Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,3,Mod(116,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.116");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.w (of order \(6\), 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: | \(7.43871121704\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16 x^{14} - 176 x^{13} + 344 x^{12} + 4576 x^{11} + 11040 x^{10} - 37664 x^{9} + \cdots + 97900608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 116.7 | ||
Root | \(-1.95177 + 4.07201i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.116 |
Dual form | 273.3.w.c.233.7 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70956 | + | 2.96105i | 0.854781 | + | 1.48052i | 0.876848 | + | 0.480768i | \(0.159642\pi\) |
−0.0220666 | + | 0.999757i | \(0.507025\pi\) | |||||||
\(3\) | −2.79279 | + | 1.09560i | −0.930930 | + | 0.365198i | ||||
\(4\) | −3.84521 | + | 6.66010i | −0.961302 | + | 1.66502i | ||||
\(5\) | −3.81256 | − | 6.60355i | −0.762512 | − | 1.32071i | −0.941552 | − | 0.336868i | \(-0.890632\pi\) |
0.179040 | − | 0.983842i | \(-0.442701\pi\) | |||||||
\(6\) | −8.01856 | − | 6.39660i | −1.33643 | − | 1.06610i | ||||
\(7\) | 4.11804 | − | 5.66055i | 0.588291 | − | 0.808649i | ||||
\(8\) | −12.6180 | −1.57725 | ||||||||
\(9\) | 6.59934 | − | 6.11953i | 0.733260 | − | 0.679948i | ||||
\(10\) | 13.0356 | − | 22.5784i | 1.30356 | − | 2.25784i | ||||
\(11\) | 1.31613 | − | 2.27960i | 0.119648 | − | 0.207236i | −0.799980 | − | 0.600026i | \(-0.795157\pi\) |
0.919628 | + | 0.392790i | \(0.128490\pi\) | |||||||
\(12\) | 3.44209 | − | 22.8130i | 0.286840 | − | 1.90109i | ||||
\(13\) | −13.0000 | −1.00000 | ||||||||
\(14\) | 23.8012 | + | 2.51665i | 1.70009 | + | 0.179761i | ||||
\(15\) | 17.8825 | + | 14.2653i | 1.19217 | + | 0.951020i | ||||
\(16\) | −6.19042 | − | 10.7221i | −0.386901 | − | 0.670132i | ||||
\(17\) | −23.8012 | − | 13.7416i | −1.40007 | − | 0.808331i | −0.405671 | − | 0.914019i | \(-0.632962\pi\) |
−0.994399 | + | 0.105688i | \(0.966295\pi\) | |||||||
\(18\) | 29.4022 | + | 9.07925i | 1.63346 | + | 0.504403i | ||||
\(19\) | −1.27488 | + | 0.736052i | −0.0670989 | + | 0.0387396i | −0.533174 | − | 0.846006i | \(-0.679001\pi\) |
0.466075 | + | 0.884745i | \(0.345668\pi\) | |||||||
\(20\) | 58.6404 | 2.93202 | ||||||||
\(21\) | −5.29914 | + | 20.3204i | −0.252340 | + | 0.967639i | ||||
\(22\) | 9.00000 | 0.409091 | ||||||||
\(23\) | 28.1602 | − | 16.2583i | 1.22436 | − | 0.706882i | 0.258512 | − | 0.966008i | \(-0.416768\pi\) |
0.965843 | + | 0.259126i | \(0.0834346\pi\) | |||||||
\(24\) | 35.2394 | − | 13.8242i | 1.46831 | − | 0.576009i | ||||
\(25\) | −16.5712 | + | 28.7022i | −0.662850 | + | 1.14809i | ||||
\(26\) | −22.2243 | − | 38.4936i | −0.854781 | − | 1.48052i | ||||
\(27\) | −11.7260 | + | 24.3208i | −0.434298 | + | 0.900769i | ||||
\(28\) | 21.8651 | + | 49.1925i | 0.780895 | + | 1.75687i | ||||
\(29\) | − | 38.7082i | − | 1.33477i | −0.744715 | − | 0.667383i | \(-0.767414\pi\) | ||
0.744715 | − | 0.667383i | \(-0.232586\pi\) | |||||||
\(30\) | −11.6690 | + | 77.3384i | −0.388967 | + | 2.57795i | ||||
\(31\) | −13.6290 | − | 7.86870i | −0.439645 | − | 0.253829i | 0.263802 | − | 0.964577i | \(-0.415023\pi\) |
−0.703447 | + | 0.710748i | \(0.748357\pi\) | |||||||
\(32\) | −4.07018 | + | 7.04976i | −0.127193 | + | 0.220305i | ||||
\(33\) | −1.17815 | + | 7.80838i | −0.0357014 | + | 0.236617i | ||||
\(34\) | − | 93.9687i | − | 2.76378i | ||||||
\(35\) | −53.0800 | − | 5.61249i | −1.51657 | − | 0.160357i | ||||
\(36\) | 15.3808 | + | 67.4831i | 0.427245 | + | 1.87453i | ||||
\(37\) | −5.09952 | + | 2.94421i | −0.137825 | + | 0.0795732i | −0.567327 | − | 0.823493i | \(-0.692022\pi\) |
0.429502 | + | 0.903066i | \(0.358689\pi\) | |||||||
\(38\) | −4.35897 | − | 2.51665i | −0.114710 | − | 0.0662277i | ||||
\(39\) | 36.3063 | − | 14.2427i | 0.930930 | − | 0.365198i | ||||
\(40\) | 48.1069 | + | 83.3235i | 1.20267 | + | 2.08309i | ||||
\(41\) | 47.3245 | 1.15426 | 0.577128 | − | 0.816654i | \(-0.304173\pi\) | ||||
0.577128 | + | 0.816654i | \(0.304173\pi\) | |||||||
\(42\) | −69.2289 | + | 19.0480i | −1.64831 | + | 0.453524i | ||||
\(43\) | −12.6904 | −0.295126 | −0.147563 | − | 0.989053i | \(-0.547143\pi\) | ||||
−0.147563 | + | 0.989053i | \(0.547143\pi\) | |||||||
\(44\) | 10.1216 | + | 17.5311i | 0.230035 | + | 0.398433i | ||||
\(45\) | −65.5710 | − | 20.2480i | −1.45713 | − | 0.449955i | ||||
\(46\) | 96.2831 | + | 55.5891i | 2.09311 | + | 1.20846i | ||||
\(47\) | −11.4237 | − | 19.7864i | −0.243057 | − | 0.420987i | 0.718527 | − | 0.695499i | \(-0.244817\pi\) |
−0.961583 | + | 0.274513i | \(0.911483\pi\) | |||||||
\(48\) | 29.0356 | + | 23.1624i | 0.604909 | + | 0.482550i | ||||
\(49\) | −15.0835 | − | 46.6207i | −0.307827 | − | 0.951442i | ||||
\(50\) | −113.318 | −2.26637 | ||||||||
\(51\) | 81.5270 | + | 12.3010i | 1.59857 | + | 0.241196i | ||||
\(52\) | 49.9877 | − | 86.5812i | 0.961302 | − | 1.66502i | ||||
\(53\) | −78.1152 | − | 45.0998i | −1.47387 | − | 0.850940i | −0.474304 | − | 0.880361i | \(-0.657300\pi\) |
−0.999567 | + | 0.0294208i | \(0.990634\pi\) | |||||||
\(54\) | −92.0614 | + | 6.85650i | −1.70484 | + | 0.126972i | ||||
\(55\) | −20.0712 | −0.364932 | ||||||||
\(56\) | −51.9614 | + | 71.4247i | −0.927881 | + | 1.27544i | ||||
\(57\) | 2.75405 | − | 3.45239i | 0.0483167 | − | 0.0605682i | ||||
\(58\) | 114.617 | − | 66.1741i | 1.97615 | − | 1.14093i | ||||
\(59\) | 18.1401 | − | 31.4196i | 0.307460 | − | 0.532536i | −0.670346 | − | 0.742048i | \(-0.733854\pi\) |
0.977806 | + | 0.209513i | \(0.0671878\pi\) | |||||||
\(60\) | −163.770 | + | 64.2461i | −2.72950 | + | 1.07077i | ||||
\(61\) | 32.6069 | + | 56.4768i | 0.534539 | + | 0.925848i | 0.999186 | + | 0.0403523i | \(0.0128480\pi\) |
−0.464647 | + | 0.885496i | \(0.653819\pi\) | |||||||
\(62\) | − | 53.8081i | − | 0.867873i | ||||||
\(63\) | −7.46356 | − | 62.5563i | −0.118469 | − | 0.992958i | ||||
\(64\) | −77.3562 | −1.20869 | ||||||||
\(65\) | 49.5633 | + | 85.8461i | 0.762512 | + | 1.32071i | ||||
\(66\) | −25.1351 | + | 9.86036i | −0.380835 | + | 0.149399i | ||||
\(67\) | 8.13479 | + | 4.69662i | 0.121415 | + | 0.0700989i | 0.559477 | − | 0.828846i | \(-0.311002\pi\) |
−0.438063 | + | 0.898944i | \(0.644335\pi\) | |||||||
\(68\) | 183.041 | − | 105.679i | 2.69178 | − | 1.55410i | ||||
\(69\) | −60.8329 | + | 76.2581i | −0.881636 | + | 1.10519i | ||||
\(70\) | −74.1247 | − | 166.767i | −1.05892 | − | 2.38239i | ||||
\(71\) | −94.6770 | −1.33348 | −0.666739 | − | 0.745291i | \(-0.732311\pi\) | ||||
−0.666739 | + | 0.745291i | \(0.732311\pi\) | |||||||
\(72\) | −83.2705 | + | 77.2162i | −1.15653 | + | 1.07245i | ||||
\(73\) | 92.0638 | + | 53.1531i | 1.26115 | + | 0.728124i | 0.973297 | − | 0.229551i | \(-0.0737258\pi\) |
0.287851 | + | 0.957675i | \(0.407059\pi\) | |||||||
\(74\) | −17.4359 | − | 10.0666i | −0.235620 | − | 0.136035i | ||||
\(75\) | 14.8340 | − | 98.3147i | 0.197786 | − | 1.31086i | ||||
\(76\) | − | 11.3211i | − | 0.148962i | ||||||
\(77\) | −7.48391 | − | 16.8375i | −0.0971936 | − | 0.218668i | ||||
\(78\) | 104.241 | + | 83.1558i | 1.33643 | + | 1.06610i | ||||
\(79\) | −18.4521 | − | 31.9599i | −0.233571 | − | 0.404556i | 0.725286 | − | 0.688448i | \(-0.241708\pi\) |
−0.958856 | + | 0.283892i | \(0.908374\pi\) | |||||||
\(80\) | −47.2027 | + | 81.7574i | −0.590033 | + | 1.02197i | ||||
\(81\) | 6.10263 | − | 80.7698i | 0.0753411 | − | 0.997158i | ||||
\(82\) | 80.9042 | + | 140.130i | 0.986636 | + | 1.70890i | ||||
\(83\) | 11.2598 | 0.135660 | 0.0678302 | − | 0.997697i | \(-0.478392\pi\) | ||||
0.0678302 | + | 0.997697i | \(0.478392\pi\) | |||||||
\(84\) | −114.960 | − | 113.429i | −1.36857 | − | 1.35035i | ||||
\(85\) | 209.563i | 2.46545i | ||||||||
\(86\) | −21.6951 | − | 37.5769i | −0.252268 | − | 0.436941i | ||||
\(87\) | 42.4085 | + | 108.104i | 0.487455 | + | 1.24257i | ||||
\(88\) | −16.6069 | + | 28.7639i | −0.188714 | + | 0.326863i | ||||
\(89\) | 77.0661 | + | 133.482i | 0.865912 | + | 1.49980i | 0.866139 | + | 0.499803i | \(0.166594\pi\) |
−0.000227621 | 1.00000i | \(0.500072\pi\) | ||||||||
\(90\) | −52.1425 | − | 228.774i | −0.579361 | − | 2.54194i | ||||
\(91\) | −53.5345 | + | 73.5871i | −0.588291 | + | 0.808649i | ||||
\(92\) | 250.066i | 2.71811i | ||||||||
\(93\) | 46.6838 | + | 7.04377i | 0.501976 | + | 0.0757394i | ||||
\(94\) | 39.0589 | − | 67.6521i | 0.415521 | − | 0.719703i | ||||
\(95\) | 9.72111 | + | 5.61249i | 0.102327 | + | 0.0590788i | ||||
\(96\) | 3.64347 | − | 24.1478i | 0.0379528 | − | 0.251539i | ||||
\(97\) | − | 22.6422i | − | 0.233425i | −0.993166 | − | 0.116712i | \(-0.962764\pi\) | ||
0.993166 | − | 0.116712i | \(-0.0372355\pi\) | |||||||
\(98\) | 112.260 | − | 124.364i | 1.14551 | − | 1.26902i | ||||
\(99\) | −5.26450 | − | 23.0979i | −0.0531768 | − | 0.233312i | ||||
\(100\) | −127.440 | − | 220.732i | −1.27440 | − | 2.20732i | ||||
\(101\) | −23.4549 | − | 13.5417i | −0.232227 | − | 0.134076i | 0.379372 | − | 0.925244i | \(-0.376140\pi\) |
−0.611599 | + | 0.791168i | \(0.709473\pi\) | |||||||
\(102\) | 102.952 | + | 262.435i | 1.00933 | + | 2.57289i | ||||
\(103\) | −53.9644 | − | 93.4690i | −0.523926 | − | 0.907466i | −0.999612 | − | 0.0278513i | \(-0.991134\pi\) |
0.475686 | − | 0.879615i | \(-0.342200\pi\) | |||||||
\(104\) | 164.034 | 1.57725 | ||||||||
\(105\) | 154.390 | − | 42.4797i | 1.47038 | − | 0.404568i | ||||
\(106\) | − | 308.404i | − | 2.90947i | ||||||
\(107\) | −12.7306 | + | 7.35002i | −0.118978 | + | 0.0686918i | −0.558308 | − | 0.829634i | \(-0.688549\pi\) |
0.439330 | + | 0.898326i | \(0.355216\pi\) | |||||||
\(108\) | −116.890 | − | 171.615i | −1.08231 | − | 1.58903i | ||||
\(109\) | −125.211 | − | 72.2904i | −1.14872 | − | 0.663215i | −0.200146 | − | 0.979766i | \(-0.564142\pi\) |
−0.948575 | + | 0.316551i | \(0.897475\pi\) | |||||||
\(110\) | −34.3131 | − | 59.4319i | −0.311937 | − | 0.540290i | ||||
\(111\) | 11.0162 | − | 13.8096i | 0.0992452 | − | 0.124410i | ||||
\(112\) | −86.1854 | − | 9.11293i | −0.769512 | − | 0.0813655i | ||||
