Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.4 | ||
Root | \(-0.186243 - 0.0499037i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.901 |
Dual form | 1078.2.i.c.1011.4 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 2.70809 | − | 1.56352i | 1.56352 | − | 0.902696i | 0.566618 | − | 0.823980i | \(-0.308251\pi\) |
0.996897 | − | 0.0787156i | \(-0.0250819\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.90775 | + | 1.10144i | 0.853171 | + | 0.492579i | 0.861720 | − | 0.507385i | \(-0.169388\pi\) |
−0.00854833 | + | 0.999963i | \(0.502721\pi\) | |||||||
\(6\) | −3.12703 | −1.27660 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 3.38916 | − | 5.87020i | 1.12972 | − | 1.95673i | ||||
\(10\) | −1.10144 | − | 1.90775i | −0.348306 | − | 0.603283i | ||||
\(11\) | 3.31114 | − | 0.190575i | 0.998348 | − | 0.0574605i | ||||
\(12\) | 2.70809 | + | 1.56352i | 0.781758 | + | 0.451348i | ||||
\(13\) | −1.45937 | −0.404757 | −0.202378 | − | 0.979307i | \(-0.564867\pi\) | ||||
−0.202378 | + | 0.979307i | \(0.564867\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.88847 | 1.77860 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.80366 | + | 6.58813i | 0.922523 | + | 1.59786i | 0.795498 | + | 0.605957i | \(0.207210\pi\) |
0.127025 | + | 0.991899i | \(0.459457\pi\) | |||||||
\(18\) | −5.87020 | + | 3.38916i | −1.38362 | + | 0.798833i | ||||
\(19\) | 0.0903227 | − | 0.156443i | 0.0207214 | − | 0.0358906i | −0.855479 | − | 0.517838i | \(-0.826737\pi\) |
0.876200 | + | 0.481947i | \(0.160070\pi\) | |||||||
\(20\) | 2.20288i | 0.492579i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.96282 | − | 1.49053i | −0.631676 | − | 0.317782i | ||||
\(23\) | −1.14390 | + | 1.98129i | −0.238519 | + | 0.413127i | −0.960289 | − | 0.279006i | \(-0.909995\pi\) |
0.721771 | + | 0.692132i | \(0.243329\pi\) | |||||||
\(24\) | −1.56352 | − | 2.70809i | −0.319151 | − | 0.552786i | ||||
\(25\) | −0.0736626 | − | 0.127587i | −0.0147325 | − | 0.0255175i | ||||
\(26\) | 1.26385 | + | 0.729686i | 0.247862 | + | 0.143103i | ||||
\(27\) | − | 11.8149i | − | 2.27378i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.45335i | − | 0.826967i | −0.910512 | − | 0.413483i | \(-0.864312\pi\) | ||
0.910512 | − | 0.413483i | \(-0.135688\pi\) | |||||||
\(30\) | −5.96559 | − | 3.44423i | −1.08916 | − | 0.628828i | ||||
\(31\) | −7.40363 | + | 4.27449i | −1.32973 | + | 0.767720i | −0.985258 | − | 0.171076i | \(-0.945276\pi\) |
−0.344473 | + | 0.938796i | \(0.611942\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 8.66891 | − | 5.69312i | 1.50906 | − | 0.991045i | ||||
\(34\) | − | 7.60732i | − | 1.30464i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.77832 | 1.12972 | ||||||||
\(37\) | −0.754735 | + | 1.30724i | −0.124078 | + | 0.214909i | −0.921372 | − | 0.388682i | \(-0.872931\pi\) |
0.797294 | + | 0.603591i | \(0.206264\pi\) | |||||||
\(38\) | −0.156443 | + | 0.0903227i | −0.0253785 | + | 0.0146523i | ||||
\(39\) | −3.95211 | + | 2.28175i | −0.632844 | + | 0.365373i | ||||
\(40\) | 1.10144 | − | 1.90775i | 0.174153 | − | 0.301642i | ||||
\(41\) | −7.10368 | −1.10941 | −0.554705 | − | 0.832047i | \(-0.687169\pi\) | ||||
−0.554705 | + | 0.832047i | \(0.687169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.58174i | − | 0.241213i | −0.992700 | − | 0.120606i | \(-0.961516\pi\) | ||
0.992700 | − | 0.120606i | \(-0.0384839\pi\) | |||||||
\(44\) | 1.82062 | + | 2.77225i | 0.274468 | + | 0.417932i | ||||
\(45\) | 12.9313 | − | 7.46591i | 1.92769 | − | 1.11295i | ||||
\(46\) | 1.98129 | − | 1.14390i | 0.292125 | − | 0.168658i | ||||
\(47\) | 0.472293 | + | 0.272679i | 0.0688911 | + | 0.0397743i | 0.534050 | − | 0.845453i | \(-0.320669\pi\) |
−0.465159 | + | 0.885227i | \(0.654003\pi\) | |||||||
\(48\) | 3.12703i | 0.451348i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.147325i | 0.0208349i | ||||||||
\(51\) | 20.6013 | + | 11.8942i | 2.88476 | + | 1.66552i | ||||
\(52\) | −0.729686 | − | 1.26385i | −0.101189 | − | 0.175265i | ||||
\(53\) | −2.41722 | − | 4.18675i | −0.332031 | − | 0.575094i | 0.650879 | − | 0.759181i | \(-0.274400\pi\) |
−0.982910 | + | 0.184087i | \(0.941067\pi\) | |||||||
\(54\) | −5.90746 | + | 10.2320i | −0.803904 | + | 1.39240i | ||||
\(55\) | 6.52674 | + | 3.28346i | 0.880065 | + | 0.442741i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.564883i | − | 0.0748206i | ||||||
\(58\) | −2.22668 | + | 3.85672i | −0.292377 | + | 0.506412i | ||||
\(59\) | 5.36041 | − | 3.09483i | 0.697866 | − | 0.402913i | −0.108686 | − | 0.994076i | \(-0.534664\pi\) |
0.806552 | + | 0.591163i | \(0.201331\pi\) | |||||||
\(60\) | 3.44423 | + | 5.96559i | 0.444649 | + | 0.770154i | ||||
\(61\) | 2.86310 | − | 4.95904i | 0.366583 | − | 0.634940i | −0.622446 | − | 0.782663i | \(-0.713861\pi\) |
0.989029 | + | 0.147723i | \(0.0471943\pi\) | |||||||
\(62\) | 8.54897 | 1.08572 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.78412 | − | 1.60741i | −0.345327 | − | 0.199375i | ||||
\(66\) | −10.3541 | + | 0.595934i | −1.27450 | + | 0.0733544i | ||||
\(67\) | 1.49088 | + | 2.58228i | 0.182140 | + | 0.315476i | 0.942609 | − | 0.333898i | \(-0.108364\pi\) |
−0.760469 | + | 0.649374i | \(0.775031\pi\) | |||||||
\(68\) | −3.80366 | + | 6.58813i | −0.461261 | + | 0.798928i | ||||
\(69\) | 7.15399i | 0.861240i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.57488 | −0.898973 | −0.449486 | − | 0.893287i | \(-0.648393\pi\) | ||||
−0.449486 | + | 0.893287i | \(0.648393\pi\) | |||||||
\(72\) | −5.87020 | − | 3.38916i | −0.691809 | − | 0.399416i | ||||
\(73\) | 4.83822 | + | 8.38004i | 0.566271 | + | 0.980810i | 0.996930 | + | 0.0782953i | \(0.0249477\pi\) |
−0.430659 | + | 0.902515i | \(0.641719\pi\) | |||||||
\(74\) | 1.30724 | − | 0.754735i | 0.151964 | − | 0.0877362i | ||||
\(75\) | −0.398970 | − | 0.230345i | −0.0460691 | − | 0.0265980i | ||||
\(76\) | 0.180645 | 0.0207214 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.56350 | 0.516715 | ||||||||
\(79\) | −5.99185 | − | 3.45939i | −0.674135 | − | 0.389212i | 0.123506 | − | 0.992344i | \(-0.460586\pi\) |
−0.797642 | + | 0.603132i | \(0.793919\pi\) | |||||||
\(80\) | −1.90775 | + | 1.10144i | −0.213293 | + | 0.123145i | ||||
\(81\) | −8.30534 | − | 14.3853i | −0.922815 | − | 1.59836i | ||||
\(82\) | 6.15197 | + | 3.55184i | 0.679372 | + | 0.392235i | ||||
\(83\) | −5.84246 | −0.641293 | −0.320647 | − | 0.947199i | \(-0.603900\pi\) | ||||
−0.320647 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.7580i | 1.81766i | ||||||||
\(86\) | −0.790869 | + | 1.36983i | −0.0852816 | + | 0.147712i | ||||
\(87\) | −6.96289 | − | 12.0601i | −0.746500 | − | 1.29298i | ||||
\(88\) | −0.190575 | − | 3.31114i | −0.0203154 | − | 0.352969i | ||||
\(89\) | −13.9527 | − | 8.05557i | −1.47898 | − | 0.853889i | −0.479262 | − | 0.877672i | \(-0.659096\pi\) |
−0.999717 | + | 0.0237828i | \(0.992429\pi\) | |||||||
\(90\) | −14.9318 | −1.57395 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.28779 | −0.238519 | ||||||||
\(93\) | −13.3665 | + | 23.1514i | −1.38604 | + | 2.40069i | ||||
\(94\) | −0.272679 | − | 0.472293i | −0.0281247 | − | 0.0487133i | ||||
\(95\) | 0.344626 | − | 0.198970i | 0.0353579 | − | 0.0204139i | ||||
\(96\) | 1.56352 | − | 2.70809i | 0.159576 | − | 0.276393i | ||||
\(97\) | − | 11.3012i | − | 1.14746i | −0.819045 | − | 0.573729i | \(-0.805496\pi\) | ||
0.819045 | − | 0.573729i | \(-0.194504\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.1033 | − | 20.0830i | 1.01542 | − | 2.01841i | ||||
\(100\) | 0.0736626 | − | 0.127587i | 0.00736626 | − | 0.0127587i | ||||
\(101\) | 0.258858 | + | 0.448355i | 0.0257573 | + | 0.0446130i | 0.878617 | − | 0.477528i | \(-0.158467\pi\) |
−0.852859 | + | 0.522141i | \(0.825134\pi\) | |||||||
\(102\) | −11.8942 | − | 20.6013i | −1.17770 | − | 2.03983i | ||||
\(103\) | 2.50035 | + | 1.44358i | 0.246367 | + | 0.142240i | 0.618100 | − | 0.786100i | \(-0.287903\pi\) |
−0.371733 | + | 0.928340i | \(0.621236\pi\) | |||||||
\(104\) | 1.45937i | 0.143103i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.83444i | 0.469562i | ||||||||
\(107\) | −4.52030 | − | 2.60980i | −0.436994 | − | 0.252299i | 0.265328 | − | 0.964158i | \(-0.414520\pi\) |
−0.702322 | + | 0.711860i | \(0.747853\pi\) | |||||||
\(108\) | 10.2320 | − | 5.90746i | 0.984577 | − | 0.568446i | ||||
\(109\) | 8.70705 | − | 5.02702i | 0.833984 | − | 0.481501i | −0.0212309 | − | 0.999775i | \(-0.506759\pi\) |
0.855215 | + | 0.518274i | \(0.173425\pi\) | |||||||
\(110\) | −4.01059 | − | 6.10693i | −0.382395 | − | 0.582273i | ||||
\(111\) | 4.72016i | 0.448018i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.83235 | 0.736806 | 0.368403 | − | 0.929666i | \(-0.379905\pi\) | ||||
0.368403 | + | 0.929666i | \(0.379905\pi\) | |||||||
\(114\) | −0.282442 | + | 0.489203i | −0.0264531 | + | 0.0458181i | ||||
\(115\) | −4.36453 | + | 2.51986i | −0.406995 | + | 0.234978i | ||||
\(116\) | 3.85672 | − | 2.22668i | 0.358087 | − | 0.206742i | ||||
\(117\) | −4.94605 | + | 8.56680i | −0.457262 | + | 0.792001i | ||||
\(118\) | −6.18967 | −0.569805 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 6.88847i | − | 0.628828i | ||||||
\(121\) | 10.9274 | − | 1.26204i | 0.993397 | − | 0.114731i | ||||
