Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(55,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.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: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + 21016320 x^{2} + 24920064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.1 | ||
Root | \(-2.69794 + 4.67298i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.100 |
Dual form | 117.4.g.f.55.1 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69794 | + | 4.67298i | −0.953868 | + | 1.65215i | −0.216929 | + | 0.976187i | \(0.569604\pi\) |
−0.736939 | + | 0.675960i | \(0.763729\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −10.5578 | − | 18.2867i | −1.31973 | − | 2.28583i | ||||
\(5\) | 13.0421 | 1.16653 | 0.583263 | − | 0.812284i | \(-0.301776\pi\) | ||||
0.583263 | + | 0.812284i | \(0.301776\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.21247 | + | 5.56416i | 0.173457 | + | 0.300437i | 0.939626 | − | 0.342202i | \(-0.111173\pi\) |
−0.766169 | + | 0.642639i | \(0.777840\pi\) | |||||||
\(8\) | 70.7705 | 3.12764 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −35.1870 | + | 60.9457i | −1.11271 | + | 1.92727i | ||||
\(11\) | −13.1028 | + | 22.6947i | −0.359149 | + | 0.622065i | −0.987819 | − | 0.155608i | \(-0.950266\pi\) |
0.628670 | + | 0.777672i | \(0.283600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.2448 | + | 18.0800i | 0.922612 | + | 0.385730i | ||||
\(14\) | −34.6683 | −0.661820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −106.472 | + | 184.416i | −1.66363 | + | 2.88149i | ||||
\(17\) | 61.9384 | + | 107.280i | 0.883663 | + | 1.53055i | 0.847239 | + | 0.531213i | \(0.178263\pi\) |
0.0364243 | + | 0.999336i | \(0.488403\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −54.8333 | − | 94.9741i | −0.662086 | − | 1.14677i | −0.980067 | − | 0.198669i | \(-0.936338\pi\) |
0.317981 | − | 0.948097i | \(-0.396995\pi\) | |||||||
\(20\) | −137.697 | − | 238.497i | −1.53949 | − | 2.66648i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −70.7012 | − | 122.458i | −0.685162 | − | 1.18673i | ||||
\(23\) | 31.7047 | − | 54.9141i | 0.287430 | − | 0.497843i | −0.685766 | − | 0.727822i | \(-0.740533\pi\) |
0.973196 | + | 0.229979i | \(0.0738658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 45.0976 | 0.360781 | ||||||||
\(26\) | −201.160 | + | 153.303i | −1.51733 | + | 1.15635i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 67.8333 | − | 117.491i | 0.457832 | − | 0.792988i | ||||
\(29\) | −112.705 | + | 195.211i | −0.721683 | + | 1.24999i | 0.238642 | + | 0.971108i | \(0.423298\pi\) |
−0.960325 | + | 0.278884i | \(0.910036\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 200.732 | 1.16298 | 0.581491 | − | 0.813553i | \(-0.302470\pi\) | ||||
0.581491 | + | 0.813553i | \(0.302470\pi\) | |||||||
\(32\) | −291.431 | − | 504.774i | −1.60995 | − | 2.78851i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −668.426 | −3.37159 | ||||||||
\(35\) | 41.8975 | + | 72.5686i | 0.202342 | + | 0.350467i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −126.254 | + | 218.679i | −0.560976 | + | 0.971638i | 0.436436 | + | 0.899735i | \(0.356241\pi\) |
−0.997412 | + | 0.0719031i | \(0.977093\pi\) | |||||||
\(38\) | 591.749 | 2.52617 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 922.999 | 3.64847 | ||||||||
\(41\) | −113.712 | + | 196.955i | −0.433141 | + | 0.750223i | −0.997142 | − | 0.0755517i | \(-0.975928\pi\) |
0.564001 | + | 0.825774i | \(0.309262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 192.016 | + | 332.581i | 0.680980 | + | 1.17949i | 0.974682 | + | 0.223595i | \(0.0717794\pi\) |
−0.293702 | + | 0.955897i | \(0.594887\pi\) | |||||||
\(44\) | 553.348 | 1.89592 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 171.075 | + | 296.311i | 0.548340 | + | 0.949753i | ||||
\(47\) | 34.6646 | 0.107582 | 0.0537910 | − | 0.998552i | \(-0.482870\pi\) | ||||
0.0537910 | + | 0.998552i | \(0.482870\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 150.860 | − | 261.297i | 0.439825 | − | 0.761800i | ||||
\(50\) | −121.671 | + | 210.740i | −0.344137 | + | 0.596063i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −125.948 | − | 981.689i | −0.335881 | − | 2.61800i | ||||
\(53\) | −61.0601 | −0.158250 | −0.0791251 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791251 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −170.889 | + | 295.988i | −0.418957 | + | 0.725654i | ||||
\(56\) | 227.348 | + | 393.778i | 0.542512 | + | 0.939658i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −608.144 | − | 1053.34i | −1.37678 | − | 2.38465i | ||||
\(59\) | 40.2781 | + | 69.7637i | 0.0888774 | + | 0.153940i | 0.907037 | − | 0.421051i | \(-0.138339\pi\) |
−0.818159 | + | 0.574991i | \(0.805005\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0692 | + | 22.6364i | 0.0274317 | + | 0.0475131i | 0.879415 | − | 0.476055i | \(-0.157934\pi\) |
−0.851984 | + | 0.523568i | \(0.824600\pi\) | |||||||
\(62\) | −541.563 | + | 938.014i | −1.10933 | + | 1.92142i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1441.50 | 2.81544 | ||||||||
\(65\) | 564.005 | + | 235.802i | 1.07625 | + | 0.449964i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 465.755 | − | 806.711i | 0.849269 | − | 1.47098i | −0.0325921 | − | 0.999469i | \(-0.510376\pi\) |
0.881861 | − | 0.471509i | \(-0.156290\pi\) | |||||||
\(68\) | 1307.87 | − | 2265.29i | 2.33239 | − | 4.03981i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −452.149 | −0.772030 | ||||||||
\(71\) | −213.804 | − | 370.320i | −0.357379 | − | 0.618998i | 0.630143 | − | 0.776479i | \(-0.282996\pi\) |
−0.987522 | + | 0.157481i | \(0.949663\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 108.518 | 0.173987 | 0.0869935 | − | 0.996209i | \(-0.472274\pi\) | ||||
0.0869935 | + | 0.996209i | \(0.472274\pi\) | |||||||
\(74\) | −681.255 | − | 1179.97i | −1.07019 | − | 1.85363i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1157.84 | + | 2005.44i | −1.74754 | + | 3.02684i | ||||
\(77\) | −168.369 | −0.249188 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 384.590 | 0.547718 | 0.273859 | − | 0.961770i | \(-0.411700\pi\) | ||||
0.273859 | + | 0.961770i | \(0.411700\pi\) | |||||||
\(80\) | −1388.63 | + | 2405.17i | −1.94067 | + | 3.36133i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −613.576 | − | 1062.74i | −0.826319 | − | 1.43123i | ||||
\(83\) | −85.9758 | −0.113700 | −0.0568498 | − | 0.998383i | \(-0.518106\pi\) | ||||
−0.0568498 | + | 0.998383i | \(0.518106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 807.810 | + | 1399.17i | 1.03081 | + | 1.78542i | ||||
\(86\) | −2072.19 | −2.59826 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −927.291 | + | 1606.12i | −1.12329 | + | 1.94560i | ||||
\(89\) | 247.952 | − | 429.465i | 0.295313 | − | 0.511497i | −0.679745 | − | 0.733449i | \(-0.737910\pi\) |
0.975058 | + | 0.221952i | \(0.0712428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38.3226 | + | 298.703i | 0.0441462 | + | 0.344094i | ||||
\(92\) | −1338.93 | −1.51732 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −93.5232 | + | 161.987i | −0.102619 | + | 0.177741i | ||||
\(95\) | −715.144 | − | 1238.67i | −0.772340 | − | 1.33773i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −95.4286 | − | 165.287i | −0.0998898 | − | 0.173014i | 0.811749 | − | 0.584006i | \(-0.198516\pi\) |
−0.911639 | + | 0.410992i | \(0.865182\pi\) | |||||||
\(98\) | 814.024 | + | 1409.93i | 0.839070 | + | 1.45331i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −476.132 | − | 824.685i | −0.476132 | − | 0.824685i | ||||
\(101\) | 425.490 | − | 736.970i | 0.419186 | − | 0.726052i | −0.576671 | − | 0.816976i | \(-0.695649\pi\) |
0.995858 | + | 0.0909241i | \(0.0289821\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1309.50 | −1.25270 | −0.626352 | − | 0.779540i | \(-0.715453\pi\) | ||||
−0.626352 | + | 0.779540i | \(0.715453\pi\) | |||||||
\(104\) | 3060.46 | + | 1279.53i | 2.88560 | + | 1.20643i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 164.737 | − | 285.333i | 0.150950 | − | 0.261452i | ||||
\(107\) | 481.151 | − | 833.378i | 0.434716 | − | 0.752951i | −0.562556 | − | 0.826759i | \(-0.690182\pi\) |
0.997272 | + | 0.0738085i | \(0.0235153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 891.973 | 0.783812 | 0.391906 | − | 0.920005i | \(-0.371816\pi\) | ||||
0.391906 | + | 0.920005i | \(0.371816\pi\) | |||||||
