Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (of order \(3\), 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: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 48x^{6} + 157x^{5} + 1944x^{4} + 3005x^{3} + 12895x^{2} - 11550x + 44100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 63.1 | ||
Root | \(3.81550 - 6.60864i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.63 |
Dual form | 74.4.c.a.47.1 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | −4.31550 | + | 7.47467i | −0.830519 | + | 1.43850i | 0.0671091 | + | 0.997746i | \(0.478622\pi\) |
−0.897628 | + | 0.440755i | \(0.854711\pi\) | |||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −2.90148 | + | 5.02551i | −0.259516 | + | 0.449495i | −0.966112 | − | 0.258122i | \(-0.916896\pi\) |
0.706596 | + | 0.707617i | \(0.250230\pi\) | |||||||
\(6\) | −17.2620 | −1.17453 | ||||||||
\(7\) | 8.58362 | − | 14.8673i | 0.463472 | − | 0.802756i | −0.535659 | − | 0.844434i | \(-0.679937\pi\) |
0.999131 | + | 0.0416776i | \(0.0132702\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.7471 | − | 41.1312i | −0.879522 | − | 1.52338i | ||||
\(10\) | −11.6059 | −0.367011 | ||||||||
\(11\) | 9.76027 | 0.267530 | 0.133765 | − | 0.991013i | \(-0.457293\pi\) | ||||
0.133765 | + | 0.991013i | \(0.457293\pi\) | |||||||
\(12\) | −17.2620 | − | 29.8987i | −0.415259 | − | 0.719250i | ||||
\(13\) | −32.6872 | + | 56.6158i | −0.697368 | + | 1.20788i | 0.272007 | + | 0.962295i | \(0.412312\pi\) |
−0.969376 | + | 0.245582i | \(0.921021\pi\) | |||||||
\(14\) | 34.3345 | 0.655448 | ||||||||
\(15\) | −25.0427 | − | 43.3752i | −0.431066 | − | 0.746628i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 12.0789 | + | 20.9213i | 0.172327 | + | 0.298480i | 0.939233 | − | 0.343280i | \(-0.111538\pi\) |
−0.766906 | + | 0.641760i | \(0.778205\pi\) | |||||||
\(18\) | 47.4942 | − | 82.2624i | 0.621916 | − | 1.07719i | ||||
\(19\) | −34.7123 | + | 60.1234i | −0.419134 | + | 0.725961i | −0.995853 | − | 0.0909820i | \(-0.970999\pi\) |
0.576719 | + | 0.816943i | \(0.304333\pi\) | |||||||
\(20\) | −11.6059 | − | 20.1020i | −0.129758 | − | 0.224748i | ||||
\(21\) | 74.0852 | + | 128.319i | 0.769844 | + | 1.33341i | ||||
\(22\) | 9.76027 | + | 16.9053i | 0.0945862 | + | 0.163828i | ||||
\(23\) | −68.4060 | −0.620158 | −0.310079 | − | 0.950711i | \(-0.600356\pi\) | ||||
−0.310079 | + | 0.950711i | \(0.600356\pi\) | |||||||
\(24\) | 34.5240 | − | 59.7973i | 0.293633 | − | 0.508587i | ||||
\(25\) | 45.6628 | + | 79.0904i | 0.365303 | + | 0.632723i | ||||
\(26\) | −130.749 | −0.986228 | ||||||||
\(27\) | 176.885 | 1.26080 | ||||||||
\(28\) | 34.3345 | + | 59.4690i | 0.231736 | + | 0.401378i | ||||
\(29\) | 229.161 | 1.46738 | 0.733691 | − | 0.679483i | \(-0.237796\pi\) | ||||
0.733691 | + | 0.679483i | \(0.237796\pi\) | |||||||
\(30\) | 50.0853 | − | 86.7503i | 0.304810 | − | 0.527946i | ||||
\(31\) | −271.380 | −1.57230 | −0.786149 | − | 0.618036i | \(-0.787928\pi\) | ||||
−0.786149 | + | 0.618036i | \(0.787928\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −42.1205 | + | 72.9548i | −0.222189 | + | 0.384842i | ||||
\(34\) | −24.1578 | + | 41.8426i | −0.121854 | + | 0.211057i | ||||
\(35\) | 49.8103 | + | 86.2740i | 0.240557 | + | 0.416656i | ||||
\(36\) | 189.977 | 0.879522 | ||||||||
\(37\) | 207.031 | − | 88.2672i | 0.919884 | − | 0.392190i | ||||
\(38\) | −138.849 | −0.592744 | ||||||||
\(39\) | −282.123 | − | 488.651i | −1.15835 | − | 2.00633i | ||||
\(40\) | 23.2118 | − | 40.2041i | 0.0917528 | − | 0.158920i | ||||
\(41\) | −121.151 | + | 209.839i | −0.461477 | + | 0.799301i | −0.999035 | − | 0.0439258i | \(-0.986013\pi\) |
0.537558 | + | 0.843227i | \(0.319347\pi\) | |||||||
\(42\) | −148.170 | + | 256.639i | −0.544362 | + | 0.942862i | ||||
\(43\) | 189.254 | 0.671185 | 0.335593 | − | 0.942007i | \(-0.391063\pi\) | ||||
0.335593 | + | 0.942007i | \(0.391063\pi\) | |||||||
\(44\) | −19.5205 | + | 33.8106i | −0.0668826 | + | 0.115844i | ||||
\(45\) | 275.607 | 0.913001 | ||||||||
\(46\) | −68.4060 | − | 118.483i | −0.219259 | − | 0.379768i | ||||
\(47\) | 506.929 | 1.57326 | 0.786630 | − | 0.617424i | \(-0.211824\pi\) | ||||
0.786630 | + | 0.617424i | \(0.211824\pi\) | |||||||
\(48\) | 138.096 | 0.415259 | ||||||||
\(49\) | 24.1431 | + | 41.8171i | 0.0703880 | + | 0.121916i | ||||
\(50\) | −91.3257 | + | 158.181i | −0.258308 | + | 0.447403i | ||||
\(51\) | −208.506 | −0.572484 | ||||||||
\(52\) | −130.749 | − | 226.463i | −0.348684 | − | 0.603939i | ||||
\(53\) | 183.223 | + | 317.352i | 0.474862 | + | 0.822485i | 0.999586 | − | 0.0287878i | \(-0.00916471\pi\) |
−0.524724 | + | 0.851273i | \(0.675831\pi\) | |||||||
\(54\) | 176.885 | + | 306.375i | 0.445760 | + | 0.772080i | ||||
\(55\) | −28.3192 | + | 49.0503i | −0.0694284 | + | 0.120254i | ||||
\(56\) | −68.6689 | + | 118.938i | −0.163862 | + | 0.283817i | ||||
\(57\) | −299.602 | − | 518.925i | −0.696196 | − | 1.20585i | ||||
\(58\) | 229.161 | + | 396.918i | 0.518798 | + | 0.898584i | ||||
\(59\) | −444.496 | − | 769.890i | −0.980822 | − | 1.69883i | −0.659206 | − | 0.751963i | \(-0.729107\pi\) |
−0.321616 | − | 0.946870i | \(-0.604226\pi\) | |||||||
\(60\) | 200.341 | 0.431066 | ||||||||
\(61\) | −303.061 | + | 524.918i | −0.636115 | + | 1.10178i | 0.350163 | + | 0.936689i | \(0.386126\pi\) |
−0.986278 | + | 0.165095i | \(0.947207\pi\) | |||||||
\(62\) | −271.380 | − | 470.044i | −0.555892 | − | 0.962832i | ||||
\(63\) | −815.344 | −1.63053 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −189.682 | − | 328.539i | −0.361957 | − | 0.626927i | ||||
\(66\) | −168.482 | −0.314223 | ||||||||
\(67\) | −125.813 | + | 217.914i | −0.229410 | + | 0.397349i | −0.957633 | − | 0.287990i | \(-0.907013\pi\) |
0.728224 | + | 0.685340i | \(0.240346\pi\) | |||||||
\(68\) | −96.6313 | −0.172327 | ||||||||
\(69\) | 295.206 | − | 511.312i | 0.515053 | − | 0.892098i | ||||
\(70\) | −99.6207 | + | 172.548i | −0.170099 | + | 0.294621i | ||||
\(71\) | 356.160 | − | 616.887i | 0.595329 | − | 1.03114i | −0.398171 | − | 0.917311i | \(-0.630355\pi\) |
0.993500 | − | 0.113829i | \(-0.0363116\pi\) | |||||||
\(72\) | 189.977 | + | 329.049i | 0.310958 | + | 0.538595i | ||||
\(73\) | −87.8669 | −0.140877 | −0.0704387 | − | 0.997516i | \(-0.522440\pi\) | ||||
−0.0704387 | + | 0.997516i | \(0.522440\pi\) | |||||||
\(74\) | 359.914 | + | 270.321i | 0.565395 | + | 0.424652i | ||||
\(75\) | −788.232 | −1.21356 | ||||||||
\(76\) | −138.849 | − | 240.494i | −0.209567 | − | 0.362980i | ||||
\(77\) | 83.7784 | − | 145.109i | 0.123993 | − | 0.214762i | ||||
\(78\) | 564.246 | − | 977.303i | 0.819080 | − | 1.41869i | ||||
\(79\) | −216.786 | + | 375.485i | −0.308739 | + | 0.534751i | −0.978087 | − | 0.208198i | \(-0.933240\pi\) |
0.669348 | + | 0.742949i | \(0.266574\pi\) | |||||||
\(80\) | 92.8473 | 0.129758 | ||||||||
\(81\) | −122.178 | + | 211.618i | −0.167596 | + | 0.290285i | ||||
\(82\) | −484.602 | −0.652626 | ||||||||
\(83\) | 455.726 | + | 789.341i | 0.602680 | + | 1.04387i | 0.992413 | + | 0.122945i | \(0.0392339\pi\) |
−0.389733 | + | 0.920928i | \(0.627433\pi\) | |||||||
\(84\) | −592.682 | −0.769844 | ||||||||
\(85\) | −140.187 | −0.178887 | ||||||||
\(86\) | 189.254 | + | 327.798i | 0.237300 | + | 0.411015i | ||||
\(87\) | −988.943 | + | 1712.90i | −1.21869 | + | 2.11083i | ||||
\(88\) | −78.0822 | −0.0945862 | ||||||||
\(89\) | −370.719 | − | 642.105i | −0.441530 | − | 0.764752i | 0.556273 | − | 0.830999i | \(-0.312231\pi\) |
−0.997803 | + | 0.0662470i | \(0.978897\pi\) | |||||||
\(90\) | 275.607 | + | 477.365i | 0.322794 | + | 0.559096i | ||||
\(91\) | 561.148 | + | 971.937i | 0.646421 | + | 1.11963i | ||||
\(92\) | 136.812 | − | 236.965i | 0.155040 | − | 0.268536i | ||||
\(93\) | 1171.14 | − | 2028.47i | 1.30582 | − | 2.26175i | ||||
\(94\) | 506.929 | + | 878.027i | 0.556232 | + | 0.963421i | ||||
\(95\) | −201.434 | − | 348.893i | −0.217544 | − | 0.376797i | ||||
\(96\) | 138.096 | + | 239.189i | 0.146816 | + | 0.254293i | ||||
\(97\) | 1383.10 | 1.44775 | 0.723877 | − | 0.689929i | \(-0.242358\pi\) | ||||
0.723877 | + | 0.689929i | \(0.242358\pi\) | |||||||
\(98\) | −48.2862 | + | 83.6341i | −0.0497719 | + | 0.0862074i | ||||
\(99\) | −231.778 | − | 401.452i | −0.235299 | − | 0.407550i | ||||
\(100\) | −365.303 | −0.365303 | ||||||||
\(101\) | 1171.73 | 1.15437 | 0.577186 | − | 0.816613i | \(-0.304151\pi\) | ||||
0.577186 | + | 0.816613i | \(0.304151\pi\) | |||||||
\(102\) | −208.506 | − | 361.143i | −0.202404 | − | 0.350574i | ||||
\(103\) | 1351.30 | 1.29270 | 0.646349 | − | 0.763042i | \(-0.276295\pi\) | ||||
0.646349 | + | 0.763042i | \(0.276295\pi\) | |||||||
\(104\) | 261.497 | − | 452.927i | 0.246557 | − | 0.427049i | ||||
\(105\) | −859.826 | −0.799147 | ||||||||
\(106\) | −366.447 | + | 634.705i | −0.335778 | + | 0.581585i | ||||
\(107\) | 711.235 | − | 1231.89i | 0.642595 | − | 1.11301i | −0.342257 | − | 0.939607i | \(-0.611191\pi\) |
0.984851 | − | 0.173400i | \(-0.0554754\pi\) | |||||||
\(108\) | −353.771 | + | 612.749i | −0.315200 | + | 0.545943i | ||||
\(109\) | 929.141 | + | 1609.32i | 0.816473 | + | 1.41417i | 0.908266 | + | 0.418394i | \(0.137407\pi\) |
−0.0917929 | + | 0.995778i | \(0.529260\pi\) | |||||||
\(110\) | −113.277 | −0.0981866 | ||||||||
\(111\) | −233.676 | + | 1928.41i | −0.199815 | + | 1.64897i | ||||
\(112\) | −274.676 | −0.231736 | ||||||||
\(113\) | −351.085 | − | 608.097i | −0.292277 | − | 0.506238i | 0.682071 | − | 0.731286i | \(-0.261080\pi\) |
