Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.59308 | −0.919763 | −0.459881 | − | 0.887980i | \(-0.652108\pi\) | ||||
−0.459881 | + | 0.887980i | \(0.652108\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.75433 | 1.23177 | 0.615886 | − | 0.787835i | \(-0.288798\pi\) | ||||
0.615886 | + | 0.787835i | \(0.288798\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.46360 | −0.553189 | −0.276594 | − | 0.960987i | \(-0.589206\pi\) | ||||
−0.276594 | + | 0.960987i | \(0.589206\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.462108 | −0.154036 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.86989 | 1.76984 | 0.884920 | − | 0.465743i | \(-0.154213\pi\) | ||||
0.884920 | + | 0.465743i | \(0.154213\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.69840 | −1.85780 | −0.928901 | − | 0.370328i | \(-0.879245\pi\) | ||||
−0.928901 | + | 0.370328i | \(0.879245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.38785 | −1.13294 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.07288 | −1.47289 | −0.736445 | − | 0.676497i | \(-0.763497\pi\) | ||||
−0.736445 | + | 0.676497i | \(0.763497\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.48446 | 0.340558 | 0.170279 | − | 0.985396i | \(-0.445533\pi\) | ||||
0.170279 | + | 0.985396i | \(0.445533\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.33163 | 0.508802 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.40969 | −0.919483 | −0.459742 | − | 0.888053i | \(-0.652058\pi\) | ||||
−0.459742 | + | 0.888053i | \(0.652058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.58632 | 0.517264 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.51540 | 1.06144 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.17517 | 1.51809 | 0.759045 | − | 0.651038i | \(-0.225666\pi\) | ||||
0.759045 | + | 0.651038i | \(0.225666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.84800 | 1.58915 | 0.794574 | − | 0.607168i | \(-0.207694\pi\) | ||||
0.794574 | + | 0.607168i | \(0.207694\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.35119 | −1.62783 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.03123 | −0.681403 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.89315 | −1.29763 | −0.648813 | − | 0.760948i | \(-0.724734\pi\) | ||||
−0.648813 | + | 0.760948i | \(0.724734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.6711 | 1.70874 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.35916 | 0.836961 | 0.418480 | − | 0.908226i | \(-0.362563\pi\) | ||||
0.418480 | + | 0.908226i | \(0.362563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.36082 | 1.27501 | 0.637507 | − | 0.770445i | \(-0.279966\pi\) | ||||
0.637507 | + | 0.770445i | \(0.279966\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.27280 | −0.189738 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.07330 | −1.32348 | −0.661739 | − | 0.749735i | \(-0.730181\pi\) | ||||
−0.661739 | + | 0.749735i | \(0.730181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.85788 | −0.693982 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.67456 | 1.35471 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.3433 | 1.69549 | 0.847743 | − | 0.530406i | \(-0.177961\pi\) | ||||
0.847743 | + | 0.530406i | \(0.177961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.1676 | 2.18004 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.36485 | −0.313232 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.57315 | 0.334996 | 0.167498 | − | 0.985872i | \(-0.446431\pi\) | ||||
0.167498 | + | 0.985872i | \(0.446431\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.03940 | 0.389156 | 0.194578 | − | 0.980887i | \(-0.437666\pi\) | ||||
0.194578 | + | 0.980887i | \(0.437666\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.676342 | 0.0852110 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.4496 | −2.28839 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.68264 | −0.205568 | −0.102784 | − | 0.994704i | \(-0.532775\pi\) | ||||
−0.102784 | + | 0.994704i | \(0.532775\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.02497 | 0.845707 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.21882 | −0.500681 | −0.250341 | − | 0.968158i | \(-0.580543\pi\) | ||||
−0.250341 | + | 0.968158i | \(0.580543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5331 | −1.46689 | −0.733445 | − | 0.679749i | \(-0.762089\pi\) | ||||
−0.733445 | + | 0.679749i | \(0.762089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.12021 | −0.475761 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.59118 | −0.979055 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2617 | −1.60457 | −0.802284 | − | 0.596943i | \(-0.796382\pi\) | ||||
−0.802284 | + | 0.596943i | \(0.796382\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.40013 | −0.822237 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.2574 | 1.89425 | 0.947124 | − | 0.320868i | \(-0.103975\pi\) | ||||
0.947124 | + | 0.320868i | \(0.103975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.7267 | −1.81427 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.0237 | −1.39628 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.75945 | −0.928500 | −0.464250 | − | 0.885704i | \(-0.653676\pi\) | ||||
−0.464250 | + | 0.885704i | \(0.653676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.80378 | 1.02772 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.0955 | −1.46164 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.08868 | 0.419490 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.54144 | 0.258044 | 0.129022 | − | 0.991642i | \(-0.458816\pi\) | ||||
0.129022 | + | 0.991642i | \(0.458816\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.71253 | −0.272619 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5172 | −1.14600 | −0.573001 | − | 0.819554i | \(-0.694221\pi\) | ||||
−0.573001 | + | 0.819554i | \(0.694221\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.61935 | −0.159559 | −0.0797797 | − | 0.996813i | \(-0.525422\pi\) | ||||
−0.0797797 | + | 0.996813i | \(0.525422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.42206 | 0.626729 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.13438 | −0.399685 | −0.199843 | − | 0.979828i | \(-0.564043\pi\) | ||||
−0.199843 | + | 0.979828i | \(0.564043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.4290 | −1.76518 | −0.882588 | − | 0.470147i | \(-0.844201\pi\) | ||||
