Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, 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("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.723996 | −0.511942 | −0.255971 | − | 0.966684i | \(-0.582395\pi\) | ||||
−0.255971 | + | 0.966684i | \(0.582395\pi\) | |||||||
\(3\) | 3.01745 | 1.74212 | 0.871062 | − | 0.491173i | \(-0.163432\pi\) | ||||
0.871062 | + | 0.491173i | \(0.163432\pi\) | |||||||
\(4\) | −1.47583 | −0.737915 | ||||||||
\(5\) | −2.02994 | −0.907815 | −0.453908 | − | 0.891049i | \(-0.649970\pi\) | ||||
−0.453908 | + | 0.891049i | \(0.649970\pi\) | |||||||
\(6\) | −2.18462 | −0.891867 | ||||||||
\(7\) | −2.86695 | −1.08361 | −0.541803 | − | 0.840505i | \(-0.682258\pi\) | ||||
−0.541803 | + | 0.840505i | \(0.682258\pi\) | |||||||
\(8\) | 2.51649 | 0.889712 | ||||||||
\(9\) | 6.10499 | 2.03500 | ||||||||
\(10\) | 1.46966 | 0.464749 | ||||||||
\(11\) | −5.18357 | −1.56291 | −0.781453 | − | 0.623964i | \(-0.785521\pi\) | ||||
−0.781453 | + | 0.623964i | \(0.785521\pi\) | |||||||
\(12\) | −4.45324 | −1.28554 | ||||||||
\(13\) | −4.90825 | −1.36130 | −0.680652 | − | 0.732607i | \(-0.738303\pi\) | ||||
−0.680652 | + | 0.732607i | \(0.738303\pi\) | |||||||
\(14\) | 2.07566 | 0.554744 | ||||||||
\(15\) | −6.12522 | −1.58153 | ||||||||
\(16\) | 1.12974 | 0.282434 | ||||||||
\(17\) | 7.18967 | 1.74375 | 0.871875 | − | 0.489728i | \(-0.162904\pi\) | ||||
0.871875 | + | 0.489728i | \(0.162904\pi\) | |||||||
\(18\) | −4.41998 | −1.04180 | ||||||||
\(19\) | −2.17482 | −0.498938 | −0.249469 | − | 0.968383i | \(-0.580256\pi\) | ||||
−0.249469 | + | 0.968383i | \(0.580256\pi\) | |||||||
\(20\) | 2.99584 | 0.669890 | ||||||||
\(21\) | −8.65088 | −1.88778 | ||||||||
\(22\) | 3.75288 | 0.800118 | ||||||||
\(23\) | −7.89290 | −1.64578 | −0.822892 | − | 0.568198i | \(-0.807641\pi\) | ||||
−0.822892 | + | 0.568198i | \(0.807641\pi\) | |||||||
\(24\) | 7.59336 | 1.54999 | ||||||||
\(25\) | −0.879360 | −0.175872 | ||||||||
\(26\) | 3.55355 | 0.696909 | ||||||||
\(27\) | 9.36913 | 1.80309 | ||||||||
\(28\) | 4.23113 | 0.799609 | ||||||||
\(29\) | −7.73709 | −1.43674 | −0.718370 | − | 0.695661i | \(-0.755112\pi\) | ||||
−0.718370 | + | 0.695661i | \(0.755112\pi\) | |||||||
\(30\) | 4.43464 | 0.809650 | ||||||||
\(31\) | 4.00031 | 0.718477 | 0.359238 | − | 0.933246i | \(-0.383037\pi\) | ||||
0.359238 | + | 0.933246i | \(0.383037\pi\) | |||||||
\(32\) | −5.85090 | −1.03430 | ||||||||
\(33\) | −15.6412 | −2.72278 | ||||||||
\(34\) | −5.20529 | −0.892700 | ||||||||
\(35\) | 5.81973 | 0.983714 | ||||||||
\(36\) | −9.00992 | −1.50165 | ||||||||
\(37\) | −9.16541 | −1.50678 | −0.753392 | − | 0.657572i | \(-0.771584\pi\) | ||||
−0.753392 | + | 0.657572i | \(0.771584\pi\) | |||||||
\(38\) | 1.57456 | 0.255427 | ||||||||
\(39\) | −14.8104 | −2.37156 | ||||||||
\(40\) | −5.10831 | −0.807694 | ||||||||
\(41\) | 3.94489 | 0.616088 | 0.308044 | − | 0.951372i | \(-0.400326\pi\) | ||||
0.308044 | + | 0.951372i | \(0.400326\pi\) | |||||||
\(42\) | 6.26320 | 0.966432 | ||||||||
\(43\) | 7.18177 | 1.09521 | 0.547605 | − | 0.836737i | \(-0.315540\pi\) | ||||
0.547605 | + | 0.836737i | \(0.315540\pi\) | |||||||
\(44\) | 7.65007 | 1.15329 | ||||||||
\(45\) | −12.3927 | −1.84740 | ||||||||
\(46\) | 5.71442 | 0.842546 | ||||||||
\(47\) | 3.57199 | 0.521028 | 0.260514 | − | 0.965470i | \(-0.416108\pi\) | ||||
0.260514 | + | 0.965470i | \(0.416108\pi\) | |||||||
\(48\) | 3.40892 | 0.492035 | ||||||||
\(49\) | 1.21942 | 0.174202 | ||||||||
\(50\) | 0.636652 | 0.0900363 | ||||||||
\(51\) | 21.6944 | 3.03783 | ||||||||
\(52\) | 7.24375 | 1.00453 | ||||||||
\(53\) | 4.73766 | 0.650768 | 0.325384 | − | 0.945582i | \(-0.394506\pi\) | ||||
0.325384 | + | 0.945582i | \(0.394506\pi\) | |||||||
\(54\) | −6.78321 | −0.923078 | ||||||||
\(55\) | 10.5223 | 1.41883 | ||||||||
\(56\) | −7.21465 | −0.964098 | ||||||||
\(57\) | −6.56241 | −0.869212 | ||||||||
\(58\) | 5.60162 | 0.735528 | ||||||||
\(59\) | −8.30292 | −1.08095 | −0.540474 | − | 0.841361i | \(-0.681755\pi\) | ||||
−0.540474 | + | 0.841361i | \(0.681755\pi\) | |||||||
\(60\) | 9.03979 | 1.16703 | ||||||||
\(61\) | 1.43844 | 0.184173 | 0.0920865 | − | 0.995751i | \(-0.470646\pi\) | ||||
0.0920865 | + | 0.995751i | \(0.470646\pi\) | |||||||
\(62\) | −2.89621 | −0.367818 | ||||||||
\(63\) | −17.5027 | −2.20513 | ||||||||
\(64\) | 1.97655 | 0.247069 | ||||||||
\(65\) | 9.96344 | 1.23581 | ||||||||
\(66\) | 11.3241 | 1.39390 | ||||||||
\(67\) | 10.0813 | 1.23163 | 0.615814 | − | 0.787891i | \(-0.288827\pi\) | ||||
0.615814 | + | 0.787891i | \(0.288827\pi\) | |||||||
\(68\) | −10.6107 | −1.28674 | ||||||||
\(69\) | −23.8164 | −2.86716 | ||||||||
\(70\) | −4.21346 | −0.503605 | ||||||||
\(71\) | 6.02509 | 0.715046 | 0.357523 | − | 0.933904i | \(-0.383621\pi\) | ||||
0.357523 | + | 0.933904i | \(0.383621\pi\) | |||||||
\(72\) | 15.3631 | 1.81056 | ||||||||
\(73\) | −2.63460 | −0.308356 | −0.154178 | − | 0.988043i | \(-0.549273\pi\) | ||||
−0.154178 | + | 0.988043i | \(0.549273\pi\) | |||||||
\(74\) | 6.63571 | 0.771386 | ||||||||
\(75\) | −2.65342 | −0.306391 | ||||||||
\(76\) | 3.20967 | 0.368174 | ||||||||
\(77\) | 14.8611 | 1.69357 | ||||||||
\(78\) | 10.7227 | 1.21410 | ||||||||
\(79\) | 14.9656 | 1.68376 | 0.841880 | − | 0.539665i | \(-0.181449\pi\) | ||||
0.841880 | + | 0.539665i | \(0.181449\pi\) | |||||||
\(80\) | −2.29329 | −0.256398 | ||||||||
\(81\) | 9.95591 | 1.10621 | ||||||||
\(82\) | −2.85608 | −0.315402 | ||||||||
\(83\) | −9.64957 | −1.05918 | −0.529589 | − | 0.848255i | \(-0.677654\pi\) | ||||
−0.529589 | + | 0.848255i | \(0.677654\pi\) | |||||||
\(84\) | 12.7672 | 1.39302 | ||||||||
\(85\) | −14.5946 | −1.58300 | ||||||||
\(86\) | −5.19957 | −0.560684 | ||||||||
\(87\) | −23.3462 | −2.50298 | ||||||||
\(88\) | −13.0444 | −1.39054 | ||||||||
\(89\) | −6.74228 | −0.714680 | −0.357340 | − | 0.933974i | \(-0.616316\pi\) | ||||
−0.357340 | + | 0.933974i | \(0.616316\pi\) | |||||||
\(90\) | 8.97229 | 0.945762 | ||||||||
\(91\) | 14.0717 | 1.47512 | ||||||||
\(92\) | 11.6486 | 1.21445 | ||||||||
\(93\) | 12.0707 | 1.25168 | ||||||||
\(94\) | −2.58610 | −0.266736 | ||||||||
\(95\) | 4.41475 | 0.452943 | ||||||||
\(96\) | −17.6548 | −1.80188 | ||||||||
\(97\) | 2.43425 | 0.247161 | 0.123580 | − | 0.992335i | \(-0.460562\pi\) | ||||
0.123580 | + | 0.992335i | \(0.460562\pi\) | |||||||
\(98\) | −0.882851 | −0.0891814 | ||||||||
\(99\) | −31.6456 | −3.18051 | ||||||||
\(100\) | 1.29779 | 0.129779 | ||||||||
\(101\) | −5.04301 | −0.501798 | −0.250899 | − | 0.968013i | \(-0.580726\pi\) | ||||
−0.250899 | + | 0.968013i | \(0.580726\pi\) | |||||||
\(102\) | −15.7067 | −1.55519 | ||||||||
\(103\) | 3.31694 | 0.326828 | 0.163414 | − | 0.986558i | \(-0.447749\pi\) | ||||
0.163414 | + | 0.986558i | \(0.447749\pi\) | |||||||
\(104\) | −12.3515 | −1.21117 | ||||||||
\(105\) | 17.5607 | 1.71375 | ||||||||
\(106\) | −3.43005 | −0.333155 | ||||||||
\(107\) | −7.73295 | −0.747573 | −0.373786 | − | 0.927515i | \(-0.621941\pi\) | ||||
−0.373786 | + | 0.927515i | \(0.621941\pi\) | |||||||
\(108\) | −13.8273 | −1.33053 | ||||||||
\(109\) | −4.04022 | −0.386983 | −0.193491 | − | 0.981102i | \(-0.561981\pi\) | ||||
