Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.50 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.584752 | 0.413482 | 0.206741 | − | 0.978396i | \(-0.433714\pi\) | ||||
0.206741 | + | 0.978396i | \(0.433714\pi\) | |||||||
\(3\) | 2.27809 | 1.31525 | 0.657627 | − | 0.753343i | \(-0.271560\pi\) | ||||
0.657627 | + | 0.753343i | \(0.271560\pi\) | |||||||
\(4\) | −1.65806 | −0.829032 | ||||||||
\(5\) | 3.02229 | 1.35161 | 0.675805 | − | 0.737080i | \(-0.263796\pi\) | ||||
0.675805 | + | 0.737080i | \(0.263796\pi\) | |||||||
\(6\) | 1.33212 | 0.543835 | ||||||||
\(7\) | 0.0896254 | 0.0338752 | 0.0169376 | − | 0.999857i | \(-0.494608\pi\) | ||||
0.0169376 | + | 0.999857i | \(0.494608\pi\) | |||||||
\(8\) | −2.13906 | −0.756273 | ||||||||
\(9\) | 2.18969 | 0.729895 | ||||||||
\(10\) | 1.76729 | 0.558867 | ||||||||
\(11\) | −3.86153 | −1.16429 | −0.582147 | − | 0.813083i | \(-0.697787\pi\) | ||||
−0.582147 | + | 0.813083i | \(0.697787\pi\) | |||||||
\(12\) | −3.77722 | −1.09039 | ||||||||
\(13\) | −6.59562 | −1.82930 | −0.914648 | − | 0.404252i | \(-0.867532\pi\) | ||||
−0.914648 | + | 0.404252i | \(0.867532\pi\) | |||||||
\(14\) | 0.0524087 | 0.0140068 | ||||||||
\(15\) | 6.88505 | 1.77771 | ||||||||
\(16\) | 2.06531 | 0.516327 | ||||||||
\(17\) | −0.733954 | −0.178010 | −0.0890050 | − | 0.996031i | \(-0.528369\pi\) | ||||
−0.0890050 | + | 0.996031i | \(0.528369\pi\) | |||||||
\(18\) | 1.28042 | 0.301799 | ||||||||
\(19\) | −5.01007 | −1.14939 | −0.574694 | − | 0.818368i | \(-0.694879\pi\) | ||||
−0.574694 | + | 0.818368i | \(0.694879\pi\) | |||||||
\(20\) | −5.01115 | −1.12053 | ||||||||
\(21\) | 0.204175 | 0.0445545 | ||||||||
\(22\) | −2.25804 | −0.481415 | ||||||||
\(23\) | −3.76339 | −0.784722 | −0.392361 | − | 0.919811i | \(-0.628342\pi\) | ||||
−0.392361 | + | 0.919811i | \(0.628342\pi\) | |||||||
\(24\) | −4.87297 | −0.994691 | ||||||||
\(25\) | 4.13425 | 0.826850 | ||||||||
\(26\) | −3.85680 | −0.756381 | ||||||||
\(27\) | −1.84597 | −0.355257 | ||||||||
\(28\) | −0.148605 | −0.0280836 | ||||||||
\(29\) | −1.81605 | −0.337232 | −0.168616 | − | 0.985682i | \(-0.553930\pi\) | ||||
−0.168616 | + | 0.985682i | \(0.553930\pi\) | |||||||
\(30\) | 4.02605 | 0.735052 | ||||||||
\(31\) | 7.32599 | 1.31579 | 0.657893 | − | 0.753111i | \(-0.271448\pi\) | ||||
0.657893 | + | 0.753111i | \(0.271448\pi\) | |||||||
\(32\) | 5.48582 | 0.969765 | ||||||||
\(33\) | −8.79690 | −1.53134 | ||||||||
\(34\) | −0.429181 | −0.0736040 | ||||||||
\(35\) | 0.270874 | 0.0457861 | ||||||||
\(36\) | −3.63064 | −0.605107 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −2.92965 | −0.475252 | ||||||||
\(39\) | −15.0254 | −2.40599 | ||||||||
\(40\) | −6.46487 | −1.02219 | ||||||||
\(41\) | −0.475858 | −0.0743166 | −0.0371583 | − | 0.999309i | \(-0.511831\pi\) | ||||
−0.0371583 | + | 0.999309i | \(0.511831\pi\) | |||||||
\(42\) | 0.119392 | 0.0184225 | ||||||||
\(43\) | −2.90575 | −0.443123 | −0.221562 | − | 0.975146i | \(-0.571115\pi\) | ||||
−0.221562 | + | 0.975146i | \(0.571115\pi\) | |||||||
\(44\) | 6.40266 | 0.965238 | ||||||||
\(45\) | 6.61787 | 0.986533 | ||||||||
\(46\) | −2.20065 | −0.324469 | ||||||||
\(47\) | −8.22868 | −1.20028 | −0.600138 | − | 0.799897i | \(-0.704888\pi\) | ||||
−0.600138 | + | 0.799897i | \(0.704888\pi\) | |||||||
\(48\) | 4.70495 | 0.679101 | ||||||||
\(49\) | −6.99197 | −0.998852 | ||||||||
\(50\) | 2.41751 | 0.341888 | ||||||||
\(51\) | −1.67201 | −0.234129 | ||||||||
\(52\) | 10.9360 | 1.51654 | ||||||||
\(53\) | 6.94011 | 0.953298 | 0.476649 | − | 0.879094i | \(-0.341851\pi\) | ||||
0.476649 | + | 0.879094i | \(0.341851\pi\) | |||||||
\(54\) | −1.07943 | −0.146892 | ||||||||
\(55\) | −11.6707 | −1.57367 | ||||||||
\(56\) | −0.191714 | −0.0256189 | ||||||||
\(57\) | −11.4134 | −1.51174 | ||||||||
\(58\) | −1.06194 | −0.139440 | ||||||||
\(59\) | −4.15253 | −0.540613 | −0.270306 | − | 0.962774i | \(-0.587125\pi\) | ||||
−0.270306 | + | 0.962774i | \(0.587125\pi\) | |||||||
\(60\) | −11.4159 | −1.47378 | ||||||||
\(61\) | 13.3176 | 1.70514 | 0.852569 | − | 0.522615i | \(-0.175043\pi\) | ||||
0.852569 | + | 0.522615i | \(0.175043\pi\) | |||||||
\(62\) | 4.28389 | 0.544055 | ||||||||
\(63\) | 0.196251 | 0.0247254 | ||||||||
\(64\) | −0.922769 | −0.115346 | ||||||||
\(65\) | −19.9339 | −2.47249 | ||||||||
\(66\) | −5.14401 | −0.633184 | ||||||||
\(67\) | −7.64367 | −0.933823 | −0.466911 | − | 0.884304i | \(-0.654633\pi\) | ||||
−0.466911 | + | 0.884304i | \(0.654633\pi\) | |||||||
\(68\) | 1.21694 | 0.147576 | ||||||||
\(69\) | −8.57334 | −1.03211 | ||||||||
\(70\) | 0.158394 | 0.0189317 | ||||||||
\(71\) | −9.03134 | −1.07182 | −0.535912 | − | 0.844274i | \(-0.680032\pi\) | ||||
−0.535912 | + | 0.844274i | \(0.680032\pi\) | |||||||
\(72\) | −4.68387 | −0.552000 | ||||||||
\(73\) | 7.08752 | 0.829531 | 0.414766 | − | 0.909928i | \(-0.363864\pi\) | ||||
0.414766 | + | 0.909928i | \(0.363864\pi\) | |||||||
\(74\) | −0.584752 | −0.0679761 | ||||||||
\(75\) | 9.41818 | 1.08752 | ||||||||
\(76\) | 8.30701 | 0.952880 | ||||||||
\(77\) | −0.346091 | −0.0394407 | ||||||||
\(78\) | −8.78614 | −0.994834 | ||||||||
\(79\) | −1.66015 | −0.186781 | −0.0933907 | − | 0.995630i | \(-0.529771\pi\) | ||||
−0.0933907 | + | 0.995630i | \(0.529771\pi\) | |||||||
\(80\) | 6.24196 | 0.697872 | ||||||||
\(81\) | −10.7743 | −1.19715 | ||||||||
\(82\) | −0.278259 | −0.0307286 | ||||||||
\(83\) | −8.76145 | −0.961694 | −0.480847 | − | 0.876805i | \(-0.659671\pi\) | ||||
−0.480847 | + | 0.876805i | \(0.659671\pi\) | |||||||
\(84\) | −0.338535 | −0.0369372 | ||||||||
\(85\) | −2.21822 | −0.240600 | ||||||||
\(86\) | −1.69915 | −0.183224 | ||||||||
\(87\) | −4.13713 | −0.443546 | ||||||||
\(88\) | 8.26005 | 0.880524 | ||||||||
\(89\) | 12.6360 | 1.33941 | 0.669706 | − | 0.742626i | \(-0.266420\pi\) | ||||
0.669706 | + | 0.742626i | \(0.266420\pi\) | |||||||
\(90\) | 3.86981 | 0.407914 | ||||||||
\(91\) | −0.591135 | −0.0619678 | ||||||||
\(92\) | 6.23995 | 0.650560 | ||||||||
\(93\) | 16.6892 | 1.73059 | ||||||||
\(94\) | −4.81174 | −0.496293 | ||||||||
\(95\) | −15.1419 | −1.55352 | ||||||||
\(96\) | 12.4972 | 1.27549 | ||||||||
\(97\) | 1.57745 | 0.160165 | 0.0800827 | − | 0.996788i | \(-0.474482\pi\) | ||||
0.0800827 | + | 0.996788i | \(0.474482\pi\) | |||||||
\(98\) | −4.08857 | −0.413008 | ||||||||
\(99\) | −8.45553 | −0.849813 | ||||||||
\(100\) | −6.85485 | −0.685485 | ||||||||
\(101\) | −3.82740 | −0.380841 | −0.190420 | − | 0.981703i | \(-0.560985\pi\) | ||||
−0.190420 | + | 0.981703i | \(0.560985\pi\) | |||||||
\(102\) | −0.977713 | −0.0968080 | ||||||||
\(103\) | 6.12856 | 0.603865 | 0.301932 | − | 0.953329i | \(-0.402368\pi\) | ||||
0.301932 | + | 0.953329i | \(0.402368\pi\) | |||||||
\(104\) | 14.1084 | 1.38345 | ||||||||
\(105\) | 0.617075 | 0.0602204 | ||||||||
\(106\) | 4.05825 | 0.394172 | ||||||||
\(107\) | 5.43938 | 0.525844 | 0.262922 | − | 0.964817i | \(-0.415314\pi\) | ||||
0.262922 | + | 0.964817i | \(0.415314\pi\) | |||||||
\(108\) | 3.06074 | 0.294519 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −6.82445 | −0.650686 | ||||||||
\(111\) | −2.27809 | −0.216227 | ||||||||
\(112\) | 0.185104 | 0.0174907 | ||||||||
