Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91059 | −1.35099 | −0.675494 | − | 0.737366i | \(-0.736070\pi\) | ||||
−0.675494 | + | 0.737366i | \(0.736070\pi\) | |||||||
\(3\) | −2.10440 | −1.21497 | −0.607487 | − | 0.794329i | \(-0.707822\pi\) | ||||
−0.607487 | + | 0.794329i | \(0.707822\pi\) | |||||||
\(4\) | 1.65034 | 0.825168 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.02063 | 1.64142 | ||||||||
\(7\) | −2.16427 | −0.818017 | −0.409008 | − | 0.912531i | \(-0.634125\pi\) | ||||
−0.409008 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(8\) | 0.668063 | 0.236196 | ||||||||
\(9\) | 1.42849 | 0.476164 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.26801 | −1.28685 | −0.643427 | − | 0.765508i | \(-0.722488\pi\) | ||||
−0.643427 | + | 0.765508i | \(0.722488\pi\) | |||||||
\(12\) | −3.47296 | −1.00256 | ||||||||
\(13\) | −4.06225 | −1.12667 | −0.563333 | − | 0.826230i | \(-0.690481\pi\) | ||||
−0.563333 | + | 0.826230i | \(0.690481\pi\) | |||||||
\(14\) | 4.13502 | 1.10513 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.57706 | −1.14427 | ||||||||
\(17\) | −5.01513 | −1.21635 | −0.608174 | − | 0.793804i | \(-0.708098\pi\) | ||||
−0.608174 | + | 0.793804i | \(0.708098\pi\) | |||||||
\(18\) | −2.72925 | −0.643291 | ||||||||
\(19\) | −0.180581 | −0.0414281 | −0.0207140 | − | 0.999785i | \(-0.506594\pi\) | ||||
−0.0207140 | + | 0.999785i | \(0.506594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.55448 | 0.993870 | ||||||||
\(22\) | 8.15439 | 1.73852 | ||||||||
\(23\) | −2.32572 | −0.484945 | −0.242473 | − | 0.970158i | \(-0.577958\pi\) | ||||
−0.242473 | + | 0.970158i | \(0.577958\pi\) | |||||||
\(24\) | −1.40587 | −0.286972 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.76128 | 1.52211 | ||||||||
\(27\) | 3.30708 | 0.636448 | ||||||||
\(28\) | −3.57177 | −0.675001 | ||||||||
\(29\) | −0.555774 | −0.103205 | −0.0516024 | − | 0.998668i | \(-0.516433\pi\) | ||||
−0.0516024 | + | 0.998668i | \(0.516433\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.29164 | 0.591197 | 0.295598 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295598 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(32\) | 7.40874 | 1.30969 | ||||||||
\(33\) | 8.98159 | 1.56349 | ||||||||
\(34\) | 9.58183 | 1.64327 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.35749 | 0.392915 | ||||||||
\(37\) | 9.51931 | 1.56497 | 0.782483 | − | 0.622672i | \(-0.213953\pi\) | ||||
0.782483 | + | 0.622672i | \(0.213953\pi\) | |||||||
\(38\) | 0.345015 | 0.0559688 | ||||||||
\(39\) | 8.54860 | 1.36887 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.48136 | 0.543697 | 0.271849 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271849 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(42\) | −8.70173 | −1.34271 | ||||||||
\(43\) | −2.90132 | −0.442447 | −0.221223 | − | 0.975223i | \(-0.571005\pi\) | ||||
−0.221223 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(44\) | −7.04365 | −1.06187 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.44348 | 0.655155 | ||||||||
\(47\) | 4.61707 | 0.673469 | 0.336734 | − | 0.941600i | \(-0.390678\pi\) | ||||
0.336734 | + | 0.941600i | \(0.390678\pi\) | |||||||
\(48\) | 9.63196 | 1.39025 | ||||||||
\(49\) | −2.31594 | −0.330848 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.5538 | 1.47783 | ||||||||
\(52\) | −6.70409 | −0.929689 | ||||||||
\(53\) | 3.83516 | 0.526800 | 0.263400 | − | 0.964687i | \(-0.415156\pi\) | ||||
0.263400 | + | 0.964687i | \(0.415156\pi\) | |||||||
\(54\) | −6.31846 | −0.859833 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.44587 | −0.193212 | ||||||||
\(57\) | 0.380014 | 0.0503340 | ||||||||
\(58\) | 1.06185 | 0.139428 | ||||||||
\(59\) | −10.5916 | −1.37891 | −0.689454 | − | 0.724330i | \(-0.742149\pi\) | ||||
−0.689454 | + | 0.724330i | \(0.742149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.62418 | −0.335992 | −0.167996 | − | 0.985788i | \(-0.553730\pi\) | ||||
−0.167996 | + | 0.985788i | \(0.553730\pi\) | |||||||
\(62\) | −6.28897 | −0.798700 | ||||||||
\(63\) | −3.09164 | −0.389510 | ||||||||
\(64\) | −5.00091 | −0.625114 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −17.1601 | −2.11226 | ||||||||
\(67\) | 1.18895 | 0.145254 | 0.0726268 | − | 0.997359i | \(-0.476862\pi\) | ||||
0.0726268 | + | 0.997359i | \(0.476862\pi\) | |||||||
\(68\) | −8.27665 | −1.00369 | ||||||||
\(69\) | 4.89423 | 0.589196 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8729 | 1.40905 | 0.704525 | − | 0.709679i | \(-0.251160\pi\) | ||||
0.704525 | + | 0.709679i | \(0.251160\pi\) | |||||||
\(72\) | 0.954321 | 0.112468 | ||||||||
\(73\) | 13.5936 | 1.59101 | 0.795505 | − | 0.605947i | \(-0.207206\pi\) | ||||
0.795505 | + | 0.605947i | \(0.207206\pi\) | |||||||
\(74\) | −18.1875 | −2.11425 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.298019 | −0.0341851 | ||||||||
\(77\) | 9.23712 | 1.05267 | ||||||||
\(78\) | −16.3328 | −1.84933 | ||||||||
\(79\) | −1.52109 | −0.171136 | −0.0855680 | − | 0.996332i | \(-0.527270\pi\) | ||||
−0.0855680 | + | 0.996332i | \(0.527270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2449 | −1.24943 | ||||||||
\(82\) | −6.65144 | −0.734528 | ||||||||
\(83\) | 8.04914 | 0.883507 | 0.441754 | − | 0.897136i | \(-0.354357\pi\) | ||||
0.441754 | + | 0.897136i | \(0.354357\pi\) | |||||||
\(84\) | 7.51643 | 0.820110 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.54321 | 0.597740 | ||||||||
\(87\) | 1.16957 | 0.125391 | ||||||||
\(88\) | −2.85130 | −0.303949 | ||||||||
\(89\) | −15.8320 | −1.67819 | −0.839094 | − | 0.543986i | \(-0.816915\pi\) | ||||
−0.839094 | + | 0.543986i | \(0.816915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.79181 | 0.921632 | ||||||||
\(92\) | −3.83821 | −0.400161 | ||||||||
\(93\) | −6.92693 | −0.718289 | ||||||||
\(94\) | −8.82130 | −0.909848 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.5909 | −1.59124 | ||||||||
\(97\) | −10.6203 | −1.07833 | −0.539165 | − | 0.842200i | \(-0.681260\pi\) | ||||
−0.539165 | + | 0.842200i | \(0.681260\pi\) | |||||||
\(98\) | 4.42480 | 0.446972 | ||||||||
\(99\) | −6.09681 | −0.612753 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0821711 | −0.00817633 | −0.00408816 | − | 0.999992i | \(-0.501301\pi\) | ||||
−0.00408816 | + | 0.999992i | \(0.501301\pi\) | |||||||
\(102\) | −20.1640 | −1.99653 | ||||||||
\(103\) | 1.27297 | 0.125429 | 0.0627147 | − | 0.998031i | \(-0.480024\pi\) | ||||
0.0627147 | + | 0.998031i | \(0.480024\pi\) | |||||||
\(104\) | −2.71384 | −0.266114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.32741 | −0.711701 | ||||||||
\(107\) | −20.1502 | −1.94799 | −0.973995 | − | 0.226569i | \(-0.927249\pi\) | ||||
−0.973995 | + | 0.226569i | \(0.927249\pi\) | |||||||
\(108\) | 5.45779 | 0.525177 | ||||||||
\(109\) | 16.2615 | 1.55757 | 0.778787 | − | 0.627289i | \(-0.215835\pi\) | ||||
