Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.78421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78421 | −1.26162 | −0.630812 | − | 0.775936i | \(-0.717278\pi\) | ||||
−0.630812 | + | 0.775936i | \(0.717278\pi\) | |||||||
\(3\) | 2.96672 | 1.71284 | 0.856419 | − | 0.516281i | \(-0.172684\pi\) | ||||
0.856419 | + | 0.516281i | \(0.172684\pi\) | |||||||
\(4\) | 1.18339 | 0.591696 | ||||||||
\(5\) | −0.596316 | −0.266681 | −0.133340 | − | 0.991070i | \(-0.542570\pi\) | ||||
−0.133340 | + | 0.991070i | \(0.542570\pi\) | |||||||
\(6\) | −5.29325 | −2.16096 | ||||||||
\(7\) | −4.36308 | −1.64909 | −0.824544 | − | 0.565797i | \(-0.808568\pi\) | ||||
−0.824544 | + | 0.565797i | \(0.808568\pi\) | |||||||
\(8\) | 1.45700 | 0.515126 | ||||||||
\(9\) | 5.80145 | 1.93382 | ||||||||
\(10\) | 1.06395 | 0.336451 | ||||||||
\(11\) | 2.03573 | 0.613796 | 0.306898 | − | 0.951742i | \(-0.400709\pi\) | ||||
0.306898 | + | 0.951742i | \(0.400709\pi\) | |||||||
\(12\) | 3.51080 | 1.01348 | ||||||||
\(13\) | −1.74313 | −0.483458 | −0.241729 | − | 0.970344i | \(-0.577714\pi\) | ||||
−0.241729 | + | 0.970344i | \(0.577714\pi\) | |||||||
\(14\) | 7.78463 | 2.08053 | ||||||||
\(15\) | −1.76911 | −0.456781 | ||||||||
\(16\) | −4.96637 | −1.24159 | ||||||||
\(17\) | 1.46763 | 0.355953 | 0.177976 | − | 0.984035i | \(-0.443045\pi\) | ||||
0.177976 | + | 0.984035i | \(0.443045\pi\) | |||||||
\(18\) | −10.3510 | −2.43975 | ||||||||
\(19\) | −2.17572 | −0.499144 | −0.249572 | − | 0.968356i | \(-0.580290\pi\) | ||||
−0.249572 | + | 0.968356i | \(0.580290\pi\) | |||||||
\(20\) | −0.705676 | −0.157794 | ||||||||
\(21\) | −12.9440 | −2.82462 | ||||||||
\(22\) | −3.63216 | −0.774380 | ||||||||
\(23\) | −2.72236 | −0.567650 | −0.283825 | − | 0.958876i | \(-0.591604\pi\) | ||||
−0.283825 | + | 0.958876i | \(0.591604\pi\) | |||||||
\(24\) | 4.32250 | 0.882328 | ||||||||
\(25\) | −4.64441 | −0.928881 | ||||||||
\(26\) | 3.11011 | 0.609942 | ||||||||
\(27\) | 8.31113 | 1.59948 | ||||||||
\(28\) | −5.16324 | −0.975760 | ||||||||
\(29\) | −7.57422 | −1.40650 | −0.703249 | − | 0.710944i | \(-0.748268\pi\) | ||||
−0.703249 | + | 0.710944i | \(0.748268\pi\) | |||||||
\(30\) | 3.15645 | 0.576286 | ||||||||
\(31\) | −0.569957 | −0.102367 | −0.0511837 | − | 0.998689i | \(-0.516299\pi\) | ||||
−0.0511837 | + | 0.998689i | \(0.516299\pi\) | |||||||
\(32\) | 5.94703 | 1.05130 | ||||||||
\(33\) | 6.03945 | 1.05133 | ||||||||
\(34\) | −2.61856 | −0.449079 | ||||||||
\(35\) | 2.60177 | 0.439780 | ||||||||
\(36\) | 6.86539 | 1.14423 | ||||||||
\(37\) | −3.96167 | −0.651294 | −0.325647 | − | 0.945491i | \(-0.605582\pi\) | ||||
−0.325647 | + | 0.945491i | \(0.605582\pi\) | |||||||
\(38\) | 3.88193 | 0.629733 | ||||||||
\(39\) | −5.17139 | −0.828086 | ||||||||
\(40\) | −0.868830 | −0.137374 | ||||||||
\(41\) | 2.12568 | 0.331976 | 0.165988 | − | 0.986128i | \(-0.446919\pi\) | ||||
0.165988 | + | 0.986128i | \(0.446919\pi\) | |||||||
\(42\) | 23.0949 | 3.56361 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 2.40907 | 0.363181 | ||||||||
\(45\) | −3.45950 | −0.515712 | ||||||||
\(46\) | 4.85724 | 0.716161 | ||||||||
\(47\) | 9.36309 | 1.36575 | 0.682874 | − | 0.730536i | \(-0.260730\pi\) | ||||
0.682874 | + | 0.730536i | \(0.260730\pi\) | |||||||
\(48\) | −14.7338 | −2.12665 | ||||||||
\(49\) | 12.0365 | 1.71949 | ||||||||
\(50\) | 8.28658 | 1.17190 | ||||||||
\(51\) | 4.35406 | 0.609690 | ||||||||
\(52\) | −2.06281 | −0.286060 | ||||||||
\(53\) | −5.90594 | −0.811243 | −0.405621 | − | 0.914041i | \(-0.632945\pi\) | ||||
−0.405621 | + | 0.914041i | \(0.632945\pi\) | |||||||
\(54\) | −14.8288 | −2.01794 | ||||||||
\(55\) | −1.21394 | −0.163687 | ||||||||
\(56\) | −6.35699 | −0.849488 | ||||||||
\(57\) | −6.45476 | −0.854954 | ||||||||
\(58\) | 13.5140 | 1.77447 | ||||||||
\(59\) | 5.11026 | 0.665299 | 0.332649 | − | 0.943051i | \(-0.392057\pi\) | ||||
0.332649 | + | 0.943051i | \(0.392057\pi\) | |||||||
\(60\) | −2.09355 | −0.270276 | ||||||||
\(61\) | −9.78609 | −1.25298 | −0.626490 | − | 0.779429i | \(-0.715509\pi\) | ||||
−0.626490 | + | 0.779429i | \(0.715509\pi\) | |||||||
\(62\) | 1.01692 | 0.129149 | ||||||||
\(63\) | −25.3122 | −3.18904 | ||||||||
\(64\) | −0.678000 | −0.0847500 | ||||||||
\(65\) | 1.03946 | 0.128929 | ||||||||
\(66\) | −10.7756 | −1.32639 | ||||||||
\(67\) | −0.530129 | −0.0647656 | −0.0323828 | − | 0.999476i | \(-0.510310\pi\) | ||||
−0.0323828 | + | 0.999476i | \(0.510310\pi\) | |||||||
\(68\) | 1.73678 | 0.210616 | ||||||||
\(69\) | −8.07648 | −0.972293 | ||||||||
\(70\) | −4.64210 | −0.554837 | ||||||||
\(71\) | −5.33822 | −0.633530 | −0.316765 | − | 0.948504i | \(-0.602597\pi\) | ||||
−0.316765 | + | 0.948504i | \(0.602597\pi\) | |||||||
\(72\) | 8.45269 | 0.996159 | ||||||||
\(73\) | −14.0584 | −1.64541 | −0.822703 | − | 0.568471i | \(-0.807535\pi\) | ||||
−0.822703 | + | 0.568471i | \(0.807535\pi\) | |||||||
\(74\) | 7.06843 | 0.821688 | ||||||||
\(75\) | −13.7787 | −1.59102 | ||||||||
\(76\) | −2.57473 | −0.295342 | ||||||||
\(77\) | −8.88205 | −1.01220 | ||||||||
\(78\) | 9.22683 | 1.04473 | ||||||||
\(79\) | 3.65266 | 0.410957 | 0.205478 | − | 0.978662i | \(-0.434125\pi\) | ||||
0.205478 | + | 0.978662i | \(0.434125\pi\) | |||||||
\(80\) | 2.96153 | 0.331109 | ||||||||
\(81\) | 7.25248 | 0.805831 | ||||||||
\(82\) | −3.79266 | −0.418829 | ||||||||
\(83\) | −10.3460 | −1.13562 | −0.567812 | − | 0.823159i | \(-0.692210\pi\) | ||||
−0.567812 | + | 0.823159i | \(0.692210\pi\) | |||||||
\(84\) | −15.3179 | −1.67132 | ||||||||
\(85\) | −0.875173 | −0.0949258 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.4706 | −2.40910 | ||||||||
\(88\) | 2.96605 | 0.316182 | ||||||||
\(89\) | −6.03765 | −0.639990 | −0.319995 | − | 0.947419i | \(-0.603681\pi\) | ||||
−0.319995 | + | 0.947419i | \(0.603681\pi\) | |||||||
\(90\) | 6.17246 | 0.650634 | ||||||||
\(91\) | 7.60542 | 0.797265 | ||||||||
\(92\) | −3.22162 | −0.335877 | ||||||||
\(93\) | −1.69091 | −0.175339 | ||||||||
\(94\) | −16.7057 | −1.72306 | ||||||||
\(95\) | 1.29742 | 0.133112 | ||||||||
\(96\) | 17.6432 | 1.80070 | ||||||||
\(97\) | 10.2551 | 1.04125 | 0.520624 | − | 0.853786i | \(-0.325699\pi\) | ||||
0.520624 | + | 0.853786i | \(0.325699\pi\) | |||||||
\(98\) | −21.4755 | −2.16936 | ||||||||
\(99\) | 11.8102 | 1.18697 | ||||||||
\(100\) | −5.49616 | −0.549616 | ||||||||
\(101\) | −11.1802 | −1.11247 | −0.556234 | − | 0.831026i | \(-0.687754\pi\) | ||||
−0.556234 | + | 0.831026i | \(0.687754\pi\) | |||||||
\(102\) | −7.76854 | −0.769200 | ||||||||
\(103\) | −0.139535 | −0.0137488 | −0.00687442 | − | 0.999976i | \(-0.502188\pi\) | ||||
−0.00687442 | + | 0.999976i | \(0.502188\pi\) | |||||||
\(104\) | −2.53974 | −0.249042 | ||||||||
\(105\) | 7.71875 | 0.753272 | ||||||||
\(106\) | 10.5374 | 1.02348 | ||||||||
\(107\) | 5.84873 | 0.565418 | 0.282709 | − | 0.959206i | \(-0.408767\pi\) | ||||
0.282709 | + | 0.959206i | \(0.408767\pi\) | |||||||
\(108\) | 9.83533 | 0.946405 | ||||||||
\(109\) | 0.788682 | 0.0755420 | 0.0377710 | − | 0.999286i | \(-0.487974\pi\) | ||||
0.0377710 | + | 0.999286i | \(0.487974\pi\) | |||||||
\(110\) | 2.16592 | 0.206512 | ||||||||
\(111\) | −11.7532 | −1.11556 | ||||||||
