Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, 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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 26x^{16} + 281x^{14} - 1632x^{12} + 5482x^{10} - 10620x^{8} + 11052x^{6} - 5165x^{4} + 760x^{2} - 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 845) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(1.76651\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.76651 | 1.24911 | 0.624556 | − | 0.780980i | \(-0.285280\pi\) | ||||
0.624556 | + | 0.780980i | \(0.285280\pi\) | |||||||
\(3\) | 0.691389 | 0.399174 | 0.199587 | − | 0.979880i | \(-0.436040\pi\) | ||||
0.199587 | + | 0.979880i | \(0.436040\pi\) | |||||||
\(4\) | 1.12056 | 0.560281 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.22135 | 0.498613 | ||||||||
\(7\) | 4.36221 | 1.64876 | 0.824380 | − | 0.566037i | \(-0.191524\pi\) | ||||
0.824380 | + | 0.566037i | \(0.191524\pi\) | |||||||
\(8\) | −1.55354 | −0.549258 | ||||||||
\(9\) | −2.52198 | −0.840660 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.43722 | −1.63938 | −0.819692 | − | 0.572805i | \(-0.805855\pi\) | ||||
−0.819692 | + | 0.572805i | \(0.805855\pi\) | |||||||
\(12\) | 0.774744 | 0.223649 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 7.70589 | 2.05949 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98546 | −1.24637 | ||||||||
\(17\) | −3.63696 | −0.882094 | −0.441047 | − | 0.897484i | \(-0.645393\pi\) | ||||
−0.441047 | + | 0.897484i | \(0.645393\pi\) | |||||||
\(18\) | −4.45511 | −1.05008 | ||||||||
\(19\) | −1.01251 | −0.232286 | −0.116143 | − | 0.993232i | \(-0.537053\pi\) | ||||
−0.116143 | + | 0.993232i | \(0.537053\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.01598 | 0.658141 | ||||||||
\(22\) | −9.60491 | −2.04777 | ||||||||
\(23\) | −3.79639 | −0.791602 | −0.395801 | − | 0.918336i | \(-0.629533\pi\) | ||||
−0.395801 | + | 0.918336i | \(0.629533\pi\) | |||||||
\(24\) | −1.07410 | −0.219249 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.81784 | −0.734743 | ||||||||
\(28\) | 4.88812 | 0.923769 | ||||||||
\(29\) | −1.36562 | −0.253590 | −0.126795 | − | 0.991929i | \(-0.540469\pi\) | ||||
−0.126795 | + | 0.991929i | \(0.540469\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.129618 | −0.0232801 | −0.0116400 | − | 0.999932i | \(-0.503705\pi\) | ||||
−0.0116400 | + | 0.999932i | \(0.503705\pi\) | |||||||
\(32\) | −5.69981 | −1.00759 | ||||||||
\(33\) | −3.75923 | −0.654399 | ||||||||
\(34\) | −6.42474 | −1.10183 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.82604 | −0.471006 | ||||||||
\(37\) | −5.24159 | −0.861712 | −0.430856 | − | 0.902421i | \(-0.641788\pi\) | ||||
−0.430856 | + | 0.902421i | \(0.641788\pi\) | |||||||
\(38\) | −1.78862 | −0.290152 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.70850 | 0.735343 | 0.367672 | − | 0.929956i | \(-0.380155\pi\) | ||||
0.367672 | + | 0.929956i | \(0.380155\pi\) | |||||||
\(42\) | 5.32777 | 0.822092 | ||||||||
\(43\) | 0.0572302 | 0.00872753 | 0.00436377 | − | 0.999990i | \(-0.498611\pi\) | ||||
0.00436377 | + | 0.999990i | \(0.498611\pi\) | |||||||
\(44\) | −6.09274 | −0.918515 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.70637 | −0.988800 | ||||||||
\(47\) | −7.23270 | −1.05500 | −0.527499 | − | 0.849556i | \(-0.676870\pi\) | ||||
−0.527499 | + | 0.849556i | \(0.676870\pi\) | |||||||
\(48\) | −3.44690 | −0.497517 | ||||||||
\(49\) | 12.0289 | 1.71841 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.51456 | −0.352108 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7513 | −1.47680 | −0.738402 | − | 0.674360i | \(-0.764420\pi\) | ||||
−0.738402 | + | 0.674360i | \(0.764420\pi\) | |||||||
\(54\) | −6.74425 | −0.917776 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.77685 | −0.905595 | ||||||||
\(57\) | −0.700040 | −0.0927226 | ||||||||
\(58\) | −2.41239 | −0.316762 | ||||||||
\(59\) | 2.80801 | 0.365572 | 0.182786 | − | 0.983153i | \(-0.441488\pi\) | ||||
0.182786 | + | 0.983153i | \(0.441488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.30435 | 0.679153 | 0.339576 | − | 0.940579i | \(-0.389716\pi\) | ||||
0.339576 | + | 0.940579i | \(0.389716\pi\) | |||||||
\(62\) | −0.228972 | −0.0290794 | ||||||||
\(63\) | −11.0014 | −1.38605 | ||||||||
\(64\) | −0.0978416 | −0.0122302 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.64073 | −0.817417 | ||||||||
\(67\) | 7.94184 | 0.970250 | 0.485125 | − | 0.874445i | \(-0.338774\pi\) | ||||
0.485125 | + | 0.874445i | \(0.338774\pi\) | |||||||
\(68\) | −4.07545 | −0.494220 | ||||||||
\(69\) | −2.62478 | −0.315987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.88508 | −0.461074 | −0.230537 | − | 0.973064i | \(-0.574048\pi\) | ||||
−0.230537 | + | 0.973064i | \(0.574048\pi\) | |||||||
\(72\) | 3.91799 | 0.461740 | ||||||||
\(73\) | −4.44994 | −0.520826 | −0.260413 | − | 0.965497i | \(-0.583859\pi\) | ||||
−0.260413 | + | 0.965497i | \(0.583859\pi\) | |||||||
\(74\) | −9.25933 | −1.07637 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.13458 | −0.130146 | ||||||||
\(77\) | −23.7183 | −2.70295 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.43195 | −0.611142 | −0.305571 | − | 0.952169i | \(-0.598847\pi\) | ||||
−0.305571 | + | 0.952169i | \(0.598847\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.92633 | 0.547370 | ||||||||
\(82\) | 8.31761 | 0.918526 | ||||||||
\(83\) | 14.1012 | 1.54781 | 0.773906 | − | 0.633301i | \(-0.218300\pi\) | ||||
0.773906 | + | 0.633301i | \(0.218300\pi\) | |||||||
\(84\) | 3.37960 | 0.368744 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.101098 | 0.0109017 | ||||||||
\(87\) | −0.944176 | −0.101226 | ||||||||
\(88\) | 8.44692 | 0.900445 | ||||||||
\(89\) | −6.84215 | −0.725267 | −0.362633 | − | 0.931932i | \(-0.618122\pi\) | ||||
−0.362633 | + | 0.931932i | \(0.618122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.25409 | −0.443520 | ||||||||
\(93\) | −0.0896165 | −0.00929280 | ||||||||
\(94\) | −12.7766 | −1.31781 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.94078 | −0.402204 | ||||||||
\(97\) | 13.1040 | 1.33051 | 0.665256 | − | 0.746616i | \(-0.268322\pi\) | ||||
0.665256 | + | 0.746616i | \(0.268322\pi\) | |||||||
\(98\) | 21.2491 | 2.14648 | ||||||||
\(99\) | 13.7126 | 1.37816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.59542 | 0.158750 | 0.0793750 | − | 0.996845i | \(-0.474708\pi\) | ||||
0.0793750 | + | 0.996845i | \(0.474708\pi\) | |||||||
\(102\) | −4.44199 | −0.439823 | ||||||||
\(103\) | −2.66136 | −0.262232 | −0.131116 | − | 0.991367i | \(-0.541856\pi\) | ||||
−0.131116 | + | 0.991367i | \(0.541856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.9923 | −1.84469 | ||||||||
\(107\) | 2.01632 | 0.194925 | 0.0974626 | − | 0.995239i | \(-0.468927\pi\) | ||||
0.0974626 | + | 0.995239i | \(0.468927\pi\) | |||||||
\(108\) | −4.27812 | −0.411663 | ||||||||
\(109\) | −14.6022 | −1.39864 | −0.699321 | − | 0.714808i | \(-0.746514\pi\) | ||||
−0.699321 | + | 0.714808i | \(0.746514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.62398 | −0.343973 | ||||||||
