Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not 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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.4.e.h.136.1 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.176777 | + | 0.306186i | 0.940775 | − | 0.339032i | \(-0.110100\pi\) |
−0.763998 | + | 0.645219i | \(0.776766\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.50000 | − | 6.06218i | 0.437500 | − | 0.757772i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | + | 5.19615i | 0.161985 | + | 0.280566i | 0.935580 | − | 0.353114i | \(-0.114877\pi\) |
−0.773596 | + | 0.633680i | \(0.781544\pi\) | |||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | 0.158114 | ||||||||
\(11\) | −23.5000 | − | 40.7032i | −0.644138 | − | 1.11568i | −0.984500 | − | 0.175385i | \(-0.943883\pi\) |
0.340362 | − | 0.940294i | \(-0.389450\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | − | 4.33013i | 0.0533366 | − | 0.0923816i | −0.838124 | − | 0.545479i | \(-0.816348\pi\) |
0.891461 | + | 0.453097i | \(0.149681\pi\) | |||||||
\(14\) | −3.00000 | + | 5.19615i | −0.0572703 | + | 0.0991950i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20.5000 | − | 35.5070i | −0.320312 | − | 0.554798i | ||||
\(17\) | 131.000 | 1.86895 | 0.934475 | − | 0.356027i | \(-0.115869\pi\) | ||||
0.934475 | + | 0.356027i | \(0.115869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −56.0000 | −0.676173 | −0.338086 | − | 0.941115i | \(-0.609780\pi\) | ||||
−0.338086 | + | 0.941115i | \(0.609780\pi\) | |||||||
\(20\) | −17.5000 | − | 30.3109i | −0.195656 | − | 0.338886i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 23.5000 | − | 40.7032i | 0.227737 | − | 0.394452i | ||||
\(23\) | 1.50000 | − | 2.59808i | 0.0135988 | − | 0.0235538i | −0.859146 | − | 0.511731i | \(-0.829005\pi\) |
0.872745 | + | 0.488177i | \(0.162338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 5.00000 | 0.0377146 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 42.0000 | 0.283473 | ||||||||
\(29\) | −78.5000 | − | 135.966i | −0.502658 | − | 0.870629i | −0.999995 | − | 0.00307200i | \(-0.999022\pi\) |
0.497337 | − | 0.867557i | \(-0.334311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −112.500 | + | 194.856i | −0.651793 | + | 1.12894i | 0.330894 | + | 0.943668i | \(0.392650\pi\) |
−0.982687 | + | 0.185271i | \(0.940684\pi\) | |||||||
\(32\) | 80.5000 | − | 139.430i | 0.444704 | − | 0.770250i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 65.5000 | + | 113.449i | 0.330387 | + | 0.572247i | ||||
\(35\) | 30.0000 | 0.144884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −70.0000 | −0.311025 | −0.155513 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155513 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(38\) | −28.0000 | − | 48.4974i | −0.119532 | − | 0.207035i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 37.5000 | − | 64.9519i | 0.148232 | − | 0.256745i | ||||
\(41\) | 70.0000 | − | 121.244i | 0.266638 | − | 0.461831i | −0.701353 | − | 0.712814i | \(-0.747420\pi\) |
0.967992 | + | 0.250983i | \(0.0807538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −198.500 | − | 343.812i | −0.703976 | − | 1.21932i | −0.967060 | − | 0.254549i | \(-0.918073\pi\) |
0.263084 | − | 0.964773i | \(-0.415260\pi\) | |||||||
\(44\) | −329.000 | −1.12724 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | 0.00961578 | ||||||||
\(47\) | −173.500 | − | 300.511i | −0.538459 | − | 0.932638i | −0.998987 | − | 0.0449934i | \(-0.985673\pi\) |
0.460528 | − | 0.887645i | \(-0.347660\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 153.500 | − | 265.870i | 0.447522 | − | 0.775131i | ||||
\(50\) | 12.5000 | − | 21.6506i | 0.0353553 | − | 0.0612372i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17.5000 | − | 30.3109i | −0.0466695 | − | 0.0808339i | ||||
\(53\) | −4.00000 | −0.0103668 | −0.00518342 | − | 0.999987i | \(-0.501650\pi\) | ||||
−0.00518342 | + | 0.999987i | \(0.501650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −235.000 | −0.576134 | ||||||||
\(56\) | 45.0000 | + | 77.9423i | 0.107382 | + | 0.185991i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 78.5000 | − | 135.966i | 0.177716 | − | 0.307814i | ||||
\(59\) | 374.000 | − | 647.787i | 0.825265 | − | 1.42940i | −0.0764511 | − | 0.997073i | \(-0.524359\pi\) |
0.901716 | − | 0.432328i | \(-0.142308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 169.000 | + | 292.717i | 0.354725 | + | 0.614402i | 0.987071 | − | 0.160284i | \(-0.0512411\pi\) |
−0.632346 | + | 0.774686i | \(0.717908\pi\) | |||||||
\(62\) | −225.000 | −0.460888 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | −12.5000 | − | 21.6506i | −0.0238528 | − | 0.0413143i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −246.000 | + | 426.084i | −0.448562 | + | 0.776933i | −0.998293 | − | 0.0584093i | \(-0.981397\pi\) |
0.549730 | + | 0.835342i | \(0.314730\pi\) | |||||||
\(68\) | 458.500 | − | 794.145i | 0.817666 | − | 1.41624i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.0000 | + | 25.9808i | 0.0256120 | + | 0.0443614i | ||||
\(71\) | −32.0000 | −0.0534888 | −0.0267444 | − | 0.999642i | \(-0.508514\pi\) | ||||
−0.0267444 | + | 0.999642i | \(0.508514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 970.000 | 1.55520 | 0.777602 | − | 0.628757i | \(-0.216436\pi\) | ||||
0.777602 | + | 0.628757i | \(0.216436\pi\) | |||||||
\(74\) | −35.0000 | − | 60.6218i | −0.0549820 | − | 0.0952316i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −196.000 | + | 339.482i | −0.295826 | + | 0.512385i | ||||
\(77\) | 141.000 | − | 244.219i | 0.208681 | − | 0.361446i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 628.500 | + | 1088.59i | 0.895086 | + | 1.55033i | 0.833698 | + | 0.552220i | \(0.186219\pi\) |
0.0613873 | + | 0.998114i | \(0.480448\pi\) | |||||||
\(80\) | −205.000 | −0.286496 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 140.000 | 0.188542 | ||||||||
\(83\) | −51.0000 | − | 88.3346i | −0.0674455 | − | 0.116819i | 0.830331 | − | 0.557271i | \(-0.188152\pi\) |
−0.897776 | + | 0.440452i | \(0.854818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 327.500 | − | 567.247i | 0.417910 | − | 0.723842i | ||||
\(86\) | 198.500 | − | 343.812i | 0.248893 | − | 0.431095i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −352.500 | − | 610.548i | −0.427007 | − | 0.739598i | ||||
\(89\) | 1488.00 | 1.77222 | 0.886111 | − | 0.463474i | \(-0.153397\pi\) | ||||
0.886111 | + | 0.463474i | \(0.153397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.0000 | 0.0345588 | ||||||||
\(92\) | −10.5000 | − | 18.1865i | −0.0118989 | − | 0.0206095i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 173.500 | − | 300.511i | 0.190374 | − | 0.329737i | ||||
\(95\) | −140.000 | + | 242.487i | −0.151197 | + | 0.261881i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −487.000 | − | 843.509i | −0.509767 | − | 0.882942i | −0.999936 | − | 0.0113144i | \(-0.996398\pi\) |
0.490169 | − | 0.871627i | \(-0.336935\pi\) | |||||||
\(98\) | 307.000 | 0.316446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −175.000 | −0.175000 | ||||||||
\(101\) | −667.500 | − | 1156.14i | −0.657611 | − | 1.13902i | −0.981232 | − | 0.192829i | \(-0.938234\pi\) |
0.323621 | − | 0.946187i | \(-0.395100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −343.000 | + | 594.093i | −0.328124 | + | 0.568328i | −0.982140 | − | 0.188153i | \(-0.939750\pi\) |
0.654015 | + | 0.756481i | \(0.273083\pi\) | |||||||
\(104\) | 37.5000 | − | 64.9519i | 0.0353575 | − | 0.0612409i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | − | 3.46410i | −0.00183261 | − | 0.00317418i | ||||
\(107\) | 1098.00 | 0.992034 | 0.496017 | − | 0.868313i | \(-0.334795\pi\) | ||||
0.496017 | + | 0.868313i | \(0.334795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −700.000 | −0.615118 | −0.307559 | − | 0.951529i | \(-0.599512\pi\) | ||||
−0.307559 | + | 0.951529i | \(0.599512\pi\) | |||||||
\(110\) | −117.500 | − | 203.516i | −0.101847 | − | 0.176404i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 123.000 | − | 213.042i | 0.103771 | − | 0.179738i | ||||
\(113\) | −527.500 | + | 913.657i | −0.439142 | + | 0.760616i | −0.997624 | − | 0.0689009i | \(-0.978051\pi\) |
0.558482 | + | 0.829517i | \(0.311384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.50000 | − | 12.9904i | −0.00608155 | − | 0.0105336i | ||||