\(112\) | 21.6687 | 2.04750 | ||||||||
\(113\) | −6.02142 | −0.566448 | −0.283224 | − | 0.959054i | \(-0.591404\pi\) | ||||
−0.283224 | + | 0.959054i | \(0.591404\pi\) | |||||||
\(114\) | 11.5166 | 1.07863 | ||||||||
\(115\) | 1.62338 | 0.151381 | ||||||||
\(116\) | −8.96328 | −0.832220 | ||||||||
\(117\) | −10.1127 | −0.934919 | ||||||||
\(118\) | −9.11775 | −0.839357 | ||||||||
\(119\) | −6.40339 | −0.586998 | ||||||||
\(120\) | −2.57758 | −0.235300 | ||||||||
\(121\) | −6.85580 | −0.623255 | ||||||||
\(122\) | 17.4604 | 1.58079 | ||||||||
\(123\) | 6.30632 | 0.568622 | ||||||||
\(124\) | −0.674483 | −0.0605704 | ||||||||
\(125\) | 5.75112 | 0.514395 | ||||||||
\(126\) | 45.1622 | 4.02337 | ||||||||
\(127\) | −3.78116 | −0.335523 | −0.167762 | − | 0.985828i | \(-0.553654\pi\) | ||||
−0.167762 | + | 0.985828i | \(0.553654\pi\) | |||||||
\(128\) | −10.6844 | −0.944374 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.85461 | −0.162660 | ||||||||
\(131\) | −17.3598 | −1.51673 | −0.758367 | − | 0.651827i | \(-0.774003\pi\) | ||||
−0.758367 | + | 0.651827i | \(0.774003\pi\) | |||||||
\(132\) | 7.14704 | 0.622070 | ||||||||
\(133\) | 9.49284 | 0.823133 | ||||||||
\(134\) | 0.945859 | 0.0817098 | ||||||||
\(135\) | −4.95606 | −0.426550 | ||||||||
\(136\) | 2.13833 | 0.183361 | ||||||||
\(137\) | 3.11074 | 0.265768 | 0.132884 | − | 0.991132i | \(-0.457576\pi\) | ||||
0.132884 | + | 0.991132i | \(0.457576\pi\) | |||||||
\(138\) | 14.4101 | 1.22667 | ||||||||
\(139\) | 5.22160 | 0.442891 | 0.221445 | − | 0.975173i | \(-0.428923\pi\) | ||||
0.221445 | + | 0.975173i | \(0.428923\pi\) | |||||||
\(140\) | 3.07892 | 0.260216 | ||||||||
\(141\) | 27.7777 | 2.33931 | ||||||||
\(142\) | 9.52449 | 0.799277 | ||||||||
\(143\) | −3.54855 | −0.296744 | ||||||||
\(144\) | −28.8121 | −2.40101 | ||||||||
\(145\) | 4.51663 | 0.375086 | ||||||||
\(146\) | 25.0830 | 2.07589 | ||||||||
\(147\) | 35.7088 | 2.94522 | ||||||||
\(148\) | −4.68821 | −0.385368 | ||||||||
\(149\) | 20.3627 | 1.66818 | 0.834090 | − | 0.551628i | \(-0.185993\pi\) | ||||
0.834090 | + | 0.551628i | \(0.185993\pi\) | |||||||
\(150\) | 24.5840 | 2.00728 | ||||||||
\(151\) | −19.9663 | −1.62484 | −0.812418 | − | 0.583076i | \(-0.801849\pi\) | ||||
−0.812418 | + | 0.583076i | \(0.801849\pi\) | |||||||
\(152\) | −3.17001 | −0.257122 | ||||||||
\(153\) | 8.51439 | 0.688348 | ||||||||
\(154\) | 15.8474 | 1.27702 | ||||||||
\(155\) | 0.339875 | 0.0272994 | ||||||||
\(156\) | −6.11979 | −0.489975 | ||||||||
\(157\) | 17.2137 | 1.37380 | 0.686902 | − | 0.726750i | \(-0.258970\pi\) | ||||
0.686902 | + | 0.726750i | \(0.258970\pi\) | |||||||
\(158\) | −6.51711 | −0.518473 | ||||||||
\(159\) | −17.5213 | −1.38953 | ||||||||
\(160\) | −3.54631 | −0.280361 | ||||||||
\(161\) | 11.8778 | 0.936106 | ||||||||
\(162\) | −12.9399 | −1.01666 | ||||||||
\(163\) | 21.8239 | 1.70938 | 0.854689 | − | 0.519140i | \(-0.173748\pi\) | ||||
0.854689 | + | 0.519140i | \(0.173748\pi\) | |||||||
\(164\) | 2.51552 | 0.196429 | ||||||||
\(165\) | −3.60142 | −0.280370 | ||||||||
\(166\) | 18.4594 | 1.43273 | ||||||||
\(167\) | 8.47992 | 0.656196 | 0.328098 | − | 0.944644i | \(-0.393592\pi\) | ||||
0.328098 | + | 0.944644i | \(0.393592\pi\) | |||||||
\(168\) | −18.8594 | −1.45504 | ||||||||
\(169\) | −9.96149 | −0.766268 | ||||||||
\(170\) | 1.56149 | 0.119761 | ||||||||
\(171\) | −12.6223 | −0.965254 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0837 | −0.842677 | −0.421338 | − | 0.906904i | \(-0.638439\pi\) | ||||
−0.421338 | + | 0.906904i | \(0.638439\pi\) | |||||||
\(174\) | 40.0922 | 3.03939 | ||||||||
\(175\) | 20.2639 | 1.53181 | ||||||||
\(176\) | −10.1102 | −0.762084 | ||||||||
\(177\) | 15.1607 | 1.13955 | ||||||||
\(178\) | 10.7724 | 0.807427 | ||||||||
\(179\) | −15.4163 | −1.15227 | −0.576135 | − | 0.817354i | \(-0.695440\pi\) | ||||
−0.576135 | + | 0.817354i | \(0.695440\pi\) | |||||||
\(180\) | −4.09395 | −0.305145 | ||||||||
\(181\) | −3.20803 | −0.238451 | −0.119225 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119225 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(182\) | −13.5696 | −1.00585 | ||||||||
\(183\) | −29.0326 | −2.14615 | ||||||||
\(184\) | −3.96646 | −0.292411 | ||||||||
\(185\) | 2.36241 | 0.173688 | ||||||||
\(186\) | 3.01693 | 0.221212 | ||||||||
\(187\) | 2.98770 | 0.218482 | ||||||||
\(188\) | 11.0802 | 0.808108 | ||||||||
\(189\) | −36.2621 | −2.63768 | ||||||||
\(190\) | −2.31486 | −0.167938 | ||||||||
\(191\) | −5.33299 | −0.385881 | −0.192941 | − | 0.981210i | \(-0.561802\pi\) | ||||
−0.192941 | + | 0.981210i | \(0.561802\pi\) | |||||||
\(192\) | −2.01144 | −0.145163 | ||||||||
\(193\) | −6.72178 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(194\) | −18.2972 | −1.31366 | ||||||||
\(195\) | 3.08379 | 0.220834 | ||||||||
\(196\) | 14.2439 | 1.01742 | ||||||||
\(197\) | −4.86122 | −0.346347 | −0.173174 | − | 0.984891i | \(-0.555402\pi\) | ||||
−0.173174 | + | 0.984891i | \(0.555402\pi\) | |||||||
\(198\) | −21.0718 | −1.49751 | ||||||||
\(199\) | −22.6663 | −1.60677 | −0.803384 | − | 0.595461i | \(-0.796969\pi\) | ||||
−0.803384 | + | 0.595461i | \(0.796969\pi\) | |||||||
\(200\) | −6.76688 | −0.478491 | ||||||||
\(201\) | −1.57275 | −0.110933 | ||||||||
\(202\) | 19.9477 | 1.40352 | ||||||||
\(203\) | 33.0469 | 2.31944 | ||||||||
\(204\) | 5.15256 | 0.360751 | ||||||||
\(205\) | −1.26758 | −0.0885316 | ||||||||
\(206\) | 0.248960 | 0.0173459 | ||||||||
\(207\) | −15.7936 | −1.09773 | ||||||||
\(208\) | 8.65704 | 0.600257 | ||||||||
\(209\) | −4.42918 | −0.306373 | ||||||||
\(210\) | −13.7718 | −0.950347 | ||||||||
\(211\) | 18.9770 | 1.30643 | 0.653214 | − | 0.757174i | \(-0.273420\pi\) | ||||
0.653214 | + | 0.757174i | \(0.273420\pi\) | |||||||
\(212\) | −6.98904 | −0.480009 | ||||||||
\(213\) | −15.8370 | −1.08513 | ||||||||
\(214\) | −10.4353 | −0.713346 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.1093 | 0.823932 | ||||||||
\(217\) | 2.48677 | 0.168813 | ||||||||
\(218\) | −1.40717 | −0.0953057 | ||||||||
\(219\) | −41.7073 | −2.81832 | ||||||||
\(220\) | −1.43657 | −0.0968533 | ||||||||
\(221\) | −2.55828 | −0.172088 | ||||||||
\(222\) | 20.9701 | 1.40742 | ||||||||
\(223\) | 9.66301 | 0.647083 | 0.323541 | − | 0.946214i | \(-0.395126\pi\) | ||||
0.323541 | + | 0.946214i | \(0.395126\pi\) | |||||||
\(224\) | −25.9474 | −1.73368 | ||||||||
\(225\) | −26.9443 | −1.79629 | ||||||||
\(226\) | 10.7435 | 0.714644 | ||||||||
\(227\) | −17.6565 | −1.17190 | −0.585952 | − | 0.810346i | \(-0.699279\pi\) | ||||
−0.585952 | + | 0.810346i | \(0.699279\pi\) | |||||||
\(228\) | −7.63852 | −0.505873 | ||||||||
\(229\) | −0.236812 | −0.0156490 | −0.00782449 | − | 0.999969i | \(-0.502491\pi\) | ||||
−0.00782449 | + | 0.999969i | \(0.502491\pi\) | |||||||
\(230\) | −2.89645 | −0.190986 | ||||||||
\(231\) | −26.3506 | −1.73374 | ||||||||
\(232\) | −11.0356 | −0.724524 | ||||||||
\(233\) | 6.96814 | 0.456498 | 0.228249 | − | 0.973603i | \(-0.426700\pi\) | ||||
0.228249 | + | 0.973603i | \(0.426700\pi\) | |||||||
\(234\) | 18.0431 | 1.17952 | ||||||||
\(235\) | −5.58336 | −0.364219 | ||||||||
\(236\) | 6.04744 | 0.393655 | ||||||||
\(237\) | 10.8364 | 0.703903 | ||||||||
