Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,4,Mod(163,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.163");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.1786532220\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.627014547.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 26x^{4} + 169x^{2} + 147 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 235.2 | ||
Root | \(-4.00355i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.235 |
Dual form | 342.4.g.h.163.2 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.09405 | + | 3.62701i | 0.187298 | + | 0.324409i | 0.944348 | − | 0.328947i | \(-0.106694\pi\) |
−0.757051 | + | 0.653356i | \(0.773360\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.18810 | 0.172141 | 0.0860707 | − | 0.996289i | \(-0.472569\pi\) | ||||
0.0860707 | + | 0.996289i | \(0.472569\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.18810 | + | 7.25401i | −0.132440 | + | 0.229392i | ||||
\(11\) | −69.4003 | −1.90227 | −0.951135 | − | 0.308774i | \(-0.900081\pi\) | ||||
−0.951135 | + | 0.308774i | \(0.900081\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.06431 | − | 7.03960i | 0.0867106 | − | 0.150187i | −0.819408 | − | 0.573210i | \(-0.805698\pi\) |
0.906119 | + | 0.423023i | \(0.139031\pi\) | |||||||
\(14\) | 3.18810 | + | 5.52196i | 0.0608612 | + | 0.105415i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −53.0418 | − | 91.8711i | −0.756737 | − | 1.31071i | −0.944506 | − | 0.328493i | \(-0.893459\pi\) |
0.187770 | − | 0.982213i | \(-0.439874\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 42.6656 | + | 70.9834i | 0.515166 | + | 0.857090i | ||||
\(20\) | −16.7524 | −0.187298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −69.4003 | − | 120.205i | −0.672554 | − | 1.16490i | ||||
\(23\) | −88.2468 | + | 152.848i | −0.800031 | + | 1.38570i | 0.119563 | + | 0.992827i | \(0.461851\pi\) |
−0.919595 | + | 0.392869i | \(0.871483\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 53.7299 | − | 93.0629i | 0.429839 | − | 0.744503i | ||||
\(26\) | 16.2573 | 0.122627 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.37621 | + | 11.0439i | −0.0430354 | + | 0.0745394i | ||||
\(29\) | −33.1109 | + | 57.3498i | −0.212019 | + | 0.367227i | −0.952346 | − | 0.305019i | \(-0.901337\pi\) |
0.740327 | + | 0.672247i | \(0.234670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −140.915 | −0.816421 | −0.408210 | − | 0.912888i | \(-0.633847\pi\) | ||||
−0.408210 | + | 0.912888i | \(0.633847\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 106.084 | − | 183.742i | 0.535094 | − | 0.926809i | ||||
\(35\) | 6.67606 | + | 11.5633i | 0.0322417 | + | 0.0558443i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −156.003 | −0.693156 | −0.346578 | − | 0.938021i | \(-0.612656\pi\) | ||||
−0.346578 | + | 0.938021i | \(0.612656\pi\) | |||||||
\(38\) | −80.2814 | + | 144.882i | −0.342720 | + | 0.618501i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16.7524 | − | 29.0160i | −0.0662198 | − | 0.114696i | ||||
\(41\) | −207.281 | − | 359.022i | −0.789559 | − | 1.36756i | −0.926238 | − | 0.376940i | \(-0.876976\pi\) |
0.136679 | − | 0.990615i | \(-0.456357\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −57.9252 | − | 100.329i | −0.205430 | − | 0.355816i | 0.744839 | − | 0.667244i | \(-0.232526\pi\) |
−0.950270 | + | 0.311428i | \(0.899193\pi\) | |||||||
\(44\) | 138.801 | − | 240.410i | 0.475568 | − | 0.823707i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −352.987 | −1.13142 | ||||||||
\(47\) | 310.141 | − | 537.181i | 0.962527 | − | 1.66715i | 0.246410 | − | 0.969166i | \(-0.420749\pi\) |
0.716117 | − | 0.697980i | \(-0.245918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −332.836 | −0.970367 | ||||||||
\(50\) | 214.920 | 0.607884 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.2573 | + | 28.1584i | 0.0433553 | + | 0.0750936i | ||||
\(53\) | −185.993 | + | 322.149i | −0.482039 | + | 0.834916i | −0.999787 | − | 0.0206167i | \(-0.993437\pi\) |
0.517748 | + | 0.855533i | \(0.326770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −145.328 | − | 251.715i | −0.356291 | − | 0.617114i | ||||
\(56\) | −25.5048 | −0.0608612 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −132.444 | −0.299840 | ||||||||
\(59\) | 45.8465 | + | 79.4084i | 0.101164 | + | 0.175222i | 0.912165 | − | 0.409824i | \(-0.134410\pi\) |
−0.811000 | + | 0.585046i | \(0.801077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −109.310 | + | 189.331i | −0.229438 | + | 0.397399i | −0.957642 | − | 0.287962i | \(-0.907022\pi\) |
0.728203 | + | 0.685361i | \(0.240356\pi\) | |||||||
\(62\) | −140.915 | − | 244.072i | −0.288648 | − | 0.499954i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 34.0436 | 0.0649628 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 72.6712 | − | 125.870i | 0.132510 | − | 0.229515i | −0.792133 | − | 0.610348i | \(-0.791030\pi\) |
0.924644 | + | 0.380833i | \(0.124363\pi\) | |||||||
\(68\) | 424.334 | 0.756737 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.3521 | + | 23.1265i | −0.0227983 | + | 0.0394879i | ||||
\(71\) | 443.915 | + | 768.883i | 0.742014 | + | 1.28521i | 0.951577 | + | 0.307410i | \(0.0994625\pi\) |
−0.209563 | + | 0.977795i | \(0.567204\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −99.5081 | − | 172.353i | −0.159542 | − | 0.276334i | 0.775162 | − | 0.631763i | \(-0.217668\pi\) |
−0.934703 | + | 0.355429i | \(0.884335\pi\) | |||||||
\(74\) | −156.003 | − | 270.205i | −0.245067 | − | 0.424469i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −331.225 | + | 5.83100i | −0.499923 | + | 0.00880082i | ||||
\(77\) | −221.255 | −0.327460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 194.779 | + | 337.367i | 0.277397 | + | 0.480465i | 0.970737 | − | 0.240145i | \(-0.0771951\pi\) |
−0.693340 | + | 0.720610i | \(0.743862\pi\) | |||||||
\(80\) | 33.5048 | − | 58.0321i | 0.0468244 | − | 0.0811023i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 414.563 | − | 718.044i | 0.558302 | − | 0.967008i | ||||
\(83\) | −380.039 | −0.502586 | −0.251293 | − | 0.967911i | \(-0.580856\pi\) | ||||
−0.251293 | + | 0.967911i | \(0.580856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 222.145 | − | 384.766i | 0.283470 | − | 0.490985i | ||||
\(86\) | 115.850 | − | 200.659i | 0.145261 | − | 0.251600i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 555.202 | 0.672554 | ||||||||
\(89\) | −212.899 | + | 368.753i | −0.253565 | + | 0.439188i | −0.964505 | − | 0.264065i | \(-0.914937\pi\) |
0.710940 | + | 0.703253i | \(0.248270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.9575 | − | 22.4430i | 0.0149265 | − | 0.0258534i | ||||
\(92\) | −352.987 | − | 611.392i | −0.400016 | − | 0.692848i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1240.57 | 1.36122 | ||||||||
\(95\) | −168.113 | + | 303.391i | −0.181559 | + | 0.327656i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −209.923 | − | 363.597i | −0.219736 | − | 0.380595i | 0.734991 | − | 0.678077i | \(-0.237186\pi\) |
−0.954727 | + | 0.297482i | \(0.903853\pi\) | |||||||
\(98\) | −332.836 | − | 576.489i | −0.343077 | − | 0.594226i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 214.920 | + | 372.252i | 0.214920 | + | 0.372252i | ||||
\(101\) | −620.855 | + | 1075.35i | −0.611657 | + | 1.05942i | 0.379304 | + | 0.925272i | \(0.376164\pi\) |
−0.990961 | + | 0.134150i | \(0.957170\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −593.606 | −0.567862 | −0.283931 | − | 0.958845i | \(-0.591639\pi\) | ||||
−0.283931 | + | 0.958845i | \(0.591639\pi\) | |||||||
\(104\) | −32.5145 | + | 56.3168i | −0.0306568 | + | 0.0530992i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −743.971 | −0.681706 | ||||||||
\(107\) | 1778.56 | 1.60691 | 0.803457 | − | 0.595363i | \(-0.202992\pi\) | ||||
0.803457 | + | 0.595363i | \(0.202992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 534.995 | + | 926.639i | 0.470121 | + | 0.814274i | 0.999416 | − | 0.0341638i | \(-0.0108768\pi\) |
−0.529295 | + | 0.848438i | \(0.677543\pi\) | |||||||
\(110\) | 290.656 | − | 503.431i | 0.251936 | − | 0.436366i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −25.5048 | − | 44.1757i | −0.0215177 | − | 0.0372697i | ||||
\(113\) | −583.197 | −0.485510 | −0.242755 | − | 0.970088i | \(-0.578051\pi\) | ||||
