Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.64000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.2 | ||
Root | \(-0.437016 - 1.34500i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.81 |
Dual form | 605.2.g.f.366.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.335106 | + | 0.243469i | 0.236956 | + | 0.172158i | 0.699926 | − | 0.714215i | \(-0.253216\pi\) |
−0.462970 | + | 0.886374i | \(0.653216\pi\) | |||||||
\(3\) | 0.874032 | − | 2.68999i | 0.504623 | − | 1.55307i | −0.296781 | − | 0.954945i | \(-0.595913\pi\) |
0.801404 | − | 0.598123i | \(-0.204087\pi\) | |||||||
\(4\) | −0.565015 | − | 1.73894i | −0.282508 | − | 0.869469i | ||||
\(5\) | 0.809017 | − | 0.587785i | 0.361803 | − | 0.262866i | ||||
\(6\) | 0.947822 | − | 0.688633i | 0.386947 | − | 0.281133i | ||||
\(7\) | −0.618034 | − | 1.90211i | −0.233595 | − | 0.718931i | −0.997305 | − | 0.0733714i | \(-0.976624\pi\) |
0.763710 | − | 0.645560i | \(-0.223376\pi\) | |||||||
\(8\) | 0.490035 | − | 1.50817i | 0.173254 | − | 0.533220i | ||||
\(9\) | −4.04508 | − | 2.93893i | −1.34836 | − | 0.979642i | ||||
\(10\) | 0.414214 | 0.130986 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −5.17157 | −1.49290 | ||||||||
\(13\) | 5.52431 | + | 4.01365i | 1.53217 | + | 1.11319i | 0.955018 | + | 0.296549i | \(0.0958356\pi\) |
0.577151 | + | 0.816637i | \(0.304164\pi\) | |||||||
\(14\) | 0.255998 | − | 0.787881i | 0.0684184 | − | 0.210570i | ||||
\(15\) | −0.874032 | − | 2.68999i | −0.225674 | − | 0.694553i | ||||
\(16\) | −2.42705 | + | 1.76336i | −0.606763 | + | 0.440839i | ||||
\(17\) | −0.947822 | + | 0.688633i | −0.229881 | + | 0.167018i | −0.696763 | − | 0.717301i | \(-0.745377\pi\) |
0.466882 | + | 0.884319i | \(0.345377\pi\) | |||||||
\(18\) | −0.639995 | − | 1.96970i | −0.150848 | − | 0.464263i | ||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | −1.47923 | − | 1.07472i | −0.330766 | − | 0.240315i | ||||
\(21\) | −5.65685 | −1.23443 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | −3.62867 | − | 2.63638i | −0.740699 | − | 0.538149i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 0.874032 | + | 2.68999i | 0.171412 | + | 0.527551i | ||||
\(27\) | −4.57649 | + | 3.32502i | −0.880746 | + | 0.639900i | ||||
\(28\) | −2.95846 | + | 2.14944i | −0.559096 | + | 0.406207i | ||||
\(29\) | 2.36610 | + | 7.28210i | 0.439373 | + | 1.35225i | 0.888538 | + | 0.458803i | \(0.151722\pi\) |
−0.449165 | + | 0.893449i | \(0.648278\pi\) | |||||||
\(30\) | 0.362036 | − | 1.11423i | 0.0660984 | − | 0.203430i | ||||
\(31\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.485281 | −0.0832251 | ||||||||
\(35\) | −1.61803 | − | 1.17557i | −0.273498 | − | 0.198708i | ||||
\(36\) | −2.82508 | + | 8.69469i | −0.470846 | + | 1.44911i | ||||
\(37\) | 1.13003 | + | 3.47788i | 0.185776 | + | 0.571759i | 0.999961 | − | 0.00884630i | \(-0.00281590\pi\) |
−0.814185 | + | 0.580605i | \(0.802816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.6251 | − | 11.3523i | 2.50202 | − | 1.81782i | ||||
\(40\) | −0.490035 | − | 1.50817i | −0.0774813 | − | 0.238463i | ||||
\(41\) | 1.85410 | − | 5.70634i | 0.289562 | − | 0.891180i | −0.695432 | − | 0.718592i | \(-0.744787\pi\) |
0.984994 | − | 0.172588i | \(-0.0552131\pi\) | |||||||
\(42\) | −1.89564 | − | 1.37727i | −0.292504 | − | 0.212517i | ||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.00000 | −0.745356 | ||||||||
\(46\) | 0.947822 | + | 0.688633i | 0.139749 | + | 0.101533i | ||||
\(47\) | −0.874032 | + | 2.68999i | −0.127491 | + | 0.392376i | −0.994347 | − | 0.106183i | \(-0.966137\pi\) |
0.866856 | + | 0.498559i | \(0.166137\pi\) | |||||||
\(48\) | 2.62210 | + | 8.06998i | 0.378467 | + | 1.16480i | ||||
\(49\) | 2.42705 | − | 1.76336i | 0.346722 | − | 0.251908i | ||||
\(50\) | 0.335106 | − | 0.243469i | 0.0473911 | − | 0.0344317i | ||||
\(51\) | 1.02399 | + | 3.15152i | 0.143388 | + | 0.441302i | ||||
\(52\) | 3.85816 | − | 11.8742i | 0.535031 | − | 1.64666i | ||||
\(53\) | −0.277611 | − | 0.201696i | −0.0381328 | − | 0.0277051i | 0.568556 | − | 0.822645i | \(-0.307502\pi\) |
−0.606688 | + | 0.794940i | \(0.707502\pi\) | |||||||
\(54\) | −2.34315 | −0.318862 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.17157 | −0.423819 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.980070 | + | 3.01635i | −0.128689 | + | 0.396066i | ||||
\(59\) | −2.98413 | − | 9.18421i | −0.388501 | − | 1.19568i | −0.933909 | − | 0.357512i | \(-0.883625\pi\) |
0.545408 | − | 0.838171i | \(-0.316375\pi\) | |||||||
\(60\) | −4.18389 | + | 3.03977i | −0.540138 | + | 0.392433i | ||||
\(61\) | −10.7710 | + | 7.82560i | −1.37909 | + | 1.00197i | −0.382123 | + | 0.924112i | \(0.624807\pi\) |
−0.996965 | + | 0.0778539i | \(0.975193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.09017 | + | 9.51057i | −0.389325 | + | 1.19822i | ||||
\(64\) | 3.37487 | + | 2.45199i | 0.421859 | + | 0.306499i | ||||
\(65\) | 6.82843 | 0.846962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48528 | −0.547964 | −0.273982 | − | 0.961735i | \(-0.588341\pi\) | ||||
−0.273982 | + | 0.961735i | \(0.588341\pi\) | |||||||
\(68\) | 1.73302 | + | 1.25912i | 0.210160 | + | 0.152690i | ||||
\(69\) | 2.47214 | − | 7.60845i | 0.297610 | − | 0.915950i | ||||
\(70\) | −0.255998 | − | 0.787881i | −0.0305976 | − | 0.0941698i | ||||
\(71\) | 9.15298 | − | 6.65003i | 1.08626 | − | 0.789213i | 0.107496 | − | 0.994206i | \(-0.465717\pi\) |
0.978764 | + | 0.204992i | \(0.0657169\pi\) | |||||||
\(72\) | −6.41464 | + | 4.66051i | −0.755973 | + | 0.549246i | ||||
\(73\) | −2.11010 | − | 6.49422i | −0.246969 | − | 0.760091i | −0.995306 | − | 0.0967733i | \(-0.969148\pi\) |
0.748338 | − | 0.663318i | \(-0.230852\pi\) | |||||||
\(74\) | −0.468074 | + | 1.44058i | −0.0544125 | + | 0.167464i | ||||
\(75\) | −2.28825 | − | 1.66251i | −0.264224 | − | 0.191970i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.00000 | 0.905822 | ||||||||
\(79\) | −3.23607 | − | 2.35114i | −0.364086 | − | 0.264524i | 0.390668 | − | 0.920532i | \(-0.372244\pi\) |
−0.754754 | + | 0.656007i | \(0.772244\pi\) | |||||||
\(80\) | −0.927051 | + | 2.85317i | −0.103647 | + | 0.318994i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 2.01063 | − | 1.46081i | 0.222037 | − | 0.161320i | ||||
\(83\) | 4.85410 | − | 3.52671i | 0.532807 | − | 0.387107i | −0.288600 | − | 0.957450i | \(-0.593190\pi\) |
0.821407 | + | 0.570343i | \(0.193190\pi\) | |||||||
\(84\) | 3.19621 | + | 9.83692i | 0.348735 | + | 1.07330i | ||||
\(85\) | −0.362036 | + | 1.11423i | −0.0392683 | + | 0.120855i | ||||
\(86\) | −2.01063 | − | 1.46081i | −0.216812 | − | 0.157523i | ||||
\(87\) | 21.6569 | 2.32186 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.31371 | 0.987251 | 0.493626 | − | 0.869675i | \(-0.335671\pi\) | ||||
0.493626 | + | 0.869675i | \(0.335671\pi\) | |||||||
\(90\) | −1.67553 | − | 1.21734i | −0.176616 | − | 0.128319i | ||||
\(91\) | 4.22020 | − | 12.9884i | 0.442397 | − | 1.36156i | ||||
\(92\) | −1.59810 | − | 4.91846i | −0.166614 | − | 0.512785i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.947822 | + | 0.688633i | −0.0977604 | + | 0.0710271i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.85816 | + | 11.8742i | −0.393772 | + | 1.21191i | ||||
\(97\) | 6.19453 | + | 4.50059i | 0.628959 | + | 0.456965i | 0.856039 | − | 0.516911i | \(-0.172918\pi\) |
−0.227081 | + | 0.973876i | \(0.572918\pi\) | |||||||
\(98\) | 1.24264 | 0.125526 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.82843 | −0.182843 | ||||||||
\(101\) | 10.7710 | + | 7.82560i | 1.07176 | + | 0.778676i | 0.976227 | − | 0.216750i | \(-0.0695457\pi\) |
0.0955291 | + | 0.995427i | \(0.469546\pi\) | |||||||
\(102\) | −0.424151 | + | 1.30540i | −0.0419973 | + | 0.129254i | ||||
\(103\) | 0.362036 | + | 1.11423i | 0.0356725 | + | 0.109789i | 0.967307 | − | 0.253608i | \(-0.0816172\pi\) |
−0.931635 | + | 0.363396i | \(0.881617\pi\) | |||||||
\(104\) | 8.76038 | − | 6.36479i | 0.859026 | − | 0.624119i | ||||
\(105\) | −4.57649 | + | 3.32502i | −0.446620 | + | 0.324488i | ||||
\(106\) | −0.0439223 | − | 0.135179i | −0.00426611 | − | 0.0131297i | ||||
\(107\) | −1.13003 | + | 3.47788i | −0.109244 | + | 0.336219i | −0.990703 | − | 0.136042i | \(-0.956562\pi\) |
0.881459 | + | 0.472261i | \(0.156562\pi\) | |||||||
\(108\) | 8.36778 | + | 6.07955i | 0.805190 | + | 0.585005i | ||||
\(109\) | 3.65685 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3431 | 0.981728 | ||||||||
\(112\) | 4.85410 | + | 3.52671i | 0.458670 | + | 0.333243i | ||||
\(113\) | 2.57817 | − | 7.93480i | 0.242534 | − | 0.746443i | −0.753498 | − | 0.657450i | \(-0.771635\pi\) |
0.996032 | − | 0.0889933i | \(-0.0283650\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.28825 | − | 1.66251i | 0.213380 | − | 0.155030i | ||||
\(116\) | 11.3262 | − | 8.22899i | 1.05161 | − | 0.764043i | ||||
\(117\) | −10.5505 | − | 32.4711i | −0.975394 | − | 3.00195i | ||||
\(118\) | 1.23607 | − | 3.80423i | 0.113789 | − | 0.350207i | ||||
\(119\) | 1.89564 | + | 1.37727i | 0.173773 | + | 0.126254i | ||||
\(120\) | −4.48528 | −0.409448 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.51472 | −0.499279 | ||||||||
\(123\) | −13.7295 | − | 9.97505i | −1.23794 | − | 0.899420i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.309017 | − | 0.951057i | −0.0276393 | − | 0.0850651i | ||||
