||||
\(106\) | 3.68255 | 0.357681 | ||||||||
\(107\) | 17.9762 | 1.73782 | 0.868911 | − | 0.494968i | \(-0.164820\pi\) | ||||
0.868911 | + | 0.494968i | \(0.164820\pi\) | |||||||
\(108\) | 1.33681 | 0.128635 | ||||||||
\(109\) | −1.80745 | −0.173122 | −0.0865610 | − | 0.996247i | \(-0.527588\pi\) | ||||
−0.0865610 | + | 0.996247i | \(0.527588\pi\) | |||||||
\(110\) | 12.8657 | 1.22669 | ||||||||
\(111\) | 3.48968 | 0.331226 | ||||||||
\(112\) | 0.839554 | 0.0793304 | ||||||||
\(113\) | −10.3727 | −0.975785 | −0.487892 | − | 0.872904i | \(-0.662234\pi\) | ||||
−0.487892 | + | 0.872904i | \(0.662234\pi\) | |||||||
\(114\) | −8.64608 | −0.809779 | ||||||||
\(115\) | 2.62435 | 0.244722 | ||||||||
\(116\) | 8.71254 | 0.808939 | ||||||||
\(117\) | −2.00632 | −0.185484 | ||||||||
\(118\) | 2.81044 | 0.258722 | ||||||||
\(119\) | 1.00280 | 0.0919264 | ||||||||
\(120\) | 5.67174 | 0.517756 | ||||||||
\(121\) | 16.9203 | 1.53821 | ||||||||
\(122\) | 14.9799 | 1.35622 | ||||||||
\(123\) | 1.41971 | 0.128011 | ||||||||
\(124\) | −1.57356 | −0.141310 | ||||||||
\(125\) | 9.91353 | 0.886693 | ||||||||
\(126\) | 2.03685 | 0.181457 | ||||||||
\(127\) | −0.603915 | −0.0535888 | −0.0267944 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267944 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.72070 | 0.503680 | ||||||||
\(130\) | 2.01354 | 0.176599 | ||||||||
\(131\) | −13.6610 | −1.19357 | −0.596784 | − | 0.802402i | \(-0.703555\pi\) | ||||
−0.596784 | + | 0.802402i | \(0.703555\pi\) | |||||||
\(132\) | 12.3085 | 1.07132 | ||||||||
\(133\) | 3.11618 | 0.270208 | ||||||||
\(134\) | −6.07332 | −0.524655 | ||||||||
\(135\) | −3.25493 | −0.280140 | ||||||||
\(136\) | 1.19444 | 0.102423 | ||||||||
\(137\) | −5.93477 | −0.507042 | −0.253521 | − | 0.967330i | \(-0.581589\pi\) | ||||
−0.253521 | + | 0.967330i | \(0.581589\pi\) | |||||||
\(138\) | 2.51070 | 0.213725 | ||||||||
\(139\) | −1.81978 | −0.154352 | −0.0771759 | − | 0.997017i | \(-0.524590\pi\) | ||||
−0.0771759 | + | 0.997017i | \(0.524590\pi\) | |||||||
\(140\) | −2.04418 | −0.172765 | ||||||||
\(141\) | −11.2988 | −0.951531 | ||||||||
\(142\) | 10.5814 | 0.887972 | ||||||||
\(143\) | 4.36967 | 0.365410 | ||||||||
\(144\) | 2.42611 | 0.202176 | ||||||||
\(145\) | −21.2137 | −1.76170 | ||||||||
\(146\) | −12.0486 | −0.997148 | ||||||||
\(147\) | 14.6639 | 1.20946 | ||||||||
\(148\) | −1.49810 | −0.123143 | ||||||||
\(149\) | 13.0036 | 1.06529 | 0.532646 | − | 0.846338i | \(-0.321198\pi\) | ||||
0.532646 | + | 0.846338i | \(0.321198\pi\) | |||||||
\(150\) | −2.16280 | −0.176592 | ||||||||
\(151\) | −9.41130 | −0.765881 | −0.382940 | − | 0.923773i | \(-0.625089\pi\) | ||||
−0.382940 | + | 0.923773i | \(0.625089\pi\) | |||||||
\(152\) | 3.71172 | 0.301060 | ||||||||
\(153\) | 2.89785 | 0.234278 | ||||||||
\(154\) | −4.43618 | −0.357477 | ||||||||
\(155\) | 3.83138 | 0.307744 | ||||||||
\(156\) | 1.92634 | 0.154230 | ||||||||
\(157\) | −7.04207 | −0.562018 | −0.281009 | − | 0.959705i | \(-0.590669\pi\) | ||||
−0.281009 | + | 0.959705i | \(0.590669\pi\) | |||||||
\(158\) | 11.2960 | 0.898658 | ||||||||
\(159\) | −8.57815 | −0.680291 | ||||||||
\(160\) | −2.43485 | −0.192492 | ||||||||
\(161\) | −0.904895 | −0.0713157 | ||||||||
\(162\) | −10.3923 | −0.816497 | ||||||||
\(163\) | 6.87365 | 0.538386 | 0.269193 | − | 0.963086i | \(-0.413243\pi\) | ||||
0.269193 | + | 0.963086i | \(0.413243\pi\) | |||||||
\(164\) | −0.609475 | −0.0475920 | ||||||||
\(165\) | −29.9693 | −2.33310 | ||||||||
\(166\) | −1.64570 | −0.127731 | ||||||||
\(167\) | −5.22780 | −0.404539 | −0.202270 | − | 0.979330i | \(-0.564832\pi\) | ||||
−0.202270 | + | 0.979330i | \(0.564832\pi\) | |||||||
\(168\) | −1.95566 | −0.150882 | ||||||||
\(169\) | −12.3161 | −0.947394 | ||||||||
\(170\) | −2.90828 | −0.223055 | ||||||||
\(171\) | 9.00504 | 0.688633 | ||||||||
\(172\) | −2.45587 | −0.187258 | ||||||||
\(173\) | 11.4441 | 0.870077 | 0.435038 | − | 0.900412i | \(-0.356735\pi\) | ||||
0.435038 | + | 0.900412i | \(0.356735\pi\) | |||||||
\(174\) | −20.2950 | −1.53856 | ||||||||
\(175\) | 0.779508 | 0.0589252 | ||||||||
\(176\) | −5.28397 | −0.398294 | ||||||||
\(177\) | −6.54664 | −0.492075 | ||||||||
\(178\) | 3.88182 | 0.290955 | ||||||||
\(179\) | −1.65368 | −0.123602 | −0.0618009 | − | 0.998088i | \(-0.519684\pi\) | ||||
−0.0618009 | + | 0.998088i | \(0.519684\pi\) | |||||||
\(180\) | −5.90722 | −0.440298 | ||||||||
\(181\) | −8.36335 | −0.621643 | −0.310821 | − | 0.950468i | \(-0.600604\pi\) | ||||
−0.310821 | + | 0.950468i | \(0.600604\pi\) | |||||||
\(182\) | −0.694283 | −0.0514637 | ||||||||
\(183\) | −34.8943 | −2.57946 | ||||||||
\(184\) | −1.07783 | −0.0794585 | ||||||||
\(185\) | 3.64765 | 0.268180 | ||||||||
\(186\) | 3.66546 | 0.268764 | ||||||||
\(187\) | −6.31139 | −0.461535 | ||||||||
\(188\) | 4.85052 | 0.353760 | ||||||||
\(189\) | 1.12232 | 0.0816371 | ||||||||
\(190\) | −9.03746 | −0.655646 | ||||||||
\(191\) | −9.06744 | −0.656097 | −0.328048 | − | 0.944661i | \(-0.606391\pi\) | ||||
−0.328048 | + | 0.944661i | \(0.606391\pi\) | |||||||
\(192\) | −2.32940 | −0.168110 | ||||||||
\(193\) | −4.66340 | −0.335679 | −0.167839 | − | 0.985814i | \(-0.553679\pi\) | ||||
−0.167839 | + | 0.985814i | \(0.553679\pi\) | |||||||
\(194\) | −8.04003 | −0.577241 | ||||||||
\(195\) | −4.69034 | −0.335882 | ||||||||
\(196\) | −6.29515 | −0.449654 | ||||||||
\(197\) | −13.6852 | −0.975033 | −0.487516 | − | 0.873114i | \(-0.662097\pi\) | ||||
−0.487516 | + | 0.873114i | \(0.662097\pi\) | |||||||
\(198\) | −12.8195 | −0.911043 | ||||||||
\(199\) | −12.0896 | −0.857007 | −0.428504 | − | 0.903540i | \(-0.640959\pi\) | ||||
−0.428504 | + | 0.903540i | \(0.640959\pi\) | |||||||
\(200\) | 0.928478 | 0.0656533 | ||||||||
\(201\) | 14.1472 | 0.997866 | ||||||||
\(202\) | −12.2146 | −0.859416 | ||||||||
\(203\) | 7.31465 | 0.513388 | ||||||||
\(204\) | −2.78234 | −0.194803 | ||||||||
\(205\) | 1.48398 | 0.103645 | ||||||||
\(206\) | −1.71547 | −0.119522 | ||||||||
\(207\) | −2.61493 | −0.181750 | ||||||||
\(208\) | −0.826967 | −0.0573398 | ||||||||
\(209\) | −19.6126 | −1.35663 | ||||||||
\(210\) | 4.76173 | 0.328590 | ||||||||
\(211\) | −6.42797 | −0.442520 | −0.221260 | − | 0.975215i | \(-0.571017\pi\) | ||||
−0.221260 | + | 0.975215i | \(0.571017\pi\) | |||||||
\(212\) | 3.68255 | 0.252919 | ||||||||
