Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, 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("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56153 | −1.81127 | −0.905636 | − | 0.424055i | \(-0.860606\pi\) | ||||
−0.905636 | + | 0.424055i | \(0.860606\pi\) | |||||||
\(3\) | 2.54144 | 1.46730 | 0.733650 | − | 0.679527i | \(-0.237815\pi\) | ||||
0.733650 | + | 0.679527i | \(0.237815\pi\) | |||||||
\(4\) | 4.56142 | 2.28071 | ||||||||
\(5\) | −3.00625 | −1.34443 | −0.672217 | − | 0.740354i | \(-0.734658\pi\) | ||||
−0.672217 | + | 0.740354i | \(0.734658\pi\) | |||||||
\(6\) | −6.50997 | −2.65768 | ||||||||
\(7\) | −3.61687 | −1.36705 | −0.683523 | − | 0.729929i | \(-0.739553\pi\) | ||||
−0.683523 | + | 0.729929i | \(0.739553\pi\) | |||||||
\(8\) | −6.56114 | −2.31971 | ||||||||
\(9\) | 3.45892 | 1.15297 | ||||||||
\(10\) | 7.70058 | 2.43514 | ||||||||
\(11\) | 2.20426 | 0.664610 | 0.332305 | − | 0.943172i | \(-0.392174\pi\) | ||||
0.332305 | + | 0.943172i | \(0.392174\pi\) | |||||||
\(12\) | 11.5926 | 3.34649 | ||||||||
\(13\) | −3.81806 | −1.05894 | −0.529470 | − | 0.848328i | \(-0.677609\pi\) | ||||
−0.529470 | + | 0.848328i | \(0.677609\pi\) | |||||||
\(14\) | 9.26470 | 2.47609 | ||||||||
\(15\) | −7.64019 | −1.97269 | ||||||||
\(16\) | 7.68370 | 1.92093 | ||||||||
\(17\) | −7.79644 | −1.89091 | −0.945457 | − | 0.325746i | \(-0.894384\pi\) | ||||
−0.945457 | + | 0.325746i | \(0.894384\pi\) | |||||||
\(18\) | −8.86010 | −2.08835 | ||||||||
\(19\) | 1.99752 | 0.458263 | 0.229131 | − | 0.973396i | \(-0.426411\pi\) | ||||
0.229131 | + | 0.973396i | \(0.426411\pi\) | |||||||
\(20\) | −13.7127 | −3.06626 | ||||||||
\(21\) | −9.19204 | −2.00587 | ||||||||
\(22\) | −5.64628 | −1.20379 | ||||||||
\(23\) | 2.98541 | 0.622502 | 0.311251 | − | 0.950328i | \(-0.399252\pi\) | ||||
0.311251 | + | 0.950328i | \(0.399252\pi\) | |||||||
\(24\) | −16.6747 | −3.40372 | ||||||||
\(25\) | 4.03751 | 0.807503 | ||||||||
\(26\) | 9.78007 | 1.91803 | ||||||||
\(27\) | 1.16631 | 0.224456 | ||||||||
\(28\) | −16.4980 | −3.11784 | ||||||||
\(29\) | 8.31482 | 1.54402 | 0.772012 | − | 0.635608i | \(-0.219251\pi\) | ||||
0.772012 | + | 0.635608i | \(0.219251\pi\) | |||||||
\(30\) | 19.5706 | 3.57308 | ||||||||
\(31\) | −2.64647 | −0.475320 | −0.237660 | − | 0.971348i | \(-0.576380\pi\) | ||||
−0.237660 | + | 0.971348i | \(0.576380\pi\) | |||||||
\(32\) | −6.55973 | −1.15961 | ||||||||
\(33\) | 5.60200 | 0.975183 | ||||||||
\(34\) | 19.9708 | 3.42496 | ||||||||
\(35\) | 10.8732 | 1.83790 | ||||||||
\(36\) | 15.7776 | 2.62959 | ||||||||
\(37\) | −10.7166 | −1.76179 | −0.880896 | − | 0.473310i | \(-0.843059\pi\) | ||||
−0.880896 | + | 0.473310i | \(0.843059\pi\) | |||||||
\(38\) | −5.11670 | −0.830039 | ||||||||
\(39\) | −9.70338 | −1.55378 | ||||||||
\(40\) | 19.7244 | 3.11870 | ||||||||
\(41\) | −11.2502 | −1.75698 | −0.878489 | − | 0.477762i | \(-0.841448\pi\) | ||||
−0.878489 | + | 0.477762i | \(0.841448\pi\) | |||||||
\(42\) | 23.5457 | 3.63318 | ||||||||
\(43\) | 3.57514 | 0.545204 | 0.272602 | − | 0.962127i | \(-0.412116\pi\) | ||||
0.272602 | + | 0.962127i | \(0.412116\pi\) | |||||||
\(44\) | 10.0546 | 1.51578 | ||||||||
\(45\) | −10.3983 | −1.55009 | ||||||||
\(46\) | −7.64721 | −1.12752 | ||||||||
\(47\) | −9.63306 | −1.40513 | −0.702563 | − | 0.711622i | \(-0.747961\pi\) | ||||
−0.702563 | + | 0.711622i | \(0.747961\pi\) | |||||||
\(48\) | 19.5277 | 2.81858 | ||||||||
\(49\) | 6.08171 | 0.868816 | ||||||||
\(50\) | −10.3422 | −1.46261 | ||||||||
\(51\) | −19.8142 | −2.77454 | ||||||||
\(52\) | −17.4158 | −2.41514 | ||||||||
\(53\) | 7.38262 | 1.01408 | 0.507041 | − | 0.861922i | \(-0.330739\pi\) | ||||
0.507041 | + | 0.861922i | \(0.330739\pi\) | |||||||
\(54\) | −2.98752 | −0.406550 | ||||||||
\(55\) | −6.62656 | −0.893525 | ||||||||
\(56\) | 23.7308 | 3.17116 | ||||||||
\(57\) | 5.07658 | 0.672409 | ||||||||
\(58\) | −21.2986 | −2.79665 | ||||||||
\(59\) | −8.73893 | −1.13771 | −0.568856 | − | 0.822437i | \(-0.692614\pi\) | ||||
−0.568856 | + | 0.822437i | \(0.692614\pi\) | |||||||
\(60\) | −34.8501 | −4.49913 | ||||||||
\(61\) | 2.57776 | 0.330048 | 0.165024 | − | 0.986290i | \(-0.447230\pi\) | ||||
0.165024 | + | 0.986290i | \(0.447230\pi\) | |||||||
\(62\) | 6.77901 | 0.860935 | ||||||||
\(63\) | −12.5104 | −1.57617 | ||||||||
\(64\) | 1.43551 | 0.179438 | ||||||||
\(65\) | 11.4780 | 1.42368 | ||||||||
\(66\) | −14.3497 | −1.76632 | ||||||||
\(67\) | −9.40824 | −1.14940 | −0.574700 | − | 0.818364i | \(-0.694881\pi\) | ||||
−0.574700 | + | 0.818364i | \(0.694881\pi\) | |||||||
\(68\) | −35.5628 | −4.31263 | ||||||||
\(69\) | 7.58725 | 0.913397 | ||||||||
\(70\) | −27.8520 | −3.32895 | ||||||||
\(71\) | 13.8414 | 1.64267 | 0.821333 | − | 0.570449i | \(-0.193231\pi\) | ||||
0.821333 | + | 0.570449i | \(0.193231\pi\) | |||||||
\(72\) | −22.6944 | −2.67456 | ||||||||
\(73\) | −6.32605 | −0.740408 | −0.370204 | − | 0.928950i | \(-0.620712\pi\) | ||||
−0.370204 | + | 0.928950i | \(0.620712\pi\) | |||||||
\(74\) | 27.4508 | 3.19109 | ||||||||
\(75\) | 10.2611 | 1.18485 | ||||||||
\(76\) | 9.11153 | 1.04516 | ||||||||
\(77\) | −7.97252 | −0.908553 | ||||||||
\(78\) | 24.8555 | 2.81433 | ||||||||
\(79\) | 10.0733 | 1.13333 | 0.566666 | − | 0.823948i | \(-0.308233\pi\) | ||||
0.566666 | + | 0.823948i | \(0.308233\pi\) | |||||||
\(80\) | −23.0991 | −2.58256 | ||||||||
\(81\) | −7.41265 | −0.823628 | ||||||||
\(82\) | 28.8176 | 3.18237 | ||||||||
\(83\) | 7.40492 | 0.812796 | 0.406398 | − | 0.913696i | \(-0.366785\pi\) | ||||
0.406398 | + | 0.913696i | \(0.366785\pi\) | |||||||
\(84\) | −41.9288 | −4.57480 | ||||||||
\(85\) | 23.4380 | 2.54221 | ||||||||
\(86\) | −9.15782 | −0.987513 | ||||||||
\(87\) | 21.1316 | 2.26555 | ||||||||
\(88\) | −14.4625 | −1.54171 | ||||||||
\(89\) | −13.9660 | −1.48040 | −0.740198 | − | 0.672389i | \(-0.765268\pi\) | ||||
−0.740198 | + | 0.672389i | \(0.765268\pi\) | |||||||
\(90\) | 26.6356 | 2.80764 | ||||||||
\(91\) | 13.8094 | 1.44762 | ||||||||
\(92\) | 13.6177 | 1.41975 | ||||||||
\(93\) | −6.72585 | −0.697438 | ||||||||
\(94\) | 24.6753 | 2.54507 | ||||||||
\(95\) | −6.00504 | −0.616104 | ||||||||
\(96\) | −16.6711 | −1.70149 | ||||||||
\(97\) | −1.11229 | −0.112936 | −0.0564679 | − | 0.998404i | \(-0.517984\pi\) | ||||
−0.0564679 | + | 0.998404i | \(0.517984\pi\) | |||||||
\(98\) | −15.5785 | −1.57366 | ||||||||
\(99\) | 7.62436 | 0.766277 | ||||||||
\(100\) | 18.4168 | 1.84168 | ||||||||
\(101\) | 16.7103 | 1.66274 | 0.831368 | − | 0.555723i | \(-0.187558\pi\) | ||||
0.831368 | + | 0.555723i | \(0.187558\pi\) | |||||||
\(102\) | 50.7546 | 5.02545 | ||||||||
\(103\) | −16.0534 | −1.58179 | −0.790894 | − | 0.611953i | \(-0.790384\pi\) | ||||
−0.790894 | + | 0.611953i | \(0.790384\pi\) | |||||||
\(104\) | 25.0509 | 2.45644 | ||||||||
\(105\) | 27.6335 | 2.69676 | ||||||||
\(106\) | −18.9108 | −1.83678 | ||||||||
\(107\) | 3.00288 | 0.290299 | 0.145149 | − | 0.989410i | \(-0.453634\pi\) | ||||
0.145149 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(108\) | 5.32001 | 0.511918 | ||||||||
