Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.18186 | −1.83705 | −0.918525 | − | 0.395363i | \(-0.870619\pi\) | ||||
−0.918525 | + | 0.395363i | \(0.870619\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.25833 | 1.45717 | 0.728585 | − | 0.684956i | \(-0.240179\pi\) | ||||
0.728585 | + | 0.684956i | \(0.240179\pi\) | |||||||
\(6\) | −3.18186 | −1.29899 | ||||||||
\(7\) | 0.730955 | 0.276275 | 0.138137 | − | 0.990413i | \(-0.455888\pi\) | ||||
0.138137 | + | 0.990413i | \(0.455888\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.12426 | 2.37475 | ||||||||
\(10\) | 3.25833 | 1.03037 | ||||||||
\(11\) | −5.75818 | −1.73616 | −0.868078 | − | 0.496428i | \(-0.834645\pi\) | ||||
−0.868078 | + | 0.496428i | \(0.834645\pi\) | |||||||
\(12\) | −3.18186 | −0.918525 | ||||||||
\(13\) | 6.39012 | 1.77230 | 0.886151 | − | 0.463397i | \(-0.153370\pi\) | ||||
0.886151 | + | 0.463397i | \(0.153370\pi\) | |||||||
\(14\) | 0.730955 | 0.195356 | ||||||||
\(15\) | −10.3676 | −2.67689 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.49152 | −0.846817 | −0.423408 | − | 0.905939i | \(-0.639166\pi\) | ||||
−0.423408 | + | 0.905939i | \(0.639166\pi\) | |||||||
\(18\) | 7.12426 | 1.67920 | ||||||||
\(19\) | −4.71735 | −1.08224 | −0.541118 | − | 0.840947i | \(-0.681999\pi\) | ||||
−0.541118 | + | 0.840947i | \(0.681999\pi\) | |||||||
\(20\) | 3.25833 | 0.728585 | ||||||||
\(21\) | −2.32580 | −0.507531 | ||||||||
\(22\) | −5.75818 | −1.22765 | ||||||||
\(23\) | 3.36271 | 0.701173 | 0.350586 | − | 0.936530i | \(-0.385982\pi\) | ||||
0.350586 | + | 0.936530i | \(0.385982\pi\) | |||||||
\(24\) | −3.18186 | −0.649495 | ||||||||
\(25\) | 5.61671 | 1.12334 | ||||||||
\(26\) | 6.39012 | 1.25321 | ||||||||
\(27\) | −13.1228 | −2.52549 | ||||||||
\(28\) | 0.730955 | 0.138137 | ||||||||
\(29\) | −8.76673 | −1.62794 | −0.813971 | − | 0.580906i | \(-0.802698\pi\) | ||||
−0.813971 | + | 0.580906i | \(0.802698\pi\) | |||||||
\(30\) | −10.3676 | −1.89285 | ||||||||
\(31\) | −2.41031 | −0.432905 | −0.216452 | − | 0.976293i | \(-0.569449\pi\) | ||||
−0.216452 | + | 0.976293i | \(0.569449\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 18.3217 | 3.18940 | ||||||||
\(34\) | −3.49152 | −0.598790 | ||||||||
\(35\) | 2.38169 | 0.402579 | ||||||||
\(36\) | 7.12426 | 1.18738 | ||||||||
\(37\) | −1.65316 | −0.271778 | −0.135889 | − | 0.990724i | \(-0.543389\pi\) | ||||
−0.135889 | + | 0.990724i | \(0.543389\pi\) | |||||||
\(38\) | −4.71735 | −0.765256 | ||||||||
\(39\) | −20.3325 | −3.25581 | ||||||||
\(40\) | 3.25833 | 0.515187 | ||||||||
\(41\) | 9.18948 | 1.43516 | 0.717578 | − | 0.696478i | \(-0.245251\pi\) | ||||
0.717578 | + | 0.696478i | \(0.245251\pi\) | |||||||
\(42\) | −2.32580 | −0.358879 | ||||||||
\(43\) | −10.1578 | −1.54904 | −0.774522 | − | 0.632547i | \(-0.782010\pi\) | ||||
−0.774522 | + | 0.632547i | \(0.782010\pi\) | |||||||
\(44\) | −5.75818 | −0.868078 | ||||||||
\(45\) | 23.2132 | 3.46042 | ||||||||
\(46\) | 3.36271 | 0.495804 | ||||||||
\(47\) | −5.76558 | −0.840996 | −0.420498 | − | 0.907293i | \(-0.638145\pi\) | ||||
−0.420498 | + | 0.907293i | \(0.638145\pi\) | |||||||
\(48\) | −3.18186 | −0.459263 | ||||||||
\(49\) | −6.46571 | −0.923672 | ||||||||
\(50\) | 5.61671 | 0.794323 | ||||||||
\(51\) | 11.1095 | 1.55565 | ||||||||
\(52\) | 6.39012 | 0.886151 | ||||||||
\(53\) | −12.3589 | −1.69762 | −0.848810 | − | 0.528698i | \(-0.822680\pi\) | ||||
−0.848810 | + | 0.528698i | \(0.822680\pi\) | |||||||
\(54\) | −13.1228 | −1.78579 | ||||||||
\(55\) | −18.7620 | −2.52987 | ||||||||
\(56\) | 0.730955 | 0.0976779 | ||||||||
\(57\) | 15.0100 | 1.98812 | ||||||||
\(58\) | −8.76673 | −1.15113 | ||||||||
\(59\) | −3.29878 | −0.429465 | −0.214732 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214732 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(60\) | −10.3676 | −1.33845 | ||||||||
\(61\) | −3.47464 | −0.444882 | −0.222441 | − | 0.974946i | \(-0.571402\pi\) | ||||
−0.222441 | + | 0.974946i | \(0.571402\pi\) | |||||||
\(62\) | −2.41031 | −0.306110 | ||||||||
\(63\) | 5.20751 | 0.656085 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 20.8211 | 2.58254 | ||||||||
\(66\) | 18.3217 | 2.25525 | ||||||||
\(67\) | −6.19459 | −0.756789 | −0.378395 | − | 0.925644i | \(-0.623524\pi\) | ||||
−0.378395 | + | 0.925644i | \(0.623524\pi\) | |||||||
\(68\) | −3.49152 | −0.423408 | ||||||||
\(69\) | −10.6997 | −1.28809 | ||||||||
\(70\) | 2.38169 | 0.284667 | ||||||||
\(71\) | 3.91510 | 0.464637 | 0.232319 | − | 0.972640i | \(-0.425369\pi\) | ||||
0.232319 | + | 0.972640i | \(0.425369\pi\) | |||||||
\(72\) | 7.12426 | 0.839602 | ||||||||
\(73\) | −13.0659 | −1.52925 | −0.764626 | − | 0.644474i | \(-0.777076\pi\) | ||||
−0.764626 | + | 0.644474i | \(0.777076\pi\) | |||||||
\(74\) | −1.65316 | −0.192176 | ||||||||
\(75\) | −17.8716 | −2.06364 | ||||||||
\(76\) | −4.71735 | −0.541118 | ||||||||
\(77\) | −4.20897 | −0.479656 | ||||||||
\(78\) | −20.3325 | −2.30220 | ||||||||
\(79\) | 5.70341 | 0.641684 | 0.320842 | − | 0.947133i | \(-0.396034\pi\) | ||||
0.320842 | + | 0.947133i | \(0.396034\pi\) | |||||||
\(80\) | 3.25833 | 0.364292 | ||||||||
\(81\) | 20.3823 | 2.26470 | ||||||||
\(82\) | 9.18948 | 1.01481 | ||||||||
\(83\) | 5.97097 | 0.655399 | 0.327700 | − | 0.944782i | \(-0.393727\pi\) | ||||
0.327700 | + | 0.944782i | \(0.393727\pi\) | |||||||
\(84\) | −2.32580 | −0.253765 | ||||||||
\(85\) | −11.3765 | −1.23396 | ||||||||
\(86\) | −10.1578 | −1.09534 | ||||||||
\(87\) | 27.8946 | 2.99061 | ||||||||
\(88\) | −5.75818 | −0.613824 | ||||||||
\(89\) | −6.76257 | −0.716831 | −0.358415 | − | 0.933562i | \(-0.616683\pi\) | ||||
−0.358415 | + | 0.933562i | \(0.616683\pi\) | |||||||
\(90\) | 23.2132 | 2.44689 | ||||||||
\(91\) | 4.67089 | 0.489642 | ||||||||
\(92\) | 3.36271 | 0.350586 | ||||||||
\(93\) | 7.66929 | 0.795268 | ||||||||
\(94\) | −5.76558 | −0.594674 | ||||||||
\(95\) | −15.3707 | −1.57700 | ||||||||
\(96\) | −3.18186 | −0.324748 | ||||||||
\(97\) | −18.9015 | −1.91916 | −0.959579 | − | 0.281441i | \(-0.909188\pi\) | ||||
−0.959579 | + | 0.281441i | \(0.909188\pi\) | |||||||
\(98\) | −6.46571 | −0.653135 | ||||||||
\(99\) | −41.0228 | −4.12294 | ||||||||
\(100\) | 5.61671 | 0.561671 | ||||||||
\(101\) | 6.91866 | 0.688432 | 0.344216 | − | 0.938890i | \(-0.388145\pi\) | ||||
0.344216 | + | 0.938890i | \(0.388145\pi\) | |||||||
\(102\) | 11.1095 | 1.10001 | ||||||||
\(103\) | 10.4480 | 1.02947 | 0.514735 | − | 0.857349i | \(-0.327890\pi\) | ||||
0.514735 | + | 0.857349i | \(0.327890\pi\) | |||||||
\(104\) | 6.39012 | 0.626603 | ||||||||
\(105\) | −7.57822 | −0.739558 | ||||||||
\(106\) | −12.3589 | −1.20040 | ||||||||
\(107\) | 4.80472 | 0.464490 | 0.232245 | − | 0.972657i | \(-0.425393\pi\) | ||||
0.232245 | + | 0.972657i | \(0.425393\pi\) | |||||||
\(108\) | −13.1228 | −1.26275 | ||||||||
\(109\) | 9.08343 | 0.870034 | 0.435017 | − | 0.900422i | \(-0.356742\pi\) | ||||
0.435017 | + | 0.900422i | \(0.356742\pi\) | |||||||
\(110\) | −18.7620 | −1.78889 | ||||||||
\(111\) | 5.26014 | 0.499270 | ||||||||
\(112\) | 0.730955 | 0.0690687 | ||||||||