\(213\) | −24.6484 | −1.68888 | ||||||||
\(214\) | 17.9762 | 1.22883 | ||||||||
\(215\) | 5.97966 | 0.407809 | ||||||||
\(216\) | 1.33681 | 0.0909585 | ||||||||
\(217\) | −1.32109 | −0.0896814 | ||||||||
\(218\) | −1.80745 | −0.122416 | ||||||||
\(219\) | 28.0660 | 1.89652 | ||||||||
\(220\) | 12.8657 | 0.867402 | ||||||||
\(221\) | −0.987764 | −0.0664442 | ||||||||
\(222\) | 3.48968 | 0.234212 | ||||||||
\(223\) | 24.1728 | 1.61873 | 0.809364 | − | 0.587308i | \(-0.199812\pi\) | ||||
0.809364 | + | 0.587308i | \(0.199812\pi\) | |||||||
\(224\) | 0.839554 | 0.0560950 | ||||||||
\(225\) | 2.25259 | 0.150173 | ||||||||
\(226\) | −10.3727 | −0.689984 | ||||||||
\(227\) | −17.2841 | −1.14719 | −0.573593 | − | 0.819140i | \(-0.694451\pi\) | ||||
−0.573593 | + | 0.819140i | \(0.694451\pi\) | |||||||
\(228\) | −8.64608 | −0.572600 | ||||||||
\(229\) | 29.0334 | 1.91858 | 0.959291 | − | 0.282419i | \(-0.0911369\pi\) | ||||
0.959291 | + | 0.282419i | \(0.0911369\pi\) | |||||||
\(230\) | 2.62435 | 0.173044 | ||||||||
\(231\) | 10.3336 | 0.679903 | ||||||||
\(232\) | 8.71254 | 0.572006 | ||||||||
\(233\) | 9.67858 | 0.634065 | 0.317032 | − | 0.948415i | \(-0.397314\pi\) | ||||
0.317032 | + | 0.948415i | \(0.397314\pi\) | |||||||
\(234\) | −2.00632 | −0.131157 | ||||||||
\(235\) | −11.8103 | −0.770417 | ||||||||
\(236\) | 2.81044 | 0.182944 | ||||||||
\(237\) | −26.3128 | −1.70920 | ||||||||
\(238\) | 1.00280 | 0.0650018 | ||||||||
\(239\) | −22.7208 | −1.46968 | −0.734842 | − | 0.678239i | \(-0.762744\pi\) | ||||
−0.734842 | + | 0.678239i | \(0.762744\pi\) | |||||||
\(240\) | 5.67174 | 0.366109 | ||||||||
\(241\) | −28.6211 | −1.84365 | −0.921824 | − | 0.387610i | \(-0.873301\pi\) | ||||
−0.921824 | + | 0.387610i | \(0.873301\pi\) | |||||||
\(242\) | 16.9203 | 1.08768 | ||||||||
\(243\) | 20.1974 | 1.29567 | ||||||||
\(244\) | 14.9799 | 0.958992 | ||||||||
\(245\) | 15.3277 | 0.979252 | ||||||||
\(246\) | 1.41971 | 0.0905175 | ||||||||
\(247\) | −3.06947 | −0.195305 | ||||||||
\(248\) | −1.57356 | −0.0999213 | ||||||||
\(249\) | 3.83350 | 0.242938 | ||||||||
\(250\) | 9.91353 | 0.626987 | ||||||||
\(251\) | 9.58402 | 0.604938 | 0.302469 | − | 0.953159i | \(-0.402189\pi\) | ||||
0.302469 | + | 0.953159i | \(0.402189\pi\) | |||||||
\(252\) | 2.03685 | 0.128310 | ||||||||
\(253\) | 5.69521 | 0.358055 | ||||||||
\(254\) | −0.603915 | −0.0378930 | ||||||||
\(255\) | 6.77456 | 0.424240 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.3218 | −1.82905 | −0.914523 | − | 0.404533i | \(-0.867434\pi\) | ||||
−0.914523 | + | 0.404533i | \(0.867434\pi\) | |||||||
\(258\) | 5.72070 | 0.356155 | ||||||||
\(259\) | −1.25774 | −0.0781519 | ||||||||
\(260\) | 2.01354 | 0.124874 | ||||||||
\(261\) | 21.1376 | 1.30839 | ||||||||
\(262\) | −13.6610 | −0.843980 | ||||||||
\(263\) | −6.18250 | −0.381229 | −0.190615 | − | 0.981665i | \(-0.561048\pi\) | ||||
−0.190615 | + | 0.981665i | \(0.561048\pi\) | |||||||
\(264\) | 12.3085 | 0.757535 | ||||||||
\(265\) | −8.96645 | −0.550805 | ||||||||
\(266\) | 3.11618 | 0.191066 | ||||||||
\(267\) | −9.04232 | −0.553381 | ||||||||
\(268\) | −6.07332 | −0.370987 | ||||||||
\(269\) | 5.97166 | 0.364099 | 0.182049 | − | 0.983289i | \(-0.441727\pi\) | ||||
0.182049 | + | 0.983289i | \(0.441727\pi\) | |||||||
\(270\) | −3.25493 | −0.198089 | ||||||||
\(271\) | 15.4945 | 0.941222 | 0.470611 | − | 0.882341i | \(-0.344034\pi\) | ||||
0.470611 | + | 0.882341i | \(0.344034\pi\) | |||||||
\(272\) | 1.19444 | 0.0724237 | ||||||||
\(273\) | 1.61726 | 0.0978813 | ||||||||
\(274\) | −5.93477 | −0.358533 | ||||||||
\(275\) | −4.90605 | −0.295846 | ||||||||
\(276\) | 2.51070 | 0.151126 | ||||||||
\(277\) | 17.7529 | 1.06667 | 0.533334 | − | 0.845905i | \(-0.320939\pi\) | ||||
0.533334 | + | 0.845905i | \(0.320939\pi\) | |||||||
\(278\) | −1.81978 | −0.109143 | ||||||||
\(279\) | −3.81764 | −0.228556 | ||||||||
\(280\) | −2.04418 | −0.122163 | ||||||||
\(281\) | −10.3974 | −0.620258 | −0.310129 | − | 0.950694i | \(-0.600372\pi\) | ||||
−0.310129 | + | 0.950694i | \(0.600372\pi\) | |||||||
\(282\) | −11.2988 | −0.672834 | ||||||||
\(283\) | 6.89539 | 0.409889 | 0.204944 | − | 0.978774i | \(-0.434299\pi\) | ||||
0.204944 | + | 0.978774i | \(0.434299\pi\) | |||||||
\(284\) | 10.5814 | 0.627891 | ||||||||
\(285\) | 21.0519 | 1.24701 | ||||||||
\(286\) | 4.36967 | 0.258384 | ||||||||
\(287\) | −0.511687 | −0.0302039 | ||||||||
\(288\) | 2.42611 | 0.142960 | ||||||||
\(289\) | −15.5733 | −0.916077 | ||||||||
\(290\) | −21.2137 | −1.24571 | ||||||||
\(291\) | 18.7285 | 1.09788 | ||||||||
\(292\) | −12.0486 | −0.705090 | ||||||||
\(293\) | 8.75954 | 0.511738 | 0.255869 | − | 0.966711i | \(-0.417638\pi\) | ||||
0.255869 | + | 0.966711i | \(0.417638\pi\) | |||||||
\(294\) | 14.6639 | 0.855218 | ||||||||
\(295\) | −6.84298 | −0.398414 | ||||||||
\(296\) | −1.49810 | −0.0870753 | ||||||||
\(297\) | −7.06367 | −0.409876 | ||||||||
\(298\) | 13.0036 | 0.753276 | ||||||||
\(299\) | 0.891328 | 0.0515468 | ||||||||
\(300\) | −2.16280 | −0.124869 | ||||||||
\(301\) | −2.06183 | −0.118842 | ||||||||
\(302\) | −9.41130 | −0.541560 | ||||||||
\(303\) | 28.4527 | 1.63457 | ||||||||
\(304\) | 3.71172 | 0.212881 | ||||||||
\(305\) | −36.4739 | −2.08849 | ||||||||
\(306\) | 2.89785 | 0.165659 | ||||||||
\(307\) | −2.88547 | −0.164683 | −0.0823413 | − | 0.996604i | \(-0.526240\pi\) | ||||
−0.0823413 | + | 0.996604i | \(0.526240\pi\) | |||||||
\(308\) | −4.43618 | −0.252775 | ||||||||
\(309\) | 3.99601 | 0.227325 | ||||||||
\(310\) | 3.83138 | 0.217608 | ||||||||
\(311\) | 31.2564 | 1.77239 | 0.886195 | − | 0.463313i | \(-0.153339\pi\) | ||||
0.886195 | + | 0.463313i | \(0.153339\pi\) | |||||||
\(312\) | 1.92634 | 0.109057 | ||||||||
\(313\) | −29.2113 | −1.65112 | −0.825559 | − | 0.564316i | \(-0.809140\pi\) | ||||
−0.825559 | + | 0.564316i | \(0.809140\pi\) | |||||||
\(314\) | −7.04207 | −0.397407 | ||||||||
\(315\) | −4.95943 | −0.279432 | ||||||||
\(316\) | 11.2960 | 0.635447 | ||||||||
\(317\) | 19.4126 | 1.09032 | 0.545159 | − | 0.838333i | \(-0.316469\pi\) | ||||
0.545159 | + | 0.838333i | \(0.316469\pi\) | |||||||
\(318\) | −8.57815 | −0.481039 | ||||||||
\(319\) | −46.0368 | −2.57756 | ||||||||
\(320\) | −2.43485 | −0.136112 | ||||||||
\(321\) | −41.8737 | −2.33716 | ||||||||
\(322\) | −0.904895 | −0.0504278 | ||||||||
