Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 499.2 | ||
Root | \(-0.701538 - 0.227943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.499 |
Dual form | 825.2.bx.f.124.2 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.154211 | + | 0.212253i | −0.109044 | + | 0.150086i | −0.860051 | − | 0.510208i | \(-0.829568\pi\) |
0.751007 | + | 0.660294i | \(0.229568\pi\) | |||||||
\(3\) | −0.951057 | − | 0.309017i | −0.549093 | − | 0.178411i | ||||
\(4\) | 0.596764 | + | 1.83665i | 0.298382 | + | 0.918325i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.212253 | − | 0.154211i | 0.0866521 | − | 0.0629564i | ||||
\(7\) | 3.03722 | − | 0.986854i | 1.14796 | − | 0.372996i | 0.327587 | − | 0.944821i | \(-0.393764\pi\) |
0.820376 | + | 0.571825i | \(0.193764\pi\) | |||||||
\(8\) | −0.980901 | − | 0.318714i | −0.346801 | − | 0.112682i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.27115 | + | 0.547326i | 0.986289 | + | 0.165025i | ||||
\(12\) | − | 1.93117i | − | 0.557480i | ||||||
\(13\) | 0.658088 | − | 0.905781i | 0.182521 | − | 0.251218i | −0.707946 | − | 0.706267i | \(-0.750378\pi\) |
0.890467 | + | 0.455048i | \(0.150378\pi\) | |||||||
\(14\) | −0.258911 | + | 0.796845i | −0.0691968 | + | 0.212966i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.90578 | + | 2.11117i | −0.726445 | + | 0.527793i | ||||
\(17\) | 0.0518582 | + | 0.0713767i | 0.0125775 | + | 0.0173114i | 0.815259 | − | 0.579096i | \(-0.196594\pi\) |
−0.802682 | + | 0.596407i | \(0.796594\pi\) | |||||||
\(18\) | −0.249519 | + | 0.0810736i | −0.0588122 | + | 0.0191092i | ||||
\(19\) | 0.0212704 | − | 0.0654637i | 0.00487977 | − | 0.0150184i | −0.948587 | − | 0.316517i | \(-0.897487\pi\) |
0.953467 | + | 0.301498i | \(0.0974867\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.19353 | −0.696885 | ||||||||
\(22\) | −0.620620 | + | 0.609909i | −0.132317 | + | 0.130033i | ||||
\(23\) | − | 6.65450i | − | 1.38756i | −0.720187 | − | 0.693780i | \(-0.755944\pi\) | ||
0.720187 | − | 0.693780i | \(-0.244056\pi\) | |||||||
\(24\) | 0.834404 | + | 0.606230i | 0.170322 | + | 0.123746i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0907705 | + | 0.279363i | 0.0178016 | + | 0.0547876i | ||||
\(27\) | −0.587785 | − | 0.809017i | −0.113119 | − | 0.155695i | ||||
\(28\) | 3.62501 | + | 4.98940i | 0.685062 | + | 0.942908i | ||||
\(29\) | −1.15444 | − | 3.55299i | −0.214373 | − | 0.659773i | −0.999197 | − | 0.0400546i | \(-0.987247\pi\) |
0.784824 | − | 0.619718i | \(-0.212753\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.75430 | + | 5.63383i | 1.39271 | + | 1.01187i | 0.995562 | + | 0.0941130i | \(0.0300015\pi\) |
0.397152 | + | 0.917753i | \(0.369998\pi\) | |||||||
\(32\) | − | 3.00509i | − | 0.531230i | ||||||
\(33\) | −2.94192 | − | 1.53138i | −0.512122 | − | 0.266579i | ||||
\(34\) | −0.0231471 | −0.00396969 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.596764 | + | 1.83665i | −0.0994606 | + | 0.306108i | ||||
\(37\) | 7.92250 | − | 2.57418i | 1.30245 | − | 0.423192i | 0.426017 | − | 0.904715i | \(-0.359916\pi\) |
0.876433 | + | 0.481523i | \(0.159916\pi\) | |||||||
\(38\) | 0.0106148 | + | 0.0146100i | 0.00172194 | + | 0.00237005i | ||||
\(39\) | −0.905781 | + | 0.658088i | −0.145041 | + | 0.105378i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.60489 | + | 11.0947i | −0.562989 | + | 1.73270i | 0.110863 | + | 0.993836i | \(0.464638\pi\) |
−0.673852 | + | 0.738866i | \(0.735362\pi\) | |||||||
\(42\) | 0.492478 | − | 0.677837i | 0.0759909 | − | 0.104593i | ||||
\(43\) | 11.8217i | 1.80280i | 0.432989 | + | 0.901399i | \(0.357459\pi\) | ||||
−0.432989 | + | 0.901399i | \(0.642541\pi\) | |||||||
\(44\) | 0.946857 | + | 6.33458i | 0.142744 | + | 0.954974i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.41244 | + | 1.02620i | 0.208253 | + | 0.151305i | ||||
\(47\) | 0.863579 | + | 0.280594i | 0.125966 | + | 0.0409288i | 0.371322 | − | 0.928504i | \(-0.378905\pi\) |
−0.245356 | + | 0.969433i | \(0.578905\pi\) | |||||||
\(48\) | 3.41595 | − | 1.10991i | 0.493050 | − | 0.160202i | ||||
\(49\) | 2.58773 | − | 1.88010i | 0.369676 | − | 0.268586i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0272635 | − | 0.0839083i | −0.00381765 | − | 0.0117495i | ||||
\(52\) | 2.05632 | + | 0.668140i | 0.285161 | + | 0.0926544i | ||||
\(53\) | −0.512771 | + | 0.705768i | −0.0704344 | + | 0.0969447i | −0.842781 | − | 0.538257i | \(-0.819083\pi\) |
0.772346 | + | 0.635202i | \(0.219083\pi\) | |||||||
\(54\) | 0.262360 | 0.0357026 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.29374 | −0.440144 | ||||||||
\(57\) | −0.0404588 | + | 0.0556868i | −0.00535890 | + | 0.00737589i | ||||
\(58\) | 0.932160 | + | 0.302877i | 0.122399 | + | 0.0397697i | ||||
\(59\) | −0.567369 | − | 1.74618i | −0.0738651 | − | 0.227333i | 0.907307 | − | 0.420469i | \(-0.138134\pi\) |
−0.981172 | + | 0.193135i | \(0.938134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.13881 | − | 5.91319i | 1.04207 | − | 0.757107i | 0.0713799 | − | 0.997449i | \(-0.477260\pi\) |
0.970688 | + | 0.240342i | \(0.0772597\pi\) | |||||||
\(62\) | −2.39160 | + | 0.777078i | −0.303733 | + | 0.0986890i | ||||
\(63\) | 3.03722 | + | 0.986854i | 0.382654 | + | 0.124332i | ||||
\(64\) | −5.17372 | − | 3.75893i | −0.646715 | − | 0.469866i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.778717 | − | 0.388276i | 0.0958534 | − | 0.0477935i | ||||
\(67\) | 9.53916i | 1.16539i | 0.812690 | + | 0.582697i | \(0.198003\pi\) | ||||
−0.812690 | + | 0.582697i | \(0.801997\pi\) | |||||||
\(68\) | −0.100147 | + | 0.137840i | −0.0121446 | + | 0.0167156i | ||||
\(69\) | −2.05635 | + | 6.32881i | −0.247556 | + | 0.761899i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.77370 | − | 2.74175i | 0.447855 | − | 0.325386i | −0.340893 | − | 0.940102i | \(-0.610729\pi\) |
0.788748 | + | 0.614716i | \(0.210729\pi\) | |||||||
\(72\) | −0.606230 | − | 0.834404i | −0.0714449 | − | 0.0983354i | ||||
\(73\) | −6.80989 | + | 2.21267i | −0.797037 | + | 0.258973i | −0.679098 | − | 0.734048i | \(-0.737629\pi\) |
−0.117939 | + | 0.993021i | \(0.537629\pi\) | |||||||
\(74\) | −0.675360 | + | 2.07854i | −0.0785090 | + | 0.241626i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.132927 | 0.0152478 | ||||||||
\(77\) | 10.4754 | − | 1.56580i | 1.19378 | − | 0.178439i | ||||
\(78\) | − | 0.293740i | − | 0.0332595i | ||||||
\(79\) | 0.640209 | + | 0.465139i | 0.0720292 | + | 0.0523323i | 0.623217 | − | 0.782049i | \(-0.285825\pi\) |
−0.551188 | + | 0.834381i | \(0.685825\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −1.79898 | − | 2.47608i | −0.198664 | − | 0.273437i | ||||
\(83\) | 0.145318 | + | 0.200012i | 0.0159507 | + | 0.0219542i | 0.816918 | − | 0.576754i | \(-0.195681\pi\) |
−0.800967 | + | 0.598708i | \(0.795681\pi\) | |||||||
\(84\) | −1.90578 | − | 5.86539i | −0.207938 | − | 0.639966i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.50920 | − | 1.82304i | −0.270574 | − | 0.196584i | ||||
\(87\) | 3.73583i | 0.400523i | ||||||||
\(88\) | −3.03423 | − | 1.57943i | −0.323450 | − | 0.168368i | ||||
\(89\) | 14.5788 | 1.54535 | 0.772673 | − | 0.634804i | \(-0.218919\pi\) | ||||
0.772673 | + | 0.634804i | \(0.218919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.10489 | − | 3.40050i | 0.115824 | − | 0.356469i | ||||
\(92\) | 12.2220 | − | 3.97116i | 1.27423 | − | 0.414022i | ||||
\(93\) | −5.63383 | − | 7.75430i | −0.584201 | − | 0.804084i | ||||
\(94\) | −0.192730 | + | 0.140027i | −0.0198786 | + | 0.0144427i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.928623 | + | 2.85801i | −0.0947772 | + | 0.291694i | ||||
\(97\) | −2.40521 | + | 3.31048i | −0.244212 | + | 0.336128i | −0.913474 | − | 0.406898i | \(-0.866610\pi\) |
0.669262 | + | 0.743027i | \(0.266610\pi\) | |||||||
\(98\) | 0.839188i | 0.0847708i | ||||||||
\(99\) | 2.32471 | + | 2.36553i | 0.233642 | + | 0.237745i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.47207 | − | 2.52261i | −0.345484 | − | 0.251009i | 0.401488 | − | 0.915864i | \(-0.368493\pi\) |
−0.746972 | + | 0.664856i | \(0.768493\pi\) | |||||||
\(102\) | 0.0220142 | + | 0.00715284i | 0.00217973 | + | 0.000708236i | ||||
\(103\) | 1.99038 | − | 0.646712i | 0.196118 | − | 0.0637224i | −0.209311 | − | 0.977849i | \(-0.567122\pi\) |
0.405429 | + | 0.914127i | \(0.367122\pi\) | |||||||
\(104\) | −0.934204 | + | 0.678739i | −0.0916062 | + | 0.0665558i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0707268 | − | 0.217675i | −0.00686959 | − | 0.0211424i | ||||
\(107\) | −14.9705 | − | 4.86421i | −1.44725 | − | 0.470241i | −0.523103 | − | 0.852270i | \(-0.675226\pi\) |
−0.924151 | + | 0.382029i | \(0.875226\pi\) | |||||||
\(108\) | 1.13511 | − | 1.56235i | 0.109226 | − | 0.150337i | ||||
\(109\) | 4.13271 | 0.395842 | 0.197921 | − | 0.980218i | \(-0.436581\pi\) | ||||
0.197921 | + | 0.980218i | \(0.436581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.33021 | −0.790668 | ||||||||
\(112\) | −6.74209 | + | 9.27969i | −0.637067 | + | 0.876848i | ||||
\(113\) | −13.0818 | − | 4.25053i | −1.23063 | − | 0.399856i | −0.379688 | − | 0.925114i | \(-0.623969\pi\) |
−0.850943 | + | 0.525258i | \(0.823969\pi\) | |||||||
\(114\) | −0.00558051 | − | 0.0171750i | −0.000522662 | − | 0.00160859i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.83666 | − | 4.24059i | 0.541921 | − | 0.393728i | ||||
\(117\) | 1.06481 | − | 0.345977i | 0.0984416 | − | 0.0319856i | ||||