\(109\) | 11.4788 | 1.09947 | 0.549733 | − | 0.835340i | \(-0.314729\pi\) | ||||
0.549733 | + | 0.835340i | \(0.314729\pi\) | |||||||
\(110\) | 16.9741 | 1.61842 | ||||||||
\(111\) | −27.2355 | −2.58508 | ||||||||
\(112\) | −27.7909 | −2.62599 | ||||||||
\(113\) | −1.71065 | −0.160924 | −0.0804621 | − | 0.996758i | \(-0.525640\pi\) | ||||
−0.0804621 | + | 0.996758i | \(0.525640\pi\) | |||||||
\(114\) | −13.0038 | −1.21792 | ||||||||
\(115\) | −8.97488 | −0.836912 | ||||||||
\(116\) | 37.9274 | 3.52147 | ||||||||
\(117\) | −13.2064 | −1.22093 | ||||||||
\(118\) | 22.3850 | 2.06071 | ||||||||
\(119\) | 28.1987 | 2.58497 | ||||||||
\(120\) | 50.1284 | 4.57607 | ||||||||
\(121\) | −6.14122 | −0.558293 | ||||||||
\(122\) | −6.60299 | −0.597807 | ||||||||
\(123\) | −28.5916 | −2.57802 | ||||||||
\(124\) | −12.0717 | −1.08407 | ||||||||
\(125\) | 2.89347 | 0.258800 | ||||||||
\(126\) | 32.0458 | 2.85487 | ||||||||
\(127\) | −15.1212 | −1.34179 | −0.670896 | − | 0.741552i | \(-0.734090\pi\) | ||||
−0.670896 | + | 0.741552i | \(0.734090\pi\) | |||||||
\(128\) | 9.44237 | 0.834595 | ||||||||
\(129\) | 9.08601 | 0.799978 | ||||||||
\(130\) | −29.4013 | −2.57867 | ||||||||
\(131\) | −22.2083 | −1.94035 | −0.970175 | − | 0.242404i | \(-0.922064\pi\) | ||||
−0.970175 | + | 0.242404i | \(0.922064\pi\) | |||||||
\(132\) | 25.5531 | 2.22411 | ||||||||
\(133\) | −7.22476 | −0.626466 | ||||||||
\(134\) | 24.0995 | 2.08188 | ||||||||
\(135\) | −3.50620 | −0.301766 | ||||||||
\(136\) | 51.1536 | 4.38638 | ||||||||
\(137\) | −1.16754 | −0.0997500 | −0.0498750 | − | 0.998755i | \(-0.515882\pi\) | ||||
−0.0498750 | + | 0.998755i | \(0.515882\pi\) | |||||||
\(138\) | −19.4349 | −1.65441 | ||||||||
\(139\) | −3.10551 | −0.263406 | −0.131703 | − | 0.991289i | \(-0.542044\pi\) | ||||
−0.131703 | + | 0.991289i | \(0.542044\pi\) | |||||||
\(140\) | 49.5971 | 4.19172 | ||||||||
\(141\) | −24.4818 | −2.06174 | ||||||||
\(142\) | −35.4550 | −2.97532 | ||||||||
\(143\) | −8.41602 | −0.703783 | ||||||||
\(144\) | 26.5773 | 2.21477 | ||||||||
\(145\) | −24.9964 | −2.07584 | ||||||||
\(146\) | 16.2044 | 1.34108 | ||||||||
\(147\) | 15.4563 | 1.27481 | ||||||||
\(148\) | −48.8827 | −4.01814 | ||||||||
\(149\) | 14.7707 | 1.21006 | 0.605029 | − | 0.796203i | \(-0.293161\pi\) | ||||
0.605029 | + | 0.796203i | \(0.293161\pi\) | |||||||
\(150\) | −26.2841 | −2.14609 | ||||||||
\(151\) | 5.66785 | 0.461243 | 0.230622 | − | 0.973044i | \(-0.425924\pi\) | ||||
0.230622 | + | 0.973044i | \(0.425924\pi\) | |||||||
\(152\) | −13.1060 | −1.06304 | ||||||||
\(153\) | −26.9672 | −2.18017 | ||||||||
\(154\) | 20.4218 | 1.64564 | ||||||||
\(155\) | 7.95594 | 0.639037 | ||||||||
\(156\) | −44.2612 | −3.54373 | ||||||||
\(157\) | −8.78474 | −0.701099 | −0.350549 | − | 0.936544i | \(-0.614005\pi\) | ||||
−0.350549 | + | 0.936544i | \(0.614005\pi\) | |||||||
\(158\) | −25.8030 | −2.05277 | ||||||||
\(159\) | 18.7625 | 1.48796 | ||||||||
\(160\) | 19.7201 | 1.55901 | ||||||||
\(161\) | −10.7978 | −0.850989 | ||||||||
\(162\) | 18.9877 | 1.49181 | ||||||||
\(163\) | 9.38215 | 0.734866 | 0.367433 | − | 0.930050i | \(-0.380237\pi\) | ||||
0.367433 | + | 0.930050i | \(0.380237\pi\) | |||||||
\(164\) | −51.3167 | −4.00716 | ||||||||
\(165\) | −16.8410 | −1.31107 | ||||||||
\(166\) | −18.9679 | −1.47219 | ||||||||
\(167\) | 17.8900 | 1.38437 | 0.692185 | − | 0.721720i | \(-0.256648\pi\) | ||||
0.692185 | + | 0.721720i | \(0.256648\pi\) | |||||||
\(168\) | 60.3103 | 4.65304 | ||||||||
\(169\) | 1.57762 | 0.121355 | ||||||||
\(170\) | −60.0371 | −4.60464 | ||||||||
\(171\) | 6.90925 | 0.528364 | ||||||||
\(172\) | 16.3077 | 1.24345 | ||||||||
\(173\) | 17.5847 | 1.33694 | 0.668471 | − | 0.743738i | \(-0.266949\pi\) | ||||
0.668471 | + | 0.743738i | \(0.266949\pi\) | |||||||
\(174\) | −54.1292 | −4.10352 | ||||||||
\(175\) | −14.6031 | −1.10389 | ||||||||
\(176\) | 16.9369 | 1.27667 | ||||||||
\(177\) | −22.2095 | −1.66937 | ||||||||
\(178\) | 35.7743 | 2.68140 | ||||||||
\(179\) | −11.6772 | −0.872796 | −0.436398 | − | 0.899754i | \(-0.643746\pi\) | ||||
−0.436398 | + | 0.899754i | \(0.643746\pi\) | |||||||
\(180\) | −47.4312 | −3.53531 | ||||||||
\(181\) | −0.837814 | −0.0622742 | −0.0311371 | − | 0.999515i | \(-0.509913\pi\) | ||||
−0.0311371 | + | 0.999515i | \(0.509913\pi\) | |||||||
\(182\) | −35.3732 | −2.62204 | ||||||||
\(183\) | 6.55121 | 0.484280 | ||||||||
\(184\) | −19.5877 | −1.44403 | ||||||||
\(185\) | 32.2166 | 2.36861 | ||||||||
\(186\) | 17.2284 | 1.26325 | ||||||||
\(187\) | −17.1854 | −1.25672 | ||||||||
\(188\) | −43.9404 | −3.20468 | ||||||||
\(189\) | −4.21837 | −0.306841 | ||||||||
\(190\) | 15.3821 | 1.11593 | ||||||||
\(191\) | −7.66133 | −0.554354 | −0.277177 | − | 0.960819i | \(-0.589399\pi\) | ||||
−0.277177 | + | 0.960819i | \(0.589399\pi\) | |||||||
\(192\) | 3.64825 | 0.263290 | ||||||||
\(193\) | 13.9158 | 1.00168 | 0.500842 | − | 0.865539i | \(-0.333024\pi\) | ||||
0.500842 | + | 0.865539i | \(0.333024\pi\) | |||||||
\(194\) | 2.84916 | 0.204558 | ||||||||
\(195\) | 29.1707 | 2.08896 | ||||||||
\(196\) | 27.7412 | 1.98152 | ||||||||
\(197\) | −19.7394 | −1.40637 | −0.703186 | − | 0.711006i | \(-0.748240\pi\) | ||||
−0.703186 | + | 0.711006i | \(0.748240\pi\) | |||||||
\(198\) | −19.5300 | −1.38794 | ||||||||
\(199\) | −1.56272 | −0.110779 | −0.0553893 | − | 0.998465i | \(-0.517640\pi\) | ||||
−0.0553893 | + | 0.998465i | \(0.517640\pi\) | |||||||
\(200\) | −26.4907 | −1.87317 | ||||||||
\(201\) | −23.9105 | −1.68652 | ||||||||
\(202\) | −42.8038 | −3.01167 | ||||||||
\(203\) | −30.0736 | −2.11075 | ||||||||
\(204\) | −90.3808 | −6.32792 | ||||||||
\(205\) | 33.8207 | 2.36214 | ||||||||
\(206\) | 41.1212 | 2.86505 | ||||||||
\(207\) | 10.3263 | 0.717727 | ||||||||
\(208\) | −29.3369 | −2.03415 | ||||||||
\(209\) | 4.40306 | 0.304566 | ||||||||
\(210\) | −70.7841 | −4.88456 | ||||||||
\(211\) | −0.459529 | −0.0316353 | −0.0158176 | − | 0.999875i | \(-0.505035\pi\) | ||||
−0.0158176 | + | 0.999875i | \(0.505035\pi\) | |||||||
\(212\) | 33.6752 | 2.31282 | ||||||||
\(213\) | 35.1770 | 2.41029 | ||||||||
\(214\) | −7.69195 | −0.525811 | ||||||||
\(215\) | −10.7478 | −0.732991 | ||||||||
\(216\) | −7.65230 | −0.520673 | ||||||||
\(217\) | 9.57193 | 0.649785 | ||||||||
\(218\) | −29.4032 | −1.99143 | ||||||||
\(219\) | −16.0773 | −1.08640 | ||||||||
\(220\) | −30.2265 | −2.03787 | ||||||||
\(221\) | 29.7673 | 2.00237 | ||||||||
\(222\) | 69.7644 | 4.68228 | ||||||||
\(223\) | 21.1560 | 1.41671 | 0.708354 | − | 0.705857i | \(-0.249438\pi\) | ||||
0.708354 | + | 0.705857i | \(0.249438\pi\) | |||||||
\(224\) | 23.7256 | 1.58524 | ||||||||
\(225\) | 13.9654 | 0.931028 | ||||||||
\(226\) | 4.38187 | 0.291478 | ||||||||
\(227\) | 15.9982 | 1.06184 | 0.530920 | − | 0.847422i | \(-0.321847\pi\) | ||||
0.530920 | + | 0.847422i | \(0.321847\pi\) | |||||||
\(228\) | 23.1564 | 1.53357 | ||||||||
\(229\) | −27.4724 | −1.81543 | −0.907714 | − | 0.419590i | \(-0.862174\pi\) | ||||
−0.907714 | + | 0.419590i | \(0.862174\pi\) | |||||||
\(230\) | 22.9894 | 1.51588 | ||||||||
\(231\) | −20.2617 | −1.33312 | ||||||||