0.778787 | + | 0.627289i | \(0.215835\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.0324 | −1.90139 | ||||||||
\(112\) | 9.90600 | 0.936029 | ||||||||
\(113\) | 20.1200 | 1.89273 | 0.946365 | − | 0.323098i | \(-0.104724\pi\) | ||||
0.946365 | + | 0.323098i | \(0.104724\pi\) | |||||||
\(114\) | −0.726049 | −0.0680007 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.917215 | −0.0851612 | ||||||||
\(117\) | −5.80289 | −0.536478 | ||||||||
\(118\) | 20.2361 | 1.86289 | ||||||||
\(119\) | 10.8541 | 0.994993 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.21590 | 0.655991 | ||||||||
\(122\) | 5.01372 | 0.453921 | ||||||||
\(123\) | −7.32617 | −0.660579 | ||||||||
\(124\) | 5.43232 | 0.487837 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.90684 | 0.526223 | ||||||||
\(127\) | −16.4735 | −1.46179 | −0.730896 | − | 0.682489i | \(-0.760897\pi\) | ||||
−0.730896 | + | 0.682489i | \(0.760897\pi\) | |||||||
\(128\) | −5.26282 | −0.465172 | ||||||||
\(129\) | 6.10552 | 0.537561 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3756 | 1.51811 | 0.759057 | − | 0.651024i | \(-0.225660\pi\) | ||||
0.759057 | + | 0.651024i | \(0.225660\pi\) | |||||||
\(132\) | 14.8226 | 1.29015 | ||||||||
\(133\) | 0.390825 | 0.0338889 | ||||||||
\(134\) | −2.27159 | −0.196236 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.35042 | −0.287296 | ||||||||
\(137\) | 11.3396 | 0.968807 | 0.484403 | − | 0.874845i | \(-0.339037\pi\) | ||||
0.484403 | + | 0.874845i | \(0.339037\pi\) | |||||||
\(138\) | −9.35085 | −0.795997 | ||||||||
\(139\) | 5.24580 | 0.444943 | 0.222472 | − | 0.974939i | \(-0.428588\pi\) | ||||
0.222472 | + | 0.974939i | \(0.428588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.71615 | −0.818247 | ||||||||
\(142\) | −22.6841 | −1.90361 | ||||||||
\(143\) | 17.3377 | 1.44985 | ||||||||
\(144\) | −6.53829 | −0.544858 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −25.9717 | −2.14944 | ||||||||
\(147\) | 4.87366 | 0.401973 | ||||||||
\(148\) | 15.7101 | 1.29136 | ||||||||
\(149\) | 5.14511 | 0.421504 | 0.210752 | − | 0.977540i | \(-0.432409\pi\) | ||||
0.210752 | + | 0.977540i | \(0.432409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0727 | 1.55211 | 0.776057 | − | 0.630663i | \(-0.217217\pi\) | ||||
0.776057 | + | 0.630663i | \(0.217217\pi\) | |||||||
\(152\) | −0.120639 | −0.00978513 | ||||||||
\(153\) | −7.16406 | −0.579180 | ||||||||
\(154\) | −17.6483 | −1.42214 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.1081 | 1.12955 | ||||||||
\(157\) | −6.58683 | −0.525687 | −0.262843 | − | 0.964839i | \(-0.584660\pi\) | ||||
−0.262843 | + | 0.964839i | \(0.584660\pi\) | |||||||
\(158\) | 2.90617 | 0.231203 | ||||||||
\(159\) | −8.07071 | −0.640049 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.03347 | 0.396693 | ||||||||
\(162\) | 21.4843 | 1.68797 | ||||||||
\(163\) | −5.49881 | −0.430700 | −0.215350 | − | 0.976537i | \(-0.569089\pi\) | ||||
−0.215350 | + | 0.976537i | \(0.569089\pi\) | |||||||
\(164\) | 5.74542 | 0.448642 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.3786 | −1.19361 | ||||||||
\(167\) | 18.3921 | 1.42322 | 0.711612 | − | 0.702573i | \(-0.247966\pi\) | ||||
0.711612 | + | 0.702573i | \(0.247966\pi\) | |||||||
\(168\) | 3.04268 | 0.234748 | ||||||||
\(169\) | 3.50191 | 0.269378 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.257958 | −0.0197265 | ||||||||
\(172\) | −4.78815 | −0.365093 | ||||||||
\(173\) | −1.33142 | −0.101226 | −0.0506129 | − | 0.998718i | \(-0.516117\pi\) | ||||
−0.0506129 | + | 0.998718i | \(0.516117\pi\) | |||||||
\(174\) | −2.23456 | −0.169402 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.5349 | 1.47250 | ||||||||
\(177\) | 22.2889 | 1.67534 | ||||||||
\(178\) | 30.2484 | 2.26721 | ||||||||
\(179\) | −21.1070 | −1.57761 | −0.788805 | − | 0.614644i | \(-0.789300\pi\) | ||||
−0.788805 | + | 0.614644i | \(0.789300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.3428 | 1.88372 | 0.941859 | − | 0.336007i | \(-0.109077\pi\) | ||||
0.941859 | + | 0.336007i | \(0.109077\pi\) | |||||||
\(182\) | −16.7975 | −1.24511 | ||||||||
\(183\) | 5.52232 | 0.408222 | ||||||||
\(184\) | −1.55372 | −0.114542 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.2345 | 0.970400 | ||||||||
\(187\) | 21.4046 | 1.56526 | ||||||||
\(188\) | 7.61972 | 0.555725 | ||||||||
\(189\) | −7.15741 | −0.520625 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.53179 | −0.255551 | −0.127776 | − | 0.991803i | \(-0.540784\pi\) | ||||
−0.127776 | + | 0.991803i | \(0.540784\pi\) | |||||||
\(192\) | 10.5239 | 0.759498 | ||||||||
\(193\) | 3.22749 | 0.232320 | 0.116160 | − | 0.993231i | \(-0.462941\pi\) | ||||
0.116160 | + | 0.993231i | \(0.462941\pi\) | |||||||
\(194\) | 20.2910 | 1.45681 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.82208 | −0.273006 | ||||||||
\(197\) | 11.8399 | 0.843558 | 0.421779 | − | 0.906699i | \(-0.361406\pi\) | ||||
0.421779 | + | 0.906699i | \(0.361406\pi\) | |||||||
\(198\) | 11.6485 | 0.827821 | ||||||||
\(199\) | −7.98476 | −0.566025 | −0.283012 | − | 0.959116i | \(-0.591334\pi\) | ||||
−0.283012 | + | 0.959116i | \(0.591334\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50203 | −0.176479 | ||||||||
\(202\) | 0.156995 | 0.0110461 | ||||||||
\(203\) | 1.20285 | 0.0844232 | ||||||||
\(204\) | 17.4174 | 1.21946 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.43212 | −0.169454 | ||||||||
\(207\) | −3.32226 | −0.230913 | ||||||||
\(208\) | 18.5932 | 1.28921 | ||||||||
\(209\) | 0.770720 | 0.0533118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.80349 | 0.261843 | 0.130922 | − | 0.991393i | \(-0.458206\pi\) | ||||
0.130922 | + | 0.991393i | \(0.458206\pi\) | |||||||
\(212\) | 6.32931 | 0.434699 | ||||||||
\(213\) | −24.9852 | −1.71196 | ||||||||
\(214\) | 38.4986 | 2.63171 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.20934 | 0.150326 | ||||||||
\(217\) | −7.12401 | −0.483609 | ||||||||
\(218\) | −31.0691 | −2.10426 | ||||||||
\(219\) | −28.6063 | −1.93304 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.3727 | 1.37042 | ||||||||
\(222\) | 38.2736 | 2.56876 | ||||||||
\(223\) | 1.07200 | 0.0717865 | 0.0358932 | − | 0.999356i | \(-0.488572\pi\) | ||||
0.0358932 | + | 0.999356i | \(0.488572\pi\) | |||||||
\(224\) | −16.0345 | −1.07135 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −38.4410 | −2.55706 | ||||||||
\(227\) | −21.2385 | −1.40965 | −0.704826 | − | 0.709380i | \(-0.748975\pi\) | ||||
−0.704826 | + | 0.709380i | \(0.748975\pi\) | |||||||
\(228\) | 0.627150 | 0.0415340 | ||||||||
\(229\) | 7.29747 | 0.482230 | 0.241115 | − | 0.970497i | \(-0.422487\pi\) | ||||
0.241115 | + | 0.970497i | \(0.422487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.4386 | −1.27896 | ||||||||
\(232\) | −0.371292 | −0.0243765 | ||||||||
\(233\) | −21.8917 | −1.43417 | −0.717087 | − | 0.696983i | \(-0.754525\pi\) | ||||
