Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(214,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.q (of order \(15\), degree \(8\), 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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 312.2 | ||
Character | \(\chi\) | \(=\) | 539.312 |
Dual form | 539.2.q.g.520.2 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.116493 | + | 1.10836i | −0.0823733 | + | 0.783730i | 0.872879 | + | 0.487937i | \(0.162250\pi\) |
−0.955252 | + | 0.295793i | \(0.904416\pi\) | |||||||
\(3\) | −1.91292 | − | 2.12452i | −1.10443 | − | 1.22659i | −0.971896 | − | 0.235411i | \(-0.924356\pi\) |
−0.132530 | − | 0.991179i | \(-0.542310\pi\) | |||||||
\(4\) | 0.741401 | + | 0.157590i | 0.370700 | + | 0.0787948i | ||||
\(5\) | 3.15728 | + | 1.40571i | 1.41198 | + | 0.628654i | 0.964124 | − | 0.265451i | \(-0.0855210\pi\) |
0.447856 | + | 0.894106i | \(0.352188\pi\) | |||||||
\(6\) | 2.57757 | − | 1.87272i | 1.05229 | − | 0.764534i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.949813 | + | 2.92322i | −0.335810 | + | 1.03352i | ||||
\(9\) | −0.540709 | + | 5.14450i | −0.180236 | + | 1.71483i | ||||
\(10\) | −1.92584 | + | 3.33566i | −0.609005 | + | 1.05483i | ||||
\(11\) | −1.57633 | + | 2.91808i | −0.475282 | + | 0.879834i | ||||
\(12\) | −1.08344 | − | 1.87657i | −0.312762 | − | 0.541720i | ||||
\(13\) | 1.66629 | + | 1.21063i | 0.462147 | + | 0.335769i | 0.794373 | − | 0.607430i | \(-0.207800\pi\) |
−0.332226 | + | 0.943200i | \(0.607800\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.05318 | − | 9.39672i | −0.788328 | − | 2.42622i | ||||
\(16\) | −1.74447 | − | 0.776689i | −0.436118 | − | 0.194172i | ||||
\(17\) | −0.202130 | − | 1.92314i | −0.0490237 | − | 0.466429i | −0.991303 | − | 0.131601i | \(-0.957988\pi\) |
0.942279 | − | 0.334828i | \(-0.108678\pi\) | |||||||
\(18\) | −5.63898 | − | 1.19860i | −1.32912 | − | 0.282513i | ||||
\(19\) | −1.58749 | + | 0.337432i | −0.364196 | + | 0.0774123i | −0.386375 | − | 0.922342i | \(-0.626273\pi\) |
0.0221790 | + | 0.999754i | \(0.492940\pi\) | |||||||
\(20\) | 2.11929 | + | 1.53975i | 0.473887 | + | 0.344299i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.05065 | − | 2.08708i | −0.650401 | − | 0.444967i | ||||
\(23\) | 0.403568 | + | 0.699000i | 0.0841497 | + | 0.145752i | 0.905029 | − | 0.425351i | \(-0.139849\pi\) |
−0.820879 | + | 0.571102i | \(0.806516\pi\) | |||||||
\(24\) | 8.02735 | − | 3.57401i | 1.63858 | − | 0.729541i | ||||
\(25\) | 4.64676 | + | 5.16075i | 0.929352 | + | 1.03215i | ||||
\(26\) | −1.53593 | + | 1.70583i | −0.301221 | + | 0.334540i | ||||
\(27\) | 5.02542 | − | 3.65118i | 0.967142 | − | 0.702670i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.46400 | + | 7.58342i | 0.457554 | + | 1.40821i | 0.868111 | + | 0.496371i | \(0.165334\pi\) |
−0.410557 | + | 0.911835i | \(0.634666\pi\) | |||||||
\(30\) | 10.7706 | − | 2.28937i | 1.96644 | − | 0.417980i | ||||
\(31\) | 0.720257 | − | 0.320679i | 0.129362 | − | 0.0575957i | −0.341035 | − | 0.940051i | \(-0.610777\pi\) |
0.470397 | + | 0.882455i | \(0.344111\pi\) | |||||||
\(32\) | −2.00959 | + | 3.48071i | −0.355248 | + | 0.615308i | ||||
\(33\) | 9.21490 | − | 2.23312i | 1.60411 | − | 0.388736i | ||||
\(34\) | 2.15508 | 0.369592 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.21160 | + | 3.72893i | −0.201934 | + | 0.621488i | ||||
\(37\) | 6.73264 | − | 7.47735i | 1.10684 | − | 1.22927i | 0.135701 | − | 0.990750i | \(-0.456671\pi\) |
0.971138 | − | 0.238519i | \(-0.0766620\pi\) | |||||||
\(38\) | −0.189064 | − | 1.79883i | −0.0306703 | − | 0.291808i | ||||
\(39\) | −0.615482 | − | 5.85592i | −0.0985559 | − | 0.937697i | ||||
\(40\) | −7.10804 | + | 7.89428i | −1.12388 | + | 1.24820i | ||||
\(41\) | −0.657011 | + | 2.02207i | −0.102608 | + | 0.315795i | −0.989162 | − | 0.146831i | \(-0.953093\pi\) |
0.886554 | + | 0.462626i | \(0.153093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.08043 | 0.469761 | 0.234880 | − | 0.972024i | \(-0.424530\pi\) | ||||
0.234880 | + | 0.972024i | \(0.424530\pi\) | |||||||
\(44\) | −1.62855 | + | 1.91505i | −0.245513 | + | 0.288705i | ||||
\(45\) | −8.93887 | + | 15.4826i | −1.33253 | + | 2.30801i | ||||
\(46\) | −0.821758 | + | 0.365870i | −0.121162 | + | 0.0539446i | ||||
\(47\) | −7.40098 | + | 1.57313i | −1.07954 | + | 0.229464i | −0.713161 | − | 0.701000i | \(-0.752737\pi\) |
−0.366382 | + | 0.930464i | \(0.619404\pi\) | |||||||
\(48\) | 1.68695 | + | 5.19190i | 0.243490 | + | 0.749387i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.26129 | + | 4.54910i | −0.885481 | + | 0.643339i | ||||
\(51\) | −3.69907 | + | 4.10824i | −0.517974 | + | 0.575268i | ||||
\(52\) | 1.04461 | + | 1.16016i | 0.144861 | + | 0.160885i | ||||
\(53\) | 9.88680 | − | 4.40189i | 1.35806 | − | 0.604645i | 0.406933 | − | 0.913458i | \(-0.366598\pi\) |
0.951123 | + | 0.308812i | \(0.0999316\pi\) | |||||||
\(54\) | 3.46140 | + | 5.99532i | 0.471037 | + | 0.815859i | ||||
\(55\) | −9.07891 | + | 6.99733i | −1.22420 | + | 0.943520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.75363 | + | 2.72717i | 0.497181 | + | 0.361223i | ||||
\(58\) | −8.69221 | + | 1.84759i | −1.14134 | + | 0.242600i | ||||
\(59\) | 3.22460 | + | 0.685409i | 0.419807 | + | 0.0892327i | 0.412972 | − | 0.910744i | \(-0.364491\pi\) |
0.00683535 | + | 0.999977i | \(0.497824\pi\) | |||||||
\(60\) | −0.782805 | − | 7.44789i | −0.101060 | − | 0.961518i | ||||
\(61\) | −0.983548 | − | 0.437904i | −0.125930 | − | 0.0560678i | 0.342804 | − | 0.939407i | \(-0.388623\pi\) |
−0.468735 | + | 0.883339i | \(0.655290\pi\) | |||||||
\(62\) | 0.271523 | + | 0.835662i | 0.0344835 | + | 0.106129i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.71351 | − | 4.87765i | −0.839189 | − | 0.609707i | ||||
\(65\) | 3.55916 | + | 6.16465i | 0.441459 | + | 0.764630i | ||||
\(66\) | 1.40163 | + | 10.4736i | 0.172528 | + | 1.28921i | ||||
\(67\) | −1.20157 | + | 2.08118i | −0.146795 | + | 0.254257i | −0.930041 | − | 0.367455i | \(-0.880229\pi\) |
0.783246 | + | 0.621712i | \(0.213562\pi\) | |||||||
\(68\) | 0.153207 | − | 1.45767i | 0.0185791 | − | 0.176768i | ||||
\(69\) | 0.713042 | − | 2.19452i | 0.0858402 | − | 0.264189i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.57963 | − | 1.87421i | 0.306145 | − | 0.222428i | −0.424095 | − | 0.905618i | \(-0.639408\pi\) |
0.730241 | + | 0.683190i | \(0.239408\pi\) | |||||||
\(72\) | −14.5250 | − | 6.46693i | −1.71178 | − | 0.762135i | ||||
\(73\) | −1.19948 | − | 0.254957i | −0.140388 | − | 0.0298405i | 0.137181 | − | 0.990546i | \(-0.456196\pi\) |
−0.277570 | + | 0.960705i | \(0.589529\pi\) | |||||||
\(74\) | 7.50330 | + | 8.33326i | 0.872241 | + | 0.968722i | ||||
\(75\) | 2.07520 | − | 19.7442i | 0.239624 | − | 2.27987i | ||||
\(76\) | −1.23015 | −0.141107 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.56217 | 0.743020 | ||||||||
\(79\) | 0.991120 | − | 9.42988i | 0.111510 | − | 1.06094i | −0.785478 | − | 0.618889i | \(-0.787583\pi\) |
0.896988 | − | 0.442055i | \(-0.145750\pi\) | |||||||
\(80\) | −4.41599 | − | 4.90445i | −0.493723 | − | 0.548335i | ||||
\(81\) | −2.19082 | − | 0.465673i | −0.243424 | − | 0.0517414i | ||||
\(82\) | −2.16465 | − | 0.963764i | −0.239046 | − | 0.106430i | ||||
\(83\) | 13.0004 | − | 9.44536i | 1.42698 | − | 1.03676i | 0.436412 | − | 0.899747i | \(-0.356249\pi\) |
0.990569 | − | 0.137016i | \(-0.0437511\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.06520 | − | 6.35602i | 0.224002 | − | 0.689407i | ||||
\(86\) | −0.358850 | + | 3.41423i | −0.0386958 | + | 0.368165i | ||||
\(87\) | 11.3976 | − | 19.7413i | 1.22196 | − | 2.11649i | ||||
\(88\) | −7.03298 | − | 7.37959i | −0.749718 | − | 0.786667i | ||||
\(89\) | 2.21915 | + | 3.84368i | 0.235230 | + | 0.407430i | 0.959339 | − | 0.282255i | \(-0.0910825\pi\) |
−0.724110 | + | 0.689685i | \(0.757749\pi\) | |||||||
\(90\) | −16.1190 | − | 11.7111i | −1.69909 | − | 1.23446i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.189050 | + | 0.581837i | 0.0197099 | + | 0.0606607i | ||||
\(93\) | −2.05908 | − | 0.916763i | −0.213517 | − | 0.0950639i | ||||
\(94\) | −0.881427 | − | 8.38622i | −0.0909122 | − | 0.864972i | ||||
\(95\) | −5.48650 | − | 1.16619i | −0.562903 | − | 0.119649i | ||||
\(96\) | 11.2390 | − | 2.38892i | 1.14708 | − | 0.243819i | ||||
\(97\) | −5.23278 | − | 3.80184i | −0.531308 | − | 0.386018i | 0.289539 | − | 0.957166i | \(-0.406498\pi\) |
−0.820847 | + | 0.571148i | \(0.806498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.1597 | − | 9.68727i | −1.42311 | − | 0.973607i | ||||
\(100\) | 2.63183 | + | 4.55847i | 0.263183 | + | 0.455847i | ||||
\(101\) | −14.1096 | + | 6.28201i | −1.40396 | + | 0.625083i | −0.962273 | − | 0.272086i | \(-0.912286\pi\) |
−0.441687 | + | 0.897169i | \(0.645620\pi\) | |||||||
\(102\) | −4.12249 | − | 4.57849i | −0.408188 | − | 0.453338i | ||||
\(103\) | 5.96070 | − | 6.62003i | 0.587325 | − | 0.652291i | −0.374090 | − | 0.927392i | \(-0.622045\pi\) |
0.961415 | + | 0.275102i | \(0.0887116\pi\) | |||||||
\(104\) | −5.12162 | + | 3.72107i | −0.502216 | + | 0.364881i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.72713 | + | 11.4709i | 0.362011 | + | 1.11416i | ||||
\(107\) | −3.43544 | + | 0.730225i | −0.332117 | + | 0.0705936i | −0.370952 | − | 0.928652i | \(-0.620969\pi\) |
0.0388354 | + | 0.999246i | \(0.487635\pi\) | |||||||
\(108\) | 4.30124 | − | 1.91503i | 0.413887 | − | 0.184274i | ||||
\(109\) | −1.93827 | + | 3.35719i | −0.185653 | + | 0.321560i | −0.943796 | − | 0.330527i | \(-0.892773\pi\) |
0.758143 | + | 0.652088i | \(0.226107\pi\) | |||||||
\(110\) | −6.69794 | − | 10.8779i | −0.638624 | − | 1.03716i | ||||
\(111\) | −28.7648 | −2.73023 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.29224 | − | 10.1325i | 0.309708 | − | 0.953183i | −0.668170 | − | 0.744008i | \(-0.732922\pi\) |
0.977878 | − | 0.209175i | \(-0.0670777\pi\) | |||||||
\(114\) | −3.45997 | + | 3.84269i | −0.324056 | + | 0.359900i | ||||
\(115\) | 0.291585 | + | 2.77424i | 0.0271904 | + | 0.258699i | ||||
