Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), degree \(2\), not 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.4 | ||
Root | \(1.09445 + 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.217 |
Dual form | 324.4.e.i.109.4 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.5353 | + | 18.2477i | 0.942309 | + | 1.63213i | 0.761052 | + | 0.648690i | \(0.224683\pi\) |
0.181256 | + | 0.983436i | \(0.441984\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.7477 | − | 27.2759i | 0.850297 | − | 1.47276i | −0.0306428 | − | 0.999530i | \(-0.509755\pi\) |
0.880940 | − | 0.473228i | \(-0.156911\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.3296 | − | 31.7477i | 0.502415 | − | 0.870209i | −0.497581 | − | 0.867418i | \(-0.665778\pi\) |
0.999996 | − | 0.00279137i | \(-0.000888521\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.2477 | − | 48.9265i | −0.602655 | − | 1.04383i | −0.992417 | − | 0.122913i | \(-0.960776\pi\) |
0.389763 | − | 0.920915i | \(-0.372557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 35.8010 | 0.510765 | 0.255383 | − | 0.966840i | \(-0.417799\pi\) | ||||
0.255383 | + | 0.966840i | \(0.417799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 83.4955 | 1.00817 | 0.504083 | − | 0.863655i | \(-0.331830\pi\) | ||||
0.504083 | + | 0.863655i | \(0.331830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −34.7762 | − | 60.2341i | −0.315275 | − | 0.546073i | 0.664221 | − | 0.747537i | \(-0.268764\pi\) |
−0.979496 | + | 0.201464i | \(0.935430\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −159.486 | + | 276.238i | −1.27589 | + | 2.20991i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.8541 | − | 70.7614i | 0.261601 | − | 0.453105i | −0.705067 | − | 0.709141i | \(-0.749083\pi\) |
0.966667 | + | 0.256035i | \(0.0824164\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.4864 | + | 63.1962i | 0.211392 | + | 0.366141i | 0.952150 | − | 0.305630i | \(-0.0988671\pi\) |
−0.740759 | + | 0.671771i | \(0.765534\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 663.630 | 3.20497 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −25.4682 | −0.113161 | −0.0565803 | − | 0.998398i | \(-0.518020\pi\) | ||||
−0.0565803 | + | 0.998398i | \(0.518020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 199.742 | + | 345.964i | 0.760841 | + | 1.31782i | 0.942417 | + | 0.334439i | \(0.108547\pi\) |
−0.181576 | + | 0.983377i | \(0.558120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.7295 | − | 72.2777i | 0.147993 | − | 0.256331i | −0.782493 | − | 0.622660i | \(-0.786052\pi\) |
0.930486 | + | 0.366329i | \(0.119385\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 155.885 | − | 270.000i | 0.483789 | − | 0.837948i | −0.516037 | − | 0.856566i | \(-0.672593\pi\) |
0.999827 | + | 0.0186183i | \(0.00592674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −324.482 | − | 562.019i | −0.946011 | − | 1.63854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.09919 | 0.0106239 | 0.00531196 | − | 0.999986i | \(-0.498309\pi\) | ||||
0.00531196 | + | 0.999986i | \(0.498309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 772.432 | 1.89372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 176.097 | + | 305.009i | 0.388574 | + | 0.673031i | 0.992258 | − | 0.124193i | \(-0.0396343\pi\) |
−0.603684 | + | 0.797224i | \(0.706301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.77046 | + | 3.06652i | −0.00371613 | + | 0.00643652i | −0.867877 | − | 0.496778i | \(-0.834516\pi\) |
0.864161 | + | 0.503215i | \(0.167850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 595.198 | − | 1030.91i | 1.13577 | − | 1.96722i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −246.216 | − | 426.458i | −0.448956 | − | 0.777615i | 0.549362 | − | 0.835584i | \(-0.314871\pi\) |
−0.998318 | + | 0.0579695i | \(0.981537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 154.502 | 0.258253 | 0.129126 | − | 0.991628i | \(-0.458783\pi\) | ||||
0.129126 | + | 0.991628i | \(0.458783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 305.000 | 0.489008 | 0.244504 | − | 0.969648i | \(-0.421375\pi\) | ||||
0.244504 | + | 0.969648i | \(0.421375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −577.298 | − | 999.909i | −0.854405 | − | 1.47987i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −335.693 | + | 581.438i | −0.478081 | + | 0.828061i | −0.999684 | − | 0.0251271i | \(-0.992001\pi\) |
0.521603 | + | 0.853188i | \(0.325334\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −646.850 | + | 1120.38i | −0.855434 | + | 1.48166i | 0.0208078 | + | 0.999783i | \(0.493376\pi\) |
−0.876242 | + | 0.481872i | \(0.839957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 377.175 | + | 653.286i | 0.481298 | + | 0.833633i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1183.91 | 1.41005 | 0.705026 | − | 0.709181i | \(-0.250935\pi\) | ||||
0.705026 | + | 0.709181i | \(0.250935\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1779.35 | −2.04974 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 879.652 | + | 1523.60i | 0.950004 | + | 1.64546i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −307.991 | + | 533.456i | −0.322389 | + | 0.558394i | −0.980980 | − | 0.194107i | \(-0.937819\pi\) |
0.658591 | + | 0.752501i | \(0.271153\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −593.744 | + | 1028.40i | −0.584948 | + | 1.01316i | 0.409934 | + | 0.912115i | \(0.365552\pi\) |
−0.994882 | + | 0.101045i | \(0.967781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 693.459 | + | 1201.11i | 0.663384 | + | 1.14901i | 0.979721 | + | 0.200368i | \(0.0642137\pi\) |
−0.316337 | + | 0.948647i | \(0.602453\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −678.360 | −0.612893 | −0.306447 | − | 0.951888i | \(-0.599140\pi\) | ||||
