Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 4x^{3} - 12x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 133) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.27137\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13506 | 0.802611 | 0.401305 | − | 0.915944i | \(-0.368557\pi\) | ||||
0.401305 | + | 0.915944i | \(0.368557\pi\) | |||||||
\(3\) | 2.19453 | 1.26701 | 0.633505 | − | 0.773738i | \(-0.281616\pi\) | ||||
0.633505 | + | 0.773738i | \(0.281616\pi\) | |||||||
\(4\) | −0.711632 | −0.355816 | ||||||||
\(5\) | 1.83111 | 0.818895 | 0.409448 | − | 0.912334i | \(-0.365721\pi\) | ||||
0.409448 | + | 0.912334i | \(0.365721\pi\) | |||||||
\(6\) | 2.49093 | 1.01692 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.07787 | −1.08819 | ||||||||
\(9\) | 1.81594 | 0.605315 | ||||||||
\(10\) | 2.07842 | 0.657254 | ||||||||
\(11\) | 4.13788 | 1.24762 | 0.623809 | − | 0.781576i | \(-0.285584\pi\) | ||||
0.623809 | + | 0.781576i | \(0.285584\pi\) | |||||||
\(12\) | −1.56170 | −0.450823 | ||||||||
\(13\) | 4.73726 | 1.31388 | 0.656940 | − | 0.753943i | \(-0.271850\pi\) | ||||
0.656940 | + | 0.753943i | \(0.271850\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.01841 | 1.03755 | ||||||||
\(16\) | −2.07032 | −0.517579 | ||||||||
\(17\) | −1.16889 | −0.283498 | −0.141749 | − | 0.989903i | \(-0.545273\pi\) | ||||
−0.141749 | + | 0.989903i | \(0.545273\pi\) | |||||||
\(18\) | 2.06121 | 0.485832 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −1.30307 | −0.291376 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.69676 | 1.00135 | ||||||||
\(23\) | −0.834902 | −0.174089 | −0.0870446 | − | 0.996204i | \(-0.527742\pi\) | ||||
−0.0870446 | + | 0.996204i | \(0.527742\pi\) | |||||||
\(24\) | −6.75447 | −1.37875 | ||||||||
\(25\) | −1.64705 | −0.329410 | ||||||||
\(26\) | 5.37709 | 1.05453 | ||||||||
\(27\) | −2.59844 | −0.500070 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.47567 | 0.645416 | 0.322708 | − | 0.946499i | \(-0.395407\pi\) | ||||
0.322708 | + | 0.946499i | \(0.395407\pi\) | |||||||
\(30\) | 4.56115 | 0.832748 | ||||||||
\(31\) | −7.88792 | −1.41671 | −0.708356 | − | 0.705856i | \(-0.750563\pi\) | ||||
−0.708356 | + | 0.705856i | \(0.750563\pi\) | |||||||
\(32\) | 3.80581 | 0.672778 | ||||||||
\(33\) | 9.08069 | 1.58075 | ||||||||
\(34\) | −1.32677 | −0.227539 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.29228 | −0.215381 | ||||||||
\(37\) | 9.51182 | 1.56373 | 0.781867 | − | 0.623446i | \(-0.214268\pi\) | ||||
0.781867 | + | 0.623446i | \(0.214268\pi\) | |||||||
\(38\) | −1.13506 | −0.184132 | ||||||||
\(39\) | 10.3961 | 1.66470 | ||||||||
\(40\) | −5.63591 | −0.891116 | ||||||||
\(41\) | 2.27013 | 0.354534 | 0.177267 | − | 0.984163i | \(-0.443274\pi\) | ||||
0.177267 | + | 0.984163i | \(0.443274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.77566 | 1.33828 | 0.669138 | − | 0.743138i | \(-0.266663\pi\) | ||||
0.669138 | + | 0.743138i | \(0.266663\pi\) | |||||||
\(44\) | −2.94465 | −0.443923 | ||||||||
\(45\) | 3.32519 | 0.495690 | ||||||||
\(46\) | −0.947667 | −0.139726 | ||||||||
\(47\) | −4.49711 | −0.655972 | −0.327986 | − | 0.944683i | \(-0.606370\pi\) | ||||
−0.327986 | + | 0.944683i | \(0.606370\pi\) | |||||||
\(48\) | −4.54336 | −0.655778 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.86951 | −0.264388 | ||||||||
\(51\) | −2.56517 | −0.359195 | ||||||||
\(52\) | −3.37119 | −0.467500 | ||||||||
\(53\) | −7.62095 | −1.04682 | −0.523409 | − | 0.852082i | \(-0.675340\pi\) | ||||
−0.523409 | + | 0.852082i | \(0.675340\pi\) | |||||||
\(54\) | −2.94939 | −0.401361 | ||||||||
\(55\) | 7.57690 | 1.02167 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.19453 | −0.290672 | ||||||||
\(58\) | 3.94511 | 0.518018 | ||||||||
\(59\) | −3.26159 | −0.424623 | −0.212312 | − | 0.977202i | \(-0.568099\pi\) | ||||
−0.212312 | + | 0.977202i | \(0.568099\pi\) | |||||||
\(60\) | −2.85963 | −0.369177 | ||||||||
\(61\) | −7.85276 | −1.00544 | −0.502722 | − | 0.864448i | \(-0.667668\pi\) | ||||
−0.502722 | + | 0.864448i | \(0.667668\pi\) | |||||||
\(62\) | −8.95328 | −1.13707 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.46046 | 1.05756 | ||||||||
\(65\) | 8.67443 | 1.07593 | ||||||||
\(66\) | 10.3072 | 1.26872 | ||||||||
\(67\) | −11.7522 | −1.43577 | −0.717883 | − | 0.696164i | \(-0.754889\pi\) | ||||
−0.717883 | + | 0.696164i | \(0.754889\pi\) | |||||||
\(68\) | 0.831823 | 0.100873 | ||||||||
\(69\) | −1.83221 | −0.220573 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.72597 | −1.03558 | −0.517791 | − | 0.855507i | \(-0.673246\pi\) | ||||
−0.517791 | + | 0.855507i | \(0.673246\pi\) | |||||||
\(72\) | −5.58925 | −0.658699 | ||||||||
\(73\) | −7.69908 | −0.901109 | −0.450555 | − | 0.892749i | \(-0.648774\pi\) | ||||
−0.450555 | + | 0.892749i | \(0.648774\pi\) | |||||||
\(74\) | 10.7965 | 1.25507 | ||||||||
\(75\) | −3.61450 | −0.417366 | ||||||||
\(76\) | 0.711632 | 0.0816298 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.8002 | 1.33611 | ||||||||
\(79\) | −6.90625 | −0.777014 | −0.388507 | − | 0.921446i | \(-0.627009\pi\) | ||||
−0.388507 | + | 0.921446i | \(0.627009\pi\) | |||||||
\(80\) | −3.79097 | −0.423843 | ||||||||
\(81\) | −11.1502 | −1.23891 | ||||||||
\(82\) | 2.57674 | 0.284553 | ||||||||
\(83\) | 15.0920 | 1.65656 | 0.828280 | − | 0.560315i | \(-0.189320\pi\) | ||||
0.828280 | + | 0.560315i | \(0.189320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.14037 | −0.232156 | ||||||||
\(86\) | 9.96093 | 1.07411 | ||||||||
\(87\) | 7.62745 | 0.817749 | ||||||||
\(88\) | −12.7359 | −1.35765 | ||||||||
\(89\) | −3.40801 | −0.361248 | −0.180624 | − | 0.983552i | \(-0.557812\pi\) | ||||
−0.180624 | + | 0.983552i | \(0.557812\pi\) | |||||||
\(90\) | 3.77430 | 0.397846 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.594143 | 0.0619437 | ||||||||
\(93\) | −17.3102 | −1.79499 | ||||||||
\(94\) | −5.10451 | −0.526490 | ||||||||
\(95\) | −1.83111 | −0.187868 | ||||||||
\(96\) | 8.35195 | 0.852417 | ||||||||
\(97\) | −3.04535 | −0.309209 | −0.154604 | − | 0.987976i | \(-0.549410\pi\) | ||||
−0.154604 | + | 0.987976i | \(0.549410\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.51417 | 0.755202 | ||||||||
\(100\) | 1.17209 | 0.117209 | ||||||||
\(101\) | −11.9906 | −1.19311 | −0.596557 | − | 0.802571i | \(-0.703465\pi\) | ||||
−0.596557 | + | 0.802571i | \(0.703465\pi\) | |||||||
\(102\) | −2.91163 | −0.288294 | ||||||||
\(103\) | 14.4675 | 1.42553 | 0.712764 | − | 0.701404i | \(-0.247443\pi\) | ||||
0.712764 | + | 0.701404i | \(0.247443\pi\) | |||||||
\(104\) | −14.5807 | −1.42976 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.65025 | −0.840187 | ||||||||
\(107\) | −4.64077 | −0.448640 | −0.224320 | − | 0.974516i | \(-0.572016\pi\) | ||||
−0.224320 | + | 0.974516i | \(0.572016\pi\) | |||||||
\(108\) | 1.84913 | 0.177933 | ||||||||
\(109\) | 7.76669 | 0.743914 | 0.371957 | − | 0.928250i | \(-0.378687\pi\) | ||||
0.371957 | + | 0.928250i | \(0.378687\pi\) | |||||||
\(110\) | 8.60026 | 0.820003 | ||||||||
