Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3025,2,Mod(1,3025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, 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("3025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3025 = 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3025.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: | \(24.1547466114\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 7x^{6} + 18x^{5} + 16x^{4} - 30x^{3} - 12x^{2} + 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 275) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56247\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56247 | −1.81194 | −0.905970 | − | 0.423342i | \(-0.860857\pi\) | ||||
−0.905970 | + | 0.423342i | \(0.860857\pi\) | |||||||
\(3\) | 1.79260 | 1.03496 | 0.517478 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517478 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(4\) | 4.56626 | 2.28313 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.59347 | −1.87528 | ||||||||
\(7\) | −3.80088 | −1.43660 | −0.718298 | − | 0.695735i | \(-0.755079\pi\) | ||||
−0.718298 | + | 0.695735i | \(0.755079\pi\) | |||||||
\(8\) | −6.57595 | −2.32495 | ||||||||
\(9\) | 0.213399 | 0.0711330 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 8.18545 | 2.36294 | ||||||||
\(13\) | 4.49758 | 1.24740 | 0.623702 | − | 0.781663i | \(-0.285628\pi\) | ||||
0.623702 | + | 0.781663i | \(0.285628\pi\) | |||||||
\(14\) | 9.73964 | 2.60303 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.71818 | 1.92955 | ||||||||
\(17\) | −5.01207 | −1.21560 | −0.607802 | − | 0.794088i | \(-0.707949\pi\) | ||||
−0.607802 | + | 0.794088i | \(0.707949\pi\) | |||||||
\(18\) | −0.546828 | −0.128889 | ||||||||
\(19\) | 3.46053 | 0.793900 | 0.396950 | − | 0.917840i | \(-0.370069\pi\) | ||||
0.396950 | + | 0.917840i | \(0.370069\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.81344 | −1.48681 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.105727 | 0.0220456 | 0.0110228 | − | 0.999939i | \(-0.496491\pi\) | ||||
0.0110228 | + | 0.999939i | \(0.496491\pi\) | |||||||
\(24\) | −11.7880 | −2.40622 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.5249 | −2.26022 | ||||||||
\(27\) | −4.99525 | −0.961336 | ||||||||
\(28\) | −17.3558 | −3.27993 | ||||||||
\(29\) | 2.35008 | 0.436398 | 0.218199 | − | 0.975904i | \(-0.429982\pi\) | ||||
0.218199 | + | 0.975904i | \(0.429982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74526 | 0.852274 | 0.426137 | − | 0.904659i | \(-0.359874\pi\) | ||||
0.426137 | + | 0.904659i | \(0.359874\pi\) | |||||||
\(32\) | −6.62570 | −1.17127 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.8433 | 2.20260 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.974434 | 0.162406 | ||||||||
\(37\) | −5.60088 | −0.920779 | −0.460390 | − | 0.887717i | \(-0.652290\pi\) | ||||
−0.460390 | + | 0.887717i | \(0.652290\pi\) | |||||||
\(38\) | −8.86750 | −1.43850 | ||||||||
\(39\) | 8.06233 | 1.29101 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.916922 | −0.143199 | −0.0715996 | − | 0.997433i | \(-0.522810\pi\) | ||||
−0.0715996 | + | 0.997433i | \(0.522810\pi\) | |||||||
\(42\) | 17.4592 | 2.69402 | ||||||||
\(43\) | 4.46162 | 0.680390 | 0.340195 | − | 0.940355i | \(-0.389507\pi\) | ||||
0.340195 | + | 0.940355i | \(0.389507\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.270922 | −0.0399453 | ||||||||
\(47\) | 1.25360 | 0.182857 | 0.0914283 | − | 0.995812i | \(-0.470857\pi\) | ||||
0.0914283 | + | 0.995812i | \(0.470857\pi\) | |||||||
\(48\) | 13.8356 | 1.99699 | ||||||||
\(49\) | 7.44667 | 1.06381 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.98461 | −1.25810 | ||||||||
\(52\) | 20.5371 | 2.84798 | ||||||||
\(53\) | −5.49861 | −0.755292 | −0.377646 | − | 0.925950i | \(-0.623266\pi\) | ||||
−0.377646 | + | 0.925950i | \(0.623266\pi\) | |||||||
\(54\) | 12.8002 | 1.74188 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 24.9944 | 3.34002 | ||||||||
\(57\) | 6.20333 | 0.821651 | ||||||||
\(58\) | −6.02200 | −0.790728 | ||||||||
\(59\) | −1.18305 | −0.154020 | −0.0770099 | − | 0.997030i | \(-0.524537\pi\) | ||||
−0.0770099 | + | 0.997030i | \(0.524537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.32605 | 0.938004 | 0.469002 | − | 0.883197i | \(-0.344614\pi\) | ||||
0.469002 | + | 0.883197i | \(0.344614\pi\) | |||||||
\(62\) | −12.1596 | −1.54427 | ||||||||
\(63\) | −0.811103 | −0.102189 | ||||||||
\(64\) | 1.54180 | 0.192725 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.84414 | 0.958315 | 0.479157 | − | 0.877729i | \(-0.340942\pi\) | ||||
0.479157 | + | 0.877729i | \(0.340942\pi\) | |||||||
\(68\) | −22.8864 | −2.77538 | ||||||||
\(69\) | 0.189526 | 0.0228162 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.18022 | −0.258745 | −0.129372 | − | 0.991596i | \(-0.541296\pi\) | ||||
−0.129372 | + | 0.991596i | \(0.541296\pi\) | |||||||
\(72\) | −1.40330 | −0.165381 | ||||||||
\(73\) | −8.95263 | −1.04783 | −0.523913 | − | 0.851772i | \(-0.675528\pi\) | ||||
−0.523913 | + | 0.851772i | \(0.675528\pi\) | |||||||
\(74\) | 14.3521 | 1.66840 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.8017 | 1.81257 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −20.6595 | −2.33923 | ||||||||
\(79\) | −14.3825 | −1.61815 | −0.809077 | − | 0.587702i | \(-0.800033\pi\) | ||||
−0.809077 | + | 0.587702i | \(0.800033\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.59466 | −1.06607 | ||||||||
\(82\) | 2.34959 | 0.259468 | ||||||||
\(83\) | 4.71142 | 0.517146 | 0.258573 | − | 0.965992i | \(-0.416748\pi\) | ||||
0.258573 | + | 0.965992i | \(0.416748\pi\) | |||||||
\(84\) | −31.1119 | −3.39459 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.4328 | −1.23283 | ||||||||
\(87\) | 4.21274 | 0.451653 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.172993 | −0.0183372 | −0.00916862 | − | 0.999958i | \(-0.502919\pi\) | ||||
−0.00916862 | + | 0.999958i | \(0.502919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.0947 | −1.79202 | ||||||||
\(92\) | 0.482777 | 0.0503330 | ||||||||
\(93\) | 8.50634 | 0.882066 | ||||||||
\(94\) | −3.21232 | −0.331325 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −11.8772 | −1.21221 | ||||||||
\(97\) | −4.46043 | −0.452888 | −0.226444 | − | 0.974024i | \(-0.572710\pi\) | ||||
−0.226444 | + | 0.974024i | \(0.572710\pi\) | |||||||
\(98\) | −19.0819 | −1.92756 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.80519 | −0.876149 | −0.438074 | − | 0.898939i | \(-0.644339\pi\) | ||||
−0.438074 | + | 0.898939i | \(0.644339\pi\) | |||||||
\(102\) | 23.0228 | 2.27960 | ||||||||
\(103\) | −16.4740 | −1.62323 | −0.811615 | − | 0.584193i | \(-0.801411\pi\) | ||||
−0.811615 | + | 0.584193i | \(0.801411\pi\) | |||||||
