Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(11,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.e (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 346 x^{18} + 50697 x^{16} + 4104768 x^{14} + 200532432 x^{12} + 6039270720 x^{10} + \cdots + 1118416232704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.10 | ||
Root | \(-7.08776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.11 |
Dual form | 74.4.e.a.27.10 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.00000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 3.54388 | − | 6.13818i | 0.682020 | − | 1.18129i | −0.292343 | − | 0.956313i | \(-0.594435\pi\) |
0.974363 | − | 0.224980i | \(-0.0722317\pi\) | |||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 13.1273 | + | 7.57908i | 1.17415 | + | 0.677893i | 0.954653 | − | 0.297721i | \(-0.0962264\pi\) |
0.219493 | + | 0.975614i | \(0.429560\pi\) | |||||||
\(6\) | − | 14.1755i | − | 0.964522i | ||||||
\(7\) | −5.28959 | + | 9.16184i | −0.285611 | + | 0.494693i | −0.972757 | − | 0.231826i | \(-0.925530\pi\) |
0.687146 | + | 0.726519i | \(0.258863\pi\) | |||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −11.6182 | − | 20.1233i | −0.430303 | − | 0.745306i | ||||
\(10\) | 30.3163 | 0.958686 | ||||||||
\(11\) | −26.3884 | −0.723310 | −0.361655 | − | 0.932312i | \(-0.617788\pi\) | ||||
−0.361655 | + | 0.932312i | \(0.617788\pi\) | |||||||
\(12\) | −14.1755 | − | 24.5527i | −0.341010 | − | 0.590647i | ||||
\(13\) | −38.4353 | − | 22.1906i | −0.820002 | − | 0.473428i | 0.0304151 | − | 0.999537i | \(-0.490317\pi\) |
−0.850417 | + | 0.526109i | \(0.823650\pi\) | |||||||
\(14\) | 21.1584i | 0.403915i | ||||||||
\(15\) | 93.0435 | − | 53.7187i | 1.60158 | − | 0.924674i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −65.3877 | + | 37.7516i | −0.932873 | + | 0.538595i | −0.887719 | − | 0.460385i | \(-0.847711\pi\) |
−0.0451541 | + | 0.998980i | \(0.514378\pi\) | |||||||
\(18\) | −40.2465 | − | 23.2364i | −0.527011 | − | 0.304270i | ||||
\(19\) | 90.0514 | + | 51.9912i | 1.08733 | + | 0.627768i | 0.932863 | − | 0.360230i | \(-0.117302\pi\) |
0.154463 | + | 0.987999i | \(0.450635\pi\) | |||||||
\(20\) | 52.5094 | − | 30.3163i | 0.587073 | − | 0.338947i | ||||
\(21\) | 37.4913 | + | 64.9369i | 0.389585 | + | 0.674781i | ||||
\(22\) | −45.7061 | + | 26.3884i | −0.442935 | + | 0.255729i | ||||
\(23\) | 43.3057i | 0.392603i | 0.980544 | + | 0.196302i | \(0.0628931\pi\) | ||||
−0.980544 | + | 0.196302i | \(0.937107\pi\) | |||||||
\(24\) | −49.1054 | − | 28.3510i | −0.417650 | − | 0.241131i | ||||
\(25\) | 52.3849 | + | 90.7332i | 0.419079 | + | 0.725866i | ||||
\(26\) | −88.7625 | −0.669529 | ||||||||
\(27\) | 26.6758 | 0.190139 | ||||||||
\(28\) | 21.1584 | + | 36.6474i | 0.142805 | + | 0.247346i | ||||
\(29\) | 78.7083i | 0.503992i | 0.967728 | + | 0.251996i | \(0.0810870\pi\) | ||||
−0.967728 | + | 0.251996i | \(0.918913\pi\) | |||||||
\(30\) | 107.437 | − | 186.087i | 0.653843 | − | 1.13249i | ||||
\(31\) | − | 264.403i | − | 1.53188i | −0.642913 | − | 0.765940i | \(-0.722274\pi\) | ||
0.642913 | − | 0.765940i | \(-0.277726\pi\) | |||||||
\(32\) | −27.7128 | − | 16.0000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −93.5174 | + | 161.977i | −0.493312 | + | 0.854442i | ||||
\(34\) | −75.5032 | + | 130.775i | −0.380844 | + | 0.659641i | ||||
\(35\) | −138.877 | + | 80.1804i | −0.670698 | + | 0.387228i | ||||
\(36\) | −92.9454 | −0.430303 | ||||||||
\(37\) | −85.8315 | + | 208.053i | −0.381368 | + | 0.924423i | ||||
\(38\) | 207.965 | 0.887798 | ||||||||
\(39\) | −272.420 | + | 157.282i | −1.11852 | + | 0.645775i | ||||
\(40\) | 60.6326 | − | 105.019i | 0.239672 | − | 0.415123i | ||||
\(41\) | −89.5746 | + | 155.148i | −0.341200 | + | 0.590976i | −0.984656 | − | 0.174508i | \(-0.944167\pi\) |
0.643456 | + | 0.765483i | \(0.277500\pi\) | |||||||
\(42\) | 129.874 | + | 74.9827i | 0.477142 | + | 0.275478i | ||||
\(43\) | − | 208.041i | − | 0.737813i | −0.929466 | − | 0.368907i | \(-0.879732\pi\) | ||
0.929466 | − | 0.368907i | \(-0.120268\pi\) | |||||||
\(44\) | −52.7769 | + | 91.4122i | −0.180828 | + | 0.313202i | ||||
\(45\) | − | 352.220i | − | 1.16680i | ||||||
\(46\) | 43.3057 | + | 75.0077i | 0.138806 | + | 0.240419i | ||||
\(47\) | 529.657 | 1.64379 | 0.821897 | − | 0.569636i | \(-0.192916\pi\) | ||||
0.821897 | + | 0.569636i | \(0.192916\pi\) | |||||||
\(48\) | −113.404 | −0.341010 | ||||||||
\(49\) | 115.540 | + | 200.122i | 0.336853 | + | 0.583446i | ||||
\(50\) | 181.466 | + | 104.770i | 0.513265 | + | 0.296334i | ||||
\(51\) | 535.149i | 1.46933i | ||||||||
\(52\) | −153.741 | + | 88.7625i | −0.410001 | + | 0.236714i | ||||
\(53\) | −307.660 | − | 532.883i | −0.797365 | − | 1.38108i | −0.921326 | − | 0.388790i | \(-0.872893\pi\) |
0.123961 | − | 0.992287i | \(-0.460440\pi\) | |||||||
\(54\) | 46.2039 | − | 26.6758i | 0.116436 | − | 0.0672244i | ||||
\(55\) | −346.410 | − | 200.000i | −0.849272 | − | 0.490327i | ||||
\(56\) | 73.2947 | + | 42.3167i | 0.174900 | + | 0.100979i | ||||
\(57\) | 638.263 | − | 368.501i | 1.48316 | − | 0.856301i | ||||
\(58\) | 78.7083 | + | 136.327i | 0.178188 | + | 0.308631i | ||||
\(59\) | 340.581 | − | 196.635i | 0.751524 | − | 0.433892i | −0.0747204 | − | 0.997205i | \(-0.523806\pi\) |
0.826244 | + | 0.563312i | \(0.190473\pi\) | |||||||
\(60\) | − | 429.750i | − | 0.924674i | ||||||
\(61\) | −650.586 | − | 375.616i | −1.36556 | − | 0.788405i | −0.375201 | − | 0.926944i | \(-0.622426\pi\) |
−0.990357 | + | 0.138539i | \(0.955760\pi\) | |||||||
\(62\) | −264.403 | − | 457.960i | −0.541601 | − | 0.938081i | ||||
\(63\) | 245.822 | 0.491597 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −336.369 | − | 582.608i | −0.641868 | − | 1.11175i | ||||
\(66\) | 374.070i | 0.697649i | ||||||||
\(67\) | −424.457 | + | 735.181i | −0.773965 | + | 1.34055i | 0.161410 | + | 0.986888i | \(0.448396\pi\) |
−0.935374 | + | 0.353659i | \(0.884937\pi\) | |||||||
\(68\) | 302.013i | 0.538595i | ||||||||
\(69\) | 265.818 | + | 153.470i | 0.463779 | + | 0.267763i | ||||
\(70\) | −160.361 | + | 277.753i | −0.273811 | + | 0.474255i | ||||
\(71\) | 508.963 | − | 881.550i | 0.850744 | − | 1.47353i | −0.0297940 | − | 0.999556i | \(-0.509485\pi\) |
0.880538 | − | 0.473976i | \(-0.157182\pi\) | |||||||
\(72\) | −160.986 | + | 92.9454i | −0.263506 | + | 0.152135i | ||||
\(73\) | 653.543 | 1.04783 | 0.523914 | − | 0.851771i | \(-0.324471\pi\) | ||||
0.523914 | + | 0.851771i | \(0.324471\pi\) | |||||||
\(74\) | 59.3882 | + | 446.189i | 0.0932937 | + | 0.700925i | ||||
\(75\) | 742.583 | 1.14328 | ||||||||
\(76\) | 360.206 | − | 207.965i | 0.543663 | − | 0.313884i | ||||
\(77\) | 139.584 | − | 241.767i | 0.206585 | − | 0.357816i | ||||
\(78\) | −314.564 | + | 544.840i | −0.456632 | + | 0.790910i | ||||
\(79\) | −716.925 | − | 413.917i | −1.02102 | − | 0.589485i | −0.106619 | − | 0.994300i | \(-0.534002\pi\) |
−0.914398 | + | 0.404815i | \(0.867336\pi\) | |||||||
\(80\) | − | 242.531i | − | 0.338947i | ||||||
\(81\) | 408.227 | − | 707.069i | 0.559982 | − | 0.969917i | ||||
\(82\) | 358.298i | 0.482530i | ||||||||
\(83\) | 67.5310 | + | 116.967i | 0.0893071 | + | 0.154684i | 0.907218 | − | 0.420660i | \(-0.138201\pi\) |
−0.817911 | + | 0.575344i | \(0.804868\pi\) | |||||||
\(84\) | 299.931 | 0.389585 | ||||||||
\(85\) | −1144.49 | −1.46044 | ||||||||
\(86\) | −208.041 | − | 360.338i | −0.260856 | − | 0.451816i | ||||
\(87\) | 483.126 | + | 278.933i | 0.595363 | + | 0.343733i | ||||
\(88\) | 211.107i | 0.255729i | ||||||||
\(89\) | −302.917 | + | 174.889i | −0.360777 | + | 0.208295i | −0.669421 | − | 0.742883i | \(-0.733458\pi\) |
0.308645 | + | 0.951177i | \(0.400125\pi\) | |||||||
\(90\) | −352.220 | − | 610.064i | −0.412525 | − | 0.714515i | ||||
\(91\) | 406.614 | − | 234.759i | 0.468403 | − | 0.270433i | ||||
\(92\) | 150.015 | + | 86.6115i | 0.170002 | + | 0.0981508i | ||||
\(93\) | −1622.96 | − | 937.014i | −1.80960 | − | 1.04477i | ||||
\(94\) | 917.392 | − | 529.657i | 1.00661 | − | 0.581169i | ||||
\(95\) | 788.091 | + | 1365.01i | 0.851120 | + | 1.47418i | ||||
\(96\) | −196.422 | + | 113.404i | −0.208825 | + | 0.120565i | ||||
\(97\) | 95.4794i | 0.0999429i | 0.998751 | + | 0.0499714i | \(0.0159130\pi\) | ||||
−0.998751 | + | 0.0499714i | \(0.984087\pi\) | |||||||
\(98\) | 400.244 | + | 231.081i | 0.412559 | + | 0.238191i | ||||
\(99\) | 306.585 | + | 531.022i | 0.311242 | + | 0.539088i | ||||
\(100\) | 419.079 | 0.419079 | ||||||||
\(101\) | −765.362 | −0.754023 | −0.377012 | − | 0.926208i | \(-0.623048\pi\) | ||||
−0.377012 | + | 0.926208i | \(0.623048\pi\) | |||||||
\(102\) | 535.149 | + | 926.905i | 0.519486 | + | 0.899777i | ||||
\(103\) | 1067.44i | 1.02114i | 0.859835 | + | 0.510572i | \(0.170566\pi\) | ||||
−0.859835 | + | 0.510572i | \(0.829434\pi\) | |||||||
\(104\) | −177.525 | + | 307.482i | −0.167382 | + | 0.289915i | ||||
\(105\) | 1136.60i | 1.05639i | ||||||||
\(106\) | −1065.77 | − | 615.320i | −0.976569 | − | 0.563823i | ||||
\(107\) | −392.900 | + | 680.523i | −0.354982 | + | 0.614847i | −0.987115 | − | 0.160013i | \(-0.948846\pi\) |
0.632133 | + | 0.774860i | \(0.282180\pi\) | |||||||
\(108\) | 53.3516 | − | 92.4077i | 0.0475348 | − | 0.0823328i | ||||
\(109\) | −1035.81 | + | 598.024i | −0.910205 | + | 0.525507i | −0.880497 | − | 0.474052i | \(-0.842791\pi\) |
−0.0297078 | + | 0.999559i | \(0.509458\pi\) | |||||||
\(110\) | −800.000 | −0.693427 | ||||||||
\(111\) | 972.889 | + | 1264.16i | 0.831915 | + | 1.08098i | ||||
\(112\) | 169.267 | 0.142805 | ||||||||
