Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.11 | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.f.151.11 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39440 | + | 4.14722i | 0.846549 | + | 1.46627i | 0.884269 | + | 0.466977i | \(0.154657\pi\) |
−0.0377207 | + | 0.999288i | \(0.512010\pi\) | |||||||
\(3\) | −1.75824 | + | 4.88964i | −0.338373 | + | 0.941012i | ||||
\(4\) | −7.46632 | + | 12.9320i | −0.933290 | + | 1.61650i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −24.4884 | + | 4.41595i | −1.66622 | + | 0.300467i | ||||
\(7\) | 15.3349 | + | 26.5609i | 0.828008 | + | 1.43415i | 0.899599 | + | 0.436718i | \(0.143859\pi\) |
−0.0715906 | + | 0.997434i | \(0.522808\pi\) | |||||||
\(8\) | −33.1990 | −1.46720 | ||||||||
\(9\) | −20.8172 | − | 17.1943i | −0.771007 | − | 0.636827i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.3952 | − | 37.0576i | −0.586445 | − | 1.01575i | −0.994694 | − | 0.102882i | \(-0.967194\pi\) |
0.408248 | − | 0.912871i | \(-0.366140\pi\) | |||||||
\(12\) | −50.1055 | − | 59.2452i | −1.20535 | − | 1.42522i | ||||
\(13\) | −26.7209 | + | 46.2820i | −0.570081 | + | 0.987409i | 0.426476 | + | 0.904499i | \(0.359755\pi\) |
−0.996557 | + | 0.0829101i | \(0.973579\pi\) | |||||||
\(14\) | −73.4359 | + | 127.195i | −1.40190 | + | 2.42816i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.7612 | − | 34.2274i | −0.308769 | − | 0.534804i | ||||
\(17\) | 0.609730 | 0.00869890 | 0.00434945 | − | 0.999991i | \(-0.498616\pi\) | ||||
0.00434945 | + | 0.999991i | \(0.498616\pi\) | |||||||
\(18\) | 21.4640 | − | 127.504i | 0.281062 | − | 1.66961i | ||||
\(19\) | 94.5419 | 1.14155 | 0.570774 | − | 0.821107i | \(-0.306643\pi\) | ||||
0.570774 | + | 0.821107i | \(0.306643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −156.836 | + | 28.2819i | −1.62973 | + | 0.293887i | ||||
\(22\) | 102.457 | − | 177.462i | 0.992909 | − | 1.71977i | ||||
\(23\) | 76.3811 | − | 132.296i | 0.692459 | − | 1.19937i | −0.278571 | − | 0.960416i | \(-0.589861\pi\) |
0.971030 | − | 0.238958i | \(-0.0768059\pi\) | |||||||
\(24\) | 58.3718 | − | 162.331i | 0.496462 | − | 1.38066i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −255.922 | −1.93040 | ||||||||
\(27\) | 120.676 | − | 71.5568i | 0.860150 | − | 0.510042i | ||||
\(28\) | −457.982 | −3.09108 | ||||||||
\(29\) | 71.6738 | + | 124.143i | 0.458948 | + | 0.794921i | 0.998906 | − | 0.0467712i | \(-0.0148932\pi\) |
−0.539958 | + | 0.841692i | \(0.681560\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.6894 | + | 32.3711i | −0.108281 | + | 0.187549i | −0.915074 | − | 0.403286i | \(-0.867868\pi\) |
0.806793 | + | 0.590835i | \(0.201201\pi\) | |||||||
\(32\) | −38.1634 | + | 66.1010i | −0.210825 | + | 0.365160i | ||||
\(33\) | 218.816 | − | 39.4588i | 1.15427 | − | 0.208148i | ||||
\(34\) | 1.45994 | + | 2.52869i | 0.00736404 | + | 0.0127549i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 377.785 | − | 140.830i | 1.74901 | − | 0.651993i | ||||
\(37\) | −274.029 | −1.21757 | −0.608785 | − | 0.793335i | \(-0.708343\pi\) | ||||
−0.608785 | + | 0.793335i | \(0.708343\pi\) | |||||||
\(38\) | 226.371 | + | 392.087i | 0.966375 | + | 1.67381i | ||||
\(39\) | −179.321 | − | 212.031i | −0.736263 | − | 0.870566i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 136.746 | − | 236.851i | 0.520881 | − | 0.902193i | −0.478824 | − | 0.877911i | \(-0.658937\pi\) |
0.999705 | − | 0.0242820i | \(-0.00772998\pi\) | |||||||
\(42\) | −492.819 | − | 582.714i | −1.81056 | − | 2.14083i | ||||
\(43\) | −92.6811 | − | 160.528i | −0.328691 | − | 0.569310i | 0.653561 | − | 0.756874i | \(-0.273274\pi\) |
−0.982252 | + | 0.187564i | \(0.939941\pi\) | |||||||
\(44\) | 638.974 | 2.18929 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 731.548 | 2.34480 | ||||||||
\(47\) | 219.007 | + | 379.331i | 0.679689 | + | 1.17726i | 0.975074 | + | 0.221878i | \(0.0712188\pi\) |
−0.295385 | + | 0.955378i | \(0.595448\pi\) | |||||||
\(48\) | 202.105 | − | 36.4453i | 0.607736 | − | 0.109592i | ||||
\(49\) | −298.820 | + | 517.571i | −0.871194 | + | 1.50895i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.07205 | + | 2.98136i | −0.00294347 | + | 0.00818576i | ||||
\(52\) | −399.014 | − | 691.112i | −1.06410 | − | 1.84308i | ||||
\(53\) | 211.483 | 0.548103 | 0.274051 | − | 0.961715i | \(-0.411636\pi\) | ||||
0.274051 | + | 0.961715i | \(0.411636\pi\) | |||||||
\(54\) | 585.708 | + | 329.133i | 1.47601 | + | 0.829433i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −509.104 | − | 881.794i | −1.21486 | − | 2.10419i | ||||
\(57\) | −166.227 | + | 462.276i | −0.386269 | + | 1.07421i | ||||
\(58\) | −343.232 | + | 594.494i | −0.777043 | + | 1.34588i | ||||
\(59\) | −248.523 | + | 430.455i | −0.548389 | + | 0.949838i | 0.449996 | + | 0.893031i | \(0.351425\pi\) |
−0.998385 | + | 0.0568073i | \(0.981908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 104.685 | + | 181.319i | 0.219730 | + | 0.380583i | 0.954725 | − | 0.297489i | \(-0.0961492\pi\) |
−0.734996 | + | 0.678072i | \(0.762816\pi\) | |||||||
\(62\) | −179.000 | −0.366662 | ||||||||
\(63\) | 137.466 | − | 816.596i | 0.274906 | − | 1.63304i | ||||
\(64\) | −681.694 | −1.33143 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 687.578 | + | 813.000i | 1.28235 | + | 1.51626i | ||||
\(67\) | −483.805 | + | 837.976i | −0.882183 | + | 1.52799i | −0.0332735 | + | 0.999446i | \(0.510593\pi\) |
−0.848909 | + | 0.528539i | \(0.822740\pi\) | |||||||
\(68\) | −4.55244 | + | 7.88505i | −0.00811859 | + | 0.0140618i | ||||
\(69\) | 512.583 | + | 606.084i | 0.894315 | + | 1.05745i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −401.080 | −0.670415 | −0.335208 | − | 0.942144i | \(-0.608806\pi\) | ||||
−0.335208 | + | 0.942144i | \(0.608806\pi\) | |||||||
\(72\) | 691.110 | + | 570.834i | 1.13122 | + | 0.934354i | ||||
\(73\) | 97.6223 | 0.156518 | 0.0782591 | − | 0.996933i | \(-0.475064\pi\) | ||||
0.0782591 | + | 0.996933i | \(0.475064\pi\) | |||||||
\(74\) | −656.135 | − | 1136.46i | −1.03073 | − | 1.78528i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −705.880 | + | 1222.62i | −1.06539 | + | 1.84532i | ||||
\(77\) | 656.188 | − | 1136.55i | 0.971163 | − | 1.68210i | ||||
\(78\) | 449.973 | − | 1251.37i | 0.653197 | − | 1.81653i | ||||
\(79\) | −566.159 | − | 980.617i | −0.806302 | − | 1.39656i | −0.915408 | − | 0.402527i | \(-0.868132\pi\) |
0.109106 | − | 0.994030i | \(-0.465201\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 137.711 | + | 715.875i | 0.188903 | + | 0.981996i | ||||
\(82\) | 1309.70 | 1.76381 | ||||||||
\(83\) | 286.610 | + | 496.422i | 0.379030 | + | 0.656499i | 0.990921 | − | 0.134443i | \(-0.0429244\pi\) |
−0.611891 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(84\) | 805.241 | − | 2239.37i | 1.04594 | − | 2.90875i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 443.831 | − | 768.738i | 0.556507 | − | 0.963898i | ||||
\(87\) | −733.033 | + | 132.187i | −0.903326 | + | 0.162895i | ||||
\(88\) | 710.300 | + | 1230.28i | 0.860434 | + | 1.49032i | ||||
\(89\) | −90.6612 | −0.107978 | −0.0539891 | − | 0.998542i | \(-0.517194\pi\) | ||||
−0.0539891 | + | 0.998542i | \(0.517194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1639.05 | −1.88813 | ||||||||
\(92\) | 1140.57 | + | 1975.53i | 1.29253 | + | 2.23873i | ||||
\(93\) | −125.422 | − | 148.301i | −0.139846 | − | 0.165356i | ||||
\(94\) | −1048.78 | + | 1816.54i | −1.15078 | + | 1.99321i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −256.110 | − | 302.827i | −0.272282 | − | 0.321949i | ||||
\(97\) | 4.62320 | + | 8.00762i | 0.00483933 | + | 0.00838197i | 0.868435 | − | 0.495803i | \(-0.165126\pi\) |
−0.863596 | + | 0.504185i | \(0.831793\pi\) | |||||||
\(98\) | −2861.98 | −2.95003 | ||||||||
\(99\) | −191.792 | + | 1139.31i | −0.194705 | + | 1.15662i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 108.537 | + | 187.992i | 0.106929 | + | 0.185207i | 0.914525 | − | 0.404530i | \(-0.132565\pi\) |
−0.807596 | + | 0.589737i | \(0.799232\pi\) | |||||||
\(102\) | −14.9313 | + | 2.69254i | −0.0144943 | + | 0.00261373i | ||||
\(103\) | 217.245 | − | 376.279i | 0.207823 | − | 0.359960i | −0.743205 | − | 0.669063i | \(-0.766696\pi\) |
0.951028 | + | 0.309103i | \(0.100029\pi\) | |||||||
\(104\) | 887.108 | − | 1536.52i | 0.836424 | − | 1.44873i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 506.376 | + | 877.068i | 0.463996 | + | 0.803664i | ||||
\(107\) | 193.254 | 0.174604 | 0.0873018 | − | 0.996182i | \(-0.472176\pi\) | ||||
0.0873018 | + | 0.996182i | \(0.472176\pi\) | |||||||
\(108\) | 24.3733 | + | 2094.85i | 0.0217159 | + | 1.86645i | ||||
\(109\) | 1703.14 | 1.49662 | 0.748308 | − | 0.663351i | \(-0.230866\pi\) | ||||
0.748308 | + | 0.663351i | \(0.230866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 481.809 | − | 1339.90i | 0.411993 | − | 1.14575i | ||||
\(112\) | 606.074 | − | 1049.75i | 0.511327 | − | 0.885644i | ||||
\(113\) | 304.784 | − | 527.901i | 0.253731 | − | 0.439476i | −0.710819 | − | 0.703375i | \(-0.751675\pi\) |
0.964550 | + | 0.263899i | \(0.0850087\pi\) | |||||||