\(104\) | −29.5759 | −2.90015 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.0900 | 1.36854 | ||||||||
\(107\) | −17.1724 | −1.66012 | −0.830060 | − | 0.557674i | \(-0.811694\pi\) | ||||
−0.830060 | + | 0.557674i | \(0.811694\pi\) | |||||||
\(108\) | −22.8096 | −2.19485 | ||||||||
\(109\) | −17.9060 | −1.71508 | −0.857542 | − | 0.514414i | \(-0.828009\pi\) | ||||
−0.857542 | + | 0.514414i | \(0.828009\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0401 | −0.952965 | ||||||||
\(112\) | −29.3359 | −2.77198 | ||||||||
\(113\) | −14.3161 | −1.34675 | −0.673374 | − | 0.739302i | \(-0.735156\pi\) | ||||
−0.673374 | + | 0.739302i | \(0.735156\pi\) | |||||||
\(114\) | −15.8958 | −1.48878 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.7311 | 0.996353 | ||||||||
\(117\) | 0.959778 | 0.0887315 | ||||||||
\(118\) | 3.03153 | 0.279075 | ||||||||
\(119\) | 19.0503 | 1.74633 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −18.7728 | −1.69961 | ||||||||
\(123\) | −1.64367 | −0.148205 | ||||||||
\(124\) | 21.6681 | 1.94585 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.07843 | 0.185161 | ||||||||
\(127\) | 5.57000 | 0.494257 | 0.247129 | − | 0.968983i | \(-0.420513\pi\) | ||||
0.247129 | + | 0.968983i | \(0.420513\pi\) | |||||||
\(128\) | 9.30058 | 0.822063 | ||||||||
\(129\) | 7.99788 | 0.704174 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8367 | 1.20892 | 0.604458 | − | 0.796637i | \(-0.293390\pi\) | ||||
0.604458 | + | 0.796637i | \(0.293390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.1530 | −1.14051 | ||||||||
\(134\) | −20.1004 | −1.73641 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 32.9591 | 2.82622 | ||||||||
\(137\) | −9.94447 | −0.849614 | −0.424807 | − | 0.905284i | \(-0.639658\pi\) | ||||
−0.424807 | + | 0.905284i | \(0.639658\pi\) | |||||||
\(138\) | −0.485654 | −0.0413417 | ||||||||
\(139\) | −2.03061 | −0.172234 | −0.0861170 | − | 0.996285i | \(-0.527446\pi\) | ||||
−0.0861170 | + | 0.996285i | \(0.527446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.24720 | 0.189248 | ||||||||
\(142\) | 5.58676 | 0.468830 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.64705 | 0.137254 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 22.9408 | 1.89860 | ||||||||
\(147\) | 13.3489 | 1.10100 | ||||||||
\(148\) | −25.5751 | −2.10226 | ||||||||
\(149\) | −10.6201 | −0.870033 | −0.435017 | − | 0.900422i | \(-0.643258\pi\) | ||||
−0.435017 | + | 0.900422i | \(0.643258\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.43448 | 0.279494 | 0.139747 | − | 0.990187i | \(-0.455371\pi\) | ||||
0.139747 | + | 0.990187i | \(0.455371\pi\) | |||||||
\(152\) | −22.7563 | −1.84578 | ||||||||
\(153\) | −1.06957 | −0.0864696 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 36.8147 | 2.94753 | ||||||||
\(157\) | −0.298585 | −0.0238296 | −0.0119148 | − | 0.999929i | \(-0.503793\pi\) | ||||
−0.0119148 | + | 0.999929i | \(0.503793\pi\) | |||||||
\(158\) | 36.8547 | 2.93200 | ||||||||
\(159\) | −9.85678 | −0.781693 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.401856 | −0.0316707 | ||||||||
\(162\) | 24.5860 | 1.93166 | ||||||||
\(163\) | 14.2597 | 1.11691 | 0.558454 | − | 0.829536i | \(-0.311395\pi\) | ||||
0.558454 | + | 0.829536i | \(0.311395\pi\) | |||||||
\(164\) | −4.18690 | −0.326942 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0729 | −0.937037 | ||||||||
\(167\) | −17.9977 | −1.39270 | −0.696352 | − | 0.717700i | \(-0.745195\pi\) | ||||
−0.696352 | + | 0.717700i | \(0.745195\pi\) | |||||||
\(168\) | 44.8049 | 3.45677 | ||||||||
\(169\) | 7.22819 | 0.556014 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.738473 | 0.0564724 | ||||||||
\(172\) | 20.3729 | 1.55342 | ||||||||
\(173\) | 8.75353 | 0.665519 | 0.332759 | − | 0.943012i | \(-0.392020\pi\) | ||||
0.332759 | + | 0.943012i | \(0.392020\pi\) | |||||||
\(174\) | −10.7950 | −0.818368 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.12073 | −0.159404 | ||||||||
\(178\) | 0.443290 | 0.0332260 | ||||||||
\(179\) | −22.8999 | −1.71162 | −0.855811 | − | 0.517289i | \(-0.826941\pi\) | ||||
−0.855811 | + | 0.517289i | \(0.826941\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2705 | 1.28370 | 0.641852 | − | 0.766828i | \(-0.278166\pi\) | ||||
0.641852 | + | 0.766828i | \(0.278166\pi\) | |||||||
\(182\) | 43.8048 | 3.24702 | ||||||||
\(183\) | 13.1326 | 0.970793 | ||||||||
\(184\) | −0.695256 | −0.0512550 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −21.7972 | −1.59825 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.72427 | 0.417485 | ||||||||
\(189\) | 18.9863 | 1.38105 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.2017 | −1.31703 | −0.658513 | − | 0.752569i | \(-0.728814\pi\) | ||||
−0.658513 | + | 0.752569i | \(0.728814\pi\) | |||||||
\(192\) | 2.76383 | 0.199462 | ||||||||
\(193\) | 11.0361 | 0.794397 | 0.397199 | − | 0.917733i | \(-0.369982\pi\) | ||||
0.397199 | + | 0.917733i | \(0.369982\pi\) | |||||||
\(194\) | 11.4297 | 0.820607 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 34.0034 | 2.42882 | ||||||||
\(197\) | 15.7213 | 1.12009 | 0.560047 | − | 0.828461i | \(-0.310783\pi\) | ||||
0.560047 | + | 0.828461i | \(0.310783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.44523 | 0.315114 | 0.157557 | − | 0.987510i | \(-0.449638\pi\) | ||||
0.157557 | + | 0.987510i | \(0.449638\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0614 | 0.991813 | ||||||||
\(202\) | 22.5630 | 1.58753 | ||||||||
\(203\) | −8.93236 | −0.626929 | ||||||||
\(204\) | −41.0260 | −2.87240 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 42.2141 | 2.94119 | ||||||||
\(207\) | 0.0225620 | 0.00156817 | ||||||||
\(208\) | 34.7131 | 2.40692 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.31213 | −0.159173 | −0.0795866 | − | 0.996828i | \(-0.525360\pi\) | ||||
−0.0795866 | + | 0.996828i | \(0.525360\pi\) | |||||||
\(212\) | −25.1080 | −1.72443 | ||||||||
\(213\) | −3.90826 | −0.267790 | ||||||||
\(214\) | 44.0038 | 3.00804 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 32.8485 | 2.23506 | ||||||||
\(217\) | −18.0362 | −1.22437 | ||||||||
\(218\) | 45.8836 | 3.10763 | ||||||||
\(219\) | −16.0484 | −1.08445 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5422 | −1.51635 | ||||||||
\(222\) | 25.7275 | 1.72672 | ||||||||
\(223\) | 10.2973 | 0.689555 | 0.344777 | − | 0.938684i | \(-0.387954\pi\) | ||||
0.344777 | + | 0.938684i | \(0.387954\pi\) | |||||||
\(224\) | 25.1835 | 1.68264 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 36.6847 | 2.44023 | ||||||||
\(227\) | 7.17833 | 0.476442 | 0.238221 | − | 0.971211i | \(-0.423436\pi\) | ||||
0.238221 | + | 0.971211i | \(0.423436\pi\) | |||||||
\(228\) | 28.3260 | 1.87593 | ||||||||
\(229\) | 2.05937 | 0.136087 | 0.0680435 | − | 0.997682i | \(-0.478324\pi\) | ||||
