Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, 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("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70464 | −1.91247 | −0.956235 | − | 0.292600i | \(-0.905480\pi\) | ||||
−0.956235 | + | 0.292600i | \(0.905480\pi\) | |||||||
\(3\) | 1.55203 | 0.896065 | 0.448032 | − | 0.894017i | \(-0.352125\pi\) | ||||
0.448032 | + | 0.894017i | \(0.352125\pi\) | |||||||
\(4\) | 5.31508 | 2.65754 | ||||||||
\(5\) | 0.654263 | 0.292595 | 0.146298 | − | 0.989241i | \(-0.453264\pi\) | ||||
0.146298 | + | 0.989241i | \(0.453264\pi\) | |||||||
\(6\) | −4.19768 | −1.71370 | ||||||||
\(7\) | 0.835894 | 0.315938 | 0.157969 | − | 0.987444i | \(-0.449505\pi\) | ||||
0.157969 | + | 0.987444i | \(0.449505\pi\) | |||||||
\(8\) | −8.96611 | −3.17000 | ||||||||
\(9\) | −0.591204 | −0.197068 | ||||||||
\(10\) | −1.76955 | −0.559580 | ||||||||
\(11\) | −0.688569 | −0.207611 | −0.103806 | − | 0.994598i | \(-0.533102\pi\) | ||||
−0.103806 | + | 0.994598i | \(0.533102\pi\) | |||||||
\(12\) | 8.24917 | 2.38133 | ||||||||
\(13\) | 3.20921 | 0.890073 | 0.445037 | − | 0.895512i | \(-0.353191\pi\) | ||||
0.445037 | + | 0.895512i | \(0.353191\pi\) | |||||||
\(14\) | −2.26079 | −0.604222 | ||||||||
\(15\) | 1.01544 | 0.262184 | ||||||||
\(16\) | 13.6199 | 3.40499 | ||||||||
\(17\) | −3.02864 | −0.734553 | −0.367276 | − | 0.930112i | \(-0.619710\pi\) | ||||
−0.367276 | + | 0.930112i | \(0.619710\pi\) | |||||||
\(18\) | 1.59900 | 0.376887 | ||||||||
\(19\) | 5.64870 | 1.29590 | 0.647950 | − | 0.761683i | \(-0.275627\pi\) | ||||
0.647950 | + | 0.761683i | \(0.275627\pi\) | |||||||
\(20\) | 3.47746 | 0.777584 | ||||||||
\(21\) | 1.29733 | 0.283101 | ||||||||
\(22\) | 1.86233 | 0.397051 | ||||||||
\(23\) | 3.99803 | 0.833647 | 0.416823 | − | 0.908988i | \(-0.363143\pi\) | ||||
0.416823 | + | 0.908988i | \(0.363143\pi\) | |||||||
\(24\) | −13.9157 | −2.84052 | ||||||||
\(25\) | −4.57194 | −0.914388 | ||||||||
\(26\) | −8.67975 | −1.70224 | ||||||||
\(27\) | −5.57366 | −1.07265 | ||||||||
\(28\) | 4.44285 | 0.839619 | ||||||||
\(29\) | −7.24035 | −1.34450 | −0.672250 | − | 0.740324i | \(-0.734672\pi\) | ||||
−0.672250 | + | 0.740324i | \(0.734672\pi\) | |||||||
\(30\) | −2.74639 | −0.501419 | ||||||||
\(31\) | 7.60677 | 1.36622 | 0.683108 | − | 0.730318i | \(-0.260628\pi\) | ||||
0.683108 | + | 0.730318i | \(0.260628\pi\) | |||||||
\(32\) | −18.9048 | −3.34193 | ||||||||
\(33\) | −1.06868 | −0.186033 | ||||||||
\(34\) | 8.19138 | 1.40481 | ||||||||
\(35\) | 0.546894 | 0.0924420 | ||||||||
\(36\) | −3.14230 | −0.523717 | ||||||||
\(37\) | 3.41844 | 0.561988 | 0.280994 | − | 0.959710i | \(-0.409336\pi\) | ||||
0.280994 | + | 0.959710i | \(0.409336\pi\) | |||||||
\(38\) | −15.2777 | −2.47837 | ||||||||
\(39\) | 4.98078 | 0.797563 | ||||||||
\(40\) | −5.86619 | −0.927526 | ||||||||
\(41\) | −10.6857 | −1.66883 | −0.834414 | − | 0.551139i | \(-0.814194\pi\) | ||||
−0.834414 | + | 0.551139i | \(0.814194\pi\) | |||||||
\(42\) | −3.50882 | −0.541422 | ||||||||
\(43\) | −10.2333 | −1.56057 | −0.780285 | − | 0.625424i | \(-0.784926\pi\) | ||||
−0.780285 | + | 0.625424i | \(0.784926\pi\) | |||||||
\(44\) | −3.65980 | −0.551736 | ||||||||
\(45\) | −0.386803 | −0.0576612 | ||||||||
\(46\) | −10.8132 | −1.59432 | ||||||||
\(47\) | −12.6153 | −1.84013 | −0.920065 | − | 0.391767i | \(-0.871864\pi\) | ||||
−0.920065 | + | 0.391767i | \(0.871864\pi\) | |||||||
\(48\) | 21.1385 | 3.05109 | ||||||||
\(49\) | −6.30128 | −0.900183 | ||||||||
\(50\) | 12.3655 | 1.74874 | ||||||||
\(51\) | −4.70054 | −0.658207 | ||||||||
\(52\) | 17.0572 | 2.36541 | ||||||||
\(53\) | −4.49378 | −0.617269 | −0.308634 | − | 0.951181i | \(-0.599872\pi\) | ||||
−0.308634 | + | 0.951181i | \(0.599872\pi\) | |||||||
\(54\) | 15.0747 | 2.05141 | ||||||||
\(55\) | −0.450505 | −0.0607461 | ||||||||
\(56\) | −7.49472 | −1.00152 | ||||||||
\(57\) | 8.76694 | 1.16121 | ||||||||
\(58\) | 19.5825 | 2.57131 | ||||||||
\(59\) | −5.22377 | −0.680078 | −0.340039 | − | 0.940411i | \(-0.610440\pi\) | ||||
−0.340039 | + | 0.940411i | \(0.610440\pi\) | |||||||
\(60\) | 5.39712 | 0.696765 | ||||||||
\(61\) | −0.140427 | −0.0179799 | −0.00898993 | − | 0.999960i | \(-0.502862\pi\) | ||||
−0.00898993 | + | 0.999960i | \(0.502862\pi\) | |||||||
\(62\) | −20.5736 | −2.61285 | ||||||||
\(63\) | −0.494184 | −0.0622613 | ||||||||
\(64\) | 23.8909 | 2.98636 | ||||||||
\(65\) | 2.09966 | 0.260431 | ||||||||
\(66\) | 2.89040 | 0.355783 | ||||||||
\(67\) | 7.99352 | 0.976564 | 0.488282 | − | 0.872686i | \(-0.337624\pi\) | ||||
0.488282 | + | 0.872686i | \(0.337624\pi\) | |||||||
\(68\) | −16.0975 | −1.95210 | ||||||||
\(69\) | 6.20506 | 0.747001 | ||||||||
\(70\) | −1.47915 | −0.176793 | ||||||||
\(71\) | 2.56581 | 0.304506 | 0.152253 | − | 0.988342i | \(-0.451347\pi\) | ||||
0.152253 | + | 0.988342i | \(0.451347\pi\) | |||||||
\(72\) | 5.30080 | 0.624705 | ||||||||
\(73\) | −13.1396 | −1.53788 | −0.768938 | − | 0.639324i | \(-0.779214\pi\) | ||||
−0.768938 | + | 0.639324i | \(0.779214\pi\) | |||||||
\(74\) | −9.24565 | −1.07478 | ||||||||
\(75\) | −7.09579 | −0.819351 | ||||||||
\(76\) | 30.0233 | 3.44391 | ||||||||
\(77\) | −0.575571 | −0.0655924 | ||||||||
\(78\) | −13.4712 | −1.52532 | ||||||||
\(79\) | −9.21355 | −1.03661 | −0.518303 | − | 0.855197i | \(-0.673436\pi\) | ||||
−0.518303 | + | 0.855197i | \(0.673436\pi\) | |||||||
\(80\) | 8.91102 | 0.996282 | ||||||||
\(81\) | −6.87686 | −0.764096 | ||||||||
\(82\) | 28.9010 | 3.19158 | ||||||||
\(83\) | −2.19860 | −0.241327 | −0.120664 | − | 0.992693i | \(-0.538502\pi\) | ||||
−0.120664 | + | 0.992693i | \(0.538502\pi\) | |||||||
\(84\) | 6.89543 | 0.752353 | ||||||||
\(85\) | −1.98152 | −0.214927 | ||||||||
\(86\) | 27.6775 | 2.98455 | ||||||||
\(87\) | −11.2372 | −1.20476 | ||||||||
\(88\) | 6.17379 | 0.658128 | ||||||||
\(89\) | 2.93598 | 0.311213 | 0.155606 | − | 0.987819i | \(-0.450267\pi\) | ||||
0.155606 | + | 0.987819i | \(0.450267\pi\) | |||||||
\(90\) | 1.04616 | 0.110275 | ||||||||
\(91\) | 2.68256 | 0.281208 | ||||||||
\(92\) | 21.2499 | 2.21545 | ||||||||
\(93\) | 11.8059 | 1.22422 | ||||||||
\(94\) | 34.1198 | 3.51919 | ||||||||
\(95\) | 3.69573 | 0.379174 | ||||||||
\(96\) | −29.3409 | −2.99459 | ||||||||
\(97\) | 0.535520 | 0.0543738 | 0.0271869 | − | 0.999630i | \(-0.491345\pi\) | ||||
0.0271869 | + | 0.999630i | \(0.491345\pi\) | |||||||
\(98\) | 17.0427 | 1.72157 | ||||||||
\(99\) | 0.407085 | 0.0409136 | ||||||||
\(100\) | −24.3002 | −2.43002 | ||||||||
\(101\) | 6.65835 | 0.662530 | 0.331265 | − | 0.943538i | \(-0.392525\pi\) | ||||
0.331265 | + | 0.943538i | \(0.392525\pi\) | |||||||
\(102\) | 12.7133 | 1.25880 | ||||||||
\(103\) | 1.66958 | 0.164508 | 0.0822542 | − | 0.996611i | \(-0.473788\pi\) | ||||
0.0822542 | + | 0.996611i | \(0.473788\pi\) | |||||||
\(104\) | −28.7741 | −2.82153 | ||||||||
\(105\) | 0.848796 | 0.0828340 | ||||||||
\(106\) | 12.1541 | 1.18051 | ||||||||
\(107\) | 13.7829 | 1.33245 | 0.666223 | − | 0.745752i | \(-0.267910\pi\) | ||||
0.666223 | + | 0.745752i | \(0.267910\pi\) | |||||||
\(108\) | −29.6244 | −2.85061 | ||||||||
\(109\) | −3.00420 | −0.287750 | −0.143875 | − | 0.989596i | \(-0.545956\pi\) | ||||
