Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32584 | −0.937513 | −0.468757 | − | 0.883327i | \(-0.655298\pi\) | ||||
−0.468757 | + | 0.883327i | \(0.655298\pi\) | |||||||
\(3\) | 2.02466 | 1.16894 | 0.584470 | − | 0.811415i | \(-0.301302\pi\) | ||||
0.584470 | + | 0.811415i | \(0.301302\pi\) | |||||||
\(4\) | −0.242137 | −0.121069 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.68439 | −1.09590 | ||||||||
\(7\) | −3.04433 | −1.15065 | −0.575323 | − | 0.817926i | \(-0.695124\pi\) | ||||
−0.575323 | + | 0.817926i | \(0.695124\pi\) | |||||||
\(8\) | 2.97272 | 1.05102 | ||||||||
\(9\) | 1.09926 | 0.366420 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.79607 | 0.541534 | 0.270767 | − | 0.962645i | \(-0.412723\pi\) | ||||
0.270767 | + | 0.962645i | \(0.412723\pi\) | |||||||
\(12\) | −0.490247 | −0.141522 | ||||||||
\(13\) | 0.100045 | 0.0277474 | 0.0138737 | − | 0.999904i | \(-0.495584\pi\) | ||||
0.0138737 | + | 0.999904i | \(0.495584\pi\) | |||||||
\(14\) | 4.03630 | 1.07875 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.45709 | −0.864274 | ||||||||
\(17\) | 0.353668 | 0.0857771 | 0.0428886 | − | 0.999080i | \(-0.486344\pi\) | ||||
0.0428886 | + | 0.999080i | \(0.486344\pi\) | |||||||
\(18\) | −1.45745 | −0.343524 | ||||||||
\(19\) | −2.02746 | −0.465130 | −0.232565 | − | 0.972581i | \(-0.574712\pi\) | ||||
−0.232565 | + | 0.972581i | \(0.574712\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.16373 | −1.34504 | ||||||||
\(22\) | −2.38130 | −0.507696 | ||||||||
\(23\) | 4.43970 | 0.925741 | 0.462871 | − | 0.886426i | \(-0.346819\pi\) | ||||
0.462871 | + | 0.886426i | \(0.346819\pi\) | |||||||
\(24\) | 6.01877 | 1.22858 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.132644 | −0.0260136 | ||||||||
\(27\) | −3.84836 | −0.740617 | ||||||||
\(28\) | 0.737145 | 0.139307 | ||||||||
\(29\) | 8.69145 | 1.61396 | 0.806981 | − | 0.590577i | \(-0.201100\pi\) | ||||
0.806981 | + | 0.590577i | \(0.201100\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.94070 | 1.24659 | 0.623293 | − | 0.781988i | \(-0.285794\pi\) | ||||
0.623293 | + | 0.781988i | \(0.285794\pi\) | |||||||
\(32\) | −1.36188 | −0.240749 | ||||||||
\(33\) | 3.63643 | 0.633021 | ||||||||
\(34\) | −0.468909 | −0.0804172 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.266172 | −0.0443620 | ||||||||
\(37\) | −3.30485 | −0.543313 | −0.271657 | − | 0.962394i | \(-0.587572\pi\) | ||||
−0.271657 | + | 0.962394i | \(0.587572\pi\) | |||||||
\(38\) | 2.68809 | 0.436066 | ||||||||
\(39\) | 0.202557 | 0.0324351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.34644 | 0.366452 | 0.183226 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183226 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(42\) | 8.17215 | 1.26099 | ||||||||
\(43\) | −2.63050 | −0.401147 | −0.200574 | − | 0.979679i | \(-0.564281\pi\) | ||||
−0.200574 | + | 0.979679i | \(0.564281\pi\) | |||||||
\(44\) | −0.434895 | −0.0655628 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.88635 | −0.867895 | ||||||||
\(47\) | −13.2780 | −1.93679 | −0.968395 | − | 0.249421i | \(-0.919760\pi\) | ||||
−0.968395 | + | 0.249421i | \(0.919760\pi\) | |||||||
\(48\) | −6.99945 | −1.01028 | ||||||||
\(49\) | 2.26792 | 0.323988 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.716059 | 0.100268 | ||||||||
\(52\) | −0.0242246 | −0.00335934 | ||||||||
\(53\) | −8.92645 | −1.22614 | −0.613071 | − | 0.790028i | \(-0.710066\pi\) | ||||
−0.613071 | + | 0.790028i | \(0.710066\pi\) | |||||||
\(54\) | 5.10232 | 0.694338 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.04994 | −1.20935 | ||||||||
\(57\) | −4.10492 | −0.543710 | ||||||||
\(58\) | −11.5235 | −1.51311 | ||||||||
\(59\) | −0.729581 | −0.0949834 | −0.0474917 | − | 0.998872i | \(-0.515123\pi\) | ||||
−0.0474917 | + | 0.998872i | \(0.515123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0485 | 1.79873 | 0.899363 | − | 0.437202i | \(-0.144031\pi\) | ||||
0.899363 | + | 0.437202i | \(0.144031\pi\) | |||||||
\(62\) | −9.20229 | −1.16869 | ||||||||
\(63\) | −3.34651 | −0.421620 | ||||||||
\(64\) | 8.71983 | 1.08998 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.82134 | −0.593466 | ||||||||
\(67\) | 8.35024 | 1.02014 | 0.510072 | − | 0.860132i | \(-0.329619\pi\) | ||||
0.510072 | + | 0.860132i | \(0.329619\pi\) | |||||||
\(68\) | −0.0856363 | −0.0103849 | ||||||||
\(69\) | 8.98890 | 1.08214 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.35552 | −0.872940 | −0.436470 | − | 0.899719i | \(-0.643772\pi\) | ||||
−0.436470 | + | 0.899719i | \(0.643772\pi\) | |||||||
\(72\) | 3.26780 | 0.385114 | ||||||||
\(73\) | −6.30530 | −0.737979 | −0.368990 | − | 0.929433i | \(-0.620296\pi\) | ||||
−0.368990 | + | 0.929433i | \(0.620296\pi\) | |||||||
\(74\) | 4.38171 | 0.509363 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.490923 | 0.0563127 | ||||||||
\(77\) | −5.46781 | −0.623115 | ||||||||
\(78\) | −0.268559 | −0.0304083 | ||||||||
\(79\) | 1.38656 | 0.156000 | 0.0780000 | − | 0.996953i | \(-0.475147\pi\) | ||||
0.0780000 | + | 0.996953i | \(0.475147\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0894 | −1.23216 | ||||||||
\(82\) | −3.11101 | −0.343554 | ||||||||
\(83\) | 10.8019 | 1.18566 | 0.592830 | − | 0.805328i | \(-0.298011\pi\) | ||||
0.592830 | + | 0.805328i | \(0.298011\pi\) | |||||||
\(84\) | 1.49247 | 0.162842 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.48763 | 0.376081 | ||||||||
\(87\) | 17.5973 | 1.88663 | ||||||||
\(88\) | 5.33921 | 0.569162 | ||||||||
\(89\) | −3.55647 | −0.376985 | −0.188492 | − | 0.982075i | \(-0.560360\pi\) | ||||
−0.188492 | + | 0.982075i | \(0.560360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.304569 | −0.0319275 | ||||||||
\(92\) | −1.07502 | −0.112078 | ||||||||
\(93\) | 14.0526 | 1.45718 | ||||||||
\(94\) | 17.6045 | 1.81577 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.75735 | −0.281421 | ||||||||
\(97\) | 13.9809 | 1.41955 | 0.709774 | − | 0.704429i | \(-0.248797\pi\) | ||||
0.709774 | + | 0.704429i | \(0.248797\pi\) | |||||||
\(98\) | −3.00690 | −0.303743 | ||||||||
\(99\) | 1.97435 | 0.198429 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1770 | −1.21166 | −0.605830 | − | 0.795594i | \(-0.707159\pi\) | ||||
−0.605830 | + | 0.795594i | \(0.707159\pi\) | |||||||
\(102\) | −0.949382 | −0.0940029 | ||||||||
\(103\) | 4.12347 | 0.406297 | 0.203149 | − | 0.979148i | \(-0.434883\pi\) | ||||
0.203149 | + | 0.979148i | \(0.434883\pi\) | |||||||
\(104\) | 0.297405 | 0.0291630 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.8351 | 1.14952 | ||||||||
\(107\) | 0.755504 | 0.0730374 | 0.0365187 | − | 0.999333i | \(-0.488373\pi\) | ||||
0.0365187 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(108\) | 0.931831 | 0.0896655 | ||||||||
\(109\) | 14.2543 | 1.36532 | 0.682659 | − | 0.730737i | \(-0.260823\pi\) | ||||
