Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1425,2,Mod(1,1425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1425, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1425.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1425 = 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1425.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(11.3786822880\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1425.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | −2.23607 | −0.845154 | −0.422577 | − | 0.906327i | \(-0.638874\pi\) | ||||
−0.422577 | + | 0.906327i | \(0.638874\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | 6.47214 | 1.79505 | 0.897524 | − | 0.440966i | \(-0.145364\pi\) | ||||
0.897524 | + | 0.440966i | \(0.145364\pi\) | |||||||
\(14\) | 1.38197 | 0.369346 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 1.23607 | 0.299791 | 0.149895 | − | 0.988702i | \(-0.452106\pi\) | ||||
0.149895 | + | 0.988702i | \(0.452106\pi\) | |||||||
\(18\) | −0.618034 | −0.145672 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.23607 | 0.487950 | ||||||||
\(22\) | 2.47214 | 0.527061 | ||||||||
\(23\) | 3.23607 | 0.674767 | 0.337383 | − | 0.941367i | \(-0.390458\pi\) | ||||
0.337383 | + | 0.941367i | \(0.390458\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.61803 | 0.683744 | ||||||||
\(29\) | 7.47214 | 1.38754 | 0.693770 | − | 0.720196i | \(-0.255948\pi\) | ||||
0.693770 | + | 0.720196i | \(0.255948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4721 | −1.88085 | −0.940426 | − | 0.340000i | \(-0.889573\pi\) | ||||
−0.940426 | + | 0.340000i | \(0.889573\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | −0.763932 | −0.131013 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | 2.76393 | 0.454388 | 0.227194 | − | 0.973850i | \(-0.427045\pi\) | ||||
0.227194 | + | 0.973850i | \(0.427045\pi\) | |||||||
\(38\) | 0.618034 | 0.100258 | ||||||||
\(39\) | −6.47214 | −1.03637 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | −0.780869 | −0.390434 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390434 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(42\) | −1.38197 | −0.213242 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 6.47214 | 0.975711 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 0.472136 | 0.0688681 | 0.0344341 | − | 0.999407i | \(-0.489037\pi\) | ||||
0.0344341 | + | 0.999407i | \(0.489037\pi\) | |||||||
\(48\) | −1.85410 | −0.267617 | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23607 | −0.173084 | ||||||||
\(52\) | −10.4721 | −1.45222 | ||||||||
\(53\) | −5.00000 | −0.686803 | −0.343401 | − | 0.939189i | \(-0.611579\pi\) | ||||
−0.343401 | + | 0.939189i | \(0.611579\pi\) | |||||||
\(54\) | 0.618034 | 0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.00000 | −0.668153 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −4.61803 | −0.606378 | ||||||||
\(59\) | −14.7082 | −1.91485 | −0.957423 | − | 0.288690i | \(-0.906780\pi\) | ||||
−0.957423 | + | 0.288690i | \(0.906780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.94427 | 1.01716 | 0.508580 | − | 0.861015i | \(-0.330171\pi\) | ||||
0.508580 | + | 0.861015i | \(0.330171\pi\) | |||||||
\(62\) | 6.47214 | 0.821962 | ||||||||
\(63\) | −2.23607 | −0.281718 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.47214 | −0.304299 | ||||||||
\(67\) | −10.9443 | −1.33706 | −0.668528 | − | 0.743687i | \(-0.733075\pi\) | ||||
−0.668528 | + | 0.743687i | \(0.733075\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | −3.23607 | −0.389577 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.18034 | 1.08951 | 0.544753 | − | 0.838597i | \(-0.316623\pi\) | ||||
0.544753 | + | 0.838597i | \(0.316623\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 3.47214 | 0.406383 | 0.203191 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203191 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(74\) | −1.70820 | −0.198575 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.61803 | 0.185601 | ||||||||
\(77\) | 8.94427 | 1.01929 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | −2.29180 | −0.257847 | −0.128924 | − | 0.991655i | \(-0.541152\pi\) | ||||
−0.128924 | + | 0.991655i | \(0.541152\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.09017 | 0.341252 | ||||||||
\(83\) | −6.94427 | −0.762233 | −0.381116 | − | 0.924527i | \(-0.624460\pi\) | ||||
−0.381116 | + | 0.924527i | \(0.624460\pi\) | |||||||
\(84\) | −3.61803 | −0.394760 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.47214 | −0.266577 | ||||||||
\(87\) | −7.47214 | −0.801097 | ||||||||
\(88\) | −8.94427 | −0.953463 | ||||||||
\(89\) | −9.94427 | −1.05409 | −0.527045 | − | 0.849837i | \(-0.676700\pi\) | ||||
−0.527045 | + | 0.849837i | \(0.676700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.4721 | −1.51709 | ||||||||
\(92\) | −5.23607 | −0.545898 | ||||||||
\(93\) | 10.4721 | 1.08591 | ||||||||
\(94\) | −0.291796 | −0.0300965 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.61803 | 0.573388 | ||||||||
\(97\) | −1.70820 | −0.173442 | −0.0867209 | − | 0.996233i | \(-0.527639\pi\) | ||||
−0.0867209 | + | 0.996233i | \(0.527639\pi\) | |||||||
\(98\) | 1.23607 | 0.124862 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.1803 | −1.41100 | −0.705498 | − | 0.708712i | \(-0.749277\pi\) | ||||
−0.705498 | + | 0.708712i | \(0.749277\pi\) | |||||||
\(102\) | 0.763932 | 0.0756405 | ||||||||
\(103\) | 16.9443 | 1.66957 | 0.834784 | − | 0.550577i | \(-0.185592\pi\) | ||||
0.834784 | + | 0.550577i | \(0.185592\pi\) | |||||||
\(104\) | 14.4721 | 1.41911 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.09017 | 0.300144 | ||||||||
\(107\) | −16.2361 | −1.56960 | −0.784800 | − | 0.619749i | \(-0.787234\pi\) | ||||
−0.784800 | + | 0.619749i | \(0.787234\pi\) | |||||||
\(108\) | 1.61803 | 0.155695 | ||||||||
\(109\) | −7.70820 | −0.738312 | −0.369156 | − | 0.929367i | \(-0.620353\pi\) | ||||
−0.369156 | + | 0.929367i | \(0.620353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.76393 | −0.262341 | ||||||||
\(112\) | −4.14590 | −0.391751 | ||||||||
\(113\) | −12.4721 | −1.17328 | −0.586640 | − | 0.809848i | \(-0.699550\pi\) | ||||
−0.586640 | + | 0.809848i | \(0.699550\pi\) | |||||||
\(114\) | −0.618034 | −0.0578842 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.0902 | −1.12254 | ||||||||
\(117\) | 6.47214 | 0.598349 | ||||||||
\(118\) | 9.09017 | 0.836818 | ||||||||
\(119\) | −2.76393 | −0.253369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | −4.90983 | −0.444515 | ||||||||
\(123\) | 5.00000 | 0.450835 | ||||||||
\(124\) | 16.9443 | 1.52164 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.38197 | 0.123115 | ||||||||
