Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(199,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.f (of order \(2\), degree \(1\), not 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: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.15 | ||
Root | \(-1.28061 - 0.600040i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.199 |
Dual form | 300.3.f.b.199.16 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.95141 | − | 0.438172i | 0.975706 | − | 0.219086i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 3.61601 | − | 1.71011i | 0.904003 | − | 0.427526i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.37994 | + | 0.758935i | −0.563324 | + | 0.126489i | ||||
\(7\) | 6.33166 | 0.904523 | 0.452262 | − | 0.891885i | \(-0.350617\pi\) | ||||
0.452262 | + | 0.891885i | \(0.350617\pi\) | |||||||
\(8\) | 6.30701 | − | 4.92155i | 0.788376 | − | 0.615194i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 9.27963i | − | 0.843602i | −0.906688 | − | 0.421801i | \(-0.861398\pi\) | ||
0.906688 | − | 0.421801i | \(-0.138602\pi\) | |||||||
\(12\) | −6.26312 | + | 2.96199i | −0.521926 | + | 0.246833i | ||||
\(13\) | 18.5674i | 1.42826i | 0.700012 | + | 0.714131i | \(0.253178\pi\) | ||||
−0.700012 | + | 0.714131i | \(0.746822\pi\) | |||||||
\(14\) | 12.3557 | − | 2.77436i | 0.882549 | − | 0.198168i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.1511 | − | 12.3675i | 0.634442 | − | 0.772970i | ||||
\(17\) | − | 13.9110i | − | 0.818296i | −0.912468 | − | 0.409148i | \(-0.865826\pi\) | ||
0.912468 | − | 0.409148i | \(-0.134174\pi\) | |||||||
\(18\) | 5.85423 | − | 1.31451i | 0.325235 | − | 0.0730286i | ||||
\(19\) | − | 17.2468i | − | 0.907727i | −0.891071 | − | 0.453864i | \(-0.850045\pi\) | ||
0.891071 | − | 0.453864i | \(-0.149955\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.9668 | −0.522227 | ||||||||
\(22\) | −4.06607 | − | 18.1084i | −0.184821 | − | 0.823108i | ||||
\(23\) | 33.7148 | 1.46586 | 0.732931 | − | 0.680303i | \(-0.238152\pi\) | ||||
0.732931 | + | 0.680303i | \(0.238152\pi\) | |||||||
\(24\) | −10.9241 | + | 8.52438i | −0.455169 | + | 0.355183i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.13571 | + | 36.2327i | 0.312912 | + | 1.39356i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 22.8954 | − | 10.8278i | 0.817692 | − | 0.386708i | ||||
\(29\) | 28.6177 | 0.986817 | 0.493409 | − | 0.869798i | \(-0.335751\pi\) | ||||
0.493409 | + | 0.869798i | \(0.335751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 23.4939i | − | 0.757866i | −0.925424 | − | 0.378933i | \(-0.876291\pi\) | ||
0.925424 | − | 0.378933i | \(-0.123709\pi\) | |||||||
\(32\) | 14.3898 | − | 28.5820i | 0.449682 | − | 0.893189i | ||||
\(33\) | 16.0728i | 0.487054i | ||||||||
\(34\) | −6.09542 | − | 27.1461i | −0.179277 | − | 0.798416i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.8480 | − | 5.13032i | 0.301334 | − | 0.142509i | ||||
\(37\) | 67.3338i | 1.81983i | 0.414793 | + | 0.909916i | \(0.363854\pi\) | ||||
−0.414793 | + | 0.909916i | \(0.636146\pi\) | |||||||
\(38\) | −7.55706 | − | 33.6556i | −0.198870 | − | 0.885674i | ||||
\(39\) | − | 32.1597i | − | 0.824608i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −44.0791 | −1.07510 | −0.537550 | − | 0.843232i | \(-0.680650\pi\) | ||||
−0.537550 | + | 0.843232i | \(0.680650\pi\) | |||||||
\(42\) | −21.4007 | + | 4.80532i | −0.509540 | + | 0.114412i | ||||
\(43\) | −50.2937 | −1.16962 | −0.584811 | − | 0.811170i | \(-0.698831\pi\) | ||||
−0.584811 | + | 0.811170i | \(0.698831\pi\) | |||||||
\(44\) | −15.8691 | − | 33.5552i | −0.360662 | − | 0.762619i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 65.7915 | − | 14.7729i | 1.43025 | − | 0.321150i | ||||
\(47\) | −31.1594 | −0.662967 | −0.331483 | − | 0.943461i | \(-0.607549\pi\) | ||||
−0.331483 | + | 0.943461i | \(0.607549\pi\) | |||||||
\(48\) | −17.5822 | + | 21.4212i | −0.366295 | + | 0.446275i | ||||
\(49\) | −8.91003 | −0.181837 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24.0946i | 0.472444i | ||||||||
\(52\) | 31.7522 | + | 67.1400i | 0.610620 | + | 1.29115i | ||||
\(53\) | 81.6070i | 1.53975i | 0.638192 | + | 0.769877i | \(0.279682\pi\) | ||||
−0.638192 | + | 0.769877i | \(0.720318\pi\) | |||||||
\(54\) | −10.1398 | + | 2.27681i | −0.187775 | + | 0.0421631i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 39.9338 | − | 31.1616i | 0.713104 | − | 0.556457i | ||||
\(57\) | 29.8724i | 0.524077i | ||||||||
\(58\) | 55.8449 | − | 12.5395i | 0.962843 | − | 0.216198i | ||||
\(59\) | 19.2751i | 0.326697i | 0.986568 | + | 0.163349i | \(0.0522296\pi\) | ||||
−0.986568 | + | 0.163349i | \(0.947770\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53.1563 | −0.871415 | −0.435707 | − | 0.900088i | \(-0.643502\pi\) | ||||
−0.435707 | + | 0.900088i | \(0.643502\pi\) | |||||||
\(62\) | −10.2943 | − | 45.8462i | −0.166038 | − | 0.739455i | ||||
\(63\) | 18.9950 | 0.301508 | ||||||||
\(64\) | 15.5566 | − | 62.0805i | 0.243072 | − | 0.970008i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.04264 | + | 31.3646i | 0.106707 | + | 0.475221i | ||||
\(67\) | −4.49911 | −0.0671509 | −0.0335754 | − | 0.999436i | \(-0.510689\pi\) | ||||
−0.0335754 | + | 0.999436i | \(0.510689\pi\) | |||||||
\(68\) | −23.7893 | − | 50.3025i | −0.349843 | − | 0.739742i | ||||
\(69\) | −58.3958 | −0.846316 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.3360i | − | 0.187832i | −0.995580 | − | 0.0939158i | \(-0.970062\pi\) | ||
0.995580 | − | 0.0939158i | \(-0.0299385\pi\) | |||||||
\(72\) | 18.9210 | − | 14.7647i | 0.262792 | − | 0.205065i | ||||
\(73\) | 40.8904i | 0.560143i | 0.959979 | + | 0.280071i | \(0.0903581\pi\) | ||||
−0.959979 | + | 0.280071i | \(0.909642\pi\) | |||||||
\(74\) | 29.5037 | + | 131.396i | 0.398699 | + | 1.77562i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29.4939 | − | 62.3647i | −0.388077 | − | 0.820588i | ||||
\(77\) | − | 58.7555i | − | 0.763058i | ||||||
\(78\) | −14.0915 | − | 62.7568i | −0.180660 | − | 0.804574i | ||||
\(79\) | 141.309i | 1.78872i | 0.447352 | + | 0.894358i | \(0.352367\pi\) | ||||
−0.447352 | + | 0.894358i | \(0.647633\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −86.0164 | + | 19.3142i | −1.04898 | + | 0.235539i | ||||
\(83\) | −69.8503 | −0.841570 | −0.420785 | − | 0.907160i | \(-0.638245\pi\) | ||||
−0.420785 | + | 0.907160i | \(0.638245\pi\) | |||||||
\(84\) | −39.6559 | + | 18.7543i | −0.472095 | + | 0.223266i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −98.1438 | + | 22.0373i | −1.14121 | + | 0.256248i | ||||
\(87\) | −49.5673 | −0.569739 | ||||||||
\(88\) | −45.6702 | − | 58.5266i | −0.518979 | − | 0.665076i | ||||
\(89\) | 46.3079 | 0.520313 | 0.260157 | − | 0.965566i | \(-0.416226\pi\) | ||||
0.260157 | + | 0.965566i | \(0.416226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 117.563i | 1.29190i | ||||||||
\(92\) | 121.913 | − | 57.6559i | 1.32514 | − | 0.626695i | ||||
\(93\) | 40.6926i | 0.437554i | ||||||||
\(94\) | −60.8049 | + | 13.6532i | −0.646860 | + | 0.145247i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −24.9239 | + | 49.5055i | −0.259624 | + | 0.515683i | ||||
\(97\) | − | 68.5543i | − | 0.706745i | −0.935483 | − | 0.353373i | \(-0.885035\pi\) | ||
0.935483 | − | 0.353373i | \(-0.114965\pi\) | |||||||
\(98\) | −17.3871 | + | 3.90412i | −0.177420 | + | 0.0398380i | ||||
\(99\) | − | 27.8389i | − | 0.281201i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −43.3949 | −0.429653 | −0.214826 | − | 0.976652i | \(-0.568919\pi\) | ||||
−0.214826 | + | 0.976652i | \(0.568919\pi\) | |||||||
\(102\) | 10.5576 | + | 47.0185i | 0.103506 | + | 0.460966i | ||||
\(103\) | −85.7919 | −0.832931 | −0.416465 | − | 0.909152i | \(-0.636731\pi\) | ||||
−0.416465 | + | 0.909152i | \(0.636731\pi\) | |||||||
\(104\) | 91.3805 | + | 117.105i | 0.878659 | + | 1.12601i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 35.7579 | + | 159.249i | 0.337338 | + | 1.50235i | ||||
\(107\) | 183.075 | 1.71098 | 0.855491 | − | 0.517818i | \(-0.173255\pi\) | ||||
0.855491 | + | 0.517818i | \(0.173255\pi\) | |||||||
\(108\) | −18.7893 | + | 8.88597i | −0.173975 | + | 0.0822775i | ||||
\(109\) | −81.4798 | −0.747521 | −0.373761 | − | 0.927525i | \(-0.621932\pi\) | ||||
−0.373761 | + | 0.927525i | \(0.621932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 116.625i | − | 1.05068i | ||||||
\(112\) | 64.2732 | − | 78.3070i | 0.573868 | − | 0.699170i | ||||
\(113\) | − | 172.814i | − | 1.52933i | −0.644429 | − | 0.764664i | \(-0.722905\pi\) | ||
0.644429 | − | 0.764664i | \(-0.277095\pi\) | |||||||