\(112\) | −21.7476 | −2.05496 | ||||||||
\(113\) | 4.29215 | 0.403772 | 0.201886 | − | 0.979409i | \(-0.435293\pi\) | ||||
0.201886 | + | 0.979409i | \(0.435293\pi\) | |||||||
\(114\) | −1.23663 | −0.115821 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.53026 | −0.142081 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.96038 | 0.456640 | ||||||||
\(119\) | −15.8652 | −1.45436 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.5633 | 1.68758 | ||||||||
\(122\) | 9.37020 | 0.848338 | ||||||||
\(123\) | 3.25540 | 0.293530 | ||||||||
\(124\) | −0.145245 | −0.0130434 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −19.4341 | −1.73133 | ||||||||
\(127\) | 3.27565 | 0.290667 | 0.145333 | − | 0.989383i | \(-0.453575\pi\) | ||||
0.145333 | + | 0.989383i | \(0.453575\pi\) | |||||||
\(128\) | 11.2268 | 0.992316 | ||||||||
\(129\) | 0.0395684 | 0.00348380 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5462 | 1.27091 | 0.635455 | − | 0.772138i | \(-0.280812\pi\) | ||||
0.635455 | + | 0.772138i | \(0.280812\pi\) | |||||||
\(132\) | −4.21245 | −0.366647 | ||||||||
\(133\) | −4.41679 | −0.382985 | ||||||||
\(134\) | 14.0293 | 1.21195 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.65016 | 0.484497 | ||||||||
\(137\) | −1.88763 | −0.161272 | −0.0806358 | − | 0.996744i | \(-0.525695\pi\) | ||||
−0.0806358 | + | 0.996744i | \(0.525695\pi\) | |||||||
\(138\) | −4.63671 | −0.394703 | ||||||||
\(139\) | −10.0693 | −0.854069 | −0.427034 | − | 0.904235i | \(-0.640442\pi\) | ||||
−0.427034 | + | 0.904235i | \(0.640442\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00061 | −0.421127 | ||||||||
\(142\) | −6.86304 | −0.575934 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.5732 | 1.04777 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.86086 | −0.650570 | ||||||||
\(147\) | 8.31662 | 0.685943 | ||||||||
\(148\) | −5.87353 | −0.482801 | ||||||||
\(149\) | 15.6539 | 1.28242 | 0.641210 | − | 0.767365i | \(-0.278433\pi\) | ||||
0.641210 | + | 0.767365i | \(0.278433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.41670 | −0.603563 | −0.301781 | − | 0.953377i | \(-0.597581\pi\) | ||||
−0.301781 | + | 0.953377i | \(0.597581\pi\) | |||||||
\(152\) | 1.57298 | 0.127585 | ||||||||
\(153\) | 9.17236 | 0.741541 | ||||||||
\(154\) | −41.8986 | −3.37629 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2365 | −0.976582 | −0.488291 | − | 0.872681i | \(-0.662380\pi\) | ||||
−0.488291 | + | 0.872681i | \(0.662380\pi\) | |||||||
\(158\) | −9.59559 | −0.763384 | ||||||||
\(159\) | −7.43333 | −0.589502 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.5606 | −1.30516 | ||||||||
\(162\) | 8.70242 | 0.683727 | ||||||||
\(163\) | −19.4961 | −1.52705 | −0.763525 | − | 0.645778i | \(-0.776533\pi\) | ||||
−0.763525 | + | 0.645778i | \(0.776533\pi\) | |||||||
\(164\) | 5.27616 | 0.411999 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.9100 | 1.93339 | ||||||||
\(167\) | −19.6198 | −1.51822 | −0.759111 | − | 0.650961i | \(-0.774366\pi\) | ||||
−0.759111 | + | 0.650961i | \(0.774366\pi\) | |||||||
\(168\) | −4.68544 | −0.361490 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.55354 | 0.195274 | ||||||||
\(172\) | 0.0641300 | 0.00488987 | ||||||||
\(173\) | 22.9374 | 1.74390 | 0.871949 | − | 0.489597i | \(-0.162856\pi\) | ||||
0.871949 | + | 0.489597i | \(0.162856\pi\) | |||||||
\(174\) | −1.66790 | −0.126443 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 27.1071 | 2.04327 | ||||||||
\(177\) | 1.94143 | 0.145927 | ||||||||
\(178\) | −12.0867 | −0.905940 | ||||||||
\(179\) | −14.3131 | −1.06981 | −0.534905 | − | 0.844912i | \(-0.679653\pi\) | ||||
−0.534905 | + | 0.844912i | \(0.679653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1550 | 1.05214 | 0.526068 | − | 0.850442i | \(-0.323666\pi\) | ||||
0.526068 | + | 0.850442i | \(0.323666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.66737 | 0.271100 | ||||||||
\(184\) | 5.89783 | 0.434794 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.158309 | −0.0116077 | ||||||||
\(187\) | 19.7750 | 1.44609 | ||||||||
\(188\) | −8.10469 | −0.591095 | ||||||||
\(189\) | −16.6542 | −1.21141 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0345 | −0.943141 | −0.471571 | − | 0.881828i | \(-0.656313\pi\) | ||||
−0.471571 | + | 0.881828i | \(0.656313\pi\) | |||||||
\(192\) | −0.0676466 | −0.00488198 | ||||||||
\(193\) | −3.81266 | −0.274441 | −0.137221 | − | 0.990541i | \(-0.543817\pi\) | ||||
−0.137221 | + | 0.990541i | \(0.543817\pi\) | |||||||
\(194\) | 23.1484 | 1.66196 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4791 | 0.962792 | ||||||||
\(197\) | −6.91512 | −0.492682 | −0.246341 | − | 0.969183i | \(-0.579228\pi\) | ||||
−0.246341 | + | 0.969183i | \(0.579228\pi\) | |||||||
\(198\) | 24.2234 | 1.72148 | ||||||||
\(199\) | 23.3248 | 1.65345 | 0.826726 | − | 0.562604i | \(-0.190200\pi\) | ||||
0.826726 | + | 0.562604i | \(0.190200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.49090 | 0.387298 | ||||||||
\(202\) | 2.81832 | 0.198296 | ||||||||
\(203\) | −5.95713 | −0.418108 | ||||||||
\(204\) | −2.81772 | −0.197280 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.70133 | −0.327557 | ||||||||
\(207\) | 9.57442 | 0.665468 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.50526 | 0.380806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.02673 | −0.0706831 | −0.0353415 | − | 0.999375i | \(-0.511252\pi\) | ||||
−0.0353415 | + | 0.999375i | \(0.511252\pi\) | |||||||
\(212\) | −12.0475 | −0.827426 | ||||||||
\(213\) | −2.68610 | −0.184049 | ||||||||
\(214\) | 3.56186 | 0.243484 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.93115 | 0.403564 | ||||||||
\(217\) | −0.565421 | −0.0383833 | ||||||||
\(218\) | −25.7950 | −1.74706 | ||||||||
\(219\) | −3.07664 | −0.207900 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.40180 | −0.429660 | ||||||||
\(223\) | 5.61855 | 0.376246 | 0.188123 | − | 0.982146i | \(-0.439760\pi\) | ||||
0.188123 | + | 0.982146i | \(0.439760\pi\) | |||||||
\(224\) | −24.8637 | −1.66128 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.58214 | 0.504356 | ||||||||
\(227\) | −12.3749 | −0.821348 | −0.410674 | − | 0.911782i | \(-0.634707\pi\) | ||||
−0.410674 | + | 0.911782i | \(0.634707\pi\) | |||||||
\(228\) | −0.784439 | −0.0519507 | ||||||||
\(229\) | −19.7494 | −1.30508 | −0.652538 | − | 0.757756i | \(-0.726296\pi\) | ||||
−0.652538 | + | 0.757756i | \(0.726296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.3986 | −1.07895 | ||||||||
\(232\) | 2.12154 | 0.139286 | ||||||||
\(233\) | −16.2048 | −1.06161 | −0.530804 | − | 0.847494i | \(-0.678110\pi\) | ||||
−0.530804 | + | 0.847494i | \(0.678110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.14655 | 0.204823 | ||||||||
\(237\) | −3.75559 | −0.243952 | ||||||||
\(238\) | −28.0261 | −1.81666 | ||||||||
\(239\) | −21.8233 | −1.41163 | −0.705816 | − | 0.708395i | \(-0.749419\pi\) | ||||