−0.193491 | + | 0.981102i | \(0.561981\pi\) | |||||||
\(110\) | −7.61812 | −0.726359 | ||||||||
\(111\) | −27.6561 | −2.62500 | ||||||||
\(112\) | −3.23890 | −0.306047 | ||||||||
\(113\) | −12.4332 | −1.16961 | −0.584807 | − | 0.811173i | \(-0.698830\pi\) | ||||
−0.584807 | + | 0.811173i | \(0.698830\pi\) | |||||||
\(114\) | 4.75115 | 0.444986 | ||||||||
\(115\) | 16.0221 | 1.49407 | ||||||||
\(116\) | 11.4186 | 1.06019 | ||||||||
\(117\) | −29.9648 | −2.77025 | ||||||||
\(118\) | 6.01128 | 0.553383 | ||||||||
\(119\) | −20.6124 | −1.88954 | ||||||||
\(120\) | −15.4140 | −1.40710 | ||||||||
\(121\) | 15.8694 | 1.44268 | ||||||||
\(122\) | −1.04142 | −0.0942859 | ||||||||
\(123\) | 11.9035 | 1.07330 | ||||||||
\(124\) | −5.90378 | −0.530175 | ||||||||
\(125\) | 11.9347 | 1.06747 | ||||||||
\(126\) | 12.6719 | 1.12890 | ||||||||
\(127\) | 5.40366 | 0.479498 | 0.239749 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239749 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(128\) | 10.2708 | 0.907817 | ||||||||
\(129\) | 21.6706 | 1.90799 | ||||||||
\(130\) | −7.21349 | −0.632665 | ||||||||
\(131\) | −6.97739 | −0.609618 | −0.304809 | − | 0.952414i | \(-0.598593\pi\) | ||||
−0.304809 | + | 0.952414i | \(0.598593\pi\) | |||||||
\(132\) | 23.0837 | 2.00918 | ||||||||
\(133\) | 6.23511 | 0.540652 | ||||||||
\(134\) | −7.29883 | −0.630523 | ||||||||
\(135\) | −19.0187 | −1.63687 | ||||||||
\(136\) | 18.0927 | 1.55144 | ||||||||
\(137\) | 10.6937 | 0.913625 | 0.456812 | − | 0.889563i | \(-0.348991\pi\) | ||||
0.456812 | + | 0.889563i | \(0.348991\pi\) | |||||||
\(138\) | 17.2430 | 1.46782 | ||||||||
\(139\) | −1.23971 | −0.105151 | −0.0525756 | − | 0.998617i | \(-0.516743\pi\) | ||||
−0.0525756 | + | 0.998617i | \(0.516743\pi\) | |||||||
\(140\) | −8.58893 | −0.725897 | ||||||||
\(141\) | 10.7783 | 0.907695 | ||||||||
\(142\) | −4.36214 | −0.366062 | ||||||||
\(143\) | 25.4423 | 2.12759 | ||||||||
\(144\) | 6.89702 | 0.574752 | ||||||||
\(145\) | 15.7058 | 1.30429 | ||||||||
\(146\) | 1.90744 | 0.157861 | ||||||||
\(147\) | 3.67952 | 0.303482 | ||||||||
\(148\) | 13.5266 | 1.11188 | ||||||||
\(149\) | −16.2201 | −1.32880 | −0.664402 | − | 0.747375i | \(-0.731314\pi\) | ||||
−0.664402 | + | 0.747375i | \(0.731314\pi\) | |||||||
\(150\) | 1.92107 | 0.156854 | ||||||||
\(151\) | 2.09958 | 0.170861 | 0.0854306 | − | 0.996344i | \(-0.472773\pi\) | ||||
0.0854306 | + | 0.996344i | \(0.472773\pi\) | |||||||
\(152\) | −5.47291 | −0.443911 | ||||||||
\(153\) | 43.8928 | 3.54852 | ||||||||
\(154\) | −10.7593 | −0.867012 | ||||||||
\(155\) | −8.12037 | −0.652244 | ||||||||
\(156\) | 21.8576 | 1.75001 | ||||||||
\(157\) | −2.50097 | −0.199599 | −0.0997995 | − | 0.995008i | \(-0.531820\pi\) | ||||
−0.0997995 | + | 0.995008i | \(0.531820\pi\) | |||||||
\(158\) | −10.8350 | −0.861988 | ||||||||
\(159\) | 14.2956 | 1.13372 | ||||||||
\(160\) | 11.8769 | 0.938955 | ||||||||
\(161\) | 22.6286 | 1.78338 | ||||||||
\(162\) | −7.20803 | −0.566317 | ||||||||
\(163\) | 0.785063 | 0.0614909 | 0.0307454 | − | 0.999527i | \(-0.490212\pi\) | ||||
0.0307454 | + | 0.999527i | \(0.490212\pi\) | |||||||
\(164\) | −5.82199 | −0.454621 | ||||||||
\(165\) | 31.7506 | 2.47178 | ||||||||
\(166\) | 6.98624 | 0.542238 | ||||||||
\(167\) | −21.4744 | −1.66174 | −0.830869 | − | 0.556468i | \(-0.812156\pi\) | ||||
−0.830869 | + | 0.556468i | \(0.812156\pi\) | |||||||
\(168\) | −21.7698 | −1.67958 | ||||||||
\(169\) | 11.0909 | 0.853149 | ||||||||
\(170\) | 10.5664 | 0.810406 | ||||||||
\(171\) | −13.2773 | −1.01534 | ||||||||
\(172\) | −10.5991 | −0.808171 | ||||||||
\(173\) | −15.8400 | −1.20429 | −0.602145 | − | 0.798387i | \(-0.705687\pi\) | ||||
−0.602145 | + | 0.798387i | \(0.705687\pi\) | |||||||
\(174\) | 16.9026 | 1.28138 | ||||||||
\(175\) | 2.52108 | 0.190576 | ||||||||
\(176\) | −5.85607 | −0.441418 | ||||||||
\(177\) | −25.0536 | −1.88315 | ||||||||
\(178\) | 4.88138 | 0.365875 | ||||||||
\(179\) | 18.1996 | 1.36031 | 0.680153 | − | 0.733071i | \(-0.261914\pi\) | ||||
0.680153 | + | 0.733071i | \(0.261914\pi\) | |||||||
\(180\) | 18.2896 | 1.36322 | ||||||||
\(181\) | 11.9843 | 0.890784 | 0.445392 | − | 0.895336i | \(-0.353064\pi\) | ||||
0.445392 | + | 0.895336i | \(0.353064\pi\) | |||||||
\(182\) | −10.1879 | −0.755175 | ||||||||
\(183\) | 4.34041 | 0.320852 | ||||||||
\(184\) | −19.8624 | −1.46427 | ||||||||
\(185\) | 18.6052 | 1.36788 | ||||||||
\(186\) | −8.73915 | −0.640785 | ||||||||
\(187\) | −37.2682 | −2.72532 | ||||||||
\(188\) | −5.27164 | −0.384474 | ||||||||
\(189\) | −26.8609 | −1.95384 | ||||||||
\(190\) | −3.19626 | −0.231881 | ||||||||
\(191\) | 25.2836 | 1.82946 | 0.914728 | − | 0.404071i | \(-0.132405\pi\) | ||||
0.914728 | + | 0.404071i | \(0.132405\pi\) | |||||||
\(192\) | 5.96414 | 0.430425 | ||||||||
\(193\) | −3.69290 | −0.265821 | −0.132910 | − | 0.991128i | \(-0.542432\pi\) | ||||
−0.132910 | + | 0.991128i | \(0.542432\pi\) | |||||||
\(194\) | −1.76239 | −0.126532 | ||||||||
\(195\) | 30.0641 | 2.15294 | ||||||||
\(196\) | −1.79965 | −0.128546 | ||||||||
\(197\) | 7.91038 | 0.563592 | 0.281796 | − | 0.959474i | \(-0.409070\pi\) | ||||
0.281796 | + | 0.959474i | \(0.409070\pi\) | |||||||
\(198\) | 22.9113 | 1.62824 | ||||||||
\(199\) | 3.74720 | 0.265632 | 0.132816 | − | 0.991141i | \(-0.457598\pi\) | ||||
0.132816 | + | 0.991141i | \(0.457598\pi\) | |||||||
\(200\) | −2.21290 | −0.156475 | ||||||||
\(201\) | 30.4198 | 2.14565 | ||||||||
\(202\) | 3.65112 | 0.256892 | ||||||||
\(203\) | 22.1819 | 1.55686 | ||||||||
\(204\) | −32.0173 | −2.24166 | ||||||||
\(205\) | −8.00787 | −0.559294 | ||||||||
\(206\) | −2.40145 | −0.167317 | ||||||||
\(207\) | −48.1860 | −3.34916 | ||||||||
\(208\) | −5.54503 | −0.384478 | ||||||||
\(209\) | 11.2733 | 0.779793 | ||||||||
\(210\) | −12.7139 | −0.877342 | ||||||||
\(211\) | −23.8535 | −1.64214 | −0.821072 | − | 0.570825i | \(-0.806623\pi\) | ||||
−0.821072 | + | 0.570825i | \(0.806623\pi\) | |||||||
\(212\) | −6.99198 | −0.480211 | ||||||||
\(213\) | 18.1804 | 1.24570 | ||||||||
\(214\) | 5.59863 | 0.382714 | ||||||||
\(215\) | −14.5785 | −0.994247 | ||||||||
\(216\) | 23.5773 | 1.60423 | ||||||||
\(217\) | −11.4687 | −0.778546 | ||||||||
\(218\) | 2.92510 | 0.198113 | ||||||||
\(219\) | −7.94976 | −0.537195 | ||||||||
\(220\) | −15.5292 | −1.04698 | ||||||||
\(221\) | −35.2887 | −2.37378 | ||||||||
\(222\) | 20.0229 | 1.34385 | ||||||||
\(223\) | −4.04669 | −0.270986 | −0.135493 | − | 0.990778i | \(-0.543262\pi\) | ||||
−0.135493 | + | 0.990778i | \(0.543262\pi\) | |||||||
\(224\) | 16.7742 | 1.12078 | ||||||||
\(225\) | −5.36848 | −0.357899 | ||||||||
\(226\) | 9.00156 | 0.598775 | ||||||||
\(227\) | −18.5395 | −1.23051 | −0.615256 | − | 0.788328i | \(-0.710947\pi\) | ||||
−0.615256 | + | 0.788328i | \(0.710947\pi\) | |||||||
\(228\) | 9.68500 | 0.641405 | ||||||||
\(229\) | −8.56190 | −0.565786 | −0.282893 | − | 0.959151i | \(-0.591294\pi\) | ||||
−0.282893 | + | 0.959151i | \(0.591294\pi\) | |||||||
\(230\) | −11.5999 | −0.764876 | ||||||||
\(231\) | 44.8425 | 2.95042 | ||||||||
\(232\) | −19.4703 | −1.27829 | ||||||||