\(116\) | −1099.00 | −0.879652 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 748.000 | 0.583551 | ||||||||
\(119\) | 393.000 | + | 680.696i | 0.302742 | + | 0.524364i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −439.000 | + | 760.370i | −0.329827 | + | 0.571277i | ||||
\(122\) | −169.000 | + | 292.717i | −0.125414 | + | 0.217224i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 787.500 | + | 1363.99i | 0.570319 | + | 0.987822i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1646.00 | −1.15007 | −0.575035 | − | 0.818129i | \(-0.695012\pi\) | ||||
−0.575035 | + | 0.818129i | \(0.695012\pi\) | |||||||
\(128\) | −727.500 | − | 1260.07i | −0.502363 | − | 0.870119i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.5000 | − | 21.6506i | 0.00843325 | − | 0.0146068i | ||||
\(131\) | −916.500 | + | 1587.42i | −0.611259 | + | 1.05873i | 0.379769 | + | 0.925081i | \(0.376003\pi\) |
−0.991028 | + | 0.133651i | \(0.957330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −168.000 | − | 290.985i | −0.109530 | − | 0.189711i | ||||
\(134\) | −492.000 | −0.317182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1965.00 | 1.23895 | ||||||||
\(137\) | 549.000 | + | 950.896i | 0.342367 | + | 0.592996i | 0.984872 | − | 0.173285i | \(-0.0554382\pi\) |
−0.642505 | + | 0.766281i | \(0.722105\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 521.000 | − | 902.398i | 0.317918 | − | 0.550651i | −0.662135 | − | 0.749384i | \(-0.730350\pi\) |
0.980054 | + | 0.198734i | \(0.0636829\pi\) | |||||||
\(140\) | 105.000 | − | 181.865i | 0.0633866 | − | 0.109789i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.0000 | − | 27.7128i | −0.00945556 | − | 0.0163775i | ||||
\(143\) | −235.000 | −0.137424 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −785.000 | −0.449591 | ||||||||
\(146\) | 485.000 | + | 840.045i | 0.274924 | + | 0.476182i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −245.000 | + | 424.352i | −0.136073 | + | 0.235686i | ||||
\(149\) | −1470.50 | + | 2546.98i | −0.808510 | + | 1.40038i | 0.105385 | + | 0.994431i | \(0.466393\pi\) |
−0.913895 | + | 0.405950i | \(0.866941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −255.500 | − | 442.539i | −0.137697 | − | 0.238499i | 0.788927 | − | 0.614487i | \(-0.210637\pi\) |
−0.926625 | + | 0.375988i | \(0.877303\pi\) | |||||||
\(152\) | −840.000 | −0.448243 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 282.000 | 0.147560 | ||||||||
\(155\) | 562.500 | + | 974.279i | 0.291491 | + | 0.504877i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 285.500 | − | 494.501i | 0.145130 | − | 0.251372i | −0.784292 | − | 0.620392i | \(-0.786973\pi\) |
0.929421 | + | 0.369020i | \(0.120307\pi\) | |||||||
\(158\) | −628.500 | + | 1088.59i | −0.316461 | + | 0.548126i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −402.500 | − | 697.150i | −0.198878 | − | 0.344466i | ||||
\(161\) | 18.0000 | 0.00881117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 713.000 | 0.342616 | 0.171308 | − | 0.985217i | \(-0.445201\pi\) | ||||
0.171308 | + | 0.985217i | \(0.445201\pi\) | |||||||
\(164\) | −490.000 | − | 848.705i | −0.233308 | − | 0.404102i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 51.0000 | − | 88.3346i | 0.0238456 | − | 0.0413018i | ||||
\(167\) | 798.000 | − | 1382.18i | 0.369767 | − | 0.640455i | −0.619762 | − | 0.784790i | \(-0.712771\pi\) |
0.989529 | + | 0.144335i | \(0.0461042\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1086.00 | + | 1881.01i | 0.494310 | + | 0.856171i | ||||
\(170\) | 655.000 | 0.295507 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2779.00 | −1.23196 | ||||||||
\(173\) | 2067.00 | + | 3580.15i | 0.908388 | + | 1.57337i | 0.816304 | + | 0.577623i | \(0.196019\pi\) |
0.0920840 | + | 0.995751i | \(0.470647\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 75.0000 | − | 129.904i | 0.0323970 | − | 0.0561132i | ||||
\(176\) | −963.500 | + | 1668.83i | −0.412651 | + | 0.714732i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 744.000 | + | 1288.65i | 0.313287 | + | 0.542630i | ||||
\(179\) | −1828.00 | −0.763302 | −0.381651 | − | 0.924306i | \(-0.624644\pi\) | ||||
−0.381651 | + | 0.924306i | \(0.624644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −520.000 | −0.213543 | −0.106772 | − | 0.994284i | \(-0.534051\pi\) | ||||
−0.106772 | + | 0.994284i | \(0.534051\pi\) | |||||||
\(182\) | 15.0000 | + | 25.9808i | 0.00610920 | + | 0.0105814i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 22.5000 | − | 38.9711i | 0.00901479 | − | 0.0156141i | ||||
\(185\) | −175.000 | + | 303.109i | −0.0695473 | + | 0.120460i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3078.50 | − | 5332.12i | −1.20386 | − | 2.08515i | ||||
\(188\) | −2429.00 | −0.942303 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −280.000 | −0.106912 | ||||||||
\(191\) | 2413.00 | + | 4179.44i | 0.914129 | + | 1.58332i | 0.808172 | + | 0.588946i | \(0.200457\pi\) |
0.105956 | + | 0.994371i | \(0.466210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −835.000 | + | 1446.26i | −0.311423 | + | 0.539400i | −0.978671 | − | 0.205436i | \(-0.934139\pi\) |
0.667248 | + | 0.744836i | \(0.267472\pi\) | |||||||
\(194\) | 487.000 | − | 843.509i | 0.180230 | − | 0.312167i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1074.50 | − | 1861.09i | −0.391582 | − | 0.678239i | ||||
\(197\) | 1380.00 | 0.499091 | 0.249546 | − | 0.968363i | \(-0.419719\pi\) | ||||
0.249546 | + | 0.968363i | \(0.419719\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4357.00 | 1.55206 | 0.776029 | − | 0.630697i | \(-0.217231\pi\) | ||||
0.776029 | + | 0.630697i | \(0.217231\pi\) | |||||||
\(200\) | −187.500 | − | 324.760i | −0.0662913 | − | 0.114820i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 667.500 | − | 1156.14i | 0.232501 | − | 0.402703i | ||||
\(203\) | 471.000 | − | 815.796i | 0.162846 | − | 0.282057i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −350.000 | − | 606.218i | −0.119244 | − | 0.206537i | ||||
\(206\) | −686.000 | −0.232019 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −205.000 | −0.0683375 | ||||||||
\(209\) | 1316.00 | + | 2279.38i | 0.435548 | + | 0.754392i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2081.00 | − | 3604.40i | 0.678967 | − | 1.17600i | −0.296326 | − | 0.955087i | \(-0.595761\pi\) |
0.975292 | − | 0.220918i | \(-0.0709052\pi\) | |||||||
\(212\) | −14.0000 | + | 24.2487i | −0.00453549 | + | 0.00785570i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 549.000 | + | 950.896i | 0.175369 | + | 0.303747i | ||||
\(215\) | −1985.00 | −0.629655 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1350.00 | −0.422322 | ||||||||
\(218\) | −350.000 | − | 606.218i | −0.108738 | − | 0.188341i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −822.500 | + | 1424.61i | −0.252059 | + | 0.436579i | ||||
\(221\) | 327.500 | − | 567.247i | 0.0996834 | − | 0.172657i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2978.00 | + | 5158.05i | 0.894267 | + | 1.54892i | 0.834709 | + | 0.550692i | \(0.185636\pi\) |
0.0595587 | + | 0.998225i | \(0.481031\pi\) | |||||||
\(224\) | 966.000 | 0.288141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1055.00 | −0.310520 | ||||||||
\(227\) | 2470.00 | + | 4278.17i | 0.722201 | + | 1.25089i | 0.960116 | + | 0.279603i | \(0.0902028\pi\) |
−0.237915 | + | 0.971286i | \(0.576464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2172.00 | + | 3762.01i | −0.626768 | + | 1.08559i | 0.361429 | + | 0.932400i | \(0.382289\pi\) |
−0.988196 | + | 0.153194i | \(0.951044\pi\) | |||||||
\(230\) | 7.50000 | − | 12.9904i | 0.00215015 | − | 0.00372418i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1177.50 | − | 2039.49i | −0.333218 | − | 0.577151i | ||||
\(233\) | 5202.00 | 1.46264 | 0.731318 | − | 0.682036i | \(-0.238905\pi\) | ||||
0.731318 | + | 0.682036i | \(0.238905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1735.00 | −0.481612 | ||||||||
\(236\) | −2618.00 | − | 4534.51i | −0.722107 | − | 1.25073i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −393.000 | + | 680.696i | −0.107035 | + | 0.185391i | ||||
\(239\) | 773.000 | − | 1338.88i | 0.209210 | − | 0.362363i | −0.742256 | − | 0.670117i | \(-0.766244\pi\) |
0.951466 | + | 0.307754i | \(0.0995774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1829.50 | + | 3168.79i | 0.488998 | + | 0.846969i | 0.999920 | − | 0.0126581i | \(-0.00402929\pi\) |
