Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.361.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.28514\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50702 | −1.77273 | −0.886365 | − | 0.462987i | \(-0.846778\pi\) | ||||
−0.886365 | + | 0.462987i | \(0.846778\pi\) | |||||||
\(3\) | 1.22188 | 0.705451 | 0.352725 | − | 0.935727i | \(-0.385255\pi\) | ||||
0.352725 | + | 0.935727i | \(0.385255\pi\) | |||||||
\(4\) | 4.28514 | 2.14257 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.06327 | −1.25057 | ||||||||
\(7\) | 0.221876 | 0.0838613 | 0.0419307 | − | 0.999121i | \(-0.486649\pi\) | ||||
0.0419307 | + | 0.999121i | \(0.486649\pi\) | |||||||
\(8\) | −5.72889 | −2.02547 | ||||||||
\(9\) | −1.50702 | −0.502340 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.778124 | −0.234613 | −0.117307 | − | 0.993096i | \(-0.537426\pi\) | ||||
−0.117307 | + | 0.993096i | \(0.537426\pi\) | |||||||
\(12\) | 5.23591 | 1.51148 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | −0.556248 | −0.148663 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.79216 | 1.44804 | ||||||||
\(17\) | −7.07730 | −1.71650 | −0.858249 | − | 0.513233i | \(-0.828448\pi\) | ||||
−0.858249 | + | 0.513233i | \(0.828448\pi\) | |||||||
\(18\) | 3.77812 | 0.890512 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.271105 | 0.0591600 | ||||||||
\(22\) | 1.95077 | 0.415906 | ||||||||
\(23\) | −8.07730 | −1.68423 | −0.842117 | − | 0.539295i | \(-0.818691\pi\) | ||||
−0.842117 | + | 0.539295i | \(0.818691\pi\) | |||||||
\(24\) | −7.00000 | −1.42887 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.5351 | 2.45833 | ||||||||
\(27\) | −5.50702 | −1.05983 | ||||||||
\(28\) | 0.950771 | 0.179679 | ||||||||
\(29\) | −0.221876 | −0.0412014 | −0.0206007 | − | 0.999788i | \(-0.506558\pi\) | ||||
−0.0206007 | + | 0.999788i | \(0.506558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50702 | −0.450274 | −0.225137 | − | 0.974327i | \(-0.572283\pi\) | ||||
−0.225137 | + | 0.974327i | \(0.572283\pi\) | |||||||
\(32\) | −3.06327 | −0.541514 | ||||||||
\(33\) | −0.950771 | −0.165508 | ||||||||
\(34\) | 17.7429 | 3.04289 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.45779 | −1.07630 | ||||||||
\(37\) | −1.90466 | −0.313124 | −0.156562 | − | 0.987668i | \(-0.550041\pi\) | ||||
−0.156562 | + | 0.987668i | \(0.550041\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.10938 | −0.978284 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.23591 | 1.13006 | 0.565030 | − | 0.825070i | \(-0.308865\pi\) | ||||
0.565030 | + | 0.825070i | \(0.308865\pi\) | |||||||
\(42\) | −0.679666 | −0.104875 | ||||||||
\(43\) | −7.29918 | −1.11311 | −0.556557 | − | 0.830809i | \(-0.687878\pi\) | ||||
−0.556557 | + | 0.830809i | \(0.687878\pi\) | |||||||
\(44\) | −3.33437 | −0.502675 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20.2500 | 2.98569 | ||||||||
\(47\) | 2.79216 | 0.407279 | 0.203639 | − | 0.979046i | \(-0.434723\pi\) | ||||
0.203639 | + | 0.979046i | \(0.434723\pi\) | |||||||
\(48\) | 7.07730 | 1.02152 | ||||||||
\(49\) | −6.95077 | −0.992967 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.64759 | −1.21090 | ||||||||
\(52\) | −21.4257 | −2.97121 | ||||||||
\(53\) | 4.38049 | 0.601706 | 0.300853 | − | 0.953671i | \(-0.402729\pi\) | ||||
0.300853 | + | 0.953671i | \(0.402729\pi\) | |||||||
\(54\) | 13.8062 | 1.87879 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.27111 | −0.169859 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.556248 | 0.0730389 | ||||||||
\(59\) | 2.79216 | 0.363508 | 0.181754 | − | 0.983344i | \(-0.441822\pi\) | ||||
0.181754 | + | 0.983344i | \(0.441822\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.5843 | −1.61126 | −0.805629 | − | 0.592421i | \(-0.798172\pi\) | ||||
−0.805629 | + | 0.592421i | \(0.798172\pi\) | |||||||
\(62\) | 6.28514 | 0.798214 | ||||||||
\(63\) | −0.334372 | −0.0421269 | ||||||||
\(64\) | −3.90466 | −0.488082 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.38360 | 0.293401 | ||||||||
\(67\) | −10.5703 | −1.29137 | −0.645683 | − | 0.763606i | \(-0.723427\pi\) | ||||
−0.645683 | + | 0.763606i | \(0.723427\pi\) | |||||||
\(68\) | −30.3273 | −3.67772 | ||||||||
\(69\) | −9.86946 | −1.18814 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.84139 | 1.16796 | 0.583979 | − | 0.811769i | \(-0.301495\pi\) | ||||
0.583979 | + | 0.811769i | \(0.301495\pi\) | |||||||
\(72\) | 8.63355 | 1.01747 | ||||||||
\(73\) | 14.0773 | 1.64762 | 0.823812 | − | 0.566863i | \(-0.191843\pi\) | ||||
0.823812 | + | 0.566863i | \(0.191843\pi\) | |||||||
\(74\) | 4.77501 | 0.555084 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.172647 | −0.0196750 | ||||||||
\(78\) | 15.3163 | 1.73423 | ||||||||
\(79\) | −1.58432 | −0.178250 | −0.0891251 | − | 0.996020i | \(-0.528407\pi\) | ||||
−0.0891251 | + | 0.996020i | \(0.528407\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.20784 | −0.245315 | ||||||||
\(82\) | −18.1406 | −2.00329 | ||||||||
\(83\) | 9.52106 | 1.04507 | 0.522536 | − | 0.852617i | \(-0.324986\pi\) | ||||
0.522536 | + | 0.852617i | \(0.324986\pi\) | |||||||
\(84\) | 1.16172 | 0.126755 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.2992 | 1.97325 | ||||||||
\(87\) | −0.271105 | −0.0290655 | ||||||||
\(88\) | 4.45779 | 0.475202 | ||||||||
\(89\) | −3.14057 | −0.332900 | −0.166450 | − | 0.986050i | \(-0.553230\pi\) | ||||
−0.166450 | + | 0.986050i | \(0.553230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10938 | −0.116295 | ||||||||
\(92\) | −34.6124 | −3.60859 | ||||||||
\(93\) | −3.06327 | −0.317646 | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.74293 | −0.382011 | ||||||||
\(97\) | −6.36245 | −0.646009 | −0.323004 | − | 0.946398i | \(-0.604693\pi\) | ||||
−0.323004 | + | 0.946398i | \(0.604693\pi\) | |||||||
\(98\) | 17.4257 | 1.76026 | ||||||||
\(99\) | 1.17265 | 0.117855 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.39452 | −0.735783 | −0.367891 | − | 0.929869i | \(-0.619920\pi\) | ||||
−0.367891 | + | 0.929869i | \(0.619920\pi\) | |||||||
\(102\) | 21.6797 | 2.14661 | ||||||||
\(103\) | 12.2038 | 1.20248 | 0.601240 | − | 0.799069i | \(-0.294674\pi\) | ||||
0.601240 | + | 0.799069i | \(0.294674\pi\) | |||||||
\(104\) | 28.6445 | 2.80882 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.9820 | −1.06666 | ||||||||
\(107\) | −1.63355 | −0.157921 | −0.0789607 | − | 0.996878i | \(-0.525160\pi\) | ||||
−0.0789607 | + | 0.996878i | \(0.525160\pi\) | |||||||
\(108\) | −23.5984 | −2.27075 | ||||||||
\(109\) | 7.61640 | 0.729519 | 0.364759 | − | 0.931102i | \(-0.381151\pi\) | ||||
0.364759 | + | 0.931102i | \(0.381151\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.32725 | −0.220893 | ||||||||
\(112\) | 1.28514 | 0.121435 | ||||||||
\(113\) | 12.4890 | 1.17486 | 0.587432 | − | 0.809273i | \(-0.300139\pi\) | ||||