−0.306447 | + | 0.951888i | \(0.599140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 945.432 | 0.830788 | 0.415394 | − | 0.909641i | \(-0.363644\pi\) | ||||
0.415394 | + | 0.909641i | \(0.363644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −993.300 | − | 1720.45i | −0.826918 | − | 1.43226i | −0.900444 | − | 0.434971i | \(-0.856759\pi\) |
0.0735260 | − | 0.997293i | \(-0.476575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 732.757 | − | 1269.17i | 0.594173 | − | 1.02914i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 563.784 | − | 976.502i | 0.434302 | − | 0.752234i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.44545 | − | 11.1638i | −0.00484256 | − | 0.00838756i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4087.13 | −2.92451 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1496.54 | −1.04564 | −0.522821 | − | 0.852442i | \(-0.675120\pi\) | ||||
−0.522821 | + | 0.852442i | \(0.675120\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 42.6413 | + | 73.8568i | 0.0284396 | + | 0.0492588i | 0.879895 | − | 0.475168i | \(-0.157613\pi\) |
−0.851455 | + | 0.524427i | \(0.824280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1314.86 | − | 2277.41i | 0.857242 | − | 1.48479i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −449.753 | + | 778.995i | −0.280475 | + | 0.485796i | −0.971502 | − | 0.237033i | \(-0.923825\pi\) |
0.691027 | + | 0.722829i | \(0.257158\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1000.30 | − | 1732.58i | −0.610394 | − | 1.05723i | −0.991174 | − | 0.132567i | \(-0.957678\pi\) |
0.380780 | − | 0.924666i | \(-0.375655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2071.07 | −1.21113 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1721.65 | 0.986034 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −737.186 | − | 1276.84i | −0.405320 | − | 0.702034i | 0.589039 | − | 0.808105i | \(-0.299506\pi\) |
−0.994359 | + | 0.106071i | \(0.966173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 546.486 | − | 946.542i | 0.294519 | − | 0.510123i | −0.680354 | − | 0.732884i | \(-0.738174\pi\) |
0.974873 | + | 0.222761i | \(0.0715071\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −768.792 | + | 1331.59i | −0.398393 | + | 0.690036i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −270.257 | − | 468.099i | −0.137381 | − | 0.237951i | 0.789123 | − | 0.614235i | \(-0.210535\pi\) |
−0.926505 | + | 0.376284i | \(0.877202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2190.58 | −1.07231 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3251.60 | −1.56248 | −0.781242 | − | 0.624228i | \(-0.785414\pi\) | ||||
−0.781242 | + | 0.624228i | \(0.785414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 854.291 | + | 1479.67i | 0.395850 | + | 0.685633i | 0.993209 | − | 0.116341i | \(-0.0371166\pi\) |
−0.597359 | + | 0.801974i | \(0.703783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −497.368 | + | 861.467i | −0.226385 | + | 0.392111i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1314.87 | + | 2277.42i | −0.577847 | + | 1.00086i | 0.417879 | + | 0.908503i | \(0.362773\pi\) |
−0.995726 | + | 0.0923571i | \(0.970560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5023.10 | + | 8700.26i | 2.16977 | + | 3.75816i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4532.77 | 1.89271 | 0.946354 | − | 0.323131i | \(-0.104735\pi\) | ||||
0.946354 | + | 0.323131i | \(0.104735\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2327.65 | −0.955874 | −0.477937 | − | 0.878394i | \(-0.658615\pi\) | ||||
−0.477937 | + | 0.878394i | \(0.658615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −268.316 | − | 464.736i | −0.106632 | − | 0.184692i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 656.216 | − | 1136.60i | 0.256616 | − | 0.444473i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −615.840 | + | 1066.67i | −0.233302 | + | 0.404090i | −0.958778 | − | 0.284157i | \(-0.908286\pi\) |
0.725476 | + | 0.688247i | \(0.241620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1071.99 | − | 1856.73i | −0.399810 | − | 0.692491i | 0.593892 | − | 0.804544i | \(-0.297590\pi\) |
−0.993702 | + | 0.112054i | \(0.964257\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1984.55 | −0.717733 | −0.358866 | − | 0.933389i | \(-0.616837\pi\) | ||||
−0.358866 | + | 0.933389i | \(0.616837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −224.400 | −0.0799362 | −0.0399681 | − | 0.999201i | \(-0.512726\pi\) | ||||
−0.0399681 | + | 0.999201i | \(0.512726\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1286.72 | − | 2228.66i | −0.444876 | − | 0.770549i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4208.70 | + | 7289.68i | −1.43389 | + | 2.48358i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1530.43 | − | 2650.79i | 0.506519 | − | 0.877316i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1892.61 | − | 3278.10i | −0.617501 | − | 1.06954i | −0.989940 | − | 0.141487i | \(-0.954812\pi\) |
0.372439 | − | 0.928057i | \(-0.378522\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1758.54 | 0.557820 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2298.31 | 0.718983 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1011.30 | − | 1751.62i | −0.307815 | − | 0.533151i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2704.16 | − | 4683.74i | 0.812036 | − | 1.40649i | −0.0994007 | − | 0.995047i | \(-0.531693\pi\) |
0.911437 | − | 0.411440i | \(-0.134974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2244.95 | + | 3888.37i | −0.656400 | + | 1.13692i | 0.325141 | + | 0.945666i | \(0.394588\pi\) |
−0.981541 | + | 0.191253i | \(0.938745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1558.50 | − | 2699.40i | −0.449731 | − | 0.778957i | 0.548637 | − | 0.836061i | \(-0.315147\pi\) |
