Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(364,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(8.69570878012\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 727.9 | ||
Character | \(\chi\) | \(=\) | 1089.727 |
Dual form | 1089.2.e.p.364.9 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.142574 | + | 0.246946i | −0.100815 | + | 0.174617i | −0.912021 | − | 0.410144i | \(-0.865478\pi\) |
0.811206 | + | 0.584761i | \(0.198812\pi\) | |||||||
\(3\) | 0.0364826 | − | 1.73167i | 0.0210632 | − | 0.999778i | ||||
\(4\) | 0.959345 | + | 1.66163i | 0.479673 | + | 0.830817i | ||||
\(5\) | −1.35437 | − | 2.34583i | −0.605691 | − | 1.04909i | −0.991942 | − | 0.126694i | \(-0.959563\pi\) |
0.386251 | − | 0.922394i | \(-0.373770\pi\) | |||||||
\(6\) | 0.422426 | + | 0.255900i | 0.172455 | + | 0.104471i | ||||
\(7\) | 2.03667 | − | 3.52761i | 0.769788 | − | 1.33331i | −0.167890 | − | 0.985806i | \(-0.553695\pi\) |
0.937678 | − | 0.347506i | \(-0.112971\pi\) | |||||||
\(8\) | −1.11741 | −0.395063 | ||||||||
\(9\) | −2.99734 | − | 0.126351i | −0.999113 | − | 0.0421171i | ||||
\(10\) | 0.772391 | 0.244251 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.91240 | − | 1.60065i | 0.840736 | − | 0.462066i | ||||
\(13\) | −1.92548 | − | 3.33503i | −0.534032 | − | 0.924970i | −0.999210 | − | 0.0397526i | \(-0.987343\pi\) |
0.465178 | − | 0.885217i | \(-0.345990\pi\) | |||||||
\(14\) | 0.580752 | + | 1.00589i | 0.155213 | + | 0.268836i | ||||
\(15\) | −4.11161 | + | 2.25973i | −1.06161 | + | 0.583460i | ||||
\(16\) | −1.75938 | + | 3.04733i | −0.439844 | + | 0.761833i | ||||
\(17\) | −4.32020 | −1.04780 | −0.523902 | − | 0.851779i | \(-0.675524\pi\) | ||||
−0.523902 | + | 0.851779i | \(0.675524\pi\) | |||||||
\(18\) | 0.458545 | − | 0.722165i | 0.108080 | − | 0.170216i | ||||
\(19\) | −1.62229 | −0.372180 | −0.186090 | − | 0.982533i | \(-0.559582\pi\) | ||||
−0.186090 | + | 0.982533i | \(0.559582\pi\) | |||||||
\(20\) | 2.59861 | − | 4.50093i | 0.581067 | − | 1.00644i | ||||
\(21\) | −6.03434 | − | 3.65553i | −1.31680 | − | 0.797701i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.932117 | + | 1.61447i | 0.194360 | + | 0.336641i | 0.946691 | − | 0.322145i | \(-0.104404\pi\) |
−0.752331 | + | 0.658786i | \(0.771070\pi\) | |||||||
\(24\) | −0.0407660 | + | 1.93498i | −0.00832132 | + | 0.394976i | ||||
\(25\) | −1.16862 | + | 2.02411i | −0.233724 | + | 0.404822i | ||||
\(26\) | 1.09809 | 0.215354 | ||||||||
\(27\) | −0.328149 | + | 5.18578i | −0.0631523 | + | 0.998004i | ||||
\(28\) | 7.81547 | 1.47698 | ||||||||
\(29\) | −1.77667 | + | 3.07729i | −0.329920 | + | 0.571438i | −0.982496 | − | 0.186286i | \(-0.940355\pi\) |
0.652576 | + | 0.757723i | \(0.273688\pi\) | |||||||
\(30\) | 0.0281788 | − | 1.33752i | 0.00514473 | − | 0.244197i | ||||
\(31\) | 2.43230 | + | 4.21286i | 0.436853 | + | 0.756652i | 0.997445 | − | 0.0714406i | \(-0.0227596\pi\) |
−0.560592 | + | 0.828092i | \(0.689426\pi\) | |||||||
\(32\) | −1.61909 | − | 2.80435i | −0.286218 | − | 0.495744i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.615950 | − | 1.06686i | 0.105634 | − | 0.182964i | ||||
\(35\) | −11.0336 | −1.86502 | ||||||||
\(36\) | −2.66553 | − | 5.10170i | −0.444255 | − | 0.850283i | ||||
\(37\) | 7.74449 | 1.27319 | 0.636593 | − | 0.771200i | \(-0.280343\pi\) | ||||
0.636593 | + | 0.771200i | \(0.280343\pi\) | |||||||
\(38\) | 0.231297 | − | 0.400619i | 0.0375214 | − | 0.0649889i | ||||
\(39\) | −5.84540 | + | 3.21262i | −0.936013 | + | 0.514430i | ||||
\(40\) | 1.51338 | + | 2.62125i | 0.239286 | + | 0.414456i | ||||
\(41\) | −3.43607 | − | 5.95145i | −0.536624 | − | 0.929461i | −0.999083 | − | 0.0428197i | \(-0.986366\pi\) |
0.462458 | − | 0.886641i | \(-0.346967\pi\) | |||||||
\(42\) | 1.76306 | − | 0.968972i | 0.272046 | − | 0.149516i | ||||
\(43\) | −0.492496 | + | 0.853027i | −0.0751049 | + | 0.130085i | −0.901132 | − | 0.433545i | \(-0.857262\pi\) |
0.826027 | + | 0.563631i | \(0.190596\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.76310 | + | 7.20238i | 0.560969 | + | 1.07367i | ||||
\(46\) | −0.531584 | −0.0783777 | ||||||||
\(47\) | −2.93317 | + | 5.08041i | −0.427847 | + | 0.741054i | −0.996682 | − | 0.0813987i | \(-0.974061\pi\) |
0.568834 | + | 0.822452i | \(0.307395\pi\) | |||||||
\(48\) | 5.21277 | + | 3.15783i | 0.752399 | + | 0.455793i | ||||
\(49\) | −4.79603 | − | 8.30697i | −0.685147 | − | 1.18671i | ||||
\(50\) | −0.333230 | − | 0.577171i | −0.0471258 | − | 0.0816243i | ||||
\(51\) | −0.157612 | + | 7.48115i | −0.0220701 | + | 1.04757i | ||||
\(52\) | 3.69440 | − | 6.39888i | 0.512321 | − | 0.887365i | ||||
\(53\) | −1.57183 | −0.215907 | −0.107953 | − | 0.994156i | \(-0.534430\pi\) | ||||
−0.107953 | + | 0.994156i | \(0.534430\pi\) | |||||||
\(54\) | −1.23382 | − | 0.820393i | −0.167902 | − | 0.111641i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.27579 | + | 3.94178i | −0.304115 | + | 0.526743i | ||||
\(57\) | −0.0591855 | + | 2.80927i | −0.00783931 | + | 0.372097i | ||||
\(58\) | −0.506615 | − | 0.877483i | −0.0665218 | − | 0.115219i | ||||
\(59\) | −5.68125 | − | 9.84021i | −0.739635 | − | 1.28109i | −0.952660 | − | 0.304039i | \(-0.901665\pi\) |
0.213024 | − | 0.977047i | \(-0.431669\pi\) | |||||||
\(60\) | −7.69930 | − | 4.66413i | −0.993975 | − | 0.602137i | ||||
\(61\) | 4.30374 | − | 7.45430i | 0.551037 | − | 0.954425i | −0.447163 | − | 0.894453i | \(-0.647566\pi\) |
0.998200 | − | 0.0599721i | \(-0.0191012\pi\) | |||||||
\(62\) | −1.38713 | −0.176166 | ||||||||
\(63\) | −6.55030 | + | 10.3161i | −0.825260 | + | 1.29971i | ||||
\(64\) | −6.11414 | −0.764268 | ||||||||
\(65\) | −5.21561 | + | 9.03370i | −0.646916 | + | 1.12049i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.870282 | + | 1.50737i | 0.106322 | + | 0.184155i | 0.914277 | − | 0.405088i | \(-0.132759\pi\) |
−0.807956 | + | 0.589243i | \(0.799426\pi\) | |||||||
\(68\) | −4.14457 | − | 7.17860i | −0.502603 | − | 0.870533i | ||||
\(69\) | 2.82974 | − | 1.55522i | 0.340660 | − | 0.187226i | ||||
\(70\) | 1.57310 | − | 2.72470i | 0.188022 | − | 0.325663i | ||||
\(71\) | −5.74136 | −0.681374 | −0.340687 | − | 0.940177i | \(-0.610660\pi\) | ||||
−0.340687 | + | 0.940177i | \(0.610660\pi\) | |||||||
\(72\) | 3.34925 | + | 0.141186i | 0.394713 | + | 0.0166389i | ||||
\(73\) | −4.04662 | −0.473622 | −0.236811 | − | 0.971556i | \(-0.576102\pi\) | ||||
−0.236811 | + | 0.971556i | \(0.576102\pi\) | |||||||
\(74\) | −1.10416 | + | 1.91247i | −0.128356 | + | 0.222320i | ||||
\(75\) | 3.46245 | + | 2.09750i | 0.399809 | + | 0.242199i | ||||
\(76\) | −1.55634 | − | 2.69566i | −0.178524 | − | 0.309213i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0400613 | − | 1.90153i | 0.00453605 | − | 0.215306i | ||||
\(79\) | 2.14007 | − | 3.70672i | 0.240777 | − | 0.417038i | −0.720159 | − | 0.693809i | \(-0.755931\pi\) |
0.960936 | + | 0.276771i | \(0.0892644\pi\) | |||||||
\(80\) | 9.53137 | 1.06564 | ||||||||
\(81\) | 8.96807 | + | 0.757436i | 0.996452 | + | 0.0841595i | ||||
\(82\) | 1.95958 | 0.216400 | ||||||||
\(83\) | 3.25009 | − | 5.62933i | 0.356744 | − | 0.617899i | −0.630671 | − | 0.776050i | \(-0.717220\pi\) |
0.987415 | + | 0.158152i | \(0.0505535\pi\) | |||||||
\(84\) | 0.285129 | − | 13.5338i | 0.0311101 | − | 1.47666i | ||||
\(85\) | 5.85114 | + | 10.1345i | 0.634645 | + | 1.09924i | ||||
\(86\) | −0.140434 | − | 0.243239i | −0.0151434 | − | 0.0262292i | ||||
\(87\) | 5.26402 | + | 3.18887i | 0.564362 | + | 0.341883i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.26243 | 0.981816 | 0.490908 | − | 0.871211i | \(-0.336665\pi\) | ||||
0.490908 | + | 0.871211i | \(0.336665\pi\) | |||||||
\(90\) | −2.31512 | − | 0.0975927i | −0.244035 | − | 0.0102872i | ||||
\(91\) | −15.6862 | −1.64436 | ||||||||
\(92\) | −1.78844 | + | 3.09768i | −0.186458 | + | 0.322955i | ||||
\(93\) | 7.38400 | − | 4.05823i | 0.765685 | − | 0.420819i | ||||
\(94\) | −0.836390 | − | 1.44867i | −0.0862670 | − | 0.149419i | ||||
\(95\) | 2.19718 | + | 3.80563i | 0.225426 | + | 0.390449i | ||||
\(96\) | −4.91527 | + | 2.70142i | −0.501662 | + | 0.275712i | ||||
\(97\) | 3.70634 | − | 6.41957i | 0.376322 | − | 0.651809i | −0.614202 | − | 0.789149i | \(-0.710522\pi\) |
0.990524 | + | 0.137340i | \(0.0438553\pi\) | |||||||
\(98\) | 2.73516 | 0.276293 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.48444 | −0.448444 | ||||||||
\(101\) | 6.85880 | − | 11.8798i | 0.682476 | − | 1.18208i | −0.291747 | − | 0.956496i | \(-0.594236\pi\) |
0.974223 | − | 0.225588i | \(-0.0724303\pi\) | |||||||
\(102\) | −1.82497 | − | 1.10554i | −0.180699 | − | 0.109465i | ||||
\(103\) | −2.53762 | − | 4.39529i | −0.250039 | − | 0.433081i | 0.713497 | − | 0.700658i | \(-0.247110\pi\) |
−0.963536 | + | 0.267577i | \(0.913777\pi\) | |||||||
\(104\) | 2.15154 | + | 3.72659i | 0.210976 | + | 0.365422i | ||||
\(105\) | −0.402534 | + | 19.1065i | −0.0392833 | + | 1.86460i | ||||
\(106\) | 0.224102 | − | 0.388156i | 0.0217667 | − | 0.0377010i | ||||
\(107\) | −2.77898 | −0.268654 | −0.134327 | − | 0.990937i | \(-0.542887\pi\) | ||||
−0.134327 | + | 0.990937i | \(0.542887\pi\) | |||||||
\(108\) | −8.93168 | + | 4.42969i | −0.859451 | + | 0.426247i | ||||
\(109\) | −17.3573 | −1.66253 | −0.831263 | − | 0.555879i | \(-0.812382\pi\) | ||||
−0.831263 | + | 0.555879i | \(0.812382\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.282539 | − | 13.4109i | 0.0268174 | − | 1.27290i | ||||
\(112\) | 7.16653 | + | 12.4128i | 0.677174 | + | 1.17290i | ||||
\(113\) | −0.471827 | − | 0.817228i | −0.0443858 | − | 0.0768784i | 0.842979 | − | 0.537946i | \(-0.180800\pi\) |
−0.887365 | + | 0.461068i | \(0.847466\pi\) | |||||||
\(114\) | −0.685300 | − | 0.415145i | −0.0641842 | − | 0.0388819i | ||||
