Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(215,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.215");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.k (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: | \(22.3027219822\) |
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: | \( x^{16} - 178 x^{14} + 23185 x^{12} - 1395488 x^{10} + 61706754 x^{8} - 468877357 x^{6} + 2731971910 x^{4} - 4899926507 x^{2} + 6975757441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.3 | ||
Root | \(2.11897 - 1.22339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.269 |
Dual form | 378.4.k.c.215.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | + | 1.00000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 3.89811 | + | 6.75173i | 0.348658 | + | 0.603893i | 0.986011 | − | 0.166679i | \(-0.0533042\pi\) |
−0.637354 | + | 0.770572i | \(0.719971\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.4219 | − | 10.2550i | 0.832704 | − | 0.553719i | ||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −13.5035 | − | 7.79622i | −0.427017 | − | 0.246538i | ||||
\(11\) | −44.0180 | − | 25.4138i | −1.20654 | − | 0.696595i | −0.244537 | − | 0.969640i | \(-0.578636\pi\) |
−0.962001 | + | 0.273045i | \(0.911969\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 50.9038i | − | 1.08601i | −0.839729 | − | 0.543006i | \(-0.817286\pi\) | ||
0.839729 | − | 0.543006i | \(-0.182714\pi\) | |||||||
\(14\) | −16.4565 | + | 33.1841i | −0.314156 | + | 0.633487i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.37255 | − | 7.57348i | 0.0623823 | − | 0.108049i | −0.833148 | − | 0.553051i | \(-0.813464\pi\) |
0.895530 | + | 0.445001i | \(0.146797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −87.9687 | + | 50.7888i | −1.06218 | + | 0.613250i | −0.926034 | − | 0.377439i | \(-0.876805\pi\) |
−0.136145 | + | 0.990689i | \(0.543471\pi\) | |||||||
\(20\) | 31.1849 | 0.348658 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 101.655 | 0.985135 | ||||||||
\(23\) | −36.9867 | + | 21.3543i | −0.335315 | + | 0.193594i | −0.658198 | − | 0.752844i | \(-0.728681\pi\) |
0.322883 | + | 0.946439i | \(0.395348\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 32.1094 | − | 55.6152i | 0.256876 | − | 0.444921i | ||||
\(26\) | 50.9038 | + | 88.1679i | 0.383964 | + | 0.665044i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.68064 | − | 73.9330i | −0.0315914 | − | 0.499001i | ||||
\(29\) | 218.184i | 1.39710i | 0.715563 | + | 0.698548i | \(0.246170\pi\) | ||||
−0.715563 | + | 0.698548i | \(0.753830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −87.6221 | − | 50.5886i | −0.507658 | − | 0.293096i | 0.224213 | − | 0.974540i | \(-0.428019\pi\) |
−0.731870 | + | 0.681444i | \(0.761352\pi\) | |||||||
\(32\) | 27.7128 | + | 16.0000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 17.4902i | 0.0882219i | ||||||||
\(35\) | 129.355 | + | 64.1492i | 0.624715 | + | 0.309806i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −137.147 | − | 237.545i | −0.609373 | − | 1.05546i | −0.991344 | − | 0.131290i | \(-0.958088\pi\) |
0.381971 | − | 0.924174i | \(-0.375245\pi\) | |||||||
\(38\) | 101.578 | − | 175.937i | 0.433633 | − | 0.751074i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −54.0138 | + | 31.1849i | −0.213508 | + | 0.123269i | ||||
\(41\) | −6.40338 | −0.0243912 | −0.0121956 | − | 0.999926i | \(-0.503882\pi\) | ||||
−0.0121956 | + | 0.999926i | \(0.503882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −262.501 | −0.930955 | −0.465477 | − | 0.885060i | \(-0.654117\pi\) | ||||
−0.465477 | + | 0.885060i | \(0.654117\pi\) | |||||||
\(44\) | −176.072 | + | 101.655i | −0.603269 | + | 0.348298i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 42.7085 | − | 73.9733i | 0.136892 | − | 0.237104i | ||||
\(47\) | −53.2835 | − | 92.2898i | −0.165366 | − | 0.286422i | 0.771419 | − | 0.636327i | \(-0.219547\pi\) |
−0.936785 | + | 0.349905i | \(0.886214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 132.669 | − | 316.303i | 0.386791 | − | 0.922167i | ||||
\(50\) | 128.438i | 0.363277i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −176.336 | − | 101.808i | −0.470257 | − | 0.271503i | ||||
\(53\) | −555.867 | − | 320.930i | −1.44065 | − | 0.831758i | −0.442754 | − | 0.896643i | \(-0.645998\pi\) |
−0.997893 | + | 0.0648858i | \(0.979332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 396.263i | − | 0.971494i | ||||||
\(56\) | 82.0401 | + | 123.375i | 0.195769 | + | 0.294405i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −218.184 | − | 377.906i | −0.493948 | − | 0.855543i | ||||
\(59\) | −52.5654 | + | 91.0459i | −0.115990 | + | 0.200901i | −0.918175 | − | 0.396175i | \(-0.870338\pi\) |
0.802185 | + | 0.597076i | \(0.203671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 471.522 | − | 272.233i | 0.989707 | − | 0.571408i | 0.0845205 | − | 0.996422i | \(-0.473064\pi\) |
0.905187 | + | 0.425014i | \(0.139731\pi\) | |||||||
\(62\) | 202.354 | 0.414501 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 343.688 | − | 198.429i | 0.655835 | − | 0.378647i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 109.449 | − | 189.572i | 0.199572 | − | 0.345670i | −0.748817 | − | 0.662776i | \(-0.769378\pi\) |
0.948390 | + | 0.317107i | \(0.102711\pi\) | |||||||
\(68\) | −17.4902 | − | 30.2939i | −0.0311912 | − | 0.0540247i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −288.199 | + | 18.2457i | −0.492091 | + | 0.0311539i | ||||
\(71\) | − | 542.115i | − | 0.906158i | −0.891470 | − | 0.453079i | \(-0.850326\pi\) | ||
0.891470 | − | 0.453079i | \(-0.149674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −778.156 | − | 449.268i | −1.24762 | − | 0.720314i | −0.276986 | − | 0.960874i | \(-0.589335\pi\) |
−0.970634 | + | 0.240561i | \(0.922669\pi\) | |||||||
\(74\) | 475.090 | + | 274.293i | 0.746326 | + | 0.430891i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 406.310i | 0.613250i | ||||||||
\(77\) | −939.460 | + | 59.4764i | −1.39041 | + | 0.0880256i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 561.113 | + | 971.876i | 0.799115 | + | 1.38411i | 0.920193 | + | 0.391465i | \(0.128032\pi\) |
−0.121078 | + | 0.992643i | \(0.538635\pi\) | |||||||
\(80\) | 62.3698 | − | 108.028i | 0.0871644 | − | 0.150973i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.0910 | − | 6.40338i | 0.0149365 | − | 0.00862360i | ||||
\(83\) | 855.676 | 1.13160 | 0.565799 | − | 0.824543i | \(-0.308568\pi\) | ||||
0.565799 | + | 0.824543i | \(0.308568\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 68.1788 | 0.0870003 | ||||||||
\(86\) | 454.665 | − | 262.501i | 0.570091 | − | 0.329142i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 203.310 | − | 352.144i | 0.246284 | − | 0.426576i | ||||
\(89\) | −658.192 | − | 1140.02i | −0.783913 | − | 1.35778i | −0.929646 | − | 0.368453i | \(-0.879888\pi\) |
0.145733 | − | 0.989324i | \(-0.453446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −522.019 | − | 785.032i | −0.601346 | − | 0.904327i | ||||
\(92\) | 170.834i | 0.193594i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 184.580 | + | 106.567i | 0.202531 | + | 0.116931i | ||||
\(95\) | −685.824 | − | 395.961i | −0.740674 | − | 0.427628i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1240.73i | − | 1.29873i | −0.760475 | − | 0.649367i | \(-0.775034\pi\) | ||
0.760475 | − | 0.649367i | \(-0.224966\pi\) | |||||||
\(98\) | 86.5135 | + | 680.523i | 0.0891753 | + | 0.701461i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −128.438 | − | 222.461i | −0.128438 | − | 0.222461i | ||||
\(101\) | 250.942 | − | 434.645i | 0.247225 | − | 0.428206i | −0.715530 | − | 0.698582i | \(-0.753815\pi\) |
0.962755 | + | 0.270376i | \(0.0871480\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −305.111 | + | 176.156i | −0.291878 | + | 0.168516i | −0.638789 | − | 0.769382i | \(-0.720564\pi\) |
0.346910 | + | 0.937898i | \(0.387231\pi\) | |||||||
\(104\) | 407.230 | 0.383964 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1283.72 | 1.17628 | ||||||||
\(107\) | −935.207 | + | 539.942i | −0.844952 | + | 0.487833i | −0.858944 | − | 0.512069i | \(-0.828879\pi\) |
0.0139923 | + | 0.999902i | \(0.495546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −242.598 | + | 420.192i | −0.213180 | + | 0.369239i | −0.952708 | − | 0.303887i | \(-0.901716\pi\) |
0.739528 | + | 0.673126i | \(0.235049\pi\) | |||||||
\(110\) | 396.263 | + | 686.348i | 0.343475 | + | 0.594916i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −265.473 | − | 131.652i | −0.223972 | − | 0.111071i | ||||