\(323\) | 4.43343 | 0.246683 | ||||||||
\(324\) | −10.3923 | −0.577351 | ||||||||
\(325\) | −0.767821 | −0.0425910 | ||||||||
\(326\) | 6.87365 | 0.380696 | ||||||||
\(327\) | 4.21027 | 0.232828 | ||||||||
\(328\) | −0.609475 | −0.0336526 | ||||||||
\(329\) | 4.07227 | 0.224511 | ||||||||
\(330\) | −29.9693 | −1.64975 | ||||||||
\(331\) | −8.75448 | −0.481190 | −0.240595 | − | 0.970626i | \(-0.577342\pi\) | ||||
−0.240595 | + | 0.970626i | \(0.577342\pi\) | |||||||
\(332\) | −1.64570 | −0.0903195 | ||||||||
\(333\) | −3.63456 | −0.199173 | ||||||||
\(334\) | −5.22780 | −0.286053 | ||||||||
\(335\) | 14.7876 | 0.807933 | ||||||||
\(336\) | −1.95566 | −0.106690 | ||||||||
\(337\) | −24.9438 | −1.35878 | −0.679388 | − | 0.733779i | \(-0.737755\pi\) | ||||
−0.679388 | + | 0.733779i | \(0.737755\pi\) | |||||||
\(338\) | −12.3161 | −0.669909 | ||||||||
\(339\) | 24.1623 | 1.31231 | ||||||||
\(340\) | −2.90828 | −0.157724 | ||||||||
\(341\) | 8.31465 | 0.450264 | ||||||||
\(342\) | 9.00504 | 0.486937 | ||||||||
\(343\) | −11.1620 | −0.602691 | ||||||||
\(344\) | −2.45587 | −0.132411 | ||||||||
\(345\) | −6.11316 | −0.329121 | ||||||||
\(346\) | 11.4441 | 0.615237 | ||||||||
\(347\) | −29.1632 | −1.56556 | −0.782782 | − | 0.622296i | \(-0.786200\pi\) | ||||
−0.782782 | + | 0.622296i | \(0.786200\pi\) | |||||||
\(348\) | −20.2950 | −1.08793 | ||||||||
\(349\) | 0.661633 | 0.0354164 | 0.0177082 | − | 0.999843i | \(-0.494363\pi\) | ||||
0.0177082 | + | 0.999843i | \(0.494363\pi\) | |||||||
\(350\) | 0.779508 | 0.0416664 | ||||||||
\(351\) | −1.10550 | −0.0590071 | ||||||||
\(352\) | −5.28397 | −0.281636 | ||||||||
\(353\) | 21.1964 | 1.12817 | 0.564086 | − | 0.825716i | \(-0.309229\pi\) | ||||
0.564086 | + | 0.825716i | \(0.309229\pi\) | |||||||
\(354\) | −6.54664 | −0.347950 | ||||||||
\(355\) | −25.7641 | −1.36742 | ||||||||
\(356\) | 3.88182 | 0.205736 | ||||||||
\(357\) | −2.33592 | −0.123630 | ||||||||
\(358\) | −1.65368 | −0.0873996 | ||||||||
\(359\) | −31.5311 | −1.66415 | −0.832073 | − | 0.554666i | \(-0.812846\pi\) | ||||
−0.832073 | + | 0.554666i | \(0.812846\pi\) | |||||||
\(360\) | −5.90722 | −0.311338 | ||||||||
\(361\) | −5.22317 | −0.274904 | ||||||||
\(362\) | −8.36335 | −0.439568 | ||||||||
\(363\) | −39.4142 | −2.06871 | ||||||||
\(364\) | −0.694283 | −0.0363903 | ||||||||
\(365\) | 29.3364 | 1.53554 | ||||||||
\(366\) | −34.8943 | −1.82395 | ||||||||
\(367\) | −17.7182 | −0.924884 | −0.462442 | − | 0.886650i | \(-0.653027\pi\) | ||||
−0.462442 | + | 0.886650i | \(0.653027\pi\) | |||||||
\(368\) | −1.07783 | −0.0561857 | ||||||||
\(369\) | −1.47865 | −0.0769757 | ||||||||
\(370\) | 3.64765 | 0.189632 | ||||||||
\(371\) | 3.09170 | 0.160513 | ||||||||
\(372\) | 3.66546 | 0.190045 | ||||||||
\(373\) | −26.0262 | −1.34759 | −0.673794 | − | 0.738920i | \(-0.735336\pi\) | ||||
−0.673794 | + | 0.738920i | \(0.735336\pi\) | |||||||
\(374\) | −6.31139 | −0.326354 | ||||||||
\(375\) | −23.0926 | −1.19250 | ||||||||
\(376\) | 4.85052 | 0.250146 | ||||||||
\(377\) | −7.20498 | −0.371075 | ||||||||
\(378\) | 1.12232 | 0.0577262 | ||||||||
\(379\) | −0.634769 | −0.0326059 | −0.0163029 | − | 0.999867i | \(-0.505190\pi\) | ||||
−0.0163029 | + | 0.999867i | \(0.505190\pi\) | |||||||
\(380\) | −9.03746 | −0.463612 | ||||||||
\(381\) | 1.40676 | 0.0720706 | ||||||||
\(382\) | −9.06744 | −0.463931 | ||||||||
\(383\) | 8.55509 | 0.437145 | 0.218572 | − | 0.975821i | \(-0.429860\pi\) | ||||
0.218572 | + | 0.975821i | \(0.429860\pi\) | |||||||
\(384\) | −2.32940 | −0.118872 | ||||||||
\(385\) | 10.8014 | 0.550491 | ||||||||
\(386\) | −4.66340 | −0.237361 | ||||||||
\(387\) | −5.95821 | −0.302873 | ||||||||
\(388\) | −8.04003 | −0.408171 | ||||||||
\(389\) | 7.48402 | 0.379455 | 0.189728 | − | 0.981837i | \(-0.439240\pi\) | ||||
0.189728 | + | 0.981837i | \(0.439240\pi\) | |||||||
\(390\) | −4.69034 | −0.237504 | ||||||||
\(391\) | −1.28740 | −0.0651068 | ||||||||
\(392\) | −6.29515 | −0.317953 | ||||||||
\(393\) | 31.8220 | 1.60521 | ||||||||
\(394\) | −13.6852 | −0.689452 | ||||||||
\(395\) | −27.5039 | −1.38387 | ||||||||
\(396\) | −12.8195 | −0.644205 | ||||||||
\(397\) | −0.224964 | −0.0112906 | −0.00564532 | − | 0.999984i | \(-0.501797\pi\) | ||||
−0.00564532 | + | 0.999984i | \(0.501797\pi\) | |||||||
\(398\) | −12.0896 | −0.605996 | ||||||||
\(399\) | −7.25885 | −0.363397 | ||||||||
\(400\) | 0.928478 | 0.0464239 | ||||||||
\(401\) | 11.8662 | 0.592569 | 0.296284 | − | 0.955100i | \(-0.404252\pi\) | ||||
0.296284 | + | 0.955100i | \(0.404252\pi\) | |||||||
\(402\) | 14.1472 | 0.705598 | ||||||||
\(403\) | 1.30128 | 0.0648215 | ||||||||
\(404\) | −12.2146 | −0.607699 | ||||||||
\(405\) | 25.3037 | 1.25735 | ||||||||
\(406\) | 7.31465 | 0.363020 | ||||||||
\(407\) | 7.91592 | 0.392377 | ||||||||
\(408\) | −2.78234 | −0.137746 | ||||||||
\(409\) | −1.66699 | −0.0824275 | −0.0412137 | − | 0.999150i | \(-0.513122\pi\) | ||||
−0.0412137 | + | 0.999150i | \(0.513122\pi\) | |||||||
\(410\) | 1.48398 | 0.0732884 | ||||||||
\(411\) | 13.8245 | 0.681911 | ||||||||
\(412\) | −1.71547 | −0.0845150 | ||||||||
\(413\) | 2.35951 | 0.116104 | ||||||||
\(414\) | −2.61493 | −0.128517 | ||||||||
\(415\) | 4.00703 | 0.196697 | ||||||||
\(416\) | −0.826967 | −0.0405454 | ||||||||
\(417\) | 4.23900 | 0.207585 | ||||||||
\(418\) | −19.6126 | −0.959283 | ||||||||
\(419\) | −12.6731 | −0.619122 | −0.309561 | − | 0.950880i | \(-0.600182\pi\) | ||||
−0.309561 | + | 0.950880i | \(0.600182\pi\) | |||||||
\(420\) | 4.76173 | 0.232349 | ||||||||
\(421\) | −25.5422 | −1.24485 | −0.622426 | − | 0.782679i | \(-0.713853\pi\) | ||||
−0.622426 | + | 0.782679i | \(0.713853\pi\) | |||||||
\(422\) | −6.42797 | −0.312909 | ||||||||
\(423\) | 11.7679 | 0.572175 | ||||||||
\(424\) | 3.68255 | 0.178841 | ||||||||
\(425\) | 1.10901 | 0.0537951 | ||||||||
\(426\) | −24.6484 | −1.19422 | ||||||||
\(427\) | 12.5765 | 0.608618 | ||||||||
\(428\) | 17.9762 | 0.868911 | ||||||||
\(429\) | −10.1787 | −0.491433 | ||||||||
\(430\) | 5.97966 | 0.288365 | ||||||||
\(431\) | 30.7220 | 1.47982 | 0.739912 | − | 0.672703i | \(-0.234867\pi\) | ||||
0.739912 | + | 0.672703i | \(0.234867\pi\) | |||||||
\(432\) | 1.33681 | 0.0643174 | ||||||||
\(433\) | 2.16933 | 0.104252 | 0.0521258 | − | 0.998641i | \(-0.483400\pi\) | ||||
