Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(4.82290067918\) |
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: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.20 | ||
Root | \(3.65759i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.1 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.65759i | 1.82880i | 0.404816 | + | 0.914398i | \(0.367335\pi\) | ||||
−0.404816 | + | 0.914398i | \(0.632665\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −9.37798 | −2.34450 | ||||||||
\(5\) | 0.395869 | 0.0791737 | 0.0395869 | − | 0.999216i | \(-0.487396\pi\) | ||||
0.0395869 | + | 0.999216i | \(0.487396\pi\) | |||||||
\(6\) | − | 6.33514i | − | 1.05586i | ||||||
\(7\) | −6.20847 | −0.886924 | −0.443462 | − | 0.896293i | \(-0.646250\pi\) | ||||
−0.443462 | + | 0.896293i | \(0.646250\pi\) | |||||||
\(8\) | − | 19.6705i | − | 2.45881i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 1.44793i | 0.144793i | ||||||||
\(11\) | − | 8.54756i | − | 0.777051i | −0.921438 | − | 0.388525i | \(-0.872985\pi\) | ||
0.921438 | − | 0.388525i | \(-0.127015\pi\) | |||||||
\(12\) | 16.2431 | 1.35359 | ||||||||
\(13\) | − | 0.0887419i | − | 0.00682630i | −0.999994 | − | 0.00341315i | \(-0.998914\pi\) | ||
0.999994 | − | 0.00341315i | \(-0.00108644\pi\) | |||||||
\(14\) | − | 22.7081i | − | 1.62200i | ||||||
\(15\) | −0.685665 | −0.0457110 | ||||||||
\(16\) | 34.4346 | 2.15216 | ||||||||
\(17\) | −8.10940 | −0.477023 | −0.238512 | − | 0.971140i | \(-0.576660\pi\) | ||||
−0.238512 | + | 0.971140i | \(0.576660\pi\) | |||||||
\(18\) | 10.9728i | 0.609599i | ||||||||
\(19\) | 10.5067 | 0.552984 | 0.276492 | − | 0.961016i | \(-0.410828\pi\) | ||||
0.276492 | + | 0.961016i | \(0.410828\pi\) | |||||||
\(20\) | −3.71245 | −0.185622 | ||||||||
\(21\) | 10.7534 | 0.512066 | ||||||||
\(22\) | 31.2635 | 1.42107 | ||||||||
\(23\) | − | 14.0307i | − | 0.610032i | −0.952347 | − | 0.305016i | \(-0.901338\pi\) | ||
0.952347 | − | 0.305016i | \(-0.0986618\pi\) | |||||||
\(24\) | 34.0702i | 1.41959i | ||||||||
\(25\) | −24.8433 | −0.993732 | ||||||||
\(26\) | 0.324582 | 0.0124839 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 58.2229 | 2.07939 | ||||||||
\(29\) | −56.9344 | −1.96325 | −0.981627 | − | 0.190808i | \(-0.938889\pi\) | ||||
−0.981627 | + | 0.190808i | \(0.938889\pi\) | |||||||
\(30\) | − | 2.50788i | − | 0.0835960i | ||||||
\(31\) | 0.471045i | 0.0151950i | 0.999971 | + | 0.00759751i | \(0.00241838\pi\) | ||||
−0.999971 | + | 0.00759751i | \(0.997582\pi\) | |||||||
\(32\) | 47.2659i | 1.47706i | ||||||||
\(33\) | 14.8048i | 0.448631i | ||||||||
\(34\) | − | 29.6609i | − | 0.872378i | ||||||
\(35\) | −2.45774 | −0.0702211 | ||||||||
\(36\) | −28.1339 | −0.781498 | ||||||||
\(37\) | 43.8322i | 1.18465i | 0.805698 | + | 0.592327i | \(0.201791\pi\) | ||||
−0.805698 | + | 0.592327i | \(0.798209\pi\) | |||||||
\(38\) | 38.4292i | 1.01129i | ||||||||
\(39\) | 0.153705i | 0.00394117i | ||||||||
\(40\) | − | 7.78692i | − | 0.194673i | ||||||
\(41\) | 13.8735 | 0.338378 | 0.169189 | − | 0.985584i | \(-0.445885\pi\) | ||||
0.169189 | + | 0.985584i | \(0.445885\pi\) | |||||||
\(42\) | 39.3315i | 0.936464i | ||||||||
\(43\) | − | 53.7675i | − | 1.25041i | −0.780462 | − | 0.625204i | \(-0.785016\pi\) | ||
0.780462 | − | 0.625204i | \(-0.214984\pi\) | |||||||
\(44\) | 80.1588i | 1.82179i | ||||||||
\(45\) | 1.18761 | 0.0263912 | ||||||||
\(46\) | 51.3187 | 1.11562 | ||||||||
\(47\) | − | 34.1786i | − | 0.727205i | −0.931554 | − | 0.363602i | \(-0.881547\pi\) | ||
0.931554 | − | 0.363602i | \(-0.118453\pi\) | |||||||
\(48\) | −59.6425 | −1.24255 | ||||||||
\(49\) | −10.4549 | −0.213365 | ||||||||
\(50\) | − | 90.8666i | − | 1.81733i | ||||||
\(51\) | 14.0459 | 0.275410 | ||||||||
\(52\) | 0.832220i | 0.0160042i | ||||||||
\(53\) | −79.3757 | −1.49765 | −0.748827 | − | 0.662765i | \(-0.769383\pi\) | ||||
−0.748827 | + | 0.662765i | \(0.769383\pi\) | |||||||
\(54\) | − | 19.0054i | − | 0.351952i | ||||||
\(55\) | − | 3.38371i | − | 0.0615220i | ||||||
\(56\) | 122.123i | 2.18078i | ||||||||
\(57\) | −18.1981 | −0.319265 | ||||||||
\(58\) | − | 208.243i | − | 3.59039i | ||||||
\(59\) | −41.5316 | − | 41.9061i | −0.703926 | − | 0.710273i | ||||
\(60\) | 6.43015 | 0.107169 | ||||||||
\(61\) | − | 45.7782i | − | 0.750462i | −0.926931 | − | 0.375231i | \(-0.877563\pi\) | ||
0.926931 | − | 0.375231i | \(-0.122437\pi\) | |||||||
\(62\) | −1.72289 | −0.0277886 | ||||||||
\(63\) | −18.6254 | −0.295641 | ||||||||
\(64\) | −35.1409 | −0.549077 | ||||||||
\(65\) | − | 0.0351301i | − | 0.000540463i | ||||||
\(66\) | −54.1499 | −0.820454 | ||||||||
\(67\) | 104.453i | 1.55900i | 0.626403 | + | 0.779499i | \(0.284526\pi\) | ||||
−0.626403 | + | 0.779499i | \(0.715474\pi\) | |||||||
\(68\) | 76.0498 | 1.11838 | ||||||||
\(69\) | 24.3019i | 0.352202i | ||||||||
\(70\) | − | 8.98940i | − | 0.128420i | ||||||
\(71\) | 74.0325 | 1.04271 | 0.521356 | − | 0.853340i | \(-0.325427\pi\) | ||||
0.521356 | + | 0.853340i | \(0.325427\pi\) | |||||||
\(72\) | − | 59.0114i | − | 0.819602i | ||||||
\(73\) | 109.458i | 1.49943i | 0.661761 | + | 0.749715i | \(0.269810\pi\) | ||||
−0.661761 | + | 0.749715i | \(0.730190\pi\) | |||||||
\(74\) | −160.320 | −2.16649 | ||||||||
\(75\) | 43.0298 | 0.573731 | ||||||||
\(76\) | −98.5316 | −1.29647 | ||||||||
\(77\) | 53.0673i | 0.689185i | ||||||||
\(78\) | −0.562192 | −0.00720759 | ||||||||
\(79\) | −74.2528 | −0.939909 | −0.469954 | − | 0.882691i | \(-0.655730\pi\) | ||||
−0.469954 | + | 0.882691i | \(0.655730\pi\) | |||||||
\(80\) | 13.6316 | 0.170395 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 50.7436i | 0.618825i | ||||||||
\(83\) | 88.8936i | 1.07101i | 0.844533 | + | 0.535503i | \(0.179878\pi\) | ||||
−0.844533 | + | 0.535503i | \(0.820122\pi\) | |||||||
\(84\) | −100.845 | −1.20054 | ||||||||
\(85\) | −3.21026 | −0.0377677 | ||||||||
\(86\) | 196.660 | 2.28674 | ||||||||
\(87\) | 98.6133 | 1.13349 | ||||||||
\(88\) | −168.134 | −1.91062 | ||||||||
\(89\) | − | 142.879i | − | 1.60538i | −0.596394 | − | 0.802692i | \(-0.703400\pi\) | ||
0.596394 | − | 0.802692i | \(-0.296600\pi\) | |||||||
\(90\) | 4.34378i | 0.0482642i | ||||||||
\(91\) | 0.550951i | 0.00605441i | ||||||||
\(92\) | 131.580i | 1.43022i | ||||||||
\(93\) | − | 0.815874i | − | 0.00877284i | ||||||
\(94\) | 125.012 | 1.32991 | ||||||||
\(95\) | 4.15927 | 0.0437818 | ||||||||
\(96\) | − | 81.8669i | − | 0.852780i | ||||||
\(97\) | 81.4737i | 0.839935i | 0.907539 | + | 0.419968i | \(0.137959\pi\) | ||||
−0.907539 | + | 0.419968i | \(0.862041\pi\) | |||||||
\(98\) | − | 38.2398i | − | 0.390202i | ||||||
\(99\) | − | 25.6427i | − | 0.259017i | ||||||
\(100\) | 232.980 | 2.32980 | ||||||||
\(101\) | 92.0885i | 0.911768i | 0.890039 | + | 0.455884i | \(0.150677\pi\) | ||||
−0.890039 | + | 0.455884i | \(0.849323\pi\) | |||||||
\(102\) | 51.3741i | 0.503668i | ||||||||
\(103\) | 147.520i | 1.43223i | 0.697982 | + | 0.716115i | \(0.254082\pi\) | ||||
−0.697982 | + | 0.716115i | \(0.745918\pi\) | |||||||
\(104\) | −1.74559 | −0.0167846 | ||||||||
\(105\) | 4.25693 | 0.0405422 | ||||||||
\(106\) | − | 290.324i | − | 2.73891i | ||||||
\(107\) | 68.9648 | 0.644530 | 0.322265 | − | 0.946649i | \(-0.395556\pi\) | ||||
0.322265 | + | 0.946649i | \(0.395556\pi\) | |||||||
\(108\) | 48.7294 | 0.451198 | ||||||||
\(109\) | 57.3299i | 0.525963i | 0.964801 | + | 0.262981i | \(0.0847058\pi\) | ||||
−0.964801 | + | 0.262981i | \(0.915294\pi\) | |||||||
\(110\) | 12.3762 | 0.112511 | ||||||||