−0.143875 | + | 0.989596i | \(0.545956\pi\) | |||||||
\(110\) | 1.21846 | 0.116175 | ||||||||
\(111\) | 5.30552 | 0.503577 | ||||||||
\(112\) | 11.3848 | 1.07576 | ||||||||
\(113\) | 5.49088 | 0.516539 | 0.258269 | − | 0.966073i | \(-0.416848\pi\) | ||||
0.258269 | + | 0.966073i | \(0.416848\pi\) | |||||||
\(114\) | −23.7114 | −2.22078 | ||||||||
\(115\) | 2.61576 | 0.243921 | ||||||||
\(116\) | −38.4831 | −3.57306 | ||||||||
\(117\) | −1.89730 | −0.175405 | ||||||||
\(118\) | 14.1284 | 1.30063 | ||||||||
\(119\) | −2.53162 | −0.232073 | ||||||||
\(120\) | −9.10450 | −0.831124 | ||||||||
\(121\) | −10.5259 | −0.956897 | ||||||||
\(122\) | 0.379805 | 0.0343859 | ||||||||
\(123\) | −16.5845 | −1.49538 | ||||||||
\(124\) | 40.4306 | 3.63077 | ||||||||
\(125\) | −6.26256 | −0.560141 | ||||||||
\(126\) | 1.33659 | 0.119073 | ||||||||
\(127\) | −9.42358 | −0.836208 | −0.418104 | − | 0.908399i | \(-0.637305\pi\) | ||||
−0.418104 | + | 0.908399i | \(0.637305\pi\) | |||||||
\(128\) | −26.8066 | −2.36939 | ||||||||
\(129\) | −15.8825 | −1.39837 | ||||||||
\(130\) | −5.67884 | −0.498067 | ||||||||
\(131\) | 12.7971 | 1.11809 | 0.559043 | − | 0.829138i | \(-0.311169\pi\) | ||||
0.559043 | + | 0.829138i | \(0.311169\pi\) | |||||||
\(132\) | −5.68012 | −0.494391 | ||||||||
\(133\) | 4.72171 | 0.409424 | ||||||||
\(134\) | −21.6196 | −1.86765 | ||||||||
\(135\) | −3.64664 | −0.313852 | ||||||||
\(136\) | 27.1551 | 2.32853 | ||||||||
\(137\) | 1.71417 | 0.146451 | 0.0732255 | − | 0.997315i | \(-0.476671\pi\) | ||||
0.0732255 | + | 0.997315i | \(0.476671\pi\) | |||||||
\(138\) | −16.7825 | −1.42862 | ||||||||
\(139\) | 6.58532 | 0.558560 | 0.279280 | − | 0.960210i | \(-0.409904\pi\) | ||||
0.279280 | + | 0.960210i | \(0.409904\pi\) | |||||||
\(140\) | 2.90679 | 0.245668 | ||||||||
\(141\) | −19.5793 | −1.64887 | ||||||||
\(142\) | −6.93961 | −0.582359 | ||||||||
\(143\) | −2.20976 | −0.184789 | ||||||||
\(144\) | −8.05217 | −0.671014 | ||||||||
\(145\) | −4.73709 | −0.393394 | ||||||||
\(146\) | 35.5379 | 2.94114 | ||||||||
\(147\) | −9.77977 | −0.806622 | ||||||||
\(148\) | 18.1693 | 1.49351 | ||||||||
\(149\) | 11.8037 | 0.966999 | 0.483499 | − | 0.875345i | \(-0.339366\pi\) | ||||
0.483499 | + | 0.875345i | \(0.339366\pi\) | |||||||
\(150\) | 19.1916 | 1.56698 | ||||||||
\(151\) | −7.95433 | −0.647314 | −0.323657 | − | 0.946174i | \(-0.604912\pi\) | ||||
−0.323657 | + | 0.946174i | \(0.604912\pi\) | |||||||
\(152\) | −50.6468 | −4.10800 | ||||||||
\(153\) | 1.79054 | 0.144757 | ||||||||
\(154\) | 1.55671 | 0.125444 | ||||||||
\(155\) | 4.97682 | 0.399748 | ||||||||
\(156\) | 26.4733 | 2.11956 | ||||||||
\(157\) | −19.5433 | −1.55973 | −0.779864 | − | 0.625949i | \(-0.784712\pi\) | ||||
−0.779864 | + | 0.625949i | \(0.784712\pi\) | |||||||
\(158\) | 24.9193 | 1.98248 | ||||||||
\(159\) | −6.97448 | −0.553113 | ||||||||
\(160\) | −12.3687 | −0.977834 | ||||||||
\(161\) | 3.34193 | 0.263381 | ||||||||
\(162\) | 18.5995 | 1.46131 | ||||||||
\(163\) | 23.3689 | 1.83040 | 0.915198 | − | 0.403005i | \(-0.132034\pi\) | ||||
0.915198 | + | 0.403005i | \(0.132034\pi\) | |||||||
\(164\) | −56.7954 | −4.43498 | ||||||||
\(165\) | −0.699198 | −0.0544325 | ||||||||
\(166\) | 5.94641 | 0.461531 | ||||||||
\(167\) | −10.7475 | −0.831668 | −0.415834 | − | 0.909440i | \(-0.636510\pi\) | ||||
−0.415834 | + | 0.909440i | \(0.636510\pi\) | |||||||
\(168\) | −11.6320 | −0.897430 | ||||||||
\(169\) | −2.70100 | −0.207769 | ||||||||
\(170\) | 5.35931 | 0.411041 | ||||||||
\(171\) | −3.33953 | −0.255381 | ||||||||
\(172\) | −54.3911 | −4.14728 | ||||||||
\(173\) | −10.9088 | −0.829380 | −0.414690 | − | 0.909963i | \(-0.636110\pi\) | ||||
−0.414690 | + | 0.909963i | \(0.636110\pi\) | |||||||
\(174\) | 30.3927 | 2.30406 | ||||||||
\(175\) | −3.82166 | −0.288890 | ||||||||
\(176\) | −9.37827 | −0.706914 | ||||||||
\(177\) | −8.10745 | −0.609393 | ||||||||
\(178\) | −7.94076 | −0.595185 | ||||||||
\(179\) | 3.53078 | 0.263903 | 0.131951 | − | 0.991256i | \(-0.457876\pi\) | ||||
0.131951 | + | 0.991256i | \(0.457876\pi\) | |||||||
\(180\) | −2.05589 | −0.153237 | ||||||||
\(181\) | −14.9201 | −1.10900 | −0.554501 | − | 0.832183i | \(-0.687091\pi\) | ||||
−0.554501 | + | 0.832183i | \(0.687091\pi\) | |||||||
\(182\) | −7.25535 | −0.537802 | ||||||||
\(183\) | −0.217947 | −0.0161111 | ||||||||
\(184\) | −35.8468 | −2.64266 | ||||||||
\(185\) | 2.23656 | 0.164435 | ||||||||
\(186\) | −31.9308 | −2.34128 | ||||||||
\(187\) | 2.08543 | 0.152502 | ||||||||
\(188\) | −67.0513 | −4.89022 | ||||||||
\(189\) | −4.65898 | −0.338891 | ||||||||
\(190\) | −9.99563 | −0.725159 | ||||||||
\(191\) | 12.7505 | 0.922594 | 0.461297 | − | 0.887246i | \(-0.347384\pi\) | ||||
0.461297 | + | 0.887246i | \(0.347384\pi\) | |||||||
\(192\) | 37.0794 | 2.67597 | ||||||||
\(193\) | −7.64286 | −0.550145 | −0.275073 | − | 0.961423i | \(-0.588702\pi\) | ||||
−0.275073 | + | 0.961423i | \(0.588702\pi\) | |||||||
\(194\) | −1.44839 | −0.103988 | ||||||||
\(195\) | 3.25874 | 0.233363 | ||||||||
\(196\) | −33.4918 | −2.39227 | ||||||||
\(197\) | −15.2449 | −1.08615 | −0.543076 | − | 0.839684i | \(-0.682740\pi\) | ||||
−0.543076 | + | 0.839684i | \(0.682740\pi\) | |||||||
\(198\) | −1.10102 | −0.0782460 | ||||||||
\(199\) | 7.76084 | 0.550152 | 0.275076 | − | 0.961423i | \(-0.411297\pi\) | ||||
0.275076 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(200\) | 40.9925 | 2.89861 | ||||||||
\(201\) | 12.4062 | 0.875065 | ||||||||
\(202\) | −18.0084 | −1.26707 | ||||||||
\(203\) | −6.05217 | −0.424779 | ||||||||
\(204\) | −24.9837 | −1.74921 | ||||||||
\(205\) | −6.99126 | −0.488291 | ||||||||
\(206\) | −4.51561 | −0.314617 | ||||||||
\(207\) | −2.36365 | −0.164285 | ||||||||
\(208\) | 43.7092 | 3.03069 | ||||||||
\(209\) | −3.88952 | −0.269044 | ||||||||
\(210\) | −2.29569 | −0.158418 | ||||||||
\(211\) | −16.2574 | −1.11921 | −0.559604 | − | 0.828760i | \(-0.689047\pi\) | ||||
−0.559604 | + | 0.828760i | \(0.689047\pi\) | |||||||
\(212\) | −23.8848 | −1.64042 | ||||||||
\(213\) | 3.98222 | 0.272857 | ||||||||
\(214\) | −37.2779 | −2.54826 | ||||||||
\(215\) | −6.69530 | −0.456616 | ||||||||
\(216\) | 49.9740 | 3.40030 | ||||||||
\(217\) | 6.35845 | 0.431640 | ||||||||
\(218\) | 8.12529 | 0.550314 | ||||||||
\(219\) | −20.3931 | −1.37804 | ||||||||
\(220\) | −2.39447 | −0.161435 | ||||||||
\(221\) | −9.71952 | −0.653806 | ||||||||
\(222\) | −14.3495 | −0.963077 | ||||||||
\(223\) | −8.31067 | −0.556524 | −0.278262 | − | 0.960505i | \(-0.589758\pi\) | ||||
−0.278262 | + | 0.960505i | \(0.589758\pi\) | |||||||
\(224\) | −15.8024 | −1.05584 | ||||||||
\(225\) | 2.70295 | 0.180197 | ||||||||
\(226\) | −14.8509 | −0.987865 | ||||||||
\(227\) | 22.4587 | 1.49063 | 0.745317 | − | 0.666710i | \(-0.232298\pi\) | ||||
0.745317 | + | 0.666710i | \(0.232298\pi\) | |||||||
\(228\) | 46.5970 | 3.08596 | ||||||||
\(229\) | 15.8696 | 1.04869 | 0.524345 | − | 0.851506i | \(-0.324310\pi\) | ||||
0.524345 | + | 0.851506i | \(0.324310\pi\) | |||||||
\(230\) | −7.07470 | −0.466492 | ||||||||
\(231\) | −0.893303 | −0.0587750 | ||||||||
\(232\) | 64.9178 | 4.26206 | ||||||||
