Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,4,Mod(11,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.b (of order \(2\), degree \(1\), 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: | \(7.08022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.5 | ||
Character | \(\chi\) | \(=\) | 120.11 |
Dual form | 120.4.b.a.11.6 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40201 | − | 1.49343i | −0.849240 | − | 0.528007i | ||||
\(3\) | −1.49310 | − | 4.97701i | −0.287346 | − | 0.957827i | ||||
\(4\) | 3.53933 | + | 7.17448i | 0.442417 | + | 0.896810i | ||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −3.84639 | + | 14.1847i | −0.261714 | + | 0.965146i | ||||
\(7\) | 14.5956i | 0.788089i | 0.919091 | + | 0.394044i | \(0.128924\pi\) | ||||
−0.919091 | + | 0.394044i | \(0.871076\pi\) | |||||||
\(8\) | 2.21306 | − | 22.5189i | 0.0978042 | − | 0.995206i | ||||
\(9\) | −22.5413 | + | 14.8623i | −0.834864 | + | 0.550456i | ||||
\(10\) | −12.0101 | − | 7.46715i | −0.379792 | − | 0.236132i | ||||
\(11\) | 58.0556i | 1.59131i | 0.605750 | + | 0.795655i | \(0.292873\pi\) | ||||
−0.605750 | + | 0.795655i | \(0.707127\pi\) | |||||||
\(12\) | 30.4229 | − | 28.3275i | 0.731861 | − | 0.681453i | ||||
\(13\) | 43.9441i | 0.937532i | 0.883322 | + | 0.468766i | \(0.155301\pi\) | ||||
−0.883322 | + | 0.468766i | \(0.844699\pi\) | |||||||
\(14\) | 21.7975 | − | 35.0588i | 0.416117 | − | 0.669276i | ||||
\(15\) | −7.46548 | − | 24.8851i | −0.128505 | − | 0.428353i | ||||
\(16\) | −38.9462 | + | 50.7857i | −0.608535 | + | 0.793527i | ||||
\(17\) | − | 78.8045i | − | 1.12429i | −0.827039 | − | 0.562144i | \(-0.809977\pi\) | ||
0.827039 | − | 0.562144i | \(-0.190023\pi\) | |||||||
\(18\) | 76.3404 | − | 2.03556i | 0.999645 | − | 0.0266548i | ||||
\(19\) | 103.306 | 1.24737 | 0.623687 | − | 0.781674i | \(-0.285634\pi\) | ||||
0.623687 | + | 0.781674i | \(0.285634\pi\) | |||||||
\(20\) | 17.6967 | + | 35.8724i | 0.197855 | + | 0.401065i | ||||
\(21\) | 72.6425 | − | 21.7926i | 0.754852 | − | 0.226454i | ||||
\(22\) | 86.7019 | − | 139.450i | 0.840223 | − | 1.35140i | ||||
\(23\) | 163.945 | 1.48630 | 0.743151 | − | 0.669123i | \(-0.233330\pi\) | ||||
0.743151 | + | 0.669123i | \(0.233330\pi\) | |||||||
\(24\) | −115.381 | + | 22.6085i | −0.981338 | + | 0.192289i | ||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 65.6275 | − | 105.554i | 0.495024 | − | 0.796189i | ||||
\(27\) | 107.626 | + | 89.9977i | 0.767137 | + | 0.641484i | ||||
\(28\) | −104.716 | + | 51.6587i | −0.706766 | + | 0.348664i | ||||
\(29\) | −247.735 | −1.58632 | −0.793160 | − | 0.609013i | \(-0.791566\pi\) | ||||
−0.793160 | + | 0.609013i | \(0.791566\pi\) | |||||||
\(30\) | −19.2319 | + | 70.9234i | −0.117042 | + | 0.431626i | ||||
\(31\) | 153.271i | 0.888009i | 0.896025 | + | 0.444004i | \(0.146443\pi\) | ||||
−0.896025 | + | 0.444004i | \(0.853557\pi\) | |||||||
\(32\) | 169.394 | − | 63.8245i | 0.935780 | − | 0.352584i | ||||
\(33\) | 288.943 | − | 86.6825i | 1.52420 | − | 0.457257i | ||||
\(34\) | −117.689 | + | 189.289i | −0.593632 | + | 0.954790i | ||||
\(35\) | 72.9780i | 0.352444i | ||||||||
\(36\) | −186.411 | − | 109.120i | −0.863012 | − | 0.505183i | ||||
\(37\) | 153.638i | 0.682646i | 0.939946 | + | 0.341323i | \(0.110875\pi\) | ||||
−0.939946 | + | 0.341323i | \(0.889125\pi\) | |||||||
\(38\) | −248.143 | − | 154.281i | −1.05932 | − | 0.658623i | ||||
\(39\) | 218.711 | − | 65.6128i | 0.897993 | − | 0.269396i | ||||
\(40\) | 11.0653 | − | 112.595i | 0.0437394 | − | 0.445070i | ||||
\(41\) | − | 27.0586i | − | 0.103070i | −0.998671 | − | 0.0515348i | \(-0.983589\pi\) | ||
0.998671 | − | 0.0515348i | \(-0.0164113\pi\) | |||||||
\(42\) | −207.034 | − | 56.1404i | −0.760620 | − | 0.206253i | ||||
\(43\) | 246.934 | 0.875746 | 0.437873 | − | 0.899037i | \(-0.355732\pi\) | ||||
0.437873 | + | 0.899037i | \(0.355732\pi\) | |||||||
\(44\) | −416.518 | + | 205.478i | −1.42710 | + | 0.704022i | ||||
\(45\) | −112.707 | + | 74.3116i | −0.373363 | + | 0.246171i | ||||
\(46\) | −393.799 | − | 244.841i | −1.26223 | − | 0.784779i | ||||
\(47\) | −411.901 | −1.27834 | −0.639170 | − | 0.769065i | \(-0.720722\pi\) | ||||
−0.639170 | + | 0.769065i | \(0.720722\pi\) | |||||||
\(48\) | 310.912 | + | 118.008i | 0.934922 | + | 0.354854i | ||||
\(49\) | 129.968 | 0.378916 | ||||||||
\(50\) | −60.0503 | − | 37.3358i | −0.169848 | − | 0.105601i | ||||
\(51\) | −392.211 | + | 117.663i | −1.07687 | + | 0.323060i | ||||
\(52\) | −315.276 | + | 155.533i | −0.840788 | + | 0.414780i | ||||
\(53\) | −80.1737 | −0.207787 | −0.103893 | − | 0.994588i | \(-0.533130\pi\) | ||||
−0.103893 | + | 0.994588i | \(0.533130\pi\) | |||||||
\(54\) | −124.115 | − | 376.908i | −0.312775 | − | 0.949827i | ||||
\(55\) | 290.278i | 0.711656i | ||||||||
\(56\) | 328.678 | + | 32.3009i | 0.784310 | + | 0.0770784i | ||||
\(57\) | −154.246 | − | 514.157i | −0.358428 | − | 1.19477i | ||||
\(58\) | 595.063 | + | 369.975i | 1.34717 | + | 0.837589i | ||||
\(59\) | 513.612i | 1.13333i | 0.823947 | + | 0.566666i | \(0.191767\pi\) | ||||
−0.823947 | + | 0.566666i | \(0.808233\pi\) | |||||||
\(60\) | 152.115 | − | 141.637i | 0.327298 | − | 0.304755i | ||||
\(61\) | 27.0460i | 0.0567686i | 0.999597 | + | 0.0283843i | \(0.00903622\pi\) | ||||
−0.999597 | + | 0.0283843i | \(0.990964\pi\) | |||||||
\(62\) | 228.899 | − | 368.159i | 0.468875 | − | 0.754133i | ||||
\(63\) | −216.924 | − | 329.004i | −0.433808 | − | 0.657947i | ||||
\(64\) | −502.205 | − | 99.6713i | −0.980869 | − | 0.194671i | ||||
\(65\) | 219.721i | 0.419277i | ||||||||
\(66\) | −823.500 | − | 223.304i | −1.53585 | − | 0.416467i | ||||
\(67\) | −453.089 | −0.826173 | −0.413087 | − | 0.910692i | \(-0.635549\pi\) | ||||
−0.413087 | + | 0.910692i | \(0.635549\pi\) | |||||||
\(68\) | 565.381 | − | 278.915i | 1.00827 | − | 0.497404i | ||||
\(69\) | −244.786 | − | 815.958i | −0.427084 | − | 1.42362i | ||||
\(70\) | 108.988 | − | 175.294i | 0.186093 | − | 0.299309i | ||||
\(71\) | 446.258 | 0.745930 | 0.372965 | − | 0.927845i | \(-0.378341\pi\) | ||||
0.372965 | + | 0.927845i | \(0.378341\pi\) | |||||||
\(72\) | 284.798 | + | 540.498i | 0.466164 | + | 0.884698i | ||||
\(73\) | 524.821 | 0.841447 | 0.420724 | − | 0.907189i | \(-0.361776\pi\) | ||||
0.420724 | + | 0.907189i | \(0.361776\pi\) | |||||||
\(74\) | 229.447 | − | 369.040i | 0.360442 | − | 0.579730i | ||||
\(75\) | −37.3274 | − | 124.425i | −0.0574693 | − | 0.191565i | ||||
\(76\) | 365.636 | + | 741.169i | 0.551859 | + | 1.11866i | ||||
\(77\) | −847.356 | −1.25409 | ||||||||
\(78\) | −623.334 | − | 169.026i | −0.904855 | − | 0.245365i | ||||
\(79\) | − | 93.4259i | − | 0.133054i | −0.997785 | − | 0.0665268i | \(-0.978808\pi\) | ||
0.997785 | − | 0.0665268i | \(-0.0211918\pi\) | |||||||
\(80\) | −194.731 | + | 253.929i | −0.272145 | + | 0.354876i | ||||
\(81\) | 287.223 | − | 670.033i | 0.393996 | − | 0.919112i | ||||
\(82\) | −40.4102 | + | 64.9952i | −0.0544215 | + | 0.0875308i | ||||
\(83\) | 1249.95i | 1.65301i | 0.562933 | + | 0.826503i | \(0.309673\pi\) | ||||
−0.562933 | + | 0.826503i | \(0.690327\pi\) | |||||||
\(84\) | 413.457 | + | 444.041i | 0.537046 | + | 0.576772i | ||||
\(85\) | − | 394.023i | − | 0.502797i | ||||||
\(86\) | −593.139 | − | 368.779i | −0.743719 | − | 0.462400i | ||||
\(87\) | 369.892 | + | 1232.98i | 0.455823 | + | 1.51942i | ||||
\(88\) | 1307.35 | + | 128.480i | 1.58368 | + | 0.155637i | ||||
\(89\) | 267.674i | 0.318803i | 0.987214 | + | 0.159401i | \(0.0509564\pi\) | ||||
−0.987214 | + | 0.159401i | \(0.949044\pi\) | |||||||
\(90\) | 381.702 | − | 10.1778i | 0.447055 | − | 0.0119204i | ||||
\(91\) | −641.391 | −0.738858 | ||||||||
\(92\) | 580.257 | + | 1176.22i | 0.657565 | + | 1.33293i | ||||
\(93\) | 762.832 | − | 228.848i | 0.850559 | − | 0.255166i | ||||
\(94\) | 989.392 | + | 615.146i | 1.08562 | + | 0.674973i | ||||
\(95\) | 516.532 | 0.557843 | ||||||||
\(96\) | −570.577 | − | 747.782i | −0.606607 | − | 0.795002i | ||||
\(97\) | −897.223 | −0.939167 | −0.469584 | − | 0.882888i | \(-0.655596\pi\) | ||||
−0.469584 | + | 0.882888i | \(0.655596\pi\) | |||||||
\(98\) | −312.185 | − | 194.098i | −0.321791 | − | 0.200070i | ||||
\(99\) | −862.840 | − | 1308.65i | −0.875946 | − | 1.32853i | ||||
\(100\) | 88.4833 | + | 179.362i | 0.0884833 | + | 0.179362i | ||||
\(101\) | 1086.03 | 1.06994 | 0.534972 | − | 0.844870i | \(-0.320322\pi\) | ||||
0.534972 | + | 0.844870i | \(0.320322\pi\) | |||||||
\(102\) | 1117.82 | + | 303.113i | 1.08510 | + | 0.294241i | ||||
\(103\) | − | 602.598i | − | 0.576464i | −0.957561 | − | 0.288232i | \(-0.906933\pi\) | ||
0.957561 | − | 0.288232i | \(-0.0930674\pi\) | |||||||
\(104\) | 989.575 | + | 97.2509i | 0.933037 | + | 0.0916945i | ||||
\(105\) | 363.213 | − | 108.963i | 0.337580 | − | 0.101273i | ||||
\(106\) | 192.578 | + | 119.734i | 0.176461 | + | 0.109713i | ||||
\(107\) | − | 209.243i | − | 0.189050i | −0.995522 | − | 0.0945249i | \(-0.969867\pi\) | ||
0.995522 | − | 0.0945249i | \(-0.0301332\pi\) | |||||||
\(108\) | −264.761 | + | 1090.69i | −0.235895 | + | 0.971779i | ||||
\(109\) | 866.438i | 0.761374i | 0.924704 | + | 0.380687i | \(0.124312\pi\) | ||||
−0.924704 | + | 0.380687i | \(0.875688\pi\) | |||||||
\(110\) | 433.510 | − | 697.251i | 0.375759 | − | 0.604366i | ||||
\(111\) | 764.657 | − | 229.396i | 0.653856 | − | 0.196156i | ||||
\(112\) | −741.249 | − | 568.444i | −0.625370 | − | 0.479580i | ||||
\(113\) | − | 1455.92i | − | 1.21205i | −0.795445 | − | 0.606026i | \(-0.792763\pi\) | ||
0.795445 | − | 0.606026i | \(-0.207237\pi\) | |||||||