−0.974348 | + | 0.225048i | \(0.927746\pi\) | |||||||
\(114\) | 599.203 | − | 1037.85i | 0.492285 | − | 0.852663i | ||||
\(115\) | 198.479 | − | 343.775i | 0.160941 | − | 0.278758i | ||||
\(116\) | −458.321 | + | 793.836i | −0.366846 | + | 0.635395i | ||||
\(117\) | 3104.90 | 2.45340 | ||||||||
\(118\) | 888.992 | − | 1539.78i | 0.693546 | − | 1.20126i | ||||
\(119\) | 414.723 | 0.319476 | ||||||||
\(120\) | 200.341 | + | 347.001i | 0.152405 | + | 0.263973i | ||||
\(121\) | −1235.74 | −0.928428 | ||||||||
\(122\) | −1212.25 | −0.899603 | ||||||||
\(123\) | −1045.65 | − | 1811.12i | −0.766530 | − | 1.32767i | ||||
\(124\) | 542.760 | − | 940.087i | 0.393075 | − | 0.680825i | ||||
\(125\) | −1255.33 | −0.898240 | ||||||||
\(126\) | −815.344 | − | 1412.22i | −0.576481 | − | 0.998494i | ||||
\(127\) | −859.202 | − | 1488.18i | −0.600329 | − | 1.03980i | −0.992771 | − | 0.120024i | \(-0.961703\pi\) |
0.392442 | − | 0.919777i | \(-0.371631\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −816.726 | + | 1414.61i | −0.557432 | + | 0.965500i | ||||
\(130\) | 379.364 | − | 657.078i | 0.255942 | − | 0.443305i | ||||
\(131\) | −96.2362 | − | 166.686i | −0.0641847 | − | 0.111171i | 0.832147 | − | 0.554555i | \(-0.187111\pi\) |
−0.896332 | + | 0.443383i | \(0.853778\pi\) | |||||||
\(132\) | −168.482 | − | 291.819i | −0.111094 | − | 0.192421i | ||||
\(133\) | 595.913 | + | 1032.15i | 0.388513 | + | 0.672924i | ||||
\(134\) | −503.250 | −0.324434 | ||||||||
\(135\) | −513.229 | + | 888.939i | −0.327198 | + | 0.566724i | ||||
\(136\) | −96.6313 | − | 167.370i | −0.0609269 | − | 0.105529i | ||||
\(137\) | 92.2200 | 0.0575101 | 0.0287551 | − | 0.999586i | \(-0.490846\pi\) | ||||
0.0287551 | + | 0.999586i | \(0.490846\pi\) | |||||||
\(138\) | 1180.82 | 0.728395 | ||||||||
\(139\) | 311.822 | + | 540.091i | 0.190276 | + | 0.329568i | 0.945342 | − | 0.326081i | \(-0.105728\pi\) |
−0.755066 | + | 0.655649i | \(0.772395\pi\) | |||||||
\(140\) | −398.483 | −0.240557 | ||||||||
\(141\) | −2187.65 | + | 3789.13i | −1.30662 | + | 2.26314i | ||||
\(142\) | 1424.64 | 0.841922 | ||||||||
\(143\) | −319.036 | + | 552.586i | −0.186567 | + | 0.323144i | ||||
\(144\) | −379.954 | + | 658.099i | −0.219881 | + | 0.380844i | ||||
\(145\) | −664.905 | + | 1151.65i | −0.380809 | + | 0.659581i | ||||
\(146\) | −87.8669 | − | 152.190i | −0.0498077 | − | 0.0862694i | ||||
\(147\) | −416.758 | −0.233834 | ||||||||
\(148\) | −108.296 | + | 893.711i | −0.0601478 | + | 0.496369i | ||||
\(149\) | 58.8320 | 0.0323470 | 0.0161735 | − | 0.999869i | \(-0.494852\pi\) | ||||
0.0161735 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(150\) | −788.232 | − | 1365.26i | −0.429059 | − | 0.743153i | ||||
\(151\) | −757.096 | + | 1311.33i | −0.408024 | + | 0.706718i | −0.994668 | − | 0.103127i | \(-0.967115\pi\) |
0.586644 | + | 0.809845i | \(0.300449\pi\) | |||||||
\(152\) | 277.698 | − | 480.987i | 0.148186 | − | 0.256666i | ||||
\(153\) | 573.678 | − | 993.640i | 0.303132 | − | 0.525039i | ||||
\(154\) | 335.114 | 0.175352 | ||||||||
\(155\) | 787.403 | − | 1363.82i | 0.408037 | − | 0.706741i | ||||
\(156\) | 2256.98 | 1.15835 | ||||||||
\(157\) | 569.365 | + | 986.169i | 0.289428 | + | 0.501305i | 0.973673 | − | 0.227947i | \(-0.0732015\pi\) |
−0.684245 | + | 0.729252i | \(0.739868\pi\) | |||||||
\(158\) | −867.145 | −0.436622 | ||||||||
\(159\) | −3162.80 | −1.57753 | ||||||||
\(160\) | 92.8473 | + | 160.816i | 0.0458764 | + | 0.0794602i | ||||
\(161\) | −587.171 | + | 1017.01i | −0.287426 | + | 0.497836i | ||||
\(162\) | −488.711 | −0.237017 | ||||||||
\(163\) | −879.922 | − | 1524.07i | −0.422827 | − | 0.732358i | 0.573388 | − | 0.819284i | \(-0.305629\pi\) |
−0.996215 | + | 0.0869262i | \(0.972296\pi\) | |||||||
\(164\) | −484.602 | − | 839.356i | −0.230738 | − | 0.399650i | ||||
\(165\) | −244.423 | − | 423.354i | −0.115323 | − | 0.199746i | ||||
\(166\) | −911.453 | + | 1578.68i | −0.426159 | + | 0.738130i | ||||
\(167\) | 44.9020 | − | 77.7726i | 0.0208061 | − | 0.0360373i | −0.855435 | − | 0.517910i | \(-0.826710\pi\) |
0.876241 | + | 0.481873i | \(0.160043\pi\) | |||||||
\(168\) | −592.682 | − | 1026.55i | −0.272181 | − | 0.471431i | ||||
\(169\) | −1038.40 | − | 1798.56i | −0.472645 | − | 0.818646i | ||||
\(170\) | −140.187 | − | 242.811i | −0.0632461 | − | 0.109545i | ||||
\(171\) | 3297.26 | 1.47455 | ||||||||
\(172\) | −378.508 | + | 655.595i | −0.167796 | + | 0.290632i | ||||
\(173\) | −1894.94 | − | 3282.13i | −0.832773 | − | 1.44241i | −0.895831 | − | 0.444395i | \(-0.853419\pi\) |
0.0630579 | − | 0.998010i | \(-0.479915\pi\) | |||||||
\(174\) | −3955.77 | −1.72349 | ||||||||
\(175\) | 1567.81 | 0.677230 | ||||||||
\(176\) | −78.0822 | − | 135.242i | −0.0334413 | − | 0.0579220i | ||||
\(177\) | 7672.90 | 3.25836 | ||||||||
\(178\) | 741.439 | − | 1284.21i | 0.312209 | − | 0.540762i | ||||
\(179\) | −3592.46 | −1.50007 | −0.750036 | − | 0.661398i | \(-0.769964\pi\) | ||||
−0.750036 | + | 0.661398i | \(0.769964\pi\) | |||||||
\(180\) | −551.213 | + | 954.730i | −0.228250 | + | 0.395341i | ||||
\(181\) | 148.612 | − | 257.403i | 0.0610289 | − | 0.105705i | −0.833897 | − | 0.551921i | \(-0.813895\pi\) |
0.894926 | + | 0.446215i | \(0.147228\pi\) | |||||||
\(182\) | −1122.30 | + | 1943.87i | −0.457089 | + | 0.791701i | ||||
\(183\) | −2615.72 | − | 4530.56i | −1.05661 | − | 1.83010i | ||||
\(184\) | 547.248 | 0.219259 | ||||||||
\(185\) | −157.109 | + | 1296.54i | −0.0624373 | + | 0.515263i | ||||
\(186\) | 4684.56 | 1.84671 | ||||||||
\(187\) | 117.893 | + | 204.197i | 0.0461028 | + | 0.0798524i | ||||
\(188\) | −1013.86 | + | 1756.05i | −0.393315 | + | 0.681242i | ||||
\(189\) | 1518.32 | − | 2629.80i | 0.584345 | − | 1.01212i | ||||
\(190\) | 402.867 | − | 697.787i | 0.153827 | − | 0.266436i | ||||
\(191\) | 2865.50 | 1.08555 | 0.542775 | − | 0.839878i | \(-0.317374\pi\) | ||||
0.542775 | + | 0.839878i | \(0.317374\pi\) | |||||||
\(192\) | −276.192 | + | 478.379i | −0.103815 | + | 0.179813i | ||||
\(193\) | −4810.44 | −1.79411 | −0.897054 | − | 0.441921i | \(-0.854297\pi\) | ||||
−0.897054 | + | 0.441921i | \(0.854297\pi\) | |||||||
\(194\) | 1383.10 | + | 2395.59i | 0.511858 | + | 0.886565i | ||||
\(195\) | 3274.29 | 1.20245 | ||||||||
\(196\) | −193.145 | −0.0703880 | ||||||||
\(197\) | 212.593 | + | 368.221i | 0.0768863 | + | 0.133171i | 0.901905 | − | 0.431934i | \(-0.142169\pi\) |
−0.825019 | + | 0.565105i | \(0.808836\pi\) | |||||||
\(198\) | 463.556 | − | 802.903i | 0.166381 | − | 0.288181i | ||||
\(199\) | −243.177 | −0.0866248 | −0.0433124 | − | 0.999062i | \(-0.513791\pi\) | ||||
−0.0433124 | + | 0.999062i | \(0.513791\pi\) | |||||||
\(200\) | −365.303 | − | 632.723i | −0.129154 | − | 0.223701i | ||||
\(201\) | −1085.89 | − | 1880.81i | −0.381058 | − | 0.660012i | ||||
\(202\) | 1171.73 | + | 2029.50i | 0.408132 | + | 0.706905i | ||||
\(203\) | 1967.03 | − | 3406.99i | 0.680090 | − | 1.17795i | ||||
\(204\) | 417.012 | − | 722.287i | 0.143121 | − | 0.247893i | ||||
\(205\) | −703.031 | − | 1217.69i | −0.239521 | − | 0.414863i | ||||
\(206\) | 1351.30 | + | 2340.53i | 0.457038 | + | 0.791613i | ||||
\(207\) | 1624.44 | + | 2813.62i | 0.545443 | + | 0.944735i | ||||
\(208\) | 1045.99 | 0.348684 | ||||||||
\(209\) | −338.801 | + | 586.821i | −0.112131 | + | 0.194216i | ||||
\(210\) | −859.826 | − | 1489.26i | −0.282541 | − | 0.489376i | ||||
\(211\) | 1994.72 | 0.650817 | 0.325409 | − | 0.945573i | \(-0.394498\pi\) | ||||
0.325409 | + | 0.945573i | \(0.394498\pi\) | |||||||
\(212\) | −1465.79 | −0.474862 | ||||||||
\(213\) | 3074.01 | + | 5324.35i | 0.988864 | + | 1.71276i | ||||
\(214\) | 2844.94 | 0.908766 | ||||||||
\(215\) | −549.117 | + | 951.098i | −0.174183 | + | 0.301695i | ||||
\(216\) | −1415.08 | −0.445760 | ||||||||
\(217\) | −2329.42 | + | 4034.67i | −0.728716 | + | 1.26217i | ||||
\(218\) | −1858.28 | + | 3218.64i | −0.577333 | + | 0.999971i | ||||
\(219\) | 379.190 | − | 656.776i | 0.117001 | − | 0.202652i | ||||
\(220\) | −113.277 | − | 196.201i | −0.0347142 | − | 0.0601268i | ||||
\(221\) | −1579.30 | −0.480703 | ||||||||
\(222\) | −3573.77 | + | 1523.67i | −1.08043 | + | 0.460639i | ||||
\(223\) | 88.6288 | 0.0266145 | 0.0133072 | − | 0.999911i | \(-0.495764\pi\) | ||||
0.0133072 | + | 0.999911i | \(0.495764\pi\) | |||||||
\(224\) | −274.676 | − | 475.752i | −0.0819310 | − | 0.141909i | ||||
\(225\) | 2168.72 | − | 3756.33i | 0.642584 | − | 1.11299i | ||||
\(226\) | 702.170 | − | 1216.19i | 0.206671 | − | 0.357965i | ||||
\(227\) | −2024.37 | + | 3506.31i | −0.591903 | + | 1.02521i | 0.402073 | + | 0.915608i | \(0.368290\pi\) |
−0.993976 | + | 0.109599i | \(0.965043\pi\) | |||||||
\(228\) | 2396.81 | 0.696196 | ||||||||
\(229\) | −1795.58 | + | 3110.04i | −0.518145 | + | 0.897454i | 0.481632 | + | 0.876373i | \(0.340044\pi\) |
−0.999778 | + | 0.0210808i | \(0.993289\pi\) | |||||||
\(230\) | 793.914 | 0.227605 | ||||||||
\(231\) | 723.092 | + | 1252.43i | 0.205957 | + | 0.356727i | ||||
\(232\) | −1833.29 | −0.518798 | ||||||||
\(233\) | 6048.01 | 1.70051 | 0.850253 | − | 0.526374i | \(-0.176449\pi\) | ||||
0.850253 | + | 0.526374i | \(0.176449\pi\) | |||||||
\(234\) | 3104.90 | + | 5377.85i | 0.867409 | + | 1.50240i | ||||
\(235\) | −1470.84 | + | 2547.58i | −0.408286 | + | 0.707173i | ||||
\(236\) | 3555.97 | 0.980822 | ||||||||
\(237\) | −1871.08 | − | 3240.81i | −0.512826 | − | 0.888241i | ||||
\(238\) | 414.723 | + | 718.321i | 0.112952 | + | 0.195638i | ||||