\(122\) | −4.95904 | + | 2.86310i | −0.448971 | + | 0.259213i | ||||
\(123\) | −19.2374 | + | 11.1067i | −1.73458 | + | 1.00146i | ||||
\(124\) | −7.40363 | − | 4.27449i | −0.664865 | − | 0.383860i | ||||
\(125\) | − | 11.3389i | − | 1.01419i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4702i | 1.19529i | 0.801762 | + | 0.597644i | \(0.203896\pi\) | ||||
−0.801762 | + | 0.597644i | \(0.796104\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −2.47307 | − | 4.28348i | −0.217742 | − | 0.377140i | ||||
\(130\) | 1.60741 | + | 2.78412i | 0.140979 | + | 0.244183i | ||||
\(131\) | 1.31231 | − | 2.27298i | 0.114657 | − | 0.198592i | −0.802986 | − | 0.595998i | \(-0.796756\pi\) |
0.917643 | + | 0.397407i | \(0.130090\pi\) | |||||||
\(132\) | 9.26484 | + | 4.66093i | 0.806401 | + | 0.405682i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.98176i | − | 0.257585i | ||||||
\(135\) | 13.0134 | − | 22.5399i | 1.12002 | − | 1.93993i | ||||
\(136\) | 6.58813 | − | 3.80366i | 0.564928 | − | 0.326161i | ||||
\(137\) | 4.36145 | + | 7.55426i | 0.372624 | + | 0.645404i | 0.989968 | − | 0.141289i | \(-0.0451247\pi\) |
−0.617344 | + | 0.786693i | \(0.711791\pi\) | |||||||
\(138\) | 3.57700 | − | 6.19554i | 0.304494 | − | 0.527399i | ||||
\(139\) | 4.09291 | 0.347156 | 0.173578 | − | 0.984820i | \(-0.444467\pi\) | ||||
0.173578 | + | 0.984820i | \(0.444467\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.70535 | 0.143616 | ||||||||
\(142\) | 6.56004 | + | 3.78744i | 0.550506 | + | 0.317835i | ||||
\(143\) | −4.83219 | + | 0.278120i | −0.404088 | + | 0.0232575i | ||||
\(144\) | 3.38916 | + | 5.87020i | 0.282430 | + | 0.489183i | ||||
\(145\) | 4.90510 | − | 8.49588i | 0.407346 | − | 0.705544i | ||||
\(146\) | − | 9.67644i | − | 0.800828i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.50947 | −0.124078 | ||||||||
\(149\) | −16.1009 | − | 9.29587i | −1.31904 | − | 0.761547i | −0.335464 | − | 0.942053i | \(-0.608893\pi\) |
−0.983574 | + | 0.180506i | \(0.942227\pi\) | |||||||
\(150\) | 0.230345 | + | 0.398970i | 0.0188076 | + | 0.0325757i | ||||
\(151\) | −11.4354 | + | 6.60225i | −0.930602 | + | 0.537283i | −0.887002 | − | 0.461766i | \(-0.847216\pi\) |
−0.0435999 | + | 0.999049i | \(0.513883\pi\) | |||||||
\(152\) | −0.156443 | − | 0.0903227i | −0.0126892 | − | 0.00732613i | ||||
\(153\) | 51.5648 | 4.16877 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.8324 | −1.51265 | ||||||||
\(156\) | −3.95211 | − | 2.28175i | −0.316422 | − | 0.182686i | ||||
\(157\) | −4.98745 | + | 2.87951i | −0.398042 | + | 0.229810i | −0.685639 | − | 0.727942i | \(-0.740477\pi\) |
0.287597 | + | 0.957752i | \(0.407144\pi\) | |||||||
\(158\) | 3.45939 | + | 5.99185i | 0.275215 | + | 0.476686i | ||||
\(159\) | −13.0921 | − | 7.55872i | −1.03827 | − | 0.599445i | ||||
\(160\) | 2.20288 | 0.174153 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 16.6107i | 1.30506i | ||||||||
\(163\) | 2.65644 | − | 4.60109i | 0.208069 | − | 0.360386i | −0.743037 | − | 0.669250i | \(-0.766616\pi\) |
0.951106 | + | 0.308864i | \(0.0999489\pi\) | |||||||
\(164\) | −3.55184 | − | 6.15197i | −0.277352 | − | 0.480388i | ||||
\(165\) | 22.8087 | − | 1.31277i | 1.77566 | − | 0.102199i | ||||
\(166\) | 5.05972 | + | 2.92123i | 0.392710 | + | 0.226731i | ||||
\(167\) | −16.0519 | −1.24213 | −0.621067 | − | 0.783757i | \(-0.713301\pi\) | ||||
−0.621067 | + | 0.783757i | \(0.713301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8702 | −0.836172 | ||||||||
\(170\) | 8.37900 | − | 14.5129i | 0.642640 | − | 1.11308i | ||||
\(171\) | −0.612236 | − | 1.06042i | −0.0468189 | − | 0.0810926i | ||||
\(172\) | 1.36983 | − | 0.790869i | 0.104448 | − | 0.0603032i | ||||
\(173\) | 3.54738 | − | 6.14425i | 0.269703 | − | 0.467139i | −0.699082 | − | 0.715041i | \(-0.746408\pi\) |
0.968785 | + | 0.247903i | \(0.0797413\pi\) | |||||||
\(174\) | 13.9258i | 1.05571i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.49053 | + | 2.96282i | −0.112353 | + | 0.223331i | ||||
\(177\) | 9.67764 | − | 16.7622i | 0.727416 | − | 1.25992i | ||||
\(178\) | 8.05557 | + | 13.9527i | 0.603791 | + | 1.04580i | ||||
\(179\) | 12.4864 | + | 21.6271i | 0.933278 | + | 1.61648i | 0.777676 | + | 0.628665i | \(0.216398\pi\) |
0.155602 | + | 0.987820i | \(0.450268\pi\) | |||||||
\(180\) | 12.9313 | + | 7.46591i | 0.963845 | + | 0.556476i | ||||
\(181\) | 19.3579i | 1.43886i | 0.694566 | + | 0.719429i | \(0.255596\pi\) | ||||
−0.694566 | + | 0.719429i | \(0.744404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 17.9060i | − | 1.32365i | ||||||
\(184\) | 1.98129 | + | 1.14390i | 0.146062 | + | 0.0843291i | ||||
\(185\) | −2.87969 | + | 1.66259i | −0.211719 | + | 0.122236i | ||||
\(186\) | 23.1514 | − | 13.3665i | 1.69754 | − | 0.980076i | ||||
\(187\) | 13.8500 | + | 21.0894i | 1.01281 | + | 1.54221i | ||||
\(188\) | 0.545357i | 0.0397743i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.397940 | −0.0288696 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | −2.70809 | + | 1.56352i | −0.195439 | + | 0.112837i | ||||
\(193\) | 14.3859 | − | 8.30569i | 1.03552 | − | 0.597857i | 0.116957 | − | 0.993137i | \(-0.462686\pi\) |
0.918561 | + | 0.395280i | \(0.129353\pi\) | |||||||
\(194\) | −5.65058 | + | 9.78709i | −0.405688 | + | 0.702672i | ||||
\(195\) | −10.0528 | −0.719899 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.6396i | − | 1.47051i | −0.677790 | − | 0.735256i | \(-0.737062\pi\) | ||
0.677790 | − | 0.735256i | \(-0.262938\pi\) | |||||||
\(198\) | −18.7912 | + | 12.3407i | −1.33543 | + | 0.877016i | ||||
\(199\) | −0.628737 | + | 0.363001i | −0.0445700 | + | 0.0257325i | −0.522119 | − | 0.852872i | \(-0.674858\pi\) |
0.477549 | + | 0.878605i | \(0.341525\pi\) | |||||||
\(200\) | −0.127587 | + | 0.0736626i | −0.00902179 | + | 0.00520873i | ||||
\(201\) | 8.07488 | + | 4.66203i | 0.569558 | + | 0.328834i | ||||
\(202\) | − | 0.517716i | − | 0.0364264i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 23.7883i | 1.66552i | ||||||||
\(205\) | −13.5520 | − | 7.82428i | −0.946516 | − | 0.546471i | ||||
\(206\) | −1.44358 | − | 2.50035i | −0.100579 | − | 0.174208i | ||||
\(207\) | 7.75369 | + | 13.4298i | 0.538919 | + | 0.933435i | ||||
\(208\) | 0.729686 | − | 1.26385i | 0.0505946 | − | 0.0876325i | ||||
\(209\) | 0.269257 | − | 0.535220i | 0.0186249 | − | 0.0370219i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.2878i | − | 0.708241i | −0.935200 | − | 0.354120i | \(-0.884780\pi\) | ||
0.935200 | − | 0.354120i | \(-0.115220\pi\) | |||||||
\(212\) | 2.41722 | − | 4.18675i | 0.166015 | − | 0.287547i | ||||
\(213\) | −20.5134 | + | 11.8434i | −1.40556 | + | 0.811499i | ||||
\(214\) | 2.60980 | + | 4.52030i | 0.178402 | + | 0.309001i | ||||
\(215\) | 1.74219 | − | 3.01756i | 0.118816 | − | 0.205796i | ||||
\(216\) | −11.8149 | −0.803904 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0540 | −0.680945 | ||||||||
\(219\) | 26.2046 | + | 15.1293i | 1.77075 | + | 1.02234i | ||||
\(220\) | 0.419814 | + | 7.29405i | 0.0283038 | + | 0.491765i | ||||
\(221\) | −5.55095 | − | 9.61453i | −0.373398 | − | 0.646744i | ||||
\(222\) | 2.36008 | − | 4.08778i | 0.158398 | − | 0.274354i | ||||
\(223\) | − | 0.894768i | − | 0.0599181i | −0.999551 | − | 0.0299590i | \(-0.990462\pi\) | ||
0.999551 | − | 0.0299590i | \(-0.00953768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.998618 | −0.0665745 | ||||||||
\(226\) | −6.78302 | − | 3.91618i | −0.451200 | − | 0.260500i | ||||
\(227\) | −6.74239 | − | 11.6782i | −0.447508 | − | 0.775107i | 0.550715 | − | 0.834693i | \(-0.314355\pi\) |
−0.998223 | + | 0.0595863i | \(0.981022\pi\) | |||||||
\(228\) | 0.489203 | − | 0.282442i | 0.0323983 | − | 0.0187052i | ||||
\(229\) | 4.23097 | + | 2.44275i | 0.279590 | + | 0.161422i | 0.633238 | − | 0.773957i | \(-0.281725\pi\) |
−0.353648 | + | 0.935379i | \(0.615059\pi\) | |||||||
\(230\) | 5.03973 | 0.332310 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.45335 | −0.292377 | ||||||||
\(233\) | 19.6247 | + | 11.3303i | 1.28566 | + | 0.742274i | 0.977876 | − | 0.209184i | \(-0.0670807\pi\) |
0.307780 | + | 0.951458i | \(0.400414\pi\) | |||||||
\(234\) | 8.56680 | − | 4.94605i | 0.560029 | − | 0.323333i | ||||
\(235\) | 0.600678 | + | 1.04041i | 0.0391839 | + | 0.0678685i | ||||
\(236\) | 5.36041 | + | 3.09483i | 0.348933 | + | 0.201457i | ||||
\(237\) | −21.6353 | −1.40536 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.2410i | 1.63270i | 0.577556 | + | 0.816351i | \(0.304007\pi\) | ||||
−0.577556 | + | 0.816351i | \(0.695993\pi\) | |||||||
\(240\) | −3.44423 | + | 5.96559i | −0.222324 | + | 0.385077i | ||||
\(241\) | 7.03345 | + | 12.1823i | 0.453064 | + | 0.784730i | 0.998575 | − | 0.0533739i | \(-0.0169975\pi\) |
−0.545510 | + | 0.838104i | \(0.683664\pi\) | |||||||
\(242\) | −10.0944 | − | 4.37072i | −0.648892 | − | 0.280961i | ||||
\(243\) | −14.2871 | − | 8.24865i | −0.916517 | − | 0.529151i | ||||
\(244\) | 5.72621 | 0.366583 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 22.2134 | 1.41628 | ||||||||
\(247\) | −0.131814 | + | 0.228309i | −0.00838715 | + | 0.0145270i | ||||
\(248\) | 4.27449 | + | 7.40363i | 0.271430 | + | 0.470131i | ||||
\(249\) | −15.8219 | + | 9.13478i | −1.00267 | + | 0.578893i | ||||