\(114\) | −397.356 | + | 1465.37i | −0.326455 | + | 1.20390i | ||||
\(115\) | 819.727 | 0.664695 | ||||||||
\(116\) | −876.818 | − | 1777.37i | −0.701814 | − | 1.42263i | ||||
\(117\) | −653.112 | − | 990.560i | −0.516070 | − | 0.782712i | ||||
\(118\) | 767.044 | − | 1233.70i | 0.598408 | − | 0.962471i | ||||
\(119\) | 1150.20 | 0.886039 | ||||||||
\(120\) | −576.907 | + | 113.043i | −0.438868 | + | 0.0859944i | ||||
\(121\) | −2039.45 | −1.53227 | ||||||||
\(122\) | 40.3913 | − | 64.9648i | 0.0299742 | − | 0.0482102i | ||||
\(123\) | −134.671 | + | 40.4011i | −0.0987228 | + | 0.0296167i | ||||
\(124\) | −1099.64 | + | 542.477i | −0.796375 | + | 0.392870i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 29.7103 | + | 1114.23i | 0.0210064 | + | 0.787809i | ||||
\(127\) | − | 1710.12i | − | 1.19487i | −0.801917 | − | 0.597435i | \(-0.796186\pi\) | ||
0.801917 | − | 0.597435i | \(-0.203814\pi\) | |||||||
\(128\) | 1057.45 | + | 989.420i | 0.730205 | + | 0.683228i | ||||
\(129\) | −368.696 | − | 1228.99i | −0.251642 | − | 0.838813i | ||||
\(130\) | 328.138 | − | 527.772i | 0.221381 | − | 0.356067i | ||||
\(131\) | 994.011i | 0.662955i | 0.943463 | + | 0.331478i | \(0.107547\pi\) | ||||
−0.943463 | + | 0.331478i | \(0.892453\pi\) | |||||||
\(132\) | 1644.57 | + | 1766.22i | 1.08440 | + | 1.16462i | ||||
\(133\) | 1507.82i | 0.983041i | ||||||||
\(134\) | 1088.33 | + | 676.656i | 0.701619 | + | 0.436225i | ||||
\(135\) | 538.131 | + | 449.988i | 0.343074 | + | 0.286880i | ||||
\(136\) | −1774.59 | − | 174.399i | −1.11890 | − | 0.109960i | ||||
\(137\) | − | 218.135i | − | 0.136033i | −0.997684 | − | 0.0680166i | \(-0.978333\pi\) | ||
0.997684 | − | 0.0680166i | \(-0.0216671\pi\) | |||||||
\(138\) | −630.597 | + | 2325.51i | −0.388986 | + | 1.43450i | ||||
\(139\) | 871.961 | 0.532078 | 0.266039 | − | 0.963962i | \(-0.414285\pi\) | ||||
0.266039 | + | 0.963962i | \(0.414285\pi\) | |||||||
\(140\) | −523.579 | + | 258.294i | −0.316075 | + | 0.155927i | ||||
\(141\) | 615.008 | + | 2050.04i | 0.367326 | + | 1.22443i | ||||
\(142\) | −1071.92 | − | 666.455i | −0.633474 | − | 0.393857i | ||||
\(143\) | −2551.20 | −1.49190 | ||||||||
\(144\) | 123.107 | − | 1723.61i | 0.0712424 | − | 0.997459i | ||||
\(145\) | −1238.68 | −0.709424 | ||||||||
\(146\) | −1260.63 | − | 783.783i | −0.714590 | − | 0.444290i | ||||
\(147\) | −194.055 | − | 646.854i | −0.108880 | − | 0.362936i | ||||
\(148\) | −1102.27 | + | 543.775i | −0.612203 | + | 0.302014i | ||||
\(149\) | −2649.54 | −1.45677 | −0.728385 | − | 0.685168i | \(-0.759729\pi\) | ||||
−0.728385 | + | 0.685168i | \(0.759729\pi\) | |||||||
\(150\) | −96.1597 | + | 354.617i | −0.0523427 | + | 0.193029i | ||||
\(151\) | − | 717.633i | − | 0.386756i | −0.981124 | − | 0.193378i | \(-0.938056\pi\) | ||
0.981124 | − | 0.193378i | \(-0.0619443\pi\) | |||||||
\(152\) | 228.623 | − | 2326.35i | 0.121998 | − | 1.24139i | ||||
\(153\) | 1171.22 | + | 1776.36i | 0.618871 | + | 0.938628i | ||||
\(154\) | 2035.36 | + | 1265.47i | 1.06503 | + | 0.662171i | ||||
\(155\) | 766.355i | 0.397130i | ||||||||
\(156\) | 1244.83 | + | 1336.91i | 0.638884 | + | 0.686143i | ||||
\(157\) | − | 3251.75i | − | 1.65298i | −0.562951 | − | 0.826490i | \(-0.690334\pi\) | ||
0.562951 | − | 0.826490i | \(-0.309666\pi\) | |||||||
\(158\) | −139.525 | + | 224.410i | −0.0702533 | + | 0.112994i | ||||
\(159\) | 119.707 | + | 399.026i | 0.0597068 | + | 0.199024i | ||||
\(160\) | 846.972 | − | 319.122i | 0.418494 | − | 0.157680i | ||||
\(161\) | 2392.88i | 1.17134i | ||||||||
\(162\) | −1690.56 | + | 1180.48i | −0.819895 | + | 0.572514i | ||||
\(163\) | −180.616 | −0.0867912 | −0.0433956 | − | 0.999058i | \(-0.513818\pi\) | ||||
−0.0433956 | + | 0.999058i | \(0.513818\pi\) | |||||||
\(164\) | 194.132 | − | 95.7696i | 0.0924338 | − | 0.0455997i | ||||
\(165\) | 1444.72 | − | 433.413i | 0.681643 | − | 0.204492i | ||||
\(166\) | 1866.71 | − | 3002.39i | 0.872799 | − | 1.40380i | ||||
\(167\) | −3583.90 | −1.66066 | −0.830332 | − | 0.557269i | \(-0.811849\pi\) | ||||
−0.830332 | + | 0.557269i | \(0.811849\pi\) | |||||||
\(168\) | −329.985 | − | 1684.06i | −0.151541 | − | 0.773382i | ||||
\(169\) | 265.912 | 0.121034 | ||||||||
\(170\) | −588.445 | + | 946.447i | −0.265480 | + | 0.426995i | ||||
\(171\) | −2328.66 | + | 1535.37i | −1.04139 | + | 0.686625i | ||||
\(172\) | 873.982 | + | 1771.62i | 0.387445 | + | 0.785378i | ||||
\(173\) | −529.974 | −0.232909 | −0.116454 | − | 0.993196i | \(-0.537153\pi\) | ||||
−0.116454 | + | 0.993196i | \(0.537153\pi\) | |||||||
\(174\) | 952.886 | − | 3514.05i | 0.415161 | − | 1.53103i | ||||
\(175\) | 364.890i | 0.157618i | ||||||||
\(176\) | −2948.39 | − | 2261.05i | −1.26275 | − | 0.968368i | ||||
\(177\) | 2556.26 | − | 766.872i | 1.08554 | − | 0.325659i | ||||
\(178\) | 399.753 | − | 642.957i | 0.168330 | − | 0.270740i | ||||
\(179\) | − | 2272.25i | − | 0.948805i | −0.880308 | − | 0.474402i | \(-0.842664\pi\) | ||
0.880308 | − | 0.474402i | \(-0.157336\pi\) | |||||||
\(180\) | −932.053 | − | 545.598i | −0.385951 | − | 0.225925i | ||||
\(181\) | 768.299i | 0.315509i | 0.987478 | + | 0.157755i | \(0.0504255\pi\) | ||||
−0.987478 | + | 0.157755i | \(0.949574\pi\) | |||||||
\(182\) | 1540.63 | + | 957.873i | 0.627468 | + | 0.390123i | ||||
\(183\) | 134.608 | − | 40.3823i | 0.0543745 | − | 0.0163123i | ||||
\(184\) | 362.820 | − | 3691.87i | 0.145367 | − | 1.47918i | ||||
\(185\) | 768.189i | 0.305288i | ||||||||
\(186\) | −2174.10 | − | 589.539i | −0.857058 | − | 0.232404i | ||||
\(187\) | 4575.04 | 1.78909 | ||||||||
\(188\) | −1457.86 | − | 2955.18i | −0.565559 | − | 1.14643i | ||||
\(189\) | −1313.57 | + | 1570.87i | −0.505546 | + | 0.604572i | ||||
\(190\) | −1240.72 | − | 771.404i | −0.473742 | − | 0.294545i | ||||
\(191\) | 1338.21 | 0.506962 | 0.253481 | − | 0.967340i | \(-0.418424\pi\) | ||||
0.253481 | + | 0.967340i | \(0.418424\pi\) | |||||||
\(192\) | 253.774 | + | 2648.30i | 0.0953883 | + | 0.995440i | ||||
\(193\) | −858.809 | −0.320303 | −0.160151 | − | 0.987092i | \(-0.551198\pi\) | ||||
−0.160151 | + | 0.987092i | \(0.551198\pi\) | |||||||
\(194\) | 2155.14 | + | 1339.94i | 0.797578 | + | 0.495887i | ||||
\(195\) | 1093.55 | − | 328.064i | 0.401595 | − | 0.120478i | ||||
\(196\) | 460.001 | + | 932.454i | 0.167639 | + | 0.339816i | ||||
\(197\) | 3040.41 | 1.09960 | 0.549798 | − | 0.835298i | \(-0.314705\pi\) | ||||
0.549798 | + | 0.835298i | \(0.314705\pi\) | |||||||
\(198\) | 118.176 | + | 4431.99i | 0.0424161 | + | 1.59075i | ||||
\(199\) | − | 1636.95i | − | 0.583118i | −0.956553 | − | 0.291559i | \(-0.905826\pi\) | ||
0.956553 | − | 0.291559i | \(-0.0941740\pi\) | |||||||
\(200\) | 55.3264 | − | 562.973i | 0.0195608 | − | 0.199041i | ||||
\(201\) | 676.505 | + | 2255.03i | 0.237398 | + | 0.791331i | ||||
\(202\) | −2608.67 | − | 1621.92i | −0.908639 | − | 0.564938i | ||||
\(203\) | − | 3615.85i | − | 1.25016i | ||||||
\(204\) | −2232.33 | − | 2397.46i | −0.766150 | − | 0.822823i | ||||
\(205\) | − | 135.293i | − | 0.0460941i | ||||||
\(206\) | −899.938 | + | 1447.45i | −0.304377 | + | 0.489556i | ||||
\(207\) | −3695.55 | + | 2436.61i | −1.24086 | + | 0.818144i | ||||
\(208\) | −2231.74 | − | 1711.46i | −0.743957 | − | 0.570521i | ||||
\(209\) | 5997.51i | 1.98496i | ||||||||
\(210\) | −1035.17 | − | 280.702i | −0.340160 | − | 0.0922394i | ||||
\(211\) | 6036.05 | 1.96938 | 0.984689 | − | 0.174322i | \(-0.0557734\pi\) | ||||
0.984689 | + | 0.174322i | \(0.0557734\pi\) | |||||||
\(212\) | −283.762 | − | 575.205i | −0.0919284 | − | 0.186345i | ||||
\(213\) | −666.305 | − | 2221.03i | −0.214340 | − | 0.714472i | ||||
\(214\) | −312.490 | + | 502.605i | −0.0998196 | + | 0.160549i | ||||
\(215\) | 1234.67 | 0.391646 | ||||||||
\(216\) | 2264.83 | − | 2224.46i | 0.713437 | − | 0.700719i | ||||
\(217\) | −2237.08 | −0.699830 | ||||||||
\(218\) | 1293.97 | − | 2081.20i | 0.402011 | − | 0.646589i | ||||
\(219\) | −783.608 | − | 2612.04i | −0.241787 | − | 0.805961i | ||||
\(220\) | −2082.59 | + | 1027.39i | −0.638220 | + | 0.314848i | ||||
\(221\) | 3463.00 | 1.05406 | ||||||||
\(222\) | −2179.30 | − | 590.950i | −0.658853 | − | 0.178658i | ||||
\(223\) | − | 1524.61i | − | 0.457828i | −0.973447 | − | 0.228914i | \(-0.926483\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735175\pi\) | |||||||
\(224\) | 931.557 | + | 2472.41i | 0.277867 | + | 0.737478i | ||||
\(225\) | −563.533 | + | 371.558i | −0.166973 | + | 0.110091i | ||||
\(226\) | −2174.32 | + | 3497.15i | −0.639972 | + | 1.02932i | ||||
\(227\) | − | 472.571i | − | 0.138174i | −0.997611 | − | 0.0690872i | \(-0.977991\pi\) | ||
0.997611 | − | 0.0690872i | \(-0.0220087\pi\) | |||||||
\(228\) | 3142.88 | − | 2926.41i | 0.912905 | − | 0.850027i | ||||
\(229\) | 3068.70i | 0.885526i | 0.896639 | + | 0.442763i | \(0.146002\pi\) | ||||
−0.896639 | + | 0.442763i | \(0.853998\pi\) | |||||||
\(230\) | −1968.99 | − | 1224.20i | −0.564485 | − | 0.350964i | ||||
\(231\) | 1265.18 | + | 4217.30i | 0.360359 | + | 1.20120i | ||||
\(232\) | −548.252 | + | 5578.73i | −0.155149 | + | 1.57871i | ||||
\(233\) | − | 141.515i | − | 0.0397895i | −0.999802 | − | 0.0198947i | \(-0.993667\pi\) | ||
0.999802 | − | 0.0198947i | \(-0.00633311\pi\) | |||||||
\(234\) | 89.4511 | + | 3354.71i | 0.0249898 | + | 0.937199i | ||||
\(235\) | −2059.51 | −0.571691 | ||||||||
\(236\) | −3684.90 | + | 1817.85i | −1.01638 | + | 0.501405i | ||||
\(237\) | −464.982 | + | 139.494i | −0.127442 | + | 0.0382325i | ||||
\(238\) | −2762.79 | − | 1717.74i | −0.752460 | − | 0.467835i | ||||
\(239\) | −3911.18 | −1.05855 | −0.529274 | − | 0.848451i | \(-0.677536\pi\) | ||||