\(113\) | − | 1686.83i | − | 1.40428i | −0.712038 | − | 0.702140i | \(-0.752228\pi\) | ||
0.712038 | − | 0.702140i | \(-0.247772\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −288.356 | − | 166.483i | −0.233821 | − | 0.134996i | ||||
\(116\) | 755.812 | + | 436.368i | 0.604960 | + | 0.349274i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 210.262i | − | 0.164035i | ||||||
\(119\) | −10.2332 | − | 161.638i | −0.00788297 | − | 0.124515i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 626.222 | + | 1084.65i | 0.470490 | + | 0.814913i | ||||
\(122\) | −544.466 | + | 943.043i | −0.404046 | + | 0.699829i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −350.488 | + | 202.354i | −0.253829 | + | 0.146548i | ||||
\(125\) | 1475.19 | 1.05556 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1425.59 | 0.996070 | 0.498035 | − | 0.867157i | \(-0.334055\pi\) | ||||
0.498035 | + | 0.867157i | \(0.334055\pi\) | |||||||
\(128\) | 110.851 | − | 64.0000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −396.857 | + | 687.377i | −0.267744 | + | 0.463746i | ||||
\(131\) | −576.837 | − | 999.111i | −0.384721 | − | 0.666357i | 0.607009 | − | 0.794695i | \(-0.292369\pi\) |
−0.991730 | + | 0.128338i | \(0.959036\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −835.804 | + | 1685.38i | −0.544913 | + | 1.09880i | ||||
\(134\) | 437.797i | 0.282238i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 60.5878 | + | 34.9804i | 0.0382012 | + | 0.0220555i | ||||
\(137\) | 1704.44 | + | 984.057i | 1.06292 | + | 0.613676i | 0.926238 | − | 0.376939i | \(-0.123023\pi\) |
0.136681 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 821.420i | 0.501237i | 0.968086 | + | 0.250619i | \(0.0806340\pi\) | ||||
−0.968086 | + | 0.250619i | \(0.919366\pi\) | |||||||
\(140\) | 480.930 | − | 319.802i | 0.290329 | − | 0.193058i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 542.115 | + | 938.971i | 0.320375 | + | 0.554906i | ||||
\(143\) | −1293.66 | + | 2240.68i | −0.756511 | + | 1.31032i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1473.12 | + | 850.506i | −0.843696 | + | 0.487108i | ||||
\(146\) | 1797.07 | 1.01868 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1097.17 | −0.609373 | ||||||||
\(149\) | −2337.37 | + | 1349.48i | −1.28513 | + | 0.741971i | −0.977782 | − | 0.209626i | \(-0.932775\pi\) |
−0.307350 | + | 0.951597i | \(0.599442\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −636.455 | + | 1102.37i | −0.343007 | + | 0.594105i | −0.984990 | − | 0.172614i | \(-0.944779\pi\) |
0.641983 | + | 0.766719i | \(0.278112\pi\) | |||||||
\(152\) | −406.310 | − | 703.750i | −0.216816 | − | 0.375537i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1567.72 | − | 1042.48i | 0.820325 | − | 0.545488i | ||||
\(155\) | − | 788.800i | − | 0.408761i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2684.88 | + | 1550.11i | 1.36482 | + | 0.787979i | 0.990261 | − | 0.139225i | \(-0.0444611\pi\) |
0.374558 | + | 0.927203i | \(0.377794\pi\) | |||||||
\(158\) | −1943.75 | − | 1122.23i | −0.978712 | − | 0.565060i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 249.479i | 0.123269i | ||||||||
\(161\) | −351.416 | + | 708.622i | −0.172021 | + | 0.346877i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1415.80 | + | 2452.24i | 0.680333 | + | 1.17837i | 0.974879 | + | 0.222735i | \(0.0714983\pi\) |
−0.294546 | + | 0.955637i | \(0.595168\pi\) | |||||||
\(164\) | −12.8068 | + | 22.1820i | −0.00609780 | + | 0.0105617i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1482.07 | + | 855.676i | −0.692959 | + | 0.400080i | ||||
\(167\) | −3845.26 | −1.78177 | −0.890883 | − | 0.454234i | \(-0.849913\pi\) | ||||
−0.890883 | + | 0.454234i | \(0.849913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −394.194 | −0.179424 | ||||||||
\(170\) | −118.089 | + | 68.1788i | −0.0532766 | + | 0.0307593i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −525.002 | + | 909.331i | −0.232739 | + | 0.403115i | ||||
\(173\) | 1098.40 | + | 1902.48i | 0.482714 | + | 0.836084i | 0.999803 | − | 0.0198470i | \(-0.00631791\pi\) |
−0.517090 | + | 0.855931i | \(0.672985\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −75.1464 | − | 1186.97i | −0.0324602 | − | 0.512725i | ||||
\(176\) | 813.242i | 0.348298i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2280.05 | + | 1316.38i | 0.960093 | + | 0.554310i | ||||
\(179\) | −2000.24 | − | 1154.84i | −0.835222 | − | 0.482216i | 0.0204150 | − | 0.999792i | \(-0.493501\pi\) |
−0.855637 | + | 0.517576i | \(0.826835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3240.23i | 1.33063i | 0.746561 | + | 0.665317i | \(0.231704\pi\) | ||||
−0.746561 | + | 0.665317i | \(0.768296\pi\) | |||||||
\(182\) | 1689.20 | + | 837.697i | 0.687975 | + | 0.341177i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −170.834 | − | 295.893i | −0.0684459 | − | 0.118552i | ||||
\(185\) | 1069.23 | − | 1851.95i | 0.424925 | − | 0.735992i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −384.942 | + | 222.246i | −0.150533 | + | 0.0869105i | ||||
\(188\) | −426.268 | −0.165366 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1583.84 | 0.604758 | ||||||||
\(191\) | −95.2419 | + | 54.9879i | −0.0360809 | + | 0.0208313i | −0.517932 | − | 0.855422i | \(-0.673298\pi\) |
0.481851 | + | 0.876253i | \(0.339965\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2499.43 | − | 4329.13i | 0.932190 | − | 1.61460i | 0.152621 | − | 0.988285i | \(-0.451229\pi\) |
0.779569 | − | 0.626316i | \(-0.215438\pi\) | |||||||
\(194\) | 1240.73 | + | 2149.01i | 0.459172 | + | 0.795308i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −830.369 | − | 1092.19i | −0.302612 | − | 0.398027i | ||||
\(197\) | − | 508.689i | − | 0.183973i | −0.995760 | − | 0.0919863i | \(-0.970678\pi\) | ||
0.995760 | − | 0.0919863i | \(-0.0293216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1043.93 | − | 602.713i | −0.371871 | − | 0.214700i | 0.302405 | − | 0.953180i | \(-0.402211\pi\) |
−0.674275 | + | 0.738480i | \(0.735544\pi\) | |||||||
\(200\) | 444.921 | + | 256.876i | 0.157304 | + | 0.0908192i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1003.77i | 0.349629i | ||||||||
\(203\) | 2237.48 | + | 3364.81i | 0.773598 | + | 1.16337i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.9611 | − | 43.2339i | −0.00850419 | − | 0.0147297i | ||||
\(206\) | 352.311 | − | 610.221i | 0.119159 | − | 0.206389i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −705.343 | + | 407.230i | −0.235129 | + | 0.135752i | ||||
\(209\) | 5162.94 | 1.70875 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3127.48 | 1.02040 | 0.510200 | − | 0.860056i | \(-0.329571\pi\) | ||||
0.510200 | + | 0.860056i | \(0.329571\pi\) | |||||||
\(212\) | −2223.47 | + | 1283.72i | −0.720323 | + | 0.415879i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1079.88 | − | 1870.41i | 0.344950 | − | 0.597471i | ||||
\(215\) | −1023.26 | − | 1772.34i | −0.324585 | − | 0.562197i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1870.08 | + | 118.394i | −0.585021 | + | 0.0370372i | ||||
\(218\) | − | 970.391i | − | 0.301483i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1372.70 | − | 792.527i | −0.420669 | − | 0.242873i | ||||
\(221\) | −385.519 | − | 222.579i | −0.117343 | − | 0.0677480i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1206.04i | 0.362164i | 0.983468 | + | 0.181082i | \(0.0579599\pi\) | ||||
−0.983468 | + | 0.181082i | \(0.942040\pi\) | |||||||
\(224\) | 591.464 | − | 37.4451i | 0.176423 | − | 0.0111692i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1686.83 | + | 2921.68i | 0.496488 | + | 0.859943i | ||||
\(227\) | −236.529 | + | 409.681i | −0.0691586 | + | 0.119786i | −0.898531 | − | 0.438910i | \(-0.855365\pi\) |
0.829373 | + | 0.558696i | \(0.188698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1774.94 | + | 1024.76i | −0.512188 | + | 0.295712i | −0.733733 | − | 0.679438i | \(-0.762223\pi\) |
0.221545 | + | 0.975150i | \(0.428890\pi\) | |||||||
\(230\) | 665.930 | 0.190914 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1745.47 | −0.493948 | ||||||||
\(233\) | 1548.92 | − | 894.267i | 0.435506 | − | 0.251439i | −0.266184 | − | 0.963922i | \(-0.585763\pi\) |
0.701689 | + | 0.712483i | \(0.252429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 415.410 | − | 719.512i | 0.115312 | − | 0.199727i | ||||