−0.705816 | + | 0.708395i | \(0.749419\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.301660 | 0.0194317 | 0.00971583 | − | 0.999953i | \(-0.496907\pi\) | ||||
0.00971583 | + | 0.999953i | \(0.496907\pi\) | |||||||
\(242\) | 32.7924 | 2.10797 | ||||||||
\(243\) | 14.8595 | 0.953239 | ||||||||
\(244\) | 5.94385 | 0.380516 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.75070 | 0.366652 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.201366 | 0.0127868 | ||||||||
\(249\) | 9.74944 | 0.617845 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.05366 | 0.129626 | 0.0648129 | − | 0.997897i | \(-0.479355\pi\) | ||||
0.0648129 | + | 0.997897i | \(0.479355\pi\) | |||||||
\(252\) | −12.3278 | −0.776576 | ||||||||
\(253\) | 20.6418 | 1.29774 | ||||||||
\(254\) | 5.78646 | 0.363075 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.0279 | 1.25174 | ||||||||
\(257\) | 3.60458 | 0.224847 | 0.112424 | − | 0.993660i | \(-0.464139\pi\) | ||||
0.112424 | + | 0.993660i | \(0.464139\pi\) | |||||||
\(258\) | 0.0698980 | 0.00435166 | ||||||||
\(259\) | −22.8649 | −1.42076 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.44407 | 0.213183 | ||||||||
\(262\) | 25.6961 | 1.58751 | ||||||||
\(263\) | −2.36961 | −0.146117 | −0.0730583 | − | 0.997328i | \(-0.523276\pi\) | ||||
−0.0730583 | + | 0.997328i | \(0.523276\pi\) | |||||||
\(264\) | 5.84011 | 0.359434 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.80231 | −0.478391 | ||||||||
\(267\) | −4.73059 | −0.289507 | ||||||||
\(268\) | 8.89932 | 0.543613 | ||||||||
\(269\) | 6.16524 | 0.375901 | 0.187951 | − | 0.982178i | \(-0.439816\pi\) | ||||
0.187951 | + | 0.982178i | \(0.439816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.6859 | 1.86403 | 0.932017 | − | 0.362414i | \(-0.118048\pi\) | ||||
0.932017 | + | 0.362414i | \(0.118048\pi\) | |||||||
\(272\) | 18.1320 | 1.09941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.33453 | −0.201446 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.94123 | −0.177041 | ||||||||
\(277\) | −21.4700 | −1.29001 | −0.645004 | − | 0.764180i | \(-0.723144\pi\) | ||||
−0.645004 | + | 0.764180i | \(0.723144\pi\) | |||||||
\(278\) | −17.7876 | −1.06683 | ||||||||
\(279\) | 0.326894 | 0.0195706 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.1639 | −1.79943 | −0.899714 | − | 0.436480i | \(-0.856225\pi\) | ||||
−0.899714 | + | 0.436480i | \(0.856225\pi\) | |||||||
\(282\) | −8.83363 | −0.526035 | ||||||||
\(283\) | 11.3752 | 0.676185 | 0.338092 | − | 0.941113i | \(-0.390218\pi\) | ||||
0.338092 | + | 0.941113i | \(0.390218\pi\) | |||||||
\(284\) | −4.35348 | −0.258331 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.5394 | 1.21240 | ||||||||
\(288\) | 14.3748 | 0.847043 | ||||||||
\(289\) | −3.77249 | −0.221911 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.05997 | 0.531105 | ||||||||
\(292\) | −4.98643 | −0.291809 | ||||||||
\(293\) | 16.6684 | 0.973778 | 0.486889 | − | 0.873464i | \(-0.338132\pi\) | ||||
0.486889 | + | 0.873464i | \(0.338132\pi\) | |||||||
\(294\) | 14.6914 | 0.856820 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.14300 | 0.473302 | ||||||||
\(297\) | 20.7584 | 1.20453 | ||||||||
\(298\) | 27.6528 | 1.60189 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.249650 | 0.0143896 | ||||||||
\(302\) | −13.1017 | −0.753918 | ||||||||
\(303\) | 1.10305 | 0.0633688 | ||||||||
\(304\) | 5.04785 | 0.289514 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.2031 | 0.926268 | ||||||||
\(307\) | 8.83409 | 0.504188 | 0.252094 | − | 0.967703i | \(-0.418881\pi\) | ||||
0.252094 | + | 0.967703i | \(0.418881\pi\) | |||||||
\(308\) | −26.5778 | −1.51441 | ||||||||
\(309\) | −1.84004 | −0.104676 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.9186 | −0.902661 | −0.451331 | − | 0.892357i | \(-0.649051\pi\) | ||||
−0.451331 | + | 0.892357i | \(0.649051\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.6188 | 1.56111 | 0.780554 | − | 0.625089i | \(-0.214937\pi\) | ||||
0.780554 | + | 0.625089i | \(0.214937\pi\) | |||||||
\(314\) | −21.6160 | −1.21986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.08683 | −0.342411 | ||||||||
\(317\) | −30.9950 | −1.74086 | −0.870428 | − | 0.492296i | \(-0.836158\pi\) | ||||
−0.870428 | + | 0.492296i | \(0.836158\pi\) | |||||||
\(318\) | −13.1311 | −0.736354 | ||||||||
\(319\) | 7.42518 | 0.415731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.39406 | 0.0778090 | ||||||||
\(322\) | −29.2546 | −1.63029 | ||||||||
\(323\) | 3.68247 | 0.204898 | ||||||||
\(324\) | 5.52026 | 0.306681 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −34.4400 | −1.90746 | ||||||||
\(327\) | −10.0958 | −0.558301 | ||||||||
\(328\) | −7.31482 | −0.403893 | ||||||||
\(329\) | −31.5505 | −1.73944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1915 | 1.05486 | 0.527431 | − | 0.849598i | \(-0.323155\pi\) | ||||
0.527431 | + | 0.849598i | \(0.323155\pi\) | |||||||
\(332\) | 15.8013 | 0.867209 | ||||||||
\(333\) | 13.2192 | 0.724407 | ||||||||
\(334\) | −34.6585 | −1.89643 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.0361 | −0.820285 | ||||||||
\(337\) | 15.6473 | 0.852362 | 0.426181 | − | 0.904638i | \(-0.359859\pi\) | ||||
0.426181 | + | 0.904638i | \(0.359859\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.96755 | 0.161175 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.704762 | 0.0381650 | ||||||||
\(342\) | 4.51086 | 0.243919 | ||||||||
\(343\) | 21.9369 | 1.18448 | ||||||||
\(344\) | −0.0889093 | −0.00479367 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 40.5192 | 2.17832 | ||||||||
\(347\) | 9.61628 | 0.516229 | 0.258115 | − | 0.966114i | \(-0.416899\pi\) | ||||
0.258115 | + | 0.966114i | \(0.416899\pi\) | |||||||
\(348\) | −1.05801 | −0.0567152 | ||||||||
\(349\) | 13.3991 | 0.717240 | 0.358620 | − | 0.933484i | \(-0.383247\pi\) | ||||
0.358620 | + | 0.933484i | \(0.383247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30.9911 | 1.65183 | ||||||||
\(353\) | −24.9985 | −1.33054 | −0.665269 | − | 0.746604i | \(-0.731683\pi\) | ||||
−0.665269 | + | 0.746604i | \(0.731683\pi\) | |||||||
\(354\) | 3.42955 | 0.182279 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.66706 | −0.406353 | ||||||||
\(357\) | −10.9690 | −0.580542 | ||||||||
\(358\) | −25.2842 | −1.33631 | ||||||||
\(359\) | −12.4028 | −0.654596 | −0.327298 | − | 0.944921i | \(-0.606138\pi\) | ||||
−0.327298 | + | 0.944921i | \(0.606138\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9748 | −0.946043 | ||||||||
\(362\) | 25.0051 | 1.31424 | ||||||||
\(363\) | 12.8345 | 0.673636 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.47845 | 0.338634 | ||||||||
\(367\) | 11.1223 | 0.580581 | 0.290290 | − | 0.956939i | \(-0.406248\pi\) | ||||
0.290290 | + | 0.956939i | \(0.406248\pi\) | |||||||
\(368\) | 18.9268 | 0.986626 | ||||||||
\(369\) | −11.8747 | −0.618174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −46.8994 | −2.43490 | ||||||||
\(372\) | −0.100421 | −0.00520658 | ||||||||
\(373\) | 18.6801 | 0.967218 | 0.483609 | − | 0.875284i | \(-0.339326\pi\) | ||||