\(113\) | −183.741 | + | 106.083i | −0.152964 | + | 0.0883136i | −0.574528 | − | 0.818485i | \(-0.694814\pi\) |
0.421565 | + | 0.906798i | \(0.361481\pi\) | |||||||
\(114\) | 737.002 | − | 1276.53i | 0.605496 | − | 1.04875i | ||||
\(115\) | −328.218 | + | 568.490i | −0.266143 | + | 0.460973i | ||||
\(116\) | 272.654 | + | 157.417i | 0.218235 | + | 0.125998i | ||||
\(117\) | 1031.26i | 0.814870i | ||||||||
\(118\) | 393.269 | − | 681.163i | 0.306808 | − | 0.531408i | ||||
\(119\) | − | 798.762i | − | 0.615314i | ||||||
\(120\) | −429.750 | − | 744.348i | −0.326922 | − | 0.566245i | ||||
\(121\) | −634.651 | −0.476822 | ||||||||
\(122\) | −1502.46 | −1.11497 | ||||||||
\(123\) | 634.883 | + | 1099.65i | 0.465410 | + | 0.806114i | ||||
\(124\) | −915.920 | − | 528.807i | −0.663323 | − | 0.382970i | ||||
\(125\) | − | 306.654i | − | 0.219423i | ||||||
\(126\) | 425.775 | − | 245.822i | 0.301040 | − | 0.173806i | ||||
\(127\) | −685.911 | − | 1188.03i | −0.479250 | − | 0.830085i | 0.520467 | − | 0.853882i | \(-0.325758\pi\) |
−0.999717 | + | 0.0237968i | \(0.992425\pi\) | |||||||
\(128\) | −110.851 | + | 64.0000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −1276.99 | − | 737.273i | −0.871574 | − | 0.503203i | ||||
\(130\) | −1165.22 | − | 672.738i | −0.786125 | − | 0.453869i | ||||
\(131\) | 768.109 | − | 443.468i | 0.512290 | − | 0.295771i | −0.221485 | − | 0.975164i | \(-0.571090\pi\) |
0.733774 | + | 0.679393i | \(0.237757\pi\) | |||||||
\(132\) | 374.070 | + | 647.908i | 0.246656 | + | 0.427221i | ||||
\(133\) | −952.670 | + | 550.024i | −0.621105 | + | 0.358595i | ||||
\(134\) | 1697.83i | 1.09455i | ||||||||
\(135\) | 350.183 | + | 202.178i | 0.223251 | + | 0.128894i | ||||
\(136\) | 302.013 | + | 523.102i | 0.190422 | + | 0.329821i | ||||
\(137\) | 2562.76 | 1.59819 | 0.799093 | − | 0.601208i | \(-0.205313\pi\) | ||||
0.799093 | + | 0.601208i | \(0.205313\pi\) | |||||||
\(138\) | 613.881 | 0.378674 | ||||||||
\(139\) | −1533.45 | − | 2656.01i | −0.935722 | − | 1.62072i | −0.773342 | − | 0.633989i | \(-0.781416\pi\) |
−0.162380 | − | 0.986728i | \(-0.551917\pi\) | |||||||
\(140\) | 641.443i | 0.387228i | ||||||||
\(141\) | 1877.04 | − | 3251.13i | 1.12110 | − | 1.94180i | ||||
\(142\) | − | 2035.85i | − | 1.20313i | ||||||
\(143\) | 1014.25 | + | 585.576i | 0.593116 | + | 0.342436i | ||||
\(144\) | −185.891 | + | 321.972i | −0.107576 | + | 0.186327i | ||||
\(145\) | −596.537 | + | 1033.23i | −0.341653 | + | 0.591760i | ||||
\(146\) | 1131.97 | − | 653.543i | 0.641661 | − | 0.370463i | ||||
\(147\) | 1637.85 | 0.918961 | ||||||||
\(148\) | 549.053 | + | 713.435i | 0.304945 | + | 0.396243i | ||||
\(149\) | 3237.63 | 1.78012 | 0.890058 | − | 0.455848i | \(-0.150664\pi\) | ||||
0.890058 | + | 0.455848i | \(0.150664\pi\) | |||||||
\(150\) | 1286.19 | − | 742.583i | 0.700114 | − | 0.404211i | ||||
\(151\) | −401.578 | + | 695.553i | −0.216423 | + | 0.374856i | −0.953712 | − | 0.300722i | \(-0.902772\pi\) |
0.737289 | + | 0.675578i | \(0.236106\pi\) | |||||||
\(152\) | 415.929 | − | 720.411i | 0.221950 | − | 0.384428i | ||||
\(153\) | 1519.37 | + | 877.210i | 0.802836 | + | 0.463518i | ||||
\(154\) | − | 558.336i | − | 0.292156i | ||||||
\(155\) | 2003.93 | − | 3470.92i | 1.03845 | − | 1.79865i | ||||
\(156\) | 1258.25i | 0.645775i | ||||||||
\(157\) | 1226.19 | + | 2123.82i | 0.623315 | + | 1.07961i | 0.988864 | + | 0.148821i | \(0.0475478\pi\) |
−0.365549 | + | 0.930792i | \(0.619119\pi\) | |||||||
\(158\) | −1655.67 | −0.833657 | ||||||||
\(159\) | −4361.24 | −2.17528 | ||||||||
\(160\) | −242.531 | − | 420.075i | −0.119836 | − | 0.207562i | ||||
\(161\) | −396.760 | − | 229.070i | −0.194218 | − | 0.112132i | ||||
\(162\) | − | 1632.91i | − | 0.791934i | ||||||
\(163\) | 0.392102 | − | 0.226380i | 0.000188416 | − | 0.000108782i | −0.499906 | − | 0.866080i | \(-0.666632\pi\) |
0.500094 | + | 0.865971i | \(0.333299\pi\) | |||||||
\(164\) | 358.298 | + | 620.591i | 0.170600 | + | 0.295488i | ||||
\(165\) | −2455.27 | + | 1417.55i | −1.15844 | + | 0.668826i | ||||
\(166\) | 233.934 | + | 135.062i | 0.109378 | + | 0.0631496i | ||||
\(167\) | 879.725 | + | 507.909i | 0.407636 | + | 0.235348i | 0.689773 | − | 0.724025i | \(-0.257710\pi\) |
−0.282138 | + | 0.959374i | \(0.591044\pi\) | |||||||
\(168\) | 519.495 | − | 299.931i | 0.238571 | − | 0.137739i | ||||
\(169\) | −113.653 | − | 196.853i | −0.0517310 | − | 0.0896008i | ||||
\(170\) | −1982.31 | + | 1144.49i | −0.894333 | + | 0.516343i | ||||
\(171\) | − | 2416.17i | − | 1.08052i | ||||||
\(172\) | −720.675 | − | 416.082i | −0.319482 | − | 0.184453i | ||||
\(173\) | 161.521 | + | 279.762i | 0.0709839 | + | 0.122948i | 0.899333 | − | 0.437265i | \(-0.144053\pi\) |
−0.828349 | + | 0.560213i | \(0.810719\pi\) | |||||||
\(174\) | 1115.73 | 0.486112 | ||||||||
\(175\) | −1108.38 | −0.478774 | ||||||||
\(176\) | 211.107 | + | 365.649i | 0.0904138 | + | 0.156601i | ||||
\(177\) | − | 2787.40i | − | 1.18369i | ||||||
\(178\) | −349.778 | + | 605.834i | −0.147286 | + | 0.255108i | ||||
\(179\) | − | 253.165i | − | 0.105712i | −0.998602 | − | 0.0528560i | \(-0.983168\pi\) | ||
0.998602 | − | 0.0528560i | \(-0.0168324\pi\) | |||||||
\(180\) | −1220.13 | − | 704.441i | −0.505238 | − | 0.291699i | ||||
\(181\) | 1571.02 | − | 2721.08i | 0.645153 | − | 1.11744i | −0.339113 | − | 0.940746i | \(-0.610127\pi\) |
0.984266 | − | 0.176693i | \(-0.0565399\pi\) | |||||||
\(182\) | 469.517 | − | 813.227i | 0.191225 | − | 0.331211i | ||||
\(183\) | −4611.20 | + | 2662.28i | −1.86268 | + | 1.07542i | ||||
\(184\) | 346.446 | 0.138806 | ||||||||
\(185\) | −2703.59 | + | 2080.66i | −1.07444 | + | 0.826881i | ||||
\(186\) | −3748.06 | −1.47753 | ||||||||
\(187\) | 1725.48 | − | 996.206i | 0.674757 | − | 0.389571i | ||||
\(188\) | 1059.31 | − | 1834.78i | 0.410949 | − | 0.711784i | ||||
\(189\) | −141.104 | + | 244.399i | −0.0543059 | + | 0.0940606i | ||||
\(190\) | 2730.03 | + | 1576.18i | 1.04240 | + | 0.601833i | ||||
\(191\) | 680.510i | 0.257801i | 0.991658 | + | 0.128900i | \(0.0411448\pi\) | ||||
−0.991658 | + | 0.128900i | \(0.958855\pi\) | |||||||
\(192\) | −226.808 | + | 392.844i | −0.0852525 | + | 0.147662i | ||||
\(193\) | 1363.63i | 0.508580i | 0.967128 | + | 0.254290i | \(0.0818418\pi\) | ||||
−0.967128 | + | 0.254290i | \(0.918158\pi\) | |||||||
\(194\) | 95.4794 | + | 165.375i | 0.0353352 | + | 0.0612023i | ||||
\(195\) | −4768.20 | −1.75107 | ||||||||
\(196\) | 924.324 | 0.336853 | ||||||||
\(197\) | 1064.69 | + | 1844.09i | 0.385055 | + | 0.666935i | 0.991777 | − | 0.127980i | \(-0.0408492\pi\) |
−0.606722 | + | 0.794914i | \(0.707516\pi\) | |||||||
\(198\) | 1062.04 | + | 613.171i | 0.381193 | + | 0.220082i | ||||
\(199\) | 2582.54i | 0.919956i | 0.887930 | + | 0.459978i | \(0.152143\pi\) | ||||
−0.887930 | + | 0.459978i | \(0.847857\pi\) | |||||||
\(200\) | 725.866 | − | 419.079i | 0.256632 | − | 0.148167i | ||||
\(201\) | 3008.45 | + | 5210.78i | 1.05572 | + | 1.82856i | ||||
\(202\) | −1325.65 | + | 765.362i | −0.461743 | + | 0.266588i | ||||
\(203\) | −721.113 | − | 416.335i | −0.249321 | − | 0.143946i | ||||
\(204\) | 1853.81 | + | 1070.30i | 0.636238 | + | 0.367332i | ||||
\(205\) | −2351.75 | + | 1357.79i | −0.801237 | + | 0.462594i | ||||
\(206\) | 1067.44 | + | 1848.86i | 0.361029 | + | 0.625321i | ||||
\(207\) | 871.453 | − | 503.134i | 0.292610 | − | 0.168938i | ||||
\(208\) | 710.100i | 0.236714i | ||||||||
\(209\) | −2376.31 | − | 1371.97i | −0.786474 | − | 0.454071i | ||||
\(210\) | 1136.60 | + | 1968.65i | 0.373490 | + | 0.646903i | ||||
\(211\) | 5519.10 | 1.80071 | 0.900356 | − | 0.435154i | \(-0.143306\pi\) | ||||
0.900356 | + | 0.435154i | \(0.143306\pi\) | |||||||
\(212\) | −2461.28 | −0.797365 | ||||||||
\(213\) | −3607.41 | − | 6248.22i | −1.16045 | − | 2.00996i | ||||
\(214\) | 1571.60i | 0.502021i | ||||||||
\(215\) | 1576.76 | − | 2731.03i | 0.500159 | − | 0.866300i | ||||
\(216\) | − | 213.407i | − | 0.0672244i | ||||||
\(217\) | 2422.42 | + | 1398.59i | 0.757810 | + | 0.437522i | ||||
\(218\) | −1196.05 | + | 2071.61i | −0.371590 | + | 0.643612i | ||||
\(219\) | 2316.08 | − | 4011.57i | 0.714640 | − | 1.23779i | ||||
\(220\) | −1385.64 | + | 800.000i | −0.424636 | + | 0.245164i | ||||
\(221\) | 3350.93 | 1.01994 | ||||||||
\(222\) | 2949.26 | + | 1216.71i | 0.891627 | + | 0.367838i | ||||
\(223\) | −5847.34 | −1.75591 | −0.877953 | − | 0.478747i | \(-0.841091\pi\) | ||||
−0.877953 | + | 0.478747i | \(0.841091\pi\) | |||||||
\(224\) | 293.179 | − | 169.267i | 0.0874501 | − | 0.0504894i | ||||
\(225\) | 1217.23 | − | 2108.31i | 0.360662 | − | 0.624684i | ||||
\(226\) | −212.166 | + | 367.482i | −0.0624471 | + | 0.108162i | ||||
\(227\) | −1523.35 | − | 879.506i | −0.445411 | − | 0.257158i | 0.260479 | − | 0.965479i | \(-0.416119\pi\) |
−0.705890 | + | 0.708321i | \(0.749453\pi\) | |||||||
\(228\) | − | 2948.01i | − | 0.856301i | ||||||
\(229\) | 115.522 | − | 200.091i | 0.0333359 | − | 0.0577396i | −0.848876 | − | 0.528592i | \(-0.822720\pi\) |
0.882212 | + | 0.470852i | \(0.156054\pi\) | |||||||
\(230\) | 1312.87i | 0.376383i | ||||||||
\(231\) | −989.338 | − | 1713.58i | −0.281791 | − | 0.488076i | ||||
\(232\) | 629.667 | 0.178188 | ||||||||
\(233\) | 3146.43 | 0.884676 | 0.442338 | − | 0.896848i | \(-0.354149\pi\) | ||||
0.442338 | + | 0.896848i | \(0.354149\pi\) | |||||||
\(234\) | 1031.26 | + | 1786.19i | 0.288100 | + | 0.499004i | ||||
\(235\) | 6952.99 | + | 4014.31i | 1.93005 | + | 1.11432i | ||||
\(236\) | − | 1573.08i | − | 0.433892i | ||||||
\(237\) | −5081.39 | + | 2933.74i | −1.39271 | + | 0.804081i | ||||