\(115\) | 2.52486 | − | 4.37318i | 0.235444 | − | 0.407801i | ||||
\(116\) | −6.81777 | −0.633014 | ||||||||
\(117\) | 5.34992 | + | 10.2395i | 0.494601 | + | 0.946641i | ||||
\(118\) | 3.24000 | 0.298266 | ||||||||
\(119\) | −8.79882 | + | 15.2400i | −0.806587 | + | 1.39705i | ||||
\(120\) | 4.59435 | − | 2.52504i | 0.419405 | − | 0.230504i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.22720 | + | 2.12558i | 0.111106 | + | 0.192441i | ||||
\(123\) | −10.4313 | + | 5.73301i | −0.940558 | + | 0.516928i | ||||
\(124\) | −4.66682 | + | 8.08317i | −0.419093 | + | 0.725890i | ||||
\(125\) | −7.21271 | −0.645125 | ||||||||
\(126\) | −1.61362 | − | 3.08838i | −0.143752 | − | 0.275135i | ||||
\(127\) | 2.45040 | 0.217438 | 0.108719 | − | 0.994073i | \(-0.465325\pi\) | ||||
0.108719 | + | 0.994073i | \(0.465325\pi\) | |||||||
\(128\) | 4.10990 | − | 7.11856i | 0.363267 | − | 0.629198i | ||||
\(129\) | 1.45919 | + | 0.883959i | 0.128475 | + | 0.0778282i | ||||
\(130\) | −1.48722 | − | 2.57594i | −0.130438 | − | 0.225925i | ||||
\(131\) | −1.99869 | − | 3.46183i | −0.174626 | − | 0.302461i | 0.765406 | − | 0.643548i | \(-0.222538\pi\) |
−0.940032 | + | 0.341087i | \(0.889205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.30407 | + | 5.72282i | −0.286500 | + | 0.496232i | ||||
\(134\) | −0.496319 | −0.0428754 | ||||||||
\(135\) | 12.6094 | − | 6.25367i | 1.08524 | − | 0.538230i | ||||
\(136\) | 4.82743 | 0.413949 | ||||||||
\(137\) | −0.544628 | + | 0.943324i | −0.0465307 | + | 0.0805936i | −0.888353 | − | 0.459162i | \(-0.848150\pi\) |
0.841822 | + | 0.539755i | \(0.181483\pi\) | |||||||
\(138\) | −0.0193935 | + | 0.920525i | −0.00165089 | + | 0.0783603i | ||||
\(139\) | −1.44246 | − | 2.49842i | −0.122348 | − | 0.211913i | 0.798345 | − | 0.602200i | \(-0.205709\pi\) |
−0.920693 | + | 0.390287i | \(0.872376\pi\) | |||||||
\(140\) | −10.5850 | − | 18.3338i | −0.894597 | − | 1.54949i | ||||
\(141\) | 8.69056 | + | 5.26463i | 0.731877 | + | 0.443362i | ||||
\(142\) | 0.818570 | − | 1.41780i | 0.0686929 | − | 0.118980i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.65848 | − | 8.91158i | 0.471540 | − | 0.742632i | ||||
\(145\) | 9.62506 | 0.799318 | ||||||||
\(146\) | 0.576944 | − | 0.999297i | 0.0477482 | − | 0.0827024i | ||||
\(147\) | −14.5599 | + | 8.00206i | −1.20088 | + | 0.659999i | ||||
\(148\) | 7.42964 | + | 12.8685i | 0.610712 | + | 1.05778i | ||||
\(149\) | −10.0874 | − | 17.4719i | −0.826393 | − | 1.43135i | −0.900850 | − | 0.434130i | \(-0.857056\pi\) |
0.0744578 | − | 0.997224i | \(-0.476277\pi\) | |||||||
\(150\) | −1.01163 | + | 0.555986i | −0.0825988 | + | 0.0453961i | ||||
\(151\) | 5.53918 | − | 9.59414i | 0.450772 | − | 0.780760i | −0.547662 | − | 0.836700i | \(-0.684482\pi\) |
0.998434 | + | 0.0559396i | \(0.0178154\pi\) | |||||||
\(152\) | 1.81276 | 0.147035 | ||||||||
\(153\) | 12.9491 | + | 0.545864i | 1.04687 | + | 0.0441305i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.58844 | − | 11.4115i | 0.529196 | − | 0.916595i | ||||
\(156\) | −10.9459 | − | 6.63091i | −0.876377 | − | 0.530898i | ||||
\(157\) | −0.166392 | − | 0.288200i | −0.0132795 | − | 0.0230008i | 0.859309 | − | 0.511456i | \(-0.170894\pi\) |
−0.872589 | + | 0.488455i | \(0.837560\pi\) | |||||||
\(158\) | 0.610238 | + | 1.05696i | 0.0485480 | + | 0.0840875i | ||||
\(159\) | −0.0573443 | + | 2.72188i | −0.00454770 | + | 0.215859i | ||||
\(160\) | −4.38569 | + | 7.59623i | −0.346719 | + | 0.600535i | ||||
\(161\) | 7.59365 | 0.598464 | ||||||||
\(162\) | −1.46566 | + | 2.10664i | −0.115153 | + | 0.165513i | ||||
\(163\) | 13.3380 | 1.04472 | 0.522358 | − | 0.852726i | \(-0.325053\pi\) | ||||
0.522358 | + | 0.852726i | \(0.325053\pi\) | |||||||
\(164\) | 6.59276 | − | 11.4190i | 0.514808 | − | 0.891674i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.926759 | + | 1.60519i | 0.0719304 | + | 0.124587i | ||||
\(167\) | 9.45758 | + | 16.3810i | 0.731849 | + | 1.26760i | 0.956092 | + | 0.293067i | \(0.0946758\pi\) |
−0.224243 | + | 0.974533i | \(0.571991\pi\) | |||||||
\(168\) | 6.74283 | + | 4.08471i | 0.520220 | + | 0.315143i | ||||
\(169\) | −0.914932 | + | 1.58471i | −0.0703794 | + | 0.121901i | ||||
\(170\) | −3.33689 | −0.255928 | ||||||||
\(171\) | 4.86256 | + | 0.204979i | 0.371850 | + | 0.0156751i | ||||
\(172\) | −1.88989 | −0.144103 | ||||||||
\(173\) | 0.757044 | − | 1.31124i | 0.0575570 | − | 0.0996916i | −0.835811 | − | 0.549017i | \(-0.815002\pi\) |
0.893368 | + | 0.449325i | \(0.148336\pi\) | |||||||
\(174\) | −1.53799 | + | 0.845276i | −0.116595 | + | 0.0640802i | ||||
\(175\) | 4.76018 | + | 8.24487i | 0.359836 | + | 0.623254i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.2472 | + | 9.47903i | −1.29638 | + | 0.712487i | ||||
\(178\) | −1.32058 | + | 2.28732i | −0.0989819 | + | 0.171442i | ||||
\(179\) | 13.1892 | 0.985810 | 0.492905 | − | 0.870083i | \(-0.335935\pi\) | ||||
0.492905 | + | 0.870083i | \(0.335935\pi\) | |||||||
\(180\) | −8.35761 | + | 13.1625i | −0.622940 | + | 0.981072i | ||||
\(181\) | 2.79883 | 0.208035 | 0.104018 | − | 0.994575i | \(-0.466830\pi\) | ||||
0.104018 | + | 0.994575i | \(0.466830\pi\) | |||||||
\(182\) | 2.23645 | − | 3.87365i | 0.165777 | − | 0.287134i | ||||
\(183\) | −12.7513 | − | 7.72459i | −0.942606 | − | 0.571018i | ||||
\(184\) | −1.04156 | − | 1.80403i | −0.0767845 | − | 0.132995i | ||||
\(185\) | −10.4889 | − | 18.1673i | −0.771158 | − | 1.33568i | ||||
\(186\) | −0.0506061 | + | 2.40205i | −0.00371062 | + | 0.176127i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −11.2557 | −0.820907 | ||||||||
\(189\) | 17.6251 | + | 11.7193i | 1.28204 | + | 0.852453i | ||||
\(190\) | −1.25305 | −0.0909055 | ||||||||
\(191\) | 8.37078 | − | 14.4986i | 0.605688 | − | 1.04908i | −0.386254 | − | 0.922392i | \(-0.626231\pi\) |
0.991942 | − | 0.126690i | \(-0.0404354\pi\) | |||||||
\(192\) | −0.223060 | + | 10.5877i | −0.0160980 | + | 0.764099i | ||||
\(193\) | 11.0197 | + | 19.0867i | 0.793214 | + | 1.37389i | 0.923967 | + | 0.382473i | \(0.124927\pi\) |
−0.130752 | + | 0.991415i | \(0.541739\pi\) | |||||||
\(194\) | 1.05686 | + | 1.83053i | 0.0758779 | + | 0.131424i | ||||
\(195\) | 15.4531 | + | 9.36127i | 1.10662 | + | 0.670374i | ||||
\(196\) | 9.20210 | − | 15.9385i | 0.657293 | − | 1.13846i | ||||
\(197\) | 18.2247 | 1.29845 | 0.649227 | − | 0.760595i | \(-0.275093\pi\) | ||||
0.649227 | + | 0.760595i | \(0.275093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.0958 | −1.77899 | −0.889497 | − | 0.456942i | \(-0.848945\pi\) | ||||
−0.889497 | + | 0.456942i | \(0.848945\pi\) | |||||||
\(200\) | 1.30582 | − | 2.26176i | 0.0923358 | − | 0.159930i | ||||
\(201\) | 2.64202 | − | 1.45204i | 0.186353 | − | 0.102419i | ||||
\(202\) | 1.95578 | + | 3.38750i | 0.137608 | + | 0.238344i | ||||
\(203\) | 7.23698 | + | 12.5348i | 0.507937 | + | 0.879772i | ||||
\(204\) | −12.5821 | + | 6.91512i | −0.880927 | + | 0.484155i | ||||
\(205\) | −9.30741 | + | 16.1209i | −0.650057 | + | 1.12593i | ||||
\(206\) | 1.44720 | 0.100831 | ||||||||
\(207\) | −2.58988 | − | 4.95690i | −0.180009 | − | 0.344528i | ||||
\(208\) | 13.5506 | 0.939563 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.66087 | − | 2.82350i | −0.321631 | − | 0.194840i | ||||
\(211\) | −4.13501 | − | 7.16205i | −0.284666 | − | 0.493056i | 0.687862 | − | 0.725841i | \(-0.258549\pi\) |
−0.972528 | + | 0.232785i | \(0.925216\pi\) | |||||||
\(212\) | −1.50792 | − | 2.61180i | −0.103565 | − | 0.179379i | ||||
\(213\) | −0.209460 | + | 9.94213i | −0.0143520 | + | 0.681223i | ||||
\(214\) | 0.396210 | − | 0.686257i | 0.0270844 | − | 0.0469115i | ||||
\(215\) | 2.66808 | 0.181961 | ||||||||
\(216\) | 0.366677 | − | 5.79463i | 0.0249492 | − | 0.394275i | ||||
\(217\) | 19.8151 | 1.34514 | ||||||||
\(218\) | 2.47470 | − | 4.28631i | 0.167608 | − | 0.290305i | ||||
\(219\) | −0.147631 | + | 7.00740i | −0.00997600 | + | 0.473516i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.31846 | + | 14.4080i | 0.559560 | + | 0.969187i | ||||
\(222\) | 3.27147 | + | 1.98182i | 0.219567 | + | 0.133011i | ||||
\(223\) | 3.67604 | − | 6.36709i | 0.246166 | − | 0.426372i | −0.716293 | − | 0.697800i | \(-0.754163\pi\) |
0.962459 | + | 0.271428i | \(0.0874959\pi\) | |||||||
\(224\) | −13.1902 | −0.881308 | ||||||||
\(225\) | 3.75850 | − | 5.91928i | 0.250566 | − | 0.394619i | ||||
\(226\) | 0.269081 | 0.0178990 | ||||||||
\(227\) | 9.47060 | − | 16.4036i | 0.628586 | − | 1.08874i | −0.359250 | − | 0.933241i | \(-0.616968\pi\) |
0.987836 | − | 0.155501i | \(-0.0496992\pi\) | |||||||
\(228\) | −4.72476 | + | 2.59672i | −0.312905 | + | 0.171972i | ||||
\(229\) | 3.92972 | + | 6.80648i | 0.259683 | + | 0.449785i | 0.966157 | − | 0.257954i | \(-0.0830485\pi\) |
−0.706474 | + | 0.707739i | \(0.749715\pi\) | |||||||
\(230\) | 0.719959 | + | 1.24701i | 0.0474727 | + | 0.0822251i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.98527 | − | 3.43859i | 0.130339 | − | 0.225754i | ||||
\(233\) | −6.56942 | −0.430377 | −0.215188 | − | 0.976573i | \(-0.569037\pi\) | ||||
−0.215188 | + | 0.976573i | \(0.569037\pi\) | |||||||
\(234\) | −3.29136 | − | 0.138746i | −0.215163 | − | 0.00907009i | ||||
\(235\) | 15.8904 | 1.03657 | ||||||||
\(236\) | 10.9006 | − | 18.8803i | 0.709566 | − | 1.22900i | ||||
\(237\) | −6.34072 | − | 3.84112i | −0.411874 | − | 0.249508i | ||||
\(238\) | −2.50897 | − | 4.34566i | −0.162632 | − | 0.281687i | ||||
\(239\) | 12.7731 | + | 22.1237i | 0.826226 | + | 1.43107i | 0.900979 | + | 0.433863i | \(0.142850\pi\) |
−0.0747530 | + | 0.997202i | \(0.523817\pi\) | |||||||
\(240\) | 0.347729 | − | 16.5051i | 0.0224458 | − | 1.06540i | ||||
\(241\) | 1.49099 | − | 2.58247i | 0.0960432 | − | 0.166352i | −0.814000 | − | 0.580864i | \(-0.802715\pi\) |