\(113\) | 8.54599 | 0.803939 | 0.401969 | − | 0.915653i | \(-0.368326\pi\) | ||||
0.401969 | + | 0.915653i | \(0.368326\pi\) | |||||||
\(114\) | −6.67400 | −0.625077 | ||||||||
\(115\) | −11.3741 | −1.06064 | ||||||||
\(116\) | 3.01113 | 0.279577 | ||||||||
\(117\) | −14.4423 | −1.33519 | ||||||||
\(118\) | −2.42820 | −0.223534 | ||||||||
\(119\) | −0.0657809 | −0.00603013 | ||||||||
\(120\) | −14.7275 | −1.34443 | ||||||||
\(121\) | 3.91141 | 0.355582 | ||||||||
\(122\) | 7.78747 | 0.705045 | ||||||||
\(123\) | −1.08405 | −0.0977452 | ||||||||
\(124\) | −12.1470 | −1.09083 | ||||||||
\(125\) | −2.61656 | −0.234032 | ||||||||
\(126\) | 0.114758 | 0.0102235 | ||||||||
\(127\) | 3.19202 | 0.283246 | 0.141623 | − | 0.989921i | \(-0.454768\pi\) | ||||
0.141623 | + | 0.989921i | \(0.454768\pi\) | |||||||
\(128\) | −11.5112 | −1.01746 | ||||||||
\(129\) | −6.61956 | −0.582820 | ||||||||
\(130\) | −11.6564 | −1.02233 | ||||||||
\(131\) | 16.0710 | 1.40413 | 0.702064 | − | 0.712114i | \(-0.252262\pi\) | ||||
0.702064 | + | 0.712114i | \(0.252262\pi\) | |||||||
\(132\) | 14.5858 | 1.26953 | ||||||||
\(133\) | −0.449029 | −0.0389358 | ||||||||
\(134\) | −4.46965 | −0.386119 | ||||||||
\(135\) | −5.57906 | −0.480169 | ||||||||
\(136\) | 1.56997 | 0.134624 | ||||||||
\(137\) | −19.6588 | −1.67957 | −0.839784 | − | 0.542921i | \(-0.817318\pi\) | ||||
−0.839784 | + | 0.542921i | \(0.817318\pi\) | |||||||
\(138\) | −5.01328 | −0.426759 | ||||||||
\(139\) | 1.73228 | 0.146930 | 0.0734651 | − | 0.997298i | \(-0.476594\pi\) | ||||
0.0734651 | + | 0.997298i | \(0.476594\pi\) | |||||||
\(140\) | −0.449127 | −0.0379581 | ||||||||
\(141\) | −18.7457 | −1.57867 | ||||||||
\(142\) | −5.28110 | −0.443180 | ||||||||
\(143\) | 25.4692 | 2.12984 | ||||||||
\(144\) | 4.52237 | 0.376864 | ||||||||
\(145\) | −5.48864 | −0.455807 | ||||||||
\(146\) | 4.14444 | 0.342997 | ||||||||
\(147\) | −15.9283 | −1.31375 | ||||||||
\(148\) | 1.65806 | 0.136292 | ||||||||
\(149\) | 12.1107 | 0.992151 | 0.496075 | − | 0.868279i | \(-0.334774\pi\) | ||||
0.496075 | + | 0.868279i | \(0.334774\pi\) | |||||||
\(150\) | 5.50730 | 0.449669 | ||||||||
\(151\) | 9.88185 | 0.804173 | 0.402087 | − | 0.915602i | \(-0.368285\pi\) | ||||
0.402087 | + | 0.915602i | \(0.368285\pi\) | |||||||
\(152\) | 10.7168 | 0.869251 | ||||||||
\(153\) | −1.60713 | −0.129929 | ||||||||
\(154\) | −0.202378 | −0.0163081 | ||||||||
\(155\) | 22.1413 | 1.77843 | ||||||||
\(156\) | 24.9131 | 1.99464 | ||||||||
\(157\) | −9.83495 | −0.784915 | −0.392457 | − | 0.919770i | \(-0.628375\pi\) | ||||
−0.392457 | + | 0.919770i | \(0.628375\pi\) | |||||||
\(158\) | −0.970776 | −0.0772308 | ||||||||
\(159\) | 15.8102 | 1.25383 | ||||||||
\(160\) | 16.5797 | 1.31074 | ||||||||
\(161\) | −0.337296 | −0.0265826 | ||||||||
\(162\) | −6.30032 | −0.495000 | ||||||||
\(163\) | −9.29509 | −0.728048 | −0.364024 | − | 0.931390i | \(-0.618597\pi\) | ||||
−0.364024 | + | 0.931390i | \(0.618597\pi\) | |||||||
\(164\) | 0.789004 | 0.0616108 | ||||||||
\(165\) | −26.5868 | −2.06978 | ||||||||
\(166\) | −5.12328 | −0.397644 | ||||||||
\(167\) | 2.25508 | 0.174503 | 0.0872515 | − | 0.996186i | \(-0.472192\pi\) | ||||
0.0872515 | + | 0.996186i | \(0.472192\pi\) | |||||||
\(168\) | −0.436742 | −0.0336954 | ||||||||
\(169\) | 30.5022 | 2.34632 | ||||||||
\(170\) | −1.29711 | −0.0994839 | ||||||||
\(171\) | −10.9705 | −0.838933 | ||||||||
\(172\) | 4.81793 | 0.367363 | ||||||||
\(173\) | 23.3800 | 1.77755 | 0.888775 | − | 0.458344i | \(-0.151557\pi\) | ||||
0.888775 | + | 0.458344i | \(0.151557\pi\) | |||||||
\(174\) | −2.41919 | −0.183399 | ||||||||
\(175\) | 0.370534 | 0.0280097 | ||||||||
\(176\) | −7.97524 | −0.601157 | ||||||||
\(177\) | −9.45982 | −0.711044 | ||||||||
\(178\) | 7.38892 | 0.553823 | ||||||||
\(179\) | −24.3241 | −1.81807 | −0.909034 | − | 0.416721i | \(-0.863179\pi\) | ||||
−0.909034 | + | 0.416721i | \(0.863179\pi\) | |||||||
\(180\) | −10.9729 | −0.817868 | ||||||||
\(181\) | −14.8469 | −1.10356 | −0.551779 | − | 0.833990i | \(-0.686051\pi\) | ||||
−0.551779 | + | 0.833990i | \(0.686051\pi\) | |||||||
\(182\) | −0.345668 | −0.0256226 | ||||||||
\(183\) | 30.3386 | 2.24269 | ||||||||
\(184\) | 8.05013 | 0.593464 | ||||||||
\(185\) | −3.02229 | −0.222203 | ||||||||
\(186\) | 9.75908 | 0.715570 | ||||||||
\(187\) | 2.83419 | 0.207256 | ||||||||
\(188\) | 13.6437 | 0.995067 | ||||||||
\(189\) | −0.165446 | −0.0120344 | ||||||||
\(190\) | −8.85425 | −0.642355 | ||||||||
\(191\) | 1.84155 | 0.133250 | 0.0666249 | − | 0.997778i | \(-0.478777\pi\) | ||||
0.0666249 | + | 0.997778i | \(0.478777\pi\) | |||||||
\(192\) | −2.10215 | −0.151710 | ||||||||
\(193\) | 7.17013 | 0.516118 | 0.258059 | − | 0.966129i | \(-0.416917\pi\) | ||||
0.258059 | + | 0.966129i | \(0.416917\pi\) | |||||||
\(194\) | 0.922416 | 0.0662256 | ||||||||
\(195\) | −45.4111 | −3.25196 | ||||||||
\(196\) | 11.5931 | 0.828081 | ||||||||
\(197\) | 16.3347 | 1.16380 | 0.581898 | − | 0.813262i | \(-0.302310\pi\) | ||||
0.581898 | + | 0.813262i | \(0.302310\pi\) | |||||||
\(198\) | −4.94439 | −0.351383 | ||||||||
\(199\) | −7.10890 | −0.503937 | −0.251968 | − | 0.967735i | \(-0.581078\pi\) | ||||
−0.251968 | + | 0.967735i | \(0.581078\pi\) | |||||||
\(200\) | −8.84341 | −0.625324 | ||||||||
\(201\) | −17.4130 | −1.22821 | ||||||||
\(202\) | −2.23808 | −0.157471 | ||||||||
\(203\) | −0.162764 | −0.0114238 | ||||||||
\(204\) | 2.77230 | 0.194100 | ||||||||
\(205\) | −1.43818 | −0.100447 | ||||||||
\(206\) | 3.58369 | 0.249688 | ||||||||
\(207\) | −8.24065 | −0.572765 | ||||||||
\(208\) | −13.6220 | −0.944514 | ||||||||
\(209\) | 19.3465 | 1.33823 | ||||||||
\(210\) | 0.360836 | 0.0249001 | ||||||||
\(211\) | 5.37546 | 0.370062 | 0.185031 | − | 0.982733i | \(-0.440761\pi\) | ||||
0.185031 | + | 0.982733i | \(0.440761\pi\) | |||||||
\(212\) | −11.5072 | −0.790314 | ||||||||
\(213\) | −20.5742 | −1.40972 | ||||||||
\(214\) | 3.18069 | 0.217427 | ||||||||
\(215\) | −8.78203 | −0.598930 | ||||||||
\(216\) | 3.94864 | 0.268671 | ||||||||
\(217\) | 0.656595 | 0.0445725 | ||||||||
\(218\) | −0.584752 | −0.0396044 | ||||||||
\(219\) | 16.1460 | 1.09104 | ||||||||
\(220\) | 19.3507 | 1.30463 | ||||||||
\(221\) | 4.84088 | 0.325633 | ||||||||
\(222\) | −1.33212 | −0.0894059 | ||||||||
\(223\) | 17.6815 | 1.18404 | 0.592020 | − | 0.805923i | \(-0.298331\pi\) | ||||
0.592020 | + | 0.805923i | \(0.298331\pi\) | |||||||
\(224\) | 0.491669 | 0.0328510 | ||||||||
\(225\) | 9.05270 | 0.603513 | ||||||||
\(226\) | 4.99729 | 0.332415 | ||||||||
\(227\) | −12.6060 | −0.836687 | −0.418344 | − | 0.908289i | \(-0.637389\pi\) | ||||
−0.418344 | + | 0.908289i | \(0.637389\pi\) | |||||||
\(228\) | 18.9241 | 1.25328 | ||||||||
\(229\) | −6.19156 | −0.409149 | −0.204575 | − | 0.978851i | \(-0.565581\pi\) | ||||
−0.204575 | + | 0.978851i | \(0.565581\pi\) | |||||||
\(230\) | −6.65102 | −0.438555 | ||||||||
\(231\) | −0.788426 | −0.0518746 | ||||||||
\(232\) | 3.88465 | 0.255040 | ||||||||
\(233\) | −19.6366 | −1.28644 | −0.643219 | − | 0.765682i | \(-0.722402\pi\) | ||||
−0.643219 | + | 0.765682i | \(0.722402\pi\) | |||||||
\(234\) | −8.44519 | −0.552079 | ||||||||
