Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
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 | 1.2 | ||
Root | \(0.814115\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.185885 | 0.131441 | 0.0657204 | − | 0.997838i | \(-0.479065\pi\) | ||||
0.0657204 | + | 0.997838i | \(0.479065\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.96545 | −0.982723 | ||||||||
\(5\) | 0.737118 | 0.329649 | 0.164825 | − | 0.986323i | \(-0.447294\pi\) | ||||
0.164825 | + | 0.986323i | \(0.447294\pi\) | |||||||
\(6\) | −0.185885 | −0.0758874 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.737118 | −0.260611 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.137020 | 0.0433294 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.96545 | 0.567376 | ||||||||
\(13\) | 1.45666 | 0.404004 | 0.202002 | − | 0.979385i | \(-0.435255\pi\) | ||||
0.202002 | + | 0.979385i | \(0.435255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.737118 | −0.190323 | ||||||||
\(16\) | 3.79387 | 0.948468 | ||||||||
\(17\) | −0.694676 | −0.168484 | −0.0842418 | − | 0.996445i | \(-0.526847\pi\) | ||||
−0.0842418 | + | 0.996445i | \(0.526847\pi\) | |||||||
\(18\) | 0.185885 | 0.0438136 | ||||||||
\(19\) | −2.62823 | −0.602957 | −0.301479 | − | 0.953473i | \(-0.597480\pi\) | ||||
−0.301479 | + | 0.953473i | \(0.597480\pi\) | |||||||
\(20\) | −1.44877 | −0.323954 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.185885 | −0.0396309 | ||||||||
\(23\) | 4.77956 | 0.996607 | 0.498304 | − | 0.867003i | \(-0.333956\pi\) | ||||
0.498304 | + | 0.867003i | \(0.333956\pi\) | |||||||
\(24\) | 0.737118 | 0.150464 | ||||||||
\(25\) | −4.45666 | −0.891331 | ||||||||
\(26\) | 0.270771 | 0.0531026 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.434454 | 0.0806762 | 0.0403381 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403381 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(30\) | −0.137020 | −0.0250162 | ||||||||
\(31\) | −2.04887 | −0.367987 | −0.183994 | − | 0.982927i | \(-0.558903\pi\) | ||||
−0.183994 | + | 0.982927i | \(0.558903\pi\) | |||||||
\(32\) | 2.17946 | 0.385278 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −0.129130 | −0.0221456 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96545 | −0.327574 | ||||||||
\(37\) | 7.38755 | 1.21451 | 0.607253 | − | 0.794509i | \(-0.292272\pi\) | ||||
0.607253 | + | 0.794509i | \(0.292272\pi\) | |||||||
\(38\) | −0.488549 | −0.0792532 | ||||||||
\(39\) | −1.45666 | −0.233252 | ||||||||
\(40\) | −0.543344 | −0.0859102 | ||||||||
\(41\) | −9.34511 | −1.45946 | −0.729730 | − | 0.683735i | \(-0.760354\pi\) | ||||
−0.729730 | + | 0.683735i | \(0.760354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.108889 | −0.0166054 | −0.00830272 | − | 0.999966i | \(-0.502643\pi\) | ||||
−0.00830272 | + | 0.999966i | \(0.502643\pi\) | |||||||
\(44\) | 1.96545 | 0.296302 | ||||||||
\(45\) | 0.737118 | 0.109883 | ||||||||
\(46\) | 0.888450 | 0.130995 | ||||||||
\(47\) | −2.28046 | −0.332640 | −0.166320 | − | 0.986072i | \(-0.553188\pi\) | ||||
−0.166320 | + | 0.986072i | \(0.553188\pi\) | |||||||
\(48\) | −3.79387 | −0.547599 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.828427 | −0.117157 | ||||||||
\(51\) | 0.694676 | 0.0972740 | ||||||||
\(52\) | −2.86298 | −0.397024 | ||||||||
\(53\) | −0.877293 | −0.120505 | −0.0602527 | − | 0.998183i | \(-0.519191\pi\) | ||||
−0.0602527 | + | 0.998183i | \(0.519191\pi\) | |||||||
\(54\) | −0.185885 | −0.0252958 | ||||||||
\(55\) | −0.737118 | −0.0993930 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.62823 | 0.348117 | ||||||||
\(58\) | 0.0807587 | 0.0106041 | ||||||||
\(59\) | −4.21136 | −0.548272 | −0.274136 | − | 0.961691i | \(-0.588392\pi\) | ||||
−0.274136 | + | 0.961691i | \(0.588392\pi\) | |||||||
\(60\) | 1.44877 | 0.187035 | ||||||||
\(61\) | −13.6035 | −1.74175 | −0.870877 | − | 0.491502i | \(-0.836448\pi\) | ||||
−0.870877 | + | 0.491502i | \(0.836448\pi\) | |||||||
\(62\) | −0.380854 | −0.0483685 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.18262 | −0.897827 | ||||||||
\(65\) | 1.07373 | 0.133180 | ||||||||
\(66\) | 0.185885 | 0.0228809 | ||||||||
\(67\) | −4.05153 | −0.494973 | −0.247486 | − | 0.968891i | \(-0.579605\pi\) | ||||
−0.247486 | + | 0.968891i | \(0.579605\pi\) | |||||||
\(68\) | 1.36535 | 0.165573 | ||||||||
\(69\) | −4.77956 | −0.575392 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.42999 | −0.881778 | −0.440889 | − | 0.897562i | \(-0.645337\pi\) | ||||
−0.440889 | + | 0.897562i | \(0.645337\pi\) | |||||||
\(72\) | −0.737118 | −0.0868702 | ||||||||
\(73\) | −3.52576 | −0.412659 | −0.206330 | − | 0.978483i | \(-0.566152\pi\) | ||||
−0.206330 | + | 0.978483i | \(0.566152\pi\) | |||||||
\(74\) | 1.37324 | 0.159636 | ||||||||
\(75\) | 4.45666 | 0.514610 | ||||||||
\(76\) | 5.16564 | 0.592540 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.270771 | −0.0306588 | ||||||||
\(79\) | 0.0977317 | 0.0109957 | 0.00549784 | − | 0.999985i | \(-0.498250\pi\) | ||||
0.00549784 | + | 0.999985i | \(0.498250\pi\) | |||||||
\(80\) | 2.79653 | 0.312662 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.73712 | −0.191833 | ||||||||
\(83\) | −16.3387 | −1.79340 | −0.896702 | − | 0.442635i | \(-0.854044\pi\) | ||||
−0.896702 | + | 0.442635i | \(0.854044\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.512058 | −0.0555405 | ||||||||
\(86\) | −0.0202409 | −0.00218263 | ||||||||
\(87\) | −0.434454 | −0.0465784 | ||||||||
\(88\) | 0.737118 | 0.0785771 | ||||||||
\(89\) | −5.71312 | −0.605589 | −0.302794 | − | 0.953056i | \(-0.597920\pi\) | ||||
−0.302794 | + | 0.953056i | \(0.597920\pi\) | |||||||
\(90\) | 0.137020 | 0.0144431 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.39397 | −0.979389 | ||||||||
\(93\) | 2.04887 | 0.212457 | ||||||||
\(94\) | −0.423904 | −0.0437224 | ||||||||
\(95\) | −1.93732 | −0.198764 | ||||||||
\(96\) | −2.17946 | −0.222440 | ||||||||
\(97\) | 5.14225 | 0.522116 | 0.261058 | − | 0.965323i | \(-0.415929\pi\) | ||||
0.261058 | + | 0.965323i | \(0.415929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 8.75932 | 0.875932 | ||||||||
\(101\) | 6.23148 | 0.620056 | 0.310028 | − | 0.950727i | \(-0.399662\pi\) | ||||
0.310028 | + | 0.950727i | \(0.399662\pi\) | |||||||
\(102\) | 0.129130 | 0.0127858 | ||||||||
\(103\) | −14.0195 | −1.38139 | −0.690693 | − | 0.723148i | \(-0.742694\pi\) | ||||
−0.690693 | + | 0.723148i | \(0.742694\pi\) | |||||||
\(104\) | −1.07373 | −0.105288 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.163076 | −0.0158393 | ||||||||
\(107\) | −7.98826 | −0.772254 | −0.386127 | − | 0.922446i | \(-0.626187\pi\) | ||||
−0.386127 | + | 0.922446i | \(0.626187\pi\) | |||||||
\(108\) | 1.96545 | 0.189125 | ||||||||
\(109\) | −6.26664 | −0.600236 | −0.300118 | − | 0.953902i | \(-0.597026\pi\) | ||||
−0.300118 | + | 0.953902i | \(0.597026\pi\) | |||||||
\(110\) | −0.137020 | −0.0130643 | ||||||||
\(111\) | −7.38755 | −0.701195 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.8304 | 1.11291 | 0.556455 | − | 0.830878i | \(-0.312161\pi\) | ||||
