Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 \) |
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 | 1.7 | ||
Root | \(2.19791\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.19791 | 1.55416 | 0.777080 | − | 0.629402i | \(-0.216700\pi\) | ||||
0.777080 | + | 0.629402i | \(0.216700\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.83083 | 1.41541 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.19791 | −0.897295 | ||||||||
\(7\) | −1.05086 | −0.397189 | −0.198595 | − | 0.980082i | \(-0.563638\pi\) | ||||
−0.198595 | + | 0.980082i | \(0.563638\pi\) | |||||||
\(8\) | 1.82609 | 0.645619 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.22580 | −0.972614 | −0.486307 | − | 0.873788i | \(-0.661656\pi\) | ||||
−0.486307 | + | 0.873788i | \(0.661656\pi\) | |||||||
\(12\) | −2.83083 | −0.817189 | ||||||||
\(13\) | −2.58899 | −0.718056 | −0.359028 | − | 0.933327i | \(-0.616892\pi\) | ||||
−0.359028 | + | 0.933327i | \(0.616892\pi\) | |||||||
\(14\) | −2.30971 | −0.617295 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.64807 | −0.412018 | ||||||||
\(17\) | 7.50374 | 1.81992 | 0.909962 | − | 0.414691i | \(-0.136110\pi\) | ||||
0.909962 | + | 0.414691i | \(0.136110\pi\) | |||||||
\(18\) | 2.19791 | 0.518053 | ||||||||
\(19\) | 1.70135 | 0.390316 | 0.195158 | − | 0.980772i | \(-0.437478\pi\) | ||||
0.195158 | + | 0.980772i | \(0.437478\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.05086 | 0.229317 | ||||||||
\(22\) | −7.09002 | −1.51160 | ||||||||
\(23\) | 2.21428 | 0.461710 | 0.230855 | − | 0.972988i | \(-0.425848\pi\) | ||||
0.230855 | + | 0.972988i | \(0.425848\pi\) | |||||||
\(24\) | −1.82609 | −0.372748 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.69038 | −1.11597 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.97481 | −0.562187 | ||||||||
\(29\) | 6.74234 | 1.25202 | 0.626010 | − | 0.779815i | \(-0.284687\pi\) | ||||
0.626010 | + | 0.779815i | \(0.284687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.8019 | 1.94008 | 0.970041 | − | 0.242942i | \(-0.0781123\pi\) | ||||
0.970041 | + | 0.242942i | \(0.0781123\pi\) | |||||||
\(32\) | −7.27449 | −1.28596 | ||||||||
\(33\) | 3.22580 | 0.561539 | ||||||||
\(34\) | 16.4926 | 2.82845 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.83083 | 0.471804 | ||||||||
\(37\) | 11.7806 | 1.93672 | 0.968361 | − | 0.249552i | \(-0.0802835\pi\) | ||||
0.968361 | + | 0.249552i | \(0.0802835\pi\) | |||||||
\(38\) | 3.73942 | 0.606614 | ||||||||
\(39\) | 2.58899 | 0.414570 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.81601 | −0.908308 | −0.454154 | − | 0.890923i | \(-0.650058\pi\) | ||||
−0.454154 | + | 0.890923i | \(0.650058\pi\) | |||||||
\(42\) | 2.30971 | 0.356396 | ||||||||
\(43\) | 3.39497 | 0.517728 | 0.258864 | − | 0.965914i | \(-0.416652\pi\) | ||||
0.258864 | + | 0.965914i | \(0.416652\pi\) | |||||||
\(44\) | −9.13167 | −1.37665 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.86680 | 0.717571 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 1.64807 | 0.237879 | ||||||||
\(49\) | −5.89569 | −0.842241 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.50374 | −1.05073 | ||||||||
\(52\) | −7.32898 | −1.01635 | ||||||||
\(53\) | 11.1690 | 1.53418 | 0.767090 | − | 0.641539i | \(-0.221704\pi\) | ||||
0.767090 | + | 0.641539i | \(0.221704\pi\) | |||||||
\(54\) | −2.19791 | −0.299098 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.91897 | −0.256433 | ||||||||
\(57\) | −1.70135 | −0.225349 | ||||||||
\(58\) | 14.8191 | 1.94584 | ||||||||
\(59\) | 12.3261 | 1.60472 | 0.802361 | − | 0.596839i | \(-0.203577\pi\) | ||||
0.802361 | + | 0.596839i | \(0.203577\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.55166 | −0.838854 | −0.419427 | − | 0.907789i | \(-0.637769\pi\) | ||||
−0.419427 | + | 0.907789i | \(0.637769\pi\) | |||||||
\(62\) | 23.7417 | 3.01520 | ||||||||
\(63\) | −1.05086 | −0.132396 | ||||||||
\(64\) | −12.6926 | −1.58657 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.09002 | 0.872722 | ||||||||
\(67\) | −0.750116 | −0.0916412 | −0.0458206 | − | 0.998950i | \(-0.514590\pi\) | ||||
−0.0458206 | + | 0.998950i | \(0.514590\pi\) | |||||||
\(68\) | 21.2418 | 2.57595 | ||||||||
\(69\) | −2.21428 | −0.266568 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.09231 | 0.248311 | 0.124156 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124156 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(72\) | 1.82609 | 0.215206 | ||||||||
\(73\) | −4.80219 | −0.562054 | −0.281027 | − | 0.959700i | \(-0.590675\pi\) | ||||
−0.281027 | + | 0.959700i | \(0.590675\pi\) | |||||||
\(74\) | 25.8928 | 3.00998 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.81623 | 0.552459 | ||||||||
\(77\) | 3.38987 | 0.386312 | ||||||||
\(78\) | 5.69038 | 0.644308 | ||||||||
\(79\) | 6.59991 | 0.742548 | 0.371274 | − | 0.928523i | \(-0.378921\pi\) | ||||
0.371274 | + | 0.928523i | \(0.378921\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.7831 | −1.41166 | ||||||||
\(83\) | 15.6214 | 1.71467 | 0.857334 | − | 0.514761i | \(-0.172119\pi\) | ||||
0.857334 | + | 0.514761i | \(0.172119\pi\) | |||||||
\(84\) | 2.97481 | 0.324579 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.46185 | 0.804632 | ||||||||
\(87\) | −6.74234 | −0.722854 | ||||||||
\(88\) | −5.89058 | −0.627938 | ||||||||
\(89\) | −15.4144 | −1.63392 | −0.816960 | − | 0.576694i | \(-0.804343\pi\) | ||||
−0.816960 | + | 0.576694i | \(0.804343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.72067 | 0.285204 | ||||||||
\(92\) | 6.26825 | 0.653510 | ||||||||
\(93\) | −10.8019 | −1.12011 | ||||||||
\(94\) | 2.19791 | 0.226698 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.27449 | 0.742450 | ||||||||
\(97\) | −11.6829 | −1.18622 | −0.593109 | − | 0.805122i | \(-0.702100\pi\) | ||||
−0.593109 | + | 0.805122i | \(0.702100\pi\) | |||||||
\(98\) | −12.9582 | −1.30898 | ||||||||
\(99\) | −3.22580 | −0.324205 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.43631 | −0.341925 | −0.170963 | − | 0.985278i | \(-0.554688\pi\) | ||||
−0.170963 | + | 0.985278i | \(0.554688\pi\) | |||||||
\(102\) | −16.4926 | −1.63301 | ||||||||
\(103\) | 12.4894 | 1.23061 | 0.615307 | − | 0.788288i | \(-0.289032\pi\) | ||||
0.615307 | + | 0.788288i | \(0.289032\pi\) | |||||||
\(104\) | −4.72772 | −0.463591 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.5485 | 2.38436 | ||||||||
\(107\) | −20.2622 | −1.95882 | −0.979410 | − | 0.201879i | \(-0.935295\pi\) | ||||
−0.979410 | + | 0.201879i | \(0.935295\pi\) | |||||||
\(108\) | −2.83083 | −0.272396 | ||||||||
\(109\) | −12.9693 | −1.24224 | −0.621118 | − | 0.783717i | \(-0.713321\pi\) | ||||
−0.621118 | + | 0.783717i | \(0.713321\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.7806 | −1.11817 | ||||||||
\(112\) | 1.73190 | 0.163649 | ||||||||
