Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(560,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.560");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 29 x^{18} + 358 x^{16} + 2458 x^{14} + 10298 x^{12} + 27188 x^{10} + 45053 x^{8} + 44980 x^{6} + 24400 x^{4} + 5448 x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 560.4 | ||
Root | \(-1.23843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.560 |
Dual form | 731.2.d.c.560.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33801 | −1.65322 | −0.826611 | − | 0.562774i | \(-0.809734\pi\) | ||||
−0.826611 | + | 0.562774i | \(0.809734\pi\) | |||||||
\(3\) | 3.08166i | 1.77920i | 0.456742 | + | 0.889599i | \(0.349016\pi\) | ||||
−0.456742 | + | 0.889599i | \(0.650984\pi\) | |||||||
\(4\) | 3.46629 | 1.73314 | ||||||||
\(5\) | − | 3.53522i | − | 1.58100i | −0.612464 | − | 0.790499i | \(-0.709821\pi\) | ||
0.612464 | − | 0.790499i | \(-0.290179\pi\) | |||||||
\(6\) | − | 7.20495i | − | 2.94141i | ||||||
\(7\) | 0.740145i | 0.279748i | 0.990169 | + | 0.139874i | \(0.0446698\pi\) | ||||
−0.990169 | + | 0.139874i | \(0.955330\pi\) | |||||||
\(8\) | −3.42819 | −1.21205 | ||||||||
\(9\) | −6.49664 | −2.16555 | ||||||||
\(10\) | 8.26537i | 2.61374i | ||||||||
\(11\) | 0.0284320i | 0.00857258i | 0.999991 | + | 0.00428629i | \(0.00136437\pi\) | ||||
−0.999991 | + | 0.00428629i | \(0.998636\pi\) | |||||||
\(12\) | 10.6819i | 3.08361i | ||||||||
\(13\) | −6.23701 | −1.72983 | −0.864917 | − | 0.501915i | \(-0.832629\pi\) | ||||
−0.864917 | + | 0.501915i | \(0.832629\pi\) | |||||||
\(14\) | − | 1.73047i | − | 0.462486i | ||||||
\(15\) | 10.8943 | 2.81291 | ||||||||
\(16\) | 1.08257 | 0.270642 | ||||||||
\(17\) | 4.09808 | + | 0.453556i | 0.993931 | + | 0.110003i | ||||
\(18\) | 15.1892 | 3.58013 | ||||||||
\(19\) | 4.71182 | 1.08097 | 0.540483 | − | 0.841355i | \(-0.318241\pi\) | ||||
0.540483 | + | 0.841355i | \(0.318241\pi\) | |||||||
\(20\) | − | 12.2541i | − | 2.74010i | ||||||
\(21\) | −2.28088 | −0.497728 | ||||||||
\(22\) | − | 0.0664743i | − | 0.0141724i | ||||||
\(23\) | − | 0.160027i | − | 0.0333680i | −0.999861 | − | 0.0166840i | \(-0.994689\pi\) | ||
0.999861 | − | 0.0166840i | \(-0.00531093\pi\) | |||||||
\(24\) | − | 10.5645i | − | 2.15648i | ||||||
\(25\) | −7.49777 | −1.49955 | ||||||||
\(26\) | 14.5822 | 2.85980 | ||||||||
\(27\) | − | 10.7755i | − | 2.07374i | ||||||
\(28\) | 2.56555i | 0.484844i | ||||||||
\(29\) | − | 2.33996i | − | 0.434521i | −0.976114 | − | 0.217260i | \(-0.930288\pi\) | ||
0.976114 | − | 0.217260i | \(-0.0697120\pi\) | |||||||
\(30\) | −25.4711 | −4.65036 | ||||||||
\(31\) | − | 5.83878i | − | 1.04868i | −0.851510 | − | 0.524338i | \(-0.824313\pi\) | ||
0.851510 | − | 0.524338i | \(-0.175687\pi\) | |||||||
\(32\) | 4.32533 | 0.764617 | ||||||||
\(33\) | −0.0876179 | −0.0152523 | ||||||||
\(34\) | −9.58136 | − | 1.06042i | −1.64319 | − | 0.181860i | ||||
\(35\) | 2.61657 | 0.442282 | ||||||||
\(36\) | −22.5192 | −3.75320 | ||||||||
\(37\) | 1.79732i | 0.295477i | 0.989026 | + | 0.147739i | \(0.0471995\pi\) | ||||
−0.989026 | + | 0.147739i | \(0.952801\pi\) | |||||||
\(38\) | −11.0163 | −1.78708 | ||||||||
\(39\) | − | 19.2203i | − | 3.07772i | ||||||
\(40\) | 12.1194i | 1.91625i | ||||||||
\(41\) | − | 11.7697i | − | 1.83812i | −0.394116 | − | 0.919061i | \(-0.628949\pi\) | ||
0.394116 | − | 0.919061i | \(-0.371051\pi\) | |||||||
\(42\) | 5.33271 | 0.822855 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0.0985535i | 0.0148575i | ||||||||
\(45\) | 22.9671i | 3.42373i | ||||||||
\(46\) | 0.374145i | 0.0551647i | ||||||||
\(47\) | 6.13569 | 0.894983 | 0.447491 | − | 0.894288i | \(-0.352318\pi\) | ||||
0.447491 | + | 0.894288i | \(0.352318\pi\) | |||||||
\(48\) | 3.33611i | 0.481526i | ||||||||
\(49\) | 6.45219 | 0.921741 | ||||||||
\(50\) | 17.5298 | 2.47909 | ||||||||
\(51\) | −1.39771 | + | 12.6289i | −0.195718 | + | 1.76840i | ||||
\(52\) | −21.6193 | −2.99805 | ||||||||
\(53\) | 4.23655 | 0.581934 | 0.290967 | − | 0.956733i | \(-0.406023\pi\) | ||||
0.290967 | + | 0.956733i | \(0.406023\pi\) | |||||||
\(54\) | 25.1932i | 3.42836i | ||||||||
\(55\) | 0.100513 | 0.0135532 | ||||||||
\(56\) | − | 2.53736i | − | 0.339069i | ||||||
\(57\) | 14.5202i | 1.92325i | ||||||||
\(58\) | 5.47086i | 0.718359i | ||||||||
\(59\) | 12.6400 | 1.64558 | 0.822791 | − | 0.568344i | \(-0.192416\pi\) | ||||
0.822791 | + | 0.568344i | \(0.192416\pi\) | |||||||
\(60\) | 37.7629 | 4.87517 | ||||||||
\(61\) | − | 3.46012i | − | 0.443023i | −0.975158 | − | 0.221511i | \(-0.928901\pi\) | ||
0.975158 | − | 0.221511i | \(-0.0710990\pi\) | |||||||
\(62\) | 13.6511i | 1.73369i | ||||||||
\(63\) | − | 4.80846i | − | 0.605809i | ||||||
\(64\) | −12.2778 | −1.53472 | ||||||||
\(65\) | 22.0492i | 2.73486i | ||||||||
\(66\) | 0.204851 | 0.0252155 | ||||||||
\(67\) | 4.99453 | 0.610178 | 0.305089 | − | 0.952324i | \(-0.401314\pi\) | ||||
0.305089 | + | 0.952324i | \(0.401314\pi\) | |||||||
\(68\) | 14.2051 | + | 1.57215i | 1.72263 | + | 0.190652i | ||||
\(69\) | 0.493150 | 0.0593683 | ||||||||
\(70\) | −6.11757 | −0.731190 | ||||||||
\(71\) | − | 7.82497i | − | 0.928653i | −0.885664 | − | 0.464326i | \(-0.846296\pi\) | ||
0.885664 | − | 0.464326i | \(-0.153704\pi\) | |||||||
\(72\) | 22.2717 | 2.62475 | ||||||||
\(73\) | − | 10.4028i | − | 1.21756i | −0.793340 | − | 0.608778i | \(-0.791660\pi\) | ||
0.793340 | − | 0.608778i | \(-0.208340\pi\) | |||||||
\(74\) | − | 4.20215i | − | 0.488490i | ||||||
\(75\) | − | 23.1056i | − | 2.66800i | ||||||
\(76\) | 16.3325 | 1.87347 | ||||||||
\(77\) | −0.0210438 | −0.00239817 | ||||||||
\(78\) | 44.9374i | 5.08815i | ||||||||
\(79\) | 3.94100i | 0.443397i | 0.975115 | + | 0.221698i | \(0.0711600\pi\) | ||||
−0.975115 | + | 0.221698i | \(0.928840\pi\) | |||||||
\(80\) | − | 3.82711i | − | 0.427884i | ||||||
\(81\) | 13.7165 | 1.52405 | ||||||||
\(82\) | 27.5177i | 3.03882i | ||||||||
\(83\) | 8.01134 | 0.879359 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(84\) | −7.90617 | −0.862634 | ||||||||
\(85\) | 1.60342 | − | 14.4876i | 0.173915 | − | 1.57140i | ||||
\(86\) | −2.33801 | −0.252114 | ||||||||
\(87\) | 7.21098 | 0.773098 | ||||||||
\(88\) | − | 0.0974704i | − | 0.0103904i | ||||||
\(89\) | −5.50806 | −0.583853 | −0.291927 | − | 0.956441i | \(-0.594296\pi\) | ||||
−0.291927 | + | 0.956441i | \(0.594296\pi\) | |||||||
\(90\) | − | 53.6972i | − | 5.66018i | ||||||
\(91\) | − | 4.61629i | − | 0.483918i | ||||||
\(92\) | − | 0.554701i | − | 0.0578315i | ||||||
\(93\) | 17.9931 | 1.86580 | ||||||||
\(94\) | −14.3453 | −1.47961 | ||||||||
\(95\) | − | 16.6573i | − | 1.70901i | ||||||
\(96\) | 13.3292i | 1.36041i | ||||||||
\(97\) | 13.6758i | 1.38857i | 0.719700 | + | 0.694285i | \(0.244279\pi\) | ||||
−0.719700 | + | 0.694285i | \(0.755721\pi\) | |||||||
\(98\) | −15.0853 | −1.52384 | ||||||||
\(99\) | − | 0.184713i | − | 0.0185643i | ||||||
\(100\) | −25.9894 | −2.59894 | ||||||||
\(101\) | −6.19857 | −0.616781 | −0.308390 | − | 0.951260i | \(-0.599790\pi\) | ||||
−0.308390 | + | 0.951260i | \(0.599790\pi\) | |||||||
\(102\) | 3.26785 | − | 29.5265i | 0.323565 | − | 2.92356i | ||||
\(103\) | −17.1868 | −1.69347 | −0.846733 | − | 0.532018i | \(-0.821434\pi\) | ||||
−0.846733 | + | 0.532018i | \(0.821434\pi\) | |||||||
\(104\) | 21.3816 | 2.09664 | ||||||||
\(105\) | 8.06340i | 0.786907i | ||||||||
\(106\) | −9.90508 | −0.962067 | ||||||||
\(107\) | 5.41292i | 0.523287i | 0.965165 | + | 0.261644i | \(0.0842645\pi\) | ||||
−0.965165 | + | 0.261644i | \(0.915736\pi\) | |||||||
\(108\) | − | 37.3509i | − | 3.59409i | ||||||