\(235\) | −24.8695 | −1.62230 | ||||||||
\(236\) | 6.88516 | 0.448186 | ||||||||
\(237\) | −3.78197 | −0.245665 | ||||||||
\(238\) | −0.0384656 | −0.00249335 | ||||||||
\(239\) | 6.39489 | 0.413651 | 0.206826 | − | 0.978378i | \(-0.433687\pi\) | ||||
0.206826 | + | 0.978378i | \(0.433687\pi\) | |||||||
\(240\) | 14.2197 | 0.917880 | ||||||||
\(241\) | 20.8834 | 1.34522 | 0.672610 | − | 0.739997i | \(-0.265173\pi\) | ||||
0.672610 | + | 0.739997i | \(0.265173\pi\) | |||||||
\(242\) | 2.28720 | 0.147027 | ||||||||
\(243\) | −19.0070 | −1.21930 | ||||||||
\(244\) | −22.0814 | −1.41361 | ||||||||
\(245\) | −21.1318 | −1.35006 | ||||||||
\(246\) | −0.633899 | −0.0404159 | ||||||||
\(247\) | 33.0445 | 2.10257 | ||||||||
\(248\) | −15.6707 | −0.995093 | ||||||||
\(249\) | −19.9594 | −1.26487 | ||||||||
\(250\) | −1.53004 | −0.0967681 | ||||||||
\(251\) | 12.2115 | 0.770785 | 0.385392 | − | 0.922753i | \(-0.374066\pi\) | ||||
0.385392 | + | 0.922753i | \(0.374066\pi\) | |||||||
\(252\) | −0.325397 | −0.0204981 | ||||||||
\(253\) | 14.5325 | 0.913648 | ||||||||
\(254\) | 1.86654 | 0.117117 | ||||||||
\(255\) | −5.05331 | −0.316450 | ||||||||
\(256\) | −4.88568 | −0.305355 | ||||||||
\(257\) | −23.1327 | −1.44298 | −0.721491 | − | 0.692424i | \(-0.756543\pi\) | ||||
−0.721491 | + | 0.692424i | \(0.756543\pi\) | |||||||
\(258\) | −3.87080 | −0.240986 | ||||||||
\(259\) | −0.0896254 | −0.00556905 | ||||||||
\(260\) | 33.0517 | 2.04978 | ||||||||
\(261\) | −3.97658 | −0.246144 | ||||||||
\(262\) | 9.39754 | 0.580582 | ||||||||
\(263\) | −25.5161 | −1.57339 | −0.786696 | − | 0.617340i | \(-0.788210\pi\) | ||||
−0.786696 | + | 0.617340i | \(0.788210\pi\) | |||||||
\(264\) | 18.8171 | 1.15811 | ||||||||
\(265\) | 20.9750 | 1.28849 | ||||||||
\(266\) | −0.262571 | −0.0160993 | ||||||||
\(267\) | 28.7859 | 1.76167 | ||||||||
\(268\) | 12.6737 | 0.774169 | ||||||||
\(269\) | 14.1168 | 0.860717 | 0.430359 | − | 0.902658i | \(-0.358387\pi\) | ||||
0.430359 | + | 0.902658i | \(0.358387\pi\) | |||||||
\(270\) | −3.26237 | −0.198541 | ||||||||
\(271\) | 10.9707 | 0.666425 | 0.333213 | − | 0.942852i | \(-0.391867\pi\) | ||||
0.333213 | + | 0.942852i | \(0.391867\pi\) | |||||||
\(272\) | −1.51584 | −0.0919114 | ||||||||
\(273\) | −1.34666 | −0.0815034 | ||||||||
\(274\) | −11.4955 | −0.694472 | ||||||||
\(275\) | −15.9645 | −0.962697 | ||||||||
\(276\) | 14.2152 | 0.855652 | ||||||||
\(277\) | −29.6396 | −1.78087 | −0.890437 | − | 0.455107i | \(-0.849601\pi\) | ||||
−0.890437 | + | 0.455107i | \(0.849601\pi\) | |||||||
\(278\) | 1.01296 | 0.0607530 | ||||||||
\(279\) | 16.0416 | 0.960386 | ||||||||
\(280\) | −0.579417 | −0.0346268 | ||||||||
\(281\) | −18.6285 | −1.11128 | −0.555642 | − | 0.831421i | \(-0.687528\pi\) | ||||
−0.555642 | + | 0.831421i | \(0.687528\pi\) | |||||||
\(282\) | −10.9616 | −0.652752 | ||||||||
\(283\) | −2.28873 | −0.136051 | −0.0680255 | − | 0.997684i | \(-0.521670\pi\) | ||||
−0.0680255 | + | 0.997684i | \(0.521670\pi\) | |||||||
\(284\) | 14.9746 | 0.888576 | ||||||||
\(285\) | −34.4945 | −2.04328 | ||||||||
\(286\) | 14.8932 | 0.880651 | ||||||||
\(287\) | −0.0426490 | −0.00251749 | ||||||||
\(288\) | 12.0122 | 0.707826 | ||||||||
\(289\) | −16.4613 | −0.968312 | ||||||||
\(290\) | −3.20949 | −0.188468 | ||||||||
\(291\) | 3.59356 | 0.210658 | ||||||||
\(292\) | −11.7516 | −0.687708 | ||||||||
\(293\) | 14.5485 | 0.849935 | 0.424967 | − | 0.905209i | \(-0.360286\pi\) | ||||
0.424967 | + | 0.905209i | \(0.360286\pi\) | |||||||
\(294\) | −9.31412 | −0.543211 | ||||||||
\(295\) | −12.5501 | −0.730698 | ||||||||
\(296\) | 2.13906 | 0.124330 | ||||||||
\(297\) | 7.12826 | 0.413624 | ||||||||
\(298\) | 7.08179 | 0.410237 | ||||||||
\(299\) | 24.8219 | 1.43549 | ||||||||
\(300\) | −15.6160 | −0.901587 | ||||||||
\(301\) | −0.260429 | −0.0150109 | ||||||||
\(302\) | 5.77843 | 0.332512 | ||||||||
\(303\) | −8.71916 | −0.500903 | ||||||||
\(304\) | −10.3473 | −0.593460 | ||||||||
\(305\) | 40.2495 | 2.30468 | ||||||||
\(306\) | −0.939772 | −0.0537232 | ||||||||
\(307\) | −6.01746 | −0.343434 | −0.171717 | − | 0.985146i | \(-0.554932\pi\) | ||||
−0.171717 | + | 0.985146i | \(0.554932\pi\) | |||||||
\(308\) | 0.573841 | 0.0326976 | ||||||||
\(309\) | 13.9614 | 0.794236 | ||||||||
\(310\) | 12.9472 | 0.735350 | ||||||||
\(311\) | −2.84267 | −0.161193 | −0.0805966 | − | 0.996747i | \(-0.525683\pi\) | ||||
−0.0805966 | + | 0.996747i | \(0.525683\pi\) | |||||||
\(312\) | 32.1403 | 1.81958 | ||||||||
\(313\) | 14.0729 | 0.795448 | 0.397724 | − | 0.917505i | \(-0.369800\pi\) | ||||
0.397724 | + | 0.917505i | \(0.369800\pi\) | |||||||
\(314\) | −5.75101 | −0.324548 | ||||||||
\(315\) | 0.593129 | 0.0334190 | ||||||||
\(316\) | 2.75263 | 0.154848 | ||||||||
\(317\) | 11.7646 | 0.660765 | 0.330383 | − | 0.943847i | \(-0.392822\pi\) | ||||
0.330383 | + | 0.943847i | \(0.392822\pi\) | |||||||
\(318\) | 9.24504 | 0.518436 | ||||||||
\(319\) | 7.01274 | 0.392638 | ||||||||
\(320\) | −2.78888 | −0.155903 | ||||||||
\(321\) | 12.3914 | 0.691619 | ||||||||
\(322\) | −0.197234 | −0.0109914 | ||||||||
\(323\) | 3.67716 | 0.204603 | ||||||||
\(324\) | 17.8645 | 0.992475 | ||||||||
\(325\) | −27.2679 | −1.51255 | ||||||||
\(326\) | −5.43533 | −0.301035 | ||||||||
\(327\) | −2.27809 | −0.125979 | ||||||||
\(328\) | 1.01789 | 0.0562036 | ||||||||
\(329\) | −0.737498 | −0.0406596 | ||||||||
\(330\) | −15.5467 | −0.855818 | ||||||||
\(331\) | −29.7412 | −1.63473 | −0.817363 | − | 0.576123i | \(-0.804565\pi\) | ||||
−0.817363 | + | 0.576123i | \(0.804565\pi\) | |||||||
\(332\) | 14.5270 | 0.797275 | ||||||||
\(333\) | −2.18969 | −0.119994 | ||||||||
\(334\) | 1.31866 | 0.0721539 | ||||||||
\(335\) | −23.1014 | −1.26216 | ||||||||
\(336\) | 0.421683 | 0.0230047 | ||||||||
\(337\) | −11.6416 | −0.634157 | −0.317079 | − | 0.948399i | \(-0.602702\pi\) | ||||
−0.317079 | + | 0.948399i | \(0.602702\pi\) | |||||||
\(338\) | 17.8362 | 0.970163 | ||||||||
\(339\) | 19.4685 | 1.05738 | ||||||||
\(340\) | 3.67796 | 0.199465 | ||||||||
\(341\) | −28.2895 | −1.53196 | ||||||||
\(342\) | −6.41501 | −0.346884 | ||||||||
\(343\) | −1.25404 | −0.0677116 | ||||||||
\(344\) | 6.21559 | 0.335122 | ||||||||
\(345\) | −25.9111 | −1.39501 | ||||||||
\(346\) | 13.6715 | 0.734986 | ||||||||
\(347\) | 20.3437 | 1.09211 | 0.546054 | − | 0.837750i | \(-0.316129\pi\) | ||||
0.546054 | + | 0.837750i | \(0.316129\pi\) | |||||||
\(348\) | 6.85962 | 0.367714 | ||||||||
\(349\) | −33.4609 | −1.79112 | −0.895560 | − | 0.444940i | \(-0.853225\pi\) | ||||
−0.895560 | + | 0.444940i | \(0.853225\pi\) | |||||||
\(350\) | 0.216670 | 0.0115815 | ||||||||
\(351\) | 12.1753 | 0.649870 | ||||||||
\(352\) | −21.1836 | −1.12909 | ||||||||
\(353\) | −27.7137 | −1.47505 | −0.737527 | − | 0.675318i | \(-0.764006\pi\) | ||||
−0.737527 | + | 0.675318i | \(0.764006\pi\) | |||||||
\(354\) | −5.53165 | −0.294004 | ||||||||
\(355\) | −27.2954 | −1.44869 | ||||||||
\(356\) | −20.9513 | −1.11042 | ||||||||
\(357\) | −0.149855 | −0.00793115 | ||||||||
\(358\) | −14.2236 | −0.751739 | ||||||||
\(359\) | 19.7742 | 1.04364 | 0.521822 | − | 0.853054i | \(-0.325252\pi\) | ||||
0.521822 | + | 0.853054i | \(0.325252\pi\) | |||||||
