Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 103 x^{10} + 14 x^{9} + 7600 x^{8} + 1474 x^{7} + 229961 x^{6} + 442438 x^{5} + \cdots + 69739201 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.10 | ||
Root | \(-3.88205 - 6.72390i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.c.601.7 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −5.11242 | − | 4.78154i | −0.730346 | − | 0.683078i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.3587 | 0.941702 | 0.470851 | − | 0.882213i | \(-0.343947\pi\) | ||||
0.470851 | + | 0.882213i | \(0.343947\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − | 0.605169i | − | 0.0465515i | −0.999729 | − | 0.0232757i | \(-0.992590\pi\) | ||
0.999729 | − | 0.0232757i | \(-0.00740956\pi\) | |||||||
\(14\) | −7.23005 | − | 6.76212i | −0.516432 | − | 0.483009i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 5.49382i | 0.323166i | 0.986859 | + | 0.161583i | \(0.0516599\pi\) | ||||
−0.986859 | + | 0.161583i | \(0.948340\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 33.2186i | 1.74835i | 0.485612 | + | 0.874175i | \(0.338597\pi\) | ||||
−0.485612 | + | 0.874175i | \(0.661403\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.28188 | − | 8.85497i | 0.394375 | − | 0.421665i | ||||
\(22\) | 14.6495 | 0.665884 | ||||||||
\(23\) | 14.4299 | 0.627385 | 0.313693 | − | 0.949525i | \(-0.398434\pi\) | ||||
0.313693 | + | 0.949525i | \(0.398434\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.855838i | − | 0.0329169i | ||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −10.2248 | − | 9.56309i | −0.365173 | − | 0.341539i | ||||
\(29\) | 42.0972 | 1.45163 | 0.725814 | − | 0.687891i | \(-0.241464\pi\) | ||||
0.725814 | + | 0.687891i | \(0.241464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.540656i | − | 0.0174405i | −0.999962 | − | 0.00872026i | \(-0.997224\pi\) | ||
0.999962 | − | 0.00872026i | \(-0.00277578\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 17.9418i | 0.543692i | ||||||||
\(34\) | 7.76943i | 0.228513i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 13.6996 | 0.370260 | 0.185130 | − | 0.982714i | \(-0.440729\pi\) | ||||
0.185130 | + | 0.982714i | \(0.440729\pi\) | |||||||
\(38\) | 46.9782i | 1.23627i | ||||||||
\(39\) | 1.04818 | 0.0268765 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13.7668i | 0.335777i | 0.985806 | + | 0.167888i | \(0.0536948\pi\) | ||||
−0.985806 | + | 0.167888i | \(0.946305\pi\) | |||||||
\(42\) | 11.7123 | − | 12.5228i | 0.278865 | − | 0.298162i | ||||
\(43\) | 82.3938 | 1.91614 | 0.958068 | − | 0.286541i | \(-0.0925056\pi\) | ||||
0.958068 | + | 0.286541i | \(0.0925056\pi\) | |||||||
\(44\) | 20.7175 | 0.470851 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20.4069 | 0.443628 | ||||||||
\(47\) | − | 53.0228i | − | 1.12814i | −0.825725 | − | 0.564072i | \(-0.809234\pi\) | ||
0.825725 | − | 0.564072i | \(-0.190766\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 3.27369 | + | 48.8905i | 0.0668101 | + | 0.997766i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.51557 | −0.186580 | ||||||||
\(52\) | − | 1.21034i | − | 0.0232757i | ||||||
\(53\) | 19.4291 | 0.366587 | 0.183294 | − | 0.983058i | \(-0.441324\pi\) | ||||
0.183294 | + | 0.983058i | \(0.441324\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14.4601 | − | 13.5242i | −0.258216 | − | 0.241504i | ||||
\(57\) | −57.5364 | −1.00941 | ||||||||
\(58\) | 59.5344 | 1.02646 | ||||||||
\(59\) | 29.4240i | 0.498713i | 0.968412 | + | 0.249356i | \(0.0802190\pi\) | ||||
−0.968412 | + | 0.249356i | \(0.919781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.7188i | 1.22490i | 0.790510 | + | 0.612449i | \(0.209815\pi\) | ||||
−0.790510 | + | 0.612449i | \(0.790185\pi\) | |||||||
\(62\) | − | 0.764604i | − | 0.0123323i | ||||||
\(63\) | 15.3373 | + | 14.3446i | 0.243449 | + | 0.227693i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 25.3736i | 0.384448i | ||||||||
\(67\) | −12.1937 | −0.181996 | −0.0909981 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909981 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(68\) | 10.9876i | 0.161583i | ||||||||
\(69\) | 24.9933i | 0.362221i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42.3945 | 0.597105 | 0.298553 | − | 0.954393i | \(-0.403496\pi\) | ||||
0.298553 | + | 0.954393i | \(0.403496\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | 66.9179i | 0.916683i | 0.888776 | + | 0.458342i | \(0.151556\pi\) | ||||
−0.888776 | + | 0.458342i | \(0.848444\pi\) | |||||||
\(74\) | 19.3742 | 0.261813 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 66.4373i | 0.874175i | ||||||||
\(77\) | −52.9582 | − | 49.5307i | −0.687768 | − | 0.643256i | ||||
\(78\) | 1.48236 | 0.0190046 | ||||||||
\(79\) | −27.0962 | −0.342990 | −0.171495 | − | 0.985185i | \(-0.554860\pi\) | ||||
−0.171495 | + | 0.985185i | \(0.554860\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 19.4693i | 0.237430i | ||||||||
\(83\) | 126.850i | 1.52831i | 0.645031 | + | 0.764156i | \(0.276844\pi\) | ||||
−0.645031 | + | 0.764156i | \(0.723156\pi\) | |||||||
\(84\) | 16.5638 | − | 17.7099i | 0.197188 | − | 0.210833i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 116.522 | 1.35491 | ||||||||
\(87\) | 72.9145i | 0.838097i | ||||||||
\(88\) | 29.2989 | 0.332942 | ||||||||
\(89\) | − | 30.1856i | − | 0.339164i | −0.985516 | − | 0.169582i | \(-0.945758\pi\) | ||
0.985516 | − | 0.169582i | \(-0.0542417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.89364 | + | 3.09388i | −0.0317983 | + | 0.0339987i | ||||
\(92\) | 28.8597 | 0.313693 | ||||||||
\(93\) | 0.936444 | 0.0100693 | ||||||||
\(94\) | − | 74.9856i | − | 0.797719i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | − | 164.602i | − | 1.69693i | −0.529251 | − | 0.848465i | \(-0.677527\pi\) | ||
0.529251 | − | 0.848465i | \(-0.322473\pi\) | |||||||
\(98\) | 4.62970 | + | 69.1416i | 0.0472419 | + | 0.705527i | ||||
\(99\) | −31.0762 | −0.313901 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.5033i | 0.193102i | 0.995328 | + | 0.0965508i | \(0.0307810\pi\) | ||||
−0.995328 | + | 0.0965508i | \(0.969219\pi\) | |||||||
\(102\) | −13.4570 | −0.131932 | ||||||||
\(103\) | − | 108.949i | − | 1.05775i | −0.848699 | − | 0.528877i | \(-0.822613\pi\) | ||
0.848699 | − | 0.528877i | \(-0.177387\pi\) | |||||||
\(104\) | − | 1.71168i | − | 0.0164584i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 27.4769 | 0.259216 | ||||||||
\(107\) | −120.784 | −1.12882 | −0.564409 | − | 0.825495i | \(-0.690896\pi\) | ||||
−0.564409 | + | 0.825495i | \(0.690896\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | 123.855 | 1.13628 | 0.568141 | − | 0.822931i | \(-0.307663\pi\) | ||||
0.568141 | + | 0.822931i | \(0.307663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.7284i | 0.213770i | ||||||||
\(112\) | −20.4497 | − | 19.1262i | −0.182586 | − | 0.170769i | ||||
\(113\) | −201.420 | −1.78248 | −0.891239 | − | 0.453534i | \(-0.850163\pi\) | ||||
−0.891239 | + | 0.453534i | \(0.850163\pi\) | |||||||
\(114\) | −81.3687 | −0.713761 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 84.1944 | 0.725814 | ||||||||
\(117\) | 1.81551i | 0.0155172i | ||||||||
\(118\) | 41.6119i | 0.352643i | ||||||||
\(119\) | 26.2689 | − | 28.0867i | 0.220747 | − | 0.236023i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.6968 | −0.113196 | ||||||||
\(122\) | 105.668i | 0.866133i | ||||||||
\(123\) | −23.8449 | −0.193861 | ||||||||