−0.882588 | + | 0.470147i | \(0.844201\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.5744 | 1.19351 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.13298 | 0.576943 | 0.288471 | − | 0.957489i | \(-0.406853\pi\) | ||||
0.288471 | + | 0.957489i | \(0.406853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.1457 | −1.13259 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.09539 | 0.286169 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.88827 | 0.814786 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.4557 | 2.13233 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.53756 | −0.769806 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.64806 | −0.594621 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1025 | −1.51760 | −0.758802 | − | 0.651322i | \(-0.774215\pi\) | ||||
−0.758802 | + | 0.651322i | \(0.774215\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.3194 | −1.17271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.3670 | −1.08051 | −0.540256 | − | 0.841500i | \(-0.681673\pi\) | ||||
−0.540256 | + | 0.841500i | \(0.681673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17265 | −0.188393 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.1912 | 1.30745 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.35637 | 0.115882 | 0.0579411 | − | 0.998320i | \(-0.481546\pi\) | ||||
0.0579411 | + | 0.998320i | \(0.481546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.42003 | 0.798996 | 0.399498 | − | 0.916734i | \(-0.369184\pi\) | ||||
0.399498 | + | 0.916734i | \(0.369184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.4545 | 1.21729 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −39.3189 | −3.28801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.5171 | 1.86994 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.73897 | 0.638299 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0620 | −1.15201 | −0.576003 | − | 0.817448i | \(-0.695388\pi\) | ||||
−0.576003 | + | 0.817448i | \(0.695388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.72194 | 0.791161 | 0.395580 | − | 0.918431i | \(-0.370543\pi\) | ||||
0.395580 | + | 0.918431i | \(0.370543\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.80633 | 0.226878 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.3703 | 1.95747 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3959 | 1.62777 | 0.813886 | − | 0.581025i | \(-0.197348\pi\) | ||||
0.813886 | + | 0.581025i | \(0.197348\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.6639 | −1.55945 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.45402 | 0.508648 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.02566 | −0.471966 | −0.235983 | − | 0.971757i | \(-0.575831\pi\) | ||||
−0.235983 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.7562 | −2.00512 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.04988 | 0.313389 | 0.156695 | − | 0.987647i | \(-0.449916\pi\) | ||||
0.156695 | + | 0.987647i | \(0.449916\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.8686 | 2.45143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.685979 | −0.0524582 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.38104 | 0.713227 | 0.356614 | − | 0.934252i | \(-0.383931\pi\) | ||||
0.356614 | + | 0.934252i | \(0.383931\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.78534 | −0.286145 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.09923 | −0.308117 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00076 | −0.672748 | −0.336374 | − | 0.941728i | \(-0.609201\pi\) | ||||
−0.336374 | + | 0.941728i | \(0.609201\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.30418 | 0.394257 | 0.197128 | − | 0.980378i | \(-0.436838\pi\) | ||||
0.197128 | + | 0.980378i | \(0.436838\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.84200 | −0.357931 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.7403 | −1.59838 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −35.6472 | −2.60678 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.07234 | −0.587176 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5843 | −1.05529 | −0.527643 | − | 0.849466i | \(-0.676924\pi\) | ||||
−0.527643 | + | 0.849466i | \(0.676924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.26930 | −0.0913665 | −0.0456833 | − | 0.998956i | \(-0.514546\pi\) | ||||
−0.0456833 | + | 0.998956i | \(0.514546\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 29.3916 | 2.10478 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.7100 | −0.976795 | −0.488397 | − | 0.872621i | \(-0.662418\pi\) | ||||
−0.488397 | + | 0.872621i | \(0.662418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2227 | −1.29177 | −0.645887 | − | 0.763433i | \(-0.723512\pi\) | ||||
−0.645887 | + | 0.763433i | \(0.723512\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.68058 | 0.189074 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.9652 | −0.839790 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.7609 | 1.03095 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.03775 | 0.141634 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.71360 | 0.602732 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1444 | 0.698373 | 0.349186 | − | 0.937053i | \(-0.386458\pi\) | ||||
0.349186 | + | 0.937053i | \(0.386458\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.72090 | 0.460508 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.0284 | 1.57053 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.9499 | −0.879098 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.9662 | 1.34919 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.6786 | 2.73634 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.35840 | −0.626685 | −0.313342 | − | 0.949640i | \(-0.601449\pi\) | ||||
−0.313342 | + | 0.949640i | \(0.601449\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.19516 | −0.0796774 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4970 | −0.895825 | −0.447913 | − | 0.894077i | \(-0.647832\pi\) | ||||
−0.447913 | + | 0.894077i | \(0.647832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.85673 | 0.254860 | 0.127430 | − | 0.991848i | \(-0.459327\pi\) | ||||
0.127430 | + | 0.991848i | \(0.459327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6864 | 0.900499 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.6606 | −1.74659 | −0.873296 | − | 0.487190i | \(-0.838022\pi\) | ||||