\(110\) | −922.096 | − | 1597.12i | −0.799258 | − | 1.38436i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1368.16 | −1.15427 | ||||||||
\(113\) | 131.920 | + | 228.491i | 0.109823 | + | 0.190218i | 0.915698 | − | 0.401867i | \(-0.131638\pi\) |
−0.805876 | + | 0.592085i | \(0.798305\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 413.497 | − | 716.198i | 0.335294 | − | 0.580746i | ||||
\(116\) | 4759.68 | 3.80970 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −434.673 | −0.339109 | ||||||||
\(119\) | −397.951 | + | 689.271i | −0.306555 | + | 0.530969i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 322.133 | + | 557.952i | 0.242024 | + | 0.419197i | ||||
\(122\) | −141.039 | −0.104665 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2119.29 | − | 3670.71i | −1.53482 | − | 2.65838i | ||||
\(125\) | −1042.10 | −0.745665 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 771.986 | − | 1337.12i | 0.539391 | − | 0.934252i | −0.459546 | − | 0.888154i | \(-0.651988\pi\) |
0.998937 | − | 0.0460984i | \(-0.0146788\pi\) | |||||||
\(128\) | −1557.65 | + | 2697.93i | −1.07561 | + | 1.86301i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2623.55 | + | 1999.40i | −1.77001 | + | 1.34892i | ||||
\(131\) | 776.790 | 0.518080 | 0.259040 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259040 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 352.301 | − | 610.203i | 0.229687 | − | 0.397829i | ||||
\(134\) | 2513.16 | + | 4352.93i | 1.62018 | + | 2.80624i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4383.41 | + | 7592.29i | 2.76378 | + | 4.78701i | ||||
\(137\) | −1217.36 | − | 2108.52i | −0.759166 | − | 1.31491i | −0.943276 | − | 0.332009i | \(-0.892274\pi\) |
0.184110 | − | 0.982906i | \(-0.441060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −625.700 | − | 1083.74i | −0.381807 | − | 0.661310i | 0.609513 | − | 0.792776i | \(-0.291365\pi\) |
−0.991321 | + | 0.131466i | \(0.958032\pi\) | |||||||
\(140\) | 884.692 | − | 1532.33i | 0.534072 | − | 0.925041i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2307.33 | 1.36357 | ||||||||
\(143\) | −976.948 | + | 744.530i | −0.571304 | + | 0.435390i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1469.92 | + | 2545.97i | −0.841861 | + | 1.45815i | ||||
\(146\) | −292.775 | + | 507.101i | −0.165961 | + | 0.287452i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5331.88 | 2.96134 | ||||||||
\(149\) | −391.810 | − | 678.634i | −0.215425 | − | 0.373127i | 0.737979 | − | 0.674824i | \(-0.235780\pi\) |
−0.953404 | + | 0.301697i | \(0.902447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 162.220 | 0.0874255 | 0.0437128 | − | 0.999044i | \(-0.486081\pi\) | ||||
0.0437128 | + | 0.999044i | \(0.486081\pi\) | |||||||
\(152\) | −3880.58 | − | 6721.37i | −2.07077 | − | 3.58668i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 454.251 | − | 786.786i | 0.237692 | − | 0.411695i | ||||
\(155\) | 2617.97 | 1.35665 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2355.76 | −1.19752 | −0.598758 | − | 0.800930i | \(-0.704339\pi\) | ||||
−0.598758 | + | 0.800930i | \(0.704339\pi\) | |||||||
\(158\) | −1037.60 | + | 1797.18i | −0.522451 | + | 0.904911i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3800.89 | − | 6583.33i | −1.87804 | − | 3.25286i | ||||
\(161\) | 407.402 | 0.199427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −787.143 | − | 1363.37i | −0.378244 | − | 0.655138i | 0.612563 | − | 0.790422i | \(-0.290139\pi\) |
−0.990807 | + | 0.135284i | \(0.956805\pi\) | |||||||
\(164\) | 4802.19 | 2.28651 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 231.958 | − | 401.763i | 0.108454 | − | 0.187849i | ||||
\(167\) | −1787.28 | + | 3095.66i | −0.828166 | + | 1.43443i | 0.0713090 | + | 0.997454i | \(0.477282\pi\) |
−0.899475 | + | 0.436972i | \(0.856051\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1543.23 | + | 1563.73i | 0.702425 | + | 0.711758i | ||||
\(170\) | −8717.70 | −3.93304 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4054.54 | − | 7022.66i | 1.79742 | − | 3.11322i | ||||
\(173\) | −0.720540 | − | 1.24801i | −0.000316657 | − | 0.000548466i | 0.865867 | − | 0.500274i | \(-0.166767\pi\) |
−0.866184 | + | 0.499726i | \(0.833434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 144.875 | + | 250.930i | 0.0625800 | + | 0.108392i | ||||
\(176\) | −2790.17 | − | 4832.72i | −1.19498 | − | 2.06977i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1337.92 | + | 2317.35i | 0.563378 | + | 0.975800i | ||||
\(179\) | 1041.14 | − | 1803.30i | 0.434739 | − | 0.752990i | −0.562535 | − | 0.826773i | \(-0.690174\pi\) |
0.997274 | + | 0.0737830i | \(0.0235072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −464.500 | −0.190751 | −0.0953756 | − | 0.995441i | \(-0.530405\pi\) | ||||
−0.0953756 | + | 0.995441i | \(0.530405\pi\) | |||||||
\(182\) | −1499.22 | − | 626.802i | −0.610603 | − | 0.255284i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2243.76 | − | 3886.30i | 0.898978 | − | 1.55708i | ||||
\(185\) | −1646.63 | + | 2852.04i | −0.654392 | + | 1.13344i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3246.26 | −1.26947 | ||||||||
\(188\) | −365.982 | − | 633.900i | −0.141979 | − | 0.245914i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7717.68 | 2.94684 | ||||||||
\(191\) | 2433.14 | + | 4214.32i | 0.921758 | + | 1.59653i | 0.796693 | + | 0.604384i | \(0.206581\pi\) |
0.125065 | + | 0.992149i | \(0.460086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 428.169 | − | 741.611i | 0.159691 | − | 0.276592i | −0.775066 | − | 0.631880i | \(-0.782284\pi\) |
0.934757 | + | 0.355287i | \(0.115617\pi\) | |||||||
\(194\) | 1029.84 | 0.381127 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6371.01 | −2.32180 | ||||||||
\(197\) | 785.965 | − | 1361.33i | 0.284252 | − | 0.492339i | −0.688175 | − | 0.725544i | \(-0.741588\pi\) |
0.972428 | + | 0.233205i | \(0.0749214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1563.30 | − | 2707.72i | −0.556883 | − | 0.964549i | −0.997754 | − | 0.0669791i | \(-0.978664\pi\) |
0.440872 | − | 0.897570i | \(-0.354669\pi\) | |||||||
\(200\) | 3191.58 | 1.12839 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2295.90 | + | 3976.61i | 0.799697 | + | 1.38512i | ||||
\(203\) | −1448.25 | −0.500724 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1483.05 | + | 2568.71i | −0.505270 | + | 0.875153i | ||||
\(206\) | 3532.95 | − | 6119.25i | 1.19491 | − | 2.06965i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7938.61 | + | 6050.00i | −2.64636 | + | 2.01679i | ||||
\(209\) | 2873.88 | 0.951150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −61.6959 | + | 106.860i | −0.0201295 | + | 0.0348653i | −0.875915 | − | 0.482466i | \(-0.839741\pi\) |
0.855785 | + | 0.517331i | \(0.173075\pi\) | |||||||
\(212\) | 644.662 | + | 1116.59i | 0.208847 | + | 0.361733i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2596.24 | + | 4496.82i | 0.829323 | + | 1.43643i | ||||
\(215\) | 2504.30 | + | 4337.57i | 0.794380 | + | 1.37591i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 644.844 | + | 1116.90i | 0.201728 | + | 0.349402i | ||||
\(218\) | −2406.49 | + | 4168.17i | −0.747653 | + | 1.29497i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7216.84 | 2.21163 | ||||||||
\(221\) | 738.884 | + | 5759.17i | 0.224899 | + | 1.75296i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1251.84 | − | 2168.26i | 0.375918 | − | 0.651109i | −0.614546 | − | 0.788881i | \(-0.710661\pi\) |
0.990464 | + | 0.137772i | \(0.0439941\pi\) | |||||||
\(224\) | 1872.43 | − | 3243.14i | 0.558513 | − | 0.967373i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1423.65 | −0.419025 | ||||||||
\(227\) | −289.635 | − | 501.662i | −0.0846861 | − | 0.146681i | 0.820571 | − | 0.571544i | \(-0.193655\pi\) |
−0.905257 | + | 0.424864i | \(0.860322\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −768.922 | −0.221886 | −0.110943 | − | 0.993827i | \(-0.535387\pi\) | ||||
−0.110943 | + | 0.993827i | \(0.535387\pi\) | |||||||
\(230\) | 2231.19 | + | 3864.53i | 0.639652 | + | 1.10791i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7976.19 | + | 13815.2i | −2.25717 | + | 3.90953i | ||||
\(233\) | 845.695 | 0.237783 | 0.118891 | − | 0.992907i | \(-0.462066\pi\) | ||||
0.118891 | + | 0.992907i | \(0.462066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 452.101 | 0.125497 | ||||||||