\(124\) | − | 1.08131i | − | 0.00872026i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 21.6902 | + | 20.2864i | 0.172144 | + | 0.161003i | ||||
\(127\) | −213.378 | −1.68014 | −0.840071 | − | 0.542476i | \(-0.817487\pi\) | ||||
−0.840071 | + | 0.542476i | \(0.817487\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 142.710i | 1.10628i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 139.162i | 1.06231i | 0.847276 | + | 0.531153i | \(0.178241\pi\) | ||||
−0.847276 | + | 0.531153i | \(0.821759\pi\) | |||||||
\(132\) | 35.8837i | 0.271846i | ||||||||
\(133\) | 158.836 | − | 169.828i | 1.19426 | − | 1.27690i | ||||
\(134\) | −17.2446 | −0.128691 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.5389i | 0.114256i | ||||||||
\(137\) | 18.2823 | 0.133448 | 0.0667238 | − | 0.997771i | \(-0.478745\pi\) | ||||
0.0667238 | + | 0.997771i | \(0.478745\pi\) | |||||||
\(138\) | 35.3458i | 0.256129i | ||||||||
\(139\) | − | 38.7265i | − | 0.278608i | −0.990250 | − | 0.139304i | \(-0.955513\pi\) | ||
0.990250 | − | 0.139304i | \(-0.0444865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 91.8382 | 0.651335 | ||||||||
\(142\) | 59.9548 | 0.422217 | ||||||||
\(143\) | − | 6.26878i | − | 0.0438376i | ||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 94.6362i | 0.648193i | ||||||||
\(147\) | −84.6809 | + | 5.67021i | −0.576060 | + | 0.0385728i | ||||
\(148\) | 27.3992 | 0.185130 | ||||||||
\(149\) | −20.1135 | −0.134990 | −0.0674950 | − | 0.997720i | \(-0.521501\pi\) | ||||
−0.0674950 | + | 0.997720i | \(0.521501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3257 | 0.0750047 | 0.0375023 | − | 0.999297i | \(-0.488060\pi\) | ||||
0.0375023 | + | 0.999297i | \(0.488060\pi\) | |||||||
\(152\) | 93.9565i | 0.618135i | ||||||||
\(153\) | − | 16.4814i | − | 0.107722i | ||||||
\(154\) | −74.8942 | − | 70.0470i | −0.486326 | − | 0.454851i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.09637 | 0.0134382 | ||||||||
\(157\) | − | 108.422i | − | 0.690589i | −0.938494 | − | 0.345294i | \(-0.887779\pi\) | ||
0.938494 | − | 0.345294i | \(-0.112221\pi\) | |||||||
\(158\) | −38.3198 | −0.242531 | ||||||||
\(159\) | 33.6522i | 0.211649i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −73.7715 | − | 68.9970i | −0.458208 | − | 0.428553i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | 82.1443 | 0.503953 | 0.251976 | − | 0.967733i | \(-0.418919\pi\) | ||||
0.251976 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(164\) | 27.5337i | 0.167888i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 179.393i | 1.08068i | ||||||||
\(167\) | − | 314.645i | − | 1.88410i | −0.335472 | − | 0.942050i | \(-0.608896\pi\) | ||
0.335472 | − | 0.942050i | \(-0.391104\pi\) | |||||||
\(168\) | 23.4247 | − | 25.0456i | 0.139433 | − | 0.149081i | ||||
\(169\) | 168.634 | 0.997833 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 99.6559i | − | 0.582783i | ||||||
\(172\) | 164.788 | 0.958068 | ||||||||
\(173\) | 188.637i | 1.09039i | 0.838311 | + | 0.545193i | \(0.183544\pi\) | ||||
−0.838311 | + | 0.545193i | \(0.816456\pi\) | |||||||
\(174\) | 103.117i | 0.592624i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 41.4349 | 0.235426 | ||||||||
\(177\) | −50.9639 | −0.287932 | ||||||||
\(178\) | − | 42.6889i | − | 0.239825i | ||||||
\(179\) | 254.112 | 1.41962 | 0.709810 | − | 0.704393i | \(-0.248781\pi\) | ||||
0.709810 | + | 0.704393i | \(0.248781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 138.747i | 0.766560i | 0.923632 | + | 0.383280i | \(0.125206\pi\) | ||||
−0.923632 | + | 0.383280i | \(0.874794\pi\) | |||||||
\(182\) | −4.09223 | + | 4.37540i | −0.0224848 | + | 0.0240407i | ||||
\(183\) | −129.417 | −0.707195 | ||||||||
\(184\) | 40.8138 | 0.221814 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.32433 | 0.00712007 | ||||||||
\(187\) | 56.9089i | 0.304326i | ||||||||
\(188\) | − | 106.046i | − | 0.564072i | ||||||
\(189\) | −24.8456 | + | 26.5649i | −0.131458 | + | 0.140555i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 178.907 | 0.936685 | 0.468342 | − | 0.883547i | \(-0.344851\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344851\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −3.65902 | −0.0189587 | −0.00947933 | − | 0.999955i | \(-0.503017\pi\) | ||||
−0.00947933 | + | 0.999955i | \(0.503017\pi\) | |||||||
\(194\) | − | 232.783i | − | 1.19991i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.54739 | + | 97.7810i | 0.0334051 | + | 0.498883i | ||||
\(197\) | 201.822 | 1.02447 | 0.512237 | − | 0.858844i | \(-0.328817\pi\) | ||||
0.512237 | + | 0.858844i | \(0.328817\pi\) | |||||||
\(198\) | −43.9484 | −0.221961 | ||||||||
\(199\) | − | 97.5792i | − | 0.490348i | −0.969479 | − | 0.245174i | \(-0.921155\pi\) | ||
0.969479 | − | 0.245174i | \(-0.0788451\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 21.1202i | − | 0.105076i | ||||||
\(202\) | 27.5818i | 0.136543i | ||||||||
\(203\) | −215.219 | − | 201.290i | −1.06019 | − | 0.991574i | ||||
\(204\) | −19.0311 | −0.0932899 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 154.077i | − | 0.747945i | ||||||
\(207\) | −43.2896 | −0.209128 | ||||||||
\(208\) | − | 2.42068i | − | 0.0116379i | ||||||
\(209\) | 344.103i | 1.64642i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −104.122 | −0.493469 | −0.246734 | − | 0.969083i | \(-0.579357\pi\) | ||||
−0.246734 | + | 0.969083i | \(0.579357\pi\) | |||||||
\(212\) | 38.8582 | 0.183294 | ||||||||
\(213\) | 73.4294i | 0.344739i | ||||||||
\(214\) | −170.814 | −0.798196 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −2.58517 | + | 2.76406i | −0.0119132 | + | 0.0127376i | ||||
\(218\) | 175.157 | 0.803473 | ||||||||
\(219\) | −115.905 | −0.529247 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.32469 | 0.0150438 | ||||||||
\(222\) | 33.5571i | 0.151158i | ||||||||
\(223\) | − | 255.861i | − | 1.14736i | −0.819080 | − | 0.573679i | \(-0.805516\pi\) | ||
0.819080 | − | 0.573679i | \(-0.194484\pi\) | |||||||
\(224\) | −28.9202 | − | 27.0485i | −0.129108 | − | 0.120752i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −284.851 | −1.26040 | ||||||||
\(227\) | − | 102.642i | − | 0.452168i | −0.974108 | − | 0.226084i | \(-0.927408\pi\) | ||
0.974108 | − | 0.226084i | \(-0.0725924\pi\) | |||||||
\(228\) | −115.073 | −0.504705 | ||||||||
\(229\) | − | 254.063i | − | 1.10945i | −0.832035 | − | 0.554723i | \(-0.812824\pi\) | ||
0.832035 | − | 0.554723i | \(-0.187176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 85.7897 | − | 91.7262i | 0.371384 | − | 0.397083i | ||||
\(232\) | 119.069 | 0.513228 | ||||||||
\(233\) | −87.3948 | −0.375085 | −0.187543 | − | 0.982256i | \(-0.560052\pi\) | ||||
−0.187543 | + | 0.982256i | \(0.560052\pi\) | |||||||
\(234\) | 2.56751i | 0.0109723i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 58.8481i | 0.249356i | ||||||||
\(237\) | − | 46.9320i | − | 0.198025i | ||||||
\(238\) | 37.1499 | − | 39.7206i | 0.156092 | − | 0.166893i | ||||
\(239\) | −238.165 | −0.996505 | −0.498253 | − | 0.867032i | \(-0.666025\pi\) | ||||
−0.498253 | + | 0.867032i | \(0.666025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 235.615i | − | 0.977655i | −0.872381 | − | 0.488827i | \(-0.837425\pi\) | ||
0.872381 | − | 0.488827i | \(-0.162575\pi\) | |||||||
\(242\) | −19.3702 | −0.0800420 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 149.438i | 0.612449i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −33.7217 | −0.137080 | ||||||||