0.0680435 | + | 0.997682i | \(0.478324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.4540 | −1.01461 | ||||||||
\(233\) | −17.5865 | −1.15213 | −0.576065 | − | 0.817404i | \(-0.695413\pi\) | ||||
−0.576065 | + | 0.817404i | \(0.695413\pi\) | |||||||
\(234\) | −2.45940 | −0.160776 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.40210 | −0.351647 | ||||||||
\(237\) | −25.7820 | −1.67472 | ||||||||
\(238\) | −48.8157 | −3.16425 | ||||||||
\(239\) | −18.6889 | −1.20888 | −0.604442 | − | 0.796649i | \(-0.706604\pi\) | ||||
−0.604442 | + | 0.796649i | \(0.706604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.1916 | −1.94481 | −0.972406 | − | 0.233296i | \(-0.925049\pi\) | ||||
−0.972406 | + | 0.233296i | \(0.925049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.21359 | −0.142002 | ||||||||
\(244\) | 33.4526 | 2.14158 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.21186 | 0.268538 | ||||||||
\(247\) | 15.5640 | 0.990313 | ||||||||
\(248\) | −31.2046 | −1.98150 | ||||||||
\(249\) | 8.44568 | 0.535223 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.5114 | −1.61026 | −0.805132 | − | 0.593096i | \(-0.797906\pi\) | ||||
−0.805132 | + | 0.593096i | \(0.797906\pi\) | |||||||
\(252\) | −3.70370 | −0.233311 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −14.2730 | −0.895565 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.9161 | −1.68225 | ||||||||
\(257\) | 23.9417 | 1.49344 | 0.746721 | − | 0.665137i | \(-0.231627\pi\) | ||||
0.746721 | + | 0.665137i | \(0.231627\pi\) | |||||||
\(258\) | −20.4943 | −1.27592 | ||||||||
\(259\) | 21.2883 | 1.32279 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.501504 | 0.0310423 | ||||||||
\(262\) | −35.4561 | −2.19048 | ||||||||
\(263\) | −26.7696 | −1.65069 | −0.825343 | − | 0.564631i | \(-0.809018\pi\) | ||||
−0.825343 | + | 0.564631i | \(0.809018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 33.7043 | 2.06654 | ||||||||
\(267\) | −0.310107 | −0.0189782 | ||||||||
\(268\) | 35.8184 | 2.18796 | ||||||||
\(269\) | −5.96585 | −0.363744 | −0.181872 | − | 0.983322i | \(-0.558216\pi\) | ||||
−0.181872 | + | 0.983322i | \(0.558216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.49365 | 0.455207 | 0.227603 | − | 0.973754i | \(-0.426911\pi\) | ||||
0.227603 | + | 0.973754i | \(0.426911\pi\) | |||||||
\(272\) | −38.6840 | −2.34556 | ||||||||
\(273\) | −30.6439 | −1.85466 | ||||||||
\(274\) | 25.4824 | 1.53945 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.865424 | 0.0520924 | ||||||||
\(277\) | −1.44255 | −0.0866742 | −0.0433371 | − | 0.999061i | \(-0.513799\pi\) | ||||
−0.0433371 | + | 0.999061i | \(0.513799\pi\) | |||||||
\(278\) | 5.20338 | 0.312078 | ||||||||
\(279\) | 1.01263 | 0.0606248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.239273 | 0.0142738 | 0.00713691 | − | 0.999975i | \(-0.497728\pi\) | ||||
0.00713691 | + | 0.999975i | \(0.497728\pi\) | |||||||
\(282\) | −5.75839 | −0.342907 | ||||||||
\(283\) | −5.27885 | −0.313795 | −0.156898 | − | 0.987615i | \(-0.550149\pi\) | ||||
−0.156898 | + | 0.987615i | \(0.550149\pi\) | |||||||
\(284\) | −9.95546 | −0.590748 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.48511 | 0.205720 | ||||||||
\(288\) | −1.41392 | −0.0833159 | ||||||||
\(289\) | 8.12082 | 0.477695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.99575 | −0.468719 | ||||||||
\(292\) | −40.8800 | −2.39232 | ||||||||
\(293\) | −14.9959 | −0.876069 | −0.438035 | − | 0.898958i | \(-0.644325\pi\) | ||||
−0.438035 | + | 0.898958i | \(0.644325\pi\) | |||||||
\(294\) | −34.2061 | −1.99494 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 36.8311 | 2.14077 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.2137 | 1.57645 | ||||||||
\(299\) | 0.475515 | 0.0274998 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.9581 | −0.977447 | ||||||||
\(302\) | −8.80076 | −0.506427 | ||||||||
\(303\) | −15.7841 | −0.906775 | ||||||||
\(304\) | 26.7090 | 1.53187 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.74074 | 0.156678 | ||||||||
\(307\) | 2.11034 | 0.120443 | 0.0602217 | − | 0.998185i | \(-0.480819\pi\) | ||||
0.0602217 | + | 0.998185i | \(0.480819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.5312 | −1.67997 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.6612 | −0.944768 | −0.472384 | − | 0.881393i | \(-0.656606\pi\) | ||||
−0.472384 | + | 0.881393i | \(0.656606\pi\) | |||||||
\(312\) | −53.0175 | −3.00153 | ||||||||
\(313\) | 29.0799 | 1.64369 | 0.821845 | − | 0.569710i | \(-0.192945\pi\) | ||||
0.821845 | + | 0.569710i | \(0.192945\pi\) | |||||||
\(314\) | 0.765114 | 0.0431779 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −65.6740 | −3.69445 | ||||||||
\(317\) | 18.3165 | 1.02876 | 0.514379 | − | 0.857563i | \(-0.328023\pi\) | ||||
0.514379 | + | 0.857563i | \(0.328023\pi\) | |||||||
\(318\) | 25.2577 | 1.41638 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.7832 | −1.71815 | ||||||||
\(322\) | 1.02974 | 0.0573854 | ||||||||
\(323\) | −17.3444 | −0.965068 | ||||||||
\(324\) | −43.8117 | −2.43398 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −36.5401 | −2.02377 | ||||||||
\(327\) | −32.0982 | −1.77504 | ||||||||
\(328\) | 6.02964 | 0.332931 | ||||||||
\(329\) | −4.76479 | −0.262691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5599 | 1.18504 | 0.592520 | − | 0.805556i | \(-0.298133\pi\) | ||||
0.592520 | + | 0.805556i | \(0.298133\pi\) | |||||||
\(332\) | 21.5136 | 1.18071 | ||||||||
\(333\) | −1.19522 | −0.0654977 | ||||||||
\(334\) | 46.1186 | 2.52350 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −52.5873 | −2.86887 | ||||||||
\(337\) | 14.0614 | 0.765973 | 0.382986 | − | 0.923754i | \(-0.374896\pi\) | ||||
0.382986 | + | 0.923754i | \(0.374896\pi\) | |||||||
\(338\) | −18.5220 | −1.00746 | ||||||||
\(339\) | −25.6630 | −1.39382 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.89232 | −0.102325 | ||||||||
\(343\) | −1.69775 | −0.0916699 | ||||||||
\(344\) | −29.3394 | −1.58187 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.4307 | −1.20588 | ||||||||
\(347\) | −28.6497 | −1.53800 | −0.768999 | − | 0.639250i | \(-0.779245\pi\) | ||||
−0.768999 | + | 0.639250i | \(0.779245\pi\) | |||||||
\(348\) | 19.2364 | 1.03118 | ||||||||
\(349\) | 17.9222 | 0.959353 | 0.479676 | − | 0.877446i | \(-0.340754\pi\) | ||||
0.479676 | + | 0.877446i | \(0.340754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.4665 | −1.19917 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.7757 | 1.31868 | 0.659339 | − | 0.751845i | \(-0.270836\pi\) | ||||
0.659339 | + | 0.751845i | \(0.270836\pi\) | |||||||
\(354\) | 5.43430 | 0.288830 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.789931 | −0.0418663 | ||||||||
\(357\) | 34.1494 | 1.80738 | ||||||||
\(358\) | 58.6804 | 3.10136 | ||||||||
