Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, 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("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 76.2 | ||
Root | \(1.33631 + 0.462894i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.76 |
Dual form | 375.2.g.b.301.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18949 | + | 1.59076i | 1.54821 | + | 1.12484i | 0.944915 | + | 0.327315i | \(0.106144\pi\) |
0.603290 | + | 0.797522i | \(0.293856\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | 1.64533 | + | 5.06380i | 0.822664 | + | 2.53190i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.836312 | − | 2.57390i | 0.341423 | − | 1.05079i | ||||
\(7\) | −0.470294 | −0.177754 | −0.0888772 | − | 0.996043i | \(-0.528328\pi\) | ||||
−0.0888772 | + | 0.996043i | \(0.528328\pi\) | |||||||
\(8\) | −2.78023 | + | 8.55667i | −0.982960 | + | 3.02524i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.57387 | + | 1.87003i | 0.776051 | + | 0.563834i | 0.903791 | − | 0.427974i | \(-0.140772\pi\) |
−0.127740 | + | 0.991808i | \(0.540772\pi\) | |||||||
\(12\) | 4.30753 | − | 3.12960i | 1.24348 | − | 0.903438i | ||||
\(13\) | 0.455836 | − | 0.331184i | 0.126426 | − | 0.0918540i | −0.522775 | − | 0.852471i | \(-0.675103\pi\) |
0.649201 | + | 0.760617i | \(0.275103\pi\) | |||||||
\(14\) | −1.02971 | − | 0.748125i | −0.275200 | − | 0.199945i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −11.0839 | + | 8.05289i | −2.77096 | + | 2.01322i | ||||
\(17\) | 0.527295 | − | 1.62285i | 0.127888 | − | 0.393598i | −0.866528 | − | 0.499128i | \(-0.833654\pi\) |
0.994416 | + | 0.105530i | \(0.0336538\pi\) | |||||||
\(18\) | −2.70636 | −0.637896 | ||||||||
\(19\) | 1.15575 | − | 3.55705i | 0.265148 | − | 0.816043i | −0.726511 | − | 0.687155i | \(-0.758859\pi\) |
0.991659 | − | 0.128888i | \(-0.0411406\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.145329 | + | 0.447276i | 0.0317134 | + | 0.0976037i | ||||
\(22\) | 2.66071 | + | 8.18882i | 0.567265 | + | 1.74586i | ||||
\(23\) | −1.83631 | − | 1.33416i | −0.382898 | − | 0.278191i | 0.379641 | − | 0.925134i | \(-0.376047\pi\) |
−0.762539 | + | 0.646942i | \(0.776047\pi\) | |||||||
\(24\) | 8.99702 | 1.83651 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.52488 | 0.299054 | ||||||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | −0.773789 | − | 2.38148i | −0.146232 | − | 0.450057i | ||||
\(29\) | −2.57238 | − | 7.91697i | −0.477679 | − | 1.47014i | −0.842310 | − | 0.538993i | \(-0.818805\pi\) |
0.364631 | − | 0.931152i | \(-0.381195\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.67999 | − | 5.17047i | 0.301735 | − | 0.928644i | −0.679141 | − | 0.734008i | \(-0.737647\pi\) |
0.980876 | − | 0.194636i | \(-0.0623526\pi\) | |||||||
\(32\) | −19.0842 | −3.37364 | ||||||||
\(33\) | 0.983131 | − | 3.02577i | 0.171141 | − | 0.526718i | ||||
\(34\) | 3.73607 | − | 2.71441i | 0.640730 | − | 0.465518i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.30753 | − | 3.12960i | −0.717921 | − | 0.521600i | ||||
\(37\) | 0.825886 | − | 0.600041i | 0.135775 | − | 0.0986462i | −0.517825 | − | 0.855487i | \(-0.673258\pi\) |