0.587432 | + | 0.809273i | \(0.300139\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.950771 | −0.0882769 | ||||||||
\(117\) | 7.53509 | 0.696620 | ||||||||
\(118\) | −7.00000 | −0.644402 | ||||||||
\(119\) | −1.57028 | −0.143948 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3945 | −0.944957 | ||||||||
\(122\) | 31.5491 | 2.85632 | ||||||||
\(123\) | 8.84139 | 0.797201 | ||||||||
\(124\) | −10.7429 | −0.964744 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.838276 | 0.0746795 | ||||||||
\(127\) | −13.0421 | −1.15730 | −0.578650 | − | 0.815576i | \(-0.696420\pi\) | ||||
−0.578650 | + | 0.815576i | \(0.696420\pi\) | |||||||
\(128\) | 15.9156 | 1.40675 | ||||||||
\(129\) | −8.91869 | −0.785247 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.10938 | 0.621149 | 0.310575 | − | 0.950549i | \(-0.399478\pi\) | ||||
0.310575 | + | 0.950549i | \(0.399478\pi\) | |||||||
\(132\) | −4.07419 | −0.354613 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 26.4999 | 2.28924 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 40.5451 | 3.47672 | ||||||||
\(137\) | −5.42571 | −0.463550 | −0.231775 | − | 0.972769i | \(-0.574453\pi\) | ||||
−0.231775 | + | 0.972769i | \(0.574453\pi\) | |||||||
\(138\) | 24.7429 | 2.10626 | ||||||||
\(139\) | 3.57028 | 0.302828 | 0.151414 | − | 0.988470i | \(-0.451617\pi\) | ||||
0.151414 | + | 0.988470i | \(0.451617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.41168 | 0.287315 | ||||||||
\(142\) | −24.6725 | −2.07047 | ||||||||
\(143\) | 3.89062 | 0.325350 | ||||||||
\(144\) | −8.72889 | −0.727408 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −35.2921 | −2.92079 | ||||||||
\(147\) | −8.49298 | −0.700489 | ||||||||
\(148\) | −8.16172 | −0.670890 | ||||||||
\(149\) | −0.936734 | −0.0767402 | −0.0383701 | − | 0.999264i | \(-0.512217\pi\) | ||||
−0.0383701 | + | 0.999264i | \(0.512217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.971925 | 0.0790942 | 0.0395471 | − | 0.999218i | \(-0.487408\pi\) | ||||
0.0395471 | + | 0.999218i | \(0.487408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.6656 | 0.862265 | ||||||||
\(154\) | 0.432830 | 0.0348784 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −26.1796 | −2.09604 | ||||||||
\(157\) | −2.71486 | −0.216669 | −0.108335 | − | 0.994114i | \(-0.534552\pi\) | ||||
−0.108335 | + | 0.994114i | \(0.534552\pi\) | |||||||
\(158\) | 3.97193 | 0.315989 | ||||||||
\(159\) | 5.35241 | 0.424474 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.79216 | −0.141242 | ||||||||
\(162\) | 5.53509 | 0.434878 | ||||||||
\(163\) | 3.20384 | 0.250944 | 0.125472 | − | 0.992097i | \(-0.459956\pi\) | ||||
0.125472 | + | 0.992097i | \(0.459956\pi\) | |||||||
\(164\) | 31.0069 | 2.42123 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −23.8695 | −1.85263 | ||||||||
\(167\) | 10.2219 | 0.790993 | 0.395496 | − | 0.918468i | \(-0.370573\pi\) | ||||
0.395496 | + | 0.918468i | \(0.370573\pi\) | |||||||
\(168\) | −1.55313 | −0.119827 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −31.2780 | −2.38493 | ||||||||
\(173\) | −2.66563 | −0.202664 | −0.101332 | − | 0.994853i | \(-0.532310\pi\) | ||||
−0.101332 | + | 0.994853i | \(0.532310\pi\) | |||||||
\(174\) | 0.679666 | 0.0515253 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.50702 | −0.339729 | ||||||||
\(177\) | 3.41168 | 0.256437 | ||||||||
\(178\) | 7.87347 | 0.590141 | ||||||||
\(179\) | 12.9367 | 0.966937 | 0.483468 | − | 0.875362i | \(-0.339377\pi\) | ||||
0.483468 | + | 0.875362i | \(0.339377\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6124 | 1.38345 | 0.691724 | − | 0.722162i | \(-0.256851\pi\) | ||||
0.691724 | + | 0.722162i | \(0.256851\pi\) | |||||||
\(182\) | 2.78124 | 0.206159 | ||||||||
\(183\) | −15.3765 | −1.13666 | ||||||||
\(184\) | 46.2740 | 3.41137 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.67967 | 0.563100 | ||||||||
\(187\) | 5.50702 | 0.402713 | ||||||||
\(188\) | 11.9648 | 0.872623 | ||||||||
\(189\) | −1.22188 | −0.0888784 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.0421 | −1.66727 | −0.833634 | − | 0.552317i | \(-0.813744\pi\) | ||||
−0.833634 | + | 0.552317i | \(0.813744\pi\) | |||||||
\(192\) | −4.77101 | −0.344318 | ||||||||
\(193\) | −17.0773 | −1.22925 | −0.614626 | − | 0.788819i | \(-0.710693\pi\) | ||||
−0.614626 | + | 0.788819i | \(0.710693\pi\) | |||||||
\(194\) | 15.9508 | 1.14520 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.7850 | −2.12750 | ||||||||
\(197\) | 8.82024 | 0.628416 | 0.314208 | − | 0.949354i | \(-0.398261\pi\) | ||||
0.314208 | + | 0.949354i | \(0.398261\pi\) | |||||||
\(198\) | −2.93985 | −0.208926 | ||||||||
\(199\) | −2.85543 | −0.202416 | −0.101208 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101208 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9156 | −0.910995 | ||||||||
\(202\) | 18.5382 | 1.30434 | ||||||||
\(203\) | −0.0492290 | −0.00345520 | ||||||||
\(204\) | −37.0561 | −2.59445 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −30.5952 | −2.13167 | ||||||||
\(207\) | 12.1726 | 0.846057 | ||||||||
\(208\) | −28.9608 | −2.00807 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8875 | 0.887212 | 0.443606 | − | 0.896222i | \(-0.353699\pi\) | ||||
0.443606 | + | 0.896222i | \(0.353699\pi\) | |||||||
\(212\) | 18.7710 | 1.28920 | ||||||||
\(213\) | 12.0250 | 0.823937 | ||||||||
\(214\) | 4.09534 | 0.279952 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 31.5491 | 2.14665 | ||||||||
\(217\) | −0.556248 | −0.0377606 | ||||||||
\(218\) | −19.0945 | −1.29324 | ||||||||
\(219\) | 17.2007 | 1.16232 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.3865 | 2.38035 | ||||||||
\(222\) | 5.83447 | 0.391584 | ||||||||
\(223\) | 20.7077 | 1.38669 | 0.693346 | − | 0.720604i | \(-0.256136\pi\) | ||||
0.693346 | + | 0.720604i | \(0.256136\pi\) | |||||||
\(224\) | −0.679666 | −0.0454121 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.3101 | −2.08272 | ||||||||
\(227\) | 4.00000 | 0.265489 | 0.132745 | − | 0.991150i | \(-0.457621\pi\) | ||||
0.132745 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.53910 | 0.233870 | 0.116935 | − | 0.993140i | \(-0.462693\pi\) | ||||
0.116935 | + | 0.993140i | \(0.462693\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.210953 | −0.0138797 | ||||||||
\(232\) | 1.27111 | 0.0834521 | ||||||||
\(233\) | 19.7850 | 1.29616 | 0.648081 | − | 0.761572i | \(-0.275572\pi\) | ||||
0.648081 | + | 0.761572i | \(0.275572\pi\) | |||||||
\(234\) | −18.8906 | −1.23492 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.9648 | 0.778843 | ||||||||
\(237\) | −1.93585 | −0.125747 | ||||||||
\(238\) | 3.93673 | 0.255181 | ||||||||
\(239\) | 23.7741 | 1.53782 | 0.768910 | − | 0.639357i | \(-0.220799\pi\) | ||||
0.768910 | + | 0.639357i | \(0.220799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.54221 | 0.292589 | 0.146295 | − | 0.989241i | \(-0.453265\pi\) | ||||