\(232\) | −54.5547 | −3.58169 | ||||||||
\(233\) | 0.954541 | 0.0625341 | 0.0312670 | − | 0.999511i | \(-0.490046\pi\) | ||||
0.0312670 | + | 0.999511i | \(0.490046\pi\) | |||||||
\(234\) | 33.8284 | 2.21143 | ||||||||
\(235\) | 28.9593 | 1.88910 | ||||||||
\(236\) | −39.8619 | −2.59479 | ||||||||
\(237\) | 25.6006 | 1.66294 | ||||||||
\(238\) | −72.2317 | −4.68208 | ||||||||
\(239\) | 11.2833 | 0.729856 | 0.364928 | − | 0.931036i | \(-0.381094\pi\) | ||||
0.364928 | + | 0.931036i | \(0.381094\pi\) | |||||||
\(240\) | −58.7050 | −3.78939 | ||||||||
\(241\) | −18.4650 | −1.18944 | −0.594718 | − | 0.803934i | \(-0.702736\pi\) | ||||
−0.594718 | + | 0.803934i | \(0.702736\pi\) | |||||||
\(242\) | 15.7309 | 1.01122 | ||||||||
\(243\) | −22.3377 | −1.43297 | ||||||||
\(244\) | 11.7582 | 0.752743 | ||||||||
\(245\) | −18.2831 | −1.16807 | ||||||||
\(246\) | 73.2381 | 4.66949 | ||||||||
\(247\) | −7.62666 | −0.485273 | ||||||||
\(248\) | 17.3639 | 1.10261 | ||||||||
\(249\) | 18.8192 | 1.19262 | ||||||||
\(250\) | −7.41171 | −0.468758 | ||||||||
\(251\) | 27.3617 | 1.72706 | 0.863529 | − | 0.504299i | \(-0.168249\pi\) | ||||
0.863529 | + | 0.504299i | \(0.168249\pi\) | |||||||
\(252\) | −57.0653 | −3.59478 | ||||||||
\(253\) | 6.58063 | 0.413721 | ||||||||
\(254\) | 38.7334 | 2.43035 | ||||||||
\(255\) | 59.5663 | 3.73019 | ||||||||
\(256\) | −27.0579 | −1.69112 | ||||||||
\(257\) | 22.5196 | 1.40473 | 0.702367 | − | 0.711815i | \(-0.252127\pi\) | ||||
0.702367 | + | 0.711815i | \(0.252127\pi\) | |||||||
\(258\) | −23.2741 | −1.44898 | ||||||||
\(259\) | 38.7604 | 2.40845 | ||||||||
\(260\) | 52.3561 | 3.24699 | ||||||||
\(261\) | 28.7603 | 1.78022 | ||||||||
\(262\) | 56.8872 | 3.51450 | ||||||||
\(263\) | 1.37032 | 0.0844976 | 0.0422488 | − | 0.999107i | \(-0.486548\pi\) | ||||
0.0422488 | + | 0.999107i | \(0.486548\pi\) | |||||||
\(264\) | −36.7555 | −2.26215 | ||||||||
\(265\) | −22.1940 | −1.36336 | ||||||||
\(266\) | 18.5064 | 1.13470 | ||||||||
\(267\) | −35.4938 | −2.17219 | ||||||||
\(268\) | −42.9149 | −2.62145 | ||||||||
\(269\) | 5.74852 | 0.350493 | 0.175247 | − | 0.984525i | \(-0.443928\pi\) | ||||
0.175247 | + | 0.984525i | \(0.443928\pi\) | |||||||
\(270\) | 8.98123 | 0.546580 | ||||||||
\(271\) | 25.7719 | 1.56553 | 0.782765 | − | 0.622317i | \(-0.213809\pi\) | ||||
0.782765 | + | 0.622317i | \(0.213809\pi\) | |||||||
\(272\) | −59.9055 | −3.63231 | ||||||||
\(273\) | 35.0958 | 2.12410 | ||||||||
\(274\) | 2.99069 | 0.180674 | ||||||||
\(275\) | 8.89974 | 0.536674 | ||||||||
\(276\) | 34.6086 | 2.08319 | ||||||||
\(277\) | −16.3149 | −0.980266 | −0.490133 | − | 0.871648i | \(-0.663052\pi\) | ||||
−0.490133 | + | 0.871648i | \(0.663052\pi\) | |||||||
\(278\) | 7.95484 | 0.477099 | ||||||||
\(279\) | −9.15392 | −0.548031 | ||||||||
\(280\) | −71.3405 | −4.26341 | ||||||||
\(281\) | −11.2518 | −0.671226 | −0.335613 | − | 0.942000i | \(-0.608943\pi\) | ||||
−0.335613 | + | 0.942000i | \(0.608943\pi\) | |||||||
\(282\) | 62.7109 | 3.73438 | ||||||||
\(283\) | 19.2045 | 1.14159 | 0.570795 | − | 0.821093i | \(-0.306635\pi\) | ||||
0.570795 | + | 0.821093i | \(0.306635\pi\) | |||||||
\(284\) | 63.1362 | 3.74644 | ||||||||
\(285\) | −15.2614 | −0.904010 | ||||||||
\(286\) | 21.5579 | 1.27474 | ||||||||
\(287\) | 40.6903 | 2.40187 | ||||||||
\(288\) | −22.6895 | −1.33699 | ||||||||
\(289\) | 43.7845 | 2.57556 | ||||||||
\(290\) | 64.0289 | 3.75991 | ||||||||
\(291\) | −2.82682 | −0.165711 | ||||||||
\(292\) | −28.8558 | −1.68866 | ||||||||
\(293\) | −12.5841 | −0.735172 | −0.367586 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367586 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(294\) | −39.5917 | −2.30904 | ||||||||
\(295\) | 26.2714 | 1.52958 | ||||||||
\(296\) | 70.3129 | 4.08685 | ||||||||
\(297\) | 2.57084 | 0.149175 | ||||||||
\(298\) | −37.8354 | −2.19175 | ||||||||
\(299\) | −11.3985 | −0.659192 | ||||||||
\(300\) | 46.8051 | 2.70230 | ||||||||
\(301\) | −12.9308 | −0.745319 | ||||||||
\(302\) | −14.5183 | −0.835437 | ||||||||
\(303\) | 42.4682 | 2.43973 | ||||||||
\(304\) | 15.3484 | 0.880289 | ||||||||
\(305\) | −7.74937 | −0.443728 | ||||||||
\(306\) | 69.0773 | 3.94888 | ||||||||
\(307\) | −29.6428 | −1.69180 | −0.845902 | − | 0.533338i | \(-0.820937\pi\) | ||||
−0.845902 | + | 0.533338i | \(0.820937\pi\) | |||||||
\(308\) | −36.3660 | −2.07215 | ||||||||
\(309\) | −40.7987 | −2.32096 | ||||||||
\(310\) | −20.3794 | −1.15747 | ||||||||
\(311\) | 7.71994 | 0.437757 | 0.218879 | − | 0.975752i | \(-0.429760\pi\) | ||||
0.218879 | + | 0.975752i | \(0.429760\pi\) | |||||||
\(312\) | 63.6653 | 3.60434 | ||||||||
\(313\) | 12.6853 | 0.717017 | 0.358508 | − | 0.933527i | \(-0.383285\pi\) | ||||
0.358508 | + | 0.933527i | \(0.383285\pi\) | |||||||
\(314\) | 22.5024 | 1.26988 | ||||||||
\(315\) | 37.6094 | 2.11905 | ||||||||
\(316\) | 45.9484 | 2.58480 | ||||||||
\(317\) | 15.5382 | 0.872712 | 0.436356 | − | 0.899774i | \(-0.356269\pi\) | ||||
0.436356 | + | 0.899774i | \(0.356269\pi\) | |||||||
\(318\) | −48.0606 | −2.69511 | ||||||||
\(319\) | 18.3281 | 1.02617 | ||||||||
\(320\) | −4.31548 | −0.241243 | ||||||||
\(321\) | 7.63163 | 0.425956 | ||||||||
\(322\) | 27.6589 | 1.54137 | ||||||||
\(323\) | −15.5736 | −0.866536 | ||||||||
\(324\) | −33.8122 | −1.87846 | ||||||||
\(325\) | −15.4155 | −0.855097 | ||||||||
\(326\) | −24.0326 | −1.33104 | ||||||||
\(327\) | 29.1726 | 1.61325 | ||||||||
\(328\) | 73.8138 | 4.07569 | ||||||||
\(329\) | 34.8415 | 1.92087 | ||||||||
\(330\) | 43.1386 | 2.37470 | ||||||||
\(331\) | 0.378075 | 0.0207809 | 0.0103904 | − | 0.999946i | \(-0.496693\pi\) | ||||
0.0103904 | + | 0.999946i | \(0.496693\pi\) | |||||||
\(332\) | 33.7769 | 1.85375 | ||||||||
\(333\) | −37.0677 | −2.03130 | ||||||||
\(334\) | −45.8257 | −2.50747 | ||||||||
\(335\) | 28.2835 | 1.54529 | ||||||||
\(336\) | −70.6289 | −3.85312 | ||||||||
\(337\) | 10.4593 | 0.569752 | 0.284876 | − | 0.958564i | \(-0.408048\pi\) | ||||
0.284876 | + | 0.958564i | \(0.408048\pi\) | |||||||
\(338\) | −4.04111 | −0.219808 | ||||||||
\(339\) | −4.34751 | −0.236124 | ||||||||
\(340\) | 106.911 | 5.79804 | ||||||||
\(341\) | −5.83352 | −0.315903 | ||||||||
\(342\) | −17.6982 | −0.957011 | ||||||||
\(343\) | 3.32132 | 0.179334 | ||||||||
\(344\) | −23.4570 | −1.26472 | ||||||||
\(345\) | −22.8091 | −1.22800 | ||||||||
\(346\) | −45.0437 | −2.42157 | ||||||||
\(347\) | 23.7289 | 1.27384 | 0.636918 | − | 0.770932i | \(-0.280209\pi\) | ||||
0.636918 | + | 0.770932i | \(0.280209\pi\) | |||||||
\(348\) | 96.3902 | 5.16705 | ||||||||
\(349\) | −9.93055 | −0.531570 | −0.265785 | − | 0.964032i | \(-0.585631\pi\) | ||||
−0.265785 | + | 0.964032i | \(0.585631\pi\) | |||||||
\(350\) | 37.4063 | 1.99945 | ||||||||
\(351\) | −4.45303 | −0.237685 | ||||||||
\(352\) | −14.4594 | −0.770686 | ||||||||
\(353\) | 11.0081 | 0.585902 | 0.292951 | − | 0.956127i | \(-0.405363\pi\) | ||||
0.292951 | + | 0.956127i | \(0.405363\pi\) | |||||||
\(354\) | 56.8901 | 3.02368 | ||||||||
\(355\) | −41.6105 | −2.20846 | ||||||||
\(356\) | −63.7049 | −3.37635 | ||||||||
\(357\) | 71.6652 | 3.79293 | ||||||||