\(127\) | 10.7639 | 0.955145 | 0.477572 | − | 0.878592i | \(-0.341517\pi\) | ||||
0.477572 | + | 0.878592i | \(0.341517\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.94427 | −0.606724 | −0.303362 | − | 0.952875i | \(-0.598109\pi\) | ||||
−0.303362 | + | 0.952875i | \(0.598109\pi\) | |||||||
\(132\) | −6.47214 | −0.563327 | ||||||||
\(133\) | 2.23607 | 0.193892 | ||||||||
\(134\) | 6.76393 | 0.584315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.76393 | 0.237005 | ||||||||
\(137\) | 4.29180 | 0.366673 | 0.183336 | − | 0.983050i | \(-0.441310\pi\) | ||||
0.183336 | + | 0.983050i | \(0.441310\pi\) | |||||||
\(138\) | 2.00000 | 0.170251 | ||||||||
\(139\) | −15.7639 | −1.33708 | −0.668540 | − | 0.743677i | \(-0.733080\pi\) | ||||
−0.668540 | + | 0.743677i | \(0.733080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.472136 | −0.0397610 | ||||||||
\(142\) | −5.67376 | −0.476132 | ||||||||
\(143\) | −25.8885 | −2.16491 | ||||||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.14590 | −0.177596 | ||||||||
\(147\) | 2.00000 | 0.164957 | ||||||||
\(148\) | −4.47214 | −0.367607 | ||||||||
\(149\) | −19.4164 | −1.59065 | −0.795327 | − | 0.606181i | \(-0.792701\pi\) | ||||
−0.795327 | + | 0.606181i | \(0.792701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7082 | 0.952800 | 0.476400 | − | 0.879229i | \(-0.341941\pi\) | ||||
0.476400 | + | 0.879229i | \(0.341941\pi\) | |||||||
\(152\) | −2.23607 | −0.181369 | ||||||||
\(153\) | 1.23607 | 0.0999302 | ||||||||
\(154\) | −5.52786 | −0.445448 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.4721 | 0.838442 | ||||||||
\(157\) | 7.00000 | 0.558661 | 0.279330 | − | 0.960195i | \(-0.409888\pi\) | ||||
0.279330 | + | 0.960195i | \(0.409888\pi\) | |||||||
\(158\) | 1.41641 | 0.112683 | ||||||||
\(159\) | 5.00000 | 0.396526 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.23607 | −0.570282 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | −11.1803 | −0.875712 | −0.437856 | − | 0.899045i | \(-0.644262\pi\) | ||||
−0.437856 | + | 0.899045i | \(0.644262\pi\) | |||||||
\(164\) | 8.09017 | 0.631736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.29180 | 0.333108 | ||||||||
\(167\) | −24.5967 | −1.90335 | −0.951677 | − | 0.307102i | \(-0.900641\pi\) | ||||
−0.951677 | + | 0.307102i | \(0.900641\pi\) | |||||||
\(168\) | 5.00000 | 0.385758 | ||||||||
\(169\) | 28.8885 | 2.22220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −6.47214 | −0.493496 | ||||||||
\(173\) | −13.4721 | −1.02427 | −0.512134 | − | 0.858906i | \(-0.671145\pi\) | ||||
−0.512134 | + | 0.858906i | \(0.671145\pi\) | |||||||
\(174\) | 4.61803 | 0.350092 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.41641 | −0.559033 | ||||||||
\(177\) | 14.7082 | 1.10554 | ||||||||
\(178\) | 6.14590 | 0.460655 | ||||||||
\(179\) | 22.1246 | 1.65367 | 0.826836 | − | 0.562444i | \(-0.190139\pi\) | ||||
0.826836 | + | 0.562444i | \(0.190139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4721 | 0.778388 | 0.389194 | − | 0.921156i | \(-0.372754\pi\) | ||||
0.389194 | + | 0.921156i | \(0.372754\pi\) | |||||||
\(182\) | 8.94427 | 0.662994 | ||||||||
\(183\) | −7.94427 | −0.587257 | ||||||||
\(184\) | 7.23607 | 0.533450 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.47214 | −0.474560 | ||||||||
\(187\) | −4.94427 | −0.361561 | ||||||||
\(188\) | −0.763932 | −0.0557155 | ||||||||
\(189\) | 2.23607 | 0.162650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.41641 | 0.536632 | 0.268316 | − | 0.963331i | \(-0.413533\pi\) | ||||
0.268316 | + | 0.963331i | \(0.413533\pi\) | |||||||
\(192\) | 0.236068 | 0.0170367 | ||||||||
\(193\) | −3.23607 | −0.232937 | −0.116469 | − | 0.993194i | \(-0.537157\pi\) | ||||
−0.116469 | + | 0.993194i | \(0.537157\pi\) | |||||||
\(194\) | 1.05573 | 0.0757969 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.23607 | 0.231148 | ||||||||
\(197\) | −22.6525 | −1.61392 | −0.806961 | − | 0.590605i | \(-0.798889\pi\) | ||||
−0.806961 | + | 0.590605i | \(0.798889\pi\) | |||||||
\(198\) | 2.47214 | 0.175687 | ||||||||
\(199\) | 1.76393 | 0.125042 | 0.0625209 | − | 0.998044i | \(-0.480086\pi\) | ||||
0.0625209 | + | 0.998044i | \(0.480086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.9443 | 0.771949 | ||||||||
\(202\) | 8.76393 | 0.616628 | ||||||||
\(203\) | −16.7082 | −1.17269 | ||||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.4721 | −0.729628 | ||||||||
\(207\) | 3.23607 | 0.224922 | ||||||||
\(208\) | 12.0000 | 0.832050 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.81966 | 0.400642 | 0.200321 | − | 0.979730i | \(-0.435802\pi\) | ||||
0.200321 | + | 0.979730i | \(0.435802\pi\) | |||||||
\(212\) | 8.09017 | 0.555635 | ||||||||
\(213\) | −9.18034 | −0.629027 | ||||||||
\(214\) | 10.0344 | 0.685940 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 23.4164 | 1.58961 | ||||||||
\(218\) | 4.76393 | 0.322654 | ||||||||
\(219\) | −3.47214 | −0.234625 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | 1.70820 | 0.114647 | ||||||||
\(223\) | 9.23607 | 0.618493 | 0.309246 | − | 0.950982i | \(-0.399923\pi\) | ||||
0.309246 | + | 0.950982i | \(0.399923\pi\) | |||||||
\(224\) | 12.5623 | 0.839354 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.70820 | 0.512742 | ||||||||
\(227\) | 28.1246 | 1.86670 | 0.933348 | − | 0.358973i | \(-0.116873\pi\) | ||||
0.933348 | + | 0.358973i | \(0.116873\pi\) | |||||||
\(228\) | −1.61803 | −0.107157 | ||||||||
\(229\) | −4.47214 | −0.295527 | −0.147764 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.94427 | −0.588490 | ||||||||
\(232\) | 16.7082 | 1.09695 | ||||||||
\(233\) | 2.94427 | 0.192886 | 0.0964428 | − | 0.995339i | \(-0.469254\pi\) | ||||
0.0964428 | + | 0.995339i | \(0.469254\pi\) | |||||||
\(234\) | −4.00000 | −0.261488 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 23.7984 | 1.54914 | ||||||||
\(237\) | 2.29180 | 0.148868 | ||||||||
\(238\) | 1.70820 | 0.110726 | ||||||||
\(239\) | 0.291796 | 0.0188747 | 0.00943736 | − | 0.999955i | \(-0.496996\pi\) | ||||
0.00943736 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1803 | −1.04227 | −0.521134 | − | 0.853475i | \(-0.674491\pi\) | ||||
−0.521134 | + | 0.853475i | \(0.674491\pi\) | |||||||
\(242\) | −3.09017 | −0.198644 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.8541 | −0.822900 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.09017 | −0.197022 | ||||||||
\(247\) | −6.47214 | −0.411812 | ||||||||
\(248\) | −23.4164 | −1.48694 | ||||||||
\(249\) | 6.94427 | 0.440075 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.70820 | 0.234060 | 0.117030 | − | 0.993128i | \(-0.462663\pi\) | ||||
