Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32242 | −1.64220 | −0.821101 | − | 0.570783i | \(-0.806640\pi\) | ||||
−0.821101 | + | 0.570783i | \(0.806640\pi\) | |||||||
\(3\) | 2.86947 | 1.65669 | 0.828345 | − | 0.560218i | \(-0.189283\pi\) | ||||
0.828345 | + | 0.560218i | \(0.189283\pi\) | |||||||
\(4\) | 3.39365 | 1.69683 | ||||||||
\(5\) | 0.571930 | 0.255775 | 0.127888 | − | 0.991789i | \(-0.459180\pi\) | ||||
0.127888 | + | 0.991789i | \(0.459180\pi\) | |||||||
\(6\) | −6.66413 | −2.72062 | ||||||||
\(7\) | −0.979167 | −0.370090 | −0.185045 | − | 0.982730i | \(-0.559243\pi\) | ||||
−0.185045 | + | 0.982730i | \(0.559243\pi\) | |||||||
\(8\) | −3.23665 | −1.14433 | ||||||||
\(9\) | 5.23387 | 1.74462 | ||||||||
\(10\) | −1.32826 | −0.420034 | ||||||||
\(11\) | 2.35621 | 0.710424 | 0.355212 | − | 0.934786i | \(-0.384409\pi\) | ||||
0.355212 | + | 0.934786i | \(0.384409\pi\) | |||||||
\(12\) | 9.73799 | 2.81111 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.27404 | 0.607763 | ||||||||
\(15\) | 1.64114 | 0.423740 | ||||||||
\(16\) | 0.729563 | 0.182391 | ||||||||
\(17\) | −4.66455 | −1.13132 | −0.565660 | − | 0.824639i | \(-0.691378\pi\) | ||||
−0.565660 | + | 0.824639i | \(0.691378\pi\) | |||||||
\(18\) | −12.1553 | −2.86502 | ||||||||
\(19\) | −4.95588 | −1.13696 | −0.568479 | − | 0.822698i | \(-0.692468\pi\) | ||||
−0.568479 | + | 0.822698i | \(0.692468\pi\) | |||||||
\(20\) | 1.94093 | 0.434006 | ||||||||
\(21\) | −2.80969 | −0.613125 | ||||||||
\(22\) | −5.47212 | −1.16666 | ||||||||
\(23\) | −3.34642 | −0.697778 | −0.348889 | − | 0.937164i | \(-0.613441\pi\) | ||||
−0.348889 | + | 0.937164i | \(0.613441\pi\) | |||||||
\(24\) | −9.28747 | −1.89580 | ||||||||
\(25\) | −4.67290 | −0.934579 | ||||||||
\(26\) | −2.32242 | −0.455465 | ||||||||
\(27\) | 6.41003 | 1.23361 | ||||||||
\(28\) | −3.32295 | −0.627978 | ||||||||
\(29\) | −3.01230 | −0.559371 | −0.279685 | − | 0.960092i | \(-0.590230\pi\) | ||||
−0.279685 | + | 0.960092i | \(0.590230\pi\) | |||||||
\(30\) | −3.81142 | −0.695867 | ||||||||
\(31\) | −3.57054 | −0.641288 | −0.320644 | − | 0.947200i | \(-0.603899\pi\) | ||||
−0.320644 | + | 0.947200i | \(0.603899\pi\) | |||||||
\(32\) | 4.77894 | 0.844805 | ||||||||
\(33\) | 6.76108 | 1.17695 | ||||||||
\(34\) | 10.8331 | 1.85785 | ||||||||
\(35\) | −0.560015 | −0.0946598 | ||||||||
\(36\) | 17.7619 | 2.96032 | ||||||||
\(37\) | 7.40235 | 1.21694 | 0.608470 | − | 0.793577i | \(-0.291784\pi\) | ||||
0.608470 | + | 0.793577i | \(0.291784\pi\) | |||||||
\(38\) | 11.5097 | 1.86711 | ||||||||
\(39\) | 2.86947 | 0.459483 | ||||||||
\(40\) | −1.85114 | −0.292690 | ||||||||
\(41\) | 10.6844 | 1.66862 | 0.834308 | − | 0.551299i | \(-0.185868\pi\) | ||||
0.834308 | + | 0.551299i | \(0.185868\pi\) | |||||||
\(42\) | 6.52529 | 1.00687 | ||||||||
\(43\) | −4.49197 | −0.685019 | −0.342510 | − | 0.939514i | \(-0.611277\pi\) | ||||
−0.342510 | + | 0.939514i | \(0.611277\pi\) | |||||||
\(44\) | 7.99615 | 1.20547 | ||||||||
\(45\) | 2.99341 | 0.446231 | ||||||||
\(46\) | 7.77181 | 1.14589 | ||||||||
\(47\) | −8.78651 | −1.28164 | −0.640822 | − | 0.767690i | \(-0.721406\pi\) | ||||
−0.640822 | + | 0.767690i | \(0.721406\pi\) | |||||||
\(48\) | 2.09346 | 0.302165 | ||||||||
\(49\) | −6.04123 | −0.863033 | ||||||||
\(50\) | 10.8524 | 1.53477 | ||||||||
\(51\) | −13.3848 | −1.87425 | ||||||||
\(52\) | 3.39365 | 0.470615 | ||||||||
\(53\) | −0.840938 | −0.115512 | −0.0577558 | − | 0.998331i | \(-0.518394\pi\) | ||||
−0.0577558 | + | 0.998331i | \(0.518394\pi\) | |||||||
\(54\) | −14.8868 | −2.02584 | ||||||||
\(55\) | 1.34759 | 0.181709 | ||||||||
\(56\) | 3.16922 | 0.423504 | ||||||||
\(57\) | −14.2208 | −1.88359 | ||||||||
\(58\) | 6.99584 | 0.918599 | ||||||||
\(59\) | −12.4051 | −1.61501 | −0.807503 | − | 0.589863i | \(-0.799182\pi\) | ||||
−0.807503 | + | 0.589863i | \(0.799182\pi\) | |||||||
\(60\) | 5.56945 | 0.719013 | ||||||||
\(61\) | −3.72827 | −0.477356 | −0.238678 | − | 0.971099i | \(-0.576714\pi\) | ||||
−0.238678 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(62\) | 8.29230 | 1.05312 | ||||||||
\(63\) | −5.12483 | −0.645668 | ||||||||
\(64\) | −12.5578 | −1.56973 | ||||||||
\(65\) | 0.571930 | 0.0709392 | ||||||||
\(66\) | −15.7021 | −1.93279 | ||||||||
\(67\) | 0.970763 | 0.118598 | 0.0592988 | − | 0.998240i | \(-0.481114\pi\) | ||||
0.0592988 | + | 0.998240i | \(0.481114\pi\) | |||||||
\(68\) | −15.8299 | −1.91965 | ||||||||
\(69\) | −9.60247 | −1.15600 | ||||||||
\(70\) | 1.30059 | 0.155450 | ||||||||
\(71\) | −7.34122 | −0.871243 | −0.435621 | − | 0.900130i | \(-0.643471\pi\) | ||||
−0.435621 | + | 0.900130i | \(0.643471\pi\) | |||||||
\(72\) | −16.9402 | −1.99642 | ||||||||
\(73\) | −6.41439 | −0.750748 | −0.375374 | − | 0.926873i | \(-0.622486\pi\) | ||||
−0.375374 | + | 0.926873i | \(0.622486\pi\) | |||||||
\(74\) | −17.1914 | −1.99846 | ||||||||
\(75\) | −13.4087 | −1.54831 | ||||||||
\(76\) | −16.8185 | −1.92922 | ||||||||
\(77\) | −2.30712 | −0.262921 | ||||||||
\(78\) | −6.66413 | −0.754564 | ||||||||
\(79\) | 13.2468 | 1.49038 | 0.745192 | − | 0.666850i | \(-0.232358\pi\) | ||||
0.745192 | + | 0.666850i | \(0.232358\pi\) | |||||||
\(80\) | 0.417259 | 0.0466510 | ||||||||
\(81\) | 2.69180 | 0.299089 | ||||||||
\(82\) | −24.8136 | −2.74020 | ||||||||
\(83\) | 2.87692 | 0.315783 | 0.157892 | − | 0.987456i | \(-0.449530\pi\) | ||||
0.157892 | + | 0.987456i | \(0.449530\pi\) | |||||||
\(84\) | −9.53511 | −1.04037 | ||||||||
\(85\) | −2.66780 | −0.289363 | ||||||||
\(86\) | 10.4323 | 1.12494 | ||||||||
\(87\) | −8.64372 | −0.926704 | ||||||||
\(88\) | −7.62622 | −0.812958 | ||||||||
\(89\) | 1.52562 | 0.161716 | 0.0808579 | − | 0.996726i | \(-0.474234\pi\) | ||||
0.0808579 | + | 0.996726i | \(0.474234\pi\) | |||||||
\(90\) | −6.95197 | −0.732802 | ||||||||
\(91\) | −0.979167 | −0.102645 | ||||||||
\(92\) | −11.3566 | −1.18401 | ||||||||
\(93\) | −10.2456 | −1.06242 | ||||||||
\(94\) | 20.4060 | 2.10472 | ||||||||
\(95\) | −2.83442 | −0.290805 | ||||||||
\(96\) | 13.7130 | 1.39958 | ||||||||
\(97\) | 0.356445 | 0.0361915 | 0.0180957 | − | 0.999836i | \(-0.494240\pi\) | ||||
0.0180957 | + | 0.999836i | \(0.494240\pi\) | |||||||
\(98\) | 14.0303 | 1.41727 | ||||||||
\(99\) | 12.3321 | 1.23942 | ||||||||
\(100\) | −15.8582 | −1.58582 | ||||||||
\(101\) | −12.1221 | −1.20619 | −0.603096 | − | 0.797668i | \(-0.706067\pi\) | ||||
−0.603096 | + | 0.797668i | \(0.706067\pi\) | |||||||
\(102\) | 31.0852 | 3.07789 | ||||||||
\(103\) | −5.21941 | −0.514283 | −0.257142 | − | 0.966374i | \(-0.582781\pi\) | ||||
−0.257142 | + | 0.966374i | \(0.582781\pi\) | |||||||
\(104\) | −3.23665 | −0.317379 | ||||||||
\(105\) | −1.60695 | −0.156822 | ||||||||
\(106\) | 1.95301 | 0.189693 | ||||||||
\(107\) | 4.63827 | 0.448399 | 0.224199 | − | 0.974543i | \(-0.428023\pi\) | ||||
0.224199 | + | 0.974543i | \(0.428023\pi\) | |||||||
\(108\) | 21.7534 | 2.09322 | ||||||||
\(109\) | 8.74712 | 0.837822 | 0.418911 | − | 0.908027i | \(-0.362412\pi\) | ||||
0.418911 | + | 0.908027i | \(0.362412\pi\) | |||||||
\(110\) | −3.12967 | −0.298402 | ||||||||