0.682659 | + | 0.730737i | \(0.260823\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.69120 | −0.635101 | ||||||||
\(112\) | 10.5245 | 0.994474 | ||||||||
\(113\) | −0.609697 | −0.0573555 | −0.0286777 | − | 0.999589i | \(-0.509130\pi\) | ||||
−0.0286777 | + | 0.999589i | \(0.509130\pi\) | |||||||
\(114\) | 5.44248 | 0.509735 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.10453 | −0.195400 | ||||||||
\(117\) | 0.109975 | 0.0101672 | ||||||||
\(118\) | 0.967311 | 0.0890482 | ||||||||
\(119\) | −1.07668 | −0.0986992 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.77415 | −0.706740 | ||||||||
\(122\) | −18.6261 | −1.68633 | ||||||||
\(123\) | 4.75075 | 0.428361 | ||||||||
\(124\) | −1.68060 | −0.150923 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.43695 | 0.395275 | ||||||||
\(127\) | −17.9310 | −1.59112 | −0.795558 | − | 0.605877i | \(-0.792822\pi\) | ||||
−0.795558 | + | 0.605877i | \(0.792822\pi\) | |||||||
\(128\) | −8.83738 | −0.781121 | ||||||||
\(129\) | −5.32587 | −0.468917 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.5465 | 1.53304 | 0.766521 | − | 0.642219i | \(-0.221986\pi\) | ||||
0.766521 | + | 0.642219i | \(0.221986\pi\) | |||||||
\(132\) | −0.880515 | −0.0766390 | ||||||||
\(133\) | 6.17224 | 0.535201 | ||||||||
\(134\) | −11.0711 | −0.956399 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.05136 | 0.0901532 | ||||||||
\(137\) | 20.6648 | 1.76551 | 0.882757 | − | 0.469829i | \(-0.155685\pi\) | ||||
0.882757 | + | 0.469829i | \(0.155685\pi\) | |||||||
\(138\) | −11.9179 | −1.01452 | ||||||||
\(139\) | 19.1212 | 1.62184 | 0.810921 | − | 0.585155i | \(-0.198966\pi\) | ||||
0.810921 | + | 0.585155i | \(0.198966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −26.8834 | −2.26399 | ||||||||
\(142\) | 9.75228 | 0.818393 | ||||||||
\(143\) | 0.179687 | 0.0150262 | ||||||||
\(144\) | −3.80025 | −0.316687 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.35984 | 0.691866 | ||||||||
\(147\) | 4.59176 | 0.378722 | ||||||||
\(148\) | 0.800227 | 0.0657782 | ||||||||
\(149\) | −9.67814 | −0.792864 | −0.396432 | − | 0.918064i | \(-0.629752\pi\) | ||||
−0.396432 | + | 0.918064i | \(0.629752\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7919 | 0.878235 | 0.439118 | − | 0.898430i | \(-0.355291\pi\) | ||||
0.439118 | + | 0.898430i | \(0.355291\pi\) | |||||||
\(152\) | −6.02707 | −0.488860 | ||||||||
\(153\) | 0.388774 | 0.0314305 | ||||||||
\(154\) | 7.24946 | 0.584178 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0490466 | −0.00392687 | ||||||||
\(157\) | −5.75595 | −0.459375 | −0.229687 | − | 0.973264i | \(-0.573770\pi\) | ||||
−0.229687 | + | 0.973264i | \(0.573770\pi\) | |||||||
\(158\) | −1.83836 | −0.146252 | ||||||||
\(159\) | −18.0731 | −1.43329 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.5159 | −1.06520 | ||||||||
\(162\) | 14.7028 | 1.15516 | ||||||||
\(163\) | 3.54323 | 0.277527 | 0.138764 | − | 0.990326i | \(-0.455687\pi\) | ||||
0.138764 | + | 0.990326i | \(0.455687\pi\) | |||||||
\(164\) | −0.568161 | −0.0443659 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.3216 | −1.11157 | ||||||||
\(167\) | −5.31456 | −0.411253 | −0.205626 | − | 0.978631i | \(-0.565923\pi\) | ||||
−0.205626 | + | 0.978631i | \(0.565923\pi\) | |||||||
\(168\) | −18.3231 | −1.41366 | ||||||||
\(169\) | −12.9900 | −0.999230 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.22870 | −0.170433 | ||||||||
\(172\) | 0.636942 | 0.0485664 | ||||||||
\(173\) | 4.17054 | 0.317080 | 0.158540 | − | 0.987353i | \(-0.449321\pi\) | ||||
0.158540 | + | 0.987353i | \(0.449321\pi\) | |||||||
\(174\) | −23.3312 | −1.76874 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.20917 | −0.468034 | ||||||||
\(177\) | −1.47716 | −0.111030 | ||||||||
\(178\) | 4.71532 | 0.353428 | ||||||||
\(179\) | 3.52748 | 0.263656 | 0.131828 | − | 0.991273i | \(-0.457915\pi\) | ||||
0.131828 | + | 0.991273i | \(0.457915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4705 | 1.22425 | 0.612123 | − | 0.790763i | \(-0.290316\pi\) | ||||
0.612123 | + | 0.790763i | \(0.290316\pi\) | |||||||
\(182\) | 0.403811 | 0.0299324 | ||||||||
\(183\) | 28.4435 | 2.10260 | ||||||||
\(184\) | 13.1980 | 0.972970 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −18.6315 | −1.36613 | ||||||||
\(187\) | 0.635211 | 0.0464513 | ||||||||
\(188\) | 3.21509 | 0.234485 | ||||||||
\(189\) | 11.7156 | 0.852188 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.82609 | 0.638633 | 0.319317 | − | 0.947648i | \(-0.396547\pi\) | ||||
0.319317 | + | 0.947648i | \(0.396547\pi\) | |||||||
\(192\) | 17.6547 | 1.27412 | ||||||||
\(193\) | −2.05717 | −0.148078 | −0.0740391 | − | 0.997255i | \(-0.523589\pi\) | ||||
−0.0740391 | + | 0.997255i | \(0.523589\pi\) | |||||||
\(194\) | −18.5365 | −1.33085 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.549147 | −0.0392248 | ||||||||
\(197\) | 15.8660 | 1.13040 | 0.565202 | − | 0.824953i | \(-0.308798\pi\) | ||||
0.565202 | + | 0.824953i | \(0.308798\pi\) | |||||||
\(198\) | −2.61767 | −0.186030 | ||||||||
\(199\) | 5.91176 | 0.419074 | 0.209537 | − | 0.977801i | \(-0.432804\pi\) | ||||
0.209537 | + | 0.977801i | \(0.432804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.9064 | 1.19249 | ||||||||
\(202\) | 16.1448 | 1.13595 | ||||||||
\(203\) | −26.4596 | −1.85710 | ||||||||
\(204\) | −0.173385 | −0.0121393 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.46708 | −0.380909 | ||||||||
\(207\) | 4.88039 | 0.339210 | ||||||||
\(208\) | −0.345864 | −0.0239814 | ||||||||
\(209\) | −3.64145 | −0.251884 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3940 | 0.922082 | 0.461041 | − | 0.887379i | \(-0.347476\pi\) | ||||
0.461041 | + | 0.887379i | \(0.347476\pi\) | |||||||
\(212\) | 2.16143 | 0.148447 | ||||||||
\(213\) | −14.8925 | −1.02041 | ||||||||
\(214\) | −1.00168 | −0.0684735 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −11.4401 | −0.778400 | ||||||||
\(217\) | −21.1297 | −1.43438 | ||||||||
\(218\) | −18.8990 | −1.28000 | ||||||||
\(219\) | −12.7661 | −0.862654 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0353826 | 0.00238009 | ||||||||
\(222\) | 8.87149 | 0.595415 | ||||||||
\(223\) | 12.4802 | 0.835733 | 0.417866 | − | 0.908508i | \(-0.362778\pi\) | ||||
0.417866 | + | 0.908508i | \(0.362778\pi\) | |||||||
\(224\) | 4.14601 | 0.277017 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.808364 | 0.0537715 | ||||||||
\(227\) | 14.2706 | 0.947170 | 0.473585 | − | 0.880748i | \(-0.342960\pi\) | ||||
0.473585 | + | 0.880748i | \(0.342960\pi\) | |||||||
\(228\) | 0.993954 | 0.0658262 | ||||||||
\(229\) | 13.8257 | 0.913629 | 0.456815 | − | 0.889562i | \(-0.348990\pi\) | ||||
0.456815 | + | 0.889562i | \(0.348990\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.0705 | −0.728384 | ||||||||
\(232\) | 25.8373 | 1.69630 | ||||||||
\(233\) | 0.638926 | 0.0418575 | 0.0209287 | − | 0.999781i | \(-0.493338\pi\) | ||||