\(113\) | 14.6725 | 1.38027 | 0.690136 | − | 0.723680i | \(-0.257551\pi\) | ||||
0.690136 | + | 0.723680i | \(0.257551\pi\) | |||||||
\(114\) | −3.73942 | −0.350229 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 19.0864 | 1.77213 | ||||||||
\(117\) | −2.58899 | −0.239352 | ||||||||
\(118\) | 27.0917 | 2.49400 | ||||||||
\(119\) | −7.88541 | −0.722854 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.594237 | −0.0540216 | ||||||||
\(122\) | −14.4000 | −1.30371 | ||||||||
\(123\) | 5.81601 | 0.524412 | ||||||||
\(124\) | 30.5784 | 2.74602 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.30971 | −0.205765 | ||||||||
\(127\) | 14.6756 | 1.30225 | 0.651123 | − | 0.758972i | \(-0.274298\pi\) | ||||
0.651123 | + | 0.758972i | \(0.274298\pi\) | |||||||
\(128\) | −13.3482 | −1.17982 | ||||||||
\(129\) | −3.39497 | −0.298910 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1152 | −1.32062 | −0.660309 | − | 0.750994i | \(-0.729575\pi\) | ||||
−0.660309 | + | 0.750994i | \(0.729575\pi\) | |||||||
\(132\) | 9.13167 | 0.794810 | ||||||||
\(133\) | −1.78789 | −0.155029 | ||||||||
\(134\) | −1.64869 | −0.142425 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.7025 | 1.17498 | ||||||||
\(137\) | −17.6256 | −1.50585 | −0.752927 | − | 0.658104i | \(-0.771359\pi\) | ||||
−0.752927 | + | 0.658104i | \(0.771359\pi\) | |||||||
\(138\) | −4.86680 | −0.414290 | ||||||||
\(139\) | 9.44352 | 0.800989 | 0.400495 | − | 0.916299i | \(-0.368838\pi\) | ||||
0.400495 | + | 0.916299i | \(0.368838\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 4.59871 | 0.385916 | ||||||||
\(143\) | 8.35155 | 0.698392 | ||||||||
\(144\) | −1.64807 | −0.137339 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.5548 | −0.873521 | ||||||||
\(147\) | 5.89569 | 0.486268 | ||||||||
\(148\) | 33.3489 | 2.74126 | ||||||||
\(149\) | 5.63097 | 0.461307 | 0.230653 | − | 0.973036i | \(-0.425914\pi\) | ||||
0.230653 | + | 0.973036i | \(0.425914\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8349 | 1.12587 | 0.562933 | − | 0.826503i | \(-0.309673\pi\) | ||||
0.562933 | + | 0.826503i | \(0.309673\pi\) | |||||||
\(152\) | 3.10681 | 0.251996 | ||||||||
\(153\) | 7.50374 | 0.606641 | ||||||||
\(154\) | 7.45065 | 0.600390 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.32898 | 0.586788 | ||||||||
\(157\) | 4.25611 | 0.339675 | 0.169837 | − | 0.985472i | \(-0.445676\pi\) | ||||
0.169837 | + | 0.985472i | \(0.445676\pi\) | |||||||
\(158\) | 14.5060 | 1.15404 | ||||||||
\(159\) | −11.1690 | −0.885760 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.32691 | −0.183386 | ||||||||
\(162\) | 2.19791 | 0.172684 | ||||||||
\(163\) | −7.80011 | −0.610952 | −0.305476 | − | 0.952200i | \(-0.598816\pi\) | ||||
−0.305476 | + | 0.952200i | \(0.598816\pi\) | |||||||
\(164\) | −16.4641 | −1.28563 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 34.3344 | 2.66487 | ||||||||
\(167\) | 11.0275 | 0.853336 | 0.426668 | − | 0.904408i | \(-0.359687\pi\) | ||||
0.426668 | + | 0.904408i | \(0.359687\pi\) | |||||||
\(168\) | 1.91897 | 0.148052 | ||||||||
\(169\) | −6.29713 | −0.484395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.70135 | 0.130105 | ||||||||
\(172\) | 9.61057 | 0.732799 | ||||||||
\(173\) | −3.88852 | −0.295639 | −0.147819 | − | 0.989014i | \(-0.547225\pi\) | ||||
−0.147819 | + | 0.989014i | \(0.547225\pi\) | |||||||
\(174\) | −14.8191 | −1.12343 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.31635 | 0.400735 | ||||||||
\(177\) | −12.3261 | −0.926487 | ||||||||
\(178\) | −33.8795 | −2.53937 | ||||||||
\(179\) | 0.395968 | 0.0295961 | 0.0147980 | − | 0.999891i | \(-0.495289\pi\) | ||||
0.0147980 | + | 0.999891i | \(0.495289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9286 | −1.03530 | −0.517651 | − | 0.855592i | \(-0.673194\pi\) | ||||
−0.517651 | + | 0.855592i | \(0.673194\pi\) | |||||||
\(182\) | 5.97981 | 0.443253 | ||||||||
\(183\) | 6.55166 | 0.484312 | ||||||||
\(184\) | 4.04347 | 0.298089 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −23.7417 | −1.74083 | ||||||||
\(187\) | −24.2055 | −1.77008 | ||||||||
\(188\) | 2.83083 | 0.206459 | ||||||||
\(189\) | 1.05086 | 0.0764391 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.94141 | −0.574620 | −0.287310 | − | 0.957838i | \(-0.592761\pi\) | ||||
−0.287310 | + | 0.957838i | \(0.592761\pi\) | |||||||
\(192\) | 12.6926 | 0.916007 | ||||||||
\(193\) | −12.8812 | −0.927211 | −0.463606 | − | 0.886042i | \(-0.653445\pi\) | ||||
−0.463606 | + | 0.886042i | \(0.653445\pi\) | |||||||
\(194\) | −25.6780 | −1.84357 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.6897 | −1.19212 | ||||||||
\(197\) | 8.58344 | 0.611545 | 0.305772 | − | 0.952105i | \(-0.401085\pi\) | ||||
0.305772 | + | 0.952105i | \(0.401085\pi\) | |||||||
\(198\) | −7.09002 | −0.503866 | ||||||||
\(199\) | 11.9505 | 0.847149 | 0.423574 | − | 0.905861i | \(-0.360775\pi\) | ||||
0.423574 | + | 0.905861i | \(0.360775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.750116 | 0.0529091 | ||||||||
\(202\) | −7.55271 | −0.531407 | ||||||||
\(203\) | −7.08528 | −0.497289 | ||||||||
\(204\) | −21.2418 | −1.48722 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 27.4506 | 1.91257 | ||||||||
\(207\) | 2.21428 | 0.153903 | ||||||||
\(208\) | 4.26684 | 0.295852 | ||||||||
\(209\) | −5.48821 | −0.379627 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.97104 | 0.411063 | 0.205532 | − | 0.978650i | \(-0.434108\pi\) | ||||
0.205532 | + | 0.978650i | \(0.434108\pi\) | |||||||
\(212\) | 31.6175 | 2.17150 | ||||||||
\(213\) | −2.09231 | −0.143363 | ||||||||
\(214\) | −44.5346 | −3.04432 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.82609 | −0.124249 | ||||||||
\(217\) | −11.3513 | −0.770579 | ||||||||
\(218\) | −28.5055 | −1.93063 | ||||||||
\(219\) | 4.80219 | 0.324502 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.4271 | −1.30681 | ||||||||
\(222\) | −25.8928 | −1.73781 | ||||||||
\(223\) | 12.1892 | 0.816247 | 0.408124 | − | 0.912927i | \(-0.366183\pi\) | ||||
0.408124 | + | 0.912927i | \(0.366183\pi\) | |||||||
\(224\) | 7.64450 | 0.510770 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.2489 | 2.14516 | ||||||||
\(227\) | 25.3158 | 1.68027 | 0.840136 | − | 0.542376i | \(-0.182475\pi\) | ||||
0.840136 | + | 0.542376i | \(0.182475\pi\) | |||||||
\(228\) | −4.81623 | −0.318962 | ||||||||
\(229\) | 13.1238 | 0.867247 | 0.433623 | − | 0.901094i | \(-0.357235\pi\) | ||||
0.433623 | + | 0.901094i | \(0.357235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.38987 | −0.223037 | ||||||||
\(232\) | 12.3121 | 0.808328 | ||||||||
\(233\) | −20.8072 | −1.36313 | −0.681563 | − | 0.731759i | \(-0.738700\pi\) | ||||
−0.681563 | + | 0.731759i | \(0.738700\pi\) | |||||||
\(234\) | −5.69038 | −0.371992 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 34.8931 | 2.27135 | ||||||||