\(118\) | 0.458127 | + | 0.148855i | 0.0421740 | + | 0.0137032i | ||||
\(119\) | 0.227943 | + | 0.165611i | 0.0208955 | + | 0.0151815i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4009 | + | 3.58078i | 0.945533 | + | 0.325525i | ||||
\(122\) | 2.63937i | 0.238957i | ||||||||
\(123\) | 6.85690 | − | 9.43772i | 0.618266 | − | 0.850971i | ||||
\(124\) | −5.71989 | + | 17.6040i | −0.513661 | + | 1.58089i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.677837 | + | 0.492478i | −0.0603865 | + | 0.0438734i | ||||
\(127\) | −4.64338 | − | 6.39106i | −0.412033 | − | 0.567115i | 0.551680 | − | 0.834056i | \(-0.313987\pi\) |
−0.963713 | + | 0.266941i | \(0.913987\pi\) | |||||||
\(128\) | 7.31171 | − | 2.37572i | 0.646270 | − | 0.209986i | ||||
\(129\) | 3.65312 | − | 11.2431i | 0.321639 | − | 0.989903i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.3539 | −1.42884 | −0.714422 | − | 0.699715i | \(-0.753310\pi\) | ||||
−0.714422 | + | 0.699715i | \(0.753310\pi\) | |||||||
\(132\) | 1.05698 | − | 6.31714i | 0.0919982 | − | 0.549837i | ||||
\(133\) | − | 0.219819i | − | 0.0190607i | ||||||
\(134\) | −2.02472 | − | 1.47104i | −0.174909 | − | 0.127079i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0281190 | − | 0.0865414i | −0.00241118 | − | 0.00742086i | ||||
\(137\) | −4.54480 | − | 6.25538i | −0.388289 | − | 0.534433i | 0.569468 | − | 0.822013i | \(-0.307149\pi\) |
−0.957757 | + | 0.287580i | \(0.907149\pi\) | |||||||
\(138\) | −1.02620 | − | 1.41244i | −0.0873558 | − | 0.120235i | ||||
\(139\) | −6.23796 | − | 19.1985i | −0.529097 | − | 1.62839i | −0.756069 | − | 0.654492i | \(-0.772883\pi\) |
0.226972 | − | 0.973901i | \(-0.427117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.734604 | − | 0.533721i | −0.0618648 | − | 0.0449474i | ||||
\(142\) | 1.22379i | 0.102698i | ||||||||
\(143\) | 2.64846 | − | 2.60276i | 0.221476 | − | 0.217653i | ||||
\(144\) | −3.59174 | −0.299312 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.580514 | − | 1.78664i | 0.0480437 | − | 0.147863i | ||||
\(147\) | −3.04206 | + | 0.988426i | −0.250905 | + | 0.0815240i | ||||
\(148\) | 9.45572 | + | 13.0147i | 0.777255 | + | 1.06980i | ||||
\(149\) | 7.84361 | − | 5.69872i | 0.642573 | − | 0.466857i | −0.218160 | − | 0.975913i | \(-0.570005\pi\) |
0.860733 | + | 0.509056i | \(0.170005\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.68515 | − | 14.4194i | 0.381272 | − | 1.17343i | −0.557877 | − | 0.829924i | \(-0.688384\pi\) |
0.939149 | − | 0.343511i | \(-0.111616\pi\) | |||||||
\(152\) | −0.0417284 | + | 0.0574342i | −0.00338462 | + | 0.00465853i | ||||
\(153\) | 0.0882264i | 0.00713268i | ||||||||
\(154\) | −1.28307 | + | 2.46489i | −0.103393 | + | 0.198627i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.74921 | − | 1.27088i | −0.140049 | − | 0.101752i | ||||
\(157\) | −14.1522 | − | 4.59834i | −1.12947 | − | 0.366987i | −0.316096 | − | 0.948727i | \(-0.602372\pi\) |
−0.813375 | + | 0.581740i | \(0.802372\pi\) | |||||||
\(158\) | −0.197455 | + | 0.0641570i | −0.0157087 | + | 0.00510405i | ||||
\(159\) | 0.705768 | − | 0.512771i | 0.0559710 | − | 0.0406653i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.56702 | − | 20.2112i | −0.517554 | − | 1.59287i | ||||
\(162\) | −0.249519 | − | 0.0810736i | −0.0196041 | − | 0.00636974i | ||||
\(163\) | −1.99914 | + | 2.75158i | −0.156585 | + | 0.215521i | −0.880101 | − | 0.474787i | \(-0.842525\pi\) |
0.723516 | + | 0.690308i | \(0.242525\pi\) | |||||||
\(164\) | −22.5283 | −1.75917 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0648629 | −0.00503434 | ||||||||
\(167\) | −13.2936 | + | 18.2970i | −1.02869 | + | 1.41587i | −0.122757 | + | 0.992437i | \(0.539174\pi\) |
−0.905929 | + | 0.423429i | \(0.860826\pi\) | |||||||
\(168\) | 3.13253 | + | 1.01782i | 0.241680 | + | 0.0785266i | ||||
\(169\) | 3.62986 | + | 11.1716i | 0.279220 | + | 0.859351i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0556868 | − | 0.0404588i | 0.00425847 | − | 0.00309396i | ||||
\(172\) | −21.7124 | + | 7.05478i | −1.65555 | + | 0.537922i | ||||
\(173\) | 12.4506 | + | 4.04543i | 0.946598 | + | 0.307568i | 0.741333 | − | 0.671138i | \(-0.234194\pi\) |
0.205266 | + | 0.978706i | \(0.434194\pi\) | |||||||
\(174\) | −0.792943 | − | 0.576107i | −0.0601128 | − | 0.0436745i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.6607 | + | 5.31556i | −0.803584 | + | 0.400675i | ||||
\(177\) | 1.83604i | 0.138005i | ||||||||
\(178\) | −2.24821 | + | 3.09439i | −0.168510 | + | 0.231935i | ||||
\(179\) | 4.69008 | − | 14.4346i | 0.350553 | − | 1.07889i | −0.607990 | − | 0.793944i | \(-0.708024\pi\) |
0.958543 | − | 0.284947i | \(-0.0919759\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.14353 | + | 0.830823i | −0.0849978 | + | 0.0617546i | −0.629473 | − | 0.777023i | \(-0.716729\pi\) |
0.544475 | + | 0.838777i | \(0.316729\pi\) | |||||||
\(182\) | 0.551381 | + | 0.758911i | 0.0408711 | + | 0.0562542i | ||||
\(183\) | −9.56775 | + | 3.10875i | −0.707268 | + | 0.229805i | ||||
\(184\) | −2.12088 | + | 6.52740i | −0.156354 | + | 0.481207i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.51468 | 0.184385 | ||||||||
\(187\) | 0.130570 | + | 0.261867i | 0.00954820 | + | 0.0191496i | ||||
\(188\) | 1.75354i | 0.127890i | ||||||||
\(189\) | −2.58362 | − | 1.87711i | −0.187931 | − | 0.136540i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.51701 | + | 4.66887i | 0.109767 | + | 0.337827i | 0.990820 | − | 0.135190i | \(-0.0431646\pi\) |
−0.881053 | + | 0.473018i | \(0.843165\pi\) | |||||||
\(192\) | 3.75893 | + | 5.17372i | 0.271277 | + | 0.373381i | ||||
\(193\) | 5.71320 | + | 7.86354i | 0.411245 | + | 0.566030i | 0.963522 | − | 0.267631i | \(-0.0862407\pi\) |
−0.552276 | + | 0.833661i | \(0.686241\pi\) | |||||||
\(194\) | −0.331752 | − | 1.02103i | −0.0238184 | − | 0.0733054i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.99735 | + | 3.63079i | 0.356953 | + | 0.259342i | ||||
\(197\) | − | 8.88764i | − | 0.633218i | −0.948556 | − | 0.316609i | \(-0.897456\pi\) | ||
0.948556 | − | 0.316609i | \(-0.102544\pi\) | |||||||
\(198\) | −0.860588 | + | 0.128636i | −0.0611593 | + | 0.00914175i | ||||
\(199\) | −18.0381 | −1.27869 | −0.639343 | − | 0.768921i | \(-0.720794\pi\) | ||||
−0.639343 | + | 0.768921i | \(0.720794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.94776 | − | 9.07228i | 0.207919 | − | 0.639909i | ||||
\(202\) | 1.07086 | − | 0.347945i | 0.0753457 | − | 0.0244813i | ||||
\(203\) | −7.01256 | − | 9.65196i | −0.492185 | − | 0.677435i | ||||
\(204\) | 0.137840 | − | 0.100147i | 0.00965075 | − | 0.00701168i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.169671 | + | 0.522194i | −0.0118216 | + | 0.0363830i | ||||
\(207\) | 3.91142 | − | 5.38361i | 0.271862 | − | 0.374186i | ||||
\(208\) | 4.02134i | 0.278830i | ||||||||
\(209\) | 0.105409 | − | 0.202500i | 0.00729128 | − | 0.0140072i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5444 | − | 10.5671i | −1.00127 | − | 0.727469i | −0.0389136 | − | 0.999243i | \(-0.512390\pi\) |
−0.962361 | + | 0.271774i | \(0.912390\pi\) | |||||||
\(212\) | −1.60225 | − | 0.520603i | −0.110043 | − | 0.0357552i | ||||
\(213\) | −4.43625 | + | 1.44142i | −0.303967 | + | 0.0987647i | ||||
\(214\) | 3.34106 | − | 2.42743i | 0.228390 | − | 0.165935i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.318714 | + | 0.980901i | 0.0216857 | + | 0.0667418i | ||||
\(217\) | 29.1113 | + | 9.45884i | 1.97621 | + | 0.642108i | ||||
\(218\) | −0.637310 | + | 0.877182i | −0.0431641 | + | 0.0594103i | ||||
\(219\) | 7.16034 | 0.483851 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0987789 | 0.00664459 | ||||||||
\(222\) | 1.28461 | − | 1.76812i | 0.0862174 | − | 0.118668i | ||||
\(223\) | 13.0760 | + | 4.24865i | 0.875635 | + | 0.284511i | 0.712144 | − | 0.702034i | \(-0.247724\pi\) |
0.163491 | + | 0.986545i | \(0.447724\pi\) | |||||||
\(224\) | −2.96558 | − | 9.12713i | −0.198146 | − | 0.609832i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.91955 | − | 2.12118i | 0.194205 | − | 0.141099i | ||||
\(227\) | −0.630298 | + | 0.204796i | −0.0418344 | + | 0.0135928i | −0.329859 | − | 0.944030i | \(-0.607001\pi\) |
0.288025 | + | 0.957623i | \(0.407001\pi\) | |||||||
\(228\) | −0.126421 | − | 0.0410768i | −0.00837246 | − | 0.00272038i | ||||
\(229\) | −6.05987 | − | 4.40275i | −0.400447 | − | 0.290942i | 0.369276 | − | 0.929320i | \(-0.379606\pi\) |
−0.769723 | + | 0.638378i | \(0.779606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4465 | − | 1.74790i | −0.687330 | − | 0.115004i | ||||
\(232\) | 3.85306i | 0.252966i | ||||||||
\(233\) | −6.18665 | + | 8.51520i | −0.405301 | + | 0.557849i | −0.962065 | − | 0.272822i | \(-0.912043\pi\) |
0.556763 | + | 0.830671i | \(0.312043\pi\) | |||||||
\(234\) | −0.0907705 | + | 0.279363i | −0.00593385 | + | 0.0182625i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.86854 | − | 2.08411i | 0.186726 | − | 0.135664i | ||||
\(237\) | −0.465139 | − | 0.640209i | −0.0302140 | − | 0.0415861i | ||||
\(238\) | −0.0703028 | + | 0.0228428i | −0.00455706 | + | 0.00148068i | ||||
\(239\) | −5.27684 | + | 16.2404i | −0.341330 | + | 1.05051i | 0.622189 | + | 0.782867i | \(0.286244\pi\) |
−0.963519 | + | 0.267640i | \(0.913756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.7082 | −1.07627 | −0.538135 | − | 0.842859i | \(-0.680871\pi\) | ||||
−0.538135 | + | 0.842859i | \(0.680871\pi\) | |||||||