0.0209287 | + | 0.999781i | \(0.493338\pi\) | |||||||
\(234\) | −0.145810 | −0.00953190 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.176659 | 0.0114995 | ||||||||
\(237\) | 2.80731 | 0.182355 | ||||||||
\(238\) | 1.42751 | 0.0925318 | ||||||||
\(239\) | 5.56073 | 0.359694 | 0.179847 | − | 0.983695i | \(-0.442440\pi\) | ||||
0.179847 | + | 0.983695i | \(0.442440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 10.3073 | 0.662579 | ||||||||
\(243\) | −10.9072 | −0.699700 | ||||||||
\(244\) | −3.40167 | −0.217769 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.29876 | −0.401594 | ||||||||
\(247\) | −0.202836 | −0.0129062 | ||||||||
\(248\) | 20.6328 | 1.31018 | ||||||||
\(249\) | 21.8702 | 1.38597 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.9313 | 1.06869 | 0.534347 | − | 0.845265i | \(-0.320558\pi\) | ||||
0.534347 | + | 0.845265i | \(0.320558\pi\) | |||||||
\(252\) | 0.810314 | 0.0510450 | ||||||||
\(253\) | 7.97400 | 0.501321 | ||||||||
\(254\) | 23.7737 | 1.49169 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.72268 | −0.357667 | ||||||||
\(257\) | 11.9189 | 0.743479 | 0.371740 | − | 0.928337i | \(-0.378761\pi\) | ||||
0.371740 | + | 0.928337i | \(0.378761\pi\) | |||||||
\(258\) | 7.06128 | 0.439616 | ||||||||
\(259\) | 10.0610 | 0.625162 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.55418 | 0.591389 | ||||||||
\(262\) | −23.2639 | −1.43725 | ||||||||
\(263\) | 13.4726 | 0.830753 | 0.415377 | − | 0.909650i | \(-0.363650\pi\) | ||||
0.415377 | + | 0.909650i | \(0.363650\pi\) | |||||||
\(264\) | 10.8101 | 0.665316 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.18342 | −0.501758 | ||||||||
\(267\) | −7.20065 | −0.440673 | ||||||||
\(268\) | −2.02190 | −0.123507 | ||||||||
\(269\) | 13.9885 | 0.852897 | 0.426448 | − | 0.904512i | \(-0.359765\pi\) | ||||
0.426448 | + | 0.904512i | \(0.359765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.9386 | 1.21118 | 0.605591 | − | 0.795776i | \(-0.292937\pi\) | ||||
0.605591 | + | 0.795776i | \(0.292937\pi\) | |||||||
\(272\) | −1.22266 | −0.0741349 | ||||||||
\(273\) | −0.616649 | −0.0373213 | ||||||||
\(274\) | −27.3983 | −1.65519 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.17655 | −0.131013 | ||||||||
\(277\) | 31.1614 | 1.87231 | 0.936154 | − | 0.351590i | \(-0.114359\pi\) | ||||
0.936154 | + | 0.351590i | \(0.114359\pi\) | |||||||
\(278\) | −25.3518 | −1.52050 | ||||||||
\(279\) | 7.62964 | 0.456775 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.57349 | −0.511452 | −0.255726 | − | 0.966749i | \(-0.582314\pi\) | ||||
−0.255726 | + | 0.966749i | \(0.582314\pi\) | |||||||
\(282\) | 35.6432 | 2.12252 | ||||||||
\(283\) | −30.9341 | −1.83884 | −0.919420 | − | 0.393278i | \(-0.871341\pi\) | ||||
−0.919420 | + | 0.393278i | \(0.871341\pi\) | |||||||
\(284\) | 1.78105 | 0.105686 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.238237 | −0.0140872 | ||||||||
\(287\) | −7.14333 | −0.421657 | ||||||||
\(288\) | −1.49706 | −0.0882152 | ||||||||
\(289\) | −16.8749 | −0.992642 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.3067 | 1.65937 | ||||||||
\(292\) | 1.52675 | 0.0893462 | ||||||||
\(293\) | 11.0505 | 0.645579 | 0.322789 | − | 0.946471i | \(-0.395379\pi\) | ||||
0.322789 | + | 0.946471i | \(0.395379\pi\) | |||||||
\(294\) | −6.08796 | −0.355057 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.82440 | −0.571031 | ||||||||
\(297\) | −6.91190 | −0.401069 | ||||||||
\(298\) | 12.8317 | 0.743321 | ||||||||
\(299\) | 0.444169 | 0.0256869 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00809 | 0.461579 | ||||||||
\(302\) | −14.3084 | −0.823357 | ||||||||
\(303\) | −24.6544 | −1.41636 | ||||||||
\(304\) | 7.00911 | 0.402000 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.515453 | −0.0294665 | ||||||||
\(307\) | 11.9129 | 0.679907 | 0.339954 | − | 0.940442i | \(-0.389589\pi\) | ||||
0.339954 | + | 0.940442i | \(0.389589\pi\) | |||||||
\(308\) | 1.32396 | 0.0754397 | ||||||||
\(309\) | 8.34864 | 0.474937 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5262 | 1.22064 | 0.610320 | − | 0.792155i | \(-0.291041\pi\) | ||||
0.610320 | + | 0.792155i | \(0.291041\pi\) | |||||||
\(312\) | 0.602146 | 0.0340898 | ||||||||
\(313\) | 4.47097 | 0.252714 | 0.126357 | − | 0.991985i | \(-0.459672\pi\) | ||||
0.126357 | + | 0.991985i | \(0.459672\pi\) | |||||||
\(314\) | 7.63150 | 0.430670 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.335737 | −0.0188867 | ||||||||
\(317\) | 3.55620 | 0.199736 | 0.0998679 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998679 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(318\) | 23.9621 | 1.34373 | ||||||||
\(319\) | 15.6104 | 0.874016 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.52964 | 0.0853763 | ||||||||
\(322\) | 17.9200 | 0.998640 | ||||||||
\(323\) | −0.717047 | −0.0398975 | ||||||||
\(324\) | 2.68516 | 0.149176 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.69777 | −0.260186 | ||||||||
\(327\) | 28.8602 | 1.59597 | ||||||||
\(328\) | 6.97532 | 0.385148 | ||||||||
\(329\) | 40.4224 | 2.22856 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.0961 | −1.21451 | −0.607255 | − | 0.794507i | \(-0.707729\pi\) | ||||
−0.607255 | + | 0.794507i | \(0.707729\pi\) | |||||||
\(332\) | −2.61554 | −0.143546 | ||||||||
\(333\) | −3.63289 | −0.199081 | ||||||||
\(334\) | 7.04627 | 0.385555 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 21.3086 | 1.16248 | ||||||||
\(337\) | −13.2631 | −0.722486 | −0.361243 | − | 0.932472i | \(-0.617648\pi\) | ||||
−0.361243 | + | 0.932472i | \(0.617648\pi\) | |||||||
\(338\) | 17.2227 | 0.936792 | ||||||||
\(339\) | −1.23443 | −0.0670451 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4660 | 0.675070 | ||||||||
\(342\) | 2.95491 | 0.159783 | ||||||||
\(343\) | 14.4060 | 0.777851 | ||||||||
\(344\) | −7.81975 | −0.421612 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.52948 | −0.297267 | ||||||||
\(347\) | −31.6800 | −1.70067 | −0.850336 | − | 0.526240i | \(-0.823601\pi\) | ||||
−0.850336 | + | 0.526240i | \(0.823601\pi\) | |||||||
\(348\) | −4.26096 | −0.228411 | ||||||||
\(349\) | 17.1323 | 0.917070 | 0.458535 | − | 0.888676i | \(-0.348374\pi\) | ||||
0.458535 | + | 0.888676i | \(0.348374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.385008 | −0.0205502 | ||||||||
\(352\) | −2.44603 | −0.130374 | ||||||||
\(353\) | −12.1058 | −0.644327 | −0.322163 | − | 0.946684i | \(-0.604410\pi\) | ||||
−0.322163 | + | 0.946684i | \(0.604410\pi\) | |||||||
\(354\) | 1.95848 | 0.104092 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.861154 | 0.0456411 | ||||||||
\(357\) | −2.17992 | −0.115373 | ||||||||
\(358\) | −4.67689 | −0.247181 | ||||||||
\(359\) | −32.1356 | −1.69605 | −0.848025 | − | 0.529956i | \(-0.822209\pi\) | ||||
−0.848025 | + | 0.529956i | \(0.822209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.8894 | −0.783654 | ||||||||