−0.717087 | + | 0.696983i | \(0.754525\pi\) | |||||||
\(234\) | 11.0869 | 0.724775 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −17.4797 | −1.13783 | ||||||||
\(237\) | 3.20098 | 0.207926 | ||||||||
\(238\) | −20.7377 | −1.34422 | ||||||||
\(239\) | −4.98696 | −0.322580 | −0.161290 | − | 0.986907i | \(-0.551565\pi\) | ||||
−0.161290 | + | 0.986907i | \(0.551565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −13.7866 | −0.886235 | ||||||||
\(243\) | 13.7425 | 0.881580 | ||||||||
\(244\) | −4.33078 | −0.277250 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.9973 | 0.892434 | ||||||||
\(247\) | 0.733565 | 0.0466756 | ||||||||
\(248\) | 2.19903 | 0.139638 | ||||||||
\(249\) | −16.9386 | −1.07344 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.4761 | 1.16620 | 0.583102 | − | 0.812399i | \(-0.301839\pi\) | ||||
0.583102 | + | 0.812399i | \(0.301839\pi\) | |||||||
\(252\) | −5.10224 | −0.321411 | ||||||||
\(253\) | 9.92618 | 0.624053 | ||||||||
\(254\) | 31.4741 | 1.97486 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.0569 | 1.25356 | ||||||||
\(257\) | 12.8264 | 0.800091 | 0.400045 | − | 0.916495i | \(-0.368994\pi\) | ||||
0.400045 | + | 0.916495i | \(0.368994\pi\) | |||||||
\(258\) | −11.6651 | −0.726239 | ||||||||
\(259\) | −20.6024 | −1.28017 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.793919 | −0.0491423 | ||||||||
\(262\) | −33.1976 | −2.05095 | ||||||||
\(263\) | −22.0689 | −1.36083 | −0.680414 | − | 0.732828i | \(-0.738200\pi\) | ||||
−0.680414 | + | 0.732828i | \(0.738200\pi\) | |||||||
\(264\) | 6.00026 | 0.369291 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.746705 | −0.0457834 | ||||||||
\(267\) | 33.3168 | 2.03896 | ||||||||
\(268\) | 1.96217 | 0.119859 | ||||||||
\(269\) | 6.36707 | 0.388207 | 0.194104 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194104 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.2942 | −1.41502 | −0.707510 | − | 0.706704i | \(-0.750181\pi\) | ||||
−0.707510 | + | 0.706704i | \(0.750181\pi\) | |||||||
\(272\) | 22.9546 | 1.39182 | ||||||||
\(273\) | −18.5015 | −1.11976 | ||||||||
\(274\) | −21.6653 | −1.30885 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.07713 | 0.486186 | ||||||||
\(277\) | 22.1400 | 1.33026 | 0.665131 | − | 0.746727i | \(-0.268376\pi\) | ||||
0.665131 | + | 0.746727i | \(0.268376\pi\) | |||||||
\(278\) | −10.0226 | −0.601113 | ||||||||
\(279\) | 4.70208 | 0.281506 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.60586 | 0.513383 | 0.256691 | − | 0.966493i | \(-0.417368\pi\) | ||||
0.256691 | + | 0.966493i | \(0.417368\pi\) | |||||||
\(282\) | 18.5635 | 1.10544 | ||||||||
\(283\) | 15.0374 | 0.893882 | 0.446941 | − | 0.894563i | \(-0.352513\pi\) | ||||
0.446941 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(284\) | 19.5942 | 1.16270 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.1252 | −1.95874 | ||||||||
\(287\) | −7.53460 | −0.444754 | ||||||||
\(288\) | 10.5833 | 0.623628 | ||||||||
\(289\) | 8.15151 | 0.479501 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.3494 | 1.31014 | ||||||||
\(292\) | 22.4340 | 1.31285 | ||||||||
\(293\) | −6.18210 | −0.361162 | −0.180581 | − | 0.983560i | \(-0.557798\pi\) | ||||
−0.180581 | + | 0.983560i | \(0.557798\pi\) | |||||||
\(294\) | −9.31154 | −0.543060 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.35950 | 0.369638 | ||||||||
\(297\) | −14.1146 | −0.819015 | ||||||||
\(298\) | −9.83017 | −0.569446 | ||||||||
\(299\) | 9.44765 | 0.546372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.27923 | 0.361929 | ||||||||
\(302\) | −36.4400 | −2.09689 | ||||||||
\(303\) | 0.172921 | 0.00993403 | ||||||||
\(304\) | 0.826529 | 0.0474047 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.6876 | 0.782465 | ||||||||
\(307\) | −13.4882 | −0.769812 | −0.384906 | − | 0.922956i | \(-0.625766\pi\) | ||||
−0.384906 | + | 0.922956i | \(0.625766\pi\) | |||||||
\(308\) | 15.2444 | 0.868628 | ||||||||
\(309\) | −2.67884 | −0.152394 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.02889 | 0.171752 | 0.0858762 | − | 0.996306i | \(-0.472631\pi\) | ||||
0.0858762 | + | 0.996306i | \(0.472631\pi\) | |||||||
\(312\) | 5.71100 | 0.323322 | ||||||||
\(313\) | −17.6844 | −0.999582 | −0.499791 | − | 0.866146i | \(-0.666590\pi\) | ||||
−0.499791 | + | 0.866146i | \(0.666590\pi\) | |||||||
\(314\) | 12.5847 | 0.710196 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.51031 | −0.141216 | ||||||||
\(317\) | −8.57911 | −0.481851 | −0.240925 | − | 0.970544i | \(-0.577451\pi\) | ||||
−0.240925 | + | 0.970544i | \(0.577451\pi\) | |||||||
\(318\) | 15.4198 | 0.864698 | ||||||||
\(319\) | 2.37205 | 0.132809 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 42.4040 | 2.36676 | ||||||||
\(322\) | −9.61688 | −0.535928 | ||||||||
\(323\) | 0.905635 | 0.0503909 | ||||||||
\(324\) | −18.5578 | −1.03099 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.5059 | 0.581870 | ||||||||
\(327\) | −34.2208 | −1.89241 | ||||||||
\(328\) | 2.32577 | 0.128419 | ||||||||
\(329\) | −9.99258 | −0.550909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.1132 | 1.27042 | 0.635208 | − | 0.772341i | \(-0.280914\pi\) | ||||
0.635208 | + | 0.772341i | \(0.280914\pi\) | |||||||
\(332\) | 13.2838 | 0.729042 | ||||||||
\(333\) | 13.5982 | 0.745179 | ||||||||
\(334\) | −35.1397 | −1.92276 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −20.8462 | −1.13725 | ||||||||
\(337\) | −10.9314 | −0.595472 | −0.297736 | − | 0.954648i | \(-0.596232\pi\) | ||||
−0.297736 | + | 0.954648i | \(0.596232\pi\) | |||||||
\(338\) | −6.69071 | −0.363926 | ||||||||
\(339\) | −42.3405 | −2.29962 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.0488 | −0.760783 | ||||||||
\(342\) | 0.492851 | 0.0266503 | ||||||||
\(343\) | 20.1622 | 1.08866 | ||||||||
\(344\) | −1.93826 | −0.104504 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.54379 | 0.136755 | ||||||||
\(347\) | −5.04505 | −0.270832 | −0.135416 | − | 0.990789i | \(-0.543237\pi\) | ||||
−0.135416 | + | 0.990789i | \(0.543237\pi\) | |||||||
\(348\) | 1.93018 | 0.103469 | ||||||||
\(349\) | 34.7248 | 1.85878 | 0.929389 | − | 0.369102i | \(-0.120335\pi\) | ||||
0.929389 | + | 0.369102i | \(0.120335\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.4342 | −0.717065 | ||||||||
\(352\) | −31.6206 | −1.68538 | ||||||||
\(353\) | 16.3883 | 0.872264 | 0.436132 | − | 0.899883i | \(-0.356348\pi\) | ||||
0.436132 | + | 0.899883i | \(0.356348\pi\) | |||||||
\(354\) | −42.5849 | −2.26336 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −26.1281 | −1.38479 | ||||||||
\(357\) | −22.8413 | −1.20889 | ||||||||
\(358\) | 40.3267 | 2.13133 | ||||||||
\(359\) | −22.0003 | −1.16113 | −0.580565 | − | 0.814214i | \(-0.697168\pi\) | ||||
−0.580565 | + | 0.814214i | \(0.697168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9674 | −0.998284 | ||||||||