\(111\) | 21.2408 | 2.01609 | ||||||||
\(112\) | −0.714363 | −0.0675010 | ||||||||
\(113\) | −9.23182 | −0.868456 | −0.434228 | − | 0.900803i | \(-0.642979\pi\) | ||||
−0.434228 | + | 0.900803i | \(0.642979\pi\) | |||||||
\(114\) | 33.0267 | 3.09323 | ||||||||
\(115\) | −1.91392 | −0.178474 | ||||||||
\(116\) | −10.2227 | −0.949154 | ||||||||
\(117\) | 5.23387 | 0.483872 | ||||||||
\(118\) | 28.8099 | 2.65217 | ||||||||
\(119\) | 4.56737 | 0.418690 | ||||||||
\(120\) | −5.31179 | −0.484897 | ||||||||
\(121\) | −5.44828 | −0.495298 | ||||||||
\(122\) | 8.65862 | 0.783914 | ||||||||
\(123\) | 30.6585 | 2.76438 | ||||||||
\(124\) | −12.1172 | −1.08815 | ||||||||
\(125\) | −5.53222 | −0.494817 | ||||||||
\(126\) | 11.9020 | 1.06032 | ||||||||
\(127\) | −8.11639 | −0.720213 | −0.360106 | − | 0.932911i | \(-0.617260\pi\) | ||||
−0.360106 | + | 0.932911i | \(0.617260\pi\) | |||||||
\(128\) | 19.6068 | 1.73301 | ||||||||
\(129\) | −12.8896 | −1.13486 | ||||||||
\(130\) | −1.32826 | −0.116497 | ||||||||
\(131\) | 3.87412 | 0.338483 | 0.169242 | − | 0.985575i | \(-0.445868\pi\) | ||||
0.169242 | + | 0.985575i | \(0.445868\pi\) | |||||||
\(132\) | 22.9447 | 1.99708 | ||||||||
\(133\) | 4.85264 | 0.420777 | ||||||||
\(134\) | −2.25452 | −0.194761 | ||||||||
\(135\) | 3.66609 | 0.315527 | ||||||||
\(136\) | 15.0975 | 1.29460 | ||||||||
\(137\) | 1.71028 | 0.146119 | 0.0730594 | − | 0.997328i | \(-0.476724\pi\) | ||||
0.0730594 | + | 0.997328i | \(0.476724\pi\) | |||||||
\(138\) | 22.3010 | 1.89839 | ||||||||
\(139\) | 8.30153 | 0.704127 | 0.352063 | − | 0.935976i | \(-0.385480\pi\) | ||||
0.352063 | + | 0.935976i | \(0.385480\pi\) | |||||||
\(140\) | −1.90050 | −0.160621 | ||||||||
\(141\) | −25.2126 | −2.12329 | ||||||||
\(142\) | 17.0494 | 1.43076 | ||||||||
\(143\) | 2.35621 | 0.197036 | ||||||||
\(144\) | 3.81844 | 0.318203 | ||||||||
\(145\) | −1.72283 | −0.143073 | ||||||||
\(146\) | 14.8969 | 1.23288 | ||||||||
\(147\) | −17.3352 | −1.42978 | ||||||||
\(148\) | 25.1210 | 2.06493 | ||||||||
\(149\) | −5.26818 | −0.431586 | −0.215793 | − | 0.976439i | \(-0.569234\pi\) | ||||
−0.215793 | + | 0.976439i | \(0.569234\pi\) | |||||||
\(150\) | 31.1408 | 2.54263 | ||||||||
\(151\) | −1.61261 | −0.131233 | −0.0656163 | − | 0.997845i | \(-0.520901\pi\) | ||||
−0.0656163 | + | 0.997845i | \(0.520901\pi\) | |||||||
\(152\) | 16.0404 | 1.30105 | ||||||||
\(153\) | −24.4137 | −1.97373 | ||||||||
\(154\) | 5.35811 | 0.431769 | ||||||||
\(155\) | −2.04210 | −0.164025 | ||||||||
\(156\) | 9.73799 | 0.779663 | ||||||||
\(157\) | −12.4824 | −0.996201 | −0.498101 | − | 0.867119i | \(-0.665969\pi\) | ||||
−0.498101 | + | 0.867119i | \(0.665969\pi\) | |||||||
\(158\) | −30.7647 | −2.44751 | ||||||||
\(159\) | −2.41305 | −0.191367 | ||||||||
\(160\) | 2.73322 | 0.216080 | ||||||||
\(161\) | 3.27671 | 0.258241 | ||||||||
\(162\) | −6.25149 | −0.491164 | ||||||||
\(163\) | 14.9418 | 1.17033 | 0.585166 | − | 0.810914i | \(-0.301029\pi\) | ||||
0.585166 | + | 0.810914i | \(0.301029\pi\) | |||||||
\(164\) | 36.2590 | 2.83135 | ||||||||
\(165\) | 3.86687 | 0.301035 | ||||||||
\(166\) | −6.68143 | −0.518580 | ||||||||
\(167\) | −5.22044 | −0.403970 | −0.201985 | − | 0.979389i | \(-0.564739\pi\) | ||||
−0.201985 | + | 0.979389i | \(0.564739\pi\) | |||||||
\(168\) | 9.09398 | 0.701616 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.19576 | 0.475193 | ||||||||
\(171\) | −25.9385 | −1.98356 | ||||||||
\(172\) | −15.2442 | −1.16236 | ||||||||
\(173\) | −17.5933 | −1.33759 | −0.668796 | − | 0.743446i | \(-0.733190\pi\) | ||||
−0.668796 | + | 0.743446i | \(0.733190\pi\) | |||||||
\(174\) | 20.0744 | 1.52184 | ||||||||
\(175\) | 4.57554 | 0.345879 | ||||||||
\(176\) | 1.71900 | 0.129575 | ||||||||
\(177\) | −35.5961 | −2.67557 | ||||||||
\(178\) | −3.54315 | −0.265570 | ||||||||
\(179\) | −6.04528 | −0.451845 | −0.225923 | − | 0.974145i | \(-0.572540\pi\) | ||||
−0.225923 | + | 0.974145i | \(0.572540\pi\) | |||||||
\(180\) | 10.1586 | 0.757176 | ||||||||
\(181\) | −15.4866 | −1.15111 | −0.575555 | − | 0.817763i | \(-0.695214\pi\) | ||||
−0.575555 | + | 0.817763i | \(0.695214\pi\) | |||||||
\(182\) | 2.27404 | 0.168563 | ||||||||
\(183\) | −10.6982 | −0.790831 | ||||||||
\(184\) | 10.8312 | 0.798486 | ||||||||
\(185\) | 4.23363 | 0.311263 | ||||||||
\(186\) | 23.7945 | 1.74470 | ||||||||
\(187\) | −10.9907 | −0.803717 | ||||||||
\(188\) | −29.8183 | −2.17473 | ||||||||
\(189\) | −6.27649 | −0.456547 | ||||||||
\(190\) | 6.58272 | 0.477561 | ||||||||
\(191\) | −12.8714 | −0.931343 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(192\) | −36.0344 | −2.60056 | ||||||||
\(193\) | −0.860241 | −0.0619215 | −0.0309607 | − | 0.999521i | \(-0.509857\pi\) | ||||
−0.0309607 | + | 0.999521i | \(0.509857\pi\) | |||||||
\(194\) | −0.827815 | −0.0594337 | ||||||||
\(195\) | 1.64114 | 0.117524 | ||||||||
\(196\) | −20.5018 | −1.46442 | ||||||||
\(197\) | 21.4849 | 1.53074 | 0.765369 | − | 0.643591i | \(-0.222556\pi\) | ||||
0.765369 | + | 0.643591i | \(0.222556\pi\) | |||||||
\(198\) | −28.6404 | −2.03538 | ||||||||
\(199\) | 13.4535 | 0.953695 | 0.476847 | − | 0.878986i | \(-0.341779\pi\) | ||||
0.476847 | + | 0.878986i | \(0.341779\pi\) | |||||||
\(200\) | 15.1245 | 1.06946 | ||||||||
\(201\) | 2.78558 | 0.196479 | ||||||||
\(202\) | 28.1526 | 1.98081 | ||||||||
\(203\) | 2.94955 | 0.207018 | ||||||||
\(204\) | −45.4233 | −3.18027 | ||||||||
\(205\) | 6.11071 | 0.426790 | ||||||||
\(206\) | 12.1217 | 0.844557 | ||||||||
\(207\) | −17.5148 | −1.21736 | ||||||||
\(208\) | 0.729563 | 0.0505861 | ||||||||
\(209\) | −11.6771 | −0.807722 | ||||||||
\(210\) | 3.73201 | 0.257533 | ||||||||
\(211\) | 27.8756 | 1.91903 | 0.959517 | − | 0.281652i | \(-0.0908823\pi\) | ||||
0.959517 | + | 0.281652i | \(0.0908823\pi\) | |||||||
\(212\) | −2.85385 | −0.196003 | ||||||||
\(213\) | −21.0654 | −1.44338 | ||||||||
\(214\) | −10.7720 | −0.736361 | ||||||||
\(215\) | −2.56909 | −0.175211 | ||||||||
\(216\) | −20.7470 | −1.41166 | ||||||||
\(217\) | 3.49615 | 0.237334 | ||||||||
\(218\) | −20.3145 | −1.37587 | ||||||||
\(219\) | −18.4059 | −1.24376 | ||||||||
\(220\) | 4.57324 | 0.308328 | ||||||||
\(221\) | −4.66455 | −0.313772 | ||||||||
\(222\) | −49.3302 | −3.31083 | ||||||||
\(223\) | 5.50400 | 0.368575 | 0.184287 | − | 0.982872i | \(-0.441002\pi\) | ||||
0.184287 | + | 0.982872i | \(0.441002\pi\) | |||||||
\(224\) | −4.67938 | −0.312654 | ||||||||
\(225\) | −24.4573 | −1.63049 | ||||||||
\(226\) | 21.4402 | 1.42618 | ||||||||
\(227\) | 25.2791 | 1.67783 | 0.838916 | − | 0.544260i | \(-0.183190\pi\) | ||||
0.838916 | + | 0.544260i | \(0.183190\pi\) | |||||||
\(228\) | −48.2603 | −3.19612 | ||||||||
\(229\) | 14.9970 | 0.991031 | 0.495515 | − | 0.868599i | \(-0.334979\pi\) | ||||
0.495515 | + | 0.868599i | \(0.334979\pi\) | |||||||
\(230\) | 4.44494 | 0.293090 | ||||||||
\(231\) | −6.62022 | −0.435579 | ||||||||
\(232\) | 9.74976 | 0.640103 | ||||||||
\(233\) | −11.4853 | −0.752426 | −0.376213 | − | 0.926533i | \(-0.622774\pi\) | ||||
−0.376213 | + | 0.926533i | \(0.622774\pi\) | |||||||
\(234\) | −12.1553 | −0.794615 | ||||||||