\(238\) | −798.762 | − | 1383.50i | −0.217546 | − | 0.376801i | ||||
\(239\) | 1590.28 | − | 918.151i | 0.430405 | − | 0.248495i | −0.269114 | − | 0.963108i | \(-0.586731\pi\) |
0.699519 | + | 0.714614i | \(0.253397\pi\) | |||||||
\(240\) | −1488.70 | − | 859.499i | −0.400396 | − | 0.231168i | ||||
\(241\) | 2655.97 | + | 1533.43i | 0.709902 | + | 0.409862i | 0.811025 | − | 0.585012i | \(-0.198910\pi\) |
−0.101123 | + | 0.994874i | \(0.532244\pi\) | |||||||
\(242\) | −1099.25 | + | 634.651i | −0.291993 | + | 0.168582i | ||||
\(243\) | −2533.29 | − | 4387.79i | −0.668768 | − | 1.15834i | ||||
\(244\) | −2602.34 | + | 1502.46i | −0.682779 | + | 0.394203i | ||||
\(245\) | 3502.76i | 0.913401i | ||||||||
\(246\) | 2199.30 | + | 1269.77i | 0.570009 | + | 0.329095i | ||||
\(247\) | −2307.43 | − | 3996.59i | −0.594407 | − | 1.02954i | ||||
\(248\) | −2115.23 | −0.541601 | ||||||||
\(249\) | 957.287 | 0.243637 | ||||||||
\(250\) | −306.654 | − | 531.140i | −0.0775779 | − | 0.134369i | ||||
\(251\) | 4267.04i | 1.07304i | 0.843888 | + | 0.536520i | \(0.180261\pi\) | ||||
−0.843888 | + | 0.536520i | \(0.819739\pi\) | |||||||
\(252\) | 491.643 | − | 851.551i | 0.122899 | − | 0.212868i | ||||
\(253\) | − | 1142.77i | − | 0.283974i | ||||||
\(254\) | −2376.06 | − | 1371.82i | −0.586959 | − | 0.338881i | ||||
\(255\) | −4055.93 | + | 7025.08i | −0.996049 | + | 1.72521i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 364.681 | − | 210.549i | 0.0885142 | − | 0.0511037i | −0.455090 | − | 0.890446i | \(-0.650393\pi\) |
0.543604 | + | 0.839342i | \(0.317059\pi\) | |||||||
\(258\) | −2949.09 | −0.711637 | ||||||||
\(259\) | −1452.13 | − | 1886.89i | −0.348383 | − | 0.452685i | ||||
\(260\) | −2690.95 | −0.641868 | ||||||||
\(261\) | 1583.87 | − | 914.448i | 0.375629 | − | 0.216869i | ||||
\(262\) | 886.936 | − | 1536.22i | 0.209141 | − | 0.362244i | ||||
\(263\) | 24.8852 | − | 43.1025i | 0.00583456 | − | 0.0101058i | −0.863093 | − | 0.505044i | \(-0.831476\pi\) |
0.868928 | + | 0.494939i | \(0.164809\pi\) | |||||||
\(264\) | 1295.82 | + | 748.140i | 0.302091 | + | 0.174412i | ||||
\(265\) | − | 9327.12i | − | 2.16212i | ||||||
\(266\) | −1100.05 | + | 1905.34i | −0.253565 | + | 0.439187i | ||||
\(267\) | 2479.14i | 0.568244i | ||||||||
\(268\) | 1697.83 | + | 2940.72i | 0.386982 | + | 0.670273i | ||||
\(269\) | −5546.79 | −1.25722 | −0.628612 | − | 0.777719i | \(-0.716377\pi\) | ||||
−0.628612 | + | 0.777719i | \(0.716377\pi\) | |||||||
\(270\) | 808.712 | 0.182284 | ||||||||
\(271\) | 817.446 | + | 1415.86i | 0.183234 | + | 0.317370i | 0.942980 | − | 0.332850i | \(-0.108010\pi\) |
−0.759746 | + | 0.650220i | \(0.774677\pi\) | |||||||
\(272\) | 1046.20 | + | 604.026i | 0.233218 | + | 0.134649i | ||||
\(273\) | − | 3327.82i | − | 0.737762i | ||||||
\(274\) | 4438.83 | − | 2562.76i | 0.978685 | − | 0.565044i | ||||
\(275\) | −1382.35 | − | 2394.31i | −0.303124 | − | 0.525026i | ||||
\(276\) | 1063.27 | − | 613.881i | 0.231890 | − | 0.133882i | ||||
\(277\) | 6965.83 | + | 4021.72i | 1.51096 | + | 0.872354i | 0.999918 | + | 0.0127983i | \(0.00407394\pi\) |
0.511043 | + | 0.859555i | \(0.329259\pi\) | |||||||
\(278\) | −5312.02 | − | 3066.89i | −1.14602 | − | 0.661655i | ||||
\(279\) | −5320.66 | + | 3071.89i | −1.14172 | + | 0.659172i | ||||
\(280\) | 641.443 | + | 1111.01i | 0.136906 | + | 0.237128i | ||||
\(281\) | −3817.25 | + | 2203.89i | −0.810384 | + | 0.467875i | −0.847089 | − | 0.531451i | \(-0.821647\pi\) |
0.0367053 | + | 0.999326i | \(0.488314\pi\) | |||||||
\(282\) | − | 7508.16i | − | 1.58548i | ||||||
\(283\) | 397.542 | + | 229.521i | 0.0835033 | + | 0.0482106i | 0.541170 | − | 0.840913i | \(-0.317981\pi\) |
−0.457667 | + | 0.889124i | \(0.651315\pi\) | |||||||
\(284\) | −2035.85 | − | 3526.20i | −0.425372 | − | 0.736766i | ||||
\(285\) | 11171.6 | 2.32192 | ||||||||
\(286\) | 2342.30 | 0.484277 | ||||||||
\(287\) | −947.625 | − | 1641.34i | −0.194901 | − | 0.337578i | ||||
\(288\) | 743.563i | 0.152135i | ||||||||
\(289\) | 393.867 | − | 682.198i | 0.0801684 | − | 0.138856i | ||||
\(290\) | 2386.15i | 0.483170i | ||||||||
\(291\) | 586.070 | + | 338.367i | 0.118062 | + | 0.0681631i | ||||
\(292\) | 1307.09 | − | 2263.94i | 0.261957 | − | 0.453723i | ||||
\(293\) | −575.059 | + | 996.031i | −0.114660 | + | 0.198596i | −0.917644 | − | 0.397404i | \(-0.869911\pi\) |
0.802984 | + | 0.596001i | \(0.203244\pi\) | |||||||
\(294\) | 2836.83 | − | 1637.85i | 0.562747 | − | 0.324902i | ||||
\(295\) | 5961.24 | 1.17653 | ||||||||
\(296\) | 1664.42 | + | 686.652i | 0.326833 | + | 0.134834i | ||||
\(297\) | −703.933 | −0.137530 | ||||||||
\(298\) | 5607.74 | − | 3237.63i | 1.09009 | − | 0.629366i | ||||
\(299\) | 960.981 | − | 1664.47i | 0.185869 | − | 0.321935i | ||||
\(300\) | 1485.17 | − | 2572.38i | 0.285820 | − | 0.495055i | ||||
\(301\) | 1906.04 | + | 1100.45i | 0.364991 | + | 0.210728i | ||||
\(302\) | 1606.31i | 0.306069i | ||||||||
\(303\) | −2712.35 | + | 4697.93i | −0.514259 | + | 0.890723i | ||||
\(304\) | − | 1663.72i | − | 0.313884i | ||||||
\(305\) | −5693.65 | − | 9861.69i | −1.06891 | − | 1.85141i | ||||
\(306\) | 3508.84 | 0.655513 | ||||||||
\(307\) | −2503.94 | −0.465497 | −0.232749 | − | 0.972537i | \(-0.574772\pi\) | ||||
−0.232749 | + | 0.972537i | \(0.574772\pi\) | |||||||
\(308\) | −558.336 | − | 967.066i | −0.103293 | − | 0.178908i | ||||
\(309\) | 6552.13 | + | 3782.87i | 1.20627 | + | 0.696441i | ||||
\(310\) | − | 8015.74i | − | 1.46859i | ||||||
\(311\) | 7958.00 | − | 4594.55i | 1.45099 | − | 0.837727i | 0.452449 | − | 0.891790i | \(-0.350551\pi\) |
0.998538 | + | 0.0540630i | \(0.0172172\pi\) | |||||||
\(312\) | 1258.25 | + | 2179.36i | 0.228316 | + | 0.395455i | ||||
\(313\) | −4988.95 | + | 2880.37i | −0.900934 | + | 0.520155i | −0.877503 | − | 0.479571i | \(-0.840792\pi\) |
−0.0234309 | + | 0.999725i | \(0.507459\pi\) | |||||||
\(314\) | 4247.64 | + | 2452.37i | 0.763402 | + | 0.440750i | ||||
\(315\) | 3226.99 | + | 1863.10i | 0.577206 | + | 0.333250i | ||||
\(316\) | −2867.70 | + | 1655.67i | −0.510509 | + | 0.294742i | ||||
\(317\) | −3628.85 | − | 6285.35i | −0.642955 | − | 1.11363i | −0.984770 | − | 0.173863i | \(-0.944375\pi\) |
0.341815 | − | 0.939767i | \(-0.388958\pi\) | |||||||
\(318\) | −7553.89 | + | 4361.24i | −1.33208 | + | 0.769077i | ||||
\(319\) | − | 2076.99i | − | 0.364543i | ||||||
\(320\) | −840.150 | − | 485.061i | −0.146768 | − | 0.0847367i | ||||
\(321\) | 2784.78 | + | 4823.39i | 0.484210 | + | 0.838676i | ||||
\(322\) | −916.278 | −0.158578 | ||||||||
\(323\) | −7851.00 | −1.35245 | ||||||||
\(324\) | −1632.91 | − | 2828.28i | −0.279991 | − | 0.484958i | ||||
\(325\) | − | 4649.81i | − | 0.793616i | ||||||
\(326\) | 0.452760 | − | 0.784203i | 7.69204e−5 | − | 0.000133230i | ||||
\(327\) | 8477.30i | 1.43363i | ||||||||
\(328\) | 1241.18 | + | 716.596i | 0.208941 | + | 0.120632i | ||||
\(329\) | −2801.67 | + | 4852.63i | −0.469486 | + | 0.813173i | ||||
\(330\) | −2835.10 | + | 4910.54i | −0.472931 | + | 0.819141i | ||||
\(331\) | 1905.02 | − | 1099.86i | 0.316342 | − | 0.182640i | −0.333419 | − | 0.942779i | \(-0.608202\pi\) |
0.649761 | + | 0.760138i | \(0.274869\pi\) | |||||||
\(332\) | 540.248 | 0.0893071 | ||||||||
\(333\) | 5183.91 | − | 689.983i | 0.853082 | − | 0.113546i | ||||
\(334\) | 2031.64 | 0.332833 | ||||||||
\(335\) | −11144.0 | + | 6433.98i | −1.81750 | + | 1.04933i | ||||
\(336\) | 599.862 | − | 1038.99i | 0.0973962 | − | 0.168695i | ||||
\(337\) | −2296.24 | + | 3977.20i | −0.371169 | + | 0.642884i | −0.989746 | − | 0.142841i | \(-0.954376\pi\) |
0.618577 | + | 0.785724i | \(0.287710\pi\) | |||||||
\(338\) | −393.706 | − | 227.306i | −0.0633573 | − | 0.0365794i | ||||
\(339\) | 1503.78i | 0.240927i | ||||||||
\(340\) | −2288.98 | + | 3964.63i | −0.365110 | + | 0.632389i | ||||
\(341\) | 6977.19i | 1.10802i | ||||||||
\(342\) | −2416.17 | − | 4184.93i | −0.382022 | − | 0.661682i | ||||
\(343\) | −6073.31 | −0.956057 | ||||||||
\(344\) | −1664.33 | −0.260856 | ||||||||
\(345\) | 2326.33 | + | 4029.32i | 0.363030 | + | 0.628786i | ||||
\(346\) | 559.525 | + | 323.042i | 0.0869371 | + | 0.0501932i | ||||
\(347\) | − | 5311.90i | − | 0.821780i | −0.911685 | − | 0.410890i | \(-0.865218\pi\) | ||
0.911685 | − | 0.410890i | \(-0.134782\pi\) | |||||||
\(348\) | 1932.50 | − | 1115.73i | 0.297681 | − | 0.171866i | ||||
\(349\) | −899.057 | − | 1557.21i | −0.137895 | − | 0.238841i | 0.788805 | − | 0.614644i | \(-0.210700\pi\) |
−0.926700 | + | 0.375803i | \(0.877367\pi\) | |||||||
\(350\) | −1919.77 | + | 1108.38i | −0.293188 | + | 0.169272i | ||||
\(351\) | −1025.29 | − | 591.953i | −0.155915 | − | 0.0900174i | ||||
\(352\) | 731.298 | + | 422.215i | 0.110734 | + | 0.0639322i | ||||
\(353\) | 2761.25 | − | 1594.21i | 0.416335 | − | 0.240371i | −0.277173 | − | 0.960820i | \(-0.589397\pi\) |
0.693508 | + | 0.720449i | \(0.256064\pi\) | |||||||
\(354\) | −2787.40 | − | 4827.92i | −0.418499 | − | 0.724861i | ||||
\(355\) | 13362.7 | − | 7714.94i | 1.99779 | − | 1.15343i | ||||
\(356\) | 1399.11i | 0.208295i | ||||||||
\(357\) | −4902.95 | − | 2830.72i | −0.726867 | − | 0.419657i | ||||
\(358\) | −253.165 | − | 438.495i | −0.0373748 | − | 0.0647351i | ||||
\(359\) | −2540.58 | −0.373500 | −0.186750 | − | 0.982407i | \(-0.559795\pi\) | ||||
−0.186750 | + | 0.982407i | \(0.559795\pi\) | |||||||
\(360\) | −2817.76 | −0.412525 | ||||||||
\(361\) | 1976.67 | + | 3423.69i | 0.288186 | + | 0.499153i | ||||
\(362\) | − | 6284.07i | − | 0.912385i | ||||||
\(363\) | −2249.13 | + | 3895.60i | −0.325203 | + | 0.563267i | ||||
