Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5225,2,Mod(1,5225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5225 = 5^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5225.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: | \(41.7218350561\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 11 x^{13} + 87 x^{12} - 4 x^{11} - 545 x^{10} + 431 x^{9} + 1480 x^{8} - 1763 x^{7} + \cdots + 15 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.40444\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.40444 | 1.70020 | 0.850098 | − | 0.526625i | \(-0.176543\pi\) | ||||
0.850098 | + | 0.526625i | \(0.176543\pi\) | |||||||
\(3\) | 1.94792 | 1.12463 | 0.562316 | − | 0.826923i | \(-0.309911\pi\) | ||||
0.562316 | + | 0.826923i | \(0.309911\pi\) | |||||||
\(4\) | 3.78133 | 1.89066 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.68365 | 1.91209 | ||||||||
\(7\) | −0.665236 | −0.251436 | −0.125718 | − | 0.992066i | \(-0.540123\pi\) | ||||
−0.125718 | + | 0.992066i | \(0.540123\pi\) | |||||||
\(8\) | 4.28310 | 1.51430 | ||||||||
\(9\) | 0.794388 | 0.264796 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 7.36572 | 2.12630 | ||||||||
\(13\) | 3.05467 | 0.847214 | 0.423607 | − | 0.905846i | \(-0.360764\pi\) | ||||
0.423607 | + | 0.905846i | \(0.360764\pi\) | |||||||
\(14\) | −1.59952 | −0.427490 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.73579 | 0.683948 | ||||||||
\(17\) | 4.49220 | 1.08952 | 0.544759 | − | 0.838592i | \(-0.316621\pi\) | ||||
0.544759 | + | 0.838592i | \(0.316621\pi\) | |||||||
\(18\) | 1.91006 | 0.450205 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.29583 | −0.282773 | ||||||||
\(22\) | 2.40444 | 0.512628 | ||||||||
\(23\) | 0.205258 | 0.0427993 | 0.0213996 | − | 0.999771i | \(-0.493188\pi\) | ||||
0.0213996 | + | 0.999771i | \(0.493188\pi\) | |||||||
\(24\) | 8.34313 | 1.70303 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.34478 | 1.44043 | ||||||||
\(27\) | −4.29635 | −0.826833 | ||||||||
\(28\) | −2.51548 | −0.475381 | ||||||||
\(29\) | 0.0417920 | 0.00776057 | 0.00388029 | − | 0.999992i | \(-0.498765\pi\) | ||||
0.00388029 | + | 0.999992i | \(0.498765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.76694 | 1.21538 | 0.607690 | − | 0.794175i | \(-0.292097\pi\) | ||||
0.607690 | + | 0.794175i | \(0.292097\pi\) | |||||||
\(32\) | −1.98815 | −0.351459 | ||||||||
\(33\) | 1.94792 | 0.339089 | ||||||||
\(34\) | 10.8012 | 1.85240 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00384 | 0.500641 | ||||||||
\(37\) | 7.60762 | 1.25069 | 0.625343 | − | 0.780350i | \(-0.284959\pi\) | ||||
0.625343 | + | 0.780350i | \(0.284959\pi\) | |||||||
\(38\) | 2.40444 | 0.390052 | ||||||||
\(39\) | 5.95026 | 0.952804 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.90733 | 0.922569 | 0.461285 | − | 0.887252i | \(-0.347389\pi\) | ||||
0.461285 | + | 0.887252i | \(0.347389\pi\) | |||||||
\(42\) | −3.11574 | −0.480769 | ||||||||
\(43\) | −1.77676 | −0.270953 | −0.135477 | − | 0.990781i | \(-0.543257\pi\) | ||||
−0.135477 | + | 0.990781i | \(0.543257\pi\) | |||||||
\(44\) | 3.78133 | 0.570057 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.493531 | 0.0727671 | ||||||||
\(47\) | −2.44032 | −0.355957 | −0.177978 | − | 0.984034i | \(-0.556956\pi\) | ||||
−0.177978 | + | 0.984034i | \(0.556956\pi\) | |||||||
\(48\) | 5.32910 | 0.769189 | ||||||||
\(49\) | −6.55746 | −0.936780 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.75045 | 1.22531 | ||||||||
\(52\) | 11.5507 | 1.60180 | ||||||||
\(53\) | −3.34793 | −0.459874 | −0.229937 | − | 0.973205i | \(-0.573852\pi\) | ||||
−0.229937 | + | 0.973205i | \(0.573852\pi\) | |||||||
\(54\) | −10.3303 | −1.40578 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.84927 | −0.380750 | ||||||||
\(57\) | 1.94792 | 0.258008 | ||||||||
\(58\) | 0.100486 | 0.0131945 | ||||||||
\(59\) | 7.44003 | 0.968610 | 0.484305 | − | 0.874899i | \(-0.339073\pi\) | ||||
0.484305 | + | 0.874899i | \(0.339073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7720 | −1.50725 | −0.753623 | − | 0.657307i | \(-0.771695\pi\) | ||||
−0.753623 | + | 0.657307i | \(0.771695\pi\) | |||||||
\(62\) | 16.2707 | 2.06638 | ||||||||
\(63\) | −0.528456 | −0.0665792 | ||||||||
\(64\) | −10.2520 | −1.28150 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.68365 | 0.576518 | ||||||||
\(67\) | −7.55329 | −0.922781 | −0.461390 | − | 0.887197i | \(-0.652649\pi\) | ||||
−0.461390 | + | 0.887197i | \(0.652649\pi\) | |||||||
\(68\) | 16.9865 | 2.05991 | ||||||||
\(69\) | 0.399826 | 0.0481334 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.36041 | 0.280129 | 0.140065 | − | 0.990142i | \(-0.455269\pi\) | ||||
0.140065 | + | 0.990142i | \(0.455269\pi\) | |||||||
\(72\) | 3.40244 | 0.400982 | ||||||||
\(73\) | −1.57148 | −0.183928 | −0.0919639 | − | 0.995762i | \(-0.529314\pi\) | ||||
−0.0919639 | + | 0.995762i | \(0.529314\pi\) | |||||||
\(74\) | 18.2921 | 2.12641 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.78133 | 0.433748 | ||||||||
\(77\) | −0.665236 | −0.0758107 | ||||||||
\(78\) | 14.3070 | 1.61995 | ||||||||
\(79\) | −4.66885 | −0.525287 | −0.262643 | − | 0.964893i | \(-0.584594\pi\) | ||||
−0.262643 | + | 0.964893i | \(0.584594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7521 | −1.19468 | ||||||||
\(82\) | 14.2038 | 1.56855 | ||||||||
\(83\) | 12.5787 | 1.38069 | 0.690347 | − | 0.723478i | \(-0.257458\pi\) | ||||
0.690347 | + | 0.723478i | \(0.257458\pi\) | |||||||
\(84\) | −4.89995 | −0.534628 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.27211 | −0.460673 | ||||||||
\(87\) | 0.0814074 | 0.00872779 | ||||||||
\(88\) | 4.28310 | 0.456580 | ||||||||
\(89\) | 6.06754 | 0.643158 | 0.321579 | − | 0.946883i | \(-0.395786\pi\) | ||||
0.321579 | + | 0.946883i | \(0.395786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.03208 | −0.213020 | ||||||||
\(92\) | 0.776148 | 0.0809191 | ||||||||
\(93\) | 13.1815 | 1.36685 | ||||||||
\(94\) | −5.86759 | −0.605196 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.87276 | −0.395262 | ||||||||
\(97\) | 8.44105 | 0.857059 | 0.428529 | − | 0.903528i | \(-0.359032\pi\) | ||||
0.428529 | + | 0.903528i | \(0.359032\pi\) | |||||||
\(98\) | −15.7670 | −1.59271 | ||||||||
\(99\) | 0.794388 | 0.0798390 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8688 | 1.37999 | 0.689997 | − | 0.723813i | \(-0.257612\pi\) | ||||
0.689997 | + | 0.723813i | \(0.257612\pi\) | |||||||
\(102\) | 21.0399 | 2.08326 | ||||||||
\(103\) | 4.43412 | 0.436906 | 0.218453 | − | 0.975847i | \(-0.429899\pi\) | ||||
0.218453 | + | 0.975847i | \(0.429899\pi\) | |||||||
\(104\) | 13.0835 | 1.28294 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.04991 | −0.781876 | ||||||||
\(107\) | −16.9555 | −1.63915 | −0.819574 | − | 0.572973i | \(-0.805790\pi\) | ||||
−0.819574 | + | 0.572973i | \(0.805790\pi\) | |||||||
\(108\) | −16.2459 | −1.56326 | ||||||||