\(236\) | 850.498 | − | 1473.11i | 0.234588 | − | 0.406318i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2147.30 | − | 3719.23i | −0.584826 | − | 1.01295i | ||||
\(239\) | −6552.78 | −1.77349 | −0.886744 | − | 0.462260i | \(-0.847039\pi\) | ||||
−0.886744 | + | 0.462260i | \(0.847039\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2588.38 | − | 4483.20i | −0.691834 | − | 1.19829i | −0.971236 | − | 0.238118i | \(-0.923470\pi\) |
0.279402 | − | 0.960174i | \(-0.409864\pi\) | |||||||
\(242\) | −3476.39 | −0.923434 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 275.963 | − | 477.983i | 0.0724047 | − | 0.125409i | ||||
\(245\) | 1967.54 | − | 3407.88i | 0.513067 | − | 0.888658i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −654.125 | − | 5098.52i | −0.168506 | − | 1.31341i | ||||
\(248\) | 14205.9 | 3.63739 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2811.53 | − | 4869.70i | 0.711266 | − | 1.23195i | ||||
\(251\) | −2148.41 | − | 3721.15i | −0.540264 | − | 0.935765i | −0.998889 | − | 0.0471349i | \(-0.984991\pi\) |
0.458624 | − | 0.888630i | \(-0.348342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 830.840 | + | 1439.06i | 0.206460 | + | 0.357600i | ||||
\(254\) | 4165.55 | + | 7214.94i | 1.02901 | + | 1.78231i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2638.88 | − | 4570.68i | −0.644259 | − | 1.11589i | ||||
\(257\) | 691.970 | − | 1198.53i | 0.167953 | − | 0.290903i | −0.769747 | − | 0.638349i | \(-0.779618\pi\) |
0.937700 | + | 0.347446i | \(0.112951\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1622.35 | −0.389221 | ||||||||
\(260\) | −1642.63 | − | 12803.3i | −0.391813 | − | 3.05396i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2095.74 | + | 3629.92i | −0.494180 | + | 0.855944i | ||||
\(263\) | 1239.34 | − | 2146.60i | 0.290574 | − | 0.503288i | −0.683372 | − | 0.730070i | \(-0.739487\pi\) |
0.973945 | + | 0.226782i | \(0.0728206\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −796.355 | −0.184603 | ||||||||
\(266\) | 1900.98 | + | 3292.59i | 0.438182 | + | 0.758953i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −19669.4 | −4.48321 | ||||||||
\(269\) | 1226.32 | + | 2124.05i | 0.277956 | + | 0.481433i | 0.970877 | − | 0.239580i | \(-0.0770099\pi\) |
−0.692921 | + | 0.721014i | \(0.743677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2990.37 | − | 5179.47i | 0.670302 | − | 1.16100i | −0.307516 | − | 0.951543i | \(-0.599498\pi\) |
0.977818 | − | 0.209455i | \(-0.0671689\pi\) | |||||||
\(272\) | −26378.9 | −5.88036 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13137.4 | 2.89658 | ||||||||
\(275\) | −590.905 | + | 1023.48i | −0.129574 | + | 0.224429i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3689.00 | + | 6389.53i | 0.800182 | + | 1.38596i | 0.919496 | + | 0.393099i | \(0.128597\pi\) |
−0.119314 | + | 0.992857i | \(0.538070\pi\) | |||||||
\(278\) | 6752.42 | 1.45677 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2965.11 | + | 5135.72i | 0.632854 | + | 1.09613i | ||||
\(281\) | −5937.17 | −1.26043 | −0.630217 | − | 0.776419i | \(-0.717034\pi\) | ||||
−0.630217 | + | 0.776419i | \(0.717034\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −743.259 | + | 1287.36i | −0.156121 | + | 0.270409i | −0.933467 | − | 0.358664i | \(-0.883232\pi\) |
0.777346 | + | 0.629074i | \(0.216566\pi\) | |||||||
\(284\) | −4514.61 | + | 7819.53i | −0.943284 | + | 1.63382i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −843.419 | − | 6573.96i | −0.174379 | − | 1.35918i | ||||
\(287\) | −1461.18 | −0.300526 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5216.23 | + | 9034.78i | −1.06172 | + | 1.83895i | ||||
\(290\) | −7931.50 | − | 13737.8i | −1.60605 | − | 2.78176i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1145.71 | − | 1984.43i | −0.229615 | − | 0.397705i | ||||
\(293\) | −1790.02 | − | 3100.41i | −0.356909 | − | 0.618185i | 0.630534 | − | 0.776162i | \(-0.282836\pi\) |
−0.987443 | + | 0.157977i | \(0.949503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 525.313 | + | 909.869i | 0.103678 | + | 0.179575i | ||||
\(296\) | −8935.09 | + | 15476.0i | −1.75453 | + | 3.03894i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4228.32 | 0.821947 | ||||||||
\(299\) | 2363.91 | − | 1801.53i | 0.457219 | − | 0.348446i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1233.69 | + | 2136.81i | −0.236242 | + | 0.409183i | ||||
\(302\) | −437.660 | + | 758.049i | −0.0833924 | + | 0.144440i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23352.9 | 4.40587 | ||||||||
\(305\) | 170.450 | + | 295.228i | 0.0319998 | + | 0.0554252i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −415.013 | −0.0771533 | −0.0385767 | − | 0.999256i | \(-0.512282\pi\) | ||||
−0.0385767 | + | 0.999256i | \(0.512282\pi\) | |||||||
\(308\) | 1777.61 | + | 3078.92i | 0.328860 | + | 0.569602i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7063.14 | + | 12233.7i | −1.29406 | + | 2.24138i | ||||
\(311\) | −3009.05 | −0.548642 | −0.274321 | − | 0.961638i | \(-0.588453\pi\) | ||||
−0.274321 | + | 0.961638i | \(0.588453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3760.84 | 0.679154 | 0.339577 | − | 0.940578i | \(-0.389716\pi\) | ||||
0.339577 | + | 0.940578i | \(0.389716\pi\) | |||||||
\(314\) | 6355.70 | − | 11008.4i | 1.14227 | − | 1.97847i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4060.43 | − | 7032.87i | −0.722838 | − | 1.25199i | ||||
\(317\) | −2772.04 | −0.491146 | −0.245573 | − | 0.969378i | \(-0.578976\pi\) | ||||
−0.245573 | + | 0.969378i | \(0.578976\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2953.50 | − | 5115.62i | −0.518384 | − | 0.897867i | ||||
\(320\) | 18800.3 | 3.28428 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1099.15 | + | 1903.78i | −0.190227 | + | 0.329483i | ||||
\(323\) | 6792.58 | − | 11765.1i | 1.17012 | − | 2.02671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1950.24 | + | 815.365i | 0.332861 | + | 0.139164i | ||||
\(326\) | 8494.67 | 1.44318 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8047.44 | + | 13938.6i | −1.35471 | + | 2.34643i | ||||
\(329\) | 111.359 | + | 192.879i | 0.0186608 | + | 0.0323215i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3279.08 | − | 5679.53i | −0.544515 | − | 0.943128i | −0.998637 | − | 0.0521882i | \(-0.983380\pi\) |
0.454122 | − | 0.890939i | \(-0.349953\pi\) | |||||||
\(332\) | 907.716 | + | 1572.21i | 0.150052 | + | 0.259898i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9643.96 | − | 16703.8i | −1.57992 | − | 2.73650i | ||||
\(335\) | 6074.45 | − | 10521.2i | 0.990694 | − | 1.71593i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9509.17 | 1.53708 | 0.768542 | − | 0.639799i | \(-0.220983\pi\) | ||||
0.768542 | + | 0.639799i | \(0.220983\pi\) | |||||||
\(338\) | −11470.8 | + | 2992.60i | −1.84595 | + | 0.481586i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 17057.4 | − | 29544.3i | 2.72079 | − | 4.71254i | ||||
\(341\) | −2630.14 | + | 4555.54i | −0.417684 | + | 0.723450i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4142.29 | 0.652077 | ||||||||
\(344\) | 13589.1 | + | 23536.9i | 2.12986 | + | 3.68903i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.77591 | 0.00120820 | ||||||||
\(347\) | 4904.39 | + | 8494.66i | 0.758736 | + | 1.31417i | 0.943495 | + | 0.331386i | \(0.107516\pi\) |
−0.184759 | + | 0.982784i | \(0.559150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −397.476 | + | 688.449i | −0.0609639 | + | 0.105593i | −0.894897 | − | 0.446274i | \(-0.852751\pi\) |
0.833933 | + | 0.551866i | \(0.186084\pi\) | |||||||
\(350\) | −1563.46 | −0.238772 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15274.3 | 2.31284 | ||||||||
\(353\) | 3557.80 | − | 6162.29i | 0.536438 | − | 0.929138i | −0.462654 | − | 0.886539i | \(-0.653103\pi\) |
0.999092 | − | 0.0425989i | \(-0.0135638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2788.46 | − | 4829.76i | −0.416891 | − | 0.722077i | ||||
\(356\) | −10471.3 | −1.55893 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5617.87 | + | 9730.43i | 0.829367 | + | 1.43651i | ||||
\(359\) | −6907.19 | −1.01545 | −0.507726 | − | 0.861518i | \(-0.669514\pi\) | ||||
−0.507726 | + | 0.861518i | \(0.669514\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2583.89 | + | 4475.43i | −0.376715 | + | 0.652490i | ||||
\(362\) | 1253.19 | − | 2170.60i | 0.181951 | − | 0.315149i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5057.67 | − | 3854.44i | 0.728280 | − | 0.555021i | ||||