\(116\) | 0.631745 | + | 6.01065i | 0.0586561 | + | 0.558075i | ||||
\(117\) | −7.12909 | + | 7.91766i | −0.659085 | + | 0.731987i | ||||
\(118\) | −1.13533 | + | 3.49417i | −0.104515 | + | 0.321665i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 30.3687 | 2.77227 | ||||||||
\(121\) | −6.03036 | − | 9.19971i | −0.548215 | − | 0.836337i | ||||
\(122\) | 0.599933 | − | 1.03911i | 0.0543154 | − | 0.0940769i | ||||
\(123\) | 5.55274 | − | 2.47224i | 0.500674 | − | 0.222914i | ||||
\(124\) | 0.584535 | − | 0.124247i | 0.0524928 | − | 0.0111577i | ||||
\(125\) | 2.07667 | + | 6.39134i | 0.185743 | + | 0.571659i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7361 | + | 11.4330i | −1.39635 | + | 1.01451i | −0.401220 | + | 0.915982i | \(0.631414\pi\) |
−0.995134 | + | 0.0985289i | \(0.968586\pi\) | |||||||
\(128\) | 0.809577 | − | 0.899127i | 0.0715572 | − | 0.0794723i | ||||
\(129\) | −5.89262 | − | 6.54442i | −0.518816 | − | 0.576204i | ||||
\(130\) | −7.24727 | + | 3.22669i | −0.635628 | + | 0.283000i | ||||
\(131\) | −2.55642 | − | 4.42785i | −0.223355 | − | 0.386863i | 0.732469 | − | 0.680800i | \(-0.238368\pi\) |
−0.955825 | + | 0.293937i | \(0.905034\pi\) | |||||||
\(132\) | 7.18385 | − | 0.203464i | 0.625274 | − | 0.0177092i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.16672 | − | 1.57422i | −0.187176 | − | 0.135992i | ||||
\(135\) | 20.9992 | − | 4.46351i | 1.80732 | − | 0.384158i | ||||
\(136\) | 5.81374 | + | 1.23575i | 0.498524 | + | 0.105965i | ||||
\(137\) | −0.951263 | − | 9.05066i | −0.0812719 | − | 0.773250i | −0.956930 | − | 0.290319i | \(-0.906239\pi\) |
0.875658 | − | 0.482932i | \(-0.160428\pi\) | |||||||
\(138\) | 2.34926 | + | 1.04596i | 0.199982 | + | 0.0890377i | ||||
\(139\) | −4.02234 | − | 12.3795i | −0.341171 | − | 1.05002i | −0.963602 | − | 0.267341i | \(-0.913855\pi\) |
0.622431 | − | 0.782675i | \(-0.286145\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.4996 | + | 12.7142i | 1.47373 | + | 1.07073i | ||||
\(142\) | 1.77679 | + | 3.07749i | 0.149105 | + | 0.258257i | ||||
\(143\) | −6.15935 | + | 2.95402i | −0.515071 | + | 0.247027i | ||||
\(144\) | 4.93893 | − | 8.55448i | 0.411577 | − | 0.712873i | ||||
\(145\) | −2.88056 | + | 27.4067i | −0.239217 | + | 2.27600i | ||||
\(146\) | 0.422316 | − | 1.29975i | 0.0349511 | − | 0.107568i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.16994 | − | 4.48272i | 0.507166 | − | 0.368477i | ||||
\(149\) | −2.87447 | − | 1.27980i | −0.235486 | − | 0.104845i | 0.285601 | − | 0.958348i | \(-0.407807\pi\) |
−0.521087 | + | 0.853504i | \(0.674473\pi\) | |||||||
\(150\) | 21.6420 | + | 4.60015i | 1.76706 | + | 0.375601i | ||||
\(151\) | 1.91837 | + | 2.13057i | 0.156115 | + | 0.173383i | 0.816128 | − | 0.577871i | \(-0.196116\pi\) |
−0.660014 | + | 0.751254i | \(0.729449\pi\) | |||||||
\(152\) | 0.521432 | − | 4.96110i | 0.0422938 | − | 0.402398i | ||||
\(153\) | 10.0029 | 0.808684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.72484 | 0.218864 | ||||||||
\(156\) | 0.466513 | − | 4.43858i | 0.0373509 | − | 0.355370i | ||||
\(157\) | −14.3793 | − | 15.9698i | −1.14759 | − | 1.27453i | −0.956102 | − | 0.293035i | \(-0.905335\pi\) |
−0.191490 | − | 0.981495i | \(-0.561332\pi\) | |||||||
\(158\) | 10.3363 | + | 2.19704i | 0.822308 | + | 0.174787i | ||||
\(159\) | −28.2646 | − | 12.5842i | −2.24152 | − | 0.997991i | ||||
\(160\) | −11.2377 | + | 8.16468i | −0.888420 | + | 0.645475i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.771349 | − | 2.37397i | 0.0606029 | − | 0.186517i | ||||
\(163\) | 0.859480 | − | 8.17741i | 0.0673197 | − | 0.640504i | −0.907888 | − | 0.419213i | \(-0.862306\pi\) |
0.975208 | − | 0.221291i | \(-0.0710272\pi\) | |||||||
\(164\) | −0.805767 | + | 1.39563i | −0.0629198 | + | 0.108980i | ||||
\(165\) | 32.2332 | + | 5.90292i | 2.50935 | + | 0.459542i | ||||
\(166\) | 8.95440 | + | 15.5095i | 0.694997 | + | 1.20377i | ||||
\(167\) | 17.5626 | + | 12.7600i | 1.35904 | + | 0.987397i | 0.998506 | + | 0.0546489i | \(0.0174040\pi\) |
0.360529 | + | 0.932748i | \(0.382596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70632 | − | 8.32919i | −0.208178 | − | 0.640707i | ||||
\(170\) | 6.80419 | + | 3.02942i | 0.521857 | + | 0.232346i | ||||
\(171\) | −0.877549 | − | 8.34932i | −0.0671079 | − | 0.638489i | ||||
\(172\) | 2.28383 | + | 0.485443i | 0.174141 | + | 0.0370147i | ||||
\(173\) | 7.86982 | − | 1.67278i | 0.598331 | − | 0.127179i | 0.101217 | − | 0.994864i | \(-0.467726\pi\) |
0.497114 | + | 0.867685i | \(0.334393\pi\) | |||||||
\(174\) | 20.5527 | + | 14.9324i | 1.55810 | + | 1.13203i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.01630 | − | 3.86619i | 0.378118 | − | 0.291425i | ||||
\(177\) | −4.71224 | − | 8.16184i | −0.354194 | − | 0.613482i | ||||
\(178\) | −4.51871 | + | 2.01186i | −0.338691 | + | 0.150795i | ||||
\(179\) | −2.42286 | − | 2.69086i | −0.181093 | − | 0.201124i | 0.645763 | − | 0.763538i | \(-0.276540\pi\) |
−0.826856 | + | 0.562414i | \(0.809873\pi\) | |||||||
\(180\) | −9.06718 | + | 10.0701i | −0.675828 | + | 0.750583i | ||||
\(181\) | −12.7970 | + | 9.29753i | −0.951190 | + | 0.691080i | −0.951088 | − | 0.308920i | \(-0.900033\pi\) |
−0.000102207 | 1.00000i | \(0.500033\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.951118 | + | 2.92724i | 0.0703087 | + | 0.216388i | ||||
\(184\) | −2.42665 | + | 0.515800i | −0.178895 | + | 0.0380253i | ||||
\(185\) | 31.7679 | − | 14.1440i | 2.33562 | − | 1.03988i | ||||
\(186\) | 1.25598 | − | 2.17541i | 0.0920926 | − | 0.159509i | ||||
\(187\) | 5.93048 | + | 2.44167i | 0.433680 | + | 0.178552i | ||||
\(188\) | −5.73500 | −0.418268 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.93170 | − | 5.94518i | 0.140141 | − | 0.431308i | ||||
\(191\) | 0.287111 | − | 0.318869i | 0.0207746 | − | 0.0230726i | −0.732668 | − | 0.680586i | \(-0.761725\pi\) |
0.753443 | + | 0.657514i | \(0.228392\pi\) | |||||||
\(192\) | 2.47978 | + | 23.5935i | 0.178963 | + | 1.70272i | ||||
\(193\) | 1.58620 | + | 15.0917i | 0.114177 | + | 1.08632i | 0.890185 | + | 0.455600i | \(0.150575\pi\) |
−0.776007 | + | 0.630724i | \(0.782758\pi\) | |||||||
\(194\) | 4.82339 | − | 5.35692i | 0.346299 | − | 0.384604i | ||||
\(195\) | 6.28849 | − | 19.3540i | 0.450328 | − | 1.38597i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.8082 | −1.48252 | −0.741262 | − | 0.671216i | \(-0.765772\pi\) | ||||
−0.741262 | + | 0.671216i | \(0.765772\pi\) | |||||||
\(198\) | 12.3865 | − | 14.5656i | 0.880271 | − | 1.03513i | ||||
\(199\) | −4.22284 | + | 7.31417i | −0.299349 | + | 0.518488i | −0.975987 | − | 0.217828i | \(-0.930103\pi\) |
0.676638 | + | 0.736316i | \(0.263436\pi\) | |||||||
\(200\) | −19.4996 | + | 8.68177i | −1.37883 | + | 0.613894i | ||||
\(201\) | 6.72001 | − | 1.42838i | 0.473993 | − | 0.100750i | ||||
\(202\) | −5.31906 | − | 16.3704i | −0.374247 | − | 1.15182i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.38991 | + | 2.46292i | −0.237341 | + | 0.172439i | ||||
\(205\) | −4.91683 | + | 5.46069i | −0.343406 | + | 0.381391i | ||||
\(206\) | 6.64300 | + | 7.37780i | 0.462840 | + | 0.514035i | ||||
\(207\) | −3.81422 | + | 1.69820i | −0.265107 | + | 0.118033i | ||||
\(208\) | −1.96652 | − | 3.40611i | −0.136353 | − | 0.236171i | ||||
\(209\) | 1.51776 | − | 5.16434i | 0.104986 | − | 0.357225i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.97632 | + | 5.79513i | 0.549112 | + | 0.398953i | 0.827458 | − | 0.561528i | \(-0.189786\pi\) |
−0.278346 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(212\) | 8.02377 | − | 1.70551i | 0.551075 | − | 0.117135i | ||||
\(213\) | −8.91641 | − | 1.89524i | −0.610943 | − | 0.129860i | ||||
\(214\) | −0.409147 | − | 3.89278i | −0.0279687 | − | 0.266105i | ||||
\(215\) | 9.72578 | + | 4.33020i | 0.663293 | + | 0.295317i | ||||
\(216\) | 5.90001 | + | 18.1584i | 0.401445 | + | 1.23552i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.49518 | − | 2.53940i | −0.236724 | − | 0.171990i | ||||
\(219\) | 1.75285 | + | 3.03602i | 0.118447 | + | 0.205156i | ||||
\(220\) | −7.83382 | + | 3.75709i | −0.528156 | + | 0.253303i | ||||
\(221\) | 1.99140 | − | 3.44921i | 0.133956 | − | 0.232019i | ||||
\(222\) | 3.35091 | − | 31.8818i | 0.224898 | − | 2.13976i | ||||
\(223\) | 5.37562 | − | 16.5445i | 0.359978 | − | 1.10790i | −0.593088 | − | 0.805138i | \(-0.702091\pi\) |
0.953066 | − | 0.302762i | \(-0.0979087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29.0620 | + | 21.1148i | −1.93747 | + | 1.40765i | ||||
\(226\) | 10.8469 | + | 4.82936i | 0.721526 | + | 0.321244i | ||||
\(227\) | 12.3555 | + | 2.62623i | 0.820060 | + | 0.174309i | 0.598793 | − | 0.800904i | \(-0.295647\pi\) |
0.221267 | + | 0.975213i | \(0.428981\pi\) | |||||||
\(228\) | 2.35317 | + | 2.61346i | 0.155843 | + | 0.173081i | ||||
\(229\) | −0.478052 | + | 4.54836i | −0.0315906 | + | 0.300564i | 0.967306 | + | 0.253610i | \(0.0816181\pi\) |
−0.998897 | + | 0.0469539i | \(0.985049\pi\) | |||||||
\(230\) | −3.10883 | −0.204990 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.5084 | −1.60905 | ||||||||
\(233\) | −2.49372 | + | 23.7262i | −0.163369 | + | 1.55436i | 0.538855 | + | 0.842399i | \(0.318857\pi\) |
−0.702224 | + | 0.711956i | \(0.747809\pi\) | |||||||
\(234\) | −7.94513 | − | 8.82396i | −0.519389 | − | 0.576840i | ||||
\(235\) | −25.5784 | − | 5.43685i | −1.66855 | − | 0.354661i | ||||
\(236\) | 2.28271 | + | 1.01633i | 0.148592 | + | 0.0661572i | ||||
\(237\) | −21.9299 | + | 15.9330i | −1.42450 | + | 1.03496i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.73114 | − | 8.40558i | 0.176663 | − | 0.543711i | −0.823043 | − | 0.567979i | \(-0.807725\pi\) |
0.999705 | + | 0.0242677i | \(0.00772541\pi\) | |||||||
\(240\) | −1.97214 | + | 18.7637i | −0.127301 | + | 1.21119i | ||||
\(241\) | −9.47322 | + | 16.4081i | −0.610224 | + | 1.05694i | 0.380978 | + | 0.924584i | \(0.375587\pi\) |
−0.991202 | + | 0.132355i | \(0.957746\pi\) | |||||||
\(242\) | 10.8991 | − | 5.61212i | 0.700621 | − | 0.360761i | ||||