\(109\) | −9.27495 | −0.888379 | −0.444189 | − | 0.895933i | \(-0.646508\pi\) | ||||
−0.444189 | + | 0.895933i | \(0.646508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.8190 | 1.40656 | ||||||||
\(112\) | −1.81995 | −0.171969 | ||||||||
\(113\) | 2.93718 | 0.276307 | 0.138153 | − | 0.990411i | \(-0.455883\pi\) | ||||
0.138153 | + | 0.990411i | \(0.455883\pi\) | |||||||
\(114\) | 4.68365 | 0.438664 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.158029 | 0.0146726 | ||||||||
\(117\) | 2.42660 | 0.224339 | ||||||||
\(118\) | 17.8891 | 1.64683 | ||||||||
\(119\) | −2.98838 | −0.273944 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −28.3050 | −2.56261 | ||||||||
\(123\) | 11.5070 | 1.03755 | ||||||||
\(124\) | 25.5880 | 2.29787 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.27064 | −0.113198 | ||||||||
\(127\) | −9.66723 | −0.857828 | −0.428914 | − | 0.903345i | \(-0.641104\pi\) | ||||
−0.428914 | + | 0.903345i | \(0.641104\pi\) | |||||||
\(128\) | −20.6739 | −1.82734 | ||||||||
\(129\) | −3.46098 | −0.304722 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.82740 | −0.858624 | −0.429312 | − | 0.903156i | \(-0.641244\pi\) | ||||
−0.429312 | + | 0.903156i | \(0.641244\pi\) | |||||||
\(132\) | 7.36572 | 0.641104 | ||||||||
\(133\) | −0.665236 | −0.0576833 | ||||||||
\(134\) | −18.1614 | −1.56891 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.2405 | 1.64986 | ||||||||
\(137\) | −5.19124 | −0.443517 | −0.221759 | − | 0.975102i | \(-0.571180\pi\) | ||||
−0.221759 | + | 0.975102i | \(0.571180\pi\) | |||||||
\(138\) | 0.961358 | 0.0818362 | ||||||||
\(139\) | −12.5477 | −1.06428 | −0.532142 | − | 0.846655i | \(-0.678613\pi\) | ||||
−0.532142 | + | 0.846655i | \(0.678613\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.75354 | −0.400320 | ||||||||
\(142\) | 5.67546 | 0.476274 | ||||||||
\(143\) | 3.05467 | 0.255445 | ||||||||
\(144\) | 2.17328 | 0.181107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.77853 | −0.312713 | ||||||||
\(147\) | −12.7734 | −1.05353 | ||||||||
\(148\) | 28.7669 | 2.36463 | ||||||||
\(149\) | −12.9080 | −1.05746 | −0.528731 | − | 0.848790i | \(-0.677332\pi\) | ||||
−0.528731 | + | 0.848790i | \(0.677332\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1347 | 1.15027 | 0.575134 | − | 0.818059i | \(-0.304950\pi\) | ||||
0.575134 | + | 0.818059i | \(0.304950\pi\) | |||||||
\(152\) | 4.28310 | 0.347405 | ||||||||
\(153\) | 3.56855 | 0.288500 | ||||||||
\(154\) | −1.59952 | −0.128893 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 22.4999 | 1.80143 | ||||||||
\(157\) | −18.3892 | −1.46762 | −0.733810 | − | 0.679354i | \(-0.762260\pi\) | ||||
−0.733810 | + | 0.679354i | \(0.762260\pi\) | |||||||
\(158\) | −11.2260 | −0.893090 | ||||||||
\(159\) | −6.52150 | −0.517189 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.136545 | −0.0107613 | ||||||||
\(162\) | −25.8528 | −2.03119 | ||||||||
\(163\) | −8.81855 | −0.690722 | −0.345361 | − | 0.938470i | \(-0.612244\pi\) | ||||
−0.345361 | + | 0.938470i | \(0.612244\pi\) | |||||||
\(164\) | 22.3375 | 1.74427 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.2448 | 2.34745 | ||||||||
\(167\) | 1.12696 | 0.0872065 | 0.0436033 | − | 0.999049i | \(-0.486116\pi\) | ||||
0.0436033 | + | 0.999049i | \(0.486116\pi\) | |||||||
\(168\) | −5.55015 | −0.428203 | ||||||||
\(169\) | −3.66897 | −0.282228 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.794388 | 0.0607484 | ||||||||
\(172\) | −6.71851 | −0.512281 | ||||||||
\(173\) | −10.7254 | −0.815439 | −0.407719 | − | 0.913107i | \(-0.633676\pi\) | ||||
−0.407719 | + | 0.913107i | \(0.633676\pi\) | |||||||
\(174\) | 0.195739 | 0.0148389 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.73579 | 0.206218 | ||||||||
\(177\) | 14.4926 | 1.08933 | ||||||||
\(178\) | 14.5890 | 1.09349 | ||||||||
\(179\) | −7.65684 | −0.572299 | −0.286150 | − | 0.958185i | \(-0.592375\pi\) | ||||
−0.286150 | + | 0.958185i | \(0.592375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.9423 | 1.40797 | 0.703986 | − | 0.710213i | \(-0.251402\pi\) | ||||
0.703986 | + | 0.710213i | \(0.251402\pi\) | |||||||
\(182\) | −4.88601 | −0.362175 | ||||||||
\(183\) | −22.9308 | −1.69510 | ||||||||
\(184\) | 0.879140 | 0.0648111 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 31.6940 | 2.32392 | ||||||||
\(187\) | 4.49220 | 0.328502 | ||||||||
\(188\) | −9.22763 | −0.672994 | ||||||||
\(189\) | 2.85809 | 0.207895 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50113 | −0.542763 | −0.271382 | − | 0.962472i | \(-0.587481\pi\) | ||||
−0.271382 | + | 0.962472i | \(0.587481\pi\) | |||||||
\(192\) | −19.9700 | −1.44121 | ||||||||
\(193\) | 20.2215 | 1.45557 | 0.727786 | − | 0.685804i | \(-0.240549\pi\) | ||||
0.727786 | + | 0.685804i | \(0.240549\pi\) | |||||||
\(194\) | 20.2960 | 1.45717 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.7959 | −1.77114 | ||||||||
\(197\) | −24.5070 | −1.74605 | −0.873024 | − | 0.487676i | \(-0.837845\pi\) | ||||
−0.873024 | + | 0.487676i | \(0.837845\pi\) | |||||||
\(198\) | 1.91006 | 0.135742 | ||||||||
\(199\) | 9.96226 | 0.706206 | 0.353103 | − | 0.935584i | \(-0.385127\pi\) | ||||
0.353103 | + | 0.935584i | \(0.385127\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.7132 | −1.03779 | ||||||||
\(202\) | 33.3466 | 2.34626 | ||||||||
\(203\) | −0.0278015 | −0.00195129 | ||||||||
\(204\) | 33.0883 | 2.31665 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.6616 | 0.742826 | ||||||||
\(207\) | 0.163055 | 0.0113331 | ||||||||
\(208\) | 8.35695 | 0.579450 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.15413 | 0.492511 | 0.246255 | − | 0.969205i | \(-0.420800\pi\) | ||||
0.246255 | + | 0.969205i | \(0.420800\pi\) | |||||||
\(212\) | −12.6596 | −0.869468 | ||||||||
\(213\) | 4.59789 | 0.315042 | ||||||||
\(214\) | −40.7684 | −2.78687 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −18.4017 | −1.25208 | ||||||||
\(217\) | −4.50162 | −0.305590 | ||||||||
\(218\) | −22.3010 | −1.51042 | ||||||||
\(219\) | −3.06111 | −0.206851 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.7222 | 0.923056 | ||||||||
\(222\) | 35.6315 | 2.39143 | ||||||||
\(223\) | 11.2847 | 0.755680 | 0.377840 | − | 0.925871i | \(-0.376667\pi\) | ||||
0.377840 | + | 0.925871i | \(0.376667\pi\) | |||||||
\(224\) | 1.32259 | 0.0883693 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.06228 | 0.469776 | ||||||||
\(227\) | 11.0481 | 0.733291 | 0.366646 | − | 0.930361i | \(-0.380506\pi\) | ||||
0.366646 | + | 0.930361i | \(0.380506\pi\) | |||||||
\(228\) | 7.36572 | 0.487807 | ||||||||
\(229\) | −21.0370 | −1.39016 | −0.695081 | − | 0.718932i | \(-0.744631\pi\) | ||||
−0.695081 | + | 0.718932i | \(0.744631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.29583 | −0.0852591 | ||||||||
\(232\) | 0.178999 | 0.0117519 | ||||||||
\(233\) | −4.59419 | −0.300975 | −0.150488 | − | 0.988612i | \(-0.548084\pi\) | ||||