\(126\) | −3.35106 | + | 2.43469i | −0.298536 | + | 0.216899i | ||||
\(127\) | −12.6667 | + | 9.20287i | −1.12398 | + | 0.816622i | −0.984808 | − | 0.173645i | \(-0.944445\pi\) |
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(128\) | 3.26209 | + | 10.0397i | 0.288331 | + | 0.887391i | ||||
\(129\) | −5.24419 | + | 16.1400i | −0.461725 | + | 1.42104i | ||||
\(130\) | 2.28825 | + | 1.66251i | 0.200692 | + | 0.145812i | ||||
\(131\) | 11.3137 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.50304 | − | 1.09203i | −0.129843 | − | 0.0943366i | ||||
\(135\) | −1.74806 | + | 5.37999i | −0.150449 | + | 0.463036i | ||||
\(136\) | 0.574112 | + | 1.76693i | 0.0492297 | + | 0.151513i | ||||
\(137\) | −18.5836 | + | 13.5018i | −1.58770 | + | 1.15353i | −0.680573 | + | 0.732680i | \(0.738269\pi\) |
−0.907129 | + | 0.420853i | \(0.861731\pi\) | |||||||
\(138\) | 2.68085 | − | 1.94775i | 0.228209 | − | 0.165803i | ||||
\(139\) | −1.23607 | − | 3.80423i | −0.104842 | − | 0.322670i | 0.884851 | − | 0.465873i | \(-0.154260\pi\) |
−0.989693 | + | 0.143203i | \(0.954260\pi\) | |||||||
\(140\) | −1.13003 | + | 3.47788i | −0.0955050 | + | 0.293934i | ||||
\(141\) | 6.47214 | + | 4.70228i | 0.545052 | + | 0.396004i | ||||
\(142\) | 4.68629 | 0.393265 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | 6.19453 | + | 4.50059i | 0.514427 | + | 0.373753i | ||||
\(146\) | 0.874032 | − | 2.68999i | 0.0723354 | − | 0.222625i | ||||
\(147\) | −2.62210 | − | 8.06998i | −0.216267 | − | 0.665601i | ||||
\(148\) | 5.40932 | − | 3.93010i | 0.444644 | − | 0.323053i | ||||
\(149\) | −9.43059 | + | 6.85173i | −0.772584 | + | 0.561315i | −0.902744 | − | 0.430178i | \(-0.858451\pi\) |
0.130160 | + | 0.991493i | \(0.458451\pi\) | |||||||
\(150\) | −0.362036 | − | 1.11423i | −0.0295601 | − | 0.0909767i | ||||
\(151\) | −3.70820 | + | 11.4127i | −0.301769 | + | 0.928751i | 0.679094 | + | 0.734052i | \(0.262373\pi\) |
−0.980863 | + | 0.194699i | \(0.937627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.85786 | 0.473580 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −28.5694 | − | 20.7569i | −2.28738 | − | 1.66188i | ||||
\(157\) | −4.32624 | + | 13.3148i | −0.345271 | + | 1.06264i | 0.616167 | + | 0.787616i | \(0.288685\pi\) |
−0.961438 | + | 0.275020i | \(0.911315\pi\) | |||||||
\(158\) | −0.511996 | − | 1.57576i | −0.0407322 | − | 0.125361i | ||||
\(159\) | −0.785202 | + | 0.570482i | −0.0622705 | + | 0.0452422i | ||||
\(160\) | −3.57117 | + | 2.59461i | −0.282326 | + | 0.205122i | ||||
\(161\) | −1.74806 | − | 5.37999i | −0.137767 | − | 0.424002i | ||||
\(162\) | −0.127999 | + | 0.393941i | −0.0100566 | + | 0.0309509i | ||||
\(163\) | 0.392601 | + | 0.285241i | 0.0307509 | + | 0.0223418i | 0.603055 | − | 0.797700i | \(-0.293950\pi\) |
−0.572304 | + | 0.820042i | \(0.693950\pi\) | |||||||
\(164\) | −10.9706 | −0.856657 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.48528 | 0.192895 | ||||||||
\(167\) | −8.87537 | − | 6.44833i | −0.686797 | − | 0.498987i | 0.188809 | − | 0.982014i | \(-0.439537\pi\) |
−0.875606 | + | 0.483027i | \(0.839537\pi\) | |||||||
\(168\) | −2.77206 | + | 8.53151i | −0.213869 | + | 0.658220i | ||||
\(169\) | 10.3914 | + | 31.9816i | 0.799342 | + | 2.46012i | ||||
\(170\) | −0.392601 | + | 0.285241i | −0.0301111 | + | 0.0218770i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.39009 | + | 10.4336i | 0.258492 | + | 0.795556i | ||||
\(173\) | 1.89802 | − | 5.84152i | 0.144304 | − | 0.444122i | −0.852617 | − | 0.522537i | \(-0.824986\pi\) |
0.996921 | + | 0.0784144i | \(0.0249857\pi\) | |||||||
\(174\) | 7.25734 | + | 5.27276i | 0.550177 | + | 0.399727i | ||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.3137 | −2.05302 | ||||||||
\(178\) | 3.12108 | + | 2.26760i | 0.233935 | + | 0.169963i | ||||
\(179\) | −0.511996 | + | 1.57576i | −0.0382684 | + | 0.117778i | −0.968366 | − | 0.249535i | \(-0.919722\pi\) |
0.930097 | + | 0.367313i | \(0.119722\pi\) | |||||||
\(180\) | 2.82508 | + | 8.69469i | 0.210569 | + | 0.648064i | ||||
\(181\) | 1.06281 | − | 0.772178i | 0.0789982 | − | 0.0573956i | −0.547585 | − | 0.836750i | \(-0.684453\pi\) |
0.626583 | + | 0.779354i | \(0.284453\pi\) | |||||||
\(182\) | 4.57649 | − | 3.32502i | 0.339232 | − | 0.246467i | ||||
\(183\) | 11.6366 | + | 35.8138i | 0.860203 | + | 2.64743i | ||||
\(184\) | 1.38603 | − | 4.26576i | 0.102179 | − | 0.314476i | ||||
\(185\) | 2.95846 | + | 2.14944i | 0.217510 | + | 0.158030i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.17157 | 0.377176 | ||||||||
\(189\) | 9.15298 | + | 6.65003i | 0.665782 | + | 0.483719i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.96826 | − | 18.3684i | −0.431848 | − | 1.32909i | −0.896282 | − | 0.443485i | \(-0.853742\pi\) |
0.464433 | − | 0.885608i | \(-0.346258\pi\) | |||||||
\(192\) | 9.54558 | − | 6.93527i | 0.688893 | − | 0.500510i | ||||
\(193\) | 5.52431 | − | 4.01365i | 0.397649 | − | 0.288909i | −0.370934 | − | 0.928659i | \(-0.620962\pi\) |
0.768583 | + | 0.639751i | \(0.220962\pi\) | |||||||
\(194\) | 0.980070 | + | 3.01635i | 0.0703649 | + | 0.216561i | ||||
\(195\) | 5.96826 | − | 18.3684i | 0.427396 | − | 1.31539i | ||||
\(196\) | −4.43769 | − | 3.22417i | −0.316978 | − | 0.230298i | ||||
\(197\) | −5.17157 | −0.368459 | −0.184230 | − | 0.982883i | \(-0.558979\pi\) | ||||
−0.184230 | + | 0.982883i | \(0.558979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6569 | 1.53521 | 0.767607 | − | 0.640921i | \(-0.221447\pi\) | ||||
0.767607 | + | 0.640921i | \(0.221447\pi\) | |||||||
\(200\) | −1.28293 | − | 0.932102i | −0.0907167 | − | 0.0659096i | ||||
\(201\) | −3.92028 | + | 12.0654i | −0.276515 | + | 0.851026i | ||||
\(202\) | 1.70414 | + | 5.24481i | 0.119903 | + | 0.369023i | ||||
\(203\) | 12.3891 | − | 9.00117i | 0.869541 | − | 0.631758i | ||||
\(204\) | 4.90173 | − | 3.56132i | 0.343190 | − | 0.249342i | ||||
\(205\) | −1.85410 | − | 5.70634i | −0.129496 | − | 0.398548i | ||||
\(206\) | −0.149960 | + | 0.461530i | −0.0104482 | + | 0.0321563i | ||||
\(207\) | −11.4412 | − | 8.31254i | −0.795220 | − | 0.577761i | ||||
\(208\) | −20.4853 | −1.42040 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.34315 | −0.161692 | ||||||||
\(211\) | 12.9443 | + | 9.40456i | 0.891120 | + | 0.647437i | 0.936170 | − | 0.351548i | \(-0.114345\pi\) |
−0.0450495 | + | 0.998985i | \(0.514345\pi\) | |||||||
\(212\) | −0.193883 | + | 0.596709i | −0.0133159 | + | 0.0409821i | ||||
\(213\) | −9.88854 | − | 30.4338i | −0.677552 | − | 2.08529i | ||||
\(214\) | −1.22543 | + | 0.890329i | −0.0837689 | + | 0.0608617i | ||||
\(215\) | −4.85410 | + | 3.52671i | −0.331047 | + | 0.240520i | ||||
\(216\) | 2.77206 | + | 8.53151i | 0.188615 | + | 0.580496i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.22543 | + | 0.890329i | 0.0829968 | + | 0.0603007i | ||||
\(219\) | −19.3137 | −1.30510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 3.46605 | + | 2.51823i | 0.232626 | + | 0.169013i | ||||
\(223\) | −1.59810 | + | 4.91846i | −0.107017 | + | 0.329364i | −0.990199 | − | 0.139667i | \(-0.955397\pi\) |
0.883182 | + | 0.469031i | \(0.155397\pi\) | |||||||
\(224\) | 2.72813 | + | 8.39633i | 0.182281 | + | 0.561004i | ||||
\(225\) | −4.04508 | + | 2.93893i | −0.269672 | + | 0.195928i | ||||
\(226\) | 2.79584 | − | 2.03129i | 0.185976 | − | 0.135120i | ||||
\(227\) | 0.830110 | + | 2.55482i | 0.0550963 | + | 0.169569i | 0.974818 | − | 0.223002i | \(-0.0715857\pi\) |
−0.919722 | + | 0.392571i | \(0.871586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.2432 | + | 12.5279i | 1.13946 | + | 0.827866i | 0.987044 | − | 0.160451i | \(-0.0512947\pi\) |
0.152416 | + | 0.988316i | \(0.451295\pi\) | |||||||
\(230\) | 1.17157 | 0.0772512 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.1421 | 0.797170 | ||||||||
\(233\) | −17.9134 | − | 13.0148i | −1.17354 | − | 0.852629i | −0.182115 | − | 0.983277i | \(-0.558294\pi\) |
−0.991429 | + | 0.130648i | \(0.958294\pi\) | |||||||
\(234\) | 4.37016 | − | 13.4500i | 0.285686 | − | 0.879252i | ||||
\(235\) | 0.874032 | + | 2.68999i | 0.0570156 | + | 0.175476i | ||||
\(236\) | −14.2847 | + | 10.3784i | −0.929854 | + | 0.675579i | ||||
\(237\) | −9.15298 | + | 6.65003i | −0.594550 | + | 0.431966i | ||||
\(238\) | 0.299920 | + | 0.923060i | 0.0194410 | + | 0.0598331i | ||||
\(239\) | −0.212076 | + | 0.652702i | −0.0137180 | + | 0.0422198i | −0.957681 | − | 0.287831i | \(-0.907066\pi\) |
0.943963 | + | 0.330051i | \(0.107066\pi\) | |||||||
\(240\) | 6.86474 | + | 4.98752i | 0.443117 | + | 0.321943i | ||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1421 | −0.907218 | ||||||||
\(244\) | 19.6940 | + | 14.3085i | 1.26078 | + | 0.916011i | ||||
\(245\) | 0.927051 | − | 2.85317i | 0.0592271 | − | 0.182282i | ||||
\(246\) | −2.17222 | − | 6.68539i | −0.138495 | − | 0.426245i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.24419 | − | 16.1400i | −0.332337 | − | 1.02283i | ||||
\(250\) | 0.127999 | − | 0.393941i | 0.00809537 | − | 0.0249150i | ||||
\(251\) | −9.70820 | − | 7.05342i | −0.612776 | − | 0.445208i | 0.237614 | − | 0.971360i | \(-0.423635\pi\) |
−0.850391 | + | 0.526151i | \(0.823635\pi\) | |||||||
\(252\) | 18.2843 | 1.15180 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.48528 | −0.406923 | ||||||||