\(235\) | −5.02527 | −0.327813 | ||||||||
\(236\) | −42.0986 | −2.74038 | ||||||||
\(237\) | 38.0114 | 2.46911 | ||||||||
\(238\) | −10.6074 | −0.687574 | ||||||||
\(239\) | 2.97256 | 0.192279 | 0.0961394 | − | 0.995368i | \(-0.469351\pi\) | ||||
0.0961394 | + | 0.995368i | \(0.469351\pi\) | |||||||
\(240\) | 1.19731 | 0.0772862 | ||||||||
\(241\) | 16.6307 | 1.07128 | 0.535639 | − | 0.844447i | \(-0.320071\pi\) | ||||
0.535639 | + | 0.844447i | \(0.320071\pi\) | |||||||
\(242\) | 12.6532 | 0.813379 | ||||||||
\(243\) | −11.5061 | −0.738114 | ||||||||
\(244\) | −12.6524 | −0.809989 | ||||||||
\(245\) | −3.45516 | −0.220742 | ||||||||
\(246\) | −71.2019 | −4.53967 | ||||||||
\(247\) | −4.95588 | −0.315335 | ||||||||
\(248\) | 11.5566 | 0.733843 | ||||||||
\(249\) | 8.25525 | 0.523155 | ||||||||
\(250\) | 12.8482 | 0.812589 | ||||||||
\(251\) | −8.49727 | −0.536343 | −0.268172 | − | 0.963371i | \(-0.586419\pi\) | ||||
−0.268172 | + | 0.963371i | \(0.586419\pi\) | |||||||
\(252\) | −17.3919 | −1.09559 | ||||||||
\(253\) | −7.88488 | −0.495718 | ||||||||
\(254\) | 18.8497 | 1.18273 | ||||||||
\(255\) | −7.65517 | −0.479386 | ||||||||
\(256\) | −20.4195 | −1.27622 | ||||||||
\(257\) | 22.0383 | 1.37471 | 0.687357 | − | 0.726320i | \(-0.258771\pi\) | ||||
0.687357 | + | 0.726320i | \(0.258771\pi\) | |||||||
\(258\) | 29.9351 | 1.86368 | ||||||||
\(259\) | −7.24813 | −0.450377 | ||||||||
\(260\) | 1.94093 | 0.120371 | ||||||||
\(261\) | −15.7660 | −0.975892 | ||||||||
\(262\) | −8.99734 | −0.555858 | ||||||||
\(263\) | 11.2609 | 0.694375 | 0.347188 | − | 0.937796i | \(-0.387137\pi\) | ||||
0.347188 | + | 0.937796i | \(0.387137\pi\) | |||||||
\(264\) | −21.8832 | −1.34682 | ||||||||
\(265\) | −0.480958 | −0.0295450 | ||||||||
\(266\) | −11.2699 | −0.691000 | ||||||||
\(267\) | 4.37774 | 0.267913 | ||||||||
\(268\) | 3.29443 | 0.201239 | ||||||||
\(269\) | −10.4366 | −0.636330 | −0.318165 | − | 0.948035i | \(-0.603067\pi\) | ||||
−0.318165 | + | 0.948035i | \(0.603067\pi\) | |||||||
\(270\) | −8.51422 | −0.518159 | ||||||||
\(271\) | −17.3213 | −1.05219 | −0.526097 | − | 0.850425i | \(-0.676345\pi\) | ||||
−0.526097 | + | 0.850425i | \(0.676345\pi\) | |||||||
\(272\) | −3.40308 | −0.206342 | ||||||||
\(273\) | −2.80969 | −0.170050 | ||||||||
\(274\) | −3.97199 | −0.239957 | ||||||||
\(275\) | −11.0103 | −0.663947 | ||||||||
\(276\) | −32.5874 | −1.96153 | ||||||||
\(277\) | 8.67340 | 0.521134 | 0.260567 | − | 0.965456i | \(-0.416090\pi\) | ||||
0.260567 | + | 0.965456i | \(0.416090\pi\) | |||||||
\(278\) | −19.2797 | −1.15632 | ||||||||
\(279\) | −18.6877 | −1.11881 | ||||||||
\(280\) | 1.81257 | 0.108322 | ||||||||
\(281\) | −28.4321 | −1.69612 | −0.848058 | − | 0.529904i | \(-0.822228\pi\) | ||||
−0.848058 | + | 0.529904i | \(0.822228\pi\) | |||||||
\(282\) | 58.5544 | 3.48687 | ||||||||
\(283\) | 20.2386 | 1.20306 | 0.601531 | − | 0.798850i | \(-0.294558\pi\) | ||||
0.601531 | + | 0.798850i | \(0.294558\pi\) | |||||||
\(284\) | −24.9135 | −1.47835 | ||||||||
\(285\) | −8.13329 | −0.481775 | ||||||||
\(286\) | −5.47212 | −0.323573 | ||||||||
\(287\) | −10.4618 | −0.617538 | ||||||||
\(288\) | 25.0124 | 1.47387 | ||||||||
\(289\) | 4.75803 | 0.279884 | ||||||||
\(290\) | 4.00114 | 0.234955 | ||||||||
\(291\) | 1.02281 | 0.0599581 | ||||||||
\(292\) | −21.7682 | −1.27389 | ||||||||
\(293\) | 4.22798 | 0.247001 | 0.123501 | − | 0.992344i | \(-0.460588\pi\) | ||||
0.123501 | + | 0.992344i | \(0.460588\pi\) | |||||||
\(294\) | 40.2596 | 2.34799 | ||||||||
\(295\) | −7.09486 | −0.413078 | ||||||||
\(296\) | −23.9588 | −1.39258 | ||||||||
\(297\) | 15.1034 | 0.876387 | ||||||||
\(298\) | 12.2349 | 0.708751 | ||||||||
\(299\) | −3.34642 | −0.193529 | ||||||||
\(300\) | −45.5046 | −2.62721 | ||||||||
\(301\) | 4.39839 | 0.253519 | ||||||||
\(302\) | 3.74517 | 0.215510 | ||||||||
\(303\) | −34.7840 | −1.99829 | ||||||||
\(304\) | −3.61563 | −0.207370 | ||||||||
\(305\) | −2.13231 | −0.122096 | ||||||||
\(306\) | 56.6989 | 3.24126 | ||||||||
\(307\) | −26.0448 | −1.48646 | −0.743229 | − | 0.669038i | \(-0.766707\pi\) | ||||
−0.743229 | + | 0.669038i | \(0.766707\pi\) | |||||||
\(308\) | −7.82956 | −0.446131 | ||||||||
\(309\) | −14.9769 | −0.852009 | ||||||||
\(310\) | 4.74262 | 0.269363 | ||||||||
\(311\) | −1.84577 | −0.104664 | −0.0523320 | − | 0.998630i | \(-0.516665\pi\) | ||||
−0.0523320 | + | 0.998630i | \(0.516665\pi\) | |||||||
\(312\) | −9.28747 | −0.525799 | ||||||||
\(313\) | 14.3900 | 0.813369 | 0.406685 | − | 0.913569i | \(-0.366685\pi\) | ||||
0.406685 | + | 0.913569i | \(0.366685\pi\) | |||||||
\(314\) | 28.9893 | 1.63596 | ||||||||
\(315\) | −2.93105 | −0.165146 | ||||||||
\(316\) | 44.9551 | 2.52892 | ||||||||
\(317\) | −15.0050 | −0.842766 | −0.421383 | − | 0.906883i | \(-0.638455\pi\) | ||||
−0.421383 | + | 0.906883i | \(0.638455\pi\) | |||||||
\(318\) | 5.60412 | 0.314263 | ||||||||
\(319\) | −7.09762 | −0.397390 | ||||||||
\(320\) | −7.18221 | −0.401498 | ||||||||
\(321\) | 13.3094 | 0.742858 | ||||||||
\(322\) | −7.60990 | −0.424083 | ||||||||
\(323\) | 23.1170 | 1.28626 | ||||||||
\(324\) | 9.13502 | 0.507501 | ||||||||
\(325\) | −4.67290 | −0.259206 | ||||||||
\(326\) | −34.7012 | −1.92192 | ||||||||
\(327\) | 25.0996 | 1.38801 | ||||||||
\(328\) | −34.5815 | −1.90944 | ||||||||
\(329\) | 8.60345 | 0.474324 | ||||||||
\(330\) | −8.98050 | −0.494360 | ||||||||
\(331\) | 5.14142 | 0.282598 | 0.141299 | − | 0.989967i | \(-0.454872\pi\) | ||||
0.141299 | + | 0.989967i | \(0.454872\pi\) | |||||||
\(332\) | 9.76327 | 0.535829 | ||||||||
\(333\) | 38.7430 | 2.12310 | ||||||||
\(334\) | 12.1241 | 0.663400 | ||||||||
\(335\) | 0.555209 | 0.0303343 | ||||||||
\(336\) | −2.04985 | −0.111828 | ||||||||
\(337\) | 16.4429 | 0.895700 | 0.447850 | − | 0.894109i | \(-0.352190\pi\) | ||||
0.447850 | + | 0.894109i | \(0.352190\pi\) | |||||||
\(338\) | −2.32242 | −0.126323 | ||||||||
\(339\) | −26.4904 | −1.43876 | ||||||||
\(340\) | −9.05357 | −0.490999 | ||||||||
\(341\) | −8.41294 | −0.455586 | ||||||||
\(342\) | 60.2401 | 3.25741 | ||||||||
\(343\) | 12.7695 | 0.689490 | ||||||||
\(344\) | 14.5389 | 0.783886 | ||||||||
\(345\) | −5.49194 | −0.295676 | ||||||||
\(346\) | 40.8590 | 2.19660 | ||||||||
\(347\) | −32.8934 | −1.76581 | −0.882905 | − | 0.469551i | \(-0.844416\pi\) | ||||
−0.882905 | + | 0.469551i | \(0.844416\pi\) | |||||||
\(348\) | −29.3338 | −1.57246 | ||||||||
\(349\) | −16.7956 | −0.899046 | −0.449523 | − | 0.893269i | \(-0.648406\pi\) | ||||
−0.449523 | + | 0.893269i | \(0.648406\pi\) | |||||||
\(350\) | −10.6263 | −0.568002 | ||||||||
\(351\) | 6.41003 | 0.342142 | ||||||||
\(352\) | 11.2602 | 0.600170 | ||||||||
\(353\) | −24.4411 | −1.30087 | −0.650435 | − | 0.759562i | \(-0.725413\pi\) | ||||
−0.650435 | + | 0.759562i | \(0.725413\pi\) | |||||||
\(354\) | 82.6692 | 4.39382 | ||||||||
\(355\) | −4.19867 | −0.222842 | ||||||||
\(356\) | 5.17744 | 0.274404 | ||||||||
\(357\) | 13.1059 | 0.693640 | ||||||||
\(358\) | 14.0397 | 0.742021 | ||||||||
\(359\) | 34.3641 | 1.81367 | 0.906833 | − | 0.421490i | \(-0.138493\pi\) | ||||