\(109\) | 12.2793i | 1.17615i | 0.808807 | + | 0.588074i | \(0.200114\pi\) | ||||
−0.808807 | + | 0.588074i | \(0.799886\pi\) | |||||||
\(110\) | −0.235001 | −0.0224065 | ||||||||
\(111\) | −5.53873 | −0.525713 | ||||||||
\(112\) | 0.801257i | 0.0757117i | ||||||||
\(113\) | − | 14.1098i | − | 1.32734i | −0.748027 | − | 0.663668i | \(-0.768999\pi\) | ||
0.748027 | − | 0.663668i | \(-0.231001\pi\) | |||||||
\(114\) | − | 33.9485i | − | 3.17957i | ||||||
\(115\) | −0.565732 | −0.0527547 | ||||||||
\(116\) | − | 8.11099i | − | 0.753086i | ||||||
\(117\) | 40.5196 | 3.74604 | ||||||||
\(118\) | −29.5523 | −2.72051 | ||||||||
\(119\) | −0.335697 | + | 3.03318i | −0.0307733 | + | 0.278051i | ||||
\(120\) | −37.3479 | −3.40938 | ||||||||
\(121\) | 10.9992 | 0.999927 | ||||||||
\(122\) | 8.08979i | 0.732415i | ||||||||
\(123\) | 36.2703 | 3.27038 | ||||||||
\(124\) | − | 20.2389i | − | 1.81751i | ||||||
\(125\) | 8.83015i | 0.789793i | ||||||||
\(126\) | 11.2422i | 1.00154i | ||||||||
\(127\) | 2.88776 | 0.256248 | 0.128124 | − | 0.991758i | \(-0.459105\pi\) | ||||
0.128124 | + | 0.991758i | \(0.459105\pi\) | |||||||
\(128\) | 20.0549 | 1.77262 | ||||||||
\(129\) | 3.08166i | 0.271325i | ||||||||
\(130\) | − | 51.5512i | − | 4.52134i | ||||||
\(131\) | − | 4.11440i | − | 0.359477i | −0.983714 | − | 0.179738i | \(-0.942475\pi\) | ||
0.983714 | − | 0.179738i | \(-0.0575251\pi\) | |||||||
\(132\) | −0.303709 | −0.0264345 | ||||||||
\(133\) | 3.48743i | 0.302399i | ||||||||
\(134\) | −11.6772 | −1.00876 | ||||||||
\(135\) | −38.0937 | −3.27858 | ||||||||
\(136\) | −14.0490 | − | 1.55487i | −1.20469 | − | 0.133329i | ||||
\(137\) | 16.0702 | 1.37297 | 0.686487 | − | 0.727142i | \(-0.259152\pi\) | ||||
0.686487 | + | 0.727142i | \(0.259152\pi\) | |||||||
\(138\) | −1.15299 | −0.0981490 | ||||||||
\(139\) | − | 13.4527i | − | 1.14105i | −0.821282 | − | 0.570523i | \(-0.806741\pi\) | ||
0.821282 | − | 0.570523i | \(-0.193259\pi\) | |||||||
\(140\) | 9.06979 | 0.766537 | ||||||||
\(141\) | 18.9081i | 1.59235i | ||||||||
\(142\) | 18.2948i | 1.53527i | ||||||||
\(143\) | − | 0.177331i | − | 0.0148291i | ||||||
\(144\) | −7.03306 | −0.586088 | ||||||||
\(145\) | −8.27229 | −0.686976 | ||||||||
\(146\) | 24.3219i | 2.01289i | ||||||||
\(147\) | 19.8835i | 1.63996i | ||||||||
\(148\) | 6.23002i | 0.512105i | ||||||||
\(149\) | −15.6285 | −1.28033 | −0.640167 | − | 0.768236i | \(-0.721135\pi\) | ||||
−0.640167 | + | 0.768236i | \(0.721135\pi\) | |||||||
\(150\) | 54.0211i | 4.41080i | ||||||||
\(151\) | −16.6485 | −1.35484 | −0.677419 | − | 0.735597i | \(-0.736902\pi\) | ||||
−0.677419 | + | 0.735597i | \(0.736902\pi\) | |||||||
\(152\) | −16.1530 | −1.31018 | ||||||||
\(153\) | −26.6238 | − | 2.94659i | −2.15241 | − | 0.238218i | ||||
\(154\) | 0.0492006 | 0.00396470 | ||||||||
\(155\) | −20.6414 | −1.65795 | ||||||||
\(156\) | − | 66.6232i | − | 5.33413i | ||||||
\(157\) | 12.3538 | 0.985938 | 0.492969 | − | 0.870047i | \(-0.335912\pi\) | ||||
0.492969 | + | 0.870047i | \(0.335912\pi\) | |||||||
\(158\) | − | 9.21408i | − | 0.733033i | ||||||
\(159\) | 13.0556i | 1.03538i | ||||||||
\(160\) | − | 15.2910i | − | 1.20886i | ||||||
\(161\) | 0.118443 | 0.00933465 | ||||||||
\(162\) | −32.0692 | −2.51959 | ||||||||
\(163\) | − | 10.8178i | − | 0.847317i | −0.905822 | − | 0.423659i | \(-0.860746\pi\) | ||
0.905822 | − | 0.423659i | \(-0.139254\pi\) | |||||||
\(164\) | − | 40.7972i | − | 3.18573i | ||||||
\(165\) | 0.309748i | 0.0241139i | ||||||||
\(166\) | −18.7306 | −1.45377 | ||||||||
\(167\) | 23.8242i | 1.84357i | 0.387701 | + | 0.921785i | \(0.373269\pi\) | ||||
−0.387701 | + | 0.921785i | \(0.626731\pi\) | |||||||
\(168\) | 7.81928 | 0.603271 | ||||||||
\(169\) | 25.9003 | 1.99233 | ||||||||
\(170\) | −3.74881 | + | 33.8722i | −0.287520 | + | 2.59788i | ||||
\(171\) | −30.6110 | −2.34088 | ||||||||
\(172\) | 3.46629 | 0.264302 | ||||||||
\(173\) | 1.83963i | 0.139864i | 0.997552 | + | 0.0699321i | \(0.0222783\pi\) | ||||
−0.997552 | + | 0.0699321i | \(0.977722\pi\) | |||||||
\(174\) | −16.8593 | −1.27810 | ||||||||
\(175\) | − | 5.54943i | − | 0.419498i | ||||||
\(176\) | 0.0307796i | 0.00232010i | ||||||||
\(177\) | 38.9521i | 2.92782i | ||||||||
\(178\) | 12.8779 | 0.965239 | ||||||||
\(179\) | −9.36447 | −0.699933 | −0.349966 | − | 0.936762i | \(-0.613807\pi\) | ||||
−0.349966 | + | 0.936762i | \(0.613807\pi\) | |||||||
\(180\) | 79.6104i | 5.93381i | ||||||||
\(181\) | − | 18.7895i | − | 1.39661i | −0.715799 | − | 0.698306i | \(-0.753938\pi\) | ||
0.715799 | − | 0.698306i | \(-0.246062\pi\) | |||||||
\(182\) | 10.7929i | 0.800025i | ||||||||
\(183\) | 10.6629 | 0.788226 | ||||||||
\(184\) | 0.548604i | 0.0404436i | ||||||||
\(185\) | 6.35392 | 0.467149 | ||||||||
\(186\) | −42.0681 | −3.08459 | ||||||||
\(187\) | −0.0128955 | + | 0.116517i | −0.000943013 | + | 0.00852055i | ||||
\(188\) | 21.2681 | 1.55113 | ||||||||
\(189\) | 7.97541 | 0.580126 | ||||||||
\(190\) | 38.9450i | 2.82537i | ||||||||
\(191\) | −9.59380 | −0.694183 | −0.347092 | − | 0.937831i | \(-0.612831\pi\) | ||||
−0.347092 | + | 0.937831i | \(0.612831\pi\) | |||||||
\(192\) | − | 37.8360i | − | 2.73058i | ||||||
\(193\) | − | 3.84327i | − | 0.276645i | −0.990387 | − | 0.138322i | \(-0.955829\pi\) | ||
0.990387 | − | 0.138322i | \(-0.0441710\pi\) | |||||||
\(194\) | − | 31.9742i | − | 2.29561i | ||||||
\(195\) | −67.9481 | −4.86587 | ||||||||
\(196\) | 22.3651 | 1.59751 | ||||||||
\(197\) | − | 9.10325i | − | 0.648580i | −0.945958 | − | 0.324290i | \(-0.894875\pi\) | ||
0.945958 | − | 0.324290i | \(-0.105125\pi\) | |||||||
\(198\) | 0.431860i | 0.0306910i | ||||||||
\(199\) | − | 23.0246i | − | 1.63217i | −0.577931 | − | 0.816085i | \(-0.696140\pi\) | ||
0.577931 | − | 0.816085i | \(-0.303860\pi\) | |||||||
\(200\) | 25.7038 | 1.81753 | ||||||||
\(201\) | 15.3914i | 1.08563i | ||||||||
\(202\) | 14.4923 | 1.01968 | ||||||||
\(203\) | 1.73191 | 0.121556 | ||||||||
\(204\) | −4.84485 | + | 43.7754i | −0.339207 | + | 3.06489i | ||||
\(205\) | −41.6085 | −2.90607 | ||||||||
\(206\) | 40.1829 | 2.79968 | ||||||||
\(207\) | 1.03964i | 0.0722600i | ||||||||
\(208\) | −6.75198 | −0.468166 | ||||||||
\(209\) | 0.133967i | 0.00926667i | ||||||||
\(210\) | − | 18.8523i | − | 1.30093i | ||||||
\(211\) | 23.6068i | 1.62516i | 0.582849 | + | 0.812581i | \(0.301938\pi\) | ||||
−0.582849 | + | 0.812581i | \(0.698062\pi\) | |||||||
\(212\) | 14.6851 | 1.00858 | ||||||||
\(213\) | 24.1139 | 1.65226 | ||||||||
\(214\) | − | 12.6555i | − | 0.865110i | ||||||
\(215\) | − | 3.53522i | − | 0.241100i | ||||||
\(216\) | 36.9404i | 2.51348i | ||||||||
\(217\) | 4.32154 | 0.293365 | ||||||||
\(218\) | − | 28.7092i | − | 1.94443i | ||||||
\(219\) | 32.0579 | 2.16627 | ||||||||
\(220\) | 0.348408 | 0.0234897 | ||||||||
\(221\) | −25.5598 | − | 2.82883i | −1.71934 | − | 0.190288i | ||||
\(222\) | 12.9496 | 0.869121 | ||||||||
\(223\) | −8.36153 | −0.559930 | −0.279965 | − | 0.960010i | \(-0.590323\pi\) | ||||
−0.279965 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(224\) | 3.20137i | 0.213900i | ||||||||
\(225\) | 48.7103 | 3.24736 | ||||||||
\(226\) | 32.9888i | 2.19438i | ||||||||
\(227\) | − | 20.8368i | − | 1.38298i | −0.722384 | − | 0.691492i | \(-0.756954\pi\) | ||
0.722384 | − | 0.691492i | \(-0.243046\pi\) | |||||||
\(228\) | 50.3313i | 3.33327i | ||||||||
\(229\) | 18.1669 | 1.20050 | 0.600252 | − | 0.799811i | \(-0.295067\pi\) | ||||
0.600252 | + | 0.799811i | \(0.295067\pi\) | |||||||
\(230\) | 1.32269 | 0.0872153 | ||||||||
\(231\) | − | 0.0648499i | − | 0.00426681i | ||||||
\(232\) | 8.02184i | 0.526660i | ||||||||