−0.150488 | + | 0.988612i | \(0.548084\pi\) | |||||||
\(234\) | 5.83461 | 0.381420 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 28.1332 | 1.83132 | ||||||||
\(237\) | −9.09454 | −0.590754 | ||||||||
\(238\) | −7.18537 | −0.465758 | ||||||||
\(239\) | 10.8821 | 0.703904 | 0.351952 | − | 0.936018i | \(-0.385518\pi\) | ||||
0.351952 | + | 0.936018i | \(0.385518\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.13644 | 0.202036 | 0.101018 | − | 0.994885i | \(-0.467790\pi\) | ||||
0.101018 | + | 0.994885i | \(0.467790\pi\) | |||||||
\(242\) | 2.40444 | 0.154563 | ||||||||
\(243\) | −8.05519 | −0.516740 | ||||||||
\(244\) | −44.5137 | −2.84970 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 27.6679 | 1.76404 | ||||||||
\(247\) | 3.05467 | 0.194364 | ||||||||
\(248\) | 28.9835 | 1.84045 | ||||||||
\(249\) | 24.5023 | 1.55277 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9263 | 0.815899 | 0.407950 | − | 0.913004i | \(-0.366244\pi\) | ||||
0.407950 | + | 0.913004i | \(0.366244\pi\) | |||||||
\(252\) | −1.99827 | −0.125879 | ||||||||
\(253\) | 0.205258 | 0.0129045 | ||||||||
\(254\) | −23.2443 | −1.45848 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.2053 | −1.82533 | ||||||||
\(257\) | −27.5153 | −1.71635 | −0.858177 | − | 0.513353i | \(-0.828403\pi\) | ||||
−0.858177 | + | 0.513353i | \(0.828403\pi\) | |||||||
\(258\) | −8.32172 | −0.518088 | ||||||||
\(259\) | −5.06087 | −0.314467 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0331991 | 0.00205497 | ||||||||
\(262\) | −23.6294 | −1.45983 | ||||||||
\(263\) | 26.7289 | 1.64818 | 0.824088 | − | 0.566462i | \(-0.191688\pi\) | ||||
0.824088 | + | 0.566462i | \(0.191688\pi\) | |||||||
\(264\) | 8.34313 | 0.513484 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.59952 | −0.0980729 | ||||||||
\(267\) | 11.8191 | 0.723316 | ||||||||
\(268\) | −28.5615 | −1.74467 | ||||||||
\(269\) | −10.8583 | −0.662044 | −0.331022 | − | 0.943623i | \(-0.607393\pi\) | ||||
−0.331022 | + | 0.943623i | \(0.607393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.99688 | −0.425030 | −0.212515 | − | 0.977158i | \(-0.568166\pi\) | ||||
−0.212515 | + | 0.977158i | \(0.568166\pi\) | |||||||
\(272\) | 12.2897 | 0.745174 | ||||||||
\(273\) | −3.95833 | −0.239569 | ||||||||
\(274\) | −12.4820 | −0.754066 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.51187 | 0.0910041 | ||||||||
\(277\) | −5.93902 | −0.356841 | −0.178420 | − | 0.983954i | \(-0.557099\pi\) | ||||
−0.178420 | + | 0.983954i | \(0.557099\pi\) | |||||||
\(278\) | −30.1702 | −1.80949 | ||||||||
\(279\) | 5.37558 | 0.321828 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.12274 | −0.544217 | −0.272109 | − | 0.962267i | \(-0.587721\pi\) | ||||
−0.272109 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(282\) | −11.4296 | −0.680622 | ||||||||
\(283\) | −9.66343 | −0.574431 | −0.287216 | − | 0.957866i | \(-0.592730\pi\) | ||||
−0.287216 | + | 0.957866i | \(0.592730\pi\) | |||||||
\(284\) | 8.92549 | 0.529630 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.34478 | 0.434306 | ||||||||
\(287\) | −3.92977 | −0.231967 | ||||||||
\(288\) | −1.57937 | −0.0930650 | ||||||||
\(289\) | 3.17988 | 0.187052 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.4425 | 0.963876 | ||||||||
\(292\) | −5.94228 | −0.347746 | ||||||||
\(293\) | 8.88003 | 0.518777 | 0.259389 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259389 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(294\) | −30.7129 | −1.79121 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 32.5842 | 1.89392 | ||||||||
\(297\) | −4.29635 | −0.249300 | ||||||||
\(298\) | −31.0364 | −1.79789 | ||||||||
\(299\) | 0.626996 | 0.0362601 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.18196 | 0.0681273 | ||||||||
\(302\) | 33.9861 | 1.95568 | ||||||||
\(303\) | 27.0152 | 1.55198 | ||||||||
\(304\) | 2.73579 | 0.156908 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.58037 | 0.490507 | ||||||||
\(307\) | −5.48367 | −0.312969 | −0.156485 | − | 0.987680i | \(-0.550016\pi\) | ||||
−0.156485 | + | 0.987680i | \(0.550016\pi\) | |||||||
\(308\) | −2.51548 | −0.143333 | ||||||||
\(309\) | 8.63730 | 0.491359 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.4687 | −1.04726 | −0.523632 | − | 0.851945i | \(-0.675423\pi\) | ||||
−0.523632 | + | 0.851945i | \(0.675423\pi\) | |||||||
\(312\) | 25.4855 | 1.44283 | ||||||||
\(313\) | −19.9848 | −1.12961 | −0.564805 | − | 0.825225i | \(-0.691049\pi\) | ||||
−0.564805 | + | 0.825225i | \(0.691049\pi\) | |||||||
\(314\) | −44.2158 | −2.49524 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.6545 | −0.993141 | ||||||||
\(317\) | 7.52151 | 0.422450 | 0.211225 | − | 0.977437i | \(-0.432255\pi\) | ||||
0.211225 | + | 0.977437i | \(0.432255\pi\) | |||||||
\(318\) | −15.6806 | −0.879322 | ||||||||
\(319\) | 0.0417920 | 0.00233990 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.0279 | −1.84344 | ||||||||
\(322\) | −0.328315 | −0.0182963 | ||||||||
\(323\) | 4.49220 | 0.249953 | ||||||||
\(324\) | −40.6573 | −2.25874 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.2037 | −1.17436 | ||||||||
\(327\) | −18.0668 | −0.999099 | ||||||||
\(328\) | 25.3017 | 1.39705 | ||||||||
\(329\) | 1.62339 | 0.0895002 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.7743 | 1.36172 | 0.680860 | − | 0.732414i | \(-0.261606\pi\) | ||||
0.680860 | + | 0.732414i | \(0.261606\pi\) | |||||||
\(332\) | 47.5643 | 2.61043 | ||||||||
\(333\) | 6.04341 | 0.331177 | ||||||||
\(334\) | 2.70970 | 0.148268 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.54511 | −0.193402 | ||||||||
\(337\) | 20.7859 | 1.13228 | 0.566140 | − | 0.824309i | \(-0.308436\pi\) | ||||
0.566140 | + | 0.824309i | \(0.308436\pi\) | |||||||
\(338\) | −8.82182 | −0.479844 | ||||||||
\(339\) | 5.72139 | 0.310743 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.76694 | 0.366451 | ||||||||
\(342\) | 1.91006 | 0.103284 | ||||||||
\(343\) | 9.01891 | 0.486976 | ||||||||
\(344\) | −7.61003 | −0.410305 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.7886 | −1.38640 | ||||||||
\(347\) | −5.29461 | −0.284230 | −0.142115 | − | 0.989850i | \(-0.545390\pi\) | ||||
−0.142115 | + | 0.989850i | \(0.545390\pi\) | |||||||
\(348\) | 0.307828 | 0.0165013 | ||||||||
\(349\) | −5.79324 | −0.310105 | −0.155053 | − | 0.987906i | \(-0.549555\pi\) | ||||
−0.155053 | + | 0.987906i | \(0.549555\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.1240 | −0.700505 | ||||||||
\(352\) | −1.98815 | −0.105969 | ||||||||
\(353\) | −24.4881 | −1.30337 | −0.651686 | − | 0.758489i | \(-0.725938\pi\) | ||||
−0.651686 | + | 0.758489i | \(0.725938\pi\) | |||||||
\(354\) | 34.8465 | 1.85207 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 22.9434 | 1.21600 | ||||||||
\(357\) | −5.82111 | −0.308086 | ||||||||
\(358\) | −18.4104 | −0.973021 | ||||||||