0.556455 | + | 0.830878i | \(0.312161\pi\) | |||||||
\(114\) | 0.488549 | 0.0457568 | ||||||||
\(115\) | 3.52310 | 0.328531 | ||||||||
\(116\) | −0.853897 | −0.0792824 | ||||||||
\(117\) | 1.45666 | 0.134668 | ||||||||
\(118\) | −0.782829 | −0.0720653 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.543344 | 0.0496003 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.52870 | −0.228937 | ||||||||
\(123\) | 9.34511 | 0.842620 | ||||||||
\(124\) | 4.02694 | 0.361630 | ||||||||
\(125\) | −6.97068 | −0.623476 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.46308 | 0.129827 | 0.0649137 | − | 0.997891i | \(-0.479323\pi\) | ||||
0.0649137 | + | 0.997891i | \(0.479323\pi\) | |||||||
\(128\) | −5.69407 | −0.503289 | ||||||||
\(129\) | 0.108889 | 0.00958715 | ||||||||
\(130\) | 0.199590 | 0.0175052 | ||||||||
\(131\) | −9.75082 | −0.851933 | −0.425967 | − | 0.904739i | \(-0.640066\pi\) | ||||
−0.425967 | + | 0.904739i | \(0.640066\pi\) | |||||||
\(132\) | −1.96545 | −0.171070 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.753119 | −0.0650596 | ||||||||
\(135\) | −0.737118 | −0.0634411 | ||||||||
\(136\) | 0.512058 | 0.0439086 | ||||||||
\(137\) | 7.91065 | 0.675853 | 0.337926 | − | 0.941173i | \(-0.390275\pi\) | ||||
0.337926 | + | 0.941173i | \(0.390275\pi\) | |||||||
\(138\) | −0.888450 | −0.0756299 | ||||||||
\(139\) | 2.63927 | 0.223860 | 0.111930 | − | 0.993716i | \(-0.464297\pi\) | ||||
0.111930 | + | 0.993716i | \(0.464297\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.28046 | 0.192050 | ||||||||
\(142\) | −1.38113 | −0.115902 | ||||||||
\(143\) | −1.45666 | −0.121812 | ||||||||
\(144\) | 3.79387 | 0.316156 | ||||||||
\(145\) | 0.320244 | 0.0265948 | ||||||||
\(146\) | −0.655388 | −0.0542403 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.5198 | −1.19352 | ||||||||
\(149\) | 15.8554 | 1.29892 | 0.649461 | − | 0.760395i | \(-0.274995\pi\) | ||||
0.649461 | + | 0.760395i | \(0.274995\pi\) | |||||||
\(150\) | 0.828427 | 0.0676408 | ||||||||
\(151\) | −17.5728 | −1.43006 | −0.715028 | − | 0.699096i | \(-0.753586\pi\) | ||||
−0.715028 | + | 0.699096i | \(0.753586\pi\) | |||||||
\(152\) | 1.93732 | 0.157137 | ||||||||
\(153\) | −0.694676 | −0.0561612 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.51026 | −0.121307 | ||||||||
\(156\) | 2.86298 | 0.229222 | ||||||||
\(157\) | −13.3009 | −1.06152 | −0.530762 | − | 0.847521i | \(-0.678094\pi\) | ||||
−0.530762 | + | 0.847521i | \(0.678094\pi\) | |||||||
\(158\) | 0.0181669 | 0.00144528 | ||||||||
\(159\) | 0.877293 | 0.0695739 | ||||||||
\(160\) | 1.60652 | 0.127007 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.185885 | 0.0146045 | ||||||||
\(163\) | −16.8618 | −1.32072 | −0.660359 | − | 0.750950i | \(-0.729596\pi\) | ||||
−0.660359 | + | 0.750950i | \(0.729596\pi\) | |||||||
\(164\) | 18.3673 | 1.43425 | ||||||||
\(165\) | 0.737118 | 0.0573846 | ||||||||
\(166\) | −3.03712 | −0.235726 | ||||||||
\(167\) | 11.6876 | 0.904410 | 0.452205 | − | 0.891914i | \(-0.350638\pi\) | ||||
0.452205 | + | 0.891914i | \(0.350638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8782 | −0.836781 | ||||||||
\(170\) | −0.0951841 | −0.00730029 | ||||||||
\(171\) | −2.62823 | −0.200986 | ||||||||
\(172\) | 0.214016 | 0.0163185 | ||||||||
\(173\) | 18.4800 | 1.40501 | 0.702503 | − | 0.711681i | \(-0.252066\pi\) | ||||
0.702503 | + | 0.711681i | \(0.252066\pi\) | |||||||
\(174\) | −0.0807587 | −0.00612230 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.79387 | −0.285974 | ||||||||
\(177\) | 4.21136 | 0.316545 | ||||||||
\(178\) | −1.06198 | −0.0795991 | ||||||||
\(179\) | −6.81026 | −0.509023 | −0.254511 | − | 0.967070i | \(-0.581915\pi\) | ||||
−0.254511 | + | 0.967070i | \(0.581915\pi\) | |||||||
\(180\) | −1.44877 | −0.107985 | ||||||||
\(181\) | 6.93732 | 0.515647 | 0.257823 | − | 0.966192i | \(-0.416995\pi\) | ||||
0.257823 | + | 0.966192i | \(0.416995\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6035 | 1.00560 | ||||||||
\(184\) | −3.52310 | −0.259727 | ||||||||
\(185\) | 5.44550 | 0.400361 | ||||||||
\(186\) | 0.380854 | 0.0279256 | ||||||||
\(187\) | 0.694676 | 0.0507997 | ||||||||
\(188\) | 4.48213 | 0.326893 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.360119 | −0.0261258 | ||||||||
\(191\) | 16.6727 | 1.20640 | 0.603199 | − | 0.797591i | \(-0.293893\pi\) | ||||
0.603199 | + | 0.797591i | \(0.293893\pi\) | |||||||
\(192\) | 7.18262 | 0.518361 | ||||||||
\(193\) | −26.5031 | −1.90774 | −0.953869 | − | 0.300224i | \(-0.902939\pi\) | ||||
−0.953869 | + | 0.300224i | \(0.902939\pi\) | |||||||
\(194\) | 0.955869 | 0.0686274 | ||||||||
\(195\) | −1.07373 | −0.0768913 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2336 | 1.15659 | 0.578297 | − | 0.815827i | \(-0.303718\pi\) | ||||
0.578297 | + | 0.815827i | \(0.303718\pi\) | |||||||
\(198\) | −0.185885 | −0.0132103 | ||||||||
\(199\) | −0.199096 | −0.0141135 | −0.00705676 | − | 0.999975i | \(-0.502246\pi\) | ||||
−0.00705676 | + | 0.999975i | \(0.502246\pi\) | |||||||
\(200\) | 3.28508 | 0.232290 | ||||||||
\(201\) | 4.05153 | 0.285773 | ||||||||
\(202\) | 1.15834 | 0.0815006 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.36535 | −0.0955935 | ||||||||
\(205\) | −6.88845 | −0.481110 | ||||||||
\(206\) | −2.60603 | −0.181571 | ||||||||
\(207\) | 4.77956 | 0.332202 | ||||||||
\(208\) | 5.52637 | 0.383185 | ||||||||
\(209\) | 2.62823 | 0.181798 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.86179 | −0.403542 | −0.201771 | − | 0.979433i | \(-0.564670\pi\) | ||||
−0.201771 | + | 0.979433i | \(0.564670\pi\) | |||||||
\(212\) | 1.72427 | 0.118424 | ||||||||
\(213\) | 7.42999 | 0.509095 | ||||||||
\(214\) | −1.48490 | −0.101506 | ||||||||
\(215\) | −0.0802642 | −0.00547397 | ||||||||
\(216\) | 0.737118 | 0.0501546 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.16488 | −0.0788954 | ||||||||
\(219\) | 3.52576 | 0.238249 | ||||||||
\(220\) | 1.44877 | 0.0976758 | ||||||||
\(221\) | −1.01190 | −0.0680680 | ||||||||
\(222\) | −1.37324 | −0.0921656 | ||||||||
\(223\) | 4.26218 | 0.285417 | 0.142708 | − | 0.989765i | \(-0.454419\pi\) | ||||
0.142708 | + | 0.989765i | \(0.454419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.45666 | −0.297110 | ||||||||
\(226\) | 2.19910 | 0.146282 | ||||||||
\(227\) | −13.9558 | −0.926276 | −0.463138 | − | 0.886286i | \(-0.653277\pi\) | ||||
−0.463138 | + | 0.886286i | \(0.653277\pi\) | |||||||
\(228\) | −5.16564 | −0.342103 | ||||||||
\(229\) | 20.0804 | 1.32695 | 0.663476 | − | 0.748198i | \(-0.269081\pi\) | ||||
0.663476 | + | 0.748198i | \(0.269081\pi\) | |||||||
\(230\) | 0.654893 | 0.0431824 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.320244 | −0.0210251 | ||||||||
\(233\) | −12.6211 | −0.826836 | −0.413418 | − | 0.910541i | \(-0.635665\pi\) | ||||
−0.413418 | + | 0.910541i | \(0.635665\pi\) | |||||||
\(234\) | 0.270771 | 0.0177009 | ||||||||
\(235\) | −1.68097 | −0.109654 | ||||||||
\(236\) | 8.27719 | 0.538799 | ||||||||