0.653600 | + | 0.756841i | \(0.273258\pi\) | |||||||
\(38\) | 8.18892 | − | 5.94960i | 1.32842 | − | 0.965153i | ||||
\(39\) | −0.455836 | − | 0.331184i | −0.0729922 | − | 0.0530319i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.19098 | + | 0.865300i | −0.186000 | + | 0.135137i | −0.676889 | − | 0.736085i | \(-0.736672\pi\) |
0.490889 | + | 0.871222i | \(0.336672\pi\) | |||||||
\(42\) | −0.393313 | + | 1.21049i | −0.0606895 | + | 0.186783i | ||||
\(43\) | −6.72721 | −1.02589 | −0.512945 | − | 0.858421i | \(-0.671446\pi\) | ||||
−0.512945 | + | 0.858421i | \(0.671446\pi\) | |||||||
\(44\) | −5.23458 | + | 16.1104i | −0.789142 | + | 2.42873i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.89827 | − | 5.84226i | −0.279884 | − | 0.861395i | ||||
\(47\) | 1.37005 | + | 4.21658i | 0.199842 | + | 0.615052i | 0.999886 | + | 0.0151095i | \(0.00480970\pi\) |
−0.800043 | + | 0.599942i | \(0.795190\pi\) | |||||||
\(48\) | 11.0839 | + | 8.05289i | 1.59982 | + | 1.16234i | ||||
\(49\) | −6.77882 | −0.968403 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.70636 | −0.238938 | ||||||||
\(52\) | 2.42705 | + | 1.76336i | 0.336571 | + | 0.244533i | ||||
\(53\) | 2.17907 | + | 6.70648i | 0.299318 | + | 0.921206i | 0.981737 | + | 0.190244i | \(0.0609281\pi\) |
−0.682419 | + | 0.730961i | \(0.739072\pi\) | |||||||
\(54\) | 0.836312 | + | 2.57390i | 0.113808 | + | 0.350264i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.30753 | − | 4.02415i | 0.174726 | − | 0.537750i | ||||
\(57\) | −3.74010 | −0.495388 | ||||||||
\(58\) | 6.96179 | − | 21.4262i | 0.914128 | − | 2.81340i | ||||
\(59\) | 10.4136 | − | 7.56596i | 1.35574 | − | 0.985004i | 0.357038 | − | 0.934090i | \(-0.383787\pi\) |
0.998703 | − | 0.0509138i | \(-0.0162134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.102655 | − | 0.0745831i | −0.0131436 | − | 0.00954939i | 0.581194 | − | 0.813765i | \(-0.302586\pi\) |
−0.594338 | + | 0.804216i | \(0.702586\pi\) | |||||||
\(62\) | 11.9033 | − | 8.64825i | 1.51172 | − | 1.09833i | ||||
\(63\) | 0.380476 | − | 0.276432i | 0.0479355 | − | 0.0348272i | ||||
\(64\) | −19.6170 | − | 14.2526i | −2.45213 | − | 1.78158i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.96582 | − | 5.06097i | 0.857434 | − | 0.622962i | ||||
\(67\) | 0.863607 | − | 2.65791i | 0.105506 | − | 0.324715i | −0.884343 | − | 0.466838i | \(-0.845393\pi\) |
0.989849 | + | 0.142123i | \(0.0453929\pi\) | |||||||
\(68\) | 9.08535 | 1.10176 | ||||||||
\(69\) | −0.701409 | + | 2.15871i | −0.0844397 | + | 0.259879i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.95838 | + | 15.2603i | 0.588451 | + | 1.81107i | 0.584945 | + | 0.811073i | \(0.301116\pi\) |
0.00350617 | + | 0.999994i | \(0.498884\pi\) | |||||||
\(72\) | −2.78023 | − | 8.55667i | −0.327653 | − | 1.00841i | ||||
\(73\) | −7.91925 | − | 5.75367i | −0.926878 | − | 0.673416i | 0.0183484 | − | 0.999832i | \(-0.494159\pi\) |
−0.945226 | + | 0.326415i | \(0.894159\pi\) | |||||||
\(74\) | 2.76279 | 0.321168 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.9138 | 2.28427 | ||||||||
\(77\) | −1.21048 | − | 0.879462i | −0.137947 | − | 0.100224i | ||||