\(359\) | 10.4523 | 0.551651 | 0.275826 | − | 0.961208i | \(-0.411049\pi\) | ||||
0.275826 | + | 0.961208i | \(0.411049\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.02474 | −0.369723 | ||||||||
\(362\) | −44.2551 | −2.32600 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −78.0589 | −4.09140 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −33.6520 | −1.75902 | ||||||||
\(367\) | −15.1951 | −0.793176 | −0.396588 | − | 0.917997i | \(-0.629806\pi\) | ||||
−0.396588 | + | 0.917997i | \(0.629806\pi\) | |||||||
\(368\) | 0.816020 | 0.0425380 | ||||||||
\(369\) | −0.195670 | −0.0101862 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.8995 | 1.08505 | ||||||||
\(372\) | 38.8421 | 2.01387 | ||||||||
\(373\) | 21.1774 | 1.09653 | 0.548263 | − | 0.836306i | \(-0.315289\pi\) | ||||
0.548263 | + | 0.836306i | \(0.315289\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.24363 | −0.425133 | ||||||||
\(377\) | 10.5697 | 0.544365 | ||||||||
\(378\) | −48.6519 | −2.50238 | ||||||||
\(379\) | −35.1644 | −1.80627 | −0.903137 | − | 0.429351i | \(-0.858742\pi\) | ||||
−0.903137 | + | 0.429351i | \(0.858742\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.98475 | 0.511534 | ||||||||
\(382\) | 46.6412 | 2.38637 | ||||||||
\(383\) | −1.98986 | −0.101677 | −0.0508385 | − | 0.998707i | \(-0.516189\pi\) | ||||
−0.0508385 | + | 0.998707i | \(0.516189\pi\) | |||||||
\(384\) | 16.6722 | 0.850799 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.2797 | −1.43940 | ||||||||
\(387\) | 0.952104 | 0.0483982 | ||||||||
\(388\) | −20.3675 | −1.03400 | ||||||||
\(389\) | −6.05849 | −0.307178 | −0.153589 | − | 0.988135i | \(-0.549083\pi\) | ||||
−0.153589 | + | 0.988135i | \(0.549083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.529911 | −0.0267988 | ||||||||
\(392\) | −48.9690 | −2.47331 | ||||||||
\(393\) | 24.8036 | 1.25118 | ||||||||
\(394\) | −40.2853 | −2.02954 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.0663 | 1.75993 | 0.879964 | − | 0.475040i | \(-0.157566\pi\) | ||||
0.879964 | + | 0.475040i | \(0.157566\pi\) | |||||||
\(398\) | −11.3908 | −0.570968 | ||||||||
\(399\) | −23.5781 | −1.18038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.4747 | 0.822708 | 0.411354 | − | 0.911476i | \(-0.365056\pi\) | ||||
0.411354 | + | 0.911476i | \(0.365056\pi\) | |||||||
\(402\) | −36.0319 | −1.79711 | ||||||||
\(403\) | 21.3422 | 1.06313 | ||||||||
\(404\) | −40.2067 | −2.00036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.8889 | 1.13596 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 59.0824 | 2.92501 | ||||||||
\(409\) | −4.31034 | −0.213133 | −0.106566 | − | 0.994306i | \(-0.533986\pi\) | ||||
−0.106566 | + | 0.994306i | \(0.533986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.8264 | −0.879312 | ||||||||
\(412\) | −75.2244 | −3.70604 | ||||||||
\(413\) | 4.49662 | 0.221264 | ||||||||
\(414\) | −0.0578146 | −0.00284143 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −29.7996 | −1.46104 | ||||||||
\(417\) | −3.64006 | −0.178255 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.7114 | −0.914110 | −0.457055 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457055 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.5078 | −1.48686 | −0.743429 | − | 0.668815i | \(-0.766802\pi\) | ||||
−0.743429 | + | 0.668815i | \(0.766802\pi\) | |||||||
\(422\) | 5.92475 | 0.288412 | ||||||||
\(423\) | 0.267517 | 0.0130071 | ||||||||
\(424\) | 36.1586 | 1.75602 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.0148 | 0.485219 | ||||||||
\(427\) | −27.8454 | −1.34753 | ||||||||
\(428\) | −78.4136 | −3.79027 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.31340 | −0.400442 | −0.200221 | − | 0.979751i | \(-0.564166\pi\) | ||||
−0.200221 | + | 0.979751i | \(0.564166\pi\) | |||||||
\(432\) | −38.5542 | −1.85494 | ||||||||
\(433\) | −27.4497 | −1.31915 | −0.659574 | − | 0.751640i | \(-0.729263\pi\) | ||||
−0.659574 | + | 0.751640i | \(0.729263\pi\) | |||||||
\(434\) | 46.2171 | 2.21849 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −81.7634 | −3.91576 | ||||||||
\(437\) | 0.365872 | 0.0175020 | ||||||||
\(438\) | 41.1237 | 1.96496 | ||||||||
\(439\) | 23.1527 | 1.10502 | 0.552510 | − | 0.833506i | \(-0.313670\pi\) | ||||
0.552510 | + | 0.833506i | \(0.313670\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.58911 | 0.0756720 | ||||||||
\(442\) | 57.7636 | 2.74753 | ||||||||
\(443\) | −20.1835 | −0.958947 | −0.479474 | − | 0.877556i | \(-0.659172\pi\) | ||||
−0.479474 | + | 0.877556i | \(0.659172\pi\) | |||||||
\(444\) | −45.8457 | −2.17574 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −26.3864 | −1.24943 | ||||||||
\(447\) | −19.0376 | −0.900446 | ||||||||
\(448\) | −5.86020 | −0.276868 | ||||||||
\(449\) | 14.0341 | 0.662312 | 0.331156 | − | 0.943576i | \(-0.392561\pi\) | ||||
0.331156 | + | 0.943576i | \(0.392561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −65.3711 | −3.07480 | ||||||||
\(453\) | 6.15664 | 0.289264 | ||||||||
\(454\) | −18.3943 | −0.863285 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −40.7928 | −1.91030 | ||||||||
\(457\) | 15.6236 | 0.730843 | 0.365421 | − | 0.930842i | \(-0.380925\pi\) | ||||
0.365421 | + | 0.930842i | \(0.380925\pi\) | |||||||
\(458\) | −5.27707 | −0.246581 | ||||||||
\(459\) | 25.0365 | 1.16860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.6082 | −1.37899 | −0.689496 | − | 0.724289i | \(-0.742168\pi\) | ||||
−0.689496 | + | 0.724289i | \(0.742168\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.31629 | 0.0611730 | 0.0305865 | − | 0.999532i | \(-0.490262\pi\) | ||||
0.0305865 | + | 0.999532i | \(0.490262\pi\) | |||||||
\(464\) | 18.1383 | 0.842050 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 45.0649 | 2.08759 | ||||||||
\(467\) | 12.0995 | 0.559898 | 0.279949 | − | 0.960015i | \(-0.409682\pi\) | ||||
0.279949 | + | 0.960015i | \(0.409682\pi\) | |||||||
\(468\) | 4.38259 | 0.202585 | ||||||||
\(469\) | −29.8146 | −1.37671 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.535242 | −0.0246626 | ||||||||
\(472\) | 7.77967 | 0.358088 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 66.0655 | 3.03449 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 86.9883 | 3.98710 | ||||||||
\(477\) | −1.17340 | −0.0537261 | ||||||||
\(478\) | 47.8897 | 2.19043 | ||||||||
\(479\) | −3.05400 | −0.139541 | −0.0697703 | − | 0.997563i | \(-0.522227\pi\) | ||||
−0.0697703 | + | 0.997563i | \(0.522227\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.1904 | −1.14858 | ||||||||
\(482\) | 77.3651 | 3.52388 | ||||||||
\(483\) | −0.720365 | −0.0327777 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.67227 | 0.257299 | ||||||||
\(487\) | −24.2398 | −1.09841 | −0.549205 | − | 0.835688i | \(-0.685069\pi\) | ||||
−0.549205 | + | 0.835688i | \(0.685069\pi\) | |||||||