\(255\) | 2.68085 | + | 1.94775i | 0.167881 | + | 0.121973i | ||||
\(256\) | 1.22697 | − | 3.77623i | 0.0766857 | − | 0.236014i | ||||
\(257\) | 4.11416 | + | 12.6621i | 0.256634 | + | 0.789839i | 0.993503 | + | 0.113804i | \(0.0363035\pi\) |
−0.736869 | + | 0.676036i | \(0.763696\pi\) | |||||||
\(258\) | −5.68693 | + | 4.13180i | −0.354053 | + | 0.257235i | ||||
\(259\) | 5.91691 | − | 4.29889i | 0.367659 | − | 0.267120i | ||||
\(260\) | −3.85816 | − | 11.8742i | −0.239273 | − | 0.736407i | ||||
\(261\) | 11.8305 | − | 36.4105i | 0.732289 | − | 2.25375i | ||||
\(262\) | 3.79129 | + | 2.75453i | 0.234227 | + | 0.170176i | ||||
\(263\) | 22.9706 | 1.41643 | 0.708213 | − | 0.705999i | \(-0.249502\pi\) | ||||
0.708213 | + | 0.705999i | \(0.249502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.343146 | −0.0210793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.14048 | − | 25.0538i | 0.498189 | − | 1.53327i | ||||
\(268\) | 2.53425 | + | 7.79962i | 0.154804 | + | 0.476438i | ||||
\(269\) | 4.29888 | − | 3.12332i | 0.262107 | − | 0.190432i | −0.448968 | − | 0.893548i | \(-0.648208\pi\) |
0.711076 | + | 0.703116i | \(0.248208\pi\) | |||||||
\(270\) | −1.89564 | + | 1.37727i | −0.115365 | + | 0.0838178i | ||||
\(271\) | −4.73220 | − | 14.5642i | −0.287460 | − | 0.884712i | −0.985650 | − | 0.168800i | \(-0.946011\pi\) |
0.698190 | − | 0.715913i | \(-0.253989\pi\) | |||||||
\(272\) | 1.08611 | − | 3.34270i | 0.0658550 | − | 0.202681i | ||||
\(273\) | −31.2502 | − | 22.7046i | −1.89135 | − | 1.37415i | ||||
\(274\) | −9.51472 | −0.574805 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.6274 | −0.880467 | ||||||||
\(277\) | −0.947822 | − | 0.688633i | −0.0569491 | − | 0.0413760i | 0.558947 | − | 0.829204i | \(-0.311206\pi\) |
−0.615896 | + | 0.787828i | \(0.711206\pi\) | |||||||
\(278\) | 0.511996 | − | 1.57576i | 0.0307075 | − | 0.0945079i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.56586 | + | 1.86420i | −0.153339 | + | 0.111407i | ||||
\(281\) | 4.29888 | − | 3.12332i | 0.256450 | − | 0.186322i | −0.452131 | − | 0.891952i | \(-0.649336\pi\) |
0.708580 | + | 0.705630i | \(0.249336\pi\) | |||||||
\(282\) | 1.02399 | + | 3.15152i | 0.0609779 | + | 0.187671i | ||||
\(283\) | −3.90209 | + | 12.0094i | −0.231955 | + | 0.713884i | 0.765556 | + | 0.643370i | \(0.222464\pi\) |
−0.997511 | + | 0.0705145i | \(0.977536\pi\) | |||||||
\(284\) | −16.7356 | − | 12.1591i | −0.993073 | − | 0.721510i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 17.8559 | + | 12.9730i | 1.05217 | + | 0.764444i | ||||
\(289\) | −4.82914 | + | 14.8626i | −0.284067 | + | 0.874268i | ||||
\(290\) | 0.980070 | + | 3.01635i | 0.0575517 | + | 0.177126i | ||||
\(291\) | 17.5208 | − | 12.7296i | 1.02709 | − | 0.746221i | ||||
\(292\) | −10.1008 | + | 7.33866i | −0.591105 | + | 0.429463i | ||||
\(293\) | −4.58224 | − | 14.1027i | −0.267697 | − | 0.823887i | −0.991060 | − | 0.133419i | \(-0.957405\pi\) |
0.723363 | − | 0.690468i | \(-0.242595\pi\) | |||||||
\(294\) | 1.08611 | − | 3.34270i | 0.0633431 | − | 0.194950i | ||||
\(295\) | −7.81256 | − | 5.67616i | −0.454865 | − | 0.330479i | ||||
\(296\) | 5.79899 | 0.337059 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.82843 | −0.279703 | ||||||||
\(299\) | 15.6251 | + | 11.3523i | 0.903624 | + | 0.656521i | ||||
\(300\) | −1.59810 | + | 4.91846i | −0.0922666 | + | 0.283967i | ||||
\(301\) | 3.70820 | + | 11.4127i | 0.213737 | + | 0.657816i | ||||
\(302\) | −4.02127 | + | 2.92162i | −0.231398 | + | 0.168121i | ||||
\(303\) | 30.4650 | − | 22.1341i | 1.75017 | − | 1.27157i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.11416 | + | 12.6621i | −0.235576 | + | 0.725029i | ||||
\(306\) | 1.96300 | + | 1.42621i | 0.112217 | + | 0.0815308i | ||||
\(307\) | −27.6569 | −1.57846 | −0.789230 | − | 0.614098i | \(-0.789520\pi\) | ||||
−0.789230 | + | 0.614098i | \(0.789520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.31371 | 0.188510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.44040 | − | 25.9769i | 0.478611 | − | 1.47301i | −0.362414 | − | 0.932017i | \(-0.618047\pi\) |
0.841025 | − | 0.540996i | \(-0.181953\pi\) | |||||||
\(312\) | −9.46439 | − | 29.1284i | −0.535816 | − | 1.64907i | ||||
\(313\) | −17.2432 | + | 12.5279i | −0.974641 | + | 0.708118i | −0.956504 | − | 0.291718i | \(-0.905773\pi\) |
−0.0181361 | + | 0.999836i | \(0.505773\pi\) | |||||||
\(314\) | −4.69148 | + | 3.40856i | −0.264756 | + | 0.192356i | ||||
\(315\) | 3.09017 | + | 9.51057i | 0.174111 | + | 0.535860i | ||||
\(316\) | −2.26006 | + | 6.95575i | −0.127138 | + | 0.391292i | ||||
\(317\) | −17.2432 | − | 12.5279i | −0.968472 | − | 0.703636i | −0.0133691 | − | 0.999911i | \(-0.504256\pi\) |
−0.955103 | + | 0.296275i | \(0.904256\pi\) | |||||||
\(318\) | −0.402020 | −0.0225442 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.17157 | 0.233198 | ||||||||
\(321\) | 8.36778 | + | 6.07955i | 0.467044 | + | 0.339327i | ||||
\(322\) | 0.724072 | − | 2.22846i | 0.0403509 | − | 0.124187i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.47923 | − | 1.07472i | 0.0821794 | − | 0.0597068i | ||||
\(325\) | 5.52431 | − | 4.01365i | 0.306434 | − | 0.222637i | ||||
\(326\) | 0.0621155 | + | 0.191172i | 0.00344026 | + | 0.0105880i | ||||
\(327\) | 3.19621 | − | 9.83692i | 0.176751 | − | 0.543983i | ||||
\(328\) | −7.69757 | − | 5.59261i | −0.425027 | − | 0.308800i | ||||
\(329\) | 5.65685 | 0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3137 | 0.841718 | 0.420859 | − | 0.907126i | \(-0.361729\pi\) | ||||
0.420859 | + | 0.907126i | \(0.361729\pi\) | |||||||
\(332\) | −8.87537 | − | 6.44833i | −0.487099 | − | 0.353898i | ||||
\(333\) | 5.65015 | − | 17.3894i | 0.309626 | − | 0.952932i | ||||
\(334\) | −1.40422 | − | 4.32175i | −0.0768356 | − | 0.236476i | ||||
\(335\) | −3.62867 | + | 2.63638i | −0.198255 | + | 0.144041i | ||||
\(336\) | 13.7295 | − | 9.97505i | 0.749004 | − | 0.544183i | ||||
\(337\) | −1.08611 | − | 3.34270i | −0.0591641 | − | 0.182088i | 0.917107 | − | 0.398642i | \(-0.130518\pi\) |
−0.976271 | + | 0.216554i | \(0.930518\pi\) | |||||||
\(338\) | −4.30428 | + | 13.2472i | −0.234122 | + | 0.720553i | ||||
\(339\) | −19.0912 | − | 13.8705i | −1.03689 | − | 0.753345i | ||||
\(340\) | 2.14214 | 0.116174 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1803 | − | 11.7557i | −0.873656 | − | 0.634748i | ||||
\(344\) | −2.94021 | + | 9.04904i | −0.158525 | + | 0.487891i | ||||
\(345\) | −2.47214 | − | 7.60845i | −0.133095 | − | 0.409625i | ||||
\(346\) | 2.05827 | − | 1.49542i | 0.110653 | − | 0.0803941i | ||||
\(347\) | 18.5836 | − | 13.5018i | 0.997619 | − | 0.724812i | 0.0360423 | − | 0.999350i | \(-0.488525\pi\) |
0.961576 | + | 0.274538i | \(0.0885249\pi\) | |||||||
\(348\) | −12.2364 | − | 37.6599i | −0.655943 | − | 2.01878i | ||||
\(349\) | −2.15402 | + | 6.62940i | −0.115302 | + | 0.354864i | −0.992010 | − | 0.126160i | \(-0.959735\pi\) |
0.876708 | + | 0.481023i | \(0.159735\pi\) | |||||||
\(350\) | −0.670212 | − | 0.486937i | −0.0358243 | − | 0.0260279i | ||||
\(351\) | −38.6274 | −2.06178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.31371 | −0.0699216 | −0.0349608 | − | 0.999389i | \(-0.511131\pi\) | ||||
−0.0349608 | + | 0.999389i | \(0.511131\pi\) | |||||||
\(354\) | −9.15298 | − | 6.65003i | −0.486476 | − | 0.353445i | ||||
\(355\) | 3.49613 | − | 10.7600i | 0.185555 | − | 0.571080i | ||||
\(356\) | −5.26239 | − | 16.1960i | −0.278906 | − | 0.858384i | ||||
\(357\) | 5.36169 | − | 3.89550i | 0.283771 | − | 0.206172i | ||||
\(358\) | −0.555221 | + | 0.403392i | −0.0293444 | + | 0.0213199i | ||||
\(359\) | 7.20433 | + | 22.1727i | 0.380230 | + | 1.17023i | 0.939882 | + | 0.341500i | \(0.110935\pi\) |
−0.559652 | + | 0.828728i | \(0.689065\pi\) | |||||||
\(360\) | −2.45017 | + | 7.54086i | −0.129136 | + | 0.397438i | ||||
\(361\) | 15.3713 | + | 11.1679i | 0.809017 | + | 0.587785i | ||||
\(362\) | 0.544156 | 0.0286002 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.9706 | −1.30881 | ||||||||
\(365\) | −5.52431 | − | 4.01365i | −0.289156 | − | 0.210084i | ||||
\(366\) | −4.82004 | + | 14.8346i | −0.251948 | + | 0.775415i | ||||
\(367\) | 2.62210 | + | 8.06998i | 0.136872 | + | 0.421250i | 0.995877 | − | 0.0907188i | \(-0.0289165\pi\) |
−0.859004 | + | 0.511968i | \(0.828916\pi\) | |||||||
\(368\) | −6.86474 | + | 4.98752i | −0.357849 | + | 0.259993i | ||||
\(369\) | −24.2705 | + | 17.6336i | −1.26347 | + | 0.917966i | ||||
\(370\) | 0.468074 | + | 1.44058i | 0.0243340 | + | 0.0748923i | ||||
\(371\) | −0.212076 | + | 0.652702i | −0.0110104 | + | 0.0338866i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.79899 | −0.196704 | −0.0983521 | − | 0.995152i | \(-0.531357\pi\) | ||||
−0.0983521 | + | 0.995152i | \(0.531357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.82843 | −0.146059 | ||||||||
\(376\) | 3.62867 | + | 2.63638i | 0.187134 | + | 0.135961i | ||||
\(377\) | −16.1567 | + | 49.7253i | −0.832114 | + | 2.56098i | ||||
\(378\) | 1.44814 | + | 4.45693i | 0.0744845 | + | 0.229240i | ||||
\(379\) | −18.0760 | + | 13.1330i | −0.928501 | + | 0.674595i | −0.945625 | − | 0.325258i | \(-0.894549\pi\) |
0.0171244 | + | 0.999853i | \(0.494549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6846 | + | 42.1168i | 0.701083 | + | 2.15771i | ||||