\(358\) | 29.9115 | 1.58087 | ||||||||
\(359\) | 25.7066 | 1.35674 | 0.678372 | − | 0.734718i | \(-0.262686\pi\) | ||||
0.678372 | + | 0.734718i | \(0.262686\pi\) | |||||||
\(360\) | 68.2250 | 3.59578 | ||||||||
\(361\) | −15.0099 | −0.789995 | ||||||||
\(362\) | 2.14608 | 0.112796 | ||||||||
\(363\) | −15.6076 | −0.819184 | ||||||||
\(364\) | 62.9906 | 3.30160 | ||||||||
\(365\) | 19.0177 | 0.995430 | ||||||||
\(366\) | −16.7811 | −0.877162 | ||||||||
\(367\) | 15.4100 | 0.804395 | 0.402197 | − | 0.915553i | \(-0.368247\pi\) | ||||
0.402197 | + | 0.915553i | \(0.368247\pi\) | |||||||
\(368\) | 22.9390 | 1.19578 | ||||||||
\(369\) | −38.9133 | −2.02575 | ||||||||
\(370\) | −82.5237 | −4.29020 | ||||||||
\(371\) | −26.7019 | −1.38630 | ||||||||
\(372\) | −30.6794 | −1.59065 | ||||||||
\(373\) | −1.50176 | −0.0777582 | −0.0388791 | − | 0.999244i | \(-0.512379\pi\) | ||||
−0.0388791 | + | 0.999244i | \(0.512379\pi\) | |||||||
\(374\) | 44.0209 | 2.27626 | ||||||||
\(375\) | 7.35359 | 0.379738 | ||||||||
\(376\) | 63.2039 | 3.25949 | ||||||||
\(377\) | −31.7465 | −1.63503 | ||||||||
\(378\) | 10.8055 | 0.555773 | ||||||||
\(379\) | 14.6246 | 0.751217 | 0.375608 | − | 0.926778i | \(-0.377434\pi\) | ||||
0.375608 | + | 0.926778i | \(0.377434\pi\) | |||||||
\(380\) | −27.3915 | −1.40515 | ||||||||
\(381\) | −38.4297 | −1.96881 | ||||||||
\(382\) | 19.6247 | 1.00409 | ||||||||
\(383\) | −4.12778 | −0.210920 | −0.105460 | − | 0.994424i | \(-0.533631\pi\) | ||||
−0.105460 | + | 0.994424i | \(0.533631\pi\) | |||||||
\(384\) | 23.9972 | 1.22460 | ||||||||
\(385\) | 23.9674 | 1.22149 | ||||||||
\(386\) | −35.6458 | −1.81432 | ||||||||
\(387\) | 12.3661 | 0.628605 | ||||||||
\(388\) | −5.07362 | −0.257574 | ||||||||
\(389\) | −22.3662 | −1.13401 | −0.567006 | − | 0.823714i | \(-0.691898\pi\) | ||||
−0.567006 | + | 0.823714i | \(0.691898\pi\) | |||||||
\(390\) | −74.7216 | −3.78368 | ||||||||
\(391\) | −23.2756 | −1.17710 | ||||||||
\(392\) | −39.9030 | −2.01541 | ||||||||
\(393\) | −56.4411 | −2.84708 | ||||||||
\(394\) | 50.5630 | 2.54732 | ||||||||
\(395\) | −30.2827 | −1.52369 | ||||||||
\(396\) | 34.7779 | 1.74765 | ||||||||
\(397\) | 6.41105 | 0.321762 | 0.160881 | − | 0.986974i | \(-0.448567\pi\) | ||||
0.160881 | + | 0.986974i | \(0.448567\pi\) | |||||||
\(398\) | 4.00296 | 0.200650 | ||||||||
\(399\) | −18.3613 | −0.919215 | ||||||||
\(400\) | 31.0230 | 1.55115 | ||||||||
\(401\) | 1.93305 | 0.0965319 | 0.0482659 | − | 0.998835i | \(-0.484631\pi\) | ||||
0.0482659 | + | 0.998835i | \(0.484631\pi\) | |||||||
\(402\) | 61.2473 | 3.05474 | ||||||||
\(403\) | 10.1044 | 0.503336 | ||||||||
\(404\) | 76.2226 | 3.79222 | ||||||||
\(405\) | 22.2842 | 1.10731 | ||||||||
\(406\) | 77.0343 | 3.82315 | ||||||||
\(407\) | −23.6221 | −1.17091 | ||||||||
\(408\) | 130.004 | 6.43614 | ||||||||
\(409\) | 3.27687 | 0.162031 | 0.0810153 | − | 0.996713i | \(-0.474184\pi\) | ||||
0.0810153 | + | 0.996713i | \(0.474184\pi\) | |||||||
\(410\) | −86.6327 | −4.27848 | ||||||||
\(411\) | −2.96724 | −0.146363 | ||||||||
\(412\) | −73.2263 | −3.60760 | ||||||||
\(413\) | 31.6075 | 1.55531 | ||||||||
\(414\) | −26.4511 | −1.30000 | ||||||||
\(415\) | −22.2610 | −1.09275 | ||||||||
\(416\) | 25.0455 | 1.22795 | ||||||||
\(417\) | −7.89246 | −0.386495 | ||||||||
\(418\) | −11.2786 | −0.551652 | ||||||||
\(419\) | 34.7357 | 1.69695 | 0.848475 | − | 0.529236i | \(-0.177521\pi\) | ||||
0.848475 | + | 0.529236i | \(0.177521\pi\) | |||||||
\(420\) | 126.048 | 6.15052 | ||||||||
\(421\) | −29.7591 | −1.45037 | −0.725185 | − | 0.688554i | \(-0.758246\pi\) | ||||
−0.725185 | + | 0.688554i | \(0.758246\pi\) | |||||||
\(422\) | 1.17710 | 0.0573002 | ||||||||
\(423\) | −33.3199 | −1.62007 | ||||||||
\(424\) | −48.4384 | −2.35238 | ||||||||
\(425\) | −31.4782 | −1.52692 | ||||||||
\(426\) | −90.1067 | −4.36568 | ||||||||
\(427\) | −9.32340 | −0.451191 | ||||||||
\(428\) | 13.6974 | 0.662087 | ||||||||
\(429\) | −21.3888 | −1.03266 | ||||||||
\(430\) | 27.5307 | 1.32765 | ||||||||
\(431\) | 26.0204 | 1.25336 | 0.626680 | − | 0.779277i | \(-0.284413\pi\) | ||||
0.626680 | + | 0.779277i | \(0.284413\pi\) | |||||||
\(432\) | 8.96154 | 0.431162 | ||||||||
\(433\) | −19.6649 | −0.945037 | −0.472518 | − | 0.881321i | \(-0.656655\pi\) | ||||
−0.472518 | + | 0.881321i | \(0.656655\pi\) | |||||||
\(434\) | −24.5188 | −1.17694 | ||||||||
\(435\) | −63.5268 | −3.04588 | ||||||||
\(436\) | 52.3594 | 2.50756 | ||||||||
\(437\) | 5.96342 | 0.285269 | ||||||||
\(438\) | 41.1824 | 1.96777 | ||||||||
\(439\) | 28.5104 | 1.36073 | 0.680365 | − | 0.732874i | \(-0.261821\pi\) | ||||
0.680365 | + | 0.732874i | \(0.261821\pi\) | |||||||
\(440\) | 43.4778 | 2.07272 | ||||||||
\(441\) | 21.0361 | 1.00172 | ||||||||
\(442\) | −76.2498 | −3.62683 | ||||||||
\(443\) | −0.529187 | −0.0251424 | −0.0125712 | − | 0.999921i | \(-0.504002\pi\) | ||||
−0.0125712 | + | 0.999921i | \(0.504002\pi\) | |||||||
\(444\) | −124.232 | −5.89581 | ||||||||
\(445\) | 41.9853 | 1.99029 | ||||||||
\(446\) | −54.1916 | −2.56605 | ||||||||
\(447\) | 37.5387 | 1.77552 | ||||||||
\(448\) | −5.19203 | −0.245300 | ||||||||
\(449\) | 20.3954 | 0.962520 | 0.481260 | − | 0.876578i | \(-0.340179\pi\) | ||||
0.481260 | + | 0.876578i | \(0.340179\pi\) | |||||||
\(450\) | −35.7728 | −1.68634 | ||||||||
\(451\) | −24.7983 | −1.16771 | ||||||||
\(452\) | −7.80298 | −0.367022 | ||||||||
\(453\) | 14.4045 | 0.676782 | ||||||||
\(454\) | −40.9799 | −1.92328 | ||||||||
\(455\) | −41.5145 | −1.94623 | ||||||||
\(456\) | −33.3082 | −1.55980 | ||||||||
\(457\) | 1.88618 | 0.0882317 | 0.0441158 | − | 0.999026i | \(-0.485953\pi\) | ||||
0.0441158 | + | 0.999026i | \(0.485953\pi\) | |||||||
\(458\) | 70.3713 | 3.28823 | ||||||||
\(459\) | −9.09303 | −0.424426 | ||||||||
\(460\) | −40.9382 | −1.90875 | ||||||||
\(461\) | 17.2168 | 0.801864 | 0.400932 | − | 0.916108i | \(-0.368686\pi\) | ||||
0.400932 | + | 0.916108i | \(0.368686\pi\) | |||||||
\(462\) | 51.9008 | 2.41465 | ||||||||
\(463\) | 14.3910 | 0.668806 | 0.334403 | − | 0.942430i | \(-0.391465\pi\) | ||||
0.334403 | + | 0.942430i | \(0.391465\pi\) | |||||||
\(464\) | 63.8886 | 2.96595 | ||||||||
\(465\) | 20.2196 | 0.937659 | ||||||||
\(466\) | −2.44508 | −0.113266 | ||||||||
\(467\) | 2.69015 | 0.124485 | 0.0622427 | − | 0.998061i | \(-0.480175\pi\) | ||||
0.0622427 | + | 0.998061i | \(0.480175\pi\) | |||||||
\(468\) | −60.2397 | −2.78458 | ||||||||
\(469\) | 34.0284 | 1.57128 | ||||||||
\(470\) | −74.1801 | −3.42167 | ||||||||
\(471\) | −22.3259 | −1.02872 | ||||||||
\(472\) | 57.3374 | 2.63917 | ||||||||
\(473\) | 7.88055 | 0.362348 | ||||||||
\(474\) | −65.5767 | −3.01204 | ||||||||
\(475\) | 8.06502 | 0.370048 | ||||||||
\(476\) | 128.626 | 5.89556 | ||||||||
\(477\) | 25.5359 | 1.16921 | ||||||||
\(478\) | −28.9025 | −1.32197 | ||||||||
\(479\) | 19.0487 | 0.870357 | 0.435179 | − | 0.900344i | \(-0.356685\pi\) | ||||
0.435179 | + | 0.900344i | \(0.356685\pi\) | |||||||
\(480\) | 50.1176 | 2.28754 | ||||||||
\(481\) | 40.9165 | 1.86563 | ||||||||
\(482\) | 47.2986 | 2.15439 | ||||||||