0.910044 | + | 0.414513i | \(0.136048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.63880 | − | 15.5021i | 0.105129 | − | 0.994459i | ||||
\(244\) | 16.5151 | 1.05727 | ||||||||
\(245\) | −12.9912 | + | 22.5014i | −0.829975 | + | 1.43756i | ||||
\(246\) | 0.0714906 | − | 3.39334i | 0.00455807 | − | 0.216352i | ||||
\(247\) | 3.12369 | + | 5.41039i | 0.198756 | + | 0.344255i | ||||
\(248\) | −2.71787 | − | 4.70748i | −0.172585 | − | 0.298925i | ||||
\(249\) | −9.62954 | − | 5.83345i | −0.610248 | − | 0.369680i | ||||
\(250\) | 1.02835 | − | 1.78115i | 0.0650383 | − | 0.112650i | ||||
\(251\) | 11.6685 | 0.736510 | 0.368255 | − | 0.929725i | \(-0.379955\pi\) | ||||
0.368255 | + | 0.929725i | \(0.379955\pi\) | |||||||
\(252\) | −23.4256 | − | 0.987495i | −1.47567 | − | 0.0622064i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.349364 | + | 0.605116i | −0.0219211 | + | 0.0379684i | ||||
\(255\) | 17.7630 | − | 9.76250i | 1.11236 | − | 0.611351i | ||||
\(256\) | −4.94221 | − | 8.56016i | −0.308888 | − | 0.535010i | ||||
\(257\) | −10.3622 | − | 17.9479i | −0.646378 | − | 1.11956i | −0.983981 | − | 0.178271i | \(-0.942950\pi\) |
0.337604 | − | 0.941288i | \(-0.390384\pi\) | |||||||
\(258\) | −0.426333 | + | 0.234311i | −0.0265423 | + | 0.0145876i | ||||
\(259\) | 15.7729 | − | 27.3195i | 0.980083 | − | 1.69755i | ||||
\(260\) | −20.0143 | −1.24123 | ||||||||
\(261\) | 5.71411 | − | 8.99918i | 0.353694 | − | 0.557035i | ||||
\(262\) | 1.13984 | 0.0704198 | ||||||||
\(263\) | −4.54273 | + | 7.86823i | −0.280117 | + | 0.485176i | −0.971413 | − | 0.237395i | \(-0.923706\pi\) |
0.691297 | + | 0.722571i | \(0.257040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.12883 | + | 3.68724i | 0.130773 | + | 0.226505i | ||||
\(266\) | −0.942151 | − | 1.63185i | −0.0577670 | − | 0.100055i | ||||
\(267\) | 0.337918 | − | 16.0394i | 0.0206802 | − | 0.981598i | ||||
\(268\) | −1.66980 | + | 2.89218i | −0.101999 | + | 0.176668i | ||||
\(269\) | 7.94129 | 0.484189 | 0.242094 | − | 0.970253i | \(-0.422166\pi\) | ||||
0.242094 | + | 0.970253i | \(0.422166\pi\) | |||||||
\(270\) | −0.253459 | + | 4.00545i | −0.0154251 | + | 0.243764i | ||||
\(271\) | 3.72364 | 0.226195 | 0.113097 | − | 0.993584i | \(-0.463923\pi\) | ||||
0.113097 | + | 0.993584i | \(0.463923\pi\) | |||||||
\(272\) | 7.60087 | − | 13.1651i | 0.460870 | − | 0.798251i | ||||
\(273\) | −0.572275 | + | 27.1633i | −0.0346356 | + | 1.64400i | ||||
\(274\) | −0.155300 | − | 0.268987i | −0.00938201 | − | 0.0162501i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.29890 | + | 3.21000i | 0.318956 | + | 0.193219i | ||||
\(277\) | 1.95032 | − | 3.37805i | 0.117183 | − | 0.202967i | −0.801467 | − | 0.598039i | \(-0.795947\pi\) |
0.918650 | + | 0.395071i | \(0.129280\pi\) | |||||||
\(278\) | 0.822632 | 0.0493382 | ||||||||
\(279\) | −6.75811 | − | 12.9347i | −0.404597 | − | 0.774379i | ||||
\(280\) | 12.3290 | 0.736799 | ||||||||
\(281\) | −0.0198115 | + | 0.0343146i | −0.00118186 | + | 0.00204704i | −0.866616 | − | 0.498976i | \(-0.833710\pi\) |
0.865434 | + | 0.501023i | \(0.167043\pi\) | |||||||
\(282\) | −2.53913 | + | 1.39550i | −0.151203 | + | 0.0831006i | ||||
\(283\) | −3.19694 | − | 5.53725i | −0.190038 | − | 0.329156i | 0.755225 | − | 0.655466i | \(-0.227528\pi\) |
−0.945263 | + | 0.326311i | \(0.894194\pi\) | |||||||
\(284\) | −5.50795 | − | 9.54005i | −0.326837 | − | 0.566098i | ||||
\(285\) | 6.67024 | − | 3.66595i | 0.395111 | − | 0.217152i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.9925 | −1.65235 | ||||||||
\(288\) | 4.49863 | + | 8.61016i | 0.265084 | + | 0.507358i | ||||
\(289\) | 1.66417 | 0.0978923 | ||||||||
\(290\) | −1.37229 | + | 2.37687i | −0.0805834 | + | 0.139575i | ||||
\(291\) | −10.9813 | − | 6.65235i | −0.643738 | − | 0.389968i | ||||
\(292\) | −3.88211 | − | 6.72401i | −0.227183 | − | 0.393493i | ||||
\(293\) | 11.7037 | + | 20.2714i | 0.683738 | + | 1.18427i | 0.973832 | + | 0.227271i | \(0.0729802\pi\) |
−0.290094 | + | 0.956998i | \(0.593686\pi\) | |||||||
\(294\) | 0.0997857 | − | 4.73638i | 0.00581962 | − | 0.276232i | ||||
\(295\) | −15.3890 | + | 26.6545i | −0.895981 | + | 1.55189i | ||||
\(296\) | −8.65375 | −0.502989 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.75282 | 0.333252 | ||||||||
\(299\) | 3.58954 | − | 6.21727i | 0.207589 | − | 0.359554i | ||||
\(300\) | −0.163604 | + | 7.76555i | −0.00944568 | + | 0.448344i | ||||
\(301\) | 2.00610 | + | 3.47467i | 0.115630 | + | 0.200276i | ||||
\(302\) | 1.57949 | + | 2.73575i | 0.0908893 | + | 0.157425i | ||||
\(303\) | −20.3216 | − | 12.3106i | −1.16745 | − | 0.707223i | ||||
\(304\) | 2.85423 | − | 4.94367i | 0.163701 | − | 0.283539i | ||||
\(305\) | −23.3154 | −1.33503 | ||||||||
\(306\) | −1.98101 | + | 3.11990i | −0.113247 | + | 0.178353i | ||||
\(307\) | 29.1494 | 1.66365 | 0.831823 | − | 0.555042i | \(-0.187298\pi\) | ||||
0.831823 | + | 0.555042i | \(0.187298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.70376 | + | 4.23397i | −0.438252 | + | 0.240862i | ||||
\(310\) | 1.87868 | + | 3.25397i | 0.106702 | + | 0.184813i | ||||
\(311\) | 9.85287 | + | 17.0657i | 0.558705 | + | 0.967705i | 0.997605 | + | 0.0691692i | \(0.0220348\pi\) |
−0.438900 | + | 0.898536i | \(0.644632\pi\) | |||||||
\(312\) | 6.53170 | − | 3.58980i | 0.369785 | − | 0.203233i | ||||
\(313\) | −0.669188 | + | 1.15907i | −0.0378248 | + | 0.0655144i | −0.884318 | − | 0.466885i | \(-0.845376\pi\) |
0.846493 | + | 0.532399i | \(0.178710\pi\) | |||||||
\(314\) | 0.0948929 | 0.00535511 | ||||||||
\(315\) | 33.0714 | + | 1.39411i | 1.86336 | + | 0.0785491i | ||||
\(316\) | 8.21228 | 0.461977 | ||||||||
\(317\) | −2.00045 | + | 3.46487i | −0.112356 | + | 0.194607i | −0.916720 | − | 0.399531i | \(-0.869173\pi\) |
0.804364 | + | 0.594137i | \(0.202506\pi\) | |||||||
\(318\) | −0.663980 | − | 0.402230i | −0.0372342 | − | 0.0225560i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.28080 | + | 14.3428i | 0.462911 | + | 0.801785i | ||||
\(321\) | −0.101384 | + | 4.81226i | −0.00565872 | + | 0.268594i | ||||
\(322\) | −1.08266 | + | 1.87522i | −0.0603342 | + | 0.104502i | ||||
\(323\) | 7.00864 | 0.389971 | ||||||||
\(324\) | 7.34489 | + | 15.6283i | 0.408050 | + | 0.868239i | ||||
\(325\) | 9.00060 | 0.499264 | ||||||||
\(326\) | −1.90166 | + | 3.29377i | −0.105323 | + | 0.182425i | ||||
\(327\) | −0.633239 | + | 30.0570i | −0.0350182 | + | 1.66216i | ||||
\(328\) | 3.83950 | + | 6.65020i | 0.212001 | + | 0.367196i | ||||
\(329\) | 11.9478 | + | 20.6942i | 0.658704 | + | 1.14091i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.59017 | + | 2.75425i | −0.0874034 | + | 0.151387i | −0.906413 | − | 0.422393i | \(-0.861190\pi\) |
0.819009 | + | 0.573780i | \(0.194524\pi\) | |||||||
\(332\) | 12.4718 | 0.684481 | ||||||||
\(333\) | −23.2128 | − | 0.978527i | −1.27206 | − | 0.0536229i | ||||
\(334\) | −5.39362 | −0.295126 | ||||||||
\(335\) | 2.35736 | − | 4.08307i | 0.128796 | − | 0.223082i | ||||
\(336\) | 21.7563 | − | 11.9572i | 1.18690 | − | 0.652318i | ||||
\(337\) | 9.09890 | + | 15.7598i | 0.495649 | + | 0.858489i | 0.999987 | − | 0.00501702i | \(-0.00159698\pi\) |
−0.504339 | + | 0.863506i | \(0.668264\pi\) | |||||||
\(338\) | −0.260891 | − | 0.451877i | −0.0141906 | − | 0.0245789i | ||||
\(339\) | −1.43238 | + | 0.787232i | −0.0777962 | + | 0.0427566i | ||||
\(340\) | −11.2265 | + | 19.4449i | −0.608844 | + | 1.05455i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.743895 | + | 1.17156i | −0.0402252 | + | 0.0633510i | ||||
\(343\) | −10.5583 | −0.570096 | ||||||||
\(344\) | 0.550319 | − | 0.953180i | 0.0296712 | − | 0.0513920i | ||||
\(345\) | −7.48078 | − | 4.53176i | −0.402752 | − | 0.243982i | ||||
\(346\) | 0.215870 | + | 0.373898i | 0.0116052 | + | 0.0201009i | ||||
\(347\) | 13.7071 | + | 23.7413i | 0.735833 | + | 1.27450i | 0.954357 | + | 0.298669i | \(0.0965425\pi\) |
−0.218524 | + | 0.975832i | \(0.570124\pi\) | |||||||
\(348\) | −0.248730 | + | 11.8061i | −0.0133333 | + | 0.632873i | ||||
\(349\) | −11.4528 | + | 19.8368i | −0.613052 | + | 1.06184i | 0.377671 | + | 0.925940i | \(0.376725\pi\) |
−0.990723 | + | 0.135898i | \(0.956608\pi\) | |||||||
\(350\) | −2.71471 | −0.145108 | ||||||||
\(351\) | 17.9266 | − | 8.89072i | 0.956849 | − | 0.474552i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.8524 | − | 25.7250i | 0.790511 | − | 1.36921i | −0.135140 | − | 0.990827i | \(-0.543148\pi\) |
0.925651 | − | 0.378379i | \(-0.123518\pi\) | |||||||
\(354\) | 0.118204 | − | 5.61059i | 0.00628245 | − | 0.298200i | ||||
\(355\) | 7.77591 | + | 13.4683i | 0.412703 | + | 0.714822i | ||||
\(356\) | 8.88587 | + | 15.3908i | 0.470950 | + | 0.815710i | ||||
\(357\) | 26.0696 | + | 15.7926i | 1.37975 | + | 0.835834i | ||||
\(358\) | −1.88045 | + | 3.25703i | −0.0993846 | + | 0.172139i | ||||
\(359\) | −36.8574 | −1.94526 | −0.972631 | − | 0.232356i | \(-0.925356\pi\) | ||||
−0.972631 | + | 0.232356i | \(0.925356\pi\) | |||||||
\(360\) | −4.20491 | − | 8.04800i | −0.221618 | − | 0.424167i | ||||
\(361\) | −16.3682 | −0.861482 | ||||||||
\(362\) | −0.399041 | + | 0.691159i | −0.0209731 | + | 0.0363265i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.0485 | − | 26.0648i | −0.788756 | − | 1.36617i | ||||
\(365\) | 5.48061 | + | 9.49270i | 0.286868 | + | 0.496871i | ||||
\(366\) | 3.72557 | − | 2.04756i | 0.194739 | − | 0.107028i | ||||
\(367\) | 12.4303 | − | 21.5299i | 0.648857 | − | 1.12385i | −0.334539 | − | 0.942382i | \(-0.608581\pi\) |
0.983396 | − | 0.181472i | \(-0.0580860\pi\) | |||||||
\(368\) | −6.55978 | −0.341952 | ||||||||
\(369\) | 9.54710 | + | 18.2727i | 0.497002 | + | 0.951237i | ||||
\(370\) | 5.98177 | 0.310978 | ||||||||
\(371\) | −3.20129 | + | 5.54479i | −0.166202 | + | 0.287871i | ||||