\(114\) | 13.0892 | + | 58.2933i | 0.114818 | + | 0.511344i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 103.482 | − | 48.9393i | 0.892086 | − | 0.421891i | ||||
\(117\) | 55.7022i | 0.476087i | ||||||||
\(118\) | 8.44582 | + | 37.6137i | 0.0715748 | + | 0.318760i | ||||
\(119\) | − | 88.0800i | − | 0.740168i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34.8885 | 0.288335 | ||||||||
\(122\) | −103.730 | + | 23.2916i | −0.850244 | + | 0.190915i | ||||
\(123\) | 76.3472 | 0.620709 | ||||||||
\(124\) | −40.1770 | − | 84.9541i | −0.324008 | − | 0.685113i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 37.0670 | − | 8.32307i | 0.294183 | − | 0.0660561i | ||||
\(127\) | −22.3785 | −0.176208 | −0.0881041 | − | 0.996111i | \(-0.528081\pi\) | ||||
−0.0881041 | + | 0.996111i | \(0.528081\pi\) | |||||||
\(128\) | 3.15546 | − | 127.961i | 0.0246520 | − | 0.999696i | ||||
\(129\) | 87.1113 | 0.675282 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.75315i | 0.0133828i | 0.999978 | + | 0.00669141i | \(0.00212996\pi\) | ||||
−0.999978 | + | 0.00669141i | \(0.997870\pi\) | |||||||
\(132\) | 27.4862 | + | 58.1194i | 0.208228 | + | 0.440298i | ||||
\(133\) | − | 109.201i | − | 0.821060i | ||||||
\(134\) | −8.77961 | + | 1.97138i | −0.0655195 | + | 0.0147118i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −68.4639 | − | 87.7370i | −0.503411 | − | 0.645125i | ||||
\(137\) | 19.5084i | 0.142397i | 0.997462 | + | 0.0711987i | \(0.0226824\pi\) | ||||
−0.997462 | + | 0.0711987i | \(0.977318\pi\) | |||||||
\(138\) | −113.954 | + | 25.5874i | −0.825755 | + | 0.185416i | ||||
\(139\) | 257.370i | 1.85158i | 0.378038 | + | 0.925790i | \(0.376599\pi\) | ||||
−0.378038 | + | 0.925790i | \(0.623401\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 53.9697 | 0.382764 | ||||||||
\(142\) | −5.84348 | − | 26.0241i | −0.0411512 | − | 0.183268i | ||||
\(143\) | 172.299 | 1.20489 | ||||||||
\(144\) | 30.4532 | − | 37.1026i | 0.211481 | − | 0.257657i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.9170 | + | 79.7940i | 0.122719 | + | 0.546534i | ||||
\(147\) | 15.4326 | 0.104984 | ||||||||
\(148\) | 115.148 | + | 243.480i | 0.778026 | + | 1.64513i | ||||
\(149\) | 111.673 | 0.749486 | 0.374743 | − | 0.927129i | \(-0.377731\pi\) | ||||
0.374743 | + | 0.927129i | \(0.377731\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.45275i | − | 0.0427335i | −0.999772 | − | 0.0213667i | \(-0.993198\pi\) | ||
0.999772 | − | 0.0213667i | \(-0.00680176\pi\) | |||||||
\(152\) | −84.8811 | − | 108.776i | −0.558428 | − | 0.715630i | ||||
\(153\) | − | 41.7331i | − | 0.272765i | ||||||
\(154\) | −25.7450 | − | 114.656i | −0.167175 | − | 0.744520i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −54.9965 | − | 116.290i | −0.352542 | − | 0.745448i | ||||
\(157\) | 75.9075i | 0.483488i | 0.970340 | + | 0.241744i | \(0.0777193\pi\) | ||||
−0.970340 | + | 0.241744i | \(0.922281\pi\) | |||||||
\(158\) | 61.9174 | + | 275.751i | 0.391882 | + | 1.74526i | ||||
\(159\) | − | 141.347i | − | 0.888977i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 213.471 | 1.32591 | ||||||||
\(162\) | 17.5627 | − | 3.94354i | 0.108412 | − | 0.0243429i | ||||
\(163\) | −249.298 | −1.52944 | −0.764719 | − | 0.644364i | \(-0.777122\pi\) | ||||
−0.764719 | + | 0.644364i | \(0.777122\pi\) | |||||||
\(164\) | −159.391 | + | 75.3799i | −0.971893 | + | 0.459634i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −136.307 | + | 30.6064i | −0.821124 | + | 0.184376i | ||||
\(167\) | −79.1883 | −0.474182 | −0.237091 | − | 0.971487i | \(-0.576194\pi\) | ||||
−0.237091 | + | 0.971487i | \(0.576194\pi\) | |||||||
\(168\) | −69.1674 | + | 53.9735i | −0.411711 | + | 0.321271i | ||||
\(169\) | −175.749 | −1.03993 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 51.7404i | − | 0.302576i | ||||||
\(172\) | −181.863 | + | 86.0076i | −1.05734 | + | 0.500044i | ||||
\(173\) | − | 27.7204i | − | 0.160234i | −0.996785 | − | 0.0801168i | \(-0.974471\pi\) | ||
0.996785 | − | 0.0801168i | \(-0.0255293\pi\) | |||||||
\(174\) | −96.7262 | + | 21.7190i | −0.555898 | + | 0.124822i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −114.766 | − | 94.1982i | −0.652080 | − | 0.535217i | ||||
\(177\) | − | 33.3855i | − | 0.188619i | ||||||
\(178\) | 90.3657 | − | 20.2908i | 0.507673 | − | 0.113993i | ||||
\(179\) | − | 204.324i | − | 1.14147i | −0.821133 | − | 0.570737i | \(-0.806658\pi\) | ||
0.821133 | − | 0.570737i | \(-0.193342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −49.8262 | −0.275283 | −0.137641 | − | 0.990482i | \(-0.543952\pi\) | ||||
−0.137641 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(182\) | 51.5126 | + | 229.413i | 0.283036 | + | 1.26051i | ||||
\(183\) | 92.0694 | 0.503112 | ||||||||
\(184\) | 212.640 | − | 165.929i | 1.15565 | − | 0.901790i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 17.8303 | + | 79.4079i | 0.0958620 | + | 0.426924i | ||||
\(187\) | −129.089 | −0.690317 | ||||||||
\(188\) | −112.673 | + | 53.2859i | −0.599324 | + | 0.283436i | ||||
\(189\) | −32.9003 | −0.174076 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.13703i | − | 0.00595301i | −0.999996 | − | 0.00297651i | \(-0.999053\pi\) | ||
0.999996 | − | 0.00297651i | \(-0.000947453\pi\) | |||||||
\(192\) | −26.9449 | + | 107.527i | −0.140338 | + | 0.560034i | ||||
\(193\) | − | 76.6452i | − | 0.397126i | −0.980088 | − | 0.198563i | \(-0.936373\pi\) | ||
0.980088 | − | 0.198563i | \(-0.0636274\pi\) | |||||||
\(194\) | −30.0385 | − | 133.778i | −0.154838 | − | 0.689575i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32.2188 | + | 15.2371i | −0.164382 | + | 0.0777403i | ||||
\(197\) | − | 134.496i | − | 0.682719i | −0.939933 | − | 0.341359i | \(-0.889113\pi\) | ||
0.939933 | − | 0.341359i | \(-0.110887\pi\) | |||||||
\(198\) | −12.1982 | − | 54.3251i | −0.0616071 | − | 0.274369i | ||||
\(199\) | − | 176.014i | − | 0.884491i | −0.896894 | − | 0.442245i | \(-0.854182\pi\) | ||
0.896894 | − | 0.442245i | \(-0.145818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.79269 | 0.0387696 | ||||||||
\(202\) | −84.6813 | + | 19.0144i | −0.419214 | + | 0.0941308i | ||||
\(203\) | 181.198 | 0.892599 | ||||||||
\(204\) | 41.2044 | + | 87.1264i | 0.201982 | + | 0.427090i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −167.415 | + | 37.5916i | −0.812695 | + | 0.182483i | ||||
\(207\) | 101.144 | 0.488621 | ||||||||
\(208\) | 229.633 | + | 188.479i | 1.10400 | + | 0.906150i | ||||
\(209\) | −160.044 | −0.765761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 218.087i | 1.03359i | 0.856110 | + | 0.516793i | \(0.172874\pi\) | ||||
−0.856110 | + | 0.516793i | \(0.827126\pi\) | |||||||
\(212\) | 139.557 | + | 295.092i | 0.658286 | + | 1.39194i | ||||
\(213\) | 23.0987i | 0.108445i | ||||||||
\(214\) | 357.255 | − | 80.2183i | 1.66941 | − | 0.374852i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −32.7722 | + | 25.5731i | −0.151723 | + | 0.118394i | ||||
\(217\) | − | 148.755i | − | 0.685508i | ||||||
\(218\) | −159.001 | + | 35.7021i | −0.729361 | + | 0.163771i | ||||
\(219\) | − | 70.8243i | − | 0.323399i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 258.292 | 1.16874 | ||||||||
\(222\) | −51.1020 | − | 227.584i | −0.230189 | − | 1.02515i | ||||
\(223\) | 328.579 | 1.47345 | 0.736724 | − | 0.676193i | \(-0.236372\pi\) | ||||
0.736724 | + | 0.676193i | \(0.236372\pi\) | |||||||
\(224\) | 91.1115 | − | 180.972i | 0.406748 | − | 0.807910i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −75.7222 | − | 337.231i | −0.335054 | − | 1.49217i | ||||
\(227\) | −157.649 | −0.694491 | −0.347245 | − | 0.937774i | \(-0.612883\pi\) | ||||
−0.347245 | + | 0.937774i | \(0.612883\pi\) | |||||||
\(228\) | 51.0849 | + | 108.019i | 0.224057 | + | 0.473767i | ||||
\(229\) | 273.148 | 1.19279 | 0.596393 | − | 0.802692i | \(-0.296600\pi\) | ||||
0.596393 | + | 0.802692i | \(0.296600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 101.767i | 0.440552i | ||||||||
\(232\) | 180.492 | − | 140.844i | 0.777983 | − | 0.607084i | ||||
\(233\) | 108.746i | 0.466720i | 0.972390 | + | 0.233360i | \(0.0749721\pi\) | ||||
−0.972390 | + | 0.233360i | \(0.925028\pi\) | |||||||
\(234\) | 24.4071 | + | 108.698i | 0.104304 | + | 0.464521i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32.9625 | + | 69.6992i | 0.139672 | + | 0.295335i | ||||
\(237\) | − | 244.754i | − | 1.03272i | ||||||
\(238\) | −38.5942 | − | 171.880i | −0.162160 | − | 0.722186i | ||||
\(239\) | − | 178.994i | − | 0.748927i | −0.927242 | − | 0.374464i | \(-0.877827\pi\) | ||
0.927242 | − | 0.374464i | \(-0.122173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 358.623 | 1.48806 | 0.744032 | − | 0.668144i | \(-0.232911\pi\) | ||||