\(364\) | − | 1878.07i | − | 0.270433i | ||||||
\(365\) | 8579.29 | + | 4953.26i | 1.23030 | + | 0.710316i | ||||
\(366\) | −5324.55 | + | 9222.40i | −0.760434 | + | 1.31711i | ||||
\(367\) | −2944.45 | + | 5099.95i | −0.418799 | + | 0.725381i | −0.995819 | − | 0.0913487i | \(-0.970882\pi\) |
0.577020 | + | 0.816730i | \(0.304216\pi\) | |||||||
\(368\) | 600.062 | − | 346.446i | 0.0850011 | − | 0.0490754i | ||||
\(369\) | 4162.77 | 0.587277 | ||||||||
\(370\) | −2602.10 | + | 6307.39i | −0.365612 | + | 0.886232i | ||||
\(371\) | 6509.58 | 0.910945 | ||||||||
\(372\) | −6491.82 | + | 3748.06i | −0.904799 | + | 0.522386i | ||||
\(373\) | −3663.73 | + | 6345.77i | −0.508582 | + | 0.880889i | 0.491369 | + | 0.870951i | \(0.336497\pi\) |
−0.999951 | + | 0.00993769i | \(0.996837\pi\) | |||||||
\(374\) | 1992.41 | − | 3450.96i | 0.275468 | − | 0.477125i | ||||
\(375\) | −1882.30 | − | 1086.74i | −0.259204 | − | 0.149651i | ||||
\(376\) | − | 4237.25i | − | 0.581169i | ||||||
\(377\) | 1746.59 | − | 3025.18i | 0.238604 | − | 0.413275i | ||||
\(378\) | 564.416i | 0.0768001i | ||||||||
\(379\) | −290.710 | − | 503.524i | −0.0394004 | − | 0.0682435i | 0.845653 | − | 0.533733i | \(-0.179211\pi\) |
−0.885053 | + | 0.465490i | \(0.845878\pi\) | |||||||
\(380\) | 6304.72 | 0.851120 | ||||||||
\(381\) | −9723.14 | −1.30743 | ||||||||
\(382\) | 680.510 | + | 1178.68i | 0.0911464 | + | 0.157870i | ||||
\(383\) | −1830.06 | − | 1056.59i | −0.244157 | − | 0.140964i | 0.372929 | − | 0.927860i | \(-0.378353\pi\) |
−0.617086 | + | 0.786896i | \(0.711687\pi\) | |||||||
\(384\) | 907.233i | 0.120565i | ||||||||
\(385\) | 3664.73 | − | 2115.84i | 0.485123 | − | 0.280086i | ||||
\(386\) | 1363.63 | + | 2361.87i | 0.179810 | + | 0.311440i | ||||
\(387\) | −4186.47 | + | 2417.06i | −0.549897 | + | 0.317483i | ||||
\(388\) | 330.750 | + | 190.959i | 0.0432765 | + | 0.0249857i | ||||
\(389\) | 10477.7 | + | 6049.30i | 1.36566 | + | 0.788461i | 0.990370 | − | 0.138448i | \(-0.0442114\pi\) |
0.375285 | + | 0.926909i | \(0.377545\pi\) | |||||||
\(390\) | −8258.77 | + | 4768.20i | −1.07231 | + | 0.619096i | ||||
\(391\) | −1634.86 | − | 2831.66i | −0.211454 | − | 0.366249i | ||||
\(392\) | 1600.98 | − | 924.324i | 0.206279 | − | 0.119095i | ||||
\(393\) | − | 6286.39i | − | 0.806886i | ||||||
\(394\) | 3688.18 | + | 2129.37i | 0.471594 | + | 0.272275i | ||||
\(395\) | −6274.22 | − | 10867.3i | −0.799215 | − | 1.38428i | ||||
\(396\) | 2452.68 | 0.311242 | ||||||||
\(397\) | 2751.46 | 0.347838 | 0.173919 | − | 0.984760i | \(-0.444357\pi\) | ||||
0.173919 | + | 0.984760i | \(0.444357\pi\) | |||||||
\(398\) | 2582.54 | + | 4473.09i | 0.325254 | + | 0.563356i | ||||
\(399\) | 7796.88i | 0.978276i | ||||||||
\(400\) | 838.158 | − | 1451.73i | 0.104770 | − | 0.181466i | ||||
\(401\) | 1553.48i | 0.193459i | 0.995311 | + | 0.0967293i | \(0.0308381\pi\) | ||||
−0.995311 | + | 0.0967293i | \(0.969162\pi\) | |||||||
\(402\) | 10421.6 | + | 6016.90i | 1.29299 | + | 0.746506i | ||||
\(403\) | −5867.27 | + | 10162.4i | −0.725235 | + | 1.25614i | ||||
\(404\) | −1530.72 | + | 2651.29i | −0.188506 | + | 0.326502i | ||||
\(405\) | 10717.9 | − | 6187.96i | 1.31500 | − | 0.759216i | ||||
\(406\) | −1665.34 | −0.203570 | ||||||||
\(407\) | 2264.96 | − | 5490.19i | 0.275847 | − | 0.668645i | ||||
\(408\) | 4281.19 | 0.519486 | ||||||||
\(409\) | −10847.6 | + | 6262.89i | −1.31145 | + | 0.757163i | −0.982335 | − | 0.187129i | \(-0.940082\pi\) |
−0.329110 | + | 0.944292i | \(0.606749\pi\) | |||||||
\(410\) | −2715.57 | + | 4703.51i | −0.327104 | + | 0.566560i | ||||
\(411\) | 9082.12 | − | 15730.7i | 1.08999 | − | 1.88793i | ||||
\(412\) | 3697.72 | + | 2134.88i | 0.442168 | + | 0.255286i | ||||
\(413\) | 4160.47i | 0.495698i | ||||||||
\(414\) | 1006.27 | − | 1742.91i | 0.119457 | − | 0.206906i | ||||
\(415\) | 2047.29i | 0.242163i | ||||||||
\(416\) | 710.100 | + | 1229.93i | 0.0836911 | + | 0.144957i | ||||
\(417\) | −21737.4 | −2.55272 | ||||||||
\(418\) | −5487.86 | −0.642154 | ||||||||
\(419\) | 432.299 | + | 748.764i | 0.0504038 | + | 0.0873020i | 0.890127 | − | 0.455713i | \(-0.150616\pi\) |
−0.839723 | + | 0.543015i | \(0.817283\pi\) | |||||||
\(420\) | 3937.30 | + | 2273.20i | 0.457429 | + | 0.264097i | ||||
\(421\) | − | 12693.3i | − | 1.46943i | −0.678374 | − | 0.734717i | \(-0.737315\pi\) | ||
0.678374 | − | 0.734717i | \(-0.262685\pi\) | |||||||
\(422\) | 9559.36 | − | 5519.10i | 1.10271 | − | 0.636648i | ||||
\(423\) | −6153.64 | − | 10658.4i | −0.707330 | − | 1.22513i | ||||
\(424\) | −4263.06 | + | 2461.28i | −0.488285 | + | 0.281911i | ||||
\(425\) | −6850.65 | − | 3955.23i | −0.781895 | − | 0.451427i | ||||
\(426\) | −12496.4 | − | 7214.82i | −1.42125 | − | 0.820561i | ||||
\(427\) | 6882.67 | − | 3973.71i | 0.780037 | − | 0.450354i | ||||
\(428\) | 1571.60 | + | 2722.09i | 0.177491 | + | 0.307424i | ||||
\(429\) | 7188.74 | − | 4150.42i | 0.809034 | − | 0.467096i | ||||
\(430\) | − | 6307.04i | − | 0.707331i | ||||||
\(431\) | −7316.54 | − | 4224.21i | −0.817692 | − | 0.472095i | 0.0319277 | − | 0.999490i | \(-0.489835\pi\) |
−0.849620 | + | 0.527395i | \(0.823169\pi\) | |||||||
\(432\) | −213.407 | − | 369.631i | −0.0237674 | − | 0.0411664i | ||||
\(433\) | −10838.1 | −1.20288 | −0.601439 | − | 0.798919i | \(-0.705406\pi\) | ||||
−0.601439 | + | 0.798919i | \(0.705406\pi\) | |||||||
\(434\) | 5594.34 | 0.618749 | ||||||||
\(435\) | 4228.11 | + | 7323.30i | 0.466028 | + | 0.807185i | ||||
\(436\) | 4784.19i | 0.525507i | ||||||||
\(437\) | −2251.52 | + | 3899.74i | −0.246464 | + | 0.426888i | ||||
\(438\) | − | 9264.32i | − | 1.01065i | ||||||
\(439\) | 7920.18 | + | 4572.72i | 0.861069 | + | 0.497139i | 0.864370 | − | 0.502856i | \(-0.167717\pi\) |
−0.00330099 | + | 0.999995i | \(0.501051\pi\) | |||||||
\(440\) | −1600.00 | + | 2771.28i | −0.173357 | + | 0.300263i | ||||
\(441\) | 2684.74 | − | 4650.11i | 0.289897 | − | 0.502117i | ||||
\(442\) | 5803.97 | − | 3350.93i | 0.624586 | − | 0.360605i | ||||
\(443\) | 8297.95 | 0.889950 | 0.444975 | − | 0.895543i | \(-0.353213\pi\) | ||||
0.444975 | + | 0.895543i | \(0.353213\pi\) | |||||||
\(444\) | 6324.97 | − | 841.859i | 0.676058 | − | 0.0899839i | ||||
\(445\) | −5301.99 | −0.564806 | ||||||||
\(446\) | −10127.9 | + | 5847.34i | −1.07527 | + | 0.620806i | ||||
\(447\) | 11473.8 | − | 19873.2i | 1.21407 | − | 2.10284i | ||||
\(448\) | 338.534 | − | 586.358i | 0.0357014 | − | 0.0618366i | ||||
\(449\) | 11443.8 | + | 6607.08i | 1.20282 | + | 0.694448i | 0.961181 | − | 0.275918i | \(-0.0889818\pi\) |
0.241639 | + | 0.970366i | \(0.422315\pi\) | |||||||
\(450\) | − | 4868.93i | − | 0.510053i | ||||||
\(451\) | 2363.73 | − | 4094.10i | 0.246793 | − | 0.427459i | ||||
\(452\) | 848.663i | 0.0883136i | ||||||||
\(453\) | 2846.29 | + | 4929.91i | 0.295210 | + | 0.511319i | ||||
\(454\) | −3518.02 | −0.363676 | ||||||||
\(455\) | 7117.01 | 0.733298 | ||||||||
\(456\) | −2948.01 | − | 5106.10i | −0.302748 | − | 0.524375i | ||||
\(457\) | 7782.89 | + | 4493.46i | 0.796649 | + | 0.459945i | 0.842298 | − | 0.539012i | \(-0.181202\pi\) |
−0.0456494 | + | 0.998958i | \(0.514536\pi\) | |||||||
\(458\) | − | 462.089i | − | 0.0471442i | ||||||
\(459\) | −1744.27 | + | 1007.05i | −0.177376 | + | 0.102408i | ||||
\(460\) | 1312.87 | + | 2273.96i | 0.133072 | + | 0.230487i | ||||
\(461\) | −14559.6 | + | 8405.98i | −1.47095 | + | 0.849253i | −0.999468 | − | 0.0326229i | \(-0.989614\pi\) |
−0.471482 | + | 0.881876i | \(0.656281\pi\) | |||||||
\(462\) | −3427.17 | − | 1978.68i | −0.345122 | − | 0.199256i | ||||
\(463\) | −1980.56 | − | 1143.48i | −0.198800 | − | 0.114777i | 0.397296 | − | 0.917691i | \(-0.369949\pi\) |
−0.596096 | + | 0.802913i | \(0.703282\pi\) | |||||||
\(464\) | 1090.61 | − | 629.667i | 0.109118 | − | 0.0629990i | ||||
\(465\) | −14203.4 | − | 24601.0i | −1.41649 | − | 2.45343i | ||||
\(466\) | 5449.78 | − | 3146.43i | 0.541751 | − | 0.312780i | ||||
\(467\) | − | 10278.1i | − | 1.01845i | −0.860634 | − | 0.509224i | \(-0.829932\pi\) | ||
0.860634 | − | 0.509224i | \(-0.170068\pi\) | |||||||
\(468\) | 3572.38 | + | 2062.52i | 0.352849 | + | 0.203718i | ||||
\(469\) | −4490.40 | − | 7777.61i | −0.442106 | − | 0.765750i | ||||
\(470\) | 16057.2 | 1.57588 | ||||||||
\(471\) | 17381.8 | 1.70045 | ||||||||
\(472\) | −1573.08 | − | 2724.65i | −0.153404 | − | 0.265704i | ||||
\(473\) | 5489.88i | 0.533668i | ||||||||
\(474\) | −5867.49 | + | 10162.8i | −0.568571 | + | 0.984794i | ||||
\(475\) | 10894.2i | 1.05234i | ||||||||
\(476\) | −2766.99 | − | 1597.52i | −0.266439 | − | 0.153829i | ||||
\(477\) | −7148.90 | + | 12382.3i | −0.686217 | + | 1.18856i | ||||
\(478\) | 1836.30 | − | 3180.57i | 0.175712 | − | 0.304343i | ||||
\(479\) | −4680.36 | + | 2702.21i | −0.446453 | + | 0.257760i | −0.706331 | − | 0.707882i | \(-0.749651\pi\) |
0.259878 | + | 0.965642i | \(0.416318\pi\) | |||||||
\(480\) | −3438.00 | −0.326922 | ||||||||
\(481\) | 7915.78 | − | 6091.91i | 0.750371 | − | 0.577479i | ||||
\(482\) | 6133.71 | 0.579632 | ||||||||
\(483\) | −2812.14 | + | 1623.59i | −0.264921 | + | 0.152952i | ||||
\(484\) | −1269.30 | + | 2198.49i | −0.119206 | + | 0.206470i | ||||
\(485\) | −723.646 | + | 1253.39i | −0.0677506 | + | 0.117348i | ||||
\(486\) | −8775.57 | − | 5066.58i | −0.819070 | − | 0.472890i | ||||
\(487\) | − | 6495.44i | − | 0.604387i | −0.953247 | − | 0.302194i | \(-0.902281\pi\) | ||
0.953247 | − | 0.302194i | \(-0.0977190\pi\) | |||||||
\(488\) | −3004.93 | + | 5204.69i | −0.278743 | + | 0.482798i | ||||
\(489\) | − | 3.20905i | − | 0.000296766i | ||||||