\(233\) | 11.1417 | 0.729915 | 0.364957 | − | 0.931024i | \(-0.381084\pi\) | ||||
0.364957 | + | 0.931024i | \(0.381084\pi\) | |||||||
\(234\) | 5.13150 | 0.335457 | ||||||||
\(235\) | −8.25371 | −0.538413 | ||||||||
\(236\) | −27.7648 | −1.80733 | ||||||||
\(237\) | −14.2997 | −0.928865 | ||||||||
\(238\) | 6.84712 | 0.443833 | ||||||||
\(239\) | −13.9636 | −0.903232 | −0.451616 | − | 0.892212i | \(-0.649152\pi\) | ||||
−0.451616 | + | 0.892212i | \(0.649152\pi\) | |||||||
\(240\) | 13.8302 | 0.892733 | ||||||||
\(241\) | −2.34834 | −0.151270 | −0.0756350 | − | 0.997136i | \(-0.524098\pi\) | ||||
−0.0756350 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(242\) | 28.4687 | 1.83004 | ||||||||
\(243\) | 6.04787 | 0.387971 | ||||||||
\(244\) | −0.746382 | −0.0477822 | ||||||||
\(245\) | −4.12269 | −0.263389 | ||||||||
\(246\) | 44.8552 | 2.85986 | ||||||||
\(247\) | 18.1278 | 1.15345 | ||||||||
\(248\) | −68.2031 | −4.33090 | ||||||||
\(249\) | −3.41229 | −0.216245 | ||||||||
\(250\) | 16.9380 | 1.07125 | ||||||||
\(251\) | 24.9145 | 1.57259 | 0.786294 | − | 0.617853i | \(-0.211997\pi\) | ||||
0.786294 | + | 0.617853i | \(0.211997\pi\) | |||||||
\(252\) | −2.62663 | −0.165462 | ||||||||
\(253\) | −2.75292 | −0.173075 | ||||||||
\(254\) | 25.4874 | 1.59922 | ||||||||
\(255\) | −3.07539 | −0.192588 | ||||||||
\(256\) | 24.7205 | 1.54503 | ||||||||
\(257\) | −7.69580 | −0.480051 | −0.240025 | − | 0.970767i | \(-0.577156\pi\) | ||||
−0.240025 | + | 0.970767i | \(0.577156\pi\) | |||||||
\(258\) | 42.9563 | 2.67435 | ||||||||
\(259\) | 2.85745 | 0.177553 | ||||||||
\(260\) | 11.1599 | 0.692107 | ||||||||
\(261\) | 4.28053 | 0.264958 | ||||||||
\(262\) | −34.6115 | −2.13831 | ||||||||
\(263\) | −13.8659 | −0.855006 | −0.427503 | − | 0.904014i | \(-0.640607\pi\) | ||||
−0.427503 | + | 0.904014i | \(0.640607\pi\) | |||||||
\(264\) | 9.58190 | 0.589725 | ||||||||
\(265\) | −2.94012 | −0.180610 | ||||||||
\(266\) | −12.7705 | −0.783012 | ||||||||
\(267\) | 4.55672 | 0.278867 | ||||||||
\(268\) | 42.4862 | 2.59526 | ||||||||
\(269\) | −18.5358 | −1.13015 | −0.565073 | − | 0.825041i | \(-0.691152\pi\) | ||||
−0.565073 | + | 0.825041i | \(0.691152\pi\) | |||||||
\(270\) | 9.86284 | 0.600233 | ||||||||
\(271\) | 19.9446 | 1.21155 | 0.605774 | − | 0.795637i | \(-0.292864\pi\) | ||||
0.605774 | + | 0.795637i | \(0.292864\pi\) | |||||||
\(272\) | −41.2499 | −2.50114 | ||||||||
\(273\) | 4.16340 | 0.251981 | ||||||||
\(274\) | −4.63620 | −0.280083 | ||||||||
\(275\) | 3.14810 | 0.189837 | ||||||||
\(276\) | 32.9804 | 1.98519 | ||||||||
\(277\) | 11.7613 | 0.706666 | 0.353333 | − | 0.935498i | \(-0.385048\pi\) | ||||
0.353333 | + | 0.935498i | \(0.385048\pi\) | |||||||
\(278\) | −17.8109 | −1.06823 | ||||||||
\(279\) | −4.49715 | −0.269237 | ||||||||
\(280\) | −4.90351 | −0.293041 | ||||||||
\(281\) | 4.16348 | 0.248372 | 0.124186 | − | 0.992259i | \(-0.460368\pi\) | ||||
0.124186 | + | 0.992259i | \(0.460368\pi\) | |||||||
\(282\) | 52.9550 | 3.15342 | ||||||||
\(283\) | 12.7844 | 0.759951 | 0.379976 | − | 0.924997i | \(-0.375932\pi\) | ||||
0.379976 | + | 0.924997i | \(0.375932\pi\) | |||||||
\(284\) | 13.6375 | 0.809238 | ||||||||
\(285\) | 5.73589 | 0.339765 | ||||||||
\(286\) | 5.97661 | 0.353404 | ||||||||
\(287\) | −8.93212 | −0.527246 | ||||||||
\(288\) | 11.1766 | 0.658588 | ||||||||
\(289\) | −7.82735 | −0.460433 | ||||||||
\(290\) | 12.8121 | 0.752354 | ||||||||
\(291\) | 0.831142 | 0.0487224 | ||||||||
\(292\) | −69.8381 | −4.08697 | ||||||||
\(293\) | −12.0790 | −0.705661 | −0.352831 | − | 0.935687i | \(-0.614781\pi\) | ||||
−0.352831 | + | 0.935687i | \(0.614781\pi\) | |||||||
\(294\) | 26.4508 | 1.54264 | ||||||||
\(295\) | −3.41772 | −0.198987 | ||||||||
\(296\) | −30.6501 | −1.78150 | ||||||||
\(297\) | 3.83785 | 0.222695 | ||||||||
\(298\) | −31.9248 | −1.84936 | ||||||||
\(299\) | 12.8305 | 0.742007 | ||||||||
\(300\) | −37.7147 | −2.17746 | ||||||||
\(301\) | −8.55399 | −0.493044 | ||||||||
\(302\) | 21.5136 | 1.23797 | ||||||||
\(303\) | 10.3340 | 0.593670 | ||||||||
\(304\) | 76.9349 | 4.41252 | ||||||||
\(305\) | −0.0918763 | −0.00526082 | ||||||||
\(306\) | −4.84278 | −0.276843 | ||||||||
\(307\) | −7.88088 | −0.449786 | −0.224893 | − | 0.974383i | \(-0.572203\pi\) | ||||
−0.224893 | + | 0.974383i | \(0.572203\pi\) | |||||||
\(308\) | −3.05921 | −0.174315 | ||||||||
\(309\) | 2.59123 | 0.147410 | ||||||||
\(310\) | −13.4605 | −0.764506 | ||||||||
\(311\) | −3.30939 | −0.187658 | −0.0938290 | − | 0.995588i | \(-0.529911\pi\) | ||||
−0.0938290 | + | 0.995588i | \(0.529911\pi\) | |||||||
\(312\) | −44.6582 | −2.52827 | ||||||||
\(313\) | −16.2966 | −0.921140 | −0.460570 | − | 0.887623i | \(-0.652355\pi\) | ||||
−0.460570 | + | 0.887623i | \(0.652355\pi\) | |||||||
\(314\) | 52.8577 | 2.98293 | ||||||||
\(315\) | −0.323326 | −0.0182174 | ||||||||
\(316\) | −48.9708 | −2.75482 | ||||||||
\(317\) | −14.7029 | −0.825795 | −0.412897 | − | 0.910778i | \(-0.635483\pi\) | ||||
−0.412897 | + | 0.910778i | \(0.635483\pi\) | |||||||
\(318\) | 18.8635 | 1.05781 | ||||||||
\(319\) | 4.98548 | 0.279134 | ||||||||
\(320\) | 15.6309 | 0.873795 | ||||||||
\(321\) | 21.3915 | 1.19396 | ||||||||
\(322\) | −9.03871 | −0.503708 | ||||||||
\(323\) | −17.1079 | −0.951907 | ||||||||
\(324\) | −36.5511 | −2.03062 | ||||||||
\(325\) | −14.6723 | −0.813872 | ||||||||
\(326\) | −63.2045 | −3.50058 | ||||||||
\(327\) | −4.66261 | −0.257843 | ||||||||
\(328\) | 95.8092 | 5.29018 | ||||||||
\(329\) | −10.5450 | −0.581367 | ||||||||
\(330\) | 1.89108 | 0.104100 | ||||||||
\(331\) | 26.6607 | 1.46541 | 0.732703 | − | 0.680548i | \(-0.238258\pi\) | ||||
0.732703 | + | 0.680548i | \(0.238258\pi\) | |||||||
\(332\) | −11.6857 | −0.641337 | ||||||||
\(333\) | −2.02100 | −0.110750 | ||||||||
\(334\) | 29.0682 | 1.59054 | ||||||||
\(335\) | 5.22986 | 0.285738 | ||||||||
\(336\) | 17.6696 | 0.963955 | ||||||||
\(337\) | 9.65859 | 0.526137 | 0.263069 | − | 0.964777i | \(-0.415265\pi\) | ||||
0.263069 | + | 0.964777i | \(0.415265\pi\) | |||||||
\(338\) | 7.30524 | 0.397353 | ||||||||
\(339\) | 8.52201 | 0.462852 | ||||||||
\(340\) | −10.5320 | −0.571176 | ||||||||
\(341\) | −5.23779 | −0.283642 | ||||||||
\(342\) | 9.03224 | 0.488408 | ||||||||
\(343\) | −11.1185 | −0.600340 | ||||||||
\(344\) | 91.7533 | 4.94701 | ||||||||
\(345\) | 4.05974 | 0.218569 | ||||||||
\(346\) | 29.5044 | 1.58616 | ||||||||
\(347\) | 15.1418 | 0.812856 | 0.406428 | − | 0.913683i | \(-0.366774\pi\) | ||||
0.406428 | + | 0.913683i | \(0.366774\pi\) | |||||||
\(348\) | −59.7269 | −3.20170 | ||||||||
\(349\) | 30.2124 | 1.61723 | 0.808617 | − | 0.588335i | \(-0.200217\pi\) | ||||
0.808617 | + | 0.588335i | \(0.200217\pi\) | |||||||
\(350\) | 10.3362 | 0.552494 | ||||||||
\(351\) | −17.8870 | −0.954738 | ||||||||
\(352\) | 13.0173 | 0.693824 | ||||||||
\(353\) | −37.2669 | −1.98352 | −0.991758 | − | 0.128124i | \(-0.959105\pi\) | ||||
−0.991758 | + | 0.128124i | \(0.959105\pi\) | |||||||
\(354\) | 21.9277 | 1.16545 | ||||||||
\(355\) | 1.67872 | 0.0890970 | ||||||||
\(356\) | 15.6050 | 0.827061 | ||||||||
\(357\) | −3.92915 | −0.207953 | ||||||||