\(236\) | 210.262 | + | 364.184i | 0.0579952 | + | 0.100451i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 179.362 | + | 269.732i | 0.0488501 | + | 0.0734627i | ||||
\(239\) | − | 4369.08i | − | 1.18248i | −0.806496 | − | 0.591239i | \(-0.798639\pi\) | ||
0.806496 | − | 0.591239i | \(-0.201361\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2425.16 | + | 1400.17i | 0.648208 | + | 0.374243i | 0.787769 | − | 0.615970i | \(-0.211236\pi\) |
−0.139561 | + | 0.990213i | \(0.544569\pi\) | |||||||
\(242\) | −2169.30 | − | 1252.44i | −0.576230 | − | 0.332687i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2177.86i | − | 0.571408i | ||||||
\(245\) | 2652.75 | − | 337.239i | 0.691748 | − | 0.0879405i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2585.34 | + | 4477.94i | 0.665997 | + | 1.15354i | ||||
\(248\) | 404.709 | − | 700.976i | 0.103625 | − | 0.179484i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2555.11 | + | 1475.19i | −0.646397 | + | 0.373198i | ||||
\(251\) | −3078.51 | −0.774159 | −0.387080 | − | 0.922046i | \(-0.626516\pi\) | ||||
−0.387080 | + | 0.922046i | \(0.626516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2170.77 | 0.539428 | ||||||||
\(254\) | −2469.20 | + | 1425.59i | −0.609966 | + | 0.352164i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.62749 | − | 8.01505i | −0.00112317 | − | 0.00194539i | 0.865463 | − | 0.500972i | \(-0.167024\pi\) |
−0.866586 | + | 0.499027i | \(0.833691\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4551.09 | − | 2256.95i | −1.09186 | − | 0.541468i | ||||
\(260\) | − | 1587.43i | − | 0.378647i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1998.22 | + | 1153.67i | 0.471185 | + | 0.272039i | ||||
\(263\) | 650.240 | + | 375.416i | 0.152454 | + | 0.0880196i | 0.574287 | − | 0.818654i | \(-0.305280\pi\) |
−0.421832 | + | 0.906674i | \(0.638613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5004.09i | − | 1.15999i | ||||||
\(266\) | −237.724 | − | 3754.97i | −0.0547962 | − | 0.865533i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −437.797 | − | 758.287i | −0.0997862 | − | 0.172835i | ||||
\(269\) | −332.781 | + | 576.394i | −0.0754276 | + | 0.130644i | −0.901272 | − | 0.433253i | \(-0.857365\pi\) |
0.825845 | + | 0.563898i | \(0.190699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2885.66 | + | 1666.04i | −0.646832 | + | 0.373449i | −0.787242 | − | 0.616645i | \(-0.788491\pi\) |
0.140409 | + | 0.990094i | \(0.455158\pi\) | |||||||
\(272\) | −139.922 | −0.0311912 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3936.23 | −0.867870 | ||||||||
\(275\) | −2826.79 | + | 1632.05i | −0.619861 | + | 0.357877i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2828.26 | − | 4898.68i | 0.613478 | − | 1.06258i | −0.377171 | − | 0.926144i | \(-0.623103\pi\) |
0.990649 | − | 0.136432i | \(-0.0435635\pi\) | |||||||
\(278\) | −821.420 | − | 1422.74i | −0.177214 | − | 0.306944i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −513.194 | + | 1034.84i | −0.109533 | + | 0.220870i | ||||
\(281\) | − | 4156.44i | − | 0.882392i | −0.897411 | − | 0.441196i | \(-0.854554\pi\) | ||
0.897411 | − | 0.441196i | \(-0.145446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5249.78 | − | 3030.96i | −1.10271 | − | 0.636650i | −0.165779 | − | 0.986163i | \(-0.553014\pi\) |
−0.936932 | + | 0.349512i | \(0.886347\pi\) | |||||||
\(284\) | −1877.94 | − | 1084.23i | −0.392378 | − | 0.226540i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 5174.63i | − | 1.06987i | ||||||
\(287\) | −98.7522 | + | 65.6668i | −0.0203107 | + | 0.0135059i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2418.26 | + | 4188.55i | 0.492217 | + | 0.852545i | ||||
\(290\) | 1701.01 | − | 2946.24i | 0.344438 | − | 0.596583i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3112.62 | + | 1797.07i | −0.623810 | + | 0.360157i | ||||
\(293\) | 5099.64 | 1.01681 | 0.508403 | − | 0.861119i | \(-0.330236\pi\) | ||||
0.508403 | + | 0.861119i | \(0.330236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −819.623 | −0.161764 | ||||||||
\(296\) | 1900.36 | − | 1097.17i | 0.373163 | − | 0.215446i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2698.96 | − | 4674.73i | 0.524653 | − | 0.908725i | ||||
\(299\) | 1087.01 | + | 1882.76i | 0.210246 | + | 0.364157i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4048.26 | + | 2691.95i | −0.775210 | + | 0.515487i | ||||
\(302\) | − | 2545.82i | − | 0.485085i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1407.50 | + | 812.620i | 0.265545 | + | 0.153312i | ||||
\(305\) | 3676.09 | + | 2122.39i | 0.690138 | + | 0.398451i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4775.43i | − | 0.887778i | −0.896082 | − | 0.443889i | \(-0.853598\pi\) | ||
0.896082 | − | 0.443889i | \(-0.146402\pi\) | |||||||
\(308\) | −1672.89 | + | 3373.34i | −0.309486 | + | 0.624070i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 788.800 | + | 1366.24i | 0.144519 | + | 0.250314i | ||||
\(311\) | −5031.96 | + | 8715.62i | −0.917481 | + | 1.58912i | −0.114253 | + | 0.993452i | \(0.536447\pi\) |
−0.803228 | + | 0.595672i | \(0.796886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8486.84 | + | 4899.88i | −1.53260 | + | 0.884848i | −0.533361 | + | 0.845888i | \(0.679071\pi\) |
−0.999241 | + | 0.0389605i | \(0.987595\pi\) | |||||||
\(314\) | −6200.46 | −1.11437 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4488.90 | 0.799115 | ||||||||
\(317\) | 3218.25 | − | 1858.06i | 0.570205 | − | 0.329208i | −0.187026 | − | 0.982355i | \(-0.559885\pi\) |
0.757231 | + | 0.653147i | \(0.226552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5544.89 | − | 9604.03i | 0.973211 | − | 1.68565i | ||||
\(320\) | −249.479 | − | 432.111i | −0.0435822 | − | 0.0754866i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −99.9516 | − | 1578.78i | −0.0172984 | − | 0.273237i | ||||
\(323\) | 888.306i | 0.153024i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2831.02 | − | 1634.49i | −0.483190 | − | 0.278970i | ||||
\(326\) | −4904.49 | − | 2831.61i | −0.833235 | − | 0.481068i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 51.2270i | − | 0.00862360i | ||||||
\(329\) | −1768.17 | − | 876.859i | −0.296298 | − | 0.146939i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3354.20 | − | 5809.64i | −0.556989 | − | 0.964734i | −0.997746 | − | 0.0671070i | \(-0.978623\pi\) |
0.440757 | − | 0.897627i | \(-0.354710\pi\) | |||||||
\(332\) | 1711.35 | − | 2964.15i | 0.282899 | − | 0.489996i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6660.18 | − | 3845.26i | 1.09110 | − | 0.629949i | ||||
\(335\) | 1706.58 | 0.278330 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −735.278 | −0.118852 | −0.0594260 | − | 0.998233i | \(-0.518927\pi\) | ||||
−0.0594260 | + | 0.998233i | \(0.518927\pi\) | |||||||
\(338\) | 682.764 | − | 394.194i | 0.109874 | − | 0.0634359i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 136.358 | − | 236.178i | 0.0217501 | − | 0.0376722i | ||||
\(341\) | 2571.30 | + | 4453.62i | 0.408339 | + | 0.707264i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1197.69 | − | 6238.52i | −0.188539 | − | 0.982066i | ||||
\(344\) | − | 2100.01i | − | 0.329142i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3804.95 | − | 2196.79i | −0.591201 | − | 0.341330i | ||||
\(347\) | 9227.87 | + | 5327.71i | 1.42760 | + | 0.824226i | 0.996931 | − | 0.0782826i | \(-0.0249437\pi\) |
0.430671 | + | 0.902509i | \(0.358277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10961.2i | − | 1.68120i | −0.541653 | − | 0.840602i | \(-0.682201\pi\) | ||
0.541653 | − | 0.840602i | \(-0.317799\pi\) | |||||||
\(350\) | 1317.13 | + | 1980.75i | 0.201153 | + | 0.302502i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −813.242 | − | 1408.58i | −0.123142 | − | 0.213288i | ||||
\(353\) | −1529.90 | + | 2649.87i | −0.230676 | + | 0.399542i | −0.958007 | − | 0.286744i | \(-0.907427\pi\) |
0.727331 | + | 0.686286i | \(0.240760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3660.21 | − | 2113.23i | 0.547223 | − | 0.315939i | ||||
\(356\) | −5265.54 | −0.783913 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4619.35 | 0.681956 | ||||||||
\(359\) | 5412.09 | − | 3124.67i | 0.795653 | − | 0.459370i | −0.0462959 | − | 0.998928i | \(-0.514742\pi\) |
0.841949 | + | 0.539557i | \(0.181408\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1729.50 | − | 2995.58i | 0.252150 | − | 0.436736i | ||||