−0.873296 | + | 0.487190i | \(0.838022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.9908 | −1.63022 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.7200 | 1.47582 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6255 | 0.687304 | 0.343652 | − | 0.939097i | \(-0.388336\pi\) | ||||
0.343652 | + | 0.939097i | \(0.388336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2402 | −1.36820 | −0.684102 | − | 0.729387i | \(-0.739806\pi\) | ||||
−0.684102 | + | 0.729387i | \(0.739806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.75724 | −0.305177 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.3802 | −0.854828 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.94348 | −0.632688 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.4924 | −1.74226 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.6652 | 1.24126 | 0.620629 | − | 0.784105i | \(-0.286878\pi\) | ||||
0.620629 | + | 0.784105i | \(0.286878\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.8844 | −1.62734 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26.6469 | 1.66869 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.6914 | −1.47783 | −0.738916 | − | 0.673798i | \(-0.764662\pi\) | ||||
−0.738916 | + | 0.673798i | \(0.764662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.5524 | 0.717832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.77781 | −0.233841 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.08534 | 0.0669247 | 0.0334624 | − | 0.999440i | \(-0.489347\pi\) | ||||
0.0334624 | + | 0.999440i | \(0.489347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.9976 | 2.08845 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.9545 | 0.854000 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.92937 | 0.544433 | 0.272217 | − | 0.962236i | \(-0.412243\pi\) | ||||
0.272217 | + | 0.962236i | \(0.412243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.03612 | −0.488160 | −0.244080 | − | 0.969755i | \(-0.578486\pi\) | ||||
−0.244080 | + | 0.969755i | \(0.578486\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.6182 | −0.945254 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.1814 | 0.915475 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7093 | 0.643458 | 0.321729 | − | 0.946832i | \(-0.395736\pi\) | ||||
0.321729 | + | 0.946832i | \(0.395736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.08873 | −0.244786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.6054 | −0.632663 | −0.316332 | − | 0.948649i | \(-0.602451\pi\) | ||||
−0.316332 | + | 0.948649i | \(0.602451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.63639 | −0.156717 | −0.0783586 | − | 0.996925i | \(-0.524968\pi\) | ||||
−0.0783586 | + | 0.996925i | \(0.524968\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.51358 | −0.385831 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.84367 | −0.462997 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.8799 | 1.16941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.04870 | −0.237339 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.32611 | 0.427996 | 0.213998 | − | 0.976834i | \(-0.431351\pi\) | ||||
0.213998 | + | 0.976834i | \(0.431351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.08731 | 0.412639 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 32.3748 | 1.87858 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.5379 | 1.70822 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.2369 | −0.705323 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.3477 | 1.05405 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.37152 | 0.479352 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.2865 | 0.758301 | 0.379151 | − | 0.925335i | \(-0.376216\pi\) | ||||
0.379151 | + | 0.925335i | \(0.376216\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.57975 | 0.146757 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.6292 | −1.28318 | −0.641591 | − | 0.767047i | \(-0.721725\pi\) | ||||
−0.641591 | + | 0.767047i | \(0.721725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.01120 | 0.113680 | 0.0568399 | − | 0.998383i | \(-0.481898\pi\) | ||||
0.0568399 | + | 0.998383i | \(0.481898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.86287 | 0.104961 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.4277 | −1.70899 | −0.854495 | − | 0.519460i | \(-0.826133\pi\) | ||||
−0.854495 | + | 0.519460i | \(0.826133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.9874 | 2.68678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.58638 | 0.367616 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.01493 | −0.501604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.3242 | −0.960975 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.3588 | 1.62354 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2797 | 0.732133 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.921540 | −0.0506524 | −0.0253262 | − | 0.999679i | \(-0.508062\pi\) | ||||
−0.0253262 | + | 0.999679i | \(0.508062\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.64749 | 0.199881 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.63455 | −0.253213 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.03118 | 0.110646 | 0.0553228 | − | 0.998469i | \(-0.482381\pi\) | ||||
0.0553228 | + | 0.998469i | \(0.482381\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.77031 | −0.530650 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.9368 | 2.81254 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3552 | 0.937092 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.3491 | 1.04172 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.1452 | −0.598305 | −0.299152 | − | 0.954205i | \(-0.596704\pi\) | ||||
−0.299152 | + | 0.954205i | \(0.596704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.5827 | 1.58352 | 0.791762 | − | 0.610829i | \(-0.209164\pi\) | ||||
0.791762 | + | 0.610829i | \(0.209164\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.9444 | −1.97194 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.527017 | −0.0280503 | −0.0140251 | − | 0.999902i | \(-0.504464\pi\) | ||||
−0.0140251 | + | 0.999902i | \(0.504464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.6200 | −0.616726 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.1597 | −0.749410 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.171064 | 0.00902843 | 0.00451422 | − | 0.999990i | \(-0.498563\pi\) | ||||