\(113\) | 29.8000i | 0.263717i | 0.991269 | + | 0.131858i | \(0.0420944\pi\) | ||||
−0.991269 | + | 0.131858i | \(0.957906\pi\) | |||||||
\(114\) | 14.9309 | + | 2.25281i | 0.130973 | + | 0.0197615i | ||||
\(115\) | −214.725 | − | 123.971i | −1.86717 | − | 1.07801i | ||||
\(116\) | 257.800 | + | 148.841i | 2.22242 | + | 1.28311i | ||||
\(117\) | −85.7914 | + | 79.5539i | −0.733260 | + | 0.679948i | ||||
\(118\) | 124.047 | 1.05124 | ||||||||
\(119\) | −175.799 | + | 78.1392i | −1.47730 | + | 0.656632i | ||||
\(120\) | −225.641 | − | 179.999i | −1.88034 | − | 1.50000i | ||||
\(121\) | 57.0356 | + | 98.7886i | 0.471369 | + | 0.816435i | ||||
\(122\) | −111.487 | + | 193.101i | −0.913828 | + | 1.58280i | ||||
\(123\) | −132.167 | + | 51.8485i | −1.07453 | + | 0.421532i | ||||
\(124\) | 104.813 | − | 60.5136i | 0.845263 | − | 0.488013i | ||||
\(125\) | 62.0875 | 0.496700 | ||||||||
\(126\) | 172.473 | − | 129.044i | 1.36883 | − | 1.02416i | ||||
\(127\) | −35.1179 | −0.276519 | −0.138259 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138259 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(128\) | −115.965 | − | 200.857i | −0.905973 | − | 1.56919i | ||||
\(129\) | 35.4417 | − | 13.9036i | 0.274742 | − | 0.107780i | ||||
\(130\) | −169.463 | + | 293.519i | −1.30356 | + | 2.25784i | ||||
\(131\) | −127.067 | + | 73.3622i | −0.969977 | + | 0.560017i | −0.899229 | − | 0.437477i | \(-0.855872\pi\) |
−0.0707481 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(132\) | −47.4743 | − | 37.8714i | −0.359654 | − | 0.286905i | ||||
\(133\) | −1.08354 | + | 10.2476i | −0.00814695 | + | 0.0770496i | ||||
\(134\) | 32.1167i | 0.239677i | ||||||||
\(135\) | 205.310 | − | 15.2910i | 1.52081 | − | 0.113266i | ||||
\(136\) | 300.323 | + | 173.392i | 2.20826 | + | 1.27494i | ||||
\(137\) | 46.2002 | − | 80.0212i | 0.337228 | − | 0.584096i | −0.646682 | − | 0.762760i | \(-0.723844\pi\) |
0.983910 | + | 0.178664i | \(0.0571773\pi\) | |||||||
\(138\) | −329.802 | − | 49.7613i | −2.38987 | − | 0.360589i | ||||
\(139\) | 203.118 | 1.46128 | 0.730640 | − | 0.682763i | \(-0.239222\pi\) | ||||
0.730640 | + | 0.682763i | \(0.239222\pi\) | |||||||
\(140\) | 241.483 | − | 331.936i | 1.72488 | − | 2.37097i | ||||
\(141\) | 53.5818 | + | 42.7435i | 0.380012 | + | 0.303145i | ||||
\(142\) | −161.856 | − | 280.343i | −1.13983 | − | 1.97425i | ||||
\(143\) | −17.1096 | + | 29.6348i | −0.119648 | + | 0.207236i | ||||
\(144\) | −106.467 | − | 32.8764i | −0.739354 | − | 0.228309i | ||||
\(145\) | −255.612 | + | 147.577i | −1.76284 | + | 1.01778i | ||||
\(146\) | 363.474i | 2.48955i | ||||||||
\(147\) | 93.2025 | + | 113.676i | 0.634031 | + | 0.773308i | ||||
\(148\) | − | 45.2844i | − | 0.305975i | ||||||
\(149\) | 56.6732 | + | 98.1608i | 0.380357 | + | 0.658798i | 0.991113 | − | 0.133021i | \(-0.0424678\pi\) |
−0.610756 | + | 0.791819i | \(0.709134\pi\) | |||||||
\(150\) | 316.474 | − | 124.151i | 2.10983 | − | 0.827674i | ||||
\(151\) | 108.637 | + | 62.7217i | 0.719452 | + | 0.415376i | 0.814551 | − | 0.580092i | \(-0.196983\pi\) |
−0.0950990 | + | 0.995468i | \(0.530317\pi\) | |||||||
\(152\) | 16.0864 | − | 9.28750i | 0.105832 | − | 0.0611020i | ||||
\(153\) | −241.165 | + | 54.9665i | −1.57624 | + | 0.359258i | ||||
\(154\) | 37.0623 | − | 50.9449i | 0.240664 | − | 0.330811i | ||||
\(155\) | 120.000i | 0.774191i | ||||||||
\(156\) | −44.7471 | + | 296.569i | −0.286840 | + | 1.90109i | ||||
\(157\) | −72.7383 | + | 125.986i | −0.463302 | + | 0.802462i | −0.999123 | − | 0.0418695i | \(-0.986669\pi\) |
0.535822 | + | 0.844331i | \(0.320002\pi\) | |||||||
\(158\) | 63.0900 | − | 109.275i | 0.399304 | − | 0.691614i | ||||
\(159\) | 267.570 | + | 40.3717i | 1.68283 | + | 0.253910i | ||||
\(160\) | 62.0712 | 0.387945 | ||||||||
\(161\) | 23.9339 | − | 226.354i | 0.148658 | − | 1.40593i | ||||
\(162\) | 249.596 | − | 120.011i | 1.54072 | − | 0.740807i | ||||
\(163\) | 210.900 | − | 121.763i | 1.29387 | − | 0.747014i | 0.314528 | − | 0.949248i | \(-0.398154\pi\) |
0.979337 | + | 0.202234i | \(0.0648203\pi\) | |||||||
\(164\) | −181.972 | + | 315.186i | −1.10959 | + | 1.92186i | ||||
\(165\) | 56.0548 | − | 21.9900i | 0.339726 | − | 0.133273i | ||||
\(166\) | 19.2494 | + | 33.3409i | 0.115960 | + | 0.200849i | ||||
\(167\) | 67.4361 | 0.403809 | 0.201905 | − | 0.979405i | \(-0.435287\pi\) | ||||
0.201905 | + | 0.979405i | \(0.435287\pi\) | |||||||
\(168\) | 66.8645 | − | 256.403i | 0.398003 | − | 1.52621i | ||||
\(169\) | 169.000 | 1.00000 | ||||||||
\(170\) | −620.527 | + | 358.261i | −3.65016 | + | 2.10742i | ||||
\(171\) | −3.90907 | + | 12.6591i | −0.0228601 | + | 0.0740300i | ||||
\(172\) | 48.7973 | − | 84.5194i | 0.283705 | − | 0.491392i | ||||
\(173\) | −39.2307 | + | 22.6499i | −0.226767 | + | 0.130924i | −0.609080 | − | 0.793109i | \(-0.708461\pi\) |
0.382313 | + | 0.924033i | \(0.375128\pi\) | |||||||
\(174\) | −247.601 | + | 310.384i | −1.42299 | + | 1.78382i | ||||
\(175\) | 94.2293 | + | 211.999i | 0.538453 | + | 1.21142i | ||||
\(176\) | −32.5895 | −0.185167 | ||||||||
\(177\) | −16.2384 | + | 107.623i | −0.0917421 | + | 0.608037i | ||||
\(178\) | −263.499 | + | 456.393i | −1.48033 | + | 2.56401i | ||||
\(179\) | −98.2143 | − | 56.7040i | −0.548683 | − | 0.316782i | 0.199908 | − | 0.979815i | \(-0.435936\pi\) |
−0.748591 | + | 0.663032i | \(0.769269\pi\) | |||||||
\(180\) | 386.988 | − | 358.852i | 2.14993 | − | 1.99362i | ||||
\(181\) | 108.047 | 0.596943 | 0.298471 | − | 0.954419i | \(-0.403523\pi\) | ||||
0.298471 | + | 0.954419i | \(0.403523\pi\) | |||||||
\(182\) | −309.416 | − | 32.7165i | −1.70009 | − | 0.179761i | ||||
\(183\) | −152.940 | − | 122.004i | −0.835737 | − | 0.666687i | ||||
\(184\) | −355.325 | + | 205.147i | −1.93111 | + | 1.11493i | ||||
\(185\) | 38.8844 | + | 22.4499i | 0.210186 | + | 0.121351i | ||||
\(186\) | 58.9519 | + | 150.275i | 0.316946 | + | 0.807929i | ||||
\(187\) | −62.6507 | + | 36.1714i | −0.335031 | + | 0.193430i | ||||
\(188\) | 175.706 | 0.934604 | ||||||||
\(189\) | 89.3806 | + | 166.530i | 0.472913 | + | 0.881109i | ||||
\(190\) | 38.3796i | 0.201998i | ||||||||
\(191\) | −99.9100 | + | 57.6831i | −0.523089 | + | 0.302006i | −0.738198 | − | 0.674584i | \(-0.764323\pi\) |
0.215108 | + | 0.976590i | \(0.430990\pi\) | |||||||
\(192\) | 216.040 | − | 84.7511i | 1.12521 | − | 0.441412i | ||||
\(193\) | 139.629 | + | 80.6149i | 0.723466 | + | 0.417694i | 0.816027 | − | 0.578013i | \(-0.196172\pi\) |
−0.0925608 | + | 0.995707i | \(0.529505\pi\) | |||||||
\(194\) | 67.0446 | − | 38.7082i | 0.345591 | − | 0.199527i | ||||
\(195\) | −232.472 | − | 185.449i | −1.19217 | − | 0.951020i | ||||
\(196\) | 368.497 | + | 78.8083i | 1.88009 | + | 0.402083i | ||||
\(197\) | −5.26450 | −0.0267234 | −0.0133617 | − | 0.999911i | \(-0.504253\pi\) | ||||
−0.0133617 | + | 0.999911i | \(0.504253\pi\) | |||||||
\(198\) | 59.3941 | − | 55.0758i | 0.299970 | − | 0.278161i | ||||
\(199\) | 150.499 | − | 260.671i | 0.756275 | − | 1.30991i | −0.188463 | − | 0.982080i | \(-0.560351\pi\) |
0.944738 | − | 0.327826i | \(-0.106316\pi\) | |||||||
\(200\) | 209.096 | − | 362.165i | 1.04548 | − | 1.81082i | ||||
\(201\) | −27.8644 | − | 4.20424i | −0.138629 | − | 0.0209166i | ||||
\(202\) | − | 92.6015i | − | 0.458423i | ||||||
\(203\) | −219.110 | − | 159.402i | −1.07936 | − | 0.785231i | ||||
\(204\) | −395.414 | + | 495.678i | −1.93830 | + | 2.42979i | ||||
\(205\) | −180.427 | − | 312.510i | −0.880134 | − | 1.52444i | ||||
\(206\) | 184.511 | − | 319.582i | 0.895684 | − | 1.55137i | ||||
\(207\) | 86.3455 | − | 279.621i | 0.417128 | − | 1.35083i | ||||
\(208\) | 80.4754 | + | 139.387i | 0.386901 | + | 0.670132i | ||||
\(209\) | 3.87495i | 0.0185404i | ||||||||
\(210\) | 389.724 | + | 384.535i | 1.85583 | + | 1.83112i | ||||
\(211\) | 38.9533 | 0.184613 | 0.0923065 | − | 0.995731i | \(-0.470576\pi\) | ||||
0.0923065 | + | 0.995731i | \(0.470576\pi\) | |||||||
\(212\) | 600.738 | − | 346.836i | 2.83367 | − | 1.63602i | ||||
\(213\) | 264.413 | − | 103.728i | 1.24137 | − | 0.486984i | ||||
\(214\) | −43.5276 | − | 25.1306i | −0.203400 | − | 0.117433i | ||||
\(215\) | 48.3830 | + | 83.8018i | 0.225037 | + | 0.389776i | ||||
\(216\) | 147.959 | − | 306.879i | 0.684996 | − | 1.42074i | ||||
\(217\) | −100.666 | + | 44.7439i | −0.463898 | + | 0.206193i | ||||
\(218\) | − | 494.340i | − | 2.26761i | ||||||
\(219\) | −315.349 | − | 47.5806i | −1.43995 | − | 0.217263i | ||||
\(220\) | 77.1781 | − | 133.676i | 0.350810 | − | 0.607620i | ||||
\(221\) | 309.416 | + | 178.641i | 1.40007 | + | 0.808331i | ||||
\(222\) | 59.7237 | + | 9.01126i | 0.269026 | + | 0.0405912i | ||||
\(223\) | − | 102.696i | − | 0.460522i | −0.973129 | − | 0.230261i | \(-0.926042\pi\) | ||
0.973129 | − | 0.230261i | \(-0.0739580\pi\) | |||||||
\(224\) | 23.1443 | + | 52.0706i | 0.103323 | + | 0.232458i | ||||
\(225\) | 66.2850 | + | 290.824i | 0.294600 | + | 1.29255i | ||||
\(226\) | −88.2392 | + | 50.9449i | −0.390439 | + | 0.225420i | ||||
\(227\) | 62.7246 | − | 108.642i | 0.276320 | − | 0.478600i | −0.694148 | − | 0.719833i | \(-0.744218\pi\) |
0.970467 | + | 0.241233i | \(0.0775518\pi\) | |||||||
\(228\) | 12.4033 | + | 31.6174i | 0.0544006 | + | 0.138673i | ||||
\(229\) | 374.053 | − | 215.960i | 1.63342 | − | 0.943056i | 0.650393 | − | 0.759598i | \(-0.274604\pi\) |
0.983028 | − | 0.183458i | \(-0.0587290\pi\) | |||||||
\(230\) | − | 847.747i | − | 3.68586i | ||||||
\(231\) | 39.3480 | + | 38.8241i | 0.170338 | + | 0.168070i | ||||
\(232\) | 488.420i | 2.10526i | ||||||||
\(233\) | 116.689 | − | 67.3705i | 0.500811 | − | 0.289144i | −0.228237 | − | 0.973606i | \(-0.573296\pi\) |
0.729049 | + | 0.684462i | \(0.239963\pi\) | |||||||
\(234\) | −382.229 | − | 118.030i | −1.63346 | − | 0.504403i | ||||
\(235\) | −87.1069 | + | 150.874i | −0.370668 | + | 0.642015i | ||||
\(236\) | 139.505 | + | 241.630i | 0.591123 | + | 1.02386i | ||||
\(237\) | 86.5479 | + | 69.0414i | 0.365181 | + | 0.291314i | ||||
\(238\) | −531.914 | − | 386.966i | −2.23493 | − | 1.62591i | ||||