\(111\) | 20.8739 | 1.98127 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.3900 | 1.54184 | 0.770921 | − | 0.636931i | \(-0.219796\pi\) | ||||
0.770921 | + | 0.636931i | \(0.219796\pi\) | |||||||
\(114\) | −2.49093 | −0.233297 | ||||||||
\(115\) | −1.52879 | −0.142561 | ||||||||
\(116\) | −2.47340 | −0.229649 | ||||||||
\(117\) | 8.60261 | 0.795312 | ||||||||
\(118\) | −3.70211 | −0.340807 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.3682 | −1.12905 | ||||||||
\(121\) | 6.12208 | 0.556553 | ||||||||
\(122\) | −8.91338 | −0.806980 | ||||||||
\(123\) | 4.98185 | 0.449198 | ||||||||
\(124\) | 5.61330 | 0.504089 | ||||||||
\(125\) | −12.1715 | −1.08865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.55496 | −0.847866 | −0.423933 | − | 0.905694i | \(-0.639351\pi\) | ||||
−0.423933 | + | 0.905694i | \(0.639351\pi\) | |||||||
\(128\) | 1.99154 | 0.176029 | ||||||||
\(129\) | 19.2584 | 1.69561 | ||||||||
\(130\) | 9.84603 | 0.863554 | ||||||||
\(131\) | −20.1432 | −1.75992 | −0.879961 | − | 0.475046i | \(-0.842431\pi\) | ||||
−0.879961 | + | 0.475046i | \(0.842431\pi\) | |||||||
\(132\) | −6.46211 | −0.562455 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.3395 | −1.15236 | ||||||||
\(135\) | −4.75802 | −0.409505 | ||||||||
\(136\) | 3.59771 | 0.308501 | ||||||||
\(137\) | −2.57311 | −0.219835 | −0.109918 | − | 0.993941i | \(-0.535059\pi\) | ||||
−0.109918 | + | 0.993941i | \(0.535059\pi\) | |||||||
\(138\) | −2.07968 | −0.177034 | ||||||||
\(139\) | 0.592800 | 0.0502806 | 0.0251403 | − | 0.999684i | \(-0.491997\pi\) | ||||
0.0251403 | + | 0.999684i | \(0.491997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.86903 | −0.831123 | ||||||||
\(142\) | −9.90453 | −0.831170 | ||||||||
\(143\) | 19.6022 | 1.63922 | ||||||||
\(144\) | −3.75958 | −0.313298 | ||||||||
\(145\) | 6.36432 | 0.528528 | ||||||||
\(146\) | −8.73894 | −0.723240 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.76892 | −0.556402 | ||||||||
\(149\) | 14.5460 | 1.19165 | 0.595827 | − | 0.803113i | \(-0.296824\pi\) | ||||
0.595827 | + | 0.803113i | \(0.296824\pi\) | |||||||
\(150\) | −4.10268 | −0.334982 | ||||||||
\(151\) | 23.5597 | 1.91726 | 0.958632 | − | 0.284649i | \(-0.0918769\pi\) | ||||
0.958632 | + | 0.284649i | \(0.0918769\pi\) | |||||||
\(152\) | 3.07787 | 0.249648 | ||||||||
\(153\) | −2.12265 | −0.171606 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.4436 | −1.16014 | ||||||||
\(156\) | −7.39816 | −0.592327 | ||||||||
\(157\) | −0.391072 | −0.0312109 | −0.0156055 | − | 0.999878i | \(-0.504968\pi\) | ||||
−0.0156055 | + | 0.999878i | \(0.504968\pi\) | |||||||
\(158\) | −7.83903 | −0.623640 | ||||||||
\(159\) | −16.7244 | −1.32633 | ||||||||
\(160\) | 6.96884 | 0.550935 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.6562 | −0.994361 | ||||||||
\(163\) | −4.73291 | −0.370710 | −0.185355 | − | 0.982672i | \(-0.559343\pi\) | ||||
−0.185355 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(164\) | −1.61549 | −0.126149 | ||||||||
\(165\) | 16.6277 | 1.29447 | ||||||||
\(166\) | 17.1303 | 1.32957 | ||||||||
\(167\) | −24.4555 | −1.89242 | −0.946212 | − | 0.323547i | \(-0.895125\pi\) | ||||
−0.946212 | + | 0.323547i | \(0.895125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.44167 | 0.726283 | ||||||||
\(170\) | −2.42945 | −0.186331 | ||||||||
\(171\) | −1.81594 | −0.138869 | ||||||||
\(172\) | −6.24505 | −0.476180 | ||||||||
\(173\) | −9.56007 | −0.726839 | −0.363419 | − | 0.931626i | \(-0.618391\pi\) | ||||
−0.363419 | + | 0.931626i | \(0.618391\pi\) | |||||||
\(174\) | 8.65764 | 0.656334 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.56672 | −0.645741 | ||||||||
\(177\) | −7.15765 | −0.538002 | ||||||||
\(178\) | −3.86831 | −0.289942 | ||||||||
\(179\) | 4.05719 | 0.303249 | 0.151624 | − | 0.988438i | \(-0.451550\pi\) | ||||
0.151624 | + | 0.988438i | \(0.451550\pi\) | |||||||
\(180\) | −2.36631 | −0.176374 | ||||||||
\(181\) | 7.19110 | 0.534510 | 0.267255 | − | 0.963626i | \(-0.413883\pi\) | ||||
0.267255 | + | 0.963626i | \(0.413883\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.2331 | −1.27391 | ||||||||
\(184\) | 2.56972 | 0.189442 | ||||||||
\(185\) | 17.4172 | 1.28053 | ||||||||
\(186\) | −19.6482 | −1.44068 | ||||||||
\(187\) | −4.83675 | −0.353698 | ||||||||
\(188\) | 3.20029 | 0.233405 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.07842 | −0.150784 | ||||||||
\(191\) | −4.60668 | −0.333328 | −0.166664 | − | 0.986014i | \(-0.553299\pi\) | ||||
−0.166664 | + | 0.986014i | \(0.553299\pi\) | |||||||
\(192\) | 18.5667 | 1.33994 | ||||||||
\(193\) | −18.7579 | −1.35022 | −0.675111 | − | 0.737717i | \(-0.735904\pi\) | ||||
−0.675111 | + | 0.737717i | \(0.735904\pi\) | |||||||
\(194\) | −3.45667 | −0.248174 | ||||||||
\(195\) | 19.0363 | 1.36322 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.23257 | 0.159064 | 0.0795321 | − | 0.996832i | \(-0.474657\pi\) | ||||
0.0795321 | + | 0.996832i | \(0.474657\pi\) | |||||||
\(198\) | 8.52905 | 0.606134 | ||||||||
\(199\) | 6.30872 | 0.447213 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(200\) | 5.06941 | 0.358462 | ||||||||
\(201\) | −25.7906 | −1.81913 | ||||||||
\(202\) | −13.6101 | −0.957606 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.82546 | 0.127808 | ||||||||
\(205\) | 4.15684 | 0.290326 | ||||||||
\(206\) | 16.4215 | 1.14414 | ||||||||
\(207\) | −1.51614 | −0.105379 | ||||||||
\(208\) | −9.80763 | −0.680037 | ||||||||
\(209\) | −4.13788 | −0.286223 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2973 | 1.32848 | 0.664241 | − | 0.747519i | \(-0.268755\pi\) | ||||
0.664241 | + | 0.747519i | \(0.268755\pi\) | |||||||
\(212\) | 5.42331 | 0.372474 | ||||||||
\(213\) | −19.1494 | −1.31209 | ||||||||
\(214\) | −5.26756 | −0.360083 | ||||||||
\(215\) | 16.0692 | 1.09591 | ||||||||
\(216\) | 7.99767 | 0.544172 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.81569 | 0.597074 | ||||||||
\(219\) | −16.8958 | −1.14171 | ||||||||
\(220\) | −5.39197 | −0.363526 | ||||||||
\(221\) | −5.53736 | −0.372483 | ||||||||
\(222\) | 23.6932 | 1.59019 | ||||||||
\(223\) | −1.58264 | −0.105981 | −0.0529906 | − | 0.998595i | \(-0.516875\pi\) | ||||
−0.0529906 | + | 0.998595i | \(0.516875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.99095 | −0.199397 | ||||||||
\(226\) | 18.6037 | 1.23750 | ||||||||
\(227\) | −2.42883 | −0.161207 | −0.0806036 | − | 0.996746i | \(-0.525685\pi\) | ||||
−0.0806036 | + | 0.996746i | \(0.525685\pi\) | |||||||
\(228\) | 1.56170 | 0.103426 | ||||||||
\(229\) | −2.80764 | −0.185534 | −0.0927669 | − | 0.995688i | \(-0.529571\pi\) | ||||
−0.0927669 | + | 0.995688i | \(0.529571\pi\) | |||||||
\(230\) | −1.73528 | −0.114421 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.6977 | −0.702337 | ||||||||
\(233\) | 22.1168 | 1.44892 | 0.724461 | − | 0.689316i | \(-0.242089\pi\) | ||||
0.724461 | + | 0.689316i | \(0.242089\pi\) | |||||||
\(234\) | 9.76450 | 0.638326 | ||||||||
\(235\) | −8.23469 | −0.537172 | ||||||||
\(236\) | 2.32105 | 0.151088 | ||||||||