\(239\) | −96.0036 | − | 166.283i | −0.0259831 | − | 0.0450040i | 0.852741 | − | 0.522333i | \(-0.174938\pi\) |
−0.878725 | + | 0.477329i | \(0.841605\pi\) | |||||||
\(240\) | −400.683 | + | 694.003i | −0.107766 | + | 0.186657i | ||||
\(241\) | 632.495 | − | 1095.51i | 0.169056 | − | 0.292814i | −0.769032 | − | 0.639210i | \(-0.779261\pi\) |
0.938088 | + | 0.346396i | \(0.112595\pi\) | |||||||
\(242\) | −1235.74 | − | 2140.36i | −0.328249 | − | 0.568543i | ||||
\(243\) | 1333.44 | + | 2309.58i | 0.352017 | + | 0.609711i | ||||
\(244\) | −1212.25 | − | 2099.67i | −0.318058 | − | 0.550892i | ||||
\(245\) | −280.203 | −0.0730673 | ||||||||
\(246\) | 2091.30 | − | 3622.24i | 0.542018 | − | 0.938803i | ||||
\(247\) | −2269.29 | − | 3930.53i | −0.584581 | − | 1.01252i | ||||
\(248\) | 2171.04 | 0.555892 | ||||||||
\(249\) | −7866.75 | −2.00215 | ||||||||
\(250\) | −1255.33 | − | 2174.29i | −0.317576 | − | 0.550057i | ||||
\(251\) | 3414.91 | 0.858754 | 0.429377 | − | 0.903125i | \(-0.358733\pi\) | ||||
0.429377 | + | 0.903125i | \(0.358733\pi\) | |||||||
\(252\) | 1630.69 | − | 2824.43i | 0.407634 | − | 0.706042i | ||||
\(253\) | −667.662 | −0.165911 | ||||||||
\(254\) | 1718.40 | − | 2976.36i | 0.424497 | − | 0.735250i | ||||
\(255\) | 604.976 | − | 1047.85i | 0.148569 | − | 0.257329i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −512.189 | − | 887.138i | −0.124317 | − | 0.215323i | 0.797149 | − | 0.603783i | \(-0.206341\pi\) |
−0.921466 | + | 0.388460i | \(0.873007\pi\) | |||||||
\(258\) | −3266.90 | −0.788328 | ||||||||
\(259\) | 464.786 | − | 3835.64i | 0.111507 | − | 0.920212i | ||||
\(260\) | 1517.46 | 0.361957 | ||||||||
\(261\) | −5441.90 | − | 9425.65i | −1.29060 | − | 2.23538i | ||||
\(262\) | 192.472 | − | 333.372i | 0.0453854 | − | 0.0786099i | ||||
\(263\) | −693.678 | + | 1201.49i | −0.162639 | + | 0.281699i | −0.935814 | − | 0.352493i | \(-0.885334\pi\) |
0.773175 | + | 0.634192i | \(0.218667\pi\) | |||||||
\(264\) | 336.964 | − | 583.638i | 0.0785556 | − | 0.136062i | ||||
\(265\) | −2126.48 | −0.492937 | ||||||||
\(266\) | −1191.83 | + | 2064.30i | −0.274720 | + | 0.475829i | ||||
\(267\) | 6399.36 | 1.46680 | ||||||||
\(268\) | −503.250 | − | 871.655i | −0.114705 | − | 0.198675i | ||||
\(269\) | −2176.91 | −0.493415 | −0.246708 | − | 0.969090i | \(-0.579349\pi\) | ||||
−0.246708 | + | 0.969090i | \(0.579349\pi\) | |||||||
\(270\) | −2052.92 | −0.462728 | ||||||||
\(271\) | −2806.93 | − | 4861.75i | −0.629184 | − | 1.08978i | −0.987716 | − | 0.156261i | \(-0.950056\pi\) |
0.358532 | − | 0.933518i | \(-0.383278\pi\) | |||||||
\(272\) | 193.263 | − | 334.741i | 0.0430819 | − | 0.0746200i | ||||
\(273\) | −9686.54 | −2.14746 | ||||||||
\(274\) | 92.2200 | + | 159.730i | 0.0203329 | + | 0.0352176i | ||||
\(275\) | 445.682 | + | 771.944i | 0.0977296 | + | 0.169273i | ||||
\(276\) | 1180.82 | + | 2045.25i | 0.257526 | + | 0.446049i | ||||
\(277\) | −857.615 | + | 1485.43i | −0.186026 | + | 0.322206i | −0.943922 | − | 0.330170i | \(-0.892894\pi\) |
0.757896 | + | 0.652375i | \(0.226227\pi\) | |||||||
\(278\) | −623.644 | + | 1080.18i | −0.134546 | + | 0.233040i | ||||
\(279\) | 6444.48 | + | 11162.2i | 1.38287 | + | 2.39520i | ||||
\(280\) | −398.483 | − | 690.192i | −0.0850496 | − | 0.147310i | ||||
\(281\) | 1966.75 | + | 3406.51i | 0.417531 | + | 0.723185i | 0.995690 | − | 0.0927386i | \(-0.0295621\pi\) |
−0.578159 | + | 0.815924i | \(0.696229\pi\) | |||||||
\(282\) | −8750.62 | −1.84784 | ||||||||
\(283\) | 2183.88 | − | 3782.59i | 0.458721 | − | 0.794528i | −0.540173 | − | 0.841554i | \(-0.681641\pi\) |
0.998894 | + | 0.0470263i | \(0.0149744\pi\) | |||||||
\(284\) | 1424.64 | + | 2467.55i | 0.297665 | + | 0.515570i | ||||
\(285\) | 3477.15 | 0.722697 | ||||||||
\(286\) | −1276.14 | −0.263846 | ||||||||
\(287\) | 2079.82 | + | 3602.35i | 0.427763 | + | 0.740907i | ||||
\(288\) | −1519.81 | −0.310958 | ||||||||
\(289\) | 2164.70 | − | 3749.37i | 0.440607 | − | 0.763153i | ||||
\(290\) | −2659.62 | −0.538546 | ||||||||
\(291\) | −5968.75 | + | 10338.2i | −1.20239 | + | 2.08259i | ||||
\(292\) | 175.734 | − | 304.380i | 0.0352193 | − | 0.0610017i | ||||
\(293\) | 4265.97 | − | 7388.89i | 0.850583 | − | 1.47325i | −0.0300994 | − | 0.999547i | \(-0.509582\pi\) |
0.880683 | − | 0.473707i | \(-0.157084\pi\) | |||||||
\(294\) | −416.758 | − | 721.846i | −0.0826729 | − | 0.143194i | ||||
\(295\) | 5158.78 | 1.01816 | ||||||||
\(296\) | −1656.25 | + | 706.137i | −0.325228 | + | 0.138660i | ||||
\(297\) | 1726.45 | 0.337302 | ||||||||
\(298\) | 58.8320 | + | 101.900i | 0.0114364 | + | 0.0198084i | ||||
\(299\) | 2236.00 | − | 3872.86i | 0.432479 | − | 0.749075i | ||||
\(300\) | 1576.46 | − | 2730.52i | 0.303391 | − | 0.525488i | ||||
\(301\) | 1624.48 | − | 2813.69i | 0.311075 | − | 0.538798i | ||||
\(302\) | −3028.38 | −0.577033 | ||||||||
\(303\) | −5056.60 | + | 8758.30i | −0.958727 | + | 1.66056i | ||||
\(304\) | 1110.79 | 0.209567 | ||||||||
\(305\) | −1758.65 | − | 3046.07i | −0.330164 | − | 0.571861i | ||||
\(306\) | 2294.71 | 0.428693 | ||||||||
\(307\) | −2528.60 | −0.470081 | −0.235041 | − | 0.971986i | \(-0.575522\pi\) | ||||
−0.235041 | + | 0.971986i | \(0.575522\pi\) | |||||||
\(308\) | 335.114 | + | 580.434i | 0.0619964 | + | 0.107381i | ||||
\(309\) | −5831.55 | + | 10100.5i | −1.07361 | + | 1.85955i | ||||
\(310\) | 3149.61 | 0.577051 | ||||||||
\(311\) | 3170.22 | + | 5490.98i | 0.578028 | + | 1.00117i | 0.995705 | + | 0.0925779i | \(0.0295107\pi\) |
−0.417678 | + | 0.908595i | \(0.637156\pi\) | |||||||
\(312\) | 2256.98 | + | 3909.21i | 0.409540 | + | 0.709344i | ||||
\(313\) | −1270.57 | − | 2200.70i | −0.229448 | − | 0.397415i | 0.728197 | − | 0.685368i | \(-0.240359\pi\) |
−0.957645 | + | 0.287953i | \(0.907025\pi\) | |||||||
\(314\) | −1138.73 | + | 1972.34i | −0.204657 | + | 0.354476i | ||||
\(315\) | 2365.70 | − | 4097.52i | 0.423150 | − | 0.732917i | ||||
\(316\) | −867.145 | − | 1501.94i | −0.154369 | − | 0.267376i | ||||
\(317\) | 1346.25 | + | 2331.77i | 0.238526 | + | 0.413140i | 0.960292 | − | 0.278998i | \(-0.0900024\pi\) |
−0.721765 | + | 0.692138i | \(0.756669\pi\) | |||||||
\(318\) | −3162.80 | − | 5478.14i | −0.557740 | − | 0.966034i | ||||
\(319\) | 2236.67 | 0.392569 | ||||||||
\(320\) | −185.695 | + | 321.632i | −0.0324395 | + | 0.0561869i | ||||
\(321\) | 6138.67 | + | 10632.5i | 1.06737 | + | 1.84875i | ||||
\(322\) | −2348.68 | −0.406481 | ||||||||
\(323\) | −1677.14 | −0.288913 | ||||||||
\(324\) | −488.711 | − | 846.471i | −0.0837981 | − | 0.145143i | ||||
\(325\) | −5970.36 | −1.01900 | ||||||||
\(326\) | 1759.84 | − | 3048.14i | 0.298984 | − | 0.517855i | ||||
\(327\) | −16038.8 | −2.71238 | ||||||||
\(328\) | 969.204 | − | 1678.71i | 0.163157 | − | 0.282596i | ||||
\(329\) | 4351.29 | − | 7536.65i | 0.729162 | − | 1.26295i | ||||
\(330\) | 488.847 | − | 846.707i | 0.0815458 | − | 0.141241i | ||||
\(331\) | −2620.44 | − | 4538.73i | −0.435143 | − | 0.753689i | 0.562165 | − | 0.827025i | \(-0.309969\pi\) |
−0.997307 | + | 0.0733361i | \(0.976635\pi\) | |||||||
\(332\) | −3645.81 | −0.602680 | ||||||||
\(333\) | −8546.92 | − | 6419.35i | −1.40651 | − | 1.05639i | ||||
\(334\) | 179.608 | 0.0294243 | ||||||||
\(335\) | −730.085 | − | 1264.54i | −0.119071 | − | 0.206237i | ||||
\(336\) | 1185.36 | − | 2053.11i | 0.192461 | − | 0.333352i | ||||
\(337\) | 4870.76 | − | 8436.41i | 0.787322 | − | 1.36368i | −0.140280 | − | 0.990112i | \(-0.544800\pi\) |
0.927602 | − | 0.373570i | \(-0.121866\pi\) | |||||||
\(338\) | 2076.80 | − | 3597.13i | 0.334211 | − | 0.578870i | ||||
\(339\) | 6060.43 | 0.970965 | ||||||||
\(340\) | 280.374 | − | 485.621i | 0.0447217 | − | 0.0774603i | ||||
\(341\) | −2648.74 | −0.420638 | ||||||||
\(342\) | 3297.26 | + | 5711.02i | 0.521332 | + | 0.902973i | ||||
\(343\) | 6717.30 | 1.05743 | ||||||||
\(344\) | −1514.03 | −0.237300 | ||||||||
\(345\) | 1713.07 | + | 2967.12i | 0.267329 | + | 0.463028i | ||||
\(346\) | 3789.88 | − | 6564.27i | 0.588859 | − | 1.01993i | ||||
\(347\) | 8864.95 | 1.37146 | 0.685728 | − | 0.727858i | \(-0.259484\pi\) | ||||
0.685728 | + | 0.727858i | \(0.259484\pi\) | |||||||
\(348\) | −3955.77 | − | 6851.60i | −0.609344 | − | 1.05541i | ||||
\(349\) | 297.082 | + | 514.561i | 0.0455657 | + | 0.0789221i | 0.887909 | − | 0.460020i | \(-0.152158\pi\) |
−0.842343 | + | 0.538942i | \(0.818824\pi\) | |||||||
\(350\) | 1567.81 | + | 2715.53i | 0.239437 | + | 0.414717i | ||||
\(351\) | −5781.88 | + | 10014.5i | −0.879242 | + | 1.52289i | ||||
\(352\) | 156.164 | − | 270.485i | 0.0236466 | − | 0.0409570i | ||||
\(353\) | 1504.59 | + | 2606.02i | 0.226859 | + | 0.392931i | 0.956875 | − | 0.290498i | \(-0.0938211\pi\) |
−0.730017 | + | 0.683429i | \(0.760488\pi\) | |||||||
\(354\) | 7672.90 | + | 13289.8i | 1.15201 | + | 1.99533i | ||||
\(355\) | 2066.78 | + | 3579.77i | 0.308995 | + | 0.535195i | ||||
\(356\) | 2965.75 | 0.441530 | ||||||||
\(357\) | −1789.74 | + | 3099.92i | −0.265330 | + | 0.459566i | ||||
\(358\) | −3592.46 | − | 6222.32i | −0.530355 | − | 0.918602i | ||||
\(359\) | 2508.18 | 0.368737 | 0.184368 | − | 0.982857i | \(-0.440976\pi\) | ||||
0.184368 | + | 0.982857i | \(0.440976\pi\) | |||||||
\(360\) | −2204.85 | −0.322794 | ||||||||
\(361\) | 1019.62 | + | 1766.03i | 0.148654 | + | 0.257476i | ||||
\(362\) | 594.448 | 0.0863080 | ||||||||
\(363\) | 5332.82 | − | 9236.72i | 0.771076 | − | 1.33554i | ||||
\(364\) | −4489.18 | −0.646421 | ||||||||
\(365\) | 254.944 | − | 441.576i | 0.0365599 | − | 0.0633237i | ||||