0.117030 | + | 0.993128i | \(0.462663\pi\) | |||||||
\(252\) | 3.61803 | 0.227915 | ||||||||
\(253\) | −12.9443 | −0.813799 | ||||||||
\(254\) | −6.65248 | −0.417413 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −13.0000 | −0.810918 | −0.405459 | − | 0.914113i | \(-0.632888\pi\) | ||||
−0.405459 | + | 0.914113i | \(0.632888\pi\) | |||||||
\(258\) | 2.47214 | 0.153908 | ||||||||
\(259\) | −6.18034 | −0.384028 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.47214 | 0.462514 | ||||||||
\(262\) | 4.29180 | 0.265148 | ||||||||
\(263\) | −10.2918 | −0.634619 | −0.317310 | − | 0.948322i | \(-0.602779\pi\) | ||||
−0.317310 | + | 0.948322i | \(0.602779\pi\) | |||||||
\(264\) | 8.94427 | 0.550482 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.38197 | −0.0847338 | ||||||||
\(267\) | 9.94427 | 0.608580 | ||||||||
\(268\) | 17.7082 | 1.08170 | ||||||||
\(269\) | 20.4721 | 1.24821 | 0.624104 | − | 0.781341i | \(-0.285464\pi\) | ||||
0.624104 | + | 0.781341i | \(0.285464\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.18034 | 0.193192 | 0.0965959 | − | 0.995324i | \(-0.469205\pi\) | ||||
0.0965959 | + | 0.995324i | \(0.469205\pi\) | |||||||
\(272\) | 2.29180 | 0.138961 | ||||||||
\(273\) | 14.4721 | 0.875894 | ||||||||
\(274\) | −2.65248 | −0.160242 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.23607 | 0.315174 | ||||||||
\(277\) | 5.58359 | 0.335486 | 0.167743 | − | 0.985831i | \(-0.446352\pi\) | ||||
0.167743 | + | 0.985831i | \(0.446352\pi\) | |||||||
\(278\) | 9.74265 | 0.584325 | ||||||||
\(279\) | −10.4721 | −0.626950 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.88854 | 0.470591 | 0.235296 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235296 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(282\) | 0.291796 | 0.0173762 | ||||||||
\(283\) | 9.88854 | 0.587813 | 0.293906 | − | 0.955834i | \(-0.405045\pi\) | ||||
0.293906 | + | 0.955834i | \(0.405045\pi\) | |||||||
\(284\) | −14.8541 | −0.881429 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.0000 | 0.946100 | ||||||||
\(287\) | 11.1803 | 0.659955 | ||||||||
\(288\) | −5.61803 | −0.331046 | ||||||||
\(289\) | −15.4721 | −0.910126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.70820 | 0.100137 | ||||||||
\(292\) | −5.61803 | −0.328771 | ||||||||
\(293\) | 2.00000 | 0.116841 | 0.0584206 | − | 0.998292i | \(-0.481394\pi\) | ||||
0.0584206 | + | 0.998292i | \(0.481394\pi\) | |||||||
\(294\) | −1.23607 | −0.0720889 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.18034 | 0.359225 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 12.0000 | 0.695141 | ||||||||
\(299\) | 20.9443 | 1.21124 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.94427 | −0.515539 | ||||||||
\(302\) | −7.23607 | −0.416389 | ||||||||
\(303\) | 14.1803 | 0.814639 | ||||||||
\(304\) | −1.85410 | −0.106340 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.763932 | −0.0436711 | ||||||||
\(307\) | −3.05573 | −0.174400 | −0.0871998 | − | 0.996191i | \(-0.527792\pi\) | ||||
−0.0871998 | + | 0.996191i | \(0.527792\pi\) | |||||||
\(308\) | −14.4721 | −0.824626 | ||||||||
\(309\) | −16.9443 | −0.963926 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | −14.4721 | −0.819323 | ||||||||
\(313\) | −30.9443 | −1.74907 | −0.874537 | − | 0.484959i | \(-0.838834\pi\) | ||||
−0.874537 | + | 0.484959i | \(0.838834\pi\) | |||||||
\(314\) | −4.32624 | −0.244144 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.70820 | 0.208603 | ||||||||
\(317\) | −7.94427 | −0.446195 | −0.223097 | − | 0.974796i | \(-0.571617\pi\) | ||||
−0.223097 | + | 0.974796i | \(0.571617\pi\) | |||||||
\(318\) | −3.09017 | −0.173288 | ||||||||
\(319\) | −29.8885 | −1.67344 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.2361 | 0.906209 | ||||||||
\(322\) | 4.47214 | 0.249222 | ||||||||
\(323\) | −1.23607 | −0.0687767 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.90983 | 0.382700 | ||||||||
\(327\) | 7.70820 | 0.426265 | ||||||||
\(328\) | −11.1803 | −0.617331 | ||||||||
\(329\) | −1.05573 | −0.0582042 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.3607 | −1.44891 | −0.724457 | − | 0.689320i | \(-0.757909\pi\) | ||||
−0.724457 | + | 0.689320i | \(0.757909\pi\) | |||||||
\(332\) | 11.2361 | 0.616659 | ||||||||
\(333\) | 2.76393 | 0.151463 | ||||||||
\(334\) | 15.2016 | 0.831796 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.14590 | 0.226177 | ||||||||
\(337\) | −8.47214 | −0.461507 | −0.230753 | − | 0.973012i | \(-0.574119\pi\) | ||||
−0.230753 | + | 0.973012i | \(0.574119\pi\) | |||||||
\(338\) | −17.8541 | −0.971135 | ||||||||
\(339\) | 12.4721 | 0.677393 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.8885 | 2.26839 | ||||||||
\(342\) | 0.618034 | 0.0334195 | ||||||||
\(343\) | 20.1246 | 1.08663 | ||||||||
\(344\) | 8.94427 | 0.482243 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.32624 | 0.447621 | ||||||||
\(347\) | −1.70820 | −0.0917012 | −0.0458506 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458506 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(348\) | 12.0902 | 0.648101 | ||||||||
\(349\) | −17.8328 | −0.954569 | −0.477284 | − | 0.878749i | \(-0.658379\pi\) | ||||
−0.477284 | + | 0.878749i | \(0.658379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.47214 | −0.345457 | ||||||||
\(352\) | 22.4721 | 1.19777 | ||||||||
\(353\) | −26.4721 | −1.40897 | −0.704485 | − | 0.709719i | \(-0.748822\pi\) | ||||
−0.704485 | + | 0.709719i | \(0.748822\pi\) | |||||||
\(354\) | −9.09017 | −0.483137 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.0902 | 0.852777 | ||||||||
\(357\) | 2.76393 | 0.146283 | ||||||||
\(358\) | −13.6738 | −0.722681 | ||||||||
\(359\) | −25.2361 | −1.33191 | −0.665954 | − | 0.745992i | \(-0.731975\pi\) | ||||
−0.665954 | + | 0.745992i | \(0.731975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −6.47214 | −0.340168 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 23.4164 | 1.22735 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.90983 | 0.256641 | ||||||||
\(367\) | 33.3050 | 1.73850 | 0.869252 | − | 0.494369i | \(-0.164601\pi\) | ||||
0.869252 | + | 0.494369i | \(0.164601\pi\) | |||||||
\(368\) | 6.00000 | 0.312772 | ||||||||
\(369\) | −5.00000 | −0.260290 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.1803 | 0.580454 | ||||||||
\(372\) | −16.9443 | −0.878520 | ||||||||
\(373\) | 12.1803 | 0.630674 | 0.315337 | − | 0.948980i | \(-0.397882\pi\) | ||||
0.315337 | + | 0.948980i | \(0.397882\pi\) | |||||||
\(374\) | 3.05573 | 0.158008 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.05573 | 0.0544450 | ||||||||
\(377\) | 48.3607 | 2.49070 | ||||||||
\(378\) | −1.38197 | −0.0710807 | ||||||||