0.483609 | + | 0.875284i | \(0.339326\pi\) | |||||||
\(374\) | 34.9327 | 1.80633 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.2363 | 0.579466 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −29.4198 | −1.51319 | ||||||||
\(379\) | −26.5107 | −1.36176 | −0.680881 | − | 0.732394i | \(-0.738403\pi\) | ||||
−0.680881 | + | 0.732394i | \(0.738403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.26475 | 0.116026 | ||||||||
\(382\) | −23.0255 | −1.17809 | ||||||||
\(383\) | 3.72734 | 0.190458 | 0.0952291 | − | 0.995455i | \(-0.469642\pi\) | ||||
0.0952291 | + | 0.995455i | \(0.469642\pi\) | |||||||
\(384\) | 7.76207 | 0.396106 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.73510 | −0.342808 | ||||||||
\(387\) | −0.144334 | −0.00733689 | ||||||||
\(388\) | 14.6839 | 0.745460 | ||||||||
\(389\) | 11.5239 | 0.584287 | 0.292144 | − | 0.956374i | \(-0.405631\pi\) | ||||
0.292144 | + | 0.956374i | \(0.405631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.8073 | 0.698267 | ||||||||
\(392\) | −18.6873 | −0.943850 | ||||||||
\(393\) | 10.0571 | 0.507314 | ||||||||
\(394\) | −12.2156 | −0.615415 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.3658 | 0.772159 | ||||||||
\(397\) | −31.2706 | −1.56943 | −0.784714 | − | 0.619858i | \(-0.787190\pi\) | ||||
−0.784714 | + | 0.619858i | \(0.787190\pi\) | |||||||
\(398\) | 41.2036 | 2.06535 | ||||||||
\(399\) | −3.05372 | −0.152877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.2171 | −1.10947 | −0.554734 | − | 0.832028i | \(-0.687180\pi\) | ||||
−0.554734 | + | 0.832028i | \(0.687180\pi\) | |||||||
\(402\) | 9.69974 | 0.483779 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.78776 | 0.0889446 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.5233 | −0.522264 | ||||||||
\(407\) | 28.4997 | 1.41268 | ||||||||
\(408\) | 3.90646 | 0.193398 | ||||||||
\(409\) | 22.4733 | 1.11123 | 0.555617 | − | 0.831439i | \(-0.312482\pi\) | ||||
0.555617 | + | 0.831439i | \(0.312482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.30509 | −0.0643753 | ||||||||
\(412\) | −2.98222 | −0.146924 | ||||||||
\(413\) | 12.2491 | 0.602740 | ||||||||
\(414\) | 16.9133 | 0.831245 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.96182 | −0.340922 | ||||||||
\(418\) | 9.72510 | 0.475670 | ||||||||
\(419\) | 7.08755 | 0.346249 | 0.173125 | − | 0.984900i | \(-0.444614\pi\) | ||||
0.173125 | + | 0.984900i | \(0.444614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.8537 | −1.50372 | −0.751858 | − | 0.659325i | \(-0.770842\pi\) | ||||
−0.751858 | + | 0.659325i | \(0.770842\pi\) | |||||||
\(422\) | −1.81373 | −0.0882911 | ||||||||
\(423\) | 18.2407 | 0.886895 | ||||||||
\(424\) | 16.7025 | 0.811147 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.74503 | −0.229898 | ||||||||
\(427\) | 23.1387 | 1.11976 | ||||||||
\(428\) | 2.25941 | 0.109213 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.2922 | −1.21828 | −0.609142 | − | 0.793062i | \(-0.708486\pi\) | ||||
−0.609142 | + | 0.793062i | \(0.708486\pi\) | |||||||
\(432\) | 19.0337 | 0.915759 | ||||||||
\(433\) | −37.5017 | −1.80222 | −0.901109 | − | 0.433592i | \(-0.857246\pi\) | ||||
−0.901109 | + | 0.433592i | \(0.857246\pi\) | |||||||
\(434\) | −0.998822 | −0.0479450 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.3627 | −0.783632 | ||||||||
\(437\) | 3.84389 | 0.183878 | ||||||||
\(438\) | −5.43491 | −0.259690 | ||||||||
\(439\) | 7.55770 | 0.360709 | 0.180355 | − | 0.983602i | \(-0.442275\pi\) | ||||
0.180355 | + | 0.983602i | \(0.442275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.3366 | −1.44460 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.24630 | 0.439305 | 0.219652 | − | 0.975578i | \(-0.429508\pi\) | ||||
0.219652 | + | 0.975578i | \(0.429508\pi\) | |||||||
\(444\) | −4.06089 | −0.192721 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.92522 | 0.469973 | ||||||||
\(447\) | 10.8230 | 0.511908 | ||||||||
\(448\) | −0.426806 | −0.0201647 | ||||||||
\(449\) | −2.01940 | −0.0953012 | −0.0476506 | − | 0.998864i | \(-0.515173\pi\) | ||||
−0.0476506 | + | 0.998864i | \(0.515173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.6011 | −1.20551 | ||||||||
\(452\) | 4.80963 | 0.226226 | ||||||||
\(453\) | −5.12783 | −0.240926 | ||||||||
\(454\) | −21.8603 | −1.02596 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.08754 | 0.0509287 | ||||||||
\(457\) | −32.6478 | −1.52720 | −0.763600 | − | 0.645690i | \(-0.776570\pi\) | ||||
−0.763600 | + | 0.645690i | \(0.776570\pi\) | |||||||
\(458\) | −34.8875 | −1.63019 | ||||||||
\(459\) | 13.8853 | 0.648112 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.4978 | −1.28070 | −0.640350 | − | 0.768083i | \(-0.721211\pi\) | ||||
−0.640350 | + | 0.768083i | \(0.721211\pi\) | |||||||
\(462\) | −28.9682 | −1.34772 | ||||||||
\(463\) | −26.0866 | −1.21235 | −0.606174 | − | 0.795332i | \(-0.707297\pi\) | ||||
−0.606174 | + | 0.795332i | \(0.707297\pi\) | |||||||
\(464\) | 6.80826 | 0.316066 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.6259 | −1.32607 | ||||||||
\(467\) | 9.04138 | 0.418385 | 0.209193 | − | 0.977874i | \(-0.432916\pi\) | ||||
0.209193 | + | 0.977874i | \(0.432916\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.6440 | 1.59971 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.46021 | −0.389826 | ||||||||
\(472\) | −4.36235 | −0.200793 | ||||||||
\(473\) | −0.311173 | −0.0143078 | ||||||||
\(474\) | −6.63429 | −0.304723 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −17.7779 | −0.814850 | ||||||||
\(477\) | 27.1146 | 1.24149 | ||||||||
\(478\) | −38.5511 | −1.76329 | ||||||||
\(479\) | −14.6976 | −0.671550 | −0.335775 | − | 0.941942i | \(-0.608998\pi\) | ||||
−0.335775 | + | 0.941942i | \(0.608998\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.532887 | 0.0242723 | ||||||||
\(483\) | −11.4498 | −0.520986 | ||||||||
\(484\) | 20.8014 | 0.945517 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 26.2495 | 1.19070 | ||||||||
\(487\) | −1.08011 | −0.0489443 | −0.0244722 | − | 0.999701i | \(-0.507791\pi\) | ||||
−0.0244722 | + | 0.999701i | \(0.507791\pi\) | |||||||
\(488\) | −8.24051 | −0.373030 | ||||||||
\(489\) | −13.4794 | −0.609558 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.17260 | −0.0980479 | −0.0490239 | − | 0.998798i | \(-0.515611\pi\) | ||||
−0.0490239 | + | 0.998798i | \(0.515611\pi\) | |||||||
\(492\) | 3.64788 | 0.164459 | ||||||||
\(493\) | 4.96672 | 0.223690 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.646206 | 0.0290155 | ||||||||
\(497\) | −16.9475 | −0.760201 | ||||||||
\(498\) | 17.2225 | 0.771758 | ||||||||
\(499\) | 28.5639 | 1.27869 | 0.639347 | − | 0.768918i | \(-0.279205\pi\) | ||||
0.639347 | + | 0.768918i | \(0.279205\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5649 | −0.606034 | ||||||||
\(502\) | 3.62781 | 0.161917 | ||||||||
\(503\) | 37.4525 | 1.66992 | 0.834962 | − | 0.550307i | \(-0.185489\pi\) | ||||
0.834962 | + | 0.550307i | \(0.185489\pi\) | |||||||