\(359\) | −1.29578 | −0.0683884 | −0.0341942 | − | 0.999415i | \(-0.510886\pi\) | ||||
−0.0341942 | + | 0.999415i | \(0.510886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 45.5457 | 2.39383 | ||||||||
\(363\) | 1.94792 | 0.102239 | ||||||||
\(364\) | −7.68396 | −0.402749 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −55.1358 | −2.88199 | ||||||||
\(367\) | −1.48217 | −0.0773688 | −0.0386844 | − | 0.999251i | \(-0.512317\pi\) | ||||
−0.0386844 | + | 0.999251i | \(0.512317\pi\) | |||||||
\(368\) | 0.561543 | 0.0292725 | ||||||||
\(369\) | 4.69271 | 0.244293 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.22717 | 0.115629 | ||||||||
\(372\) | 49.8434 | 2.58426 | ||||||||
\(373\) | −21.1434 | −1.09477 | −0.547383 | − | 0.836882i | \(-0.684376\pi\) | ||||
−0.547383 | + | 0.836882i | \(0.684376\pi\) | |||||||
\(374\) | 10.8012 | 0.558518 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.4521 | −0.539026 | ||||||||
\(377\) | 0.127661 | 0.00657487 | ||||||||
\(378\) | 6.87210 | 0.353463 | ||||||||
\(379\) | −7.09981 | −0.364693 | −0.182346 | − | 0.983234i | \(-0.558369\pi\) | ||||
−0.182346 | + | 0.983234i | \(0.558369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.8310 | −0.964740 | ||||||||
\(382\) | −18.0360 | −0.922803 | ||||||||
\(383\) | −0.626205 | −0.0319976 | −0.0159988 | − | 0.999872i | \(-0.505093\pi\) | ||||
−0.0159988 | + | 0.999872i | \(0.505093\pi\) | |||||||
\(384\) | −40.2712 | −2.05508 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 48.6213 | 2.47476 | ||||||||
\(387\) | −1.41144 | −0.0717473 | ||||||||
\(388\) | 31.9184 | 1.62041 | ||||||||
\(389\) | −0.689943 | −0.0349815 | −0.0174907 | − | 0.999847i | \(-0.505568\pi\) | ||||
−0.0174907 | + | 0.999847i | \(0.505568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.922061 | 0.0466306 | ||||||||
\(392\) | −28.0862 | −1.41857 | ||||||||
\(393\) | −19.1430 | −0.965636 | ||||||||
\(394\) | −58.9255 | −2.96862 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.00384 | 0.150949 | ||||||||
\(397\) | 27.4815 | 1.37926 | 0.689628 | − | 0.724164i | \(-0.257774\pi\) | ||||
0.689628 | + | 0.724164i | \(0.257774\pi\) | |||||||
\(398\) | 23.9537 | 1.20069 | ||||||||
\(399\) | −1.29583 | −0.0648725 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.6174 | 1.37915 | 0.689574 | − | 0.724215i | \(-0.257798\pi\) | ||||
0.689574 | + | 0.724215i | \(0.257798\pi\) | |||||||
\(402\) | −35.3770 | −1.76444 | ||||||||
\(403\) | 20.6708 | 1.02969 | ||||||||
\(404\) | 52.4423 | 2.60910 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0668471 | −0.00331757 | ||||||||
\(407\) | 7.60762 | 0.377096 | ||||||||
\(408\) | 37.4790 | 1.85549 | ||||||||
\(409\) | −8.03757 | −0.397432 | −0.198716 | − | 0.980057i | \(-0.563677\pi\) | ||||
−0.198716 | + | 0.980057i | \(0.563677\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1121 | −0.498793 | ||||||||
\(412\) | 16.7669 | 0.826043 | ||||||||
\(413\) | −4.94938 | −0.243543 | ||||||||
\(414\) | 0.392055 | 0.0192685 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.07316 | −0.297761 | ||||||||
\(417\) | −24.4419 | −1.19693 | ||||||||
\(418\) | 2.40444 | 0.117605 | ||||||||
\(419\) | −17.7286 | −0.866101 | −0.433050 | − | 0.901370i | \(-0.642563\pi\) | ||||
−0.433050 | + | 0.901370i | \(0.642563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5510 | −0.757908 | −0.378954 | − | 0.925416i | \(-0.623716\pi\) | ||||
−0.378954 | + | 0.925416i | \(0.623716\pi\) | |||||||
\(422\) | 17.2017 | 0.837364 | ||||||||
\(423\) | −1.93856 | −0.0942559 | ||||||||
\(424\) | −14.3395 | −0.696389 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.0553 | 0.535633 | ||||||||
\(427\) | 7.83114 | 0.378975 | ||||||||
\(428\) | −64.1142 | −3.09908 | ||||||||
\(429\) | 5.95026 | 0.287281 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.1423 | −1.64458 | −0.822288 | − | 0.569072i | \(-0.807303\pi\) | ||||
−0.822288 | + | 0.569072i | \(0.807303\pi\) | |||||||
\(432\) | −11.7539 | −0.565511 | ||||||||
\(433\) | 5.06729 | 0.243519 | 0.121759 | − | 0.992560i | \(-0.461146\pi\) | ||||
0.121759 | + | 0.992560i | \(0.461146\pi\) | |||||||
\(434\) | −10.8239 | −0.519562 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.0716 | −1.67963 | ||||||||
\(437\) | 0.205258 | 0.00981883 | ||||||||
\(438\) | −7.36027 | −0.351687 | ||||||||
\(439\) | −23.7809 | −1.13500 | −0.567500 | − | 0.823374i | \(-0.692089\pi\) | ||||
−0.567500 | + | 0.823374i | \(0.692089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.20917 | −0.248056 | ||||||||
\(442\) | 32.9942 | 1.56938 | ||||||||
\(443\) | −13.0487 | −0.619961 | −0.309981 | − | 0.950743i | \(-0.600323\pi\) | ||||
−0.309981 | + | 0.950743i | \(0.600323\pi\) | |||||||
\(444\) | 56.0356 | 2.65933 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.1334 | 1.28480 | ||||||||
\(447\) | −25.1437 | −1.18925 | ||||||||
\(448\) | 6.81998 | 0.322214 | ||||||||
\(449\) | −26.5900 | −1.25486 | −0.627430 | − | 0.778673i | \(-0.715893\pi\) | ||||
−0.627430 | + | 0.778673i | \(0.715893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.90733 | 0.278165 | ||||||||
\(452\) | 11.1064 | 0.522403 | ||||||||
\(453\) | 27.5333 | 1.29363 | ||||||||
\(454\) | 26.5646 | 1.24674 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.34313 | 0.390703 | ||||||||
\(457\) | −0.764032 | −0.0357399 | −0.0178700 | − | 0.999840i | \(-0.505688\pi\) | ||||
−0.0178700 | + | 0.999840i | \(0.505688\pi\) | |||||||
\(458\) | −50.5821 | −2.36355 | ||||||||
\(459\) | −19.3001 | −0.900851 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.17462 | −0.241006 | −0.120503 | − | 0.992713i | \(-0.538451\pi\) | ||||
−0.120503 | + | 0.992713i | \(0.538451\pi\) | |||||||
\(462\) | −3.11574 | −0.144957 | ||||||||
\(463\) | 14.9993 | 0.697078 | 0.348539 | − | 0.937294i | \(-0.386678\pi\) | ||||
0.348539 | + | 0.937294i | \(0.386678\pi\) | |||||||
\(464\) | 0.114334 | 0.00530783 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0465 | −0.511717 | ||||||||
\(467\) | −8.46795 | −0.391850 | −0.195925 | − | 0.980619i | \(-0.562771\pi\) | ||||
−0.195925 | + | 0.980619i | \(0.562771\pi\) | |||||||
\(468\) | 9.17576 | 0.424150 | ||||||||
\(469\) | 5.02472 | 0.232020 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.8207 | −1.65053 | ||||||||
\(472\) | 31.8664 | 1.46677 | ||||||||
\(473\) | −1.77676 | −0.0816954 | ||||||||
\(474\) | −21.8673 | −1.00440 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −11.3000 | −0.517936 | ||||||||
\(477\) | −2.65956 | −0.121773 | ||||||||
\(478\) | 26.1653 | 1.19677 | ||||||||
\(479\) | 11.4343 | 0.522446 | 0.261223 | − | 0.965278i | \(-0.415874\pi\) | ||||
0.261223 | + | 0.965278i | \(0.415874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.2388 | 1.05960 | ||||||||
\(482\) | 7.54139 | 0.343501 | ||||||||
\(483\) | −0.265979 | −0.0121025 | ||||||||
\(484\) | 3.78133 | 0.171879 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.3682 | −0.878560 | ||||||||