\(242\) | −2.36396 | + | 1.65542i | −0.151961 | + | 0.106415i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 15.7174 | + | 11.4194i | 1.00620 | + | 0.731050i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.945777 | + | 2.91080i | 0.0603006 | + | 0.185586i | ||||
\(247\) | −0.0452979 | − | 0.0623472i | −0.00288224 | − | 0.00396706i | ||||
\(248\) | −5.81062 | − | 7.99763i | −0.368975 | − | 0.507850i | ||||
\(249\) | −0.0763980 | − | 0.235129i | −0.00484152 | − | 0.0149007i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.15646 | + | 3.01984i | 0.262353 | + | 0.190611i | 0.711184 | − | 0.703006i | \(-0.248159\pi\) |
−0.448831 | + | 0.893617i | \(0.648159\pi\) | |||||||
\(252\) | 6.16724i | 0.388499i | ||||||||
\(253\) | 3.64219 | − | 21.7679i | 0.228982 | − | 1.36854i | ||||
\(254\) | 2.07259 | 0.130046 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.32908 | − | 10.2458i | 0.208067 | − | 0.640366i | ||||
\(257\) | 3.51724 | − | 1.14282i | 0.219399 | − | 0.0712872i | −0.197255 | − | 0.980352i | \(-0.563203\pi\) |
0.416654 | + | 0.909065i | \(0.363203\pi\) | |||||||
\(258\) | 1.82304 | + | 2.50920i | 0.113498 | + | 0.156216i | ||||
\(259\) | 21.5221 | − | 15.6367i | 1.33732 | − | 0.971617i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.15444 | − | 3.55299i | 0.0714577 | − | 0.219924i | ||||
\(262\) | 2.52195 | − | 3.47116i | 0.155806 | − | 0.214449i | ||||
\(263\) | − | 31.6315i | − | 1.95048i | −0.221147 | − | 0.975241i | \(-0.570980\pi\) | ||
0.221147 | − | 0.975241i | \(-0.429020\pi\) | |||||||
\(264\) | 2.39766 | + | 2.43976i | 0.147566 | + | 0.150157i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0466573 | + | 0.0338985i | 0.00286074 | + | 0.00207845i | ||||
\(267\) | −13.8652 | − | 4.50509i | −0.848539 | − | 0.275707i | ||||
\(268\) | −17.5201 | + | 5.69262i | −1.07021 | + | 0.347732i | ||||
\(269\) | −11.9536 | + | 8.68479i | −0.728823 | + | 0.529521i | −0.889191 | − | 0.457536i | \(-0.848732\pi\) |
0.160368 | + | 0.987057i | \(0.448732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.05269 | − | 18.6283i | −0.367675 | − | 1.13159i | −0.948289 | − | 0.317408i | \(-0.897188\pi\) |
0.580614 | − | 0.814179i | \(-0.302812\pi\) | |||||||
\(272\) | −0.301377 | − | 0.0979234i | −0.0182737 | − | 0.00593748i | ||||
\(273\) | −2.10162 | + | 2.89263i | −0.127196 | + | 0.175070i | ||||
\(274\) | 2.02859 | 0.122551 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.8510 | −0.773537 | ||||||||
\(277\) | 15.1122 | − | 20.8001i | 0.908002 | − | 1.24976i | −0.0598418 | − | 0.998208i | \(-0.519060\pi\) |
0.967844 | − | 0.251550i | \(-0.0809404\pi\) | |||||||
\(278\) | 5.03691 | + | 1.63659i | 0.302094 | + | 0.0981561i | ||||
\(279\) | 2.96188 | + | 9.11573i | 0.177323 | + | 0.545744i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.6096 | − | 15.7003i | 1.28912 | − | 0.936599i | 0.289331 | − | 0.957229i | \(-0.406567\pi\) |
0.999787 | + | 0.0206304i | \(0.00656732\pi\) | |||||||
\(282\) | 0.226568 | − | 0.0736165i | 0.0134919 | − | 0.00438380i | ||||
\(283\) | −6.87970 | − | 2.23535i | −0.408956 | − | 0.132878i | 0.0973123 | − | 0.995254i | \(-0.468975\pi\) |
−0.506268 | + | 0.862376i | \(0.668975\pi\) | |||||||
\(284\) | 7.28764 | + | 5.29478i | 0.432442 | + | 0.314187i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.144021 | + | 0.963520i | 0.00851616 | + | 0.0569741i | ||||
\(287\) | 37.2546i | 2.19907i | ||||||||
\(288\) | 1.76635 | − | 2.43117i | 0.104083 | − | 0.143258i | ||||
\(289\) | 5.25088 | − | 16.1606i | 0.308876 | − | 0.950621i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.31048 | − | 2.40521i | 0.194064 | − | 0.140996i | ||||
\(292\) | −8.12778 | − | 11.1869i | −0.475643 | − | 0.654666i | ||||
\(293\) | 13.8804 | − | 4.51002i | 0.810902 | − | 0.263478i | 0.125922 | − | 0.992040i | \(-0.459811\pi\) |
0.684980 | + | 0.728562i | \(0.259811\pi\) | |||||||
\(294\) | 0.259323 | − | 0.798115i | 0.0151240 | − | 0.0465470i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.59161 | −0.499377 | ||||||||
\(297\) | −1.47994 | − | 2.96813i | −0.0858747 | − | 0.172228i | ||||
\(298\) | 2.54364i | 0.147349i | ||||||||
\(299\) | −6.02752 | − | 4.37925i | −0.348580 | − | 0.253258i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.6663 | + | 35.9053i | 0.672436 | + | 2.06955i | ||||
\(302\) | 2.33807 | + | 3.21807i | 0.134541 | + | 0.185179i | ||||
\(303\) | 2.52261 | + | 3.47207i | 0.144920 | + | 0.199465i | ||||
\(304\) | 0.0763980 | + | 0.235129i | 0.00438172 | + | 0.0134856i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0187264 | − | 0.0136055i | −0.00107052 | − | 0.000777775i | ||||
\(307\) | 28.5445i | 1.62912i | 0.580080 | + | 0.814559i | \(0.303021\pi\) | ||||
−0.580080 | + | 0.814559i | \(0.696979\pi\) | |||||||
\(308\) | 9.12713 | + | 18.3051i | 0.520066 | + | 1.04303i | ||||
\(309\) | −2.09280 | −0.119055 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.07411 | + | 9.46113i | −0.174317 | + | 0.536492i | −0.999602 | − | 0.0282249i | \(-0.991015\pi\) |
0.825285 | + | 0.564717i | \(0.191015\pi\) | |||||||
\(312\) | 1.09822 | − | 0.356834i | 0.0621746 | − | 0.0202018i | ||||
\(313\) | −9.65786 | − | 13.2929i | −0.545894 | − | 0.751359i | 0.443554 | − | 0.896248i | \(-0.353718\pi\) |
−0.989448 | + | 0.144889i | \(0.953718\pi\) | |||||||
\(314\) | 3.15844 | − | 2.29474i | 0.178241 | − | 0.129500i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.472244 | + | 1.45342i | −0.0265658 | + | 0.0817612i | ||||
\(317\) | 8.35278 | − | 11.4966i | 0.469139 | − | 0.645714i | −0.507234 | − | 0.861809i | \(-0.669332\pi\) |
0.976373 | + | 0.216094i | \(0.0693318\pi\) | |||||||
\(318\) | 0.228877i | 0.0128348i | ||||||||
\(319\) | −1.83169 | − | 12.2542i | −0.102555 | − | 0.686104i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7347 | + | 9.25228i | 0.710780 | + | 0.516412i | ||||
\(322\) | 5.30261 | + | 1.72292i | 0.295503 | + | 0.0960147i | ||||
\(323\) | 0.00577563 | − | 0.00187662i | 0.000321365 | − | 0.000104418i | ||||
\(324\) | −1.56235 | + | 1.13511i | −0.0867971 | + | 0.0630618i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.275743 | − | 0.848650i | −0.0152720 | − | 0.0470024i | ||||
\(327\) | −3.93044 | − | 1.27708i | −0.217354 | − | 0.0706226i | ||||
\(328\) | 7.07207 | − | 9.73387i | 0.390490 | − | 0.537463i | ||||
\(329\) | 2.89979 | 0.159870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9119 | −0.599773 | −0.299886 | − | 0.953975i | \(-0.596949\pi\) | ||||
−0.299886 | + | 0.953975i | \(0.596949\pi\) | |||||||
\(332\) | −0.280633 | + | 0.386258i | −0.0154017 | + | 0.0211986i | ||||
\(333\) | 7.92250 | + | 2.57418i | 0.434150 | + | 0.141064i | ||||
\(334\) | −1.83359 | − | 5.64321i | −0.100330 | − | 0.308783i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.27969 | − | 6.74209i | 0.506249 | − | 0.367811i | ||||
\(337\) | 5.59800 | − | 1.81890i | 0.304943 | − | 0.0990819i | −0.152549 | − | 0.988296i | \(-0.548748\pi\) |
0.457491 | + | 0.889214i | \(0.348748\pi\) | |||||||
\(338\) | −2.93097 | − | 0.952330i | −0.159424 | − | 0.0517999i | ||||
\(339\) | 11.1280 | + | 8.08499i | 0.604392 | + | 0.439116i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.2820 | + | 22.6732i | 1.20664 | + | 1.22783i | ||||
\(342\) | 0.0180589i | 0.000976514i | ||||||||
\(343\) | −7.13561 | + | 9.82132i | −0.385287 | + | 0.530302i | ||||
\(344\) | 3.76775 | − | 11.5959i | 0.203144 | − | 0.625212i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.77867 | + | 2.01882i | −0.149382 | + | 0.108533i | ||||
\(347\) | −20.2811 | − | 27.9145i | −1.08875 | − | 1.49853i | −0.849512 | − | 0.527569i | \(-0.823104\pi\) |
−0.239234 | − | 0.970962i | \(-0.576896\pi\) | |||||||
\(348\) | −6.86141 | + | 2.22941i | −0.367810 | + | 0.119509i | ||||
\(349\) | 1.70378 | − | 5.24371i | 0.0912014 | − | 0.280689i | −0.895044 | − | 0.445978i | \(-0.852856\pi\) |
0.986245 | + | 0.165289i | \(0.0528558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.11961 | −0.0597602 | ||||||||
\(352\) | 1.64476 | − | 9.83010i | 0.0876662 | − | 0.523946i | ||||
\(353\) | 29.8740i | 1.59003i | 0.606589 | + | 0.795016i | \(0.292537\pi\) | ||||
−0.606589 | + | 0.795016i | \(0.707463\pi\) | |||||||
\(354\) | −0.389706 | − | 0.283138i | −0.0207127 | − | 0.0150486i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.70008 | + | 26.7761i | 0.461103 | + | 1.41913i | ||||
\(357\) | −0.165611 | − | 0.227943i | −0.00876504 | − | 0.0120640i | ||||
\(358\) | 2.34053 | + | 3.22146i | 0.123701 | + | 0.170259i | ||||
\(359\) | 11.0978 | + | 34.1554i | 0.585717 | + | 1.80265i | 0.596372 | + | 0.802708i | \(0.296608\pi\) |
−0.0106548 | + | 0.999943i | \(0.503392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3675 | + | 11.1651i | 0.808815 | + | 0.587639i | ||||
\(362\) | − | 0.370840i | − | 0.0194909i | ||||||
\(363\) | −8.78529 | − | 6.61956i | −0.461108 | − | 0.347437i | ||||
\(364\) | 6.90488 | 0.361914 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.815611 | − | 2.51019i | 0.0426326 | − | 0.131210i | ||||
\(367\) | 8.58887 | − | 2.79069i | 0.448335 | − | 0.145673i | −0.0761428 | − | 0.997097i | \(-0.524260\pi\) |
0.524478 | + | 0.851424i | \(0.324260\pi\) | |||||||
\(368\) | 14.0488 | + | 19.3365i | 0.732345 | + | 1.00799i | ||||
\(369\) | −9.43772 | + | 6.85690i | −0.491308 | + | 0.356956i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.860909 | + | 2.64961i | −0.0446962 | + | 0.137561i | ||||