0.00451422 | + | 0.999990i | \(0.498563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7964 | −0.884021 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −37.3667 | −1.96124 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.5203 | −1.80687 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.35445 | −0.175101 | −0.0875506 | − | 0.996160i | \(-0.527904\pi\) | ||||
−0.0875506 | + | 0.996160i | \(0.527904\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.47651 | −0.128922 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0657 | −0.937924 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.2102 | −1.20178 | −0.600890 | − | 0.799332i | \(-0.705187\pi\) | ||||
−0.600890 | + | 0.799332i | \(0.705187\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.5909 | 0.546910 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −54.7605 | −2.82031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.0589 | 1.28719 | 0.643594 | − | 0.765367i | \(-0.277442\pi\) | ||||
0.643594 | + | 0.765367i | \(0.277442\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.2456 | 1.39584 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5652 | 0.693148 | 0.346574 | − | 0.938023i | \(-0.387345\pi\) | ||||
0.346574 | + | 0.938023i | \(0.387345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.6629 | −1.20597 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.86361 | −0.196398 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.9073 | −1.26285 | −0.631424 | − | 0.775438i | \(-0.717529\pi\) | ||||
−0.631424 | + | 0.775438i | \(0.717529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.7795 | 1.35430 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.7016 | 0.993816 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −39.2814 | −1.97646 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.8957 | −1.19929 | −0.599647 | − | 0.800265i | \(-0.704692\pi\) | ||||
−0.599647 | + | 0.800265i | \(0.704692\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.46120 | 0.173277 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.2689 | −1.31181 | −0.655903 | − | 0.754845i | \(-0.727712\pi\) | ||||
−0.655903 | + | 0.754845i | \(0.727712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −59.2674 | −2.95232 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.3824 | −1.01281 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −46.3320 | −2.29659 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.9584 | 0.789093 | 0.394546 | − | 0.918876i | \(-0.370902\pi\) | ||||
0.394546 | + | 0.918876i | \(0.370902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.16079 | −0.106584 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.76607 | −0.185316 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.5326 | 2.33328 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.0068 | −0.734887 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.96030 | 0.291180 | 0.145590 | − | 0.989345i | \(-0.453492\pi\) | ||||
0.145590 | + | 0.989345i | \(0.453492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.1846 | −1.03247 | −0.516236 | − | 0.856446i | \(-0.672667\pi\) | ||||
−0.516236 | + | 0.856446i | \(0.672667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.19285 | 0.203863 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.7064 | −0.761874 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.44847 | −0.215277 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 62.6380 | 3.02419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.38874 | −0.115062 | −0.0575309 | − | 0.998344i | \(-0.518323\pi\) | ||||
−0.0575309 | + | 0.998344i | \(0.518323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.90143 | 0.187491 | 0.0937455 | − | 0.995596i | \(-0.470116\pi\) | ||||
0.0937455 | + | 0.995596i | \(0.470116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −35.8714 | −1.71990 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.54599 | −0.313137 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.34917 | 0.255302 | 0.127651 | − | 0.991819i | \(-0.459256\pi\) | ||||
0.127651 | + | 0.991819i | \(0.459256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.24487 | 0.106898 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8298 | −1.08467 | −0.542337 | − | 0.840161i | \(-0.682461\pi\) | ||||
−0.542337 | + | 0.840161i | \(0.682461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.1264 | −1.14370 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.4019 | 1.05957 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.5053 | −1.48683 | −0.743413 | − | 0.668833i | \(-0.766794\pi\) | ||||
−0.743413 | + | 0.668833i | \(0.766794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.4577 | 1.48129 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.4878 | −0.727680 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.0028 | 1.26591 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.1928 | 0.757469 | 0.378734 | − | 0.925505i | \(-0.376359\pi\) | ||||
0.378734 | + | 0.925505i | \(0.376359\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.4944 | −1.56338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.9691 | −1.20950 | −0.604751 | − | 0.796415i | \(-0.706727\pi\) | ||||
−0.604751 | + | 0.796415i | \(0.706727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1706 | 1.03036 | 0.515179 | − | 0.857083i | \(-0.327726\pi\) | ||||
0.515179 | + | 0.857083i | \(0.327726\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −38.8237 | −1.80041 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.5908 | −1.36930 | −0.684649 | − | 0.728873i | \(-0.740044\pi\) | ||||
−0.684649 | + | 0.728873i | \(0.740044\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.46272 | 0.113718 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.4923 | −1.49716 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 49.0772 | 2.25657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.83928 | 0.176158 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.70396 | −0.261166 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.2331 | −1.15293 | −0.576465 | − | 0.817122i | \(-0.695568\pi\) | ||||