\(379\) | 6.76393 | 0.347440 | 0.173720 | − | 0.984795i | \(-0.444421\pi\) | ||||
0.173720 | + | 0.984795i | \(0.444421\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.7639 | −0.551453 | ||||||||
\(382\) | −4.58359 | −0.234517 | ||||||||
\(383\) | 16.1246 | 0.823929 | 0.411965 | − | 0.911200i | \(-0.364843\pi\) | ||||
0.411965 | + | 0.911200i | \(0.364843\pi\) | |||||||
\(384\) | −11.3820 | −0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 4.00000 | 0.203331 | ||||||||
\(388\) | 2.76393 | 0.140317 | ||||||||
\(389\) | 8.00000 | 0.405616 | 0.202808 | − | 0.979219i | \(-0.434993\pi\) | ||||
0.202808 | + | 0.979219i | \(0.434993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | −4.47214 | −0.225877 | ||||||||
\(393\) | 6.94427 | 0.350292 | ||||||||
\(394\) | 14.0000 | 0.705310 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.47214 | 0.325237 | ||||||||
\(397\) | 22.3607 | 1.12225 | 0.561125 | − | 0.827731i | \(-0.310369\pi\) | ||||
0.561125 | + | 0.827731i | \(0.310369\pi\) | |||||||
\(398\) | −1.09017 | −0.0546453 | ||||||||
\(399\) | −2.23607 | −0.111943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.8328 | −1.04034 | −0.520171 | − | 0.854062i | \(-0.674132\pi\) | ||||
−0.520171 | + | 0.854062i | \(0.674132\pi\) | |||||||
\(402\) | −6.76393 | −0.337354 | ||||||||
\(403\) | −67.7771 | −3.37622 | ||||||||
\(404\) | 22.9443 | 1.14152 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.3262 | 0.512483 | ||||||||
\(407\) | −11.0557 | −0.548012 | ||||||||
\(408\) | −2.76393 | −0.136835 | ||||||||
\(409\) | 8.76393 | 0.433349 | 0.216674 | − | 0.976244i | \(-0.430479\pi\) | ||||
0.216674 | + | 0.976244i | \(0.430479\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.29180 | −0.211699 | ||||||||
\(412\) | −27.4164 | −1.35071 | ||||||||
\(413\) | 32.8885 | 1.61834 | ||||||||
\(414\) | −2.00000 | −0.0982946 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −36.3607 | −1.78273 | ||||||||
\(417\) | 15.7639 | 0.771963 | ||||||||
\(418\) | −2.47214 | −0.120916 | ||||||||
\(419\) | 39.3050 | 1.92017 | 0.960086 | − | 0.279704i | \(-0.0902363\pi\) | ||||
0.960086 | + | 0.279704i | \(0.0902363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5279 | 0.561834 | 0.280917 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280917 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(422\) | −3.59675 | −0.175087 | ||||||||
\(423\) | 0.472136 | 0.0229560 | ||||||||
\(424\) | −11.1803 | −0.542965 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.67376 | 0.274895 | ||||||||
\(427\) | −17.7639 | −0.859657 | ||||||||
\(428\) | 26.2705 | 1.26983 | ||||||||
\(429\) | 25.8885 | 1.24991 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.18034 | −0.249528 | −0.124764 | − | 0.992186i | \(-0.539817\pi\) | ||||
−0.124764 | + | 0.992186i | \(0.539817\pi\) | |||||||
\(432\) | −1.85410 | −0.0892055 | ||||||||
\(433\) | −19.5279 | −0.938449 | −0.469225 | − | 0.883079i | \(-0.655467\pi\) | ||||
−0.469225 | + | 0.883079i | \(0.655467\pi\) | |||||||
\(434\) | −14.4721 | −0.694685 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.4721 | 0.597307 | ||||||||
\(437\) | −3.23607 | −0.154802 | ||||||||
\(438\) | 2.14590 | 0.102535 | ||||||||
\(439\) | −16.7639 | −0.800099 | −0.400049 | − | 0.916494i | \(-0.631007\pi\) | ||||
−0.400049 | + | 0.916494i | \(0.631007\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | −4.94427 | −0.235175 | ||||||||
\(443\) | 13.4164 | 0.637433 | 0.318716 | − | 0.947850i | \(-0.396748\pi\) | ||||
0.318716 | + | 0.947850i | \(0.396748\pi\) | |||||||
\(444\) | 4.47214 | 0.212238 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.70820 | −0.270291 | ||||||||
\(447\) | 19.4164 | 0.918365 | ||||||||
\(448\) | 0.527864 | 0.0249392 | ||||||||
\(449\) | −25.4721 | −1.20210 | −0.601052 | − | 0.799210i | \(-0.705252\pi\) | ||||
−0.601052 | + | 0.799210i | \(0.705252\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0000 | 0.941763 | ||||||||
\(452\) | 20.1803 | 0.949203 | ||||||||
\(453\) | −11.7082 | −0.550099 | ||||||||
\(454\) | −17.3820 | −0.815776 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23607 | 0.104713 | ||||||||
\(457\) | 8.88854 | 0.415789 | 0.207894 | − | 0.978151i | \(-0.433339\pi\) | ||||
0.207894 | + | 0.978151i | \(0.433339\pi\) | |||||||
\(458\) | 2.76393 | 0.129150 | ||||||||
\(459\) | −1.23607 | −0.0576947 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.81966 | −0.0847500 | −0.0423750 | − | 0.999102i | \(-0.513492\pi\) | ||||
−0.0423750 | + | 0.999102i | \(0.513492\pi\) | |||||||
\(462\) | 5.52786 | 0.257180 | ||||||||
\(463\) | 8.58359 | 0.398913 | 0.199457 | − | 0.979907i | \(-0.436082\pi\) | ||||
0.199457 | + | 0.979907i | \(0.436082\pi\) | |||||||
\(464\) | 13.8541 | 0.643161 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.81966 | −0.0842941 | ||||||||
\(467\) | −26.1803 | −1.21148 | −0.605741 | − | 0.795662i | \(-0.707123\pi\) | ||||
−0.605741 | + | 0.795662i | \(0.707123\pi\) | |||||||
\(468\) | −10.4721 | −0.484075 | ||||||||
\(469\) | 24.4721 | 1.13002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | −0.322543 | ||||||||
\(472\) | −32.8885 | −1.51382 | ||||||||
\(473\) | −16.0000 | −0.735681 | ||||||||
\(474\) | −1.41641 | −0.0650578 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.47214 | 0.204980 | ||||||||
\(477\) | −5.00000 | −0.228934 | ||||||||
\(478\) | −0.180340 | −0.00824855 | ||||||||
\(479\) | −38.7639 | −1.77117 | −0.885585 | − | 0.464478i | \(-0.846242\pi\) | ||||
−0.885585 | + | 0.464478i | \(0.846242\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.8885 | 0.815647 | ||||||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 7.23607 | 0.329252 | ||||||||
\(484\) | −8.09017 | −0.367735 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.618034 | 0.0280346 | ||||||||
\(487\) | 24.0000 | 1.08754 | 0.543772 | − | 0.839233i | \(-0.316996\pi\) | ||||
0.543772 | + | 0.839233i | \(0.316996\pi\) | |||||||
\(488\) | 17.7639 | 0.804135 | ||||||||
\(489\) | 11.1803 | 0.505592 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.29180 | −0.374204 | −0.187102 | − | 0.982341i | \(-0.559909\pi\) | ||||
−0.187102 | + | 0.982341i | \(0.559909\pi\) | |||||||
\(492\) | −8.09017 | −0.364733 | ||||||||
\(493\) | 9.23607 | 0.415972 | ||||||||
\(494\) | 4.00000 | 0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.4164 | −0.871822 | ||||||||
\(497\) | −20.5279 | −0.920801 | ||||||||
\(498\) | −4.29180 | −0.192320 | ||||||||
\(499\) | −31.1803 | −1.39582 | −0.697912 | − | 0.716184i | \(-0.745887\pi\) | ||||
−0.697912 | + | 0.716184i | \(0.745887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5967 | 1.09890 | ||||||||
\(502\) | −2.29180 | −0.102288 | ||||||||