\(382\) | 2.47214 | − | 7.60845i | 0.126485 | − | 0.389282i | ||||
\(383\) | 27.6216 | + | 20.0682i | 1.41140 | + | 1.02544i | 0.993118 | + | 0.117121i | \(0.0373664\pi\) |
0.418278 | + | 0.908319i | \(0.362634\pi\) | |||||||
\(384\) | 29.8579 | 1.52368 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.82843 | 0.143963 | ||||||||
\(387\) | 24.2705 | + | 17.6336i | 1.23374 | + | 0.896364i | ||||
\(388\) | 4.32624 | − | 13.3148i | 0.219631 | − | 0.675956i | ||||
\(389\) | −7.61029 | − | 23.4221i | −0.385857 | − | 1.18755i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.550000 | − | 0.835165i | \(-0.314628\pi\) | |||||||
\(390\) | 6.47214 | − | 4.70228i | 0.327729 | − | 0.238109i | ||||
\(391\) | −2.68085 | + | 1.94775i | −0.135576 | + | 0.0985019i | ||||
\(392\) | −1.47010 | − | 4.52452i | −0.0742515 | − | 0.228523i | ||||
\(393\) | 9.88854 | − | 30.4338i | 0.498811 | − | 1.53518i | ||||
\(394\) | −1.73302 | − | 1.25912i | −0.0873085 | − | 0.0634333i | ||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3137 | 0.668196 | 0.334098 | − | 0.942538i | \(-0.391568\pi\) | ||||
0.334098 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(398\) | 7.25734 | + | 5.27276i | 0.363777 | + | 0.264300i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.927051 | + | 2.85317i | 0.0463525 | + | 0.142658i | ||||
\(401\) | −14.0071 | + | 10.1767i | −0.699480 | + | 0.508202i | −0.879763 | − | 0.475413i | \(-0.842299\pi\) |
0.180283 | + | 0.983615i | \(0.442299\pi\) | |||||||
\(402\) | −4.25125 | + | 3.08871i | −0.212033 | + | 0.154051i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7.52245 | − | 23.1517i | 0.374256 | − | 1.15184i | ||||
\(405\) | 0.809017 | + | 0.587785i | 0.0402004 | + | 0.0292073i | ||||
\(406\) | 6.34315 | 0.314805 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.25483 | 0.260153 | ||||||||
\(409\) | −28.2918 | − | 20.5552i | −1.39894 | − | 1.01639i | −0.994817 | − | 0.101683i | \(-0.967577\pi\) |
−0.404122 | − | 0.914705i | \(-0.632423\pi\) | |||||||
\(410\) | 0.767994 | − | 2.36364i | 0.0379285 | − | 0.116732i | ||||
\(411\) | 20.0770 | + | 61.7907i | 0.990326 | + | 3.04791i | ||||
\(412\) | 1.73302 | − | 1.25912i | 0.0853800 | − | 0.0620322i | ||||
\(413\) | −15.6251 | + | 11.3523i | −0.768862 | + | 0.558611i | ||||
\(414\) | −1.81018 | − | 5.57116i | −0.0889655 | − | 0.273808i | ||||
\(415\) | 1.85410 | − | 5.70634i | 0.0910143 | − | 0.280113i | ||||
\(416\) | −24.3855 | − | 17.7171i | −1.19560 | − | 0.868652i | ||||
\(417\) | −11.3137 | −0.554035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.3431 | −0.700709 | −0.350354 | − | 0.936617i | \(-0.613939\pi\) | ||||
−0.350354 | + | 0.936617i | \(0.613939\pi\) | |||||||
\(420\) | 8.36778 | + | 6.07955i | 0.408306 | + | 0.296652i | ||||
\(421\) | −1.85410 | + | 5.70634i | −0.0903634 | + | 0.278110i | −0.986018 | − | 0.166641i | \(-0.946708\pi\) |
0.895654 | + | 0.444751i | \(0.146708\pi\) | |||||||
\(422\) | 2.04798 | + | 6.30305i | 0.0996943 | + | 0.306828i | ||||
\(423\) | 11.4412 | − | 8.31254i | 0.556292 | − | 0.404169i | ||||
\(424\) | −0.440231 | + | 0.319847i | −0.0213795 | + | 0.0155331i | ||||
\(425\) | 0.362036 | + | 1.11423i | 0.0175613 | + | 0.0540482i | ||||
\(426\) | 4.09597 | − | 12.6061i | 0.198450 | − | 0.610767i | ||||
\(427\) | 21.5420 | + | 15.6512i | 1.04249 | + | 0.757415i | ||||
\(428\) | 6.68629 | 0.323194 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.48528 | −0.119851 | ||||||||
\(431\) | −9.15298 | − | 6.65003i | −0.440884 | − | 0.320321i | 0.345102 | − | 0.938565i | \(-0.387844\pi\) |
−0.785986 | + | 0.618244i | \(0.787844\pi\) | |||||||
\(432\) | 5.24419 | − | 16.1400i | 0.252311 | − | 0.776534i | ||||
\(433\) | 1.13003 | + | 3.47788i | 0.0543058 | + | 0.167136i | 0.974531 | − | 0.224254i | \(-0.0719944\pi\) |
−0.920225 | + | 0.391390i | \(0.871994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.5208 | − | 12.7296i | 0.840056 | − | 0.610337i | ||||
\(436\) | −2.06618 | − | 6.35904i | −0.0989520 | − | 0.304543i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.47214 | − | 4.70228i | −0.309251 | − | 0.224684i | ||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | −2.68085 | − | 1.94775i | −0.127515 | − | 0.0926450i | ||||
\(443\) | −6.54238 | + | 20.1354i | −0.310838 | + | 0.956660i | 0.666596 | + | 0.745419i | \(0.267751\pi\) |
−0.977434 | + | 0.211241i | \(0.932249\pi\) | |||||||
\(444\) | −5.84403 | − | 17.9861i | −0.277346 | − | 0.853582i | ||||
\(445\) | 7.53495 | − | 5.47446i | 0.357191 | − | 0.259514i | ||||
\(446\) | −1.73302 | + | 1.25912i | −0.0820611 | + | 0.0596209i | ||||
\(447\) | 10.1885 | + | 31.3569i | 0.481898 | + | 1.48313i | ||||
\(448\) | 2.57817 | − | 7.93480i | 0.121807 | − | 0.374884i | ||||
\(449\) | 13.4519 | + | 9.77335i | 0.634833 | + | 0.461233i | 0.858071 | − | 0.513531i | \(-0.171663\pi\) |
−0.223238 | + | 0.974764i | \(0.571663\pi\) | |||||||
\(450\) | −2.07107 | −0.0976311 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −15.2548 | −0.717527 | ||||||||
\(453\) | 27.4589 | + | 19.9501i | 1.29013 | + | 0.937337i | ||||
\(454\) | −0.343843 | + | 1.05824i | −0.0161373 | + | 0.0496656i | ||||
\(455\) | −4.22020 | − | 12.9884i | −0.197846 | − | 0.608907i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3369 | − | 9.68981i | 0.623873 | − | 0.453270i | −0.230399 | − | 0.973096i | \(-0.574003\pi\) |
0.854272 | + | 0.519826i | \(0.174003\pi\) | |||||||
\(458\) | 2.72813 | + | 8.39633i | 0.127477 | + | 0.392335i | ||||
\(459\) | 2.04798 | − | 6.30305i | 0.0955917 | − | 0.294201i | ||||
\(460\) | −4.18389 | − | 3.03977i | −0.195075 | − | 0.141730i | ||||
\(461\) | −32.6274 | −1.51961 | −0.759805 | − | 0.650151i | \(-0.774706\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1421 | 1.02903 | 0.514516 | − | 0.857481i | \(-0.327972\pi\) | ||||
0.514516 | + | 0.857481i | \(0.327972\pi\) | |||||||
\(464\) | −18.5836 | − | 13.5018i | −0.862721 | − | 0.626803i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.83417 | − | 8.72268i | −0.131290 | − | 0.404071i | ||||
\(467\) | 7.41996 | − | 5.39092i | 0.343355 | − | 0.249462i | −0.402721 | − | 0.915323i | \(-0.631936\pi\) |
0.746076 | + | 0.665861i | \(0.231936\pi\) | |||||||
\(468\) | −50.5040 | + | 36.6933i | −2.33455 | + | 1.69615i | ||||
\(469\) | 2.77206 | + | 8.53151i | 0.128002 | + | 0.393949i | ||||
\(470\) | −0.362036 | + | 1.11423i | −0.0166995 | + | 0.0513957i | ||||
\(471\) | 32.0354 | + | 23.2751i | 1.47612 | + | 1.07246i | ||||
\(472\) | −15.3137 | −0.704871 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4.68629 | −0.215248 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.32391 | − | 4.07458i | 0.0606814 | − | 0.186758i | ||||
\(477\) | 0.530189 | + | 1.63176i | 0.0242757 | + | 0.0747129i | ||||
\(478\) | −0.229980 | + | 0.167090i | −0.0105191 | + | 0.00764254i | ||||
\(479\) | 29.1246 | − | 21.1603i | 1.33074 | − | 0.966837i | 0.331007 | − | 0.943628i | \(-0.392612\pi\) |
0.999731 | − | 0.0232090i | \(-0.00738832\pi\) | |||||||
\(480\) | 3.85816 | + | 11.8742i | 0.176100 | + | 0.541981i | ||||
\(481\) | −7.71633 | + | 23.7484i | −0.351834 | + | 1.08283i | ||||
\(482\) | 2.01063 | + | 1.46081i | 0.0915819 | + | 0.0665382i | ||||
\(483\) | −16.0000 | −0.728025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.65685 | 0.347680 | ||||||||
\(486\) | −4.73911 | − | 3.44317i | −0.214970 | − | 0.156185i | ||||
\(487\) | −2.32218 | + | 7.14692i | −0.105228 | + | 0.323858i | −0.989784 | − | 0.142576i | \(-0.954461\pi\) |
0.884556 | + | 0.466434i | \(0.154461\pi\) | |||||||
\(488\) | 6.52418 | + | 20.0794i | 0.295336 | + | 0.908950i | ||||
\(489\) | 1.11044 | − | 0.806784i | 0.0502160 | − | 0.0364840i | ||||
\(490\) | 1.00532 | − | 0.730406i | 0.0454156 | − | 0.0329964i | ||||
\(491\) | −7.20433 | − | 22.1727i | −0.325127 | − | 1.00064i | −0.971383 | − | 0.237517i | \(-0.923666\pi\) |
0.646256 | − | 0.763120i | \(-0.276334\pi\) | |||||||
\(492\) | −9.58862 | + | 29.5107i | −0.432289 | + | 1.33045i | ||||
\(493\) | −7.25734 | − | 5.27276i | −0.326854 | − | 0.237473i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3060 | − | 13.3001i | −0.821135 | − | 0.596589i | ||||
\(498\) | 2.17222 | − | 6.68539i | 0.0973393 | − | 0.299580i | ||||
\(499\) | −0.511996 | − | 1.57576i | −0.0229201 | − | 0.0705408i | 0.938942 | − | 0.344075i | \(-0.111807\pi\) |
−0.961862 | + | 0.273534i | \(0.911807\pi\) | |||||||
\(500\) | −1.47923 | + | 1.07472i | −0.0661531 | + | 0.0480631i | ||||
\(501\) | −25.1033 | + | 18.2386i | −1.12153 | + | 0.814843i | ||||
\(502\) | −1.53599 | − | 4.72729i | −0.0685545 | − | 0.210989i | ||||
\(503\) | −8.84636 | + | 27.2263i | −0.394440 | + | 1.21396i | 0.534957 | + | 0.844879i | \(0.320328\pi\) |
−0.929397 | + | 0.369081i | \(0.879672\pi\) | |||||||
\(504\) | 12.8293 | + | 9.32102i | 0.571462 | + | 0.415191i | ||||
\(505\) | 13.3137 | 0.592452 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 95.1127 | 4.22410 | ||||||||
\(508\) | 23.1601 | + | 16.8268i | 1.02756 | + | 0.746567i | ||||
\(509\) | 2.87809 | − | 8.85786i | 0.127569 | − | 0.392618i | −0.866791 | − | 0.498671i | \(-0.833821\pi\) |
0.994360 | + | 0.106053i | \(0.0338215\pi\) | |||||||
\(510\) | 0.424151 | + | 1.30540i | 0.0187817 | + | 0.0578043i | ||||
\(511\) | −11.0486 | + | 8.02730i | −0.488762 | + | 0.355107i | ||||