\(247\) | 20.1029 | 0.0813882 | ||||||||
\(248\) | − | 1.52921i | − | 0.00616616i | ||||||
\(249\) | −219.710 | −0.882371 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 281.571i | − | 1.12180i | −0.827884 | − | 0.560899i | \(-0.810456\pi\) | ||
0.827884 | − | 0.560899i | \(-0.189544\pi\) | |||||||
\(252\) | 30.6745 | + | 28.6893i | 0.121724 | + | 0.113846i | ||||
\(253\) | 149.475 | 0.590810 | ||||||||
\(254\) | −301.762 | −1.18804 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 253.540i | 0.986539i | 0.869877 | + | 0.493269i | \(0.164198\pi\) | ||||
−0.869877 | + | 0.493269i | \(0.835802\pi\) | |||||||
\(258\) | 201.823i | 0.782259i | ||||||||
\(259\) | −70.0382 | − | 65.5053i | −0.270418 | − | 0.252916i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −126.292 | −0.483876 | ||||||||
\(262\) | 196.805i | 0.751163i | ||||||||
\(263\) | −264.972 | −1.00750 | −0.503749 | − | 0.863850i | \(-0.668046\pi\) | ||||
−0.503749 | + | 0.863850i | \(0.668046\pi\) | |||||||
\(264\) | 50.7472i | 0.192224i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 224.628 | − | 240.173i | 0.844468 | − | 0.902904i | ||||
\(267\) | 52.2830 | 0.195816 | ||||||||
\(268\) | −24.3875 | −0.0909981 | ||||||||
\(269\) | − | 189.680i | − | 0.705130i | −0.935787 | − | 0.352565i | \(-0.885310\pi\) | ||
0.935787 | − | 0.352565i | \(-0.114690\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 286.595i | 1.05755i | 0.848763 | + | 0.528773i | \(0.177348\pi\) | ||||
−0.848763 | + | 0.528773i | \(0.822652\pi\) | |||||||
\(272\) | 21.9753i | 0.0807914i | ||||||||
\(273\) | −5.35875 | − | 5.01193i | −0.0196291 | − | 0.0183587i | ||||
\(274\) | 25.8551 | 0.0943617 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 49.9865i | 0.181111i | ||||||||
\(277\) | 82.5341 | 0.297957 | 0.148979 | − | 0.988840i | \(-0.452401\pi\) | ||||
0.148979 | + | 0.988840i | \(0.452401\pi\) | |||||||
\(278\) | − | 54.7676i | − | 0.197006i | ||||||
\(279\) | 1.62197i | 0.00581351i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −384.926 | −1.36984 | −0.684922 | − | 0.728617i | \(-0.740164\pi\) | ||||
−0.684922 | + | 0.728617i | \(0.740164\pi\) | |||||||
\(282\) | 129.879 | 0.460563 | ||||||||
\(283\) | − | 514.332i | − | 1.81743i | −0.417419 | − | 0.908714i | \(-0.637065\pi\) | ||
0.417419 | − | 0.908714i | \(-0.362935\pi\) | |||||||
\(284\) | 84.7889 | 0.298553 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 8.86539i | − | 0.0309979i | ||||||
\(287\) | 65.8268 | − | 70.3819i | 0.229362 | − | 0.245233i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | 258.818 | 0.895564 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 285.099 | 0.979723 | ||||||||
\(292\) | 133.836i | 0.458342i | ||||||||
\(293\) | 431.273i | 1.47192i | 0.677023 | + | 0.735962i | \(0.263270\pi\) | ||||
−0.677023 | + | 0.735962i | \(0.736730\pi\) | |||||||
\(294\) | −119.757 | + | 8.01888i | −0.407336 | + | 0.0272751i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 38.7484 | 0.130907 | ||||||||
\(297\) | − | 53.8255i | − | 0.181231i | ||||||
\(298\) | −28.4448 | −0.0954524 | ||||||||
\(299\) | − | 8.73251i | − | 0.0292057i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −421.232 | − | 393.970i | −1.39944 | − | 1.30887i | ||||
\(302\) | 16.0170 | 0.0530363 | ||||||||
\(303\) | −33.7806 | −0.111487 | ||||||||
\(304\) | 132.875i | 0.437087i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 23.3083i | − | 0.0761709i | ||||||
\(307\) | − | 341.103i | − | 1.11108i | −0.831489 | − | 0.555542i | \(-0.812511\pi\) | ||
0.831489 | − | 0.555542i | \(-0.187489\pi\) | |||||||
\(308\) | −105.916 | − | 99.0614i | −0.343884 | − | 0.321628i | ||||
\(309\) | 188.705 | 0.610694 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 545.710i | − | 1.75469i | −0.479857 | − | 0.877347i | \(-0.659311\pi\) | ||
0.479857 | − | 0.877347i | \(-0.340689\pi\) | |||||||
\(312\) | 2.96471 | 0.00950228 | ||||||||
\(313\) | − | 98.7397i | − | 0.315462i | −0.987482 | − | 0.157731i | \(-0.949582\pi\) | ||
0.987482 | − | 0.157731i | \(-0.0504179\pi\) | |||||||
\(314\) | − | 153.332i | − | 0.488320i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −54.1924 | −0.171495 | ||||||||
\(317\) | −165.058 | −0.520689 | −0.260344 | − | 0.965516i | \(-0.583836\pi\) | ||||
−0.260344 | + | 0.965516i | \(0.583836\pi\) | |||||||
\(318\) | 47.5914i | 0.149659i | ||||||||
\(319\) | 436.073 | 1.36700 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 209.203i | − | 0.651724i | ||||||
\(322\) | −104.329 | − | 97.5765i | −0.324002 | − | 0.303033i | ||||
\(323\) | −182.497 | −0.565006 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 116.170 | 0.356349 | ||||||||
\(327\) | 214.523i | 0.656033i | ||||||||
\(328\) | 38.9385i | 0.118715i | ||||||||
\(329\) | −253.531 | + | 271.075i | −0.770610 | + | 0.823936i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −230.662 | −0.696863 | −0.348431 | − | 0.937334i | \(-0.613286\pi\) | ||||
−0.348431 | + | 0.937334i | \(0.613286\pi\) | |||||||
\(332\) | 253.700i | 0.764156i | ||||||||
\(333\) | −41.0988 | −0.123420 | ||||||||
\(334\) | − | 444.975i | − | 1.33226i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 33.1275 | − | 35.4199i | 0.0985938 | − | 0.105416i | ||||
\(337\) | 144.633 | 0.429179 | 0.214590 | − | 0.976704i | \(-0.431159\pi\) | ||||
0.214590 | + | 0.976704i | \(0.431159\pi\) | |||||||
\(338\) | 238.484 | 0.705574 | ||||||||
\(339\) | − | 348.870i | − | 1.02911i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.60051i | − | 0.0164238i | ||||||
\(342\) | − | 140.935i | − | 0.412090i | ||||||
\(343\) | 217.036 | − | 265.602i | 0.632757 | − | 0.774351i | ||||
\(344\) | 233.045 | 0.677456 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 266.773i | 0.771019i | ||||||||
\(347\) | 162.310 | 0.467751 | 0.233875 | − | 0.972267i | \(-0.424859\pi\) | ||||
0.233875 | + | 0.972267i | \(0.424859\pi\) | |||||||
\(348\) | 145.829i | 0.419049i | ||||||||
\(349\) | 313.404i | 0.898006i | 0.893530 | + | 0.449003i | \(0.148221\pi\) | ||||
−0.893530 | + | 0.449003i | \(0.851779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.14455 | −0.00895883 | ||||||||
\(352\) | 58.5978 | 0.166471 | ||||||||
\(353\) | 343.028i | 0.971752i | 0.874028 | + | 0.485876i | \(0.161499\pi\) | ||||
−0.874028 | + | 0.485876i | \(0.838501\pi\) | |||||||
\(354\) | −72.0739 | −0.203599 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 60.3712i | − | 0.169582i | ||||||
\(357\) | 48.6476 | + | 45.4991i | 0.136268 | + | 0.127448i | ||||
\(358\) | 359.369 | 1.00382 | ||||||||
\(359\) | −357.293 | −0.995244 | −0.497622 | − | 0.867394i | \(-0.665793\pi\) | ||||
−0.497622 | + | 0.867394i | \(0.665793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −742.478 | −2.05672 | ||||||||
\(362\) | 196.218i | 0.542040i | ||||||||
\(363\) | − | 23.7235i | − | 0.0653540i | ||||||
\(364\) | −5.78728 | + | 6.18776i | −0.0158991 | + | 0.0169993i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −183.023 | −0.500062 | ||||||||
\(367\) | 617.139i | 1.68158i | 0.541363 | + | 0.840789i | \(0.317909\pi\) | ||||
−0.541363 | + | 0.840789i | \(0.682091\pi\) | |||||||
\(368\) | 57.7195 | 0.156846 | ||||||||
\(369\) | − | 41.3005i | − | 0.111926i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −99.3298 | − | 92.9011i | −0.267735 | − | 0.250407i | ||||
\(372\) | 1.87289 | 0.00503465 | ||||||||