−0.529274 | + | 0.848451i | \(0.677536\pi\) | |||||||
\(240\) | 1554.56 | + | 590.040i | 0.418110 | + | 0.158696i | ||||
\(241\) | 4114.37 | 1.09971 | 0.549855 | − | 0.835260i | \(-0.314683\pi\) | ||||
0.549855 | + | 0.835260i | \(0.314683\pi\) | |||||||
\(242\) | 4898.79 | + | 3045.78i | 1.30126 | + | 0.809049i | ||||
\(243\) | −3763.61 | − | 429.092i | −0.993563 | − | 0.113277i | ||||
\(244\) | −194.041 | + | 95.7248i | −0.0509106 | + | 0.0251154i | ||||
\(245\) | 649.841 | 0.169456 | ||||||||
\(246\) | 383.818 | + | 104.078i | 0.0994771 | + | 0.0269747i | ||||
\(247\) | 4539.71i | 1.16945i | ||||||||
\(248\) | 3451.50 | + | 339.197i | 0.883751 | + | 0.0868510i | ||||
\(249\) | 6221.00 | − | 1866.29i | 1.58329 | − | 0.474985i | ||||
\(250\) | −300.252 | − | 186.679i | −0.0759583 | − | 0.0472264i | ||||
\(251\) | − | 5279.91i | − | 1.32775i | −0.747844 | − | 0.663874i | \(-0.768911\pi\) | ||
0.747844 | − | 0.663874i | \(-0.231089\pi\) | |||||||
\(252\) | 1592.67 | − | 2720.78i | 0.398129 | − | 0.680130i | ||||
\(253\) | 9517.94i | 2.36517i | ||||||||
\(254\) | −2553.94 | + | 4107.73i | −0.630901 | + | 1.01473i | ||||
\(255\) | −1961.06 | + | 588.313i | −0.481592 | + | 0.144477i | ||||
\(256\) | −1062.38 | − | 3955.83i | −0.259370 | − | 0.965778i | ||||
\(257\) | − | 2278.07i | − | 0.552928i | −0.961024 | − | 0.276464i | \(-0.910837\pi\) | ||
0.961024 | − | 0.276464i | \(-0.0891626\pi\) | |||||||
\(258\) | −949.804 | + | 3502.68i | −0.229195 | + | 0.845223i | ||||
\(259\) | −2242.44 | −0.537985 | ||||||||
\(260\) | −1576.38 | + | 777.665i | −0.376012 | + | 0.185495i | ||||
\(261\) | 5584.28 | − | 3681.92i | 1.32436 | − | 0.873199i | ||||
\(262\) | 1484.49 | − | 2387.63i | 0.350045 | − | 0.563008i | ||||
\(263\) | 6017.98 | 1.41097 | 0.705484 | − | 0.708726i | \(-0.250730\pi\) | ||||
0.705484 | + | 0.708726i | \(0.250730\pi\) | |||||||
\(264\) | −1312.55 | − | 6698.53i | −0.305992 | − | 1.56161i | ||||
\(265\) | −400.869 | −0.0929252 | ||||||||
\(266\) | 2251.82 | − | 3621.80i | 0.519053 | − | 0.834838i | ||||
\(267\) | 1332.22 | − | 399.663i | 0.305358 | − | 0.0916067i | ||||
\(268\) | −1603.63 | − | 3250.67i | −0.365513 | − | 0.740920i | ||||
\(269\) | 3008.84 | 0.681979 | 0.340989 | − | 0.940067i | \(-0.389238\pi\) | ||||
0.340989 | + | 0.940067i | \(0.389238\pi\) | |||||||
\(270\) | −620.573 | − | 1884.54i | −0.139877 | − | 0.424776i | ||||
\(271\) | − | 2907.26i | − | 0.651673i | −0.945426 | − | 0.325836i | \(-0.894354\pi\) | ||
0.945426 | − | 0.325836i | \(-0.105646\pi\) | |||||||
\(272\) | 4002.14 | + | 3069.14i | 0.892153 | + | 0.684169i | ||||
\(273\) | 957.659 | + | 3192.21i | 0.212308 | + | 0.707698i | ||||
\(274\) | −325.770 | + | 523.963i | −0.0718265 | + | 0.115525i | ||||
\(275\) | 1451.39i | 0.318262i | ||||||||
\(276\) | 4987.69 | − | 4644.16i | 1.08777 | − | 1.01285i | ||||
\(277\) | − | 7971.57i | − | 1.72912i | −0.502532 | − | 0.864558i | \(-0.667598\pi\) | ||
0.502532 | − | 0.864558i | \(-0.332402\pi\) | |||||||
\(278\) | −2094.46 | − | 1302.21i | −0.451861 | − | 0.280941i | ||||
\(279\) | −2277.96 | − | 3454.93i | −0.488810 | − | 0.741367i | ||||
\(280\) | 1643.39 | + | 161.505i | 0.350754 | + | 0.0344705i | ||||
\(281\) | − | 913.436i | − | 0.193918i | −0.995288 | − | 0.0969591i | \(-0.969088\pi\) | ||
0.995288 | − | 0.0969591i | \(-0.0309116\pi\) | |||||||
\(282\) | 1584.33 | − | 5842.69i | 0.334559 | − | 1.23378i | ||||
\(283\) | −1838.40 | −0.386154 | −0.193077 | − | 0.981184i | \(-0.561847\pi\) | ||||
−0.193077 | + | 0.981184i | \(0.561847\pi\) | |||||||
\(284\) | 1579.45 | + | 3201.67i | 0.330012 | + | 0.668957i | ||||
\(285\) | −771.231 | − | 2570.79i | −0.160294 | − | 0.534317i | ||||
\(286\) | 6128.02 | + | 3810.04i | 1.26698 | + | 0.787736i | ||||
\(287\) | 394.937 | 0.0812279 | ||||||||
\(288\) | −2869.79 | + | 3956.28i | −0.587168 | + | 0.809465i | ||||
\(289\) | −1297.15 | −0.264024 | ||||||||
\(290\) | 2975.32 | + | 1849.88i | 0.602471 | + | 0.374581i | ||||
\(291\) | 1339.64 | + | 4465.49i | 0.269866 | + | 0.899559i | ||||
\(292\) | 1857.52 | + | 3765.32i | 0.372270 | + | 0.754618i | ||||
\(293\) | 742.598 | 0.148065 | 0.0740324 | − | 0.997256i | \(-0.476413\pi\) | ||||
0.0740324 | + | 0.997256i | \(0.476413\pi\) | |||||||
\(294\) | −499.908 | + | 1843.56i | −0.0991675 | + | 0.365709i | ||||
\(295\) | 2568.06i | 0.506842i | ||||||||
\(296\) | 3459.76 | + | 340.009i | 0.679373 | + | 0.0667656i | ||||
\(297\) | −5224.87 | + | 6248.31i | −1.02080 | + | 1.22075i | ||||
\(298\) | 6364.23 | + | 3956.90i | 1.23715 | + | 0.769185i | ||||
\(299\) | 7204.44i | 1.39346i | ||||||||
\(300\) | 760.573 | − | 708.187i | 0.146372 | − | 0.136291i | ||||
\(301\) | 3604.15i | 0.690166i | ||||||||
\(302\) | −1071.73 | + | 1723.76i | −0.204210 | + | 0.328448i | ||||
\(303\) | −1621.55 | − | 5405.20i | −0.307445 | − | 1.02482i | ||||
\(304\) | −4023.40 | + | 5246.49i | −0.759071 | + | 0.989825i | ||||
\(305\) | 135.230i | 0.0253877i | ||||||||
\(306\) | −160.412 | − | 6015.97i | −0.0299677 | − | 1.12389i | ||||
\(307\) | 8317.65 | 1.54630 | 0.773149 | − | 0.634225i | \(-0.218681\pi\) | ||||
0.773149 | + | 0.634225i | \(0.218681\pi\) | |||||||
\(308\) | −2999.08 | − | 6079.34i | −0.554832 | − | 1.12468i | ||||
\(309\) | −2999.14 | + | 899.736i | −0.552152 | + | 0.165645i | ||||
\(310\) | 1144.50 | − | 1840.79i | 0.209687 | − | 0.337258i | ||||
\(311\) | 3016.33 | 0.549970 | 0.274985 | − | 0.961449i | \(-0.411327\pi\) | ||||
0.274985 | + | 0.961449i | \(0.411327\pi\) | |||||||
\(312\) | −993.511 | − | 5070.33i | −0.180277 | − | 0.920036i | ||||
\(313\) | −9400.48 | −1.69759 | −0.848797 | − | 0.528720i | \(-0.822672\pi\) | ||||
−0.848797 | + | 0.528720i | \(0.822672\pi\) | |||||||
\(314\) | −4856.26 | + | 7810.74i | −0.872785 | + | 1.40378i | ||||
\(315\) | −1084.62 | − | 1645.02i | −0.194005 | − | 0.294243i | ||||
\(316\) | 670.282 | − | 330.665i | 0.119324 | − | 0.0588651i | ||||
\(317\) | −5801.88 | −1.02797 | −0.513985 | − | 0.857799i | \(-0.671831\pi\) | ||||
−0.513985 | + | 0.857799i | \(0.671831\pi\) | |||||||
\(318\) | 308.379 | − | 1137.24i | 0.0543807 | − | 0.200545i | ||||
\(319\) | − | 14382.4i | − | 2.52433i | ||||||
\(320\) | −2511.02 | − | 498.357i | −0.438658 | − | 0.0870593i | ||||
\(321\) | −1041.41 | + | 312.420i | −0.181077 | + | 0.0543228i | ||||
\(322\) | 3573.60 | − | 5747.73i | 0.618475 | − | 0.994747i | ||||
\(323\) | − | 8141.01i | − | 1.40241i | ||||||
\(324\) | 5823.71 | − | 310.792i | 0.998579 | − | 0.0532907i | ||||
\(325\) | 1098.60i | 0.187506i | ||||||||
\(326\) | 433.843 | + | 269.738i | 0.0737066 | + | 0.0458264i | ||||
\(327\) | 4312.28 | − | 1293.68i | 0.729264 | − | 0.218778i | ||||
\(328\) | −609.332 | − | 59.8823i | −0.102575 | − | 0.0100806i | ||||
\(329\) | − | 6011.95i | − | 1.00745i | ||||||
\(330\) | −4117.50 | − | 1116.52i | −0.686851 | − | 0.186250i | ||||
\(331\) | −5997.26 | −0.995888 | −0.497944 | − | 0.867209i | \(-0.665912\pi\) | ||||
−0.497944 | + | 0.867209i | \(0.665912\pi\) | |||||||
\(332\) | −8967.71 | + | 4423.98i | −1.48243 | + | 0.731317i | ||||
\(333\) | −2283.41 | − | 3463.20i | −0.375766 | − | 0.569916i | ||||
\(334\) | 8608.58 | + | 5352.31i | 1.41030 | + | 0.876842i | ||||
\(335\) | −2265.44 | −0.369476 | ||||||||
\(336\) | −1722.40 | + | 4537.95i | −0.279656 | + | 0.736801i | ||||
\(337\) | −8013.40 | −1.29531 | −0.647653 | − | 0.761936i | \(-0.724249\pi\) | ||||
−0.647653 | + | 0.761936i | \(0.724249\pi\) | |||||||
\(338\) | −638.724 | − | 397.121i | −0.102787 | − | 0.0639069i | ||||
\(339\) | −7246.16 | + | 2173.83i | −1.16094 | + | 0.348279i | ||||
\(340\) | 2826.91 | − | 1394.58i | 0.450913 | − | 0.222446i | ||||
\(341\) | −8898.23 | −1.41310 | ||||||||
\(342\) | 7886.45 | − | 210.287i | 1.24693 | − | 0.0332486i | ||||
\(343\) | 6903.26i | 1.08671i | ||||||||
\(344\) | 546.479 | − | 5560.69i | 0.0856516 | − | 0.871548i | ||||
\(345\) | −1223.93 | − | 4079.79i | −0.190998 | − | 0.636663i | ||||
\(346\) | 1273.00 | + | 791.479i | 0.197795 | + | 0.122977i | ||||
\(347\) | 249.070i | 0.0385325i | 0.999814 | + | 0.0192662i | \(0.00613301\pi\) | ||||
−0.999814 | + | 0.0192662i | \(0.993867\pi\) | |||||||
\(348\) | −7536.83 | + | 7017.72i | −1.16097 | + | 1.08100i | ||||
\(349\) | 8681.38i | 1.33153i | 0.746162 | + | 0.665764i | \(0.231894\pi\) | ||||
−0.746162 | + | 0.665764i | \(0.768106\pi\) | |||||||
\(350\) | 544.938 | − | 876.471i | 0.0832233 | − | 0.133855i | ||||
\(351\) | −3954.87 | + | 4729.55i | −0.601411 | + | 0.719215i | ||||
\(352\) | 3705.37 | + | 9834.28i | 0.561070 | + | 1.48912i | ||||
\(353\) | − | 6747.03i | − | 1.01730i | −0.860972 | − | 0.508652i | \(-0.830144\pi\) | ||
0.860972 | − | 0.508652i | \(-0.169856\pi\) | |||||||
\(354\) | −7285.43 | − | 1975.55i | −1.09383 | − | 0.296609i | ||||
\(355\) | 2231.29 | 0.333590 | ||||||||
\(356\) | −1920.42 | + | 947.389i | −0.285905 | + | 0.141044i | ||||
\(357\) | −1717.36 | − | 5724.56i | −0.254600 | − | 0.848672i | ||||
\(358\) | −3393.45 | + | 5457.98i | −0.500976 | + | 0.805763i | ||||
\(359\) | 1559.98 | 0.229339 | 0.114669 | − | 0.993404i | \(-0.463419\pi\) | ||||
0.114669 | + | 0.993404i | \(0.463419\pi\) | |||||||
\(360\) | 1423.99 | + | 2702.49i | 0.208475 | + | 0.395649i | ||||
\(361\) | 3813.21 | 0.555942 | ||||||||
\(362\) | 1147.40 | − | 1845.46i | 0.166591 | − | 0.267943i | ||||
\(363\) | 3045.09 | + | 10150.4i | 0.440292 | + | 1.46765i | ||||
\(364\) | −2270.10 | − | 4601.65i | −0.326883 | − | 0.662615i | ||||
\(365\) | 2624.10 | 0.376307 | ||||||||
\(366\) | −383.639 | − | 104.029i | −0.0547900 | − | 0.0148571i | ||||