\(114\) | −2315.18 | + | 417.492i | −1.90207 | + | 0.342998i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2140.56 | −1.71332 | ||||||||
\(117\) | 1352.04 | − | 504.013i | 1.06834 | − | 0.398256i | ||||
\(118\) | −2380.26 | −1.85695 | ||||||||
\(119\) | 9.35016 | + | 16.1950i | 0.00720275 | + | 0.0124755i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −250.010 | + | 433.030i | −0.187836 | + | 0.325342i | ||||
\(122\) | −501.314 | + | 868.302i | −0.372024 | + | 0.644364i | ||||
\(123\) | 917.684 | + | 1085.08i | 0.672722 | + | 0.795434i | ||||
\(124\) | −279.083 | − | 483.385i | −0.202116 | − | 0.350075i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3715.76 | − | 1385.16i | 2.62719 | − | 0.979361i | ||||
\(127\) | 1372.33 | 0.958857 | 0.479429 | − | 0.877581i | \(-0.340844\pi\) | ||||
0.479429 | + | 0.877581i | \(0.340844\pi\) | |||||||
\(128\) | −1326.94 | − | 2298.33i | −0.916298 | − | 1.58707i | ||||
\(129\) | 947.881 | − | 170.930i | 0.646948 | − | 0.116663i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −537.087 | + | 930.262i | −0.358210 | + | 0.620438i | −0.987662 | − | 0.156601i | \(-0.949946\pi\) |
0.629452 | + | 0.777040i | \(0.283280\pi\) | |||||||
\(132\) | −1123.47 | + | 3124.35i | −0.740798 | + | 2.06015i | ||||
\(133\) | 1449.79 | + | 2511.11i | 0.945210 | + | 1.63715i | ||||
\(134\) | −4633.70 | −2.98724 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.2424 | −0.0127630 | ||||||||
\(137\) | 991.784 | + | 1717.82i | 0.618495 | + | 1.07127i | 0.989760 | + | 0.142738i | \(0.0455908\pi\) |
−0.371265 | + | 0.928527i | \(0.621076\pi\) | |||||||
\(138\) | −1286.24 | + | 3577.01i | −0.793418 | + | 2.20649i | ||||
\(139\) | 1025.49 | − | 1776.20i | 0.625761 | − | 1.08385i | −0.362632 | − | 0.931932i | \(-0.618122\pi\) |
0.988393 | − | 0.151918i | \(-0.0485448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2239.86 | + | 403.910i | −1.33780 | + | 0.241244i | ||||
\(142\) | −960.347 | − | 1663.37i | −0.567539 | − | 0.983007i | ||||
\(143\) | 2286.80 | 1.33728 | ||||||||
\(144\) | −177.145 | + | 1052.30i | −0.102514 | + | 0.608970i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 233.747 | + | 404.862i | 0.132500 | + | 0.229497i | ||||
\(147\) | −2005.34 | − | 2371.13i | −1.12515 | − | 1.33039i | ||||
\(148\) | 2045.99 | − | 3543.75i | 1.13635 | − | 1.96821i | ||||
\(149\) | 290.144 | − | 502.544i | 0.159527 | − | 0.276309i | −0.775171 | − | 0.631751i | \(-0.782336\pi\) |
0.934698 | + | 0.355442i | \(0.115670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 804.674 | + | 1393.74i | 0.433665 | + | 0.751130i | 0.997186 | − | 0.0749720i | \(-0.0238868\pi\) |
−0.563520 | + | 0.826102i | \(0.690553\pi\) | |||||||
\(152\) | −3138.70 | −1.67488 | ||||||||
\(153\) | −12.6929 | − | 10.4839i | −0.00670691 | − | 0.00553969i | ||||
\(154\) | 6284.71 | 3.28855 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4080.85 | − | 735.893i | 2.09442 | − | 0.377684i | ||||
\(157\) | −103.480 | + | 179.233i | −0.0526026 | + | 0.0911103i | −0.891128 | − | 0.453753i | \(-0.850085\pi\) |
0.838525 | + | 0.544863i | \(0.183418\pi\) | |||||||
\(158\) | 2711.23 | − | 4695.98i | 1.36515 | − | 2.36451i | ||||
\(159\) | −371.838 | + | 1034.08i | −0.185463 | + | 0.515771i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4685.19 | 2.29345 | ||||||||
\(162\) | −2639.16 | + | 2285.21i | −1.27995 | + | 1.10829i | ||||
\(163\) | 2104.04 | 1.01105 | 0.505525 | − | 0.862812i | \(-0.331299\pi\) | ||||
0.505525 | + | 0.862812i | \(0.331299\pi\) | |||||||
\(164\) | 2041.98 | + | 3536.81i | 0.972266 | + | 1.68401i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1372.52 | + | 2377.27i | −0.641735 | + | 1.11152i | ||||
\(167\) | 517.426 | − | 896.209i | 0.239758 | − | 0.415274i | −0.720886 | − | 0.693053i | \(-0.756265\pi\) |
0.960645 | + | 0.277779i | \(0.0895984\pi\) | |||||||
\(168\) | 5206.79 | − | 938.931i | 2.39114 | − | 0.431191i | ||||
\(169\) | −329.515 | − | 570.737i | −0.149984 | − | 0.259780i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1968.10 | − | 1625.58i | −0.880141 | − | 0.726968i | ||||
\(172\) | 2767.94 | 1.22706 | ||||||||
\(173\) | −1760.62 | − | 3049.48i | −0.773741 | − | 1.34016i | −0.935499 | − | 0.353329i | \(-0.885050\pi\) |
0.161758 | − | 0.986830i | \(-0.448284\pi\) | |||||||
\(174\) | −2303.38 | − | 2723.54i | −1.00356 | − | 1.18662i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −845.591 | + | 1464.61i | −0.362152 | + | 0.627266i | ||||
\(177\) | −1667.81 | − | 1972.03i | −0.708249 | − | 0.837441i | ||||
\(178\) | −217.079 | − | 375.992i | −0.0914089 | − | 0.158325i | ||||
\(179\) | 961.672 | 0.401557 | 0.200779 | − | 0.979637i | \(-0.435653\pi\) | ||||
0.200779 | + | 0.979637i | \(0.435653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1493.35 | 0.613258 | 0.306629 | − | 0.951829i | \(-0.400799\pi\) | ||||
0.306629 | + | 0.951829i | \(0.400799\pi\) | |||||||
\(182\) | −3924.55 | − | 6797.52i | −1.59839 | − | 2.76849i | ||||
\(183\) | −1070.65 | + | 193.068i | −0.432483 | + | 0.0779891i | ||||
\(184\) | −2535.78 | + | 4392.09i | −1.01598 | + | 1.75972i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 314.725 | − | 875.246i | 0.124069 | − | 0.345033i | ||||
\(187\) | −13.0453 | − | 22.5951i | −0.00510143 | − | 0.00883593i | ||||
\(188\) | −6540.69 | −2.53739 | ||||||||
\(189\) | 3751.16 | + | 2107.93i | 1.44369 | + | 0.811267i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −828.719 | − | 1435.38i | −0.313948 | − | 0.543773i | 0.665266 | − | 0.746607i | \(-0.268318\pi\) |
−0.979213 | + | 0.202834i | \(0.934985\pi\) | |||||||
\(192\) | 1198.58 | − | 3333.24i | 0.450522 | − | 1.25289i | ||||
\(193\) | −508.384 | + | 880.546i | −0.189608 | + | 0.328410i | −0.945119 | − | 0.326725i | \(-0.894055\pi\) |
0.755512 | + | 0.655135i | \(0.227388\pi\) | |||||||
\(194\) | −22.1396 | + | 38.3469i | −0.00819346 | + | 0.0141915i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4462.16 | − | 7728.70i | −1.62615 | − | 2.81658i | ||||
\(197\) | 4594.73 | 1.66173 | 0.830865 | − | 0.556475i | \(-0.187846\pi\) | ||||
0.830865 | + | 0.556475i | \(0.187846\pi\) | |||||||
\(198\) | −5184.21 | + | 1932.56i | −1.86073 | + | 0.693643i | ||||
\(199\) | −832.746 | −0.296642 | −0.148321 | − | 0.988939i | \(-0.547387\pi\) | ||||
−0.148321 | + | 0.988939i | \(0.547387\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3246.75 | − | 3839.00i | −1.13935 | − | 1.34717i | ||||
\(202\) | −519.763 | + | 900.255i | −0.181041 | + | 0.313573i | ||||
\(203\) | −2198.22 | + | 3807.43i | −0.760025 | + | 1.31640i | ||||
\(204\) | −30.5508 | − | 36.1236i | −0.0104852 | − | 0.0123978i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2080.69 | 0.703729 | ||||||||
\(207\) | −3864.78 | + | 1440.71i | −1.29768 | + | 0.483749i | ||||
\(208\) | 2112.15 | 0.704093 | ||||||||
\(209\) | −2022.74 | − | 3503.50i | −0.669455 | − | 1.15953i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1212.40 | + | 2099.94i | −0.395568 | + | 0.685145i | −0.993174 | − | 0.116646i | \(-0.962786\pi\) |
0.597605 | + | 0.801791i | \(0.296119\pi\) | |||||||
\(212\) | −1579.00 | + | 2734.91i | −0.511539 | + | 0.886011i | ||||
\(213\) | 705.195 | − | 1961.14i | 0.226851 | − | 0.630869i | ||||
\(214\) | 462.728 | + | 801.468i | 0.147810 | + | 0.256015i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4006.31 | + | 2375.62i | −1.26201 | + | 0.748334i | ||||
\(217\) | −1146.40 | −0.358631 | ||||||||
\(218\) | 4078.00 | + | 7063.30i | 1.26696 | + | 2.19444i | ||||
\(219\) | −171.643 | + | 477.338i | −0.0529616 | + | 0.147286i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.2925 | + | 28.2195i | −0.00495907 | + | 0.00858937i | ||||
\(222\) | 6710.52 | − | 1210.10i | 2.02874 | − | 0.365840i | ||||
\(223\) | 1505.39 | + | 2607.41i | 0.452056 | + | 0.782983i | 0.998514 | − | 0.0545031i | \(-0.0173575\pi\) |
−0.546458 | + | 0.837487i | \(0.684024\pi\) | |||||||
\(224\) | −2340.93 | −0.698260 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2919.10 | 0.859184 | ||||||||
\(227\) | −39.8202 | − | 68.9706i | −0.0116430 | − | 0.0201663i | 0.860145 | − | 0.510049i | \(-0.170373\pi\) |
−0.871788 | + | 0.489883i | \(0.837039\pi\) | |||||||
\(228\) | −4737.07 | − | 5601.16i | −1.37596 | − | 1.62695i | ||||
\(229\) | 1157.98 | − | 2005.67i | 0.334154 | − | 0.578771i | −0.649168 | − | 0.760645i | \(-0.724883\pi\) |
0.983322 | + | 0.181874i | \(0.0582162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4403.59 | + | 5206.85i | 1.25426 | + | 1.48305i | ||||
\(232\) | −2379.50 | − | 4121.41i | −0.673369 | − | 1.16631i | ||||
\(233\) | −2055.15 | −0.577842 | −0.288921 | − | 0.957353i | \(-0.593297\pi\) | ||||
−0.288921 | + | 0.957353i | \(0.593297\pi\) | |||||||
\(234\) | 5327.59 | + | 4400.41i | 1.48836 | + | 1.22933i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3711.10 | − | 6427.82i | −1.02361 | − | 1.77295i | ||||
\(237\) | 5790.31 | − | 1044.16i | 1.58701 | − | 0.286183i | ||||
\(238\) | −44.7761 | + | 77.5544i | −0.0121950 | + | 0.0211223i | ||||
\(239\) | 2279.90 | − | 3948.90i | 0.617048 | − | 1.06876i | −0.372974 | − | 0.927842i | \(-0.621662\pi\) |