\(239\) | 219.958 | 0.920326 | 0.460163 | − | 0.887834i | \(-0.347791\pi\) | ||||
0.460163 | + | 0.887834i | \(0.347791\pi\) | |||||||
\(240\) | 42.2541 | − | 280.046i | 0.176059 | − | 1.16686i | ||||
\(241\) | −112.644 | − | 65.0348i | −0.467401 | − | 0.269854i | 0.247750 | − | 0.968824i | \(-0.420309\pi\) |
−0.715151 | + | 0.698970i | \(0.753642\pi\) | |||||||
\(242\) | −195.012 | + | 337.771i | −0.805834 | + | 1.39575i | ||||
\(243\) | 71.4476 | + | 232.259i | 0.294023 | + | 0.955798i | ||||
\(244\) | −501.521 | −2.05541 | ||||||||
\(245\) | −250.355 | + | 277.349i | −1.02186 | + | 1.13204i | ||||
\(246\) | −379.474 | − | 302.716i | −1.54258 | − | 1.23055i | ||||
\(247\) | 16.5734 | − | 9.56867i | 0.0670989 | − | 0.0387396i | ||||
\(248\) | 171.970 | + | 99.2872i | 0.693429 | + | 0.400352i | ||||
\(249\) | −31.4463 | + | 12.3362i | −0.126290 | + | 0.0495430i | ||||
\(250\) | 106.142 | + | 183.844i | 0.424570 | + | 0.735377i | ||||
\(251\) | 217.191i | 0.865302i | 0.901562 | + | 0.432651i | \(0.142422\pi\) | ||||
−0.901562 | + | 0.432651i | \(0.857578\pi\) | |||||||
\(252\) | 445.330 | + | 190.834i | 1.76718 | + | 0.757278i | ||||
\(253\) | − | 85.5918i | − | 0.338307i | ||||||
\(254\) | −60.0362 | − | 103.986i | −0.236363 | − | 0.409393i | ||||
\(255\) | −229.596 | − | 585.266i | −0.900378 | − | 2.29516i | ||||
\(256\) | 241.785 | − | 418.784i | 0.944473 | − | 1.63587i | ||||
\(257\) | 363.383 | − | 209.799i | 1.41394 | − | 0.816340i | 0.418185 | − | 0.908362i | \(-0.362666\pi\) |
0.995757 | + | 0.0920216i | \(0.0293329\pi\) | |||||||
\(258\) | 101.759 | + | 81.1755i | 0.394414 | + | 0.314634i | ||||
\(259\) | −4.33418 | + | 40.9904i | −0.0167343 | + | 0.158264i | ||||
\(260\) | −762.325 | −2.93202 | ||||||||
\(261\) | −236.876 | − | 255.449i | −0.907572 | − | 0.978731i | ||||
\(262\) | −434.458 | − | 250.835i | −1.65824 | − | 0.957384i | ||||
\(263\) | −296.339 | − | 171.091i | −1.12676 | − | 0.650537i | −0.183644 | − | 0.982993i | \(-0.558789\pi\) |
−0.943119 | + | 0.332456i | \(0.892123\pi\) | |||||||
\(264\) | 14.8658 | − | 98.5260i | 0.0563100 | − | 0.373205i | ||||
\(265\) | 687.783i | 2.59541i | ||||||||
\(266\) | −32.1960 | + | 14.3105i | −0.121038 | + | 0.0537988i | ||||
\(267\) | −361.472 | − | 288.355i | −1.35383 | − | 1.07998i | ||||
\(268\) | −62.5599 | + | 36.1190i | −0.233433 | + | 0.134772i | ||||
\(269\) | −71.7141 | − | 41.4042i | −0.266595 | − | 0.153919i | 0.360744 | − | 0.932665i | \(-0.382523\pi\) |
−0.627339 | + | 0.778746i | \(0.715856\pi\) | |||||||
\(270\) | 396.267 | + | 581.791i | 1.46766 | + | 2.15478i | ||||
\(271\) | 451.032 | − | 260.403i | 1.66432 | − | 0.960897i | 0.693709 | − | 0.720255i | \(-0.255975\pi\) |
0.970614 | − | 0.240642i | \(-0.0773580\pi\) | |||||||
\(272\) | 340.266i | 1.25098i | ||||||||
\(273\) | 68.8888 | − | 264.165i | 0.252340 | − | 0.967639i | ||||
\(274\) | 315.929 | 1.15302 | ||||||||
\(275\) | 43.6197 | + | 75.5515i | 0.158617 | + | 0.274733i | ||||
\(276\) | −273.971 | − | 698.381i | −0.992648 | − | 2.53037i | ||||
\(277\) | −76.3685 | + | 132.274i | −0.275699 | + | 0.477524i | −0.970311 | − | 0.241860i | \(-0.922243\pi\) |
0.694612 | + | 0.719384i | \(0.255576\pi\) | |||||||
\(278\) | 347.243 | + | 601.442i | 1.24907 | + | 2.16346i | ||||
\(279\) | −138.095 | + | 31.4748i | −0.494965 | + | 0.112813i | ||||
\(280\) | 669.763 | + | 70.8183i | 2.39201 | + | 0.252923i | ||||
\(281\) | 321.417 | 1.14383 | 0.571917 | − | 0.820312i | \(-0.306200\pi\) | ||||
0.571917 | + | 0.820312i | \(0.306200\pi\) | |||||||
\(282\) | −34.9641 | + | 231.731i | −0.123986 | + | 0.821740i | ||||
\(283\) | 27.7973 | − | 48.1463i | 0.0982236 | − | 0.170128i | −0.812726 | − | 0.582646i | \(-0.802017\pi\) |
0.910949 | + | 0.412518i | \(0.135351\pi\) | |||||||
\(284\) | 364.053 | − | 630.558i | 1.28188 | − | 2.22027i | ||||
\(285\) | −33.2980 | − | 5.02409i | −0.116835 | − | 0.0176284i | ||||
\(286\) | −117.000 | −0.409091 | ||||||||
\(287\) | 194.884 | − | 267.882i | 0.679038 | − | 0.933388i | ||||
\(288\) | 16.2807 | + | 71.4314i | 0.0565303 | + | 0.248026i | ||||
\(289\) | 233.165 | + | 403.853i | 0.806798 | + | 1.39741i | ||||
\(290\) | −873.968 | − | 504.586i | −3.01368 | − | 1.73995i | ||||
\(291\) | 24.8067 | + | 63.2348i | 0.0852463 | + | 0.217302i | ||||
\(292\) | −708.009 | + | 408.769i | −2.42469 | + | 1.39989i | ||||
\(293\) | −506.781 | −1.72963 | −0.864813 | − | 0.502093i | \(-0.832563\pi\) | ||||
−0.864813 | + | 0.502093i | \(0.832563\pi\) | |||||||
\(294\) | −177.265 | + | 470.314i | −0.602943 | + | 1.59971i | ||||
\(295\) | −276.641 | −0.937767 | ||||||||
\(296\) | 64.3457 | − | 37.1500i | 0.217384 | − | 0.125507i | ||||
\(297\) | 40.0086 | + | 58.7399i | 0.134709 | + | 0.197777i | ||||
\(298\) | −193.773 | + | 335.624i | −0.650244 | + | 1.12626i | ||||
\(299\) | −366.082 | + | 211.358i | −1.22436 | + | 0.706882i | ||||
\(300\) | 597.746 | + | 476.836i | 1.99249 | + | 1.58945i | ||||
\(301\) | −52.2596 | + | 71.8347i | −0.173620 | + | 0.238653i | ||||
\(302\) | 428.907i | 1.42022i | ||||||||
\(303\) | 80.3408 | + | 12.1220i | 0.265151 | + | 0.0400066i | ||||
\(304\) | 15.7841 | + | 9.11293i | 0.0519213 | + | 0.0299768i | ||||
\(305\) | 248.631 | − | 430.642i | 0.815185 | − | 1.41194i | ||||
\(306\) | −575.044 | − | 620.131i | −1.87923 | − | 2.02657i | ||||
\(307\) | 199.468i | 0.649734i | 0.945760 | + | 0.324867i | \(0.105319\pi\) | ||||
−0.945760 | + | 0.324867i | \(0.894681\pi\) | |||||||
\(308\) | 140.916 | + | 14.9000i | 0.457520 | + | 0.0483766i | ||||
\(309\) | 253.115 | + | 201.916i | 0.819144 | + | 0.653451i | ||||
\(310\) | −355.325 | + | 205.147i | −1.14621 | + | 0.661764i | ||||
\(311\) | 140.108 | + | 80.8915i | 0.450509 | + | 0.260101i | 0.708045 | − | 0.706167i | \(-0.249577\pi\) |
−0.257536 | + | 0.966269i | \(0.582911\pi\) | |||||||
\(312\) | −458.112 | + | 179.715i | −1.46831 | + | 0.576009i | ||||
\(313\) | −195.142 | − | 337.997i | −0.623458 | − | 1.07986i | −0.988837 | − | 0.149003i | \(-0.952394\pi\) |
0.365378 | − | 0.930859i | \(-0.380940\pi\) | |||||||
\(314\) | −497.403 | −1.58409 | ||||||||
\(315\) | −384.639 | + | 287.786i | −1.22107 | + | 0.913606i | ||||
\(316\) | 283.808 | 0.898128 | ||||||||
\(317\) | 22.9875 | + | 39.8155i | 0.0725158 | + | 0.125601i | 0.900003 | − | 0.435883i | \(-0.143564\pi\) |
−0.827488 | + | 0.561484i | \(0.810231\pi\) | |||||||
\(318\) | 337.886 | + | 861.307i | 1.06253 | + | 2.70851i | ||||
\(319\) | −88.2392 | − | 50.9449i | −0.276612 | − | 0.159702i | ||||
\(320\) | 294.925 | + | 510.826i | 0.921642 | + | 1.59633i | ||||
\(321\) | 27.5013 | − | 34.4747i | 0.0856737 | − | 0.107398i | ||||
\(322\) | 711.162 | − | 316.097i | 2.20858 | − | 0.981668i | ||||
\(323\) | 40.4582 | 0.125258 | ||||||||
\(324\) | 514.469 | + | 351.221i | 1.58787 | + | 1.08401i | ||||
\(325\) | 215.426 | − | 373.129i | 0.662850 | − | 1.14809i | ||||
\(326\) | 721.094 | + | 416.324i | 2.21194 | + | 1.27707i | ||||
\(327\) | 428.888 | + | 64.7117i | 1.31158 | + | 0.197895i | ||||
\(328\) | −597.140 | −1.82055 | ||||||||
\(329\) | −159.045 | − | 16.8168i | −0.483419 | − | 0.0511150i | ||||
\(330\) | 160.942 | + | 128.388i | 0.487704 | + | 0.389054i | ||||
\(331\) | −42.8290 | + | 24.7274i | −0.129393 | + | 0.0747050i | −0.563299 | − | 0.826253i | \(-0.690468\pi\) |
0.433906 | + | 0.900958i | \(0.357135\pi\) | |||||||
\(332\) | −43.2963 | + | 74.9915i | −0.130411 | + | 0.225878i | ||||
\(333\) | −15.6363 | + | 50.6365i | −0.0469558 | + | 0.152062i | ||||
\(334\) | 115.286 | + | 199.682i | 0.345168 | + | 0.597849i | ||||
\(335\) | − | 71.6247i | − | 0.213805i | ||||||
\(336\) | 250.682 | − | 68.9738i | 0.746076 | − | 0.205279i | ||||
\(337\) | 111.882 | 0.331994 | 0.165997 | − | 0.986126i | \(-0.446916\pi\) | ||||
0.165997 | + | 0.986126i | \(0.446916\pi\) | |||||||
\(338\) | 288.916 | + | 500.417i | 0.854781 | + | 1.48052i | ||||
\(339\) | −32.6487 | − | 83.2250i | −0.0963089 | − | 0.245502i | ||||
\(340\) | −1395.71 | − | 805.814i | −4.10503 | − | 2.37004i | ||||
\(341\) | −35.8749 | + | 20.7124i | −0.105205 | + | 0.0607402i | ||||
\(342\) | −44.1671 | + | 10.0666i | −0.129144 | + | 0.0294345i | ||||
\(343\) | −326.013 | − | 106.605i | −0.950475 | − | 0.310800i | ||||
\(344\) | 160.128 | 0.465487 | ||||||||
\(345\) | 735.503 | + | 110.975i | 2.13189 | + | 0.321665i | ||||
\(346\) | −134.135 | − | 77.4428i | −0.387673 | − | 0.223823i | ||||
\(347\) | −481.422 | − | 277.949i | −1.38738 | − | 0.801006i | −0.394363 | − | 0.918955i | \(-0.629035\pi\) |
−0.993020 | + | 0.117949i | \(0.962368\pi\) | |||||||
\(348\) | −883.052 | − | 133.237i | −2.53751 | − | 0.382865i | ||||
\(349\) | 121.834i | 0.349094i | 0.984649 | + | 0.174547i | \(0.0558461\pi\) | ||||
−0.984649 | + | 0.174547i | \(0.944154\pi\) | |||||||
\(350\) | −466.649 | + | 641.444i | −1.33328 | + | 1.83270i | ||||
\(351\) | 152.439 | − | 316.170i | 0.434298 | − | 0.900769i | ||||
\(352\) | 10.7137 | + | 18.5567i | 0.0304368 | + | 0.0527180i | ||||
\(353\) | 177.017 | − | 306.603i | 0.501465 | − | 0.868564i | −0.498533 | − | 0.866871i | \(-0.666128\pi\) |
0.999999 | − | 0.00169298i | \(-0.000538894\pi\) | |||||||
\(354\) | −346.436 | + | 135.905i | −0.978633 | + | 0.383912i | ||||
\(355\) | 360.962 | + | 625.204i | 1.01679 | + | 1.76114i | ||||
\(356\) | −1185.34 | −3.32961 | ||||||||
\(357\) | 405.361 | − | 410.831i | 1.13547 | − | 1.15079i | ||||
\(358\) | − | 387.756i | − | 1.08312i | ||||||
\(359\) | −230.318 | − | 398.922i | −0.641554 | − | 1.11120i | −0.985086 | − | 0.172063i | \(-0.944957\pi\) |
0.343532 | − | 0.939141i | \(-0.388376\pi\) | |||||||
\(360\) | 827.375 | + | 255.489i | 2.29826 | + | 0.709692i | ||||
\(361\) | −179.416 | + | 310.758i | −0.496998 | + | 0.860827i | ||||
\(362\) | 184.713 | + | 319.931i | 0.510256 | + | 0.883789i | ||||
\(363\) | −267.521 | − | 213.408i | −0.736972 | − | 0.587900i | ||||
\(364\) | −284.246 | − | 639.502i | −0.780895 | − | 1.75687i | ||||
\(365\) | − | 810.597i | − | 2.22081i | ||||||
\(366\) | 99.7989 | − | 661.435i | 0.272675 | − | 1.80720i | ||||