−0.998368 | + | 0.0571034i | \(0.981814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1675.60 | −0.471124 | −0.235562 | − | 0.971859i | \(-0.575693\pi\) | ||||
−0.235562 | + | 0.971859i | \(0.575693\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6569.18 | 1.82352 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2875.86 | + | 4981.13i | 0.778342 | + | 1.34813i | 0.932897 | + | 0.360144i | \(0.117272\pi\) |
−0.154555 | + | 0.987984i | \(0.549394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 902.705 | − | 1563.53i | 0.241279 | − | 0.417908i | −0.719800 | − | 0.694182i | \(-0.755766\pi\) |
0.961079 | + | 0.276274i | \(0.0890997\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6837.05 | − | 11842.1i | 1.78287 | − | 3.08802i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2358.56 | − | 4085.14i | −0.607576 | − | 1.05235i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −32.6596 | −0.00821297 | −0.00410649 | − | 0.999992i | \(-0.501307\pi\) | ||||
−0.00410649 | + | 0.999992i | \(0.501307\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2549.73 | −0.633597 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −574.128 | − | 994.418i | −0.139351 | − | 0.241362i | 0.787900 | − | 0.615803i | \(-0.211168\pi\) |
−0.927251 | + | 0.374440i | \(0.877835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −401.066 | + | 694.667i | −0.0962202 | + | 0.166658i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2317.01 | − | 4013.17i | 0.543242 | − | 0.940923i | −0.455473 | − | 0.890250i | \(-0.650530\pi\) |
0.998715 | − | 0.0506737i | \(-0.0161368\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 43.1863 | + | 74.8009i | 0.0100110 | + | 0.0173396i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8134.42 | 1.84373 | 0.921866 | − | 0.387508i | \(-0.126664\pi\) | ||||
0.921866 | + | 0.387508i | \(0.126664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6891.35 | 1.54472 | 0.772361 | − | 0.635184i | \(-0.219076\pi\) | ||||
0.772361 | + | 0.635184i | \(0.219076\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5846.63 | + | 10126.7i | 1.28205 | + | 2.22058i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 910.891 | − | 1577.71i | 0.197582 | − | 0.342222i | −0.750162 | − | 0.661254i | \(-0.770025\pi\) |
0.947744 | + | 0.319032i | \(0.103358\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2270.60 | + | 3932.80i | −0.482039 | + | 0.834915i | −0.999787 | − | 0.0206174i | \(-0.993437\pi\) |
0.517749 | + | 0.855533i | \(0.326770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1378.97 | + | 2388.45i | 0.289652 | + | 0.501691i | 0.973727 | − | 0.227720i | \(-0.0731272\pi\) |
−0.684075 | + | 0.729412i | \(0.739794\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12581.9 | 2.58777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3631.29 | −0.739119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 834.532 | + | 1445.45i | 0.166396 | + | 0.288206i | 0.937150 | − | 0.348927i | \(-0.113454\pi\) |
−0.770754 | + | 0.637132i | \(0.780120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3710.48 | + | 6426.74i | −0.732314 | + | 1.26840i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1964.70 | + | 3402.95i | −0.380004 | + | 0.658187i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1314.29 | − | 2276.42i | −0.251676 | − | 0.435916i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −74.6094 | −0.0140069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7500.21 | −1.39433 | −0.697165 | − | 0.716910i | \(-0.745556\pi\) | ||||
−0.697165 | + | 0.716910i | \(0.745556\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4243.26 | − | 7349.54i | −0.773676 | − | 1.34005i | −0.935536 | − | 0.353232i | \(-0.885083\pi\) |
0.161860 | − | 0.986814i | \(-0.448251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4682.83 | + | 8110.90i | −0.845653 | + | 1.46471i | 0.0394004 | + | 0.999224i | \(0.487455\pi\) |
−0.885053 | + | 0.465490i | \(0.845878\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −252.944 | + | 438.111i | −0.0448162 | + | 0.0776239i | −0.887563 | − | 0.460686i | \(-0.847604\pi\) |
0.842747 | + | 0.538310i | \(0.180937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1497.67 | − | 2594.05i | −0.262864 | − | 0.455294i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2989.22 | 0.514937 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18020.5 | 3.07569 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4909.66 | − | 8503.77i | −0.822730 | − | 1.42501i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3299.26 | + | 5714.48i | −0.547866 | + | 0.948931i | 0.450555 | + | 0.892749i | \(0.351226\pi\) |
−0.998421 | + | 0.0561825i | \(0.982107\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5187.93 | − | 8985.76i | 0.846110 | − | 1.46551i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1806.21 | + | 3128.45i | 0.291960 | + | 0.505689i | 0.974273 | − | 0.225371i | \(-0.0723593\pi\) |
−0.682313 | + | 0.731060i | \(0.739026\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2675.12 | 0.424826 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9636.46 | −1.51697 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1304.78 | + | 2259.95i | 0.201857 | + | 0.349626i | 0.949127 | − | 0.314894i | \(-0.101969\pi\) |
−0.747270 | + | 0.664521i | \(0.768636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −338.764 | + | 586.756i | −0.0519587 | + | 0.0899952i | −0.890835 | − | 0.454327i | \(-0.849880\pi\) |
0.838876 | + | 0.544322i | \(0.183213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 774.941 | − | 1342.24i | 0.116844 | − | 0.202380i | −0.801671 | − | 0.597765i | \(-0.796056\pi\) |
0.918515 | + | 0.395385i | \(0.129389\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1627.72 | + | 2819.30i | 0.243354 | + | 0.421501i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8381.31 | −1.23217 | −0.616084 | − | 0.787680i | \(-0.711282\pi\) | ||||