0.990022 | − | 0.140916i | \(-0.0450048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1946.62 | − | 3371.64i | −0.520301 | − | 0.901188i | −0.999721 | − | 0.0236025i | \(-0.992486\pi\) |
0.479420 | − | 0.877585i | \(-0.340847\pi\) | |||||||
\(242\) | −2394.50 | −0.636050 | ||||||||
\(243\) | −3742.50 | − | 585.324i | −0.987990 | − | 0.154521i | ||||
\(244\) | −3126.44 | −0.820285 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2302.77 | + | 6403.96i | −0.596825 | + | 1.65976i | ||||
\(247\) | −2526.25 | + | 4375.59i | −0.650774 | + | 1.12717i | ||||
\(248\) | 620.471 | − | 1074.69i | 0.158871 | − | 0.275172i | ||||
\(249\) | −2931.26 | + | 528.589i | −0.746027 | + | 0.134530i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1560.52 | 0.392426 | 0.196213 | − | 0.980561i | \(-0.437136\pi\) | ||||
0.196213 | + | 0.980561i | \(0.437136\pi\) | |||||||
\(252\) | 9533.89 | + | 7874.68i | 2.38325 | + | 1.96849i | ||||
\(253\) | −6536.76 | −1.62436 | ||||||||
\(254\) | 3285.92 | + | 5691.37i | 0.811719 | + | 1.40594i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3627.68 | − | 6283.33i | 0.885665 | − | 1.53402i | ||||
\(257\) | 3094.87 | − | 5360.47i | 0.751177 | − | 1.30108i | −0.196076 | − | 0.980589i | \(-0.562820\pi\) |
0.947253 | − | 0.320488i | \(-0.103847\pi\) | |||||||
\(258\) | 2978.49 | + | 3521.80i | 0.718732 | + | 0.849837i | ||||
\(259\) | −4202.21 | − | 7278.45i | −1.00816 | − | 1.74618i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 642.502 | − | 3816.68i | 0.152375 | − | 0.905160i | ||||
\(262\) | −5144.01 | −1.21297 | ||||||||
\(263\) | 2976.03 | + | 5154.64i | 0.697757 | + | 1.20855i | 0.969243 | + | 0.246108i | \(0.0791516\pi\) |
−0.271486 | + | 0.962442i | \(0.587515\pi\) | |||||||
\(264\) | −7264.48 | + | 1309.99i | −1.69355 | + | 0.305396i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6942.77 | + | 12025.2i | −1.60033 | + | 2.77186i | ||||
\(267\) | 159.404 | − | 443.301i | 0.0365370 | − | 0.101609i | ||||
\(268\) | −7224.49 | − | 12513.2i | −1.64666 | − | 2.85211i | ||||
\(269\) | 5228.45 | 1.18507 | 0.592536 | − | 0.805544i | \(-0.298127\pi\) | ||||
0.592536 | + | 0.805544i | \(0.298127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5868.44 | −1.31543 | −0.657717 | − | 0.753265i | \(-0.728478\pi\) | ||||
−0.657717 | + | 0.753265i | \(0.728478\pi\) | |||||||
\(272\) | −12.0490 | − | 20.8695i | −0.00268595 | − | 0.00465220i | ||||
\(273\) | 2881.85 | − | 8014.38i | 0.638891 | − | 1.77675i | ||||
\(274\) | −4749.46 | + | 8226.31i | −1.04717 | + | 1.81376i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11665.0 | + | 2103.53i | −2.54403 | + | 0.458760i | ||||
\(277\) | 838.841 | + | 1452.91i | 0.181953 | + | 0.315152i | 0.942546 | − | 0.334077i | \(-0.108425\pi\) |
−0.760592 | + | 0.649230i | \(0.775091\pi\) | |||||||
\(278\) | 9821.72 | 2.11895 | ||||||||
\(279\) | 945.660 | − | 352.522i | 0.202922 | − | 0.0756450i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −589.278 | − | 1020.66i | −0.125101 | − | 0.216681i | 0.796671 | − | 0.604413i | \(-0.206592\pi\) |
−0.921772 | + | 0.387731i | \(0.873259\pi\) | |||||||
\(282\) | −7038.22 | − | 8322.07i | −1.48624 | − | 1.75735i | ||||
\(283\) | 1870.28 | − | 3239.41i | 0.392849 | − | 0.680435i | −0.599975 | − | 0.800019i | \(-0.704823\pi\) |
0.992824 | + | 0.119584i | \(0.0381560\pi\) | |||||||
\(284\) | 2994.59 | − | 5186.79i | 0.625692 | − | 1.08373i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5475.51 | + | 9483.87i | 1.13208 | + | 1.96081i | ||||
\(287\) | 8387.96 | 1.72518 | ||||||||
\(288\) | 1931.02 | − | 719.843i | 0.395091 | − | 0.147282i | ||||
\(289\) | −4912.63 | −0.999924 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −47.2831 | + | 8.52648i | −0.00952503 | + | 0.00171763i | ||||
\(292\) | −728.879 | + | 1262.46i | −0.146077 | + | 0.253012i | ||||
\(293\) | 1358.07 | − | 2352.25i | 0.270783 | − | 0.469009i | −0.698280 | − | 0.715825i | \(-0.746051\pi\) |
0.969062 | + | 0.246816i | \(0.0793842\pi\) | |||||||
\(294\) | 5032.04 | − | 13994.0i | 0.998213 | − | 2.77602i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9097.49 | 1.78642 | ||||||||
\(297\) | −5233.61 | − | 2940.98i | −1.02251 | − | 0.574588i | ||||
\(298\) | 2778.88 | 0.540189 | ||||||||
\(299\) | 4081.94 | + | 7070.13i | 0.789515 | + | 1.36748i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2842.51 | − | 4923.38i | 0.544318 | − | 0.942787i | ||||
\(302\) | −3853.42 | + | 6674.33i | −0.734237 | + | 1.27174i | ||||
\(303\) | −1110.05 | + | 200.173i | −0.210464 | + | 0.0379526i | ||||
\(304\) | −1868.26 | − | 3235.93i | −0.352475 | − | 0.610504i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.0873 | − | 77.7428i | 0.00244493 | − | 0.0145237i | ||||
\(307\) | −4308.59 | −0.800992 | −0.400496 | − | 0.916299i | \(-0.631162\pi\) | ||||
−0.400496 | + | 0.916299i | \(0.631162\pi\) | |||||||
\(308\) | 9798.61 | + | 16971.7i | 1.81275 | + | 3.13978i | ||||
\(309\) | 1457.90 | + | 1723.84i | 0.268405 | + | 0.317365i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3153.11 | − | 5461.35i | 0.574908 | − | 0.995770i | −0.421143 | − | 0.906994i | \(-0.638371\pi\) |
0.996052 | − | 0.0887763i | \(-0.0282956\pi\) | |||||||
\(312\) | 5953.26 | + | 7039.20i | 1.08025 | + | 1.27730i | ||||
\(313\) | 2381.80 | + | 4125.40i | 0.430120 | + | 0.744989i | 0.996883 | − | 0.0788914i | \(-0.0251380\pi\) |
−0.566764 | + | 0.823881i | \(0.691805\pi\) | |||||||
\(314\) | −991.091 | −0.178123 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16908.5 | 3.01005 | ||||||||
\(317\) | −731.473 | − | 1266.95i | −0.129601 | − | 0.224476i | 0.793921 | − | 0.608021i | \(-0.208036\pi\) |
−0.923522 | + | 0.383545i | \(0.874703\pi\) | |||||||
\(318\) | −5178.88 | + | 933.899i | −0.913261 | + | 0.164687i | ||||
\(319\) | 3066.95 | − | 5312.11i | 0.538296 | − | 0.932355i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −339.787 | + | 944.943i | −0.0590812 | + | 0.164304i | ||||
\(322\) | 11218.2 | + | 19430.5i | 1.94151 | + | 3.36280i | ||||
\(323\) | 57.6450 | 0.00993020 | ||||||||
\(324\) | −10285.9 | − | 3564.07i | −1.76370 | − | 0.611123i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5037.92 | + | 8725.93i | 0.855903 | + | 1.48247i | ||||
\(327\) | −2994.53 | + | 8327.74i | −0.506415 | + | 1.40833i | ||||
\(328\) | −4539.83 | + | 7863.22i | −0.764239 | + | 1.32370i | ||||
\(329\) | −6716.90 | + | 11634.0i | −1.12558 | + | 1.94956i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2888.59 | + | 5003.18i | 0.479671 | + | 0.830814i | 0.999728 | − | 0.0233171i | \(-0.00742273\pi\) |
−0.520057 | + | 0.854131i | \(0.674089\pi\) | |||||||
\(332\) | −8559.67 | −1.41498 | ||||||||
\(333\) | 5704.51 | + | 4711.74i | 0.938755 | + | 0.775381i | ||||
\(334\) | 4955.71 | 0.811869 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4067.28 | + | 4809.20i | 0.660382 | + | 0.780843i | ||||
\(337\) | −1468.77 | + | 2543.98i | −0.237415 | + | 0.411214i | −0.959972 | − | 0.280097i | \(-0.909633\pi\) |
0.722557 | + | 0.691311i | \(0.242967\pi\) | |||||||
\(338\) | 1577.98 | − | 2733.15i | 0.253938 | − | 0.439833i | ||||
\(339\) | 2045.36 | + | 2418.46i | 0.327696 | + | 0.387471i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1599.46 | 0.254004 | ||||||||
\(342\) | 2029.25 | − | 12054.4i | 0.320846 | − | 1.90593i | ||||
\(343\) | −7809.75 | −1.22941 | ||||||||
\(344\) | 3076.92 | + | 5329.38i | 0.482257 | + | 0.835293i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8431.25 | − | 14603.3i | 1.31002 | − | 2.26902i | ||||
\(347\) | −3495.56 | + | 6054.49i | −0.540783 | + | 0.936663i | 0.458077 | + | 0.888913i | \(0.348539\pi\) |
−0.998859 | + | 0.0477504i | \(0.984795\pi\) | |||||||
\(348\) | 3763.61 | − | 10466.6i | 0.579743 | − | 1.61226i | ||||
\(349\) | 2676.15 | + | 4635.24i | 0.410462 | + | 0.710941i | 0.994940 | − | 0.100468i | \(-0.0320341\pi\) |
−0.584478 | + | 0.811409i | \(0.698701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 87.2286 | + | 7497.17i | 0.0132647 | + | 1.14008i | ||||
\(352\) | 3266.06 | 0.494550 | ||||||||
\(353\) | 517.078 | + | 895.605i | 0.0779639 | + | 0.135037i | 0.902371 | − | 0.430959i | \(-0.141825\pi\) |
−0.824407 | + | 0.565997i | \(0.808491\pi\) | |||||||
\(354\) | 4185.06 | − | 11638.6i | 0.628343 | − | 1.74741i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 676.905 | − | 1172.43i | 0.100775 | − | 0.174547i | ||||
\(357\) | −95.6273 | + | 17.2443i | −0.0141768 | + | 0.00255649i | ||||
\(358\) | 2302.63 | + | 3988.27i | 0.339938 | + | 0.588789i | ||||
\(359\) | −7870.36 | −1.15705 | −0.578526 | − | 0.815664i | \(-0.696372\pi\) | ||||
−0.578526 | + | 0.815664i | \(0.696372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2079.17 | 0.303130 | ||||||||
\(362\) | 3575.68 | + | 6193.25i | 0.519153 | + | 0.899199i | ||||
\(363\) | −1677.78 | − | 1983.83i | −0.242592 | − | 0.286843i | ||||
\(364\) | 12237.7 | − | 21196.3i | 1.76217 | − | 3.05216i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3364.25 | − | 3977.93i | −0.480471 | − | 0.568114i | ||||
\(367\) | −6625.85 | − | 11476.3i | −0.942416 | − | 1.63231i | −0.760845 | − | 0.648934i | \(-0.775215\pi\) |
−0.181571 | − | 0.983378i | \(-0.558118\pi\) | |||||||