\(490\) | 3502.76 | + | 6066.96i | 0.322936 | + | 0.559342i | ||||
\(491\) | 15466.9 | 1.42161 | 0.710807 | − | 0.703387i | \(-0.248330\pi\) | ||||
0.710807 | + | 0.703387i | \(0.248330\pi\) | |||||||
\(492\) | 5079.06 | 0.465410 | ||||||||
\(493\) | −2971.37 | − | 5146.56i | −0.271447 | − | 0.470161i | ||||
\(494\) | −7993.18 | − | 4614.87i | −0.727997 | − | 0.420309i | ||||
\(495\) | 9294.54i | 0.843957i | ||||||||
\(496\) | −3663.68 | + | 2115.23i | −0.331662 | + | 0.191485i | ||||
\(497\) | 5384.41 | + | 9326.08i | 0.485964 | + | 0.841714i | ||||
\(498\) | 1658.07 | − | 957.287i | 0.149197 | − | 0.0861387i | ||||
\(499\) | 13070.5 | + | 7546.24i | 1.17257 | + | 0.676986i | 0.954285 | − | 0.298898i | \(-0.0966192\pi\) |
0.218289 | + | 0.975884i | \(0.429953\pi\) | |||||||
\(500\) | −1062.28 | − | 613.307i | −0.0950132 | − | 0.0548559i | ||||
\(501\) | 6235.28 | − | 3599.94i | 0.556031 | − | 0.321025i | ||||
\(502\) | 4267.04 | + | 7390.72i | 0.379377 | + | 0.657100i | ||||
\(503\) | −1968.78 | + | 1136.68i | −0.174520 | + | 0.100759i | −0.584715 | − | 0.811238i | \(-0.698794\pi\) |
0.410195 | + | 0.911998i | \(0.365460\pi\) | |||||||
\(504\) | − | 1966.57i | − | 0.173806i | ||||||
\(505\) | −10047.2 | − | 5800.74i | −0.885334 | − | 0.511148i | ||||
\(506\) | −1142.77 | − | 1979.34i | −0.100400 | − | 0.173898i | ||||
\(507\) | −1611.09 | −0.141126 | ||||||||
\(508\) | −5487.28 | −0.479250 | ||||||||
\(509\) | −4905.93 | − | 8497.31i | −0.427213 | − | 0.739954i | 0.569411 | − | 0.822053i | \(-0.307171\pi\) |
−0.996624 | + | 0.0820983i | \(0.973838\pi\) | |||||||
\(510\) | 16223.7i | 1.40863i | ||||||||
\(511\) | −3456.98 | + | 5987.66i | −0.299271 | + | 0.518353i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 2402.19 | + | 1386.91i | 0.206744 | + | 0.119363i | ||||
\(514\) | 421.097 | − | 729.361i | 0.0361358 | − | 0.0625890i | ||||
\(515\) | −8090.20 | + | 14012.6i | −0.692227 | + | 1.19897i | ||||
\(516\) | −5107.98 | + | 2949.09i | −0.435787 | + | 0.251602i | ||||
\(517\) | −13976.8 | −1.18897 | ||||||||
\(518\) | −4402.05 | − | 1816.05i | −0.373388 | − | 0.154040i | ||||
\(519\) | 2289.64 | 0.193650 | ||||||||
\(520\) | −4660.86 | + | 2690.95i | −0.393062 | + | 0.226935i | ||||
\(521\) | 5109.78 | − | 8850.40i | 0.429680 | − | 0.744228i | −0.567164 | − | 0.823605i | \(-0.691960\pi\) |
0.996845 | + | 0.0793763i | \(0.0252929\pi\) | |||||||
\(522\) | 1828.90 | − | 3167.74i | 0.153350 | − | 0.265610i | ||||
\(523\) | 1256.36 | + | 725.358i | 0.105041 | + | 0.0606457i | 0.551600 | − | 0.834109i | \(-0.314017\pi\) |
−0.446559 | + | 0.894754i | \(0.647351\pi\) | |||||||
\(524\) | − | 3547.74i | − | 0.295771i | ||||||
\(525\) | −3927.96 | + | 6803.42i | −0.326534 | + | 0.565573i | ||||
\(526\) | − | 99.5409i | − | 0.00825131i | ||||||
\(527\) | 9981.65 | + | 17288.7i | 0.825062 | + | 1.42905i | ||||
\(528\) | 2992.56 | 0.246656 | ||||||||
\(529\) | 10291.6 | 0.845863 | ||||||||
\(530\) | −9327.12 | − | 16155.0i | −0.764423 | − | 1.32402i | ||||
\(531\) | −7913.87 | − | 4569.07i | −0.646766 | − | 0.373410i | ||||
\(532\) | 4400.19i | 0.358595i | ||||||||
\(533\) | 6885.65 | − | 3975.43i | 0.559569 | − | 0.323067i | ||||
\(534\) | 2479.14 | + | 4294.00i | 0.200905 | + | 0.347977i | ||||
\(535\) | −10315.5 | + | 5955.64i | −0.833602 | + | 0.481280i | ||||
\(536\) | 5881.45 | + | 3395.65i | 0.473955 | + | 0.273638i | ||||
\(537\) | −1553.97 | − | 897.187i | −0.124877 | − | 0.0720977i | ||||
\(538\) | −9607.31 | + | 5546.79i | −0.769890 | + | 0.444496i | ||||
\(539\) | −3048.93 | − | 5280.91i | −0.243649 | − | 0.422012i | ||||
\(540\) | 1400.73 | − | 808.712i | 0.111626 | − | 0.0644471i | ||||
\(541\) | − | 12067.4i | − | 0.959002i | −0.877541 | − | 0.479501i | \(-0.840818\pi\) | ||
0.877541 | − | 0.479501i | \(-0.159182\pi\) | |||||||
\(542\) | 2831.72 | + | 1634.89i | 0.224415 | + | 0.129566i | ||||
\(543\) | −11135.0 | − | 19286.4i | −0.880015 | − | 1.52423i | ||||
\(544\) | 2416.10 | 0.190422 | ||||||||
\(545\) | −18129.9 | −1.42495 | ||||||||
\(546\) | −3327.82 | − | 5763.96i | −0.260838 | − | 0.451785i | ||||
\(547\) | 12947.2i | 1.01204i | 0.862523 | + | 0.506018i | \(0.168883\pi\) | ||||
−0.862523 | + | 0.506018i | \(0.831117\pi\) | |||||||
\(548\) | 5125.52 | − | 8877.67i | 0.399546 | − | 0.692035i | ||||
\(549\) | 17455.9i | 1.35701i | ||||||||
\(550\) | −4788.62 | − | 2764.71i | −0.371250 | − | 0.214341i | ||||
\(551\) | −4092.14 | + | 7087.80i | −0.316390 | + | 0.548004i | ||||
\(552\) | 1227.76 | − | 2126.55i | 0.0946686 | − | 0.163971i | ||||
\(553\) | 7584.48 | − | 4378.90i | 0.583227 | − | 0.336727i | ||||
\(554\) | 16086.9 | 1.23369 | ||||||||
\(555\) | 3190.26 | + | 23968.7i | 0.243998 | + | 1.83318i | ||||
\(556\) | −12267.6 | −0.935722 | ||||||||
\(557\) | 1846.29 | − | 1065.96i | 0.140449 | − | 0.0810880i | −0.428129 | − | 0.903718i | \(-0.640827\pi\) |
0.568578 | + | 0.822630i | \(0.307494\pi\) | |||||||
\(558\) | −6143.77 | + | 10641.3i | −0.466105 | + | 0.807318i | ||||
\(559\) | −4616.56 | + | 7996.12i | −0.349302 | + | 0.605008i | ||||
\(560\) | 2222.03 | + | 1282.89i | 0.167674 | + | 0.0968069i | ||||
\(561\) | − | 14121.7i | − | 1.06278i | ||||||
\(562\) | −4407.78 | + | 7634.49i | −0.330838 | + | 0.573028i | ||||
\(563\) | 22392.2i | 1.67623i | 0.545490 | + | 0.838117i | \(0.316344\pi\) | ||||
−0.545490 | + | 0.838117i | \(0.683656\pi\) | |||||||
\(564\) | −7508.16 | − | 13004.5i | −0.560551 | − | 0.970902i | ||||
\(565\) | −3216.04 | −0.239469 | ||||||||
\(566\) | 918.084 | 0.0681801 | ||||||||
\(567\) | 4318.70 | + | 7480.21i | 0.319874 | + | 0.554038i | ||||
\(568\) | −7052.40 | − | 4071.71i | −0.520972 | − | 0.300783i | ||||
\(569\) | 14343.5i | 1.05679i | 0.848999 | + | 0.528394i | \(0.177206\pi\) | ||||
−0.848999 | + | 0.528394i | \(0.822794\pi\) | |||||||
\(570\) | 19349.8 | − | 11171.6i | 1.42188 | − | 0.820924i | ||||
\(571\) | −10466.3 | − | 18128.2i | −0.767077 | − | 1.32862i | −0.939141 | − | 0.343531i | \(-0.888377\pi\) |
0.172064 | − | 0.985086i | \(-0.444956\pi\) | |||||||
\(572\) | 4056.99 | − | 2342.30i | 0.296558 | − | 0.171218i | ||||
\(573\) | 4177.09 | + | 2411.65i | 0.304538 | + | 0.175825i | ||||
\(574\) | −3282.67 | − | 1895.25i | −0.238704 | − | 0.137816i | ||||
\(575\) | −3929.27 | + | 2268.57i | −0.284977 | + | 0.164532i | ||||
\(576\) | 743.563 | + | 1287.89i | 0.0537879 | + | 0.0931633i | ||||
\(577\) | −22977.6 | + | 13266.1i | −1.65783 | + | 0.957150i | −0.684120 | + | 0.729370i | \(0.739813\pi\) |
−0.973713 | + | 0.227780i | \(0.926853\pi\) | |||||||
\(578\) | − | 1575.47i | − | 0.113375i | ||||||
\(579\) | 8370.18 | + | 4832.53i | 0.600782 | + | 0.346862i | ||||
\(580\) | 2386.15 | + | 4132.93i | 0.170826 | + | 0.295880i | ||||
\(581\) | −1428.84 | −0.102028 | ||||||||
\(582\) | 1353.47 | 0.0963971 | ||||||||
\(583\) | 8118.67 | + | 14061.9i | 0.576743 | + | 0.998947i | ||||
\(584\) | − | 5228.35i | − | 0.370463i | ||||||
\(585\) | −7815.99 | + | 13537.7i | −0.552395 | + | 0.956777i | ||||
\(586\) | 2300.23i | 0.162153i | ||||||||
\(587\) | −7352.14 | − | 4244.76i | −0.516960 | − | 0.298467i | 0.218730 | − | 0.975785i | \(-0.429809\pi\) |
−0.735690 | + | 0.677318i | \(0.763142\pi\) | |||||||
\(588\) | 3275.69 | − | 5673.67i | 0.229740 | − | 0.397922i | ||||
\(589\) | 13746.6 | − | 23809.9i | 0.961665 | − | 1.66565i | ||||
\(590\) | 10325.2 | − | 5961.24i | 0.720475 | − | 0.415967i | ||||
\(591\) | 15092.5 | 1.05046 | ||||||||
\(592\) | 3569.52 | − | 475.106i | 0.247815 | − | 0.0329843i | ||||
\(593\) | 18980.5 | 1.31440 | 0.657198 | − | 0.753718i | \(-0.271742\pi\) | ||||
0.657198 | + | 0.753718i | \(0.271742\pi\) | |||||||
\(594\) | −1219.25 | + | 703.933i | −0.0842194 | + | 0.0486241i | ||||
\(595\) | 6053.88 | − | 10485.6i | 0.417117 | − | 0.722469i | ||||
\(596\) | 6475.27 | − | 11215.5i | 0.445029 | − | 0.770813i | ||||
\(597\) | 15852.1 | + | 9152.21i | 1.08674 | + | 0.627429i | ||||
\(598\) | − | 3843.92i | − | 0.262859i | ||||||
\(599\) | 8131.62 | − | 14084.4i | 0.554673 | − | 0.960721i | −0.443256 | − | 0.896395i | \(-0.646177\pi\) |
0.997929 | − | 0.0643262i | \(-0.0204898\pi\) | |||||||
\(600\) | − | 5940.66i | − | 0.404211i | ||||||
\(601\) | 2603.31 | + | 4509.07i | 0.176691 | + | 0.306038i | 0.940745 | − | 0.339114i | \(-0.110127\pi\) |
−0.764054 | + | 0.645152i | \(0.776794\pi\) | |||||||
\(602\) | 4401.81 | 0.298014 | ||||||||
\(603\) | 19725.7 | 1.33216 | ||||||||
\(604\) | 1606.31 | + | 2782.21i | 0.108212 | + | 0.187428i | ||||
\(605\) | −8331.28 | − | 4810.07i | −0.559859 | − | 0.323235i | ||||
\(606\) | 10849.4i | 0.727272i | ||||||||
\(607\) | −14421.2 | + | 8326.06i | −0.964311 | + | 0.556745i | −0.897497 | − | 0.441020i | \(-0.854617\pi\) |
−0.0668136 | + | 0.997765i | \(0.521283\pi\) | |||||||
\(608\) | −1663.72 | − | 2881.64i | −0.110975 | − | 0.192214i | ||||
\(609\) | −5111.08 | + | 2950.88i | −0.340084 | + | 0.196348i | ||||
\(610\) | −19723.4 | − | 11387.3i | −1.30914 | − | 0.755833i | ||||
\(611\) | −20357.5 | − | 11753.4i | −1.34792 | − | 0.778219i | ||||
\(612\) | 6077.49 | − | 3508.84i | 0.401418 | − | 0.231759i | ||||
\(613\) | −7117.27 | − | 12327.5i | −0.468946 | − | 0.812238i | 0.530424 | − | 0.847733i | \(-0.322033\pi\) |
−0.999370 | + | 0.0354942i | \(0.988699\pi\) | |||||||
\(614\) | −4336.96 | + | 2503.94i | −0.285058 | + | 0.164578i | ||||
\(615\) | 19247.3i | 1.26199i | ||||||||
\(616\) | −1934.13 | − | 1116.67i | −0.126507 | − | 0.0730389i | ||||
\(617\) | 10392.4 | + | 18000.2i | 0.678092 | + | 1.17449i | 0.975555 | + | 0.219756i | \(0.0705262\pi\) |