\(488\) | −48.1758 | −2.18081 | ||||||||
\(489\) | 25.5619 | 1.15595 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6796 | 1.47481 | 0.737404 | − | 0.675452i | \(-0.236051\pi\) | ||||
0.737404 | + | 0.675452i | \(0.236051\pi\) | |||||||
\(492\) | −7.50542 | −0.338370 | ||||||||
\(493\) | −11.7787 | −0.530488 | ||||||||
\(494\) | −39.8823 | −1.79439 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.6248 | 1.64450 | ||||||||
\(497\) | 8.28676 | 0.371712 | ||||||||
\(498\) | −21.6418 | −0.969792 | ||||||||
\(499\) | −30.0059 | −1.34325 | −0.671625 | − | 0.740891i | \(-0.734403\pi\) | ||||
−0.671625 | + | 0.740891i | \(0.734403\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.2626 | −1.44139 | ||||||||
\(502\) | 65.3721 | 2.91770 | ||||||||
\(503\) | 13.5516 | 0.604236 | 0.302118 | − | 0.953271i | \(-0.402306\pi\) | ||||
0.302118 | + | 0.953271i | \(0.402306\pi\) | |||||||
\(504\) | 5.33378 | 0.237585 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9572 | 0.575450 | ||||||||
\(508\) | 25.4340 | 1.12845 | ||||||||
\(509\) | 38.0843 | 1.68806 | 0.844028 | − | 0.536299i | \(-0.180178\pi\) | ||||
0.844028 | + | 0.536299i | \(0.180178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.0278 | 1.50530 | ||||||||
\(512\) | 50.3705 | 2.22608 | ||||||||
\(513\) | −17.2862 | −0.763204 | ||||||||
\(514\) | −61.3499 | −2.70603 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 36.5203 | 1.60772 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −54.5505 | −2.39681 | ||||||||
\(519\) | 15.6915 | 0.688782 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.20872 | 0.0967658 | 0.0483829 | − | 0.998829i | \(-0.484593\pi\) | ||||
0.0483829 | + | 0.998829i | \(0.484593\pi\) | |||||||
\(522\) | −1.28509 | −0.0562468 | ||||||||
\(523\) | −2.40261 | −0.105059 | −0.0525294 | − | 0.998619i | \(-0.516728\pi\) | ||||
−0.0525294 | + | 0.998619i | \(0.516728\pi\) | |||||||
\(524\) | 63.1818 | 2.76011 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 68.5964 | 2.99095 | ||||||||
\(527\) | −23.7836 | −1.03603 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9888 | −0.999514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.252461 | −0.0109559 | ||||||||
\(532\) | −60.0602 | −2.60394 | ||||||||
\(533\) | −4.12393 | −0.178627 | ||||||||
\(534\) | 0.794639 | 0.0343874 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −51.5827 | −2.22804 | ||||||||
\(537\) | −41.0503 | −1.77145 | ||||||||
\(538\) | 15.2873 | 0.659083 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.5101 | 1.01078 | 0.505388 | − | 0.862892i | \(-0.331349\pi\) | ||||
0.505388 | + | 0.862892i | \(0.331349\pi\) | |||||||
\(542\) | −19.2023 | −0.824807 | ||||||||
\(543\) | 30.9590 | 1.32858 | ||||||||
\(544\) | 33.2085 | 1.42380 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 78.5242 | 3.36053 | ||||||||
\(547\) | −1.41425 | −0.0604688 | −0.0302344 | − | 0.999543i | \(-0.509625\pi\) | ||||
−0.0302344 | + | 0.999543i | \(0.509625\pi\) | |||||||
\(548\) | −45.4090 | −1.93978 | ||||||||
\(549\) | 1.56337 | 0.0667230 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.13251 | 0.346457 | ||||||||
\(552\) | −1.24631 | −0.0530466 | ||||||||
\(553\) | 54.6660 | 2.32464 | ||||||||
\(554\) | 3.69648 | 0.157049 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.27228 | −0.393232 | ||||||||
\(557\) | −4.96462 | −0.210358 | −0.105179 | − | 0.994453i | \(-0.533542\pi\) | ||||
−0.105179 | + | 0.994453i | \(0.533542\pi\) | |||||||
\(558\) | −2.59484 | −0.109849 | ||||||||
\(559\) | 20.0665 | 0.848721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.613129 | −0.0258633 | ||||||||
\(563\) | −16.6024 | −0.699707 | −0.349853 | − | 0.936804i | \(-0.613769\pi\) | ||||
−0.349853 | + | 0.936804i | \(0.613769\pi\) | |||||||
\(564\) | 10.2613 | 0.432078 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.5269 | 0.568578 | ||||||||
\(567\) | 36.4681 | 1.53152 | ||||||||
\(568\) | 14.3371 | 0.601569 | ||||||||
\(569\) | 27.0868 | 1.13554 | 0.567768 | − | 0.823189i | \(-0.307807\pi\) | ||||
0.567768 | + | 0.823189i | \(0.307807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.9648 | 1.08659 | 0.543296 | − | 0.839541i | \(-0.317176\pi\) | ||||
0.543296 | + | 0.839541i | \(0.317176\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.6282 | −1.36306 | ||||||||
\(574\) | −8.93049 | −0.372751 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.329019 | 0.0137091 | ||||||||
\(577\) | −0.746507 | −0.0310775 | −0.0155388 | − | 0.999879i | \(-0.504946\pi\) | ||||
−0.0155388 | + | 0.999879i | \(0.504946\pi\) | |||||||
\(578\) | −20.8094 | −0.865555 | ||||||||
\(579\) | 19.7833 | 0.822166 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.9075 | −0.742930 | ||||||||
\(582\) | 20.4889 | 0.849291 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 58.8721 | 2.43614 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.4265 | 1.58738 | ||||||||
\(587\) | 17.9002 | 0.738819 | 0.369409 | − | 0.929267i | \(-0.379560\pi\) | ||||
0.369409 | + | 0.929267i | \(0.379560\pi\) | |||||||
\(588\) | 60.9544 | 2.51372 | ||||||||
\(589\) | 16.4211 | 0.676620 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.1819 | 1.15925 | ||||||||
\(592\) | −43.2286 | −1.77668 | ||||||||
\(593\) | −11.1992 | −0.459895 | −0.229948 | − | 0.973203i | \(-0.573855\pi\) | ||||
−0.229948 | + | 0.973203i | \(0.573855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −48.4941 | −1.98640 | ||||||||
\(597\) | 7.96851 | 0.326129 | ||||||||
\(598\) | −1.21849 | −0.0498279 | ||||||||
\(599\) | −1.81590 | −0.0741958 | −0.0370979 | − | 0.999312i | \(-0.511811\pi\) | ||||
−0.0370979 | + | 0.999312i | \(0.511811\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.8125 | −1.90952 | −0.954761 | − | 0.297373i | \(-0.903889\pi\) | ||||
−0.954761 | + | 0.297373i | \(0.903889\pi\) | |||||||
\(602\) | 43.4545 | 1.77107 | ||||||||
\(603\) | 1.67393 | 0.0681678 | ||||||||
\(604\) | 15.6827 | 0.638121 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 40.4464 | 1.64302 | ||||||||
\(607\) | −32.8999 | −1.33537 | −0.667683 | − | 0.744446i | \(-0.732714\pi\) | ||||
−0.667683 | + | 0.744446i | \(0.732714\pi\) | |||||||
\(608\) | −22.9284 | −0.929870 | ||||||||
\(609\) | −16.0121 | −0.648843 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.63817 | 0.228096 | ||||||||
\(612\) | −4.88393 | −0.197421 | ||||||||
\(613\) | −14.8860 | −0.601240 | −0.300620 | − | 0.953744i | \(-0.597194\pi\) | ||||
−0.300620 | + | 0.953744i | \(0.597194\pi\) | |||||||
\(614\) | −5.40768 | −0.218236 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.4741 | 1.50865 | 0.754324 | − | 0.656502i | \(-0.227965\pi\) | ||||
0.754324 | + | 0.656502i | \(0.227965\pi\) | |||||||
\(618\) | 75.6728 | 3.04401 | ||||||||
\(619\) | −12.3920 | −0.498077 | −0.249039 | − | 0.968494i | \(-0.580115\pi\) | ||||