\(237\) | −6.59991 | −0.428710 | ||||||||
\(238\) | −17.3314 | −1.12343 | ||||||||
\(239\) | 0.988409 | 0.0639349 | 0.0319674 | − | 0.999489i | \(-0.489823\pi\) | ||||
0.0319674 | + | 0.999489i | \(0.489823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0839 | 1.03606 | 0.518028 | − | 0.855364i | \(-0.326666\pi\) | ||||
0.518028 | + | 0.855364i | \(0.326666\pi\) | |||||||
\(242\) | −1.30608 | −0.0839582 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −18.5466 | −1.18732 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.7831 | 0.815020 | ||||||||
\(247\) | −4.40478 | −0.280269 | ||||||||
\(248\) | 19.7252 | 1.25255 | ||||||||
\(249\) | −15.6214 | −0.989964 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5672 | −0.666997 | −0.333498 | − | 0.942751i | \(-0.608229\pi\) | ||||
−0.333498 | + | 0.942751i | \(0.608229\pi\) | |||||||
\(252\) | −2.97481 | −0.187396 | ||||||||
\(253\) | −7.14282 | −0.449066 | ||||||||
\(254\) | 32.2556 | 2.02390 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.95304 | −0.247065 | ||||||||
\(257\) | 23.9740 | 1.49546 | 0.747728 | − | 0.664005i | \(-0.231145\pi\) | ||||
0.747728 | + | 0.664005i | \(0.231145\pi\) | |||||||
\(258\) | −7.46185 | −0.464555 | ||||||||
\(259\) | −12.3798 | −0.769245 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.74234 | 0.417340 | ||||||||
\(262\) | −33.2218 | −2.05245 | ||||||||
\(263\) | 2.96013 | 0.182530 | 0.0912649 | − | 0.995827i | \(-0.470909\pi\) | ||||
0.0912649 | + | 0.995827i | \(0.470909\pi\) | |||||||
\(264\) | 5.89058 | 0.362540 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.92962 | −0.240941 | ||||||||
\(267\) | 15.4144 | 0.943345 | ||||||||
\(268\) | −2.12345 | −0.129710 | ||||||||
\(269\) | 30.7826 | 1.87685 | 0.938423 | − | 0.345489i | \(-0.112287\pi\) | ||||
0.938423 | + | 0.345489i | \(0.112287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6106 | −0.705296 | −0.352648 | − | 0.935756i | \(-0.614719\pi\) | ||||
−0.352648 | + | 0.935756i | \(0.614719\pi\) | |||||||
\(272\) | −12.3667 | −0.749842 | ||||||||
\(273\) | −2.72067 | −0.164663 | ||||||||
\(274\) | −38.7395 | −2.34034 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.26825 | −0.377304 | ||||||||
\(277\) | 0.511633 | 0.0307410 | 0.0153705 | − | 0.999882i | \(-0.495107\pi\) | ||||
0.0153705 | + | 0.999882i | \(0.495107\pi\) | |||||||
\(278\) | 20.7561 | 1.24487 | ||||||||
\(279\) | 10.8019 | 0.646694 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.0058 | −1.49172 | −0.745862 | − | 0.666101i | \(-0.767962\pi\) | ||||
−0.745862 | + | 0.666101i | \(0.767962\pi\) | |||||||
\(282\) | −2.19791 | −0.130884 | ||||||||
\(283\) | 31.8811 | 1.89513 | 0.947567 | − | 0.319556i | \(-0.103534\pi\) | ||||
0.947567 | + | 0.319556i | \(0.103534\pi\) | |||||||
\(284\) | 5.92296 | 0.351463 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.3560 | 1.08541 | ||||||||
\(287\) | 6.11183 | 0.360770 | ||||||||
\(288\) | −7.27449 | −0.428654 | ||||||||
\(289\) | 39.3061 | 2.31212 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.6829 | 0.684863 | ||||||||
\(292\) | −13.5942 | −0.795538 | ||||||||
\(293\) | −11.7501 | −0.686447 | −0.343223 | − | 0.939254i | \(-0.611519\pi\) | ||||
−0.343223 | + | 0.939254i | \(0.611519\pi\) | |||||||
\(294\) | 12.9582 | 0.755738 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 21.5124 | 1.25039 | ||||||||
\(297\) | 3.22580 | 0.187180 | ||||||||
\(298\) | 12.3764 | 0.716944 | ||||||||
\(299\) | −5.73275 | −0.331534 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.56765 | −0.205636 | ||||||||
\(302\) | 30.4078 | 1.74978 | ||||||||
\(303\) | 3.43631 | 0.197411 | ||||||||
\(304\) | −2.80395 | −0.160817 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.4926 | 0.942818 | ||||||||
\(307\) | 14.3166 | 0.817092 | 0.408546 | − | 0.912738i | \(-0.366036\pi\) | ||||
0.408546 | + | 0.912738i | \(0.366036\pi\) | |||||||
\(308\) | 9.59614 | 0.546791 | ||||||||
\(309\) | −12.4894 | −0.710495 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.9784 | −0.906050 | −0.453025 | − | 0.891498i | \(-0.649655\pi\) | ||||
−0.453025 | + | 0.891498i | \(0.649655\pi\) | |||||||
\(312\) | 4.72772 | 0.267654 | ||||||||
\(313\) | −17.1969 | −0.972025 | −0.486013 | − | 0.873952i | \(-0.661549\pi\) | ||||
−0.486013 | + | 0.873952i | \(0.661549\pi\) | |||||||
\(314\) | 9.35458 | 0.527909 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.6832 | 1.05101 | ||||||||
\(317\) | 24.6354 | 1.38366 | 0.691830 | − | 0.722061i | \(-0.256805\pi\) | ||||
0.691830 | + | 0.722061i | \(0.256805\pi\) | |||||||
\(318\) | −24.5485 | −1.37661 | ||||||||
\(319\) | −21.7494 | −1.21773 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.2622 | 1.13093 | ||||||||
\(322\) | −5.11435 | −0.285011 | ||||||||
\(323\) | 12.7665 | 0.710346 | ||||||||
\(324\) | 2.83083 | 0.157268 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.1440 | −0.949517 | ||||||||
\(327\) | 12.9693 | 0.717205 | ||||||||
\(328\) | −10.6205 | −0.586421 | ||||||||
\(329\) | −1.05086 | −0.0579360 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.11931 | −0.391313 | −0.195656 | − | 0.980673i | \(-0.562684\pi\) | ||||
−0.195656 | + | 0.980673i | \(0.562684\pi\) | |||||||
\(332\) | 44.2214 | 2.42696 | ||||||||
\(333\) | 11.7806 | 0.645574 | ||||||||
\(334\) | 24.2376 | 1.32622 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.73190 | −0.0944828 | ||||||||
\(337\) | 7.95185 | 0.433165 | 0.216582 | − | 0.976264i | \(-0.430509\pi\) | ||||
0.216582 | + | 0.976264i | \(0.430509\pi\) | |||||||
\(338\) | −13.8406 | −0.752827 | ||||||||
\(339\) | −14.6725 | −0.796900 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.8448 | −1.88695 | ||||||||
\(342\) | 3.73942 | 0.202205 | ||||||||
\(343\) | 13.5516 | 0.731718 | ||||||||
\(344\) | 6.19951 | 0.334255 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.54664 | −0.459470 | ||||||||
\(347\) | 1.56985 | 0.0842738 | 0.0421369 | − | 0.999112i | \(-0.486583\pi\) | ||||
0.0421369 | + | 0.999112i | \(0.486583\pi\) | |||||||
\(348\) | −19.0864 | −1.02314 | ||||||||
\(349\) | −20.9148 | −1.11954 | −0.559771 | − | 0.828647i | \(-0.689111\pi\) | ||||
−0.559771 | + | 0.828647i | \(0.689111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.58899 | 0.138190 | ||||||||
\(352\) | 23.4660 | 1.25074 | ||||||||
\(353\) | −11.0677 | −0.589075 | −0.294537 | − | 0.955640i | \(-0.595166\pi\) | ||||
−0.294537 | + | 0.955640i | \(0.595166\pi\) | |||||||
\(354\) | −27.0917 | −1.43991 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −43.6354 | −2.31267 | ||||||||
\(357\) | 7.88541 | 0.417340 | ||||||||
\(358\) | 0.870304 | 0.0459970 | ||||||||
\(359\) | −21.3955 | −1.12921 | −0.564607 | − | 0.825360i | \(-0.690972\pi\) | ||||
−0.564607 | + | 0.825360i | \(0.690972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1054 | −0.847653 | ||||||||