−0.616084 | + | 0.787680i | \(0.711282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 112.491 | 0.0164005 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3213.28 | + | 5565.56i | 0.460796 | + | 0.798122i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2102.91 | − | 3642.35i | 0.299104 | − | 0.518063i | −0.676827 | − | 0.736142i | \(-0.736646\pi\) |
0.975931 | + | 0.218079i | \(0.0699789\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 64.5530 | − | 111.809i | 0.00903348 | − | 0.0156465i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4006.42 | − | 6939.32i | −0.556151 | − | 0.963282i | −0.997813 | − | 0.0661007i | \(-0.978944\pi\) |
0.441662 | − | 0.897182i | \(-0.354389\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4616.14 | −0.630619 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8049.26 | 1.09093 | 0.545466 | − | 0.838133i | \(-0.316353\pi\) | ||||
0.545466 | + | 0.838133i | \(0.316353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1613.73 | − | 2795.07i | −0.215295 | − | 0.372902i | 0.738069 | − | 0.674725i | \(-0.235738\pi\) |
−0.953364 | + | 0.301824i | \(0.902405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12164.0 | − | 21068.7i | 1.61023 | − | 2.78899i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4455.97 | + | 7717.96i | −0.580788 | + | 1.00595i | 0.414598 | + | 0.910004i | \(0.363922\pi\) |
−0.995386 | + | 0.0959494i | \(0.969411\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1245.02 | − | 2156.44i | −0.161032 | − | 0.278915i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14146.6 | −1.80200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2972.50 | 0.375783 | 0.187891 | − | 0.982190i | \(-0.439835\pi\) | ||||
0.187891 | + | 0.982190i | \(0.439835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6136.59 | + | 10628.9i | 0.764206 | + | 1.32364i | 0.940665 | + | 0.339336i | \(0.110202\pi\) |
−0.176459 | + | 0.984308i | \(0.556464\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2061.31 | − | 3570.30i | 0.254792 | − | 0.441313i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −466.820 | + | 808.557i | −0.0568536 | + | 0.0984734i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1124.65 | + | 1947.95i | 0.135967 | + | 0.235501i | 0.925966 | − | 0.377606i | \(-0.123253\pi\) |
−0.790000 | + | 0.613107i | \(0.789919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11092.5 | 1.32161 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27259.1 | −3.22433 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4730.46 | + | 8193.40i | 0.551547 | + | 0.955307i | 0.998163 | + | 0.0605814i | \(0.0192955\pi\) |
−0.446617 | + | 0.894725i | \(0.647371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −767.457 | + | 1329.27i | −0.0888446 | + | 0.153883i | −0.907023 | − | 0.421081i | \(-0.861651\pi\) |
0.818178 | + | 0.574964i | \(0.194984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5709.77 | + | 9889.60i | −0.651681 | + | 1.12874i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 55.7613 | + | 96.5814i | 0.00631962 | + | 0.0109459i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3991.88 | −0.446130 | −0.223065 | − | 0.974804i | \(-0.571606\pi\) | ||||
−0.223065 | + | 0.974804i | \(0.571606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3058.08 | −0.339404 | −0.169702 | − | 0.985495i | \(-0.554281\pi\) | ||||
−0.169702 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2903.65 | − | 5029.27i | −0.317850 | − | 0.550533i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7381.89 | − | 12785.8i | 0.802548 | − | 1.39005i | −0.115387 | − | 0.993321i | \(-0.536811\pi\) |
0.917934 | − | 0.396733i | \(-0.129856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5782.33 | − | 10015.3i | 0.620150 | − | 1.07413i | −0.369307 | − | 0.929307i | \(-0.620405\pi\) |
0.989457 | − | 0.144824i | \(-0.0462617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12472.9 | + | 21603.7i | 1.32870 | + | 2.30138i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17266.9 | −1.81486 | −0.907432 | − | 0.420198i | \(-0.861961\pi\) | ||||
−0.907432 | + | 0.420198i | \(0.861961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14644.7 | 1.52903 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18746.0 | − | 32469.1i | −1.93149 | − | 3.34544i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6350.76 | + | 10999.8i | −0.650057 | + | 1.12593i | 0.333052 | + | 0.942909i | \(0.391922\pi\) |
−0.983109 | + | 0.183023i | \(0.941412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8249.92 | + | 14289.3i | −0.833486 | + | 1.44364i | 0.0617714 | + | 0.998090i | \(0.480325\pi\) |
−0.895257 | + | 0.445550i | \(0.853008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 682.418 | + | 1181.98i | 0.0684982 | + | 0.118642i | 0.898240 | − | 0.439504i | \(-0.144846\pi\) |
−0.829742 | + | 0.558147i | \(0.811513\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10333.5 | −1.02393 | −0.511966 | − | 0.859006i | \(-0.671083\pi\) | ||||
−0.511966 | + | 0.859006i | \(0.671083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15509.4 | −1.52698 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1529.77 | − | 2649.64i | −0.148708 | − | 0.257570i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13316.4 | + | 23064.7i | −1.28631 | + | 2.22796i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6094.31 | + | 10555.7i | −0.581328 | + | 1.00689i | 0.413994 | + | 0.910280i | \(0.364133\pi\) |
−0.995322 | + | 0.0966103i | \(0.969200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 719.418 | + | 1246.07i | 0.0681968 | + | 0.118120i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12979.1 | −1.21516 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9816.46 | 0.913401 | 0.456701 | − | 0.889620i | \(-0.349031\pi\) | ||||