\(367\) | −197.260 | + | 341.665i | −0.537494 | + | 0.930967i | 0.461544 | + | 0.887117i | \(0.347296\pi\) |
−0.999038 | + | 0.0438500i | \(0.986038\pi\) | |||||||
\(368\) | −348.646 | − | 201.291i | −0.947408 | − | 0.546986i | ||||
\(369\) | 312.310 | − | 289.604i | 0.846370 | − | 0.784834i | ||||
\(370\) | 153.518i | 0.414914i | ||||||||
\(371\) | −576.971 | + | 256.452i | −1.55518 | + | 0.691245i | ||||
\(372\) | −226.421 | + | 283.834i | −0.608659 | + | 0.762994i | ||||
\(373\) | 8.71374 | + | 15.0926i | 0.0233612 | + | 0.0404629i | 0.877470 | − | 0.479632i | \(-0.159230\pi\) |
−0.854108 | + | 0.520095i | \(0.825897\pi\) | |||||||
\(374\) | −214.211 | − | 123.675i | −0.572756 | − | 0.330681i | ||||
\(375\) | −173.397 | + | 68.0228i | −0.462393 | + | 0.181394i | ||||
\(376\) | 144.144 | + | 249.664i | 0.383361 | + | 0.664001i | ||||
\(377\) | 503.207i | 1.33477i | ||||||||
\(378\) | −340.301 | + | 549.353i | −0.900266 | + | 1.45331i | ||||
\(379\) | − | 364.695i | − | 0.962255i | −0.876651 | − | 0.481128i | \(-0.840227\pi\) | ||
0.876651 | − | 0.481128i | \(-0.159773\pi\) | |||||||
\(380\) | −74.7594 | + | 43.1624i | −0.196735 | + | 0.113585i | ||||
\(381\) | 98.0769 | − | 38.4750i | 0.257420 | − | 0.100984i | ||||
\(382\) | −341.605 | − | 197.226i | −0.894254 | − | 0.516298i | ||||
\(383\) | −189.775 | − | 328.701i | −0.495497 | − | 0.858226i | 0.504489 | − | 0.863418i | \(-0.331681\pi\) |
−0.999987 | + | 0.00519153i | \(0.998347\pi\) | |||||||
\(384\) | 543.922 | + | 433.900i | 1.41646 | + | 1.12995i | ||||
\(385\) | −82.6541 | + | 113.614i | −0.214686 | + | 0.295102i | ||||
\(386\) | 551.265i | 1.42815i | ||||||||
\(387\) | −83.7484 | + | 77.6594i | −0.216404 | + | 0.200670i | ||||
\(388\) | 150.799 | + | 87.0639i | 0.388657 | + | 0.224391i | ||||
\(389\) | 3.35580 | + | 1.93747i | 0.00862675 | + | 0.00498065i | 0.504307 | − | 0.863524i | \(-0.331748\pi\) |
−0.495680 | + | 0.868505i | \(0.665081\pi\) | |||||||
\(390\) | 151.697 | − | 1005.40i | 0.388967 | − | 2.57795i | ||||
\(391\) | −893.661 | −2.28558 | ||||||||
\(392\) | 190.324 | + | 588.259i | 0.485521 | + | 1.50066i | ||||
\(393\) | 274.496 | − | 344.099i | 0.698464 | − | 0.875570i | ||||
\(394\) | −9.00000 | − | 15.5885i | −0.0228426 | − | 0.0395646i | ||||
\(395\) | −140.699 | + | 243.698i | −0.356201 | + | 0.616958i | ||||
\(396\) | 174.077 | + | 53.7542i | 0.439590 | + | 0.135743i | ||||
\(397\) | −566.438 | + | 327.033i | −1.42680 | + | 0.823761i | −0.996867 | − | 0.0791018i | \(-0.974795\pi\) |
−0.429929 | + | 0.902863i | \(0.641461\pi\) | |||||||
\(398\) | 1029.15 | 2.58580 | ||||||||
\(399\) | −8.20111 | − | 29.8065i | −0.0205542 | − | 0.0747030i | ||||
\(400\) | 410.332 | 1.02583 | ||||||||
\(401\) | 49.3294 | + | 85.4410i | 0.123016 | + | 0.213070i | 0.920956 | − | 0.389667i | \(-0.127410\pi\) |
−0.797940 | + | 0.602737i | \(0.794077\pi\) | |||||||
\(402\) | −35.1869 | − | 89.6951i | −0.0875296 | − | 0.223122i | ||||
\(403\) | 177.177 | + | 102.293i | 0.439645 | + | 0.253829i | ||||
\(404\) | 180.378 | − | 104.141i | 0.446480 | − | 0.257775i | ||||
\(405\) | −556.634 | + | 267.641i | −1.37440 | + | 0.660841i | ||||
\(406\) | 97.4152 | − | 921.302i | 0.239939 | − | 2.26922i | ||||
\(407\) | 15.4998i | 0.0380830i | ||||||||
\(408\) | −1028.71 | − | 155.214i | −2.52134 | − | 0.380426i | ||||
\(409\) | 337.204 | + | 194.685i | 0.824460 | + | 0.476002i | 0.851952 | − | 0.523620i | \(-0.175419\pi\) |
−0.0274923 | + | 0.999622i | \(0.508752\pi\) | |||||||
\(410\) | 616.904 | − | 1068.51i | 1.50464 | − | 2.60612i | ||||
\(411\) | −41.3567 | + | 274.099i | −0.100625 | + | 0.666907i | ||||
\(412\) | 830.017 | 2.01460 | ||||||||
\(413\) | −103.150 | − | 232.070i | −0.249759 | − | 0.561913i | ||||
\(414\) | 975.585 | − | 222.356i | 2.35648 | − | 0.537093i | ||||
\(415\) | −42.9288 | − | 74.3548i | −0.103443 | − | 0.179168i | ||||
\(416\) | 52.9123 | − | 91.6469i | 0.127193 | − | 0.220305i | ||||
\(417\) | −567.265 | + | 222.535i | −1.36035 | + | 0.533657i | ||||
\(418\) | −11.4739 | + | 6.62447i | −0.0274496 | + | 0.0158480i | ||||
\(419\) | 101.383i | 0.241965i | 0.992655 | + | 0.120983i | \(0.0386045\pi\) | ||||
−0.992655 | + | 0.120983i | \(0.961395\pi\) | |||||||
\(420\) | −310.744 | + | 1191.60i | −0.739866 | + | 2.83713i | ||||
\(421\) | − | 89.7621i | − | 0.213212i | −0.994301 | − | 0.106606i | \(-0.966002\pi\) | ||
0.994301 | − | 0.106606i | \(-0.0339983\pi\) | |||||||
\(422\) | 66.5932 | + | 115.343i | 0.157804 | + | 0.273324i | ||||
\(423\) | −196.472 | − | 60.6695i | −0.464473 | − | 0.143427i | ||||
\(424\) | 985.657 | + | 569.069i | 2.32466 | + | 1.34214i | ||||
\(425\) | 788.831 | − | 455.432i | 1.85607 | − | 1.07160i | ||||
\(426\) | 759.173 | + | 605.611i | 1.78210 | + | 1.42162i | ||||
\(427\) | 453.966 | + | 48.0007i | 1.06315 | + | 0.112414i | ||||
\(428\) | − | 113.049i | − | 0.264134i | ||||||
\(429\) | 15.3159 | − | 101.509i | 0.0357014 | − | 0.236617i | ||||
\(430\) | −165.427 | + | 286.529i | −0.384715 | + | 0.666346i | ||||
\(431\) | −323.225 | + | 559.842i | −0.749941 | + | 1.29894i | 0.197909 | + | 0.980220i | \(0.436585\pi\) |
−0.947850 | + | 0.318716i | \(0.896748\pi\) | |||||||
\(432\) | 333.359 | − | 24.8278i | 0.771665 | − | 0.0574717i | ||||
\(433\) | −571.521 | −1.31991 | −0.659955 | − | 0.751305i | \(-0.729425\pi\) | ||||
−0.659955 | + | 0.751305i | \(0.729425\pi\) | |||||||
\(434\) | −304.583 | − | 221.584i | −0.701805 | − | 0.510562i | ||||
\(435\) | 552.184 | − | 692.200i | 1.26939 | − | 1.59126i | ||||
\(436\) | 962.922 | − | 555.943i | 2.20854 | − | 1.27510i | ||||
\(437\) | −23.9339 | + | 41.4547i | −0.0547686 | + | 0.0948620i | ||||
\(438\) | −398.220 | − | 1015.11i | −0.909179 | − | 2.31759i | ||||
\(439\) | −192.296 | − | 333.066i | −0.438032 | − | 0.758694i | 0.559506 | − | 0.828826i | \(-0.310991\pi\) |
−0.997538 | + | 0.0701329i | \(0.977658\pi\) | |||||||
\(440\) | 253.259 | 0.575588 | ||||||||
\(441\) | −384.838 | − | 215.361i | −0.872649 | − | 0.488348i | ||||
\(442\) | 1221.59i | 2.76378i | ||||||||
\(443\) | 429.496 | − | 247.970i | 0.969517 | − | 0.559751i | 0.0704282 | − | 0.997517i | \(-0.477563\pi\) |
0.899089 | + | 0.437766i | \(0.144230\pi\) | |||||||
\(444\) | 49.6133 | + | 126.470i | 0.111742 | + | 0.284842i | ||||
\(445\) | 587.639 | − | 1017.82i | 1.32054 | − | 2.28724i | ||||
\(446\) | 304.089 | − | 175.566i | 0.681814 | − | 0.393646i | ||||
\(447\) | −265.821 | − | 212.052i | −0.594677 | − | 0.474388i | ||||
\(448\) | −318.556 | + | 437.878i | −0.711062 | + | 0.977407i | ||||
\(449\) | 568.342 | 1.26580 | 0.632898 | − | 0.774235i | \(-0.281865\pi\) | ||||
0.632898 | + | 0.774235i | \(0.281865\pi\) | |||||||
\(450\) | −747.826 | + | 693.455i | −1.66184 | + | 1.54101i | ||||
\(451\) | 62.2850 | − | 107.881i | 0.138104 | − | 0.239203i | ||||
\(452\) | −198.471 | − | 114.587i | −0.439094 | − | 0.253511i | ||||
\(453\) | −372.119 | − | 56.1461i | −0.821454 | − | 0.123943i | ||||
\(454\) | 428.926 | 0.944771 | ||||||||
\(455\) | 690.039 | + | 72.9623i | 1.51657 | + | 0.160357i | ||||
\(456\) | −34.7506 | + | 43.5622i | −0.0762075 | + | 0.0955312i | ||||
\(457\) | −178.846 | + | 103.257i | −0.391349 | + | 0.225945i | −0.682744 | − | 0.730657i | \(-0.739214\pi\) |
0.291396 | + | 0.956603i | \(0.405880\pi\) | |||||||
\(458\) | 1278.93 | + | 738.393i | 2.79243 | + | 1.61221i | ||||
\(459\) | 613.301 | − | 417.729i | 1.33617 | − | 0.910084i | ||||
\(460\) | 1651.32 | − | 953.391i | 3.58983 | − | 2.07259i | ||||
\(461\) | 223.957 | 0.485807 | 0.242903 | − | 0.970050i | \(-0.421900\pi\) | ||||
0.242903 | + | 0.970050i | \(0.421900\pi\) | |||||||
\(462\) | −47.6923 | + | 182.884i | −0.103230 | + | 0.395852i | ||||
\(463\) | − | 779.264i | − | 1.68307i | −0.540199 | − | 0.841537i | \(-0.681651\pi\) | ||
0.540199 | − | 0.841537i | \(-0.318349\pi\) | |||||||
\(464\) | −415.034 | + | 239.620i | −0.894470 | + | 0.516422i | ||||
\(465\) | −131.471 | − | 335.134i | −0.282733 | − | 0.720717i | ||||
\(466\) | 398.975 | + | 230.348i | 0.856168 | + | 0.494309i | ||||
\(467\) | −125.682 | + | 72.5624i | −0.269126 | + | 0.155380i | −0.628490 | − | 0.777817i | \(-0.716327\pi\) |
0.359364 | + | 0.933197i | \(0.382994\pi\) | |||||||
\(468\) | −199.951 | − | 877.281i | −0.427245 | − | 1.87453i | ||||
\(469\) | 60.0848 | − | 26.7065i | 0.128113 | − | 0.0569435i | ||||
\(470\) | −595.659 | −1.26736 | ||||||||
\(471\) | 65.1126 | − | 431.545i | 0.138243 | − | 0.916232i | ||||
\(472\) | −228.892 | + | 396.452i | −0.484940 | + | 0.839941i | ||||
\(473\) | −16.7022 | + | 28.9290i | −0.0353112 | + | 0.0611608i | ||||
\(474\) | −56.4758 | + | 374.303i | −0.119147 | + | 0.789669i | ||||
\(475\) | − | 48.7892i | − | 0.102714i | ||||||
\(476\) | 155.570 | − | 1471.30i | 0.326828 | − | 3.09097i | ||||
\(477\) | −791.499 | + | 180.399i | −1.65933 | + | 0.378196i | ||||
\(478\) | 376.032 | + | 651.306i | 0.786677 | + | 1.36257i | ||||
\(479\) | 315.482 | − | 546.431i | 0.658627 | − | 1.14077i | −0.322345 | − | 0.946622i | \(-0.604471\pi\) |
0.980971 | − | 0.194153i | \(-0.0621957\pi\) | |||||||
\(480\) | −173.352 | + | 68.0050i | −0.361150 | + | 0.141677i | ||||
\(481\) | 66.2937 | − | 38.2747i | 0.137825 | − | 0.0795732i | ||||
\(482\) | − | 444.724i | − | 0.922664i | ||||||
\(483\) | 181.150 | + | 658.381i | 0.375052 | + | 1.36311i | ||||
\(484\) | −877.255 | −1.81251 | ||||||||
\(485\) | −149.519 | + | 86.3247i | −0.308286 | + | 0.177989i | ||||
\(486\) | −565.586 | + | 608.621i | −1.16376 | + | 1.25231i | ||||
\(487\) | 398.367 | + | 229.997i | 0.818002 | + | 0.472273i | 0.849727 | − | 0.527223i | \(-0.176767\pi\) |
−0.0317252 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(488\) | −411.433 | − | 712.623i | −0.843101 | − | 1.46029i | ||||
\(489\) | −455.596 | + | 571.120i | −0.931690 | + | 1.16793i | ||||
\(490\) | −1249.24 | − | 267.168i | −2.54947 | − | 0.545240i | ||||
\(491\) | 589.214i | 1.20003i | 0.799989 | + | 0.600015i | \(0.204839\pi\) | ||||
−0.799989 | + | 0.600015i | \(0.795161\pi\) | |||||||
