Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,2,Mod(23,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.k (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(1.31753163335\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} + 19 x^{12} - 80 x^{11} + 168 x^{10} + 28 x^{9} + 119 x^{8} - 432 x^{7} + 784 x^{6} + 84 x^{5} + 169 x^{4} - 420 x^{3} + 392 x^{2} - 112 x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 122.3 | ||
Root | \(1.05652 + 1.05652i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.122 |
Dual form | 165.2.k.c.23.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.05652 | + | 1.05652i | −0.747074 | + | 0.747074i | −0.973929 | − | 0.226854i | \(-0.927156\pi\) |
0.226854 | + | 0.973929i | \(0.427156\pi\) | |||||||
\(3\) | −1.71860 | + | 0.215468i | −0.992232 | + | 0.124400i | ||||
\(4\) | − | 0.232479i | − | 0.116240i | ||||||
\(5\) | −0.158945 | − | 2.23041i | −0.0710824 | − | 0.997470i | ||||
\(6\) | 1.58809 | − | 2.04338i | 0.648335 | − | 0.834207i | ||||
\(7\) | −1.04338 | − | 1.04338i | −0.394361 | − | 0.394361i | 0.481877 | − | 0.876239i | \(-0.339955\pi\) |
−0.876239 | + | 0.481877i | \(0.839955\pi\) | |||||||
\(8\) | −1.86743 | − | 1.86743i | −0.660234 | − | 0.660234i | ||||
\(9\) | 2.90715 | − | 0.740604i | 0.969049 | − | 0.246868i | ||||
\(10\) | 2.52441 | + | 2.18855i | 0.798288 | + | 0.692081i | ||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0.0500918 | + | 0.399538i | 0.0144603 | + | 0.115337i | ||||
\(13\) | 3.37924 | − | 3.37924i | 0.937233 | − | 0.937233i | −0.0609106 | − | 0.998143i | \(-0.519400\pi\) |
0.998143 | + | 0.0609106i | \(0.0194004\pi\) | |||||||
\(14\) | 2.20471 | 0.589234 | ||||||||
\(15\) | 0.753744 | + | 3.79893i | 0.194616 | + | 0.980880i | ||||
\(16\) | 4.41091 | 1.10273 | ||||||||
\(17\) | −0.138459 | + | 0.138459i | −0.0335813 | + | 0.0335813i | −0.723698 | − | 0.690117i | \(-0.757559\pi\) |
0.690117 | + | 0.723698i | \(0.257559\pi\) | |||||||
\(18\) | −2.28900 | + | 3.85393i | −0.539523 | + | 0.908380i | ||||
\(19\) | − | 6.97457i | − | 1.60008i | −0.599949 | − | 0.800038i | \(-0.704813\pi\) | ||
0.599949 | − | 0.800038i | \(-0.295187\pi\) | |||||||
\(20\) | −0.518525 | + | 0.0369515i | −0.115946 | + | 0.00826260i | ||||
\(21\) | 2.01797 | + | 1.56834i | 0.440357 | + | 0.342239i | ||||
\(22\) | −1.05652 | − | 1.05652i | −0.225251 | − | 0.225251i | ||||
\(23\) | −2.64775 | − | 2.64775i | −0.552094 | − | 0.552094i | 0.374951 | − | 0.927045i | \(-0.377660\pi\) |
−0.927045 | + | 0.374951i | \(0.877660\pi\) | |||||||
\(24\) | 3.61172 | + | 2.80698i | 0.737239 | + | 0.572972i | ||||
\(25\) | −4.94947 | + | 0.709026i | −0.989895 | + | 0.141805i | ||||
\(26\) | 7.14049i | 1.40036i | ||||||||
\(27\) | −4.83664 | + | 1.89920i | −0.930811 | + | 0.365500i | ||||
\(28\) | −0.242565 | + | 0.242565i | −0.0458405 | + | 0.0458405i | ||||
\(29\) | −0.161760 | −0.0300381 | −0.0150190 | − | 0.999887i | \(-0.504781\pi\) | ||||
−0.0150190 | + | 0.999887i | \(0.504781\pi\) | |||||||
\(30\) | −4.81000 | − | 3.21731i | −0.878182 | − | 0.587397i | ||||
\(31\) | −7.53000 | −1.35243 | −0.676214 | − | 0.736705i | \(-0.736381\pi\) | ||||
−0.676214 | + | 0.736705i | \(0.736381\pi\) | |||||||
\(32\) | −0.925378 | + | 0.925378i | −0.163585 | + | 0.163585i | ||||
\(33\) | −0.215468 | − | 1.71860i | −0.0375081 | − | 0.299169i | ||||
\(34\) | − | 0.292570i | − | 0.0501754i | ||||||
\(35\) | −2.16133 | + | 2.49301i | −0.365332 | + | 0.421396i | ||||
\(36\) | −0.172175 | − | 0.675852i | −0.0286959 | − | 0.112642i | ||||
\(37\) | 3.94032 | + | 3.94032i | 0.647785 | + | 0.647785i | 0.952457 | − | 0.304672i | \(-0.0985470\pi\) |
−0.304672 | + | 0.952457i | \(0.598547\pi\) | |||||||
\(38\) | 7.36879 | + | 7.36879i | 1.19538 | + | 1.19538i | ||||
\(39\) | −5.07943 | + | 6.53567i | −0.813360 | + | 1.04654i | ||||
\(40\) | −3.86831 | + | 4.46195i | −0.611633 | + | 0.705495i | ||||
\(41\) | − | 8.21214i | − | 1.28252i | −0.767324 | − | 0.641260i | \(-0.778412\pi\) | ||
0.767324 | − | 0.641260i | \(-0.221588\pi\) | |||||||
\(42\) | −3.78901 | + | 0.475044i | −0.584657 | + | 0.0733009i | ||||
\(43\) | −1.14357 | + | 1.14357i | −0.174392 | + | 0.174392i | −0.788906 | − | 0.614514i | \(-0.789352\pi\) |
0.614514 | + | 0.788906i | \(0.289352\pi\) | |||||||
\(44\) | 0.232479 | 0.0350476 | ||||||||
\(45\) | −2.11393 | − | 6.36642i | −0.315126 | − | 0.949050i | ||||
\(46\) | 5.59482 | 0.824911 | ||||||||
\(47\) | −0.797409 | + | 0.797409i | −0.116314 | + | 0.116314i | −0.762868 | − | 0.646554i | \(-0.776209\pi\) |
0.646554 | + | 0.762868i | \(0.276209\pi\) | |||||||
\(48\) | −7.58058 | + | 0.950409i | −1.09416 | + | 0.137180i | ||||
\(49\) | − | 4.82271i | − | 0.688958i | ||||||
\(50\) | 4.48013 | − | 5.97833i | 0.633586 | − | 0.845464i | ||||
\(51\) | 0.208122 | − | 0.267789i | 0.0291429 | − | 0.0374979i | ||||
\(52\) | −0.785604 | − | 0.785604i | −0.108944 | − | 0.108944i | ||||
\(53\) | −0.0372189 | − | 0.0372189i | −0.00511240 | − | 0.00511240i | 0.704546 | − | 0.709658i | \(-0.251151\pi\) |
−0.709658 | + | 0.704546i | \(0.751151\pi\) | |||||||
\(54\) | 3.10347 | − | 7.11656i | 0.422329 | − | 0.968441i | ||||
\(55\) | 2.23041 | − | 0.158945i | 0.300749 | − | 0.0214322i | ||||
\(56\) | 3.89688i | 0.520742i | ||||||||
\(57\) | 1.50279 | + | 11.9865i | 0.199050 | + | 1.58765i | ||||
\(58\) | 0.170903 | − | 0.170903i | 0.0224407 | − | 0.0224407i | ||||
\(59\) | 10.3955 | 1.35338 | 0.676688 | − | 0.736270i | \(-0.263414\pi\) | ||||
0.676688 | + | 0.736270i | \(0.263414\pi\) | |||||||
\(60\) | 0.883173 | − | 0.175230i | 0.114017 | − | 0.0226221i | ||||
\(61\) | −8.33669 | −1.06740 | −0.533702 | − | 0.845673i | \(-0.679200\pi\) | ||||
−0.533702 | + | 0.845673i | \(0.679200\pi\) | |||||||
\(62\) | 7.95562 | − | 7.95562i | 1.01036 | − | 1.01036i | ||||
\(63\) | −3.80600 | − | 2.26053i | −0.479511 | − | 0.284800i | ||||
\(64\) | 6.86646i | 0.858308i | ||||||||
\(65\) | −8.07421 | − | 6.99998i | −1.00148 | − | 0.868241i | ||||
\(66\) | 2.04338 | + | 1.58809i | 0.251523 | + | 0.195480i | ||||
\(67\) | 5.41037 | + | 5.41037i | 0.660982 | + | 0.660982i | 0.955611 | − | 0.294630i | \(-0.0951963\pi\) |
−0.294630 | + | 0.955611i | \(0.595196\pi\) | |||||||
\(68\) | 0.0321889 | + | 0.0321889i | 0.00390348 | + | 0.00390348i | ||||
\(69\) | 5.12092 | + | 3.97991i | 0.616486 | + | 0.479125i | ||||
\(70\) | −0.350429 | − | 4.91742i | −0.0418842 | − | 0.587744i | ||||
\(71\) | 15.1518i | 1.79819i | 0.437755 | + | 0.899095i | \(0.355774\pi\) | ||||
−0.437755 | + | 0.899095i | \(0.644226\pi\) | |||||||
\(72\) | −6.81190 | − | 4.04586i | −0.802790 | − | 0.476809i | ||||
\(73\) | 3.98389 | − | 3.98389i | 0.466279 | − | 0.466279i | −0.434428 | − | 0.900707i | \(-0.643049\pi\) |
0.900707 | + | 0.434428i | \(0.143049\pi\) | |||||||
\(74\) | −8.32608 | −0.967887 | ||||||||
\(75\) | 8.35337 | − | 2.28498i | 0.964565 | − | 0.263847i | ||||
\(76\) | −1.62144 | −0.185992 | ||||||||
\(77\) | 1.04338 | − | 1.04338i | 0.118904 | − | 0.118904i | ||||
\(78\) | −1.53854 | − | 12.2716i | −0.174206 | − | 1.38949i | ||||
\(79\) | − | 13.5518i | − | 1.52470i | −0.647165 | − | 0.762350i | \(-0.724046\pi\) | ||
0.647165 | − | 0.762350i | \(-0.275954\pi\) | |||||||
\(80\) | −0.701093 | − | 9.83815i | −0.0783846 | − | 1.09994i | ||||
\(81\) | 7.90301 | − | 4.30609i | 0.878112 | − | 0.478454i | ||||
\(82\) | 8.67631 | + | 8.67631i | 0.958138 | + | 0.958138i | ||||
\(83\) | 5.92343 | + | 5.92343i | 0.650181 | + | 0.650181i | 0.953036 | − | 0.302856i | \(-0.0979400\pi\) |
−0.302856 | + | 0.953036i | \(0.597940\pi\) | |||||||
\(84\) | 0.364606 | − | 0.469136i | 0.0397818 | − | 0.0511869i | ||||
\(85\) | 0.330828 | + | 0.286814i | 0.0358834 | + | 0.0311093i | ||||
\(86\) | − | 2.41641i | − | 0.260568i | ||||||
\(87\) | 0.278000 | − | 0.0348540i | 0.0298047 | − | 0.00373675i | ||||
\(88\) | 1.86743 | − | 1.86743i | 0.199068 | − | 0.199068i | ||||
\(89\) | 2.98552 | 0.316464 | 0.158232 | − | 0.987402i | \(-0.449421\pi\) | ||||
0.158232 | + | 0.987402i | \(0.449421\pi\) | |||||||
\(90\) | 8.95968 | + | 4.49285i | 0.944433 | + | 0.473588i | ||||
\(91\) | −7.05168 | −0.739217 | ||||||||
\(92\) | −0.615548 | + | 0.615548i | −0.0641753 | + | 0.0641753i | ||||
\(93\) | 12.9410 | − | 1.62247i | 1.34192 | − | 0.168243i | ||||
\(94\) | − | 1.68496i | − | 0.173790i | ||||||
\(95\) | −15.5562 | + | 1.10857i | −1.59603 | + | 0.113737i | ||||
\(96\) | 1.39096 | − | 1.78974i | 0.141964 | − | 0.182665i | ||||
\(97\) | 7.94941 | + | 7.94941i | 0.807141 | + | 0.807141i | 0.984200 | − | 0.177060i | \(-0.0566585\pi\) |
−0.177060 | + | 0.984200i | \(0.556659\pi\) | |||||||
\(98\) | 5.09530 | + | 5.09530i | 0.514703 | + | 0.514703i | ||||
\(99\) | 0.740604 | + | 2.90715i | 0.0744335 | + | 0.292179i | ||||
\(100\) | 0.164834 | + | 1.15065i | 0.0164834 | + | 0.115065i | ||||
\(101\) | − | 2.33132i | − | 0.231975i | −0.993251 | − | 0.115987i | \(-0.962997\pi\) | ||
0.993251 | − | 0.115987i | \(-0.0370032\pi\) | |||||||
\(102\) | 0.0630395 | + | 0.502810i | 0.00624184 | + | 0.0497857i | ||||
\(103\) | −1.95903 | + | 1.95903i | −0.193029 | + | 0.193029i | −0.797003 | − | 0.603975i | \(-0.793583\pi\) |
0.603975 | + | 0.797003i | \(0.293583\pi\) | |||||||
\(104\) | −12.6210 | −1.23759 | ||||||||
\(105\) | 3.17729 | − | 4.75018i | 0.310072 | − | 0.463570i | ||||
\(106\) | 0.0786451 | 0.00763869 | ||||||||
\(107\) | 6.57276 | − | 6.57276i | 0.635413 | − | 0.635413i | −0.314008 | − | 0.949420i | \(-0.601672\pi\) |
0.949420 | + | 0.314008i | \(0.101672\pi\) | |||||||
\(108\) | 0.441524 | + | 1.12442i | 0.0424857 | + | 0.108197i | ||||
\(109\) | 18.5815i | 1.77979i | 0.456170 | + | 0.889893i | \(0.349221\pi\) | ||||
−0.456170 | + | 0.889893i | \(0.650779\pi\) | |||||||
\(110\) | −2.18855 | + | 2.52441i | −0.208670 | + | 0.240693i | ||||
\(111\) | −7.62083 | − | 5.92281i | −0.723338 | − | 0.562168i | ||||
\(112\) | −4.60227 | − | 4.60227i | −0.434873 | − | 0.434873i | ||||