\(358\) | −9.54949 | −0.504706 | ||||||||
\(359\) | −17.2820 | −0.912107 | −0.456053 | − | 0.889952i | \(-0.650737\pi\) | ||||
−0.456053 | + | 0.889952i | \(0.650737\pi\) | |||||||
\(360\) | 3.46812 | 0.182786 | ||||||||
\(361\) | 12.9078 | 0.679357 | ||||||||
\(362\) | 40.3535 | 2.12093 | ||||||||
\(363\) | −16.3365 | −0.857442 | ||||||||
\(364\) | 14.2580 | 0.747322 | ||||||||
\(365\) | −8.59676 | −0.449975 | ||||||||
\(366\) | 0.589469 | 0.0308120 | ||||||||
\(367\) | 30.6510 | 1.59997 | 0.799983 | − | 0.600022i | \(-0.204842\pi\) | ||||
0.799983 | + | 0.600022i | \(0.204842\pi\) | |||||||
\(368\) | 54.4529 | 2.83855 | ||||||||
\(369\) | 6.31744 | 0.328873 | ||||||||
\(370\) | −6.04908 | −0.314477 | ||||||||
\(371\) | −3.75633 | −0.195019 | ||||||||
\(372\) | 62.7495 | 3.25341 | ||||||||
\(373\) | −25.6324 | −1.32720 | −0.663598 | − | 0.748089i | \(-0.730971\pi\) | ||||
−0.663598 | + | 0.748089i | \(0.730971\pi\) | |||||||
\(374\) | −5.64033 | −0.291655 | ||||||||
\(375\) | −9.71968 | −0.501922 | ||||||||
\(376\) | 113.110 | 5.83321 | ||||||||
\(377\) | −23.2358 | −1.19670 | ||||||||
\(378\) | 12.6009 | 0.648119 | ||||||||
\(379\) | −22.3881 | −1.15000 | −0.575000 | − | 0.818153i | \(-0.694998\pi\) | ||||
−0.575000 | + | 0.818153i | \(0.694998\pi\) | |||||||
\(380\) | 19.6431 | 1.00767 | ||||||||
\(381\) | −14.6257 | −0.749296 | ||||||||
\(382\) | −34.4855 | −1.76443 | ||||||||
\(383\) | −8.02017 | −0.409811 | −0.204906 | − | 0.978782i | \(-0.565689\pi\) | ||||
−0.204906 | + | 0.978782i | \(0.565689\pi\) | |||||||
\(384\) | −41.6047 | −2.12313 | ||||||||
\(385\) | −0.376575 | −0.0191920 | ||||||||
\(386\) | 20.6712 | 1.05214 | ||||||||
\(387\) | 6.05000 | 0.307539 | ||||||||
\(388\) | 2.84633 | 0.144501 | ||||||||
\(389\) | −13.3117 | −0.674932 | −0.337466 | − | 0.941338i | \(-0.609570\pi\) | ||||
−0.337466 | + | 0.941338i | \(0.609570\pi\) | |||||||
\(390\) | −8.81372 | −0.446300 | ||||||||
\(391\) | −12.1086 | −0.612357 | ||||||||
\(392\) | 56.4980 | 2.85358 | ||||||||
\(393\) | 19.8615 | 1.00188 | ||||||||
\(394\) | 41.2319 | 2.07723 | ||||||||
\(395\) | −6.02808 | −0.303306 | ||||||||
\(396\) | 2.16369 | 0.108730 | ||||||||
\(397\) | 16.7626 | 0.841292 | 0.420646 | − | 0.907225i | \(-0.361803\pi\) | ||||
0.420646 | + | 0.907225i | \(0.361803\pi\) | |||||||
\(398\) | −20.9903 | −1.05215 | ||||||||
\(399\) | 7.32824 | 0.366871 | ||||||||
\(400\) | −62.2696 | −3.11348 | ||||||||
\(401\) | −14.0346 | −0.700853 | −0.350427 | − | 0.936590i | \(-0.613963\pi\) | ||||
−0.350427 | + | 0.936590i | \(0.613963\pi\) | |||||||
\(402\) | −33.5543 | −1.67353 | ||||||||
\(403\) | 24.4117 | 1.21603 | ||||||||
\(404\) | 35.3897 | 1.76070 | ||||||||
\(405\) | −4.49928 | −0.223571 | ||||||||
\(406\) | 16.3689 | 0.812377 | ||||||||
\(407\) | −2.35383 | −0.116675 | ||||||||
\(408\) | 42.1455 | 2.08651 | ||||||||
\(409\) | 17.9419 | 0.887170 | 0.443585 | − | 0.896232i | \(-0.353706\pi\) | ||||
0.443585 | + | 0.896232i | \(0.353706\pi\) | |||||||
\(410\) | 18.9089 | 0.933842 | ||||||||
\(411\) | 2.66044 | 0.131230 | ||||||||
\(412\) | 8.87394 | 0.437188 | ||||||||
\(413\) | −4.36652 | −0.214862 | ||||||||
\(414\) | 6.39283 | 0.314190 | ||||||||
\(415\) | −1.43846 | −0.0706112 | ||||||||
\(416\) | −60.6695 | −2.97457 | ||||||||
\(417\) | 10.2206 | 0.500505 | ||||||||
\(418\) | 10.5198 | 0.514538 | ||||||||
\(419\) | 35.8275 | 1.75029 | 0.875144 | − | 0.483862i | \(-0.160766\pi\) | ||||
0.875144 | + | 0.483862i | \(0.160766\pi\) | |||||||
\(420\) | 4.51142 | 0.220135 | ||||||||
\(421\) | 18.9888 | 0.925455 | 0.462728 | − | 0.886501i | \(-0.346871\pi\) | ||||
0.462728 | + | 0.886501i | \(0.346871\pi\) | |||||||
\(422\) | 43.9705 | 2.14045 | ||||||||
\(423\) | 7.45821 | 0.362631 | ||||||||
\(424\) | 40.2918 | 1.95674 | ||||||||
\(425\) | 13.8468 | 0.671666 | ||||||||
\(426\) | −10.7705 | −0.521831 | ||||||||
\(427\) | −0.117382 | −0.00568053 | ||||||||
\(428\) | 73.2575 | 3.54103 | ||||||||
\(429\) | −3.42961 | −0.165583 | ||||||||
\(430\) | 18.1084 | 0.873264 | ||||||||
\(431\) | −15.8086 | −0.761474 | −0.380737 | − | 0.924683i | \(-0.624330\pi\) | ||||
−0.380737 | + | 0.924683i | \(0.624330\pi\) | |||||||
\(432\) | −75.9128 | −3.65236 | ||||||||
\(433\) | −3.82261 | −0.183703 | −0.0918515 | − | 0.995773i | \(-0.529279\pi\) | ||||
−0.0918515 | + | 0.995773i | \(0.529279\pi\) | |||||||
\(434\) | −17.1973 | −0.825498 | ||||||||
\(435\) | −7.35211 | −0.352507 | ||||||||
\(436\) | −15.9676 | −0.764709 | ||||||||
\(437\) | 22.5837 | 1.08032 | ||||||||
\(438\) | 55.1559 | 2.63545 | ||||||||
\(439\) | −30.6473 | −1.46272 | −0.731359 | − | 0.681993i | \(-0.761113\pi\) | ||||
−0.731359 | + | 0.681993i | \(0.761113\pi\) | |||||||
\(440\) | 4.03928 | 0.192565 | ||||||||
\(441\) | 3.72534 | 0.177397 | ||||||||
\(442\) | 26.2878 | 1.25038 | ||||||||
\(443\) | −3.91557 | −0.186034 | −0.0930172 | − | 0.995665i | \(-0.529651\pi\) | ||||
−0.0930172 | + | 0.995665i | \(0.529651\pi\) | |||||||
\(444\) | 28.1993 | 1.33828 | ||||||||
\(445\) | 1.92090 | 0.0910594 | ||||||||
\(446\) | 22.4774 | 1.06434 | ||||||||
\(447\) | 18.3197 | 0.866494 | ||||||||
\(448\) | 19.9703 | 0.943506 | ||||||||
\(449\) | 26.6257 | 1.25655 | 0.628273 | − | 0.777993i | \(-0.283762\pi\) | ||||
0.628273 | + | 0.777993i | \(0.283762\pi\) | |||||||
\(450\) | −7.31051 | −0.344621 | ||||||||
\(451\) | 7.35785 | 0.346468 | ||||||||
\(452\) | 29.1845 | 1.37272 | ||||||||
\(453\) | −12.3454 | −0.580036 | ||||||||
\(454\) | −60.7427 | −2.85079 | ||||||||
\(455\) | 1.75510 | 0.0822802 | ||||||||
\(456\) | −78.6054 | −3.68103 | ||||||||
\(457\) | −33.3844 | −1.56166 | −0.780829 | − | 0.624745i | \(-0.785203\pi\) | ||||
−0.780829 | + | 0.624745i | \(0.785203\pi\) | |||||||
\(458\) | −42.9215 | −2.00559 | ||||||||
\(459\) | 16.8806 | 0.787918 | ||||||||
\(460\) | 13.9030 | 0.648230 | ||||||||
\(461\) | −28.4489 | −1.32500 | −0.662499 | − | 0.749062i | \(-0.730504\pi\) | ||||
−0.662499 | + | 0.749062i | \(0.730504\pi\) | |||||||
\(462\) | 2.41606 | 0.112405 | ||||||||
\(463\) | 19.0225 | 0.884052 | 0.442026 | − | 0.897002i | \(-0.354260\pi\) | ||||
0.442026 | + | 0.897002i | \(0.354260\pi\) | |||||||
\(464\) | −98.6131 | −4.57800 | ||||||||
\(465\) | 7.72418 | 0.358200 | ||||||||
\(466\) | −30.1342 | −1.39594 | ||||||||
\(467\) | 30.5109 | 1.41188 | 0.705939 | − | 0.708273i | \(-0.250525\pi\) | ||||
0.705939 | + | 0.708273i | \(0.250525\pi\) | |||||||
\(468\) | −10.0843 | −0.466146 | ||||||||
\(469\) | 6.68174 | 0.308534 | ||||||||
\(470\) | 22.3233 | 1.02970 | ||||||||
\(471\) | −30.3318 | −1.39762 | ||||||||
\(472\) | 46.8369 | 2.15584 | ||||||||
\(473\) | 7.04637 | 0.323992 | ||||||||
\(474\) | 38.6756 | 1.77643 | ||||||||
\(475\) | −25.8255 | −1.18496 | ||||||||
\(476\) | −13.4558 | −0.616744 | ||||||||
\(477\) | 2.65674 | 0.121644 | ||||||||
\(478\) | 37.7666 | 1.72740 | ||||||||
\(479\) | 17.4688 | 0.798168 | 0.399084 | − | 0.916914i | \(-0.369328\pi\) | ||||
0.399084 | + | 0.916914i | \(0.369328\pi\) | |||||||
\(480\) | −19.1966 | −0.876202 | ||||||||
\(481\) | 10.9705 | 0.500210 | ||||||||
\(482\) | 6.35142 | 0.289299 | ||||||||
\(483\) | 5.18677 | 0.236006 | ||||||||
\(484\) | −55.9459 | −2.54299 | ||||||||