\(238\) | 11.4250 | 0.740571 | ||||||||
\(239\) | −29.5224 | −1.90964 | −0.954822 | − | 0.297178i | \(-0.903954\pi\) | ||||
−0.954822 | + | 0.297178i | \(0.903954\pi\) | |||||||
\(240\) | 8.78603 | 0.567136 | ||||||||
\(241\) | 17.3820 | 1.11967 | 0.559836 | − | 0.828603i | \(-0.310864\pi\) | ||||
0.559836 | + | 0.828603i | \(0.310864\pi\) | |||||||
\(242\) | 12.2322 | 0.786314 | ||||||||
\(243\) | −3.41730 | −0.219220 | ||||||||
\(244\) | −11.5808 | −0.741384 | ||||||||
\(245\) | −7.17753 | −0.458556 | ||||||||
\(246\) | −11.2518 | −0.717387 | ||||||||
\(247\) | 3.79257 | 0.241315 | ||||||||
\(248\) | −0.830425 | −0.0527321 | ||||||||
\(249\) | −30.6938 | −1.94514 | ||||||||
\(250\) | −10.2612 | −0.648974 | ||||||||
\(251\) | −19.5637 | −1.23485 | −0.617426 | − | 0.786629i | \(-0.711824\pi\) | ||||
−0.617426 | + | 0.786629i | \(0.711824\pi\) | |||||||
\(252\) | −29.9543 | −1.88694 | ||||||||
\(253\) | −5.54198 | −0.348421 | ||||||||
\(254\) | 6.74636 | 0.423304 | ||||||||
\(255\) | −2.59640 | −0.162593 | ||||||||
\(256\) | 20.4191 | 1.27620 | ||||||||
\(257\) | 21.9755 | 1.37080 | 0.685398 | − | 0.728168i | \(-0.259628\pi\) | ||||
0.685398 | + | 0.728168i | \(0.259628\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.2851 | 1.07404 | ||||||||
\(260\) | 1.23009 | 0.0762868 | ||||||||
\(261\) | −43.9415 | −2.71991 | ||||||||
\(262\) | 30.9735 | 1.91355 | ||||||||
\(263\) | −21.1856 | −1.30636 | −0.653181 | − | 0.757202i | \(-0.726566\pi\) | ||||
−0.653181 | + | 0.757202i | \(0.726566\pi\) | |||||||
\(264\) | 8.79945 | 0.541569 | ||||||||
\(265\) | 3.52181 | 0.216343 | ||||||||
\(266\) | −16.9372 | −1.03849 | ||||||||
\(267\) | −17.9120 | −1.09620 | ||||||||
\(268\) | −0.627351 | −0.0383215 | ||||||||
\(269\) | −2.43036 | −0.148182 | −0.0740908 | − | 0.997251i | \(-0.523605\pi\) | ||||
−0.0740908 | + | 0.997251i | \(0.523605\pi\) | |||||||
\(270\) | 8.84264 | 0.538146 | ||||||||
\(271\) | 19.9289 | 1.21059 | 0.605296 | − | 0.796000i | \(-0.293055\pi\) | ||||
0.605296 | + | 0.796000i | \(0.293055\pi\) | |||||||
\(272\) | −7.28880 | −0.441948 | ||||||||
\(273\) | 22.5632 | 1.36559 | ||||||||
\(274\) | −5.55020 | −0.335300 | ||||||||
\(275\) | −9.45476 | −0.570143 | ||||||||
\(276\) | −9.55764 | −0.575303 | ||||||||
\(277\) | 15.0216 | 0.902558 | 0.451279 | − | 0.892383i | \(-0.350968\pi\) | ||||
0.451279 | + | 0.892383i | \(0.350968\pi\) | |||||||
\(278\) | −9.31642 | −0.558762 | ||||||||
\(279\) | −3.30658 | −0.197960 | ||||||||
\(280\) | 3.79077 | 0.226542 | ||||||||
\(281\) | 32.7779 | 1.95536 | 0.977682 | − | 0.210091i | \(-0.0673761\pi\) | ||||
0.977682 | + | 0.210091i | \(0.0673761\pi\) | |||||||
\(282\) | −49.5612 | −2.95133 | ||||||||
\(283\) | 12.5323 | 0.744967 | 0.372483 | − | 0.928039i | \(-0.378506\pi\) | ||||
0.372483 | + | 0.928039i | \(0.378506\pi\) | |||||||
\(284\) | −6.31721 | −0.374857 | ||||||||
\(285\) | 3.84908 | 0.228000 | ||||||||
\(286\) | 6.33134 | 0.374380 | ||||||||
\(287\) | −9.27453 | −0.547458 | ||||||||
\(288\) | 34.5014 | 2.03302 | ||||||||
\(289\) | −14.8461 | −0.873297 | ||||||||
\(290\) | −8.05861 | −0.473218 | ||||||||
\(291\) | 30.4241 | 1.78349 | ||||||||
\(292\) | −16.6366 | −0.973581 | ||||||||
\(293\) | −7.34726 | −0.429232 | −0.214616 | − | 0.976699i | \(-0.568850\pi\) | ||||
−0.214616 | + | 0.976699i | \(0.568850\pi\) | |||||||
\(294\) | −63.7119 | −3.71576 | ||||||||
\(295\) | −3.04733 | −0.177422 | ||||||||
\(296\) | −5.77213 | −0.335498 | ||||||||
\(297\) | 16.9192 | 0.981753 | ||||||||
\(298\) | −36.3313 | −2.10462 | ||||||||
\(299\) | 4.74543 | 0.274435 | ||||||||
\(300\) | −16.3056 | −0.941403 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 35.6240 | 2.04993 | ||||||||
\(303\) | −33.1685 | −1.90548 | ||||||||
\(304\) | 10.8054 | 0.619734 | ||||||||
\(305\) | 5.83560 | 0.334146 | ||||||||
\(306\) | −15.1914 | −0.868436 | ||||||||
\(307\) | 11.3798 | 0.649480 | 0.324740 | − | 0.945803i | \(-0.394723\pi\) | ||||
0.324740 | + | 0.945803i | \(0.394723\pi\) | |||||||
\(308\) | −10.5110 | −0.598917 | ||||||||
\(309\) | −0.413963 | −0.0235495 | ||||||||
\(310\) | −0.606407 | −0.0344416 | ||||||||
\(311\) | 24.8424 | 1.40868 | 0.704342 | − | 0.709861i | \(-0.251242\pi\) | ||||
0.704342 | + | 0.709861i | \(0.251242\pi\) | |||||||
\(312\) | −7.53470 | −0.426568 | ||||||||
\(313\) | 16.9309 | 0.956989 | 0.478495 | − | 0.878090i | \(-0.341183\pi\) | ||||
0.478495 | + | 0.878090i | \(0.341183\pi\) | |||||||
\(314\) | −30.7128 | −1.73322 | ||||||||
\(315\) | 15.0941 | 0.850454 | ||||||||
\(316\) | 4.32254 | 0.243162 | ||||||||
\(317\) | 23.6541 | 1.32855 | 0.664273 | − | 0.747490i | \(-0.268741\pi\) | ||||
0.664273 | + | 0.747490i | \(0.268741\pi\) | |||||||
\(318\) | 31.2616 | 1.75306 | ||||||||
\(319\) | −15.4191 | −0.863303 | ||||||||
\(320\) | 0.404302 | 0.0226012 | ||||||||
\(321\) | 17.3516 | 0.968470 | ||||||||
\(322\) | −21.1925 | −1.18101 | ||||||||
\(323\) | −3.19316 | −0.177672 | ||||||||
\(324\) | 8.58253 | 0.476807 | ||||||||
\(325\) | 8.09582 | 0.449075 | ||||||||
\(326\) | −38.9383 | −2.15659 | ||||||||
\(327\) | 2.33980 | 0.129391 | ||||||||
\(328\) | 3.09711 | 0.171010 | ||||||||
\(329\) | −40.8519 | −2.25224 | ||||||||
\(330\) | 6.42568 | 0.353722 | ||||||||
\(331\) | 24.1779 | 1.32894 | 0.664469 | − | 0.747316i | \(-0.268658\pi\) | ||||
0.664469 | + | 0.747316i | \(0.268658\pi\) | |||||||
\(332\) | −12.2434 | −0.671944 | ||||||||
\(333\) | −22.9834 | −1.25948 | ||||||||
\(334\) | −15.1299 | −0.827873 | ||||||||
\(335\) | 0.316124 | 0.0172717 | ||||||||
\(336\) | 64.2849 | 3.50703 | ||||||||
\(337\) | −15.5384 | −0.846431 | −0.423216 | − | 0.906029i | \(-0.639099\pi\) | ||||
−0.423216 | + | 0.906029i | \(0.639099\pi\) | |||||||
\(338\) | 17.7734 | 0.966743 | ||||||||
\(339\) | −17.8639 | −0.970234 | ||||||||
\(340\) | −1.03567 | −0.0561672 | ||||||||
\(341\) | −1.16028 | −0.0628326 | ||||||||
\(342\) | 22.5208 | 1.21779 | ||||||||
\(343\) | −21.9745 | −1.18651 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.81613 | 0.259292 | ||||||||
\(346\) | 19.7756 | 1.06314 | ||||||||
\(347\) | −13.7962 | −0.740618 | −0.370309 | − | 0.928909i | \(-0.620748\pi\) | ||||
−0.370309 | + | 0.928909i | \(0.620748\pi\) | |||||||
\(348\) | −26.5916 | −1.42546 | ||||||||
\(349\) | 13.4384 | 0.719341 | 0.359671 | − | 0.933079i | \(-0.382889\pi\) | ||||
0.359671 | + | 0.933079i | \(0.382889\pi\) | |||||||
\(350\) | −36.1550 | −1.93257 | ||||||||
\(351\) | −14.4874 | −0.773280 | ||||||||
\(352\) | 12.1066 | 0.645281 | ||||||||
\(353\) | 7.62634 | 0.405909 | 0.202955 | − | 0.979188i | \(-0.434946\pi\) | ||||
0.202955 | + | 0.979188i | \(0.434946\pi\) | |||||||
\(354\) | −27.0499 | −1.43768 | ||||||||
\(355\) | 3.18327 | 0.168950 | ||||||||
\(356\) | −7.14491 | −0.378680 | ||||||||
\(357\) | −18.9971 | −1.00543 | ||||||||
\(358\) | 27.5059 | 1.45373 | ||||||||
\(359\) | 16.8262 | 0.888053 | 0.444026 | − | 0.896014i | \(-0.353550\pi\) | ||||
0.444026 | + | 0.896014i | \(0.353550\pi\) | |||||||
\(360\) | −5.04048 | −0.265656 | ||||||||
\(361\) | −14.2662 | −0.750855 | ||||||||
\(362\) | 5.72379 | 0.300836 | ||||||||
\(363\) | −20.3393 | −1.06754 | ||||||||
\(364\) | 9.00020 | 0.471739 | ||||||||