\(483\) | −27.4420 | −1.24866 | ||||||||
\(484\) | −28.0127 | −1.27330 | ||||||||
\(485\) | 3.34381 | 0.151835 | ||||||||
\(486\) | 57.2187 | 2.59549 | ||||||||
\(487\) | −36.4665 | −1.65245 | −0.826227 | − | 0.563337i | \(-0.809517\pi\) | ||||
−0.826227 | + | 0.563337i | \(0.809517\pi\) | |||||||
\(488\) | −16.9130 | −0.765617 | ||||||||
\(489\) | 23.8442 | 1.07827 | ||||||||
\(490\) | 46.8327 | 2.11569 | ||||||||
\(491\) | −22.7726 | −1.02771 | −0.513857 | − | 0.857876i | \(-0.671784\pi\) | ||||
−0.513857 | + | 0.857876i | \(0.671784\pi\) | |||||||
\(492\) | −130.418 | −5.87971 | ||||||||
\(493\) | −64.8260 | −2.91962 | ||||||||
\(494\) | 19.5359 | 0.878962 | ||||||||
\(495\) | −22.9207 | −1.03021 | ||||||||
\(496\) | −20.3347 | −0.913055 | ||||||||
\(497\) | −50.0623 | −2.24560 | ||||||||
\(498\) | −48.2058 | −2.16015 | ||||||||
\(499\) | 23.6318 | 1.05791 | 0.528953 | − | 0.848651i | \(-0.322585\pi\) | ||||
0.528953 | + | 0.848651i | \(0.322585\pi\) | |||||||
\(500\) | 13.1983 | 0.590248 | ||||||||
\(501\) | 45.4664 | 2.03129 | ||||||||
\(502\) | −70.0878 | −3.12817 | ||||||||
\(503\) | −28.5638 | −1.27360 | −0.636799 | − | 0.771030i | \(-0.719742\pi\) | ||||
−0.636799 | + | 0.771030i | \(0.719742\pi\) | |||||||
\(504\) | 82.0827 | 3.65625 | ||||||||
\(505\) | −50.2352 | −2.23544 | ||||||||
\(506\) | −16.8565 | −0.749362 | ||||||||
\(507\) | 4.00942 | 0.178065 | ||||||||
\(508\) | −68.9742 | −3.06024 | ||||||||
\(509\) | 1.67049 | 0.0740431 | 0.0370215 | − | 0.999314i | \(-0.488213\pi\) | ||||
0.0370215 | + | 0.999314i | \(0.488213\pi\) | |||||||
\(510\) | −152.581 | −6.75638 | ||||||||
\(511\) | 22.8805 | 1.01217 | ||||||||
\(512\) | 50.4248 | 2.22848 | ||||||||
\(513\) | 2.32972 | 0.102860 | ||||||||
\(514\) | −57.6846 | −2.54436 | ||||||||
\(515\) | 48.2605 | 2.12661 | ||||||||
\(516\) | 41.4451 | 1.82452 | ||||||||
\(517\) | −21.2338 | −0.933861 | ||||||||
\(518\) | −99.2857 | −4.36236 | ||||||||
\(519\) | 44.6905 | 1.96170 | ||||||||
\(520\) | −75.3091 | −3.30252 | ||||||||
\(521\) | 40.1288 | 1.75808 | 0.879038 | − | 0.476752i | \(-0.158186\pi\) | ||||
0.879038 | + | 0.476752i | \(0.158186\pi\) | |||||||
\(522\) | −73.6702 | −3.22446 | ||||||||
\(523\) | 26.8145 | 1.17252 | 0.586258 | − | 0.810124i | \(-0.300601\pi\) | ||||
0.586258 | + | 0.810124i | \(0.300601\pi\) | |||||||
\(524\) | −101.301 | −4.42538 | ||||||||
\(525\) | −37.1130 | −1.61974 | ||||||||
\(526\) | −3.51011 | −0.153048 | ||||||||
\(527\) | 20.6331 | 0.898790 | ||||||||
\(528\) | 43.0441 | 1.87325 | ||||||||
\(529\) | −14.0873 | −0.612492 | ||||||||
\(530\) | 56.8505 | 2.46943 | ||||||||
\(531\) | −30.2272 | −1.31175 | ||||||||
\(532\) | −32.9552 | −1.42879 | ||||||||
\(533\) | 42.9538 | 1.86054 | ||||||||
\(534\) | 90.9183 | 3.93442 | ||||||||
\(535\) | −9.02738 | −0.390288 | ||||||||
\(536\) | 61.7288 | 2.66628 | ||||||||
\(537\) | −29.6769 | −1.28065 | ||||||||
\(538\) | −14.7250 | −0.634839 | ||||||||
\(539\) | 13.4057 | 0.577424 | ||||||||
\(540\) | −15.9932 | −0.688240 | ||||||||
\(541\) | 23.4834 | 1.00963 | 0.504815 | − | 0.863227i | \(-0.331561\pi\) | ||||
0.504815 | + | 0.863227i | \(0.331561\pi\) | |||||||
\(542\) | −66.0154 | −2.83560 | ||||||||
\(543\) | −2.12925 | −0.0913750 | ||||||||
\(544\) | 51.1425 | 2.19272 | ||||||||
\(545\) | −34.5080 | −1.47816 | ||||||||
\(546\) | −89.8989 | −3.84732 | ||||||||
\(547\) | −14.8864 | −0.636497 | −0.318248 | − | 0.948007i | \(-0.603095\pi\) | ||||
−0.318248 | + | 0.948007i | \(0.603095\pi\) | |||||||
\(548\) | −5.32566 | −0.227501 | ||||||||
\(549\) | 8.91624 | 0.380536 | ||||||||
\(550\) | −22.7969 | −0.972064 | ||||||||
\(551\) | 16.6090 | 0.707568 | ||||||||
\(552\) | −49.7810 | −2.11882 | ||||||||
\(553\) | −36.4337 | −1.54932 | ||||||||
\(554\) | 41.7910 | 1.77553 | ||||||||
\(555\) | 81.8766 | 3.47547 | ||||||||
\(556\) | −14.1655 | −0.600752 | ||||||||
\(557\) | −31.3251 | −1.32729 | −0.663643 | − | 0.748049i | \(-0.730991\pi\) | ||||
−0.663643 | + | 0.748049i | \(0.730991\pi\) | |||||||
\(558\) | 23.4480 | 0.992634 | ||||||||
\(559\) | −13.6501 | −0.577339 | ||||||||
\(560\) | 83.5463 | 3.53048 | ||||||||
\(561\) | −43.6757 | −1.84399 | ||||||||
\(562\) | 28.8218 | 1.21577 | ||||||||
\(563\) | 33.6511 | 1.41822 | 0.709112 | − | 0.705096i | \(-0.249096\pi\) | ||||
0.709112 | + | 0.705096i | \(0.249096\pi\) | |||||||
\(564\) | −111.672 | −4.70224 | ||||||||
\(565\) | 5.14263 | 0.216352 | ||||||||
\(566\) | −49.1929 | −2.06773 | ||||||||
\(567\) | 26.8106 | 1.12594 | ||||||||
\(568\) | −90.8151 | −3.81052 | ||||||||
\(569\) | 27.4804 | 1.15204 | 0.576019 | − | 0.817436i | \(-0.304605\pi\) | ||||
0.576019 | + | 0.817436i | \(0.304605\pi\) | |||||||
\(570\) | 39.0926 | 1.63741 | ||||||||
\(571\) | −22.4223 | −0.938346 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(572\) | −38.3890 | −1.60512 | ||||||||
\(573\) | −19.4708 | −0.813404 | ||||||||
\(574\) | −104.229 | −4.35044 | ||||||||
\(575\) | 12.0536 | 0.502672 | ||||||||
\(576\) | 4.96529 | 0.206887 | ||||||||
\(577\) | −1.83229 | −0.0762792 | −0.0381396 | − | 0.999272i | \(-0.512143\pi\) | ||||
−0.0381396 | + | 0.999272i | \(0.512143\pi\) | |||||||
\(578\) | −112.155 | −4.66504 | ||||||||
\(579\) | 35.3662 | 1.46977 | ||||||||
\(580\) | −114.019 | −4.73438 | ||||||||
\(581\) | −26.7826 | −1.11113 | ||||||||
\(582\) | 7.24096 | 0.300148 | ||||||||
\(583\) | 16.2732 | 0.673969 | ||||||||
\(584\) | 41.5061 | 1.71754 | ||||||||
\(585\) | 39.7016 | 1.64146 | ||||||||
\(586\) | 32.2346 | 1.33160 | ||||||||
\(587\) | 4.21437 | 0.173946 | 0.0869729 | − | 0.996211i | \(-0.472281\pi\) | ||||
0.0869729 | + | 0.996211i | \(0.472281\pi\) | |||||||
\(588\) | 70.5027 | 2.90748 | ||||||||
\(589\) | −5.28638 | −0.217822 | ||||||||
\(590\) | −67.2948 | −2.77048 | ||||||||
\(591\) | −50.1664 | −2.06357 | ||||||||
\(592\) | −82.3429 | −3.38427 | ||||||||
\(593\) | −35.3505 | −1.45167 | −0.725837 | − | 0.687867i | \(-0.758547\pi\) | ||||
−0.725837 | + | 0.687867i | \(0.758547\pi\) | |||||||
\(594\) | −6.58528 | −0.270198 | ||||||||
\(595\) | −84.7721 | −3.47532 | ||||||||
\(596\) | 67.3751 | 2.75979 | ||||||||
\(597\) | −3.97157 | −0.162545 | ||||||||
\(598\) | 29.1976 | 1.19398 | ||||||||
\(599\) | 2.19553 | 0.0897070 | 0.0448535 | − | 0.998994i | \(-0.485718\pi\) | ||||
0.0448535 | + | 0.998994i | \(0.485718\pi\) | |||||||
\(600\) | −67.3245 | −2.74851 | ||||||||
\(601\) | −10.8225 | −0.441460 | −0.220730 | − | 0.975335i | \(-0.570844\pi\) | ||||
−0.220730 | + | 0.975335i | \(0.570844\pi\) | |||||||
\(602\) | 33.1226 | 1.34998 | ||||||||
\(603\) | −32.5423 | −1.32523 | ||||||||
\(604\) | 25.8534 | 1.05196 | ||||||||
\(605\) | 18.4620 | 0.750588 | ||||||||
\(606\) | −108.783 | −4.41902 | ||||||||
\(607\) | 17.2143 | 0.698707 | 0.349353 | − | 0.936991i | \(-0.386401\pi\) | ||||
0.349353 | + | 0.936991i | \(0.386401\pi\) | |||||||
\(608\) | −13.1032 | −0.531404 | ||||||||
\(609\) | −76.4302 | −3.09711 | ||||||||
\(610\) | 19.8502 | 0.803712 | ||||||||
\(611\) | 36.7796 | 1.48794 | ||||||||
\(612\) | −123.009 | −4.97234 | ||||||||
\(613\) | 14.1562 | 0.571763 | 0.285881 | − | 0.958265i | \(-0.407714\pi\) | ||||