\(233\) | −24.0792 | −1.57748 | −0.788739 | − | 0.614728i | \(-0.789266\pi\) | ||||
−0.788739 | + | 0.614728i | \(0.789266\pi\) | |||||||
\(234\) | 21.6944 | 1.41821 | ||||||||
\(235\) | −7.25090 | −0.472997 | ||||||||
\(236\) | 12.2537 | 0.797648 | ||||||||
\(237\) | 45.1579 | 2.93332 | ||||||||
\(238\) | 14.9233 | 0.967335 | ||||||||
\(239\) | 11.4142 | 0.738322 | 0.369161 | − | 0.929366i | \(-0.379645\pi\) | ||||
0.369161 | + | 0.929366i | \(0.379645\pi\) | |||||||
\(240\) | −6.91988 | −0.446677 | ||||||||
\(241\) | 11.1865 | 0.720588 | 0.360294 | − | 0.932839i | \(-0.382676\pi\) | ||||
0.360294 | + | 0.932839i | \(0.382676\pi\) | |||||||
\(242\) | −11.4894 | −0.738567 | ||||||||
\(243\) | 1.93402 | 0.124067 | ||||||||
\(244\) | −2.12289 | −0.135904 | ||||||||
\(245\) | −2.47533 | −0.158143 | ||||||||
\(246\) | −8.61808 | −0.549469 | ||||||||
\(247\) | 10.6746 | 0.679207 | ||||||||
\(248\) | 10.0667 | 0.639237 | ||||||||
\(249\) | −29.1171 | −1.84522 | ||||||||
\(250\) | −8.64069 | −0.546485 | ||||||||
\(251\) | −7.05319 | −0.445194 | −0.222597 | − | 0.974911i | \(-0.571453\pi\) | ||||
−0.222597 | + | 0.974911i | \(0.571453\pi\) | |||||||
\(252\) | 25.8310 | 1.62720 | ||||||||
\(253\) | 40.9134 | 2.57220 | ||||||||
\(254\) | −3.91223 | −0.245475 | ||||||||
\(255\) | −44.0383 | −2.75779 | ||||||||
\(256\) | −11.3891 | −0.711819 | ||||||||
\(257\) | −4.15606 | −0.259248 | −0.129624 | − | 0.991563i | \(-0.541377\pi\) | ||||
−0.129624 | + | 0.991563i | \(0.541377\pi\) | |||||||
\(258\) | −15.6894 | −0.976781 | ||||||||
\(259\) | 26.2768 | 1.63276 | ||||||||
\(260\) | −14.7043 | −0.911925 | ||||||||
\(261\) | −47.2348 | −2.92376 | ||||||||
\(262\) | 5.05160 | 0.312089 | ||||||||
\(263\) | −4.84381 | −0.298682 | −0.149341 | − | 0.988786i | \(-0.547715\pi\) | ||||
−0.149341 | + | 0.988786i | \(0.547715\pi\) | |||||||
\(264\) | −39.3608 | −2.42249 | ||||||||
\(265\) | −9.61715 | −0.590777 | ||||||||
\(266\) | −4.51419 | −0.276783 | ||||||||
\(267\) | −20.3445 | −1.24506 | ||||||||
\(268\) | −14.8783 | −0.908837 | ||||||||
\(269\) | −21.0700 | −1.28466 | −0.642329 | − | 0.766429i | \(-0.722032\pi\) | ||||
−0.642329 | + | 0.766429i | \(0.722032\pi\) | |||||||
\(270\) | 13.7695 | 0.837984 | ||||||||
\(271\) | 13.2461 | 0.804644 | 0.402322 | − | 0.915498i | \(-0.368203\pi\) | ||||
0.402322 | + | 0.915498i | \(0.368203\pi\) | |||||||
\(272\) | 8.12242 | 0.492494 | ||||||||
\(273\) | 42.4607 | 2.56984 | ||||||||
\(274\) | −7.74220 | −0.467723 | ||||||||
\(275\) | 4.55822 | 0.274871 | ||||||||
\(276\) | 35.1490 | 2.11572 | ||||||||
\(277\) | 32.4384 | 1.94903 | 0.974516 | − | 0.224319i | \(-0.0720157\pi\) | ||||
0.974516 | + | 0.224319i | \(0.0720157\pi\) | |||||||
\(278\) | 0.897548 | 0.0538313 | ||||||||
\(279\) | 24.4218 | 1.46210 | ||||||||
\(280\) | 14.6453 | 0.875222 | ||||||||
\(281\) | −16.6018 | −0.990382 | −0.495191 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495191 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(282\) | −7.80343 | −0.464687 | ||||||||
\(283\) | 10.2724 | 0.610630 | 0.305315 | − | 0.952251i | \(-0.401238\pi\) | ||||
0.305315 | + | 0.952251i | \(0.401238\pi\) | |||||||
\(284\) | −8.89201 | −0.527643 | ||||||||
\(285\) | 13.3213 | 0.789084 | ||||||||
\(286\) | −18.4201 | −1.08920 | ||||||||
\(287\) | −11.3098 | −0.667597 | ||||||||
\(288\) | −35.7196 | −2.10480 | ||||||||
\(289\) | 34.6913 | 2.04067 | ||||||||
\(290\) | −11.3709 | −0.667724 | ||||||||
\(291\) | 7.34522 | 0.430584 | ||||||||
\(292\) | 3.88822 | 0.227541 | ||||||||
\(293\) | −16.9631 | −0.990997 | −0.495499 | − | 0.868609i | \(-0.665015\pi\) | ||||
−0.495499 | + | 0.868609i | \(0.665015\pi\) | |||||||
\(294\) | −2.66396 | −0.155365 | ||||||||
\(295\) | 16.8544 | 0.981301 | ||||||||
\(296\) | −23.0646 | −1.34060 | ||||||||
\(297\) | −48.5656 | −2.81806 | ||||||||
\(298\) | 11.7433 | 0.680271 | ||||||||
\(299\) | 38.7403 | 2.24041 | ||||||||
\(300\) | 3.91600 | 0.226090 | ||||||||
\(301\) | −20.5898 | −1.18678 | ||||||||
\(302\) | −1.52009 | −0.0874711 | ||||||||
\(303\) | −15.2170 | −0.874195 | ||||||||
\(304\) | −2.45697 | −0.140917 | ||||||||
\(305\) | −2.91993 | −0.167195 | ||||||||
\(306\) | −31.7782 | −1.81664 | ||||||||
\(307\) | −34.1607 | −1.94965 | −0.974826 | − | 0.222967i | \(-0.928426\pi\) | ||||
−0.974826 | + | 0.222967i | \(0.928426\pi\) | |||||||
\(308\) | −21.9324 | −1.24971 | ||||||||
\(309\) | 10.0087 | 0.569374 | ||||||||
\(310\) | 5.87911 | 0.333911 | ||||||||
\(311\) | 21.4133 | 1.21424 | 0.607120 | − | 0.794610i | \(-0.292325\pi\) | ||||
0.607120 | + | 0.794610i | \(0.292325\pi\) | |||||||
\(312\) | −37.2701 | −2.11001 | ||||||||
\(313\) | −15.9294 | −0.900381 | −0.450191 | − | 0.892932i | \(-0.648644\pi\) | ||||
−0.450191 | + | 0.892932i | \(0.648644\pi\) | |||||||
\(314\) | 1.81069 | 0.102183 | ||||||||
\(315\) | 35.5294 | 2.00185 | ||||||||
\(316\) | −22.0867 | −1.24247 | ||||||||
\(317\) | −4.07966 | −0.229136 | −0.114568 | − | 0.993415i | \(-0.536548\pi\) | ||||
−0.114568 | + | 0.993415i | \(0.536548\pi\) | |||||||
\(318\) | −10.3500 | −0.580398 | ||||||||
\(319\) | 40.1058 | 2.24549 | ||||||||
\(320\) | −4.01227 | −0.224293 | ||||||||
\(321\) | −23.3338 | −1.30236 | ||||||||
\(322\) | −16.3830 | −0.912988 | ||||||||
\(323\) | −15.6362 | −0.870024 | ||||||||
\(324\) | −14.6932 | −0.816290 | ||||||||
\(325\) | 4.31612 | 0.239415 | ||||||||
\(326\) | −0.568382 | −0.0314798 | ||||||||
\(327\) | −12.1912 | −0.674172 | ||||||||
\(328\) | 9.92726 | 0.548141 | ||||||||
\(329\) | −10.2407 | −0.564589 | ||||||||
\(330\) | −22.9873 | −1.26541 | ||||||||
\(331\) | −7.12795 | −0.391787 | −0.195894 | − | 0.980625i | \(-0.562761\pi\) | ||||
−0.195894 | + | 0.980625i | \(0.562761\pi\) | |||||||
\(332\) | 14.2411 | 0.781583 | ||||||||
\(333\) | −55.9547 | −3.06630 | ||||||||
\(334\) | 15.5474 | 0.850714 | ||||||||
\(335\) | −20.4644 | −1.11809 | ||||||||
\(336\) | −9.77320 | −0.533172 | ||||||||
\(337\) | −1.19451 | −0.0650689 | −0.0325345 | − | 0.999471i | \(-0.510358\pi\) | ||||
−0.0325345 | + | 0.999471i | \(0.510358\pi\) | |||||||
\(338\) | −8.02979 | −0.436763 | ||||||||
\(339\) | −37.5164 | −2.03761 | ||||||||
\(340\) | 21.5391 | 1.16812 | ||||||||
\(341\) | −20.7359 | −1.12291 | ||||||||
\(342\) | 9.61267 | 0.519794 | ||||||||
\(343\) | 16.5727 | 0.894840 | ||||||||
\(344\) | 18.0728 | 0.974421 | ||||||||
\(345\) | 48.3458 | 2.60285 | ||||||||
\(346\) | 11.4681 | 0.616527 | ||||||||
\(347\) | −8.45278 | −0.453769 | −0.226884 | − | 0.973922i | \(-0.572854\pi\) | ||||
−0.226884 | + | 0.973922i | \(0.572854\pi\) | |||||||
\(348\) | 34.4551 | 1.84699 | ||||||||
\(349\) | −18.6796 | −0.999895 | −0.499948 | − | 0.866056i | \(-0.666647\pi\) | ||||
−0.499948 | + | 0.866056i | \(0.666647\pi\) | |||||||
\(350\) | −1.82525 | −0.0975638 | ||||||||
\(351\) | −45.9861 | −2.45456 | ||||||||
\(352\) | 30.3285 | 1.61652 | ||||||||
\(353\) | 0.0957780 | 0.00509775 | 0.00254887 | − | 0.999997i | \(-0.499189\pi\) | ||||
0.00254887 | + | 0.999997i | \(0.499189\pi\) | |||||||
\(354\) | 18.1387 | 0.964062 | ||||||||
\(355\) | −12.2305 | −0.649130 | ||||||||
\(356\) | 9.95045 | 0.527373 | ||||||||
\(357\) | −62.1969 | −3.29181 | ||||||||