\(366\) | 5231.45 | − | 9061.13i | 0.747137 | − | 1.29408i | ||||
\(367\) | −4818.85 | + | 8346.50i | −0.685401 | + | 1.18715i | 0.287910 | + | 0.957657i | \(0.407040\pi\) |
−0.973311 | + | 0.229491i | \(0.926294\pi\) | |||||||
\(368\) | 547.248 | + | 947.862i | 0.0775198 | + | 0.134268i | ||||
\(369\) | 11507.9 | 1.62352 | ||||||||
\(370\) | −2402.79 | + | 1024.42i | −0.337608 | + | 0.143938i | ||||
\(371\) | 6290.88 | 0.880340 | ||||||||
\(372\) | 4684.56 | + | 8113.90i | 0.652912 | + | 1.13088i | ||||
\(373\) | −5551.33 | + | 9615.19i | −0.770609 | + | 1.33473i | 0.166621 | + | 0.986021i | \(0.446714\pi\) |
−0.937230 | + | 0.348712i | \(0.886619\pi\) | |||||||
\(374\) | −235.787 | + | 408.395i | −0.0325996 | + | 0.0564642i | ||||
\(375\) | 5417.37 | − | 9383.16i | 0.746005 | − | 1.29212i | ||||
\(376\) | −4055.44 | −0.556232 | ||||||||
\(377\) | −7490.62 | + | 12974.1i | −1.02331 | + | 1.77242i | ||||
\(378\) | 6073.27 | 0.826389 | ||||||||
\(379\) | −3690.26 | − | 6391.71i | −0.500147 | − | 0.866280i | −1.00000 | 0.000169856i | \(-0.999946\pi\) | |
0.499853 | − | 0.866110i | \(-0.333387\pi\) | |||||||
\(380\) | 1611.47 | 0.217544 | ||||||||
\(381\) | 14831.5 | 1.99434 | ||||||||
\(382\) | 2865.50 | + | 4963.19i | 0.383800 | + | 0.664761i | ||||
\(383\) | −1862.27 | + | 3225.55i | −0.248454 | + | 0.430334i | −0.963097 | − | 0.269155i | \(-0.913256\pi\) |
0.714643 | + | 0.699489i | \(0.246589\pi\) | |||||||
\(384\) | −1104.77 | −0.146816 | ||||||||
\(385\) | 486.163 | + | 842.058i | 0.0643562 | + | 0.111468i | ||||
\(386\) | −4810.44 | − | 8331.92i | −0.634313 | − | 1.09866i | ||||
\(387\) | −4494.23 | − | 7784.24i | −0.590322 | − | 1.02247i | ||||
\(388\) | −2766.19 | + | 4791.19i | −0.361938 | + | 0.626896i | ||||
\(389\) | −1634.82 | + | 2831.59i | −0.213081 | + | 0.369067i | −0.952677 | − | 0.303984i | \(-0.901683\pi\) |
0.739596 | + | 0.673051i | \(0.235017\pi\) | |||||||
\(390\) | 3274.29 | + | 5671.24i | 0.425129 | + | 0.736345i | ||||
\(391\) | −826.270 | − | 1431.14i | −0.106870 | − | 0.185105i | ||||
\(392\) | −193.145 | − | 334.537i | −0.0248859 | − | 0.0431037i | ||||
\(393\) | 1661.23 | 0.213226 | ||||||||
\(394\) | −425.185 | + | 736.442i | −0.0543668 | + | 0.0941661i | ||||
\(395\) | −1258.00 | − | 2178.92i | −0.160245 | − | 0.277553i | ||||
\(396\) | 1854.23 | 0.235299 | ||||||||
\(397\) | 12159.0 | 1.53714 | 0.768570 | − | 0.639765i | \(-0.220968\pi\) | ||||
0.768570 | + | 0.639765i | \(0.220968\pi\) | |||||||
\(398\) | −243.177 | − | 421.194i | −0.0306265 | − | 0.0530467i | ||||
\(399\) | −10286.7 | −1.29067 | ||||||||
\(400\) | 730.606 | − | 1265.45i | 0.0913257 | − | 0.158181i | ||||
\(401\) | −179.867 | −0.0223994 | −0.0111997 | − | 0.999937i | \(-0.503565\pi\) | ||||
−0.0111997 | + | 0.999937i | \(0.503565\pi\) | |||||||
\(402\) | 2171.78 | − | 3761.63i | 0.269449 | − | 0.466699i | ||||
\(403\) | 8870.64 | − | 15364.4i | 1.09647 | − | 1.89914i | ||||
\(404\) | −2343.46 | + | 4058.99i | −0.288593 | + | 0.499858i | ||||
\(405\) | −708.991 | − | 1228.01i | −0.0869878 | − | 0.150667i | ||||
\(406\) | 7868.11 | 0.961793 | ||||||||
\(407\) | 2020.68 | − | 861.512i | 0.246097 | − | 0.104923i | ||||
\(408\) | 1668.05 | 0.202404 | ||||||||
\(409\) | 2272.68 | + | 3936.39i | 0.274759 | + | 0.475897i | 0.970074 | − | 0.242808i | \(-0.0780684\pi\) |
−0.695315 | + | 0.718705i | \(0.744735\pi\) | |||||||
\(410\) | 1406.06 | − | 2435.37i | 0.169367 | − | 0.293352i | ||||
\(411\) | −397.976 | + | 689.314i | −0.0477632 | + | 0.0827284i | ||||
\(412\) | −2702.61 | + | 4681.06i | −0.323175 | + | 0.559755i | ||||
\(413\) | −15261.5 | −1.81833 | ||||||||
\(414\) | −3248.89 | + | 5627.24i | −0.385686 | + | 0.668028i | ||||
\(415\) | −5289.12 | −0.625621 | ||||||||
\(416\) | 1045.99 | + | 1811.71i | 0.123278 | + | 0.213525i | ||||
\(417\) | −5382.67 | −0.632112 | ||||||||
\(418\) | −1355.20 | −0.158577 | ||||||||
\(419\) | −417.523 | − | 723.170i | −0.0486809 | − | 0.0843179i | 0.840658 | − | 0.541566i | \(-0.182168\pi\) |
−0.889339 | + | 0.457248i | \(0.848835\pi\) | |||||||
\(420\) | 1719.65 | − | 2978.53i | 0.199787 | − | 0.346041i | ||||
\(421\) | −16250.4 | −1.88122 | −0.940611 | − | 0.339486i | \(-0.889747\pi\) | ||||
−0.940611 | + | 0.339486i | \(0.889747\pi\) | |||||||
\(422\) | 1994.72 | + | 3454.96i | 0.230099 | + | 0.398543i | ||||
\(423\) | −12038.1 | − | 20850.6i | −1.38372 | − | 2.39667i | ||||
\(424\) | −1465.79 | − | 2538.82i | −0.167889 | − | 0.290792i | ||||
\(425\) | −1103.11 | + | 1910.65i | −0.125903 | + | 0.218071i | ||||
\(426\) | −6148.03 | + | 10648.7i | −0.699232 | + | 1.21111i | ||||
\(427\) | 5202.72 | + | 9011.38i | 0.589643 | + | 1.02129i | ||||
\(428\) | 2844.94 | + | 4927.58i | 0.321297 | + | 0.556503i | ||||
\(429\) | −2753.60 | − | 4769.37i | −0.309895 | − | 0.536754i | ||||
\(430\) | −2196.47 | −0.246333 | ||||||||
\(431\) | −5307.38 | + | 9192.65i | −0.593150 | + | 1.02737i | 0.400656 | + | 0.916229i | \(0.368782\pi\) |
−0.993805 | + | 0.111137i | \(0.964551\pi\) | |||||||
\(432\) | −1415.08 | − | 2451.00i | −0.157600 | − | 0.272971i | ||||
\(433\) | 12682.2 | 1.40754 | 0.703772 | − | 0.710426i | \(-0.251498\pi\) | ||||
0.703772 | + | 0.710426i | \(0.251498\pi\) | |||||||
\(434\) | −9317.68 | −1.03056 | ||||||||
\(435\) | −5738.80 | − | 9939.88i | −0.632538 | − | 1.09559i | ||||
\(436\) | −7433.12 | −0.816473 | ||||||||
\(437\) | 2374.53 | − | 4112.80i | 0.259929 | − | 0.450211i | ||||
\(438\) | 1516.76 | 0.165465 | ||||||||
\(439\) | 6302.87 | − | 10916.9i | 0.685238 | − | 1.18687i | −0.288124 | − | 0.957593i | \(-0.593031\pi\) |
0.973362 | − | 0.229274i | \(-0.0736352\pi\) | |||||||
\(440\) | 226.554 | − | 392.403i | 0.0245467 | − | 0.0425161i | ||||
\(441\) | 1146.66 | − | 1986.07i | 0.123816 | − | 0.214455i | ||||
\(442\) | −1579.30 | − | 2735.43i | −0.169954 | − | 0.294369i | ||||
\(443\) | 6136.72 | 0.658159 | 0.329080 | − | 0.944302i | \(-0.393262\pi\) | ||||
0.329080 | + | 0.944302i | \(0.393262\pi\) | |||||||
\(444\) | −6212.84 | − | 4666.29i | −0.664073 | − | 0.498766i | ||||
\(445\) | 4302.54 | 0.458337 | ||||||||
\(446\) | 88.6288 | + | 153.510i | 0.00940963 | + | 0.0162980i | ||||
\(447\) | −253.890 | + | 439.750i | −0.0268648 | + | 0.0465312i | ||||
\(448\) | 549.351 | − | 951.504i | 0.0579340 | − | 0.100345i | ||||
\(449\) | 1808.77 | − | 3132.89i | 0.190114 | − | 0.329288i | −0.755174 | − | 0.655525i | \(-0.772447\pi\) |
0.945288 | + | 0.326237i | \(0.105781\pi\) | |||||||
\(450\) | 8674.88 | 0.908751 | ||||||||
\(451\) | −1182.46 | + | 2048.09i | −0.123459 | + | 0.213837i | ||||
\(452\) | 2808.68 | 0.292277 | ||||||||
\(453\) | −6534.50 | − | 11318.1i | −0.677743 | − | 1.17388i | ||||
\(454\) | −8097.47 | −0.837077 | ||||||||
\(455\) | −6512.64 | −0.671027 | ||||||||
\(456\) | 2396.81 | + | 4151.40i | 0.246143 | + | 0.426331i | ||||
\(457\) | 4963.05 | − | 8596.25i | 0.508012 | − | 0.879903i | −0.491945 | − | 0.870626i | \(-0.663714\pi\) |
0.999957 | − | 0.00927627i | \(-0.00295277\pi\) | |||||||
\(458\) | −7182.32 | −0.732768 | ||||||||
\(459\) | 2136.58 | + | 3700.67i | 0.217271 | + | 0.376324i | ||||
\(460\) | 793.914 | + | 1375.10i | 0.0804705 | + | 0.139379i | ||||
\(461\) | 374.446 | + | 648.560i | 0.0378302 | + | 0.0655237i | 0.884321 | − | 0.466880i | \(-0.154622\pi\) |
−0.846490 | + | 0.532404i | \(0.821289\pi\) | |||||||
\(462\) | −1446.18 | + | 2504.86i | −0.145633 | + | 0.252244i | ||||
\(463\) | −6416.71 | + | 11114.1i | −0.644081 | + | 1.11558i | 0.340432 | + | 0.940269i | \(0.389427\pi\) |
−0.984513 | + | 0.175312i | \(0.943907\pi\) | |||||||
\(464\) | −1833.29 | − | 3175.34i | −0.183423 | − | 0.317698i | ||||
\(465\) | 6796.07 | + | 11771.1i | 0.677764 | + | 1.17392i | ||||
\(466\) | 6048.01 | + | 10475.5i | 0.601220 | + | 1.04134i | ||||
\(467\) | −10067.2 | −0.997551 | −0.498775 | − | 0.866731i | \(-0.666217\pi\) | ||||
−0.498775 | + | 0.866731i | \(0.666217\pi\) | |||||||
\(468\) | −6209.80 | + | 10755.7i | −0.613351 | + | 1.06235i | ||||
\(469\) | 2159.85 | + | 3740.98i | 0.212650 | + | 0.368320i | ||||
\(470\) | −5883.38 | −0.577404 | ||||||||
\(471\) | −9828.38 | −0.961503 | ||||||||
\(472\) | 3555.97 | + | 6159.12i | 0.346773 | + | 0.600628i | ||||
\(473\) | 1847.17 | 0.179562 | ||||||||
\(474\) | 3742.16 | − | 6481.62i | 0.362623 | − | 0.628081i | ||||
\(475\) | −6340.24 | −0.612443 | ||||||||
\(476\) | −829.446 | + | 1436.64i | −0.0798689 | + | 0.138337i | ||||
\(477\) | 8702.05 | − | 15072.4i | 0.835303 | − | 1.44679i | ||||
\(478\) | 192.007 | − | 332.566i | 0.0183728 | − | 0.0318226i | ||||
\(479\) | −4530.90 | − | 7847.75i | −0.432196 | − | 0.748586i | 0.564866 | − | 0.825183i | \(-0.308928\pi\) |
−0.997062 | + | 0.0765967i | \(0.975595\pi\) | |||||||
\(480\) | −1602.73 | −0.152405 | ||||||||
\(481\) | −1769.94 | + | 14606.4i | −0.167781 | + | 1.38461i | ||||
\(482\) | 2529.98 | 0.239082 | ||||||||
\(483\) | −5067.87 | − | 8777.81i | −0.477425 | − | 0.826924i | ||||
\(484\) | 2471.47 | − | 4280.72i | 0.232107 | − | 0.402021i | ||||
\(485\) | −4013.02 | + | 6950.76i | −0.375715 | + | 0.650758i | ||||
\(486\) | −2666.88 | + | 4619.16i | −0.248913 | + | 0.431131i | ||||
\(487\) | −10696.1 | −0.995250 | −0.497625 | − | 0.867392i | \(-0.665795\pi\) | ||||
−0.497625 | + | 0.867392i | \(0.665795\pi\) | |||||||
\(488\) | 2424.49 | − | 4199.34i | 0.224901 | − | 0.389539i | ||||
\(489\) | 15189.2 | 1.40466 | ||||||||
\(490\) | −280.203 | − | 485.325i | −0.0258332 | − | 0.0447444i | ||||