\(111\) | − | 75.9196i | − | 0.683961i | ||||||
\(112\) | −213.786 | −1.90881 | ||||||||
\(113\) | 19.6848i | 0.174201i | 0.996200 | + | 0.0871007i | \(0.0277602\pi\) | ||||
−0.996200 | + | 0.0871007i | \(0.972240\pi\) | |||||||
\(114\) | − | 66.5613i | − | 0.583871i | ||||||
\(115\) | − | 5.55433i | − | 0.0482985i | ||||||
\(116\) | 533.930 | 4.60284 | ||||||||
\(117\) | − | 0.266226i | − | 0.00227543i | ||||||
\(118\) | 153.276 | − | 151.906i | 1.29894 | − | 1.28734i | ||||
\(119\) | 50.3469 | 0.423084 | ||||||||
\(120\) | 13.4873i | 0.112394i | ||||||||
\(121\) | 47.9392 | 0.396192 | ||||||||
\(122\) | 167.438 | 1.37244 | ||||||||
\(123\) | −24.0296 | −0.195363 | ||||||||
\(124\) | − | 4.41745i | − | 0.0356246i | ||||||
\(125\) | −19.7314 | −0.157851 | ||||||||
\(126\) | − | 68.1242i | − | 0.540668i | ||||||
\(127\) | 5.95404 | 0.0468822 | 0.0234411 | − | 0.999725i | \(-0.492538\pi\) | ||||
0.0234411 | + | 0.999725i | \(0.492538\pi\) | |||||||
\(128\) | 60.5324i | 0.472909i | ||||||||
\(129\) | 93.1281i | 0.721923i | ||||||||
\(130\) | 0.128492 | 0.000988397 | ||||||||
\(131\) | − | 207.532i | − | 1.58421i | −0.610384 | − | 0.792106i | \(-0.708985\pi\) | ||
0.610384 | − | 0.792106i | \(-0.291015\pi\) | |||||||
\(132\) | − | 138.839i | − | 1.05181i | ||||||
\(133\) | −65.2305 | −0.490455 | ||||||||
\(134\) | −382.046 | −2.85109 | ||||||||
\(135\) | −2.05699 | −0.0152370 | ||||||||
\(136\) | 159.516i | 1.17291i | ||||||||
\(137\) | −62.5295 | −0.456419 | −0.228210 | − | 0.973612i | \(-0.573287\pi\) | ||||
−0.228210 | + | 0.973612i | \(0.573287\pi\) | |||||||
\(138\) | −88.8866 | −0.644106 | ||||||||
\(139\) | −101.500 | −0.730217 | −0.365108 | − | 0.930965i | \(-0.618968\pi\) | ||||
−0.365108 | + | 0.930965i | \(0.618968\pi\) | |||||||
\(140\) | 23.0486 | 0.164633 | ||||||||
\(141\) | 59.1991i | 0.419852i | ||||||||
\(142\) | 270.781i | 1.90691i | ||||||||
\(143\) | −0.758526 | −0.00530438 | ||||||||
\(144\) | 103.304 | 0.717387 | ||||||||
\(145\) | −22.5385 | −0.155438 | ||||||||
\(146\) | −400.354 | −2.74215 | ||||||||
\(147\) | 18.1084 | 0.123187 | ||||||||
\(148\) | − | 411.058i | − | 2.77742i | ||||||
\(149\) | 15.5533i | 0.104385i | 0.998637 | + | 0.0521924i | \(0.0166209\pi\) | ||||
−0.998637 | + | 0.0521924i | \(0.983379\pi\) | |||||||
\(150\) | 157.386i | 1.04924i | ||||||||
\(151\) | 48.2391i | 0.319464i | 0.987160 | + | 0.159732i | \(0.0510631\pi\) | ||||
−0.987160 | + | 0.159732i | \(0.948937\pi\) | |||||||
\(152\) | − | 206.671i | − | 1.35968i | ||||||
\(153\) | −24.3282 | −0.159008 | ||||||||
\(154\) | −194.098 | −1.26038 | ||||||||
\(155\) | 0.186472i | 0.00120305i | ||||||||
\(156\) | − | 1.44145i | − | 0.00924004i | ||||||
\(157\) | − | 218.253i | − | 1.39014i | −0.718940 | − | 0.695072i | \(-0.755372\pi\) | ||
0.718940 | − | 0.695072i | \(-0.244628\pi\) | |||||||
\(158\) | − | 271.586i | − | 1.71890i | ||||||
\(159\) | 137.483 | 0.864671 | ||||||||
\(160\) | 18.7111i | 0.116944i | ||||||||
\(161\) | 87.1094i | 0.541052i | ||||||||
\(162\) | 32.9183i | 0.203200i | ||||||||
\(163\) | 300.810 | 1.84546 | 0.922729 | − | 0.385449i | \(-0.125953\pi\) | ||||
0.922729 | + | 0.385449i | \(0.125953\pi\) | |||||||
\(164\) | −130.106 | −0.793326 | ||||||||
\(165\) | 5.86076i | 0.0355197i | ||||||||
\(166\) | −325.136 | −1.95865 | ||||||||
\(167\) | −285.372 | −1.70881 | −0.854407 | − | 0.519605i | \(-0.826079\pi\) | ||||
−0.854407 | + | 0.519605i | \(0.826079\pi\) | |||||||
\(168\) | − | 211.524i | − | 1.25907i | ||||||
\(169\) | 168.992 | 0.999953 | ||||||||
\(170\) | − | 11.7418i | − | 0.0690694i | ||||||
\(171\) | 31.5201 | 0.184328 | ||||||||
\(172\) | 504.231i | 2.93157i | ||||||||
\(173\) | − | 115.450i | − | 0.667344i | −0.942689 | − | 0.333672i | \(-0.891712\pi\) | ||
0.942689 | − | 0.333672i | \(-0.108288\pi\) | |||||||
\(174\) | 360.687i | 2.07291i | ||||||||
\(175\) | 154.239 | 0.881365 | ||||||||
\(176\) | − | 294.332i | − | 1.67234i | ||||||
\(177\) | 71.9349 | + | 72.5835i | 0.406412 | + | 0.410076i | ||||
\(178\) | 522.594 | 2.93592 | ||||||||
\(179\) | − | 145.888i | − | 0.815016i | −0.913202 | − | 0.407508i | \(-0.866398\pi\) | ||
0.913202 | − | 0.407508i | \(-0.133602\pi\) | |||||||
\(180\) | −11.1373 | −0.0618741 | ||||||||
\(181\) | −40.9343 | −0.226157 | −0.113078 | − | 0.993586i | \(-0.536071\pi\) | ||||
−0.113078 | + | 0.993586i | \(0.536071\pi\) | |||||||
\(182\) | −2.01516 | −0.0110723 | ||||||||
\(183\) | 79.2901i | 0.433280i | ||||||||
\(184\) | −275.991 | −1.49995 | ||||||||
\(185\) | 17.3518i | 0.0937935i | ||||||||
\(186\) | 2.98414 | 0.0160437 | ||||||||
\(187\) | 69.3155i | 0.370671i | ||||||||
\(188\) | 320.527i | 1.70493i | ||||||||
\(189\) | 32.2602 | 0.170689 | ||||||||
\(190\) | 15.2129i | 0.0800680i | ||||||||
\(191\) | − | 281.121i | − | 1.47184i | −0.677070 | − | 0.735919i | \(-0.736751\pi\) | ||
0.677070 | − | 0.735919i | \(-0.263249\pi\) | |||||||
\(192\) | 60.8658 | 0.317010 | ||||||||
\(193\) | 46.9362 | 0.243193 | 0.121596 | − | 0.992580i | \(-0.461199\pi\) | ||||
0.121596 | + | 0.992580i | \(0.461199\pi\) | |||||||
\(194\) | −297.998 | −1.53607 | ||||||||
\(195\) | 0.0608472i | 0.000312037i | ||||||||
\(196\) | 98.0459 | 0.500234 | ||||||||
\(197\) | 20.8170 | 0.105670 | 0.0528350 | − | 0.998603i | \(-0.483174\pi\) | ||||
0.0528350 | + | 0.998603i | \(0.483174\pi\) | |||||||
\(198\) | 93.7905 | 0.473689 | ||||||||
\(199\) | −206.378 | −1.03707 | −0.518537 | − | 0.855055i | \(-0.673523\pi\) | ||||
−0.518537 | + | 0.855055i | \(0.673523\pi\) | |||||||
\(200\) | 488.679i | 2.44339i | ||||||||
\(201\) | − | 180.918i | − | 0.900088i | ||||||
\(202\) | −336.822 | −1.66744 | ||||||||
\(203\) | 353.475 | 1.74126 | ||||||||
\(204\) | −131.722 | −0.645696 | ||||||||
\(205\) | 5.49209 | 0.0267907 | ||||||||
\(206\) | −539.567 | −2.61926 | ||||||||
\(207\) | − | 42.0922i | − | 0.203344i | ||||||
\(208\) | − | 3.05579i | − | 0.0146913i | ||||||
\(209\) | − | 89.8066i | − | 0.429697i | ||||||
\(210\) | 15.5701i | 0.0741434i | ||||||||
\(211\) | − | 200.660i | − | 0.950993i | −0.879718 | − | 0.475497i | \(-0.842268\pi\) | ||
0.879718 | − | 0.475497i | \(-0.157732\pi\) | |||||||
\(212\) | 744.384 | 3.51124 | ||||||||
\(213\) | −128.228 | −0.602010 | ||||||||
\(214\) | 252.245i | 1.17871i | ||||||||
\(215\) | − | 21.2849i | − | 0.0989994i | ||||||
\(216\) | 102.211i | 0.473198i | ||||||||
\(217\) | − | 2.92447i | − | 0.0134768i | ||||||
\(218\) | −209.690 | −0.961879 | ||||||||
\(219\) | − | 189.588i | − | 0.865697i | ||||||
\(220\) | 31.7324i | 0.144238i | ||||||||
\(221\) | 0.719643i | 0.00325630i | ||||||||
\(222\) | 277.683 | 1.25082 | ||||||||
\(223\) | −271.603 | −1.21795 | −0.608976 | − | 0.793189i | \(-0.708419\pi\) | ||||
−0.608976 | + | 0.793189i | \(0.708419\pi\) | |||||||
\(224\) | − | 293.449i | − | 1.31004i | ||||||
\(225\) | −74.5299 | −0.331244 | ||||||||
\(226\) | −71.9989 | −0.318579 | ||||||||
\(227\) | − | 124.072i | − | 0.546571i | −0.961933 | − | 0.273286i | \(-0.911890\pi\) | ||
0.961933 | − | 0.273286i | \(-0.0881104\pi\) | |||||||
\(228\) | 170.662 | 0.748516 | ||||||||
\(229\) | 269.653i | 1.17752i | 0.808307 | + | 0.588762i | \(0.200384\pi\) | ||||
−0.808307 | + | 0.588762i | \(0.799616\pi\) | |||||||
\(230\) | 20.3155 | 0.0883281 | ||||||||
\(231\) | − | 91.9152i | − | 0.397901i | ||||||
\(232\) | 1119.93i | 4.82727i | ||||||||
\(233\) | 432.383i | 1.85572i | 0.372928 | + | 0.927860i | \(0.378354\pi\) | ||||
−0.372928 | + | 0.927860i | \(0.621646\pi\) | |||||||
\(234\) | 0.973745 | 0.00416130 | ||||||||