−0.510922 | + | 0.859627i | \(0.670696\pi\) | |||||||
\(242\) | −878.000 | −0.233223 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2366.00 | 0.620769 | ||||||||
\(245\) | −767.500 | − | 1329.35i | −0.200138 | − | 0.346649i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −140.000 | + | 242.487i | −0.0360647 | + | 0.0624659i | ||||
\(248\) | −1687.50 | + | 2922.84i | −0.432082 | + | 0.748388i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −62.5000 | − | 108.253i | −0.0158114 | − | 0.0273861i | ||||
\(251\) | −1221.00 | −0.307047 | −0.153524 | − | 0.988145i | \(-0.549062\pi\) | ||||
−0.153524 | + | 0.988145i | \(0.549062\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −141.000 | −0.0350379 | ||||||||
\(254\) | −823.000 | − | 1425.48i | −0.203306 | − | 0.352136i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 59.5000 | − | 103.057i | 0.0145264 | − | 0.0251604i | ||||
\(257\) | −3127.50 | + | 5416.99i | −0.759098 | + | 1.31480i | 0.184214 | + | 0.982886i | \(0.441026\pi\) |
−0.943311 | + | 0.331909i | \(0.892307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −210.000 | − | 363.731i | −0.0503813 | − | 0.0872630i | ||||
\(260\) | −175.000 | −0.0417425 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1833.00 | −0.432226 | ||||||||
\(263\) | 418.000 | + | 723.997i | 0.0980037 | + | 0.169747i | 0.910858 | − | 0.412719i | \(-0.135421\pi\) |
−0.812855 | + | 0.582467i | \(0.802088\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0000 | + | 17.3205i | −0.00231809 | + | 0.00401506i | ||||
\(266\) | 168.000 | − | 290.985i | 0.0387246 | − | 0.0670730i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1722.00 | + | 2982.59i | 0.392492 | + | 0.679816i | ||||
\(269\) | 2231.00 | 0.505675 | 0.252837 | − | 0.967509i | \(-0.418636\pi\) | ||||
0.252837 | + | 0.967509i | \(0.418636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4832.00 | −1.08311 | −0.541556 | − | 0.840665i | \(-0.682164\pi\) | ||||
−0.541556 | + | 0.840665i | \(0.682164\pi\) | |||||||
\(272\) | −2685.50 | − | 4651.42i | −0.598648 | − | 1.03689i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −549.000 | + | 950.896i | −0.121045 | + | 0.209656i | ||||
\(275\) | −587.500 | + | 1017.58i | −0.128828 | + | 0.223136i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3225.00 | − | 5585.86i | −0.699536 | − | 1.21163i | −0.968627 | − | 0.248517i | \(-0.920057\pi\) |
0.269091 | − | 0.963115i | \(-0.413277\pi\) | |||||||
\(278\) | 1042.00 | 0.224802 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 450.000 | 0.0960452 | ||||||||
\(281\) | −525.000 | − | 909.327i | −0.111455 | − | 0.193046i | 0.804902 | − | 0.593408i | \(-0.202218\pi\) |
−0.916357 | + | 0.400362i | \(0.868884\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 792.000 | − | 1371.78i | 0.166359 | − | 0.288142i | −0.770778 | − | 0.637104i | \(-0.780132\pi\) |
0.937137 | + | 0.348962i | \(0.113466\pi\) | |||||||
\(284\) | −112.000 | + | 193.990i | −0.0234013 | + | 0.0405323i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −117.500 | − | 203.516i | −0.0242934 | − | 0.0420775i | ||||
\(287\) | 840.000 | 0.172765 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12248.0 | 2.49298 | ||||||||
\(290\) | −392.500 | − | 679.830i | −0.0794772 | − | 0.137659i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3395.00 | − | 5880.31i | 0.680402 | − | 1.17849i | ||||
\(293\) | 3297.00 | − | 5710.57i | 0.657382 | − | 1.13862i | −0.323909 | − | 0.946088i | \(-0.604997\pi\) |
0.981291 | − | 0.192530i | \(-0.0616693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1870.00 | − | 3238.94i | −0.369070 | − | 0.639248i | ||||
\(296\) | −1050.00 | −0.206182 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2941.00 | −0.571703 | ||||||||
\(299\) | −7.50000 | − | 12.9904i | −0.00145062 | − | 0.00251255i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1191.00 | − | 2062.87i | 0.228067 | − | 0.395023i | ||||
\(302\) | 255.500 | − | 442.539i | 0.0486834 | − | 0.0843220i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1148.00 | + | 1988.39i | 0.216587 | + | 0.375139i | ||||
\(305\) | 1690.00 | 0.317276 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4343.00 | −0.807388 | −0.403694 | − | 0.914894i | \(-0.632274\pi\) | ||||
−0.403694 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(308\) | −987.000 | − | 1709.53i | −0.182596 | − | 0.316265i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −562.500 | + | 974.279i | −0.103058 | + | 0.178501i | ||||
\(311\) | −1062.00 | + | 1839.44i | −0.193635 | + | 0.335386i | −0.946452 | − | 0.322844i | \(-0.895361\pi\) |
0.752817 | + | 0.658230i | \(0.228694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3758.00 | + | 6509.05i | 0.678641 | + | 1.17544i | 0.975390 | + | 0.220486i | \(0.0707642\pi\) |
−0.296749 | + | 0.954956i | \(0.595902\pi\) | |||||||
\(314\) | 571.000 | 0.102622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8799.00 | 1.56640 | ||||||||
\(317\) | −3440.00 | − | 5958.25i | −0.609494 | − | 1.05567i | −0.991324 | − | 0.131442i | \(-0.958039\pi\) |
0.381830 | − | 0.924233i | \(-0.375294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3689.50 | + | 6390.40i | −0.647562 | + | 1.12161i | ||||
\(320\) | −417.500 | + | 723.131i | −0.0729342 | + | 0.126326i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.00000 | + | 15.5885i | 0.00155761 | + | 0.00269786i | ||||
\(323\) | −7336.00 | −1.26373 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −125.000 | −0.0213346 | ||||||||
\(326\) | 356.500 | + | 617.476i | 0.0605666 | + | 0.104904i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1050.00 | − | 1818.65i | 0.176758 | − | 0.306153i | ||||
\(329\) | 1041.00 | − | 1803.06i | 0.174444 | − | 0.302146i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2493.00 | + | 4318.00i | 0.413981 | + | 0.717036i | 0.995321 | − | 0.0966248i | \(-0.0308047\pi\) |
−0.581340 | + | 0.813661i | \(0.697471\pi\) | |||||||
\(332\) | −714.000 | −0.118030 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1596.00 | 0.261465 | ||||||||
\(335\) | 1230.00 | + | 2130.42i | 0.200603 | + | 0.347455i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −452.000 | + | 782.887i | −0.0730623 | + | 0.126548i | −0.900242 | − | 0.435390i | \(-0.856611\pi\) |
0.827180 | + | 0.561938i | \(0.189944\pi\) | |||||||
\(338\) | −1086.00 | + | 1881.01i | −0.174765 | + | 0.302702i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2292.50 | − | 3970.73i | −0.365671 | − | 0.633361i | ||||
\(341\) | 10575.0 | 1.67938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3900.00 | 0.613936 | ||||||||
\(344\) | −2977.50 | − | 5157.18i | −0.466675 | − | 0.808304i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2067.00 | + | 3580.15i | −0.321164 | + | 0.556272i | ||||
\(347\) | 4430.00 | − | 7672.99i | 0.685345 | − | 1.18705i | −0.287983 | − | 0.957636i | \(-0.592985\pi\) |
0.973328 | − | 0.229417i | \(-0.0736821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2227.00 | + | 3857.28i | 0.341572 | + | 0.591620i | 0.984725 | − | 0.174118i | \(-0.0557074\pi\) |
−0.643153 | + | 0.765738i | \(0.722374\pi\) | |||||||
\(350\) | 150.000 | 0.0229081 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7567.00 | −1.14580 | ||||||||
\(353\) | −4390.50 | − | 7604.57i | −0.661991 | − | 1.14660i | −0.980092 | − | 0.198545i | \(-0.936378\pi\) |
0.318101 | − | 0.948057i | \(-0.396955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −80.0000 | + | 138.564i | −0.0119604 | + | 0.0207161i | ||||
\(356\) | 5208.00 | − | 9020.52i | 0.775347 | − | 1.34294i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −914.000 | − | 1583.09i | −0.134934 | − | 0.233713i | ||||
\(359\) | −2928.00 | −0.430457 | −0.215228 | − | 0.976564i | \(-0.569050\pi\) | ||||
−0.215228 | + | 0.976564i | \(0.569050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3723.00 | −0.542790 | ||||||||
\(362\) | −260.000 | − | 450.333i | −0.0377494 | − | 0.0653839i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 105.000 | − | 181.865i | 0.0151195 | − | 0.0261877i | ||||
\(365\) | 2425.00 | − | 4200.22i | 0.347754 | − | 0.602328i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4551.00 | − | 7882.56i | −0.647303 | − | 1.12116i | −0.983764 | − | 0.179465i | \(-0.942563\pi\) |
0.336461 | − | 0.941697i | \(-0.390770\pi\) | |||||||