\(485\) | 0.350371 | 0.0159095 | ||||||||
\(486\) | −16.3573 | −0.741983 | ||||||||
\(487\) | −17.3114 | −0.784455 | −0.392227 | − | 0.919868i | \(-0.628295\pi\) | ||||
−0.392227 | + | 0.919868i | \(0.628295\pi\) | |||||||
\(488\) | 1.25909 | 0.0569961 | ||||||||
\(489\) | 36.2693 | 1.64015 | ||||||||
\(490\) | 11.1504 | 0.503724 | ||||||||
\(491\) | 31.5606 | 1.42431 | 0.712154 | − | 0.702023i | \(-0.247720\pi\) | ||||
0.712154 | + | 0.702023i | \(0.247720\pi\) | |||||||
\(492\) | −88.1482 | −3.97403 | ||||||||
\(493\) | 21.9284 | 0.987605 | ||||||||
\(494\) | −49.0293 | −2.20593 | ||||||||
\(495\) | 0.266341 | 0.0119711 | ||||||||
\(496\) | 103.604 | 4.65194 | ||||||||
\(497\) | 2.14475 | 0.0962051 | ||||||||
\(498\) | 9.22901 | 0.413562 | ||||||||
\(499\) | −31.0560 | −1.39026 | −0.695129 | − | 0.718885i | \(-0.744653\pi\) | ||||
−0.695129 | + | 0.718885i | \(0.744653\pi\) | |||||||
\(500\) | −33.2860 | −1.48860 | ||||||||
\(501\) | −16.6805 | −0.745229 | ||||||||
\(502\) | −67.3847 | −3.00753 | ||||||||
\(503\) | −3.95821 | −0.176488 | −0.0882439 | − | 0.996099i | \(-0.528125\pi\) | ||||
−0.0882439 | + | 0.996099i | \(0.528125\pi\) | |||||||
\(504\) | 4.43091 | 0.197368 | ||||||||
\(505\) | 4.35631 | 0.193853 | ||||||||
\(506\) | 7.44566 | 0.331000 | ||||||||
\(507\) | −4.19204 | −0.186175 | ||||||||
\(508\) | −50.0871 | −2.22226 | ||||||||
\(509\) | −24.0115 | −1.06429 | −0.532144 | − | 0.846654i | \(-0.678614\pi\) | ||||
−0.532144 | + | 0.846654i | \(0.678614\pi\) | |||||||
\(510\) | 8.31781 | 0.368319 | ||||||||
\(511\) | −10.9833 | −0.485874 | ||||||||
\(512\) | −13.2469 | −0.585437 | ||||||||
\(513\) | −31.4839 | −1.39005 | ||||||||
\(514\) | 20.8144 | 0.918082 | ||||||||
\(515\) | 1.09234 | 0.0481343 | ||||||||
\(516\) | −84.4166 | −3.71623 | ||||||||
\(517\) | 8.68650 | 0.382032 | ||||||||
\(518\) | −7.72838 | −0.339566 | ||||||||
\(519\) | −16.9308 | −0.743178 | ||||||||
\(520\) | −18.8258 | −0.825566 | ||||||||
\(521\) | −36.3650 | −1.59318 | −0.796591 | − | 0.604519i | \(-0.793365\pi\) | ||||
−0.796591 | + | 0.604519i | \(0.793365\pi\) | |||||||
\(522\) | −11.5773 | −0.506724 | ||||||||
\(523\) | 15.9132 | 0.695834 | 0.347917 | − | 0.937525i | \(-0.386889\pi\) | ||||
0.347917 | + | 0.937525i | \(0.386889\pi\) | |||||||
\(524\) | 68.0176 | 2.97136 | ||||||||
\(525\) | −5.93132 | −0.258864 | ||||||||
\(526\) | 37.5022 | 1.63517 | ||||||||
\(527\) | −23.0381 | −1.00356 | ||||||||
\(528\) | −14.5554 | −0.633441 | ||||||||
\(529\) | −7.01577 | −0.305033 | ||||||||
\(530\) | 7.95196 | 0.345411 | ||||||||
\(531\) | 3.08832 | 0.134022 | ||||||||
\(532\) | 25.0963 | 1.08806 | ||||||||
\(533\) | −34.2926 | −1.48538 | ||||||||
\(534\) | −12.3243 | −0.533325 | ||||||||
\(535\) | 9.01766 | 0.389868 | ||||||||
\(536\) | −71.6708 | −3.09571 | ||||||||
\(537\) | 5.47988 | 0.236474 | ||||||||
\(538\) | 50.1326 | 2.16137 | ||||||||
\(539\) | 4.33887 | 0.186888 | ||||||||
\(540\) | −19.3822 | −0.834076 | ||||||||
\(541\) | 16.6370 | 0.715283 | 0.357641 | − | 0.933859i | \(-0.383581\pi\) | ||||
0.357641 | + | 0.933859i | \(0.383581\pi\) | |||||||
\(542\) | −53.9430 | −2.31705 | ||||||||
\(543\) | −23.1564 | −0.993738 | ||||||||
\(544\) | 57.2559 | 2.45483 | ||||||||
\(545\) | −1.96554 | −0.0841944 | ||||||||
\(546\) | −11.2605 | −0.481906 | ||||||||
\(547\) | −16.2060 | −0.692917 | −0.346458 | − | 0.938065i | \(-0.612616\pi\) | ||||
−0.346458 | + | 0.938065i | \(0.612616\pi\) | |||||||
\(548\) | 9.11093 | 0.389200 | ||||||||
\(549\) | 0.0830212 | 0.00354326 | ||||||||
\(550\) | −8.51448 | −0.363058 | ||||||||
\(551\) | −40.8985 | −1.74234 | ||||||||
\(552\) | −55.6352 | −2.36799 | ||||||||
\(553\) | −7.70155 | −0.327503 | ||||||||
\(554\) | −31.8100 | −1.35148 | ||||||||
\(555\) | 3.47120 | 0.147344 | ||||||||
\(556\) | 35.0015 | 1.48440 | ||||||||
\(557\) | −20.6060 | −0.873103 | −0.436551 | − | 0.899679i | \(-0.643800\pi\) | ||||
−0.436551 | + | 0.899679i | \(0.643800\pi\) | |||||||
\(558\) | 12.1632 | 0.514909 | ||||||||
\(559\) | −32.8409 | −1.38902 | ||||||||
\(560\) | 7.44867 | 0.314764 | ||||||||
\(561\) | 3.23664 | 0.136651 | ||||||||
\(562\) | −11.2607 | −0.475005 | ||||||||
\(563\) | 13.4340 | 0.566176 | 0.283088 | − | 0.959094i | \(-0.408641\pi\) | ||||
0.283088 | + | 0.959094i | \(0.408641\pi\) | |||||||
\(564\) | −104.066 | −4.38195 | ||||||||
\(565\) | 3.59248 | 0.151137 | ||||||||
\(566\) | −34.5771 | −1.45338 | ||||||||
\(567\) | −5.74833 | −0.241407 | ||||||||
\(568\) | −23.0054 | −0.965284 | ||||||||
\(569\) | −33.9557 | −1.42350 | −0.711748 | − | 0.702435i | \(-0.752096\pi\) | ||||
−0.711748 | + | 0.702435i | \(0.752096\pi\) | |||||||
\(570\) | −15.5135 | −0.649789 | ||||||||
\(571\) | −12.7729 | −0.534529 | −0.267265 | − | 0.963623i | \(-0.586120\pi\) | ||||
−0.267265 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(572\) | −11.7451 | −0.491086 | ||||||||
\(573\) | 19.7892 | 0.826704 | ||||||||
\(574\) | 24.1582 | 1.00834 | ||||||||
\(575\) | −18.2787 | −0.762276 | ||||||||
\(576\) | −14.1244 | −0.588517 | ||||||||
\(577\) | 9.15746 | 0.381230 | 0.190615 | − | 0.981665i | \(-0.438952\pi\) | ||||
0.190615 | + | 0.981665i | \(0.438952\pi\) | |||||||
\(578\) | 21.1702 | 0.880563 | ||||||||
\(579\) | −11.8620 | −0.492966 | ||||||||
\(580\) | −25.1780 | −1.04546 | ||||||||
\(581\) | −1.83779 | −0.0762445 | ||||||||
\(582\) | −2.24794 | −0.0931802 | ||||||||
\(583\) | 3.09428 | 0.128152 | ||||||||
\(584\) | 117.811 | 4.87506 | ||||||||
\(585\) | −1.24133 | −0.0513227 | ||||||||
\(586\) | 32.6693 | 1.34956 | ||||||||
\(587\) | −39.8011 | −1.64277 | −0.821384 | − | 0.570375i | \(-0.806798\pi\) | ||||
−0.821384 | + | 0.570375i | \(0.806798\pi\) | |||||||
\(588\) | −51.9803 | −2.14363 | ||||||||
\(589\) | 42.9683 | 1.77048 | ||||||||
\(590\) | 9.24371 | 0.380557 | ||||||||
\(591\) | −23.6605 | −0.973262 | ||||||||
\(592\) | 46.5589 | 1.91356 | ||||||||
\(593\) | 4.95233 | 0.203368 | 0.101684 | − | 0.994817i | \(-0.467577\pi\) | ||||
0.101684 | + | 0.994817i | \(0.467577\pi\) | |||||||
\(594\) | −10.3800 | −0.425897 | ||||||||
\(595\) | −1.65634 | −0.0679035 | ||||||||
\(596\) | 62.7378 | 2.56984 | ||||||||
\(597\) | 12.0451 | 0.492971 | ||||||||
\(598\) | −34.7019 | −1.41907 | ||||||||
\(599\) | 24.3121 | 0.993367 | 0.496683 | − | 0.867932i | \(-0.334551\pi\) | ||||
0.496683 | + | 0.867932i | \(0.334551\pi\) | |||||||
\(600\) | 63.6216 | 2.59734 | ||||||||
\(601\) | 8.05050 | 0.328387 | 0.164193 | − | 0.986428i | \(-0.447498\pi\) | ||||
0.164193 | + | 0.986428i | \(0.447498\pi\) | |||||||
\(602\) | 23.1355 | 0.942932 | ||||||||
\(603\) | −4.72580 | −0.192450 | ||||||||
\(604\) | −42.2779 | −1.72026 | ||||||||
\(605\) | −6.88669 | −0.279984 | ||||||||
\(606\) | −27.9496 | −1.13538 | ||||||||
\(607\) | 20.6685 | 0.838907 | 0.419453 | − | 0.907777i | \(-0.362222\pi\) | ||||
0.419453 | + | 0.907777i | \(0.362222\pi\) | |||||||
\(608\) | −106.788 | −4.33081 | ||||||||
\(609\) | −9.39314 | −0.380629 | ||||||||
\(610\) | 0.248492 | 0.0100612 | ||||||||
\(611\) | −40.4851 | −1.63785 | ||||||||
\(612\) | 9.51689 | 0.384697 | ||||||||
\(613\) | −29.4090 | −1.18782 | −0.593909 | − | 0.804532i | \(-0.702416\pi\) | ||||