\(372\) | 10.8799 | − | 14.9749i | 0.564095 | − | 0.776410i | ||||
\(373\) | − | 17.1994i | − | 0.890553i | −0.895393 | − | 0.445277i | \(-0.853105\pi\) | ||
0.895393 | − | 0.445277i | \(-0.146895\pi\) | |||||||
\(374\) | −0.0757176 | − | 0.0126690i | −0.00391526 | − | 0.000655098i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.757656 | − | 0.550469i | −0.0390731 | − | 0.0283883i | ||||
\(377\) | −3.97795 | − | 1.29251i | −0.204875 | − | 0.0665678i | ||||
\(378\) | 0.796845 | − | 0.258911i | 0.0409853 | − | 0.0133169i | ||||
\(379\) | −6.47382 | + | 4.70350i | −0.332538 | + | 0.241603i | −0.741507 | − | 0.670946i | \(-0.765888\pi\) |
0.408969 | + | 0.912548i | \(0.365888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.44117 | + | 7.51314i | 0.125065 | + | 0.384910i | ||||
\(382\) | −1.22492 | − | 0.398002i | −0.0626725 | − | 0.0203635i | ||||
\(383\) | −17.4649 | + | 24.0384i | −0.892417 | + | 1.22831i | 0.0804076 | + | 0.996762i | \(0.474378\pi\) |
−0.972824 | + | 0.231544i | \(0.925622\pi\) | |||||||
\(384\) | −7.68799 | −0.392326 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.55010 | −0.129797 | ||||||||
\(387\) | −6.94864 | + | 9.56399i | −0.353219 | + | 0.486165i | ||||
\(388\) | −7.51553 | − | 2.44194i | −0.381543 | − | 0.123971i | ||||
\(389\) | 0.183988 | + | 0.566256i | 0.00932855 | + | 0.0287103i | 0.955612 | − | 0.294627i | \(-0.0951953\pi\) |
−0.946284 | + | 0.323337i | \(0.895195\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.474976 | − | 0.345090i | 0.0240206 | − | 0.0174520i | ||||
\(392\) | −3.13752 | + | 1.01944i | −0.158469 | + | 0.0514897i | ||||
\(393\) | 15.5534 | + | 5.05362i | 0.784568 | + | 0.254922i | ||||
\(394\) | 1.88643 | + | 1.37057i | 0.0950371 | + | 0.0690485i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.95735 | + | 5.68133i | −0.148612 | + | 0.285498i | ||||
\(397\) | 1.66950i | 0.0837898i | 0.999122 | + | 0.0418949i | \(0.0133395\pi\) | ||||
−0.999122 | + | 0.0418949i | \(0.986661\pi\) | |||||||
\(398\) | 2.78168 | − | 3.82865i | 0.139433 | − | 0.191913i | ||||
\(399\) | −0.0679277 | + | 0.209060i | −0.00340064 | + | 0.0104661i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.19771 | − | 6.68253i | 0.459312 | − | 0.333710i | −0.333949 | − | 0.942591i | \(-0.608381\pi\) |
0.793261 | + | 0.608881i | \(0.208381\pi\) | |||||||
\(402\) | 1.47104 | + | 2.02472i | 0.0733690 | + | 0.100984i | ||||
\(403\) | 10.2060 | − | 3.31614i | 0.508398 | − | 0.165189i | ||||
\(404\) | 2.56114 | − | 7.88237i | 0.127421 | − | 0.392163i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.13008 | 0.155343 | ||||||||
\(407\) | 27.3246 | − | 4.08433i | 1.35443 | − | 0.202453i | ||||
\(408\) | 0.0909950i | 0.00450492i | ||||||||
\(409\) | −6.95565 | − | 5.05358i | −0.343935 | − | 0.249883i | 0.402385 | − | 0.915470i | \(-0.368181\pi\) |
−0.746320 | + | 0.665587i | \(0.768181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.38934 | + | 7.35364i | 0.117858 | + | 0.362728i | ||||
\(412\) | 2.37557 | + | 3.26969i | 0.117036 | + | 0.161086i | ||||
\(413\) | −3.44645 | − | 4.74363i | −0.169589 | − | 0.233419i | ||||
\(414\) | 0.539504 | + | 1.66042i | 0.0265152 | + | 0.0816054i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.72195 | − | 1.97761i | −0.133455 | − | 0.0969604i | ||||
\(417\) | 20.1865i | 0.988536i | ||||||||
\(418\) | 0.0267261 | + | 0.0536011i | 0.00130721 | + | 0.00262172i | ||||
\(419\) | −31.3915 | −1.53358 | −0.766789 | − | 0.641899i | \(-0.778147\pi\) | ||||
−0.766789 | + | 0.641899i | \(0.778147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.41497 | + | 4.35482i | −0.0689613 | + | 0.212241i | −0.979598 | − | 0.200967i | \(-0.935592\pi\) |
0.910637 | + | 0.413208i | \(0.135592\pi\) | |||||||
\(422\) | 4.48580 | − | 1.45753i | 0.218366 | − | 0.0709513i | ||||
\(423\) | 0.533721 | + | 0.734604i | 0.0259504 | + | 0.0357177i | ||||
\(424\) | 0.727915 | − | 0.528861i | 0.0353507 | − | 0.0256838i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.378171 | − | 1.16389i | 0.0183225 | − | 0.0563908i | ||||
\(427\) | 18.8839 | − | 25.9915i | 0.913858 | − | 1.25782i | ||||
\(428\) | − | 30.3983i | − | 1.46936i | ||||||
\(429\) | −3.32313 | + | 1.65695i | −0.160442 | + | 0.0799982i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.8694 | − | 9.35015i | −0.619896 | − | 0.450381i | 0.232989 | − | 0.972479i | \(-0.425149\pi\) |
−0.852885 | + | 0.522098i | \(0.825149\pi\) | |||||||
\(432\) | 3.41595 | + | 1.10991i | 0.164350 | + | 0.0534005i | ||||
\(433\) | 15.0295 | − | 4.88338i | 0.722272 | − | 0.234680i | 0.0752639 | − | 0.997164i | \(-0.476020\pi\) |
0.647008 | + | 0.762483i | \(0.276020\pi\) | |||||||
\(434\) | −6.49696 | + | 4.72032i | −0.311864 | + | 0.226583i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.46625 | + | 7.59034i | 0.118112 | + | 0.363511i | ||||
\(437\) | −0.435628 | − | 0.141544i | −0.0208389 | − | 0.00677098i | ||||
\(438\) | −1.10420 | + | 1.51981i | −0.0527609 | + | 0.0726192i | ||||
\(439\) | −21.5227 | −1.02722 | −0.513611 | − | 0.858023i | \(-0.671693\pi\) | ||||
−0.513611 | + | 0.858023i | \(0.671693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.19862 | 0.152315 | ||||||||
\(442\) | −0.0152328 | + | 0.0209662i | −0.000724551 | + | 0.000997258i | ||||
\(443\) | −9.67881 | − | 3.14484i | −0.459854 | − | 0.149416i | 0.0699233 | − | 0.997552i | \(-0.477725\pi\) |
−0.529777 | + | 0.848137i | \(0.677725\pi\) | |||||||
\(444\) | −4.97116 | − | 15.2997i | −0.235921 | − | 0.726090i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.91826 | + | 2.12024i | −0.138184 | + | 0.100396i | ||||
\(447\) | −9.22071 | + | 2.99599i | −0.436125 | + | 0.141706i | ||||
\(448\) | −19.4233 | − | 6.31100i | −0.917663 | − | 0.298167i | ||||
\(449\) | 31.2352 | + | 22.6937i | 1.47408 | + | 1.07098i | 0.979406 | + | 0.201902i | \(0.0647121\pi\) |
0.494673 | + | 0.869079i | \(0.335288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.8646 | + | 34.3194i | −0.841209 | + | 1.61604i | ||||
\(452\) | − | 26.5632i | − | 1.24943i | ||||||
\(453\) | −8.91168 | + | 12.2659i | −0.418707 | + | 0.576301i | ||||
\(454\) | 0.0537303 | − | 0.165365i | 0.00252169 | − | 0.00776096i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0574342 | − | 0.0417284i | 0.00268960 | − | 0.00195411i | ||||
\(457\) | −13.7329 | − | 18.9017i | −0.642396 | − | 0.884183i | 0.356344 | − | 0.934355i | \(-0.384023\pi\) |
−0.998741 | + | 0.0501720i | \(0.984023\pi\) | |||||||
\(458\) | 1.86900 | − | 0.607275i | 0.0873326 | − | 0.0283761i | ||||
\(459\) | 0.0272635 | − | 0.0839083i | 0.00127255 | − | 0.00391651i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.93120 | 0.229669 | 0.114834 | − | 0.993385i | \(-0.463366\pi\) | ||||
0.114834 | + | 0.993385i | \(0.463366\pi\) | |||||||
\(462\) | 1.98197 | − | 1.94776i | 0.0922094 | − | 0.0906181i | ||||
\(463\) | − | 26.9648i | − | 1.25316i | −0.779357 | − | 0.626580i | \(-0.784454\pi\) | ||
0.779357 | − | 0.626580i | \(-0.215546\pi\) | |||||||
\(464\) | 10.8555 | + | 7.88699i | 0.503954 | + | 0.366144i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.853329 | − | 2.62628i | −0.0395297 | − | 0.121660i | ||||
\(467\) | 13.9175 | + | 19.1558i | 0.644024 | + | 0.886423i | 0.998822 | − | 0.0485201i | \(-0.0154505\pi\) |
−0.354798 | + | 0.934943i | \(0.615450\pi\) | |||||||
\(468\) | 1.27088 | + | 1.74921i | 0.0587464 | + | 0.0808574i | ||||
\(469\) | 9.41376 | + | 28.9726i | 0.434687 | + | 1.33783i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0386 | + | 8.74655i | 0.554709 | + | 0.403020i | ||||
\(472\) | 1.89366i | 0.0871627i | ||||||||
\(473\) | −6.47035 | + | 38.6707i | −0.297507 | + | 1.77808i | ||||
\(474\) | 0.207616 | 0.00953613 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.168140 | + | 0.517482i | −0.00770669 | + | 0.0237188i | ||||
\(477\) | −0.829680 | + | 0.269579i | −0.0379884 | + | 0.0123432i | ||||
\(478\) | −2.63334 | − | 3.62449i | −0.120446 | − | 0.165780i | ||||
\(479\) | −10.9412 | + | 7.94922i | −0.499915 | + | 0.363209i | −0.808984 | − | 0.587830i | \(-0.799982\pi\) |
0.309070 | + | 0.951039i | \(0.399982\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.88206 | − | 8.87008i | 0.131411 | − | 0.404441i | ||||
\(482\) | 2.57659 | − | 3.54637i | 0.117361 | − | 0.161533i | ||||
\(483\) | 21.2513i | 0.966969i | ||||||||
\(484\) | −0.369771 | + | 21.2396i | −0.0168078 | + | 0.965437i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.212253 | + | 0.154211i | 0.00962801 | + | 0.00699516i | ||||
\(487\) | −8.20480 | − | 2.66590i | −0.371795 | − | 0.120803i | 0.117159 | − | 0.993113i | \(-0.462621\pi\) |
−0.488954 | + | 0.872310i | \(0.662621\pi\) | |||||||
\(488\) | −9.86798 | + | 3.20630i | −0.446703 | + | 0.145142i | ||||
\(489\) | 2.75158 | − | 1.99914i | 0.124431 | − | 0.0904043i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00565 | − | 24.6388i | −0.361290 | − | 1.11194i | −0.952272 | − | 0.305251i | \(-0.901260\pi\) |
0.590982 | − | 0.806685i | \(-0.298740\pi\) | |||||||
\(492\) | 21.4257 | + | 6.96164i | 0.965947 | + | 0.313855i | ||||
\(493\) | 0.193733 | − | 0.266651i | 0.00872532 | − | 0.0120094i | ||||
\(494\) | 0.0202189 | 0.000909690 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.4263 | −1.54579 | ||||||||
\(497\) | 8.75585 | − | 12.0514i | 0.392754 | − | 0.540579i | ||||
\(498\) | 0.0616883 | + | 0.0200437i | 0.00276432 | + | 0.000898182i | ||||