\(365\) | 1415.31 | 0.202960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 229.767 | − | 397.967i | 0.0326804 | − | 0.0566042i | −0.849223 | − | 0.528035i | \(-0.822929\pi\) |
0.881903 | + | 0.471431i | \(0.156262\pi\) | |||||||
\(368\) | 6751.35 | + | 11693.7i | 0.956354 | + | 1.65645i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8885.03 | − | 15389.3i | −1.24841 | − | 2.16230i | ||||
\(371\) | −196.154 | − | 339.749i | −0.0274496 | − | 0.0475441i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2679.96 | − | 4641.83i | −0.372019 | − | 0.644355i | 0.617857 | − | 0.786290i | \(-0.288001\pi\) |
−0.989876 | + | 0.141935i | \(0.954668\pi\) | |||||||
\(374\) | 8758.24 | − | 15169.7i | 1.21090 | − | 2.09735i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2453.23 | 0.336478 | ||||||||
\(377\) | −8403.32 | + | 6404.15i | −1.14799 | + | 0.874882i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4297.03 | + | 7442.68i | −0.582384 | + | 1.00872i | 0.412812 | + | 0.910816i | \(0.364547\pi\) |
−0.995196 | + | 0.0979028i | \(0.968787\pi\) | |||||||
\(380\) | −15100.7 | + | 26155.2i | −2.03855 | + | 3.53088i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26257.9 | −3.51694 | ||||||||
\(383\) | −4668.24 | − | 8085.63i | −0.622810 | − | 1.07874i | −0.988960 | − | 0.148182i | \(-0.952658\pi\) |
0.366151 | − | 0.930556i | \(-0.380676\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2195.90 | −0.290684 | ||||||||
\(386\) | 2310.35 | + | 4001.65i | 0.304648 | + | 0.527665i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2015.04 | + | 3490.14i | −0.263654 | + | 0.456663i | ||||
\(389\) | 12792.1 | 1.66732 | 0.833659 | − | 0.552279i | \(-0.186242\pi\) | ||||
0.833659 | + | 0.552279i | \(0.186242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7854.95 | 1.01596 | ||||||||
\(392\) | 10676.4 | − | 18492.1i | 1.37562 | − | 2.38264i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4240.98 | + | 7345.59i | 0.542278 | + | 0.939253i | ||||
\(395\) | 5015.88 | 0.638927 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6692.24 | + | 11591.3i | 0.846030 | + | 1.46537i | 0.884723 | + | 0.466116i | \(0.154347\pi\) |
−0.0386932 | + | 0.999251i | \(0.512319\pi\) | |||||||
\(398\) | 16870.8 | 2.12477 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4801.65 | + | 8316.70i | −0.600206 | + | 1.03959i | ||||
\(401\) | 3178.71 | − | 5505.68i | 0.395853 | − | 0.685637i | −0.597357 | − | 0.801976i | \(-0.703782\pi\) |
0.993210 | + | 0.116338i | \(0.0371157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8680.60 | + | 3629.23i | 1.07298 | + | 0.448597i | ||||
\(404\) | −17969.0 | −2.21285 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3907.29 | − | 6767.62i | 0.477624 | − | 0.827270i | ||||
\(407\) | −3308.57 | − | 5730.62i | −0.402948 | − | 0.697926i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2650.81 | + | 4591.35i | 0.320475 | + | 0.555079i | 0.980586 | − | 0.196089i | \(-0.0628241\pi\) |
−0.660111 | + | 0.751168i | \(0.729491\pi\) | |||||||
\(410\) | −8002.35 | − | 13860.5i | −0.963922 | − | 1.66956i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13825.4 | + | 23946.3i | 1.65323 | + | 2.86347i | ||||
\(413\) | −258.785 | + | 448.228i | −0.0308328 | + | 0.0534040i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1121.31 | −0.132633 | ||||||||
\(416\) | −3476.58 | − | 27097.9i | −0.409744 | − | 3.19371i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7753.57 | + | 13429.6i | −0.907272 | + | 1.57144i | ||||
\(419\) | −8197.92 | + | 14199.2i | −0.955835 | + | 1.65555i | −0.223388 | + | 0.974730i | \(0.571712\pi\) |
−0.732447 | + | 0.680824i | \(0.761622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8484.68 | 0.982227 | 0.491114 | − | 0.871095i | \(-0.336590\pi\) | ||||
0.491114 | + | 0.871095i | \(0.336590\pi\) | |||||||
\(422\) | −332.904 | − | 576.607i | −0.0384017 | − | 0.0665137i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4321.26 | −0.494950 | ||||||||
\(425\) | 2793.27 | + | 4838.09i | 0.318809 | + | 0.552193i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −83.9685 | + | 145.438i | −0.00951645 | + | 0.0164830i | ||||
\(428\) | −20319.6 | −2.29483 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −27025.8 | −3.03094 | ||||||||
\(431\) | −797.370 | + | 1381.09i | −0.0891136 | + | 0.154349i | −0.907137 | − | 0.420836i | \(-0.861737\pi\) |
0.818023 | + | 0.575185i | \(0.195070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1693.79 | + | 2933.73i | 0.187987 | + | 0.325602i | 0.944579 | − | 0.328285i | \(-0.106471\pi\) |
−0.756592 | + | 0.653887i | \(0.773137\pi\) | |||||||
\(434\) | −6959.02 | −0.769685 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9417.29 | − | 16311.2i | −1.03442 | − | 1.79166i | ||||
\(437\) | −6953.90 | −0.761213 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3605.77 | − | 6245.37i | 0.392014 | − | 0.678987i | −0.600701 | − | 0.799473i | \(-0.705112\pi\) |
0.992715 | + | 0.120486i | \(0.0384453\pi\) | |||||||
\(440\) | −12093.9 | + | 20947.2i | −1.31035 | + | 2.26959i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28905.9 | − | 12085.1i | −3.11067 | − | 1.30052i | ||||
\(443\) | −7500.66 | −0.804441 | −0.402220 | − | 0.915543i | \(-0.631761\pi\) | ||||
−0.402220 | + | 0.915543i | \(0.631761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3233.82 | − | 5601.15i | 0.344490 | − | 0.596674i | ||||
\(446\) | 6754.82 | + | 11699.7i | 0.717152 | + | 1.24214i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4630.79 | + | 8020.76i | 0.488358 | + | 0.845860i | ||||
\(449\) | 3824.77 | + | 6624.69i | 0.402009 | + | 0.696299i | 0.993968 | − | 0.109668i | \(-0.0349789\pi\) |
−0.591960 | + | 0.805968i | \(0.701646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2979.88 | − | 5161.31i | −0.311125 | − | 0.538884i | ||||
\(452\) | 2785.56 | − | 4824.74i | 0.289871 | − | 0.502072i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3125.67 | 0.323117 | ||||||||
\(455\) | 499.809 | + | 3895.72i | 0.0514976 | + | 0.401394i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4500.90 | − | 7795.78i | 0.460707 | − | 0.797968i | −0.538290 | − | 0.842760i | \(-0.680929\pi\) |
0.998996 | + | 0.0447924i | \(0.0142626\pi\) | |||||||
\(458\) | 2074.51 | − | 3593.16i | 0.211649 | − | 0.366588i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17462.5 | −1.76999 | ||||||||
\(461\) | 673.916 | + | 1167.26i | 0.0680854 | + | 0.117927i | 0.898059 | − | 0.439876i | \(-0.144978\pi\) |
−0.829973 | + | 0.557803i | \(0.811644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −94.9035 | −0.00952600 | −0.00476300 | − | 0.999989i | \(-0.501516\pi\) | ||||
−0.00476300 | + | 0.999989i | \(0.501516\pi\) | |||||||
\(464\) | −24000.0 | − | 41569.1i | −2.40123 | − | 4.15905i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2281.64 | + | 3951.92i | −0.226813 | + | 0.392852i | ||||
\(467\) | 13290.9 | 1.31698 | 0.658489 | − | 0.752591i | \(-0.271196\pi\) | ||||
0.658489 | + | 0.752591i | \(0.271196\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5984.90 | 0.589247 | ||||||||
\(470\) | −1219.74 | + | 2112.66i | −0.119708 | + | 0.207340i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2850.50 | + | 4937.21i | 0.277977 | + | 0.481470i | ||||
\(473\) | −10063.8 | −0.978294 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2472.85 | − | 4283.10i | −0.238868 | − | 0.413731i | ||||
\(476\) | 16806.0 | 1.61828 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17679.0 | − | 30621.0i | 1.69167 | − | 2.93006i | ||||
\(479\) | 1900.79 | − | 3292.27i | 0.181314 | − | 0.314045i | −0.761014 | − | 0.648735i | \(-0.775298\pi\) |
0.942328 | + | 0.334690i | \(0.108632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9413.57 | + | 7174.06i | −0.892353 | + | 0.680060i | ||||
\(482\) | 27933.2 | 2.63967 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6802.05 | − | 11781.5i | 0.638810 | − | 1.10645i | ||||
\(485\) | −1244.59 | − | 2155.70i | −0.116524 | − | 0.201825i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4373.67 | + | 7575.42i | 0.406961 | + | 0.704877i | 0.994548 | − | 0.104284i | \(-0.0332552\pi\) |
−0.587587 | + | 0.809161i | \(0.699922\pi\) | |||||||
\(488\) | 924.911 | + | 1601.99i | 0.0857966 | + | 0.148604i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10616.6 | + | 18388.5i | 0.978796 | + | 1.69533i | ||||