0.744032 | + | 0.668144i | \(0.232911\pi\) | |||||||
\(242\) | 68.0819 | − | 15.2872i | 0.281330 | − | 0.0631701i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | −192.214 | + | 90.9029i | −0.787762 | + | 0.372553i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 148.985 | − | 33.4532i | 0.605629 | − | 0.135989i | ||||
\(247\) | 320.229 | 1.29647 | ||||||||
\(248\) | −115.626 | − | 148.176i | −0.466235 | − | 0.597483i | ||||
\(249\) | 120.984 | 0.485881 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 306.220i | − | 1.22000i | −0.792401 | − | 0.610000i | \(-0.791169\pi\) | ||
0.792401 | − | 0.610000i | \(-0.208831\pi\) | |||||||
\(252\) | 68.6861 | − | 32.4834i | 0.272564 | − | 0.128903i | ||||
\(253\) | − | 312.861i | − | 1.23660i | ||||||
\(254\) | −43.6696 | + | 9.80560i | −0.171927 | + | 0.0386047i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −49.9113 | − | 251.087i | −0.194966 | − | 0.980810i | ||||
\(257\) | 251.062i | 0.976895i | 0.872593 | + | 0.488447i | \(0.162437\pi\) | ||||
−0.872593 | + | 0.488447i | \(0.837563\pi\) | |||||||
\(258\) | 169.990 | − | 38.1697i | 0.658876 | − | 0.147945i | ||||
\(259\) | 426.335i | 1.64608i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 85.8531 | 0.328939 | ||||||||
\(262\) | 0.768181 | + | 3.42112i | 0.00293199 | + | 0.0130577i | ||||
\(263\) | 48.7645 | 0.185416 | 0.0927082 | − | 0.995693i | \(-0.470448\pi\) | ||||
0.0927082 | + | 0.995693i | \(0.470448\pi\) | |||||||
\(264\) | 79.1031 | + | 101.371i | 0.299633 | + | 0.383982i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −47.8488 | − | 213.096i | −0.179883 | − | 0.801113i | ||||
\(267\) | −80.2076 | −0.300403 | ||||||||
\(268\) | −16.2688 | + | 7.69395i | −0.0607046 | + | 0.0287088i | ||||
\(269\) | −148.696 | −0.552772 | −0.276386 | − | 0.961047i | \(-0.589137\pi\) | ||||
−0.276386 | + | 0.961047i | \(0.589137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 83.3415i | 0.307533i | 0.988107 | + | 0.153767i | \(0.0491404\pi\) | ||||
−0.988107 | + | 0.153767i | \(0.950860\pi\) | |||||||
\(272\) | −172.045 | − | 141.212i | −0.632519 | − | 0.519162i | ||||
\(273\) | − | 203.624i | − | 0.745877i | ||||||
\(274\) | 8.54805 | + | 38.0690i | 0.0311972 | + | 0.138938i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −211.160 | + | 99.8630i | −0.765072 | + | 0.361822i | ||||
\(277\) | − | 144.080i | − | 0.520146i | −0.965589 | − | 0.260073i | \(-0.916253\pi\) | ||
0.965589 | − | 0.260073i | \(-0.0837466\pi\) | |||||||
\(278\) | 112.772 | + | 502.234i | 0.405655 | + | 1.80660i | ||||
\(279\) | − | 70.4816i | − | 0.252622i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −343.671 | −1.22303 | −0.611514 | − | 0.791233i | \(-0.709439\pi\) | ||||
−0.611514 | + | 0.791233i | \(0.709439\pi\) | |||||||
\(282\) | 105.317 | − | 23.6480i | 0.373465 | − | 0.0838581i | ||||
\(283\) | −314.955 | −1.11292 | −0.556458 | − | 0.830876i | \(-0.687840\pi\) | ||||
−0.556458 | + | 0.830876i | \(0.687840\pi\) | |||||||
\(284\) | −22.8061 | − | 48.2233i | −0.0803030 | − | 0.169800i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 336.225 | − | 75.4964i | 1.17561 | − | 0.263973i | ||||
\(287\) | −279.094 | −0.972453 | ||||||||
\(288\) | 43.1695 | − | 85.7461i | 0.149894 | − | 0.297730i | ||||
\(289\) | 95.4831 | 0.330391 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 118.740i | 0.408040i | ||||||||
\(292\) | 69.9269 | + | 147.860i | 0.239476 | + | 0.506371i | ||||
\(293\) | − | 6.55421i | − | 0.0223693i | −0.999937 | − | 0.0111847i | \(-0.996440\pi\) | ||
0.999937 | − | 0.0111847i | \(-0.00356026\pi\) | |||||||
\(294\) | 30.1154 | − | 6.76214i | 0.102433 | − | 0.0230005i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 331.387 | + | 424.674i | 1.11955 | + | 1.43471i | ||||
\(297\) | 48.2184i | 0.162351i | ||||||||
\(298\) | 217.921 | − | 48.9321i | 0.731278 | − | 0.164202i | ||||
\(299\) | 625.997i | 2.09364i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −318.443 | −1.05795 | ||||||||
\(302\) | −2.82741 | − | 12.5920i | −0.00936229 | − | 0.0416953i | ||||
\(303\) | 75.1622 | 0.248060 | ||||||||
\(304\) | −213.300 | − | 175.074i | −0.701646 | − | 0.575900i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −18.2863 | − | 81.4384i | −0.0597590 | − | 0.266139i | ||||
\(307\) | 354.559 | 1.15492 | 0.577458 | − | 0.816420i | \(-0.304045\pi\) | ||||
0.577458 | + | 0.816420i | \(0.304045\pi\) | |||||||
\(308\) | −100.478 | − | 212.460i | −0.326228 | − | 0.689807i | ||||
\(309\) | 148.596 | 0.480893 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 193.387i | 0.621823i | 0.950439 | + | 0.310912i | \(0.100634\pi\) | ||||
−0.950439 | + | 0.310912i | \(0.899366\pi\) | |||||||
\(312\) | −158.276 | − | 202.831i | −0.507294 | − | 0.650101i | ||||
\(313\) | − | 23.5224i | − | 0.0751514i | −0.999294 | − | 0.0375757i | \(-0.988036\pi\) | ||
0.999294 | − | 0.0375757i | \(-0.0119635\pi\) | |||||||
\(314\) | 33.2605 | + | 148.127i | 0.105925 | + | 0.471742i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 241.653 | + | 510.973i | 0.764724 | + | 1.61700i | ||||
\(317\) | 214.004i | 0.675092i | 0.941309 | + | 0.337546i | \(0.109597\pi\) | ||||
−0.941309 | + | 0.337546i | \(0.890403\pi\) | |||||||
\(318\) | −61.9344 | − | 275.827i | −0.194762 | − | 0.867380i | ||||
\(319\) | − | 265.562i | − | 0.832481i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −317.095 | −0.987836 | ||||||||
\(322\) | 416.570 | − | 93.5369i | 1.29369 | − | 0.290487i | ||||
\(323\) | −239.921 | −0.742790 | ||||||||
\(324\) | 32.5441 | − | 15.3910i | 0.100445 | − | 0.0475029i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −486.483 | + | 109.235i | −1.49228 | + | 0.335078i | ||||
\(327\) | 141.127 | 0.431582 | ||||||||
\(328\) | −278.007 | + | 216.938i | −0.847583 | + | 0.661395i | ||||
\(329\) | −197.291 | −0.599669 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 412.454i | − | 1.24609i | −0.782188 | − | 0.623043i | \(-0.785896\pi\) | ||
0.782188 | − | 0.623043i | \(-0.214104\pi\) | |||||||
\(332\) | −252.579 | + | 119.451i | −0.760782 | + | 0.359793i | ||||
\(333\) | 202.001i | 0.606610i | ||||||||
\(334\) | −154.529 | + | 34.6981i | −0.462662 | + | 0.103886i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −111.324 | + | 135.632i | −0.331323 | + | 0.403666i | ||||
\(337\) | − | 103.268i | − | 0.306433i | −0.988193 | − | 0.153216i | \(-0.951037\pi\) | ||
0.988193 | − | 0.153216i | \(-0.0489631\pi\) | |||||||
\(338\) | −342.958 | + | 77.0081i | −1.01467 | + | 0.227835i | ||||
\(339\) | 299.323i | 0.882958i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −218.014 | −0.639338 | ||||||||
\(342\) | −22.6712 | − | 100.967i | −0.0662900 | − | 0.295225i | ||||
\(343\) | −366.667 | −1.06900 | ||||||||
\(344\) | −317.203 | + | 247.523i | −0.922102 | + | 0.719545i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.1463 | − | 54.0939i | −0.0351049 | − | 0.156341i | ||||
\(347\) | −153.211 | −0.441531 | −0.220766 | − | 0.975327i | \(-0.570856\pi\) | ||||
−0.220766 | + | 0.975327i | \(0.570856\pi\) | |||||||
\(348\) | −179.236 | + | 84.7654i | −0.515046 | + | 0.243579i | ||||
\(349\) | 84.7317 | 0.242784 | 0.121392 | − | 0.992605i | \(-0.461264\pi\) | ||||
0.121392 | + | 0.992605i | \(0.461264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 96.4791i | − | 0.274869i | ||||||
\(352\) | −265.231 | − | 133.532i | −0.753496 | − | 0.379353i | ||||
\(353\) | 256.065i | 0.725396i | 0.931907 | + | 0.362698i | \(0.118144\pi\) | ||||
−0.931907 | + | 0.362698i | \(0.881856\pi\) | |||||||
\(354\) | −14.6286 | − | 65.1489i | −0.0413237 | − | 0.184036i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 167.450 | − | 79.1914i | 0.470365 | − | 0.222448i | ||||
\(357\) | 152.559i | 0.427336i | ||||||||
\(358\) | −89.5289 | − | 398.720i | −0.250081 | − | 1.11374i | ||||
\(359\) | − | 667.258i | − | 1.85866i | −0.369253 | − | 0.929329i | \(-0.620386\pi\) | ||
0.369253 | − | 0.929329i | \(-0.379614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 63.5473 | 0.176031 | ||||||||
\(362\) | −97.2314 | + | 21.8324i | −0.268595 | + | 0.0603106i | ||||
\(363\) | −60.4287 | −0.166470 | ||||||||
\(364\) | 201.044 | + | 425.108i | 0.552320 | + | 1.16788i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 179.665 | − | 40.3422i | 0.490889 | − | 0.110225i | ||||
\(367\) | −245.301 | −0.668396 | −0.334198 | − | 0.942503i | \(-0.608465\pi\) | ||||
−0.334198 | + | 0.942503i | \(0.608465\pi\) | |||||||
\(368\) | 342.242 | − | 416.969i | 0.930005 | − | 1.13307i | ||||
\(369\) | −132.237 | −0.358367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 516.708i | 1.39274i | ||||||||