−0.242755 | + | 0.970088i | \(0.578051\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −739.173 | −0.599376 | ||||||||
\(116\) | −132.444 | − | 229.399i | −0.106009 | − | 0.183614i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −91.6929 | + | 158.817i | −0.0715341 | + | 0.123901i | ||||
\(119\) | −169.103 | − | 292.895i | −0.130266 | − | 0.225627i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3485.40 | 2.61863 | ||||||||
\(122\) | −437.241 | −0.324475 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 281.830 | − | 488.143i | 0.204105 | − | 0.353521i | ||||
\(125\) | 973.566 | 0.696627 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −829.677 | + | 1437.04i | −0.579700 | + | 1.00407i | 0.415814 | + | 0.909450i | \(0.363497\pi\) |
−0.995513 | + | 0.0946199i | \(0.969836\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 34.0436 | + | 58.9652i | 0.0229678 | + | 0.0397814i | ||||
\(131\) | 298.773 | + | 517.490i | 0.199267 | + | 0.345140i | 0.948291 | − | 0.317403i | \(-0.102811\pi\) |
−0.749024 | + | 0.662543i | \(0.769477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 136.022 | + | 226.303i | 0.0886814 | + | 0.147541i | ||||
\(134\) | 290.685 | 0.187398 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 424.334 | + | 734.969i | 0.267547 | + | 0.463405i | ||||
\(137\) | −888.654 | + | 1539.19i | −0.554182 | + | 0.959871i | 0.443785 | + | 0.896133i | \(0.353635\pi\) |
−0.997967 | + | 0.0637373i | \(0.979698\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −81.7836 | + | 141.653i | −0.0499050 | + | 0.0864379i | −0.889899 | − | 0.456158i | \(-0.849225\pi\) |
0.839994 | + | 0.542596i | \(0.182559\pi\) | |||||||
\(140\) | −53.4085 | −0.0322417 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −887.829 | + | 1537.77i | −0.524683 | + | 0.908778i | ||||
\(143\) | −282.065 | + | 488.550i | −0.164947 | + | 0.285697i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −277.344 | −0.158843 | ||||||||
\(146\) | 199.016 | − | 344.706i | 0.112813 | − | 0.195398i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 312.006 | − | 540.411i | 0.173289 | − | 0.300145i | ||||
\(149\) | −559.899 | − | 969.774i | −0.307844 | − | 0.533201i | 0.670047 | − | 0.742319i | \(-0.266274\pi\) |
−0.977890 | + | 0.209118i | \(0.932941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2807.15 | −1.51286 | −0.756432 | − | 0.654073i | \(-0.773059\pi\) | ||||
−0.756432 | + | 0.654073i | \(0.773059\pi\) | |||||||
\(152\) | −341.325 | − | 567.868i | −0.182139 | − | 0.303027i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −221.255 | − | 383.226i | −0.115774 | − | 0.200527i | ||||
\(155\) | −295.083 | − | 511.099i | −0.152914 | − | 0.264854i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −501.971 | − | 869.439i | −0.255170 | − | 0.441967i | 0.709772 | − | 0.704432i | \(-0.248798\pi\) |
−0.964942 | + | 0.262465i | \(0.915465\pi\) | |||||||
\(158\) | −389.558 | + | 674.734i | −0.196149 | + | 0.339740i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 134.019 | 0.0662198 | ||||||||
\(161\) | −281.340 | + | 487.295i | −0.137719 | + | 0.238536i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1271.99 | 0.611225 | 0.305612 | − | 0.952156i | \(-0.401139\pi\) | ||||
0.305612 | + | 0.952156i | \(0.401139\pi\) | |||||||
\(164\) | 1658.25 | 0.789559 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −380.039 | − | 658.246i | −0.177691 | − | 0.307770i | ||||
\(167\) | −1492.49 | + | 2585.07i | −0.691572 | + | 1.19784i | 0.279751 | + | 0.960073i | \(0.409748\pi\) |
−0.971323 | + | 0.237765i | \(0.923585\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1065.46 | + | 1845.44i | 0.484963 | + | 0.839980i | ||||
\(170\) | 888.578 | 0.400887 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 463.402 | 0.205430 | ||||||||
\(173\) | 28.3873 | + | 49.1683i | 0.0124754 | + | 0.0216081i | 0.872196 | − | 0.489157i | \(-0.162696\pi\) |
−0.859720 | + | 0.510765i | \(0.829362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 171.297 | − | 296.694i | 0.0739931 | − | 0.128160i | ||||
\(176\) | 555.202 | + | 961.639i | 0.237784 | + | 0.411854i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −851.598 | −0.358595 | ||||||||
\(179\) | 4640.98 | 1.93790 | 0.968948 | − | 0.247266i | \(-0.0795323\pi\) | ||||
0.968948 | + | 0.247266i | \(0.0795323\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1887.70 | + | 3269.60i | −0.775204 | + | 1.34269i | 0.159476 | + | 0.987202i | \(0.449020\pi\) |
−0.934680 | + | 0.355491i | \(0.884314\pi\) | |||||||
\(182\) | 51.8298 | 0.0211093 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 705.974 | − | 1222.78i | 0.282854 | − | 0.489917i | ||||
\(185\) | −326.679 | − | 565.824i | −0.129826 | − | 0.224866i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3681.12 | + | 6375.88i | 1.43952 | + | 2.49332i | ||||
\(188\) | 1240.57 | + | 2148.72i | 0.481264 | + | 0.833573i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −693.603 | + | 12.2104i | −0.264838 | + | 0.00466230i | ||||
\(191\) | 2762.53 | 1.04654 | 0.523271 | − | 0.852166i | \(-0.324712\pi\) | ||||
0.523271 | + | 0.852166i | \(0.324712\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1030.76 | − | 1785.32i | −0.384433 | − | 0.665857i | 0.607258 | − | 0.794505i | \(-0.292270\pi\) |
−0.991690 | + | 0.128648i | \(0.958936\pi\) | |||||||
\(194\) | 419.846 | − | 727.194i | 0.155377 | − | 0.269121i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 665.672 | − | 1152.98i | 0.242592 | − | 0.420181i | ||||
\(197\) | −2094.82 | −0.757614 | −0.378807 | − | 0.925476i | \(-0.623666\pi\) | ||||
−0.378807 | + | 0.925476i | \(0.623666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 858.681 | − | 1487.28i | 0.305881 | − | 0.529801i | −0.671576 | − | 0.740935i | \(-0.734382\pi\) |
0.977457 | + | 0.211134i | \(0.0677158\pi\) | |||||||
\(200\) | −429.839 | + | 744.503i | −0.151971 | + | 0.263222i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2483.42 | −0.865014 | ||||||||
\(203\) | −105.561 | + | 182.837i | −0.0364972 | + | 0.0632151i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 868.116 | − | 1503.62i | 0.295765 | − | 0.512280i | ||||
\(206\) | −593.606 | − | 1028.16i | −0.200769 | − | 0.347743i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −130.058 | −0.0433553 | ||||||||
\(209\) | −2961.00 | − | 4926.27i | −0.979985 | − | 1.63042i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1145.53 | + | 1984.11i | 0.373750 | + | 0.647354i | 0.990139 | − | 0.140088i | \(-0.0447384\pi\) |
−0.616389 | + | 0.787442i | \(0.711405\pi\) | |||||||
\(212\) | −743.971 | − | 1288.60i | −0.241020 | − | 0.417458i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1778.56 | + | 3080.55i | 0.568130 | + | 0.984030i | ||||
\(215\) | 242.597 | − | 420.190i | 0.0769533 | − | 0.133287i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −449.251 | −0.140540 | ||||||||
\(218\) | −1069.99 | + | 1853.28i | −0.332426 | + | 0.575779i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1162.62 | 0.356291 | ||||||||
\(221\) | −862.314 | −0.262468 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1628.09 | − | 2819.94i | −0.488902 | − | 0.846804i | 0.511016 | − | 0.859571i | \(-0.329269\pi\) |
−0.999918 | + | 0.0127673i | \(0.995936\pi\) | |||||||
\(224\) | 51.0097 | − | 88.3514i | 0.0152153 | − | 0.0263537i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −583.197 | − | 1010.13i | −0.171654 | − | 0.297313i | ||||
\(227\) | 998.044 | 0.291817 | 0.145909 | − | 0.989298i | \(-0.453389\pi\) | ||||
0.145909 | + | 0.989298i | \(0.453389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1028.59 | −0.296816 | −0.148408 | − | 0.988926i | \(-0.547415\pi\) | ||||
−0.148408 | + | 0.988926i | \(0.547415\pi\) | |||||||
\(230\) | −739.173 | − | 1280.29i | −0.211912 | − | 0.367042i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 264.887 | − | 458.799i | 0.0749600 | − | 0.129835i | ||||
\(233\) | −62.7431 | − | 108.674i | −0.0176414 | − | 0.0305557i | 0.857070 | − | 0.515200i | \(-0.172282\pi\) |
−0.874711 | + | 0.484644i | \(0.838949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2597.81 | 0.721117 | ||||||||
\(236\) | −366.772 | −0.101164 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 338.206 | − | 585.789i | 0.0921118 | − | 0.159542i | ||||
\(239\) | −3591.03 | −0.971901 | −0.485950 | − | 0.873986i | \(-0.661526\pi\) | ||||