\(250\) | −5.66947 | + | 9.81980i | −0.358569 | + | 0.621059i | ||||
\(251\) | 3.03720i | 0.191706i | 0.995395 | + | 0.0958532i | \(0.0305579\pi\) | ||||
−0.995395 | + | 0.0958532i | \(0.969442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.41002 | + | 6.77832i | −0.214386 | + | 0.426149i | ||||
\(254\) | 6.73510 | − | 11.6655i | 0.422598 | − | 0.731961i | ||||
\(255\) | 26.2014 | + | 45.3821i | 1.64079 | + | 2.84194i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −22.3160 | − | 12.8842i | −1.39204 | − | 0.803692i | −0.398496 | − | 0.917170i | \(-0.630468\pi\) |
−0.993541 | + | 0.113478i | \(0.963801\pi\) | |||||||
\(258\) | 4.94614i | 0.307933i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 3.21482i | − | 0.199375i | ||||||
\(261\) | −26.1421 | − | 15.0931i | −1.61815 | − | 0.934241i | ||||
\(262\) | −2.27298 | + | 1.31231i | −0.140425 | + | 0.0810747i | ||||
\(263\) | −5.55124 | + | 3.20501i | −0.342304 | + | 0.197629i | −0.661290 | − | 0.750130i | \(-0.729991\pi\) |
0.318986 | + | 0.947759i | \(0.396658\pi\) | |||||||
\(264\) | −5.69312 | − | 8.66891i | −0.350387 | − | 0.533534i | ||||
\(265\) | − | 10.6497i | − | 0.654205i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −50.3800 | −3.08321 | ||||||||
\(268\) | −1.49088 | + | 2.58228i | −0.0910701 | + | 0.157738i | ||||
\(269\) | −2.37423 | + | 1.37076i | −0.144759 | + | 0.0835767i | −0.570630 | − | 0.821207i | \(-0.693301\pi\) |
0.425871 | + | 0.904784i | \(0.359968\pi\) | |||||||
\(270\) | −22.5399 | + | 13.0134i | −1.37174 | + | 0.791972i | ||||
\(271\) | −14.3001 | + | 24.7685i | −0.868670 | + | 1.50458i | −0.00531291 | + | 0.999986i | \(0.501691\pi\) |
−0.863357 | + | 0.504594i | \(0.831642\pi\) | |||||||
\(272\) | −7.60732 | −0.461261 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 8.72291i | − | 0.526970i | ||||||
\(275\) | −0.268223 | − | 0.408422i | −0.0161744 | − | 0.0246288i | ||||
\(276\) | −6.19554 | + | 3.57700i | −0.372928 | + | 0.215310i | ||||
\(277\) | −9.32564 | + | 5.38416i | −0.560324 | + | 0.323503i | −0.753275 | − | 0.657705i | \(-0.771527\pi\) |
0.192952 | + | 0.981208i | \(0.438194\pi\) | |||||||
\(278\) | −3.54456 | − | 2.04645i | −0.212589 | − | 0.122738i | ||||
\(279\) | 57.9477i | 3.46924i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.6289i | 1.17096i | 0.810686 | + | 0.585481i | \(0.199094\pi\) | ||||
−0.810686 | + | 0.585481i | \(0.800906\pi\) | |||||||
\(282\) | −1.47688 | − | 0.852675i | −0.0879467 | − | 0.0507760i | ||||
\(283\) | −5.31163 | − | 9.20001i | −0.315744 | − | 0.546884i | 0.663852 | − | 0.747864i | \(-0.268921\pi\) |
−0.979595 | + | 0.200980i | \(0.935587\pi\) | |||||||
\(284\) | −3.78744 | − | 6.56004i | −0.224743 | − | 0.389267i | ||||
\(285\) | 0.622185 | − | 1.07766i | 0.0368551 | − | 0.0638348i | ||||
\(286\) | 4.32386 | + | 2.17524i | 0.255675 | + | 0.128624i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 6.77832i | − | 0.399416i | ||||||
\(289\) | −20.4356 | + | 35.3956i | −1.20210 | + | 2.08209i | ||||
\(290\) | −8.49588 | + | 4.90510i | −0.498895 | + | 0.288037i | ||||
\(291\) | −17.6695 | − | 30.6045i | −1.03581 | − | 1.79407i | ||||
\(292\) | −4.83822 | + | 8.38004i | −0.283135 | + | 0.490405i | ||||
\(293\) | 0.277651 | 0.0162206 | 0.00811028 | − | 0.999967i | \(-0.497418\pi\) | ||||
0.00811028 | + | 0.999967i | \(0.497418\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6351 | 0.793866 | ||||||||
\(296\) | 1.30724 | + | 0.754735i | 0.0759818 | + | 0.0438681i | ||||
\(297\) | −2.25163 | − | 39.1209i | −0.130653 | − | 2.27003i | ||||
\(298\) | 9.29587 | + | 16.1009i | 0.538495 | + | 0.932701i | ||||
\(299\) | 1.66937 | − | 2.89143i | 0.0965421 | − | 0.167216i | ||||
\(300\) | − | 0.460691i | − | 0.0265980i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.2045 | 0.759833 | ||||||||
\(303\) | 1.40202 | + | 0.809457i | 0.0805440 | + | 0.0465021i | ||||
\(304\) | 0.0903227 | + | 0.156443i | 0.00518036 | + | 0.00897265i | ||||
\(305\) | 10.9242 | − | 6.30707i | 0.625516 | − | 0.361142i | ||||
\(306\) | −44.6565 | − | 25.7824i | −2.55284 | − | 1.47388i | ||||
\(307\) | 6.41443 | 0.366091 | 0.183045 | − | 0.983104i | \(-0.441404\pi\) | ||||
0.183045 | + | 0.983104i | \(0.441404\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.02823 | 0.513598 | ||||||||
\(310\) | 16.3093 | + | 9.41618i | 0.926306 | + | 0.534803i | ||||
\(311\) | 9.78814 | − | 5.65119i | 0.555035 | − | 0.320449i | −0.196115 | − | 0.980581i | \(-0.562833\pi\) |
0.751150 | + | 0.660131i | \(0.229499\pi\) | |||||||
\(312\) | 2.28175 | + | 3.95211i | 0.129179 | + | 0.223744i | ||||
\(313\) | 14.2432 | + | 8.22333i | 0.805075 | + | 0.464810i | 0.845243 | − | 0.534383i | \(-0.179456\pi\) |
−0.0401677 | + | 0.999193i | \(0.512789\pi\) | |||||||
\(314\) | 5.75901 | 0.325000 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 6.91879i | − | 0.389212i | ||||||
\(317\) | 14.0955 | − | 24.4141i | 0.791683 | − | 1.37124i | −0.133241 | − | 0.991084i | \(-0.542539\pi\) |
0.924924 | − | 0.380151i | \(-0.124128\pi\) | |||||||
\(318\) | 7.55872 | + | 13.0921i | 0.423872 | + | 0.734168i | ||||
\(319\) | −0.848697 | − | 14.7457i | −0.0475179 | − | 0.825601i | ||||
\(320\) | −1.90775 | − | 1.10144i | −0.106646 | − | 0.0615723i | ||||
\(321\) | −16.3218 | −0.910996 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.37423 | 0.0764640 | ||||||||
\(324\) | 8.30534 | − | 14.3853i | 0.461408 | − | 0.799181i | ||||
\(325\) | 0.107501 | + | 0.186198i | 0.00596309 | + | 0.0103284i | ||||
\(326\) | −4.60109 | + | 2.65644i | −0.254831 | + | 0.147127i | ||||
\(327\) | 15.7196 | − | 27.2272i | 0.869298 | − | 1.50567i | ||||
\(328\) | 7.10368i | 0.392235i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −20.4093 | − | 10.2675i | −1.12350 | − | 0.565206i | ||||
\(331\) | −9.55629 | + | 16.5520i | −0.525261 | + | 0.909779i | 0.474306 | + | 0.880360i | \(0.342699\pi\) |
−0.999567 | + | 0.0294190i | \(0.990634\pi\) | |||||||
\(332\) | −2.92123 | − | 5.05972i | −0.160323 | − | 0.277688i | ||||
\(333\) | 5.11584 | + | 8.86089i | 0.280346 | + | 0.485574i | ||||
\(334\) | 13.9014 | + | 8.02596i | 0.760649 | + | 0.439161i | ||||
\(335\) | 6.56846i | 0.358874i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0358i | 0.873525i | 0.899577 | + | 0.436763i | \(0.143875\pi\) | ||||
−0.899577 | + | 0.436763i | \(0.856125\pi\) | |||||||
\(338\) | 9.41390 | + | 5.43512i | 0.512049 | + | 0.295631i | ||||
\(339\) | 21.2107 | − | 12.2460i | 1.15201 | − | 0.665112i | ||||
\(340\) | −14.5129 | + | 8.37900i | −0.787070 | + | 0.454415i | ||||
\(341\) | −23.6999 | + | 15.5644i | −1.28342 | + | 0.842859i | ||||
\(342\) | 1.22447i | 0.0662119i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.58174 | −0.0852816 | ||||||||
\(345\) | −7.87969 | + | 13.6480i | −0.424228 | + | 0.734785i | ||||
\(346\) | −6.14425 | + | 3.54738i | −0.330317 | + | 0.190708i | ||||
\(347\) | −8.54848 | + | 4.93547i | −0.458907 | + | 0.264950i | −0.711584 | − | 0.702601i | \(-0.752022\pi\) |
0.252678 | + | 0.967550i | \(0.418689\pi\) | |||||||
\(348\) | 6.96289 | − | 12.0601i | 0.373250 | − | 0.646488i | ||||
\(349\) | 31.1871 | 1.66940 | 0.834702 | − | 0.550701i | \(-0.185640\pi\) | ||||
0.834702 | + | 0.550701i | \(0.185640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.2424i | 0.920330i | ||||||||
\(352\) | 2.77225 | − | 1.82062i | 0.147761 | − | 0.0970391i | ||||
\(353\) | 22.4891 | − | 12.9841i | 1.19698 | − | 0.691075i | 0.237097 | − | 0.971486i | \(-0.423804\pi\) |
0.959880 | + | 0.280411i | \(0.0904709\pi\) | |||||||
\(354\) | −16.7622 | + | 9.67764i | −0.890899 | + | 0.514361i | ||||
\(355\) | −14.4510 | − | 8.34327i | −0.766978 | − | 0.442815i | ||||
\(356\) | − | 16.1111i | − | 0.853889i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 24.9728i | − | 1.31985i | ||||||
\(359\) | −3.47334 | − | 2.00534i | −0.183316 | − | 0.105838i | 0.405534 | − | 0.914080i | \(-0.367086\pi\) |
−0.588850 | + | 0.808243i | \(0.700419\pi\) | |||||||
\(360\) | −7.46591 | − | 12.9313i | −0.393488 | − | 0.681541i | ||||
\(361\) | 9.48368 | + | 16.4262i | 0.499141 | + | 0.864538i | ||||
\(362\) | 9.67893 | − | 16.7644i | 0.508713 | − | 0.881117i | ||||
\(363\) | 27.6190 | − | 20.5028i | 1.44962 | − | 1.07612i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.3160i | 1.11573i | ||||||||
\(366\) | −8.95301 | + | 15.5071i | −0.467982 | + | 0.810568i | ||||
\(367\) | −16.6148 | + | 9.59255i | −0.867284 | + | 0.500727i | −0.866445 | − | 0.499273i | \(-0.833601\pi\) |
−0.000839598 | 1.00000i | \(0.500267\pi\) | ||||||||
\(368\) | −1.14390 | − | 1.98129i | −0.0596297 | − | 0.103282i | ||||
\(369\) | −24.0755 | + | 41.7000i | −1.25332 | + | 2.17082i | ||||
\(370\) | 3.32518 | 0.172868 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.7329 | −1.38604 | ||||||||
\(373\) | 18.2116 | + | 10.5145i | 0.942961 | + | 0.544419i | 0.890887 | − | 0.454225i | \(-0.150084\pi\) |
0.0520734 | + | 0.998643i | \(0.483417\pi\) | |||||||
\(374\) | −1.44976 | − | 25.1889i | −0.0749655 | − | 1.30249i | ||||
\(375\) | −17.7286 | − | 30.7068i | −0.915501 | − | 1.58569i | ||||
\(376\) | 0.272679 | − | 0.472293i | 0.0140623 | − | 0.0243567i | ||||