0.146295 | + | 0.989241i | \(0.453265\pi\) | |||||||
\(242\) | 26.0593 | 1.67515 | ||||||||
\(243\) | 13.8234 | 0.886768 | ||||||||
\(244\) | −53.9256 | −3.45223 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −22.1655 | −1.41322 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14.3624 | 0.912016 | ||||||||
\(249\) | 11.6336 | 0.737246 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.5030 | −1.23102 | −0.615510 | − | 0.788129i | \(-0.711050\pi\) | ||||
−0.615510 | + | 0.788129i | \(0.711050\pi\) | |||||||
\(252\) | −1.43283 | −0.0902598 | ||||||||
\(253\) | 6.28514 | 0.395144 | ||||||||
\(254\) | 32.6968 | 2.05158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0913 | −2.00571 | ||||||||
\(257\) | 1.76409 | 0.110041 | 0.0550203 | − | 0.998485i | \(-0.482478\pi\) | ||||
0.0550203 | + | 0.998485i | \(0.482478\pi\) | |||||||
\(258\) | 22.3593 | 1.39203 | ||||||||
\(259\) | −0.422598 | −0.0262590 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.334372 | 0.0206971 | ||||||||
\(262\) | −17.8234 | −1.10113 | ||||||||
\(263\) | 6.47183 | 0.399070 | 0.199535 | − | 0.979891i | \(-0.436057\pi\) | ||||
0.199535 | + | 0.979891i | \(0.436057\pi\) | |||||||
\(264\) | 5.44687 | 0.335231 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.83739 | −0.234844 | ||||||||
\(268\) | −45.2952 | −2.76684 | ||||||||
\(269\) | −28.4859 | −1.73681 | −0.868407 | − | 0.495852i | \(-0.834856\pi\) | ||||
−0.868407 | + | 0.495852i | \(0.834856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.492981 | −0.0299465 | −0.0149732 | − | 0.999888i | \(-0.504766\pi\) | ||||
−0.0149732 | + | 0.999888i | \(0.504766\pi\) | |||||||
\(272\) | −40.9929 | −2.48556 | ||||||||
\(273\) | −1.35553 | −0.0820402 | ||||||||
\(274\) | 13.6024 | 0.821749 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −42.2921 | −2.54568 | ||||||||
\(277\) | 8.78905 | 0.528083 | 0.264041 | − | 0.964511i | \(-0.414944\pi\) | ||||
0.264041 | + | 0.964511i | \(0.414944\pi\) | |||||||
\(278\) | −8.95077 | −0.536832 | ||||||||
\(279\) | 3.77812 | 0.226190 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.74293 | 0.282940 | 0.141470 | − | 0.989943i | \(-0.454817\pi\) | ||||
0.141470 | + | 0.989943i | \(0.454817\pi\) | |||||||
\(282\) | −8.55313 | −0.509332 | ||||||||
\(283\) | −16.8695 | −1.00279 | −0.501393 | − | 0.865220i | \(-0.667179\pi\) | ||||
−0.501393 | + | 0.865220i | \(0.667179\pi\) | |||||||
\(284\) | 42.1718 | 2.50243 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.75385 | −0.576758 | ||||||||
\(287\) | 1.60548 | 0.0947683 | ||||||||
\(288\) | 4.61640 | 0.272024 | ||||||||
\(289\) | 33.0882 | 1.94637 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.77412 | −0.455727 | ||||||||
\(292\) | 60.3233 | 3.53015 | ||||||||
\(293\) | 11.6336 | 0.679639 | 0.339820 | − | 0.940491i | \(-0.389634\pi\) | ||||
0.339820 | + | 0.940491i | \(0.389634\pi\) | |||||||
\(294\) | 21.2921 | 1.24178 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.9116 | 0.634223 | ||||||||
\(297\) | 4.28514 | 0.248649 | ||||||||
\(298\) | 2.34841 | 0.136040 | ||||||||
\(299\) | 40.3865 | 2.33561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.61951 | −0.0933472 | ||||||||
\(302\) | −2.43664 | −0.140213 | ||||||||
\(303\) | −9.03519 | −0.519058 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −26.7389 | −1.52856 | ||||||||
\(307\) | 5.89062 | 0.336195 | 0.168098 | − | 0.985770i | \(-0.446238\pi\) | ||||
0.168098 | + | 0.985770i | \(0.446238\pi\) | |||||||
\(308\) | −0.739818 | −0.0421550 | ||||||||
\(309\) | 14.9116 | 0.848290 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8202 | 0.840378 | 0.420189 | − | 0.907437i | \(-0.361964\pi\) | ||||
0.420189 | + | 0.907437i | \(0.361964\pi\) | |||||||
\(312\) | 35.0000 | 1.98148 | ||||||||
\(313\) | 5.89462 | 0.333184 | 0.166592 | − | 0.986026i | \(-0.446724\pi\) | ||||
0.166592 | + | 0.986026i | \(0.446724\pi\) | |||||||
\(314\) | 6.80620 | 0.384096 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.78905 | −0.381914 | ||||||||
\(317\) | −4.15861 | −0.233571 | −0.116785 | − | 0.993157i | \(-0.537259\pi\) | ||||
−0.116785 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(318\) | −13.4186 | −0.752477 | ||||||||
\(319\) | 0.172647 | 0.00966638 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.99600 | −0.111406 | ||||||||
\(322\) | 4.49298 | 0.250384 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.46090 | −0.525606 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.03208 | −0.444856 | ||||||||
\(327\) | 9.30630 | 0.514639 | ||||||||
\(328\) | −41.4538 | −2.28890 | ||||||||
\(329\) | 0.619514 | 0.0341549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.6797 | −0.587008 | −0.293504 | − | 0.955958i | \(-0.594821\pi\) | ||||
−0.293504 | + | 0.955958i | \(0.594821\pi\) | |||||||
\(332\) | 40.7991 | 2.23914 | ||||||||
\(333\) | 2.87035 | 0.157294 | ||||||||
\(334\) | −25.6264 | −1.40222 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.57028 | 0.0856661 | ||||||||
\(337\) | −26.3453 | −1.43512 | −0.717560 | − | 0.696497i | \(-0.754741\pi\) | ||||
−0.717560 | + | 0.696497i | \(0.754741\pi\) | |||||||
\(338\) | −30.0842 | −1.63637 | ||||||||
\(339\) | 15.2600 | 0.828809 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.95077 | 0.105640 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.09534 | −0.167133 | ||||||||
\(344\) | 41.8162 | 2.25458 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.68278 | 0.359268 | ||||||||
\(347\) | 16.8835 | 0.906354 | 0.453177 | − | 0.891421i | \(-0.350291\pi\) | ||||
0.453177 | + | 0.891421i | \(0.350291\pi\) | |||||||
\(348\) | −1.16172 | −0.0622750 | ||||||||
\(349\) | 4.61640 | 0.247110 | 0.123555 | − | 0.992338i | \(-0.460570\pi\) | ||||
0.123555 | + | 0.992338i | \(0.460570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.5351 | 1.46971 | ||||||||
\(352\) | 2.38360 | 0.127046 | ||||||||
\(353\) | 24.9508 | 1.32800 | 0.663998 | − | 0.747735i | \(-0.268858\pi\) | ||||
0.663998 | + | 0.747735i | \(0.268858\pi\) | |||||||
\(354\) | −8.55313 | −0.454594 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.4578 | −0.713261 | ||||||||
\(357\) | −1.91869 | −0.101548 | ||||||||
\(358\) | −32.4326 | −1.71412 | ||||||||
\(359\) | 11.8022 | 0.622896 | 0.311448 | − | 0.950263i | \(-0.399186\pi\) | ||||
0.311448 | + | 0.950263i | \(0.399186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −46.6616 | −2.45248 | ||||||||
\(363\) | −12.7008 | −0.666620 | ||||||||
\(364\) | −4.75385 | −0.249170 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 38.5491 | 2.01500 | ||||||||
\(367\) | −26.2328 | −1.36934 | −0.684670 | − | 0.728853i | \(-0.740054\pi\) | ||||
−0.684670 | + | 0.728853i | \(0.740054\pi\) | |||||||
\(368\) | −46.7850 | −2.43884 | ||||||||
\(369\) | −10.9047 | −0.567674 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.971925 | 0.0504599 | ||||||||