0.906833 | + | 0.421490i | \(0.138493\pi\) | |||||||
\(360\) | −9.68861 | −0.510635 | ||||||||
\(361\) | 5.56078 | 0.292673 | ||||||||
\(362\) | 35.9664 | 1.89035 | ||||||||
\(363\) | −15.6337 | −0.820555 | ||||||||
\(364\) | −3.32295 | −0.174170 | ||||||||
\(365\) | −3.66859 | −0.192023 | ||||||||
\(366\) | 24.8457 | 1.29870 | ||||||||
\(367\) | 28.9391 | 1.51061 | 0.755305 | − | 0.655373i | \(-0.227489\pi\) | ||||
0.755305 | + | 0.655373i | \(0.227489\pi\) | |||||||
\(368\) | −2.44143 | −0.127268 | ||||||||
\(369\) | 55.9205 | 2.91111 | ||||||||
\(370\) | −9.83228 | −0.511156 | ||||||||
\(371\) | 0.823418 | 0.0427497 | ||||||||
\(372\) | −34.7699 | −1.80273 | ||||||||
\(373\) | −6.61730 | −0.342631 | −0.171315 | − | 0.985216i | \(-0.554802\pi\) | ||||
−0.171315 | + | 0.985216i | \(0.554802\pi\) | |||||||
\(374\) | 25.5250 | 1.31986 | ||||||||
\(375\) | −15.8746 | −0.819759 | ||||||||
\(376\) | 28.4388 | 1.46662 | ||||||||
\(377\) | −3.01230 | −0.155142 | ||||||||
\(378\) | 14.5767 | 0.749743 | ||||||||
\(379\) | 2.43718 | 0.125190 | 0.0625948 | − | 0.998039i | \(-0.480062\pi\) | ||||
0.0625948 | + | 0.998039i | \(0.480062\pi\) | |||||||
\(380\) | −9.61903 | −0.493446 | ||||||||
\(381\) | −23.2897 | −1.19317 | ||||||||
\(382\) | 29.8929 | 1.52945 | ||||||||
\(383\) | 3.34133 | 0.170734 | 0.0853671 | − | 0.996350i | \(-0.472794\pi\) | ||||
0.0853671 | + | 0.996350i | \(0.472794\pi\) | |||||||
\(384\) | 56.2610 | 2.87106 | ||||||||
\(385\) | −1.31951 | −0.0672486 | ||||||||
\(386\) | 1.99784 | 0.101688 | ||||||||
\(387\) | −23.5104 | −1.19510 | ||||||||
\(388\) | 1.20965 | 0.0614106 | ||||||||
\(389\) | 28.4636 | 1.44316 | 0.721580 | − | 0.692331i | \(-0.243416\pi\) | ||||
0.721580 | + | 0.692331i | \(0.243416\pi\) | |||||||
\(390\) | −3.81142 | −0.192999 | ||||||||
\(391\) | 15.6096 | 0.789409 | ||||||||
\(392\) | 19.5533 | 0.987593 | ||||||||
\(393\) | 11.1167 | 0.560762 | ||||||||
\(394\) | −49.8971 | −2.51378 | ||||||||
\(395\) | 7.57626 | 0.381203 | ||||||||
\(396\) | 41.8508 | 2.10308 | ||||||||
\(397\) | 26.5099 | 1.33049 | 0.665246 | − | 0.746624i | \(-0.268327\pi\) | ||||
0.665246 | + | 0.746624i | \(0.268327\pi\) | |||||||
\(398\) | −31.2448 | −1.56616 | ||||||||
\(399\) | 13.9245 | 0.697097 | ||||||||
\(400\) | −3.40917 | −0.170459 | ||||||||
\(401\) | 2.59226 | 0.129451 | 0.0647256 | − | 0.997903i | \(-0.479383\pi\) | ||||
0.0647256 | + | 0.997903i | \(0.479383\pi\) | |||||||
\(402\) | −6.46929 | −0.322659 | ||||||||
\(403\) | −3.57054 | −0.177861 | ||||||||
\(404\) | −41.1381 | −2.04670 | ||||||||
\(405\) | 1.53952 | 0.0764994 | ||||||||
\(406\) | −6.85010 | −0.339965 | ||||||||
\(407\) | 17.4415 | 0.864543 | ||||||||
\(408\) | 43.3219 | 2.14475 | ||||||||
\(409\) | 27.2328 | 1.34658 | 0.673288 | − | 0.739381i | \(-0.264882\pi\) | ||||
0.673288 | + | 0.739381i | \(0.264882\pi\) | |||||||
\(410\) | −14.1916 | −0.700875 | ||||||||
\(411\) | 4.90759 | 0.242074 | ||||||||
\(412\) | −17.7128 | −0.872649 | ||||||||
\(413\) | 12.1467 | 0.597698 | ||||||||
\(414\) | 40.6767 | 1.99915 | ||||||||
\(415\) | 1.64540 | 0.0807695 | ||||||||
\(416\) | 4.77894 | 0.234307 | ||||||||
\(417\) | 23.8210 | 1.16652 | ||||||||
\(418\) | 27.1192 | 1.32644 | ||||||||
\(419\) | −17.1980 | −0.840177 | −0.420089 | − | 0.907483i | \(-0.638001\pi\) | ||||
−0.420089 | + | 0.907483i | \(0.638001\pi\) | |||||||
\(420\) | −5.45342 | −0.266100 | ||||||||
\(421\) | −6.94089 | −0.338278 | −0.169139 | − | 0.985592i | \(-0.554099\pi\) | ||||
−0.169139 | + | 0.985592i | \(0.554099\pi\) | |||||||
\(422\) | −64.7389 | −3.15144 | ||||||||
\(423\) | −45.9875 | −2.23599 | ||||||||
\(424\) | 2.72182 | 0.132183 | ||||||||
\(425\) | 21.7970 | 1.05731 | ||||||||
\(426\) | 48.9228 | 2.37032 | ||||||||
\(427\) | 3.65059 | 0.176665 | ||||||||
\(428\) | 15.7407 | 0.760854 | ||||||||
\(429\) | 6.76108 | 0.326428 | ||||||||
\(430\) | 5.96653 | 0.287731 | ||||||||
\(431\) | −37.5906 | −1.81068 | −0.905338 | − | 0.424692i | \(-0.860383\pi\) | ||||
−0.905338 | + | 0.424692i | \(0.860383\pi\) | |||||||
\(432\) | 4.67652 | 0.224999 | ||||||||
\(433\) | −27.5733 | −1.32509 | −0.662545 | − | 0.749022i | \(-0.730524\pi\) | ||||
−0.662545 | + | 0.749022i | \(0.730524\pi\) | |||||||
\(434\) | −8.11954 | −0.389751 | ||||||||
\(435\) | −4.94361 | −0.237028 | ||||||||
\(436\) | 29.6847 | 1.42164 | ||||||||
\(437\) | 16.5845 | 0.793344 | ||||||||
\(438\) | 42.7463 | 2.04250 | ||||||||
\(439\) | 7.25912 | 0.346459 | 0.173229 | − | 0.984882i | \(-0.444580\pi\) | ||||
0.173229 | + | 0.984882i | \(0.444580\pi\) | |||||||
\(440\) | −4.36167 | −0.207934 | ||||||||
\(441\) | −31.6190 | −1.50567 | ||||||||
\(442\) | 10.8331 | 0.515276 | ||||||||
\(443\) | −16.1892 | −0.769173 | −0.384586 | − | 0.923089i | \(-0.625656\pi\) | ||||
−0.384586 | + | 0.923089i | \(0.625656\pi\) | |||||||
\(444\) | 72.0840 | 3.42095 | ||||||||
\(445\) | 0.872551 | 0.0413629 | ||||||||
\(446\) | −12.7826 | −0.605274 | ||||||||
\(447\) | −15.1169 | −0.715004 | ||||||||
\(448\) | 12.2962 | 0.580942 | ||||||||
\(449\) | −8.45649 | −0.399087 | −0.199543 | − | 0.979889i | \(-0.563946\pi\) | ||||
−0.199543 | + | 0.979889i | \(0.563946\pi\) | |||||||
\(450\) | 56.8003 | 2.67759 | ||||||||
\(451\) | 25.1746 | 1.18542 | ||||||||
\(452\) | −31.3296 | −1.47362 | ||||||||
\(453\) | −4.62735 | −0.217412 | ||||||||
\(454\) | −58.7088 | −2.75534 | ||||||||
\(455\) | −0.560015 | −0.0262539 | ||||||||
\(456\) | 46.0276 | 2.15544 | ||||||||
\(457\) | −4.60629 | −0.215473 | −0.107737 | − | 0.994179i | \(-0.534360\pi\) | ||||
−0.107737 | + | 0.994179i | \(0.534360\pi\) | |||||||
\(458\) | −34.8294 | −1.62747 | ||||||||
\(459\) | −29.8999 | −1.39561 | ||||||||
\(460\) | −6.49518 | −0.302839 | ||||||||
\(461\) | −14.6700 | −0.683250 | −0.341625 | − | 0.939836i | \(-0.610977\pi\) | ||||
−0.341625 | + | 0.939836i | \(0.610977\pi\) | |||||||
\(462\) | 15.3750 | 0.715308 | ||||||||
\(463\) | 1.00000 | 0.0464739 | ||||||||
\(464\) | −2.19766 | −0.102024 | ||||||||
\(465\) | −5.85975 | −0.271739 | ||||||||
\(466\) | 26.6737 | 1.23564 | ||||||||
\(467\) | 26.9256 | 1.24597 | 0.622983 | − | 0.782235i | \(-0.285920\pi\) | ||||
0.622983 | + | 0.782235i | \(0.285920\pi\) | |||||||
\(468\) | 17.7619 | 0.821046 | ||||||||
\(469\) | −0.950538 | −0.0438918 | ||||||||
\(470\) | 11.6708 | 0.538334 | ||||||||
\(471\) | −35.8178 | −1.65040 | ||||||||
\(472\) | 40.1509 | 1.84810 | ||||||||
\(473\) | −10.5840 | −0.486654 | ||||||||
\(474\) | −88.2786 | −4.05477 | ||||||||
\(475\) | 23.1583 | 1.06258 | ||||||||
\(476\) | 15.5001 | 0.710444 | ||||||||
\(477\) | −4.40136 | −0.201524 | ||||||||
\(478\) | −6.90354 | −0.315761 | ||||||||
\(479\) | 14.9843 | 0.684649 | 0.342325 | − | 0.939582i | \(-0.388786\pi\) | ||||
0.342325 | + | 0.939582i | \(0.388786\pi\) | |||||||
\(480\) | 7.84290 | 0.357978 | ||||||||
\(481\) | 7.40235 | 0.337518 | ||||||||
\(482\) | −38.6236 | −1.75926 | ||||||||
\(483\) | 9.40242 | 0.427825 | ||||||||
\(484\) | −18.4895 | −0.840434 | ||||||||
\(485\) | 0.203862 | 0.00925688 | ||||||||
\(486\) | 26.7219 | 1.21213 | ||||||||
\(487\) | −12.6809 | −0.574624 | −0.287312 | − | 0.957837i | \(-0.592762\pi\) | ||||