\(362\) | −48.4197 | −2.54488 | ||||||||
\(363\) | −15.1851 | −0.797012 | ||||||||
\(364\) | 14.5094 | 0.760502 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.5509 | −0.551502 | ||||||||
\(367\) | 13.4672 | 0.702985 | 0.351492 | − | 0.936191i | \(-0.385674\pi\) | ||||
0.351492 | + | 0.936191i | \(0.385674\pi\) | |||||||
\(368\) | 10.6449 | 0.554906 | ||||||||
\(369\) | 4.97309 | 0.258889 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.30032 | −0.430931 | ||||||||
\(372\) | −11.4318 | −0.592709 | ||||||||
\(373\) | 1.45356 | 0.0752624 | 0.0376312 | − | 0.999292i | \(-0.488019\pi\) | ||||
0.0376312 | + | 0.999292i | \(0.488019\pi\) | |||||||
\(374\) | −40.8953 | −2.11465 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.08449 | 0.159070 | ||||||||
\(377\) | 2.25770 | 0.116277 | ||||||||
\(378\) | 13.6748 | 0.703358 | ||||||||
\(379\) | 5.98669 | 0.307516 | 0.153758 | − | 0.988109i | \(-0.450862\pi\) | ||||
0.153758 | + | 0.988109i | \(0.450862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.6669 | 1.77604 | ||||||||
\(382\) | 6.74778 | 0.345246 | ||||||||
\(383\) | 8.66966 | 0.442999 | 0.221499 | − | 0.975161i | \(-0.428905\pi\) | ||||
0.221499 | + | 0.975161i | \(0.428905\pi\) | |||||||
\(384\) | 11.0751 | 0.565172 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.16640 | −0.313861 | ||||||||
\(387\) | −4.14450 | −0.210677 | ||||||||
\(388\) | −17.5271 | −0.889803 | ||||||||
\(389\) | −6.51323 | −0.330234 | −0.165117 | − | 0.986274i | \(-0.552800\pi\) | ||||
−0.165117 | + | 0.986274i | \(0.552800\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.6638 | 0.589862 | ||||||||
\(392\) | −1.54719 | −0.0781450 | ||||||||
\(393\) | −36.5652 | −1.84447 | ||||||||
\(394\) | −22.6211 | −1.13964 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.0618 | −0.505624 | ||||||||
\(397\) | 14.5951 | 0.732506 | 0.366253 | − | 0.930515i | \(-0.380641\pi\) | ||||
0.366253 | + | 0.930515i | \(0.380641\pi\) | |||||||
\(398\) | 15.2556 | 0.764693 | ||||||||
\(399\) | −0.822452 | −0.0411741 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.1126 | −0.604874 | −0.302437 | − | 0.953169i | \(-0.597800\pi\) | ||||
−0.302437 | + | 0.953169i | \(0.597800\pi\) | |||||||
\(402\) | 4.78034 | 0.238422 | ||||||||
\(403\) | −13.3715 | −0.666082 | ||||||||
\(404\) | −0.135610 | −0.00674684 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.29814 | −0.114055 | ||||||||
\(407\) | −40.6285 | −2.01388 | ||||||||
\(408\) | 7.05062 | 0.349058 | ||||||||
\(409\) | −9.38475 | −0.464046 | −0.232023 | − | 0.972710i | \(-0.574535\pi\) | ||||
−0.232023 | + | 0.972710i | \(0.574535\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.8630 | −1.17708 | ||||||||
\(412\) | 2.10083 | 0.103500 | ||||||||
\(413\) | 22.9231 | 1.12797 | ||||||||
\(414\) | 6.34747 | 0.311961 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −30.0962 | −1.47559 | ||||||||
\(417\) | −11.0393 | −0.540595 | ||||||||
\(418\) | −1.47253 | −0.0720236 | ||||||||
\(419\) | −24.2224 | −1.18334 | −0.591671 | − | 0.806180i | \(-0.701531\pi\) | ||||
−0.591671 | + | 0.806180i | \(0.701531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.1092 | 1.22375 | 0.611873 | − | 0.790956i | \(-0.290416\pi\) | ||||
0.611873 | + | 0.790956i | \(0.290416\pi\) | |||||||
\(422\) | −7.26690 | −0.353747 | ||||||||
\(423\) | 6.59544 | 0.320681 | ||||||||
\(424\) | 2.56213 | 0.124428 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 47.7365 | 2.31284 | ||||||||
\(427\) | 5.67943 | 0.274847 | ||||||||
\(428\) | −33.2545 | −1.60742 | ||||||||
\(429\) | −36.4855 | −1.76154 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.77815 | −0.422829 | −0.211414 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211414 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(432\) | −15.1367 | −0.728266 | ||||||||
\(433\) | −0.611398 | −0.0293819 | −0.0146910 | − | 0.999892i | \(-0.504676\pi\) | ||||
−0.0146910 | + | 0.999892i | \(0.504676\pi\) | |||||||
\(434\) | 13.6110 | 0.653350 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.8370 | 1.28526 | ||||||||
\(437\) | 0.419979 | 0.0200903 | ||||||||
\(438\) | 54.6549 | 2.61151 | ||||||||
\(439\) | 16.2646 | 0.776268 | 0.388134 | − | 0.921603i | \(-0.373120\pi\) | ||||
0.388134 | + | 0.921603i | \(0.373120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.30830 | −0.157538 | ||||||||
\(442\) | −38.9238 | −1.85142 | ||||||||
\(443\) | −31.4243 | −1.49301 | −0.746507 | − | 0.665377i | \(-0.768271\pi\) | ||||
−0.746507 | + | 0.665377i | \(0.768271\pi\) | |||||||
\(444\) | −33.0602 | −1.56897 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.04815 | −0.0969826 | ||||||||
\(447\) | −10.8274 | −0.512116 | ||||||||
\(448\) | 10.8233 | 0.511354 | ||||||||
\(449\) | −14.4936 | −0.683995 | −0.341998 | − | 0.939701i | \(-0.611104\pi\) | ||||
−0.341998 | + | 0.939701i | \(0.611104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8585 | −0.699659 | ||||||||
\(452\) | 33.2048 | 1.56182 | ||||||||
\(453\) | −40.1365 | −1.88578 | ||||||||
\(454\) | 40.5780 | 1.90442 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.253873 | 0.0118887 | ||||||||
\(457\) | 11.6660 | 0.545711 | 0.272855 | − | 0.962055i | \(-0.412032\pi\) | ||||
0.272855 | + | 0.962055i | \(0.412032\pi\) | |||||||
\(458\) | −13.9424 | −0.651487 | ||||||||
\(459\) | −16.5854 | −0.774142 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.47727 | −0.208527 | −0.104264 | − | 0.994550i | \(-0.533249\pi\) | ||||
−0.104264 | + | 0.994550i | \(0.533249\pi\) | |||||||
\(462\) | 37.1391 | 1.72787 | ||||||||
\(463\) | 17.5232 | 0.814370 | 0.407185 | − | 0.913346i | \(-0.366510\pi\) | ||||
0.407185 | + | 0.913346i | \(0.366510\pi\) | |||||||
\(464\) | 2.54381 | 0.118094 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 41.8260 | 1.93755 | ||||||||
\(467\) | −5.20074 | −0.240661 | −0.120331 | − | 0.992734i | \(-0.538395\pi\) | ||||
−0.120331 | + | 0.992734i | \(0.538395\pi\) | |||||||
\(468\) | −9.57672 | −0.442684 | ||||||||
\(469\) | −2.57321 | −0.118820 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8613 | 0.638696 | ||||||||
\(472\) | −7.07585 | −0.325692 | ||||||||
\(473\) | 12.3828 | 0.569364 | ||||||||
\(474\) | −6.11574 | −0.280905 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.9129 | 0.821036 | ||||||||
\(477\) | 5.47849 | 0.250843 | ||||||||
\(478\) | 9.52802 | 0.435801 | ||||||||
\(479\) | 24.6586 | 1.12668 | 0.563340 | − | 0.826225i | \(-0.309516\pi\) | ||||
0.563340 | + | 0.826225i | \(0.309516\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.6699 | −1.76319 | ||||||||
\(482\) | 1.91059 | 0.0870248 | ||||||||
\(483\) | −10.5924 | −0.481972 | ||||||||
\(484\) | 11.9087 | 0.541303 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −26.2562 | −1.19100 | ||||||||
\(487\) | −33.7896 | −1.53115 | −0.765576 | − | 0.643346i | \(-0.777546\pi\) | ||||