\(362\) | −21.8374 | −1.14775 | ||||||||
\(363\) | −15.7400 | −0.826137 | ||||||||
\(364\) | 0.0737475 | 0.00386542 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −37.7116 | −1.97122 | ||||||||
\(367\) | −7.48127 | −0.390519 | −0.195259 | − | 0.980752i | \(-0.562555\pi\) | ||||
−0.195259 | + | 0.980752i | \(0.562555\pi\) | |||||||
\(368\) | −15.3485 | −0.800094 | ||||||||
\(369\) | 2.57935 | 0.134276 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.1750 | 1.41086 | ||||||||
\(372\) | −3.40265 | −0.176419 | ||||||||
\(373\) | −23.2022 | −1.20137 | −0.600683 | − | 0.799487i | \(-0.705105\pi\) | ||||
−0.600683 | + | 0.799487i | \(0.705105\pi\) | |||||||
\(374\) | −0.842191 | −0.0435487 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −39.4717 | −2.03560 | ||||||||
\(377\) | 0.869534 | 0.0447833 | ||||||||
\(378\) | −15.5331 | −0.798938 | ||||||||
\(379\) | −13.0230 | −0.668948 | −0.334474 | − | 0.942405i | \(-0.608559\pi\) | ||||
−0.334474 | + | 0.942405i | \(0.608559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.3042 | −1.85992 | ||||||||
\(382\) | −11.7020 | −0.598727 | ||||||||
\(383\) | 8.52674 | 0.435696 | 0.217848 | − | 0.975983i | \(-0.430096\pi\) | ||||
0.217848 | + | 0.975983i | \(0.430096\pi\) | |||||||
\(384\) | −17.8927 | −0.913083 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.72749 | 0.138825 | ||||||||
\(387\) | −2.89160 | −0.146988 | ||||||||
\(388\) | −3.38531 | −0.171863 | ||||||||
\(389\) | −9.47661 | −0.480483 | −0.240242 | − | 0.970713i | \(-0.577227\pi\) | ||||
−0.240242 | + | 0.970713i | \(0.577227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.57018 | 0.0794074 | ||||||||
\(392\) | 6.74189 | 0.340517 | ||||||||
\(393\) | 35.5257 | 1.79203 | ||||||||
\(394\) | −21.0358 | −1.05977 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.478063 | −0.0240236 | ||||||||
\(397\) | 21.7239 | 1.09029 | 0.545145 | − | 0.838341i | \(-0.316474\pi\) | ||||
0.545145 | + | 0.838341i | \(0.316474\pi\) | |||||||
\(398\) | −7.83807 | −0.392887 | ||||||||
\(399\) | 12.4967 | 0.625618 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0902 | −0.903381 | −0.451691 | − | 0.892175i | \(-0.649179\pi\) | ||||
−0.451691 | + | 0.892175i | \(0.649179\pi\) | |||||||
\(402\) | −22.4153 | −1.11797 | ||||||||
\(403\) | 0.694381 | 0.0345896 | ||||||||
\(404\) | 2.94851 | 0.146694 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35.0813 | 1.74106 | ||||||||
\(407\) | −5.93572 | −0.294223 | ||||||||
\(408\) | 2.12865 | 0.105384 | ||||||||
\(409\) | −2.85438 | −0.141140 | −0.0705701 | − | 0.997507i | \(-0.522482\pi\) | ||||
−0.0705701 | + | 0.997507i | \(0.522482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.8393 | 2.06378 | ||||||||
\(412\) | −0.998446 | −0.0491899 | ||||||||
\(413\) | 2.22108 | 0.109292 | ||||||||
\(414\) | −6.47063 | −0.318014 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.136249 | −0.00668016 | ||||||||
\(417\) | 38.7141 | 1.89584 | ||||||||
\(418\) | 4.82799 | 0.236145 | ||||||||
\(419\) | 30.9992 | 1.51441 | 0.757205 | − | 0.653178i | \(-0.226565\pi\) | ||||
0.757205 | + | 0.653178i | \(0.226565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9371 | 0.922939 | 0.461470 | − | 0.887156i | \(-0.347322\pi\) | ||||
0.461470 | + | 0.887156i | \(0.347322\pi\) | |||||||
\(422\) | −17.7584 | −0.864465 | ||||||||
\(423\) | −14.5959 | −0.709679 | ||||||||
\(424\) | −26.5359 | −1.28870 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 19.7451 | 0.956652 | ||||||||
\(427\) | −42.7682 | −2.06970 | ||||||||
\(428\) | −0.182936 | −0.00884254 | ||||||||
\(429\) | 0.363806 | 0.0175647 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8655 | 0.716047 | 0.358023 | − | 0.933713i | \(-0.383451\pi\) | ||||
0.358023 | + | 0.933713i | \(0.383451\pi\) | |||||||
\(432\) | 13.3041 | 0.640095 | ||||||||
\(433\) | −14.5262 | −0.698083 | −0.349041 | − | 0.937107i | \(-0.613493\pi\) | ||||
−0.349041 | + | 0.937107i | \(0.613493\pi\) | |||||||
\(434\) | 28.0148 | 1.34475 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.45151 | −0.165297 | ||||||||
\(437\) | −9.00130 | −0.430590 | ||||||||
\(438\) | 16.9259 | 0.808749 | ||||||||
\(439\) | −12.0153 | −0.573461 | −0.286731 | − | 0.958011i | \(-0.592568\pi\) | ||||
−0.286731 | + | 0.958011i | \(0.592568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.49303 | 0.118716 | ||||||||
\(442\) | −0.0469119 | −0.00223137 | ||||||||
\(443\) | 12.2129 | 0.580252 | 0.290126 | − | 0.956988i | \(-0.406303\pi\) | ||||
0.290126 | + | 0.956988i | \(0.406303\pi\) | |||||||
\(444\) | 1.62019 | 0.0768908 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.5467 | −0.783511 | ||||||||
\(447\) | −19.5950 | −0.926811 | ||||||||
\(448\) | −26.5460 | −1.25418 | ||||||||
\(449\) | 23.0221 | 1.08648 | 0.543241 | − | 0.839577i | \(-0.317197\pi\) | ||||
0.543241 | + | 0.839577i | \(0.317197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.21436 | 0.198447 | ||||||||
\(452\) | 0.147630 | 0.00694395 | ||||||||
\(453\) | 21.8500 | 1.02660 | ||||||||
\(454\) | −18.9205 | −0.887984 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.2028 | −0.571448 | ||||||||
\(457\) | 4.97076 | 0.232523 | 0.116261 | − | 0.993219i | \(-0.462909\pi\) | ||||
0.116261 | + | 0.993219i | \(0.462909\pi\) | |||||||
\(458\) | −18.3307 | −0.856539 | ||||||||
\(459\) | −1.36104 | −0.0635279 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.2971 | 1.03848 | 0.519241 | − | 0.854628i | \(-0.326215\pi\) | ||||
0.519241 | + | 0.854628i | \(0.326215\pi\) | |||||||
\(462\) | 14.6777 | 0.682869 | ||||||||
\(463\) | −7.31113 | −0.339777 | −0.169888 | − | 0.985463i | \(-0.554341\pi\) | ||||
−0.169888 | + | 0.985463i | \(0.554341\pi\) | |||||||
\(464\) | −30.0472 | −1.39491 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.847117 | −0.0392419 | ||||||||
\(467\) | 37.5955 | 1.73971 | 0.869855 | − | 0.493307i | \(-0.164212\pi\) | ||||
0.869855 | + | 0.493307i | \(0.164212\pi\) | |||||||
\(468\) | −0.0266291 | −0.00123093 | ||||||||
\(469\) | −25.4208 | −1.17383 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.6539 | −0.536982 | ||||||||
\(472\) | −2.16884 | −0.0998291 | ||||||||
\(473\) | −4.72455 | −0.217235 | ||||||||
\(474\) | −3.72206 | −0.170960 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.260705 | 0.0119494 | ||||||||
\(477\) | −9.81250 | −0.449283 | ||||||||
\(478\) | −7.37266 | −0.337218 | ||||||||
\(479\) | 19.1132 | 0.873306 | 0.436653 | − | 0.899630i | \(-0.356164\pi\) | ||||
0.436653 | + | 0.899630i | \(0.356164\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.330632 | −0.0150755 | ||||||||
\(482\) | −1.32584 | −0.0603905 | ||||||||
\(483\) | −27.3651 | −1.24516 | ||||||||
\(484\) | 1.88241 | 0.0855641 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.4613 | 0.655978 | ||||||||