\(492\) | 162.895 | − | 1079.61i | 0.331087 | − | 2.19434i | ||||
\(493\) | −531.914 | + | 921.302i | −1.07893 | + | 1.86877i | ||||
\(494\) | 56.6666 | + | 32.7165i | 0.114710 | + | 0.0662277i | ||||
\(495\) | −132.457 | + | 122.827i | −0.267590 | + | 0.248135i | ||||
\(496\) | 194.842i | 0.392827i | ||||||||
\(497\) | −389.883 | + | 535.923i | −0.784474 | + | 1.07832i | ||||
\(498\) | −90.2875 | − | 72.0245i | −0.181300 | − | 0.144628i | ||||
\(499\) | −217.184 | + | 125.391i | −0.435238 | + | 0.251285i | −0.701575 | − | 0.712595i | \(-0.747520\pi\) |
0.266338 | + | 0.963880i | \(0.414186\pi\) | |||||||
\(500\) | −238.739 | + | 413.509i | −0.477479 | + | 0.827018i | ||||
\(501\) | −188.335 | + | 73.8827i | −0.375918 | + | 0.147470i | ||||
\(502\) | −643.112 | + | 371.301i | −1.28110 | + | 0.739644i | ||||
\(503\) | − | 312.424i | − | 0.621121i | −0.950554 | − | 0.310560i | \(-0.899483\pi\) | ||
0.950554 | − | 0.310560i | \(-0.100517\pi\) | |||||||
\(504\) | 94.1751 | + | 789.335i | 0.186855 | + | 1.56614i | ||||
\(505\) | 206.514i | 0.408939i | ||||||||
\(506\) | 253.441 | − | 146.325i | 0.500873 | − | 0.289179i | ||||
\(507\) | −471.981 | + | 185.156i | −0.930930 | + | 0.365198i | ||||
\(508\) | 135.036 | − | 233.889i | 0.265818 | − | 0.460411i | ||||
\(509\) | −20.4403 | − | 35.4037i | −0.0401578 | − | 0.0695554i | 0.845248 | − | 0.534374i | \(-0.179453\pi\) |
−0.885406 | + | 0.464819i | \(0.846119\pi\) | |||||||
\(510\) | 1340.49 | − | 1680.39i | 2.62841 | − | 3.29489i | ||||
\(511\) | 679.997 | − | 302.245i | 1.33072 | − | 0.591478i | ||||
\(512\) | 725.669 | 1.41732 | ||||||||
\(513\) | −2.95207 | − | 39.6370i | −0.00575452 | − | 0.0772652i | ||||
\(514\) | 1242.45 | + | 717.330i | 2.41722 | + | 1.39558i | ||||
\(515\) | −411.485 | + | 712.713i | −0.799000 | + | 1.38391i | ||||
\(516\) | −43.6815 | + | 289.507i | −0.0846541 | + | 0.561060i | ||||
\(517\) | −60.1400 | −0.116325 | ||||||||
\(518\) | −128.784 | + | 57.2419i | −0.248618 | + | 0.110506i | ||||
\(519\) | 84.7481 | − | 106.237i | 0.163291 | − | 0.204696i | ||||
\(520\) | −625.389 | − | 1083.21i | −1.20267 | − | 2.08309i | ||||
\(521\) | −356.672 | − | 205.924i | −0.684590 | − | 0.395248i | 0.116992 | − | 0.993133i | \(-0.462675\pi\) |
−0.801582 | + | 0.597884i | \(0.796008\pi\) | |||||||
\(522\) | 351.442 | − | 1138.11i | 0.673260 | − | 2.18028i | ||||
\(523\) | −22.1289 | − | 38.3284i | −0.0423115 | − | 0.0732857i | 0.844094 | − | 0.536195i | \(-0.180139\pi\) |
−0.886406 | + | 0.462909i | \(0.846806\pi\) | |||||||
\(524\) | − | 1128.37i | − | 2.15338i | ||||||
\(525\) | −495.428 | − | 488.832i | −0.943672 | − | 0.931108i | ||||
\(526\) | − | 1169.96i | − | 2.22427i | ||||||
\(527\) | 216.257 | + | 374.569i | 0.410356 | + | 0.710757i | ||||
\(528\) | 91.0155 | − | 35.7049i | 0.172378 | − | 0.0676229i | ||||
\(529\) | 264.163 | − | 457.544i | 0.499363 | − | 0.864923i | ||||
\(530\) | −2036.56 | + | 1175.81i | −3.84257 | + | 2.21851i | ||||
\(531\) | −72.5605 | − | 318.358i | −0.136649 | − | 0.599544i | ||||
\(532\) | −64.0835 | − | 46.6207i | −0.120458 | − | 0.0876328i | ||||
\(533\) | −615.218 | −1.15426 | ||||||||
\(534\) | 235.874 | − | 1563.30i | 0.441712 | − | 2.92752i | ||||
\(535\) | 97.0725 | + | 56.0448i | 0.181444 | + | 0.104757i | ||||
\(536\) | −102.645 | − | 59.2620i | −0.191501 | − | 0.110563i | ||||
\(537\) | 336.416 | + | 50.7593i | 0.626474 | + | 0.0945239i | ||||
\(538\) | − | 283.132i | − | 0.526268i | ||||||
\(539\) | −126.128 | − | 26.9743i | −0.234004 | − | 0.0500450i | ||||
\(540\) | −687.619 | + | 1426.18i | −1.27337 | + | 2.64107i | ||||
\(541\) | 570.140 | − | 329.171i | 1.05386 | − | 0.608449i | 0.130135 | − | 0.991496i | \(-0.458459\pi\) |
0.923729 | + | 0.383048i | \(0.125126\pi\) | |||||||
\(542\) | 1542.13 | + | 890.351i | 2.84526 | + | 1.64271i | ||||
\(543\) | −301.752 | + | 118.375i | −0.555712 | + | 0.218003i | ||||
\(544\) | 193.750 | − | 111.862i | 0.356159 | − | 0.205628i | ||||
\(545\) | 1102.45i | 2.02284i | ||||||||
\(546\) | 899.976 | − | 247.624i | 1.64831 | − | 0.453524i | ||||
\(547\) | 188.044 | 0.343774 | 0.171887 | − | 0.985117i | \(-0.445014\pi\) | ||||
0.171887 | + | 0.985117i | \(0.445014\pi\) | |||||||
\(548\) | 355.299 | + | 615.396i | 0.648356 | + | 1.12299i | ||||
\(549\) | 560.795 | + | 173.171i | 1.02149 | + | 0.315429i | ||||
\(550\) | −149.141 | + | 258.320i | −0.271166 | + | 0.469673i | ||||
\(551\) | 28.4913 | + | 49.3483i | 0.0517083 | + | 0.0895614i | ||||
\(552\) | 767.589 | − | 962.224i | 1.39056 | − | 1.74316i | ||||
\(553\) | −256.897 | − | 27.1634i | −0.464552 | − | 0.0491200i | ||||
\(554\) | −522.227 | −0.942648 | ||||||||
\(555\) | −133.192 | − | 20.0963i | −0.239986 | − | 0.0362096i | ||||
\(556\) | −781.031 | + | 1352.78i | −1.40473 | + | 2.43307i | ||||
\(557\) | 89.8156 | − | 155.565i | 0.161249 | − | 0.279291i | −0.774068 | − | 0.633102i | \(-0.781781\pi\) |
0.935317 | + | 0.353811i | \(0.115114\pi\) | |||||||
\(558\) | −329.281 | − | 355.098i | −0.590109 | − | 0.636377i | ||||
\(559\) | 164.975 | 0.295126 | ||||||||
\(560\) | 268.409 | + | 603.873i | 0.479302 | + | 1.07834i | ||||
\(561\) | 135.341 | − | 169.659i | 0.241250 | − | 0.302423i | ||||
\(562\) | 549.483 | + | 951.732i | 0.977727 | + | 1.69347i | ||||
\(563\) | 559.119 | + | 322.808i | 0.993107 | + | 0.573371i | 0.906202 | − | 0.422846i | \(-0.138969\pi\) |
0.0869053 | + | 0.996217i | \(0.472302\pi\) | |||||||
\(564\) | −490.708 | + | 192.502i | −0.870050 | + | 0.341316i | ||||
\(565\) | 196.786 | − | 113.614i | 0.348293 | − | 0.201087i | ||||
\(566\) | 190.085 | 0.335839 | ||||||||
\(567\) | −432.070 | − | 367.157i | −0.762028 | − | 0.647544i | ||||
\(568\) | 1194.63 | 2.10323 | ||||||||
\(569\) | −293.747 | + | 169.595i | −0.516251 | + | 0.298058i | −0.735399 | − | 0.677634i | \(-0.763005\pi\) |
0.219148 | + | 0.975692i | \(0.429672\pi\) | |||||||
\(570\) | −42.0485 | − | 107.186i | −0.0737693 | − | 0.188046i | ||||
\(571\) | 236.817 | − | 410.179i | 0.414740 | − | 0.718352i | −0.580661 | − | 0.814146i | \(-0.697206\pi\) |
0.995401 | + | 0.0957941i | \(0.0305390\pi\) | |||||||
\(572\) | −131.580 | − | 227.904i | −0.230035 | − | 0.398433i | ||||
\(573\) | 215.830 | − | 270.558i | 0.376667 | − | 0.472177i | ||||
\(574\) | 1126.38 | + | 119.099i | 1.96233 | + | 0.207490i | ||||
\(575\) | 1077.68i | 1.87423i | ||||||||
\(576\) | −510.500 | + | 473.384i | −0.886285 | + | 0.821847i | ||||
\(577\) | −428.206 | − | 247.225i | −0.742125 | − | 0.428466i | 0.0807167 | − | 0.996737i | \(-0.474279\pi\) |
−0.822841 | + | 0.568271i | \(0.807612\pi\) | |||||||
\(578\) | −797.219 | + | 1380.82i | −1.37927 | + | 2.38897i | ||||
\(579\) | −478.276 | − | 72.1634i | −0.826037 | − | 0.124635i | ||||
\(580\) | − | 2269.86i | − | 3.91356i | ||||||
\(581\) | 46.3684 | − | 63.7367i | 0.0798078 | − | 0.109702i | ||||
\(582\) | −144.833 | + | 181.558i | −0.248854 | + | 0.311955i | ||||
\(583\) | −205.619 | + | 118.714i | −0.352691 | + | 0.203626i | ||||
\(584\) | −1161.66 | − | 670.685i | −1.98914 | − | 1.14843i | ||||
\(585\) | 852.423 | + | 263.224i | 1.45713 | + | 0.449955i | ||||
\(586\) | −866.373 | − | 1500.60i | −1.47845 | − | 2.56076i | ||||
\(587\) | 805.107 | 1.37156 | 0.685781 | − | 0.727808i | \(-0.259461\pi\) | ||||
0.685781 | + | 0.727808i | \(0.259461\pi\) | |||||||
\(588\) | −1115.48 | + | 183.629i | −1.89707 | + | 0.312294i | ||||
\(589\) | 23.1671 | 0.0393329 | ||||||||
\(590\) | −472.935 | − | 819.148i | −0.801586 | − | 1.38839i | ||||
\(591\) | 14.7027 | − | 5.76777i | 0.0248776 | − | 0.00975933i | ||||
\(592\) | 63.1363 | + | 36.4517i | 0.106649 | + | 0.0615739i | ||||
\(593\) | −234.927 | − | 406.905i | −0.396167 | − | 0.686181i | 0.597083 | − | 0.802180i | \(-0.296326\pi\) |
−0.993249 | + | 0.115999i | \(0.962993\pi\) | |||||||
\(594\) | −105.534 | + | 218.887i | −0.177667 | + | 0.368497i | ||||
\(595\) | 1186.24 | + | 862.989i | 1.99368 | + | 1.45040i | ||||
\(596\) | −871.681 | −1.46255 | ||||||||
\(597\) | −134.721 | + | 892.886i | −0.225663 | + | 1.49562i | ||||
\(598\) | −1251.68 | − | 722.658i | −2.09311 | − | 1.20846i | ||||
\(599\) | 331.592 | + | 191.445i | 0.553577 | + | 0.319608i | 0.750563 | − | 0.660799i | \(-0.229782\pi\) |
−0.196987 | + | 0.980406i | \(0.563116\pi\) | |||||||
\(600\) | −187.175 | + | 1240.53i | −0.311958 | + | 2.06756i | ||||
\(601\) | −136.830 | −0.227671 | −0.113836 | − | 0.993500i | \(-0.536314\pi\) | ||||
−0.113836 | + | 0.993500i | \(0.536314\pi\) | |||||||
\(602\) | −302.047 | − | 31.9374i | −0.501739 | − | 0.0530521i | ||||
\(603\) | 82.4254 | − | 18.7865i | 0.136692 | − | 0.0311550i | ||||
\(604\) | −835.466 | + | 482.356i | −1.38322 | + | 0.798603i | ||||
\(605\) | 434.904 | − | 753.275i | 0.718849 | − | 1.24508i | ||||
\(606\) | 101.454 | + | 258.616i | 0.167415 | + | 0.426760i | ||||
\(607\) | 163.797 | + | 283.705i | 0.269847 | + | 0.467389i | 0.968822 | − | 0.247757i | \(-0.0796935\pi\) |
−0.698975 | + | 0.715146i | \(0.746360\pi\) | |||||||
\(608\) | − | 11.9835i | − | 0.0197096i | ||||||
\(609\) | 786.567 | + | 205.120i | 1.29157 | + | 0.336815i | ||||
\(610\) | 1700.20 | 2.78722 | ||||||||
\(611\) | 148.508 | + | 257.223i | 0.243057 | + | 0.420987i | ||||
\(612\) | 561.246 | − | 1817.54i | 0.917068 | − | 2.96983i | ||||
\(613\) | 606.899 | + | 350.393i | 0.990047 | + | 0.571604i | 0.905288 | − | 0.424798i | \(-0.139655\pi\) |
0.0847586 | + | 0.996402i | \(0.472988\pi\) | |||||||
\(614\) | −590.635 | + | 341.003i | −0.961946 | + | 0.555380i | ||||
\(615\) | 846.280 | + | 675.098i | 1.37606 | + | 1.09772i | ||||
\(616\) | 94.4319 | + | 212.455i | 0.153299 | + | 0.344894i | ||||
\(617\) | 197.729 | 0.320469 | 0.160234 | − | 0.987079i | \(-0.448775\pi\) | ||||
0.160234 | + | 0.987079i | \(0.448775\pi\) | |||||||
\(618\) | −165.167 | + | 1094.68i | −0.267261 | + | 1.77132i | ||||
\(619\) | 353.048 | + | 203.832i | 0.570351 | + | 0.329293i | 0.757290 | − | 0.653079i | \(-0.226523\pi\) |
−0.186938 | + | 0.982372i | \(0.559856\pi\) | |||||||
\(620\) | −799.209 | − | 461.423i | −1.28905 | − | 0.744231i | ||||