\(368\) | −123.000 | −0.0174234 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −350.000 | −0.0491774 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.00167927 | − | 0.00290858i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4091.50 | − | 7086.69i | 0.567962 | − | 0.983739i | −0.428805 | − | 0.903397i | \(-0.641065\pi\) |
0.996767 | − | 0.0803422i | \(-0.0256013\pi\) | |||||||
\(374\) | 3078.50 | − | 5332.12i | 0.425630 | − | 0.737212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2602.50 | − | 4507.66i | −0.356951 | − | 0.618258i | ||||
\(377\) | −785.000 | −0.107240 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6136.00 | 0.831623 | 0.415812 | − | 0.909451i | \(-0.363498\pi\) | ||||
0.415812 | + | 0.909451i | \(0.363498\pi\) | |||||||
\(380\) | 980.000 | + | 1697.41i | 0.132297 | + | 0.229145i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2413.00 | + | 4179.44i | −0.323193 | + | 0.559787i | ||||
\(383\) | 2821.50 | − | 4886.98i | 0.376428 | − | 0.651992i | −0.614112 | − | 0.789219i | \(-0.710486\pi\) |
0.990540 | + | 0.137227i | \(0.0438189\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −705.000 | − | 1221.10i | −0.0933250 | − | 0.161644i | ||||
\(386\) | −1670.00 | −0.220209 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6818.00 | −0.892092 | ||||||||
\(389\) | 4495.50 | + | 7786.43i | 0.585941 | + | 1.01488i | 0.994757 | + | 0.102262i | \(0.0326082\pi\) |
−0.408817 | + | 0.912616i | \(0.634059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 196.500 | − | 340.348i | 0.0254154 | − | 0.0440208i | ||||
\(392\) | 2302.50 | − | 3988.05i | 0.296668 | − | 0.513844i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 690.000 | + | 1195.12i | 0.0882277 | + | 0.152815i | ||||
\(395\) | 6285.00 | 0.800589 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12449.0 | −1.57380 | −0.786898 | − | 0.617082i | \(-0.788314\pi\) | ||||
−0.786898 | + | 0.617082i | \(0.788314\pi\) | |||||||
\(398\) | 2178.50 | + | 3773.27i | 0.274368 | + | 0.475219i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −512.500 | + | 887.676i | −0.0640625 | + | 0.110960i | ||||
\(401\) | 4038.00 | − | 6994.02i | 0.502863 | − | 0.870984i | −0.497131 | − | 0.867675i | \(-0.665613\pi\) |
0.999995 | − | 0.00330917i | \(-0.00105334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 562.500 | + | 974.279i | 0.0695288 | + | 0.120427i | ||||
\(404\) | −9345.00 | −1.15082 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 942.000 | 0.115149 | ||||||||
\(407\) | 1645.00 | + | 2849.22i | 0.200343 | + | 0.347004i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1416.50 | − | 2453.45i | 0.171250 | − | 0.296614i | −0.767607 | − | 0.640921i | \(-0.778553\pi\) |
0.938857 | + | 0.344307i | \(0.111886\pi\) | |||||||
\(410\) | 350.000 | − | 606.218i | 0.0421592 | − | 0.0730219i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2401.00 | + | 4158.65i | 0.287109 | + | 0.497287i | ||||
\(413\) | 4488.00 | 0.534722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −510.000 | −0.0603251 | ||||||||
\(416\) | −402.500 | − | 697.150i | −0.0474379 | − | 0.0821649i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1316.00 | + | 2279.38i | −0.153990 | + | 0.266718i | ||||
\(419\) | −2388.50 | + | 4137.00i | −0.278487 | + | 0.482353i | −0.971009 | − | 0.239044i | \(-0.923166\pi\) |
0.692522 | + | 0.721396i | \(0.256499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3232.00 | + | 5597.99i | 0.374152 | + | 0.648050i | 0.990200 | − | 0.139658i | \(-0.0446005\pi\) |
−0.616048 | + | 0.787709i | \(0.711267\pi\) | |||||||
\(422\) | 4162.00 | 0.480102 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −60.0000 | −0.00687231 | ||||||||
\(425\) | −1637.50 | − | 2836.23i | −0.186895 | − | 0.323712i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1014.00 | + | 1756.30i | −0.114920 | + | 0.199048i | ||||
\(428\) | 3843.00 | − | 6656.27i | 0.434015 | − | 0.751736i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −992.500 | − | 1719.06i | −0.111308 | − | 0.192792i | ||||
\(431\) | −10680.0 | −1.19359 | −0.596795 | − | 0.802394i | \(-0.703560\pi\) | ||||
−0.596795 | + | 0.802394i | \(0.703560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11566.0 | 1.28366 | 0.641832 | − | 0.766845i | \(-0.278175\pi\) | ||||
0.641832 | + | 0.766845i | \(0.278175\pi\) | |||||||
\(434\) | −675.000 | − | 1169.13i | −0.0746568 | − | 0.129309i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2450.00 | + | 4243.52i | −0.269114 | + | 0.466119i | ||||
\(437\) | −84.0000 | + | 145.492i | −0.00919511 | + | 0.0159264i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 724.000 | + | 1254.00i | 0.0787122 | + | 0.136333i | 0.902695 | − | 0.430282i | \(-0.141586\pi\) |
−0.823982 | + | 0.566615i | \(0.808253\pi\) | |||||||
\(440\) | −3525.00 | −0.381927 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 655.000 | 0.0704868 | ||||||||
\(443\) | −1188.00 | − | 2057.68i | −0.127412 | − | 0.220684i | 0.795261 | − | 0.606267i | \(-0.207334\pi\) |
−0.922673 | + | 0.385583i | \(0.874000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3720.00 | − | 6443.23i | 0.396281 | − | 0.686378i | ||||
\(446\) | −2978.00 | + | 5158.05i | −0.316171 | + | 0.547625i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −501.000 | − | 867.757i | −0.0528349 | − | 0.0915127i | ||||
\(449\) | 14894.0 | 1.56546 | 0.782730 | − | 0.622362i | \(-0.213827\pi\) | ||||
0.782730 | + | 0.622362i | \(0.213827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6580.00 | −0.687007 | ||||||||
\(452\) | 3692.50 | + | 6395.60i | 0.384249 | + | 0.665539i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2470.00 | + | 4278.17i | −0.255337 | + | 0.442256i | ||||
\(455\) | 75.0000 | − | 129.904i | 0.00772759 | − | 0.0133846i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8102.00 | − | 14033.1i | −0.829312 | − | 1.43641i | −0.898579 | − | 0.438812i | \(-0.855399\pi\) |
0.0692668 | − | 0.997598i | \(-0.477934\pi\) | |||||||
\(458\) | −4344.00 | −0.443192 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −105.000 | −0.0106427 | ||||||||
\(461\) | −2541.00 | − | 4401.14i | −0.256716 | − | 0.444646i | 0.708644 | − | 0.705566i | \(-0.249307\pi\) |
−0.965360 | + | 0.260921i | \(0.915974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5163.00 | − | 8942.58i | 0.518240 | − | 0.897617i | −0.481536 | − | 0.876426i | \(-0.659921\pi\) |
0.999775 | − | 0.0211910i | \(-0.00674580\pi\) | |||||||
\(464\) | −3218.50 | + | 5574.61i | −0.322015 | + | 0.557747i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2601.00 | + | 4505.06i | 0.258560 | + | 0.447839i | ||||
\(467\) | −4184.00 | −0.414588 | −0.207294 | − | 0.978279i | \(-0.566466\pi\) | ||||
−0.207294 | + | 0.978279i | \(0.566466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2952.00 | −0.290641 | ||||||||
\(470\) | −867.500 | − | 1502.55i | −0.0851379 | − | 0.147463i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5610.00 | − | 9716.81i | 0.547079 | − | 0.947568i | ||||
\(473\) | −9329.50 | + | 16159.2i | −0.906915 | + | 1.57082i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 700.000 | + | 1212.44i | 0.0676173 | + | 0.117117i | ||||
\(476\) | 5502.00 | 0.529798 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1546.00 | 0.147934 | ||||||||
\(479\) | −7788.00 | − | 13489.2i | −0.742887 | − | 1.28672i | −0.951176 | − | 0.308650i | \(-0.900123\pi\) |
0.208289 | − | 0.978067i | \(-0.433211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −175.000 | + | 303.109i | −0.0165890 | + | 0.0287330i | ||||
\(482\) | −1829.50 | + | 3168.79i | −0.172887 | + | 0.299449i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3073.00 | + | 5322.59i | 0.288599 | + | 0.499868i | ||||
\(485\) | −4870.00 | −0.455949 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10220.0 | 0.950949 | 0.475475 | − | 0.879729i | \(-0.342276\pi\) | ||||
0.475475 | + | 0.879729i | \(0.342276\pi\) | |||||||
\(488\) | 2535.00 | + | 4390.75i | 0.235152 | + | 0.407295i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 767.500 | − | 1329.35i | 0.0707594 | − | 0.122559i | ||||
\(491\) | −1346.00 | + | 2331.34i | −0.123715 | + | 0.214281i | −0.921230 | − | 0.389018i | \(-0.872814\pi\) |
0.797515 | + | 0.603299i | \(0.206148\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10283.5 | − | 17811.5i | −0.939443 | − | 1.62716i | ||||
\(494\) | −280.000 | −0.0255016 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9225.00 | 0.835110 | ||||||||