\(487\) | 21.8759 | 0.991292 | 0.495646 | − | 0.868525i | \(-0.334931\pi\) | ||||
0.495646 | + | 0.868525i | \(0.334931\pi\) | |||||||
\(488\) | 41.7623 | 1.89049 | ||||||||
\(489\) | 7.17385 | 0.324413 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.2959 | −1.32211 | −0.661054 | − | 0.750339i | \(-0.729890\pi\) | ||||
−0.661054 | + | 0.750339i | \(0.729890\pi\) | |||||||
\(492\) | −1.15033 | −0.0518611 | ||||||||
\(493\) | 3.07389 | 0.138441 | ||||||||
\(494\) | 0.268929 | 0.0120997 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.9947 | −1.07739 | ||||||||
\(497\) | 22.3926 | 1.00445 | ||||||||
\(498\) | −28.9964 | −1.29936 | ||||||||
\(499\) | 4.44924 | 0.199175 | 0.0995876 | − | 0.995029i | \(-0.468248\pi\) | ||||
0.0995876 | + | 0.995029i | \(0.468248\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.7602 | −0.480730 | ||||||||
\(502\) | −22.4482 | −1.00191 | ||||||||
\(503\) | −28.9684 | −1.29164 | −0.645820 | − | 0.763490i | \(-0.723484\pi\) | ||||
−0.645820 | + | 0.763490i | \(0.723484\pi\) | |||||||
\(504\) | −9.94825 | −0.443130 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.5723 | −0.469995 | ||||||||
\(507\) | −26.3004 | −1.16804 | ||||||||
\(508\) | 4.34176 | 0.192634 | ||||||||
\(509\) | −19.0593 | −0.844791 | −0.422395 | − | 0.906412i | \(-0.638811\pi\) | ||||
−0.422395 | + | 0.906412i | \(0.638811\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.1954 | 0.849154 | ||||||||
\(512\) | 25.2621 | 1.11644 | ||||||||
\(513\) | 7.80238 | 0.344483 | ||||||||
\(514\) | −15.8026 | −0.697022 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.28959 | 0.0567712 | ||||||||
\(517\) | −23.8481 | −1.04884 | ||||||||
\(518\) | −13.3394 | −0.586097 | ||||||||
\(519\) | 8.44393 | 0.370647 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2343 | −0.448373 | −0.224187 | − | 0.974546i | \(-0.571973\pi\) | ||||
−0.224187 | + | 0.974546i | \(0.571973\pi\) | |||||||
\(522\) | −12.6673 | −0.554435 | ||||||||
\(523\) | −11.2295 | −0.491033 | −0.245517 | − | 0.969392i | \(-0.578958\pi\) | ||||
−0.245517 | + | 0.969392i | \(0.578958\pi\) | |||||||
\(524\) | −4.24866 | −0.185603 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.8625 | −0.778842 | ||||||||
\(527\) | 2.45470 | 0.106929 | ||||||||
\(528\) | −12.5715 | −0.547104 | ||||||||
\(529\) | −3.28907 | −0.143003 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.802000 | −0.0348038 | ||||||||
\(532\) | −1.49453 | −0.0647961 | ||||||||
\(533\) | 0.234749 | 0.0101681 | ||||||||
\(534\) | 9.54694 | 0.413137 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.8230 | 1.07219 | ||||||||
\(537\) | 7.14195 | 0.308198 | ||||||||
\(538\) | −18.5466 | −0.799602 | ||||||||
\(539\) | 4.07333 | 0.175451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3237 | 0.959769 | 0.479885 | − | 0.877332i | \(-0.340679\pi\) | ||||
0.479885 | + | 0.877332i | \(0.340679\pi\) | |||||||
\(542\) | −26.4354 | −1.13550 | ||||||||
\(543\) | 33.3473 | 1.43107 | ||||||||
\(544\) | −0.481654 | −0.0206507 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.817581 | 0.0349892 | ||||||||
\(547\) | −19.2895 | −0.824758 | −0.412379 | − | 0.911012i | \(-0.635302\pi\) | ||||
−0.412379 | + | 0.911012i | \(0.635302\pi\) | |||||||
\(548\) | −5.00372 | −0.213749 | ||||||||
\(549\) | 15.4430 | 0.659090 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.6215 | −0.750703 | ||||||||
\(552\) | 26.7215 | 1.13734 | ||||||||
\(553\) | −4.22113 | −0.179501 | ||||||||
\(554\) | −41.3152 | −1.75531 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.62997 | −0.196354 | ||||||||
\(557\) | −18.3152 | −0.776038 | −0.388019 | − | 0.921651i | \(-0.626841\pi\) | ||||
−0.388019 | + | 0.921651i | \(0.626841\pi\) | |||||||
\(558\) | −10.1157 | −0.428232 | ||||||||
\(559\) | −0.263168 | −0.0111308 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.28609 | 0.0542987 | ||||||||
\(562\) | 11.3671 | 0.479493 | ||||||||
\(563\) | 7.82106 | 0.329618 | 0.164809 | − | 0.986325i | \(-0.447299\pi\) | ||||
0.164809 | + | 0.986325i | \(0.447299\pi\) | |||||||
\(564\) | 6.50948 | 0.274098 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 41.0138 | 1.72394 | ||||||||
\(567\) | 33.7598 | 1.41778 | ||||||||
\(568\) | −21.8659 | −0.917475 | ||||||||
\(569\) | −28.1832 | −1.18150 | −0.590751 | − | 0.806854i | \(-0.701169\pi\) | ||||
−0.590751 | + | 0.806854i | \(0.701169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.2412 | 1.05631 | 0.528155 | − | 0.849148i | \(-0.322884\pi\) | ||||
0.528155 | + | 0.849148i | \(0.322884\pi\) | |||||||
\(572\) | −0.0435089 | −0.00181920 | ||||||||
\(573\) | 17.8699 | 0.746524 | ||||||||
\(574\) | 9.47094 | 0.395309 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.58537 | 0.399390 | ||||||||
\(577\) | 19.3497 | 0.805537 | 0.402768 | − | 0.915302i | \(-0.368048\pi\) | ||||
0.402768 | + | 0.915302i | \(0.368048\pi\) | |||||||
\(578\) | 22.3735 | 0.930615 | ||||||||
\(579\) | −4.16507 | −0.173095 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.8844 | −1.36428 | ||||||||
\(582\) | −37.5303 | −1.55568 | ||||||||
\(583\) | −16.0325 | −0.663998 | ||||||||
\(584\) | −18.7439 | −0.775629 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6513 | −0.605239 | ||||||||
\(587\) | 10.0485 | 0.414747 | 0.207373 | − | 0.978262i | \(-0.433508\pi\) | ||||
0.207373 | + | 0.978262i | \(0.433508\pi\) | |||||||
\(588\) | −1.11184 | −0.0458514 | ||||||||
\(589\) | −14.0720 | −0.579825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.1233 | 1.32137 | ||||||||
\(592\) | 11.4252 | 0.469571 | ||||||||
\(593\) | 38.4349 | 1.57833 | 0.789166 | − | 0.614179i | \(-0.210513\pi\) | ||||
0.789166 | + | 0.614179i | \(0.210513\pi\) | |||||||
\(594\) | 9.16411 | 0.376008 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.34344 | 0.0959910 | ||||||||
\(597\) | 11.9693 | 0.489872 | ||||||||
\(598\) | −0.588898 | −0.0240818 | ||||||||
\(599\) | −0.0858525 | −0.00350784 | −0.00175392 | − | 0.999998i | \(-0.500558\pi\) | ||||
−0.00175392 | + | 0.999998i | \(0.500558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.5160 | 0.428955 | 0.214477 | − | 0.976729i | \(-0.431195\pi\) | ||||
0.214477 | + | 0.976729i | \(0.431195\pi\) | |||||||
\(602\) | −10.6175 | −0.432736 | ||||||||
\(603\) | 9.17909 | 0.373801 | ||||||||
\(604\) | −2.61313 | −0.106327 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 32.6879 | 1.32785 | ||||||||
\(607\) | 11.5035 | 0.466914 | 0.233457 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233457 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(608\) | 2.76115 | 0.111980 | ||||||||
\(609\) | −53.5718 | −2.17084 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.32839 | −0.0537409 | ||||||||
\(612\) | −0.0941366 | −0.00380525 | ||||||||
\(613\) | 13.1760 | 0.532175 | 0.266087 | − | 0.963949i | \(-0.414269\pi\) | ||||
0.266087 | + | 0.963949i | \(0.414269\pi\) | |||||||