\(372\) | −13.1265 | −0.680579 | ||||||||
\(373\) | 11.9960 | 0.621129 | 0.310565 | − | 0.950552i | \(-0.399482\pi\) | ||||
0.310565 | + | 0.950552i | \(0.399482\pi\) | |||||||
\(374\) | −13.8062 | −0.713902 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.9960 | −0.824931 | ||||||||
\(377\) | 1.10938 | 0.0571360 | ||||||||
\(378\) | 3.06327 | 0.157557 | ||||||||
\(379\) | −0.313217 | −0.0160889 | −0.00804444 | − | 0.999968i | \(-0.502561\pi\) | ||||
−0.00804444 | + | 0.999968i | \(0.502561\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.9358 | −0.816418 | ||||||||
\(382\) | 57.7670 | 2.95562 | ||||||||
\(383\) | 30.0882 | 1.53744 | 0.768718 | − | 0.639588i | \(-0.220895\pi\) | ||||
0.768718 | + | 0.639588i | \(0.220895\pi\) | |||||||
\(384\) | 19.4469 | 0.992394 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 42.8131 | 2.17913 | ||||||||
\(387\) | 11.0000 | 0.559161 | ||||||||
\(388\) | −27.2640 | −1.38412 | ||||||||
\(389\) | −35.7218 | −1.81117 | −0.905583 | − | 0.424169i | \(-0.860566\pi\) | ||||
−0.905583 | + | 0.424169i | \(0.860566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.1655 | 2.89099 | ||||||||
\(392\) | 39.8202 | 2.01123 | ||||||||
\(393\) | 8.68678 | 0.438190 | ||||||||
\(394\) | −22.1125 | −1.11401 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.02496 | 0.252514 | ||||||||
\(397\) | −9.55313 | −0.479458 | −0.239729 | − | 0.970840i | \(-0.577059\pi\) | ||||
−0.239729 | + | 0.970840i | \(0.577059\pi\) | |||||||
\(398\) | 7.15861 | 0.358829 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.8835 | −1.54225 | −0.771124 | − | 0.636685i | \(-0.780305\pi\) | ||||
−0.771124 | + | 0.636685i | \(0.780305\pi\) | |||||||
\(402\) | 32.3796 | 1.61495 | ||||||||
\(403\) | 12.5351 | 0.624417 | ||||||||
\(404\) | −31.6866 | −1.57647 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.123418 | 0.00612514 | ||||||||
\(407\) | 1.48206 | 0.0734629 | ||||||||
\(408\) | 49.5411 | 2.45265 | ||||||||
\(409\) | −31.5632 | −1.56070 | −0.780349 | − | 0.625344i | \(-0.784959\pi\) | ||||
−0.780349 | + | 0.625344i | \(0.784959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.62955 | −0.327012 | ||||||||
\(412\) | 52.2952 | 2.57640 | ||||||||
\(413\) | 0.619514 | 0.0304843 | ||||||||
\(414\) | −30.5171 | −1.49983 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.3163 | 0.750945 | ||||||||
\(417\) | 4.36245 | 0.213630 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.5070 | −1.29495 | −0.647476 | − | 0.762086i | \(-0.724176\pi\) | ||||
−0.647476 | + | 0.762086i | \(0.724176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.2359 | 0.986238 | 0.493119 | − | 0.869962i | \(-0.335857\pi\) | ||||
0.493119 | + | 0.869962i | \(0.335857\pi\) | |||||||
\(422\) | −32.3092 | −1.57279 | ||||||||
\(423\) | −4.20784 | −0.204592 | ||||||||
\(424\) | −25.0953 | −1.21874 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −30.1468 | −1.46062 | ||||||||
\(427\) | −2.79216 | −0.135122 | ||||||||
\(428\) | −7.00000 | −0.338358 | ||||||||
\(429\) | 4.75385 | 0.229518 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4609 | 0.552052 | 0.276026 | − | 0.961150i | \(-0.410982\pi\) | ||||
0.276026 | + | 0.961150i | \(0.410982\pi\) | |||||||
\(432\) | −31.8975 | −1.53467 | ||||||||
\(433\) | 25.9468 | 1.24692 | 0.623461 | − | 0.781854i | \(-0.285726\pi\) | ||||
0.623461 | + | 0.781854i | \(0.285726\pi\) | |||||||
\(434\) | 1.39452 | 0.0669393 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 32.6374 | 1.56305 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −43.1225 | −2.06047 | ||||||||
\(439\) | −25.3123 | −1.20809 | −0.604046 | − | 0.796950i | \(-0.706446\pi\) | ||||
−0.604046 | + | 0.796950i | \(0.706446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.4749 | 0.498807 | ||||||||
\(442\) | −88.7147 | −4.21973 | ||||||||
\(443\) | −20.0250 | −0.951415 | −0.475707 | − | 0.879604i | \(-0.657808\pi\) | ||||
−0.475707 | + | 0.879604i | \(0.657808\pi\) | |||||||
\(444\) | −9.97262 | −0.473279 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −51.9147 | −2.45823 | ||||||||
\(447\) | −1.14457 | −0.0541364 | ||||||||
\(448\) | −0.866350 | −0.0409312 | ||||||||
\(449\) | −19.7601 | −0.932536 | −0.466268 | − | 0.884644i | \(-0.654402\pi\) | ||||
−0.466268 | + | 0.884644i | \(0.654402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.63044 | −0.265127 | ||||||||
\(452\) | 53.5171 | 2.51723 | ||||||||
\(453\) | 1.18757 | 0.0557970 | ||||||||
\(454\) | −10.0281 | −0.470641 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.4647 | 1.61219 | 0.806096 | − | 0.591785i | \(-0.201577\pi\) | ||||
0.806096 | + | 0.591785i | \(0.201577\pi\) | |||||||
\(458\) | −8.87258 | −0.414588 | ||||||||
\(459\) | 38.9748 | 1.81919 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.93273 | −0.369464 | −0.184732 | − | 0.982789i | \(-0.559142\pi\) | ||||
−0.184732 | + | 0.982789i | \(0.559142\pi\) | |||||||
\(462\) | 0.528864 | 0.0246050 | ||||||||
\(463\) | −9.25395 | −0.430068 | −0.215034 | − | 0.976607i | \(-0.568986\pi\) | ||||
−0.215034 | + | 0.976607i | \(0.568986\pi\) | |||||||
\(464\) | −1.28514 | −0.0596612 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −49.6015 | −2.29774 | ||||||||
\(467\) | −9.47183 | −0.438304 | −0.219152 | − | 0.975691i | \(-0.570329\pi\) | ||||
−0.219152 | + | 0.975691i | \(0.570329\pi\) | |||||||
\(468\) | 32.2889 | 1.49256 | ||||||||
\(469\) | −2.34529 | −0.108296 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.31722 | −0.152849 | ||||||||
\(472\) | −15.9960 | −0.736275 | ||||||||
\(473\) | 5.67967 | 0.261151 | ||||||||
\(474\) | 4.85320 | 0.222915 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.72889 | −0.308418 | ||||||||
\(477\) | −6.60147 | −0.302261 | ||||||||
\(478\) | −59.6022 | −2.72614 | ||||||||
\(479\) | −34.7149 | −1.58616 | −0.793081 | − | 0.609116i | \(-0.791524\pi\) | ||||
−0.793081 | + | 0.609116i | \(0.791524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.52328 | 0.434224 | ||||||||
\(482\) | −11.3874 | −0.518682 | ||||||||
\(483\) | −2.18980 | −0.0996393 | ||||||||
\(484\) | −44.5420 | −2.02464 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −34.6554 | −1.57200 | ||||||||
\(487\) | −28.5070 | −1.29178 | −0.645888 | − | 0.763432i | \(-0.723513\pi\) | ||||
−0.645888 | + | 0.763432i | \(0.723513\pi\) | |||||||
\(488\) | 72.0943 | 3.26355 | ||||||||
\(489\) | 3.91469 | 0.177028 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.1898 | −1.40758 | −0.703788 | − | 0.710410i | \(-0.748509\pi\) | ||||
−0.703788 | + | 0.710410i | \(0.748509\pi\) | |||||||
\(492\) | 37.8866 | 1.70806 | ||||||||
\(493\) | 1.57028 | 0.0707221 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.5211 | −0.652015 | ||||||||
\(497\) | 2.18357 | 0.0979465 | ||||||||
\(498\) | −29.1655 | −1.30694 | ||||||||
\(499\) | 16.1867 | 0.724616 | 0.362308 | − | 0.932059i | \(-0.381989\pi\) | ||||