\(358\) | −13.1765 | −0.696398 | ||||||||
\(359\) | −34.0926 | −1.79934 | −0.899669 | − | 0.436572i | \(-0.856192\pi\) | ||||
−0.899669 | + | 0.436572i | \(0.856192\pi\) | |||||||
\(360\) | −31.1861 | −1.64365 | ||||||||
\(361\) | −14.2702 | −0.751061 | ||||||||
\(362\) | −8.67656 | −0.456030 | ||||||||
\(363\) | 47.8852 | 2.51332 | ||||||||
\(364\) | −20.7675 | −1.08851 | ||||||||
\(365\) | 5.34807 | 0.279931 | ||||||||
\(366\) | −3.14244 | −0.164258 | ||||||||
\(367\) | 20.9122 | 1.09161 | 0.545804 | − | 0.837913i | \(-0.316224\pi\) | ||||
0.545804 | + | 0.837913i | \(0.316224\pi\) | |||||||
\(368\) | −8.91689 | −0.464825 | ||||||||
\(369\) | 24.0835 | 1.25374 | ||||||||
\(370\) | −13.4701 | −0.700276 | ||||||||
\(371\) | −13.5826 | −0.705176 | ||||||||
\(372\) | −17.8143 | −0.923630 | ||||||||
\(373\) | 11.3183 | 0.586039 | 0.293020 | − | 0.956106i | \(-0.405340\pi\) | ||||
0.293020 | + | 0.956106i | \(0.405340\pi\) | |||||||
\(374\) | 26.9820 | 1.39521 | ||||||||
\(375\) | 36.0124 | 1.85967 | ||||||||
\(376\) | 8.98885 | 0.463565 | ||||||||
\(377\) | 37.9756 | 1.95584 | ||||||||
\(378\) | 19.4471 | 1.00025 | ||||||||
\(379\) | 25.6376 | 1.31691 | 0.658456 | − | 0.752619i | \(-0.271210\pi\) | ||||
0.658456 | + | 0.752619i | \(0.271210\pi\) | |||||||
\(380\) | −6.51542 | −0.334234 | ||||||||
\(381\) | 16.3053 | 0.835344 | ||||||||
\(382\) | −18.3052 | −0.936576 | ||||||||
\(383\) | −4.30051 | −0.219746 | −0.109873 | − | 0.993946i | \(-0.535044\pi\) | ||||
−0.109873 | + | 0.993946i | \(0.535044\pi\) | |||||||
\(384\) | 30.9915 | 1.58153 | ||||||||
\(385\) | −30.1670 | −1.53745 | ||||||||
\(386\) | 2.67364 | 0.136085 | ||||||||
\(387\) | 43.8446 | 2.22875 | ||||||||
\(388\) | −3.59254 | −0.182383 | ||||||||
\(389\) | −24.8065 | −1.25774 | −0.628870 | − | 0.777510i | \(-0.716482\pi\) | ||||
−0.628870 | + | 0.777510i | \(0.716482\pi\) | |||||||
\(390\) | −21.7663 | −1.10218 | ||||||||
\(391\) | −56.7473 | −2.86984 | ||||||||
\(392\) | 3.06864 | 0.154990 | ||||||||
\(393\) | −21.0539 | −1.06203 | ||||||||
\(394\) | −5.72708 | −0.288526 | ||||||||
\(395\) | −30.3792 | −1.52854 | ||||||||
\(396\) | 46.7036 | 2.34694 | ||||||||
\(397\) | −26.1155 | −1.31070 | −0.655349 | − | 0.755326i | \(-0.727479\pi\) | ||||
−0.655349 | + | 0.755326i | \(0.727479\pi\) | |||||||
\(398\) | −2.71295 | −0.135988 | ||||||||
\(399\) | 18.8141 | 0.941883 | ||||||||
\(400\) | −0.993444 | −0.0496722 | ||||||||
\(401\) | −1.61342 | −0.0805704 | −0.0402852 | − | 0.999188i | \(-0.512827\pi\) | ||||
−0.0402852 | + | 0.999188i | \(0.512827\pi\) | |||||||
\(402\) | −22.0238 | −1.09845 | ||||||||
\(403\) | −19.6345 | −0.978065 | ||||||||
\(404\) | 7.44263 | 0.370285 | ||||||||
\(405\) | −20.2099 | −1.00424 | ||||||||
\(406\) | −16.0596 | −0.797023 | ||||||||
\(407\) | 47.5096 | 2.35496 | ||||||||
\(408\) | 54.5938 | 2.70279 | ||||||||
\(409\) | −19.2122 | −0.949981 | −0.474990 | − | 0.879991i | \(-0.657548\pi\) | ||||
−0.474990 | + | 0.879991i | \(0.657548\pi\) | |||||||
\(410\) | 5.79767 | 0.286326 | ||||||||
\(411\) | 32.2677 | 1.59165 | ||||||||
\(412\) | −4.89524 | −0.241171 | ||||||||
\(413\) | 23.8041 | 1.17132 | ||||||||
\(414\) | 34.8865 | 1.71458 | ||||||||
\(415\) | 19.5880 | 0.961537 | ||||||||
\(416\) | 28.7177 | 1.40800 | ||||||||
\(417\) | −3.74077 | −0.183186 | ||||||||
\(418\) | −8.16185 | −0.399209 | ||||||||
\(419\) | −23.6883 | −1.15725 | −0.578625 | − | 0.815594i | \(-0.696410\pi\) | ||||
−0.578625 | + | 0.815594i | \(0.696410\pi\) | |||||||
\(420\) | −25.9167 | −1.26460 | ||||||||
\(421\) | 14.8015 | 0.721381 | 0.360690 | − | 0.932686i | \(-0.382541\pi\) | ||||
0.360690 | + | 0.932686i | \(0.382541\pi\) | |||||||
\(422\) | 17.2698 | 0.840683 | ||||||||
\(423\) | 21.8069 | 1.06029 | ||||||||
\(424\) | 11.9223 | 0.578996 | ||||||||
\(425\) | −6.32230 | −0.306677 | ||||||||
\(426\) | −13.1625 | −0.637726 | ||||||||
\(427\) | −4.12393 | −0.199571 | ||||||||
\(428\) | 11.4125 | 0.551645 | ||||||||
\(429\) | 76.7708 | 3.70653 | ||||||||
\(430\) | 10.5548 | 0.508997 | ||||||||
\(431\) | −16.3188 | −0.786048 | −0.393024 | − | 0.919528i | \(-0.628571\pi\) | ||||
−0.393024 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(432\) | 10.5846 | 0.509254 | ||||||||
\(433\) | −0.0993936 | −0.00477655 | −0.00238828 | − | 0.999997i | \(-0.500760\pi\) | ||||
−0.00238828 | + | 0.999997i | \(0.500760\pi\) | |||||||
\(434\) | 8.30328 | 0.398570 | ||||||||
\(435\) | 47.3914 | 2.27224 | ||||||||
\(436\) | 5.96268 | 0.285561 | ||||||||
\(437\) | 17.1656 | 0.821144 | ||||||||
\(438\) | 5.75559 | 0.275013 | ||||||||
\(439\) | −22.9969 | −1.09758 | −0.548791 | − | 0.835960i | \(-0.684912\pi\) | ||||
−0.548791 | + | 0.835960i | \(0.684912\pi\) | |||||||
\(440\) | 26.4793 | 1.26235 | ||||||||
\(441\) | 7.44451 | 0.354501 | ||||||||
\(442\) | 25.5489 | 1.21524 | ||||||||
\(443\) | 10.5680 | 0.502100 | 0.251050 | − | 0.967974i | \(-0.419224\pi\) | ||||
0.251050 | + | 0.967974i | \(0.419224\pi\) | |||||||
\(444\) | 40.8157 | 1.93703 | ||||||||
\(445\) | 13.6864 | 0.648797 | ||||||||
\(446\) | 2.92978 | 0.138729 | ||||||||
\(447\) | −48.9434 | −2.31494 | ||||||||
\(448\) | −5.66668 | −0.267726 | ||||||||
\(449\) | −37.6403 | −1.77636 | −0.888178 | − | 0.459500i | \(-0.848029\pi\) | ||||
−0.888178 | + | 0.459500i | \(0.848029\pi\) | |||||||
\(450\) | 3.88676 | 0.183223 | ||||||||
\(451\) | −20.4486 | −0.962888 | ||||||||
\(452\) | 18.3492 | 0.863076 | ||||||||
\(453\) | 6.33537 | 0.297661 | ||||||||
\(454\) | 13.4225 | 0.629951 | ||||||||
\(455\) | −28.5647 | −1.33913 | ||||||||
\(456\) | −16.5142 | −0.773348 | ||||||||
\(457\) | −9.61456 | −0.449750 | −0.224875 | − | 0.974388i | \(-0.572197\pi\) | ||||
−0.224875 | + | 0.974388i | \(0.572197\pi\) | |||||||
\(458\) | 6.19878 | 0.289650 | ||||||||
\(459\) | 67.3610 | 3.14414 | ||||||||
\(460\) | −23.6459 | −1.10249 | ||||||||
\(461\) | −2.72760 | −0.127037 | −0.0635185 | − | 0.997981i | \(-0.520232\pi\) | ||||
−0.0635185 | + | 0.997981i | \(0.520232\pi\) | |||||||
\(462\) | −32.4657 | −1.51044 | ||||||||
\(463\) | −21.3890 | −0.994030 | −0.497015 | − | 0.867742i | \(-0.665571\pi\) | ||||
−0.497015 | + | 0.867742i | \(0.665571\pi\) | |||||||
\(464\) | −8.74086 | −0.405784 | ||||||||
\(465\) | −24.5028 | −1.13629 | ||||||||
\(466\) | 17.4332 | 0.807578 | ||||||||
\(467\) | 29.3105 | 1.35633 | 0.678165 | − | 0.734910i | \(-0.262776\pi\) | ||||
0.678165 | + | 0.734910i | \(0.262776\pi\) | |||||||
\(468\) | 44.2230 | 2.04421 | ||||||||
\(469\) | −28.9026 | −1.33460 | ||||||||
\(470\) | 5.24962 | 0.242147 | ||||||||
\(471\) | −7.54654 | −0.347726 | ||||||||
\(472\) | −20.8942 | −0.961733 | ||||||||
\(473\) | −37.2272 | −1.71171 | ||||||||
\(474\) | −32.6941 | −1.50169 | ||||||||
\(475\) | 1.91245 | 0.0877492 | ||||||||
\(476\) | 30.4205 | 1.39432 | ||||||||
\(477\) | 28.9234 | 1.32431 | ||||||||
\(478\) | −8.26381 | −0.377978 | ||||||||
\(479\) | −16.8279 | −0.768885 | −0.384442 | − | 0.923149i | \(-0.625606\pi\) | ||||
−0.384442 | + | 0.923149i | \(0.625606\pi\) | |||||||
\(480\) | 35.8381 | 1.63578 | ||||||||
\(481\) | 44.9861 | 2.05119 | ||||||||
\(482\) | −8.09900 | −0.368899 | ||||||||
\(483\) | 68.2805 | 3.10687 | ||||||||