−0.485950 | + | 0.873986i | \(0.661526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1845.92 | − | 3197.23i | 0.493386 | − | 0.854570i | −0.506585 | − | 0.862190i | \(-0.669092\pi\) |
0.999971 | + | 0.00762002i | \(0.00242555\pi\) | |||||||
\(242\) | 3485.40 | + | 6036.89i | 0.925827 | + | 1.60358i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −437.241 | − | 757.324i | −0.114719 | − | 0.198700i | ||||
\(245\) | −696.976 | − | 1207.20i | −0.181748 | − | 0.314796i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 673.101 | − | 11.8495i | 0.173394 | − | 0.00305250i | ||||
\(248\) | 1127.32 | 0.288648 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 973.566 | + | 1686.27i | 0.246295 | + | 0.426595i | ||||
\(251\) | 3647.44 | − | 6317.55i | 0.917228 | − | 1.58869i | 0.113622 | − | 0.993524i | \(-0.463755\pi\) |
0.803606 | − | 0.595162i | \(-0.202912\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6124.35 | − | 10607.7i | 1.52188 | − | 2.63597i | ||||
\(254\) | −3318.71 | −0.819820 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1151.60 | − | 1994.63i | 0.279513 | − | 0.484131i | −0.691751 | − | 0.722136i | \(-0.743160\pi\) |
0.971264 | + | 0.238006i | \(0.0764937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −497.354 | −0.119321 | ||||||||
\(260\) | −68.0871 | + | 117.930i | −0.0162407 | + | 0.0281297i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −597.546 | + | 1034.98i | −0.140903 | + | 0.244051i | ||||
\(263\) | 3569.19 | + | 6182.01i | 0.836827 | + | 1.44943i | 0.892534 | + | 0.450980i | \(0.148925\pi\) |
−0.0557070 | + | 0.998447i | \(0.517741\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1557.91 | −0.361139 | ||||||||
\(266\) | −255.945 | + | 461.900i | −0.0589963 | + | 0.106470i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 290.685 | + | 503.481i | 0.0662552 | + | 0.114757i | ||||
\(269\) | −2723.33 | − | 4716.95i | −0.617265 | − | 1.06913i | −0.989983 | − | 0.141190i | \(-0.954907\pi\) |
0.372717 | − | 0.927945i | \(-0.378426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1701.84 | + | 2947.67i | 0.381474 | + | 0.660732i | 0.991273 | − | 0.131824i | \(-0.0420834\pi\) |
−0.609799 | + | 0.792556i | \(0.708750\pi\) | |||||||
\(272\) | −848.669 | + | 1469.94i | −0.189184 | + | 0.327677i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3554.62 | −0.783731 | ||||||||
\(275\) | −3728.87 | + | 6458.59i | −0.817670 | + | 1.41625i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5131.93 | −1.11317 | −0.556584 | − | 0.830791i | \(-0.687888\pi\) | ||||
−0.556584 | + | 0.830791i | \(0.687888\pi\) | |||||||
\(278\) | −327.134 | −0.0705763 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −53.4085 | − | 92.5062i | −0.0113992 | − | 0.0197439i | ||||
\(281\) | 1683.34 | − | 2915.63i | 0.357365 | − | 0.618975i | −0.630154 | − | 0.776470i | \(-0.717008\pi\) |
0.987520 | + | 0.157495i | \(0.0503417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3342.88 | − | 5790.04i | −0.702168 | − | 1.21619i | −0.967704 | − | 0.252090i | \(-0.918882\pi\) |
0.265535 | − | 0.964101i | \(-0.414451\pi\) | |||||||
\(284\) | −3551.32 | −0.742014 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1128.26 | −0.233270 | ||||||||
\(287\) | −660.835 | − | 1144.60i | −0.135916 | − | 0.235413i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3170.36 | + | 5491.23i | −0.645301 | + | 1.11769i | ||||
\(290\) | −277.344 | − | 480.374i | −0.0561593 | − | 0.0972708i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 796.065 | 0.159542 | ||||||||
\(293\) | 5625.93 | 1.12174 | 0.560871 | − | 0.827903i | \(-0.310466\pi\) | ||||
0.560871 | + | 0.827903i | \(0.310466\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −192.010 | + | 332.571i | −0.0378957 | + | 0.0656374i | ||||
\(296\) | 1248.02 | 0.245067 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1119.80 | − | 1939.55i | 0.217678 | − | 0.377030i | ||||
\(299\) | 717.325 | + | 1242.44i | 0.138742 | + | 0.240309i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −184.672 | − | 319.861i | −0.0353631 | − | 0.0612507i | ||||
\(302\) | −2807.15 | − | 4862.12i | −0.534878 | − | 0.926436i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 642.251 | − | 1159.06i | 0.121170 | − | 0.218673i | ||||
\(305\) | −915.606 | −0.171893 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2801.77 | − | 4852.81i | −0.520865 | − | 0.902164i | −0.999706 | − | 0.0242627i | \(-0.992276\pi\) |
0.478841 | − | 0.877902i | \(-0.341057\pi\) | |||||||
\(308\) | 442.511 | − | 766.451i | 0.0818649 | − | 0.141794i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 590.166 | − | 1022.20i | 0.108126 | − | 0.187280i | ||||
\(311\) | −6668.20 | −1.21582 | −0.607908 | − | 0.794008i | \(-0.707991\pi\) | ||||
−0.607908 | + | 0.794008i | \(0.707991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2245.70 | + | 3889.67i | −0.405541 | + | 0.702418i | −0.994384 | − | 0.105829i | \(-0.966250\pi\) |
0.588843 | + | 0.808247i | \(0.299584\pi\) | |||||||
\(314\) | 1003.94 | − | 1738.88i | 0.180432 | − | 0.312518i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1558.23 | −0.277397 | ||||||||
\(317\) | −633.023 | + | 1096.43i | −0.112158 | + | 0.194264i | −0.916640 | − | 0.399713i | \(-0.869110\pi\) |
0.804482 | + | 0.593977i | \(0.202443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2297.91 | − | 3980.10i | 0.403317 | − | 0.698566i | ||||
\(320\) | 134.019 | + | 232.128i | 0.0234122 | + | 0.0405512i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1125.36 | −0.194764 | ||||||||
\(323\) | 4258.27 | − | 7684.82i | 0.733549 | − | 1.32382i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −436.750 | − | 756.474i | −0.0745432 | − | 0.129113i | ||||
\(326\) | 1271.99 | + | 2203.14i | 0.216101 | + | 0.374297i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1658.25 | + | 2872.17i | 0.279151 | + | 0.483504i | ||||
\(329\) | 988.763 | − | 1712.59i | 0.165691 | − | 0.286985i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5068.09 | −0.841594 | −0.420797 | − | 0.907155i | \(-0.638249\pi\) | ||||
−0.420797 | + | 0.907155i | \(0.638249\pi\) | |||||||
\(332\) | 760.077 | − | 1316.49i | 0.125647 | − | 0.217626i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5969.97 | −0.978031 | ||||||||
\(335\) | 608.709 | 0.0992757 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5372.06 | − | 9304.68i | −0.868352 | − | 1.50403i | −0.863680 | − | 0.504041i | \(-0.831846\pi\) |
−0.00467268 | − | 0.999989i | \(-0.501487\pi\) | |||||||
\(338\) | −2130.93 | + | 3690.87i | −0.342920 | + | 0.593955i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 888.578 | + | 1539.06i | 0.141735 | + | 0.245492i | ||||
\(341\) | 9779.53 | 1.55305 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2154.64 | −0.339182 | ||||||||
\(344\) | 463.402 | + | 802.635i | 0.0726306 | + | 0.125800i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −56.7747 | + | 98.3367i | −0.00882146 | + | 0.0152792i | ||||
\(347\) | −2425.67 | − | 4201.38i | −0.375264 | − | 0.649977i | 0.615102 | − | 0.788447i | \(-0.289115\pi\) |
−0.990367 | + | 0.138471i | \(0.955781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7611.35 | −1.16741 | −0.583705 | − | 0.811966i | \(-0.698398\pi\) | ||||
−0.583705 | + | 0.811966i | \(0.698398\pi\) | |||||||
\(350\) | 685.186 | 0.104642 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1110.40 | + | 1923.28i | −0.168139 | + | 0.291225i | ||||
\(353\) | −5567.64 | −0.839477 | −0.419739 | − | 0.907645i | \(-0.637878\pi\) | ||||
−0.419739 | + | 0.907645i | \(0.637878\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1859.16 | + | 3220.16i | −0.277955 | + | 0.481432i | ||||
\(356\) | −851.598 | − | 1475.01i | −0.126783 | − | 0.219594i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4640.98 | + | 8038.42i | 0.685149 | + | 1.18671i | ||||
\(359\) | 2170.66 | + | 3759.69i | 0.319116 | + | 0.552726i | 0.980304 | − | 0.197495i | \(-0.0632805\pi\) |
−0.661187 | + | 0.750221i | \(0.729947\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3218.30 | + | 6057.10i | −0.469208 | + | 0.883088i | ||||
\(362\) | −7550.82 | −1.09630 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 51.8298 | + | 89.7719i | 0.00746325 | + | 0.0129267i | ||||