\(367\) | 13670.5i | 1.94440i | 0.234144 | + | 0.972202i | \(0.424771\pi\) | ||||
−0.234144 | + | 0.972202i | \(0.575229\pi\) | |||||||
\(368\) | −6385.06 | + | 8326.08i | −0.904467 | + | 1.17942i | ||||
\(369\) | 402.154 | + | 609.938i | 0.0567352 | + | 0.0860491i | ||||
\(370\) | 1147.24 | − | 1845.20i | 0.161195 | − | 0.259263i | ||||
\(371\) | − | 1170.18i | − | 0.163755i | ||||||
\(372\) | 4341.78 | + | 4662.95i | 0.605137 | + | 0.649899i | ||||
\(373\) | − | 10962.3i | − | 1.52173i | −0.648909 | − | 0.760866i | \(-0.724774\pi\) | ||
0.648909 | − | 0.760866i | \(-0.275226\pi\) | |||||||
\(374\) | −10989.3 | − | 6832.50i | −1.51937 | − | 0.944653i | ||||
\(375\) | −186.637 | − | 622.127i | −0.0257010 | − | 0.0856706i | ||||
\(376\) | −911.561 | + | 9275.58i | −0.125027 | + | 1.27221i | ||||
\(377\) | − | 10886.5i | − | 1.48723i | ||||||
\(378\) | 5501.20 | − | 1811.53i | 0.748548 | − | 0.246494i | ||||
\(379\) | −221.741 | −0.0300529 | −0.0150265 | − | 0.999887i | \(-0.504783\pi\) | ||||
−0.0150265 | + | 0.999887i | \(0.504783\pi\) | |||||||
\(380\) | 1828.18 | + | 3705.85i | 0.246799 | + | 0.500279i | ||||
\(381\) | −8511.29 | + | 2553.37i | −1.14448 | + | 0.343342i | ||||
\(382\) | −3214.41 | − | 1998.53i | −0.430532 | − | 0.267680i | ||||
\(383\) | 567.176 | 0.0756694 | 0.0378347 | − | 0.999284i | \(-0.487954\pi\) | ||||
0.0378347 | + | 0.999284i | \(0.487954\pi\) | |||||||
\(384\) | 3345.48 | − | 6740.24i | 0.444592 | − | 0.895733i | ||||
\(385\) | −4236.78 | −0.560848 | ||||||||
\(386\) | 2062.87 | + | 1282.57i | 0.272014 | + | 0.169122i | ||||
\(387\) | −5566.22 | + | 3670.01i | −0.731129 | + | 0.482060i | ||||
\(388\) | −3175.57 | − | 6437.11i | −0.415503 | − | 0.842254i | ||||
\(389\) | 10143.0 | 1.32204 | 0.661019 | − | 0.750369i | \(-0.270124\pi\) | ||||
0.661019 | + | 0.750369i | \(0.270124\pi\) | |||||||
\(390\) | −3116.67 | − | 845.131i | −0.404663 | − | 0.109730i | ||||
\(391\) | − | 12919.6i | − | 1.67103i | ||||||
\(392\) | 287.627 | − | 2926.75i | 0.0370596 | − | 0.377100i | ||||
\(393\) | 4947.21 | − | 1484.15i | 0.634996 | − | 0.190498i | ||||
\(394\) | −7303.11 | − | 4540.64i | −0.933821 | − | 0.580595i | ||||
\(395\) | − | 467.129i | − | 0.0595034i | ||||||
\(396\) | 6335.00 | − | 10822.2i | 0.803903 | − | 1.37332i | ||||
\(397\) | 4548.29i | 0.574992i | 0.957782 | + | 0.287496i | \(0.0928228\pi\) | ||||
−0.957782 | + | 0.287496i | \(0.907177\pi\) | |||||||
\(398\) | −2444.67 | + | 3931.98i | −0.307891 | + | 0.495207i | ||||
\(399\) | 7504.44 | − | 2251.32i | 0.941583 | − | 0.282473i | ||||
\(400\) | −973.656 | + | 1269.64i | −0.121707 | + | 0.158705i | ||||
\(401\) | 141.751i | 0.0176526i | 0.999961 | + | 0.00882632i | \(0.00280954\pi\) | ||||
−0.999961 | + | 0.00882632i | \(0.997190\pi\) | |||||||
\(402\) | 1742.75 | − | 6426.92i | 0.216221 | − | 0.797377i | ||||
\(403\) | −6735.36 | −0.832537 | ||||||||
\(404\) | 3843.83 | + | 7791.72i | 0.473361 | + | 0.959536i | ||||
\(405\) | 1436.12 | − | 3350.16i | 0.176201 | − | 0.411039i | ||||
\(406\) | −5400.01 | + | 8685.31i | −0.660094 | + | 1.06169i | ||||
\(407\) | −8919.53 | −1.08630 | ||||||||
\(408\) | 1781.65 | + | 9092.57i | 0.216189 | + | 1.10331i | ||||
\(409\) | 10767.4 | 1.30175 | 0.650873 | − | 0.759186i | \(-0.274403\pi\) | ||||
0.650873 | + | 0.759186i | \(0.274403\pi\) | |||||||
\(410\) | −202.051 | + | 324.976i | −0.0243380 | + | 0.0391449i | ||||
\(411\) | −1085.66 | + | 325.697i | −0.130296 | + | 0.0390886i | ||||
\(412\) | 4323.33 | − | 2132.80i | 0.516978 | − | 0.255037i | ||||
\(413\) | −7496.48 | −0.893167 | ||||||||
\(414\) | 12515.7 | − | 333.721i | 1.48577 | − | 0.0396172i | ||||
\(415\) | 6249.73i | 0.739246i | ||||||||
\(416\) | 2804.71 | + | 7443.89i | 0.330559 | + | 0.877324i | ||||
\(417\) | −1301.92 | − | 4339.76i | −0.152891 | − | 0.509638i | ||||
\(418\) | 8956.86 | − | 14406.1i | 1.04807 | − | 1.68571i | ||||
\(419\) | 1276.55i | 0.148840i | 0.997227 | + | 0.0744198i | \(0.0237105\pi\) | ||||
−0.997227 | + | 0.0744198i | \(0.976290\pi\) | |||||||
\(420\) | 2067.28 | + | 2220.20i | 0.240174 | + | 0.257940i | ||||
\(421\) | − | 14268.0i | − | 1.65173i | −0.563869 | − | 0.825864i | \(-0.690688\pi\) | ||
0.563869 | − | 0.825864i | \(-0.309312\pi\) | |||||||
\(422\) | −14498.7 | − | 9014.41i | −1.67247 | − | 1.03985i | ||||
\(423\) | 9284.81 | − | 6121.81i | 1.06724 | − | 0.703670i | ||||
\(424\) | −177.429 | + | 1805.43i | −0.0203224 | + | 0.206791i | ||||
\(425\) | − | 1970.11i | − | 0.224858i | ||||||
\(426\) | −1716.48 | + | 6330.03i | −0.195220 | + | 0.719931i | ||||
\(427\) | −394.753 | −0.0447387 | ||||||||
\(428\) | 1501.21 | − | 740.582i | 0.169542 | − | 0.0836388i | ||||
\(429\) | 3809.19 | + | 12697.4i | 0.428693 | + | 1.42899i | ||||
\(430\) | −2965.69 | − | 1843.89i | −0.332601 | − | 0.206792i | ||||
\(431\) | 15402.6 | 1.72139 | 0.860695 | − | 0.509120i | \(-0.170029\pi\) | ||||
0.860695 | + | 0.509120i | \(0.170029\pi\) | |||||||
\(432\) | −8762.24 | + | 1960.81i | −0.975864 | + | 0.218378i | ||||
\(433\) | 9528.41 | 1.05752 | 0.528760 | − | 0.848771i | \(-0.322657\pi\) | ||||
0.528760 | + | 0.848771i | \(0.322657\pi\) | |||||||
\(434\) | 5373.50 | + | 3340.93i | 0.594323 | + | 0.369515i | ||||
\(435\) | 1849.46 | + | 6164.91i | 0.203850 | + | 0.679505i | ||||
\(436\) | −6216.24 | + | 3066.61i | −0.682807 | + | 0.336844i | ||||
\(437\) | 16936.6 | 1.85398 | ||||||||
\(438\) | −2018.66 | + | 7444.42i | −0.220218 | + | 0.812119i | ||||
\(439\) | − | 2811.08i | − | 0.305616i | −0.988256 | − | 0.152808i | \(-0.951168\pi\) | ||
0.988256 | − | 0.152808i | \(-0.0488317\pi\) | |||||||
\(440\) | 6536.75 | + | 642.401i | 0.708244 | + | 0.0696029i | ||||
\(441\) | −2929.66 | + | 1931.63i | −0.316344 | + | 0.208577i | ||||
\(442\) | −8318.16 | − | 5171.74i | −0.895146 | − | 0.556549i | ||||
\(443\) | 4207.40i | 0.451241i | 0.974215 | + | 0.225620i | \(0.0724409\pi\) | ||||
−0.974215 | + | 0.225620i | \(0.927559\pi\) | |||||||
\(444\) | 4352.17 | + | 4674.11i | 0.465191 | + | 0.499602i | ||||
\(445\) | 1338.37i | 0.142573i | ||||||||
\(446\) | −2276.90 | + | 3662.14i | −0.241737 | + | 0.388806i | ||||
\(447\) | 3956.02 | + | 13186.8i | 0.418598 | + | 1.39533i | ||||
\(448\) | 1454.76 | − | 7329.98i | 0.153418 | − | 0.773012i | ||||
\(449\) | − | 5099.95i | − | 0.536040i | −0.963413 | − | 0.268020i | \(-0.913631\pi\) | ||
0.963413 | − | 0.268020i | \(-0.0863693\pi\) | |||||||
\(450\) | 1908.51 | − | 50.8891i | 0.199929 | − | 0.00533097i | ||||
\(451\) | 1570.91 | 0.164016 | ||||||||
\(452\) | 10445.5 | − | 5153.00i | 1.08698 | − | 0.536232i | ||||
\(453\) | −3571.67 | + | 1071.49i | −0.370445 | + | 0.111133i | ||||
\(454\) | −705.751 | + | 1135.12i | −0.0729571 | + | 0.117343i | ||||
\(455\) | −3206.96 | −0.330427 | ||||||||
\(456\) | −11919.6 | + | 2335.60i | −1.22410 | + | 0.239857i | ||||
\(457\) | 8660.31 | 0.886460 | 0.443230 | − | 0.896408i | \(-0.353833\pi\) | ||||
0.443230 | + | 0.896408i | \(0.353833\pi\) | |||||||
\(458\) | 4582.89 | − | 7371.06i | 0.467564 | − | 0.752024i | ||||
\(459\) | 7092.22 | − | 8481.44i | 0.721213 | − | 0.862483i | ||||
\(460\) | 2901.29 | + | 5881.11i | 0.294072 | + | 0.596105i | ||||
\(461\) | −11202.5 | −1.13179 | −0.565893 | − | 0.824479i | \(-0.691468\pi\) | ||||
−0.565893 | + | 0.824479i | \(0.691468\pi\) | |||||||
\(462\) | 3259.26 | − | 12019.5i | 0.328213 | − | 1.21038i | ||||
\(463\) | 2975.15i | 0.298633i | 0.988789 | + | 0.149316i | \(0.0477073\pi\) | ||||
−0.988789 | + | 0.149316i | \(0.952293\pi\) | |||||||
\(464\) | 9648.36 | − | 12581.4i | 0.965331 | − | 1.25879i | ||||
\(465\) | 3814.16 | − | 1144.24i | 0.380381 | − | 0.114114i | ||||
\(466\) | −211.342 | + | 339.920i | −0.0210091 | + | 0.0337908i | ||||
\(467\) | 13454.8i | 1.33322i | 0.745406 | + | 0.666611i | \(0.232256\pi\) | ||||
−0.745406 | + | 0.666611i | \(0.767744\pi\) | |||||||
\(468\) | 4795.17 | − | 8191.65i | 0.473625 | − | 0.809101i | ||||
\(469\) | − | 6613.11i | − | 0.651098i | ||||||
\(470\) | 4946.96 | + | 3075.73i | 0.485503 | + | 0.301857i | ||||
\(471\) | −16184.0 | + | 4855.17i | −1.58327 | + | 0.474978i | ||||
\(472\) | 11566.0 | + | 1136.65i | 1.12790 | + | 0.110845i | ||||
\(473\) | 14335.9i | 1.39358i | ||||||||
\(474\) | 1325.22 | + | 359.352i | 0.128416 | + | 0.0348219i | ||||
\(475\) | 2582.66 | 0.249475 | ||||||||
\(476\) | 4070.94 | + | 8252.08i | 0.391998 | + | 0.794608i | ||||
\(477\) | 1807.22 | − | 1191.57i | 0.173474 | − | 0.114378i | ||||
\(478\) | 9394.70 | + | 5841.07i | 0.898961 | + | 0.558921i | ||||
\(479\) | 11128.5 | 1.06153 | 0.530765 | − | 0.847519i | \(-0.321905\pi\) | ||||
0.530765 | + | 0.847519i | \(0.321905\pi\) | |||||||
\(480\) | −2852.89 | − | 3738.91i | −0.271283 | − | 0.355536i | ||||
\(481\) | −6751.48 | −0.640002 | ||||||||
\(482\) | −9882.78 | − | 6144.53i | −0.933918 | − | 0.580655i | ||||
\(483\) | 11909.4 | − | 3572.80i | 1.12194 | − | 0.336580i | ||||
\(484\) | −7218.29 | − | 14632.0i | −0.677901 | − | 1.37415i | ||||
\(485\) | −4486.12 | −0.420008 | ||||||||
\(486\) | 8399.43 | + | 6651.38i | 0.783963 | + | 0.620808i | ||||
\(487\) | 2167.65i | 0.201695i | 0.994902 | + | 0.100848i | \(0.0321555\pi\) | ||||
−0.994902 | + | 0.100848i | \(0.967845\pi\) | |||||||
\(488\) | 609.047 | + | 59.8543i | 0.0564964 | + | 0.00555221i | ||||
\(489\) | 269.677 | + | 898.930i | 0.0249391 | + | 0.0831309i | ||||
\(490\) | −1560.93 | − | 970.492i | −0.143909 | − | 0.0894742i | ||||
\(491\) | 4706.59i | 0.432597i | 0.976327 | + | 0.216299i | \(0.0693985\pi\) | ||||
−0.976327 | + | 0.216299i | \(0.930601\pi\) | |||||||