\(497\) | −96.0000 | − | 166.277i | −0.00866436 | − | 0.0150071i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2882.00 | + | 4991.77i | −0.258549 | + | 0.447820i | −0.965853 | − | 0.259089i | \(-0.916578\pi\) |
0.707304 | + | 0.706909i | \(0.249911\pi\) | |||||||
\(500\) | −437.500 | + | 757.772i | −0.0391312 | + | 0.0677772i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −610.500 | − | 1057.42i | −0.0542788 | − | 0.0940136i | ||||
\(503\) | 2437.00 | 0.216025 | 0.108012 | − | 0.994150i | \(-0.465551\pi\) | ||||
0.108012 | + | 0.994150i | \(0.465551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6675.00 | −0.588185 | ||||||||
\(506\) | −70.5000 | − | 122.110i | −0.00619389 | − | 0.0107281i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5761.00 | + | 9978.34i | −0.503156 | + | 0.871491i | ||||
\(509\) | −2924.50 | + | 5065.38i | −0.254668 | + | 0.441098i | −0.964805 | − | 0.262965i | \(-0.915300\pi\) |
0.710137 | + | 0.704063i | \(0.248633\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2910.00 | + | 5040.27i | 0.251919 | + | 0.436337i | ||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6255.00 | −0.536763 | ||||||||
\(515\) | 1715.00 | + | 2970.47i | 0.146742 | + | 0.254164i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8154.50 | + | 14124.0i | −0.693684 | + | 1.20150i | ||||
\(518\) | 210.000 | − | 363.731i | 0.0178125 | − | 0.0308521i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −187.500 | − | 324.760i | −0.0158123 | − | 0.0273878i | ||||
\(521\) | 17032.0 | 1.43222 | 0.716109 | − | 0.697989i | \(-0.245921\pi\) | ||||
0.716109 | + | 0.697989i | \(0.245921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4147.00 | 0.346722 | 0.173361 | − | 0.984858i | \(-0.444537\pi\) | ||||
0.173361 | + | 0.984858i | \(0.444537\pi\) | |||||||
\(524\) | 6415.50 | + | 11112.0i | 0.534852 | + | 0.926391i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −418.000 | + | 723.997i | −0.0346496 | + | 0.0600148i | ||||
\(527\) | −14737.5 | + | 25526.1i | −1.21817 | + | 2.10993i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6079.00 | + | 10529.1i | 0.499630 | + | 0.865385i | ||||
\(530\) | −20.0000 | −0.00163914 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2352.00 | −0.191677 | ||||||||
\(533\) | −350.000 | − | 606.218i | −0.0284431 | − | 0.0492649i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2745.00 | − | 4754.48i | 0.221826 | − | 0.384213i | ||||
\(536\) | −3690.00 | + | 6391.27i | −0.297358 | + | 0.515039i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1115.50 | + | 1932.10i | 0.0893915 | + | 0.154831i | ||||
\(539\) | −14429.0 | −1.15306 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3942.00 | −0.313271 | −0.156636 | − | 0.987656i | \(-0.550065\pi\) | ||||
−0.156636 | + | 0.987656i | \(0.550065\pi\) | |||||||
\(542\) | −2416.00 | − | 4184.63i | −0.191469 | − | 0.331634i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10545.5 | − | 18265.3i | 0.831130 | − | 1.43956i | ||||
\(545\) | −1750.00 | + | 3031.09i | −0.137545 | + | 0.238234i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6875.50 | + | 11908.7i | 0.537432 | + | 0.930859i | 0.999041 | + | 0.0437759i | \(0.0139388\pi\) |
−0.461610 | + | 0.887083i | \(0.652728\pi\) | |||||||
\(548\) | 7686.00 | 0.599142 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1175.00 | −0.0910949 | ||||||||
\(551\) | 4396.00 | + | 7614.10i | 0.339884 | + | 0.588696i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3771.00 | + | 6531.56i | −0.289981 | + | 0.502261i | ||||
\(554\) | 3225.00 | − | 5585.86i | 0.247323 | − | 0.428377i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3647.00 | − | 6316.79i | −0.278179 | − | 0.481819i | ||||
\(557\) | −7944.00 | −0.604305 | −0.302153 | − | 0.953260i | \(-0.597705\pi\) | ||||
−0.302153 | + | 0.953260i | \(0.597705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1985.00 | −0.150191 | ||||||||
\(560\) | −615.000 | − | 1065.21i | −0.0464080 | − | 0.0803811i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 525.000 | − | 909.327i | 0.0394053 | − | 0.0682520i | ||||
\(563\) | −3351.00 | + | 5804.10i | −0.250849 | + | 0.434483i | −0.963760 | − | 0.266772i | \(-0.914043\pi\) |
0.712911 | + | 0.701254i | \(0.247376\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2637.50 | + | 4568.28i | 0.196390 | + | 0.340158i | ||||
\(566\) | 1584.00 | 0.117633 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −480.000 | −0.0354584 | ||||||||
\(569\) | −1380.00 | − | 2390.23i | −0.101674 | − | 0.176105i | 0.810700 | − | 0.585461i | \(-0.199087\pi\) |
−0.912375 | + | 0.409356i | \(0.865753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4465.00 | + | 7733.61i | −0.327241 | + | 0.566798i | −0.981963 | − | 0.189072i | \(-0.939452\pi\) |
0.654723 | + | 0.755869i | \(0.272785\pi\) | |||||||
\(572\) | −822.500 | + | 1424.61i | −0.0601232 | + | 0.104136i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 420.000 | + | 727.461i | 0.0305409 | + | 0.0528983i | ||||
\(575\) | −75.0000 | −0.00543951 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6944.00 | 0.501010 | 0.250505 | − | 0.968115i | \(-0.419403\pi\) | ||||
0.250505 | + | 0.968115i | \(0.419403\pi\) | |||||||
\(578\) | 6124.00 | + | 10607.1i | 0.440700 | + | 0.763315i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2747.50 | + | 4758.81i | −0.196696 | + | 0.340688i | ||||
\(581\) | 306.000 | − | 530.008i | 0.0218503 | − | 0.0378458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 94.0000 | + | 162.813i | 0.00667767 | + | 0.0115661i | ||||
\(584\) | 14550.0 | 1.03096 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6594.00 | 0.464839 | ||||||||
\(587\) | −2103.00 | − | 3642.50i | −0.147871 | − | 0.256120i | 0.782570 | − | 0.622563i | \(-0.213909\pi\) |
−0.930440 | + | 0.366444i | \(0.880575\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6300.00 | − | 10911.9i | 0.440725 | − | 0.763358i | ||||
\(590\) | 1870.00 | − | 3238.94i | 0.130486 | − | 0.226008i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1435.00 | + | 2485.49i | 0.0996252 | + | 0.172556i | ||||
\(593\) | 6571.00 | 0.455040 | 0.227520 | − | 0.973773i | \(-0.426938\pi\) | ||||
0.227520 | + | 0.973773i | \(0.426938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3930.00 | 0.270780 | ||||||||
\(596\) | 10293.5 | + | 17828.9i | 0.707447 | + | 1.22533i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.50000 | − | 12.9904i | 0.000512873 | − | 0.000888321i | ||||
\(599\) | −4745.00 | + | 8218.58i | −0.323665 | + | 0.560605i | −0.981241 | − | 0.192784i | \(-0.938248\pi\) |
0.657576 | + | 0.753388i | \(0.271582\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5930.50 | − | 10271.9i | −0.402513 | − | 0.697172i | 0.591516 | − | 0.806293i | \(-0.298530\pi\) |
−0.994028 | + | 0.109121i | \(0.965196\pi\) | |||||||
\(602\) | 2382.00 | 0.161268 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3577.00 | −0.240970 | ||||||||
\(605\) | 2195.00 | + | 3801.85i | 0.147503 | + | 0.255483i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 259.000 | − | 448.601i | 0.0173188 | − | 0.0299970i | −0.857236 | − | 0.514923i | \(-0.827820\pi\) |
0.874555 | + | 0.484927i | \(0.161154\pi\) | |||||||
\(608\) | −4508.00 | + | 7808.09i | −0.300697 | + | 0.520822i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 845.000 | + | 1463.58i | 0.0560870 | + | 0.0971455i | ||||
\(611\) | −1735.00 | −0.114878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15163.0 | 0.999067 | 0.499533 | − | 0.866295i | \(-0.333505\pi\) | ||||
0.499533 | + | 0.866295i | \(0.333505\pi\) | |||||||
\(614\) | −2171.50 | − | 3761.15i | −0.142727 | − | 0.247211i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2115.00 | − | 3663.29i | 0.138337 | − | 0.239607i | ||||
\(617\) | 9505.50 | − | 16464.0i | 0.620222 | − | 1.07426i | −0.369222 | − | 0.929341i | \(-0.620376\pi\) |
0.989444 | − | 0.144915i | \(-0.0462909\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3953.00 | + | 6846.80i | 0.256679 | + | 0.444582i | 0.965350 | − | 0.260958i | \(-0.0840383\pi\) |
−0.708671 | + | 0.705539i | \(0.750705\pi\) | |||||||
\(620\) | 7875.00 | 0.510109 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2124.00 | −0.136921 | ||||||||
\(623\) | 4464.00 | + | 7731.87i | 0.287073 | + | 0.497225i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −3758.00 | + | 6509.05i | −0.239936 | + | 0.415581i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1998.50 | − | 3461.50i | −0.126989 | − | 0.219951i | ||||