\(365\) | 416.750 | − | 721.833i | 0.0597636 | − | 0.103514i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4482.24 | − | 7763.47i | 0.637524 | − | 1.10422i | −0.348451 | − | 0.937327i | \(-0.613292\pi\) |
0.985974 | − | 0.166896i | \(-0.0533745\pi\) | |||||||
\(368\) | 2823.90 | 0.400016 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 653.357 | − | 1131.65i | 0.0918012 | − | 0.159004i | ||||
\(371\) | −592.965 | + | 1027.04i | −0.0829789 | + | 0.143724i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5048.11 | 0.700755 | 0.350377 | − | 0.936609i | \(-0.386053\pi\) | ||||
0.350377 | + | 0.936609i | \(0.386053\pi\) | |||||||
\(374\) | −7362.23 | + | 12751.8i | −1.01789 | + | 1.76304i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2481.13 | + | 4297.45i | −0.340305 | + | 0.589425i | ||||
\(377\) | 269.147 | + | 466.175i | 0.0367686 | + | 0.0636850i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9290.41 | −1.25915 | −0.629573 | − | 0.776941i | \(-0.716770\pi\) | ||||
−0.629573 | + | 0.776941i | \(0.716770\pi\) | |||||||
\(380\) | −714.752 | − | 1189.14i | −0.0964894 | − | 0.160531i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2762.53 | + | 4784.84i | 0.370009 | + | 0.640874i | ||||
\(383\) | 2081.13 | + | 3604.62i | 0.277652 | + | 0.480907i | 0.970801 | − | 0.239887i | \(-0.0771105\pi\) |
−0.693149 | + | 0.720794i | \(0.743777\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −463.320 | − | 802.495i | −0.0613325 | − | 0.106231i | ||||
\(386\) | 2061.51 | − | 3570.65i | 0.271835 | − | 0.470832i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1679.38 | 0.219736 | ||||||||
\(389\) | 2092.61 | − | 3624.51i | 0.272750 | − | 0.472417i | −0.696815 | − | 0.717251i | \(-0.745400\pi\) |
0.969565 | + | 0.244834i | \(0.0787335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18723.1 | 2.42165 | ||||||||
\(392\) | 2662.69 | 0.343077 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2094.82 | − | 3628.34i | −0.267857 | − | 0.463942i | ||||
\(395\) | −815.754 | + | 1412.93i | −0.103912 | + | 0.179980i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2264.88 | + | 3922.89i | 0.286325 | + | 0.495930i | 0.972930 | − | 0.231101i | \(-0.0742329\pi\) |
−0.686605 | + | 0.727031i | \(0.740900\pi\) | |||||||
\(398\) | 3434.72 | 0.432581 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1719.36 | −0.214920 | ||||||||
\(401\) | −4748.53 | − | 8224.69i | −0.591347 | − | 1.02424i | −0.994051 | − | 0.108913i | \(-0.965263\pi\) |
0.402704 | − | 0.915330i | \(-0.368070\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −572.722 | + | 991.984i | −0.0707924 | + | 0.122616i | ||||
\(404\) | −2483.42 | − | 4301.41i | −0.305829 | − | 0.529711i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −422.245 | −0.0516149 | ||||||||
\(407\) | 10826.7 | 1.31857 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2677.22 | − | 4637.08i | 0.323667 | − | 0.560608i | −0.657574 | − | 0.753390i | \(-0.728417\pi\) |
0.981242 | + | 0.192781i | \(0.0617508\pi\) | |||||||
\(410\) | 3472.46 | 0.418275 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1187.21 | − | 2056.31i | 0.141965 | − | 0.245891i | ||||
\(413\) | 146.163 | + | 253.162i | 0.0174146 | + | 0.0301630i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −795.821 | − | 1378.40i | −0.0941333 | − | 0.163044i | ||||
\(416\) | −130.058 | − | 225.267i | −0.0153284 | − | 0.0265496i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5571.55 | − | 10054.9i | 0.651946 | − | 1.17656i | ||||
\(419\) | −14506.1 | −1.69134 | −0.845668 | − | 0.533709i | \(-0.820798\pi\) | ||||
−0.845668 | + | 0.533709i | \(0.820798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 631.724 | + | 1094.18i | 0.0731315 | + | 0.126667i | 0.900272 | − | 0.435327i | \(-0.143367\pi\) |
−0.827141 | + | 0.561995i | \(0.810034\pi\) | |||||||
\(422\) | −2291.05 | + | 3968.22i | −0.264281 | + | 0.457749i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1487.94 | − | 2577.19i | 0.170427 | − | 0.295187i | ||||
\(425\) | −11399.7 | −1.30110 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −348.493 | + | 603.607i | −0.0394959 | + | 0.0684089i | ||||
\(428\) | −3557.12 | + | 6161.11i | −0.401729 | + | 0.695814i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 970.387 | 0.108828 | ||||||||
\(431\) | −4093.81 | + | 7090.69i | −0.457522 | + | 0.792451i | −0.998829 | − | 0.0483738i | \(-0.984596\pi\) |
0.541308 | + | 0.840825i | \(0.317929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4621.47 | − | 8004.63i | 0.512919 | − | 0.888401i | −0.486969 | − | 0.873419i | \(-0.661898\pi\) |
0.999888 | − | 0.0149820i | \(-0.00476910\pi\) | |||||||
\(434\) | −449.251 | − | 778.126i | −0.0496884 | − | 0.0860628i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4279.96 | −0.470121 | ||||||||
\(437\) | −14614.8 | + | 257.284i | −1.59982 | + | 0.0281637i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1021.52 | + | 1769.33i | 0.111059 | + | 0.192359i | 0.916197 | − | 0.400727i | \(-0.131243\pi\) |
−0.805139 | + | 0.593086i | \(0.797909\pi\) | |||||||
\(440\) | 1162.62 | + | 2013.72i | 0.125968 | + | 0.218183i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −862.314 | − | 1493.57i | −0.0927966 | − | 0.160728i | ||||
\(443\) | −4834.57 | + | 8373.71i | −0.518504 | + | 0.898075i | 0.481265 | + | 0.876575i | \(0.340177\pi\) |
−0.999769 | + | 0.0214998i | \(0.993156\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1783.29 | −0.189969 | ||||||||
\(446\) | 3256.19 | − | 5639.88i | 0.345706 | − | 0.598781i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 204.039 | 0.0215177 | ||||||||
\(449\) | 13227.2 | 1.39027 | 0.695134 | − | 0.718881i | \(-0.255345\pi\) | ||||
0.695134 | + | 0.718881i | \(0.255345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14385.4 | + | 24916.2i | 1.50195 | + | 2.60146i | ||||
\(452\) | 1166.39 | − | 2020.26i | 0.121377 | − | 0.210232i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 998.044 | + | 1728.66i | 0.103173 | + | 0.178701i | ||||
\(455\) | 108.534 | 0.0111828 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5380.98 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(458\) | −1028.59 | − | 1781.56i | −0.104940 | − | 0.181762i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1478.35 | − | 2560.57i | 0.149844 | − | 0.259538i | ||||
\(461\) | −1422.33 | − | 2463.55i | −0.143698 | − | 0.248892i | 0.785189 | − | 0.619257i | \(-0.212566\pi\) |
−0.928886 | + | 0.370365i | \(0.879233\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6625.39 | 0.665028 | 0.332514 | − | 0.943098i | \(-0.392103\pi\) | ||||
0.332514 | + | 0.943098i | \(0.392103\pi\) | |||||||
\(464\) | 1059.55 | 0.106009 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 125.486 | − | 217.348i | 0.0124743 | − | 0.0216062i | ||||
\(467\) | 18635.1 | 1.84653 | 0.923264 | − | 0.384167i | \(-0.125511\pi\) | ||||
0.923264 | + | 0.384167i | \(0.125511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 231.683 | − | 401.288i | 0.0228106 | − | 0.0395090i | ||||
\(470\) | 2597.81 | + | 4499.54i | 0.254953 | + | 0.441592i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −366.772 | − | 635.267i | −0.0357670 | − | 0.0619503i | ||||
\(473\) | 4020.03 | + | 6962.89i | 0.390784 | + | 0.676858i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8898.34 | − | 156.650i | 0.859545 | − | 0.0151317i | ||||
\(476\) | 1352.82 | 0.130266 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3591.03 | − | 6219.84i | −0.343619 | − | 0.595165i | ||||
\(479\) | 778.310 | − | 1348.07i | 0.0742420 | − | 0.128591i | −0.826514 | − | 0.562916i | \(-0.809680\pi\) |
0.900756 | + | 0.434325i | \(0.143013\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −634.046 | + | 1098.20i | −0.0601039 | + | 0.104103i | ||||
\(482\) | 7383.68 | 0.697754 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6970.80 | + | 12073.8i | −0.654659 | + | 1.13390i | ||||
\(485\) | 879.179 | − | 1522.78i | 0.0823123 | − | 0.142569i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19339.5 | 1.79950 | 0.899751 | − | 0.436405i | \(-0.143748\pi\) | ||||
0.899751 | + | 0.436405i | \(0.143748\pi\) | |||||||
\(488\) | 874.482 | − | 1514.65i | 0.0811188 | − | 0.140502i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1393.95 | − | 2414.40i | 0.128515 | − | 0.222594i | ||||
\(491\) | −3419.12 | − | 5922.10i | −0.314262 | − | 0.544319i | 0.665018 | − | 0.746827i | \(-0.268424\pi\) |