−0.297463 | + | 0.954733i | \(0.596141\pi\) | |||||||
\(618\) | 15131.5 | 0.984916 | ||||||||
\(619\) | 21684.9 | 1.40806 | 0.704031 | − | 0.710169i | \(-0.251381\pi\) | ||||
0.704031 | + | 0.710169i | \(0.251381\pi\) | |||||||
\(620\) | −8015.74 | − | 13883.7i | −0.519225 | − | 0.899325i | ||||
\(621\) | 1155.22i | 0.0746493i | ||||||||
\(622\) | 9189.11 | − | 15916.0i | 0.592363 | − | 1.02600i | ||||
\(623\) | − | 3700.37i | − | 0.237965i | ||||||
\(624\) | 4358.72 | + | 2516.51i | 0.279629 | + | 0.161444i | ||||
\(625\) | 8872.26 | − | 15367.2i | 0.567825 | − | 0.983501i | ||||
\(626\) | −5760.75 | + | 9977.91i | −0.367805 | + | 0.637057i | ||||
\(627\) | −16842.7 | + | 9724.17i | −1.07278 | + | 0.619371i | ||||
\(628\) | 9809.50 | 0.623315 | ||||||||
\(629\) | −2242.00 | − | 16844.4i | −0.142121 | − | 1.06777i | ||||
\(630\) | 7452.40 | 0.471287 | ||||||||
\(631\) | −17673.9 | + | 10204.1i | −1.11504 | + | 0.643767i | −0.940129 | − | 0.340818i | \(-0.889296\pi\) |
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(632\) | −3311.33 | + | 5735.40i | −0.208414 | + | 0.360984i | ||||
\(633\) | 19559.0 | − | 33877.2i | 1.22812 | − | 2.12717i | ||||
\(634\) | −12570.7 | − | 7257.70i | −0.787455 | − | 0.454638i | ||||
\(635\) | − | 20794.3i | − | 1.29952i | ||||||
\(636\) | −8722.49 | + | 15107.8i | −0.543819 | + | 0.941923i | ||||
\(637\) | − | 10255.7i | − | 0.637903i | ||||||
\(638\) | −2076.99 | − | 3597.45i | −0.128885 | − | 0.223236i | ||||
\(639\) | −23652.9 | −1.46431 | ||||||||
\(640\) | −1940.24 | −0.119836 | ||||||||
\(641\) | 13731.7 | + | 23784.1i | 0.846133 | + | 1.46554i | 0.884634 | + | 0.466286i | \(0.154408\pi\) |
−0.0385015 | + | 0.999259i | \(0.512258\pi\) | |||||||
\(642\) | 9646.77 | + | 5569.57i | 0.593034 | + | 0.342388i | ||||
\(643\) | 2214.77i | 0.135835i | 0.997691 | + | 0.0679176i | \(0.0216355\pi\) | ||||
−0.997691 | + | 0.0679176i | \(0.978365\pi\) | |||||||
\(644\) | −1587.04 | + | 916.278i | −0.0971089 | + | 0.0560659i | ||||
\(645\) | −11175.7 | − | 19356.9i | −0.682237 | − | 1.18167i | ||||
\(646\) | −13598.3 | + | 7851.00i | −0.828203 | + | 0.478163i | ||||
\(647\) | 4530.24 | + | 2615.54i | 0.275274 | + | 0.158930i | 0.631282 | − | 0.775553i | \(-0.282529\pi\) |
−0.356008 | + | 0.934483i | \(0.615862\pi\) | |||||||
\(648\) | −5656.55 | − | 3265.81i | −0.342917 | − | 0.197983i | ||||
\(649\) | −8987.41 | + | 5188.88i | −0.543585 | + | 0.313839i | ||||
\(650\) | −4649.81 | − | 8053.71i | −0.280585 | − | 0.485988i | ||||
\(651\) | 17169.5 | − | 9912.84i | 1.03368 | − | 0.596797i | ||||
\(652\) | − | 1.81104i | − | 0.000108782i | ||||||
\(653\) | 11787.9 | + | 6805.77i | 0.706428 | + | 0.407857i | 0.809737 | − | 0.586793i | \(-0.199610\pi\) |
−0.103309 | + | 0.994649i | \(0.532943\pi\) | |||||||
\(654\) | 8477.30 | + | 14683.1i | 0.506863 | + | 0.877913i | ||||
\(655\) | 13444.3 | 0.802004 | ||||||||
\(656\) | 2866.39 | 0.170600 | ||||||||
\(657\) | −7592.98 | − | 13151.4i | −0.450884 | − | 0.780953i | ||||
\(658\) | 11206.7i | 0.663953i | ||||||||
\(659\) | 15964.0 | − | 27650.4i | 0.943654 | − | 1.63446i | 0.185230 | − | 0.982695i | \(-0.440697\pi\) |
0.758424 | − | 0.651761i | \(-0.225970\pi\) | |||||||
\(660\) | 11340.4i | 0.668826i | ||||||||
\(661\) | −22388.1 | − | 12925.8i | −1.31739 | − | 0.760598i | −0.334086 | − | 0.942543i | \(-0.608428\pi\) |
−0.983309 | + | 0.181944i | \(0.941761\pi\) | |||||||
\(662\) | 2199.73 | − | 3810.04i | 0.129146 | − | 0.223688i | ||||
\(663\) | 11875.3 | − | 20568.6i | 0.695622 | − | 1.20485i | ||||
\(664\) | 935.737 | − | 540.248i | 0.0546892 | − | 0.0315748i | ||||
\(665\) | −16674.7 | −0.972357 | ||||||||
\(666\) | 8288.81 | − | 6378.99i | 0.482260 | − | 0.371143i | ||||
\(667\) | −3408.52 | −0.197869 | ||||||||
\(668\) | 3518.90 | − | 2031.64i | 0.203818 | − | 0.117674i | ||||
\(669\) | −20722.3 | + | 35892.0i | −1.19756 | + | 2.07424i | ||||
\(670\) | −12868.0 | + | 22288.0i | −0.741989 | + | 1.28516i | ||||
\(671\) | 17167.9 | + | 9911.92i | 0.987722 | + | 0.570261i | ||||
\(672\) | − | 2399.45i | − | 0.137739i | ||||||
\(673\) | 56.5304 | − | 97.9136i | 0.00323787 | − | 0.00560816i | −0.864402 | − | 0.502801i | \(-0.832303\pi\) |
0.867640 | + | 0.497193i | \(0.165636\pi\) | |||||||
\(674\) | 9184.94i | 0.524912i | ||||||||
\(675\) | 1397.41 | + | 2420.38i | 0.0796834 | + | 0.138016i | ||||
\(676\) | −909.225 | −0.0517310 | ||||||||
\(677\) | −29282.0 | −1.66233 | −0.831167 | − | 0.556023i | \(-0.812326\pi\) | ||||
−0.831167 | + | 0.556023i | \(0.812326\pi\) | |||||||
\(678\) | 1503.78 | + | 2604.62i | 0.0851804 | + | 0.147537i | ||||
\(679\) | −874.766 | − | 505.047i | −0.0494410 | − | 0.0285448i | ||||
\(680\) | 9155.92i | 0.516343i | ||||||||
\(681\) | −10797.1 | + | 6233.73i | −0.607558 | + | 0.350774i | ||||
\(682\) | 6977.19 | + | 12084.8i | 0.391746 | + | 0.678523i | ||||
\(683\) | −11482.7 | + | 6629.53i | −0.643298 | + | 0.371409i | −0.785884 | − | 0.618374i | \(-0.787792\pi\) |
0.142586 | + | 0.989782i | \(0.454458\pi\) | |||||||
\(684\) | −8369.86 | − | 4832.34i | −0.467880 | − | 0.270130i | ||||
\(685\) | 33642.3 | + | 19423.4i | 1.87650 | + | 1.08340i | ||||
\(686\) | −10519.3 | + | 6073.31i | −0.585463 | + | 0.338017i | ||||
\(687\) | −818.795 | − | 1418.19i | −0.0454716 | − | 0.0787591i | ||||
\(688\) | −2882.70 | + | 1664.33i | −0.159741 | + | 0.0922266i | ||||
\(689\) | 27308.7i | 1.50998i | ||||||||
\(690\) | 8058.64 | + | 4652.66i | 0.444619 | + | 0.256701i | ||||
\(691\) | −6512.48 | − | 11279.9i | −0.358533 | − | 0.620998i | 0.629183 | − | 0.777257i | \(-0.283390\pi\) |
−0.987716 | + | 0.156260i | \(0.950056\pi\) | |||||||
\(692\) | 1292.17 | 0.0709839 | ||||||||
\(693\) | −6486.85 | −0.355577 | ||||||||
\(694\) | −5311.90 | − | 9200.47i | −0.290543 | − | 0.503235i | ||||
\(695\) | − | 46488.5i | − | 2.53728i | ||||||
\(696\) | 2231.46 | − | 3865.01i | 0.121528 | − | 0.210493i | ||||
\(697\) | − | 13526.3i | − | 0.735074i | ||||||
\(698\) | −3114.42 | − | 1798.11i | −0.168886 | − | 0.0975066i | ||||
\(699\) | 11150.6 | − | 19313.4i | 0.603367 | − | 1.04506i | ||||
\(700\) | −2216.76 | + | 3839.53i | −0.119694 | + | 0.207315i | ||||
\(701\) | −10205.0 | + | 5891.88i | −0.549841 | + | 0.317451i | −0.749058 | − | 0.662504i | \(-0.769494\pi\) |
0.199217 | + | 0.979955i | \(0.436160\pi\) | |||||||
\(702\) | −2367.81 | −0.127304 | ||||||||
\(703\) | −18546.2 | + | 14273.0i | −0.994995 | + | 0.765739i | ||||
\(704\) | 1688.86 | 0.0904138 | ||||||||
\(705\) | 49281.1 | − | 28452.5i | 2.63267 | − | 1.51997i | ||||
\(706\) | 3188.42 | − | 5522.50i | 0.169968 | − | 0.294394i | ||||
\(707\) | 4048.45 | − | 7012.12i | 0.215357 | − | 0.373010i | ||||
\(708\) | −9655.83 | − | 5574.80i | −0.512554 | − | 0.295923i | ||||
\(709\) | − | 7108.31i | − | 0.376528i | −0.982118 | − | 0.188264i | \(-0.939714\pi\) | ||
0.982118 | − | 0.188264i | \(-0.0602860\pi\) | |||||||
\(710\) | 15429.9 | − | 26725.4i | 0.815596 | − | 1.41265i | ||||
\(711\) | 19235.8i | 1.01463i | ||||||||
\(712\) | 1399.11 | + | 2423.33i | 0.0736432 | + | 0.127554i | ||||
\(713\) | 11450.2 | 0.601420 | ||||||||
\(714\) | −11322.9 | −0.593484 | ||||||||
\(715\) | 8876.25 | + | 15374.1i | 0.464270 | + | 0.804139i | ||||
\(716\) | −876.990 | − | 506.330i | −0.0457746 | − | 0.0264280i | ||||
\(717\) | − | 13015.3i | − | 0.677913i | ||||||
\(718\) | −4400.41 | + | 2540.58i | −0.228721 | + | 0.132052i | ||||
\(719\) | −10204.4 | − | 17674.6i | −0.529293 | − | 0.916763i | −0.999416 | − | 0.0341617i | \(-0.989124\pi\) |
0.470123 | − | 0.882601i | \(-0.344209\pi\) | |||||||
\(720\) | −4880.51 | + | 2817.76i | −0.252619 | + | 0.145850i | ||||
\(721\) | −9779.70 | − | 5646.31i | −0.505153 | − | 0.291650i | ||||
\(722\) | 6847.38 | + | 3953.33i | 0.352954 | + | 0.203778i | ||||
\(723\) | 18824.9 | − | 10868.6i | 0.968335 | − | 0.559068i | ||||
\(724\) | −6284.07 | − | 10884.3i | −0.322577 | − | 0.558719i | ||||
\(725\) | −7141.46 | + | 4123.13i | −0.365831 | + | 0.211213i | ||||
\(726\) | 8996.51i | 0.459906i | ||||||||
\(727\) | 3249.94 | + | 1876.35i | 0.165796 | + | 0.0957223i | 0.580602 | − | 0.814188i | \(-0.302817\pi\) |
−0.414806 | + | 0.909910i | \(0.636151\pi\) | |||||||
\(728\) | −1878.07 | − | 3252.91i | −0.0956124 | − | 0.165606i | ||||
\(729\) | −13866.5 | −0.704489 | ||||||||
\(730\) | 19813.0 | 1.00454 | ||||||||
\(731\) | 7853.88 | + | 13603.3i | 0.397382 | + | 0.688286i | ||||
\(732\) | 21298.2i | 1.07542i | ||||||||
\(733\) | −8309.57 | + | 14392.6i | −0.418719 | + | 0.725242i | −0.995811 | − | 0.0914370i | \(-0.970854\pi\) |
0.577092 | + | 0.816679i | \(0.304187\pi\) | |||||||
\(734\) | 11777.8i | 0.592271i | ||||||||
\(735\) | 21500.6 | + | 12413.4i | 1.07899 | + | 0.622958i | ||||
\(736\) | 692.892 | − | 1200.12i | 0.0347015 | − | 0.0601048i | ||||
\(737\) | 11200.7 | − | 19400.3i | 0.559817 | − | 0.969631i | ||||
\(738\) | 7210.13 | − | 4162.77i | 0.359632 | − | 0.207634i | ||||
\(739\) | −18100.3 | −0.900988 | −0.450494 | − | 0.892779i | \(-0.648752\pi\) | ||||
−0.450494 | + | 0.892779i | \(0.648752\pi\) | |||||||
\(740\) | 1800.43 | + | 13526.8i | 0.0894394 | + | 0.671967i | ||||
\(741\) | −32709.1 | −1.62159 | ||||||||
\(742\) | 11274.9 | − | 6509.58i | 0.557838 | − | 0.322068i | ||||
\(743\) | −1820.01 | + | 3152.36i | −0.0898652 | + | 0.155651i | −0.907454 | − | 0.420151i | \(-0.861977\pi\) |
0.817589 | + | 0.575803i | \(0.195310\pi\) | |||||||
\(744\) | −7496.11 | + | 12983.6i | −0.369383 | + | 0.639790i | ||||
\(745\) | 42501.5 | + | 24538.3i | 2.09012 | + | 1.20673i | ||||
\(746\) | 14654.9i | 0.719243i | ||||||||