\(233\) | − | 16.1982i | − | 1.06118i | −0.847628 | − | 0.530590i | \(-0.821970\pi\) | ||
0.847628 | − | 0.530590i | \(-0.178030\pi\) | |||||||
\(234\) | −94.7352 | −6.19304 | ||||||||
\(235\) | − | 21.6910i | − | 1.41497i | ||||||
\(236\) | 43.8137 | 2.85203 | ||||||||
\(237\) | −12.1448 | −0.788891 | ||||||||
\(238\) | 0.784862 | − | 7.09159i | 0.0508751 | − | 0.459680i | ||||
\(239\) | 3.56099 | 0.230342 | 0.115171 | − | 0.993346i | \(-0.463258\pi\) | ||||
0.115171 | + | 0.993346i | \(0.463258\pi\) | |||||||
\(240\) | 11.7939 | 0.761291 | ||||||||
\(241\) | 3.98278i | 0.256553i | 0.991738 | + | 0.128277i | \(0.0409445\pi\) | ||||
−0.991738 | + | 0.128277i | \(0.959055\pi\) | |||||||
\(242\) | −25.7162 | −1.65310 | ||||||||
\(243\) | 9.94305i | 0.637847i | ||||||||
\(244\) | − | 11.9938i | − | 0.767822i | ||||||
\(245\) | − | 22.8099i | − | 1.45727i | ||||||
\(246\) | −84.8003 | −5.40667 | ||||||||
\(247\) | −29.3877 | −1.86989 | ||||||||
\(248\) | 20.0164i | 1.27105i | ||||||||
\(249\) | 24.6882i | 1.56455i | ||||||||
\(250\) | − | 20.6450i | − | 1.30570i | ||||||
\(251\) | 24.1344 | 1.52335 | 0.761676 | − | 0.647958i | \(-0.224377\pi\) | ||||
0.761676 | + | 0.647958i | \(0.224377\pi\) | |||||||
\(252\) | − | 16.6675i | − | 1.04995i | ||||||
\(253\) | 0.00454990 | 0.000286050 | ||||||||
\(254\) | −6.75162 | −0.423634 | ||||||||
\(255\) | 44.6460 | + | 4.94119i | 2.79584 | + | 0.309429i | ||||
\(256\) | −22.3330 | −1.39581 | ||||||||
\(257\) | −20.7034 | −1.29144 | −0.645720 | − | 0.763574i | \(-0.723443\pi\) | ||||
−0.645720 | + | 0.763574i | \(0.723443\pi\) | |||||||
\(258\) | − | 7.20495i | − | 0.448561i | ||||||
\(259\) | −1.33028 | −0.0826594 | ||||||||
\(260\) | 76.4288i | 4.73991i | ||||||||
\(261\) | 15.2019i | 0.940975i | ||||||||
\(262\) | 9.61950i | 0.594295i | ||||||||
\(263\) | 0.500679 | 0.0308732 | 0.0154366 | − | 0.999881i | \(-0.495086\pi\) | ||||
0.0154366 | + | 0.999881i | \(0.495086\pi\) | |||||||
\(264\) | 0.300371 | 0.0184865 | ||||||||
\(265\) | − | 14.9771i | − | 0.920037i | ||||||
\(266\) | − | 8.15365i | − | 0.499932i | ||||||
\(267\) | − | 16.9740i | − | 1.03879i | ||||||
\(268\) | 17.3125 | 1.05753 | ||||||||
\(269\) | − | 13.4633i | − | 0.820873i | −0.911889 | − | 0.410437i | \(-0.865376\pi\) | ||
0.911889 | − | 0.410437i | \(-0.134624\pi\) | |||||||
\(270\) | 89.0633 | 5.42022 | ||||||||
\(271\) | −12.7952 | −0.777253 | −0.388626 | − | 0.921395i | \(-0.627050\pi\) | ||||
−0.388626 | + | 0.921395i | \(0.627050\pi\) | |||||||
\(272\) | 4.43645 | + | 0.491005i | 0.269000 | + | 0.0297715i | ||||
\(273\) | 14.2258 | 0.860987 | ||||||||
\(274\) | −37.5724 | −2.26983 | ||||||||
\(275\) | − | 0.213177i | − | 0.0128550i | ||||||
\(276\) | 1.70940 | 0.102894 | ||||||||
\(277\) | 7.42987i | 0.446418i | 0.974771 | + | 0.223209i | \(0.0716532\pi\) | ||||
−0.974771 | + | 0.223209i | \(0.928347\pi\) | |||||||
\(278\) | 31.4526i | 1.88640i | ||||||||
\(279\) | 37.9325i | 2.27096i | ||||||||
\(280\) | −8.97011 | −0.536067 | ||||||||
\(281\) | 0.280317 | 0.0167223 | 0.00836115 | − | 0.999965i | \(-0.497339\pi\) | ||||
0.00836115 | + | 0.999965i | \(0.497339\pi\) | |||||||
\(282\) | − | 44.2074i | − | 2.63251i | ||||||
\(283\) | 17.5709i | 1.04448i | 0.852798 | + | 0.522240i | \(0.174904\pi\) | ||||
−0.852798 | + | 0.522240i | \(0.825096\pi\) | |||||||
\(284\) | − | 27.1236i | − | 1.60949i | ||||||
\(285\) | 51.3323 | 3.04066 | ||||||||
\(286\) | 0.414601i | 0.0245159i | ||||||||
\(287\) | 8.71130 | 0.514212 | ||||||||
\(288\) | −28.1001 | −1.65581 | ||||||||
\(289\) | 16.5886 | + | 3.71742i | 0.975799 | + | 0.218672i | ||||
\(290\) | 19.3407 | 1.13572 | ||||||||
\(291\) | −42.1443 | −2.47054 | ||||||||
\(292\) | − | 36.0591i | − | 2.11020i | ||||||
\(293\) | −6.68485 | −0.390533 | −0.195267 | − | 0.980750i | \(-0.562557\pi\) | ||||
−0.195267 | + | 0.980750i | \(0.562557\pi\) | |||||||
\(294\) | − | 46.4877i | − | 2.71122i | ||||||
\(295\) | − | 44.6850i | − | 2.60166i | ||||||
\(296\) | − | 6.16155i | − | 0.358133i | ||||||
\(297\) | 0.306369 | 0.0177773 | ||||||||
\(298\) | 36.5395 | 2.11668 | ||||||||
\(299\) | 0.998092i | 0.0577211i | ||||||||
\(300\) | − | 80.0906i | − | 4.62403i | ||||||
\(301\) | 0.740145i | 0.0426612i | ||||||||
\(302\) | 38.9244 | 2.23985 | ||||||||
\(303\) | − | 19.1019i | − | 1.09738i | ||||||
\(304\) | 5.10087 | 0.292555 | ||||||||
\(305\) | −12.2323 | −0.700418 | ||||||||
\(306\) | 62.2467 | + | 6.88915i | 3.55840 | + | 0.393827i | ||||
\(307\) | 16.1286 | 0.920506 | 0.460253 | − | 0.887788i | \(-0.347759\pi\) | ||||
0.460253 | + | 0.887788i | \(0.347759\pi\) | |||||||
\(308\) | −0.0729439 | −0.00415636 | ||||||||
\(309\) | − | 52.9639i | − | 3.01301i | ||||||
\(310\) | 48.2597 | 2.74097 | ||||||||
\(311\) | − | 12.0595i | − | 0.683831i | −0.939731 | − | 0.341916i | \(-0.888924\pi\) | ||
0.939731 | − | 0.341916i | \(-0.111076\pi\) | |||||||
\(312\) | 65.8910i | 3.73034i | ||||||||
\(313\) | 28.1473i | 1.59098i | 0.605966 | + | 0.795490i | \(0.292787\pi\) | ||||
−0.605966 | + | 0.795490i | \(0.707213\pi\) | |||||||
\(314\) | −28.8832 | −1.62997 | ||||||||
\(315\) | −16.9989 | −0.957782 | ||||||||
\(316\) | 13.6606i | 0.768470i | ||||||||
\(317\) | − | 24.1025i | − | 1.35373i | −0.736107 | − | 0.676865i | \(-0.763338\pi\) | ||
0.736107 | − | 0.676865i | \(-0.236662\pi\) | |||||||
\(318\) | − | 30.5241i | − | 1.71171i | ||||||
\(319\) | 0.0665299 | 0.00372496 | ||||||||
\(320\) | 43.4047i | 2.42639i | ||||||||
\(321\) | −16.6808 | −0.931032 | ||||||||
\(322\) | −0.276922 | −0.0154322 | ||||||||
\(323\) | 19.3094 | + | 2.13707i | 1.07441 | + | 0.118910i | ||||
\(324\) | 47.5452 | 2.64140 | ||||||||
\(325\) | 46.7636 | 2.59398 | ||||||||
\(326\) | 25.2922i | 1.40080i | ||||||||
\(327\) | −37.8408 | −2.09260 | ||||||||
\(328\) | 40.3488i | 2.22789i | ||||||||
\(329\) | 4.54130i | 0.250370i | ||||||||
\(330\) | − | 0.724195i | − | 0.0398656i | ||||||
\(331\) | 2.10977 | 0.115964 | 0.0579818 | − | 0.998318i | \(-0.481533\pi\) | ||||
0.0579818 | + | 0.998318i | \(0.481533\pi\) | |||||||
\(332\) | 27.7696 | 1.52405 | ||||||||
\(333\) | − | 11.6765i | − | 0.639871i | ||||||
\(334\) | − | 55.7011i | − | 3.04783i | ||||||
\(335\) | − | 17.6567i | − | 0.964691i | ||||||
\(336\) | −2.46920 | −0.134706 | ||||||||
\(337\) | 25.7371i | 1.40199i | 0.713165 | + | 0.700996i | \(0.247261\pi\) | ||||
−0.713165 | + | 0.700996i | \(0.752739\pi\) | |||||||
\(338\) | −60.5550 | −3.29376 | ||||||||
\(339\) | 43.4816 | 2.36159 | ||||||||
\(340\) | 5.55791 | − | 50.2182i | 0.301420 | − | 2.72347i | ||||
\(341\) | 0.166008 | 0.00898985 | ||||||||
\(342\) | 71.5689 | 3.87000 | ||||||||
\(343\) | 9.95657i | 0.537604i | ||||||||
\(344\) | −3.42819 | −0.184836 | ||||||||
\(345\) | − | 1.74339i | − | 0.0938612i | ||||||
\(346\) | − | 4.30106i | − | 0.231227i | ||||||
\(347\) | − | 20.9754i | − | 1.12602i | −0.826451 | − | 0.563009i | \(-0.809644\pi\) | ||
0.826451 | − | 0.563009i | \(-0.190356\pi\) | |||||||
\(348\) | 24.9953 | 1.33989 | ||||||||
\(349\) | 7.92514 | 0.424223 | 0.212112 | − | 0.977245i | \(-0.431966\pi\) | ||||
0.212112 | + | 0.977245i | \(0.431966\pi\) | |||||||
\(350\) | 12.9746i | 0.693523i | ||||||||
\(351\) | 67.2067i | 3.58723i | ||||||||
\(352\) | 0.122978i | 0.00655474i | ||||||||
\(353\) | −28.9441 | −1.54054 | −0.770269 | − | 0.637720i | \(-0.779878\pi\) | ||||
−0.770269 | + | 0.637720i | \(0.779878\pi\) | |||||||
\(354\) | − | 91.0703i | − | 4.84033i | ||||||
\(355\) | −27.6630 | −1.46820 | ||||||||
\(356\) | −19.0925 | −1.01190 | ||||||||
\(357\) | −9.34722 | − | 1.03450i | −0.494707 | − | 0.0547518i | ||||
\(358\) | 21.8942 | 1.15714 | ||||||||