\(360\) | −14.1560 | −0.746088 | ||||||||
\(361\) | 6.10077 | 0.321093 | ||||||||
\(362\) | −8.68174 | −0.456302 | ||||||||
\(363\) | 8.91053 | 0.467681 | ||||||||
\(364\) | 0.980140 | 0.0513733 | ||||||||
\(365\) | 21.4205 | 1.12120 | ||||||||
\(366\) | 17.7405 | 0.927313 | ||||||||
\(367\) | −11.4015 | −0.595152 | −0.297576 | − | 0.954698i | \(-0.596178\pi\) | ||||
−0.297576 | + | 0.954698i | \(0.596178\pi\) | |||||||
\(368\) | −7.77257 | −0.405173 | ||||||||
\(369\) | −1.04198 | −0.0542433 | ||||||||
\(370\) | −1.76729 | −0.0918772 | ||||||||
\(371\) | 0.622010 | 0.0322932 | ||||||||
\(372\) | −27.6718 | −1.43472 | ||||||||
\(373\) | −28.3847 | −1.46970 | −0.734852 | − | 0.678228i | \(-0.762748\pi\) | ||||
−0.734852 | + | 0.678228i | \(0.762748\pi\) | |||||||
\(374\) | 1.65730 | 0.0856968 | ||||||||
\(375\) | −5.96075 | −0.307812 | ||||||||
\(376\) | 17.6017 | 0.907736 | ||||||||
\(377\) | 11.9780 | 0.616898 | ||||||||
\(378\) | −0.0967448 | −0.00497601 | ||||||||
\(379\) | 18.5290 | 0.951769 | 0.475885 | − | 0.879508i | \(-0.342128\pi\) | ||||
0.475885 | + | 0.879508i | \(0.342128\pi\) | |||||||
\(380\) | 25.1062 | 1.28792 | ||||||||
\(381\) | 7.27171 | 0.372541 | ||||||||
\(382\) | 1.07685 | 0.0550965 | ||||||||
\(383\) | −33.9131 | −1.73288 | −0.866440 | − | 0.499282i | \(-0.833597\pi\) | ||||
−0.866440 | + | 0.499282i | \(0.833597\pi\) | |||||||
\(384\) | −26.2236 | −1.33822 | ||||||||
\(385\) | −1.04599 | −0.0533085 | ||||||||
\(386\) | 4.19275 | 0.213406 | ||||||||
\(387\) | −6.36268 | −0.323433 | ||||||||
\(388\) | −2.61551 | −0.132782 | ||||||||
\(389\) | −14.5294 | −0.736669 | −0.368335 | − | 0.929693i | \(-0.620072\pi\) | ||||
−0.368335 | + | 0.929693i | \(0.620072\pi\) | |||||||
\(390\) | −26.5543 | −1.34463 | ||||||||
\(391\) | 2.76216 | 0.139688 | ||||||||
\(392\) | 14.9563 | 0.755405 | ||||||||
\(393\) | 36.6111 | 1.84679 | ||||||||
\(394\) | 9.55174 | 0.481209 | ||||||||
\(395\) | −5.01745 | −0.252456 | ||||||||
\(396\) | 14.0198 | 0.704522 | ||||||||
\(397\) | −19.1823 | −0.962731 | −0.481365 | − | 0.876520i | \(-0.659859\pi\) | ||||
−0.481365 | + | 0.876520i | \(0.659859\pi\) | |||||||
\(398\) | −4.15695 | −0.208369 | ||||||||
\(399\) | −1.02293 | −0.0512105 | ||||||||
\(400\) | 8.53849 | 0.426925 | ||||||||
\(401\) | 5.34862 | 0.267097 | 0.133549 | − | 0.991042i | \(-0.457363\pi\) | ||||
0.133549 | + | 0.991042i | \(0.457363\pi\) | |||||||
\(402\) | −10.1823 | −0.507845 | ||||||||
\(403\) | −48.3194 | −2.40696 | ||||||||
\(404\) | 6.34608 | 0.315729 | ||||||||
\(405\) | −32.5632 | −1.61808 | ||||||||
\(406\) | −0.0951769 | −0.00472355 | ||||||||
\(407\) | 3.86153 | 0.191409 | ||||||||
\(408\) | 3.57654 | 0.177065 | ||||||||
\(409\) | −9.42415 | −0.465994 | −0.232997 | − | 0.972477i | \(-0.574853\pi\) | ||||
−0.232997 | + | 0.972477i | \(0.574853\pi\) | |||||||
\(410\) | −0.840981 | −0.0415331 | ||||||||
\(411\) | −44.7845 | −2.20906 | ||||||||
\(412\) | −10.1615 | −0.500624 | ||||||||
\(413\) | −0.372172 | −0.0183134 | ||||||||
\(414\) | −4.81874 | −0.236828 | ||||||||
\(415\) | −26.4797 | −1.29984 | ||||||||
\(416\) | −36.1824 | −1.77399 | ||||||||
\(417\) | 3.94629 | 0.193251 | ||||||||
\(418\) | 11.3129 | 0.553333 | ||||||||
\(419\) | −18.4384 | −0.900777 | −0.450388 | − | 0.892833i | \(-0.648714\pi\) | ||||
−0.450388 | + | 0.892833i | \(0.648714\pi\) | |||||||
\(420\) | −1.02315 | −0.0499246 | ||||||||
\(421\) | 37.1984 | 1.81294 | 0.906469 | − | 0.422273i | \(-0.138768\pi\) | ||||
0.906469 | + | 0.422273i | \(0.138768\pi\) | |||||||
\(422\) | 3.14332 | 0.153014 | ||||||||
\(423\) | −18.0182 | −0.876075 | ||||||||
\(424\) | −14.8453 | −0.720953 | ||||||||
\(425\) | −3.03435 | −0.147188 | ||||||||
\(426\) | −12.0308 | −0.582895 | ||||||||
\(427\) | 1.19359 | 0.0577619 | ||||||||
\(428\) | −9.01884 | −0.435942 | ||||||||
\(429\) | 58.0210 | 2.80128 | ||||||||
\(430\) | −5.13532 | −0.247647 | ||||||||
\(431\) | 11.9586 | 0.576028 | 0.288014 | − | 0.957626i | \(-0.407005\pi\) | ||||
0.288014 | + | 0.957626i | \(0.407005\pi\) | |||||||
\(432\) | −3.81249 | −0.183429 | ||||||||
\(433\) | 18.9425 | 0.910317 | 0.455158 | − | 0.890411i | \(-0.349583\pi\) | ||||
0.455158 | + | 0.890411i | \(0.349583\pi\) | |||||||
\(434\) | 0.383945 | 0.0184300 | ||||||||
\(435\) | −12.5036 | −0.599502 | ||||||||
\(436\) | 1.65806 | 0.0794069 | ||||||||
\(437\) | 18.8549 | 0.901950 | ||||||||
\(438\) | 9.44141 | 0.451128 | ||||||||
\(439\) | −34.1528 | −1.63003 | −0.815013 | − | 0.579443i | \(-0.803270\pi\) | ||||
−0.815013 | + | 0.579443i | \(0.803270\pi\) | |||||||
\(440\) | 24.9643 | 1.19013 | ||||||||
\(441\) | −15.3102 | −0.729057 | ||||||||
\(442\) | 2.83072 | 0.134643 | ||||||||
\(443\) | 31.5637 | 1.49964 | 0.749818 | − | 0.661644i | \(-0.230141\pi\) | ||||
0.749818 | + | 0.661644i | \(0.230141\pi\) | |||||||
\(444\) | 3.77722 | 0.179259 | ||||||||
\(445\) | 38.1896 | 1.81036 | ||||||||
\(446\) | 10.3393 | 0.489580 | ||||||||
\(447\) | 27.5893 | 1.30493 | ||||||||
\(448\) | −0.0827035 | −0.00390738 | ||||||||
\(449\) | −19.3841 | −0.914790 | −0.457395 | − | 0.889264i | \(-0.651218\pi\) | ||||
−0.457395 | + | 0.889264i | \(0.651218\pi\) | |||||||
\(450\) | 5.29359 | 0.249542 | ||||||||
\(451\) | 1.83754 | 0.0865264 | ||||||||
\(452\) | −14.1698 | −0.666491 | ||||||||
\(453\) | 22.5117 | 1.05769 | ||||||||
\(454\) | −7.37137 | −0.345955 | ||||||||
\(455\) | −1.78658 | −0.0837563 | ||||||||
\(456\) | 24.4139 | 1.14329 | ||||||||
\(457\) | −1.26750 | −0.0592910 | −0.0296455 | − | 0.999560i | \(-0.509438\pi\) | ||||
−0.0296455 | + | 0.999560i | \(0.509438\pi\) | |||||||
\(458\) | −3.62053 | −0.169176 | ||||||||
\(459\) | 1.35486 | 0.0632393 | ||||||||
\(460\) | 18.8590 | 0.879303 | ||||||||
\(461\) | −1.33108 | −0.0619947 | −0.0309974 | − | 0.999519i | \(-0.509868\pi\) | ||||
−0.0309974 | + | 0.999519i | \(0.509868\pi\) | |||||||
\(462\) | −0.461034 | −0.0214492 | ||||||||
\(463\) | −5.47601 | −0.254492 | −0.127246 | − | 0.991871i | \(-0.540614\pi\) | ||||
−0.127246 | + | 0.991871i | \(0.540614\pi\) | |||||||
\(464\) | −3.75070 | −0.174122 | ||||||||
\(465\) | 50.4398 | 2.33909 | ||||||||
\(466\) | −11.4826 | −0.531920 | ||||||||
\(467\) | −21.0263 | −0.972980 | −0.486490 | − | 0.873686i | \(-0.661723\pi\) | ||||
−0.486490 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(468\) | 23.9463 | 1.10692 | ||||||||
\(469\) | −0.685067 | −0.0316335 | ||||||||
\(470\) | −14.5425 | −0.670795 | ||||||||
\(471\) | −22.4049 | −1.03236 | ||||||||
\(472\) | 8.88251 | 0.408851 | ||||||||
\(473\) | 11.2206 | 0.515926 | ||||||||
\(474\) | −2.21151 | −0.101578 | ||||||||
\(475\) | −20.7129 | −0.950371 | ||||||||
\(476\) | 0.109069 | 0.00499917 | ||||||||
\(477\) | 15.1967 | 0.695807 | ||||||||
\(478\) | 3.73943 | 0.171038 | ||||||||
\(479\) | 35.4804 | 1.62114 | 0.810571 | − | 0.585640i | \(-0.199157\pi\) | ||||
0.810571 | + | 0.585640i | \(0.199157\pi\) | |||||||
\(480\) | 37.7701 | 1.72396 | ||||||||
\(481\) | 6.59562 | 0.300734 | ||||||||
\(482\) | 12.2116 | 0.556225 | ||||||||
\(483\) | −0.768389 | −0.0349629 | ||||||||
\(484\) | −6.48536 | −0.294789 | ||||||||
\(485\) | 4.76750 | 0.216481 | ||||||||