0.0521258 | + | 0.998641i | \(0.483400\pi\) | |||||||
\(434\) | −1.32109 | −0.0634143 | ||||||||
\(435\) | 49.4152 | 2.36928 | ||||||||
\(436\) | −1.80745 | −0.0865610 | ||||||||
\(437\) | −4.00059 | −0.191374 | ||||||||
\(438\) | 28.0660 | 1.34104 | ||||||||
\(439\) | 11.2301 | 0.535984 | 0.267992 | − | 0.963421i | \(-0.413640\pi\) | ||||
0.267992 | + | 0.963421i | \(0.413640\pi\) | |||||||
\(440\) | 12.8657 | 0.613346 | ||||||||
\(441\) | −15.2728 | −0.727274 | ||||||||
\(442\) | −0.987764 | −0.0469831 | ||||||||
\(443\) | −15.0579 | −0.715423 | −0.357711 | − | 0.933832i | \(-0.616443\pi\) | ||||
−0.357711 | + | 0.933832i | \(0.616443\pi\) | |||||||
\(444\) | 3.48968 | 0.165613 | ||||||||
\(445\) | −9.45164 | −0.448051 | ||||||||
\(446\) | 24.1728 | 1.14461 | ||||||||
\(447\) | −30.2905 | −1.43269 | ||||||||
\(448\) | 0.839554 | 0.0396652 | ||||||||
\(449\) | −4.70643 | −0.222110 | −0.111055 | − | 0.993814i | \(-0.535423\pi\) | ||||
−0.111055 | + | 0.993814i | \(0.535423\pi\) | |||||||
\(450\) | 2.25259 | 0.106188 | ||||||||
\(451\) | 3.22044 | 0.151645 | ||||||||
\(452\) | −10.3727 | −0.487892 | ||||||||
\(453\) | 21.9227 | 1.03002 | ||||||||
\(454\) | −17.2841 | −0.811183 | ||||||||
\(455\) | 1.69047 | 0.0792506 | ||||||||
\(456\) | −8.64608 | −0.404890 | ||||||||
\(457\) | −33.9258 | −1.58698 | −0.793491 | − | 0.608582i | \(-0.791739\pi\) | ||||
−0.793491 | + | 0.608582i | \(0.791739\pi\) | |||||||
\(458\) | 29.0334 | 1.35664 | ||||||||
\(459\) | 1.59674 | 0.0745296 | ||||||||
\(460\) | 2.62435 | 0.122361 | ||||||||
\(461\) | −14.5339 | −0.676909 | −0.338455 | − | 0.940983i | \(-0.609904\pi\) | ||||
−0.338455 | + | 0.940983i | \(0.609904\pi\) | |||||||
\(462\) | 10.3336 | 0.480764 | ||||||||
\(463\) | 17.3313 | 0.805453 | 0.402726 | − | 0.915320i | \(-0.368063\pi\) | ||||
0.402726 | + | 0.915320i | \(0.368063\pi\) | |||||||
\(464\) | 8.71254 | 0.404470 | ||||||||
\(465\) | −8.92483 | −0.413879 | ||||||||
\(466\) | 9.67858 | 0.448351 | ||||||||
\(467\) | 6.04447 | 0.279705 | 0.139852 | − | 0.990172i | \(-0.455337\pi\) | ||||
0.139852 | + | 0.990172i | \(0.455337\pi\) | |||||||
\(468\) | −2.00632 | −0.0927420 | ||||||||
\(469\) | −5.09888 | −0.235444 | ||||||||
\(470\) | −11.8103 | −0.544767 | ||||||||
\(471\) | 16.4038 | 0.755847 | ||||||||
\(472\) | 2.81044 | 0.129361 | ||||||||
\(473\) | 12.9767 | 0.596670 | ||||||||
\(474\) | −26.3128 | −1.20859 | ||||||||
\(475\) | 3.44625 | 0.158125 | ||||||||
\(476\) | 1.00280 | 0.0459632 | ||||||||
\(477\) | 8.93429 | 0.409073 | ||||||||
\(478\) | −22.7208 | −1.03922 | ||||||||
\(479\) | 32.2044 | 1.47146 | 0.735728 | − | 0.677277i | \(-0.236840\pi\) | ||||
0.735728 | + | 0.677277i | \(0.236840\pi\) | |||||||
\(480\) | 5.67174 | 0.258878 | ||||||||
\(481\) | 1.23888 | 0.0564880 | ||||||||
\(482\) | −28.6211 | −1.30366 | ||||||||
\(483\) | 2.10786 | 0.0959111 | ||||||||
\(484\) | 16.9203 | 0.769105 | ||||||||
\(485\) | 19.5762 | 0.888912 | ||||||||
\(486\) | 20.1974 | 0.916175 | ||||||||
\(487\) | −31.7527 | −1.43885 | −0.719426 | − | 0.694569i | \(-0.755595\pi\) | ||||
−0.719426 | + | 0.694569i | \(0.755595\pi\) | |||||||
\(488\) | 14.9799 | 0.678110 | ||||||||
\(489\) | −16.0115 | −0.724065 | ||||||||
\(490\) | 15.3277 | 0.692436 | ||||||||
\(491\) | −23.6489 | −1.06726 | −0.533629 | − | 0.845718i | \(-0.679172\pi\) | ||||
−0.533629 | + | 0.845718i | \(0.679172\pi\) | |||||||
\(492\) | 1.41971 | 0.0640055 | ||||||||
\(493\) | 10.4066 | 0.468691 | ||||||||
\(494\) | −3.06947 | −0.138102 | ||||||||
\(495\) | 31.2135 | 1.40294 | ||||||||
\(496\) | −1.57356 | −0.0706550 | ||||||||
\(497\) | 8.88367 | 0.398487 | ||||||||
\(498\) | 3.83350 | 0.171783 | ||||||||
\(499\) | −24.6965 | −1.10557 | −0.552783 | − | 0.833325i | \(-0.686434\pi\) | ||||
−0.552783 | + | 0.833325i | \(0.686434\pi\) | |||||||
\(500\) | 9.91353 | 0.443347 | ||||||||
\(501\) | 12.1777 | 0.544057 | ||||||||
\(502\) | 9.58402 | 0.427756 | ||||||||
\(503\) | −6.93249 | −0.309105 | −0.154552 | − | 0.987985i | \(-0.549393\pi\) | ||||
−0.154552 | + | 0.987985i | \(0.549393\pi\) | |||||||
\(504\) | 2.03685 | 0.0907287 | ||||||||
\(505\) | 29.7407 | 1.32344 | ||||||||
\(506\) | 5.69521 | 0.253183 | ||||||||
\(507\) | 28.6892 | 1.27413 | ||||||||
\(508\) | −0.603915 | −0.0267944 | ||||||||
\(509\) | −15.2412 | −0.675556 | −0.337778 | − | 0.941226i | \(-0.609675\pi\) | ||||
−0.337778 | + | 0.941226i | \(0.609675\pi\) | |||||||
\(510\) | 6.77456 | 0.299983 | ||||||||
\(511\) | −10.1154 | −0.447480 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.96186 | 0.219072 | ||||||||
\(514\) | −29.3218 | −1.29333 | ||||||||
\(515\) | 4.17690 | 0.184056 | ||||||||
\(516\) | 5.72070 | 0.251840 | ||||||||
\(517\) | −25.6300 | −1.12720 | ||||||||
\(518\) | −1.25774 | −0.0552618 | ||||||||
\(519\) | −26.6578 | −1.17015 | ||||||||
\(520\) | 2.01354 | 0.0882994 | ||||||||
\(521\) | 20.9887 | 0.919532 | 0.459766 | − | 0.888040i | \(-0.347933\pi\) | ||||
0.459766 | + | 0.888040i | \(0.347933\pi\) | |||||||
\(522\) | 21.1376 | 0.925168 | ||||||||
\(523\) | −11.2784 | −0.493170 | −0.246585 | − | 0.969121i | \(-0.579308\pi\) | ||||
−0.246585 | + | 0.969121i | \(0.579308\pi\) | |||||||
\(524\) | −13.6610 | −0.596784 | ||||||||
\(525\) | −1.81579 | −0.0792474 | ||||||||
\(526\) | −6.18250 | −0.269570 | ||||||||
\(527\) | −1.87953 | −0.0818736 | ||||||||
\(528\) | 12.3085 | 0.535658 | ||||||||
\(529\) | −21.8383 | −0.949491 | ||||||||
\(530\) | −8.96645 | −0.389478 | ||||||||
\(531\) | 6.81844 | 0.295895 | ||||||||
\(532\) | 3.11618 | 0.135104 | ||||||||
\(533\) | 0.504015 | 0.0218313 | ||||||||
\(534\) | −9.04232 | −0.391300 | ||||||||
\(535\) | −43.7692 | −1.89231 | ||||||||
\(536\) | −6.07332 | −0.262327 | ||||||||
\(537\) | 3.85208 | 0.166230 | ||||||||
\(538\) | 5.97166 | 0.257457 | ||||||||
\(539\) | 33.2634 | 1.43275 | ||||||||
\(540\) | −3.25493 | −0.140070 | ||||||||
\(541\) | −40.0672 | −1.72263 | −0.861313 | − | 0.508075i | \(-0.830357\pi\) | ||||
−0.861313 | + | 0.508075i | \(0.830357\pi\) | |||||||
\(542\) | 15.4945 | 0.665545 | ||||||||
\(543\) | 19.4816 | 0.836036 | ||||||||
\(544\) | 1.19444 | 0.0512113 | ||||||||
\(545\) | 4.40085 | 0.188512 | ||||||||
\(546\) | 1.61726 | 0.0692125 | ||||||||
\(547\) | 19.0009 | 0.812420 | 0.406210 | − | 0.913780i | \(-0.366850\pi\) | ||||
0.406210 | + | 0.913780i | \(0.366850\pi\) | |||||||