\(362\) | −3240.23 | − | 5612.25i | −0.470450 | − | 0.814844i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3763.47 | + | 238.262i | −0.541921 | + | 0.0343086i | ||||
\(365\) | − | 7005.19i | − | 1.00457i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10383.2 | + | 5994.76i | 1.47684 | + | 0.852654i | 0.999658 | − | 0.0261512i | \(-0.00832512\pi\) |
0.477181 | + | 0.878805i | \(0.341658\pi\) | |||||||
\(368\) | 591.787 | + | 341.668i | 0.0838288 | + | 0.0483986i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4276.91i | 0.600935i | ||||||||
\(371\) | −11863.7 | + | 751.079i | −1.66019 | + | 0.105105i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1431.68 | + | 2479.73i | 0.198738 | + | 0.344225i | 0.948120 | − | 0.317914i | \(-0.102982\pi\) |
−0.749381 | + | 0.662139i | \(0.769649\pi\) | |||||||
\(374\) | 444.493 | − | 769.884i | 0.0614550 | − | 0.106443i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 738.318 | − | 426.268i | 0.101266 | − | 0.0584657i | ||||
\(377\) | 11106.4 | 1.51726 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7545.36 | −1.02264 | −0.511318 | − | 0.859392i | \(-0.670843\pi\) | ||||
−0.511318 | + | 0.859392i | \(0.670843\pi\) | |||||||
\(380\) | −2743.30 | + | 1583.84i | −0.370337 | + | 0.213814i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 109.976 | − | 190.484i | 0.0147300 | − | 0.0255131i | ||||
\(383\) | 1640.98 | + | 2842.25i | 0.218929 | + | 0.379197i | 0.954481 | − | 0.298272i | \(-0.0964102\pi\) |
−0.735552 | + | 0.677469i | \(0.763077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4063.69 | − | 6111.13i | −0.537934 | − | 0.808966i | ||||
\(386\) | 9997.71i | 1.31832i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4298.02 | − | 2481.46i | −0.562368 | − | 0.324683i | ||||
\(389\) | 1010.94 | + | 583.664i | 0.131765 | + | 0.0760744i | 0.564433 | − | 0.825479i | \(-0.309095\pi\) |
−0.432669 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 373.490i | 0.0483075i | ||||||||
\(392\) | 2530.43 | + | 1061.35i | 0.326035 | + | 0.136751i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 508.689 | + | 881.076i | 0.0650441 | + | 0.112660i | ||||
\(395\) | −4374.56 | + | 7576.96i | −0.557235 | + | 0.965160i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11853.7 | + | 6843.75i | −1.49854 | + | 0.865183i | −0.999999 | − | 0.00168199i | \(-0.999465\pi\) |
−0.498543 | + | 0.866865i | \(0.666131\pi\) | |||||||
\(398\) | 2410.85 | 0.303631 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1027.50 | −0.128438 | ||||||||
\(401\) | 3691.74 | − | 2131.42i | 0.459742 | − | 0.265432i | −0.252194 | − | 0.967677i | \(-0.581152\pi\) |
0.711936 | + | 0.702245i | \(0.247819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2575.15 | + | 4460.29i | −0.318306 | + | 0.551323i | ||||
\(404\) | −1003.77 | − | 1738.58i | −0.123612 | − | 0.214103i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7240.25 | − | 3590.54i | −0.885043 | − | 0.438906i | ||||
\(407\) | 13941.7i | 1.69794i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9296.72 | + | 5367.46i | 1.12394 | + | 0.648909i | 0.942405 | − | 0.334474i | \(-0.108559\pi\) |
0.181539 | + | 0.983384i | \(0.441892\pi\) | |||||||
\(410\) | 86.4678 | + | 49.9222i | 0.0104155 | + | 0.00601337i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1409.25i | 0.168516i | ||||||||
\(413\) | 123.020 | + | 1943.16i | 0.0146572 | + | 0.231517i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3335.52 | + | 5777.29i | 0.394540 | + | 0.683364i | ||||
\(416\) | 814.460 | − | 1410.69i | 0.0959909 | − | 0.166261i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8942.48 | + | 5162.94i | −1.04639 | + | 0.604133i | ||||
\(419\) | 894.104 | 0.104248 | 0.0521239 | − | 0.998641i | \(-0.483401\pi\) | ||||
0.0521239 | + | 0.998641i | \(0.483401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4275.53 | 0.494956 | 0.247478 | − | 0.968893i | \(-0.420398\pi\) | ||||
0.247478 | + | 0.968893i | \(0.420398\pi\) | |||||||
\(422\) | −5416.95 | + | 3127.48i | −0.624865 | + | 0.360766i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2567.44 | − | 4446.94i | 0.294071 | − | 0.509345i | ||||
\(425\) | −280.800 | − | 486.360i | −0.0320490 | − | 0.0555105i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4480.00 | − | 9033.81i | 0.507734 | − | 1.02383i | ||||
\(428\) | 4319.54i | 0.487833i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3544.67 | + | 2046.52i | 0.397533 | + | 0.229516i | ||||
\(431\) | −4324.96 | − | 2497.01i | −0.483355 | − | 0.279065i | 0.238459 | − | 0.971153i | \(-0.423358\pi\) |
−0.721813 | + | 0.692088i | \(0.756691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2469.93i | − | 0.274128i | −0.990562 | − | 0.137064i | \(-0.956233\pi\) | ||
0.990562 | − | 0.137064i | \(-0.0437666\pi\) | |||||||
\(434\) | 3120.69 | − | 2075.15i | 0.345156 | − | 0.229517i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 970.391 | + | 1680.77i | 0.106590 | + | 0.184620i | ||||
\(437\) | 2169.11 | − | 3757.01i | 0.237443 | − | 0.411264i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7186.67 | + | 4149.22i | −0.781323 | + | 0.451097i | −0.836899 | − | 0.547357i | \(-0.815634\pi\) |
0.0555758 | + | 0.998454i | \(0.482301\pi\) | |||||||
\(440\) | 3170.11 | 0.343475 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 890.317 | 0.0958101 | ||||||||
\(443\) | −10784.7 | + | 6226.57i | −1.15666 | + | 0.667795i | −0.950500 | − | 0.310724i | \(-0.899428\pi\) |
−0.206155 | + | 0.978519i | \(0.566095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5131.42 | − | 8887.87i | 0.546635 | − | 0.946799i | ||||
\(446\) | −1206.04 | − | 2088.93i | −0.128044 | − | 0.221779i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −987.001 | + | 656.321i | −0.104088 | + | 0.0692149i | ||||
\(449\) | 7411.31i | 0.778979i | 0.921031 | + | 0.389489i | \(0.127348\pi\) | ||||
−0.921031 | + | 0.389489i | \(0.872652\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 281.864 | + | 162.734i | 0.0294289 | + | 0.0169908i | ||||
\(452\) | −5843.36 | − | 3373.66i | −0.608072 | − | 0.351070i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 946.118i | − | 0.0978051i | ||||||
\(455\) | 3265.44 | − | 6584.67i | 0.336453 | − | 0.678449i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6156.75 | + | 10663.8i | 0.630198 | + | 1.09154i | 0.987511 | + | 0.157551i | \(0.0503597\pi\) |
−0.357313 | + | 0.933985i | \(0.616307\pi\) | |||||||
\(458\) | 2049.52 | − | 3549.87i | 0.209100 | − | 0.362171i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1153.43 | + | 665.930i | −0.116910 | + | 0.0674982i | ||||
\(461\) | −16338.5 | −1.65067 | −0.825334 | − | 0.564645i | \(-0.809013\pi\) | ||||
−0.825334 | + | 0.564645i | \(0.809013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13862.3 | 1.39144 | 0.695720 | − | 0.718313i | \(-0.255086\pi\) | ||||
0.695720 | + | 0.718313i | \(0.255086\pi\) | |||||||
\(464\) | 3023.25 | − | 1745.47i | 0.302480 | − | 0.174637i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1788.53 | + | 3097.83i | −0.177794 | + | 0.307949i | ||||
\(467\) | −8822.10 | − | 15280.3i | −0.874172 | − | 1.51411i | −0.857643 | − | 0.514246i | \(-0.828072\pi\) |
−0.0165291 | − | 0.999863i | \(-0.505262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −256.146 | − | 4045.96i | −0.0252191 | − | 0.398347i | ||||
\(470\) | 1661.64i | 0.163076i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −728.368 | − | 420.523i | −0.0710293 | − | 0.0410088i | ||||
\(473\) | 11554.8 | + | 6671.15i | 1.12323 | + | 0.648499i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6523.20i | 0.630115i | ||||||||
\(476\) | −580.397 | − | 287.827i | −0.0558875 | − | 0.0277154i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4369.08 | + | 7567.47i | 0.418069 | + | 0.724117i | ||||
\(479\) | 2801.64 | − | 4852.59i | 0.267245 | − | 0.462882i | −0.700904 | − | 0.713255i | \(-0.747220\pi\) |
0.968149 | + | 0.250373i | \(0.0805534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12091.9 | + | 6981.29i | −1.14625 | + | 0.661786i | ||||
\(482\) | −5600.66 | −0.529260 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5009.78 | 0.470490 | ||||||||
\(485\) | 8377.08 | − | 4836.51i | 0.784296 | − | 0.452813i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 733.532 | − | 1270.51i | 0.0682536 | − | 0.118219i | −0.829879 | − | 0.557943i | \(-0.811591\pi\) |
0.898133 | + | 0.439725i | \(0.144924\pi\) | |||||||