\(235\) | − | 13.5302i | − | 0.0575755i | ||||||
\(236\) | 389.483 | + | 392.995i | 1.65035 | + | 1.66523i | ||||
\(237\) | 128.610 | 0.542657 | ||||||||
\(238\) | 184.149i | 0.773733i | ||||||||
\(239\) | 345.014 | 1.44357 | 0.721787 | − | 0.692115i | \(-0.243321\pi\) | ||||
0.721787 | + | 0.692115i | \(0.243321\pi\) | |||||||
\(240\) | −23.6106 | −0.0983774 | ||||||||
\(241\) | −395.883 | −1.64267 | −0.821334 | − | 0.570447i | \(-0.806770\pi\) | ||||
−0.821334 | + | 0.570447i | \(0.806770\pi\) | |||||||
\(242\) | 175.342i | 0.724554i | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 429.307i | 1.75945i | ||||||||
\(245\) | −4.13877 | −0.0168929 | ||||||||
\(246\) | − | 87.8906i | − | 0.357279i | ||||||
\(247\) | − | 0.932384i | − | 0.00377483i | ||||||
\(248\) | 9.26568 | 0.0373616 | ||||||||
\(249\) | − | 153.968i | − | 0.618346i | ||||||
\(250\) | − | 72.1694i | − | 0.288678i | ||||||
\(251\) | 98.2846 | 0.391572 | 0.195786 | − | 0.980647i | \(-0.437274\pi\) | ||||
0.195786 | + | 0.980647i | \(0.437274\pi\) | |||||||
\(252\) | 174.669 | 0.693130 | ||||||||
\(253\) | −119.929 | −0.474026 | ||||||||
\(254\) | 21.7774i | 0.0857379i | ||||||||
\(255\) | 5.56033 | 0.0218052 | ||||||||
\(256\) | −361.966 | −1.41393 | ||||||||
\(257\) | −248.162 | −0.965609 | −0.482805 | − | 0.875728i | \(-0.660382\pi\) | ||||
−0.482805 | + | 0.875728i | \(0.660382\pi\) | |||||||
\(258\) | −340.625 | −1.32025 | ||||||||
\(259\) | − | 272.131i | − | 1.05070i | ||||||
\(260\) | 0.329450i | 0.00126711i | ||||||||
\(261\) | −170.803 | −0.654418 | ||||||||
\(262\) | 759.066 | 2.89720 | ||||||||
\(263\) | 194.073 | 0.737919 | 0.368959 | − | 0.929446i | \(-0.379714\pi\) | ||||
0.368959 | + | 0.929446i | \(0.379714\pi\) | |||||||
\(264\) | 291.217 | 1.10310 | ||||||||
\(265\) | −31.4224 | −0.118575 | ||||||||
\(266\) | − | 238.587i | − | 0.896942i | ||||||
\(267\) | 247.474i | 0.926869i | ||||||||
\(268\) | − | 979.557i | − | 3.65506i | ||||||
\(269\) | − | 213.661i | − | 0.794278i | −0.917758 | − | 0.397139i | \(-0.870003\pi\) | ||
0.917758 | − | 0.397139i | \(-0.129997\pi\) | |||||||
\(270\) | − | 7.52364i | − | 0.0278653i | ||||||
\(271\) | −56.3572 | −0.207960 | −0.103980 | − | 0.994579i | \(-0.533158\pi\) | ||||
−0.103980 | + | 0.994579i | \(0.533158\pi\) | |||||||
\(272\) | −279.244 | −1.02663 | ||||||||
\(273\) | − | 0.954276i | − | 0.00349552i | ||||||
\(274\) | − | 228.707i | − | 0.834698i | ||||||
\(275\) | 212.349i | 0.772180i | ||||||||
\(276\) | − | 227.903i | − | 0.825736i | ||||||
\(277\) | 170.342 | 0.614953 | 0.307476 | − | 0.951556i | \(-0.400515\pi\) | ||||
0.307476 | + | 0.951556i | \(0.400515\pi\) | |||||||
\(278\) | − | 371.246i | − | 1.33542i | ||||||
\(279\) | 1.41314i | 0.00506500i | ||||||||
\(280\) | 48.3448i | 0.172660i | ||||||||
\(281\) | −39.9961 | −0.142335 | −0.0711674 | − | 0.997464i | \(-0.522672\pi\) | ||||
−0.0711674 | + | 0.997464i | \(0.522672\pi\) | |||||||
\(282\) | −216.526 | −0.767824 | ||||||||
\(283\) | − | 357.475i | − | 1.26316i | −0.775309 | − | 0.631581i | \(-0.782406\pi\) | ||
0.775309 | − | 0.631581i | \(-0.217594\pi\) | |||||||
\(284\) | −694.275 | −2.44463 | ||||||||
\(285\) | −7.20407 | −0.0252774 | ||||||||
\(286\) | − | 2.77438i | − | 0.00970063i | ||||||
\(287\) | −86.1333 | −0.300116 | ||||||||
\(288\) | 141.798i | 0.492353i | ||||||||
\(289\) | −223.238 | −0.772449 | ||||||||
\(290\) | − | 82.4368i | − | 0.284265i | ||||||
\(291\) | − | 141.117i | − | 0.484937i | ||||||
\(292\) | − | 1026.50i | − | 3.51541i | ||||||
\(293\) | 67.1472 | 0.229171 | 0.114586 | − | 0.993413i | \(-0.463446\pi\) | ||||
0.114586 | + | 0.993413i | \(0.463446\pi\) | |||||||
\(294\) | 66.2332i | 0.225283i | ||||||||
\(295\) | −16.4411 | − | 16.5893i | −0.0557324 | − | 0.0562350i | ||||
\(296\) | 862.200 | 2.91284 | ||||||||
\(297\) | 44.4144i | 0.149544i | ||||||||
\(298\) | −56.8878 | −0.190899 | ||||||||
\(299\) | −1.24511 | −0.00416426 | ||||||||
\(300\) | −403.533 | −1.34511 | ||||||||
\(301\) | 333.814i | 1.10902i | ||||||||
\(302\) | −176.439 | −0.584235 | ||||||||
\(303\) | − | 159.502i | − | 0.526409i | ||||||
\(304\) | 361.794 | 1.19011 | ||||||||
\(305\) | − | 18.1221i | − | 0.0594169i | ||||||
\(306\) | − | 88.9826i | − | 0.290793i | ||||||
\(307\) | 123.299 | 0.401626 | 0.200813 | − | 0.979630i | \(-0.435642\pi\) | ||||
0.200813 | + | 0.979630i | \(0.435642\pi\) | |||||||
\(308\) | − | 497.664i | − | 1.61579i | ||||||
\(309\) | − | 255.512i | − | 0.826899i | ||||||
\(310\) | −0.682039 | −0.00220013 | ||||||||
\(311\) | −246.230 | −0.791737 | −0.395868 | − | 0.918307i | \(-0.629556\pi\) | ||||
−0.395868 | + | 0.918307i | \(0.629556\pi\) | |||||||
\(312\) | 3.02346 | 0.00969057 | ||||||||
\(313\) | − | 489.577i | − | 1.56414i | −0.623189 | − | 0.782071i | \(-0.714163\pi\) | ||
0.623189 | − | 0.782071i | \(-0.285837\pi\) | |||||||
\(314\) | 798.280 | 2.54229 | ||||||||
\(315\) | −7.37322 | −0.0234070 | ||||||||
\(316\) | 696.341 | 2.20361 | ||||||||
\(317\) | 319.318 | 1.00731 | 0.503656 | − | 0.863904i | \(-0.331988\pi\) | ||||
0.503656 | + | 0.863904i | \(0.331988\pi\) | |||||||
\(318\) | 502.856i | 1.58131i | ||||||||
\(319\) | 486.650i | 1.52555i | ||||||||
\(320\) | −13.9112 | −0.0434725 | ||||||||
\(321\) | −119.450 | −0.372120 | ||||||||
\(322\) | −318.611 | −0.989474 | ||||||||
\(323\) | −85.2029 | −0.263786 | ||||||||
\(324\) | −84.4018 | −0.260499 | ||||||||
\(325\) | 2.20464i | 0.00678351i | ||||||||
\(326\) | 1100.24i | 3.37497i | ||||||||
\(327\) | − | 99.2984i | − | 0.303665i | ||||||
\(328\) | − | 272.898i | − | 0.832007i | ||||||
\(329\) | 212.197i | 0.644976i | ||||||||
\(330\) | −21.4363 | −0.0649584 | ||||||||
\(331\) | −222.382 | −0.671850 | −0.335925 | − | 0.941889i | \(-0.609049\pi\) | ||||
−0.335925 | + | 0.941889i | \(0.609049\pi\) | |||||||
\(332\) | − | 833.642i | − | 2.51097i | ||||||
\(333\) | 131.497i | 0.394885i | ||||||||
\(334\) | − | 1043.77i | − | 3.12507i | ||||||
\(335\) | 41.3496i | 0.123432i | ||||||||
\(336\) | 370.288 | 1.10205 | ||||||||
\(337\) | − | 285.028i | − | 0.845781i | −0.906181 | − | 0.422890i | \(-0.861016\pi\) | ||
0.906181 | − | 0.422890i | \(-0.138984\pi\) | |||||||
\(338\) | 618.104i | 1.82871i | ||||||||
\(339\) | − | 34.0950i | − | 0.100575i | ||||||
\(340\) | 30.1057 | 0.0885462 | ||||||||
\(341\) | 4.02629 | 0.0118073 | ||||||||
\(342\) | 115.288i | 0.337098i | ||||||||
\(343\) | 369.124 | 1.07616 | ||||||||
\(344\) | −1057.63 | −3.07451 | ||||||||
\(345\) | 9.62037i | 0.0278851i | ||||||||
\(346\) | 422.271 | 1.22044 | ||||||||
\(347\) | 62.2130i | 0.179288i | 0.995974 | + | 0.0896441i | \(0.0285730\pi\) | ||||
−0.995974 | + | 0.0896441i | \(0.971427\pi\) | |||||||
\(348\) | −924.793 | −2.65745 | ||||||||
\(349\) | − | 291.454i | − | 0.835112i | −0.908651 | − | 0.417556i | \(-0.862887\pi\) | ||
0.908651 | − | 0.417556i | \(-0.137113\pi\) | |||||||
\(350\) | 564.143i | 1.61184i | ||||||||
\(351\) | 0.461116i | 0.00131372i | ||||||||
\(352\) | 404.008 | 1.14775 | ||||||||
\(353\) | 306.106i | 0.867156i | 0.901116 | + | 0.433578i | \(0.142749\pi\) | ||||
−0.901116 | + | 0.433578i | \(0.857251\pi\) | |||||||
\(354\) | −265.481 | + | 263.109i | −0.749946 | + | 0.743245i | ||||
\(355\) | 29.3071 | 0.0825553 | ||||||||
\(356\) | 1339.92i | 3.76382i | ||||||||
\(357\) | −87.2035 | −0.244267 | ||||||||
\(358\) | 533.598 | 1.49050 | ||||||||
\(359\) | 461.119 | 1.28445 | 0.642226 | − | 0.766515i | \(-0.278011\pi\) | ||||
0.642226 | + | 0.766515i | \(0.278011\pi\) | |||||||
\(360\) | − | 23.3608i | − | 0.0648910i | ||||||