\(487\) | 34.9001 | 1.58148 | 0.790738 | − | 0.612155i | \(-0.209697\pi\) | ||||
0.790738 | + | 0.612155i | \(0.209697\pi\) | |||||||
\(488\) | −50.4205 | −2.28243 | ||||||||
\(489\) | −17.1778 | −0.776808 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5534 | 0.701917 | 0.350958 | − | 0.936391i | \(-0.385856\pi\) | ||||
0.350958 | + | 0.936391i | \(0.385856\pi\) | |||||||
\(492\) | 43.5117 | 1.96166 | ||||||||
\(493\) | 0.187738 | 0.00845529 | ||||||||
\(494\) | 7.34478 | 0.330457 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.5129 | 0.831256 | ||||||||
\(497\) | −1.57023 | −0.0704345 | ||||||||
\(498\) | 58.9144 | 2.64002 | ||||||||
\(499\) | −29.1290 | −1.30399 | −0.651996 | − | 0.758222i | \(-0.726068\pi\) | ||||
−0.651996 | + | 0.758222i | \(0.726068\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.19522 | 0.0980752 | ||||||||
\(502\) | 31.0804 | 1.38719 | ||||||||
\(503\) | 5.76237 | 0.256931 | 0.128466 | − | 0.991714i | \(-0.458995\pi\) | ||||
0.128466 | + | 0.991714i | \(0.458995\pi\) | |||||||
\(504\) | −2.26343 | −0.100821 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.493531 | 0.0219401 | ||||||||
\(507\) | −7.14686 | −0.317403 | ||||||||
\(508\) | −36.5550 | −1.62186 | ||||||||
\(509\) | 20.3839 | 0.903502 | 0.451751 | − | 0.892144i | \(-0.350799\pi\) | ||||
0.451751 | + | 0.892144i | \(0.350799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.04541 | 0.0462460 | ||||||||
\(512\) | −28.8745 | −1.27608 | ||||||||
\(513\) | −4.29635 | −0.189689 | ||||||||
\(514\) | −66.1588 | −2.91814 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.0871 | −0.576128 | ||||||||
\(517\) | −2.44032 | −0.107325 | ||||||||
\(518\) | −12.1685 | −0.534655 | ||||||||
\(519\) | −20.8922 | −0.917068 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.9184 | 0.960262 | 0.480131 | − | 0.877197i | \(-0.340589\pi\) | ||||
0.480131 | + | 0.877197i | \(0.340589\pi\) | |||||||
\(522\) | 0.0798251 | 0.00349385 | ||||||||
\(523\) | 3.65894 | 0.159994 | 0.0799972 | − | 0.996795i | \(-0.474509\pi\) | ||||
0.0799972 | + | 0.996795i | \(0.474509\pi\) | |||||||
\(524\) | −37.1606 | −1.62337 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 64.2681 | 2.80222 | ||||||||
\(527\) | 30.3985 | 1.32418 | ||||||||
\(528\) | 5.32910 | 0.231919 | ||||||||
\(529\) | −22.9579 | −0.998168 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.91027 | 0.256484 | ||||||||
\(532\) | −2.51548 | −0.109060 | ||||||||
\(533\) | 18.0450 | 0.781614 | ||||||||
\(534\) | 28.4182 | 1.22978 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −32.3515 | −1.39737 | ||||||||
\(537\) | −14.9149 | −0.643626 | ||||||||
\(538\) | −26.1082 | −1.12560 | ||||||||
\(539\) | −6.55746 | −0.282450 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.6166 | −1.27332 | −0.636659 | − | 0.771145i | \(-0.719684\pi\) | ||||
−0.636659 | + | 0.771145i | \(0.719684\pi\) | |||||||
\(542\) | −16.8236 | −0.722635 | ||||||||
\(543\) | 36.8981 | 1.58345 | ||||||||
\(544\) | −8.93118 | −0.382921 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.51756 | −0.407314 | ||||||||
\(547\) | 0.893755 | 0.0382142 | 0.0191071 | − | 0.999817i | \(-0.493918\pi\) | ||||
0.0191071 | + | 0.999817i | \(0.493918\pi\) | |||||||
\(548\) | −19.6298 | −0.838542 | ||||||||
\(549\) | −9.35151 | −0.399113 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0417920 | 0.00178040 | ||||||||
\(552\) | 1.71249 | 0.0728886 | ||||||||
\(553\) | 3.10589 | 0.132076 | ||||||||
\(554\) | −14.2800 | −0.606699 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −47.4470 | −2.01220 | ||||||||
\(557\) | −2.52940 | −0.107174 | −0.0535870 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535870 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(558\) | 12.9253 | 0.547170 | ||||||||
\(559\) | −5.42742 | −0.229555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.75045 | 0.369444 | ||||||||
\(562\) | −21.9351 | −0.925276 | ||||||||
\(563\) | 26.4031 | 1.11276 | 0.556379 | − | 0.830929i | \(-0.312190\pi\) | ||||
0.556379 | + | 0.830929i | \(0.312190\pi\) | |||||||
\(564\) | −17.9747 | −0.756871 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.2351 | −0.976645 | ||||||||
\(567\) | 7.15270 | 0.300385 | ||||||||
\(568\) | 10.1099 | 0.424201 | ||||||||
\(569\) | 25.7456 | 1.07931 | 0.539656 | − | 0.841886i | \(-0.318554\pi\) | ||||
0.539656 | + | 0.841886i | \(0.318554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.1904 | −1.34712 | −0.673562 | − | 0.739131i | \(-0.735237\pi\) | ||||
−0.673562 | + | 0.739131i | \(0.735237\pi\) | |||||||
\(572\) | 11.5507 | 0.482960 | ||||||||
\(573\) | −14.6116 | −0.610408 | ||||||||
\(574\) | −9.44889 | −0.394389 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.14405 | −0.339335 | ||||||||
\(577\) | 44.7621 | 1.86347 | 0.931735 | − | 0.363138i | \(-0.118295\pi\) | ||||
0.931735 | + | 0.363138i | \(0.118295\pi\) | |||||||
\(578\) | 7.64582 | 0.318024 | ||||||||
\(579\) | 39.3898 | 1.63698 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.36783 | −0.347156 | ||||||||
\(582\) | 39.5350 | 1.63878 | ||||||||
\(583\) | −3.34793 | −0.138657 | ||||||||
\(584\) | −6.73080 | −0.278522 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3515 | 0.882022 | ||||||||
\(587\) | 20.5841 | 0.849597 | 0.424799 | − | 0.905288i | \(-0.360345\pi\) | ||||
0.424799 | + | 0.905288i | \(0.360345\pi\) | |||||||
\(588\) | −48.3004 | −1.99188 | ||||||||
\(589\) | 6.76694 | 0.278827 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47.7376 | −1.96366 | ||||||||
\(592\) | 20.8129 | 0.855403 | ||||||||
\(593\) | 37.6866 | 1.54760 | 0.773802 | − | 0.633428i | \(-0.218353\pi\) | ||||
0.773802 | + | 0.633428i | \(0.218353\pi\) | |||||||
\(594\) | −10.3303 | −0.423858 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −48.8092 | −1.99930 | ||||||||
\(597\) | 19.4057 | 0.794222 | ||||||||
\(598\) | 1.50758 | 0.0616493 | ||||||||
\(599\) | −29.3217 | −1.19805 | −0.599027 | − | 0.800729i | \(-0.704446\pi\) | ||||
−0.599027 | + | 0.800729i | \(0.704446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.4596 | −0.712190 | −0.356095 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356095 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(602\) | 2.84196 | 0.115830 | ||||||||
\(603\) | −6.00024 | −0.244349 | ||||||||
\(604\) | 53.4481 | 2.17477 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 64.9565 | 2.63868 | ||||||||
\(607\) | 39.4241 | 1.60017 | 0.800087 | − | 0.599884i | \(-0.204787\pi\) | ||||
0.800087 | + | 0.599884i | \(0.204787\pi\) | |||||||
\(608\) | −1.98815 | −0.0806302 | ||||||||
\(609\) | −0.0541551 | −0.00219448 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.45437 | −0.301571 | ||||||||
\(612\) | 13.4939 | 0.545457 | ||||||||
\(613\) | 24.8034 | 1.00180 | 0.500901 | − | 0.865505i | \(-0.333002\pi\) | ||||