\(243\) | −6.11610 | − | 10.5934i | −0.392348 | − | 0.679567i | ||||
\(244\) | −0.660194 | − | 0.479659i | −0.0422646 | − | 0.0307070i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.09328 | + | 6.44244i | 0.133462 | + | 0.410755i | ||||
\(247\) | −3.05374 | − | 1.35961i | −0.194305 | − | 0.0865101i | ||||
\(248\) | 0.253307 | + | 2.41006i | 0.0160850 | + | 0.153039i | ||||
\(249\) | −44.9356 | − | 9.55136i | −2.84768 | − | 0.605293i | ||||
\(250\) | −7.32584 | + | 1.55715i | −0.463327 | + | 0.0984831i | ||||
\(251\) | 2.31938 | + | 1.68513i | 0.146398 | + | 0.106364i | 0.658573 | − | 0.752516i | \(-0.271160\pi\) |
−0.512175 | + | 0.858881i | \(0.671160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.67589 | + | 0.0757876i | −0.168232 | + | 0.00476473i | ||||
\(254\) | −10.8387 | − | 18.7732i | −0.680080 | − | 1.17793i | ||||
\(255\) | −17.4540 | + | 7.77104i | −1.09301 | + | 0.486641i | ||||
\(256\) | −10.2031 | − | 11.3317i | −0.637695 | − | 0.708232i | ||||
\(257\) | 14.9991 | − | 16.6582i | 0.935621 | − | 1.03911i | −0.0635326 | − | 0.997980i | \(-0.520237\pi\) |
0.999154 | − | 0.0411328i | \(-0.0130967\pi\) | |||||||
\(258\) | 7.94003 | − | 5.76877i | 0.494325 | − | 0.359148i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.66728 | + | 5.13136i | 0.103400 | + | 0.318234i | ||||
\(261\) | −40.3452 | + | 8.57564i | −2.49731 | + | 0.530819i | ||||
\(262\) | 5.20546 | − | 2.31762i | 0.321594 | − | 0.143183i | ||||
\(263\) | −0.495353 | + | 0.857976i | −0.0305448 | + | 0.0529051i | −0.880894 | − | 0.473314i | \(-0.843058\pi\) |
0.850349 | + | 0.526219i | \(0.176391\pi\) | |||||||
\(264\) | −2.22453 | + | 29.0583i | −0.136910 | + | 1.78841i | ||||
\(265\) | 37.4032 | 2.29766 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.92090 | − | 12.0673i | 0.239955 | − | 0.738506i | ||||
\(268\) | −1.21882 | + | 1.35363i | −0.0744511 | + | 0.0826863i | ||||
\(269\) | 0.751598 | + | 7.15098i | 0.0458257 | + | 0.436003i | 0.993247 | + | 0.116015i | \(0.0370121\pi\) |
−0.947422 | + | 0.319988i | \(0.896321\pi\) | |||||||
\(270\) | 2.50092 | + | 23.7947i | 0.152201 | + | 1.44810i | ||||
\(271\) | −18.1765 | + | 20.1870i | −1.10414 | + | 1.22627i | −0.132156 | + | 0.991229i | \(0.542190\pi\) |
−0.971985 | + | 0.235044i | \(0.924477\pi\) | |||||||
\(272\) | −1.14107 | + | 3.51185i | −0.0691874 | + | 0.212937i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.1422 | 0.612714 | ||||||||
\(275\) | −22.3843 | + | 5.42456i | −1.34982 | + | 0.327113i | ||||
\(276\) | 0.874484 | − | 1.51465i | 0.0526377 | − | 0.0911712i | ||||
\(277\) | 19.1713 | − | 8.53561i | 1.15189 | − | 0.512855i | 0.260225 | − | 0.965548i | \(-0.416203\pi\) |
0.891667 | + | 0.452693i | \(0.149536\pi\) | |||||||
\(278\) | 14.1895 | − | 3.01608i | 0.851032 | − | 0.180892i | ||||
\(279\) | 1.26029 | + | 3.87876i | 0.0754513 | + | 0.232215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7803 | − | 16.5509i | 1.35896 | − | 0.987341i | 0.360448 | − | 0.932779i | \(-0.382624\pi\) |
0.998510 | − | 0.0545621i | \(-0.0173763\pi\) | |||||||
\(282\) | −16.1305 | + | 17.9148i | −0.960560 | + | 1.06681i | ||||
\(283\) | −17.5257 | − | 19.4643i | −1.04179 | − | 1.15703i | −0.987357 | − | 0.158512i | \(-0.949330\pi\) |
−0.0544372 | − | 0.998517i | \(-0.517336\pi\) | |||||||
\(284\) | 2.20789 | − | 0.983018i | 0.131014 | − | 0.0583314i | ||||
\(285\) | 8.01766 | + | 13.8870i | 0.474925 | + | 0.822595i | ||||
\(286\) | −2.55660 | − | 7.17091i | −0.151175 | − | 0.424025i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.8199 | − | 12.2204i | −0.991123 | − | 0.720093i | ||||
\(289\) | 12.9709 | − | 2.75705i | 0.762995 | − | 0.162180i | ||||
\(290\) | −30.0410 | − | 6.38540i | −1.76407 | − | 0.374964i | ||||
\(291\) | 1.93284 | + | 18.3897i | 0.113305 | + | 1.07803i | ||||
\(292\) | −0.849116 | − | 0.378051i | −0.0496907 | − | 0.0221237i | ||||
\(293\) | −1.37941 | − | 4.24538i | −0.0805858 | − | 0.248017i | 0.902644 | − | 0.430388i | \(-0.141623\pi\) |
−0.983230 | + | 0.182370i | \(0.941623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.21748 | + | 6.69689i | 0.536663 | + | 0.389908i | ||||
\(296\) | 15.4632 | + | 26.7831i | 0.898782 | + | 1.55674i | ||||
\(297\) | 2.73271 | + | 20.4200i | 0.158568 | + | 1.18489i | ||||
\(298\) | 1.75333 | − | 3.03686i | 0.101568 | − | 0.175921i | ||||
\(299\) | −0.173770 | + | 1.65331i | −0.0100494 | + | 0.0956135i | ||||
\(300\) | 4.65004 | − | 14.3114i | 0.268470 | − | 0.826267i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.58492 | + | 1.87805i | −0.148745 | + | 0.108070i | ||||
\(303\) | 40.3368 | + | 17.9591i | 2.31729 | + | 1.03172i | ||||
\(304\) | 3.03142 | + | 0.644348i | 0.173864 | + | 0.0369559i | ||||
\(305\) | −2.48977 | − | 2.76517i | −0.142564 | − | 0.158333i | ||||
\(306\) | −1.16527 | + | 11.0868i | −0.0666140 | + | 0.633790i | ||||
\(307\) | 12.8841 | 0.735334 | 0.367667 | − | 0.929957i | \(-0.380157\pi\) | ||||
0.367667 | + | 0.929957i | \(0.380157\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.4667 | −1.44875 | ||||||||
\(310\) | −0.317426 | + | 3.02011i | −0.0180286 | + | 0.171531i | ||||
\(311\) | 17.9460 | + | 19.9310i | 1.01762 | + | 1.13019i | 0.991445 | + | 0.130528i | \(0.0416672\pi\) |
0.0261787 | + | 0.999657i | \(0.491666\pi\) | |||||||
\(312\) | 17.7027 | + | 3.76283i | 1.00222 | + | 0.213029i | ||||
\(313\) | 3.27843 | + | 1.45965i | 0.185308 | + | 0.0825043i | 0.497293 | − | 0.867583i | \(-0.334327\pi\) |
−0.311985 | + | 0.950087i | \(0.600994\pi\) | |||||||
\(314\) | 19.3754 | − | 14.0771i | 1.09342 | − | 0.794415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.22087 | − | 6.83513i | 0.124934 | − | 0.384506i | ||||
\(317\) | 1.76842 | − | 16.8254i | 0.0993243 | − | 0.945007i | −0.825446 | − | 0.564481i | \(-0.809076\pi\) |
0.924770 | − | 0.380526i | \(-0.124257\pi\) | |||||||
\(318\) | 17.2405 | − | 29.8614i | 0.966797 | − | 1.67454i | ||||
\(319\) | −26.0131 | − | 4.76382i | −1.45645 | − | 0.266723i | ||||
\(320\) | −14.3399 | − | 24.8374i | −0.801624 | − | 1.38845i | ||||
\(321\) | 8.12311 | + | 5.90178i | 0.453388 | + | 0.329405i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.969808 | + | 2.98476i | 0.0539616 | + | 0.166077i | ||||
\(324\) | −1.55089 | − | 0.690500i | −0.0861605 | − | 0.0383611i | ||||
\(325\) | 1.49509 | + | 14.2249i | 0.0829328 | + | 0.789053i | ||||
\(326\) | 8.96340 | + | 1.90523i | 0.496437 | + | 0.105521i | ||||
\(327\) | 10.8402 | − | 2.30415i | 0.599463 | − | 0.127420i | ||||
\(328\) | −5.28693 | − | 3.84118i | −0.291922 | − | 0.212094i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.2975 | + | 35.0384i | −0.566860 | + | 1.92880i | ||||
\(331\) | 0.619131 | + | 1.07237i | 0.0340305 | + | 0.0589426i | 0.882539 | − | 0.470239i | \(-0.155832\pi\) |
−0.848509 | + | 0.529182i | \(0.822499\pi\) | |||||||
\(332\) | 11.1270 | − | 4.95406i | 0.610674 | − | 0.271890i | ||||
\(333\) | 34.8269 | + | 38.6792i | 1.90850 | + | 2.11960i | ||||
\(334\) | −16.1886 | + | 17.9793i | −0.885801 | + | 0.983781i | ||||
\(335\) | −6.71924 | + | 4.88181i | −0.367111 | + | 0.266722i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.32885 | − | 19.4782i | −0.344754 | − | 1.06104i | −0.961715 | − | 0.274051i | \(-0.911636\pi\) |
0.616961 | − | 0.786994i | \(-0.288364\pi\) | |||||||
\(338\) | 9.54702 | − | 2.02928i | 0.519290 | − | 0.110378i | ||||
\(339\) | −27.8244 | + | 12.3882i | −1.51121 | + | 0.672836i | ||||
\(340\) | 2.53278 | − | 4.38691i | 0.137359 | − | 0.237913i | ||||
\(341\) | −0.199596 | + | 2.60726i | −0.0108088 | + | 0.141191i | ||||
\(342\) | 9.35630 | 0.505931 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.92583 | + | 9.00478i | −0.157750 | + | 0.485505i | ||||
\(345\) | 5.33614 | − | 5.92639i | 0.287288 | − | 0.319066i | ||||
\(346\) | 0.937264 | + | 8.91747i | 0.0503876 | + | 0.479406i | ||||
\(347\) | −2.85048 | − | 27.1205i | −0.153022 | − | 1.45590i | −0.754125 | − | 0.656731i | \(-0.771939\pi\) |
0.601103 | − | 0.799171i | \(-0.294728\pi\) | |||||||
\(348\) | 11.5613 | − | 12.8401i | 0.619748 | − | 0.688300i | ||||
\(349\) | 2.46730 | − | 7.59356i | 0.132071 | − | 0.406474i | −0.863052 | − | 0.505116i | \(-0.831450\pi\) |
0.995123 | + | 0.0986418i | \(0.0314498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7941 | 0.682897 | ||||||||
\(352\) | −6.98920 | − | 11.3509i | −0.372526 | − | 0.605004i | ||||
\(353\) | −2.96736 | + | 5.13961i | −0.157937 | + | 0.273554i | −0.934124 | − | 0.356948i | \(-0.883817\pi\) |
0.776188 | + | 0.630502i | \(0.217151\pi\) | |||||||
\(354\) | 9.59522 | − | 4.27207i | 0.509980 | − | 0.227058i | ||||
\(355\) | 10.7792 | − | 2.29119i | 0.572102 | − | 0.121604i | ||||
\(356\) | 1.03956 | + | 3.19942i | 0.0550964 | + | 0.169569i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.26469 | − | 2.37194i | 0.172544 | − | 0.125361i | ||||
\(359\) | 19.0169 | − | 21.1204i | 1.00367 | − | 1.11469i | 0.0102773 | − | 0.999947i | \(-0.496729\pi\) |
0.993395 | − | 0.114744i | \(-0.0366048\pi\) | |||||||
\(360\) | −36.7688 | − | 40.8359i | −1.93788 | − | 2.15224i | ||||
\(361\) | −14.9511 | + | 6.65665i | −0.786899 | + | 0.350350i | ||||
\(362\) | −8.81427 | − | 15.2668i | −0.463267 | − | 0.802403i | ||||
\(363\) | −8.00931 | + | 30.4099i | −0.420380 | + | 1.59611i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.42870 | − | 2.49109i | −0.179466 | − | 0.130390i | ||||
\(366\) | −3.35524 | + | 0.713178i | −0.175381 | + | 0.0372784i | ||||
\(367\) | 29.7371 | + | 6.32081i | 1.55226 | + | 0.329944i | 0.902668 | − | 0.430337i | \(-0.141605\pi\) |
0.649595 | + | 0.760281i | \(0.274939\pi\) | |||||||
\(368\) | −0.161107 | − | 1.53283i | −0.00839829 | − | 0.0799044i | ||||
\(369\) | −10.0473 | − | 4.47335i | −0.523042 | − | 0.232873i | ||||
\(370\) | 11.9759 | + | 36.8580i | 0.622596 | + | 1.91615i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.38213 | − | 1.00418i | −0.0716603 | − | 0.0520643i | ||||
\(373\) | −7.21128 | − | 12.4903i | −0.373386 | − | 0.646723i | 0.616698 | − | 0.787200i | \(-0.288470\pi\) |