\(362\) | −30.6138 | −1.60903 | ||||||||
\(363\) | 0.594237 | 0.0311894 | ||||||||
\(364\) | 7.70176 | 0.403682 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.4000 | 0.752699 | ||||||||
\(367\) | −22.9905 | −1.20009 | −0.600046 | − | 0.799965i | \(-0.704851\pi\) | ||||
−0.600046 | + | 0.799965i | \(0.704851\pi\) | |||||||
\(368\) | −3.64930 | −0.190233 | ||||||||
\(369\) | −5.81601 | −0.302769 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.7371 | −0.609360 | ||||||||
\(372\) | −30.5784 | −1.58541 | ||||||||
\(373\) | 30.8418 | 1.59693 | 0.798464 | − | 0.602042i | \(-0.205646\pi\) | ||||
0.798464 | + | 0.602042i | \(0.205646\pi\) | |||||||
\(374\) | −53.2017 | −2.75099 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.82609 | 0.0941732 | ||||||||
\(377\) | −17.4558 | −0.899021 | ||||||||
\(378\) | 2.30971 | 0.118799 | ||||||||
\(379\) | −18.6754 | −0.959290 | −0.479645 | − | 0.877463i | \(-0.659235\pi\) | ||||
−0.479645 | + | 0.877463i | \(0.659235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.6756 | −0.751852 | ||||||||
\(382\) | −17.4545 | −0.893052 | ||||||||
\(383\) | 11.9269 | 0.609438 | 0.304719 | − | 0.952442i | \(-0.401438\pi\) | ||||
0.304719 | + | 0.952442i | \(0.401438\pi\) | |||||||
\(384\) | 13.3482 | 0.681172 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.3118 | −1.44104 | ||||||||
\(387\) | 3.39497 | 0.172576 | ||||||||
\(388\) | −33.0722 | −1.67899 | ||||||||
\(389\) | 3.23480 | 0.164011 | 0.0820054 | − | 0.996632i | \(-0.473868\pi\) | ||||
0.0820054 | + | 0.996632i | \(0.473868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6154 | 0.840277 | ||||||||
\(392\) | −10.7660 | −0.543767 | ||||||||
\(393\) | 15.1152 | 0.762459 | ||||||||
\(394\) | 18.8657 | 0.950438 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.13167 | −0.458884 | ||||||||
\(397\) | 0.211311 | 0.0106054 | 0.00530270 | − | 0.999986i | \(-0.498312\pi\) | ||||
0.00530270 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(398\) | 26.2662 | 1.31661 | ||||||||
\(399\) | 1.78789 | 0.0895063 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.7778 | 1.43710 | 0.718548 | − | 0.695478i | \(-0.244807\pi\) | ||||
0.718548 | + | 0.695478i | \(0.244807\pi\) | |||||||
\(402\) | 1.64869 | 0.0822292 | ||||||||
\(403\) | −27.9661 | −1.39309 | ||||||||
\(404\) | −9.72759 | −0.483966 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.5728 | −0.772866 | ||||||||
\(407\) | −38.0019 | −1.88368 | ||||||||
\(408\) | −13.7025 | −0.678374 | ||||||||
\(409\) | 3.37349 | 0.166808 | 0.0834042 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834042 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.6256 | 0.869406 | ||||||||
\(412\) | 35.3552 | 1.74183 | ||||||||
\(413\) | −12.9531 | −0.637378 | ||||||||
\(414\) | 4.86680 | 0.239190 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 18.8336 | 0.923393 | ||||||||
\(417\) | −9.44352 | −0.462451 | ||||||||
\(418\) | −12.0626 | −0.590002 | ||||||||
\(419\) | 8.59815 | 0.420047 | 0.210024 | − | 0.977696i | \(-0.432646\pi\) | ||||
0.210024 | + | 0.977696i | \(0.432646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.4340 | −1.62947 | −0.814737 | − | 0.579831i | \(-0.803118\pi\) | ||||
−0.814737 | + | 0.579831i | \(0.803118\pi\) | |||||||
\(422\) | 13.1238 | 0.638858 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 20.3956 | 0.990496 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.59871 | −0.222808 | ||||||||
\(427\) | 6.88490 | 0.333183 | ||||||||
\(428\) | −57.3588 | −2.77254 | ||||||||
\(429\) | −8.35155 | −0.403217 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7133 | −0.997726 | −0.498863 | − | 0.866681i | \(-0.666249\pi\) | ||||
−0.498863 | + | 0.866681i | \(0.666249\pi\) | |||||||
\(432\) | 1.64807 | 0.0792929 | ||||||||
\(433\) | −25.6067 | −1.23058 | −0.615291 | − | 0.788300i | \(-0.710961\pi\) | ||||
−0.615291 | + | 0.788300i | \(0.710961\pi\) | |||||||
\(434\) | −24.9493 | −1.19760 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.7139 | −1.75828 | ||||||||
\(437\) | 3.76727 | 0.180213 | ||||||||
\(438\) | 10.5548 | 0.504328 | ||||||||
\(439\) | −2.07924 | −0.0992367 | −0.0496183 | − | 0.998768i | \(-0.515800\pi\) | ||||
−0.0496183 | + | 0.998768i | \(0.515800\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.89569 | −0.280747 | ||||||||
\(442\) | −42.6991 | −2.03099 | ||||||||
\(443\) | −21.9500 | −1.04287 | −0.521437 | − | 0.853290i | \(-0.674604\pi\) | ||||
−0.521437 | + | 0.853290i | \(0.674604\pi\) | |||||||
\(444\) | −33.3489 | −1.58267 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.7907 | 1.26858 | ||||||||
\(447\) | −5.63097 | −0.266336 | ||||||||
\(448\) | 13.3382 | 0.630169 | ||||||||
\(449\) | 2.61869 | 0.123583 | 0.0617917 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617917 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.7613 | 0.883433 | ||||||||
\(452\) | 41.5353 | 1.95365 | ||||||||
\(453\) | −13.8349 | −0.650019 | ||||||||
\(454\) | 55.6421 | 2.61141 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.10681 | −0.145490 | ||||||||
\(457\) | 31.5801 | 1.47726 | 0.738628 | − | 0.674113i | \(-0.235474\pi\) | ||||
0.738628 | + | 0.674113i | \(0.235474\pi\) | |||||||
\(458\) | 28.8450 | 1.34784 | ||||||||
\(459\) | −7.50374 | −0.350245 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.891136 | 0.0415043 | 0.0207522 | − | 0.999785i | \(-0.493394\pi\) | ||||
0.0207522 | + | 0.999785i | \(0.493394\pi\) | |||||||
\(462\) | −7.45065 | −0.346635 | ||||||||
\(463\) | 15.1369 | 0.703470 | 0.351735 | − | 0.936100i | \(-0.385592\pi\) | ||||
0.351735 | + | 0.936100i | \(0.385592\pi\) | |||||||
\(464\) | −11.1119 | −0.515855 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −45.7325 | −2.11852 | ||||||||
\(467\) | 2.92279 | 0.135251 | 0.0676253 | − | 0.997711i | \(-0.478458\pi\) | ||||
0.0676253 | + | 0.997711i | \(0.478458\pi\) | |||||||
\(468\) | −7.32898 | −0.338782 | ||||||||
\(469\) | 0.788269 | 0.0363989 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.25611 | −0.196111 | ||||||||
\(472\) | 22.5085 | 1.03604 | ||||||||
\(473\) | −10.9515 | −0.503550 | ||||||||
\(474\) | −14.5060 | −0.666284 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −22.3222 | −1.02314 | ||||||||
\(477\) | 11.1690 | 0.511394 | ||||||||
\(478\) | 2.17244 | 0.0993650 | ||||||||
\(479\) | −13.3779 | −0.611252 | −0.305626 | − | 0.952152i | \(-0.598866\pi\) | ||||
−0.305626 | + | 0.952152i | \(0.598866\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.4999 | −1.39068 | ||||||||
\(482\) | 35.3511 | 1.61020 | ||||||||
\(483\) | 2.32691 | 0.105878 | ||||||||
\(484\) | −1.68218 | −0.0764629 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.19791 | −0.0996994 | ||||||||
\(487\) | 36.9084 | 1.67248 | 0.836239 | − | 0.548365i | \(-0.184749\pi\) | ||||