−0.287312 | + | 0.957837i | \(0.592762\pi\) | |||||||
\(488\) | 12.0671 | 0.546251 | ||||||||
\(489\) | 42.8751 | 1.93888 | ||||||||
\(490\) | 8.02436 | 0.362503 | ||||||||
\(491\) | −29.5808 | −1.33496 | −0.667481 | − | 0.744627i | \(-0.732627\pi\) | ||||
−0.667481 | + | 0.744627i | \(0.732627\pi\) | |||||||
\(492\) | 104.044 | 4.69067 | ||||||||
\(493\) | 14.0510 | 0.632827 | ||||||||
\(494\) | 11.5097 | 0.517844 | ||||||||
\(495\) | 7.05310 | 0.317013 | ||||||||
\(496\) | −2.60493 | −0.116965 | ||||||||
\(497\) | 7.18828 | 0.322438 | ||||||||
\(498\) | −19.1722 | −0.859126 | ||||||||
\(499\) | −13.2261 | −0.592082 | −0.296041 | − | 0.955175i | \(-0.595666\pi\) | ||||
−0.296041 | + | 0.955175i | \(0.595666\pi\) | |||||||
\(500\) | −18.7744 | −0.839618 | ||||||||
\(501\) | −14.9799 | −0.669254 | ||||||||
\(502\) | 19.7343 | 0.880783 | ||||||||
\(503\) | −2.93051 | −0.130665 | −0.0653324 | − | 0.997864i | \(-0.520811\pi\) | ||||
−0.0653324 | + | 0.997864i | \(0.520811\pi\) | |||||||
\(504\) | 16.5873 | 0.738856 | ||||||||
\(505\) | −6.93299 | −0.308514 | ||||||||
\(506\) | 18.3120 | 0.814069 | ||||||||
\(507\) | 2.86947 | 0.127438 | ||||||||
\(508\) | −27.5442 | −1.22208 | ||||||||
\(509\) | 32.9616 | 1.46100 | 0.730498 | − | 0.682915i | \(-0.239288\pi\) | ||||
0.730498 | + | 0.682915i | \(0.239288\pi\) | |||||||
\(510\) | 17.7786 | 0.787248 | ||||||||
\(511\) | 6.28076 | 0.277844 | ||||||||
\(512\) | 8.20921 | 0.362799 | ||||||||
\(513\) | −31.7674 | −1.40256 | ||||||||
\(514\) | −51.1824 | −2.25756 | ||||||||
\(515\) | −2.98514 | −0.131541 | ||||||||
\(516\) | −43.7428 | −1.92567 | ||||||||
\(517\) | −20.7029 | −0.910511 | ||||||||
\(518\) | 16.8332 | 0.739610 | ||||||||
\(519\) | −50.4834 | −2.21598 | ||||||||
\(520\) | −1.85114 | −0.0811777 | ||||||||
\(521\) | −16.0345 | −0.702486 | −0.351243 | − | 0.936284i | \(-0.614241\pi\) | ||||
−0.351243 | + | 0.936284i | \(0.614241\pi\) | |||||||
\(522\) | 36.6154 | 1.60261 | ||||||||
\(523\) | 17.3235 | 0.757505 | 0.378753 | − | 0.925498i | \(-0.376353\pi\) | ||||
0.378753 | + | 0.925498i | \(0.376353\pi\) | |||||||
\(524\) | 13.1474 | 0.574347 | ||||||||
\(525\) | 13.1294 | 0.573014 | ||||||||
\(526\) | −26.1525 | −1.14030 | ||||||||
\(527\) | 16.6550 | 0.725501 | ||||||||
\(528\) | 4.93263 | 0.214665 | ||||||||
\(529\) | −11.8014 | −0.513106 | ||||||||
\(530\) | 1.11699 | 0.0485188 | ||||||||
\(531\) | −64.9267 | −2.81758 | ||||||||
\(532\) | 16.4681 | 0.713985 | ||||||||
\(533\) | 10.6844 | 0.462791 | ||||||||
\(534\) | −10.1670 | −0.439967 | ||||||||
\(535\) | 2.65277 | 0.114689 | ||||||||
\(536\) | −3.14202 | −0.135714 | ||||||||
\(537\) | −17.3468 | −0.748568 | ||||||||
\(538\) | 24.2382 | 1.04498 | ||||||||
\(539\) | −14.2344 | −0.613120 | ||||||||
\(540\) | 12.4414 | 0.535394 | ||||||||
\(541\) | 4.91193 | 0.211180 | 0.105590 | − | 0.994410i | \(-0.466327\pi\) | ||||
0.105590 | + | 0.994410i | \(0.466327\pi\) | |||||||
\(542\) | 40.2274 | 1.72791 | ||||||||
\(543\) | −44.4384 | −1.90703 | ||||||||
\(544\) | −22.2916 | −0.955745 | ||||||||
\(545\) | 5.00274 | 0.214294 | ||||||||
\(546\) | 6.52529 | 0.279257 | ||||||||
\(547\) | −0.290860 | −0.0124363 | −0.00621814 | − | 0.999981i | \(-0.501979\pi\) | ||||
−0.00621814 | + | 0.999981i | \(0.501979\pi\) | |||||||
\(548\) | 5.80408 | 0.247938 | ||||||||
\(549\) | −19.5133 | −0.832806 | ||||||||
\(550\) | 25.5706 | 1.09034 | ||||||||
\(551\) | 14.9286 | 0.635981 | ||||||||
\(552\) | 31.0798 | 1.32284 | ||||||||
\(553\) | −12.9709 | −0.551577 | ||||||||
\(554\) | −20.1433 | −0.855807 | ||||||||
\(555\) | 12.1483 | 0.515666 | ||||||||
\(556\) | 28.1725 | 1.19478 | ||||||||
\(557\) | −1.49971 | −0.0635449 | −0.0317724 | − | 0.999495i | \(-0.510115\pi\) | ||||
−0.0317724 | + | 0.999495i | \(0.510115\pi\) | |||||||
\(558\) | 43.4008 | 1.83730 | ||||||||
\(559\) | −4.49197 | −0.189990 | ||||||||
\(560\) | −0.408566 | −0.0172651 | ||||||||
\(561\) | −31.5374 | −1.33151 | ||||||||
\(562\) | 66.0313 | 2.78536 | ||||||||
\(563\) | 23.2439 | 0.979612 | 0.489806 | − | 0.871831i | \(-0.337068\pi\) | ||||
0.489806 | + | 0.871831i | \(0.337068\pi\) | |||||||
\(564\) | −85.5629 | −3.60285 | ||||||||
\(565\) | −5.27996 | −0.222129 | ||||||||
\(566\) | −47.0027 | −1.97567 | ||||||||
\(567\) | −2.63572 | −0.110690 | ||||||||
\(568\) | 23.7609 | 0.996987 | ||||||||
\(569\) | −24.4067 | −1.02318 | −0.511590 | − | 0.859230i | \(-0.670943\pi\) | ||||
−0.511590 | + | 0.859230i | \(0.670943\pi\) | |||||||
\(570\) | 18.8889 | 0.791171 | ||||||||
\(571\) | 32.4328 | 1.35727 | 0.678636 | − | 0.734475i | \(-0.262572\pi\) | ||||
0.678636 | + | 0.734475i | \(0.262572\pi\) | |||||||
\(572\) | 7.99615 | 0.334336 | ||||||||
\(573\) | −36.9342 | −1.54295 | ||||||||
\(574\) | 24.2966 | 1.01412 | ||||||||
\(575\) | 15.6375 | 0.652128 | ||||||||
\(576\) | −65.7262 | −2.73859 | ||||||||
\(577\) | 23.1097 | 0.962068 | 0.481034 | − | 0.876702i | \(-0.340261\pi\) | ||||
0.481034 | + | 0.876702i | \(0.340261\pi\) | |||||||
\(578\) | −11.0502 | −0.459626 | ||||||||
\(579\) | −2.46844 | −0.102585 | ||||||||
\(580\) | −5.84668 | −0.242770 | ||||||||
\(581\) | −2.81699 | −0.116868 | ||||||||
\(582\) | −2.37539 | −0.0984632 | ||||||||
\(583\) | −1.98143 | −0.0820623 | ||||||||
\(584\) | 20.7611 | 0.859101 | ||||||||
\(585\) | 2.99341 | 0.123762 | ||||||||
\(586\) | −9.81917 | −0.405626 | ||||||||
\(587\) | 15.2383 | 0.628951 | 0.314476 | − | 0.949266i | \(-0.398171\pi\) | ||||
0.314476 | + | 0.949266i | \(0.398171\pi\) | |||||||
\(588\) | −58.8294 | −2.42609 | ||||||||
\(589\) | 17.6952 | 0.729117 | ||||||||
\(590\) | 16.4773 | 0.678358 | ||||||||
\(591\) | 61.6505 | 2.53596 | ||||||||
\(592\) | 5.40048 | 0.221958 | ||||||||
\(593\) | −6.77311 | −0.278138 | −0.139069 | − | 0.990283i | \(-0.544411\pi\) | ||||
−0.139069 | + | 0.990283i | \(0.544411\pi\) | |||||||
\(594\) | −35.0765 | −1.43920 | ||||||||
\(595\) | 2.61222 | 0.107091 | ||||||||
\(596\) | −17.8783 | −0.732326 | ||||||||
\(597\) | 38.6045 | 1.57998 | ||||||||
\(598\) | 7.77181 | 0.317813 | ||||||||
\(599\) | −34.8707 | −1.42478 | −0.712390 | − | 0.701784i | \(-0.752387\pi\) | ||||
−0.712390 | + | 0.701784i | \(0.752387\pi\) | |||||||
\(600\) | 43.3994 | 1.77177 | ||||||||
\(601\) | −6.82519 | −0.278405 | −0.139203 | − | 0.990264i | \(-0.544454\pi\) | ||||
−0.139203 | + | 0.990264i | \(0.544454\pi\) | |||||||
\(602\) | −10.2149 | −0.416329 | ||||||||
\(603\) | 5.08085 | 0.206908 | ||||||||
\(604\) | −5.47265 | −0.222679 | ||||||||
\(605\) | −3.11603 | −0.126685 | ||||||||
\(606\) | 80.7832 | 3.28159 | ||||||||
\(607\) | 38.1504 | 1.54848 | 0.774238 | − | 0.632895i | \(-0.218134\pi\) | ||||
0.774238 | + | 0.632895i | \(0.218134\pi\) | |||||||
\(608\) | −23.6839 | −0.960508 | ||||||||
\(609\) | 8.46364 | 0.342964 | ||||||||
\(610\) | 4.95213 | 0.200506 | ||||||||
\(611\) | −8.78651 | −0.355464 | ||||||||
\(612\) | −82.8514 | −3.34907 | ||||||||
\(613\) | 4.58957 | 0.185371 | 0.0926856 | − | 0.995695i | \(-0.470455\pi\) | ||||
0.0926856 | + | 0.995695i | \(0.470455\pi\) | |||||||
\(614\) | 60.4871 | 2.44106 | ||||||||