\(503\) | −9.52786 | −0.424826 | −0.212413 | − | 0.977180i | \(-0.568132\pi\) | ||||
−0.212413 | + | 0.977180i | \(0.568132\pi\) | |||||||
\(504\) | −5.00000 | −0.222718 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.00000 | 0.355643 | ||||||||
\(507\) | −28.8885 | −1.28299 | ||||||||
\(508\) | −17.4164 | −0.772728 | ||||||||
\(509\) | −9.00000 | −0.398918 | −0.199459 | − | 0.979906i | \(-0.563918\pi\) | ||||
−0.199459 | + | 0.979906i | \(0.563918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.76393 | −0.343456 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 8.03444 | 0.354384 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.47214 | 0.284920 | ||||||||
\(517\) | −1.88854 | −0.0830581 | ||||||||
\(518\) | 3.81966 | 0.167826 | ||||||||
\(519\) | 13.4721 | 0.591361 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.8328 | −1.56986 | −0.784932 | − | 0.619582i | \(-0.787302\pi\) | ||||
−0.784932 | + | 0.619582i | \(0.787302\pi\) | |||||||
\(522\) | −4.61803 | −0.202126 | ||||||||
\(523\) | 41.1246 | 1.79825 | 0.899127 | − | 0.437688i | \(-0.144203\pi\) | ||||
0.899127 | + | 0.437688i | \(0.144203\pi\) | |||||||
\(524\) | 11.2361 | 0.490850 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.36068 | 0.277339 | ||||||||
\(527\) | −12.9443 | −0.563861 | ||||||||
\(528\) | 7.41641 | 0.322758 | ||||||||
\(529\) | −12.5279 | −0.544690 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.7082 | −0.638282 | ||||||||
\(532\) | −3.61803 | −0.156862 | ||||||||
\(533\) | −32.3607 | −1.40170 | ||||||||
\(534\) | −6.14590 | −0.265959 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.4721 | −1.05704 | ||||||||
\(537\) | −22.1246 | −0.954747 | ||||||||
\(538\) | −12.6525 | −0.545487 | ||||||||
\(539\) | 8.00000 | 0.344584 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.8328 | 1.06765 | 0.533823 | − | 0.845596i | \(-0.320755\pi\) | ||||
0.533823 | + | 0.845596i | \(0.320755\pi\) | |||||||
\(542\) | −1.96556 | −0.0844280 | ||||||||
\(543\) | −10.4721 | −0.449402 | ||||||||
\(544\) | −6.94427 | −0.297733 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.94427 | −0.382780 | ||||||||
\(547\) | −7.70820 | −0.329579 | −0.164790 | − | 0.986329i | \(-0.552694\pi\) | ||||
−0.164790 | + | 0.986329i | \(0.552694\pi\) | |||||||
\(548\) | −6.94427 | −0.296645 | ||||||||
\(549\) | 7.94427 | 0.339053 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.47214 | −0.318324 | ||||||||
\(552\) | −7.23607 | −0.307988 | ||||||||
\(553\) | 5.12461 | 0.217921 | ||||||||
\(554\) | −3.45085 | −0.146613 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.5066 | 1.08172 | ||||||||
\(557\) | −33.8885 | −1.43590 | −0.717952 | − | 0.696093i | \(-0.754920\pi\) | ||||
−0.717952 | + | 0.696093i | \(0.754920\pi\) | |||||||
\(558\) | 6.47214 | 0.273987 | ||||||||
\(559\) | 25.8885 | 1.09497 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.94427 | 0.208747 | ||||||||
\(562\) | −4.87539 | −0.205656 | ||||||||
\(563\) | 23.6525 | 0.996833 | 0.498417 | − | 0.866938i | \(-0.333915\pi\) | ||||
0.498417 | + | 0.866938i | \(0.333915\pi\) | |||||||
\(564\) | 0.763932 | 0.0321673 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.11146 | −0.256884 | ||||||||
\(567\) | −2.23607 | −0.0939060 | ||||||||
\(568\) | 20.5279 | 0.861330 | ||||||||
\(569\) | −20.8885 | −0.875693 | −0.437847 | − | 0.899050i | \(-0.644259\pi\) | ||||
−0.437847 | + | 0.899050i | \(0.644259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.6525 | −0.655036 | −0.327518 | − | 0.944845i | \(-0.606212\pi\) | ||||
−0.327518 | + | 0.944845i | \(0.606212\pi\) | |||||||
\(572\) | 41.8885 | 1.75145 | ||||||||
\(573\) | −7.41641 | −0.309825 | ||||||||
\(574\) | −6.90983 | −0.288411 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.236068 | −0.00983617 | ||||||||
\(577\) | −1.41641 | −0.0589658 | −0.0294829 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294829 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(578\) | 9.56231 | 0.397739 | ||||||||
\(579\) | 3.23607 | 0.134486 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.5279 | 0.644204 | ||||||||
\(582\) | −1.05573 | −0.0437613 | ||||||||
\(583\) | 20.0000 | 0.828315 | ||||||||
\(584\) | 7.76393 | 0.321274 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.23607 | −0.0510615 | ||||||||
\(587\) | 12.6525 | 0.522224 | 0.261112 | − | 0.965309i | \(-0.415911\pi\) | ||||
0.261112 | + | 0.965309i | \(0.415911\pi\) | |||||||
\(588\) | −3.23607 | −0.133453 | ||||||||
\(589\) | 10.4721 | 0.431497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.6525 | 0.931798 | ||||||||
\(592\) | 5.12461 | 0.210620 | ||||||||
\(593\) | −13.8885 | −0.570334 | −0.285167 | − | 0.958478i | \(-0.592049\pi\) | ||||
−0.285167 | + | 0.958478i | \(0.592049\pi\) | |||||||
\(594\) | −2.47214 | −0.101433 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 31.4164 | 1.28687 | ||||||||
\(597\) | −1.76393 | −0.0721929 | ||||||||
\(598\) | −12.9443 | −0.529331 | ||||||||
\(599\) | −20.0000 | −0.817178 | −0.408589 | − | 0.912719i | \(-0.633979\pi\) | ||||
−0.408589 | + | 0.912719i | \(0.633979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.7771 | −1.45938 | −0.729689 | − | 0.683779i | \(-0.760335\pi\) | ||||
−0.729689 | + | 0.683779i | \(0.760335\pi\) | |||||||
\(602\) | 5.52786 | 0.225299 | ||||||||
\(603\) | −10.9443 | −0.445685 | ||||||||
\(604\) | −18.9443 | −0.770831 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.76393 | −0.356010 | ||||||||
\(607\) | −19.1246 | −0.776244 | −0.388122 | − | 0.921608i | \(-0.626876\pi\) | ||||
−0.388122 | + | 0.921608i | \(0.626876\pi\) | |||||||
\(608\) | 5.61803 | 0.227841 | ||||||||
\(609\) | 16.7082 | 0.677051 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.05573 | 0.123622 | ||||||||
\(612\) | −2.00000 | −0.0808452 | ||||||||
\(613\) | 23.0000 | 0.928961 | 0.464481 | − | 0.885583i | \(-0.346241\pi\) | ||||
0.464481 | + | 0.885583i | \(0.346241\pi\) | |||||||
\(614\) | 1.88854 | 0.0762154 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.0000 | 0.805823 | ||||||||
\(617\) | 22.0000 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(618\) | 10.4721 | 0.421251 | ||||||||
\(619\) | 30.7082 | 1.23427 | 0.617133 | − | 0.786858i | \(-0.288294\pi\) | ||||
0.617133 | + | 0.786858i | \(0.288294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.23607 | −0.129859 | ||||||||
\(622\) | −2.47214 | −0.0991236 | ||||||||
\(623\) | 22.2361 | 0.890869 | ||||||||
\(624\) | −12.0000 | −0.480384 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.1246 | 0.764373 | ||||||||
\(627\) | −4.00000 | −0.159745 | ||||||||
\(628\) | −11.3262 | −0.451966 | ||||||||