\(113\) | 15.9610 | 1.50149 | 0.750743 | − | 0.660594i | \(-0.229696\pi\) | ||||
0.750743 | + | 0.660594i | \(0.229696\pi\) | |||||||
\(114\) | 15.0100 | 1.40581 | ||||||||
\(115\) | 10.9568 | 1.02173 | ||||||||
\(116\) | −8.76673 | −0.813971 | ||||||||
\(117\) | 45.5249 | 4.20878 | ||||||||
\(118\) | −3.29878 | −0.303678 | ||||||||
\(119\) | −2.55214 | −0.233954 | ||||||||
\(120\) | −10.3676 | −0.946425 | ||||||||
\(121\) | 22.1566 | 2.01424 | ||||||||
\(122\) | −3.47464 | −0.314579 | ||||||||
\(123\) | −29.2397 | −2.63645 | ||||||||
\(124\) | −2.41031 | −0.216452 | ||||||||
\(125\) | 2.00944 | 0.179730 | ||||||||
\(126\) | 5.20751 | 0.463922 | ||||||||
\(127\) | 14.8746 | 1.31991 | 0.659953 | − | 0.751307i | \(-0.270576\pi\) | ||||
0.659953 | + | 0.751307i | \(0.270576\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 32.3206 | 2.84567 | ||||||||
\(130\) | 20.8211 | 1.82613 | ||||||||
\(131\) | 1.43415 | 0.125303 | 0.0626513 | − | 0.998035i | \(-0.480044\pi\) | ||||
0.0626513 | + | 0.998035i | \(0.480044\pi\) | |||||||
\(132\) | 18.3217 | 1.59470 | ||||||||
\(133\) | −3.44817 | −0.298994 | ||||||||
\(134\) | −6.19459 | −0.535131 | ||||||||
\(135\) | −42.7585 | −3.68007 | ||||||||
\(136\) | −3.49152 | −0.299395 | ||||||||
\(137\) | 10.0698 | 0.860319 | 0.430159 | − | 0.902753i | \(-0.358457\pi\) | ||||
0.430159 | + | 0.902753i | \(0.358457\pi\) | |||||||
\(138\) | −10.6997 | −0.910817 | ||||||||
\(139\) | −7.96726 | −0.675774 | −0.337887 | − | 0.941187i | \(-0.609712\pi\) | ||||
−0.337887 | + | 0.941187i | \(0.609712\pi\) | |||||||
\(140\) | 2.38169 | 0.201290 | ||||||||
\(141\) | 18.3453 | 1.54495 | ||||||||
\(142\) | 3.91510 | 0.328548 | ||||||||
\(143\) | −36.7955 | −3.07699 | ||||||||
\(144\) | 7.12426 | 0.593688 | ||||||||
\(145\) | −28.5649 | −2.37219 | ||||||||
\(146\) | −13.0659 | −1.08135 | ||||||||
\(147\) | 20.5730 | 1.69683 | ||||||||
\(148\) | −1.65316 | −0.135889 | ||||||||
\(149\) | 3.90248 | 0.319704 | 0.159852 | − | 0.987141i | \(-0.448898\pi\) | ||||
0.159852 | + | 0.987141i | \(0.448898\pi\) | |||||||
\(150\) | −17.8716 | −1.45921 | ||||||||
\(151\) | 2.76698 | 0.225173 | 0.112587 | − | 0.993642i | \(-0.464086\pi\) | ||||
0.112587 | + | 0.993642i | \(0.464086\pi\) | |||||||
\(152\) | −4.71735 | −0.382628 | ||||||||
\(153\) | −24.8745 | −2.01098 | ||||||||
\(154\) | −4.20897 | −0.339168 | ||||||||
\(155\) | −7.85359 | −0.630816 | ||||||||
\(156\) | −20.3325 | −1.62790 | ||||||||
\(157\) | −15.8994 | −1.26891 | −0.634454 | − | 0.772961i | \(-0.718775\pi\) | ||||
−0.634454 | + | 0.772961i | \(0.718775\pi\) | |||||||
\(158\) | 5.70341 | 0.453739 | ||||||||
\(159\) | 39.3242 | 3.11861 | ||||||||
\(160\) | 3.25833 | 0.257594 | ||||||||
\(161\) | 2.45799 | 0.193717 | ||||||||
\(162\) | 20.3823 | 1.60139 | ||||||||
\(163\) | −3.17193 | −0.248444 | −0.124222 | − | 0.992254i | \(-0.539644\pi\) | ||||
−0.124222 | + | 0.992254i | \(0.539644\pi\) | |||||||
\(164\) | 9.18948 | 0.717578 | ||||||||
\(165\) | 59.6983 | 4.64750 | ||||||||
\(166\) | 5.97097 | 0.463437 | ||||||||
\(167\) | −14.2730 | −1.10448 | −0.552239 | − | 0.833686i | \(-0.686226\pi\) | ||||
−0.552239 | + | 0.833686i | \(0.686226\pi\) | |||||||
\(168\) | −2.32580 | −0.179439 | ||||||||
\(169\) | 27.8337 | 2.14105 | ||||||||
\(170\) | −11.3765 | −0.872538 | ||||||||
\(171\) | −33.6077 | −2.57004 | ||||||||
\(172\) | −10.1578 | −0.774522 | ||||||||
\(173\) | −12.2135 | −0.928574 | −0.464287 | − | 0.885685i | \(-0.653689\pi\) | ||||
−0.464287 | + | 0.885685i | \(0.653689\pi\) | |||||||
\(174\) | 27.8946 | 2.11468 | ||||||||
\(175\) | 4.10556 | 0.310351 | ||||||||
\(176\) | −5.75818 | −0.434039 | ||||||||
\(177\) | 10.4963 | 0.788949 | ||||||||
\(178\) | −6.76257 | −0.506876 | ||||||||
\(179\) | 16.6232 | 1.24248 | 0.621238 | − | 0.783622i | \(-0.286630\pi\) | ||||
0.621238 | + | 0.783622i | \(0.286630\pi\) | |||||||
\(180\) | 23.2132 | 1.73021 | ||||||||
\(181\) | 4.65824 | 0.346244 | 0.173122 | − | 0.984900i | \(-0.444614\pi\) | ||||
0.173122 | + | 0.984900i | \(0.444614\pi\) | |||||||
\(182\) | 4.67089 | 0.346229 | ||||||||
\(183\) | 11.0558 | 0.817270 | ||||||||
\(184\) | 3.36271 | 0.247902 | ||||||||
\(185\) | −5.38655 | −0.396027 | ||||||||
\(186\) | 7.66929 | 0.562339 | ||||||||
\(187\) | 20.1048 | 1.47021 | ||||||||
\(188\) | −5.76558 | −0.420498 | ||||||||
\(189\) | −9.59220 | −0.697730 | ||||||||
\(190\) | −15.3707 | −1.11511 | ||||||||
\(191\) | −16.9489 | −1.22638 | −0.613190 | − | 0.789936i | \(-0.710114\pi\) | ||||
−0.613190 | + | 0.789936i | \(0.710114\pi\) | |||||||
\(192\) | −3.18186 | −0.229631 | ||||||||
\(193\) | 17.4848 | 1.25858 | 0.629291 | − | 0.777170i | \(-0.283345\pi\) | ||||
0.629291 | + | 0.777170i | \(0.283345\pi\) | |||||||
\(194\) | −18.9015 | −1.35705 | ||||||||
\(195\) | −66.2500 | −4.74426 | ||||||||
\(196\) | −6.46571 | −0.461836 | ||||||||
\(197\) | −13.3981 | −0.954576 | −0.477288 | − | 0.878747i | \(-0.658380\pi\) | ||||
−0.477288 | + | 0.878747i | \(0.658380\pi\) | |||||||
\(198\) | −41.0228 | −2.91536 | ||||||||
\(199\) | −3.66238 | −0.259619 | −0.129810 | − | 0.991539i | \(-0.541437\pi\) | ||||
−0.129810 | + | 0.991539i | \(0.541437\pi\) | |||||||
\(200\) | 5.61671 | 0.397161 | ||||||||
\(201\) | 19.7103 | 1.39026 | ||||||||
\(202\) | 6.91866 | 0.486795 | ||||||||
\(203\) | −6.40808 | −0.449759 | ||||||||
\(204\) | 11.1095 | 0.777823 | ||||||||
\(205\) | 29.9423 | 2.09126 | ||||||||
\(206\) | 10.4480 | 0.727946 | ||||||||
\(207\) | 23.9568 | 1.66511 | ||||||||
\(208\) | 6.39012 | 0.443075 | ||||||||
\(209\) | 27.1634 | 1.87893 | ||||||||
\(210\) | −7.57822 | −0.522947 | ||||||||
\(211\) | 16.6422 | 1.14569 | 0.572847 | − | 0.819662i | \(-0.305839\pi\) | ||||
0.572847 | + | 0.819662i | \(0.305839\pi\) | |||||||
\(212\) | −12.3589 | −0.848810 | ||||||||
\(213\) | −12.4573 | −0.853562 | ||||||||
\(214\) | 4.80472 | 0.328444 | ||||||||
\(215\) | −33.0973 | −2.25722 | ||||||||
\(216\) | −13.1228 | −0.892896 | ||||||||
\(217\) | −1.76183 | −0.119601 | ||||||||
\(218\) | 9.08343 | 0.615207 | ||||||||
\(219\) | 41.5741 | 2.80931 | ||||||||
\(220\) | −18.7620 | −1.26494 | ||||||||
\(221\) | −22.3112 | −1.50081 | ||||||||
\(222\) | 5.26014 | 0.353037 | ||||||||
\(223\) | −15.6933 | −1.05090 | −0.525452 | − | 0.850823i | \(-0.676104\pi\) | ||||
−0.525452 | + | 0.850823i | \(0.676104\pi\) | |||||||
\(224\) | 0.730955 | 0.0488390 | ||||||||
\(225\) | 40.0149 | 2.66766 | ||||||||
\(226\) | 15.9610 | 1.06171 | ||||||||
\(227\) | −21.4540 | −1.42395 | −0.711974 | − | 0.702205i | \(-0.752199\pi\) | ||||
−0.711974 | + | 0.702205i | \(0.752199\pi\) | |||||||
\(228\) | 15.0100 | 0.994060 | ||||||||
\(229\) | −0.269337 | −0.0177983 | −0.00889913 | − | 0.999960i | \(-0.502833\pi\) | ||||
−0.00889913 | + | 0.999960i | \(0.502833\pi\) | |||||||
\(230\) | 10.9568 | 0.722470 | ||||||||
\(231\) | 13.3924 | 0.881153 | ||||||||
\(232\) | −8.76673 | −0.575564 | ||||||||
\(233\) | −24.5826 | −1.61046 | −0.805230 | − | 0.592962i | \(-0.797958\pi\) | ||||
−0.805230 | + | 0.592962i | \(0.797958\pi\) | |||||||
\(234\) | 45.5249 | 2.97606 | ||||||||
\(235\) | −18.7862 | −1.22547 | ||||||||