\(237\) | −0.0977317 | −0.00634835 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4384 | 1.32205 | 0.661024 | − | 0.750364i | \(-0.270122\pi\) | ||||
0.661024 | + | 0.750364i | \(0.270122\pi\) | |||||||
\(240\) | −2.79653 | −0.180516 | ||||||||
\(241\) | −4.97138 | −0.320234 | −0.160117 | − | 0.987098i | \(-0.551187\pi\) | ||||
−0.160117 | + | 0.987098i | \(0.551187\pi\) | |||||||
\(242\) | 0.185885 | 0.0119492 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 26.7370 | 1.71166 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.73712 | 0.110755 | ||||||||
\(247\) | −3.82843 | −0.243597 | ||||||||
\(248\) | 1.51026 | 0.0959014 | ||||||||
\(249\) | 16.3387 | 1.03542 | ||||||||
\(250\) | −1.29575 | −0.0819502 | ||||||||
\(251\) | −5.12467 | −0.323466 | −0.161733 | − | 0.986835i | \(-0.551708\pi\) | ||||
−0.161733 | + | 0.986835i | \(0.551708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.77956 | −0.300488 | ||||||||
\(254\) | 0.271965 | 0.0170646 | ||||||||
\(255\) | 0.512058 | 0.0320663 | ||||||||
\(256\) | 13.3068 | 0.831674 | ||||||||
\(257\) | 2.25184 | 0.140466 | 0.0702329 | − | 0.997531i | \(-0.477626\pi\) | ||||
0.0702329 | + | 0.997531i | \(0.477626\pi\) | |||||||
\(258\) | 0.0202409 | 0.00126014 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.11036 | −0.130879 | ||||||||
\(261\) | 0.434454 | 0.0268921 | ||||||||
\(262\) | −1.81254 | −0.111979 | ||||||||
\(263\) | 12.1018 | 0.746227 | 0.373113 | − | 0.927786i | \(-0.378290\pi\) | ||||
0.373113 | + | 0.927786i | \(0.378290\pi\) | |||||||
\(264\) | −0.737118 | −0.0453665 | ||||||||
\(265\) | −0.646669 | −0.0397245 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.71312 | 0.349637 | ||||||||
\(268\) | 7.96306 | 0.486421 | ||||||||
\(269\) | 30.7974 | 1.87775 | 0.938876 | − | 0.344256i | \(-0.111869\pi\) | ||||
0.938876 | + | 0.344256i | \(0.111869\pi\) | |||||||
\(270\) | −0.137020 | −0.00833874 | ||||||||
\(271\) | 1.29514 | 0.0786741 | 0.0393370 | − | 0.999226i | \(-0.487475\pi\) | ||||
0.0393370 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(272\) | −2.63551 | −0.159801 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.47047 | 0.0888346 | ||||||||
\(275\) | 4.45666 | 0.268746 | ||||||||
\(276\) | 9.39397 | 0.565451 | ||||||||
\(277\) | 10.9680 | 0.659004 | 0.329502 | − | 0.944155i | \(-0.393119\pi\) | ||||
0.329502 | + | 0.944155i | \(0.393119\pi\) | |||||||
\(278\) | 0.490602 | 0.0294244 | ||||||||
\(279\) | −2.04887 | −0.122662 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.6386 | 1.64878 | 0.824390 | − | 0.566023i | \(-0.191519\pi\) | ||||
0.824390 | + | 0.566023i | \(0.191519\pi\) | |||||||
\(282\) | 0.423904 | 0.0252431 | ||||||||
\(283\) | −31.1516 | −1.85177 | −0.925885 | − | 0.377805i | \(-0.876679\pi\) | ||||
−0.925885 | + | 0.377805i | \(0.876679\pi\) | |||||||
\(284\) | 14.6033 | 0.866544 | ||||||||
\(285\) | 1.93732 | 0.114757 | ||||||||
\(286\) | −0.270771 | −0.0160110 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.17946 | 0.128426 | ||||||||
\(289\) | −16.5174 | −0.971613 | ||||||||
\(290\) | 0.0595287 | 0.00349565 | ||||||||
\(291\) | −5.14225 | −0.301444 | ||||||||
\(292\) | 6.92970 | 0.405530 | ||||||||
\(293\) | 5.88942 | 0.344064 | 0.172032 | − | 0.985091i | \(-0.444967\pi\) | ||||
0.172032 | + | 0.985091i | \(0.444967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.10427 | −0.180737 | ||||||||
\(296\) | −5.44550 | −0.316513 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 2.94728 | 0.170731 | ||||||||
\(299\) | 6.96218 | 0.402633 | ||||||||
\(300\) | −8.75932 | −0.505720 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.26653 | −0.187968 | ||||||||
\(303\) | −6.23148 | −0.357989 | ||||||||
\(304\) | −9.97117 | −0.571886 | ||||||||
\(305\) | −10.0274 | −0.574168 | ||||||||
\(306\) | −0.129130 | −0.00738187 | ||||||||
\(307\) | 26.2089 | 1.49582 | 0.747909 | − | 0.663801i | \(-0.231058\pi\) | ||||
0.747909 | + | 0.663801i | \(0.231058\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0195 | 0.797544 | ||||||||
\(310\) | −0.280735 | −0.0159447 | ||||||||
\(311\) | −17.2002 | −0.975334 | −0.487667 | − | 0.873030i | \(-0.662152\pi\) | ||||
−0.487667 | + | 0.873030i | \(0.662152\pi\) | |||||||
\(312\) | 1.07373 | 0.0607879 | ||||||||
\(313\) | 7.62616 | 0.431056 | 0.215528 | − | 0.976498i | \(-0.430853\pi\) | ||||
0.215528 | + | 0.976498i | \(0.430853\pi\) | |||||||
\(314\) | −2.47244 | −0.139528 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.192086 | −0.0108057 | ||||||||
\(317\) | −16.7353 | −0.939949 | −0.469975 | − | 0.882680i | \(-0.655737\pi\) | ||||
−0.469975 | + | 0.882680i | \(0.655737\pi\) | |||||||
\(318\) | 0.163076 | 0.00914484 | ||||||||
\(319\) | −0.434454 | −0.0243248 | ||||||||
\(320\) | −5.29444 | −0.295968 | ||||||||
\(321\) | 7.98826 | 0.445861 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.82577 | 0.101588 | ||||||||
\(324\) | −1.96545 | −0.109191 | ||||||||
\(325\) | −6.49182 | −0.360101 | ||||||||
\(326\) | −3.13436 | −0.173596 | ||||||||
\(327\) | 6.26664 | 0.346546 | ||||||||
\(328\) | 6.88845 | 0.380351 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.137020 | 0.00754268 | ||||||||
\(331\) | −12.1550 | −0.668098 | −0.334049 | − | 0.942556i | \(-0.608415\pi\) | ||||
−0.334049 | + | 0.942556i | \(0.608415\pi\) | |||||||
\(332\) | 32.1128 | 1.76242 | ||||||||
\(333\) | 7.38755 | 0.404835 | ||||||||
\(334\) | 2.17254 | 0.118876 | ||||||||
\(335\) | −2.98645 | −0.163167 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6634 | 1.12561 | 0.562805 | − | 0.826590i | \(-0.309722\pi\) | ||||
0.562805 | + | 0.826590i | \(0.309722\pi\) | |||||||
\(338\) | −2.02209 | −0.109987 | ||||||||
\(339\) | −11.8304 | −0.642538 | ||||||||
\(340\) | 1.00642 | 0.0545809 | ||||||||
\(341\) | 2.04887 | 0.110952 | ||||||||
\(342\) | −0.488549 | −0.0264177 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.0802642 | 0.00432755 | ||||||||
\(345\) | −3.52310 | −0.189677 | ||||||||
\(346\) | 3.43515 | 0.184675 | ||||||||
\(347\) | 24.4829 | 1.31431 | 0.657155 | − | 0.753755i | \(-0.271760\pi\) | ||||
0.657155 | + | 0.753755i | \(0.271760\pi\) | |||||||
\(348\) | 0.853897 | 0.0457737 | ||||||||
\(349\) | −4.48708 | −0.240188 | −0.120094 | − | 0.992763i | \(-0.538320\pi\) | ||||
−0.120094 | + | 0.992763i | \(0.538320\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.45666 | −0.0777506 | ||||||||
\(352\) | −2.17946 | −0.116166 | ||||||||
\(353\) | −27.5632 | −1.46704 | −0.733519 | − | 0.679668i | \(-0.762124\pi\) | ||||
−0.733519 | + | 0.679668i | \(0.762124\pi\) | |||||||
\(354\) | 0.782829 | 0.0416069 | ||||||||
\(355\) | −5.47678 | −0.290678 | ||||||||
\(356\) | 11.2288 | 0.595126 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.26593 | −0.0669064 | ||||||||
\(359\) | −29.9273 | −1.57950 | −0.789751 | − | 0.613428i | \(-0.789790\pi\) | ||||
−0.789751 | + | 0.613428i | \(0.789790\pi\) | |||||||
\(360\) | −0.543344 | −0.0286367 | ||||||||
\(361\) | −12.0924 | −0.636443 | ||||||||