\(614\) | −15.7947 | −0.637422 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.2543 | −0.654904 | ||||||||
\(617\) | −11.8470 | −0.476941 | −0.238471 | − | 0.971150i | \(-0.576646\pi\) | ||||
−0.238471 | + | 0.971150i | \(0.576646\pi\) | |||||||
\(618\) | −11.0690 | −0.445260 | ||||||||
\(619\) | −12.7910 | −0.514114 | −0.257057 | − | 0.966396i | \(-0.582753\pi\) | ||||
−0.257057 | + | 0.966396i | \(0.582753\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.0855 | −0.685619 | ||||||||
\(622\) | −28.5404 | −1.14437 | ||||||||
\(623\) | 10.8270 | 0.433776 | ||||||||
\(624\) | −0.700258 | −0.0280328 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.92781 | −0.236923 | ||||||||
\(627\) | −7.37270 | −0.294437 | ||||||||
\(628\) | 1.39373 | 0.0556159 | ||||||||
\(629\) | −1.16882 | −0.0466038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1203 | 0.562121 | 0.281060 | − | 0.959690i | \(-0.409314\pi\) | ||||
0.281060 | + | 0.959690i | \(0.409314\pi\) | |||||||
\(632\) | 4.12185 | 0.163959 | ||||||||
\(633\) | 27.1184 | 1.07786 | ||||||||
\(634\) | −4.71496 | −0.187255 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.37616 | 0.173526 | ||||||||
\(637\) | 0.226893 | 0.00898983 | ||||||||
\(638\) | −20.6970 | −0.819402 | ||||||||
\(639\) | −8.08564 | −0.319863 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.7254 | 0.976593 | 0.488297 | − | 0.872678i | \(-0.337618\pi\) | ||||
0.488297 | + | 0.872678i | \(0.337618\pi\) | |||||||
\(642\) | −2.02807 | −0.0800414 | ||||||||
\(643\) | 16.9975 | 0.670318 | 0.335159 | − | 0.942162i | \(-0.391210\pi\) | ||||
0.335159 | + | 0.942162i | \(0.391210\pi\) | |||||||
\(644\) | 3.27270 | 0.128962 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.950692 | 0.0374045 | ||||||||
\(647\) | 1.38493 | 0.0544470 | 0.0272235 | − | 0.999629i | \(-0.491333\pi\) | ||||
0.0272235 | + | 0.999629i | \(0.491333\pi\) | |||||||
\(648\) | −32.9658 | −1.29502 | ||||||||
\(649\) | −1.31038 | −0.0514368 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.7806 | −1.67670 | ||||||||
\(652\) | −0.857949 | −0.0335999 | ||||||||
\(653\) | 24.3154 | 0.951534 | 0.475767 | − | 0.879571i | \(-0.342171\pi\) | ||||
0.475767 | + | 0.879571i | \(0.342171\pi\) | |||||||
\(654\) | −38.2642 | −1.49625 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.11187 | −0.316715 | ||||||||
\(657\) | −6.93117 | −0.270411 | ||||||||
\(658\) | −53.5939 | −2.08931 | ||||||||
\(659\) | 35.7071 | 1.39095 | 0.695475 | − | 0.718550i | \(-0.255194\pi\) | ||||
0.695475 | + | 0.718550i | \(0.255194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.4094 | 1.18279 | 0.591395 | − | 0.806382i | \(-0.298578\pi\) | ||||
0.591395 | + | 0.806382i | \(0.298578\pi\) | |||||||
\(662\) | 29.2960 | 1.13862 | ||||||||
\(663\) | 0.0716379 | 0.00278219 | ||||||||
\(664\) | 32.1110 | 1.24615 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.81664 | 0.186641 | ||||||||
\(667\) | 38.5874 | 1.49411 | ||||||||
\(668\) | 1.28685 | 0.0497898 | ||||||||
\(669\) | 25.2681 | 0.976921 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.2320 | 0.974072 | ||||||||
\(672\) | 8.39427 | 0.323816 | ||||||||
\(673\) | 10.4201 | 0.401666 | 0.200833 | − | 0.979625i | \(-0.435635\pi\) | ||||
0.200833 | + | 0.979625i | \(0.435635\pi\) | |||||||
\(674\) | 17.5848 | 0.677340 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.14536 | 0.120975 | ||||||||
\(677\) | −24.0844 | −0.925640 | −0.462820 | − | 0.886452i | \(-0.653162\pi\) | ||||
−0.462820 | + | 0.886452i | \(0.653162\pi\) | |||||||
\(678\) | 1.63666 | 0.0628557 | ||||||||
\(679\) | −42.5625 | −1.63340 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.8931 | 1.10718 | ||||||||
\(682\) | −16.5279 | −0.632887 | ||||||||
\(683\) | 22.2056 | 0.849674 | 0.424837 | − | 0.905270i | \(-0.360331\pi\) | ||||
0.424837 | + | 0.905270i | \(0.360331\pi\) | |||||||
\(684\) | 0.539652 | 0.0206341 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.1001 | −0.729246 | ||||||||
\(687\) | 27.9924 | 1.06798 | ||||||||
\(688\) | 9.09388 | 0.346701 | ||||||||
\(689\) | −0.893045 | −0.0340223 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.8898 | −0.870768 | −0.435384 | − | 0.900245i | \(-0.643387\pi\) | ||||
−0.435384 | + | 0.900245i | \(0.643387\pi\) | |||||||
\(692\) | −1.00984 | −0.0383885 | ||||||||
\(693\) | −6.01055 | −0.228322 | ||||||||
\(694\) | 42.0028 | 1.59440 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 52.3118 | 1.98287 | ||||||||
\(697\) | 0.829861 | 0.0314332 | ||||||||
\(698\) | −22.7147 | −0.859765 | ||||||||
\(699\) | 1.29361 | 0.0489289 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.2327 | 0.839718 | 0.419859 | − | 0.907589i | \(-0.362080\pi\) | ||||
0.419859 | + | 0.907589i | \(0.362080\pi\) | |||||||
\(702\) | 0.510460 | 0.0192661 | ||||||||
\(703\) | 6.70043 | 0.252712 | ||||||||
\(704\) | 15.6614 | 0.590261 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.0504 | 0.604065 | ||||||||
\(707\) | 37.0708 | 1.39419 | ||||||||
\(708\) | 0.357675 | 0.0134422 | ||||||||
\(709\) | −36.0658 | −1.35448 | −0.677241 | − | 0.735762i | \(-0.736824\pi\) | ||||
−0.677241 | + | 0.735762i | \(0.736824\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.52419 | 0.0571615 | ||||||||
\(712\) | −10.5724 | −0.396217 | ||||||||
\(713\) | 30.8146 | 1.15402 | ||||||||
\(714\) | 2.89023 | 0.108164 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.854134 | −0.0319205 | ||||||||
\(717\) | 11.2586 | 0.420460 | ||||||||
\(718\) | 42.6068 | 1.59007 | ||||||||
\(719\) | −41.4592 | −1.54617 | −0.773083 | − | 0.634305i | \(-0.781286\pi\) | ||||
−0.773083 | + | 0.634305i | \(0.781286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5532 | −0.467505 | ||||||||
\(722\) | 19.7410 | 0.734686 | ||||||||
\(723\) | 2.02466 | 0.0752980 | ||||||||
\(724\) | −3.98813 | −0.148218 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.8688 | 0.774515 | ||||||||
\(727\) | −36.9815 | −1.37157 | −0.685784 | − | 0.727805i | \(-0.740541\pi\) | ||||
−0.685784 | + | 0.727805i | \(0.740541\pi\) | |||||||
\(728\) | −0.905399 | −0.0335563 | ||||||||
\(729\) | 11.1847 | 0.414249 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.930323 | −0.0344093 | ||||||||
\(732\) | −6.88723 | −0.254559 | ||||||||
\(733\) | −13.8389 | −0.511152 | −0.255576 | − | 0.966789i | \(-0.582265\pi\) | ||||
−0.255576 | + | 0.966789i | \(0.582265\pi\) | |||||||
\(734\) | 9.91899 | 0.366117 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.04634 | −0.222871 | ||||||||
\(737\) | 14.9976 | 0.552443 | ||||||||
\(738\) | −3.41982 | −0.125885 | ||||||||
\(739\) | 34.7385 | 1.27788 | 0.638939 | − | 0.769257i | \(-0.279374\pi\) | ||||
0.638939 | + | 0.769257i | \(0.279374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.410675 | −0.0150865 | ||||||||
\(742\) | −36.0298 | −1.32270 | ||||||||
\(743\) | −8.59167 | −0.315198 | −0.157599 | − | 0.987503i | \(-0.550375\pi\) | ||||