\(488\) | 2177.86 | + | 3772.17i | 0.202023 | + | 0.349914i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4257.47 | + | 3236.87i | −0.392516 | + | 0.298422i | ||||
\(491\) | 379.554i | 0.0348860i | 0.999848 | + | 0.0174430i | \(0.00555256\pi\) | ||||
−0.999848 | + | 0.0174430i | \(0.994447\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1652.41 | + | 954.021i | 0.150955 | + | 0.0871541i | ||||
\(494\) | −8955.88 | − | 5170.68i | −0.815676 | − | 0.470931i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1618.84i | 0.146548i | ||||||||
\(497\) | −5559.40 | − | 8360.44i | −0.501757 | − | 0.754561i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6499.43 | + | 11257.3i | 0.583075 | + | 1.00992i | 0.995112 | + | 0.0987491i | \(0.0314841\pi\) |
−0.412037 | + | 0.911167i | \(0.635183\pi\) | |||||||
\(500\) | 2950.39 | − | 5110.22i | 0.263891 | − | 0.457072i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5332.14 | − | 3078.51i | 0.474074 | − | 0.273707i | ||||
\(503\) | 10899.0 | 0.966129 | 0.483064 | − | 0.875585i | \(-0.339524\pi\) | ||||
0.483064 | + | 0.875585i | \(0.339524\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3912.81 | 0.344787 | ||||||||
\(506\) | −3759.89 | + | 2170.77i | −0.330331 | + | 0.190717i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2851.19 | − | 4938.40i | 0.249018 | − | 0.431311i | ||||
\(509\) | 8142.34 | + | 14103.0i | 0.709043 | + | 1.22810i | 0.965212 | + | 0.261467i | \(0.0842062\pi\) |
−0.256169 | + | 0.966632i | \(0.582460\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16607.9 | + | 1051.43i | −1.43775 | + | 0.0910227i | ||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.0301 | + | 9.25498i | 0.00137560 | + | 0.000794201i | ||||
\(515\) | −2378.71 | − | 1373.35i | −0.203531 | − | 0.117509i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5416.55i | 0.460773i | ||||||||
\(518\) | 10139.7 | − | 641.935i | 0.860061 | − | 0.0544498i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1587.43 | + | 2749.51i | 0.133872 | + | 0.231873i | ||||
\(521\) | 7475.64 | − | 12948.2i | 0.628626 | − | 1.08881i | −0.359202 | − | 0.933260i | \(-0.616951\pi\) |
0.987828 | − | 0.155552i | \(-0.0497155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11840.7 | + | 6836.22i | −0.989975 | + | 0.571562i | −0.905267 | − | 0.424844i | \(-0.860329\pi\) |
−0.0847081 | + | 0.996406i | \(0.526996\pi\) | |||||||
\(524\) | −4614.70 | −0.384721 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1501.66 | −0.124478 | ||||||||
\(527\) | −766.264 | + | 442.403i | −0.0633377 | + | 0.0365680i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5171.49 | + | 8957.29i | −0.425042 | + | 0.736195i | ||||
\(530\) | 5004.09 | + | 8667.33i | 0.410120 | + | 0.710349i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4166.72 | + | 6266.07i | 0.339568 | + | 0.510655i | ||||
\(533\) | 325.956i | 0.0264892i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7291.08 | − | 4209.51i | −0.589198 | − | 0.340174i | ||||
\(536\) | 1516.57 | + | 875.594i | 0.122213 | + | 0.0705595i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1331.12i | − | 0.106671i | ||||||
\(539\) | −13878.3 | + | 10551.4i | −1.10906 | + | 0.843194i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3105.32 | − | 5378.57i | −0.246780 | − | 0.427436i | 0.715850 | − | 0.698254i | \(-0.246039\pi\) |
−0.962631 | + | 0.270818i | \(0.912706\pi\) | |||||||
\(542\) | 3332.08 | − | 5771.33i | 0.264068 | − | 0.457379i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 242.351 | − | 139.922i | 0.0191006 | − | 0.0110277i | ||||
\(545\) | −3782.69 | −0.297308 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10396.4 | 0.812649 | 0.406324 | − | 0.913729i | \(-0.366810\pi\) | ||||
0.406324 | + | 0.913729i | \(0.366810\pi\) | |||||||
\(548\) | 6817.75 | − | 3936.23i | 0.531459 | − | 0.306838i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3264.09 | − | 5653.57i | 0.253057 | − | 0.438308i | ||||
\(551\) | −11081.3 | − | 19193.4i | −0.856768 | − | 1.48397i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18620.0 | + | 9233.94i | 1.43183 | + | 0.710067i | ||||
\(554\) | 11313.0i | 0.867589i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2845.48 | + | 1642.84i | 0.217042 | + | 0.125309i | ||||
\(557\) | 11076.9 | + | 6395.26i | 0.842628 | + | 0.486492i | 0.858157 | − | 0.513388i | \(-0.171610\pi\) |
−0.0155285 | + | 0.999879i | \(0.504943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13362.3i | 1.01103i | ||||||||
\(560\) | −145.965 | − | 2305.59i | −0.0110146 | − | 0.173981i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4156.44 | + | 7199.16i | 0.311973 | + | 0.540353i | ||||
\(563\) | −3100.58 | + | 5370.36i | −0.232103 | + | 0.402014i | −0.958427 | − | 0.285339i | \(-0.907894\pi\) |
0.726324 | + | 0.687353i | \(0.241227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11389.0 | − | 6575.46i | 0.848035 | − | 0.489613i | ||||
\(566\) | 12123.9 | 0.900360 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4336.92 | 0.320375 | ||||||||
\(569\) | 22006.0 | − | 12705.2i | 1.62134 | − | 0.936079i | 0.634774 | − | 0.772698i | \(-0.281093\pi\) |
0.986563 | − | 0.163381i | \(-0.0522401\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4142.12 | + | 7174.37i | −0.303577 | + | 0.525811i | −0.976944 | − | 0.213498i | \(-0.931514\pi\) |
0.673366 | + | 0.739309i | \(0.264848\pi\) | |||||||
\(572\) | 5174.63 | + | 8962.73i | 0.378256 | + | 0.655158i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 105.377 | − | 212.490i | 0.00766264 | − | 0.0154515i | ||||
\(575\) | 2742.69i | 0.198919i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1424.66 | − | 822.525i | −0.102789 | − | 0.0593452i | 0.447724 | − | 0.894172i | \(-0.352235\pi\) |
−0.550513 | + | 0.834826i | \(0.685568\pi\) | |||||||
\(578\) | −8377.10 | − | 4836.52i | −0.602840 | − | 0.348050i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6804.05i | 0.487108i | ||||||||
\(581\) | 13196.1 | − | 8774.97i | 0.942286 | − | 0.626587i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16312.1 | + | 28253.4i | 1.15880 | + | 2.00710i | ||||
\(584\) | 3594.15 | − | 6225.25i | 0.254669 | − | 0.441100i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8832.83 | + | 5099.64i | −0.622664 | + | 0.359495i | ||||
\(587\) | −21115.2 | −1.48470 | −0.742350 | − | 0.670013i | \(-0.766289\pi\) | ||||
−0.742350 | + | 0.670013i | \(0.766289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10277.3 | 0.718964 | ||||||||
\(590\) | 1419.63 | − | 819.623i | 0.0990597 | − | 0.0571921i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2194.35 | + | 3800.72i | −0.152343 | + | 0.263866i | ||||
\(593\) | −6622.57 | − | 11470.6i | −0.458611 | − | 0.794338i | 0.540277 | − | 0.841488i | \(-0.318320\pi\) |
−0.998888 | + | 0.0471494i | \(0.984986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1051.45 | − | 699.174i | 0.0724455 | − | 0.0481737i | ||||
\(596\) | 10795.8i | 0.741971i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3765.52 | − | 2174.02i | −0.257498 | − | 0.148666i | ||||
\(599\) | −11800.0 | − | 6812.73i | −0.804900 | − | 0.464709i | 0.0402819 | − | 0.999188i | \(-0.487174\pi\) |
−0.845182 | + | 0.534479i | \(0.820508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15150.8i | − | 1.02831i | −0.857697 | − | 0.514156i | \(-0.828105\pi\) | ||
0.857697 | − | 0.514156i | \(-0.171895\pi\) | |||||||
\(602\) | 4319.85 | − | 8710.87i | 0.292465 | − | 0.589748i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2545.82 | + | 4409.49i | 0.171503 | + | 0.297052i | ||||
\(605\) | −4882.17 | + | 8456.17i | −0.328080 | + | 0.568251i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3988.38 | + | 2302.69i | −0.266694 | + | 0.153976i | −0.627384 | − | 0.778710i | \(-0.715875\pi\) |
0.360690 | + | 0.932686i | \(0.382541\pi\) | |||||||
\(608\) | −3250.48 | −0.216816 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8489.56 | −0.563495 | ||||||||
\(611\) | −4697.90 | + | 2712.33i | −0.311058 | + | 0.179590i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2333.08 | − | 4041.01i | 0.153723 | − | 0.266256i | −0.778870 | − | 0.627185i | \(-0.784207\pi\) |
0.932593 | + | 0.360929i | \(0.117540\pi\) | |||||||
\(614\) | 4775.43 | + | 8271.28i | 0.313877 | + | 0.543651i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −475.811 | − | 7515.68i | −0.0311217 | − | 0.491583i | ||||
\(617\) | − | 16316.4i | − | 1.06463i | −0.846548 | − | 0.532313i | \(-0.821323\pi\) | ||