\(486\) | −11.1144 | −0.504158 | ||||||||
\(487\) | −33.7090 | −1.52750 | −0.763750 | − | 0.645512i | \(-0.776644\pi\) | ||||
−0.763750 | + | 0.645512i | \(0.776644\pi\) | |||||||
\(488\) | −28.4871 | −1.28955 | ||||||||
\(489\) | −21.1750 | −0.957569 | ||||||||
\(490\) | −12.3569 | −0.558226 | ||||||||
\(491\) | 13.4574 | 0.607325 | 0.303662 | − | 0.952780i | \(-0.401790\pi\) | ||||
0.303662 | + | 0.952780i | \(0.401790\pi\) | |||||||
\(492\) | 1.79742 | 0.0810339 | ||||||||
\(493\) | 1.33290 | 0.0600307 | ||||||||
\(494\) | 19.3228 | 0.869376 | ||||||||
\(495\) | −25.5551 | −1.14862 | ||||||||
\(496\) | 15.1304 | 0.679376 | ||||||||
\(497\) | −0.809438 | −0.0363083 | ||||||||
\(498\) | −11.6713 | −0.523003 | ||||||||
\(499\) | 24.3761 | 1.09122 | 0.545612 | − | 0.838038i | \(-0.316297\pi\) | ||||
0.545612 | + | 0.838038i | \(0.316297\pi\) | |||||||
\(500\) | 4.33842 | 0.194020 | ||||||||
\(501\) | 5.13726 | 0.229516 | ||||||||
\(502\) | 7.14072 | 0.318706 | ||||||||
\(503\) | −6.81572 | −0.303898 | −0.151949 | − | 0.988388i | \(-0.548555\pi\) | ||||
−0.151949 | + | 0.988388i | \(0.548555\pi\) | |||||||
\(504\) | −0.419794 | −0.0186991 | ||||||||
\(505\) | −11.5675 | −0.514748 | ||||||||
\(506\) | 8.49789 | 0.377777 | ||||||||
\(507\) | 69.4867 | 3.08601 | ||||||||
\(508\) | −5.29258 | −0.234820 | ||||||||
\(509\) | 14.5328 | 0.644154 | 0.322077 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322077 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(510\) | −2.95493 | −0.130847 | ||||||||
\(511\) | 0.635222 | 0.0281005 | ||||||||
\(512\) | 20.1655 | 0.891199 | ||||||||
\(513\) | 9.24843 | 0.408328 | ||||||||
\(514\) | −13.5269 | −0.596647 | ||||||||
\(515\) | 18.5223 | 0.816190 | ||||||||
\(516\) | 10.9757 | 0.483176 | ||||||||
\(517\) | 31.7753 | 1.39747 | ||||||||
\(518\) | −0.0524087 | −0.00230270 | ||||||||
\(519\) | 53.2617 | 2.33793 | ||||||||
\(520\) | 42.6398 | 1.86988 | ||||||||
\(521\) | 42.2720 | 1.85197 | 0.925985 | − | 0.377561i | \(-0.123237\pi\) | ||||
0.925985 | + | 0.377561i | \(0.123237\pi\) | |||||||
\(522\) | −2.32532 | −0.101776 | ||||||||
\(523\) | 10.6812 | 0.467058 | 0.233529 | − | 0.972350i | \(-0.424973\pi\) | ||||
0.233529 | + | 0.972350i | \(0.424973\pi\) | |||||||
\(524\) | −26.6467 | −1.16407 | ||||||||
\(525\) | 0.844108 | 0.0368399 | ||||||||
\(526\) | −14.9206 | −0.650570 | ||||||||
\(527\) | −5.37694 | −0.234223 | ||||||||
\(528\) | −18.1683 | −0.790674 | ||||||||
\(529\) | −8.83686 | −0.384211 | ||||||||
\(530\) | 12.2652 | 0.532766 | ||||||||
\(531\) | −9.09273 | −0.394591 | ||||||||
\(532\) | 0.744519 | 0.0322790 | ||||||||
\(533\) | 3.13858 | 0.135947 | ||||||||
\(534\) | 16.8326 | 0.728419 | ||||||||
\(535\) | 16.4394 | 0.710736 | ||||||||
\(536\) | 16.3503 | 0.706225 | ||||||||
\(537\) | −55.4124 | −2.39122 | ||||||||
\(538\) | 8.25484 | 0.355891 | ||||||||
\(539\) | 26.9997 | 1.16296 | ||||||||
\(540\) | 9.25044 | 0.398075 | ||||||||
\(541\) | 19.7921 | 0.850930 | 0.425465 | − | 0.904975i | \(-0.360111\pi\) | ||||
0.425465 | + | 0.904975i | \(0.360111\pi\) | |||||||
\(542\) | 6.41517 | 0.275555 | ||||||||
\(543\) | −33.8225 | −1.45146 | ||||||||
\(544\) | −4.02634 | −0.172628 | ||||||||
\(545\) | −3.02229 | −0.129461 | ||||||||
\(546\) | −0.787461 | −0.0337002 | ||||||||
\(547\) | 20.6735 | 0.883935 | 0.441968 | − | 0.897031i | \(-0.354281\pi\) | ||||
0.441968 | + | 0.897031i | \(0.354281\pi\) | |||||||
\(548\) | 32.5956 | 1.39242 | ||||||||
\(549\) | 29.1612 | 1.24457 | ||||||||
\(550\) | −9.33529 | −0.398058 | ||||||||
\(551\) | 9.09854 | 0.387611 | ||||||||
\(552\) | 18.3389 | 0.780556 | ||||||||
\(553\) | −0.148792 | −0.00632726 | ||||||||
\(554\) | −17.3319 | −0.736360 | ||||||||
\(555\) | −6.88505 | −0.292254 | ||||||||
\(556\) | −2.87223 | −0.121810 | ||||||||
\(557\) | −8.87489 | −0.376041 | −0.188021 | − | 0.982165i | \(-0.560207\pi\) | ||||
−0.188021 | + | 0.982165i | \(0.560207\pi\) | |||||||
\(558\) | 9.38037 | 0.397103 | ||||||||
\(559\) | 19.1652 | 0.810603 | ||||||||
\(560\) | 0.559438 | 0.0236406 | ||||||||
\(561\) | 6.45652 | 0.272595 | ||||||||
\(562\) | −10.8931 | −0.459497 | ||||||||
\(563\) | 39.4753 | 1.66369 | 0.831843 | − | 0.555011i | \(-0.187286\pi\) | ||||
0.831843 | + | 0.555011i | \(0.187286\pi\) | |||||||
\(564\) | 31.0815 | 1.30877 | ||||||||
\(565\) | 25.8285 | 1.08661 | ||||||||
\(566\) | −1.33834 | −0.0562547 | ||||||||
\(567\) | −0.965654 | −0.0405537 | ||||||||
\(568\) | 19.3186 | 0.810591 | ||||||||
\(569\) | 23.1213 | 0.969294 | 0.484647 | − | 0.874710i | \(-0.338948\pi\) | ||||
0.484647 | + | 0.874710i | \(0.338948\pi\) | |||||||
\(570\) | −20.1708 | −0.844861 | ||||||||
\(571\) | −33.3786 | −1.39685 | −0.698425 | − | 0.715683i | \(-0.746115\pi\) | ||||
−0.698425 | + | 0.715683i | \(0.746115\pi\) | |||||||
\(572\) | −42.2295 | −1.76571 | ||||||||
\(573\) | 4.19521 | 0.175257 | ||||||||
\(574\) | −0.0249391 | −0.00104094 | ||||||||
\(575\) | −15.5588 | −0.648847 | ||||||||
\(576\) | −2.02057 | −0.0841906 | ||||||||
\(577\) | −20.3857 | −0.848667 | −0.424333 | − | 0.905506i | \(-0.639492\pi\) | ||||
−0.424333 | + | 0.905506i | \(0.639492\pi\) | |||||||
\(578\) | −9.62579 | −0.400380 | ||||||||
\(579\) | 16.3342 | 0.678826 | ||||||||
\(580\) | 9.10052 | 0.377878 | ||||||||
\(581\) | −0.785248 | −0.0325776 | ||||||||
\(582\) | 2.10134 | 0.0871035 | ||||||||
\(583\) | −26.7994 | −1.10992 | ||||||||
\(584\) | −15.1606 | −0.627352 | ||||||||
\(585\) | −43.6489 | −1.80466 | ||||||||
\(586\) | 8.50729 | 0.351433 | ||||||||
\(587\) | −12.1035 | −0.499565 | −0.249782 | − | 0.968302i | \(-0.580359\pi\) | ||||
−0.249782 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(588\) | 26.4102 | 1.08914 | ||||||||
\(589\) | −36.7037 | −1.51235 | ||||||||
\(590\) | −7.33873 | −0.302131 | ||||||||
\(591\) | 37.2118 | 1.53069 | ||||||||
\(592\) | −2.06531 | −0.0848836 | ||||||||
\(593\) | −29.0891 | −1.19455 | −0.597273 | − | 0.802038i | \(-0.703749\pi\) | ||||
−0.597273 | + | 0.802038i | \(0.703749\pi\) | |||||||
\(594\) | 4.16827 | 0.171026 | ||||||||
\(595\) | −0.198809 | −0.00815038 | ||||||||
\(596\) | −20.0804 | −0.822525 | ||||||||
\(597\) | −16.1947 | −0.662805 | ||||||||
\(598\) | 14.5147 | 0.593549 | ||||||||
\(599\) | 1.75083 | 0.0715368 | 0.0357684 | − | 0.999360i | \(-0.488612\pi\) | ||||
0.0357684 | + | 0.999360i | \(0.488612\pi\) | |||||||
\(600\) | −20.1461 | −0.822460 | ||||||||
\(601\) | −26.3868 | −1.07634 | −0.538170 | − | 0.842836i | \(-0.680884\pi\) | ||||
−0.538170 | + | 0.842836i | \(0.680884\pi\) | |||||||
\(602\) | −0.152287 | −0.00620674 | ||||||||
\(603\) | −16.7372 | −0.681593 | ||||||||
\(604\) | −16.3847 | −0.666686 | ||||||||
\(605\) | 11.8214 | 0.480609 | ||||||||
\(606\) | −5.09855 | −0.207114 | ||||||||
\(607\) | 7.96874 | 0.323441 | 0.161721 | − | 0.986837i | \(-0.448296\pi\) | ||||
0.161721 | + | 0.986837i | \(0.448296\pi\) | |||||||
\(608\) | −27.4843 | −1.11464 | ||||||||
\(609\) | −0.370792 | −0.0150252 | ||||||||
\(610\) | 23.5360 | 0.952945 | ||||||||
\(611\) | 54.2732 | 2.19566 | ||||||||
\(612\) | 2.66472 | 0.107715 | ||||||||
\(613\) | 17.6987 | 0.714846 | 0.357423 | − | 0.933943i | \(-0.383656\pi\) | ||||