\(629\) | −9170.00 | −0.581291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3416.00 | −0.215513 | −0.107757 | − | 0.994177i | \(-0.534367\pi\) | ||||
−0.107757 | + | 0.994177i | \(0.534367\pi\) | |||||||
\(632\) | 9427.50 | + | 16328.9i | 0.593364 | + | 1.02774i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3440.00 | − | 5958.25i | 0.215489 | − | 0.373237i | ||||
\(635\) | −4115.00 | + | 7127.39i | −0.257163 | + | 0.445420i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −767.500 | − | 1329.35i | −0.0477386 | − | 0.0826856i | ||||
\(638\) | −7379.00 | −0.457896 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7275.00 | −0.449328 | ||||||||
\(641\) | 2415.00 | + | 4182.90i | 0.148809 | + | 0.257745i | 0.930788 | − | 0.365560i | \(-0.119123\pi\) |
−0.781978 | + | 0.623306i | \(0.785789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6274.50 | + | 10867.8i | −0.384824 | + | 0.666536i | −0.991745 | − | 0.128227i | \(-0.959071\pi\) |
0.606920 | + | 0.794763i | \(0.292405\pi\) | |||||||
\(644\) | 63.0000 | − | 109.119i | 0.00385489 | − | 0.00667686i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3668.00 | − | 6353.16i | −0.223399 | − | 0.386938i | ||||
\(647\) | −8164.00 | −0.496074 | −0.248037 | − | 0.968751i | \(-0.579785\pi\) | ||||
−0.248037 | + | 0.968751i | \(0.579785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35156.0 | −2.12634 | ||||||||
\(650\) | −62.5000 | − | 108.253i | −0.00377146 | − | 0.00653237i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2495.50 | − | 4322.33i | 0.149895 | − | 0.259625i | ||||
\(653\) | 11884.0 | − | 20583.7i | 0.712185 | − | 1.23354i | −0.251850 | − | 0.967766i | \(-0.581039\pi\) |
0.964035 | − | 0.265774i | \(-0.0856277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4582.50 | + | 7937.12i | 0.273363 | + | 0.473479i | ||||
\(656\) | −5740.00 | −0.341630 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2082.00 | 0.123351 | ||||||||
\(659\) | 10736.0 | + | 18595.3i | 0.634621 | + | 1.09920i | 0.986595 | + | 0.163186i | \(0.0521771\pi\) |
−0.351974 | + | 0.936010i | \(0.614490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6491.00 | + | 11242.7i | −0.381953 | + | 0.661561i | −0.991341 | − | 0.131310i | \(-0.958082\pi\) |
0.609389 | + | 0.792872i | \(0.291415\pi\) | |||||||
\(662\) | −2493.00 | + | 4318.00i | −0.146364 | + | 0.253510i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −765.000 | − | 1325.02i | −0.0447105 | − | 0.0774408i | ||||
\(665\) | −1680.00 | −0.0979663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −471.000 | −0.0273421 | ||||||||
\(668\) | −5586.00 | − | 9675.24i | −0.323546 | − | 0.560398i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1230.00 | + | 2130.42i | −0.0709239 | + | 0.122844i | ||||
\(671\) | 7943.00 | − | 13757.7i | 0.456984 | − | 0.791519i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3003.00 | + | 5201.35i | 0.172002 | + | 0.297916i | 0.939120 | − | 0.343590i | \(-0.111643\pi\) |
−0.767118 | + | 0.641506i | \(0.778310\pi\) | |||||||
\(674\) | −904.000 | −0.0516629 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15204.0 | 0.865043 | ||||||||
\(677\) | 582.000 | + | 1008.05i | 0.0330400 | + | 0.0572270i | 0.882073 | − | 0.471114i | \(-0.156148\pi\) |
−0.849033 | + | 0.528340i | \(0.822814\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2922.00 | − | 5061.05i | 0.165149 | − | 0.286046i | ||||
\(680\) | 4912.50 | − | 8508.70i | 0.277038 | − | 0.479844i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5287.50 | + | 9158.22i | 0.296875 | + | 0.514203i | ||||
\(683\) | −26496.0 | −1.48439 | −0.742197 | − | 0.670182i | \(-0.766216\pi\) | ||||
−0.742197 | + | 0.670182i | \(0.766216\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5490.00 | 0.306222 | ||||||||
\(686\) | 1950.00 | + | 3377.50i | 0.108530 | + | 0.187979i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8138.50 | + | 14096.3i | −0.450985 | + | 0.781128i | ||||
\(689\) | −10.0000 | + | 17.3205i | −0.000552931 | + | 0.000957705i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8555.00 | − | 14817.7i | −0.470981 | − | 0.815762i | 0.528469 | − | 0.848953i | \(-0.322766\pi\) |
−0.999449 | + | 0.0331907i | \(0.989433\pi\) | |||||||
\(692\) | 28938.0 | 1.58968 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8860.00 | 0.484612 | ||||||||
\(695\) | −2605.00 | − | 4511.99i | −0.142177 | − | 0.246258i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9170.00 | − | 15882.9i | 0.498334 | − | 0.863139i | ||||
\(698\) | −2227.00 | + | 3857.28i | −0.120764 | + | 0.209169i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −525.000 | − | 909.327i | −0.0283473 | − | 0.0490990i | ||||
\(701\) | −30251.0 | −1.62991 | −0.814953 | − | 0.579527i | \(-0.803237\pi\) | ||||
−0.814953 | + | 0.579527i | \(0.803237\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3920.00 | 0.210307 | ||||||||
\(704\) | 3924.50 | + | 6797.43i | 0.210100 | + | 0.363903i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4390.50 | − | 7604.57i | 0.234049 | − | 0.405385i | ||||
\(707\) | 4005.00 | − | 6936.86i | 0.213046 | − | 0.369007i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9410.00 | − | 16298.6i | −0.498448 | − | 0.863338i | 0.501550 | − | 0.865129i | \(-0.332763\pi\) |
−0.999998 | + | 0.00179062i | \(0.999430\pi\) | |||||||
\(710\) | −160.000 | −0.00845731 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22320.0 | 1.17483 | ||||||||
\(713\) | 337.500 | + | 584.567i | 0.0177272 | + | 0.0307044i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −587.500 | + | 1017.58i | −0.0307290 | + | 0.0532242i | ||||
\(716\) | −6398.00 | + | 11081.7i | −0.333945 | + | 0.578409i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1464.00 | − | 2535.72i | −0.0760947 | − | 0.131800i | ||||
\(719\) | −31890.0 | −1.65410 | −0.827049 | − | 0.562130i | \(-0.809982\pi\) | ||||
−0.827049 | + | 0.562130i | \(0.809982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4116.00 | −0.212605 | ||||||||
\(722\) | −1861.50 | − | 3224.21i | −0.0959527 | − | 0.166195i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1820.00 | + | 3152.33i | −0.0934251 | + | 0.161817i | ||||
\(725\) | −1962.50 | + | 3399.15i | −0.100532 | + | 0.174126i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5726.00 | + | 9917.72i | 0.292112 | + | 0.505953i | 0.974309 | − | 0.225215i | \(-0.0723086\pi\) |
−0.682197 | + | 0.731169i | \(0.738975\pi\) | |||||||
\(728\) | 450.000 | 0.0229095 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4850.00 | 0.245899 | ||||||||
\(731\) | −26003.5 | − | 45039.4i | −1.31570 | − | 2.27885i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3547.00 | + | 6143.58i | −0.178733 | + | 0.309575i | −0.941447 | − | 0.337161i | \(-0.890533\pi\) |
0.762714 | + | 0.646736i | \(0.223867\pi\) | |||||||
\(734\) | 4551.00 | − | 7882.56i | 0.228856 | − | 0.396391i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −241.500 | − | 418.290i | −0.0120948 | − | 0.0209489i | ||||
\(737\) | 23124.0 | 1.15574 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3200.00 | −0.159288 | −0.0796440 | − | 0.996823i | \(-0.525378\pi\) | ||||
−0.0796440 | + | 0.996823i | \(0.525378\pi\) | |||||||
\(740\) | 1225.00 | + | 2121.76i | 0.0608539 | + | 0.105402i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | − | 20.7846i | 0.000593711 | − | 0.00102834i | ||||
\(743\) | −10415.5 | + | 18040.2i | −0.514277 | + | 0.890753i | 0.485586 | + | 0.874189i | \(0.338606\pi\) |
−0.999863 | + | 0.0165646i | \(0.994727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7352.50 | + | 12734.9i | 0.361577 | + | 0.626269i | ||||
\(746\) | 8183.00 | 0.401610 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −43099.0 | −2.10676 | ||||||||
\(749\) | 3294.00 | + | 5705.38i | 0.160694 | + | 0.278331i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7802.50 | − | 13514.3i | 0.379118 | − | 0.656651i | −0.611817 | − | 0.791000i | \(-0.709561\pi\) |
0.990934 | + | 0.134349i | \(0.0428943\pi\) | |||||||
\(752\) | −7113.50 | + | 12320.9i | −0.344950 | + | 0.597472i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −392.500 | − | 679.830i | −0.0189576 | − | 0.0328355i | ||||
\(755\) | −2555.00 | −0.123160 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21349.0 | 1.02502 | 0.512512 | − | 0.858680i | \(-0.328715\pi\) | ||||