\(236\) | −3.29878 | −0.214732 | ||||||||
\(237\) | −18.1475 | −1.17881 | ||||||||
\(238\) | −2.55214 | −0.165431 | ||||||||
\(239\) | −23.0023 | −1.48789 | −0.743947 | − | 0.668239i | \(-0.767049\pi\) | ||||
−0.743947 | + | 0.668239i | \(0.767049\pi\) | |||||||
\(240\) | −10.3676 | −0.669223 | ||||||||
\(241\) | −7.66395 | −0.493679 | −0.246839 | − | 0.969056i | \(-0.579392\pi\) | ||||
−0.246839 | + | 0.969056i | \(0.579392\pi\) | |||||||
\(242\) | 22.1566 | 1.42428 | ||||||||
\(243\) | −25.4852 | −1.63488 | ||||||||
\(244\) | −3.47464 | −0.222441 | ||||||||
\(245\) | −21.0674 | −1.34595 | ||||||||
\(246\) | −29.2397 | −1.86425 | ||||||||
\(247\) | −30.1445 | −1.91805 | ||||||||
\(248\) | −2.41031 | −0.153055 | ||||||||
\(249\) | −18.9988 | −1.20400 | ||||||||
\(250\) | 2.00944 | 0.127088 | ||||||||
\(251\) | −2.40741 | −0.151955 | −0.0759773 | − | 0.997110i | \(-0.524208\pi\) | ||||
−0.0759773 | + | 0.997110i | \(0.524208\pi\) | |||||||
\(252\) | 5.20751 | 0.328042 | ||||||||
\(253\) | −19.3631 | −1.21735 | ||||||||
\(254\) | 14.8746 | 0.933315 | ||||||||
\(255\) | 36.1985 | 2.26684 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.2530 | 1.01384 | 0.506918 | − | 0.861994i | \(-0.330785\pi\) | ||||
0.506918 | + | 0.861994i | \(0.330785\pi\) | |||||||
\(258\) | 32.3206 | 2.01219 | ||||||||
\(259\) | −1.20839 | −0.0750855 | ||||||||
\(260\) | 20.8211 | 1.29127 | ||||||||
\(261\) | −62.4565 | −3.86596 | ||||||||
\(262\) | 1.43415 | 0.0886024 | ||||||||
\(263\) | −8.95933 | −0.552456 | −0.276228 | − | 0.961092i | \(-0.589085\pi\) | ||||
−0.276228 | + | 0.961092i | \(0.589085\pi\) | |||||||
\(264\) | 18.3217 | 1.12762 | ||||||||
\(265\) | −40.2692 | −2.47372 | ||||||||
\(266\) | −3.44817 | −0.211421 | ||||||||
\(267\) | 21.5176 | 1.31685 | ||||||||
\(268\) | −6.19459 | −0.378395 | ||||||||
\(269\) | −11.0489 | −0.673661 | −0.336831 | − | 0.941565i | \(-0.609355\pi\) | ||||
−0.336831 | + | 0.941565i | \(0.609355\pi\) | |||||||
\(270\) | −42.7585 | −2.60220 | ||||||||
\(271\) | 20.2615 | 1.23080 | 0.615399 | − | 0.788216i | \(-0.288995\pi\) | ||||
0.615399 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(272\) | −3.49152 | −0.211704 | ||||||||
\(273\) | −14.8621 | −0.899498 | ||||||||
\(274\) | 10.0698 | 0.608337 | ||||||||
\(275\) | −32.3420 | −1.95030 | ||||||||
\(276\) | −10.6997 | −0.644045 | ||||||||
\(277\) | −16.0554 | −0.964678 | −0.482339 | − | 0.875985i | \(-0.660213\pi\) | ||||
−0.482339 | + | 0.875985i | \(0.660213\pi\) | |||||||
\(278\) | −7.96726 | −0.477845 | ||||||||
\(279\) | −17.1717 | −1.02804 | ||||||||
\(280\) | 2.38169 | 0.142333 | ||||||||
\(281\) | 14.6147 | 0.871842 | 0.435921 | − | 0.899985i | \(-0.356423\pi\) | ||||
0.435921 | + | 0.899985i | \(0.356423\pi\) | |||||||
\(282\) | 18.3453 | 1.09245 | ||||||||
\(283\) | 18.9708 | 1.12769 | 0.563847 | − | 0.825879i | \(-0.309321\pi\) | ||||
0.563847 | + | 0.825879i | \(0.309321\pi\) | |||||||
\(284\) | 3.91510 | 0.232319 | ||||||||
\(285\) | 48.9075 | 2.89703 | ||||||||
\(286\) | −36.7955 | −2.17576 | ||||||||
\(287\) | 6.71709 | 0.396497 | ||||||||
\(288\) | 7.12426 | 0.419801 | ||||||||
\(289\) | −4.80932 | −0.282901 | ||||||||
\(290\) | −28.5649 | −1.67739 | ||||||||
\(291\) | 60.1420 | 3.52559 | ||||||||
\(292\) | −13.0659 | −0.764626 | ||||||||
\(293\) | −11.3485 | −0.662988 | −0.331494 | − | 0.943457i | \(-0.607553\pi\) | ||||
−0.331494 | + | 0.943457i | \(0.607553\pi\) | |||||||
\(294\) | 20.5730 | 1.19984 | ||||||||
\(295\) | −10.7485 | −0.625803 | ||||||||
\(296\) | −1.65316 | −0.0960881 | ||||||||
\(297\) | 75.5636 | 4.38465 | ||||||||
\(298\) | 3.90248 | 0.226065 | ||||||||
\(299\) | 21.4881 | 1.24269 | ||||||||
\(300\) | −17.8716 | −1.03182 | ||||||||
\(301\) | −7.42487 | −0.427962 | ||||||||
\(302\) | 2.76698 | 0.159222 | ||||||||
\(303\) | −22.0142 | −1.26469 | ||||||||
\(304\) | −4.71735 | −0.270559 | ||||||||
\(305\) | −11.3215 | −0.648268 | ||||||||
\(306\) | −24.8745 | −1.42198 | ||||||||
\(307\) | 33.8698 | 1.93305 | 0.966527 | − | 0.256564i | \(-0.0825905\pi\) | ||||
0.966527 | + | 0.256564i | \(0.0825905\pi\) | |||||||
\(308\) | −4.20897 | −0.239828 | ||||||||
\(309\) | −33.2441 | −1.89119 | ||||||||
\(310\) | −7.85359 | −0.446054 | ||||||||
\(311\) | 4.54087 | 0.257489 | 0.128745 | − | 0.991678i | \(-0.458905\pi\) | ||||
0.128745 | + | 0.991678i | \(0.458905\pi\) | |||||||
\(312\) | −20.3325 | −1.15110 | ||||||||
\(313\) | 9.53960 | 0.539210 | 0.269605 | − | 0.962971i | \(-0.413107\pi\) | ||||
0.269605 | + | 0.962971i | \(0.413107\pi\) | |||||||
\(314\) | −15.8994 | −0.897254 | ||||||||
\(315\) | 16.9678 | 0.956027 | ||||||||
\(316\) | 5.70341 | 0.320842 | ||||||||
\(317\) | −24.1254 | −1.35502 | −0.677510 | − | 0.735514i | \(-0.736941\pi\) | ||||
−0.677510 | + | 0.735514i | \(0.736941\pi\) | |||||||
\(318\) | 39.3242 | 2.20519 | ||||||||
\(319\) | 50.4804 | 2.82636 | ||||||||
\(320\) | 3.25833 | 0.182146 | ||||||||
\(321\) | −15.2880 | −0.853291 | ||||||||
\(322\) | 2.45799 | 0.136978 | ||||||||
\(323\) | 16.4707 | 0.916455 | ||||||||
\(324\) | 20.3823 | 1.13235 | ||||||||
\(325\) | 35.8915 | 1.99090 | ||||||||
\(326\) | −3.17193 | −0.175677 | ||||||||
\(327\) | −28.9022 | −1.59830 | ||||||||
\(328\) | 9.18948 | 0.507404 | ||||||||
\(329\) | −4.21438 | −0.232346 | ||||||||
\(330\) | 59.6983 | 3.28628 | ||||||||
\(331\) | −27.3148 | −1.50136 | −0.750679 | − | 0.660667i | \(-0.770273\pi\) | ||||
−0.750679 | + | 0.660667i | \(0.770273\pi\) | |||||||
\(332\) | 5.97097 | 0.327700 | ||||||||
\(333\) | −11.7776 | −0.645406 | ||||||||
\(334\) | −14.2730 | −0.780984 | ||||||||
\(335\) | −20.1840 | −1.10277 | ||||||||
\(336\) | −2.32580 | −0.126883 | ||||||||
\(337\) | 3.25159 | 0.177125 | 0.0885627 | − | 0.996071i | \(-0.471773\pi\) | ||||
0.0885627 | + | 0.996071i | \(0.471773\pi\) | |||||||
\(338\) | 27.8337 | 1.51395 | ||||||||
\(339\) | −50.7858 | −2.75831 | ||||||||
\(340\) | −11.3765 | −0.616978 | ||||||||
\(341\) | 13.8790 | 0.751590 | ||||||||
\(342\) | −33.6077 | −1.81729 | ||||||||
\(343\) | −9.84282 | −0.531462 | ||||||||
\(344\) | −10.1578 | −0.547670 | ||||||||
\(345\) | −34.8631 | −1.87696 | ||||||||
\(346\) | −12.2135 | −0.656601 | ||||||||
\(347\) | 6.76218 | 0.363013 | 0.181506 | − | 0.983390i | \(-0.441903\pi\) | ||||
0.181506 | + | 0.983390i | \(0.441903\pi\) | |||||||
\(348\) | 27.8946 | 1.49530 | ||||||||
\(349\) | −21.6154 | −1.15704 | −0.578522 | − | 0.815667i | \(-0.696370\pi\) | ||||
−0.578522 | + | 0.815667i | \(0.696370\pi\) | |||||||
\(350\) | 4.10556 | 0.219451 | ||||||||
\(351\) | −83.8566 | −4.47593 | ||||||||
\(352\) | −5.75818 | −0.306912 | ||||||||
\(353\) | 13.4774 | 0.717331 | 0.358666 | − | 0.933466i | \(-0.383232\pi\) | ||||
0.358666 | + | 0.933466i | \(0.383232\pi\) | |||||||
\(354\) | 10.4963 | 0.557871 | ||||||||
\(355\) | 12.7567 | 0.677055 | ||||||||
\(356\) | −6.76257 | −0.358415 | ||||||||
\(357\) | 8.12056 | 0.429786 | ||||||||
\(358\) | 16.6232 | 0.878563 | ||||||||
\(359\) | 6.90181 | 0.364264 | 0.182132 | − | 0.983274i | \(-0.441700\pi\) | ||||
0.182132 | + | 0.983274i | \(0.441700\pi\) | |||||||