0.357423 | + | 0.933943i | \(0.383656\pi\) | |||||||
\(614\) | −3.51872 | −0.142004 | ||||||||
\(615\) | −3.27631 | −0.132113 | ||||||||
\(616\) | 0.740310 | 0.0298280 | ||||||||
\(617\) | 25.2186 | 1.01526 | 0.507631 | − | 0.861574i | \(-0.330521\pi\) | ||||
0.507631 | + | 0.861574i | \(0.330521\pi\) | |||||||
\(618\) | 8.16396 | 0.328403 | ||||||||
\(619\) | −28.6527 | −1.15165 | −0.575825 | − | 0.817573i | \(-0.695319\pi\) | ||||
−0.575825 | + | 0.817573i | \(0.695319\pi\) | |||||||
\(620\) | −36.7117 | −1.47438 | ||||||||
\(621\) | 6.94711 | 0.278778 | ||||||||
\(622\) | −1.66226 | −0.0666506 | ||||||||
\(623\) | 1.13251 | 0.0453729 | ||||||||
\(624\) | −31.0321 | −1.24228 | ||||||||
\(625\) | −28.5792 | −1.14317 | ||||||||
\(626\) | 8.22917 | 0.328904 | ||||||||
\(627\) | 44.0731 | 1.76011 | ||||||||
\(628\) | 16.3070 | 0.650720 | ||||||||
\(629\) | 0.733954 | 0.0292647 | ||||||||
\(630\) | 0.346834 | 0.0138182 | ||||||||
\(631\) | 26.2067 | 1.04327 | 0.521636 | − | 0.853168i | \(-0.325322\pi\) | ||||
0.521636 | + | 0.853168i | \(0.325322\pi\) | |||||||
\(632\) | 3.55116 | 0.141258 | ||||||||
\(633\) | 12.2458 | 0.486726 | ||||||||
\(634\) | 6.87937 | 0.273215 | ||||||||
\(635\) | 9.64723 | 0.382839 | ||||||||
\(636\) | −26.2143 | −1.03946 | ||||||||
\(637\) | 46.1163 | 1.82720 | ||||||||
\(638\) | 4.10071 | 0.162349 | ||||||||
\(639\) | −19.7758 | −0.782319 | ||||||||
\(640\) | −34.7903 | −1.37521 | ||||||||
\(641\) | 18.6295 | 0.735819 | 0.367910 | − | 0.929862i | \(-0.380074\pi\) | ||||
0.367910 | + | 0.929862i | \(0.380074\pi\) | |||||||
\(642\) | 7.24589 | 0.285972 | ||||||||
\(643\) | −29.1929 | −1.15126 | −0.575628 | − | 0.817712i | \(-0.695242\pi\) | ||||
−0.575628 | + | 0.817712i | \(0.695242\pi\) | |||||||
\(644\) | 0.559258 | 0.0220379 | ||||||||
\(645\) | −20.0062 | −0.787745 | ||||||||
\(646\) | 2.15023 | 0.0845996 | ||||||||
\(647\) | −47.4581 | −1.86577 | −0.932885 | − | 0.360175i | \(-0.882717\pi\) | ||||
−0.932885 | + | 0.360175i | \(0.882717\pi\) | |||||||
\(648\) | 23.0470 | 0.905371 | ||||||||
\(649\) | 16.0351 | 0.629433 | ||||||||
\(650\) | −15.9450 | −0.625414 | ||||||||
\(651\) | 1.49578 | 0.0586243 | ||||||||
\(652\) | 15.4119 | 0.603575 | ||||||||
\(653\) | −5.68593 | −0.222508 | −0.111254 | − | 0.993792i | \(-0.535487\pi\) | ||||
−0.111254 | + | 0.993792i | \(0.535487\pi\) | |||||||
\(654\) | −1.33212 | −0.0520899 | ||||||||
\(655\) | 48.5712 | 1.89783 | ||||||||
\(656\) | −0.982793 | −0.0383716 | ||||||||
\(657\) | 15.5194 | 0.605471 | ||||||||
\(658\) | −0.431254 | −0.0168120 | ||||||||
\(659\) | −9.92443 | −0.386601 | −0.193300 | − | 0.981140i | \(-0.561919\pi\) | ||||
−0.193300 | + | 0.981140i | \(0.561919\pi\) | |||||||
\(660\) | 44.0826 | 1.71591 | ||||||||
\(661\) | −7.26866 | −0.282718 | −0.141359 | − | 0.989958i | \(-0.545147\pi\) | ||||
−0.141359 | + | 0.989958i | \(0.545147\pi\) | |||||||
\(662\) | −17.3913 | −0.675931 | ||||||||
\(663\) | 11.0280 | 0.428290 | ||||||||
\(664\) | 18.7413 | 0.727303 | ||||||||
\(665\) | −1.35710 | −0.0526260 | ||||||||
\(666\) | −1.28042 | −0.0496154 | ||||||||
\(667\) | 6.83452 | 0.264634 | ||||||||
\(668\) | −3.73906 | −0.144669 | ||||||||
\(669\) | 40.2800 | 1.55731 | ||||||||
\(670\) | −13.5086 | −0.521883 | ||||||||
\(671\) | −51.4261 | −1.98528 | ||||||||
\(672\) | 1.12006 | 0.0432074 | ||||||||
\(673\) | 14.1466 | 0.545310 | 0.272655 | − | 0.962112i | \(-0.412098\pi\) | ||||
0.272655 | + | 0.962112i | \(0.412098\pi\) | |||||||
\(674\) | −6.80744 | −0.262213 | ||||||||
\(675\) | −7.63169 | −0.293744 | ||||||||
\(676\) | −50.5746 | −1.94518 | ||||||||
\(677\) | 32.1454 | 1.23545 | 0.617725 | − | 0.786395i | \(-0.288055\pi\) | ||||
0.617725 | + | 0.786395i | \(0.288055\pi\) | |||||||
\(678\) | 11.3843 | 0.437210 | ||||||||
\(679\) | 0.141379 | 0.00542564 | ||||||||
\(680\) | 4.74492 | 0.181959 | ||||||||
\(681\) | −28.7175 | −1.10046 | ||||||||
\(682\) | −16.5424 | −0.633440 | ||||||||
\(683\) | −37.0433 | −1.41742 | −0.708712 | − | 0.705498i | \(-0.750723\pi\) | ||||
−0.708712 | + | 0.705498i | \(0.750723\pi\) | |||||||
\(684\) | 18.1897 | 0.695502 | ||||||||
\(685\) | −59.4147 | −2.27012 | ||||||||
\(686\) | −0.733300 | −0.0279975 | ||||||||
\(687\) | −14.1049 | −0.538136 | ||||||||
\(688\) | −6.00127 | −0.228796 | ||||||||
\(689\) | −45.7743 | −1.74386 | ||||||||
\(690\) | −15.1516 | −0.576812 | ||||||||
\(691\) | 12.7318 | 0.484341 | 0.242170 | − | 0.970234i | \(-0.422141\pi\) | ||||
0.242170 | + | 0.970234i | \(0.422141\pi\) | |||||||
\(692\) | −38.7656 | −1.47365 | ||||||||
\(693\) | −0.757830 | −0.0287876 | ||||||||
\(694\) | 11.8960 | 0.451567 | ||||||||
\(695\) | 5.23546 | 0.198592 | ||||||||
\(696\) | 8.84957 | 0.335442 | ||||||||
\(697\) | 0.349258 | 0.0132291 | ||||||||
\(698\) | −19.5663 | −0.740597 | ||||||||
\(699\) | −44.7340 | −1.69199 | ||||||||
\(700\) | −0.614369 | −0.0232210 | ||||||||
\(701\) | −1.40835 | −0.0531927 | −0.0265964 | − | 0.999646i | \(-0.508467\pi\) | ||||
−0.0265964 | + | 0.999646i | \(0.508467\pi\) | |||||||
\(702\) | 7.11954 | 0.268710 | ||||||||
\(703\) | 5.01007 | 0.188958 | ||||||||
\(704\) | 3.56330 | 0.134297 | ||||||||
\(705\) | −56.6548 | −2.13374 | ||||||||
\(706\) | −16.2057 | −0.609909 | ||||||||
\(707\) | −0.343032 | −0.0129011 | ||||||||
\(708\) | 15.6850 | 0.589478 | ||||||||
\(709\) | −20.2078 | −0.758920 | −0.379460 | − | 0.925208i | \(-0.623890\pi\) | ||||
−0.379460 | + | 0.925208i | \(0.623890\pi\) | |||||||
\(710\) | −15.9610 | −0.599007 | ||||||||
\(711\) | −3.63520 | −0.136331 | ||||||||
\(712\) | −27.0292 | −1.01296 | ||||||||
\(713\) | −27.5706 | −1.03253 | ||||||||
\(714\) | −0.0876279 | −0.00327939 | ||||||||
\(715\) | 76.9753 | 2.87871 | ||||||||
\(716\) | 40.3309 | 1.50724 | ||||||||
\(717\) | 14.5681 | 0.544057 | ||||||||
\(718\) | 11.5630 | 0.431529 | ||||||||
\(719\) | −9.45831 | −0.352735 | −0.176368 | − | 0.984324i | \(-0.556435\pi\) | ||||
−0.176368 | + | 0.984324i | \(0.556435\pi\) | |||||||
\(720\) | 13.6679 | 0.509374 | ||||||||
\(721\) | 0.549275 | 0.0204561 | ||||||||
\(722\) | 3.56744 | 0.132766 | ||||||||
\(723\) | 47.5743 | 1.76931 | ||||||||
\(724\) | 24.6171 | 0.914886 | ||||||||
\(725\) | −7.50801 | −0.278840 | ||||||||
\(726\) | 5.21045 | 0.193378 | ||||||||
\(727\) | 23.4752 | 0.870647 | 0.435324 | − | 0.900274i | \(-0.356634\pi\) | ||||
0.435324 | + | 0.900274i | \(0.356634\pi\) | |||||||
\(728\) | 1.26447 | 0.0468645 | ||||||||
\(729\) | −10.9766 | −0.406539 | ||||||||
\(730\) | 12.5257 | 0.463598 | ||||||||
\(731\) | 2.13269 | 0.0788804 | ||||||||
\(732\) | −50.3033 | −1.85926 | ||||||||
\(733\) | −23.6122 | −0.872138 | −0.436069 | − | 0.899913i | \(-0.643630\pi\) | ||||
−0.436069 | + | 0.899913i | \(0.643630\pi\) | |||||||
\(734\) | −6.66703 | −0.246085 | ||||||||
\(735\) | −48.1400 | −1.77567 | ||||||||
\(736\) | −20.6453 | −0.760996 | ||||||||
\(737\) | 29.5163 | 1.08725 | ||||||||
\(738\) | −0.609300 | −0.0224286 | ||||||||
\(739\) | −16.4596 | −0.605478 | −0.302739 | − | 0.953074i | \(-0.597901\pi\) | ||||
−0.302739 | + | 0.953074i | \(0.597901\pi\) | |||||||
\(740\) | 5.01115 | 0.184214 | ||||||||
\(741\) | 75.2783 | 2.76542 | ||||||||