\(484\) | −23.4206 | −1.06457 | ||||||||
\(485\) | −4.94137 | −0.224376 | ||||||||
\(486\) | −1.40022 | −0.0635152 | ||||||||
\(487\) | −9.26965 | −0.420048 | −0.210024 | − | 0.977696i | \(-0.567354\pi\) | ||||
−0.210024 | + | 0.977696i | \(0.567354\pi\) | |||||||
\(488\) | 3.61981 | 0.163861 | ||||||||
\(489\) | 2.36889 | 0.107125 | ||||||||
\(490\) | 1.79213 | 0.0809602 | ||||||||
\(491\) | 7.02225 | 0.316910 | 0.158455 | − | 0.987366i | \(-0.449349\pi\) | ||||
0.158455 | + | 0.987366i | \(0.449349\pi\) | |||||||
\(492\) | −17.5675 | −0.792006 | ||||||||
\(493\) | −55.6271 | −2.50532 | ||||||||
\(494\) | −7.72834 | −0.347715 | ||||||||
\(495\) | 64.2386 | 2.88731 | ||||||||
\(496\) | 4.51929 | 0.202922 | ||||||||
\(497\) | −17.2736 | −0.774829 | ||||||||
\(498\) | 21.0806 | 0.944645 | ||||||||
\(499\) | 0.207296 | 0.00927984 | 0.00463992 | − | 0.999989i | \(-0.498523\pi\) | ||||
0.00463992 | + | 0.999989i | \(0.498523\pi\) | |||||||
\(500\) | −17.6136 | −0.787705 | ||||||||
\(501\) | −64.7978 | −2.89495 | ||||||||
\(502\) | 5.10648 | 0.227913 | ||||||||
\(503\) | 22.9333 | 1.02254 | 0.511272 | − | 0.859419i | \(-0.329175\pi\) | ||||
0.511272 | + | 0.859419i | \(0.329175\pi\) | |||||||
\(504\) | −44.0453 | −1.96193 | ||||||||
\(505\) | 10.2370 | 0.455540 | ||||||||
\(506\) | −29.6211 | −1.31682 | ||||||||
\(507\) | 33.4663 | 1.48629 | ||||||||
\(508\) | −7.97489 | −0.353829 | ||||||||
\(509\) | 34.6558 | 1.53609 | 0.768046 | − | 0.640394i | \(-0.221229\pi\) | ||||
0.768046 | + | 0.640394i | \(0.221229\pi\) | |||||||
\(510\) | 31.8836 | 1.41183 | ||||||||
\(511\) | 7.55327 | 0.334137 | ||||||||
\(512\) | −12.2959 | −0.543407 | ||||||||
\(513\) | −20.3762 | −0.899631 | ||||||||
\(514\) | 3.00897 | 0.132720 | ||||||||
\(515\) | −6.73318 | −0.296699 | ||||||||
\(516\) | −31.9821 | −1.40793 | ||||||||
\(517\) | −18.5156 | −0.814317 | ||||||||
\(518\) | −19.0243 | −0.835879 | ||||||||
\(519\) | −47.7962 | −2.09802 | ||||||||
\(520\) | 25.0729 | 1.09952 | ||||||||
\(521\) | 27.2351 | 1.19319 | 0.596596 | − | 0.802542i | \(-0.296520\pi\) | ||||
0.596596 | + | 0.802542i | \(0.296520\pi\) | |||||||
\(522\) | 34.1978 | 1.49680 | ||||||||
\(523\) | 13.6302 | 0.596006 | 0.298003 | − | 0.954565i | \(-0.403679\pi\) | ||||
0.298003 | + | 0.954565i | \(0.403679\pi\) | |||||||
\(524\) | 10.2974 | 0.449846 | ||||||||
\(525\) | 7.60723 | 0.332007 | ||||||||
\(526\) | 3.50690 | 0.152908 | ||||||||
\(527\) | 28.7609 | 1.25284 | ||||||||
\(528\) | −17.6704 | −0.769004 | ||||||||
\(529\) | 39.2979 | 1.70860 | ||||||||
\(530\) | 6.96277 | 0.302444 | ||||||||
\(531\) | −50.6892 | −2.19973 | ||||||||
\(532\) | −9.20196 | −0.398956 | ||||||||
\(533\) | −19.3625 | −0.838684 | ||||||||
\(534\) | 14.7293 | 0.637399 | ||||||||
\(535\) | 15.6974 | 0.678658 | ||||||||
\(536\) | 25.3695 | 1.09579 | ||||||||
\(537\) | 54.9165 | 2.36982 | ||||||||
\(538\) | 15.2546 | 0.657670 | ||||||||
\(539\) | −6.32093 | −0.272262 | ||||||||
\(540\) | 28.0684 | 1.20787 | ||||||||
\(541\) | 25.8331 | 1.11065 | 0.555325 | − | 0.831634i | \(-0.312594\pi\) | ||||
0.555325 | + | 0.831634i | \(0.312594\pi\) | |||||||
\(542\) | −9.59013 | −0.411931 | ||||||||
\(543\) | 36.1619 | 1.55186 | ||||||||
\(544\) | −42.0660 | −1.80356 | ||||||||
\(545\) | 8.20139 | 0.351309 | ||||||||
\(546\) | −30.7414 | −1.31561 | ||||||||
\(547\) | −34.8074 | −1.48826 | −0.744129 | − | 0.668036i | \(-0.767135\pi\) | ||||
−0.744129 | + | 0.668036i | \(0.767135\pi\) | |||||||
\(548\) | −15.7821 | −0.674178 | ||||||||
\(549\) | 8.78164 | 0.374791 | ||||||||
\(550\) | −3.30013 | −0.140718 | ||||||||
\(551\) | 16.8268 | 0.716845 | ||||||||
\(552\) | −59.9337 | −2.55095 | ||||||||
\(553\) | −42.9056 | −1.82453 | ||||||||
\(554\) | −23.4852 | −0.997792 | ||||||||
\(555\) | 56.1402 | 2.38302 | ||||||||
\(556\) | 1.82961 | 0.0775926 | ||||||||
\(557\) | 12.8327 | 0.543737 | 0.271869 | − | 0.962334i | \(-0.412358\pi\) | ||||
0.271869 | + | 0.962334i | \(0.412358\pi\) | |||||||
\(558\) | −17.6813 | −0.748509 | ||||||||
\(559\) | −35.2499 | −1.49091 | ||||||||
\(560\) | 6.57476 | 0.277834 | ||||||||
\(561\) | −112.455 | −4.74784 | ||||||||
\(562\) | 12.0196 | 0.507018 | ||||||||
\(563\) | 6.10554 | 0.257318 | 0.128659 | − | 0.991689i | \(-0.458933\pi\) | ||||
0.128659 | + | 0.991689i | \(0.458933\pi\) | |||||||
\(564\) | −15.9069 | −0.669802 | ||||||||
\(565\) | 25.2385 | 1.06179 | ||||||||
\(566\) | −7.43716 | −0.312607 | ||||||||
\(567\) | −28.5431 | −1.19870 | ||||||||
\(568\) | 15.1620 | 0.636185 | ||||||||
\(569\) | −23.9940 | −1.00588 | −0.502940 | − | 0.864321i | \(-0.667748\pi\) | ||||
−0.502940 | + | 0.864321i | \(0.667748\pi\) | |||||||
\(570\) | −9.64454 | −0.403965 | ||||||||
\(571\) | 35.8875 | 1.50184 | 0.750922 | − | 0.660390i | \(-0.229609\pi\) | ||||
0.750922 | + | 0.660390i | \(0.229609\pi\) | |||||||
\(572\) | −37.5485 | −1.56998 | ||||||||
\(573\) | 76.2919 | 3.18714 | ||||||||
\(574\) | 8.18825 | 0.341771 | ||||||||
\(575\) | 6.94070 | 0.289447 | ||||||||
\(576\) | 12.0668 | 0.502784 | ||||||||
\(577\) | 20.8231 | 0.866876 | 0.433438 | − | 0.901183i | \(-0.357300\pi\) | ||||
0.433438 | + | 0.901183i | \(0.357300\pi\) | |||||||
\(578\) | −25.1164 | −1.04470 | ||||||||
\(579\) | −11.1431 | −0.463093 | ||||||||
\(580\) | −23.1791 | −0.962459 | ||||||||
\(581\) | 27.6648 | 1.14773 | ||||||||
\(582\) | −5.31791 | −0.220434 | ||||||||
\(583\) | −24.5580 | −1.01709 | ||||||||
\(584\) | −6.62993 | −0.274349 | ||||||||
\(585\) | 60.8267 | 2.51487 | ||||||||
\(586\) | 12.2812 | 0.507333 | ||||||||
\(587\) | −5.35770 | −0.221136 | −0.110568 | − | 0.993869i | \(-0.535267\pi\) | ||||
−0.110568 | + | 0.993869i | \(0.535267\pi\) | |||||||
\(588\) | −5.43035 | −0.223944 | ||||||||
\(589\) | −8.69995 | −0.358475 | ||||||||
\(590\) | −12.2025 | −0.502370 | ||||||||
\(591\) | 23.8692 | 0.981846 | ||||||||
\(592\) | −10.3545 | −0.425567 | ||||||||
\(593\) | 30.9114 | 1.26938 | 0.634690 | − | 0.772767i | \(-0.281128\pi\) | ||||
0.634690 | + | 0.772767i | \(0.281128\pi\) | |||||||
\(594\) | 35.1613 | 1.44268 | ||||||||
\(595\) | 41.8419 | 1.71535 | ||||||||
\(596\) | 23.9381 | 0.980545 | ||||||||
\(597\) | 11.3070 | 0.462763 | ||||||||
\(598\) | −28.0478 | −1.14696 | ||||||||
\(599\) | 4.77015 | 0.194903 | 0.0974515 | − | 0.995240i | \(-0.468931\pi\) | ||||
0.0974515 | + | 0.995240i | \(0.468931\pi\) | |||||||
\(600\) | −6.67730 | −0.272599 | ||||||||
\(601\) | −44.5777 | −1.81836 | −0.909181 | − | 0.416402i | \(-0.863291\pi\) | ||||
−0.909181 | + | 0.416402i | \(0.863291\pi\) | |||||||
\(602\) | 14.9069 | 0.607560 | ||||||||
\(603\) | 61.5463 | 2.50636 | ||||||||
\(604\) | −3.09862 | −0.126081 | ||||||||
\(605\) | −32.2139 | −1.30968 | ||||||||
\(606\) | 11.0171 | 0.447537 | ||||||||
\(607\) | 8.95911 | 0.363639 | 0.181819 | − | 0.983332i | \(-0.441801\pi\) | ||||
0.181819 | + | 0.983332i | \(0.441801\pi\) | |||||||
\(608\) | 12.7246 | 0.516053 | ||||||||
\(609\) | 66.9326 | 2.71225 | ||||||||
\(610\) | 2.11402 | 0.0855942 | ||||||||
\(611\) | −17.5322 | −0.709277 | ||||||||
\(612\) | −64.7784 | −2.61851 | ||||||||
\(613\) | 23.4711 | 0.947989 | 0.473995 | − | 0.880528i | \(-0.342812\pi\) | ||||