\(621\) | 65.2067 | + | 875.522i | 0.105003 | + | 1.40986i | ||||
\(622\) | 553.156i | 0.889319i | ||||||||
\(623\) | 1072.94 | + | 113.449i | 1.72222 | + | 0.182102i | ||||
\(624\) | −377.463 | − | 301.111i | −0.604909 | − | 0.482550i | ||||
\(625\) | 177.569 | + | 307.558i | 0.284110 | + | 0.492093i | ||||
\(626\) | 667.217 | − | 1155.65i | 1.06584 | − | 1.84609i | ||||
\(627\) | −4.24538 | − | 10.8219i | −0.00677093 | − | 0.0172598i | ||||
\(628\) | −559.388 | − | 968.889i | −0.890745 | − | 1.54282i | ||||
\(629\) | 161.833 | 0.257286 | ||||||||
\(630\) | −1509.71 | − | 646.946i | −2.39637 | − | 1.02690i | ||||
\(631\) | 974.420i | 1.54425i | 0.635472 | + | 0.772124i | \(0.280806\pi\) | ||||
−0.635472 | + | 0.772124i | \(0.719194\pi\) | |||||||
\(632\) | 232.828 | + | 403.270i | 0.368399 | + | 0.638086i | ||||
\(633\) | −108.788 | + | 42.6771i | −0.171862 | + | 0.0674204i | ||||
\(634\) | −78.5971 | + | 136.134i | −0.123970 | + | 0.214723i | ||||
\(635\) | 133.889 | + | 231.903i | 0.210849 | + | 0.365201i | ||||
\(636\) | −1297.74 | + | 1626.81i | −2.04048 | + | 2.55787i | ||||
\(637\) | 196.086 | + | 606.069i | 0.307827 | + | 0.951442i | ||||
\(638\) | − | 348.374i | − | 0.546041i | ||||||
\(639\) | −624.806 | + | 579.379i | −0.977787 | + | 0.906696i | ||||
\(640\) | −884.244 | + | 1531.56i | −1.38163 | + | 2.39306i | ||||
\(641\) | −436.447 | − | 251.983i | −0.680884 | − | 0.393109i | 0.119304 | − | 0.992858i | \(-0.461934\pi\) |
−0.800188 | + | 0.599749i | \(0.795267\pi\) | |||||||
\(642\) | 149.096 | + | 22.4960i | 0.232237 | + | 0.0350405i | ||||
\(643\) | − | 806.217i | − | 1.25384i | −0.779085 | − | 0.626919i | \(-0.784316\pi\) | ||
0.779085 | − | 0.626919i | \(-0.215684\pi\) | |||||||
\(644\) | 1415.51 | + | 1029.78i | 2.19800 | + | 1.59904i | ||||
\(645\) | −226.936 | − | 181.033i | −0.351839 | − | 0.280671i | ||||
\(646\) | 69.1658 | + | 119.799i | 0.107068 | + | 0.185447i | ||||
\(647\) | −415.070 | − | 239.641i | −0.641530 | − | 0.370387i | 0.143674 | − | 0.989625i | \(-0.454108\pi\) |
−0.785204 | + | 0.619238i | \(0.787442\pi\) | |||||||
\(648\) | −77.0030 | + | 1019.15i | −0.118832 | + | 1.57277i | ||||
\(649\) | −47.7494 | − | 82.7043i | −0.0735738 | − | 0.127433i | ||||
\(650\) | 1473.14 | 2.26637 | ||||||||
\(651\) | 232.117 | − | 235.249i | 0.356555 | − | 0.361366i | ||||
\(652\) | 1872.82i | 2.87242i | ||||||||
\(653\) | −440.531 | + | 254.341i | −0.674626 | + | 0.389496i | −0.797827 | − | 0.602886i | \(-0.794017\pi\) |
0.123201 | + | 0.992382i | \(0.460684\pi\) | |||||||
\(654\) | 541.596 | + | 1380.59i | 0.828129 | + | 2.11099i | ||||
\(655\) | 968.902 | + | 559.396i | 1.47924 | + | 0.854039i | ||||
\(656\) | −292.958 | − | 507.419i | −0.446583 | − | 0.773504i | ||||
\(657\) | 932.832 | − | 212.612i | 1.41984 | − | 0.323611i | ||||
\(658\) | −222.101 | − | 499.689i | −0.337540 | − | 0.759405i | ||||
\(659\) | − | 443.924i | − | 0.673633i | −0.941570 | − | 0.336817i | \(-0.890650\pi\) | ||
0.941570 | − | 0.336817i | \(-0.109350\pi\) | |||||||
\(660\) | −69.0870 | + | 457.886i | −0.104677 | + | 0.693767i | ||||
\(661\) | −508.855 | − | 293.788i | −0.769826 | − | 0.444459i | 0.0629863 | − | 0.998014i | \(-0.479938\pi\) |
−0.832813 | + | 0.553555i | \(0.813271\pi\) | |||||||
\(662\) | −146.438 | − | 84.5459i | −0.221205 | − | 0.127713i | ||||
\(663\) | −1059.85 | − | 159.913i | −1.59857 | − | 0.241196i | ||||
\(664\) | −142.076 | −0.213970 | ||||||||
\(665\) | 71.8016 | − | 31.9144i | 0.107972 | − | 0.0479915i | ||||
\(666\) | −176.668 | + | 40.2665i | −0.265268 | + | 0.0604601i | ||||
\(667\) | −629.329 | − | 1090.03i | −0.943522 | − | 1.63423i | ||||
\(668\) | −259.306 | + | 449.131i | −0.388182 | + | 0.672352i | ||||
\(669\) | 112.514 | + | 286.809i | 0.168182 | + | 0.428714i | ||||
\(670\) | 212.084 | − | 122.447i | 0.316543 | − | 0.182756i | ||||
\(671\) | 171.659 | 0.255826 | ||||||||
\(672\) | −121.686 | − | 120.065i | −0.181080 | − | 0.178669i | ||||
\(673\) | 986.044 | 1.46515 | 0.732574 | − | 0.680688i | \(-0.238319\pi\) | ||||
0.732574 | + | 0.680688i | \(0.238319\pi\) | |||||||
\(674\) | 191.269 | + | 331.288i | 0.283783 | + | 0.491526i | ||||
\(675\) | −503.746 | − | 739.589i | −0.746290 | − | 1.09569i | ||||
\(676\) | −649.840 | + | 1125.56i | −0.961302 | + | 1.66502i | ||||
\(677\) | −129.730 | + | 74.8998i | −0.191625 | + | 0.110635i | −0.592743 | − | 0.805392i | \(-0.701955\pi\) |
0.401118 | + | 0.916026i | \(0.368622\pi\) | |||||||
\(678\) | 190.618 | − | 238.953i | 0.281148 | − | 0.352438i | ||||
\(679\) | −128.167 | − | 93.2413i | −0.188759 | − | 0.137322i | ||||
\(680\) | − | 2644.27i | − | 3.88863i | ||||||
\(681\) | −56.1487 | + | 372.135i | −0.0824503 | + | 0.546454i | ||||
\(682\) | −122.661 | − | 70.8183i | −0.179855 | − | 0.103839i | ||||
\(683\) | −320.414 | + | 554.973i | −0.469127 | + | 0.812552i | −0.999377 | − | 0.0352896i | \(-0.988765\pi\) |
0.530250 | + | 0.847841i | \(0.322098\pi\) | |||||||
\(684\) | −69.2798 | − | 74.7117i | −0.101286 | − | 0.109228i | ||||
\(685\) | −704.565 | −1.02856 | ||||||||
\(686\) | −241.678 | − | 1147.59i | −0.352301 | − | 1.67287i | ||||
\(687\) | −808.047 | + | 1012.94i | −1.17620 | + | 1.47444i | ||||
\(688\) | 78.5589 | + | 136.068i | 0.114185 | + | 0.197773i | ||||
\(689\) | 1015.50 | + | 586.298i | 1.47387 | + | 0.850940i | ||||
\(690\) | 928.788 | + | 2367.58i | 1.34607 | + | 3.43127i | ||||
\(691\) | −666.727 | + | 384.935i | −0.964873 | + | 0.557070i | −0.897669 | − | 0.440670i | \(-0.854741\pi\) |
−0.0672037 | + | 0.997739i | \(0.521408\pi\) | |||||||
\(692\) | − | 348.374i | − | 0.503431i | ||||||
\(693\) | −152.426 | − | 65.3181i | −0.219951 | − | 0.0942541i | ||||
\(694\) | − | 1900.68i | − | 2.73874i | ||||||
\(695\) | −774.399 | − | 1341.30i | −1.11424 | − | 1.92993i | ||||
\(696\) | −535.111 | − | 1364.05i | −0.768837 | − | 1.95985i | ||||
\(697\) | −1126.38 | − | 650.315i | −1.61604 | − | 0.933021i | ||||
\(698\) | −360.756 | + | 208.282i | −0.516842 | + | 0.298399i | ||||
\(699\) | −252.077 | + | 315.995i | −0.360625 | + | 0.452068i | ||||
\(700\) | −1774.27 | − | 187.605i | −2.53467 | − | 0.268007i | ||||
\(701\) | − | 1220.21i | − | 1.74067i | −0.492457 | − | 0.870337i | \(-0.663901\pi\) | ||
0.492457 | − | 0.870337i | \(-0.336099\pi\) | |||||||
\(702\) | 1196.80 | − | 89.1345i | 1.70484 | − | 0.126972i | ||||
\(703\) | 4.33418 | − | 7.50702i | 0.00616526 | − | 0.0106785i | ||||
\(704\) | −101.811 | + | 176.341i | −0.144617 | + | 0.250484i | ||||
\(705\) | 77.9748 | − | 516.792i | 0.110603 | − | 0.733038i | ||||
\(706\) | 1210.49 | 1.71457 | ||||||||
\(707\) | −173.241 | + | 77.0023i | −0.245037 | + | 0.108914i | ||||
\(708\) | −654.337 | − | 521.980i | −0.924204 | − | 0.737260i | ||||
\(709\) | 612.879 | − | 353.846i | 0.864427 | − | 0.499077i | −0.00106550 | − | 0.999999i | \(-0.500339\pi\) |
0.865492 | + | 0.500922i | \(0.167006\pi\) | |||||||
\(710\) | −1234.17 | + | 2137.65i | −1.73827 | + | 3.01078i | ||||
\(711\) | −317.351 | − | 97.9965i | −0.446345 | − | 0.137829i | ||||
\(712\) | −972.420 | − | 1684.28i | −1.36576 | − | 2.36556i | ||||
\(713\) | −511.726 | −0.717708 | ||||||||
\(714\) | 1909.48 | + | 497.953i | 2.67434 | + | 0.697414i | ||||
\(715\) | 260.926 | 0.364932 | ||||||||
\(716\) | 755.309 | − | 436.078i | 1.05490 | − | 0.609047i | ||||
\(717\) | −614.296 | + | 240.985i | −0.856759 | + | 0.336102i | ||||
\(718\) | 787.485 | − | 1363.96i | 1.09678 | − | 1.89967i | ||||
\(719\) | 1030.82 | − | 595.144i | 1.43369 | − | 0.827739i | 0.436286 | − | 0.899808i | \(-0.356294\pi\) |
0.997400 | + | 0.0720695i | \(0.0229603\pi\) | |||||||
\(720\) | 188.811 | + | 828.404i | 0.262237 | + | 1.15056i | ||||
\(721\) | −751.313 | − | 79.4412i | −1.04204 | − | 0.110182i | ||||
\(722\) | −1226.89 | −1.69930 | ||||||||
\(723\) | 385.841 | + | 58.2167i | 0.533667 | + | 0.0805210i | ||||
\(724\) | −415.462 | + | 719.601i | −0.573842 | + | 0.993924i | ||||
\(725\) | 1111.01 | + | 641.444i | 1.53243 | + | 0.884750i | ||||
\(726\) | 174.567 | − | 1156.98i | 0.240451 | − | 1.59363i | ||||
\(727\) | −301.359 | −0.414524 | −0.207262 | − | 0.978285i | \(-0.566455\pi\) | ||||
−0.207262 | + | 0.978285i | \(0.566455\pi\) | |||||||
\(728\) | 675.498 | − | 928.521i | 0.927881 | − | 1.27544i | ||||
\(729\) | −454.000 | − | 570.373i | −0.622771 | − | 0.782404i | ||||
\(730\) | 2400.22 | − | 1385.77i | 3.28797 | − | 1.89831i | ||||
\(731\) | 302.047 | + | 174.387i | 0.413197 | + | 0.238559i | ||||
\(732\) | 1400.64 | − | 549.464i | 1.91345 | − | 0.750634i | ||||
\(733\) | −879.905 | + | 508.013i | −1.20042 | + | 0.693060i | −0.960648 | − | 0.277770i | \(-0.910405\pi\) |
−0.239768 | + | 0.970830i | \(0.577071\pi\) | |||||||
\(734\) | −1348.92 | −1.83776 | ||||||||
\(735\) | 395.326 | − | 1048.87i | 0.537859 | − | 1.42703i | ||||
\(736\) | 264.697i | 0.359642i | ||||||||
\(737\) | 21.4128 | − | 12.3627i | 0.0290540 | − | 0.0167744i | ||||
\(738\) | 1391.45 | + | 429.671i | 1.88543 | + | 0.582210i | ||||
\(739\) | −930.201 | − | 537.052i | −1.25873 | − | 0.726728i | −0.285902 | − | 0.958259i | \(-0.592293\pi\) |
−0.972828 | + | 0.231531i | \(0.925627\pi\) | |||||||
\(740\) | −299.038 | + | 172.649i | −0.404105 | + | 0.233310i | ||||
\(741\) | −35.8027 | + | 44.8811i | −0.0483167 | + | 0.0605682i | ||||
\(742\) | −1745.73 | − | 1270.02i | −2.35274 | − | 1.71162i | ||||
\(743\) | 530.788 | 0.714385 | 0.357192 | − | 0.934031i | \(-0.383734\pi\) | ||||
0.357192 | + | 0.934031i | \(0.383734\pi\) | |||||||
\(744\) | −589.056 | − | 88.8782i | −0.791742 | − | 0.119460i | ||||
\(745\) | 432.140 | − | 748.488i | 0.580054 | − | 1.00468i | ||||
\(746\) | −29.7934 | + | 51.6036i | −0.0399375 | + | 0.0691738i | ||||
\(747\) | 74.3074 | − | 68.9048i | 0.0994744 | − | 0.0922421i | ||||
\(748\) | − | 556.347i | − | 0.743779i | ||||||
\(749\) | −10.8200 | + | 102.330i | −0.0144459 | + | 0.136622i | ||||
\(750\) | −497.852 | − | 397.149i | −0.663803 | − | 0.529532i | ||||
\(751\) | 259.436 | + | 449.356i | 0.345454 | + | 0.598344i | 0.985436 | − | 0.170046i | \(-0.0543916\pi\) |