\(499\) | 8.66717 | + | 26.6748i | 0.387996 | + | 1.19413i | 0.934284 | + | 0.356531i | \(0.116040\pi\) |
−0.546288 | + | 0.837597i | \(0.683960\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.2970 | − | 13.2936i | 0.817450 | − | 0.593913i | ||||
\(502\) | −1.28194 | + | 0.416529i | −0.0572160 | + | 0.0185906i | ||||
\(503\) | −27.9610 | − | 9.08507i | −1.24672 | − | 0.405083i | −0.389974 | − | 0.920826i | \(-0.627516\pi\) |
−0.856744 | + | 0.515743i | \(0.827516\pi\) | |||||||
\(504\) | −2.66469 | − | 1.93601i | −0.118695 | − | 0.0862368i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.05864 | + | 4.12992i | 0.180429 | + | 0.183597i | ||||
\(507\) | − | 11.7465i | − | 0.521680i | ||||||
\(508\) | 8.96714 | − | 12.3422i | 0.397853 | − | 0.547597i | ||||
\(509\) | 5.99195 | − | 18.4413i | 0.265589 | − | 0.817398i | −0.725969 | − | 0.687728i | \(-0.758608\pi\) |
0.991557 | − | 0.129670i | \(-0.0413918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.4996 | + | 13.4407i | −0.818373 | + | 0.594583i | ||||
\(512\) | 10.6991 | + | 14.7261i | 0.472838 | + | 0.650806i | ||||
\(513\) | −0.0654637 | + | 0.0212704i | −0.00289029 | + | 0.000939113i | ||||
\(514\) | −0.299830 | + | 0.922782i | −0.0132249 | + | 0.0407022i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 22.8298 | 1.00502 | ||||||||
\(517\) | 2.67132 | + | 1.39052i | 0.117485 | + | 0.0611552i | ||||
\(518\) | 6.97949i | 0.306661i | ||||||||
\(519\) | −10.5911 | − | 7.69487i | −0.464897 | − | 0.337767i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.72734 | + | 23.7823i | 0.338541 | + | 1.04192i | 0.964951 | + | 0.262429i | \(0.0845235\pi\) |
−0.626410 | + | 0.779493i | \(0.715477\pi\) | |||||||
\(522\) | 0.576107 | + | 0.792943i | 0.0252155 | + | 0.0347062i | ||||
\(523\) | −1.28585 | − | 1.76982i | −0.0562262 | − | 0.0773887i | 0.779978 | − | 0.625807i | \(-0.215230\pi\) |
−0.836204 | + | 0.548418i | \(0.815230\pi\) | |||||||
\(524\) | −9.75939 | − | 30.0363i | −0.426341 | − | 1.31214i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.71389 | + | 4.87793i | 0.292740 | + | 0.212688i | ||||
\(527\) | 0.845637i | 0.0368365i | ||||||||
\(528\) | 11.7816 | − | 1.76104i | 0.512727 | − | 0.0766395i | ||||
\(529\) | −21.2824 | −0.925322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.567369 | − | 1.74618i | 0.0246217 | − | 0.0757778i | ||||
\(532\) | 0.403730 | − | 0.131180i | 0.0175039 | − | 0.00568737i | ||||
\(533\) | 7.67703 | + | 10.5665i | 0.332529 | + | 0.457687i | ||||
\(534\) | 3.09439 | − | 2.24821i | 0.133908 | − | 0.0972895i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.04026 | − | 9.35697i | 0.131319 | − | 0.404159i | ||||
\(537\) | −8.92106 | + | 12.2788i | −0.384972 | + | 0.529869i | ||||
\(538\) | − | 3.87648i | − | 0.167127i | ||||||
\(539\) | 9.49390 | − | 4.73375i | 0.408931 | − | 0.203897i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.9689 | − | 7.96939i | −0.471591 | − | 0.342631i | 0.326470 | − | 0.945208i | \(-0.394141\pi\) |
−0.798061 | + | 0.602577i | \(0.794141\pi\) | |||||||
\(542\) | 4.88731 | + | 1.58798i | 0.209928 | + | 0.0682097i | ||||
\(543\) | 1.34430 | − | 0.436789i | 0.0576894 | − | 0.0187444i | ||||
\(544\) | 0.214493 | − | 0.155838i | 0.00919632 | − | 0.00668152i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.289878 | − | 0.892153i | −0.0124056 | − | 0.0381806i | ||||
\(547\) | −3.53110 | − | 1.14732i | −0.150979 | − | 0.0490560i | 0.232553 | − | 0.972584i | \(-0.425292\pi\) |
−0.383531 | + | 0.923528i | \(0.625292\pi\) | |||||||
\(548\) | 8.77677 | − | 12.0802i | 0.374925 | − | 0.516040i | ||||
\(549\) | 10.0601 | 0.429356 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.257147 | −0.0109548 | ||||||||
\(552\) | 4.03416 | − | 5.55254i | 0.171705 | − | 0.236332i | ||||
\(553\) | 2.40348 | + | 0.780939i | 0.102207 | + | 0.0332089i | ||||
\(554\) | 2.08443 | + | 6.41522i | 0.0885590 | + | 0.272557i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.5383 | − | 22.9139i | 1.33752 | − | 0.971766i | ||||
\(557\) | −6.25339 | + | 2.03185i | −0.264964 | + | 0.0860922i | −0.438486 | − | 0.898738i | \(-0.644485\pi\) |
0.173522 | + | 0.984830i | \(0.444485\pi\) | |||||||
\(558\) | −2.39160 | − | 0.777078i | −0.101244 | − | 0.0328963i | ||||
\(559\) | 10.7079 | + | 7.77974i | 0.452896 | + | 0.329048i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0432577 | − | 0.289399i | −0.00182634 | − | 0.0122184i | ||||
\(562\) | 7.00786i | 0.295609i | ||||||||
\(563\) | 4.06087 | − | 5.58931i | 0.171145 | − | 0.235561i | −0.714825 | − | 0.699303i | \(-0.753494\pi\) |
0.885970 | + | 0.463742i | \(0.153494\pi\) | |||||||
\(564\) | 0.541873 | − | 1.66771i | 0.0228170 | − | 0.0702235i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.53539 | − | 1.11552i | 0.0645372 | − | 0.0468890i | ||||
\(567\) | 1.87711 | + | 2.58362i | 0.0788311 | + | 0.108502i | ||||
\(568\) | −4.57545 | + | 1.48666i | −0.191982 | + | 0.0623787i | ||||
\(569\) | 2.08515 | − | 6.41743i | 0.0874140 | − | 0.269033i | −0.897789 | − | 0.440427i | \(-0.854827\pi\) |
0.985203 | + | 0.171394i | \(0.0548272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.68928 | 0.405484 | 0.202742 | − | 0.979232i | \(-0.435015\pi\) | ||||
0.202742 | + | 0.979232i | \(0.435015\pi\) | |||||||
\(572\) | 6.36086 | + | 3.31107i | 0.265961 | + | 0.138443i | ||||
\(573\) | − | 4.90914i | − | 0.205082i | ||||||
\(574\) | −7.90742 | − | 5.74508i | −0.330049 | − | 0.239795i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.97619 | − | 6.08207i | −0.0823411 | − | 0.253420i | ||||
\(577\) | −8.90484 | − | 12.2565i | −0.370713 | − | 0.510243i | 0.582381 | − | 0.812916i | \(-0.302121\pi\) |
−0.953095 | + | 0.302673i | \(0.902121\pi\) | |||||||
\(578\) | 2.62039 | + | 3.60666i | 0.108994 | + | 0.150017i | ||||
\(579\) | −3.00361 | − | 9.24415i | −0.124826 | − | 0.384174i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.638745 | + | 0.464076i | 0.0264996 | + | 0.0192531i | ||||
\(582\) | 1.07357i | 0.0445009i | ||||||||
\(583\) | −2.06364 | + | 2.02802i | −0.0854671 | + | 0.0839921i | ||||
\(584\) | 7.38503 | 0.305595 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.18325 | + | 3.64166i | −0.0488795 | + | 0.150436i | ||||
\(587\) | 25.6892 | − | 8.34693i | 1.06031 | − | 0.344514i | 0.273601 | − | 0.961843i | \(-0.411785\pi\) |
0.786705 | + | 0.617329i | \(0.211785\pi\) | |||||||
\(588\) | −3.63079 | − | 4.99735i | −0.149731 | − | 0.206087i | ||||
\(589\) | 0.533749 | − | 0.387791i | 0.0219927 | − | 0.0159787i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.74643 | + | 8.45265i | −0.112973 | + | 0.347696i | ||||
\(592\) | −17.5865 | + | 24.2058i | −0.722801 | + | 0.994850i | ||||
\(593\) | 22.1863i | 0.911084i | 0.890214 | + | 0.455542i | \(0.150554\pi\) | ||||
−0.890214 | + | 0.455542i | \(0.849446\pi\) | |||||||
\(594\) | 0.858218 | + | 0.143596i | 0.0352131 | + | 0.00589183i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.1473 | + | 11.0052i | 0.620458 | + | 0.450789i | ||||
\(597\) | 17.1552 | + | 5.57408i | 0.702118 | + | 0.228132i | ||||
\(598\) | 1.85902 | − | 0.604033i | 0.0760210 | − | 0.0247007i | ||||
\(599\) | 9.50487 | − | 6.90569i | 0.388359 | − | 0.282159i | −0.376424 | − | 0.926448i | \(-0.622846\pi\) |
0.764783 | + | 0.644289i | \(0.222846\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6242 | + | 32.6979i | 0.433370 | + | 1.33378i | 0.894747 | + | 0.446572i | \(0.147355\pi\) |
−0.461377 | + | 0.887204i | \(0.652645\pi\) | |||||||
\(602\) | −9.42010 | − | 3.06077i | −0.383934 | − | 0.124748i | ||||
\(603\) | −5.60698 | + | 7.71734i | −0.228334 | + | 0.314274i | ||||
\(604\) | 29.2793 | 1.19136 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.12597 | −0.0457395 | ||||||||
\(607\) | 8.01137 | − | 11.0267i | 0.325172 | − | 0.447560i | −0.614866 | − | 0.788632i | \(-0.710790\pi\) |
0.940037 | + | 0.341071i | \(0.110790\pi\) | |||||||
\(608\) | −0.196724 | − | 0.0639196i | −0.00797822 | − | 0.00259228i | ||||
\(609\) | 3.68672 | + | 11.3466i | 0.149393 | + | 0.459786i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.822467 | − | 0.597557i | 0.0332735 | − | 0.0241746i | ||||
\(612\) | −0.162041 | + | 0.0526503i | −0.00655012 | + | 0.00212826i | ||||
\(613\) | 6.49565 | + | 2.11057i | 0.262357 | + | 0.0852450i | 0.437242 | − | 0.899344i | \(-0.355955\pi\) |
−0.174885 | + | 0.984589i | \(0.555955\pi\) | |||||||
\(614\) | −6.05866 | − | 4.40187i | −0.244508 | − | 0.177645i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.7743 | − | 1.80275i | −0.434110 | − | 0.0726349i | ||||
\(617\) | 30.3730i | 1.22277i | 0.791333 | + | 0.611386i | \(0.209388\pi\) | ||||
−0.791333 | + | 0.611386i | \(0.790612\pi\) | |||||||
\(618\) | 0.322734 | − | 0.444205i | 0.0129823 | − | 0.0178685i | ||||
\(619\) | 7.96890 | − | 24.5258i | 0.320297 | − | 0.985773i | −0.653222 | − | 0.757167i | \(-0.726583\pi\) |
0.973519 | − | 0.228607i | \(-0.0734170\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.38361 | + | 3.91142i | −0.216037 | + | 0.156960i | ||||
\(622\) | −1.53410 | − | 2.11150i | −0.0615117 | − | 0.0846635i | ||||
\(623\) | 44.2790 | − | 14.3871i | 1.77400 | − | 0.576408i | ||||
\(624\) | 1.24266 | − | 3.82452i | 0.0497463 | − | 0.153103i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.31081 | 0.172295 | ||||||||
\(627\) | −0.162826 | + | 0.160016i | −0.00650263 | + | 0.00639041i | ||||
\(628\) | − | 28.7368i | − | 1.14672i | ||||||