\(237\) | −15.1559 | −0.984485 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.0161 | 0.841944 | 0.420972 | − | 0.907074i | \(-0.361689\pi\) | ||||
0.420972 | + | 0.907074i | \(0.361689\pi\) | |||||||
\(240\) | −8.31938 | −0.537013 | ||||||||
\(241\) | 11.4453 | 0.737254 | 0.368627 | − | 0.929577i | \(-0.379828\pi\) | ||||
0.368627 | + | 0.929577i | \(0.379828\pi\) | |||||||
\(242\) | 6.94895 | 0.446695 | ||||||||
\(243\) | −16.6740 | −1.06964 | ||||||||
\(244\) | 5.58828 | 0.357753 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.65471 | 0.360531 | ||||||||
\(247\) | −4.73726 | −0.301425 | ||||||||
\(248\) | 24.2780 | 1.54165 | ||||||||
\(249\) | 33.1197 | 2.09888 | ||||||||
\(250\) | −13.8154 | −0.873761 | ||||||||
\(251\) | 2.29536 | 0.144882 | 0.0724411 | − | 0.997373i | \(-0.476921\pi\) | ||||
0.0724411 | + | 0.997373i | \(0.476921\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.45473 | −0.217197 | ||||||||
\(254\) | −10.8455 | −0.680506 | ||||||||
\(255\) | −4.69710 | −0.294144 | ||||||||
\(256\) | −14.6604 | −0.916275 | ||||||||
\(257\) | 12.9349 | 0.806857 | 0.403428 | − | 0.915011i | \(-0.367818\pi\) | ||||
0.403428 | + | 0.915011i | \(0.367818\pi\) | |||||||
\(258\) | 21.8595 | 1.36091 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.17301 | −0.382834 | ||||||||
\(261\) | 6.31163 | 0.390680 | ||||||||
\(262\) | −22.8638 | −1.41253 | ||||||||
\(263\) | 18.8105 | 1.15990 | 0.579951 | − | 0.814651i | \(-0.303072\pi\) | ||||
0.579951 | + | 0.814651i | \(0.303072\pi\) | |||||||
\(264\) | −27.9492 | −1.72016 | ||||||||
\(265\) | −13.9548 | −0.857234 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.47897 | −0.457705 | ||||||||
\(268\) | 8.36328 | 0.510868 | ||||||||
\(269\) | 3.19124 | 0.194573 | 0.0972866 | − | 0.995256i | \(-0.468984\pi\) | ||||
0.0972866 | + | 0.995256i | \(0.468984\pi\) | |||||||
\(270\) | −5.40065 | −0.328673 | ||||||||
\(271\) | 0.534528 | 0.0324703 | 0.0162351 | − | 0.999868i | \(-0.494832\pi\) | ||||
0.0162351 | + | 0.999868i | \(0.494832\pi\) | |||||||
\(272\) | 2.41998 | 0.146733 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.92064 | −0.176442 | ||||||||
\(275\) | −6.81531 | −0.410978 | ||||||||
\(276\) | 1.30386 | 0.0784833 | ||||||||
\(277\) | 26.8067 | 1.61066 | 0.805328 | − | 0.592829i | \(-0.201989\pi\) | ||||
0.805328 | + | 0.592829i | \(0.201989\pi\) | |||||||
\(278\) | 0.672865 | 0.0403557 | ||||||||
\(279\) | −14.3240 | −0.857557 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.86099 | 0.111017 | 0.0555087 | − | 0.998458i | \(-0.482322\pi\) | ||||
0.0555087 | + | 0.998458i | \(0.482322\pi\) | |||||||
\(282\) | −11.2020 | −0.667068 | ||||||||
\(283\) | −12.4410 | −0.739543 | −0.369771 | − | 0.929123i | \(-0.620564\pi\) | ||||
−0.369771 | + | 0.929123i | \(0.620564\pi\) | |||||||
\(284\) | 6.20968 | 0.368477 | ||||||||
\(285\) | −4.01841 | −0.238030 | ||||||||
\(286\) | 22.2498 | 1.31566 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.91114 | 0.407243 | ||||||||
\(289\) | −15.6337 | −0.919629 | ||||||||
\(290\) | 7.22391 | 0.424202 | ||||||||
\(291\) | −6.68311 | −0.391771 | ||||||||
\(292\) | 5.47891 | 0.320629 | ||||||||
\(293\) | −4.08101 | −0.238415 | −0.119208 | − | 0.992869i | \(-0.538035\pi\) | ||||
−0.119208 | + | 0.992869i | \(0.538035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.97232 | −0.347722 | ||||||||
\(296\) | −29.2762 | −1.70164 | ||||||||
\(297\) | −10.7520 | −0.623897 | ||||||||
\(298\) | 16.5106 | 0.956434 | ||||||||
\(299\) | −3.95515 | −0.228732 | ||||||||
\(300\) | 2.57219 | 0.148506 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 26.7418 | 1.53882 | ||||||||
\(303\) | −26.3138 | −1.51169 | ||||||||
\(304\) | 2.07032 | 0.118741 | ||||||||
\(305\) | −14.3792 | −0.823353 | ||||||||
\(306\) | −2.40934 | −0.137733 | ||||||||
\(307\) | 13.6881 | 0.781223 | 0.390612 | − | 0.920556i | \(-0.372264\pi\) | ||||
0.390612 | + | 0.920556i | \(0.372264\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.7494 | 1.80616 | ||||||||
\(310\) | −16.3944 | −0.931140 | ||||||||
\(311\) | −13.0057 | −0.737488 | −0.368744 | − | 0.929531i | \(-0.620212\pi\) | ||||
−0.368744 | + | 0.929531i | \(0.620212\pi\) | |||||||
\(312\) | −31.9977 | −1.81151 | ||||||||
\(313\) | 1.65165 | 0.0933571 | 0.0466785 | − | 0.998910i | \(-0.485136\pi\) | ||||
0.0466785 | + | 0.998910i | \(0.485136\pi\) | |||||||
\(314\) | −0.443891 | −0.0250502 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.91471 | 0.276474 | ||||||||
\(317\) | 35.0878 | 1.97073 | 0.985363 | − | 0.170471i | \(-0.0545290\pi\) | ||||
0.985363 | + | 0.170471i | \(0.0545290\pi\) | |||||||
\(318\) | −18.9832 | −1.06453 | ||||||||
\(319\) | 14.3819 | 0.805233 | ||||||||
\(320\) | 15.4920 | 0.866029 | ||||||||
\(321\) | −10.1843 | −0.568431 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.16889 | 0.0650390 | ||||||||
\(324\) | 7.93483 | 0.440824 | ||||||||
\(325\) | −7.80252 | −0.432806 | ||||||||
\(326\) | −5.37215 | −0.297536 | ||||||||
\(327\) | 17.0442 | 0.942547 | ||||||||
\(328\) | −6.98716 | −0.385801 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 18.8735 | 1.03895 | ||||||||
\(331\) | −16.5046 | −0.907174 | −0.453587 | − | 0.891212i | \(-0.649856\pi\) | ||||
−0.453587 | + | 0.891212i | \(0.649856\pi\) | |||||||
\(332\) | −10.7399 | −0.589430 | ||||||||
\(333\) | 17.2729 | 0.946551 | ||||||||
\(334\) | −27.7585 | −1.51888 | ||||||||
\(335\) | −21.5196 | −1.17574 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0546 | −0.547710 | −0.273855 | − | 0.961771i | \(-0.588299\pi\) | ||||
−0.273855 | + | 0.961771i | \(0.588299\pi\) | |||||||
\(338\) | 10.7169 | 0.582922 | ||||||||
\(339\) | 35.9683 | 1.95353 | ||||||||
\(340\) | 1.52316 | 0.0826047 | ||||||||
\(341\) | −32.6393 | −1.76752 | ||||||||
\(342\) | −2.06121 | −0.111458 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −27.0104 | −1.45630 | ||||||||
\(345\) | −3.35498 | −0.180626 | ||||||||
\(346\) | −10.8513 | −0.583368 | ||||||||
\(347\) | −27.7296 | −1.48860 | −0.744301 | − | 0.667845i | \(-0.767217\pi\) | ||||
−0.744301 | + | 0.667845i | \(0.767217\pi\) | |||||||
\(348\) | −5.42794 | −0.290968 | ||||||||
\(349\) | −21.4865 | −1.15014 | −0.575072 | − | 0.818103i | \(-0.695026\pi\) | ||||
−0.575072 | + | 0.818103i | \(0.695026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3095 | −0.657032 | ||||||||
\(352\) | 15.7480 | 0.839371 | ||||||||
\(353\) | 31.2690 | 1.66428 | 0.832140 | − | 0.554566i | \(-0.187116\pi\) | ||||
0.832140 | + | 0.554566i | \(0.187116\pi\) | |||||||
\(354\) | −8.12438 | −0.431806 | ||||||||
\(355\) | −15.9782 | −0.848034 | ||||||||
\(356\) | 2.42525 | 0.128538 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.60517 | 0.243391 | ||||||||
\(359\) | −1.16328 | −0.0613957 | −0.0306979 | − | 0.999529i | \(-0.509773\pi\) | ||||
−0.0306979 | + | 0.999529i | \(0.509773\pi\) | |||||||
\(360\) | −10.2345 | −0.539406 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 8.16235 | 0.429004 | ||||||||
\(363\) | 13.4351 | 0.705158 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0978 | −0.737914 | ||||||||