−0.979280 | + | 0.202509i | \(0.935091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7025.05 | 0.641770 | ||||||||
\(494\) | 693.625 | + | 1154.00i | 0.0631734 | + | 0.105103i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1127.32 | + | 1952.57i | 0.102053 | + | 0.176760i | ||||
\(497\) | 1415.25 | + | 2451.28i | 0.127731 | + | 0.221237i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9057.49 | + | 15688.0i | 0.812563 | + | 1.40740i | 0.911065 | + | 0.412263i | \(0.135262\pi\) |
−0.0985021 | + | 0.995137i | \(0.531405\pi\) | |||||||
\(500\) | −1947.13 | + | 3372.53i | −0.174157 | + | 0.301648i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14589.8 | 1.29716 | ||||||||
\(503\) | −2915.92 | + | 5050.53i | −0.258478 | + | 0.447698i | −0.965834 | − | 0.259160i | \(-0.916554\pi\) |
0.707356 | + | 0.706857i | \(0.249888\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5200.41 | −0.458248 | ||||||||
\(506\) | 24497.4 | 2.15226 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3318.71 | − | 5748.17i | −0.289850 | − | 0.502035i | ||||
\(509\) | 4957.32 | − | 8586.34i | 0.431689 | − | 0.747707i | −0.565330 | − | 0.824865i | \(-0.691251\pi\) |
0.997019 | + | 0.0771579i | \(0.0245846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −317.242 | − | 549.480i | −0.0274637 | − | 0.0475686i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4606.40 | 0.395291 | ||||||||
\(515\) | −1243.04 | − | 2153.01i | −0.106359 | − | 0.184220i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21523.9 | + | 37280.5i | −1.83099 | + | 3.17136i | ||||
\(518\) | −497.354 | − | 861.443i | −0.0421863 | − | 0.0730688i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −272.348 | −0.0229678 | ||||||||
\(521\) | 5851.91 | 0.492086 | 0.246043 | − | 0.969259i | \(-0.420869\pi\) | ||||
0.246043 | + | 0.969259i | \(0.420869\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3447.05 | + | 5970.46i | −0.288200 | + | 0.499178i | −0.973380 | − | 0.229196i | \(-0.926390\pi\) |
0.685180 | + | 0.728374i | \(0.259724\pi\) | |||||||
\(524\) | −2390.19 | −0.199267 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7138.38 | + | 12364.0i | −0.591726 | + | 1.02490i | ||||
\(527\) | 7474.37 | + | 12946.0i | 0.617816 | + | 1.07009i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9491.49 | − | 16439.7i | −0.780101 | − | 1.35117i | ||||
\(530\) | −1557.91 | − | 2698.39i | −0.127682 | − | 0.221152i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1055.98 | + | 18.5899i | −0.0860574 | + | 0.00151499i | ||||
\(533\) | −3369.83 | −0.273853 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3724.40 | + | 6450.84i | 0.300971 | + | 0.521298i | ||||
\(536\) | −581.370 | + | 1006.96i | −0.0468495 | + | 0.0811458i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5446.66 | − | 9433.89i | 0.436472 | − | 0.755992i | ||||
\(539\) | 23098.9 | 1.84590 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2812.50 | − | 4871.39i | 0.223509 | − | 0.387130i | −0.732362 | − | 0.680916i | \(-0.761582\pi\) |
0.955871 | + | 0.293786i | \(0.0949153\pi\) | |||||||
\(542\) | −3403.68 | + | 5895.34i | −0.269743 | + | 0.467208i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3394.67 | −0.267547 | ||||||||
\(545\) | −2240.62 | + | 3880.86i | −0.176105 | + | 0.305023i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1798.07 | + | 3114.35i | −0.140548 | + | 0.243437i | −0.927703 | − | 0.373319i | \(-0.878220\pi\) |
0.787155 | + | 0.616755i | \(0.211553\pi\) | |||||||
\(548\) | −3554.62 | − | 6156.78i | −0.277091 | − | 0.479935i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14915.5 | −1.15636 | ||||||||
\(551\) | −5483.59 | + | 96.5350i | −0.423972 | + | 0.00746376i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 620.975 | + | 1075.56i | 0.0477515 | + | 0.0827080i | ||||
\(554\) | −5131.93 | − | 8888.76i | −0.393564 | − | 0.681674i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −327.134 | − | 566.613i | −0.0249525 | − | 0.0432190i | ||||
\(557\) | 9190.73 | − | 15918.8i | 0.699145 | − | 1.21095i | −0.269618 | − | 0.962967i | \(-0.586897\pi\) |
0.968763 | − | 0.247987i | \(-0.0797692\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −941.705 | −0.0712520 | ||||||||
\(560\) | 106.817 | − | 185.012i | 0.00806043 | − | 0.0139611i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6733.36 | 0.505391 | ||||||||
\(563\) | −5578.33 | −0.417582 | −0.208791 | − | 0.977960i | \(-0.566953\pi\) | ||||
−0.208791 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1221.25 | − | 2115.26i | −0.0909349 | − | 0.157504i | ||||
\(566\) | 6685.76 | − | 11580.1i | 0.496508 | − | 0.859977i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3551.32 | − | 6151.06i | −0.262341 | − | 0.454389i | ||||
\(569\) | −16981.3 | −1.25113 | −0.625564 | − | 0.780173i | \(-0.715131\pi\) | ||||
−0.625564 | + | 0.780173i | \(0.715131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19520.5 | −1.43066 | −0.715332 | − | 0.698785i | \(-0.753724\pi\) | ||||
−0.715332 | + | 0.698785i | \(0.753724\pi\) | |||||||
\(572\) | −1128.26 | − | 1954.20i | −0.0824735 | − | 0.142848i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1321.67 | − | 2289.20i | 0.0961070 | − | 0.166462i | ||||
\(575\) | 9482.98 | + | 16425.0i | 0.687770 | + | 1.19125i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6371.35 | 0.459693 | 0.229846 | − | 0.973227i | \(-0.426178\pi\) | ||||
0.229846 | + | 0.973227i | \(0.426178\pi\) | |||||||
\(578\) | −12681.4 | −0.912593 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 554.688 | − | 960.748i | 0.0397107 | − | 0.0687809i | ||||
\(581\) | −1211.60 | −0.0865159 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12908.0 | − | 22357.2i | 0.916969 | − | 1.58824i | ||||
\(584\) | 796.065 | + | 1378.82i | 0.0564065 | + | 0.0976989i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5625.93 | + | 9744.39i | 0.396596 | + | 0.686924i | ||||
\(587\) | 5379.52 | + | 9317.61i | 0.378257 | + | 0.655160i | 0.990809 | − | 0.135271i | \(-0.0431904\pi\) |
−0.612552 | + | 0.790430i | \(0.709857\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6012.21 | − | 10002.6i | −0.420592 | − | 0.699747i | ||||
\(590\) | −768.039 | −0.0535927 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1248.02 | + | 2161.64i | 0.0866444 | + | 0.150073i | ||||
\(593\) | 1805.88 | − | 3127.87i | 0.125057 | − | 0.216604i | −0.796698 | − | 0.604377i | \(-0.793422\pi\) |
0.921755 | + | 0.387773i | \(0.126755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 708.220 | − | 1226.67i | 0.0487970 | − | 0.0845188i | ||||
\(596\) | 4479.19 | 0.307844 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1434.65 | + | 2484.89i | −0.0981057 | + | 0.169924i | ||||
\(599\) | −4590.12 | + | 7950.31i | −0.313100 | + | 0.542306i | −0.979032 | − | 0.203707i | \(-0.934701\pi\) |
0.665932 | + | 0.746013i | \(0.268034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12700.4 | 0.862000 | 0.431000 | − | 0.902352i | \(-0.358161\pi\) | ||||
0.431000 | + | 0.902352i | \(0.358161\pi\) | |||||||
\(602\) | 369.343 | − | 639.721i | 0.0250055 | − | 0.0433108i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5614.29 | − | 9724.24i | 0.378216 | − | 0.655089i | ||||
\(605\) | 7298.61 | + | 12641.6i | 0.490464 | + | 0.849509i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24227.5 | −1.62004 | −0.810019 | − | 0.586404i | \(-0.800543\pi\) | ||||
−0.810019 | + | 0.586404i | \(0.800543\pi\) | |||||||
\(608\) | 2649.80 | − | 46.6480i | 0.176749 | − | 0.00311156i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −915.606 | − | 1585.88i | −0.0607734 | − | 0.105263i | ||||
\(611\) | −2521.02 | − | 4366.54i | −0.166923 | − | 0.289119i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8106.74 | + | 14041.3i | 0.534141 | + | 0.925159i | 0.999204 | + | 0.0398814i | \(0.0126980\pi\) |
−0.465064 | + | 0.885277i | \(0.653969\pi\) | |||||||
\(614\) | 5603.54 | − | 9705.62i | 0.368307 | − | 0.637927i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1770.04 | 0.115774 | ||||||||
\(617\) | −10757.7 | + | 18632.8i | −0.701924 | + | 1.21577i | 0.265866 | + | 0.964010i | \(0.414342\pi\) |
−0.967790 | + | 0.251758i | \(0.918991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15878.5 | −1.03103 | −0.515516 | − | 0.856880i | \(-0.672400\pi\) | ||||
−0.515516 | + | 0.856880i | \(0.672400\pi\) | |||||||