−0.576465 | + | 0.817122i | \(0.695568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.8715 | 2.41073 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.2817 | −0.467835 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.99995 | 0.317851 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.4539 | 0.881542 | 0.440771 | − | 0.897620i | \(-0.354705\pi\) | ||||
0.440771 | + | 0.897620i | \(0.354705\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.59934 | 0.434097 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.65848 | 0.210234 | 0.105117 | − | 0.994460i | \(-0.466478\pi\) | ||||
0.105117 | + | 0.994460i | \(0.466478\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −49.6468 | −2.23598 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.47119 | −0.335805 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.17466 | 0.276971 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.16907 | 0.410464 | 0.205232 | − | 0.978713i | \(-0.434205\pi\) | ||||
0.205232 | + | 0.978713i | \(0.434205\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.45177 | −0.288244 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.7221 | −1.41161 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −50.7691 | −2.25473 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.6477 | 0.516275 | 0.258137 | − | 0.966108i | \(-0.416891\pi\) | ||||
0.258137 | + | 0.966108i | \(0.416891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.3435 | 0.811467 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.18737 | 0.361481 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.46023 | −0.196541 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −53.2593 | −2.34234 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9447 | −0.656000 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4805 | 0.722024 | 0.361012 | − | 0.932561i | \(-0.382431\pi\) | ||||
0.361012 | + | 0.932561i | \(0.382431\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.75352 | −0.382765 | −0.191382 | − | 0.981516i | \(-0.561297\pi\) | ||||
−0.191382 | + | 0.981516i | \(0.561297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.03033 | 0.263185 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −53.7328 | −2.34064 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.55465 | −0.154550 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.18908 | −0.0516015 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −35.8978 | −1.55491 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3874 | −0.492321 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.3389 | 0.618769 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.5152 | −1.22824 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3348 | 0.960248 | 0.480124 | − | 0.877201i | \(-0.340592\pi\) | ||||
0.480124 | + | 0.877201i | \(0.340592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.44997 | −0.362623 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −50.7595 | −2.17430 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9067 | −0.551849 | −0.275925 | − | 0.961179i | \(-0.588984\pi\) | ||||
−0.275925 | + | 0.961179i | \(0.588984\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.40453 | −0.0599441 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1357 | 0.516997 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.8734 | 0.887629 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.6340 | 1.47013 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.56576 | −0.151086 | −0.0755430 | − | 0.997143i | \(-0.524069\pi\) | ||||
−0.0755430 | + | 0.997143i | \(0.524069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.0041 | −2.36872 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 56.7887 | 2.39762 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.6331 | 1.50176 | 0.750878 | − | 0.660441i | \(-0.229631\pi\) | ||||
0.750878 | + | 0.660441i | \(0.229631\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.8922 | 0.710662 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.8308 | 0.454852 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.2523 | −0.471721 | −0.235861 | − | 0.971787i | \(-0.575791\pi\) | ||||
−0.235861 | + | 0.971787i | \(0.575791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2326 | 0.511918 | 0.255959 | − | 0.966688i | \(-0.417609\pi\) | ||||
0.255959 | + | 0.966688i | \(0.417609\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.2340 | 0.970613 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.4049 | −0.475616 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.9930 | −0.624167 | −0.312083 | − | 0.950055i | \(-0.601027\pi\) | ||||
−0.312083 | + | 0.950055i | \(0.601027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.02210 | 0.0840355 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.2580 | −1.04788 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 72.4541 | 3.00074 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.52571 | 0.352495 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.7141 | −1.88682 | −0.943412 | − | 0.331622i | \(-0.892404\pi\) | ||||
−0.943412 | + | 0.331622i | \(0.892404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1345 | 0.541196 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.8410 | 0.898419 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.8233 | 1.10150 | 0.550750 | − | 0.834670i | \(-0.314342\pi\) | ||||
0.550750 | + | 0.834670i | \(0.314342\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.4812 | 1.00363 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.0302 | 1.18813 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.0654 | 0.533837 | 0.266918 | − | 0.963719i | \(-0.413995\pi\) | ||||
0.266918 | + | 0.963719i | \(0.413995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.45943 | 0.345068 | 0.172534 | − | 0.985004i | \(-0.444805\pi\) | ||||
0.172534 | + | 0.985004i | \(0.444805\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.777564 | 0.0316648 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 64.6046 | 2.62655 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.3103 | −1.27085 | −0.635423 | − | 0.772164i | \(-0.719174\pi\) | ||||
−0.635423 | + | 0.772164i | \(0.719174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.0614 | 0.772408 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60.7766 | 2.45876 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.9304 | −0.562642 | −0.281321 | − | 0.959614i | \(-0.590773\pi\) | ||||