\(366\) | −19.5606 | −1.02245 | ||||||||
\(367\) | 10.6069 | 0.553675 | 0.276838 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276838 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(368\) | 1.72851 | 0.0901049 | ||||||||
\(369\) | 4.12242 | 0.214605 | ||||||||
\(370\) | 19.7696 | 1.02777 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.3185 | 0.638686 | ||||||||
\(373\) | 0.424629 | 0.0219864 | 0.0109932 | − | 0.999940i | \(-0.496501\pi\) | ||||
0.0109932 | + | 0.999940i | \(0.496501\pi\) | |||||||
\(374\) | −5.49001 | −0.283882 | ||||||||
\(375\) | −26.7106 | −1.37933 | ||||||||
\(376\) | 13.8415 | 0.713823 | ||||||||
\(377\) | 16.4652 | 0.848000 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.337918 | −0.0173577 | −0.00867885 | − | 0.999962i | \(-0.502763\pi\) | ||||
−0.00867885 | + | 0.999962i | \(0.502763\pi\) | |||||||
\(380\) | 1.30307 | 0.0668463 | ||||||||
\(381\) | −20.9686 | −1.07425 | ||||||||
\(382\) | −5.22887 | −0.267532 | ||||||||
\(383\) | 27.9380 | 1.42756 | 0.713782 | − | 0.700368i | \(-0.246981\pi\) | ||||
0.713782 | + | 0.700368i | \(0.246981\pi\) | |||||||
\(384\) | 4.37049 | 0.223031 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.2914 | −1.08370 | ||||||||
\(387\) | 15.9361 | 0.810079 | ||||||||
\(388\) | 2.16717 | 0.110021 | ||||||||
\(389\) | 30.8591 | 1.56462 | 0.782308 | − | 0.622892i | \(-0.214042\pi\) | ||||
0.782308 | + | 0.622892i | \(0.214042\pi\) | |||||||
\(390\) | 21.6074 | 1.09413 | ||||||||
\(391\) | 0.975912 | 0.0493540 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.2048 | −2.22984 | ||||||||
\(394\) | 2.53411 | 0.127667 | ||||||||
\(395\) | −12.6461 | −0.636293 | ||||||||
\(396\) | −5.34732 | −0.268713 | ||||||||
\(397\) | −28.7758 | −1.44422 | −0.722109 | − | 0.691779i | \(-0.756827\pi\) | ||||
−0.722109 | + | 0.691779i | \(0.756827\pi\) | |||||||
\(398\) | 7.16079 | 0.358938 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.40991 | 0.170496 | ||||||||
\(401\) | 12.4489 | 0.621668 | 0.310834 | − | 0.950464i | \(-0.399392\pi\) | ||||
0.310834 | + | 0.950464i | \(0.399392\pi\) | |||||||
\(402\) | −29.2740 | −1.46005 | ||||||||
\(403\) | −37.3671 | −1.86139 | ||||||||
\(404\) | 8.53293 | 0.424529 | ||||||||
\(405\) | −20.4172 | −1.01454 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.3588 | 1.95094 | ||||||||
\(408\) | 7.89526 | 0.390874 | ||||||||
\(409\) | −17.8715 | −0.883689 | −0.441845 | − | 0.897092i | \(-0.645676\pi\) | ||||
−0.441845 | + | 0.897092i | \(0.645676\pi\) | |||||||
\(410\) | 4.71828 | 0.233019 | ||||||||
\(411\) | −5.64675 | −0.278534 | ||||||||
\(412\) | −10.2956 | −0.507225 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.72091 | −0.0845781 | ||||||||
\(415\) | 27.6350 | 1.35655 | ||||||||
\(416\) | 18.0291 | 0.883950 | ||||||||
\(417\) | 1.30091 | 0.0637060 | ||||||||
\(418\) | −4.69676 | −0.229726 | ||||||||
\(419\) | −20.2060 | −0.987126 | −0.493563 | − | 0.869710i | \(-0.664306\pi\) | ||||
−0.493563 | + | 0.869710i | \(0.664306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.33097 | 0.357290 | 0.178645 | − | 0.983914i | \(-0.442829\pi\) | ||||
0.178645 | + | 0.983914i | \(0.442829\pi\) | |||||||
\(422\) | 21.9037 | 1.06625 | ||||||||
\(423\) | −8.16651 | −0.397069 | ||||||||
\(424\) | 23.4563 | 1.13914 | ||||||||
\(425\) | 1.92523 | 0.0933873 | ||||||||
\(426\) | −21.7358 | −1.05310 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.30252 | 0.159633 | ||||||||
\(429\) | 43.0176 | 2.07691 | ||||||||
\(430\) | 18.2395 | 0.879588 | ||||||||
\(431\) | −7.60358 | −0.366252 | −0.183126 | − | 0.983089i | \(-0.558622\pi\) | ||||
−0.183126 | + | 0.983089i | \(0.558622\pi\) | |||||||
\(432\) | 5.37959 | 0.258826 | ||||||||
\(433\) | 25.0990 | 1.20618 | 0.603092 | − | 0.797672i | \(-0.293935\pi\) | ||||
0.603092 | + | 0.797672i | \(0.293935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.9667 | 0.669651 | ||||||||
\(436\) | −5.52703 | −0.264697 | ||||||||
\(437\) | 0.834902 | 0.0399388 | ||||||||
\(438\) | −19.1778 | −0.916352 | ||||||||
\(439\) | 35.8632 | 1.71166 | 0.855829 | − | 0.517259i | \(-0.173047\pi\) | ||||
0.855829 | + | 0.517259i | \(0.173047\pi\) | |||||||
\(440\) | −23.3207 | −1.11177 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.28525 | −0.298959 | ||||||||
\(443\) | 29.1136 | 1.38323 | 0.691615 | − | 0.722266i | \(-0.256899\pi\) | ||||
0.691615 | + | 0.722266i | \(0.256899\pi\) | |||||||
\(444\) | −14.8546 | −0.704967 | ||||||||
\(445\) | −6.24043 | −0.295825 | ||||||||
\(446\) | −1.79639 | −0.0850617 | ||||||||
\(447\) | 31.9215 | 1.50984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.10596 | −0.382544 | −0.191272 | − | 0.981537i | \(-0.561261\pi\) | ||||
−0.191272 | + | 0.981537i | \(0.561261\pi\) | |||||||
\(450\) | −3.39492 | −0.160038 | ||||||||
\(451\) | 9.39352 | 0.442323 | ||||||||
\(452\) | −11.6637 | −0.548612 | ||||||||
\(453\) | 51.7024 | 2.42919 | ||||||||
\(454\) | −2.75688 | −0.129387 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.75447 | 0.316307 | ||||||||
\(457\) | −12.2443 | −0.572764 | −0.286382 | − | 0.958115i | \(-0.592453\pi\) | ||||
−0.286382 | + | 0.958115i | \(0.592453\pi\) | |||||||
\(458\) | −3.18684 | −0.148911 | ||||||||
\(459\) | 3.03730 | 0.141769 | ||||||||
\(460\) | 1.08794 | 0.0507254 | ||||||||
\(461\) | 35.0498 | 1.63243 | 0.816216 | − | 0.577747i | \(-0.196068\pi\) | ||||
0.816216 | + | 0.577747i | \(0.196068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.8700 | 1.34170 | 0.670852 | − | 0.741591i | \(-0.265929\pi\) | ||||
0.670852 | + | 0.741591i | \(0.265929\pi\) | |||||||
\(464\) | −7.19574 | −0.334054 | ||||||||
\(465\) | −31.6969 | −1.46991 | ||||||||
\(466\) | 25.1040 | 1.16292 | ||||||||
\(467\) | 34.8463 | 1.61249 | 0.806247 | − | 0.591580i | \(-0.201496\pi\) | ||||
0.806247 | + | 0.591580i | \(0.201496\pi\) | |||||||
\(468\) | −6.12189 | −0.282985 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.34689 | −0.431140 | ||||||||
\(471\) | −0.858217 | −0.0395446 | ||||||||
\(472\) | 10.0388 | 0.462072 | ||||||||
\(473\) | 36.3127 | 1.66966 | ||||||||
\(474\) | −17.2030 | −0.790158 | ||||||||
\(475\) | 1.64705 | 0.0755719 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.8392 | −0.633654 | ||||||||
\(478\) | 14.7741 | 0.675753 | ||||||||
\(479\) | 18.8948 | 0.863326 | 0.431663 | − | 0.902035i | \(-0.357927\pi\) | ||||
0.431663 | + | 0.902035i | \(0.357927\pi\) | |||||||
\(480\) | 15.2933 | 0.698040 | ||||||||
\(481\) | 45.0600 | 2.05456 | ||||||||
\(482\) | 12.9911 | 0.591728 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.35667 | −0.198030 | ||||||||
\(485\) | −5.57636 | −0.253210 | ||||||||
\(486\) | −18.9261 | −0.858505 | ||||||||
\(487\) | −0.314082 | −0.0142324 | −0.00711620 | − | 0.999975i | \(-0.502265\pi\) | ||||
−0.00711620 | + | 0.999975i | \(0.502265\pi\) | |||||||
\(488\) | 24.1698 | 1.09412 | ||||||||
\(489\) | −10.3865 | −0.469693 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.2050 | 1.67904 | 0.839519 | − | 0.543330i | \(-0.182837\pi\) | ||||