\(113\) | −8.98496 | − | 8.98496i | −0.845234 | − | 0.845234i | 0.144300 | − | 0.989534i | \(-0.453907\pi\) |
−0.989534 | + | 0.144300i | \(0.953907\pi\) | |||||||
\(114\) | −14.2517 | − | 11.0762i | −1.33479 | − | 1.03738i | ||||
\(115\) | −5.48473 | + | 6.32642i | −0.511454 | + | 0.589942i | ||||
\(116\) | 0.0376059i | 0.00349162i | ||||||||
\(117\) | 7.32127 | − | 12.3266i | 0.676852 | − | 1.13960i | ||||
\(118\) | −10.9831 | + | 10.9831i | −1.01107 | + | 1.01107i | ||||
\(119\) | 0.288932 | 0.0264863 | ||||||||
\(120\) | 5.68666 | − | 8.50178i | 0.519118 | − | 0.776103i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 8.80791 | − | 8.80791i | 0.797430 | − | 0.797430i | ||||
\(123\) | 1.76945 | + | 14.1133i | 0.159546 | + | 1.27256i | ||||
\(124\) | 1.75057i | 0.157206i | ||||||||
\(125\) | 2.36812 | + | 10.9267i | 0.211811 | + | 0.977311i | ||||
\(126\) | 6.40943 | − | 1.63282i | 0.570997 | − | 0.145463i | ||||
\(127\) | −5.97520 | − | 5.97520i | −0.530213 | − | 0.530213i | 0.390422 | − | 0.920636i | \(-0.372329\pi\) |
−0.920636 | + | 0.390422i | \(0.872329\pi\) | |||||||
\(128\) | −9.10532 | − | 9.10532i | −0.804805 | − | 0.804805i | ||||
\(129\) | 1.71893 | − | 2.21173i | 0.151343 | − | 0.194732i | ||||
\(130\) | 15.9262 | − | 1.13495i | 1.39682 | − | 0.0995413i | ||||
\(131\) | − | 2.56196i | − | 0.223839i | −0.993717 | − | 0.111920i | \(-0.964300\pi\) | ||
0.993717 | − | 0.111920i | \(-0.0357000\pi\) | |||||||
\(132\) | −0.399538 | + | 0.0500918i | −0.0347754 | + | 0.00435993i | ||||
\(133\) | −7.27714 | + | 7.27714i | −0.631008 | + | 0.631008i | ||||
\(134\) | −11.4323 | −0.987605 | ||||||||
\(135\) | 5.00475 | + | 10.4858i | 0.430740 | + | 0.902476i | ||||
\(136\) | 0.517124 | 0.0443430 | ||||||||
\(137\) | 6.89566 | − | 6.89566i | 0.589136 | − | 0.589136i | −0.348261 | − | 0.937397i | \(-0.613228\pi\) |
0.937397 | + | 0.348261i | \(0.113228\pi\) | |||||||
\(138\) | −9.61523 | + | 1.20550i | −0.818503 | + | 0.102619i | ||||
\(139\) | 4.80305i | 0.407389i | 0.979034 | + | 0.203695i | \(0.0652950\pi\) | ||||
−0.979034 | + | 0.203695i | \(0.934705\pi\) | |||||||
\(140\) | 0.579574 | + | 0.502465i | 0.0489830 | + | 0.0424661i | ||||
\(141\) | 1.19861 | − | 1.54224i | 0.100941 | − | 0.129880i | ||||
\(142\) | −16.0082 | − | 16.0082i | −1.34338 | − | 1.34338i | ||||
\(143\) | 3.37924 | + | 3.37924i | 0.282586 | + | 0.282586i | ||||
\(144\) | 12.8232 | − | 3.26674i | 1.06860 | − | 0.272228i | ||||
\(145\) | 0.0257110 | + | 0.360791i | 0.00213518 | + | 0.0299621i | ||||
\(146\) | 8.41813i | 0.696689i | ||||||||
\(147\) | 1.03914 | + | 8.28829i | 0.0857066 | + | 0.683606i | ||||
\(148\) | 0.916044 | − | 0.916044i | 0.0752983 | − | 0.0752983i | ||||
\(149\) | −9.35238 | −0.766177 | −0.383088 | − | 0.923712i | \(-0.625140\pi\) | ||||
−0.383088 | + | 0.923712i | \(0.625140\pi\) | |||||||
\(150\) | −6.41139 | + | 11.2397i | −0.523488 | + | 0.917715i | ||||
\(151\) | −2.84779 | −0.231750 | −0.115875 | − | 0.993264i | \(-0.536967\pi\) | ||||
−0.115875 | + | 0.993264i | \(0.536967\pi\) | |||||||
\(152\) | −13.0245 | + | 13.0245i | −1.05643 | + | 1.05643i | ||||
\(153\) | −0.299978 | + | 0.505065i | −0.0242518 | + | 0.0408320i | ||||
\(154\) | 2.20471i | 0.177661i | ||||||||
\(155\) | 1.19686 | + | 16.7950i | 0.0961339 | + | 1.34901i | ||||
\(156\) | 1.51941 | + | 1.18086i | 0.121650 | + | 0.0945448i | ||||
\(157\) | −11.7887 | − | 11.7887i | −0.940838 | − | 0.940838i | 0.0575074 | − | 0.998345i | \(-0.481685\pi\) |
−0.998345 | + | 0.0575074i | \(0.981685\pi\) | |||||||
\(158\) | 14.3178 | + | 14.3178i | 1.13906 | + | 1.13906i | ||||
\(159\) | 0.0719837 | + | 0.0559447i | 0.00570868 | + | 0.00443671i | ||||
\(160\) | 2.21106 | + | 1.91689i | 0.174799 | + | 0.151543i | ||||
\(161\) | 5.52523i | 0.435449i | ||||||||
\(162\) | −3.80023 | + | 12.8992i | −0.298574 | + | 1.01346i | ||||
\(163\) | −1.02307 | + | 1.02307i | −0.0801327 | + | 0.0801327i | −0.746037 | − | 0.665904i | \(-0.768046\pi\) |
0.665904 | + | 0.746037i | \(0.268046\pi\) | |||||||
\(164\) | −1.90915 | −0.149080 | ||||||||
\(165\) | −3.79893 | + | 0.753744i | −0.295746 | + | 0.0586789i | ||||
\(166\) | −12.5165 | −0.971467 | ||||||||
\(167\) | −0.279986 | + | 0.279986i | −0.0216660 | + | 0.0216660i | −0.717857 | − | 0.696191i | \(-0.754877\pi\) |
0.696191 | + | 0.717857i | \(0.254877\pi\) | |||||||
\(168\) | −0.839651 | − | 6.69716i | −0.0647805 | − | 0.516697i | ||||
\(169\) | − | 9.83853i | − | 0.756810i | ||||||
\(170\) | −0.652552 | + | 0.0465027i | −0.0500485 | + | 0.00356659i | ||||
\(171\) | −5.16539 | − | 20.2761i | −0.395007 | − | 1.55055i | ||||
\(172\) | 0.265856 | + | 0.265856i | 0.0202713 | + | 0.0202713i | ||||
\(173\) | 13.8099 | + | 13.8099i | 1.04995 | + | 1.04995i | 0.998685 | + | 0.0512647i | \(0.0163252\pi\) |
0.0512647 | + | 0.998685i | \(0.483675\pi\) | |||||||
\(174\) | −0.256889 | + | 0.330537i | −0.0194747 | + | 0.0250580i | ||||
\(175\) | 5.90398 | + | 4.42441i | 0.446299 | + | 0.334454i | ||||
\(176\) | 4.41091i | 0.332485i | ||||||||
\(177\) | −17.8656 | + | 2.23989i | −1.34286 | + | 0.168360i | ||||
\(178\) | −3.15427 | + | 3.15427i | −0.236422 | + | 0.236422i | ||||
\(179\) | 8.00740 | 0.598501 | 0.299250 | − | 0.954175i | \(-0.403263\pi\) | ||||
0.299250 | + | 0.954175i | \(0.403263\pi\) | |||||||
\(180\) | −1.48006 | + | 0.491445i | −0.110317 | + | 0.0366301i | ||||
\(181\) | 16.9227 | 1.25785 | 0.628927 | − | 0.777464i | \(-0.283494\pi\) | ||||
0.628927 | + | 0.777464i | \(0.283494\pi\) | |||||||
\(182\) | 7.45026 | − | 7.45026i | 0.552250 | − | 0.552250i | ||||
\(183\) | 14.3274 | − | 1.79629i | 1.05911 | − | 0.132785i | ||||
\(184\) | 9.88895i | 0.729023i | ||||||||
\(185\) | 8.16224 | − | 9.41483i | 0.600100 | − | 0.692192i | ||||
\(186\) | −11.9583 | + | 15.3867i | −0.876827 | + | 1.12821i | ||||
\(187\) | −0.138459 | − | 0.138459i | −0.0101251 | − | 0.0101251i | ||||
\(188\) | 0.185381 | + | 0.185381i | 0.0135203 | + | 0.0135203i | ||||
\(189\) | 7.02805 | + | 3.06487i | 0.511215 | + | 0.222937i | ||||
\(190\) | 15.2642 | − | 17.6067i | 1.10738 | − | 1.27732i | ||||
\(191\) | − | 21.2773i | − | 1.53957i | −0.638301 | − | 0.769787i | \(-0.720362\pi\) | ||
0.638301 | − | 0.769787i | \(-0.279638\pi\) | |||||||
\(192\) | −1.47950 | − | 11.8007i | −0.106774 | − | 0.851640i | ||||
\(193\) | 6.92019 | − | 6.92019i | 0.498126 | − | 0.498126i | −0.412728 | − | 0.910854i | \(-0.635424\pi\) |
0.910854 | + | 0.412728i | \(0.135424\pi\) | |||||||
\(194\) | −16.7975 | −1.20599 | ||||||||
\(195\) | 15.3846 | + | 10.2904i | 1.10171 | + | 0.736912i | ||||
\(196\) | −1.12118 | −0.0800843 | ||||||||
\(197\) | −1.80376 | + | 1.80376i | −0.128513 | + | 0.128513i | −0.768438 | − | 0.639925i | \(-0.778966\pi\) |
0.639925 | + | 0.768438i | \(0.278966\pi\) | |||||||
\(198\) | −3.85393 | − | 2.28900i | −0.273887 | − | 0.162672i | ||||
\(199\) | 14.5849i | 1.03390i | 0.856016 | + | 0.516949i | \(0.172932\pi\) | ||||
−0.856016 | + | 0.516949i | \(0.827068\pi\) | |||||||
\(200\) | 10.5668 | + | 7.91872i | 0.747187 | + | 0.559938i | ||||
\(201\) | −10.4640 | − | 8.13248i | −0.738073 | − | 0.573621i | ||||
\(202\) | 2.46309 | + | 2.46309i | 0.173302 | + | 0.173302i | ||||
\(203\) | 0.168777 | + | 0.168777i | 0.0118459 | + | 0.0118459i | ||||
\(204\) | −0.0622554 | − | 0.0483841i | −0.00435875 | − | 0.00338756i | ||||
\(205\) | −18.3164 | + | 1.30528i | −1.27928 | + | 0.0911647i | ||||
\(206\) | − | 4.13951i | − | 0.288414i | ||||||
\(207\) | −9.65834 | − | 5.73647i | −0.671301 | − | 0.398712i | ||||
\(208\) | 14.9055 | − | 14.9055i | 1.03351 | − | 1.03351i | ||||
\(209\) | 6.97457 | 0.482441 | ||||||||
\(210\) | 1.66179 | + | 8.37555i | 0.114674 | + | 0.577968i | ||||
\(211\) | −5.42436 | −0.373428 | −0.186714 | − | 0.982414i | \(-0.559784\pi\) | ||||
−0.186714 | + | 0.982414i | \(0.559784\pi\) | |||||||
\(212\) | −0.00865262 | + | 0.00865262i | −0.000594265 | + | 0.000594265i | ||||
\(213\) | −3.26472 | − | 26.0398i | −0.223695 | − | 1.78422i | ||||
\(214\) | 13.8885i | 0.949401i | ||||||||
\(215\) | 2.73239 | + | 2.36886i | 0.186347 | + | 0.161555i | ||||
\(216\) | 12.5787 | + | 5.48545i | 0.855870 | + | 0.373238i | ||||
\(217\) | 7.85667 | + | 7.85667i | 0.533346 | + | 0.533346i | ||||
\(218\) | −19.6318 | − | 19.6318i | −1.32963 | − | 1.32963i | ||||
\(219\) | −5.98829 | + | 7.70509i | −0.404651 | + | 0.520662i | ||||
\(220\) | −0.0369515 | − | 0.518525i | −0.00249127 | − | 0.0349589i | ||||
\(221\) | 0.935774i | 0.0629469i | ||||||||
\(222\) | 14.3092 | − | 1.79400i | 0.960368 | − | 0.120405i | ||||
\(223\) | 10.3117 | − | 10.3117i | 0.690525 | − | 0.690525i | −0.271823 | − | 0.962347i | \(-0.587626\pi\) |
0.962347 | + | 0.271823i | \(0.0876264\pi\) | |||||||
\(224\) | 1.93104 | 0.129023 | ||||||||
\(225\) | −13.8637 | + | 5.72684i | −0.924249 | + | 0.381790i | ||||
\(226\) | 18.9856 | 1.26291 | ||||||||
\(227\) | 18.3744 | − | 18.3744i | 1.21955 | − | 1.21955i | 0.251766 | − | 0.967788i | \(-0.418989\pi\) |
0.967788 | − | 0.251766i | \(-0.0810113\pi\) | |||||||
\(228\) | 2.78661 | − | 0.349369i | 0.184548 | − | 0.0231375i | ||||
\(229\) | − | 14.3877i | − | 0.950765i | −0.879779 | − | 0.475382i | \(-0.842310\pi\) | ||
0.879779 | − | 0.475382i | \(-0.157690\pi\) | |||||||
\(230\) | −0.889269 | − | 12.4787i | −0.0586367 | − | 0.822824i | ||||
\(231\) | −1.56834 | + | 2.01797i | −0.103189 | + | 0.132773i | ||||
\(232\) | 0.302075 | + | 0.302075i | 0.0198322 | + | 0.0198322i | ||||
\(233\) | −12.8401 | − | 12.8401i | −0.841181 | − | 0.841181i | 0.147832 | − | 0.989012i | \(-0.452771\pi\) |
−0.989012 | + | 0.147832i | \(0.952771\pi\) | |||||||
\(234\) | 5.28827 | + | 20.7584i | 0.345705 | + | 1.35702i | ||||
\(235\) | 1.90529 | + | 1.65181i | 0.124288 | + | 0.107752i | ||||
\(236\) | − | 2.41674i | − | 0.157316i | ||||||
\(237\) | 2.91998 | + | 23.2901i | 0.189673 | + | 1.51286i | ||||