\(373\) | 338.873 | 0.908506 | 0.454253 | − | 0.890873i | \(-0.349906\pi\) | ||||
0.454253 | + | 0.890873i | \(0.349906\pi\) | |||||||
\(374\) | 80.4814i | 0.215191i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 149.971i | − | 0.398859i | ||||||
\(377\) | − | 25.4759i | − | 0.0675754i | ||||||
\(378\) | −35.1370 | + | 37.5685i | −0.0929551 | + | 0.0993875i | ||||
\(379\) | −211.631 | −0.558392 | −0.279196 | − | 0.960234i | \(-0.590068\pi\) | ||||
−0.279196 | + | 0.960234i | \(0.590068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 369.582i | − | 0.970031i | ||||||
\(382\) | 253.012 | 0.662336 | ||||||||
\(383\) | 238.751i | 0.623370i | 0.950185 | + | 0.311685i | \(0.100893\pi\) | ||||
−0.950185 | + | 0.311685i | \(0.899107\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.17464 | −0.0134058 | ||||||||
\(387\) | −247.182 | −0.638712 | ||||||||
\(388\) | − | 329.204i | − | 0.848465i | ||||||
\(389\) | −21.7723 | −0.0559700 | −0.0279850 | − | 0.999608i | \(-0.508909\pi\) | ||||
−0.0279850 | + | 0.999608i | \(0.508909\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 79.2750i | 0.202749i | ||||||||
\(392\) | 9.25941 | + | 138.283i | 0.0236209 | + | 0.352763i | ||||
\(393\) | −241.036 | −0.613322 | ||||||||
\(394\) | 285.419 | 0.724413 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −62.1524 | −0.156950 | ||||||||
\(397\) | 552.917i | 1.39274i | 0.717684 | + | 0.696369i | \(0.245202\pi\) | ||||
−0.717684 | + | 0.696369i | \(0.754798\pi\) | |||||||
\(398\) | − | 137.998i | − | 0.346728i | ||||||
\(399\) | 294.150 | + | 275.113i | 0.737218 | + | 0.689505i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −636.205 | −1.58655 | −0.793273 | − | 0.608866i | \(-0.791625\pi\) | ||||
−0.793273 | + | 0.608866i | \(0.791625\pi\) | |||||||
\(402\) | − | 29.8685i | − | 0.0742997i | ||||||
\(403\) | −0.327188 | −0.000811882 | ||||||||
\(404\) | 39.0065i | 0.0965508i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −304.365 | − | 284.666i | −0.749667 | − | 0.701149i | ||||
\(407\) | 141.911 | 0.348675 | ||||||||
\(408\) | −26.9141 | −0.0659659 | ||||||||
\(409\) | − | 358.386i | − | 0.876249i | −0.898914 | − | 0.438124i | \(-0.855643\pi\) | ||
0.898914 | − | 0.438124i | \(-0.144357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.6659i | 0.0770460i | ||||||||
\(412\) | − | 217.897i | − | 0.528877i | ||||||
\(413\) | 140.692 | − | 150.428i | 0.340659 | − | 0.364233i | ||||
\(414\) | −61.2207 | −0.147876 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 3.42335i | − | 0.00822921i | ||||||
\(417\) | 67.0763 | 0.160854 | ||||||||
\(418\) | 486.635i | 1.16420i | ||||||||
\(419\) | 391.544i | 0.934472i | 0.884133 | + | 0.467236i | \(0.154750\pi\) | ||||
−0.884133 | + | 0.467236i | \(0.845250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 472.677 | 1.12275 | 0.561374 | − | 0.827563i | \(-0.310273\pi\) | ||||
0.561374 | + | 0.827563i | \(0.310273\pi\) | |||||||
\(422\) | −147.251 | −0.348935 | ||||||||
\(423\) | 159.068i | 0.376048i | ||||||||
\(424\) | 54.9538 | 0.129608 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 103.845i | 0.243767i | ||||||||
\(427\) | 357.271 | − | 381.994i | 0.836700 | − | 0.894599i | ||||
\(428\) | −241.567 | −0.564409 | ||||||||
\(429\) | 10.8578 | 0.0253097 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −671.160 | −1.55721 | −0.778607 | − | 0.627511i | \(-0.784074\pi\) | ||||
−0.778607 | + | 0.627511i | \(0.784074\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | − | 113.211i | − | 0.261456i | −0.991418 | − | 0.130728i | \(-0.958268\pi\) | ||
0.991418 | − | 0.130728i | \(-0.0417315\pi\) | |||||||
\(434\) | −3.65599 | + | 3.90898i | −0.00842393 | + | 0.00900686i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 247.710 | 0.568141 | ||||||||
\(437\) | 479.340i | 1.09689i | ||||||||
\(438\) | −163.915 | −0.374234 | ||||||||
\(439\) | − | 603.089i | − | 1.37378i | −0.726762 | − | 0.686890i | \(-0.758976\pi\) | ||
0.726762 | − | 0.686890i | \(-0.241024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.82108 | − | 146.672i | −0.0222700 | − | 0.332589i | ||||
\(442\) | 4.70182 | 0.0106376 | ||||||||
\(443\) | −853.722 | −1.92714 | −0.963569 | − | 0.267459i | \(-0.913816\pi\) | ||||
−0.963569 | + | 0.267459i | \(0.913816\pi\) | |||||||
\(444\) | 47.4569i | 0.106885i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 361.842i | − | 0.811305i | ||||||
\(447\) | − | 34.8376i | − | 0.0779366i | ||||||
\(448\) | −40.8994 | − | 38.2523i | −0.0912932 | − | 0.0853847i | ||||
\(449\) | −232.558 | −0.517946 | −0.258973 | − | 0.965885i | \(-0.583384\pi\) | ||||
−0.258973 | + | 0.965885i | \(0.583384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 142.607i | 0.316202i | ||||||||
\(452\) | −402.840 | −0.891239 | ||||||||
\(453\) | 19.6167i | 0.0433040i | ||||||||
\(454\) | − | 145.158i | − | 0.319731i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −162.737 | −0.356880 | ||||||||
\(457\) | 389.899 | 0.853170 | 0.426585 | − | 0.904448i | \(-0.359717\pi\) | ||||
0.426585 | + | 0.904448i | \(0.359717\pi\) | |||||||
\(458\) | − | 359.299i | − | 0.784496i | ||||||
\(459\) | 28.5467 | 0.0621932 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 599.713i | 1.30090i | 0.759551 | + | 0.650448i | \(0.225419\pi\) | ||||
−0.759551 | + | 0.650448i | \(0.774581\pi\) | |||||||
\(462\) | 121.325 | − | 129.721i | 0.262608 | − | 0.280780i | ||||
\(463\) | −211.263 | −0.456292 | −0.228146 | − | 0.973627i | \(-0.573266\pi\) | ||||
−0.228146 | + | 0.973627i | \(0.573266\pi\) | |||||||
\(464\) | 168.389 | 0.362907 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −123.595 | −0.265225 | ||||||||
\(467\) | 796.828i | 1.70627i | 0.521690 | + | 0.853135i | \(0.325302\pi\) | ||||
−0.521690 | + | 0.853135i | \(0.674698\pi\) | |||||||
\(468\) | 3.63101i | 0.00775858i | ||||||||
\(469\) | 62.3396 | + | 58.3049i | 0.132920 | + | 0.124318i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 187.793 | 0.398712 | ||||||||
\(472\) | 83.2238i | 0.176322i | ||||||||
\(473\) | 853.495 | 1.80443 | ||||||||
\(474\) | − | 66.3719i | − | 0.140025i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 52.5378 | − | 56.1734i | 0.110374 | − | 0.118011i | ||||
\(477\) | −58.2873 | −0.122196 | ||||||||
\(478\) | −336.816 | −0.704636 | ||||||||
\(479\) | − | 522.525i | − | 1.09087i | −0.838154 | − | 0.545433i | \(-0.816365\pi\) | ||
0.838154 | − | 0.545433i | \(-0.183635\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 8.29058i | − | 0.0172361i | ||||||
\(482\) | − | 333.210i | − | 0.691306i | ||||||
\(483\) | 119.506 | − | 127.776i | 0.247425 | − | 0.264547i | ||||
\(484\) | −27.3935 | −0.0565982 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | 216.781 | 0.445135 | 0.222568 | − | 0.974917i | \(-0.428556\pi\) | ||||
0.222568 | + | 0.974917i | \(0.428556\pi\) | |||||||
\(488\) | 211.337i | 0.433067i | ||||||||
\(489\) | 142.278i | 0.290957i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 451.246 | 0.919035 | 0.459517 | − | 0.888169i | \(-0.348022\pi\) | ||||
0.459517 | + | 0.888169i | \(0.348022\pi\) | |||||||
\(492\) | −47.6897 | −0.0969304 | ||||||||
\(493\) | 231.274i | 0.469116i | ||||||||
\(494\) | 28.4298 | 0.0575501 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.16263i | − | 0.00436013i | ||||||
\(497\) | −216.738 | − | 202.711i | −0.436093 | − | 0.407869i | ||||
\(498\) | −310.718 | −0.623931 | ||||||||