\(615\) | 17.5345 | 0.707059 | ||||||||
\(616\) | 7.46734 | 0.300868 | ||||||||
\(617\) | 14.7453 | 0.593623 | 0.296812 | − | 0.954936i | \(-0.404077\pi\) | ||||
0.296812 | + | 0.954936i | \(0.404077\pi\) | |||||||
\(618\) | 34.7828 | 1.39917 | ||||||||
\(619\) | −28.3322 | −1.13877 | −0.569384 | − | 0.822072i | \(-0.692818\pi\) | ||||
−0.569384 | + | 0.822072i | \(0.692818\pi\) | |||||||
\(620\) | −6.93017 | −0.278322 | ||||||||
\(621\) | −21.4507 | −0.860786 | ||||||||
\(622\) | 4.28666 | 0.171879 | ||||||||
\(623\) | −1.49384 | −0.0598495 | ||||||||
\(624\) | 2.09346 | 0.0838055 | ||||||||
\(625\) | 20.2004 | 0.808017 | ||||||||
\(626\) | −33.4196 | −1.33572 | ||||||||
\(627\) | −33.5071 | −1.33815 | ||||||||
\(628\) | −42.3608 | −1.69038 | ||||||||
\(629\) | −34.5286 | −1.37675 | ||||||||
\(630\) | 6.80713 | 0.271203 | ||||||||
\(631\) | 25.7618 | 1.02556 | 0.512780 | − | 0.858520i | \(-0.328616\pi\) | ||||
0.512780 | + | 0.858520i | \(0.328616\pi\) | |||||||
\(632\) | −42.8753 | −1.70549 | ||||||||
\(633\) | 79.9882 | 3.17924 | ||||||||
\(634\) | 34.8480 | 1.38399 | ||||||||
\(635\) | −4.64201 | −0.184212 | ||||||||
\(636\) | −8.18904 | −0.324717 | ||||||||
\(637\) | −6.04123 | −0.239362 | ||||||||
\(638\) | 16.4837 | 0.652595 | ||||||||
\(639\) | −38.4230 | −1.51999 | ||||||||
\(640\) | 11.2137 | 0.443260 | ||||||||
\(641\) | −10.9491 | −0.432462 | −0.216231 | − | 0.976342i | \(-0.569376\pi\) | ||||
−0.216231 | + | 0.976342i | \(0.569376\pi\) | |||||||
\(642\) | −30.9100 | −1.21992 | ||||||||
\(643\) | 26.4676 | 1.04378 | 0.521890 | − | 0.853013i | \(-0.325227\pi\) | ||||
0.521890 | + | 0.853013i | \(0.325227\pi\) | |||||||
\(644\) | 11.1200 | 0.438189 | ||||||||
\(645\) | −7.37195 | −0.290270 | ||||||||
\(646\) | −53.6874 | −2.11230 | ||||||||
\(647\) | −17.7380 | −0.697351 | −0.348676 | − | 0.937243i | \(-0.613369\pi\) | ||||
−0.348676 | + | 0.937243i | \(0.613369\pi\) | |||||||
\(648\) | −8.71240 | −0.342255 | ||||||||
\(649\) | −29.2290 | −1.14734 | ||||||||
\(650\) | 10.8524 | 0.425668 | ||||||||
\(651\) | 10.0321 | 0.393189 | ||||||||
\(652\) | 50.7072 | 1.98585 | ||||||||
\(653\) | 13.2646 | 0.519083 | 0.259541 | − | 0.965732i | \(-0.416429\pi\) | ||||
0.259541 | + | 0.965732i | \(0.416429\pi\) | |||||||
\(654\) | −58.2919 | −2.27939 | ||||||||
\(655\) | 2.21573 | 0.0865756 | ||||||||
\(656\) | 7.79491 | 0.304340 | ||||||||
\(657\) | −33.5721 | −1.30977 | ||||||||
\(658\) | −19.9809 | −0.778935 | ||||||||
\(659\) | 1.22113 | 0.0475686 | 0.0237843 | − | 0.999717i | \(-0.492429\pi\) | ||||
0.0237843 | + | 0.999717i | \(0.492429\pi\) | |||||||
\(660\) | 13.1228 | 0.510804 | ||||||||
\(661\) | −0.861660 | −0.0335147 | −0.0167574 | − | 0.999860i | \(-0.505334\pi\) | ||||
−0.0167574 | + | 0.999860i | \(0.505334\pi\) | |||||||
\(662\) | −11.9406 | −0.464083 | ||||||||
\(663\) | −13.3848 | −0.519822 | ||||||||
\(664\) | −9.31158 | −0.361359 | ||||||||
\(665\) | 2.77537 | 0.107624 | ||||||||
\(666\) | −89.9775 | −3.48656 | ||||||||
\(667\) | 10.0804 | 0.390316 | ||||||||
\(668\) | −17.7164 | −0.685467 | ||||||||
\(669\) | 15.7936 | 0.610615 | ||||||||
\(670\) | −1.28943 | −0.0498150 | ||||||||
\(671\) | −8.78458 | −0.339125 | ||||||||
\(672\) | −13.4273 | −0.517971 | ||||||||
\(673\) | 6.65418 | 0.256500 | 0.128250 | − | 0.991742i | \(-0.459064\pi\) | ||||
0.128250 | + | 0.991742i | \(0.459064\pi\) | |||||||
\(674\) | −38.1873 | −1.47092 | ||||||||
\(675\) | −29.9534 | −1.15291 | ||||||||
\(676\) | 3.39365 | 0.130525 | ||||||||
\(677\) | −37.9495 | −1.45852 | −0.729258 | − | 0.684238i | \(-0.760135\pi\) | ||||
−0.729258 | + | 0.684238i | \(0.760135\pi\) | |||||||
\(678\) | 61.5220 | 2.36274 | ||||||||
\(679\) | −0.349019 | −0.0133941 | ||||||||
\(680\) | 8.63472 | 0.331126 | ||||||||
\(681\) | 72.5377 | 2.77965 | ||||||||
\(682\) | 19.5384 | 0.748164 | ||||||||
\(683\) | 18.2028 | 0.696511 | 0.348256 | − | 0.937400i | \(-0.386774\pi\) | ||||
0.348256 | + | 0.937400i | \(0.386774\pi\) | |||||||
\(684\) | −88.0261 | −3.36576 | ||||||||
\(685\) | 0.978160 | 0.0373736 | ||||||||
\(686\) | −29.6563 | −1.13228 | ||||||||
\(687\) | 43.0335 | 1.64183 | ||||||||
\(688\) | −3.27717 | −0.124941 | ||||||||
\(689\) | −0.840938 | −0.0320372 | ||||||||
\(690\) | 12.7546 | 0.485560 | ||||||||
\(691\) | −14.4140 | −0.548335 | −0.274168 | − | 0.961682i | \(-0.588402\pi\) | ||||
−0.274168 | + | 0.961682i | \(0.588402\pi\) | |||||||
\(692\) | −59.7054 | −2.26966 | ||||||||
\(693\) | −12.0752 | −0.458698 | ||||||||
\(694\) | 76.3924 | 2.89982 | ||||||||
\(695\) | 4.74790 | 0.180098 | ||||||||
\(696\) | 27.9767 | 1.06045 | ||||||||
\(697\) | −49.8377 | −1.88774 | ||||||||
\(698\) | 39.0064 | 1.47641 | ||||||||
\(699\) | −32.9567 | −1.24654 | ||||||||
\(700\) | 15.5278 | 0.586895 | ||||||||
\(701\) | 8.09220 | 0.305638 | 0.152819 | − | 0.988254i | \(-0.451165\pi\) | ||||
0.152819 | + | 0.988254i | \(0.451165\pi\) | |||||||
\(702\) | −14.8868 | −0.561866 | ||||||||
\(703\) | −36.6852 | −1.38361 | ||||||||
\(704\) | −29.5889 | −1.11517 | ||||||||
\(705\) | −14.4199 | −0.543084 | ||||||||
\(706\) | 56.7626 | 2.13629 | ||||||||
\(707\) | 11.8695 | 0.446400 | ||||||||
\(708\) | −120.801 | −4.53997 | ||||||||
\(709\) | −13.8050 | −0.518459 | −0.259230 | − | 0.965816i | \(-0.583469\pi\) | ||||
−0.259230 | + | 0.965816i | \(0.583469\pi\) | |||||||
\(710\) | 9.75108 | 0.365952 | ||||||||
\(711\) | 69.3322 | 2.60016 | ||||||||
\(712\) | −4.93791 | −0.185056 | ||||||||
\(713\) | 11.9485 | 0.447476 | ||||||||
\(714\) | −30.4376 | −1.13910 | ||||||||
\(715\) | 1.34759 | 0.0503969 | ||||||||
\(716\) | −20.5156 | −0.766703 | ||||||||
\(717\) | 8.52967 | 0.318546 | ||||||||
\(718\) | −79.8079 | −2.97840 | ||||||||
\(719\) | 0.573972 | 0.0214056 | 0.0107028 | − | 0.999943i | \(-0.496593\pi\) | ||||
0.0107028 | + | 0.999943i | \(0.496593\pi\) | |||||||
\(720\) | 2.18388 | 0.0813884 | ||||||||
\(721\) | 5.11067 | 0.190331 | ||||||||
\(722\) | −12.9145 | −0.480627 | ||||||||
\(723\) | 47.7214 | 1.77478 | ||||||||
\(724\) | −52.5561 | −1.95323 | ||||||||
\(725\) | 14.0762 | 0.522776 | ||||||||
\(726\) | 36.3080 | 1.34752 | ||||||||
\(727\) | −7.89664 | −0.292870 | −0.146435 | − | 0.989220i | \(-0.546780\pi\) | ||||
−0.146435 | + | 0.989220i | \(0.546780\pi\) | |||||||
\(728\) | 3.16922 | 0.117459 | ||||||||
\(729\) | −41.0917 | −1.52192 | ||||||||
\(730\) | 8.52001 | 0.315340 | ||||||||
\(731\) | 20.9530 | 0.774976 | ||||||||
\(732\) | −36.3058 | −1.34190 | ||||||||
\(733\) | −52.5363 | −1.94047 | −0.970236 | − | 0.242161i | \(-0.922144\pi\) | ||||
−0.970236 | + | 0.242161i | \(0.922144\pi\) | |||||||
\(734\) | −67.2089 | −2.48073 | ||||||||
\(735\) | −9.91450 | −0.365702 | ||||||||
\(736\) | −15.9924 | −0.589486 | ||||||||
\(737\) | 2.28732 | 0.0842545 | ||||||||
\(738\) | −129.871 | −4.78062 | ||||||||
\(739\) | 24.8907 | 0.915621 | 0.457810 | − | 0.889050i | \(-0.348634\pi\) | ||||
0.457810 | + | 0.889050i | \(0.348634\pi\) | |||||||
\(740\) | 14.3675 | 0.528158 | ||||||||
\(741\) | −14.2208 | −0.522413 | ||||||||
\(742\) | −1.91233 | −0.0702037 | ||||||||