\(362\) | 1.28955 | 0.0677770 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.59890 | −0.136033 | ||||||||
\(366\) | 2.52870 | 0.132177 | ||||||||
\(367\) | 12.8782 | 0.672234 | 0.336117 | − | 0.941820i | \(-0.390886\pi\) | ||||
0.336117 | + | 0.941820i | \(0.390886\pi\) | |||||||
\(368\) | 18.1331 | 0.945251 | ||||||||
\(369\) | −9.34511 | −0.486487 | ||||||||
\(370\) | 1.01224 | 0.0526238 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.02694 | −0.208787 | ||||||||
\(373\) | −20.5408 | −1.06356 | −0.531782 | − | 0.846881i | \(-0.678478\pi\) | ||||
−0.531782 | + | 0.846881i | \(0.678478\pi\) | |||||||
\(374\) | 0.129130 | 0.00667715 | ||||||||
\(375\) | 6.97068 | 0.359964 | ||||||||
\(376\) | 1.68097 | 0.0866894 | ||||||||
\(377\) | 0.632851 | 0.0325935 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.8961 | −1.63839 | −0.819197 | − | 0.573512i | \(-0.805581\pi\) | ||||
−0.819197 | + | 0.573512i | \(0.805581\pi\) | |||||||
\(380\) | 3.80769 | 0.195330 | ||||||||
\(381\) | −1.46308 | −0.0749558 | ||||||||
\(382\) | 3.09922 | 0.158570 | ||||||||
\(383\) | 4.18555 | 0.213872 | 0.106936 | − | 0.994266i | \(-0.465896\pi\) | ||||
0.106936 | + | 0.994266i | \(0.465896\pi\) | |||||||
\(384\) | 5.69407 | 0.290574 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.92654 | −0.250755 | ||||||||
\(387\) | −0.108889 | −0.00553514 | ||||||||
\(388\) | −10.1068 | −0.513096 | ||||||||
\(389\) | 22.1789 | 1.12451 | 0.562256 | − | 0.826963i | \(-0.309933\pi\) | ||||
0.562256 | + | 0.826963i | \(0.309933\pi\) | |||||||
\(390\) | −0.199590 | −0.0101067 | ||||||||
\(391\) | −3.32024 | −0.167912 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.75082 | 0.491864 | ||||||||
\(394\) | 3.01758 | 0.152024 | ||||||||
\(395\) | 0.0720398 | 0.00362472 | ||||||||
\(396\) | 1.96545 | 0.0987674 | ||||||||
\(397\) | −1.37736 | −0.0691279 | −0.0345640 | − | 0.999402i | \(-0.511004\pi\) | ||||
−0.0345640 | + | 0.999402i | \(0.511004\pi\) | |||||||
\(398\) | −0.0370090 | −0.00185509 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.9080 | −0.845400 | ||||||||
\(401\) | 19.1656 | 0.957082 | 0.478541 | − | 0.878065i | \(-0.341166\pi\) | ||||
0.478541 | + | 0.878065i | \(0.341166\pi\) | |||||||
\(402\) | 0.753119 | 0.0375622 | ||||||||
\(403\) | −2.98449 | −0.148668 | ||||||||
\(404\) | −12.2476 | −0.609343 | ||||||||
\(405\) | 0.737118 | 0.0366277 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.38755 | −0.366187 | ||||||||
\(408\) | −0.512058 | −0.0253507 | ||||||||
\(409\) | 29.4900 | 1.45819 | 0.729094 | − | 0.684414i | \(-0.239942\pi\) | ||||
0.729094 | + | 0.684414i | \(0.239942\pi\) | |||||||
\(410\) | −1.28046 | −0.0632375 | ||||||||
\(411\) | −7.91065 | −0.390204 | ||||||||
\(412\) | 27.5547 | 1.35752 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.888450 | 0.0436650 | ||||||||
\(415\) | −12.0435 | −0.591194 | ||||||||
\(416\) | 3.17473 | 0.155654 | ||||||||
\(417\) | −2.63927 | −0.129246 | ||||||||
\(418\) | 0.488549 | 0.0238957 | ||||||||
\(419\) | 28.8026 | 1.40710 | 0.703550 | − | 0.710646i | \(-0.251597\pi\) | ||||
0.703550 | + | 0.710646i | \(0.251597\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8452 | 1.06467 | 0.532335 | − | 0.846534i | \(-0.321315\pi\) | ||||
0.532335 | + | 0.846534i | \(0.321315\pi\) | |||||||
\(422\) | −1.08962 | −0.0530419 | ||||||||
\(423\) | −2.28046 | −0.110880 | ||||||||
\(424\) | 0.646669 | 0.0314050 | ||||||||
\(425\) | 3.09593 | 0.150175 | ||||||||
\(426\) | 1.38113 | 0.0669158 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.7005 | 0.758912 | ||||||||
\(429\) | 1.45666 | 0.0703280 | ||||||||
\(430\) | −0.0149199 | −0.000719503 0 | ||||||||
\(431\) | 5.93078 | 0.285676 | 0.142838 | − | 0.989746i | \(-0.454377\pi\) | ||||
0.142838 | + | 0.989746i | \(0.454377\pi\) | |||||||
\(432\) | −3.79387 | −0.182533 | ||||||||
\(433\) | −12.3728 | −0.594597 | −0.297298 | − | 0.954785i | \(-0.596086\pi\) | ||||
−0.297298 | + | 0.954785i | \(0.596086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.320244 | −0.0153545 | ||||||||
\(436\) | 12.3168 | 0.589866 | ||||||||
\(437\) | −12.5618 | −0.600912 | ||||||||
\(438\) | 0.655388 | 0.0313156 | ||||||||
\(439\) | −15.3102 | −0.730715 | −0.365358 | − | 0.930867i | \(-0.619053\pi\) | ||||
−0.365358 | + | 0.930867i | \(0.619053\pi\) | |||||||
\(440\) | 0.543344 | 0.0259029 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.188098 | −0.00894691 | ||||||||
\(443\) | −24.0535 | −1.14282 | −0.571408 | − | 0.820666i | \(-0.693603\pi\) | ||||
−0.571408 | + | 0.820666i | \(0.693603\pi\) | |||||||
\(444\) | 14.5198 | 0.689081 | ||||||||
\(445\) | −4.21124 | −0.199632 | ||||||||
\(446\) | 0.792277 | 0.0375154 | ||||||||
\(447\) | −15.8554 | −0.749933 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9447 | −0.516513 | −0.258256 | − | 0.966076i | \(-0.583148\pi\) | ||||
−0.258256 | + | 0.966076i | \(0.583148\pi\) | |||||||
\(450\) | −0.828427 | −0.0390524 | ||||||||
\(451\) | 9.34511 | 0.440044 | ||||||||
\(452\) | −23.2520 | −1.09368 | ||||||||
\(453\) | 17.5728 | 0.825643 | ||||||||
\(454\) | −2.59417 | −0.121750 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.93732 | −0.0907231 | ||||||||
\(457\) | −29.2520 | −1.36835 | −0.684175 | − | 0.729318i | \(-0.739838\pi\) | ||||
−0.684175 | + | 0.729318i | \(0.739838\pi\) | |||||||
\(458\) | 3.73266 | 0.174416 | ||||||||
\(459\) | 0.694676 | 0.0324247 | ||||||||
\(460\) | −6.92447 | −0.322855 | ||||||||
\(461\) | −13.8527 | −0.645185 | −0.322592 | − | 0.946538i | \(-0.604554\pi\) | ||||
−0.322592 | + | 0.946538i | \(0.604554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.3553 | 0.806570 | 0.403285 | − | 0.915074i | \(-0.367868\pi\) | ||||
0.403285 | + | 0.915074i | \(0.367868\pi\) | |||||||
\(464\) | 1.64827 | 0.0765188 | ||||||||
\(465\) | 1.51026 | 0.0700365 | ||||||||
\(466\) | −2.34608 | −0.108680 | ||||||||
\(467\) | 11.0749 | 0.512487 | 0.256244 | − | 0.966612i | \(-0.417515\pi\) | ||||
0.256244 | + | 0.966612i | \(0.417515\pi\) | |||||||
\(468\) | −2.86298 | −0.132341 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.312468 | −0.0144131 | ||||||||
\(471\) | 13.3009 | 0.612871 | ||||||||
\(472\) | 3.10427 | 0.142885 | ||||||||
\(473\) | 0.108889 | 0.00500673 | ||||||||
\(474\) | −0.0181669 | −0.000834433 0 | ||||||||
\(475\) | 11.7131 | 0.537435 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.877293 | −0.0401685 | ||||||||
\(478\) | 3.79919 | 0.173771 | ||||||||
\(479\) | −35.1983 | −1.60825 | −0.804125 | − | 0.594460i | \(-0.797366\pi\) | ||||
−0.804125 | + | 0.594460i | \(0.797366\pi\) | |||||||
\(480\) | −1.60652 | −0.0733274 | ||||||||
\(481\) | 10.7611 | 0.490665 | ||||||||
\(482\) | −0.924106 | −0.0420919 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.96545 | −0.0893385 | ||||||||
\(485\) | 3.79045 | 0.172115 | ||||||||
\(486\) | −0.185885 | −0.00843193 | ||||||||
\(487\) | −7.00180 | −0.317282 | −0.158641 | − | 0.987336i | \(-0.550711\pi\) | ||||
−0.158641 | + | 0.987336i | \(0.550711\pi\) | |||||||