\(359\) | −7.44895 | −0.393141 | −0.196570 | − | 0.980490i | \(-0.562980\pi\) | ||||
−0.196570 | + | 0.980490i | \(0.562980\pi\) | |||||||
\(360\) | − | 78.7354i | − | 4.14972i | ||||||
\(361\) | 3.20128 | 0.168488 | ||||||||
\(362\) | 43.9300i | 2.30891i | ||||||||
\(363\) | 33.8958i | 1.77907i | ||||||||
\(364\) | − | 16.0014i | − | 0.838700i | ||||||
\(365\) | −36.7762 | −1.92495 | ||||||||
\(366\) | −24.9300 | −1.30311 | ||||||||
\(367\) | − | 33.9690i | − | 1.77317i | −0.462567 | − | 0.886584i | \(-0.653072\pi\) | ||
0.462567 | − | 0.886584i | \(-0.346928\pi\) | |||||||
\(368\) | − | 0.173240i | − | 0.00903078i | ||||||
\(369\) | 76.4637i | 3.98054i | ||||||||
\(370\) | −14.8555 | −0.772301 | ||||||||
\(371\) | 3.13566i | 0.162795i | ||||||||
\(372\) | 62.3694 | 3.23370 | ||||||||
\(373\) | −21.6025 | −1.11853 | −0.559267 | − | 0.828988i | \(-0.688917\pi\) | ||||
−0.559267 | + | 0.828988i | \(0.688917\pi\) | |||||||
\(374\) | 0.0301498 | − | 0.272417i | 0.00155901 | − | 0.0140864i | ||||
\(375\) | −27.2115 | −1.40520 | ||||||||
\(376\) | −21.0343 | −1.08476 | ||||||||
\(377\) | 14.5944i | 0.751649i | ||||||||
\(378\) | −18.6466 | −0.959077 | ||||||||
\(379\) | 11.1463i | 0.572549i | 0.958148 | + | 0.286275i | \(0.0924170\pi\) | ||||
−0.958148 | + | 0.286275i | \(0.907583\pi\) | |||||||
\(380\) | − | 57.7391i | − | 2.96195i | ||||||
\(381\) | 8.89911i | 0.455915i | ||||||||
\(382\) | 22.4304 | 1.14764 | ||||||||
\(383\) | 11.5891 | 0.592177 | 0.296088 | − | 0.955161i | \(-0.404318\pi\) | ||||
0.296088 | + | 0.955161i | \(0.404318\pi\) | |||||||
\(384\) | 61.8025i | 3.15385i | ||||||||
\(385\) | 0.0743945i | 0.00379149i | ||||||||
\(386\) | 8.98560i | 0.457355i | ||||||||
\(387\) | −6.49664 | −0.330243 | ||||||||
\(388\) | 47.4043i | 2.40659i | ||||||||
\(389\) | 3.94673 | 0.200107 | 0.100054 | − | 0.994982i | \(-0.468099\pi\) | ||||
0.100054 | + | 0.994982i | \(0.468099\pi\) | |||||||
\(390\) | 158.863 | 8.04436 | ||||||||
\(391\) | 0.0725813 | − | 0.655805i | 0.00367059 | − | 0.0331655i | ||||
\(392\) | −22.1193 | −1.11719 | ||||||||
\(393\) | 12.6792 | 0.639580 | ||||||||
\(394\) | 21.2835i | 1.07225i | ||||||||
\(395\) | 13.9323 | 0.701009 | ||||||||
\(396\) | − | 0.640267i | − | 0.0321746i | ||||||
\(397\) | 28.5059i | 1.43067i | 0.698782 | + | 0.715335i | \(0.253726\pi\) | ||||
−0.698782 | + | 0.715335i | \(0.746274\pi\) | |||||||
\(398\) | 53.8317i | 2.69834i | ||||||||
\(399\) | −10.7471 | −0.538027 | ||||||||
\(400\) | −8.11684 | −0.405842 | ||||||||
\(401\) | − | 21.5476i | − | 1.07604i | −0.842933 | − | 0.538019i | \(-0.819173\pi\) | ||
0.842933 | − | 0.538019i | \(-0.180827\pi\) | |||||||
\(402\) | − | 35.9853i | − | 1.79479i | ||||||
\(403\) | 36.4165i | 1.81404i | ||||||||
\(404\) | −21.4860 | −1.06897 | ||||||||
\(405\) | − | 48.4907i | − | 2.40952i | ||||||
\(406\) | −4.04923 | −0.200960 | ||||||||
\(407\) | −0.0511014 | −0.00253300 | ||||||||
\(408\) | 4.79160 | − | 43.2943i | 0.237220 | − | 2.14339i | ||||
\(409\) | 4.93591 | 0.244065 | 0.122033 | − | 0.992526i | \(-0.461059\pi\) | ||||
0.122033 | + | 0.992526i | \(0.461059\pi\) | |||||||
\(410\) | 97.2811 | 4.80437 | ||||||||
\(411\) | 49.5231i | 2.44279i | ||||||||
\(412\) | −59.5744 | −2.93502 | ||||||||
\(413\) | 9.35540i | 0.460349i | ||||||||
\(414\) | − | 2.43069i | − | 0.119462i | ||||||
\(415\) | − | 28.3218i | − | 1.39026i | ||||||
\(416\) | −26.9771 | −1.32266 | ||||||||
\(417\) | 41.4568 | 2.03015 | ||||||||
\(418\) | − | 0.313215i | − | 0.0153199i | ||||||
\(419\) | 19.1063i | 0.933403i | 0.884415 | + | 0.466701i | \(0.154558\pi\) | ||||
−0.884415 | + | 0.466701i | \(0.845442\pi\) | |||||||
\(420\) | 27.9500i | 1.36382i | ||||||||
\(421\) | −12.5866 | −0.613433 | −0.306716 | − | 0.951801i | \(-0.599230\pi\) | ||||
−0.306716 | + | 0.951801i | \(0.599230\pi\) | |||||||
\(422\) | − | 55.1930i | − | 2.68675i | ||||||
\(423\) | −39.8614 | −1.93813 | ||||||||
\(424\) | −14.5237 | −0.705333 | ||||||||
\(425\) | −30.7265 | − | 3.40065i | −1.49045 | − | 0.164956i | ||||
\(426\) | −56.3785 | −2.73155 | ||||||||
\(427\) | 2.56099 | 0.123935 | ||||||||
\(428\) | 18.7627i | 0.906932i | ||||||||
\(429\) | 0.546473 | 0.0263840 | ||||||||
\(430\) | 8.26537i | 0.398592i | ||||||||
\(431\) | 7.68277i | 0.370066i | 0.982732 | + | 0.185033i | \(0.0592392\pi\) | ||||
−0.982732 | + | 0.185033i | \(0.940761\pi\) | |||||||
\(432\) | − | 11.6652i | − | 0.561242i | ||||||
\(433\) | −9.31844 | −0.447816 | −0.223908 | − | 0.974610i | \(-0.571881\pi\) | ||||
−0.223908 | + | 0.974610i | \(0.571881\pi\) | |||||||
\(434\) | −10.1038 | −0.484998 | ||||||||
\(435\) | − | 25.4924i | − | 1.22227i | ||||||
\(436\) | 42.5637i | 2.03843i | ||||||||
\(437\) | − | 0.754021i | − | 0.0360697i | ||||||
\(438\) | −74.9518 | −3.58133 | ||||||||
\(439\) | 13.6524i | 0.651592i | 0.945440 | + | 0.325796i | \(0.105632\pi\) | ||||
−0.945440 | + | 0.325796i | \(0.894368\pi\) | |||||||
\(440\) | −0.344579 | −0.0164272 | ||||||||
\(441\) | −41.9176 | −1.99607 | ||||||||
\(442\) | 59.7590 | + | 6.61383i | 2.84244 | + | 0.314588i | ||||
\(443\) | −11.1088 | −0.527794 | −0.263897 | − | 0.964551i | \(-0.585008\pi\) | ||||
−0.263897 | + | 0.964551i | \(0.585008\pi\) | |||||||
\(444\) | −19.1988 | −0.911136 | ||||||||
\(445\) | 19.4722i | 0.923071i | ||||||||
\(446\) | 19.5493 | 0.925688 | ||||||||
\(447\) | − | 48.1617i | − | 2.27797i | ||||||
\(448\) | − | 9.08734i | − | 0.429337i | ||||||
\(449\) | − | 6.26601i | − | 0.295711i | −0.989009 | − | 0.147856i | \(-0.952763\pi\) | ||
0.989009 | − | 0.147856i | \(-0.0472371\pi\) | |||||||
\(450\) | −113.885 | −5.36860 | ||||||||
\(451\) | 0.334637 | 0.0157574 | ||||||||
\(452\) | − | 48.9085i | − | 2.30046i | ||||||
\(453\) | − | 51.3052i | − | 2.41053i | ||||||
\(454\) | 48.7165i | 2.28638i | ||||||||
\(455\) | −16.3196 | −0.765074 | ||||||||
\(456\) | − | 49.7782i | − | 2.33108i | ||||||
\(457\) | −31.9074 | −1.49257 | −0.746283 | − | 0.665628i | \(-0.768164\pi\) | ||||
−0.746283 | + | 0.665628i | \(0.768164\pi\) | |||||||
\(458\) | −42.4744 | −1.98470 | ||||||||
\(459\) | 4.88728 | − | 44.1588i | 0.228119 | − | 2.06116i | ||||
\(460\) | −1.96099 | −0.0914315 | ||||||||
\(461\) | 15.2512 | 0.710318 | 0.355159 | − | 0.934806i | \(-0.384427\pi\) | ||||
0.355159 | + | 0.934806i | \(0.384427\pi\) | |||||||
\(462\) | 0.151620i | 0.00705399i | ||||||||
\(463\) | 41.8252 | 1.94378 | 0.971891 | − | 0.235432i | \(-0.0756506\pi\) | ||||
0.971891 | + | 0.235432i | \(0.0756506\pi\) | |||||||
\(464\) | − | 2.53317i | − | 0.117600i | ||||||
\(465\) | − | 63.6097i | − | 2.94983i | ||||||
\(466\) | 37.8716i | 1.75437i | ||||||||
\(467\) | 23.4463 | 1.08496 | 0.542482 | − | 0.840067i | \(-0.317485\pi\) | ||||
0.542482 | + | 0.840067i | \(0.317485\pi\) | |||||||
\(468\) | 140.453 | 6.49242 | ||||||||
\(469\) | 3.69667i | 0.170696i | ||||||||
\(470\) | 50.7138i | 2.33925i | ||||||||
\(471\) | 38.0701i | 1.75418i | ||||||||
\(472\) | −43.3322 | −1.99453 | ||||||||
\(473\) | 0.0284320i | 0.00130731i | ||||||||
\(474\) | 28.3947 | 1.30421 | ||||||||
\(475\) | −35.3282 | −1.62097 | ||||||||
\(476\) | −1.16362 | + | 10.5139i | −0.0533345 | + | 0.481902i | ||||
\(477\) | −27.5233 | −1.26021 | ||||||||
\(478\) | −8.32564 | −0.380806 | ||||||||
\(479\) | 10.4477i | 0.477369i | 0.971097 | + | 0.238684i | \(0.0767161\pi\) | ||||
−0.971097 | + | 0.238684i | \(0.923284\pi\) | |||||||
\(480\) | 47.1216 | 2.15080 | ||||||||
\(481\) | − | 11.2099i | − | 0.511127i | ||||||
\(482\) | − | 9.31177i | − | 0.424140i | ||||||
\(483\) | 0.365003i | 0.0166082i | ||||||||
\(484\) | 38.1263 | 1.73302 | ||||||||
\(485\) | 48.3470 | 2.19533 | ||||||||