0.362308 | + | 0.932059i | \(0.381989\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4899 | 0.558006 | ||||||||
\(502\) | 48.8944 | 2.18226 | ||||||||
\(503\) | −17.2219 | −0.767886 | −0.383943 | − | 0.923357i | \(-0.625434\pi\) | ||||
−0.383943 | + | 0.923357i | \(0.625434\pi\) | |||||||
\(504\) | 1.91558 | 0.0853267 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.7570 | −0.700483 | ||||||||
\(507\) | 14.6625 | 0.651185 | ||||||||
\(508\) | −55.8873 | −2.47960 | ||||||||
\(509\) | 36.5912 | 1.62188 | 0.810939 | − | 0.585130i | \(-0.198957\pi\) | ||||
0.810939 | + | 0.585130i | \(0.198957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.12342 | 0.138172 | ||||||||
\(512\) | 48.6224 | 2.14883 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.42260 | −0.195072 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −38.2179 | −1.68245 | ||||||||
\(517\) | −2.17265 | −0.0955529 | ||||||||
\(518\) | 1.05946 | 0.0465500 | ||||||||
\(519\) | −3.25707 | −0.142969 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.63667 | 0.159325 | 0.0796626 | − | 0.996822i | \(-0.474616\pi\) | ||||
0.0796626 | + | 0.996822i | \(0.474616\pi\) | |||||||
\(522\) | −0.838276 | −0.0366903 | ||||||||
\(523\) | −35.6233 | −1.55770 | −0.778850 | − | 0.627211i | \(-0.784196\pi\) | ||||
−0.778850 | + | 0.627211i | \(0.784196\pi\) | |||||||
\(524\) | 30.4647 | 1.33086 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.2250 | −0.707443 | ||||||||
\(527\) | 17.7429 | 0.772894 | ||||||||
\(528\) | −5.50702 | −0.239662 | ||||||||
\(529\) | 42.2428 | 1.83664 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.20784 | −0.182605 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.1796 | −1.56711 | ||||||||
\(534\) | 9.62040 | 0.416316 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 60.5561 | 2.61562 | ||||||||
\(537\) | 15.8071 | 0.682126 | ||||||||
\(538\) | 71.4146 | 3.07890 | ||||||||
\(539\) | 5.40856 | 0.232963 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.17265 | 0.136403 | 0.0682014 | − | 0.997672i | \(-0.478274\pi\) | ||||
0.0682014 | + | 0.997672i | \(0.478274\pi\) | |||||||
\(542\) | 1.23591 | 0.0530870 | ||||||||
\(543\) | 22.7420 | 0.975955 | ||||||||
\(544\) | 21.6797 | 0.929508 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.39833 | 0.145435 | ||||||||
\(547\) | −28.3805 | −1.21346 | −0.606731 | − | 0.794907i | \(-0.707519\pi\) | ||||
−0.606731 | + | 0.794907i | \(0.707519\pi\) | |||||||
\(548\) | −23.2500 | −0.993189 | ||||||||
\(549\) | 18.9648 | 0.809398 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 56.5411 | 2.40655 | ||||||||
\(553\) | −0.351523 | −0.0149483 | ||||||||
\(554\) | −22.0343 | −0.936148 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.2992 | 0.648830 | ||||||||
\(557\) | −2.13054 | −0.0902737 | −0.0451368 | − | 0.998981i | \(-0.514372\pi\) | ||||
−0.0451368 | + | 0.998981i | \(0.514372\pi\) | |||||||
\(558\) | −9.47183 | −0.400974 | ||||||||
\(559\) | 36.4959 | 1.54361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.72889 | 0.284094 | ||||||||
\(562\) | −11.8906 | −0.501575 | ||||||||
\(563\) | −20.2609 | −0.853894 | −0.426947 | − | 0.904277i | \(-0.640411\pi\) | ||||
−0.426947 | + | 0.904277i | \(0.640411\pi\) | |||||||
\(564\) | 14.6195 | 0.615593 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 42.2921 | 1.77767 | ||||||||
\(567\) | −0.489867 | −0.0205725 | ||||||||
\(568\) | −56.3803 | −2.36566 | ||||||||
\(569\) | 34.7530 | 1.45692 | 0.728460 | − | 0.685088i | \(-0.240236\pi\) | ||||
0.728460 | + | 0.685088i | \(0.240236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0702 | 1.34210 | 0.671048 | − | 0.741414i | \(-0.265845\pi\) | ||||
0.671048 | + | 0.741414i | \(0.265845\pi\) | |||||||
\(572\) | 16.6719 | 0.697085 | ||||||||
\(573\) | −28.1546 | −1.17618 | ||||||||
\(574\) | −4.02496 | −0.167999 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.88439 | 0.245183 | ||||||||
\(577\) | −30.2740 | −1.26032 | −0.630162 | − | 0.776464i | \(-0.717012\pi\) | ||||
−0.630162 | + | 0.776464i | \(0.717012\pi\) | |||||||
\(578\) | −82.9528 | −3.45038 | ||||||||
\(579\) | −20.8664 | −0.867176 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.11250 | 0.0876411 | ||||||||
\(582\) | 19.4899 | 0.807881 | ||||||||
\(583\) | −3.40856 | −0.141168 | ||||||||
\(584\) | −80.6474 | −3.33721 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.1655 | −1.20482 | ||||||||
\(587\) | −2.49610 | −0.103025 | −0.0515125 | − | 0.998672i | \(-0.516404\pi\) | ||||
−0.0515125 | + | 0.998672i | \(0.516404\pi\) | |||||||
\(588\) | −36.3936 | −1.50085 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.7772 | 0.443316 | ||||||||
\(592\) | −11.0321 | −0.453416 | ||||||||
\(593\) | 9.96392 | 0.409169 | 0.204585 | − | 0.978849i | \(-0.434416\pi\) | ||||
0.204585 | + | 0.978849i | \(0.434416\pi\) | |||||||
\(594\) | −10.7429 | −0.440788 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.01404 | −0.164421 | ||||||||
\(597\) | −3.48898 | −0.142794 | ||||||||
\(598\) | −101.250 | −4.14041 | ||||||||
\(599\) | −32.0702 | −1.31035 | −0.655176 | − | 0.755476i | \(-0.727406\pi\) | ||||
−0.655176 | + | 0.755476i | \(0.727406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.68278 | −0.150224 | −0.0751119 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751119 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(602\) | 4.06015 | 0.165479 | ||||||||
\(603\) | 15.9296 | 0.648704 | ||||||||
\(604\) | 4.16484 | 0.169465 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22.6514 | 0.920150 | ||||||||
\(607\) | −20.4850 | −0.831460 | −0.415730 | − | 0.909488i | \(-0.636474\pi\) | ||||
−0.415730 | + | 0.909488i | \(0.636474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0601518 | −0.00243747 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.9608 | −0.564794 | ||||||||
\(612\) | 45.7037 | 1.84746 | ||||||||
\(613\) | −10.7117 | −0.432643 | −0.216322 | − | 0.976322i | \(-0.569406\pi\) | ||||
−0.216322 | + | 0.976322i | \(0.569406\pi\) | |||||||
\(614\) | −14.7679 | −0.595984 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.989077 | 0.0398511 | ||||||||
\(617\) | 17.7320 | 0.713864 | 0.356932 | − | 0.934130i | \(-0.383823\pi\) | ||||
0.356932 | + | 0.934130i | \(0.383823\pi\) | |||||||
\(618\) | −37.3836 | −1.50379 | ||||||||
\(619\) | −13.2780 | −0.533689 | −0.266844 | − | 0.963740i | \(-0.585981\pi\) | ||||
−0.266844 | + | 0.963740i | \(0.585981\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.4819 | 1.78500 | ||||||||
\(622\) | −37.1546 | −1.48976 | ||||||||
\(623\) | −0.696818 | −0.0279174 | ||||||||
\(624\) | −35.3865 | −1.41659 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.7779 | −0.590645 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.6336 | −0.464229 | ||||||||