\(492\) | −766.504 | − | 823.203i | −0.0702371 | − | 0.0754326i | ||||
\(493\) | 19522.7i | 1.78348i | ||||||||
\(494\) | 6779.74 | − | 10904.4i | 0.617480 | − | 0.993146i | ||||
\(495\) | −4314.20 | − | 6543.25i | −0.391735 | − | 0.594136i | ||||
\(496\) | −7783.98 | − | 5969.33i | −0.704659 | − | 0.540385i | ||||
\(497\) | 6513.40i | 0.587859i | ||||||||
\(498\) | −17730.1 | − | 4807.78i | −1.59539 | − | 0.432614i | ||||
\(499\) | −21594.1 | −1.93724 | −0.968620 | − | 0.248546i | \(-0.920047\pi\) | ||||
−0.968620 | + | 0.248546i | \(0.920047\pi\) | |||||||
\(500\) | 442.417 | + | 896.810i | 0.0395709 | + | 0.0802131i | ||||
\(501\) | 5351.11 | + | 17837.1i | 0.477186 | + | 1.59063i | ||||
\(502\) | −7885.17 | + | 12682.4i | −0.701061 | + | 1.12758i | ||||
\(503\) | −3910.09 | −0.346605 | −0.173303 | − | 0.984869i | \(-0.555444\pi\) | ||||
−0.173303 | + | 0.984869i | \(0.555444\pi\) | |||||||
\(504\) | −7888.90 | + | 4156.80i | −0.697221 | + | 0.367378i | ||||
\(505\) | 5430.17 | 0.478494 | ||||||||
\(506\) | 14214.4 | − | 22862.2i | 1.24883 | − | 2.00860i | ||||
\(507\) | −397.032 | − | 1323.45i | −0.0347787 | − | 0.115930i | ||||
\(508\) | 12269.2 | − | 6052.68i | 1.07157 | − | 0.528631i | ||||
\(509\) | −18113.4 | −1.57733 | −0.788667 | − | 0.614821i | \(-0.789228\pi\) | ||||
−0.788667 | + | 0.614821i | \(0.789228\pi\) | |||||||
\(510\) | 5589.09 | + | 1515.56i | 0.485272 | + | 0.131589i | ||||
\(511\) | 7660.08i | 0.663135i | ||||||||
\(512\) | −3355.90 | + | 11088.5i | −0.289670 | + | 0.957126i | ||||
\(513\) | 11118.5 | + | 9297.33i | 0.956906 | + | 0.800170i | ||||
\(514\) | −3402.15 | + | 5471.97i | −0.291950 | + | 0.469568i | ||||
\(515\) | − | 3012.99i | − | 0.257802i | ||||||
\(516\) | 7512.45 | − | 6995.02i | 0.640925 | − | 0.596780i | ||||
\(517\) | − | 23913.2i | − | 2.03424i | ||||||
\(518\) | 5386.36 | + | 3348.92i | 0.456879 | + | 0.284060i | ||||
\(519\) | 791.302 | + | 2637.69i | 0.0669254 | + | 0.223086i | ||||
\(520\) | 4947.88 | + | 486.254i | 0.417267 | + | 0.0410070i | ||||
\(521\) | − | 16469.0i | − | 1.38487i | −0.721480 | − | 0.692436i | \(-0.756538\pi\) | ||
0.721480 | − | 0.692436i | \(-0.243462\pi\) | |||||||
\(522\) | −18912.2 | + | 504.281i | −1.58576 | + | 0.0422831i | ||||
\(523\) | 380.198 | 0.0317876 | 0.0158938 | − | 0.999874i | \(-0.494941\pi\) | ||||
0.0158938 | + | 0.999874i | \(0.494941\pi\) | |||||||
\(524\) | −7131.51 | + | 3518.14i | −0.594545 | + | 0.293303i | ||||
\(525\) | 1816.06 | − | 544.816i | 0.150970 | − | 0.0452909i | ||||
\(526\) | −14455.3 | − | 8987.43i | −1.19825 | − | 0.745001i | ||||
\(527\) | 12078.4 | 0.998378 | ||||||||
\(528\) | −6851.03 | + | 18050.2i | −0.564683 | + | 1.48775i | ||||
\(529\) | 14711.1 | 1.20910 | ||||||||
\(530\) | 962.892 | + | 598.669i | 0.0789157 | + | 0.0490652i | ||||
\(531\) | −7633.47 | − | 11577.5i | −0.623850 | − | 0.946179i | ||||
\(532\) | −10817.8 | + | 5336.67i | −0.881601 | + | 0.434914i | ||||
\(533\) | 1189.07 | 0.0966310 | ||||||||
\(534\) | −3796.88 | − | 1029.58i | −0.307691 | − | 0.0834349i | ||||
\(535\) | − | 1046.22i | − | 0.0845456i | ||||||
\(536\) | −1002.71 | + | 10203.1i | −0.0808032 | + | 0.822212i | ||||
\(537\) | −11309.0 | + | 3392.69i | −0.908791 | + | 0.272636i | ||||
\(538\) | −7227.28 | − | 4493.49i | −0.579164 | − | 0.360090i | ||||
\(539\) | 7545.38i | 0.602973i | ||||||||
\(540\) | −1323.80 | + | 5453.47i | −0.105495 | + | 0.434593i | ||||
\(541\) | − | 5985.34i | − | 0.475656i | −0.971307 | − | 0.237828i | \(-0.923565\pi\) | ||
0.971307 | − | 0.237828i | \(-0.0764354\pi\) | |||||||
\(542\) | −4341.79 | + | 6983.27i | −0.344088 | + | 0.553427i | ||||
\(543\) | 3823.83 | − | 1147.14i | 0.302203 | − | 0.0906605i | ||||
\(544\) | −5029.66 | − | 13349.0i | −0.396406 | − | 1.05209i | ||||
\(545\) | 4332.19i | 0.340497i | ||||||||
\(546\) | 2467.04 | − | 9097.94i | 0.193369 | − | 0.713106i | ||||
\(547\) | 6496.76 | 0.507827 | 0.253914 | − | 0.967227i | \(-0.418282\pi\) | ||||
0.253914 | + | 0.967227i | \(0.418282\pi\) | |||||||
\(548\) | 1565.01 | − | 772.053i | 0.121996 | − | 0.0601833i | ||||
\(549\) | −401.966 | − | 609.653i | −0.0312486 | − | 0.0473941i | ||||
\(550\) | 2167.55 | − | 3486.26i | 0.168045 | − | 0.270281i | ||||
\(551\) | −25592.6 | −1.97873 | ||||||||
\(552\) | −18916.2 | + | 3706.56i | −1.45857 | + | 0.285800i | ||||
\(553\) | 1363.61 | 0.104858 | ||||||||
\(554\) | −11905.0 | + | 19147.8i | −0.912986 | + | 1.46843i | ||||
\(555\) | 3823.29 | − | 1146.98i | 0.292413 | − | 0.0877235i | ||||
\(556\) | 3086.16 | + | 6255.87i | 0.235400 | + | 0.477172i | ||||
\(557\) | 22280.1 | 1.69486 | 0.847431 | − | 0.530905i | \(-0.178148\pi\) | ||||
0.847431 | + | 0.530905i | \(0.178148\pi\) | |||||||
\(558\) | 311.993 | + | 11700.8i | 0.0236697 | + | 0.887693i | ||||
\(559\) | 10851.3i | 0.821040i | ||||||||
\(560\) | −3706.24 | − | 2842.22i | −0.279674 | − | 0.214475i | ||||
\(561\) | −6830.97 | − | 22770.0i | −0.514089 | − | 1.71364i | ||||
\(562\) | −1364.15 | + | 2194.08i | −0.102390 | + | 0.164683i | ||||
\(563\) | 10370.5i | 0.776317i | 0.921593 | + | 0.388158i | \(0.126889\pi\) | ||||
−0.921593 | + | 0.388158i | \(0.873111\pi\) | |||||||
\(564\) | −12531.2 | + | 11668.1i | −0.935568 | + | 0.871129i | ||||
\(565\) | − | 7279.62i | − | 0.542046i | ||||||
\(566\) | 4415.86 | + | 2745.52i | 0.327937 | + | 0.203892i | ||||
\(567\) | 9779.53 | + | 4192.20i | 0.724342 | + | 0.310504i | ||||
\(568\) | 987.593 | − | 10049.2i | 0.0729551 | − | 0.742354i | ||||
\(569\) | 15791.9i | 1.16350i | 0.813368 | + | 0.581750i | \(0.197632\pi\) | ||||
−0.813368 | + | 0.581750i | \(0.802368\pi\) | |||||||
\(570\) | −1986.78 | + | 7326.84i | −0.145995 | + | 0.538399i | ||||
\(571\) | 14459.2 | 1.05972 | 0.529858 | − | 0.848087i | \(-0.322245\pi\) | ||||
0.529858 | + | 0.848087i | \(0.322245\pi\) | |||||||
\(572\) | −9029.56 | − | 18303.5i | −0.660043 | − | 1.33795i | ||||
\(573\) | −1998.08 | − | 6660.31i | −0.145674 | − | 0.485582i | ||||
\(574\) | −948.645 | − | 589.811i | −0.0689820 | − | 0.0428889i | ||||
\(575\) | 4098.63 | 0.297261 | ||||||||
\(576\) | 12801.7 | − | 5217.20i | 0.926050 | − | 0.377402i | ||||
\(577\) | −1179.27 | −0.0850845 | −0.0425423 | − | 0.999095i | \(-0.513546\pi\) | ||||
−0.0425423 | + | 0.999095i | \(0.513546\pi\) | |||||||
\(578\) | 3115.77 | + | 1937.20i | 0.224220 | + | 0.139407i | ||||
\(579\) | 1282.28 | + | 4274.30i | 0.0920378 | + | 0.306795i | ||||
\(580\) | −4384.09 | − | 8886.85i | −0.313861 | − | 0.636218i | ||||
\(581\) | −18243.7 | −1.30271 | ||||||||
\(582\) | 3451.07 | − | 12726.8i | 0.245793 | − | 0.906433i | ||||
\(583\) | − | 4654.53i | − | 0.330654i | ||||||
\(584\) | 1161.46 | − | 11818.4i | 0.0822971 | − | 0.837413i | ||||
\(585\) | −3265.56 | − | 4952.80i | −0.230794 | − | 0.350039i | ||||
\(586\) | −1783.73 | − | 1109.02i | −0.125743 | − | 0.0781793i | ||||
\(587\) | 3761.00i | 0.264451i | 0.991220 | + | 0.132226i | \(0.0422124\pi\) | ||||
−0.991220 | + | 0.132226i | \(0.957788\pi\) | |||||||
\(588\) | 3954.01 | − | 3681.67i | 0.277314 | − | 0.258214i | ||||
\(589\) | 15833.9i | 1.10768i | ||||||||
\(590\) | 3835.22 | − | 6168.52i | 0.267616 | − | 0.430430i | ||||
\(591\) | −4539.63 | − | 15132.2i | −0.315965 | − | 1.05322i | ||||
\(592\) | −7802.61 | − | 5983.61i | −0.541698 | − | 0.415414i | ||||
\(593\) | − | 7912.85i | − | 0.547962i | −0.961735 | − | 0.273981i | \(-0.911659\pi\) | ||
0.961735 | − | 0.273981i | \(-0.0883406\pi\) | |||||||
\(594\) | 21881.6 | − | 7205.54i | 1.51147 | − | 0.497722i | ||||
\(595\) | 5751.00 | 0.396249 | ||||||||
\(596\) | −9377.60 | − | 19009.1i | −0.644499 | − | 1.30645i | ||||
\(597\) | −8147.14 | + | 2444.13i | −0.558526 | + | 0.167557i | ||||
\(598\) | 10759.3 | − | 17305.2i | 0.735755 | − | 1.18338i | ||||
\(599\) | −13018.4 | −0.888012 | −0.444006 | − | 0.896024i | \(-0.646443\pi\) | ||||
−0.444006 | + | 0.896024i | \(0.646443\pi\) | |||||||
\(600\) | −2884.53 | + | 565.213i | −0.196268 | + | 0.0384578i | ||||
\(601\) | 6784.23 | 0.460457 | 0.230228 | − | 0.973137i | \(-0.426053\pi\) | ||||
0.230228 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(602\) | 5382.55 | − | 8657.22i | 0.364412 | − | 0.586116i | ||||
\(603\) | 10213.2 | − | 6733.95i | 0.689742 | − | 0.454772i | ||||
\(604\) | 5148.64 | − | 2539.94i | 0.346846 | − | 0.171107i | ||||
\(605\) | −10197.2 | −0.685251 | ||||||||
\(606\) | −4177.31 | + | 15405.0i | −0.280019 | + | 1.03265i | ||||
\(607\) | − | 16589.8i | − | 1.10932i | −0.832077 | − | 0.554661i | \(-0.812848\pi\) | ||
0.832077 | − | 0.554661i | \(-0.187152\pi\) | |||||||
\(608\) | 17499.5 | − | 6593.48i | 1.16727 | − | 0.439804i | ||||
\(609\) | −17996.1 | + | 5398.80i | −1.19744 | + | 0.359229i | ||||
\(610\) | 201.957 | − | 324.824i | 0.0134049 | − | 0.0215602i | ||||
\(611\) | − | 18100.7i | − | 1.19848i | ||||||
\(612\) | −8599.12 | + | 14690.0i | −0.567972 | + | 0.970274i | ||||
\(613\) | 16207.7i | 1.06790i | 0.845516 | + | 0.533950i | \(0.179293\pi\) | ||||
−0.845516 | + | 0.533950i | \(0.820707\pi\) | |||||||
\(614\) | −19979.1 | − | 12421.8i | −1.31318 | − | 0.816456i | ||||
\(615\) | −673.356 | + | 202.006i | −0.0441502 | + | 0.0132450i | ||||
\(616\) | −1875.25 | + | 19081.6i | −0.122656 | + | 1.24808i | ||||
\(617\) | 17461.9i | 1.13936i | 0.821865 | + | 0.569682i | \(0.192934\pi\) | ||||
−0.821865 | + | 0.569682i | \(0.807066\pi\) | |||||||
\(618\) | 8547.66 | + | 2317.83i | 0.556371 | + | 0.150868i | ||||
\(619\) | 5700.52 | 0.370151 | 0.185075 | − | 0.982724i | \(-0.440747\pi\) | ||||
0.185075 | + | 0.982724i | \(0.440747\pi\) | |||||||
\(620\) | −5498.19 | + | 2712.38i | −0.356150 | + | 0.175697i | ||||