−0.593909 | + | 0.804532i | \(0.702416\pi\) | |||||||
\(614\) | 21.3150 | 0.860202 | ||||||||
\(615\) | −10.8506 | −0.437540 | ||||||||
\(616\) | 5.16063 | 0.207928 | ||||||||
\(617\) | 29.8885 | 1.20327 | 0.601633 | − | 0.798773i | \(-0.294517\pi\) | ||||
0.601633 | + | 0.798773i | \(0.294517\pi\) | |||||||
\(618\) | −7.00835 | −0.281917 | ||||||||
\(619\) | −44.2827 | −1.77987 | −0.889935 | − | 0.456087i | \(-0.849251\pi\) | ||||
−0.889935 | + | 0.456087i | \(0.849251\pi\) | |||||||
\(620\) | 26.4522 | 1.06235 | ||||||||
\(621\) | −22.2836 | −0.894211 | ||||||||
\(622\) | 8.95070 | 0.358890 | ||||||||
\(623\) | 2.45417 | 0.0983241 | ||||||||
\(624\) | 67.8379 | 2.71569 | ||||||||
\(625\) | 18.7623 | 0.750494 | ||||||||
\(626\) | 44.0765 | 1.76165 | ||||||||
\(627\) | −6.03665 | −0.241081 | ||||||||
\(628\) | −103.874 | −4.14504 | ||||||||
\(629\) | −10.3532 | −0.412810 | ||||||||
\(630\) | 0.874481 | 0.0348402 | ||||||||
\(631\) | 27.5192 | 1.09552 | 0.547762 | − | 0.836634i | \(-0.315480\pi\) | ||||
0.547762 | + | 0.836634i | \(0.315480\pi\) | |||||||
\(632\) | 82.6097 | 3.28604 | ||||||||
\(633\) | −25.2320 | −1.00288 | ||||||||
\(634\) | 39.7660 | 1.57931 | ||||||||
\(635\) | −6.16550 | −0.244670 | ||||||||
\(636\) | −37.0700 | −1.46992 | ||||||||
\(637\) | −20.2221 | −0.801229 | ||||||||
\(638\) | −13.4839 | −0.533834 | ||||||||
\(639\) | −1.51692 | −0.0600084 | ||||||||
\(640\) | −17.5386 | −0.693274 | ||||||||
\(641\) | −5.30090 | −0.209373 | −0.104686 | − | 0.994505i | \(-0.533384\pi\) | ||||
−0.104686 | + | 0.994505i | \(0.533384\pi\) | |||||||
\(642\) | −57.8564 | −2.28341 | ||||||||
\(643\) | −12.5243 | −0.493912 | −0.246956 | − | 0.969027i | \(-0.579430\pi\) | ||||
−0.246956 | + | 0.969027i | \(0.579430\pi\) | |||||||
\(644\) | 17.7626 | 0.699945 | ||||||||
\(645\) | −10.3913 | −0.409157 | ||||||||
\(646\) | 46.2706 | 1.82049 | ||||||||
\(647\) | −27.9216 | −1.09771 | −0.548855 | − | 0.835918i | \(-0.684936\pi\) | ||||
−0.548855 | + | 0.835918i | \(0.684936\pi\) | |||||||
\(648\) | 61.6587 | 2.42218 | ||||||||
\(649\) | 3.59693 | 0.141192 | ||||||||
\(650\) | 39.6833 | 1.55651 | ||||||||
\(651\) | 9.86850 | 0.386777 | ||||||||
\(652\) | 124.208 | 4.86435 | ||||||||
\(653\) | −17.1866 | −0.672565 | −0.336282 | − | 0.941761i | \(-0.609170\pi\) | ||||
−0.336282 | + | 0.941761i | \(0.609170\pi\) | |||||||
\(654\) | 12.6107 | 0.493117 | ||||||||
\(655\) | 8.37266 | 0.327147 | ||||||||
\(656\) | −145.539 | −5.68233 | ||||||||
\(657\) | 7.76820 | 0.303066 | ||||||||
\(658\) | 28.5206 | 1.11185 | ||||||||
\(659\) | −33.3224 | −1.29806 | −0.649028 | − | 0.760765i | \(-0.724824\pi\) | ||||
−0.649028 | + | 0.760765i | \(0.724824\pi\) | |||||||
\(660\) | −3.71629 | −0.144657 | ||||||||
\(661\) | 34.8130 | 1.35407 | 0.677034 | − | 0.735951i | \(-0.263265\pi\) | ||||
0.677034 | + | 0.735951i | \(0.263265\pi\) | |||||||
\(662\) | −72.1077 | −2.80255 | ||||||||
\(663\) | −15.0850 | −0.585852 | ||||||||
\(664\) | 19.7128 | 0.765007 | ||||||||
\(665\) | 3.08924 | 0.119796 | ||||||||
\(666\) | 5.46607 | 0.211806 | ||||||||
\(667\) | −28.9471 | −1.12084 | ||||||||
\(668\) | −57.1240 | −2.21019 | ||||||||
\(669\) | −12.8984 | −0.498681 | ||||||||
\(670\) | −14.1449 | −0.546465 | ||||||||
\(671\) | 0.0966939 | 0.00373283 | ||||||||
\(672\) | −24.5258 | −0.946105 | ||||||||
\(673\) | −25.7025 | −0.990758 | −0.495379 | − | 0.868677i | \(-0.664971\pi\) | ||||
−0.495379 | + | 0.868677i | \(0.664971\pi\) | |||||||
\(674\) | −26.1230 | −1.00622 | ||||||||
\(675\) | 25.4824 | 0.980819 | ||||||||
\(676\) | −14.3561 | −0.552156 | ||||||||
\(677\) | 37.7711 | 1.45166 | 0.725830 | − | 0.687874i | \(-0.241456\pi\) | ||||
0.725830 | + | 0.687874i | \(0.241456\pi\) | |||||||
\(678\) | −23.0490 | −0.885191 | ||||||||
\(679\) | 0.447638 | 0.0171788 | ||||||||
\(680\) | 17.7666 | 0.681317 | ||||||||
\(681\) | 34.8565 | 1.33571 | ||||||||
\(682\) | 14.1663 | 0.542457 | ||||||||
\(683\) | −11.0102 | −0.421295 | −0.210648 | − | 0.977562i | \(-0.567557\pi\) | ||||
−0.210648 | + | 0.977562i | \(0.567557\pi\) | |||||||
\(684\) | −17.7499 | −0.678684 | ||||||||
\(685\) | 1.12151 | 0.0428509 | ||||||||
\(686\) | 30.0714 | 1.14813 | ||||||||
\(687\) | 24.6300 | 0.939694 | ||||||||
\(688\) | −139.378 | −5.31372 | ||||||||
\(689\) | −14.4215 | −0.549414 | ||||||||
\(690\) | −10.9801 | −0.418007 | ||||||||
\(691\) | 37.8684 | 1.44058 | 0.720291 | − | 0.693672i | \(-0.244008\pi\) | ||||
0.720291 | + | 0.693672i | \(0.244008\pi\) | |||||||
\(692\) | −57.9811 | −2.20411 | ||||||||
\(693\) | 0.340280 | 0.0129262 | ||||||||
\(694\) | −40.9532 | −1.55456 | ||||||||
\(695\) | 4.30853 | 0.163432 | ||||||||
\(696\) | 100.754 | 3.81908 | ||||||||
\(697\) | 32.3631 | 1.22584 | ||||||||
\(698\) | −81.7138 | −3.09291 | ||||||||
\(699\) | 17.2922 | 0.654051 | ||||||||
\(700\) | −20.3124 | −0.767737 | ||||||||
\(701\) | −14.7412 | −0.556766 | −0.278383 | − | 0.960470i | \(-0.589798\pi\) | ||||
−0.278383 | + | 0.960470i | \(0.589798\pi\) | |||||||
\(702\) | 48.3779 | 1.82591 | ||||||||
\(703\) | 19.3097 | 0.728280 | ||||||||
\(704\) | −16.4505 | −0.620003 | ||||||||
\(705\) | −12.8100 | −0.482453 | ||||||||
\(706\) | 100.794 | 3.79342 | ||||||||
\(707\) | 5.56567 | 0.209319 | ||||||||
\(708\) | −43.0918 | −1.61949 | ||||||||
\(709\) | −10.9142 | −0.409893 | −0.204946 | − | 0.978773i | \(-0.565702\pi\) | ||||
−0.204946 | + | 0.978773i | \(0.565702\pi\) | |||||||
\(710\) | −4.54033 | −0.170395 | ||||||||
\(711\) | 5.44709 | 0.204282 | ||||||||
\(712\) | −26.3243 | −0.986544 | ||||||||
\(713\) | 30.4121 | 1.13894 | ||||||||
\(714\) | 10.6269 | 0.397703 | ||||||||
\(715\) | −1.44576 | −0.0540685 | ||||||||
\(716\) | 18.7664 | 0.701333 | ||||||||
\(717\) | −21.6720 | −0.809355 | ||||||||
\(718\) | 46.7415 | 1.74438 | ||||||||
\(719\) | −11.6753 | −0.435415 | −0.217707 | − | 0.976014i | \(-0.569858\pi\) | ||||
−0.217707 | + | 0.976014i | \(0.569858\pi\) | |||||||
\(720\) | −5.26823 | −0.196335 | ||||||||
\(721\) | 1.39559 | 0.0519745 | ||||||||
\(722\) | −34.9109 | −1.29925 | ||||||||
\(723\) | −3.64470 | −0.135548 | ||||||||
\(724\) | −79.3016 | −2.94722 | ||||||||
\(725\) | 33.1025 | 1.22939 | ||||||||
\(726\) | 44.1843 | 1.63983 | ||||||||
\(727\) | −28.5063 | −1.05724 | −0.528621 | − | 0.848858i | \(-0.677291\pi\) | ||||
−0.528621 | + | 0.848858i | \(0.677291\pi\) | |||||||
\(728\) | −24.0521 | −0.891429 | ||||||||
\(729\) | 30.0171 | 1.11174 | ||||||||
\(730\) | 23.2512 | 0.860564 | ||||||||
\(731\) | 30.9931 | 1.14632 | ||||||||
\(732\) | −1.15841 | −0.0428160 | ||||||||
\(733\) | −37.6163 | −1.38939 | −0.694695 | − | 0.719305i | \(-0.744461\pi\) | ||||
−0.694695 | + | 0.719305i | \(0.744461\pi\) | |||||||
\(734\) | −82.8998 | −3.05989 | ||||||||
\(735\) | −6.39854 | −0.236014 | ||||||||
\(736\) | −75.5820 | −2.78599 | ||||||||
\(737\) | −5.50409 | −0.202746 | ||||||||
\(738\) | −17.0864 | −0.628959 | ||||||||
\(739\) | −4.89899 | −0.180212 | −0.0901062 | − | 0.995932i | \(-0.528721\pi\) | ||||
−0.0901062 | + | 0.995932i | \(0.528721\pi\) | |||||||
\(740\) | 11.8875 | 0.436993 | ||||||||
\(741\) | 28.1349 | 1.03356 | ||||||||