\(368\) | −6037.53 | −0.855239 | ||||||||
\(369\) | −6919.16 | + | 2579.32i | −0.976144 | + | 0.363886i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3243.08 | + | 5617.18i | 0.453834 | + | 0.786063i | ||||
\(372\) | 2854.27 | − | 514.707i | 0.397815 | − | 0.0717374i | ||||
\(373\) | −1044.92 | + | 1809.85i | −0.145051 | + | 0.251235i | −0.929392 | − | 0.369095i | \(-0.879668\pi\) |
0.784341 | + | 0.620330i | \(0.213001\pi\) | |||||||
\(374\) | 62.4714 | − | 108.204i | 0.00863721 | − | 0.0149601i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7270.80 | − | 12593.4i | −0.997242 | − | 1.72727i | ||||
\(377\) | −7660.76 | −1.04655 | ||||||||
\(378\) | 239.726 | + | 20604.2i | 0.0326196 | + | 2.80361i | ||||
\(379\) | −4197.61 | −0.568909 | −0.284455 | − | 0.958690i | \(-0.591812\pi\) | ||||
−0.284455 | + | 0.958690i | \(0.591812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2412.89 | + | 6710.22i | −0.324452 | + | 0.902296i | ||||
\(382\) | 3968.57 | − | 6873.77i | 0.531544 | − | 0.920661i | ||||
\(383\) | 3856.67 | − | 6679.94i | 0.514534 | − | 0.891199i | −0.485324 | − | 0.874334i | \(-0.661298\pi\) |
0.999858 | − | 0.0168643i | \(-0.00536833\pi\) | |||||||
\(384\) | 13571.1 | − | 2447.25i | 1.80351 | − | 0.325224i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4869.10 | −0.642048 | ||||||||
\(387\) | −830.816 | + | 4935.34i | −0.109129 | + | 0.648262i | ||||
\(388\) | −138.073 | −0.0180660 | ||||||||
\(389\) | −571.797 | − | 990.381i | −0.0745276 | − | 0.129086i | 0.826353 | − | 0.563152i | \(-0.190412\pi\) |
−0.900881 | + | 0.434067i | \(0.857078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 46.5718 | − | 80.6648i | 0.00602363 | − | 0.0104332i | ||||
\(392\) | 9920.52 | − | 17182.8i | 1.27822 | − | 2.21394i | ||||
\(393\) | −3604.32 | − | 4261.79i | −0.462631 | − | 0.547020i | ||||
\(394\) | 11001.6 | + | 19055.4i | 1.40673 | + | 2.43654i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −13301.6 | − | 10986.7i | −1.68796 | − | 1.39420i | ||||
\(397\) | 2122.39 | 0.268311 | 0.134156 | − | 0.990960i | \(-0.457168\pi\) | ||||
0.134156 | + | 0.990960i | \(0.457168\pi\) | |||||||
\(398\) | −1993.93 | − | 3453.59i | −0.251122 | − | 0.434956i | ||||
\(399\) | −14827.5 | + | 2673.83i | −1.86041 | + | 0.335485i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −164.782 | + | 285.411i | −0.0205208 | + | 0.0355430i | −0.876103 | − | 0.482123i | \(-0.839866\pi\) |
0.855583 | + | 0.517666i | \(0.173199\pi\) | |||||||
\(402\) | 8147.15 | − | 22657.1i | 1.01080 | − | 2.81103i | ||||
\(403\) | −998.798 | − | 1729.97i | −0.123458 | − | 0.213836i | ||||
\(404\) | −3241.49 | −0.399183 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21053.7 | −2.57359 | ||||||||
\(407\) | 5862.91 | + | 10154.9i | 0.714038 | + | 1.23675i | ||||
\(408\) | 35.5910 | − | 98.9782i | 0.00431867 | − | 0.0120102i | ||||
\(409\) | 593.799 | − | 1028.49i | 0.0717884 | − | 0.124341i | −0.827897 | − | 0.560881i | \(-0.810463\pi\) |
0.899685 | + | 0.436539i | \(0.143796\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10143.3 | + | 1829.13i | −1.21736 | + | 0.219524i | ||||
\(412\) | 3244.04 | + | 5618.84i | 0.387918 | + | 0.671894i | ||||
\(413\) | −15244.3 | −1.81628 | ||||||||
\(414\) | −15228.8 | − | 12578.5i | −1.80786 | − | 1.49323i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2039.52 | − | 3532.56i | −0.240375 | − | 0.416341i | ||||
\(417\) | 6881.92 | + | 8137.25i | 0.808175 | + | 0.955595i | ||||
\(418\) | 9686.52 | − | 16777.5i | 1.13345 | − | 1.96320i | ||||
\(419\) | 5986.83 | − | 10369.5i | 0.698032 | − | 1.20903i | −0.271115 | − | 0.962547i | \(-0.587392\pi\) |
0.969148 | − | 0.246481i | \(-0.0792742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4318.23 | + | 7479.40i | 0.499900 | + | 0.865851i | 1.00000 | 0.000115960i | \(-3.69112e-5\pi\) | |
−0.500100 | + | 0.865967i | \(0.666704\pi\) | |||||||
\(422\) | −11611.9 | −1.33947 | ||||||||
\(423\) | 1963.23 | − | 11662.3i | 0.225663 | − | 1.34052i | ||||
\(424\) | −7021.03 | −0.804178 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9821.81 | − | 1771.15i | 1.11706 | − | 0.201438i | ||||
\(427\) | −3210.66 | + | 5561.03i | −0.363876 | + | 0.630251i | ||||
\(428\) | −1442.90 | + | 2499.17i | −0.162956 | + | 0.282248i | ||||
\(429\) | −4020.74 | + | 11181.6i | −0.452502 | + | 1.25840i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4589.22 | −0.512889 | −0.256445 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256445 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(432\) | −4833.91 | − | 2716.37i | −0.538360 | − | 0.302526i | ||||
\(433\) | 16279.0 | 1.80674 | 0.903369 | − | 0.428864i | \(-0.141086\pi\) | ||||
0.903369 | + | 0.428864i | \(0.141086\pi\) | |||||||
\(434\) | −2744.95 | − | 4754.40i | −0.303599 | − | 0.525849i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12716.2 | + | 22025.1i | −1.39678 | + | 2.41929i | ||||
\(437\) | 7221.21 | − | 12507.5i | 0.790474 | − | 1.36914i | ||||
\(438\) | −2390.61 | + | 431.095i | −0.260794 | + | 0.0470286i | ||||
\(439\) | 5261.48 | + | 9113.15i | 0.572020 | + | 0.990767i | 0.996358 | + | 0.0852636i | \(0.0271732\pi\) |
−0.424339 | + | 0.905503i | \(0.639493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15119.9 | − | 5636.37i | 1.63264 | − | 0.608613i | ||||
\(442\) | −156.044 | −0.0167924 | ||||||||
\(443\) | −7878.97 | − | 13646.8i | −0.845014 | − | 1.46361i | −0.885609 | − | 0.464432i | \(-0.846259\pi\) |
0.0405945 | − | 0.999176i | \(-0.487075\pi\) | |||||||
\(444\) | 13730.3 | + | 16234.9i | 1.46760 | + | 1.73530i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7209.02 | + | 12486.4i | −0.765374 | + | 1.32567i | ||||
\(447\) | 1947.12 | + | 2302.29i | 0.206030 | + | 0.243612i | ||||
\(448\) | −10453.7 | − | 18106.4i | −1.10244 | − | 1.90948i | ||||
\(449\) | 10964.2 | 1.15241 | 0.576206 | − | 0.817305i | \(-0.304533\pi\) | ||||
0.576206 | + | 0.817305i | \(0.304533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11702.8 | −1.22187 | ||||||||
\(452\) | 4551.23 | + | 7882.95i | 0.473610 | + | 0.820316i | ||||
\(453\) | −8229.68 | + | 1484.05i | −0.853563 | + | 0.153922i | ||||
\(454\) | 190.691 | − | 330.287i | 0.0197127 | − | 0.0341434i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5518.58 | − | 15347.1i | 0.566735 | − | 1.57608i | ||||
\(457\) | −6739.14 | − | 11672.5i | −0.689811 | − | 1.19479i | −0.971899 | − | 0.235400i | \(-0.924360\pi\) |
0.282087 | − | 0.959389i | \(-0.408973\pi\) | |||||||
\(458\) | 11090.6 | 1.13151 | ||||||||
\(459\) | 73.5796 | − | 43.6304i | 0.00748235 | − | 0.00443680i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5179.15 | + | 8970.55i | 0.523248 | + | 0.906291i | 0.999634 | + | 0.0270553i | \(0.00861302\pi\) |
−0.476386 | + | 0.879236i | \(0.658054\pi\) | |||||||
\(462\) | −11050.0 | + | 30730.0i | −1.11276 | + | 3.09456i | ||||
\(463\) | −7199.29 | + | 12469.5i | −0.722634 | + | 1.25164i | 0.237307 | + | 0.971435i | \(0.423735\pi\) |
−0.959941 | + | 0.280203i | \(0.909598\pi\) | |||||||
\(464\) | 2832.72 | − | 4906.42i | 0.283418 | − | 0.490894i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4920.85 | − | 8523.16i | −0.489172 | − | 0.847270i | ||||
\(467\) | −18838.8 | −1.86671 | −0.933356 | − | 0.358953i | \(-0.883134\pi\) | ||||
−0.933356 | + | 0.358953i | \(0.883134\pi\) | |||||||
\(468\) | −3576.86 | + | 21247.8i | −0.353291 | + | 2.09867i | ||||
\(469\) | −29676.5 | −2.92182 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −694.441 | − | 821.114i | −0.0679366 | − | 0.0803290i | ||||
\(472\) | 8250.72 | − | 14290.7i | 0.804598 | − | 1.39360i | ||||
\(473\) | −3965.86 | + | 6869.07i | −0.385519 | + | 0.667739i | ||||
\(474\) | 18194.7 | + | 21513.6i | 1.76310 | + | 2.08471i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −279.245 | −0.0268890 | ||||||||
\(477\) | −4402.49 | − | 3636.31i | −0.422591 | − | 0.349047i | ||||
\(478\) | 21836.0 | 2.08944 | ||||||||
\(479\) | −3181.96 | − | 5511.31i | −0.303523 | − | 0.525717i | 0.673409 | − | 0.739271i | \(-0.264830\pi\) |
−0.976931 | + | 0.213554i | \(0.931496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7322.31 | − | 12682.6i | 0.694113 | − | 1.20224i | ||||
\(482\) | 9321.96 | − | 16146.1i | 0.880920 | − | 1.52580i | ||||
\(483\) | −8237.69 | + | 22908.9i | −0.776041 | + | 2.15816i | ||||
\(484\) | −3733.31 | − | 6466.28i | −0.350611 | − | 0.607277i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6533.58 | − | 16922.5i | −0.609813 | − | 1.57946i | ||||
\(487\) | 1556.53 | 0.144832 | 0.0724158 | − | 0.997375i | \(-0.476929\pi\) | ||||
0.0724158 | + | 0.997375i | \(0.476929\pi\) | |||||||
\(488\) | −3475.43 | − | 6019.62i | −0.322388 | − | 0.558392i | ||||
\(489\) | −3699.41 | + | 10288.0i | −0.342112 | + | 0.951410i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6817.36 | − | 11808.0i | 0.626605 | − | 1.08531i | −0.361623 | − | 0.932324i | \(-0.617777\pi\) |
0.988228 | − | 0.152987i | \(-0.0488893\pi\) | |||||||
\(492\) | −20884.0 | + | 3765.98i | −1.91367 | + | 0.345089i | ||||
\(493\) | 43.7016 | + | 75.6935i | 0.00399234 | + | 0.00691493i | ||||
\(494\) | −24195.4 | −2.20365 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1477.30 | 0.133736 | ||||||||