−0.990084 | + | 0.140476i | \(0.955137\pi\) | |||||||
\(374\) | −3.39711 | + | 6.28868i | −0.175660 | + | 0.325180i | ||||
\(375\) | 9.60599 | − | 16.6381i | 0.496051 | − | 0.859186i | ||||
\(376\) | 2.43094 | − | 23.1289i | 0.125366 | − | 1.19278i | ||||
\(377\) | −5.07499 | + | 15.6192i | −0.261375 | + | 0.804430i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.1278 | − | 13.1706i | 0.931163 | − | 0.676529i | −0.0151144 | − | 0.999886i | \(-0.504811\pi\) |
0.946277 | + | 0.323356i | \(0.104811\pi\) | |||||||
\(380\) | −3.88392 | − | 1.72923i | −0.199241 | − | 0.0887077i | ||||
\(381\) | 54.3915 | + | 11.5613i | 2.78656 | + | 0.592301i | ||||
\(382\) | 0.319976 | + | 0.355369i | 0.0163714 | + | 0.0181823i | ||||
\(383\) | −3.52037 | + | 33.4940i | −0.179882 | + | 1.71147i | 0.416808 | + | 0.908994i | \(0.363149\pi\) |
−0.596691 | + | 0.802471i | \(0.703518\pi\) | |||||||
\(384\) | −3.45887 | −0.176510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.9118 | −0.860790 | ||||||||
\(387\) | −1.66561 | + | 15.8473i | −0.0846680 | + | 0.805562i | ||||
\(388\) | −3.28046 | − | 3.64332i | −0.166540 | − | 0.184961i | ||||
\(389\) | −2.37478 | − | 0.504774i | −0.120406 | − | 0.0255931i | 0.147315 | − | 0.989090i | \(-0.452937\pi\) |
−0.267720 | + | 0.963497i | \(0.586270\pi\) | |||||||
\(390\) | 20.7186 | + | 9.22453i | 1.04913 | + | 0.467102i | ||||
\(391\) | 1.26270 | − | 0.917404i | 0.0638574 | − | 0.0463951i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.51680 | + | 13.9013i | −0.227842 | + | 0.701227i | ||||
\(394\) | 2.42402 | − | 23.0630i | 0.122120 | − | 1.16190i | ||||
\(395\) | 16.3850 | − | 28.3796i | 0.824417 | − | 1.42793i | ||||
\(396\) | −8.97142 | − | 9.41358i | −0.450831 | − | 0.473050i | ||||
\(397\) | 2.94848 | + | 5.10692i | 0.147980 | + | 0.256309i | 0.930481 | − | 0.366341i | \(-0.119390\pi\) |
−0.782501 | + | 0.622650i | \(0.786056\pi\) | |||||||
\(398\) | −7.61481 | − | 5.53248i | −0.381696 | − | 0.277318i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.09784 | − | 12.6119i | −0.204892 | − | 0.630593i | ||||
\(401\) | 10.2679 | + | 4.57155i | 0.512753 | + | 0.228292i | 0.646768 | − | 0.762687i | \(-0.276120\pi\) |
−0.134015 | + | 0.990979i | \(0.542787\pi\) | |||||||
\(402\) | 0.800326 | + | 7.61460i | 0.0399166 | + | 0.379782i | ||||
\(403\) | 1.58839 | + | 0.337622i | 0.0791231 | + | 0.0168181i | ||||
\(404\) | −11.4509 | + | 2.43396i | −0.569702 | + | 0.121094i | ||||
\(405\) | −6.26243 | − | 4.54992i | −0.311183 | − | 0.226087i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2066 | + | 31.4331i | 0.555492 | + | 1.55808i | ||||
\(408\) | −8.49587 | − | 14.7153i | −0.420608 | − | 0.728515i | ||||
\(409\) | 26.7983 | − | 11.9314i | 1.32509 | − | 0.589968i | 0.382511 | − | 0.923951i | \(-0.375059\pi\) |
0.942579 | + | 0.333983i | \(0.108393\pi\) | |||||||
\(410\) | −5.47964 | − | 6.08576i | −0.270620 | − | 0.300554i | ||||
\(411\) | −17.4086 | + | 19.3342i | −0.858702 | + | 0.953685i | ||||
\(412\) | 5.46251 | − | 3.96875i | 0.269119 | − | 0.195526i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.43789 | − | 4.42536i | −0.0706683 | − | 0.217495i | ||||
\(415\) | 54.3235 | − | 11.5468i | 2.66663 | − | 0.566811i | ||||
\(416\) | −7.56243 | + | 3.36701i | −0.370778 | + | 0.165081i | ||||
\(417\) | −18.6060 | + | 32.2266i | −0.911140 | + | 1.57814i | ||||
\(418\) | 5.54714 | + | 2.28384i | 0.271320 | + | 0.111706i | ||||
\(419\) | −20.2858 | −0.991027 | −0.495514 | − | 0.868600i | \(-0.665020\pi\) | ||||
−0.495514 | + | 0.868600i | \(0.665020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.945600 | + | 2.91026i | −0.0460857 | + | 0.141837i | −0.971452 | − | 0.237238i | \(-0.923758\pi\) |
0.925366 | + | 0.379075i | \(0.123758\pi\) | |||||||
\(422\) | −7.35229 | + | 8.16555i | −0.357904 | + | 0.397493i | ||||
\(423\) | −4.09118 | − | 38.9250i | −0.198920 | − | 1.89260i | ||||
\(424\) | 3.47709 | + | 33.0823i | 0.168862 | + | 1.60662i | ||||
\(425\) | 8.98557 | − | 9.97949i | 0.435864 | − | 0.484076i | ||||
\(426\) | 3.13932 | − | 9.66183i | 0.152100 | − | 0.468117i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.66211 | −0.128678 | ||||||||
\(429\) | 18.0582 | + | 7.43484i | 0.871859 | + | 0.358957i | ||||
\(430\) | −5.93241 | + | 10.2752i | −0.286086 | + | 0.495516i | ||||
\(431\) | 6.88993 | − | 3.06759i | 0.331876 | − | 0.147761i | −0.234032 | − | 0.972229i | \(-0.575192\pi\) |
0.565909 | + | 0.824468i | \(0.308526\pi\) | |||||||
\(432\) | −11.6025 | + | 2.46619i | −0.558227 | + | 0.118655i | ||||
\(433\) | −9.93848 | − | 30.5875i | −0.477613 | − | 1.46994i | −0.842401 | − | 0.538851i | \(-0.818859\pi\) |
0.364788 | − | 0.931091i | \(-0.381141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 63.7362 | − | 46.3071i | 3.05592 | − | 2.22025i | ||||
\(436\) | −1.96610 | + | 2.18357i | −0.0941589 | + | 0.104574i | ||||
\(437\) | −0.876527 | − | 0.973482i | −0.0419300 | − | 0.0465679i | ||||
\(438\) | −3.56921 | + | 1.58911i | −0.170543 | + | 0.0759308i | ||||
\(439\) | 2.33363 | + | 4.04196i | 0.111378 | + | 0.192912i | 0.916326 | − | 0.400433i | \(-0.131140\pi\) |
−0.804948 | + | 0.593345i | \(0.797807\pi\) | |||||||
\(440\) | −11.8315 | − | 33.1858i | −0.564045 | − | 1.58207i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.59099 | + | 2.60901i | 0.170806 | + | 0.124098i | ||||
\(443\) | −16.8996 | + | 3.59212i | −0.802924 | + | 0.170667i | −0.591055 | − | 0.806631i | \(-0.701288\pi\) |
−0.211869 | + | 0.977298i | \(0.567955\pi\) | |||||||
\(444\) | −21.3262 | − | 4.53303i | −1.01210 | − | 0.215128i | ||||
\(445\) | 1.60337 | + | 15.2551i | 0.0760072 | + | 0.723161i | ||||
\(446\) | 17.7110 | + | 7.88546i | 0.838642 | + | 0.373387i | ||||
\(447\) | 2.77969 | + | 8.55501i | 0.131475 | + | 0.404638i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.5430 | + | 9.83957i | 0.639134 | + | 0.464358i | 0.859553 | − | 0.511047i | \(-0.170742\pi\) |
−0.220418 | + | 0.975405i | \(0.570742\pi\) | |||||||
\(450\) | −20.0173 | − | 34.6710i | −0.943625 | − | 1.63441i | ||||
\(451\) | −4.86490 | − | 5.10467i | −0.229079 | − | 0.240369i | ||||
\(452\) | 4.03764 | − | 6.99340i | 0.189915 | − | 0.328942i | ||||
\(453\) | 0.856728 | − | 8.15123i | 0.0402526 | − | 0.382978i | ||||
\(454\) | −4.35015 | + | 13.3884i | −0.204162 | + | 0.628347i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.5374 | + | 8.38241i | −0.540288 | + | 0.392542i | ||||
\(457\) | −19.8216 | − | 8.82513i | −0.927214 | − | 0.412822i | −0.113137 | − | 0.993579i | \(-0.536090\pi\) |
−0.814077 | + | 0.580757i | \(0.802757\pi\) | |||||||
\(458\) | −4.98554 | − | 1.05971i | −0.232959 | − | 0.0495169i | ||||
\(459\) | −8.03750 | − | 8.92655i | −0.375158 | − | 0.416656i | ||||
\(460\) | −0.221011 | + | 2.10278i | −0.0103047 | + | 0.0980425i | ||||
\(461\) | −6.07778 | −0.283070 | −0.141535 | − | 0.989933i | \(-0.545204\pi\) | ||||
−0.141535 | + | 0.989933i | \(0.545204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.14719 | −0.239210 | −0.119605 | − | 0.992822i | \(-0.538163\pi\) | ||||
−0.119605 | + | 0.992822i | \(0.538163\pi\) | |||||||
\(464\) | 1.59157 | − | 15.1428i | 0.0738870 | − | 0.702988i | ||||
\(465\) | −5.21241 | − | 5.78897i | −0.241720 | − | 0.268457i | ||||
\(466\) | −26.0067 | − | 5.52789i | −1.20474 | − | 0.256075i | ||||
\(467\) | −3.58044 | − | 1.59411i | −0.165683 | − | 0.0737667i | 0.322219 | − | 0.946665i | \(-0.395571\pi\) |
−0.487902 | + | 0.872898i | \(0.662238\pi\) | |||||||
\(468\) | −6.53325 | + | 4.74669i | −0.302000 | + | 0.219416i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.00570 | − | 27.7167i | 0.415402 | − | 1.27848i | ||||
\(471\) | −6.42166 | + | 61.0980i | −0.295895 | + | 2.81525i | ||||
\(472\) | −5.06637 | + | 8.77521i | −0.233199 | + | 0.403912i | ||||
\(473\) | −4.85577 | + | 8.98893i | −0.223269 | + | 0.413311i | ||||
\(474\) | −15.1048 | − | 26.1623i | −0.693787 | − | 1.20167i | ||||
\(475\) | −9.11811 | − | 6.62469i | −0.418368 | − | 0.303962i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.2996 | + | 53.2428i | 0.792096 | + | 2.43782i | ||||
\(478\) | 8.99826 | + | 4.00628i | 0.411571 | + | 0.183243i | ||||
\(479\) | 1.57973 | + | 15.0301i | 0.0721797 | + | 0.686744i | 0.969454 | + | 0.245271i | \(0.0788771\pi\) |
−0.897275 | + | 0.441473i | \(0.854456\pi\) | |||||||
\(480\) | 38.8429 | + | 8.25631i | 1.77293 | + | 0.376847i | ||||
\(481\) | 20.2709 | − | 4.30871i | 0.924273 | − | 0.196460i | ||||
\(482\) | −17.0825 | − | 12.4112i | −0.778088 | − | 0.565314i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.02114 | − | 7.77100i | −0.137324 | − | 0.353227i | ||||
\(485\) | −11.1771 | − | 19.3593i | −0.507525 | − | 0.879059i | ||||
\(486\) | 12.4538 | − | 5.54479i | 0.564916 | − | 0.251517i | ||||
\(487\) | 16.7797 | + | 18.6357i | 0.760359 | + | 0.844464i | 0.991722 | − | 0.128404i | \(-0.0409853\pi\) |
−0.231363 | + | 0.972867i | \(0.574319\pi\) | |||||||
\(488\) | 2.21428 | − | 2.45920i | 0.100236 | − | 0.111323i | ||||
\(489\) | −19.0172 | + | 13.8168i | −0.859985 | + | 0.624816i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.5019 | + | 35.3991i | 0.519071 | + | 1.59754i | 0.775750 | + | 0.631040i | \(0.217372\pi\) |
−0.256679 | + | 0.966497i | \(0.582628\pi\) | |||||||
\(492\) | 4.50641 | − | 0.957866i | 0.203164 | − | 0.0431839i | ||||
\(493\) | 14.0859 | − | 6.27144i | 0.634397 | − | 0.282452i | ||||
\(494\) | 1.86268 | − | 3.22626i | 0.0838060 | − | 0.145156i | ||||
\(495\) | −31.0888 | − | 50.4900i | −1.39734 | − | 2.26936i | ||||
\(496\) | −1.50554 | −0.0676006 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.8211 | − | 48.6922i | 0.708959 | − | 2.18195i | ||||
\(499\) | −21.2873 | + | 23.6419i | −0.952950 | + | 1.05836i | 0.0452852 | + | 0.998974i | \(0.485580\pi\) |
−0.998235 | + | 0.0593841i | \(0.981086\pi\) | |||||||
\(500\) | 0.532438 | + | 5.06581i | 0.0238114 | + | 0.226550i | ||||
\(501\) | −6.48713 | − | 61.7209i | −0.289823 | − | 2.75749i | ||||
\(502\) | −2.13792 | + | 2.37441i | −0.0954203 | + | 0.105975i | ||||