\(743\) | −45.6196 | −1.67362 | −0.836810 | − | 0.547494i | \(-0.815582\pi\) | ||||
−0.836810 | + | 0.547494i | \(0.815582\pi\) | |||||||
\(744\) | 33.1613 | 1.21575 | ||||||||
\(745\) | −3.01303 | −0.110389 | ||||||||
\(746\) | 15.3682 | 0.562669 | ||||||||
\(747\) | 15.0574 | 0.550923 | ||||||||
\(748\) | −37.2985 | −1.36377 | ||||||||
\(749\) | −4.54164 | −0.165948 | ||||||||
\(750\) | 36.8675 | 1.34621 | ||||||||
\(751\) | −36.8924 | −1.34622 | −0.673112 | − | 0.739541i | \(-0.735043\pi\) | ||||
−0.673112 | + | 0.739541i | \(0.735043\pi\) | |||||||
\(752\) | −6.41031 | −0.233760 | ||||||||
\(753\) | −24.3827 | −0.888555 | ||||||||
\(754\) | 6.99584 | 0.254774 | ||||||||
\(755\) | −0.922303 | −0.0335660 | ||||||||
\(756\) | −21.3002 | −0.774681 | ||||||||
\(757\) | 8.30946 | 0.302012 | 0.151006 | − | 0.988533i | \(-0.451749\pi\) | ||||
0.151006 | + | 0.988533i | \(0.451749\pi\) | |||||||
\(758\) | −5.66017 | −0.205587 | ||||||||
\(759\) | −22.6254 | −0.821251 | ||||||||
\(760\) | 9.17402 | 0.332777 | ||||||||
\(761\) | 17.9599 | 0.651045 | 0.325523 | − | 0.945534i | \(-0.394460\pi\) | ||||
0.325523 | + | 0.945534i | \(0.394460\pi\) | |||||||
\(762\) | 54.0886 | 1.95942 | ||||||||
\(763\) | −8.56488 | −0.310070 | ||||||||
\(764\) | −43.6811 | −1.58033 | ||||||||
\(765\) | −13.9629 | −0.504830 | ||||||||
\(766\) | −7.75999 | −0.280380 | ||||||||
\(767\) | −12.4051 | −0.447922 | ||||||||
\(768\) | −58.5932 | −2.11430 | ||||||||
\(769\) | 19.4730 | 0.702216 | 0.351108 | − | 0.936335i | \(-0.385805\pi\) | ||||
0.351108 | + | 0.936335i | \(0.385805\pi\) | |||||||
\(770\) | 3.06447 | 0.110436 | ||||||||
\(771\) | 63.2384 | 2.27748 | ||||||||
\(772\) | −2.91936 | −0.105070 | ||||||||
\(773\) | −54.8489 | −1.97278 | −0.986390 | − | 0.164424i | \(-0.947423\pi\) | ||||
−0.986390 | + | 0.164424i | \(0.947423\pi\) | |||||||
\(774\) | 54.6011 | 1.96260 | ||||||||
\(775\) | 16.6848 | 0.599334 | ||||||||
\(776\) | −1.15369 | −0.0414149 | ||||||||
\(777\) | −20.7983 | −0.746136 | ||||||||
\(778\) | −66.1044 | −2.36996 | ||||||||
\(779\) | −52.9504 | −1.89715 | ||||||||
\(780\) | 5.56945 | 0.199418 | ||||||||
\(781\) | −17.2975 | −0.618952 | ||||||||
\(782\) | −36.2520 | −1.29637 | ||||||||
\(783\) | −19.3090 | −0.690046 | ||||||||
\(784\) | −4.40746 | −0.157409 | ||||||||
\(785\) | −7.13904 | −0.254803 | ||||||||
\(786\) | −25.8176 | −0.920884 | ||||||||
\(787\) | 9.50916 | 0.338965 | 0.169482 | − | 0.985533i | \(-0.445790\pi\) | ||||
0.169482 | + | 0.985533i | \(0.445790\pi\) | |||||||
\(788\) | 72.9124 | 2.59740 | ||||||||
\(789\) | 32.3128 | 1.15036 | ||||||||
\(790\) | −17.5953 | −0.626012 | ||||||||
\(791\) | 9.03949 | 0.321407 | ||||||||
\(792\) | −39.9146 | −1.41831 | ||||||||
\(793\) | −3.72827 | −0.132395 | ||||||||
\(794\) | −61.5671 | −2.18494 | ||||||||
\(795\) | −1.38009 | −0.0489469 | ||||||||
\(796\) | 45.6565 | 1.61825 | ||||||||
\(797\) | −32.0224 | −1.13429 | −0.567146 | − | 0.823618i | \(-0.691952\pi\) | ||||
−0.567146 | + | 0.823618i | \(0.691952\pi\) | |||||||
\(798\) | −32.3386 | −1.14477 | ||||||||
\(799\) | 40.9851 | 1.44995 | ||||||||
\(800\) | −22.3315 | −0.789537 | ||||||||
\(801\) | 7.98492 | 0.282133 | ||||||||
\(802\) | −6.02032 | −0.212585 | ||||||||
\(803\) | −15.1137 | −0.533349 | ||||||||
\(804\) | 9.45327 | 0.333391 | ||||||||
\(805\) | 1.87405 | 0.0660515 | ||||||||
\(806\) | 8.29230 | 0.292084 | ||||||||
\(807\) | −29.9475 | −1.05420 | ||||||||
\(808\) | 39.2349 | 1.38028 | ||||||||
\(809\) | −3.65769 | −0.128598 | −0.0642988 | − | 0.997931i | \(-0.520481\pi\) | ||||
−0.0642988 | + | 0.997931i | \(0.520481\pi\) | |||||||
\(810\) | −3.57542 | −0.125627 | ||||||||
\(811\) | −45.3660 | −1.59302 | −0.796508 | − | 0.604628i | \(-0.793322\pi\) | ||||
−0.796508 | + | 0.604628i | \(0.793322\pi\) | |||||||
\(812\) | 10.0097 | 0.351273 | ||||||||
\(813\) | −49.7030 | −1.74316 | ||||||||
\(814\) | −40.5065 | −1.41975 | ||||||||
\(815\) | 8.54567 | 0.299342 | ||||||||
\(816\) | −9.76505 | −0.341845 | ||||||||
\(817\) | 22.2617 | 0.778838 | ||||||||
\(818\) | −63.2461 | −2.21135 | ||||||||
\(819\) | −5.12483 | −0.179076 | ||||||||
\(820\) | 20.7376 | 0.724188 | ||||||||
\(821\) | 35.6698 | 1.24489 | 0.622443 | − | 0.782665i | \(-0.286140\pi\) | ||||
0.622443 | + | 0.782665i | \(0.286140\pi\) | |||||||
\(822\) | −11.3975 | −0.397534 | ||||||||
\(823\) | −43.4128 | −1.51327 | −0.756637 | − | 0.653835i | \(-0.773159\pi\) | ||||
−0.756637 | + | 0.653835i | \(0.773159\pi\) | |||||||
\(824\) | 16.8934 | 0.588509 | ||||||||
\(825\) | −31.5938 | −1.09996 | ||||||||
\(826\) | −28.2097 | −0.981541 | ||||||||
\(827\) | 26.5291 | 0.922508 | 0.461254 | − | 0.887268i | \(-0.347400\pi\) | ||||
0.461254 | + | 0.887268i | \(0.347400\pi\) | |||||||
\(828\) | −59.4389 | −2.06565 | ||||||||
\(829\) | −50.6791 | −1.76016 | −0.880078 | − | 0.474828i | \(-0.842510\pi\) | ||||
−0.880078 | + | 0.474828i | \(0.842510\pi\) | |||||||
\(830\) | −3.82131 | −0.132640 | ||||||||
\(831\) | 24.8881 | 0.863358 | ||||||||
\(832\) | −12.5578 | −0.435365 | ||||||||
\(833\) | 28.1796 | 0.976366 | ||||||||
\(834\) | −55.3225 | −1.91566 | ||||||||
\(835\) | −2.98573 | −0.103325 | ||||||||
\(836\) | −39.6280 | −1.37056 | ||||||||
\(837\) | −22.8873 | −0.791100 | ||||||||
\(838\) | 39.9410 | 1.37974 | ||||||||
\(839\) | 11.1416 | 0.384650 | 0.192325 | − | 0.981331i | \(-0.438397\pi\) | ||||
0.192325 | + | 0.981331i | \(0.438397\pi\) | |||||||
\(840\) | 5.20112 | 0.179456 | ||||||||
\(841\) | −19.9260 | −0.687104 | ||||||||
\(842\) | 16.1197 | 0.555521 | ||||||||
\(843\) | −81.5850 | −2.80994 | ||||||||
\(844\) | 94.5999 | 3.25626 | ||||||||
\(845\) | 0.571930 | 0.0196750 | ||||||||
\(846\) | 106.802 | 3.67194 | ||||||||
\(847\) | 5.33477 | 0.183305 | ||||||||
\(848\) | −0.613517 | −0.0210682 | ||||||||
\(849\) | 58.0742 | 1.99310 | ||||||||
\(850\) | −50.6218 | −1.73631 | ||||||||
\(851\) | −24.7714 | −0.849153 | ||||||||
\(852\) | −71.4887 | −2.44916 | ||||||||
\(853\) | −11.8635 | −0.406197 | −0.203099 | − | 0.979158i | \(-0.565101\pi\) | ||||
−0.203099 | + | 0.979158i | \(0.565101\pi\) | |||||||
\(854\) | −8.47823 | −0.290119 | ||||||||
\(855\) | −14.8350 | −0.507346 | ||||||||
\(856\) | −15.0124 | −0.513115 | ||||||||
\(857\) | 17.2528 | 0.589344 | 0.294672 | − | 0.955599i | \(-0.404790\pi\) | ||||
0.294672 | + | 0.955599i | \(0.404790\pi\) | |||||||
\(858\) | −15.7021 | −0.536060 | ||||||||
\(859\) | 30.2049 | 1.03058 | 0.515288 | − | 0.857017i | \(-0.327685\pi\) | ||||
0.515288 | + | 0.857017i | \(0.327685\pi\) | |||||||
\(860\) | −8.71861 | −0.297302 | ||||||||
\(861\) | −30.0197 | −1.02307 | ||||||||
\(862\) | 87.3013 | 2.97349 | ||||||||
\(863\) | −12.4538 | −0.423933 | −0.211967 | − | 0.977277i | \(-0.567987\pi\) | ||||
−0.211967 | + | 0.977277i | \(0.567987\pi\) | |||||||
\(864\) | 30.6332 | 1.04216 | ||||||||
\(865\) | −10.0621 | −0.342123 | ||||||||
\(866\) | 64.0370 | 2.17606 | ||||||||
\(867\) | 13.6530 | 0.463681 | ||||||||
\(868\) | 11.8647 | 0.402715 | ||||||||
\(869\) | 31.2123 | 1.05881 | ||||||||
\(870\) | 11.4811 | 0.389247 | ||||||||
\(871\) | 0.970763 | 0.0328930 | ||||||||