\(548\) | −5.93477 | −0.253521 | ||||||||
\(549\) | 36.3430 | 1.55108 | ||||||||
\(550\) | −4.90605 | −0.209195 | ||||||||
\(551\) | 32.3385 | 1.37767 | ||||||||
\(552\) | 2.51070 | 0.106862 | ||||||||
\(553\) | 9.48356 | 0.403282 | ||||||||
\(554\) | 17.7529 | 0.754248 | ||||||||
\(555\) | −8.49683 | −0.360671 | ||||||||
\(556\) | −1.81978 | −0.0771759 | ||||||||
\(557\) | −8.37592 | −0.354899 | −0.177450 | − | 0.984130i | \(-0.556785\pi\) | ||||
−0.177450 | + | 0.984130i | \(0.556785\pi\) | |||||||
\(558\) | −3.81764 | −0.161614 | ||||||||
\(559\) | 2.03092 | 0.0858988 | ||||||||
\(560\) | −2.04418 | −0.0863826 | ||||||||
\(561\) | 14.7018 | 0.620709 | ||||||||
\(562\) | −10.3974 | −0.438589 | ||||||||
\(563\) | −29.2806 | −1.23403 | −0.617015 | − | 0.786952i | \(-0.711658\pi\) | ||||
−0.617015 | + | 0.786952i | \(0.711658\pi\) | |||||||
\(564\) | −11.2988 | −0.475765 | ||||||||
\(565\) | 25.2560 | 1.06253 | ||||||||
\(566\) | 6.89539 | 0.289835 | ||||||||
\(567\) | −8.72491 | −0.366412 | ||||||||
\(568\) | 10.5814 | 0.443986 | ||||||||
\(569\) | −35.7409 | −1.49834 | −0.749168 | − | 0.662380i | \(-0.769546\pi\) | ||||
−0.749168 | + | 0.662380i | \(0.769546\pi\) | |||||||
\(570\) | 21.0519 | 0.881766 | ||||||||
\(571\) | 39.1562 | 1.63864 | 0.819319 | − | 0.573338i | \(-0.194352\pi\) | ||||
0.819319 | + | 0.573338i | \(0.194352\pi\) | |||||||
\(572\) | 4.36967 | 0.182705 | ||||||||
\(573\) | 21.1217 | 0.882372 | ||||||||
\(574\) | −0.511687 | −0.0213574 | ||||||||
\(575\) | −1.00074 | −0.0417337 | ||||||||
\(576\) | 2.42611 | 0.101088 | ||||||||
\(577\) | 19.5386 | 0.813402 | 0.406701 | − | 0.913561i | \(-0.366679\pi\) | ||||
0.406701 | + | 0.913561i | \(0.366679\pi\) | |||||||
\(578\) | −15.5733 | −0.647764 | ||||||||
\(579\) | 10.8629 | 0.451448 | ||||||||
\(580\) | −21.2137 | −0.880851 | ||||||||
\(581\) | −1.38165 | −0.0573206 | ||||||||
\(582\) | 18.7285 | 0.776320 | ||||||||
\(583\) | −19.4585 | −0.805889 | ||||||||
\(584\) | −12.0486 | −0.498574 | ||||||||
\(585\) | 4.88507 | 0.201973 | ||||||||
\(586\) | 8.75954 | 0.361853 | ||||||||
\(587\) | 6.93614 | 0.286285 | 0.143143 | − | 0.989702i | \(-0.454279\pi\) | ||||
0.143143 | + | 0.989702i | \(0.454279\pi\) | |||||||
\(588\) | 14.6639 | 0.604730 | ||||||||
\(589\) | −5.84061 | −0.240658 | ||||||||
\(590\) | −6.84298 | −0.281721 | ||||||||
\(591\) | 31.8784 | 1.31130 | ||||||||
\(592\) | −1.49810 | −0.0615716 | ||||||||
\(593\) | 34.9109 | 1.43362 | 0.716810 | − | 0.697268i | \(-0.245601\pi\) | ||||
0.716810 | + | 0.697268i | \(0.245601\pi\) | |||||||
\(594\) | −7.06367 | −0.289826 | ||||||||
\(595\) | −2.44166 | −0.100098 | ||||||||
\(596\) | 13.0036 | 0.532646 | ||||||||
\(597\) | 28.1615 | 1.15257 | ||||||||
\(598\) | 0.891328 | 0.0364491 | ||||||||
\(599\) | −6.07663 | −0.248284 | −0.124142 | − | 0.992264i | \(-0.539618\pi\) | ||||
−0.124142 | + | 0.992264i | \(0.539618\pi\) | |||||||
\(600\) | −2.16280 | −0.0882959 | ||||||||
\(601\) | −10.3947 | −0.424010 | −0.212005 | − | 0.977269i | \(-0.567999\pi\) | ||||
−0.212005 | + | 0.977269i | \(0.567999\pi\) | |||||||
\(602\) | −2.06183 | −0.0840340 | ||||||||
\(603\) | −14.7346 | −0.600038 | ||||||||
\(604\) | −9.41130 | −0.382940 | ||||||||
\(605\) | −41.1984 | −1.67495 | ||||||||
\(606\) | 28.4527 | 1.15581 | ||||||||
\(607\) | −33.3950 | −1.35546 | −0.677731 | − | 0.735310i | \(-0.737037\pi\) | ||||
−0.677731 | + | 0.735310i | \(0.737037\pi\) | |||||||
\(608\) | 3.71172 | 0.150530 | ||||||||
\(609\) | −17.0388 | −0.690445 | ||||||||
\(610\) | −36.4739 | −1.47678 | ||||||||
\(611\) | −4.01121 | −0.162276 | ||||||||
\(612\) | 2.89785 | 0.117139 | ||||||||
\(613\) | 8.51003 | 0.343717 | 0.171859 | − | 0.985122i | \(-0.445023\pi\) | ||||
0.171859 | + | 0.985122i | \(0.445023\pi\) | |||||||
\(614\) | −2.88547 | −0.116448 | ||||||||
\(615\) | −3.45678 | −0.139391 | ||||||||
\(616\) | −4.43618 | −0.178739 | ||||||||
\(617\) | 5.27523 | 0.212373 | 0.106186 | − | 0.994346i | \(-0.466136\pi\) | ||||
0.106186 | + | 0.994346i | \(0.466136\pi\) | |||||||
\(618\) | 3.99601 | 0.160743 | ||||||||
\(619\) | −18.7411 | −0.753267 | −0.376634 | − | 0.926362i | \(-0.622918\pi\) | ||||
−0.376634 | + | 0.926362i | \(0.622918\pi\) | |||||||
\(620\) | 3.83138 | 0.153872 | ||||||||
\(621\) | −1.44085 | −0.0578194 | ||||||||
\(622\) | 31.2564 | 1.25327 | ||||||||
\(623\) | 3.25900 | 0.130569 | ||||||||
\(624\) | 1.92634 | 0.0771152 | ||||||||
\(625\) | −28.7803 | −1.15121 | ||||||||
\(626\) | −29.2113 | −1.16752 | ||||||||
\(627\) | 45.6856 | 1.82451 | ||||||||
\(628\) | −7.04207 | −0.281009 | ||||||||
\(629\) | −1.78940 | −0.0713479 | ||||||||
\(630\) | −4.95943 | −0.197588 | ||||||||
\(631\) | −9.07510 | −0.361274 | −0.180637 | − | 0.983550i | \(-0.557816\pi\) | ||||
−0.180637 | + | 0.983550i | \(0.557816\pi\) | |||||||
\(632\) | 11.2960 | 0.449329 | ||||||||
\(633\) | 14.9733 | 0.595137 | ||||||||
\(634\) | 19.4126 | 0.770972 | ||||||||
\(635\) | 1.47044 | 0.0583527 | ||||||||
\(636\) | −8.57815 | −0.340146 | ||||||||
\(637\) | 5.20588 | 0.206264 | ||||||||
\(638\) | −46.0368 | −1.82261 | ||||||||
\(639\) | 25.6717 | 1.01556 | ||||||||
\(640\) | −2.43485 | −0.0962458 | ||||||||
\(641\) | −38.7985 | −1.53245 | −0.766225 | − | 0.642573i | \(-0.777867\pi\) | ||||
−0.766225 | + | 0.642573i | \(0.777867\pi\) | |||||||
\(642\) | −41.8737 | −1.65262 | ||||||||
\(643\) | −45.6826 | −1.80154 | −0.900772 | − | 0.434291i | \(-0.856999\pi\) | ||||
−0.900772 | + | 0.434291i | \(0.856999\pi\) | |||||||
\(644\) | −0.904895 | −0.0356578 | ||||||||
\(645\) | −13.9290 | −0.548455 | ||||||||
\(646\) | 4.43343 | 0.174431 | ||||||||
\(647\) | −7.20417 | −0.283225 | −0.141613 | − | 0.989922i | \(-0.545229\pi\) | ||||
−0.141613 | + | 0.989922i | \(0.545229\pi\) | |||||||
\(648\) | −10.3923 | −0.408249 | ||||||||
\(649\) | −14.8503 | −0.582924 | ||||||||
\(650\) | −0.767821 | −0.0301164 | ||||||||
\(651\) | 3.07735 | 0.120611 | ||||||||
\(652\) | 6.87365 | 0.269193 | ||||||||
\(653\) | −7.03589 | −0.275336 | −0.137668 | − | 0.990478i | \(-0.543961\pi\) | ||||
−0.137668 | + | 0.990478i | \(0.543961\pi\) | |||||||
\(654\) | 4.21027 | 0.164635 | ||||||||
\(655\) | 33.2625 | 1.29967 | ||||||||
\(656\) | −0.609475 | −0.0237960 | ||||||||
\(657\) | −29.2312 | −1.14042 | ||||||||
\(658\) | 4.07227 | 0.158754 | ||||||||