\(486\) | − | 23.2469i | − | 1.05450i | ||||||
\(487\) | 6.19164i | 0.280570i | 0.990111 | + | 0.140285i | \(0.0448019\pi\) | ||||
−0.990111 | + | 0.140285i | \(0.955198\pi\) | |||||||
\(488\) | 11.8619i | 0.536965i | ||||||||
\(489\) | 33.3369 | 1.50755 | ||||||||
\(490\) | 53.3297i | 2.40919i | ||||||||
\(491\) | 0.704438 | 0.0317908 | 0.0158954 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158954 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(492\) | 125.723 | 5.66804 | ||||||||
\(493\) | 1.06130 | − | 9.58937i | 0.0477987 | − | 0.431883i | ||||
\(494\) | 68.7086 | 3.09135 | ||||||||
\(495\) | −0.653000 | −0.0293502 | ||||||||
\(496\) | − | 6.32088i | − | 0.283816i | ||||||
\(497\) | 5.79161 | 0.259789 | ||||||||
\(498\) | − | 57.7213i | − | 2.58655i | ||||||
\(499\) | 1.40530i | 0.0629100i | 0.999505 | + | 0.0314550i | \(0.0100141\pi\) | ||||
−0.999505 | + | 0.0314550i | \(0.989986\pi\) | |||||||
\(500\) | 30.6078i | 1.36882i | ||||||||
\(501\) | −73.4181 | −3.28008 | ||||||||
\(502\) | −56.4265 | −2.51844 | ||||||||
\(503\) | − | 32.2080i | − | 1.43609i | −0.695999 | − | 0.718043i | \(-0.745038\pi\) | ||
0.695999 | − | 0.718043i | \(-0.254962\pi\) | |||||||
\(504\) | 16.4843i | 0.734269i | ||||||||
\(505\) | 21.9133i | 0.975129i | ||||||||
\(506\) | −0.0106377 | −0.000472904 | ||||||||
\(507\) | 79.8158i | 3.54475i | ||||||||
\(508\) | 10.0098 | 0.444114 | ||||||||
\(509\) | −8.34894 | −0.370060 | −0.185030 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185030 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(510\) | −104.383 | − | 11.5526i | −4.62214 | − | 0.511556i | ||||
\(511\) | 7.69958 | 0.340610 | ||||||||
\(512\) | 12.1050 | 0.534969 | ||||||||
\(513\) | − | 50.7721i | − | 2.24165i | ||||||
\(514\) | 48.4047 | 2.13504 | ||||||||
\(515\) | 60.7591i | 2.67737i | ||||||||
\(516\) | 10.6819i | 0.470246i | ||||||||
\(517\) | 0.174450i | 0.00767231i | ||||||||
\(518\) | 3.11020 | 0.136654 | ||||||||
\(519\) | −5.66911 | −0.248846 | ||||||||
\(520\) | − | 75.5888i | − | 3.31479i | ||||||
\(521\) | 1.54030i | 0.0674818i | 0.999431 | + | 0.0337409i | \(0.0107421\pi\) | ||||
−0.999431 | + | 0.0337409i | \(0.989258\pi\) | |||||||
\(522\) | − | 35.5422i | − | 1.55564i | ||||||
\(523\) | 18.3697 | 0.803253 | 0.401626 | − | 0.915804i | \(-0.368445\pi\) | ||||
0.401626 | + | 0.915804i | \(0.368445\pi\) | |||||||
\(524\) | − | 14.2617i | − | 0.623024i | ||||||
\(525\) | 17.1015 | 0.746370 | ||||||||
\(526\) | −1.17059 | −0.0510403 | ||||||||
\(527\) | 2.64821 | − | 23.9278i | 0.115358 | − | 1.04231i | ||||
\(528\) | −0.0948523 | −0.00412792 | ||||||||
\(529\) | 22.9744 | 0.998887 | ||||||||
\(530\) | 35.0166i | 1.52103i | ||||||||
\(531\) | −82.1173 | −3.56359 | ||||||||
\(532\) | 12.0884i | 0.524100i | ||||||||
\(533\) | 73.4078i | 3.17965i | ||||||||
\(534\) | 39.6853i | 1.71735i | ||||||||
\(535\) | 19.1359 | 0.827316 | ||||||||
\(536\) | −17.1222 | −0.739566 | ||||||||
\(537\) | − | 28.8581i | − | 1.24532i | ||||||
\(538\) | 31.4774i | 1.35709i | ||||||||
\(539\) | 0.183449i | 0.00790169i | ||||||||
\(540\) | −132.044 | −5.68225 | ||||||||
\(541\) | 27.4232i | 1.17901i | 0.807763 | + | 0.589507i | \(0.200678\pi\) | ||||
−0.807763 | + | 0.589507i | \(0.799322\pi\) | |||||||
\(542\) | 29.9153 | 1.28497 | ||||||||
\(543\) | 57.9029 | 2.48485 | ||||||||
\(544\) | 17.7256 | + | 1.96178i | 0.759977 | + | 0.0841105i | ||||
\(545\) | 43.4102 | 1.85949 | ||||||||
\(546\) | −33.2601 | −1.42340 | ||||||||
\(547\) | − | 2.44485i | − | 0.104534i | −0.998633 | − | 0.0522672i | \(-0.983355\pi\) | ||
0.998633 | − | 0.0522672i | \(-0.0166448\pi\) | |||||||
\(548\) | 55.7041 | 2.37956 | ||||||||
\(549\) | 22.4792i | 0.959387i | ||||||||
\(550\) | 0.498409i | 0.0212522i | ||||||||
\(551\) | − | 11.0255i | − | 0.469702i | ||||||
\(552\) | −1.69061 | −0.0719573 | ||||||||
\(553\) | −2.91691 | −0.124040 | ||||||||
\(554\) | − | 17.3711i | − | 0.738028i | ||||||
\(555\) | 19.5806i | 0.831151i | ||||||||
\(556\) | − | 46.6310i | − | 1.97760i | ||||||
\(557\) | −23.3813 | −0.990698 | −0.495349 | − | 0.868694i | \(-0.664960\pi\) | ||||
−0.495349 | + | 0.868694i | \(0.664960\pi\) | |||||||
\(558\) | − | 88.6865i | − | 3.75440i | ||||||
\(559\) | −6.23701 | −0.263797 | ||||||||
\(560\) | 2.83262 | 0.119700 | ||||||||
\(561\) | −0.359065 | − | 0.0397396i | −0.0151598 | − | 0.00167781i | ||||
\(562\) | −0.655383 | −0.0276457 | ||||||||
\(563\) | −18.6416 | −0.785648 | −0.392824 | − | 0.919614i | \(-0.628502\pi\) | ||||
−0.392824 | + | 0.919614i | \(0.628502\pi\) | |||||||
\(564\) | 65.5410i | 2.75977i | ||||||||
\(565\) | −49.8811 | −2.09852 | ||||||||
\(566\) | − | 41.0809i | − | 1.72676i | ||||||
\(567\) | 10.1522i | 0.426351i | ||||||||
\(568\) | 26.8255i | 1.12557i | ||||||||
\(569\) | −7.73787 | −0.324389 | −0.162194 | − | 0.986759i | \(-0.551857\pi\) | ||||
−0.162194 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(570\) | −120.015 | −5.02689 | ||||||||
\(571\) | 32.1225i | 1.34429i | 0.740421 | + | 0.672143i | \(0.234626\pi\) | ||||
−0.740421 | + | 0.672143i | \(0.765374\pi\) | |||||||
\(572\) | − | 0.614679i | − | 0.0257010i | ||||||
\(573\) | − | 29.5649i | − | 1.23509i | ||||||
\(574\) | −20.3671 | −0.850106 | ||||||||
\(575\) | 1.19985i | 0.0500371i | ||||||||
\(576\) | 79.7644 | 3.32352 | ||||||||
\(577\) | −27.5133 | −1.14539 | −0.572696 | − | 0.819768i | \(-0.694102\pi\) | ||||
−0.572696 | + | 0.819768i | \(0.694102\pi\) | |||||||
\(578\) | −38.7842 | − | 8.69135i | −1.61321 | − | 0.361513i | ||||
\(579\) | 11.8437 | 0.492206 | ||||||||
\(580\) | −28.6741 | −1.19063 | ||||||||
\(581\) | 5.92955i | 0.245999i | ||||||||
\(582\) | 98.5337 | 4.08435 | ||||||||
\(583\) | 0.120454i | 0.00498868i | ||||||||
\(584\) | 35.6628i | 1.47574i | ||||||||
\(585\) | − | 143.246i | − | 5.92248i | ||||||
\(586\) | 15.6292 | 0.645638 | ||||||||
\(587\) | 13.3509 | 0.551051 | 0.275525 | − | 0.961294i | \(-0.411148\pi\) | ||||
0.275525 | + | 0.961294i | \(0.411148\pi\) | |||||||
\(588\) | 68.9218i | 2.84229i | ||||||||
\(589\) | − | 27.5113i | − | 1.13358i | ||||||
\(590\) | 104.474i | 4.30112i | ||||||||
\(591\) | 28.0532 | 1.15395 | ||||||||
\(592\) | 1.94572i | 0.0799686i | ||||||||
\(593\) | −35.8906 | −1.47385 | −0.736924 | − | 0.675975i | \(-0.763723\pi\) | ||||
−0.736924 | + | 0.675975i | \(0.763723\pi\) | |||||||
\(594\) | −0.716293 | −0.0293898 | ||||||||
\(595\) | 10.7229 | + | 1.18676i | 0.439598 | + | 0.0486525i | ||||
\(596\) | −54.1727 | −2.21900 | ||||||||
\(597\) | 70.9540 | 2.90396 | ||||||||
\(598\) | − | 2.33355i | − | 0.0954258i | ||||||
\(599\) | 18.0369 | 0.736969 | 0.368484 | − | 0.929634i | \(-0.379877\pi\) | ||||
0.368484 | + | 0.929634i | \(0.379877\pi\) | |||||||
\(600\) | 79.2104i | 3.23375i | ||||||||
\(601\) | 0.185843i | 0.00758069i | 0.999993 | + | 0.00379035i | \(0.00120651\pi\) | ||||
−0.999993 | + | 0.00379035i | \(0.998793\pi\) | |||||||
\(602\) | − | 1.73047i | − | 0.0705285i | ||||||
\(603\) | −32.4477 | −1.32137 | ||||||||
\(604\) | −57.7086 | −2.34813 | ||||||||
\(605\) | − | 38.8845i | − | 1.58088i | ||||||
\(606\) | 44.6604i | 1.81421i | ||||||||
\(607\) | − | 8.62574i | − | 0.350108i | −0.984559 | − | 0.175054i | \(-0.943990\pi\) | ||
0.984559 | − | 0.175054i | \(-0.0560100\pi\) | |||||||
\(608\) | 20.3802 | 0.826525 | ||||||||
\(609\) | 5.33717i | 0.216273i | ||||||||
\(610\) | 28.5992 | 1.15795 | ||||||||
\(611\) | −38.2684 | −1.54817 | ||||||||
\(612\) | −92.2857 | − | 10.2137i | −3.73043 | − | 0.412865i | ||||
\(613\) | 46.7758 | 1.88926 | 0.944628 | − | 0.328143i | \(-0.106423\pi\) | ||||
0.944628 | + | 0.328143i | \(0.106423\pi\) | |||||||