\(872\) | −28.3113 | −0.958743 | ||||||||
\(873\) | 1.86559 | 0.0631405 | ||||||||
\(874\) | −38.5162 | −1.30283 | ||||||||
\(875\) | 5.41697 | 0.183127 | ||||||||
\(876\) | −62.4633 | −2.11044 | ||||||||
\(877\) | 53.5856 | 1.80946 | 0.904729 | − | 0.425987i | \(-0.140073\pi\) | ||||
0.904729 | + | 0.425987i | \(0.140073\pi\) | |||||||
\(878\) | −16.8587 | −0.568955 | ||||||||
\(879\) | 12.1321 | 0.409205 | ||||||||
\(880\) | 0.983150 | 0.0331420 | ||||||||
\(881\) | 8.96305 | 0.301973 | 0.150986 | − | 0.988536i | \(-0.451755\pi\) | ||||
0.150986 | + | 0.988536i | \(0.451755\pi\) | |||||||
\(882\) | 73.4328 | 2.47261 | ||||||||
\(883\) | 11.7289 | 0.394710 | 0.197355 | − | 0.980332i | \(-0.436765\pi\) | ||||
0.197355 | + | 0.980332i | \(0.436765\pi\) | |||||||
\(884\) | −15.8299 | −0.532416 | ||||||||
\(885\) | −20.3585 | −0.684343 | ||||||||
\(886\) | 37.5982 | 1.26314 | ||||||||
\(887\) | −4.40709 | −0.147975 | −0.0739877 | − | 0.997259i | \(-0.523573\pi\) | ||||
−0.0739877 | + | 0.997259i | \(0.523573\pi\) | |||||||
\(888\) | −68.7491 | −2.30707 | ||||||||
\(889\) | 7.94729 | 0.266544 | ||||||||
\(890\) | −2.02643 | −0.0679262 | ||||||||
\(891\) | 6.34244 | 0.212480 | ||||||||
\(892\) | 18.6786 | 0.625407 | ||||||||
\(893\) | 43.5449 | 1.45717 | ||||||||
\(894\) | 35.1078 | 1.17418 | ||||||||
\(895\) | −3.45748 | −0.115571 | ||||||||
\(896\) | −19.1983 | −0.641370 | ||||||||
\(897\) | −9.60247 | −0.320617 | ||||||||
\(898\) | 19.6396 | 0.655380 | ||||||||
\(899\) | 10.7555 | 0.358718 | ||||||||
\(900\) | −82.9997 | −2.76666 | ||||||||
\(901\) | 3.92260 | 0.130681 | ||||||||
\(902\) | −58.4660 | −1.94671 | ||||||||
\(903\) | 12.6211 | 0.420002 | ||||||||
\(904\) | 29.8801 | 0.993798 | ||||||||
\(905\) | −8.85726 | −0.294425 | ||||||||
\(906\) | 10.7467 | 0.357034 | ||||||||
\(907\) | −36.9735 | −1.22768 | −0.613842 | − | 0.789429i | \(-0.710377\pi\) | ||||
−0.613842 | + | 0.789429i | \(0.710377\pi\) | |||||||
\(908\) | 85.7884 | 2.84699 | ||||||||
\(909\) | −63.4454 | −2.10435 | ||||||||
\(910\) | 1.30059 | 0.0431142 | ||||||||
\(911\) | 8.83375 | 0.292675 | 0.146338 | − | 0.989235i | \(-0.453251\pi\) | ||||
0.146338 | + | 0.989235i | \(0.453251\pi\) | |||||||
\(912\) | −10.3749 | −0.343549 | ||||||||
\(913\) | 6.77863 | 0.224340 | ||||||||
\(914\) | 10.6978 | 0.353850 | ||||||||
\(915\) | −6.11860 | −0.202275 | ||||||||
\(916\) | 50.8946 | 1.68161 | ||||||||
\(917\) | −3.79341 | −0.125269 | ||||||||
\(918\) | 69.4403 | 2.29187 | ||||||||
\(919\) | −1.21791 | −0.0401750 | −0.0200875 | − | 0.999798i | \(-0.506394\pi\) | ||||
−0.0200875 | + | 0.999798i | \(0.506394\pi\) | |||||||
\(920\) | 6.19469 | 0.204233 | ||||||||
\(921\) | −74.7349 | −2.46260 | ||||||||
\(922\) | 34.0700 | 1.12203 | ||||||||
\(923\) | −7.34122 | −0.241639 | ||||||||
\(924\) | −22.4667 | −0.739101 | ||||||||
\(925\) | −34.5904 | −1.13733 | ||||||||
\(926\) | −2.32242 | −0.0763196 | ||||||||
\(927\) | −27.3177 | −0.897231 | ||||||||
\(928\) | −14.3956 | −0.472559 | ||||||||
\(929\) | −46.7273 | −1.53307 | −0.766536 | − | 0.642202i | \(-0.778021\pi\) | ||||
−0.766536 | + | 0.642202i | \(0.778021\pi\) | |||||||
\(930\) | 13.6088 | 0.446251 | ||||||||
\(931\) | 29.9396 | 0.981232 | ||||||||
\(932\) | −38.9771 | −1.27674 | ||||||||
\(933\) | −5.29638 | −0.173396 | ||||||||
\(934\) | −62.5326 | −2.04613 | ||||||||
\(935\) | −6.28589 | −0.205571 | ||||||||
\(936\) | −16.9402 | −0.553708 | ||||||||
\(937\) | 39.7903 | 1.29989 | 0.649946 | − | 0.759980i | \(-0.274791\pi\) | ||||
0.649946 | + | 0.759980i | \(0.274791\pi\) | |||||||
\(938\) | 2.20755 | 0.0720791 | ||||||||
\(939\) | 41.2916 | 1.34750 | ||||||||
\(940\) | −17.0540 | −0.556241 | ||||||||
\(941\) | −19.9305 | −0.649717 | −0.324859 | − | 0.945763i | \(-0.605317\pi\) | ||||
−0.324859 | + | 0.945763i | \(0.605317\pi\) | |||||||
\(942\) | 83.1841 | 2.71028 | ||||||||
\(943\) | −35.7544 | −1.16432 | ||||||||
\(944\) | −9.05030 | −0.294562 | ||||||||
\(945\) | −3.58972 | −0.116773 | ||||||||
\(946\) | 24.5806 | 0.799184 | ||||||||
\(947\) | 32.2991 | 1.04958 | 0.524790 | − | 0.851232i | \(-0.324144\pi\) | ||||
0.524790 | + | 0.851232i | \(0.324144\pi\) | |||||||
\(948\) | 128.997 | 4.18964 | ||||||||
\(949\) | −6.41439 | −0.208220 | ||||||||
\(950\) | −53.7834 | −1.74497 | ||||||||
\(951\) | −43.0565 | −1.39620 | ||||||||
\(952\) | −14.7830 | −0.479119 | ||||||||
\(953\) | −26.7351 | −0.866035 | −0.433017 | − | 0.901386i | \(-0.642551\pi\) | ||||
−0.433017 | + | 0.901386i | \(0.642551\pi\) | |||||||
\(954\) | 10.2218 | 0.330944 | ||||||||
\(955\) | −7.36155 | −0.238214 | ||||||||
\(956\) | 10.0878 | 0.326264 | ||||||||
\(957\) | −20.3664 | −0.658353 | ||||||||
\(958\) | −34.7999 | −1.12433 | ||||||||
\(959\) | −1.67465 | −0.0540772 | ||||||||
\(960\) | −20.6092 | −0.665158 | ||||||||
\(961\) | −18.2513 | −0.588750 | ||||||||
\(962\) | −17.1914 | −0.554273 | ||||||||
\(963\) | 24.2761 | 0.782287 | ||||||||
\(964\) | 56.4388 | 1.81777 | ||||||||
\(965\) | −0.491998 | −0.0158380 | ||||||||
\(966\) | −21.8364 | −0.702574 | ||||||||
\(967\) | 26.6867 | 0.858186 | 0.429093 | − | 0.903260i | \(-0.358833\pi\) | ||||
0.429093 | + | 0.903260i | \(0.358833\pi\) | |||||||
\(968\) | 17.6341 | 0.566783 | ||||||||
\(969\) | 66.3335 | 2.13094 | ||||||||
\(970\) | −0.473453 | −0.0152017 | ||||||||
\(971\) | −17.5028 | −0.561692 | −0.280846 | − | 0.959753i | \(-0.590615\pi\) | ||||
−0.280846 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(972\) | −39.0475 | −1.25245 | ||||||||
\(973\) | −8.12858 | −0.260590 | ||||||||
\(974\) | 29.4503 | 0.943649 | ||||||||
\(975\) | −13.4087 | −0.429424 | ||||||||
\(976\) | −2.72001 | −0.0870652 | ||||||||
\(977\) | −5.03697 | −0.161147 | −0.0805734 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805734 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(978\) | −99.5741 | −3.18403 | ||||||||
\(979\) | 3.59469 | 0.114887 | ||||||||
\(980\) | −11.7256 | −0.374561 | ||||||||
\(981\) | 45.7813 | 1.46168 | ||||||||
\(982\) | 68.6991 | 2.19228 | ||||||||
\(983\) | 3.41467 | 0.108911 | 0.0544555 | − | 0.998516i | \(-0.482658\pi\) | ||||
0.0544555 | + | 0.998516i | \(0.482658\pi\) | |||||||
\(984\) | −99.2306 | −3.16336 | ||||||||
\(985\) | 12.2879 | 0.391525 | ||||||||
\(986\) | −32.6325 | −1.03923 | ||||||||
\(987\) | 24.6874 | 0.785808 | ||||||||
\(988\) | −16.8185 | −0.535069 | ||||||||
\(989\) | 15.0320 | 0.477991 | ||||||||
\(990\) | −16.3803 | −0.520600 | ||||||||
\(991\) | −28.2617 | −0.897761 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(992\) | −17.0634 | −0.541763 | ||||||||
\(993\) | 14.7532 | 0.468177 | ||||||||
\(994\) | −16.6942 | −0.529509 | ||||||||
\(995\) | 7.69448 | 0.243931 | ||||||||
\(996\) | 28.0154 | 0.887703 | ||||||||
\(997\) | 21.7739 | 0.689587 | 0.344793 | − | 0.938679i | \(-0.387949\pi\) | ||||
0.344793 | + | 0.938679i | \(0.387949\pi\) | |||||||
\(998\) | 30.7166 | 0.972317 | ||||||||
\(999\) | 47.4493 | 1.50123 |
(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 | 6019.2.a.b.1.12 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.b.1.12 | ✓ | 101 | 1.1 | even | 1 | trivial |