\(365\) | 8.38323 | 0.438798 | ||||||||
\(366\) | 51.8002 | 2.70764 | ||||||||
\(367\) | 0.0729401 | 0.00380744 | 0.00190372 | − | 0.999998i | \(-0.499394\pi\) | ||||
0.00190372 | + | 0.999998i | \(0.499394\pi\) | |||||||
\(368\) | 13.5202 | 0.704790 | ||||||||
\(369\) | 12.3321 | 0.641981 | ||||||||
\(370\) | −4.21502 | −0.219128 | ||||||||
\(371\) | 25.7681 | 1.33781 | ||||||||
\(372\) | −2.00101 | −0.103747 | ||||||||
\(373\) | 25.7567 | 1.33363 | 0.666817 | − | 0.745222i | \(-0.267656\pi\) | ||||
0.666817 | + | 0.745222i | \(0.267656\pi\) | |||||||
\(374\) | −5.33068 | −0.275643 | ||||||||
\(375\) | 17.0620 | 0.881076 | ||||||||
\(376\) | 13.6420 | 0.703532 | ||||||||
\(377\) | 13.2029 | 0.679983 | ||||||||
\(378\) | 64.6991 | 3.32776 | ||||||||
\(379\) | −16.0471 | −0.824284 | −0.412142 | − | 0.911120i | \(-0.635219\pi\) | ||||
−0.412142 | + | 0.911120i | \(0.635219\pi\) | |||||||
\(380\) | 1.53535 | 0.0787620 | ||||||||
\(381\) | −11.2176 | −0.574697 | ||||||||
\(382\) | 9.51515 | 0.486837 | ||||||||
\(383\) | −24.1300 | −1.23299 | −0.616493 | − | 0.787360i | \(-0.711447\pi\) | ||||
−0.616493 | + | 0.787360i | \(0.711447\pi\) | |||||||
\(384\) | −31.6976 | −1.61756 | ||||||||
\(385\) | 5.29651 | 0.269935 | ||||||||
\(386\) | 11.9930 | 0.610430 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.1358 | 0.616103 | ||||||||
\(389\) | 16.4021 | 0.831621 | 0.415810 | − | 0.909451i | \(-0.363498\pi\) | ||||
0.415810 | + | 0.909451i | \(0.363498\pi\) | |||||||
\(390\) | −5.50211 | −0.278610 | ||||||||
\(391\) | −3.99541 | −0.202057 | ||||||||
\(392\) | 17.5371 | 0.885756 | ||||||||
\(393\) | −51.5018 | −2.59792 | ||||||||
\(394\) | 8.67342 | 0.436960 | ||||||||
\(395\) | −2.17814 | −0.109594 | ||||||||
\(396\) | 13.9761 | 0.702325 | ||||||||
\(397\) | −7.70285 | −0.386595 | −0.193298 | − | 0.981140i | \(-0.561918\pi\) | ||||
−0.193298 | + | 0.981140i | \(0.561918\pi\) | |||||||
\(398\) | 40.4413 | 2.02714 | ||||||||
\(399\) | 28.1626 | 1.40989 | ||||||||
\(400\) | 23.0658 | 1.15329 | ||||||||
\(401\) | 1.41296 | 0.0705600 | 0.0352800 | − | 0.999377i | \(-0.488768\pi\) | ||||
0.0352800 | + | 0.999377i | \(0.488768\pi\) | |||||||
\(402\) | 2.80610 | 0.139956 | ||||||||
\(403\) | 0.993511 | 0.0494903 | ||||||||
\(404\) | −13.2305 | −0.658244 | ||||||||
\(405\) | −4.32477 | −0.214899 | ||||||||
\(406\) | −58.9626 | −2.92626 | ||||||||
\(407\) | −8.06488 | −0.399761 | ||||||||
\(408\) | 6.34384 | 0.314067 | ||||||||
\(409\) | −7.12388 | −0.352253 | −0.176127 | − | 0.984368i | \(-0.556357\pi\) | ||||
−0.176127 | + | 0.984368i | \(0.556357\pi\) | |||||||
\(410\) | 2.26162 | 0.111694 | ||||||||
\(411\) | 9.22869 | 0.455218 | ||||||||
\(412\) | −0.165125 | −0.00813513 | ||||||||
\(413\) | −22.2965 | −1.09714 | ||||||||
\(414\) | 28.1791 | 1.38493 | ||||||||
\(415\) | 6.16950 | 0.302849 | ||||||||
\(416\) | −10.3665 | −0.508258 | ||||||||
\(417\) | 15.4911 | 0.758600 | ||||||||
\(418\) | 7.90257 | 0.386527 | ||||||||
\(419\) | 13.7080 | 0.669679 | 0.334840 | − | 0.942275i | \(-0.391318\pi\) | ||||
0.334840 | + | 0.942275i | \(0.391318\pi\) | |||||||
\(420\) | 9.13431 | 0.445709 | ||||||||
\(421\) | −1.86680 | −0.0909825 | −0.0454912 | − | 0.998965i | \(-0.514485\pi\) | ||||
−0.0454912 | + | 0.998965i | \(0.514485\pi\) | |||||||
\(422\) | −33.8588 | −1.64822 | ||||||||
\(423\) | 54.3195 | 2.64111 | ||||||||
\(424\) | −8.60492 | −0.417892 | ||||||||
\(425\) | −6.81628 | −0.330638 | ||||||||
\(426\) | 28.2565 | 1.36903 | ||||||||
\(427\) | 42.6975 | 2.06628 | ||||||||
\(428\) | 6.92135 | 0.334556 | ||||||||
\(429\) | −10.5276 | −0.508275 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.8277 | −1.14774 | −0.573871 | − | 0.818946i | \(-0.694559\pi\) | ||||
−0.573871 | + | 0.818946i | \(0.694559\pi\) | |||||||
\(432\) | −41.2761 | −1.98590 | ||||||||
\(433\) | 40.0874 | 1.92648 | 0.963240 | − | 0.268643i | \(-0.0865753\pi\) | ||||
0.963240 | + | 0.268643i | \(0.0865753\pi\) | |||||||
\(434\) | −4.43691 | −0.212978 | ||||||||
\(435\) | 13.3996 | 0.642462 | ||||||||
\(436\) | 0.933320 | 0.0446979 | ||||||||
\(437\) | 5.92308 | 0.283339 | ||||||||
\(438\) | 74.4144 | 3.55566 | ||||||||
\(439\) | 8.29016 | 0.395668 | 0.197834 | − | 0.980236i | \(-0.436609\pi\) | ||||
0.197834 | + | 0.980236i | \(0.436609\pi\) | |||||||
\(440\) | −1.76870 | −0.0843196 | ||||||||
\(441\) | 69.8289 | 3.32519 | ||||||||
\(442\) | 4.56449 | 0.217111 | ||||||||
\(443\) | −31.4964 | −1.49644 | −0.748219 | − | 0.663452i | \(-0.769091\pi\) | ||||
−0.748219 | + | 0.663452i | \(0.769091\pi\) | |||||||
\(444\) | −13.9086 | −0.660074 | ||||||||
\(445\) | 3.60035 | 0.170673 | ||||||||
\(446\) | −17.2408 | −0.816376 | ||||||||
\(447\) | 60.4106 | 2.85732 | ||||||||
\(448\) | 2.95817 | 0.139760 | ||||||||
\(449\) | 15.4315 | 0.728257 | 0.364129 | − | 0.931349i | \(-0.381367\pi\) | ||||
0.364129 | + | 0.931349i | \(0.381367\pi\) | |||||||
\(450\) | 48.0742 | 2.26624 | ||||||||
\(451\) | 4.32732 | 0.203766 | ||||||||
\(452\) | −7.12571 | −0.335165 | ||||||||
\(453\) | −59.2345 | −2.78308 | ||||||||
\(454\) | 31.5029 | 1.47850 | ||||||||
\(455\) | −4.53524 | −0.212615 | ||||||||
\(456\) | −9.40456 | −0.440409 | ||||||||
\(457\) | −9.28539 | −0.434352 | −0.217176 | − | 0.976132i | \(-0.569685\pi\) | ||||
−0.217176 | + | 0.976132i | \(0.569685\pi\) | |||||||
\(458\) | 0.422521 | 0.0197431 | ||||||||
\(459\) | 12.1977 | 0.569339 | ||||||||
\(460\) | 1.92110 | 0.0895718 | ||||||||
\(461\) | −20.9145 | −0.974085 | −0.487043 | − | 0.873378i | \(-0.661924\pi\) | ||||
−0.487043 | + | 0.873378i | \(0.661924\pi\) | |||||||
\(462\) | 47.0149 | 2.18733 | ||||||||
\(463\) | 2.18915 | 0.101738 | 0.0508692 | − | 0.998705i | \(-0.483801\pi\) | ||||
0.0508692 | + | 0.998705i | \(0.483801\pi\) | |||||||
\(464\) | 37.6164 | 1.74630 | ||||||||
\(465\) | 1.00831 | 0.0467595 | ||||||||
\(466\) | −12.4326 | −0.575929 | ||||||||
\(467\) | −0.230966 | −0.0106878 | −0.00534391 | − | 0.999986i | \(-0.501701\pi\) | ||||
−0.00534391 | + | 0.999986i | \(0.501701\pi\) | |||||||
\(468\) | −11.9673 | −0.553188 | ||||||||
\(469\) | 2.31299 | 0.106804 | ||||||||
\(470\) | 9.96188 | 0.459507 | ||||||||
\(471\) | 51.0683 | 2.35310 | ||||||||
\(472\) | 7.44562 | 0.342713 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −19.3345 | −0.888061 | ||||||||
\(475\) | 10.1049 | 0.463646 | ||||||||
\(476\) | −7.57773 | −0.347325 | ||||||||
\(477\) | −34.2630 | −1.56879 | ||||||||
\(478\) | 52.6740 | 2.40925 | ||||||||
\(479\) | 5.00954 | 0.228892 | 0.114446 | − | 0.993429i | \(-0.463491\pi\) | ||||
0.114446 | + | 0.993429i | \(0.463491\pi\) | |||||||
\(480\) | −10.5209 | −0.480212 | ||||||||
\(481\) | 6.90571 | 0.314873 | ||||||||
\(482\) | −31.0131 | −1.41261 | ||||||||
\(483\) | 35.2383 | 1.60340 | ||||||||
\(484\) | −8.11311 | −0.368778 | ||||||||
\(485\) | −6.11529 | −0.277681 | ||||||||
\(486\) | 6.09716 | 0.276573 | ||||||||
\(487\) | −13.0400 | −0.590899 | −0.295450 | − | 0.955358i | \(-0.595469\pi\) | ||||
−0.295450 | + | 0.955358i | \(0.595469\pi\) | |||||||
\(488\) | −14.2583 | −0.645442 | ||||||||
\(489\) | 64.7454 | 2.92789 | ||||||||
\(490\) | 12.8062 | 0.578525 | ||||||||