0.456701 | + | 0.889620i | \(0.349031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1732.01 | + | 2999.93i | 0.159195 | + | 0.275733i | 0.934578 | − | 0.355757i | \(-0.115777\pi\) |
−0.775384 | + | 0.631490i | \(0.782444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1462.62 | − | 2533.33i | 0.133616 | − | 0.231430i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2433.05 | − | 4214.16i | 0.219592 | − | 0.380344i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6183.45 | + | 10710.1i | 0.554728 | + | 0.960817i | 0.997925 | + | 0.0643928i | \(0.0205111\pi\) |
−0.443196 | + | 0.896424i | \(0.646156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6249.98 | 0.554021 | 0.277011 | − | 0.960867i | \(-0.410656\pi\) | ||||
0.277011 | + | 0.960867i | \(0.410656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25021.2 | −2.20481 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3740.71 | − | 6479.10i | −0.325745 | − | 0.564207i | 0.655918 | − | 0.754832i | \(-0.272282\pi\) |
−0.981663 | + | 0.190625i | \(0.938948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4803.06 | − | 8319.14i | 0.415802 | − | 0.720190i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14611.6 | + | 25308.1i | −1.25022 | + | 2.16545i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5714.59 | − | 9897.96i | −0.486127 | − | 0.841996i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17700.1 | 1.48840 | 0.744200 | − | 0.667957i | \(-0.232831\pi\) | ||||
0.744200 | + | 0.667957i | \(0.232831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21707.9 | 1.81495 | 0.907475 | − | 0.420107i | \(-0.138007\pi\) | ||||
0.907475 | + | 0.420107i | \(0.138007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1306.25 | + | 2262.49i | 0.107972 | + | 0.187012i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3664.74 | − | 6347.51i | 0.301203 | − | 0.521699i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11284.5 | − | 19545.4i | 0.917049 | − | 1.58838i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7146.75 | − | 12378.5i | −0.577534 | − | 1.00032i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23790.4 | −1.90116 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19282.0 | −1.53235 | −0.766173 | − | 0.642634i | \(-0.777841\pi\) | ||||
−0.766173 | + | 0.642634i | \(0.777841\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9960.44 | + | 17252.0i | 0.782859 | + | 1.35595i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3892.26 | − | 6741.60i | 0.304243 | − | 0.526965i | −0.672849 | − | 0.739780i | \(-0.734930\pi\) |
0.977093 | + | 0.212815i | \(0.0682630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3411.13 | − | 5908.25i | 0.263737 | − | 0.456806i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10572.8 | + | 18312.6i | 0.813023 | + | 1.40820i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8556.03 | −0.650863 | −0.325431 | − | 0.945566i | \(-0.605510\pi\) | ||||
−0.325431 | + | 0.945566i | \(0.605510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4715.06 | −0.356754 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1481.61 | − | 2566.23i | −0.110910 | − | 0.192102i | 0.805227 | − | 0.592966i | \(-0.202043\pi\) |
−0.916138 | + | 0.400864i | \(0.868710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20929.5 | − | 36250.9i | 1.55842 | − | 2.69927i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7242.04 | − | 12543.6i | 0.533571 | − | 0.924172i | −0.465660 | − | 0.884964i | \(-0.654183\pi\) |
0.999231 | − | 0.0392086i | \(-0.0124837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8324.90 | − | 14419.1i | −0.610133 | − | 1.05678i | −0.991217 | − | 0.132242i | \(-0.957782\pi\) |
0.381084 | − | 0.924540i | \(-0.375551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22185.3 | 1.60903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14355.4 | 1.03574 | 0.517872 | − | 0.855458i | \(-0.326724\pi\) | ||||
0.517872 | + | 0.855458i | \(0.326724\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20372.8 | + | 35286.8i | 1.45475 | + | 2.51969i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 75.1364 | − | 130.140i | 0.00533762 | − | 0.00924502i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4003.11 | + | 6933.59i | −0.281475 | + | 0.487530i | −0.971748 | − | 0.236019i | \(-0.924157\pi\) |
0.690273 | + | 0.723549i | \(0.257490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3046.45 | + | 5276.60i | 0.213118 | + | 0.369131i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17866.7 | 1.23726 | 0.618632 | − | 0.785681i | \(-0.287687\pi\) | ||||
0.618632 | + | 0.785681i | \(0.287687\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23758.6 | 1.63699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7906.02 | − | 13693.6i | −0.539284 | − | 0.934068i | −0.998943 | − | 0.0459720i | \(-0.985361\pi\) |
0.459658 | − | 0.888096i | \(-0.347972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11455.2 | + | 19840.9i | −0.777481 | + | 1.34664i | 0.155909 | + | 0.987771i | \(0.450169\pi\) |
−0.933390 | + | 0.358865i | \(0.883164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 135.810 | − | 235.230i | 0.00912638 | − | 0.0158073i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.36137 | − | 14.4823i | −0.000559107 | − | 0.000968401i | 0.865746 | − | 0.500484i | \(-0.166845\pi\) |
−0.866305 | + | 0.499516i | \(0.833511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17613.5 | −1.16623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 162.745 | 0.0107230 | 0.00536152 | − | 0.999986i | \(-0.498293\pi\) | ||||
0.00536152 | + | 0.999986i | \(0.498293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4446.59 | + | 7701.72i | 0.290134 | + | 0.502528i | 0.973841 | − | 0.227229i | \(-0.0729666\pi\) |