0.512512 | + | 0.858680i | \(0.328715\pi\) | |||||||
\(758\) | 3068.00 | + | 5313.93i | 0.147012 | + | 0.254632i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2100.00 | + | 3637.31i | −0.100230 | + | 0.173604i | ||||
\(761\) | 1851.00 | − | 3206.03i | 0.0881717 | − | 0.152718i | −0.818567 | − | 0.574412i | \(-0.805231\pi\) |
0.906738 | + | 0.421694i | \(0.138564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2100.00 | − | 3637.31i | −0.0996397 | − | 0.172581i | ||||
\(764\) | 33782.0 | 1.59972 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5643.00 | 0.266175 | ||||||||
\(767\) | −1870.00 | − | 3238.94i | −0.0880336 | − | 0.152479i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 696.500 | − | 1206.37i | 0.0326612 | − | 0.0565708i | −0.849233 | − | 0.528019i | \(-0.822935\pi\) |
0.881894 | + | 0.471448i | \(0.156268\pi\) | |||||||
\(770\) | 705.000 | − | 1221.10i | 0.0329954 | − | 0.0571497i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5845.00 | + | 10123.8i | 0.272495 | + | 0.471975i | ||||
\(773\) | 6906.00 | 0.321334 | 0.160667 | − | 0.987009i | \(-0.448635\pi\) | ||||
0.160667 | + | 0.987009i | \(0.448635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5625.00 | 0.260717 | ||||||||
\(776\) | −7305.00 | − | 12652.6i | −0.337931 | − | 0.585313i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4495.50 | + | 7786.43i | −0.207161 | + | 0.358814i | ||||
\(779\) | −3920.00 | + | 6789.64i | −0.180293 | + | 0.312277i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 752.000 | + | 1302.50i | 0.0344541 | + | 0.0596763i | ||||
\(782\) | 393.000 | 0.0179714 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12587.0 | −0.573387 | ||||||||
\(785\) | −1427.50 | − | 2472.50i | −0.0649040 | − | 0.112417i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15246.5 | + | 26407.7i | −0.690571 | + | 1.19610i | 0.281081 | + | 0.959684i | \(0.409307\pi\) |
−0.971651 | + | 0.236419i | \(0.924026\pi\) | |||||||
\(788\) | 4830.00 | − | 8365.81i | 0.218352 | − | 0.378197i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3142.50 | + | 5442.97i | 0.141525 | + | 0.245129i | ||||
\(791\) | −6330.00 | −0.284537 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1690.00 | 0.0756793 | ||||||||
\(794\) | −6224.50 | − | 10781.2i | −0.278211 | − | 0.481875i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15249.5 | − | 26412.9i | 0.679025 | − | 1.17611i | ||||
\(797\) | 16744.0 | − | 29001.5i | 0.744169 | − | 1.28894i | −0.206413 | − | 0.978465i | \(-0.566179\pi\) |
0.950582 | − | 0.310474i | \(-0.100488\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22728.5 | − | 39366.9i | −1.00635 | − | 1.74306i | ||||
\(800\) | −4025.00 | −0.177882 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8076.00 | 0.355578 | ||||||||
\(803\) | −22795.0 | − | 39482.1i | −1.00177 | − | 1.73511i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.0000 | − | 77.9423i | 0.00197024 | − | 0.00341255i | ||||
\(806\) | −562.500 | + | 974.279i | −0.0245822 | + | 0.0425775i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10012.5 | − | 17342.2i | −0.435939 | − | 0.755068i | ||||
\(809\) | 15304.0 | 0.665093 | 0.332546 | − | 0.943087i | \(-0.392092\pi\) | ||||
0.332546 | + | 0.943087i | \(0.392092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40122.0 | −1.73721 | −0.868603 | − | 0.495509i | \(-0.834982\pi\) | ||||
−0.868603 | + | 0.495509i | \(0.834982\pi\) | |||||||
\(812\) | −3297.00 | − | 5710.57i | −0.142490 | − | 0.246800i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1645.00 | + | 2849.22i | −0.0708320 | + | 0.122685i | ||||
\(815\) | 1782.50 | − | 3087.38i | 0.0766114 | − | 0.132695i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11116.0 | + | 19253.5i | 0.476009 | + | 0.824472i | ||||
\(818\) | 2833.00 | 0.121092 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4900.00 | −0.208677 | ||||||||
\(821\) | 12549.0 | + | 21735.5i | 0.533451 | + | 0.923964i | 0.999237 | + | 0.0390664i | \(0.0124384\pi\) |
−0.465786 | + | 0.884898i | \(0.654228\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21746.0 | − | 37665.2i | 0.921042 | − | 1.59529i | 0.123237 | − | 0.992377i | \(-0.460672\pi\) |
0.797805 | − | 0.602915i | \(-0.205994\pi\) | |||||||
\(824\) | −5145.00 | + | 8911.40i | −0.217518 | + | 0.376752i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2244.00 | + | 3886.72i | 0.0945263 | + | 0.163724i | ||||
\(827\) | −11206.0 | −0.471186 | −0.235593 | − | 0.971852i | \(-0.575703\pi\) | ||||
−0.235593 | + | 0.971852i | \(0.575703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23964.0 | −1.00399 | −0.501993 | − | 0.864872i | \(-0.667400\pi\) | ||||
−0.501993 | + | 0.864872i | \(0.667400\pi\) | |||||||
\(830\) | −255.000 | − | 441.673i | −0.0106641 | − | 0.0184707i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −417.500 | + | 723.131i | −0.0173969 | + | 0.0301323i | ||||
\(833\) | 20108.5 | − | 34828.9i | 0.836396 | − | 1.44868i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3990.00 | − | 6910.88i | −0.165365 | − | 0.286420i | ||||
\(836\) | 18424.0 | 0.762210 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4777.00 | −0.196920 | ||||||||
\(839\) | −17303.0 | − | 29969.7i | −0.711997 | − | 1.23322i | −0.964106 | − | 0.265517i | \(-0.914457\pi\) |
0.252109 | − | 0.967699i | \(-0.418876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −130.000 | + | 225.167i | −0.00533027 | + | 0.00923230i | ||||
\(842\) | −3232.00 | + | 5597.99i | −0.132283 | + | 0.229120i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14567.0 | − | 25230.8i | −0.594096 | − | 1.02900i | ||||
\(845\) | 10860.0 | 0.442125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5268.00 | −0.213708 | ||||||||
\(848\) | 82.0000 | + | 142.028i | 0.00332063 | + | 0.00575149i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1637.50 | − | 2836.23i | 0.0660774 | − | 0.114449i | ||||
\(851\) | −105.000 | + | 181.865i | −0.00422956 | + | 0.00732581i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9238.50 | + | 16001.6i | 0.370833 | + | 0.642301i | 0.989694 | − | 0.143199i | \(-0.0457390\pi\) |
−0.618861 | + | 0.785500i | \(0.712406\pi\) | |||||||
\(854\) | −2028.00 | −0.0812608 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16470.0 | 0.657632 | ||||||||
\(857\) | −20671.0 | − | 35803.2i | −0.823930 | − | 1.42709i | −0.902734 | − | 0.430198i | \(-0.858444\pi\) |
0.0788045 | − | 0.996890i | \(-0.474890\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10949.0 | + | 18964.2i | −0.434895 | + | 0.753261i | −0.997287 | − | 0.0736101i | \(-0.976548\pi\) |
0.562392 | + | 0.826871i | \(0.309881\pi\) | |||||||
\(860\) | −6947.50 | + | 12033.4i | −0.275474 | + | 0.477135i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5340.00 | − | 9249.15i | −0.210999 | − | 0.365461i | ||||
\(863\) | 18487.0 | 0.729206 | 0.364603 | − | 0.931163i | \(-0.381205\pi\) | ||||
0.364603 | + | 0.931163i | \(0.381205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20670.0 | 0.812487 | ||||||||
\(866\) | 5783.00 | + | 10016.4i | 0.226922 | + | 0.393040i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4725.00 | + | 8183.94i | −0.184766 | + | 0.320024i | ||||
\(869\) | 29539.5 | − | 51163.9i | 1.15312 | − | 1.99726i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1230.00 | + | 2130.42i | 0.0478496 | + | 0.0828779i | ||||
\(872\) | −10500.0 | −0.407769 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −168.000 | −0.00650193 | ||||||||
\(875\) | −375.000 | − | 649.519i | −0.0144884 | − | 0.0250946i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3796.50 | + | 6575.73i | −0.146179 | + | 0.253189i | −0.929812 | − | 0.368035i | \(-0.880031\pi\) |
0.783633 | + | 0.621224i | \(0.213364\pi\) | |||||||
\(878\) | −724.000 | + | 1254.00i | −0.0278289 | + | 0.0482012i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4817.50 | + | 8344.15i | 0.184543 | + | 0.319638i | ||||
\(881\) | 3038.00 | 0.116178 | 0.0580890 | − | 0.998311i | \(-0.481499\pi\) | ||||
0.0580890 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16732.0 | −0.637686 | −0.318843 | − | 0.947808i | \(-0.603294\pi\) | ||||
−0.318843 | + | 0.947808i | \(0.603294\pi\) | |||||||
\(884\) | −2292.50 | − | 3970.73i | −0.0872230 | − | 0.151075i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1188.00 | − | 2057.68i | 0.0450470 | − | 0.0780237i | ||||