\(491\) | 25.3230 | 1.14281 | 0.571406 | − | 0.820668i | \(-0.306398\pi\) | ||||
0.571406 | + | 0.820668i | \(0.306398\pi\) | |||||||
\(492\) | 7.46285 | 0.336451 | ||||||||
\(493\) | −11.1162 | −0.500647 | ||||||||
\(494\) | −6.76672 | −0.304449 | ||||||||
\(495\) | −7.04261 | −0.316542 | ||||||||
\(496\) | 2.83062 | 0.127098 | ||||||||
\(497\) | 23.2911 | 1.04475 | ||||||||
\(498\) | 54.7640 | 2.45404 | ||||||||
\(499\) | 8.68477 | 0.388784 | 0.194392 | − | 0.980924i | \(-0.437727\pi\) | ||||
0.194392 | + | 0.980924i | \(0.437727\pi\) | |||||||
\(500\) | 6.80583 | 0.304366 | ||||||||
\(501\) | 25.1576 | 1.12396 | ||||||||
\(502\) | 34.9057 | 1.55792 | ||||||||
\(503\) | 28.7691 | 1.28275 | 0.641374 | − | 0.767228i | \(-0.278365\pi\) | ||||
0.641374 | + | 0.767228i | \(0.278365\pi\) | |||||||
\(504\) | −36.8797 | −1.64275 | ||||||||
\(505\) | 6.66692 | 0.296674 | ||||||||
\(506\) | 9.88804 | 0.439577 | ||||||||
\(507\) | −29.5530 | −1.31249 | ||||||||
\(508\) | −4.47459 | −0.198528 | ||||||||
\(509\) | 26.5391 | 1.17632 | 0.588162 | − | 0.808743i | \(-0.299852\pi\) | ||||
0.588162 | + | 0.808743i | \(0.299852\pi\) | |||||||
\(510\) | 4.63251 | 0.205131 | ||||||||
\(511\) | 61.3377 | 2.71342 | ||||||||
\(512\) | −15.0632 | −0.665705 | ||||||||
\(513\) | −18.0827 | −0.798370 | ||||||||
\(514\) | −39.2089 | −1.72943 | ||||||||
\(515\) | 0.0832072 | 0.00366655 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.0607 | 0.838290 | ||||||||
\(518\) | −30.8401 | −1.35504 | ||||||||
\(519\) | −32.8822 | −1.44337 | ||||||||
\(520\) | 1.51449 | 0.0664146 | ||||||||
\(521\) | −35.6883 | −1.56353 | −0.781766 | − | 0.623572i | \(-0.785681\pi\) | ||||
−0.781766 | + | 0.623572i | \(0.785681\pi\) | |||||||
\(522\) | 78.4007 | 3.43150 | ||||||||
\(523\) | −38.8890 | −1.70050 | −0.850249 | − | 0.526381i | \(-0.823549\pi\) | ||||
−0.850249 | + | 0.526381i | \(0.823549\pi\) | |||||||
\(524\) | −20.5435 | −0.897447 | ||||||||
\(525\) | 60.1174 | 2.62374 | ||||||||
\(526\) | 37.7995 | 1.64814 | ||||||||
\(527\) | −0.836487 | −0.0364380 | ||||||||
\(528\) | −29.9941 | −1.30533 | ||||||||
\(529\) | −15.5888 | −0.677773 | ||||||||
\(530\) | −6.28363 | −0.272943 | ||||||||
\(531\) | 29.6469 | 1.28657 | ||||||||
\(532\) | 11.2338 | 0.487045 | ||||||||
\(533\) | −3.70535 | −0.160497 | ||||||||
\(534\) | 31.9588 | 1.38299 | ||||||||
\(535\) | −3.48769 | −0.150786 | ||||||||
\(536\) | −0.772396 | −0.0333624 | ||||||||
\(537\) | −45.7360 | −1.97365 | ||||||||
\(538\) | 4.33626 | 0.186950 | ||||||||
\(539\) | 24.5030 | 1.05542 | ||||||||
\(540\) | −5.86497 | −0.252388 | ||||||||
\(541\) | 19.1568 | 0.823615 | 0.411807 | − | 0.911271i | \(-0.364898\pi\) | ||||
0.411807 | + | 0.911271i | \(0.364898\pi\) | |||||||
\(542\) | −35.5572 | −1.52731 | ||||||||
\(543\) | −9.51734 | −0.408428 | ||||||||
\(544\) | 8.72805 | 0.374212 | ||||||||
\(545\) | −0.470304 | −0.0201456 | ||||||||
\(546\) | −40.2574 | −1.72286 | ||||||||
\(547\) | −2.41686 | −0.103337 | −0.0516687 | − | 0.998664i | \(-0.516454\pi\) | ||||
−0.0516687 | + | 0.998664i | \(0.516454\pi\) | |||||||
\(548\) | 3.68122 | 0.157254 | ||||||||
\(549\) | −56.7735 | −2.42303 | ||||||||
\(550\) | 16.8692 | 0.719307 | ||||||||
\(551\) | 16.4794 | 0.702046 | ||||||||
\(552\) | −11.7674 | −0.500853 | ||||||||
\(553\) | −15.9369 | −0.677704 | ||||||||
\(554\) | −26.8016 | −1.13869 | ||||||||
\(555\) | 7.00861 | 0.297499 | ||||||||
\(556\) | 6.17921 | 0.262057 | ||||||||
\(557\) | 2.65074 | 0.112315 | 0.0561576 | − | 0.998422i | \(-0.482115\pi\) | ||||
0.0561576 | + | 0.998422i | \(0.482115\pi\) | |||||||
\(558\) | 5.89962 | 0.249751 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −12.9214 | −0.546027 | ||||||||
\(561\) | 8.86369 | 0.374225 | ||||||||
\(562\) | −58.4825 | −2.46693 | ||||||||
\(563\) | 4.82635 | 0.203407 | 0.101703 | − | 0.994815i | \(-0.467571\pi\) | ||||
0.101703 | + | 0.994815i | \(0.467571\pi\) | |||||||
\(564\) | 32.8719 | 1.38416 | ||||||||
\(565\) | 3.59067 | 0.151061 | ||||||||
\(566\) | −22.3602 | −0.939868 | ||||||||
\(567\) | −31.6431 | −1.32889 | ||||||||
\(568\) | −7.77776 | −0.326348 | ||||||||
\(569\) | 12.1025 | 0.507364 | 0.253682 | − | 0.967288i | \(-0.418358\pi\) | ||||
0.253682 | + | 0.967288i | \(0.418358\pi\) | |||||||
\(570\) | −6.86755 | −0.287650 | ||||||||
\(571\) | −28.1047 | −1.17614 | −0.588072 | − | 0.808809i | \(-0.700113\pi\) | ||||
−0.588072 | + | 0.808809i | \(0.700113\pi\) | |||||||
\(572\) | −4.19932 | −0.175583 | ||||||||
\(573\) | −15.8215 | −0.660952 | ||||||||
\(574\) | 16.5477 | 0.690687 | ||||||||
\(575\) | 12.6437 | 0.527280 | ||||||||
\(576\) | −3.93338 | −0.163891 | ||||||||
\(577\) | −23.2153 | −0.966467 | −0.483233 | − | 0.875492i | \(-0.660538\pi\) | ||||
−0.483233 | + | 0.875492i | \(0.660538\pi\) | |||||||
\(578\) | 26.4884 | 1.10177 | ||||||||
\(579\) | −19.9417 | −0.828747 | ||||||||
\(580\) | 5.34495 | 0.221937 | ||||||||
\(581\) | 45.1405 | 1.87274 | ||||||||
\(582\) | −54.2828 | −2.25010 | ||||||||
\(583\) | −12.0229 | −0.497937 | ||||||||
\(584\) | −20.4830 | −0.847591 | ||||||||
\(585\) | 6.03036 | 0.249325 | ||||||||
\(586\) | 13.1090 | 0.541529 | ||||||||
\(587\) | 34.5213 | 1.42485 | 0.712424 | − | 0.701749i | \(-0.247597\pi\) | ||||
0.712424 | + | 0.701749i | \(0.247597\pi\) | |||||||
\(588\) | 42.2576 | 1.74267 | ||||||||
\(589\) | 1.24007 | 0.0510961 | ||||||||
\(590\) | 5.43706 | 0.223840 | ||||||||
\(591\) | −14.4219 | −0.593237 | ||||||||
\(592\) | 19.6751 | 0.808641 | ||||||||
\(593\) | 27.1159 | 1.11352 | 0.556758 | − | 0.830675i | \(-0.312045\pi\) | ||||
0.556758 | + | 0.830675i | \(0.312045\pi\) | |||||||
\(594\) | −30.1874 | −1.23860 | ||||||||
\(595\) | 3.81845 | 0.156541 | ||||||||
\(596\) | 24.0971 | 0.987056 | ||||||||
\(597\) | −67.2445 | −2.75214 | ||||||||
\(598\) | −8.46682 | −0.346234 | ||||||||
\(599\) | 7.69678 | 0.314482 | 0.157241 | − | 0.987560i | \(-0.449740\pi\) | ||||
0.157241 | + | 0.987560i | \(0.449740\pi\) | |||||||
\(600\) | −20.0755 | −0.819578 | ||||||||
\(601\) | −31.0119 | −1.26500 | −0.632500 | − | 0.774560i | \(-0.717971\pi\) | ||||
−0.632500 | + | 0.774560i | \(0.717971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.07552 | −0.125245 | ||||||||
\(604\) | −23.6280 | −0.961410 | ||||||||
\(605\) | 4.08823 | 0.166210 | ||||||||
\(606\) | 59.1794 | 2.40400 | ||||||||
\(607\) | 4.76958 | 0.193591 | 0.0967957 | − | 0.995304i | \(-0.469141\pi\) | ||||
0.0967957 | + | 0.995304i | \(0.469141\pi\) | |||||||
\(608\) | −12.9391 | −0.524749 | ||||||||
\(609\) | 98.0411 | 3.97283 | ||||||||
\(610\) | −10.4119 | −0.421566 | ||||||||
\(611\) | −16.3211 | −0.660282 | ||||||||
\(612\) | 10.0759 | 0.407293 | ||||||||
\(613\) | −34.2509 | −1.38338 | −0.691691 | − | 0.722194i | \(-0.743134\pi\) | ||||
−0.691691 | + | 0.722194i | \(0.743134\pi\) | |||||||
\(614\) | −20.3039 | −0.819400 | ||||||||
\(615\) | −3.76056 | −0.151640 | ||||||||
\(616\) | −12.9411 | −0.521412 | ||||||||
\(617\) | 22.8354 | 0.919319 | 0.459659 | − | 0.888095i | \(-0.347972\pi\) | ||||
0.459659 | + | 0.888095i | \(0.347972\pi\) | |||||||
\(618\) | 0.738595 | 0.0297107 | ||||||||
\(619\) | 16.2615 | 0.653607 | 0.326803 | − | 0.945092i | \(-0.394029\pi\) | ||||