\(372\) | 13.8271 | + | 8.37627i | 0.716902 | + | 0.434290i | ||||
\(373\) | −9.13952 | − | 15.8301i | −0.473227 | − | 0.819653i | 0.526304 | − | 0.850297i | \(-0.323578\pi\) |
−0.999530 | + | 0.0306440i | \(0.990244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.263138 | + | 12.4900i | −0.0135884 | + | 0.644981i | ||||
\(376\) | 3.27755 | − | 5.67689i | 0.169027 | − | 0.292763i | ||||
\(377\) | 13.6838 | 0.704750 | ||||||||
\(378\) | −5.40691 | + | 2.68157i | −0.278102 | + | 0.137925i | ||||
\(379\) | −31.4593 | −1.61595 | −0.807977 | − | 0.589213i | \(-0.799438\pi\) | ||||
−0.807977 | + | 0.589213i | \(0.799438\pi\) | |||||||
\(380\) | −4.21571 | + | 7.30183i | −0.216261 | + | 0.374576i | ||||
\(381\) | 0.0893970 | − | 4.24328i | 0.00457995 | − | 0.217390i | ||||
\(382\) | 2.38691 | + | 4.13425i | 0.122125 | + | 0.211527i | ||||
\(383\) | 6.21588 | + | 10.7662i | 0.317617 | + | 0.550129i | 0.979990 | − | 0.199045i | \(-0.0637841\pi\) |
−0.662373 | + | 0.749174i | \(0.730451\pi\) | |||||||
\(384\) | −12.1770 | − | 7.37668i | −0.621407 | − | 0.376440i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.28449 | −0.319872 | ||||||||
\(387\) | 1.58396 | − | 2.49458i | 0.0805170 | − | 0.126807i | ||||
\(388\) | 14.2226 | 0.722045 | ||||||||
\(389\) | −3.65984 | + | 6.33903i | −0.185561 | + | 0.321402i | −0.943766 | − | 0.330616i | \(-0.892744\pi\) |
0.758204 | + | 0.652017i | \(0.226077\pi\) | |||||||
\(390\) | −4.51493 | + | 2.48140i | −0.228623 | + | 0.125650i | ||||
\(391\) | −4.02694 | − | 6.97486i | −0.203651 | − | 0.352734i | ||||
\(392\) | 5.35912 | + | 9.28227i | 0.270677 | + | 0.468826i | ||||
\(393\) | −6.06765 | + | 3.33476i | −0.306072 | + | 0.168217i | ||||
\(394\) | −2.59837 | + | 4.50050i | −0.130904 | + | 0.226732i | ||||
\(395\) | −11.5938 | −0.583346 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.2087 | 1.71688 | 0.858442 | − | 0.512911i | \(-0.171433\pi\) | ||||
0.858442 | + | 0.512911i | \(0.171433\pi\) | |||||||
\(398\) | 3.57801 | − | 6.19730i | 0.179350 | − | 0.310642i | ||||
\(399\) | 9.78948 | + | 5.93034i | 0.490087 | + | 0.296888i | ||||
\(400\) | −4.11208 | − | 7.12234i | −0.205604 | − | 0.356117i | ||||
\(401\) | −3.73789 | − | 6.47421i | −0.186661 | − | 0.323307i | 0.757474 | − | 0.652865i | \(-0.226433\pi\) |
−0.944135 | + | 0.329559i | \(0.893100\pi\) | |||||||
\(402\) | −0.0181070 | + | 0.859459i | −0.000903095 | + | 0.0428659i | ||||
\(403\) | 9.36666 | − | 16.2235i | 0.466587 | − | 0.808152i | ||||
\(404\) | 26.3198 | 1.30946 | ||||||||
\(405\) | −10.3692 | − | 22.0634i | −0.515252 | − | 1.09634i | ||||
\(406\) | −4.12723 | −0.204831 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.176117 | − | 8.35950i | 0.00871910 | − | 0.413857i | ||||
\(409\) | −1.20510 | − | 2.08729i | −0.0595883 | − | 0.103210i | 0.834692 | − | 0.550717i | \(-0.185645\pi\) |
−0.894281 | + | 0.447507i | \(0.852312\pi\) | |||||||
\(410\) | −2.65399 | − | 4.59685i | −0.131071 | − | 0.227022i | ||||
\(411\) | 1.61365 | + | 0.977529i | 0.0795956 | + | 0.0482180i | ||||
\(412\) | 4.86891 | − | 8.43321i | 0.239874 | − | 0.415474i | ||||
\(413\) | −46.2832 | −2.27745 | ||||||||
\(414\) | 1.59334 | + | 0.0671663i | 0.0783082 | + | 0.00330104i | ||||
\(415\) | −17.6073 | −0.864307 | ||||||||
\(416\) | −6.23505 | + | 10.7994i | −0.305699 | + | 0.529485i | ||||
\(417\) | −4.37905 | + | 2.40672i | −0.214443 | + | 0.117857i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.60088 | + | 9.70101i | 0.273621 | + | 0.473925i | 0.969786 | − | 0.243956i | \(-0.0784453\pi\) |
−0.696165 | + | 0.717881i | \(0.745112\pi\) | |||||||
\(420\) | −32.1342 | + | 17.6608i | −1.56799 | + | 0.861761i | ||||
\(421\) | 3.45243 | − | 5.97979i | 0.168261 | − | 0.291437i | −0.769547 | − | 0.638590i | \(-0.779518\pi\) |
0.937809 | + | 0.347153i | \(0.112851\pi\) | |||||||
\(422\) | 2.35818 | 0.114795 | ||||||||
\(423\) | 9.43363 | − | 14.8571i | 0.458679 | − | 0.722376i | ||||
\(424\) | 1.75637 | 0.0852969 | ||||||||
\(425\) | 5.04868 | − | 8.74456i | 0.244897 | − | 0.424174i | ||||
\(426\) | −2.42530 | − | 1.46922i | −0.117506 | − | 0.0711837i | ||||
\(427\) | −17.5306 | − | 30.3638i | −0.848364 | − | 1.46941i | ||||
\(428\) | −2.66600 | − | 4.61765i | −0.128866 | − | 0.223202i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.380399 | + | 0.658871i | −0.0183445 | + | 0.0317736i | ||||
\(431\) | −29.1806 | −1.40558 | −0.702789 | − | 0.711398i | \(-0.748062\pi\) | ||||
−0.702789 | + | 0.711398i | \(0.748062\pi\) | |||||||
\(432\) | −15.2254 | − | 10.1237i | −0.732535 | − | 0.487078i | ||||
\(433\) | −36.5360 | −1.75581 | −0.877903 | − | 0.478838i | \(-0.841058\pi\) | ||||
−0.877903 | + | 0.478838i | \(0.841058\pi\) | |||||||
\(434\) | −2.82512 | + | 4.89326i | −0.135610 | + | 0.234884i | ||||
\(435\) | 0.351147 | − | 16.6674i | 0.0168362 | − | 0.799141i | ||||
\(436\) | −16.6516 | − | 28.8415i | −0.797468 | − | 1.38126i | ||||
\(437\) | −1.51217 | − | 2.61915i | −0.0723368 | − | 0.125291i | ||||
\(438\) | −1.70940 | − | 1.03553i | −0.0816783 | − | 0.0494796i | ||||
\(439\) | 10.7487 | − | 18.6173i | 0.513009 | − | 0.888557i | −0.486877 | − | 0.873470i | \(-0.661864\pi\) |
0.999886 | − | 0.0150869i | \(-0.00480250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.3257 | + | 25.5048i | 0.634558 | + | 1.21451i | ||||
\(442\) | −4.74399 | −0.225649 | ||||||||
\(443\) | 16.7225 | − | 28.9642i | 0.794510 | − | 1.37613i | −0.128640 | − | 0.991691i | \(-0.541061\pi\) |
0.923150 | − | 0.384440i | \(-0.125605\pi\) | |||||||
\(444\) | 22.5550 | − | 12.3962i | 1.07041 | − | 0.588297i | ||||
\(445\) | −12.5447 | − | 21.7281i | −0.594677 | − | 1.03001i | ||||
\(446\) | 1.04822 | + | 1.81557i | 0.0496345 | + | 0.0859695i | ||||
\(447\) | −30.6235 | + | 16.8306i | −1.44844 | + | 0.796060i | ||||
\(448\) | −12.4525 | + | 21.5683i | −0.588324 | + | 1.01901i | ||||
\(449\) | 39.5333 | 1.86569 | 0.932846 | − | 0.360276i | \(-0.117318\pi\) | ||||
0.932846 | + | 0.360276i | \(0.117318\pi\) | |||||||
\(450\) | 0.925876 | + | 1.77208i | 0.0436462 | + | 0.0835367i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.905290 | − | 1.56801i | 0.0425813 | − | 0.0737529i | ||||
\(453\) | −16.4118 | − | 9.94203i | −0.771092 | − | 0.467117i | ||||
\(454\) | 2.70053 | + | 4.67745i | 0.126742 | + | 0.219523i | ||||
\(455\) | 21.2449 | + | 36.7973i | 0.995977 | + | 1.72508i | ||||
\(456\) | 0.0661344 | − | 3.13910i | 0.00309703 | − | 0.147002i | ||||
\(457\) | −18.7562 | + | 32.4866i | −0.877376 | + | 1.51966i | −0.0231665 | + | 0.999732i | \(0.507375\pi\) |
−0.854210 | + | 0.519929i | \(0.825959\pi\) | |||||||
\(458\) | −2.24111 | −0.104720 | ||||||||
\(459\) | 1.41767 | − | 22.4036i | 0.0661712 | − | 1.04571i | ||||
\(460\) | 9.68884 | 0.451745 | ||||||||
\(461\) | −9.68265 | + | 16.7708i | −0.450966 | + | 0.781096i | −0.998446 | − | 0.0557228i | \(-0.982254\pi\) |
0.547480 | + | 0.836818i | \(0.315587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.17464 | + | 12.4268i | 0.333434 | + | 0.577524i | 0.983183 | − | 0.182625i | \(-0.0584594\pi\) |
−0.649749 | + | 0.760149i | \(0.725126\pi\) | |||||||
\(464\) | −6.25167 | − | 10.8282i | −0.290227 | − | 0.502687i | ||||
\(465\) | −19.5206 | − | 11.8253i | −0.905245 | − | 0.548385i | ||||
\(466\) | 0.936629 | − | 1.62229i | 0.0433885 | − | 0.0751511i | ||||
\(467\) | −22.3209 | −1.03289 | −0.516445 | − | 0.856320i | \(-0.672745\pi\) | ||||
−0.516445 | + | 0.856320i | \(0.672745\pi\) | |||||||
\(468\) | −11.8819 | + | 18.7128i | −0.549239 | + | 0.865000i | ||||
\(469\) | 7.08990 | 0.327381 | ||||||||
\(470\) | −2.26556 | + | 3.92406i | −0.104502 | + | 0.181003i | ||||
\(471\) | −0.505136 | + | 0.277621i | −0.0232754 | + | 0.0127921i | ||||
\(472\) | 6.34827 | + | 10.9955i | 0.292203 | + | 0.506110i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.85257 | − | 1.01817i | 0.0850915 | − | 0.0467660i | ||||
\(475\) | 1.89584 | − | 3.28370i | 0.0869873 | − | 0.150666i | ||||
\(476\) | −33.7644 | −1.54759 | ||||||||
\(477\) | 4.71129 | + | 0.198602i | 0.215715 | + | 0.00909338i | ||||
\(478\) | −7.28448 | −0.333184 | ||||||||
\(479\) | 11.6308 | − | 20.1452i | 0.531426 | − | 0.920456i | −0.467902 | − | 0.883781i | \(-0.654990\pi\) |
0.999327 | − | 0.0366756i | \(-0.0116768\pi\) | |||||||
\(480\) | 12.9941 | + | 7.87168i | 0.593099 | + | 0.359291i | ||||
\(481\) | −14.9118 | − | 25.8281i | −0.679921 | − | 1.17766i | ||||
\(482\) | 0.425154 | + | 0.736388i | 0.0193652 | + | 0.0335416i | ||||
\(483\) | 0.277036 | − | 13.1497i | 0.0126056 | − | 0.598331i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.0790 | −0.911740 | ||||||||
\(486\) | 3.59452 | + | 2.61489i | 0.163051 | + | 0.118614i | ||||
\(487\) | 0.270802 | 0.0122712 | 0.00613559 | − | 0.999981i | \(-0.498047\pi\) | ||||
0.00613559 | + | 0.999981i | \(0.498047\pi\) | |||||||
\(488\) | −4.80903 | + | 8.32949i | −0.217695 | + | 0.377058i | ||||
\(489\) | 0.486606 | − | 23.0970i | 0.0220051 | − | 1.04448i | ||||
\(490\) | −3.70441 | − | 6.41623i | −0.167348 | − | 0.289856i | ||||
\(491\) | 2.10328 | + | 3.64298i | 0.0949196 | + | 0.164406i | 0.909575 | − | 0.415540i | \(-0.136407\pi\) |
−0.814655 | + | 0.579945i | \(0.803074\pi\) | |||||||
\(492\) | −19.5334 | − | 11.8331i | −0.880632 | − | 0.533475i | ||||
\(493\) | 7.67559 | − | 13.2945i | 0.345691 | − | 0.598755i | ||||
\(494\) | −1.78143 | −0.0801504 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.1173 | −0.768589 | ||||||||
\(497\) | −11.6932 | + | 20.2533i | −0.524514 | + | 0.908485i | ||||
\(498\) | 2.81347 | − | 1.54628i | 0.126075 | − | 0.0692903i | ||||
\(499\) | 7.68212 | + | 13.3058i | 0.343899 | + | 0.595650i | 0.985153 | − | 0.171678i | \(-0.0549189\pi\) |