\(361\) | −250.609 | −0.694209 | ||||||||
\(362\) | − | 149.721i | − | 0.413594i | ||||||
\(363\) | −83.0332 | −0.228742 | ||||||||
\(364\) | − | 5.16681i | − | 0.0141945i | ||||||
\(365\) | 43.3312i | 0.118715i | ||||||||
\(366\) | −290.011 | −0.792380 | ||||||||
\(367\) | 232.591i | 0.633763i | 0.948465 | + | 0.316881i | \(0.102636\pi\) | ||||
−0.948465 | + | 0.316881i | \(0.897364\pi\) | |||||||
\(368\) | − | 483.143i | − | 1.31289i | ||||||
\(369\) | 41.6205 | 0.112793 | ||||||||
\(370\) | −63.4658 | −0.171529 | ||||||||
\(371\) | 492.802 | 1.32831 | ||||||||
\(372\) | 7.65125i | 0.0205679i | ||||||||
\(373\) | −36.2600 | −0.0972117 | −0.0486058 | − | 0.998818i | \(-0.515478\pi\) | ||||
−0.0486058 | + | 0.998818i | \(0.515478\pi\) | |||||||
\(374\) | −253.528 | −0.677882 | ||||||||
\(375\) | 34.1758 | 0.0911354 | ||||||||
\(376\) | −672.309 | −1.78806 | ||||||||
\(377\) | 5.05246i | 0.0134018i | ||||||||
\(378\) | 117.994i | 0.312155i | ||||||||
\(379\) | −37.4494 | −0.0988110 | −0.0494055 | − | 0.998779i | \(-0.515733\pi\) | ||||
−0.0494055 | + | 0.998779i | \(0.515733\pi\) | |||||||
\(380\) | −39.0056 | −0.102646 | ||||||||
\(381\) | −10.3127 | −0.0270674 | ||||||||
\(382\) | 1028.23 | 2.69169 | ||||||||
\(383\) | −487.151 | −1.27193 | −0.635967 | − | 0.771716i | \(-0.719399\pi\) | ||||
−0.635967 | + | 0.771716i | \(0.719399\pi\) | |||||||
\(384\) | − | 104.845i | − | 0.273034i | ||||||
\(385\) | 21.0077i | 0.0545654i | ||||||||
\(386\) | 171.673i | 0.444750i | ||||||||
\(387\) | − | 161.303i | − | 0.416802i | ||||||
\(388\) | − | 764.059i | − | 1.96922i | ||||||
\(389\) | 377.266 | 0.969834 | 0.484917 | − | 0.874560i | \(-0.338850\pi\) | ||||
0.484917 | + | 0.874560i | \(0.338850\pi\) | |||||||
\(390\) | −0.222554 | −0.000570652 | ||||||||
\(391\) | 113.781i | 0.290999i | ||||||||
\(392\) | 205.653i | 0.524624i | ||||||||
\(393\) | 359.455i | 0.914645i | ||||||||
\(394\) | 76.1400i | 0.193249i | ||||||||
\(395\) | −29.3944 | −0.0744161 | ||||||||
\(396\) | 240.477i | 0.607264i | ||||||||
\(397\) | 457.106i | 1.15140i | 0.817661 | + | 0.575700i | \(0.195270\pi\) | ||||
−0.817661 | + | 0.575700i | \(0.804730\pi\) | |||||||
\(398\) | − | 754.845i | − | 1.89660i | ||||||
\(399\) | 112.983 | 0.283164 | ||||||||
\(400\) | −855.469 | −2.13867 | ||||||||
\(401\) | 242.627i | 0.605056i | 0.953141 | + | 0.302528i | \(0.0978305\pi\) | ||||
−0.953141 | + | 0.302528i | \(0.902169\pi\) | |||||||
\(402\) | 661.723 | 1.64608 | ||||||||
\(403\) | 0.0418014 | 0.000103726 | ||||||||
\(404\) | − | 863.605i | − | 2.13764i | ||||||
\(405\) | 3.56282 | 0.00879708 | ||||||||
\(406\) | 1292.87i | 3.18441i | ||||||||
\(407\) | 374.658 | 0.920537 | ||||||||
\(408\) | − | 276.289i | − | 0.677179i | ||||||
\(409\) | 362.561i | 0.886458i | 0.896408 | + | 0.443229i | \(0.146167\pi\) | ||||
−0.896408 | + | 0.443229i | \(0.853833\pi\) | |||||||
\(410\) | 20.0878i | 0.0489947i | ||||||||
\(411\) | 108.304 | 0.263514 | ||||||||
\(412\) | − | 1383.44i | − | 3.35786i | ||||||
\(413\) | 257.848 | + | 260.173i | 0.624329 | + | 0.629959i | ||||
\(414\) | 153.956 | 0.371875 | ||||||||
\(415\) | 35.1902i | 0.0847956i | ||||||||
\(416\) | 4.19446 | 0.0100828 | ||||||||
\(417\) | 175.803 | 0.421591 | ||||||||
\(418\) | 328.476 | 0.785827 | ||||||||
\(419\) | 818.928i | 1.95448i | 0.212133 | + | 0.977241i | \(0.431959\pi\) | ||||
−0.212133 | + | 0.977241i | \(0.568041\pi\) | |||||||
\(420\) | −39.9214 | −0.0950509 | ||||||||
\(421\) | 329.980i | 0.783801i | 0.920008 | + | 0.391901i | \(0.128182\pi\) | ||||
−0.920008 | + | 0.391901i | \(0.871818\pi\) | |||||||
\(422\) | 733.931 | 1.73917 | ||||||||
\(423\) | − | 102.536i | − | 0.242402i | ||||||
\(424\) | 1561.36i | 3.68244i | ||||||||
\(425\) | 201.464 | 0.474033 | ||||||||
\(426\) | − | 469.006i | − | 1.10095i | ||||||
\(427\) | 284.213i | 0.665603i | ||||||||
\(428\) | −646.750 | −1.51110 | ||||||||
\(429\) | 1.31381 | 0.00306249 | ||||||||
\(430\) | 77.8514 | 0.181050 | ||||||||
\(431\) | − | 713.566i | − | 1.65561i | −0.561019 | − | 0.827803i | \(-0.689590\pi\) | ||
0.561019 | − | 0.827803i | \(-0.310410\pi\) | |||||||
\(432\) | −178.927 | −0.414184 | ||||||||
\(433\) | 625.618 | 1.44485 | 0.722423 | − | 0.691452i | \(-0.243029\pi\) | ||||
0.722423 | + | 0.691452i | \(0.243029\pi\) | |||||||
\(434\) | 10.6965 | 0.0246464 | ||||||||
\(435\) | 39.0379 | 0.0897423 | ||||||||
\(436\) | − | 537.639i | − | 1.23312i | ||||||
\(437\) | − | 147.417i | − | 0.337338i | ||||||
\(438\) | 693.434 | 1.58318 | ||||||||
\(439\) | −461.737 | −1.05179 | −0.525897 | − | 0.850548i | \(-0.676270\pi\) | ||||
−0.525897 | + | 0.850548i | \(0.676270\pi\) | |||||||
\(440\) | −66.5591 | −0.151271 | ||||||||
\(441\) | −31.3647 | −0.0711218 | ||||||||
\(442\) | −2.63216 | −0.00595511 | ||||||||
\(443\) | − | 255.246i | − | 0.576175i | −0.957604 | − | 0.288088i | \(-0.906981\pi\) | ||
0.957604 | − | 0.288088i | \(-0.0930195\pi\) | |||||||
\(444\) | 711.973i | 1.60354i | ||||||||
\(445\) | − | 56.5614i | − | 0.127104i | ||||||
\(446\) | − | 993.413i | − | 2.22738i | ||||||
\(447\) | − | 26.9392i | − | 0.0602666i | ||||||
\(448\) | 218.171 | 0.486989 | ||||||||
\(449\) | −224.485 | −0.499966 | −0.249983 | − | 0.968250i | \(-0.580425\pi\) | ||||
−0.249983 | + | 0.968250i | \(0.580425\pi\) | |||||||
\(450\) | − | 272.600i | − | 0.605777i | ||||||
\(451\) | − | 118.585i | − | 0.262937i | ||||||
\(452\) | − | 184.603i | − | 0.408415i | ||||||
\(453\) | − | 83.5526i | − | 0.184443i | ||||||
\(454\) | 453.804 | 0.999568 | ||||||||
\(455\) | 0.218104i | 0.000479350i | ||||||||
\(456\) | 357.966i | 0.785012i | ||||||||
\(457\) | 64.2869i | 0.140671i | 0.997523 | + | 0.0703357i | \(0.0224071\pi\) | ||||
−0.997523 | + | 0.0703357i | \(0.977593\pi\) | |||||||
\(458\) | −986.281 | −2.15345 | ||||||||
\(459\) | 42.1377 | 0.0918032 | ||||||||
\(460\) | 52.0884i | 0.113236i | ||||||||
\(461\) | −212.758 | −0.461513 | −0.230757 | − | 0.973012i | \(-0.574120\pi\) | ||||
−0.230757 | + | 0.973012i | \(0.574120\pi\) | |||||||
\(462\) | 336.188 | 0.727680 | ||||||||
\(463\) | 291.329i | 0.629221i | 0.949221 | + | 0.314610i | \(0.101874\pi\) | ||||
−0.949221 | + | 0.314610i | \(0.898126\pi\) | |||||||
\(464\) | −1960.51 | −4.22524 | ||||||||
\(465\) | − | 0.322979i | − | 0.000694579i | ||||||
\(466\) | −1581.48 | −3.39373 | ||||||||
\(467\) | − | 31.5294i | − | 0.0675148i | −0.999430 | − | 0.0337574i | \(-0.989253\pi\) | ||
0.999430 | − | 0.0337574i | \(-0.0107474\pi\) | |||||||
\(468\) | 2.49666i | 0.00533474i | ||||||||
\(469\) | − | 648.493i | − | 1.38271i | ||||||
\(470\) | 49.4881 | 0.105294 | ||||||||
\(471\) | 378.025i | 0.802600i | ||||||||
\(472\) | −824.313 | + | 816.946i | −1.74643 | + | 1.73082i | ||||
\(473\) | −459.581 | −0.971630 | ||||||||
\(474\) | 470.402i | 0.992408i | ||||||||
\(475\) | −261.021 | −0.549518 | ||||||||
\(476\) | −472.153 | −0.991917 | ||||||||
\(477\) | −238.127 | −0.499218 | ||||||||
\(478\) | 1261.92i | 2.64000i | ||||||||
\(479\) | −172.294 | −0.359695 | −0.179848 | − | 0.983694i | \(-0.557560\pi\) | ||||
−0.179848 | + | 0.983694i | \(0.557560\pi\) | |||||||
\(480\) | − | 32.4085i | − | 0.0675178i | ||||||
\(481\) | 3.88975 | 0.00808680 | ||||||||
\(482\) | − | 1447.98i | − | 3.00411i | ||||||
\(483\) | − | 150.878i | − | 0.312376i | ||||||
\(484\) | −449.573 | −0.928870 | ||||||||
\(485\) | 32.2529i | 0.0665008i | ||||||||
\(486\) | − | 57.0162i | − | 0.117317i | ||||||
\(487\) | −403.087 | −0.827694 | −0.413847 | − | 0.910347i | \(-0.635815\pi\) | ||||