\(629\) | 13.4798 | 0.537476 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.06415 | 0.161791 | 0.0808957 | − | 0.996723i | \(-0.474222\pi\) | ||||
0.0808957 | + | 0.996723i | \(0.474222\pi\) | |||||||
\(632\) | 9.07642 | 0.361040 | ||||||||
\(633\) | 15.7469 | 0.625884 | ||||||||
\(634\) | 10.4257 | 0.414058 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 22.9358 | 0.909465 | ||||||||
\(637\) | 34.7539 | 1.37700 | ||||||||
\(638\) | −0.432830 | −0.0171359 | ||||||||
\(639\) | −14.8312 | −0.586712 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.98507 | −0.196899 | −0.0984493 | − | 0.995142i | \(-0.531388\pi\) | ||||
−0.0984493 | + | 0.995142i | \(0.531388\pi\) | |||||||
\(642\) | 5.00400 | 0.197492 | ||||||||
\(643\) | 5.87658 | 0.231750 | 0.115875 | − | 0.993264i | \(-0.463033\pi\) | ||||
0.115875 | + | 0.993264i | \(0.463033\pi\) | |||||||
\(644\) | −7.67967 | −0.302621 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.9757 | −0.667385 | −0.333692 | − | 0.942682i | \(-0.608295\pi\) | ||||
−0.333692 | + | 0.942682i | \(0.608295\pi\) | |||||||
\(648\) | 12.6485 | 0.496879 | ||||||||
\(649\) | −2.17265 | −0.0852839 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.679666 | −0.0266382 | ||||||||
\(652\) | 13.7289 | 0.537665 | ||||||||
\(653\) | −24.6797 | −0.965790 | −0.482895 | − | 0.875678i | \(-0.660415\pi\) | ||||
−0.482895 | + | 0.875678i | \(0.660415\pi\) | |||||||
\(654\) | −23.3311 | −0.912317 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.9116 | 1.63637 | ||||||||
\(657\) | −21.2148 | −0.827667 | ||||||||
\(658\) | −1.55313 | −0.0605474 | ||||||||
\(659\) | −1.88662 | −0.0734921 | −0.0367461 | − | 0.999325i | \(-0.511699\pi\) | ||||
−0.0367461 | + | 0.999325i | \(0.511699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.7499 | −1.74057 | −0.870284 | − | 0.492551i | \(-0.836065\pi\) | ||||
−0.870284 | + | 0.492551i | \(0.836065\pi\) | |||||||
\(662\) | 26.7741 | 1.04061 | ||||||||
\(663\) | 43.2379 | 1.67922 | ||||||||
\(664\) | −54.5451 | −2.11676 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.19603 | −0.278840 | ||||||||
\(667\) | 1.79216 | 0.0693928 | ||||||||
\(668\) | 43.8022 | 1.69476 | ||||||||
\(669\) | 25.3023 | 0.978243 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.79216 | 0.378022 | ||||||||
\(672\) | −0.830467 | −0.0320360 | ||||||||
\(673\) | 25.4046 | 0.979274 | 0.489637 | − | 0.871926i | \(-0.337129\pi\) | ||||
0.489637 | + | 0.871926i | \(0.337129\pi\) | |||||||
\(674\) | 66.0481 | 2.54408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 51.4217 | 1.97776 | ||||||||
\(677\) | −3.86946 | −0.148716 | −0.0743578 | − | 0.997232i | \(-0.523691\pi\) | ||||
−0.0743578 | + | 0.997232i | \(0.523691\pi\) | |||||||
\(678\) | −38.2571 | −1.46925 | ||||||||
\(679\) | −1.41168 | −0.0541751 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.88750 | 0.187290 | ||||||||
\(682\) | −4.89062 | −0.187271 | ||||||||
\(683\) | −48.5171 | −1.85645 | −0.928227 | − | 0.372015i | \(-0.878667\pi\) | ||||
−0.928227 | + | 0.372015i | \(0.878667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.76008 | 0.296281 | ||||||||
\(687\) | 4.32434 | 0.164984 | ||||||||
\(688\) | −42.2780 | −1.61183 | ||||||||
\(689\) | −21.9024 | −0.834416 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.6374 | −1.81221 | −0.906105 | − | 0.423052i | \(-0.860959\pi\) | ||||
−0.906105 | + | 0.423052i | \(0.860959\pi\) | |||||||
\(692\) | −11.4226 | −0.434222 | ||||||||
\(693\) | 0.260182 | 0.00988351 | ||||||||
\(694\) | −42.3273 | −1.60672 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.55313 | 0.0588714 | ||||||||
\(697\) | −51.2108 | −1.93975 | ||||||||
\(698\) | −11.5734 | −0.438060 | ||||||||
\(699\) | 24.1749 | 0.914378 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.5531 | 1.07844 | 0.539218 | − | 0.842166i | \(-0.318720\pi\) | ||||
0.539218 | + | 0.842166i | \(0.318720\pi\) | |||||||
\(702\) | −69.0310 | −2.60541 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.03831 | 0.114510 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −62.5520 | −2.35418 | ||||||||
\(707\) | −1.64067 | −0.0617037 | ||||||||
\(708\) | 14.6195 | 0.549435 | ||||||||
\(709\) | 19.4827 | 0.731690 | 0.365845 | − | 0.930676i | \(-0.380780\pi\) | ||||
0.365845 | + | 0.930676i | \(0.380780\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.38760 | 0.0895421 | ||||||||
\(712\) | 17.9920 | 0.674279 | ||||||||
\(713\) | 20.2500 | 0.758367 | ||||||||
\(714\) | 4.81020 | 0.180017 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 55.4357 | 2.07173 | ||||||||
\(717\) | 29.0490 | 1.08486 | ||||||||
\(718\) | −29.5883 | −1.10423 | ||||||||
\(719\) | 4.10627 | 0.153138 | 0.0765689 | − | 0.997064i | \(-0.475603\pi\) | ||||
0.0765689 | + | 0.997064i | \(0.475603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.70774 | 0.100842 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.55002 | 0.206407 | ||||||||
\(724\) | 79.7568 | 2.96414 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.8412 | 1.18174 | ||||||||
\(727\) | 12.4117 | 0.460324 | 0.230162 | − | 0.973152i | \(-0.426074\pi\) | ||||
0.230162 | + | 0.973152i | \(0.426074\pi\) | |||||||
\(728\) | 6.35553 | 0.235551 | ||||||||
\(729\) | 23.5139 | 0.870887 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.6585 | 1.91066 | ||||||||
\(732\) | −65.8904 | −2.43538 | ||||||||
\(733\) | 16.3985 | 0.605693 | 0.302847 | − | 0.953039i | \(-0.402063\pi\) | ||||
0.302847 | + | 0.953039i | \(0.402063\pi\) | |||||||
\(734\) | 65.7661 | 2.42747 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.7429 | 0.912037 | ||||||||
\(737\) | 8.22499 | 0.302971 | ||||||||
\(738\) | 27.3382 | 1.00633 | ||||||||
\(739\) | −46.2036 | −1.69963 | −0.849814 | − | 0.527082i | \(-0.823286\pi\) | ||||
−0.849814 | + | 0.527082i | \(0.823286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.43664 | −0.0894517 | ||||||||
\(743\) | −24.8131 | −0.910305 | −0.455153 | − | 0.890413i | \(-0.650415\pi\) | ||||
−0.455153 | + | 0.890413i | \(0.650415\pi\) | |||||||
\(744\) | 17.5491 | 0.643382 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.0742 | −1.10109 | ||||||||
\(747\) | −14.3484 | −0.524981 | ||||||||
\(748\) | 23.5984 | 0.862841 | ||||||||
\(749\) | −0.362446 | −0.0132435 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5391 | 0.384577 | 0.192289 | − | 0.981338i | \(-0.438409\pi\) | ||||
0.192289 | + | 0.981338i | \(0.438409\pi\) | |||||||
\(752\) | 16.1726 | 0.589756 | ||||||||
\(753\) | −23.8303 | −0.868423 | ||||||||
\(754\) | −2.78124 | −0.101287 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.23591 | −0.190428 | ||||||||
\(757\) | 6.19672 | 0.225224 | 0.112612 | − | 0.993639i | \(-0.464078\pi\) | ||||
0.112612 | + | 0.993639i | \(0.464078\pi\) | |||||||
\(758\) | 0.785241 | 0.0285212 | ||||||||
\(759\) | 7.67967 | 0.278754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.6084 | 1.29080 | 0.645402 | − | 0.763843i | \(-0.276690\pi\) | ||||