−0.281321 | + | 0.959614i | \(0.590773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.5152 | −0.948226 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.0125 | −1.89265 | −0.946325 | − | 0.323215i | \(-0.895236\pi\) | ||||
−0.946325 | + | 0.323215i | \(0.895236\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.3762 | −1.34150 | −0.670751 | − | 0.741682i | \(-0.734028\pi\) | ||||
−0.670751 | + | 0.741682i | \(0.734028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.3212 | −0.975976 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.8203 | 0.513636 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2425 | −1.24970 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.8814 | −0.554371 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.9342 | 1.91126 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.74341 | −0.149023 | −0.0745114 | − | 0.997220i | \(-0.523740\pi\) | ||||
−0.0745114 | + | 0.997220i | \(0.523740\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.1609 | −0.642337 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −47.1059 | −1.86934 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.5400 | 1.28928 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.94955 | 0.0771230 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.81336 | −0.0716234 | −0.0358117 | − | 0.999359i | \(-0.511402\pi\) | ||||
−0.0358117 | + | 0.999359i | \(0.511402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6210 | 0.537160 | 0.268580 | − | 0.963257i | \(-0.413446\pi\) | ||||
0.268580 | + | 0.963257i | \(0.413446\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −36.6861 | −1.44451 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6018 | 0.652685 | 0.326342 | − | 0.945252i | \(-0.394184\pi\) | ||||
0.326342 | + | 0.945252i | \(0.394184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.1041 | 0.592889 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.6302 | 0.808562 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.76542 | −0.225618 | −0.112809 | − | 0.993617i | \(-0.535985\pi\) | ||||
−0.112809 | + | 0.993617i | \(0.535985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.0629 | −1.33095 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.79166 | 0.225954 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.3602 | 0.754168 | 0.377084 | − | 0.926179i | \(-0.376927\pi\) | ||||
0.377084 | + | 0.926179i | \(0.376927\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.17780 | −0.201393 | −0.100697 | − | 0.994917i | \(-0.532107\pi\) | ||||
−0.100697 | + | 0.994917i | \(0.532107\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −64.8041 | −2.51678 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.98419 | −0.232057 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.0499 | −1.39586 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.9086 | 0.576401 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.8410 | 0.688744 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.58114 | 0.0994958 | 0.0497479 | − | 0.998762i | \(-0.484158\pi\) | ||||
0.0497479 | + | 0.998762i | \(0.484158\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.2646 | 0.549045 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.2830 | 1.66350 | 0.831751 | − | 0.555149i | \(-0.187339\pi\) | ||||
0.831751 | + | 0.555149i | \(0.187339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.71965 | −0.142747 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.5017 | 0.823947 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.8597 | 0.568590 | 0.284295 | − | 0.958737i | \(-0.408240\pi\) | ||||
0.284295 | + | 0.958737i | \(0.408240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.73588 | 0.142741 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.14406 | −0.234411 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −82.6806 | −3.14988 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.7070 | −1.32032 | −0.660158 | − | 0.751127i | \(-0.729511\pi\) | ||||
−0.660158 | + | 0.751127i | \(0.729511\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.97005 | 0.150810 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.9458 | 0.984182 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.5456 | −1.23275 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42.4723 | 1.60645 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6514 | 0.477838 | 0.238919 | − | 0.971040i | \(-0.423207\pi\) | ||||
0.238919 | + | 0.971040i | \(0.423207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.7170 | −0.441917 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.8123 | 1.49942 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.8565 | 0.633956 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.358275 | −0.0134553 | −0.00672765 | − | 0.999977i | \(-0.502141\pi\) | ||||
−0.00672765 | + | 0.999977i | \(0.502141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.59046 | 0.247161 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.0169 | −1.46119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −108.297 | −4.05008 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.9272 | −0.632157 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.9993 | 0.895024 | 0.447512 | − | 0.894278i | \(-0.352310\pi\) | ||||
0.447512 | + | 0.894278i | \(0.352310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.37008 | 0.0882665 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33.8373 | 1.25842 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.1436 | 0.785254 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.0953 | 1.41288 | 0.706438 | − | 0.707775i | \(-0.250301\pi\) | ||||
0.706438 | + | 0.707775i | \(0.250301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7790 | 1.10293 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50.7743 | −1.87796 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.7757 | 1.87544 | 0.937721 | − | 0.347388i | \(-0.112931\pi\) | ||||
0.937721 | + | 0.347388i | \(0.112931\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.3156 | 0.786240 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.87694 | −0.363822 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.7456 | −1.13099 | −0.565497 | − | 0.824750i | \(-0.691316\pi\) | ||||
−0.565497 | + | 0.824750i | \(0.691316\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.8407 | 0.581923 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.3272 | 0.635673 | 0.317837 | − | 0.948146i | \(-0.397044\pi\) | ||||