−0.641254 | + | 0.767328i | \(0.721586\pi\) | |||||||
\(500\) | −6.91948 | − | 11.9849i | −0.309449 | − | 0.535981i | ||||
\(501\) | 28.7115 | − | 15.7797i | 1.28273 | − | 0.704987i | ||||
\(502\) | −1.66363 | + | 2.88149i | −0.0742514 | + | 0.128607i | ||||
\(503\) | 3.91570 | 0.174592 | 0.0872961 | − | 0.996182i | \(-0.472177\pi\) | ||||
0.0872961 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(504\) | 7.31936 | − | 11.5273i | 0.326030 | − | 0.513467i | ||||
\(505\) | −37.1573 | −1.65348 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.71081 | + | 1.64217i | 0.120391 | + | 0.0729314i | ||||
\(508\) | 2.35078 | + | 4.07167i | 0.104299 | + | 0.180651i | ||||
\(509\) | −14.2747 | − | 24.7245i | −0.632715 | − | 1.09589i | −0.986994 | − | 0.160754i | \(-0.948607\pi\) |
0.354280 | − | 0.935139i | \(-0.384726\pi\) | |||||||
\(510\) | −0.121738 | + | 5.77838i | −0.00539066 | + | 0.255871i | ||||
\(511\) | −8.24163 | + | 14.2749i | −0.364588 | + | 0.631485i | ||||
\(512\) | 19.2581 | 0.851097 | ||||||||
\(513\) | 0.532354 | − | 8.41286i | 0.0235040 | − | 0.371437i | ||||
\(514\) | 5.90954 | 0.260659 | ||||||||
\(515\) | −6.87375 | + | 11.9057i | −0.302893 | + | 0.524627i | ||||
\(516\) | −0.0689482 | + | 3.27266i | −0.00303528 | + | 0.144071i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.49763 | + | 7.79012i | 0.197615 | + | 0.342278i | ||||
\(519\) | −2.24301 | − | 1.35878i | −0.0984572 | − | 0.0596440i | ||||
\(520\) | 5.82796 | − | 10.0943i | 0.255573 | − | 0.442666i | ||||
\(521\) | −14.2748 | −0.625388 | −0.312694 | − | 0.949854i | \(-0.601232\pi\) | ||||
−0.312694 | + | 0.949854i | \(0.601232\pi\) | |||||||
\(522\) | 1.40763 | + | 2.69413i | 0.0616101 | + | 0.117919i | ||||
\(523\) | −33.1573 | −1.44987 | −0.724934 | − | 0.688818i | \(-0.758130\pi\) | ||||
−0.724934 | + | 0.688818i | \(0.758130\pi\) | |||||||
\(524\) | 3.83486 | − | 6.64217i | 0.167527 | − | 0.290165i | ||||
\(525\) | 14.4510 | − | 7.94225i | 0.630695 | − | 0.346628i | ||||
\(526\) | −1.29535 | − | 2.24361i | −0.0564800 | − | 0.0978262i | ||||
\(527\) | −10.5080 | − | 18.2004i | −0.457736 | − | 0.792822i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.76231 | − | 16.9088i | 0.424448 | − | 0.735166i | ||||
\(530\) | −1.21406 | −0.0527356 | ||||||||
\(531\) | 15.7853 | + | 30.2123i | 0.685023 | + | 1.31110i | ||||
\(532\) | −12.6790 | −0.549704 | ||||||||
\(533\) | −13.2322 | + | 22.9188i | −0.573149 | + | 0.992723i | ||||
\(534\) | 3.91269 | + | 2.37026i | 0.169319 | + | 0.102571i | ||||
\(535\) | 3.76376 | + | 6.51902i | 0.162721 | + | 0.281842i | ||||
\(536\) | −0.972460 | − | 1.68435i | −0.0420039 | − | 0.0727528i | ||||
\(537\) | 0.481178 | − | 22.8394i | 0.0207644 | − | 0.985591i | ||||
\(538\) | −1.13222 | + | 1.96107i | −0.0488136 | + | 0.0845476i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 22.4881 | + | 14.9528i | 0.967733 | + | 0.643466i | ||||
\(541\) | −28.4609 | −1.22363 | −0.611815 | − | 0.791001i | \(-0.709560\pi\) | ||||
−0.611815 | + | 0.791001i | \(0.709560\pi\) | |||||||
\(542\) | −0.530894 | + | 0.919536i | −0.0228039 | + | 0.0394975i | ||||
\(543\) | 0.102109 | − | 4.84664i | 0.00438190 | − | 0.207989i | ||||
\(544\) | 6.99481 | + | 12.1154i | 0.299900 | + | 0.519442i | ||||
\(545\) | 23.5081 | + | 40.7173i | 1.00698 | + | 1.74414i | ||||
\(546\) | −6.62628 | − | 4.01411i | −0.283578 | − | 0.171788i | ||||
\(547\) | 15.3733 | − | 26.6274i | 0.657316 | − | 1.13850i | −0.323992 | − | 0.946060i | \(-0.605025\pi\) |
0.981308 | − | 0.192444i | \(-0.0616415\pi\) | |||||||
\(548\) | −2.08995 | −0.0892781 | ||||||||
\(549\) | −13.8416 | + | 21.7993i | −0.590746 | + | 0.930370i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.88228 | − | 4.99226i | 0.122789 | − | 0.212678i | ||||
\(552\) | −3.16197 | + | 1.73781i | −0.134582 | + | 0.0739662i | ||||
\(553\) | −8.71724 | − | 15.0987i | −0.370695 | − | 0.642062i | ||||
\(554\) | 0.556130 | + | 0.963246i | 0.0236277 | + | 0.0409244i | ||||
\(555\) | −31.8423 | + | 17.5004i | −1.35163 | + | 0.742853i | ||||
\(556\) | 2.76764 | − | 4.79369i | 0.117374 | − | 0.203298i | ||||
\(557\) | −7.29459 | −0.309082 | −0.154541 | − | 0.987986i | \(-0.549390\pi\) | ||||
−0.154541 | + | 0.987986i | \(0.549390\pi\) | |||||||
\(558\) | 4.15770 | + | 0.175266i | 0.176009 | + | 0.00741959i | ||||
\(559\) | 3.79316 | 0.160433 | ||||||||
\(560\) | 19.4122 | − | 33.6230i | 0.820316 | − | 1.42083i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.00564923 | − | 0.00978475i | −0.000238298 | − | 0.000412745i | ||||
\(563\) | 18.2867 | + | 31.6735i | 0.770693 | + | 1.33488i | 0.937183 | + | 0.348837i | \(0.113423\pi\) |
−0.166490 | + | 0.986043i | \(0.553243\pi\) | |||||||
\(564\) | −0.410637 | + | 19.4911i | −0.0172910 | + | 0.820725i | ||||
\(565\) | −1.27805 | + | 2.21365i | −0.0537681 | + | 0.0931291i | ||||
\(566\) | 1.82320 | 0.0766349 | ||||||||
\(567\) | 20.9369 | − | 30.0932i | 0.879268 | − | 1.26380i | ||||
\(568\) | 6.41545 | 0.269186 | ||||||||
\(569\) | −0.0757419 | + | 0.131189i | −0.00317527 | + | 0.00549972i | −0.867609 | − | 0.497248i | \(-0.834344\pi\) |
0.864433 | + | 0.502747i | \(0.167677\pi\) | |||||||
\(570\) | −0.0457144 | + | 2.16986i | −0.00191476 | + | 0.0908853i | ||||
\(571\) | −21.6127 | − | 37.4343i | −0.904463 | − | 1.56658i | −0.821637 | − | 0.570012i | \(-0.806939\pi\) |
−0.0828262 | − | 0.996564i | \(-0.526395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.8014 | − | 15.0243i | −1.03609 | − | 0.627651i | ||||
\(574\) | 3.99101 | − | 6.91264i | 0.166582 | − | 0.288528i | ||||
\(575\) | −4.35716 | −0.181706 | ||||||||
\(576\) | 18.3262 | + | 0.772531i | 0.763590 | + | 0.0321888i | ||||
\(577\) | 29.1251 | 1.21250 | 0.606248 | − | 0.795276i | \(-0.292674\pi\) | ||||
0.606248 | + | 0.795276i | \(0.292674\pi\) | |||||||
\(578\) | −0.237268 | + | 0.410959i | −0.00986903 | + | 0.0170937i | ||||
\(579\) | 33.4538 | − | 18.3861i | 1.39029 | − | 0.764100i | ||||
\(580\) | 9.23376 | + | 15.9933i | 0.383411 | + | 0.664087i | ||||
\(581\) | −13.2387 | − | 22.9301i | −0.549235 | − | 0.951302i | ||||
\(582\) | 3.20842 | − | 1.76334i | 0.132993 | − | 0.0730929i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.52173 | 0.187111 | ||||||||
\(585\) | 16.7744 | − | 26.4180i | 0.693534 | − | 1.09225i | ||||
\(586\) | −6.67459 | −0.275725 | ||||||||
\(587\) | 11.3474 | − | 19.6543i | 0.468359 | − | 0.811221i | −0.530987 | − | 0.847380i | \(-0.678179\pi\) |
0.999346 | + | 0.0361584i | \(0.0115121\pi\) | |||||||
\(588\) | −27.2644 | − | 16.5164i | −1.12437 | − | 0.681126i | ||||
\(589\) | −3.94590 | − | 6.83450i | −0.162588 | − | 0.281610i | ||||
\(590\) | −4.38814 | − | 7.60049i | −0.180657 | − | 0.312907i | ||||
\(591\) | 0.664883 | − | 31.5590i | 0.0273496 | − | 1.29817i | ||||
\(592\) | −13.6255 | + | 23.6000i | −0.560003 | + | 0.969954i | ||||
\(593\) | −22.9308 | −0.941656 | −0.470828 | − | 0.882225i | \(-0.656045\pi\) | ||||
−0.470828 | + | 0.882225i | \(0.656045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 47.6673 | 1.95417 | ||||||||
\(596\) | 19.3546 | − | 33.5232i | 0.792796 | − | 1.37316i | ||||
\(597\) | −0.915560 | + | 43.4575i | −0.0374714 | + | 1.77860i | ||||
\(598\) | 1.02355 | + | 1.77284i | 0.0418562 | + | 0.0724970i | ||||
\(599\) | 6.25035 | + | 10.8259i | 0.255382 | + | 0.442335i | 0.964999 | − | 0.262253i | \(-0.0844654\pi\) |
−0.709617 | + | 0.704588i | \(0.751132\pi\) | |||||||
\(600\) | −3.86897 | − | 2.34377i | −0.157950 | − | 0.0956839i | ||||
\(601\) | −11.2394 | + | 19.4672i | −0.458465 | + | 0.794085i | −0.998880 | − | 0.0473137i | \(-0.984934\pi\) |
0.540415 | + | 0.841399i | \(0.318267\pi\) | |||||||
\(602\) | −1.14407 | −0.0466289 | ||||||||
\(603\) | −2.41807 | − | 4.62806i | −0.0984714 | − | 0.188469i | ||||
\(604\) | 21.2559 | 0.864892 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.93738 | − | 3.26317i | 0.241190 | − | 0.132557i | ||||
\(607\) | −13.3524 | − | 23.1270i | −0.541956 | − | 0.938695i | −0.998792 | − | 0.0491443i | \(-0.984351\pi\) |
0.456836 | − | 0.889551i | \(-0.348983\pi\) | |||||||
\(608\) | 2.62664 | + | 4.54948i | 0.106524 | + | 0.184506i | ||||
\(609\) | 21.9702 | − | 12.0747i | 0.890275 | − | 0.489293i | ||||
\(610\) | 3.32417 | − | 5.75763i | 0.134592 | − | 0.233120i | ||||
\(611\) | 22.5911 | 0.913936 | ||||||||
\(612\) | 11.5156 | + | 22.0404i | 0.465492 | + | 0.890929i | ||||
\(613\) | −43.4844 | −1.75632 | −0.878160 | − | 0.478367i | \(-0.841229\pi\) | ||||
−0.878160 | + | 0.478367i | \(0.841229\pi\) | |||||||
\(614\) | −4.15595 | + | 7.19832i | −0.167721 | + | 0.290501i | ||||
\(615\) | 27.5765 | + | 16.7055i | 1.11199 | + | 0.673629i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.7128 | − | 35.8756i | −0.833864 | − | 1.44430i | −0.894952 | − | 0.446163i | \(-0.852790\pi\) |
0.0610871 | − | 0.998132i | \(-0.480543\pi\) | |||||||
\(618\) | 0.0527976 | − | 2.50606i | 0.00212383 | − | 0.100809i | ||||
\(619\) | −4.45588 | + | 7.71780i | −0.179097 | + | 0.310205i | −0.941571 | − | 0.336813i | \(-0.890651\pi\) |
0.762475 | + | 0.647018i | \(0.223984\pi\) | |||||||
\(620\) | 25.2824 | 1.01536 | ||||||||
\(621\) | −8.67818 | + | 4.30397i | −0.348244 | + | 0.172712i | ||||
\(622\) | −5.61906 | −0.225304 | ||||||||
\(623\) | 18.8645 | − | 32.6743i | 0.755790 | − | 1.30907i | ||||
\(624\) | 0.494360 | − | 23.4651i | 0.0197902 | − | 0.939354i | ||||
\(625\) | 15.6118 | + | 27.0404i | 0.624470 | + | 1.08161i | ||||
\(626\) | −0.190818 | − | 0.330506i | −0.00762662 | − | 0.0132097i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.319255 | − | 0.552966i | 0.0127397 | − | 0.0220657i | ||||
\(629\) | −33.4578 | −1.33405 | ||||||||
\(630\) | −5.05939 | + | 7.96807i | −0.201571 | + | 0.317456i | ||||