\(238\) | −0.305263 | + | 0.305263i | −0.0197872 | + | 0.0197872i | ||||
\(239\) | −6.03008 | −0.390054 | −0.195027 | − | 0.980798i | \(-0.562479\pi\) | ||||
−0.195027 | + | 0.980798i | \(0.562479\pi\) | |||||||
\(240\) | 3.32470 | + | 16.7567i | 0.214608 | + | 1.08164i | ||||
\(241\) | 8.19817 | 0.528091 | 0.264045 | − | 0.964510i | \(-0.414943\pi\) | ||||
0.264045 | + | 0.964510i | \(0.414943\pi\) | |||||||
\(242\) | 1.05652 | − | 1.05652i | 0.0679158 | − | 0.0679158i | ||||
\(243\) | −12.6543 | + | 9.10327i | −0.811771 | + | 0.583975i | ||||
\(244\) | 1.93811i | 0.124075i | ||||||||
\(245\) | −10.7566 | + | 0.766546i | −0.687215 | + | 0.0489728i | ||||
\(246\) | −16.7805 | − | 13.0416i | −1.06989 | − | 0.831502i | ||||
\(247\) | −23.5687 | − | 23.5687i | −1.49964 | − | 1.49964i | ||||
\(248\) | 14.0617 | + | 14.0617i | 0.892920 | + | 0.892920i | ||||
\(249\) | −11.4563 | − | 8.90368i | −0.726013 | − | 0.564248i | ||||
\(250\) | −14.0462 | − | 9.04230i | −0.888362 | − | 0.571885i | ||||
\(251\) | − | 9.14311i | − | 0.577108i | −0.957464 | − | 0.288554i | \(-0.906825\pi\) | ||
0.957464 | − | 0.288554i | \(-0.0931745\pi\) | |||||||
\(252\) | −0.525527 | + | 0.884817i | −0.0331051 | + | 0.0557382i | ||||
\(253\) | 2.64775 | − | 2.64775i | 0.166463 | − | 0.166463i | ||||
\(254\) | 12.6259 | 0.792218 | ||||||||
\(255\) | −0.630359 | − | 0.421634i | −0.0394746 | − | 0.0264037i | ||||
\(256\) | 5.50704 | 0.344190 | ||||||||
\(257\) | −8.53152 | + | 8.53152i | −0.532182 | + | 0.532182i | −0.921221 | − | 0.389039i | \(-0.872807\pi\) |
0.389039 | + | 0.921221i | \(0.372807\pi\) | |||||||
\(258\) | 0.520657 | + | 4.15283i | 0.0324147 | + | 0.258544i | ||||
\(259\) | − | 8.22252i | − | 0.510923i | ||||||
\(260\) | −1.62735 | + | 1.87709i | −0.100924 | + | 0.116412i | ||||
\(261\) | −0.470260 | + | 0.119800i | −0.0291084 | + | 0.00741544i | ||||
\(262\) | 2.70677 | + | 2.70677i | 0.167225 | + | 0.167225i | ||||
\(263\) | 1.80302 | + | 1.80302i | 0.111179 | + | 0.111179i | 0.760508 | − | 0.649329i | \(-0.224950\pi\) |
−0.649329 | + | 0.760508i | \(0.724950\pi\) | |||||||
\(264\) | −2.80698 | + | 3.61172i | −0.172758 | + | 0.222286i | ||||
\(265\) | −0.0770976 | + | 0.0889292i | −0.00473607 | + | 0.00546287i | ||||
\(266\) | − | 15.3769i | − | 0.942820i | ||||||
\(267\) | −5.13090 | + | 0.643283i | −0.314006 | + | 0.0393683i | ||||
\(268\) | 1.25780 | − | 1.25780i | 0.0768323 | − | 0.0768323i | ||||
\(269\) | 3.78908 | 0.231024 | 0.115512 | − | 0.993306i | \(-0.463149\pi\) | ||||
0.115512 | + | 0.993306i | \(0.463149\pi\) | |||||||
\(270\) | −16.3661 | − | 5.79088i | −0.996011 | − | 0.352422i | ||||
\(271\) | 28.8342 | 1.75155 | 0.875776 | − | 0.482718i | \(-0.160350\pi\) | ||||
0.875776 | + | 0.482718i | \(0.160350\pi\) | |||||||
\(272\) | −0.610731 | + | 0.610731i | −0.0370310 | + | 0.0370310i | ||||
\(273\) | 12.1190 | − | 1.51941i | 0.733475 | − | 0.0919588i | ||||
\(274\) | 14.5708i | 0.880257i | ||||||||
\(275\) | −0.709026 | − | 4.94947i | −0.0427559 | − | 0.298464i | ||||
\(276\) | 0.925248 | − | 1.19051i | 0.0556934 | − | 0.0716602i | ||||
\(277\) | 14.3716 | + | 14.3716i | 0.863507 | + | 0.863507i | 0.991744 | − | 0.128236i | \(-0.0409316\pi\) |
−0.128236 | + | 0.991744i | \(0.540932\pi\) | |||||||
\(278\) | −5.07453 | − | 5.07453i | −0.304350 | − | 0.304350i | ||||
\(279\) | −21.8908 | + | 5.57675i | −1.31057 | + | 0.333871i | ||||
\(280\) | 8.69164 | − | 0.619390i | 0.519425 | − | 0.0370156i | ||||
\(281\) | 21.9763i | 1.31099i | 0.755197 | + | 0.655497i | \(0.227541\pi\) | ||||
−0.755197 | + | 0.655497i | \(0.772459\pi\) | |||||||
\(282\) | 0.363054 | + | 2.89577i | 0.0216196 | + | 0.172440i | ||||
\(283\) | 5.65151 | − | 5.65151i | 0.335947 | − | 0.335947i | −0.518892 | − | 0.854840i | \(-0.673655\pi\) |
0.854840 | + | 0.518892i | \(0.173655\pi\) | |||||||
\(284\) | 3.52248 | 0.209021 | ||||||||
\(285\) | 26.4959 | − | 5.25704i | 1.56948 | − | 0.311400i | ||||
\(286\) | −7.14049 | −0.422226 | ||||||||
\(287\) | −8.56840 | + | 8.56840i | −0.505776 | + | 0.505776i | ||||
\(288\) | −2.00487 | + | 3.37555i | −0.118138 | + | 0.198906i | ||||
\(289\) | 16.9617i | 0.997745i | ||||||||
\(290\) | −0.408348 | − | 0.354020i | −0.0239790 | − | 0.0207888i | ||||
\(291\) | −15.3747 | − | 11.9490i | −0.901279 | − | 0.700462i | ||||
\(292\) | −0.926172 | − | 0.926172i | −0.0542001 | − | 0.0542001i | ||||
\(293\) | 13.8329 | + | 13.8329i | 0.808128 | + | 0.808128i | 0.984350 | − | 0.176223i | \(-0.0563878\pi\) |
−0.176223 | + | 0.984350i | \(0.556388\pi\) | |||||||
\(294\) | −9.85463 | − | 7.65889i | −0.574734 | − | 0.446676i | ||||
\(295\) | −1.65231 | − | 23.1862i | −0.0962013 | − | 1.34995i | ||||
\(296\) | − | 14.7165i | − | 0.855380i | ||||||
\(297\) | −1.89920 | − | 4.83664i | −0.110202 | − | 0.280650i | ||||
\(298\) | 9.88100 | − | 9.88100i | 0.572391 | − | 0.572391i | ||||
\(299\) | −17.8948 | −1.03488 | ||||||||
\(300\) | −0.531211 | − | 1.94199i | −0.0306695 | − | 0.112121i | ||||
\(301\) | 2.38635 | 0.137547 | ||||||||
\(302\) | 3.00876 | − | 3.00876i | 0.173134 | − | 0.173134i | ||||
\(303\) | 0.502323 | + | 4.00659i | 0.0288577 | + | 0.230173i | ||||
\(304\) | − | 30.7642i | − | 1.76445i | ||||||
\(305\) | 1.32508 | + | 18.5943i | 0.0758737 | + | 1.06470i | ||||
\(306\) | −0.216679 | − | 0.850545i | −0.0123867 | − | 0.0486224i | ||||
\(307\) | 2.68221 | + | 2.68221i | 0.153082 | + | 0.153082i | 0.779493 | − | 0.626411i | \(-0.215477\pi\) |
−0.626411 | + | 0.779493i | \(0.715477\pi\) | |||||||
\(308\) | −0.242565 | − | 0.242565i | −0.0138214 | − | 0.0138214i | ||||
\(309\) | 2.94467 | − | 3.78889i | 0.167516 | − | 0.215542i | ||||
\(310\) | −19.0088 | − | 16.4798i | −1.07963 | − | 0.935990i | ||||
\(311\) | 27.6326i | 1.56690i | 0.621453 | + | 0.783452i | \(0.286543\pi\) | ||||
−0.621453 | + | 0.783452i | \(0.713457\pi\) | |||||||
\(312\) | 21.6903 | − | 2.71941i | 1.22797 | − | 0.153956i | ||||
\(313\) | −12.8540 | + | 12.8540i | −0.726549 | + | 0.726549i | −0.969931 | − | 0.243382i | \(-0.921743\pi\) |
0.243382 | + | 0.969931i | \(0.421743\pi\) | |||||||
\(314\) | 24.9100 | 1.40575 | ||||||||
\(315\) | −4.43697 | + | 8.84824i | −0.249995 | + | 0.498542i | ||||
\(316\) | −3.15052 | −0.177231 | ||||||||
\(317\) | −3.24834 | + | 3.24834i | −0.182445 | + | 0.182445i | −0.792420 | − | 0.609975i | \(-0.791179\pi\) |
0.609975 | + | 0.792420i | \(0.291179\pi\) | |||||||
\(318\) | −0.135159 | + | 0.0169455i | −0.00757935 | + | 0.000950255i | ||||
\(319\) | − | 0.161760i | − | 0.00905682i | ||||||
\(320\) | 15.3150 | − | 1.09139i | 0.856136 | − | 0.0610106i | ||||
\(321\) | −9.87971 | + | 12.7121i | −0.551431 | + | 0.709522i | ||||
\(322\) | −5.83753 | − | 5.83753i | −0.325313 | − | 0.325313i | ||||
\(323\) | 0.965693 | + | 0.965693i | 0.0537326 | + | 0.0537326i | ||||
\(324\) | −1.00108 | − | 1.83729i | −0.0556154 | − | 0.102072i | ||||
\(325\) | −14.3295 | + | 19.1214i | −0.794857 | + | 1.06067i | ||||
\(326\) | − | 2.16178i | − | 0.119730i | ||||||
\(327\) | −4.00371 | − | 31.9341i | −0.221406 | − | 1.76596i | ||||
\(328\) | −15.3355 | + | 15.3355i | −0.846764 | + | 0.846764i | ||||
\(329\) | 1.66400 | 0.0917395 | ||||||||
\(330\) | 3.21731 | − | 4.81000i | 0.177107 | − | 0.264782i | ||||
\(331\) | 33.0142 | 1.81463 | 0.907314 | − | 0.420455i | \(-0.138129\pi\) | ||||
0.907314 | + | 0.420455i | \(0.138129\pi\) | |||||||
\(332\) | 1.37708 | − | 1.37708i | 0.0755769 | − | 0.0755769i | ||||
\(333\) | 14.3733 | + | 8.53688i | 0.787653 | + | 0.467818i | ||||
\(334\) | − | 0.591624i | − | 0.0323722i | ||||||
\(335\) | 11.2074 | − | 12.9273i | 0.612325 | − | 0.706294i | ||||
\(336\) | 8.90108 | + | 6.91780i | 0.485594 | + | 0.377397i | ||||
\(337\) | 7.43583 | + | 7.43583i | 0.405055 | + | 0.405055i | 0.880010 | − | 0.474955i | \(-0.157536\pi\) |
−0.474955 | + | 0.880010i | \(0.657536\pi\) | |||||||
\(338\) | 10.3946 | + | 10.3946i | 0.565393 | + | 0.565393i | ||||
\(339\) | 17.3775 | + | 13.5056i | 0.943816 | + | 0.733521i | ||||
\(340\) | 0.0666783 | − | 0.0769108i | 0.00361614 | − | 0.00417107i | ||||
\(341\) | − | 7.53000i | − | 0.407773i | ||||||
\(342\) | 26.8795 | + | 15.9648i | 1.45348 | + | 0.863278i | ||||
\(343\) | −12.3356 | + | 12.3356i | −0.666060 | + | 0.666060i | ||||
\(344\) | 4.27105 | 0.230279 | ||||||||
\(345\) | 8.06289 | − | 12.0543i | 0.434092 | − | 0.648984i | ||||
\(346\) | −29.1810 | −1.56878 | ||||||||
\(347\) | −12.6263 | + | 12.6263i | −0.677815 | + | 0.677815i | −0.959505 | − | 0.281690i | \(-0.909105\pi\) |
0.281690 | + | 0.959505i | \(0.409105\pi\) | |||||||
\(348\) | −0.00810285 | − | 0.0646293i | −0.000434358 | − | 0.00346450i | ||||
\(349\) | − | 22.9188i | − | 1.22682i | −0.789766 | − | 0.613408i | \(-0.789798\pi\) | ||
0.789766 | − | 0.613408i | \(-0.210202\pi\) | |||||||
\(350\) | −10.9122 | + | 1.56320i | −0.583280 | + | 0.0835565i | ||||
\(351\) | −9.92632 | + | 22.7620i | −0.529828 | + | 1.21495i | ||||
\(352\) | −0.925378 | − | 0.925378i | −0.0493228 | − | 0.0493228i | ||||
\(353\) | −12.5661 | − | 12.5661i | −0.668826 | − | 0.668826i | 0.288618 | − | 0.957444i | \(-0.406804\pi\) |
−0.957444 | + | 0.288618i | \(0.906804\pi\) | |||||||
\(354\) | 16.5090 | − | 21.2419i | 0.877441 | − | 1.12900i | ||||
\(355\) | 33.7948 | − | 2.40831i | 1.79364 | − | 0.127820i | ||||
\(356\) | − | 0.694072i | − | 0.0367857i | ||||||
\(357\) | −0.496557 | + | 0.0622554i | −0.0262806 | + | 0.00329491i | ||||
\(358\) | −8.45999 | + | 8.45999i | −0.447125 | + | 0.447125i | ||||
\(359\) | −18.3875 | −0.970455 | −0.485227 | − | 0.874388i | \(-0.661263\pi\) | ||||
−0.485227 | + | 0.874388i | \(0.661263\pi\) | |||||||
\(360\) | −7.94121 | + | 15.8364i | −0.418539 | + | 0.834652i | ||||
\(361\) | −29.6446 | −1.56024 | ||||||||
\(362\) | −17.8792 | + | 17.8792i | −0.939710 | + | 0.939710i | ||||
\(363\) | 1.71860 | − | 0.215468i | 0.0902029 | − | 0.0113091i | ||||
\(364\) | 1.63937i | 0.0859264i | ||||||||