0.317837 | + | 0.948146i | \(0.397044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.7314 | −1.41901 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.97480 | −0.291783 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.05107 | 0.221101 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.6584 | −1.22821 | −0.614106 | − | 0.789224i | \(-0.710483\pi\) | ||||
−0.614106 | + | 0.789224i | \(0.710483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.3282 | −1.14166 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.7774 | 0.974530 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.1538 | −1.24134 | −0.620671 | − | 0.784071i | \(-0.713140\pi\) | ||||
−0.620671 | + | 0.784071i | \(0.713140\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 41.2358 | 1.49677 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.3681 | 0.520842 | 0.260421 | − | 0.965495i | \(-0.416139\pi\) | ||||
0.260421 | + | 0.965495i | \(0.416139\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.9727 | 0.976476 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.72955 | 0.279463 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.2360 | −0.622356 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.4962 | 0.991537 | 0.495768 | − | 0.868455i | \(-0.334887\pi\) | ||||
0.495768 | + | 0.868455i | \(0.334887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.7423 | 1.35925 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.75525 | −0.278937 | −0.139469 | − | 0.990226i | \(-0.544539\pi\) | ||||
−0.139469 | + | 0.990226i | \(0.544539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.8838 | 0.822009 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.4039 | −0.660236 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.95544 | 0.285033 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.7640 | −0.886126 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 45.0893 | 1.61136 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.1770 | 2.00504 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.6903 | 0.701885 | 0.350942 | − | 0.936397i | \(-0.385861\pi\) | ||||
0.350942 | + | 0.936397i | \(0.385861\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.72902 | −0.0615549 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.97623 | −0.319158 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.3591 | −0.722975 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −54.1607 | −1.92088 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.9546 | −0.777671 | −0.388835 | − | 0.921307i | \(-0.627123\pi\) | ||||
−0.388835 | + | 0.921307i | \(0.627123\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.1011 | 1.94934 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.04782 | 0.143023 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −73.5680 | −2.59616 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.7765 | 0.626539 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.2252 | −0.500750 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.3431 | −0.363644 | −0.181822 | − | 0.983331i | \(-0.558199\pi\) | ||||
−0.181822 | + | 0.983331i | \(0.558199\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4712 | 1.14022 | 0.570109 | − | 0.821569i | \(-0.306901\pi\) | ||||
0.570109 | + | 0.821569i | \(0.306901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.8022 | 0.448991 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.5967 | −0.581355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.4113 | 0.434215 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.53041 | −0.158305 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.2464 | −1.89321 | −0.946606 | − | 0.322394i | \(-0.895513\pi\) | ||||
−0.946606 | + | 0.322394i | \(0.895513\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.1896 | −1.71464 | −0.857322 | − | 0.514781i | \(-0.827873\pi\) | ||||
−0.857322 | + | 0.514781i | \(0.827873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.1852 | −0.842020 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.9413 | −1.49322 | −0.746608 | − | 0.665265i | \(-0.768319\pi\) | ||||
−0.746608 | + | 0.665265i | \(0.768319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.5437 | −0.748245 | −0.374122 | − | 0.927379i | \(-0.622056\pi\) | ||||
−0.374122 | + | 0.927379i | \(0.622056\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.0607 | −0.591829 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.5013 | 1.02216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.1547 | 0.386025 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.8003 | 1.68678 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.6657 | −0.644410 | −0.322205 | − | 0.946670i | \(-0.604424\pi\) | ||||
−0.322205 | + | 0.946670i | \(0.604424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.8333 | 1.30460 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.8952 | 0.581900 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 87.7765 | 3.01960 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.3297 | −1.17958 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.19997 | 0.144143 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.8063 | 1.19315 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.7303 | −1.01795 | −0.508974 | − | 0.860782i | \(-0.669975\pi\) | ||||
−0.508974 | + | 0.860782i | \(0.669975\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.88941 | −0.0646165 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.9356 | −0.783465 | −0.391733 | − | 0.920079i | \(-0.628124\pi\) | ||||
−0.391733 | + | 0.920079i | \(0.628124\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.3777 | −0.729397 | −0.364698 | − | 0.931126i | \(-0.618828\pi\) | ||||
−0.364698 | + | 0.931126i | \(0.618828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.4956 | 0.425848 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.1528 | 1.84338 | 0.921692 | − | 0.387922i | \(-0.126807\pi\) | ||||
0.921692 | + | 0.387922i | \(0.126807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.8385 | 0.878534 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.6702 | −1.07558 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −83.7147 | −2.83983 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.2710 | 0.381904 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.17442 | −0.0397481 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.73010 | 0.328937 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.5204 | −1.03060 | −0.515300 | − | 0.857010i | \(-0.672319\pi\) | ||||