\(659\) | 21.4415 | 0.835243 | 0.417621 | − | 0.908621i | \(-0.362864\pi\) | ||||
0.417621 | + | 0.908621i | \(0.362864\pi\) | |||||||
\(660\) | −29.9693 | −1.16655 | ||||||||
\(661\) | 48.3581 | 1.88091 | 0.940456 | − | 0.339915i | \(-0.110398\pi\) | ||||
0.940456 | + | 0.339915i | \(0.110398\pi\) | |||||||
\(662\) | −8.75448 | −0.340252 | ||||||||
\(663\) | 2.30090 | 0.0893595 | ||||||||
\(664\) | −1.64570 | −0.0638655 | ||||||||
\(665\) | −7.58743 | −0.294228 | ||||||||
\(666\) | −3.63456 | −0.140836 | ||||||||
\(667\) | −9.39062 | −0.363606 | ||||||||
\(668\) | −5.22780 | −0.202270 | ||||||||
\(669\) | −56.3081 | −2.17700 | ||||||||
\(670\) | 14.7876 | 0.571295 | ||||||||
\(671\) | −79.1535 | −3.05569 | ||||||||
\(672\) | −1.95566 | −0.0754412 | ||||||||
\(673\) | 20.5451 | 0.791956 | 0.395978 | − | 0.918260i | \(-0.370406\pi\) | ||||
0.395978 | + | 0.918260i | \(0.370406\pi\) | |||||||
\(674\) | −24.9438 | −0.960800 | ||||||||
\(675\) | 1.24120 | 0.0477738 | ||||||||
\(676\) | −12.3161 | −0.473697 | ||||||||
\(677\) | 30.6479 | 1.17789 | 0.588947 | − | 0.808172i | \(-0.299543\pi\) | ||||
0.588947 | + | 0.808172i | \(0.299543\pi\) | |||||||
\(678\) | 24.1623 | 0.927947 | ||||||||
\(679\) | −6.75004 | −0.259043 | ||||||||
\(680\) | −2.90828 | −0.111528 | ||||||||
\(681\) | 40.2616 | 1.54283 | ||||||||
\(682\) | 8.31465 | 0.318384 | ||||||||
\(683\) | 20.5442 | 0.786102 | 0.393051 | − | 0.919517i | \(-0.371420\pi\) | ||||
0.393051 | + | 0.919517i | \(0.371420\pi\) | |||||||
\(684\) | 9.00504 | 0.344316 | ||||||||
\(685\) | 14.4503 | 0.552116 | ||||||||
\(686\) | −11.1620 | −0.426167 | ||||||||
\(687\) | −67.6305 | −2.58026 | ||||||||
\(688\) | −2.45587 | −0.0936291 | ||||||||
\(689\) | −3.04535 | −0.116019 | ||||||||
\(690\) | −6.11316 | −0.232724 | ||||||||
\(691\) | 9.15226 | 0.348168 | 0.174084 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174084 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(692\) | 11.4441 | 0.435038 | ||||||||
\(693\) | −10.7627 | −0.408840 | ||||||||
\(694\) | −29.1632 | −1.10702 | ||||||||
\(695\) | 4.43089 | 0.168073 | ||||||||
\(696\) | −20.2950 | −0.769280 | ||||||||
\(697\) | −0.727982 | −0.0275743 | ||||||||
\(698\) | 0.661633 | 0.0250432 | ||||||||
\(699\) | −22.5453 | −0.852742 | ||||||||
\(700\) | 0.779508 | 0.0294626 | ||||||||
\(701\) | −43.0248 | −1.62502 | −0.812512 | − | 0.582945i | \(-0.801900\pi\) | ||||
−0.812512 | + | 0.582945i | \(0.801900\pi\) | |||||||
\(702\) | −1.10550 | −0.0417243 | ||||||||
\(703\) | −5.56052 | −0.209719 | ||||||||
\(704\) | −5.28397 | −0.199147 | ||||||||
\(705\) | 27.5108 | 1.03612 | ||||||||
\(706\) | 21.1964 | 0.797738 | ||||||||
\(707\) | −10.2548 | −0.385672 | ||||||||
\(708\) | −6.54664 | −0.246038 | ||||||||
\(709\) | −36.0122 | −1.35247 | −0.676233 | − | 0.736688i | \(-0.736389\pi\) | ||||
−0.676233 | + | 0.736688i | \(0.736389\pi\) | |||||||
\(710\) | −25.7641 | −0.966910 | ||||||||
\(711\) | 27.4053 | 1.02778 | ||||||||
\(712\) | 3.88182 | 0.145477 | ||||||||
\(713\) | 1.69603 | 0.0635168 | ||||||||
\(714\) | −2.33592 | −0.0874196 | ||||||||
\(715\) | −10.6395 | −0.397893 | ||||||||
\(716\) | −1.65368 | −0.0618009 | ||||||||
\(717\) | 52.9258 | 1.97655 | ||||||||
\(718\) | −31.5311 | −1.17673 | ||||||||
\(719\) | −46.1319 | −1.72043 | −0.860214 | − | 0.509932i | \(-0.829670\pi\) | ||||
−0.860214 | + | 0.509932i | \(0.829670\pi\) | |||||||
\(720\) | −5.90722 | −0.220149 | ||||||||
\(721\) | −1.44023 | −0.0536369 | ||||||||
\(722\) | −5.22317 | −0.194386 | ||||||||
\(723\) | 66.6701 | 2.47949 | ||||||||
\(724\) | −8.36335 | −0.310821 | ||||||||
\(725\) | 8.08941 | 0.300433 | ||||||||
\(726\) | −39.4142 | −1.46280 | ||||||||
\(727\) | 17.3359 | 0.642953 | 0.321476 | − | 0.946918i | \(-0.395821\pi\) | ||||
0.321476 | + | 0.946918i | \(0.395821\pi\) | |||||||
\(728\) | −0.694283 | −0.0257318 | ||||||||
\(729\) | −15.8710 | −0.587816 | ||||||||
\(730\) | 29.3364 | 1.08579 | ||||||||
\(731\) | −2.93339 | −0.108495 | ||||||||
\(732\) | −34.8943 | −1.28973 | ||||||||
\(733\) | −7.93149 | −0.292956 | −0.146478 | − | 0.989214i | \(-0.546794\pi\) | ||||
−0.146478 | + | 0.989214i | \(0.546794\pi\) | |||||||
\(734\) | −17.7182 | −0.653992 | ||||||||
\(735\) | −35.7044 | −1.31698 | ||||||||
\(736\) | −1.07783 | −0.0397293 | ||||||||
\(737\) | 32.0912 | 1.18209 | ||||||||
\(738\) | −1.47865 | −0.0544300 | ||||||||
\(739\) | −3.96053 | −0.145691 | −0.0728453 | − | 0.997343i | \(-0.523208\pi\) | ||||
−0.0728453 | + | 0.997343i | \(0.523208\pi\) | |||||||
\(740\) | 3.64765 | 0.134090 | ||||||||
\(741\) | 7.15002 | 0.262662 | ||||||||
\(742\) | 3.09170 | 0.113500 | ||||||||
\(743\) | −8.63437 | −0.316764 | −0.158382 | − | 0.987378i | \(-0.550628\pi\) | ||||
−0.158382 | + | 0.987378i | \(0.550628\pi\) | |||||||
\(744\) | 3.66546 | 0.134382 | ||||||||
\(745\) | −31.6617 | −1.15999 | ||||||||
\(746\) | −26.0262 | −0.952888 | ||||||||
\(747\) | −3.99265 | −0.146084 | ||||||||
\(748\) | −6.31139 | −0.230767 | ||||||||
\(749\) | 15.0920 | 0.551448 | ||||||||
\(750\) | −23.0926 | −0.843223 | ||||||||
\(751\) | 12.2092 | 0.445519 | 0.222759 | − | 0.974873i | \(-0.428494\pi\) | ||||
0.222759 | + | 0.974873i | \(0.428494\pi\) | |||||||
\(752\) | 4.85052 | 0.176880 | ||||||||
\(753\) | −22.3250 | −0.813569 | ||||||||
\(754\) | −7.20498 | −0.262390 | ||||||||
\(755\) | 22.9151 | 0.833965 | ||||||||
\(756\) | 1.12232 | 0.0408186 | ||||||||
\(757\) | −17.9274 | −0.651583 | −0.325791 | − | 0.945442i | \(-0.605631\pi\) | ||||
−0.325791 | + | 0.945442i | \(0.605631\pi\) | |||||||
\(758\) | −0.634769 | −0.0230558 | ||||||||
\(759\) | −13.2664 | −0.481541 | ||||||||
\(760\) | −9.03746 | −0.327823 | ||||||||
\(761\) | −27.4872 | −0.996408 | −0.498204 | − | 0.867060i | \(-0.666007\pi\) | ||||
−0.498204 | + | 0.867060i | \(0.666007\pi\) | |||||||
\(762\) | 1.40676 | 0.0509616 | ||||||||
\(763\) | −1.51745 | −0.0549353 | ||||||||
\(764\) | −9.06744 | −0.328048 | ||||||||
\(765\) | −7.05583 | −0.255104 | ||||||||
\(766\) | 8.55509 | 0.309108 | ||||||||
\(767\) | −2.32414 | −0.0839197 | ||||||||
\(768\) | −2.32940 | −0.0840551 | ||||||||
\(769\) | −27.7383 | −1.00027 | −0.500134 | − | 0.865948i | \(-0.666716\pi\) | ||||
−0.500134 | + | 0.865948i | \(0.666716\pi\) | |||||||
\(770\) | 10.8014 | 0.389256 | ||||||||
\(771\) | 68.3024 | 2.45985 | ||||||||