\(614\) | −37.7087 | −1.52180 | ||||||||
\(615\) | − | 128.223i | − | 5.17047i | ||||||
\(616\) | 0.0721422 | 0.00290669 | ||||||||
\(617\) | − | 22.7804i | − | 0.917105i | −0.888667 | − | 0.458552i | \(-0.848368\pi\) | ||
0.888667 | − | 0.458552i | \(-0.151632\pi\) | |||||||
\(618\) | 123.830i | 4.98118i | ||||||||
\(619\) | − | 2.07620i | − | 0.0834496i | −0.999129 | − | 0.0417248i | \(-0.986715\pi\) | ||
0.999129 | − | 0.0417248i | \(-0.0132853\pi\) | |||||||
\(620\) | −71.5489 | −2.87347 | ||||||||
\(621\) | −1.72437 | −0.0691966 | ||||||||
\(622\) | 28.1952i | 1.13052i | ||||||||
\(623\) | − | 4.07676i | − | 0.163332i | ||||||
\(624\) | − | 20.8073i | − | 0.832960i | ||||||
\(625\) | −6.27232 | −0.250893 | ||||||||
\(626\) | − | 65.8087i | − | 2.63024i | ||||||
\(627\) | −0.412840 | −0.0164872 | ||||||||
\(628\) | 42.8217 | 1.70877 | ||||||||
\(629\) | −0.815184 | + | 7.36556i | −0.0325035 | + | 0.293684i | ||||
\(630\) | 39.7437 | 1.58343 | ||||||||
\(631\) | −0.316738 | −0.0126091 | −0.00630457 | − | 0.999980i | \(-0.502007\pi\) | ||||
−0.00630457 | + | 0.999980i | \(0.502007\pi\) | |||||||
\(632\) | − | 13.5105i | − | 0.537418i | ||||||
\(633\) | −72.7483 | −2.89149 | ||||||||
\(634\) | 56.3518i | 2.23802i | ||||||||
\(635\) | − | 10.2089i | − | 0.405127i | ||||||
\(636\) | 45.2545i | 1.79446i | ||||||||
\(637\) | −40.2423 | −1.59446 | ||||||||
\(638\) | −0.155548 | −0.00615819 | ||||||||
\(639\) | 50.8360i | 2.01104i | ||||||||
\(640\) | − | 70.8986i | − | 2.80251i | ||||||
\(641\) | − | 13.6477i | − | 0.539053i | −0.962993 | − | 0.269527i | \(-0.913133\pi\) | ||
0.962993 | − | 0.269527i | \(-0.0868672\pi\) | |||||||
\(642\) | 38.9999 | 1.53920 | ||||||||
\(643\) | 10.1344i | 0.399662i | 0.979830 | + | 0.199831i | \(0.0640394\pi\) | ||||
−0.979830 | + | 0.199831i | \(0.935961\pi\) | |||||||
\(644\) | 0.410559 | 0.0161783 | ||||||||
\(645\) | 10.8943 | 0.428965 | ||||||||
\(646\) | −45.1457 | − | 4.99650i | −1.77623 | − | 0.196585i | ||||
\(647\) | −3.28860 | −0.129288 | −0.0646442 | − | 0.997908i | \(-0.520591\pi\) | ||||
−0.0646442 | + | 0.997908i | \(0.520591\pi\) | |||||||
\(648\) | −47.0226 | −1.84722 | ||||||||
\(649\) | 0.359380i | 0.0141069i | ||||||||
\(650\) | −109.334 | −4.28842 | ||||||||
\(651\) | 13.3175i | 0.521955i | ||||||||
\(652\) | − | 37.4977i | − | 1.46852i | ||||||
\(653\) | 13.1836i | 0.515915i | 0.966156 | + | 0.257958i | \(0.0830495\pi\) | ||||
−0.966156 | + | 0.257958i | \(0.916951\pi\) | |||||||
\(654\) | 88.4721 | 3.45953 | ||||||||
\(655\) | −14.5453 | −0.568332 | ||||||||
\(656\) | − | 12.7415i | − | 0.497473i | ||||||
\(657\) | 67.5833i | 2.63668i | ||||||||
\(658\) | − | 10.6176i | − | 0.413917i | ||||||
\(659\) | 14.3758 | 0.560003 | 0.280001 | − | 0.960000i | \(-0.409665\pi\) | ||||
0.280001 | + | 0.960000i | \(0.409665\pi\) | |||||||
\(660\) | 1.07368i | 0.0417928i | ||||||||
\(661\) | 43.2280 | 1.68138 | 0.840688 | − | 0.541520i | \(-0.182151\pi\) | ||||
0.840688 | + | 0.541520i | \(0.182151\pi\) | |||||||
\(662\) | −4.93267 | −0.191714 | ||||||||
\(663\) | 8.71750 | − | 78.7666i | 0.338560 | − | 3.05904i | ||||
\(664\) | −27.4644 | −1.06583 | ||||||||
\(665\) | 12.3288 | 0.478092 | ||||||||
\(666\) | 27.2999i | 1.05785i | ||||||||
\(667\) | −0.374458 | −0.0144991 | ||||||||
\(668\) | 82.5814i | 3.19517i | ||||||||
\(669\) | − | 25.7674i | − | 0.996226i | ||||||
\(670\) | 41.2816i | 1.59485i | ||||||||
\(671\) | 0.0983782 | 0.00379785 | ||||||||
\(672\) | −9.86554 | −0.380571 | ||||||||
\(673\) | − | 17.3709i | − | 0.669600i | −0.942289 | − | 0.334800i | \(-0.891331\pi\) | ||
0.942289 | − | 0.334800i | \(-0.108669\pi\) | |||||||
\(674\) | − | 60.1737i | − | 2.31780i | ||||||
\(675\) | 80.7920i | 3.10969i | ||||||||
\(676\) | 89.7777 | 3.45299 | ||||||||
\(677\) | 32.2397i | 1.23907i | 0.784967 | + | 0.619537i | \(0.212680\pi\) | ||||
−0.784967 | + | 0.619537i | \(0.787320\pi\) | |||||||
\(678\) | −101.660 | −3.90424 | ||||||||
\(679\) | −10.1221 | −0.388450 | ||||||||
\(680\) | −5.49682 | + | 49.6663i | −0.210794 | + | 1.90462i | ||||
\(681\) | 64.2119 | 2.46060 | ||||||||
\(682\) | −0.388129 | −0.0148622 | ||||||||
\(683\) | 7.03066i | 0.269021i | 0.990912 | + | 0.134510i | \(0.0429462\pi\) | ||||
−0.990912 | + | 0.134510i | \(0.957054\pi\) | |||||||
\(684\) | −106.107 | −4.05709 | ||||||||
\(685\) | − | 56.8118i | − | 2.17067i | ||||||
\(686\) | − | 23.2785i | − | 0.888779i | ||||||
\(687\) | 55.9843i | 2.13593i | ||||||||
\(688\) | 1.08257 | 0.0412725 | ||||||||
\(689\) | −26.4234 | −1.00665 | ||||||||
\(690\) | 4.07607i | 0.155173i | ||||||||
\(691\) | − | 46.9553i | − | 1.78626i | −0.449796 | − | 0.893131i | \(-0.648503\pi\) | ||
0.449796 | − | 0.893131i | \(-0.351497\pi\) | |||||||
\(692\) | 6.37667i | 0.242405i | ||||||||
\(693\) | 0.136714 | 0.00519334 | ||||||||
\(694\) | 49.0406i | 1.86156i | ||||||||
\(695\) | −47.5584 | −1.80399 | ||||||||
\(696\) | −24.7206 | −0.937033 | ||||||||
\(697\) | 5.33822 | − | 48.2333i | 0.202200 | − | 1.82697i | ||||
\(698\) | −18.5291 | −0.701335 | ||||||||
\(699\) | 49.9174 | 1.88805 | ||||||||
\(700\) | − | 19.2359i | − | 0.727050i | ||||||
\(701\) | −4.15009 | −0.156747 | −0.0783734 | − | 0.996924i | \(-0.524973\pi\) | ||||
−0.0783734 | + | 0.996924i | \(0.524973\pi\) | |||||||
\(702\) | − | 157.130i | − | 5.93049i | ||||||
\(703\) | 8.46865i | 0.319401i | ||||||||
\(704\) | − | 0.349082i | − | 0.0131565i | ||||||
\(705\) | 66.8444 | 2.51751 | ||||||||
\(706\) | 67.6715 | 2.54685 | ||||||||
\(707\) | − | 4.58784i | − | 0.172543i | ||||||
\(708\) | 135.019i | 5.07433i | ||||||||
\(709\) | − | 38.8785i | − | 1.46011i | −0.683388 | − | 0.730056i | \(-0.739494\pi\) | ||
0.683388 | − | 0.730056i | \(-0.260506\pi\) | |||||||
\(710\) | 64.6763 | 2.42726 | ||||||||
\(711\) | − | 25.6032i | − | 0.960197i | ||||||
\(712\) | 18.8827 | 0.707658 | ||||||||
\(713\) | −0.934364 | −0.0349922 | ||||||||
\(714\) | 21.8539 | + | 2.41868i | 0.817861 | + | 0.0905168i | ||||
\(715\) | −0.626903 | −0.0234448 | ||||||||
\(716\) | −32.4599 | −1.21308 | ||||||||
\(717\) | 10.9738i | 0.409823i | ||||||||
\(718\) | 17.4157 | 0.649949 | ||||||||
\(719\) | − | 46.9497i | − | 1.75093i | −0.483284 | − | 0.875463i | \(-0.660556\pi\) | ||
0.483284 | − | 0.875463i | \(-0.339444\pi\) | |||||||
\(720\) | 24.8634i | 0.926604i | ||||||||
\(721\) | − | 12.7207i | − | 0.473744i | ||||||
\(722\) | −7.48462 | −0.278549 | ||||||||
\(723\) | −12.2736 | −0.456459 | ||||||||
\(724\) | − | 65.1298i | − | 2.42053i | ||||||
\(725\) | 17.5445i | 0.651587i | ||||||||
\(726\) | − | 79.2487i | − | 2.94119i | ||||||
\(727\) | −34.6046 | −1.28341 | −0.641706 | − | 0.766950i | \(-0.721773\pi\) | ||||
−0.641706 | + | 0.766950i | \(0.721773\pi\) | |||||||
\(728\) | 15.8255i | 0.586533i | ||||||||
\(729\) | 10.5082 | 0.389194 | ||||||||
\(730\) | 85.9831 | 3.18238 | ||||||||
\(731\) | 4.09808 | + | 0.453556i | 0.151573 | + | 0.0167754i | ||||
\(732\) | 36.9607 | 1.36611 | ||||||||
\(733\) | −36.5440 | −1.34978 | −0.674892 | − | 0.737917i | \(-0.735810\pi\) | ||||
−0.674892 | + | 0.737917i | \(0.735810\pi\) | |||||||
\(734\) | 79.4199i | 2.93144i | ||||||||
\(735\) | 70.2924 | 2.59277 | ||||||||
\(736\) | − | 0.692171i | − | 0.0255137i | ||||||
\(737\) | 0.142004i | 0.00523080i | ||||||||
\(738\) | − | 178.773i | − | 6.58072i | ||||||
\(739\) | 11.2321 | 0.413178 | 0.206589 | − | 0.978428i | \(-0.433764\pi\) | ||||
0.206589 | + | 0.978428i | \(0.433764\pi\) | |||||||
\(740\) | 22.0245 | 0.809636 | ||||||||
\(741\) | − | 90.5629i | − | 3.32691i | ||||||
\(742\) | − | 7.33120i | − | 0.269137i | ||||||