\(512\) | 18.4111 | − | 13.3764i | 0.813663 | − | 0.591161i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.70414 | + | 5.24481i | −0.0751665 | + | 0.231339i | ||||
\(515\) | 0.947822 | + | 0.688633i | 0.0417660 | + | 0.0303448i | ||||
\(516\) | 31.0294 | 1.36599 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.02944 | 0.133106 | ||||||||
\(519\) | −14.0547 | − | 10.2113i | −0.616934 | − | 0.448228i | ||||
\(520\) | 3.34617 | − | 10.2984i | 0.146739 | − | 0.451617i | ||||
\(521\) | 0.830110 | + | 2.55482i | 0.0363678 | + | 0.111928i | 0.967592 | − | 0.252517i | \(-0.0812585\pi\) |
−0.931225 | + | 0.364446i | \(0.881258\pi\) | |||||||
\(522\) | 12.8293 | − | 9.32102i | 0.561522 | − | 0.407970i | ||||
\(523\) | −30.4174 | + | 22.0995i | −1.33006 | + | 0.966345i | −0.330313 | + | 0.943872i | \(0.607154\pi\) |
−0.999747 | + | 0.0224738i | \(0.992846\pi\) | |||||||
\(524\) | −6.39242 | − | 19.6738i | −0.279254 | − | 0.859455i | ||||
\(525\) | −1.74806 | + | 5.37999i | −0.0762918 | + | 0.234802i | ||||
\(526\) | 7.69757 | + | 5.59261i | 0.335630 | + | 0.243849i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | −0.114990 | − | 0.0835452i | −0.00499485 | − | 0.00362897i | ||||
\(531\) | −14.9207 | + | 45.9211i | −0.647502 | + | 1.99280i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.1459 | − | 24.0819i | 1.43571 | − | 1.04310i | ||||
\(534\) | 8.82774 | − | 6.41373i | 0.382014 | − | 0.277549i | ||||
\(535\) | 1.13003 | + | 3.47788i | 0.0488555 | + | 0.150362i | ||||
\(536\) | −2.19794 | + | 6.76458i | −0.0949368 | + | 0.292185i | ||||
\(537\) | 3.79129 | + | 2.75453i | 0.163606 | + | 0.118867i | ||||
\(538\) | 2.20101 | 0.0948923 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.3431 | 0.445098 | ||||||||
\(541\) | −4.85410 | − | 3.52671i | −0.208694 | − | 0.151625i | 0.478529 | − | 0.878072i | \(-0.341170\pi\) |
−0.687223 | + | 0.726447i | \(0.741170\pi\) | |||||||
\(542\) | 1.96014 | − | 6.03269i | 0.0841952 | − | 0.259126i | ||||
\(543\) | −1.14822 | − | 3.53387i | −0.0492750 | − | 0.151653i | ||||
\(544\) | 4.18389 | − | 3.03977i | 0.179383 | − | 0.130329i | ||||
\(545\) | 2.95846 | − | 2.14944i | 0.126726 | − | 0.0920721i | ||||
\(546\) | −4.94427 | − | 15.2169i | −0.211595 | − | 0.651223i | ||||
\(547\) | −10.5066 | + | 32.3359i | −0.449229 | + | 1.38258i | 0.428550 | + | 0.903518i | \(0.359025\pi\) |
−0.877779 | + | 0.479066i | \(0.840975\pi\) | |||||||
\(548\) | 33.9787 | + | 24.6870i | 1.45150 | + | 1.05458i | ||||
\(549\) | 66.5685 | 2.84108 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −10.2634 | − | 7.45682i | −0.436840 | − | 0.317383i | ||||
\(553\) | −2.47214 | + | 7.60845i | −0.105126 | + | 0.323544i | ||||
\(554\) | −0.149960 | − | 0.461530i | −0.00637120 | − | 0.0196085i | ||||
\(555\) | 8.36778 | − | 6.07955i | 0.355193 | − | 0.258062i | ||||
\(556\) | −5.91691 | + | 4.29889i | −0.250933 | + | 0.182314i | ||||
\(557\) | 11.7866 | + | 36.2753i | 0.499413 | + | 1.53703i | 0.809965 | + | 0.586478i | \(0.199486\pi\) |
−0.310552 | + | 0.950556i | \(0.600514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.1459 | − | 24.0819i | −1.40192 | − | 1.01856i | ||||
\(560\) | 6.00000 | 0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.20101 | 0.0928440 | ||||||||
\(563\) | −9.43059 | − | 6.85173i | −0.397452 | − | 0.288766i | 0.371050 | − | 0.928613i | \(-0.378998\pi\) |
−0.768502 | + | 0.639847i | \(0.778998\pi\) | |||||||
\(564\) | 4.52012 | − | 13.9115i | 0.190331 | − | 0.585780i | ||||
\(565\) | −2.57817 | − | 7.93480i | −0.108465 | − | 0.333820i | ||||
\(566\) | −4.23152 | + | 3.07438i | −0.177864 | + | 0.129226i | ||||
\(567\) | 1.61803 | − | 1.17557i | 0.0679510 | − | 0.0493693i | ||||
\(568\) | −5.54411 | − | 17.0630i | −0.232626 | − | 0.715949i | ||||
\(569\) | 6.28638 | − | 19.3475i | 0.263539 | − | 0.811089i | −0.728488 | − | 0.685059i | \(-0.759776\pi\) |
0.992026 | − | 0.126030i | \(-0.0402235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.9411 | 1.92258 | 0.961288 | − | 0.275545i | \(-0.0888584\pi\) | ||||
0.961288 | + | 0.275545i | \(0.0888584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.6274 | −2.28209 | ||||||||
\(574\) | −4.02127 | − | 2.92162i | −0.167845 | − | 0.121946i | ||||
\(575\) | 0.874032 | − | 2.68999i | 0.0364497 | − | 0.112181i | ||||
\(576\) | −6.44543 | − | 19.8370i | −0.268560 | − | 0.826542i | ||||
\(577\) | −5.63930 | + | 4.09719i | −0.234767 | + | 0.170568i | −0.698949 | − | 0.715172i | \(-0.746349\pi\) |
0.464182 | + | 0.885740i | \(0.346349\pi\) | |||||||
\(578\) | −5.23684 | + | 3.80479i | −0.217824 | + | 0.158258i | ||||
\(579\) | −5.96826 | − | 18.3684i | −0.248033 | − | 0.763366i | ||||
\(580\) | 4.32624 | − | 13.3148i | 0.179637 | − | 0.552867i | ||||
\(581\) | −9.70820 | − | 7.05342i | −0.402764 | − | 0.292625i | ||||
\(582\) | 8.97056 | 0.371842 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.8284 | −0.448084 | ||||||||
\(585\) | −27.6216 | − | 20.0682i | −1.14201 | − | 0.829720i | ||||
\(586\) | 1.89802 | − | 5.84152i | 0.0784067 | − | 0.241311i | ||||
\(587\) | 8.07836 | + | 24.8626i | 0.333430 | + | 1.02619i | 0.967490 | + | 0.252908i | \(0.0813870\pi\) |
−0.634061 | + | 0.773283i | \(0.718613\pi\) | |||||||
\(588\) | −12.5517 | + | 9.11932i | −0.517622 | + | 0.376075i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.23607 | − | 3.80423i | −0.0508881 | − | 0.156618i | ||||
\(591\) | −4.52012 | + | 13.9115i | −0.185933 | + | 0.572243i | ||||
\(592\) | −8.87537 | − | 6.44833i | −0.364776 | − | 0.265025i | ||||
\(593\) | 20.4853 | 0.841230 | 0.420615 | − | 0.907239i | \(-0.361814\pi\) | ||||
0.420615 | + | 0.907239i | \(0.361814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.34315 | 0.0960596 | ||||||||
\(596\) | 17.2432 | + | 12.5279i | 0.706307 | + | 0.513162i | ||||
\(597\) | 18.9288 | − | 58.2568i | 0.774704 | − | 2.38429i | ||||
\(598\) | 2.47214 | + | 7.60845i | 0.101093 | + | 0.311133i | ||||
\(599\) | −4.57649 | + | 3.32502i | −0.186990 | + | 0.135856i | −0.677342 | − | 0.735668i | \(-0.736868\pi\) |
0.490352 | + | 0.871525i | \(0.336868\pi\) | |||||||
\(600\) | −3.62867 | + | 2.63638i | −0.148140 | + | 0.107630i | ||||
\(601\) | −13.5786 | − | 41.7905i | −0.553881 | − | 1.70467i | −0.698881 | − | 0.715238i | \(-0.746318\pi\) |
0.145000 | − | 0.989432i | \(-0.453682\pi\) | |||||||
\(602\) | −1.53599 | + | 4.72729i | −0.0626022 | + | 0.192670i | ||||
\(603\) | 18.1433 | + | 13.1819i | 0.738854 | + | 0.536809i | ||||
\(604\) | 21.9411 | 0.892772 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.5980 | 0.633625 | ||||||||
\(607\) | 14.7923 | + | 10.7472i | 0.600400 | + | 0.436216i | 0.846021 | − | 0.533150i | \(-0.178992\pi\) |
−0.245621 | + | 0.969366i | \(0.578992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.3847 | − | 41.1938i | −0.542374 | − | 1.66926i | ||||
\(610\) | −4.46150 | + | 3.24147i | −0.180641 | + | 0.131243i | ||||
\(611\) | −15.6251 | + | 11.3523i | −0.632125 | + | 0.459265i | ||||
\(612\) | −3.30978 | − | 10.1865i | −0.133790 | − | 0.411763i | ||||
\(613\) | 7.86629 | − | 24.2099i | 0.317716 | − | 0.977831i | −0.656905 | − | 0.753973i | \(-0.728135\pi\) |
0.974622 | − | 0.223858i | \(-0.0718650\pi\) | |||||||
\(614\) | −9.26797 | − | 6.73358i | −0.374025 | − | 0.271745i | ||||
\(615\) | −16.9706 | −0.684319 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.6569 | 0.469287 | 0.234644 | − | 0.972081i | \(-0.424608\pi\) | ||||
0.234644 | + | 0.972081i | \(0.424608\pi\) | |||||||
\(618\) | 1.11044 | + | 0.806784i | 0.0446686 | + | 0.0324536i | ||||
\(619\) | −7.92840 | + | 24.4011i | −0.318669 | + | 0.980764i | 0.655548 | + | 0.755153i | \(0.272438\pi\) |
−0.974218 | + | 0.225610i | \(0.927562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.9443 | + | 9.40456i | −0.519436 | + | 0.377392i | ||||
\(622\) | 9.15298 | − | 6.65003i | 0.367001 | − | 0.266642i | ||||
\(623\) | −5.75619 | − | 17.7157i | −0.230617 | − | 0.709766i | ||||
\(624\) | −17.9048 | + | 55.1053i | −0.716765 | + | 2.20598i | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | −8.82843 | −0.352855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25.5980 | 1.02147 | ||||||||
\(629\) | −3.46605 | − | 2.51823i | −0.138200 | − | 0.100408i | ||||
\(630\) | −1.27999 | + | 3.93941i | −0.0509960 | + | 0.156950i | ||||
\(631\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(632\) | −5.13171 | + | 3.72841i | −0.204129 | + | 0.148308i | ||||
\(633\) | 36.6119 | − | 26.6001i | 1.45519 | − | 1.05726i | ||||
\(634\) | −2.72813 | − | 8.39633i | −0.108348 | − | 0.333461i | ||||
\(635\) | −4.83823 | + | 14.8906i | −0.191999 | + | 0.590914i | ||||
\(636\) | 1.43568 | + | 1.04309i | 0.0569286 | + | 0.0413610i | ||||
\(637\) | 20.4853 | 0.811656 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −56.5685 | −2.23782 | ||||||||
\(640\) | 8.54027 | + | 6.20487i | 0.337584 | + | 0.245269i | ||||
\(641\) | 9.27051 | − | 28.5317i | 0.366163 | − | 1.12693i | −0.583086 | − | 0.812410i | \(-0.698155\pi\) |
0.949250 | − | 0.314524i | \(-0.101845\pi\) | |||||||
\(642\) | 1.32391 | + | 4.07458i | 0.0522507 | + | 0.160811i | ||||
\(643\) | −40.0106 | + | 29.0694i | −1.57786 | + | 1.14639i | −0.658773 | + | 0.752341i | \(0.728924\pi\) |
−0.919091 | + | 0.394044i | \(0.871076\pi\) | |||||||