\(742\) | 0.363722 | 0.0133527 | ||||||||
\(743\) | −25.0956 | −0.920667 | −0.460333 | − | 0.887746i | \(-0.652270\pi\) | ||||
−0.460333 | + | 0.887746i | \(0.652270\pi\) | |||||||
\(744\) | −35.6993 | −1.30880 | ||||||||
\(745\) | 36.6022 | 1.34100 | ||||||||
\(746\) | −16.5980 | −0.607697 | ||||||||
\(747\) | −19.1848 | −0.701936 | ||||||||
\(748\) | −4.69926 | −0.171822 | ||||||||
\(749\) | 0.487506 | 0.0178131 | ||||||||
\(750\) | −3.48556 | −0.127275 | ||||||||
\(751\) | −23.2231 | −0.847422 | −0.423711 | − | 0.905797i | \(-0.639273\pi\) | ||||
−0.423711 | + | 0.905797i | \(0.639273\pi\) | |||||||
\(752\) | −16.9947 | −0.619735 | ||||||||
\(753\) | 27.8189 | 1.01378 | ||||||||
\(754\) | 7.00416 | 0.255076 | ||||||||
\(755\) | 29.8658 | 1.08693 | ||||||||
\(756\) | 0.274320 | 0.00997691 | ||||||||
\(757\) | 24.5149 | 0.891011 | 0.445505 | − | 0.895279i | \(-0.353024\pi\) | ||||
0.445505 | + | 0.895279i | \(0.353024\pi\) | |||||||
\(758\) | 10.8349 | 0.393540 | ||||||||
\(759\) | 33.1062 | 1.20168 | ||||||||
\(760\) | 32.3894 | 1.17489 | ||||||||
\(761\) | 12.7152 | 0.460925 | 0.230463 | − | 0.973081i | \(-0.425976\pi\) | ||||
0.230463 | + | 0.973081i | \(0.425976\pi\) | |||||||
\(762\) | 4.25215 | 0.154039 | ||||||||
\(763\) | −0.0896254 | −0.00324466 | ||||||||
\(764\) | −3.05341 | −0.110468 | ||||||||
\(765\) | −4.85721 | −0.175613 | ||||||||
\(766\) | −19.8308 | −0.716515 | ||||||||
\(767\) | 27.3885 | 0.988941 | ||||||||
\(768\) | −11.1300 | −0.401620 | ||||||||
\(769\) | 23.5298 | 0.848505 | 0.424252 | − | 0.905544i | \(-0.360537\pi\) | ||||
0.424252 | + | 0.905544i | \(0.360537\pi\) | |||||||
\(770\) | −0.611644 | −0.0220421 | ||||||||
\(771\) | −52.6984 | −1.89789 | ||||||||
\(772\) | −11.8885 | −0.427878 | ||||||||
\(773\) | −30.3911 | −1.09309 | −0.546546 | − | 0.837429i | \(-0.684058\pi\) | ||||
−0.546546 | + | 0.837429i | \(0.684058\pi\) | |||||||
\(774\) | −3.72059 | −0.133734 | ||||||||
\(775\) | 30.2874 | 1.08796 | ||||||||
\(776\) | −3.37426 | −0.121129 | ||||||||
\(777\) | −0.204175 | −0.00732472 | ||||||||
\(778\) | −8.49610 | −0.304600 | ||||||||
\(779\) | 2.38408 | 0.0854186 | ||||||||
\(780\) | 75.2946 | 2.69598 | ||||||||
\(781\) | 34.8748 | 1.24792 | ||||||||
\(782\) | 1.61518 | 0.0577587 | ||||||||
\(783\) | 3.35237 | 0.119804 | ||||||||
\(784\) | −14.4406 | −0.515734 | ||||||||
\(785\) | −29.7241 | −1.06090 | ||||||||
\(786\) | 21.4084 | 0.763613 | ||||||||
\(787\) | −12.9196 | −0.460534 | −0.230267 | − | 0.973128i | \(-0.573960\pi\) | ||||
−0.230267 | + | 0.973128i | \(0.573960\pi\) | |||||||
\(788\) | −27.0839 | −0.964825 | ||||||||
\(789\) | −58.1280 | −2.06941 | ||||||||
\(790\) | −2.93397 | −0.104386 | ||||||||
\(791\) | 0.765937 | 0.0272336 | ||||||||
\(792\) | 18.0869 | 0.642690 | ||||||||
\(793\) | −87.8375 | −3.11920 | ||||||||
\(794\) | −11.2169 | −0.398072 | ||||||||
\(795\) | 47.7830 | 1.69469 | ||||||||
\(796\) | 11.7870 | 0.417780 | ||||||||
\(797\) | 55.3286 | 1.95984 | 0.979920 | − | 0.199392i | \(-0.0638967\pi\) | ||||
0.979920 | + | 0.199392i | \(0.0638967\pi\) | |||||||
\(798\) | −0.598160 | −0.0211746 | ||||||||
\(799\) | 6.03947 | 0.213661 | ||||||||
\(800\) | 22.6797 | 0.801850 | ||||||||
\(801\) | 27.6688 | 0.977630 | ||||||||
\(802\) | 3.12762 | 0.110440 | ||||||||
\(803\) | −27.3687 | −0.965819 | ||||||||
\(804\) | 28.8718 | 1.01823 | ||||||||
\(805\) | −1.01941 | −0.0359293 | ||||||||
\(806\) | −28.2549 | −0.995236 | ||||||||
\(807\) | 32.1593 | 1.13206 | ||||||||
\(808\) | 8.18705 | 0.288019 | ||||||||
\(809\) | −28.5850 | −1.00499 | −0.502497 | − | 0.864579i | \(-0.667585\pi\) | ||||
−0.502497 | + | 0.864579i | \(0.667585\pi\) | |||||||
\(810\) | −19.0414 | −0.669047 | ||||||||
\(811\) | 35.6691 | 1.25251 | 0.626255 | − | 0.779618i | \(-0.284587\pi\) | ||||
0.626255 | + | 0.779618i | \(0.284587\pi\) | |||||||
\(812\) | 0.269874 | 0.00947071 | ||||||||
\(813\) | 24.9923 | 0.876519 | ||||||||
\(814\) | 2.25804 | 0.0791442 | ||||||||
\(815\) | −28.0925 | −0.984037 | ||||||||
\(816\) | −3.45322 | −0.120887 | ||||||||
\(817\) | 14.5580 | 0.509320 | ||||||||
\(818\) | −5.51080 | −0.192680 | ||||||||
\(819\) | −1.29440 | −0.0452300 | ||||||||
\(820\) | 2.38460 | 0.0832738 | ||||||||
\(821\) | 28.6649 | 1.00041 | 0.500207 | − | 0.865906i | \(-0.333257\pi\) | ||||
0.500207 | + | 0.865906i | \(0.333257\pi\) | |||||||
\(822\) | −26.1879 | −0.913407 | ||||||||
\(823\) | −27.1376 | −0.945958 | −0.472979 | − | 0.881074i | \(-0.656821\pi\) | ||||
−0.472979 | + | 0.881074i | \(0.656821\pi\) | |||||||
\(824\) | −13.1094 | −0.456687 | ||||||||
\(825\) | −36.3686 | −1.26619 | ||||||||
\(826\) | −0.217628 | −0.00757226 | ||||||||
\(827\) | 12.2489 | 0.425936 | 0.212968 | − | 0.977059i | \(-0.431687\pi\) | ||||
0.212968 | + | 0.977059i | \(0.431687\pi\) | |||||||
\(828\) | 13.6635 | 0.474840 | ||||||||
\(829\) | 30.6128 | 1.06323 | 0.531614 | − | 0.846987i | \(-0.321586\pi\) | ||||
0.531614 | + | 0.846987i | \(0.321586\pi\) | |||||||
\(830\) | −15.4840 | −0.537459 | ||||||||
\(831\) | −67.5217 | −2.34230 | ||||||||
\(832\) | 6.08623 | 0.211002 | ||||||||
\(833\) | 5.13178 | 0.177806 | ||||||||
\(834\) | 2.30760 | 0.0799057 | ||||||||
\(835\) | 6.81550 | 0.235860 | ||||||||
\(836\) | −32.0778 | −1.10943 | ||||||||
\(837\) | −13.5235 | −0.467442 | ||||||||
\(838\) | −10.7819 | −0.372455 | ||||||||
\(839\) | 23.0314 | 0.795131 | 0.397566 | − | 0.917574i | \(-0.369855\pi\) | ||||
0.397566 | + | 0.917574i | \(0.369855\pi\) | |||||||
\(840\) | −1.31996 | −0.0455430 | ||||||||
\(841\) | −25.7020 | −0.886274 | ||||||||
\(842\) | 21.7518 | 0.749618 | ||||||||
\(843\) | −42.4374 | −1.46162 | ||||||||
\(844\) | −8.91287 | −0.306794 | ||||||||
\(845\) | 92.1865 | 3.17131 | ||||||||
\(846\) | −10.5362 | −0.362242 | ||||||||
\(847\) | 0.350561 | 0.0120454 | ||||||||
\(848\) | 14.3335 | 0.492213 | ||||||||
\(849\) | −5.21393 | −0.178942 | ||||||||
\(850\) | −1.77434 | −0.0608594 | ||||||||
\(851\) | 3.76339 | 0.129007 | ||||||||
\(852\) | 34.1133 | 1.16870 | ||||||||
\(853\) | 11.4143 | 0.390817 | 0.195408 | − | 0.980722i | \(-0.437397\pi\) | ||||
0.195408 | + | 0.980722i | \(0.437397\pi\) | |||||||
\(854\) | 0.697955 | 0.0238835 | ||||||||
\(855\) | −33.1560 | −1.13391 | ||||||||
\(856\) | −11.6352 | −0.397682 | ||||||||
\(857\) | −3.21516 | −0.109828 | −0.0549139 | − | 0.998491i | \(-0.517488\pi\) | ||||
−0.0549139 | + | 0.998491i | \(0.517488\pi\) | |||||||
\(858\) | 33.9279 | 1.15828 | ||||||||
\(859\) | 29.2317 | 0.997374 | 0.498687 | − | 0.866782i | \(-0.333816\pi\) | ||||
0.498687 | + | 0.866782i | \(0.333816\pi\) | |||||||
\(860\) | 14.5612 | 0.496532 | ||||||||
\(861\) | −0.0971581 | −0.00331114 | ||||||||
\(862\) | 6.99285 | 0.238177 | ||||||||
\(863\) | −22.2295 | −0.756702 | −0.378351 | − | 0.925662i | \(-0.623509\pi\) | ||||
−0.378351 | + | 0.925662i | \(0.623509\pi\) | |||||||
\(864\) | −10.1266 | −0.344516 | ||||||||
\(865\) | 70.6612 | 2.40255 | ||||||||
\(866\) | 11.0767 | 0.376400 | ||||||||
\(867\) | −37.5003 | −1.27358 | ||||||||
\(868\) | −1.08868 | −0.0369521 | ||||||||
\(869\) | 6.41071 | 0.217469 | ||||||||
\(870\) | −7.31151 | −0.247883 | ||||||||
\(871\) | 50.4147 | 1.70824 | ||||||||