−0.765576 | + | 0.643346i | \(0.777546\pi\) | |||||||
\(488\) | −1.75312 | −0.0793599 | ||||||||
\(489\) | 11.5717 | 0.523289 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.93113 | 0.222539 | 0.111269 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111269 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(492\) | −12.0906 | −0.545088 | ||||||||
\(493\) | 2.78728 | 0.125533 | ||||||||
\(494\) | −1.40154 | −0.0630582 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.0661 | −0.676486 | ||||||||
\(497\) | −25.6961 | −1.15263 | ||||||||
\(498\) | 32.3626 | 1.45020 | ||||||||
\(499\) | −7.66605 | −0.343179 | −0.171590 | − | 0.985169i | \(-0.554890\pi\) | ||||
−0.171590 | + | 0.985169i | \(0.554890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.7043 | −1.72918 | ||||||||
\(502\) | −35.3002 | −1.57553 | ||||||||
\(503\) | −1.96005 | −0.0873942 | −0.0436971 | − | 0.999045i | \(-0.513914\pi\) | ||||
−0.0436971 | + | 0.999045i | \(0.513914\pi\) | |||||||
\(504\) | −2.06541 | −0.0920006 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −18.9648 | −0.843088 | ||||||||
\(507\) | −7.36942 | −0.327288 | ||||||||
\(508\) | −27.1869 | −1.20622 | ||||||||
\(509\) | 5.20406 | 0.230666 | 0.115333 | − | 0.993327i | \(-0.463206\pi\) | ||||
0.115333 | + | 0.993327i | \(0.463206\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.4202 | −1.30147 | ||||||||
\(512\) | −27.7948 | −1.22837 | ||||||||
\(513\) | −0.597195 | −0.0263668 | ||||||||
\(514\) | −24.5060 | −1.08091 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.0762 | 0.443578 | ||||||||
\(517\) | −19.7057 | −0.866655 | ||||||||
\(518\) | 39.3626 | 1.72949 | ||||||||
\(519\) | 2.80183 | 0.122987 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.1820 | −1.19086 | −0.595432 | − | 0.803405i | \(-0.703019\pi\) | ||||
−0.595432 | + | 0.803405i | \(0.703019\pi\) | |||||||
\(522\) | 1.51685 | 0.0663907 | ||||||||
\(523\) | −26.6139 | −1.16374 | −0.581872 | − | 0.813281i | \(-0.697679\pi\) | ||||
−0.581872 | + | 0.813281i | \(0.697679\pi\) | |||||||
\(524\) | 28.6756 | 1.25270 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.1646 | 1.83846 | ||||||||
\(527\) | −16.5080 | −0.719101 | ||||||||
\(528\) | −41.1093 | −1.78905 | ||||||||
\(529\) | −17.5910 | −0.764828 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.1300 | −0.656586 | ||||||||
\(532\) | 0.644993 | 0.0279640 | ||||||||
\(533\) | −14.1422 | −0.612566 | ||||||||
\(534\) | −63.6547 | −2.75461 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.794294 | 0.0343083 | ||||||||
\(537\) | 44.4175 | 1.91676 | ||||||||
\(538\) | −12.1648 | −0.524463 | ||||||||
\(539\) | 9.88445 | 0.425753 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.7687 | 1.27986 | 0.639928 | − | 0.768435i | \(-0.278964\pi\) | ||||
0.639928 | + | 0.768435i | \(0.278964\pi\) | |||||||
\(542\) | 44.5055 | 1.91167 | ||||||||
\(543\) | −53.3314 | −2.28867 | ||||||||
\(544\) | −37.1558 | −1.59304 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 35.3486 | 1.51278 | ||||||||
\(547\) | −15.7917 | −0.675204 | −0.337602 | − | 0.941289i | \(-0.609616\pi\) | ||||
−0.337602 | + | 0.941289i | \(0.609616\pi\) | |||||||
\(548\) | 18.7141 | 0.799428 | ||||||||
\(549\) | −3.74862 | −0.159987 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.100362 | 0.00427557 | ||||||||
\(552\) | 3.26965 | 0.139166 | ||||||||
\(553\) | 3.29205 | 0.139992 | ||||||||
\(554\) | −42.3003 | −1.79717 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.65734 | 0.367153 | ||||||||
\(557\) | 28.0554 | 1.18874 | 0.594372 | − | 0.804190i | \(-0.297401\pi\) | ||||
0.594372 | + | 0.804190i | \(0.297401\pi\) | |||||||
\(558\) | −8.98373 | −0.380312 | ||||||||
\(559\) | 11.7859 | 0.498490 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −45.0438 | −1.90175 | ||||||||
\(562\) | −16.4422 | −0.693574 | ||||||||
\(563\) | −16.3809 | −0.690374 | −0.345187 | − | 0.938534i | \(-0.612185\pi\) | ||||
−0.345187 | + | 0.938534i | \(0.612185\pi\) | |||||||
\(564\) | −16.0349 | −0.675192 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −28.7303 | −1.20762 | ||||||||
\(567\) | 24.3370 | 1.02206 | ||||||||
\(568\) | 7.93182 | 0.332812 | ||||||||
\(569\) | −0.387204 | −0.0162324 | −0.00811621 | − | 0.999967i | \(-0.502583\pi\) | ||||
−0.00811621 | + | 0.999967i | \(0.502583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.8102 | 1.20567 | 0.602835 | − | 0.797866i | \(-0.294038\pi\) | ||||
0.602835 | + | 0.797866i | \(0.294038\pi\) | |||||||
\(572\) | 28.6131 | 1.19637 | ||||||||
\(573\) | 7.43228 | 0.310488 | ||||||||
\(574\) | 14.3955 | 0.600857 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.14376 | −0.297656 | ||||||||
\(577\) | −12.9248 | −0.538064 | −0.269032 | − | 0.963131i | \(-0.586704\pi\) | ||||
−0.269032 | + | 0.963131i | \(0.586704\pi\) | |||||||
\(578\) | −15.5742 | −0.647799 | ||||||||
\(579\) | −6.79193 | −0.282263 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.4205 | −0.722724 | ||||||||
\(582\) | −42.7004 | −1.76999 | ||||||||
\(583\) | −16.3685 | −0.677914 | ||||||||
\(584\) | 9.08138 | 0.375790 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.8114 | 0.487925 | ||||||||
\(587\) | −36.3915 | −1.50204 | −0.751018 | − | 0.660282i | \(-0.770437\pi\) | ||||
−0.751018 | + | 0.660282i | \(0.770437\pi\) | |||||||
\(588\) | 8.04317 | 0.331695 | ||||||||
\(589\) | −0.594408 | −0.0244921 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.9159 | −1.02490 | ||||||||
\(592\) | −43.5705 | −1.79074 | ||||||||
\(593\) | 35.8670 | 1.47288 | 0.736440 | − | 0.676502i | \(-0.236505\pi\) | ||||
0.736440 | + | 0.676502i | \(0.236505\pi\) | |||||||
\(594\) | 26.9672 | 1.10648 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.49116 | 0.347811 | ||||||||
\(597\) | 16.8031 | 0.687706 | ||||||||
\(598\) | −18.0505 | −0.738142 | ||||||||
\(599\) | −0.855742 | −0.0349647 | −0.0174823 | − | 0.999847i | \(-0.505565\pi\) | ||||
−0.0174823 | + | 0.999847i | \(0.505565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.2622 | 1.19363 | 0.596815 | − | 0.802379i | \(-0.296432\pi\) | ||||
0.596815 | + | 0.802379i | \(0.296432\pi\) | |||||||
\(602\) | −11.9970 | −0.488961 | ||||||||
\(603\) | 1.69841 | 0.0691645 | ||||||||
\(604\) | 31.4764 | 1.28075 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.330380 | −0.0134208 | ||||||||
\(607\) | 25.5599 | 1.03745 | 0.518723 | − | 0.854942i | \(-0.326408\pi\) | ||||
0.518723 | + | 0.854942i | \(0.326408\pi\) | |||||||
\(608\) | −1.33788 | −0.0542581 | ||||||||
\(609\) | −2.53127 | −0.102572 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.7557 | −0.758775 | ||||||||
\(612\) | −11.8231 | −0.477921 | ||||||||
\(613\) | 9.50489 | 0.383899 | 0.191950 | − | 0.981405i | \(-0.438519\pi\) | ||||
0.191950 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(614\) | 25.7703 | 1.04001 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.17097 | 0.248636 | ||||||||