\(491\) | −2824.19 | −0.259580 | −0.129790 | − | 0.991541i | \(-0.541430\pi\) | ||||
−0.129790 | + | 0.991541i | \(0.541430\pi\) | |||||||
\(492\) | 8365.21 | 0.766530 | ||||||||
\(493\) | 2768.01 | + | 4794.34i | 0.252870 | + | 0.437984i | ||||
\(494\) | 4538.58 | − | 7861.05i | 0.413361 | − | 0.715963i | ||||
\(495\) | 2690.00 | 0.244255 | ||||||||
\(496\) | 2171.04 | + | 3760.35i | 0.196537 | + | 0.340413i | ||||
\(497\) | −6114.27 | − | 10590.2i | −0.551836 | − | 0.955809i | ||||
\(498\) | −7866.75 | − | 13625.6i | −0.707866 | − | 1.22606i | ||||
\(499\) | −8289.68 | + | 14358.1i | −0.743681 | + | 1.28809i | 0.207127 | + | 0.978314i | \(0.433589\pi\) |
−0.950808 | + | 0.309780i | \(0.899745\pi\) | |||||||
\(500\) | 2510.66 | − | 4348.59i | 0.224560 | − | 0.388949i | ||||
\(501\) | 387.549 | + | 671.255i | 0.0345597 | + | 0.0598592i | ||||
\(502\) | 3414.91 | + | 5914.80i | 0.303615 | + | 0.525877i | ||||
\(503\) | 5577.78 | + | 9661.00i | 0.494435 | + | 0.856387i | 0.999979 | − | 0.00641365i | \(-0.00204154\pi\) |
−0.505544 | + | 0.862801i | \(0.668708\pi\) | |||||||
\(504\) | 6522.75 | 0.576481 | ||||||||
\(505\) | −3399.75 | + | 5888.54i | −0.299578 | + | 0.518884i | ||||
\(506\) | −667.662 | − | 1156.42i | −0.0586584 | − | 0.101599i | ||||
\(507\) | 17924.9 | 1.57016 | ||||||||
\(508\) | 6873.61 | 0.600329 | ||||||||
\(509\) | 5068.07 | + | 8778.16i | 0.441333 | + | 0.764411i | 0.997789 | − | 0.0664665i | \(-0.0211725\pi\) |
−0.556456 | + | 0.830877i | \(0.687839\pi\) | |||||||
\(510\) | 2419.90 | 0.210108 | ||||||||
\(511\) | −754.216 | + | 1306.34i | −0.0652927 | + | 0.113090i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −6140.09 | + | 10635.0i | −0.528444 | + | 0.915292i | ||||
\(514\) | 1024.38 | − | 1774.28i | 0.0879054 | − | 0.152257i | ||||
\(515\) | −3920.78 | + | 6790.99i | −0.335476 | + | 0.581062i | ||||
\(516\) | −3266.90 | − | 5658.44i | −0.278716 | − | 0.482750i | ||||
\(517\) | 4947.77 | 0.420895 | ||||||||
\(518\) | 7108.30 | − | 3030.61i | 0.602936 | − | 0.257060i | ||||
\(519\) | 32710.5 | 2.76653 | ||||||||
\(520\) | 1517.46 | + | 2628.31i | 0.127971 | + | 0.221652i | ||||
\(521\) | 10618.9 | − | 18392.4i | 0.892940 | − | 1.54662i | 0.0566057 | − | 0.998397i | \(-0.481972\pi\) |
0.836334 | − | 0.548220i | \(-0.184694\pi\) | |||||||
\(522\) | 10883.8 | − | 18851.3i | 0.912588 | − | 1.58065i | ||||
\(523\) | 9472.09 | − | 16406.1i | 0.791942 | − | 1.37168i | −0.132821 | − | 0.991140i | \(-0.542404\pi\) |
0.924763 | − | 0.380543i | \(-0.124263\pi\) | |||||||
\(524\) | 769.890 | 0.0641847 | ||||||||
\(525\) | −6765.88 | + | 11718.9i | −0.562452 | + | 0.974196i | ||||
\(526\) | −2774.71 | −0.230006 | ||||||||
\(527\) | −3277.97 | − | 5677.62i | −0.270950 | − | 0.469300i | ||||
\(528\) | 1347.86 | 0.111094 | ||||||||
\(529\) | −7487.62 | −0.615404 | ||||||||
\(530\) | −2126.48 | − | 3683.16i | −0.174280 | − | 0.301861i | ||||
\(531\) | −21111.0 | + | 36565.3i | −1.72531 | + | 2.98832i | ||||
\(532\) | −4767.31 | −0.388513 | ||||||||
\(533\) | −7920.14 | − | 13718.1i | −0.643638 | − | 1.11481i | ||||
\(534\) | 6399.36 | + | 11084.0i | 0.518591 | + | 0.898225i | ||||
\(535\) | 4127.26 | + | 7148.63i | 0.333527 | + | 0.577686i | ||||
\(536\) | 1006.50 | − | 1743.31i | 0.0811086 | − | 0.140484i | ||||
\(537\) | 15503.2 | − | 26852.4i | 1.24584 | − | 2.15785i | ||||
\(538\) | −2176.91 | − | 3770.52i | −0.174449 | − | 0.302154i | ||||
\(539\) | 235.643 | + | 408.146i | 0.0188309 | + | 0.0326161i | ||||
\(540\) | −2052.92 | − | 3555.76i | −0.163599 | − | 0.283362i | ||||
\(541\) | 1085.07 | 0.0862304 | 0.0431152 | − | 0.999070i | \(-0.486272\pi\) | ||||
0.0431152 | + | 0.999070i | \(0.486272\pi\) | |||||||
\(542\) | 5613.86 | − | 9723.49i | 0.444900 | − | 0.770590i | ||||
\(543\) | 1282.67 | + | 2221.65i | 0.101371 | + | 0.175580i | ||||
\(544\) | 773.050 | 0.0609269 | ||||||||
\(545\) | −10783.5 | −0.847551 | ||||||||
\(546\) | −9686.54 | − | 16777.6i | −0.759241 | − | 1.31504i | ||||
\(547\) | 10779.7 | 0.842608 | 0.421304 | − | 0.906920i | \(-0.361573\pi\) | ||||
0.421304 | + | 0.906920i | \(0.361573\pi\) | |||||||
\(548\) | −184.440 | + | 319.460i | −0.0143775 | + | 0.0249026i | ||||
\(549\) | 28787.3 | 2.23791 | ||||||||
\(550\) | −891.364 | + | 1543.89i | −0.0691052 | + | 0.119694i | ||||
\(551\) | −7954.69 | + | 13777.9i | −0.615029 | + | 1.06526i | ||||
\(552\) | −2361.65 | + | 4090.50i | −0.182099 | + | 0.315404i | ||||
\(553\) | 3721.62 | + | 6446.03i | 0.286183 | + | 0.495684i | ||||
\(554\) | −3430.46 | −0.263080 | ||||||||
\(555\) | −9013.21 | − | 6769.57i | −0.689351 | − | 0.517752i | ||||
\(556\) | −2494.58 | −0.190276 | ||||||||
\(557\) | −1075.60 | − | 1862.99i | −0.0818213 | − | 0.141719i | 0.822211 | − | 0.569183i | \(-0.192740\pi\) |
−0.904032 | + | 0.427464i | \(0.859407\pi\) | |||||||
\(558\) | −12889.0 | + | 22324.3i | −0.977838 | + | 1.69366i | ||||
\(559\) | −6186.18 | + | 10714.8i | −0.468063 | + | 0.810710i | ||||
\(560\) | 796.965 | − | 1380.38i | 0.0601392 | − | 0.104164i | ||||
\(561\) | −2035.08 | −0.153157 | ||||||||
\(562\) | −3933.49 | + | 6813.01i | −0.295239 | + | 0.511369i | ||||
\(563\) | 7635.94 | 0.571610 | 0.285805 | − | 0.958288i | \(-0.407739\pi\) | ||||
0.285805 | + | 0.958288i | \(0.407739\pi\) | |||||||
\(564\) | −8750.62 | − | 15156.5i | −0.653311 | − | 1.13157i | ||||
\(565\) | 4074.66 | 0.303402 | ||||||||
\(566\) | 8735.51 | 0.648729 | ||||||||
\(567\) | 2097.45 | + | 3632.89i | 0.155352 | + | 0.269078i | ||||
\(568\) | −2849.28 | + | 4935.09i | −0.210481 | + | 0.364563i | ||||
\(569\) | 1746.95 | 0.128710 | 0.0643549 | − | 0.997927i | \(-0.479501\pi\) | ||||
0.0643549 | + | 0.997927i | \(0.479501\pi\) | |||||||
\(570\) | 3477.15 | + | 6022.60i | 0.255512 | + | 0.442560i | ||||
\(571\) | −3220.40 | − | 5577.90i | −0.236024 | − | 0.408805i | 0.723546 | − | 0.690276i | \(-0.242511\pi\) |
−0.959570 | + | 0.281471i | \(0.909178\pi\) | |||||||
\(572\) | −1276.14 | − | 2210.34i | −0.0932836 | − | 0.161572i | ||||
\(573\) | −12366.1 | + | 21418.6i | −0.901570 | + | 1.56156i | ||||
\(574\) | −4159.64 | + | 7204.71i | −0.302474 | + | 0.523900i | ||||
\(575\) | −3123.61 | − | 5410.26i | −0.226546 | − | 0.392388i | ||||
\(576\) | −1519.81 | − | 2632.40i | −0.109940 | − | 0.190422i | ||||
\(577\) | −4957.97 | − | 8587.46i | −0.357718 | − | 0.619585i | 0.629862 | − | 0.776707i | \(-0.283112\pi\) |
−0.987579 | + | 0.157122i | \(0.949778\pi\) | |||||||
\(578\) | 8658.80 | 0.623112 | ||||||||
\(579\) | 20759.4 | − | 35956.4i | 1.49004 | − | 2.58082i | ||||
\(580\) | −2659.62 | − | 4606.60i | −0.190405 | − | 0.329790i | ||||
\(581\) | 15647.1 | 1.11730 | ||||||||
\(582\) | −23875.0 | −1.70043 | ||||||||
\(583\) | 1788.31 | + | 3097.45i | 0.127040 | + | 0.220040i | ||||
\(584\) | 702.935 | 0.0498077 | ||||||||
\(585\) | −9008.80 | + | 15603.7i | −0.636698 | + | 1.10279i | ||||
\(586\) | 17063.9 | 1.20291 | ||||||||
\(587\) | −6992.60 | + | 12111.5i | −0.491679 | + | 0.851613i | −0.999954 | − | 0.00958162i | \(-0.996950\pi\) |
0.508275 | + | 0.861195i | \(0.330283\pi\) | |||||||
\(588\) | 833.516 | − | 1443.69i | 0.0584586 | − | 0.101253i | ||||
\(589\) | 9420.21 | − | 16316.3i | 0.659003 | − | 1.14143i | ||||
\(590\) | 5158.78 | + | 8935.28i | 0.359973 | + | 0.623491i | ||||
\(591\) | −3669.77 | −0.255422 | ||||||||
\(592\) | −2879.31 | − | 2162.57i | −0.199897 | − | 0.150137i | ||||
\(593\) | −11166.1 | −0.773252 | −0.386626 | − | 0.922236i | \(-0.626360\pi\) | ||||
−0.386626 | + | 0.922236i | \(0.626360\pi\) | |||||||
\(594\) | 1726.45 | + | 2990.30i | 0.119254 | + | 0.206555i | ||||
\(595\) | −1203.31 | + | 2084.19i | −0.0829090 | + | 0.143603i | ||||
\(596\) | −117.664 | + | 203.800i | −0.00808676 | + | 0.0140067i | ||||
\(597\) | 1049.43 | − | 1817.66i | 0.0719435 | − | 0.124610i | ||||
\(598\) | 8944.00 | 0.611617 | ||||||||
\(599\) | 7696.15 | − | 13330.1i | 0.524969 | − | 0.909272i | −0.474609 | − | 0.880197i | \(-0.657410\pi\) |
0.999577 | − | 0.0290754i | \(-0.00925630\pi\) | |||||||
\(600\) | 6305.86 | 0.429059 | ||||||||
\(601\) | −1141.95 | − | 1977.92i | −0.0775062 | − | 0.134245i | 0.824667 | − | 0.565618i | \(-0.191362\pi\) |
−0.902173 | + | 0.431374i | \(0.858029\pi\) | |||||||
\(602\) | 6497.94 | 0.439927 | ||||||||
\(603\) | 11950.7 | 0.807084 | ||||||||
\(604\) | −3028.38 | − | 5245.31i | −0.204012 | − | 0.353359i | ||||
\(605\) | 3585.46 | − | 6210.21i | 0.240942 | − | 0.417324i | ||||
\(606\) | −20226.4 | −1.35585 | ||||||||
\(607\) | 1113.58 | + | 1928.78i | 0.0744628 | + | 0.128973i | 0.900853 | − | 0.434125i | \(-0.142942\pi\) |
−0.826390 | + | 0.563099i | \(0.809609\pi\) | |||||||
\(608\) | 1110.79 | + | 1923.95i | 0.0740930 | + | 0.128333i | ||||
\(609\) | 16977.4 | + | 29405.8i | 1.12965 | + | 1.95662i | ||||
\(610\) | 3517.30 | − | 6092.15i | 0.233461 | − | 0.404367i | ||||
\(611\) | −16570.1 | + | 28700.2i | −1.09714 | + | 1.90031i | ||||
\(612\) | 2294.71 | + | 3974.56i | 0.151566 | + | 0.262520i | ||||
\(613\) | 14749.7 | + | 25547.3i | 0.971838 | + | 1.68327i | 0.689999 | + | 0.723810i | \(0.257611\pi\) |
0.281838 | + | 0.959462i | \(0.409056\pi\) | |||||||
\(614\) | −2528.60 | − | 4379.67i | −0.166199 | − | 0.287865i | ||||
\(615\) | 12135.7 | 0.795707 | ||||||||
\(616\) | −670.228 | + | 1160.87i | −0.0438380 | + | 0.0759297i | ||||
\(617\) | −10116.8 | − | 17522.8i | −0.660109 | − | 1.14334i | −0.980587 | − | 0.196086i | \(-0.937177\pi\) |
0.320478 | − | 0.947256i | \(-0.396156\pi\) | |||||||