0.500901 | + | 0.865505i | \(0.333002\pi\) | |||||||
\(614\) | −13.1851 | −0.532109 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.84927 | −0.114800 | ||||||||
\(617\) | −44.9932 | −1.81136 | −0.905678 | − | 0.423966i | \(-0.860638\pi\) | ||||
−0.905678 | + | 0.423966i | \(0.860638\pi\) | |||||||
\(618\) | 20.7679 | 0.835406 | ||||||||
\(619\) | 4.48348 | 0.180206 | 0.0901031 | − | 0.995932i | \(-0.471280\pi\) | ||||
0.0901031 | + | 0.995932i | \(0.471280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.881861 | −0.0353879 | ||||||||
\(622\) | −44.4069 | −1.78055 | ||||||||
\(623\) | −4.03635 | −0.161713 | ||||||||
\(624\) | 16.2787 | 0.651668 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −48.0523 | −1.92056 | ||||||||
\(627\) | 1.94792 | 0.0777924 | ||||||||
\(628\) | −69.5358 | −2.77478 | ||||||||
\(629\) | 34.1750 | 1.36265 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.6458 | 1.65789 | 0.828947 | − | 0.559327i | \(-0.188941\pi\) | ||||
0.828947 | + | 0.559327i | \(0.188941\pi\) | |||||||
\(632\) | −19.9971 | −0.795444 | ||||||||
\(633\) | 13.9357 | 0.553893 | ||||||||
\(634\) | 18.0850 | 0.718247 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.6600 | −0.977831 | ||||||||
\(637\) | −20.0309 | −0.793653 | ||||||||
\(638\) | 0.100486 | 0.00397829 | ||||||||
\(639\) | 1.87508 | 0.0741771 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.0569 | −1.10818 | −0.554090 | − | 0.832457i | \(-0.686934\pi\) | ||||
−0.554090 | + | 0.832457i | \(0.686934\pi\) | |||||||
\(642\) | −79.4136 | −3.13420 | ||||||||
\(643\) | 22.4021 | 0.883453 | 0.441727 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441727 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(644\) | −0.516322 | −0.0203459 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.8012 | 0.424969 | ||||||||
\(647\) | −25.5651 | −1.00507 | −0.502533 | − | 0.864558i | \(-0.667599\pi\) | ||||
−0.502533 | + | 0.864558i | \(0.667599\pi\) | |||||||
\(648\) | −46.0523 | −1.80911 | ||||||||
\(649\) | 7.44003 | 0.292047 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.76879 | −0.343676 | ||||||||
\(652\) | −33.3458 | −1.30592 | ||||||||
\(653\) | 11.9470 | 0.467523 | 0.233761 | − | 0.972294i | \(-0.424897\pi\) | ||||
0.233761 | + | 0.972294i | \(0.424897\pi\) | |||||||
\(654\) | −43.4406 | −1.69866 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 16.1612 | 0.630989 | ||||||||
\(657\) | −1.24837 | −0.0487034 | ||||||||
\(658\) | 3.90333 | 0.152168 | ||||||||
\(659\) | 17.3208 | 0.674724 | 0.337362 | − | 0.941375i | \(-0.390465\pi\) | ||||
0.337362 | + | 0.941375i | \(0.390465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.6524 | 0.725495 | 0.362748 | − | 0.931887i | \(-0.381839\pi\) | ||||
0.362748 | + | 0.931887i | \(0.381839\pi\) | |||||||
\(662\) | 59.5683 | 2.31519 | ||||||||
\(663\) | 26.7298 | 1.03810 | ||||||||
\(664\) | 53.8759 | 2.09079 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.5310 | 0.563065 | ||||||||
\(667\) | 0.00857814 | 0.000332147 0 | ||||||||
\(668\) | 4.26139 | 0.164878 | ||||||||
\(669\) | 21.9817 | 0.849862 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7720 | −0.454452 | ||||||||
\(672\) | 2.57630 | 0.0993830 | ||||||||
\(673\) | 47.6707 | 1.83757 | 0.918785 | − | 0.394758i | \(-0.129171\pi\) | ||||
0.918785 | + | 0.394758i | \(0.129171\pi\) | |||||||
\(674\) | 49.9784 | 1.92510 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.8736 | −0.533599 | ||||||||
\(677\) | 4.64806 | 0.178639 | 0.0893197 | − | 0.996003i | \(-0.471531\pi\) | ||||
0.0893197 | + | 0.996003i | \(0.471531\pi\) | |||||||
\(678\) | 13.7567 | 0.528324 | ||||||||
\(679\) | −5.61529 | −0.215495 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.5209 | 0.824683 | ||||||||
\(682\) | 16.2707 | 0.623038 | ||||||||
\(683\) | 25.0058 | 0.956820 | 0.478410 | − | 0.878137i | \(-0.341213\pi\) | ||||
0.478410 | + | 0.878137i | \(0.341213\pi\) | |||||||
\(684\) | 3.00384 | 0.114855 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 21.6854 | 0.827954 | ||||||||
\(687\) | −40.9783 | −1.56342 | ||||||||
\(688\) | −4.86084 | −0.185318 | ||||||||
\(689\) | −10.2268 | −0.389612 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9866 | −0.760328 | −0.380164 | − | 0.924919i | \(-0.624132\pi\) | ||||
−0.380164 | + | 0.924919i | \(0.624132\pi\) | |||||||
\(692\) | −40.5563 | −1.54172 | ||||||||
\(693\) | −0.528456 | −0.0200744 | ||||||||
\(694\) | −12.7306 | −0.483246 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.348676 | 0.0132165 | ||||||||
\(697\) | 26.5369 | 1.00516 | ||||||||
\(698\) | −13.9295 | −0.527239 | ||||||||
\(699\) | −8.94911 | −0.338487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.2573 | −1.06726 | −0.533632 | − | 0.845717i | \(-0.679173\pi\) | ||||
−0.533632 | + | 0.845717i | \(0.679173\pi\) | |||||||
\(702\) | −31.5558 | −1.19100 | ||||||||
\(703\) | 7.60762 | 0.286927 | ||||||||
\(704\) | −10.2520 | −0.386386 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −58.8803 | −2.21599 | ||||||||
\(707\) | −9.22600 | −0.346980 | ||||||||
\(708\) | 54.8012 | 2.05956 | ||||||||
\(709\) | −20.5903 | −0.773287 | −0.386643 | − | 0.922229i | \(-0.626366\pi\) | ||||
−0.386643 | + | 0.922229i | \(0.626366\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.70888 | −0.139094 | ||||||||
\(712\) | 25.9879 | 0.973936 | ||||||||
\(713\) | 1.38897 | 0.0520173 | ||||||||
\(714\) | −13.9965 | −0.523806 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.9530 | −1.08203 | ||||||||
\(717\) | 21.1974 | 0.791632 | ||||||||
\(718\) | −3.11561 | −0.116274 | ||||||||
\(719\) | 36.7987 | 1.37236 | 0.686179 | − | 0.727433i | \(-0.259287\pi\) | ||||
0.686179 | + | 0.727433i | \(0.259287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.94973 | −0.109854 | ||||||||
\(722\) | 2.40444 | 0.0894840 | ||||||||
\(723\) | 6.10954 | 0.227216 | ||||||||
\(724\) | 71.6272 | 2.66200 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.68365 | 0.173827 | ||||||||
\(727\) | 7.19540 | 0.266862 | 0.133431 | − | 0.991058i | \(-0.457400\pi\) | ||||
0.133431 | + | 0.991058i | \(0.457400\pi\) | |||||||
\(728\) | −8.70360 | −0.322577 | ||||||||
\(729\) | 16.5655 | 0.613537 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.98156 | −0.295208 | ||||||||
\(732\) | −86.7090 | −3.20486 | ||||||||
\(733\) | 23.2371 | 0.858282 | 0.429141 | − | 0.903237i | \(-0.358816\pi\) | ||||
0.429141 | + | 0.903237i | \(0.358816\pi\) | |||||||
\(734\) | −3.56379 | −0.131542 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.408084 | −0.0150422 | ||||||||
\(737\) | −7.55329 | −0.278229 | ||||||||
\(738\) | 11.2833 | 0.415345 | ||||||||
\(739\) | 8.05244 | 0.296214 | 0.148107 | − | 0.988971i | \(-0.452682\pi\) | ||||
0.148107 | + | 0.988971i | \(0.452682\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.95026 | 0.218588 | ||||||||
\(742\) | 5.35509 | 0.196592 | ||||||||