\(503\) | −5.93493 | + | 18.2658i | −0.264626 | + | 0.814434i | 0.727154 | + | 0.686474i | \(0.240843\pi\) |
−0.991779 | + | 0.127959i | \(0.959157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.3788 | −2.37532 | ||||||||
\(506\) | 0.227724 | − | 2.97469i | 0.0101236 | − | 0.132241i | ||||
\(507\) | −12.5185 | + | 21.6827i | −0.555967 | + | 0.962963i | ||||
\(508\) | −13.4685 | + | 5.99655i | −0.597567 | + | 0.266054i | ||||
\(509\) | −2.46052 | + | 0.522999i | −0.109061 | + | 0.0231815i | −0.262119 | − | 0.965036i | \(-0.584421\pi\) |
0.153058 | + | 0.988217i | \(0.451088\pi\) | |||||||
\(510\) | −6.57984 | − | 20.2506i | −0.291360 | − | 0.896714i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 15.7059 | − | 11.4110i | 0.694109 | − | 0.504300i | ||||
\(513\) | −6.74580 | + | 7.49196i | −0.297834 | + | 0.330778i | ||||
\(514\) | 16.7160 | + | 18.5651i | 0.737313 | + | 0.818869i | ||||
\(515\) | 28.1255 | − | 12.5223i | 1.23936 | − | 0.551797i | ||||
\(516\) | −3.33746 | − | 5.78065i | −0.146924 | − | 0.254479i | ||||
\(517\) | 7.07588 | − | 24.0764i | 0.311197 | − | 1.05888i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.6082 | − | 13.5196i | −0.816809 | − | 0.593447i | ||||
\(520\) | −21.4012 | + | 4.54896i | −0.938504 | + | 0.199485i | ||||
\(521\) | −14.5712 | − | 3.09721i | −0.638377 | − | 0.135691i | −0.122658 | − | 0.992449i | \(-0.539142\pi\) |
−0.515719 | + | 0.856758i | \(0.672475\pi\) | |||||||
\(522\) | −4.80496 | − | 45.7161i | −0.210307 | − | 2.00094i | ||||
\(523\) | −9.04869 | − | 4.02874i | −0.395672 | − | 0.176164i | 0.199249 | − | 0.979949i | \(-0.436150\pi\) |
−0.594920 | + | 0.803785i | \(0.702816\pi\) | |||||||
\(524\) | −1.19755 | − | 3.68567i | −0.0523151 | − | 0.161009i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.893242 | − | 0.648979i | −0.0389472 | − | 0.0282968i | ||||
\(527\) | −0.762295 | − | 1.32033i | −0.0332061 | − | 0.0575146i | ||||
\(528\) | −17.8096 | − | 3.26150i | −0.775062 | − | 0.141938i | ||||
\(529\) | 11.1743 | − | 19.3544i | 0.485838 | − | 0.841496i | ||||
\(530\) | −4.35723 | + | 41.4563i | −0.189266 | + | 1.80075i | ||||
\(531\) | −5.26966 | + | 16.2183i | −0.228684 | + | 0.703816i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.54276 | + | 2.57397i | −0.153454 | + | 0.111491i | ||||
\(534\) | 12.9182 | + | 5.75153i | 0.559023 | + | 0.248893i | ||||
\(535\) | −11.8731 | − | 2.52372i | −0.513321 | − | 0.109110i | ||||
\(536\) | −4.94249 | − | 5.48919i | −0.213483 | − | 0.237097i | ||||
\(537\) | −1.08203 | + | 10.2948i | −0.0466930 | + | 0.444254i | ||||
\(538\) | −8.01342 | −0.345483 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.2722 | 0.700245 | ||||||||
\(541\) | 2.30050 | − | 21.8878i | 0.0989063 | − | 0.941031i | −0.826726 | − | 0.562605i | \(-0.809799\pi\) |
0.925632 | − | 0.378425i | \(-0.123534\pi\) | |||||||
\(542\) | −20.2571 | − | 22.4977i | −0.870115 | − | 0.966361i | ||||
\(543\) | 44.2323 | + | 9.40188i | 1.89819 | + | 0.403473i | ||||
\(544\) | 7.10007 | + | 3.16116i | 0.304413 | + | 0.135533i | ||||
\(545\) | −10.8389 | + | 7.87494i | −0.464289 | + | 0.337325i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.35724 | + | 10.3325i | −0.143545 | + | 0.441787i | −0.996821 | − | 0.0796728i | \(-0.974612\pi\) |
0.853276 | + | 0.521460i | \(0.174612\pi\) | |||||||
\(548\) | 0.721023 | − | 6.86008i | 0.0308006 | − | 0.293048i | ||||
\(549\) | 2.78461 | − | 4.82309i | 0.118844 | − | 0.205844i | ||||
\(550\) | −3.40475 | − | 25.4418i | −0.145179 | − | 1.08484i | ||||
\(551\) | −6.47048 | − | 11.2072i | −0.275652 | − | 0.477443i | ||||
\(552\) | 5.73781 | + | 4.16876i | 0.244218 | + | 0.177434i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.22721 | + | 22.2431i | 0.307055 | + | 0.945018i | ||||
\(555\) | −90.8185 | − | 40.4350i | −3.85503 | − | 1.71637i | ||||
\(556\) | −1.03129 | − | 9.81205i | −0.0437364 | − | 0.416124i | ||||
\(557\) | −32.8781 | − | 6.98845i | −1.39309 | − | 0.296110i | −0.550575 | − | 0.834786i | \(-0.685592\pi\) |
−0.842513 | + | 0.538675i | \(0.818925\pi\) | |||||||
\(558\) | −4.44588 | + | 0.945002i | −0.188209 | + | 0.0400051i | ||||
\(559\) | 5.13290 | + | 3.72927i | 0.217098 | + | 0.157731i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.15720 | − | 17.2701i | −0.259957 | − | 0.729145i | ||||
\(562\) | 15.6906 | + | 27.1769i | 0.661867 | + | 1.14639i | ||||
\(563\) | −1.87595 | + | 0.835227i | −0.0790619 | + | 0.0352006i | −0.445887 | − | 0.895089i | \(-0.647112\pi\) |
0.366825 | + | 0.930290i | \(0.380445\pi\) | |||||||
\(564\) | 10.9706 | + | 12.1841i | 0.461946 | + | 0.513043i | ||||
\(565\) | 24.6379 | − | 27.3632i | 1.03652 | − | 1.15118i | ||||
\(566\) | 23.6151 | − | 17.1573i | 0.992615 | − | 0.721177i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.02857 | + | 9.32098i | 0.127076 | + | 0.391099i | ||||
\(569\) | −3.20261 | + | 0.680736i | −0.134260 | + | 0.0285379i | −0.274552 | − | 0.961572i | \(-0.588529\pi\) |
0.140291 | + | 0.990110i | \(0.455196\pi\) | |||||||
\(570\) | −16.3258 | + | 7.26872i | −0.683813 | + | 0.304453i | ||||
\(571\) | 21.9448 | − | 38.0096i | 0.918363 | − | 1.59065i | 0.116462 | − | 0.993195i | \(-0.462845\pi\) |
0.801901 | − | 0.597457i | \(-0.203822\pi\) | |||||||
\(572\) | −5.03207 | + | 1.21946i | −0.210402 | + | 0.0509883i | ||||
\(573\) | −1.22666 | −0.0512446 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.73208 | + | 5.33080i | −0.0722328 | + | 0.222310i | ||||
\(576\) | 28.7232 | − | 31.9003i | 1.19680 | − | 1.32918i | ||||
\(577\) | 4.58780 | + | 43.6500i | 0.190992 | + | 1.81717i | 0.499904 | + | 0.866081i | \(0.333369\pi\) |
−0.308912 | + | 0.951091i | \(0.599965\pi\) | |||||||
\(578\) | 1.54478 | + | 14.6976i | 0.0642546 | + | 0.611341i | ||||
\(579\) | 29.0283 | − | 32.2392i | 1.20637 | − | 1.33981i | ||||
\(580\) | −6.45466 | + | 19.8654i | −0.268015 | + | 0.824866i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −20.6076 | −0.854214 | ||||||||
\(583\) | −2.73981 | + | 35.7893i | −0.113471 | + | 1.48224i | ||||
\(584\) | 1.88458 | − | 3.26418i | 0.0779843 | − | 0.135073i | ||||
\(585\) | −33.6385 | + | 14.9768i | −1.39078 | + | 0.619216i | ||||
\(586\) | 4.86610 | − | 1.03432i | 0.201017 | − | 0.0427274i | ||||
\(587\) | 0.862670 | + | 2.65503i | 0.0356062 | + | 0.109585i | 0.967280 | − | 0.253711i | \(-0.0816513\pi\) |
−0.931674 | + | 0.363296i | \(0.881651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03520 | + | 0.752114i | −0.0426545 | + | 0.0309903i | ||||
\(590\) | −8.49635 | + | 9.43616i | −0.349789 | + | 0.388480i | ||||
\(591\) | 39.8045 | + | 44.2074i | 1.63734 | + | 1.81845i | ||||
\(592\) | −17.5525 | + | 7.81486i | −0.721402 | + | 0.321189i | ||||
\(593\) | −11.6263 | − | 20.1374i | −0.477435 | − | 0.826942i | 0.522230 | − | 0.852805i | \(-0.325100\pi\) |
−0.999666 | + | 0.0258622i | \(0.991767\pi\) | |||||||
\(594\) | −22.9511 | + | 0.650030i | −0.941696 | + | 0.0266710i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.92945 | − | 1.40183i | −0.0790334 | − | 0.0574211i | ||||
\(597\) | 23.6170 | − | 5.01995i | 0.966581 | − | 0.205453i | ||||
\(598\) | −1.81222 | − | 0.385200i | −0.0741074 | − | 0.0157520i | ||||
\(599\) | −1.09331 | − | 10.4022i | −0.0446715 | − | 0.425021i | −0.993888 | − | 0.110396i | \(-0.964788\pi\) |
0.949216 | − | 0.314624i | \(-0.101879\pi\) | |||||||
\(600\) | 55.7457 | + | 24.8196i | 2.27581 | + | 1.01326i | ||||
\(601\) | 6.89406 | + | 21.2177i | 0.281215 | + | 0.865489i | 0.987508 | + | 0.157570i | \(0.0503660\pi\) |
−0.706293 | + | 0.707919i | \(0.749634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0569 | − | 7.30679i | −0.409550 | − | 0.297556i | ||||
\(604\) | 1.08653 | + | 1.88192i | 0.0442102 | + | 0.0765743i | ||||
\(605\) | −6.10741 | − | 37.5231i | −0.248302 | − | 1.52553i | ||||
\(606\) | −24.6042 | + | 42.6157i | −0.999476 | + | 1.73114i | ||||
\(607\) | −1.98483 | + | 18.8844i | −0.0805617 | + | 0.766494i | 0.877431 | + | 0.479702i | \(0.159255\pi\) |
−0.957993 | + | 0.286791i | \(0.907411\pi\) | |||||||
\(608\) | 2.01571 | − | 6.20370i | 0.0817477 | − | 0.251593i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.35485 | − | 2.43744i | 0.135834 | − | 0.0986892i | ||||
\(611\) | −14.2367 | − | 6.33858i | −0.575955 | − | 0.256431i | ||||
\(612\) | 7.41614 | + | 1.57635i | 0.299780 | + | 0.0637201i | ||||
\(613\) | 13.4908 | + | 14.9830i | 0.544888 | + | 0.605160i | 0.951200 | − | 0.308575i | \(-0.0998520\pi\) |
−0.406312 | + | 0.913734i | \(0.633185\pi\) | |||||||
\(614\) | −1.50091 | + | 14.2802i | −0.0605719 | + | 0.576303i | ||||
\(615\) | 21.0068 | 0.847077 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.03919 | 0.283387 | 0.141694 | − | 0.989911i | \(-0.454745\pi\) | ||||
0.141694 | + | 0.989911i | \(0.454745\pi\) | |||||||
\(618\) | 2.96670 | − | 28.2263i | 0.119338 | − | 1.13543i | ||||
\(619\) | −20.7986 | − | 23.0992i | −0.835968 | − | 0.928436i | 0.162331 | − | 0.986736i | \(-0.448099\pi\) |
−0.998299 | + | 0.0582999i | \(0.981432\pi\) | |||||||
\(620\) | 2.02020 | + | 0.429407i | 0.0811331 | + | 0.0172454i | ||||
\(621\) | 4.58027 | + | 2.03927i | 0.183800 | + | 0.0818330i | ||||
\(622\) | −24.1814 | + | 17.5688i | −0.969585 | + | 0.704445i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.47453 | + | 10.6935i | −0.139093 | + | 0.428083i | ||||
\(625\) | 1.20173 | − | 11.4337i | 0.0480691 | − | 0.457347i | ||||
\(626\) | −1.99974 | + | 3.46364i | −0.0799255 | + | 0.138435i | ||||
\(627\) | −13.8751 | + | 6.65447i | −0.554117 | + | 0.265754i | ||||
\(628\) | −8.14414 | − | 14.1061i | −0.324986 | − | 0.562893i | ||||
\(629\) | −15.7408 | − | 11.4364i | −0.627628 | − | 0.455998i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.78971 | + | 20.8966i | 0.270294 | + | 0.831880i | 0.990426 | + | 0.138043i | \(0.0440812\pi\) |
−0.720132 | + | 0.693837i | \(0.755919\pi\) | |||||||
\(632\) | 26.6243 | + | 11.8539i | 1.05906 | + | 0.471522i | ||||
\(633\) | −2.94622 | − | 28.0314i | −0.117102 | − | 1.11415i | ||||
\(634\) | 18.4426 | + | 3.92009i | 0.732449 | + | 0.155687i | ||||