0.846548 | − | 0.532313i | \(-0.178677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4523.82 | + | 2611.83i | 0.293744 | + | 0.169593i | 0.639629 | − | 0.768684i | \(-0.279088\pi\) |
−0.345885 | + | 0.938277i | \(0.612421\pi\) | |||||||
\(620\) | −2732.48 | − | 1577.60i | −0.176999 | − | 0.102190i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 20127.9i | − | 1.29751i | ||||||
\(623\) | −21841.5 | − | 10831.5i | −1.40459 | − | 0.696559i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1736.79 | + | 3008.20i | 0.111154 | + | 0.192525i | ||||
\(626\) | 9799.76 | − | 16973.7i | 0.625682 | − | 1.08371i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10739.5 | − | 6200.46i | 0.682409 | − | 0.393989i | ||||
\(629\) | −2398.72 | −0.152056 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12467.8 | −0.786584 | −0.393292 | − | 0.919414i | \(-0.628664\pi\) | ||||
−0.393292 | + | 0.919414i | \(0.628664\pi\) | |||||||
\(632\) | −7775.00 | + | 4488.90i | −0.489356 | + | 0.282530i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3716.11 | + | 6436.50i | −0.232785 | + | 0.403196i | ||||
\(635\) | 5557.12 | + | 9625.22i | 0.347288 | + | 0.601520i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16101.0 | − | 6753.37i | −1.00149 | − | 0.420060i | ||||
\(638\) | 22179.6i | 1.37633i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 864.221 | + | 498.958i | 0.0533771 | + | 0.0308173i | ||||
\(641\) | 5896.71 | + | 3404.47i | 0.363348 | + | 0.209779i | 0.670548 | − | 0.741866i | \(-0.266059\pi\) |
−0.307200 | + | 0.951645i | \(0.599392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8746.71i | 0.536449i | 0.963356 | + | 0.268224i | \(0.0864369\pi\) | ||||
−0.963356 | + | 0.268224i | \(0.913563\pi\) | |||||||
\(644\) | 1751.91 | + | 2634.58i | 0.107197 | + | 0.161207i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −888.306 | − | 1538.59i | −0.0541020 | − | 0.0937075i | ||||
\(647\) | −5728.79 | + | 9922.55i | −0.348102 | + | 0.602930i | −0.985912 | − | 0.167263i | \(-0.946507\pi\) |
0.637810 | + | 0.770193i | \(0.279840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4627.65 | − | 2671.77i | 0.279894 | − | 0.161597i | ||||
\(650\) | 6537.97 | 0.394523 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11326.4 | 0.680333 | ||||||||
\(653\) | 19349.2 | − | 11171.3i | 1.15956 | − | 0.669472i | 0.208361 | − | 0.978052i | \(-0.433187\pi\) |
0.951198 | + | 0.308580i | \(0.0998537\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4497.15 | − | 7789.29i | 0.268272 | − | 0.464661i | ||||
\(656\) | 51.2270 | + | 88.7278i | 0.00304890 | + | 0.00528085i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3939.41 | − | 249.401i | 0.233395 | − | 0.0147761i | ||||
\(659\) | − | 6944.96i | − | 0.410527i | −0.978707 | − | 0.205263i | \(-0.934195\pi\) | ||
0.978707 | − | 0.205263i | \(-0.0658051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16338.1 | − | 9432.82i | −0.961391 | − | 0.555059i | −0.0647898 | − | 0.997899i | \(-0.520638\pi\) |
−0.896601 | + | 0.442840i | \(0.853971\pi\) | |||||||
\(662\) | 11619.3 | + | 6708.40i | 0.682170 | + | 0.393851i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6845.41i | 0.400080i | ||||||||
\(665\) | −14637.3 | + | 926.675i | −0.853548 | + | 0.0540374i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4659.16 | − | 8069.90i | −0.270470 | − | 0.468468i | ||||
\(668\) | −7690.51 | + | 13320.4i | −0.445441 | + | 0.771527i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2955.89 | + | 1706.58i | −0.170442 | + | 0.0984045i | ||||
\(671\) | −27673.9 | −1.59216 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5622.15 | 0.322018 | 0.161009 | − | 0.986953i | \(-0.448525\pi\) | ||||
0.161009 | + | 0.986953i | \(0.448525\pi\) | |||||||
\(674\) | 1273.54 | − | 735.278i | 0.0727817 | − | 0.0420206i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −788.388 | + | 1365.53i | −0.0448560 | + | 0.0776928i | ||||
\(677\) | −13723.5 | − | 23769.8i | −0.779081 | − | 1.34941i | −0.932472 | − | 0.361243i | \(-0.882353\pi\) |
0.153391 | − | 0.988166i | \(-0.450981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12723.7 | − | 19134.4i | −0.719133 | − | 1.08146i | ||||
\(680\) | 545.430i | 0.0307593i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8907.24 | − | 5142.60i | −0.500111 | − | 0.288739i | ||||
\(683\) | 27472.6 | + | 15861.3i | 1.53911 | + | 0.888604i | 0.998891 | + | 0.0470784i | \(0.0149911\pi\) |
0.540217 | + | 0.841526i | \(0.318342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15343.9i | 0.855852i | ||||||||
\(686\) | 8312.97 | + | 9607.75i | 0.462669 | + | 0.534731i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2100.01 | + | 3637.32i | 0.116369 | + | 0.201558i | ||||
\(689\) | −16336.6 | + | 28295.7i | −0.903299 | + | 1.56456i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6896.96 | − | 3981.96i | 0.379700 | − | 0.219220i | −0.297988 | − | 0.954570i | \(-0.596315\pi\) |
0.677688 | + | 0.735350i | \(0.262982\pi\) | |||||||
\(692\) | 8787.16 | 0.482714 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21310.8 | −1.16563 | ||||||||
\(695\) | −5546.01 | + | 3201.99i | −0.302694 | + | 0.174760i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.9991 | + | 48.4959i | −0.00152158 | + | 0.00263545i | ||||
\(698\) | 10961.2 | + | 18985.4i | 0.594395 | + | 1.02952i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4262.09 | − | 2113.63i | −0.230131 | − | 0.114125i | ||||
\(701\) | − | 21374.8i | − | 1.15166i | −0.817568 | − | 0.575831i | \(-0.804678\pi\) | ||
0.817568 | − | 0.575831i | \(-0.195322\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24129.2 | + | 13931.0i | 1.29453 | + | 0.747395i | ||||
\(704\) | 2817.15 | + | 1626.48i | 0.150817 | + | 0.0870744i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 6119.61i | − | 0.326225i | ||||||
\(707\) | −587.286 | − | 9276.47i | −0.0312407 | − | 0.493462i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3514.63 | − | 6087.51i | −0.186170 | − | 0.322456i | 0.757800 | − | 0.652487i | \(-0.226274\pi\) |
−0.943970 | + | 0.330031i | \(0.892941\pi\) | |||||||
\(710\) | −4226.45 | + | 7320.43i | −0.223403 | + | 0.386945i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9120.18 | − | 5265.54i | 0.480047 | − | 0.277155i | ||||
\(713\) | 4321.13 | 0.226967 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20171.3 | −1.05505 | ||||||||
\(716\) | −8000.95 | + | 4619.35i | −0.417611 | + | 0.241108i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6249.35 | + | 10824.2i | −0.324824 | + | 0.562612i | ||||
\(719\) | 5369.20 | + | 9299.72i | 0.278494 | + | 0.482366i | 0.971011 | − | 0.239036i | \(-0.0768314\pi\) |
−0.692517 | + | 0.721402i | \(0.743498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2898.90 | + | 5845.57i | −0.149738 | + | 0.301942i | ||||
\(722\) | 6917.98i | 0.356594i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11224.5 | + | 6480.47i | 0.576181 | + | 0.332658i | ||||
\(725\) | 12134.4 | + | 7005.77i | 0.621598 | + | 0.358880i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 15722.6i | − | 0.802092i | −0.916058 | − | 0.401046i | \(-0.868647\pi\) | ||
0.916058 | − | 0.401046i | \(-0.131353\pi\) | |||||||
\(728\) | 6280.26 | − | 4176.15i | 0.319728 | − | 0.212608i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7005.19 | + | 12133.4i | 0.355170 | + | 0.615172i | ||||
\(731\) | −1147.80 | + | 1988.05i | −0.0580751 | + | 0.100589i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14966.9 | + | 8641.17i | −0.754184 | + | 0.435428i | −0.827204 | − | 0.561902i | \(-0.810070\pi\) |
0.0730197 | + | 0.997331i | \(0.476736\pi\) | |||||||
\(734\) | −23979.0 | −1.20583 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1366.67 | −0.0684459 | ||||||||
\(737\) | −9635.47 | + | 5563.04i | −0.481584 | + | 0.278043i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17235.3 | − | 29852.5i | 0.857932 | − | 1.48598i | −0.0159660 | − | 0.999873i | \(-0.505082\pi\) |
0.873898 | − | 0.486109i | \(-0.161584\pi\) | |||||||
\(740\) | −4276.91 | − | 7407.82i | −0.212462 | − | 0.367996i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19797.4 | − | 13164.6i | 0.979495 | − | 0.651330i | ||||
\(743\) | − | 33600.2i | − | 1.65904i | −0.558474 | − | 0.829522i | \(-0.688613\pi\) | ||
0.558474 | − | 0.829522i | \(-0.311387\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18222.6 | − | 10520.8i | −0.896142 | − | 0.517388i | ||||
\(746\) | −4959.47 | − | 2863.35i | −0.243404 | − | 0.140529i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1777.97i | 0.0869105i | ||||||||