\(618\) | −23326.2 | −1.51831 | ||||||||
\(619\) | −12667.8 | −0.822554 | −0.411277 | − | 0.911510i | \(-0.634917\pi\) | ||||
−0.411277 | + | 0.911510i | \(0.634917\pi\) | |||||||
\(620\) | 3149.61 | + | 5455.29i | 0.204018 | + | 0.353370i | ||||
\(621\) | −12100.0 | −0.781896 | ||||||||
\(622\) | −6340.44 | + | 10982.0i | −0.408727 | + | 0.707936i | ||||
\(623\) | −12728.4 | −0.818547 | ||||||||
\(624\) | −4513.97 | + | 7818.42i | −0.289589 | + | 0.501582i | ||||
\(625\) | −2065.55 | + | 3577.63i | −0.132195 | + | 0.228969i | ||||
\(626\) | 2541.15 | − | 4401.40i | 0.162244 | − | 0.281015i | ||||
\(627\) | −2924.19 | − | 5064.85i | −0.186254 | − | 0.322601i | ||||
\(628\) | −4554.92 | −0.289428 | ||||||||
\(629\) | 4347.37 | + | 3265.19i | 0.275582 | + | 0.206982i | ||||
\(630\) | 9462.81 | 0.598424 | ||||||||
\(631\) | −2369.66 | − | 4104.37i | −0.149500 | − | 0.258942i | 0.781543 | − | 0.623852i | \(-0.214433\pi\) |
−0.931043 | + | 0.364910i | \(0.881100\pi\) | |||||||
\(632\) | 1734.29 | − | 3003.88i | 0.109156 | − | 0.189063i | ||||
\(633\) | −8608.23 | + | 14909.9i | −0.540516 | + | 0.936201i | ||||
\(634\) | −2692.50 | + | 4663.54i | −0.168663 | + | 0.292134i | ||||
\(635\) | 9971.82 | 0.623181 | ||||||||
\(636\) | 6325.61 | − | 10956.3i | 0.394382 | − | 0.683089i | ||||
\(637\) | −3156.68 | −0.196346 | ||||||||
\(638\) | 2236.67 | + | 3874.03i | 0.138794 | + | 0.240399i | ||||
\(639\) | −33831.0 | −2.09442 | ||||||||
\(640\) | −742.778 | −0.0458764 | ||||||||
\(641\) | −6554.62 | − | 11352.9i | −0.403888 | − | 0.699554i | 0.590303 | − | 0.807181i | \(-0.299008\pi\) |
−0.994191 | + | 0.107627i | \(0.965675\pi\) | |||||||
\(642\) | −12277.3 | + | 21265.0i | −0.754747 | + | 1.30726i | ||||
\(643\) | 27918.1 | 1.71226 | 0.856130 | − | 0.516761i | \(-0.172862\pi\) | ||||
0.856130 | + | 0.516761i | \(0.172862\pi\) | |||||||
\(644\) | −2348.68 | − | 4068.04i | −0.143713 | − | 0.248918i | ||||
\(645\) | −4739.43 | − | 8208.93i | −0.289325 | − | 0.501126i | ||||
\(646\) | −1677.14 | − | 2904.90i | −0.102146 | − | 0.176922i | ||||
\(647\) | 1084.15 | − | 1877.80i | 0.0658767 | − | 0.114102i | −0.831206 | − | 0.555965i | \(-0.812349\pi\) |
0.897083 | + | 0.441863i | \(0.145682\pi\) | |||||||
\(648\) | 977.421 | − | 1692.94i | 0.0592542 | − | 0.102631i | ||||
\(649\) | −4338.40 | − | 7514.34i | −0.262400 | − | 0.454489i | ||||
\(650\) | −5970.36 | − | 10341.0i | −0.360272 | − | 0.624009i | ||||
\(651\) | −20105.2 | − | 34823.3i | −1.21042 | − | 2.09652i | ||||
\(652\) | 7039.38 | 0.422827 | ||||||||
\(653\) | 9783.46 | − | 16945.4i | 0.586304 | − | 1.01551i | −0.408408 | − | 0.912800i | \(-0.633916\pi\) |
0.994712 | − | 0.102708i | \(-0.0327508\pi\) | |||||||
\(654\) | −16038.8 | − | 27780.1i | −0.958972 | − | 1.66099i | ||||
\(655\) | 1116.91 | 0.0666278 | ||||||||
\(656\) | 3876.82 | 0.230738 | ||||||||
\(657\) | 2086.58 | + | 3614.07i | 0.123905 | + | 0.214609i | ||||
\(658\) | 17405.1 | 1.03119 | ||||||||
\(659\) | −8235.94 | + | 14265.1i | −0.486839 | + | 0.843230i | −0.999886 | − | 0.0151310i | \(-0.995183\pi\) |
0.513047 | + | 0.858361i | \(0.328517\pi\) | |||||||
\(660\) | 1955.39 | 0.115323 | ||||||||
\(661\) | 83.0511 | − | 143.849i | 0.00488701 | − | 0.00846455i | −0.863572 | − | 0.504226i | \(-0.831778\pi\) |
0.868459 | + | 0.495762i | \(0.165111\pi\) | |||||||
\(662\) | 5240.87 | − | 9077.46i | 0.307692 | − | 0.532939i | ||||
\(663\) | 6815.48 | − | 11804.8i | 0.399233 | − | 0.691491i | ||||
\(664\) | −3645.81 | − | 6314.73i | −0.213080 | − | 0.369065i | ||||
\(665\) | −6916.12 | −0.403302 | ||||||||
\(666\) | 2571.72 | − | 21223.1i | 0.149628 | − | 1.23480i | ||||
\(667\) | −15676.0 | −0.910009 | ||||||||
\(668\) | 179.608 | + | 311.090i | 0.0104031 | + | 0.0180186i | ||||
\(669\) | −382.478 | + | 662.471i | −0.0221038 | + | 0.0382849i | ||||
\(670\) | 1460.17 | − | 2529.09i | 0.0841959 | − | 0.145832i | ||||
\(671\) | −2957.96 | + | 5123.34i | −0.170180 | + | 0.294761i | ||||
\(672\) | 4741.45 | 0.272181 | ||||||||
\(673\) | 1696.38 | − | 2938.21i | 0.0971628 | − | 0.168291i | −0.813346 | − | 0.581780i | \(-0.802357\pi\) |
0.910509 | + | 0.413489i | \(0.135690\pi\) | |||||||
\(674\) | 19483.1 | 1.11344 | ||||||||
\(675\) | 8077.09 | + | 13989.9i | 0.460574 | + | 0.797738i | ||||
\(676\) | 8307.21 | 0.472645 | ||||||||
\(677\) | 5580.22 | 0.316787 | 0.158394 | − | 0.987376i | \(-0.449368\pi\) | ||||
0.158394 | + | 0.987376i | \(0.449368\pi\) | |||||||
\(678\) | 6060.43 | + | 10497.0i | 0.343288 | + | 0.594592i | ||||
\(679\) | 11872.0 | − | 20562.8i | 0.670993 | − | 1.16219i | ||||
\(680\) | 1121.49 | 0.0632461 | ||||||||
\(681\) | −17472.3 | − | 30262.9i | −0.983173 | − | 1.70291i | ||||
\(682\) | −2648.74 | − | 4587.76i | −0.148718 | − | 0.257587i | ||||
\(683\) | 6641.24 | + | 11503.0i | 0.372065 | + | 0.644435i | 0.989883 | − | 0.141886i | \(-0.0453167\pi\) |
−0.617818 | + | 0.786321i | \(0.711983\pi\) | |||||||
\(684\) | −6594.52 | + | 11422.0i | −0.368637 | + | 0.638498i | ||||
\(685\) | −267.574 | + | 463.453i | −0.0149248 | + | 0.0258505i | ||||
\(686\) | 6717.30 | + | 11634.7i | 0.373860 | + | 0.647544i | ||||
\(687\) | −15497.7 | − | 26842.7i | −0.860659 | − | 1.49070i | ||||
\(688\) | −1514.03 | − | 2622.38i | −0.0838982 | − | 0.145316i | ||||
\(689\) | −23956.2 | −1.32461 | ||||||||
\(690\) | −3426.14 | + | 5934.24i | −0.189030 | + | 0.327410i | ||||
\(691\) | −6948.98 | − | 12036.0i | −0.382564 | − | 0.662620i | 0.608864 | − | 0.793274i | \(-0.291625\pi\) |
−0.991428 | + | 0.130655i | \(0.958292\pi\) | |||||||
\(692\) | 15159.5 | 0.832773 | ||||||||
\(693\) | −7957.98 | −0.436217 | ||||||||
\(694\) | 8864.95 | + | 15354.5i | 0.484883 | + | 0.839842i | ||||
\(695\) | −3618.98 | −0.197519 | ||||||||
\(696\) | 7911.55 | − | 13703.2i | 0.430871 | − | 0.746291i | ||||
\(697\) | −5853.47 | −0.318100 | ||||||||
\(698\) | −594.163 | + | 1029.12i | −0.0322198 | + | 0.0558063i | ||||
\(699\) | −26100.2 | + | 45206.8i | −1.41230 | + | 2.44618i | ||||
\(700\) | −3135.62 | + | 5431.05i | −0.169307 | + | 0.293249i | ||||
\(701\) | 4649.93 | + | 8053.91i | 0.250535 | + | 0.433940i | 0.963673 | − | 0.267084i | \(-0.0860600\pi\) |
−0.713138 | + | 0.701024i | \(0.752727\pi\) | |||||||
\(702\) | −23127.5 | −1.24344 | ||||||||
\(703\) | −1879.60 | + | 15511.4i | −0.100840 | + | 0.832180i | ||||
\(704\) | 624.658 | 0.0334413 | ||||||||
\(705\) | −12694.9 | − | 21988.1i | −0.678179 | − | 1.17464i | ||||
\(706\) | −3009.17 | + | 5212.04i | −0.160413 | + | 0.277844i | ||||
\(707\) | 10057.7 | − | 17420.4i | 0.535019 | − | 0.926679i | ||||
\(708\) | −15345.8 | + | 26579.7i | −0.814591 | + | 1.41091i | ||||
\(709\) | 29471.3 | 1.56110 | 0.780550 | − | 0.625094i | \(-0.214939\pi\) | ||||
0.780550 | + | 0.625094i | \(0.214939\pi\) | |||||||
\(710\) | −4133.56 | + | 7159.53i | −0.218492 | + | 0.378440i | ||||
\(711\) | 20592.2 | 1.08617 | ||||||||
\(712\) | 2965.75 | + | 5136.84i | 0.156104 | + | 0.270381i | ||||
\(713\) | 18564.0 | 0.975074 | ||||||||
\(714\) | −7158.95 | −0.375234 | ||||||||
\(715\) | −1851.35 | − | 3206.63i | −0.0968344 | − | 0.167722i | ||||
\(716\) | 7184.91 | − | 12444.6i | 0.375018 | − | 0.649550i | ||||
\(717\) | 1657.21 | 0.0863177 | ||||||||
\(718\) | 2508.18 | + | 4344.29i | 0.130368 | + | 0.225804i | ||||
\(719\) | 13186.0 | + | 22838.8i | 0.683942 | + | 1.18462i | 0.973768 | + | 0.227543i | \(0.0730693\pi\) |
−0.289826 | + | 0.957079i | \(0.593597\pi\) | |||||||
\(720\) | −2204.85 | − | 3818.92i | −0.114125 | − | 0.197670i | ||||
\(721\) | 11599.1 | − | 20090.2i | 0.599129 | − | 1.03772i | ||||
\(722\) | −2039.24 | + | 3532.06i | −0.105114 | + | 0.182063i | ||||
\(723\) | 5459.06 | + | 9455.37i | 0.280809 | + | 0.486375i | ||||
\(724\) | 594.448 | + | 1029.61i | 0.0305145 | + | 0.0528526i | ||||
\(725\) | 10464.1 | + | 18124.4i | 0.536039 | + | 0.928446i | ||||
\(726\) | 21331.3 | 1.09047 | ||||||||
\(727\) | −10798.3 | + | 18703.3i | −0.550878 | + | 0.954149i | 0.447333 | + | 0.894367i | \(0.352374\pi\) |
−0.998211 | + | 0.0597816i | \(0.980960\pi\) | |||||||
\(728\) | −4489.18 | − | 7775.50i | −0.228544 | − | 0.395850i | ||||
\(729\) | −29615.4 | −1.50462 | ||||||||
\(730\) | 1019.78 | 0.0517036 | ||||||||
\(731\) | 2285.98 | + | 3959.44i | 0.115664 | + | 0.200335i | ||||
\(732\) | 20925.8 | 1.05661 | ||||||||
\(733\) | −9413.89 | + | 16305.3i | −0.474366 | + | 0.821625i | −0.999569 | − | 0.0293513i | \(-0.990656\pi\) |
0.525204 | + | 0.850977i | \(0.323989\pi\) | |||||||
\(734\) | −19275.4 | −0.969303 | ||||||||
\(735\) | 1209.21 | − | 2094.42i | 0.0606838 | − | 0.105107i | ||||
\(736\) | −1094.50 | + | 1895.72i | −0.0548148 | + | 0.0949420i | ||||
\(737\) | −1227.97 | + | 2126.90i | −0.0613741 | + | 0.106303i | ||||
\(738\) | 11507.9 | + | 19932.3i | 0.573999 | + | 0.994196i | ||||
\(739\) | −6510.06 | −0.324055 | −0.162027 | − | 0.986786i | \(-0.551803\pi\) | ||||
−0.162027 | + | 0.986786i | \(0.551803\pi\) | |||||||
\(740\) | −4177.13 | − | 3137.33i | −0.207506 | − | 0.155852i | ||||
\(741\) | 39172.5 | 1.94202 | ||||||||
\(742\) | 6290.88 | + | 10896.1i | 0.311247 | + | 0.539096i | ||||
\(743\) | 4517.91 | − | 7825.26i | 0.223077 | − | 0.386381i | −0.732664 | − | 0.680591i | \(-0.761723\pi\) |
0.955741 | + | 0.294210i | \(0.0950565\pi\) | |||||||
\(744\) | −9369.12 | + | 16227.8i | −0.461678 | + | 0.799650i | ||||
\(745\) | −170.700 | + | 295.661i | −0.00839457 | + | 0.0145398i | ||||
\(746\) | −22205.3 | −1.08981 | ||||||||