0.645402 | + | 0.763843i | \(0.276690\pi\) | |||||||
\(762\) | 39.9515 | 1.44729 | ||||||||
\(763\) | 1.68990 | 0.0611784 | ||||||||
\(764\) | −98.7387 | −3.57224 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −75.4317 | −2.72546 | ||||||||
\(767\) | −13.9608 | −0.504095 | ||||||||
\(768\) | −39.2116 | −1.41493 | ||||||||
\(769\) | −0.155495 | −0.00560730 | −0.00280365 | − | 0.999996i | \(-0.500892\pi\) | ||||
−0.00280365 | + | 0.999996i | \(0.500892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.15550 | 0.0776283 | ||||||||
\(772\) | −73.1787 | −2.63376 | ||||||||
\(773\) | −5.08823 | −0.183011 | −0.0915054 | − | 0.995805i | \(-0.529168\pi\) | ||||
−0.0915054 | + | 0.995805i | \(0.529168\pi\) | |||||||
\(774\) | −27.5772 | −0.991242 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.4498 | 1.30847 | ||||||||
\(777\) | −0.516362 | −0.0185244 | ||||||||
\(778\) | 89.5552 | 3.21071 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.65782 | −0.274018 | ||||||||
\(782\) | −143.315 | −5.12494 | ||||||||
\(783\) | 1.22188 | 0.0436663 | ||||||||
\(784\) | −40.2600 | −1.43786 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.7779 | −0.776793 | ||||||||
\(787\) | −22.5070 | −0.802289 | −0.401144 | − | 0.916015i | \(-0.631387\pi\) | ||||
−0.401144 | + | 0.916015i | \(0.631387\pi\) | |||||||
\(788\) | 37.7960 | 1.34643 | ||||||||
\(789\) | 7.90777 | 0.281524 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.77101 | 0.0985257 | ||||||||
\(792\) | −6.71797 | −0.238713 | ||||||||
\(793\) | 62.9216 | 2.23441 | ||||||||
\(794\) | 23.9499 | 0.849950 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.2359 | −0.433690 | ||||||||
\(797\) | 29.2219 | 1.03509 | 0.517546 | − | 0.855655i | \(-0.326846\pi\) | ||||
0.517546 | + | 0.855655i | \(0.326846\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.7610 | −0.699093 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.73290 | 0.167229 | ||||||||
\(802\) | 77.4255 | 2.73399 | ||||||||
\(803\) | −10.9539 | −0.386554 | ||||||||
\(804\) | −55.3451 | −1.95187 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31.4257 | −1.10692 | ||||||||
\(807\) | −34.8062 | −1.22524 | ||||||||
\(808\) | 42.3624 | 1.49031 | ||||||||
\(809\) | 25.8664 | 0.909412 | 0.454706 | − | 0.890641i | \(-0.349744\pi\) | ||||
0.454706 | + | 0.890641i | \(0.349744\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6968 | 0.691649 | 0.345824 | − | 0.938299i | \(-0.387599\pi\) | ||||
0.345824 | + | 0.938299i | \(0.387599\pi\) | |||||||
\(812\) | −0.210953 | −0.00740301 | ||||||||
\(813\) | −0.602362 | −0.0211258 | ||||||||
\(814\) | −3.71555 | −0.130230 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −50.0882 | −1.75344 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 79.1295 | 2.76670 | ||||||||
\(819\) | 1.67186 | 0.0584194 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.08042 | 0.142408 | 0.0712038 | − | 0.997462i | \(-0.477316\pi\) | ||||
0.0712038 | + | 0.997462i | \(0.477316\pi\) | |||||||
\(822\) | 16.6204 | 0.579703 | ||||||||
\(823\) | −10.6064 | −0.369715 | −0.184857 | − | 0.982765i | \(-0.559182\pi\) | ||||
−0.184857 | + | 0.982765i | \(0.559182\pi\) | |||||||
\(824\) | −69.9145 | −2.43559 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.55313 | −0.0540404 | ||||||||
\(827\) | 15.4046 | 0.535669 | 0.267834 | − | 0.963465i | \(-0.413692\pi\) | ||||
0.267834 | + | 0.963465i | \(0.413692\pi\) | |||||||
\(828\) | 52.1615 | 1.81274 | ||||||||
\(829\) | −21.2350 | −0.737523 | −0.368761 | − | 0.929524i | \(-0.620218\pi\) | ||||
−0.368761 | + | 0.929524i | \(0.620218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7391 | 0.372536 | ||||||||
\(832\) | 19.5233 | 0.676848 | ||||||||
\(833\) | 49.1927 | 1.70443 | ||||||||
\(834\) | −10.9367 | −0.378708 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.8062 | 0.477212 | ||||||||
\(838\) | 66.4536 | 2.29560 | ||||||||
\(839\) | 6.09134 | 0.210296 | 0.105148 | − | 0.994457i | \(-0.466468\pi\) | ||||
0.105148 | + | 0.994457i | \(0.466468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9508 | −0.998302 | ||||||||
\(842\) | −50.7318 | −1.74833 | ||||||||
\(843\) | 5.79528 | 0.199600 | ||||||||
\(844\) | 55.2248 | 1.90092 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.5491 | 0.362687 | ||||||||
\(847\) | −2.30630 | −0.0792453 | ||||||||
\(848\) | 25.3725 | 0.871295 | ||||||||
\(849\) | −20.6124 | −0.707416 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.3845 | 0.527373 | ||||||||
\(852\) | 51.5287 | 1.76534 | ||||||||
\(853\) | 34.9648 | 1.19717 | 0.598586 | − | 0.801058i | \(-0.295729\pi\) | ||||
0.598586 | + | 0.801058i | \(0.295729\pi\) | |||||||
\(854\) | 7.00000 | 0.239535 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.35844 | 0.319865 | ||||||||
\(857\) | 4.15149 | 0.141812 | 0.0709061 | − | 0.997483i | \(-0.477411\pi\) | ||||
0.0709061 | + | 0.997483i | \(0.477411\pi\) | |||||||
\(858\) | −11.9180 | −0.406874 | ||||||||
\(859\) | 28.2491 | 0.963846 | 0.481923 | − | 0.876214i | \(-0.339939\pi\) | ||||
0.481923 | + | 0.876214i | \(0.339939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.96169 | 0.0668543 | ||||||||
\(862\) | −28.7327 | −0.978640 | ||||||||
\(863\) | 51.8272 | 1.76422 | 0.882108 | − | 0.471046i | \(-0.156124\pi\) | ||||
0.882108 | + | 0.471046i | \(0.156124\pi\) | |||||||
\(864\) | 16.8695 | 0.573911 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −65.0490 | −2.21046 | ||||||||
\(867\) | 40.4297 | 1.37307 | ||||||||
\(868\) | −2.38360 | −0.0809047 | ||||||||
\(869\) | 1.23280 | 0.0418198 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.8514 | 1.79080 | ||||||||
\(872\) | −43.6336 | −1.47762 | ||||||||
\(873\) | 9.58832 | 0.324516 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 73.7075 | 2.49035 | ||||||||
\(877\) | −47.1998 | −1.59383 | −0.796913 | − | 0.604095i | \(-0.793535\pi\) | ||||
−0.796913 | + | 0.604095i | \(0.793535\pi\) | |||||||
\(878\) | 63.4585 | 2.14162 | ||||||||
\(879\) | 14.2148 | 0.479452 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.8935 | −1.14190 | −0.570951 | − | 0.820984i | \(-0.693425\pi\) | ||||
−0.570951 | + | 0.820984i | \(0.693425\pi\) | |||||||
\(882\) | −26.2609 | −0.884250 | ||||||||
\(883\) | −21.0662 | −0.708934 | −0.354467 | − | 0.935069i | \(-0.615338\pi\) | ||||
−0.354467 | + | 0.935069i | \(0.615338\pi\) | |||||||
\(884\) | 151.636 | 5.10008 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 50.2029 | 1.68660 | ||||||||
\(887\) | 7.21476 | 0.242248 | 0.121124 | − | 0.992637i | \(-0.461350\pi\) | ||||
0.121124 | + | 0.992637i | \(0.461350\pi\) | |||||||
\(888\) | 13.3326 | 0.447413 | ||||||||
\(889\) | −2.89373 | −0.0970527 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.71797 | 0.0575542 | ||||||||