\(620\) | 2360.66 | 0.152914 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6668.20 | − | 11549.7i | −0.429856 | − | 0.744532i | ||||
\(623\) | −678.746 | + | 1175.62i | −0.0436491 | + | 0.0756024i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4677.54 | − | 8101.73i | −0.299362 | − | 0.518511i | ||||
\(626\) | −8982.80 | −0.573522 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4015.77 | 0.255170 | ||||||||
\(629\) | 8274.68 | + | 14332.2i | 0.524536 | + | 0.908523i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2779.87 | + | 4814.88i | −0.175380 | + | 0.303768i | −0.940293 | − | 0.340366i | \(-0.889449\pi\) |
0.764912 | + | 0.644134i | \(0.222782\pi\) | |||||||
\(632\) | −1558.23 | − | 2698.94i | −0.0980745 | − | 0.169870i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2532.09 | −0.158616 | ||||||||
\(635\) | −6949.55 | −0.434306 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1352.75 | + | 2343.03i | −0.0841412 | + | 0.145737i | ||||
\(638\) | 9191.64 | 0.570377 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −268.039 | + | 464.257i | −0.0165549 | + | 0.0286740i | ||||
\(641\) | −10243.5 | − | 17742.2i | −0.631190 | − | 1.09325i | −0.987309 | − | 0.158812i | \(-0.949234\pi\) |
0.356119 | − | 0.934441i | \(-0.384100\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2051.15 | + | 3552.69i | 0.125800 | + | 0.217892i | 0.922045 | − | 0.387082i | \(-0.126517\pi\) |
−0.796245 | + | 0.604974i | \(0.793184\pi\) | |||||||
\(644\) | −1125.36 | − | 1949.18i | −0.0688593 | − | 0.119268i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17568.8 | − | 309.287i | 1.07002 | − | 0.0188370i | ||||
\(647\) | −22860.4 | −1.38908 | −0.694539 | − | 0.719455i | \(-0.744392\pi\) | ||||
−0.694539 | + | 0.719455i | \(0.744392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3181.76 | − | 5510.97i | −0.192442 | − | 0.333320i | ||||
\(650\) | 873.501 | − | 1512.95i | 0.0527100 | − | 0.0912964i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2543.97 | + | 4406.29i | −0.152806 | + | 0.264668i | ||||
\(653\) | −26388.5 | −1.58141 | −0.790706 | − | 0.612197i | \(-0.790286\pi\) | ||||
−0.790706 | + | 0.612197i | \(0.790286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1251.29 | + | 2167.30i | −0.0746444 | + | 0.129288i | ||||
\(656\) | −3316.50 | + | 5744.35i | −0.197390 | + | 0.341889i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3955.05 | 0.234322 | ||||||||
\(659\) | 1611.65 | − | 2791.45i | 0.0952668 | − | 0.165007i | −0.814453 | − | 0.580229i | \(-0.802963\pi\) |
0.909720 | + | 0.415222i | \(0.136296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13740.1 | − | 23798.5i | 0.808513 | − | 1.40039i | −0.105381 | − | 0.994432i | \(-0.533606\pi\) |
0.913894 | − | 0.405953i | \(-0.133060\pi\) | |||||||
\(662\) | −5068.09 | − | 8778.19i | −0.297548 | − | 0.515369i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3040.31 | 0.177691 | ||||||||
\(665\) | −535.963 | + | 967.243i | −0.0312538 | + | 0.0564031i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5843.87 | − | 10121.9i | −0.339244 | − | 0.587587i | ||||
\(668\) | −5969.97 | − | 10340.3i | −0.345786 | − | 0.598919i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 608.709 | + | 1054.32i | 0.0350992 | + | 0.0607937i | ||||
\(671\) | 7586.17 | − | 13139.6i | 0.436454 | − | 0.755961i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2165.00 | −0.124004 | −0.0620020 | − | 0.998076i | \(-0.519749\pi\) | ||||
−0.0620020 | + | 0.998076i | \(0.519749\pi\) | |||||||
\(674\) | 10744.1 | − | 18609.4i | 0.614018 | − | 1.06351i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8523.70 | −0.484963 | ||||||||
\(677\) | −11999.0 | −0.681179 | −0.340589 | − | 0.940212i | \(-0.610627\pi\) | ||||
−0.340589 | + | 0.940212i | \(0.610627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −669.256 | − | 1159.19i | −0.0378258 | − | 0.0655161i | ||||
\(680\) | −1777.16 | + | 3078.13i | −0.100222 | + | 0.173589i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9779.53 | + | 16938.6i | 0.549087 | + | 0.951047i | ||||
\(683\) | −5234.35 | −0.293246 | −0.146623 | − | 0.989192i | \(-0.546840\pi\) | ||||
−0.146623 | + | 0.989192i | \(0.546840\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7443.56 | −0.415188 | ||||||||
\(686\) | −2154.64 | − | 3731.94i | −0.119919 | − | 0.207706i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −926.803 | + | 1605.27i | −0.0513576 | + | 0.0889540i | ||||
\(689\) | 1511.87 | + | 2618.63i | 0.0835958 | + | 0.144792i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5160.63 | −0.284109 | −0.142055 | − | 0.989859i | \(-0.545371\pi\) | ||||
−0.142055 | + | 0.989859i | \(0.545371\pi\) | |||||||
\(692\) | −227.099 | −0.0124754 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4851.34 | − | 8402.76i | 0.265352 | − | 0.459603i | ||||
\(695\) | −685.036 | −0.0373884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21989.1 | + | 38086.3i | −1.19498 | + | 2.06976i | ||||
\(698\) | −7611.35 | − | 13183.2i | −0.412742 | − | 0.714890i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 685.186 | + | 1186.78i | 0.0369966 | + | 0.0640799i | ||||
\(701\) | −1657.51 | − | 2870.90i | −0.0893059 | − | 0.154682i | 0.817912 | − | 0.575343i | \(-0.195132\pi\) |
−0.907218 | + | 0.420661i | \(0.861798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6655.96 | − | 11073.6i | −0.357090 | − | 0.594097i | ||||
\(704\) | −4441.62 | −0.237784 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5567.64 | − | 9643.43i | −0.296800 | − | 0.514073i | ||||
\(707\) | −1979.35 | + | 3428.34i | −0.105292 | + | 0.182370i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9166.60 | − | 15877.0i | 0.485555 | − | 0.841007i | −0.514307 | − | 0.857606i | \(-0.671951\pi\) |
0.999862 | + | 0.0165995i | \(0.00528404\pi\) | |||||||
\(710\) | −7436.64 | −0.393088 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1703.20 | − | 2950.02i | 0.0896488 | − | 0.155276i | ||||
\(713\) | 12435.3 | − | 21538.5i | 0.653162 | − | 1.13131i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2362.63 | −0.123577 | ||||||||
\(716\) | −9281.96 | + | 16076.8i | −0.484474 | + | 0.839133i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4341.31 | + | 7519.37i | −0.225649 | + | 0.390836i | ||||
\(719\) | 4873.50 | + | 8441.15i | 0.252783 | + | 0.437833i | 0.964291 | − | 0.264845i | \(-0.0853208\pi\) |
−0.711508 | + | 0.702678i | \(0.751987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1892.48 | −0.0977526 | ||||||||
\(722\) | −13709.5 | + | 482.844i | −0.706669 | + | 0.0248886i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7550.82 | − | 13078.4i | −0.387602 | − | 0.671346i | ||||
\(725\) | 3558.09 | + | 6162.80i | 0.182268 | + | 0.315697i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16361.8 | − | 28339.4i | −0.834697 | − | 1.44574i | −0.894277 | − | 0.447515i | \(-0.852309\pi\) |
0.0595791 | − | 0.998224i | \(-0.481024\pi\) | |||||||
\(728\) | −103.660 | + | 179.544i | −0.00527731 | + | 0.00914057i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1667.00 | 0.0845185 | ||||||||
\(731\) | −6144.91 | + | 10643.3i | −0.310914 | + | 0.538518i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36938.2 | 1.86131 | 0.930657 | − | 0.365894i | \(-0.119237\pi\) | ||||
0.930657 | + | 0.365894i | \(0.119237\pi\) | |||||||
\(734\) | 17929.0 | 0.901594 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2823.90 | + | 4891.13i | 0.141427 | + | 0.244959i | ||||
\(737\) | −5043.40 | + | 8735.43i | −0.252071 | + | 0.436599i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4993.60 | + | 8649.16i | 0.248569 | + | 0.430534i | 0.963129 | − | 0.269040i | \(-0.0867064\pi\) |
−0.714560 | + | 0.699574i | \(0.753373\pi\) | |||||||
\(740\) | 2613.43 | 0.129826 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2371.86 | −0.117350 | ||||||||
\(743\) | 10869.9 | + | 18827.2i | 0.536713 | + | 0.929615i | 0.999078 | + | 0.0429249i | \(0.0136676\pi\) |
−0.462365 | + | 0.886690i | \(0.652999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2344.92 | − | 4061.51i | 0.115317 | − | 0.199735i | ||||
\(746\) | 5048.11 | + | 8743.59i | 0.247754 | + | 0.429123i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29448.9 | −1.43952 | ||||||||