0.326803 | + | 0.945092i | \(0.394029\pi\) | |||||||
\(620\) | 0.402205 | 0.0161530 | ||||||||
\(621\) | −22.6258 | −0.907944 | ||||||||
\(622\) | −44.3240 | −1.77723 | ||||||||
\(623\) | 26.3427 | 1.05540 | ||||||||
\(624\) | 25.6830 | 1.02814 | ||||||||
\(625\) | 19.7926 | 0.791702 | ||||||||
\(626\) | −30.2082 | −1.20736 | ||||||||
\(627\) | −13.1401 | −0.524767 | ||||||||
\(628\) | 20.3706 | 0.812874 | ||||||||
\(629\) | −5.81427 | −0.231830 | ||||||||
\(630\) | −26.9309 | −1.07295 | ||||||||
\(631\) | −1.91996 | −0.0764323 | −0.0382162 | − | 0.999269i | \(-0.512168\pi\) | ||||
−0.0382162 | + | 0.999269i | \(0.512168\pi\) | |||||||
\(632\) | 5.32192 | 0.211695 | ||||||||
\(633\) | 56.2994 | 2.23770 | ||||||||
\(634\) | −42.2038 | −1.67613 | ||||||||
\(635\) | 2.25476 | 0.0894776 | ||||||||
\(636\) | −20.7346 | −0.822179 | ||||||||
\(637\) | −20.9811 | −0.831303 | ||||||||
\(638\) | 27.5108 | 1.08916 | ||||||||
\(639\) | −30.9694 | −1.22513 | ||||||||
\(640\) | 6.37126 | 0.251846 | ||||||||
\(641\) | −29.6154 | −1.16974 | −0.584869 | − | 0.811128i | \(-0.698854\pi\) | ||||
−0.584869 | + | 0.811128i | \(0.698854\pi\) | |||||||
\(642\) | −30.9588 | −1.22185 | ||||||||
\(643\) | −10.3385 | −0.407710 | −0.203855 | − | 0.979001i | \(-0.565347\pi\) | ||||
−0.203855 | + | 0.979001i | \(0.565347\pi\) | |||||||
\(644\) | 14.0562 | 0.553890 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.69725 | 0.224155 | ||||||||
\(647\) | 15.2577 | 0.599843 | 0.299921 | − | 0.953964i | \(-0.403040\pi\) | ||||
0.299921 | + | 0.953964i | \(0.403040\pi\) | |||||||
\(648\) | 10.5668 | 0.415104 | ||||||||
\(649\) | 10.4031 | 0.408358 | ||||||||
\(650\) | −14.4446 | −0.566564 | ||||||||
\(651\) | 7.37756 | 0.289149 | ||||||||
\(652\) | 25.8262 | 1.01143 | ||||||||
\(653\) | −1.96573 | −0.0769249 | −0.0384625 | − | 0.999260i | \(-0.512246\pi\) | ||||
−0.0384625 | + | 0.999260i | \(0.512246\pi\) | |||||||
\(654\) | −4.17469 | −0.163243 | ||||||||
\(655\) | 10.3519 | 0.404484 | ||||||||
\(656\) | −10.5569 | −0.412179 | ||||||||
\(657\) | −81.5589 | −3.18192 | ||||||||
\(658\) | 72.8883 | 2.84148 | ||||||||
\(659\) | −29.7073 | −1.15723 | −0.578616 | − | 0.815600i | \(-0.696407\pi\) | ||||
−0.578616 | + | 0.815600i | \(0.696407\pi\) | |||||||
\(660\) | −4.26190 | −0.165894 | ||||||||
\(661\) | −11.8003 | −0.458978 | −0.229489 | − | 0.973311i | \(-0.573705\pi\) | ||||
−0.229489 | + | 0.973311i | \(0.573705\pi\) | |||||||
\(662\) | −43.1384 | −1.67662 | ||||||||
\(663\) | −7.58970 | −0.294759 | ||||||||
\(664\) | −15.0741 | −0.584989 | ||||||||
\(665\) | −5.66073 | −0.219514 | ||||||||
\(666\) | 41.0072 | 1.58899 | ||||||||
\(667\) | 20.6197 | 0.798399 | ||||||||
\(668\) | 10.0351 | 0.388269 | ||||||||
\(669\) | 28.6675 | 1.10835 | ||||||||
\(670\) | −0.564031 | −0.0217904 | ||||||||
\(671\) | −19.9218 | −0.769074 | ||||||||
\(672\) | −76.9787 | −2.96952 | ||||||||
\(673\) | 20.3486 | 0.784383 | 0.392191 | − | 0.919884i | \(-0.371717\pi\) | ||||
0.392191 | + | 0.919884i | \(0.371717\pi\) | |||||||
\(674\) | 27.7237 | 1.06788 | ||||||||
\(675\) | −38.6003 | −1.48573 | ||||||||
\(676\) | −11.7884 | −0.453398 | ||||||||
\(677\) | −23.8419 | −0.916320 | −0.458160 | − | 0.888870i | \(-0.651491\pi\) | ||||
−0.458160 | + | 0.888870i | \(0.651491\pi\) | |||||||
\(678\) | 31.8729 | 1.22407 | ||||||||
\(679\) | −44.7438 | −1.71711 | ||||||||
\(680\) | −1.27512 | −0.0488987 | ||||||||
\(681\) | −52.3820 | −2.00728 | ||||||||
\(682\) | 2.07018 | 0.0792712 | ||||||||
\(683\) | 35.4165 | 1.35518 | 0.677588 | − | 0.735442i | \(-0.263025\pi\) | ||||
0.677588 | + | 0.735442i | \(0.263025\pi\) | |||||||
\(684\) | −14.9372 | −0.571137 | ||||||||
\(685\) | −1.85498 | −0.0708752 | ||||||||
\(686\) | 39.2070 | 1.49693 | ||||||||
\(687\) | −0.702556 | −0.0268042 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.2948 | 0.392202 | ||||||||
\(690\) | −8.59298 | −0.327129 | ||||||||
\(691\) | 15.5979 | 0.593373 | 0.296687 | − | 0.954975i | \(-0.404118\pi\) | ||||
0.296687 | + | 0.954975i | \(0.404118\pi\) | |||||||
\(692\) | −13.1163 | −0.498609 | ||||||||
\(693\) | −51.5288 | −1.95742 | ||||||||
\(694\) | 24.6152 | 0.934382 | ||||||||
\(695\) | −3.11373 | −0.118110 | ||||||||
\(696\) | −32.7396 | −1.24099 | ||||||||
\(697\) | 3.11972 | 0.118168 | ||||||||
\(698\) | −23.9769 | −0.907539 | ||||||||
\(699\) | 20.6725 | 0.781908 | ||||||||
\(700\) | 23.9802 | 0.906365 | ||||||||
\(701\) | 10.9798 | 0.414702 | 0.207351 | − | 0.978267i | \(-0.433516\pi\) | ||||
0.207351 | + | 0.978267i | \(0.433516\pi\) | |||||||
\(702\) | 25.8485 | 0.975589 | ||||||||
\(703\) | 8.61948 | 0.325090 | ||||||||
\(704\) | −1.38022 | −0.0520192 | ||||||||
\(705\) | −16.5643 | −0.623848 | ||||||||
\(706\) | −13.6070 | −0.512105 | ||||||||
\(707\) | 48.7800 | 1.83456 | ||||||||
\(708\) | 17.9411 | 0.674267 | ||||||||
\(709\) | 33.2542 | 1.24889 | 0.624445 | − | 0.781069i | \(-0.285325\pi\) | ||||
0.624445 | + | 0.781069i | \(0.285325\pi\) | |||||||
\(710\) | −5.67961 | −0.213152 | ||||||||
\(711\) | 21.1908 | 0.794715 | ||||||||
\(712\) | −8.79683 | −0.329675 | ||||||||
\(713\) | 1.55163 | 0.0581089 | ||||||||
\(714\) | 33.8947 | 1.26848 | ||||||||
\(715\) | 2.11606 | 0.0791360 | ||||||||
\(716\) | −18.2436 | −0.681795 | ||||||||
\(717\) | −87.5847 | −3.27091 | ||||||||
\(718\) | −30.0214 | −1.12039 | ||||||||
\(719\) | −23.0531 | −0.859734 | −0.429867 | − | 0.902892i | \(-0.641440\pi\) | ||||
−0.429867 | + | 0.902892i | \(0.641440\pi\) | |||||||
\(720\) | 17.1811 | 0.640303 | ||||||||
\(721\) | 0.608804 | 0.0226730 | ||||||||
\(722\) | 25.4539 | 0.947297 | ||||||||
\(723\) | 51.5676 | 1.91782 | ||||||||
\(724\) | −3.79636 | −0.141091 | ||||||||
\(725\) | 35.1778 | 1.30647 | ||||||||
\(726\) | 36.2895 | 1.34683 | ||||||||
\(727\) | 27.9375 | 1.03614 | 0.518072 | − | 0.855337i | \(-0.326650\pi\) | ||||
0.518072 | + | 0.855337i | \(0.326650\pi\) | |||||||
\(728\) | 11.0811 | 0.410692 | ||||||||
\(729\) | −31.8956 | −1.18132 | ||||||||
\(730\) | −14.9574 | −0.553599 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −34.3570 | −1.26987 | ||||||||
\(733\) | 6.77186 | 0.250124 | 0.125062 | − | 0.992149i | \(-0.460087\pi\) | ||||
0.125062 | + | 0.992149i | \(0.460087\pi\) | |||||||
\(734\) | −0.130140 | −0.00480356 | ||||||||
\(735\) | −21.2938 | −0.785432 | ||||||||
\(736\) | −16.1899 | −0.596769 | ||||||||
\(737\) | −1.07920 | −0.0397528 | ||||||||
\(738\) | −22.0029 | −0.809939 | ||||||||
\(739\) | 15.0999 | 0.555458 | 0.277729 | − | 0.960660i | \(-0.410418\pi\) | ||||
0.277729 | + | 0.960660i | \(0.410418\pi\) | |||||||
\(740\) | 2.79565 | 0.102770 | ||||||||
\(741\) | 11.2515 | 0.413334 | ||||||||
\(742\) | −45.9755 | −1.68782 | ||||||||
\(743\) | 25.5817 | 0.938501 | 0.469250 | − | 0.883065i | \(-0.344524\pi\) | ||||
0.469250 | + | 0.883065i | \(0.344524\pi\) | |||||||
\(744\) | −2.46364 | −0.0903215 | ||||||||
\(745\) | −12.1426 | −0.444871 | ||||||||
\(746\) | −45.9553 | −1.68254 | ||||||||
\(747\) | −60.0219 | −2.19609 | ||||||||
\(748\) | 3.53562 | 0.129275 | ||||||||
\(749\) | −25.5185 | −0.932425 | ||||||||
\(750\) | −30.4421 | −1.11159 | ||||||||
\(751\) | 26.5575 | 0.969097 | 0.484548 | − | 0.874764i | \(-0.338984\pi\) | ||||