\(360\) | 23.2132 | 1.22344 | ||||||||
\(361\) | 3.25343 | 0.171233 | ||||||||
\(362\) | 4.65824 | 0.244832 | ||||||||
\(363\) | −70.4993 | −3.70025 | ||||||||
\(364\) | 4.67089 | 0.244821 | ||||||||
\(365\) | −42.5731 | −2.22838 | ||||||||
\(366\) | 11.0558 | 0.577897 | ||||||||
\(367\) | 13.5564 | 0.707641 | 0.353820 | − | 0.935313i | \(-0.384882\pi\) | ||||
0.353820 | + | 0.935313i | \(0.384882\pi\) | |||||||
\(368\) | 3.36271 | 0.175293 | ||||||||
\(369\) | 65.4682 | 3.40814 | ||||||||
\(370\) | −5.38655 | −0.280033 | ||||||||
\(371\) | −9.03376 | −0.469010 | ||||||||
\(372\) | 7.66929 | 0.397634 | ||||||||
\(373\) | −16.4605 | −0.852291 | −0.426145 | − | 0.904655i | \(-0.640129\pi\) | ||||
−0.426145 | + | 0.904655i | \(0.640129\pi\) | |||||||
\(374\) | 20.1048 | 1.03959 | ||||||||
\(375\) | −6.39378 | −0.330173 | ||||||||
\(376\) | −5.76558 | −0.297337 | ||||||||
\(377\) | −56.0205 | −2.88520 | ||||||||
\(378\) | −9.59220 | −0.493370 | ||||||||
\(379\) | −35.4651 | −1.82172 | −0.910860 | − | 0.412716i | \(-0.864580\pi\) | ||||
−0.910860 | + | 0.412716i | \(0.864580\pi\) | |||||||
\(380\) | −15.3707 | −0.788500 | ||||||||
\(381\) | −47.3289 | −2.42473 | ||||||||
\(382\) | −16.9489 | −0.867181 | ||||||||
\(383\) | 28.2598 | 1.44401 | 0.722004 | − | 0.691889i | \(-0.243221\pi\) | ||||
0.722004 | + | 0.691889i | \(0.243221\pi\) | |||||||
\(384\) | −3.18186 | −0.162374 | ||||||||
\(385\) | −13.7142 | −0.698940 | ||||||||
\(386\) | 17.4848 | 0.889951 | ||||||||
\(387\) | −72.3666 | −3.67860 | ||||||||
\(388\) | −18.9015 | −0.959579 | ||||||||
\(389\) | −28.6301 | −1.45160 | −0.725801 | − | 0.687905i | \(-0.758531\pi\) | ||||
−0.725801 | + | 0.687905i | \(0.758531\pi\) | |||||||
\(390\) | −66.2500 | −3.35470 | ||||||||
\(391\) | −11.7409 | −0.593765 | ||||||||
\(392\) | −6.46571 | −0.326567 | ||||||||
\(393\) | −4.56329 | −0.230187 | ||||||||
\(394\) | −13.3981 | −0.674987 | ||||||||
\(395\) | 18.5836 | 0.935043 | ||||||||
\(396\) | −41.0228 | −2.06147 | ||||||||
\(397\) | 29.1457 | 1.46278 | 0.731390 | − | 0.681960i | \(-0.238872\pi\) | ||||
0.731390 | + | 0.681960i | \(0.238872\pi\) | |||||||
\(398\) | −3.66238 | −0.183579 | ||||||||
\(399\) | 10.9716 | 0.549268 | ||||||||
\(400\) | 5.61671 | 0.280836 | ||||||||
\(401\) | 2.03995 | 0.101870 | 0.0509352 | − | 0.998702i | \(-0.483780\pi\) | ||||
0.0509352 | + | 0.998702i | \(0.483780\pi\) | |||||||
\(402\) | 19.7103 | 0.983062 | ||||||||
\(403\) | −15.4022 | −0.767238 | ||||||||
\(404\) | 6.91866 | 0.344216 | ||||||||
\(405\) | 66.4123 | 3.30005 | ||||||||
\(406\) | −6.40808 | −0.318028 | ||||||||
\(407\) | 9.51920 | 0.471849 | ||||||||
\(408\) | 11.1095 | 0.550004 | ||||||||
\(409\) | 13.0344 | 0.644509 | 0.322254 | − | 0.946653i | \(-0.395559\pi\) | ||||
0.322254 | + | 0.946653i | \(0.395559\pi\) | |||||||
\(410\) | 29.9423 | 1.47875 | ||||||||
\(411\) | −32.0406 | −1.58045 | ||||||||
\(412\) | 10.4480 | 0.514735 | ||||||||
\(413\) | −2.41126 | −0.118650 | ||||||||
\(414\) | 23.9568 | 1.17741 | ||||||||
\(415\) | 19.4554 | 0.955028 | ||||||||
\(416\) | 6.39012 | 0.313302 | ||||||||
\(417\) | 25.3508 | 1.24143 | ||||||||
\(418\) | 27.1634 | 1.32860 | ||||||||
\(419\) | 10.4099 | 0.508558 | 0.254279 | − | 0.967131i | \(-0.418162\pi\) | ||||
0.254279 | + | 0.967131i | \(0.418162\pi\) | |||||||
\(420\) | −7.57822 | −0.369779 | ||||||||
\(421\) | 2.74094 | 0.133585 | 0.0667927 | − | 0.997767i | \(-0.478723\pi\) | ||||
0.0667927 | + | 0.997767i | \(0.478723\pi\) | |||||||
\(422\) | 16.6422 | 0.810129 | ||||||||
\(423\) | −41.0755 | −1.99716 | ||||||||
\(424\) | −12.3589 | −0.600199 | ||||||||
\(425\) | −19.6108 | −0.951265 | ||||||||
\(426\) | −12.4573 | −0.603559 | ||||||||
\(427\) | −2.53980 | −0.122910 | ||||||||
\(428\) | 4.80472 | 0.232245 | ||||||||
\(429\) | 117.078 | 5.65259 | ||||||||
\(430\) | −33.0973 | −1.59610 | ||||||||
\(431\) | −18.7175 | −0.901588 | −0.450794 | − | 0.892628i | \(-0.648859\pi\) | ||||
−0.450794 | + | 0.892628i | \(0.648859\pi\) | |||||||
\(432\) | −13.1228 | −0.631373 | ||||||||
\(433\) | 33.0512 | 1.58834 | 0.794170 | − | 0.607696i | \(-0.207906\pi\) | ||||
0.794170 | + | 0.607696i | \(0.207906\pi\) | |||||||
\(434\) | −1.76183 | −0.0845705 | ||||||||
\(435\) | 90.8896 | 4.35782 | ||||||||
\(436\) | 9.08343 | 0.435017 | ||||||||
\(437\) | −15.8631 | −0.758834 | ||||||||
\(438\) | 41.5741 | 1.98649 | ||||||||
\(439\) | −16.9884 | −0.810812 | −0.405406 | − | 0.914137i | \(-0.632870\pi\) | ||||
−0.405406 | + | 0.914137i | \(0.632870\pi\) | |||||||
\(440\) | −18.7620 | −0.894445 | ||||||||
\(441\) | −46.0634 | −2.19349 | ||||||||
\(442\) | −22.3112 | −1.06124 | ||||||||
\(443\) | 8.95033 | 0.425243 | 0.212621 | − | 0.977135i | \(-0.431800\pi\) | ||||
0.212621 | + | 0.977135i | \(0.431800\pi\) | |||||||
\(444\) | 5.26014 | 0.249635 | ||||||||
\(445\) | −22.0347 | −1.04454 | ||||||||
\(446\) | −15.6933 | −0.743101 | ||||||||
\(447\) | −12.4172 | −0.587312 | ||||||||
\(448\) | 0.730955 | 0.0345344 | ||||||||
\(449\) | −40.1425 | −1.89444 | −0.947221 | − | 0.320583i | \(-0.896121\pi\) | ||||
−0.947221 | + | 0.320583i | \(0.896121\pi\) | |||||||
\(450\) | 40.0149 | 1.88632 | ||||||||
\(451\) | −52.9146 | −2.49165 | ||||||||
\(452\) | 15.9610 | 0.750743 | ||||||||
\(453\) | −8.80414 | −0.413655 | ||||||||
\(454\) | −21.4540 | −1.00688 | ||||||||
\(455\) | 15.2193 | 0.713492 | ||||||||
\(456\) | 15.0100 | 0.702907 | ||||||||
\(457\) | 7.34381 | 0.343529 | 0.171764 | − | 0.985138i | \(-0.445053\pi\) | ||||
0.171764 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(458\) | −0.269337 | −0.0125853 | ||||||||
\(459\) | 45.8186 | 2.13863 | ||||||||
\(460\) | 10.9568 | 0.510864 | ||||||||
\(461\) | −28.4444 | −1.32479 | −0.662395 | − | 0.749155i | \(-0.730460\pi\) | ||||
−0.662395 | + | 0.749155i | \(0.730460\pi\) | |||||||
\(462\) | 13.3924 | 0.623069 | ||||||||
\(463\) | −18.5267 | −0.861008 | −0.430504 | − | 0.902589i | \(-0.641664\pi\) | ||||
−0.430504 | + | 0.902589i | \(0.641664\pi\) | |||||||
\(464\) | −8.76673 | −0.406985 | ||||||||
\(465\) | 24.9891 | 1.15884 | ||||||||
\(466\) | −24.5826 | −1.13877 | ||||||||
\(467\) | −7.41094 | −0.342937 | −0.171469 | − | 0.985190i | \(-0.554851\pi\) | ||||
−0.171469 | + | 0.985190i | \(0.554851\pi\) | |||||||
\(468\) | 45.5249 | 2.10439 | ||||||||
\(469\) | −4.52796 | −0.209082 | ||||||||
\(470\) | −18.7862 | −0.866541 | ||||||||
\(471\) | 50.5896 | 2.33105 | ||||||||
\(472\) | −3.29878 | −0.151839 | ||||||||
\(473\) | 58.4902 | 2.68938 | ||||||||
\(474\) | −18.1475 | −0.833542 | ||||||||
\(475\) | −26.4960 | −1.21572 | ||||||||
\(476\) | −2.55214 | −0.116977 | ||||||||
\(477\) | −88.0477 | −4.03143 | ||||||||
\(478\) | −23.0023 | −1.05210 | ||||||||
\(479\) | 40.0605 | 1.83041 | 0.915206 | − | 0.402987i | \(-0.132028\pi\) | ||||
0.915206 | + | 0.402987i | \(0.132028\pi\) | |||||||
\(480\) | −10.3676 | −0.473212 | ||||||||
\(481\) | −10.5639 | −0.481673 | ||||||||
\(482\) | −7.66395 | −0.349084 | ||||||||
\(483\) | −7.82098 | −0.355867 | ||||||||
\(484\) | 22.1566 | 1.00712 | ||||||||
\(485\) | −61.5873 | −2.79654 | ||||||||
\(486\) | −25.4852 | −1.15603 | ||||||||