\(747\) | 21644.4 | − | 37489.1i | 1.06014 | − | 1.83622i | ||||
\(748\) | −943.148 | −0.0461028 | ||||||||
\(749\) | −12209.9 | − | 21148.2i | −0.595649 | − | 1.03169i | ||||
\(750\) | 21669.5 | 1.05501 | ||||||||
\(751\) | −12387.2 | −0.601884 | −0.300942 | − | 0.953642i | \(-0.597301\pi\) | ||||
−0.300942 | + | 0.953642i | \(0.597301\pi\) | |||||||
\(752\) | −4055.44 | − | 7024.22i | −0.196658 | − | 0.340621i | ||||
\(753\) | −14737.0 | + | 25525.3i | −0.713211 | + | 1.23532i | ||||
\(754\) | −29962.5 | −1.44717 | ||||||||
\(755\) | −4393.39 | − | 7609.58i | −0.211777 | − | 0.366809i | ||||
\(756\) | 6073.27 | + | 10519.2i | 0.292173 | + | 0.506058i | ||||
\(757\) | 8643.24 | + | 14970.5i | 0.414985 | + | 0.718776i | 0.995427 | − | 0.0955263i | \(-0.0304534\pi\) |
−0.580442 | + | 0.814302i | \(0.697120\pi\) | |||||||
\(758\) | 7380.51 | − | 12783.4i | 0.353657 | − | 0.612553i | ||||
\(759\) | 2881.29 | − | 4990.55i | 0.137792 | − | 0.238663i | ||||
\(760\) | 1611.47 | + | 2791.15i | 0.0769133 | + | 0.133218i | ||||
\(761\) | 9167.51 | + | 15878.6i | 0.436691 | + | 0.756371i | 0.997432 | − | 0.0716201i | \(-0.0228169\pi\) |
−0.560741 | + | 0.827991i | \(0.689484\pi\) | |||||||
\(762\) | 14831.5 | + | 25689.0i | 0.705105 | + | 1.22128i | ||||
\(763\) | 31901.5 | 1.51365 | ||||||||
\(764\) | −5731.00 | + | 9926.38i | −0.271388 | + | 0.470057i | ||||
\(765\) | 3329.03 | + | 5766.05i | 0.157335 | + | 0.272512i | ||||
\(766\) | −7449.10 | −0.351367 | ||||||||
\(767\) | 58117.3 | 2.73598 | ||||||||
\(768\) | −1104.77 | − | 1913.51i | −0.0519074 | − | 0.0899063i | ||||
\(769\) | −27200.0 | −1.27550 | −0.637748 | − | 0.770245i | \(-0.720134\pi\) | ||||
−0.637748 | + | 0.770245i | \(0.720134\pi\) | |||||||
\(770\) | −972.325 | + | 1684.12i | −0.0455067 | + | 0.0788199i | ||||
\(771\) | 8841.41 | 0.412990 | ||||||||
\(772\) | 9620.87 | − | 16663.8i | 0.448527 | − | 0.776871i | ||||
\(773\) | −13160.6 | + | 22794.9i | −0.612360 | + | 1.06064i | 0.378481 | + | 0.925609i | \(0.376446\pi\) |
−0.990841 | + | 0.135030i | \(0.956887\pi\) | |||||||
\(774\) | 8988.47 | − | 15568.5i | 0.417421 | − | 0.722994i | ||||
\(775\) | −12392.0 | − | 21463.5i | −0.574365 | − | 0.994830i | ||||
\(776\) | −11064.8 | −0.511858 | ||||||||
\(777\) | 26664.3 | + | 20026.8i | 1.23112 | + | 0.924656i | ||||
\(778\) | −6539.27 | −0.301342 | ||||||||
\(779\) | −8410.82 | − | 14568.0i | −0.386841 | − | 0.670028i | ||||
\(780\) | −6548.59 | + | 11342.5i | −0.300612 | + | 0.520675i | ||||
\(781\) | 3476.22 | − | 6020.98i | 0.159269 | − | 0.275861i | ||||
\(782\) | 1652.54 | − | 2862.28i | 0.0755687 | − | 0.130889i | ||||
\(783\) | 40535.2 | 1.85008 | ||||||||
\(784\) | 386.290 | − | 669.073i | 0.0175970 | − | 0.0304789i | ||||
\(785\) | −6608.00 | −0.300445 | ||||||||
\(786\) | 1661.23 | + | 2877.33i | 0.0753869 | + | 0.130574i | ||||
\(787\) | −36881.0 | −1.67048 | −0.835239 | − | 0.549887i | \(-0.814671\pi\) | ||||
−0.835239 | + | 0.549887i | \(0.814671\pi\) | |||||||
\(788\) | −1700.74 | −0.0768863 | ||||||||
\(789\) | −5987.14 | − | 10370.0i | −0.270149 | − | 0.467912i | ||||
\(790\) | 2516.00 | − | 4357.84i | 0.113311 | − | 0.196260i | ||||
\(791\) | −12054.3 | −0.541848 | ||||||||
\(792\) | 1854.23 | + | 3211.61i | 0.0831907 | + | 0.144091i | ||||
\(793\) | −19812.4 | − | 34316.1i | −0.887213 | − | 1.53670i | ||||
\(794\) | 12159.0 | + | 21060.1i | 0.543461 | + | 0.941303i | ||||
\(795\) | 9176.81 | − | 15894.7i | 0.409393 | − | 0.709090i | ||||
\(796\) | 486.353 | − | 842.389i | 0.0216562 | − | 0.0375096i | ||||
\(797\) | −10624.1 | − | 18401.5i | −0.472178 | − | 0.817835i | 0.527316 | − | 0.849669i | \(-0.323199\pi\) |
−0.999493 | + | 0.0318340i | \(0.989865\pi\) | |||||||
\(798\) | −10286.7 | − | 17817.0i | −0.456320 | − | 0.790370i | ||||
\(799\) | 6123.15 | + | 10605.6i | 0.271116 | + | 0.469587i | ||||
\(800\) | 2922.42 | 0.129154 | ||||||||
\(801\) | −17607.0 | + | 30496.2i | −0.776671 | + | 1.34523i | ||||
\(802\) | −179.867 | − | 311.539i | −0.00791937 | − | 0.0137168i | ||||
\(803\) | −857.605 | −0.0376890 | ||||||||
\(804\) | 8687.11 | 0.381058 | ||||||||
\(805\) | −3407.33 | − | 5901.66i | −0.149183 | − | 0.258393i | ||||
\(806\) | 35482.6 | 1.55064 | ||||||||
\(807\) | 9394.47 | − | 16271.7i | 0.409791 | − | 0.709778i | ||||
\(808\) | −9373.84 | −0.408132 | ||||||||
\(809\) | −3592.39 | + | 6222.20i | −0.156121 | + | 0.270409i | −0.933467 | − | 0.358665i | \(-0.883232\pi\) |
0.777346 | + | 0.629073i | \(0.216566\pi\) | |||||||
\(810\) | 1417.98 | − | 2456.02i | 0.0615097 | − | 0.106538i | ||||
\(811\) | 13130.3 | − | 22742.3i | 0.568515 | − | 0.984697i | −0.428198 | − | 0.903685i | \(-0.640852\pi\) |
0.996713 | − | 0.0810118i | \(-0.0258151\pi\) | |||||||
\(812\) | 7868.11 | + | 13628.0i | 0.340045 | + | 0.588975i | ||||
\(813\) | 48453.3 | 2.09020 | ||||||||
\(814\) | 3512.86 | + | 2638.41i | 0.151260 | + | 0.113607i | ||||
\(815\) | 10212.3 | 0.438922 | ||||||||
\(816\) | 1668.05 | + | 2889.15i | 0.0715606 | + | 0.123947i | ||||
\(817\) | −6569.44 | + | 11378.6i | −0.281316 | + | 0.487254i | ||||
\(818\) | −4545.35 | + | 7872.78i | −0.194284 | + | 0.336510i | ||||
\(819\) | 26651.3 | − | 46161.4i | 1.13708 | − | 1.96949i | ||||
\(820\) | 5624.25 | 0.239521 | ||||||||
\(821\) | 14746.3 | − | 25541.3i | 0.626855 | − | 1.08574i | −0.361324 | − | 0.932440i | \(-0.617675\pi\) |
0.988179 | − | 0.153304i | \(-0.0489914\pi\) | |||||||
\(822\) | −1591.90 | −0.0675474 | ||||||||
\(823\) | 12857.6 | + | 22270.0i | 0.544579 | + | 0.943238i | 0.998633 | + | 0.0522641i | \(0.0166438\pi\) |
−0.454055 | + | 0.890974i | \(0.650023\pi\) | |||||||
\(824\) | −10810.4 | −0.457038 | ||||||||
\(825\) | −7693.36 | −0.324665 | ||||||||
\(826\) | −15261.5 | − | 26433.8i | −0.642877 | − | 1.11350i | ||||
\(827\) | −15481.9 | + | 26815.4i | −0.650976 | + | 1.12752i | 0.331911 | + | 0.943311i | \(0.392307\pi\) |
−0.982886 | + | 0.184212i | \(0.941027\pi\) | |||||||
\(828\) | −12995.6 | −0.545443 | ||||||||
\(829\) | −10660.9 | − | 18465.3i | −0.446646 | − | 0.773614i | 0.551519 | − | 0.834162i | \(-0.314048\pi\) |
−0.998165 | + | 0.0605482i | \(0.980715\pi\) | |||||||
\(830\) | −5289.12 | − | 9161.02i | −0.221190 | − | 0.383113i | ||||
\(831\) | −7402.08 | − | 12820.8i | −0.308995 | − | 0.535196i | ||||
\(832\) | −2091.98 | + | 3623.41i | −0.0871710 | + | 0.150985i | ||||
\(833\) | −583.245 | + | 1010.21i | −0.0242596 | + | 0.0420188i | ||||
\(834\) | −5382.67 | − | 9323.06i | −0.223485 | − | 0.387088i | ||||
\(835\) | 260.564 | + | 451.311i | 0.0107990 | + | 0.0187045i | ||||
\(836\) | −1355.20 | − | 2347.28i | −0.0560655 | − | 0.0971082i | ||||
\(837\) | −48003.1 | −1.98236 | ||||||||
\(838\) | 835.045 | − | 1446.34i | 0.0344226 | − | 0.0596217i | ||||
\(839\) | −15727.2 | − | 27240.3i | −0.647156 | − | 1.12091i | −0.983799 | − | 0.179274i | \(-0.942625\pi\) |
0.336643 | − | 0.941632i | \(-0.390708\pi\) | |||||||
\(840\) | 6878.61 | 0.282541 | ||||||||
\(841\) | 28125.6 | 1.15321 | ||||||||
\(842\) | −16250.4 | − | 28146.5i | −0.665113 | − | 1.15201i | ||||
\(843\) | −33950.0 | −1.38707 | ||||||||
\(844\) | −3989.45 | + | 6909.93i | −0.162704 | + | 0.281812i | ||||
\(845\) | 12051.6 | 0.490636 | ||||||||
\(846\) | 24076.2 | − | 41701.2i | 0.978436 | − | 1.69470i | ||||
\(847\) | −10607.1 | + | 18372.0i | −0.430300 | + | 0.745301i | ||||
\(848\) | 2931.58 | − | 5077.64i | 0.118715 | − | 0.205621i | ||||
\(849\) | 18849.0 | + | 32647.5i | 0.761952 | + | 1.31974i | ||||
\(850\) | −4412.46 | −0.178054 | ||||||||
\(851\) | −14162.2 | + | 6038.00i | −0.570474 | + | 0.243220i | ||||
\(852\) | −24592.1 | −0.988864 | ||||||||
\(853\) | 23005.2 | + | 39846.2i | 0.923427 | + | 1.59942i | 0.794072 | + | 0.607824i | \(0.207958\pi\) |
0.129356 | + | 0.991598i | \(0.458709\pi\) | |||||||
\(854\) | −10405.4 | + | 18022.8i | −0.416940 | + | 0.722162i | ||||
\(855\) | −9566.93 | + | 16570.4i | −0.382669 | + | 0.662802i | ||||
\(856\) | −5689.88 | + | 9855.16i | −0.227192 | + | 0.393507i | ||||
\(857\) | −16592.5 | −0.661365 | −0.330682 | − | 0.943742i | \(-0.607279\pi\) | ||||
−0.330682 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(858\) | 5507.20 | − | 9538.74i | 0.219129 | − | 0.379542i | ||||
\(859\) | −9563.88 | −0.379878 | −0.189939 | − | 0.981796i | \(-0.560829\pi\) | ||||
−0.189939 | + | 0.981796i | \(0.560829\pi\) | |||||||
\(860\) | −2196.47 | − | 3804.39i | −0.0870917 | − | 0.150847i | ||||
\(861\) | −35901.9 | −1.42106 | ||||||||
\(862\) | −21229.5 | −0.838840 | ||||||||
\(863\) | 13590.1 | + | 23538.7i | 0.536051 | + | 0.928467i | 0.999112 | + | 0.0421407i | \(0.0134178\pi\) |
−0.463061 | + | 0.886326i | \(0.653249\pi\) | |||||||
\(864\) | 2830.17 | − | 4901.99i | 0.111440 | − | 0.193020i | ||||
\(865\) | 21992.5 | 0.864472 | ||||||||
\(866\) | 12682.2 | + | 21966.2i | 0.497642 | + | 0.861941i | ||||
\(867\) | 18683.5 | + | 32360.8i | 0.731864 | + | 1.26763i | ||||
\(868\) | −9317.68 | − | 16138.7i | −0.364358 | − | 0.631087i | ||||
\(869\) | −2115.89 | + | 3664.83i | −0.0825969 | + | 0.143062i | ||||
\(870\) | 11477.6 | − | 19879.8i | 0.447272 | − | 0.774698i | ||||
\(871\) | −8224.91 | − | 14246.0i | −0.319966 | − | 0.554198i | ||||
\(872\) | −7433.12 | − | 12874.5i | −0.288667 | − | 0.499985i | ||||
\(873\) | −32844.5 | − | 56888.4i | −1.27333 | − | 2.20548i | ||||
\(874\) | 9498.11 | 0.367595 | ||||||||
\(875\) | −10775.3 | + | 18663.3i | −0.416309 | + | 0.721068i | ||||
\(876\) | 1516.76 | + | 2627.10i | 0.0585006 | + | 0.101326i | ||||