0.836239 | + | 0.548365i | \(0.184749\pi\) | |||||||
\(488\) | −11.9639 | −0.541580 | ||||||||
\(489\) | 7.80011 | 0.352733 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.79535 | 0.306670 | 0.153335 | − | 0.988174i | \(-0.450999\pi\) | ||||
0.153335 | + | 0.988174i | \(0.450999\pi\) | |||||||
\(492\) | 16.4641 | 0.742259 | ||||||||
\(493\) | 50.5927 | 2.27858 | ||||||||
\(494\) | −9.68132 | −0.435583 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.8023 | −0.799349 | ||||||||
\(497\) | −2.19873 | −0.0986265 | ||||||||
\(498\) | −34.3344 | −1.53856 | ||||||||
\(499\) | −5.04952 | −0.226047 | −0.113024 | − | 0.993592i | \(-0.536054\pi\) | ||||
−0.113024 | + | 0.993592i | \(0.536054\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0275 | −0.492674 | ||||||||
\(502\) | −23.2258 | −1.03662 | ||||||||
\(503\) | −18.6865 | −0.833191 | −0.416595 | − | 0.909092i | \(-0.636777\pi\) | ||||
−0.416595 | + | 0.909092i | \(0.636777\pi\) | |||||||
\(504\) | −1.91897 | −0.0854776 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.6993 | −0.697920 | ||||||||
\(507\) | 6.29713 | 0.279666 | ||||||||
\(508\) | 41.5440 | 1.84322 | ||||||||
\(509\) | 26.5029 | 1.17472 | 0.587360 | − | 0.809326i | \(-0.300167\pi\) | ||||
0.587360 | + | 0.809326i | \(0.300167\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.04644 | 0.223242 | ||||||||
\(512\) | 18.0079 | 0.795846 | ||||||||
\(513\) | −1.70135 | −0.0751164 | ||||||||
\(514\) | 52.6928 | 2.32418 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.61057 | −0.423082 | ||||||||
\(517\) | −3.22580 | −0.141870 | ||||||||
\(518\) | −27.2098 | −1.19553 | ||||||||
\(519\) | 3.88852 | 0.170687 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.1654 | −0.620600 | −0.310300 | − | 0.950639i | \(-0.600429\pi\) | ||||
−0.310300 | + | 0.950639i | \(0.600429\pi\) | |||||||
\(522\) | 14.8191 | 0.648613 | ||||||||
\(523\) | −14.9461 | −0.653549 | −0.326775 | − | 0.945102i | \(-0.605962\pi\) | ||||
−0.326775 | + | 0.945102i | \(0.605962\pi\) | |||||||
\(524\) | −42.7884 | −1.86922 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.50612 | 0.283680 | ||||||||
\(527\) | 81.0548 | 3.53080 | ||||||||
\(528\) | −5.31635 | −0.231364 | ||||||||
\(529\) | −18.0970 | −0.786824 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.3261 | 0.534907 | ||||||||
\(532\) | −5.06120 | −0.219431 | ||||||||
\(533\) | 15.0576 | 0.652216 | ||||||||
\(534\) | 33.8795 | 1.46611 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.36978 | −0.0591653 | ||||||||
\(537\) | −0.395968 | −0.0170873 | ||||||||
\(538\) | 67.6574 | 2.91692 | ||||||||
\(539\) | 19.0183 | 0.819175 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.91744 | 0.383391 | 0.191695 | − | 0.981454i | \(-0.438601\pi\) | ||||
0.191695 | + | 0.981454i | \(0.438601\pi\) | |||||||
\(542\) | −25.5192 | −1.09614 | ||||||||
\(543\) | 13.9286 | 0.597732 | ||||||||
\(544\) | −54.5859 | −2.34035 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.97981 | −0.255912 | ||||||||
\(547\) | 8.89021 | 0.380118 | 0.190059 | − | 0.981773i | \(-0.439132\pi\) | ||||
0.190059 | + | 0.981773i | \(0.439132\pi\) | |||||||
\(548\) | −49.8950 | −2.13141 | ||||||||
\(549\) | −6.55166 | −0.279618 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4711 | 0.488684 | ||||||||
\(552\) | −4.04347 | −0.172102 | ||||||||
\(553\) | −6.93560 | −0.294932 | ||||||||
\(554\) | 1.12452 | 0.0477765 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.7330 | 1.13373 | ||||||||
\(557\) | −35.1323 | −1.48860 | −0.744301 | − | 0.667844i | \(-0.767217\pi\) | ||||
−0.744301 | + | 0.667844i | \(0.767217\pi\) | |||||||
\(558\) | 23.7417 | 1.00507 | ||||||||
\(559\) | −8.78954 | −0.371758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.2055 | 1.02196 | ||||||||
\(562\) | −54.9607 | −2.31838 | ||||||||
\(563\) | −29.2562 | −1.23300 | −0.616502 | − | 0.787354i | \(-0.711451\pi\) | ||||
−0.616502 | + | 0.787354i | \(0.711451\pi\) | |||||||
\(564\) | −2.83083 | −0.119199 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 70.0719 | 2.94534 | ||||||||
\(567\) | −1.05086 | −0.0441321 | ||||||||
\(568\) | 3.82074 | 0.160315 | ||||||||
\(569\) | −9.51183 | −0.398756 | −0.199378 | − | 0.979923i | \(-0.563892\pi\) | ||||
−0.199378 | + | 0.979923i | \(0.563892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.71387 | 0.0717231 | 0.0358615 | − | 0.999357i | \(-0.488582\pi\) | ||||
0.0358615 | + | 0.999357i | \(0.488582\pi\) | |||||||
\(572\) | 23.6418 | 0.988513 | ||||||||
\(573\) | 7.94141 | 0.331757 | ||||||||
\(574\) | 13.4333 | 0.560694 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.6926 | −0.528857 | ||||||||
\(577\) | −22.3271 | −0.929491 | −0.464746 | − | 0.885444i | \(-0.653854\pi\) | ||||
−0.464746 | + | 0.885444i | \(0.653854\pi\) | |||||||
\(578\) | 86.3915 | 3.59341 | ||||||||
\(579\) | 12.8812 | 0.535326 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.4159 | −0.681047 | ||||||||
\(582\) | 25.6780 | 1.06439 | ||||||||
\(583\) | −36.0289 | −1.49217 | ||||||||
\(584\) | −8.76921 | −0.362873 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.8257 | −1.06685 | ||||||||
\(587\) | −15.3439 | −0.633311 | −0.316655 | − | 0.948541i | \(-0.602560\pi\) | ||||
−0.316655 | + | 0.948541i | \(0.602560\pi\) | |||||||
\(588\) | 16.6897 | 0.688270 | ||||||||
\(589\) | 18.3778 | 0.757246 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.58344 | −0.353075 | ||||||||
\(592\) | −19.4153 | −0.797965 | ||||||||
\(593\) | 25.0738 | 1.02966 | 0.514830 | − | 0.857293i | \(-0.327855\pi\) | ||||
0.514830 | + | 0.857293i | \(0.327855\pi\) | |||||||
\(594\) | 7.09002 | 0.290907 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.9403 | 0.652940 | ||||||||
\(597\) | −11.9505 | −0.489102 | ||||||||
\(598\) | −12.6001 | −0.515256 | ||||||||
\(599\) | −45.9704 | −1.87830 | −0.939150 | − | 0.343506i | \(-0.888385\pi\) | ||||
−0.939150 | + | 0.343506i | \(0.888385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2362 | −0.825453 | −0.412727 | − | 0.910855i | \(-0.635423\pi\) | ||||
−0.412727 | + | 0.910855i | \(0.635423\pi\) | |||||||
\(602\) | −7.84139 | −0.319591 | ||||||||
\(603\) | −0.750116 | −0.0305471 | ||||||||
\(604\) | 39.1641 | 1.59357 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.55271 | 0.306808 | ||||||||
\(607\) | −2.94855 | −0.119678 | −0.0598389 | − | 0.998208i | \(-0.519059\pi\) | ||||
−0.0598389 | + | 0.998208i | \(0.519059\pi\) | |||||||
\(608\) | −12.3765 | −0.501932 | ||||||||
\(609\) | 7.08528 | 0.287110 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.58899 | −0.104739 | ||||||||
\(612\) | 21.2418 | 0.858649 | ||||||||
\(613\) | −21.0447 | −0.849987 | −0.424993 | − | 0.905196i | \(-0.639724\pi\) | ||||
−0.424993 | + | 0.905196i | \(0.639724\pi\) | |||||||
\(614\) | 31.4667 | 1.26989 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.19020 | 0.249410 | ||||||||