\(372\) | 69.5886 | + | 147.145i | 0.187066 | + | 0.395550i | ||||
\(373\) | 698.787i | 1.87342i | 0.350101 | + | 0.936712i | \(0.386147\pi\) | ||||
−0.350101 | + | 0.936712i | \(0.613853\pi\) | |||||||
\(374\) | −251.906 | + | 56.5632i | −0.673546 | + | 0.151239i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −196.523 | + | 153.353i | −0.522667 | + | 0.407853i | ||||
\(377\) | 531.357i | 1.40943i | ||||||||
\(378\) | −64.2020 | + | 14.4160i | −0.169847 | + | 0.0381375i | ||||
\(379\) | 208.691i | 0.550636i | 0.961353 | + | 0.275318i | \(0.0887831\pi\) | ||||
−0.961353 | + | 0.275318i | \(0.911217\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.7606 | 0.101734 | ||||||||
\(382\) | −0.498212 | − | 2.21880i | −0.00130422 | − | 0.00580839i | ||||
\(383\) | −156.524 | −0.408680 | −0.204340 | − | 0.978900i | \(-0.565505\pi\) | ||||
−0.204340 | + | 0.978900i | \(0.565505\pi\) | |||||||
\(384\) | −5.46541 | + | 221.635i | −0.0142328 | + | 0.577175i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −33.5838 | − | 149.566i | −0.0870046 | − | 0.387478i | ||||
\(387\) | −150.881 | −0.389874 | ||||||||
\(388\) | −117.235 | − | 247.893i | −0.302152 | − | 0.638900i | ||||
\(389\) | −386.588 | −0.993801 | −0.496900 | − | 0.867808i | \(-0.665529\pi\) | ||||
−0.496900 | + | 0.867808i | \(0.665529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 469.008i | − | 1.19951i | ||||||
\(392\) | −56.1956 | + | 43.8512i | −0.143356 | + | 0.111865i | ||||
\(393\) | − | 3.03655i | − | 0.00772658i | ||||||
\(394\) | −58.9322 | − | 262.456i | −0.149574 | − | 0.666133i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −47.6074 | − | 100.666i | −0.120221 | − | 0.254206i | ||||
\(397\) | 561.155i | 1.41349i | 0.707470 | + | 0.706744i | \(0.249837\pi\) | ||||
−0.707470 | + | 0.706744i | \(0.750163\pi\) | |||||||
\(398\) | −77.1242 | − | 343.475i | −0.193779 | − | 0.863002i | ||||
\(399\) | 189.142i | 0.474039i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9333 | 0.0422276 | 0.0211138 | − | 0.999777i | \(-0.493279\pi\) | ||||
0.0211138 | + | 0.999777i | \(0.493279\pi\) | |||||||
\(402\) | 15.2067 | − | 3.41453i | 0.0378277 | − | 0.00849387i | ||||
\(403\) | 436.220 | 1.08243 | ||||||||
\(404\) | −156.917 | + | 74.2099i | −0.388407 | + | 0.183688i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 353.591 | − | 79.3957i | 0.870914 | − | 0.195556i | ||||
\(407\) | 624.832 | 1.53521 | ||||||||
\(408\) | 118.583 | + | 151.965i | 0.290644 | + | 0.372463i | ||||
\(409\) | −258.490 | −0.632006 | −0.316003 | − | 0.948758i | \(-0.602341\pi\) | ||||
−0.316003 | + | 0.948758i | \(0.602341\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 33.7896i | − | 0.0822132i | ||||||
\(412\) | −310.224 | + | 146.713i | −0.752972 | + | 0.356100i | ||||
\(413\) | 122.044i | 0.295505i | ||||||||
\(414\) | 197.374 | − | 44.3186i | 0.476750 | − | 0.107050i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 530.694 | + | 267.182i | 1.27571 | + | 0.642264i | ||||
\(417\) | − | 445.777i | − | 1.06901i | ||||||
\(418\) | −312.312 | + | 70.1267i | −0.747157 | + | 0.167767i | ||||
\(419\) | 258.917i | 0.617941i | 0.951072 | + | 0.308970i | \(0.0999844\pi\) | ||||
−0.951072 | + | 0.308970i | \(0.900016\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 97.4654 | 0.231509 | 0.115755 | − | 0.993278i | \(-0.463071\pi\) | ||||
0.115755 | + | 0.993278i | \(0.463071\pi\) | |||||||
\(422\) | 95.5594 | + | 425.577i | 0.226444 | + | 1.00848i | ||||
\(423\) | −93.4783 | −0.220989 | ||||||||
\(424\) | 401.633 | + | 514.696i | 0.947248 | + | 1.21390i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.1212 | + | 45.0751i | 0.0237587 | + | 0.105810i | ||||
\(427\) | −336.568 | −0.788215 | ||||||||
\(428\) | 662.002 | − | 313.078i | 1.54673 | − | 0.731490i | ||||
\(429\) | −298.430 | −0.695641 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 389.968i | − | 0.904799i | −0.891815 | − | 0.452399i | \(-0.850568\pi\) | ||
0.891815 | − | 0.452399i | \(-0.149432\pi\) | |||||||
\(432\) | −52.7465 | + | 64.2635i | −0.122098 | + | 0.148758i | ||||
\(433\) | 275.893i | 0.637166i | 0.947895 | + | 0.318583i | \(0.103207\pi\) | ||||
−0.947895 | + | 0.318583i | \(0.896793\pi\) | |||||||
\(434\) | −65.1803 | − | 290.283i | −0.150185 | − | 0.668854i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −294.632 | + | 139.339i | −0.675761 | + | 0.319585i | ||||
\(437\) | − | 581.473i | − | 1.33060i | ||||||
\(438\) | −31.0332 | − | 138.207i | −0.0708520 | − | 0.315542i | ||||
\(439\) | − | 446.143i | − | 1.01627i | −0.861277 | − | 0.508136i | \(-0.830335\pi\) | ||
0.861277 | − | 0.508136i | \(-0.169665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.7301 | −0.0606125 | ||||||||
\(442\) | 504.034 | − | 113.176i | 1.14035 | − | 0.256055i | ||||
\(443\) | −794.679 | −1.79386 | −0.896929 | − | 0.442174i | \(-0.854207\pi\) | ||||
−0.896929 | + | 0.442174i | \(0.854207\pi\) | |||||||
\(444\) | −199.442 | − | 421.719i | −0.449194 | − | 0.949818i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 641.193 | − | 143.974i | 1.43765 | − | 0.322812i | ||||
\(447\) | −193.424 | −0.432716 | ||||||||
\(448\) | 98.4993 | − | 393.073i | 0.219865 | − | 0.877395i | ||||
\(449\) | 750.226 | 1.67088 | 0.835441 | − | 0.549581i | \(-0.185212\pi\) | ||||
0.835441 | + | 0.549581i | \(0.185212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 409.037i | 0.906957i | ||||||||
\(452\) | −295.530 | − | 624.898i | −0.653828 | − | 1.38252i | ||||
\(453\) | 11.1765i | 0.0246722i | ||||||||
\(454\) | −307.639 | + | 69.0775i | −0.677619 | + | 0.152153i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 147.018 | + | 188.405i | 0.322409 | + | 0.413169i | ||||
\(457\) | − | 101.092i | − | 0.221209i | −0.993865 | − | 0.110604i | \(-0.964721\pi\) | ||
0.993865 | − | 0.110604i | \(-0.0352787\pi\) | |||||||
\(458\) | 533.024 | − | 119.686i | 1.16381 | − | 0.261323i | ||||
\(459\) | 72.2839i | 0.157481i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.48690 | −0.00973297 | −0.00486648 | − | 0.999988i | \(-0.501549\pi\) | ||||
−0.00486648 | + | 0.999988i | \(0.501549\pi\) | |||||||
\(462\) | 44.5916 | + | 198.590i | 0.0965186 | + | 0.429849i | ||||
\(463\) | 515.108 | 1.11254 | 0.556272 | − | 0.831000i | \(-0.312231\pi\) | ||||
0.556272 | + | 0.831000i | \(0.312231\pi\) | |||||||
\(464\) | 290.500 | − | 353.930i | 0.626079 | − | 0.762780i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 47.6493 | + | 212.208i | 0.102252 | + | 0.455382i | ||||
\(467\) | 295.498 | 0.632758 | 0.316379 | − | 0.948633i | \(-0.397533\pi\) | ||||
0.316379 | + | 0.948633i | \(0.397533\pi\) | |||||||
\(468\) | 95.2567 | + | 201.420i | 0.203540 | + | 0.430384i | ||||
\(469\) | −28.4869 | −0.0607396 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 131.476i | − | 0.279142i | ||||||
\(472\) | 94.8637 | + | 121.568i | 0.200982 | + | 0.257560i | ||||
\(473\) | 466.707i | 0.986696i | ||||||||
\(474\) | −107.244 | − | 477.615i | −0.226253 | − | 1.00763i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −150.626 | − | 318.498i | −0.316441 | − | 0.669114i | ||||
\(477\) | 244.821i | 0.513251i | ||||||||
\(478\) | −78.4299 | − | 349.290i | −0.164079 | − | 0.730732i | ||||
\(479\) | 273.155i | 0.570260i | 0.958489 | + | 0.285130i | \(0.0920368\pi\) | ||||
−0.958489 | + | 0.285130i | \(0.907963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1250.21 | −2.59920 | ||||||||
\(482\) | 699.822 | − | 157.139i | 1.45191 | − | 0.326014i | ||||
\(483\) | −369.743 | −0.765512 | ||||||||
\(484\) | 126.157 | − | 59.6631i | 0.260656 | − | 0.123271i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −30.4195 | + | 6.83042i | −0.0625915 | + | 0.0140544i | ||||
\(487\) | −357.751 | −0.734601 | −0.367301 | − | 0.930102i | \(-0.619718\pi\) | ||||
−0.367301 | + | 0.930102i | \(0.619718\pi\) | |||||||
\(488\) | −335.257 | + | 261.612i | −0.687002 | + | 0.536089i | ||||
\(489\) | 431.797 | 0.883021 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 422.379i | 0.860242i | 0.902771 | + | 0.430121i | \(0.141529\pi\) | ||||
−0.902771 | + | 0.430121i | \(0.858471\pi\) | |||||||
\(492\) | 276.072 | − | 130.562i | 0.561123 | − | 0.265370i | ||||
\(493\) | − | 398.102i | − | 0.807509i | ||||||
\(494\) | 624.898 | − | 140.315i | 1.26498 | − | 0.284039i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −290.561 | − | 238.488i | −0.585808 | − | 0.480822i | ||||
\(497\) | − | 84.4394i | − | 0.169898i | ||||||
\(498\) | 236.090 | − | 53.0119i | 0.474076 | − | 0.106450i | ||||
\(499\) | − | 207.096i | − | 0.415021i | −0.978233 | − | 0.207511i | \(-0.933464\pi\) | ||