\(747\) | 1569.17 | − | 2717.89i | 0.0768582 | − | 0.133122i | ||||
\(748\) | − | 7969.64i | − | 0.389571i | ||||||
\(749\) | −4156.56 | − | 7199.38i | −0.202774 | − | 0.351214i | ||||
\(750\) | −4346.98 | −0.211639 | ||||||||
\(751\) | −24991.0 | −1.21429 | −0.607146 | − | 0.794590i | \(-0.707686\pi\) | ||||
−0.607146 | + | 0.794590i | \(0.707686\pi\) | |||||||
\(752\) | −4237.25 | − | 7339.14i | −0.205474 | − | 0.355892i | ||||
\(753\) | 26191.8 | + | 15121.9i | 1.26757 | + | 0.731834i | ||||
\(754\) | − | 6986.35i | − | 0.337437i | ||||||
\(755\) | −10543.3 | + | 6087.18i | −0.508225 | + | 0.293424i | ||||
\(756\) | 564.416 | + | 977.598i | 0.0271529 | + | 0.0470303i | ||||
\(757\) | 14813.5 | − | 8552.57i | 0.711235 | − | 0.410632i | −0.100283 | − | 0.994959i | \(-0.531975\pi\) |
0.811518 | + | 0.584327i | \(0.198641\pi\) | |||||||
\(758\) | −1007.05 | − | 581.419i | −0.0482554 | − | 0.0278603i | ||||
\(759\) | −7014.53 | − | 4049.84i | −0.335456 | − | 0.193676i | ||||
\(760\) | 10920.1 | − | 6304.72i | 0.521202 | − | 0.300916i | ||||
\(761\) | 13499.5 | + | 23381.9i | 0.643046 | + | 1.11379i | 0.984749 | + | 0.173980i | \(0.0556628\pi\) |
−0.341703 | + | 0.939808i | \(0.611004\pi\) | |||||||
\(762\) | −16841.0 | + | 9723.14i | −0.800635 | + | 0.462247i | ||||
\(763\) | − | 12653.2i | − | 0.600362i | ||||||
\(764\) | 2357.35 | + | 1361.02i | 0.111631 | + | 0.0644502i | ||||
\(765\) | 13296.9 | + | 23030.9i | 0.628431 | + | 1.08847i | ||||
\(766\) | −4226.35 | −0.199353 | ||||||||
\(767\) | −17453.8 | −0.821668 | ||||||||
\(768\) | 907.233 | + | 1571.37i | 0.0426263 | + | 0.0738308i | ||||
\(769\) | − | 7750.65i | − | 0.363453i | −0.983349 | − | 0.181727i | \(-0.941831\pi\) | ||
0.983349 | − | 0.181727i | \(-0.0581686\pi\) | |||||||
\(770\) | 4231.67 | − | 7329.47i | 0.198050 | − | 0.343033i | ||||
\(771\) | − | 2984.63i | − | 0.139415i | ||||||
\(772\) | 4723.74 | + | 2727.25i | 0.220222 | + | 0.127145i | ||||
\(773\) | 7779.78 | − | 13475.0i | 0.361991 | − | 0.626987i | −0.626297 | − | 0.779584i | \(-0.715430\pi\) |
0.988288 | + | 0.152597i | \(0.0487636\pi\) | |||||||
\(774\) | −4834.12 | + | 8372.94i | −0.224494 | + | 0.388836i | ||||
\(775\) | 23990.2 | − | 13850.7i | 1.11194 | − | 0.641978i | ||||
\(776\) | 763.835 | 0.0353352 | ||||||||
\(777\) | −16728.2 | + | 2226.54i | −0.772358 | + | 0.102802i | ||||
\(778\) | 24197.2 | 1.11505 | ||||||||
\(779\) | −16132.6 | + | 9314.18i | −0.741991 | + | 0.428389i | ||||
\(780\) | −9536.41 | + | 16517.5i | −0.437767 | + | 0.758235i | ||||
\(781\) | −13430.7 | + | 23262.7i | −0.615352 | + | 1.06582i | ||||
\(782\) | −5663.32 | − | 3269.72i | −0.258977 | − | 0.149520i | ||||
\(783\) | 2099.61i | 0.0958287i | ||||||||
\(784\) | 1848.65 | − | 3201.95i | 0.0842132 | − | 0.145862i | ||||
\(785\) | 37173.5i | 1.69016i | ||||||||
\(786\) | −6286.39 | − | 10888.3i | −0.285277 | − | 0.494115i | ||||
\(787\) | 1226.45 | 0.0555504 | 0.0277752 | − | 0.999614i | \(-0.491158\pi\) | ||||
0.0277752 | + | 0.999614i | \(0.491158\pi\) | |||||||
\(788\) | 8517.50 | 0.385055 | ||||||||
\(789\) | −176.381 | − | 305.500i | −0.00795857 | − | 0.0137847i | ||||
\(790\) | −21734.5 | − | 12548.4i | −0.978835 | − | 0.565131i | ||||
\(791\) | − | 2244.54i | − | 0.100893i | ||||||
\(792\) | 4248.17 | − | 2452.68i | 0.190596 | − | 0.110041i | ||||
\(793\) | 16670.3 | + | 28873.8i | 0.746507 | + | 1.29299i | ||||
\(794\) | 4765.66 | − | 2751.46i | 0.213006 | − | 0.122979i | ||||
\(795\) | −57251.6 | − | 33054.2i | −2.55409 | − | 1.47461i | ||||
\(796\) | 8946.18 | + | 5165.08i | 0.398353 | + | 0.229989i | ||||
\(797\) | −18366.4 | + | 10603.8i | −0.816275 | + | 0.471277i | −0.849130 | − | 0.528184i | \(-0.822873\pi\) |
0.0328552 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(798\) | 7796.88 | + | 13504.6i | 0.345873 | + | 0.599069i | ||||
\(799\) | −34633.0 | + | 19995.4i | −1.53345 | + | 0.885339i | ||||
\(800\) | − | 3352.63i | − | 0.148167i | ||||||
\(801\) | 7038.68 | + | 4063.79i | 0.310486 | + | 0.179259i | ||||
\(802\) | 1553.48 | + | 2690.70i | 0.0683980 | + | 0.118469i | ||||
\(803\) | −17246.0 | −0.757905 | ||||||||
\(804\) | 24067.6 | 1.05572 | ||||||||
\(805\) | −3472.27 | − | 6014.15i | −0.152027 | − | 0.263318i | ||||
\(806\) | 23469.1i | 1.02564i | ||||||||
\(807\) | −19657.1 | + | 34047.2i | −0.857453 | + | 1.48515i | ||||
\(808\) | 6122.90i | 0.266588i | ||||||||
\(809\) | −25414.4 | − | 14673.0i | −1.10448 | − | 0.637671i | −0.167085 | − | 0.985943i | \(-0.553435\pi\) |
−0.937394 | + | 0.348271i | \(0.886769\pi\) | |||||||
\(810\) | 12375.9 | − | 21435.7i | 0.536847 | − | 0.929846i | ||||
\(811\) | 7454.84 | − | 12912.2i | 0.322780 | − | 0.559072i | −0.658280 | − | 0.752773i | \(-0.728716\pi\) |
0.981061 | + | 0.193701i | \(0.0620492\pi\) | |||||||
\(812\) | −2884.45 | + | 1665.34i | −0.124661 | + | 0.0719729i | ||||
\(813\) | 11587.7 | 0.499876 | ||||||||
\(814\) | −1567.16 | − | 11774.2i | −0.0674803 | − | 0.506986i | ||||
\(815\) | 6.86301 | 0.000294970 | ||||||||
\(816\) | 7415.24 | − | 4281.19i | 0.318119 | − | 0.183666i | ||||
\(817\) | 10816.3 | − | 18734.4i | 0.463176 | − | 0.802244i | ||||
\(818\) | −12525.8 | + | 21695.3i | −0.535395 | + | 0.927332i | ||||
\(819\) | −9448.22 | − | 5454.93i | −0.403111 | − | 0.232736i | ||||
\(820\) | 10862.3i | 0.462594i | ||||||||
\(821\) | 10738.7 | − | 18599.9i | 0.456494 | − | 0.790671i | −0.542279 | − | 0.840199i | \(-0.682438\pi\) |
0.998773 | + | 0.0495277i | \(0.0157716\pi\) | |||||||
\(822\) | − | 36328.5i | − | 1.54149i | ||||||
\(823\) | 4792.84 | + | 8301.45i | 0.202999 | + | 0.351604i | 0.949493 | − | 0.313787i | \(-0.101598\pi\) |
−0.746494 | + | 0.665392i | \(0.768265\pi\) | |||||||
\(824\) | 8539.51 | 0.361029 | ||||||||
\(825\) | −19595.6 | −0.826947 | ||||||||
\(826\) | 4160.47 | + | 7206.14i | 0.175256 | + | 0.303552i | ||||
\(827\) | −23113.9 | − | 13344.8i | −0.971885 | − | 0.561118i | −0.0720749 | − | 0.997399i | \(-0.522962\pi\) |
−0.899811 | + | 0.436281i | \(0.856295\pi\) | |||||||
\(828\) | − | 4025.07i | − | 0.168938i | ||||||
\(829\) | −15777.6 | + | 9109.22i | −0.661013 | + | 0.381636i | −0.792663 | − | 0.609660i | \(-0.791306\pi\) |
0.131650 | + | 0.991296i | \(0.457973\pi\) | |||||||
\(830\) | 2047.29 | + | 3546.01i | 0.0856175 | + | 0.148294i | ||||
\(831\) | 49372.1 | − | 28505.0i | 2.06101 | − | 1.18993i | ||||
\(832\) | 2459.86 | + | 1420.20i | 0.102500 | + | 0.0591786i | ||||
\(833\) | −15109.9 | − | 8723.68i | −0.628482 | − | 0.362854i | ||||
\(834\) | −37650.3 | + | 21737.4i | −1.56322 | + | 0.902524i | ||||
\(835\) | 7698.97 | + | 13335.0i | 0.319082 | + | 0.552667i | ||||
\(836\) | −9505.26 | + | 5487.86i | −0.393237 | + | 0.227036i | ||||
\(837\) | − | 7053.18i | − | 0.291271i | ||||||
\(838\) | 1497.53 | + | 864.598i | 0.0617318 | + | 0.0356409i | ||||
\(839\) | −14003.6 | − | 24254.9i | −0.576230 | − | 0.998059i | −0.995907 | − | 0.0903859i | \(-0.971190\pi\) |
0.419677 | − | 0.907674i | \(-0.362143\pi\) | |||||||
\(840\) | 9092.80 | 0.373490 | ||||||||
\(841\) | 18194.0 | 0.745992 | ||||||||
\(842\) | −12693.3 | − | 21985.4i | −0.519523 | − | 0.899840i | ||||
\(843\) | 31241.3i | 1.27640i | ||||||||
\(844\) | 11038.2 | − | 19118.7i | 0.450178 | − | 0.779731i | ||||
\(845\) | − | 3445.54i | − | 0.140272i | ||||||
\(846\) | −21316.8 | − | 12307.3i | −0.866298 | − | 0.500158i | ||||
\(847\) | 3357.04 | − | 5814.57i | 0.136186 | − | 0.235881i | ||||
\(848\) | −4922.56 | + | 8526.13i | −0.199341 | + | 0.345269i | ||||
\(849\) | 2817.68 | − | 1626.79i | 0.113902 | − | 0.0657612i | ||||
\(850\) | −15820.9 | −0.638415 | ||||||||
\(851\) | −9009.88 | − | 3717.00i | −0.362931 | − | 0.149726i | ||||
\(852\) | −28859.3 | −1.16045 | ||||||||
\(853\) | 23919.8 | − | 13810.1i | 0.960141 | − | 0.554337i | 0.0639243 | − | 0.997955i | \(-0.479638\pi\) |
0.896216 | + | 0.443617i | \(0.146305\pi\) | |||||||
\(854\) | 7947.42 | − | 13765.3i | 0.318449 | − | 0.551569i | ||||
\(855\) | 18312.4 | − | 31717.9i | 0.732479 | − | 1.26869i | ||||
\(856\) | 5444.19 | + | 3143.20i | 0.217381 | + | 0.125505i | ||||
\(857\) | 41760.7i | 1.66455i | 0.554363 | + | 0.832275i | \(0.312962\pi\) | ||||
−0.554363 | + | 0.832275i | \(0.687038\pi\) | |||||||
\(858\) | 8300.84 | − | 14377.5i | 0.330287 | − | 0.572073i | ||||
\(859\) | 16328.2i | 0.648558i | 0.945962 | + | 0.324279i | \(0.105122\pi\) | ||||
−0.945962 | + | 0.324279i | \(0.894878\pi\) | |||||||
\(860\) | −6307.04 | − | 10924.1i | −0.250079 | − | 0.433150i | ||||
\(861\) | −13433.1 | −0.531705 | ||||||||
\(862\) | −16896.8 | −0.667643 | ||||||||
\(863\) | 10894.4 | + | 18869.7i | 0.429722 | + | 0.744300i | 0.996848 | − | 0.0793304i | \(-0.0252782\pi\) |
−0.567126 | + | 0.823631i | \(0.691945\pi\) | |||||||
\(864\) | −739.262 | − | 426.813i | −0.0291090 | − | 0.0168061i | ||||
\(865\) | 4896.72i | 0.192478i | ||||||||
\(866\) | −18772.1 | + | 10838.1i | −0.736609 | + | 0.425281i | ||||
\(867\) | −2791.64 | − | 4835.26i | −0.109353 | − | 0.189405i | ||||
\(868\) | 9689.68 | − | 5594.34i | 0.378905 | − | 0.218761i | ||||
\(869\) | 18918.5 | + | 10922.6i | 0.738512 | + | 0.426380i | ||||
\(870\) | 14646.6 | + | 8456.22i | 0.570766 | + | 0.329532i | ||||
\(871\) | 32628.2 | − | 18837.9i | 1.26931 | − | 0.732834i | ||||
\(872\) | 4784.19 | + | 8286.46i | 0.185795 | + | 0.321806i | ||||
\(873\) | 1921.36 | − | 1109.30i | 0.0744881 | − | 0.0430057i | ||||
\(874\) | 9006.07i | 0.348552i | ||||||||
\(875\) | 2809.51 | + | 1622.07i | 0.108547 | + | 0.0626698i | ||||
\(876\) | −9264.32 | − | 16046.3i | −0.357320 | − | 0.618896i | ||||