\(377\) | 6.49910i | 0.334721i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7525 | 1.06599 | 0.532993 | − | 0.846120i | \(-0.321067\pi\) | ||||
0.532993 | + | 0.846120i | \(0.321067\pi\) | |||||||
\(380\) | 0.344626 | + | 0.198970i | 0.0176789 | + | 0.0102069i | ||||
\(381\) | 21.0609 | + | 36.4785i | 1.07898 | + | 1.86885i | ||||
\(382\) | 5.19615 | − | 3.00000i | 0.265858 | − | 0.153493i | ||||
\(383\) | 1.08778 | + | 0.628029i | 0.0555829 | + | 0.0320908i | 0.527534 | − | 0.849534i | \(-0.323117\pi\) |
−0.471951 | + | 0.881625i | \(0.656450\pi\) | |||||||
\(384\) | 3.12703 | 0.159576 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.6114 | −0.845497 | ||||||||
\(387\) | −9.28511 | − | 5.36076i | −0.471989 | − | 0.272503i | ||||
\(388\) | 9.78709 | − | 5.65058i | 0.496864 | − | 0.286865i | ||||
\(389\) | 8.32393 | + | 14.4175i | 0.422040 | + | 0.730994i | 0.996139 | − | 0.0877915i | \(-0.0279809\pi\) |
−0.574099 | + | 0.818786i | \(0.694648\pi\) | |||||||
\(390\) | 8.70601 | + | 5.02642i | 0.440846 | + | 0.254523i | ||||
\(391\) | −17.4040 | −0.880156 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8.20726i | − | 0.414001i | ||||||
\(394\) | −10.3198 | + | 17.8744i | −0.519904 | + | 0.900501i | ||||
\(395\) | −7.62062 | − | 13.1993i | −0.383435 | − | 0.664129i | ||||
\(396\) | 22.4440 | − | 1.29178i | 1.12785 | − | 0.0649143i | ||||
\(397\) | −12.2752 | − | 7.08712i | −0.616077 | − | 0.355692i | 0.159263 | − | 0.987236i | \(-0.449088\pi\) |
−0.775340 | + | 0.631544i | \(0.782421\pi\) | |||||||
\(398\) | 0.726003 | 0.0363912 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.147325 | 0.00736626 | ||||||||
\(401\) | 2.42635 | − | 4.20256i | 0.121166 | − | 0.209866i | −0.799062 | − | 0.601249i | \(-0.794670\pi\) |
0.920228 | + | 0.391383i | \(0.128003\pi\) | |||||||
\(402\) | −4.66203 | − | 8.07488i | −0.232521 | − | 0.402738i | ||||
\(403\) | 10.8046 | − | 6.23807i | 0.538218 | − | 0.310740i | ||||
\(404\) | −0.258858 | + | 0.448355i | −0.0128787 | + | 0.0223065i | ||||
\(405\) | − | 36.5913i | − | 1.81824i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.24991 | + | 4.47229i | −0.111524 | + | 0.221683i | ||||
\(408\) | 11.8942 | − | 20.6013i | 0.588849 | − | 1.01992i | ||||
\(409\) | −5.31402 | − | 9.20415i | −0.262761 | − | 0.455116i | 0.704213 | − | 0.709988i | \(-0.251300\pi\) |
−0.966975 | + | 0.254872i | \(0.917967\pi\) | |||||||
\(410\) | 7.82428 | + | 13.5520i | 0.386414 | + | 0.669288i | ||||
\(411\) | 23.6224 | + | 13.6384i | 1.16521 | + | 0.672733i | ||||
\(412\) | 2.88716i | 0.142240i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 15.5074i | − | 0.762146i | ||||||
\(415\) | −11.1459 | − | 6.43512i | −0.547133 | − | 0.315887i | ||||
\(416\) | −1.26385 | + | 0.729686i | −0.0619655 | + | 0.0357758i | ||||
\(417\) | 11.0840 | − | 6.39932i | 0.542783 | − | 0.313376i | ||||
\(418\) | −0.500794 | + | 0.328886i | −0.0244946 | + | 0.0160863i | ||||
\(419\) | 11.3690i | 0.555410i | 0.960666 | + | 0.277705i | \(0.0895739\pi\) | ||||
−0.960666 | + | 0.277705i | \(0.910426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.2464 | 1.32791 | 0.663955 | − | 0.747772i | \(-0.268877\pi\) | ||||
0.663955 | + | 0.747772i | \(0.268877\pi\) | |||||||
\(422\) | −5.14390 | + | 8.90949i | −0.250401 | + | 0.433707i | ||||
\(423\) | 3.20136 | − | 1.84830i | 0.155655 | − | 0.0898676i | ||||
\(424\) | −4.18675 | + | 2.41722i | −0.203326 | + | 0.117391i | ||||
\(425\) | 0.560375 | − | 0.970598i | 0.0271822 | − | 0.0470809i | ||||
\(426\) | 23.6869 | 1.14763 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 5.21959i | − | 0.252299i | ||||||
\(429\) | −12.6512 | + | 8.30838i | −0.610804 | + | 0.401132i | ||||
\(430\) | −3.01756 | + | 1.74219i | −0.145520 | + | 0.0840158i | ||||
\(431\) | −13.1818 | + | 7.61049i | −0.634943 | + | 0.366584i | −0.782664 | − | 0.622445i | \(-0.786140\pi\) |
0.147721 | + | 0.989029i | \(0.452806\pi\) | |||||||
\(432\) | 10.2320 | + | 5.90746i | 0.492289 | + | 0.284223i | ||||
\(433\) | 1.85534i | 0.0891619i | 0.999006 | + | 0.0445810i | \(0.0141953\pi\) | ||||
−0.999006 | + | 0.0445810i | \(0.985805\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 30.6768i | − | 1.47084i | ||||||
\(436\) | 8.70705 | + | 5.02702i | 0.416992 | + | 0.240750i | ||||
\(437\) | 0.206639 | + | 0.357910i | 0.00988490 | + | 0.0171212i | ||||
\(438\) | −15.1293 | − | 26.2046i | −0.722904 | − | 1.25211i | ||||
\(439\) | 16.4702 | − | 28.5272i | 0.786079 | − | 1.36153i | −0.142274 | − | 0.989827i | \(-0.545441\pi\) |
0.928352 | − | 0.371701i | \(-0.121225\pi\) | |||||||
\(440\) | 3.28346 | − | 6.52674i | 0.156533 | − | 0.311150i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.1019i | 0.528064i | ||||||||
\(443\) | 16.4306 | − | 28.4587i | 0.780643 | − | 1.35211i | −0.150924 | − | 0.988545i | \(-0.548225\pi\) |
0.931567 | − | 0.363569i | \(-0.118442\pi\) | |||||||
\(444\) | −4.08778 | + | 2.36008i | −0.193997 | + | 0.112004i | ||||
\(445\) | −17.7455 | − | 30.7360i | −0.841215 | − | 1.45703i | ||||
\(446\) | −0.447384 | + | 0.774891i | −0.0211842 | + | 0.0366922i | ||||
\(447\) | −58.1369 | −2.74978 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.62716 | 0.171176 | 0.0855880 | − | 0.996331i | \(-0.472723\pi\) | ||||
0.0855880 | + | 0.996331i | \(0.472723\pi\) | |||||||
\(450\) | 0.864828 | + | 0.499309i | 0.0407684 | + | 0.0235376i | ||||
\(451\) | −23.5213 | + | 1.35378i | −1.10758 | + | 0.0637472i | ||||
\(452\) | 3.91618 | + | 6.78302i | 0.184201 | + | 0.319046i | ||||
\(453\) | −20.6454 | + | 35.7589i | −0.970007 | + | 1.68010i | ||||
\(454\) | 13.4848i | 0.632872i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.564883 | −0.0264531 | ||||||||
\(457\) | 2.36916 | + | 1.36783i | 0.110825 | + | 0.0639846i | 0.554388 | − | 0.832259i | \(-0.312952\pi\) |
−0.443563 | + | 0.896243i | \(0.646286\pi\) | |||||||
\(458\) | −2.44275 | − | 4.23097i | −0.114142 | − | 0.197700i | ||||
\(459\) | 77.8383 | − | 44.9399i | 3.63318 | − | 2.09762i | ||||
\(460\) | −4.36453 | − | 2.51986i | −0.203497 | − | 0.117489i | ||||
\(461\) | −20.4439 | −0.952169 | −0.476084 | − | 0.879400i | \(-0.657944\pi\) | ||||
−0.476084 | + | 0.879400i | \(0.657944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.1701 | 1.40212 | 0.701062 | − | 0.713100i | \(-0.252710\pi\) | ||||
0.701062 | + | 0.713100i | \(0.252710\pi\) | |||||||
\(464\) | 3.85672 | + | 2.22668i | 0.179044 | + | 0.103371i | ||||
\(465\) | −50.9997 | + | 29.4447i | −2.36505 | + | 1.36546i | ||||
\(466\) | −11.3303 | − | 19.6247i | −0.524867 | − | 0.909096i | ||||
\(467\) | −23.5318 | − | 13.5861i | −1.08892 | − | 0.628691i | −0.155634 | − | 0.987815i | \(-0.549742\pi\) |
−0.933290 | + | 0.359124i | \(0.883075\pi\) | |||||||
\(468\) | −9.89209 | −0.457262 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1.20136i | − | 0.0554144i | ||||||
\(471\) | −9.00431 | + | 15.5959i | −0.414897 | + | 0.718622i | ||||
\(472\) | −3.09483 | − | 5.36041i | −0.142451 | − | 0.246733i | ||||
\(473\) | −0.301440 | − | 5.23736i | −0.0138602 | − | 0.240814i | ||||
\(474\) | 18.7367 | + | 10.8176i | 0.860604 | + | 0.496870i | ||||
\(475\) | −0.0266136 | −0.00122112 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.7694 | −1.50041 | ||||||||
\(478\) | 12.6205 | − | 21.8593i | 0.577247 | − | 0.999822i | ||||
\(479\) | 10.8092 | + | 18.7221i | 0.493885 | + | 0.855434i | 0.999975 | − | 0.00704654i | \(-0.00224300\pi\) |
−0.506090 | + | 0.862481i | \(0.668910\pi\) | |||||||
\(480\) | 5.96559 | − | 3.44423i | 0.272291 | − | 0.157207i | ||||
\(481\) | 1.10144 | − | 1.90775i | 0.0502213 | − | 0.0869859i | ||||
\(482\) | − | 14.0669i | − | 0.640730i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.55664 | + | 8.83235i | 0.298029 | + | 0.401471i | ||||
\(485\) | 12.4475 | − | 21.5598i | 0.565214 | − | 0.978979i | ||||
\(486\) | 8.24865 | + | 14.2871i | 0.374167 | + | 0.648075i | ||||
\(487\) | −1.04287 | − | 1.80630i | −0.0472567 | − | 0.0818511i | 0.841429 | − | 0.540367i | \(-0.181715\pi\) |
−0.888686 | + | 0.458516i | \(0.848381\pi\) | |||||||
\(488\) | −4.95904 | − | 2.86310i | −0.224485 | − | 0.129607i | ||||
\(489\) | − | 16.6136i | − | 0.751291i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.47983i | − | 0.111913i | −0.998433 | − | 0.0559566i | \(-0.982179\pi\) | ||
0.998433 | − | 0.0559566i | \(-0.0178208\pi\) | |||||||
\(492\) | −19.2374 | − | 11.1067i | −0.867289 | − | 0.500730i | ||||
\(493\) | 29.3393 | − | 16.9390i | 1.32137 | − | 0.762896i | ||||
\(494\) | 0.228309 | − | 0.131814i | 0.0102721 | − | 0.00593061i | ||||
\(495\) | 41.3947 | − | 27.1851i | 1.86055 | − | 1.22188i | ||||
\(496\) | − | 8.54897i | − | 0.383860i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 18.2696 | 0.818678 | ||||||||
\(499\) | −7.69189 | + | 13.3227i | −0.344336 | + | 0.596408i | −0.985233 | − | 0.171219i | \(-0.945229\pi\) |
0.640897 | + | 0.767627i | \(0.278563\pi\) | |||||||
\(500\) | 9.81980 | − | 5.66947i | 0.439155 | − | 0.253546i | ||||
\(501\) | −43.4700 | + | 25.0974i | −1.94210 | + | 1.12127i | ||||
\(502\) | 1.51860 | − | 2.63029i | 0.0677784 | − | 0.117396i | ||||
\(503\) | −15.5714 | −0.694295 | −0.347147 | − | 0.937811i | \(-0.612850\pi\) | ||||