0.978233 | − | 0.207511i | \(-0.0665362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 137.158 | 0.273769 | ||||||||
\(502\) | −134.177 | − | 597.562i | −0.267285 | − | 1.19036i | ||||
\(503\) | 702.853 | 1.39732 | 0.698661 | − | 0.715452i | \(-0.253779\pi\) | ||||
0.698661 | + | 0.715452i | \(0.253779\pi\) | |||||||
\(504\) | 119.802 | − | 93.4849i | 0.237701 | − | 0.185486i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −137.087 | − | 610.520i | −0.270923 | − | 1.20656i | ||||
\(507\) | 304.406 | 0.600406 | ||||||||
\(508\) | −80.9207 | + | 38.2695i | −0.159293 | + | 0.0753337i | ||||
\(509\) | 389.029 | 0.764300 | 0.382150 | − | 0.924100i | \(-0.375184\pi\) | ||||
0.382150 | + | 0.924100i | \(0.375184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 258.904i | 0.506662i | ||||||||
\(512\) | −207.417 | − | 468.105i | −0.405111 | − | 0.914267i | ||||
\(513\) | 89.6171i | 0.174692i | ||||||||
\(514\) | 110.008 | + | 489.925i | 0.214024 | + | 0.953162i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 314.996 | − | 148.970i | 0.610457 | − | 0.288701i | ||||
\(517\) | 289.148i | 0.559280i | ||||||||
\(518\) | 186.808 | + | 831.954i | 0.360633 | + | 1.60609i | ||||
\(519\) | 48.0132i | 0.0925109i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −151.753 | −0.291273 | −0.145637 | − | 0.989338i | \(-0.546523\pi\) | ||||
−0.145637 | + | 0.989338i | \(0.546523\pi\) | |||||||
\(522\) | 167.535 | − | 37.6184i | 0.320948 | − | 0.0720659i | ||||
\(523\) | 557.762 | 1.06647 | 0.533234 | − | 0.845968i | \(-0.320977\pi\) | ||||
0.533234 | + | 0.845968i | \(0.320977\pi\) | |||||||
\(524\) | 2.99807 | + | 6.33941i | 0.00572151 | + | 0.0120981i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 95.1596 | − | 21.3672i | 0.180912 | − | 0.0406221i | ||||
\(527\) | −326.824 | −0.620159 | ||||||||
\(528\) | 198.781 | + | 163.156i | 0.376478 | + | 0.309008i | ||||
\(529\) | 607.689 | 1.14875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 57.8254i | 0.108899i | ||||||||
\(532\) | −186.745 | − | 394.872i | −0.351025 | − | 0.742241i | ||||
\(533\) | − | 818.435i | − | 1.53552i | ||||||
\(534\) | −156.518 | + | 35.1447i | −0.293105 | + | 0.0658141i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −28.3759 | + | 22.1426i | −0.0529401 | + | 0.0413108i | ||||
\(537\) | 353.899i | 0.659030i | ||||||||
\(538\) | −290.166 | + | 65.1542i | −0.539342 | + | 0.121104i | ||||
\(539\) | 82.6818i | 0.153398i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 340.979 | 0.630275 | 0.315137 | − | 0.949046i | \(-0.397949\pi\) | ||||
0.315137 | + | 0.949046i | \(0.397949\pi\) | |||||||
\(542\) | 36.5179 | + | 162.633i | 0.0673761 | + | 0.300062i | ||||
\(543\) | 86.3015 | 0.158935 | ||||||||
\(544\) | −397.606 | − | 200.177i | −0.730893 | − | 0.367973i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −89.2224 | − | 397.355i | −0.163411 | − | 0.727756i | ||||
\(547\) | 113.651 | 0.207771 | 0.103885 | − | 0.994589i | \(-0.466872\pi\) | ||||
0.103885 | + | 0.994589i | \(0.466872\pi\) | |||||||
\(548\) | 33.3615 | + | 70.5428i | 0.0608787 | + | 0.128728i | ||||
\(549\) | −159.469 | −0.290472 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 493.564i | − | 0.895761i | ||||||
\(552\) | −368.303 | + | 287.398i | −0.667215 | + | 0.520649i | ||||
\(553\) | 894.718i | 1.61794i | ||||||||
\(554\) | −63.1319 | − | 281.160i | −0.113957 | − | 0.507509i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 440.129 | + | 930.651i | 0.791599 | + | 1.67383i | ||||
\(557\) | − | 233.232i | − | 0.418728i | −0.977838 | − | 0.209364i | \(-0.932861\pi\) | ||
0.977838 | − | 0.209364i | \(-0.0671394\pi\) | |||||||
\(558\) | −30.8830 | − | 137.539i | −0.0553459 | − | 0.246485i | ||||
\(559\) | − | 933.825i | − | 1.67053i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 223.589 | 0.398554 | ||||||||
\(562\) | −670.644 | + | 150.587i | −1.19332 | + | 0.267948i | ||||
\(563\) | −167.786 | −0.298021 | −0.149011 | − | 0.988836i | \(-0.547609\pi\) | ||||
−0.149011 | + | 0.988836i | \(0.547609\pi\) | |||||||
\(564\) | 195.155 | − | 92.2939i | 0.346020 | − | 0.163642i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −614.607 | + | 138.004i | −1.08588 | + | 0.243824i | ||||
\(567\) | 56.9850 | 0.100503 | ||||||||
\(568\) | −65.6341 | − | 84.1105i | −0.115553 | − | 0.148082i | ||||
\(569\) | −381.089 | −0.669752 | −0.334876 | − | 0.942262i | \(-0.608694\pi\) | ||||
−0.334876 | + | 0.942262i | \(0.608694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 453.871i | − | 0.794870i | −0.917630 | − | 0.397435i | \(-0.869900\pi\) | ||
0.917630 | − | 0.397435i | \(-0.130100\pi\) | |||||||
\(572\) | 623.034 | − | 294.649i | 1.08922 | − | 0.515120i | ||||
\(573\) | 1.96939i | 0.00343697i | ||||||||
\(574\) | −544.627 | + | 122.291i | −0.948828 | + | 0.213051i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 46.6699 | − | 186.242i | 0.0810241 | − | 0.323336i | ||||
\(577\) | − | 688.294i | − | 1.19288i | −0.802656 | − | 0.596442i | \(-0.796581\pi\) | ||
0.802656 | − | 0.596442i | \(-0.203419\pi\) | |||||||
\(578\) | 186.327 | − | 41.8380i | 0.322365 | − | 0.0723841i | ||||
\(579\) | 132.753i | 0.229281i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −442.269 | −0.761220 | ||||||||
\(582\) | 52.0283 | + | 231.710i | 0.0893957 | + | 0.398127i | ||||
\(583\) | 757.282 | 1.29894 | ||||||||
\(584\) | 201.244 | + | 257.896i | 0.344597 | + | 0.441603i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.87187 | − | 12.7900i | −0.00490080 | − | 0.0218259i | ||||
\(587\) | −249.163 | −0.424468 | −0.212234 | − | 0.977219i | \(-0.568074\pi\) | ||||
−0.212234 | + | 0.977219i | \(0.568074\pi\) | |||||||
\(588\) | 55.8046 | − | 26.3914i | 0.0949057 | − | 0.0448834i | ||||
\(589\) | −405.194 | −0.687936 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 232.953i | 0.394168i | ||||||||
\(592\) | 832.752 | + | 683.510i | 1.40668 | + | 1.15458i | ||||
\(593\) | − | 163.937i | − | 0.276454i | −0.990401 | − | 0.138227i | \(-0.955860\pi\) | ||
0.990401 | − | 0.138227i | \(-0.0441404\pi\) | |||||||
\(594\) | 21.1279 | + | 94.0938i | 0.0355689 | + | 0.158407i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 403.812 | − | 190.973i | 0.677538 | − | 0.320425i | ||||
\(597\) | 304.865i | 0.510661i | ||||||||
\(598\) | 274.294 | + | 1221.58i | 0.458686 | + | 2.04277i | ||||
\(599\) | 170.412i | 0.284494i | 0.989831 | + | 0.142247i | \(0.0454327\pi\) | ||||
−0.989831 | + | 0.142247i | \(0.954567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1119.87 | 1.86335 | 0.931674 | − | 0.363295i | \(-0.118348\pi\) | ||||
0.931674 | + | 0.363295i | \(0.118348\pi\) | |||||||
\(602\) | −621.413 | + | 139.533i | −1.03225 | + | 0.231782i | ||||
\(603\) | −13.4973 | −0.0223836 | ||||||||
\(604\) | −11.0349 | − | 23.3332i | −0.0182697 | − | 0.0386312i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 146.672 | − | 32.9339i | 0.242034 | − | 0.0543464i | ||||
\(607\) | −660.957 | −1.08889 | −0.544445 | − | 0.838796i | \(-0.683260\pi\) | ||||
−0.544445 | + | 0.838796i | \(0.683260\pi\) | |||||||
\(608\) | −492.949 | − | 248.179i | −0.810772 | − | 0.408189i | ||||
\(609\) | −313.844 | −0.515342 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 578.550i | − | 0.946890i | ||||||
\(612\) | −71.3680 | − | 150.907i | −0.116614 | − | 0.246581i | ||||
\(613\) | − | 179.315i | − | 0.292520i | −0.989246 | − | 0.146260i | \(-0.953276\pi\) | ||
0.989246 | − | 0.146260i | \(-0.0467236\pi\) | |||||||
\(614\) | 691.891 | − | 155.358i | 1.12686 | − | 0.253026i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −289.168 | − | 370.571i | −0.469429 | − | 0.601576i | ||||
\(617\) | 63.6752i | 0.103201i | 0.998668 | + | 0.0516007i | \(0.0164323\pi\) | ||||
−0.998668 | + | 0.0516007i | \(0.983568\pi\) | |||||||
\(618\) | 289.972 | − | 65.1105i | 0.469210 | − | 0.105357i | ||||
\(619\) | − | 872.350i | − | 1.40929i | −0.709561 | − | 0.704644i | \(-0.751107\pi\) | ||
0.709561 | − | 0.704644i | \(-0.248893\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −175.187 | −0.282105 | ||||||||
\(622\) | 84.7367 | + | 377.378i | 0.136233 | + | 0.606716i | ||||
\(623\) | 293.206 | 0.470636 | ||||||||
\(624\) | −397.736 | − | 326.456i | −0.637397 | − | 0.523166i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.3068 | − | 45.9019i | −0.0164646 | − | 0.0733257i | ||||
\(627\) | 277.204 | 0.442112 | ||||||||
\(628\) | 129.810 | + | 274.483i | 0.206704 | + | 0.437074i | ||||
\(629\) | 936.682 | 1.48916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 340.783i | − | 0.540068i | −0.962851 | − | 0.270034i | \(-0.912965\pi\) | ||