\(487\) | −23.3099 | −1.05627 | −0.528137 | − | 0.849159i | \(-0.677109\pi\) | ||||
−0.528137 | + | 0.849159i | \(0.677109\pi\) | |||||||
\(488\) | −3.47464 | −0.157290 | ||||||||
\(489\) | 10.0926 | 0.456405 | ||||||||
\(490\) | −21.0674 | −0.951728 | ||||||||
\(491\) | −20.7248 | −0.935295 | −0.467648 | − | 0.883915i | \(-0.654898\pi\) | ||||
−0.467648 | + | 0.883915i | \(0.654898\pi\) | |||||||
\(492\) | −29.2397 | −1.31823 | ||||||||
\(493\) | 30.6092 | 1.37857 | ||||||||
\(494\) | −30.1445 | −1.35626 | ||||||||
\(495\) | −133.666 | −6.00782 | ||||||||
\(496\) | −2.41031 | −0.108226 | ||||||||
\(497\) | 2.86176 | 0.128368 | ||||||||
\(498\) | −18.9988 | −0.851358 | ||||||||
\(499\) | 32.6856 | 1.46321 | 0.731604 | − | 0.681730i | \(-0.238772\pi\) | ||||
0.731604 | + | 0.681730i | \(0.238772\pi\) | |||||||
\(500\) | 2.00944 | 0.0898651 | ||||||||
\(501\) | 45.4147 | 2.02898 | ||||||||
\(502\) | −2.40741 | −0.107448 | ||||||||
\(503\) | −22.8957 | −1.02087 | −0.510434 | − | 0.859917i | \(-0.670515\pi\) | ||||
−0.510434 | + | 0.859917i | \(0.670515\pi\) | |||||||
\(504\) | 5.20751 | 0.231961 | ||||||||
\(505\) | 22.5433 | 1.00316 | ||||||||
\(506\) | −19.3631 | −0.860793 | ||||||||
\(507\) | −88.5630 | −3.93322 | ||||||||
\(508\) | 14.8746 | 0.659953 | ||||||||
\(509\) | −21.0881 | −0.934715 | −0.467357 | − | 0.884068i | \(-0.654794\pi\) | ||||
−0.467357 | + | 0.884068i | \(0.654794\pi\) | |||||||
\(510\) | 36.1985 | 1.60290 | ||||||||
\(511\) | −9.55061 | −0.422494 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 61.9051 | 2.73318 | ||||||||
\(514\) | 16.2530 | 0.716891 | ||||||||
\(515\) | 34.0430 | 1.50011 | ||||||||
\(516\) | 32.3206 | 1.42284 | ||||||||
\(517\) | 33.1992 | 1.46010 | ||||||||
\(518\) | −1.20839 | −0.0530935 | ||||||||
\(519\) | 38.8616 | 1.70584 | ||||||||
\(520\) | 20.8211 | 0.913067 | ||||||||
\(521\) | −30.1264 | −1.31986 | −0.659931 | − | 0.751326i | \(-0.729415\pi\) | ||||
−0.659931 | + | 0.751326i | \(0.729415\pi\) | |||||||
\(522\) | −62.4565 | −2.73365 | ||||||||
\(523\) | 36.4701 | 1.59472 | 0.797362 | − | 0.603501i | \(-0.206228\pi\) | ||||
0.797362 | + | 0.603501i | \(0.206228\pi\) | |||||||
\(524\) | 1.43415 | 0.0626513 | ||||||||
\(525\) | −13.0633 | −0.570131 | ||||||||
\(526\) | −8.95933 | −0.390646 | ||||||||
\(527\) | 8.41564 | 0.366591 | ||||||||
\(528\) | 18.3217 | 0.797351 | ||||||||
\(529\) | −11.6922 | −0.508357 | ||||||||
\(530\) | −40.2692 | −1.74918 | ||||||||
\(531\) | −23.5014 | −1.01987 | ||||||||
\(532\) | −3.44817 | −0.149497 | ||||||||
\(533\) | 58.7219 | 2.54353 | ||||||||
\(534\) | 21.5176 | 0.931157 | ||||||||
\(535\) | 15.6554 | 0.676840 | ||||||||
\(536\) | −6.19459 | −0.267565 | ||||||||
\(537\) | −52.8927 | −2.28249 | ||||||||
\(538\) | −11.0489 | −0.476350 | ||||||||
\(539\) | 37.2307 | 1.60364 | ||||||||
\(540\) | −42.7585 | −1.84003 | ||||||||
\(541\) | 14.1947 | 0.610277 | 0.305138 | − | 0.952308i | \(-0.401297\pi\) | ||||
0.305138 | + | 0.952308i | \(0.401297\pi\) | |||||||
\(542\) | 20.2615 | 0.870306 | ||||||||
\(543\) | −14.8219 | −0.636068 | ||||||||
\(544\) | −3.49152 | −0.149697 | ||||||||
\(545\) | 29.5968 | 1.26779 | ||||||||
\(546\) | −14.8621 | −0.636041 | ||||||||
\(547\) | 11.1207 | 0.475486 | 0.237743 | − | 0.971328i | \(-0.423592\pi\) | ||||
0.237743 | + | 0.971328i | \(0.423592\pi\) | |||||||
\(548\) | 10.0698 | 0.430159 | ||||||||
\(549\) | −24.7542 | −1.05649 | ||||||||
\(550\) | −32.3420 | −1.37907 | ||||||||
\(551\) | 41.3558 | 1.76182 | ||||||||
\(552\) | −10.6997 | −0.455409 | ||||||||
\(553\) | 4.16894 | 0.177281 | ||||||||
\(554\) | −16.0554 | −0.682130 | ||||||||
\(555\) | 17.1393 | 0.727521 | ||||||||
\(556\) | −7.96726 | −0.337887 | ||||||||
\(557\) | −2.95092 | −0.125034 | −0.0625172 | − | 0.998044i | \(-0.519913\pi\) | ||||
−0.0625172 | + | 0.998044i | \(0.519913\pi\) | |||||||
\(558\) | −17.1717 | −0.726936 | ||||||||
\(559\) | −64.9094 | −2.74537 | ||||||||
\(560\) | 2.38169 | 0.100645 | ||||||||
\(561\) | −63.9706 | −2.70084 | ||||||||
\(562\) | 14.6147 | 0.616485 | ||||||||
\(563\) | −9.11591 | −0.384190 | −0.192095 | − | 0.981376i | \(-0.561528\pi\) | ||||
−0.192095 | + | 0.981376i | \(0.561528\pi\) | |||||||
\(564\) | 18.3453 | 0.772476 | ||||||||
\(565\) | 52.0063 | 2.18792 | ||||||||
\(566\) | 18.9708 | 0.797400 | ||||||||
\(567\) | 14.8986 | 0.625680 | ||||||||
\(568\) | 3.91510 | 0.164274 | ||||||||
\(569\) | 14.0235 | 0.587894 | 0.293947 | − | 0.955822i | \(-0.405031\pi\) | ||||
0.293947 | + | 0.955822i | \(0.405031\pi\) | |||||||
\(570\) | 48.9075 | 2.04851 | ||||||||
\(571\) | 32.8245 | 1.37366 | 0.686831 | − | 0.726817i | \(-0.259001\pi\) | ||||
0.686831 | + | 0.726817i | \(0.259001\pi\) | |||||||
\(572\) | −36.7955 | −1.53850 | ||||||||
\(573\) | 53.9291 | 2.25292 | ||||||||
\(574\) | 6.71709 | 0.280366 | ||||||||
\(575\) | 18.8874 | 0.787657 | ||||||||
\(576\) | 7.12426 | 0.296844 | ||||||||
\(577\) | 24.8871 | 1.03607 | 0.518033 | − | 0.855361i | \(-0.326665\pi\) | ||||
0.518033 | + | 0.855361i | \(0.326665\pi\) | |||||||
\(578\) | −4.80932 | −0.200041 | ||||||||
\(579\) | −55.6342 | −2.31208 | ||||||||
\(580\) | −28.5649 | −1.18609 | ||||||||
\(581\) | 4.36451 | 0.181070 | ||||||||
\(582\) | 60.1420 | 2.49297 | ||||||||
\(583\) | 71.1645 | 2.94733 | ||||||||
\(584\) | −13.0659 | −0.540673 | ||||||||
\(585\) | 148.335 | 6.13290 | ||||||||
\(586\) | −11.3485 | −0.468804 | ||||||||
\(587\) | 37.7809 | 1.55938 | 0.779692 | − | 0.626163i | \(-0.215376\pi\) | ||||
0.779692 | + | 0.626163i | \(0.215376\pi\) | |||||||
\(588\) | 20.5730 | 0.848416 | ||||||||
\(589\) | 11.3703 | 0.468505 | ||||||||
\(590\) | −10.7485 | −0.442510 | ||||||||
\(591\) | 42.6310 | 1.75360 | ||||||||
\(592\) | −1.65316 | −0.0679445 | ||||||||
\(593\) | 13.2399 | 0.543696 | 0.271848 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271848 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(594\) | 75.5636 | 3.10041 | ||||||||
\(595\) | −8.31571 | −0.340911 | ||||||||
\(596\) | 3.90248 | 0.159852 | ||||||||
\(597\) | 11.6532 | 0.476934 | ||||||||
\(598\) | 21.4881 | 0.878714 | ||||||||
\(599\) | −7.42702 | −0.303460 | −0.151730 | − | 0.988422i | \(-0.548484\pi\) | ||||
−0.151730 | + | 0.988422i | \(0.548484\pi\) | |||||||
\(600\) | −17.8716 | −0.729605 | ||||||||
\(601\) | −40.0027 | −1.63174 | −0.815872 | − | 0.578232i | \(-0.803743\pi\) | ||||
−0.815872 | + | 0.578232i | \(0.803743\pi\) | |||||||
\(602\) | −7.42487 | −0.302615 | ||||||||
\(603\) | −44.1318 | −1.79719 | ||||||||
\(604\) | 2.76698 | 0.112587 | ||||||||
\(605\) | 72.1935 | 2.93508 | ||||||||
\(606\) | −22.0142 | −0.894267 | ||||||||
\(607\) | −29.1085 | −1.18148 | −0.590740 | − | 0.806862i | \(-0.701164\pi\) | ||||
−0.590740 | + | 0.806862i | \(0.701164\pi\) | |||||||
\(608\) | −4.71735 | −0.191314 | ||||||||
\(609\) | 20.3897 | 0.826231 | ||||||||
\(610\) | −11.3215 | −0.458395 | ||||||||
\(611\) | −36.8428 | −1.49050 | ||||||||
\(612\) | −24.8745 | −1.00549 | ||||||||
\(613\) | 26.7990 | 1.08240 | 0.541200 | − | 0.840894i | \(-0.317970\pi\) | ||||
0.541200 | + | 0.840894i | \(0.317970\pi\) | |||||||