\(504\) | 17.0911 | 0.761298 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 36.4640 | 1.62102 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.67056 | 0.162855 | ||||||||
\(509\) | 21.3881 | 0.948011 | 0.474005 | − | 0.880522i | \(-0.342808\pi\) | ||||
0.474005 | + | 0.880522i | \(0.342808\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.4116 | −0.858716 | ||||||||
\(512\) | 12.9260 | 0.571253 | ||||||||
\(513\) | 3.86561 | 0.170671 | ||||||||
\(514\) | 6.36753 | 0.280860 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0443388 | 0.00195191 | ||||||||
\(517\) | 39.3258 | 1.72955 | ||||||||
\(518\) | −40.3911 | −1.77468 | ||||||||
\(519\) | 15.8587 | 0.696118 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.6689 | −1.29982 | −0.649910 | − | 0.760011i | \(-0.725193\pi\) | ||||
−0.649910 | + | 0.760011i | \(0.725193\pi\) | |||||||
\(522\) | 6.08399 | 0.266289 | ||||||||
\(523\) | −17.7702 | −0.777036 | −0.388518 | − | 0.921441i | \(-0.627013\pi\) | ||||
−0.388518 | + | 0.921441i | \(0.627013\pi\) | |||||||
\(524\) | 16.3000 | 0.712067 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.18595 | −0.182516 | ||||||||
\(527\) | 0.471416 | 0.0205352 | ||||||||
\(528\) | 18.7415 | 0.815620 | ||||||||
\(529\) | −8.58743 | −0.373366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.08175 | −0.307322 | ||||||||
\(532\) | −4.94929 | −0.214579 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.35664 | −0.361627 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.3379 | −0.532918 | ||||||||
\(537\) | −9.89591 | −0.427040 | ||||||||
\(538\) | 10.8910 | 0.469543 | ||||||||
\(539\) | −65.4035 | −2.81713 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.9280 | 1.20072 | 0.600358 | − | 0.799731i | \(-0.295025\pi\) | ||||
0.600358 | + | 0.799731i | \(0.295025\pi\) | |||||||
\(542\) | 54.2069 | 2.32839 | ||||||||
\(543\) | 9.78664 | 0.419985 | ||||||||
\(544\) | 20.7300 | 0.888791 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.7436 | 1.78483 | 0.892414 | − | 0.451218i | \(-0.149010\pi\) | ||||
0.892414 | + | 0.451218i | \(0.149010\pi\) | |||||||
\(548\) | −2.11521 | −0.0903574 | ||||||||
\(549\) | −13.3775 | −0.570937 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.38271 | 0.0589054 | ||||||||
\(552\) | 4.07770 | 0.173558 | ||||||||
\(553\) | −23.6953 | −1.00763 | ||||||||
\(554\) | −37.9270 | −1.61136 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.2833 | −0.478518 | ||||||||
\(557\) | 10.3200 | 0.437273 | 0.218636 | − | 0.975806i | \(-0.429839\pi\) | ||||
0.218636 | + | 0.975806i | \(0.429839\pi\) | |||||||
\(558\) | 0.577462 | 0.0244459 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.6722 | 0.577241 | ||||||||
\(562\) | −53.2849 | −2.24769 | ||||||||
\(563\) | 20.3028 | 0.855660 | 0.427830 | − | 0.903859i | \(-0.359278\pi\) | ||||
0.427830 | + | 0.903859i | \(0.359278\pi\) | |||||||
\(564\) | −5.60349 | −0.235950 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.0944 | 0.844630 | ||||||||
\(567\) | 21.4897 | 0.902482 | ||||||||
\(568\) | 6.03562 | 0.253249 | ||||||||
\(569\) | −17.2259 | −0.722148 | −0.361074 | − | 0.932537i | \(-0.617590\pi\) | ||||
−0.361074 | + | 0.932537i | \(0.617590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0786 | −0.463626 | −0.231813 | − | 0.972760i | \(-0.574466\pi\) | ||||
−0.231813 | + | 0.972760i | \(0.574466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.01189 | −0.376477 | ||||||||
\(574\) | 36.2831 | 1.51443 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.246755 | 0.0102814 | ||||||||
\(577\) | 16.1346 | 0.671691 | 0.335845 | − | 0.941917i | \(-0.390978\pi\) | ||||
0.335845 | + | 0.941917i | \(0.390978\pi\) | |||||||
\(578\) | −6.66414 | −0.277192 | ||||||||
\(579\) | −2.63603 | −0.109550 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 61.5125 | 2.55197 | ||||||||
\(582\) | 16.0045 | 0.663410 | ||||||||
\(583\) | 58.4572 | 2.42105 | ||||||||
\(584\) | 6.91314 | 0.286068 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.4449 | 1.21636 | ||||||||
\(587\) | 3.29336 | 0.135932 | 0.0679658 | − | 0.997688i | \(-0.478349\pi\) | ||||
0.0679658 | + | 0.997688i | \(0.478349\pi\) | |||||||
\(588\) | 9.31929 | 0.384321 | ||||||||
\(589\) | 0.131240 | 0.00540765 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.78104 | −0.196666 | ||||||||
\(592\) | 26.1318 | 1.07401 | ||||||||
\(593\) | −4.66535 | −0.191583 | −0.0957915 | − | 0.995401i | \(-0.530538\pi\) | ||||
−0.0957915 | + | 0.995401i | \(0.530538\pi\) | |||||||
\(594\) | 36.6700 | 1.50459 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.5412 | 0.718516 | ||||||||
\(597\) | 16.1265 | 0.660015 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.3301 | −0.544651 | −0.272326 | − | 0.962205i | \(-0.587793\pi\) | ||||
−0.272326 | + | 0.962205i | \(0.587793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.4692 | 1.32445 | 0.662223 | − | 0.749307i | \(-0.269613\pi\) | ||||
0.662223 | + | 0.749307i | \(0.269613\pi\) | |||||||
\(602\) | 0.441010 | 0.0179742 | ||||||||
\(603\) | −20.0292 | −0.815651 | ||||||||
\(604\) | −8.31088 | −0.338165 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.94856 | 0.0791547 | ||||||||
\(607\) | 35.5116 | 1.44137 | 0.720686 | − | 0.693262i | \(-0.243827\pi\) | ||||
0.720686 | + | 0.693262i | \(0.243827\pi\) | |||||||
\(608\) | 5.77113 | 0.234050 | ||||||||
\(609\) | −4.11869 | −0.166898 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.2782 | 0.415471 | ||||||||
\(613\) | −13.2854 | −0.536593 | −0.268296 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268296 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(614\) | 15.6055 | 0.629788 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.8472 | 1.48462 | ||||||||
\(617\) | 32.4545 | 1.30657 | 0.653284 | − | 0.757113i | \(-0.273391\pi\) | ||||
0.653284 | + | 0.757113i | \(0.273391\pi\) | |||||||
\(618\) | −3.25045 | −0.130752 | ||||||||
\(619\) | 27.8149 | 1.11797 | 0.558987 | − | 0.829176i | \(-0.311190\pi\) | ||||
0.558987 | + | 0.829176i | \(0.311190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.4940 | 0.581624 | ||||||||
\(622\) | −28.1204 | −1.12753 | ||||||||
\(623\) | −29.8469 | −1.19579 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 48.7889 | 1.95000 | ||||||||
\(627\) | 3.80627 | 0.152008 | ||||||||
\(628\) | −13.7118 | −0.547160 | ||||||||
\(629\) | 19.0635 | 0.760110 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6301 | 0.502796 | 0.251398 | − | 0.967884i | \(-0.419110\pi\) | ||||
0.251398 | + | 0.967884i | \(0.419110\pi\) | |||||||
\(632\) | 8.43873 | 0.335675 | ||||||||
\(633\) | −0.709870 | −0.0282148 | ||||||||
\(634\) | −54.7531 | −2.17452 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.32951 | −0.330287 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.1167 | 0.519294 | ||||||||
\(639\) | 9.79811 | 0.387607 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.25209 | 0.286440 | 0.143220 | − | 0.989691i | \(-0.454254\pi\) | ||||
0.143220 | + | 0.989691i | \(0.454254\pi\) | |||||||
\(642\) | 2.46263 | 0.0971922 | ||||||||