0.839519 | + | 0.543330i | \(0.182837\pi\) | |||||||
\(492\) | −3.54525 | −0.159832 | ||||||||
\(493\) | −4.06269 | −0.182974 | ||||||||
\(494\) | −5.37709 | −0.241927 | ||||||||
\(495\) | 13.7592 | 0.618432 | ||||||||
\(496\) | 16.3305 | 0.733260 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 37.5930 | 1.68458 | ||||||||
\(499\) | −30.3987 | −1.36083 | −0.680416 | − | 0.732826i | \(-0.738201\pi\) | ||||
−0.680416 | + | 0.732826i | \(0.738201\pi\) | |||||||
\(500\) | 8.66160 | 0.387358 | ||||||||
\(501\) | −53.6683 | −2.39772 | ||||||||
\(502\) | 2.60538 | 0.116284 | ||||||||
\(503\) | 12.1197 | 0.540390 | 0.270195 | − | 0.962806i | \(-0.412912\pi\) | ||||
0.270195 | + | 0.962806i | \(0.412912\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.9561 | −0.977036 | ||||||||
\(506\) | −3.92133 | −0.174325 | ||||||||
\(507\) | 20.7200 | 0.920207 | ||||||||
\(508\) | 6.79962 | 0.301684 | ||||||||
\(509\) | 3.72098 | 0.164929 | 0.0824647 | − | 0.996594i | \(-0.473721\pi\) | ||||
0.0824647 | + | 0.996594i | \(0.473721\pi\) | |||||||
\(510\) | −5.33150 | −0.236083 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.6236 | −0.911441 | ||||||||
\(513\) | 2.59844 | 0.114724 | ||||||||
\(514\) | 14.6819 | 0.647592 | ||||||||
\(515\) | 26.4916 | 1.16736 | ||||||||
\(516\) | −13.7049 | −0.603325 | ||||||||
\(517\) | −18.6085 | −0.818402 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.9798 | −0.920912 | ||||||||
\(520\) | −26.6988 | −1.17082 | ||||||||
\(521\) | −8.36054 | −0.366282 | −0.183141 | − | 0.983087i | \(-0.558626\pi\) | ||||
−0.183141 | + | 0.983087i | \(0.558626\pi\) | |||||||
\(522\) | 7.16410 | 0.313564 | ||||||||
\(523\) | −13.5948 | −0.594459 | −0.297229 | − | 0.954806i | \(-0.596063\pi\) | ||||
−0.297229 | + | 0.954806i | \(0.596063\pi\) | |||||||
\(524\) | 14.3346 | 0.626209 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.3511 | 0.930950 | ||||||||
\(527\) | 9.22014 | 0.401636 | ||||||||
\(528\) | −18.7999 | −0.818161 | ||||||||
\(529\) | −22.3029 | −0.969693 | ||||||||
\(530\) | −15.8395 | −0.688025 | ||||||||
\(531\) | −5.92287 | −0.257031 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7542 | 0.465816 | ||||||||
\(534\) | −8.48910 | −0.367359 | ||||||||
\(535\) | −8.49774 | −0.367389 | ||||||||
\(536\) | 36.1719 | 1.56239 | ||||||||
\(537\) | 8.90361 | 0.384219 | ||||||||
\(538\) | 3.62226 | 0.156167 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.38596 | 0.145708 | ||||||||
\(541\) | −17.8176 | −0.766038 | −0.383019 | − | 0.923740i | \(-0.625116\pi\) | ||||
−0.383019 | + | 0.923740i | \(0.625116\pi\) | |||||||
\(542\) | 0.606723 | 0.0260610 | ||||||||
\(543\) | 15.7811 | 0.677230 | ||||||||
\(544\) | −4.44859 | −0.190732 | ||||||||
\(545\) | 14.2216 | 0.609188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.1622 | −0.947587 | −0.473793 | − | 0.880636i | \(-0.657116\pi\) | ||||
−0.473793 | + | 0.880636i | \(0.657116\pi\) | |||||||
\(548\) | 1.83111 | 0.0782210 | ||||||||
\(549\) | −14.2602 | −0.608610 | ||||||||
\(550\) | −7.73580 | −0.329856 | ||||||||
\(551\) | −3.47567 | −0.148069 | ||||||||
\(552\) | 5.63932 | 0.240026 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.4273 | 1.29273 | ||||||||
\(555\) | 38.2224 | 1.62245 | ||||||||
\(556\) | −0.421855 | −0.0178906 | ||||||||
\(557\) | 20.2402 | 0.857606 | 0.428803 | − | 0.903398i | \(-0.358935\pi\) | ||||
0.428803 | + | 0.903398i | \(0.358935\pi\) | |||||||
\(558\) | −16.2587 | −0.688284 | ||||||||
\(559\) | 41.5726 | 1.75834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6144 | −0.448139 | ||||||||
\(562\) | 2.11234 | 0.0891037 | ||||||||
\(563\) | −37.3471 | −1.57399 | −0.786995 | − | 0.616959i | \(-0.788364\pi\) | ||||
−0.786995 | + | 0.616959i | \(0.788364\pi\) | |||||||
\(564\) | 7.02312 | 0.295727 | ||||||||
\(565\) | 30.0118 | 1.26261 | ||||||||
\(566\) | −14.1214 | −0.593565 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.8574 | 1.12691 | ||||||||
\(569\) | 5.01882 | 0.210400 | 0.105200 | − | 0.994451i | \(-0.466452\pi\) | ||||
0.105200 | + | 0.994451i | \(0.466452\pi\) | |||||||
\(570\) | −4.56115 | −0.191045 | ||||||||
\(571\) | −11.1874 | −0.468177 | −0.234089 | − | 0.972215i | \(-0.575211\pi\) | ||||
−0.234089 | + | 0.972215i | \(0.575211\pi\) | |||||||
\(572\) | −13.9496 | −0.583262 | ||||||||
\(573\) | −10.1095 | −0.422329 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.37513 | 0.0573467 | ||||||||
\(576\) | 15.3637 | 0.640156 | ||||||||
\(577\) | 18.9610 | 0.789356 | 0.394678 | − | 0.918819i | \(-0.370856\pi\) | ||||
0.394678 | + | 0.918819i | \(0.370856\pi\) | |||||||
\(578\) | −17.7452 | −0.738104 | ||||||||
\(579\) | −41.1646 | −1.71074 | ||||||||
\(580\) | −4.52906 | −0.188059 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.58575 | −0.314439 | ||||||||
\(583\) | −31.5346 | −1.30603 | ||||||||
\(584\) | 23.6968 | 0.980580 | ||||||||
\(585\) | 15.7523 | 0.651277 | ||||||||
\(586\) | −4.63221 | −0.191355 | ||||||||
\(587\) | −35.2670 | −1.45562 | −0.727812 | − | 0.685777i | \(-0.759463\pi\) | ||||
−0.727812 | + | 0.685777i | \(0.759463\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.88792 | 0.325016 | ||||||||
\(590\) | −6.77896 | −0.279085 | ||||||||
\(591\) | 4.89944 | 0.201536 | ||||||||
\(592\) | −19.6925 | −0.809355 | ||||||||
\(593\) | −16.0376 | −0.658585 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(594\) | −12.2042 | −0.500746 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.3514 | −0.424010 | ||||||||
\(597\) | 13.8446 | 0.566624 | ||||||||
\(598\) | −4.48935 | −0.183583 | ||||||||
\(599\) | 4.77170 | 0.194966 | 0.0974831 | − | 0.995237i | \(-0.468921\pi\) | ||||
0.0974831 | + | 0.995237i | \(0.468921\pi\) | |||||||
\(600\) | 11.1250 | 0.454175 | ||||||||
\(601\) | −3.18521 | −0.129928 | −0.0649638 | − | 0.997888i | \(-0.520693\pi\) | ||||
−0.0649638 | + | 0.997888i | \(0.520693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.3414 | −0.869090 | ||||||||
\(604\) | −16.7659 | −0.682193 | ||||||||
\(605\) | 11.2102 | 0.455759 | ||||||||
\(606\) | −29.8678 | −1.21330 | ||||||||
\(607\) | −32.6945 | −1.32703 | −0.663514 | − | 0.748164i | \(-0.730936\pi\) | ||||
−0.663514 | + | 0.748164i | \(0.730936\pi\) | |||||||
\(608\) | −3.80581 | −0.154346 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.3213 | −0.660832 | ||||||||
\(611\) | −21.3040 | −0.861868 | ||||||||
\(612\) | 1.51054 | 0.0610601 | ||||||||
\(613\) | −8.69213 | −0.351072 | −0.175536 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175536 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(614\) | 15.5369 | 0.627018 | ||||||||
\(615\) | 9.12230 | 0.367846 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.5546 | 1.35086 | 0.675429 | − | 0.737425i | \(-0.263959\pi\) | ||||
0.675429 | + | 0.737425i | \(0.263959\pi\) | |||||||
\(618\) | 36.0375 | 1.44964 | ||||||||
\(619\) | −26.0101 | −1.04544 | −0.522718 | − | 0.852506i | \(-0.675082\pi\) | ||||
−0.522718 | + | 0.852506i | \(0.675082\pi\) | |||||||
\(620\) | 10.2785 | 0.412796 | ||||||||