\(617\) | −16.6437 | −0.670051 | −0.335026 | − | 0.942209i | \(-0.608745\pi\) | ||||
−0.335026 | + | 0.942209i | \(0.608745\pi\) | |||||||
\(618\) | −27.4506 | −1.10422 | ||||||||
\(619\) | 38.9234 | 1.56446 | 0.782232 | − | 0.622987i | \(-0.214081\pi\) | ||||
0.782232 | + | 0.622987i | \(0.214081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.21428 | −0.0888561 | ||||||||
\(622\) | −35.1191 | −1.40815 | ||||||||
\(623\) | 16.1984 | 0.648975 | ||||||||
\(624\) | −4.26684 | −0.170810 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −37.7973 | −1.51068 | ||||||||
\(627\) | 5.48821 | 0.219178 | ||||||||
\(628\) | 12.0483 | 0.480780 | ||||||||
\(629\) | 88.3987 | 3.52469 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6963 | −0.784097 | −0.392049 | − | 0.919945i | \(-0.628233\pi\) | ||||
−0.392049 | + | 0.919945i | \(0.628233\pi\) | |||||||
\(632\) | 12.0520 | 0.479403 | ||||||||
\(633\) | −5.97104 | −0.237328 | ||||||||
\(634\) | 54.1464 | 2.15043 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −31.6175 | −1.25372 | ||||||||
\(637\) | 15.2639 | 0.604776 | ||||||||
\(638\) | −47.8033 | −1.89255 | ||||||||
\(639\) | 2.09231 | 0.0827704 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.39022 | −0.252399 | −0.126199 | − | 0.992005i | \(-0.540278\pi\) | ||||
−0.126199 | + | 0.992005i | \(0.540278\pi\) | |||||||
\(642\) | 44.5346 | 1.75764 | ||||||||
\(643\) | 39.9323 | 1.57477 | 0.787387 | − | 0.616459i | \(-0.211433\pi\) | ||||
0.787387 | + | 0.616459i | \(0.211433\pi\) | |||||||
\(644\) | −6.58708 | −0.259567 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.0596 | 1.10399 | ||||||||
\(647\) | −28.4879 | −1.11998 | −0.559988 | − | 0.828501i | \(-0.689194\pi\) | ||||
−0.559988 | + | 0.828501i | \(0.689194\pi\) | |||||||
\(648\) | 1.82609 | 0.0717355 | ||||||||
\(649\) | −39.7615 | −1.56078 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3513 | 0.444894 | ||||||||
\(652\) | −22.0808 | −0.864750 | ||||||||
\(653\) | −38.6045 | −1.51071 | −0.755355 | − | 0.655316i | \(-0.772535\pi\) | ||||
−0.755355 | + | 0.655316i | \(0.772535\pi\) | |||||||
\(654\) | 28.5055 | 1.11465 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.58520 | 0.374239 | ||||||||
\(657\) | −4.80219 | −0.187351 | ||||||||
\(658\) | −2.30971 | −0.0900418 | ||||||||
\(659\) | −18.9279 | −0.737324 | −0.368662 | − | 0.929563i | \(-0.620184\pi\) | ||||
−0.368662 | + | 0.929563i | \(0.620184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.518381 | −0.0201627 | −0.0100813 | − | 0.999949i | \(-0.503209\pi\) | ||||
−0.0100813 | + | 0.999949i | \(0.503209\pi\) | |||||||
\(662\) | −15.6476 | −0.608162 | ||||||||
\(663\) | 19.4271 | 0.754486 | ||||||||
\(664\) | 28.5260 | 1.10702 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25.8928 | 1.00333 | ||||||||
\(667\) | 14.9294 | 0.578070 | ||||||||
\(668\) | 31.2170 | 1.20782 | ||||||||
\(669\) | −12.1892 | −0.471260 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1343 | 0.815881 | ||||||||
\(672\) | −7.64450 | −0.294893 | ||||||||
\(673\) | 17.7260 | 0.683288 | 0.341644 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(674\) | 17.4775 | 0.673207 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.8261 | −0.685619 | ||||||||
\(677\) | −3.62115 | −0.139172 | −0.0695861 | − | 0.997576i | \(-0.522168\pi\) | ||||
−0.0695861 | + | 0.997576i | \(0.522168\pi\) | |||||||
\(678\) | −32.2489 | −1.23851 | ||||||||
\(679\) | 12.2771 | 0.471153 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.3158 | −0.970105 | ||||||||
\(682\) | −76.5859 | −2.93262 | ||||||||
\(683\) | 1.75071 | 0.0669889 | 0.0334944 | − | 0.999439i | \(-0.489336\pi\) | ||||
0.0334944 | + | 0.999439i | \(0.489336\pi\) | |||||||
\(684\) | 4.81623 | 0.184153 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 29.7853 | 1.13721 | ||||||||
\(687\) | −13.1238 | −0.500705 | ||||||||
\(688\) | −5.59516 | −0.213313 | ||||||||
\(689\) | −28.9164 | −1.10163 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.3812 | 0.432963 | 0.216481 | − | 0.976287i | \(-0.430542\pi\) | ||||
0.216481 | + | 0.976287i | \(0.430542\pi\) | |||||||
\(692\) | −11.0077 | −0.418451 | ||||||||
\(693\) | 3.38987 | 0.128771 | ||||||||
\(694\) | 3.45039 | 0.130975 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.3121 | −0.466689 | ||||||||
\(697\) | −43.6418 | −1.65305 | ||||||||
\(698\) | −45.9689 | −1.73995 | ||||||||
\(699\) | 20.8072 | 0.787001 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.5746 | 0.550476 | 0.275238 | − | 0.961376i | \(-0.411243\pi\) | ||||
0.275238 | + | 0.961376i | \(0.411243\pi\) | |||||||
\(702\) | 5.69038 | 0.214769 | ||||||||
\(703\) | 20.0430 | 0.755935 | ||||||||
\(704\) | 40.9437 | 1.54312 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.3259 | −0.915516 | ||||||||
\(707\) | 3.61109 | 0.135809 | ||||||||
\(708\) | −34.8931 | −1.31136 | ||||||||
\(709\) | −18.7870 | −0.705561 | −0.352780 | − | 0.935706i | \(-0.614764\pi\) | ||||
−0.352780 | + | 0.935706i | \(0.614764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.59991 | 0.247516 | ||||||||
\(712\) | −28.1480 | −1.05489 | ||||||||
\(713\) | 23.9185 | 0.895755 | ||||||||
\(714\) | 17.3314 | 0.648613 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.12092 | 0.0418907 | ||||||||
\(717\) | −0.988409 | −0.0369128 | ||||||||
\(718\) | −47.0256 | −1.75498 | ||||||||
\(719\) | −9.79963 | −0.365465 | −0.182732 | − | 0.983163i | \(-0.558494\pi\) | ||||
−0.182732 | + | 0.983163i | \(0.558494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.1246 | −0.488786 | ||||||||
\(722\) | −35.3983 | −1.31739 | ||||||||
\(723\) | −16.0839 | −0.598167 | ||||||||
\(724\) | −39.4294 | −1.46538 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.30608 | 0.0484733 | ||||||||
\(727\) | 25.5912 | 0.949126 | 0.474563 | − | 0.880221i | \(-0.342606\pi\) | ||||
0.474563 | + | 0.880221i | \(0.342606\pi\) | |||||||
\(728\) | 4.96819 | 0.184133 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.4750 | 0.942226 | ||||||||
\(732\) | 18.5466 | 0.685502 | ||||||||
\(733\) | 42.3314 | 1.56354 | 0.781772 | − | 0.623564i | \(-0.214316\pi\) | ||||
0.781772 | + | 0.623564i | \(0.214316\pi\) | |||||||
\(734\) | −50.5311 | −1.86514 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.1078 | −0.593741 | ||||||||
\(737\) | 2.41972 | 0.0891316 | ||||||||
\(738\) | −12.7831 | −0.470552 | ||||||||
\(739\) | −1.65177 | −0.0607612 | −0.0303806 | − | 0.999538i | \(-0.509672\pi\) | ||||
−0.0303806 | + | 0.999538i | \(0.509672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.40478 | 0.161814 | ||||||||
\(742\) | −25.7971 | −0.947043 | ||||||||
\(743\) | −30.1467 | −1.10597 | −0.552987 | − | 0.833190i | \(-0.686512\pi\) | ||||
−0.552987 | + | 0.833190i | \(0.686512\pi\) | |||||||