\(629\) | 0.594583 | + | 0.431990i | 0.0237076 | + | 0.0172246i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.90021 | − | 24.3143i | −0.314502 | − | 0.967939i | −0.975959 | − | 0.217955i | \(-0.930061\pi\) |
0.661456 | − | 0.749984i | \(-0.269939\pi\) | |||||||
\(632\) | −0.479735 | − | 0.660299i | −0.0190828 | − | 0.0262653i | ||||
\(633\) | 10.5671 | + | 14.5444i | 0.420004 | + | 0.578086i | ||||
\(634\) | 1.15210 | + | 3.54581i | 0.0457559 | + | 0.140822i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.36296 | + | 0.990246i | 0.0540447 | + | 0.0392658i | ||||
\(637\) | − | 3.58119i | − | 0.141892i | ||||||
\(638\) | 2.88347 | + | 1.50095i | 0.114157 | + | 0.0594233i | ||||
\(639\) | 4.66454 | 0.184527 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.25851 | + | 3.87329i | −0.0497081 | + | 0.152986i | −0.972829 | − | 0.231523i | \(-0.925629\pi\) |
0.923121 | + | 0.384509i | \(0.125629\pi\) | |||||||
\(642\) | −3.92766 | + | 1.27617i | −0.155012 | + | 0.0503665i | ||||
\(643\) | 6.65950 | + | 9.16601i | 0.262625 | + | 0.361472i | 0.919883 | − | 0.392194i | \(-0.128284\pi\) |
−0.657258 | + | 0.753666i | \(0.728284\pi\) | |||||||
\(644\) | 33.2020 | − | 24.1226i | 1.30834 | − | 0.950565i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.000492348 | 0.00151529i | −1.93712e−5 | 5.96184e-5i | ||||||
\(647\) | −21.6587 | + | 29.8107i | −0.851492 | + | 1.17198i | 0.132040 | + | 0.991244i | \(0.457847\pi\) |
−0.983532 | + | 0.180734i | \(0.942153\pi\) | |||||||
\(648\) | − | 1.03138i | − | 0.0405164i | ||||||
\(649\) | −0.900218 | − | 6.02256i | −0.0353366 | − | 0.236406i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.7636 | − | 17.9918i | −0.970561 | − | 0.705154i | ||||
\(652\) | −6.24671 | − | 2.02968i | −0.244640 | − | 0.0794883i | ||||
\(653\) | 14.5291 | − | 4.72079i | 0.568568 | − | 0.184739i | −0.0106050 | − | 0.999944i | \(-0.503376\pi\) |
0.579173 | + | 0.815205i | \(0.303376\pi\) | |||||||
\(654\) | 0.877182 | − | 0.637310i | 0.0343005 | − | 0.0249208i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.9478 | − | 39.8493i | −0.505528 | − | 1.55585i | ||||
\(657\) | −6.80989 | − | 2.21267i | −0.265679 | − | 0.0863243i | ||||
\(658\) | −0.447180 | + | 0.615490i | −0.0174329 | + | 0.0239943i | ||||
\(659\) | −11.8996 | −0.463544 | −0.231772 | − | 0.972770i | \(-0.574452\pi\) | ||||
−0.231772 | + | 0.972770i | \(0.574452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.8648 | −1.74504 | −0.872520 | − | 0.488578i | \(-0.837516\pi\) | ||||
−0.872520 | + | 0.488578i | \(0.837516\pi\) | |||||||
\(662\) | 1.68274 | − | 2.31609i | 0.0654015 | − | 0.0900174i | ||||
\(663\) | −0.0939443 | − | 0.0305244i | −0.00364849 | − | 0.00118547i | ||||
\(664\) | −0.0787953 | − | 0.242507i | −0.00305785 | − | 0.00941110i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.76812 | + | 1.28461i | −0.0685131 | + | 0.0497777i | ||||
\(667\) | −23.6434 | + | 7.68219i | −0.915474 | + | 0.297456i | ||||
\(668\) | −41.5383 | − | 13.4966i | −1.60717 | − | 0.522200i | ||||
\(669\) | −11.1231 | − | 8.08142i | −0.430045 | − | 0.312446i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.8597 | − | 14.8884i | 1.15272 | − | 0.574759i | ||||
\(672\) | 9.59683i | 0.370206i | ||||||||
\(673\) | 11.2306 | − | 15.4576i | 0.432909 | − | 0.595848i | −0.535709 | − | 0.844403i | \(-0.679956\pi\) |
0.968618 | + | 0.248555i | \(0.0799557\pi\) | |||||||
\(674\) | −0.477207 | + | 1.46869i | −0.0183813 | + | 0.0565719i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.3521 | + | 13.3336i | −0.705849 | + | 0.512830i | ||||
\(677\) | −27.3093 | − | 37.5881i | −1.04958 | − | 1.44463i | −0.889170 | − | 0.457578i | \(-0.848717\pi\) |
−0.160414 | − | 0.987050i | \(-0.551283\pi\) | |||||||
\(678\) | −3.43213 | + | 1.11517i | −0.131810 | + | 0.0428278i | ||||
\(679\) | −4.03819 | + | 12.4283i | −0.154971 | + | 0.476953i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.662735 | 0.0253961 | ||||||||
\(682\) | −8.24860 | + | 1.23295i | −0.315855 | + | 0.0472122i | ||||
\(683\) | 42.5651i | 1.62871i | 0.580367 | + | 0.814355i | \(0.302909\pi\) | ||||
−0.580367 | + | 0.814355i | \(0.697091\pi\) | |||||||
\(684\) | 0.107540 | + | 0.0781327i | 0.00411191 | + | 0.00298748i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.984219 | − | 3.02912i | −0.0375777 | − | 0.115652i | ||||
\(687\) | 4.40275 | + | 6.05987i | 0.167976 | + | 0.231198i | ||||
\(688\) | −24.9577 | − | 34.3514i | −0.951505 | − | 1.30963i | ||||
\(689\) | 0.301823 | + | 0.928915i | 0.0114985 | + | 0.0353888i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.4249 | − | 20.6519i | −1.08134 | − | 0.785636i | −0.103420 | − | 0.994638i | \(-0.532979\pi\) |
−0.977915 | + | 0.209001i | \(0.932979\pi\) | |||||||
\(692\) | 25.2815i | 0.961057i | ||||||||
\(693\) | 9.39509 | + | 4.89050i | 0.356890 | + | 0.185775i | ||||
\(694\) | 9.05253 | 0.343629 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.19066 | − | 3.66448i | 0.0451319 | − | 0.138902i | ||||
\(697\) | −0.978846 | + | 0.318046i | −0.0370764 | + | 0.0120469i | ||||
\(698\) | 0.850252 | + | 1.17027i | 0.0321825 | + | 0.0442954i | ||||
\(699\) | 8.51520 | − | 6.18665i | 0.322074 | − | 0.234001i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.47794 | + | 29.1701i | −0.357977 | + | 1.10174i | 0.596286 | + | 0.802772i | \(0.296642\pi\) |
−0.954263 | + | 0.298968i | \(0.903358\pi\) | |||||||
\(702\) | 0.172656 | − | 0.237640i | 0.00651647 | − | 0.00896916i | ||||
\(703\) | − | 0.573390i | − | 0.0216258i | ||||||
\(704\) | −14.8667 | − | 15.1277i | −0.560309 | − | 0.570148i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.34086 | − | 4.60690i | −0.238641 | − | 0.173383i | ||||
\(707\) | −13.0349 | − | 4.23530i | −0.490228 | − | 0.159285i | ||||
\(708\) | −3.37217 | + | 1.09568i | −0.126734 | + | 0.0411783i | ||||
\(709\) | 12.2100 | − | 8.87107i | 0.458555 | − | 0.333160i | −0.334409 | − | 0.942428i | \(-0.608537\pi\) |
0.792964 | + | 0.609268i | \(0.208537\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.244538 | + | 0.752611i | 0.00917090 | + | 0.0282251i | ||||
\(712\) | −14.3003 | − | 4.64646i | −0.535927 | − | 0.174133i | ||||
\(713\) | 37.4903 | − | 51.6010i | 1.40402 | − | 1.93247i | ||||
\(714\) | 0.0739208 | 0.00276642 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.3101 | 1.09537 | ||||||||
\(717\) | 10.0371 | − | 13.8149i | 0.374844 | − | 0.515929i | ||||
\(718\) | −8.96099 | − | 2.91160i | −0.334421 | − | 0.108660i | ||||
\(719\) | 1.91288 | + | 5.88723i | 0.0713383 | + | 0.219557i | 0.980369 | − | 0.197173i | \(-0.0631761\pi\) |
−0.909030 | + | 0.416730i | \(0.863176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.40701 | − | 3.92842i | 0.201367 | − | 0.146302i | ||||
\(722\) | −4.73968 | + | 1.54001i | −0.176393 | + | 0.0573134i | ||||
\(723\) | 15.8904 | + | 5.16312i | 0.590972 | + | 0.192018i | ||||
\(724\) | −2.20835 | − | 1.60446i | −0.0820725 | − | 0.0596292i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.75982 | − | 0.843898i | 0.102426 | − | 0.0313200i | ||||
\(727\) | − | 18.1515i | − | 0.673200i | −0.941648 | − | 0.336600i | \(-0.890723\pi\) | ||
0.941648 | − | 0.336600i | \(-0.109277\pi\) | |||||||
\(728\) | −2.16757 | + | 2.98341i | −0.0803355 | + | 0.110572i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.843796 | + | 0.613054i | −0.0312089 | + | 0.0226746i | ||||
\(732\) | −11.4194 | − | 15.7174i | −0.422072 | − | 0.580932i | ||||
\(733\) | −27.3342 | + | 8.88142i | −1.00961 | + | 0.328043i | −0.766700 | − | 0.642005i | \(-0.778103\pi\) |
−0.242912 | + | 0.970048i | \(0.578103\pi\) | |||||||
\(734\) | −0.732165 | + | 2.25337i | −0.0270247 | + | 0.0831735i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.9974 | −0.737113 | ||||||||
\(737\) | −5.22103 | + | 31.2040i | −0.192319 | + | 1.14942i | ||||
\(738\) | − | 3.06060i | − | 0.112662i | ||||||
\(739\) | −37.8896 | − | 27.5284i | −1.39379 | − | 1.01265i | −0.995437 | − | 0.0954172i | \(-0.969581\pi\) |
−0.398354 | − | 0.917232i | \(-0.630419\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0238145 | + | 0.0732936i | 0.000874848 | + | 0.00269251i | ||||
\(742\) | −0.429626 | − | 0.591330i | −0.0157721 | − | 0.0217084i | ||||
\(743\) | 15.6414 | + | 21.5286i | 0.573828 | + | 0.789806i | 0.993002 | − | 0.118100i | \(-0.0376803\pi\) |
−0.419174 | + | 0.907906i | \(0.637680\pi\) | |||||||
\(744\) | 3.05482 | + | 9.40178i | 0.111995 | + | 0.344686i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.65064 | + | 2.65235i | 0.133659 | + | 0.0971093i | ||||
\(747\) | 0.247229i | 0.00904564i | ||||||||
\(748\) | −0.403039 | + | 0.396084i | −0.0147366 | + | 0.0144823i | ||||
\(749\) | −50.2691 | −1.83679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5406 | − | 38.5959i | 0.457612 | − | 1.40838i | −0.410430 | − | 0.911892i | \(-0.634621\pi\) |
0.868041 | − | 0.496492i | \(-0.165379\pi\) | |||||||
\(752\) | −3.10175 | + | 1.00782i | −0.113109 | + | 0.0367514i | ||||
\(753\) | −3.01984 | − | 4.15646i | −0.110049 | − | 0.151470i | ||||
\(754\) | 0.887784 | − | 0.645013i | 0.0323312 | − | 0.0234900i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.90578 | − | 5.86539i | 0.0693126 | − | 0.213322i | ||||
\(757\) | 19.2311 | − | 26.4693i | 0.698966 | − | 0.962045i | −0.300998 | − | 0.953625i | \(-0.597320\pi\) |
0.999965 | − | 0.00841989i | \(-0.00268017\pi\) | |||||||
\(758\) | − | 2.09942i | − | 0.0762545i | ||||||