\(749\) | −8885.55 | + | 17917.5i | −0.433472 | + | 0.874087i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17479.2 | − | 30274.9i | −0.849303 | − | 1.47104i | −0.881831 | − | 0.471565i | \(-0.843689\pi\) |
0.0325279 | − | 0.999471i | \(-0.489644\pi\) | |||||||
\(752\) | −852.536 | + | 1476.64i | −0.0413415 | + | 0.0716056i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19236.8 | + | 11106.4i | −0.929131 | + | 0.536434i | ||||
\(755\) | −9923.90 | −0.478368 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38297.1 | 1.83875 | 0.919374 | − | 0.393386i | \(-0.128696\pi\) | ||||
0.919374 | + | 0.393386i | \(0.128696\pi\) | |||||||
\(758\) | 13068.9 | − | 7545.36i | 0.626234 | − | 0.361556i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3167.68 | − | 5486.59i | 0.151189 | − | 0.261868i | ||||
\(761\) | 9539.02 | + | 16522.1i | 0.454388 | + | 0.787023i | 0.998653 | − | 0.0518907i | \(-0.0165247\pi\) |
−0.544265 | + | 0.838913i | \(0.683191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 567.757 | + | 8967.99i | 0.0269386 | + | 0.425509i | ||||
\(764\) | 439.903i | 0.0208313i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5684.51 | − | 3281.95i | −0.268133 | − | 0.154806i | ||||
\(767\) | 4634.58 | + | 2675.78i | 0.218181 | + | 0.125967i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12553.3i | 0.588667i | 0.955703 | + | 0.294334i | \(0.0950977\pi\) | ||||
−0.955703 | + | 0.294334i | \(0.904902\pi\) | |||||||
\(770\) | 13149.6 | + | 6521.10i | 0.615429 | + | 0.305200i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9997.71 | − | 17316.5i | −0.466095 | − | 0.807300i | ||||
\(773\) | 4533.66 | − | 7852.53i | 0.210950 | − | 0.365376i | −0.741062 | − | 0.671437i | \(-0.765678\pi\) |
0.952012 | + | 0.306060i | \(0.0990109\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5626.99 | + | 3248.74i | −0.260810 | + | 0.150579i | ||||
\(776\) | 9925.85 | 0.459172 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2334.66 | −0.107585 | ||||||||
\(779\) | 563.297 | − | 325.220i | 0.0259078 | − | 0.0149579i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13777.2 | + | 23862.8i | −0.631226 | + | 1.09331i | ||||
\(782\) | −373.490 | − | 646.904i | −0.0170793 | − | 0.0295822i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5444.18 | + | 692.108i | −0.248004 | + | 0.0315282i | ||||
\(785\) | 24170.1i | 1.09894i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1848.67 | + | 1067.33i | 0.0837333 | + | 0.0483435i | 0.541282 | − | 0.840841i | \(-0.317939\pi\) |
−0.457549 | + | 0.889185i | \(0.651272\pi\) | |||||||
\(788\) | −1762.15 | − | 1017.38i | −0.0796625 | − | 0.0459932i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 17498.2i | − | 0.788050i | ||||||
\(791\) | −17298.5 | − | 26014.1i | −0.777577 | − | 1.16935i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13857.7 | − | 24002.2i | −0.620556 | − | 1.07483i | ||||
\(794\) | 13687.5 | − | 23707.4i | 0.611777 | − | 1.05963i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4175.72 | + | 2410.85i | −0.185935 | + | 0.107350i | ||||
\(797\) | −16730.6 | −0.743574 | −0.371787 | − | 0.928318i | \(-0.621255\pi\) | ||||
−0.371787 | + | 0.928318i | \(0.621255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −931.939 | −0.0412636 | ||||||||
\(800\) | 1779.69 | − | 1027.50i | 0.0786518 | − | 0.0454096i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4262.85 | + | 7383.47i | −0.187689 | + | 0.325087i | ||||
\(803\) | 22835.2 | + | 39551.8i | 1.00353 | + | 1.73817i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6154.28 | + | 389.623i | −0.269453 | + | 0.0170589i | ||||
\(806\) | − | 10300.6i | − | 0.450153i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3477.16 | + | 2007.54i | 0.151394 | + | 0.0874072i | ||||
\(809\) | −21928.9 | − | 12660.6i | −0.953001 | − | 0.550215i | −0.0589890 | − | 0.998259i | \(-0.518788\pi\) |
−0.894012 | + | 0.448043i | \(0.852121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23863.6i | − | 1.03325i | −0.856212 | − | 0.516625i | \(-0.827188\pi\) | ||
0.856212 | − | 0.516625i | \(-0.172812\pi\) | |||||||
\(812\) | 16131.0 | − | 1021.24i | 0.697152 | − | 0.0441362i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13941.7 | − | 24147.7i | −0.600314 | − | 1.03977i | ||||
\(815\) | −11037.9 | + | 19118.3i | −0.474407 | + | 0.821697i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23091.9 | − | 13332.1i | 0.988841 | − | 0.570908i | ||||
\(818\) | −21469.8 | −0.917696 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −199.689 | −0.00850419 | ||||||||
\(821\) | 20798.2 | − | 12007.9i | 0.884121 | − | 0.510447i | 0.0121059 | − | 0.999927i | \(-0.496146\pi\) |
0.872015 | + | 0.489479i | \(0.162813\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16008.0 | − | 27726.6i | 0.678011 | − | 1.17435i | −0.297569 | − | 0.954700i | \(-0.596176\pi\) |
0.975579 | − | 0.219648i | \(-0.0704910\pi\) | |||||||
\(824\) | −1409.25 | − | 2440.89i | −0.0595794 | − | 0.103195i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2156.24 | − | 3242.63i | −0.0908294 | − | 0.136593i | ||||
\(827\) | 33661.4i | 1.41538i | 0.706522 | + | 0.707691i | \(0.250263\pi\) | ||||
−0.706522 | + | 0.707691i | \(0.749737\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2750.33 | + | 1587.90i | 0.115227 | + | 0.0665261i | 0.556506 | − | 0.830844i | \(-0.312142\pi\) |
−0.441279 | + | 0.897370i | \(0.645475\pi\) | |||||||
\(830\) | −11554.6 | − | 6671.04i | −0.483211 | − | 0.278982i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3257.84i | 0.135752i | ||||||||
\(833\) | −1815.41 | − | 2387.82i | −0.0755107 | − | 0.0993194i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14989.2 | − | 25962.1i | −0.621226 | − | 1.07600i | ||||
\(836\) | 10325.9 | − | 17885.0i | 0.427187 | − | 0.739909i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1548.63 | + | 894.104i | −0.0638385 | + | 0.0368572i | ||||
\(839\) | 40349.4 | 1.66033 | 0.830165 | − | 0.557518i | \(-0.188246\pi\) | ||||
0.830165 | + | 0.557518i | \(0.188246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23215.3 | −0.951877 | ||||||||
\(842\) | −7405.43 | + | 4275.53i | −0.303097 | + | 0.174993i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6254.96 | − | 10833.9i | 0.255100 | − | 0.441846i | ||||
\(845\) | −1536.61 | − | 2661.49i | −0.0625575 | − | 0.108353i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20780.6 | + | 10305.4i | 0.843012 | + | 0.418062i | ||||
\(848\) | 10269.8i | 0.415879i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 972.721 | + | 561.601i | 0.0392518 | + | 0.0226621i | ||||
\(851\) | 10145.2 | + | 5857.33i | 0.408664 | + | 0.235942i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46022.2i | − | 1.84733i | −0.383204 | − | 0.923664i | \(-0.625179\pi\) | ||
0.383204 | − | 0.923664i | \(-0.374821\pi\) | |||||||
\(854\) | 1274.23 | + | 20127.0i | 0.0510575 | + | 0.806478i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4319.54 | − | 7481.66i | −0.172475 | − | 0.298736i | ||||
\(857\) | −7564.70 | + | 13102.4i | −0.301523 | + | 0.522253i | −0.976481 | − | 0.215603i | \(-0.930828\pi\) |
0.674958 | + | 0.737856i | \(0.264162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39374.0 | − | 22732.6i | 1.56394 | − | 0.902941i | 0.567087 | − | 0.823658i | \(-0.308070\pi\) |
0.996852 | − | 0.0792832i | \(-0.0252631\pi\) | |||||||
\(860\) | −8186.07 | −0.324585 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9988.06 | 0.394657 | ||||||||
\(863\) | 5596.89 | − | 3231.36i | 0.220765 | − | 0.127459i | −0.385539 | − | 0.922691i | \(-0.625985\pi\) |
0.606304 | + | 0.795233i | \(0.292651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8563.34 | + | 14832.1i | −0.336604 | + | 0.583015i | ||||
\(866\) | 2469.93 | + | 4278.05i | 0.0969189 | + | 0.167868i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3330.04 | + | 6714.95i | −0.130218 | + | 0.262581i | ||||
\(869\) | − | 57040.0i | − | 2.22664i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9649.91 | − | 5571.38i | −0.375402 | − | 0.216738i | ||||
\(872\) | −3361.53 | − | 1940.78i | −0.130546 | − | 0.0753706i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8676.45i | 0.335796i | ||||||||
\(875\) | 22750.3 | − | 15128.1i | 0.878970 | − | 0.584485i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16030.7 | + | 27766.0i | 0.617240 | + | 1.06909i | 0.989987 | + | 0.141158i | \(0.0450826\pi\) |