\(621\) | 2.16944 | 0.0870568 | ||||||||
\(622\) | −14.7623 | −0.591915 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −21.5231 | −0.861614 | ||||||||
\(625\) | −14.0520 | −0.562079 | ||||||||
\(626\) | 1.87473 | 0.0749294 | ||||||||
\(627\) | −9.08069 | −0.362648 | ||||||||
\(628\) | 0.278299 | 0.0111053 | ||||||||
\(629\) | −11.1183 | −0.443316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.86026 | −0.273102 | −0.136551 | − | 0.990633i | \(-0.543602\pi\) | ||||
−0.136551 | + | 0.990633i | \(0.543602\pi\) | |||||||
\(632\) | 21.2566 | 0.845541 | ||||||||
\(633\) | 42.3485 | 1.68320 | ||||||||
\(634\) | 39.8268 | 1.58173 | ||||||||
\(635\) | −17.4961 | −0.694313 | ||||||||
\(636\) | 11.9016 | 0.471929 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.3244 | 0.646289 | ||||||||
\(639\) | −15.8459 | −0.626854 | ||||||||
\(640\) | 3.64672 | 0.144149 | ||||||||
\(641\) | 35.0868 | 1.38585 | 0.692923 | − | 0.721012i | \(-0.256323\pi\) | ||||
0.692923 | + | 0.721012i | \(0.256323\pi\) | |||||||
\(642\) | −11.5598 | −0.456229 | ||||||||
\(643\) | 12.6069 | 0.497166 | 0.248583 | − | 0.968611i | \(-0.420035\pi\) | ||||
0.248583 | + | 0.968611i | \(0.420035\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 35.2642 | 1.38853 | ||||||||
\(646\) | 1.32677 | 0.0522010 | ||||||||
\(647\) | −16.3733 | −0.643701 | −0.321850 | − | 0.946791i | \(-0.604305\pi\) | ||||
−0.321850 | + | 0.946791i | \(0.604305\pi\) | |||||||
\(648\) | 34.3188 | 1.34817 | ||||||||
\(649\) | −13.4961 | −0.529768 | ||||||||
\(650\) | −8.85635 | −0.347374 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.36809 | 0.131905 | ||||||||
\(653\) | 43.9868 | 1.72134 | 0.860668 | − | 0.509167i | \(-0.170046\pi\) | ||||
0.860668 | + | 0.509167i | \(0.170046\pi\) | |||||||
\(654\) | 19.3463 | 0.756498 | ||||||||
\(655\) | −36.8844 | −1.44119 | ||||||||
\(656\) | −4.69988 | −0.183499 | ||||||||
\(657\) | −13.9811 | −0.545455 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.67382 | 0.298930 | 0.149465 | − | 0.988767i | \(-0.452245\pi\) | ||||
0.149465 | + | 0.988767i | \(0.452245\pi\) | |||||||
\(660\) | −11.8328 | −0.460592 | ||||||||
\(661\) | 5.24677 | 0.204076 | 0.102038 | − | 0.994781i | \(-0.467464\pi\) | ||||
0.102038 | + | 0.994781i | \(0.467464\pi\) | |||||||
\(662\) | −18.7337 | −0.728107 | ||||||||
\(663\) | −12.1519 | −0.471940 | ||||||||
\(664\) | −46.4512 | −1.80266 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.6059 | 0.759712 | ||||||||
\(667\) | −2.90185 | −0.112360 | ||||||||
\(668\) | 17.4033 | 0.673355 | ||||||||
\(669\) | −3.47314 | −0.134279 | ||||||||
\(670\) | −24.4261 | −0.943663 | ||||||||
\(671\) | −32.4938 | −1.25441 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.86577 | −0.149015 | −0.0745073 | − | 0.997220i | \(-0.523738\pi\) | ||||
−0.0745073 | + | 0.997220i | \(0.523738\pi\) | |||||||
\(674\) | −11.4126 | −0.439598 | ||||||||
\(675\) | 4.27976 | 0.164728 | ||||||||
\(676\) | −6.71900 | −0.258423 | ||||||||
\(677\) | −1.43146 | −0.0550153 | −0.0275077 | − | 0.999622i | \(-0.508757\pi\) | ||||
−0.0275077 | + | 0.999622i | \(0.508757\pi\) | |||||||
\(678\) | 40.8263 | 1.56792 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.58778 | 0.252630 | ||||||||
\(681\) | −5.33013 | −0.204251 | ||||||||
\(682\) | −37.0476 | −1.41863 | ||||||||
\(683\) | −25.8187 | −0.987925 | −0.493962 | − | 0.869483i | \(-0.664452\pi\) | ||||
−0.493962 | + | 0.869483i | \(0.664452\pi\) | |||||||
\(684\) | 1.29228 | 0.0494117 | ||||||||
\(685\) | −4.71163 | −0.180022 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.16143 | −0.235073 | ||||||||
\(688\) | −18.1684 | −0.692663 | ||||||||
\(689\) | −36.1024 | −1.37539 | ||||||||
\(690\) | −3.80811 | −0.144972 | ||||||||
\(691\) | −19.3172 | −0.734862 | −0.367431 | − | 0.930051i | \(-0.619763\pi\) | ||||
−0.367431 | + | 0.930051i | \(0.619763\pi\) | |||||||
\(692\) | 6.80325 | 0.258621 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.4748 | −1.19477 | ||||||||
\(695\) | 1.08548 | 0.0411746 | ||||||||
\(696\) | −23.4763 | −0.889868 | ||||||||
\(697\) | −2.65354 | −0.100510 | ||||||||
\(698\) | −24.3885 | −0.923117 | ||||||||
\(699\) | 48.5359 | 1.83580 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3256 | 1.25869 | 0.629345 | − | 0.777126i | \(-0.283323\pi\) | ||||
0.629345 | + | 0.777126i | \(0.283323\pi\) | |||||||
\(702\) | −13.9721 | −0.527341 | ||||||||
\(703\) | −9.51182 | −0.358745 | ||||||||
\(704\) | 35.0084 | 1.31943 | ||||||||
\(705\) | −18.0712 | −0.680603 | ||||||||
\(706\) | 35.4923 | 1.33577 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.09361 | 0.191430 | ||||||||
\(709\) | 37.3750 | 1.40365 | 0.701824 | − | 0.712351i | \(-0.252369\pi\) | ||||
0.701824 | + | 0.712351i | \(0.252369\pi\) | |||||||
\(710\) | −18.1362 | −0.680641 | ||||||||
\(711\) | −12.5414 | −0.470338 | ||||||||
\(712\) | 10.4894 | 0.393108 | ||||||||
\(713\) | 6.58564 | 0.246634 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.8938 | 1.34235 | ||||||||
\(716\) | −2.88723 | −0.107901 | ||||||||
\(717\) | 28.5643 | 1.06675 | ||||||||
\(718\) | −1.32040 | −0.0492769 | ||||||||
\(719\) | −17.6638 | −0.658748 | −0.329374 | − | 0.944200i | \(-0.606838\pi\) | ||||
−0.329374 | + | 0.944200i | \(0.606838\pi\) | |||||||
\(720\) | −6.88419 | −0.256558 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.13506 | 0.0422427 | ||||||||
\(723\) | 25.1169 | 0.934108 | ||||||||
\(724\) | −5.11742 | −0.190187 | ||||||||
\(725\) | −5.72461 | −0.212607 | ||||||||
\(726\) | 15.2496 | 0.565967 | ||||||||
\(727\) | 18.7835 | 0.696640 | 0.348320 | − | 0.937376i | \(-0.386752\pi\) | ||||
0.348320 | + | 0.937376i | \(0.386752\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.14108 | −0.116336 | ||||||||
\(730\) | −16.0019 | −0.592258 | ||||||||
\(731\) | −10.2578 | −0.379399 | ||||||||
\(732\) | 12.2636 | 0.453277 | ||||||||
\(733\) | 17.3943 | 0.642474 | 0.321237 | − | 0.946999i | \(-0.395901\pi\) | ||||
0.321237 | + | 0.946999i | \(0.395901\pi\) | |||||||
\(734\) | 12.0395 | 0.444386 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.17748 | −0.117123 | ||||||||
\(737\) | −48.6294 | −1.79129 | ||||||||
\(738\) | 4.67921 | 0.172244 | ||||||||
\(739\) | −28.1262 | −1.03464 | −0.517319 | − | 0.855793i | \(-0.673070\pi\) | ||||
−0.517319 | + | 0.855793i | \(0.673070\pi\) | |||||||
\(740\) | −12.3946 | −0.455635 | ||||||||
\(741\) | −10.3961 | −0.381908 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.3940 | −1.18842 | −0.594211 | − | 0.804310i | \(-0.702535\pi\) | ||||
−0.594211 | + | 0.804310i | \(0.702535\pi\) | |||||||
\(744\) | 53.2787 | 1.95329 | ||||||||
\(745\) | 26.6352 | 0.975840 | ||||||||
\(746\) | 0.481980 | 0.0176465 | ||||||||
\(747\) | 27.4062 | 1.00274 | ||||||||
\(748\) | 3.44199 | 0.125851 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −30.3182 | −1.10706 | ||||||||
\(751\) | −5.91823 | −0.215959 | −0.107980 | − | 0.994153i | \(-0.534438\pi\) | ||||
−0.107980 | + | 0.994153i | \(0.534438\pi\) | |||||||