\(365\) | −9.51893 | − | 8.25249i | −0.498243 | − | 0.431955i | ||||
\(366\) | −13.2394 | + | 17.0351i | −0.692035 | + | 0.890436i | ||||
\(367\) | −2.00228 | − | 2.00228i | −0.104518 | − | 0.104518i | 0.652914 | − | 0.757432i | \(-0.273546\pi\) |
−0.757432 | + | 0.652914i | \(0.773546\pi\) | |||||||
\(368\) | −11.6790 | − | 11.6790i | −0.608810 | − | 0.608810i | ||||
\(369\) | −6.08194 | − | 23.8739i | −0.316613 | − | 1.24283i | ||||
\(370\) | 1.32339 | + | 18.5706i | 0.0687998 | + | 0.965438i | ||||
\(371\) | 0.0776670i | 0.00403227i | ||||||||
\(372\) | −0.377192 | − | 3.00853i | −0.0195565 | − | 0.155985i | ||||
\(373\) | 1.42819 | − | 1.42819i | 0.0739491 | − | 0.0739491i | −0.669165 | − | 0.743114i | \(-0.733348\pi\) |
0.743114 | + | 0.669165i | \(0.233348\pi\) | |||||||
\(374\) | 0.292570 | 0.0151285 | ||||||||
\(375\) | −6.42418 | − | 18.2683i | −0.331743 | − | 0.943370i | ||||
\(376\) | 2.97820 | 0.153589 | ||||||||
\(377\) | −0.546626 | + | 0.546626i | −0.0281527 | + | 0.0281527i | ||||
\(378\) | −10.6634 | + | 4.18718i | −0.548466 | + | 0.215365i | ||||
\(379\) | − | 7.51540i | − | 0.386040i | −0.981195 | − | 0.193020i | \(-0.938172\pi\) | ||
0.981195 | − | 0.193020i | \(-0.0618282\pi\) | |||||||
\(380\) | 0.257721 | + | 3.61649i | 0.0132208 | + | 0.185522i | ||||
\(381\) | 11.5564 | + | 8.98150i | 0.592054 | + | 0.460136i | ||||
\(382\) | 22.4800 | + | 22.4800i | 1.15018 | + | 1.15018i | ||||
\(383\) | 0.239638 | + | 0.239638i | 0.0122450 | + | 0.0122450i | 0.713203 | − | 0.700958i | \(-0.247244\pi\) |
−0.700958 | + | 0.713203i | \(0.747244\pi\) | |||||||
\(384\) | 17.6103 | + | 13.6865i | 0.898671 | + | 0.698435i | ||||
\(385\) | −2.49301 | − | 2.16133i | −0.127056 | − | 0.110152i | ||||
\(386\) | 14.6227i | 0.744275i | ||||||||
\(387\) | −2.47759 | + | 4.17144i | −0.125943 | + | 0.212046i | ||||
\(388\) | 1.84808 | − | 1.84808i | 0.0938218 | − | 0.0938218i | ||||
\(389\) | 28.0738 | 1.42340 | 0.711699 | − | 0.702485i | \(-0.247926\pi\) | ||||
0.711699 | + | 0.702485i | \(0.247926\pi\) | |||||||
\(390\) | −27.1262 | + | 5.38210i | −1.37359 | + | 0.272533i | ||||
\(391\) | 0.733211 | 0.0370801 | ||||||||
\(392\) | −9.00605 | + | 9.00605i | −0.454874 | + | 0.454874i | ||||
\(393\) | 0.552019 | + | 4.40298i | 0.0278457 | + | 0.222101i | ||||
\(394\) | − | 3.81143i | − | 0.192017i | ||||||
\(395\) | −30.2262 | + | 2.15400i | −1.52084 | + | 0.108379i | ||||
\(396\) | 0.675852 | − | 0.172175i | 0.0339628 | − | 0.00865213i | ||||
\(397\) | −13.0553 | − | 13.0553i | −0.655226 | − | 0.655226i | 0.299021 | − | 0.954247i | \(-0.403340\pi\) |
−0.954247 | + | 0.299021i | \(0.903340\pi\) | |||||||
\(398\) | −15.4093 | − | 15.4093i | −0.772398 | − | 0.772398i | ||||
\(399\) | 10.9385 | − | 14.0745i | 0.547609 | − | 0.704604i | ||||
\(400\) | −21.8317 | + | 3.12745i | −1.09158 | + | 0.156373i | ||||
\(401\) | 2.07860i | 0.103800i | 0.998652 | + | 0.0519001i | \(0.0165277\pi\) | ||||
−0.998652 | + | 0.0519001i | \(0.983472\pi\) | |||||||
\(402\) | 19.6476 | − | 2.46330i | 0.979933 | − | 0.122858i | ||||
\(403\) | −25.4457 | + | 25.4457i | −1.26754 | + | 1.26754i | ||||
\(404\) | −0.541983 | −0.0269647 | ||||||||
\(405\) | −10.8605 | − | 16.9425i | −0.539662 | − | 0.841881i | ||||
\(406\) | −0.356634 | −0.0176995 | ||||||||
\(407\) | −3.94032 | + | 3.94032i | −0.195314 | + | 0.195314i | ||||
\(408\) | −0.888728 | + | 0.111424i | −0.0439986 | + | 0.00551629i | ||||
\(409\) | 1.39211i | 0.0688354i | 0.999408 | + | 0.0344177i | \(0.0109577\pi\) | ||||
−0.999408 | + | 0.0344177i | \(0.989042\pi\) | |||||||
\(410\) | 17.9727 | − | 20.7308i | 0.887607 | − | 1.02382i | ||||
\(411\) | −10.3651 | + | 13.3366i | −0.511271 | + | 0.657848i | ||||
\(412\) | 0.455434 | + | 0.455434i | 0.0224376 | + | 0.0224376i | ||||
\(413\) | −10.8465 | − | 10.8465i | −0.533719 | − | 0.533719i | ||||
\(414\) | 16.2650 | − | 4.14354i | 0.799379 | − | 0.203644i | ||||
\(415\) | 12.2702 | − | 14.1532i | 0.602320 | − | 0.694753i | ||||
\(416\) | 6.25415i | 0.306635i | ||||||||
\(417\) | −1.03490 | − | 8.25450i | −0.0506794 | − | 0.404225i | ||||
\(418\) | −7.36879 | + | 7.36879i | −0.360419 | + | 0.360419i | ||||
\(419\) | −8.51722 | −0.416093 | −0.208047 | − | 0.978119i | \(-0.566711\pi\) | ||||
−0.208047 | + | 0.978119i | \(0.566711\pi\) | |||||||
\(420\) | −1.10432 | − | 0.738655i | −0.0538853 | − | 0.0360427i | ||||
\(421\) | −19.3495 | −0.943039 | −0.471519 | − | 0.881856i | \(-0.656294\pi\) | ||||
−0.471519 | + | 0.881856i | \(0.656294\pi\) | |||||||
\(422\) | 5.73095 | − | 5.73095i | 0.278979 | − | 0.278979i | ||||
\(423\) | −1.72762 | + | 2.90875i | −0.0839998 | + | 0.141428i | ||||
\(424\) | 0.139007i | 0.00675077i | ||||||||
\(425\) | 0.587129 | − | 0.783471i | 0.0284799 | − | 0.0380039i | ||||
\(426\) | 30.9609 | + | 24.0624i | 1.50006 | + | 1.16583i | ||||
\(427\) | 8.69836 | + | 8.69836i | 0.420943 | + | 0.420943i | ||||
\(428\) | −1.52803 | − | 1.52803i | −0.0738602 | − | 0.0738602i | ||||
\(429\) | −6.53567 | − | 5.07943i | −0.315545 | − | 0.245237i | ||||
\(430\) | −5.38958 | + | 0.384076i | −0.259909 | + | 0.0185218i | ||||
\(431\) | − | 28.5298i | − | 1.37423i | −0.726548 | − | 0.687116i | \(-0.758876\pi\) | ||
0.726548 | − | 0.687116i | \(-0.241124\pi\) | |||||||
\(432\) | −21.3340 | + | 8.37718i | −1.02643 | + | 0.403047i | ||||
\(433\) | −29.2496 | + | 29.2496i | −1.40564 | + | 1.40564i | −0.625099 | + | 0.780545i | \(0.714941\pi\) |
−0.780545 | + | 0.625099i | \(0.785059\pi\) | |||||||
\(434\) | −16.6015 | −0.796898 | ||||||||
\(435\) | −0.121926 | − | 0.614515i | −0.00584589 | − | 0.0294637i | ||||
\(436\) | 4.31982 | 0.206882 | ||||||||
\(437\) | −18.4669 | + | 18.4669i | −0.883393 | + | 0.883393i | ||||
\(438\) | −1.81383 | − | 14.4674i | −0.0866684 | − | 0.691278i | ||||
\(439\) | − | 5.90310i | − | 0.281740i | −0.990028 | − | 0.140870i | \(-0.955010\pi\) | ||
0.990028 | − | 0.140870i | \(-0.0449899\pi\) | |||||||
\(440\) | −4.46195 | − | 3.86831i | −0.212715 | − | 0.184414i | ||||
\(441\) | −3.57172 | − | 14.0203i | −0.170082 | − | 0.667634i | ||||
\(442\) | −0.988666 | − | 0.988666i | −0.0470260 | − | 0.0470260i | ||||
\(443\) | −0.198416 | − | 0.198416i | −0.00942704 | − | 0.00942704i | 0.702378 | − | 0.711805i | \(-0.252122\pi\) |
−0.711805 | + | 0.702378i | \(0.752122\pi\) | |||||||
\(444\) | −1.37693 | + | 1.77169i | −0.0653463 | + | 0.0840806i | ||||
\(445\) | −0.474534 | − | 6.65894i | −0.0224951 | − | 0.315664i | ||||
\(446\) | 21.7892i | 1.03175i | ||||||||
\(447\) | 16.0730 | − | 2.01513i | 0.760225 | − | 0.0953126i | ||||
\(448\) | 7.16434 | − | 7.16434i | 0.338483 | − | 0.338483i | ||||
\(449\) | 24.8090 | 1.17081 | 0.585404 | − | 0.810741i | \(-0.300936\pi\) | ||||
0.585404 | + | 0.810741i | \(0.300936\pi\) | |||||||
\(450\) | 8.59681 | − | 20.6979i | 0.405258 | − | 0.975708i | ||||
\(451\) | 8.21214 | 0.386694 | ||||||||
\(452\) | −2.08882 | + | 2.08882i | −0.0982498 | + | 0.0982498i | ||||
\(453\) | 4.89420 | − | 0.613607i | 0.229950 | − | 0.0288298i | ||||
\(454\) | 38.8260i | 1.82219i | ||||||||
\(455\) | 1.12083 | + | 15.7281i | 0.0525453 | + | 0.737347i | ||||
\(456\) | 19.5775 | − | 25.1902i | 0.916800 | − | 1.17964i | ||||
\(457\) | 13.7125 | + | 13.7125i | 0.641443 | + | 0.641443i | 0.950910 | − | 0.309467i | \(-0.100151\pi\) |
−0.309467 | + | 0.950910i | \(0.600151\pi\) | |||||||
\(458\) | 15.2009 | + | 15.2009i | 0.710292 | + | 0.710292i | ||||
\(459\) | 0.406716 | − | 0.932638i | 0.0189839 | − | 0.0435318i | ||||
\(460\) | 1.47076 | + | 1.27509i | 0.0685747 | + | 0.0594512i | ||||
\(461\) | 8.41541i | 0.391945i | 0.980609 | + | 0.195972i | \(0.0627863\pi\) | ||||
−0.980609 | + | 0.195972i | \(0.937214\pi\) | |||||||
\(462\) | −0.475044 | − | 3.78901i | −0.0221011 | − | 0.176281i | ||||
\(463\) | 23.8342 | − | 23.8342i | 1.10767 | − | 1.10767i | 0.114212 | − | 0.993456i | \(-0.463566\pi\) |
0.993456 | − | 0.114212i | \(-0.0364342\pi\) | |||||||
\(464\) | −0.713509 | −0.0331238 | ||||||||
\(465\) | −5.67570 | − | 28.6060i | −0.263204 | − | 1.32657i | ||||
\(466\) | 27.1316 | 1.25685 | ||||||||
\(467\) | 27.3489 | − | 27.3489i | 1.26556 | − | 1.26556i | 0.317196 | − | 0.948360i | \(-0.397259\pi\) |
0.948360 | − | 0.317196i | \(-0.102741\pi\) | |||||||
\(468\) | −2.86569 | − | 1.70205i | −0.132466 | − | 0.0786771i | ||||
\(469\) | − | 11.2902i | − | 0.521331i | ||||||
\(470\) | −3.75816 | + | 0.267816i | −0.173351 | + | 0.0123534i | ||||
\(471\) | 22.8000 | + | 17.7199i | 1.05057 | + | 0.816489i | ||||
\(472\) | −19.4128 | − | 19.4128i | −0.893546 | − | 0.893546i | ||||
\(473\) | −1.14357 | − | 1.14357i | −0.0525812 | − | 0.0525812i | ||||
\(474\) | −27.6916 | − | 21.5215i | −1.27192 | − | 0.988516i | ||||
\(475\) | 4.94515 | + | 34.5204i | 0.226899 | + | 1.58391i | ||||
\(476\) | − | 0.0671707i | − | 0.00307876i | ||||||
\(477\) | −0.135765 | − | 0.0806363i | −0.00621626 | − | 0.00369208i | ||||
\(478\) | 6.37092 | − | 6.37092i | 0.291399 | − | 0.291399i | ||||
\(479\) | −4.45179 | −0.203407 | −0.101704 | − | 0.994815i | \(-0.532429\pi\) | ||||
−0.101704 | + | 0.994815i | \(0.532429\pi\) | |||||||
\(480\) | −4.21294 | − | 2.81795i | −0.192294 | − | 0.128621i | ||||
\(481\) | 26.6306 | 1.21425 | ||||||||
\(482\) | −8.66155 | + | 8.66155i | −0.394523 | + | 0.394523i | ||||
\(483\) | −1.19051 | − | 9.49565i | −0.0541700 | − | 0.432067i | ||||
\(484\) | 0.232479i | 0.0105672i | ||||||||
\(485\) | 16.4669 | − | 18.9940i | 0.747725 | − | 0.862472i | ||||
\(486\) | 3.75170 | − | 22.9873i | 0.170181 | − | 1.04273i | ||||
\(487\) | 3.97415 | + | 3.97415i | 0.180086 | + | 0.180086i | 0.791393 | − | 0.611307i | \(-0.209356\pi\) |
−0.611307 | + | 0.791393i | \(0.709356\pi\) | |||||||
\(488\) | 15.5682 | + | 15.5682i | 0.704737 | + | 0.704737i | ||||
\(489\) | 1.53780 | − | 1.97867i | 0.0695417 | − | 0.0894788i | ||||
\(490\) | 10.5547 | − | 12.1745i | 0.476815 | − | 0.549987i | ||||