\(631\) | −5.67049 | −0.225739 | −0.112869 | − | 0.993610i | \(-0.536004\pi\) | ||||
−0.112869 | + | 0.993610i | \(0.536004\pi\) | |||||||
\(632\) | −2.39134 | + | 4.14192i | −0.0951222 | + | 0.164757i | ||||
\(633\) | −12.5531 | + | 6.89917i | −0.498942 | + | 0.274217i | ||||
\(634\) | −0.570424 | − | 0.988003i | −0.0226544 | − | 0.0392386i | ||||
\(635\) | −3.31874 | − | 5.74823i | −0.131700 | − | 0.228112i | ||||
\(636\) | −4.57778 | + | 2.51594i | −0.181521 | + | 0.0997633i | ||||
\(637\) | −18.4693 | + | 31.9898i | −0.731780 | + | 1.26748i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.2088 | + | 0.725429i | 0.680770 | + | 0.0286975i | ||||
\(640\) | −22.2653 | −0.880112 | ||||||||
\(641\) | −13.4091 | + | 23.2252i | −0.529628 | + | 0.917342i | 0.469775 | + | 0.882786i | \(0.344335\pi\) |
−0.999403 | + | 0.0345558i | \(0.988998\pi\) | |||||||
\(642\) | −1.17391 | − | 0.711141i | −0.0463306 | − | 0.0280665i | ||||
\(643\) | −7.06923 | − | 12.2443i | −0.278783 | − | 0.482866i | 0.692299 | − | 0.721610i | \(-0.256598\pi\) |
−0.971083 | + | 0.238744i | \(0.923264\pi\) | |||||||
\(644\) | 7.28493 | + | 12.6179i | 0.287067 | + | 0.497214i | ||||
\(645\) | 0.0973384 | − | 4.62022i | 0.00383270 | − | 0.181921i | ||||
\(646\) | −0.999252 | + | 1.73075i | −0.0393150 | + | 0.0680956i | ||||
\(647\) | −1.27403 | −0.0500875 | −0.0250437 | − | 0.999686i | \(-0.507973\pi\) | ||||
−0.0250437 | + | 0.999686i | \(0.507973\pi\) | |||||||
\(648\) | −10.0210 | − | 0.846365i | −0.393662 | − | 0.0332484i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.28325 | + | 2.22266i | −0.0503334 | + | 0.0871799i | ||||
\(651\) | 0.722907 | − | 34.3132i | 0.0283329 | − | 1.34484i | ||||
\(652\) | 12.7958 | + | 22.1629i | 0.501121 | + | 0.867968i | ||||
\(653\) | 2.41417 | + | 4.18146i | 0.0944736 | + | 0.163633i | 0.909389 | − | 0.415947i | \(-0.136550\pi\) |
−0.814915 | + | 0.579580i | \(0.803217\pi\) | |||||||
\(654\) | −7.33217 | − | 4.44173i | −0.286711 | − | 0.173685i | ||||
\(655\) | −5.41391 | + | 9.37717i | −0.211539 | + | 0.366396i | ||||
\(656\) | 24.1814 | 0.944124 | ||||||||
\(657\) | 12.1291 | + | 0.511297i | 0.473201 | + | 0.0199476i | ||||
\(658\) | −6.81379 | −0.265629 | ||||||||
\(659\) | 11.0889 | − | 19.2065i | 0.431961 | − | 0.748178i | −0.565082 | − | 0.825035i | \(-0.691155\pi\) |
0.997042 | + | 0.0768574i | \(0.0244886\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6987 | + | 23.7269i | 0.532820 | + | 0.922871i | 0.999265 | + | 0.0383209i | \(0.0122009\pi\) |
−0.466446 | + | 0.884550i | \(0.654466\pi\) | |||||||
\(662\) | −0.453433 | − | 0.785369i | −0.0176232 | − | 0.0305242i | ||||
\(663\) | 25.2533 | − | 13.8792i | 0.980758 | − | 0.539022i | ||||
\(664\) | −3.63168 | + | 6.29025i | −0.140937 | + | 0.244109i | ||||
\(665\) | 17.8997 | 0.694121 | ||||||||
\(666\) | 3.55120 | − | 5.59280i | 0.137606 | − | 0.216717i | ||||
\(667\) | −6.62427 | −0.256493 | ||||||||
\(668\) | −18.1462 | + | 31.4301i | −0.702096 | + | 1.21607i | ||||
\(669\) | −10.8916 | − | 6.59797i | −0.421092 | − | 0.255092i | ||||
\(670\) | 0.672198 | + | 1.16428i | 0.0259693 | + | 0.0449801i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.481213 | + | 22.8410i | −0.0185632 | + | 0.881112i | ||||
\(673\) | −17.6218 | + | 30.5218i | −0.679269 | + | 1.17653i | 0.295932 | + | 0.955209i | \(0.404370\pi\) |
−0.975201 | + | 0.221320i | \(0.928963\pi\) | |||||||
\(674\) | −5.18907 | −0.199876 | ||||||||
\(675\) | −10.1131 | − | 6.72441i | −0.389253 | − | 0.258823i | ||||
\(676\) | −3.51094 | −0.135036 | ||||||||
\(677\) | 22.0250 | − | 38.1484i | 0.846489 | − | 1.46616i | −0.0378328 | − | 0.999284i | \(-0.512045\pi\) |
0.884322 | − | 0.466878i | \(-0.154621\pi\) | |||||||
\(678\) | 0.00981679 | − | 0.465959i | 0.000377012 | − | 0.0178951i | ||||
\(679\) | −15.0972 | − | 26.1491i | −0.579376 | − | 1.00351i | ||||
\(680\) | −6.53811 | − | 11.3243i | −0.250725 | − | 0.434269i | ||||
\(681\) | −28.0600 | − | 16.9984i | −1.07526 | − | 0.651379i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.2845 | 1.61797 | 0.808985 | − | 0.587829i | \(-0.200017\pi\) | ||||
0.808985 | + | 0.587829i | \(0.200017\pi\) | |||||||
\(684\) | 4.32428 | + | 8.27645i | 0.165343 | + | 0.316458i | ||||
\(685\) | 2.95051 | 0.112733 | ||||||||
\(686\) | 1.50534 | − | 2.60733i | 0.0574743 | − | 0.0995484i | ||||
\(687\) | 11.9299 | − | 6.55665i | 0.455155 | − | 0.250152i | ||||
\(688\) | −1.73297 | − | 3.00159i | −0.0660689 | − | 0.114435i | ||||
\(689\) | 3.02652 | + | 5.24208i | 0.115301 | + | 0.199707i | ||||
\(690\) | 2.18566 | − | 1.20124i | 0.0832068 | − | 0.0457302i | ||||
\(691\) | 4.23344 | − | 7.33253i | 0.161048 | − | 0.278943i | −0.774197 | − | 0.632945i | \(-0.781846\pi\) |
0.935245 | + | 0.354002i | \(0.115179\pi\) | |||||||
\(692\) | 2.90507 | 0.110434 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.81709 | −0.296733 | ||||||||
\(695\) | −3.90725 | + | 6.76755i | −0.148210 | + | 0.256708i | ||||
\(696\) | −5.88206 | − | 3.56327i | −0.222959 | − | 0.135065i | ||||
\(697\) | 14.8445 | + | 25.7115i | 0.562277 | + | 0.973892i | ||||
\(698\) | −3.26574 | − | 5.65642i | −0.123610 | − | 0.214099i | ||||
\(699\) | −0.239669 | + | 11.3760i | −0.00906513 | + | 0.430281i | ||||
\(700\) | −9.13331 | + | 15.8194i | −0.345207 | + | 0.597915i | ||||
\(701\) | 43.5518 | 1.64493 | 0.822465 | − | 0.568816i | \(-0.192599\pi\) | ||||
0.822465 | + | 0.568816i | \(0.192599\pi\) | |||||||
\(702\) | −0.360339 | + | 5.69447i | −0.0136001 | + | 0.214924i | ||||
\(703\) | −12.5638 | −0.473854 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.579722 | − | 27.5168i | 0.0218336 | − | 1.03634i | ||||
\(706\) | 4.23512 | + | 7.33545i | 0.159391 | + | 0.276073i | ||||
\(707\) | −27.9382 | − | 48.3904i | −1.05072 | − | 1.81991i | ||||
\(708\) | −32.2967 | − | 19.5649i | −1.21379 | − | 0.735295i | ||||
\(709\) | 3.01364 | − | 5.21978i | 0.113180 | − | 0.196033i | −0.803871 | − | 0.594804i | \(-0.797230\pi\) |
0.917051 | + | 0.398771i | \(0.130563\pi\) | |||||||
\(710\) | −4.43458 | −0.166427 | ||||||||
\(711\) | −6.88287 | + | 10.8399i | −0.258128 | + | 0.406527i | ||||
\(712\) | −10.3499 | −0.387880 | ||||||||
\(713\) | −4.53437 | + | 7.85376i | −0.169813 | + | 0.294126i | ||||
\(714\) | −7.61677 | + | 4.18616i | −0.285051 | + | 0.156663i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.6530 | + | 21.9157i | 0.472866 | + | 0.819028i | ||||
\(717\) | 38.7769 | − | 21.3117i | 1.44815 | − | 0.795900i | ||||
\(718\) | 5.25492 | − | 9.10179i | 0.196112 | − | 0.339676i | ||||
\(719\) | 40.4066 | 1.50691 | 0.753457 | − | 0.657498i | \(-0.228385\pi\) | ||||
0.753457 | + | 0.657498i | \(0.228385\pi\) | |||||||
\(720\) | −28.5687 | − | 1.20430i | −1.06469 | − | 0.0448817i | ||||
\(721\) | −20.6732 | −0.769909 | ||||||||
\(722\) | 2.33368 | − | 4.04205i | 0.0868505 | − | 0.150429i | ||||
\(723\) | −4.41759 | − | 2.67612i | −0.164292 | − | 0.0995258i | ||||
\(724\) | 2.68504 | + | 4.65063i | 0.0997889 | + | 0.172839i | ||||
\(725\) | −4.15251 | − | 7.19235i | −0.154220 | − | 0.267117i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.36031 | + | 16.2125i | −0.347155 | + | 0.601290i | −0.985743 | − | 0.168259i | \(-0.946185\pi\) |
0.638588 | + | 0.769549i | \(0.279519\pi\) | |||||||
\(728\) | 17.5279 | 0.649628 | ||||||||
\(729\) | −26.7846 | − | 3.40342i | −0.992024 | − | 0.126053i | ||||
\(730\) | −3.12558 | −0.115683 | ||||||||
\(731\) | 2.12768 | − | 3.68525i | 0.0786951 | − | 0.136304i | ||||
\(732\) | 0.602513 | − | 28.5986i | 0.0222695 | − | 1.05704i | ||||
\(733\) | −0.282096 | − | 0.488604i | −0.0104194 | − | 0.0180470i | 0.860769 | − | 0.508996i | \(-0.169983\pi\) |
−0.871188 | + | 0.490949i | \(0.836650\pi\) | |||||||
\(734\) | 3.54448 | + | 6.13923i | 0.130829 | + | 0.226603i | ||||
\(735\) | 38.4909 | + | 23.3173i | 1.41976 | + | 0.860071i | ||||
\(736\) | 3.01837 | − | 5.22796i | 0.111258 | − | 0.192705i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.87353 | − | 0.247596i | −0.216208 | − | 0.00911413i | ||||
\(739\) | 1.94812 | 0.0716629 | 0.0358315 | − | 0.999358i | \(-0.488592\pi\) | ||||
0.0358315 | + | 0.999358i | \(0.488592\pi\) | |||||||
\(740\) | 20.1249 | − | 34.8574i | 0.739806 | − | 1.28138i | ||||
\(741\) | 9.48296 | − | 5.21181i | 0.348365 | − | 0.191461i | ||||
\(742\) | −0.912842 | − | 1.58109i | −0.0335115 | − | 0.0580436i | ||||
\(743\) | 13.6313 | + | 23.6102i | 0.500086 | + | 0.866174i | 1.00000 | 9.89898e-5i | \(3.15094e-5\pi\) | |
−0.499914 | + | 0.866075i | \(0.666635\pi\) | |||||||
\(744\) | −8.25095 | + | 4.53470i | −0.302494 | + | 0.166250i | ||||
\(745\) | −27.3241 | + | 47.3267i | −1.00108 | + | 1.73392i | ||||
\(746\) | 5.21224 | 0.190834 | ||||||||
\(747\) | −10.4529 | + | 16.4623i | −0.382452 | + | 0.602325i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.65985 | + | 9.80315i | −0.206807 | + | 0.358199i | ||||
\(750\) | −3.04684 | − | 1.84573i | −0.111255 | − | 0.0673967i | ||||
\(751\) | −15.1531 | − | 26.2460i | −0.552946 | − | 0.957730i | −0.998060 | − | 0.0622562i | \(-0.980170\pi\) |
0.445115 | − | 0.895474i | \(-0.353163\pi\) | |||||||
\(752\) | −10.3211 | − | 17.8767i | −0.376372 | − | 0.651896i | ||||
\(753\) | 0.425698 | − | 20.2060i | 0.0155133 | − | 0.736347i | ||||
\(754\) | −1.95095 | + | 3.37915i | −0.0710495 | + | 0.123061i | ||||
\(755\) | −30.0083 | −1.09211 | ||||||||
\(756\) | −2.56464 | + | 40.5293i | −0.0932750 | + | 1.47404i | ||||
\(757\) | 11.1070 | 0.403689 | 0.201845 | − | 0.979418i | \(-0.435306\pi\) | ||||
0.201845 | + | 0.979418i | \(0.435306\pi\) | |||||||
\(758\) | 4.48528 | − | 7.76874i | 0.162913 | − | 0.282173i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.45515 | − | 4.25244i | −0.0890576 | − | 0.154252i | ||||