\(497\) | −6150.54 | − | 10653.0i | −0.555109 | − | 0.961477i | ||||
\(498\) | −9210.78 | − | 10890.9i | −0.828805 | − | 0.979988i | ||||
\(499\) | −1132.45 | + | 1961.47i | −0.101594 | + | 0.175967i | −0.912342 | − | 0.409430i | \(-0.865728\pi\) |
0.810747 | + | 0.585396i | \(0.199061\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3472.38 | + | 4105.78i | 0.309650 | + | 0.366133i | ||||
\(502\) | 3736.51 | + | 6471.82i | 0.332208 | + | 0.575401i | ||||
\(503\) | −20004.6 | −1.77329 | −0.886643 | − | 0.462455i | \(-0.846969\pi\) | ||||
−0.886643 | + | 0.462455i | \(0.846969\pi\) | |||||||
\(504\) | −4563.74 | + | 27110.2i | −0.403343 | + | 2.39600i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15651.6 | − | 27109.4i | −1.37510 | − | 2.38174i | ||||
\(507\) | 3370.06 | − | 607.718i | 0.295207 | − | 0.0532342i | ||||
\(508\) | −10246.3 | + | 17747.1i | −0.894891 | + | 1.55000i | ||||
\(509\) | 361.966 | − | 626.944i | 0.0315204 | − | 0.0545949i | −0.849835 | − | 0.527049i | \(-0.823298\pi\) |
0.881355 | + | 0.472454i | \(0.156632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1497.03 | + | 2592.93i | 0.129598 | + | 0.224471i | ||||
\(512\) | 13513.5 | 1.16644 | ||||||||
\(513\) | 11408.9 | − | 6765.12i | 0.981902 | − | 0.582237i | ||||
\(514\) | 29641.4 | 2.54363 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4866.71 | + | 13534.3i | −0.415203 | + | 1.15468i | ||||
\(517\) | 9371.39 | − | 16231.7i | 0.797201 | − | 1.38079i | ||||
\(518\) | 20123.6 | − | 34855.0i | 1.70691 | − | 2.95645i | ||||
\(519\) | 18006.4 | − | 3247.07i | 1.52292 | − | 0.274626i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2150.30 | −0.180818 | −0.0904090 | − | 0.995905i | \(-0.528817\pi\) | ||||
−0.0904090 | + | 0.995905i | \(0.528817\pi\) | |||||||
\(522\) | 17367.0 | − | 6474.07i | 1.45620 | − | 0.542840i | ||||
\(523\) | 12696.4 | 1.06152 | 0.530760 | − | 0.847522i | \(-0.321907\pi\) | ||||
0.530760 | + | 0.847522i | \(0.321907\pi\) | |||||||
\(524\) | −8020.12 | − | 13891.3i | −0.668627 | − | 1.15810i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14251.6 | + | 24684.5i | −1.18137 | + | 2.04619i | ||||
\(527\) | −11.3955 | + | 19.7376i | −0.000941929 | + | 0.00163147i | ||||
\(528\) | −5674.65 | − | 6709.77i | −0.467722 | − | 0.553040i | ||||
\(529\) | −5584.63 | − | 9672.87i | −0.458998 | − | 0.795008i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12574.9 | − | 4687.67i | 1.02769 | − | 0.383103i | ||||
\(532\) | −43298.4 | −3.52862 | ||||||||
\(533\) | 7307.96 | + | 12657.8i | 0.593889 | + | 1.02865i | ||||
\(534\) | 2220.14 | − | 400.355i | 0.179916 | − | 0.0324439i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16061.9 | − | 27820.0i | 1.29434 | − | 2.24186i | ||||
\(537\) | −1690.85 | + | 4702.23i | −0.135876 | + | 0.377870i | ||||
\(538\) | 12519.0 | + | 21683.6i | 1.00322 | + | 1.73763i | ||||
\(539\) | 25573.2 | 2.04363 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12233.1 | −0.972167 | −0.486083 | − | 0.873912i | \(-0.661575\pi\) | ||||
−0.486083 | + | 0.873912i | \(0.661575\pi\) | |||||||
\(542\) | −14051.4 | − | 24337.7i | −1.11358 | − | 1.92877i | ||||
\(543\) | −2625.67 | + | 7301.94i | −0.207510 | + | 0.577083i | ||||
\(544\) | −23.2694 | + | 40.3038i | −0.00183395 | + | 0.00317649i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 40137.7 | − | 7237.98i | 3.14604 | − | 0.567320i | ||||
\(547\) | 9043.15 | + | 15663.2i | 0.706868 | + | 1.22433i | 0.966013 | + | 0.258493i | \(0.0832260\pi\) |
−0.259145 | + | 0.965839i | \(0.583441\pi\) | |||||||
\(548\) | −29619.9 | −2.30894 | ||||||||
\(549\) | 938.420 | − | 5574.54i | 0.0729522 | − | 0.433362i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6776.17 | + | 11736.7i | 0.523911 | + | 0.907440i | ||||
\(552\) | −17017.3 | − | 20121.4i | −1.31214 | − | 1.55149i | ||||
\(553\) | 17364.0 | − | 30075.4i | 1.33525 | − | 2.31272i | ||||
\(554\) | −4017.04 | + | 6957.72i | −0.308065 | + | 0.533584i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15313.2 | + | 26523.3i | 1.16803 | + | 2.02309i | ||||
\(557\) | 9106.96 | 0.692773 | 0.346386 | − | 0.938092i | \(-0.387409\pi\) | ||||
0.346386 | + | 0.938092i | \(0.387409\pi\) | |||||||
\(558\) | 3726.28 | + | 3077.79i | 0.282699 | + | 0.233500i | ||||
\(559\) | 9906.09 | 0.749523 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 133.419 | − | 24.0592i | 0.0100409 | − | 0.00181066i | ||||
\(562\) | 2821.93 | − | 4887.73i | 0.211808 | − | 0.366862i | ||||
\(563\) | −7355.90 | + | 12740.8i | −0.550647 | + | 0.953749i | 0.447581 | + | 0.894243i | \(0.352286\pi\) |
−0.998228 | + | 0.0595052i | \(0.981048\pi\) | |||||||
\(564\) | 11500.1 | − | 31981.6i | 0.858584 | − | 2.38771i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17912.8 | 1.33026 | ||||||||
\(567\) | −16902.5 | + | 14635.6i | −1.25192 | + | 1.08402i | ||||
\(568\) | 13315.5 | 0.983635 | ||||||||
\(569\) | −986.825 | − | 1709.23i | −0.0727062 | − | 0.125931i | 0.827380 | − | 0.561642i | \(-0.189830\pi\) |
−0.900086 | + | 0.435711i | \(0.856497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13097.0 | − | 22684.7i | 0.959881 | − | 1.66256i | 0.237101 | − | 0.971485i | \(-0.423803\pi\) |
0.722780 | − | 0.691078i | \(-0.242864\pi\) | |||||||
\(572\) | −17074.0 | + | 29573.0i | −1.24807 | + | 2.16173i | ||||
\(573\) | 8475.59 | − | 1528.39i | 0.617928 | − | 0.111430i | ||||
\(574\) | 20084.1 | + | 34786.7i | 1.46045 | + | 2.52957i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 14190.9 | + | 11721.3i | 1.02654 | + | 0.847892i | ||||
\(577\) | 8674.57 | 0.625870 | 0.312935 | − | 0.949775i | \(-0.398688\pi\) | ||||
0.312935 | + | 0.949775i | \(0.398688\pi\) | |||||||
\(578\) | −11762.8 | − | 20373.8i | −0.846485 | − | 1.46615i | ||||
\(579\) | −3411.69 | − | 4034.02i | −0.244879 | − | 0.289548i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8790.27 | + | 15225.2i | −0.627680 | + | 1.08717i | ||||
\(582\) | −148.576 | − | 175.678i | −0.0105819 | − | 0.0125122i | ||||
\(583\) | −4524.73 | − | 7837.06i | −0.321432 | − | 0.556737i | ||||
\(584\) | −3240.96 | −0.229644 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13007.1 | 0.916923 | ||||||||
\(587\) | 12191.9 | + | 21117.0i | 0.857263 | + | 1.48482i | 0.874530 | + | 0.484972i | \(0.161170\pi\) |
−0.0172666 | + | 0.999851i | \(0.505496\pi\) | |||||||
\(588\) | 45636.1 | − | 8229.49i | 3.20068 | − | 0.577174i | ||||
\(589\) | −1766.94 | + | 3060.42i | −0.123608 | + | 0.214096i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8078.63 | + | 22466.6i | −0.562285 | + | 1.56371i | ||||
\(592\) | 5415.15 | + | 9379.31i | 0.375948 | + | 0.651161i | ||||
\(593\) | 12980.5 | 0.898895 | 0.449447 | − | 0.893307i | \(-0.351621\pi\) | ||||
0.449447 | + | 0.893307i | \(0.351621\pi\) | |||||||
\(594\) | −334.465 | − | 28746.8i | −0.0231032 | − | 1.98568i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4332.61 | + | 7504.30i | 0.297770 | + | 0.515752i | ||||
\(597\) | 1464.17 | − | 4071.83i | 0.100376 | − | 0.279144i | ||||
\(598\) | −19547.6 | + | 33857.5i | −1.33673 | + | 2.31528i | ||||
\(599\) | 12502.4 | − | 21654.7i | 0.852808 | − | 1.47711i | −0.0258550 | − | 0.999666i | \(-0.508231\pi\) |
0.878663 | − | 0.477442i | \(-0.158436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4154.50 | − | 7195.81i | −0.281973 | − | 0.488391i | 0.689898 | − | 0.723907i | \(-0.257655\pi\) |
−0.971871 | + | 0.235516i | \(0.924322\pi\) | |||||||
\(602\) | 27224.5 | 1.84317 | ||||||||
\(603\) | 24479.9 | − | 9125.59i | 1.65323 | − | 0.616290i | ||||
\(604\) | −24031.8 | −1.61894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3488.06 | − | 4124.32i | −0.233816 | − | 0.276467i | ||||
\(607\) | 11891.8 | − | 20597.2i | 0.795177 | − | 1.37729i | −0.127549 | − | 0.991832i | \(-0.540711\pi\) |
0.922726 | − | 0.385456i | \(-0.125956\pi\) | |||||||
\(608\) | −3608.04 | + | 6249.31i | −0.240667 | + | 0.416847i | ||||
\(609\) | −14752.0 | − | 17442.9i | −0.981577 | − | 1.16063i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23408.2 | −1.54991 | ||||||||
\(612\) | 230.347 | − | 85.8685i | 0.0152144 | − | 0.00567162i | ||||
\(613\) | −13900.8 | −0.915903 | −0.457951 | − | 0.888977i | \(-0.651417\pi\) | ||||
−0.457951 | + | 0.888977i | \(0.651417\pi\) | |||||||
\(614\) | −10316.5 | − | 17868.7i | −0.678078 | − | 1.17447i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21784.8 | + | 37732.4i | −1.42489 | + | 2.46799i | ||||
\(617\) | −10100.7 | + | 17495.0i | −0.659061 | + | 1.14153i | 0.321798 | + | 0.946808i | \(0.395713\pi\) |
−0.980859 | + | 0.194719i | \(0.937621\pi\) | |||||||
\(618\) | −3658.34 | + | 10173.8i | −0.238123 | + | 0.662218i | ||||
\(619\) | −5720.45 | − | 9908.11i | −0.371445 | − | 0.643361i | 0.618343 | − | 0.785908i | \(-0.287804\pi\) |
−0.989788 | + | 0.142547i | \(0.954471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −249.341 | − | 21430.5i | −0.0161122 | − | 1.38482i | ||||
\(622\) | 30199.2 | 1.94675 | ||||||||
\(623\) | −1390.28 | − | 2408.04i | −0.0894069 | − | 0.154857i | ||||