\(644\) | −8.36778 | + | 6.07955i | −0.329737 | + | 0.239568i | ||||
\(645\) | 5.24419 | + | 16.1400i | 0.206490 | + | 0.635510i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.4068 | + | 20.6387i | 1.11679 | + | 0.811392i | 0.983719 | − | 0.179715i | \(-0.0575176\pi\) |
0.133067 | + | 0.991107i | \(0.457518\pi\) | |||||||
\(648\) | 1.58579 | 0.0622956 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.82843 | 0.110940 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.274191 | − | 0.843874i | 0.0107382 | − | 0.0330487i | ||||
\(653\) | 0.106038 | + | 0.326351i | 0.00414958 | + | 0.0127711i | 0.953110 | − | 0.302624i | \(-0.0978628\pi\) |
−0.948960 | + | 0.315396i | \(0.897863\pi\) | |||||||
\(654\) | 3.46605 | − | 2.51823i | 0.135533 | − | 0.0984706i | ||||
\(655\) | 9.15298 | − | 6.65003i | 0.357637 | − | 0.259838i | ||||
\(656\) | 5.56231 | + | 17.1190i | 0.217172 | + | 0.668385i | ||||
\(657\) | −10.5505 | + | 32.4711i | −0.411614 | + | 1.26682i | ||||
\(658\) | 1.89564 | + | 1.37727i | 0.0738999 | + | 0.0536914i | ||||
\(659\) | −21.9411 | −0.854705 | −0.427352 | − | 0.904085i | \(-0.640554\pi\) | ||||
−0.427352 | + | 0.904085i | \(0.640554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.627417 | −0.0244037 | −0.0122018 | − | 0.999926i | \(-0.503884\pi\) | ||||
−0.0122018 | + | 0.999926i | \(0.503884\pi\) | |||||||
\(662\) | 5.13171 | + | 3.72841i | 0.199450 | + | 0.144909i | ||||
\(663\) | −6.99226 | + | 21.5200i | −0.271557 | + | 0.835766i | ||||
\(664\) | −2.94021 | − | 9.04904i | −0.114102 | − | 0.351171i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.12717 | − | 4.45165i | 0.237423 | − | 0.172498i | ||||
\(667\) | 6.69234 | + | 20.5969i | 0.259128 | + | 0.797515i | ||||
\(668\) | −6.19853 | + | 19.0771i | −0.239828 | + | 0.738116i | ||||
\(669\) | 11.8338 | + | 8.59778i | 0.457522 | + | 0.332409i | ||||
\(670\) | −1.85786 | −0.0717756 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 24.9706 | 0.963260 | ||||||||
\(673\) | −3.62867 | − | 2.63638i | −0.139875 | − | 0.101625i | 0.515647 | − | 0.856801i | \(-0.327551\pi\) |
−0.655522 | + | 0.755176i | \(0.727551\pi\) | |||||||
\(674\) | 0.449881 | − | 1.38459i | 0.0173288 | − | 0.0533324i | ||||
\(675\) | 1.74806 | + | 5.37999i | 0.0672830 | + | 0.207076i | ||||
\(676\) | 49.7426 | − | 36.1401i | 1.91318 | − | 1.39001i | ||||
\(677\) | −13.8921 | + | 10.0932i | −0.533917 | + | 0.387913i | −0.821821 | − | 0.569746i | \(-0.807042\pi\) |
0.287904 | + | 0.957659i | \(0.407042\pi\) | |||||||
\(678\) | −3.02052 | − | 9.29620i | −0.116002 | − | 0.357018i | ||||
\(679\) | 4.73220 | − | 14.5642i | 0.181605 | − | 0.558923i | ||||
\(680\) | 1.50304 | + | 1.09203i | 0.0576391 | + | 0.0418773i | ||||
\(681\) | 7.59798 | 0.291155 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7990 | 1.21675 | 0.608377 | − | 0.793648i | \(-0.291821\pi\) | ||||
0.608377 | + | 0.793648i | \(0.291821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.09829 | + | 21.8463i | −0.271212 | + | 0.834704i | ||||
\(686\) | −2.55998 | − | 7.87881i | −0.0977405 | − | 0.300814i | ||||
\(687\) | 48.7710 | − | 35.4342i | 1.86073 | − | 1.35190i | ||||
\(688\) | 14.5623 | − | 10.5801i | 0.555183 | − | 0.403364i | ||||
\(689\) | −0.724072 | − | 2.22846i | −0.0275849 | − | 0.0848977i | ||||
\(690\) | 1.02399 | − | 3.15152i | 0.0389827 | − | 0.119976i | ||||
\(691\) | 13.4995 | + | 9.80796i | 0.513545 | + | 0.373112i | 0.814167 | − | 0.580631i | \(-0.197194\pi\) |
−0.300622 | + | 0.953743i | \(0.597194\pi\) | |||||||
\(692\) | −11.2304 | −0.426918 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.51472 | 0.361174 | ||||||||
\(695\) | −3.23607 | − | 2.35114i | −0.122751 | − | 0.0891839i | ||||
\(696\) | 10.6126 | − | 32.6623i | 0.402270 | − | 1.23806i | ||||
\(697\) | 2.17222 | + | 6.68539i | 0.0822785 | + | 0.253227i | ||||
\(698\) | −2.33588 | + | 1.69711i | −0.0884142 | + | 0.0642367i | ||||
\(699\) | −50.6666 | + | 36.8115i | −1.91639 | + | 1.39234i | ||||
\(700\) | 1.13003 | + | 3.47788i | 0.0427111 | + | 0.131451i | ||||
\(701\) | 10.0824 | − | 31.0305i | 0.380808 | − | 1.17201i | −0.558668 | − | 0.829391i | \(-0.688687\pi\) |
0.939476 | − | 0.342615i | \(-0.111313\pi\) | |||||||
\(702\) | −12.9443 | − | 9.40456i | −0.488550 | − | 0.354952i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | −0.440231 | − | 0.319847i | −0.0165683 | − | 0.0120376i | ||||
\(707\) | 8.22832 | − | 25.3242i | 0.309458 | − | 0.952414i | ||||
\(708\) | 15.4327 | + | 47.4968i | 0.579995 | + | 1.78504i | ||||
\(709\) | 16.6879 | − | 12.1245i | 0.626728 | − | 0.455345i | −0.228537 | − | 0.973535i | \(-0.573394\pi\) |
0.855265 | + | 0.518190i | \(0.173394\pi\) | |||||||
\(710\) | 3.79129 | − | 2.75453i | 0.142285 | − | 0.103376i | ||||
\(711\) | 6.18034 | + | 19.0211i | 0.231781 | + | 0.713348i | ||||
\(712\) | 4.56404 | − | 14.0467i | 0.171045 | − | 0.526422i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 2.74517 | 0.102735 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.02944 | 0.113215 | ||||||||
\(717\) | 1.57040 | + | 1.14096i | 0.0586478 | + | 0.0426101i | ||||
\(718\) | −2.98413 | + | 9.18421i | −0.111367 | + | 0.342752i | ||||
\(719\) | 9.16447 | + | 28.2053i | 0.341777 | + | 1.05188i | 0.963287 | + | 0.268475i | \(0.0865197\pi\) |
−0.621509 | + | 0.783407i | \(0.713480\pi\) | |||||||
\(720\) | 12.1353 | − | 8.81678i | 0.452254 | − | 0.328582i | ||||
\(721\) | 1.89564 | − | 1.37727i | 0.0705975 | − | 0.0512921i | ||||
\(722\) | 2.43198 | + | 7.48487i | 0.0905090 | + | 0.278558i | ||||
\(723\) | 5.24419 | − | 16.1400i | 0.195034 | − | 0.600252i | ||||
\(724\) | −1.94328 | − | 1.41187i | −0.0722213 | − | 0.0524718i | ||||
\(725\) | 7.65685 | 0.284368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.4853 | −1.35316 | −0.676582 | − | 0.736367i | \(-0.736540\pi\) | ||||
−0.676582 | + | 0.736367i | \(0.736540\pi\) | |||||||
\(728\) | −17.5208 | − | 12.7296i | −0.649363 | − | 0.471790i | ||||
\(729\) | −13.2877 | + | 40.8954i | −0.492138 | + | 1.51465i | ||||
\(730\) | −0.874032 | − | 2.68999i | −0.0323494 | − | 0.0995611i | ||||
\(731\) | 5.68693 | − | 4.13180i | 0.210339 | − | 0.152820i | ||||
\(732\) | 55.7031 | − | 40.4707i | 2.05885 | − | 1.49584i | ||||
\(733\) | 10.3384 | + | 31.8184i | 0.381858 | + | 1.17524i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
−0.556875 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(734\) | −1.08611 | + | 3.34270i | −0.0400890 | + | 0.123381i | ||||
\(735\) | −6.86474 | − | 4.98752i | −0.253210 | − | 0.183968i | ||||
\(736\) | −12.4853 | −0.460214 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.4264 | −0.457422 | ||||||||
\(739\) | 30.6950 | + | 22.3012i | 1.12913 | + | 0.820364i | 0.985569 | − | 0.169277i | \(-0.0541431\pi\) |
0.143566 | + | 0.989641i | \(0.454143\pi\) | |||||||
\(740\) | 2.06618 | − | 6.35904i | 0.0759542 | − | 0.233763i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.229980 | + | 0.167090i | −0.00844284 | + | 0.00613408i | ||||
\(743\) | −23.9453 | + | 17.3973i | −0.878467 | + | 0.638243i | −0.932845 | − | 0.360277i | \(-0.882682\pi\) |
0.0543787 | + | 0.998520i | \(0.482682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.60217 | + | 11.0863i | −0.131973 | + | 0.406172i | ||||
\(746\) | −1.27306 | − | 0.924935i | −0.0466102 | − | 0.0338643i | ||||
\(747\) | −30.0000 | −1.09764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.31371 | 0.267237 | ||||||||
\(750\) | −0.947822 | − | 0.688633i | −0.0346096 | − | 0.0251453i | ||||
\(751\) | −4.94427 | + | 15.2169i | −0.180419 | + | 0.555273i | −0.999839 | − | 0.0179203i | \(-0.994295\pi\) |
0.819420 | + | 0.573193i | \(0.194295\pi\) | |||||||
\(752\) | −2.62210 | − | 8.06998i | −0.0956180 | − | 0.294282i | ||||
\(753\) | −27.4589 | + | 19.9501i | −1.00066 | + | 0.727022i | ||||
\(754\) | −17.5208 | + | 12.7296i | −0.638069 | + | 0.463584i | ||||
\(755\) | 3.70820 | + | 11.4127i | 0.134955 | + | 0.415350i | ||||
\(756\) | 6.39242 | − | 19.6738i | 0.232490 | − | 0.715530i | ||||
\(757\) | 7.53495 | + | 5.47446i | 0.273862 | + | 0.198973i | 0.716236 | − | 0.697858i | \(-0.245863\pi\) |
−0.442374 | + | 0.896831i | \(0.645863\pi\) | |||||||
\(758\) | −9.25483 | −0.336151 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2705 | + | 17.6336i | 0.879805 | + | 0.639216i | 0.933200 | − | 0.359358i | \(-0.117004\pi\) |
−0.0533947 | + | 0.998573i | \(0.517004\pi\) | |||||||
\(762\) | −5.66834 | + | 17.4454i | −0.205342 | + | 0.631979i | ||||
\(763\) | −2.26006 | − | 6.95575i | −0.0818197 | − | 0.251815i | ||||
\(764\) | −28.5694 | + | 20.7569i | −1.03360 | + | 0.750957i | ||||
\(765\) | 4.73911 | − | 3.44317i | 0.171343 | − | 0.124488i | ||||
\(766\) | 4.37016 | + | 13.4500i | 0.157900 | + | 0.485967i | ||||
\(767\) | 20.3769 | − | 62.7137i | 0.735768 | − | 2.26446i | ||||
\(768\) | −9.08562 | − | 6.60109i | −0.327849 | − | 0.238196i | ||||
\(769\) | 14.9706 | 0.539852 | 0.269926 | − | 0.962881i | \(-0.413001\pi\) | ||||
0.269926 | + | 0.962881i | \(0.413001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.6569 | 1.35618 | ||||||||
\(772\) | −10.1008 | − | 7.33866i | −0.363536 | − | 0.264124i | ||||
\(773\) | −9.35835 | + | 28.8021i | −0.336597 | + | 1.03594i | 0.629334 | + | 0.777135i | \(0.283328\pi\) |