−0.157599 | + | 0.987503i | \(0.550375\pi\) | |||||||
\(744\) | 41.7745 | 1.53153 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 30.7625 | 1.12630 | ||||||||
\(747\) | 11.8741 | 0.434450 | ||||||||
\(748\) | −0.153808 | −0.00562379 | ||||||||
\(749\) | −2.30000 | −0.0840402 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3458 | 0.778919 | 0.389459 | − | 0.921044i | \(-0.372662\pi\) | ||||
0.389459 | + | 0.921044i | \(0.372662\pi\) | |||||||
\(752\) | 45.9032 | 1.67392 | ||||||||
\(753\) | 34.2802 | 1.24924 | ||||||||
\(754\) | −1.15287 | −0.0419849 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.83680 | −0.103173 | ||||||||
\(757\) | −49.0973 | −1.78447 | −0.892237 | − | 0.451568i | \(-0.850865\pi\) | ||||
−0.892237 | + | 0.451568i | \(0.850865\pi\) | |||||||
\(758\) | 17.2665 | 0.627148 | ||||||||
\(759\) | 16.1447 | 0.586014 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.9688 | −1.81137 | −0.905683 | − | 0.423955i | \(-0.860642\pi\) | ||||
−0.905683 | + | 0.423955i | \(0.860642\pi\) | |||||||
\(762\) | 48.1337 | 1.74370 | ||||||||
\(763\) | −43.3948 | −1.57100 | ||||||||
\(764\) | −2.13713 | −0.0773185 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.3051 | −0.408471 | ||||||||
\(767\) | −0.0729907 | −0.00263554 | ||||||||
\(768\) | −11.5865 | −0.418092 | ||||||||
\(769\) | −19.4741 | −0.702255 | −0.351128 | − | 0.936328i | \(-0.614202\pi\) | ||||
−0.351128 | + | 0.936328i | \(0.614202\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1317 | 0.869083 | ||||||||
\(772\) | 0.498117 | 0.0179276 | ||||||||
\(773\) | 7.87928 | 0.283398 | 0.141699 | − | 0.989910i | \(-0.454743\pi\) | ||||
0.141699 | + | 0.989910i | \(0.454743\pi\) | |||||||
\(774\) | 3.83382 | 0.137804 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 41.5615 | 1.49197 | ||||||||
\(777\) | 20.3702 | 0.730776 | ||||||||
\(778\) | 12.5645 | 0.450459 | ||||||||
\(779\) | −4.75731 | −0.170448 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2110 | −0.472727 | ||||||||
\(782\) | −2.08181 | −0.0744455 | ||||||||
\(783\) | −33.4478 | −1.19533 | ||||||||
\(784\) | −7.84040 | −0.280014 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −47.1015 | −1.68006 | ||||||||
\(787\) | −48.7404 | −1.73741 | −0.868703 | − | 0.495333i | \(-0.835046\pi\) | ||||
−0.868703 | + | 0.495333i | \(0.835046\pi\) | |||||||
\(788\) | −3.84174 | −0.136856 | ||||||||
\(789\) | 27.2774 | 0.971101 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.85612 | 0.0659959 | ||||||||
\(792\) | 5.86919 | 0.208552 | ||||||||
\(793\) | 1.40548 | 0.0499100 | ||||||||
\(794\) | −28.8025 | −1.02216 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.43146 | −0.0507367 | ||||||||
\(797\) | 2.61718 | 0.0927051 | 0.0463526 | − | 0.998925i | \(-0.485240\pi\) | ||||
0.0463526 | + | 0.998925i | \(0.485240\pi\) | |||||||
\(798\) | −16.5687 | −0.586525 | ||||||||
\(799\) | −4.69599 | −0.166132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.90949 | −0.138135 | ||||||||
\(802\) | 23.9848 | 0.846932 | ||||||||
\(803\) | −11.3247 | −0.399641 | ||||||||
\(804\) | −4.09368 | −0.144373 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.920641 | −0.0324282 | ||||||||
\(807\) | 28.3221 | 0.996985 | ||||||||
\(808\) | −36.1989 | −1.27347 | ||||||||
\(809\) | −41.0761 | −1.44416 | −0.722080 | − | 0.691809i | \(-0.756814\pi\) | ||||
−0.722080 | + | 0.691809i | \(0.756814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.6245 | 0.653993 | 0.326996 | − | 0.945026i | \(-0.393963\pi\) | ||||
0.326996 | + | 0.945026i | \(0.393963\pi\) | |||||||
\(812\) | 6.40686 | 0.224837 | ||||||||
\(813\) | 40.3689 | 1.41580 | ||||||||
\(814\) | 7.86984 | 0.275838 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.47548 | −0.0866592 | ||||||||
\(817\) | 5.33322 | 0.186586 | ||||||||
\(818\) | 3.78447 | 0.132321 | ||||||||
\(819\) | −0.334801 | −0.0116989 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.4848 | −1.34313 | −0.671564 | − | 0.740946i | \(-0.734377\pi\) | ||||
−0.671564 | + | 0.740946i | \(0.734377\pi\) | |||||||
\(822\) | −55.4724 | −1.93482 | ||||||||
\(823\) | −29.9573 | −1.04425 | −0.522123 | − | 0.852870i | \(-0.674860\pi\) | ||||
−0.522123 | + | 0.852870i | \(0.674860\pi\) | |||||||
\(824\) | 12.2579 | 0.427026 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.94481 | −0.102463 | ||||||||
\(827\) | 17.3939 | 0.604844 | 0.302422 | − | 0.953174i | \(-0.402205\pi\) | ||||
0.302422 | + | 0.953174i | \(0.402205\pi\) | |||||||
\(828\) | −1.18172 | −0.0410678 | ||||||||
\(829\) | 41.4644 | 1.44012 | 0.720060 | − | 0.693912i | \(-0.244114\pi\) | ||||
0.720060 | + | 0.693912i | \(0.244114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 63.0914 | 2.18862 | ||||||||
\(832\) | 0.872373 | 0.0302441 | ||||||||
\(833\) | 0.802089 | 0.0277907 | ||||||||
\(834\) | −51.3288 | −1.77737 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.881730 | 0.0304953 | ||||||||
\(837\) | −26.7103 | −0.923243 | ||||||||
\(838\) | −41.1001 | −1.41978 | ||||||||
\(839\) | 12.5173 | 0.432145 | 0.216072 | − | 0.976377i | \(-0.430675\pi\) | ||||
0.216072 | + | 0.976377i | \(0.430675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.5414 | 1.60487 | ||||||||
\(842\) | −25.1077 | −0.865268 | ||||||||
\(843\) | −17.3584 | −0.597856 | ||||||||
\(844\) | −3.24319 | −0.111635 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 19.3520 | 0.665334 | ||||||||
\(847\) | 23.6670 | 0.813209 | ||||||||
\(848\) | 30.8596 | 1.05972 | ||||||||
\(849\) | −62.6311 | −2.14949 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.6725 | −0.502968 | ||||||||
\(852\) | 3.60602 | 0.123540 | ||||||||
\(853\) | −40.5026 | −1.38678 | −0.693392 | − | 0.720561i | \(-0.743885\pi\) | ||||
−0.693392 | + | 0.720561i | \(0.743885\pi\) | |||||||
\(854\) | 56.7040 | 1.94037 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.24591 | 0.0767635 | ||||||||
\(857\) | −4.42595 | −0.151188 | −0.0755939 | − | 0.997139i | \(-0.524085\pi\) | ||||
−0.0755939 | + | 0.997139i | \(0.524085\pi\) | |||||||
\(858\) | −0.482350 | −0.0164671 | ||||||||
\(859\) | 34.9029 | 1.19087 | 0.595437 | − | 0.803402i | \(-0.296979\pi\) | ||||
0.595437 | + | 0.803402i | \(0.296979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.4628 | −0.492892 | ||||||||
\(862\) | −19.7094 | −0.671303 | ||||||||
\(863\) | 10.9055 | 0.371227 | 0.185614 | − | 0.982623i | \(-0.440573\pi\) | ||||
0.185614 | + | 0.982623i | \(0.440573\pi\) | |||||||
\(864\) | 5.24100 | 0.178302 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.2594 | 0.654462 | ||||||||
\(867\) | −34.1660 | −1.16034 | ||||||||
\(868\) | 5.11630 | 0.173659 | ||||||||
\(869\) | 2.49035 | 0.0844793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.835397 | 0.0283064 | ||||||||
\(872\) | 42.3742 | 1.43497 | ||||||||
\(873\) | 15.3687 | 0.520152 | ||||||||