\(491\) | − | 17.5760i | − | 0.793192i | −0.917993 | − | 0.396596i | \(-0.870191\pi\) | ||
0.917993 | − | 0.396596i | \(-0.129809\pi\) | |||||||
\(492\) | 3.28106 | − | 0.411361i | 0.147922 | − | 0.0185456i | ||||
\(493\) | 0.0223972 | − | 0.0223972i | 0.00100872 | − | 0.00100872i | ||||
\(494\) | 49.8018 | 2.24069 | ||||||||
\(495\) | 6.36642 | − | 2.11393i | 0.286149 | − | 0.0950140i | ||||
\(496\) | −33.2142 | −1.49136 | ||||||||
\(497\) | 15.8091 | − | 15.8091i | 0.709136 | − | 0.709136i | ||||
\(498\) | 21.5108 | − | 2.69690i | 0.963921 | − | 0.120851i | ||||
\(499\) | − | 8.21295i | − | 0.367662i | −0.982958 | − | 0.183831i | \(-0.941150\pi\) | ||
0.982958 | − | 0.183831i | \(-0.0588499\pi\) | |||||||
\(500\) | 2.54023 | − | 0.550538i | 0.113602 | − | 0.0246208i | ||||
\(501\) | 0.420855 | − | 0.541511i | 0.0188024 | − | 0.0241929i | ||||
\(502\) | 9.65991 | + | 9.65991i | 0.431143 | + | 0.431143i | ||||
\(503\) | −18.7472 | − | 18.7472i | −0.835895 | − | 0.835895i | 0.152420 | − | 0.988316i | \(-0.451293\pi\) |
−0.988316 | + | 0.152420i | \(0.951293\pi\) | |||||||
\(504\) | 2.88604 | + | 11.3288i | 0.128555 | + | 0.504625i | ||||
\(505\) | −5.19980 | + | 0.370551i | −0.231388 | + | 0.0164893i | ||||
\(506\) | 5.59482i | 0.248720i | ||||||||
\(507\) | 2.11989 | + | 16.9085i | 0.0941474 | + | 0.750931i | ||||
\(508\) | −1.38911 | + | 1.38911i | −0.0616319 | + | 0.0616319i | ||||
\(509\) | 24.0212 | 1.06472 | 0.532361 | − | 0.846518i | \(-0.321305\pi\) | ||||
0.532361 | + | 0.846518i | \(0.321305\pi\) | |||||||
\(510\) | 1.11145 | − | 0.220523i | 0.0492160 | − | 0.00976493i | ||||
\(511\) | −8.31343 | −0.367765 | ||||||||
\(512\) | 12.3923 | − | 12.3923i | 0.547669 | − | 0.547669i | ||||
\(513\) | 13.2461 | + | 33.7335i | 0.584828 | + | 1.48937i | ||||
\(514\) | − | 18.0275i | − | 0.795159i | ||||||
\(515\) | 4.68082 | + | 4.05806i | 0.206261 | + | 0.178820i | ||||
\(516\) | −0.514182 | − | 0.399615i | −0.0226356 | − | 0.0175921i | ||||
\(517\) | −0.797409 | − | 0.797409i | −0.0350700 | − | 0.0350700i | ||||
\(518\) | 8.68728 | + | 8.68728i | 0.381697 | + | 0.381697i | ||||
\(519\) | −26.7093 | − | 20.7581i | −1.17241 | − | 0.911180i | ||||
\(520\) | 2.00604 | + | 28.1499i | 0.0879707 | + | 1.23446i | ||||
\(521\) | − | 12.0705i | − | 0.528817i | −0.964411 | − | 0.264408i | \(-0.914823\pi\) | ||
0.964411 | − | 0.264408i | \(-0.0851767\pi\) | |||||||
\(522\) | 0.370269 | − | 0.623412i | 0.0162062 | − | 0.0272860i | ||||
\(523\) | 22.4783 | − | 22.4783i | 0.982908 | − | 0.982908i | −0.0169486 | − | 0.999856i | \(-0.505395\pi\) |
0.999856 | + | 0.0169486i | \(0.00539517\pi\) | |||||||
\(524\) | −0.595603 | −0.0260190 | ||||||||
\(525\) | −11.0999 | − | 6.33165i | −0.484438 | − | 0.276336i | ||||
\(526\) | −3.80986 | −0.166118 | ||||||||
\(527\) | 1.04260 | − | 1.04260i | 0.0454163 | − | 0.0454163i | ||||
\(528\) | −0.950409 | − | 7.58058i | −0.0413612 | − | 0.329902i | ||||
\(529\) | − | 8.97883i | − | 0.390384i | ||||||
\(530\) | −0.0125003 | − | 0.175411i | −0.000542977 | − | 0.00761937i | ||||
\(531\) | 30.2212 | − | 7.69893i | 1.31149 | − | 0.334105i | ||||
\(532\) | 1.69179 | + | 1.69179i | 0.0733482 | + | 0.0733482i | ||||
\(533\) | −27.7508 | − | 27.7508i | −1.20202 | − | 1.20202i | ||||
\(534\) | 4.74127 | − | 6.10056i | 0.205175 | − | 0.263997i | ||||
\(535\) | −15.7047 | − | 13.6153i | −0.678972 | − | 0.588639i | ||||
\(536\) | − | 20.2069i | − | 0.872806i | ||||||
\(537\) | −13.7615 | + | 1.72533i | −0.593852 | + | 0.0744537i | ||||
\(538\) | −4.00325 | + | 4.00325i | −0.172592 | + | 0.172592i | ||||
\(539\) | 4.82271 | 0.207729 | ||||||||
\(540\) | 2.43774 | − | 1.16350i | 0.104904 | − | 0.0500691i | ||||
\(541\) | 4.15229 | 0.178521 | 0.0892605 | − | 0.996008i | \(-0.471550\pi\) | ||||
0.0892605 | + | 0.996008i | \(0.471550\pi\) | |||||||
\(542\) | −30.4640 | + | 30.4640i | −1.30854 | + | 1.30854i | ||||
\(543\) | −29.0833 | + | 3.64629i | −1.24808 | + | 0.156477i | ||||
\(544\) | − | 0.256254i | − | 0.0109868i | ||||||
\(545\) | 41.4444 | − | 2.95344i | 1.77528 | − | 0.126511i | ||||
\(546\) | −11.1987 | + | 14.4093i | −0.479260 | + | 0.616660i | ||||
\(547\) | 13.9478 | + | 13.9478i | 0.596365 | + | 0.596365i | 0.939343 | − | 0.342978i | \(-0.111436\pi\) |
−0.342978 | + | 0.939343i | \(0.611436\pi\) | |||||||
\(548\) | −1.60310 | − | 1.60310i | −0.0684810 | − | 0.0684810i | ||||
\(549\) | −24.2360 | + | 6.17419i | −1.03437 | + | 0.263508i | ||||
\(550\) | 5.97833 | + | 4.48013i | 0.254917 | + | 0.191033i | ||||
\(551\) | 1.12821i | 0.0480632i | ||||||||
\(552\) | −2.13075 | − | 16.9951i | −0.0906907 | − | 0.723360i | ||||
\(553\) | −14.1397 | + | 14.1397i | −0.601283 | + | 0.601283i | ||||
\(554\) | −30.3679 | −1.29021 | ||||||||
\(555\) | −11.9990 | + | 17.9390i | −0.509330 | + | 0.761468i | ||||
\(556\) | 1.11661 | 0.0473548 | ||||||||
\(557\) | −32.3534 | + | 32.3534i | −1.37086 | + | 1.37086i | −0.511682 | + | 0.859175i | \(0.670977\pi\) |
−0.859175 | + | 0.511682i | \(0.829023\pi\) | |||||||
\(558\) | 17.2362 | − | 29.0201i | 0.729666 | − | 1.22852i | ||||
\(559\) | 7.72877i | 0.326892i | ||||||||
\(560\) | −9.53344 | + | 10.9965i | −0.402861 | + | 0.464685i | ||||
\(561\) | 0.267789 | + | 0.208122i | 0.0113061 | + | 0.00878692i | ||||
\(562\) | −23.2184 | − | 23.2184i | −0.979410 | − | 0.979410i | ||||
\(563\) | 15.8283 | + | 15.8283i | 0.667083 | + | 0.667083i | 0.957040 | − | 0.289957i | \(-0.0936410\pi\) |
−0.289957 | + | 0.957040i | \(0.593641\pi\) | |||||||
\(564\) | −0.358539 | − | 0.278652i | −0.0150972 | − | 0.0117334i | ||||
\(565\) | −18.6121 | + | 21.4683i | −0.783015 | + | 0.903177i | ||||
\(566\) | 11.9419i | 0.501955i | ||||||||
\(567\) | −12.7388 | − | 3.75297i | −0.534978 | − | 0.157610i | ||||
\(568\) | 28.2949 | − | 28.2949i | 1.18723 | − | 1.18723i | ||||
\(569\) | 23.3745 | 0.979912 | 0.489956 | − | 0.871747i | \(-0.337013\pi\) | ||||
0.489956 | + | 0.871747i | \(0.337013\pi\) | |||||||
\(570\) | −22.4393 | + | 33.5477i | −0.939880 | + | 1.40516i | ||||
\(571\) | −14.3694 | −0.601339 | −0.300669 | − | 0.953728i | \(-0.597210\pi\) | ||||
−0.300669 | + | 0.953728i | \(0.597210\pi\) | |||||||
\(572\) | 0.785604 | − | 0.785604i | 0.0328478 | − | 0.0328478i | ||||
\(573\) | 4.58458 | + | 36.5672i | 0.191524 | + | 1.52762i | ||||
\(574\) | − | 18.1054i | − | 0.755705i | ||||||
\(575\) | 14.9823 | + | 11.2276i | 0.624805 | + | 0.468225i | ||||
\(576\) | 5.08533 | + | 19.9618i | 0.211889 | + | 0.831742i | ||||
\(577\) | 27.3648 | + | 27.3648i | 1.13921 | + | 1.13921i | 0.988592 | + | 0.150621i | \(0.0481272\pi\) |
0.150621 | + | 0.988592i | \(0.451873\pi\) | |||||||
\(578\) | −17.9204 | − | 17.9204i | −0.745389 | − | 0.745389i | ||||
\(579\) | −10.4019 | + | 13.3841i | −0.432290 | + | 0.556224i | ||||
\(580\) | 0.0838766 | − | 0.00597727i | 0.00348279 | − | 0.000248193i | ||||
\(581\) | − | 12.3608i | − | 0.512813i | ||||||
\(582\) | 28.8681 | − | 3.61931i | 1.19662 | − | 0.150025i | ||||
\(583\) | 0.0372189 | − | 0.0372189i | 0.00154145 | − | 0.00154145i | ||||
\(584\) | −14.8792 | −0.615706 | ||||||||
\(585\) | −28.6571 | − | 14.3702i | −1.18483 | − | 0.594134i | ||||
\(586\) | −29.2296 | −1.20746 | ||||||||
\(587\) | 10.8344 | − | 10.8344i | 0.447183 | − | 0.447183i | −0.447234 | − | 0.894417i | \(-0.647591\pi\) |
0.894417 | + | 0.447234i | \(0.147591\pi\) | |||||||
\(588\) | 1.92686 | − | 0.241578i | 0.0794622 | − | 0.00996251i | ||||
\(589\) | 52.5185i | 2.16399i | ||||||||
\(590\) | 26.2425 | + | 22.7510i | 1.08038 | + | 0.936646i | ||||
\(591\) | 2.71129 | − | 3.48860i | 0.111528 | − | 0.143502i | ||||
\(592\) | 17.3804 | + | 17.3804i | 0.714331 | + | 0.714331i | ||||
\(593\) | −29.3036 | − | 29.3036i | −1.20335 | − | 1.20335i | −0.973140 | − | 0.230214i | \(-0.926057\pi\) |
−0.230214 | − | 0.973140i | \(-0.573943\pi\) | |||||||
\(594\) | 7.11656 | + | 3.10347i | 0.291996 | + | 0.127337i | ||||
\(595\) | −0.0459243 | − | 0.644436i | −0.00188271 | − | 0.0264193i | ||||
\(596\) | 2.17424i | 0.0890602i | ||||||||
\(597\) | −3.14258 | − | 25.0656i | −0.128617 | − | 1.02587i | ||||
\(598\) | 18.9062 | − | 18.9062i | 0.773133 | − | 0.773133i | ||||
\(599\) | −3.87877 | −0.158482 | −0.0792411 | − | 0.996855i | \(-0.525250\pi\) | ||||
−0.0792411 | + | 0.996855i | \(0.525250\pi\) | |||||||
\(600\) | −19.8663 | − | 11.3323i | −0.811040 | − | 0.462638i | ||||
\(601\) | −5.52177 | −0.225238 | −0.112619 | − | 0.993638i | \(-0.535924\pi\) | ||||
−0.112619 | + | 0.993638i | \(0.535924\pi\) | |||||||
\(602\) | −2.52123 | + | 2.52123i | −0.102758 | + | 0.102758i | ||||
\(603\) | 19.7357 | + | 11.7218i | 0.803699 | + | 0.477348i | ||||
\(604\) | 0.662053i | 0.0269386i | ||||||||
\(605\) | 0.158945 | + | 2.23041i | 0.00646204 | + | 0.0906791i | ||||
\(606\) | −4.76377 | − | 3.70234i | −0.193515 | − | 0.150397i | ||||
\(607\) | −8.91423 | − | 8.91423i | −0.361817 | − | 0.361817i | 0.502664 | − | 0.864482i | \(-0.332353\pi\) |
−0.864482 | + | 0.502664i | \(0.832353\pi\) | |||||||
\(608\) | 6.45411 | + | 6.45411i | 0.261749 | + | 0.261749i | ||||
\(609\) | −0.326426 | − | 0.253694i | −0.0132275 | − | 0.0102802i | ||||
\(610\) | −21.0452 | − | 18.2453i | −0.852096 | − | 0.738730i | ||||
\(611\) | 5.38927i | 0.218027i | ||||||||
\(612\) | 0.117417 | + | 0.0697387i | 0.00474631 | + | 0.00281902i | ||||
\(613\) | −11.8416 | + | 11.8416i | −0.478277 | + | 0.478277i | −0.904580 | − | 0.426303i | \(-0.859816\pi\) |
0.426303 | + | 0.904580i | \(0.359816\pi\) | |||||||
\(614\) | −5.66764 | −0.228727 | ||||||||
\(615\) | 31.1973 | − | 6.18985i | 1.25800 | − | 0.249599i | ||||
\(616\) | −3.89688 | −0.157010 | ||||||||
\(617\) | −12.9487 | + | 12.9487i | −0.521295 | + | 0.521295i | −0.917962 | − | 0.396668i | \(-0.870167\pi\) |
0.396668 | + | 0.917962i | \(0.370167\pi\) | |||||||
\(618\) | 0.891931 | + | 7.11415i | 0.0358787 | + | 0.286173i | ||||
\(619\) | 22.4360i | 0.901777i | 0.892580 | + | 0.450889i | \(0.148893\pi\) | ||||