\(749\) | 5670.23 | 0.276617 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19033.7 | − | 32967.3i | 0.924833 | − | 1.60186i | 0.133003 | − | 0.991116i | \(-0.457538\pi\) |
0.791830 | − | 0.610742i | \(-0.209129\pi\) | |||||||
\(752\) | −9924.53 | −0.481264 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −538.293 | + | 932.351i | −0.0259993 | + | 0.0450321i | ||||
\(755\) | −5878.31 | − | 10181.5i | −0.283356 | − | 0.490787i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5682.61 | + | 9842.58i | 0.272838 | + | 0.472569i | 0.969587 | − | 0.244746i | \(-0.0787045\pi\) |
−0.696750 | + | 0.717314i | \(0.745371\pi\) | |||||||
\(758\) | −9290.41 | − | 16091.5i | −0.445176 | − | 0.771067i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1344.91 | − | 2427.13i | 0.0641907 | − | 0.115844i | ||||
\(761\) | −24549.3 | −1.16940 | −0.584699 | − | 0.811250i | \(-0.698787\pi\) | ||||
−0.584699 | + | 0.811250i | \(0.698787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1705.62 | + | 2954.22i | 0.0809274 | + | 0.140170i | ||||
\(764\) | −5525.06 | + | 9569.68i | −0.261636 | + | 0.453166i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4162.26 | + | 7209.24i | −0.196330 | + | 0.340053i | ||||
\(767\) | 745.338 | 0.0350881 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7111.27 | + | 12317.1i | −0.333471 | + | 0.577588i | −0.983190 | − | 0.182586i | \(-0.941553\pi\) |
0.649719 | + | 0.760174i | \(0.274886\pi\) | |||||||
\(770\) | 926.641 | − | 1604.99i | 0.0433686 | − | 0.0751166i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8246.06 | 0.384433 | ||||||||
\(773\) | 8041.29 | − | 13927.9i | 0.374159 | − | 0.648063i | −0.616041 | − | 0.787714i | \(-0.711265\pi\) |
0.990201 | + | 0.139651i | \(0.0445980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7571.34 | + | 13113.9i | −0.350930 | + | 0.607828i | ||||
\(776\) | 1679.38 | + | 2908.78i | 0.0776886 | + | 0.134561i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8370.46 | 0.385727 | ||||||||
\(779\) | 16640.8 | − | 30031.4i | 0.765365 | − | 1.38124i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30807.8 | − | 53360.7i | −1.41151 | − | 2.44481i | ||||
\(782\) | 18723.1 | + | 32429.3i | 0.856183 | + | 1.48295i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2662.69 | + | 4611.91i | 0.121296 | + | 0.210091i | ||||
\(785\) | 2102.31 | − | 3641.30i | 0.0955854 | − | 0.165559i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30058.0 | 1.36144 | 0.680720 | − | 0.732544i | \(-0.261667\pi\) | ||||
0.680720 | + | 0.732544i | \(0.261667\pi\) | |||||||
\(788\) | 4189.64 | − | 7256.68i | 0.189403 | − | 0.328056i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3263.02 | −0.146953 | ||||||||
\(791\) | −1859.29 | −0.0835764 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 888.543 | + | 1539.00i | 0.0397895 | + | 0.0689174i | ||||
\(794\) | −4529.76 | + | 7845.77i | −0.202462 | + | 0.350675i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3434.72 | + | 5949.12i | 0.152940 | + | 0.264901i | ||||
\(797\) | 20008.2 | 0.889243 | 0.444621 | − | 0.895719i | \(-0.353338\pi\) | ||||
0.444621 | + | 0.895719i | \(0.353338\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −65801.8 | −2.91352 | ||||||||
\(800\) | −1719.36 | − | 2978.01i | −0.0759855 | − | 0.131611i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9497.05 | − | 16449.4i | 0.418145 | − | 0.724249i | ||||
\(803\) | 6905.89 | + | 11961.4i | 0.303491 | + | 0.525662i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2356.56 | −0.103178 | ||||||||
\(806\) | −2290.89 | −0.100116 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4966.84 | − | 8602.82i | 0.216254 | − | 0.374562i | ||||
\(809\) | −35302.3 | −1.53419 | −0.767097 | − | 0.641532i | \(-0.778299\pi\) | ||||
−0.767097 | + | 0.641532i | \(0.778299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5490.38 | + | 9509.61i | −0.237723 | + | 0.411748i | −0.960060 | − | 0.279793i | \(-0.909734\pi\) |
0.722338 | + | 0.691540i | \(0.243068\pi\) | |||||||
\(812\) | −422.245 | − | 731.349i | −0.0182486 | − | 0.0316075i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10826.7 | + | 18752.3i | 0.466185 | + | 0.807456i | ||||
\(815\) | 2663.60 | + | 4613.50i | 0.114481 | + | 0.198287i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4650.31 | − | 8392.34i | 0.199136 | − | 0.359377i | ||||
\(818\) | 10708.9 | 0.457735 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3472.46 | + | 6014.48i | 0.147883 | + | 0.256140i | ||||
\(821\) | −2813.34 | + | 4872.85i | −0.119594 | + | 0.207142i | −0.919607 | − | 0.392840i | \(-0.871492\pi\) |
0.800013 | + | 0.599983i | \(0.204826\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14383.1 | + | 24912.3i | −0.609191 | + | 1.05515i | 0.382183 | + | 0.924087i | \(0.375172\pi\) |
−0.991374 | + | 0.131063i | \(0.958161\pi\) | |||||||
\(824\) | 4748.85 | 0.200769 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −292.327 | + | 506.325i | −0.0123140 | + | 0.0213284i | ||||
\(827\) | 22241.2 | − | 38522.9i | 0.935191 | − | 1.61980i | 0.160897 | − | 0.986971i | \(-0.448561\pi\) |
0.774294 | − | 0.632827i | \(-0.218105\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23302.5 | 0.976271 | 0.488136 | − | 0.872768i | \(-0.337677\pi\) | ||||
0.488136 | + | 0.872768i | \(0.337677\pi\) | |||||||
\(830\) | 1591.64 | − | 2756.80i | 0.0665623 | − | 0.115289i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 260.116 | − | 450.534i | 0.0108388 | − | 0.0187734i | ||||
\(833\) | 17654.2 | + | 30578.0i | 0.734312 | + | 1.27187i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12501.4 | −0.518120 | ||||||||
\(836\) | 22987.1 | − | 404.673i | 0.950988 | − | 0.0167415i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14506.1 | − | 25125.3i | −0.597978 | − | 1.03573i | ||||
\(839\) | −13841.8 | − | 23974.8i | −0.569575 | − | 0.986533i | −0.996608 | − | 0.0822969i | \(-0.973774\pi\) |
0.427033 | − | 0.904236i | \(-0.359559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10001.8 | + | 17323.7i | 0.410096 | + | 0.710307i | ||||
\(842\) | −1263.45 | + | 2188.36i | −0.0517118 | + | 0.0895674i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9164.21 | −0.373750 | ||||||||
\(845\) | −4462.27 | + | 7728.88i | −0.181665 | + | 0.314653i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11111.8 | 0.450776 | ||||||||
\(848\) | 5951.77 | 0.241020 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11399.7 | − | 19744.9i | −0.460008 | − | 0.796758i | ||||
\(851\) | 13766.8 | − | 23844.7i | 0.554546 | − | 0.960502i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15304.7 | + | 26508.6i | 0.614331 | + | 1.06405i | 0.990502 | + | 0.137502i | \(0.0439072\pi\) |
−0.376171 | + | 0.926550i | \(0.622759\pi\) | |||||||
\(854\) | −1393.97 | −0.0558556 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14228.5 | −0.568130 | ||||||||
\(857\) | 5459.14 | + | 9455.50i | 0.217597 | + | 0.376889i | 0.954073 | − | 0.299575i | \(-0.0968449\pi\) |
−0.736476 | + | 0.676464i | \(0.763512\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7319.75 | + | 12678.2i | −0.290741 | + | 0.503578i | −0.973985 | − | 0.226612i | \(-0.927235\pi\) |
0.683244 | + | 0.730190i | \(0.260569\pi\) | |||||||
\(860\) | 970.387 | + | 1680.76i | 0.0384767 | + | 0.0666435i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16375.2 | −0.647033 | ||||||||
\(863\) | 22775.2 | 0.898353 | 0.449176 | − | 0.893443i | \(-0.351717\pi\) | ||||
0.449176 | + | 0.893443i | \(0.351717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −118.889 | + | 205.922i | −0.00467324 | + | 0.00809429i | ||||
\(866\) | 18485.9 | 0.725377 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 898.502 | − | 1556.25i | 0.0351350 | − | 0.0608556i | ||||
\(869\) | −13517.7 | − | 23413.4i | −0.527684 | − | 0.913975i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −590.717 | − | 1023.15i | −0.0229801 | − | 0.0398028i | ||||
\(872\) | −4279.96 | − | 7413.11i | −0.166213 | − | 0.287889i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15060.4 | − | 25056.2i | −0.582867 | − | 0.969725i | ||||
\(875\) | 3103.83 | 0.119918 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −402.954 | − | 697.937i | −0.0155152 | − | 0.0268730i | 0.858164 | − | 0.513376i | \(-0.171605\pi\) |
−0.873679 | + | 0.486503i | \(0.838272\pi\) | |||||||