−0.639982 | + | 0.768390i | \(0.721058\pi\) | |||||||
\(752\) | −141.435 | + | 244.972i | −0.188078 | + | 0.325760i | ||||
\(753\) | −237.953 | − | 606.568i | −0.316007 | − | 0.805535i | ||||
\(754\) | −1490.02 | + | 860.264i | −1.97615 | + | 1.14093i | ||||
\(755\) | − | 956.522i | − | 1.26692i | ||||||
\(756\) | −1452.79 | − | 45.0578i | −1.92168 | − | 0.0596003i | ||||
\(757\) | 216.211 | 0.285616 | 0.142808 | − | 0.989750i | \(-0.454387\pi\) | ||||
0.142808 | + | 0.989750i | \(0.454387\pi\) | |||||||
\(758\) | 1079.88 | − | 623.468i | 1.42464 | − | 0.822518i | ||||
\(759\) | 93.7740 | + | 239.040i | 0.123549 | + | 0.314940i | ||||
\(760\) | −122.661 | − | 70.8183i | −0.161396 | − | 0.0931820i | ||||
\(761\) | 316.996 | + | 549.052i | 0.416551 | + | 0.721488i | 0.995590 | − | 0.0938121i | \(-0.0299053\pi\) |
−0.579039 | + | 0.815300i | \(0.696572\pi\) | |||||||
\(762\) | 281.595 | + | 224.635i | 0.369547 | + | 0.294797i | ||||
\(763\) | −924.825 | + | 411.066i | −1.21209 | + | 0.538750i | ||||
\(764\) | − | 887.214i | − | 1.16127i | ||||||
\(765\) | 1282.43 | + | 1382.98i | 1.67638 | + | 1.80782i | ||||
\(766\) | 648.866 | − | 1123.87i | 0.847084 | − | 1.46719i | ||||
\(767\) | −235.822 | + | 408.455i | −0.307460 | + | 0.532536i | ||||
\(768\) | −216.437 | + | 1434.47i | −0.281819 | + | 1.86780i | ||||
\(769\) | 819.151i | 1.06522i | 0.846362 | + | 0.532608i | \(0.178788\pi\) | ||||
−0.846362 | + | 0.532608i | \(0.821212\pi\) | |||||||
\(770\) | −477.720 | − | 50.5124i | −0.620415 | − | 0.0656005i | ||||
\(771\) | −784.997 | + | 984.046i | −1.01815 | + | 1.27632i | ||||
\(772\) | −1073.81 | + | 619.962i | −1.39094 | + | 0.803059i | ||||
\(773\) | −568.343 | + | 984.399i | −0.735244 | + | 1.27348i | 0.219373 | + | 0.975641i | \(0.429599\pi\) |
−0.954616 | + | 0.297838i | \(0.903734\pi\) | |||||||
\(774\) | −373.126 | − | 115.219i | −0.482076 | − | 0.148862i | ||||
\(775\) | 451.699 | − | 260.788i | 0.582837 | − | 0.336501i | ||||
\(776\) | 285.699i | 0.368169i | ||||||||
\(777\) | −32.8044 | − | 119.226i | −0.0422194 | − | 0.153444i | ||||
\(778\) | 13.2489i | 0.0170295i | ||||||||
\(779\) | −60.3330 | + | 34.8333i | −0.0774493 | + | 0.0447154i | ||||
\(780\) | 2129.01 | − | 835.199i | 2.72950 | − | 1.07077i | ||||
\(781\) | −124.607 | + | 215.825i | −0.159548 | + | 0.276345i | ||||
\(782\) | −1527.77 | − | 2646.17i | −1.95367 | − | 3.38385i | ||||
\(783\) | 941.414 | + | 453.894i | 1.20232 | + | 0.579686i | ||||
\(784\) | −406.499 | + | 450.329i | −0.518493 | + | 0.574399i | ||||
\(785\) | 1109.28 | 1.41309 | ||||||||
\(786\) | 1488.16 | + | 224.538i | 1.89334 | + | 0.285671i | ||||
\(787\) | −930.596 | − | 537.280i | −1.18246 | − | 0.682694i | −0.225878 | − | 0.974156i | \(-0.572525\pi\) |
−0.956582 | + | 0.291462i | \(0.905858\pi\) | |||||||
\(788\) | 20.2431 | − | 35.0621i | 0.0256892 | − | 0.0444951i | ||||
\(789\) | 1015.06 | + | 153.154i | 1.28651 | + | 0.194112i | ||||
\(790\) | −962.137 | −1.21790 | ||||||||
\(791\) | 168.684 | + | 122.717i | 0.213254 | + | 0.155142i | ||||
\(792\) | 66.4275 | + | 291.449i | 0.0838731 | + | 0.367992i | ||||
\(793\) | −423.889 | − | 734.198i | −0.534539 | − | 0.925848i | ||||
\(794\) | −1936.72 | − | 1118.17i | −2.43920 | − | 1.40827i | ||||
\(795\) | −753.532 | − | 1920.83i | −0.947839 | − | 2.41614i | ||||
\(796\) | 1157.40 | + | 2004.67i | 1.45402 | + | 2.51843i | ||||
\(797\) | − | 119.200i | − | 0.149561i | −0.997200 | − | 0.0747803i | \(-0.976174\pi\) | ||
0.997200 | − | 0.0747803i | \(-0.0238256\pi\) | |||||||
\(798\) | 74.2382 | − | 75.2400i | 0.0930304 | − | 0.0942857i | ||||
\(799\) | 627.919i | 0.785881i | ||||||||
\(800\) | −134.896 | − | 233.647i | −0.168620 | − | 0.292058i | ||||
\(801\) | 1325.44 | + | 409.288i | 1.65473 | + | 0.510971i | ||||
\(802\) | −168.663 | + | 292.133i | −0.210303 | + | 0.364256i | ||||
\(803\) | 242.335 | − | 139.912i | 0.301787 | − | 0.174237i | ||||
\(804\) | 135.145 | − | 169.413i | 0.168091 | − | 0.210713i | ||||
\(805\) | −1585.99 | + | 704.940i | −1.97017 | + | 0.875702i | ||||
\(806\) | 699.506i | 0.867873i | ||||||||
\(807\) | 245.645 | + | 37.0635i | 0.304392 | + | 0.0459275i | ||||
\(808\) | 295.954 | + | 170.869i | 0.366279 | + | 0.211471i | ||||
\(809\) | −348.228 | − | 201.050i | −0.430443 | − | 0.248516i | 0.269092 | − | 0.963114i | \(-0.413276\pi\) |
−0.699535 | + | 0.714598i | \(0.746610\pi\) | |||||||
\(810\) | −1744.10 | − | 1190.67i | −2.15321 | − | 1.46997i | ||||
\(811\) | − | 1280.62i | − | 1.57906i | −0.613712 | − | 0.789530i | \(-0.710324\pi\) | ||
0.613712 | − | 0.789530i | \(-0.289676\pi\) | |||||||
\(812\) | 1904.15 | − | 846.358i | 2.34502 | − | 1.04231i | ||||
\(813\) | −974.339 | + | 1221.40i | −1.19845 | + | 1.50234i | ||||
\(814\) | −45.8957 | + | 26.4979i | −0.0563829 | + | 0.0325527i | ||||
\(815\) | −1608.14 | − | 928.459i | −1.97318 | − | 1.13921i | ||||
\(816\) | −372.793 | − | 950.290i | −0.456854 | − | 1.16457i | ||||
\(817\) | 16.1787 | − | 9.34080i | 0.0198026 | − | 0.0114331i | ||||
\(818\) | 1331.30i | 1.62751i | ||||||||
\(819\) | 97.0263 | + | 813.232i | 0.118469 | + | 0.992958i | ||||
\(820\) | 2775.12 | 3.38430 | ||||||||
\(821\) | 404.665 | + | 700.900i | 0.492893 | + | 0.853716i | 0.999966 | − | 0.00818719i | \(-0.00260609\pi\) |
−0.507074 | + | 0.861903i | \(0.669273\pi\) | |||||||
\(822\) | −882.322 | + | 346.130i | −1.07338 | + | 0.421083i | ||||
\(823\) | 36.0687 | − | 62.4728i | 0.0438259 | − | 0.0759087i | −0.843280 | − | 0.537474i | \(-0.819379\pi\) |
0.887106 | + | 0.461565i | \(0.152712\pi\) | |||||||
\(824\) | 680.922 | + | 1179.39i | 0.826362 | + | 1.43130i | ||||
\(825\) | −204.595 | − | 163.210i | −0.247993 | − | 0.197830i | ||||
\(826\) | 510.829 | − | 702.172i | 0.618437 | − | 0.850087i | ||||
\(827\) | 645.671 | 0.780739 | 0.390370 | − | 0.920658i | \(-0.372347\pi\) | ||||
0.390370 | + | 0.920658i | \(0.372347\pi\) | |||||||
\(828\) | 1530.29 | + | 1650.27i | 1.84817 | + | 1.99308i | ||||
\(829\) | 468.985 | − | 812.306i | 0.565724 | − | 0.979863i | −0.431258 | − | 0.902229i | \(-0.641930\pi\) |
0.996982 | − | 0.0776340i | \(-0.0247366\pi\) | |||||||
\(830\) | 146.779 | − | 254.228i | 0.176842 | − | 0.306299i | ||||
\(831\) | 68.3622 | − | 453.083i | 0.0822650 | − | 0.545226i | ||||
\(832\) | 1005.63 | 1.20869 | ||||||||
\(833\) | −281.637 | + | 1316.90i | −0.338100 | + | 1.58091i | ||||
\(834\) | −1628.71 | − | 1299.26i | −1.95289 | − | 1.55787i | ||||
\(835\) | −257.104 | − | 445.318i | −0.307909 | − | 0.533315i | ||||
\(836\) | −25.8075 | − | 14.9000i | −0.0308703 | − | 0.0178229i | ||||
\(837\) | 351.187 | − | 239.199i | 0.419578 | − | 0.285781i | ||||
\(838\) | −300.201 | + | 173.321i | −0.358235 | + | 0.206827i | ||||
\(839\) | 743.899 | 0.886650 | 0.443325 | − | 0.896361i | \(-0.353799\pi\) | ||||
0.443325 | + | 0.896361i | \(0.353799\pi\) | |||||||
\(840\) | −1948.09 | + | 536.008i | −2.31916 | + | 0.638105i | ||||
\(841\) | −657.327 | −0.781601 | ||||||||
\(842\) | 265.790 | − | 153.454i | 0.315665 | − | 0.182249i | ||||
\(843\) | −897.650 | + | 352.143i | −1.06483 | + | 0.417726i | ||||
\(844\) | −149.784 | + | 259.433i | −0.177469 | + | 0.307385i | ||||
\(845\) | −644.323 | − | 1116.00i | −0.762512 | − | 1.32071i | ||||
\(846\) | −156.236 | − | 685.482i | −0.184676 | − | 0.810262i | ||||
\(847\) | 794.072 | + | 83.9624i | 0.937511 | + | 0.0991291i | ||||
\(848\) | 1116.75i | 1.31692i | ||||||||
\(849\) | −24.8831 | + | 164.917i | −0.0293087 | + | 0.194249i | ||||
\(850\) | 2697.11 | + | 1557.18i | 3.17307 | + | 1.83197i | ||||
\(851\) | −95.7355 | + | 165.819i | −0.112498 | + | 0.194852i | ||||
\(852\) | −325.886 | + | 2159.87i | −0.382496 | + | 2.53506i | ||||
\(853\) | 857.426i | 1.00519i | 0.864522 | + | 0.502594i | \(0.167621\pi\) | ||||
−0.864522 | + | 0.502594i | \(0.832379\pi\) | |||||||
\(854\) | 633.950 | + | 1426.27i | 0.742330 | + | 1.67011i | ||||
\(855\) | 98.4987 | − | 22.4499i | 0.115203 | − | 0.0262572i | ||||
\(856\) | 160.635 | − | 92.7425i | 0.187657 | − | 0.108344i | ||||
\(857\) | −604.822 | − | 349.194i | −0.705744 | − | 0.407461i | 0.103739 | − | 0.994605i | \(-0.466919\pi\) |
−0.809483 | + | 0.587143i | \(0.800253\pi\) | |||||||
\(858\) | 326.756 | − | 128.185i | 0.380835 | − | 0.149399i | ||||
\(859\) | −50.3096 | − | 87.1388i | −0.0585676 | − | 0.101442i | 0.835255 | − | 0.549863i | \(-0.185320\pi\) |
−0.893823 | + | 0.448421i | \(0.851987\pi\) | |||||||
\(860\) | −744.171 | −0.865315 | ||||||||
\(861\) | −250.779 | + | 961.653i | −0.291265 | + | 1.11690i | ||||
\(862\) | −2210.29 | −2.56414 | ||||||||
\(863\) | −426.398 | − | 738.543i | −0.494088 | − | 0.855785i | 0.505889 | − | 0.862599i | \(-0.331165\pi\) |
−0.999977 | + | 0.00681331i | \(0.997831\pi\) | |||||||
\(864\) | −123.728 | − | 181.656i | −0.143204 | − | 0.210250i | ||||
\(865\) | 299.139 | + | 172.708i | 0.345826 | + | 0.199663i | ||||
\(866\) | −977.051 | − | 1692.30i | −1.12823 | − | 1.95416i | ||||
\(867\) | −1093.64 | − | 872.422i | −1.26141 | − | 1.00625i | ||||
\(868\) | 89.0823 | − | 842.494i | 0.102629 | − | 0.970615i | ||||
\(869\) | −97.1411 | −0.111785 | ||||||||
\(870\) | 2993.63 | + | 451.686i | 3.44096 | + | 0.519180i | ||||
\(871\) | −105.752 | − | 61.0561i | −0.121415 | − | 0.0700989i | ||||
\(872\) | 1579.91 | + | 912.160i | 1.81182 | + | 1.04605i | ||||
\(873\) | −138.560 | − | 149.423i | −0.158717 | − | 0.171161i | ||||
\(874\) | −163.666 | −0.187261 | ||||||||
\(875\) | 255.679 | − | 351.449i | 0.292204 | − | 0.401656i | ||||
\(876\) | 1529.47 | − | 1917.30i | 1.74598 | − | 2.18870i | ||||
\(877\) | −408.625 | + | 235.920i | −0.465935 | + | 0.269008i | −0.714537 | − | 0.699598i | \(-0.753362\pi\) |
0.248601 | + | 0.968606i | \(0.420029\pi\) | |||||||
\(878\) | 657.484 | − | 1138.80i | 0.748843 | − | 1.29703i | ||||
\(879\) | 1415.33 | − | 555.226i | 1.61016 | − | 0.631657i | ||||
\(880\) | 124.249 | + | 215.206i | 0.141192 | + | 0.244553i | ||||
\(881\) | 702.898i | 0.797842i | 0.916985 | + | 0.398921i | \(0.130615\pi\) | ||||