−0.249039 | + | 0.968494i | \(0.580115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.528133 | −0.0211932 | ||||||||
\(622\) | 42.6937 | 1.71186 | ||||||||
\(623\) | 0.657526 | 0.0263432 | ||||||||
\(624\) | 62.2265 | 2.49106 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −74.5163 | −2.97827 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.36341 | −0.0544061 | ||||||||
\(629\) | 28.0720 | 1.11930 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.54279 | 0.0614174 | 0.0307087 | − | 0.999528i | \(-0.490224\pi\) | ||||
0.0307087 | + | 0.999528i | \(0.490224\pi\) | |||||||
\(632\) | 94.5785 | 3.76213 | ||||||||
\(633\) | −4.14471 | −0.164737 | ||||||||
\(634\) | −46.9355 | −1.86405 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −45.0086 | −1.78471 | ||||||||
\(637\) | 33.4920 | 1.32700 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.465257 | −0.0184053 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.2172 | 1.23300 | 0.616502 | − | 0.787353i | \(-0.288549\pi\) | ||||
0.616502 | + | 0.787353i | \(0.288549\pi\) | |||||||
\(642\) | 78.8810 | 3.11319 | ||||||||
\(643\) | 20.3183 | 0.801275 | 0.400638 | − | 0.916237i | \(-0.368789\pi\) | ||||
0.400638 | + | 0.916237i | \(0.368789\pi\) | |||||||
\(644\) | −1.83498 | −0.0723082 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 44.4445 | 1.74865 | ||||||||
\(647\) | −22.1687 | −0.871541 | −0.435771 | − | 0.900058i | \(-0.643524\pi\) | ||||
−0.435771 | + | 0.900058i | \(0.643524\pi\) | |||||||
\(648\) | 63.0940 | 2.47857 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.3316 | −1.26717 | ||||||||
\(652\) | 65.1135 | 2.55004 | ||||||||
\(653\) | −11.8719 | −0.464583 | −0.232292 | − | 0.972646i | \(-0.574622\pi\) | ||||
−0.232292 | + | 0.972646i | \(0.574622\pi\) | |||||||
\(654\) | 82.2507 | 3.21626 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.07697 | −0.276309 | ||||||||
\(657\) | −1.91048 | −0.0745349 | ||||||||
\(658\) | 12.2096 | 0.475981 | ||||||||
\(659\) | −13.3368 | −0.519527 | −0.259764 | − | 0.965672i | \(-0.583645\pi\) | ||||
−0.259764 | + | 0.965672i | \(0.583645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.8817 | −1.74570 | −0.872848 | − | 0.487992i | \(-0.837730\pi\) | ||||
−0.872848 | + | 0.487992i | \(0.837730\pi\) | |||||||
\(662\) | −55.2467 | −2.14722 | ||||||||
\(663\) | −40.4090 | −1.56935 | ||||||||
\(664\) | −30.9821 | −1.20234 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.06272 | 0.118678 | ||||||||
\(667\) | 0.248467 | 0.00962067 | ||||||||
\(668\) | −82.1821 | −3.17972 | ||||||||
\(669\) | 18.4588 | 0.713659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 45.1438 | 1.74146 | ||||||||
\(673\) | −5.88475 | −0.226840 | −0.113420 | − | 0.993547i | \(-0.536181\pi\) | ||||
−0.113420 | + | 0.993547i | \(0.536181\pi\) | |||||||
\(674\) | −36.0319 | −1.38790 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.0057 | 1.26945 | ||||||||
\(677\) | −29.6008 | −1.13765 | −0.568825 | − | 0.822458i | \(-0.692602\pi\) | ||||
−0.568825 | + | 0.822458i | \(0.692602\pi\) | |||||||
\(678\) | 65.7608 | 2.52553 | ||||||||
\(679\) | 16.9536 | 0.650618 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.8678 | 0.493097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.1257 | 0.502239 | 0.251120 | − | 0.967956i | \(-0.419201\pi\) | ||||
0.251120 | + | 0.967956i | \(0.419201\pi\) | |||||||
\(684\) | 3.37206 | 0.128934 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.35043 | 0.166100 | ||||||||
\(687\) | 3.69162 | 0.140844 | ||||||||
\(688\) | 34.4356 | 1.31284 | ||||||||
\(689\) | −24.7304 | −0.942153 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.04276 | −0.267919 | −0.133960 | − | 0.990987i | \(-0.542769\pi\) | ||||
−0.133960 | + | 0.990987i | \(0.542769\pi\) | |||||||
\(692\) | 39.9709 | 1.51946 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 73.4141 | 2.78676 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −27.7028 | −1.05007 | ||||||||
\(697\) | 4.59568 | 0.174074 | ||||||||
\(698\) | −45.9251 | −1.73829 | ||||||||
\(699\) | −31.5255 | −1.19240 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.3634 | −1.67558 | −0.837791 | − | 0.545992i | \(-0.816153\pi\) | ||||
−0.837791 | + | 0.545992i | \(0.816153\pi\) | |||||||
\(702\) | 57.5698 | 2.17283 | ||||||||
\(703\) | −19.3820 | −0.731006 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −63.4871 | −2.38937 | ||||||||
\(707\) | 33.4674 | 1.25867 | ||||||||
\(708\) | −9.68378 | −0.363939 | ||||||||
\(709\) | −19.5161 | −0.732943 | −0.366471 | − | 0.930429i | \(-0.619434\pi\) | ||||
−0.366471 | + | 0.930429i | \(0.619434\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.06920 | −0.115104 | ||||||||
\(712\) | 1.13760 | 0.0426332 | ||||||||
\(713\) | 0.501703 | 0.0187889 | ||||||||
\(714\) | −87.5068 | −3.27486 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −104.567 | −3.90785 | ||||||||
\(717\) | −33.5016 | −1.25114 | ||||||||
\(718\) | −26.7837 | −0.999560 | ||||||||
\(719\) | 47.4024 | 1.76781 | 0.883906 | − | 0.467665i | \(-0.154905\pi\) | ||||
0.883906 | + | 0.467665i | \(0.154905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.6156 | 2.33193 | ||||||||
\(722\) | 18.0007 | 0.669916 | ||||||||
\(723\) | −54.1213 | −2.01279 | ||||||||
\(724\) | 78.8614 | 2.93086 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.2483 | −1.38146 | −0.690731 | − | 0.723112i | \(-0.742711\pi\) | ||||
−0.690731 | + | 0.723112i | \(0.742711\pi\) | |||||||
\(728\) | 112.414 | 4.16635 | ||||||||
\(729\) | 24.8159 | 0.919107 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.3619 | −0.827086 | ||||||||
\(732\) | 59.9670 | 2.21644 | ||||||||
\(733\) | 11.6209 | 0.429226 | 0.214613 | − | 0.976699i | \(-0.431151\pi\) | ||||
0.214613 | + | 0.976699i | \(0.431151\pi\) | |||||||
\(734\) | 38.9369 | 1.43719 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.700516 | −0.0258214 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.501399 | 0.0184568 | ||||||||
\(739\) | −37.9801 | −1.39712 | −0.698560 | − | 0.715551i | \(-0.746176\pi\) | ||||
−0.698560 | + | 0.715551i | \(0.746176\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.8999 | 1.02493 | ||||||||
\(742\) | −53.5544 | −1.96605 | ||||||||
\(743\) | −7.71703 | −0.283111 | −0.141555 | − | 0.989930i | \(-0.545210\pi\) | ||||
−0.141555 | + | 0.989930i | \(0.545210\pi\) | |||||||
\(744\) | −55.9373 | −2.05076 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −54.2665 | −1.98684 | ||||||||
\(747\) | 1.00541 | 0.0367861 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 65.2703 | 2.38492 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0280 | 0.584870 | 0.292435 | − | 0.956285i | \(-0.405534\pi\) | ||||
0.292435 | + | 0.956285i | \(0.405534\pi\) | |||||||
\(752\) | 9.67552 | 0.352830 | ||||||||