\(874\) | 11.9343 | 0.403684 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.09115 | 0.104440 | ||||||||
\(877\) | −8.18855 | −0.276508 | −0.138254 | − | 0.990397i | \(-0.544149\pi\) | ||||
−0.138254 | + | 0.990397i | \(0.544149\pi\) | |||||||
\(878\) | 15.9305 | 0.537628 | ||||||||
\(879\) | 22.3736 | 0.754643 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.93204 | 0.300928 | 0.150464 | − | 0.988615i | \(-0.451923\pi\) | ||||
0.150464 | + | 0.988615i | \(0.451923\pi\) | |||||||
\(882\) | −3.30537 | −0.111298 | ||||||||
\(883\) | −40.4510 | −1.36129 | −0.680643 | − | 0.732615i | \(-0.738299\pi\) | ||||
−0.680643 | + | 0.732615i | \(0.738299\pi\) | |||||||
\(884\) | −0.00856746 | −0.000288155 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.1924 | −0.543994 | ||||||||
\(887\) | −58.8126 | −1.97473 | −0.987366 | − | 0.158455i | \(-0.949349\pi\) | ||||
−0.987366 | + | 0.158455i | \(0.949349\pi\) | |||||||
\(888\) | −19.8911 | −0.667501 | ||||||||
\(889\) | 54.5877 | 1.83081 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.9173 | −0.667255 | ||||||||
\(892\) | −3.02191 | −0.101181 | ||||||||
\(893\) | 26.9205 | 0.900860 | ||||||||
\(894\) | 25.9799 | 0.868898 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 26.9038 | 0.898794 | ||||||||
\(897\) | 0.899292 | 0.0300265 | ||||||||
\(898\) | −30.5238 | −1.01859 | ||||||||
\(899\) | 60.3248 | 2.01194 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.15700 | −0.105175 | ||||||||
\(902\) | −5.58759 | −0.186046 | ||||||||
\(903\) | 16.2137 | 0.539558 | ||||||||
\(904\) | −1.81246 | −0.0602816 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −28.9697 | −0.962455 | ||||||||
\(907\) | 19.5914 | 0.650522 | 0.325261 | − | 0.945624i | \(-0.394548\pi\) | ||||
0.325261 | + | 0.945624i | \(0.394548\pi\) | |||||||
\(908\) | −3.45543 | −0.114673 | ||||||||
\(909\) | −13.3857 | −0.443977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.8647 | −1.22138 | −0.610692 | − | 0.791868i | \(-0.709109\pi\) | ||||
−0.610692 | + | 0.791868i | \(0.709109\pi\) | |||||||
\(912\) | 14.1911 | 0.469914 | ||||||||
\(913\) | 19.4009 | 0.642076 | ||||||||
\(914\) | −6.59046 | −0.217993 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.34772 | −0.110612 | ||||||||
\(917\) | −53.4172 | −1.76399 | ||||||||
\(918\) | 1.80453 | 0.0595583 | ||||||||
\(919\) | 21.4022 | 0.705995 | 0.352997 | − | 0.935624i | \(-0.385162\pi\) | ||||
0.352997 | + | 0.935624i | \(0.385162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.1197 | 0.794771 | ||||||||
\(922\) | −29.5625 | −0.973590 | ||||||||
\(923\) | −0.735881 | −0.0242218 | ||||||||
\(924\) | 2.68057 | 0.0881844 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.69342 | 0.318545 | ||||||||
\(927\) | 4.53277 | 0.148876 | ||||||||
\(928\) | −11.8367 | −0.388559 | ||||||||
\(929\) | 12.6133 | 0.413828 | 0.206914 | − | 0.978359i | \(-0.433658\pi\) | ||||
0.206914 | + | 0.978359i | \(0.433658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.59810 | −0.150697 | ||||||||
\(932\) | −0.154708 | −0.00506763 | ||||||||
\(933\) | 43.5834 | 1.42686 | ||||||||
\(934\) | −49.8457 | −1.63100 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.326926 | 0.0106859 | ||||||||
\(937\) | 56.2291 | 1.83693 | 0.918463 | − | 0.395507i | \(-0.129431\pi\) | ||||
0.918463 | + | 0.395507i | \(0.129431\pi\) | |||||||
\(938\) | 33.7041 | 1.10048 | ||||||||
\(939\) | 9.05220 | 0.295408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.84947 | −0.321083 | −0.160542 | − | 0.987029i | \(-0.551324\pi\) | ||||
−0.160542 | + | 0.987029i | \(0.551324\pi\) | |||||||
\(942\) | 15.4512 | 0.503428 | ||||||||
\(943\) | 10.4175 | 0.339240 | ||||||||
\(944\) | 2.52223 | 0.0820916 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.26402 | 0.203661 | ||||||||
\(947\) | 3.66056 | 0.118952 | 0.0594761 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594761 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(948\) | −0.679755 | −0.0220774 | ||||||||
\(949\) | −0.630812 | −0.0204770 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.20010 | 0.233479 | ||||||||
\(952\) | −3.20068 | −0.103734 | ||||||||
\(953\) | 48.1748 | 1.56054 | 0.780268 | − | 0.625446i | \(-0.215083\pi\) | ||||
0.780268 | + | 0.625446i | \(0.215083\pi\) | |||||||
\(954\) | 13.0098 | 0.421209 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.34646 | −0.0435476 | ||||||||
\(957\) | 31.6059 | 1.02167 | ||||||||
\(958\) | −25.3412 | −0.818736 | ||||||||
\(959\) | −62.9104 | −2.03148 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1733 | 0.553978 | ||||||||
\(962\) | 0.438367 | 0.0141335 | ||||||||
\(963\) | 0.830496 | 0.0267624 | ||||||||
\(964\) | −0.242137 | −0.00779872 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 36.2819 | 1.16735 | ||||||||
\(967\) | 9.98807 | 0.321195 | 0.160597 | − | 0.987020i | \(-0.448658\pi\) | ||||
0.160597 | + | 0.987020i | \(0.448658\pi\) | |||||||
\(968\) | −23.1104 | −0.742796 | ||||||||
\(969\) | −1.45178 | −0.0466378 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.4950 | 0.882356 | 0.441178 | − | 0.897420i | \(-0.354561\pi\) | ||||
0.441178 | + | 0.897420i | \(0.354561\pi\) | |||||||
\(972\) | 2.64105 | 0.0847118 | ||||||||
\(973\) | −58.2113 | −1.86617 | ||||||||
\(974\) | −29.0041 | −0.929350 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48.5670 | −1.55459 | ||||||||
\(977\) | −31.8959 | −1.02044 | −0.510220 | − | 0.860044i | \(-0.670436\pi\) | ||||
−0.510220 | + | 0.860044i | \(0.670436\pi\) | |||||||
\(978\) | −9.51141 | −0.304141 | ||||||||
\(979\) | −6.38765 | −0.204150 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6692 | 0.500280 | ||||||||
\(982\) | 38.8418 | 1.23949 | ||||||||
\(983\) | 22.8367 | 0.728377 | 0.364189 | − | 0.931325i | \(-0.381346\pi\) | ||||
0.364189 | + | 0.931325i | \(0.381346\pi\) | |||||||
\(984\) | 14.1227 | 0.450214 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.07550 | −0.129790 | ||||||||
\(987\) | 81.8418 | 2.60505 | ||||||||
\(988\) | 0.0491143 | 0.00156253 | ||||||||
\(989\) | −11.6786 | −0.371359 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.8840 | 1.07636 | 0.538180 | − | 0.842830i | \(-0.319112\pi\) | ||||
0.538180 | + | 0.842830i | \(0.319112\pi\) | |||||||
\(992\) | −9.45240 | −0.300114 | ||||||||
\(993\) | −44.7371 | −1.41969 | ||||||||
\(994\) | −29.6891 | −0.941681 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.29558 | −0.167797 | ||||||||
\(997\) | 12.3737 | 0.391878 | 0.195939 | − | 0.980616i | \(-0.437224\pi\) | ||||
0.195939 | + | 0.980616i | \(0.437224\pi\) | |||||||
\(998\) | −5.89900 | −0.186730 | ||||||||
\(999\) | 12.7182 | 0.402387 |
(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 | 6025.2.a.k.1.8 | 25 | ||
5.4 | even | 2 | 1205.2.a.d.1.18 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.d.1.18 | ✓ | 25 | 5.4 | even | 2 | ||
6025.2.a.k.1.8 | 25 | 1.1 | even | 1 | trivial |