\(742\) | 10.1595 | 0.372968 | ||||||||
\(743\) | −10.6268 | −0.389861 | −0.194931 | − | 0.980817i | \(-0.562448\pi\) | ||||
−0.194931 | + | 0.980817i | \(0.562448\pi\) | |||||||
\(744\) | −105.853 | −3.88077 | ||||||||
\(745\) | 7.72274 | 0.282939 | ||||||||
\(746\) | 69.3265 | 2.53822 | ||||||||
\(747\) | 1.29982 | 0.0475579 | ||||||||
\(748\) | 11.0842 | 0.405279 | ||||||||
\(749\) | 11.5211 | 0.420971 | ||||||||
\(750\) | 26.2883 | 0.959911 | ||||||||
\(751\) | 14.4118 | 0.525893 | 0.262946 | − | 0.964810i | \(-0.415306\pi\) | ||||
0.262946 | + | 0.964810i | \(0.415306\pi\) | |||||||
\(752\) | −171.819 | −6.26561 | ||||||||
\(753\) | 38.6680 | 1.40914 | ||||||||
\(754\) | 62.8444 | 2.28866 | ||||||||
\(755\) | −5.20422 | −0.189401 | ||||||||
\(756\) | −24.7629 | −0.900618 | ||||||||
\(757\) | −27.5148 | −1.00004 | −0.500022 | − | 0.866013i | \(-0.666675\pi\) | ||||
−0.500022 | + | 0.866013i | \(0.666675\pi\) | |||||||
\(758\) | 60.5518 | 2.19934 | ||||||||
\(759\) | −4.27261 | −0.155086 | ||||||||
\(760\) | −33.1363 | −1.20198 | ||||||||
\(761\) | 36.1869 | 1.31177 | 0.655887 | − | 0.754859i | \(-0.272295\pi\) | ||||
0.655887 | + | 0.754859i | \(0.272295\pi\) | |||||||
\(762\) | 39.5572 | 1.43301 | ||||||||
\(763\) | −2.51120 | −0.0909114 | ||||||||
\(764\) | 67.7700 | 2.45183 | ||||||||
\(765\) | 1.17149 | 0.0423552 | ||||||||
\(766\) | 21.6917 | 0.783752 | ||||||||
\(767\) | −16.7642 | −0.605319 | ||||||||
\(768\) | 38.3670 | 1.38445 | ||||||||
\(769\) | 3.08536 | 0.111261 | 0.0556304 | − | 0.998451i | \(-0.482283\pi\) | ||||
0.0556304 | + | 0.998451i | \(0.482283\pi\) | |||||||
\(770\) | 1.01850 | 0.0367042 | ||||||||
\(771\) | −11.9441 | −0.430156 | ||||||||
\(772\) | −40.6225 | −1.46203 | ||||||||
\(773\) | 21.4675 | 0.772131 | 0.386065 | − | 0.922471i | \(-0.373834\pi\) | ||||
0.386065 | + | 0.922471i | \(0.373834\pi\) | |||||||
\(774\) | −16.3631 | −0.588159 | ||||||||
\(775\) | −34.7777 | −1.24925 | ||||||||
\(776\) | −4.80153 | −0.172365 | ||||||||
\(777\) | 4.43485 | 0.159099 | ||||||||
\(778\) | 36.0035 | 1.29079 | ||||||||
\(779\) | −60.3603 | −2.16263 | ||||||||
\(780\) | 17.3205 | 0.620172 | ||||||||
\(781\) | −1.76674 | −0.0632190 | ||||||||
\(782\) | 32.7494 | 1.17111 | ||||||||
\(783\) | 40.3552 | 1.44218 | ||||||||
\(784\) | −85.8231 | −3.06511 | ||||||||
\(785\) | −12.7865 | −0.456369 | ||||||||
\(786\) | −53.7181 | −1.91606 | ||||||||
\(787\) | 1.38563 | 0.0493922 | 0.0246961 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246961 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(788\) | −81.0277 | −2.88649 | ||||||||
\(789\) | −21.5202 | −0.766141 | ||||||||
\(790\) | 16.3038 | 0.580063 | ||||||||
\(791\) | 4.58980 | 0.163194 | ||||||||
\(792\) | −3.64997 | −0.129696 | ||||||||
\(793\) | −0.450660 | −0.0160034 | ||||||||
\(794\) | −45.3369 | −1.60895 | ||||||||
\(795\) | −4.56315 | −0.161838 | ||||||||
\(796\) | 41.2495 | 1.46205 | ||||||||
\(797\) | 25.8299 | 0.914942 | 0.457471 | − | 0.889225i | \(-0.348755\pi\) | ||||
0.457471 | + | 0.889225i | \(0.348755\pi\) | |||||||
\(798\) | −19.8202 | −0.701629 | ||||||||
\(799\) | 38.2071 | 1.35167 | ||||||||
\(800\) | 86.4318 | 3.05582 | ||||||||
\(801\) | −1.73576 | −0.0613301 | ||||||||
\(802\) | 37.9585 | 1.34036 | ||||||||
\(803\) | 9.04754 | 0.319281 | ||||||||
\(804\) | 65.9399 | 2.32552 | ||||||||
\(805\) | 2.18650 | 0.0770640 | ||||||||
\(806\) | −66.0248 | −2.32562 | ||||||||
\(807\) | −28.7681 | −1.01268 | ||||||||
\(808\) | −59.6995 | −2.10022 | ||||||||
\(809\) | 20.5729 | 0.723303 | 0.361652 | − | 0.932313i | \(-0.382213\pi\) | ||||
0.361652 | + | 0.932313i | \(0.382213\pi\) | |||||||
\(810\) | 12.1689 | 0.427573 | ||||||||
\(811\) | −45.4124 | −1.59465 | −0.797323 | − | 0.603553i | \(-0.793751\pi\) | ||||
−0.797323 | + | 0.603553i | \(0.793751\pi\) | |||||||
\(812\) | −32.1678 | −1.12887 | ||||||||
\(813\) | 30.9546 | 1.08563 | ||||||||
\(814\) | 6.36627 | 0.223138 | ||||||||
\(815\) | 15.2894 | 0.535565 | ||||||||
\(816\) | −64.0210 | −2.24118 | ||||||||
\(817\) | −57.8051 | −2.02234 | ||||||||
\(818\) | −48.5264 | −1.69669 | ||||||||
\(819\) | −1.58594 | −0.0554172 | ||||||||
\(820\) | −37.1591 | −1.29765 | ||||||||
\(821\) | 35.0243 | 1.22236 | 0.611178 | − | 0.791493i | \(-0.290696\pi\) | ||||
0.611178 | + | 0.791493i | \(0.290696\pi\) | |||||||
\(822\) | −7.19552 | −0.250973 | ||||||||
\(823\) | −8.62740 | −0.300732 | −0.150366 | − | 0.988630i | \(-0.548045\pi\) | ||||
−0.150366 | + | 0.988630i | \(0.548045\pi\) | |||||||
\(824\) | −14.9696 | −0.521491 | ||||||||
\(825\) | 4.88594 | 0.170107 | ||||||||
\(826\) | 11.8099 | 0.410918 | ||||||||
\(827\) | 18.7137 | 0.650738 | 0.325369 | − | 0.945587i | \(-0.394511\pi\) | ||||
0.325369 | + | 0.945587i | \(0.394511\pi\) | |||||||
\(828\) | −12.5630 | −0.436595 | ||||||||
\(829\) | 13.8846 | 0.482234 | 0.241117 | − | 0.970496i | \(-0.422486\pi\) | ||||
0.241117 | + | 0.970496i | \(0.422486\pi\) | |||||||
\(830\) | 3.89052 | 0.135042 | ||||||||
\(831\) | 18.2538 | 0.633218 | ||||||||
\(832\) | 76.6708 | 2.65808 | ||||||||
\(833\) | 19.0843 | 0.661232 | ||||||||
\(834\) | −27.6431 | −0.957202 | ||||||||
\(835\) | −7.03171 | −0.243342 | ||||||||
\(836\) | −20.6731 | −0.714995 | ||||||||
\(837\) | −42.3975 | −1.46547 | ||||||||
\(838\) | −96.9006 | −3.34737 | ||||||||
\(839\) | 0.0144394 | 0.000498505 0 | 0.000249252 | − | 1.00000i | \(-0.499921\pi\) | ||||
0.000249252 | 1.00000i | \(0.499921\pi\) | ||||||||
\(840\) | −7.61040 | −0.262584 | ||||||||
\(841\) | 23.4227 | 0.807679 | ||||||||
\(842\) | −51.3578 | −1.76991 | ||||||||
\(843\) | 6.46185 | 0.222558 | ||||||||
\(844\) | −86.4096 | −2.97434 | ||||||||
\(845\) | −1.76717 | −0.0607923 | ||||||||
\(846\) | −20.1718 | −0.693520 | ||||||||
\(847\) | −8.79851 | −0.302320 | ||||||||
\(848\) | −61.2051 | −2.10179 | ||||||||
\(849\) | 19.8417 | 0.680965 | ||||||||
\(850\) | −37.4505 | −1.28454 | ||||||||
\(851\) | 13.6670 | 0.468499 | ||||||||
\(852\) | 21.1658 | 0.725129 | ||||||||
\(853\) | −25.7202 | −0.880643 | −0.440321 | − | 0.897840i | \(-0.645135\pi\) | ||||
−0.440321 | + | 0.897840i | \(0.645135\pi\) | |||||||
\(854\) | 0.317477 | 0.0108638 | ||||||||
\(855\) | −2.18493 | −0.0747231 | ||||||||
\(856\) | −123.579 | −4.22385 | ||||||||
\(857\) | 39.8205 | 1.36024 | 0.680121 | − | 0.733100i | \(-0.261927\pi\) | ||||
0.680121 | + | 0.733100i | \(0.261927\pi\) | |||||||
\(858\) | 9.27587 | 0.316673 | ||||||||
\(859\) | 53.6866 | 1.83176 | 0.915882 | − | 0.401447i | \(-0.131493\pi\) | ||||
0.915882 | + | 0.401447i | \(0.131493\pi\) | |||||||
\(860\) | −35.5861 | −1.21347 | ||||||||
\(861\) | −13.8629 | −0.472447 | ||||||||
\(862\) | 42.7566 | 1.45630 | ||||||||
\(863\) | −29.1668 | −0.992850 | −0.496425 | − | 0.868080i | \(-0.665354\pi\) | ||||
−0.496425 | + | 0.868080i | \(0.665354\pi\) | |||||||
\(864\) | 105.369 | 3.58473 | ||||||||
\(865\) | −7.13722 | −0.242673 | ||||||||
\(866\) | 10.3388 | 0.351327 | ||||||||
\(867\) | −12.1483 | −0.412577 | ||||||||
\(868\) | 33.7957 | 1.14710 | ||||||||
\(869\) | 6.34417 | 0.215211 | ||||||||
\(870\) | 19.8848 | 0.674158 | ||||||||
\(871\) | 25.6529 | 0.869214 | ||||||||