\(878\) | −2043.05 | + | 3538.67i | −0.0785303 | + | 0.136018i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2325.25 | + | 4027.44i | −0.0890728 | + | 0.154279i | ||||
\(881\) | 901.690 | 0.0344821 | 0.0172410 | − | 0.999851i | \(-0.494512\pi\) | ||||
0.0172410 | + | 0.999851i | \(0.494512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12703.2 | − | 22002.5i | 0.484140 | − | 0.838554i | −0.515695 | − | 0.856773i | \(-0.672466\pi\) |
0.999834 | + | 0.0182183i | \(0.00579938\pi\) | |||||||
\(884\) | 1724.63 | − | 2987.14i | 0.0656171 | − | 0.113652i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19338.3 | −0.733275 | ||||||||
\(887\) | 14280.2 | − | 24734.1i | 0.540568 | − | 0.936291i | −0.458304 | − | 0.888796i | \(-0.651543\pi\) |
0.998871 | − | 0.0474953i | \(-0.0151239\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2645.10 | + | 4581.44i | −0.0997904 | + | 0.172842i | ||||
\(890\) | −1783.29 | − | 3088.75i | −0.0671641 | − | 0.116332i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13024.8 | 0.488902 | ||||||||
\(893\) | 51363.3 | − | 904.218i | 1.92476 | − | 0.0338841i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9718.46 | + | 16832.9i | 0.362963 | + | 0.628671i | ||||
\(896\) | 204.039 | + | 353.405i | 0.00760765 | + | 0.0131768i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13227.2 | + | 22910.2i | 0.491534 | + | 0.851361i | ||||
\(899\) | 4665.82 | − | 8081.44i | 0.173097 | − | 0.299812i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39461.6 | 1.45911 | ||||||||
\(902\) | −28770.8 | + | 49832.4i | −1.06204 | + | 1.83951i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4665.58 | 0.171654 | ||||||||
\(905\) | −15811.8 | −0.580776 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20452.7 | + | 35425.1i | 0.748755 | + | 1.29688i | 0.948420 | + | 0.317017i | \(0.102681\pi\) |
−0.199665 | + | 0.979864i | \(0.563985\pi\) | |||||||
\(908\) | −1996.09 | + | 3457.33i | −0.0729543 | + | 0.126361i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 108.534 | + | 187.987i | 0.00395372 | + | 0.00684804i | ||||
\(911\) | −30047.9 | −1.09279 | −0.546395 | − | 0.837527i | \(-0.684000\pi\) | ||||
−0.546395 | + | 0.837527i | \(0.684000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26374.8 | 0.956055 | ||||||||
\(914\) | −5380.98 | − | 9320.13i | −0.194734 | − | 0.337289i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2057.17 | − | 3563.12i | 0.0742040 | − | 0.128525i | ||||
\(917\) | 952.520 | + | 1649.81i | 0.0343021 | + | 0.0594129i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49600.1 | −1.78036 | −0.890182 | − | 0.455605i | \(-0.849423\pi\) | ||||
−0.890182 | + | 0.455605i | \(0.849423\pi\) | |||||||
\(920\) | 5913.39 | 0.211912 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2844.67 | − | 4927.11i | 0.101610 | − | 0.175993i | ||||
\(923\) | 7216.84 | 0.257362 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8382.03 | + | 14518.1i | −0.297945 | + | 0.516057i | ||||
\(926\) | 6625.39 | + | 11475.5i | 0.235123 | + | 0.407245i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1059.55 | + | 1835.19i | 0.0374800 | + | 0.0649173i | ||||
\(929\) | 13778.4 | + | 23864.8i | 0.486603 | + | 0.842821i | 0.999881 | − | 0.0154015i | \(-0.00490263\pi\) |
−0.513279 | + | 0.858222i | \(0.671569\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14200.6 | − | 23625.8i | −0.499900 | − | 0.831693i | ||||
\(932\) | 501.945 | 0.0176414 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18635.1 | + | 32276.9i | 0.652846 | + | 1.13076i | ||||
\(935\) | −15416.9 | + | 26702.9i | −0.539237 | + | 0.933986i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13440.4 | − | 23279.5i | 0.468601 | − | 0.811641i | −0.530755 | − | 0.847525i | \(-0.678092\pi\) |
0.999356 | + | 0.0358846i | \(0.0114249\pi\) | |||||||
\(938\) | 926.734 | 0.0322590 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5195.62 | + | 8999.08i | −0.180279 | + | 0.312253i | ||||
\(941\) | −3205.67 | + | 5552.38i | −0.111054 | + | 0.192351i | −0.916195 | − | 0.400732i | \(-0.868756\pi\) |
0.805142 | + | 0.593083i | \(0.202089\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 73167.6 | 2.52669 | ||||||||
\(944\) | 733.544 | − | 1270.53i | 0.0252911 | − | 0.0438055i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8040.05 | + | 13925.8i | −0.276326 | + | 0.478611i | ||||
\(947\) | −994.915 | − | 1723.24i | −0.0341398 | − | 0.0591319i | 0.848451 | − | 0.529274i | \(-0.177536\pi\) |
−0.882590 | + | 0.470143i | \(0.844202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1617.73 | −0.0553358 | ||||||||
\(950\) | 9169.67 | + | 15255.7i | 0.313161 | + | 0.521012i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1352.82 | + | 2343.16i | 0.0460559 | + | 0.0797712i | ||||
\(953\) | −19133.2 | − | 33139.7i | −0.650351 | − | 1.12644i | −0.983038 | − | 0.183404i | \(-0.941288\pi\) |
0.332686 | − | 0.943038i | \(-0.392045\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5784.88 | + | 10019.7i | 0.196015 | + | 0.339508i | ||||
\(956\) | 7182.05 | − | 12439.7i | 0.242975 | − | 0.420845i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3113.24 | 0.104994 | ||||||||
\(959\) | −2833.12 | + | 4907.11i | −0.0953976 | + | 0.165234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9934.01 | −0.333457 | ||||||||
\(962\) | −2536.18 | −0.0849998 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7383.68 | + | 12788.9i | 0.246693 | + | 0.427285i | ||||
\(965\) | 4316.92 | − | 7477.12i | 0.144007 | − | 0.249427i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −110.058 | − | 190.626i | −0.00366001 | − | 0.00633932i | 0.864190 | − | 0.503166i | \(-0.167832\pi\) |
−0.867850 | + | 0.496827i | \(0.834498\pi\) | |||||||
\(968\) | −27883.2 | −0.925827 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3516.72 | 0.116407 | ||||||||
\(971\) | 1087.68 | + | 1883.91i | 0.0359478 | + | 0.0622633i | 0.883440 | − | 0.468545i | \(-0.155222\pi\) |
−0.847492 | + | 0.530809i | \(0.821888\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −260.735 | + | 451.606i | −0.00859072 | + | 0.0148796i | ||||
\(974\) | 19339.5 | + | 33497.0i | 0.636220 | + | 1.10196i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3497.93 | 0.114719 | ||||||||
\(977\) | −13707.7 | −0.448872 | −0.224436 | − | 0.974489i | \(-0.572054\pi\) | ||||
−0.224436 | + | 0.974489i | \(0.572054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14775.3 | − | 25591.5i | 0.482350 | − | 0.835454i | ||||
\(980\) | 5575.81 | 0.181748 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6838.25 | − | 11844.2i | 0.222217 | − | 0.384891i | ||||
\(983\) | −9442.87 | − | 16355.5i | −0.306389 | − | 0.530682i | 0.671180 | − | 0.741294i | \(-0.265788\pi\) |
−0.977570 | + | 0.210612i | \(0.932454\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4386.67 | − | 7597.93i | −0.141899 | − | 0.245777i | ||||
\(986\) | 7025.05 | + | 12167.7i | 0.226900 | + | 0.393002i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1305.15 | + | 2355.39i | −0.0420268 | + | 0.0758451i | ||||
\(989\) | 20446.8 | 0.657403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20327.5 | + | 35208.3i | 0.651589 | + | 1.12858i | 0.982737 | + | 0.185006i | \(0.0592305\pi\) |
−0.331149 | + | 0.943579i | \(0.607436\pi\) | |||||||
\(992\) | −2254.64 | + | 3905.15i | −0.0721621 | + | 0.124988i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2830.49 | + | 4902.56i | −0.0903197 | + | 0.156438i | ||||
\(995\) | 7192.49 | 0.229163 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8216.65 | − | 14231.7i | 0.261007 | − | 0.452077i | −0.705503 | − | 0.708707i | \(-0.749279\pi\) |
0.966510 | + | 0.256630i | \(0.0826121\pi\) | |||||||
\(998\) | −18115.0 | + | 31376.1i | −0.574569 | + | 0.995182i | ||||
\(999\) | 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 | 342.4.g.h.235.2 | 6 | ||
3.2 | odd | 2 | 114.4.e.d.7.2 | ✓ | 6 | ||
19.11 | even | 3 | inner | 342.4.g.h.163.2 | 6 | ||
57.11 | odd | 6 | 114.4.e.d.49.2 | yes | 6 | ||
57.26 | odd | 6 | 2166.4.a.u.1.2 | 3 | |||
57.50 | even | 6 | 2166.4.a.t.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.e.d.7.2 | ✓ | 6 | 3.2 | odd | 2 | ||
114.4.e.d.49.2 | yes | 6 | 57.11 | odd | 6 | ||
342.4.g.h.163.2 | 6 | 19.11 | even | 3 | inner | ||
342.4.g.h.235.2 | 6 | 1.1 | even | 1 | trivial | ||
2166.4.a.t.1.2 | 3 | 57.50 | even | 6 | |||
2166.4.a.u.1.2 | 3 | 57.26 | odd | 6 |