\(488\) | 10.0274 | 0.453920 | ||||||||
\(489\) | 16.8618 | 0.762516 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.5894 | 0.658412 | 0.329206 | − | 0.944258i | \(-0.393219\pi\) | ||||
0.329206 | + | 0.944258i | \(0.393219\pi\) | |||||||
\(492\) | −18.3673 | −0.828062 | ||||||||
\(493\) | −0.301805 | −0.0135926 | ||||||||
\(494\) | −0.711649 | −0.0320186 | ||||||||
\(495\) | −0.737118 | −0.0331310 | ||||||||
\(496\) | −7.77314 | −0.349024 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.03712 | 0.136097 | ||||||||
\(499\) | −20.5720 | −0.920928 | −0.460464 | − | 0.887678i | \(-0.652317\pi\) | ||||
−0.460464 | + | 0.887678i | \(0.652317\pi\) | |||||||
\(500\) | 13.7005 | 0.612705 | ||||||||
\(501\) | −11.6876 | −0.522161 | ||||||||
\(502\) | −0.952601 | −0.0425167 | ||||||||
\(503\) | −29.3811 | −1.31004 | −0.655020 | − | 0.755612i | \(-0.727340\pi\) | ||||
−0.655020 | + | 0.755612i | \(0.727340\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.59334 | 0.204401 | ||||||||
\(506\) | −0.888450 | −0.0394964 | ||||||||
\(507\) | 10.8782 | 0.483116 | ||||||||
\(508\) | −2.87560 | −0.127584 | ||||||||
\(509\) | −10.2908 | −0.456132 | −0.228066 | − | 0.973646i | \(-0.573240\pi\) | ||||
−0.228066 | + | 0.973646i | \(0.573240\pi\) | |||||||
\(510\) | 0.0951841 | 0.00421482 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 13.8617 | 0.612605 | ||||||||
\(513\) | 2.62823 | 0.116039 | ||||||||
\(514\) | 0.418584 | 0.0184629 | ||||||||
\(515\) | −10.3341 | −0.455373 | ||||||||
\(516\) | −0.214016 | −0.00942152 | ||||||||
\(517\) | 2.28046 | 0.100295 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.4800 | −0.811180 | ||||||||
\(520\) | −0.791465 | −0.0347080 | ||||||||
\(521\) | −6.89210 | −0.301948 | −0.150974 | − | 0.988538i | \(-0.548241\pi\) | ||||
−0.150974 | + | 0.988538i | \(0.548241\pi\) | |||||||
\(522\) | 0.0807587 | 0.00353471 | ||||||||
\(523\) | −30.8606 | −1.34944 | −0.674719 | − | 0.738074i | \(-0.735735\pi\) | ||||
−0.674719 | + | 0.738074i | \(0.735735\pi\) | |||||||
\(524\) | 19.1647 | 0.837215 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.24954 | 0.0980847 | ||||||||
\(527\) | 1.42330 | 0.0619998 | ||||||||
\(528\) | 3.79387 | 0.165107 | ||||||||
\(529\) | −0.155794 | −0.00677365 | ||||||||
\(530\) | −0.120206 | −0.00522143 | ||||||||
\(531\) | −4.21136 | −0.182757 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6126 | −0.589628 | ||||||||
\(534\) | 1.06198 | 0.0459566 | ||||||||
\(535\) | −5.88829 | −0.254573 | ||||||||
\(536\) | 2.98645 | 0.128995 | ||||||||
\(537\) | 6.81026 | 0.293884 | ||||||||
\(538\) | 5.72479 | 0.246813 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.44877 | 0.0623450 | ||||||||
\(541\) | 31.0493 | 1.33491 | 0.667457 | − | 0.744649i | \(-0.267383\pi\) | ||||
0.667457 | + | 0.744649i | \(0.267383\pi\) | |||||||
\(542\) | 0.240747 | 0.0103410 | ||||||||
\(543\) | −6.93732 | −0.297709 | ||||||||
\(544\) | −1.51402 | −0.0649130 | ||||||||
\(545\) | −4.61926 | −0.197867 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.7208 | 1.52731 | 0.763656 | − | 0.645624i | \(-0.223403\pi\) | ||||
0.763656 | + | 0.645624i | \(0.223403\pi\) | |||||||
\(548\) | −15.5480 | −0.664176 | ||||||||
\(549\) | −13.6035 | −0.580584 | ||||||||
\(550\) | 0.828427 | 0.0353243 | ||||||||
\(551\) | −1.14185 | −0.0486443 | ||||||||
\(552\) | 3.52310 | 0.149953 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.03879 | 0.0866200 | ||||||||
\(555\) | −5.44550 | −0.231149 | ||||||||
\(556\) | −5.18735 | −0.219993 | ||||||||
\(557\) | −38.9278 | −1.64942 | −0.824712 | − | 0.565553i | \(-0.808663\pi\) | ||||
−0.824712 | + | 0.565553i | \(0.808663\pi\) | |||||||
\(558\) | −0.380854 | −0.0161228 | ||||||||
\(559\) | −0.158614 | −0.00670866 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.694676 | −0.0293292 | ||||||||
\(562\) | 5.13761 | 0.216717 | ||||||||
\(563\) | 30.6398 | 1.29131 | 0.645657 | − | 0.763628i | \(-0.276584\pi\) | ||||
0.645657 | + | 0.763628i | \(0.276584\pi\) | |||||||
\(564\) | −4.48213 | −0.188732 | ||||||||
\(565\) | 8.72040 | 0.366870 | ||||||||
\(566\) | −5.79063 | −0.243398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.47678 | 0.229801 | ||||||||
\(569\) | −3.34788 | −0.140350 | −0.0701752 | − | 0.997535i | \(-0.522356\pi\) | ||||
−0.0701752 | + | 0.997535i | \(0.522356\pi\) | |||||||
\(570\) | 0.360119 | 0.0150837 | ||||||||
\(571\) | 13.7741 | 0.576429 | 0.288215 | − | 0.957566i | \(-0.406938\pi\) | ||||
0.288215 | + | 0.957566i | \(0.406938\pi\) | |||||||
\(572\) | 2.86298 | 0.119707 | ||||||||
\(573\) | −16.6727 | −0.696514 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.3009 | −0.888307 | ||||||||
\(576\) | −7.18262 | −0.299276 | ||||||||
\(577\) | 25.1746 | 1.04803 | 0.524017 | − | 0.851708i | \(-0.324433\pi\) | ||||
0.524017 | + | 0.851708i | \(0.324433\pi\) | |||||||
\(578\) | −3.07035 | −0.127710 | ||||||||
\(579\) | 26.5031 | 1.10143 | ||||||||
\(580\) | −0.629423 | −0.0261354 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.955869 | −0.0396220 | ||||||||
\(583\) | 0.877293 | 0.0363338 | ||||||||
\(584\) | 2.59890 | 0.107543 | ||||||||
\(585\) | 1.07373 | 0.0443932 | ||||||||
\(586\) | 1.09476 | 0.0452240 | ||||||||
\(587\) | 31.2072 | 1.28806 | 0.644029 | − | 0.765001i | \(-0.277262\pi\) | ||||
0.644029 | + | 0.765001i | \(0.277262\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.38489 | 0.221880 | ||||||||
\(590\) | −0.577038 | −0.0237563 | ||||||||
\(591\) | −16.2336 | −0.667759 | ||||||||
\(592\) | 28.0274 | 1.15192 | ||||||||
\(593\) | 5.19937 | 0.213512 | 0.106756 | − | 0.994285i | \(-0.465954\pi\) | ||||
0.106756 | + | 0.994285i | \(0.465954\pi\) | |||||||
\(594\) | 0.185885 | 0.00762697 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31.1629 | −1.27648 | ||||||||
\(597\) | 0.199096 | 0.00814845 | ||||||||
\(598\) | 1.29417 | 0.0529224 | ||||||||
\(599\) | 39.2252 | 1.60270 | 0.801350 | − | 0.598196i | \(-0.204116\pi\) | ||||
0.801350 | + | 0.598196i | \(0.204116\pi\) | |||||||
\(600\) | −3.28508 | −0.134113 | ||||||||
\(601\) | −43.0250 | −1.75503 | −0.877514 | − | 0.479552i | \(-0.840799\pi\) | ||||
−0.877514 | + | 0.479552i | \(0.840799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.05153 | −0.164991 | ||||||||
\(604\) | 34.5385 | 1.40535 | ||||||||
\(605\) | 0.737118 | 0.0299681 | ||||||||
\(606\) | −1.15834 | −0.0470544 | ||||||||
\(607\) | −14.3595 | −0.582835 | −0.291417 | − | 0.956596i | \(-0.594127\pi\) | ||||
−0.291417 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(608\) | −5.72813 | −0.232306 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.86395 | −0.0754691 | ||||||||
\(611\) | −3.32185 | −0.134388 | ||||||||
\(612\) | 1.36535 | 0.0551909 | ||||||||
\(613\) | −38.9985 | −1.57513 | −0.787567 | − | 0.616229i | \(-0.788660\pi\) | ||||
−0.787567 | + | 0.616229i | \(0.788660\pi\) | |||||||
\(614\) | 4.87184 | 0.196612 | ||||||||
\(615\) | 6.88845 | 0.277769 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6511 | 0.509315 | 0.254658 | − | 0.967031i | \(-0.418037\pi\) | ||||