\(617\) | 16.9425 | 0.682081 | 0.341040 | − | 0.940049i | \(-0.389221\pi\) | ||||
0.341040 | + | 0.940049i | \(0.389221\pi\) | |||||||
\(618\) | 5.11815 | 0.205882 | ||||||||
\(619\) | 12.7691 | 0.513233 | 0.256617 | − | 0.966513i | \(-0.417392\pi\) | ||||
0.256617 | + | 0.966513i | \(0.417392\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.69133 | −0.308642 | ||||||||
\(622\) | −5.78695 | −0.232035 | ||||||||
\(623\) | 34.2647 | 1.37279 | ||||||||
\(624\) | −39.1275 | −1.56635 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 33.7876 | 1.35042 | ||||||||
\(627\) | −1.62190 | −0.0647725 | ||||||||
\(628\) | −10.8705 | −0.433780 | ||||||||
\(629\) | −47.7406 | −1.90354 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.17336 | −0.0865202 | −0.0432601 | − | 0.999064i | \(-0.513774\pi\) | ||||
−0.0432601 | + | 0.999064i | \(0.513774\pi\) | |||||||
\(632\) | −1.01618 | −0.0404216 | ||||||||
\(633\) | −8.00407 | −0.318133 | ||||||||
\(634\) | 16.3911 | 0.650975 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.3194 | −0.528148 | ||||||||
\(637\) | 9.40794 | 0.372756 | ||||||||
\(638\) | −4.53200 | −0.179424 | ||||||||
\(639\) | 16.9603 | 0.670939 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.2645 | 0.681907 | 0.340954 | − | 0.940080i | \(-0.389250\pi\) | ||||
0.340954 | + | 0.940080i | \(0.389250\pi\) | |||||||
\(642\) | −81.0164 | −3.19746 | ||||||||
\(643\) | 1.98271 | 0.0781903 | 0.0390952 | − | 0.999235i | \(-0.487552\pi\) | ||||
0.0390952 | + | 0.999235i | \(0.487552\pi\) | |||||||
\(644\) | 8.30693 | 0.327339 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.73029 | −0.0680775 | ||||||||
\(647\) | 5.08596 | 0.199950 | 0.0999749 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999749 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(648\) | −7.51229 | −0.295111 | ||||||||
\(649\) | 45.2050 | 1.77445 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.9917 | 0.587573 | ||||||||
\(652\) | −9.07488 | −0.355400 | ||||||||
\(653\) | −30.8609 | −1.20768 | −0.603841 | − | 0.797105i | \(-0.706364\pi\) | ||||
−0.603841 | + | 0.797105i | \(0.706364\pi\) | |||||||
\(654\) | 65.3817 | 2.55663 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.9344 | −0.622134 | ||||||||
\(657\) | 19.4183 | 0.757581 | ||||||||
\(658\) | 19.0917 | 0.744271 | ||||||||
\(659\) | −32.9409 | −1.28319 | −0.641597 | − | 0.767042i | \(-0.721728\pi\) | ||||
−0.641597 | + | 0.767042i | \(0.721728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.4578 | 0.795716 | 0.397858 | − | 0.917447i | \(-0.369754\pi\) | ||||
0.397858 | + | 0.917447i | \(0.369754\pi\) | |||||||
\(662\) | −44.1597 | −1.71632 | ||||||||
\(663\) | −42.8723 | −1.66502 | ||||||||
\(664\) | 5.37733 | 0.208681 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −25.9806 | −1.00673 | ||||||||
\(667\) | 1.29257 | 0.0500486 | ||||||||
\(668\) | 30.3531 | 1.17440 | ||||||||
\(669\) | −2.25592 | −0.0872187 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.2000 | 0.432372 | ||||||||
\(672\) | 33.7430 | 1.30166 | ||||||||
\(673\) | −21.2044 | −0.817368 | −0.408684 | − | 0.912676i | \(-0.634012\pi\) | ||||
−0.408684 | + | 0.912676i | \(0.634012\pi\) | |||||||
\(674\) | 20.8854 | 0.804476 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.77934 | 0.222282 | ||||||||
\(677\) | −25.9496 | −0.997326 | −0.498663 | − | 0.866796i | \(-0.666175\pi\) | ||||
−0.498663 | + | 0.866796i | \(0.666175\pi\) | |||||||
\(678\) | 80.8951 | 3.10676 | ||||||||
\(679\) | 22.9852 | 0.882092 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 44.6943 | 1.71269 | ||||||||
\(682\) | 26.8414 | 1.02781 | ||||||||
\(683\) | −26.5331 | −1.01526 | −0.507630 | − | 0.861575i | \(-0.669478\pi\) | ||||
−0.507630 | + | 0.861575i | \(0.669478\pi\) | |||||||
\(684\) | −0.425717 | −0.0162777 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −38.5216 | −1.47076 | ||||||||
\(687\) | −15.3568 | −0.585898 | ||||||||
\(688\) | 13.2795 | 0.506276 | ||||||||
\(689\) | −15.5794 | −0.593528 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.3646 | −1.30729 | −0.653645 | − | 0.756801i | \(-0.726761\pi\) | ||||
−0.653645 | + | 0.756801i | \(0.726761\pi\) | |||||||
\(692\) | −2.19729 | −0.0835284 | ||||||||
\(693\) | 13.1951 | 0.501242 | ||||||||
\(694\) | 9.63900 | 0.365891 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.781346 | 0.0296169 | ||||||||
\(697\) | −17.4595 | −0.661325 | ||||||||
\(698\) | −66.3448 | −2.51119 | ||||||||
\(699\) | 46.0689 | 1.74249 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.7634 | −1.08638 | −0.543190 | − | 0.839610i | \(-0.682784\pi\) | ||||
−0.543190 | + | 0.839610i | \(0.682784\pi\) | |||||||
\(702\) | 25.6672 | 0.968746 | ||||||||
\(703\) | −1.71900 | −0.0648335 | ||||||||
\(704\) | 21.3439 | 0.804430 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.3113 | −1.17842 | ||||||||
\(707\) | 0.177840 | 0.00668837 | ||||||||
\(708\) | 36.7842 | 1.38244 | ||||||||
\(709\) | −38.6338 | −1.45092 | −0.725462 | − | 0.688262i | \(-0.758374\pi\) | ||||
−0.725462 | + | 0.688262i | \(0.758374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.17286 | −0.0814887 | ||||||||
\(712\) | −10.5768 | −0.396381 | ||||||||
\(713\) | −7.65543 | −0.286698 | ||||||||
\(714\) | 43.6403 | 1.63320 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −34.8336 | −1.30179 | ||||||||
\(717\) | 10.4946 | 0.391926 | ||||||||
\(718\) | 42.0334 | 1.56867 | ||||||||
\(719\) | −42.0112 | −1.56675 | −0.783376 | − | 0.621548i | \(-0.786504\pi\) | ||||
−0.783376 | + | 0.621548i | \(0.786504\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.75505 | −0.102603 | ||||||||
\(722\) | 36.2388 | 1.34867 | ||||||||
\(723\) | 2.10440 | 0.0782634 | ||||||||
\(724\) | 41.8242 | 1.55438 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 29.0125 | 1.07675 | ||||||||
\(727\) | 18.3447 | 0.680367 | 0.340184 | − | 0.940359i | \(-0.389511\pi\) | ||||
0.340184 | + | 0.940359i | \(0.389511\pi\) | |||||||
\(728\) | 5.87348 | 0.217686 | ||||||||
\(729\) | 4.81503 | 0.178334 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.5505 | 0.538169 | ||||||||
\(732\) | 9.11368 | 0.336851 | ||||||||
\(733\) | −33.6042 | −1.24120 | −0.620599 | − | 0.784128i | \(-0.713111\pi\) | ||||
−0.620599 | + | 0.784128i | \(0.713111\pi\) | |||||||
\(734\) | −25.7303 | −0.949724 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.2306 | −0.635130 | ||||||||
\(737\) | −5.07446 | −0.186920 | ||||||||
\(738\) | −9.50152 | −0.349756 | ||||||||
\(739\) | 16.6117 | 0.611070 | 0.305535 | − | 0.952181i | \(-0.401165\pi\) | ||||
0.305535 | + | 0.952181i | \(0.401165\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.54371 | −0.0567097 | ||||||||
\(742\) | 15.8585 | 0.582183 | ||||||||
\(743\) | 50.1494 | 1.83980 | 0.919901 | − | 0.392151i | \(-0.128269\pi\) | ||||