\(621\) | 17644.8 | + | 14754.7i | 1.14020 | + | 0.953439i | ||||
\(622\) | −7245.27 | − | 4504.68i | −0.467056 | − | 0.290388i | ||||
\(623\) | −3906.87 | −0.251245 | ||||||||
\(624\) | −5185.76 | + | 13662.7i | −0.332687 | + | 0.876519i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 22580.1 | + | 14039.0i | 1.44166 | + | 0.896342i | ||||
\(627\) | 29849.7 | − | 8954.86i | 1.90125 | − | 0.570371i | ||||
\(628\) | 23329.6 | − | 11509.0i | 1.48241 | − | 0.731306i | ||||
\(629\) | 12107.3 | 0.767491 | ||||||||
\(630\) | 148.551 | + | 5571.17i | 0.00939434 | + | 0.352319i | ||||
\(631\) | − | 8186.74i | − | 0.516496i | −0.966079 | − | 0.258248i | \(-0.916855\pi\) | ||
0.966079 | − | 0.258248i | \(-0.0831452\pi\) | |||||||
\(632\) | −2103.85 | − | 206.757i | −0.132416 | − | 0.0130132i | ||||
\(633\) | −9012.39 | − | 30041.5i | −0.565893 | − | 1.88632i | ||||
\(634\) | 13936.2 | + | 8664.71i | 0.872992 | + | 0.542775i | ||||
\(635\) | − | 8550.60i | − | 0.534363i | ||||||
\(636\) | −2439.12 | + | 2271.12i | −0.152071 | + | 0.141597i | ||||
\(637\) | 5711.34i | 0.355246i | ||||||||
\(638\) | −21479.1 | + | 34546.7i | −1.33286 | + | 2.14376i | ||||
\(639\) | −10059.2 | + | 6632.42i | −0.622750 | + | 0.410602i | ||||
\(640\) | 5287.25 | + | 4947.10i | 0.326558 | + | 0.305549i | ||||
\(641\) | 27307.8i | 1.68267i | 0.540510 | + | 0.841337i | \(0.318231\pi\) | ||||
−0.540510 | + | 0.841337i | \(0.681769\pi\) | |||||||
\(642\) | 2968.05 | + | 804.831i | 0.182461 | + | 0.0494769i | ||||
\(643\) | −11306.2 | −0.693427 | −0.346714 | − | 0.937971i | \(-0.612702\pi\) | ||||
−0.346714 | + | 0.937971i | \(0.612702\pi\) | |||||||
\(644\) | −17167.7 | + | 8469.21i | −1.05047 | + | 0.518220i | ||||
\(645\) | −1843.48 | − | 6144.97i | −0.112538 | − | 0.375129i | ||||
\(646\) | −12158.0 | + | 19554.8i | −0.740482 | + | 1.19098i | ||||
\(647\) | −4998.32 | −0.303716 | −0.151858 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151858 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(648\) | −14452.8 | − | 7950.78i | −0.876171 | − | 0.482000i | ||||
\(649\) | −29818.1 | −1.80348 | ||||||||
\(650\) | 1640.69 | − | 2638.86i | 0.0990047 | − | 0.159238i | ||||
\(651\) | 3340.18 | + | 11134.0i | 0.201094 | + | 0.670316i | ||||
\(652\) | −639.262 | − | 1295.83i | −0.0383979 | − | 0.0778352i | ||||
\(653\) | 23047.6 | 1.38120 | 0.690599 | − | 0.723238i | \(-0.257347\pi\) | ||||
0.690599 | + | 0.723238i | \(0.257347\pi\) | |||||||
\(654\) | −12290.2 | − | 3332.66i | −0.734837 | − | 0.199262i | ||||
\(655\) | 4970.06i | 0.296483i | ||||||||
\(656\) | 1374.19 | + | 1053.83i | 0.0817885 | + | 0.0627214i | ||||
\(657\) | −11830.2 | + | 7800.05i | −0.702494 | + | 0.463180i | ||||
\(658\) | −8978.43 | + | 14440.8i | −0.531939 | + | 0.855563i | ||||
\(659\) | − | 18811.4i | − | 1.11197i | −0.831191 | − | 0.555986i | \(-0.812341\pi\) | ||
0.831191 | − | 0.555986i | \(-0.187659\pi\) | |||||||
\(660\) | 8222.84 | + | 8831.10i | 0.484960 | + | 0.520833i | ||||
\(661\) | − | 30855.3i | − | 1.81563i | −0.419370 | − | 0.907815i | \(-0.637749\pi\) | ||
0.419370 | − | 0.907815i | \(-0.362251\pi\) | |||||||
\(662\) | 14405.5 | + | 8956.48i | 0.845748 | + | 0.525836i | ||||
\(663\) | −5170.58 | − | 17235.4i | −0.302879 | − | 1.00960i | ||||
\(664\) | 28147.5 | + | 2766.20i | 1.64508 | + | 0.161671i | ||||
\(665\) | 7539.10i | 0.439629i | ||||||||
\(666\) | 312.740 | + | 11728.8i | 0.0181958 | + | 0.682403i | ||||
\(667\) | −40615.0 | −2.35775 | ||||||||
\(668\) | −12684.6 | − | 25712.6i | −0.734705 | − | 1.48930i | ||||
\(669\) | −7588.02 | + | 2276.39i | −0.438520 | + | 0.131555i | ||||
\(670\) | 5441.63 | + | 3383.28i | 0.313774 | + | 0.195086i | ||||
\(671\) | −1570.17 | −0.0903365 | ||||||||
\(672\) | 10914.3 | − | 8327.92i | 0.626532 | − | 0.478060i | ||||
\(673\) | 12293.3 | 0.704117 | 0.352058 | − | 0.935978i | \(-0.385482\pi\) | ||||
0.352058 | + | 0.935978i | \(0.385482\pi\) | |||||||
\(674\) | 19248.3 | + | 11967.5i | 1.10002 | + | 0.683931i | ||||
\(675\) | 2690.66 | + | 2249.94i | 0.153427 | + | 0.128297i | ||||
\(676\) | 941.152 | + | 1907.78i | 0.0535475 | + | 0.108545i | ||||
\(677\) | −296.947 | −0.0168576 | −0.00842881 | − | 0.999964i | \(-0.502683\pi\) | ||||
−0.00842881 | + | 0.999964i | \(0.502683\pi\) | |||||||
\(678\) | 20651.8 | + | 5600.05i | 1.16981 | + | 0.317210i | ||||
\(679\) | − | 13095.5i | − | 0.740147i | ||||||
\(680\) | −8872.97 | − | 871.994i | −0.500386 | − | 0.0491757i | ||||
\(681\) | −2351.99 | + | 705.593i | −0.132347 | + | 0.0397039i | ||||
\(682\) | 21373.7 | + | 13288.9i | 1.20006 | + | 0.746126i | ||||
\(683\) | − | 6305.85i | − | 0.353275i | −0.984276 | − | 0.176638i | \(-0.943478\pi\) | ||
0.984276 | − | 0.176638i | \(-0.0565220\pi\) | |||||||
\(684\) | −19257.4 | − | 11272.7i | −1.07650 | − | 0.630153i | ||||
\(685\) | − | 1090.68i | − | 0.0608359i | ||||||
\(686\) | 10309.5 | − | 16581.7i | 0.573790 | − | 0.922876i | ||||
\(687\) | 15273.0 | − | 4581.86i | 0.848181 | − | 0.254453i | ||||
\(688\) | −9617.15 | + | 12540.7i | −0.532922 | + | 0.694928i | ||||
\(689\) | − | 3523.17i | − | 0.194807i | ||||||
\(690\) | −3152.99 | + | 11627.6i | −0.173960 | + | 0.641527i | ||||
\(691\) | −27248.7 | −1.50013 | −0.750064 | − | 0.661365i | \(-0.769978\pi\) | ||||
−0.750064 | + | 0.661365i | \(0.769978\pi\) | |||||||
\(692\) | −1875.75 | − | 3802.29i | −0.103043 | − | 0.208875i | ||||
\(693\) | 19100.5 | − | 12593.7i | 1.04700 | − | 0.690323i | ||||
\(694\) | 371.968 | − | 598.269i | 0.0203454 | − | 0.0327233i | ||||
\(695\) | 4359.81 | 0.237952 | ||||||||
\(696\) | 28584.0 | − | 5600.92i | 1.55672 | − | 0.305032i | ||||
\(697\) | −2132.34 | −0.115880 | ||||||||
\(698\) | 12965.0 | − | 20852.8i | 0.703057 | − | 1.13079i | ||||
\(699\) | −704.321 | + | 211.295i | −0.0381114 | + | 0.0114334i | ||||
\(700\) | −2617.90 | + | 1291.47i | −0.141353 | + | 0.0697327i | ||||
\(701\) | −17919.3 | −0.965481 | −0.482741 | − | 0.875763i | \(-0.660359\pi\) | ||||
−0.482741 | + | 0.875763i | \(0.660359\pi\) | |||||||
\(702\) | 16562.9 | − | 5454.11i | 0.890493 | − | 0.293236i | ||||
\(703\) | 15871.8i | 0.851515i | ||||||||
\(704\) | 5786.48 | − | 29155.8i | 0.309781 | − | 1.56087i | ||||
\(705\) | 3075.04 | + | 10250.2i | 0.164273 | + | 0.547581i | ||||
\(706\) | −10076.2 | + | 16206.5i | −0.537144 | + | 0.863935i | ||||
\(707\) | 15851.3i | 0.843211i | ||||||||
\(708\) | 14549.3 | + | 15625.6i | 0.772313 | + | 0.829443i | ||||
\(709\) | − | 12485.0i | − | 0.661329i | −0.943748 | − | 0.330665i | \(-0.892727\pi\) | ||
0.943748 | − | 0.330665i | \(-0.107273\pi\) | |||||||
\(710\) | −5359.58 | − | 3332.27i | −0.283298 | − | 0.176138i | ||||
\(711\) | 1388.52 | + | 2105.94i | 0.0732402 | + | 0.111082i | ||||
\(712\) | 6027.74 | + | 592.378i | 0.317274 | + | 0.0311802i | ||||
\(713\) | 25128.1i | 1.31985i | ||||||||
\(714\) | −4424.11 | + | 16315.2i | −0.231888 | + | 0.855157i | ||||
\(715\) | −12756.0 | −0.667200 | ||||||||
\(716\) | 16302.2 | − | 8042.26i | 0.850897 | − | 0.419767i | ||||
\(717\) | 5839.76 | + | 19466.0i | 0.304170 | + | 1.01391i | ||||
\(718\) | −3747.09 | − | 2329.72i | −0.194763 | − | 0.121092i | ||||
\(719\) | 7727.83 | 0.400834 | 0.200417 | − | 0.979711i | \(-0.435770\pi\) | ||||
0.200417 | + | 0.979711i | \(0.435770\pi\) | |||||||
\(720\) | 615.534 | − | 8618.05i | 0.0318606 | − | 0.446077i | ||||
\(721\) | 8795.28 | 0.454304 | ||||||||
\(722\) | −9159.37 | − | 5694.76i | −0.472128 | − | 0.293541i | ||||
\(723\) | −6143.15 | − | 20477.3i | −0.315998 | − | 1.05333i | ||||
\(724\) | −5512.14 | + | 2719.27i | −0.282952 | + | 0.139587i | ||||
\(725\) | −6193.38 | −0.317264 | ||||||||
\(726\) | 7844.51 | − | 28929.0i | 0.401015 | − | 1.47886i | ||||
\(727\) | 12917.1i | 0.658964i | 0.944162 | + | 0.329482i | \(0.106874\pi\) | ||||
−0.944162 | + | 0.329482i | \(0.893126\pi\) | |||||||
\(728\) | −1419.44 | + | 14443.5i | −0.0722634 | + | 0.735316i | ||||
\(729\) | 3483.84 | + | 19372.2i | 0.176997 | + | 0.984211i | ||||
\(730\) | −6303.13 | − | 3918.92i | −0.319575 | − | 0.198693i | ||||
\(731\) | − | 19459.5i | − | 0.984591i | ||||||
\(732\) | 766.145 | + | 822.818i | 0.0386852 | + | 0.0415468i | ||||
\(733\) | 5574.53i | 0.280900i | 0.990088 | + | 0.140450i | \(0.0448550\pi\) | ||||
−0.990088 | + | 0.140450i | \(0.955145\pi\) | |||||||
\(734\) | 20416.0 | − | 32836.8i | 1.02666 | − | 1.65127i | ||||
\(735\) | −970.275 | − | 3234.27i | −0.0486927 | − | 0.162310i | ||||
\(736\) | 27771.4 | − | 10463.7i | 1.39085 | − | 0.524046i | ||||
\(737\) | − | 26304.3i | − | 1.31470i | ||||||
\(738\) | −55.0796 | − | 2065.67i | −0.00274730 | − | 0.103033i | ||||
\(739\) | 17289.1 | 0.860607 | 0.430304 | − | 0.902684i | \(-0.358406\pi\) | ||||
0.430304 | + | 0.902684i | \(0.358406\pi\) | |||||||
\(740\) | −5511.35 | + | 2718.88i | −0.273786 | + | 0.135065i | ||||
\(741\) | 22594.2 | − | 6778.22i | 1.12013 | − | 0.336038i | ||||
\(742\) | −1747.59 | + | 2810.80i | −0.0864636 | + | 0.139067i | ||||
\(743\) | −13359.7 | −0.659649 | −0.329824 | − | 0.944042i | \(-0.606990\pi\) | ||||
−0.329824 | + | 0.944042i | \(0.606990\pi\) | |||||||
\(744\) | −3465.23 | − | 17684.6i | −0.170755 | − | 0.871437i | ||||
\(745\) | −13247.7 | −0.651487 | ||||||||
\(746\) | −16371.4 | + | 26331.6i | −0.803486 | + | 1.29232i | ||||
\(747\) | −18577.1 | − | 28175.5i | −0.909907 | − | 1.38003i | ||||
\(748\) | 16192.6 | + | 32823.5i | 0.791524 | + | 1.60447i | ||||
\(749\) | 3054.03 | 0.148988 | ||||||||
\(750\) | −480.798 | + | 1773.09i | −0.0234084 | + | 0.0863252i | ||||