\(753\) | −45.7316 | −1.66655 | ||||||||
\(754\) | −27.0844 | −0.986356 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 86.6964 | 3.15312 | ||||||||
\(757\) | 6.37605 | 0.231742 | 0.115871 | − | 0.993264i | \(-0.463034\pi\) | ||||
0.115871 | + | 0.993264i | \(0.463034\pi\) | |||||||
\(758\) | 90.1078 | 3.27286 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.8646 | 0.575092 | 0.287546 | − | 0.957767i | \(-0.407161\pi\) | ||||
0.287546 | + | 0.957767i | \(0.407161\pi\) | |||||||
\(762\) | −25.5856 | −0.926870 | ||||||||
\(763\) | 68.0585 | 2.46388 | ||||||||
\(764\) | −83.1135 | −3.00694 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.09895 | 0.184233 | ||||||||
\(767\) | −5.32085 | −0.192125 | ||||||||
\(768\) | −48.2496 | −1.74106 | ||||||||
\(769\) | 51.7503 | 1.86616 | 0.933082 | − | 0.359663i | \(-0.117108\pi\) | ||||
0.933082 | + | 0.359663i | \(0.117108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.9178 | 1.54565 | ||||||||
\(772\) | 50.3937 | 1.81371 | ||||||||
\(773\) | −9.68605 | −0.348383 | −0.174192 | − | 0.984712i | \(-0.555731\pi\) | ||||
−0.174192 | + | 0.984712i | \(0.555731\pi\) | |||||||
\(774\) | −2.43974 | −0.0876946 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.3316 | 1.05294 | ||||||||
\(777\) | 38.1612 | 1.36903 | ||||||||
\(778\) | 15.5247 | 0.556588 | ||||||||
\(779\) | −3.17304 | −0.113686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.35788 | 0.0485578 | ||||||||
\(783\) | −11.7392 | −0.419526 | ||||||||
\(784\) | 57.4748 | 2.05267 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −63.5584 | −2.26705 | ||||||||
\(787\) | −18.2226 | −0.649566 | −0.324783 | − | 0.945789i | \(-0.605291\pi\) | ||||
−0.324783 | + | 0.945789i | \(0.605291\pi\) | |||||||
\(788\) | 71.7874 | 2.55732 | ||||||||
\(789\) | −47.9871 | −1.70839 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.4139 | 1.93473 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.9495 | 1.17007 | ||||||||
\(794\) | −89.8564 | −3.18889 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.2981 | 0.719446 | ||||||||
\(797\) | 20.0132 | 0.708902 | 0.354451 | − | 0.935075i | \(-0.384668\pi\) | ||||
0.354451 | + | 0.935075i | \(0.384668\pi\) | |||||||
\(798\) | 60.4182 | 2.13878 | ||||||||
\(799\) | −6.28314 | −0.222281 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0369165 | −0.00130438 | ||||||||
\(802\) | −42.2160 | −1.49070 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 64.2079 | 2.26444 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −54.6887 | −1.92633 | ||||||||
\(807\) | −10.6944 | −0.376459 | ||||||||
\(808\) | 57.9025 | 2.03700 | ||||||||
\(809\) | 31.8062 | 1.11825 | 0.559123 | − | 0.829085i | \(-0.311138\pi\) | ||||
0.559123 | + | 0.829085i | \(0.311138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.65484 | −0.128339 | −0.0641694 | − | 0.997939i | \(-0.520440\pi\) | ||||
−0.0641694 | + | 0.997939i | \(0.520440\pi\) | |||||||
\(812\) | −40.7874 | −1.43136 | ||||||||
\(813\) | 13.4331 | 0.471119 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −69.3448 | −2.42755 | ||||||||
\(817\) | 15.4396 | 0.540162 | ||||||||
\(818\) | 11.0451 | 0.386184 | ||||||||
\(819\) | −3.64800 | −0.127471 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.7678 | −0.480501 | −0.240250 | − | 0.970711i | \(-0.577230\pi\) | ||||
−0.240250 | + | 0.970711i | \(0.577230\pi\) | |||||||
\(822\) | 45.6797 | 1.59326 | ||||||||
\(823\) | 40.5760 | 1.41439 | 0.707195 | − | 0.707018i | \(-0.249960\pi\) | ||||
0.707195 | + | 0.707018i | \(0.249960\pi\) | |||||||
\(824\) | 108.332 | 3.77393 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.5225 | −0.400918 | ||||||||
\(827\) | 15.5321 | 0.540105 | 0.270052 | − | 0.962846i | \(-0.412959\pi\) | ||||
0.270052 | + | 0.962846i | \(0.412959\pi\) | |||||||
\(828\) | 0.103024 | 0.00358033 | ||||||||
\(829\) | −29.1311 | −1.01177 | −0.505883 | − | 0.862602i | \(-0.668833\pi\) | ||||
−0.505883 | + | 0.862602i | \(0.668833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.58590 | −0.0897040 | ||||||||
\(832\) | 6.93437 | 0.240406 | ||||||||
\(833\) | −37.3232 | −1.29317 | ||||||||
\(834\) | 9.32755 | 0.322987 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.7038 | −0.819322 | ||||||||
\(838\) | 47.9473 | 1.65631 | ||||||||
\(839\) | 21.7832 | 0.752041 | 0.376020 | − | 0.926611i | \(-0.377292\pi\) | ||||
0.376020 | + | 0.926611i | \(0.377292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4771 | −0.809556 | ||||||||
\(842\) | 78.1753 | 2.69410 | ||||||||
\(843\) | 0.428919 | 0.0147728 | ||||||||
\(844\) | −10.5578 | −0.363413 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.685505 | −0.0235681 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −42.4392 | −1.45737 | ||||||||
\(849\) | −9.46285 | −0.324764 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.592165 | −0.0202991 | ||||||||
\(852\) | −17.8461 | −0.611398 | ||||||||
\(853\) | 8.75293 | 0.299695 | 0.149847 | − | 0.988709i | \(-0.452122\pi\) | ||||
0.149847 | + | 0.988709i | \(0.452122\pi\) | |||||||
\(854\) | 71.3531 | 2.44165 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 112.925 | 3.85970 | ||||||||
\(857\) | 14.0273 | 0.479163 | 0.239582 | − | 0.970876i | \(-0.422990\pi\) | ||||
0.239582 | + | 0.970876i | \(0.422990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8774 | 1.08764 | 0.543822 | − | 0.839201i | \(-0.316977\pi\) | ||||
0.543822 | + | 0.839201i | \(0.316977\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.24739 | 0.212911 | ||||||||
\(862\) | 21.3028 | 0.725577 | ||||||||
\(863\) | −3.46523 | −0.117958 | −0.0589789 | − | 0.998259i | \(-0.518784\pi\) | ||||
−0.0589789 | + | 0.998259i | \(0.518784\pi\) | |||||||
\(864\) | 33.0970 | 1.12598 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 70.3390 | 2.39022 | ||||||||
\(867\) | 14.5573 | 0.494393 | ||||||||
\(868\) | −82.3577 | −2.79540 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.2796 | 1.19540 | ||||||||
\(872\) | 117.749 | 3.98749 | ||||||||
\(873\) | −0.951851 | −0.0322153 | ||||||||
\(874\) | −0.937535 | −0.0317126 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −73.2813 | −2.47594 | ||||||||
\(877\) | 19.7763 | 0.667799 | 0.333899 | − | 0.942609i | \(-0.391635\pi\) | ||||
0.333899 | + | 0.942609i | \(0.391635\pi\) | |||||||
\(878\) | −59.3282 | −2.00223 | ||||||||
\(879\) | −26.8816 | −0.906692 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.2097 | 1.92744 | 0.963722 | − | 0.266910i | \(-0.0860025\pi\) | ||||
0.963722 | + | 0.266910i | \(0.0860025\pi\) | |||||||
\(882\) | −4.07205 | −0.137113 | ||||||||
\(883\) | −57.2412 | −1.92632 | −0.963159 | − | 0.268931i | \(-0.913329\pi\) | ||||
−0.963159 | + | 0.268931i | \(0.913329\pi\) | |||||||
\(884\) | −102.933 | −3.46202 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 51.7196 | 1.73756 | ||||||||