\(872\) | 2.13906 | 0.0724378 | ||||||||
\(873\) | 3.45411 | 0.116904 | ||||||||
\(874\) | 11.0254 | 0.372941 | ||||||||
\(875\) | −0.234510 | −0.00792788 | ||||||||
\(876\) | −26.7711 | −0.904511 | ||||||||
\(877\) | 34.4329 | 1.16272 | 0.581358 | − | 0.813648i | \(-0.302522\pi\) | ||||
0.581358 | + | 0.813648i | \(0.302522\pi\) | |||||||
\(878\) | −19.9710 | −0.673987 | ||||||||
\(879\) | 33.1429 | 1.11788 | ||||||||
\(880\) | −24.1035 | −0.812529 | ||||||||
\(881\) | −28.6241 | −0.964370 | −0.482185 | − | 0.876069i | \(-0.660157\pi\) | ||||
−0.482185 | + | 0.876069i | \(0.660157\pi\) | |||||||
\(882\) | −8.95268 | −0.301452 | ||||||||
\(883\) | −26.4849 | −0.891288 | −0.445644 | − | 0.895210i | \(-0.647025\pi\) | ||||
−0.445644 | + | 0.895210i | \(0.647025\pi\) | |||||||
\(884\) | −8.02649 | −0.269960 | ||||||||
\(885\) | −28.5903 | −0.961054 | ||||||||
\(886\) | 18.4570 | 0.620073 | ||||||||
\(887\) | −10.2875 | −0.345421 | −0.172710 | − | 0.984973i | \(-0.555252\pi\) | ||||
−0.172710 | + | 0.984973i | \(0.555252\pi\) | |||||||
\(888\) | 4.87297 | 0.163526 | ||||||||
\(889\) | 0.286086 | 0.00959503 | ||||||||
\(890\) | 22.3315 | 0.748553 | ||||||||
\(891\) | 41.6054 | 1.39383 | ||||||||
\(892\) | −29.3170 | −0.981607 | ||||||||
\(893\) | 41.2262 | 1.37958 | ||||||||
\(894\) | 16.1329 | 0.539566 | ||||||||
\(895\) | −73.5145 | −2.45732 | ||||||||
\(896\) | −1.03170 | −0.0344666 | ||||||||
\(897\) | 56.5465 | 1.88803 | ||||||||
\(898\) | −11.3349 | −0.378250 | ||||||||
\(899\) | −13.3044 | −0.443726 | ||||||||
\(900\) | −15.0100 | −0.500332 | ||||||||
\(901\) | −5.09372 | −0.169697 | ||||||||
\(902\) | 1.07451 | 0.0357771 | ||||||||
\(903\) | −0.593281 | −0.0197431 | ||||||||
\(904\) | −18.2804 | −0.607997 | ||||||||
\(905\) | −44.8715 | −1.49158 | ||||||||
\(906\) | 13.1638 | 0.437337 | ||||||||
\(907\) | −28.5031 | −0.946431 | −0.473215 | − | 0.880947i | \(-0.656907\pi\) | ||||
−0.473215 | + | 0.880947i | \(0.656907\pi\) | |||||||
\(908\) | 20.9015 | 0.693641 | ||||||||
\(909\) | −8.38080 | −0.277974 | ||||||||
\(910\) | −1.04471 | −0.0346317 | ||||||||
\(911\) | −43.2998 | −1.43459 | −0.717293 | − | 0.696772i | \(-0.754619\pi\) | ||||
−0.717293 | + | 0.696772i | \(0.754619\pi\) | |||||||
\(912\) | −23.5721 | −0.780551 | ||||||||
\(913\) | 33.8326 | 1.11970 | ||||||||
\(914\) | −0.741171 | −0.0245158 | ||||||||
\(915\) | 91.6920 | 3.03124 | ||||||||
\(916\) | 10.2660 | 0.339198 | ||||||||
\(917\) | 1.44037 | 0.0475651 | ||||||||
\(918\) | 0.792256 | 0.0261483 | ||||||||
\(919\) | −21.5168 | −0.709774 | −0.354887 | − | 0.934909i | \(-0.615481\pi\) | ||||
−0.354887 | + | 0.934909i | \(0.615481\pi\) | |||||||
\(920\) | 24.3299 | 0.802132 | ||||||||
\(921\) | −13.7083 | −0.451704 | ||||||||
\(922\) | −0.778354 | −0.0256337 | ||||||||
\(923\) | 59.5673 | 1.96068 | ||||||||
\(924\) | 1.30726 | 0.0430057 | ||||||||
\(925\) | −4.13425 | −0.135933 | ||||||||
\(926\) | −3.20211 | −0.105228 | ||||||||
\(927\) | 13.4196 | 0.440758 | ||||||||
\(928\) | −9.96253 | −0.327036 | ||||||||
\(929\) | 9.74770 | 0.319812 | 0.159906 | − | 0.987132i | \(-0.448881\pi\) | ||||
0.159906 | + | 0.987132i | \(0.448881\pi\) | |||||||
\(930\) | 29.4948 | 0.967172 | ||||||||
\(931\) | 35.0302 | 1.14807 | ||||||||
\(932\) | 32.5588 | 1.06650 | ||||||||
\(933\) | −6.47586 | −0.212010 | ||||||||
\(934\) | −12.2952 | −0.402310 | ||||||||
\(935\) | 8.56573 | 0.280129 | ||||||||
\(936\) | 30.8930 | 1.00977 | ||||||||
\(937\) | −37.9518 | −1.23983 | −0.619916 | − | 0.784668i | \(-0.712833\pi\) | ||||
−0.619916 | + | 0.784668i | \(0.712833\pi\) | |||||||
\(938\) | −0.400595 | −0.0130799 | ||||||||
\(939\) | 32.0593 | 1.04622 | ||||||||
\(940\) | 41.2352 | 1.34494 | ||||||||
\(941\) | −29.6207 | −0.965607 | −0.482804 | − | 0.875729i | \(-0.660382\pi\) | ||||
−0.482804 | + | 0.875729i | \(0.660382\pi\) | |||||||
\(942\) | −13.1013 | −0.426864 | ||||||||
\(943\) | 1.79084 | 0.0583178 | ||||||||
\(944\) | −8.57624 | −0.279133 | ||||||||
\(945\) | −0.500025 | −0.0162658 | ||||||||
\(946\) | 6.56130 | 0.213326 | ||||||||
\(947\) | 37.3241 | 1.21287 | 0.606436 | − | 0.795132i | \(-0.292599\pi\) | ||||
0.606436 | + | 0.795132i | \(0.292599\pi\) | |||||||
\(948\) | 6.27074 | 0.203664 | ||||||||
\(949\) | −46.7466 | −1.51746 | ||||||||
\(950\) | −12.1119 | −0.392962 | ||||||||
\(951\) | 26.8008 | 0.869074 | ||||||||
\(952\) | 0.140710 | 0.00456042 | ||||||||
\(953\) | −52.3441 | −1.69559 | −0.847795 | − | 0.530324i | \(-0.822070\pi\) | ||||
−0.847795 | + | 0.530324i | \(0.822070\pi\) | |||||||
\(954\) | 8.88628 | 0.287704 | ||||||||
\(955\) | 5.56570 | 0.180102 | ||||||||
\(956\) | −10.6031 | −0.342930 | ||||||||
\(957\) | 15.9756 | 0.516419 | ||||||||
\(958\) | 20.7473 | 0.670314 | ||||||||
\(959\) | −1.76193 | −0.0568957 | ||||||||
\(960\) | −6.35331 | −0.205052 | ||||||||
\(961\) | 22.6701 | 0.731294 | ||||||||
\(962\) | 3.85680 | 0.124348 | ||||||||
\(963\) | 11.9105 | 0.383811 | ||||||||
\(964\) | −34.6261 | −1.11523 | ||||||||
\(965\) | 21.6702 | 0.697590 | ||||||||
\(966\) | −0.449318 | −0.0144566 | ||||||||
\(967\) | 43.3244 | 1.39322 | 0.696610 | − | 0.717450i | \(-0.254691\pi\) | ||||
0.696610 | + | 0.717450i | \(0.254691\pi\) | |||||||
\(968\) | −8.36674 | −0.268917 | ||||||||
\(969\) | 8.37689 | 0.269105 | ||||||||
\(970\) | 2.78781 | 0.0895111 | ||||||||
\(971\) | −38.4145 | −1.23278 | −0.616390 | − | 0.787441i | \(-0.711406\pi\) | ||||
−0.616390 | + | 0.787441i | \(0.711406\pi\) | |||||||
\(972\) | 31.5148 | 1.01084 | ||||||||
\(973\) | 0.155256 | 0.00497729 | ||||||||
\(974\) | −19.7114 | −0.631594 | ||||||||
\(975\) | −62.1187 | −1.98939 | ||||||||
\(976\) | 27.5048 | 0.880409 | ||||||||
\(977\) | −26.8389 | −0.858653 | −0.429326 | − | 0.903149i | \(-0.641249\pi\) | ||||
−0.429326 | + | 0.903149i | \(0.641249\pi\) | |||||||
\(978\) | −12.3822 | −0.395938 | ||||||||
\(979\) | −48.7942 | −1.55947 | ||||||||
\(980\) | 35.0378 | 1.11924 | ||||||||
\(981\) | −2.18969 | −0.0699113 | ||||||||
\(982\) | 7.86926 | 0.251118 | ||||||||
\(983\) | −29.4959 | −0.940774 | −0.470387 | − | 0.882460i | \(-0.655886\pi\) | ||||
−0.470387 | + | 0.882460i | \(0.655886\pi\) | |||||||
\(984\) | 2.31884 | 0.0739220 | ||||||||
\(985\) | 49.3681 | 1.57300 | ||||||||
\(986\) | 0.779416 | 0.0248217 | ||||||||
\(987\) | −1.68009 | −0.0534777 | ||||||||
\(988\) | −54.7899 | −1.74310 | ||||||||
\(989\) | 10.9355 | 0.347728 | ||||||||
\(990\) | −14.9434 | −0.474932 | ||||||||
\(991\) | −61.6396 | −1.95805 | −0.979024 | − | 0.203746i | \(-0.934688\pi\) | ||||
−0.979024 | + | 0.203746i | \(0.934688\pi\) | |||||||
\(992\) | 40.1890 | 1.27600 | ||||||||
\(993\) | −67.7532 | −2.15008 | ||||||||
\(994\) | −0.473321 | −0.0150128 | ||||||||
\(995\) | −21.4852 | −0.681126 | ||||||||
\(996\) | 33.0939 | 1.04862 | ||||||||
\(997\) | 33.7609 | 1.06922 | 0.534609 | − | 0.845099i | \(-0.320459\pi\) | ||||
0.534609 | + | 0.845099i | \(0.320459\pi\) | |||||||
\(998\) | 14.2540 | 0.451202 | ||||||||
\(999\) | 1.84597 | 0.0584039 |
(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 | 4033.2.a.d.1.50 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.50 | ✓ | 79 | 1.1 | even | 1 | trivial |