0.285881 | + | 0.958265i | \(0.407714\pi\) | |||||||
\(614\) | 75.9309 | 3.06432 | ||||||||
\(615\) | 85.9533 | 3.46597 | ||||||||
\(616\) | 52.3088 | 2.10758 | ||||||||
\(617\) | −11.9955 | −0.482922 | −0.241461 | − | 0.970410i | \(-0.577627\pi\) | ||||
−0.241461 | + | 0.970410i | \(0.577627\pi\) | |||||||
\(618\) | 104.507 | 4.20389 | ||||||||
\(619\) | 8.40040 | 0.337641 | 0.168820 | − | 0.985647i | \(-0.446004\pi\) | ||||
0.168820 | + | 0.985647i | \(0.446004\pi\) | |||||||
\(620\) | 36.2904 | 1.45746 | ||||||||
\(621\) | 3.48190 | 0.139724 | ||||||||
\(622\) | −19.7748 | −0.792898 | ||||||||
\(623\) | 50.5132 | 2.02377 | ||||||||
\(624\) | −74.5579 | −2.98470 | ||||||||
\(625\) | −28.8861 | −1.15544 | ||||||||
\(626\) | −32.4938 | −1.29871 | ||||||||
\(627\) | 11.1901 | 0.446890 | ||||||||
\(628\) | −40.0709 | −1.59900 | ||||||||
\(629\) | 83.5510 | 3.33140 | ||||||||
\(630\) | −96.3375 | −3.83818 | ||||||||
\(631\) | 9.95363 | 0.396248 | 0.198124 | − | 0.980177i | \(-0.436515\pi\) | ||||
0.198124 | + | 0.980177i | \(0.436515\pi\) | |||||||
\(632\) | −66.0922 | −2.62901 | ||||||||
\(633\) | −1.16787 | −0.0464185 | ||||||||
\(634\) | −39.8015 | −1.58072 | ||||||||
\(635\) | 45.4581 | 1.80395 | ||||||||
\(636\) | 85.5836 | 3.39361 | ||||||||
\(637\) | −23.2204 | −0.920025 | ||||||||
\(638\) | −46.9478 | −1.85868 | ||||||||
\(639\) | 47.8761 | 1.89395 | ||||||||
\(640\) | −28.3861 | −1.12206 | ||||||||
\(641\) | 16.5800 | 0.654869 | 0.327435 | − | 0.944874i | \(-0.393816\pi\) | ||||
0.327435 | + | 0.944874i | \(0.393816\pi\) | |||||||
\(642\) | −19.5486 | −0.771522 | ||||||||
\(643\) | −23.2968 | −0.918736 | −0.459368 | − | 0.888246i | \(-0.651924\pi\) | ||||
−0.459368 | + | 0.888246i | \(0.651924\pi\) | |||||||
\(644\) | −49.2535 | −1.94086 | ||||||||
\(645\) | −27.3148 | −1.07552 | ||||||||
\(646\) | 39.8921 | 1.56953 | ||||||||
\(647\) | −21.2826 | −0.836706 | −0.418353 | − | 0.908285i | \(-0.637392\pi\) | ||||
−0.418353 | + | 0.908285i | \(0.637392\pi\) | |||||||
\(648\) | 48.6355 | 1.91058 | ||||||||
\(649\) | −19.2629 | −0.756135 | ||||||||
\(650\) | 39.4872 | 1.54881 | ||||||||
\(651\) | 24.3265 | 0.953430 | ||||||||
\(652\) | 42.7959 | 1.67602 | ||||||||
\(653\) | −27.4555 | −1.07442 | −0.537209 | − | 0.843449i | \(-0.680521\pi\) | ||||
−0.537209 | + | 0.843449i | \(0.680521\pi\) | |||||||
\(654\) | −74.7263 | −2.92203 | ||||||||
\(655\) | 66.7637 | 2.60867 | ||||||||
\(656\) | −86.4428 | −3.37503 | ||||||||
\(657\) | −21.8813 | −0.853670 | ||||||||
\(658\) | −89.2474 | −3.47922 | ||||||||
\(659\) | −19.1374 | −0.745486 | −0.372743 | − | 0.927935i | \(-0.621583\pi\) | ||||
−0.372743 | + | 0.927935i | \(0.621583\pi\) | |||||||
\(660\) | −76.8188 | −2.99017 | ||||||||
\(661\) | −22.3987 | −0.871209 | −0.435604 | − | 0.900138i | \(-0.643465\pi\) | ||||
−0.435604 | + | 0.900138i | \(0.643465\pi\) | |||||||
\(662\) | −0.968450 | −0.0376399 | ||||||||
\(663\) | 75.6518 | 2.93807 | ||||||||
\(664\) | −48.5847 | −1.88545 | ||||||||
\(665\) | 21.7194 | 0.842243 | ||||||||
\(666\) | 94.9498 | 3.67923 | ||||||||
\(667\) | 24.8232 | 0.961157 | ||||||||
\(668\) | 81.6038 | 3.15735 | ||||||||
\(669\) | 53.7666 | 2.07874 | ||||||||
\(670\) | −72.4489 | −2.79895 | ||||||||
\(671\) | 5.68205 | 0.219353 | ||||||||
\(672\) | 60.2973 | 2.32602 | ||||||||
\(673\) | 28.5580 | 1.10083 | 0.550414 | − | 0.834892i | \(-0.314470\pi\) | ||||
0.550414 | + | 0.834892i | \(0.314470\pi\) | |||||||
\(674\) | −26.7917 | −1.03198 | ||||||||
\(675\) | 4.70897 | 0.181248 | ||||||||
\(676\) | 7.19618 | 0.276776 | ||||||||
\(677\) | −49.3503 | −1.89669 | −0.948343 | − | 0.317248i | \(-0.897241\pi\) | ||||
−0.948343 | + | 0.317248i | \(0.897241\pi\) | |||||||
\(678\) | 11.1363 | 0.427686 | ||||||||
\(679\) | 4.02300 | 0.154389 | ||||||||
\(680\) | −153.780 | −5.89720 | ||||||||
\(681\) | 40.6585 | 1.55804 | ||||||||
\(682\) | 14.9427 | 0.572186 | ||||||||
\(683\) | −15.6337 | −0.598205 | −0.299103 | − | 0.954221i | \(-0.596687\pi\) | ||||
−0.299103 | + | 0.954221i | \(0.596687\pi\) | |||||||
\(684\) | 31.5160 | 1.20504 | ||||||||
\(685\) | 3.50992 | 0.134107 | ||||||||
\(686\) | −8.50764 | −0.324823 | ||||||||
\(687\) | −69.8195 | −2.66378 | ||||||||
\(688\) | 27.4703 | 1.04730 | ||||||||
\(689\) | −28.1873 | −1.07385 | ||||||||
\(690\) | 58.4262 | 2.22425 | ||||||||
\(691\) | −26.3036 | −1.00064 | −0.500318 | − | 0.865842i | \(-0.666783\pi\) | ||||
−0.500318 | + | 0.865842i | \(0.666783\pi\) | |||||||
\(692\) | 80.2113 | 3.04918 | ||||||||
\(693\) | −27.5763 | −1.04754 | ||||||||
\(694\) | −60.7823 | −2.30726 | ||||||||
\(695\) | 9.33591 | 0.354131 | ||||||||
\(696\) | −138.648 | −5.25542 | ||||||||
\(697\) | 87.7111 | 3.32230 | ||||||||
\(698\) | 25.4374 | 0.962818 | ||||||||
\(699\) | 2.42591 | 0.0917563 | ||||||||
\(700\) | −66.6110 | −2.51766 | ||||||||
\(701\) | −2.53467 | −0.0957332 | −0.0478666 | − | 0.998854i | \(-0.515242\pi\) | ||||
−0.0478666 | + | 0.998854i | \(0.515242\pi\) | |||||||
\(702\) | 11.4066 | 0.430513 | ||||||||
\(703\) | −21.4066 | −0.807364 | ||||||||
\(704\) | 3.16423 | 0.119256 | ||||||||
\(705\) | 73.5984 | 2.77188 | ||||||||
\(706\) | −28.1976 | −1.06123 | ||||||||
\(707\) | −60.4389 | −2.27304 | ||||||||
\(708\) | −101.307 | −3.80734 | ||||||||
\(709\) | −17.9266 | −0.673246 | −0.336623 | − | 0.941639i | \(-0.609285\pi\) | ||||
−0.336623 | + | 0.941639i | \(0.609285\pi\) | |||||||
\(710\) | 106.586 | 4.00012 | ||||||||
\(711\) | 34.8426 | 1.30670 | ||||||||
\(712\) | 91.6331 | 3.43409 | ||||||||
\(713\) | −7.90081 | −0.295888 | ||||||||
\(714\) | −183.572 | −6.87002 | ||||||||
\(715\) | 25.3006 | 0.946190 | ||||||||
\(716\) | −53.2647 | −1.99059 | ||||||||
\(717\) | 28.6758 | 1.07092 | ||||||||
\(718\) | −65.8482 | −2.45743 | ||||||||
\(719\) | 42.6941 | 1.59222 | 0.796110 | − | 0.605152i | \(-0.206888\pi\) | ||||
0.796110 | + | 0.605152i | \(0.206888\pi\) | |||||||
\(720\) | −79.8978 | −2.97762 | ||||||||
\(721\) | 58.0630 | 2.16238 | ||||||||
\(722\) | 38.4483 | 1.43090 | ||||||||
\(723\) | −46.9277 | −1.74526 | ||||||||
\(724\) | −3.82162 | −0.142029 | ||||||||
\(725\) | 33.5712 | 1.24680 | ||||||||
\(726\) | 39.9792 | 1.48377 | ||||||||
\(727\) | 37.8904 | 1.40528 | 0.702639 | − | 0.711546i | \(-0.252005\pi\) | ||||
0.702639 | + | 0.711546i | \(0.252005\pi\) | |||||||
\(728\) | −90.6056 | −3.35807 | ||||||||
\(729\) | −34.5320 | −1.27896 | ||||||||
\(730\) | −48.7143 | −1.80300 | ||||||||
\(731\) | −27.8734 | −1.03093 | ||||||||
\(732\) | 29.8828 | 1.10450 | ||||||||
\(733\) | −3.71487 | −0.137212 | −0.0686059 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686059 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(734\) | −39.4731 | −1.45698 | ||||||||
\(735\) | −46.4655 | −1.71390 | ||||||||
\(736\) | −19.5835 | −0.721857 | ||||||||
\(737\) | −20.7382 | −0.763903 | ||||||||
\(738\) | 99.6775 | 3.66918 | ||||||||
\(739\) | 3.91332 | 0.143954 | 0.0719769 | − | 0.997406i | \(-0.477069\pi\) | ||||
0.0719769 | + | 0.997406i | \(0.477069\pi\) | |||||||
\(740\) | 146.953 | 5.40212 | ||||||||
\(741\) | −19.3827 | −0.712041 | ||||||||