\(629\) | 3.41641 | 0.136221 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.4164 | −1.72838 | −0.864190 | − | 0.503166i | \(-0.832169\pi\) | ||||
−0.864190 | + | 0.503166i | \(0.832169\pi\) | |||||||
\(632\) | −5.12461 | −0.203846 | ||||||||
\(633\) | −5.81966 | −0.231311 | ||||||||
\(634\) | 4.90983 | 0.194994 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.09017 | −0.320796 | ||||||||
\(637\) | −12.9443 | −0.512871 | ||||||||
\(638\) | 18.4721 | 0.731319 | ||||||||
\(639\) | 9.18034 | 0.363169 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.94427 | 0.274282 | 0.137141 | − | 0.990552i | \(-0.456209\pi\) | ||||
0.137141 | + | 0.990552i | \(0.456209\pi\) | |||||||
\(642\) | −10.0344 | −0.396028 | ||||||||
\(643\) | −17.1803 | −0.677526 | −0.338763 | − | 0.940872i | \(-0.610009\pi\) | ||||
−0.338763 | + | 0.940872i | \(0.610009\pi\) | |||||||
\(644\) | 11.7082 | 0.461368 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.763932 | 0.0300565 | ||||||||
\(647\) | 17.3050 | 0.680328 | 0.340164 | − | 0.940366i | \(-0.389517\pi\) | ||||
0.340164 | + | 0.940366i | \(0.389517\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 58.8328 | 2.30939 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.4164 | −0.917761 | ||||||||
\(652\) | 18.0902 | 0.708466 | ||||||||
\(653\) | 25.8885 | 1.01310 | 0.506549 | − | 0.862211i | \(-0.330921\pi\) | ||||
0.506549 | + | 0.862211i | \(0.330921\pi\) | |||||||
\(654\) | −4.76393 | −0.186284 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.27051 | −0.361953 | ||||||||
\(657\) | 3.47214 | 0.135461 | ||||||||
\(658\) | 0.652476 | 0.0254362 | ||||||||
\(659\) | 24.9443 | 0.971691 | 0.485845 | − | 0.874045i | \(-0.338512\pi\) | ||||
0.485845 | + | 0.874045i | \(0.338512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.1246 | −0.899443 | −0.449722 | − | 0.893169i | \(-0.648477\pi\) | ||||
−0.449722 | + | 0.893169i | \(0.648477\pi\) | |||||||
\(662\) | 16.2918 | 0.633199 | ||||||||
\(663\) | −8.00000 | −0.310694 | ||||||||
\(664\) | −15.5279 | −0.602598 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.70820 | −0.0661916 | ||||||||
\(667\) | 24.1803 | 0.936266 | ||||||||
\(668\) | 39.7984 | 1.53985 | ||||||||
\(669\) | −9.23607 | −0.357087 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.7771 | −1.22674 | ||||||||
\(672\) | −12.5623 | −0.484601 | ||||||||
\(673\) | −34.2492 | −1.32021 | −0.660105 | − | 0.751173i | \(-0.729488\pi\) | ||||
−0.660105 | + | 0.751173i | \(0.729488\pi\) | |||||||
\(674\) | 5.23607 | 0.201686 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.7426 | −1.79779 | ||||||||
\(677\) | 5.83282 | 0.224173 | 0.112087 | − | 0.993698i | \(-0.464247\pi\) | ||||
0.112087 | + | 0.993698i | \(0.464247\pi\) | |||||||
\(678\) | −7.70820 | −0.296032 | ||||||||
\(679\) | 3.81966 | 0.146585 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.1246 | −1.07774 | ||||||||
\(682\) | −25.8885 | −0.991324 | ||||||||
\(683\) | 8.34752 | 0.319409 | 0.159705 | − | 0.987165i | \(-0.448946\pi\) | ||||
0.159705 | + | 0.987165i | \(0.448946\pi\) | |||||||
\(684\) | 1.61803 | 0.0618671 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.4377 | −0.474873 | ||||||||
\(687\) | 4.47214 | 0.170623 | ||||||||
\(688\) | 7.41641 | 0.282748 | ||||||||
\(689\) | −32.3607 | −1.23284 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.05573 | −0.268413 | −0.134206 | − | 0.990953i | \(-0.542848\pi\) | ||||
−0.134206 | + | 0.990953i | \(0.542848\pi\) | |||||||
\(692\) | 21.7984 | 0.828650 | ||||||||
\(693\) | 8.94427 | 0.339765 | ||||||||
\(694\) | 1.05573 | 0.0400749 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −16.7082 | −0.633323 | ||||||||
\(697\) | −6.18034 | −0.234097 | ||||||||
\(698\) | 11.0213 | 0.417162 | ||||||||
\(699\) | −2.94427 | −0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.3475 | 0.655207 | 0.327603 | − | 0.944815i | \(-0.393759\pi\) | ||||
0.327603 | + | 0.944815i | \(0.393759\pi\) | |||||||
\(702\) | 4.00000 | 0.150970 | ||||||||
\(703\) | −2.76393 | −0.104244 | ||||||||
\(704\) | 0.944272 | 0.0355886 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.3607 | 0.615742 | ||||||||
\(707\) | 31.7082 | 1.19251 | ||||||||
\(708\) | −23.7984 | −0.894398 | ||||||||
\(709\) | −40.4164 | −1.51787 | −0.758935 | − | 0.651166i | \(-0.774280\pi\) | ||||
−0.758935 | + | 0.651166i | \(0.774280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.29180 | −0.0859491 | ||||||||
\(712\) | −22.2361 | −0.833332 | ||||||||
\(713\) | −33.8885 | −1.26914 | ||||||||
\(714\) | −1.70820 | −0.0639279 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −35.7984 | −1.33785 | ||||||||
\(717\) | −0.291796 | −0.0108973 | ||||||||
\(718\) | 15.5967 | 0.582065 | ||||||||
\(719\) | −37.5279 | −1.39955 | −0.699777 | − | 0.714362i | \(-0.746717\pi\) | ||||
−0.699777 | + | 0.714362i | \(0.746717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.8885 | −1.41104 | ||||||||
\(722\) | −0.618034 | −0.0230008 | ||||||||
\(723\) | 16.1803 | 0.601753 | ||||||||
\(724\) | −16.9443 | −0.629729 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.09017 | 0.114687 | ||||||||
\(727\) | −15.7639 | −0.584652 | −0.292326 | − | 0.956319i | \(-0.594429\pi\) | ||||
−0.292326 | + | 0.956319i | \(0.594429\pi\) | |||||||
\(728\) | −32.3607 | −1.19937 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.94427 | 0.182871 | ||||||||
\(732\) | 12.8541 | 0.475101 | ||||||||
\(733\) | −12.4164 | −0.458610 | −0.229305 | − | 0.973355i | \(-0.573645\pi\) | ||||
−0.229305 | + | 0.973355i | \(0.573645\pi\) | |||||||
\(734\) | −20.5836 | −0.759754 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.1803 | −0.670136 | ||||||||
\(737\) | 43.7771 | 1.61255 | ||||||||
\(738\) | 3.09017 | 0.113751 | ||||||||
\(739\) | −4.59675 | −0.169094 | −0.0845470 | − | 0.996419i | \(-0.526944\pi\) | ||||
−0.0845470 | + | 0.996419i | \(0.526944\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.47214 | 0.237760 | ||||||||
\(742\) | −6.90983 | −0.253668 | ||||||||
\(743\) | 42.1246 | 1.54540 | 0.772701 | − | 0.634770i | \(-0.218905\pi\) | ||||
0.772701 | + | 0.634770i | \(0.218905\pi\) | |||||||
\(744\) | 23.4164 | 0.858487 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.52786 | −0.275615 | ||||||||
\(747\) | −6.94427 | −0.254078 | ||||||||
\(748\) | 8.00000 | 0.292509 | ||||||||
\(749\) | 36.3050 | 1.32655 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.4721 | −0.747039 | −0.373519 | − | 0.927622i | \(-0.621849\pi\) | ||||
−0.373519 | + | 0.927622i | \(0.621849\pi\) | |||||||
\(752\) | 0.875388 | 0.0319221 | ||||||||
\(753\) | −3.70820 | −0.135134 | ||||||||
\(754\) | −29.8885 | −1.08848 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.61803 | −0.131587 | ||||||||