−0.413847 | + | 0.910347i | \(0.635815\pi\) | |||||||
\(488\) | −900.478 | −1.84524 | ||||||||
\(489\) | −521.018 | −1.06548 | ||||||||
\(490\) | − | 15.1379i | − | 0.0308937i | ||||||
\(491\) | 294.608 | 0.600017 | 0.300008 | − | 0.953937i | \(-0.403011\pi\) | ||||
0.300008 | + | 0.953937i | \(0.403011\pi\) | |||||||
\(492\) | 225.349 | 0.458027 | ||||||||
\(493\) | 461.703 | 0.936518 | ||||||||
\(494\) | 3.41028 | 0.00690340 | ||||||||
\(495\) | − | 10.1511i | − | 0.0205073i | ||||||
\(496\) | 16.2203i | 0.0327021i | ||||||||
\(497\) | −459.628 | −0.924806 | ||||||||
\(498\) | 563.153 | 1.13083 | ||||||||
\(499\) | 515.505 | 1.03308 | 0.516538 | − | 0.856264i | \(-0.327220\pi\) | ||||
0.516538 | + | 0.856264i | \(0.327220\pi\) | |||||||
\(500\) | 185.041 | 0.370081 | ||||||||
\(501\) | 494.279 | 0.986584 | ||||||||
\(502\) | 359.485i | 0.716105i | ||||||||
\(503\) | 618.687i | 1.22999i | 0.788529 | + | 0.614997i | \(0.210843\pi\) | ||||
−0.788529 | + | 0.614997i | \(0.789157\pi\) | |||||||
\(504\) | 366.370i | 0.726925i | ||||||||
\(505\) | 36.4550i | 0.0721881i | ||||||||
\(506\) | − | 438.650i | − | 0.866896i | ||||||
\(507\) | −292.703 | −0.577323 | ||||||||
\(508\) | −55.8368 | −0.109915 | ||||||||
\(509\) | 597.596i | 1.17406i | 0.809566 | + | 0.587029i | \(0.199703\pi\) | ||||
−0.809566 | + | 0.587029i | \(0.800297\pi\) | |||||||
\(510\) | 20.3374i | 0.0398773i | ||||||||
\(511\) | − | 679.569i | − | 1.32988i | ||||||
\(512\) | − | 1081.80i | − | 2.11288i | ||||||
\(513\) | −54.5944 | −0.106422 | ||||||||
\(514\) | − | 907.674i | − | 1.76590i | ||||||
\(515\) | 58.3984i | 0.113395i | ||||||||
\(516\) | − | 873.353i | − | 1.69255i | ||||||
\(517\) | −292.144 | −0.565075 | ||||||||
\(518\) | 995.344 | 1.92151 | ||||||||
\(519\) | 199.966i | 0.385291i | ||||||||
\(520\) | −0.691026 | −0.00132890 | ||||||||
\(521\) | −190.298 | −0.365256 | −0.182628 | − | 0.983182i | \(-0.558460\pi\) | ||||
−0.182628 | + | 0.983182i | \(0.558460\pi\) | |||||||
\(522\) | − | 624.728i | − | 1.19680i | ||||||
\(523\) | −579.438 | −1.10791 | −0.553956 | − | 0.832546i | \(-0.686882\pi\) | ||||
−0.553956 | + | 0.832546i | \(0.686882\pi\) | |||||||
\(524\) | 1946.23i | 3.71418i | ||||||||
\(525\) | −267.149 | −0.508856 | ||||||||
\(526\) | 709.838i | 1.34950i | ||||||||
\(527\) | − | 3.81989i | − | 0.00724837i | ||||||
\(528\) | 509.798i | 0.965526i | ||||||||
\(529\) | 332.139 | 0.627861 | ||||||||
\(530\) | − | 114.930i | − | 0.216849i | ||||||
\(531\) | −124.595 | − | 125.718i | −0.234642 | − | 0.236758i | ||||
\(532\) | 611.730 | 1.14987 | ||||||||
\(533\) | − | 1.23116i | − | 0.00230987i | ||||||
\(534\) | −905.159 | −1.69505 | ||||||||
\(535\) | 27.3010 | 0.0510299 | ||||||||
\(536\) | 2054.64 | 3.83328 | ||||||||
\(537\) | 252.685i | 0.470550i | ||||||||
\(538\) | 781.484 | 1.45257 | ||||||||
\(539\) | 89.3639i | 0.165796i | ||||||||
\(540\) | 19.2904 | 0.0357230 | ||||||||
\(541\) | − | 808.858i | − | 1.49512i | −0.664196 | − | 0.747558i | \(-0.731226\pi\) | ||
0.664196 | − | 0.747558i | \(-0.268774\pi\) | |||||||
\(542\) | − | 206.132i | − | 0.380317i | ||||||
\(543\) | 70.9004 | 0.130572 | ||||||||
\(544\) | − | 383.298i | − | 0.704591i | ||||||
\(545\) | 22.6951i | 0.0416424i | ||||||||
\(546\) | 3.49035 | 0.00639258 | ||||||||
\(547\) | 270.832 | 0.495122 | 0.247561 | − | 0.968872i | \(-0.420371\pi\) | ||||
0.247561 | + | 0.968872i | \(0.420371\pi\) | |||||||
\(548\) | 586.400 | 1.07007 | ||||||||
\(549\) | − | 137.335i | − | 0.250154i | ||||||
\(550\) | −776.688 | −1.41216 | ||||||||
\(551\) | −598.192 | −1.08565 | ||||||||
\(552\) | 478.030 | 0.865997 | ||||||||
\(553\) | 460.996 | 0.833628 | ||||||||
\(554\) | 623.041i | 1.12462i | ||||||||
\(555\) | − | 30.0542i | − | 0.0541517i | ||||||
\(556\) | 951.866 | 1.71199 | ||||||||
\(557\) | −519.832 | −0.933270 | −0.466635 | − | 0.884450i | \(-0.654534\pi\) | ||||
−0.466635 | + | 0.884450i | \(0.654534\pi\) | |||||||
\(558\) | −5.16868 | −0.00926286 | ||||||||
\(559\) | −4.77143 | −0.00853565 | ||||||||
\(560\) | −84.6312 | −0.151127 | ||||||||
\(561\) | − | 120.058i | − | 0.214007i | ||||||
\(562\) | − | 146.289i | − | 0.260301i | ||||||
\(563\) | − | 417.978i | − | 0.742411i | −0.928551 | − | 0.371206i | \(-0.878944\pi\) | ||
0.928551 | − | 0.371206i | \(-0.121056\pi\) | |||||||
\(564\) | − | 555.168i | − | 0.984341i | ||||||
\(565\) | 7.79258i | 0.0137922i | ||||||||
\(566\) | 1307.50 | 2.31007 | ||||||||
\(567\) | −55.8762 | −0.0985471 | ||||||||
\(568\) | − | 1456.25i | − | 2.56383i | ||||||
\(569\) | 285.720i | 0.502144i | 0.967968 | + | 0.251072i | \(0.0807831\pi\) | ||||
−0.967968 | + | 0.251072i | \(0.919217\pi\) | |||||||
\(570\) | − | 26.3495i | − | 0.0462273i | ||||||
\(571\) | 69.7739i | 0.122196i | 0.998132 | + | 0.0610980i | \(0.0194602\pi\) | ||||
−0.998132 | + | 0.0610980i | \(0.980540\pi\) | |||||||
\(572\) | 7.11345 | 0.0124361 | ||||||||
\(573\) | 486.916i | 0.849766i | ||||||||
\(574\) | − | 315.040i | − | 0.548851i | ||||||
\(575\) | 348.569i | 0.606208i | ||||||||
\(576\) | −105.423 | −0.183026 | ||||||||
\(577\) | 114.805 | 0.198968 | 0.0994840 | − | 0.995039i | \(-0.468281\pi\) | ||||
0.0994840 | + | 0.995039i | \(0.468281\pi\) | |||||||
\(578\) | − | 816.512i | − | 1.41265i | ||||||
\(579\) | −81.2959 | −0.140407 | ||||||||
\(580\) | 211.366 | 0.364424 | ||||||||
\(581\) | − | 551.893i | − | 0.949902i | ||||||
\(582\) | 516.147 | 0.886850 | ||||||||
\(583\) | 678.469i | 1.16375i | ||||||||
\(584\) | 2153.10 | 3.68681 | ||||||||
\(585\) | − | 0.105390i | − | 0.000180154i | ||||||
\(586\) | 245.597i | 0.419108i | ||||||||
\(587\) | − | 861.663i | − | 1.46791i | −0.679199 | − | 0.733954i | \(-0.737673\pi\) | ||
0.679199 | − | 0.733954i | \(-0.262327\pi\) | |||||||
\(588\) | −169.820 | −0.288810 | ||||||||
\(589\) | 4.94913i | 0.00840260i | ||||||||
\(590\) | 60.6770 | − | 60.1347i | 0.102842 | − | 0.101923i | ||||
\(591\) | −36.0561 | −0.0610085 | ||||||||
\(592\) | 1509.34i | 2.54957i | ||||||||
\(593\) | 903.733 | 1.52400 | 0.762001 | − | 0.647576i | \(-0.224217\pi\) | ||||
0.762001 | + | 0.647576i | \(0.224217\pi\) | |||||||
\(594\) | −162.450 | −0.273485 | ||||||||
\(595\) | 19.9308 | 0.0334971 | ||||||||
\(596\) | − | 145.859i | − | 0.244730i | ||||||
\(597\) | 357.457 | 0.598755 | ||||||||
\(598\) | − | 4.55412i | − | 0.00761558i | ||||||
\(599\) | 236.884 | 0.395466 | 0.197733 | − | 0.980256i | \(-0.436642\pi\) | ||||
0.197733 | + | 0.980256i | \(0.436642\pi\) | |||||||
\(600\) | − | 846.417i | − | 1.41069i | ||||||
\(601\) | − | 681.352i | − | 1.13370i | −0.823822 | − | 0.566848i | \(-0.808163\pi\) | ||
0.823822 | − | 0.566848i | \(-0.191837\pi\) | |||||||
\(602\) | −1220.96 | −2.02817 | ||||||||
\(603\) | 313.359i | 0.519666i | ||||||||
\(604\) | − | 452.386i | − | 0.748983i | ||||||
\(605\) | 18.9776 | 0.0313680 | ||||||||
\(606\) | 583.393 | 0.962695 | ||||||||
\(607\) | −855.559 | −1.40949 | −0.704744 | − | 0.709462i | \(-0.748938\pi\) | ||||
−0.704744 | + | 0.709462i | \(0.748938\pi\) | |||||||
\(608\) | 496.608i | 0.816790i | ||||||||
\(609\) | −612.237 | −1.00532 | ||||||||
\(610\) | 66.2834 | 0.108661 | ||||||||
\(611\) | −3.03308 | −0.00496412 | ||||||||
\(612\) | 228.149 | 0.372793 | ||||||||
\(613\) | − | 629.123i | − | 1.02630i | −0.858299 | − | 0.513151i | \(-0.828478\pi\) | ||
0.858299 | − | 0.513151i | \(-0.171522\pi\) | |||||||
\(614\) | 450.978i | 0.734492i | ||||||||
\(615\) | −9.51257 | −0.0154676 | ||||||||
\(616\) | 1043.86 | 1.69457 | ||||||||