−0.372747 | + | 0.927933i | \(0.621584\pi\) | |||||||
\(878\) | 8298.45 | − | 14373.3i | 0.318974 | − | 0.552479i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5490.79 | + | 3170.11i | −0.210335 | + | 0.121437i | ||||
\(881\) | 17364.4 | 0.664042 | 0.332021 | − | 0.943272i | \(-0.392270\pi\) | ||||
0.332021 | + | 0.943272i | \(0.392270\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22921.5 | −0.873578 | −0.436789 | − | 0.899564i | \(-0.643884\pi\) | ||||
−0.436789 | + | 0.899564i | \(0.643884\pi\) | |||||||
\(884\) | −1542.07 | + | 890.317i | −0.0586715 | + | 0.0338740i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12453.1 | − | 21569.5i | 0.472202 | − | 0.817879i | ||||
\(887\) | −19471.0 | − | 33724.7i | −0.737058 | − | 1.27662i | −0.953814 | − | 0.300397i | \(-0.902881\pi\) |
0.216756 | − | 0.976226i | \(-0.430452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21985.3 | − | 14619.5i | 0.829432 | − | 0.551543i | ||||
\(890\) | 20525.7i | 0.773058i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4177.85 | + | 2412.08i | 0.156822 | + | 0.0905410i | ||||
\(893\) | 9374.56 | + | 5412.41i | 0.351297 | + | 0.202821i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18006.8i | − | 0.672513i | ||||||
\(896\) | 1053.21 | − | 2123.78i | 0.0392695 | − | 0.0791859i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7411.31 | − | 12836.8i | −0.275411 | − | 0.477025i | ||||
\(899\) | 11037.6 | − | 19117.7i | 0.409484 | − | 0.709246i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4861.12 | + | 2806.57i | −0.179742 | + | 0.103774i | ||||
\(902\) | −650.937 | −0.0240286 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13494.7 | 0.496488 | ||||||||
\(905\) | −21877.2 | + | 12630.8i | −0.803560 | + | 0.463936i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19008.5 | + | 32923.6i | −0.695882 | + | 1.20530i | 0.274000 | + | 0.961730i | \(0.411653\pi\) |
−0.969882 | + | 0.243574i | \(0.921680\pi\) | |||||||
\(908\) | 946.118 | + | 1638.72i | 0.0345793 | + | 0.0598931i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 928.773 | + | 14670.4i | 0.0338335 | + | 0.534418i | ||||
\(911\) | − | 22877.1i | − | 0.832000i | −0.909365 | − | 0.416000i | \(-0.863432\pi\) | ||
0.909365 | − | 0.416000i | \(-0.136568\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37665.1 | − | 21746.0i | −1.36532 | − | 0.788266i | ||||
\(914\) | −21327.6 | − | 12313.5i | −0.771832 | − | 0.445617i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8198.07i | 0.295712i | ||||||||
\(917\) | −19141.8 | − | 9492.70i | −0.689333 | − | 0.341850i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 314.315 | + | 544.409i | 0.0112821 | + | 0.0195412i | 0.871611 | − | 0.490198i | \(-0.163075\pi\) |
−0.860329 | + | 0.509739i | \(0.829742\pi\) | |||||||
\(920\) | 1331.86 | − | 2306.85i | 0.0477284 | − | 0.0826680i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28299.0 | − | 16338.5i | 1.01082 | − | 0.583599i | ||||
\(923\) | −27595.7 | −0.984099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17614.8 | −0.626132 | ||||||||
\(926\) | −24010.2 | + | 13862.3i | −0.852079 | + | 0.491948i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3490.95 | + | 6046.50i | −0.123487 | + | 0.213886i | ||||
\(929\) | −21843.2 | − | 37833.5i | −0.771423 | − | 1.33614i | −0.936783 | − | 0.349911i | \(-0.886212\pi\) |
0.165359 | − | 0.986233i | \(-0.447122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4393.91 | + | 34562.9i | 0.154677 | + | 1.21671i | ||||
\(932\) | − | 7154.13i | − | 0.251439i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30560.7 | + | 17644.2i | 1.07064 | + | 0.618133i | ||||
\(935\) | −3001.09 | − | 1732.68i | −0.104969 | − | 0.0606040i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27163.5i | 0.947059i | 0.880778 | + | 0.473529i | \(0.157020\pi\) | ||||
−0.880778 | + | 0.473529i | \(0.842980\pi\) | |||||||
\(938\) | 4489.62 | + | 6751.66i | 0.156281 | + | 0.235021i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1661.64 | − | 2878.05i | −0.0576561 | − | 0.0998633i | ||||
\(941\) | −13299.2 | + | 23034.9i | −0.460725 | + | 0.797999i | −0.998997 | − | 0.0447721i | \(-0.985744\pi\) |
0.538272 | + | 0.842771i | \(0.319077\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 236.840 | − | 136.739i | 0.00817875 | − | 0.00472200i | ||||
\(944\) | 1682.09 | 0.0579952 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26684.6 | −0.917116 | ||||||||
\(947\) | −17614.5 | + | 10169.7i | −0.604429 | + | 0.348967i | −0.770782 | − | 0.637099i | \(-0.780134\pi\) |
0.166353 | + | 0.986066i | \(0.446801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22869.5 | + | 39611.1i | −0.782270 | + | 1.35493i | ||||
\(950\) | −6523.20 | − | 11298.5i | −0.222779 | − | 0.385865i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1293.10 | − | 81.8654i | 0.0440228 | − | 0.00278705i | ||||
\(953\) | 45566.5i | 1.54884i | 0.632673 | + | 0.774419i | \(0.281958\pi\) | ||||
−0.632673 | + | 0.774419i | \(0.718042\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −742.527 | − | 428.698i | −0.0251598 | − | 0.0145260i | ||||
\(956\) | −15134.9 | − | 8738.16i | −0.512028 | − | 0.295620i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11206.6i | 0.377942i | ||||||||
\(959\) | 36377.2 | − | 2303.01i | 1.22490 | − | 0.0775475i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9777.08 | − | 16934.4i | −0.328189 | − | 0.568440i | ||||
\(962\) | 13962.6 | − | 24183.9i | 0.467954 | − | 0.810519i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9700.63 | − | 5600.66i | 0.324104 | − | 0.187121i | ||||
\(965\) | 38972.2 | 1.30006 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34217.5 | −1.13791 | −0.568955 | − | 0.822368i | \(-0.692652\pi\) | ||||
−0.568955 | + | 0.822368i | \(0.692652\pi\) | |||||||
\(968\) | −8677.19 | + | 5009.78i | −0.288115 | + | 0.166343i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9673.02 | + | 16754.2i | −0.320187 | + | 0.554581i | ||||
\(971\) | −16355.4 | − | 28328.5i | −0.540547 | − | 0.936255i | −0.998873 | − | 0.0474705i | \(-0.984884\pi\) |
0.458326 | − | 0.888784i | \(-0.348449\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8423.68 | + | 12667.9i | 0.277544 | + | 0.417382i | ||||
\(974\) | 2934.13i | 0.0965252i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7544.34 | − | 4355.73i | −0.247427 | − | 0.142852i | ||||
\(977\) | −14095.0 | − | 8137.73i | −0.461554 | − | 0.266478i | 0.251144 | − | 0.967950i | \(-0.419193\pi\) |
−0.712697 | + | 0.701472i | \(0.752527\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66908.7i | 2.18428i | ||||||||
\(980\) | 4137.28 | − | 9863.89i | 0.134858 | − | 0.321521i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −379.554 | − | 657.406i | −0.0123341 | − | 0.0213632i | ||||
\(983\) | 16406.9 | − | 28417.6i | 0.532349 | − | 0.922056i | −0.466938 | − | 0.884290i | \(-0.654643\pi\) |
0.999287 | − | 0.0377653i | \(-0.0120239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3434.53 | − | 1982.93i | 0.111100 | − | 0.0641435i | ||||
\(986\) | −3816.09 | −0.123254 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20682.7 | 0.665997 | ||||||||
\(989\) | 9709.04 | − | 5605.52i | 0.312163 | − | 0.180228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4299.83 | − | 7447.52i | 0.137829 | − | 0.238727i | −0.788846 | − | 0.614591i | \(-0.789321\pi\) |
0.926675 | + | 0.375865i | \(0.122654\pi\) | |||||||
\(992\) | −1618.84 | − | 2803.91i | −0.0518126 | − | 0.0897420i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17989.6 | + | 8921.31i | 0.574040 | + | 0.284675i | ||||
\(995\) | − | 9397.78i | − | 0.299427i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27178.0 | + | 15691.2i | 0.863326 | + | 0.498441i | 0.865125 | − | 0.501557i | \(-0.167239\pi\) |
−0.00179867 | + | 0.999998i | \(0.500573\pi\) | |||||||
\(998\) | −22514.7 | − | 12998.9i | −0.714119 | − | 0.412297i | ||||
\(999\) | 0 | 0 |
(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 | 378.4.k.c.269.3 | yes | 16 | |
3.2 | odd | 2 | inner | 378.4.k.c.269.6 | yes | 16 | |
7.5 | odd | 6 | inner | 378.4.k.c.215.6 | yes | 16 | |
21.5 | even | 6 | inner | 378.4.k.c.215.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.k.c.215.3 | ✓ | 16 | 21.5 | even | 6 | inner | |
378.4.k.c.215.6 | yes | 16 | 7.5 | odd | 6 | inner | |
378.4.k.c.269.3 | yes | 16 | 1.1 | even | 1 | trivial | |
378.4.k.c.269.6 | yes | 16 | 3.2 | odd | 2 | inner |