0.962851 | − | 0.270034i | \(-0.0870349\pi\) | |||||||
\(632\) | 695.458 | + | 891.234i | 1.10041 | + | 1.41018i | ||||
\(633\) | − | 377.737i | − | 0.596742i | ||||||
\(634\) | 93.7705 | + | 417.610i | 0.147903 | + | 0.658691i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −241.719 | − | 511.114i | −0.380061 | − | 0.803638i | ||||
\(637\) | − | 165.436i | − | 0.259712i | ||||||
\(638\) | −116.362 | − | 518.220i | −0.182385 | − | 0.812257i | ||||
\(639\) | − | 40.0081i | − | 0.0626105i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 766.210 | 1.19534 | 0.597668 | − | 0.801744i | \(-0.296094\pi\) | ||||
0.597668 | + | 0.801744i | \(0.296094\pi\) | |||||||
\(642\) | −618.783 | + | 138.942i | −0.963837 | + | 0.216421i | ||||
\(643\) | −1163.47 | −1.80943 | −0.904717 | − | 0.426014i | \(-0.859917\pi\) | ||||
−0.904717 | + | 0.426014i | \(0.859917\pi\) | |||||||
\(644\) | 771.913 | − | 365.058i | 1.19862 | − | 0.566860i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −468.185 | + | 105.127i | −0.724744 | + | 0.162735i | ||||
\(647\) | 740.530 | 1.14456 | 0.572279 | − | 0.820059i | \(-0.306059\pi\) | ||||
0.572279 | + | 0.820059i | \(0.306059\pi\) | |||||||
\(648\) | 56.7630 | − | 44.2940i | 0.0875973 | − | 0.0683549i | ||||
\(649\) | 178.866 | 0.275603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 257.652i | 0.395778i | ||||||||
\(652\) | −901.465 | + | 426.326i | −1.38262 | + | 0.653875i | ||||
\(653\) | 109.569i | 0.167793i | 0.996474 | + | 0.0838967i | \(0.0267366\pi\) | ||||
−0.996474 | + | 0.0838967i | \(0.973263\pi\) | |||||||
\(654\) | 275.397 | − | 61.8379i | 0.421097 | − | 0.0945534i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −447.450 | + | 545.149i | −0.682089 | + | 0.831020i | ||||
\(657\) | 122.671i | 0.186714i | ||||||||
\(658\) | −384.996 | + | 86.4473i | −0.585100 | + | 0.131379i | ||||
\(659\) | 723.214i | 1.09744i | 0.836006 | + | 0.548721i | \(0.184885\pi\) | ||||
−0.836006 | + | 0.548721i | \(0.815115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 700.333 | 1.05951 | 0.529753 | − | 0.848152i | \(-0.322285\pi\) | ||||
0.529753 | + | 0.848152i | \(0.322285\pi\) | |||||||
\(662\) | −180.726 | − | 804.868i | −0.273000 | − | 1.21581i | ||||
\(663\) | −447.375 | −0.674773 | ||||||||
\(664\) | −440.546 | + | 343.772i | −0.663473 | + | 0.517729i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 88.5112 | + | 394.188i | 0.132900 | + | 0.591873i | ||||
\(667\) | 964.841 | 1.44654 | ||||||||
\(668\) | −286.346 | + | 135.420i | −0.428662 | + | 0.202725i | ||||
\(669\) | −569.116 | −0.850696 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 493.271i | 0.735128i | ||||||||
\(672\) | −157.810 | + | 313.452i | −0.234836 | + | 0.466447i | ||||
\(673\) | − | 1221.18i | − | 1.81454i | −0.420552 | − | 0.907269i | \(-0.638163\pi\) | ||
0.420552 | − | 0.907269i | \(-0.361837\pi\) | |||||||
\(674\) | −45.2490 | − | 201.518i | −0.0671350 | − | 0.298988i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −635.509 | + | 300.549i | −0.940103 | + | 0.444599i | ||||
\(677\) | − | 989.373i | − | 1.46141i | −0.682695 | − | 0.730704i | \(-0.739192\pi\) | ||
0.682695 | − | 0.730704i | \(-0.260808\pi\) | |||||||
\(678\) | 131.155 | + | 584.102i | 0.193444 | + | 0.861507i | ||||
\(679\) | − | 434.063i | − | 0.639268i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 273.057 | 0.400965 | ||||||||
\(682\) | −425.435 | + | 95.5276i | −0.623806 | + | 0.140070i | ||||
\(683\) | −307.312 | −0.449945 | −0.224972 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224972 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(684\) | −88.4816 | − | 187.094i | −0.129359 | − | 0.273529i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −715.518 | + | 160.663i | −1.04303 | + | 0.234203i | ||||
\(687\) | −473.107 | −0.688656 | ||||||||
\(688\) | −510.536 | + | 622.009i | −0.742058 | + | 0.904083i | ||||
\(689\) | −1515.23 | −2.19917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 893.378i | 1.29288i | 0.762966 | + | 0.646438i | \(0.223742\pi\) | ||||
−0.762966 | + | 0.646438i | \(0.776258\pi\) | |||||||
\(692\) | −47.4048 | − | 100.237i | −0.0685041 | − | 0.144852i | ||||
\(693\) | − | 176.266i | − | 0.254353i | ||||||
\(694\) | −298.978 | + | 67.1329i | −0.430805 | + | 0.0967332i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −312.621 | + | 243.948i | −0.449169 | + | 0.350500i | ||||
\(697\) | 613.186i | 0.879750i | ||||||||
\(698\) | 165.346 | − | 37.1270i | 0.236886 | − | 0.0531906i | ||||
\(699\) | − | 188.353i | − | 0.269461i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1127.42 | 1.60830 | 0.804149 | − | 0.594428i | \(-0.202622\pi\) | ||||
0.804149 | + | 0.594428i | \(0.202622\pi\) | |||||||
\(702\) | −42.2744 | − | 188.270i | −0.0602199 | − | 0.268191i | ||||
\(703\) | 1161.29 | 1.65191 | ||||||||
\(704\) | −576.084 | − | 144.360i | −0.818301 | − | 0.205056i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 112.200 | + | 499.688i | 0.158924 | + | 0.707773i | ||||
\(707\) | −274.762 | −0.388631 | ||||||||
\(708\) | −57.0928 | − | 120.722i | −0.0806395 | − | 0.170512i | ||||
\(709\) | −1093.27 | −1.54199 | −0.770997 | − | 0.636839i | \(-0.780242\pi\) | ||||
−0.770997 | + | 0.636839i | \(0.780242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 423.926i | 0.596239i | ||||||||
\(712\) | 292.064 | − | 227.907i | 0.410202 | − | 0.320094i | ||||
\(713\) | − | 792.091i | − | 1.11093i | ||||||
\(714\) | 66.8470 | + | 297.705i | 0.0936233 | + | 0.416954i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −349.415 | − | 738.837i | −0.488010 | − | 1.03190i | ||||
\(717\) | 310.026i | 0.432393i | ||||||||
\(718\) | −292.374 | − | 1302.10i | −0.407206 | − | 1.81350i | ||||
\(719\) | 769.690i | 1.07050i | 0.844693 | + | 0.535251i | \(0.179783\pi\) | ||||
−0.844693 | + | 0.535251i | \(0.820217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −543.205 | −0.753405 | ||||||||
\(722\) | 124.007 | − | 27.8446i | 0.171755 | − | 0.0385660i | ||||
\(723\) | −621.154 | −0.859134 | ||||||||
\(724\) | −180.172 | + | 85.2081i | −0.248857 | + | 0.117691i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −117.921 | + | 26.4782i | −0.162426 | + | 0.0364713i | ||||
\(727\) | 295.050 | 0.405846 | 0.202923 | − | 0.979195i | \(-0.434956\pi\) | ||||
0.202923 | + | 0.979195i | \(0.434956\pi\) | |||||||
\(728\) | 578.591 | + | 741.468i | 0.794767 | + | 1.01850i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 699.638i | 0.957097i | ||||||||
\(732\) | 332.924 | − | 157.448i | 0.454814 | − | 0.215094i | ||||
\(733\) | 261.200i | 0.356344i | 0.983999 | + | 0.178172i | \(0.0570184\pi\) | ||||
−0.983999 | + | 0.178172i | \(0.942982\pi\) | |||||||
\(734\) | −478.684 | + | 107.484i | −0.652158 | + | 0.146436i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 485.150 | − | 963.638i | 0.659172 | − | 1.30929i | ||||
\(737\) | 41.7501i | 0.0566487i | ||||||||
\(738\) | −258.049 | + | 57.9426i | −0.349660 | + | 0.0785130i | ||||
\(739\) | 482.679i | 0.653151i | 0.945171 | + | 0.326576i | \(0.105895\pi\) | ||||
−0.945171 | + | 0.326576i | \(0.894105\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −554.652 | −0.748519 | ||||||||
\(742\) | 226.407 | + | 1008.31i | 0.305130 | + | 1.35891i | ||||
\(743\) | 23.7067 | 0.0319067 | 0.0159534 | − | 0.999873i | \(-0.494922\pi\) | ||||
0.0159534 | + | 0.999873i | \(0.494922\pi\) | |||||||
\(744\) | 200.271 | + | 256.648i | 0.269181 | + | 0.344957i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 306.189 | + | 1363.62i | 0.410441 | + | 1.82791i | ||||
\(747\) | −209.551 | −0.280523 | ||||||||
\(748\) | −466.788 | + | 220.756i | −0.624048 | + | 0.295129i | ||||
\(749\) | 1159.17 | 1.54762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 395.508i | − | 0.526642i | −0.964708 | − | 0.263321i | \(-0.915182\pi\) | ||
0.964708 | − | 0.263321i | \(-0.0848179\pi\) | |||||||
\(752\) | −316.302 | + | 385.365i | −0.420614 | + | 0.512453i | ||||
\(753\) | 530.389i | 0.704368i | ||||||||
\(754\) | 232.825 | + | 1036.90i | 0.308787 | + | 1.37519i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −118.968 | + | 56.2630i | −0.157365 | + | 0.0744219i | ||||
\(757\) | − | 393.940i | − | 0.520396i | −0.965555 | − | 0.260198i | \(-0.916212\pi\) | ||
0.965555 | − | 0.260198i | \(-0.0837879\pi\) | |||||||
\(758\) | 91.4425 | + | 407.242i | 0.120637 | + | 0.537259i | ||||
\(759\) | 541.891i | 0.713954i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −369.354 | −0.485354 | −0.242677 | − | 0.970107i | \(-0.578025\pi\) | ||||
−0.242677 | + | 0.970107i | \(0.578025\pi\) | |||||||