0.484548 | + | 0.874764i | \(0.338984\pi\) | |||||||
\(752\) | −46.5006 | −1.69570 | ||||||||
\(753\) | −58.0402 | −2.11510 | ||||||||
\(754\) | −23.5567 | −0.857883 | ||||||||
\(755\) | 11.9062 | 0.433312 | ||||||||
\(756\) | −42.9123 | −1.56071 | ||||||||
\(757\) | −43.3142 | −1.57428 | −0.787140 | − | 0.616774i | \(-0.788439\pi\) | ||||
−0.787140 | + | 0.616774i | \(0.788439\pi\) | |||||||
\(758\) | 28.6313 | 1.03994 | ||||||||
\(759\) | −16.4415 | −0.596790 | ||||||||
\(760\) | 1.89033 | 0.0685695 | ||||||||
\(761\) | −34.7007 | −1.25790 | −0.628949 | − | 0.777446i | \(-0.716515\pi\) | ||||
−0.628949 | + | 0.777446i | \(0.716515\pi\) | |||||||
\(762\) | 20.0146 | 0.725052 | ||||||||
\(763\) | −3.44108 | −0.124576 | ||||||||
\(764\) | −6.31102 | −0.228325 | ||||||||
\(765\) | −5.07727 | −0.183569 | ||||||||
\(766\) | 43.0530 | 1.55557 | ||||||||
\(767\) | −8.90785 | −0.321644 | ||||||||
\(768\) | 60.5779 | 2.18592 | ||||||||
\(769\) | −15.6400 | −0.563992 | −0.281996 | − | 0.959416i | \(-0.590996\pi\) | ||||
−0.281996 | + | 0.959416i | \(0.590996\pi\) | |||||||
\(770\) | −9.45007 | −0.340557 | ||||||||
\(771\) | 65.1954 | 2.34795 | ||||||||
\(772\) | −7.95450 | −0.286289 | ||||||||
\(773\) | 36.9024 | 1.32729 | 0.663643 | − | 0.748049i | \(-0.269009\pi\) | ||||
0.663643 | + | 0.748049i | \(0.269009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.64711 | 0.0950871 | ||||||||
\(776\) | 14.9417 | 0.536374 | ||||||||
\(777\) | 51.2800 | 1.83966 | ||||||||
\(778\) | −29.2648 | −1.04919 | ||||||||
\(779\) | −4.62489 | −0.165704 | ||||||||
\(780\) | 3.64933 | 0.130667 | ||||||||
\(781\) | −10.8672 | −0.388858 | ||||||||
\(782\) | 7.12864 | 0.254920 | ||||||||
\(783\) | −62.9504 | −2.24966 | ||||||||
\(784\) | −59.7775 | −2.13491 | ||||||||
\(785\) | −10.2648 | −0.366367 | ||||||||
\(786\) | 91.8899 | 3.27760 | ||||||||
\(787\) | −38.7287 | −1.38053 | −0.690265 | − | 0.723557i | \(-0.742506\pi\) | ||||
−0.690265 | + | 0.723557i | \(0.742506\pi\) | |||||||
\(788\) | −5.75273 | −0.204932 | ||||||||
\(789\) | −62.8519 | −2.23759 | ||||||||
\(790\) | 3.88626 | 0.138267 | ||||||||
\(791\) | 26.2719 | 0.934123 | ||||||||
\(792\) | 17.2074 | 0.611438 | ||||||||
\(793\) | 17.0584 | 0.605763 | ||||||||
\(794\) | 13.7435 | 0.487738 | ||||||||
\(795\) | 10.4482 | 0.370560 | ||||||||
\(796\) | −26.8231 | −0.950719 | ||||||||
\(797\) | 38.7160 | 1.37139 | 0.685695 | − | 0.727889i | \(-0.259498\pi\) | ||||
0.685695 | + | 0.727889i | \(0.259498\pi\) | |||||||
\(798\) | −50.2479 | −1.77876 | ||||||||
\(799\) | 13.7416 | 0.486142 | ||||||||
\(800\) | −27.6204 | −0.976530 | ||||||||
\(801\) | −35.0271 | −1.23762 | ||||||||
\(802\) | −2.52102 | −0.0890203 | ||||||||
\(803\) | −28.6190 | −1.00994 | ||||||||
\(804\) | −1.86118 | −0.0656386 | ||||||||
\(805\) | −7.08295 | −0.249641 | ||||||||
\(806\) | −1.77263 | −0.0624382 | ||||||||
\(807\) | −7.21021 | −0.253811 | ||||||||
\(808\) | −16.2895 | −0.573061 | ||||||||
\(809\) | −25.9190 | −0.911262 | −0.455631 | − | 0.890169i | \(-0.650586\pi\) | ||||
−0.455631 | + | 0.890169i | \(0.650586\pi\) | |||||||
\(810\) | 7.71628 | 0.271122 | ||||||||
\(811\) | 11.6619 | 0.409504 | 0.204752 | − | 0.978814i | \(-0.434361\pi\) | ||||
0.204752 | + | 0.978814i | \(0.434361\pi\) | |||||||
\(812\) | 39.1075 | 1.37240 | ||||||||
\(813\) | 59.1234 | 2.07355 | ||||||||
\(814\) | 14.3894 | 0.504349 | ||||||||
\(815\) | −13.0139 | −0.455858 | ||||||||
\(816\) | −21.6238 | −0.756986 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 12.7105 | 0.444411 | ||||||||
\(819\) | 44.1225 | 1.54176 | ||||||||
\(820\) | −1.50005 | −0.0523839 | ||||||||
\(821\) | −6.92887 | −0.241819 | −0.120910 | − | 0.992664i | \(-0.538581\pi\) | ||||
−0.120910 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(822\) | −16.4659 | −0.574314 | ||||||||
\(823\) | 2.20617 | 0.0769022 | 0.0384511 | − | 0.999260i | \(-0.487758\pi\) | ||||
0.0384511 | + | 0.999260i | \(0.487758\pi\) | |||||||
\(824\) | −0.203303 | −0.00708238 | ||||||||
\(825\) | −28.0497 | −0.976564 | ||||||||
\(826\) | 39.7815 | 1.38417 | ||||||||
\(827\) | −11.5425 | −0.401373 | −0.200686 | − | 0.979656i | \(-0.564317\pi\) | ||||
−0.200686 | + | 0.979656i | \(0.564317\pi\) | |||||||
\(828\) | −18.6900 | −0.649524 | ||||||||
\(829\) | 48.7103 | 1.69178 | 0.845890 | − | 0.533358i | \(-0.179070\pi\) | ||||
0.845890 | + | 0.533358i | \(0.179070\pi\) | |||||||
\(830\) | −11.0077 | −0.382081 | ||||||||
\(831\) | 44.5648 | 1.54594 | ||||||||
\(832\) | 1.18184 | 0.0409731 | ||||||||
\(833\) | 17.6651 | 0.612059 | ||||||||
\(834\) | −27.6392 | −0.957069 | ||||||||
\(835\) | −5.05672 | −0.174995 | ||||||||
\(836\) | −5.24146 | −0.181280 | ||||||||
\(837\) | −4.73699 | −0.163734 | ||||||||
\(838\) | −24.4579 | −0.844884 | ||||||||
\(839\) | −5.82683 | −0.201164 | −0.100582 | − | 0.994929i | \(-0.532071\pi\) | ||||
−0.100582 | + | 0.994929i | \(0.532071\pi\) | |||||||
\(840\) | 11.2462 | 0.388030 | ||||||||
\(841\) | 28.3689 | 0.978237 | ||||||||
\(842\) | 3.33076 | 0.114786 | ||||||||
\(843\) | 97.2429 | 3.34922 | ||||||||
\(844\) | 22.4572 | 0.773008 | ||||||||
\(845\) | 5.94020 | 0.204349 | ||||||||
\(846\) | −96.9173 | −3.33208 | ||||||||
\(847\) | 29.9124 | 1.02780 | ||||||||
\(848\) | 29.3310 | 1.00723 | ||||||||
\(849\) | 37.1798 | 1.27601 | ||||||||
\(850\) | 12.1616 | 0.417141 | ||||||||
\(851\) | 10.7851 | 0.369707 | ||||||||
\(852\) | −18.7414 | −0.642070 | ||||||||
\(853\) | 13.2215 | 0.452694 | 0.226347 | − | 0.974047i | \(-0.427322\pi\) | ||||
0.226347 | + | 0.974047i | \(0.427322\pi\) | |||||||
\(854\) | −76.1811 | −2.60686 | ||||||||
\(855\) | 7.52690 | 0.257415 | ||||||||
\(856\) | 8.52158 | 0.291262 | ||||||||
\(857\) | 0.657370 | 0.0224553 | 0.0112277 | − | 0.999937i | \(-0.496426\pi\) | ||||
0.0112277 | + | 0.999937i | \(0.496426\pi\) | |||||||
\(858\) | 18.7833 | 0.641253 | ||||||||
\(859\) | 38.6154 | 1.31754 | 0.658771 | − | 0.752344i | \(-0.271077\pi\) | ||||
0.658771 | + | 0.752344i | \(0.271077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.5150 | −0.937708 | ||||||||
\(862\) | 42.5136 | 1.44802 | ||||||||
\(863\) | −16.5212 | −0.562390 | −0.281195 | − | 0.959651i | \(-0.590731\pi\) | ||||
−0.281195 | + | 0.959651i | \(0.590731\pi\) | |||||||
\(864\) | 49.4266 | 1.68153 | ||||||||
\(865\) | 6.60938 | 0.224726 | ||||||||
\(866\) | −71.5243 | −2.43049 | ||||||||
\(867\) | −44.0442 | −1.49582 | ||||||||
\(868\) | 2.94282 | 0.0998860 | ||||||||
\(869\) | 7.43584 | 0.252244 | ||||||||
\(870\) | −23.9077 | −0.810545 | ||||||||
\(871\) | 0.924085 | 0.0313114 | ||||||||
\(872\) | 1.14911 | 0.0389136 | ||||||||
\(873\) | 59.4945 | 2.01358 | ||||||||
\(874\) | −10.5680 | −0.357468 | ||||||||
\(875\) | −25.0926 | −0.848284 | ||||||||
\(876\) | −49.3561 | −1.66759 | ||||||||
\(877\) | −47.0958 | −1.59031 | −0.795156 | − | 0.606405i | \(-0.792611\pi\) | ||||
−0.795156 | + | 0.606405i | \(0.792611\pi\) | |||||||
\(878\) | −14.7914 | −0.499184 | ||||||||
\(879\) | −21.7973 | −0.735205 | ||||||||
\(880\) | 6.02887 | 0.203233 | ||||||||
\(881\) | 25.7188 | 0.866488 | 0.433244 | − | 0.901277i | \(-0.357369\pi\) | ||||
0.433244 | + | 0.901277i | \(0.357369\pi\) | |||||||