\(761\) | 16.6705 | + | 28.8741i | 0.604304 | + | 1.04669i | 0.992161 | + | 0.124966i | \(0.0398822\pi\) |
−0.387857 | + | 0.921720i | \(0.626784\pi\) | |||||||
\(762\) | 1.03511 | + | 0.627058i | 0.0374982 | + | 0.0227159i | ||||
\(763\) | −35.3510 | + | 61.2298i | −1.27979 | + | 2.21667i | ||||
\(764\) | 32.1219 | 1.16213 | ||||||||
\(765\) | −16.2573 | − | 31.1157i | −0.587786 | − | 1.12499i | ||||
\(766\) | −3.54490 | −0.128082 | ||||||||
\(767\) | −21.8782 | + | 37.8942i | −0.789977 | + | 1.36828i | ||||
\(768\) | −15.0037 | + | 8.24597i | −0.541398 | + | 0.297551i | ||||
\(769\) | 25.9701 | + | 44.9815i | 0.936504 | + | 1.62207i | 0.771929 | + | 0.635709i | \(0.219292\pi\) |
0.164575 | + | 0.986364i | \(0.447375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.4578 | + | 17.2891i | −1.13293 | + | 0.622653i | ||||
\(772\) | −21.1434 | + | 36.6214i | −0.760966 | + | 1.31803i | ||||
\(773\) | −7.72276 | −0.277768 | −0.138884 | − | 0.990309i | \(-0.544352\pi\) | ||||
−0.138884 | + | 0.990309i | \(0.544352\pi\) | |||||||
\(774\) | 0.390195 | + | 0.746815i | 0.0140253 | + | 0.0268437i | ||||
\(775\) | −11.3697 | −0.408412 | ||||||||
\(776\) | −4.14150 | + | 7.17328i | −0.148671 | + | 0.257506i | ||||
\(777\) | −46.7329 | − | 28.3102i | −1.67653 | − | 1.01562i | ||||
\(778\) | −1.04360 | − | 1.80756i | −0.0374148 | − | 0.0648043i | ||||
\(779\) | 5.57432 | + | 9.65501i | 0.199721 | + | 0.345926i | ||||
\(780\) | −0.730173 | + | 34.6580i | −0.0261444 | + | 1.24096i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.29655 | 0.0821244 | ||||||||
\(783\) | −15.3751 | − | 10.2232i | −0.549462 | − | 0.365349i | ||||
\(784\) | 33.7521 | 1.20543 | ||||||||
\(785\) | −0.450712 | + | 0.780656i | −0.0160866 | + | 0.0278628i | ||||
\(786\) | 0.0415845 | − | 1.97383i | 0.00148327 | − | 0.0704042i | ||||
\(787\) | 9.85316 | + | 17.0662i | 0.351227 | + | 0.608343i | 0.986465 | − | 0.163973i | \(-0.0524311\pi\) |
−0.635238 | + | 0.772317i | \(0.719098\pi\) | |||||||
\(788\) | 17.4837 | + | 30.2827i | 0.622833 | + | 1.07878i | ||||
\(789\) | 13.4594 | + | 8.15354i | 0.479168 | + | 0.290274i | ||||
\(790\) | 1.65297 | − | 2.86303i | 0.0588102 | − | 0.101862i | ||||
\(791\) | −3.84382 | −0.136670 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.1470 | −1.17709 | ||||||||
\(794\) | −4.87727 | + | 8.44768i | −0.173088 | + | 0.299797i | ||||
\(795\) | 6.46273 | − | 3.55190i | 0.229210 | − | 0.125973i | ||||
\(796\) | −24.0755 | − | 41.7000i | −0.853334 | − | 1.47802i | ||||
\(797\) | −7.01288 | − | 12.1467i | −0.248409 | − | 0.430257i | 0.714676 | − | 0.699456i | \(-0.246574\pi\) |
−0.963085 | + | 0.269199i | \(0.913241\pi\) | |||||||
\(798\) | −2.86020 | + | 1.57196i | −0.101250 | + | 0.0556467i | ||||
\(799\) | 12.6719 | − | 21.9484i | 0.448300 | − | 0.776479i | ||||
\(800\) | 7.56841 | 0.267584 | ||||||||
\(801\) | −27.7626 | − | 1.17032i | −0.980945 | − | 0.0413513i | ||||
\(802\) | 2.13170 | 0.0752731 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.94737 | + | 2.99705i | 0.174480 | + | 0.105698i | ||||
\(805\) | −10.2846 | − | 17.8134i | −0.362484 | − | 0.627841i | ||||
\(806\) | 2.67089 | + | 4.62611i | 0.0940780 | + | 0.162948i | ||||
\(807\) | 0.289719 | − | 13.7517i | 0.0101986 | − | 0.484081i | ||||
\(808\) | −7.66408 | + | 13.2746i | −0.269621 | + | 0.466998i | ||||
\(809\) | −20.9298 | −0.735854 | −0.367927 | − | 0.929855i | \(-0.619932\pi\) | ||||
−0.367927 | + | 0.929855i | \(0.619932\pi\) | |||||||
\(810\) | 6.92686 | + | 0.585037i | 0.243385 | + | 0.0205561i | ||||
\(811\) | 1.94293 | 0.0682255 | 0.0341127 | − | 0.999418i | \(-0.489139\pi\) | ||||
0.0341127 | + | 0.999418i | \(0.489139\pi\) | |||||||
\(812\) | −13.8855 | + | 24.0504i | −0.487286 | + | 0.844005i | ||||
\(813\) | 0.135848 | − | 6.44810i | 0.00476440 | − | 0.226145i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0646 | − | 31.2888i | −0.632775 | − | 1.09600i | ||||
\(816\) | −22.5202 | − | 13.6425i | −0.788366 | − | 0.477582i | ||||
\(817\) | 0.798973 | − | 1.38386i | 0.0279525 | − | 0.0484152i | ||||
\(818\) | 0.687264 | 0.0240296 | ||||||||
\(819\) | 47.0169 | + | 1.98198i | 1.64291 | + | 0.0692559i | ||||
\(820\) | −35.7161 | −1.24726 | ||||||||
\(821\) | −5.42088 | + | 9.38924i | −0.189190 | + | 0.327687i | −0.944980 | − | 0.327127i | \(-0.893920\pi\) |
0.755790 | + | 0.654814i | \(0.227253\pi\) | |||||||
\(822\) | −0.471462 | + | 0.259114i | −0.0164441 | + | 0.00903765i | ||||
\(823\) | −23.8339 | − | 41.2815i | −0.830798 | − | 1.43898i | −0.897407 | − | 0.441204i | \(-0.854551\pi\) |
0.0666091 | − | 0.997779i | \(-0.478782\pi\) | |||||||
\(824\) | 2.83556 | + | 4.91134i | 0.0987815 | + | 0.171094i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.59880 | − | 11.4295i | 0.229601 | − | 0.397681i | ||||
\(827\) | 37.4150 | 1.30105 | 0.650524 | − | 0.759486i | \(-0.274549\pi\) | ||||
0.650524 | + | 0.759486i | \(0.274549\pi\) | |||||||
\(828\) | 5.75197 | − | 9.05881i | 0.199895 | − | 0.314816i | ||||
\(829\) | 10.7069 | 0.371866 | 0.185933 | − | 0.982562i | \(-0.440469\pi\) | ||||
0.185933 | + | 0.982562i | \(0.440469\pi\) | |||||||
\(830\) | 2.51034 | − | 4.34804i | 0.0871353 | − | 0.150923i | ||||
\(831\) | −5.77850 | − | 3.50054i | −0.200454 | − | 0.121432i | ||||
\(832\) | 11.7727 | + | 20.3908i | 0.408143 | + | 0.706925i | ||||
\(833\) | 20.7198 | + | 35.8878i | 0.717900 | + | 1.24344i | ||||
\(834\) | 0.0300117 | − | 1.42452i | 0.00103922 | − | 0.0493272i | ||||
\(835\) | 25.6181 | − | 44.3718i | 0.886549 | − | 1.53555i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.6451 | + | 11.2309i | −0.782730 | + | 0.388197i | ||||
\(838\) | −3.19416 | −0.110341 | ||||||||
\(839\) | −7.68075 | + | 13.3035i | −0.265169 | + | 0.459286i | −0.967608 | − | 0.252458i | \(-0.918761\pi\) |
0.702439 | + | 0.711744i | \(0.252094\pi\) | |||||||
\(840\) | 0.449794 | − | 21.3497i | 0.0155194 | − | 0.736636i | ||||
\(841\) | 8.18687 | + | 14.1801i | 0.282306 | + | 0.488968i | ||||
\(842\) | 0.984455 | + | 1.70513i | 0.0339266 | + | 0.0587625i | ||||
\(843\) | 0.0586987 | + | 0.0355589i | 0.00202169 | + | 0.00122471i | ||||
\(844\) | 7.93381 | − | 13.7418i | 0.273093 | − | 0.473011i | ||||
\(845\) | 4.95661 | 0.170513 | ||||||||
\(846\) | 2.32390 | + | 4.44783i | 0.0798974 | + | 0.152920i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.76543 | − | 4.78987i | 0.0949654 | − | 0.164485i | ||||
\(849\) | −9.70531 | + | 5.33401i | −0.333085 | + | 0.183063i | ||||
\(850\) | 1.43962 | + | 2.49350i | 0.0493786 | + | 0.0855263i | ||||
\(851\) | 7.21877 | + | 12.5033i | 0.247456 | + | 0.428607i | ||||
\(852\) | −16.7211 | + | 9.18988i | −0.572856 | + | 0.314840i | ||||
\(853\) | −20.7321 | + | 35.9091i | −0.709854 | + | 1.22950i | 0.255057 | + | 0.966926i | \(0.417906\pi\) |
−0.964911 | + | 0.262578i | \(0.915427\pi\) | |||||||
\(854\) | 9.99763 | 0.342112 | ||||||||
\(855\) | −6.10485 | − | 11.6844i | −0.208781 | − | 0.399597i | ||||
\(856\) | 3.10525 | 0.106135 | ||||||||
\(857\) | −9.20273 | + | 15.9396i | −0.314359 | + | 0.544486i | −0.979301 | − | 0.202409i | \(-0.935123\pi\) |
0.664942 | + | 0.746895i | \(0.268456\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.52426 | + | 13.0324i | 0.256725 | + | 0.444660i | 0.965363 | − | 0.260912i | \(-0.0840233\pi\) |
−0.708638 | + | 0.705572i | \(0.750690\pi\) | |||||||
\(860\) | 2.55961 | + | 4.43337i | 0.0872819 | + | 0.151177i | ||||
\(861\) | −1.02124 | + | 48.4738i | −0.0348038 | + | 1.65198i | ||||
\(862\) | 4.16040 | − | 7.20602i | 0.141704 | − | 0.245438i | ||||
\(863\) | −14.4298 | −0.491196 | −0.245598 | − | 0.969372i | \(-0.578984\pi\) | ||||
−0.245598 | + | 0.969372i | \(0.578984\pi\) | |||||||
\(864\) | 15.0740 | − | 7.47601i | 0.512829 | − | 0.254339i | ||||
\(865\) | −4.10126 | −0.139447 | ||||||||
\(866\) | 5.20909 | − | 9.02240i | 0.177012 | − | 0.306594i | ||||
\(867\) | 0.0607132 | − | 2.88179i | 0.00206193 | − | 0.0978706i | ||||
\(868\) | 19.0095 | + | 32.9255i | 0.645225 | + | 1.11756i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.06588 | + | 2.46306i | 0.137846 | + | 0.0835054i | ||||
\(871\) | 3.35142 | − | 5.80482i | 0.113558 | − | 0.196689i | ||||
\(872\) | 19.3952 | 0.656803 | ||||||||
\(873\) | −11.9203 | + | 18.7733i | −0.403440 | + | 0.635381i | ||||
\(874\) | 0.862385 | 0.0291706 | ||||||||
\(875\) | −14.6899 | + | 25.4436i | −0.496609 | + | 0.860152i | ||||
\(876\) | −11.7854 | + | 6.47721i | −0.398191 | + | 0.218845i | ||||
\(877\) | 12.0377 | + | 20.8499i | 0.406484 | + | 0.704050i | 0.994493 | − | 0.104804i | \(-0.0334215\pi\) |
−0.588009 | + | 0.808854i | \(0.700088\pi\) | |||||||
\(878\) | 3.06498 | + | 5.30870i | 0.103438 | + | 0.179160i | ||||
\(879\) | 35.5303 | − | 19.5274i | 1.19841 | − | 0.658642i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.0956 | −0.340129 | −0.170064 | − | 0.985433i | \(-0.554398\pi\) | ||||
−0.170064 | + | 0.985433i | \(0.554398\pi\) | |||||||
\(882\) | −8.19820 | − | 0.345591i | −0.276048 | − | 0.0116367i | ||||
\(883\) | 50.7198 | 1.70686 | 0.853429 | − | 0.521209i | \(-0.174519\pi\) | ||||
0.853429 | + | 0.521209i | \(0.174519\pi\) | |||||||
\(884\) | −15.9605 | + | 27.6445i | −0.536811 | + | 0.929785i | ||||
\(885\) | 45.5953 | + | 27.6210i | 1.53267 | + | 0.928470i | ||||
\(886\) | 4.76839 | + | 8.25910i | 0.160197 | + | 0.277470i | ||||
\(887\) | 1.28635 | + | 2.22803i | 0.0431915 | + | 0.0748099i | 0.886813 | − | 0.462128i | \(-0.152914\pi\) |
−0.843621 | + | 0.536938i | \(0.819581\pi\) | |||||||
\(888\) | −0.315711 | + | 14.9854i | −0.0105946 | + | 0.502878i | ||||
\(889\) | 4.99065 | − | 8.64407i | 0.167381 | − | 0.289913i | ||||
\(890\) | 7.15422 | 0.239810 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.1064 | 0.472316 | ||||||||