\(872\) | 26.9360 | 0.912168 | ||||||||
\(873\) | −0.316602 | −0.0107153 | ||||||||
\(874\) | −61.0807 | −2.06608 | ||||||||
\(875\) | −5.23484 | −0.176970 | ||||||||
\(876\) | −108.391 | −3.66219 | ||||||||
\(877\) | −7.15580 | −0.241634 | −0.120817 | − | 0.992675i | \(-0.538551\pi\) | ||||
−0.120817 | + | 0.992675i | \(0.538551\pi\) | |||||||
\(878\) | 82.8900 | 2.79740 | ||||||||
\(879\) | −18.7469 | −0.632318 | ||||||||
\(880\) | −6.13586 | −0.206840 | ||||||||
\(881\) | −12.5202 | −0.421815 | −0.210908 | − | 0.977506i | \(-0.567642\pi\) | ||||
−0.210908 | + | 0.977506i | \(0.567642\pi\) | |||||||
\(882\) | −10.0757 | −0.339267 | ||||||||
\(883\) | 35.8067 | 1.20499 | 0.602496 | − | 0.798122i | \(-0.294173\pi\) | ||||
0.602496 | + | 0.798122i | \(0.294173\pi\) | |||||||
\(884\) | −51.6601 | −1.73752 | ||||||||
\(885\) | −5.30440 | −0.178306 | ||||||||
\(886\) | 10.5902 | 0.355785 | ||||||||
\(887\) | 13.1983 | 0.443155 | 0.221578 | − | 0.975143i | \(-0.428879\pi\) | ||||
0.221578 | + | 0.975143i | \(0.428879\pi\) | |||||||
\(888\) | −47.5699 | −1.59634 | ||||||||
\(889\) | −7.87712 | −0.264190 | ||||||||
\(890\) | −5.19535 | −0.174148 | ||||||||
\(891\) | 4.73520 | 0.158635 | ||||||||
\(892\) | −44.1719 | −1.47898 | ||||||||
\(893\) | −71.2599 | −2.38462 | ||||||||
\(894\) | −49.5483 | −1.65714 | ||||||||
\(895\) | 2.31006 | 0.0772167 | ||||||||
\(896\) | −22.4075 | −0.748582 | ||||||||
\(897\) | 19.9133 | 0.664886 | ||||||||
\(898\) | −72.0130 | −2.40311 | ||||||||
\(899\) | −55.0756 | −1.83688 | ||||||||
\(900\) | 14.3664 | 0.478880 | ||||||||
\(901\) | 13.6100 | 0.453416 | ||||||||
\(902\) | −19.9003 | −0.662609 | ||||||||
\(903\) | −13.2761 | −0.441799 | ||||||||
\(904\) | −49.2318 | −1.63743 | ||||||||
\(905\) | −9.76167 | −0.324489 | ||||||||
\(906\) | 33.3898 | 1.10930 | ||||||||
\(907\) | −45.0375 | −1.49545 | −0.747723 | − | 0.664010i | \(-0.768853\pi\) | ||||
−0.747723 | + | 0.664010i | \(0.768853\pi\) | |||||||
\(908\) | 119.370 | 3.96142 | ||||||||
\(909\) | −3.93644 | −0.130564 | ||||||||
\(910\) | −4.74690 | −0.157358 | ||||||||
\(911\) | 53.4441 | 1.77068 | 0.885341 | − | 0.464942i | \(-0.153925\pi\) | ||||
0.885341 | + | 0.464942i | \(0.153925\pi\) | |||||||
\(912\) | 119.405 | 3.95390 | ||||||||
\(913\) | 1.51389 | 0.0501023 | ||||||||
\(914\) | 90.2929 | 2.98662 | ||||||||
\(915\) | −0.142595 | −0.00471404 | ||||||||
\(916\) | 84.3480 | 2.78694 | ||||||||
\(917\) | 10.6970 | 0.353246 | ||||||||
\(918\) | −45.6559 | −1.50687 | ||||||||
\(919\) | −3.20348 | −0.105673 | −0.0528365 | − | 0.998603i | \(-0.516826\pi\) | ||||
−0.0528365 | + | 0.998603i | \(0.516826\pi\) | |||||||
\(920\) | −23.4532 | −0.773229 | ||||||||
\(921\) | −12.2314 | −0.403037 | ||||||||
\(922\) | 76.9441 | 2.53402 | ||||||||
\(923\) | 8.23422 | 0.271033 | ||||||||
\(924\) | −4.74798 | −0.156197 | ||||||||
\(925\) | −15.6289 | −0.513875 | ||||||||
\(926\) | −51.4491 | −1.69072 | ||||||||
\(927\) | −0.987061 | −0.0324193 | ||||||||
\(928\) | 136.878 | 4.49323 | ||||||||
\(929\) | −8.67341 | −0.284565 | −0.142283 | − | 0.989826i | \(-0.545444\pi\) | ||||
−0.142283 | + | 0.989826i | \(0.545444\pi\) | |||||||
\(930\) | −20.8911 | −0.685047 | ||||||||
\(931\) | −35.5940 | −1.16655 | ||||||||
\(932\) | 59.2189 | 1.93978 | ||||||||
\(933\) | −5.13627 | −0.168154 | ||||||||
\(934\) | −82.5211 | −2.70017 | ||||||||
\(935\) | 1.36442 | 0.0446212 | ||||||||
\(936\) | 17.0114 | 0.556034 | ||||||||
\(937\) | −34.3500 | −1.12217 | −0.561083 | − | 0.827760i | \(-0.689615\pi\) | ||||
−0.561083 | + | 0.827760i | \(0.689615\pi\) | |||||||
\(938\) | −18.0717 | −0.590062 | ||||||||
\(939\) | −25.2928 | −0.825401 | ||||||||
\(940\) | −43.8692 | −1.43085 | ||||||||
\(941\) | −15.5646 | −0.507392 | −0.253696 | − | 0.967284i | \(-0.581646\pi\) | ||||
−0.253696 | + | 0.967284i | \(0.581646\pi\) | |||||||
\(942\) | 82.0367 | 2.67290 | ||||||||
\(943\) | −42.7218 | −1.39121 | ||||||||
\(944\) | −71.1475 | −2.31565 | ||||||||
\(945\) | −3.04820 | −0.0991580 | ||||||||
\(946\) | −19.0579 | −0.619626 | ||||||||
\(947\) | −5.23476 | −0.170107 | −0.0850534 | − | 0.996376i | \(-0.527106\pi\) | ||||
−0.0850534 | + | 0.996376i | \(0.527106\pi\) | |||||||
\(948\) | −76.0041 | −2.46850 | ||||||||
\(949\) | −42.1677 | −1.36882 | ||||||||
\(950\) | 69.8487 | 2.26619 | ||||||||
\(951\) | −22.8193 | −0.739966 | ||||||||
\(952\) | 22.6988 | 0.735672 | ||||||||
\(953\) | 0.566532 | 0.0183518 | 0.00917589 | − | 0.999958i | \(-0.497079\pi\) | ||||
0.00917589 | + | 0.999958i | \(0.497079\pi\) | |||||||
\(954\) | −7.18554 | −0.232640 | ||||||||
\(955\) | 8.34218 | 0.269947 | ||||||||
\(956\) | −74.2179 | −2.40038 | ||||||||
\(957\) | 7.73762 | 0.250122 | ||||||||
\(958\) | −47.2467 | −1.52647 | ||||||||
\(959\) | 1.43286 | 0.0462695 | ||||||||
\(960\) | 24.2597 | 0.782977 | ||||||||
\(961\) | 26.8629 | 0.866544 | ||||||||
\(962\) | −29.6712 | −0.956637 | ||||||||
\(963\) | −8.14853 | −0.262583 | ||||||||
\(964\) | −12.4816 | −0.402006 | ||||||||
\(965\) | −5.00044 | −0.160970 | ||||||||
\(966\) | −14.0284 | −0.451355 | ||||||||
\(967\) | 6.32251 | 0.203318 | 0.101659 | − | 0.994819i | \(-0.467585\pi\) | ||||
0.101659 | + | 0.994819i | \(0.467585\pi\) | |||||||
\(968\) | 94.3761 | 3.03336 | ||||||||
\(969\) | −26.5519 | −0.852970 | ||||||||
\(970\) | −0.947627 | −0.0304265 | ||||||||
\(971\) | 35.6298 | 1.14342 | 0.571708 | − | 0.820457i | \(-0.306281\pi\) | ||||
0.571708 | + | 0.820457i | \(0.306281\pi\) | |||||||
\(972\) | 32.1449 | 1.03105 | ||||||||
\(973\) | 5.50463 | 0.176470 | ||||||||
\(974\) | 46.8211 | 1.50025 | ||||||||
\(975\) | −22.7718 | −0.729282 | ||||||||
\(976\) | −1.91261 | −0.0612212 | ||||||||
\(977\) | 29.7108 | 0.950531 | 0.475266 | − | 0.879842i | \(-0.342352\pi\) | ||||
0.475266 | + | 0.879842i | \(0.342352\pi\) | |||||||
\(978\) | −98.0953 | −3.13674 | ||||||||
\(979\) | −2.02162 | −0.0646114 | ||||||||
\(980\) | −21.9125 | −0.699968 | ||||||||
\(981\) | 1.77610 | 0.0567064 | ||||||||
\(982\) | −85.3600 | −2.72395 | ||||||||
\(983\) | −41.4137 | −1.32089 | −0.660446 | − | 0.750874i | \(-0.729633\pi\) | ||||
−0.660446 | + | 0.750874i | \(0.729633\pi\) | |||||||
\(984\) | 148.699 | 4.74034 | ||||||||
\(985\) | −9.97415 | −0.317803 | ||||||||
\(986\) | −59.3084 | −1.88877 | ||||||||
\(987\) | −16.3662 | −0.520943 | ||||||||
\(988\) | 96.3509 | 3.06533 | ||||||||
\(989\) | −40.9132 | −1.30096 | ||||||||
\(990\) | −0.720356 | −0.0228944 | ||||||||
\(991\) | 8.77873 | 0.278866 | 0.139433 | − | 0.990232i | \(-0.455472\pi\) | ||||
0.139433 | + | 0.990232i | \(0.455472\pi\) | |||||||
\(992\) | −143.805 | −4.56580 | ||||||||
\(993\) | 41.3783 | 1.31310 | ||||||||
\(994\) | −5.80077 | −0.183989 | ||||||||
\(995\) | 5.07763 | 0.160972 | ||||||||
\(996\) | −18.1366 | −0.574679 | ||||||||
\(997\) | −13.3134 | −0.421640 | −0.210820 | − | 0.977525i | \(-0.567613\pi\) | ||||
−0.210820 | + | 0.977525i | \(0.567613\pi\) | |||||||
\(998\) | 83.9953 | 2.65882 | ||||||||
\(999\) | −19.0532 | −0.602817 |
(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 | 6037.2.a.a.1.12 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.12 | ✓ | 243 | 1.1 | even | 1 | trivial |