\(743\) | − | 20.9461i | − | 0.768437i | −0.923242 | − | 0.384218i | \(-0.874471\pi\) | ||
0.923242 | − | 0.384218i | \(-0.125529\pi\) | |||||||
\(744\) | −61.6839 | −2.26144 | ||||||||
\(745\) | 55.2500i | 2.02420i | ||||||||
\(746\) | 50.5068 | 1.84918 | ||||||||
\(747\) | −52.0468 | −1.90429 | ||||||||
\(748\) | −0.0446995 | + | 0.403881i | −0.00163438 | + | 0.0147673i | ||||
\(749\) | −4.00635 | −0.146389 | ||||||||
\(750\) | 63.6208 | 2.32310 | ||||||||
\(751\) | 6.18988i | 0.225872i | 0.993602 | + | 0.112936i | \(0.0360255\pi\) | ||||
−0.993602 | + | 0.112936i | \(0.963975\pi\) | |||||||
\(752\) | 6.64231 | 0.242220 | ||||||||
\(753\) | 74.3742i | 2.71035i | ||||||||
\(754\) | − | 34.1218i | − | 1.24264i | ||||||
\(755\) | 58.8562i | 2.14200i | ||||||||
\(756\) | 27.6451 | 1.00544 | ||||||||
\(757\) | 5.23071 | 0.190113 | 0.0950566 | − | 0.995472i | \(-0.469697\pi\) | ||||
0.0950566 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(758\) | − | 26.0603i | − | 0.946551i | ||||||
\(759\) | 0.0140213i | 0.000508939i | ||||||||
\(760\) | 57.1045i | 2.07140i | ||||||||
\(761\) | 4.28808 | 0.155443 | 0.0777214 | − | 0.996975i | \(-0.475236\pi\) | ||||
0.0777214 | + | 0.996975i | \(0.475236\pi\) | |||||||
\(762\) | − | 20.8062i | − | 0.753729i | ||||||
\(763\) | −9.08849 | −0.329026 | ||||||||
\(764\) | −33.2549 | −1.20312 | ||||||||
\(765\) | −10.4168 | + | 94.1209i | −0.376621 | + | 3.40295i | ||||
\(766\) | −27.0955 | −0.978999 | ||||||||
\(767\) | −78.8355 | −2.84658 | ||||||||
\(768\) | − | 68.8229i | − | 2.48343i | ||||||
\(769\) | 0.199366 | 0.00718933 | 0.00359467 | − | 0.999994i | \(-0.498856\pi\) | ||||
0.00359467 | + | 0.999994i | \(0.498856\pi\) | |||||||
\(770\) | − | 0.173935i | − | 0.00626818i | ||||||
\(771\) | − | 63.8008i | − | 2.29773i | ||||||
\(772\) | − | 13.3219i | − | 0.479465i | ||||||
\(773\) | 34.2604 | 1.23226 | 0.616131 | − | 0.787644i | \(-0.288699\pi\) | ||||
0.616131 | + | 0.787644i | \(0.288699\pi\) | |||||||
\(774\) | 15.1892 | 0.545965 | ||||||||
\(775\) | 43.7778i | 1.57255i | ||||||||
\(776\) | − | 46.8833i | − | 1.68301i | ||||||
\(777\) | − | 4.09946i | − | 0.147067i | ||||||
\(778\) | −9.22749 | −0.330822 | ||||||||
\(779\) | − | 55.4568i | − | 1.98695i | ||||||
\(780\) | −235.528 | −8.43324 | ||||||||
\(781\) | 0.222480 | 0.00796095 | ||||||||
\(782\) | −0.169696 | + | 1.53328i | −0.00606831 | + | 0.0548299i | ||||
\(783\) | −25.2142 | −0.901083 | ||||||||
\(784\) | 6.98493 | 0.249462 | ||||||||
\(785\) | − | 43.6733i | − | 1.55877i | ||||||
\(786\) | −29.6440 | −1.05737 | ||||||||
\(787\) | 42.4321i | 1.51254i | 0.654258 | + | 0.756271i | \(0.272981\pi\) | ||||
−0.654258 | + | 0.756271i | \(0.727019\pi\) | |||||||
\(788\) | − | 31.5545i | − | 1.12408i | ||||||
\(789\) | 1.54292i | 0.0549296i | ||||||||
\(790\) | −32.5738 | −1.15892 | ||||||||
\(791\) | 10.4433 | 0.371320 | ||||||||
\(792\) | 0.633230i | 0.0225009i | ||||||||
\(793\) | 21.5808i | 0.766356i | ||||||||
\(794\) | − | 66.6470i | − | 2.36521i | ||||||
\(795\) | 46.1544 | 1.63693 | ||||||||
\(796\) | − | 79.8099i | − | 2.82879i | ||||||
\(797\) | 8.23793 | 0.291802 | 0.145901 | − | 0.989299i | \(-0.453392\pi\) | ||||
0.145901 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(798\) | 25.1268 | 0.889479 | ||||||||
\(799\) | 25.1446 | + | 2.78288i | 0.889551 | + | 0.0984511i | ||||
\(800\) | −32.4303 | −1.14658 | ||||||||
\(801\) | 35.7839 | 1.26436 | ||||||||
\(802\) | 50.3786i | 1.77893i | ||||||||
\(803\) | 0.295773 | 0.0104376 | ||||||||
\(804\) | 53.3511i | 1.88155i | ||||||||
\(805\) | − | 0.418723i | − | 0.0147581i | ||||||
\(806\) | − | 85.1421i | − | 2.99900i | ||||||
\(807\) | 41.4894 | 1.46050 | ||||||||
\(808\) | 21.2499 | 0.747568 | ||||||||
\(809\) | 33.4777i | 1.17701i | 0.808492 | + | 0.588507i | \(0.200284\pi\) | ||||
−0.808492 | + | 0.588507i | \(0.799716\pi\) | |||||||
\(810\) | 113.372i | 3.98347i | ||||||||
\(811\) | 0.513702i | 0.0180385i | 0.999959 | + | 0.00901926i | \(0.00287096\pi\) | ||||
−0.999959 | + | 0.00901926i | \(0.997129\pi\) | |||||||
\(812\) | 6.00331 | 0.210675 | ||||||||
\(813\) | − | 39.4305i | − | 1.38289i | ||||||
\(814\) | 0.119476 | 0.00418762 | ||||||||
\(815\) | −38.2434 | −1.33961 | ||||||||
\(816\) | −1.51311 | + | 13.6717i | −0.0529695 | + | 0.478604i | ||||
\(817\) | 4.71182 | 0.164846 | ||||||||
\(818\) | −11.5402 | −0.403494 | ||||||||
\(819\) | 29.9904i | 1.04795i | ||||||||
\(820\) | −144.227 | −5.03663 | ||||||||
\(821\) | 40.8842i | 1.42687i | 0.700722 | + | 0.713435i | \(0.252862\pi\) | ||||
−0.700722 | + | 0.713435i | \(0.747138\pi\) | |||||||
\(822\) | − | 115.785i | − | 4.03848i | ||||||
\(823\) | 34.3211i | 1.19636i | 0.801363 | + | 0.598179i | \(0.204109\pi\) | ||||
−0.801363 | + | 0.598179i | \(0.795891\pi\) | |||||||
\(824\) | 58.9196 | 2.05256 | ||||||||
\(825\) | 0.656939 | 0.0228717 | ||||||||
\(826\) | − | 21.8730i | − | 0.761059i | ||||||
\(827\) | 34.5180i | 1.20031i | 0.799884 | + | 0.600154i | \(0.204894\pi\) | ||||
−0.799884 | + | 0.600154i | \(0.795106\pi\) | |||||||
\(828\) | 3.60369i | 0.125237i | ||||||||
\(829\) | −37.3709 | −1.29794 | −0.648972 | − | 0.760812i | \(-0.724801\pi\) | ||||
−0.648972 | + | 0.760812i | \(0.724801\pi\) | |||||||
\(830\) | 66.2167i | 2.29841i | ||||||||
\(831\) | −22.8964 | −0.794266 | ||||||||
\(832\) | 76.5767 | 2.65482 | ||||||||
\(833\) | 26.4416 | + | 2.92642i | 0.916147 | + | 0.101395i | ||||
\(834\) | −96.9264 | −3.35629 | ||||||||
\(835\) | 84.2237 | 2.91468 | ||||||||
\(836\) | 0.464367i | 0.0160605i | ||||||||
\(837\) | −62.9156 | −2.17468 | ||||||||
\(838\) | − | 44.6706i | − | 1.54312i | ||||||
\(839\) | 33.9006i | 1.17038i | 0.810897 | + | 0.585189i | \(0.198980\pi\) | ||||
−0.810897 | + | 0.585189i | \(0.801020\pi\) | |||||||
\(840\) | − | 27.6429i | − | 0.953769i | ||||||
\(841\) | 23.5246 | 0.811192 | ||||||||
\(842\) | 29.4276 | 1.01414 | ||||||||
\(843\) | 0.863842i | 0.0297523i | ||||||||
\(844\) | 81.8280i | 2.81664i | ||||||||
\(845\) | − | 91.5630i | − | 3.14986i | ||||||
\(846\) | 93.1964 | 3.20416 | ||||||||
\(847\) | 8.14099i | 0.279728i | ||||||||
\(848\) | 4.58635 | 0.157496 | ||||||||
\(849\) | −54.1476 | −1.85834 | ||||||||
\(850\) | 71.8388 | + | 7.95076i | 2.46405 | + | 0.272709i | ||||
\(851\) | 0.287620 | 0.00985949 | ||||||||
\(852\) | 83.5857 | 2.86360 | ||||||||
\(853\) | − | 47.4275i | − | 1.62389i | −0.583737 | − | 0.811943i | \(-0.698410\pi\) | ||
0.583737 | − | 0.811943i | \(-0.301590\pi\) | |||||||
\(854\) | −5.98762 | −0.204892 | ||||||||
\(855\) | 108.217i | 3.70093i | ||||||||
\(856\) | − | 18.5565i | − | 0.634249i | ||||||
\(857\) | 29.0994i | 0.994015i | 0.867746 | + | 0.497008i | \(0.165568\pi\) | ||||
−0.867746 | + | 0.497008i | \(0.834432\pi\) | |||||||
\(858\) | −1.27766 | −0.0436186 | ||||||||
\(859\) | 25.0028 | 0.853086 | 0.426543 | − | 0.904467i | \(-0.359731\pi\) | ||||
0.426543 | + | 0.904467i | \(0.359731\pi\) | |||||||
\(860\) | − | 12.2541i | − | 0.417861i | ||||||
\(861\) | 26.8453i | 0.914885i | ||||||||
\(862\) | − | 17.9624i | − | 0.611802i | ||||||
\(863\) | −1.43734 | −0.0489275 | −0.0244638 | − | 0.999701i | \(-0.507788\pi\) | ||||
−0.0244638 | + | 0.999701i | \(0.507788\pi\) | |||||||
\(864\) | − | 46.6075i | − | 1.58562i | ||||||
\(865\) | 6.50348 | 0.221125 | ||||||||
\(866\) | 21.7866 | 0.740339 | ||||||||
\(867\) | −11.4558 | + | 51.1204i | −0.389060 | + | 1.73614i | ||||
\(868\) | 14.9797 | 0.508444 | ||||||||
\(869\) | −0.112050 | −0.00380105 | ||||||||
\(870\) | 59.6014i | 2.02068i | ||||||||
\(871\) | −31.1509 | −1.05551 | ||||||||
\(872\) | − | 42.0959i | − | 1.42555i | ||||||
\(873\) | − | 88.8470i | − | 3.00701i | ||||||