\(643\) | 3.94228 | 0.155468 | 0.0777341 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777341 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(644\) | −18.5572 | −0.731257 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.50513 | 0.255941 | ||||||||
\(647\) | −4.09732 | −0.161082 | −0.0805412 | − | 0.996751i | \(-0.525665\pi\) | ||||
−0.0805412 | + | 0.996751i | \(0.525665\pi\) | |||||||
\(648\) | −7.65324 | −0.300648 | ||||||||
\(649\) | −15.2678 | −0.599312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.390926 | −0.0153216 | ||||||||
\(652\) | −21.8466 | −0.855577 | ||||||||
\(653\) | 37.1255 | 1.45283 | 0.726416 | − | 0.687255i | \(-0.241185\pi\) | ||||
0.726416 | + | 0.687255i | \(0.241185\pi\) | |||||||
\(654\) | −17.8344 | −0.697380 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23.4740 | −0.916507 | ||||||||
\(657\) | 11.2227 | 0.437838 | ||||||||
\(658\) | −55.7344 | −2.17275 | ||||||||
\(659\) | 42.8526 | 1.66930 | 0.834651 | − | 0.550779i | \(-0.185669\pi\) | ||||
0.834651 | + | 0.550779i | \(0.185669\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.1806 | 1.40726 | 0.703632 | − | 0.710565i | \(-0.251560\pi\) | ||||
0.703632 | + | 0.710565i | \(0.251560\pi\) | |||||||
\(662\) | 33.9021 | 1.31764 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.9068 | −0.850148 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23.3518 | 0.904866 | ||||||||
\(667\) | 5.18443 | 0.200742 | ||||||||
\(668\) | −21.9852 | −0.850631 | ||||||||
\(669\) | 3.88460 | 0.150187 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.8409 | −1.11339 | ||||||||
\(672\) | −17.1905 | −0.663139 | ||||||||
\(673\) | 32.9716 | 1.27096 | 0.635481 | − | 0.772116i | \(-0.280802\pi\) | ||||
0.635481 | + | 0.772116i | \(0.280802\pi\) | |||||||
\(674\) | 27.6411 | 1.06470 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.9308 | −0.689137 | −0.344568 | − | 0.938761i | \(-0.611975\pi\) | ||||
−0.344568 | + | 0.938761i | \(0.611975\pi\) | |||||||
\(678\) | 5.24221 | 0.201326 | ||||||||
\(679\) | 57.1625 | 2.19369 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.55584 | −0.327860 | ||||||||
\(682\) | 1.24497 | 0.0476723 | ||||||||
\(683\) | −10.5968 | −0.405476 | −0.202738 | − | 0.979233i | \(-0.564984\pi\) | ||||
−0.202738 | + | 0.979233i | \(0.564984\pi\) | |||||||
\(684\) | 2.86140 | 0.109408 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 38.7518 | 1.47955 | ||||||||
\(687\) | −13.6545 | −0.520952 | ||||||||
\(688\) | −0.285319 | −0.0108777 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.11847 | −0.156674 | −0.0783369 | − | 0.996927i | \(-0.524961\pi\) | ||||
−0.0783369 | + | 0.996927i | \(0.524961\pi\) | |||||||
\(692\) | 25.7028 | 0.977073 | ||||||||
\(693\) | 59.8171 | 2.27226 | ||||||||
\(694\) | 16.9873 | 0.644828 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.46681 | 0.0555994 | ||||||||
\(697\) | −17.1246 | −0.648642 | ||||||||
\(698\) | 23.6697 | 0.895913 | ||||||||
\(699\) | −11.2038 | −0.423766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.0511 | −0.795089 | −0.397545 | − | 0.917583i | \(-0.630138\pi\) | ||||
−0.397545 | + | 0.917583i | \(0.630138\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.30718 | 0.200164 | ||||||||
\(704\) | 0.531986 | 0.0200500 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −44.1602 | −1.66199 | ||||||||
\(707\) | 6.95954 | 0.261741 | ||||||||
\(708\) | 2.17549 | 0.0817599 | ||||||||
\(709\) | 21.9555 | 0.824558 | 0.412279 | − | 0.911058i | \(-0.364733\pi\) | ||||
0.412279 | + | 0.911058i | \(0.364733\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6993 | 0.513763 | ||||||||
\(712\) | 10.6295 | 0.398359 | ||||||||
\(713\) | 0.492080 | 0.0184286 | ||||||||
\(714\) | −19.3769 | −0.725162 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.0387 | −0.599394 | ||||||||
\(717\) | −15.0884 | −0.563486 | ||||||||
\(718\) | −21.9097 | −0.817663 | ||||||||
\(719\) | 15.1917 | 0.566553 | 0.283276 | − | 0.959038i | \(-0.408579\pi\) | ||||
0.283276 | + | 0.959038i | \(0.408579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6094 | −0.432357 | ||||||||
\(722\) | −31.7527 | −1.18171 | ||||||||
\(723\) | 0.208565 | 0.00775661 | ||||||||
\(724\) | 15.8616 | 0.589492 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 22.6723 | 0.841447 | ||||||||
\(727\) | 0.952345 | 0.0353205 | 0.0176603 | − | 0.999844i | \(-0.494378\pi\) | ||||
0.0176603 | + | 0.999844i | \(0.494378\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.50529 | −0.166863 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.208144 | −0.00769850 | ||||||||
\(732\) | 4.10952 | 0.151892 | ||||||||
\(733\) | −16.5074 | −0.609716 | −0.304858 | − | 0.952398i | \(-0.598609\pi\) | ||||
−0.304858 | + | 0.952398i | \(0.598609\pi\) | |||||||
\(734\) | 19.6477 | 0.725210 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.6387 | 0.797612 | ||||||||
\(737\) | −43.1815 | −1.59061 | ||||||||
\(738\) | −20.9769 | −0.772169 | ||||||||
\(739\) | 5.66334 | 0.208329 | 0.104165 | − | 0.994560i | \(-0.466783\pi\) | ||||
0.104165 | + | 0.994560i | \(0.466783\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −82.8484 | −3.04146 | ||||||||
\(743\) | 32.3940 | 1.18842 | 0.594211 | − | 0.804309i | \(-0.297465\pi\) | ||||
0.594211 | + | 0.804309i | \(0.297465\pi\) | |||||||
\(744\) | 0.139223 | 0.00510414 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.9986 | 1.20816 | ||||||||
\(747\) | −35.5630 | −1.30118 | ||||||||
\(748\) | 22.1591 | 0.810216 | ||||||||
\(749\) | 8.79562 | 0.321385 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.7912 | −1.01412 | −0.507058 | − | 0.861912i | \(-0.669267\pi\) | ||||
−0.507058 | + | 0.861912i | \(0.669267\pi\) | |||||||
\(752\) | 36.0584 | 1.31491 | ||||||||
\(753\) | 1.41988 | 0.0517432 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.6621 | −0.678733 | ||||||||
\(757\) | 1.65955 | 0.0603173 | 0.0301586 | − | 0.999545i | \(-0.490399\pi\) | ||||
0.0301586 | + | 0.999545i | \(0.490399\pi\) | |||||||
\(758\) | −46.8314 | −1.70099 | ||||||||
\(759\) | 14.2715 | 0.518023 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.8781 | 1.69933 | 0.849665 | − | 0.527323i | \(-0.176804\pi\) | ||||
0.849665 | + | 0.527323i | \(0.176804\pi\) | |||||||
\(762\) | 4.00070 | 0.144930 | ||||||||
\(763\) | −63.6980 | −2.30602 | ||||||||
\(764\) | −14.6059 | −0.528424 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.58439 | 0.237904 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 13.8471 | 0.499663 | ||||||||
\(769\) | 33.8126 | 1.21931 | 0.609657 | − | 0.792665i | \(-0.291307\pi\) | ||||
0.609657 | + | 0.792665i | \(0.291307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.49217 | 0.0897531 | ||||||||
\(772\) | −4.27232 | −0.153764 | ||||||||
\(773\) | −35.9618 | −1.29346 | −0.646728 | − | 0.762721i | \(-0.723863\pi\) | ||||
−0.646728 | + | 0.762721i | \(0.723863\pi\) | |||||||
\(774\) | −0.254967 | −0.00916460 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.3576 | −0.730794 | ||||||||