\(614\) | 33.8698 | 1.36688 | ||||||||
\(615\) | −95.2725 | −3.84176 | ||||||||
\(616\) | −4.20897 | −0.169584 | ||||||||
\(617\) | 21.8951 | 0.881465 | 0.440733 | − | 0.897638i | \(-0.354719\pi\) | ||||
0.440733 | + | 0.897638i | \(0.354719\pi\) | |||||||
\(618\) | −33.2441 | −1.33727 | ||||||||
\(619\) | 23.6420 | 0.950254 | 0.475127 | − | 0.879917i | \(-0.342402\pi\) | ||||
0.475127 | + | 0.879917i | \(0.342402\pi\) | |||||||
\(620\) | −7.85359 | −0.315408 | ||||||||
\(621\) | −44.1283 | −1.77081 | ||||||||
\(622\) | 4.54087 | 0.182072 | ||||||||
\(623\) | −4.94313 | −0.198042 | ||||||||
\(624\) | −20.3325 | −0.813952 | ||||||||
\(625\) | −21.5361 | −0.861445 | ||||||||
\(626\) | 9.53960 | 0.381279 | ||||||||
\(627\) | −86.4301 | −3.45169 | ||||||||
\(628\) | −15.8994 | −0.634454 | ||||||||
\(629\) | 5.77204 | 0.230146 | ||||||||
\(630\) | 16.9678 | 0.676013 | ||||||||
\(631\) | −21.5790 | −0.859047 | −0.429523 | − | 0.903056i | \(-0.641318\pi\) | ||||
−0.429523 | + | 0.903056i | \(0.641318\pi\) | |||||||
\(632\) | 5.70341 | 0.226870 | ||||||||
\(633\) | −52.9532 | −2.10470 | ||||||||
\(634\) | −24.1254 | −0.958144 | ||||||||
\(635\) | 48.4663 | 1.92333 | ||||||||
\(636\) | 39.3242 | 1.55931 | ||||||||
\(637\) | −41.3167 | −1.63703 | ||||||||
\(638\) | 50.4804 | 1.99854 | ||||||||
\(639\) | 27.8922 | 1.10340 | ||||||||
\(640\) | 3.25833 | 0.128797 | ||||||||
\(641\) | 22.2160 | 0.877479 | 0.438740 | − | 0.898614i | \(-0.355425\pi\) | ||||
0.438740 | + | 0.898614i | \(0.355425\pi\) | |||||||
\(642\) | −15.2880 | −0.603368 | ||||||||
\(643\) | −16.4214 | −0.647597 | −0.323799 | − | 0.946126i | \(-0.604960\pi\) | ||||
−0.323799 | + | 0.946126i | \(0.604960\pi\) | |||||||
\(644\) | 2.45799 | 0.0968583 | ||||||||
\(645\) | 105.311 | 4.14663 | ||||||||
\(646\) | 16.4707 | 0.648032 | ||||||||
\(647\) | 8.67949 | 0.341226 | 0.170613 | − | 0.985338i | \(-0.445425\pi\) | ||||
0.170613 | + | 0.985338i | \(0.445425\pi\) | |||||||
\(648\) | 20.3823 | 0.800693 | ||||||||
\(649\) | 18.9950 | 0.745618 | ||||||||
\(650\) | 35.8915 | 1.40778 | ||||||||
\(651\) | 5.60590 | 0.219713 | ||||||||
\(652\) | −3.17193 | −0.124222 | ||||||||
\(653\) | −29.1413 | −1.14039 | −0.570194 | − | 0.821510i | \(-0.693132\pi\) | ||||
−0.570194 | + | 0.821510i | \(0.693132\pi\) | |||||||
\(654\) | −28.9022 | −1.13017 | ||||||||
\(655\) | 4.67295 | 0.182587 | ||||||||
\(656\) | 9.18948 | 0.358789 | ||||||||
\(657\) | −93.0852 | −3.63160 | ||||||||
\(658\) | −4.21438 | −0.164294 | ||||||||
\(659\) | −19.0624 | −0.742568 | −0.371284 | − | 0.928519i | \(-0.621082\pi\) | ||||
−0.371284 | + | 0.928519i | \(0.621082\pi\) | |||||||
\(660\) | 59.6983 | 2.32375 | ||||||||
\(661\) | 31.8226 | 1.23776 | 0.618879 | − | 0.785486i | \(-0.287587\pi\) | ||||
0.618879 | + | 0.785486i | \(0.287587\pi\) | |||||||
\(662\) | −27.3148 | −1.06162 | ||||||||
\(663\) | 70.9913 | 2.75707 | ||||||||
\(664\) | 5.97097 | 0.231719 | ||||||||
\(665\) | −11.2353 | −0.435686 | ||||||||
\(666\) | −11.7776 | −0.456371 | ||||||||
\(667\) | −29.4800 | −1.14147 | ||||||||
\(668\) | −14.2730 | −0.552239 | ||||||||
\(669\) | 49.9341 | 1.93056 | ||||||||
\(670\) | −20.1840 | −0.779776 | ||||||||
\(671\) | 20.0076 | 0.772384 | ||||||||
\(672\) | −2.32580 | −0.0897196 | ||||||||
\(673\) | 5.18110 | 0.199717 | 0.0998584 | − | 0.995002i | \(-0.468161\pi\) | ||||
0.0998584 | + | 0.995002i | \(0.468161\pi\) | |||||||
\(674\) | 3.25159 | 0.125247 | ||||||||
\(675\) | −73.7072 | −2.83699 | ||||||||
\(676\) | 27.8337 | 1.07053 | ||||||||
\(677\) | 48.9104 | 1.87978 | 0.939890 | − | 0.341479i | \(-0.110928\pi\) | ||||
0.939890 | + | 0.341479i | \(0.110928\pi\) | |||||||
\(678\) | −50.7858 | −1.95042 | ||||||||
\(679\) | −13.8161 | −0.530215 | ||||||||
\(680\) | −11.3765 | −0.436269 | ||||||||
\(681\) | 68.2636 | 2.61587 | ||||||||
\(682\) | 13.8790 | 0.531454 | ||||||||
\(683\) | 13.7576 | 0.526419 | 0.263209 | − | 0.964739i | \(-0.415219\pi\) | ||||
0.263209 | + | 0.964739i | \(0.415219\pi\) | |||||||
\(684\) | −33.6077 | −1.28502 | ||||||||
\(685\) | 32.8106 | 1.25363 | ||||||||
\(686\) | −9.84282 | −0.375801 | ||||||||
\(687\) | 0.856993 | 0.0326963 | ||||||||
\(688\) | −10.1578 | −0.387261 | ||||||||
\(689\) | −78.9746 | −3.00869 | ||||||||
\(690\) | −34.8631 | −1.32721 | ||||||||
\(691\) | 1.79712 | 0.0683658 | 0.0341829 | − | 0.999416i | \(-0.489117\pi\) | ||||
0.0341829 | + | 0.999416i | \(0.489117\pi\) | |||||||
\(692\) | −12.2135 | −0.464287 | ||||||||
\(693\) | −29.9858 | −1.13907 | ||||||||
\(694\) | 6.76218 | 0.256689 | ||||||||
\(695\) | −25.9600 | −0.984718 | ||||||||
\(696\) | 27.8946 | 1.05734 | ||||||||
\(697\) | −32.0852 | −1.21531 | ||||||||
\(698\) | −21.6154 | −0.818153 | ||||||||
\(699\) | 78.2185 | 2.95850 | ||||||||
\(700\) | 4.10556 | 0.155176 | ||||||||
\(701\) | −6.07857 | −0.229585 | −0.114792 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114792 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(702\) | −83.8566 | −3.16496 | ||||||||
\(703\) | 7.79855 | 0.294128 | ||||||||
\(704\) | −5.75818 | −0.217019 | ||||||||
\(705\) | 59.7750 | 2.25126 | ||||||||
\(706\) | 13.4774 | 0.507230 | ||||||||
\(707\) | 5.05723 | 0.190197 | ||||||||
\(708\) | 10.4963 | 0.394474 | ||||||||
\(709\) | 19.9584 | 0.749553 | 0.374777 | − | 0.927115i | \(-0.377719\pi\) | ||||
0.374777 | + | 0.927115i | \(0.377719\pi\) | |||||||
\(710\) | 12.7567 | 0.478750 | ||||||||
\(711\) | 40.6326 | 1.52384 | ||||||||
\(712\) | −6.76257 | −0.253438 | ||||||||
\(713\) | −8.10517 | −0.303541 | ||||||||
\(714\) | 8.12056 | 0.303904 | ||||||||
\(715\) | −119.892 | −4.48370 | ||||||||
\(716\) | 16.6232 | 0.621238 | ||||||||
\(717\) | 73.1901 | 2.73334 | ||||||||
\(718\) | 6.90181 | 0.257573 | ||||||||
\(719\) | −38.2316 | −1.42580 | −0.712898 | − | 0.701267i | \(-0.752618\pi\) | ||||
−0.712898 | + | 0.701267i | \(0.752618\pi\) | |||||||
\(720\) | 23.2132 | 0.865105 | ||||||||
\(721\) | 7.63700 | 0.284417 | ||||||||
\(722\) | 3.25343 | 0.121080 | ||||||||
\(723\) | 24.3857 | 0.906912 | ||||||||
\(724\) | 4.65824 | 0.173122 | ||||||||
\(725\) | −49.2402 | −1.82873 | ||||||||
\(726\) | −70.4993 | −2.61647 | ||||||||
\(727\) | 22.7654 | 0.844323 | 0.422162 | − | 0.906521i | \(-0.361271\pi\) | ||||
0.422162 | + | 0.906521i | \(0.361271\pi\) | |||||||
\(728\) | 4.67089 | 0.173115 | ||||||||
\(729\) | 19.9436 | 0.738653 | ||||||||
\(730\) | −42.5731 | −1.57570 | ||||||||
\(731\) | 35.4660 | 1.31176 | ||||||||
\(732\) | 11.0558 | 0.408635 | ||||||||
\(733\) | 16.0169 | 0.591599 | 0.295800 | − | 0.955250i | \(-0.404414\pi\) | ||||
0.295800 | + | 0.955250i | \(0.404414\pi\) | |||||||
\(734\) | 13.5564 | 0.500378 | ||||||||
\(735\) | 67.0336 | 2.47257 | ||||||||
\(736\) | 3.36271 | 0.123951 | ||||||||
\(737\) | 35.6695 | 1.31390 | ||||||||
\(738\) | 65.4682 | 2.40992 | ||||||||
\(739\) | −31.9413 | −1.17498 | −0.587490 | − | 0.809231i | \(-0.699884\pi\) | ||||
−0.587490 | + | 0.809231i | \(0.699884\pi\) | |||||||
\(740\) | −5.38655 | −0.198013 | ||||||||
\(741\) | 95.9156 | 3.52355 | ||||||||
\(742\) | −9.03376 | −0.331640 | ||||||||