0.254658 | + | 0.967031i | \(0.418037\pi\) | |||||||
\(618\) | 2.60603 | 0.104830 | ||||||||
\(619\) | 11.3799 | 0.457397 | 0.228699 | − | 0.973497i | \(-0.426553\pi\) | ||||
0.228699 | + | 0.973497i | \(0.426553\pi\) | |||||||
\(620\) | 2.96833 | 0.119211 | ||||||||
\(621\) | −4.77956 | −0.191797 | ||||||||
\(622\) | −3.19726 | −0.128199 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.52637 | −0.221232 | ||||||||
\(625\) | 17.1451 | 0.685803 | ||||||||
\(626\) | 1.41759 | 0.0566583 | ||||||||
\(627\) | −2.62823 | −0.104961 | ||||||||
\(628\) | 26.1421 | 1.04318 | ||||||||
\(629\) | −5.13195 | −0.204624 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.50877 | −0.0998725 | −0.0499363 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499363 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(632\) | −0.0720398 | −0.00286559 | ||||||||
\(633\) | 5.86179 | 0.232985 | ||||||||
\(634\) | −3.11085 | −0.123548 | ||||||||
\(635\) | 1.07846 | 0.0427975 | ||||||||
\(636\) | −1.72427 | −0.0683719 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.0807587 | −0.00319727 | ||||||||
\(639\) | −7.42999 | −0.293926 | ||||||||
\(640\) | −4.19720 | −0.165909 | ||||||||
\(641\) | −41.1124 | −1.62384 | −0.811921 | − | 0.583768i | \(-0.801578\pi\) | ||||
−0.811921 | + | 0.583768i | \(0.801578\pi\) | |||||||
\(642\) | 1.48490 | 0.0586043 | ||||||||
\(643\) | 7.14757 | 0.281873 | 0.140936 | − | 0.990019i | \(-0.454989\pi\) | ||||
0.140936 | + | 0.990019i | \(0.454989\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0802642 | 0.00316040 | ||||||||
\(646\) | 0.339383 | 0.0133529 | ||||||||
\(647\) | 14.6680 | 0.576659 | 0.288330 | − | 0.957531i | \(-0.406900\pi\) | ||||
0.288330 | + | 0.957531i | \(0.406900\pi\) | |||||||
\(648\) | −0.737118 | −0.0289567 | ||||||||
\(649\) | 4.21136 | 0.165310 | ||||||||
\(650\) | −1.20673 | −0.0473320 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.1409 | 1.29790 | ||||||||
\(653\) | 42.7955 | 1.67472 | 0.837358 | − | 0.546655i | \(-0.184099\pi\) | ||||
0.837358 | + | 0.546655i | \(0.184099\pi\) | |||||||
\(654\) | 1.16488 | 0.0455503 | ||||||||
\(655\) | −7.18751 | −0.280839 | ||||||||
\(656\) | −35.4542 | −1.38425 | ||||||||
\(657\) | −3.52576 | −0.137553 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.3904 | −1.88502 | −0.942511 | − | 0.334176i | \(-0.891542\pi\) | ||||
−0.942511 | + | 0.334176i | \(0.891542\pi\) | |||||||
\(660\) | −1.44877 | −0.0563932 | ||||||||
\(661\) | 27.9721 | 1.08799 | 0.543993 | − | 0.839090i | \(-0.316912\pi\) | ||||
0.543993 | + | 0.839090i | \(0.316912\pi\) | |||||||
\(662\) | −2.25943 | −0.0878154 | ||||||||
\(663\) | 1.01190 | 0.0392991 | ||||||||
\(664\) | 12.0435 | 0.467380 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.37324 | 0.0532119 | ||||||||
\(667\) | 2.07650 | 0.0804025 | ||||||||
\(668\) | −22.9713 | −0.888785 | ||||||||
\(669\) | −4.26218 | −0.164785 | ||||||||
\(670\) | −0.555138 | −0.0214469 | ||||||||
\(671\) | 13.6035 | 0.525158 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.9653 | −1.42491 | −0.712453 | − | 0.701720i | \(-0.752416\pi\) | ||||
−0.712453 | + | 0.701720i | \(0.752416\pi\) | |||||||
\(674\) | 3.84103 | 0.147951 | ||||||||
\(675\) | 4.45666 | 0.171537 | ||||||||
\(676\) | 21.3804 | 0.822324 | ||||||||
\(677\) | 36.1775 | 1.39041 | 0.695206 | − | 0.718810i | \(-0.255313\pi\) | ||||
0.695206 | + | 0.718810i | \(0.255313\pi\) | |||||||
\(678\) | −2.19910 | −0.0844558 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.377447 | 0.0144745 | ||||||||
\(681\) | 13.9558 | 0.534786 | ||||||||
\(682\) | 0.380854 | 0.0145837 | ||||||||
\(683\) | −18.1417 | −0.694171 | −0.347086 | − | 0.937833i | \(-0.612829\pi\) | ||||
−0.347086 | + | 0.937833i | \(0.612829\pi\) | |||||||
\(684\) | 5.16564 | 0.197513 | ||||||||
\(685\) | 5.83109 | 0.222794 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.0804 | −0.766116 | ||||||||
\(688\) | −0.413112 | −0.0157497 | ||||||||
\(689\) | −1.27791 | −0.0486847 | ||||||||
\(690\) | −0.654893 | −0.0249314 | ||||||||
\(691\) | −19.3125 | −0.734683 | −0.367342 | − | 0.930086i | \(-0.619732\pi\) | ||||
−0.367342 | + | 0.930086i | \(0.619732\pi\) | |||||||
\(692\) | −36.3214 | −1.38073 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.55101 | 0.172754 | ||||||||
\(695\) | 1.94546 | 0.0737954 | ||||||||
\(696\) | 0.320244 | 0.0121388 | ||||||||
\(697\) | 6.49182 | 0.245895 | ||||||||
\(698\) | −0.834083 | −0.0315705 | ||||||||
\(699\) | 12.6211 | 0.477374 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8768 | 1.54389 | 0.771947 | − | 0.635687i | \(-0.219283\pi\) | ||||
0.771947 | + | 0.635687i | \(0.219283\pi\) | |||||||
\(702\) | −0.270771 | −0.0102196 | ||||||||
\(703\) | −19.4162 | −0.732295 | ||||||||
\(704\) | 7.18262 | 0.270705 | ||||||||
\(705\) | 1.68097 | 0.0633090 | ||||||||
\(706\) | −5.12359 | −0.192829 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.27719 | −0.311076 | ||||||||
\(709\) | 29.7385 | 1.11685 | 0.558427 | − | 0.829554i | \(-0.311405\pi\) | ||||
0.558427 | + | 0.829554i | \(0.311405\pi\) | |||||||
\(710\) | −1.01805 | −0.0382069 | ||||||||
\(711\) | 0.0977317 | 0.00366522 | ||||||||
\(712\) | 4.21124 | 0.157823 | ||||||||
\(713\) | −9.79268 | −0.366739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07373 | −0.0401552 | ||||||||
\(716\) | 13.3852 | 0.500229 | ||||||||
\(717\) | −20.4384 | −0.763285 | ||||||||
\(718\) | −5.56304 | −0.207611 | ||||||||
\(719\) | 1.47174 | 0.0548865 | 0.0274432 | − | 0.999623i | \(-0.491263\pi\) | ||||
0.0274432 | + | 0.999623i | \(0.491263\pi\) | |||||||
\(720\) | 2.79653 | 0.104221 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.24780 | −0.0836545 | ||||||||
\(723\) | 4.97138 | 0.184887 | ||||||||
\(724\) | −13.6349 | −0.506738 | ||||||||
\(725\) | −1.93621 | −0.0719092 | ||||||||
\(726\) | −0.185885 | −0.00689885 | ||||||||
\(727\) | −35.9124 | −1.33192 | −0.665958 | − | 0.745989i | \(-0.731977\pi\) | ||||
−0.665958 | + | 0.745989i | \(0.731977\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.483098 | −0.0178803 | ||||||||
\(731\) | 0.0756426 | 0.00279774 | ||||||||
\(732\) | −26.7370 | −0.988228 | ||||||||
\(733\) | −6.64049 | −0.245272 | −0.122636 | − | 0.992452i | \(-0.539135\pi\) | ||||
−0.122636 | + | 0.992452i | \(0.539135\pi\) | |||||||
\(734\) | 2.39386 | 0.0883590 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.4169 | 0.383971 | ||||||||
\(737\) | 4.05153 | 0.149240 | ||||||||
\(738\) | −1.73712 | −0.0639442 | ||||||||
\(739\) | 37.9825 | 1.39721 | 0.698604 | − | 0.715509i | \(-0.253805\pi\) | ||||
0.698604 | + | 0.715509i | \(0.253805\pi\) | |||||||
\(740\) | −10.7028 | −0.393444 | ||||||||
\(741\) | 3.82843 | 0.140641 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.4601 | 1.00741 | 0.503707 | − | 0.863875i | \(-0.331969\pi\) | ||||
0.503707 | + | 0.863875i | \(0.331969\pi\) | |||||||
\(744\) | −1.51026 | −0.0553687 | ||||||||
\(745\) | 11.6873 | 0.428189 | ||||||||
\(746\) | −3.81824 | −0.139796 | ||||||||