−0.347147 | + | 0.937811i | \(0.612850\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.14047i | 0.0507501i | ||||||||
\(506\) | 6.34233 | − | 4.16519i | 0.281951 | − | 0.185165i | ||||
\(507\) | −29.4375 | + | 16.9958i | −1.30737 | + | 0.754809i | ||||
\(508\) | −11.6655 | + | 6.73510i | −0.517575 | + | 0.298822i | ||||
\(509\) | 26.6346 | + | 15.3775i | 1.18056 | + | 0.681595i | 0.956144 | − | 0.292898i | \(-0.0946198\pi\) |
0.224414 | + | 0.974494i | \(0.427953\pi\) | |||||||
\(510\) | − | 52.4028i | − | 2.32043i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.84837 | − | 1.06716i | −0.0816074 | − | 0.0471161i | ||||
\(514\) | 12.8842 | + | 22.3160i | 0.568296 | + | 0.984318i | ||||
\(515\) | 3.18003 | + | 5.50797i | 0.140129 | + | 0.242710i | ||||
\(516\) | 2.47307 | − | 4.28348i | 0.108871 | − | 0.188570i | ||||
\(517\) | 1.61580 | + | 0.812872i | 0.0710627 | + | 0.0357500i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 22.1856i | − | 0.973838i | ||||||
\(520\) | −1.60741 | + | 2.78412i | −0.0704896 | + | 0.122092i | ||||
\(521\) | 3.19850 | − | 1.84666i | 0.140129 | − | 0.0809035i | −0.428296 | − | 0.903638i | \(-0.640886\pi\) |
0.568425 | + | 0.822735i | \(0.307553\pi\) | |||||||
\(522\) | 15.0931 | + | 26.1421i | 0.660608 | + | 1.14421i | ||||
\(523\) | 14.6007 | − | 25.2891i | 0.638444 | − | 1.10582i | −0.347331 | − | 0.937743i | \(-0.612912\pi\) |
0.985774 | − | 0.168074i | \(-0.0537548\pi\) | |||||||
\(524\) | 2.62462 | 0.114657 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.41002 | 0.279490 | ||||||||
\(527\) | −56.3218 | − | 32.5174i | −2.45341 | − | 1.41648i | ||||
\(528\) | 0.595934 | + | 10.3541i | 0.0259347 | + | 0.450602i | ||||
\(529\) | 8.88301 | + | 15.3858i | 0.386218 | + | 0.668949i | ||||
\(530\) | −5.32484 | + | 9.22289i | −0.231296 | + | 0.400617i | ||||
\(531\) | − | 41.9556i | − | 1.82072i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3669 | 0.449041 | ||||||||
\(534\) | 43.6304 | + | 25.1900i | 1.88807 | + | 1.09008i | ||||
\(535\) | −5.74906 | − | 9.95767i | −0.248554 | − | 0.430508i | ||||
\(536\) | 2.58228 | − | 1.49088i | 0.111538 | − | 0.0643963i | ||||
\(537\) | 67.6286 | + | 39.0454i | 2.91839 | + | 1.68493i | ||||
\(538\) | 2.74152 | 0.118195 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 26.0268 | 1.12002 | ||||||||
\(541\) | 14.0078 | + | 8.08743i | 0.602244 | + | 0.347706i | 0.769924 | − | 0.638136i | \(-0.220294\pi\) |
−0.167680 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(542\) | 24.7685 | − | 14.3001i | 1.06390 | − | 0.614242i | ||||
\(543\) | 30.2663 | + | 52.4228i | 1.29885 | + | 2.24968i | ||||
\(544\) | 6.58813 | + | 3.80366i | 0.282464 | + | 0.163081i | ||||
\(545\) | 22.1478 | 0.948708 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 34.0719i | − | 1.45681i | −0.685146 | − | 0.728405i | \(-0.740262\pi\) | ||
0.685146 | − | 0.728405i | \(-0.259738\pi\) | |||||||
\(548\) | −4.36145 | + | 7.55426i | −0.186312 | + | 0.322702i | ||||
\(549\) | −19.4070 | − | 33.6140i | −0.828272 | − | 1.43461i | ||||
\(550\) | 0.0280765 | + | 0.487815i | 0.00119719 | + | 0.0208005i | ||||
\(551\) | −0.696698 | − | 0.402239i | −0.0296803 | − | 0.0171359i | ||||
\(552\) | 7.15399 | 0.304494 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.7683 | 0.457502 | ||||||||
\(555\) | −5.19897 | + | 9.00488i | −0.220684 | + | 0.382236i | ||||
\(556\) | 2.04645 | + | 3.54456i | 0.0867889 | + | 0.150323i | ||||
\(557\) | −22.2451 | + | 12.8432i | −0.942555 | + | 0.544185i | −0.890760 | − | 0.454473i | \(-0.849828\pi\) |
−0.0517949 | + | 0.998658i | \(0.516494\pi\) | |||||||
\(558\) | 28.9738 | − | 50.1842i | 1.22656 | − | 2.12447i | ||||
\(559\) | 2.30834i | 0.0976325i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 70.4806 | + | 35.4572i | 2.97569 | + | 1.49700i | ||||
\(562\) | 9.81445 | − | 16.9991i | 0.413998 | − | 0.717065i | ||||
\(563\) | −10.9683 | − | 18.9976i | −0.462258 | − | 0.800654i | 0.536815 | − | 0.843700i | \(-0.319627\pi\) |
−0.999073 | + | 0.0430456i | \(0.986294\pi\) | |||||||
\(564\) | 0.852675 | + | 1.47688i | 0.0359041 | + | 0.0621877i | ||||
\(565\) | 14.9422 | + | 8.62686i | 0.628621 | + | 0.362935i | ||||
\(566\) | 10.6233i | 0.446529i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.57488i | 0.317835i | ||||||||
\(569\) | −2.22306 | − | 1.28348i | −0.0931956 | − | 0.0538065i | 0.452678 | − | 0.891674i | \(-0.350469\pi\) |
−0.545873 | + | 0.837868i | \(0.683802\pi\) | |||||||
\(570\) | −1.07766 | + | 0.622185i | −0.0451380 | + | 0.0260605i | ||||
\(571\) | 29.7126 | − | 17.1546i | 1.24343 | − | 0.717897i | 0.273643 | − | 0.961831i | \(-0.411771\pi\) |
0.969792 | + | 0.243934i | \(0.0784380\pi\) | |||||||
\(572\) | −2.65696 | − | 4.04574i | −0.111093 | − | 0.169161i | ||||
\(573\) | 18.7622i | 0.783801i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.337049 | 0.0140559 | ||||||||
\(576\) | −3.38916 | + | 5.87020i | −0.141215 | + | 0.244592i | ||||
\(577\) | 17.9257 | − | 10.3494i | 0.746255 | − | 0.430851i | −0.0780842 | − | 0.996947i | \(-0.524880\pi\) |
0.824339 | + | 0.566096i | \(0.191547\pi\) | |||||||
\(578\) | 35.3956 | − | 20.4356i | 1.47226 | − | 0.850011i | ||||
\(579\) | 25.9721 | − | 44.9851i | 1.07937 | − | 1.86952i | ||||
\(580\) | 9.81020 | 0.407346 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 35.3391i | 1.46485i | ||||||||
\(583\) | −8.80165 | − | 13.4023i | −0.364527 | − | 0.555065i | ||||
\(584\) | 8.38004 | − | 4.83822i | 0.346769 | − | 0.200207i | ||||
\(585\) | −18.8716 | + | 10.8955i | −0.780246 | + | 0.450475i | ||||
\(586\) | −0.240453 | − | 0.138826i | −0.00993303 | − | 0.00573484i | ||||
\(587\) | − | 16.0435i | − | 0.662184i | −0.943598 | − | 0.331092i | \(-0.892583\pi\) | ||
0.943598 | − | 0.331092i | \(-0.107417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.54433i | 0.0636331i | ||||||||
\(590\) | −11.8083 | − | 6.81755i | −0.486141 | − | 0.280674i | ||||
\(591\) | −32.2703 | − | 55.8939i | −1.32742 | − | 2.29917i | ||||
\(592\) | −0.754735 | − | 1.30724i | −0.0310194 | − | 0.0537272i | ||||
\(593\) | −17.7436 | + | 30.7328i | −0.728641 | + | 1.26204i | 0.228816 | + | 0.973470i | \(0.426515\pi\) |
−0.957458 | + | 0.288574i | \(0.906819\pi\) | |||||||
\(594\) | −17.6105 | + | 35.0055i | −0.722568 | + | 1.43629i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 18.5917i | − | 0.761547i | ||||||
\(597\) | −1.13512 | + | 1.96608i | −0.0464572 | + | 0.0804663i | ||||
\(598\) | −2.89143 | + | 1.66937i | −0.118239 | + | 0.0682656i | ||||
\(599\) | −0.374693 | − | 0.648987i | −0.0153095 | − | 0.0265169i | 0.858269 | − | 0.513200i | \(-0.171540\pi\) |
−0.873579 | + | 0.486683i | \(0.838207\pi\) | |||||||
\(600\) | −0.230345 | + | 0.398970i | −0.00940381 | + | 0.0162879i | ||||
\(601\) | 18.5168 | 0.755317 | 0.377658 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377658 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2114 | 0.823070 | ||||||||
\(604\) | −11.4354 | − | 6.60225i | −0.465301 | − | 0.268642i | ||||
\(605\) | 22.2367 | + | 9.62817i | 0.904052 | + | 0.391441i | ||||
\(606\) | −0.809457 | − | 1.40202i | −0.0328820 | − | 0.0569532i | ||||
\(607\) | −18.4955 | + | 32.0352i | −0.750710 | + | 1.30027i | 0.196770 | + | 0.980450i | \(0.436955\pi\) |
−0.947479 | + | 0.319817i | \(0.896378\pi\) | |||||||
\(608\) | − | 0.180645i | − | 0.00732613i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.6141 | −0.510732 | ||||||||
\(611\) | −0.689252 | − | 0.397940i | −0.0278841 | − | 0.0160989i | ||||
\(612\) | 25.7824 | + | 44.6565i | 1.04219 | + | 1.80513i | ||||
\(613\) | −2.79338 | + | 1.61276i | −0.112824 | + | 0.0651387i | −0.555350 | − | 0.831617i | \(-0.687416\pi\) |
0.442526 | + | 0.896756i | \(0.354082\pi\) | |||||||
\(614\) | −5.55506 | − | 3.20722i | −0.224184 | − | 0.129433i | ||||
\(615\) | −48.9335 | −1.97319 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8351 | −0.436206 | −0.218103 | − | 0.975926i | \(-0.569987\pi\) | ||||
−0.218103 | + | 0.975926i | \(0.569987\pi\) | |||||||
\(618\) | −7.81868 | − | 4.51412i | −0.314513 | − | 0.181584i | ||||
\(619\) | −4.44127 | + | 2.56417i | −0.178510 | + | 0.103063i | −0.586592 | − | 0.809882i | \(-0.699531\pi\) |
0.408083 | + | 0.912945i | \(0.366198\pi\) | |||||||
\(620\) | −9.41618 | − | 16.3093i | −0.378163 | − | 0.654997i | ||||
\(621\) | 23.4087 | + | 13.5150i | 0.939360 | + | 0.542340i | ||||
\(622\) | −11.3024 | −0.453184 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.56350i | − | 0.182686i | ||||||
\(625\) | 12.1208 | − | 20.9939i | 0.484833 | − | 0.839756i | ||||
\(626\) | −8.22333 | − | 14.2432i | −0.328670 | − | 0.569274i | ||||
\(627\) | −0.107653 | − | 1.87041i | −0.00429923 | − | 0.0746970i | ||||
\(628\) | −4.98745 | − | 2.87951i | −0.199021 | − | 0.114905i | ||||
\(629\) | −11.4830 | −0.457858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.9567 | −1.19256 | −0.596278 | − | 0.802778i | \(-0.703354\pi\) | ||||
−0.596278 | + | 0.802778i | \(0.703354\pi\) | |||||||
\(632\) | −3.45939 | + | 5.99185i | −0.137607 | + | 0.238343i | ||||
\(633\) | −16.0851 | − | 27.8602i | −0.639326 | − | 1.10735i | ||||
\(634\) | −24.4141 | + | 14.0955i | −0.969610 | + | 0.559804i | ||||
\(635\) | −14.8366 | + | 25.6978i | −0.588773 | + | 1.01979i | ||||