\(491\) | −7542.69 | + | 13064.3i | −0.693273 | + | 1.20078i | 0.277487 | + | 0.960729i | \(0.410499\pi\) |
−0.970759 | + | 0.240054i | \(0.922835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27923.1 | −2.55090 | ||||||||
\(494\) | 25590.1 | + | 10698.8i | 2.33067 | + | 0.974419i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21372.4 | + | 37018.0i | −1.93477 | + | 3.35113i | ||||
\(497\) | 1373.68 | − | 2379.28i | 0.123980 | − | 0.214739i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14593.9 | 1.30925 | 0.654623 | − | 0.755955i | \(-0.272827\pi\) | ||||
0.654623 | + | 0.755955i | \(0.272827\pi\) | |||||||
\(500\) | 11002.3 | + | 19056.5i | 0.984074 | + | 1.70447i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23185.2 | 2.06136 | ||||||||
\(503\) | 9102.46 | + | 15765.9i | 0.806876 | + | 1.39755i | 0.915017 | + | 0.403414i | \(0.132177\pi\) |
−0.108142 | + | 0.994135i | \(0.534490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5549.30 | − | 9611.67i | 0.488991 | − | 0.846958i | ||||
\(506\) | −8966.25 | −0.787744 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32601.9 | −2.84739 | ||||||||
\(509\) | 3945.96 | − | 6834.61i | 0.343618 | − | 0.595164i | −0.641483 | − | 0.767137i | \(-0.721681\pi\) |
0.985102 | + | 0.171973i | \(0.0550140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 348.610 | + | 603.811i | 0.0301793 | + | 0.0522721i | ||||
\(512\) | 3555.88 | 0.306932 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3733.79 | + | 6467.12i | 0.320410 | + | 0.554966i | ||||
\(515\) | −17078.6 | −1.46131 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −454.203 | + | 786.703i | −0.0386380 | + | 0.0669229i | ||||
\(518\) | 4377.02 | − | 7581.23i | 0.371265 | − | 0.643050i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 39914.9 | + | 16687.8i | 3.36613 | + | 1.40733i | ||||
\(521\) | 647.902 | 0.0544820 | 0.0272410 | − | 0.999629i | \(-0.491328\pi\) | ||||
0.0272410 | + | 0.999629i | \(0.491328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4634.99 | + | 8028.04i | −0.387522 | + | 0.671208i | −0.992116 | − | 0.125326i | \(-0.960002\pi\) |
0.604593 | + | 0.796534i | \(0.293336\pi\) | |||||||
\(524\) | −8201.20 | − | 14204.9i | −0.683724 | − | 1.18424i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6687.33 | + | 11582.8i | 0.554337 | + | 0.960141i | ||||
\(527\) | 12433.0 | + | 21534.6i | 1.02768 | + | 1.78000i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4073.12 | + | 7054.86i | 0.334768 | + | 0.579835i | ||||
\(530\) | 2148.52 | − | 3721.35i | 0.176087 | − | 0.304991i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14878.1 | −1.21250 | ||||||||
\(533\) | −8478.38 | + | 6461.35i | −0.689005 | + | 0.525089i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6275.24 | − | 10869.0i | 0.507107 | − | 0.878336i | ||||
\(536\) | 32961.7 | − | 57091.4i | 2.65621 | − | 4.60069i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13234.2 | −1.06053 | ||||||||
\(539\) | 3953.38 | + | 6847.45i | 0.315926 | + | 0.547200i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3844.83 | 0.305549 | 0.152775 | − | 0.988261i | \(-0.451179\pi\) | ||||
0.152775 | + | 0.988261i | \(0.451179\pi\) | |||||||
\(542\) | 16135.7 | + | 27947.8i | 1.27876 | + | 2.21488i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 36101.6 | − | 62529.8i | 2.84530 | − | 4.92820i | ||||
\(545\) | 11633.2 | 0.914337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20245.4 | −1.58251 | −0.791253 | − | 0.611489i | \(-0.790571\pi\) | ||||
−0.791253 | + | 0.611489i | \(0.790571\pi\) | |||||||
\(548\) | −25705.2 | + | 44522.8i | −2.00378 | + | 3.47065i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3188.46 | − | 5522.57i | −0.247193 | − | 0.428151i | ||||
\(551\) | 24720.0 | 1.91126 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1235.48 | + | 2139.92i | 0.0950056 | + | 0.164555i | ||||
\(554\) | −39810.8 | −3.05307 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13212.1 | + | 22884.0i | −1.00776 | + | 1.74550i | ||||
\(557\) | 3611.67 | − | 6255.60i | 0.274742 | − | 0.475868i | −0.695328 | − | 0.718693i | \(-0.744741\pi\) |
0.970070 | + | 0.242825i | \(0.0780741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2290.62 | + | 17854.1i | 0.173315 | + | 1.35089i | ||||
\(560\) | −17843.7 | −1.34649 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16018.2 | − | 27744.3i | 1.20229 | − | 2.08242i | ||||
\(563\) | −8645.13 | − | 14973.8i | −0.647156 | − | 1.12091i | −0.983799 | − | 0.179275i | \(-0.942625\pi\) |
0.336643 | − | 0.941632i | \(-0.390708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1720.51 | + | 2980.02i | 0.128111 | + | 0.221894i | ||||
\(566\) | −4010.54 | − | 6946.47i | −0.297837 | − | 0.515869i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15131.0 | − | 26207.7i | −1.11775 | − | 1.93600i | ||||
\(569\) | 8682.00 | − | 15037.7i | 0.639663 | − | 1.10793i | −0.345843 | − | 0.938292i | \(-0.612407\pi\) |
0.985507 | − | 0.169637i | \(-0.0542595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 158.149 | 0.0115908 | 0.00579540 | − | 0.999983i | \(-0.498155\pi\) | ||||
0.00579540 | + | 0.999983i | \(0.498155\pi\) | |||||||
\(572\) | 23929.4 | + | 10004.5i | 1.74919 | + | 0.731311i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3942.19 | − | 6828.07i | 0.286662 | − | 0.496513i | ||||
\(575\) | 1429.81 | − | 2476.50i | 0.103699 | − | 0.179612i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9627.04 | 0.694591 | 0.347295 | − | 0.937756i | \(-0.387100\pi\) | ||||
0.347295 | + | 0.937756i | \(0.387100\pi\) | |||||||
\(578\) | −28146.2 | − | 48750.7i | −2.02548 | − | 3.50824i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 62076.4 | 4.44411 | ||||||||
\(581\) | −276.195 | − | 478.383i | −0.0197220 | − | 0.0341595i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 800.059 | − | 1385.74i | 0.0568354 | − | 0.0984418i | ||||
\(584\) | 7679.86 | 0.544169 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19317.6 | 1.36178 | ||||||||
\(587\) | −6660.59 | + | 11536.5i | −0.468334 | + | 0.811179i | −0.999345 | − | 0.0361864i | \(-0.988479\pi\) |
0.531011 | + | 0.847365i | \(0.321812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11006.8 | − | 19064.3i | −0.769994 | − | 1.33367i | ||||
\(590\) | −5669.06 | −0.395579 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26885.2 | − | 46566.6i | −1.86651 | − | 3.23290i | ||||
\(593\) | −16723.4 | −1.15809 | −0.579044 | − | 0.815296i | \(-0.696574\pi\) | ||||
−0.579044 | + | 0.815296i | \(0.696574\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5190.13 | + | 8989.57i | −0.357604 | + | 0.619389i | ||||
\(596\) | −8273.31 | + | 14329.8i | −0.568604 | + | 0.984850i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2040.81 | + | 15906.9i | 0.139557 | + | 1.08776i | ||||
\(599\) | −17160.0 | −1.17051 | −0.585256 | − | 0.810849i | \(-0.699006\pi\) | ||||
−0.585256 | + | 0.810849i | \(0.699006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5524.29 | + | 9568.34i | −0.374942 | + | 0.649419i | −0.990318 | − | 0.138814i | \(-0.955671\pi\) |
0.615376 | + | 0.788234i | \(0.289004\pi\) | |||||||
\(602\) | −6656.86 | − | 11530.0i | −0.450687 | − | 0.780612i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1712.69 | − | 2966.46i | −0.115378 | − | 0.199840i | ||||
\(605\) | 4201.31 | + | 7276.89i | 0.282327 | + | 0.489004i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10559.8 | − | 18290.1i | −0.706110 | − | 1.22302i | −0.966290 | − | 0.257458i | \(-0.917115\pi\) |
0.260180 | − | 0.965560i | \(-0.416218\pi\) | |||||||
\(608\) | −31960.3 | + | 55356.9i | −2.13184 | + | 3.69246i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1839.46 | −0.122094 | ||||||||
\(611\) | 1499.06 | + | 626.736i | 0.0992563 | + | 0.0414976i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3116.91 | − | 5398.65i | 0.205369 | − | 0.355709i | −0.744881 | − | 0.667197i | \(-0.767494\pi\) |
0.950250 | + | 0.311488i | \(0.100827\pi\) | |||||||
\(614\) | 1119.68 | − | 1939.35i | 0.0735940 | − | 0.127469i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11915.6 | −0.779371 | ||||||||
\(617\) | −2799.18 | − | 4848.32i | −0.182643 | − | 0.316347i | 0.760137 | − | 0.649763i | \(-0.225132\pi\) |
−0.942780 | + | 0.333416i | \(0.891799\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15874.3 | −1.03076 | −0.515382 | − | 0.856961i | \(-0.672350\pi\) | ||||