\(882\) | −124.589 | −4.19514 | ||||||||
\(883\) | −8.18378 | −0.275406 | −0.137703 | − | 0.990474i | \(-0.543972\pi\) | ||||
−0.137703 | + | 0.990474i | \(0.543972\pi\) | |||||||
\(884\) | −3.02745 | −0.101824 | ||||||||
\(885\) | −9.04058 | −0.303896 | ||||||||
\(886\) | 56.1960 | 1.88794 | ||||||||
\(887\) | 28.6814 | 0.963027 | 0.481514 | − | 0.876439i | \(-0.340087\pi\) | ||||
0.481514 | + | 0.876439i | \(0.340087\pi\) | |||||||
\(888\) | −17.1243 | −0.574655 | ||||||||
\(889\) | 16.4975 | 0.553308 | ||||||||
\(890\) | −6.42376 | −0.215325 | ||||||||
\(891\) | 14.7641 | 0.494615 | ||||||||
\(892\) | 11.4351 | 0.382877 | ||||||||
\(893\) | −20.3715 | −0.681705 | ||||||||
\(894\) | −107.785 | −3.60487 | ||||||||
\(895\) | 9.19301 | 0.307288 | ||||||||
\(896\) | 46.6168 | 1.55736 | ||||||||
\(897\) | 14.0784 | 0.470063 | ||||||||
\(898\) | −27.5330 | −0.918787 | ||||||||
\(899\) | 4.31698 | 0.143979 | ||||||||
\(900\) | −31.8857 | −1.06286 | ||||||||
\(901\) | −8.66774 | −0.288764 | ||||||||
\(902\) | −7.72083 | −0.257076 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.77319 | −0.291792 | ||||||||
\(905\) | 1.91300 | 0.0635903 | ||||||||
\(906\) | 105.687 | 3.51120 | ||||||||
\(907\) | 9.35838 | 0.310740 | 0.155370 | − | 0.987856i | \(-0.450343\pi\) | ||||
0.155370 | + | 0.987856i | \(0.450343\pi\) | |||||||
\(908\) | −20.8946 | −0.693411 | ||||||||
\(909\) | −64.8612 | −2.15131 | ||||||||
\(910\) | 8.09180 | 0.268241 | ||||||||
\(911\) | −17.3043 | −0.573318 | −0.286659 | − | 0.958033i | \(-0.592545\pi\) | ||||
−0.286659 | + | 0.958033i | \(0.592545\pi\) | |||||||
\(912\) | 32.0567 | 1.06150 | ||||||||
\(913\) | −21.0617 | −0.697041 | ||||||||
\(914\) | 16.5671 | 0.547990 | ||||||||
\(915\) | 17.3126 | 0.572338 | ||||||||
\(916\) | −0.280241 | −0.00925944 | ||||||||
\(917\) | 75.7423 | 2.50123 | ||||||||
\(918\) | −21.7632 | −0.718292 | ||||||||
\(919\) | −36.0906 | −1.19052 | −0.595259 | − | 0.803534i | \(-0.702951\pi\) | ||||
−0.595259 | + | 0.803534i | \(0.702951\pi\) | |||||||
\(920\) | 2.36526 | 0.0779805 | ||||||||
\(921\) | 33.7607 | 1.11245 | ||||||||
\(922\) | 37.3158 | 1.22893 | ||||||||
\(923\) | 9.30522 | 0.306285 | ||||||||
\(924\) | −31.1831 | −1.02585 | ||||||||
\(925\) | 18.3996 | 0.604975 | ||||||||
\(926\) | −3.90589 | −0.128356 | ||||||||
\(927\) | −0.809508 | −0.0265877 | ||||||||
\(928\) | −45.0442 | −1.47865 | ||||||||
\(929\) | 14.4903 | 0.475411 | 0.237705 | − | 0.971337i | \(-0.423605\pi\) | ||||
0.237705 | + | 0.971337i | \(0.423605\pi\) | |||||||
\(930\) | −1.79904 | −0.0589929 | ||||||||
\(931\) | −26.1880 | −0.858276 | ||||||||
\(932\) | 8.24605 | 0.270108 | ||||||||
\(933\) | 73.7006 | 2.41285 | ||||||||
\(934\) | 0.412091 | 0.0134840 | ||||||||
\(935\) | −1.78161 | −0.0582650 | ||||||||
\(936\) | −14.7342 | −0.481601 | ||||||||
\(937\) | 11.3372 | 0.370370 | 0.185185 | − | 0.982704i | \(-0.440712\pi\) | ||||
0.185185 | + | 0.982704i | \(0.440712\pi\) | |||||||
\(938\) | −4.12686 | −0.134747 | ||||||||
\(939\) | 50.2292 | 1.63917 | ||||||||
\(940\) | −6.60731 | −0.215507 | ||||||||
\(941\) | −34.8232 | −1.13520 | −0.567602 | − | 0.823303i | \(-0.692129\pi\) | ||||
−0.567602 | + | 0.823303i | \(0.692129\pi\) | |||||||
\(942\) | −91.1164 | −2.96873 | ||||||||
\(943\) | −5.78687 | −0.188446 | ||||||||
\(944\) | −25.3794 | −0.826029 | ||||||||
\(945\) | 21.6237 | 0.703419 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.7749 | 1.13003 | 0.565016 | − | 0.825080i | \(-0.308870\pi\) | ||||
0.565016 | + | 0.825080i | \(0.308870\pi\) | |||||||
\(948\) | 12.8238 | 0.416497 | ||||||||
\(949\) | 24.5056 | 0.795485 | ||||||||
\(950\) | −18.0293 | −0.584947 | ||||||||
\(951\) | 70.1752 | 2.27559 | ||||||||
\(952\) | −9.32972 | −0.302378 | ||||||||
\(953\) | 7.89785 | 0.255836 | 0.127918 | − | 0.991785i | \(-0.459171\pi\) | ||||
0.127918 | + | 0.991785i | \(0.459171\pi\) | |||||||
\(954\) | 61.1323 | 1.97923 | ||||||||
\(955\) | 3.18015 | 0.102907 | ||||||||
\(956\) | −34.9366 | −1.12993 | ||||||||
\(957\) | −45.7441 | −1.47870 | ||||||||
\(958\) | −8.93806 | −0.288776 | ||||||||
\(959\) | −13.5724 | −0.438275 | ||||||||
\(960\) | 1.19945 | 0.0387122 | ||||||||
\(961\) | −30.6751 | −0.989521 | ||||||||
\(962\) | −12.3212 | −0.397252 | ||||||||
\(963\) | 33.9311 | 1.09342 | ||||||||
\(964\) | 20.5697 | 0.662506 | ||||||||
\(965\) | 4.00831 | 0.129032 | ||||||||
\(966\) | −62.8724 | −2.02289 | ||||||||
\(967\) | −3.36262 | −0.108134 | −0.0540672 | − | 0.998537i | \(-0.517219\pi\) | ||||
−0.0540672 | + | 0.998537i | \(0.517219\pi\) | |||||||
\(968\) | −9.98888 | −0.321055 | ||||||||
\(969\) | −9.47321 | −0.304323 | ||||||||
\(970\) | 10.9109 | 0.350329 | ||||||||
\(971\) | −48.5656 | −1.55854 | −0.779272 | − | 0.626686i | \(-0.784411\pi\) | ||||
−0.779272 | + | 0.626686i | \(0.784411\pi\) | |||||||
\(972\) | −4.04400 | −0.129712 | ||||||||
\(973\) | −22.7823 | −0.730366 | ||||||||
\(974\) | 23.2661 | 0.745493 | ||||||||
\(975\) | 24.0181 | 0.769193 | ||||||||
\(976\) | 48.6013 | 1.55569 | ||||||||
\(977\) | 1.03175 | 0.0330085 | 0.0165042 | − | 0.999864i | \(-0.494746\pi\) | ||||
0.0165042 | + | 0.999864i | \(0.494746\pi\) | |||||||
\(978\) | −115.519 | −3.69390 | ||||||||
\(979\) | −12.2910 | −0.392823 | ||||||||
\(980\) | −8.49384 | −0.271326 | ||||||||
\(981\) | 4.57550 | 0.146084 | ||||||||
\(982\) | −45.1815 | −1.44180 | ||||||||
\(983\) | −55.6019 | −1.77343 | −0.886713 | − | 0.462320i | \(-0.847017\pi\) | ||||
−0.886713 | + | 0.462320i | \(0.847017\pi\) | |||||||
\(984\) | 9.18828 | 0.292912 | ||||||||
\(985\) | 2.89882 | 0.0923642 | ||||||||
\(986\) | 19.8335 | 0.631629 | ||||||||
\(987\) | −121.196 | −3.85772 | ||||||||
\(988\) | 4.48810 | 0.142785 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 12.5655 | 0.399357 | ||||||||
\(991\) | −41.7282 | −1.32554 | −0.662770 | − | 0.748823i | \(-0.730619\pi\) | ||||
−0.662770 | + | 0.748823i | \(0.730619\pi\) | |||||||
\(992\) | −3.38955 | −0.107618 | ||||||||
\(993\) | 71.7292 | 2.27626 | ||||||||
\(994\) | −41.5561 | −1.31808 | ||||||||
\(995\) | 13.5163 | 0.428494 | ||||||||
\(996\) | −36.3228 | −1.15093 | ||||||||
\(997\) | 16.7365 | 0.530050 | 0.265025 | − | 0.964242i | \(-0.414620\pi\) | ||||
0.265025 | + | 0.964242i | \(0.414620\pi\) | |||||||
\(998\) | −15.4954 | −0.490499 | ||||||||
\(999\) | −32.9259 | −1.04173 |
(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 | 1849.2.a.n.1.5 | 18 | ||
43.14 | even | 21 | 43.2.g.a.24.2 | yes | 36 | ||
43.40 | even | 21 | 43.2.g.a.9.2 | ✓ | 36 | ||
43.42 | odd | 2 | 1849.2.a.o.1.14 | 18 | |||
129.14 | odd | 42 | 387.2.y.c.325.2 | 36 | |||
129.83 | odd | 42 | 387.2.y.c.181.2 | 36 | |||
172.83 | odd | 42 | 688.2.bg.c.353.3 | 36 | |||
172.143 | odd | 42 | 688.2.bg.c.497.3 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.9.2 | ✓ | 36 | 43.40 | even | 21 | ||
43.2.g.a.24.2 | yes | 36 | 43.14 | even | 21 | ||
387.2.y.c.181.2 | 36 | 129.83 | odd | 42 | |||
387.2.y.c.325.2 | 36 | 129.14 | odd | 42 | |||
688.2.bg.c.353.3 | 36 | 172.83 | odd | 42 | |||
688.2.bg.c.497.3 | 36 | 172.143 | odd | 42 | |||
1849.2.a.n.1.5 | 18 | 1.1 | even | 1 | trivial | ||
1849.2.a.o.1.14 | 18 | 43.42 | odd | 2 |