\(757\) | 23.0000 | 0.835949 | 0.417975 | − | 0.908459i | \(-0.362740\pi\) | ||||
0.417975 | + | 0.908459i | \(0.362740\pi\) | |||||||
\(758\) | −4.18034 | −0.151837 | ||||||||
\(759\) | 12.9443 | 0.469847 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.1246 | −0.910766 | −0.455383 | − | 0.890296i | \(-0.650498\pi\) | ||||
−0.455383 | + | 0.890296i | \(0.650498\pi\) | |||||||
\(762\) | 6.65248 | 0.240994 | ||||||||
\(763\) | 17.2361 | 0.623988 | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.96556 | −0.360070 | ||||||||
\(767\) | −95.1935 | −3.43724 | ||||||||
\(768\) | 6.56231 | 0.236797 | ||||||||
\(769\) | −5.58359 | −0.201349 | −0.100675 | − | 0.994919i | \(-0.532100\pi\) | ||||
−0.100675 | + | 0.994919i | \(0.532100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.0000 | 0.468184 | ||||||||
\(772\) | 5.23607 | 0.188450 | ||||||||
\(773\) | −3.94427 | −0.141866 | −0.0709328 | − | 0.997481i | \(-0.522598\pi\) | ||||
−0.0709328 | + | 0.997481i | \(0.522598\pi\) | |||||||
\(774\) | −2.47214 | −0.0888591 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.81966 | −0.137118 | ||||||||
\(777\) | 6.18034 | 0.221718 | ||||||||
\(778\) | −4.94427 | −0.177261 | ||||||||
\(779\) | 5.00000 | 0.179144 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.7214 | −1.31399 | ||||||||
\(782\) | −2.47214 | −0.0884034 | ||||||||
\(783\) | −7.47214 | −0.267032 | ||||||||
\(784\) | −3.70820 | −0.132436 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.29180 | −0.153083 | ||||||||
\(787\) | −19.3475 | −0.689665 | −0.344832 | − | 0.938664i | \(-0.612064\pi\) | ||||
−0.344832 | + | 0.938664i | \(0.612064\pi\) | |||||||
\(788\) | 36.6525 | 1.30569 | ||||||||
\(789\) | 10.2918 | 0.366398 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.8885 | 0.991602 | ||||||||
\(792\) | −8.94427 | −0.317821 | ||||||||
\(793\) | 51.4164 | 1.82585 | ||||||||
\(794\) | −13.8197 | −0.490441 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.85410 | −0.101161 | ||||||||
\(797\) | −31.3607 | −1.11085 | −0.555426 | − | 0.831566i | \(-0.687445\pi\) | ||||
−0.555426 | + | 0.831566i | \(0.687445\pi\) | |||||||
\(798\) | 1.38197 | 0.0489211 | ||||||||
\(799\) | 0.583592 | 0.0206460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.94427 | −0.351364 | ||||||||
\(802\) | 12.8754 | 0.454646 | ||||||||
\(803\) | −13.8885 | −0.490116 | ||||||||
\(804\) | −17.7082 | −0.624520 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 41.8885 | 1.47546 | ||||||||
\(807\) | −20.4721 | −0.720653 | ||||||||
\(808\) | −31.7082 | −1.11549 | ||||||||
\(809\) | −16.8328 | −0.591810 | −0.295905 | − | 0.955217i | \(-0.595621\pi\) | ||||
−0.295905 | + | 0.955217i | \(0.595621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.7214 | 1.64061 | 0.820304 | − | 0.571927i | \(-0.193804\pi\) | ||||
0.820304 | + | 0.571927i | \(0.193804\pi\) | |||||||
\(812\) | 27.0344 | 0.948723 | ||||||||
\(813\) | −3.18034 | −0.111539 | ||||||||
\(814\) | 6.83282 | 0.239490 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.29180 | −0.0802289 | ||||||||
\(817\) | −4.00000 | −0.139942 | ||||||||
\(818\) | −5.41641 | −0.189380 | ||||||||
\(819\) | −14.4721 | −0.505697 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.12461 | 0.178850 | 0.0894251 | − | 0.995994i | \(-0.471497\pi\) | ||||
0.0894251 | + | 0.995994i | \(0.471497\pi\) | |||||||
\(822\) | 2.65248 | 0.0925157 | ||||||||
\(823\) | −33.1803 | −1.15659 | −0.578297 | − | 0.815826i | \(-0.696282\pi\) | ||||
−0.578297 | + | 0.815826i | \(0.696282\pi\) | |||||||
\(824\) | 37.8885 | 1.31991 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.3262 | −0.707240 | ||||||||
\(827\) | −36.9443 | −1.28468 | −0.642339 | − | 0.766421i | \(-0.722036\pi\) | ||||
−0.642339 | + | 0.766421i | \(0.722036\pi\) | |||||||
\(828\) | −5.23607 | −0.181966 | ||||||||
\(829\) | 55.6656 | 1.93335 | 0.966674 | − | 0.256012i | \(-0.0824086\pi\) | ||||
0.966674 | + | 0.256012i | \(0.0824086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.58359 | −0.193693 | ||||||||
\(832\) | −1.52786 | −0.0529692 | ||||||||
\(833\) | −2.47214 | −0.0856544 | ||||||||
\(834\) | −9.74265 | −0.337360 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.47214 | −0.223844 | ||||||||
\(837\) | 10.4721 | 0.361970 | ||||||||
\(838\) | −24.2918 | −0.839146 | ||||||||
\(839\) | −38.2361 | −1.32006 | −0.660028 | − | 0.751241i | \(-0.729456\pi\) | ||||
−0.660028 | + | 0.751241i | \(0.729456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8328 | 0.925270 | ||||||||
\(842\) | −7.12461 | −0.245530 | ||||||||
\(843\) | −7.88854 | −0.271696 | ||||||||
\(844\) | −9.41641 | −0.324126 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.291796 | −0.0100322 | ||||||||
\(847\) | −11.1803 | −0.384161 | ||||||||
\(848\) | −9.27051 | −0.318351 | ||||||||
\(849\) | −9.88854 | −0.339374 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.94427 | 0.306606 | ||||||||
\(852\) | 14.8541 | 0.508893 | ||||||||
\(853\) | −36.8885 | −1.26304 | −0.631520 | − | 0.775360i | \(-0.717569\pi\) | ||||
−0.631520 | + | 0.775360i | \(0.717569\pi\) | |||||||
\(854\) | 10.9787 | 0.375684 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.3050 | −1.24088 | ||||||||
\(857\) | 32.7771 | 1.11964 | 0.559822 | − | 0.828613i | \(-0.310870\pi\) | ||||
0.559822 | + | 0.828613i | \(0.310870\pi\) | |||||||
\(858\) | −16.0000 | −0.546231 | ||||||||
\(859\) | −21.2918 | −0.726467 | −0.363233 | − | 0.931698i | \(-0.618327\pi\) | ||||
−0.363233 | + | 0.931698i | \(0.618327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.1803 | −0.381025 | ||||||||
\(862\) | 3.20163 | 0.109048 | ||||||||
\(863\) | 34.8197 | 1.18528 | 0.592638 | − | 0.805469i | \(-0.298087\pi\) | ||||
0.592638 | + | 0.805469i | \(0.298087\pi\) | |||||||
\(864\) | 5.61803 | 0.191129 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.0689 | 0.410117 | ||||||||
\(867\) | 15.4721 | 0.525461 | ||||||||
\(868\) | −37.8885 | −1.28602 | ||||||||
\(869\) | 9.16718 | 0.310975 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −70.8328 | −2.40008 | ||||||||
\(872\) | −17.2361 | −0.583687 | ||||||||
\(873\) | −1.70820 | −0.0578139 | ||||||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.61803 | 0.189816 | ||||||||
\(877\) | −44.9443 | −1.51766 | −0.758830 | − | 0.651289i | \(-0.774229\pi\) | ||||
−0.758830 | + | 0.651289i | \(0.774229\pi\) | |||||||
\(878\) | 10.3607 | 0.349656 | ||||||||
\(879\) | −2.00000 | −0.0674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.944272 | −0.0318133 | −0.0159067 | − | 0.999873i | \(-0.505063\pi\) | ||||
−0.0159067 | + | 0.999873i | \(0.505063\pi\) | |||||||