\(636\) | − | 15.1174i | − | 0.599445i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.63786 | + | 13.1945i | −0.262795 | + | 0.522375i | ||||
\(639\) | −25.6725 | + | 44.4660i | −1.01559 | + | 1.75905i | ||||
\(640\) | 1.10144 | + | 1.90775i | 0.0435382 | + | 0.0754104i | ||||
\(641\) | −4.61345 | − | 7.99073i | −0.182220 | − | 0.315615i | 0.760416 | − | 0.649436i | \(-0.224995\pi\) |
−0.942636 | + | 0.333821i | \(0.891662\pi\) | |||||||
\(642\) | 14.1351 | + | 8.16091i | 0.557869 | + | 0.322086i | ||||
\(643\) | − | 1.79941i | − | 0.0709616i | −0.999370 | − | 0.0354808i | \(-0.988704\pi\) | ||
0.999370 | − | 0.0354808i | \(-0.0112963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 10.8958i | − | 0.429020i | ||||||
\(646\) | −1.19011 | − | 0.687113i | −0.0468244 | − | 0.0270341i | ||||
\(647\) | 35.2683 | − | 20.3622i | 1.38654 | − | 0.800520i | 0.393618 | − | 0.919274i | \(-0.371223\pi\) |
0.992924 | + | 0.118754i | \(0.0378899\pi\) | |||||||
\(648\) | −14.3853 | + | 8.30534i | −0.565107 | + | 0.326264i | ||||
\(649\) | 17.1593 | − | 11.2690i | 0.673561 | − | 0.442347i | ||||
\(650\) | − | 0.215002i | − | 0.00843309i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.31289 | 0.208069 | ||||||||
\(653\) | 18.8692 | − | 32.6824i | 0.738408 | − | 1.27896i | −0.214803 | − | 0.976657i | \(-0.568911\pi\) |
0.953212 | − | 0.302304i | \(-0.0977557\pi\) | |||||||
\(654\) | −27.2272 | + | 15.7196i | −1.06467 | + | 0.614686i | ||||
\(655\) | 5.00711 | − | 2.89086i | 0.195644 | − | 0.112955i | ||||
\(656\) | 3.55184 | − | 6.15197i | 0.138676 | − | 0.240194i | ||||
\(657\) | 65.5900 | 2.55891 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32.5997i | − | 1.26991i | −0.772551 | − | 0.634953i | \(-0.781019\pi\) | ||
0.772551 | − | 0.634953i | \(-0.218981\pi\) | |||||||
\(660\) | 12.5413 | + | 19.0965i | 0.488168 | + | 0.743332i | ||||
\(661\) | −10.9747 | + | 6.33624i | −0.426866 | + | 0.246451i | −0.698011 | − | 0.716087i | \(-0.745931\pi\) |
0.271145 | + | 0.962539i | \(0.412598\pi\) | |||||||
\(662\) | 16.5520 | − | 9.55629i | 0.643311 | − | 0.371416i | ||||
\(663\) | −30.0649 | − | 17.3580i | −1.16763 | − | 0.674129i | ||||
\(664\) | 5.84246i | 0.226731i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 10.2317i | − | 0.396469i | ||||||
\(667\) | 8.82336 | + | 5.09417i | 0.341642 | + | 0.197247i | ||||
\(668\) | −8.02596 | − | 13.9014i | −0.310534 | − | 0.537860i | ||||
\(669\) | −1.39898 | − | 2.42311i | −0.0540878 | − | 0.0936828i | ||||
\(670\) | 3.28423 | − | 5.68846i | 0.126881 | − | 0.219764i | ||||
\(671\) | 8.53508 | − | 16.9657i | 0.329493 | − | 0.654955i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.20344i | − | 0.0463893i | −0.999731 | − | 0.0231947i | \(-0.992616\pi\) | ||
0.999731 | − | 0.0231947i | \(-0.00738375\pi\) | |||||||
\(674\) | 8.01790 | − | 13.8874i | 0.308838 | − | 0.534923i | ||||
\(675\) | −1.50744 | + | 0.870318i | −0.0580212 | + | 0.0334986i | ||||
\(676\) | −5.43512 | − | 9.41390i | −0.209043 | − | 0.362073i | ||||
\(677\) | 13.1579 | − | 22.7902i | 0.505701 | − | 0.875900i | −0.494277 | − | 0.869304i | \(-0.664567\pi\) |
0.999978 | − | 0.00659557i | \(-0.00209945\pi\) | |||||||
\(678\) | −24.4920 | −0.940610 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.7580 | 0.642640 | ||||||||
\(681\) | −36.5180 | − | 21.0837i | −1.39937 | − | 0.807928i | ||||
\(682\) | 28.3069 | − | 1.62922i | 1.08393 | − | 0.0623861i | ||||
\(683\) | −16.4637 | − | 28.5160i | −0.629966 | − | 1.09113i | −0.987558 | − | 0.157255i | \(-0.949735\pi\) |
0.357592 | − | 0.933878i | \(-0.383598\pi\) | |||||||
\(684\) | 0.612236 | − | 1.06042i | 0.0234094 | − | 0.0405463i | ||||
\(685\) | 19.2155i | 0.734187i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.2771 | 0.582858 | ||||||||
\(688\) | 1.36983 | + | 0.790869i | 0.0522241 | + | 0.0301516i | ||||
\(689\) | 3.52762 | + | 6.11002i | 0.134392 | + | 0.232773i | ||||
\(690\) | 13.6480 | − | 7.87969i | 0.519571 | − | 0.299975i | ||||
\(691\) | −24.4510 | − | 14.1168i | −0.930159 | − | 0.537028i | −0.0432974 | − | 0.999062i | \(-0.513786\pi\) |
−0.886862 | + | 0.462034i | \(0.847120\pi\) | |||||||
\(692\) | 7.09477 | 0.269703 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.87094 | 0.374696 | ||||||||
\(695\) | 7.80824 | + | 4.50809i | 0.296183 | + | 0.171002i | ||||
\(696\) | −12.0601 | + | 6.96289i | −0.457136 | + | 0.263927i | ||||
\(697\) | −27.0200 | − | 46.8000i | −1.02346 | − | 1.77268i | ||||
\(698\) | −27.0088 | − | 15.5935i | −1.02230 | − | 0.590224i | ||||
\(699\) | 70.8605 | 2.68019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.2464i | − | 0.915775i | −0.889010 | − | 0.457888i | \(-0.848606\pi\) | ||
0.889010 | − | 0.457888i | \(-0.151394\pi\) | |||||||
\(702\) | 8.62119 | − | 14.9323i | 0.325386 | − | 0.563585i | ||||
\(703\) | 0.136339 | + | 0.236147i | 0.00514214 | + | 0.00890644i | ||||
\(704\) | −3.31114 | + | 0.190575i | −0.124793 | + | 0.00718256i | ||||
\(705\) | 3.25338 | + | 1.87834i | 0.122529 | + | 0.0707423i | ||||
\(706\) | −25.9682 | −0.977327 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 19.3553 | 0.727416 | ||||||||
\(709\) | −21.6350 | + | 37.4729i | −0.812518 | + | 1.40732i | 0.0985783 | + | 0.995129i | \(0.468571\pi\) |
−0.911096 | + | 0.412193i | \(0.864763\pi\) | |||||||
\(710\) | 8.34327 | + | 14.4510i | 0.313117 | + | 0.542335i | ||||
\(711\) | −40.6147 | + | 23.4489i | −1.52317 | + | 0.879402i | ||||
\(712\) | −8.05557 | + | 13.9527i | −0.301895 | + | 0.522898i | ||||
\(713\) | − | 19.5583i | − | 0.732463i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.52494 | − | 4.79178i | −0.356213 | − | 0.179203i | ||||
\(716\) | −12.4864 | + | 21.6271i | −0.466639 | + | 0.808242i | ||||
\(717\) | 39.4646 | + | 68.3548i | 1.47383 | + | 2.55276i | ||||
\(718\) | 2.00534 | + | 3.47334i | 0.0748385 | + | 0.129624i | ||||
\(719\) | −19.9268 | − | 11.5048i | −0.743145 | − | 0.429055i | 0.0800668 | − | 0.996790i | \(-0.474487\pi\) |
−0.823212 | + | 0.567735i | \(0.807820\pi\) | |||||||
\(720\) | 14.9318i | 0.556476i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.9674i | − | 0.705892i | ||||||
\(723\) | 38.0944 | + | 21.9938i | 1.41675 | + | 0.817958i | ||||
\(724\) | −16.7644 | + | 9.67893i | −0.623044 | + | 0.359714i | ||||
\(725\) | −0.568192 | + | 0.328046i | −0.0211021 | + | 0.0121833i | ||||
\(726\) | −34.1702 | + | 3.94645i | −1.26817 | + | 0.146466i | ||||
\(727\) | − | 39.3745i | − | 1.46032i | −0.683276 | − | 0.730160i | \(-0.739445\pi\) | ||
0.683276 | − | 0.730160i | \(-0.260555\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.75557 | −0.0650210 | ||||||||
\(730\) | 10.6580 | − | 18.4602i | 0.394471 | − | 0.683243i | ||||
\(731\) | 10.4207 | − | 6.01639i | 0.385423 | − | 0.222524i | ||||
\(732\) | 15.5071 | − | 8.95301i | 0.573158 | − | 0.330913i | ||||
\(733\) | 4.09264 | − | 7.08867i | 0.151165 | − | 0.261826i | −0.780491 | − | 0.625167i | \(-0.785031\pi\) |
0.931656 | + | 0.363341i | \(0.118364\pi\) | |||||||
\(734\) | 19.1851 | 0.708135 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.28779i | 0.0843291i | ||||||||
\(737\) | 5.42864 | + | 8.26619i | 0.199967 | + | 0.304489i | ||||
\(738\) | 41.7000 | − | 24.0755i | 1.53500 | − | 0.886232i | ||||
\(739\) | −33.0756 | + | 19.0962i | −1.21671 | + | 0.702466i | −0.964212 | − | 0.265133i | \(-0.914584\pi\) |
−0.252494 | + | 0.967598i | \(0.581251\pi\) | |||||||
\(740\) | −2.87969 | − | 1.66259i | −0.105860 | − | 0.0611180i | ||||
\(741\) | 0.824375i | 0.0302842i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.3005i | − | 1.00156i | −0.865575 | − | 0.500779i | \(-0.833047\pi\) | ||
0.865575 | − | 0.500779i | \(-0.166953\pi\) | |||||||
\(744\) | 23.1514 | + | 13.3665i | 0.848771 | + | 0.490038i | ||||
\(745\) | −20.4777 | − | 35.4684i | −0.750244 | − | 1.29946i | ||||
\(746\) | −10.5145 | − | 18.2116i | −0.384962 | − | 0.666774i | ||||
\(747\) | −19.8010 | + | 34.2964i | −0.724482 | + | 1.25484i | ||||
\(748\) | −11.3389 | + | 22.5391i | −0.414592 | + | 0.824112i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 35.4572i | 1.29471i | ||||||||
\(751\) | 1.11584 | − | 1.93269i | 0.0407175 | − | 0.0705247i | −0.844948 | − | 0.534848i | \(-0.820369\pi\) |
0.885666 | + | 0.464323i | \(0.153702\pi\) | |||||||
\(752\) | −0.472293 | + | 0.272679i | −0.0172228 | + | 0.00994357i | ||||
\(753\) | 4.74871 | + | 8.22500i | 0.173053 | + | 0.299736i | ||||
\(754\) | 3.24955 | − | 5.62838i | 0.118342 | − | 0.204974i | ||||
\(755\) | −29.0879 | −1.05862 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.6709 | −0.605913 | −0.302956 | − | 0.953004i | \(-0.597974\pi\) | ||||
−0.302956 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(758\) | −17.9722 | − | 10.3763i | −0.652780 | − | 0.376883i | ||||
\(759\) | 1.36337 | + | 23.6879i | 0.0494873 | + | 0.859817i | ||||
\(760\) | −0.198970 | − | 0.344626i | −0.00721740 | − | 0.0125009i | ||||
\(761\) | −22.8160 | + | 39.5185i | −0.827081 | + | 1.43255i | 0.0732375 | + | 0.997315i | \(0.476667\pi\) |
−0.900318 | + | 0.435232i | \(0.856666\pi\) | |||||||
\(762\) | − | 42.1218i | − | 1.52591i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 98.3728 | + | 56.7955i | 3.55668 | + | 2.05345i | ||||