\(887\) | −4015.50 | + | 6955.05i | −0.152004 | + | 0.263278i | −0.931964 | − | 0.362551i | \(-0.881906\pi\) |
0.779960 | + | 0.625829i | \(0.215239\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4938.00 | − | 8552.87i | −0.186294 | − | 0.322670i | ||||
\(890\) | 7440.00 | 0.280213 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41692.0 | 1.56497 | ||||||||
\(893\) | 9716.00 | + | 16828.6i | 0.364091 | + | 0.630625i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4570.00 | + | 7915.47i | −0.170680 | + | 0.295626i | ||||
\(896\) | 4365.00 | − | 7560.40i | 0.162750 | − | 0.281892i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7447.00 | + | 12898.6i | 0.276737 | + | 0.479322i | ||||
\(899\) | 35325.0 | 1.31052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −524.000 | −0.0193751 | ||||||||
\(902\) | −3290.00 | − | 5698.45i | −0.121447 | − | 0.210352i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7912.50 | + | 13704.9i | −0.291113 | + | 0.504222i | ||||
\(905\) | −1300.00 | + | 2251.67i | −0.0477497 | + | 0.0827049i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19243.5 | + | 33330.7i | 0.704487 | + | 1.22021i | 0.966876 | + | 0.255246i | \(0.0821563\pi\) |
−0.262389 | + | 0.964962i | \(0.584510\pi\) | |||||||
\(908\) | 34580.0 | 1.26385 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 150.000 | 0.00546423 | ||||||||
\(911\) | −2560.00 | − | 4434.05i | −0.0931027 | − | 0.161259i | 0.815712 | − | 0.578458i | \(-0.196345\pi\) |
−0.908815 | + | 0.417199i | \(0.863012\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2397.00 | + | 4151.73i | −0.0868884 | + | 0.150495i | ||||
\(914\) | 8102.00 | − | 14033.1i | 0.293206 | − | 0.507848i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15204.0 | + | 26334.1i | 0.548422 | + | 0.949894i | ||||
\(917\) | −10998.0 | −0.396059 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28075.0 | 1.00774 | 0.503868 | − | 0.863781i | \(-0.331910\pi\) | ||||
0.503868 | + | 0.863781i | \(0.331910\pi\) | |||||||
\(920\) | −112.500 | − | 194.856i | −0.00403154 | − | 0.00698283i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2541.00 | − | 4401.14i | 0.0907629 | − | 0.157206i | ||||
\(923\) | −80.0000 | + | 138.564i | −0.00285291 | + | 0.00494138i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 875.000 | + | 1515.54i | 0.0311025 | + | 0.0538711i | ||||
\(926\) | 10326.0 | 0.366451 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25277.0 | −0.894136 | ||||||||
\(929\) | −6428.00 | − | 11133.6i | −0.227014 | − | 0.393199i | 0.729908 | − | 0.683546i | \(-0.239563\pi\) |
−0.956922 | + | 0.290346i | \(0.906230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8596.00 | + | 14888.7i | −0.302602 | + | 0.524122i | ||||
\(932\) | 18207.0 | − | 31535.4i | 0.639904 | − | 1.10835i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2092.00 | − | 3623.45i | −0.0732894 | − | 0.126941i | ||||
\(935\) | −30785.0 | −1.07677 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1374.00 | −0.0479046 | −0.0239523 | − | 0.999713i | \(-0.507625\pi\) | ||||
−0.0239523 | + | 0.999713i | \(0.507625\pi\) | |||||||
\(938\) | −1476.00 | − | 2556.51i | −0.0513786 | − | 0.0889903i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6072.50 | + | 10517.9i | −0.210705 | + | 0.364953i | ||||
\(941\) | 4271.50 | − | 7398.46i | 0.147978 | − | 0.256305i | −0.782502 | − | 0.622648i | \(-0.786057\pi\) |
0.930480 | + | 0.366343i | \(0.119390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −210.000 | − | 363.731i | −0.00725190 | − | 0.0125607i | ||||
\(944\) | −30668.0 | −1.05737 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18659.0 | −0.641286 | ||||||||
\(947\) | 6753.00 | + | 11696.5i | 0.231724 | + | 0.401358i | 0.958316 | − | 0.285712i | \(-0.0922299\pi\) |
−0.726591 | + | 0.687070i | \(0.758897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2425.00 | − | 4200.22i | 0.0829492 | − | 0.143672i | ||||
\(950\) | −700.000 | + | 1212.44i | −0.0239063 | + | 0.0414070i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5895.00 | + | 10210.4i | 0.200691 | + | 0.347607i | ||||
\(953\) | −21775.0 | −0.740148 | −0.370074 | − | 0.929002i | \(-0.620668\pi\) | ||||
−0.370074 | + | 0.929002i | \(0.620668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24130.0 | 0.817621 | ||||||||
\(956\) | −5411.00 | − | 9372.13i | −0.183059 | − | 0.317067i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7788.00 | − | 13489.2i | 0.262650 | − | 0.454923i | ||||
\(959\) | −3294.00 | + | 5705.38i | −0.110916 | + | 0.192113i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10417.0 | − | 18042.8i | −0.349669 | − | 0.605645i | ||||
\(962\) | −350.000 | −0.0117302 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25613.0 | 0.855746 | ||||||||
\(965\) | 4175.00 | + | 7231.31i | 0.139273 | + | 0.241227i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1927.00 | + | 3337.66i | −0.0640829 | + | 0.110995i | −0.896287 | − | 0.443475i | \(-0.853746\pi\) |
0.832204 | + | 0.554470i | \(0.187079\pi\) | |||||||
\(968\) | −6585.00 | + | 11405.6i | −0.218647 | + | 0.378707i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2435.00 | − | 4217.54i | −0.0806012 | − | 0.139605i | ||||
\(971\) | −12933.0 | −0.427435 | −0.213718 | − | 0.976895i | \(-0.568557\pi\) | ||||
−0.213718 | + | 0.976895i | \(0.568557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6252.00 | 0.205992 | ||||||||
\(974\) | 5110.00 | + | 8850.78i | 0.168106 | + | 0.291168i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6929.00 | − | 12001.4i | 0.227246 | − | 0.393601i | ||||
\(977\) | 8760.50 | − | 15173.6i | 0.286871 | − | 0.496876i | −0.686190 | − | 0.727422i | \(-0.740718\pi\) |
0.973061 | + | 0.230547i | \(0.0740515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34968.0 | − | 60566.4i | −1.14155 | − | 1.97723i | ||||
\(980\) | −10745.0 | −0.350241 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2692.00 | −0.0874798 | ||||||||
\(983\) | −6286.50 | − | 10888.5i | −0.203976 | − | 0.353296i | 0.745830 | − | 0.666136i | \(-0.232053\pi\) |
−0.949806 | + | 0.312840i | \(0.898720\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3450.00 | − | 5975.58i | 0.111600 | − | 0.193297i | ||||
\(986\) | 10283.5 | − | 17811.5i | 0.332143 | − | 0.575289i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 980.000 | + | 1697.41i | 0.0315566 | + | 0.0546577i | ||||
\(989\) | −1191.00 | −0.0382928 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8945.00 | 0.286728 | 0.143364 | − | 0.989670i | \(-0.454208\pi\) | ||||
0.143364 | + | 0.989670i | \(0.454208\pi\) | |||||||
\(992\) | 18112.5 | + | 31371.8i | 0.579710 | + | 1.00409i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 96.0000 | − | 166.277i | 0.00306331 | − | 0.00530582i | ||||
\(995\) | 10892.5 | − | 18866.4i | 0.347051 | − | 0.601109i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29089.5 | + | 50384.5i | 0.924046 | + | 1.60049i | 0.793089 | + | 0.609106i | \(0.208472\pi\) |
0.130957 | + | 0.991388i | \(0.458195\pi\) | |||||||
\(998\) | −5764.00 | −0.182822 | ||||||||
\(999\) | 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 | 405.4.e.h.271.1 | 2 | ||
3.2 | odd | 2 | 405.4.e.f.271.1 | 2 | |||
9.2 | odd | 6 | 405.4.e.f.136.1 | 2 | |||
9.4 | even | 3 | 135.4.a.b.1.1 | ✓ | 1 | ||
9.5 | odd | 6 | 135.4.a.c.1.1 | yes | 1 | ||
9.7 | even | 3 | inner | 405.4.e.h.136.1 | 2 | ||
36.23 | even | 6 | 2160.4.a.p.1.1 | 1 | |||
36.31 | odd | 6 | 2160.4.a.f.1.1 | 1 | |||
45.4 | even | 6 | 675.4.a.h.1.1 | 1 | |||
45.13 | odd | 12 | 675.4.b.f.649.2 | 2 | |||
45.14 | odd | 6 | 675.4.a.c.1.1 | 1 | |||
45.22 | odd | 12 | 675.4.b.f.649.1 | 2 | |||
45.23 | even | 12 | 675.4.b.e.649.1 | 2 | |||
45.32 | even | 12 | 675.4.b.e.649.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.b.1.1 | ✓ | 1 | 9.4 | even | 3 | ||
135.4.a.c.1.1 | yes | 1 | 9.5 | odd | 6 | ||
405.4.e.f.136.1 | 2 | 9.2 | odd | 6 | |||
405.4.e.f.271.1 | 2 | 3.2 | odd | 2 | |||
405.4.e.h.136.1 | 2 | 9.7 | even | 3 | inner | ||
405.4.e.h.271.1 | 2 | 1.1 | even | 1 | trivial | ||
675.4.a.c.1.1 | 1 | 45.14 | odd | 6 | |||
675.4.a.h.1.1 | 1 | 45.4 | even | 6 | |||
675.4.b.e.649.1 | 2 | 45.23 | even | 12 | |||
675.4.b.e.649.2 | 2 | 45.32 | even | 12 | |||
675.4.b.f.649.1 | 2 | 45.22 | odd | 12 | |||
675.4.b.f.649.2 | 2 | 45.13 | odd | 12 | |||
2160.4.a.f.1.1 | 1 | 36.31 | odd | 6 | |||
2160.4.a.p.1.1 | 1 | 36.23 | even | 6 |