0.473995 | + | 0.880528i | \(0.342812\pi\) | |||||||
\(614\) | 24.7322 | 0.998109 | ||||||||
\(615\) | −24.1633 | −0.974360 | ||||||||
\(616\) | 37.3976 | 1.50679 | ||||||||
\(617\) | 25.6789 | 1.03379 | 0.516896 | − | 0.856048i | \(-0.327087\pi\) | ||||
0.516896 | + | 0.856048i | \(0.327087\pi\) | |||||||
\(618\) | −7.24625 | −0.291487 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | 11.9843 | 0.481301 | ||||||||
\(621\) | −73.9496 | −2.96750 | ||||||||
\(622\) | −15.5032 | −0.621620 | ||||||||
\(623\) | 19.3298 | 0.774431 | ||||||||
\(624\) | −16.7318 | −0.669809 | ||||||||
\(625\) | −19.8299 | −0.793197 | ||||||||
\(626\) | 11.5328 | 0.460943 | ||||||||
\(627\) | 34.0167 | 1.35850 | ||||||||
\(628\) | 3.69101 | 0.147287 | ||||||||
\(629\) | −65.8962 | −2.62745 | ||||||||
\(630\) | −25.7231 | −1.02483 | ||||||||
\(631\) | −11.0957 | −0.441711 | −0.220856 | − | 0.975306i | \(-0.570885\pi\) | ||||
−0.220856 | + | 0.975306i | \(0.570885\pi\) | |||||||
\(632\) | 37.6607 | 1.49806 | ||||||||
\(633\) | −71.9767 | −2.86082 | ||||||||
\(634\) | 2.95365 | 0.117305 | ||||||||
\(635\) | −10.9691 | −0.435295 | ||||||||
\(636\) | −21.0979 | −0.836588 | ||||||||
\(637\) | −5.98520 | −0.237142 | ||||||||
\(638\) | −29.0364 | −1.14956 | ||||||||
\(639\) | 36.7831 | 1.45512 | ||||||||
\(640\) | −20.8490 | −0.824130 | ||||||||
\(641\) | −36.8740 | −1.45644 | −0.728218 | − | 0.685345i | \(-0.759651\pi\) | ||||
−0.728218 | + | 0.685345i | \(0.759651\pi\) | |||||||
\(642\) | 16.8936 | 0.666736 | ||||||||
\(643\) | 26.6767 | 1.05203 | 0.526013 | − | 0.850476i | \(-0.323686\pi\) | ||||
0.526013 | + | 0.850476i | \(0.323686\pi\) | |||||||
\(644\) | −33.3959 | −1.31598 | ||||||||
\(645\) | −43.9899 | −1.73210 | ||||||||
\(646\) | 11.3206 | 0.445402 | ||||||||
\(647\) | 4.92648 | 0.193680 | 0.0968399 | − | 0.995300i | \(-0.469127\pi\) | ||||
0.0968399 | + | 0.995300i | \(0.469127\pi\) | |||||||
\(648\) | 25.0539 | 0.984210 | ||||||||
\(649\) | 43.0388 | 1.68942 | ||||||||
\(650\) | −3.12485 | −0.122567 | ||||||||
\(651\) | −34.6062 | −1.35632 | ||||||||
\(652\) | −1.15862 | −0.0453751 | ||||||||
\(653\) | 30.5281 | 1.19466 | 0.597328 | − | 0.801997i | \(-0.296229\pi\) | ||||
0.597328 | + | 0.801997i | \(0.296229\pi\) | |||||||
\(654\) | 8.82634 | 0.345137 | ||||||||
\(655\) | 14.1637 | 0.553420 | ||||||||
\(656\) | 4.45668 | 0.174004 | ||||||||
\(657\) | −16.0842 | −0.627504 | ||||||||
\(658\) | 7.41423 | 0.289037 | ||||||||
\(659\) | 5.69587 | 0.221879 | 0.110940 | − | 0.993827i | \(-0.464614\pi\) | ||||
0.110940 | + | 0.993827i | \(0.464614\pi\) | |||||||
\(660\) | −46.8584 | −1.82396 | ||||||||
\(661\) | −16.0281 | −0.623421 | −0.311711 | − | 0.950177i | \(-0.600902\pi\) | ||||
−0.311711 | + | 0.950177i | \(0.600902\pi\) | |||||||
\(662\) | 5.16060 | 0.200573 | ||||||||
\(663\) | −106.482 | −4.13541 | ||||||||
\(664\) | −24.2830 | −0.942363 | ||||||||
\(665\) | −12.6569 | −0.490812 | ||||||||
\(666\) | 40.5109 | 1.56977 | ||||||||
\(667\) | 61.0680 | 2.36456 | ||||||||
\(668\) | 31.6926 | 1.22622 | ||||||||
\(669\) | −12.2107 | −0.472091 | ||||||||
\(670\) | 14.8162 | 0.572398 | ||||||||
\(671\) | −7.45624 | −0.287845 | ||||||||
\(672\) | 50.6154 | 1.95253 | ||||||||
\(673\) | −38.4585 | −1.48247 | −0.741233 | − | 0.671247i | \(-0.765759\pi\) | ||||
−0.741233 | + | 0.671247i | \(0.765759\pi\) | |||||||
\(674\) | 0.864817 | 0.0333115 | ||||||||
\(675\) | −8.23884 | −0.317113 | ||||||||
\(676\) | −16.3683 | −0.629552 | ||||||||
\(677\) | 23.1687 | 0.890446 | 0.445223 | − | 0.895420i | \(-0.353124\pi\) | ||||
0.445223 | + | 0.895420i | \(0.353124\pi\) | |||||||
\(678\) | 27.1617 | 1.04314 | ||||||||
\(679\) | −6.97888 | −0.267825 | ||||||||
\(680\) | −36.7270 | −1.40842 | ||||||||
\(681\) | −55.9420 | −2.14370 | ||||||||
\(682\) | 15.0127 | 0.574866 | ||||||||
\(683\) | 34.7337 | 1.32905 | 0.664523 | − | 0.747267i | \(-0.268635\pi\) | ||||
0.664523 | + | 0.747267i | \(0.268635\pi\) | |||||||
\(684\) | 19.5950 | 0.749232 | ||||||||
\(685\) | −21.7075 | −0.829402 | ||||||||
\(686\) | −11.9985 | −0.458106 | ||||||||
\(687\) | −25.8351 | −0.985670 | ||||||||
\(688\) | 8.11350 | 0.309324 | ||||||||
\(689\) | −23.2536 | −0.885893 | ||||||||
\(690\) | −35.0021 | −1.33251 | ||||||||
\(691\) | 15.8030 | 0.601173 | 0.300586 | − | 0.953755i | \(-0.402818\pi\) | ||||
0.300586 | + | 0.953755i | \(0.402818\pi\) | |||||||
\(692\) | 23.3771 | 0.888664 | ||||||||
\(693\) | 90.7266 | 3.44642 | ||||||||
\(694\) | 6.11977 | 0.232303 | ||||||||
\(695\) | 2.51654 | 0.0954578 | ||||||||
\(696\) | −58.7505 | −2.22693 | ||||||||
\(697\) | 28.3624 | 1.07430 | ||||||||
\(698\) | 13.5239 | 0.511889 | ||||||||
\(699\) | −72.6576 | −2.74816 | ||||||||
\(700\) | −3.72069 | −0.140629 | ||||||||
\(701\) | −17.4822 | −0.660295 | −0.330147 | − | 0.943929i | \(-0.607098\pi\) | ||||
−0.330147 | + | 0.943929i | \(0.607098\pi\) | |||||||
\(702\) | 33.2937 | 1.25659 | ||||||||
\(703\) | 19.9331 | 0.751792 | ||||||||
\(704\) | −10.2456 | −0.386146 | ||||||||
\(705\) | −21.8792 | −0.824019 | ||||||||
\(706\) | −0.0693428 | −0.00260975 | ||||||||
\(707\) | 14.4581 | 0.543752 | ||||||||
\(708\) | 36.9749 | 1.38960 | ||||||||
\(709\) | 1.40984 | 0.0529478 | 0.0264739 | − | 0.999650i | \(-0.491572\pi\) | ||||
0.0264739 | + | 0.999650i | \(0.491572\pi\) | |||||||
\(710\) | 8.85486 | 0.332317 | ||||||||
\(711\) | 91.3647 | 3.42644 | ||||||||
\(712\) | −16.9668 | −0.635859 | ||||||||
\(713\) | −31.5740 | −1.18246 | ||||||||
\(714\) | 45.0303 | 1.68522 | ||||||||
\(715\) | −51.6462 | −1.93146 | ||||||||
\(716\) | −26.8596 | −1.00379 | ||||||||
\(717\) | 34.4417 | 1.28625 | ||||||||
\(718\) | 24.6829 | 0.921157 | ||||||||
\(719\) | −13.1497 | −0.490402 | −0.245201 | − | 0.969472i | \(-0.578854\pi\) | ||||
−0.245201 | + | 0.969472i | \(0.578854\pi\) | |||||||
\(720\) | −14.0005 | −0.521768 | ||||||||
\(721\) | −9.50951 | −0.354153 | ||||||||
\(722\) | 10.3315 | 0.384500 | ||||||||
\(723\) | 33.7548 | 1.25535 | ||||||||
\(724\) | −17.6868 | −0.657323 | ||||||||
\(725\) | 6.80368 | 0.252682 | ||||||||
\(726\) | −34.6687 | −1.28667 | ||||||||
\(727\) | 15.4676 | 0.573661 | 0.286831 | − | 0.957981i | \(-0.407398\pi\) | ||||
0.286831 | + | 0.957981i | \(0.407398\pi\) | |||||||
\(728\) | 35.4113 | 1.31243 | ||||||||
\(729\) | −24.0319 | −0.890071 | ||||||||
\(730\) | −3.87198 | −0.143308 | ||||||||
\(731\) | 51.6345 | 1.90977 | ||||||||
\(732\) | −6.40570 | −0.236762 | ||||||||
\(733\) | −5.10122 | −0.188418 | −0.0942089 | − | 0.995552i | \(-0.530032\pi\) | ||||
−0.0942089 | + | 0.995552i | \(0.530032\pi\) | |||||||
\(734\) | −15.1403 | −0.558840 | ||||||||
\(735\) | −7.46919 | −0.275505 | ||||||||
\(736\) | 46.1805 | 1.70224 | ||||||||
\(737\) | −52.2572 | −1.92492 | ||||||||
\(738\) | −17.4364 | −0.641841 | ||||||||
\(739\) | 16.1116 | 0.592673 | 0.296337 | − | 0.955084i | \(-0.404235\pi\) | ||||
0.296337 | + | 0.955084i | \(0.404235\pi\) | |||||||
\(740\) | −27.4581 | −1.00938 | ||||||||
\(741\) | 32.2099 | 1.18326 | ||||||||
\(742\) | 9.83378 | 0.361009 | ||||||||
\(743\) | 32.9642 | 1.20934 | 0.604670 | − | 0.796476i | \(-0.293305\pi\) | ||||