\(766\) | −0.628029 | − | 1.08778i | −0.0226916 | − | 0.0393030i | ||||
\(767\) | −7.82283 | + | 4.51652i | −0.282466 | + | 0.163082i | ||||
\(768\) | −2.70809 | − | 1.56352i | −0.0977197 | − | 0.0564185i | ||||
\(769\) | −51.3570 | −1.85198 | −0.925991 | − | 0.377546i | \(-0.876768\pi\) | ||||
−0.925991 | + | 0.377546i | \(0.876768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −80.5784 | −2.90196 | ||||||||
\(772\) | 14.3859 | + | 8.30569i | 0.517759 | + | 0.298928i | ||||
\(773\) | 18.9208 | − | 10.9239i | 0.680533 | − | 0.392906i | −0.119523 | − | 0.992831i | \(-0.538137\pi\) |
0.800056 | + | 0.599926i | \(0.204803\pi\) | |||||||
\(774\) | 5.36076 | + | 9.28511i | 0.192689 | + | 0.333747i | ||||
\(775\) | 1.09074 | + | 0.629740i | 0.0391806 | + | 0.0226209i | ||||
\(776\) | −11.3012 | −0.405688 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 16.6479i | − | 0.596854i | ||||||
\(779\) | −0.641624 | + | 1.11132i | −0.0229886 | + | 0.0398173i | ||||
\(780\) | −5.02642 | − | 8.70601i | −0.179975 | − | 0.311725i | ||||
\(781\) | −25.0815 | + | 1.44358i | −0.897487 | + | 0.0516554i | ||||
\(782\) | 15.0723 | + | 8.70198i | 0.538983 | + | 0.311182i | ||||
\(783\) | −52.6160 | −1.88034 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.6864 | −0.452797 | ||||||||
\(786\) | −4.10363 | + | 7.10769i | −0.146372 | + | 0.253523i | ||||
\(787\) | −10.2201 | − | 17.7017i | −0.364307 | − | 0.630998i | 0.624358 | − | 0.781138i | \(-0.285361\pi\) |
−0.988665 | + | 0.150141i | \(0.952027\pi\) | |||||||
\(788\) | 17.8744 | − | 10.3198i | 0.636750 | − | 0.367628i | ||||
\(789\) | −10.0222 | + | 17.3589i | −0.356799 | + | 0.617993i | ||||
\(790\) | 15.2412i | 0.542259i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −20.0830 | − | 10.1033i | −0.713617 | − | 0.359005i | ||||
\(793\) | −4.17833 | + | 7.23709i | −0.148377 | + | 0.256996i | ||||
\(794\) | 7.08712 | + | 12.2752i | 0.251512 | + | 0.435632i | ||||
\(795\) | −16.6509 | − | 28.8403i | −0.590548 | − | 1.02286i | ||||
\(796\) | −0.628737 | − | 0.363001i | −0.0222850 | − | 0.0128662i | ||||
\(797\) | − | 6.09214i | − | 0.215795i | −0.994162 | − | 0.107897i | \(-0.965588\pi\) | ||
0.994162 | − | 0.107897i | \(-0.0344118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.14871i | 0.146771i | ||||||||
\(800\) | −0.127587 | − | 0.0736626i | −0.00451090 | − | 0.00260437i | ||||
\(801\) | −94.5756 | + | 54.6033i | −3.34167 | + | 1.92931i | ||||
\(802\) | −4.20256 | + | 2.42635i | −0.148398 | + | 0.0856774i | ||||
\(803\) | 17.6171 | + | 26.8255i | 0.621693 | + | 0.946651i | ||||
\(804\) | 9.32407i | 0.328834i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.4761 | −0.439453 | ||||||||
\(807\) | −4.28641 | + | 7.42428i | −0.150889 | + | 0.261347i | ||||
\(808\) | 0.448355 | − | 0.258858i | 0.0157731 | − | 0.00910660i | ||||
\(809\) | 30.1186 | − | 17.3890i | 1.05891 | − | 0.611364i | 0.133783 | − | 0.991011i | \(-0.457288\pi\) |
0.925132 | + | 0.379646i | \(0.123954\pi\) | |||||||
\(810\) | −18.2956 | + | 31.6890i | −0.642844 | + | 1.11344i | ||||
\(811\) | 26.6602 | 0.936167 | 0.468083 | − | 0.883684i | \(-0.344945\pi\) | ||||
0.468083 | + | 0.883684i | \(0.344945\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 89.4337i | 3.13658i | ||||||||
\(814\) | 4.18463 | − | 2.74816i | 0.146671 | − | 0.0963231i | ||||
\(815\) | 10.1357 | − | 5.85182i | 0.355036 | − | 0.204980i | ||||
\(816\) | −20.6013 | + | 11.8942i | −0.721189 | + | 0.416379i | ||||
\(817\) | −0.247452 | − | 0.142867i | −0.00865727 | − | 0.00499827i | ||||
\(818\) | 10.6280i | 0.371601i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 15.6486i | − | 0.546471i | ||||||
\(821\) | −11.0422 | − | 6.37522i | −0.385375 | − | 0.222497i | 0.294779 | − | 0.955565i | \(-0.404754\pi\) |
−0.680154 | + | 0.733069i | \(0.738087\pi\) | |||||||
\(822\) | −13.6384 | − | 23.6224i | −0.475694 | − | 0.823926i | ||||
\(823\) | 7.93819 | + | 13.7494i | 0.276708 | + | 0.479272i | 0.970565 | − | 0.240841i | \(-0.0774232\pi\) |
−0.693857 | + | 0.720113i | \(0.744090\pi\) | |||||||
\(824\) | 1.44358 | − | 2.50035i | 0.0502895 | − | 0.0871039i | ||||
\(825\) | −1.36494 | − | 0.686673i | −0.0475213 | − | 0.0239069i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.9639i | 1.25059i | 0.780390 | + | 0.625293i | \(0.215021\pi\) | ||||
−0.780390 | + | 0.625293i | \(0.784979\pi\) | |||||||
\(828\) | −7.75369 | + | 13.4298i | −0.269459 | + | 0.466717i | ||||
\(829\) | 31.0966 | − | 17.9536i | 1.08003 | − | 0.623555i | 0.149124 | − | 0.988818i | \(-0.452355\pi\) |
0.930904 | + | 0.365264i | \(0.119021\pi\) | |||||||
\(830\) | 6.43512 | + | 11.1459i | 0.223366 | + | 0.386882i | ||||
\(831\) | −16.8364 | + | 29.1616i | −0.584050 | + | 1.01160i | ||||
\(832\) | 1.45937 | 0.0505946 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.7986 | −0.443181 | ||||||||
\(835\) | −30.6230 | − | 17.6802i | −1.05975 | − | 0.611849i | ||||
\(836\) | 0.598143 | − | 0.0344265i | 0.0206872 | − | 0.00119066i | ||||
\(837\) | 50.5027 | + | 87.4733i | 1.74563 | + | 3.02352i | ||||
\(838\) | 5.68448 | − | 9.84582i | 0.196367 | − | 0.340118i | ||||
\(839\) | 39.5137i | 1.36416i | 0.731276 | + | 0.682081i | \(0.238925\pi\) | ||||
−0.731276 | + | 0.682081i | \(0.761075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.16765 | 0.316126 | ||||||||
\(842\) | −23.5961 | − | 13.6232i | −0.813176 | − | 0.469487i | ||||
\(843\) | 30.6901 | + | 53.1568i | 1.05702 | + | 1.83082i | ||||
\(844\) | 8.90949 | − | 5.14390i | 0.306677 | − | 0.177060i | ||||
\(845\) | −20.7377 | − | 11.9729i | −0.713398 | − | 0.411880i | ||||
\(846\) | −3.69661 | −0.127092 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.83444 | 0.166015 | ||||||||
\(849\) | −28.7687 | − | 16.6096i | −0.987340 | − | 0.570041i | ||||
\(850\) | −0.970598 | + | 0.560375i | −0.0332912 | + | 0.0192207i | ||||
\(851\) | −1.72668 | − | 2.99069i | −0.0591897 | − | 0.102520i | ||||
\(852\) | −20.5134 | − | 11.8434i | −0.702779 | − | 0.405750i | ||||
\(853\) | −8.92246 | −0.305499 | −0.152750 | − | 0.988265i | \(-0.548813\pi\) | ||||
−0.152750 | + | 0.988265i | \(0.548813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.69736i | − | 0.0922479i | ||||||
\(856\) | −2.60980 | + | 4.52030i | −0.0892010 | + | 0.154501i | ||||
\(857\) | −4.37047 | − | 7.56987i | −0.149292 | − | 0.258582i | 0.781674 | − | 0.623687i | \(-0.214366\pi\) |
−0.930966 | + | 0.365106i | \(0.881033\pi\) | |||||||
\(858\) | 15.1104 | − | 0.869689i | 0.515861 | − | 0.0296907i | ||||
\(859\) | −25.7825 | − | 14.8855i | −0.879688 | − | 0.507888i | −0.00913247 | − | 0.999958i | \(-0.502907\pi\) |
−0.870556 | + | 0.492070i | \(0.836240\pi\) | |||||||
\(860\) | 3.48438 | 0.118816 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.2210 | 0.518428 | ||||||||
\(863\) | −11.4864 | + | 19.8951i | −0.391002 | + | 0.677236i | −0.992582 | − | 0.121577i | \(-0.961205\pi\) |
0.601580 | + | 0.798813i | \(0.294538\pi\) | |||||||
\(864\) | −5.90746 | − | 10.2320i | −0.200976 | − | 0.348101i | ||||
\(865\) | 13.5350 | − | 7.81445i | 0.460205 | − | 0.265699i | ||||
\(866\) | 0.927669 | − | 1.60677i | 0.0315235 | − | 0.0546003i | ||||
\(867\) | 127.806i | 4.34051i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.4991 | − | 10.3127i | −0.695386 | − | 0.349833i | ||||
\(870\) | −15.3384 | + | 26.5669i | −0.520020 | + | 0.900701i | ||||
\(871\) | −2.17575 | − | 3.76851i | −0.0737225 | − | 0.127691i | ||||
\(872\) | −5.02702 | − | 8.70705i | −0.170236 | − | 0.294858i | ||||
\(873\) | −66.3400 | − | 38.3014i | −2.24527 | − | 1.29631i | ||||
\(874\) | − | 0.413279i | − | 0.0139794i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30.2585i | 1.02234i | ||||||||
\(877\) | 28.7911 | + | 16.6225i | 0.972205 | + | 0.561303i | 0.899908 | − | 0.436080i | \(-0.143634\pi\) |
0.0722974 | + | 0.997383i | \(0.476967\pi\) | |||||||
\(878\) | −28.5272 | + | 16.4702i | −0.962746 | + | 0.555842i | ||||
\(879\) | 0.751904 | − | 0.434112i | 0.0253611 | − | 0.0146422i | ||||
\(880\) | −6.10693 | + | 4.01059i | −0.205864 | + | 0.135197i | ||||
\(881\) | 2.73248i | 0.0920594i | 0.998940 | + | 0.0460297i | \(0.0146569\pi\) | ||||
−0.998940 | + | 0.0460297i | \(0.985343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7473 | −0.664550 | −0.332275 | − | 0.943183i | \(-0.607816\pi\) | ||||
−0.332275 | + | 0.943183i | \(0.607816\pi\) | |||||||
\(884\) | 5.55095 | − | 9.61453i | 0.186699 | − | 0.323372i | ||||
\(885\) | 36.9250 | − | 21.3187i | 1.24122 | − | 0.716619i | ||||
\(886\) | −28.4587 | + | 16.4306i | −0.956089 | + | 0.551998i | ||||
\(887\) | 12.2310 | − | 21.1847i | 0.410676 | − | 0.711312i | −0.584288 | − | 0.811547i | \(-0.698626\pi\) |
0.994964 | + | 0.100235i | \(0.0319593\pi\) | |||||||
\(888\) | 4.72016 | 0.158398 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 35.4909i | 1.18966i | ||||||||
\(891\) | −30.2416 | − | 46.0489i | −1.01313 | − | 1.54270i | ||||
\(892\) | 0.774891 | − | 0.447384i | 0.0259453 | − | 0.0149795i | ||||
\(893\) | 0.0853176 | − | 0.0492581i | 0.00285504 | − | 0.00164836i | ||||
\(894\) | 50.3480 | + | 29.0685i | 1.68389 | + | 0.972195i | ||||
\(895\) | 55.0121i | 1.83885i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 10.4403i | − | 0.348593i | ||||||