\(747\) | −16.3387 | −0.597801 | ||||||||
\(748\) | −1.36535 | −0.0499221 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.29575 | 0.0473140 | ||||||||
\(751\) | 11.3194 | 0.413052 | 0.206526 | − | 0.978441i | \(-0.433784\pi\) | ||||
0.206526 | + | 0.978441i | \(0.433784\pi\) | |||||||
\(752\) | −8.65178 | −0.315498 | ||||||||
\(753\) | 5.12467 | 0.186753 | ||||||||
\(754\) | 0.117638 | 0.00428411 | ||||||||
\(755\) | −12.9533 | −0.471417 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.58955 | −0.203156 | −0.101578 | − | 0.994828i | \(-0.532389\pi\) | ||||
−0.101578 | + | 0.994828i | \(0.532389\pi\) | |||||||
\(758\) | −5.92902 | −0.215352 | ||||||||
\(759\) | 4.77956 | 0.173487 | ||||||||
\(760\) | 1.42803 | 0.0518001 | ||||||||
\(761\) | −34.8768 | −1.26428 | −0.632141 | − | 0.774854i | \(-0.717824\pi\) | ||||
−0.632141 | + | 0.774854i | \(0.717824\pi\) | |||||||
\(762\) | −0.271965 | −0.00985225 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −32.7694 | −1.18556 | ||||||||
\(765\) | −0.512058 | −0.0185135 | ||||||||
\(766\) | 0.778033 | 0.0281115 | ||||||||
\(767\) | −6.13450 | −0.221504 | ||||||||
\(768\) | −13.3068 | −0.480167 | ||||||||
\(769\) | −25.1994 | −0.908713 | −0.454357 | − | 0.890820i | \(-0.650131\pi\) | ||||
−0.454357 | + | 0.890820i | \(0.650131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.25184 | −0.0810979 | ||||||||
\(772\) | 52.0905 | 1.87478 | ||||||||
\(773\) | −44.1959 | −1.58962 | −0.794808 | − | 0.606861i | \(-0.792428\pi\) | ||||
−0.794808 | + | 0.606861i | \(0.792428\pi\) | |||||||
\(774\) | −0.0202409 | −0.000727544 0 | ||||||||
\(775\) | 9.13109 | 0.327998 | ||||||||
\(776\) | −3.79045 | −0.136069 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.12272 | 0.147807 | ||||||||
\(779\) | 24.5611 | 0.879992 | ||||||||
\(780\) | 2.11036 | 0.0755629 | ||||||||
\(781\) | 7.42999 | 0.265866 | ||||||||
\(782\) | −0.617185 | −0.0220705 | ||||||||
\(783\) | −0.434454 | −0.0155261 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.80431 | −0.349931 | ||||||||
\(786\) | 1.81254 | 0.0646510 | ||||||||
\(787\) | −13.0628 | −0.465638 | −0.232819 | − | 0.972520i | \(-0.574795\pi\) | ||||
−0.232819 | + | 0.972520i | \(0.574795\pi\) | |||||||
\(788\) | −31.9062 | −1.13661 | ||||||||
\(789\) | −12.1018 | −0.430834 | ||||||||
\(790\) | 0.0133911 | 0.000476436 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.737118 | 0.0261924 | ||||||||
\(793\) | −19.8157 | −0.703675 | ||||||||
\(794\) | −0.256032 | −0.00908623 | ||||||||
\(795\) | 0.646669 | 0.0229350 | ||||||||
\(796\) | 0.391312 | 0.0138697 | ||||||||
\(797\) | 32.9154 | 1.16592 | 0.582962 | − | 0.812500i | \(-0.301894\pi\) | ||||
0.582962 | + | 0.812500i | \(0.301894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.58418 | 0.0560443 | ||||||||
\(800\) | −9.71312 | −0.343410 | ||||||||
\(801\) | −5.71312 | −0.201863 | ||||||||
\(802\) | 3.56260 | 0.125800 | ||||||||
\(803\) | 3.52576 | 0.124421 | ||||||||
\(804\) | −7.96306 | −0.280835 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.554774 | −0.0195411 | ||||||||
\(807\) | −30.7974 | −1.08412 | ||||||||
\(808\) | −4.59334 | −0.161593 | ||||||||
\(809\) | 28.1035 | 0.988066 | 0.494033 | − | 0.869443i | \(-0.335522\pi\) | ||||
0.494033 | + | 0.869443i | \(0.335522\pi\) | |||||||
\(810\) | 0.137020 | 0.00481437 | ||||||||
\(811\) | −37.4361 | −1.31456 | −0.657280 | − | 0.753647i | \(-0.728293\pi\) | ||||
−0.657280 | + | 0.753647i | \(0.728293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.29514 | −0.0454225 | ||||||||
\(814\) | −1.37324 | −0.0481319 | ||||||||
\(815\) | −12.4291 | −0.435374 | ||||||||
\(816\) | 2.63551 | 0.0922614 | ||||||||
\(817\) | 0.286186 | 0.0100124 | ||||||||
\(818\) | 5.48176 | 0.191665 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5389 | 0.472798 | ||||||||
\(821\) | 10.1890 | 0.355600 | 0.177800 | − | 0.984067i | \(-0.443102\pi\) | ||||
0.177800 | + | 0.984067i | \(0.443102\pi\) | |||||||
\(822\) | −1.47047 | −0.0512887 | ||||||||
\(823\) | −3.80372 | −0.132589 | −0.0662947 | − | 0.997800i | \(-0.521118\pi\) | ||||
−0.0662947 | + | 0.997800i | \(0.521118\pi\) | |||||||
\(824\) | 10.3341 | 0.360004 | ||||||||
\(825\) | −4.45666 | −0.155161 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.3768 | −1.47359 | −0.736793 | − | 0.676119i | \(-0.763661\pi\) | ||||
−0.736793 | + | 0.676119i | \(0.763661\pi\) | |||||||
\(828\) | −9.39397 | −0.326463 | ||||||||
\(829\) | 44.6643 | 1.55126 | 0.775628 | − | 0.631191i | \(-0.217434\pi\) | ||||
0.775628 | + | 0.631191i | \(0.217434\pi\) | |||||||
\(830\) | −2.23872 | −0.0777071 | ||||||||
\(831\) | −10.9680 | −0.380476 | ||||||||
\(832\) | −10.4626 | −0.362726 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.490602 | −0.0169882 | ||||||||
\(835\) | 8.61511 | 0.298138 | ||||||||
\(836\) | −5.16564 | −0.178658 | ||||||||
\(837\) | 2.04887 | 0.0708192 | ||||||||
\(838\) | 5.35399 | 0.184950 | ||||||||
\(839\) | −35.5777 | −1.22828 | −0.614140 | − | 0.789197i | \(-0.710497\pi\) | ||||
−0.614140 | + | 0.789197i | \(0.710497\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8112 | −0.993491 | ||||||||
\(842\) | 4.06070 | 0.139941 | ||||||||
\(843\) | −27.6386 | −0.951923 | ||||||||
\(844\) | 11.5210 | 0.396570 | ||||||||
\(845\) | −8.01849 | −0.275844 | ||||||||
\(846\) | −0.423904 | −0.0145741 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.32834 | −0.114296 | ||||||||
\(849\) | 31.1516 | 1.06912 | ||||||||
\(850\) | 0.575488 | 0.0197391 | ||||||||
\(851\) | 35.3092 | 1.21039 | ||||||||
\(852\) | −14.6033 | −0.500299 | ||||||||
\(853\) | −8.32083 | −0.284900 | −0.142450 | − | 0.989802i | \(-0.545498\pi\) | ||||
−0.142450 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.93732 | −0.0662548 | ||||||||
\(856\) | 5.88829 | 0.201258 | ||||||||
\(857\) | 26.5648 | 0.907438 | 0.453719 | − | 0.891145i | \(-0.350097\pi\) | ||||
0.453719 | + | 0.891145i | \(0.350097\pi\) | |||||||
\(858\) | 0.270771 | 0.00924397 | ||||||||
\(859\) | −21.0501 | −0.718221 | −0.359111 | − | 0.933295i | \(-0.616920\pi\) | ||||
−0.359111 | + | 0.933295i | \(0.616920\pi\) | |||||||
\(860\) | 0.157755 | 0.00537940 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.10245 | 0.0375494 | ||||||||
\(863\) | 41.7854 | 1.42239 | 0.711197 | − | 0.702993i | \(-0.248154\pi\) | ||||
0.711197 | + | 0.702993i | \(0.248154\pi\) | |||||||
\(864\) | −2.17946 | −0.0741468 | ||||||||
\(865\) | 13.6219 | 0.463159 | ||||||||
\(866\) | −2.29991 | −0.0781543 | ||||||||
\(867\) | 16.5174 | 0.560961 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.0977317 | −0.00331532 | ||||||||
\(870\) | −0.0595287 | −0.00201821 | ||||||||
\(871\) | −5.90168 | −0.199971 | ||||||||
\(872\) | 4.61926 | 0.156428 | ||||||||
\(873\) | 5.14225 | 0.174039 | ||||||||
\(874\) | −2.33505 | −0.0789843 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.92970 | −0.234133 | ||||||||
\(877\) | 18.5386 | 0.626004 | 0.313002 | − | 0.949752i | \(-0.398665\pi\) | ||||