−0.965930 | + | 0.258803i | \(0.916672\pi\) | |||||||
\(774\) | 3.83997 | + | 11.8182i | 0.138025 | + | 0.424797i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.82319 | − | 7.13697i | 0.352632 | − | 0.256202i | ||||
\(777\) | −6.39242 | − | 19.6738i | −0.229327 | − | 0.705795i | ||||
\(778\) | 3.15229 | − | 9.70174i | 0.113015 | − | 0.347824i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −35.3137 | −1.26443 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.37258 | −0.0490835 | ||||||||
\(783\) | −35.0415 | − | 25.4592i | −1.25228 | − | 0.909836i | ||||
\(784\) | −2.78115 | + | 8.55951i | −0.0993269 | + | 0.305697i | ||||
\(785\) | 4.32624 | + | 13.3148i | 0.154410 | + | 0.475225i | ||||
\(786\) | 10.7234 | − | 7.79100i | 0.382491 | − | 0.277896i | ||||
\(787\) | −15.3475 | + | 11.1506i | −0.547080 | + | 0.397477i | −0.826708 | − | 0.562632i | \(-0.809789\pi\) |
0.279628 | + | 0.960108i | \(0.409789\pi\) | |||||||
\(788\) | 2.92202 | + | 8.99304i | 0.104093 | + | 0.320364i | ||||
\(789\) | 20.0770 | − | 61.7907i | 0.714760 | − | 2.19981i | ||||
\(790\) | −1.34042 | − | 0.973874i | −0.0476901 | − | 0.0346489i | ||||
\(791\) | −16.6863 | −0.593296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −90.9117 | −3.22837 | ||||||||
\(794\) | 4.46150 | + | 3.24147i | 0.158333 | + | 0.115035i | ||||
\(795\) | −0.299920 | + | 0.923060i | −0.0106371 | + | 0.0327376i | ||||
\(796\) | −12.2364 | − | 37.6599i | −0.433709 | − | 1.33482i | ||||
\(797\) | 10.2158 | − | 7.42221i | 0.361862 | − | 0.262908i | −0.391966 | − | 0.919980i | \(-0.628205\pi\) |
0.753828 | + | 0.657071i | \(0.228205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.02399 | − | 3.15152i | −0.0362262 | − | 0.111493i | ||||
\(800\) | −1.36407 | + | 4.19817i | −0.0482271 | + | 0.148428i | ||||
\(801\) | −37.6747 | − | 27.3723i | −1.33117 | − | 0.967153i | ||||
\(802\) | −7.17157 | −0.253237 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 23.1960 | 0.818058 | ||||||||
\(805\) | −4.57649 | − | 3.32502i | −0.161300 | − | 0.117191i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.64435 | − | 14.2938i | −0.163489 | − | 0.503167i | ||||
\(808\) | 17.0805 | − | 12.4097i | 0.600891 | − | 0.436573i | ||||
\(809\) | −18.5836 | + | 13.5018i | −0.653364 | + | 0.474697i | −0.864415 | − | 0.502778i | \(-0.832311\pi\) |
0.211052 | + | 0.977475i | \(0.432311\pi\) | |||||||
\(810\) | 0.127999 | + | 0.393941i | 0.00449743 | + | 0.0138417i | ||||
\(811\) | −4.30804 | + | 13.2588i | −0.151276 | + | 0.465579i | −0.997765 | − | 0.0668274i | \(-0.978712\pi\) |
0.846489 | + | 0.532407i | \(0.178712\pi\) | |||||||
\(812\) | −22.6525 | − | 16.4580i | −0.794946 | − | 0.577562i | ||||
\(813\) | −43.3137 | −1.51908 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.485281 | 0.0169987 | ||||||||
\(816\) | −8.04254 | − | 5.84325i | −0.281545 | − | 0.204555i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −4.47620 | − | 13.7763i | −0.156507 | − | 0.481678i | ||||
\(819\) | −55.2431 | + | 40.1365i | −1.93035 | + | 1.40248i | ||||
\(820\) | −8.87537 | + | 6.44833i | −0.309941 | + | 0.225186i | ||||
\(821\) | −5.77438 | − | 17.7717i | −0.201527 | − | 0.620237i | −0.999838 | − | 0.0179916i | \(-0.994273\pi\) |
0.798311 | − | 0.602246i | \(-0.205727\pi\) | |||||||
\(822\) | −8.31617 | + | 25.5945i | −0.290060 | + | 0.892712i | ||||
\(823\) | −29.5172 | − | 21.4455i | −1.02891 | − | 0.747543i | −0.0608161 | − | 0.998149i | \(-0.519370\pi\) |
−0.968089 | + | 0.250605i | \(0.919370\pi\) | |||||||
\(824\) | 1.85786 | 0.0647218 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 27.7366 | + | 20.1518i | 0.964495 | + | 0.700746i | 0.954190 | − | 0.299201i | \(-0.0967200\pi\) |
0.0103044 | + | 0.999947i | \(0.496720\pi\) | |||||||
\(828\) | −7.99052 | + | 24.5923i | −0.277690 | + | 0.854641i | ||||
\(829\) | 5.56231 | + | 17.1190i | 0.193187 | + | 0.594568i | 0.999993 | + | 0.00375172i | \(0.00119421\pi\) |
−0.806806 | + | 0.590816i | \(0.798806\pi\) | |||||||
\(830\) | 2.01063 | − | 1.46081i | 0.0697902 | − | 0.0507055i | ||||
\(831\) | −2.68085 | + | 1.94775i | −0.0929975 | + | 0.0675667i | ||||
\(832\) | 8.80244 | + | 27.0911i | 0.305170 | + | 0.939215i | ||||
\(833\) | −1.08611 | + | 3.34270i | −0.0376314 | + | 0.115818i | ||||
\(834\) | −3.79129 | − | 2.75453i | −0.131282 | − | 0.0953817i | ||||
\(835\) | −10.9706 | −0.379652 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.80647 | − | 3.49211i | −0.166037 | − | 0.120633i | ||||
\(839\) | 11.6366 | − | 35.8138i | 0.401740 | − | 1.23643i | −0.521846 | − | 0.853040i | \(-0.674757\pi\) |
0.923587 | − | 0.383390i | \(-0.125243\pi\) | |||||||
\(840\) | 2.77206 | + | 8.53151i | 0.0956450 | + | 0.294365i | ||||
\(841\) | −23.9691 | + | 17.4146i | −0.826520 | + | 0.600502i | ||||
\(842\) | −2.01063 | + | 1.46081i | −0.0692911 | + | 0.0503429i | ||||
\(843\) | −4.64435 | − | 14.2938i | −0.159960 | − | 0.492306i | ||||
\(844\) | 9.04024 | − | 27.8230i | 0.311178 | − | 0.957707i | ||||
\(845\) | 27.2052 | + | 19.7657i | 0.935886 | + | 0.679961i | ||||
\(846\) | 5.85786 | 0.201398 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.02944 | 0.0353510 | ||||||||
\(849\) | 28.8946 | + | 20.9932i | 0.991661 | + | 0.720484i | ||||
\(850\) | −0.149960 | + | 0.461530i | −0.00514359 | + | 0.0158303i | ||||
\(851\) | 3.19621 | + | 9.83692i | 0.109565 | + | 0.337205i | ||||
\(852\) | −47.3353 | + | 34.3911i | −1.62168 | + | 1.17822i | ||||
\(853\) | 26.2811 | − | 19.0944i | 0.899849 | − | 0.653779i | −0.0385780 | − | 0.999256i | \(-0.512283\pi\) |
0.938427 | + | 0.345477i | \(0.112283\pi\) | |||||||
\(854\) | 3.40828 | + | 10.4896i | 0.116629 | + | 0.358947i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.69148 | + | 3.40856i | 0.160352 | + | 0.116502i | ||||
\(857\) | −48.7696 | −1.66594 | −0.832968 | − | 0.553321i | \(-0.813360\pi\) | ||||
−0.832968 | + | 0.553321i | \(0.813360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2843 | −1.10153 | −0.550763 | − | 0.834662i | \(-0.685663\pi\) | ||||
−0.550763 | + | 0.834662i | \(0.685663\pi\) | |||||||
\(860\) | 8.87537 | + | 6.44833i | 0.302648 | + | 0.219886i | ||||
\(861\) | −10.4884 | + | 32.2799i | −0.357443 | + | 1.10010i | ||||
\(862\) | −1.44814 | − | 4.45693i | −0.0493240 | − | 0.151804i | ||||
\(863\) | 11.9964 | − | 8.71593i | 0.408364 | − | 0.296694i | −0.364575 | − | 0.931174i | \(-0.618786\pi\) |
0.772939 | + | 0.634480i | \(0.218786\pi\) | |||||||
\(864\) | 20.2016 | − | 14.6773i | 0.687273 | − | 0.499333i | ||||
\(865\) | −1.89802 | − | 5.84152i | −0.0645348 | − | 0.198618i | ||||
\(866\) | −0.468074 | + | 1.44058i | −0.0159058 | + | 0.0489530i | ||||
\(867\) | 35.7594 | + | 25.9807i | 1.21445 | + | 0.882351i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 8.97056 | 0.304131 | ||||||||
\(871\) | −24.7781 | − | 18.0023i | −0.839574 | − | 0.609986i | ||||
\(872\) | 1.79199 | − | 5.51517i | 0.0606843 | − | 0.186767i | ||||
\(873\) | −11.8305 | − | 36.4105i | −0.400401 | − | 1.23231i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.61803 | + | 1.17557i | −0.0546995 | + | 0.0397415i | ||||
\(876\) | 10.9125 | + | 33.5853i | 0.368700 | + | 1.13474i | ||||
\(877\) | 0.449881 | − | 1.38459i | 0.0151914 | − | 0.0467543i | −0.943173 | − | 0.332301i | \(-0.892175\pi\) |
0.958365 | + | 0.285546i | \(0.0921751\pi\) | |||||||
\(878\) | −5.36169 | − | 3.89550i | −0.180948 | − | 0.131467i | ||||
\(879\) | −41.9411 | −1.41464 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.6274 | −1.77306 | −0.886531 | − | 0.462668i | \(-0.846892\pi\) | ||||
−0.886531 | + | 0.462668i | \(0.846892\pi\) | |||||||
\(882\) | −5.02659 | − | 3.65203i | −0.169254 | − | 0.122970i | ||||
\(883\) | 13.2347 | − | 40.7323i | 0.445384 | − | 1.37075i | −0.436679 | − | 0.899617i | \(-0.643845\pi\) |
0.882063 | − | 0.471132i | \(-0.156155\pi\) | |||||||
\(884\) | 4.52012 | + | 13.9115i | 0.152028 | + | 0.467894i | ||||
\(885\) | −22.0973 | + | 16.0546i | −0.742791 | + | 0.539669i | ||||
\(886\) | −7.09472 | + | 5.15461i | −0.238352 | + | 0.173173i | ||||
\(887\) | −5.65015 | − | 17.3894i | −0.189713 | − | 0.583878i | 0.810284 | − | 0.586037i | \(-0.199313\pi\) |
−0.999998 | + | 0.00215907i | \(0.999313\pi\) | |||||||
\(888\) | 5.06850 | − | 15.5992i | 0.170088 | − | 0.523476i | ||||
\(889\) | 25.3333 | + | 18.4057i | 0.849652 | + | 0.617309i | ||||
\(890\) | 3.85786 | 0.129316 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.45584 | 0.316605 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −4.22020 | + | 12.9884i | −0.141145 | + | 0.434398i | ||||
\(895\) | 0.511996 | + | 1.57576i | 0.0171141 | + | 0.0526719i | ||||
\(896\) | 17.0805 | − | 12.4097i | 0.570621 | − | 0.414580i | ||||
\(897\) | 44.1945 | − | 32.1092i | 1.47561 | − | 1.07209i | ||||
\(898\) | 2.12829 | + | 6.55021i | 0.0710221 | + | 0.218583i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 7.39614 | + | 5.37361i | 0.246538 | + | 0.179120i | ||||
\(901\) | 0.402020 | 0.0133932 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.9411 | 1.12949 | ||||||||
\(904\) | −10.7037 | − | 7.77666i | −0.355998 | − | 0.258648i | ||||
\(905\) | 0.405958 | − | 1.24941i | 0.0134945 | − | 0.0415318i | ||||
\(906\) | 4.34443 | + | 13.3708i | 0.144334 | + | 0.444215i | ||||
\(907\) | 35.9893 | − | 26.1478i | 1.19501 | − | 0.868223i | 0.201222 | − | 0.979546i | \(-0.435509\pi\) |