\(777\) | −15.8085 | −0.567128 | ||||||||
\(778\) | 20.3572 | 0.729840 | ||||||||
\(779\) | −4.76741 | −0.170810 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.1240 | 0.755878 | ||||||||
\(782\) | 24.3908 | 0.872214 | ||||||||
\(783\) | 5.21372 | 0.186323 | ||||||||
\(784\) | −59.9694 | −2.14177 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.7660 | 0.633692 | ||||||||
\(787\) | −11.8483 | −0.422346 | −0.211173 | − | 0.977449i | \(-0.567728\pi\) | ||||
−0.211173 | + | 0.977449i | \(0.567728\pi\) | |||||||
\(788\) | −7.74883 | −0.276040 | ||||||||
\(789\) | −1.63832 | −0.0583259 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.7233 | 0.665723 | ||||||||
\(792\) | −21.3030 | −0.756968 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −55.2399 | −1.96039 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.1369 | 0.926398 | ||||||||
\(797\) | 18.5060 | 0.655517 | 0.327759 | − | 0.944761i | \(-0.393707\pi\) | ||||
0.327759 | + | 0.944761i | \(0.393707\pi\) | |||||||
\(798\) | −5.39443 | −0.190961 | ||||||||
\(799\) | 26.3051 | 0.930607 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.2558 | 0.609703 | ||||||||
\(802\) | −39.2467 | −1.38585 | ||||||||
\(803\) | 24.1953 | 0.853833 | ||||||||
\(804\) | 6.15289 | 0.216996 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.26258 | 0.150050 | ||||||||
\(808\) | −2.47854 | −0.0871947 | ||||||||
\(809\) | −17.9832 | −0.632255 | −0.316127 | − | 0.948717i | \(-0.602383\pi\) | ||||
−0.316127 | + | 0.948717i | \(0.602383\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.4247 | −1.73554 | −0.867768 | − | 0.496969i | \(-0.834446\pi\) | ||||
−0.867768 | + | 0.496969i | \(0.834446\pi\) | |||||||
\(812\) | −6.67533 | −0.234258 | ||||||||
\(813\) | 21.2159 | 0.744073 | ||||||||
\(814\) | 50.3450 | 1.76459 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.5362 | 0.438856 | ||||||||
\(817\) | −0.0579464 | −0.00202729 | ||||||||
\(818\) | 39.6993 | 1.38805 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0664 | −0.805022 | −0.402511 | − | 0.915415i | \(-0.631862\pi\) | ||||
−0.402511 | + | 0.915415i | \(0.631862\pi\) | |||||||
\(822\) | −2.30546 | −0.0804120 | ||||||||
\(823\) | −23.8292 | −0.830635 | −0.415317 | − | 0.909677i | \(-0.636329\pi\) | ||||
−0.415317 | + | 0.909677i | \(0.636329\pi\) | |||||||
\(824\) | 4.13453 | 0.144033 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.6382 | 0.752890 | ||||||||
\(827\) | −31.4303 | −1.09294 | −0.546468 | − | 0.837480i | \(-0.684028\pi\) | ||||
−0.546468 | + | 0.837480i | \(0.684028\pi\) | |||||||
\(828\) | 10.7287 | 0.372849 | ||||||||
\(829\) | −9.13940 | −0.317425 | −0.158712 | − | 0.987325i | \(-0.550734\pi\) | ||||
−0.158712 | + | 0.987325i | \(0.550734\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.8441 | −0.514937 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43.7485 | −1.51580 | ||||||||
\(834\) | −12.2981 | −0.425849 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.16898 | 0.213359 | ||||||||
\(837\) | 0.494860 | 0.0171049 | ||||||||
\(838\) | 12.5202 | 0.432504 | ||||||||
\(839\) | −38.0484 | −1.31358 | −0.656788 | − | 0.754075i | \(-0.728085\pi\) | ||||
−0.656788 | + | 0.754075i | \(0.728085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1351 | −0.935692 | ||||||||
\(842\) | −54.5034 | −1.87831 | ||||||||
\(843\) | −20.8550 | −0.718284 | ||||||||
\(844\) | −1.15052 | −0.0396024 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 32.2225 | 1.10783 | ||||||||
\(847\) | 80.9772 | 2.78241 | ||||||||
\(848\) | 53.6002 | 1.84064 | ||||||||
\(849\) | 7.86468 | 0.269915 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.8991 | 0.682133 | ||||||||
\(852\) | −3.00995 | −0.103119 | ||||||||
\(853\) | 9.60563 | 0.328891 | 0.164445 | − | 0.986386i | \(-0.447417\pi\) | ||||
0.164445 | + | 0.986386i | \(0.447417\pi\) | |||||||
\(854\) | 40.8747 | 1.39870 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.13243 | −0.107064 | ||||||||
\(857\) | −30.6098 | −1.04561 | −0.522805 | − | 0.852452i | \(-0.675114\pi\) | ||||
−0.522805 | + | 0.852452i | \(0.675114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.5778 | −1.14566 | −0.572829 | − | 0.819675i | \(-0.694154\pi\) | ||||
−0.572829 | + | 0.819675i | \(0.694154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.2007 | 0.483960 | ||||||||
\(862\) | −44.6790 | −1.52177 | ||||||||
\(863\) | 34.9343 | 1.18918 | 0.594589 | − | 0.804030i | \(-0.297315\pi\) | ||||
0.594589 | + | 0.804030i | \(0.297315\pi\) | |||||||
\(864\) | 21.7609 | 0.740322 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −66.2473 | −2.25117 | ||||||||
\(867\) | −2.60826 | −0.0885810 | ||||||||
\(868\) | −0.633589 | −0.0215054 | ||||||||
\(869\) | 29.5347 | 1.00190 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 22.6851 | 0.768215 | ||||||||
\(873\) | −33.0481 | −1.11851 | ||||||||
\(874\) | 6.79028 | 0.229685 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.44756 | −0.116482 | ||||||||
\(877\) | 22.1218 | 0.747001 | 0.373500 | − | 0.927630i | \(-0.378157\pi\) | ||||
0.373500 | + | 0.927630i | \(0.378157\pi\) | |||||||
\(878\) | 13.3508 | 0.450566 | ||||||||
\(879\) | 11.5243 | 0.388707 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.01725 | −0.101654 | −0.0508269 | − | 0.998707i | \(-0.516186\pi\) | ||||
−0.0508269 | + | 0.998707i | \(0.516186\pi\) | |||||||
\(882\) | −53.5899 | −1.80446 | ||||||||
\(883\) | 21.4931 | 0.723300 | 0.361650 | − | 0.932314i | \(-0.382214\pi\) | ||||
0.361650 | + | 0.932314i | \(0.382214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.3337 | 0.548741 | ||||||||
\(887\) | 0.273357 | 0.00917842 | 0.00458921 | − | 0.999989i | \(-0.498539\pi\) | ||||
0.00458921 | + | 0.999989i | \(0.498539\pi\) | |||||||
\(888\) | 5.62998 | 0.188930 | ||||||||
\(889\) | 14.2890 | 0.479239 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.7856 | −0.897350 | ||||||||
\(892\) | 6.29593 | 0.210803 | ||||||||
\(893\) | 7.32320 | 0.245062 | ||||||||
\(894\) | 19.1189 | 0.639431 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 48.9735 | 1.63609 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.56729 | −0.119042 | ||||||||
\(899\) | 0.177009 | 0.00590359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.1021 | 1.30268 | ||||||||
\(902\) | −45.2247 | −1.50582 | ||||||||
\(903\) | 0.172605 | 0.00574395 | ||||||||
\(904\) | −6.66802 | −0.221775 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.05837 | −0.300944 | ||||||||
\(907\) | −36.0688 | −1.19765 | −0.598823 | − | 0.800881i | \(-0.704365\pi\) | ||||
−0.598823 | + | 0.800881i | \(0.704365\pi\) | |||||||
\(908\) | −13.8668 | −0.460186 | ||||||||
\(909\) | −4.02361 | −0.133455 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0257 | −0.729744 | −0.364872 | − | 0.931058i | \(-0.618887\pi\) | ||||
−0.364872 | + | 0.931058i | \(0.618887\pi\) | |||||||
\(912\) | 3.49003 | 0.115566 | ||||||||
\(913\) | −76.6715 | −2.53746 | ||||||||
\(914\) | −57.6727 | −1.90764 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.1304 | −0.731209 | ||||||||