\(743\) | 28.2801 | 1.03750 | 0.518748 | − | 0.854927i | \(-0.326398\pi\) | ||||
0.518748 | + | 0.854927i | \(0.326398\pi\) | |||||||
\(744\) | 56.4575 | 2.06983 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −50.8381 | −1.86132 | ||||||||
\(747\) | 9.99239 | 0.365603 | ||||||||
\(748\) | 16.9865 | 0.621088 | ||||||||
\(749\) | 11.2794 | 0.412140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2029 | 0.810195 | 0.405098 | − | 0.914273i | \(-0.367238\pi\) | ||||
0.405098 | + | 0.914273i | \(0.367238\pi\) | |||||||
\(752\) | −6.67619 | −0.243456 | ||||||||
\(753\) | 25.1793 | 0.917586 | ||||||||
\(754\) | 0.306953 | 0.0111786 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.8074 | 0.393061 | ||||||||
\(757\) | −8.75295 | −0.318131 | −0.159066 | − | 0.987268i | \(-0.550848\pi\) | ||||
−0.159066 | + | 0.987268i | \(0.550848\pi\) | |||||||
\(758\) | −17.0711 | −0.620049 | ||||||||
\(759\) | 0.399826 | 0.0145128 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.4713 | −0.488334 | −0.244167 | − | 0.969733i | \(-0.578514\pi\) | ||||
−0.244167 | + | 0.969733i | \(0.578514\pi\) | |||||||
\(762\) | −45.2780 | −1.64025 | ||||||||
\(763\) | 6.17003 | 0.223370 | ||||||||
\(764\) | −28.3643 | −1.02618 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.50567 | −0.0544022 | ||||||||
\(767\) | 22.7269 | 0.820620 | ||||||||
\(768\) | −56.8896 | −2.05282 | ||||||||
\(769\) | 23.4526 | 0.845723 | 0.422862 | − | 0.906194i | \(-0.361026\pi\) | ||||
0.422862 | + | 0.906194i | \(0.361026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −53.5975 | −1.93027 | ||||||||
\(772\) | 76.4640 | 2.75200 | ||||||||
\(773\) | −36.4566 | −1.31125 | −0.655626 | − | 0.755086i | \(-0.727595\pi\) | ||||
−0.655626 | + | 0.755086i | \(0.727595\pi\) | |||||||
\(774\) | −3.39371 | −0.121984 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.1538 | 1.29785 | ||||||||
\(777\) | −9.85816 | −0.353660 | ||||||||
\(778\) | −1.65893 | −0.0594754 | ||||||||
\(779\) | 5.90733 | 0.211652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.36041 | 0.0844621 | ||||||||
\(782\) | 2.21704 | 0.0792812 | ||||||||
\(783\) | −0.179553 | −0.00641670 | ||||||||
\(784\) | −17.9398 | −0.640708 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −46.0281 | −1.64177 | ||||||||
\(787\) | 0.310043 | 0.0110519 | 0.00552593 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552593 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(788\) | −92.6689 | −3.30119 | ||||||||
\(789\) | 52.0658 | 1.85359 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.95392 | −0.0694734 | ||||||||
\(792\) | 3.40244 | 0.120901 | ||||||||
\(793\) | −35.9595 | −1.27696 | ||||||||
\(794\) | 66.0775 | 2.34500 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37.6706 | 1.33520 | ||||||||
\(797\) | 39.9134 | 1.41381 | 0.706903 | − | 0.707311i | \(-0.250092\pi\) | ||||
0.706903 | + | 0.707311i | \(0.250092\pi\) | |||||||
\(798\) | −3.11574 | −0.110296 | ||||||||
\(799\) | −10.9624 | −0.387821 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.81998 | 0.170306 | ||||||||
\(802\) | 66.4044 | 2.34482 | ||||||||
\(803\) | −1.57148 | −0.0554563 | ||||||||
\(804\) | −55.6354 | −1.96211 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 49.7017 | 1.75067 | ||||||||
\(807\) | −21.1511 | −0.744555 | ||||||||
\(808\) | 59.4012 | 2.08973 | ||||||||
\(809\) | 35.5265 | 1.24904 | 0.624522 | − | 0.781007i | \(-0.285294\pi\) | ||||
0.624522 | + | 0.781007i | \(0.285294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.44459 | −0.191185 | −0.0955927 | − | 0.995421i | \(-0.530475\pi\) | ||||
−0.0955927 | + | 0.995421i | \(0.530475\pi\) | |||||||
\(812\) | −0.105127 | −0.00368923 | ||||||||
\(813\) | −13.6294 | −0.478003 | ||||||||
\(814\) | 18.2921 | 0.641137 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 23.9394 | 0.838046 | ||||||||
\(817\) | −1.77676 | −0.0621609 | ||||||||
\(818\) | −19.3258 | −0.675712 | ||||||||
\(819\) | −1.61426 | −0.0564068 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.04790 | −0.176173 | −0.0880865 | − | 0.996113i | \(-0.528075\pi\) | ||||
−0.0880865 | + | 0.996113i | \(0.528075\pi\) | |||||||
\(822\) | −24.3139 | −0.848046 | ||||||||
\(823\) | −43.4928 | −1.51607 | −0.758033 | − | 0.652217i | \(-0.773839\pi\) | ||||
−0.758033 | + | 0.652217i | \(0.773839\pi\) | |||||||
\(824\) | 18.9918 | 0.661609 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.9005 | −0.414071 | ||||||||
\(827\) | −14.5718 | −0.506711 | −0.253356 | − | 0.967373i | \(-0.581534\pi\) | ||||
−0.253356 | + | 0.967373i | \(0.581534\pi\) | |||||||
\(828\) | 0.616563 | 0.0214271 | ||||||||
\(829\) | 42.0994 | 1.46217 | 0.731086 | − | 0.682285i | \(-0.239014\pi\) | ||||
0.731086 | + | 0.682285i | \(0.239014\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.5687 | −0.401315 | ||||||||
\(832\) | −31.3164 | −1.08570 | ||||||||
\(833\) | −29.4574 | −1.02064 | ||||||||
\(834\) | −58.7691 | −2.03501 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.78133 | 0.130780 | ||||||||
\(837\) | −29.0732 | −1.00492 | ||||||||
\(838\) | −42.6274 | −1.47254 | ||||||||
\(839\) | 39.2894 | 1.35642 | 0.678211 | − | 0.734868i | \(-0.262756\pi\) | ||||
0.678211 | + | 0.734868i | \(0.262756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9983 | −0.999940 | ||||||||
\(842\) | −37.3914 | −1.28859 | ||||||||
\(843\) | −17.7704 | −0.612044 | ||||||||
\(844\) | 27.0521 | 0.931172 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.66115 | −0.160253 | ||||||||
\(847\) | −0.665236 | −0.0228578 | ||||||||
\(848\) | −9.15925 | −0.314530 | ||||||||
\(849\) | −18.8236 | −0.646023 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.56153 | 0.0535284 | ||||||||
\(852\) | 17.3861 | 0.595639 | ||||||||
\(853\) | 40.0833 | 1.37243 | 0.686213 | − | 0.727401i | \(-0.259272\pi\) | ||||
0.686213 | + | 0.727401i | \(0.259272\pi\) | |||||||
\(854\) | 18.8295 | 0.644332 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −72.6220 | −2.48217 | ||||||||
\(857\) | 8.21405 | 0.280587 | 0.140293 | − | 0.990110i | \(-0.455195\pi\) | ||||
0.140293 | + | 0.990110i | \(0.455195\pi\) | |||||||
\(858\) | 14.3070 | 0.488434 | ||||||||
\(859\) | −47.6682 | −1.62642 | −0.813210 | − | 0.581971i | \(-0.802282\pi\) | ||||
−0.813210 | + | 0.581971i | \(0.802282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.65487 | −0.260877 | ||||||||
\(862\) | −82.0930 | −2.79610 | ||||||||
\(863\) | 1.03040 | 0.0350752 | 0.0175376 | − | 0.999846i | \(-0.494417\pi\) | ||||
0.0175376 | + | 0.999846i | \(0.494417\pi\) | |||||||
\(864\) | 8.54180 | 0.290598 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.1840 | 0.414029 | ||||||||
\(867\) | 6.19414 | 0.210364 | ||||||||
\(868\) | −17.0221 | −0.577768 | ||||||||
\(869\) | −4.66885 | −0.158380 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.0728 | −0.781793 | ||||||||
\(872\) | −39.7255 | −1.34528 | ||||||||
\(873\) | 6.70547 | 0.226946 | ||||||||