\(762\) | 75.6379 | − | 16.9838i | 0.0992623 | − | 0.0222885i | ||||
\(763\) | −515.903 | −0.676150 | ||||||||
\(764\) | −1.94443 | − | 4.11150i | −0.00254507 | − | 0.00538154i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −305.444 | + | 68.5846i | −0.398751 | + | 0.0895360i | ||||
\(767\) | −357.890 | −0.466610 | ||||||||
\(768\) | 86.4490 | + | 434.896i | 0.112564 | + | 0.566271i | ||||
\(769\) | 873.491 | 1.13588 | 0.567940 | − | 0.823070i | \(-0.307741\pi\) | ||||
0.567940 | + | 0.823070i | \(0.307741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 434.852i | − | 0.564010i | ||||||
\(772\) | −131.071 | − | 277.150i | −0.169782 | − | 0.359003i | ||||
\(773\) | − | 1176.93i | − | 1.52254i | −0.648432 | − | 0.761272i | \(-0.724575\pi\) | ||
0.648432 | − | 0.761272i | \(-0.275425\pi\) | |||||||
\(774\) | −294.431 | + | 66.1119i | −0.380402 | + | 0.0854159i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −337.394 | − | 432.372i | −0.434786 | − | 0.557181i | ||||
\(777\) | − | 738.433i | − | 0.950365i | ||||||
\(778\) | −754.393 | + | 169.392i | −0.969657 | + | 0.217728i | ||||
\(779\) | 760.224i | 0.975897i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −123.754 | −0.158455 | ||||||||
\(782\) | −205.506 | − | 915.228i | −0.262795 | − | 1.17037i | ||||
\(783\) | −148.702 | −0.189913 | ||||||||
\(784\) | −90.4464 | + | 110.195i | −0.115365 | + | 0.140555i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.33053 | − | 5.92555i | −0.00169278 | − | 0.00753887i | ||||
\(787\) | −603.482 | −0.766814 | −0.383407 | − | 0.923580i | \(-0.625249\pi\) | ||||
−0.383407 | + | 0.923580i | \(0.625249\pi\) | |||||||
\(788\) | −230.002 | − | 486.338i | −0.291880 | − | 0.617180i | ||||
\(789\) | −84.4626 | −0.107050 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1094.20i | − | 1.38331i | ||||||
\(792\) | −137.011 | − | 175.580i | −0.172993 | − | 0.221692i | ||||
\(793\) | − | 986.975i | − | 1.24461i | ||||||
\(794\) | 245.882 | + | 1095.04i | 0.309675 | + | 1.37915i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −301.002 | − | 636.467i | −0.378143 | − | 0.799582i | ||||
\(797\) | − | 860.121i | − | 1.07920i | −0.841922 | − | 0.539599i | \(-0.818576\pi\) | ||
0.841922 | − | 0.539599i | \(-0.181424\pi\) | |||||||
\(798\) | 82.8765 | + | 369.093i | 0.103855 | + | 0.462523i | ||||
\(799\) | 433.460i | 0.542503i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 138.924 | 0.173438 | ||||||||
\(802\) | 33.0437 | − | 7.41967i | 0.0412017 | − | 0.00925146i | ||||
\(803\) | 379.448 | 0.472538 | ||||||||
\(804\) | 28.1784 | − | 13.3263i | 0.0350478 | − | 0.0165750i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 851.245 | − | 191.139i | 1.05614 | − | 0.237145i | ||||
\(807\) | 257.548 | 0.319143 | ||||||||
\(808\) | −273.692 | + | 213.570i | −0.338728 | + | 0.264320i | ||||
\(809\) | −941.012 | −1.16318 | −0.581589 | − | 0.813483i | \(-0.697569\pi\) | ||||
−0.581589 | + | 0.813483i | \(0.697569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1105.29i | − | 1.36287i | −0.731878 | − | 0.681436i | \(-0.761356\pi\) | ||
0.731878 | − | 0.681436i | \(-0.238644\pi\) | |||||||
\(812\) | 655.213 | − | 309.867i | 0.806912 | − | 0.381610i | ||||
\(813\) | − | 144.352i | − | 0.177554i | ||||||
\(814\) | 1219.30 | − | 273.784i | 1.49792 | − | 0.336344i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 297.991 | + | 244.586i | 0.365185 | + | 0.299738i | ||||
\(817\) | 867.407i | 1.06170i | ||||||||
\(818\) | −504.421 | + | 113.263i | −0.616652 | + | 0.138463i | ||||
\(819\) | 352.688i | 0.430632i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −193.170 | −0.235286 | −0.117643 | − | 0.993056i | \(-0.537534\pi\) | ||||
−0.117643 | + | 0.993056i | \(0.537534\pi\) | |||||||
\(822\) | −14.8057 | − | 65.9374i | −0.0180117 | − | 0.0802159i | ||||
\(823\) | 178.778 | 0.217227 | 0.108614 | − | 0.994084i | \(-0.465359\pi\) | ||||
0.108614 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(824\) | −541.090 | + | 422.229i | −0.656662 | + | 0.512414i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 53.4761 | + | 238.158i | 0.0647410 | + | 0.288326i | ||||
\(827\) | 1558.61 | 1.88465 | 0.942326 | − | 0.334697i | \(-0.108634\pi\) | ||||
0.942326 | + | 0.334697i | \(0.108634\pi\) | |||||||
\(828\) | 365.740 | − | 172.968i | 0.441714 | − | 0.208898i | ||||
\(829\) | 565.477 | 0.682119 | 0.341059 | − | 0.940042i | \(-0.389214\pi\) | ||||
0.341059 | + | 0.940042i | \(0.389214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 249.554i | 0.300306i | ||||||||
\(832\) | 1152.67 | + | 288.846i | 1.38543 | + | 0.347171i | ||||
\(833\) | 123.948i | 0.148797i | ||||||||
\(834\) | −195.327 | − | 869.895i | −0.234205 | − | 1.04304i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −578.721 | + | 273.692i | −0.692250 | + | 0.327383i | ||||
\(837\) | 122.078i | 0.145851i | ||||||||
\(838\) | 113.450 | + | 505.254i | 0.135382 | + | 0.602928i | ||||
\(839\) | − | 1280.25i | − | 1.52592i | −0.646443 | − | 0.762962i | \(-0.723744\pi\) | ||
0.646443 | − | 0.762962i | \(-0.276256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0271 | −0.0261915 | ||||||||
\(842\) | 190.195 | − | 42.7066i | 0.225885 | − | 0.0507204i | ||||
\(843\) | 595.256 | 0.706116 | ||||||||
\(844\) | 372.952 | + | 788.604i | 0.441886 | + | 0.934365i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −182.415 | + | 40.9595i | −0.215620 | + | 0.0484155i | ||||
\(847\) | 220.903 | 0.260806 | ||||||||
\(848\) | 1009.28 | + | 828.398i | 1.19018 | + | 0.976885i | ||||
\(849\) | 545.518 | 0.642542 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2270.15i | 2.66762i | ||||||||
\(852\) | 39.5012 | + | 83.5252i | 0.0463630 | + | 0.0980343i | ||||
\(853\) | 120.366i | 0.141109i | 0.997508 | + | 0.0705546i | \(0.0224769\pi\) | ||||
−0.997508 | + | 0.0705546i | \(0.977523\pi\) | |||||||
\(854\) | −656.782 | + | 147.474i | −0.769066 | + | 0.172687i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1154.66 | − | 901.014i | 1.34890 | − | 1.05259i | ||||
\(857\) | 717.784i | 0.837554i | 0.908089 | + | 0.418777i | \(0.137541\pi\) | ||||
−0.908089 | + | 0.418777i | \(0.862459\pi\) | |||||||
\(858\) | −582.360 | + | 130.764i | −0.678741 | + | 0.152405i | ||||
\(859\) | − | 252.894i | − | 0.294405i | −0.989106 | − | 0.147203i | \(-0.952973\pi\) | ||
0.989106 | − | 0.147203i | \(-0.0470269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 483.405 | 0.561446 | ||||||||
\(862\) | −170.873 | − | 760.989i | −0.198229 | − | 0.882817i | ||||
\(863\) | −1234.73 | −1.43075 | −0.715373 | − | 0.698743i | \(-0.753743\pi\) | ||||
−0.715373 | + | 0.698743i | \(0.753743\pi\) | |||||||
\(864\) | −74.7717 | + | 148.517i | −0.0865413 | + | 0.171894i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 120.888 | + | 538.381i | 0.139594 | + | 0.621687i | ||||
\(867\) | −165.382 | −0.190752 | ||||||||
\(868\) | −254.387 | − | 537.901i | −0.293073 | − | 0.619701i | ||||
\(869\) | 1311.29 | 1.50897 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 83.5368i | − | 0.0959091i | ||||||
\(872\) | −513.894 | + | 401.007i | −0.589327 | + | 0.459871i | ||||
\(873\) | − | 205.663i | − | 0.235582i | ||||||
\(874\) | −254.785 | − | 1134.69i | −0.291516 | − | 1.29828i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −121.117 | − | 256.101i | −0.138261 | − | 0.292353i | ||||
\(877\) | 685.723i | 0.781896i | 0.920413 | + | 0.390948i | \(0.127853\pi\) | ||||
−0.920413 | + | 0.390948i | \(0.872147\pi\) | |||||||
\(878\) | −195.487 | − | 870.609i | −0.222651 | − | 0.991582i | ||||
\(879\) | 11.3522i | 0.0129149i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −458.454 | −0.520379 | −0.260189 | − | 0.965558i | \(-0.583785\pi\) | ||||
−0.260189 | + | 0.965558i | \(0.583785\pi\) | |||||||
\(882\) | −52.1614 | + | 11.7124i | −0.0591399 | + | 0.0132793i | ||||
\(883\) | 771.505 | 0.873732 | 0.436866 | − | 0.899527i | \(-0.356088\pi\) | ||||
0.436866 | + | 0.899527i | \(0.356088\pi\) | |||||||
\(884\) | 933.986 | − | 441.707i | 1.05655 | − | 0.499668i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1550.75 | + | 348.206i | −1.75028 | + | 0.393009i | ||||
\(887\) | −1161.05 | −1.30896 | −0.654480 | − | 0.756080i | \(-0.727112\pi\) | ||||
−0.654480 | + | 0.756080i | \(0.727112\pi\) | |||||||
\(888\) | −573.979 | − | 735.558i | −0.646372 | − | 0.828331i | ||||
\(889\) | −141.693 | −0.159385 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 83.5166i | − | 0.0937336i | ||||||
\(892\) | 1188.15 | − | 561.905i | 1.33200 | − | 0.629938i | ||||
\(893\) | 537.401i | 0.601793i | ||||||||