\(499\) | 347.296 | 0.695984 | 0.347992 | − | 0.937498i | \(-0.386864\pi\) | ||||
0.347992 | + | 0.937498i | \(0.386864\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 544.981 | 1.08779 | ||||||||
\(502\) | − | 398.202i | − | 0.793231i | ||||||
\(503\) | − | 684.193i | − | 1.36022i | −0.733108 | − | 0.680112i | \(-0.761931\pi\) | ||
0.733108 | − | 0.680112i | \(-0.238069\pi\) | |||||||
\(504\) | 43.3803 | + | 40.5727i | 0.0860721 | + | 0.0805015i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 211.390 | 0.417766 | ||||||||
\(507\) | 292.082i | 0.576099i | ||||||||
\(508\) | −426.756 | −0.840071 | ||||||||
\(509\) | 577.464i | 1.13451i | 0.823543 | + | 0.567253i | \(0.191994\pi\) | ||||
−0.823543 | + | 0.567253i | \(0.808006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 319.971 | − | 342.112i | 0.626166 | − | 0.669496i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 172.609 | 0.336470 | ||||||||
\(514\) | 358.560i | 0.697588i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 285.421i | 0.553141i | ||||||||
\(517\) | − | 549.249i | − | 1.06238i | ||||||
\(518\) | −99.0490 | − | 92.6385i | −0.191214 | − | 0.178839i | ||||
\(519\) | −326.728 | −0.629534 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 871.106i | 1.67199i | 0.548738 | + | 0.835994i | \(0.315109\pi\) | ||||
−0.548738 | + | 0.835994i | \(0.684891\pi\) | |||||||
\(522\) | −178.603 | −0.342152 | ||||||||
\(523\) | 108.067i | 0.206629i | 0.994649 | + | 0.103315i | \(0.0329449\pi\) | ||||
−0.994649 | + | 0.103315i | \(0.967055\pi\) | |||||||
\(524\) | 278.324i | 0.531153i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −374.727 | −0.712408 | ||||||||
\(527\) | 2.97027 | 0.00563618 | ||||||||
\(528\) | 71.7674i | 0.135923i | ||||||||
\(529\) | −320.779 | −0.606388 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 88.2721i | − | 0.166238i | ||||||
\(532\) | 317.673 | − | 339.655i | 0.597129 | − | 0.638450i | ||||
\(533\) | 8.33127 | 0.0156309 | ||||||||
\(534\) | 73.9393 | 0.138463 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −34.4891 | −0.0643454 | ||||||||
\(537\) | 440.135i | 0.819618i | ||||||||
\(538\) | − | 268.248i | − | 0.498602i | ||||||
\(539\) | 33.9113 | + | 506.444i | 0.0629152 | + | 0.939598i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 608.803 | 1.12533 | 0.562664 | − | 0.826685i | \(-0.309776\pi\) | ||||
0.562664 | + | 0.826685i | \(0.309776\pi\) | |||||||
\(542\) | 405.306i | 0.747797i | ||||||||
\(543\) | −240.318 | −0.442574 | ||||||||
\(544\) | 31.0777i | 0.0571281i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.57842 | − | 7.08794i | −0.0138799 | − | 0.0129816i | ||||
\(547\) | −1020.16 | −1.86502 | −0.932508 | − | 0.361150i | \(-0.882384\pi\) | ||||
−0.932508 | + | 0.361150i | \(0.882384\pi\) | |||||||
\(548\) | 36.5646 | 0.0667238 | ||||||||
\(549\) | − | 224.156i | − | 0.408299i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1398.41i | 2.53795i | ||||||||
\(552\) | 70.6916i | 0.128065i | ||||||||
\(553\) | 138.527 | + | 129.562i | 0.250501 | + | 0.234289i | ||||
\(554\) | 116.721 | 0.210687 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 77.4531i | − | 0.139304i | ||||||
\(557\) | 162.089 | 0.291003 | 0.145502 | − | 0.989358i | \(-0.453520\pi\) | ||||
0.145502 | + | 0.989358i | \(0.453520\pi\) | |||||||
\(558\) | 2.29381i | 0.00411077i | ||||||||
\(559\) | − | 49.8622i | − | 0.0891989i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −98.5692 | −0.175703 | ||||||||
\(562\) | −544.368 | −0.968626 | ||||||||
\(563\) | − | 273.813i | − | 0.486347i | −0.969983 | − | 0.243173i | \(-0.921812\pi\) | ||
0.969983 | − | 0.243173i | \(-0.0781884\pi\) | |||||||
\(564\) | 183.676 | 0.325667 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 727.375i | − | 1.28512i | ||||||
\(567\) | −46.0118 | − | 43.0339i | −0.0811495 | − | 0.0758975i | ||||
\(568\) | 119.910 | 0.211109 | ||||||||
\(569\) | −618.238 | −1.08653 | −0.543267 | − | 0.839560i | \(-0.682813\pi\) | ||||
−0.543267 | + | 0.839560i | \(0.682813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 602.897 | 1.05586 | 0.527931 | − | 0.849287i | \(-0.322968\pi\) | ||||
0.527931 | + | 0.849287i | \(0.322968\pi\) | |||||||
\(572\) | − | 12.5376i | − | 0.0219188i | ||||||
\(573\) | 309.876i | 0.540795i | ||||||||
\(574\) | 93.0931 | − | 99.5350i | 0.162183 | − | 0.173406i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | − | 491.145i | − | 0.851204i | −0.904911 | − | 0.425602i | \(-0.860062\pi\) | ||
0.904911 | − | 0.425602i | \(-0.139938\pi\) | |||||||
\(578\) | 366.024 | 0.633259 | ||||||||
\(579\) | − | 6.33761i | − | 0.0109458i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 606.538 | − | 648.510i | 1.04396 | − | 1.11620i | ||||
\(582\) | 403.192 | 0.692769 | ||||||||
\(583\) | 201.261 | 0.345216 | ||||||||
\(584\) | 189.272i | 0.324096i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 609.913i | 1.04081i | ||||||||
\(587\) | − | 990.289i | − | 1.68703i | −0.537102 | − | 0.843517i | \(-0.680481\pi\) | ||
0.537102 | − | 0.843517i | \(-0.319519\pi\) | |||||||
\(588\) | −169.362 | + | 11.3404i | −0.288030 | + | 0.0192864i | ||||
\(589\) | 17.9599 | 0.0304921 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 349.565i | 0.591481i | ||||||||
\(592\) | 54.7985 | 0.0925650 | ||||||||
\(593\) | 10.4613i | 0.0176414i | 0.999961 | + | 0.00882070i | \(0.00280775\pi\) | ||||
−0.999961 | + | 0.00882070i | \(0.997192\pi\) | |||||||
\(594\) | − | 76.1208i | − | 0.128149i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −40.2270 | −0.0674950 | ||||||||
\(597\) | 169.012 | 0.283102 | ||||||||
\(598\) | − | 12.3496i | − | 0.0206516i | ||||||
\(599\) | −592.559 | −0.989248 | −0.494624 | − | 0.869107i | \(-0.664694\pi\) | ||||
−0.494624 | + | 0.869107i | \(0.664694\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 595.499i | − | 0.990846i | −0.868652 | − | 0.495423i | \(-0.835013\pi\) | ||
0.868652 | − | 0.495423i | \(-0.164987\pi\) | |||||||
\(602\) | −595.712 | − | 557.157i | −0.989555 | − | 0.925510i | ||||
\(603\) | 36.5812 | 0.0606654 | ||||||||
\(604\) | 22.6514 | 0.0375023 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −47.7730 | −0.0788334 | ||||||||
\(607\) | 621.260i | 1.02349i | 0.859136 | + | 0.511747i | \(0.171001\pi\) | ||||
−0.859136 | + | 0.511747i | \(0.828999\pi\) | |||||||
\(608\) | 187.913i | 0.309067i | ||||||||
\(609\) | 348.644 | − | 372.769i | 0.572485 | − | 0.612101i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.0878 | −0.0525168 | ||||||||
\(612\) | − | 32.9629i | − | 0.0538609i | ||||||
\(613\) | −332.564 | −0.542519 | −0.271259 | − | 0.962506i | \(-0.587440\pi\) | ||||
−0.271259 | + | 0.962506i | \(0.587440\pi\) | |||||||
\(614\) | − | 482.392i | − | 0.785654i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −149.788 | − | 140.094i | −0.243163 | − | 0.227425i | ||||
\(617\) | 366.977 | 0.594776 | 0.297388 | − | 0.954757i | \(-0.403884\pi\) | ||||
0.297388 | + | 0.954757i | \(0.403884\pi\) | |||||||
\(618\) | 266.869 | 0.431826 | ||||||||
\(619\) | − | 1123.84i | − | 1.81557i | −0.419439 | − | 0.907783i | \(-0.637773\pi\) | ||
0.419439 | − | 0.907783i | \(-0.362227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 74.9798i | − | 0.120740i | ||||||
\(622\) | − | 771.750i | − | 1.24076i | ||||||
\(623\) | −144.334 | + | 154.321i | −0.231675 | + | 0.247707i | ||||
\(624\) | 4.19273 | 0.00671912 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 139.639i | − | 0.223066i | ||||||