\(893\) | 4.75847 | − | 8.24191i | 0.159236 | − | 0.275805i | ||||
\(894\) | 0.209878 | − | 9.96196i | 0.00701936 | − | 0.333178i | ||||
\(895\) | −17.8631 | − | 30.9397i | −0.597097 | − | 1.03420i | ||||
\(896\) | −16.7410 | − | 28.9963i | −0.559278 | − | 0.968698i | ||||
\(897\) | −10.6353 | − | 6.44271i | −0.355102 | − | 0.215116i | ||||
\(898\) | −5.63643 | + | 9.76258i | −0.188090 | + | 0.325781i | ||||
\(899\) | −17.2856 | −0.576506 | ||||||||
\(900\) | 13.4414 | + | 0.566615i | 0.448046 | + | 0.0188872i | ||||
\(901\) | 6.79061 | 0.226228 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.09015 | − | 3.34713i | 0.202668 | − | 0.111386i | ||||
\(904\) | 0.527223 | + | 0.913178i | 0.0175352 | + | 0.0303718i | ||||
\(905\) | −3.79064 | − | 6.56559i | −0.126005 | − | 0.218247i | ||||
\(906\) | 4.79504 | − | 2.63534i | 0.159304 | − | 0.0875533i | ||||
\(907\) | −5.14743 | + | 8.91562i | −0.170918 | + | 0.296038i | −0.938741 | − | 0.344624i | \(-0.888007\pi\) |
0.767823 | + | 0.640662i | \(0.221340\pi\) | |||||||
\(908\) | 36.3423 | 1.20606 | ||||||||
\(909\) | −22.0592 | + | 34.7411i | −0.731657 | + | 1.15229i | ||||
\(910\) | −12.1159 | −0.401638 | ||||||||
\(911\) | 7.80127 | − | 13.5122i | 0.258468 | − | 0.447679i | −0.707364 | − | 0.706850i | \(-0.750116\pi\) |
0.965832 | + | 0.259170i | \(0.0834491\pi\) | |||||||
\(912\) | −8.45665 | − | 5.12293i | −0.280028 | − | 0.169637i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.34829 | − | 9.26351i | −0.176906 | − | 0.306410i | ||||
\(915\) | −0.850605 | + | 40.3744i | −0.0281201 | + | 1.33474i | ||||
\(916\) | −7.53992 | + | 13.0595i | −0.249126 | + | 0.431499i | ||||
\(917\) | −16.2826 | −0.537700 | ||||||||
\(918\) | 5.33036 | + | 3.54427i | 0.175928 | + | 0.116978i | ||||
\(919\) | 11.2124 | 0.369864 | 0.184932 | − | 0.982751i | \(-0.440794\pi\) | ||||
0.184932 | + | 0.982751i | \(0.440794\pi\) | |||||||
\(920\) | −2.82130 | + | 4.88663i | −0.0930154 | + | 0.161107i | ||||
\(921\) | 1.06345 | − | 50.4771i | 0.0350418 | − | 1.66328i | ||||
\(922\) | −2.76099 | − | 4.78218i | −0.0909284 | − | 0.157493i | ||||
\(923\) | 11.0549 | + | 19.1476i | 0.363875 | + | 0.630251i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.05036 | + | 15.6757i | −0.297574 | + | 0.515413i | ||||
\(926\) | −4.09167 | −0.134461 | ||||||||
\(927\) | 7.05076 | + | 13.4948i | 0.231577 | + | 0.443228i | ||||
\(928\) | 11.5064 | 0.377715 | ||||||||
\(929\) | −11.7638 | + | 20.3754i | −0.385956 | + | 0.668496i | −0.991901 | − | 0.127011i | \(-0.959462\pi\) |
0.605945 | + | 0.795506i | \(0.292795\pi\) | |||||||
\(930\) | 5.70334 | − | 3.13454i | 0.187020 | − | 0.102786i | ||||
\(931\) | 7.78057 | + | 13.4763i | 0.254998 | + | 0.441669i | ||||
\(932\) | −6.30234 | − | 10.9160i | −0.206440 | − | 0.357565i | ||||
\(933\) | 29.9115 | − | 16.4393i | 0.979258 | − | 0.538198i | ||||
\(934\) | 3.18239 | − | 5.51206i | 0.104131 | − | 0.180360i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.97805 | − | 11.4417i | −0.195399 | − | 0.373983i | ||||
\(937\) | 18.6555 | 0.609448 | 0.304724 | − | 0.952441i | \(-0.401436\pi\) | ||||
0.304724 | + | 0.952441i | \(0.401436\pi\) | |||||||
\(938\) | −1.01084 | + | 1.75082i | −0.0330050 | + | 0.0571663i | ||||
\(939\) | 1.98271 | + | 1.20110i | 0.0647032 | + | 0.0391963i | ||||
\(940\) | 15.2444 | + | 26.4040i | 0.497216 | + | 0.861204i | ||||
\(941\) | 16.2463 | + | 28.1394i | 0.529615 | + | 0.917320i | 0.999403 | + | 0.0345407i | \(0.0109968\pi\) |
−0.469789 | + | 0.882779i | \(0.655670\pi\) | |||||||
\(942\) | 0.00346194 | − | 0.164323i | 0.000112796 | − | 0.00535393i | ||||
\(943\) | 6.40565 | − | 11.0949i | 0.208597 | − | 0.361300i | ||||
\(944\) | 39.9818 | 1.30130 | ||||||||
\(945\) | 3.62066 | − | 57.2177i | 0.117780 | − | 1.86129i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.92137 | − | 3.32790i | 0.0624360 | − | 0.108142i | −0.833118 | − | 0.553096i | \(-0.813446\pi\) |
0.895554 | + | 0.444953i | \(0.146780\pi\) | |||||||
\(948\) | 0.299605 | − | 14.2209i | 0.00973073 | − | 0.461874i | ||||
\(949\) | 7.79169 | + | 13.4956i | 0.252929 | + | 0.438086i | ||||
\(950\) | 0.540597 | + | 0.936341i | 0.0175393 | + | 0.0303789i | ||||
\(951\) | 5.92702 | + | 3.59051i | 0.192197 | + | 0.116430i | ||||
\(952\) | 9.83187 | − | 17.0293i | 0.318653 | − | 0.551923i | ||||
\(953\) | 19.0891 | 0.618358 | 0.309179 | − | 0.951004i | \(-0.399946\pi\) | ||||
0.309179 | + | 0.951004i | \(0.399946\pi\) | |||||||
\(954\) | −0.720753 | + | 1.13512i | −0.0233352 | + | 0.0367508i | ||||
\(955\) | −45.3484 | −1.46744 | ||||||||
\(956\) | −24.5077 | + | 42.4486i | −0.792636 | + | 1.37289i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.31651 | + | 5.74436i | 0.107152 | + | 0.185592i | ||||
\(959\) | 2.21845 | + | 3.84247i | 0.0716376 | + | 0.124080i | ||||
\(960\) | 25.1390 | − | 13.8163i | 0.811357 | − | 0.445920i | ||||
\(961\) | 3.66788 | − | 6.35296i | 0.118319 | − | 0.204934i | ||||
\(962\) | 8.50417 | 0.274186 | ||||||||
\(963\) | 8.32953 | + | 0.351128i | 0.268416 | + | 0.0113149i | ||||
\(964\) | 5.72150 | 0.184277 | ||||||||
\(965\) | 29.8494 | − | 51.7007i | 0.960886 | − | 1.66430i | ||||
\(966\) | 3.20776 | + | 1.94322i | 0.103208 | + | 0.0625220i | ||||
\(967\) | −13.2813 | − | 23.0039i | −0.427099 | − | 0.739757i | 0.569515 | − | 0.821981i | \(-0.307131\pi\) |
−0.996614 | + | 0.0822239i | \(0.973798\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.255693 | − | 12.1366i | 0.00821406 | − | 0.389885i | ||||
\(970\) | 2.86274 | − | 4.95842i | 0.0919172 | − | 0.159205i | ||||
\(971\) | −51.1079 | −1.64013 | −0.820066 | − | 0.572269i | \(-0.806063\pi\) | ||||
−0.820066 | + | 0.572269i | \(0.806063\pi\) | |||||||
\(972\) | 27.3310 | − | 12.1487i | 0.876641 | − | 0.389671i | ||||
\(973\) | −11.7513 | −0.376728 | ||||||||
\(974\) | −0.0386093 | + | 0.0668733i | −0.00123712 | + | 0.00214276i | ||||
\(975\) | 0.328365 | − | 15.5860i | 0.0105161 | − | 0.499153i | ||||
\(976\) | 15.1438 | + | 26.2298i | 0.484741 | + | 0.839596i | ||||
\(977\) | 10.5873 | + | 18.3377i | 0.338717 | + | 0.586676i | 0.984192 | − | 0.177106i | \(-0.0566736\pi\) |
−0.645474 | + | 0.763782i | \(0.723340\pi\) | |||||||
\(978\) | 5.63434 | + | 3.41321i | 0.180166 | + | 0.109142i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −49.8521 | −1.59247 | ||||||||
\(981\) | 52.0257 | + | 2.19312i | 1.66105 | + | 0.0700208i | ||||
\(982\) | −1.19949 | −0.0382774 | ||||||||
\(983\) | −25.4177 | + | 44.0248i | −0.810699 | + | 1.40417i | 0.101676 | + | 0.994818i | \(0.467579\pi\) |
−0.912375 | + | 0.409355i | \(0.865754\pi\) | |||||||
\(984\) | 11.6560 | − | 6.40611i | 0.371580 | − | 0.204219i | ||||
\(985\) | −24.6829 | − | 42.7520i | −0.786462 | − | 1.36219i | ||||
\(986\) | 2.18868 | + | 3.79091i | 0.0697018 | + | 0.120727i | ||||
\(987\) | 36.2713 | − | 19.9346i | 1.15453 | − | 0.634526i | ||||
\(988\) | −5.99340 | + | 10.3809i | −0.190675 | + | 0.330259i | ||||
\(989\) | −1.83625 | −0.0583895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1480 | −0.417662 | −0.208831 | − | 0.977952i | \(-0.566966\pi\) | ||||
−0.208831 | + | 0.977952i | \(0.566966\pi\) | |||||||
\(992\) | 7.87622 | − | 13.6420i | 0.250070 | − | 0.433134i | ||||
\(993\) | 4.71142 | + | 2.85412i | 0.149513 | + | 0.0905727i | ||||
\(994\) | −3.33431 | − | 5.77519i | −0.105758 | − | 0.183178i | ||||
\(995\) | 33.9889 | + | 58.8705i | 1.07752 | + | 1.86632i | ||||
\(996\) | 0.455005 | − | 21.5971i | 0.0144174 | − | 0.684329i | ||||
\(997\) | 18.6043 | − | 32.2237i | 0.589205 | − | 1.02053i | −0.405132 | − | 0.914258i | \(-0.632774\pi\) |
0.994337 | − | 0.106275i | \(-0.0338924\pi\) | |||||||
\(998\) | −4.38109 | −0.138681 | ||||||||
\(999\) | −2.54135 | + | 40.1612i | −0.0804047 | + | 1.27064i |
(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 | 1089.2.e.p.727.9 | 36 | ||
9.2 | odd | 6 | 9801.2.a.cp.1.9 | 18 | |||
9.4 | even | 3 | inner | 1089.2.e.p.364.9 | 36 | ||
9.7 | even | 3 | 9801.2.a.cm.1.10 | 18 | |||
11.3 | even | 5 | 99.2.m.b.97.5 | yes | 72 | ||
11.4 | even | 5 | 99.2.m.b.16.5 | ✓ | 72 | ||
11.10 | odd | 2 | 1089.2.e.o.727.10 | 36 | |||
33.14 | odd | 10 | 297.2.n.b.262.5 | 72 | |||
33.26 | odd | 10 | 297.2.n.b.181.5 | 72 | |||
99.4 | even | 15 | 99.2.m.b.49.5 | yes | 72 | ||
99.14 | odd | 30 | 297.2.n.b.64.5 | 72 | |||
99.25 | even | 15 | 891.2.f.f.163.5 | 36 | |||
99.43 | odd | 6 | 9801.2.a.co.1.9 | 18 | |||
99.47 | odd | 30 | 891.2.f.e.163.5 | 36 | |||
99.58 | even | 15 | 99.2.m.b.31.5 | yes | 72 | ||
99.59 | odd | 30 | 297.2.n.b.280.5 | 72 | |||
99.65 | even | 6 | 9801.2.a.cn.1.10 | 18 | |||
99.70 | even | 15 | 891.2.f.f.82.5 | 36 | |||
99.76 | odd | 6 | 1089.2.e.o.364.10 | 36 | |||
99.92 | odd | 30 | 891.2.f.e.82.5 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.16.5 | ✓ | 72 | 11.4 | even | 5 | ||
99.2.m.b.31.5 | yes | 72 | 99.58 | even | 15 | ||
99.2.m.b.49.5 | yes | 72 | 99.4 | even | 15 | ||
99.2.m.b.97.5 | yes | 72 | 11.3 | even | 5 | ||
297.2.n.b.64.5 | 72 | 99.14 | odd | 30 | |||
297.2.n.b.181.5 | 72 | 33.26 | odd | 10 | |||
297.2.n.b.262.5 | 72 | 33.14 | odd | 10 | |||
297.2.n.b.280.5 | 72 | 99.59 | odd | 30 | |||
891.2.f.e.82.5 | 36 | 99.92 | odd | 30 | |||
891.2.f.e.163.5 | 36 | 99.47 | odd | 30 | |||
891.2.f.f.82.5 | 36 | 99.70 | even | 15 | |||
891.2.f.f.163.5 | 36 | 99.25 | even | 15 | |||
1089.2.e.o.364.10 | 36 | 99.76 | odd | 6 | |||
1089.2.e.o.727.10 | 36 | 11.10 | odd | 2 | |||
1089.2.e.p.364.9 | 36 | 9.4 | even | 3 | inner | ||
1089.2.e.p.727.9 | 36 | 1.1 | even | 1 | trivial | ||
9801.2.a.cm.1.10 | 18 | 9.7 | even | 3 | |||
9801.2.a.cn.1.10 | 18 | 99.65 | even | 6 | |||
9801.2.a.co.1.9 | 18 | 99.43 | odd | 6 | |||
9801.2.a.cp.1.9 | 18 | 9.2 | odd | 6 |