\(751\) | 8468.05i | 0.411456i | 0.978609 | + | 0.205728i | \(0.0659563\pi\) | ||||
−0.978609 | + | 0.205728i | \(0.934044\pi\) | |||||||
\(752\) | 16042.0 | − | 20918.7i | 0.777915 | − | 1.01440i | ||||
\(753\) | −26278.2 | + | 7883.41i | −1.27175 | + | 0.381524i | ||||
\(754\) | −16258.2 | + | 26149.5i | −0.785266 | + | 1.26301i | ||||
\(755\) | − | 3588.16i | − | 0.172962i | ||||||
\(756\) | −15919.3 | − | 3864.35i | −0.765848 | − | 0.185906i | ||||
\(757\) | 6277.34i | 0.301392i | 0.988580 | + | 0.150696i | \(0.0481515\pi\) | ||||
−0.988580 | + | 0.150696i | \(0.951849\pi\) | |||||||
\(758\) | 532.624 | + | 331.154i | 0.0255221 | + | 0.0158682i | ||||
\(759\) | 47370.9 | − | 14211.2i | 2.26542 | − | 0.679623i | ||||
\(760\) | 1143.11 | − | 11631.7i | 0.0545594 | − | 0.555168i | ||||
\(761\) | 11037.7i | 0.525778i | 0.964826 | + | 0.262889i | \(0.0846752\pi\) | ||||
−0.964826 | + | 0.262889i | \(0.915325\pi\) | |||||||
\(762\) | 24257.5 | + | 6577.78i | 1.15322 | + | 0.312714i | ||||
\(763\) | −12646.2 | −0.600030 | ||||||||
\(764\) | 4736.38 | + | 9600.99i | 0.224288 | + | 0.454649i | ||||
\(765\) | 5856.09 | + | 8881.79i | 0.276768 | + | 0.419767i | ||||
\(766\) | −1362.37 | − | 847.038i | −0.0642614 | − | 0.0399540i | ||||
\(767\) | −22570.3 | −1.06254 | ||||||||
\(768\) | −18102.0 | + | 11193.9i | −0.850519 | + | 0.525944i | ||||
\(769\) | 5492.77 | 0.257574 | 0.128787 | − | 0.991672i | \(-0.458892\pi\) | ||||
0.128787 | + | 0.991672i | \(0.458892\pi\) | |||||||
\(770\) | 10176.8 | + | 6327.34i | 0.476294 | + | 0.296132i | ||||
\(771\) | −11338.0 | + | 3401.38i | −0.529609 | + | 0.158882i | ||||
\(772\) | −3039.61 | − | 6161.51i | −0.141707 | − | 0.287251i | ||||
\(773\) | 21115.4 | 0.982497 | 0.491248 | − | 0.871020i | \(-0.336541\pi\) | ||||
0.491248 | + | 0.871020i | \(0.336541\pi\) | |||||||
\(774\) | 18851.0 | − | 502.650i | 0.875435 | − | 0.0233429i | ||||
\(775\) | 3831.77i | 0.177602i | ||||||||
\(776\) | −1985.61 | + | 20204.5i | −0.0918545 | + | 0.934665i | ||||
\(777\) | 3348.17 | + | 11160.6i | 0.154588 | + | 0.515297i | ||||
\(778\) | −24363.7 | − | 15147.9i | −1.12273 | − | 0.698045i | ||||
\(779\) | − | 2795.33i | − | 0.128566i | ||||||
\(780\) | 6224.14 | + | 6684.54i | 0.285718 | + | 0.306853i | ||||
\(781\) | 25907.7i | 1.18701i | ||||||||
\(782\) | −19294.6 | + | 31033.1i | −0.882318 | + | 1.41911i | ||||
\(783\) | −26662.8 | − | 22295.6i | −1.21692 | − | 1.01760i | ||||
\(784\) | −5061.78 | + | 6600.53i | −0.230584 | + | 0.300680i | ||||
\(785\) | − | 16258.7i | − | 0.739235i | ||||||
\(786\) | −14099.7 | − | 3823.35i | −0.639849 | − | 0.173504i | ||||
\(787\) | 38018.5 | 1.72200 | 0.861000 | − | 0.508605i | \(-0.169839\pi\) | ||||
0.861000 | + | 0.508605i | \(0.169839\pi\) | |||||||
\(788\) | 10761.0 | + | 21813.4i | 0.486480 | + | 0.986128i | ||||
\(789\) | −8985.42 | − | 29951.6i | −0.405436 | − | 1.35146i | ||||
\(790\) | −697.625 | + | 1122.05i | −0.0314182 | + | 0.0505326i | ||||
\(791\) | 21250.1 | 0.955205 | ||||||||
\(792\) | −31378.9 | + | 16534.1i | −1.40783 | + | 0.741811i | ||||
\(793\) | −1188.51 | −0.0532224 | ||||||||
\(794\) | 6792.55 | − | 10925.0i | 0.303600 | − | 0.488306i | ||||
\(795\) | 598.535 | + | 1995.13i | 0.0267017 | + | 0.0890062i | ||||
\(796\) | 11744.3 | − | 5793.72i | 0.522946 | − | 0.257981i | ||||
\(797\) | 5023.82 | 0.223278 | 0.111639 | − | 0.993749i | \(-0.464390\pi\) | ||||
0.111639 | + | 0.993749i | \(0.464390\pi\) | |||||||
\(798\) | −21387.9 | − | 5799.66i | −0.948778 | − | 0.257275i | ||||
\(799\) | 32459.7i | 1.43722i | ||||||||
\(800\) | 4234.86 | − | 1595.61i | 0.187156 | − | 0.0705168i | ||||
\(801\) | −3978.26 | − | 6033.74i | −0.175487 | − | 0.266157i | ||||
\(802\) | 211.695 | − | 340.488i | 0.00932072 | − | 0.0149913i | ||||
\(803\) | 30468.8i | 1.33900i | ||||||||
\(804\) | −13784.3 | + | 12834.9i | −0.604644 | + | 0.562999i | ||||
\(805\) | 11964.4i | 0.523839i | ||||||||
\(806\) | 16178.4 | + | 10058.8i | 0.707023 | + | 0.439585i | ||||
\(807\) | −4492.49 | − | 14975.0i | −0.195964 | − | 0.653218i | ||||
\(808\) | 2403.45 | − | 24456.3i | 0.104645 | − | 1.06481i | ||||
\(809\) | − | 9928.57i | − | 0.431483i | −0.976450 | − | 0.215742i | \(-0.930783\pi\) | ||
0.976450 | − | 0.215742i | \(-0.0692169\pi\) | |||||||
\(810\) | −8452.81 | + | 5902.40i | −0.366668 | + | 0.256036i | ||||
\(811\) | 16918.7 | 0.732549 | 0.366274 | − | 0.930507i | \(-0.380633\pi\) | ||||
0.366274 | + | 0.930507i | \(0.380633\pi\) | |||||||
\(812\) | 25941.8 | − | 12797.7i | 1.12116 | − | 0.553092i | ||||
\(813\) | −14469.5 | + | 4340.81i | −0.624190 | + | 0.187256i | ||||
\(814\) | 21424.8 | + | 13320.7i | 0.922530 | + | 0.573575i | ||||
\(815\) | −903.082 | −0.0388142 | ||||||||
\(816\) | 9299.57 | − | 24501.2i | 0.398958 | − | 1.05112i | ||||
\(817\) | 25509.9 | 1.09238 | ||||||||
\(818\) | −25863.5 | − | 16080.4i | −1.10550 | − | 0.687332i | ||||
\(819\) | 14457.8 | − | 9532.56i | 0.616846 | − | 0.406709i | ||||
\(820\) | 970.658 | − | 478.848i | 0.0413376 | − | 0.0203928i | ||||
\(821\) | 18362.5 | 0.780579 | 0.390289 | − | 0.920692i | \(-0.372375\pi\) | ||||
0.390289 | + | 0.920692i | \(0.372375\pi\) | |||||||
\(822\) | 3094.18 | + | 839.032i | 0.131292 | + | 0.0356017i | ||||
\(823\) | 35007.5i | 1.48273i | 0.671103 | + | 0.741364i | \(0.265821\pi\) | ||||
−0.671103 | + | 0.741364i | \(0.734179\pi\) | |||||||
\(824\) | −13569.9 | − | 1333.58i | −0.573700 | − | 0.0563806i | ||||
\(825\) | 7223.59 | − | 2167.06i | 0.304840 | − | 0.0914514i | ||||
\(826\) | 18006.7 | + | 11195.5i | 0.758513 | + | 0.471599i | ||||
\(827\) | − | 21104.7i | − | 0.887404i | −0.896174 | − | 0.443702i | \(-0.853665\pi\) | ||
0.896174 | − | 0.443702i | \(-0.146335\pi\) | |||||||
\(828\) | −30561.2 | − | 17889.7i | −1.28270 | − | 0.750855i | ||||
\(829\) | − | 44840.3i | − | 1.87861i | −0.343085 | − | 0.939304i | \(-0.611472\pi\) | ||
0.343085 | − | 0.939304i | \(-0.388528\pi\) | |||||||
\(830\) | 9333.54 | − | 15011.9i | 0.390327 | − | 0.627797i | ||||
\(831\) | −39674.6 | + | 11902.3i | −1.65619 | + | 0.496855i | ||||
\(832\) | 4379.97 | − | 22069.0i | 0.182510 | − | 0.919596i | ||||
\(833\) | − | 10242.1i | − | 0.426011i | ||||||
\(834\) | −3353.90 | + | 12368.5i | −0.139252 | + | 0.513532i | ||||
\(835\) | −17919.5 | −0.742671 | ||||||||
\(836\) | −43029.0 | + | 21227.2i | −1.78013 | + | 0.878179i | ||||
\(837\) | −13794.0 | + | 16496.0i | −0.569643 | + | 0.681224i | ||||
\(838\) | 1906.44 | − | 3066.30i | 0.0785883 | − | 0.126400i | ||||
\(839\) | −19998.2 | −0.822900 | −0.411450 | − | 0.911432i | \(-0.634978\pi\) | ||||
−0.411450 | + | 0.911432i | \(0.634978\pi\) | |||||||
\(840\) | −1649.92 | − | 8420.30i | −0.0677712 | − | 0.345867i | ||||
\(841\) | 36983.8 | 1.51641 | ||||||||
\(842\) | −21308.2 | + | 34271.8i | −0.872125 | + | 1.40271i | ||||
\(843\) | −4546.18 | + | 1363.85i | −0.185740 | + | 0.0557217i | ||||
\(844\) | 21363.6 | + | 43305.5i | 0.871285 | + | 1.76616i | ||||
\(845\) | 1329.56 | 0.0541281 | ||||||||
\(846\) | −31444.7 | + | 838.452i | −1.27789 | + | 0.0340740i | ||||
\(847\) | − | 29767.0i | − | 1.20756i | ||||||
\(848\) | 3122.47 | − | 4071.68i | 0.126446 | − | 0.164885i | ||||
\(849\) | 2744.91 | + | 9149.75i | 0.110960 | + | 0.369869i | ||||
\(850\) | −2942.23 | + | 4732.24i | −0.118726 | + | 0.190958i | ||||
\(851\) | 25188.2i | 1.01462i | ||||||||
\(852\) | 13576.5 | − | 12641.4i | 0.545918 | − | 0.508317i | ||||
\(853\) | − | 27500.9i | − | 1.10388i | −0.833882 | − | 0.551942i | \(-0.813887\pi\) | ||
0.833882 | − | 0.551942i | \(-0.186113\pi\) | |||||||
\(854\) | 948.201 | + | 589.536i | 0.0379939 | + | 0.0236224i | ||||
\(855\) | −11643.3 | + | 7676.86i | −0.465723 | + | 0.307068i | ||||
\(856\) | −4711.94 | − | 463.067i | −0.188143 | − | 0.0184899i | ||||
\(857\) | 1250.31i | 0.0498365i | 0.999689 | + | 0.0249183i | \(0.00793255\pi\) | ||||
−0.999689 | + | 0.0249183i | \(0.992067\pi\) | |||||||
\(858\) | 9812.91 | − | 36188.0i | 0.390451 | − | 1.43990i | ||||
\(859\) | 15260.3 | 0.606142 | 0.303071 | − | 0.952968i | \(-0.401988\pi\) | ||||
0.303071 | + | 0.952968i | \(0.401988\pi\) | |||||||
\(860\) | 4369.91 | + | 8858.11i | 0.173271 | + | 0.351232i | ||||
\(861\) | −589.679 | − | 1965.61i | −0.0233406 | − | 0.0778023i | ||||
\(862\) | −36997.4 | − | 23002.8i | −1.46187 | − | 0.908907i | ||||
\(863\) | 15513.7 | 0.611926 | 0.305963 | − | 0.952043i | \(-0.401022\pi\) | ||||
0.305963 | + | 0.952043i | \(0.401022\pi\) | |||||||
\(864\) | 23975.3 | + | 8375.90i | 0.944048 | + | 0.329808i | ||||
\(865\) | −2649.87 | −0.104160 | ||||||||
\(866\) | −22887.4 | − | 14230.0i | −0.898088 | − | 0.558378i | ||||
\(867\) | 1936.77 | + | 6455.93i | 0.0758664 | + | 0.252889i | ||||
\(868\) | −7917.78 | − | 16049.9i | −0.309616 | − | 0.627614i | ||||
\(869\) | 5423.89 | 0.211730 | ||||||||
\(870\) | 4764.43 | − | 17570.2i | 0.185666 | − | 0.684697i | ||||
\(871\) | − | 19910.6i | − | 0.774564i | ||||||
\(872\) | 19511.3 | + | 1917.48i | 0.757724 | + | 0.0744656i | ||||
\(873\) | 20224.6 | − | 13334.8i | 0.784077 | − | 0.516970i | ||||
\(874\) | −40681.9 | − | 25293.6i | −1.57447 | − | 0.978913i | ||||
\(875\) | 1824.45i | 0.0704888i | ||||||||
\(876\) | 15966.6 | − | 14866.9i | 0.615823 | − | 0.573407i | ||||
\(877\) | 17948.8i | 0.691091i | 0.938402 | + | 0.345545i | \(0.112306\pi\) | ||||
−0.938402 | + | 0.345545i | \(0.887694\pi\) | |||||||
\(878\) | −4198.15 | + | 6752.25i | −0.161368 | + | 0.259542i | ||||
\(879\) | −1108.77 | − | 3695.92i | −0.0425459 | − | 0.141821i | ||||
\(880\) | −14742.0 | − | 11305.2i | −0.564718 | − | 0.433067i | ||||