\(635\) | −65.7548 | + | 13.9766i | −2.60940 | + | 0.554645i | ||||
\(636\) | −18.9722 | − | 13.7841i | −0.752298 | − | 0.546576i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.31039 | − | 28.2770i | 0.329012 | − | 1.11950i | ||||
\(639\) | 8.24705 | + | 14.2843i | 0.326248 | + | 0.565078i | ||||
\(640\) | 3.81998 | − | 1.70076i | 0.150998 | − | 0.0672286i | ||||
\(641\) | −8.89337 | − | 9.87709i | −0.351267 | − | 0.390122i | 0.541455 | − | 0.840730i | \(-0.317874\pi\) |
−0.892722 | + | 0.450608i | \(0.851207\pi\) | |||||||
\(642\) | −7.48760 | + | 8.31582i | −0.295512 | + | 0.328199i | ||||
\(643\) | −11.8848 | + | 8.63480i | −0.468690 | + | 0.340523i | −0.796930 | − | 0.604071i | \(-0.793544\pi\) |
0.328241 | + | 0.944594i | \(0.393544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.40510 | − | 28.9459i | −0.370325 | − | 1.13974i | ||||
\(646\) | −3.42117 | + | 0.727192i | −0.134604 | + | 0.0286110i | ||||
\(647\) | −5.61395 | + | 2.49949i | −0.220707 | + | 0.0982651i | −0.514112 | − | 0.857723i | \(-0.671878\pi\) |
0.293405 | + | 0.955988i | \(0.405212\pi\) | |||||||
\(648\) | 3.44213 | − | 5.96195i | 0.135220 | − | 0.234207i | ||||
\(649\) | −7.08311 | + | 8.32920i | −0.278036 | + | 0.326950i | ||||
\(650\) | −15.9404 | −0.625236 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.92589 | − | 5.92729i | 0.0754238 | − | 0.232131i | ||||
\(653\) | −27.2129 | + | 30.2230i | −1.06492 | + | 1.18272i | −0.0823978 | + | 0.996600i | \(0.526258\pi\) |
−0.982527 | + | 0.186119i | \(0.940409\pi\) | |||||||
\(654\) | 1.29102 | + | 12.2832i | 0.0504829 | + | 0.480313i | ||||
\(655\) | −1.84706 | − | 17.5736i | −0.0721704 | − | 0.686656i | ||||
\(656\) | 2.71666 | − | 3.01716i | 0.106068 | − | 0.117800i | ||||
\(657\) | 1.96020 | − | 6.03286i | 0.0764745 | − | 0.235364i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0090 | 0.701531 | 0.350765 | − | 0.936463i | \(-0.385921\pi\) | ||||
0.350765 | + | 0.936463i | \(0.385921\pi\) | |||||||
\(660\) | 22.9675 | + | 9.45605i | 0.894008 | + | 0.368076i | ||||
\(661\) | 8.57098 | − | 14.8454i | 0.333373 | − | 0.577418i | −0.649798 | − | 0.760107i | \(-0.725147\pi\) |
0.983171 | + | 0.182689i | \(0.0584800\pi\) | |||||||
\(662\) | −1.26069 | + | 0.561297i | −0.0489983 | + | 0.0218154i | ||||
\(663\) | −11.1373 | + | 2.36731i | −0.432537 | + | 0.0919387i | ||||
\(664\) | 15.2629 | + | 46.9744i | 0.592316 | + | 1.82296i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −46.9276 | + | 34.0949i | −1.81841 | + | 1.32115i | ||||
\(667\) | −4.30642 | + | 4.78276i | −0.166745 | + | 0.185189i | ||||
\(668\) | 11.0101 | + | 12.2279i | 0.425993 | + | 0.473113i | ||||
\(669\) | −45.4321 | + | 20.2277i | −1.75651 | + | 0.782048i | ||||
\(670\) | −4.62807 | − | 8.01605i | −0.178798 | − | 0.309687i | ||||
\(671\) | 2.82823 | − | 2.17979i | 0.109183 | − | 0.0841498i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.7632 | + | 13.6322i | 0.723268 | + | 0.525485i | 0.887426 | − | 0.460949i | \(-0.152491\pi\) |
−0.164159 | + | 0.986434i | \(0.552491\pi\) | |||||||
\(674\) | 22.3261 | − | 4.74557i | 0.859971 | − | 0.182792i | ||||
\(675\) | 42.1947 | + | 8.96877i | 1.62408 | + | 0.345208i | ||||
\(676\) | −0.693873 | − | 6.60176i | −0.0266874 | − | 0.253914i | ||||
\(677\) | −25.1869 | − | 11.2139i | −0.968012 | − | 0.430987i | −0.139046 | − | 0.990286i | \(-0.544404\pi\) |
−0.828966 | + | 0.559299i | \(0.811070\pi\) | |||||||
\(678\) | −10.4893 | − | 32.2826i | −0.402838 | − | 1.23981i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.6185 | + | 12.0741i | 0.637291 | + | 0.463019i | ||||
\(681\) | −18.0556 | − | 31.2731i | −0.691890 | − | 1.19839i | ||||
\(682\) | −2.86654 | − | 0.524954i | −0.109765 | − | 0.0201015i | ||||
\(683\) | −10.9675 | + | 18.9963i | −0.419661 | + | 0.726874i | −0.995905 | − | 0.0904032i | \(-0.971184\pi\) |
0.576244 | + | 0.817278i | \(0.304518\pi\) | |||||||
\(684\) | 0.665151 | − | 6.32849i | 0.0254327 | − | 0.241976i | ||||
\(685\) | 9.71923 | − | 29.9127i | 0.371353 | − | 1.14291i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.5775 | − | 7.68503i | 0.403558 | − | 0.293202i | ||||
\(688\) | −5.37372 | − | 2.39253i | −0.204871 | − | 0.0912145i | ||||
\(689\) | 21.8034 | + | 4.63445i | 0.830643 | + | 0.176559i | ||||
\(690\) | 5.94695 | + | 6.60476i | 0.226397 | + | 0.251439i | ||||
\(691\) | 2.68289 | − | 25.5260i | 0.102062 | − | 0.971055i | −0.816919 | − | 0.576753i | \(-0.804320\pi\) |
0.918981 | − | 0.394303i | \(-0.129014\pi\) | |||||||
\(692\) | 6.09830 | 0.231823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3913 | 1.15364 | ||||||||
\(695\) | 4.70235 | − | 44.7399i | 0.178370 | − | 1.69708i | ||||
\(696\) | 46.8826 | + | 52.0684i | 1.77708 | + | 1.97365i | ||||
\(697\) | 4.02152 | + | 0.854801i | 0.152326 | + | 0.0323779i | ||||
\(698\) | 8.12899 | + | 3.61926i | 0.307687 | + | 0.136991i | ||||
\(699\) | 55.1770 | − | 40.0884i | 2.08699 | − | 1.51628i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.69007 | + | 17.5122i | −0.214911 | + | 0.661428i | 0.784249 | + | 0.620446i | \(0.213049\pi\) |
−0.999160 | + | 0.0409817i | \(0.986951\pi\) | |||||||
\(702\) | −1.49042 | + | 14.1804i | −0.0562525 | + | 0.535206i | ||||
\(703\) | −8.16492 | + | 14.1421i | −0.307946 | + | 0.533378i | ||||
\(704\) | 24.8161 | − | 11.9018i | 0.935292 | − | 0.448565i | ||||
\(705\) | 37.3787 | + | 64.7419i | 1.40776 | + | 2.43832i | ||||
\(706\) | −5.35087 | − | 3.88764i | −0.201383 | − | 0.146313i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.20744 | − | 6.79380i | −0.0829607 | − | 0.255327i | ||||
\(709\) | 21.6164 | + | 9.62422i | 0.811819 | + | 0.361445i | 0.770291 | − | 0.637692i | \(-0.220111\pi\) |
0.0415280 | + | 0.999137i | \(0.486777\pi\) | |||||||
\(710\) | 1.28376 | + | 12.2142i | 0.0481787 | + | 0.458390i | ||||
\(711\) | 47.9761 | + | 10.1976i | 1.79925 | + | 0.382442i | ||||
\(712\) | −13.3437 | + | 2.83630i | −0.500077 | + | 0.106295i | ||||
\(713\) | 0.514827 | + | 0.374044i | 0.0192804 | + | 0.0140081i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.5993 | + | 0.668389i | −0.882565 | + | 0.0249963i | ||||
\(716\) | −1.37226 | − | 2.37682i | −0.0512838 | − | 0.0888261i | ||||
\(717\) | −23.0822 | + | 10.2769i | −0.862022 | + | 0.383797i | ||||
\(718\) | 21.1937 | + | 23.5380i | 0.790941 | + | 0.878429i | ||||
\(719\) | 7.44223 | − | 8.26544i | 0.277548 | − | 0.308249i | −0.588213 | − | 0.808706i | \(-0.700168\pi\) |
0.865761 | + | 0.500458i | \(0.166835\pi\) | |||||||
\(720\) | 27.6187 | − | 20.0662i | 1.02929 | − | 0.747823i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.63627 | − | 17.3467i | −0.209760 | − | 0.645576i | ||||
\(723\) | 52.9808 | − | 11.2614i | 1.97038 | − | 0.418817i | ||||
\(724\) | −10.9529 | + | 4.87653i | −0.407060 | + | 0.181235i | ||||
\(725\) | −27.6865 | + | 47.9544i | −1.02825 | + | 1.78098i | ||||
\(726\) | −32.7722 | − | 12.4198i | −1.21629 | − | 0.460941i | ||||
\(727\) | 42.4803 | 1.57551 | 0.787753 | − | 0.615991i | \(-0.211244\pi\) | ||||
0.787753 | + | 0.615991i | \(0.211244\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.8826 | + | 39.6485i | −0.477133 | + | 1.46846i | ||||
\(730\) | 3.16045 | − | 3.51004i | 0.116974 | − | 0.129912i | ||||
\(731\) | −0.622646 | − | 5.92408i | −0.0230294 | − | 0.219110i | ||||
\(732\) | 0.243857 | + | 2.32014i | 0.00901321 | + | 0.0857550i | ||||
\(733\) | 14.8470 | − | 16.4892i | 0.548385 | − | 0.609043i | −0.403695 | − | 0.914894i | \(-0.632274\pi\) |
0.952080 | + | 0.305851i | \(0.0989408\pi\) | |||||||
\(734\) | −10.4699 | + | 32.2231i | −0.386452 | + | 1.18938i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.24402 | −0.119576 | ||||||||
\(737\) | −4.17897 | − | 6.78690i | −0.153935 | − | 0.249999i | ||||
\(738\) | 6.12854 | − | 10.6149i | 0.225595 | − | 0.390741i | ||||
\(739\) | 26.9022 | − | 11.9776i | 0.989613 | − | 0.440604i | 0.152898 | − | 0.988242i | \(-0.451140\pi\) |
0.836715 | + | 0.547638i | \(0.184473\pi\) | |||||||
\(740\) | 25.7817 | − | 5.48006i | 0.947753 | − | 0.201451i | ||||
\(741\) | 2.95305 | + | 9.08855i | 0.108483 | + | 0.333876i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6772 | + | 9.93704i | −0.501766 | + | 0.364555i | −0.809691 | − | 0.586856i | \(-0.800365\pi\) |
0.307925 | + | 0.951411i | \(0.400365\pi\) | |||||||
\(744\) | 4.63565 | − | 5.14841i | 0.169951 | − | 0.188750i | ||||
\(745\) | −7.27649 | − | 8.08136i | −0.266590 | − | 0.296078i | ||||
\(746\) | 14.6838 | − | 6.53767i | 0.537613 | − | 0.239361i | ||||
\(747\) | 41.5622 | + | 71.9879i | 1.52068 | + | 2.63390i | ||||
\(748\) | 4.01208 | + | 2.74484i | 0.146696 | + | 0.100361i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.3220 | + | 12.5851i | 0.632508 | + | 0.459544i | ||||
\(751\) | 1.51756 | − | 0.322568i | 0.0553766 | − | 0.0117707i | −0.180140 | − | 0.983641i | \(-0.557655\pi\) |
0.235517 | + | 0.971870i | \(0.424322\pi\) | |||||||
\(752\) | 14.1326 | + | 3.00398i | 0.515364 | + | 0.109544i | ||||
\(753\) | −0.856713 | − | 8.15108i | −0.0312204 | − | 0.297042i | ||||
\(754\) | −16.7205 | − | 7.44446i | −0.608926 | − | 0.271111i | ||||
\(755\) | 3.06188 | + | 9.42349i | 0.111433 | + | 0.342956i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1505 | − | 7.37474i | −0.368925 | − | 0.268040i | 0.387840 | − | 0.921727i | \(-0.373221\pi\) |
−0.756765 | + | 0.653687i | \(0.773221\pi\) | |||||||
\(758\) | 12.4860 | + | 21.6265i | 0.453513 | + | 0.785508i | ||||
\(759\) | 5.27979 | + | 5.54000i | 0.191644 | + | 0.201089i | ||||
\(760\) | 8.62019 | − | 14.9306i | 0.312687 | − | 0.541590i | ||||
\(761\) | 0.944347 | − | 8.98487i | 0.0342326 | − | 0.325701i | −0.963982 | − | 0.265968i | \(-0.914308\pi\) |
0.998214 | − | 0.0597330i | \(-0.0190249\pi\) | |||||||
\(762\) | −19.1503 | + | 58.9386i | −0.693742 | + | 2.13512i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.263115 | − | 0.191164i | 0.00951916 | − | 0.00691608i | ||||
\(765\) | 31.5819 | + | 14.0612i | 1.14185 | + | 0.508383i | ||||