\(874\) | 1.76291i | 0.0596312i | ||||||||
\(875\) | −6.53559 | −0.220943 | ||||||||
\(876\) | 111.122 | 3.75446 | ||||||||
\(877\) | 15.8342i | 0.534682i | 0.963602 | + | 0.267341i | \(0.0861450\pi\) | ||||
−0.963602 | + | 0.267341i | \(0.913855\pi\) | |||||||
\(878\) | − | 31.9194i | − | 1.07723i | ||||||
\(879\) | − | 20.6005i | − | 0.694836i | ||||||
\(880\) | 0.108813 | 0.00366807 | ||||||||
\(881\) | − | 10.4114i | − | 0.350771i | −0.984500 | − | 0.175385i | \(-0.943883\pi\) | ||
0.984500 | − | 0.175385i | \(-0.0561171\pi\) | |||||||
\(882\) | 98.0036 | 3.29995 | ||||||||
\(883\) | −50.3013 | −1.69277 | −0.846386 | − | 0.532569i | \(-0.821227\pi\) | ||||
−0.846386 | + | 0.532569i | \(0.821227\pi\) | |||||||
\(884\) | −88.5975 | − | 9.80553i | −2.97986 | − | 0.329796i | ||||
\(885\) | 137.704 | 4.62887 | ||||||||
\(886\) | 25.9724 | 0.872560 | ||||||||
\(887\) | 5.92453i | 0.198926i | 0.995041 | + | 0.0994631i | \(0.0317125\pi\) | ||||
−0.995041 | + | 0.0994631i | \(0.968287\pi\) | |||||||
\(888\) | 18.9878 | 0.637190 | ||||||||
\(889\) | 2.13736i | 0.0716849i | ||||||||
\(890\) | − | 45.5262i | − | 1.52604i | ||||||
\(891\) | 0.389987i | 0.0130650i | ||||||||
\(892\) | −28.9835 | −0.970438 | ||||||||
\(893\) | 28.9103 | 0.967446 | ||||||||
\(894\) | 112.602i | 3.76599i | ||||||||
\(895\) | 33.1054i | 1.10659i | ||||||||
\(896\) | 14.8436i | 0.495888i | ||||||||
\(897\) | −3.07578 | −0.102697 | ||||||||
\(898\) | 14.6500i | 0.488877i | ||||||||
\(899\) | −13.6625 | −0.455671 | ||||||||
\(900\) | 168.844 | 5.62813 | ||||||||
\(901\) | 17.3617 | + | 1.92151i | 0.578403 | + | 0.0640148i | ||||
\(902\) | −0.782384 | −0.0260505 | ||||||||
\(903\) | −2.28088 | −0.0759028 | ||||||||
\(904\) | 48.3710i | 1.60880i | ||||||||
\(905\) | −66.4249 | −2.20804 | ||||||||
\(906\) | 119.952i | 3.98514i | ||||||||
\(907\) | − | 28.3773i | − | 0.942253i | −0.882066 | − | 0.471127i | \(-0.843847\pi\) | ||
0.882066 | − | 0.471127i | \(-0.156153\pi\) | |||||||
\(908\) | − | 72.2262i | − | 2.39691i | ||||||
\(909\) | 40.2699 | 1.33567 | ||||||||
\(910\) | 38.1553 | 1.26484 | ||||||||
\(911\) | − | 28.4514i | − | 0.942638i | −0.881963 | − | 0.471319i | \(-0.843778\pi\) | ||
0.881963 | − | 0.471319i | \(-0.156222\pi\) | |||||||
\(912\) | 15.7192i | 0.520513i | ||||||||
\(913\) | 0.227779i | 0.00753837i | ||||||||
\(914\) | 74.5999 | 2.46754 | ||||||||
\(915\) | − | 37.6957i | − | 1.24618i | ||||||
\(916\) | 62.9717 | 2.08064 | ||||||||
\(917\) | 3.04525 | 0.100563 | ||||||||
\(918\) | −11.4265 | + | 103.244i | −0.377131 | + | 3.40755i | ||||
\(919\) | −36.1952 | −1.19397 | −0.596984 | − | 0.802253i | \(-0.703635\pi\) | ||||
−0.596984 | + | 0.802253i | \(0.703635\pi\) | |||||||
\(920\) | 1.93944 | 0.0639413 | ||||||||
\(921\) | 49.7028i | 1.63776i | ||||||||
\(922\) | −35.6574 | −1.17431 | ||||||||
\(923\) | 48.8044i | 1.60642i | ||||||||
\(924\) | − | 0.224788i | − | 0.00739500i | ||||||
\(925\) | − | 13.4759i | − | 0.443084i | ||||||
\(926\) | −97.7877 | −3.21350 | ||||||||
\(927\) | 111.657 | 3.66728 | ||||||||
\(928\) | − | 10.1211i | − | 0.332242i | ||||||
\(929\) | 33.9517i | 1.11392i | 0.830540 | + | 0.556959i | \(0.188032\pi\) | ||||
−0.830540 | + | 0.556959i | \(0.811968\pi\) | |||||||
\(930\) | 148.720i | 4.87672i | ||||||||
\(931\) | 30.4016 | 0.996371 | ||||||||
\(932\) | − | 56.1477i | − | 1.83918i | ||||||
\(933\) | 37.1633 | 1.21667 | ||||||||
\(934\) | −54.8176 | −1.79369 | ||||||||
\(935\) | 0.411912 | + | 0.0455884i | 0.0134710 | + | 0.00149090i | ||||
\(936\) | −138.909 | −4.54038 | ||||||||
\(937\) | −4.22845 | −0.138137 | −0.0690686 | − | 0.997612i | \(-0.522003\pi\) | ||||
−0.0690686 | + | 0.997612i | \(0.522003\pi\) | |||||||
\(938\) | − | 8.64285i | − | 0.282199i | ||||||
\(939\) | −86.7406 | −2.83067 | ||||||||
\(940\) | − | 75.1873i | − | 2.45234i | ||||||
\(941\) | 30.8462i | 1.00556i | 0.864416 | + | 0.502778i | \(0.167689\pi\) | ||||
−0.864416 | + | 0.502778i | \(0.832311\pi\) | |||||||
\(942\) | − | 89.0083i | − | 2.90005i | ||||||
\(943\) | −1.88348 | −0.0613344 | ||||||||
\(944\) | 13.6836 | 0.445364 | ||||||||
\(945\) | − | 28.1948i | − | 0.917178i | ||||||
\(946\) | − | 0.0664743i | − | 0.00216127i | ||||||
\(947\) | − | 7.28320i | − | 0.236672i | −0.992974 | − | 0.118336i | \(-0.962244\pi\) | ||
0.992974 | − | 0.118336i | \(-0.0377560\pi\) | |||||||
\(948\) | −42.0974 | −1.36726 | ||||||||
\(949\) | 64.8824i | 2.10617i | ||||||||
\(950\) | 82.5975 | 2.67982 | ||||||||
\(951\) | 74.2757 | 2.40856 | ||||||||
\(952\) | 1.15083 | − | 10.3983i | 0.0372987 | − | 0.337011i | ||||
\(953\) | 23.6911 | 0.767429 | 0.383715 | − | 0.923452i | \(-0.374645\pi\) | ||||
0.383715 | + | 0.923452i | \(0.374645\pi\) | |||||||
\(954\) | 64.3498 | 2.08340 | ||||||||
\(955\) | 33.9162i | 1.09750i | ||||||||
\(956\) | 12.3434 | 0.399215 | ||||||||
\(957\) | 0.205023i | 0.00662745i | ||||||||
\(958\) | − | 24.4269i | − | 0.789197i | ||||||
\(959\) | 11.8943i | 0.384087i | ||||||||
\(960\) | −133.759 | −4.31704 | ||||||||
\(961\) | −3.09135 | −0.0997208 | ||||||||
\(962\) | 26.2088i | 0.845007i | ||||||||
\(963\) | − | 35.1658i | − | 1.13320i | ||||||
\(964\) | 13.8054i | 0.444644i | ||||||||
\(965\) | −13.5868 | −0.437374 | ||||||||
\(966\) | − | 0.853379i | − | 0.0274570i | ||||||
\(967\) | 14.2289 | 0.457572 | 0.228786 | − | 0.973477i | \(-0.426524\pi\) | ||||
0.228786 | + | 0.973477i | \(0.426524\pi\) | |||||||
\(968\) | −37.7073 | −1.21196 | ||||||||
\(969\) | −6.58574 | + | 59.5052i | −0.211564 | + | 1.91158i | ||||
\(970\) | −113.036 | −3.62936 | ||||||||
\(971\) | 11.8113 | 0.379041 | 0.189521 | − | 0.981877i | \(-0.439307\pi\) | ||||
0.189521 | + | 0.981877i | \(0.439307\pi\) | |||||||
\(972\) | 34.4655i | 1.10548i | ||||||||
\(973\) | 9.95697 | 0.319206 | ||||||||
\(974\) | − | 14.4761i | − | 0.463844i | ||||||
\(975\) | 144.110i | 4.61520i | ||||||||
\(976\) | − | 3.74581i | − | 0.119901i | ||||||
\(977\) | −9.59199 | −0.306875 | −0.153437 | − | 0.988158i | \(-0.549034\pi\) | ||||
−0.153437 | + | 0.988158i | \(0.549034\pi\) | |||||||
\(978\) | −77.9419 | −2.49231 | ||||||||
\(979\) | − | 0.156605i | − | 0.00500513i | ||||||
\(980\) | − | 79.0656i | − | 2.52566i | ||||||
\(981\) | − | 79.7745i | − | 2.54700i | ||||||
\(982\) | −1.64698 | −0.0525573 | ||||||||
\(983\) | 22.2300i | 0.709026i | 0.935051 | + | 0.354513i | \(0.115353\pi\) | ||||
−0.935051 | + | 0.354513i | \(0.884647\pi\) | |||||||
\(984\) | −124.342 | −3.96386 | ||||||||
\(985\) | −32.1820 | −1.02540 | ||||||||
\(986\) | −2.48134 | + | 22.4200i | −0.0790219 | + | 0.713999i | ||||
\(987\) | −13.9948 | −0.445458 | ||||||||
\(988\) | −101.866 | −3.24079 | ||||||||
\(989\) | − | 0.160027i | − | 0.00508857i | ||||||
\(990\) | 1.52672 | 0.0485223 | ||||||||
\(991\) | − | 58.9752i | − | 1.87341i | −0.350120 | − | 0.936705i | \(-0.613859\pi\) | ||
0.350120 | − | 0.936705i | \(-0.386141\pi\) | |||||||
\(992\) | − | 25.2546i | − | 0.801835i | ||||||
\(993\) | 6.50161i | 0.206322i | ||||||||
\(994\) | −13.5408 | −0.429489 | ||||||||
\(995\) | −81.3970 | −2.58046 | ||||||||
\(996\) | 85.5765i | 2.71160i | ||||||||
\(997\) | 17.1366i | 0.542720i | 0.962478 | + | 0.271360i | \(0.0874734\pi\) | ||||
−0.962478 | + | 0.271360i | \(0.912527\pi\) | |||||||
\(998\) | − | 3.28561i | − | 0.104004i | ||||||
\(999\) | 19.3670 | 0.612744 |
(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 | 731.2.d.c.560.4 | yes | 20 | |
17.16 | even | 2 | inner | 731.2.d.c.560.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.d.c.560.3 | ✓ | 20 | 17.16 | even | 2 | inner | |
731.2.d.c.560.4 | yes | 20 | 1.1 | even | 1 | trivial |