\(742\) | 68.3978 | 2.51096 | ||||||||
\(743\) | 7.39114 | 0.271155 | 0.135577 | − | 0.990767i | \(-0.456711\pi\) | ||||
0.135577 | + | 0.990767i | \(0.456711\pi\) | |||||||
\(744\) | 44.1292 | 1.61786 | ||||||||
\(745\) | −44.4042 | −1.62684 | ||||||||
\(746\) | 3.84680 | 0.140841 | ||||||||
\(747\) | 25.6130 | 0.937131 | ||||||||
\(748\) | −78.3898 | −2.86622 | ||||||||
\(749\) | −10.8610 | −0.396852 | ||||||||
\(750\) | −18.8364 | −0.687809 | ||||||||
\(751\) | −12.5849 | −0.459230 | −0.229615 | − | 0.973282i | \(-0.573747\pi\) | ||||
−0.229615 | + | 0.973282i | \(0.573747\pi\) | |||||||
\(752\) | −74.0176 | −2.69914 | ||||||||
\(753\) | 69.5382 | 2.53411 | ||||||||
\(754\) | 81.3196 | 2.96148 | ||||||||
\(755\) | −17.0389 | −0.620111 | ||||||||
\(756\) | −19.2417 | −0.699816 | ||||||||
\(757\) | −15.5271 | −0.564343 | −0.282172 | − | 0.959364i | \(-0.591055\pi\) | ||||
−0.282172 | + | 0.959364i | \(0.591055\pi\) | |||||||
\(758\) | −37.4614 | −1.36066 | ||||||||
\(759\) | 16.7243 | 0.607053 | ||||||||
\(760\) | 39.3999 | 1.42918 | ||||||||
\(761\) | 0.107011 | 0.00387916 | 0.00193958 | − | 0.999998i | \(-0.499383\pi\) | ||||
0.00193958 | + | 0.999998i | \(0.499383\pi\) | |||||||
\(762\) | 98.4386 | 3.56605 | ||||||||
\(763\) | −41.5171 | −1.50302 | ||||||||
\(764\) | −34.9465 | −1.26432 | ||||||||
\(765\) | 81.0701 | 2.93110 | ||||||||
\(766\) | 10.5734 | 0.382033 | ||||||||
\(767\) | 33.3658 | 1.20477 | ||||||||
\(768\) | −68.7660 | −2.48138 | ||||||||
\(769\) | −17.8476 | −0.643600 | −0.321800 | − | 0.946808i | \(-0.604288\pi\) | ||||
−0.321800 | + | 0.946808i | \(0.604288\pi\) | |||||||
\(770\) | −61.3930 | −2.21245 | ||||||||
\(771\) | 57.2322 | 2.06117 | ||||||||
\(772\) | 63.4759 | 2.28455 | ||||||||
\(773\) | 6.08433 | 0.218838 | 0.109419 | − | 0.993996i | \(-0.465101\pi\) | ||||
0.109419 | + | 0.993996i | \(0.465101\pi\) | |||||||
\(774\) | −31.6761 | −1.13857 | ||||||||
\(775\) | −10.6852 | −0.383822 | ||||||||
\(776\) | 7.29789 | 0.261979 | ||||||||
\(777\) | 98.5071 | 3.53392 | ||||||||
\(778\) | 57.2916 | 2.05400 | ||||||||
\(779\) | −22.4724 | −0.805158 | ||||||||
\(780\) | 133.060 | 4.76431 | ||||||||
\(781\) | 30.5100 | 1.09173 | ||||||||
\(782\) | 59.6210 | 2.13204 | ||||||||
\(783\) | 9.69762 | 0.346565 | ||||||||
\(784\) | 46.7301 | 1.66893 | ||||||||
\(785\) | 26.4091 | 0.942581 | ||||||||
\(786\) | 144.575 | 5.15684 | ||||||||
\(787\) | 31.0249 | 1.10592 | 0.552959 | − | 0.833208i | \(-0.313498\pi\) | ||||
0.552959 | + | 0.833208i | \(0.313498\pi\) | |||||||
\(788\) | −90.0396 | −3.20753 | ||||||||
\(789\) | 3.48259 | 0.123983 | ||||||||
\(790\) | 77.5701 | 2.75982 | ||||||||
\(791\) | 6.18719 | 0.219991 | ||||||||
\(792\) | −50.0245 | −1.77754 | ||||||||
\(793\) | −9.84204 | −0.349501 | ||||||||
\(794\) | −16.4221 | −0.582798 | ||||||||
\(795\) | −56.4046 | −2.00047 | ||||||||
\(796\) | −7.12823 | −0.252654 | ||||||||
\(797\) | −20.5158 | −0.726706 | −0.363353 | − | 0.931652i | \(-0.618368\pi\) | ||||
−0.363353 | + | 0.931652i | \(0.618368\pi\) | |||||||
\(798\) | 47.0330 | 1.66495 | ||||||||
\(799\) | 75.1036 | 2.65697 | ||||||||
\(800\) | −26.4850 | −0.936385 | ||||||||
\(801\) | −48.3073 | −1.70685 | ||||||||
\(802\) | −4.95156 | −0.174846 | ||||||||
\(803\) | −13.9443 | −0.492083 | ||||||||
\(804\) | −109.066 | −3.84645 | ||||||||
\(805\) | 32.4609 | 1.14410 | ||||||||
\(806\) | −25.8827 | −0.911679 | ||||||||
\(807\) | 14.6095 | 0.514279 | ||||||||
\(808\) | −109.639 | −3.85707 | ||||||||
\(809\) | 39.3255 | 1.38261 | 0.691305 | − | 0.722563i | \(-0.257036\pi\) | ||||
0.691305 | + | 0.722563i | \(0.257036\pi\) | |||||||
\(810\) | −57.0817 | −2.00565 | ||||||||
\(811\) | 28.9904 | 1.01799 | 0.508995 | − | 0.860769i | \(-0.330017\pi\) | ||||
0.508995 | + | 0.860769i | \(0.330017\pi\) | |||||||
\(812\) | −137.178 | −4.81401 | ||||||||
\(813\) | 65.4977 | 2.29710 | ||||||||
\(814\) | 60.5087 | 2.12083 | ||||||||
\(815\) | −28.2050 | −0.987979 | ||||||||
\(816\) | −152.246 | −5.32969 | ||||||||
\(817\) | 7.14142 | 0.249847 | ||||||||
\(818\) | −8.39378 | −0.293482 | ||||||||
\(819\) | 47.7656 | 1.66907 | ||||||||
\(820\) | 154.270 | 5.38736 | ||||||||
\(821\) | 12.3105 | 0.429639 | 0.214819 | − | 0.976654i | \(-0.431084\pi\) | ||||
0.214819 | + | 0.976654i | \(0.431084\pi\) | |||||||
\(822\) | 7.60067 | 0.265104 | ||||||||
\(823\) | −6.01238 | −0.209578 | −0.104789 | − | 0.994494i | \(-0.533417\pi\) | ||||
−0.104789 | + | 0.994494i | \(0.533417\pi\) | |||||||
\(824\) | 105.329 | 3.66930 | ||||||||
\(825\) | 22.6181 | 0.787463 | ||||||||
\(826\) | −80.9635 | −2.81708 | ||||||||
\(827\) | −38.1609 | −1.32699 | −0.663493 | − | 0.748183i | \(-0.730927\pi\) | ||||
−0.663493 | + | 0.748183i | \(0.730927\pi\) | |||||||
\(828\) | 47.1025 | 1.63693 | ||||||||
\(829\) | −6.76980 | −0.235125 | −0.117562 | − | 0.993066i | \(-0.537508\pi\) | ||||
−0.117562 | + | 0.993066i | \(0.537508\pi\) | |||||||
\(830\) | 57.0222 | 1.97927 | ||||||||
\(831\) | −41.4633 | −1.43834 | ||||||||
\(832\) | −5.48085 | −0.190014 | ||||||||
\(833\) | −47.4157 | −1.64286 | ||||||||
\(834\) | 20.2167 | 0.700048 | ||||||||
\(835\) | −53.7817 | −1.86119 | ||||||||
\(836\) | 20.0842 | 0.694627 | ||||||||
\(837\) | −3.08659 | −0.106688 | ||||||||
\(838\) | −88.9764 | −3.07364 | ||||||||
\(839\) | −36.7102 | −1.26738 | −0.633688 | − | 0.773589i | \(-0.718460\pi\) | ||||
−0.633688 | + | 0.773589i | \(0.718460\pi\) | |||||||
\(840\) | −181.308 | −6.25571 | ||||||||
\(841\) | 40.1363 | 1.38401 | ||||||||
\(842\) | 76.2287 | 2.62702 | ||||||||
\(843\) | −28.5958 | −0.984891 | ||||||||
\(844\) | −2.09611 | −0.0721509 | ||||||||
\(845\) | −4.74271 | −0.163154 | ||||||||
\(846\) | 85.3499 | 2.93439 | ||||||||
\(847\) | 22.2120 | 0.763213 | ||||||||
\(848\) | 56.7259 | 1.94797 | ||||||||
\(849\) | 48.8071 | 1.67506 | ||||||||
\(850\) | 80.6323 | 2.76567 | ||||||||
\(851\) | −31.9934 | −1.09672 | ||||||||
\(852\) | 160.457 | 5.49716 | ||||||||
\(853\) | −0.511245 | −0.0175047 | −0.00875235 | − | 0.999962i | \(-0.502786\pi\) | ||||
−0.00875235 | + | 0.999962i | \(0.502786\pi\) | |||||||
\(854\) | 23.8821 | 0.817230 | ||||||||
\(855\) | −20.7709 | −0.710350 | ||||||||
\(856\) | −19.7023 | −0.673411 | ||||||||
\(857\) | 30.0453 | 1.02633 | 0.513164 | − | 0.858291i | \(-0.328473\pi\) | ||||
0.513164 | + | 0.858291i | \(0.328473\pi\) | |||||||
\(858\) | 54.7880 | 1.87043 | ||||||||
\(859\) | 23.6291 | 0.806215 | 0.403107 | − | 0.915153i | \(-0.367930\pi\) | ||||
0.403107 | + | 0.915153i | \(0.367930\pi\) | |||||||
\(860\) | −49.0250 | −1.67174 | ||||||||
\(861\) | 103.412 | 3.52427 | ||||||||
\(862\) | −66.6520 | −2.27018 | ||||||||
\(863\) | −48.2324 | −1.64185 | −0.820925 | − | 0.571036i | \(-0.806542\pi\) | ||||
−0.820925 | + | 0.571036i | \(0.806542\pi\) | |||||||
\(864\) | −7.65064 | −0.260280 | ||||||||
\(865\) | −52.8640 | −1.79743 | ||||||||
\(866\) | 50.3723 | 1.71172 | ||||||||
\(867\) | 111.276 | 3.77912 | ||||||||
\(868\) | 43.6616 | 1.48197 | ||||||||
\(869\) | 22.2042 | 0.753224 | ||||||||
\(870\) | 162.726 | 5.51692 | ||||||||