\(766\) | −36.7134 | − | 7.80368i | −1.32651 | − | 0.281958i | ||||
\(767\) | 4.54335 | + | 5.04590i | 0.164051 | + | 0.182197i | ||||
\(768\) | −4.55663 | + | 43.3534i | −0.164423 | + | 1.56438i | ||||
\(769\) | −16.1383 | −0.581963 | −0.290981 | − | 0.956729i | \(-0.593982\pi\) | ||||
−0.290981 | + | 0.956729i | \(0.593982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −64.0829 | −2.30789 | ||||||||
\(772\) | −1.20228 | + | 11.4390i | −0.0432711 | + | 0.411697i | ||||
\(773\) | −12.3210 | − | 13.6839i | −0.443155 | − | 0.492174i | 0.479639 | − | 0.877466i | \(-0.340767\pi\) |
−0.922795 | + | 0.385292i | \(0.874101\pi\) | |||||||
\(774\) | −17.3705 | − | 3.69221i | −0.624369 | − | 0.132714i | ||||
\(775\) | 5.00181 | + | 2.22695i | 0.179670 | + | 0.0799943i | ||||
\(776\) | 16.0838 | − | 11.6855i | 0.577374 | − | 0.419487i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.836118 | − | 2.57331i | 0.0299763 | − | 0.0922575i | ||||
\(779\) | 0.360689 | − | 3.43173i | 0.0129230 | − | 0.122954i | ||||
\(780\) | 7.71228 | − | 13.3581i | 0.276144 | − | 0.478295i | ||||
\(781\) | 1.40274 | + | 10.4819i | 0.0501941 | + | 0.375073i | ||||
\(782\) | 0.869719 | + | 1.50640i | 0.0311011 | + | 0.0538687i | ||||
\(783\) | 40.0711 | + | 29.1133i | 1.43202 | + | 1.04043i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.9505 | − | 70.6344i | −0.819139 | − | 2.52105i | ||||
\(786\) | −14.8815 | − | 6.62565i | −0.530804 | − | 0.236329i | ||||
\(787\) | −4.91148 | − | 46.7296i | −0.175075 | − | 1.66573i | −0.631053 | − | 0.775740i | \(-0.717377\pi\) |
0.455977 | − | 0.889991i | \(-0.349290\pi\) | |||||||
\(788\) | −15.4272 | − | 3.27916i | −0.549572 | − | 0.116815i | ||||
\(789\) | 2.77036 | − | 0.588857i | 0.0986273 | − | 0.0209639i | ||||
\(790\) | 29.5461 | + | 21.4665i | 1.05120 | + | 0.763744i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 41.7671 | − | 32.1910i | 1.48413 | − | 1.14386i | ||||
\(793\) | −1.10874 | − | 1.92039i | −0.0393725 | − | 0.0681952i | ||||
\(794\) | −6.00379 | + | 2.67306i | −0.213067 | + | 0.0948634i | ||||
\(795\) | −71.5495 | − | 79.4637i | −2.53760 | − | 2.81829i | ||||
\(796\) | −4.28345 | + | 4.75726i | −0.151823 | + | 0.168616i | ||||
\(797\) | 2.52781 | − | 1.83656i | 0.0895395 | − | 0.0650543i | −0.542115 | − | 0.840304i | \(-0.682376\pi\) |
0.631654 | + | 0.775250i | \(0.282376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.52129 | + | 13.9151i | 0.159952 | + | 0.492281i | ||||
\(800\) | −27.3011 | + | 5.80304i | −0.965241 | + | 0.205168i | ||||
\(801\) | −20.9738 | + | 9.33812i | −0.741071 | + | 0.329946i | ||||
\(802\) | −6.26307 | + | 10.8480i | −0.221157 | + | 0.383055i | ||||
\(803\) | 2.63476 | − | 3.09828i | 0.0929786 | − | 0.109336i | ||||
\(804\) | 5.20732 | 0.183648 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.559243 | + | 1.72117i | −0.0196985 | + | 0.0606258i | ||||
\(807\) | 13.7546 | − | 15.2760i | 0.484185 | − | 0.537742i | ||||
\(808\) | −4.96221 | − | 47.2123i | −0.174570 | − | 1.66092i | ||||
\(809\) | 3.42076 | + | 32.5464i | 0.120268 | + | 1.14427i | 0.873605 | + | 0.486636i | \(0.161776\pi\) |
−0.753337 | + | 0.657634i | \(0.771557\pi\) | |||||||
\(810\) | 5.77249 | − | 6.41100i | 0.202825 | − | 0.225260i | ||||
\(811\) | 10.0929 | − | 31.0627i | 0.354410 | − | 1.09076i | −0.601941 | − | 0.798540i | \(-0.705606\pi\) |
0.956351 | − | 0.292220i | \(-0.0943941\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 77.6578 | 2.72358 | ||||||||
\(814\) | −36.1448 | + | 8.75925i | −1.26687 | + | 0.307011i | ||||
\(815\) | 14.2087 | − | 24.6102i | 0.497710 | − | 0.862058i | ||||
\(816\) | 9.64375 | − | 4.29367i | 0.337599 | − | 0.150309i | ||||
\(817\) | −4.89016 | + | 1.03944i | −0.171085 | + | 0.0363652i | ||||
\(818\) | 10.1024 | + | 31.0921i | 0.353224 | + | 1.08711i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.50589 | + | 3.27372i | −0.157352 | + | 0.114323i | ||||
\(821\) | −4.97259 | + | 5.52262i | −0.173545 | + | 0.192741i | −0.823642 | − | 0.567110i | \(-0.808061\pi\) |
0.650097 | + | 0.759851i | \(0.274728\pi\) | |||||||
\(822\) | −19.4013 | − | 21.5473i | −0.676698 | − | 0.751549i | ||||
\(823\) | 5.99164 | − | 2.66765i | 0.208855 | − | 0.0929884i | −0.299643 | − | 0.954051i | \(-0.596868\pi\) |
0.508498 | + | 0.861063i | \(0.330201\pi\) | |||||||
\(824\) | 13.6903 | + | 23.7122i | 0.476923 | + | 0.826055i | ||||
\(825\) | 54.3440 | + | 37.1790i | 1.89202 | + | 1.29441i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.2982 | − | 14.0209i | −0.671063 | − | 0.487556i | 0.199318 | − | 0.979935i | \(-0.436127\pi\) |
−0.870381 | + | 0.492379i | \(0.836127\pi\) | |||||||
\(828\) | −3.09549 | + | 0.657966i | −0.107576 | + | 0.0228659i | ||||
\(829\) | 25.5718 | + | 5.43546i | 0.888147 | + | 0.188781i | 0.629324 | − | 0.777143i | \(-0.283332\pi\) |
0.258823 | + | 0.965925i | \(0.416665\pi\) | |||||||
\(830\) | 6.46971 | + | 61.5552i | 0.224567 | + | 2.13661i | ||||
\(831\) | −54.8073 | − | 24.4018i | −1.90124 | − | 0.846488i | ||||
\(832\) | −5.28164 | − | 16.2552i | −0.183108 | − | 0.563548i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −33.5512 | − | 24.3764i | −1.16178 | − | 0.844085i | ||||
\(835\) | 37.5133 | + | 64.9749i | 1.29820 | + | 2.24855i | ||||
\(836\) | 1.93912 | − | 3.58966i | 0.0670657 | − | 0.124151i | ||||
\(837\) | 2.44874 | − | 4.24133i | 0.0846407 | − | 0.146602i | ||||
\(838\) | 2.36317 | − | 22.4840i | 0.0816342 | − | 0.776698i | ||||
\(839\) | 10.5959 | − | 32.6107i | 0.365810 | − | 1.12585i | −0.583662 | − | 0.811997i | \(-0.698381\pi\) |
0.949472 | − | 0.313851i | \(-0.101619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9754 | + | 20.3253i | −0.964670 | + | 0.700874i | ||||
\(842\) | −3.11546 | − | 1.38709i | −0.107366 | − | 0.0478024i | ||||
\(843\) | −78.7395 | − | 16.7366i | −2.71193 | − | 0.576439i | ||||
\(844\) | 5.00039 | + | 5.55350i | 0.172121 | + | 0.191159i | ||||
\(845\) | 3.16384 | − | 30.1019i | 0.108839 | − | 1.03554i | ||||
\(846\) | 43.6195 | 1.49967 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.6661 | −0.709678 | ||||||||
\(849\) | −7.82682 | + | 74.4672i | −0.268616 | + | 2.55571i | ||||
\(850\) | 10.0141 | + | 11.1218i | 0.343482 | + | 0.381475i | ||||
\(851\) | 7.94374 | + | 1.68849i | 0.272308 | + | 0.0578809i | ||||
\(852\) | −6.31197 | − | 2.81027i | −0.216244 | − | 0.0962782i | ||||
\(853\) | −17.3002 | + | 12.5693i | −0.592347 | + | 0.430365i | −0.843154 | − | 0.537672i | \(-0.819304\pi\) |
0.250807 | + | 0.968037i | \(0.419304\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.96608 | − | 27.5948i | 0.306634 | − | 0.943721i | ||||
\(856\) | 1.12841 | − | 10.7361i | 0.0385684 | − | 0.366954i | ||||
\(857\) | −21.4348 | + | 37.1262i | −0.732200 | + | 1.26821i | 0.223741 | + | 0.974649i | \(0.428173\pi\) |
−0.955941 | + | 0.293559i | \(0.905160\pi\) | |||||||
\(858\) | −10.3442 | + | 19.1489i | −0.353143 | + | 0.653734i | ||||
\(859\) | 15.1958 | + | 26.3198i | 0.518473 | + | 0.898022i | 0.999770 | + | 0.0214638i | \(0.00683266\pi\) |
−0.481297 | + | 0.876558i | \(0.659834\pi\) | |||||||
\(860\) | 6.52831 | + | 4.74310i | 0.222614 | + | 0.161738i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.59737 | + | 7.99389i | 0.0884668 | + | 0.272273i | ||||
\(863\) | 10.7967 | + | 4.80698i | 0.367523 | + | 0.163632i | 0.582184 | − | 0.813057i | \(-0.302198\pi\) |
−0.214662 | + | 0.976688i | \(0.568865\pi\) | |||||||
\(864\) | 2.60967 | + | 24.8294i | 0.0887829 | + | 0.844712i | ||||
\(865\) | 27.1987 | + | 5.78126i | 0.924784 | + | 0.196569i | ||||
\(866\) | 35.0598 | − | 7.45218i | 1.19138 | − | 0.253236i | ||||
\(867\) | −30.6698 | − | 22.2829i | −1.04160 | − | 0.756766i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.9548 | + | 17.7568i | 0.880456 | + | 0.602357i | ||||
\(870\) | 43.9001 | + | 76.0373i | 1.48835 | + | 2.57790i | ||||
\(871\) | −4.52171 | + | 2.01320i | −0.153212 | + | 0.0682146i | ||||
\(872\) | −7.97282 | − | 8.85471i | −0.269994 | − | 0.299858i | ||||
\(873\) | 22.3880 | − | 24.8644i | 0.757718 | − | 0.841531i | ||||
\(874\) | 1.18108 | − | 0.858104i | 0.0399506 | − | 0.0290258i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.821118 | + | 2.52714i | 0.0277430 | + | 0.0853842i | ||||
\(877\) | 9.00373 | − | 1.91380i | 0.304034 | − | 0.0646245i | −0.0533683 | − | 0.998575i | \(-0.516996\pi\) |
0.357403 | + | 0.933950i | \(0.383662\pi\) | |||||||
\(878\) | −4.75180 | + | 2.11564i | −0.160366 | + | 0.0713993i | ||||
\(879\) | −6.38067 | + | 11.0516i | −0.215215 | + | 0.372763i | ||||
\(880\) | 21.2726 | − | 5.15517i | 0.717101 | − | 0.173781i | ||||
\(881\) | −41.9030 | −1.41175 | −0.705874 | − | 0.708338i | \(-0.749445\pi\) | ||||
−0.705874 | + | 0.708338i | \(0.749445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.95906 | + | 15.2624i | −0.166886 | + | 0.513621i | −0.999170 | − | 0.0407275i | \(-0.987032\pi\) |
0.832285 | + | 0.554348i | \(0.187032\pi\) | |||||||
\(884\) | 2.01999 | − | 2.24343i | 0.0679396 | − | 0.0754546i | ||||
\(885\) | −3.40468 | − | 32.3933i | −0.114447 | − | 1.08889i | ||||
\(886\) | −2.01268 | − | 19.1493i | −0.0676172 | − | 0.643334i | ||||
\(887\) | −22.6490 | + | 25.1542i | −0.760478 | + | 0.844596i | −0.991736 | − | 0.128296i | \(-0.959049\pi\) |
0.231258 | + | 0.972892i | \(0.425716\pi\) | |||||||
\(888\) | 27.3211 | − | 84.0858i | 0.916838 | − | 2.82174i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −17.0949 | −0.573024 | ||||||||
\(891\) | 4.81232 | − | 5.65892i | 0.161219 | − | 0.189581i | ||||
\(892\) | 6.59273 | − | 11.4189i | 0.220741 | − | 0.382335i | ||||
\(893\) | 11.2182 | − | 4.99466i | 0.375402 | − | 0.167140i | ||||
\(894\) | −9.80585 | + | 2.08430i | −0.327957 | + | 0.0697094i | ||||
\(895\) | −3.86708 | − | 11.9017i | −0.129262 | − | 0.397829i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.84490 | − | 2.79348i | 0.128377 | − | 0.0932716i | ||||
\(898\) | −12.4835 | + | 13.8643i | −0.416579 | + | 0.462658i | ||||
\(899\) | 4.20656 | + | 4.67186i | 0.140297 | + | 0.155815i | ||||
\(900\) | −24.8741 | + | 11.0747i | −0.829137 | + | 0.369155i | ||||