\(752\) | 9.31044 | 0.339517 | ||||||||
\(753\) | 5.03724 | 0.183567 | ||||||||
\(754\) | 18.6890 | 0.680614 | ||||||||
\(755\) | 43.1404 | 1.57004 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.7464 | −0.863078 | −0.431539 | − | 0.902094i | \(-0.642029\pi\) | ||||
−0.431539 | + | 0.902094i | \(0.642029\pi\) | |||||||
\(758\) | −0.383559 | −0.0139315 | ||||||||
\(759\) | −7.58149 | −0.275191 | ||||||||
\(760\) | 5.63591 | 0.204436 | ||||||||
\(761\) | 0.606289 | 0.0219780 | 0.0109890 | − | 0.999940i | \(-0.496502\pi\) | ||||
0.0109890 | + | 0.999940i | \(0.496502\pi\) | |||||||
\(762\) | −23.8007 | −0.862208 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.27826 | 0.118603 | ||||||||
\(765\) | −3.88679 | −0.140527 | ||||||||
\(766\) | 31.7114 | 1.14578 | ||||||||
\(767\) | −15.4510 | −0.557904 | ||||||||
\(768\) | −32.1726 | −1.16093 | ||||||||
\(769\) | −48.3067 | −1.74199 | −0.870993 | − | 0.491296i | \(-0.836523\pi\) | ||||
−0.870993 | + | 0.491296i | \(0.836523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.3860 | 1.02230 | ||||||||
\(772\) | 13.3487 | 0.480430 | ||||||||
\(773\) | 3.31978 | 0.119404 | 0.0597021 | − | 0.998216i | \(-0.480985\pi\) | ||||
0.0597021 | + | 0.998216i | \(0.480985\pi\) | |||||||
\(774\) | 18.0885 | 0.650178 | ||||||||
\(775\) | 12.9918 | 0.466679 | ||||||||
\(776\) | 9.37321 | 0.336479 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.0270 | 1.25578 | ||||||||
\(779\) | −2.27013 | −0.0813357 | ||||||||
\(780\) | −13.5468 | −0.485054 | ||||||||
\(781\) | −36.1071 | −1.29201 | ||||||||
\(782\) | 1.10772 | 0.0396120 | ||||||||
\(783\) | −9.03132 | −0.322753 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.716094 | −0.0255585 | ||||||||
\(786\) | −50.1753 | −1.78969 | ||||||||
\(787\) | 37.2734 | 1.32865 | 0.664327 | − | 0.747442i | \(-0.268718\pi\) | ||||
0.664327 | + | 0.747442i | \(0.268718\pi\) | |||||||
\(788\) | −1.58877 | −0.0565976 | ||||||||
\(789\) | 41.2800 | 1.46961 | ||||||||
\(790\) | −14.3541 | −0.510696 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −23.1277 | −0.821806 | ||||||||
\(793\) | −37.2006 | −1.32103 | ||||||||
\(794\) | −32.6624 | −1.15914 | ||||||||
\(795\) | −30.6241 | −1.08612 | ||||||||
\(796\) | −4.48949 | −0.159126 | ||||||||
\(797\) | 32.2508 | 1.14238 | 0.571191 | − | 0.820817i | \(-0.306482\pi\) | ||||
0.571191 | + | 0.820817i | \(0.306482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.25665 | 0.185967 | ||||||||
\(800\) | −6.26836 | −0.221620 | ||||||||
\(801\) | −6.18876 | −0.218669 | ||||||||
\(802\) | 14.1303 | 0.498957 | ||||||||
\(803\) | −31.8579 | −1.12424 | ||||||||
\(804\) | 18.3534 | 0.647276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.4141 | −1.49397 | ||||||||
\(807\) | 7.00326 | 0.246526 | ||||||||
\(808\) | 36.9057 | 1.29834 | ||||||||
\(809\) | −4.37072 | −0.153666 | −0.0768332 | − | 0.997044i | \(-0.524481\pi\) | ||||
−0.0768332 | + | 0.997044i | \(0.524481\pi\) | |||||||
\(810\) | −23.1748 | −0.814278 | ||||||||
\(811\) | −24.3955 | −0.856644 | −0.428322 | − | 0.903626i | \(-0.640895\pi\) | ||||
−0.428322 | + | 0.903626i | \(0.640895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.17304 | 0.0411402 | ||||||||
\(814\) | 44.6747 | 1.56585 | ||||||||
\(815\) | −8.66645 | −0.303573 | ||||||||
\(816\) | 5.31071 | 0.185912 | ||||||||
\(817\) | −8.77566 | −0.307022 | ||||||||
\(818\) | −20.2853 | −0.709258 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.95814 | −0.103303 | ||||||||
\(821\) | −22.4555 | −0.783702 | −0.391851 | − | 0.920029i | \(-0.628165\pi\) | ||||
−0.391851 | + | 0.920029i | \(0.628165\pi\) | |||||||
\(822\) | −6.40942 | −0.223554 | ||||||||
\(823\) | 33.3905 | 1.16392 | 0.581960 | − | 0.813218i | \(-0.302286\pi\) | ||||
0.581960 | + | 0.813218i | \(0.302286\pi\) | |||||||
\(824\) | −44.5292 | −1.55125 | ||||||||
\(825\) | −14.9564 | −0.520714 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.6022 | −1.55097 | −0.775486 | − | 0.631365i | \(-0.782495\pi\) | ||||
−0.775486 | + | 0.631365i | \(0.782495\pi\) | |||||||
\(828\) | 1.07893 | 0.0374955 | ||||||||
\(829\) | 32.2868 | 1.12137 | 0.560684 | − | 0.828030i | \(-0.310538\pi\) | ||||
0.560684 | + | 0.828030i | \(0.310538\pi\) | |||||||
\(830\) | 31.3675 | 1.08878 | ||||||||
\(831\) | 58.8279 | 2.04072 | ||||||||
\(832\) | 40.0794 | 1.38950 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.47662 | 0.0511311 | ||||||||
\(835\) | −44.7806 | −1.54970 | ||||||||
\(836\) | 2.94465 | 0.101843 | ||||||||
\(837\) | 20.4963 | 0.708455 | ||||||||
\(838\) | −22.9350 | −0.792278 | ||||||||
\(839\) | 5.17125 | 0.178531 | 0.0892657 | − | 0.996008i | \(-0.471548\pi\) | ||||
0.0892657 | + | 0.996008i | \(0.471548\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.9197 | −0.583438 | ||||||||
\(842\) | 8.32111 | 0.286764 | ||||||||
\(843\) | 4.08399 | 0.140660 | ||||||||
\(844\) | −13.7326 | −0.472695 | ||||||||
\(845\) | 17.2887 | 0.594749 | ||||||||
\(846\) | −9.26950 | −0.318692 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.7778 | 0.541811 | ||||||||
\(849\) | −27.3022 | −0.937008 | ||||||||
\(850\) | 2.18525 | 0.0749536 | ||||||||
\(851\) | −7.94144 | −0.272229 | ||||||||
\(852\) | 13.6273 | 0.466864 | ||||||||
\(853\) | 3.86988 | 0.132502 | 0.0662511 | − | 0.997803i | \(-0.478896\pi\) | ||||
0.0662511 | + | 0.997803i | \(0.478896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.32519 | −0.113719 | ||||||||
\(856\) | 14.2837 | 0.488207 | ||||||||
\(857\) | 14.7977 | 0.505481 | 0.252741 | − | 0.967534i | \(-0.418668\pi\) | ||||
0.252741 | + | 0.967534i | \(0.418668\pi\) | |||||||
\(858\) | 48.8277 | 1.66695 | ||||||||
\(859\) | −37.6674 | −1.28520 | −0.642598 | − | 0.766204i | \(-0.722143\pi\) | ||||
−0.642598 | + | 0.766204i | \(0.722143\pi\) | |||||||
\(860\) | −11.4353 | −0.389942 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.63054 | −0.293957 | ||||||||
\(863\) | 0.671748 | 0.0228666 | 0.0114333 | − | 0.999935i | \(-0.496361\pi\) | ||||
0.0114333 | + | 0.999935i | \(0.496361\pi\) | |||||||
\(864\) | −9.88916 | −0.336436 | ||||||||
\(865\) | −17.5055 | −0.595205 | ||||||||
\(866\) | 28.4890 | 0.968096 | ||||||||
\(867\) | −34.3085 | −1.16518 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.5773 | −0.969417 | ||||||||
\(870\) | 15.8531 | 0.537469 | ||||||||
\(871\) | −55.6735 | −1.88642 | ||||||||
\(872\) | −23.9049 | −0.809522 | ||||||||
\(873\) | −5.53019 | −0.187169 | ||||||||
\(874\) | 0.947667 | 0.0320553 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0236 | 0.406240 | ||||||||
\(877\) | 2.39645 | 0.0809224 | 0.0404612 | − | 0.999181i | \(-0.487117\pi\) | ||||
0.0404612 | + | 0.999181i | \(0.487117\pi\) | |||||||
\(878\) | 40.7070 | 1.37380 | ||||||||
\(879\) | −8.95589 | −0.302075 | ||||||||
\(880\) | −15.6866 | −0.528794 | ||||||||
\(881\) | 4.30698 | 0.145106 | 0.0725530 | − | 0.997365i | \(-0.476885\pi\) | ||||
0.0725530 | + | 0.997365i | \(0.476885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.6998 | −0.999479 | −0.499739 | − | 0.866176i | \(-0.666571\pi\) | ||||