−0.683707 | + | 0.729757i | \(0.739633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10778.8 | + | 18669.5i | −0.699898 | + | 1.21226i | 0.268603 | + | 0.963251i | \(0.413438\pi\) |
−0.968501 | + | 0.249009i | \(0.919895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18644.0 | − | 32292.3i | 1.19896 | − | 2.07667i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23123.5 | − | 40051.1i | −1.47990 | − | 2.56327i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −911.785 | −0.0577985 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3085.90 | 0.194687 | 0.0973437 | − | 0.995251i | \(-0.468965\pi\) | ||||
0.0973437 | + | 0.995251i | \(0.468965\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15766.6 | − | 27308.5i | −0.985317 | − | 1.70662i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18331.7 | + | 31751.5i | −1.14024 | + | 1.97495i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6283.27 | + | 10882.9i | −0.387167 | + | 0.670593i | −0.992067 | − | 0.125708i | \(-0.959880\pi\) |
0.604900 | + | 0.796301i | \(0.293213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −438.114 | − | 758.835i | −0.0268702 | − | 0.0465405i | 0.852278 | − | 0.523090i | \(-0.175221\pi\) |
−0.879148 | + | 0.476549i | \(0.841887\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11125.4 | 0.676022 | 0.338011 | − | 0.941142i | \(-0.390246\pi\) | ||||
0.338011 | + | 0.941142i | \(0.390246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12911.1 | 0.780903 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10330.4 | − | 17892.8i | −0.619080 | − | 1.07228i | −0.989654 | − | 0.143475i | \(-0.954172\pi\) |
0.370574 | − | 0.928803i | \(-0.379161\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −898.479 | + | 1556.21i | −0.0535977 | + | 0.0928340i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1826.87 | + | 3164.24i | −0.107989 | + | 0.187043i | −0.914956 | − | 0.403555i | \(-0.867775\pi\) |
0.806966 | + | 0.590597i | \(0.201108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6670.38 | + | 11553.4i | 0.392508 | + | 0.679844i | 0.992780 | − | 0.119953i | \(-0.0382742\pi\) |
−0.600272 | + | 0.799796i | \(0.704941\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55410.1 | 3.23114 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5683.00 | −0.329905 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 64.9034 | + | 112.416i | 0.00373408 | + | 0.00646761i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2110.98 | − | 3656.32i | 0.120910 | − | 0.209422i | −0.799217 | − | 0.601043i | \(-0.794752\pi\) |
0.920127 | + | 0.391621i | \(0.128086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9341.03 | + | 16179.1i | −0.530288 | + | 0.918485i | 0.469088 | + | 0.883152i | \(0.344583\pi\) |
−0.999376 | + | 0.0353338i | \(0.988751\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9700.31 | + | 16801.4i | 0.548253 | + | 0.949602i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18674.1 | 1.04619 | 0.523093 | − | 0.852275i | \(-0.324778\pi\) | ||||
0.523093 | + | 0.852275i | \(0.324778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18953.2 | −1.05717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −115.793 | − | 200.559i | −0.00640255 | − | 0.0110895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17764.2 | + | 30768.4i | −0.977974 | + | 1.69390i | −0.308227 | + | 0.951313i | \(0.599735\pi\) |
−0.669748 | + | 0.742589i | \(0.733598\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21077.1 | − | 36506.6i | 1.15036 | − | 1.99248i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7150.96 | + | 12385.8i | 0.388611 | + | 0.673094i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13722.2 | 0.739346 | 0.369673 | − | 0.929162i | \(-0.379470\pi\) | ||||
0.369673 | + | 0.929162i | \(0.379470\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2126.48 | −0.114085 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18700.2 | + | 32389.8i | 0.994760 | + | 1.72297i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1476.42 | + | 2557.23i | −0.0782059 | + | 0.135457i | −0.902476 | − | 0.430740i | \(-0.858252\pi\) |
0.824270 | + | 0.566197i | \(0.191586\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2537.71 | − | 4395.45i | 0.133293 | − | 0.230871i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21819.4 | − | 37792.4i | −1.14126 | − | 1.97672i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8101.57 | 0.420219 | 0.210109 | − | 0.977678i | \(-0.432618\pi\) | ||||
0.210109 | + | 0.977678i | \(0.432618\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43681.6 | 2.25629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13031.3 | + | 22570.9i | 0.667547 | + | 1.15623i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1700.22 | + | 2944.87i | −0.0867368 | + | 0.150233i | −0.906130 | − | 0.422999i | \(-0.860977\pi\) |
0.819393 | + | 0.573232i | \(0.194311\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1493.96 | − | 2587.61i | 0.0755896 | − | 0.130925i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10207.0 | + | 17679.0i | 0.514330 | + | 0.890845i | 0.999862 | + | 0.0166265i | \(0.00529264\pi\) |
−0.485532 | + | 0.874219i | \(0.661374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18052.1 | −0.902250 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9505.82 | −0.473176 | −0.236588 | − | 0.971610i | \(-0.576029\pi\) | ||||
−0.236588 | + | 0.971610i | \(0.576029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.5803 | − | 32.1820i | −0.000917422 | − | 0.00158902i | 0.865566 | − | 0.500794i | \(-0.166959\pi\) |
−0.866484 | + | 0.499205i | \(0.833625\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15533.0 | − | 26903.9i | 0.763872 | − | 1.32307i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10682.6 | + | 18502.9i | −0.521141 | + | 0.902643i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5088.90 | − | 8814.24i | −0.247266 | − | 0.428277i | 0.715500 | − | 0.698612i | \(-0.246199\pi\) |