\(901\) | −10.4638 | − | 18.1239i | −0.348601 | − | 0.603795i | ||||
\(902\) | 6.22455 | − | 4.79741i | 0.207255 | − | 0.159736i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.4925 | + | 19.2479i | 0.881127 | + | 0.640176i | ||||
\(905\) | −53.4733 | + | 11.3661i | −1.77751 | + | 0.377822i | ||||
\(906\) | 8.93470 | + | 1.89913i | 0.296836 | + | 0.0630943i | ||||
\(907\) | 4.60985 | + | 43.8598i | 0.153067 | + | 1.45634i | 0.753913 | + | 0.656974i | \(0.228164\pi\) |
−0.600846 | + | 0.799365i | \(0.705169\pi\) | |||||||
\(908\) | 8.74648 | + | 3.89418i | 0.290262 | + | 0.129233i | ||||
\(909\) | −24.6886 | − | 75.9837i | −0.818869 | − | 2.52022i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.1075 | − | 29.1398i | −1.32882 | − | 0.965446i | −0.999777 | − | 0.0211316i | \(-0.993273\pi\) |
−0.329045 | − | 0.944314i | \(-0.606727\pi\) | |||||||
\(912\) | −4.42994 | − | 7.67288i | −0.146690 | − | 0.254075i | ||||
\(913\) | 7.06934 | + | 52.8252i | 0.233961 | + | 1.74826i | ||||
\(914\) | 12.0905 | − | 20.9414i | 0.399919 | − | 0.692680i | ||||
\(915\) | −1.11191 | + | 10.5791i | −0.0367586 | + | 0.349735i | ||||
\(916\) | −1.07120 | + | 3.29682i | −0.0353935 | + | 0.108930i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.8302 | − | 7.86857i | 0.357448 | − | 0.259701i | ||||
\(919\) | −37.2659 | − | 16.5919i | −1.22929 | − | 0.547315i | −0.313736 | − | 0.949510i | \(-0.601581\pi\) |
−0.915554 | + | 0.402195i | \(0.868247\pi\) | |||||||
\(920\) | −8.38668 | − | 1.78264i | −0.276501 | − | 0.0587720i | ||||
\(921\) | −24.6463 | − | 27.3725i | −0.812122 | − | 0.901953i | ||||
\(922\) | 0.708022 | − | 6.73638i | 0.0233175 | − | 0.221851i | ||||
\(923\) | 6.56740 | 0.216169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.8737 | 2.29743 | ||||||||
\(926\) | 0.599614 | − | 5.70495i | 0.0197045 | − | 0.187476i | ||||
\(927\) | 30.8337 | + | 34.2443i | 1.01271 | + | 1.12473i | ||||
\(928\) | −31.3473 | − | 6.66307i | −1.02903 | − | 0.218726i | ||||
\(929\) | 37.8143 | + | 16.8360i | 1.24065 | + | 0.552372i | 0.918914 | − | 0.394459i | \(-0.129068\pi\) |
0.321733 | + | 0.946830i | \(0.395735\pi\) | |||||||
\(930\) | 7.02348 | − | 5.10286i | 0.230309 | − | 0.167329i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.58785 | + | 17.1976i | −0.183036 | + | 0.563327i | ||||
\(933\) | 8.01452 | − | 76.2530i | 0.262384 | − | 2.49641i | ||||
\(934\) | 2.18395 | − | 3.78271i | 0.0714610 | − | 0.123774i | ||||
\(935\) | 15.2919 | + | 16.0456i | 0.500100 | + | 0.524747i | ||||
\(936\) | −16.3738 | − | 28.3602i | −0.535194 | − | 0.926982i | ||||
\(937\) | −1.29155 | − | 0.938364i | −0.0421930 | − | 0.0306550i | 0.566489 | − | 0.824069i | \(-0.308301\pi\) |
−0.608682 | + | 0.793414i | \(0.708301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.17033 | − | 9.75727i | −0.103460 | − | 0.318416i | ||||
\(940\) | −18.1070 | − | 8.06177i | −0.590586 | − | 0.262946i | ||||
\(941\) | −0.742975 | − | 7.06893i | −0.0242203 | − | 0.230441i | −0.999935 | − | 0.0113957i | \(-0.996373\pi\) |
0.975715 | − | 0.219045i | \(-0.0702941\pi\) | |||||||
\(942\) | −66.9706 | − | 14.2350i | −2.18202 | − | 0.463803i | ||||
\(943\) | −1.67858 | + | 0.356793i | −0.0546620 | + | 0.0116188i | ||||
\(944\) | −5.09287 | − | 3.70019i | −0.165759 | − | 0.120431i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.39731 | − | 6.42910i | −0.305533 | − | 0.209028i | ||||
\(947\) | 1.22993 | + | 2.13030i | 0.0399674 | + | 0.0692255i | 0.885317 | − | 0.464988i | \(-0.153941\pi\) |
−0.845350 | + | 0.534213i | \(0.820608\pi\) | |||||||
\(948\) | −18.7697 | + | 8.35681i | −0.609611 | + | 0.271416i | ||||
\(949\) | −1.69002 | − | 1.87696i | −0.0548605 | − | 0.0609288i | ||||
\(950\) | 8.40476 | − | 9.33443i | 0.272686 | − | 0.302849i | ||||
\(951\) | −39.1286 | + | 28.4286i | −1.26883 | + | 0.921861i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.83790 | − | 27.2003i | −0.286288 | − | 0.881103i | −0.986010 | − | 0.166688i | \(-0.946693\pi\) |
0.699722 | − | 0.714415i | \(-0.253307\pi\) | |||||||
\(954\) | −61.0276 | + | 12.9718i | −1.97584 | + | 0.419978i | ||||
\(955\) | 1.35473 | − | 0.603165i | 0.0438380 | − | 0.0195180i | ||||
\(956\) | 3.34950 | − | 5.80150i | 0.108331 | − | 0.187634i | ||||
\(957\) | 39.6402 | + | 64.3781i | 1.28139 | + | 2.08105i | ||||
\(958\) | −16.8428 | −0.544168 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −25.3364 | + | 77.9774i | −0.817728 | + | 2.51671i | ||||
\(961\) | −20.3271 | + | 22.5755i | −0.655713 | + | 0.728243i | ||||
\(962\) | 2.41418 | + | 22.9694i | 0.0778363 | + | 0.740563i | ||||
\(963\) | −1.89907 | − | 18.0685i | −0.0611968 | − | 0.582248i | ||||
\(964\) | −9.60920 | + | 10.6721i | −0.309492 | + | 0.343725i | ||||
\(965\) | −16.2065 | + | 49.8785i | −0.521706 | + | 1.60565i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.213338 | −0.00686047 | −0.00343024 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00343024 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(968\) | 32.6205 | − | 8.89010i | 1.04846 | − | 0.285739i | ||||
\(969\) | 4.48601 | − | 7.76999i | 0.144111 | − | 0.249608i | ||||
\(970\) | 22.7591 | − | 10.1330i | 0.730751 | − | 0.325351i | ||||
\(971\) | 0.810100 | − | 0.172192i | 0.0259974 | − | 0.00552591i | −0.194895 | − | 0.980824i | \(-0.562436\pi\) |
0.220892 | + | 0.975298i | \(0.429103\pi\) | |||||||
\(972\) | −2.86507 | − | 8.81779i | −0.0918973 | − | 0.282831i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.6098 | + | 16.4270i | −0.724465 | + | 0.526354i | ||||
\(975\) | 27.3609 | − | 30.3874i | 0.876251 | − | 0.973175i | ||||
\(976\) | 1.37566 | + | 1.52782i | 0.0440337 | + | 0.0489044i | ||||
\(977\) | 8.91359 | − | 3.96859i | 0.285171 | − | 0.126966i | −0.259166 | − | 0.965833i | \(-0.583448\pi\) |
0.544337 | + | 0.838866i | \(0.316781\pi\) | |||||||
\(978\) | −13.0986 | − | 22.6874i | −0.418847 | − | 0.725464i | ||||
\(979\) | −14.7143 | + | 0.416743i | −0.470271 | + | 0.0133192i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.2230 | − | 11.7867i | −0.517961 | − | 0.376321i | ||||
\(982\) | −40.5748 | + | 8.62445i | −1.29480 | + | 0.275217i | ||||
\(983\) | −44.1338 | − | 9.38093i | −1.40765 | − | 0.299205i | −0.559442 | − | 0.828870i | \(-0.688985\pi\) |
−0.848207 | + | 0.529664i | \(0.822318\pi\) | |||||||
\(984\) | 1.95284 | + | 18.5801i | 0.0622544 | + | 0.592311i | ||||
\(985\) | −65.6974 | − | 29.2504i | −2.09329 | − | 0.931994i | ||||
\(986\) | 5.31011 | + | 16.3428i | 0.169108 | + | 0.520462i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.04978 | − | 1.48926i | −0.0652123 | − | 0.0473795i | ||||
\(989\) | 1.24316 | + | 2.15322i | 0.0395302 | + | 0.0684684i | ||||
\(990\) | 59.5828 | − | 28.5758i | 1.89367 | − | 0.908200i | ||||
\(991\) | −26.7702 | + | 46.3674i | −0.850384 | + | 1.47291i | 0.0304776 | + | 0.999535i | \(0.490297\pi\) |
−0.880862 | + | 0.473373i | \(0.843036\pi\) | |||||||
\(992\) | −0.331229 | + | 3.15144i | −0.0105165 | + | 0.100058i | ||||
\(993\) | 1.09391 | − | 3.36671i | 0.0347142 | − | 0.106839i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.6143 | + | 17.1568i | −0.748624 | + | 0.543907i | ||||
\(996\) | −31.8101 | − | 14.1628i | −1.00794 | − | 0.448765i | ||||
\(997\) | 30.4798 | + | 6.47867i | 0.965304 | + | 0.205182i | 0.663490 | − | 0.748185i | \(-0.269075\pi\) |
0.301814 | + | 0.953367i | \(0.402408\pi\) | |||||||
\(998\) | −23.7240 | − | 26.3481i | −0.750969 | − | 0.834036i | ||||
\(999\) | 6.53316 | − | 62.1589i | 0.206700 | − | 1.96662i |
(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 | 539.2.q.g.312.2 | 32 | ||
7.2 | even | 3 | inner | 539.2.q.g.422.3 | 32 | ||
7.3 | odd | 6 | 539.2.f.e.246.2 | 16 | |||
7.4 | even | 3 | 77.2.f.b.15.2 | ✓ | 16 | ||
7.5 | odd | 6 | 539.2.q.f.422.3 | 32 | |||
7.6 | odd | 2 | 539.2.q.f.312.2 | 32 | |||
11.3 | even | 5 | inner | 539.2.q.g.410.3 | 32 | ||
21.11 | odd | 6 | 693.2.m.i.631.3 | 16 | |||
77.3 | odd | 30 | 539.2.f.e.344.2 | 16 | |||
77.4 | even | 15 | 847.2.f.w.372.3 | 16 | |||
77.17 | even | 30 | 5929.2.a.bs.1.3 | 8 | |||
77.18 | odd | 30 | 847.2.f.v.372.2 | 16 | |||
77.25 | even | 15 | 77.2.f.b.36.2 | yes | 16 | ||
77.32 | odd | 6 | 847.2.f.x.323.3 | 16 | |||
77.38 | odd | 30 | 5929.2.a.bt.1.6 | 8 | |||
77.39 | odd | 30 | 847.2.a.o.1.3 | 8 | |||
77.46 | odd | 30 | 847.2.f.v.148.2 | 16 | |||
77.47 | odd | 30 | 539.2.q.f.520.2 | 32 | |||
77.53 | even | 15 | 847.2.f.w.148.3 | 16 | |||
77.58 | even | 15 | inner | 539.2.q.g.520.2 | 32 | ||
77.60 | even | 15 | 847.2.a.p.1.6 | 8 | |||
77.69 | odd | 10 | 539.2.q.f.410.3 | 32 | |||
77.74 | odd | 30 | 847.2.f.x.729.3 | 16 | |||
231.116 | even | 30 | 7623.2.a.cw.1.6 | 8 | |||
231.137 | odd | 30 | 7623.2.a.ct.1.3 | 8 | |||
231.179 | odd | 30 | 693.2.m.i.190.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.2 | ✓ | 16 | 7.4 | even | 3 | ||
77.2.f.b.36.2 | yes | 16 | 77.25 | even | 15 | ||
539.2.f.e.246.2 | 16 | 7.3 | odd | 6 | |||
539.2.f.e.344.2 | 16 | 77.3 | odd | 30 | |||
539.2.q.f.312.2 | 32 | 7.6 | odd | 2 | |||
539.2.q.f.410.3 | 32 | 77.69 | odd | 10 | |||
539.2.q.f.422.3 | 32 | 7.5 | odd | 6 | |||
539.2.q.f.520.2 | 32 | 77.47 | odd | 30 | |||
539.2.q.g.312.2 | 32 | 1.1 | even | 1 | trivial | ||
539.2.q.g.410.3 | 32 | 11.3 | even | 5 | inner | ||
539.2.q.g.422.3 | 32 | 7.2 | even | 3 | inner | ||
539.2.q.g.520.2 | 32 | 77.58 | even | 15 | inner | ||
693.2.m.i.190.3 | 16 | 231.179 | odd | 30 | |||
693.2.m.i.631.3 | 16 | 21.11 | odd | 6 | |||
847.2.a.o.1.3 | 8 | 77.39 | odd | 30 | |||
847.2.a.p.1.6 | 8 | 77.60 | even | 15 | |||
847.2.f.v.148.2 | 16 | 77.46 | odd | 30 | |||
847.2.f.v.372.2 | 16 | 77.18 | odd | 30 | |||
847.2.f.w.148.3 | 16 | 77.53 | even | 15 | |||
847.2.f.w.372.3 | 16 | 77.4 | even | 15 | |||
847.2.f.x.323.3 | 16 | 77.32 | odd | 6 | |||
847.2.f.x.729.3 | 16 | 77.74 | odd | 30 | |||
5929.2.a.bs.1.3 | 8 | 77.17 | even | 30 | |||
5929.2.a.bt.1.6 | 8 | 77.38 | odd | 30 | |||
7623.2.a.ct.1.3 | 8 | 231.137 | odd | 30 | |||
7623.2.a.cw.1.6 | 8 | 231.116 | even | 30 |