0.313002 | + | 0.949752i | \(0.398665\pi\) | |||||||
\(878\) | −2.84594 | −0.0960458 | ||||||||
\(879\) | −5.88942 | −0.198645 | ||||||||
\(880\) | −2.79653 | −0.0942712 | ||||||||
\(881\) | 41.9600 | 1.41367 | 0.706833 | − | 0.707380i | \(-0.250123\pi\) | ||||
0.706833 | + | 0.707380i | \(0.250123\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.7832 | 0.497495 | 0.248747 | − | 0.968568i | \(-0.419981\pi\) | ||||
0.248747 | + | 0.968568i | \(0.419981\pi\) | |||||||
\(884\) | 1.98884 | 0.0668920 | ||||||||
\(885\) | 3.10427 | 0.104349 | ||||||||
\(886\) | −4.47119 | −0.150213 | ||||||||
\(887\) | −55.1139 | −1.85055 | −0.925273 | − | 0.379303i | \(-0.876164\pi\) | ||||
−0.925273 | + | 0.379303i | \(0.876164\pi\) | |||||||
\(888\) | 5.44550 | 0.182739 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.782808 | −0.0262398 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −8.37709 | −0.280486 | ||||||||
\(893\) | 5.99358 | 0.200567 | ||||||||
\(894\) | −2.94728 | −0.0985718 | ||||||||
\(895\) | −5.01997 | −0.167799 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.96218 | −0.232460 | ||||||||
\(898\) | −2.03446 | −0.0678909 | ||||||||
\(899\) | −0.890139 | −0.0296878 | ||||||||
\(900\) | 8.75932 | 0.291977 | ||||||||
\(901\) | 0.609434 | 0.0203032 | ||||||||
\(902\) | 1.73712 | 0.0578397 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.72040 | −0.290036 | ||||||||
\(905\) | 5.11362 | 0.169983 | ||||||||
\(906\) | 3.26653 | 0.108523 | ||||||||
\(907\) | 27.0841 | 0.899312 | 0.449656 | − | 0.893202i | \(-0.351547\pi\) | ||||
0.449656 | + | 0.893202i | \(0.351547\pi\) | |||||||
\(908\) | 27.4293 | 0.910273 | ||||||||
\(909\) | 6.23148 | 0.206685 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.2161 | −0.636659 | −0.318330 | − | 0.947980i | \(-0.603122\pi\) | ||||
−0.318330 | + | 0.947980i | \(0.603122\pi\) | |||||||
\(912\) | 9.97117 | 0.330178 | ||||||||
\(913\) | 16.3387 | 0.540732 | ||||||||
\(914\) | −5.43752 | −0.179857 | ||||||||
\(915\) | 10.0274 | 0.331496 | ||||||||
\(916\) | −39.4670 | −1.30403 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.129130 | 0.00426193 | ||||||||
\(919\) | −18.5892 | −0.613201 | −0.306600 | − | 0.951838i | \(-0.599192\pi\) | ||||
−0.306600 | + | 0.951838i | \(0.599192\pi\) | |||||||
\(920\) | −2.59694 | −0.0856187 | ||||||||
\(921\) | −26.2089 | −0.863611 | ||||||||
\(922\) | −2.57501 | −0.0848036 | ||||||||
\(923\) | −10.8229 | −0.356242 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.9238 | −1.08253 | ||||||||
\(926\) | 3.22610 | 0.106016 | ||||||||
\(927\) | −14.0195 | −0.460462 | ||||||||
\(928\) | 0.946877 | 0.0310828 | ||||||||
\(929\) | 12.5848 | 0.412895 | 0.206448 | − | 0.978458i | \(-0.433810\pi\) | ||||
0.206448 | + | 0.978458i | \(0.433810\pi\) | |||||||
\(930\) | 0.280735 | 0.00920565 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 24.8061 | 0.812551 | ||||||||
\(933\) | 17.2002 | 0.563109 | ||||||||
\(934\) | 2.05867 | 0.0673617 | ||||||||
\(935\) | 0.512058 | 0.0167461 | ||||||||
\(936\) | −1.07373 | −0.0350959 | ||||||||
\(937\) | −22.7111 | −0.741940 | −0.370970 | − | 0.928645i | \(-0.620975\pi\) | ||||
−0.370970 | + | 0.928645i | \(0.620975\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.62616 | −0.248870 | ||||||||
\(940\) | 3.30386 | 0.107760 | ||||||||
\(941\) | −37.8880 | −1.23511 | −0.617557 | − | 0.786526i | \(-0.711878\pi\) | ||||
−0.617557 | + | 0.786526i | \(0.711878\pi\) | |||||||
\(942\) | 2.47244 | 0.0805563 | ||||||||
\(943\) | −44.6655 | −1.45451 | ||||||||
\(944\) | −15.9774 | −0.520018 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0202409 | 0.000658088 0 | ||||||||
\(947\) | −25.1364 | −0.816824 | −0.408412 | − | 0.912798i | \(-0.633917\pi\) | ||||
−0.408412 | + | 0.912798i | \(0.633917\pi\) | |||||||
\(948\) | 0.192086 | 0.00623868 | ||||||||
\(949\) | −5.13583 | −0.166716 | ||||||||
\(950\) | 2.17730 | 0.0706408 | ||||||||
\(951\) | 16.7353 | 0.542680 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.35610 | −0.205894 | −0.102947 | − | 0.994687i | \(-0.532827\pi\) | ||||
−0.102947 | + | 0.994687i | \(0.532827\pi\) | |||||||
\(954\) | −0.163076 | −0.00527978 | ||||||||
\(955\) | 12.2898 | 0.397688 | ||||||||
\(956\) | −40.1705 | −1.29921 | ||||||||
\(957\) | 0.434454 | 0.0140439 | ||||||||
\(958\) | −6.54285 | −0.211390 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.29444 | 0.170877 | ||||||||
\(961\) | −26.8021 | −0.864585 | ||||||||
\(962\) | 2.00033 | 0.0644934 | ||||||||
\(963\) | −7.98826 | −0.257418 | ||||||||
\(964\) | 9.77097 | 0.314702 | ||||||||
\(965\) | −19.5359 | −0.628884 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.9034 | −0.897313 | −0.448657 | − | 0.893704i | \(-0.648097\pi\) | ||||
−0.448657 | + | 0.893704i | \(0.648097\pi\) | |||||||
\(968\) | −0.737118 | −0.0236919 | ||||||||
\(969\) | −1.82577 | −0.0586521 | ||||||||
\(970\) | 0.704588 | 0.0226230 | ||||||||
\(971\) | −1.69091 | −0.0542640 | −0.0271320 | − | 0.999632i | \(-0.508637\pi\) | ||||
−0.0271320 | + | 0.999632i | \(0.508637\pi\) | |||||||
\(972\) | 1.96545 | 0.0630417 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.30153 | −0.0417038 | ||||||||
\(975\) | 6.49182 | 0.207905 | ||||||||
\(976\) | −51.6101 | −1.65200 | ||||||||
\(977\) | −41.7981 | −1.33724 | −0.668620 | − | 0.743604i | \(-0.733115\pi\) | ||||
−0.668620 | + | 0.743604i | \(0.733115\pi\) | |||||||
\(978\) | 3.13436 | 0.100226 | ||||||||
\(979\) | 5.71312 | 0.182592 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.26664 | −0.200079 | ||||||||
\(982\) | 2.71196 | 0.0865422 | ||||||||
\(983\) | −44.7004 | −1.42572 | −0.712861 | − | 0.701305i | \(-0.752601\pi\) | ||||
−0.712861 | + | 0.701305i | \(0.752601\pi\) | |||||||
\(984\) | −6.88845 | −0.219596 | ||||||||
\(985\) | 11.9661 | 0.381270 | ||||||||
\(986\) | −0.0561011 | −0.00178662 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.52457 | 0.239388 | ||||||||
\(989\) | −0.520442 | −0.0165491 | ||||||||
\(990\) | −0.137020 | −0.00435477 | ||||||||
\(991\) | 26.0860 | 0.828650 | 0.414325 | − | 0.910129i | \(-0.364018\pi\) | ||||
0.414325 | + | 0.910129i | \(0.364018\pi\) | |||||||
\(992\) | −4.46543 | −0.141777 | ||||||||
\(993\) | 12.1550 | 0.385727 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.146757 | −0.00465252 | ||||||||
\(996\) | −32.1128 | −1.01753 | ||||||||
\(997\) | −17.2538 | −0.546435 | −0.273217 | − | 0.961952i | \(-0.588088\pi\) | ||||
−0.273217 | + | 0.961952i | \(0.588088\pi\) | |||||||
\(998\) | −3.82403 | −0.121047 | ||||||||
\(999\) | −7.38755 | −0.233732 |
(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 | 1617.2.a.w.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 4851.2.a.bs.1.3 | 4 | |||
7.6 | odd | 2 | 1617.2.a.y.1.2 | yes | 4 | ||
21.20 | even | 2 | 4851.2.a.br.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1617.2.a.w.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1617.2.a.y.1.2 | yes | 4 | 7.6 | odd | 2 | ||
4851.2.a.br.1.3 | 4 | 21.20 | even | 2 | |||
4851.2.a.bs.1.3 | 4 | 3.2 | odd | 2 |