\(627\) | −596.003 | −0.950564 | ||||||||
\(628\) | − | 216.845i | − | 0.345294i | ||||||
\(629\) | 75.2632i | 0.119655i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 782.201 | 1.23962 | 0.619810 | − | 0.784752i | \(-0.287210\pi\) | ||||
0.619810 | + | 0.784752i | \(0.287210\pi\) | |||||||
\(632\) | −76.6397 | −0.121265 | ||||||||
\(633\) | − | 180.344i | − | 0.284904i | ||||||
\(634\) | −233.428 | −0.368183 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 67.3044i | 0.105825i | ||||||||
\(637\) | 29.5870 | − | 1.98114i | 0.0464474 | − | 0.00311011i | ||||
\(638\) | 616.701 | 0.966616 | ||||||||
\(639\) | −127.183 | −0.199035 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.16909 | 0.00962416 | 0.00481208 | − | 0.999988i | \(-0.498468\pi\) | ||||
0.00481208 | + | 0.999988i | \(0.498468\pi\) | |||||||
\(642\) | − | 295.858i | − | 0.460838i | ||||||
\(643\) | 82.5062i | 0.128315i | 0.997940 | + | 0.0641573i | \(0.0204359\pi\) | ||||
−0.997940 | + | 0.0641573i | \(0.979564\pi\) | |||||||
\(644\) | −147.543 | − | 137.994i | −0.229104 | − | 0.214276i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −258.090 | −0.399520 | ||||||||
\(647\) | − | 863.567i | − | 1.33472i | −0.744733 | − | 0.667362i | \(-0.767423\pi\) | ||
0.744733 | − | 0.667362i | \(-0.232577\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | 304.796i | 0.469639i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.78750 | − | 4.47765i | −0.00735407 | − | 0.00687811i | ||||
\(652\) | 164.289 | 0.251976 | ||||||||
\(653\) | −172.088 | −0.263535 | −0.131767 | − | 0.991281i | \(-0.542065\pi\) | ||||
−0.131767 | + | 0.991281i | \(0.542065\pi\) | |||||||
\(654\) | 303.381i | 0.463885i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 55.0674i | 0.0839442i | ||||||||
\(657\) | − | 200.754i | − | 0.305561i | ||||||
\(658\) | −358.547 | + | 383.358i | −0.544904 | + | 0.582611i | ||||
\(659\) | 170.542 | 0.258789 | 0.129394 | − | 0.991593i | \(-0.458697\pi\) | ||||
0.129394 | + | 0.991593i | \(0.458697\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 53.4631i | − | 0.0808822i | −0.999182 | − | 0.0404411i | \(-0.987124\pi\) | ||
0.999182 | − | 0.0404411i | \(-0.0128763\pi\) | |||||||
\(662\) | −326.205 | −0.492756 | ||||||||
\(663\) | 5.75853i | 0.00868556i | ||||||||
\(664\) | 358.786i | 0.540340i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −58.1225 | −0.0872711 | ||||||||
\(667\) | 607.457 | 0.910730 | ||||||||
\(668\) | − | 629.290i | − | 0.942050i | ||||||
\(669\) | 443.164 | 0.662427 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 773.991i | 1.15349i | ||||||||
\(672\) | 46.8494 | − | 50.0913i | 0.0697163 | − | 0.0745406i | ||||
\(673\) | 1215.31 | 1.80581 | 0.902907 | − | 0.429836i | \(-0.141429\pi\) | ||||
0.902907 | + | 0.429836i | \(0.141429\pi\) | |||||||
\(674\) | 204.542 | 0.303475 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 337.268 | 0.498916 | ||||||||
\(677\) | 1161.52i | 1.71569i | 0.513907 | + | 0.857846i | \(0.328198\pi\) | ||||
−0.513907 | + | 0.857846i | \(0.671802\pi\) | |||||||
\(678\) | − | 493.376i | − | 0.727694i | ||||||
\(679\) | −787.053 | + | 841.516i | −1.15914 | + | 1.23935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 177.781 | 0.261059 | ||||||||
\(682\) | − | 7.92032i | − | 0.0116134i | ||||||
\(683\) | 724.141 | 1.06024 | 0.530118 | − | 0.847924i | \(-0.322148\pi\) | ||||
0.530118 | + | 0.847924i | \(0.322148\pi\) | |||||||
\(684\) | − | 199.312i | − | 0.291392i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 306.935 | − | 375.618i | 0.447427 | − | 0.547549i | ||||
\(687\) | 440.050 | 0.640539 | ||||||||
\(688\) | 329.575 | 0.479034 | ||||||||
\(689\) | − | 11.7579i | − | 0.0170652i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1084.92i | 1.57007i | 0.619450 | + | 0.785036i | \(0.287356\pi\) | ||||
−0.619450 | + | 0.785036i | \(0.712644\pi\) | |||||||
\(692\) | 377.273i | 0.545193i | ||||||||
\(693\) | 158.875 | + | 148.592i | 0.229256 | + | 0.214419i | ||||
\(694\) | 229.540 | 0.330750 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 206.233i | 0.296312i | ||||||||
\(697\) | −75.6325 | −0.108511 | ||||||||
\(698\) | 443.220i | 0.634986i | ||||||||
\(699\) | − | 151.372i | − | 0.216556i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −405.283 | −0.578150 | −0.289075 | − | 0.957307i | \(-0.593348\pi\) | ||||
−0.289075 | + | 0.957307i | \(0.593348\pi\) | |||||||
\(702\) | −4.44707 | −0.00633485 | ||||||||
\(703\) | 455.083i | 0.647344i | ||||||||
\(704\) | 82.8698 | 0.117713 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 485.115i | 0.687132i | ||||||||
\(707\) | 93.2557 | − | 99.7089i | 0.131903 | − | 0.141031i | ||||
\(708\) | −101.928 | −0.143966 | ||||||||
\(709\) | 906.179 | 1.27811 | 0.639055 | − | 0.769161i | \(-0.279326\pi\) | ||||
0.639055 | + | 0.769161i | \(0.279326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 81.2886 | 0.114330 | ||||||||
\(712\) | − | 85.3777i | − | 0.119913i | ||||||
\(713\) | − | 7.80160i | − | 0.0109419i | ||||||
\(714\) | 68.7981 | + | 64.3454i | 0.0963558 | + | 0.0901197i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 508.224 | 0.709810 | ||||||||
\(717\) | − | 412.514i | − | 0.575333i | ||||||
\(718\) | −505.288 | −0.703744 | ||||||||
\(719\) | − | 1374.58i | − | 1.91180i | −0.293693 | − | 0.955900i | \(-0.594884\pi\) | ||
0.293693 | − | 0.955900i | \(-0.405116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −520.943 | + | 556.991i | −0.722528 | + | 0.772526i | ||||
\(722\) | −1050.02 | −1.45432 | ||||||||
\(723\) | 408.097 | 0.564449 | ||||||||
\(724\) | 277.495i | 0.383280i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 33.5501i | − | 0.0462122i | ||||||
\(727\) | − | 203.600i | − | 0.280055i | −0.990148 | − | 0.140028i | \(-0.955281\pi\) | ||
0.990148 | − | 0.140028i | \(-0.0447192\pi\) | |||||||
\(728\) | −8.18445 | + | 8.75081i | −0.0112424 | + | 0.0120203i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 452.657i | 0.619229i | ||||||||
\(732\) | −258.833 | −0.353597 | ||||||||
\(733\) | 841.642i | 1.14822i | 0.818780 | + | 0.574108i | \(0.194651\pi\) | ||||
−0.818780 | + | 0.574108i | \(0.805349\pi\) | |||||||
\(734\) | 872.767i | 1.18906i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 81.6276 | 0.110907 | ||||||||
\(737\) | −126.312 | −0.171386 | ||||||||
\(738\) | − | 58.4078i | − | 0.0791433i | ||||||
\(739\) | −1251.55 | −1.69358 | −0.846788 | − | 0.531930i | \(-0.821467\pi\) | ||||
−0.846788 | + | 0.531930i | \(0.821467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.8192i | 0.0469895i | ||||||||
\(742\) | −140.474 | − | 131.382i | −0.189317 | − | 0.177065i | ||||
\(743\) | −83.5814 | −0.112492 | −0.0562459 | − | 0.998417i | \(-0.517913\pi\) | ||||
−0.0562459 | + | 0.998417i | \(0.517913\pi\) | |||||||
\(744\) | 2.64866 | 0.00356003 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 479.239 | 0.642411 | ||||||||
\(747\) | − | 380.550i | − | 0.509437i | ||||||
\(748\) | 113.818i | 0.152163i | ||||||||
\(749\) | 617.497 | + | 577.532i | 0.824428 | + | 0.771071i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1364.04 | 1.81630 | 0.908152 | − | 0.418641i | \(-0.137493\pi\) | ||||
0.908152 | + | 0.418641i | \(0.137493\pi\) | |||||||
\(752\) | − | 212.091i | − | 0.282036i | ||||||
\(753\) | 487.696 | 0.647670 | ||||||||
\(754\) | − | 36.0284i | − | 0.0477830i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −49.6913 | + | 53.1298i | −0.0657292 | + | 0.0702776i | ||||