\(887\) | −39.7251 | −1.33384 | −0.666920 | − | 0.745129i | \(-0.732388\pi\) | ||||
−0.666920 | + | 0.745129i | \(0.732388\pi\) | |||||||
\(888\) | 66.0233 | 2.21560 | ||||||||
\(889\) | −21.1709 | −0.710049 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 47.0199 | 1.57434 | ||||||||
\(893\) | 4.33812 | 0.145170 | ||||||||
\(894\) | 48.7832 | 1.63155 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −35.3504 | −1.18097 | ||||||||
\(897\) | 0.852407 | 0.0284610 | ||||||||
\(898\) | −35.9621 | −1.20007 | ||||||||
\(899\) | 11.1517 | 0.371931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.5594 | 0.918136 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.3989 | −1.01161 | ||||||||
\(904\) | 94.1422 | 3.13112 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.7762 | −0.524129 | ||||||||
\(907\) | −26.6119 | −0.883635 | −0.441817 | − | 0.897105i | \(-0.645666\pi\) | ||||
−0.441817 | + | 0.897105i | \(0.645666\pi\) | |||||||
\(908\) | 32.7781 | 1.08778 | ||||||||
\(909\) | −1.87902 | −0.0623230 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.78778 | 0.258021 | 0.129010 | − | 0.991643i | \(-0.458820\pi\) | ||||
0.129010 | + | 0.991643i | \(0.458820\pi\) | |||||||
\(912\) | 47.8784 | 1.58541 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.0351 | −1.32424 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.40361 | 0.310704 | ||||||||
\(917\) | −52.5915 | −1.73673 | ||||||||
\(918\) | −64.1554 | −2.11744 | ||||||||
\(919\) | 15.9781 | 0.527069 | 0.263535 | − | 0.964650i | \(-0.415112\pi\) | ||||
0.263535 | + | 0.964650i | \(0.415112\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.78298 | 0.124654 | ||||||||
\(922\) | 75.8702 | 2.49865 | ||||||||
\(923\) | −9.80572 | −0.322759 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.37295 | −0.110842 | ||||||||
\(927\) | −3.51553 | −0.115465 | ||||||||
\(928\) | −15.5709 | −0.511140 | ||||||||
\(929\) | 9.92533 | 0.325639 | 0.162820 | − | 0.986656i | \(-0.447941\pi\) | ||||
0.162820 | + | 0.986656i | \(0.447941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.7694 | 0.844559 | ||||||||
\(932\) | −80.3045 | −2.63046 | ||||||||
\(933\) | −29.8667 | −0.977793 | ||||||||
\(934\) | −31.0046 | −1.01450 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.31145 | −0.206296 | ||||||||
\(937\) | 8.91808 | 0.291341 | 0.145671 | − | 0.989333i | \(-0.453466\pi\) | ||||
0.145671 | + | 0.989333i | \(0.453466\pi\) | |||||||
\(938\) | 76.3991 | 2.49452 | ||||||||
\(939\) | 52.1284 | 1.70115 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.3215 | −1.21665 | −0.608323 | − | 0.793690i | \(-0.708157\pi\) | ||||
−0.608323 | + | 0.793690i | \(0.708157\pi\) | |||||||
\(942\) | 1.37154 | 0.0446872 | ||||||||
\(943\) | −0.0969435 | −0.00315691 | ||||||||
\(944\) | −9.13098 | −0.297188 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.62118 | −0.0526814 | −0.0263407 | − | 0.999653i | \(-0.508385\pi\) | ||||
−0.0263407 | + | 0.999653i | \(0.508385\pi\) | |||||||
\(948\) | −117.727 | −3.82359 | ||||||||
\(949\) | −40.2651 | −1.30706 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.8341 | 1.06472 | ||||||||
\(952\) | −125.274 | −4.06014 | ||||||||
\(953\) | −25.3420 | −0.820907 | −0.410454 | − | 0.911881i | \(-0.634630\pi\) | ||||
−0.410454 | + | 0.911881i | \(0.634630\pi\) | |||||||
\(954\) | 3.00679 | 0.0973486 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −85.3383 | −2.76004 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.82578 | 0.252839 | ||||||||
\(959\) | 37.7977 | 1.22055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48248 | −0.273628 | ||||||||
\(962\) | 64.5496 | 2.08116 | ||||||||
\(963\) | −3.66457 | −0.118089 | ||||||||
\(964\) | −137.863 | −4.44025 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.84591 | 0.0593913 | ||||||||
\(967\) | 6.70594 | 0.215648 | 0.107824 | − | 0.994170i | \(-0.465612\pi\) | ||||
0.107824 | + | 0.994170i | \(0.465612\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.0915 | −0.998803 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.81959 | 0.186760 | 0.0933798 | − | 0.995631i | \(-0.470233\pi\) | ||||
0.0933798 | + | 0.995631i | \(0.470233\pi\) | |||||||
\(972\) | −10.1078 | −0.324209 | ||||||||
\(973\) | 7.71810 | 0.247431 | ||||||||
\(974\) | 62.1137 | 1.99025 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 56.5438 | 1.80992 | ||||||||
\(977\) | 5.23201 | 0.167387 | 0.0836934 | − | 0.996492i | \(-0.473328\pi\) | ||||
0.0836934 | + | 0.996492i | \(0.473328\pi\) | |||||||
\(978\) | −65.5017 | −2.09451 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.82112 | −0.121999 | ||||||||
\(982\) | −83.7404 | −2.67227 | ||||||||
\(983\) | −14.7913 | −0.471768 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(984\) | 10.8087 | 0.344569 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 30.1827 | 0.961213 | ||||||||
\(987\) | −8.54134 | −0.271874 | ||||||||
\(988\) | 71.0692 | 2.26101 | ||||||||
\(989\) | 0.471714 | 0.0149996 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9189 | 0.791575 | 0.395788 | − | 0.918342i | \(-0.370472\pi\) | ||||
0.395788 | + | 0.918342i | \(0.370472\pi\) | |||||||
\(992\) | −31.4407 | −0.998243 | ||||||||
\(993\) | 38.6482 | 1.22646 | ||||||||
\(994\) | −21.2346 | −0.673520 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.5651 | 1.22198 | ||||||||
\(997\) | −14.8384 | −0.469937 | −0.234969 | − | 0.972003i | \(-0.575499\pi\) | ||||
−0.234969 | + | 0.972003i | \(0.575499\pi\) | |||||||
\(998\) | 76.8893 | 2.43389 | ||||||||
\(999\) | 27.9778 | 0.885178 |
(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 | 3025.2.a.bj.1.2 | 8 | ||
5.4 | even | 2 | 3025.2.a.bm.1.7 | 8 | |||
11.2 | odd | 10 | 275.2.h.e.26.1 | yes | 16 | ||
11.6 | odd | 10 | 275.2.h.e.201.1 | yes | 16 | ||
11.10 | odd | 2 | 3025.2.a.bn.1.7 | 8 | |||
55.2 | even | 20 | 275.2.z.c.224.8 | 32 | |||
55.13 | even | 20 | 275.2.z.c.224.1 | 32 | |||
55.17 | even | 20 | 275.2.z.c.124.1 | 32 | |||
55.24 | odd | 10 | 275.2.h.c.26.4 | ✓ | 16 | ||
55.28 | even | 20 | 275.2.z.c.124.8 | 32 | |||
55.39 | odd | 10 | 275.2.h.c.201.4 | yes | 16 | ||
55.54 | odd | 2 | 3025.2.a.bi.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.h.c.26.4 | ✓ | 16 | 55.24 | odd | 10 | ||
275.2.h.c.201.4 | yes | 16 | 55.39 | odd | 10 | ||
275.2.h.e.26.1 | yes | 16 | 11.2 | odd | 10 | ||
275.2.h.e.201.1 | yes | 16 | 11.6 | odd | 10 | ||
275.2.z.c.124.1 | 32 | 55.17 | even | 20 | |||
275.2.z.c.124.8 | 32 | 55.28 | even | 20 | |||
275.2.z.c.224.1 | 32 | 55.13 | even | 20 | |||
275.2.z.c.224.8 | 32 | 55.2 | even | 20 | |||
3025.2.a.bi.1.2 | 8 | 55.54 | odd | 2 | |||
3025.2.a.bj.1.2 | 8 | 1.1 | even | 1 | trivial | ||
3025.2.a.bm.1.7 | 8 | 5.4 | even | 2 | |||
3025.2.a.bn.1.7 | 8 | 11.10 | odd | 2 |