\(759\) | −10.1906 | + | 19.5770i | −0.369894 | + | 0.710600i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.12721 | + | 1.54551i | 0.0771113 | + | 0.0560246i | 0.625673 | − | 0.780085i | \(-0.284824\pi\) |
−0.548562 | + | 0.836110i | \(0.684824\pi\) | |||||||
\(762\) | −1.97115 | − | 0.640464i | −0.0714071 | − | 0.0232016i | ||||
\(763\) | 12.5520 | − | 4.07838i | 0.454412 | − | 0.147647i | ||||
\(764\) | −7.66978 | + | 5.57242i | −0.277483 | + | 0.201603i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.40895 | − | 7.41399i | −0.0870389 | − | 0.267878i | ||||
\(767\) | −1.95503 | − | 0.635229i | −0.0705922 | − | 0.0229368i | ||||
\(768\) | −6.33228 | + | 8.71564i | −0.228497 | + | 0.314499i | ||||
\(769\) | −3.23559 | −0.116678 | −0.0583392 | − | 0.998297i | \(-0.518581\pi\) | ||||
−0.0583392 | + | 0.998297i | \(0.518581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.69824 | −0.133189 | ||||||||
\(772\) | −11.0331 | + | 15.1858i | −0.397092 | + | 0.546550i | ||||
\(773\) | −41.5008 | − | 13.4844i | −1.49268 | − | 0.485001i | −0.554806 | − | 0.831980i | \(-0.687208\pi\) |
−0.937873 | + | 0.346979i | \(0.887208\pi\) | |||||||
\(774\) | −0.958431 | − | 2.94975i | −0.0344501 | − | 0.106026i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.41436 | − | 2.48068i | 0.122569 | − | 0.0890512i | ||||
\(777\) | −25.3007 | + | 8.22070i | −0.907658 | + | 0.294916i | ||||
\(778\) | −0.148563 | − | 0.0482710i | −0.00532623 | − | 0.00173060i | ||||
\(779\) | 0.649623 | + | 0.471979i | 0.0232752 | + | 0.0169104i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8450 | − | 6.90324i | 0.495412 | − | 0.247017i | ||||
\(782\) | 0.154032i | 0.00550818i | ||||||||
\(783\) | −2.19587 | + | 3.02235i | −0.0784739 | + | 0.108010i | ||||
\(784\) | −3.55017 | + | 10.9263i | −0.126792 | + | 0.390225i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.47116 | + | 2.52195i | −0.123812 | + | 0.0899549i | ||||
\(787\) | 2.68277 | + | 3.69251i | 0.0956304 | + | 0.131624i | 0.854151 | − | 0.520025i | \(-0.174077\pi\) |
−0.758521 | + | 0.651649i | \(0.774077\pi\) | |||||||
\(788\) | 16.3235 | − | 5.30382i | 0.581500 | − | 0.188941i | ||||
\(789\) | −9.77467 | + | 30.0833i | −0.347987 | + | 1.07100i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.9270 | −1.56186 | ||||||||
\(792\) | −1.52638 | − | 3.06127i | −0.0542375 | − | 0.108777i | ||||
\(793\) | − | 11.2634i | − | 0.399974i | ||||||
\(794\) | −0.354357 | − | 0.257455i | −0.0125757 | − | 0.00913675i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.7645 | − | 33.1297i | −0.381537 | − | 1.17425i | ||||
\(797\) | 6.57177 | + | 9.04526i | 0.232784 | + | 0.320400i | 0.909389 | − | 0.415946i | \(-0.136550\pi\) |
−0.676605 | + | 0.736346i | \(0.736550\pi\) | |||||||
\(798\) | −0.0338985 | − | 0.0466573i | −0.00119999 | − | 0.00165165i | ||||
\(799\) | 0.0247558 | + | 0.0761905i | 0.000875797 | + | 0.00269543i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.7945 | + | 8.56919i | 0.416737 | + | 0.302777i | ||||
\(802\) | 2.98277i | 0.105325i | ||||||||
\(803\) | −23.4872 | + | 3.51074i | −0.828846 | + | 0.123891i | ||||
\(804\) | 18.4217 | 0.649684 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.870021 | + | 2.67765i | −0.0306452 | + | 0.0943162i | ||||
\(807\) | 14.0523 | − | 4.56586i | 0.494664 | − | 0.160726i | ||||
\(808\) | 2.60176 | + | 3.58102i | 0.0915298 | + | 0.125980i | ||||
\(809\) | −36.8440 | + | 26.7687i | −1.29537 | + | 0.941139i | −0.999899 | − | 0.0142137i | \(-0.995475\pi\) |
−0.295468 | + | 0.955353i | \(0.595475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.872550 | − | 2.68543i | 0.0306394 | − | 0.0942983i | −0.934567 | − | 0.355786i | \(-0.884213\pi\) |
0.965207 | + | 0.261488i | \(0.0842131\pi\) | |||||||
\(812\) | 13.5424 | − | 18.6395i | 0.475246 | − | 0.654120i | ||||
\(813\) | 19.5869i | 0.686943i | ||||||||
\(814\) | −3.34685 | + | 6.42959i | −0.117307 | + | 0.225357i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.256367 | + | 0.186261i | 0.00897463 | + | 0.00652045i | ||||
\(817\) | 0.773895 | + | 0.251454i | 0.0270751 | + | 0.00879725i | ||||
\(818\) | 2.14528 | − | 0.697043i | 0.0750079 | − | 0.0243715i | ||||
\(819\) | 2.89263 | − | 2.10162i | 0.101077 | − | 0.0734366i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.23460 | − | 22.2658i | −0.252489 | − | 0.777083i | −0.994314 | − | 0.106488i | \(-0.966039\pi\) |
0.741825 | − | 0.670594i | \(-0.233961\pi\) | |||||||
\(822\) | −1.92930 | − | 0.626867i | −0.0672920 | − | 0.0218645i | ||||
\(823\) | −27.0996 | + | 37.2994i | −0.944633 | + | 1.30018i | 0.00923747 | + | 0.999957i | \(0.497060\pi\) |
−0.953870 | + | 0.300218i | \(0.902940\pi\) | |||||||
\(824\) | −2.15848 | −0.0751941 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.53833 | 0.0535255 | ||||||||
\(827\) | −25.5390 | + | 35.1515i | −0.888079 | + | 1.22234i | 0.0860379 | + | 0.996292i | \(0.472579\pi\) |
−0.974117 | + | 0.226044i | \(0.927421\pi\) | |||||||
\(828\) | 12.2220 | + | 3.97116i | 0.424743 | + | 0.138007i | ||||
\(829\) | −4.78085 | − | 14.7139i | −0.166046 | − | 0.511036i | 0.833066 | − | 0.553173i | \(-0.186583\pi\) |
−0.999112 | + | 0.0421372i | \(0.986583\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.8001 | + | 15.1122i | −0.721548 | + | 0.524235i | ||||
\(832\) | −6.80953 | + | 2.21255i | −0.236078 | + | 0.0767064i | ||||
\(833\) | 0.268390 | + | 0.0872053i | 0.00929918 | + | 0.00302149i | ||||
\(834\) | −4.28465 | − | 3.11298i | −0.148365 | − | 0.107794i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.434825 | + | 0.0727546i | 0.0150387 | + | 0.00251627i | ||||
\(837\) | − | 9.58484i | − | 0.331301i | ||||||
\(838\) | 4.84093 | − | 6.66296i | 0.167227 | − | 0.230168i | ||||
\(839\) | −9.33790 | + | 28.7391i | −0.322380 | + | 0.992184i | 0.650229 | + | 0.759738i | \(0.274673\pi\) |
−0.972609 | + | 0.232446i | \(0.925327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1705 | − | 8.84239i | 0.419673 | − | 0.304910i | ||||
\(842\) | −0.706122 | − | 0.971894i | −0.0243346 | − | 0.0334937i | ||||
\(843\) | −25.4036 | + | 8.25411i | −0.874945 | + | 0.284287i | ||||
\(844\) | 10.7285 | − | 33.0189i | 0.369290 | − | 1.13656i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.238228 | −0.00819045 | ||||||||
\(847\) | 35.1235 | + | 0.611482i | 1.20686 | + | 0.0210108i | ||||
\(848\) | − | 3.13335i | − | 0.107600i | ||||||
\(849\) | 5.85223 | + | 4.25189i | 0.200848 | + | 0.145925i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.1299 | − | 52.7203i | −0.587204 | − | 1.80723i | ||||
\(852\) | −5.29478 | − | 7.28764i | −0.181396 | − | 0.249670i | ||||
\(853\) | −1.18091 | − | 1.62538i | −0.0404336 | − | 0.0556521i | 0.788322 | − | 0.615263i | \(-0.210950\pi\) |
−0.828755 | + | 0.559611i | \(0.810950\pi\) | |||||||
\(854\) | 2.60467 | + | 8.01636i | 0.0891301 | + | 0.274314i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.1343 | + | 9.54262i | 0.448921 | + | 0.326160i | ||||
\(857\) | − | 33.6095i | − | 1.14808i | −0.818828 | − | 0.574039i | \(-0.805376\pi\) | ||
0.818828 | − | 0.574039i | \(-0.194624\pi\) | |||||||
\(858\) | 0.160771 | − | 0.960867i | 0.00548865 | − | 0.0328034i | ||||
\(859\) | 13.7301 | 0.468466 | 0.234233 | − | 0.972180i | \(-0.424742\pi\) | ||||
0.234233 | + | 0.972180i | \(0.424742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.5123 | − | 35.4312i | 0.392338 | − | 1.20749i | ||||
\(862\) | 3.96920 | − | 1.28967i | 0.135192 | − | 0.0439264i | ||||
\(863\) | 5.14799 | + | 7.08560i | 0.175240 | + | 0.241197i | 0.887598 | − | 0.460620i | \(-0.152373\pi\) |
−0.712358 | + | 0.701816i | \(0.752373\pi\) | |||||||
\(864\) | −2.43117 | + | 1.76635i | −0.0827100 | + | 0.0600923i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.28120 | + | 3.94314i | −0.0435370 | + | 0.133993i | ||||
\(867\) | −9.98777 | + | 13.7470i | −0.339203 | + | 0.466872i | ||||
\(868\) | 59.1120i | 2.00639i | ||||||||
\(869\) | 1.83964 | + | 1.87194i | 0.0624055 | + | 0.0635014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.64038 | + | 6.27761i | 0.292768 | + | 0.212709i | ||||
\(872\) | −4.05378 | − | 1.31715i | −0.137278 | − | 0.0446044i | ||||
\(873\) | −3.89170 | + | 1.26449i | −0.131714 | + | 0.0427965i | ||||
\(874\) | 0.0972220 | − | 0.0706359i | 0.00328858 | − | 0.00238930i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.27303 | + | 13.1510i | 0.144372 | + | 0.444332i | ||||
\(877\) | −14.5001 | − | 4.71136i | −0.489633 | − | 0.159091i | 0.0537871 | − | 0.998552i | \(-0.482871\pi\) |
−0.543420 | + | 0.839461i | \(0.682871\pi\) | |||||||
\(878\) | 3.31904 | − | 4.56827i | 0.112012 | − | 0.154172i | ||||
\(879\) | −14.5947 | −0.492268 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8486 | −0.533953 | −0.266977 | − | 0.963703i | \(-0.586025\pi\) | ||||
−0.266977 | + | 0.963703i | \(0.586025\pi\) | |||||||
\(882\) | −0.493262 | + | 0.678917i | −0.0166090 | + | 0.0228603i | ||||
\(883\) | 31.3474 | + | 10.1854i | 1.05492 | + | 0.342765i | 0.784598 | − | 0.620004i | \(-0.212869\pi\) |
0.270324 | + | 0.962769i | \(0.412869\pi\) | |||||||
\(884\) | 0.0589476 | + | 0.181422i | 0.00198262 | + | 0.00610189i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.16008 | − | 1.56939i | 0.0725694 | − | 0.0527247i | ||||
\(887\) | −10.7017 | + | 3.47720i | −0.359328 | + | 0.116753i | −0.483117 | − | 0.875556i | \(-0.660495\pi\) |
0.123789 | + | 0.992309i | \(0.460495\pi\) | |||||||