\(917\) | 63.4537 | 2.09543 | ||||||||
\(918\) | 24.5286 | 0.809565 | ||||||||
\(919\) | −8.72185 | −0.287707 | −0.143854 | − | 0.989599i | \(-0.545949\pi\) | ||||
−0.143854 | + | 0.989599i | \(0.545949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.10780 | 0.201259 | ||||||||
\(922\) | −48.5751 | −1.59974 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −18.3756 | −0.604513 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −46.0823 | −1.51436 | ||||||||
\(927\) | 6.71191 | 0.220448 | ||||||||
\(928\) | 7.78378 | 0.255515 | ||||||||
\(929\) | −30.2187 | −0.991442 | −0.495721 | − | 0.868482i | \(-0.665096\pi\) | ||||
−0.495721 | + | 0.868482i | \(0.665096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.1794 | −0.399163 | ||||||||
\(932\) | −18.1584 | −0.594799 | ||||||||
\(933\) | −11.0060 | −0.360319 | ||||||||
\(934\) | 15.9717 | 0.522610 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.7430 | 0.906323 | 0.453161 | − | 0.891428i | \(-0.350296\pi\) | ||||
0.453161 | + | 0.891428i | \(0.350296\pi\) | |||||||
\(938\) | 61.1989 | 1.99822 | ||||||||
\(939\) | 19.0953 | 0.623153 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.5726 | −1.71382 | −0.856909 | − | 0.515468i | \(-0.827618\pi\) | ||||
−0.856909 | + | 0.515468i | \(0.827618\pi\) | |||||||
\(942\) | −14.9451 | −0.486936 | ||||||||
\(943\) | −17.8753 | −0.582099 | ||||||||
\(944\) | −13.9992 | −0.455636 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.549691 | −0.0178720 | ||||||||
\(947\) | −48.2034 | −1.56640 | −0.783200 | − | 0.621770i | \(-0.786414\pi\) | ||||
−0.783200 | + | 0.621770i | \(0.786414\pi\) | |||||||
\(948\) | −4.20837 | −0.136681 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.4296 | −0.694903 | ||||||||
\(952\) | 24.6472 | 0.798819 | ||||||||
\(953\) | −39.0286 | −1.26426 | −0.632130 | − | 0.774862i | \(-0.717819\pi\) | ||||
−0.632130 | + | 0.774862i | \(0.717819\pi\) | |||||||
\(954\) | 47.8982 | 1.55076 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.4544 | −0.790911 | ||||||||
\(957\) | 5.13369 | 0.165949 | ||||||||
\(958\) | −25.9635 | −0.838841 | ||||||||
\(959\) | −8.23426 | −0.265898 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9832 | −0.999458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.08513 | −0.163866 | ||||||||
\(964\) | 0.338029 | 0.0108872 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −20.2263 | −0.650770 | ||||||||
\(967\) | −43.4644 | −1.39772 | −0.698861 | − | 0.715258i | \(-0.746309\pi\) | ||||
−0.698861 | + | 0.715258i | \(0.746309\pi\) | |||||||
\(968\) | −28.8388 | −0.926916 | ||||||||
\(969\) | 2.54602 | 0.0817900 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.6094 | 0.404655 | 0.202328 | − | 0.979318i | \(-0.435149\pi\) | ||||
0.202328 | + | 0.979318i | \(0.435149\pi\) | |||||||
\(972\) | 16.6510 | 0.534082 | ||||||||
\(973\) | −43.9245 | −1.40815 | ||||||||
\(974\) | −1.90802 | −0.0611370 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.4447 | −0.846473 | ||||||||
\(977\) | 36.8798 | 1.17989 | 0.589944 | − | 0.807444i | \(-0.299150\pi\) | ||||
0.589944 | + | 0.807444i | \(0.299150\pi\) | |||||||
\(978\) | −23.8115 | −0.761407 | ||||||||
\(979\) | 37.2023 | 1.18899 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.8266 | 1.17578 | ||||||||
\(982\) | −3.83791 | −0.122473 | ||||||||
\(983\) | 15.6468 | 0.499056 | 0.249528 | − | 0.968368i | \(-0.419725\pi\) | ||||
0.249528 | + | 0.968368i | \(0.419725\pi\) | |||||||
\(984\) | −5.05739 | −0.161224 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.77376 | 0.279414 | ||||||||
\(987\) | −21.8137 | −0.694338 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.217268 | −0.00690873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.2433 | 0.674816 | 0.337408 | − | 0.941359i | \(-0.390450\pi\) | ||||
0.337408 | + | 0.941359i | \(0.390450\pi\) | |||||||
\(992\) | 0.738798 | 0.0234568 | ||||||||
\(993\) | 13.2688 | 0.421073 | ||||||||
\(994\) | −29.9380 | −0.949576 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.9248 | 0.346167 | ||||||||
\(997\) | −17.7179 | −0.561132 | −0.280566 | − | 0.959835i | \(-0.590522\pi\) | ||||
−0.280566 | + | 0.959835i | \(0.590522\pi\) | |||||||
\(998\) | 50.4584 | 1.59723 | ||||||||
\(999\) | 20.0115 | 0.633137 |
(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 | 4225.2.a.ca.1.14 | 18 | ||
5.2 | odd | 4 | 845.2.b.g.339.14 | yes | 18 | ||
5.3 | odd | 4 | 845.2.b.g.339.5 | ✓ | 18 | ||
5.4 | even | 2 | inner | 4225.2.a.ca.1.5 | 18 | ||
13.12 | even | 2 | 4225.2.a.cb.1.5 | 18 | |||
65.2 | even | 12 | 845.2.l.g.654.10 | 72 | |||
65.3 | odd | 12 | 845.2.n.i.529.14 | 36 | |||
65.7 | even | 12 | 845.2.l.g.699.27 | 72 | |||
65.8 | even | 4 | 845.2.d.e.844.28 | 36 | |||
65.12 | odd | 4 | 845.2.b.h.339.5 | yes | 18 | ||
65.17 | odd | 12 | 845.2.n.h.484.5 | 36 | |||
65.18 | even | 4 | 845.2.d.e.844.10 | 36 | |||
65.22 | odd | 12 | 845.2.n.i.484.14 | 36 | |||
65.23 | odd | 12 | 845.2.n.h.529.5 | 36 | |||
65.28 | even | 12 | 845.2.l.g.654.27 | 72 | |||
65.32 | even | 12 | 845.2.l.g.699.9 | 72 | |||
65.33 | even | 12 | 845.2.l.g.699.10 | 72 | |||
65.37 | even | 12 | 845.2.l.g.654.28 | 72 | |||
65.38 | odd | 4 | 845.2.b.h.339.14 | yes | 18 | ||
65.42 | odd | 12 | 845.2.n.i.529.5 | 36 | |||
65.43 | odd | 12 | 845.2.n.h.484.14 | 36 | |||
65.47 | even | 4 | 845.2.d.e.844.9 | 36 | |||
65.48 | odd | 12 | 845.2.n.i.484.5 | 36 | |||
65.57 | even | 4 | 845.2.d.e.844.27 | 36 | |||
65.58 | even | 12 | 845.2.l.g.699.28 | 72 | |||
65.62 | odd | 12 | 845.2.n.h.529.14 | 36 | |||
65.63 | even | 12 | 845.2.l.g.654.9 | 72 | |||
65.64 | even | 2 | 4225.2.a.cb.1.14 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.b.g.339.5 | ✓ | 18 | 5.3 | odd | 4 | ||
845.2.b.g.339.14 | yes | 18 | 5.2 | odd | 4 | ||
845.2.b.h.339.5 | yes | 18 | 65.12 | odd | 4 | ||
845.2.b.h.339.14 | yes | 18 | 65.38 | odd | 4 | ||
845.2.d.e.844.9 | 36 | 65.47 | even | 4 | |||
845.2.d.e.844.10 | 36 | 65.18 | even | 4 | |||
845.2.d.e.844.27 | 36 | 65.57 | even | 4 | |||
845.2.d.e.844.28 | 36 | 65.8 | even | 4 | |||
845.2.l.g.654.9 | 72 | 65.63 | even | 12 | |||
845.2.l.g.654.10 | 72 | 65.2 | even | 12 | |||
845.2.l.g.654.27 | 72 | 65.28 | even | 12 | |||
845.2.l.g.654.28 | 72 | 65.37 | even | 12 | |||
845.2.l.g.699.9 | 72 | 65.32 | even | 12 | |||
845.2.l.g.699.10 | 72 | 65.33 | even | 12 | |||
845.2.l.g.699.27 | 72 | 65.7 | even | 12 | |||
845.2.l.g.699.28 | 72 | 65.58 | even | 12 | |||
845.2.n.h.484.5 | 36 | 65.17 | odd | 12 | |||
845.2.n.h.484.14 | 36 | 65.43 | odd | 12 | |||
845.2.n.h.529.5 | 36 | 65.23 | odd | 12 | |||
845.2.n.h.529.14 | 36 | 65.62 | odd | 12 | |||
845.2.n.i.484.5 | 36 | 65.48 | odd | 12 | |||
845.2.n.i.484.14 | 36 | 65.22 | odd | 12 | |||
845.2.n.i.529.5 | 36 | 65.42 | odd | 12 | |||
845.2.n.i.529.14 | 36 | 65.3 | odd | 12 | |||
4225.2.a.ca.1.5 | 18 | 5.4 | even | 2 | inner | ||
4225.2.a.ca.1.14 | 18 | 1.1 | even | 1 | trivial | ||
4225.2.a.cb.1.5 | 18 | 13.12 | even | 2 | |||
4225.2.a.cb.1.14 | 18 | 65.64 | even | 2 |