\(624\) | −3713.67 | + | 10327.7i | −0.238246 | + | 0.662560i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11406.0 | + | 19755.7i | −0.728235 | + | 1.26134i | ||||
\(627\) | 20687.3 | − | 3730.51i | 1.31766 | − | 0.237611i | ||||
\(628\) | −1545.23 | − | 2676.42i | −0.0981869 | − | 0.170065i | ||||
\(629\) | −167.084 | −0.0105915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7670.95 | −0.483955 | −0.241978 | − | 0.970282i | \(-0.577796\pi\) | ||||
−0.241978 | + | 0.970282i | \(0.577796\pi\) | |||||||
\(632\) | 18795.9 | + | 32555.5i | 1.18301 | + | 2.04903i | ||||
\(633\) | −8136.24 | − | 9620.38i | −0.510879 | − | 0.604069i | ||||
\(634\) | 3502.88 | − | 6067.16i | 0.219428 | − | 0.380060i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10596.5 | − | 12529.4i | −0.660656 | − | 0.781166i | ||||
\(637\) | −15969.5 | − | 27659.9i | −0.993302 | − | 1.72045i | ||||
\(638\) | 29374.0 | 1.82277 | ||||||||
\(639\) | 8349.37 | + | 6896.31i | 0.516895 | + | 0.426938i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11992.0 | − | 20770.7i | −0.738930 | − | 1.27986i | −0.952978 | − | 0.303040i | \(-0.901998\pi\) |
0.214048 | − | 0.976823i | \(-0.431335\pi\) | |||||||
\(642\) | −4732.48 | + | 853.401i | −0.290928 | + | 0.0524627i | ||||
\(643\) | −14295.2 | + | 24760.1i | −0.876747 | + | 1.51857i | −0.0218578 | + | 0.999761i | \(0.506958\pi\) |
−0.854890 | + | 0.518810i | \(0.826375\pi\) | |||||||
\(644\) | −34981.1 | + | 60589.1i | −2.14045 | + | 3.70737i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 138.025 | + | 239.067i | 0.00840640 | + | 0.0145603i | ||||
\(647\) | −25703.8 | −1.56186 | −0.780928 | − | 0.624621i | \(-0.785254\pi\) | ||||
−0.780928 | + | 0.624621i | \(0.785254\pi\) | |||||||
\(648\) | −4571.86 | − | 23766.3i | −0.277160 | − | 1.44079i | ||||
\(649\) | 21268.8 | 1.28640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2015.65 | − | 5605.51i | 0.121351 | − | 0.337476i | ||||
\(652\) | −15709.4 | + | 27209.5i | −0.943603 | + | 1.63437i | ||||
\(653\) | 1821.61 | − | 3155.12i | 0.109165 | − | 0.189080i | −0.806267 | − | 0.591552i | \(-0.798516\pi\) |
0.915432 | + | 0.402472i | \(0.131849\pi\) | |||||||
\(654\) | −41707.1 | + | 7520.98i | −2.49370 | + | 0.449684i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10809.1 | −0.643328 | ||||||||
\(657\) | −2032.22 | − | 1678.55i | −0.120677 | − | 0.0996750i | ||||
\(658\) | −64331.8 | −3.81142 | ||||||||
\(659\) | 9705.17 | + | 16809.9i | 0.573687 | + | 0.993655i | 0.996183 | + | 0.0872904i | \(0.0278208\pi\) |
−0.422496 | + | 0.906365i | \(0.638846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10613.7 | − | 18383.4i | 0.624544 | − | 1.08174i | −0.364085 | − | 0.931366i | \(-0.618618\pi\) |
0.988629 | − | 0.150376i | \(-0.0480485\pi\) | |||||||
\(662\) | −13832.9 | + | 23959.2i | −0.812130 | + | 1.40665i | ||||
\(663\) | −109.337 | − | 129.281i | −0.00640468 | − | 0.00757296i | ||||
\(664\) | −9515.15 | − | 16480.7i | −0.556114 | − | 0.963217i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5881.76 | + | 34939.7i | −0.342213 | + | 2.03286i | ||||
\(667\) | 21898.1 | 1.27121 | ||||||||
\(668\) | 7726.54 | + | 13382.8i | 0.447528 | + | 0.775141i | ||||
\(669\) | −15396.2 | + | 2776.36i | −0.889760 | + | 0.160449i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4479.50 | − | 7758.73i | 0.257719 | − | 0.446382i | ||||
\(672\) | 4115.92 | − | 11446.3i | 0.236272 | − | 0.657071i | ||||
\(673\) | 7116.80 | + | 12326.7i | 0.407626 | + | 0.706030i | 0.994623 | − | 0.103560i | \(-0.0330233\pi\) |
−0.586997 | + | 0.809589i | \(0.699690\pi\) | |||||||
\(674\) | −14067.3 | −0.803932 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9841.05 | 0.559914 | ||||||||
\(677\) | −8462.10 | − | 14656.8i | −0.480391 | − | 0.832062i | 0.519356 | − | 0.854558i | \(-0.326172\pi\) |
−0.999747 | + | 0.0224963i | \(0.992839\pi\) | |||||||
\(678\) | −5132.48 | + | 14273.4i | −0.290725 | + | 0.808503i | ||||
\(679\) | −141.793 | + | 245.592i | −0.00801401 | + | 0.0138807i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 407.255 | − | 73.4397i | 0.0229164 | − | 0.00413247i | ||||
\(682\) | 3829.75 | + | 6633.31i | 0.215027 | + | 0.372438i | ||||
\(683\) | −3582.98 | −0.200730 | −0.100365 | − | 0.994951i | \(-0.532001\pi\) | ||||
−0.100365 | + | 0.994951i | \(0.532001\pi\) | |||||||
\(684\) | 35716.5 | − | 13314.4i | 1.99657 | − | 0.744281i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18699.7 | − | 32388.8i | −1.04075 | − | 1.80264i | ||||
\(687\) | 7771.03 | + | 9188.54i | 0.431562 | + | 0.510284i | ||||
\(688\) | −3662.98 | + | 6344.47i | −0.202979 | + | 0.351571i | ||||
\(689\) | −5651.03 | + | 9787.86i | −0.312463 | + | 0.541202i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8929.12 | + | 15465.7i | 0.491577 | + | 0.851436i | 0.999953 | − | 0.00969887i | \(-0.00308730\pi\) |
−0.508376 | + | 0.861135i | \(0.669754\pi\) | |||||||
\(692\) | 52581.3 | 2.88850 | ||||||||
\(693\) | −33202.2 | + | 12377.1i | −1.81998 | + | 0.678451i | ||||
\(694\) | −33479.1 | −1.83120 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 24336.0 | − | 4388.46i | 1.32536 | − | 0.239000i | ||||
\(697\) | 83.3781 | − | 144.415i | 0.00453109 | − | 0.00784808i | ||||
\(698\) | −12815.6 | + | 22197.2i | −0.694952 | + | 1.20369i | ||||
\(699\) | 3613.44 | − | 10048.9i | 0.195526 | − | 0.543756i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19796.1 | −1.06660 | −0.533302 | − | 0.845925i | \(-0.679049\pi\) | ||||
−0.533302 | + | 0.845925i | \(0.679049\pi\) | |||||||
\(702\) | −30883.6 | + | 18313.0i | −1.66044 | + | 0.984587i | ||||
\(703\) | −25907.2 | −1.38991 | ||||||||
\(704\) | 14585.0 | + | 25261.9i | 0.780813 | + | 1.35241i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2476.18 | + | 4288.87i | −0.132000 | + | 0.228632i | ||||
\(707\) | −3328.81 | + | 5765.68i | −0.177076 | + | 0.306705i | ||||
\(708\) | 37954.8 | − | 6844.32i | 2.01473 | − | 0.363313i | ||||
\(709\) | 8145.36 | + | 14108.2i | 0.431460 | + | 0.747311i | 0.996999 | − | 0.0774103i | \(-0.0246651\pi\) |
−0.565539 | + | 0.824722i | \(0.691332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5075.19 | + | 30148.4i | −0.267700 | + | 1.59023i | ||||
\(712\) | 3009.86 | 0.158426 | ||||||||
\(713\) | 2855.04 | + | 4945.07i | 0.149961 | + | 0.259740i | ||||
\(714\) | −300.486 | − | 355.298i | −0.0157499 | − | 0.0186228i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7180.15 | + | 12436.4i | −0.374769 | + | 0.649119i | ||||
\(717\) | 15300.1 | + | 18091.0i | 0.796922 | + | 0.942289i | ||||
\(718\) | −18844.8 | − | 32640.1i | −0.979501 | − | 1.69655i | ||||
\(719\) | −8647.80 | −0.448551 | −0.224276 | − | 0.974526i | \(-0.572002\pi\) | ||||
−0.224276 | + | 0.974526i | \(0.572002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13325.7 | 0.688316 | ||||||||
\(722\) | 4978.37 | + | 8622.79i | 0.256615 | + | 0.444470i | ||||
\(723\) | 19908.7 | − | 3590.11i | 1.02408 | − | 0.184672i | ||||
\(724\) | −11149.8 | + | 19312.0i | −0.572348 | + | 0.991335i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4210.10 | − | 11708.2i | 0.215222 | − | 0.598531i | ||||
\(727\) | −5290.01 | − | 9162.56i | −0.269870 | − | 0.467429i | 0.698958 | − | 0.715163i | \(-0.253647\pi\) |
−0.968828 | + | 0.247734i | \(0.920314\pi\) | |||||||
\(728\) | 54414.9 | 2.77026 | ||||||||
\(729\) | 9442.23 | − | 17270.3i | 0.479715 | − | 0.877424i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −56.5104 | − | 97.8789i | −0.00285925 | − | 0.00495237i | ||||
\(732\) | 5497.02 | − | 15287.2i | 0.277563 | − | 0.771898i | ||||
\(733\) | 14098.7 | − | 24419.7i | 0.710435 | − | 1.23051i | −0.254259 | − | 0.967136i | \(-0.581832\pi\) |
0.964694 | − | 0.263373i | \(-0.0848349\pi\) | |||||||
\(734\) | 31729.9 | − | 54957.8i | 1.59560 | − | 2.76366i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5829.93 | + | 10097.7i | 0.291975 | + | 0.505716i | ||||
\(737\) | 41404.5 | 2.06941 | ||||||||
\(738\) | −27264.3 | − | 22519.4i | −1.35991 | − | 1.12324i | ||||
\(739\) | −27120.4 | −1.34998 | −0.674992 | − | 0.737825i | \(-0.735853\pi\) | ||||
−0.674992 | + | 0.737825i | \(0.735853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16953.3 | − | 20045.8i | −0.840479 | − | 0.993792i | ||||
\(742\) | −15530.5 | + | 26899.6i | −0.768384 | + | 1.33088i | ||||
\(743\) | 6332.68 | − | 10968.5i | 0.312683 | − | 0.541583i | −0.666259 | − | 0.745720i | \(-0.732106\pi\) |
0.978942 | + | 0.204137i | \(0.0654389\pi\) | |||||||
\(744\) | 4163.90 | + | 4923.44i | 0.205183 | + | 0.242610i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10007.8 | −0.491169 | ||||||||
\(747\) | 2569.24 | − | 15262.2i | 0.125841 | − | 0.747542i | ||||
\(748\) | 389.601 | 0.0190444 | ||||||||
\(749\) | 2963.54 | + | 5133.00i | 0.144573 | + | 0.250408i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4324.63 | + | 7490.47i | −0.210130 | + | 0.363956i | −0.951755 | − | 0.306859i | \(-0.900722\pi\) |
0.741625 | + | 0.670815i | \(0.234055\pi\) | |||||||
\(752\) | 8655.68 | − | 14992.1i | 0.419734 | − | 0.727001i | ||||
\(753\) | −2743.76 | + | 7630.37i | −0.132787 | + | 0.369278i | ||||