0.919901 | + | 0.392151i | \(0.128269\pi\) | |||||||
\(744\) | −4.62762 | −0.169657 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.77715 | −0.101679 | ||||||||
\(747\) | 11.4981 | 0.420694 | ||||||||
\(748\) | 35.3248 | 1.29160 | ||||||||
\(749\) | 43.6104 | 1.59349 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.60036 | 0.131379 | 0.0656896 | − | 0.997840i | \(-0.479075\pi\) | ||||
0.0656896 | + | 0.997840i | \(0.479075\pi\) | |||||||
\(752\) | −21.1326 | −0.770627 | ||||||||
\(753\) | −38.8811 | −1.41691 | ||||||||
\(754\) | −4.31352 | −0.157089 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.8121 | −0.429603 | ||||||||
\(757\) | 21.7797 | 0.791598 | 0.395799 | − | 0.918337i | \(-0.370468\pi\) | ||||
0.395799 | + | 0.918337i | \(0.370468\pi\) | |||||||
\(758\) | −11.4381 | −0.415450 | ||||||||
\(759\) | −20.8886 | −0.758209 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.60072 | −0.311776 | −0.155888 | − | 0.987775i | \(-0.549824\pi\) | ||||
−0.155888 | + | 0.987775i | \(0.549824\pi\) | |||||||
\(762\) | −66.2341 | −2.39941 | ||||||||
\(763\) | −35.1944 | −1.27412 | ||||||||
\(764\) | −5.82864 | −0.210873 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.5641 | −0.598486 | ||||||||
\(767\) | 43.0257 | 1.55357 | ||||||||
\(768\) | −42.2077 | −1.52304 | ||||||||
\(769\) | 34.1553 | 1.23167 | 0.615836 | − | 0.787874i | \(-0.288818\pi\) | ||||
0.615836 | + | 0.787874i | \(0.288818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.9919 | −0.972090 | ||||||||
\(772\) | 5.32645 | 0.191703 | ||||||||
\(773\) | −26.5165 | −0.953731 | −0.476865 | − | 0.878976i | \(-0.658227\pi\) | ||||
−0.476865 | + | 0.878976i | \(0.658227\pi\) | |||||||
\(774\) | 7.91843 | 0.284622 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.09504 | −0.254697 | ||||||||
\(777\) | 43.3555 | 1.55537 | ||||||||
\(778\) | 12.4441 | 0.446142 | ||||||||
\(779\) | −0.628667 | −0.0225243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.6735 | −1.81324 | ||||||||
\(782\) | −22.2846 | −0.796896 | ||||||||
\(783\) | −1.83799 | −0.0656844 | ||||||||
\(784\) | 10.6002 | 0.378579 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 69.8609 | 2.49186 | ||||||||
\(787\) | 32.7986 | 1.16914 | 0.584572 | − | 0.811342i | \(-0.301262\pi\) | ||||
0.584572 | + | 0.811342i | \(0.301262\pi\) | |||||||
\(788\) | 19.5398 | 0.696077 | ||||||||
\(789\) | 46.4418 | 1.65337 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.5451 | −1.54829 | ||||||||
\(792\) | −4.07305 | −0.144730 | ||||||||
\(793\) | 10.6601 | 0.378551 | ||||||||
\(794\) | −27.8851 | −0.989606 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.1775 | −0.467066 | ||||||||
\(797\) | −18.5774 | −0.658047 | −0.329024 | − | 0.944322i | \(-0.606720\pi\) | ||||
−0.329024 | + | 0.944322i | \(0.606720\pi\) | |||||||
\(798\) | 1.57136 | 0.0556257 | ||||||||
\(799\) | −23.1552 | −0.819172 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.6159 | −0.799092 | ||||||||
\(802\) | 23.1421 | 0.817177 | ||||||||
\(803\) | −58.0176 | −2.04740 | ||||||||
\(804\) | −4.12919 | −0.145625 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.5474 | 0.899869 | ||||||||
\(807\) | −13.3989 | −0.471662 | ||||||||
\(808\) | −0.0548954 | −0.00193121 | ||||||||
\(809\) | 15.1345 | 0.532100 | 0.266050 | − | 0.963959i | \(-0.414281\pi\) | ||||
0.266050 | + | 0.963959i | \(0.414281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.1559 | 0.813113 | 0.406557 | − | 0.913626i | \(-0.366729\pi\) | ||||
0.406557 | + | 0.913626i | \(0.366729\pi\) | |||||||
\(812\) | 1.98510 | 0.0696633 | ||||||||
\(813\) | 49.0202 | 1.71921 | ||||||||
\(814\) | 77.6242 | 2.72073 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −48.3055 | −1.69103 | ||||||||
\(817\) | 0.523922 | 0.0183297 | ||||||||
\(818\) | 17.9304 | 0.626921 | ||||||||
\(819\) | 12.5590 | 0.438848 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4499 | 0.399605 | 0.199803 | − | 0.979836i | \(-0.435970\pi\) | ||||
0.199803 | + | 0.979836i | \(0.435970\pi\) | |||||||
\(822\) | 45.5923 | 1.59021 | ||||||||
\(823\) | −55.2246 | −1.92501 | −0.962504 | − | 0.271269i | \(-0.912557\pi\) | ||||
−0.962504 | + | 0.271269i | \(0.912557\pi\) | |||||||
\(824\) | 0.850424 | 0.0296259 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −43.7964 | −1.52387 | ||||||||
\(827\) | −11.9420 | −0.415264 | −0.207632 | − | 0.978207i | \(-0.566576\pi\) | ||||
−0.207632 | + | 0.978207i | \(0.566576\pi\) | |||||||
\(828\) | −5.48285 | −0.190542 | ||||||||
\(829\) | −36.3476 | −1.26240 | −0.631202 | − | 0.775618i | \(-0.717438\pi\) | ||||
−0.631202 | + | 0.775618i | \(0.717438\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.5913 | −1.61623 | ||||||||
\(832\) | 20.3150 | 0.704295 | ||||||||
\(833\) | 11.6147 | 0.402427 | ||||||||
\(834\) | 21.0914 | 0.730337 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.27195 | 0.0439912 | ||||||||
\(837\) | 10.8857 | 0.376266 | ||||||||
\(838\) | 46.2789 | 1.59868 | ||||||||
\(839\) | −24.9289 | −0.860641 | −0.430320 | − | 0.902676i | \(-0.641599\pi\) | ||||
−0.430320 | + | 0.902676i | \(0.641599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6911 | −0.989349 | ||||||||
\(842\) | −47.9732 | −1.65327 | ||||||||
\(843\) | −18.1102 | −0.623747 | ||||||||
\(844\) | 6.27704 | 0.216065 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.6012 | −0.433236 | ||||||||
\(847\) | −15.6171 | −0.536611 | ||||||||
\(848\) | −17.5538 | −0.602799 | ||||||||
\(849\) | −31.6447 | −1.08604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.1392 | −0.758923 | ||||||||
\(852\) | −41.2341 | −1.41266 | ||||||||
\(853\) | 41.5695 | 1.42331 | 0.711657 | − | 0.702527i | \(-0.247945\pi\) | ||||
0.711657 | + | 0.702527i | \(0.247945\pi\) | |||||||
\(854\) | −10.8510 | −0.371315 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.4616 | −0.460107 | ||||||||
\(857\) | −28.3039 | −0.966842 | −0.483421 | − | 0.875388i | \(-0.660606\pi\) | ||||
−0.483421 | + | 0.875388i | \(0.660606\pi\) | |||||||
\(858\) | 69.7087 | 2.37981 | ||||||||
\(859\) | −12.3577 | −0.421638 | −0.210819 | − | 0.977525i | \(-0.567613\pi\) | ||||
−0.210819 | + | 0.977525i | \(0.567613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.8558 | 0.540364 | ||||||||
\(862\) | 16.7714 | 0.571237 | ||||||||
\(863\) | −20.5144 | −0.698319 | −0.349159 | − | 0.937063i | \(-0.613533\pi\) | ||||
−0.349159 | + | 0.937063i | \(0.613533\pi\) | |||||||
\(864\) | 24.5013 | 0.833552 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.16813 | 0.0396946 | ||||||||
\(867\) | −17.1540 | −0.582581 | ||||||||
\(868\) | −11.7570 | −0.399059 | ||||||||
\(869\) | 6.49203 | 0.220227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.82983 | −0.163652 | ||||||||
\(872\) | 10.8637 | 0.367892 | ||||||||
\(873\) | −15.1710 | −0.513461 | ||||||||