\(894\) | −377.450 | + | 84.7529i | −0.422203 | + | 0.0948019i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.9793 | − | 810.207i | 0.0222983 | − | 0.904248i | ||||
\(897\) | − | 1084.26i | − | 1.20876i | ||||||
\(898\) | 1464.00 | − | 328.728i | 1.63029 | − | 0.366066i | ||||
\(899\) | − | 672.340i | − | 0.747876i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1135.24 | 1.25997 | ||||||||
\(902\) | 179.229 | + | 798.200i | 0.198701 | + | 0.884923i | ||||
\(903\) | 551.560 | 0.610808 | ||||||||
\(904\) | −850.514 | − | 1089.94i | −0.940834 | − | 1.20569i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.89722 | + | 21.8099i | 0.00540532 | + | 0.0240728i | ||||
\(907\) | 392.544 | 0.432793 | 0.216397 | − | 0.976306i | \(-0.430570\pi\) | ||||
0.216397 | + | 0.976306i | \(0.430570\pi\) | |||||||
\(908\) | −570.062 | + | 269.597i | −0.627822 | + | 0.296913i | ||||
\(909\) | −130.185 | −0.143218 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1013.40i | 1.11240i | 0.831048 | + | 0.556201i | \(0.187741\pi\) | ||||
−0.831048 | + | 0.556201i | \(0.812259\pi\) | |||||||
\(912\) | 369.447 | + | 303.237i | 0.405096 | + | 0.332496i | ||||
\(913\) | 648.185i | 0.709950i | ||||||||
\(914\) | −44.2958 | − | 197.273i | −0.0484637 | − | 0.215835i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 987.707 | − | 467.112i | 1.07828 | − | 0.509948i | ||||
\(917\) | 11.1004i | 0.0121051i | ||||||||
\(918\) | 31.6727 | + | 141.056i | 0.0345019 | + | 0.153655i | ||||
\(919\) | 970.018i | 1.05551i | 0.849395 | + | 0.527757i | \(0.176967\pi\) | ||||
−0.849395 | + | 0.527757i | \(0.823033\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −614.115 | −0.666791 | ||||||||
\(922\) | −8.75578 | + | 1.96603i | −0.00949651 | + | 0.00213236i | ||||
\(923\) | 247.616 | 0.268273 | ||||||||
\(924\) | 174.033 | + | 367.992i | 0.188348 | + | 0.398260i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1005.19 | − | 225.706i | 1.08552 | − | 0.243743i | ||||
\(927\) | −257.376 | −0.277644 | ||||||||
\(928\) | 411.804 | − | 817.952i | 0.443754 | − | 0.881414i | ||||
\(929\) | −980.857 | −1.05582 | −0.527910 | − | 0.849300i | \(-0.677024\pi\) | ||||
−0.527910 | + | 0.849300i | \(0.677024\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 153.670i | 0.165059i | ||||||||
\(932\) | 185.967 | + | 393.226i | 0.199535 | + | 0.421917i | ||||
\(933\) | − | 334.956i | − | 0.359010i | ||||||
\(934\) | 576.638 | − | 129.479i | 0.617386 | − | 0.138628i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 274.141 | + | 351.314i | 0.292886 | + | 0.375336i | ||||
\(937\) | − | 964.666i | − | 1.02953i | −0.857333 | − | 0.514763i | \(-0.827880\pi\) | ||
0.857333 | − | 0.514763i | \(-0.172120\pi\) | |||||||
\(938\) | −55.5896 | + | 12.4821i | −0.0592639 | + | 0.0133072i | ||||
\(939\) | 40.7420i | 0.0433887i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1581.10 | −1.68023 | −0.840117 | − | 0.542405i | \(-0.817514\pi\) | ||||
−0.840117 | + | 0.542405i | \(0.817514\pi\) | |||||||
\(942\) | −57.6089 | − | 256.563i | −0.0611560 | − | 0.272360i | ||||
\(943\) | −1486.12 | −1.57595 | ||||||||
\(944\) | 238.386 | + | 195.663i | 0.252527 | + | 0.207271i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 204.498 | + | 910.738i | 0.216171 | + | 0.962725i | ||||
\(947\) | −1245.27 | −1.31497 | −0.657483 | − | 0.753469i | \(-0.728379\pi\) | ||||
−0.657483 | + | 0.753469i | \(0.728379\pi\) | |||||||
\(948\) | −418.555 | − | 885.032i | −0.441513 | − | 0.933578i | ||||
\(949\) | −759.229 | −0.800031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 370.666i | − | 0.389765i | ||||||
\(952\) | −433.490 | − | 555.521i | −0.455347 | − | 0.583530i | ||||
\(953\) | 1106.52i | 1.16109i | 0.814228 | + | 0.580546i | \(0.197161\pi\) | ||||
−0.814228 | + | 0.580546i | \(0.802839\pi\) | |||||||
\(954\) | 107.274 | + | 477.746i | 0.112446 | + | 0.500782i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −306.098 | − | 647.243i | −0.320186 | − | 0.677032i | ||||
\(957\) | 459.966i | 0.480633i | ||||||||
\(958\) | 119.689 | + | 533.037i | 0.124936 | + | 0.556406i | ||||
\(959\) | 123.521i | 0.128802i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 409.039 | 0.425638 | ||||||||
\(962\) | −2439.68 | + | 547.808i | −2.53605 | + | 0.569447i | ||||
\(963\) | 549.225 | 0.570327 | ||||||||
\(964\) | 1296.79 | − | 613.284i | 1.34521 | − | 0.636187i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −721.520 | + | 162.011i | −0.746915 | + | 0.167713i | ||||
\(967\) | 406.453 | 0.420324 | 0.210162 | − | 0.977667i | \(-0.432601\pi\) | ||||
0.210162 | + | 0.977667i | \(0.432601\pi\) | |||||||
\(968\) | 220.042 | − | 171.706i | 0.227316 | − | 0.177382i | ||||
\(969\) | 415.555 | 0.428850 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1815.22i | − | 1.86943i | −0.355393 | − | 0.934717i | \(-0.615653\pi\) | ||
0.355393 | − | 0.934717i | \(-0.384347\pi\) | |||||||
\(972\) | −56.3680 | + | 26.6579i | −0.0579918 | + | 0.0274258i | ||||
\(973\) | 1629.58i | 1.67480i | ||||||||
\(974\) | −698.119 | + | 156.756i | −0.716754 | + | 0.160941i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −539.594 | + | 657.412i | −0.552862 | + | 0.673578i | ||||
\(977\) | 1457.74i | 1.49205i | 0.665916 | + | 0.746027i | \(0.268041\pi\) | ||||
−0.665916 | + | 0.746027i | \(0.731959\pi\) | |||||||
\(978\) | 842.614 | − | 189.201i | 0.861568 | − | 0.193457i | ||||
\(979\) | − | 429.720i | − | 0.438938i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −244.439 | −0.249174 | ||||||||
\(982\) | 185.074 | + | 824.235i | 0.188467 | + | 0.839343i | ||||
\(983\) | −19.9496 | −0.0202946 | −0.0101473 | − | 0.999949i | \(-0.503230\pi\) | ||||
−0.0101473 | + | 0.999949i | \(0.503230\pi\) | |||||||
\(984\) | 481.522 | − | 375.747i | 0.489352 | − | 0.381857i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −174.437 | − | 776.860i | −0.176914 | − | 0.787891i | ||||
\(987\) | 341.718 | 0.346219 | ||||||||
\(988\) | 1157.95 | − | 547.625i | 1.17201 | − | 0.554276i | ||||
\(989\) | −1695.65 | −1.71450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 605.720i | 0.611221i | 0.952157 | + | 0.305611i | \(0.0988605\pi\) | ||||
−0.952157 | + | 0.305611i | \(0.901139\pi\) | |||||||
\(992\) | −671.502 | − | 338.073i | −0.676918 | − | 0.340799i | ||||
\(993\) | 714.392i | 0.719428i | ||||||||
\(994\) | −36.9989 | − | 164.776i | −0.0372223 | − | 0.165771i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 437.481 | − | 206.896i | 0.439237 | − | 0.207727i | ||||
\(997\) | − | 1238.47i | − | 1.24220i | −0.783732 | − | 0.621099i | \(-0.786686\pi\) | ||
0.783732 | − | 0.621099i | \(-0.213314\pi\) | |||||||
\(998\) | −90.7434 | − | 404.129i | −0.0909253 | − | 0.404939i | ||||
\(999\) | − | 349.876i | − | 0.350227i |
(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 | 300.3.f.b.199.15 | 16 | ||
3.2 | odd | 2 | 900.3.f.f.199.2 | 16 | |||
4.3 | odd | 2 | inner | 300.3.f.b.199.1 | 16 | ||
5.2 | odd | 4 | 60.3.c.a.31.4 | yes | 8 | ||
5.3 | odd | 4 | 300.3.c.d.151.5 | 8 | |||
5.4 | even | 2 | inner | 300.3.f.b.199.2 | 16 | ||
12.11 | even | 2 | 900.3.f.f.199.16 | 16 | |||
15.2 | even | 4 | 180.3.c.b.91.5 | 8 | |||
15.8 | even | 4 | 900.3.c.u.451.4 | 8 | |||
15.14 | odd | 2 | 900.3.f.f.199.15 | 16 | |||
20.3 | even | 4 | 300.3.c.d.151.6 | 8 | |||
20.7 | even | 4 | 60.3.c.a.31.3 | ✓ | 8 | ||
20.19 | odd | 2 | inner | 300.3.f.b.199.16 | 16 | ||
40.27 | even | 4 | 960.3.e.c.511.5 | 8 | |||
40.37 | odd | 4 | 960.3.e.c.511.2 | 8 | |||
60.23 | odd | 4 | 900.3.c.u.451.3 | 8 | |||
60.47 | odd | 4 | 180.3.c.b.91.6 | 8 | |||
60.59 | even | 2 | 900.3.f.f.199.1 | 16 | |||
120.77 | even | 4 | 2880.3.e.j.2431.8 | 8 | |||
120.107 | odd | 4 | 2880.3.e.j.2431.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.3 | ✓ | 8 | 20.7 | even | 4 | ||
60.3.c.a.31.4 | yes | 8 | 5.2 | odd | 4 | ||
180.3.c.b.91.5 | 8 | 15.2 | even | 4 | |||
180.3.c.b.91.6 | 8 | 60.47 | odd | 4 | |||
300.3.c.d.151.5 | 8 | 5.3 | odd | 4 | |||
300.3.c.d.151.6 | 8 | 20.3 | even | 4 | |||
300.3.f.b.199.1 | 16 | 4.3 | odd | 2 | inner | ||
300.3.f.b.199.2 | 16 | 5.4 | even | 2 | inner | ||
300.3.f.b.199.15 | 16 | 1.1 | even | 1 | trivial | ||
300.3.f.b.199.16 | 16 | 20.19 | odd | 2 | inner | ||
900.3.c.u.451.3 | 8 | 60.23 | odd | 4 | |||
900.3.c.u.451.4 | 8 | 15.8 | even | 4 | |||
900.3.f.f.199.1 | 16 | 60.59 | even | 2 | |||
900.3.f.f.199.2 | 16 | 3.2 | odd | 2 | |||
900.3.f.f.199.15 | 16 | 15.14 | odd | 2 | |||
900.3.f.f.199.16 | 16 | 12.11 | even | 2 | |||
960.3.e.c.511.2 | 8 | 40.37 | odd | 4 | |||
960.3.e.c.511.5 | 8 | 40.27 | even | 4 | |||
2880.3.e.j.2431.5 | 8 | 120.107 | odd | 4 | |||
2880.3.e.j.2431.8 | 8 | 120.77 | even | 4 |