0.604670 | + | 0.796476i | \(0.293305\pi\) | |||||||
\(744\) | 30.3758 | 1.11363 | ||||||||
\(745\) | 32.9258 | 1.20631 | ||||||||
\(746\) | −8.19440 | −0.300018 | ||||||||
\(747\) | −58.9105 | −2.15542 | ||||||||
\(748\) | 55.0015 | 2.01105 | ||||||||
\(749\) | 22.1700 | 0.810075 | ||||||||
\(750\) | −26.0728 | −0.952045 | ||||||||
\(751\) | 29.0599 | 1.06041 | 0.530205 | − | 0.847869i | \(-0.322115\pi\) | ||||
0.530205 | + | 0.847869i | \(0.322115\pi\) | |||||||
\(752\) | 4.03540 | 0.147156 | ||||||||
\(753\) | −21.2826 | −0.775582 | ||||||||
\(754\) | −27.4941 | −1.00128 | ||||||||
\(755\) | −4.26201 | −0.155110 | ||||||||
\(756\) | 39.6421 | 1.44177 | ||||||||
\(757\) | −51.6796 | −1.87833 | −0.939164 | − | 0.343468i | \(-0.888398\pi\) | ||||
−0.939164 | + | 0.343468i | \(0.888398\pi\) | |||||||
\(758\) | −18.5615 | −0.674183 | ||||||||
\(759\) | 123.454 | 4.48110 | ||||||||
\(760\) | 11.1096 | 0.402989 | ||||||||
\(761\) | 5.32890 | 0.193173 | 0.0965863 | − | 0.995325i | \(-0.469208\pi\) | ||||
0.0965863 | + | 0.995325i | \(0.469208\pi\) | |||||||
\(762\) | −11.8049 | −0.427648 | ||||||||
\(763\) | 11.5831 | 0.419337 | ||||||||
\(764\) | −37.3143 | −1.34998 | ||||||||
\(765\) | −89.0996 | −3.22140 | ||||||||
\(766\) | 3.11355 | 0.112497 | ||||||||
\(767\) | 40.7528 | 1.47150 | ||||||||
\(768\) | −34.3660 | −1.24008 | ||||||||
\(769\) | 5.94381 | 0.214339 | 0.107170 | − | 0.994241i | \(-0.465821\pi\) | ||||
0.107170 | + | 0.994241i | \(0.465821\pi\) | |||||||
\(770\) | 21.8408 | 0.787087 | ||||||||
\(771\) | −12.5407 | −0.451642 | ||||||||
\(772\) | 5.45009 | 0.196153 | ||||||||
\(773\) | 21.8886 | 0.787278 | 0.393639 | − | 0.919265i | \(-0.371216\pi\) | ||||
0.393639 | + | 0.919265i | \(0.371216\pi\) | |||||||
\(774\) | −31.7433 | −1.14099 | ||||||||
\(775\) | −3.51771 | −0.126360 | ||||||||
\(776\) | 6.12575 | 0.219902 | ||||||||
\(777\) | 79.2888 | 2.84447 | ||||||||
\(778\) | 17.9598 | 0.643891 | ||||||||
\(779\) | −8.57943 | −0.307390 | ||||||||
\(780\) | −44.3696 | −1.58869 | ||||||||
\(781\) | −31.2315 | −1.11755 | ||||||||
\(782\) | 41.0848 | 1.46919 | ||||||||
\(783\) | −72.4898 | −2.59057 | ||||||||
\(784\) | 1.37762 | 0.0492006 | ||||||||
\(785\) | 5.07681 | 0.181199 | ||||||||
\(786\) | 15.2429 | 0.543698 | ||||||||
\(787\) | 17.2063 | 0.613339 | 0.306670 | − | 0.951816i | \(-0.400785\pi\) | ||||
0.306670 | + | 0.951816i | \(0.400785\pi\) | |||||||
\(788\) | −11.6744 | −0.415883 | ||||||||
\(789\) | −14.6159 | −0.520341 | ||||||||
\(790\) | 21.9944 | 0.782526 | ||||||||
\(791\) | 35.6453 | 1.26740 | ||||||||
\(792\) | −79.6358 | −2.82974 | ||||||||
\(793\) | −7.06021 | −0.250715 | ||||||||
\(794\) | 18.9075 | 0.671002 | ||||||||
\(795\) | −29.0192 | −1.02921 | ||||||||
\(796\) | −5.53022 | −0.196014 | ||||||||
\(797\) | 26.2860 | 0.931099 | 0.465549 | − | 0.885022i | \(-0.345857\pi\) | ||||
0.465549 | + | 0.885022i | \(0.345857\pi\) | |||||||
\(798\) | −13.6213 | −0.482190 | ||||||||
\(799\) | 25.6814 | 0.908542 | ||||||||
\(800\) | 5.14504 | 0.181905 | ||||||||
\(801\) | −41.1615 | −1.45437 | ||||||||
\(802\) | 1.16811 | 0.0412474 | ||||||||
\(803\) | 13.6566 | 0.481932 | ||||||||
\(804\) | −44.8945 | −1.58331 | ||||||||
\(805\) | −45.9345 | −1.61898 | ||||||||
\(806\) | 14.2153 | 0.500713 | ||||||||
\(807\) | −63.5775 | −2.23803 | ||||||||
\(808\) | −12.6907 | −0.446456 | ||||||||
\(809\) | −3.27058 | −0.114987 | −0.0574937 | − | 0.998346i | \(-0.518311\pi\) | ||||
−0.0574937 | + | 0.998346i | \(0.518311\pi\) | |||||||
\(810\) | 14.6318 | 0.514111 | ||||||||
\(811\) | −11.2065 | −0.393512 | −0.196756 | − | 0.980452i | \(-0.563041\pi\) | ||||
−0.196756 | + | 0.980452i | \(0.563041\pi\) | |||||||
\(812\) | −32.7367 | −1.14883 | ||||||||
\(813\) | 39.9695 | 1.40179 | ||||||||
\(814\) | −34.3967 | −1.20560 | ||||||||
\(815\) | −1.59363 | −0.0558224 | ||||||||
\(816\) | 24.5090 | 0.857986 | ||||||||
\(817\) | −15.6191 | −0.546441 | ||||||||
\(818\) | 13.9095 | 0.486335 | ||||||||
\(819\) | 85.9077 | 3.00186 | ||||||||
\(820\) | 11.8183 | 0.412712 | ||||||||
\(821\) | −24.6391 | −0.859910 | −0.429955 | − | 0.902850i | \(-0.641471\pi\) | ||||
−0.429955 | + | 0.902850i | \(0.641471\pi\) | |||||||
\(822\) | −23.3617 | −0.814832 | ||||||||
\(823\) | −9.88862 | −0.344696 | −0.172348 | − | 0.985036i | \(-0.555135\pi\) | ||||
−0.172348 | + | 0.985036i | \(0.555135\pi\) | |||||||
\(824\) | 8.34703 | 0.290783 | ||||||||
\(825\) | 13.7542 | 0.478860 | ||||||||
\(826\) | −17.2341 | −0.599649 | ||||||||
\(827\) | 18.9840 | 0.660140 | 0.330070 | − | 0.943957i | \(-0.392928\pi\) | ||||
0.330070 | + | 0.943957i | \(0.392928\pi\) | |||||||
\(828\) | 71.1144 | 2.47140 | ||||||||
\(829\) | −23.6093 | −0.819986 | −0.409993 | − | 0.912089i | \(-0.634469\pi\) | ||||
−0.409993 | + | 0.912089i | \(0.634469\pi\) | |||||||
\(830\) | −14.1816 | −0.492252 | ||||||||
\(831\) | 97.8810 | 3.39545 | ||||||||
\(832\) | −9.70142 | −0.336336 | ||||||||
\(833\) | 8.76719 | 0.303765 | ||||||||
\(834\) | 2.70830 | 0.0937808 | ||||||||
\(835\) | 43.5916 | 1.50855 | ||||||||
\(836\) | −16.6375 | −0.575421 | ||||||||
\(837\) | 37.4794 | 1.29548 | ||||||||
\(838\) | 17.1502 | 0.592445 | ||||||||
\(839\) | −48.9383 | −1.68954 | −0.844768 | − | 0.535132i | \(-0.820262\pi\) | ||||
−0.844768 | + | 0.535132i | \(0.820262\pi\) | |||||||
\(840\) | 44.1913 | 1.52475 | ||||||||
\(841\) | 30.8625 | 1.06422 | ||||||||
\(842\) | −10.7162 | −0.369305 | ||||||||
\(843\) | −50.0951 | −1.72537 | ||||||||
\(844\) | 35.2037 | 1.21176 | ||||||||
\(845\) | −22.5139 | −0.774502 | ||||||||
\(846\) | −15.7881 | −0.542807 | ||||||||
\(847\) | −45.4969 | −1.56329 | ||||||||
\(848\) | 5.35230 | 0.183799 | ||||||||
\(849\) | 30.9964 | 1.06379 | ||||||||
\(850\) | 4.57732 | 0.157001 | ||||||||
\(851\) | 72.3416 | 2.47984 | ||||||||
\(852\) | −26.8312 | −0.919220 | ||||||||
\(853\) | 6.33675 | 0.216966 | 0.108483 | − | 0.994098i | \(-0.465401\pi\) | ||||
0.108483 | + | 0.994098i | \(0.465401\pi\) | |||||||
\(854\) | 2.98571 | 0.102169 | ||||||||
\(855\) | 26.9520 | 0.921738 | ||||||||
\(856\) | −19.4599 | −0.665125 | ||||||||
\(857\) | 2.41085 | 0.0823529 | 0.0411765 | − | 0.999152i | \(-0.486889\pi\) | ||||
0.0411765 | + | 0.999152i | \(0.486889\pi\) | |||||||
\(858\) | −55.5817 | −1.89753 | ||||||||
\(859\) | 21.5349 | 0.734760 | 0.367380 | − | 0.930071i | \(-0.380255\pi\) | ||||
0.367380 | + | 0.930071i | \(0.380255\pi\) | |||||||
\(860\) | 21.5154 | 0.733670 | ||||||||
\(861\) | −34.1268 | −1.16304 | ||||||||
\(862\) | 11.8147 | 0.402411 | ||||||||
\(863\) | 22.3824 | 0.761905 | 0.380953 | − | 0.924595i | \(-0.375596\pi\) | ||||
0.380953 | + | 0.924595i | \(0.375596\pi\) | |||||||
\(864\) | −54.8178 | −1.86494 | ||||||||
\(865\) | 32.1541 | 1.09327 | ||||||||
\(866\) | 0.0719606 | 0.00244532 | ||||||||
\(867\) | 104.679 | 3.55509 | ||||||||
\(868\) | 16.9258 | 0.574501 | ||||||||
\(869\) | −77.5752 | −2.63156 | ||||||||
\(870\) | −34.3112 | −1.16326 | ||||||||
\(871\) | −49.4816 | −1.67662 | ||||||||
\(872\) | −10.1672 | −0.344303 | ||||||||
\(873\) | 14.8611 | 0.502971 | ||||||||
\(874\) | −12.4278 | −0.420378 | ||||||||
\(875\) | −34.2163 | −1.15672 | ||||||||