\(757\) | −193.941 | −0.256196 | −0.128098 | − | 0.991761i | \(-0.540887\pi\) | ||||
−0.128098 | + | 0.991761i | \(0.540887\pi\) | |||||||
\(758\) | −299.291 | −0.394843 | ||||||||
\(759\) | 258.898i | 0.341105i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 698.879i | 0.918369i | 0.888341 | + | 0.459185i | \(0.151858\pi\) | ||||
−0.888341 | + | 0.459185i | \(0.848142\pi\) | |||||||
\(762\) | − | 522.667i | − | 0.685915i | ||||||
\(763\) | −633.198 | − | 592.217i | −0.829879 | − | 0.776169i | ||||
\(764\) | 357.814 | 0.468342 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 337.645i | 0.440789i | ||||||||
\(767\) | 17.8065 | 0.0232158 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | 335.359i | 0.436097i | 0.975938 | + | 0.218049i | \(0.0699691\pi\) | ||||
−0.975938 | + | 0.218049i | \(0.930031\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −439.145 | −0.569578 | ||||||||
\(772\) | −7.31805 | −0.00947933 | ||||||||
\(773\) | 1276.11i | 1.65085i | 0.564511 | + | 0.825426i | \(0.309065\pi\) | ||||
−0.564511 | + | 0.825426i | \(0.690935\pi\) | |||||||
\(774\) | −349.567 | −0.451638 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 465.565i | − | 0.599955i | ||||||
\(777\) | 113.459 | − | 121.310i | 0.146021 | − | 0.156126i | ||||
\(778\) | −30.7907 | −0.0395767 | ||||||||
\(779\) | −457.316 | −0.587055 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 439.153 | 0.562295 | ||||||||
\(782\) | 112.112i | 0.143365i | ||||||||
\(783\) | − | 218.743i | − | 0.279366i | ||||||
\(784\) | 13.0948 | + | 195.562i | 0.0167025 | + | 0.249441i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −340.876 | −0.433684 | ||||||||
\(787\) | − | 415.510i | − | 0.527967i | −0.964527 | − | 0.263983i | \(-0.914964\pi\) | ||
0.964527 | − | 0.263983i | \(-0.0850364\pi\) | |||||||
\(788\) | 403.643 | 0.512237 | ||||||||
\(789\) | − | 458.945i | − | 0.581679i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1029.74 | + | 963.098i | 1.30183 | + | 1.21757i | ||||
\(792\) | −87.8967 | −0.110981 | ||||||||
\(793\) | 45.2175 | 0.0570208 | ||||||||
\(794\) | 781.943i | 0.984814i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 195.158i | − | 0.245174i | ||||||
\(797\) | − | 1337.78i | − | 1.67852i | −0.543731 | − | 0.839259i | \(-0.682989\pi\) | ||
0.543731 | − | 0.839259i | \(-0.317011\pi\) | |||||||
\(798\) | 415.991 | + | 389.068i | 0.521292 | + | 0.487554i | ||||
\(799\) | 291.297 | 0.364578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 90.5568i | 0.113055i | ||||||||
\(802\) | −899.730 | −1.12186 | ||||||||
\(803\) | 693.184i | 0.863243i | ||||||||
\(804\) | − | 42.2404i | − | 0.0525378i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.462714 | −0.000574087 | ||||||||
\(807\) | 328.535 | 0.407107 | ||||||||
\(808\) | 55.1635i | 0.0682717i | ||||||||
\(809\) | 754.137 | 0.932184 | 0.466092 | − | 0.884736i | \(-0.345662\pi\) | ||||
0.466092 | + | 0.884736i | \(0.345662\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 509.569i | − | 0.628321i | −0.949370 | − | 0.314161i | \(-0.898277\pi\) | ||
0.949370 | − | 0.314161i | \(-0.101723\pi\) | |||||||
\(812\) | −430.437 | − | 402.579i | −0.530095 | − | 0.495787i | ||||
\(813\) | −496.397 | −0.610574 | ||||||||
\(814\) | 200.692 | 0.246550 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −38.0623 | −0.0466449 | ||||||||
\(817\) | 2737.01i | 3.35007i | ||||||||
\(818\) | − | 506.834i | − | 0.619602i | ||||||
\(819\) | 8.68092 | − | 9.28163i | 0.0105994 | − | 0.0113329i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −508.671 | −0.619575 | −0.309787 | − | 0.950806i | \(-0.600258\pi\) | ||||
−0.309787 | + | 0.950806i | \(0.600258\pi\) | |||||||
\(822\) | 44.7824i | 0.0544797i | ||||||||
\(823\) | −717.806 | −0.872182 | −0.436091 | − | 0.899903i | \(-0.643637\pi\) | ||||
−0.436091 | + | 0.899903i | \(0.643637\pi\) | |||||||
\(824\) | − | 308.153i | − | 0.373972i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 198.969 | − | 212.737i | 0.240883 | − | 0.257551i | ||||
\(827\) | 444.662 | 0.537681 | 0.268841 | − | 0.963185i | \(-0.413360\pi\) | ||||
0.268841 | + | 0.963185i | \(0.413360\pi\) | |||||||
\(828\) | −86.5792 | −0.104564 | ||||||||
\(829\) | − | 250.314i | − | 0.301947i | −0.988538 | − | 0.150973i | \(-0.951759\pi\) | ||
0.988538 | − | 0.150973i | \(-0.0482407\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 142.953i | 0.172026i | ||||||||
\(832\) | − | 4.84135i | − | 0.00581893i | ||||||
\(833\) | −268.595 | + | 17.9851i | −0.322444 | + | 0.0215907i | ||||
\(834\) | 94.8602 | 0.113741 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 688.206i | 0.823212i | ||||||||
\(837\) | −2.80933 | −0.00335643 | ||||||||
\(838\) | 553.726i | 0.660771i | ||||||||
\(839\) | − | 1026.45i | − | 1.22343i | −0.791080 | − | 0.611713i | \(-0.790481\pi\) | ||
0.791080 | − | 0.611713i | \(-0.209519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 931.173 | 1.10722 | ||||||||
\(842\) | 668.466 | 0.793902 | ||||||||
\(843\) | − | 666.711i | − | 0.790880i | ||||||
\(844\) | −208.244 | −0.246734 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 224.957i | 0.265906i | ||||||||
\(847\) | 70.0236 | + | 65.4917i | 0.0826725 | + | 0.0773219i | ||||
\(848\) | 77.7165 | 0.0916468 | ||||||||
\(849\) | 890.849 | 1.04929 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 197.684 | 0.232296 | ||||||||
\(852\) | 146.859i | 0.172369i | ||||||||
\(853\) | 840.837i | 0.985740i | 0.870103 | + | 0.492870i | \(0.164052\pi\) | ||||
−0.870103 | + | 0.492870i | \(0.835948\pi\) | |||||||
\(854\) | 505.257 | − | 540.221i | 0.591636 | − | 0.632577i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −341.628 | −0.399098 | ||||||||
\(857\) | 860.502i | 1.00409i | 0.864843 | + | 0.502043i | \(0.167418\pi\) | ||||
−0.864843 | + | 0.502043i | \(0.832582\pi\) | |||||||
\(858\) | 15.3553 | 0.0178966 | ||||||||
\(859\) | 1163.93i | 1.35498i | 0.735532 | + | 0.677490i | \(0.236932\pi\) | ||||
−0.735532 | + | 0.677490i | \(0.763068\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 121.905 | + | 114.015i | 0.141585 | + | 0.132422i | ||||
\(862\) | −949.163 | −1.10112 | ||||||||
\(863\) | −704.504 | −0.816343 | −0.408172 | − | 0.912905i | \(-0.633833\pi\) | ||||
−0.408172 | + | 0.912905i | \(0.633833\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 160.104i | − | 0.184878i | ||||||
\(867\) | 448.286i | 0.517054i | ||||||||
\(868\) | −5.17034 | + | 5.52813i | −0.00595662 | + | 0.00636881i | ||||
\(869\) | −280.682 | −0.322995 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.37928i | 0.00847219i | ||||||||
\(872\) | 350.314 | 0.401736 | ||||||||
\(873\) | 493.807i | 0.565643i | ||||||||
\(874\) | 677.890i | 0.775618i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −231.810 | −0.264624 | ||||||||
\(877\) | −570.744 | −0.650792 | −0.325396 | − | 0.945578i | \(-0.605498\pi\) | ||||
−0.325396 | + | 0.945578i | \(0.605498\pi\) | |||||||
\(878\) | − | 852.897i | − | 0.971409i | ||||||
\(879\) | −746.988 | −0.849815 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1241.29i | − | 1.40895i | −0.709728 | − | 0.704476i | \(-0.751182\pi\) | ||
0.709728 | − | 0.704476i | \(-0.248818\pi\) | |||||||
\(882\) | −13.8891 | − | 207.425i | −0.0157473 | − | 0.235176i | ||||
\(883\) | −907.346 | −1.02757 | −0.513786 | − | 0.857918i | \(-0.671758\pi\) | ||||