−0.499739 | + | 0.866176i | \(0.666571\pi\) | |||||||
\(884\) | 3.94056 | 0.132535 | ||||||||
\(885\) | −13.1064 | −0.440567 | ||||||||
\(886\) | 33.0458 | 1.11020 | ||||||||
\(887\) | 53.8320 | 1.80750 | 0.903751 | − | 0.428058i | \(-0.140802\pi\) | ||||
0.903751 | + | 0.428058i | \(0.140802\pi\) | |||||||
\(888\) | −64.2473 | −2.15600 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.08328 | −0.237432 | ||||||||
\(891\) | −46.1381 | −1.54569 | ||||||||
\(892\) | 1.12626 | 0.0377098 | ||||||||
\(893\) | 4.49711 | 0.150490 | ||||||||
\(894\) | 36.2330 | 1.21181 | ||||||||
\(895\) | 7.42914 | 0.248329 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.67969 | −0.289806 | ||||||||
\(898\) | −9.20078 | −0.307034 | ||||||||
\(899\) | −27.4158 | −0.914368 | ||||||||
\(900\) | 2.12846 | 0.0709486 | ||||||||
\(901\) | 8.90808 | 0.296771 | ||||||||
\(902\) | 10.6622 | 0.355014 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −50.4463 | −1.67782 | ||||||||
\(905\) | 13.1677 | 0.437708 | ||||||||
\(906\) | 58.6855 | 1.94970 | ||||||||
\(907\) | 0.718141 | 0.0238455 | 0.0119227 | − | 0.999929i | \(-0.496205\pi\) | ||||
0.0119227 | + | 0.999929i | \(0.496205\pi\) | |||||||
\(908\) | 1.72843 | 0.0573601 | ||||||||
\(909\) | −21.7744 | −0.722210 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.2647 | −1.69848 | −0.849238 | − | 0.528010i | \(-0.822939\pi\) | ||||
−0.849238 | + | 0.528010i | \(0.822939\pi\) | |||||||
\(912\) | 4.54336 | 0.150446 | ||||||||
\(913\) | 62.4488 | 2.06675 | ||||||||
\(914\) | −13.8981 | −0.459707 | ||||||||
\(915\) | −31.5556 | −1.04320 | ||||||||
\(916\) | 1.99800 | 0.0660159 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.44753 | 0.113785 | ||||||||
\(919\) | 24.0222 | 0.792420 | 0.396210 | − | 0.918160i | \(-0.370325\pi\) | ||||
0.396210 | + | 0.918160i | \(0.370325\pi\) | |||||||
\(920\) | 4.70544 | 0.155134 | ||||||||
\(921\) | 30.0390 | 0.989818 | ||||||||
\(922\) | 39.7837 | 1.31021 | ||||||||
\(923\) | −41.3372 | −1.36063 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.6665 | −0.515110 | ||||||||
\(926\) | 32.7693 | 1.07687 | ||||||||
\(927\) | 26.2722 | 0.862893 | ||||||||
\(928\) | 13.2277 | 0.434222 | ||||||||
\(929\) | 24.6046 | 0.807251 | 0.403626 | − | 0.914924i | \(-0.367750\pi\) | ||||
0.403626 | + | 0.914924i | \(0.367750\pi\) | |||||||
\(930\) | −35.9780 | −1.17976 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.7390 | −0.515549 | ||||||||
\(933\) | −28.5414 | −0.934404 | ||||||||
\(934\) | 39.5527 | 1.29420 | ||||||||
\(935\) | −8.85660 | −0.289642 | ||||||||
\(936\) | −26.4777 | −0.865452 | ||||||||
\(937\) | −2.90609 | −0.0949377 | −0.0474688 | − | 0.998873i | \(-0.515115\pi\) | ||||
−0.0474688 | + | 0.998873i | \(0.515115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.62460 | 0.118284 | ||||||||
\(940\) | 5.86007 | 0.191134 | ||||||||
\(941\) | −3.64954 | −0.118972 | −0.0594858 | − | 0.998229i | \(-0.518946\pi\) | ||||
−0.0594858 | + | 0.998229i | \(0.518946\pi\) | |||||||
\(942\) | −0.974130 | −0.0317389 | ||||||||
\(943\) | −1.89533 | −0.0617205 | ||||||||
\(944\) | 6.75252 | 0.219776 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.2172 | 1.34009 | ||||||||
\(947\) | −36.4871 | −1.18567 | −0.592836 | − | 0.805323i | \(-0.701992\pi\) | ||||
−0.592836 | + | 0.805323i | \(0.701992\pi\) | |||||||
\(948\) | 10.7855 | 0.350295 | ||||||||
\(949\) | −36.4726 | −1.18395 | ||||||||
\(950\) | 1.86951 | 0.0606548 | ||||||||
\(951\) | 77.0010 | 2.49693 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.22124 | 0.266312 | 0.133156 | − | 0.991095i | \(-0.457489\pi\) | ||||
0.133156 | + | 0.991095i | \(0.457489\pi\) | |||||||
\(954\) | −15.7084 | −0.508578 | ||||||||
\(955\) | −8.43532 | −0.272960 | ||||||||
\(956\) | −9.26270 | −0.299577 | ||||||||
\(957\) | 31.5615 | 1.02024 | ||||||||
\(958\) | 21.4468 | 0.692915 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 33.9976 | 1.09727 | ||||||||
\(961\) | 31.2192 | 1.00707 | ||||||||
\(962\) | 51.1459 | 1.64901 | ||||||||
\(963\) | −8.42738 | −0.271569 | ||||||||
\(964\) | −8.14481 | −0.262327 | ||||||||
\(965\) | −34.3476 | −1.10569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.4422 | −1.42917 | −0.714583 | − | 0.699551i | \(-0.753383\pi\) | ||||
−0.714583 | + | 0.699551i | \(0.753383\pi\) | |||||||
\(968\) | −18.8430 | −0.605637 | ||||||||
\(969\) | 2.56517 | 0.0824051 | ||||||||
\(970\) | −6.32952 | −0.203229 | ||||||||
\(971\) | 57.6556 | 1.85026 | 0.925129 | − | 0.379653i | \(-0.123957\pi\) | ||||
0.925129 | + | 0.379653i | \(0.123957\pi\) | |||||||
\(972\) | 11.8658 | 0.380595 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.356502 | −0.0114231 | ||||||||
\(975\) | −17.1228 | −0.548369 | ||||||||
\(976\) | 16.2577 | 0.520396 | ||||||||
\(977\) | 29.1680 | 0.933168 | 0.466584 | − | 0.884477i | \(-0.345485\pi\) | ||||
0.466584 | + | 0.884477i | \(0.345485\pi\) | |||||||
\(978\) | −11.7893 | −0.376981 | ||||||||
\(979\) | −14.1019 | −0.450700 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1039 | 0.450303 | ||||||||
\(982\) | 42.2300 | 1.34761 | ||||||||
\(983\) | 27.6877 | 0.883099 | 0.441549 | − | 0.897237i | \(-0.354429\pi\) | ||||
0.441549 | + | 0.897237i | \(0.354429\pi\) | |||||||
\(984\) | −15.3335 | −0.488814 | ||||||||
\(985\) | 4.08808 | 0.130257 | ||||||||
\(986\) | −4.61141 | −0.146857 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.37119 | 0.107252 | ||||||||
\(989\) | −7.32682 | −0.232979 | ||||||||
\(990\) | 15.6176 | 0.496360 | ||||||||
\(991\) | 16.6411 | 0.528623 | 0.264312 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264312 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(992\) | −30.0199 | −0.953133 | ||||||||
\(993\) | −36.2197 | −1.14940 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.5519 | 0.366221 | ||||||||
\(996\) | −23.5691 | −0.746814 | ||||||||
\(997\) | −28.2236 | −0.893851 | −0.446925 | − | 0.894571i | \(-0.647481\pi\) | ||||
−0.446925 | + | 0.894571i | \(0.647481\pi\) | |||||||
\(998\) | −34.5044 | −1.09222 | ||||||||
\(999\) | −24.7159 | −0.781976 |
(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 | 931.2.a.o.1.5 | 7 | ||
3.2 | odd | 2 | 8379.2.a.ck.1.3 | 7 | |||
7.2 | even | 3 | 931.2.f.p.704.3 | 14 | |||
7.3 | odd | 6 | 133.2.f.d.58.3 | yes | 14 | ||
7.4 | even | 3 | 931.2.f.p.324.3 | 14 | |||
7.5 | odd | 6 | 133.2.f.d.39.3 | ✓ | 14 | ||
7.6 | odd | 2 | 931.2.a.n.1.5 | 7 | |||
21.5 | even | 6 | 1197.2.j.l.172.5 | 14 | |||
21.17 | even | 6 | 1197.2.j.l.856.5 | 14 | |||
21.20 | even | 2 | 8379.2.a.cl.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.f.d.39.3 | ✓ | 14 | 7.5 | odd | 6 | ||
133.2.f.d.58.3 | yes | 14 | 7.3 | odd | 6 | ||
931.2.a.n.1.5 | 7 | 7.6 | odd | 2 | |||
931.2.a.o.1.5 | 7 | 1.1 | even | 1 | trivial | ||
931.2.f.p.324.3 | 14 | 7.4 | even | 3 | |||
931.2.f.p.704.3 | 14 | 7.2 | even | 3 | |||
1197.2.j.l.172.5 | 14 | 21.5 | even | 6 | |||
1197.2.j.l.856.5 | 14 | 21.17 | even | 6 | |||
8379.2.a.ck.1.3 | 7 | 3.2 | odd | 2 | |||
8379.2.a.cl.1.3 | 7 | 21.20 | even | 2 |