\(876\) | 11.7325 | 0.396404 | ||||||||
\(877\) | −17.6514 | −0.596045 | −0.298022 | − | 0.954559i | \(-0.596327\pi\) | ||||
−0.298022 | + | 0.954559i | \(0.596327\pi\) | |||||||
\(878\) | 16.6497 | 0.561899 | ||||||||
\(879\) | −51.1854 | −1.72644 | ||||||||
\(880\) | 11.8874 | 0.400726 | ||||||||
\(881\) | −43.5861 | −1.46845 | −0.734227 | − | 0.678904i | \(-0.762455\pi\) | ||||
−0.734227 | + | 0.678904i | \(0.762455\pi\) | |||||||
\(882\) | −5.38980 | −0.181484 | ||||||||
\(883\) | −10.0998 | −0.339887 | −0.169943 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169943 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(884\) | 52.0801 | 1.75164 | ||||||||
\(885\) | 50.8573 | 1.70955 | ||||||||
\(886\) | −7.65118 | −0.257046 | ||||||||
\(887\) | 15.5185 | 0.521060 | 0.260530 | − | 0.965466i | \(-0.416103\pi\) | ||||
0.260530 | + | 0.965466i | \(0.416103\pi\) | |||||||
\(888\) | −69.5963 | −2.33550 | ||||||||
\(889\) | −15.4920 | −0.519586 | ||||||||
\(890\) | −9.90889 | −0.332147 | ||||||||
\(891\) | −51.6072 | −1.72891 | ||||||||
\(892\) | 5.97222 | 0.199965 | ||||||||
\(893\) | −7.76843 | −0.259961 | ||||||||
\(894\) | 35.4348 | 1.18512 | ||||||||
\(895\) | −36.9441 | −1.23491 | ||||||||
\(896\) | −29.4458 | −0.983716 | ||||||||
\(897\) | 116.897 | 3.90307 | ||||||||
\(898\) | 27.2514 | 0.909392 | ||||||||
\(899\) | −30.9507 | −1.03226 | ||||||||
\(900\) | 7.92296 | 0.264099 | ||||||||
\(901\) | 34.0622 | 1.13478 | ||||||||
\(902\) | 14.8047 | 0.492943 | ||||||||
\(903\) | −62.1286 | −2.06751 | ||||||||
\(904\) | −31.2879 | −1.04062 | ||||||||
\(905\) | −24.3273 | −0.808667 | ||||||||
\(906\) | −4.58678 | −0.152385 | ||||||||
\(907\) | 2.33484 | 0.0775271 | 0.0387636 | − | 0.999248i | \(-0.487658\pi\) | ||||
0.0387636 | + | 0.999248i | \(0.487658\pi\) | |||||||
\(908\) | 27.3612 | 0.908013 | ||||||||
\(909\) | −30.7875 | −1.02116 | ||||||||
\(910\) | 20.6807 | 0.685559 | ||||||||
\(911\) | −7.30115 | −0.241898 | −0.120949 | − | 0.992659i | \(-0.538594\pi\) | ||||
−0.120949 | + | 0.992659i | \(0.538594\pi\) | |||||||
\(912\) | −7.41378 | −0.245495 | ||||||||
\(913\) | 50.0192 | 1.65540 | ||||||||
\(914\) | 6.96090 | 0.230246 | ||||||||
\(915\) | −8.81075 | −0.291274 | ||||||||
\(916\) | 12.6359 | 0.417502 | ||||||||
\(917\) | 20.0039 | 0.660585 | ||||||||
\(918\) | −48.7690 | −1.60962 | ||||||||
\(919\) | −23.9848 | −0.791185 | −0.395593 | − | 0.918426i | \(-0.629461\pi\) | ||||
−0.395593 | + | 0.918426i | \(0.629461\pi\) | |||||||
\(920\) | 40.3193 | 1.32929 | ||||||||
\(921\) | −103.078 | −3.39654 | ||||||||
\(922\) | 1.97477 | 0.0650356 | ||||||||
\(923\) | −29.5726 | −0.973396 | ||||||||
\(924\) | −66.1798 | −2.17716 | ||||||||
\(925\) | 8.05969 | 0.265001 | ||||||||
\(926\) | 15.4855 | 0.508886 | ||||||||
\(927\) | 20.2499 | 0.665093 | ||||||||
\(928\) | 45.2689 | 1.48602 | ||||||||
\(929\) | 12.0761 | 0.396204 | 0.198102 | − | 0.980181i | \(-0.436522\pi\) | ||||
0.198102 | + | 0.980181i | \(0.436522\pi\) | |||||||
\(930\) | 17.7399 | 0.581715 | ||||||||
\(931\) | −2.65201 | −0.0869161 | ||||||||
\(932\) | 35.5368 | 1.16405 | ||||||||
\(933\) | 64.6136 | 2.11536 | ||||||||
\(934\) | −21.2207 | −0.694362 | ||||||||
\(935\) | 75.6520 | 2.47409 | ||||||||
\(936\) | −75.4060 | −2.46472 | ||||||||
\(937\) | 57.3121 | 1.87230 | 0.936152 | − | 0.351595i | \(-0.114360\pi\) | ||||
0.936152 | + | 0.351595i | \(0.114360\pi\) | |||||||
\(938\) | 20.9254 | 0.683238 | ||||||||
\(939\) | −48.0660 | −1.56858 | ||||||||
\(940\) | 10.7011 | 0.349031 | ||||||||
\(941\) | 46.7239 | 1.52316 | 0.761578 | − | 0.648074i | \(-0.224425\pi\) | ||||
0.761578 | + | 0.648074i | \(0.224425\pi\) | |||||||
\(942\) | 5.46366 | 0.178016 | ||||||||
\(943\) | −31.1366 | −1.01395 | ||||||||
\(944\) | −9.38011 | −0.305296 | ||||||||
\(945\) | 54.5258 | 1.77373 | ||||||||
\(946\) | 26.9523 | 0.876296 | ||||||||
\(947\) | 45.7966 | 1.48819 | 0.744095 | − | 0.668074i | \(-0.232881\pi\) | ||||
0.744095 | + | 0.668074i | \(0.232881\pi\) | |||||||
\(948\) | −66.6454 | −2.16454 | ||||||||
\(949\) | 12.9313 | 0.419767 | ||||||||
\(950\) | −1.38460 | −0.0449225 | ||||||||
\(951\) | −12.3101 | −0.399184 | ||||||||
\(952\) | −51.8709 | −1.68115 | ||||||||
\(953\) | 8.74797 | 0.283375 | 0.141687 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141687 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(954\) | −20.9404 | −0.677970 | ||||||||
\(955\) | −51.3241 | −1.66081 | ||||||||
\(956\) | −16.8454 | −0.544819 | ||||||||
\(957\) | 121.017 | 3.91192 | ||||||||
\(958\) | 12.1833 | 0.393625 | ||||||||
\(959\) | −30.6583 | −0.990010 | ||||||||
\(960\) | −12.1068 | −0.390746 | ||||||||
\(961\) | −14.9975 | −0.483792 | ||||||||
\(962\) | −32.5698 | −1.05009 | ||||||||
\(963\) | −47.2096 | −1.52131 | ||||||||
\(964\) | −16.5094 | −0.531732 | ||||||||
\(965\) | 7.49635 | 0.241316 | ||||||||
\(966\) | −49.4348 | −1.59054 | ||||||||
\(967\) | 5.02074 | 0.161456 | 0.0807281 | − | 0.996736i | \(-0.474275\pi\) | ||||
0.0807281 | + | 0.996736i | \(0.474275\pi\) | |||||||
\(968\) | 39.9352 | 1.28357 | ||||||||
\(969\) | −47.1815 | −1.51569 | ||||||||
\(970\) | 3.57753 | 0.114868 | ||||||||
\(971\) | 49.8646 | 1.60023 | 0.800115 | − | 0.599846i | \(-0.204772\pi\) | ||||
0.800115 | + | 0.599846i | \(0.204772\pi\) | |||||||
\(972\) | −2.85428 | −0.0915510 | ||||||||
\(973\) | 3.55420 | 0.113942 | ||||||||
\(974\) | 6.71118 | 0.215040 | ||||||||
\(975\) | 13.0237 | 0.417091 | ||||||||
\(976\) | 1.62505 | 0.0520167 | ||||||||
\(977\) | 29.5958 | 0.946854 | 0.473427 | − | 0.880833i | \(-0.343017\pi\) | ||||
0.473427 | + | 0.880833i | \(0.343017\pi\) | |||||||
\(978\) | −1.71506 | −0.0548417 | ||||||||
\(979\) | 34.9491 | 1.11698 | ||||||||
\(980\) | 3.65317 | 0.116696 | ||||||||
\(981\) | −24.6655 | −0.787509 | ||||||||
\(982\) | −5.08408 | −0.162240 | ||||||||
\(983\) | −36.7308 | −1.17153 | −0.585765 | − | 0.810481i | \(-0.699206\pi\) | ||||
−0.585765 | + | 0.810481i | \(0.699206\pi\) | |||||||
\(984\) | 29.9550 | 0.954930 | ||||||||
\(985\) | −16.0576 | −0.511637 | ||||||||
\(986\) | 40.2738 | 1.28258 | ||||||||
\(987\) | −30.9008 | −0.983583 | ||||||||
\(988\) | −15.7539 | −0.501197 | ||||||||
\(989\) | −56.6850 | −1.80248 | ||||||||
\(990\) | −46.5085 | −1.47814 | ||||||||
\(991\) | 1.77182 | 0.0562838 | 0.0281419 | − | 0.999604i | \(-0.491041\pi\) | ||||
0.0281419 | + | 0.999604i | \(0.491041\pi\) | |||||||
\(992\) | −23.4054 | −0.743122 | ||||||||
\(993\) | −21.5082 | −0.682542 | ||||||||
\(994\) | 12.5060 | 0.396667 | ||||||||
\(995\) | −7.60657 | −0.241144 | ||||||||
\(996\) | 42.9718 | 1.36161 | ||||||||
\(997\) | −11.3713 | −0.360134 | −0.180067 | − | 0.983654i | \(-0.557631\pi\) | ||||
−0.180067 | + | 0.983654i | \(0.557631\pi\) | |||||||
\(998\) | −0.150081 | −0.00475074 | ||||||||
\(999\) | −85.8719 | −2.71687 |
(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 | 619.2.a.a.1.11 | ✓ | 21 | |
3.2 | odd | 2 | 5571.2.a.e.1.11 | 21 | |||
4.3 | odd | 2 | 9904.2.a.j.1.1 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.a.1.11 | ✓ | 21 | 1.1 | even | 1 | trivial | |
5571.2.a.e.1.11 | 21 | 3.2 | odd | 2 | |||
9904.2.a.j.1.1 | 21 | 4.3 | odd | 2 |