\(617\) | −909.047 | −1.47333 | −0.736667 | − | 0.676256i | \(-0.763602\pi\) | ||||
−0.736667 | + | 0.676256i | \(0.763602\pi\) | |||||||
\(618\) | 934.558 | 1.51223 | ||||||||
\(619\) | 437.303 | 0.706466 | 0.353233 | − | 0.935535i | \(-0.385082\pi\) | ||||
0.353233 | + | 0.935535i | \(0.385082\pi\) | |||||||
\(620\) | − | 1.74873i | − | 0.00282053i | ||||||
\(621\) | 72.9058i | 0.117401i | ||||||||
\(622\) | − | 900.609i | − | 1.44792i | ||||||
\(623\) | 887.061i | 1.42385i | ||||||||
\(624\) | 5.29279i | 0.00848203i | ||||||||
\(625\) | 613.271 | 0.981234 | ||||||||
\(626\) | 1790.67 | 2.86050 | ||||||||
\(627\) | 155.550i | 0.248085i | ||||||||
\(628\) | 2046.77i | 3.25919i | ||||||||
\(629\) | − | 355.453i | − | 0.565108i | ||||||
\(630\) | − | 26.9682i | − | 0.0428067i | ||||||
\(631\) | −548.459 | −0.869190 | −0.434595 | − | 0.900626i | \(-0.643108\pi\) | ||||
−0.434595 | + | 0.900626i | \(0.643108\pi\) | |||||||
\(632\) | 1460.59i | 2.31106i | ||||||||
\(633\) | 347.553i | 0.549056i | ||||||||
\(634\) | 1167.93i | 1.84217i | ||||||||
\(635\) | 2.35702 | 0.00371184 | ||||||||
\(636\) | −1289.31 | −2.02722 | ||||||||
\(637\) | 0.927788i | 0.00145650i | ||||||||
\(638\) | −1779.97 | −2.78992 | ||||||||
\(639\) | 222.097 | 0.347570 | ||||||||
\(640\) | 23.9629i | 0.0374420i | ||||||||
\(641\) | −1064.88 | −1.66128 | −0.830640 | − | 0.556810i | \(-0.812025\pi\) | ||||
−0.830640 | + | 0.556810i | \(0.812025\pi\) | |||||||
\(642\) | − | 436.901i | − | 0.680531i | ||||||
\(643\) | 1042.17 | 1.62079 | 0.810395 | − | 0.585884i | \(-0.199252\pi\) | ||||
0.810395 | + | 0.585884i | \(0.199252\pi\) | |||||||
\(644\) | − | 816.910i | − | 1.26849i | ||||||
\(645\) | 36.8665i | 0.0571573i | ||||||||
\(646\) | − | 311.638i | − | 0.482411i | ||||||
\(647\) | −144.371 | −0.223138 | −0.111569 | − | 0.993757i | \(-0.535588\pi\) | ||||
−0.111569 | + | 0.993757i | \(0.535588\pi\) | |||||||
\(648\) | − | 177.034i | − | 0.273201i | ||||||
\(649\) | −358.195 | + | 354.994i | −0.551918 | + | 0.546986i | ||||
\(650\) | −8.06367 | −0.0124057 | ||||||||
\(651\) | 5.06533i | 0.00778085i | ||||||||
\(652\) | −2820.99 | −4.32667 | ||||||||
\(653\) | −816.374 | −1.25019 | −0.625095 | − | 0.780549i | \(-0.714940\pi\) | ||||
−0.625095 | + | 0.780549i | \(0.714940\pi\) | |||||||
\(654\) | 363.193 | 0.555341 | ||||||||
\(655\) | − | 82.1553i | − | 0.125428i | ||||||
\(656\) | 477.729 | 0.728245 | ||||||||
\(657\) | 328.375i | 0.499810i | ||||||||
\(658\) | −776.130 | −1.17953 | ||||||||
\(659\) | − | 317.201i | − | 0.481337i | −0.970607 | − | 0.240669i | \(-0.922633\pi\) | ||
0.970607 | − | 0.240669i | \(-0.0773667\pi\) | |||||||
\(660\) | − | 54.9621i | − | 0.0832759i | ||||||
\(661\) | 307.730 | 0.465552 | 0.232776 | − | 0.972530i | \(-0.425219\pi\) | ||||
0.232776 | + | 0.972530i | \(0.425219\pi\) | |||||||
\(662\) | − | 813.384i | − | 1.22868i | ||||||
\(663\) | − | 1.24646i | − | 0.00188003i | ||||||
\(664\) | 1748.58 | 2.63340 | ||||||||
\(665\) | −25.8227 | −0.0388311 | ||||||||
\(666\) | −480.961 | −0.722164 | ||||||||
\(667\) | 798.831i | 1.19765i | ||||||||
\(668\) | 2676.21 | 4.00631 | ||||||||
\(669\) | 470.430 | 0.703184 | ||||||||
\(670\) | −151.240 | −0.225731 | ||||||||
\(671\) | −391.292 | −0.583147 | ||||||||
\(672\) | 508.268i | 0.756351i | ||||||||
\(673\) | 1083.95i | 1.61062i | 0.592853 | + | 0.805311i | \(0.298002\pi\) | ||||
−0.592853 | + | 0.805311i | \(0.701998\pi\) | |||||||
\(674\) | 1042.52 | 1.54676 | ||||||||
\(675\) | 129.090 | 0.191244 | ||||||||
\(676\) | −1584.80 | −2.34439 | ||||||||
\(677\) | −815.853 | −1.20510 | −0.602550 | − | 0.798081i | \(-0.705849\pi\) | ||||
−0.602550 | + | 0.798081i | \(0.705849\pi\) | |||||||
\(678\) | 124.706 | 0.183932 | ||||||||
\(679\) | − | 505.827i | − | 0.744959i | ||||||
\(680\) | 63.1472i | 0.0928635i | ||||||||
\(681\) | 214.899i | 0.315563i | ||||||||
\(682\) | 14.7265i | 0.0215931i | ||||||||
\(683\) | − | 1151.50i | − | 1.68594i | −0.537957 | − | 0.842972i | \(-0.680804\pi\) | ||
0.537957 | − | 0.842972i | \(-0.319196\pi\) | |||||||
\(684\) | −295.595 | −0.432156 | ||||||||
\(685\) | −24.7534 | −0.0361364 | ||||||||
\(686\) | 1350.10i | 1.96808i | ||||||||
\(687\) | − | 467.053i | − | 0.679844i | ||||||
\(688\) | − | 1851.46i | − | 2.69108i | ||||||
\(689\) | 7.04395i | 0.0102234i | ||||||||
\(690\) | −35.1874 | −0.0509962 | ||||||||
\(691\) | − | 939.727i | − | 1.35995i | −0.733234 | − | 0.679976i | \(-0.761990\pi\) | ||
0.733234 | − | 0.679976i | \(-0.238010\pi\) | |||||||
\(692\) | 1082.69i | 1.56458i | ||||||||
\(693\) | 159.202i | 0.229728i | ||||||||
\(694\) | −227.550 | −0.327882 | ||||||||
\(695\) | −40.1807 | −0.0578140 | ||||||||
\(696\) | − | 1939.77i | − | 2.78702i | ||||||
\(697\) | −112.506 | −0.161414 | ||||||||
\(698\) | 1066.02 | 1.52725 | ||||||||
\(699\) | − | 748.909i | − | 1.07140i | ||||||
\(700\) | −1446.45 | −2.06636 | ||||||||
\(701\) | − | 782.026i | − | 1.11559i | −0.829980 | − | 0.557793i | \(-0.811648\pi\) | ||
0.829980 | − | 0.557793i | \(-0.188352\pi\) | |||||||
\(702\) | −1.68658 | −0.00240253 | ||||||||
\(703\) | 460.532i | 0.655095i | ||||||||
\(704\) | 300.369i | 0.426661i | ||||||||
\(705\) | 23.4351i | 0.0332412i | ||||||||
\(706\) | −1119.61 | −1.58585 | ||||||||
\(707\) | − | 571.729i | − | 0.808669i | ||||||
\(708\) | −674.604 | − | 680.687i | −0.952831 | − | 0.961422i | ||||
\(709\) | −461.863 | −0.651429 | −0.325715 | − | 0.945468i | \(-0.605605\pi\) | ||||
−0.325715 | + | 0.945468i | \(0.605605\pi\) | |||||||
\(710\) | 107.194i | 0.150977i | ||||||||
\(711\) | −222.758 | −0.313303 | ||||||||
\(712\) | −2810.50 | −3.94733 | ||||||||
\(713\) | 6.60911 | 0.00926944 | ||||||||
\(714\) | − | 318.955i | − | 0.446715i | ||||||
\(715\) | −0.300277 | −0.000419968 | ||||||||
\(716\) | 1368.13i | 1.91080i | ||||||||
\(717\) | −597.582 | −0.833448 | ||||||||
\(718\) | 1686.58i | 2.34900i | ||||||||
\(719\) | 398.240i | 0.553881i | 0.960887 | + | 0.276940i | \(0.0893205\pi\) | ||||
−0.960887 | + | 0.276940i | \(0.910680\pi\) | |||||||
\(720\) | 40.8947 | 0.0567982 | ||||||||
\(721\) | − | 915.872i | − | 1.27028i | ||||||
\(722\) | − | 916.627i | − | 1.26957i | ||||||
\(723\) | 685.690 | 0.948395 | ||||||||
\(724\) | 383.881 | 0.530223 | ||||||||
\(725\) | 1414.44 | 1.95095 | ||||||||
\(726\) | − | 303.701i | − | 0.418322i | ||||||
\(727\) | −402.797 | −0.554053 | −0.277027 | − | 0.960862i | \(-0.589349\pi\) | ||||
−0.277027 | + | 0.960862i | \(0.589349\pi\) | |||||||
\(728\) | 10.8375 | 0.0148866 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −158.488 | −0.217106 | ||||||||
\(731\) | 436.022i | 0.596473i | ||||||||
\(732\) | − | 743.581i | − | 1.01582i | ||||||
\(733\) | 701.565 | 0.957114 | 0.478557 | − | 0.878056i | \(-0.341160\pi\) | ||||
0.478557 | + | 0.878056i | \(0.341160\pi\) | |||||||
\(734\) | −850.723 | −1.15902 | ||||||||
\(735\) | 7.16856 | 0.00975314 | ||||||||
\(736\) | 663.175 | 0.901053 | ||||||||
\(737\) | 892.817 | 1.21142 | ||||||||
\(738\) | 152.231i | 0.206275i | ||||||||
\(739\) | − | 952.579i | − | 1.28901i | −0.764599 | − | 0.644506i | \(-0.777063\pi\) | ||
0.764599 | − | 0.644506i | \(-0.222937\pi\) | |||||||
\(740\) | − | 162.725i | − | 0.219898i | ||||||
\(741\) | 1.61494i | 0.00217940i | ||||||||
\(742\) | 1802.47i | 2.42920i | ||||||||
\(743\) | −681.496 | −0.917222 | −0.458611 | − | 0.888637i | \(-0.651653\pi\) | ||||
−0.458611 | + | 0.888637i | \(0.651653\pi\) | |||||||
\(744\) | −16.0486 | −0.0215707 | ||||||||
\(745\) | 6.15708i | 0.00826454i | ||||||||