\(898\) | −3.14121 | − | 1.81358i | −0.104824 | − | 0.0605199i | ||||
\(899\) | 19.0358 | + | 32.9710i | 0.634879 | + | 1.09964i | ||||
\(900\) | −0.499309 | − | 0.864828i | −0.0166436 | − | 0.0288276i | ||||
\(901\) | 18.3886 | − | 31.8499i | 0.612612 | − | 1.06107i | ||||
\(902\) | 21.0470 | + | 10.5883i | 0.700787 | + | 0.352550i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.83235i | − | 0.260500i | ||||||
\(905\) | −21.3215 | + | 36.9299i | −0.708751 | + | 1.22759i | ||||
\(906\) | 35.7589 | − | 20.6454i | 1.18801 | − | 0.685898i | ||||
\(907\) | 22.3109 | + | 38.6436i | 0.740820 | + | 1.28314i | 0.952122 | + | 0.305718i | \(0.0988964\pi\) |
−0.211302 | + | 0.977421i | \(0.567770\pi\) | |||||||
\(908\) | 6.74239 | − | 11.6782i | 0.223754 | − | 0.387554i | ||||
\(909\) | 3.50925 | 0.116394 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.0868 | 1.22874 | 0.614370 | − | 0.789018i | \(-0.289410\pi\) | ||||
0.614370 | + | 0.789018i | \(0.289410\pi\) | |||||||
\(912\) | 0.489203 | + | 0.282442i | 0.0161991 | + | 0.00935258i | ||||
\(913\) | −19.3452 | + | 1.11343i | −0.640234 | + | 0.0368490i | ||||
\(914\) | −1.36783 | − | 2.36916i | −0.0452439 | − | 0.0783648i | ||||
\(915\) | 19.7224 | − | 34.1602i | 0.652003 | − | 1.12930i | ||||
\(916\) | 4.88550i | 0.161422i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −89.8799 | −2.96648 | ||||||||
\(919\) | −44.1563 | − | 25.4937i | −1.45658 | − | 0.840958i | −0.457741 | − | 0.889085i | \(-0.651341\pi\) |
−0.998841 | + | 0.0481269i | \(0.984675\pi\) | |||||||
\(920\) | 2.51986 | + | 4.36453i | 0.0830774 | + | 0.143894i | ||||
\(921\) | 17.3708 | − | 10.0291i | 0.572389 | − | 0.330469i | ||||
\(922\) | 17.7050 | + | 10.2220i | 0.583082 | + | 0.336642i | ||||
\(923\) | 11.0546 | 0.363865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.222383 | 0.00731191 | ||||||||
\(926\) | −26.1281 | − | 15.0851i | −0.858622 | − | 0.495726i | ||||
\(927\) | 16.9482 | − | 9.78504i | 0.556652 | − | 0.321383i | ||||
\(928\) | −2.22668 | − | 3.85672i | −0.0730942 | − | 0.126603i | ||||
\(929\) | −10.5567 | − | 6.09489i | −0.346353 | − | 0.199967i | 0.316725 | − | 0.948517i | \(-0.397417\pi\) |
−0.663078 | + | 0.748551i | \(0.730750\pi\) | |||||||
\(930\) | 58.8893 | 1.93106 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.6606i | 0.742274i | ||||||||
\(933\) | 17.6714 | − | 30.6078i | 0.578537 | − | 1.00206i | ||||
\(934\) | 13.5861 | + | 23.5318i | 0.444551 | + | 0.769986i | ||||
\(935\) | 3.19365 | + | 55.4882i | 0.104444 | + | 1.81466i | ||||
\(936\) | 8.56680 | + | 4.94605i | 0.280015 | + | 0.161667i | ||||
\(937\) | 17.0188 | 0.555979 | 0.277990 | − | 0.960584i | \(-0.410332\pi\) | ||||
0.277990 | + | 0.960584i | \(0.410332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 51.4292 | 1.67833 | ||||||||
\(940\) | −0.600678 | + | 1.04041i | −0.0195920 | + | 0.0339343i | ||||
\(941\) | −6.79916 | − | 11.7765i | −0.221646 | − | 0.383902i | 0.733662 | − | 0.679515i | \(-0.237810\pi\) |
−0.955308 | + | 0.295612i | \(0.904476\pi\) | |||||||
\(942\) | 15.5959 | − | 9.00431i | 0.508142 | − | 0.293376i | ||||
\(943\) | 8.12587 | − | 14.0744i | 0.264615 | − | 0.458326i | ||||
\(944\) | 6.18967i | 0.201457i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.35763 | + | 4.68641i | −0.0766531 | + | 0.152368i | ||||
\(947\) | 16.5425 | − | 28.6524i | 0.537558 | − | 0.931078i | −0.461477 | − | 0.887152i | \(-0.652680\pi\) |
0.999035 | − | 0.0439257i | \(-0.0139865\pi\) | |||||||
\(948\) | −10.8176 | − | 18.7367i | −0.351340 | − | 0.608539i | ||||
\(949\) | −7.06076 | − | 12.2296i | −0.229202 | − | 0.396990i | ||||
\(950\) | 0.0230481 | + | 0.0133068i | 0.000747778 | + | 0.000431730i | ||||
\(951\) | − | 88.1542i | − | 2.85860i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.427553i | 0.0138498i | 0.999976 | + | 0.00692490i | \(0.00220428\pi\) | ||||
−0.999976 | + | 0.00692490i | \(0.997796\pi\) | |||||||
\(954\) | 28.3791 | + | 16.3847i | 0.918808 | + | 0.530474i | ||||
\(955\) | −11.4465 | + | 6.60864i | −0.370400 | + | 0.213850i | ||||
\(956\) | −21.8593 | + | 12.6205i | −0.706981 | + | 0.408176i | ||||
\(957\) | −25.3535 | − | 38.6057i | −0.819561 | − | 1.24794i | ||||
\(958\) | − | 21.6184i | − | 0.698459i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.88847 | −0.222324 | ||||||||
\(961\) | 21.0425 | − | 36.4466i | 0.678790 | − | 1.17570i | ||||
\(962\) | −1.90775 | + | 1.10144i | −0.0615083 | + | 0.0355118i | ||||
\(963\) | −30.6400 | + | 17.6900i | −0.987362 | + | 0.570053i | ||||
\(964\) | −7.03345 | + | 12.1823i | −0.226532 | + | 0.392365i | ||||
\(965\) | 36.5928 | 1.17797 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.75935i | 0.217366i | 0.994076 | + | 0.108683i | \(0.0346634\pi\) | ||||
−0.994076 | + | 0.108683i | \(0.965337\pi\) | |||||||
\(968\) | −1.26204 | − | 10.9274i | −0.0405636 | − | 0.351219i | ||||
\(969\) | 3.72153 | − | 2.14862i | 0.119553 | − | 0.0690237i | ||||
\(970\) | −21.5598 | + | 12.4475i | −0.692242 | + | 0.399666i | ||||
\(971\) | −18.6089 | − | 10.7439i | −0.597189 | − | 0.344787i | 0.170746 | − | 0.985315i | \(-0.445382\pi\) |
−0.767935 | + | 0.640528i | \(0.778716\pi\) | |||||||
\(972\) | − | 16.4973i | − | 0.529151i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.08573i | 0.0668311i | ||||||||
\(975\) | 0.582245 | + | 0.336159i | 0.0186468 | + | 0.0107657i | ||||
\(976\) | 2.86310 | + | 4.95904i | 0.0916457 | + | 0.158735i | ||||
\(977\) | −21.6466 | − | 37.4931i | −0.692537 | − | 1.19951i | −0.971004 | − | 0.239064i | \(-0.923160\pi\) |
0.278467 | − | 0.960446i | \(-0.410174\pi\) | |||||||
\(978\) | −8.30678 | + | 14.3878i | −0.265622 | + | 0.460070i | ||||
\(979\) | −47.7345 | − | 24.0141i | −1.52560 | − | 0.767495i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 68.1495i | − | 2.17584i | ||||||
\(982\) | −1.23992 | + | 2.14760i | −0.0395673 | + | 0.0685326i | ||||
\(983\) | −18.1526 | + | 10.4804i | −0.578977 | + | 0.334273i | −0.760727 | − | 0.649072i | \(-0.775157\pi\) |
0.181750 | + | 0.983345i | \(0.441824\pi\) | |||||||
\(984\) | 11.1067 | + | 19.2374i | 0.354069 | + | 0.613266i | ||||
\(985\) | 22.7333 | − | 39.3752i | 0.724342 | − | 1.25460i | ||||
\(986\) | −33.8781 | −1.07890 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.263629 | −0.00838715 | ||||||||
\(989\) | 3.13387 | + | 1.80934i | 0.0996514 | + | 0.0575338i | ||||
\(990\) | −49.4414 | + | 2.84563i | −1.57135 | + | 0.0904401i | ||||
\(991\) | −19.2702 | − | 33.3770i | −0.612138 | − | 1.06025i | −0.990879 | − | 0.134751i | \(-0.956976\pi\) |
0.378742 | − | 0.925502i | \(-0.376357\pi\) | |||||||
\(992\) | −4.27449 | + | 7.40363i | −0.135715 | + | 0.235065i | ||||
\(993\) | 59.7656i | 1.89660i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.59930 | −0.0507011 | ||||||||
\(996\) | −15.8219 | − | 9.13478i | −0.501336 | − | 0.289447i | ||||
\(997\) | 9.72323 | + | 16.8411i | 0.307938 | + | 0.533364i | 0.977911 | − | 0.209021i | \(-0.0670278\pi\) |
−0.669973 | + | 0.742385i | \(0.733694\pi\) | |||||||
\(998\) | 13.3227 | − | 7.69189i | 0.421724 | − | 0.243482i | ||||
\(999\) | 15.4449 | + | 8.91714i | 0.488656 | + | 0.282126i |
(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 | 1078.2.i.c.901.4 | 16 | ||
7.2 | even | 3 | 1078.2.c.b.1077.16 | 16 | |||
7.3 | odd | 6 | inner | 1078.2.i.c.1011.8 | 16 | ||
7.4 | even | 3 | 154.2.i.a.87.5 | yes | 16 | ||
7.5 | odd | 6 | 1078.2.c.b.1077.9 | 16 | |||
7.6 | odd | 2 | 154.2.i.a.131.1 | yes | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.c.901.8 | 16 | ||
21.11 | odd | 6 | 1386.2.bk.c.703.3 | 16 | |||
21.20 | even | 2 | 1386.2.bk.c.901.7 | 16 | |||
28.11 | odd | 6 | 1232.2.bn.b.241.8 | 16 | |||
28.27 | even | 2 | 1232.2.bn.b.593.7 | 16 | |||
77.10 | even | 6 | inner | 1078.2.i.c.1011.4 | 16 | ||
77.32 | odd | 6 | 154.2.i.a.87.1 | ✓ | 16 | ||
77.54 | even | 6 | 1078.2.c.b.1077.1 | 16 | |||
77.65 | odd | 6 | 1078.2.c.b.1077.8 | 16 | |||
77.76 | even | 2 | 154.2.i.a.131.5 | yes | 16 | ||
231.32 | even | 6 | 1386.2.bk.c.703.7 | 16 | |||
231.230 | odd | 2 | 1386.2.bk.c.901.3 | 16 | |||
308.263 | even | 6 | 1232.2.bn.b.241.7 | 16 | |||
308.307 | odd | 2 | 1232.2.bn.b.593.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.1 | ✓ | 16 | 77.32 | odd | 6 | ||
154.2.i.a.87.5 | yes | 16 | 7.4 | even | 3 | ||
154.2.i.a.131.1 | yes | 16 | 7.6 | odd | 2 | ||
154.2.i.a.131.5 | yes | 16 | 77.76 | even | 2 | ||
1078.2.c.b.1077.1 | 16 | 77.54 | even | 6 | |||
1078.2.c.b.1077.8 | 16 | 77.65 | odd | 6 | |||
1078.2.c.b.1077.9 | 16 | 7.5 | odd | 6 | |||
1078.2.c.b.1077.16 | 16 | 7.2 | even | 3 | |||
1078.2.i.c.901.4 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.i.c.901.8 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.c.1011.4 | 16 | 77.10 | even | 6 | inner | ||
1078.2.i.c.1011.8 | 16 | 7.3 | odd | 6 | inner | ||
1232.2.bn.b.241.7 | 16 | 308.263 | even | 6 | |||
1232.2.bn.b.241.8 | 16 | 28.11 | odd | 6 | |||
1232.2.bn.b.593.7 | 16 | 28.27 | even | 2 | |||
1232.2.bn.b.593.8 | 16 | 308.307 | odd | 2 | |||
1386.2.bk.c.703.3 | 16 | 21.11 | odd | 6 | |||
1386.2.bk.c.703.7 | 16 | 231.32 | even | 6 | |||
1386.2.bk.c.901.3 | 16 | 231.230 | odd | 2 | |||
1386.2.bk.c.901.7 | 16 | 21.20 | even | 2 |