−0.892580 | + | 0.450889i | \(0.851107\pi\) | |||||||
\(620\) | 3.90450 | − | 0.278245i | 0.156808 | − | 0.0111746i | ||||
\(621\) | 17.8348 | + | 7.77761i | 0.715686 | + | 0.312105i | ||||
\(622\) | −29.1945 | − | 29.1945i | −1.17059 | − | 1.17059i | ||||
\(623\) | −3.11504 | − | 3.11504i | −0.124801 | − | 0.124801i | ||||
\(624\) | −22.4049 | + | 28.8283i | −0.896915 | + | 1.15405i | ||||
\(625\) | 23.9946 | − | 7.01861i | 0.959783 | − | 0.280745i | ||||
\(626\) | − | 27.1610i | − | 1.08557i | ||||||
\(627\) | −11.9865 | + | 1.50279i | −0.478694 | + | 0.0600158i | ||||
\(628\) | −2.74062 | + | 2.74062i | −0.109363 | + | 0.109363i | ||||
\(629\) | −1.09115 | −0.0435069 | ||||||||
\(630\) | −4.66061 | − | 14.0361i | −0.185683 | − | 0.559213i | ||||
\(631\) | −18.3686 | −0.731243 | −0.365622 | − | 0.930764i | \(-0.619144\pi\) | ||||
−0.365622 | + | 0.930764i | \(0.619144\pi\) | |||||||
\(632\) | −25.3070 | + | 25.3070i | −1.00666 | + | 1.00666i | ||||
\(633\) | 9.32228 | − | 1.16877i | 0.370527 | − | 0.0464546i | ||||
\(634\) | − | 6.86389i | − | 0.272600i | ||||||
\(635\) | −12.3774 | + | 14.2769i | −0.491183 | + | 0.566561i | ||||
\(636\) | 0.0130060 | − | 0.0167347i | 0.000515722 | − | 0.000663575i | ||||
\(637\) | −16.2971 | − | 16.2971i | −0.645714 | − | 0.645714i | ||||
\(638\) | 0.170903 | + | 0.170903i | 0.00676612 | + | 0.00676612i | ||||
\(639\) | 11.2215 | + | 44.0485i | 0.443915 | + | 1.74253i | ||||
\(640\) | −18.8614 | + | 21.7559i | −0.745561 | + | 0.859976i | ||||
\(641\) | 12.9593i | 0.511860i | 0.966695 | + | 0.255930i | \(0.0823817\pi\) | ||||
−0.966695 | + | 0.255930i | \(0.917618\pi\) | |||||||
\(642\) | −2.99253 | − | 23.8688i | −0.118106 | − | 0.942026i | ||||
\(643\) | 5.94169 | − | 5.94169i | 0.234317 | − | 0.234317i | −0.580175 | − | 0.814492i | \(-0.697016\pi\) |
0.814492 | + | 0.580175i | \(0.197016\pi\) | |||||||
\(644\) | 1.28450 | 0.0506165 | ||||||||
\(645\) | −5.20628 | − | 3.48237i | −0.204997 | − | 0.137118i | ||||
\(646\) | −2.04055 | −0.0802845 | ||||||||
\(647\) | 20.3903 | − | 20.3903i | 0.801625 | − | 0.801625i | −0.181724 | − | 0.983350i | \(-0.558168\pi\) |
0.983350 | + | 0.181724i | \(0.0581678\pi\) | |||||||
\(648\) | −22.7996 | − | 6.71698i | −0.895652 | − | 0.263868i | ||||
\(649\) | 10.3955i | 0.408058i | ||||||||
\(650\) | −5.06279 | − | 35.3416i | −0.198579 | − | 1.38621i | ||||
\(651\) | −15.1953 | − | 11.8096i | −0.595551 | − | 0.462854i | ||||
\(652\) | 0.237842 | + | 0.237842i | 0.00931460 | + | 0.00931460i | ||||
\(653\) | 0.357485 | + | 0.357485i | 0.0139895 | + | 0.0139895i | 0.714067 | − | 0.700077i | \(-0.246851\pi\) |
−0.700077 | + | 0.714067i | \(0.746851\pi\) | |||||||
\(654\) | 37.9691 | + | 29.5091i | 1.48471 | + | 1.15390i | ||||
\(655\) | −5.71423 | + | 0.407211i | −0.223273 | + | 0.0159111i | ||||
\(656\) | − | 36.2230i | − | 1.41427i | ||||||
\(657\) | 8.63126 | − | 14.5322i | 0.336738 | − | 0.566956i | ||||
\(658\) | −1.75806 | + | 1.75806i | −0.0685362 | + | 0.0685362i | ||||
\(659\) | 27.8465 | 1.08474 | 0.542372 | − | 0.840138i | \(-0.317526\pi\) | ||||
0.542372 | + | 0.840138i | \(0.317526\pi\) | |||||||
\(660\) | 0.175230 | + | 0.883173i | 0.00682082 | + | 0.0343775i | ||||
\(661\) | 16.1467 | 0.628034 | 0.314017 | − | 0.949417i | \(-0.398325\pi\) | ||||
0.314017 | + | 0.949417i | \(0.398325\pi\) | |||||||
\(662\) | −34.8803 | + | 34.8803i | −1.35566 | + | 1.35566i | ||||
\(663\) | −0.201629 | − | 1.60822i | −0.00783062 | − | 0.0624580i | ||||
\(664\) | − | 22.1231i | − | 0.858544i | ||||||
\(665\) | 17.3877 | + | 15.0744i | 0.674266 | + | 0.584558i | ||||
\(666\) | −24.2051 | + | 6.16632i | −0.937930 | + | 0.238940i | ||||
\(667\) | 0.428300 | + | 0.428300i | 0.0165839 | + | 0.0165839i | ||||
\(668\) | 0.0650911 | + | 0.0650911i | 0.00251845 | + | 0.00251845i | ||||
\(669\) | −15.4999 | + | 19.9435i | −0.599259 | + | 0.771062i | ||||
\(670\) | 1.81712 | + | 25.4988i | 0.0702013 | + | 0.985106i | ||||
\(671\) | − | 8.33669i | − | 0.321835i | ||||||
\(672\) | −3.31869 | + | 0.416078i | −0.128021 | + | 0.0160505i | ||||
\(673\) | 15.9975 | − | 15.9975i | 0.616658 | − | 0.616658i | −0.328015 | − | 0.944673i | \(-0.606380\pi\) |
0.944673 | + | 0.328015i | \(0.106380\pi\) | |||||||
\(674\) | −15.7122 | −0.605213 | ||||||||
\(675\) | 22.5922 | − | 12.8293i | 0.869575 | − | 0.493801i | ||||
\(676\) | −2.28726 | −0.0879714 | ||||||||
\(677\) | −3.58130 | + | 3.58130i | −0.137641 | + | 0.137641i | −0.772570 | − | 0.634929i | \(-0.781029\pi\) |
0.634929 | + | 0.772570i | \(0.281029\pi\) | |||||||
\(678\) | −32.6286 | + | 4.09079i | −1.25310 | + | 0.157106i | ||||
\(679\) | − | 16.5885i | − | 0.636610i | ||||||
\(680\) | −0.0821944 | − | 1.15340i | −0.00315201 | − | 0.0442309i | ||||
\(681\) | −27.6191 | + | 35.5373i | −1.05837 | + | 1.36179i | ||||
\(682\) | 7.95562 | + | 7.95562i | 0.304636 | + | 0.304636i | ||||
\(683\) | 15.0743 | + | 15.0743i | 0.576802 | + | 0.576802i | 0.934021 | − | 0.357219i | \(-0.116275\pi\) |
−0.357219 | + | 0.934021i | \(0.616275\pi\) | |||||||
\(684\) | −4.71378 | + | 1.20085i | −0.180236 | + | 0.0459156i | ||||
\(685\) | −16.4762 | − | 14.2841i | −0.629523 | − | 0.545768i | ||||
\(686\) | − | 26.0657i | − | 0.995192i | ||||||
\(687\) | 3.10008 | + | 24.7266i | 0.118275 | + | 0.943379i | ||||
\(688\) | −5.04417 | + | 5.04417i | −0.192307 | + | 0.192307i | ||||
\(689\) | −0.251543 | −0.00958302 | ||||||||
\(690\) | 4.21706 | + | 21.2543i | 0.160541 | + | 0.809138i | ||||
\(691\) | 4.01842 | 0.152868 | 0.0764340 | − | 0.997075i | \(-0.475647\pi\) | ||||
0.0764340 | + | 0.997075i | \(0.475647\pi\) | |||||||
\(692\) | 3.21053 | − | 3.21053i | 0.122046 | − | 0.122046i | ||||
\(693\) | 2.26053 | − | 3.80600i | 0.0858705 | − | 0.144578i | ||||
\(694\) | − | 26.6799i | − | 1.01276i | ||||||
\(695\) | 10.7128 | − | 0.763421i | 0.406359 | − | 0.0289582i | ||||
\(696\) | −0.584232 | − | 0.454057i | −0.0221452 | − | 0.0172110i | ||||
\(697\) | 1.13705 | + | 1.13705i | 0.0430687 | + | 0.0430687i | ||||
\(698\) | 24.2143 | + | 24.2143i | 0.916523 | + | 0.916523i | ||||
\(699\) | 24.8335 | + | 19.3003i | 0.939289 | + | 0.730003i | ||||
\(700\) | 1.02858 | − | 1.37255i | 0.0388768 | − | 0.0518776i | ||||
\(701\) | 36.2944i | 1.37082i | 0.728157 | + | 0.685410i | \(0.240377\pi\) | ||||
−0.728157 | + | 0.685410i | \(0.759623\pi\) | |||||||
\(702\) | −13.5612 | − | 34.5359i | −0.511834 | − | 1.30348i | ||||
\(703\) | 27.4820 | − | 27.4820i | 1.03651 | − | 1.03651i | ||||
\(704\) | −6.86646 | −0.258789 | ||||||||
\(705\) | −3.63034 | − | 2.42826i | −0.136727 | − | 0.0914535i | ||||
\(706\) | 26.5527 | 0.999325 | ||||||||
\(707\) | −2.43245 | + | 2.43245i | −0.0914818 | + | 0.0914818i | ||||
\(708\) | 0.520728 | + | 4.15339i | 0.0195702 | + | 0.156094i | ||||
\(709\) | − | 17.0221i | − | 0.639277i | −0.947540 | − | 0.319639i | \(-0.896438\pi\) | ||
0.947540 | − | 0.319639i | \(-0.103562\pi\) | |||||||
\(710\) | −33.1605 | + | 38.2494i | −1.24449 | + | 1.43547i | ||||
\(711\) | −10.0365 | − | 39.3972i | −0.376399 | − | 1.47751i | ||||
\(712\) | −5.57523 | − | 5.57523i | −0.208941 | − | 0.208941i | ||||
\(713\) | 19.9376 | + | 19.9376i | 0.746668 | + | 0.746668i | ||||
\(714\) | 0.458849 | − | 0.590398i | 0.0171720 | − | 0.0220951i | ||||
\(715\) | 6.99998 | − | 8.07421i | 0.261785 | − | 0.301958i | ||||
\(716\) | − | 1.86156i | − | 0.0695696i | ||||||
\(717\) | 10.3633 | − | 1.29929i | 0.387024 | − | 0.0485228i | ||||
\(718\) | 19.4268 | − | 19.4268i | 0.725002 | − | 0.725002i | ||||
\(719\) | −20.9403 | −0.780940 | −0.390470 | − | 0.920616i | \(-0.627688\pi\) | ||||
−0.390470 | + | 0.920616i | \(0.627688\pi\) | |||||||
\(720\) | −9.32435 | − | 28.0817i | −0.347498 | − | 1.04654i | ||||
\(721\) | 4.08803 | 0.152246 | ||||||||
\(722\) | 31.3202 | − | 31.3202i | 1.16562 | − | 1.16562i | ||||
\(723\) | −14.0893 | + | 1.76644i | −0.523989 | + | 0.0656946i | ||||
\(724\) | − | 3.93418i | − | 0.146213i | ||||||
\(725\) | 0.800627 | − | 0.114692i | 0.0297345 | − | 0.00425956i | ||||
\(726\) | −1.58809 | + | 2.04338i | −0.0589395 | + | 0.0758370i | ||||
\(727\) | −7.72035 | − | 7.72035i | −0.286332 | − | 0.286332i | 0.549296 | − | 0.835628i | \(-0.314896\pi\) |
−0.835628 | + | 0.549296i | \(0.814896\pi\) | |||||||
\(728\) | 13.1685 | + | 13.1685i | 0.488056 | + | 0.488056i | ||||
\(729\) | 19.7861 | − | 18.3714i | 0.732819 | − | 0.680424i | ||||
\(730\) | 18.7759 | − | 1.33802i | 0.694927 | − | 0.0495224i | ||||
\(731\) | − | 0.316674i | − | 0.0117126i | ||||||
\(732\) | −0.417600 | − | 3.33083i | −0.0154349 | − | 0.123111i | ||||
\(733\) | −0.579034 | + | 0.579034i | −0.0213871 | + | 0.0213871i | −0.717719 | − | 0.696332i | \(-0.754814\pi\) |
0.696332 | + | 0.717719i | \(0.254814\pi\) | |||||||
\(734\) | 4.23091 | 0.156166 | ||||||||
\(735\) | 18.3211 | − | 3.63509i | 0.675785 | − | 0.134082i | ||||
\(736\) | 4.90034 | 0.180629 | ||||||||
\(737\) | −5.41037 | + | 5.41037i | −0.199293 | + | 0.199293i | ||||
\(738\) | 31.6490 | + | 18.7976i | 1.16502 | + | 0.691949i | ||||
\(739\) | 40.7534i | 1.49914i | 0.661925 | + | 0.749570i | \(0.269740\pi\) | ||||
−0.661925 | + | 0.749570i | \(0.730260\pi\) | |||||||
\(740\) | −2.18876 | − | 1.89755i | −0.0804603 | − | 0.0697555i | ||||
\(741\) | 45.5835 | + | 35.4269i | 1.67455 | + | 1.30144i | ||||
\(742\) | −0.0820569 | − | 0.0820569i | −0.00301240 | − | 0.00301240i | ||||
\(743\) | −24.8882 | − | 24.8882i | −0.913060 | − | 0.913060i | 0.0834523 | − | 0.996512i | \(-0.473405\pi\) |
−0.996512 | + | 0.0834523i | \(0.973405\pi\) | |||||||
\(744\) | −27.1963 | − | 21.1366i | −0.997064 | − | 0.774905i | ||||
\(745\) | 1.48652 | + | 20.8597i | 0.0544617 | + | 0.764239i | ||||
\(746\) | 3.01784i | 0.110491i | ||||||||
\(747\) | 21.6072 | + | 12.8334i | 0.790566 | + | 0.469548i | ||||
\(748\) | −0.0321889 | + | 0.0321889i | −0.00117694 | + | 0.00117694i | ||||
\(749\) | −13.7158 | −0.501165 | ||||||||