\(874\) | 0.493531 | 0.0166939 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.5751 | −0.391086 | ||||||||
\(877\) | 25.9529 | 0.876366 | 0.438183 | − | 0.898886i | \(-0.355622\pi\) | ||||
0.438183 | + | 0.898886i | \(0.355622\pi\) | |||||||
\(878\) | −57.1797 | −1.92972 | ||||||||
\(879\) | 17.2976 | 0.583433 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.8144 | −0.499109 | −0.249554 | − | 0.968361i | \(-0.580284\pi\) | ||||
−0.249554 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(882\) | −12.5251 | −0.421743 | ||||||||
\(883\) | 1.57133 | 0.0528794 | 0.0264397 | − | 0.999650i | \(-0.491583\pi\) | ||||
0.0264397 | + | 0.999650i | \(0.491583\pi\) | |||||||
\(884\) | 51.8882 | 1.74519 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.3748 | −1.05406 | ||||||||
\(887\) | 39.1857 | 1.31573 | 0.657864 | − | 0.753137i | \(-0.271460\pi\) | ||||
0.657864 | + | 0.753137i | \(0.271460\pi\) | |||||||
\(888\) | 63.4714 | 2.12996 | ||||||||
\(889\) | 6.43099 | 0.215689 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.7521 | −0.360209 | ||||||||
\(892\) | 42.6712 | 1.42874 | ||||||||
\(893\) | −2.44032 | −0.0816620 | ||||||||
\(894\) | −60.4564 | −2.02196 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.7531 | 0.459457 | ||||||||
\(897\) | 1.22134 | 0.0407793 | ||||||||
\(898\) | −63.9340 | −2.13351 | ||||||||
\(899\) | 0.282804 | 0.00943204 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0396 | −0.501042 | ||||||||
\(902\) | 14.2038 | 0.472935 | ||||||||
\(903\) | 2.30237 | 0.0766181 | ||||||||
\(904\) | 12.5802 | 0.418412 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 66.2022 | 2.19942 | ||||||||
\(907\) | −51.6485 | −1.71496 | −0.857481 | − | 0.514516i | \(-0.827972\pi\) | ||||
−0.857481 | + | 0.514516i | \(0.827972\pi\) | |||||||
\(908\) | 41.7767 | 1.38641 | ||||||||
\(909\) | 11.0172 | 0.365417 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7905 | 0.688822 | 0.344411 | − | 0.938819i | \(-0.388079\pi\) | ||||
0.344411 | + | 0.938819i | \(0.388079\pi\) | |||||||
\(912\) | 5.32910 | 0.176464 | ||||||||
\(913\) | 12.5787 | 0.416295 | ||||||||
\(914\) | −1.83707 | −0.0607649 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −79.5477 | −2.62833 | ||||||||
\(917\) | 6.53754 | 0.215889 | ||||||||
\(918\) | −46.4059 | −1.53162 | ||||||||
\(919\) | 11.0153 | 0.363363 | 0.181681 | − | 0.983357i | \(-0.441846\pi\) | ||||
0.181681 | + | 0.983357i | \(0.441846\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.6817 | −0.351975 | ||||||||
\(922\) | −12.4421 | −0.409758 | ||||||||
\(923\) | 7.21028 | 0.237329 | ||||||||
\(924\) | −4.89995 | −0.161196 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 36.0650 | 1.18517 | ||||||||
\(927\) | 3.52241 | 0.115691 | ||||||||
\(928\) | −0.0830888 | −0.00272752 | ||||||||
\(929\) | 22.8406 | 0.749375 | 0.374687 | − | 0.927151i | \(-0.377750\pi\) | ||||
0.374687 | + | 0.927151i | \(0.377750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.55746 | −0.214912 | ||||||||
\(932\) | −17.3721 | −0.569044 | ||||||||
\(933\) | −35.9755 | −1.17779 | ||||||||
\(934\) | −20.3607 | −0.666221 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.3934 | 0.339717 | ||||||||
\(937\) | 13.4463 | 0.439270 | 0.219635 | − | 0.975582i | \(-0.429513\pi\) | ||||
0.219635 | + | 0.975582i | \(0.429513\pi\) | |||||||
\(938\) | 12.0816 | 0.394479 | ||||||||
\(939\) | −38.9288 | −1.27039 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.2843 | −0.498253 | −0.249126 | − | 0.968471i | \(-0.580143\pi\) | ||||
−0.249126 | + | 0.968471i | \(0.580143\pi\) | |||||||
\(942\) | −86.1288 | −2.80623 | ||||||||
\(943\) | 1.21253 | 0.0394853 | ||||||||
\(944\) | 20.3544 | 0.662478 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.27211 | −0.138898 | ||||||||
\(947\) | 31.6259 | 1.02770 | 0.513852 | − | 0.857879i | \(-0.328218\pi\) | ||||
0.513852 | + | 0.857879i | \(0.328218\pi\) | |||||||
\(948\) | −34.3895 | −1.11692 | ||||||||
\(949\) | −4.80036 | −0.155826 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.6513 | 0.475100 | ||||||||
\(952\) | −12.7995 | −0.414834 | ||||||||
\(953\) | −16.2564 | −0.526596 | −0.263298 | − | 0.964715i | \(-0.584810\pi\) | ||||
−0.263298 | + | 0.964715i | \(0.584810\pi\) | |||||||
\(954\) | −6.39475 | −0.207038 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 41.1488 | 1.33085 | ||||||||
\(957\) | 0.0814074 | 0.00263153 | ||||||||
\(958\) | 27.4931 | 0.888261 | ||||||||
\(959\) | 3.45340 | 0.111516 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7915 | 0.477146 | ||||||||
\(962\) | 55.8763 | 1.80152 | ||||||||
\(963\) | −13.4692 | −0.434040 | ||||||||
\(964\) | 11.8599 | 0.381983 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.639530 | −0.0205765 | ||||||||
\(967\) | 43.6663 | 1.40421 | 0.702106 | − | 0.712072i | \(-0.252243\pi\) | ||||
0.702106 | + | 0.712072i | \(0.252243\pi\) | |||||||
\(968\) | 4.28310 | 0.137664 | ||||||||
\(969\) | 8.75045 | 0.281105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.5513 | −1.04462 | −0.522311 | − | 0.852755i | \(-0.674930\pi\) | ||||
−0.522311 | + | 0.852755i | \(0.674930\pi\) | |||||||
\(972\) | −30.4593 | −0.976983 | ||||||||
\(973\) | 8.34720 | 0.267599 | ||||||||
\(974\) | 83.9153 | 2.68882 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32.2056 | −1.03088 | ||||||||
\(977\) | 37.0156 | 1.18423 | 0.592117 | − | 0.805852i | \(-0.298292\pi\) | ||||
0.592117 | + | 0.805852i | \(0.298292\pi\) | |||||||
\(978\) | −41.3030 | −1.32073 | ||||||||
\(979\) | 6.06754 | 0.193919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.36791 | −0.235239 | ||||||||
\(982\) | 37.3973 | 1.19340 | ||||||||
\(983\) | 10.3708 | 0.330777 | 0.165389 | − | 0.986228i | \(-0.447112\pi\) | ||||
0.165389 | + | 0.986228i | \(0.447112\pi\) | |||||||
\(984\) | 49.2856 | 1.57117 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.451405 | 0.0143757 | ||||||||
\(987\) | 3.16223 | 0.100655 | ||||||||
\(988\) | 11.5507 | 0.367478 | ||||||||
\(989\) | −0.364694 | −0.0115966 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4472 | −0.649525 | −0.324763 | − | 0.945796i | \(-0.605284\pi\) | ||||
−0.324763 | + | 0.945796i | \(0.605284\pi\) | |||||||
\(992\) | −13.4537 | −0.427156 | ||||||||
\(993\) | 48.2583 | 1.53143 | ||||||||
\(994\) | −3.77552 | −0.119752 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 92.6514 | 2.93577 | ||||||||
\(997\) | −51.6575 | −1.63601 | −0.818004 | − | 0.575212i | \(-0.804920\pi\) | ||||
−0.818004 | + | 0.575212i | \(0.804920\pi\) | |||||||
\(998\) | −70.0389 | −2.21704 | ||||||||
\(999\) | −32.6850 | −1.03411 |
(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 | 5225.2.a.y.1.13 | yes | 15 | |
5.4 | even | 2 | 5225.2.a.r.1.3 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5225.2.a.r.1.3 | ✓ | 15 | 5.4 | even | 2 | ||
5225.2.a.y.1.13 | yes | 15 | 1.1 | even | 1 | trivial |