−0.515382 | + | 0.856961i | \(0.672350\pi\) | |||||||
\(620\) | −27640.0 | − | 47874.0i | −1.79040 | − | 3.10107i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8118.25 | − | 14061.2i | 0.523332 | − | 0.906437i | ||||
\(623\) | 3186.15 | 0.204896 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19228.4 | −1.23062 | ||||||||
\(626\) | −10146.5 | + | 17574.3i | −0.647823 | + | 1.12206i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24871.6 | + | 43079.0i | 1.58039 | + | 2.73732i | ||||
\(629\) | −31280.0 | −1.98285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5624.51 | − | 9741.93i | −0.354846 | − | 0.614612i | 0.632245 | − | 0.774768i | \(-0.282133\pi\) |
−0.987092 | + | 0.160156i | \(0.948800\pi\) | |||||||
\(632\) | 27217.6 | 1.71307 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7478.81 | − | 12953.7i | 0.468488 | − | 0.811445i | ||||
\(635\) | 10068.3 | − | 17438.9i | 0.629213 | − | 1.08983i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11248.2 | − | 8572.20i | 0.699637 | − | 0.533192i | ||||
\(638\) | 31873.6 | 1.97788 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −20315.1 | + | 35186.8i | −1.25473 | + | 2.17325i | ||||
\(641\) | 11884.2 | + | 20584.0i | 0.732287 | + | 1.26836i | 0.955903 | + | 0.293681i | \(0.0948804\pi\) |
−0.223616 | + | 0.974677i | \(0.571786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2184.48 | + | 3783.63i | 0.133977 | + | 0.232055i | 0.925206 | − | 0.379465i | \(-0.123892\pi\) |
−0.791229 | + | 0.611520i | \(0.790558\pi\) | |||||||
\(644\) | −4301.27 | − | 7450.02i | −0.263189 | − | 0.455857i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36652.0 | + | 63483.1i | 2.23228 | + | 3.86642i | ||||
\(647\) | 10652.6 | − | 18450.8i | 0.647290 | − | 1.12114i | −0.336477 | − | 0.941692i | \(-0.609235\pi\) |
0.983767 | − | 0.179448i | \(-0.0574312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2111.02 | −0.127681 | ||||||||
\(650\) | −9071.81 | + | 6913.61i | −0.547424 | + | 0.417191i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16621.0 | + | 28788.5i | −0.998358 | + | 1.72921i | ||||
\(653\) | 13979.2 | − | 24212.6i | 0.837744 | − | 1.45101i | −0.0540335 | − | 0.998539i | \(-0.517208\pi\) |
0.891777 | − | 0.452475i | \(-0.149459\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10131.0 | 0.604353 | ||||||||
\(656\) | −24214.3 | − | 41940.4i | −1.44117 | − | 2.49619i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1201.76 | −0.0711999 | ||||||||
\(659\) | −4809.73 | − | 8330.70i | −0.284310 | − | 0.492440i | 0.688131 | − | 0.725586i | \(-0.258431\pi\) |
−0.972442 | + | 0.233146i | \(0.925098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2207.20 | + | 3822.99i | −0.129879 | + | 0.224958i | −0.923630 | − | 0.383286i | \(-0.874792\pi\) |
0.793750 | + | 0.608244i | \(0.208126\pi\) | |||||||
\(662\) | 35387.1 | 2.07758 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6084.55 | −0.355612 | ||||||||
\(665\) | 4594.76 | − | 7958.36i | 0.267936 | − | 0.464078i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7146.56 | + | 12378.2i | 0.414866 | + | 0.718570i | ||||
\(668\) | 75479.0 | 4.37181 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32777.0 | + | 56771.5i | 1.88998 | + | 3.27354i | ||||
\(671\) | −684.970 | −0.0394083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9000.88 | − | 15590.0i | 0.515540 | − | 0.892942i | −0.484297 | − | 0.874904i | \(-0.660925\pi\) |
0.999837 | − | 0.0180383i | \(-0.00574207\pi\) | |||||||
\(674\) | −25655.2 | + | 44436.1i | −1.46617 | + | 2.53949i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12302.4 | − | 44730.1i | 0.699952 | − | 2.54495i | ||||
\(677\) | −11192.0 | −0.635369 | −0.317684 | − | 0.948197i | \(-0.602905\pi\) | ||||
−0.317684 | + | 0.948197i | \(0.602905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 613.123 | − | 1061.96i | 0.0346532 | − | 0.0600211i | ||||
\(680\) | 57169.1 | + | 99019.8i | 3.22402 | + | 5.58417i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14192.0 | − | 24581.2i | −0.796831 | − | 1.38015i | ||||
\(683\) | −17561.2 | − | 30416.8i | −0.983835 | − | 1.70405i | −0.647002 | − | 0.762488i | \(-0.723978\pi\) |
−0.336833 | − | 0.941564i | \(-0.609356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15876.9 | − | 27499.7i | −0.885586 | − | 1.53388i | ||||
\(686\) | −11175.7 | + | 19356.8i | −0.621996 | + | 1.07733i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −81777.5 | −4.53160 | ||||||||
\(689\) | −2640.53 | − | 1103.97i | −0.146003 | − | 0.0610418i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14767.3 | + | 25577.7i | −0.812987 | + | 1.40813i | 0.0977773 | + | 0.995208i | \(0.468827\pi\) |
−0.910764 | + | 0.412926i | \(0.864507\pi\) | |||||||
\(692\) | −15.2147 | + | 26.3526i | −0.000835802 | + | 0.00144765i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −52927.1 | −2.89494 | ||||||||
\(695\) | −8160.48 | − | 14134.4i | −0.445388 | − | 0.771434i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28172.5 | −1.53100 | ||||||||
\(698\) | −2144.74 | − | 3714.79i | −0.116303 | − | 0.201443i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3059.12 | − | 5298.55i | 0.165177 | − | 0.286095i | ||||
\(701\) | 8804.19 | 0.474365 | 0.237182 | − | 0.971465i | \(-0.423776\pi\) | ||||
0.237182 | + | 0.971465i | \(0.423776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27691.8 | 1.48566 | ||||||||
\(704\) | −18887.7 | + | 32714.5i | −1.01116 | + | 1.75138i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19197.5 | + | 33251.0i | 1.02338 | + | 1.77255i | ||||
\(707\) | 5467.49 | 0.290843 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13569.1 | − | 23502.4i | −0.718758 | − | 1.24492i | −0.961492 | − | 0.274832i | \(-0.911378\pi\) |
0.242735 | − | 0.970093i | \(-0.421956\pi\) | |||||||
\(710\) | 30092.5 | 1.59064 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17547.7 | − | 30393.4i | 0.923633 | − | 1.59978i | ||||
\(713\) | 6364.13 | − | 11023.0i | 0.334276 | − | 0.578983i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12741.5 | + | 9710.27i | −0.666441 | + | 0.507893i | ||||
\(716\) | −43968.6 | −2.29495 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18635.2 | − | 32277.1i | 0.968607 | − | 1.67768i | ||||
\(719\) | −8668.72 | − | 15014.7i | −0.449637 | − | 0.778794i | 0.548725 | − | 0.836003i | \(-0.315113\pi\) |
−0.998362 | + | 0.0572088i | \(0.981780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4206.72 | − | 7286.25i | −0.217290 | − | 0.376358i | ||||
\(722\) | −13942.4 | − | 24148.9i | −0.718673 | − | 1.24478i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4904.10 | + | 8494.15i | 0.251740 | + | 0.436026i | ||||
\(725\) | −5082.73 | + | 8803.54i | −0.260369 | + | 0.450973i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25771.3 | 1.31473 | 0.657363 | − | 0.753574i | \(-0.271672\pi\) | ||||
0.657363 | + | 0.753574i | \(0.271672\pi\) | |||||||
\(728\) | 2712.11 | + | 21139.3i | 0.138074 | + | 1.07620i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3818.42 | + | 6613.69i | −0.193597 | + | 0.335320i | ||||
\(731\) | −23786.3 | + | 41199.1i | −1.20351 | + | 2.08455i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21784.2 | 1.09771 | 0.548853 | − | 0.835919i | \(-0.315065\pi\) | ||||
0.548853 | + | 0.835919i | \(0.315065\pi\) | |||||||
\(734\) | 1239.80 | + | 2147.39i | 0.0623456 | + | 0.107986i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36959.0 | −1.85099 | ||||||||
\(737\) | 12205.4 | + | 21140.4i | 0.610029 | + | 1.05660i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11176.9 | + | 19359.0i | −0.556360 | + | 0.963643i | 0.441437 | + | 0.897292i | \(0.354469\pi\) |
−0.997796 | + | 0.0663507i | \(0.978864\pi\) | |||||||
\(740\) | 69539.2 | 3.45448 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2116.85 | 0.104733 | ||||||||
\(743\) | 9191.31 | − | 15919.8i | 0.453831 | − | 0.786059i | −0.544789 | − | 0.838573i | \(-0.683390\pi\) |
0.998620 | + | 0.0525145i | \(0.0167236\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5110.04 | − | 8850.85i | −0.251298 | − | 0.435262i | ||||
\(746\) | 28921.5 | 1.41943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34273.5 | + | 59363.4i | 1.67535 | + | 2.90179i | ||||
\(749\) | 6182.74 | 0.301618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6891.39 | + | 11936.2i | −0.334847 | + | 0.579972i | −0.983455 | − | 0.181150i | \(-0.942018\pi\) |