\(772\) | −4.66340 | −0.167839 | ||||||||
\(773\) | 30.2622 | 1.08846 | 0.544229 | − | 0.838937i | \(-0.316822\pi\) | ||||
0.544229 | + | 0.838937i | \(0.316822\pi\) | |||||||
\(774\) | −5.95821 | −0.214164 | ||||||||
\(775\) | −1.46102 | −0.0524813 | ||||||||
\(776\) | −8.04003 | −0.288620 | ||||||||
\(777\) | 2.92977 | 0.105105 | ||||||||
\(778\) | 7.48402 | 0.268315 | ||||||||
\(779\) | −2.26220 | −0.0810516 | ||||||||
\(780\) | −4.69034 | −0.167941 | ||||||||
\(781\) | −55.9118 | −2.00068 | ||||||||
\(782\) | −1.28740 | −0.0460375 | ||||||||
\(783\) | 11.6470 | 0.416231 | ||||||||
\(784\) | −6.29515 | −0.224827 | ||||||||
\(785\) | 17.1464 | 0.611980 | ||||||||
\(786\) | 31.8220 | 1.13505 | ||||||||
\(787\) | −0.118372 | −0.00421949 | −0.00210974 | − | 0.999998i | \(-0.500672\pi\) | ||||
−0.00210974 | + | 0.999998i | \(0.500672\pi\) | |||||||
\(788\) | −13.6852 | −0.487516 | ||||||||
\(789\) | 14.4015 | 0.512708 | ||||||||
\(790\) | −27.5039 | −0.978545 | ||||||||
\(791\) | −8.70847 | −0.309638 | ||||||||
\(792\) | −12.8195 | −0.455521 | ||||||||
\(793\) | −12.3879 | −0.439908 | ||||||||
\(794\) | −0.224964 | −0.00798369 | ||||||||
\(795\) | 20.8865 | 0.740767 | ||||||||
\(796\) | −12.0896 | −0.428504 | ||||||||
\(797\) | 27.8852 | 0.987743 | 0.493872 | − | 0.869535i | \(-0.335581\pi\) | ||||
0.493872 | + | 0.869535i | \(0.335581\pi\) | |||||||
\(798\) | −7.25885 | −0.256960 | ||||||||
\(799\) | 5.79366 | 0.204965 | ||||||||
\(800\) | 0.928478 | 0.0328267 | ||||||||
\(801\) | 9.41774 | 0.332760 | ||||||||
\(802\) | 11.8662 | 0.419010 | ||||||||
\(803\) | 63.6643 | 2.24666 | ||||||||
\(804\) | 14.1472 | 0.498933 | ||||||||
\(805\) | 2.20328 | 0.0776554 | ||||||||
\(806\) | 1.30128 | 0.0458358 | ||||||||
\(807\) | −13.9104 | −0.489669 | ||||||||
\(808\) | −12.2146 | −0.429708 | ||||||||
\(809\) | −8.48860 | −0.298443 | −0.149222 | − | 0.988804i | \(-0.547677\pi\) | ||||
−0.149222 | + | 0.988804i | \(0.547677\pi\) | |||||||
\(810\) | 25.3037 | 0.889081 | ||||||||
\(811\) | 37.6517 | 1.32213 | 0.661065 | − | 0.750328i | \(-0.270105\pi\) | ||||
0.661065 | + | 0.750328i | \(0.270105\pi\) | |||||||
\(812\) | 7.31465 | 0.256694 | ||||||||
\(813\) | −36.0929 | −1.26583 | ||||||||
\(814\) | 7.91592 | 0.277453 | ||||||||
\(815\) | −16.7363 | −0.586246 | ||||||||
\(816\) | −2.78234 | −0.0974013 | ||||||||
\(817\) | −9.11548 | −0.318910 | ||||||||
\(818\) | −1.66699 | −0.0582850 | ||||||||
\(819\) | −1.68441 | −0.0588580 | ||||||||
\(820\) | 1.48398 | 0.0518227 | ||||||||
\(821\) | 26.1360 | 0.912151 | 0.456076 | − | 0.889941i | \(-0.349255\pi\) | ||||
0.456076 | + | 0.889941i | \(0.349255\pi\) | |||||||
\(822\) | 13.8245 | 0.482184 | ||||||||
\(823\) | −16.2827 | −0.567579 | −0.283789 | − | 0.958887i | \(-0.591592\pi\) | ||||
−0.283789 | + | 0.958887i | \(0.591592\pi\) | |||||||
\(824\) | −1.71547 | −0.0597611 | ||||||||
\(825\) | 11.4282 | 0.397878 | ||||||||
\(826\) | 2.35951 | 0.0820980 | ||||||||
\(827\) | 37.4397 | 1.30191 | 0.650953 | − | 0.759118i | \(-0.274370\pi\) | ||||
0.650953 | + | 0.759118i | \(0.274370\pi\) | |||||||
\(828\) | −2.61493 | −0.0908752 | ||||||||
\(829\) | −17.3493 | −0.602566 | −0.301283 | − | 0.953535i | \(-0.597415\pi\) | ||||
−0.301283 | + | 0.953535i | \(0.597415\pi\) | |||||||
\(830\) | 4.00703 | 0.139086 | ||||||||
\(831\) | −41.3536 | −1.43454 | ||||||||
\(832\) | −0.826967 | −0.0286699 | ||||||||
\(833\) | −7.51919 | −0.260525 | ||||||||
\(834\) | 4.23900 | 0.146785 | ||||||||
\(835\) | 12.7289 | 0.440502 | ||||||||
\(836\) | −19.6126 | −0.678315 | ||||||||
\(837\) | −2.10356 | −0.0727095 | ||||||||
\(838\) | −12.6731 | −0.437785 | ||||||||
\(839\) | 26.6947 | 0.921604 | 0.460802 | − | 0.887503i | \(-0.347562\pi\) | ||||
0.460802 | + | 0.887503i | \(0.347562\pi\) | |||||||
\(840\) | 4.76173 | 0.164295 | ||||||||
\(841\) | 46.9084 | 1.61753 | ||||||||
\(842\) | −25.5422 | −0.880243 | ||||||||
\(843\) | 24.2198 | 0.834174 | ||||||||
\(844\) | −6.42797 | −0.221260 | ||||||||
\(845\) | 29.9879 | 1.03161 | ||||||||
\(846\) | 11.7679 | 0.404589 | ||||||||
\(847\) | 14.2055 | 0.488107 | ||||||||
\(848\) | 3.68255 | 0.126459 | ||||||||
\(849\) | −16.0621 | −0.551251 | ||||||||
\(850\) | 1.10901 | 0.0380389 | ||||||||
\(851\) | 1.61470 | 0.0553510 | ||||||||
\(852\) | −24.6484 | −0.844439 | ||||||||
\(853\) | −56.4901 | −1.93419 | −0.967093 | − | 0.254424i | \(-0.918114\pi\) | ||||
−0.967093 | + | 0.254424i | \(0.918114\pi\) | |||||||
\(854\) | 12.5765 | 0.430358 | ||||||||
\(855\) | −21.9259 | −0.749850 | ||||||||
\(856\) | 17.9762 | 0.614413 | ||||||||
\(857\) | 21.1982 | 0.724118 | 0.362059 | − | 0.932155i | \(-0.382074\pi\) | ||||
0.362059 | + | 0.932155i | \(0.382074\pi\) | |||||||
\(858\) | −10.1787 | −0.347495 | ||||||||
\(859\) | 32.9341 | 1.12370 | 0.561849 | − | 0.827240i | \(-0.310090\pi\) | ||||
0.561849 | + | 0.827240i | \(0.310090\pi\) | |||||||
\(860\) | 5.97966 | 0.203905 | ||||||||
\(861\) | 1.19192 | 0.0406207 | ||||||||
\(862\) | 30.7220 | 1.04639 | ||||||||
\(863\) | 31.6222 | 1.07643 | 0.538217 | − | 0.842806i | \(-0.319098\pi\) | ||||
0.538217 | + | 0.842806i | \(0.319098\pi\) | |||||||
\(864\) | 1.33681 | 0.0454792 | ||||||||
\(865\) | −27.8646 | −0.947424 | ||||||||
\(866\) | 2.16933 | 0.0737170 | ||||||||
\(867\) | 36.2765 | 1.23201 | ||||||||
\(868\) | −1.32109 | −0.0448407 | ||||||||
\(869\) | −59.6874 | −2.02476 | ||||||||
\(870\) | 49.4152 | 1.67533 | ||||||||
\(871\) | 5.02243 | 0.170179 | ||||||||
\(872\) | −1.80745 | −0.0612078 | ||||||||
\(873\) | −19.5060 | −0.660179 | ||||||||
\(874\) | −4.00059 | −0.135322 | ||||||||
\(875\) | 8.32294 | 0.281367 | ||||||||
\(876\) | 28.0660 | 0.948262 | ||||||||
\(877\) | −13.1255 | −0.443215 | −0.221608 | − | 0.975136i | \(-0.571130\pi\) | ||||
−0.221608 | + | 0.975136i | \(0.571130\pi\) | |||||||
\(878\) | 11.2301 | 0.378998 | ||||||||
\(879\) | −20.4045 | −0.688227 | ||||||||
\(880\) | 12.8657 | 0.433701 | ||||||||
\(881\) | 41.6652 | 1.40373 | 0.701867 | − | 0.712308i | \(-0.252350\pi\) | ||||
0.701867 | + | 0.712308i | \(0.252350\pi\) | |||||||
\(882\) | −15.2728 | −0.514260 | ||||||||
\(883\) | −7.85921 | −0.264483 | −0.132242 | − | 0.991217i | \(-0.542218\pi\) | ||||
−0.132242 | + | 0.991217i | \(0.542218\pi\) | |||||||
\(884\) | −0.987764 | −0.0332221 | ||||||||