\(754\) | −18342.9 | − | 31770.9i | −0.885955 | − | 1.53452i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −55267.2 | + | 32771.7i | −2.65880 | + | 1.57658i | ||||
\(757\) | −11715.6 | −0.562496 | −0.281248 | − | 0.959635i | \(-0.590748\pi\) | ||||
−0.281248 | + | 0.959635i | \(0.590748\pi\) | |||||||
\(758\) | −10050.8 | − | 17408.4i | −0.481609 | − | 0.834172i | ||||
\(759\) | 11493.2 | − | 31962.4i | 0.549639 | − | 1.52854i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18256.8 | − | 31621.7i | 0.869658 | − | 1.50629i | 0.00731060 | − | 0.999973i | \(-0.497673\pi\) |
0.862347 | − | 0.506318i | \(-0.168994\pi\) | |||||||
\(762\) | −33606.2 | + | 6060.15i | −1.59767 | + | 0.288105i | ||||
\(763\) | 26117.5 | + | 45236.9i | 1.23921 | + | 2.14638i | ||||
\(764\) | 24749.9 | 1.17202 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36937.6 | 1.74231 | ||||||||
\(767\) | −13281.5 | − | 23004.3i | −0.625252 | − | 1.08297i | ||||
\(768\) | 24344.9 | + | 28785.7i | 1.14384 | + | 1.35249i | ||||
\(769\) | 11459.8 | − | 19848.9i | 0.537386 | − | 0.930779i | −0.461658 | − | 0.887058i | \(-0.652745\pi\) |
0.999044 | − | 0.0437213i | \(-0.0139214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20769.2 | + | 24557.8i | 0.970150 | + | 1.14712i | ||||
\(772\) | −7591.50 | − | 13148.9i | −0.353917 | − | 0.613003i | ||||
\(773\) | 5112.86 | 0.237900 | 0.118950 | − | 0.992900i | \(-0.462047\pi\) | ||||
0.118950 | + | 0.992900i | \(0.462047\pi\) | |||||||
\(774\) | −22457.3 | + | 8371.59i | −1.04291 | + | 0.388774i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −153.486 | − | 265.845i | −0.00710028 | − | 0.0122980i | ||||
\(777\) | 42977.5 | − | 7750.06i | 1.98431 | − | 0.357828i | ||||
\(778\) | 2738.22 | − | 4742.74i | 0.126182 | − | 0.218554i | ||||
\(779\) | 12928.2 | − | 22392.3i | 0.594611 | − | 1.02990i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8581.20 | + | 14863.1i | 0.393162 | + | 0.680976i | ||||
\(782\) | 446.046 | 0.0203972 | ||||||||
\(783\) | 17532.5 | + | 9852.24i | 0.800206 | + | 0.449669i | ||||
\(784\) | 23620.2 | 1.07599 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9044.40 | − | 25152.4i | 0.410436 | − | 1.14142i | ||||
\(787\) | −17294.3 | + | 29954.7i | −0.783324 | + | 1.35676i | 0.146671 | + | 0.989185i | \(0.453144\pi\) |
−0.929995 | + | 0.367572i | \(0.880189\pi\) | |||||||
\(788\) | −34305.7 | + | 59419.2i | −1.55087 | + | 2.68619i | ||||
\(789\) | −30436.9 | + | 5488.64i | −1.37336 | + | 0.247656i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18695.3 | 0.840367 | ||||||||
\(792\) | 6367.31 | − | 37824.0i | 0.285672 | − | 1.69699i | ||||
\(793\) | −11189.1 | −0.501054 | ||||||||
\(794\) | 5081.85 | + | 8802.02i | 0.227139 | + | 0.393416i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6217.55 | − | 10769.1i | 0.276853 | − | 0.479524i | ||||
\(797\) | 8638.99 | − | 14963.2i | 0.383951 | − | 0.665022i | −0.607672 | − | 0.794188i | \(-0.707897\pi\) |
0.991623 | + | 0.129166i | \(0.0412300\pi\) | |||||||
\(798\) | −46592.0 | − | 55090.9i | −2.06684 | − | 2.44386i | ||||
\(799\) | 133.535 | + | 231.289i | 0.00591255 | + | 0.0102408i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1887.31 | + | 1558.86i | 0.0832520 | + | 0.0687634i | ||||
\(802\) | −1578.22 | −0.0694873 | ||||||||
\(803\) | −2088.65 | − | 3617.65i | −0.0917894 | − | 0.158984i | ||||
\(804\) | 73887.3 | − | 13324.0i | 3.24105 | − | 0.584454i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4783.05 | − | 8284.48i | 0.209027 | − | 0.362045i | ||||
\(807\) | −9192.87 | + | 25565.3i | −0.400997 | + | 1.11517i | ||||
\(808\) | −3603.32 | − | 6241.14i | −0.156887 | − | 0.271736i | ||||
\(809\) | 35591.8 | 1.54677 | 0.773387 | − | 0.633934i | \(-0.218561\pi\) | ||||
0.773387 | + | 0.633934i | \(0.218561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23814.4 | −1.03112 | −0.515558 | − | 0.856854i | \(-0.672415\pi\) | ||||
−0.515558 | + | 0.856854i | \(0.672415\pi\) | |||||||
\(812\) | −32825.3 | − | 56855.0i | −1.41865 | − | 2.45717i | ||||
\(813\) | 10318.1 | − | 28694.6i | 0.445108 | − | 1.23784i | ||||
\(814\) | −28076.3 | + | 48629.6i | −1.20894 | + | 2.09394i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 123.229 | − | 22.2218i | 0.00528663 | − | 0.000953330i | ||||
\(817\) | −8762.24 | − | 15176.7i | −0.375217 | − | 0.649895i | ||||
\(818\) | 5687.17 | 0.243089 | ||||||||
\(819\) | 34120.5 | + | 28182.4i | 1.45576 | + | 1.20241i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3982.82 | − | 6898.45i | −0.169307 | − | 0.293249i | 0.768869 | − | 0.639406i | \(-0.220820\pi\) |
−0.938177 | + | 0.346157i | \(0.887486\pi\) | |||||||
\(822\) | −31873.0 | − | 37687.0i | −1.35243 | − | 1.59913i | ||||
\(823\) | 17742.1 | − | 30730.1i | 0.751457 | − | 1.30156i | −0.195659 | − | 0.980672i | \(-0.562685\pi\) |
0.947116 | − | 0.320890i | \(-0.103982\pi\) | |||||||
\(824\) | −7212.31 | + | 12492.1i | −0.304918 | + | 0.528134i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36501.1 | − | 63221.7i | −1.53757 | − | 2.66315i | ||||
\(827\) | −37867.6 | −1.59224 | −0.796122 | − | 0.605136i | \(-0.793119\pi\) | ||||
−0.796122 | + | 0.605136i | \(0.793119\pi\) | |||||||
\(828\) | 10224.4 | − | 60736.2i | 0.429132 | − | 2.54919i | ||||
\(829\) | 10136.2 | 0.424662 | 0.212331 | − | 0.977198i | \(-0.431894\pi\) | ||||
0.212331 | + | 0.977198i | \(0.431894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8579.11 | + | 1547.06i | −0.358130 | + | 0.0645811i | ||||
\(832\) | 18215.5 | − | 31550.1i | 0.759025 | − | 1.31467i | ||||
\(833\) | −182.199 | + | 315.578i | −0.00757843 | + | 0.0131262i | ||||
\(834\) | −17268.9 | + | 48024.7i | −0.716996 | + | 1.99396i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 60409.8 | 2.49918 | ||||||||
\(837\) | 61.0104 | + | 5243.76i | 0.00251951 | + | 0.216548i | ||||
\(838\) | 57339.5 | 2.36367 | ||||||||
\(839\) | −15701.7 | − | 27196.2i | −0.646106 | − | 1.11909i | −0.984045 | − | 0.177921i | \(-0.943063\pi\) |
0.337939 | − | 0.941168i | \(-0.390270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1920.24 | − | 3325.95i | 0.0787339 | − | 0.136371i | ||||
\(842\) | −20679.2 | + | 35817.4i | −0.846379 | + | 1.46597i | ||||
\(843\) | 6026.75 | − | 1086.79i | 0.246230 | − | 0.0444023i | ||||
\(844\) | −18104.3 | − | 31357.6i | −0.738360 | − | 1.27888i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 53066.8 | − | 19782.2i | 2.15659 | − | 0.803931i | ||||
\(847\) | −15335.5 | −0.622120 | ||||||||
\(848\) | −4179.17 | − | 7238.53i | −0.169237 | − | 0.293127i | ||||
\(849\) | 12551.2 | + | 14840.6i | 0.507368 | + | 0.599917i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20930.6 | + | 36252.9i | −0.843117 | + | 1.46032i | ||||
\(852\) | 20096.3 | + | 23762.1i | 0.808085 | + | 0.955488i | ||||
\(853\) | 2781.70 | + | 4818.04i | 0.111657 | + | 0.193396i | 0.916439 | − | 0.400176i | \(-0.131051\pi\) |
−0.804781 | + | 0.593571i | \(0.797718\pi\) | |||||||
\(854\) | −30750.5 | −1.23215 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6415.85 | −0.256179 | ||||||||
\(857\) | 11355.0 | + | 19667.5i | 0.452603 | + | 0.783931i | 0.998547 | − | 0.0538909i | \(-0.0171623\pi\) |
−0.545944 | + | 0.837821i | \(0.683829\pi\) | |||||||
\(858\) | −56000.0 | + | 10098.4i | −2.22821 | + | 0.401810i | ||||
\(859\) | −17391.9 | + | 30123.6i | −0.690807 | + | 1.19651i | 0.280767 | + | 0.959776i | \(0.409411\pi\) |
−0.971574 | + | 0.236737i | \(0.923922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14748.0 | + | 41014.1i | −0.583754 | + | 1.62341i | ||||
\(862\) | −10988.4 | − | 19032.5i | −0.434186 | − | 0.752031i | ||||
\(863\) | 19361.6 | 0.763705 | 0.381853 | − | 0.924223i | \(-0.375286\pi\) | ||||
0.381853 | + | 0.924223i | \(0.375286\pi\) | |||||||
\(864\) | 124.582 | + | 10707.6i | 0.00490551 | + | 0.421622i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 38978.4 | + | 67512.6i | 1.52949 | + | 2.64916i | ||||
\(867\) | 8637.58 | − | 24021.0i | 0.338348 | − | 0.940941i | ||||
\(868\) | 8559.42 | − | 14825.3i | 0.334707 | − | 0.579729i | ||||
\(869\) | −24226.2 | + | 41961.0i | −0.945705 | + | 1.63801i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25855.5 | − | 44783.0i | −1.00583 | − | 1.74215i | ||||
\(872\) | −56542.6 | −2.19584 | ||||||||
\(873\) | 41.4435 | − | 246.189i | 0.00160670 | − | 0.00954437i | ||||
\(874\) | 69161.9 | 2.67670 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4891.41 | − | 5783.66i | −0.188659 | − | 0.223073i | ||||
\(877\) | 1413.55 | − | 2448.34i | 0.0544266 | − | 0.0942696i | −0.837528 | − | 0.546394i | \(-0.816000\pi\) |
0.891955 | + | 0.452124i | \(0.149334\pi\) | |||||||
\(878\) | −25196.2 | + | 43641.1i | −0.968485 | + | 1.67747i | ||||
\(879\) | 9113.83 | + | 10776.3i | 0.349718 | + | 0.413510i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3106.28 | 0.118789 | 0.0593946 | − | 0.998235i | \(-0.481083\pi\) | ||||
0.0593946 | + | 0.998235i | \(0.481083\pi\) | |||||||
\(882\) | 59578.3 | + | 49209.8i | 2.27450 | + | 1.87866i | ||||
\(883\) | −15219.6 | −0.580045 | −0.290023 | − | 0.957020i | \(-0.593663\pi\) | ||||
−0.290023 | + | 0.957020i | \(0.593663\pi\) | |||||||