\(877\) | −17764.9 | −0.684013 | −0.342006 | − | 0.939698i | \(-0.611106\pi\) | ||||
−0.342006 | + | 0.939698i | \(0.611106\pi\) | |||||||
\(878\) | 25211.5 | 0.969073 | ||||||||
\(879\) | 36819.6 | + | 63773.5i | 1.41285 | + | 2.44713i | ||||
\(880\) | 906.215 | 0.0347142 | ||||||||
\(881\) | 12642.6 | − | 21897.7i | 0.483474 | − | 0.837401i | −0.516346 | − | 0.856380i | \(-0.672708\pi\) |
0.999820 | + | 0.0189787i | \(0.00604146\pi\) | |||||||
\(882\) | 4586.63 | 0.175102 | ||||||||
\(883\) | −2921.85 | + | 5060.80i | −0.111357 | + | 0.192876i | −0.916318 | − | 0.400452i | \(-0.868853\pi\) |
0.804961 | + | 0.593328i | \(0.202186\pi\) | |||||||
\(884\) | 3158.60 | − | 5470.86i | 0.120176 | − | 0.208150i | ||||
\(885\) | −22262.7 | + | 38560.2i | −0.845597 | + | 1.46462i | ||||
\(886\) | 6136.72 | + | 10629.1i | 0.232694 | + | 0.403039i | ||||
\(887\) | 30297.4 | 1.14688 | 0.573442 | − | 0.819246i | \(-0.305608\pi\) | ||||
0.573442 | + | 0.819246i | \(0.305608\pi\) | |||||||
\(888\) | 1869.41 | − | 15427.2i | 0.0706454 | − | 0.583001i | ||||
\(889\) | −29500.2 | −1.11294 | ||||||||
\(890\) | 4302.54 | + | 7452.21i | 0.162046 | + | 0.280673i | ||||
\(891\) | −1192.49 | + | 2065.45i | −0.0448371 | + | 0.0776601i | ||||
\(892\) | −177.258 | + | 307.019i | −0.00665362 | + | 0.0115244i | ||||
\(893\) | −17596.7 | + | 30478.3i | −0.659406 | + | 1.14213i | ||||
\(894\) | −1015.56 | −0.0379926 | ||||||||
\(895\) | 10423.4 | − | 18053.9i | 0.389293 | − | 0.674275i | ||||
\(896\) | 2197.41 | 0.0819310 | ||||||||
\(897\) | 19298.9 | + | 33426.7i | 0.718363 | + | 1.24424i | ||||
\(898\) | 7235.10 | 0.268862 | ||||||||
\(899\) | −62189.6 | −2.30716 | ||||||||
\(900\) | 8674.88 | + | 15025.3i | 0.321292 | + | 0.556494i | ||||
\(901\) | −4426.28 | + | 7666.54i | −0.163663 | + | 0.283473i | ||||
\(902\) | −4729.85 | −0.174597 | ||||||||
\(903\) | 14020.9 | + | 24285.0i | 0.516708 | + | 0.894964i | ||||
\(904\) | 2808.68 | + | 4864.77i | 0.103335 | + | 0.178982i | ||||
\(905\) | 862.389 | + | 1493.70i | 0.0316760 | + | 0.0548644i | ||||
\(906\) | 13069.0 | − | 22636.2i | 0.479236 | − | 0.830062i | ||||
\(907\) | −4720.79 | + | 8176.64i | −0.172824 | + | 0.299340i | −0.939406 | − | 0.342807i | \(-0.888622\pi\) |
0.766582 | + | 0.642146i | \(0.221956\pi\) | |||||||
\(908\) | −8097.47 | − | 14025.2i | −0.295952 | − | 0.512603i | ||||
\(909\) | −27825.2 | − | 48194.7i | −1.01530 | − | 1.75854i | ||||
\(910\) | −6512.64 | − | 11280.2i | −0.237244 | − | 0.410918i | ||||
\(911\) | −5048.65 | −0.183611 | −0.0918053 | − | 0.995777i | \(-0.529264\pi\) | ||||
−0.0918053 | + | 0.995777i | \(0.529264\pi\) | |||||||
\(912\) | −4793.62 | + | 8302.80i | −0.174049 | + | 0.301462i | ||||
\(913\) | 4448.01 | + | 7704.19i | 0.161235 | + | 0.279268i | ||||
\(914\) | 19852.2 | 0.718437 | ||||||||
\(915\) | 30357.8 | 1.09683 | ||||||||
\(916\) | −7182.32 | − | 12440.1i | −0.259073 | − | 0.448727i | ||||
\(917\) | −3304.22 | −0.118991 | ||||||||
\(918\) | −4273.17 | + | 7401.34i | −0.153633 | + | 0.266101i | ||||
\(919\) | −18619.3 | −0.668329 | −0.334164 | − | 0.942515i | \(-0.608454\pi\) | ||||
−0.334164 | + | 0.942515i | \(0.608454\pi\) | |||||||
\(920\) | −1587.83 | + | 2750.20i | −0.0569013 | + | 0.0985559i | ||||
\(921\) | 10912.2 | − | 18900.5i | 0.390411 | − | 0.676212i | ||||
\(922\) | −748.892 | + | 1297.12i | −0.0267500 | + | 0.0463323i | ||||
\(923\) | 23283.7 | + | 40328.5i | 0.830327 | + | 1.43817i | ||||
\(924\) | −5784.73 | −0.205957 | ||||||||
\(925\) | 16434.7 | + | 12343.6i | 0.584184 | + | 0.438764i | ||||
\(926\) | −25666.8 | −0.910868 | ||||||||
\(927\) | −32089.6 | − | 55580.7i | −1.13696 | − | 1.96927i | ||||
\(928\) | 3666.57 | − | 6350.69i | 0.129699 | − | 0.224646i | ||||
\(929\) | 7802.23 | − | 13513.9i | 0.275547 | − | 0.477261i | −0.694726 | − | 0.719274i | \(-0.744474\pi\) |
0.970273 | + | 0.242013i | \(0.0778078\pi\) | |||||||
\(930\) | −13592.1 | + | 23542.3i | −0.479252 | + | 0.830088i | ||||
\(931\) | −3352.25 | −0.118008 | ||||||||
\(932\) | −12096.0 | + | 20950.9i | −0.425127 | + | 0.736341i | ||||
\(933\) | −54724.3 | −1.92025 | ||||||||
\(934\) | −10067.2 | − | 17437.0i | −0.352688 | − | 0.610873i | ||||
\(935\) | −1368.26 | −0.0478577 | ||||||||
\(936\) | −24839.2 | −0.867409 | ||||||||
\(937\) | −16509.9 | − | 28596.0i | −0.575619 | − | 0.997002i | −0.995974 | − | 0.0896420i | \(-0.971428\pi\) |
0.420355 | − | 0.907360i | \(-0.361906\pi\) | |||||||
\(938\) | −4319.71 | + | 7481.95i | −0.150366 | + | 0.260442i | ||||
\(939\) | 21932.7 | 0.762242 | ||||||||
\(940\) | −5883.38 | − | 10190.3i | −0.204143 | − | 0.353586i | ||||
\(941\) | −12483.6 | − | 21622.3i | −0.432471 | − | 0.749062i | 0.564614 | − | 0.825355i | \(-0.309025\pi\) |
−0.997085 | + | 0.0762931i | \(0.975692\pi\) | |||||||
\(942\) | −9828.38 | − | 17023.2i | −0.339943 | − | 0.588798i | ||||
\(943\) | 8287.43 | − | 14354.2i | 0.286189 | − | 0.495693i | ||||
\(944\) | −7111.94 | + | 12318.2i | −0.245205 | + | 0.424708i | ||||
\(945\) | 8810.72 | + | 15260.6i | 0.303294 | + | 0.525321i | ||||
\(946\) | 1847.17 | + | 3199.40i | 0.0634849 | + | 0.109959i | ||||
\(947\) | 19195.4 | + | 33247.4i | 0.658676 | + | 1.14086i | 0.980959 | + | 0.194217i | \(0.0622166\pi\) |
−0.322282 | + | 0.946644i | \(0.604450\pi\) | |||||||
\(948\) | 14968.7 | 0.512826 | ||||||||
\(949\) | 2872.12 | − | 4974.66i | 0.0982434 | − | 0.170163i | ||||
\(950\) | −6340.24 | − | 10981.6i | −0.216531 | − | 0.375043i | ||||
\(951\) | −23238.9 | −0.792402 | ||||||||
\(952\) | −3317.78 | −0.112952 | ||||||||
\(953\) | −9401.17 | − | 16283.3i | −0.319553 | − | 0.553482i | 0.660842 | − | 0.750525i | \(-0.270199\pi\) |
−0.980395 | + | 0.197043i | \(0.936866\pi\) | |||||||
\(954\) | 34808.2 | 1.18130 | ||||||||
\(955\) | −8314.18 | + | 14400.6i | −0.281718 | + | 0.487950i | ||||
\(956\) | 768.029 | 0.0259831 | ||||||||
\(957\) | −9652.36 | + | 16718.4i | −0.326036 | + | 0.564711i | ||||
\(958\) | 9061.80 | − | 15695.5i | 0.305609 | − | 0.529330i | ||||
\(959\) | 791.581 | − | 1371.06i | 0.0266543 | − | 0.0461666i | ||||
\(960\) | −1602.73 | − | 2776.01i | −0.0538832 | − | 0.0933285i | ||||
\(961\) | 43856.0 | 1.47212 | ||||||||
\(962\) | −27069.1 | + | 11540.8i | −0.907215 | + | 0.386789i | ||||
\(963\) | −67559.0 | −2.26071 | ||||||||
\(964\) | 2529.98 | + | 4382.05i | 0.0845281 | + | 0.146407i | ||||
\(965\) | 13957.4 | − | 24174.9i | 0.465600 | − | 0.806442i | ||||
\(966\) | 10135.7 | − | 17555.6i | 0.337590 | − | 0.584724i | ||||
\(967\) | 23828.6 | − | 41272.4i | 0.792428 | − | 1.37253i | −0.132032 | − | 0.991245i | \(-0.542150\pi\) |
0.924460 | − | 0.381280i | \(-0.124517\pi\) | |||||||
\(968\) | 9885.90 | 0.328249 | ||||||||
\(969\) | 7237.72 | − | 12536.1i | 0.239947 | − | 0.415601i | ||||
\(970\) | −16052.1 | −0.531342 | ||||||||
\(971\) | 21568.8 | + | 37358.3i | 0.712848 | + | 1.23469i | 0.963784 | + | 0.266686i | \(0.0859286\pi\) |
−0.250935 | + | 0.968004i | \(0.580738\pi\) | |||||||
\(972\) | −10667.5 | −0.352017 | ||||||||
\(973\) | 10706.2 | 0.352750 | ||||||||
\(974\) | −10696.1 | − | 18526.2i | −0.351874 | − | 0.609464i | ||||
\(975\) | 25765.1 | − | 44626.4i | 0.846300 | − | 1.46584i | ||||
\(976\) | 9697.96 | 0.318058 | ||||||||
\(977\) | −11799.4 | − | 20437.1i | −0.386383 | − | 0.669234i | 0.605577 | − | 0.795786i | \(-0.292942\pi\) |
−0.991960 | + | 0.126552i | \(0.959609\pi\) | |||||||
\(978\) | 15189.2 | + | 26308.5i | 0.496623 | + | 0.860177i | ||||
\(979\) | −3618.32 | − | 6267.12i | −0.118123 | − | 0.204594i | ||||
\(980\) | 560.405 | − | 970.651i | 0.0182668 | − | 0.0316391i | ||||
\(981\) | 44128.8 | − | 76433.3i | 1.43621 | − | 2.48759i | ||||
\(982\) | −2824.19 | − | 4891.64i | −0.0917755 | − | 0.158960i | ||||
\(983\) | 10344.4 | + | 17917.0i | 0.335640 | + | 0.581346i | 0.983608 | − | 0.180322i | \(-0.0577141\pi\) |
−0.647967 | + | 0.761668i | \(0.724381\pi\) | |||||||
\(984\) | 8365.21 | + | 14489.0i | 0.271009 | + | 0.469402i | ||||
\(985\) | −2467.33 | −0.0798129 | ||||||||
\(986\) | −5536.02 | + | 9588.68i | −0.178806 | + | 0.309701i | ||||
\(987\) | 37556.0 | + | 65048.8i | 1.21116 | + | 2.09780i | ||||
\(988\) | 18154.3 | 0.584581 | ||||||||
\(989\) | −12946.1 | −0.416241 | ||||||||
\(990\) | 2690.00 | + | 4659.21i | 0.0863573 | + | 0.149575i | ||||
\(991\) | −367.111 | −0.0117676 | −0.00588378 | − | 0.999983i | \(-0.501873\pi\) | ||||
−0.00588378 | + | 0.999983i | \(0.501873\pi\) | |||||||
\(992\) | −4342.08 | + | 7520.70i | −0.138973 | + | 0.240708i | ||||
\(993\) | 45234.0 | 1.44558 | ||||||||
\(994\) | 12228.5 | − | 21180.5i | 0.390207 | − | 0.675859i | ||||
\(995\) | 705.572 | − | 1222.09i | 0.0224805 | − | 0.0389374i | ||||
\(996\) | 15733.5 | − | 27251.2i | 0.500537 | − | 0.866956i | ||||
\(997\) | −7544.87 | − | 13068.1i | −0.239667 | − | 0.415116i | 0.720951 | − | 0.692986i | \(-0.243705\pi\) |
−0.960619 | + | 0.277870i | \(0.910372\pi\) | |||||||
\(998\) | −33158.7 | −1.05172 | ||||||||
\(999\) | 36620.8 | − | 15613.2i | 1.15979 | − | 0.494473i |
(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 | 74.4.c.a.63.1 | yes | 8 | |
3.2 | odd | 2 | 666.4.f.a.433.3 | 8 | |||
37.10 | even | 3 | inner | 74.4.c.a.47.1 | ✓ | 8 | |
111.47 | odd | 6 | 666.4.f.a.343.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.c.a.47.1 | ✓ | 8 | 37.10 | even | 3 | inner | |
74.4.c.a.63.1 | yes | 8 | 1.1 | even | 1 | trivial | |
666.4.f.a.343.3 | 8 | 111.47 | odd | 6 | |||
666.4.f.a.433.3 | 8 | 3.2 | odd | 2 |