\(743\) | −35.4020 | −1.29877 | −0.649387 | − | 0.760458i | \(-0.724975\pi\) | ||||
−0.649387 | + | 0.760458i | \(0.724975\pi\) | |||||||
\(744\) | 7.66929 | 0.281170 | ||||||||
\(745\) | 12.7156 | 0.465862 | ||||||||
\(746\) | −16.4605 | −0.602661 | ||||||||
\(747\) | 42.5388 | 1.55641 | ||||||||
\(748\) | 20.1048 | 0.735103 | ||||||||
\(749\) | 3.51203 | 0.128327 | ||||||||
\(750\) | −6.39378 | −0.233468 | ||||||||
\(751\) | 39.5106 | 1.44176 | 0.720881 | − | 0.693059i | \(-0.243737\pi\) | ||||
0.720881 | + | 0.693059i | \(0.243737\pi\) | |||||||
\(752\) | −5.76558 | −0.210249 | ||||||||
\(753\) | 7.66006 | 0.279148 | ||||||||
\(754\) | −56.0205 | −2.04015 | ||||||||
\(755\) | 9.01572 | 0.328116 | ||||||||
\(756\) | −9.59220 | −0.348865 | ||||||||
\(757\) | 30.7188 | 1.11649 | 0.558247 | − | 0.829675i | \(-0.311474\pi\) | ||||
0.558247 | + | 0.829675i | \(0.311474\pi\) | |||||||
\(758\) | −35.4651 | −1.28815 | ||||||||
\(759\) | 61.6106 | 2.23632 | ||||||||
\(760\) | −15.3707 | −0.557554 | ||||||||
\(761\) | −35.7388 | −1.29553 | −0.647765 | − | 0.761840i | \(-0.724296\pi\) | ||||
−0.647765 | + | 0.761840i | \(0.724296\pi\) | |||||||
\(762\) | −47.3289 | −1.71455 | ||||||||
\(763\) | 6.63957 | 0.240369 | ||||||||
\(764\) | −16.9489 | −0.613190 | ||||||||
\(765\) | −81.0492 | −2.93034 | ||||||||
\(766\) | 28.2598 | 1.02107 | ||||||||
\(767\) | −21.0796 | −0.761141 | ||||||||
\(768\) | −3.18186 | −0.114816 | ||||||||
\(769\) | −19.3434 | −0.697540 | −0.348770 | − | 0.937208i | \(-0.613401\pi\) | ||||
−0.348770 | + | 0.937208i | \(0.613401\pi\) | |||||||
\(770\) | −13.7142 | −0.494225 | ||||||||
\(771\) | −51.7150 | −1.86247 | ||||||||
\(772\) | 17.4848 | 0.629291 | ||||||||
\(773\) | 1.06919 | 0.0384560 | 0.0192280 | − | 0.999815i | \(-0.493879\pi\) | ||||
0.0192280 | + | 0.999815i | \(0.493879\pi\) | |||||||
\(774\) | −72.3666 | −2.60116 | ||||||||
\(775\) | −13.5380 | −0.486300 | ||||||||
\(776\) | −18.9015 | −0.678525 | ||||||||
\(777\) | 3.84492 | 0.137936 | ||||||||
\(778\) | −28.6301 | −1.02644 | ||||||||
\(779\) | −43.3500 | −1.55318 | ||||||||
\(780\) | −66.2500 | −2.37213 | ||||||||
\(781\) | −22.5438 | −0.806682 | ||||||||
\(782\) | −11.7409 | −0.419855 | ||||||||
\(783\) | 115.044 | 4.11135 | ||||||||
\(784\) | −6.46571 | −0.230918 | ||||||||
\(785\) | −51.8054 | −1.84901 | ||||||||
\(786\) | −4.56329 | −0.162767 | ||||||||
\(787\) | −8.53703 | −0.304312 | −0.152156 | − | 0.988356i | \(-0.548622\pi\) | ||||
−0.152156 | + | 0.988356i | \(0.548622\pi\) | |||||||
\(788\) | −13.3981 | −0.477288 | ||||||||
\(789\) | 28.5074 | 1.01489 | ||||||||
\(790\) | 18.5836 | 0.661175 | ||||||||
\(791\) | 11.6668 | 0.414823 | ||||||||
\(792\) | −41.0228 | −1.45768 | ||||||||
\(793\) | −22.2034 | −0.788465 | ||||||||
\(794\) | 29.1457 | 1.03434 | ||||||||
\(795\) | 128.131 | 4.54435 | ||||||||
\(796\) | −3.66238 | −0.129810 | ||||||||
\(797\) | 1.34500 | 0.0476422 | 0.0238211 | − | 0.999716i | \(-0.492417\pi\) | ||||
0.0238211 | + | 0.999716i | \(0.492417\pi\) | |||||||
\(798\) | 10.9716 | 0.388391 | ||||||||
\(799\) | 20.1306 | 0.712170 | ||||||||
\(800\) | 5.61671 | 0.198581 | ||||||||
\(801\) | −48.1783 | −1.70230 | ||||||||
\(802\) | 2.03995 | 0.0720333 | ||||||||
\(803\) | 75.2360 | 2.65502 | ||||||||
\(804\) | 19.7103 | 0.695130 | ||||||||
\(805\) | 8.00893 | 0.282278 | ||||||||
\(806\) | −15.4022 | −0.542519 | ||||||||
\(807\) | 35.1560 | 1.23755 | ||||||||
\(808\) | 6.91866 | 0.243398 | ||||||||
\(809\) | 8.94182 | 0.314378 | 0.157189 | − | 0.987569i | \(-0.449757\pi\) | ||||
0.157189 | + | 0.987569i | \(0.449757\pi\) | |||||||
\(810\) | 66.4123 | 2.33349 | ||||||||
\(811\) | 44.0342 | 1.54625 | 0.773125 | − | 0.634254i | \(-0.218693\pi\) | ||||
0.773125 | + | 0.634254i | \(0.218693\pi\) | |||||||
\(812\) | −6.40808 | −0.224880 | ||||||||
\(813\) | −64.4693 | −2.26104 | ||||||||
\(814\) | 9.51920 | 0.333648 | ||||||||
\(815\) | −10.3352 | −0.362026 | ||||||||
\(816\) | 11.1095 | 0.388911 | ||||||||
\(817\) | 47.9178 | 1.67643 | ||||||||
\(818\) | 13.0344 | 0.455737 | ||||||||
\(819\) | 33.2767 | 1.16278 | ||||||||
\(820\) | 29.9423 | 1.04563 | ||||||||
\(821\) | −45.8981 | −1.60185 | −0.800927 | − | 0.598761i | \(-0.795660\pi\) | ||||
−0.800927 | + | 0.598761i | \(0.795660\pi\) | |||||||
\(822\) | −32.0406 | −1.11755 | ||||||||
\(823\) | −23.5201 | −0.819860 | −0.409930 | − | 0.912117i | \(-0.634447\pi\) | ||||
−0.409930 | + | 0.912117i | \(0.634447\pi\) | |||||||
\(824\) | 10.4480 | 0.363973 | ||||||||
\(825\) | 102.908 | 3.58279 | ||||||||
\(826\) | −2.41126 | −0.0838985 | ||||||||
\(827\) | −33.6472 | −1.17003 | −0.585014 | − | 0.811023i | \(-0.698911\pi\) | ||||
−0.585014 | + | 0.811023i | \(0.698911\pi\) | |||||||
\(828\) | 23.9568 | 0.832557 | ||||||||
\(829\) | 26.0962 | 0.906359 | 0.453179 | − | 0.891419i | \(-0.350290\pi\) | ||||
0.453179 | + | 0.891419i | \(0.350290\pi\) | |||||||
\(830\) | 19.4554 | 0.675307 | ||||||||
\(831\) | 51.0862 | 1.77216 | ||||||||
\(832\) | 6.39012 | 0.221538 | ||||||||
\(833\) | 22.5751 | 0.782181 | ||||||||
\(834\) | 25.3508 | 0.877825 | ||||||||
\(835\) | −46.5061 | −1.60941 | ||||||||
\(836\) | 27.1634 | 0.939464 | ||||||||
\(837\) | 31.6301 | 1.09330 | ||||||||
\(838\) | 10.4099 | 0.359605 | ||||||||
\(839\) | 36.8689 | 1.27286 | 0.636428 | − | 0.771336i | \(-0.280411\pi\) | ||||
0.636428 | + | 0.771336i | \(0.280411\pi\) | |||||||
\(840\) | −7.57822 | −0.261473 | ||||||||
\(841\) | 47.8556 | 1.65019 | ||||||||
\(842\) | 2.74094 | 0.0944591 | ||||||||
\(843\) | −46.5021 | −1.60162 | ||||||||
\(844\) | 16.6422 | 0.572847 | ||||||||
\(845\) | 90.6913 | 3.11988 | ||||||||
\(846\) | −41.0755 | −1.41220 | ||||||||
\(847\) | 16.1955 | 0.556483 | ||||||||
\(848\) | −12.3589 | −0.424405 | ||||||||
\(849\) | −60.3624 | −2.07163 | ||||||||
\(850\) | −19.6108 | −0.672646 | ||||||||
\(851\) | −5.55910 | −0.190563 | ||||||||
\(852\) | −12.4573 | −0.426781 | ||||||||
\(853\) | −22.5089 | −0.770689 | −0.385344 | − | 0.922773i | \(-0.625917\pi\) | ||||
−0.385344 | + | 0.922773i | \(0.625917\pi\) | |||||||
\(854\) | −2.53980 | −0.0869103 | ||||||||
\(855\) | −109.505 | −3.74499 | ||||||||
\(856\) | 4.80472 | 0.164222 | ||||||||
\(857\) | −23.3086 | −0.796207 | −0.398104 | − | 0.917340i | \(-0.630332\pi\) | ||||
−0.398104 | + | 0.917340i | \(0.630332\pi\) | |||||||
\(858\) | 117.078 | 3.99698 | ||||||||
\(859\) | 46.6021 | 1.59004 | 0.795022 | − | 0.606581i | \(-0.207459\pi\) | ||||
0.795022 | + | 0.606581i | \(0.207459\pi\) | |||||||
\(860\) | −33.0973 | −1.12861 | ||||||||
\(861\) | −21.3729 | −0.728386 | ||||||||
\(862\) | −18.7175 | −0.637519 | ||||||||
\(863\) | 30.1422 | 1.02605 | 0.513026 | − | 0.858373i | \(-0.328524\pi\) | ||||
0.513026 | + | 0.858373i | \(0.328524\pi\) | |||||||
\(864\) | −13.1228 | −0.446448 | ||||||||
\(865\) | −39.7955 | −1.35309 | ||||||||
\(866\) | 33.0512 | 1.12313 | ||||||||
\(867\) | 15.3026 | 0.519704 | ||||||||
\(868\) | −1.76183 | −0.0598004 | ||||||||
\(869\) | −32.8413 | −1.11406 | ||||||||
\(870\) | 90.8896 | 3.08145 | ||||||||
\(871\) | −39.5842 | −1.34126 | ||||||||
\(872\) | 9.08343 | 0.307604 | ||||||||