0.648608 | + | 0.761122i | \(0.275351\pi\) | |||||||
\(752\) | −3690.82 | + | 6392.69i | −0.178977 | + | 0.309997i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7254.75 | − | 56546.6i | −0.350401 | − | 2.73117i | ||||
\(755\) | 2115.69 | 0.101984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12819.7 | + | 22204.4i | −0.615510 | + | 1.06609i | 0.374785 | + | 0.927112i | \(0.377717\pi\) |
−0.990295 | + | 0.138983i | \(0.955617\pi\) | |||||||
\(758\) | −23186.3 | − | 40159.9i | −1.11104 | − | 1.92437i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −50611.1 | − | 87661.0i | −2.41560 | − | 4.18395i | ||||
\(761\) | −21.7379 | − | 37.6511i | −0.00103548 | − | 0.00179350i | 0.865507 | − | 0.500896i | \(-0.166996\pi\) |
−0.866543 | + | 0.499103i | \(0.833663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2865.44 | + | 4963.08i | 0.135958 | + | 0.235486i | ||||
\(764\) | 51377.3 | − | 88988.1i | 2.43294 | − | 4.21397i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50378.7 | 2.37631 | ||||||||
\(767\) | 480.491 | + | 3745.15i | 0.0226200 | + | 0.176310i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10242.8 | − | 17741.1i | 0.480321 | − | 0.831940i | −0.519425 | − | 0.854516i | \(-0.673854\pi\) |
0.999745 | + | 0.0225767i | \(0.00718701\pi\) | |||||||
\(770\) | 5924.41 | − | 10261.4i | 0.277274 | − | 0.480253i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18082.1 | −0.842992 | ||||||||
\(773\) | −14725.1 | − | 25504.7i | −0.685157 | − | 1.18673i | −0.973387 | − | 0.229166i | \(-0.926400\pi\) |
0.288230 | − | 0.957561i | \(-0.406933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9052.51 | 0.419582 | ||||||||
\(776\) | −6753.53 | − | 11697.5i | −0.312420 | − | 0.541127i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34512.5 | + | 59777.4i | −1.59040 | + | 2.75466i | ||||
\(779\) | 24940.8 | 1.14711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11205.7 | 0.513409 | ||||||||
\(782\) | −21192.2 | + | 36706.0i | −0.969095 | + | 1.67852i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 32124.9 | + | 55641.9i | 1.46341 | + | 2.53471i | ||||
\(785\) | −30724.1 | −1.39693 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4875.55 | − | 8444.70i | −0.220832 | − | 0.382492i | 0.734229 | − | 0.678902i | \(-0.237544\pi\) |
−0.955061 | + | 0.296410i | \(0.904211\pi\) | |||||||
\(788\) | −33192.3 | −1.50054 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13532.6 | + | 23439.1i | −0.609452 | + | 1.05560i | ||||
\(791\) | −847.575 | + | 1468.04i | −0.0380990 | + | 0.0659894i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 155.906 | + | 1215.20i | 0.00698158 | + | 0.0544174i | ||||
\(794\) | −72221.2 | −3.22800 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33010.1 | + | 57175.2i | −1.46987 | + | 2.54588i | ||||
\(797\) | 18875.4 | + | 32693.1i | 0.838896 | + | 1.45301i | 0.890818 | + | 0.454360i | \(0.150132\pi\) |
−0.0519216 | + | 0.998651i | \(0.516535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2147.07 | + | 3718.83i | 0.0950661 | + | 0.164659i | ||||
\(800\) | −13142.9 | − | 22764.1i | −0.580837 | − | 1.00604i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17152.0 | + | 29708.1i | 0.755183 | + | 1.30801i | ||||
\(803\) | −1421.89 | + | 2462.78i | −0.0624873 | + | 0.108231i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5313.39 | 0.232637 | ||||||||
\(806\) | −40379.1 | + | 30772.8i | −1.76463 | + | 1.34482i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30112.1 | − | 52155.7i | 1.31107 | − | 2.27083i | ||||
\(809\) | 3499.72 | − | 6061.70i | 0.152094 | − | 0.263434i | −0.779903 | − | 0.625900i | \(-0.784732\pi\) |
0.931997 | + | 0.362466i | \(0.118065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35792.1 | −1.54973 | −0.774864 | − | 0.632128i | \(-0.782182\pi\) | ||||
−0.774864 | + | 0.632128i | \(0.782182\pi\) | |||||||
\(812\) | 15290.3 | + | 26483.6i | 0.660819 | + | 1.14457i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 35705.4 | 1.53744 | ||||||||
\(815\) | −10266.0 | − | 17781.3i | −0.441231 | − | 0.764235i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21057.7 | − | 36473.1i | 0.901735 | − | 1.56185i | ||||
\(818\) | −28607.0 | −1.22276 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 62630.9 | 2.66727 | ||||||||
\(821\) | −4888.31 | + | 8466.80i | −0.207799 | + | 0.359919i | −0.951021 | − | 0.309126i | \(-0.899963\pi\) |
0.743222 | + | 0.669045i | \(0.233297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9831.02 | − | 17027.8i | −0.416389 | − | 0.721206i | 0.579185 | − | 0.815196i | \(-0.303371\pi\) |
−0.995573 | + | 0.0939904i | \(0.970038\pi\) | |||||||
\(824\) | −92673.7 | −3.91801 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1396.37 | − | 2418.59i | −0.0588209 | − | 0.101881i | ||||
\(827\) | 5281.22 | 0.222063 | 0.111032 | − | 0.993817i | \(-0.464585\pi\) | ||||
0.111032 | + | 0.993817i | \(0.464585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10867.7 | + | 18823.5i | −0.455310 | + | 0.788621i | −0.998706 | − | 0.0508562i | \(-0.983805\pi\) |
0.543396 | + | 0.839477i | \(0.317138\pi\) | |||||||
\(830\) | 3025.23 | − | 5239.85i | 0.126515 | − | 0.219130i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 62337.6 | + | 26062.4i | 2.59756 | + | 1.08600i | ||||
\(833\) | 37376.1 | 1.55463 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23309.9 | + | 40374.0i | −0.966077 | + | 1.67329i | ||||
\(836\) | −30341.9 | − | 52553.7i | −1.25526 | − | 2.17417i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −44235.1 | − | 76617.4i | −1.82348 | − | 3.15836i | ||||
\(839\) | 14287.4 | + | 24746.5i | 0.587908 | + | 1.01829i | 0.994506 | + | 0.104679i | \(0.0333816\pi\) |
−0.406598 | + | 0.913607i | \(0.633285\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13210.4 | − | 22881.0i | −0.541652 | − | 0.938169i | ||||
\(842\) | −22891.2 | + | 39648.7i | −0.936915 | + | 1.62278i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2605.49 | 0.106262 | ||||||||
\(845\) | 20127.0 | + | 20394.4i | 0.819396 | + | 0.830284i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2069.69 | + | 3584.81i | −0.0839614 | + | 0.145425i | ||||
\(848\) | 6501.22 | − | 11260.4i | 0.263270 | − | 0.455997i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30144.4 | −1.21640 | ||||||||
\(851\) | 8005.72 | + | 13866.3i | 0.322482 | + | 0.558556i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5251.39 | 0.210791 | 0.105395 | − | 0.994430i | \(-0.466389\pi\) | ||||
0.105395 | + | 0.994430i | \(0.466389\pi\) | |||||||
\(854\) | −453.085 | − | 784.766i | −0.0181549 | − | 0.0314451i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34051.3 | − | 58978.6i | 1.35964 | − | 2.35496i | ||||
\(857\) | −34851.0 | −1.38913 | −0.694566 | − | 0.719429i | \(-0.744404\pi\) | ||||
−0.694566 | + | 0.719429i | \(0.744404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41697.5 | 1.65623 | 0.828114 | − | 0.560559i | \(-0.189414\pi\) | ||||
0.828114 | + | 0.560559i | \(0.189414\pi\) | |||||||
\(860\) | 52879.9 | − | 91590.6i | 2.09673 | − | 3.63164i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4302.52 | − | 7452.19i | −0.170005 | − | 0.294458i | ||||
\(863\) | 28648.9 | 1.13004 | 0.565018 | − | 0.825079i | \(-0.308869\pi\) | ||||
0.565018 | + | 0.825079i | \(0.308869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.39739 | − | 16.2768i | −0.000369388 | − | 0.000639799i | ||||
\(866\) | −18279.0 | −0.717257 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13616.3 | − | 23584.1i | 0.532450 | − | 0.922231i | ||||
\(869\) | −5039.20 | + | 8728.15i | −0.196713 | + | 0.340716i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34726.8 | − | 26465.2i | 1.35095 | − | 1.02955i | ||||
\(872\) | 63125.4 | 2.45149 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18761.2 | − | 32495.4i | 0.726096 | − | 1.25764i | ||||
\(875\) | −3347.71 | − | 5798.41i | −0.129341 | − | 0.224025i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15758.4 | + | 27294.3i | 0.606754 | + | 1.05093i | 0.991772 | + | 0.128020i | \(0.0408621\pi\) |
−0.385018 | + | 0.922909i | \(0.625805\pi\) | |||||||
\(878\) | 19456.3 | + | 33699.4i | 0.747858 | + | 1.29533i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −36389.8 | − | 63029.0i | −1.39398 | − | 2.41444i | ||||