\(871\) | 35.9213 | 1.21715 | ||||||||
\(872\) | −75.3138 | −2.55045 | ||||||||
\(873\) | −3.84731 | −0.130212 | ||||||||
\(874\) | −15.2755 | −0.516700 | ||||||||
\(875\) | −10.4653 | −0.353792 | ||||||||
\(876\) | −73.3352 | −2.47777 | ||||||||
\(877\) | 55.2702 | 1.86634 | 0.933171 | − | 0.359433i | \(-0.117030\pi\) | ||||
0.933171 | + | 0.359433i | \(0.117030\pi\) | |||||||
\(878\) | −73.0303 | −2.46465 | ||||||||
\(879\) | −31.9818 | −1.07872 | ||||||||
\(880\) | −50.9165 | −1.71639 | ||||||||
\(881\) | −42.1938 | −1.42154 | −0.710772 | − | 0.703422i | \(-0.751654\pi\) | ||||
−0.710772 | + | 0.703422i | \(0.751654\pi\) | |||||||
\(882\) | −53.8846 | −1.81439 | ||||||||
\(883\) | 44.5562 | 1.49944 | 0.749718 | − | 0.661758i | \(-0.230189\pi\) | ||||
0.749718 | + | 0.661758i | \(0.230189\pi\) | |||||||
\(884\) | 135.781 | 4.56682 | ||||||||
\(885\) | 66.7671 | 2.24435 | ||||||||
\(886\) | 1.35553 | 0.0455398 | ||||||||
\(887\) | 41.9321 | 1.40794 | 0.703971 | − | 0.710229i | \(-0.251408\pi\) | ||||
0.703971 | + | 0.710229i | \(0.251408\pi\) | |||||||
\(888\) | 178.696 | 5.99664 | ||||||||
\(889\) | 54.6914 | 1.83429 | ||||||||
\(890\) | −107.546 | −3.60497 | ||||||||
\(891\) | −16.3394 | −0.547392 | ||||||||
\(892\) | 96.5013 | 3.23110 | ||||||||
\(893\) | −19.2422 | −0.643917 | ||||||||
\(894\) | −96.1564 | −3.21595 | ||||||||
\(895\) | 35.1046 | 1.17342 | ||||||||
\(896\) | −34.1518 | −1.14093 | ||||||||
\(897\) | −28.9686 | −0.967233 | ||||||||
\(898\) | −52.2434 | −1.74339 | ||||||||
\(899\) | −22.0049 | −0.733906 | ||||||||
\(900\) | 63.7021 | 2.12340 | ||||||||
\(901\) | −57.5582 | −1.91754 | ||||||||
\(902\) | 63.5215 | 2.11503 | ||||||||
\(903\) | −32.8629 | −1.09361 | ||||||||
\(904\) | 11.2238 | 0.373298 | ||||||||
\(905\) | 2.51867 | 0.0837236 | ||||||||
\(906\) | −36.8975 | −1.22584 | ||||||||
\(907\) | 32.7075 | 1.08604 | 0.543018 | − | 0.839721i | \(-0.317282\pi\) | ||||
0.543018 | + | 0.839721i | \(0.317282\pi\) | |||||||
\(908\) | 72.9746 | 2.42175 | ||||||||
\(909\) | 57.7995 | 1.91709 | ||||||||
\(910\) | 106.341 | 3.52516 | ||||||||
\(911\) | −42.1150 | −1.39533 | −0.697666 | − | 0.716423i | \(-0.745778\pi\) | ||||
−0.697666 | + | 0.716423i | \(0.745778\pi\) | |||||||
\(912\) | 39.0069 | 1.29165 | ||||||||
\(913\) | 16.3224 | 0.540192 | ||||||||
\(914\) | −4.83150 | −0.159812 | ||||||||
\(915\) | −19.6946 | −0.651082 | ||||||||
\(916\) | −125.313 | −4.14046 | ||||||||
\(917\) | 80.3245 | 2.65255 | ||||||||
\(918\) | 23.2920 | 0.768752 | ||||||||
\(919\) | −47.3855 | −1.56310 | −0.781552 | − | 0.623840i | \(-0.785572\pi\) | ||||
−0.781552 | + | 0.623840i | \(0.785572\pi\) | |||||||
\(920\) | 58.8855 | 1.94140 | ||||||||
\(921\) | −75.3354 | −2.48239 | ||||||||
\(922\) | −44.1012 | −1.45239 | ||||||||
\(923\) | −52.8472 | −1.73949 | ||||||||
\(924\) | −92.4220 | −3.04046 | ||||||||
\(925\) | −43.2683 | −1.42265 | ||||||||
\(926\) | −36.8629 | −1.21139 | ||||||||
\(927\) | −55.5273 | −1.82376 | ||||||||
\(928\) | −54.5429 | −1.79046 | ||||||||
\(929\) | −53.5664 | −1.75746 | −0.878728 | − | 0.477323i | \(-0.841607\pi\) | ||||
−0.878728 | + | 0.477323i | \(0.841607\pi\) | |||||||
\(930\) | −51.7929 | −1.69836 | ||||||||
\(931\) | 12.1484 | 0.398146 | ||||||||
\(932\) | 4.35406 | 0.142622 | ||||||||
\(933\) | 19.6197 | 0.642322 | ||||||||
\(934\) | −6.89090 | −0.225477 | ||||||||
\(935\) | 51.6635 | 1.68958 | ||||||||
\(936\) | 86.6488 | 2.83221 | ||||||||
\(937\) | −37.0292 | −1.20969 | −0.604845 | − | 0.796343i | \(-0.706765\pi\) | ||||
−0.604845 | + | 0.796343i | \(0.706765\pi\) | |||||||
\(938\) | −87.1645 | −2.84602 | ||||||||
\(939\) | 32.2390 | 1.05208 | ||||||||
\(940\) | 132.096 | 4.30849 | ||||||||
\(941\) | 42.6671 | 1.39091 | 0.695454 | − | 0.718570i | \(-0.255203\pi\) | ||||
0.695454 | + | 0.718570i | \(0.255203\pi\) | |||||||
\(942\) | 57.1884 | 1.86330 | ||||||||
\(943\) | −33.5863 | −1.09372 | ||||||||
\(944\) | −67.1473 | −2.18546 | ||||||||
\(945\) | 12.6815 | 0.412528 | ||||||||
\(946\) | −20.1862 | −0.656312 | ||||||||
\(947\) | 29.0710 | 0.944682 | 0.472341 | − | 0.881416i | \(-0.343409\pi\) | ||||
0.472341 | + | 0.881416i | \(0.343409\pi\) | |||||||
\(948\) | 116.775 | 3.79268 | ||||||||
\(949\) | 24.1533 | 0.784049 | ||||||||
\(950\) | −20.6588 | −0.670258 | ||||||||
\(951\) | 39.4894 | 1.28053 | ||||||||
\(952\) | −185.015 | −5.99639 | ||||||||
\(953\) | −6.08784 | −0.197205 | −0.0986023 | − | 0.995127i | \(-0.531437\pi\) | ||||
−0.0986023 | + | 0.995127i | \(0.531437\pi\) | |||||||
\(954\) | −65.4108 | −2.11775 | ||||||||
\(955\) | 23.0318 | 0.745292 | ||||||||
\(956\) | 51.4678 | 1.66459 | ||||||||
\(957\) | 46.5796 | 1.50571 | ||||||||
\(958\) | −48.7937 | −1.57645 | ||||||||
\(959\) | 4.22285 | 0.136363 | ||||||||
\(960\) | −10.9675 | −0.353976 | ||||||||
\(961\) | −23.9962 | −0.774071 | ||||||||
\(962\) | −104.809 | −3.37917 | ||||||||
\(963\) | 10.3867 | 0.334706 | ||||||||
\(964\) | −84.2267 | −2.71276 | ||||||||
\(965\) | −41.8344 | −1.34670 | ||||||||
\(966\) | 70.2935 | 2.26166 | ||||||||
\(967\) | −5.63642 | −0.181255 | −0.0906275 | − | 0.995885i | \(-0.528887\pi\) | ||||
−0.0906275 | + | 0.995885i | \(0.528887\pi\) | |||||||
\(968\) | 40.2934 | 1.29508 | ||||||||
\(969\) | −39.5792 | −1.27147 | ||||||||
\(970\) | −8.56527 | −0.275014 | ||||||||
\(971\) | −22.2430 | −0.713812 | −0.356906 | − | 0.934140i | \(-0.616168\pi\) | ||||
−0.356906 | + | 0.934140i | \(0.616168\pi\) | |||||||
\(972\) | −101.892 | −3.26818 | ||||||||
\(973\) | 11.2322 | 0.360088 | ||||||||
\(974\) | 93.4099 | 2.99305 | ||||||||
\(975\) | −39.1775 | −1.25468 | ||||||||
\(976\) | 19.8067 | 0.633997 | ||||||||
\(977\) | 22.6529 | 0.724731 | 0.362365 | − | 0.932036i | \(-0.381969\pi\) | ||||
0.362365 | + | 0.932036i | \(0.381969\pi\) | |||||||
\(978\) | −61.0774 | −1.95304 | ||||||||
\(979\) | −30.7848 | −0.983886 | ||||||||
\(980\) | −83.3970 | −2.66402 | ||||||||
\(981\) | 39.7041 | 1.26765 | ||||||||
\(982\) | 58.3326 | 1.86147 | ||||||||
\(983\) | 34.2767 | 1.09326 | 0.546628 | − | 0.837375i | \(-0.315911\pi\) | ||||
0.546628 | + | 0.837375i | \(0.315911\pi\) | |||||||
\(984\) | 187.593 | 5.98026 | ||||||||
\(985\) | 59.3414 | 1.89078 | ||||||||
\(986\) | 166.054 | 5.28822 | ||||||||
\(987\) | 88.5475 | 2.81850 | ||||||||
\(988\) | −34.7884 | −1.10677 | ||||||||
\(989\) | 10.6733 | 0.339390 | ||||||||
\(990\) | 58.7120 | 1.86599 | ||||||||
\(991\) | 11.7312 | 0.372655 | 0.186327 | − | 0.982488i | \(-0.440341\pi\) | ||||
0.186327 | + | 0.982488i | \(0.440341\pi\) | |||||||
\(992\) | 17.3601 | 0.551185 | ||||||||
\(993\) | 0.960855 | 0.0304918 | ||||||||
\(994\) | 128.236 | 4.06740 | ||||||||
\(995\) | 4.69793 | 0.148934 | ||||||||
\(996\) | 85.8421 | 2.72001 | ||||||||
\(997\) | −9.43404 | −0.298779 | −0.149389 | − | 0.988778i | \(-0.547731\pi\) | ||||
−0.149389 | + | 0.988778i | \(0.547731\pi\) | |||||||
\(998\) | −60.5335 | −1.91616 | ||||||||
\(999\) | −12.4988 | −0.395444 |
(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 | 8011.2.a.b.1.19 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.19 | ✓ | 358 | 1.1 | even | 1 | trivial |