−0.515300 | + | 0.857010i | \(0.672319\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.6711 | −0.393655 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.55114 | 0.119641 | 0.0598205 | − | 0.998209i | \(-0.480947\pi\) | ||||
0.0598205 | + | 0.998209i | \(0.480947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.5969 | 0.895056 | 0.447528 | − | 0.894270i | \(-0.352305\pi\) | ||||
0.447528 | + | 0.894270i | \(0.352305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.2906 | −0.379530 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.2877 | 1.58776 | 0.793882 | − | 0.608071i | \(-0.208057\pi\) | ||||
0.793882 | + | 0.608071i | \(0.208057\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.0312 | 0.839521 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −43.4380 | −1.45523 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.4689 | −0.450720 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.7910 | −0.828673 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.0561 | −1.57116 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 72.3339 | 2.41247 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74.9596 | −2.49727 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.4943 | 0.648730 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.6095 | 0.485635 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.29369 | −0.175774 | −0.0878870 | − | 0.996130i | \(-0.528011\pi\) | ||||
−0.0878870 | + | 0.996130i | \(0.528011\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.32219 | 0.176526 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4595 | 0.479064 | 0.239532 | − | 0.970888i | \(-0.423006\pi\) | ||||
0.239532 | + | 0.970888i | \(0.423006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 101.299 | 3.35252 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.3365 | −0.440890 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.1004 | 0.597727 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.00395 | −0.0990911 | −0.0495456 | − | 0.998772i | \(-0.515777\pi\) | ||||
−0.0495456 | + | 0.998772i | \(0.515777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.1664 | −0.697457 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.2593 | 0.930167 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.4142 | −0.671216 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.748316 | 0.0245779 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.1686 | 0.432047 | 0.216023 | − | 0.976388i | \(-0.430691\pi\) | ||||
0.216023 | + | 0.976388i | \(0.430691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.21130 | −0.236341 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.0500 | 1.18022 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −98.1840 | −3.21096 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.66519 | 0.250411 | 0.125205 | − | 0.992131i | \(-0.460041\pi\) | ||||
0.125205 | + | 0.992131i | \(0.460041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.20400 | −0.104559 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.8108 | −1.03700 | −0.518501 | − | 0.855077i | \(-0.673510\pi\) | ||||
−0.518501 | + | 0.855077i | \(0.673510\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.6322 | −0.769572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.2339 | −0.723268 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.1008 | 0.653189 | 0.326595 | − | 0.945165i | \(-0.394099\pi\) | ||||
0.326595 | + | 0.945165i | \(0.394099\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 83.9518 | 2.72519 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.4736 | 1.57187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.24603 | 0.0727560 | 0.0363780 | − | 0.999338i | \(-0.488418\pi\) | ||||
0.0363780 | + | 0.999338i | \(0.488418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.1701 | −1.29987 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −76.4475 | −2.47120 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.98518 | −0.0641047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.2871 | 1.52539 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.91053 | 0.0615660 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.49608 | −0.112543 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.4322 | 0.817843 | 0.408921 | − | 0.912570i | \(-0.365905\pi\) | ||||
0.408921 | + | 0.912570i | \(0.365905\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.3615 | 0.461357 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.2958 | −0.330409 | −0.165205 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.7872 | −0.441996 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.5988 | 0.883869 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.26590 | −0.0724925 | −0.0362462 | − | 0.999343i | \(-0.511540\pi\) | ||||
−0.0362462 | + | 0.999343i | \(0.511540\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.4170 | −1.64330 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.51619 | 0.271901 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.6737 | −0.627492 | −0.313746 | − | 0.949507i | \(-0.601584\pi\) | ||||
−0.313746 | + | 0.949507i | \(0.601584\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.7617 | −1.20319 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.1555 | −0.673388 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.8686 | −1.17235 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.1094 | −1.52825 | −0.764123 | − | 0.645070i | \(-0.776828\pi\) | ||||
−0.764123 | + | 0.645070i | \(0.776828\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.46808 | 0.0465882 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.1914 | −1.59117 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.90282 | −0.0602629 | −0.0301315 | − | 0.999546i | \(-0.509593\pi\) | ||||
−0.0301315 | + | 0.999546i | \(0.509593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.5339 | −1.37735 |
(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 | 8048.2.a.v.1.9 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.20 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.20 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.9 | 28 | 1.1 | even | 1 | trivial |