\(881\) | −15623.1 | + | 27059.9i | −0.597451 | + | 1.03482i | 0.395745 | + | 0.918360i | \(0.370486\pi\) |
−0.993196 | + | 0.116455i | \(0.962847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16181.8 | −0.616718 | −0.308359 | − | 0.951270i | \(-0.599780\pi\) | ||||
−0.308359 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(884\) | 97515.0 | − | 74316.0i | 3.71016 | − | 2.82751i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20236.4 | − | 35050.4i | 0.767330 | − | 1.32905i | ||||
\(887\) | 6644.52 | − | 11508.6i | 0.251523 | − | 0.435651i | −0.712422 | − | 0.701751i | \(-0.752402\pi\) |
0.963945 | + | 0.266100i | \(0.0857352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9919.92 | 0.374245 | ||||||||
\(890\) | 17449.4 | + | 30223.2i | 0.657195 | + | 1.13830i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −52867.0 | −1.98444 | ||||||||
\(893\) | −1900.78 | − | 3292.24i | −0.0712285 | − | 0.123371i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13578.7 | − | 23519.0i | 0.507134 | − | 0.878382i | ||||
\(896\) | −20015.6 | −0.746288 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41276.0 | −1.53385 | ||||||||
\(899\) | −22623.5 | + | 39185.0i | −0.839304 | + | 1.45372i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3781.97 | − | 6550.56i | −0.139840 | − | 0.242210i | ||||
\(902\) | 32158.2 | 1.18709 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9336.01 | + | 16170.4i | 0.343486 | + | 0.594935i | ||||
\(905\) | −6058.07 | −0.222516 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23564.2 | + | 40814.4i | −0.862664 | + | 1.49418i | 0.00668479 | + | 0.999978i | \(0.497872\pi\) |
−0.869348 | + | 0.494200i | \(0.835461\pi\) | |||||||
\(908\) | −6115.82 | + | 10592.9i | −0.223525 | + | 0.387157i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19553.1 | − | 8174.85i | −0.712284 | − | 0.297795i | ||||
\(911\) | −2884.69 | −0.104911 | −0.0524556 | − | 0.998623i | \(-0.516705\pi\) | ||||
−0.0524556 | + | 0.998623i | \(0.516705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1126.52 | − | 1951.20i | 0.0408351 | − | 0.0707285i | ||||
\(914\) | 24286.3 | + | 42065.2i | 0.878907 | + | 1.52231i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8118.14 | + | 14061.0i | 0.292828 | + | 0.507194i | ||||
\(917\) | 2495.41 | + | 4322.18i | 0.0898646 | + | 0.155650i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12876.1 | + | 22302.0i | 0.462179 | + | 0.800518i | 0.999069 | − | 0.0431343i | \(-0.0137343\pi\) |
−0.536890 | + | 0.843652i | \(0.680401\pi\) | |||||||
\(920\) | 29263.4 | − | 50685.7i | 1.04868 | − | 1.81637i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7272.75 | −0.259778 | ||||||||
\(923\) | −2550.54 | − | 19880.0i | −0.0909556 | − | 0.708946i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5693.77 | + | 9861.90i | −0.202389 | + | 0.350548i | ||||
\(926\) | 256.044 | − | 443.482i | 0.00908655 | − | 0.0157384i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 131383. | 4.64748 | ||||||||
\(929\) | 25697.4 | + | 44509.2i | 0.907539 | + | 1.57190i | 0.817473 | + | 0.575967i | \(0.195374\pi\) |
0.0900658 | + | 0.995936i | \(0.471292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33088.6 | −1.16481 | ||||||||
\(932\) | −8928.69 | − | 15465.0i | −0.313808 | − | 0.543532i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −35858.1 | + | 62108.0i | −1.25622 | + | 2.17584i | ||||
\(935\) | −42338.3 | −1.48087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6781.86 | 0.236450 | 0.118225 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118225 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(938\) | −16146.9 | + | 27967.3i | −0.562064 | + | 0.973523i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4773.19 | − | 8267.42i | −0.165622 | − | 0.286865i | ||||
\(941\) | 22038.2 | 0.763470 | 0.381735 | − | 0.924272i | \(-0.375327\pi\) | ||||
0.381735 | + | 0.924272i | \(0.375327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7210.39 | + | 12488.8i | 0.248995 | + | 0.431273i | ||||
\(944\) | −17154.0 | −0.591436 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27151.5 | − | 47027.8i | 0.933163 | − | 1.61629i | ||||
\(947\) | −22765.5 | + | 39431.0i | −0.781182 | + | 1.35305i | 0.150072 | + | 0.988675i | \(0.452049\pi\) |
−0.931254 | + | 0.364371i | \(0.881284\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4692.83 | + | 1962.00i | 0.160522 | + | 0.0671120i | ||||
\(950\) | 26686.5 | 0.911393 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −28163.2 | + | 48780.0i | −0.958795 | + | 1.66068i | ||||
\(953\) | −13270.6 | − | 22985.3i | −0.451077 | − | 0.781288i | 0.547376 | − | 0.836887i | \(-0.315627\pi\) |
−0.998453 | + | 0.0555985i | \(0.982293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31733.4 | + | 54963.8i | 1.07525 | + | 1.86240i | ||||
\(956\) | 69183.0 | + | 119828.i | 2.34052 | + | 4.05390i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10256.5 | + | 17764.7i | 0.345900 | + | 0.599116i | ||||
\(959\) | 7821.44 | − | 13547.1i | 0.263365 | − | 0.456162i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10502.1 | 0.352527 | ||||||||
\(962\) | −8126.92 | − | 63344.6i | −0.272372 | − | 2.12299i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −54655.2 | + | 94665.6i | −1.82606 | + | 3.16284i | ||||
\(965\) | 5584.25 | − | 9672.20i | 0.186283 | − | 0.322652i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48269.6 | 1.60522 | 0.802609 | − | 0.596506i | \(-0.203445\pi\) | ||||
0.802609 | + | 0.596506i | \(0.203445\pi\) | |||||||
\(968\) | 22797.5 | + | 39486.5i | 0.756964 | + | 1.31110i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13431.4 | 0.444594 | ||||||||
\(971\) | 17080.7 | + | 29584.6i | 0.564515 | + | 0.977769i | 0.997095 | + | 0.0761732i | \(0.0242702\pi\) |
−0.432579 | + | 0.901596i | \(0.642396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4020.09 | − | 6963.00i | 0.132454 | − | 0.229418i | ||||
\(974\) | −47199.7 | −1.55275 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5566.02 | −0.182545 | ||||||||
\(977\) | 12062.1 | − | 20892.2i | 0.394985 | − | 0.684135i | −0.598114 | − | 0.801411i | \(-0.704083\pi\) |
0.993099 | + | 0.117276i | \(0.0374164\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6497.72 | + | 11254.4i | 0.212123 | + | 0.367407i | ||||
\(980\) | −83091.7 | −2.70843 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −40699.5 | − | 70493.7i | −1.32258 | − | 2.29078i | ||||
\(983\) | 19023.4 | 0.617246 | 0.308623 | − | 0.951185i | \(-0.400132\pi\) | ||||
0.308623 | + | 0.951185i | \(0.400132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10250.7 | − | 17754.7i | 0.331587 | − | 0.574326i | ||||
\(986\) | 75334.9 | − | 130484.i | 2.43322 | − | 4.21446i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −86328.9 | + | 65791.0i | −2.77985 | + | 2.11851i | ||||
\(989\) | 24351.2 | 0.782936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 114.981 | − | 199.153i | 0.00368566 | − | 0.00638374i | −0.864177 | − | 0.503188i | \(-0.832160\pi\) |
0.867862 | + | 0.496805i | \(0.165493\pi\) | |||||||
\(992\) | −58499.4 | − | 101324.i | −1.87234 | − | 3.24298i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7412.22 | + | 12838.3i | 0.236520 | + | 0.409665i | ||||
\(995\) | −20388.8 | − | 35314.5i | −0.649618 | − | 1.12517i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13495.6 | − | 23375.0i | −0.428694 | − | 0.742521i | 0.568063 | − | 0.822985i | \(-0.307693\pi\) |
−0.996757 | + | 0.0804645i | \(0.974360\pi\) | |||||||
\(998\) | −39373.6 | + | 68197.1i | −1.24885 | + | 2.16307i | ||||
\(999\) | 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 | 117.4.g.f.100.1 | yes | 16 | |
3.2 | odd | 2 | inner | 117.4.g.f.100.8 | yes | 16 | |
13.3 | even | 3 | inner | 117.4.g.f.55.1 | ✓ | 16 | |
13.4 | even | 6 | 1521.4.a.bd.1.1 | 8 | |||
13.9 | even | 3 | 1521.4.a.bc.1.8 | 8 | |||
39.17 | odd | 6 | 1521.4.a.bd.1.8 | 8 | |||
39.29 | odd | 6 | inner | 117.4.g.f.55.8 | yes | 16 | |
39.35 | odd | 6 | 1521.4.a.bc.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.g.f.55.1 | ✓ | 16 | 13.3 | even | 3 | inner | |
117.4.g.f.55.8 | yes | 16 | 39.29 | odd | 6 | inner | |
117.4.g.f.100.1 | yes | 16 | 1.1 | even | 1 | trivial | |
117.4.g.f.100.8 | yes | 16 | 3.2 | odd | 2 | inner | |
1521.4.a.bc.1.1 | 8 | 39.35 | odd | 6 | |||
1521.4.a.bc.1.8 | 8 | 13.9 | even | 3 | |||
1521.4.a.bd.1.1 | 8 | 13.4 | even | 6 | |||
1521.4.a.bd.1.8 | 8 | 39.17 | odd | 6 |