\(874\) | −0.802407 | −0.0271418 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −47.2101 | −1.59508 | ||||||||
\(877\) | 33.0284 | 1.11529 | 0.557645 | − | 0.830079i | \(-0.311705\pi\) | ||||
0.557645 | + | 0.830079i | \(0.311705\pi\) | |||||||
\(878\) | −31.0749 | −1.04873 | ||||||||
\(879\) | 13.0096 | 0.438803 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.5997 | 0.559260 | 0.279630 | − | 0.960108i | \(-0.409788\pi\) | ||||
0.279630 | + | 0.960108i | \(0.409788\pi\) | |||||||
\(882\) | 6.32078 | 0.212832 | ||||||||
\(883\) | −49.9499 | −1.68095 | −0.840473 | − | 0.541853i | \(-0.817723\pi\) | ||||
−0.840473 | + | 0.541853i | \(0.817723\pi\) | |||||||
\(884\) | 33.6218 | 1.13083 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 60.0388 | 2.01704 | ||||||||
\(887\) | −3.83231 | −0.128677 | −0.0643383 | − | 0.997928i | \(-0.520494\pi\) | ||||
−0.0643383 | + | 0.997928i | \(0.520494\pi\) | |||||||
\(888\) | −13.3829 | −0.449101 | ||||||||
\(889\) | 35.6532 | 1.19577 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.9933 | 1.60784 | ||||||||
\(892\) | 1.76916 | 0.0592359 | ||||||||
\(893\) | −0.833754 | −0.0279005 | ||||||||
\(894\) | 20.6866 | 0.691863 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.3902 | 0.380519 | ||||||||
\(897\) | −19.8816 | −0.663828 | ||||||||
\(898\) | 27.6913 | 0.924069 | ||||||||
\(899\) | −1.82941 | −0.0610143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.2338 | −0.640772 | ||||||||
\(902\) | 28.3884 | 0.945230 | ||||||||
\(903\) | −13.2140 | −0.439734 | ||||||||
\(904\) | 13.4414 | 0.447055 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 76.6843 | 2.54766 | ||||||||
\(907\) | −33.5656 | −1.11453 | −0.557264 | − | 0.830336i | \(-0.688149\pi\) | ||||
−0.557264 | + | 0.830336i | \(0.688149\pi\) | |||||||
\(908\) | −35.0507 | −1.16320 | ||||||||
\(909\) | −0.117381 | −0.00389327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.44125 | −0.246540 | −0.123270 | − | 0.992373i | \(-0.539338\pi\) | ||||
−0.123270 | + | 0.992373i | \(0.539338\pi\) | |||||||
\(912\) | −1.73935 | −0.0575955 | ||||||||
\(913\) | −34.3538 | −1.13694 | ||||||||
\(914\) | −22.2888 | −0.737248 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.0433 | 0.397921 | ||||||||
\(917\) | −37.6055 | −1.24184 | ||||||||
\(918\) | 31.6879 | 1.04586 | ||||||||
\(919\) | 42.2789 | 1.39465 | 0.697326 | − | 0.716754i | \(-0.254373\pi\) | ||||
0.697326 | + | 0.716754i | \(0.254373\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.3845 | 0.935302 | ||||||||
\(922\) | 8.55420 | 0.281718 | ||||||||
\(923\) | −48.2306 | −1.58753 | ||||||||
\(924\) | −32.0802 | −1.05536 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33.4795 | −1.10020 | ||||||||
\(927\) | 1.81843 | 0.0597250 | ||||||||
\(928\) | −4.11759 | −0.135167 | ||||||||
\(929\) | −54.0164 | −1.77222 | −0.886110 | − | 0.463474i | \(-0.846603\pi\) | ||||
−0.886110 | + | 0.463474i | \(0.846603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.418214 | 0.0137064 | ||||||||
\(932\) | −36.1287 | −1.18344 | ||||||||
\(933\) | −6.37398 | −0.208675 | ||||||||
\(934\) | 9.93645 | 0.325131 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.87670 | −0.126714 | ||||||||
\(937\) | −5.15837 | −0.168517 | −0.0842584 | − | 0.996444i | \(-0.526852\pi\) | ||||
−0.0842584 | + | 0.996444i | \(0.526852\pi\) | |||||||
\(938\) | 4.91634 | 0.160524 | ||||||||
\(939\) | 37.2151 | 1.21447 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.7898 | −0.971119 | −0.485560 | − | 0.874204i | \(-0.661384\pi\) | ||||
−0.485560 | + | 0.874204i | \(0.661384\pi\) | |||||||
\(942\) | −26.4832 | −0.862870 | ||||||||
\(943\) | −8.09666 | −0.263663 | ||||||||
\(944\) | 48.4784 | 1.57784 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.6585 | −0.769203 | ||||||||
\(947\) | 45.5068 | 1.47877 | 0.739386 | − | 0.673282i | \(-0.235116\pi\) | ||||
0.739386 | + | 0.673282i | \(0.235116\pi\) | |||||||
\(948\) | 5.28269 | 0.171574 | ||||||||
\(949\) | −55.2207 | −1.79254 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0539 | 0.585437 | ||||||||
\(952\) | 7.25121 | 0.235013 | ||||||||
\(953\) | 25.6723 | 0.831607 | 0.415803 | − | 0.909455i | \(-0.363500\pi\) | ||||
0.415803 | + | 0.909455i | \(0.363500\pi\) | |||||||
\(954\) | −10.4671 | −0.338886 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.23016 | −0.266183 | ||||||||
\(957\) | −4.99174 | −0.161360 | ||||||||
\(958\) | −47.1123 | −1.52213 | ||||||||
\(959\) | −24.5419 | −0.792500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1651 | −0.650486 | ||||||||
\(962\) | 73.8821 | 2.38205 | ||||||||
\(963\) | −28.7843 | −0.927562 | ||||||||
\(964\) | −1.65034 | −0.0531537 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 20.2377 | 0.651139 | ||||||||
\(967\) | −7.17383 | −0.230695 | −0.115347 | − | 0.993325i | \(-0.536798\pi\) | ||||
−0.115347 | + | 0.993325i | \(0.536798\pi\) | |||||||
\(968\) | 4.82067 | 0.154942 | ||||||||
\(969\) | −1.90582 | −0.0612237 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9457 | 1.28192 | 0.640959 | − | 0.767575i | \(-0.278537\pi\) | ||||
0.640959 | + | 0.767575i | \(0.278537\pi\) | |||||||
\(972\) | 22.6797 | 0.727452 | ||||||||
\(973\) | −11.3533 | −0.363971 | ||||||||
\(974\) | 64.5578 | 2.06857 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.0110 | 0.384464 | ||||||||
\(977\) | 26.5270 | 0.848675 | 0.424338 | − | 0.905504i | \(-0.360507\pi\) | ||||
0.424338 | + | 0.905504i | \(0.360507\pi\) | |||||||
\(978\) | −22.1087 | −0.706957 | ||||||||
\(979\) | 67.5711 | 2.15958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.2295 | 0.741660 | ||||||||
\(982\) | −9.42135 | −0.300647 | ||||||||
\(983\) | −39.2874 | −1.25307 | −0.626537 | − | 0.779392i | \(-0.715528\pi\) | ||||
−0.626537 | + | 0.779392i | \(0.715528\pi\) | |||||||
\(984\) | −4.89434 | −0.156026 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.32534 | −0.169593 | ||||||||
\(987\) | 21.0284 | 0.669340 | ||||||||
\(988\) | 1.21063 | 0.0385152 | ||||||||
\(989\) | 6.74764 | 0.214562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.50257 | 0.206561 | 0.103280 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103280 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(992\) | 24.3870 | 0.774287 | ||||||||
\(993\) | −48.6394 | −1.54352 | ||||||||
\(994\) | 49.0946 | 1.55719 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −27.9544 | −0.885768 | ||||||||
\(997\) | 45.8122 | 1.45089 | 0.725444 | − | 0.688282i | \(-0.241635\pi\) | ||||
0.725444 | + | 0.688282i | \(0.241635\pi\) | |||||||
\(998\) | 14.6466 | 0.463631 | ||||||||
\(999\) | 31.4811 | 0.996019 |
(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 | 6025.2.a.j.1.8 | 25 | ||
5.4 | even | 2 | 1205.2.a.e.1.18 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.e.1.18 | ✓ | 25 | 5.4 | even | 2 | ||
6025.2.a.j.1.8 | 25 | 1.1 | even | 1 | trivial |