\(877\) | 31479.3 | 1.21207 | 0.606033 | − | 0.795440i | \(-0.292760\pi\) | ||||
0.606033 | + | 0.795440i | \(0.292760\pi\) | |||||||
\(878\) | 18290.9 | 0.703060 | ||||||||
\(879\) | 4075.88 | + | 7059.63i | 0.156400 | + | 0.270893i | ||||
\(880\) | 6400.00i | 0.245164i | ||||||||
\(881\) | 3368.11 | − | 5833.73i | 0.128802 | − | 0.223091i | −0.794411 | − | 0.607381i | \(-0.792220\pi\) |
0.923213 | + | 0.384290i | \(0.125554\pi\) | |||||||
\(882\) | − | 10739.0i | − | 0.409977i | ||||||
\(883\) | 19238.0 | + | 11107.1i | 0.733194 | + | 0.423310i | 0.819590 | − | 0.572951i | \(-0.194202\pi\) |
−0.0863954 | + | 0.996261i | \(0.527535\pi\) | |||||||
\(884\) | 6701.85 | − | 11607.9i | 0.254986 | − | 0.441649i | ||||
\(885\) | 21125.9 | − | 36591.2i | 0.802418 | − | 1.38983i | ||||
\(886\) | 14372.5 | − | 8297.95i | 0.544981 | − | 0.314645i | ||||
\(887\) | 11208.2 | 0.424278 | 0.212139 | − | 0.977239i | \(-0.431957\pi\) | ||||
0.212139 | + | 0.977239i | \(0.431957\pi\) | |||||||
\(888\) | 10113.3 | − | 7783.11i | 0.382185 | − | 0.294126i | ||||
\(889\) | 14512.7 | 0.547516 | ||||||||
\(890\) | −9183.32 | + | 5301.99i | −0.345872 | + | 0.199689i | ||||
\(891\) | −10772.5 | + | 18658.5i | −0.405040 | + | 0.701551i | ||||
\(892\) | −11694.7 | + | 20255.8i | −0.438976 | + | 0.760329i | ||||
\(893\) | 47696.3 | + | 27537.5i | 1.78734 | + | 1.03192i | ||||
\(894\) | − | 45895.1i | − | 1.71696i | ||||||
\(895\) | 1918.76 | − | 3323.39i | 0.0716615 | − | 0.124121i | ||||
\(896\) | − | 1354.13i | − | 0.0504894i | ||||||
\(897\) | −6811.20 | − | 11797.4i | −0.253533 | − | 0.439133i | ||||
\(898\) | 26428.3 | 0.982098 | ||||||||
\(899\) | 20810.8 | 0.772055 | ||||||||
\(900\) | −4868.93 | − | 8433.24i | −0.180331 | − | 0.312342i | ||||
\(901\) | 40234.4 | + | 23229.3i | 1.48768 | + | 0.858914i | ||||
\(902\) | − | 9454.93i | − | 0.349018i | ||||||
\(903\) | 13509.5 | − | 7799.74i | 0.497862 | − | 0.287441i | ||||
\(904\) | 848.663 | + | 1469.93i | 0.0312236 | + | 0.0540808i | ||||
\(905\) | 41246.6 | − | 23813.7i | 1.51501 | − | 0.874691i | ||||
\(906\) | 9859.82 | + | 5692.57i | 0.361557 | + | 0.208745i | ||||
\(907\) | −32351.2 | − | 18678.0i | −1.18435 | − | 0.683783i | −0.227331 | − | 0.973818i | \(-0.573000\pi\) |
−0.957016 | + | 0.290034i | \(0.906333\pi\) | |||||||
\(908\) | −6093.39 | + | 3518.02i | −0.222705 | + | 0.128579i | ||||
\(909\) | 8892.11 | + | 15401.6i | 0.324458 | + | 0.561979i | ||||
\(910\) | 12327.0 | − | 7117.01i | 0.449052 | − | 0.259260i | ||||
\(911\) | − | 2359.83i | − | 0.0858230i | −0.999079 | − | 0.0429115i | \(-0.986337\pi\) | ||
0.999079 | − | 0.0429115i | \(-0.0136633\pi\) | |||||||
\(912\) | −10212.2 | − | 5896.02i | −0.370789 | − | 0.214075i | ||||
\(913\) | −1782.04 | − | 3086.58i | −0.0645967 | − | 0.111885i | ||||
\(914\) | 17973.8 | 0.650461 | ||||||||
\(915\) | −80710.4 | −2.91607 | ||||||||
\(916\) | −462.089 | − | 800.362i | −0.0166680 | − | 0.0288698i | ||||
\(917\) | 9383.05i | 0.337901i | ||||||||
\(918\) | −2014.11 | + | 3488.54i | −0.0724134 | + | 0.125424i | ||||
\(919\) | − | 38964.4i | − | 1.39861i | −0.714826 | − | 0.699303i | \(-0.753494\pi\) | ||
0.714826 | − | 0.699303i | \(-0.246506\pi\) | |||||||
\(920\) | 4547.92 | + | 2625.74i | 0.162979 | + | 0.0940958i | ||||
\(921\) | −8873.68 | + | 15369.7i | −0.317478 | + | 0.549889i | ||||
\(922\) | −16812.0 | + | 29119.2i | −0.600513 | + | 1.04012i | ||||
\(923\) | −39124.3 | + | 22588.4i | −1.39522 | + | 0.805533i | ||||
\(924\) | −7914.70 | −0.281791 | ||||||||
\(925\) | −23373.6 | + | 3111.04i | −0.830831 | + | 0.110584i | ||||
\(926\) | −4573.91 | −0.162320 | ||||||||
\(927\) | 21480.4 | − | 12401.7i | 0.761065 | − | 0.439401i | ||||
\(928\) | 1259.33 | − | 2181.23i | 0.0445470 | − | 0.0771577i | ||||
\(929\) | 14960.1 | − | 25911.7i | 0.528338 | − | 0.915109i | −0.471116 | − | 0.882071i | \(-0.656149\pi\) |
0.999454 | − | 0.0330376i | \(-0.0105181\pi\) | |||||||
\(930\) | −49202.0 | − | 28406.8i | −1.73484 | − | 1.00161i | ||||
\(931\) | 24028.3i | 0.845862i | ||||||||
\(932\) | 6292.86 | − | 10899.6i | 0.221169 | − | 0.383076i | ||||
\(933\) | − | 65130.2i | − | 2.28539i | ||||||
\(934\) | −10278.1 | − | 17802.3i | −0.360076 | − | 0.623670i | ||||
\(935\) | 30201.3 | 1.05635 | ||||||||
\(936\) | 8250.06 | 0.288100 | ||||||||
\(937\) | −13750.0 | − | 23815.7i | −0.479396 | − | 0.830337i | 0.520325 | − | 0.853968i | \(-0.325811\pi\) |
−0.999721 | + | 0.0236307i | \(0.992477\pi\) | |||||||
\(938\) | −15555.2 | − | 8980.81i | −0.541467 | − | 0.312616i | ||||
\(939\) | 40830.8i | 1.41902i | ||||||||
\(940\) | 27811.9 | − | 16057.2i | 0.965027 | − | 0.557159i | ||||
\(941\) | 76.3768 | + | 132.289i | 0.00264592 | + | 0.00458287i | 0.867345 | − | 0.497707i | \(-0.165824\pi\) |
−0.864699 | + | 0.502290i | \(0.832491\pi\) | |||||||
\(942\) | 30106.2 | − | 17381.8i | 1.04131 | − | 0.601201i | ||||
\(943\) | −6718.78 | − | 3879.09i | −0.232019 | − | 0.133956i | ||||
\(944\) | −5449.30 | − | 3146.16i | −0.187881 | − | 0.108473i | ||||
\(945\) | −3704.65 | + | 2138.88i | −0.127526 | + | 0.0736272i | ||||
\(946\) | 5489.88 | + | 9508.75i | 0.188680 | + | 0.326803i | ||||
\(947\) | 1987.51 | − | 1147.49i | 0.0681999 | − | 0.0393752i | −0.465512 | − | 0.885041i | \(-0.654130\pi\) |
0.533712 | + | 0.845666i | \(0.320797\pi\) | |||||||
\(948\) | 23469.9i | 0.804081i | ||||||||
\(949\) | −25119.1 | − | 14502.5i | −0.859221 | − | 0.496072i | ||||
\(950\) | 10894.2 | + | 18869.3i | 0.372058 | + | 0.644423i | ||||
\(951\) | −51440.9 | −1.75403 | ||||||||
\(952\) | −6390.10 | −0.217546 | ||||||||
\(953\) | −24293.7 | − | 42077.9i | −0.825760 | − | 1.43026i | −0.901337 | − | 0.433118i | \(-0.857413\pi\) |
0.0755771 | − | 0.997140i | \(-0.475920\pi\) | |||||||
\(954\) | 28595.6i | 0.970458i | ||||||||
\(955\) | −5157.64 | + | 8933.29i | −0.174761 | + | 0.302696i | ||||
\(956\) | − | 7345.20i | − | 0.248495i | ||||||
\(957\) | −12748.9 | − | 7360.60i | −0.430632 | − | 0.248625i | ||||
\(958\) | −5404.41 | + | 9360.72i | −0.182264 | + | 0.315690i | ||||
\(959\) | −13556.0 | + | 23479.6i | −0.456459 | + | 0.790611i | ||||
\(960\) | −5954.78 | + | 3438.00i | −0.200198 | + | 0.115584i | ||||
\(961\) | −40118.2 | −1.34665 | ||||||||
\(962\) | 7618.62 | − | 18467.3i | 0.255337 | − | 0.618928i | ||||
\(963\) | 18259.1 | 0.610999 | ||||||||
\(964\) | 10623.9 | − | 6133.71i | 0.354951 | − | 0.204931i | ||||
\(965\) | −10335.0 | + | 17900.8i | −0.344763 | + | 0.597147i | ||||
\(966\) | −3247.18 | + | 5624.28i | −0.108154 | + | 0.187327i | ||||
\(967\) | −16794.3 | − | 9696.18i | −0.558498 | − | 0.322449i | 0.194044 | − | 0.980993i | \(-0.437839\pi\) |
−0.752542 | + | 0.658544i | \(0.771173\pi\) | |||||||
\(968\) | 5077.21i | 0.168582i | ||||||||
\(969\) | −27823.0 | + | 48190.9i | −0.922398 | + | 1.59764i | ||||
\(970\) | 2894.58i | 0.0958139i | ||||||||
\(971\) | 16316.4 | + | 28260.9i | 0.539258 | + | 0.934022i | 0.998944 | + | 0.0459406i | \(0.0146285\pi\) |
−0.459686 | + | 0.888081i | \(0.652038\pi\) | |||||||
\(972\) | −20266.3 | −0.668768 | ||||||||
\(973\) | 32445.2 | 1.06901 | ||||||||
\(974\) | −6495.44 | − | 11250.4i | −0.213683 | − | 0.370110i | ||||
\(975\) | −28541.4 | − | 16478.4i | −0.937493 | − | 0.541262i | ||||
\(976\) | 12019.7i | 0.394203i | ||||||||
\(977\) | −27826.2 | + | 16065.4i | −0.911195 | + | 0.526079i | −0.880816 | − | 0.473460i | \(-0.843005\pi\) |
−0.0303798 | + | 0.999538i | \(0.509672\pi\) | |||||||
\(978\) | −3.20905 | − | 5.55824i | −0.000104923 | − | 0.000181731i | ||||
\(979\) | 7993.50 | − | 4615.05i | 0.260953 | − | 0.150662i | ||||
\(980\) | 12133.9 | + | 7005.52i | 0.395514 | + | 0.228350i | ||||
\(981\) | 24068.4 | + | 13895.9i | 0.783328 | + | 0.452254i | ||||
\(982\) | 26789.5 | − | 15466.9i | 0.870557 | − | 0.502617i | ||||
\(983\) | 15264.9 | + | 26439.5i | 0.495293 | + | 0.857873i | 0.999985 | − | 0.00542650i | \(-0.00172732\pi\) |
−0.504692 | + | 0.863299i | \(0.668394\pi\) | |||||||
\(984\) | 8797.20 | − | 5079.06i | 0.285005 | − | 0.164547i | ||||
\(985\) | 32277.4i | 1.04410i | ||||||||
\(986\) | −10293.1 | − | 5942.73i | −0.332454 | − | 0.191942i | ||||
\(987\) | 19857.5 | + | 34394.3i | 0.640398 | + | 1.10920i | ||||
\(988\) | −18459.5 | −0.594407 | ||||||||
\(989\) | 9009.37 | 0.289668 | ||||||||
\(990\) | 9294.54 | + | 16098.6i | 0.298384 | + | 0.516816i | ||||
\(991\) | − | 42890.5i | − | 1.37483i | −0.726263 | − | 0.687417i | \(-0.758744\pi\) | ||
0.726263 | − | 0.687417i | \(-0.241256\pi\) | |||||||
\(992\) | −4230.45 | + | 7327.36i | −0.135400 | + | 0.234520i | ||||
\(993\) | − | 15591.1i | − | 0.498258i | ||||||
\(994\) | 18652.2 | + | 10768.8i | 0.595181 | + | 0.343628i | ||||
\(995\) | −19573.3 | + | 33901.9i | −0.623632 | + | 1.08016i | ||||
\(996\) | 1914.57 | − | 3316.14i | 0.0609092 | − | 0.105498i | ||||
\(997\) | −18348.9 | + | 10593.7i | −0.582863 | + | 0.336516i | −0.762270 | − | 0.647259i | \(-0.775915\pi\) |
0.179407 | + | 0.983775i | \(0.442582\pi\) | |||||||
\(998\) | 30184.9 | 0.957402 | ||||||||
\(999\) | −2289.63 | + | 5549.98i | −0.0725131 | + | 0.175769i |
(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 | 74.4.e.a.11.10 | ✓ | 20 | |
3.2 | odd | 2 | 666.4.s.d.307.1 | 20 | |||
37.27 | even | 6 | inner | 74.4.e.a.27.10 | yes | 20 | |
111.101 | odd | 6 | 666.4.s.d.397.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.e.a.11.10 | ✓ | 20 | 1.1 | even | 1 | trivial | |
74.4.e.a.27.10 | yes | 20 | 37.27 | even | 6 | inner | |
666.4.s.d.307.1 | 20 | 3.2 | odd | 2 | |||
666.4.s.d.397.1 | 20 | 111.101 | odd | 6 |