\(884\) | −243.291 | − | 421.392i | −0.00925650 | − | 0.0160327i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 37730.9 | − | 65351.7i | 1.43069 | − | 2.47803i | ||||
\(887\) | 13086.4 | − | 22666.4i | 0.495377 | − | 0.858019i | −0.504608 | − | 0.863348i | \(-0.668363\pi\) |
0.999986 | + | 0.00532957i | \(0.00169646\pi\) | |||||||
\(888\) | −15995.6 | + | 44483.5i | −0.604478 | + | 1.68104i | ||||
\(889\) | 21044.6 | + | 36450.4i | 0.793941 | + | 1.37515i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23582.3 | − | 20419.5i | 0.886684 | − | 0.767766i | ||||
\(892\) | −44958.9 | −1.68760 | ||||||||
\(893\) | 20705.3 | + | 35862.6i | 0.775898 | + | 1.34389i | ||||
\(894\) | −4885.94 | + | 13587.7i | −0.182786 | + | 0.508324i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 40697.1 | − | 70489.4i | 1.51740 | − | 2.62822i | ||||
\(897\) | −41747.5 | + | 7528.25i | −1.55397 | + | 0.280224i | ||||
\(898\) | 26252.7 | + | 45471.0i | 0.975572 | + | 1.68974i | ||||
\(899\) | −5358.17 | −0.198782 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 128.948 | 0.00476789 | ||||||||
\(902\) | −28021.3 | − | 48534.3i | −1.03438 | − | 1.79159i | ||||
\(903\) | 19075.7 | + | 22555.4i | 0.702991 | + | 0.831224i | ||||
\(904\) | −10118.5 | + | 17525.8i | −0.372275 | + | 0.644800i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −25859.8 | − | 30576.9i | −0.948273 | − | 1.12125i | ||||
\(907\) | 10012.9 | + | 17342.9i | 0.366565 | + | 0.634909i | 0.989026 | − | 0.147742i | \(-0.0472004\pi\) |
−0.622461 | + | 0.782651i | \(0.713867\pi\) | |||||||
\(908\) | 1189.24 | 0.0434651 | ||||||||
\(909\) | 972.953 | − | 5779.68i | 0.0355015 | − | 0.210891i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2432.43 | + | 4213.10i | 0.0884633 | + | 0.153223i | 0.906862 | − | 0.421428i | \(-0.138471\pi\) |
−0.818398 | + | 0.574651i | \(0.805138\pi\) | |||||||
\(912\) | 19107.4 | − | 3445.60i | 0.693759 | − | 0.125105i | ||||
\(913\) | 12264.1 | − | 21242.1i | 0.444561 | − | 0.770002i | ||||
\(914\) | 32272.4 | − | 55897.5i | 1.16792 | − | 2.02289i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17291.6 | + | 29950.0i | 0.623724 | + | 1.08032i | ||||
\(917\) | −32944.8 | −1.18640 | ||||||||
\(918\) | 357.124 | + | 200.682i | 0.0128397 | + | 0.00721515i | ||||
\(919\) | 16242.7 | 0.583021 | 0.291510 | − | 0.956568i | \(-0.405842\pi\) | ||||
0.291510 | + | 0.956568i | \(0.405842\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7575.54 | − | 21067.5i | 0.271034 | − | 0.753743i | ||||
\(922\) | −24801.9 | + | 42958.2i | −0.885909 | + | 1.53444i | ||||
\(923\) | 10717.2 | − | 18562.8i | 0.382191 | − | 0.661974i | ||||
\(924\) | −100214. | + | 18071.4i | −3.56796 | + | 0.643404i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −68952.0 | −2.44698 | ||||||||
\(927\) | −10992.3 | + | 4097.70i | −0.389465 | + | 0.145184i | ||||
\(928\) | −10941.3 | −0.387031 | ||||||||
\(929\) | 77.8488 | + | 134.838i | 0.00274934 | + | 0.00476200i | 0.867397 | − | 0.497617i | \(-0.165792\pi\) |
−0.864647 | + | 0.502379i | \(0.832458\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28251.0 | + | 48932.1i | −0.994510 | + | 1.72254i | ||||
\(932\) | 15344.4 | − | 26577.3i | 0.539294 | − | 0.934085i | ||||
\(933\) | 21160.1 | + | 25019.9i | 0.742498 | + | 0.877938i | ||||
\(934\) | −45107.6 | − | 78128.6i | −1.58026 | − | 2.73709i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −44886.4 | + | 16732.7i | −1.56748 | + | 0.584323i | ||||
\(937\) | 27195.9 | 0.948186 | 0.474093 | − | 0.880475i | \(-0.342776\pi\) | ||||
0.474093 | + | 0.880475i | \(0.342776\pi\) | |||||||
\(938\) | −71057.4 | − | 123075.i | −2.47346 | − | 4.28416i | ||||
\(939\) | −24359.5 | + | 4392.71i | −0.846585 | + | 0.152663i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18570.0 | + | 32164.2i | −0.643321 | + | 1.11426i | 0.341366 | + | 0.939931i | \(0.389111\pi\) |
−0.984687 | + | 0.174334i | \(0.944223\pi\) | |||||||
\(942\) | 1742.58 | − | 4846.08i | 0.0602719 | − | 0.167615i | ||||
\(943\) | −20889.6 | − | 36181.9i | −0.721378 | − | 1.24946i | ||||
\(944\) | 19644.5 | 0.677303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37983.5 | −1.30544 | ||||||||
\(947\) | 22875.9 | + | 39622.3i | 0.784972 | + | 1.35961i | 0.929016 | + | 0.370039i | \(0.120656\pi\) |
−0.144044 | + | 0.989571i | \(0.546011\pi\) | |||||||
\(948\) | −29729.2 | + | 82676.5i | −1.01852 | + | 2.83250i | ||||
\(949\) | −2608.56 | + | 4518.16i | −0.0892280 | + | 0.154547i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7481.03 | − | 1349.04i | 0.255088 | − | 0.0459997i | ||||
\(952\) | −310.416 | − | 537.656i | −0.0105679 | − | 0.0183041i | ||||
\(953\) | −9011.61 | −0.306311 | −0.153156 | − | 0.988202i | \(-0.548944\pi\) | ||||
−0.153156 | + | 0.988202i | \(0.548944\pi\) | |||||||
\(954\) | 4539.28 | − | 26964.9i | 0.154051 | − | 0.915116i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 34044.9 | + | 58967.5i | 1.15177 | + | 1.99492i | ||||
\(957\) | 20581.9 | + | 24336.3i | 0.695213 | + | 0.822027i | ||||
\(958\) | 15237.8 | − | 26392.6i | 0.513894 | − | 0.890090i | ||||
\(959\) | −30417.9 | + | 52685.3i | −1.02424 | + | 1.77403i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14196.9 | + | 24589.8i | 0.476550 | + | 0.825409i | ||||
\(962\) | 70130.2 | 2.35040 | ||||||||
\(963\) | −4023.01 | − | 3322.87i | −0.134621 | − | 0.111192i | ||||
\(964\) | 58136.2 | 1.94237 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −114733. | + | 20689.6i | −3.82139 | + | 0.689105i | ||||
\(967\) | −14198.0 | + | 24591.6i | −0.472158 | + | 0.817801i | −0.999492 | − | 0.0318564i | \(-0.989858\pi\) |
0.527335 | + | 0.849658i | \(0.323191\pi\) | |||||||
\(968\) | 8300.09 | − | 14376.2i | 0.275594 | − | 0.477343i | ||||
\(969\) | −101.354 | + | 281.864i | −0.00336012 | + | 0.00934444i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10379.7 | −0.343048 | −0.171524 | − | 0.985180i | \(-0.554869\pi\) | ||||
−0.171524 | + | 0.985180i | \(0.554869\pi\) | |||||||
\(972\) | 35512.1 | − | 44027.9i | 1.17186 | − | 1.45288i | ||||
\(973\) | 62903.1 | 2.07254 | ||||||||
\(974\) | 3726.95 | + | 6455.26i | 0.122607 | + | 0.212361i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4137.39 | − | 7166.18i | 0.135691 | − | 0.235024i | ||||
\(977\) | 15815.8 | − | 27393.8i | 0.517905 | − | 0.897038i | −0.481878 | − | 0.876238i | \(-0.660045\pi\) |
0.999784 | − | 0.0208002i | \(-0.00662139\pi\) | |||||||
\(978\) | −51524.5 | + | 9291.34i | −1.68463 | + | 0.303788i | ||||
\(979\) | 1939.71 | + | 3359.68i | 0.0633233 | + | 0.109679i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35454.6 | − | 29284.3i | −1.15390 | − | 0.953086i | ||||
\(982\) | 65293.9 | 2.12181 | ||||||||
\(983\) | −12647.2 | − | 21905.5i | −0.410358 | − | 0.710760i | 0.584571 | − | 0.811342i | \(-0.301263\pi\) |
−0.994929 | + | 0.100582i | \(0.967929\pi\) | |||||||
\(984\) | −30466.2 | − | 36023.6i | −0.987020 | − | 1.16706i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −209.279 | + | 362.481i | −0.00675942 | + | 0.0117077i | ||||
\(987\) | −45076.2 | − | 53298.6i | −1.45369 | − | 1.71886i | ||||
\(988\) | −37723.5 | − | 65339.0i | −1.21472 | − | 2.10396i | ||||
\(989\) | −28316.3 | −0.910421 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20172.4 | −0.646617 | −0.323308 | − | 0.946294i | \(-0.604795\pi\) | ||||
−0.323308 | + | 0.946294i | \(0.604795\pi\) | |||||||
\(992\) | −1426.51 | − | 2470.78i | −0.0456569 | − | 0.0790800i | ||||
\(993\) | −29542.6 | + | 5327.37i | −0.944114 | + | 0.170251i | ||||
\(994\) | 29453.7 | − | 51015.3i | 0.939854 | − | 1.62787i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15050.0 | − | 41853.7i | 0.478791 | − | 1.33151i | ||||
\(997\) | 28177.6 | + | 48805.0i | 0.895079 | + | 1.55032i | 0.833707 | + | 0.552206i | \(0.186214\pi\) |
0.0613712 | + | 0.998115i | \(0.480453\pi\) | |||||||
\(998\) | −10846.2 | −0.344018 | ||||||||
\(999\) | −33068.6 | + | 19608.7i | −1.04729 | + | 0.621011i |
(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 | 225.4.e.f.76.11 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.49.3 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.49.22 | 48 | |||
5.4 | even | 2 | 225.4.e.e.76.2 | ✓ | 24 | ||
9.4 | even | 3 | 2025.4.a.bf.1.2 | 12 | |||
9.5 | odd | 6 | 2025.4.a.bj.1.11 | 12 | |||
9.7 | even | 3 | inner | 225.4.e.f.151.11 | yes | 24 | |
45.4 | even | 6 | 2025.4.a.bi.1.11 | 12 | |||
45.7 | odd | 12 | 225.4.k.e.124.22 | 48 | |||
45.14 | odd | 6 | 2025.4.a.be.1.2 | 12 | |||
45.34 | even | 6 | 225.4.e.e.151.2 | yes | 24 | ||
45.43 | odd | 12 | 225.4.k.e.124.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.2 | ✓ | 24 | 5.4 | even | 2 | ||
225.4.e.e.151.2 | yes | 24 | 45.34 | even | 6 | ||
225.4.e.f.76.11 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.e.f.151.11 | yes | 24 | 9.7 | even | 3 | inner | |
225.4.k.e.49.3 | 48 | 5.2 | odd | 4 | |||
225.4.k.e.49.22 | 48 | 5.3 | odd | 4 | |||
225.4.k.e.124.3 | 48 | 45.43 | odd | 12 | |||
225.4.k.e.124.22 | 48 | 45.7 | odd | 12 | |||
2025.4.a.be.1.2 | 12 | 45.14 | odd | 6 | |||
2025.4.a.bf.1.2 | 12 | 9.4 | even | 3 | |||
2025.4.a.bi.1.11 | 12 | 45.4 | even | 6 | |||
2025.4.a.bj.1.11 | 12 | 9.5 | odd | 6 |