\(746\) | − | 132.624i | − | 0.177780i | ||||||
\(747\) | 266.681i | 0.357002i | ||||||||
\(748\) | − | 650.040i | − | 0.869037i | ||||||
\(749\) | −428.166 | −0.571650 | ||||||||
\(750\) | 125.001i | 0.166668i | ||||||||
\(751\) | 1302.06i | 1.73376i | 0.498514 | + | 0.866882i | \(0.333879\pi\) | ||||
−0.498514 | + | 0.866882i | \(0.666121\pi\) | |||||||
\(752\) | − | 1176.93i | − | 1.56506i | ||||||
\(753\) | −170.234 | −0.226074 | ||||||||
\(754\) | −18.4799 | −0.0245091 | ||||||||
\(755\) | 19.0964i | 0.0252932i | ||||||||
\(756\) | −302.535 | −0.400179 | ||||||||
\(757\) | 653.976 | 0.863904 | 0.431952 | − | 0.901896i | \(-0.357825\pi\) | ||||
0.431952 | + | 0.901896i | \(0.357825\pi\) | |||||||
\(758\) | − | 136.975i | − | 0.180705i | ||||||
\(759\) | 207.722 | 0.273679 | ||||||||
\(760\) | − | 81.8148i | − | 0.107651i | ||||||
\(761\) | 638.164 | 0.838586 | 0.419293 | − | 0.907851i | \(-0.362278\pi\) | ||||
0.419293 | + | 0.907851i | \(0.362278\pi\) | |||||||
\(762\) | − | 37.7196i | − | 0.0495008i | ||||||
\(763\) | − | 355.931i | − | 0.466489i | ||||||
\(764\) | 2636.35i | 3.45072i | ||||||||
\(765\) | −9.63077 | −0.0125892 | ||||||||
\(766\) | − | 1781.80i | − | 2.32611i | ||||||
\(767\) | −3.71883 | + | 3.68560i | −0.00484854 | + | 0.00480521i | ||||
\(768\) | 626.944 | 0.816334 | ||||||||
\(769\) | − | 1305.23i | − | 1.69730i | −0.528951 | − | 0.848652i | \(-0.677414\pi\) | ||
0.528951 | − | 0.848652i | \(-0.322586\pi\) | |||||||
\(770\) | −76.8375 | −0.0997889 | ||||||||
\(771\) | 429.829 | 0.557495 | ||||||||
\(772\) | −440.167 | −0.570164 | ||||||||
\(773\) | − | 155.891i | − | 0.201671i | −0.994903 | − | 0.100835i | \(-0.967848\pi\) | ||
0.994903 | − | 0.100835i | \(-0.0321515\pi\) | |||||||
\(774\) | 589.979 | 0.762247 | ||||||||
\(775\) | − | 11.7023i | − | 0.0150998i | ||||||
\(776\) | 1602.63 | 2.06524 | ||||||||
\(777\) | 471.345i | 0.606621i | ||||||||
\(778\) | 1379.88i | 1.77363i | ||||||||
\(779\) | 145.765 | 0.187118 | ||||||||
\(780\) | − | 0.570623i | − | 0.000731569i | ||||||
\(781\) | − | 632.797i | − | 0.810240i | ||||||
\(782\) | −416.164 | −0.532178 | ||||||||
\(783\) | 295.840 | 0.377829 | ||||||||
\(784\) | −360.010 | −0.459197 | ||||||||
\(785\) | − | 86.3994i | − | 0.110063i | ||||||
\(786\) | −1314.74 | −1.67270 | ||||||||
\(787\) | 389.653 | 0.495111 | 0.247556 | − | 0.968874i | \(-0.420373\pi\) | ||||
0.247556 | + | 0.968874i | \(0.420373\pi\) | |||||||
\(788\) | −195.221 | −0.247743 | ||||||||
\(789\) | −336.144 | −0.426037 | ||||||||
\(790\) | − | 107.513i | − | 0.136092i | ||||||
\(791\) | − | 122.212i | − | 0.154504i | ||||||
\(792\) | −504.403 | −0.636873 | ||||||||
\(793\) | −4.06244 | −0.00512288 | ||||||||
\(794\) | −1671.91 | −2.10568 | ||||||||
\(795\) | 54.4251 | 0.0684593 | ||||||||
\(796\) | 1935.41 | 2.43141 | ||||||||
\(797\) | − | 48.4897i | − | 0.0608403i | −0.999537 | − | 0.0304201i | \(-0.990315\pi\) | ||
0.999537 | − | 0.0304201i | \(-0.00968453\pi\) | |||||||
\(798\) | 413.244i | 0.517850i | ||||||||
\(799\) | 277.168i | 0.346894i | ||||||||
\(800\) | − | 1174.24i | − | 1.46780i | ||||||
\(801\) | − | 428.638i | − | 0.535128i | ||||||
\(802\) | −887.432 | −1.10652 | ||||||||
\(803\) | 935.602 | 1.16513 | ||||||||
\(804\) | 1696.64i | 2.11025i | ||||||||
\(805\) | 34.4839i | 0.0428371i | ||||||||
\(806\) | 0.152893i | 0.000189693i | ||||||||
\(807\) | 370.071i | 0.458577i | ||||||||
\(808\) | 1811.42 | 2.24186 | ||||||||
\(809\) | − | 1140.26i | − | 1.40947i | −0.709472 | − | 0.704734i | \(-0.751066\pi\) | ||
0.709472 | − | 0.704734i | \(-0.248934\pi\) | |||||||
\(810\) | 13.0313i | 0.0160881i | ||||||||
\(811\) | 30.8005i | 0.0379784i | 0.999820 | + | 0.0189892i | \(0.00604481\pi\) | ||||
−0.999820 | + | 0.0189892i | \(0.993955\pi\) | |||||||
\(812\) | −3314.89 | −4.08237 | ||||||||
\(813\) | 97.6135 | 0.120066 | ||||||||
\(814\) | 1370.35i | 1.68347i | ||||||||
\(815\) | 119.081 | 0.146112 | ||||||||
\(816\) | 483.664 | 0.592726 | ||||||||
\(817\) | − | 564.919i | − | 0.691455i | ||||||
\(818\) | −1326.10 | −1.62115 | ||||||||
\(819\) | 1.65285i | 0.00201814i | ||||||||
\(820\) | −51.5047 | −0.0628106 | ||||||||
\(821\) | 892.226i | 1.08675i | 0.839489 | + | 0.543377i | \(0.182855\pi\) | ||||
−0.839489 | + | 0.543377i | \(0.817145\pi\) | |||||||
\(822\) | 396.133i | 0.481913i | ||||||||
\(823\) | 1300.11i | 1.57972i | 0.613290 | + | 0.789858i | \(0.289846\pi\) | ||||
−0.613290 | + | 0.789858i | \(0.710154\pi\) | |||||||
\(824\) | 2901.78 | 3.52158 | ||||||||
\(825\) | − | 367.800i | − | 0.445818i | ||||||
\(826\) | −951.606 | + | 943.103i | −1.15207 | + | 1.14177i | ||||
\(827\) | −1617.28 | −1.95559 | −0.977797 | − | 0.209556i | \(-0.932798\pi\) | ||||
−0.977797 | + | 0.209556i | \(0.932798\pi\) | |||||||
\(828\) | 394.740i | 0.476739i | ||||||||
\(829\) | 353.866 | 0.426859 | 0.213430 | − | 0.976958i | \(-0.431537\pi\) | ||||
0.213430 | + | 0.976958i | \(0.431537\pi\) | |||||||
\(830\) | −128.711 | −0.155074 | ||||||||
\(831\) | −295.041 | −0.355043 | ||||||||
\(832\) | 3.11847i | 0.00374816i | ||||||||
\(833\) | 84.7829 | 0.101780 | ||||||||
\(834\) | 643.017i | 0.771003i | ||||||||
\(835\) | −112.970 | −0.135293 | ||||||||
\(836\) | 842.204i | 1.00742i | ||||||||
\(837\) | − | 2.44762i | − | 0.00292428i | ||||||
\(838\) | −2995.30 | −3.57435 | ||||||||
\(839\) | − | 968.406i | − | 1.15424i | −0.816660 | − | 0.577119i | \(-0.804177\pi\) | ||
0.816660 | − | 0.577119i | \(-0.195823\pi\) | |||||||
\(840\) | − | 83.7357i | − | 0.0996854i | ||||||
\(841\) | 2400.52 | 2.85437 | ||||||||
\(842\) | −1206.93 | −1.43341 | ||||||||
\(843\) | 69.2752 | 0.0821770 | ||||||||
\(844\) | 1881.78i | 2.22960i | ||||||||
\(845\) | 66.8987 | 0.0791700 | ||||||||
\(846\) | 375.035 | 0.443303 | ||||||||
\(847\) | −297.629 | −0.351392 | ||||||||
\(848\) | −2733.27 | −3.22320 | ||||||||
\(849\) | 619.165i | 0.729287i | ||||||||
\(850\) | 736.873i | 0.866910i | ||||||||
\(851\) | 614.998 | 0.722677 | ||||||||
\(852\) | 1202.52 | 1.41141 | ||||||||
\(853\) | −303.366 | −0.355646 | −0.177823 | − | 0.984063i | \(-0.556905\pi\) | ||||
−0.177823 | + | 0.984063i | \(0.556905\pi\) | |||||||
\(854\) | −1039.53 | −1.21725 | ||||||||
\(855\) | 12.4778 | 0.0145939 | ||||||||
\(856\) | − | 1356.57i | − | 1.58478i | ||||||
\(857\) | 662.303i | 0.772816i | 0.922328 | + | 0.386408i | \(0.126284\pi\) | ||||
−0.922328 | + | 0.386408i | \(0.873716\pi\) | |||||||
\(858\) | 4.80537i | 0.00560066i | ||||||||
\(859\) | 1317.31i | 1.53354i | 0.641924 | + | 0.766769i | \(0.278137\pi\) | ||||
−0.641924 | + | 0.766769i | \(0.721863\pi\) | |||||||
\(860\) | 199.609i | 0.232104i | ||||||||
\(861\) | 149.187 | 0.173272 | ||||||||
\(862\) | 2609.93 | 3.02777 | ||||||||
\(863\) | 248.154i | 0.287548i | 0.989611 | + | 0.143774i | \(0.0459238\pi\) | ||||
−0.989611 | + | 0.143774i | \(0.954076\pi\) | |||||||
\(864\) | − | 245.601i | − | 0.284260i | ||||||
\(865\) | − | 45.7032i | − | 0.0528361i | ||||||
\(866\) | 2288.26i | 2.64233i | ||||||||
\(867\) | 386.659 | 0.445974 | ||||||||
\(868\) | 27.4256i | 0.0315963i | ||||||||
\(869\) | 634.680i | 0.730357i | ||||||||
\(870\) | 142.785i | 0.164120i | ||||||||
\(871\) | 9.26935 | 0.0106422 | ||||||||
\(872\) | 1127.71 | 1.29324 | ||||||||
\(873\) | 244.421i | 0.279978i | ||||||||
\(874\) | 539.190 | 0.616922 | ||||||||
\(875\) | 122.502 | 0.140002 | ||||||||
\(876\) | 1777.95i | 2.02962i | ||||||||
\(877\) | 1210.94 | 1.38078 | 0.690390 | − | 0.723437i | \(-0.257439\pi\) | ||||