\(744\) | −19.7252 | −0.723162 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 67.7877 | 2.48188 | ||||||||
\(747\) | 15.6214 | 0.571556 | ||||||||
\(748\) | −68.5217 | −2.50540 | ||||||||
\(749\) | 21.2928 | 0.778022 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.44762 | −0.162296 | −0.0811479 | − | 0.996702i | \(-0.525859\pi\) | ||||
−0.0811479 | + | 0.996702i | \(0.525859\pi\) | |||||||
\(752\) | −1.64807 | −0.0600990 | ||||||||
\(753\) | 10.5672 | 0.385091 | ||||||||
\(754\) | −38.3664 | −1.39722 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.97481 | 0.108193 | ||||||||
\(757\) | −41.9419 | −1.52441 | −0.762203 | − | 0.647338i | \(-0.775882\pi\) | ||||
−0.762203 | + | 0.647338i | \(0.775882\pi\) | |||||||
\(758\) | −41.0469 | −1.49089 | ||||||||
\(759\) | 7.14282 | 0.259268 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.1036 | −0.982504 | −0.491252 | − | 0.871018i | \(-0.663461\pi\) | ||||
−0.491252 | + | 0.871018i | \(0.663461\pi\) | |||||||
\(762\) | −32.2556 | −1.16850 | ||||||||
\(763\) | 13.6290 | 0.493402 | ||||||||
\(764\) | −22.4808 | −0.813325 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.2144 | 0.947163 | ||||||||
\(767\) | −31.9122 | −1.15228 | ||||||||
\(768\) | 3.95304 | 0.142643 | ||||||||
\(769\) | 32.8683 | 1.18526 | 0.592631 | − | 0.805474i | \(-0.298089\pi\) | ||||
0.592631 | + | 0.805474i | \(0.298089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.9740 | −0.863402 | ||||||||
\(772\) | −36.4645 | −1.31239 | ||||||||
\(773\) | 21.9310 | 0.788804 | 0.394402 | − | 0.918938i | \(-0.370952\pi\) | ||||
0.394402 | + | 0.918938i | \(0.370952\pi\) | |||||||
\(774\) | 7.46185 | 0.268211 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −21.3340 | −0.765845 | ||||||||
\(777\) | 12.3798 | 0.444124 | ||||||||
\(778\) | 7.10981 | 0.254899 | ||||||||
\(779\) | −9.89506 | −0.354527 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.74936 | −0.241511 | ||||||||
\(782\) | 36.5192 | 1.30592 | ||||||||
\(783\) | −6.74234 | −0.240951 | ||||||||
\(784\) | 9.71652 | 0.347018 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 33.2218 | 1.18498 | ||||||||
\(787\) | 53.6288 | 1.91166 | 0.955830 | − | 0.293920i | \(-0.0949599\pi\) | ||||
0.955830 | + | 0.293920i | \(0.0949599\pi\) | |||||||
\(788\) | 24.2982 | 0.865588 | ||||||||
\(789\) | −2.96013 | −0.105384 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.4188 | −0.548229 | ||||||||
\(792\) | −5.89058 | −0.209313 | ||||||||
\(793\) | 16.9622 | 0.602344 | ||||||||
\(794\) | 0.464444 | 0.0164825 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.8298 | 1.19907 | ||||||||
\(797\) | −4.21744 | −0.149389 | −0.0746946 | − | 0.997206i | \(-0.523798\pi\) | ||||
−0.0746946 | + | 0.997206i | \(0.523798\pi\) | |||||||
\(798\) | 3.92962 | 0.139107 | ||||||||
\(799\) | 7.50374 | 0.265463 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4144 | −0.544640 | ||||||||
\(802\) | 63.2512 | 2.23348 | ||||||||
\(803\) | 15.4909 | 0.546661 | ||||||||
\(804\) | 2.12345 | 0.0748883 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −61.4670 | −2.16508 | ||||||||
\(807\) | −30.7826 | −1.08360 | ||||||||
\(808\) | −6.27500 | −0.220754 | ||||||||
\(809\) | −9.77548 | −0.343688 | −0.171844 | − | 0.985124i | \(-0.554972\pi\) | ||||
−0.171844 | + | 0.985124i | \(0.554972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9279 | 0.489075 | 0.244538 | − | 0.969640i | \(-0.421364\pi\) | ||||
0.244538 | + | 0.969640i | \(0.421364\pi\) | |||||||
\(812\) | −20.0572 | −0.703869 | ||||||||
\(813\) | 11.6106 | 0.407203 | ||||||||
\(814\) | −83.5249 | −2.92755 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.3667 | 0.432921 | ||||||||
\(817\) | 5.77603 | 0.202078 | ||||||||
\(818\) | 7.41465 | 0.259247 | ||||||||
\(819\) | 2.72067 | 0.0950681 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.631310 | 0.0220329 | 0.0110164 | − | 0.999939i | \(-0.496493\pi\) | ||||
0.0110164 | + | 0.999939i | \(0.496493\pi\) | |||||||
\(822\) | 38.7395 | 1.35120 | ||||||||
\(823\) | −26.9584 | −0.939711 | −0.469855 | − | 0.882743i | \(-0.655694\pi\) | ||||
−0.469855 | + | 0.882743i | \(0.655694\pi\) | |||||||
\(824\) | 22.8067 | 0.794508 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.4697 | −0.990588 | ||||||||
\(827\) | −19.3808 | −0.673937 | −0.336968 | − | 0.941516i | \(-0.609402\pi\) | ||||
−0.336968 | + | 0.941516i | \(0.609402\pi\) | |||||||
\(828\) | 6.26825 | 0.217837 | ||||||||
\(829\) | 44.6224 | 1.54980 | 0.774900 | − | 0.632083i | \(-0.217800\pi\) | ||||
0.774900 | + | 0.632083i | \(0.217800\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.511633 | −0.0177483 | ||||||||
\(832\) | 32.8609 | 1.13925 | ||||||||
\(833\) | −44.2397 | −1.53281 | ||||||||
\(834\) | −20.7561 | −0.718723 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.5362 | −0.537330 | ||||||||
\(837\) | −10.8019 | −0.373369 | ||||||||
\(838\) | 18.8980 | 0.652820 | ||||||||
\(839\) | 25.8332 | 0.891860 | 0.445930 | − | 0.895068i | \(-0.352873\pi\) | ||||
0.445930 | + | 0.895068i | \(0.352873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4591 | 0.567555 | ||||||||
\(842\) | −73.4851 | −2.53246 | ||||||||
\(843\) | 25.0058 | 0.861247 | ||||||||
\(844\) | 16.9030 | 0.581825 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.19791 | 0.0755658 | ||||||||
\(847\) | 0.624462 | 0.0214568 | ||||||||
\(848\) | −18.4073 | −0.632110 | ||||||||
\(849\) | −31.8811 | −1.09416 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.0856 | 0.894204 | ||||||||
\(852\) | −5.92296 | −0.202917 | ||||||||
\(853\) | 1.16342 | 0.0398346 | 0.0199173 | − | 0.999802i | \(-0.493660\pi\) | ||||
0.0199173 | + | 0.999802i | \(0.493660\pi\) | |||||||
\(854\) | 15.1324 | 0.517820 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −37.0005 | −1.26465 | ||||||||
\(857\) | 26.9612 | 0.920976 | 0.460488 | − | 0.887666i | \(-0.347674\pi\) | ||||
0.460488 | + | 0.887666i | \(0.347674\pi\) | |||||||
\(858\) | −18.3560 | −0.626663 | ||||||||
\(859\) | −16.1012 | −0.549367 | −0.274683 | − | 0.961535i | \(-0.588573\pi\) | ||||
−0.274683 | + | 0.961535i | \(0.588573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.11183 | −0.208291 | ||||||||
\(862\) | −45.5261 | −1.55063 | ||||||||
\(863\) | −9.69771 | −0.330114 | −0.165057 | − | 0.986284i | \(-0.552781\pi\) | ||||
−0.165057 | + | 0.986284i | \(0.552781\pi\) | |||||||
\(864\) | 7.27449 | 0.247483 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −56.2814 | −1.91252 | ||||||||
\(867\) | −39.3061 | −1.33491 | ||||||||
\(868\) | −32.1337 | −1.09069 | ||||||||
\(869\) | −21.2900 | −0.722212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.94204 | 0.0658036 | ||||||||
\(872\) | −23.6831 | −0.802011 | ||||||||
\(873\) | −11.6829 | −0.395406 | ||||||||
\(874\) | 8.28013 | 0.280080 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.5942 | 0.459304 | ||||||||