\(892\) | 88.7356 | 2.97109 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 2.86946 | 0.0959693 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.53129 | 0.117972 | ||||||||
\(897\) | 49.3473 | 1.64766 | ||||||||
\(898\) | 49.5389 | 1.65313 | ||||||||
\(899\) | 0.556248 | 0.0185519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.0020 | −1.03283 | ||||||||
\(902\) | 14.1156 | 0.469998 | ||||||||
\(903\) | −1.97885 | −0.0658519 | ||||||||
\(904\) | −71.5480 | −2.37965 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.97727 | −0.0989131 | ||||||||
\(907\) | 1.16864 | 0.0388042 | 0.0194021 | − | 0.999812i | \(-0.493824\pi\) | ||||
0.0194021 | + | 0.999812i | \(0.493824\pi\) | |||||||
\(908\) | 17.1406 | 0.568830 | ||||||||
\(909\) | 11.1437 | 0.369613 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.3313 | 0.408553 | 0.204276 | − | 0.978913i | \(-0.434516\pi\) | ||||
0.204276 | + | 0.978913i | \(0.434516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.40856 | −0.245188 | ||||||||
\(914\) | −86.4037 | −2.85798 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.1655 | 0.501083 | ||||||||
\(917\) | 1.57740 | 0.0520904 | ||||||||
\(918\) | −97.7107 | −3.22493 | ||||||||
\(919\) | 52.8895 | 1.74466 | 0.872332 | − | 0.488913i | \(-0.162607\pi\) | ||||
0.872332 | + | 0.488913i | \(0.162607\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.19761 | 0.237169 | ||||||||
\(922\) | 19.8875 | 0.654960 | ||||||||
\(923\) | −49.2070 | −1.61967 | ||||||||
\(924\) | −0.903965 | −0.0297383 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.1998 | 0.762394 | ||||||||
\(927\) | −18.3914 | −0.604053 | ||||||||
\(928\) | 0.679666 | 0.0223111 | ||||||||
\(929\) | 1.39141 | 0.0456506 | 0.0228253 | − | 0.999739i | \(-0.492734\pi\) | ||||
0.0228253 | + | 0.999739i | \(0.492734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 84.7817 | 2.77712 | ||||||||
\(933\) | 18.1085 | 0.592845 | ||||||||
\(934\) | 23.7460 | 0.776994 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −43.1678 | −1.41098 | ||||||||
\(937\) | 33.3694 | 1.09013 | 0.545065 | − | 0.838394i | \(-0.316505\pi\) | ||||
0.545065 | + | 0.838394i | \(0.316505\pi\) | |||||||
\(938\) | 5.87970 | 0.191979 | ||||||||
\(939\) | 7.20250 | 0.235045 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.3233 | −1.15151 | −0.575753 | − | 0.817624i | \(-0.695291\pi\) | ||||
−0.575753 | + | 0.817624i | \(0.695291\pi\) | |||||||
\(942\) | 8.31633 | 0.270961 | ||||||||
\(943\) | −58.4467 | −1.90329 | ||||||||
\(944\) | 16.1726 | 0.526375 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.2390 | −0.462951 | ||||||||
\(947\) | −13.2571 | −0.430797 | −0.215398 | − | 0.976526i | \(-0.569105\pi\) | ||||
−0.215398 | + | 0.976526i | \(0.569105\pi\) | |||||||
\(948\) | −8.29537 | −0.269421 | ||||||||
\(949\) | −70.3865 | −2.28484 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.08131 | −0.164773 | ||||||||
\(952\) | 8.99600 | 0.291562 | ||||||||
\(953\) | 18.2702 | 0.591830 | 0.295915 | − | 0.955214i | \(-0.404375\pi\) | ||||
0.295915 | + | 0.955214i | \(0.404375\pi\) | |||||||
\(954\) | 16.5500 | 0.535827 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 101.875 | 3.29489 | ||||||||
\(957\) | 0.210953 | 0.00681916 | ||||||||
\(958\) | 87.0308 | 2.81184 | ||||||||
\(959\) | −1.20384 | −0.0388739 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7149 | −0.797253 | ||||||||
\(962\) | −23.8750 | −0.769762 | ||||||||
\(963\) | 2.46179 | 0.0793301 | ||||||||
\(964\) | 19.4640 | 0.626894 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.48987 | 0.176634 | ||||||||
\(967\) | 45.1125 | 1.45072 | 0.725360 | − | 0.688370i | \(-0.241673\pi\) | ||||
0.725360 | + | 0.688370i | \(0.241673\pi\) | |||||||
\(968\) | 59.5491 | 1.91398 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.6024 | −0.500704 | −0.250352 | − | 0.968155i | \(-0.580546\pi\) | ||||
−0.250352 | + | 0.968155i | \(0.580546\pi\) | |||||||
\(972\) | 59.2350 | 1.89996 | ||||||||
\(973\) | 0.792161 | 0.0253955 | ||||||||
\(974\) | 71.4676 | 2.28997 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −72.8904 | −2.33317 | ||||||||
\(977\) | 26.2319 | 0.839233 | 0.419617 | − | 0.907701i | \(-0.362165\pi\) | ||||
0.419617 | + | 0.907701i | \(0.362165\pi\) | |||||||
\(978\) | −9.81420 | −0.313824 | ||||||||
\(979\) | 2.44375 | 0.0781027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.4781 | −0.366466 | ||||||||
\(982\) | 78.1934 | 2.49525 | ||||||||
\(983\) | −34.3413 | −1.09532 | −0.547659 | − | 0.836702i | \(-0.684481\pi\) | ||||
−0.547659 | + | 0.836702i | \(0.684481\pi\) | |||||||
\(984\) | −50.6514 | −1.61471 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.93673 | −0.125371 | ||||||||
\(987\) | 0.756969 | 0.0240946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.9577 | 1.87475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.30318 | −0.104929 | −0.0524645 | − | 0.998623i | \(-0.516708\pi\) | ||||
−0.0524645 | + | 0.998623i | \(0.516708\pi\) | |||||||
\(992\) | 7.67967 | 0.243830 | ||||||||
\(993\) | −13.0492 | −0.414105 | ||||||||
\(994\) | −5.47425 | −0.173633 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 49.8514 | 1.57960 | ||||||||
\(997\) | −9.82335 | −0.311109 | −0.155554 | − | 0.987827i | \(-0.549716\pi\) | ||||
−0.155554 | + | 0.987827i | \(0.549716\pi\) | |||||||
\(998\) | −40.5803 | −1.28455 | ||||||||
\(999\) | 10.4890 | 0.331857 |
(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 | 9025.2.a.ba.1.1 | 3 | ||
5.4 | even | 2 | 1805.2.a.g.1.3 | 3 | |||
19.8 | odd | 6 | 475.2.e.d.26.1 | 6 | |||
19.12 | odd | 6 | 475.2.e.d.201.1 | 6 | |||
19.18 | odd | 2 | 9025.2.a.z.1.3 | 3 | |||
95.8 | even | 12 | 475.2.j.b.349.1 | 12 | |||
95.12 | even | 12 | 475.2.j.b.49.1 | 12 | |||
95.27 | even | 12 | 475.2.j.b.349.6 | 12 | |||
95.69 | odd | 6 | 95.2.e.b.11.3 | ✓ | 6 | ||
95.84 | odd | 6 | 95.2.e.b.26.3 | yes | 6 | ||
95.88 | even | 12 | 475.2.j.b.49.6 | 12 | |||
95.94 | odd | 2 | 1805.2.a.h.1.1 | 3 | |||
285.164 | even | 6 | 855.2.k.g.676.1 | 6 | |||
285.179 | even | 6 | 855.2.k.g.406.1 | 6 | |||
380.179 | even | 6 | 1520.2.q.j.881.2 | 6 | |||
380.259 | even | 6 | 1520.2.q.j.961.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.b.11.3 | ✓ | 6 | 95.69 | odd | 6 | ||
95.2.e.b.26.3 | yes | 6 | 95.84 | odd | 6 | ||
475.2.e.d.26.1 | 6 | 19.8 | odd | 6 | |||
475.2.e.d.201.1 | 6 | 19.12 | odd | 6 | |||
475.2.j.b.49.1 | 12 | 95.12 | even | 12 | |||
475.2.j.b.49.6 | 12 | 95.88 | even | 12 | |||
475.2.j.b.349.1 | 12 | 95.8 | even | 12 | |||
475.2.j.b.349.6 | 12 | 95.27 | even | 12 | |||
855.2.k.g.406.1 | 6 | 285.179 | even | 6 | |||
855.2.k.g.676.1 | 6 | 285.164 | even | 6 | |||
1520.2.q.j.881.2 | 6 | 380.179 | even | 6 | |||
1520.2.q.j.961.2 | 6 | 380.259 | even | 6 | |||
1805.2.a.g.1.3 | 3 | 5.4 | even | 2 | |||
1805.2.a.h.1.1 | 3 | 95.94 | odd | 2 | |||
9025.2.a.z.1.3 | 3 | 19.18 | odd | 2 | |||
9025.2.a.ba.1.1 | 3 | 1.1 | even | 1 | trivial |