\(873\) | −134.659 | −4.55753 | ||||||||
\(874\) | −15.8631 | −0.536577 | ||||||||
\(875\) | 1.46881 | 0.0496550 | ||||||||
\(876\) | 41.5741 | 1.40466 | ||||||||
\(877\) | −33.3570 | −1.12639 | −0.563193 | − | 0.826325i | \(-0.690427\pi\) | ||||
−0.563193 | + | 0.826325i | \(0.690427\pi\) | |||||||
\(878\) | −16.9884 | −0.573331 | ||||||||
\(879\) | 36.1095 | 1.21794 | ||||||||
\(880\) | −18.7620 | −0.632468 | ||||||||
\(881\) | −16.7938 | −0.565797 | −0.282899 | − | 0.959150i | \(-0.591296\pi\) | ||||
−0.282899 | + | 0.959150i | \(0.591296\pi\) | |||||||
\(882\) | −46.0634 | −1.55103 | ||||||||
\(883\) | −20.8750 | −0.702501 | −0.351251 | − | 0.936281i | \(-0.614243\pi\) | ||||
−0.351251 | + | 0.936281i | \(0.614243\pi\) | |||||||
\(884\) | −22.3112 | −0.750407 | ||||||||
\(885\) | 34.2003 | 1.14963 | ||||||||
\(886\) | 8.95033 | 0.300692 | ||||||||
\(887\) | −46.8678 | −1.57367 | −0.786833 | − | 0.617166i | \(-0.788280\pi\) | ||||
−0.786833 | + | 0.617166i | \(0.788280\pi\) | |||||||
\(888\) | 5.26014 | 0.176519 | ||||||||
\(889\) | 10.8727 | 0.364657 | ||||||||
\(890\) | −22.0347 | −0.738604 | ||||||||
\(891\) | −117.365 | −3.93187 | ||||||||
\(892\) | −15.6933 | −0.525452 | ||||||||
\(893\) | 27.1983 | 0.910156 | ||||||||
\(894\) | −12.4172 | −0.415292 | ||||||||
\(895\) | 54.1638 | 1.81050 | ||||||||
\(896\) | 0.730955 | 0.0244195 | ||||||||
\(897\) | −68.3723 | −2.28288 | ||||||||
\(898\) | −40.1425 | −1.33957 | ||||||||
\(899\) | 21.1306 | 0.704744 | ||||||||
\(900\) | 40.0149 | 1.33383 | ||||||||
\(901\) | 43.1511 | 1.43757 | ||||||||
\(902\) | −52.9146 | −1.76186 | ||||||||
\(903\) | 23.6249 | 0.786188 | ||||||||
\(904\) | 15.9610 | 0.530856 | ||||||||
\(905\) | 15.1781 | 0.504537 | ||||||||
\(906\) | −8.80414 | −0.292498 | ||||||||
\(907\) | −13.8963 | −0.461419 | −0.230710 | − | 0.973023i | \(-0.574105\pi\) | ||||
−0.230710 | + | 0.973023i | \(0.574105\pi\) | |||||||
\(908\) | −21.4540 | −0.711974 | ||||||||
\(909\) | 49.2903 | 1.63486 | ||||||||
\(910\) | 15.2193 | 0.504515 | ||||||||
\(911\) | 28.4412 | 0.942301 | 0.471150 | − | 0.882053i | \(-0.343839\pi\) | ||||
0.471150 | + | 0.882053i | \(0.343839\pi\) | |||||||
\(912\) | 15.0100 | 0.497030 | ||||||||
\(913\) | −34.3819 | −1.13788 | ||||||||
\(914\) | 7.34381 | 0.242912 | ||||||||
\(915\) | 36.0235 | 1.19090 | ||||||||
\(916\) | −0.269337 | −0.00889913 | ||||||||
\(917\) | 1.04830 | 0.0346180 | ||||||||
\(918\) | 45.8186 | 1.51224 | ||||||||
\(919\) | 26.7449 | 0.882232 | 0.441116 | − | 0.897450i | \(-0.354583\pi\) | ||||
0.441116 | + | 0.897450i | \(0.354583\pi\) | |||||||
\(920\) | 10.9568 | 0.361235 | ||||||||
\(921\) | −107.769 | −3.55112 | ||||||||
\(922\) | −28.4444 | −0.936767 | ||||||||
\(923\) | 25.0180 | 0.823477 | ||||||||
\(924\) | 13.3924 | 0.440576 | ||||||||
\(925\) | −9.28533 | −0.305300 | ||||||||
\(926\) | −18.5267 | −0.608825 | ||||||||
\(927\) | 74.4342 | 2.44474 | ||||||||
\(928\) | −8.76673 | −0.287782 | ||||||||
\(929\) | 14.6015 | 0.479059 | 0.239530 | − | 0.970889i | \(-0.423007\pi\) | ||||
0.239530 | + | 0.970889i | \(0.423007\pi\) | |||||||
\(930\) | 24.9891 | 0.819424 | ||||||||
\(931\) | 30.5010 | 0.999631 | ||||||||
\(932\) | −24.5826 | −0.805230 | ||||||||
\(933\) | −14.4484 | −0.473020 | ||||||||
\(934\) | −7.41094 | −0.242493 | ||||||||
\(935\) | 65.5079 | 2.14234 | ||||||||
\(936\) | 45.5249 | 1.48803 | ||||||||
\(937\) | −36.1515 | −1.18102 | −0.590509 | − | 0.807031i | \(-0.701073\pi\) | ||||
−0.590509 | + | 0.807031i | \(0.701073\pi\) | |||||||
\(938\) | −4.52796 | −0.147843 | ||||||||
\(939\) | −30.3537 | −0.990556 | ||||||||
\(940\) | −18.7862 | −0.612737 | ||||||||
\(941\) | −36.2444 | −1.18153 | −0.590767 | − | 0.806843i | \(-0.701175\pi\) | ||||
−0.590767 | + | 0.806843i | \(0.701175\pi\) | |||||||
\(942\) | 50.5896 | 1.64830 | ||||||||
\(943\) | 30.9015 | 1.00629 | ||||||||
\(944\) | −3.29878 | −0.107366 | ||||||||
\(945\) | −31.2546 | −1.01671 | ||||||||
\(946\) | 58.4902 | 1.90168 | ||||||||
\(947\) | 14.0773 | 0.457451 | 0.228725 | − | 0.973491i | \(-0.426544\pi\) | ||||
0.228725 | + | 0.973491i | \(0.426544\pi\) | |||||||
\(948\) | −18.1475 | −0.589403 | ||||||||
\(949\) | −83.4930 | −2.71030 | ||||||||
\(950\) | −26.4960 | −0.859644 | ||||||||
\(951\) | 76.7639 | 2.48924 | ||||||||
\(952\) | −2.55214 | −0.0827153 | ||||||||
\(953\) | 26.9547 | 0.873150 | 0.436575 | − | 0.899668i | \(-0.356191\pi\) | ||||
0.436575 | + | 0.899668i | \(0.356191\pi\) | |||||||
\(954\) | −88.0477 | −2.85065 | ||||||||
\(955\) | −55.2251 | −1.78704 | ||||||||
\(956\) | −23.0023 | −0.743947 | ||||||||
\(957\) | −160.622 | −5.19216 | ||||||||
\(958\) | 40.0605 | 1.29430 | ||||||||
\(959\) | 7.36055 | 0.237684 | ||||||||
\(960\) | −10.3676 | −0.334612 | ||||||||
\(961\) | −25.1904 | −0.812593 | ||||||||
\(962\) | −10.5639 | −0.340594 | ||||||||
\(963\) | 34.2301 | 1.10305 | ||||||||
\(964\) | −7.66395 | −0.246839 | ||||||||
\(965\) | 56.9711 | 1.83397 | ||||||||
\(966\) | −7.82098 | −0.251636 | ||||||||
\(967\) | −53.5070 | −1.72067 | −0.860334 | − | 0.509731i | \(-0.829745\pi\) | ||||
−0.860334 | + | 0.509731i | \(0.829745\pi\) | |||||||
\(968\) | 22.1566 | 0.712140 | ||||||||
\(969\) | −52.4076 | −1.68357 | ||||||||
\(970\) | −61.5873 | −1.97745 | ||||||||
\(971\) | −39.4960 | −1.26749 | −0.633744 | − | 0.773543i | \(-0.718483\pi\) | ||||
−0.633744 | + | 0.773543i | \(0.718483\pi\) | |||||||
\(972\) | −25.4852 | −0.817440 | ||||||||
\(973\) | −5.82371 | −0.186700 | ||||||||
\(974\) | −23.3099 | −0.746898 | ||||||||
\(975\) | −114.202 | −3.65738 | ||||||||
\(976\) | −3.47464 | −0.111220 | ||||||||
\(977\) | 29.3663 | 0.939513 | 0.469756 | − | 0.882796i | \(-0.344342\pi\) | ||||
0.469756 | + | 0.882796i | \(0.344342\pi\) | |||||||
\(978\) | 10.0926 | 0.322727 | ||||||||
\(979\) | 38.9401 | 1.24453 | ||||||||
\(980\) | −21.0674 | −0.672973 | ||||||||
\(981\) | 64.7127 | 2.06612 | ||||||||
\(982\) | −20.7248 | −0.661354 | ||||||||
\(983\) | 13.6426 | 0.435131 | 0.217565 | − | 0.976046i | \(-0.430189\pi\) | ||||
0.217565 | + | 0.976046i | \(0.430189\pi\) | |||||||
\(984\) | −29.2397 | −0.932127 | ||||||||
\(985\) | −43.6555 | −1.39098 | ||||||||
\(986\) | 30.6092 | 0.974795 | ||||||||
\(987\) | 13.4096 | 0.426832 | ||||||||
\(988\) | −30.1445 | −0.959024 | ||||||||
\(989\) | −34.1576 | −1.08615 | ||||||||
\(990\) | −133.666 | −4.24817 | ||||||||
\(991\) | −51.5061 | −1.63614 | −0.818072 | − | 0.575115i | \(-0.804957\pi\) | ||||
−0.818072 | + | 0.575115i | \(0.804957\pi\) | |||||||
\(992\) | −2.41031 | −0.0765275 | ||||||||
\(993\) | 86.9120 | 2.75807 | ||||||||
\(994\) | 2.86176 | 0.0907696 | ||||||||
\(995\) | −11.9333 | −0.378310 | ||||||||
\(996\) | −18.9988 | −0.602001 | ||||||||
\(997\) | −12.0060 | −0.380233 | −0.190117 | − | 0.981762i | \(-0.560887\pi\) | ||||
−0.190117 | + | 0.981762i | \(0.560887\pi\) | |||||||
\(998\) | 32.6856 | 1.03464 | ||||||||
\(999\) | 21.6942 | 0.686373 |
(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 | 6046.2.a.e.1.4 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.e.1.4 | ✓ | 56 | 1.1 | even | 1 | trivial |