0.690390 | + | 0.723437i | \(0.257439\pi\) | |||||||
\(878\) | − | 1688.85i | − | 1.92352i | ||||||
\(879\) | −116.302 | −0.132312 | ||||||||
\(880\) | − | 116.517i | − | 0.132405i | ||||||
\(881\) | − | 821.372i | − | 0.932318i | −0.884701 | − | 0.466159i | \(-0.845637\pi\) | ||
0.884701 | − | 0.466159i | \(-0.154363\pi\) | |||||||
\(882\) | − | 114.719i | − | 0.130067i | ||||||
\(883\) | −121.125 | −0.137175 | −0.0685874 | − | 0.997645i | \(-0.521849\pi\) | ||||
−0.0685874 | + | 0.997645i | \(0.521849\pi\) | |||||||
\(884\) | − | 6.74880i | − | 0.00763439i | ||||||
\(885\) | 28.4768 | + | 28.7335i | 0.0321771 | + | 0.0324673i | ||||
\(886\) | 933.585 | 1.05371 | ||||||||
\(887\) | − | 385.806i | − | 0.434956i | −0.976065 | − | 0.217478i | \(-0.930217\pi\) | ||
0.976065 | − | 0.217478i | \(-0.0697830\pi\) | |||||||
\(888\) | −1493.37 | −1.68173 | ||||||||
\(889\) | −36.9655 | −0.0415809 | ||||||||
\(890\) | 206.878 | 0.232448 | ||||||||
\(891\) | − | 76.9280i | − | 0.0863390i | ||||||
\(892\) | 2547.09 | 2.85548 | ||||||||
\(893\) | − | 359.104i | − | 0.402133i | ||||||
\(894\) | 98.5326 | 0.110215 | ||||||||
\(895\) | − | 57.7524i | − | 0.0645278i | ||||||
\(896\) | − | 375.813i | − | 0.419435i | ||||||
\(897\) | 2.15660 | 0.00240424 | ||||||||
\(898\) | − | 821.073i | − | 0.914336i | ||||||
\(899\) | − | 26.8187i | − | 0.0298317i | ||||||
\(900\) | 698.940 | 0.776600 | ||||||||
\(901\) | 643.689 | 0.714416 | ||||||||
\(902\) | 433.734 | 0.480858 | ||||||||
\(903\) | − | 578.183i | − | 0.640291i | ||||||
\(904\) | 387.208 | 0.428328 | ||||||||
\(905\) | −16.2046 | −0.0179057 | ||||||||
\(906\) | 305.601 | 0.337308 | ||||||||
\(907\) | −836.228 | −0.921971 | −0.460986 | − | 0.887408i | \(-0.652504\pi\) | ||||
−0.460986 | + | 0.887408i | \(0.652504\pi\) | |||||||
\(908\) | 1163.54i | 1.28143i | ||||||||
\(909\) | 276.266i | 0.303923i | ||||||||
\(910\) | −0.797737 | −0.000876634 | ||||||||
\(911\) | 26.1105 | 0.0286614 | 0.0143307 | − | 0.999897i | \(-0.495438\pi\) | ||||
0.0143307 | + | 0.999897i | \(0.495438\pi\) | |||||||
\(912\) | −626.645 | −0.687111 | ||||||||
\(913\) | 759.823 | 0.832227 | ||||||||
\(914\) | −235.135 | −0.257259 | ||||||||
\(915\) | 31.3885i | 0.0343044i | ||||||||
\(916\) | − | 2528.80i | − | 2.76070i | ||||||
\(917\) | 1288.45i | 1.40508i | ||||||||
\(918\) | 154.122i | 0.167889i | ||||||||
\(919\) | 1116.36i | 1.21476i | 0.794412 | + | 0.607380i | \(0.207779\pi\) | ||||
−0.794412 | + | 0.607380i | \(0.792221\pi\) | |||||||
\(920\) | −109.256 | −0.118757 | ||||||||
\(921\) | −213.560 | −0.231879 | ||||||||
\(922\) | − | 778.180i | − | 0.844013i | ||||||
\(923\) | − | 6.56978i | − | 0.00711786i | ||||||
\(924\) | 861.979i | 0.932878i | ||||||||
\(925\) | − | 1088.94i | − | 1.17723i | ||||||
\(926\) | −1065.56 | −1.15072 | ||||||||
\(927\) | 442.559i | 0.477410i | ||||||||
\(928\) | − | 2691.05i | − | 2.89984i | ||||||
\(929\) | 1393.02i | 1.49949i | 0.661730 | + | 0.749743i | \(0.269823\pi\) | ||||
−0.661730 | + | 0.749743i | \(0.730177\pi\) | |||||||
\(930\) | 1.18133 | 0.00127024 | ||||||||
\(931\) | −109.846 | −0.117988 | ||||||||
\(932\) | − | 4054.88i | − | 4.35073i | ||||||
\(933\) | 426.483 | 0.457109 | ||||||||
\(934\) | 115.322 | 0.123471 | ||||||||
\(935\) | 27.4398i | 0.0293474i | ||||||||
\(936\) | −5.23678 | −0.00559485 | ||||||||
\(937\) | − | 1420.84i | − | 1.51637i | −0.652041 | − | 0.758184i | \(-0.726087\pi\) | ||
0.652041 | − | 0.758184i | \(-0.273913\pi\) | |||||||
\(938\) | 2371.92 | 2.52870 | ||||||||
\(939\) | 847.972i | 0.903058i | ||||||||
\(940\) | 126.886i | 0.134986i | ||||||||
\(941\) | − | 968.807i | − | 1.02955i | −0.857325 | − | 0.514775i | \(-0.827875\pi\) | ||
0.857325 | − | 0.514775i | \(-0.172125\pi\) | |||||||
\(942\) | −1382.66 | −1.46779 | ||||||||
\(943\) | − | 194.655i | − | 0.206422i | ||||||
\(944\) | −1430.13 | − | 1443.02i | −1.51496 | − | 1.52862i | ||||
\(945\) | 12.7708 | 0.0135141 | ||||||||
\(946\) | − | 1680.96i | − | 1.77691i | ||||||
\(947\) | −573.028 | −0.605098 | −0.302549 | − | 0.953134i | \(-0.597838\pi\) | ||||
−0.302549 | + | 0.953134i | \(0.597838\pi\) | |||||||
\(948\) | −1206.10 | −1.27226 | ||||||||
\(949\) | 9.71355 | 0.0102356 | ||||||||
\(950\) | − | 954.708i | − | 1.00496i | ||||||
\(951\) | −553.075 | −0.581572 | ||||||||
\(952\) | − | 990.347i | − | 1.04028i | ||||||
\(953\) | 834.685 | 0.875850 | 0.437925 | − | 0.899011i | \(-0.355713\pi\) | ||||
0.437925 | + | 0.899011i | \(0.355713\pi\) | |||||||
\(954\) | − | 870.972i | − | 0.912968i | ||||||
\(955\) | − | 111.287i | − | 0.116531i | ||||||
\(956\) | −3235.54 | −3.38445 | ||||||||
\(957\) | − | 842.903i | − | 0.880776i | ||||||
\(958\) | − | 630.182i | − | 0.657810i | ||||||
\(959\) | 388.212 | 0.404809 | ||||||||
\(960\) | 24.0949 | 0.0250988 | ||||||||
\(961\) | 960.778 | 0.999769 | ||||||||
\(962\) | 14.2271i | 0.0147891i | ||||||||
\(963\) | 206.894 | 0.214843 | ||||||||
\(964\) | 3712.58 | 3.85123 | ||||||||
\(965\) | 18.5806 | 0.0192545 | ||||||||
\(966\) | 551.850 | 0.571273 | ||||||||
\(967\) | − | 128.620i | − | 0.133009i | −0.997786 | − | 0.0665046i | \(-0.978815\pi\) | ||
0.997786 | − | 0.0665046i | \(-0.0211847\pi\) | |||||||
\(968\) | − | 942.987i | − | 0.974160i | ||||||
\(969\) | 147.576 | 0.152297 | ||||||||
\(970\) | −117.968 | −0.121616 | ||||||||
\(971\) | 1485.57 | 1.52994 | 0.764969 | − | 0.644067i | \(-0.222754\pi\) | ||||
0.764969 | + | 0.644067i | \(0.222754\pi\) | |||||||
\(972\) | 146.188 | 0.150399 | ||||||||
\(973\) | 630.160 | 0.647647 | ||||||||
\(974\) | − | 1474.33i | − | 1.51368i | ||||||
\(975\) | − | 3.81855i | − | 0.00391646i | ||||||
\(976\) | − | 1576.35i | − | 1.61512i | ||||||
\(977\) | − | 1.03419i | − | 0.00105854i | −1.00000 | 0.000529271i | \(-0.999832\pi\) | |||
1.00000 | 0.000529271i | \(-0.000168472\pi\) | ||||||||
\(978\) | − | 1905.67i | − | 1.94854i | ||||||
\(979\) | −1221.27 | −1.24747 | ||||||||
\(980\) | 38.8133 | 0.0396054 | ||||||||
\(981\) | 171.990i | 0.175321i | ||||||||
\(982\) | 1077.56i | 1.09731i | ||||||||
\(983\) | 941.272i | 0.957550i | 0.877938 | + | 0.478775i | \(0.158919\pi\) | ||||
−0.877938 | + | 0.478775i | \(0.841081\pi\) | |||||||
\(984\) | 472.674i | 0.480360i | ||||||||
\(985\) | 8.24079 | 0.00836628 | ||||||||
\(986\) | 1688.72i | 1.71270i | ||||||||
\(987\) | − | 367.536i | − | 0.372377i | ||||||
\(988\) | 8.74388i | 0.00885008i | ||||||||
\(989\) | −754.398 | −0.762788 | ||||||||
\(990\) | 37.1287 | 0.0375037 | ||||||||
\(991\) | 1077.04i | 1.08682i | 0.839467 | + | 0.543410i | \(0.182867\pi\) | ||||
−0.839467 | + | 0.543410i | \(0.817133\pi\) | |||||||
\(992\) | −22.2644 | −0.0224439 | ||||||||
\(993\) | 385.178 | 0.387893 | ||||||||
\(994\) | − | 1681.13i | − | 1.69128i | ||||||
\(995\) | −81.6984 | −0.0821090 | ||||||||
\(996\) | 1443.91i | 1.44971i | ||||||||
\(997\) | −1366.02 | −1.37013 | −0.685063 | − | 0.728484i | \(-0.740225\pi\) | ||||
−0.685063 | + | 0.728484i | \(0.740225\pi\) | |||||||
\(998\) | 1885.51i | 1.88929i | ||||||||
\(999\) | − | 227.759i | − | 0.227987i |
(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 | 177.3.c.a.58.20 | yes | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.1 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.1 | ✓ | 20 | |
177.176 | even | 2 | 531.3.c.c.235.20 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.1 | ✓ | 20 | 59.58 | odd | 2 | inner | |
177.3.c.a.58.20 | yes | 20 | 1.1 | even | 1 | trivial | |
531.3.c.c.235.1 | 20 | 3.2 | odd | 2 | |||
531.3.c.c.235.20 | 20 | 177.176 | even | 2 |