\(750\) | 26.0881 | + | 12.5136i | 0.952604 | + | 0.456930i | ||||
\(751\) | 18.0268 | 0.657805 | 0.328903 | − | 0.944364i | \(-0.393321\pi\) | ||||
0.328903 | + | 0.944364i | \(0.393321\pi\) | |||||||
\(752\) | −3.51730 | + | 3.51730i | −0.128263 | + | 0.128263i | ||||
\(753\) | 1.97005 | + | 15.7133i | 0.0717924 | + | 0.572625i | ||||
\(754\) | − | 1.15505i | − | 0.0420643i | ||||||
\(755\) | 0.452643 | + | 6.35175i | 0.0164734 | + | 0.231164i | ||||
\(756\) | 0.712520 | − | 1.63388i | 0.0259141 | − | 0.0594235i | ||||
\(757\) | −33.3360 | − | 33.3360i | −1.21162 | − | 1.21162i | −0.970494 | − | 0.241123i | \(-0.922484\pi\) |
−0.241123 | − | 0.970494i | \(-0.577516\pi\) | |||||||
\(758\) | 7.94019 | + | 7.94019i | 0.288401 | + | 0.288401i | ||||
\(759\) | −3.97991 | + | 5.12092i | −0.144462 | + | 0.185878i | ||||
\(760\) | 31.1201 | + | 26.9798i | 1.12885 | + | 0.978660i | ||||
\(761\) | 45.3776i | 1.64494i | 0.568811 | + | 0.822468i | \(0.307404\pi\) | ||||
−0.568811 | + | 0.822468i | \(0.692596\pi\) | |||||||
\(762\) | −21.6988 | + | 2.72047i | −0.786064 | + | 0.0985521i | ||||
\(763\) | 19.3876 | − | 19.3876i | 0.701879 | − | 0.701879i | ||||
\(764\) | −4.94654 | −0.178960 | ||||||||
\(765\) | 1.17418 | + | 0.588796i | 0.0424526 | + | 0.0212880i | ||||
\(766\) | −0.506367 | −0.0182958 | ||||||||
\(767\) | 35.1288 | − | 35.1288i | 1.26843 | − | 1.26843i | ||||
\(768\) | −9.46438 | + | 1.18659i | −0.341516 | + | 0.0428173i | ||||
\(769\) | − | 8.85728i | − | 0.319402i | −0.987165 | − | 0.159701i | \(-0.948947\pi\) | ||
0.987165 | − | 0.159701i | \(-0.0510530\pi\) | |||||||
\(770\) | 4.91742 | − | 0.350429i | 0.177211 | − | 0.0126286i | ||||
\(771\) | 12.8240 | − | 16.5005i | 0.461844 | − | 0.594251i | ||||
\(772\) | −1.60880 | − | 1.60880i | −0.0579021 | − | 0.0579021i | ||||
\(773\) | −25.8567 | − | 25.8567i | −0.930001 | − | 0.930001i | 0.0677042 | − | 0.997705i | \(-0.478433\pi\) |
−0.997705 | + | 0.0677042i | \(0.978433\pi\) | |||||||
\(774\) | −1.78960 | − | 7.02485i | −0.0643258 | − | 0.252503i | ||||
\(775\) | 37.2696 | − | 5.33897i | 1.33876 | − | 0.191782i | ||||
\(776\) | − | 29.6899i | − | 1.06580i | ||||||
\(777\) | 1.77169 | + | 14.1312i | 0.0635589 | + | 0.506954i | ||||
\(778\) | −29.6606 | + | 29.6606i | −1.06338 | + | 1.06338i | ||||
\(779\) | −57.2761 | −2.05213 | ||||||||
\(780\) | 2.39231 | − | 3.57660i | 0.0856584 | − | 0.128063i | ||||
\(781\) | −15.1518 | −0.542174 | ||||||||
\(782\) | −0.774654 | + | 0.774654i | −0.0277016 | + | 0.0277016i | ||||
\(783\) | 0.782374 | − | 0.307214i | 0.0279598 | − | 0.0109789i | ||||
\(784\) | − | 21.2725i | − | 0.759734i | ||||||
\(785\) | −24.4198 | + | 28.1673i | −0.871581 | + | 1.00533i | ||||
\(786\) | −5.23506 | − | 4.06862i | −0.186729 | − | 0.145123i | ||||
\(787\) | 2.52646 | + | 2.52646i | 0.0900586 | + | 0.0900586i | 0.750701 | − | 0.660642i | \(-0.229716\pi\) |
−0.660642 | + | 0.750701i | \(0.729716\pi\) | |||||||
\(788\) | 0.419338 | + | 0.419338i | 0.0149383 | + | 0.0149383i | ||||
\(789\) | −3.48715 | − | 2.71017i | −0.124146 | − | 0.0964845i | ||||
\(790\) | 29.6589 | − | 34.2104i | 1.05522 | − | 1.21715i | ||||
\(791\) | 18.7495i | 0.666655i | ||||||||
\(792\) | 4.04586 | − | 6.81190i | 0.143763 | − | 0.242050i | ||||
\(793\) | −28.1717 | + | 28.1717i | −1.00041 | + | 1.00041i | ||||
\(794\) | 27.5864 | 0.979004 | ||||||||
\(795\) | 0.113338 | − | 0.169445i | 0.00401970 | − | 0.00600961i | ||||
\(796\) | 3.39069 | 0.120180 | ||||||||
\(797\) | 6.73965 | − | 6.73965i | 0.238731 | − | 0.238731i | −0.577594 | − | 0.816324i | \(-0.696008\pi\) |
0.816324 | + | 0.577594i | \(0.196008\pi\) | |||||||
\(798\) | 3.31323 | + | 26.4267i | 0.117287 | + | 0.935496i | ||||
\(799\) | − | 0.220817i | − | 0.00781195i | ||||||
\(800\) | 3.92401 | − | 5.23625i | 0.138735 | − | 0.185129i | ||||
\(801\) | 8.67934 | − | 2.21109i | 0.306669 | − | 0.0781249i | ||||
\(802\) | −2.19608 | − | 2.19608i | −0.0775464 | − | 0.0775464i | ||||
\(803\) | 3.98389 | + | 3.98389i | 0.140588 | + | 0.140588i | ||||
\(804\) | −1.89063 | + | 2.43266i | −0.0666775 | + | 0.0857935i | ||||
\(805\) | 12.3235 | − | 0.878209i | 0.434348 | − | 0.0309528i | ||||
\(806\) | − | 53.7679i | − | 1.89389i | ||||||
\(807\) | −6.51190 | + | 0.816424i | −0.229230 | + | 0.0287395i | ||||
\(808\) | −4.35356 | + | 4.35356i | −0.153158 | + | 0.153158i | ||||
\(809\) | −26.6054 | −0.935397 | −0.467698 | − | 0.883888i | \(-0.654917\pi\) | ||||
−0.467698 | + | 0.883888i | \(0.654917\pi\) | |||||||
\(810\) | 29.3745 | + | 6.42581i | 1.03212 | + | 0.225780i | ||||
\(811\) | −49.2615 | −1.72980 | −0.864902 | − | 0.501941i | \(-0.832620\pi\) | ||||
−0.864902 | + | 0.501941i | \(0.832620\pi\) | |||||||
\(812\) | 0.0392373 | − | 0.0392373i | 0.00137696 | − | 0.00137696i | ||||
\(813\) | −49.5543 | + | 6.21283i | −1.73795 | + | 0.217894i | ||||
\(814\) | − | 8.32608i | − | 0.291829i | ||||||
\(815\) | 2.44447 | + | 2.11925i | 0.0856260 | + | 0.0742340i | ||||
\(816\) | 0.918008 | − | 1.18119i | 0.0321367 | − | 0.0413500i | ||||
\(817\) | 7.97588 | + | 7.97588i | 0.279041 | + | 0.279041i | ||||
\(818\) | −1.47079 | − | 1.47079i | −0.0514251 | − | 0.0514251i | ||||
\(819\) | −20.5003 | + | 5.22250i | −0.716337 | + | 0.182489i | ||||
\(820\) | 0.303451 | + | 4.25820i | 0.0105970 | + | 0.148703i | ||||
\(821\) | − | 12.0560i | − | 0.420756i | −0.977620 | − | 0.210378i | \(-0.932531\pi\) | ||
0.977620 | − | 0.210378i | \(-0.0674695\pi\) | |||||||
\(822\) | −3.13954 | − | 25.0414i | −0.109504 | − | 0.873419i | ||||
\(823\) | 24.7646 | − | 24.7646i | 0.863241 | − | 0.863241i | −0.128472 | − | 0.991713i | \(-0.541007\pi\) |
0.991713 | + | 0.128472i | \(0.0410072\pi\) | |||||||
\(824\) | 7.31668 | 0.254888 | ||||||||
\(825\) | 2.28498 | + | 8.35337i | 0.0795528 | + | 0.290827i | ||||
\(826\) | 22.9191 | 0.797456 | ||||||||
\(827\) | 29.8690 | − | 29.8690i | 1.03865 | − | 1.03865i | 0.0394242 | − | 0.999223i | \(-0.487448\pi\) |
0.999223 | − | 0.0394242i | \(-0.0125524\pi\) | |||||||
\(828\) | −1.33361 | + | 2.24537i | −0.0463462 | + | 0.0780318i | ||||
\(829\) | − | 13.4176i | − | 0.466013i | −0.972475 | − | 0.233006i | \(-0.925144\pi\) | ||
0.972475 | − | 0.233006i | \(-0.0748563\pi\) | |||||||
\(830\) | 1.98943 | + | 27.9169i | 0.0690542 | + | 0.969009i | ||||
\(831\) | −27.7956 | − | 21.6024i | −0.964220 | − | 0.749379i | ||||
\(832\) | 23.2034 | + | 23.2034i | 0.804434 | + | 0.804434i | ||||
\(833\) | 0.667748 | + | 0.667748i | 0.0231361 | + | 0.0231361i | ||||
\(834\) | 9.81446 | + | 7.62767i | 0.339847 | + | 0.264125i | ||||
\(835\) | 0.668987 | + | 0.579982i | 0.0231513 | + | 0.0200711i | ||||
\(836\) | − | 1.62144i | − | 0.0560788i | ||||||
\(837\) | 36.4199 | − | 14.3010i | 1.25886 | − | 0.494313i | ||||
\(838\) | 8.99863 | − | 8.99863i | 0.310853 | − | 0.310853i | ||||
\(839\) | −32.2680 | −1.11401 | −0.557007 | − | 0.830508i | \(-0.688050\pi\) | ||||
−0.557007 | + | 0.830508i | \(0.688050\pi\) | |||||||
\(840\) | −14.8040 | + | 2.93725i | −0.510785 | + | 0.101345i | ||||
\(841\) | −28.9738 | −0.999098 | ||||||||
\(842\) | 20.4432 | − | 20.4432i | 0.704520 | − | 0.704520i | ||||
\(843\) | −4.73518 | − | 37.7684i | −0.163088 | − | 1.30081i | ||||
\(844\) | 1.26105i | 0.0434072i | ||||||||
\(845\) | −21.9440 | + | 1.56379i | −0.754896 | + | 0.0537959i | ||||
\(846\) | −1.24789 | − | 4.89843i | −0.0429033 | − | 0.168411i | ||||
\(847\) | 1.04338 | + | 1.04338i | 0.0358510 | + | 0.0358510i | ||||
\(848\) | −0.164169 | − | 0.164169i | −0.00563759 | − | 0.00563759i | ||||
\(849\) | −8.49494 | + | 10.9304i | −0.291546 | + | 0.375129i | ||||
\(850\) | 0.207440 | + | 1.44807i | 0.00711514 | + | 0.0496684i | ||||
\(851\) | − | 20.8660i | − | 0.715277i | ||||||
\(852\) | −6.05373 | + | 0.758982i | −0.207397 | + | 0.0260023i | ||||
\(853\) | 11.1082 | − | 11.1082i | 0.380338 | − | 0.380338i | −0.490886 | − | 0.871224i | \(-0.663327\pi\) |
0.871224 | + | 0.490886i | \(0.163327\pi\) | |||||||
\(854\) | −18.3800 | −0.628951 | ||||||||
\(855\) | −44.4030 | + | 14.7437i | −1.51855 | + | 0.504225i | ||||
\(856\) | −24.5483 | −0.839043 | ||||||||
\(857\) | −25.3044 | + | 25.3044i | −0.864382 | + | 0.864382i | −0.991843 | − | 0.127462i | \(-0.959317\pi\) |
0.127462 | + | 0.991843i | \(0.459317\pi\) | |||||||
\(858\) | 12.2716 | − | 1.53854i | 0.418946 | − | 0.0525250i | ||||
\(859\) | 14.5610i | 0.496814i | 0.968656 | + | 0.248407i | \(0.0799071\pi\) | ||||
−0.968656 | + | 0.248407i | \(0.920093\pi\) | |||||||
\(860\) | 0.550711 | − | 0.635224i | 0.0187791 | − | 0.0216610i | ||||
\(861\) | 12.8794 | − | 16.5718i | 0.438929 | − | 0.564766i | ||||
\(862\) | 30.1424 | + | 30.1424i | 1.02665 | + | 1.02665i | ||||
\(863\) | −31.1659 | − | 31.1659i | −1.06090 | − | 1.06090i | −0.998021 | − | 0.0628778i | \(-0.979972\pi\) |
−0.0628778 | − | 0.998021i | \(-0.520028\pi\) | |||||||
\(864\) | 2.71824 | − | 6.23319i | 0.0924765 | − | 0.212057i | ||||
\(865\) | 28.6068 | − | 32.9969i | 0.972661 | − | 1.12193i | ||||
\(866\) | − | 61.8056i | − | 2.10024i | ||||||
\(867\) | −3.65469 | − | 29.1502i | −0.124120 | − | 0.989994i | ||||
\(868\) | 1.82652 | − | 1.82652i | 0.0619960 | − | 0.0619960i | ||||
\(869\) | 13.5518 | 0.459714 | ||||||||
\(870\) | 0.778066 | + | 0.520432i | 0.0263789 | + | 0.0176443i | ||||
\(871\) | 36.5659 | 1.23899 | ||||||||
\(872\) | 34.6996 | − | 34.6996i | 1.17508 | − | 1.17508i | ||||
\(873\) | 28.9975 | + | 17.2227i | 0.981416 | + | 0.582902i | ||||
\(874\) | − | 39.0214i | − | 1.31992i | ||||||
\(875\) | 8.92984 | − | 13.8715i | 0.301884 | − | 0.468944i | ||||
\(876\) | 1.79128 | + | 1.39216i | 0.0605216 | + | 0.0470366i | ||||
\(877\) | 5.05706 | + | 5.05706i | 0.170765 | + | 0.170765i | 0.787315 | − | 0.616551i | \(-0.211470\pi\) |
−0.616551 | + | 0.787315i | \(0.711470\pi\) | |||||||
\(878\) | 6.23676 | + | 6.23676i | 0.210481 | + | 0.210481i | ||||
\(879\) | −26.7538 | − | 20.7927i | −0.902382 | − | 0.701319i | ||||