−0.962766 | + | 0.270335i | \(0.912865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23029.7 | 1.11011 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17129.3 | 0.822425 | 0.411213 | − | 0.911539i | \(-0.365105\pi\) | ||||
0.411213 | + | 0.911539i | \(0.365105\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11468.9 | + | 19864.7i | 0.546317 | + | 0.946248i | 0.998523 | + | 0.0543348i | \(0.0173038\pi\) |
−0.452206 | + | 0.891913i | \(0.649363\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14888.4 | − | 25787.5i | 0.706417 | − | 1.22355i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9948.68 | − | 17231.6i | 0.468352 | − | 0.811210i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2635.08 | − | 4564.09i | −0.123567 | − | 0.214025i | 0.797605 | − | 0.603181i | \(-0.206100\pi\) |
−0.921172 | + | 0.389156i | \(0.872767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.1847 | −0.00145102 | −0.000725509 | − | 1.00000i | \(-0.500231\pi\) | ||||
−0.000725509 | 1.00000i | \(0.500231\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23276.3 | −1.07885 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16677.6 | + | 28886.4i | 0.767055 | + | 1.32858i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2831.95 | − | 4905.07i | 0.129750 | − | 0.224734i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5694.49 | − | 9863.15i | 0.258911 | − | 0.448447i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11531.6 | − | 19973.3i | −0.522307 | − | 0.904663i | −0.999663 | − | 0.0259526i | \(-0.991738\pi\) |
0.477356 | − | 0.878710i | \(-0.341595\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −62568.8 | −2.81251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 200.045 | 0.00895816 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17022.0 | − | 29483.1i | −0.756527 | − | 1.31034i | −0.944612 | − | 0.328190i | \(-0.893561\pi\) |
0.188085 | − | 0.982153i | \(-0.439772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5580.82 | − | 9666.26i | 0.247103 | − | 0.427995i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5590.52 | − | 9683.06i | 0.245685 | − | 0.425539i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23078.5 | − | 39973.1i | −1.01045 | − | 1.75015i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16017.6 | 0.696103 | 0.348052 | − | 0.937475i | \(-0.386843\pi\) | ||||
0.348052 | + | 0.937475i | \(0.386843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15085.2 | 0.653160 | 0.326580 | − | 0.945170i | \(-0.394104\pi\) | ||||
0.326580 | + | 0.945170i | \(0.394104\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34256.7 | − | 59334.3i | −1.47234 | − | 2.55017i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3484.23 | − | 6034.86i | 0.149202 | − | 0.258425i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5347.65 | + | 9262.39i | −0.227325 | + | 0.393739i | −0.957015 | − | 0.290040i | \(-0.906331\pi\) |
0.729689 | + | 0.683779i | \(0.239665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14691.9 | + | 25447.1i | 0.622268 | + | 1.07780i | 0.989062 | + | 0.147498i | \(0.0471219\pi\) |
−0.366794 | + | 0.930302i | \(0.619545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5402.42 | −0.227159 | −0.113580 | − | 0.993529i | \(-0.536232\pi\) | ||||
−0.113580 | + | 0.993529i | \(0.536232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25212.9 | 1.05631 | 0.528155 | − | 0.849148i | \(-0.322884\pi\) | ||||
0.528155 | + | 0.849148i | \(0.322884\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11616.8 | − | 20120.8i | −0.483190 | − | 0.836909i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18000.5 | + | 31177.7i | −0.746026 | + | 1.29216i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15158.4 | − | 26255.1i | 0.623748 | − | 1.08036i | −0.365033 | − | 0.930994i | \(-0.618942\pi\) |
0.988782 | − | 0.149369i | \(-0.0477243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8856.39 | + | 15339.7i | 0.363130 | + | 0.628960i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20959.8 | −0.853299 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −406.005 | −0.0164705 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 885.686 | + | 1534.05i | 0.0356767 | + | 0.0617939i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12664.5 | − | 21935.5i | 0.508350 | − | 0.880488i | −0.491603 | − | 0.870819i | \(-0.663589\pi\) |
0.999953 | − | 0.00966889i | \(-0.00307775\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1005.46 | − | 1741.51i | 0.0400770 | − | 0.0694154i | −0.845291 | − | 0.534306i | \(-0.820573\pi\) |
0.885368 | + | 0.464891i | \(0.153906\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3482.25 | − | 6031.43i | −0.138315 | − | 0.239569i | 0.788544 | − | 0.614979i | \(-0.210835\pi\) |
−0.926859 | + | 0.375410i | \(0.877502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14772.4 | −0.582686 | −0.291343 | − | 0.956619i | \(-0.594102\pi\) | ||||
−0.291343 | + | 0.956619i | \(0.594102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −55410.2 | −2.17804 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12306.2 | + | 21315.0i | 0.480391 | + | 0.832062i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13910.1 | + | 24093.0i | −0.541131 | + | 0.937266i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −64363.1 | + | 111480.i | −2.48671 | + | 4.30710i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12561.5 | + | 21757.1i | 0.483661 | + | 0.837726i | 0.999824 | − | 0.0187648i | \(-0.00597336\pi\) |
−0.516163 | + | 0.856491i | \(0.672640\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20881.3 | −0.798533 | −0.399267 | − | 0.916835i | \(-0.630735\pi\) | ||||