\(885\) | 15.9401 | 0.535819 | ||||||||
\(886\) | −15.0579 | −0.505880 | ||||||||
\(887\) | 26.2520 | 0.881456 | 0.440728 | − | 0.897641i | \(-0.354720\pi\) | ||||
0.440728 | + | 0.897641i | \(0.354720\pi\) | |||||||
\(888\) | 3.48968 | 0.117106 | ||||||||
\(889\) | −0.507019 | −0.0170049 | ||||||||
\(890\) | −9.45164 | −0.316820 | ||||||||
\(891\) | 54.9126 | 1.83964 | ||||||||
\(892\) | 24.1728 | 0.809364 | ||||||||
\(893\) | 18.0037 | 0.602472 | ||||||||
\(894\) | −30.2905 | −1.01307 | ||||||||
\(895\) | 4.02645 | 0.134590 | ||||||||
\(896\) | 0.839554 | 0.0280475 | ||||||||
\(897\) | −2.07626 | −0.0693243 | ||||||||
\(898\) | −4.70643 | −0.157055 | ||||||||
\(899\) | −13.7097 | −0.457245 | ||||||||
\(900\) | 2.25259 | 0.0750865 | ||||||||
\(901\) | 4.39860 | 0.146539 | ||||||||
\(902\) | 3.22044 | 0.107229 | ||||||||
\(903\) | 4.80284 | 0.159828 | ||||||||
\(904\) | −10.3727 | −0.344992 | ||||||||
\(905\) | 20.3635 | 0.676905 | ||||||||
\(906\) | 21.9227 | 0.728333 | ||||||||
\(907\) | 47.7509 | 1.58554 | 0.792772 | − | 0.609519i | \(-0.208637\pi\) | ||||
0.792772 | + | 0.609519i | \(0.208637\pi\) | |||||||
\(908\) | −17.2841 | −0.573593 | ||||||||
\(909\) | −29.6340 | −0.982898 | ||||||||
\(910\) | 1.69047 | 0.0560386 | ||||||||
\(911\) | −8.59572 | −0.284789 | −0.142395 | − | 0.989810i | \(-0.545480\pi\) | ||||
−0.142395 | + | 0.989810i | \(0.545480\pi\) | |||||||
\(912\) | −8.64608 | −0.286300 | ||||||||
\(913\) | 8.69582 | 0.287790 | ||||||||
\(914\) | −33.9258 | −1.12217 | ||||||||
\(915\) | 84.9623 | 2.80877 | ||||||||
\(916\) | 29.0334 | 0.959291 | ||||||||
\(917\) | −11.4692 | −0.378745 | ||||||||
\(918\) | 1.59674 | 0.0527004 | ||||||||
\(919\) | 35.2148 | 1.16163 | 0.580815 | − | 0.814036i | \(-0.302734\pi\) | ||||
0.580815 | + | 0.814036i | \(0.302734\pi\) | |||||||
\(920\) | 2.62435 | 0.0865221 | ||||||||
\(921\) | 6.72142 | 0.221478 | ||||||||
\(922\) | −14.5339 | −0.478647 | ||||||||
\(923\) | −8.75048 | −0.288025 | ||||||||
\(924\) | 10.3336 | 0.339952 | ||||||||
\(925\) | −1.39095 | −0.0457343 | ||||||||
\(926\) | 17.3313 | 0.569541 | ||||||||
\(927\) | −4.16192 | −0.136695 | ||||||||
\(928\) | 8.71254 | 0.286003 | ||||||||
\(929\) | 55.6573 | 1.82606 | 0.913029 | − | 0.407894i | \(-0.133737\pi\) | ||||
0.913029 | + | 0.407894i | \(0.133737\pi\) | |||||||
\(930\) | −8.92483 | −0.292657 | ||||||||
\(931\) | −23.3658 | −0.765783 | ||||||||
\(932\) | 9.67858 | 0.317032 | ||||||||
\(933\) | −72.8088 | −2.38365 | ||||||||
\(934\) | 6.04447 | 0.197781 | ||||||||
\(935\) | 15.3673 | 0.502564 | ||||||||
\(936\) | −2.00632 | −0.0655785 | ||||||||
\(937\) | −10.4278 | −0.340661 | −0.170331 | − | 0.985387i | \(-0.554484\pi\) | ||||
−0.170331 | + | 0.985387i | \(0.554484\pi\) | |||||||
\(938\) | −5.09888 | −0.166484 | ||||||||
\(939\) | 68.0447 | 2.22056 | ||||||||
\(940\) | −11.8103 | −0.385208 | ||||||||
\(941\) | −0.429183 | −0.0139910 | −0.00699548 | − | 0.999976i | \(-0.502227\pi\) | ||||
−0.00699548 | + | 0.999976i | \(0.502227\pi\) | |||||||
\(942\) | 16.4038 | 0.534465 | ||||||||
\(943\) | 0.656909 | 0.0213919 | ||||||||
\(944\) | 2.81044 | 0.0914719 | ||||||||
\(945\) | −2.73269 | −0.0888944 | ||||||||
\(946\) | 12.9767 | 0.421910 | ||||||||
\(947\) | −24.9345 | −0.810263 | −0.405132 | − | 0.914258i | \(-0.632774\pi\) | ||||
−0.405132 | + | 0.914258i | \(0.632774\pi\) | |||||||
\(948\) | −26.3128 | −0.854600 | ||||||||
\(949\) | 9.96377 | 0.323438 | ||||||||
\(950\) | 3.44625 | 0.111811 | ||||||||
\(951\) | −45.2197 | −1.46635 | ||||||||
\(952\) | 1.00280 | 0.0325009 | ||||||||
\(953\) | −9.58228 | −0.310400 | −0.155200 | − | 0.987883i | \(-0.549602\pi\) | ||||
−0.155200 | + | 0.987883i | \(0.549602\pi\) | |||||||
\(954\) | 8.93429 | 0.289258 | ||||||||
\(955\) | 22.0778 | 0.714422 | ||||||||
\(956\) | −22.7208 | −0.734842 | ||||||||
\(957\) | 107.238 | 3.46652 | ||||||||
\(958\) | 32.2044 | 1.04048 | ||||||||
\(959\) | −4.98256 | −0.160895 | ||||||||
\(960\) | 5.67174 | 0.183055 | ||||||||
\(961\) | −28.5239 | −0.920126 | ||||||||
\(962\) | 1.23888 | 0.0399431 | ||||||||
\(963\) | 43.6122 | 1.40538 | ||||||||
\(964\) | −28.6211 | −0.921824 | ||||||||
\(965\) | 11.3547 | 0.365520 | ||||||||
\(966\) | 2.10786 | 0.0678194 | ||||||||
\(967\) | −10.6500 | −0.342482 | −0.171241 | − | 0.985229i | \(-0.554778\pi\) | ||||
−0.171241 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(968\) | 16.9203 | 0.543840 | ||||||||
\(969\) | −10.3272 | −0.331759 | ||||||||
\(970\) | 19.5762 | 0.628555 | ||||||||
\(971\) | −26.7795 | −0.859394 | −0.429697 | − | 0.902973i | \(-0.641380\pi\) | ||||
−0.429697 | + | 0.902973i | \(0.641380\pi\) | |||||||
\(972\) | 20.1974 | 0.647833 | ||||||||
\(973\) | −1.52780 | −0.0489791 | ||||||||
\(974\) | −31.7527 | −1.01742 | ||||||||
\(975\) | 1.78856 | 0.0572799 | ||||||||
\(976\) | 14.9799 | 0.479496 | ||||||||
\(977\) | −13.8623 | −0.443495 | −0.221748 | − | 0.975104i | \(-0.571176\pi\) | ||||
−0.221748 | + | 0.975104i | \(0.571176\pi\) | |||||||
\(978\) | −16.0115 | −0.511991 | ||||||||
\(979\) | −20.5114 | −0.655548 | ||||||||
\(980\) | 15.3277 | 0.489626 | ||||||||
\(981\) | −4.38507 | −0.140004 | ||||||||
\(982\) | −23.6489 | −0.754666 | ||||||||
\(983\) | 39.6329 | 1.26409 | 0.632046 | − | 0.774931i | \(-0.282215\pi\) | ||||
0.632046 | + | 0.774931i | \(0.282215\pi\) | |||||||
\(984\) | 1.41971 | 0.0452587 | ||||||||
\(985\) | 33.3214 | 1.06171 | ||||||||
\(986\) | 10.4066 | 0.331414 | ||||||||
\(987\) | −9.48595 | −0.301941 | ||||||||
\(988\) | −3.06947 | −0.0976527 | ||||||||
\(989\) | 2.64700 | 0.0841698 | ||||||||
\(990\) | 31.2135 | 0.992031 | ||||||||
\(991\) | 40.3000 | 1.28017 | 0.640086 | − | 0.768303i | \(-0.278899\pi\) | ||||
0.640086 | + | 0.768303i | \(0.278899\pi\) | |||||||
\(992\) | −1.57356 | −0.0499606 | ||||||||
\(993\) | 20.3927 | 0.647143 | ||||||||
\(994\) | 8.88367 | 0.281773 | ||||||||
\(995\) | 29.4363 | 0.933192 | ||||||||
\(996\) | 3.83350 | 0.121469 | ||||||||
\(997\) | −14.8039 | −0.468844 | −0.234422 | − | 0.972135i | \(-0.575320\pi\) | ||||
−0.234422 | + | 0.972135i | \(0.575320\pi\) | |||||||
\(998\) | −24.6965 | −0.781753 | ||||||||
\(999\) | −2.00268 | −0.0633619 |
(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 | 8042.2.a.a.1.11 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.11 | ✓ | 67 | 1.1 | even | 1 | trivial |