0.993784 | + | 0.111322i | \(0.0355086\pi\) | |||||||
\(908\) | 3.97364 | − | 2.88702i | 0.131870 | − | 0.0958091i | ||||
\(909\) | −20.5708 | − | 63.3104i | −0.682291 | − | 2.09987i | ||||
\(910\) | 1.74806 | − | 5.37999i | 0.0579478 | − | 0.178345i | ||||
\(911\) | −46.8754 | − | 34.0569i | −1.55305 | − | 1.12836i | −0.941432 | − | 0.337204i | \(-0.890519\pi\) |
−0.611618 | − | 0.791153i | \(-0.709481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.82843 | 0.225864 | ||||||||
\(915\) | 30.4650 | + | 22.1341i | 1.00714 | + | 0.731732i | ||||
\(916\) | 12.0426 | − | 37.0632i | 0.397898 | − | 1.22460i | ||||
\(917\) | −6.99226 | − | 21.5200i | −0.230905 | − | 0.710651i | ||||
\(918\) | 2.22089 | − | 1.61357i | 0.0733002 | − | 0.0532557i | ||||
\(919\) | 25.8885 | − | 18.8091i | 0.853984 | − | 0.620456i | −0.0722574 | − | 0.997386i | \(-0.523020\pi\) |
0.926242 | + | 0.376930i | \(0.123020\pi\) | |||||||
\(920\) | −1.38603 | − | 4.26576i | −0.0456960 | − | 0.140638i | ||||
\(921\) | −24.1730 | + | 74.3968i | −0.796527 | + | 2.45146i | ||||
\(922\) | −10.9336 | − | 7.94375i | −0.360080 | − | 0.261614i | ||||
\(923\) | 77.2548 | 2.54287 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.65685 | 0.120237 | ||||||||
\(926\) | 7.41996 | + | 5.39092i | 0.243835 | + | 0.177156i | ||||
\(927\) | 1.81018 | − | 5.57116i | 0.0594541 | − | 0.182981i | ||||
\(928\) | −10.4445 | − | 32.1447i | −0.342856 | − | 1.05520i | ||||
\(929\) | 14.0071 | − | 10.1767i | 0.459558 | − | 0.333888i | −0.333800 | − | 0.942644i | \(-0.608331\pi\) |
0.793358 | + | 0.608756i | \(0.208331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.5106 | + | 38.5038i | −0.409800 | + | 1.26123i | ||||
\(933\) | −62.5005 | − | 45.4093i | −2.04617 | − | 1.48663i | ||||
\(934\) | 3.79899 | 0.124307 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −54.1421 | −1.76969 | ||||||||
\(937\) | −40.0106 | − | 29.0694i | −1.30709 | − | 0.949656i | −0.307092 | − | 0.951680i | \(-0.599356\pi\) |
−0.999998 | + | 0.00202342i | \(0.999356\pi\) | |||||||
\(938\) | −1.14822 | + | 3.53387i | −0.0374908 | + | 0.115385i | ||||
\(939\) | 18.6289 | + | 57.3337i | 0.607930 | + | 1.87102i | ||||
\(940\) | 4.18389 | − | 3.03977i | 0.136463 | − | 0.0991465i | ||||
\(941\) | 23.7153 | − | 17.2302i | 0.773096 | − | 0.561687i | −0.129803 | − | 0.991540i | \(-0.541434\pi\) |
0.902899 | + | 0.429852i | \(0.141434\pi\) | |||||||
\(942\) | 5.06850 | + | 15.5992i | 0.165141 | + | 0.508251i | ||||
\(943\) | 5.24419 | − | 16.1400i | 0.170774 | − | 0.525590i | ||||
\(944\) | 23.4377 | + | 17.0285i | 0.762831 | + | 0.554229i | ||||
\(945\) | 11.3137 | 0.368035 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.8284 | 1.52172 | 0.760860 | − | 0.648916i | \(-0.224778\pi\) | ||||
0.760860 | + | 0.648916i | \(0.224778\pi\) | |||||||
\(948\) | 16.7356 | + | 12.1591i | 0.543546 | + | 0.394909i | ||||
\(949\) | 14.4087 | − | 44.3453i | 0.467725 | − | 1.43951i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.7710 | + | 35.4342i | −1.58151 | + | 1.14903i | ||||
\(952\) | 3.00609 | − | 2.18405i | 0.0974279 | − | 0.0707855i | ||||
\(953\) | 18.1790 | + | 55.9492i | 0.588875 | + | 1.81237i | 0.583118 | + | 0.812388i | \(0.301833\pi\) |
0.00575724 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(954\) | −0.219612 | + | 0.675895i | −0.00711019 | + | 0.0218829i | ||||
\(955\) | −15.6251 | − | 11.3523i | −0.505617 | − | 0.367352i | ||||
\(956\) | 1.25483 | 0.0405842 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.9117 | 0.481775 | ||||||||
\(959\) | 37.1672 | + | 27.0035i | 1.20019 | + | 0.871989i | ||||
\(960\) | 3.64609 | − | 11.2215i | 0.117677 | − | 0.362173i | ||||
\(961\) | −9.57953 | − | 29.4828i | −0.309017 | − | 0.951057i | ||||
\(962\) | −8.36778 | + | 6.07955i | −0.269788 | + | 0.196013i | ||||
\(963\) | 14.7923 | − | 10.7472i | 0.476675 | − | 0.346324i | ||||
\(964\) | −3.39009 | − | 10.4336i | −0.109187 | − | 0.336044i | ||||
\(965\) | 2.11010 | − | 6.49422i | 0.0679265 | − | 0.209056i | ||||
\(966\) | −5.36169 | − | 3.89550i | −0.172510 | − | 0.125336i | ||||
\(967\) | 18.9706 | 0.610052 | 0.305026 | − | 0.952344i | \(-0.401335\pi\) | ||||
0.305026 | + | 0.952344i | \(0.401335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.56586 | + | 1.86420i | 0.0823847 | + | 0.0598560i | ||||
\(971\) | −9.67647 | + | 29.7811i | −0.310533 | + | 0.955721i | 0.667022 | + | 0.745038i | \(0.267569\pi\) |
−0.977554 | + | 0.210683i | \(0.932431\pi\) | |||||||
\(972\) | 7.99052 | + | 24.5923i | 0.256296 | + | 0.788798i | ||||
\(973\) | −6.47214 | + | 4.70228i | −0.207487 | + | 0.150748i | ||||
\(974\) | −2.51823 | + | 1.82960i | −0.0806892 | + | 0.0586241i | ||||
\(975\) | −5.96826 | − | 18.3684i | −0.191137 | − | 0.588261i | ||||
\(976\) | 12.3425 | − | 37.9863i | 0.395073 | − | 1.21591i | ||||
\(977\) | −35.3191 | − | 25.6609i | −1.12996 | − | 0.820963i | −0.144270 | − | 0.989538i | \(-0.546084\pi\) |
−0.985689 | + | 0.168575i | \(0.946084\pi\) | |||||||
\(978\) | 0.568542 | 0.0181800 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.48528 | −0.175221 | ||||||||
\(981\) | −14.7923 | − | 10.7472i | −0.472281 | − | 0.343132i | ||||
\(982\) | 2.98413 | − | 9.18421i | 0.0952275 | − | 0.293080i | ||||
\(983\) | −15.4948 | − | 47.6880i | −0.494206 | − | 1.52101i | −0.818190 | − | 0.574948i | \(-0.805022\pi\) |
0.323983 | − | 0.946063i | \(-0.394978\pi\) | |||||||
\(984\) | −21.7720 | + | 15.8183i | −0.694066 | + | 0.504269i | ||||
\(985\) | −4.18389 | + | 3.03977i | −0.133310 | + | 0.0968553i | ||||
\(986\) | −1.14822 | − | 3.53387i | −0.0365669 | − | 0.112541i | ||||
\(987\) | 4.94427 | − | 15.2169i | 0.157378 | − | 0.484359i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.9706 | −0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.94113 | 0.315790 | 0.157895 | − | 0.987456i | \(-0.449529\pi\) | ||||
0.157895 | + | 0.987456i | \(0.449529\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.3847 | − | 41.1938i | 0.424750 | − | 1.30725i | ||||
\(994\) | −2.89629 | − | 8.91386i | −0.0918647 | − | 0.282730i | ||||
\(995\) | 17.5208 | − | 12.7296i | 0.555446 | − | 0.403555i | ||||
\(996\) | −25.1033 | + | 18.2386i | −0.795430 | + | 0.577914i | ||||
\(997\) | 2.92202 | + | 8.99304i | 0.0925412 | + | 0.284813i | 0.986605 | − | 0.163127i | \(-0.0521580\pi\) |
−0.894064 | + | 0.447939i | \(0.852158\pi\) | |||||||
\(998\) | 0.212076 | − | 0.652702i | 0.00671314 | − | 0.0206609i | ||||
\(999\) | −16.7356 | − | 12.1591i | −0.529490 | − | 0.384697i |
(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 | 605.2.g.f.81.2 | 8 | ||
11.2 | odd | 10 | 605.2.g.l.511.2 | 8 | |||
11.3 | even | 5 | inner | 605.2.g.f.366.2 | 8 | ||
11.4 | even | 5 | inner | 605.2.g.f.251.1 | 8 | ||
11.5 | even | 5 | 55.2.a.b.1.1 | ✓ | 2 | ||
11.6 | odd | 10 | 605.2.a.d.1.2 | 2 | |||
11.7 | odd | 10 | 605.2.g.l.251.2 | 8 | |||
11.8 | odd | 10 | 605.2.g.l.366.1 | 8 | |||
11.9 | even | 5 | inner | 605.2.g.f.511.1 | 8 | ||
11.10 | odd | 2 | 605.2.g.l.81.1 | 8 | |||
33.5 | odd | 10 | 495.2.a.b.1.2 | 2 | |||
33.17 | even | 10 | 5445.2.a.y.1.1 | 2 | |||
44.27 | odd | 10 | 880.2.a.m.1.1 | 2 | |||
44.39 | even | 10 | 9680.2.a.bn.1.1 | 2 | |||
55.27 | odd | 20 | 275.2.b.d.199.2 | 4 | |||
55.38 | odd | 20 | 275.2.b.d.199.3 | 4 | |||
55.39 | odd | 10 | 3025.2.a.o.1.1 | 2 | |||
55.49 | even | 10 | 275.2.a.c.1.2 | 2 | |||
77.27 | odd | 10 | 2695.2.a.f.1.1 | 2 | |||
88.5 | even | 10 | 3520.2.a.bn.1.1 | 2 | |||
88.27 | odd | 10 | 3520.2.a.bo.1.2 | 2 | |||
132.71 | even | 10 | 7920.2.a.ch.1.1 | 2 | |||
143.38 | even | 10 | 9295.2.a.g.1.2 | 2 | |||
165.38 | even | 20 | 2475.2.c.l.199.2 | 4 | |||
165.104 | odd | 10 | 2475.2.a.x.1.1 | 2 | |||
165.137 | even | 20 | 2475.2.c.l.199.3 | 4 | |||
220.27 | even | 20 | 4400.2.b.q.4049.4 | 4 | |||
220.159 | odd | 10 | 4400.2.a.bn.1.2 | 2 | |||
220.203 | even | 20 | 4400.2.b.q.4049.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.1 | ✓ | 2 | 11.5 | even | 5 | ||
275.2.a.c.1.2 | 2 | 55.49 | even | 10 | |||
275.2.b.d.199.2 | 4 | 55.27 | odd | 20 | |||
275.2.b.d.199.3 | 4 | 55.38 | odd | 20 | |||
495.2.a.b.1.2 | 2 | 33.5 | odd | 10 | |||
605.2.a.d.1.2 | 2 | 11.6 | odd | 10 | |||
605.2.g.f.81.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.f.251.1 | 8 | 11.4 | even | 5 | inner | ||
605.2.g.f.366.2 | 8 | 11.3 | even | 5 | inner | ||
605.2.g.f.511.1 | 8 | 11.9 | even | 5 | inner | ||
605.2.g.l.81.1 | 8 | 11.10 | odd | 2 | |||
605.2.g.l.251.2 | 8 | 11.7 | odd | 10 | |||
605.2.g.l.366.1 | 8 | 11.8 | odd | 10 | |||
605.2.g.l.511.2 | 8 | 11.2 | odd | 10 | |||
880.2.a.m.1.1 | 2 | 44.27 | odd | 10 | |||
2475.2.a.x.1.1 | 2 | 165.104 | odd | 10 | |||
2475.2.c.l.199.2 | 4 | 165.38 | even | 20 | |||
2475.2.c.l.199.3 | 4 | 165.137 | even | 20 | |||
2695.2.a.f.1.1 | 2 | 77.27 | odd | 10 | |||
3025.2.a.o.1.1 | 2 | 55.39 | odd | 10 | |||
3520.2.a.bn.1.1 | 2 | 88.5 | even | 10 | |||
3520.2.a.bo.1.2 | 2 | 88.27 | odd | 10 | |||
4400.2.a.bn.1.2 | 2 | 220.159 | odd | 10 | |||
4400.2.b.q.4049.1 | 4 | 220.203 | even | 20 | |||
4400.2.b.q.4049.4 | 4 | 220.27 | even | 20 | |||
5445.2.a.y.1.1 | 2 | 33.17 | even | 10 | |||
7920.2.a.ch.1.1 | 2 | 132.71 | even | 10 | |||
9295.2.a.g.1.2 | 2 | 143.38 | even | 10 | |||
9680.2.a.bn.1.1 | 2 | 44.39 | even | 10 |