−0.399267 | + | 0.916835i | \(0.630735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38366.4 | −1.46221 | −0.731106 | − | 0.682264i | \(-0.760995\pi\) | ||||
−0.731106 | + | 0.682264i | \(0.760995\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20493.3 | + | 35495.4i | 0.775758 | + | 1.34365i | 0.934367 | + | 0.356311i | \(0.115966\pi\) |
−0.158609 | + | 0.987341i | \(0.550701\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23567.1 | + | 40819.4i | −0.889107 | + | 1.53998i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13015.7 | − | 22543.8i | 0.487740 | − | 0.844791i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47754.2 | + | 82712.7i | 1.78352 | + | 3.08914i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5962.47 | 0.221201 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 146.755 | 0.00542632 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24522.6 | − | 42474.4i | −0.900728 | − | 1.56011i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16897.9 | − | 29268.0i | 0.618616 | − | 1.07147i | −0.371123 | − | 0.928584i | \(-0.621027\pi\) |
0.989739 | − | 0.142890i | \(-0.0456396\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26068.8 | + | 45152.6i | −0.948078 | + | 1.64212i | −0.198612 | + | 0.980078i | \(0.563643\pi\) |
−0.749467 | + | 0.662042i | \(0.769690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23713.0 | + | 41072.0i | 0.859567 | + | 1.48881i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2686.01 | 0.0967284 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28749.5 | 1.03194 | 0.515972 | − | 0.856605i | \(-0.327431\pi\) | ||||
0.515972 | + | 0.856605i | \(0.327431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4364.32 | − | 7559.22i | −0.155637 | − | 0.269572i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4061.83 | − | 7035.29i | 0.144381 | − | 0.250075i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4030.63 | − | 6981.26i | 0.142347 | − | 0.246553i | −0.786033 | − | 0.618185i | \(-0.787868\pi\) |
0.928380 | + | 0.371632i | \(0.121202\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27092.8 | − | 46926.0i | −0.953737 | − | 1.65192i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27653.8 | 0.967247 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38362.0 | −1.33749 | −0.668746 | − | 0.743491i | \(-0.733169\pi\) | ||||
−0.668746 | + | 0.743491i | \(0.733169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12891.3 | − | 22328.4i | −0.446594 | − | 0.773523i | 0.551568 | − | 0.834130i | \(-0.314030\pi\) |
−0.998162 | + | 0.0606066i | \(0.980696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13892.5 | − | 24062.6i | 0.479749 | − | 0.830949i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24029.5 | + | 41620.3i | −0.824554 | + | 1.42817i | 0.0777053 | + | 0.996976i | \(0.475241\pi\) |
−0.902260 | + | 0.431193i | \(0.858093\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8615.56 | − | 14922.6i | −0.294703 | − | 0.510440i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49570.9 | −1.68495 | −0.842476 | − | 0.538733i | \(-0.818903\pi\) | ||||
−0.842476 | + | 0.538733i | \(0.818903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25952.3 | −0.879368 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14165.2 | + | 24534.8i | 0.476974 | + | 0.826142i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12233.0 | − | 21188.2i | 0.410627 | − | 0.711227i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22587.5 | − | 39122.6i | 0.753488 | − | 1.30508i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21589.6 | + | 37394.3i | 0.717968 | + | 1.24356i | 0.961804 | + | 0.273741i | \(0.0882610\pi\) |
−0.243836 | + | 0.969817i | \(0.578406\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23494.7 | −0.776498 | −0.388249 | − | 0.921554i | \(-0.626920\pi\) | ||||
−0.388249 | + | 0.921554i | \(0.626920\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −63010.1 | −2.07606 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10096.4 | + | 17487.4i | 0.330616 | + | 0.572643i | 0.982633 | − | 0.185561i | \(-0.0594103\pi\) |
−0.652017 | + | 0.758204i | \(0.726077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21700.6 | − | 37586.6i | 0.708432 | − | 1.22704i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24610.9 | − | 42627.4i | 0.798542 | − | 1.38312i | −0.122023 | − | 0.992527i | \(-0.538938\pi\) |
0.920566 | − | 0.390588i | \(-0.127728\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20907.9 | − | 36213.5i | −0.676326 | − | 1.17143i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5804.77 | −0.186634 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38703.5 | 1.24062 | 0.620312 | − | 0.784355i | \(-0.287006\pi\) | ||||
0.620312 | + | 0.784355i | \(0.287006\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2364.13 | − | 4094.79i | −0.0753245 | − | 0.130466i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4171.39 | + | 7225.06i | −0.132507 | + | 0.229508i | −0.924642 | − | 0.380837i | \(-0.875636\pi\) |
0.792136 | + | 0.610345i | \(0.208969\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 324.4.e.i.217.4 | 8 | ||
3.2 | odd | 2 | inner | 324.4.e.i.217.1 | 8 | ||
9.2 | odd | 6 | 324.4.a.e.1.4 | yes | 4 | ||
9.4 | even | 3 | inner | 324.4.e.i.109.4 | 8 | ||
9.5 | odd | 6 | inner | 324.4.e.i.109.1 | 8 | ||
9.7 | even | 3 | 324.4.a.e.1.1 | ✓ | 4 | ||
36.7 | odd | 6 | 1296.4.a.z.1.1 | 4 | |||
36.11 | even | 6 | 1296.4.a.z.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.4.a.e.1.1 | ✓ | 4 | 9.7 | even | 3 | ||
324.4.a.e.1.4 | yes | 4 | 9.2 | odd | 6 | ||
324.4.e.i.109.1 | 8 | 9.5 | odd | 6 | inner | ||
324.4.e.i.109.4 | 8 | 9.4 | even | 3 | inner | ||
324.4.e.i.217.1 | 8 | 3.2 | odd | 2 | inner | ||
324.4.e.i.217.4 | 8 | 1.1 | even | 1 | trivial | ||
1296.4.a.z.1.1 | 4 | 36.7 | odd | 6 | |||
1296.4.a.z.1.4 | 4 | 36.11 | even | 6 |