\(888\) | 8.17111 | + | 2.65495i | 0.274204 | + | 0.0890944i | ||||
\(889\) | −20.4100 | − | 14.8288i | −0.684530 | − | 0.497340i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.490303 | + | 3.28018i | 0.0164258 | + | 0.109890i | ||||
\(892\) | 26.5515i | 0.889010i | ||||||||
\(893\) | 0.0367374 | − | 0.0505647i | 0.00122937 | − | 0.00169208i | ||||
\(894\) | 0.786027 | − | 2.41914i | 0.0262887 | − | 0.0809083i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.8628 | − | 14.4312i | 0.663570 | − | 0.482112i | ||||
\(897\) | 4.37925 | + | 6.02752i | 0.146219 | + | 0.201253i | ||||
\(898\) | −9.63362 | + | 3.13015i | −0.321478 | + | 0.104455i | ||||
\(899\) | 11.0651 | − | 34.0548i | 0.369041 | − | 1.13579i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0769667 | −0.00256413 | ||||||||
\(902\) | −4.52950 | − | 9.08425i | −0.150816 | − | 0.302472i | ||||
\(903\) | − | 37.7530i | − | 1.25634i | ||||||
\(904\) | 11.4772 | + | 8.33870i | 0.381727 | + | 0.277341i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.22919 | − | 3.78307i | −0.0408372 | − | 0.125684i | ||||
\(907\) | 14.9147 | + | 20.5284i | 0.495236 | + | 0.681634i | 0.981343 | − | 0.192266i | \(-0.0615835\pi\) |
−0.486107 | + | 0.873899i | \(0.661583\pi\) | |||||||
\(908\) | −0.752278 | − | 1.03542i | −0.0249652 | − | 0.0343617i | ||||
\(909\) | −1.32621 | − | 4.08166i | −0.0439877 | − | 0.135380i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0825 | + | 10.2316i | 0.466575 | + | 0.338986i | 0.796105 | − | 0.605159i | \(-0.206890\pi\) |
−0.329530 | + | 0.944145i | \(0.606890\pi\) | |||||||
\(912\) | − | 0.247229i | − | 0.00818657i | ||||||
\(913\) | 0.365884 | + | 0.733807i | 0.0121090 | + | 0.0242855i | ||||
\(914\) | 6.12971 | 0.202753 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.47000 | − | 13.7573i | 0.147693 | − | 0.454553i | ||||
\(917\) | −49.6704 | + | 16.1389i | −1.64026 | + | 0.532953i | ||||
\(918\) | 0.0136055 | + | 0.0187264i | 0.000449048 | + | 0.000618062i | ||||
\(919\) | −26.6133 | + | 19.3357i | −0.877890 | + | 0.637825i | −0.932692 | − | 0.360673i | \(-0.882547\pi\) |
0.0548022 | + | 0.998497i | \(0.482547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.82072 | − | 27.1474i | 0.290653 | − | 0.894537i | ||||
\(922\) | −0.760446 | + | 1.04666i | −0.0250440 | + | 0.0344701i | ||||
\(923\) | − | 5.22245i | − | 0.171899i | ||||||
\(924\) | −3.02381 | − | 20.2297i | −0.0994762 | − | 0.665507i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.72337 | + | 4.15827i | 0.188082 | + | 0.136649i | ||||
\(927\) | 1.99038 | + | 0.646712i | 0.0653725 | + | 0.0212408i | ||||
\(928\) | −10.6770 | + | 3.46918i | −0.350491 | + | 0.113881i | ||||
\(929\) | 26.9509 | − | 19.5810i | 0.884230 | − | 0.642431i | −0.0501368 | − | 0.998742i | \(-0.515966\pi\) |
0.934367 | + | 0.356311i | \(0.115966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0680360 | − | 0.209393i | −0.00222979 | − | 0.00686258i | ||||
\(932\) | −19.3314 | − | 6.28115i | −0.633221 | − | 0.205746i | ||||
\(933\) | 5.84730 | − | 8.04812i | 0.191432 | − | 0.263484i | ||||
\(934\) | −6.21211 | −0.203266 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.15474 | −0.0377438 | ||||||||
\(937\) | −14.0267 | + | 19.3061i | −0.458233 | + | 0.630704i | −0.974141 | − | 0.225940i | \(-0.927455\pi\) |
0.515908 | + | 0.856644i | \(0.327455\pi\) | |||||||
\(938\) | −7.60123 | − | 2.46979i | −0.248189 | − | 0.0806415i | ||||
\(939\) | 5.07744 | + | 15.6267i | 0.165696 | + | 0.509959i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.41192 | − | 4.65853i | 0.209023 | − | 0.151864i | −0.478349 | − | 0.878170i | \(-0.658765\pi\) |
0.687371 | + | 0.726306i | \(0.258765\pi\) | |||||||
\(942\) | −3.71297 | + | 1.20642i | −0.120975 | + | 0.0393072i | ||||
\(943\) | 73.8297 | + | 23.9887i | 2.40423 | + | 0.781181i | ||||
\(944\) | 5.33514 | + | 3.87620i | 0.173644 | + | 0.126160i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.21019 | − | 7.33681i | −0.234423 | − | 0.238540i | ||||
\(947\) | − | 2.15429i | − | 0.0700050i | −0.999387 | − | 0.0350025i | \(-0.988856\pi\) | ||
0.999387 | − | 0.0350025i | \(-0.0111439\pi\) | |||||||
\(948\) | 0.898262 | − | 1.23635i | 0.0291742 | − | 0.0401548i | ||||
\(949\) | −2.47731 | + | 7.62439i | −0.0804170 | + | 0.247498i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.4966 | + | 8.35278i | −0.372803 | + | 0.270858i | ||||
\(952\) | −0.170807 | − | 0.235096i | −0.00553590 | − | 0.00761951i | ||||
\(953\) | −5.69971 | + | 1.85195i | −0.184632 | + | 0.0599904i | −0.399874 | − | 0.916570i | \(-0.630946\pi\) |
0.215242 | + | 0.976561i | \(0.430946\pi\) | |||||||
\(954\) | 0.0707268 | − | 0.217675i | 0.00228986 | − | 0.00704748i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −32.9770 | −1.06655 | ||||||||
\(957\) | −2.04472 | + | 12.2205i | −0.0660964 | + | 0.395032i | ||||
\(958\) | − | 3.54816i | − | 0.114636i | ||||||
\(959\) | −19.9767 | − | 14.5139i | −0.645082 | − | 0.468680i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.8096 | + | 57.8901i | 0.606762 | + | 1.86742i | ||||
\(962\) | 1.43826 | + | 1.97959i | 0.0463713 | + | 0.0638246i | ||||
\(963\) | −9.25228 | − | 12.7347i | −0.298151 | − | 0.410369i | ||||
\(964\) | −9.97085 | − | 30.6871i | −0.321139 | − | 0.988365i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.51067 | − | 3.27719i | −0.145128 | − | 0.105442i | ||||
\(967\) | 22.2784i | 0.716424i | 0.933640 | + | 0.358212i | \(0.116613\pi\) | ||||
−0.933640 | + | 0.358212i | \(0.883387\pi\) | |||||||
\(968\) | −9.06097 | − | 6.82729i | −0.291231 | − | 0.219437i | ||||
\(969\) | −0.00607286 | −0.000195088 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3381 | + | 34.8952i | −0.363858 | + | 1.11984i | 0.586835 | + | 0.809706i | \(0.300374\pi\) |
−0.950693 | + | 0.310133i | \(0.899626\pi\) | |||||||
\(972\) | 1.83665 | − | 0.596764i | 0.0589106 | − | 0.0191412i | ||||
\(973\) | −37.8922 | − | 52.1541i | −1.21477 | − | 1.67198i | ||||
\(974\) | 1.83112 | − | 1.33039i | 0.0586728 | − | 0.0426283i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.1658 | + | 34.3649i | −0.357409 | + | 1.09999i | ||||
\(977\) | 16.4018 | − | 22.5751i | 0.524739 | − | 0.722242i | −0.461578 | − | 0.887100i | \(-0.652717\pi\) |
0.986317 | + | 0.164858i | \(0.0527165\pi\) | |||||||
\(978\) | 0.892323i | 0.0285333i | ||||||||
\(979\) | 47.6894 | + | 7.97935i | 1.52416 | + | 0.255021i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.34343 | + | 2.42915i | 0.106748 | + | 0.0775567i | ||||
\(982\) | 6.46424 | + | 2.10036i | 0.206282 | + | 0.0670252i | ||||
\(983\) | 9.31294 | − | 3.02596i | 0.297037 | − | 0.0965130i | −0.156708 | − | 0.987645i | \(-0.550088\pi\) |
0.453744 | + | 0.891132i | \(0.350088\pi\) | |||||||
\(984\) | −9.73387 | + | 7.07207i | −0.310305 | + | 0.225449i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.0267218 | + | 0.0822412i | 0.000850995 | + | 0.00261909i | ||||
\(987\) | −2.75786 | − | 0.896084i | −0.0877837 | − | 0.0285227i | ||||
\(988\) | 0.0874779 | − | 0.120403i | 0.00278304 | − | 0.00383053i | ||||
\(989\) | 78.6678 | 2.50149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.9794 | 1.11116 | 0.555578 | − | 0.831464i | \(-0.312497\pi\) | ||||
0.555578 | + | 0.831464i | \(0.312497\pi\) | |||||||
\(992\) | 16.9302 | − | 23.3024i | 0.537533 | − | 0.739851i | ||||
\(993\) | 10.3778 | + | 3.37196i | 0.329331 | + | 0.107006i | ||||
\(994\) | 1.20770 | + | 3.71692i | 0.0383059 | + | 0.117894i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.386258 | − | 0.280633i | 0.0122390 | − | 0.00889218i | ||||
\(997\) | 12.1501 | − | 3.94779i | 0.384796 | − | 0.125028i | −0.110230 | − | 0.993906i | \(-0.535159\pi\) |
0.495026 | + | 0.868878i | \(0.335159\pi\) | |||||||
\(998\) | −6.99839 | − | 2.27392i | −0.221530 | − | 0.0719795i | ||||
\(999\) | −6.73928 | − | 4.89637i | −0.213221 | − | 0.154914i |
(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 | 825.2.bx.f.499.2 | 16 | ||
5.2 | odd | 4 | 825.2.n.g.301.2 | 8 | |||
5.3 | odd | 4 | 165.2.m.d.136.1 | yes | 8 | ||
5.4 | even | 2 | inner | 825.2.bx.f.499.3 | 16 | ||
11.3 | even | 5 | inner | 825.2.bx.f.124.3 | 16 | ||
15.8 | even | 4 | 495.2.n.a.136.2 | 8 | |||
55.3 | odd | 20 | 165.2.m.d.91.1 | ✓ | 8 | ||
55.14 | even | 10 | inner | 825.2.bx.f.124.2 | 16 | ||
55.17 | even | 20 | 9075.2.a.cm.1.3 | 4 | |||
55.27 | odd | 20 | 9075.2.a.di.1.2 | 4 | |||
55.28 | even | 20 | 1815.2.a.w.1.2 | 4 | |||
55.38 | odd | 20 | 1815.2.a.p.1.3 | 4 | |||
55.47 | odd | 20 | 825.2.n.g.751.2 | 8 | |||
165.38 | even | 20 | 5445.2.a.bt.1.2 | 4 | |||
165.83 | odd | 20 | 5445.2.a.bf.1.3 | 4 | |||
165.113 | even | 20 | 495.2.n.a.91.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.91.1 | ✓ | 8 | 55.3 | odd | 20 | ||
165.2.m.d.136.1 | yes | 8 | 5.3 | odd | 4 | ||
495.2.n.a.91.2 | 8 | 165.113 | even | 20 | |||
495.2.n.a.136.2 | 8 | 15.8 | even | 4 | |||
825.2.n.g.301.2 | 8 | 5.2 | odd | 4 | |||
825.2.n.g.751.2 | 8 | 55.47 | odd | 20 | |||
825.2.bx.f.124.2 | 16 | 55.14 | even | 10 | inner | ||
825.2.bx.f.124.3 | 16 | 11.3 | even | 5 | inner | ||
825.2.bx.f.499.2 | 16 | 1.1 | even | 1 | trivial | ||
825.2.bx.f.499.3 | 16 | 5.4 | even | 2 | inner | ||
1815.2.a.p.1.3 | 4 | 55.38 | odd | 20 | |||
1815.2.a.w.1.2 | 4 | 55.28 | even | 20 | |||
5445.2.a.bf.1.3 | 4 | 165.83 | odd | 20 | |||
5445.2.a.bt.1.2 | 4 | 165.38 | even | 20 | |||
9075.2.a.cm.1.3 | 4 | 55.17 | even | 20 | |||
9075.2.a.di.1.2 | 4 | 55.27 | odd | 20 |