−0.513786 | + | 0.857918i | \(0.671758\pi\) | |||||||
\(884\) | 6.64937 | 0.00752191 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1207.35 | −1.36269 | ||||||||
\(887\) | − | 132.595i | − | 0.149487i | −0.997203 | − | 0.0747437i | \(-0.976186\pi\) | ||
0.997203 | − | 0.0747437i | \(-0.0238139\pi\) | |||||||
\(888\) | 67.1141i | 0.0755790i | ||||||||
\(889\) | 1090.88 | + | 1020.28i | 1.22708 | + | 1.14767i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 93.2285 | 0.104634 | ||||||||
\(892\) | − | 511.722i | − | 0.573679i | ||||||
\(893\) | 1761.35 | 1.97239 | ||||||||
\(894\) | − | 49.2679i | − | 0.0551095i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −57.8404 | − | 54.0970i | −0.0645541 | − | 0.0603761i | ||||
\(897\) | 15.1251 | 0.0168619 | ||||||||
\(898\) | −328.887 | −0.366243 | ||||||||
\(899\) | − | 22.7601i | − | 0.0253171i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 106.740i | 0.118468i | ||||||||
\(902\) | 201.677i | 0.223588i | ||||||||
\(903\) | 682.375 | − | 729.595i | 0.755676 | − | 0.807968i | ||||
\(904\) | −569.702 | −0.630201 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 27.7422i | 0.0306205i | ||||||||
\(907\) | −1309.04 | −1.44326 | −0.721632 | − | 0.692277i | \(-0.756608\pi\) | ||||
−0.721632 | + | 0.692277i | \(0.756608\pi\) | |||||||
\(908\) | − | 205.284i | − | 0.226084i | ||||||
\(909\) | − | 58.5098i | − | 0.0643672i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1252.86 | −1.37525 | −0.687627 | − | 0.726064i | \(-0.741348\pi\) | ||||
−0.687627 | + | 0.726064i | \(0.741348\pi\) | |||||||
\(912\) | −230.145 | −0.252352 | ||||||||
\(913\) | 1314.00i | 1.43922i | ||||||||
\(914\) | 551.400 | 0.603282 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 508.126i | − | 0.554723i | ||||||
\(917\) | 665.409 | − | 711.455i | 0.725637 | − | 0.775850i | ||||
\(918\) | 40.3711 | 0.0439773 | ||||||||
\(919\) | −329.889 | −0.358966 | −0.179483 | − | 0.983761i | \(-0.557442\pi\) | ||||
−0.179483 | + | 0.983761i | \(0.557442\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 590.807 | 0.641484 | ||||||||
\(922\) | 848.122i | 0.919872i | ||||||||
\(923\) | − | 25.6558i | − | 0.0277961i | ||||||
\(924\) | 171.579 | − | 183.452i | 0.185692 | − | 0.198542i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −298.771 | −0.322647 | ||||||||
\(927\) | 326.846i | 0.352585i | ||||||||
\(928\) | 238.138 | 0.256614 | ||||||||
\(929\) | − | 12.0040i | − | 0.0129214i | −0.999979 | − | 0.00646072i | \(-0.997943\pi\) | ||
0.999979 | − | 0.00646072i | \(-0.00205653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1624.08 | + | 108.748i | −1.74444 | + | 0.116807i | ||||
\(932\) | −174.790 | −0.187543 | ||||||||
\(933\) | 945.197 | 1.01307 | ||||||||
\(934\) | 1126.89i | 1.20652i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.13503i | 0.00548614i | ||||||||
\(937\) | 300.461i | 0.320663i | 0.987063 | + | 0.160331i | \(0.0512563\pi\) | ||||
−0.987063 | + | 0.160331i | \(0.948744\pi\) | |||||||
\(938\) | 88.1615 | + | 82.4556i | 0.0939888 | + | 0.0879058i | ||||
\(939\) | 171.022 | 0.182132 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 494.625i | − | 0.525637i | −0.964845 | − | 0.262819i | \(-0.915348\pi\) | ||
0.964845 | − | 0.262819i | \(-0.0846521\pi\) | |||||||
\(942\) | 265.580 | 0.281932 | ||||||||
\(943\) | 198.654i | 0.210661i | ||||||||
\(944\) | 117.696i | 0.124678i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1207.02 | 1.27592 | ||||||||
\(947\) | 337.631 | 0.356527 | 0.178263 | − | 0.983983i | \(-0.442952\pi\) | ||||
0.178263 | + | 0.983983i | \(0.442952\pi\) | |||||||
\(948\) | − | 93.8640i | − | 0.0990127i | ||||||
\(949\) | 40.4966 | 0.0426729 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 285.889i | − | 0.300620i | ||||||
\(952\) | 74.2997 | − | 79.4412i | 0.0780459 | − | 0.0834466i | ||||
\(953\) | 635.279 | 0.666610 | 0.333305 | − | 0.942819i | \(-0.391836\pi\) | ||||
0.333305 | + | 0.942819i | \(0.391836\pi\) | |||||||
\(954\) | −82.4308 | −0.0864054 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −476.330 | −0.498253 | ||||||||
\(957\) | 755.301i | 0.789238i | ||||||||
\(958\) | − | 738.962i | − | 0.771359i | ||||||
\(959\) | −93.4669 | − | 87.4177i | −0.0974629 | − | 0.0911551i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.708 | 0.999696 | ||||||||
\(962\) | − | 11.7247i | − | 0.0121878i | ||||||
\(963\) | 362.351 | 0.376273 | ||||||||
\(964\) | − | 471.230i | − | 0.488827i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 169.007 | − | 180.703i | 0.174956 | − | 0.187063i | ||||
\(967\) | −489.313 | −0.506011 | −0.253006 | − | 0.967465i | \(-0.581419\pi\) | ||||
−0.253006 | + | 0.967465i | \(0.581419\pi\) | |||||||
\(968\) | −38.7403 | −0.0400210 | ||||||||
\(969\) | − | 316.094i | − | 0.326207i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 621.040i | 0.639588i | 0.947487 | + | 0.319794i | \(0.103614\pi\) | ||||
−0.947487 | + | 0.319794i | \(0.896386\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −185.173 | + | 197.986i | −0.190311 | + | 0.203480i | ||||
\(974\) | 306.574 | 0.314758 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 298.875i | 0.306224i | ||||||||
\(977\) | 1475.20 | 1.50993 | 0.754963 | − | 0.655768i | \(-0.227655\pi\) | ||||
0.754963 | + | 0.655768i | \(0.227655\pi\) | |||||||
\(978\) | 201.212i | 0.205738i | ||||||||
\(979\) | − | 312.684i | − | 0.319392i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −371.564 | −0.378761 | ||||||||
\(982\) | 638.158 | 0.649856 | ||||||||
\(983\) | 343.366i | 0.349304i | 0.984630 | + | 0.174652i | \(0.0558801\pi\) | ||||
−0.984630 | + | 0.174652i | \(0.944120\pi\) | |||||||
\(984\) | −67.4435 | −0.0685401 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 327.071i | 0.331715i | ||||||||
\(987\) | −469.515 | − | 439.128i | −0.475700 | − | 0.444912i | ||||
\(988\) | 40.2058 | 0.0406941 | ||||||||
\(989\) | 1188.93 | 1.20216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1389.23 | −1.40184 | −0.700921 | − | 0.713239i | \(-0.747228\pi\) | ||||
−0.700921 | + | 0.713239i | \(0.747228\pi\) | |||||||
\(992\) | − | 3.05841i | − | 0.00308308i | ||||||
\(993\) | − | 399.518i | − | 0.402334i | ||||||
\(994\) | −306.514 | − | 286.677i | −0.308364 | − | 0.288407i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −439.421 | −0.441186 | ||||||||
\(997\) | 347.412i | 0.348458i | 0.984705 | + | 0.174229i | \(0.0557432\pi\) | ||||
−0.984705 | + | 0.174229i | \(0.944257\pi\) | |||||||
\(998\) | 491.151 | 0.492135 | ||||||||
\(999\) | − | 71.1853i | − | 0.0712565i |
(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 | 1050.3.f.c.601.10 | yes | 12 | |
5.2 | odd | 4 | 1050.3.h.c.349.24 | 24 | |||
5.3 | odd | 4 | 1050.3.h.c.349.1 | 24 | |||
5.4 | even | 2 | 1050.3.f.d.601.3 | yes | 12 | ||
7.6 | odd | 2 | inner | 1050.3.f.c.601.7 | ✓ | 12 | |
35.13 | even | 4 | 1050.3.h.c.349.23 | 24 | |||
35.27 | even | 4 | 1050.3.h.c.349.2 | 24 | |||
35.34 | odd | 2 | 1050.3.f.d.601.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.f.c.601.7 | ✓ | 12 | 7.6 | odd | 2 | inner | |
1050.3.f.c.601.10 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.3.f.d.601.3 | yes | 12 | 5.4 | even | 2 | ||
1050.3.f.d.601.6 | yes | 12 | 35.34 | odd | 2 | ||
1050.3.h.c.349.1 | 24 | 5.3 | odd | 4 | |||
1050.3.h.c.349.2 | 24 | 35.27 | even | 4 | |||
1050.3.h.c.349.23 | 24 | 35.13 | even | 4 | |||
1050.3.h.c.349.24 | 24 | 5.2 | odd | 4 |