−0.916985 | + | 0.398921i | \(0.869385\pi\) | |||||||
\(882\) | −20.2090 | − | 1507.70i | −0.0229127 | − | 1.70941i | ||||
\(883\) | 936.948 | 1.06110 | 0.530548 | − | 0.847655i | \(-0.321986\pi\) | ||||
0.530548 | + | 0.847655i | \(0.321986\pi\) | |||||||
\(884\) | −2379.53 | + | 1373.82i | −2.69178 | + | 1.55410i | ||||
\(885\) | 772.601 | − | 303.087i | 0.872995 | − | 0.342471i | ||||
\(886\) | 1468.50 | + | 847.839i | 1.65745 | + | 0.956929i | ||||
\(887\) | −892.025 | + | 515.011i | −1.00567 | + | 0.580621i | −0.909920 | − | 0.414785i | \(-0.863857\pi\) |
−0.0957459 | + | 0.995406i | \(0.530524\pi\) | |||||||
\(888\) | −139.003 | + | 174.249i | −0.156534 | + | 0.196226i | ||||
\(889\) | −144.617 | + | 198.786i | −0.162674 | + | 0.223607i | ||||
\(890\) | 4018.42 | 4.51508 | ||||||||
\(891\) | −176.091 | − | 120.215i | −0.197633 | − | 0.134921i | ||||
\(892\) | 683.968 | + | 394.889i | 0.766780 | + | 0.442701i | ||||
\(893\) | 29.1276 | + | 16.8168i | 0.0326177 | + | 0.0188318i | ||||
\(894\) | 173.458 | − | 1149.62i | 0.194025 | − | 1.28593i | ||||
\(895\) | 864.751i | 0.966202i | ||||||||
\(896\) | −1614.50 | − | 170.712i | −1.80190 | − | 0.190527i | ||||
\(897\) | 790.828 | − | 991.355i | 0.881636 | − | 1.10519i | ||||
\(898\) | 971.617 | + | 1682.89i | 1.08198 | + | 1.87404i | ||||
\(899\) | −304.583 | + | 527.554i | −0.338802 | + | 0.586823i | ||||
\(900\) | −2191.80 | − | 676.815i | −2.43533 | − | 0.752017i | ||||
\(901\) | 1239.49 | + | 2146.86i | 1.37568 | + | 2.38275i | ||||
\(902\) | 425.920 | 0.472195 | ||||||||
\(903\) | 67.2483 | − | 257.874i | 0.0744721 | − | 0.285575i | ||||
\(904\) | − | 376.016i | − | 0.415947i | ||||||
\(905\) | −411.934 | − | 713.491i | −0.455176 | − | 0.788388i | ||||
\(906\) | −469.908 | − | 1197.85i | −0.518663 | − | 1.32213i | ||||
\(907\) | −454.488 | + | 787.196i | −0.501089 | + | 0.867912i | 0.498910 | + | 0.866654i | \(0.333734\pi\) |
−0.999999 | + | 0.00125790i | \(0.999600\pi\) | |||||||
\(908\) | 482.378 | + | 835.503i | 0.531253 | + | 0.920158i | ||||
\(909\) | −237.656 | + | 54.1668i | −0.261447 | + | 0.0595894i | ||||
\(910\) | 963.621 | + | 2167.97i | 1.05892 | + | 2.38239i | ||||
\(911\) | − | 80.1743i | − | 0.0880069i | −0.999031 | − | 0.0440035i | \(-0.985989\pi\) | ||
0.999031 | − | 0.0440035i | \(-0.0140113\pi\) | |||||||
\(912\) | −54.0657 | − | 8.15756i | −0.0592825 | − | 0.00894469i | ||||
\(913\) | 14.8193 | − | 25.6679i | 0.0162315 | − | 0.0281138i | ||||
\(914\) | −611.498 | − | 353.049i | −0.669035 | − | 0.386268i | ||||
\(915\) | −222.565 | + | 1475.09i | −0.243241 | + | 1.61212i | ||||
\(916\) | 3321.64i | 3.62625i | ||||||||
\(917\) | −107.997 | + | 1021.38i | −0.117772 | + | 1.11382i | ||||
\(918\) | 2285.39 | + | 1101.88i | 2.48953 | + | 1.20031i | ||||
\(919\) | −395.033 | − | 684.217i | −0.429851 | − | 0.744524i | 0.567009 | − | 0.823712i | \(-0.308101\pi\) |
−0.996860 | + | 0.0791880i | \(0.974767\pi\) | |||||||
\(920\) | 2709.39 | + | 1564.27i | 2.94499 | + | 1.70029i | ||||
\(921\) | −218.536 | − | 557.073i | −0.237282 | − | 0.604856i | ||||
\(922\) | 382.869 | + | 663.148i | 0.415259 | + | 0.719249i | ||||
\(923\) | 1230.80 | 1.33348 | ||||||||
\(924\) | −409.874 | + | 112.775i | −0.443586 | + | 0.122051i | ||||
\(925\) | − | 195.157i | − | 0.210980i | ||||||
\(926\) | 2307.44 | − | 1332.20i | 2.49183 | − | 1.43866i | ||||
\(927\) | −928.116 | − | 286.597i | −1.00120 | − | 0.309167i | ||||
\(928\) | 272.884 | + | 157.549i | 0.294056 | + | 0.169773i | ||||
\(929\) | 623.696 | + | 1080.27i | 0.671363 | + | 1.16283i | 0.977518 | + | 0.210853i | \(0.0676240\pi\) |
−0.306155 | + | 0.951982i | \(0.599043\pi\) | |||||||
\(930\) | 767.589 | − | 962.224i | 0.825365 | − | 1.03465i | ||||
\(931\) | 53.5449 | + | 48.3335i | 0.0575134 | + | 0.0519156i | ||||
\(932\) | 1036.21i | 1.11182i | ||||||||
\(933\) | −479.917 | − | 72.4111i | −0.514381 | − | 0.0776110i | ||||
\(934\) | −429.722 | − | 248.100i | −0.460088 | − | 0.265632i | ||||
\(935\) | 477.720 | + | 275.812i | 0.510930 | + | 0.294986i | ||||
\(936\) | 1082.52 | − | 1003.81i | 1.15653 | − | 1.07245i | ||||
\(937\) | −1128.28 | −1.20414 | −0.602072 | − | 0.798442i | \(-0.705658\pi\) | ||||
−0.602072 | + | 0.798442i | \(0.705658\pi\) | |||||||
\(938\) | 181.798 | + | 132.258i | 0.193814 | + | 0.141000i | ||||
\(939\) | 915.299 | + | 730.156i | 0.974760 | + | 0.777589i | ||||
\(940\) | −669.888 | − | 1160.28i | −0.712647 | − | 1.23434i | ||||
\(941\) | 190.627 | − | 330.176i | 0.202579 | − | 0.350878i | −0.746780 | − | 0.665072i | \(-0.768401\pi\) |
0.949359 | + | 0.314194i | \(0.101734\pi\) | |||||||
\(942\) | 1389.14 | − | 544.952i | 1.47467 | − | 0.578506i | ||||
\(943\) | 1332.67 | − | 769.415i | 1.41322 | − | 0.815922i | ||||
\(944\) | −449.179 | −0.475826 | ||||||||
\(945\) | 758.918 | − | 1225.13i | 0.803088 | − | 1.29644i | ||||
\(946\) | −114.214 | −0.120733 | ||||||||
\(947\) | −521.905 | − | 903.966i | −0.551114 | − | 0.954557i | −0.998195 | − | 0.0600635i | \(-0.980870\pi\) |
0.447081 | − | 0.894494i | \(-0.352464\pi\) | |||||||
\(948\) | −792.617 | + | 310.939i | −0.836094 | + | 0.327995i | ||||
\(949\) | −1196.83 | − | 690.990i | −1.26115 | − | 0.728124i | ||||
\(950\) | 144.467 | − | 83.4082i | 0.152071 | − | 0.0877981i | ||||
\(951\) | −107.821 | − | 86.0113i | −0.113376 | − | 0.0904430i | ||||
\(952\) | 2218.23 | − | 985.960i | 2.33008 | − | 1.03567i | ||||
\(953\) | 645.739i | 0.677586i | 0.940861 | + | 0.338793i | \(0.110019\pi\) | ||||
−0.940861 | + | 0.338793i | \(0.889981\pi\) | |||||||
\(954\) | −1887.29 | − | 2035.26i | −1.97829 | − | 2.13340i | ||||
\(955\) | 761.826 | + | 439.841i | 0.797724 | + | 0.460566i | ||||
\(956\) | −845.784 | + | 1464.94i | −0.884711 | + | 1.53236i | ||||
\(957\) | 302.248 | + | 45.6040i | 0.315829 | + | 0.0476531i | ||||
\(958\) | 2157.35 | 2.25193 | ||||||||
\(959\) | −262.709 | − | 591.049i | −0.273941 | − | 0.616318i | ||||
\(960\) | −1383.32 | − | 1103.51i | −1.44096 | − | 1.14949i | ||||
\(961\) | −356.667 | − | 617.766i | −0.371142 | − | 0.642836i | ||||
\(962\) | 226.667 | + | 130.866i | 0.235620 | + | 0.136035i | ||||
\(963\) | −39.0350 | + | 126.411i | −0.0405348 | + | 0.131268i | ||||
\(964\) | 866.276 | − | 500.144i | 0.898626 | − | 0.518822i | ||||
\(965\) | − | 1229.40i | − | 1.27399i | ||||||
\(966\) | −1639.81 | + | 1661.94i | −1.69753 | + | 1.72043i | ||||
\(967\) | 354.180i | 0.366267i | 0.983088 | + | 0.183134i | \(0.0586241\pi\) | ||||
−0.983088 | + | 0.183134i | \(0.941376\pi\) | |||||||
\(968\) | −719.675 | − | 1246.51i | −0.743466 | − | 1.28772i | ||||
\(969\) | −112.991 | + | 44.3258i | −0.116606 | + | 0.0457439i | ||||
\(970\) | −511.223 | − | 295.155i | −0.527034 | − | 0.304283i | ||||
\(971\) | 804.917 | − | 464.719i | 0.828957 | − | 0.478599i | −0.0245383 | − | 0.999699i | \(-0.507812\pi\) |
0.853495 | + | 0.521100i | \(0.174478\pi\) | |||||||
\(972\) | −1821.60 | − | 417.236i | −1.87407 | − | 0.429255i | ||||
\(973\) | 836.447 | − | 1149.76i | 0.859658 | − | 1.18166i | ||||
\(974\) | 1572.78i | 1.61476i | ||||||||
\(975\) | −192.841 | + | 1278.09i | −0.197786 | + | 1.31086i | ||||
\(976\) | 403.700 | − | 699.229i | 0.413627 | − | 0.716423i | ||||
\(977\) | −523.426 | + | 906.600i | −0.535748 | + | 0.927943i | 0.463379 | + | 0.886160i | \(0.346637\pi\) |
−0.999127 | + | 0.0417824i | \(0.986696\pi\) | |||||||
\(978\) | −2469.98 | − | 372.677i | −2.52555 | − | 0.381061i | ||||
\(979\) | 405.715 | 0.414418 | ||||||||
\(980\) | −884.505 | − | 2733.85i | −0.902556 | − | 2.78965i | ||||
\(981\) | −1268.69 | + | 289.162i | −1.29326 | + | 0.294762i | ||||
\(982\) | −1744.69 | + | 1007.30i | −1.77667 | + | 1.02576i | ||||
\(983\) | 439.404 | − | 761.070i | 0.447003 | − | 0.774232i | −0.551186 | − | 0.834382i | \(-0.685825\pi\) |
0.998189 | + | 0.0601503i | \(0.0191580\pi\) | |||||||
\(984\) | 1667.69 | − | 654.224i | 1.69480 | − | 0.664861i | ||||
\(985\) | 20.0712 | + | 34.7644i | 0.0203769 | + | 0.0352938i | ||||
\(986\) | −3637.36 | −3.68901 | ||||||||
\(987\) | 462.603 | − | 127.283i | 0.468696 | − | 0.128959i | ||||
\(988\) | 147.174i | 0.148962i | ||||||||
\(989\) | −357.364 | + | 206.324i | −0.361339 | + | 0.208619i | ||||
\(990\) | −590.139 | − | 182.232i | −0.596100 | − | 0.184073i | ||||
\(991\) | −257.036 | + | 445.199i | −0.259370 | + | 0.449242i | −0.966073 | − | 0.258268i | \(-0.916848\pi\) |
0.706703 | + | 0.707510i | \(0.250182\pi\) | |||||||
\(992\) | 110.945 | − | 64.0541i | 0.111840 | − | 0.0645706i | ||||
\(993\) | 92.5213 | − | 115.982i | 0.0931735 | − | 0.116799i | ||||
\(994\) | −2253.43 | − | 238.269i | −2.26703 | − | 0.239707i | ||||
\(995\) | −2295.14 | −2.30668 | ||||||||
\(996\) | 38.7573 | − | 256.871i | 0.0389129 | − | 0.257902i | ||||
\(997\) | 553.005 | − | 957.832i | 0.554669 | − | 0.960714i | −0.443261 | − | 0.896393i | \(-0.646178\pi\) |
0.997929 | − | 0.0643215i | \(-0.0204883\pi\) | |||||||
\(998\) | −742.578 | − | 428.728i | −0.744066 | − | 0.429587i | ||||
\(999\) | −11.8083 | − | 158.548i | −0.0118201 | − | 0.158707i |
(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 | 273.3.w.c.116.7 | yes | 16 | |
3.2 | odd | 2 | inner | 273.3.w.c.116.2 | yes | 16 | |
7.2 | even | 3 | inner | 273.3.w.c.233.8 | yes | 16 | |
13.12 | even | 2 | inner | 273.3.w.c.116.1 | ✓ | 16 | |
21.2 | odd | 6 | inner | 273.3.w.c.233.1 | yes | 16 | |
39.38 | odd | 2 | inner | 273.3.w.c.116.8 | yes | 16 | |
91.51 | even | 6 | inner | 273.3.w.c.233.2 | yes | 16 | |
273.233 | odd | 6 | inner | 273.3.w.c.233.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.3.w.c.116.1 | ✓ | 16 | 13.12 | even | 2 | inner | |
273.3.w.c.116.2 | yes | 16 | 3.2 | odd | 2 | inner | |
273.3.w.c.116.7 | yes | 16 | 1.1 | even | 1 | trivial | |
273.3.w.c.116.8 | yes | 16 | 39.38 | odd | 2 | inner | |
273.3.w.c.233.1 | yes | 16 | 21.2 | odd | 6 | inner | |
273.3.w.c.233.2 | yes | 16 | 91.51 | even | 6 | inner | |
273.3.w.c.233.7 | yes | 16 | 273.233 | odd | 6 | inner | |
273.3.w.c.233.8 | yes | 16 | 7.2 | even | 3 | inner |