\(881\) | 50006.7i | 1.91234i | 0.292817 | + | 0.956169i | \(0.405407\pi\) | ||||
−0.292817 | + | 0.956169i | \(0.594593\pi\) | |||||||
\(882\) | 9921.83 | − | 264.559i | 0.378782 | − | 0.0100999i | ||||
\(883\) | −2670.53 | −0.101779 | −0.0508894 | − | 0.998704i | \(-0.516206\pi\) | ||||
−0.0508894 | + | 0.998704i | \(0.516206\pi\) | |||||||
\(884\) | 12256.7 | + | 24845.2i | 0.466332 | + | 0.945288i | ||||
\(885\) | 12781.3 | − | 3834.36i | 0.485467 | − | 0.145639i | ||||
\(886\) | 6283.46 | − | 10106.2i | 0.238258 | − | 0.383212i | ||||
\(887\) | −27123.1 | −1.02672 | −0.513362 | − | 0.858172i | \(-0.671600\pi\) | ||||
−0.513362 | + | 0.858172i | \(0.671600\pi\) | |||||||
\(888\) | −3473.52 | − | 17726.9i | −0.131265 | − | 0.669906i | ||||
\(889\) | 24960.2 | 0.941664 | ||||||||
\(890\) | 1998.76 | − | 3214.79i | 0.0752795 | − | 0.121079i | ||||
\(891\) | 38899.1 | + | 16674.9i | 1.46259 | + | 0.626970i | ||||
\(892\) | 10938.3 | − | 5396.11i | 0.410585 | − | 0.202551i | ||||
\(893\) | −42552.0 | −1.59457 | ||||||||
\(894\) | 10191.2 | − | 37582.9i | 0.381256 | − | 1.40600i | ||||
\(895\) | − | 11361.3i | − | 0.424318i | ||||||
\(896\) | −14441.2 | + | 15434.1i | −0.538444 | + | 0.575467i | ||||
\(897\) | 35856.6 | − | 10756.9i | 1.33469 | − | 0.400405i | ||||
\(898\) | −7616.43 | + | 12250.2i | −0.283033 | + | 0.455226i | ||||
\(899\) | − | 37970.6i | − | 1.40867i | ||||||
\(900\) | −4660.27 | − | 2727.99i | −0.172602 | − | 0.101037i | ||||
\(901\) | 6318.05i | 0.233612i | ||||||||
\(902\) | −3773.34 | − | 2346.04i | −0.139289 | − | 0.0866014i | ||||
\(903\) | 17937.9 | − | 5381.34i | 0.661059 | − | 0.198317i | ||||
\(904\) | −32785.9 | − | 3222.04i | −1.20624 | − | 0.118544i | ||||
\(905\) | 3841.49i | 0.141100i | ||||||||
\(906\) | 10179.4 | + | 2760.29i | 0.373276 | + | 0.101219i | ||||
\(907\) | −33013.5 | −1.20860 | −0.604298 | − | 0.796759i | \(-0.706546\pi\) | ||||
−0.604298 | + | 0.796759i | \(0.706546\pi\) | |||||||
\(908\) | 3390.45 | − | 1672.58i | 0.123916 | − | 0.0611307i | ||||
\(909\) | −24480.6 | + | 16141.0i | −0.893258 | + | 0.588957i | ||||
\(910\) | 7703.15 | + | 4789.37i | 0.280612 | + | 0.174468i | ||||
\(911\) | 47241.1 | 1.71808 | 0.859038 | − | 0.511912i | \(-0.171062\pi\) | ||||
0.859038 | + | 0.511912i | \(0.171062\pi\) | |||||||
\(912\) | 32119.2 | + | 12191.0i | 1.16620 | + | 0.442636i | ||||
\(913\) | −72566.3 | −2.63044 | ||||||||
\(914\) | −20802.2 | − | 12933.6i | −0.752817 | − | 0.468057i | ||||
\(915\) | 673.041 | − | 201.911i | 0.0243170 | − | 0.00729506i | ||||
\(916\) | −22016.3 | + | 10861.2i | −0.794148 | + | 0.391772i | ||||
\(917\) | −14508.2 | −0.522468 | ||||||||
\(918\) | −29702.0 | + | 9780.78i | −1.06788 | + | 0.351649i | ||||
\(919\) | 50644.8i | 1.81787i | 0.416942 | + | 0.908933i | \(0.363102\pi\) | ||||
−0.416942 | + | 0.908933i | \(0.636898\pi\) | |||||||
\(920\) | 1814.10 | − | 18459.4i | 0.0650099 | − | 0.661508i | ||||
\(921\) | −12419.0 | − | 41397.1i | −0.444323 | − | 1.48108i | ||||
\(922\) | 26908.6 | + | 16730.2i | 0.961157 | + | 0.597591i | ||||
\(923\) | 19610.4i | 0.699333i | ||||||||
\(924\) | −25779.0 | + | 24003.5i | −0.917823 | + | 0.854607i | ||||
\(925\) | 3840.94i | 0.136529i | ||||||||
\(926\) | 4443.18 | − | 7146.35i | 0.157680 | − | 0.253611i | ||||
\(927\) | 8956.00 | + | 13583.4i | 0.317318 | + | 0.481269i | ||||
\(928\) | −41964.9 | + | 15811.6i | −1.48445 | + | 0.559311i | ||||
\(929\) | − | 36463.1i | − | 1.28774i | −0.765133 | − | 0.643872i | \(-0.777327\pi\) | ||
0.765133 | − | 0.643872i | \(-0.222673\pi\) | |||||||
\(930\) | −10870.5 | − | 2947.70i | −0.383288 | − | 0.103934i | ||||
\(931\) | 13426.5 | 0.472650 | ||||||||
\(932\) | 1015.29 | − | 500.868i | 0.0356836 | − | 0.0176035i | ||||
\(933\) | −4503.67 | − | 15012.3i | −0.158032 | − | 0.526776i | ||||
\(934\) | 20093.8 | − | 32318.6i | 0.703950 | − | 1.13222i | ||||
\(935\) | 22875.2 | 0.800106 | ||||||||
\(936\) | −23751.7 | + | 12515.2i | −0.829433 | + | 0.437043i | ||||
\(937\) | −1429.44 | −0.0498376 | −0.0249188 | − | 0.999689i | \(-0.507933\pi\) | ||||
−0.0249188 | + | 0.999689i | \(0.507933\pi\) | |||||||
\(938\) | −9876.21 | + | 15884.8i | −0.343784 | + | 0.552938i | ||||
\(939\) | 14035.8 | + | 46786.3i | 0.487797 | + | 1.62600i | ||||
\(940\) | −7289.28 | − | 14775.9i | −0.252926 | − | 0.512698i | ||||
\(941\) | −8397.60 | −0.290918 | −0.145459 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145459 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(942\) | 46125.0 | + | 12507.5i | 1.59537 | + | 0.432607i | ||||
\(943\) | − | 4436.14i | − | 0.153193i | ||||||
\(944\) | −26084.2 | − | 20003.3i | −0.899330 | − | 0.689673i | ||||
\(945\) | −6567.85 | + | 7854.36i | −0.226087 | + | 0.270373i | ||||
\(946\) | 21409.7 | − | 34435.0i | 0.735822 | − | 1.18349i | ||||
\(947\) | 43156.1i | 1.48087i | 0.672127 | + | 0.740436i | \(0.265381\pi\) | ||||
−0.672127 | + | 0.740436i | \(0.734619\pi\) | |||||||
\(948\) | −2646.52 | − | 2842.29i | −0.0906698 | − | 0.0973768i | ||||
\(949\) | 23062.8i | 0.788883i | ||||||||
\(950\) | −6203.58 | − | 3857.02i | −0.211864 | − | 0.131725i | ||||
\(951\) | 8662.77 | + | 28876.1i | 0.295383 | + | 0.984616i | ||||
\(952\) | 2545.46 | − | 25901.3i | 0.0866583 | − | 0.881791i | ||||
\(953\) | − | 20652.4i | − | 0.701991i | −0.936377 | − | 0.350995i | \(-0.885843\pi\) | ||
0.936377 | − | 0.350995i | \(-0.114157\pi\) | |||||||
\(954\) | −6120.49 | + | 163.199i | −0.207713 | + | 0.00553853i | ||||
\(955\) | 6691.07 | 0.226720 | ||||||||
\(956\) | −13843.0 | − | 28060.6i | −0.468319 | − | 0.949316i | ||||
\(957\) | −71581.5 | + | 21474.3i | −2.41787 | + | 0.725356i | ||||
\(958\) | −26730.7 | − | 16619.6i | −0.901493 | − | 0.560495i | ||||
\(959\) | 3183.81 | 0.107206 | ||||||||
\(960\) | 1268.87 | + | 13241.5i | 0.0426590 | + | 0.445174i | ||||
\(961\) | 6299.02 | 0.211440 | ||||||||
\(962\) | 16217.1 | + | 10082.9i | 0.543515 | + | 0.337926i | ||||
\(963\) | 3109.84 | + | 4716.63i | 0.104064 | + | 0.157831i | ||||
\(964\) | 14562.1 | + | 29518.5i | 0.486530 | + | 0.986231i | ||||
\(965\) | −4294.05 | −0.143244 | ||||||||
\(966\) | −33942.3 | − | 9203.95i | −1.13051 | − | 0.306555i | ||||
\(967\) | − | 27587.9i | − | 0.917443i | −0.888580 | − | 0.458721i | \(-0.848308\pi\) | ||
0.888580 | − | 0.458721i | \(-0.151692\pi\) | |||||||
\(968\) | −4513.42 | + | 45926.2i | −0.149862 | + | 1.52492i | ||||
\(969\) | −40517.9 | + | 12155.3i | −1.34326 | + | 0.402977i | ||||
\(970\) | 10775.7 | + | 6699.70i | 0.356688 | + | 0.221767i | ||||
\(971\) | 13285.7i | 0.439093i | 0.975602 | + | 0.219547i | \(0.0704578\pi\) | ||||
−0.975602 | + | 0.219547i | \(0.929542\pi\) | |||||||
\(972\) | −10242.2 | − | 28520.7i | −0.337981 | − | 0.941153i | ||||
\(973\) | 12726.8i | 0.419324i | ||||||||
\(974\) | 3237.24 | − | 5206.73i | 0.106497 | − | 0.171288i | ||||
\(975\) | 5467.77 | − | 1640.32i | 0.179599 | − | 0.0538793i | ||||
\(976\) | −1373.55 | − | 1053.34i | −0.0450474 | − | 0.0345457i | ||||
\(977\) | − | 20541.2i | − | 0.672642i | −0.941747 | − | 0.336321i | \(-0.890817\pi\) | ||
0.941747 | − | 0.336321i | \(-0.109183\pi\) | |||||||
\(978\) | 694.721 | − | 2561.99i | 0.0227144 | − | 0.0837662i | ||||
\(979\) | −15540.0 | −0.507314 | ||||||||
\(980\) | 2300.00 | + | 4662.27i | 0.0749704 | + | 0.151970i | ||||
\(981\) | −12877.3 | − | 19530.7i | −0.419103 | − | 0.635644i | ||||
\(982\) | 7028.96 | − | 11305.3i | 0.228415 | − | 0.367379i | ||||
\(983\) | −28203.9 | −0.915123 | −0.457562 | − | 0.889178i | \(-0.651277\pi\) | ||||
−0.457562 | + | 0.889178i | \(0.651277\pi\) | |||||||
\(984\) | 611.756 | + | 3122.06i | 0.0198192 | + | 0.101146i | ||||
\(985\) | 15202.1 | 0.491754 | ||||||||
\(986\) | 29155.7 | − | 46893.7i | 0.941691 | − | 1.51460i | ||||
\(987\) | −29921.6 | + | 8976.42i | −0.964958 | + | 0.289486i | ||||
\(988\) | −32570.0 | + | 16067.5i | −1.04878 | + | 0.517385i | ||||
\(989\) | 40483.7 | 1.30162 | ||||||||
\(990\) | 590.879 | + | 22159.9i | 0.0189691 | + | 0.711403i | ||||
\(991\) | − | 30236.1i | − | 0.969206i | −0.874734 | − | 0.484603i | \(-0.838964\pi\) | ||
0.874734 | − | 0.484603i | \(-0.161036\pi\) | |||||||
\(992\) | 9782.44 | + | 25963.2i | 0.313098 | + | 0.830981i | ||||
\(993\) | 8954.48 | + | 29848.4i | 0.286165 | + | 0.953888i | ||||
\(994\) | 9727.31 | − | 15645.3i | 0.310394 | − | 0.499233i | ||||
\(995\) | − | 8184.76i | − | 0.260778i | ||||||
\(996\) | 35407.8 | + | 38027.0i | 1.12645 | + | 1.20977i | ||||
\(997\) | − | 848.710i | − | 0.0269598i | −0.999909 | − | 0.0134799i | \(-0.995709\pi\) | ||
0.999909 | − | 0.0134799i | \(-0.00429091\pi\) | |||||||
\(998\) | 51869.2 | + | 32249.2i | 1.64518 | + | 1.02288i | ||||
\(999\) | −13827.0 | + | 16535.5i | −0.437906 | + | 0.523683i |
(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 | 120.4.b.a.11.5 | ✓ | 24 | |
3.2 | odd | 2 | 120.4.b.b.11.20 | yes | 24 | ||
4.3 | odd | 2 | 480.4.b.b.431.16 | 24 | |||
8.3 | odd | 2 | 120.4.b.b.11.19 | yes | 24 | ||
8.5 | even | 2 | 480.4.b.a.431.16 | 24 | |||
12.11 | even | 2 | 480.4.b.a.431.15 | 24 | |||
24.5 | odd | 2 | 480.4.b.b.431.15 | 24 | |||
24.11 | even | 2 | inner | 120.4.b.a.11.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.b.a.11.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
120.4.b.a.11.6 | yes | 24 | 24.11 | even | 2 | inner | |
120.4.b.b.11.19 | yes | 24 | 8.3 | odd | 2 | ||
120.4.b.b.11.20 | yes | 24 | 3.2 | odd | 2 | ||
480.4.b.a.431.15 | 24 | 12.11 | even | 2 | |||
480.4.b.a.431.16 | 24 | 8.5 | even | 2 | |||
480.4.b.b.431.15 | 24 | 24.5 | odd | 2 | |||
480.4.b.b.431.16 | 24 | 4.3 | odd | 2 |