\(882\) | 1.23607 | 0.0416206 | ||||||||
\(883\) | 45.6525 | 1.53633 | 0.768164 | − | 0.640253i | \(-0.221171\pi\) | ||||
0.768164 | + | 0.640253i | \(0.221171\pi\) | |||||||
\(884\) | −12.9443 | −0.435363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.29180 | −0.278568 | ||||||||
\(887\) | −18.8328 | −0.632344 | −0.316172 | − | 0.948702i | \(-0.602398\pi\) | ||||
−0.316172 | + | 0.948702i | \(0.602398\pi\) | |||||||
\(888\) | −6.18034 | −0.207399 | ||||||||
\(889\) | −24.0689 | −0.807244 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | −14.9443 | −0.500371 | ||||||||
\(893\) | −0.472136 | −0.0157994 | ||||||||
\(894\) | −12.0000 | −0.401340 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.4508 | −0.850253 | ||||||||
\(897\) | −20.9443 | −0.699309 | ||||||||
\(898\) | 15.7426 | 0.525339 | ||||||||
\(899\) | −78.2492 | −2.60976 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.18034 | −0.205897 | ||||||||
\(902\) | −12.3607 | −0.411566 | ||||||||
\(903\) | 8.94427 | 0.297647 | ||||||||
\(904\) | −27.8885 | −0.927559 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.23607 | 0.240402 | ||||||||
\(907\) | −29.8197 | −0.990146 | −0.495073 | − | 0.868852i | \(-0.664859\pi\) | ||||
−0.495073 | + | 0.868852i | \(0.664859\pi\) | |||||||
\(908\) | −45.5066 | −1.51019 | ||||||||
\(909\) | −14.1803 | −0.470332 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.7639 | 0.389756 | 0.194878 | − | 0.980827i | \(-0.437569\pi\) | ||||
0.194878 | + | 0.980827i | \(0.437569\pi\) | |||||||
\(912\) | 1.85410 | 0.0613955 | ||||||||
\(913\) | 27.7771 | 0.919287 | ||||||||
\(914\) | −5.49342 | −0.181706 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.23607 | 0.239086 | ||||||||
\(917\) | 15.5279 | 0.512775 | ||||||||
\(918\) | 0.763932 | 0.0252135 | ||||||||
\(919\) | 41.2918 | 1.36209 | 0.681045 | − | 0.732241i | \(-0.261526\pi\) | ||||
0.681045 | + | 0.732241i | \(0.261526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.05573 | 0.100690 | ||||||||
\(922\) | 1.12461 | 0.0370371 | ||||||||
\(923\) | 59.4164 | 1.95571 | ||||||||
\(924\) | 14.4721 | 0.476098 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.30495 | −0.174332 | ||||||||
\(927\) | 16.9443 | 0.556523 | ||||||||
\(928\) | −41.9787 | −1.37802 | ||||||||
\(929\) | 47.5967 | 1.56160 | 0.780799 | − | 0.624782i | \(-0.214812\pi\) | ||||
0.780799 | + | 0.624782i | \(0.214812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | −4.76393 | −0.156048 | ||||||||
\(933\) | −4.00000 | −0.130954 | ||||||||
\(934\) | 16.1803 | 0.529437 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.4721 | 0.473037 | ||||||||
\(937\) | 39.9443 | 1.30492 | 0.652461 | − | 0.757822i | \(-0.273737\pi\) | ||||
0.652461 | + | 0.757822i | \(0.273737\pi\) | |||||||
\(938\) | −15.1246 | −0.493836 | ||||||||
\(939\) | 30.9443 | 1.00983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.4721 | 1.18896 | 0.594479 | − | 0.804111i | \(-0.297358\pi\) | ||||
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(942\) | 4.32624 | 0.140956 | ||||||||
\(943\) | −16.1803 | −0.526904 | ||||||||
\(944\) | −27.2705 | −0.887579 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.88854 | 0.321504 | ||||||||
\(947\) | −36.9443 | −1.20053 | −0.600264 | − | 0.799802i | \(-0.704938\pi\) | ||||
−0.600264 | + | 0.799802i | \(0.704938\pi\) | |||||||
\(948\) | −3.70820 | −0.120437 | ||||||||
\(949\) | 22.4721 | 0.729476 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.94427 | 0.257611 | ||||||||
\(952\) | −6.18034 | −0.200306 | ||||||||
\(953\) | 53.2492 | 1.72491 | 0.862456 | − | 0.506132i | \(-0.168925\pi\) | ||||
0.862456 | + | 0.506132i | \(0.168925\pi\) | |||||||
\(954\) | 3.09017 | 0.100048 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.472136 | −0.0152700 | ||||||||
\(957\) | 29.8885 | 0.966159 | ||||||||
\(958\) | 23.9574 | 0.774029 | ||||||||
\(959\) | −9.59675 | −0.309895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.6656 | 2.53760 | ||||||||
\(962\) | −11.0557 | −0.356451 | ||||||||
\(963\) | −16.2361 | −0.523200 | ||||||||
\(964\) | 26.1803 | 0.843212 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.47214 | −0.143889 | ||||||||
\(967\) | 22.5967 | 0.726662 | 0.363331 | − | 0.931660i | \(-0.381639\pi\) | ||||
0.363331 | + | 0.931660i | \(0.381639\pi\) | |||||||
\(968\) | 11.1803 | 0.359350 | ||||||||
\(969\) | 1.23607 | 0.0397082 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0689 | 0.676133 | 0.338066 | − | 0.941122i | \(-0.390227\pi\) | ||||
0.338066 | + | 0.941122i | \(0.390227\pi\) | |||||||
\(972\) | 1.61803 | 0.0518985 | ||||||||
\(973\) | 35.2492 | 1.13004 | ||||||||
\(974\) | −14.8328 | −0.475274 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.7295 | 0.471479 | ||||||||
\(977\) | 5.05573 | 0.161747 | 0.0808735 | − | 0.996724i | \(-0.474229\pi\) | ||||
0.0808735 | + | 0.996724i | \(0.474229\pi\) | |||||||
\(978\) | −6.90983 | −0.220952 | ||||||||
\(979\) | 39.7771 | 1.27128 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.70820 | −0.246104 | ||||||||
\(982\) | 5.12461 | 0.163533 | ||||||||
\(983\) | 57.3050 | 1.82774 | 0.913872 | − | 0.406002i | \(-0.133078\pi\) | ||||
0.913872 | + | 0.406002i | \(0.133078\pi\) | |||||||
\(984\) | 11.1803 | 0.356416 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.70820 | −0.181786 | ||||||||
\(987\) | 1.05573 | 0.0336042 | ||||||||
\(988\) | 10.4721 | 0.333163 | ||||||||
\(989\) | 12.9443 | 0.411604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.0557 | −1.17711 | −0.588557 | − | 0.808456i | \(-0.700304\pi\) | ||||
−0.588557 | + | 0.808456i | \(0.700304\pi\) | |||||||
\(992\) | 58.8328 | 1.86794 | ||||||||
\(993\) | 26.3607 | 0.836531 | ||||||||
\(994\) | 12.6869 | 0.402405 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.2361 | −0.356028 | ||||||||
\(997\) | 12.4721 | 0.394997 | 0.197498 | − | 0.980303i | \(-0.436718\pi\) | ||||
0.197498 | + | 0.980303i | \(0.436718\pi\) | |||||||
\(998\) | 19.2705 | 0.609997 | ||||||||
\(999\) | −2.76393 | −0.0874469 |
(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 | 1425.2.a.q.1.1 | yes | 2 | |
3.2 | odd | 2 | 4275.2.a.s.1.2 | 2 | |||
5.2 | odd | 4 | 1425.2.c.m.799.2 | 4 | |||
5.3 | odd | 4 | 1425.2.c.m.799.3 | 4 | |||
5.4 | even | 2 | 1425.2.a.n.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 4275.2.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1425.2.a.n.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
1425.2.a.q.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1425.2.c.m.799.2 | 4 | 5.2 | odd | 4 | |||
1425.2.c.m.799.3 | 4 | 5.3 | odd | 4 | |||
4275.2.a.s.1.2 | 2 | 3.2 | odd | 2 | |||
4275.2.a.v.1.1 | 2 | 15.14 | odd | 2 |