\(877\) | 2.85277 | 0.0963312 | 0.0481656 | − | 0.998839i | \(-0.484662\pi\) | ||||
0.0481656 | + | 0.998839i | \(0.484662\pi\) | |||||||
\(878\) | −4.56999 | −0.154230 | ||||||||
\(879\) | 11.7501 | 0.396320 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.9431 | 1.07619 | 0.538095 | − | 0.842884i | \(-0.319144\pi\) | ||||
0.538095 | + | 0.842884i | \(0.319144\pi\) | |||||||
\(882\) | −12.9582 | −0.436326 | ||||||||
\(883\) | 21.5997 | 0.726886 | 0.363443 | − | 0.931616i | \(-0.381601\pi\) | ||||
0.363443 | + | 0.931616i | \(0.381601\pi\) | |||||||
\(884\) | −54.9948 | −1.84967 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48.2442 | −1.62079 | ||||||||
\(887\) | −32.1151 | −1.07832 | −0.539160 | − | 0.842203i | \(-0.681258\pi\) | ||||
−0.539160 | + | 0.842203i | \(0.681258\pi\) | |||||||
\(888\) | −21.5124 | −0.721910 | ||||||||
\(889\) | −15.4220 | −0.517238 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.22580 | −0.108068 | ||||||||
\(892\) | 34.5054 | 1.15533 | ||||||||
\(893\) | 1.70135 | 0.0569335 | ||||||||
\(894\) | −12.3764 | −0.413928 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14.0271 | 0.468613 | ||||||||
\(897\) | 5.73275 | 0.191411 | ||||||||
\(898\) | 5.75565 | 0.192068 | ||||||||
\(899\) | 72.8302 | 2.42902 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.8093 | 2.79209 | ||||||||
\(902\) | 41.2356 | 1.37300 | ||||||||
\(903\) | 3.56765 | 0.118724 | ||||||||
\(904\) | 26.7932 | 0.891129 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −30.4078 | −1.01023 | ||||||||
\(907\) | −23.2655 | −0.772519 | −0.386259 | − | 0.922390i | \(-0.626233\pi\) | ||||
−0.386259 | + | 0.922390i | \(0.626233\pi\) | |||||||
\(908\) | 71.6648 | 2.37828 | ||||||||
\(909\) | −3.43631 | −0.113975 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.7030 | −0.917841 | −0.458920 | − | 0.888477i | \(-0.651764\pi\) | ||||
−0.458920 | + | 0.888477i | \(0.651764\pi\) | |||||||
\(912\) | 2.80395 | 0.0928480 | ||||||||
\(913\) | −50.3913 | −1.66771 | ||||||||
\(914\) | 69.4104 | 2.29589 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37.1513 | 1.22751 | ||||||||
\(917\) | 15.8840 | 0.524535 | ||||||||
\(918\) | −16.4926 | −0.544336 | ||||||||
\(919\) | −3.21697 | −0.106118 | −0.0530590 | − | 0.998591i | \(-0.516897\pi\) | ||||
−0.0530590 | + | 0.998591i | \(0.516897\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.3166 | −0.471748 | ||||||||
\(922\) | 1.95864 | 0.0645044 | ||||||||
\(923\) | −5.41696 | −0.178302 | ||||||||
\(924\) | −9.59614 | −0.315690 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 33.2695 | 1.09330 | ||||||||
\(927\) | 12.4894 | 0.410205 | ||||||||
\(928\) | −49.0471 | −1.61005 | ||||||||
\(929\) | −5.48067 | −0.179815 | −0.0899075 | − | 0.995950i | \(-0.528657\pi\) | ||||
−0.0899075 | + | 0.995950i | \(0.528657\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.0306 | −0.328740 | ||||||||
\(932\) | −58.9016 | −1.92939 | ||||||||
\(933\) | 15.9784 | 0.523108 | ||||||||
\(934\) | 6.42404 | 0.210201 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.72772 | −0.154530 | ||||||||
\(937\) | −3.03424 | −0.0991242 | −0.0495621 | − | 0.998771i | \(-0.515783\pi\) | ||||
−0.0495621 | + | 0.998771i | \(0.515783\pi\) | |||||||
\(938\) | 1.73255 | 0.0565697 | ||||||||
\(939\) | 17.1969 | 0.561199 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.1897 | −1.53834 | −0.769170 | − | 0.639045i | \(-0.779330\pi\) | ||||
−0.769170 | + | 0.639045i | \(0.779330\pi\) | |||||||
\(942\) | −9.35458 | −0.304789 | ||||||||
\(943\) | −12.8783 | −0.419375 | ||||||||
\(944\) | −20.3143 | −0.661175 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0704 | −0.782597 | ||||||||
\(947\) | −38.9579 | −1.26596 | −0.632982 | − | 0.774167i | \(-0.718169\pi\) | ||||
−0.632982 | + | 0.774167i | \(0.718169\pi\) | |||||||
\(948\) | −18.6832 | −0.606802 | ||||||||
\(949\) | 12.4328 | 0.403586 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.6354 | −0.798856 | ||||||||
\(952\) | −14.3994 | −0.466688 | ||||||||
\(953\) | −21.3170 | −0.690524 | −0.345262 | − | 0.938506i | \(-0.612210\pi\) | ||||
−0.345262 | + | 0.938506i | \(0.612210\pi\) | |||||||
\(954\) | 24.5485 | 0.794788 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.79801 | 0.0904943 | ||||||||
\(957\) | 21.7494 | 0.703058 | ||||||||
\(958\) | −29.4035 | −0.949983 | ||||||||
\(959\) | 18.5221 | 0.598109 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 85.6814 | 2.76392 | ||||||||
\(962\) | −67.0362 | −2.16133 | ||||||||
\(963\) | −20.2622 | −0.652940 | ||||||||
\(964\) | 45.5308 | 1.46645 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.11435 | 0.164551 | ||||||||
\(967\) | 48.1797 | 1.54935 | 0.774677 | − | 0.632358i | \(-0.217913\pi\) | ||||
0.774677 | + | 0.632358i | \(0.217913\pi\) | |||||||
\(968\) | −1.08513 | −0.0348774 | ||||||||
\(969\) | −12.7665 | −0.410119 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.4387 | 0.944732 | 0.472366 | − | 0.881402i | \(-0.343400\pi\) | ||||
0.472366 | + | 0.881402i | \(0.343400\pi\) | |||||||
\(972\) | −2.83083 | −0.0907988 | ||||||||
\(973\) | −9.92385 | −0.318144 | ||||||||
\(974\) | 81.1215 | 2.59930 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7976 | 0.345623 | ||||||||
\(977\) | −44.7657 | −1.43218 | −0.716091 | − | 0.698007i | \(-0.754070\pi\) | ||||
−0.716091 | + | 0.698007i | \(0.754070\pi\) | |||||||
\(978\) | 17.1440 | 0.548204 | ||||||||
\(979\) | 49.7236 | 1.58917 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.9693 | −0.414079 | ||||||||
\(982\) | 14.9356 | 0.476614 | ||||||||
\(983\) | −41.8646 | −1.33527 | −0.667637 | − | 0.744487i | \(-0.732694\pi\) | ||||
−0.667637 | + | 0.744487i | \(0.732694\pi\) | |||||||
\(984\) | 10.6205 | 0.338570 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 111.199 | 3.54128 | ||||||||
\(987\) | 1.05086 | 0.0334494 | ||||||||
\(988\) | −12.4692 | −0.396697 | ||||||||
\(989\) | 7.51742 | 0.239040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.5991 | −0.908480 | −0.454240 | − | 0.890879i | \(-0.650089\pi\) | ||||
−0.454240 | + | 0.890879i | \(0.650089\pi\) | |||||||
\(992\) | −78.5785 | −2.49487 | ||||||||
\(993\) | 7.11931 | 0.225924 | ||||||||
\(994\) | −4.83262 | −0.153281 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −44.2214 | −1.40121 | ||||||||
\(997\) | −24.6378 | −0.780287 | −0.390144 | − | 0.920754i | \(-0.627575\pi\) | ||||
−0.390144 | + | 0.920754i | \(0.627575\pi\) | |||||||
\(998\) | −11.0984 | −0.351314 | ||||||||
\(999\) | −11.7806 | −0.372722 |
(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 | 3525.2.a.be.1.7 | yes | 8 | |
5.4 | even | 2 | 3525.2.a.bd.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.bd.1.2 | ✓ | 8 | 5.4 | even | 2 | ||
3525.2.a.be.1.7 | yes | 8 | 1.1 | even | 1 | trivial |