\(880\) | 9.83815 | − | 0.701093i | 0.331644 | − | 0.0236338i | ||||
\(881\) | 0.249716i | 0.00841316i | 0.999991 | + | 0.00420658i | \(0.00133900\pi\) | ||||
−0.999991 | + | 0.00420658i | \(0.998661\pi\) | |||||||
\(882\) | 18.5864 | + | 11.0392i | 0.625836 | + | 0.371709i | ||||
\(883\) | −4.25796 | + | 4.25796i | −0.143292 | + | 0.143292i | −0.775114 | − | 0.631822i | \(-0.782307\pi\) |
0.631822 | + | 0.775114i | \(0.282307\pi\) | |||||||
\(884\) | 0.217548 | 0.00731694 | ||||||||
\(885\) | 7.83553 | + | 39.4917i | 0.263389 | + | 1.32750i | ||||
\(886\) | 0.419263 | 0.0140854 | ||||||||
\(887\) | −17.6949 | + | 17.6949i | −0.594137 | + | 0.594137i | −0.938746 | − | 0.344609i | \(-0.888011\pi\) |
0.344609 | + | 0.938746i | \(0.388011\pi\) | |||||||
\(888\) | 3.17093 | + | 25.2917i | 0.106410 | + | 0.848735i | ||||
\(889\) | 12.4688i | 0.418191i | ||||||||
\(890\) | 7.53667 | + | 6.53396i | 0.252630 | + | 0.219019i | ||||
\(891\) | 4.30609 | + | 7.90301i | 0.144259 | + | 0.264761i | ||||
\(892\) | −2.39727 | − | 2.39727i | −0.0802664 | − | 0.0802664i | ||||
\(893\) | 5.56158 | + | 5.56158i | 0.186111 | + | 0.186111i | ||||
\(894\) | −14.8524 | + | 19.1105i | −0.496739 | + | 0.639150i | ||||
\(895\) | −1.27274 | − | 17.8598i | −0.0425429 | − | 0.596987i | ||||
\(896\) | 19.0007i | 0.634768i | ||||||||
\(897\) | 30.7539 | − | 3.85575i | 1.02684 | − | 0.128740i | ||||
\(898\) | −26.2113 | + | 26.2113i | −0.874681 | + | 0.874681i | ||||
\(899\) | 1.21805 | 0.0406244 | ||||||||
\(900\) | 1.33137 | + | 3.22303i | 0.0443791 | + | 0.107434i | ||||
\(901\) | 0.0103066 | 0.000343362 | ||||||||
\(902\) | −8.67631 | + | 8.67631i | −0.288889 | + | 0.288889i | ||||
\(903\) | −4.10118 | + | 0.514182i | −0.136479 | + | 0.0171109i | ||||
\(904\) | 33.5575i | 1.11611i | ||||||||
\(905\) | −2.68978 | − | 37.7446i | −0.0894113 | − | 1.25467i | ||||
\(906\) | −4.52255 | + | 5.81913i | −0.150252 | + | 0.193328i | ||||
\(907\) | 20.7669 | + | 20.7669i | 0.689555 | + | 0.689555i | 0.962134 | − | 0.272578i | \(-0.0878764\pi\) |
−0.272578 | + | 0.962134i | \(0.587876\pi\) | |||||||
\(908\) | −4.27168 | − | 4.27168i | −0.141761 | − | 0.141761i | ||||
\(909\) | −1.72658 | − | 6.77748i | −0.0572671 | − | 0.224795i | ||||
\(910\) | −17.8013 | − | 15.4330i | −0.590108 | − | 0.511598i | ||||
\(911\) | 51.3966i | 1.70285i | 0.524479 | + | 0.851423i | \(0.324260\pi\) | ||||
−0.524479 | + | 0.851423i | \(0.675740\pi\) | |||||||
\(912\) | 6.62869 | + | 52.8713i | 0.219498 | + | 1.75074i | ||||
\(913\) | −5.92343 | + | 5.92343i | −0.196037 | + | 0.196037i | ||||
\(914\) | −28.9751 | −0.958411 | ||||||||
\(915\) | −6.28373 | − | 31.6705i | −0.207734 | − | 1.04700i | ||||
\(916\) | −3.34484 | −0.110517 | ||||||||
\(917\) | −2.67310 | + | 2.67310i | −0.0882736 | + | 0.0882736i | ||||
\(918\) | 0.555648 | + | 1.41506i | 0.0183391 | + | 0.0467038i | ||||
\(919\) | 8.13299i | 0.268283i | 0.990962 | + | 0.134141i | \(0.0428276\pi\) | ||||
−0.990962 | + | 0.134141i | \(0.957172\pi\) | |||||||
\(920\) | 22.0564 | − | 1.57180i | 0.727179 | − | 0.0518208i | ||||
\(921\) | −5.18757 | − | 4.03171i | −0.170936 | − | 0.132849i | ||||
\(922\) | −8.89107 | − | 8.89107i | −0.292812 | − | 0.292812i | ||||
\(923\) | 51.2016 | + | 51.2016i | 1.68532 | + | 1.68532i | ||||
\(924\) | 0.469136 | + | 0.364606i | 0.0154334 | + | 0.0119947i | ||||
\(925\) | −22.2963 | − | 16.7087i | −0.733098 | − | 0.549379i | ||||
\(926\) | 50.3627i | 1.65502i | ||||||||
\(927\) | −4.24432 | + | 7.14605i | −0.139402 | + | 0.234707i | ||||
\(928\) | 0.149689 | − | 0.149689i | 0.00491378 | − | 0.00491378i | ||||
\(929\) | 58.9243 | 1.93324 | 0.966622 | − | 0.256208i | \(-0.0824733\pi\) | ||||
0.966622 | + | 0.256208i | \(0.0824733\pi\) | |||||||
\(930\) | 36.2193 | + | 24.2263i | 1.18768 | + | 0.794413i | ||||
\(931\) | −33.6363 | −1.10239 | ||||||||
\(932\) | −2.98505 | + | 2.98505i | −0.0977786 | + | 0.0977786i | ||||
\(933\) | −5.95394 | − | 47.4894i | −0.194923 | − | 1.55473i | ||||
\(934\) | 57.7895i | 1.89093i | ||||||||
\(935\) | −0.286814 | + | 0.330828i | −0.00937980 | + | 0.0108192i | ||||
\(936\) | −36.6910 | + | 9.34713i | −1.19928 | + | 0.305520i | ||||
\(937\) | −25.4166 | − | 25.4166i | −0.830325 | − | 0.830325i | 0.157236 | − | 0.987561i | \(-0.449742\pi\) |
−0.987561 | + | 0.157236i | \(0.949742\pi\) | |||||||
\(938\) | 11.9283 | + | 11.9283i | 0.389473 | + | 0.389473i | ||||
\(939\) | 19.3212 | − | 24.8604i | 0.630522 | − | 0.811288i | ||||
\(940\) | 0.384011 | − | 0.442942i | 0.0125251 | − | 0.0144472i | ||||
\(941\) | − | 13.9714i | − | 0.455454i | −0.973725 | − | 0.227727i | \(-0.926871\pi\) | ||
0.973725 | − | 0.227727i | \(-0.0731294\pi\) | |||||||
\(942\) | −42.8102 | + | 5.36729i | −1.39483 | + | 0.174876i | ||||
\(943\) | −21.7437 | + | 21.7437i | −0.708072 | + | 0.708072i | ||||
\(944\) | 45.8536 | 1.49241 | ||||||||
\(945\) | 5.71886 | − | 16.1626i | 0.186034 | − | 0.525769i | ||||
\(946\) | 2.41641 | 0.0785641 | ||||||||
\(947\) | 16.9086 | − | 16.9086i | 0.549455 | − | 0.549455i | −0.376828 | − | 0.926283i | \(-0.622985\pi\) |
0.926283 | + | 0.376828i | \(0.122985\pi\) | |||||||
\(948\) | 5.41447 | − | 0.678835i | 0.175854 | − | 0.0220476i | ||||
\(949\) | − | 26.9250i | − | 0.874023i | ||||||
\(950\) | −41.6963 | − | 31.2470i | −1.35281 | − | 1.01379i | ||||
\(951\) | 4.88268 | − | 6.28250i | 0.158332 | − | 0.203724i | ||||
\(952\) | −0.539558 | − | 0.539558i | −0.0174872 | − | 0.0174872i | ||||
\(953\) | −1.08828 | − | 1.08828i | −0.0352529 | − | 0.0352529i | 0.689261 | − | 0.724513i | \(-0.257936\pi\) |
−0.724513 | + | 0.689261i | \(0.757936\pi\) | |||||||
\(954\) | 0.228633 | − | 0.0582449i | 0.00740227 | − | 0.00188575i | ||||
\(955\) | −47.4572 | + | 3.38193i | −1.53568 | + | 0.109437i | ||||
\(956\) | 1.40187i | 0.0453397i | ||||||||
\(957\) | 0.0348540 | + | 0.278000i | 0.00112667 | + | 0.00898647i | ||||
\(958\) | 4.70341 | − | 4.70341i | 0.151960 | − | 0.151960i | ||||
\(959\) | −14.3896 | −0.464665 | ||||||||
\(960\) | −26.0852 | + | 5.17555i | −0.841896 | + | 0.167040i | ||||
\(961\) | 25.7010 | 0.829064 | ||||||||
\(962\) | −28.1358 | + | 28.1358i | −0.907135 | + | 0.907135i | ||||
\(963\) | 14.2402 | − | 23.9758i | 0.458883 | − | 0.772609i | ||||
\(964\) | − | 1.90591i | − | 0.0613851i | ||||||
\(965\) | −16.5348 | − | 14.3350i | −0.532275 | − | 0.461458i | ||||
\(966\) | 11.2902 | + | 8.77456i | 0.363255 | + | 0.282317i | ||||
\(967\) | −8.46891 | − | 8.46891i | −0.272342 | − | 0.272342i | 0.557701 | − | 0.830042i | \(-0.311684\pi\) |
−0.830042 | + | 0.557701i | \(0.811684\pi\) | |||||||
\(968\) | 1.86743 | + | 1.86743i | 0.0600213 | + | 0.0600213i | ||||
\(969\) | −1.86771 | − | 1.45156i | −0.0599996 | − | 0.0466309i | ||||
\(970\) | 2.66988 | + | 37.4653i | 0.0857246 | + | 1.20294i | ||||
\(971\) | 23.1322i | 0.742347i | 0.928564 | + | 0.371173i | \(0.121044\pi\) | ||||
−0.928564 | + | 0.371173i | \(0.878956\pi\) | |||||||
\(972\) | 2.11632 | + | 2.94186i | 0.0678811 | + | 0.0943601i | ||||
\(973\) | 5.01142 | − | 5.01142i | 0.160659 | − | 0.160659i | ||||
\(974\) | −8.39756 | −0.269075 | ||||||||
\(975\) | 20.5066 | − | 35.9496i | 0.656735 | − | 1.15131i | ||||
\(976\) | −36.7724 | −1.17706 | ||||||||
\(977\) | 26.7706 | − | 26.7706i | 0.856468 | − | 0.856468i | −0.134452 | − | 0.990920i | \(-0.542927\pi\) |
0.990920 | + | 0.134452i | \(0.0429273\pi\) | |||||||
\(978\) | 0.465795 | + | 3.71523i | 0.0148945 | + | 0.118800i | ||||
\(979\) | 2.98552i | 0.0954176i | ||||||||
\(980\) | 0.178206 | + | 2.50069i | 0.00569259 | + | 0.0798817i | ||||
\(981\) | 13.7615 | + | 54.0192i | 0.439372 | + | 1.72470i | ||||
\(982\) | 18.5694 | + | 18.5694i | 0.592573 | + | 0.592573i | ||||
\(983\) | 2.19423 | + | 2.19423i | 0.0699849 | + | 0.0699849i | 0.741233 | − | 0.671248i | \(-0.234241\pi\) |
−0.671248 | + | 0.741233i | \(0.734241\pi\) | |||||||
\(984\) | 23.0513 | − | 29.6599i | 0.734849 | − | 0.945524i | ||||
\(985\) | 4.30984 | + | 3.73644i | 0.137323 | + | 0.119053i | ||||
\(986\) | 0.0473262i | 0.00150717i | ||||||||
\(987\) | −2.85975 | + | 0.358539i | −0.0910269 | + | 0.0114124i | ||||
\(988\) | −5.47925 | + | 5.47925i | −0.174318 | + | 0.174318i | ||||
\(989\) | 6.05576 | 0.192562 | ||||||||
\(990\) | −4.49285 | + | 8.95968i | −0.142792 | + | 0.284757i | ||||
\(991\) | −5.63682 | −0.179059 | −0.0895297 | − | 0.995984i | \(-0.528536\pi\) | ||||
−0.0895297 | + | 0.995984i | \(0.528536\pi\) | |||||||
\(992\) | 6.96810 | − | 6.96810i | 0.221237 | − | 0.221237i | ||||
\(993\) | −56.7382 | + | 7.11350i | −1.80053 | + | 0.225740i | ||||
\(994\) | 33.4054i | 1.05955i | ||||||||
\(995\) | 32.5304 | − | 2.31820i | 1.03128 | − | 0.0734920i | ||||
\(996\) | −2.06992 | + | 2.66335i | −0.0655880 | + | 0.0843916i | ||||
\(997\) | −30.3894 | − | 30.3894i | −0.962443 | − | 0.962443i | 0.0368765 | − | 0.999320i | \(-0.488259\pi\) |
−0.999320 | + | 0.0368765i | \(0.988259\pi\) | |||||||
\(998\) | 8.67716 | + | 8.67716i | 0.274671 | + | 0.274671i | ||||
\(999\) | −26.5413 | − | 11.5745i | −0.839731 | − | 0.366200i |
(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 | 165.2.k.c.122.3 | yes | 16 | |
3.2 | odd | 2 | 165.2.k.d.122.6 | yes | 16 | ||
5.2 | odd | 4 | 825.2.k.i.518.3 | 16 | |||
5.3 | odd | 4 | 165.2.k.d.23.6 | yes | 16 | ||
5.4 | even | 2 | 825.2.k.j.782.6 | 16 | |||
15.2 | even | 4 | 825.2.k.j.518.6 | 16 | |||
15.8 | even | 4 | inner | 165.2.k.c.23.3 | ✓ | 16 | |
15.14 | odd | 2 | 825.2.k.i.782.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.k.c.23.3 | ✓ | 16 | 15.8 | even | 4 | inner | |
165.2.k.c.122.3 | yes | 16 | 1.1 | even | 1 | trivial | |
165.2.k.d.23.6 | yes | 16 | 5.3 | odd | 4 | ||
165.2.k.d.122.6 | yes | 16 | 3.2 | odd | 2 | ||
825.2.k.i.518.3 | 16 | 5.2 | odd | 4 | |||
825.2.k.i.782.3 | 16 | 15.14 | odd | 2 | |||
825.2.k.j.518.6 | 16 | 15.2 | even | 4 | |||
825.2.k.j.782.6 | 16 | 5.4 | even | 2 |