\(78\) | −0.471215 | − | 1.45025i | −0.0533546 | − | 0.164209i | ||||
\(79\) | −1.46937 | − | 4.52227i | −0.165317 | − | 0.508795i | 0.833742 | − | 0.552154i | \(-0.186194\pi\) |
−0.999060 | + | 0.0433593i | \(0.986194\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −3.98413 | −0.439974 | ||||||||
\(83\) | −3.61256 | + | 11.1183i | −0.396530 | + | 1.22039i | 0.531233 | + | 0.847226i | \(0.321729\pi\) |
−0.927763 | + | 0.373169i | \(0.878271\pi\) | |||||||
\(84\) | −2.02580 | + | 1.47183i | −0.221033 | + | 0.160590i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.7292 | − | 10.7014i | −1.58829 | − | 1.15396i | ||||
\(87\) | −6.73458 | + | 4.89296i | −0.722023 | + | 0.524580i | ||||
\(88\) | −23.1572 | + | 16.8247i | −2.46856 | + | 1.79351i | ||||
\(89\) | 5.01630 | + | 3.64456i | 0.531727 | + | 0.386322i | 0.821003 | − | 0.570923i | \(-0.193415\pi\) |
−0.289277 | + | 0.957246i | \(0.593415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.214377 | + | 0.155754i | −0.0224728 | + | 0.0163275i | ||||
\(92\) | 3.73458 | − | 11.4938i | 0.389357 | − | 1.19832i | ||||
\(93\) | −5.43656 | −0.563745 | ||||||||
\(94\) | −3.70785 | + | 11.4116i | −0.382436 | + | 1.17702i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.89735 | + | 18.1502i | 0.601895 | + | 1.85244i | ||||
\(97\) | −2.61256 | − | 8.04064i | −0.265265 | − | 0.816403i | −0.991632 | − | 0.129096i | \(-0.958793\pi\) |
0.726367 | − | 0.687307i | \(-0.241207\pi\) | |||||||
\(98\) | −14.8422 | − | 10.7835i | −1.49929 | − | 1.08930i | ||||
\(99\) | −3.18148 | −0.319751 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.83325 | −0.580430 | −0.290215 | − | 0.956961i | \(-0.593727\pi\) | ||||
−0.290215 | + | 0.956961i | \(0.593727\pi\) | |||||||
\(102\) | −3.73607 | − | 2.71441i | −0.369926 | − | 0.268767i | ||||
\(103\) | 4.35077 | + | 13.3903i | 0.428694 | + | 1.31938i | 0.899412 | + | 0.437101i | \(0.143995\pi\) |
−0.470718 | + | 0.882284i | \(0.656005\pi\) | |||||||
\(104\) | 1.56651 | + | 4.82121i | 0.153609 | + | 0.472758i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.89735 | + | 18.1502i | −0.572801 | + | 1.76290i | ||||
\(107\) | 8.61207 | 0.832561 | 0.416280 | − | 0.909236i | \(-0.363334\pi\) | ||||
0.416280 | + | 0.909236i | \(0.363334\pi\) | |||||||
\(108\) | −1.64533 | + | 5.06380i | −0.158322 | + | 0.487265i | ||||
\(109\) | −13.5005 | + | 9.80868i | −1.29311 | + | 0.939501i | −0.999863 | − | 0.0165355i | \(-0.994736\pi\) |
−0.293249 | + | 0.956036i | \(0.594736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.825886 | − | 0.600041i | −0.0783896 | − | 0.0569534i | ||||
\(112\) | 5.21267 | − | 3.78723i | 0.492551 | − | 0.357860i | ||||
\(113\) | 9.52686 | − | 6.92167i | 0.896211 | − | 0.651136i | −0.0412787 | − | 0.999148i | \(-0.513143\pi\) |
0.937490 | + | 0.348012i | \(0.113143\pi\) | |||||||
\(114\) | −8.18892 | − | 5.94960i | −0.766963 | − | 0.557231i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 35.8576 | − | 26.0520i | 3.32929 | − | 2.41887i | ||||
\(117\) | −0.174114 | + | 0.535867i | −0.0160968 | + | 0.0495409i | ||||
\(118\) | 34.8362 | 3.20693 | ||||||||
\(119\) | −0.247984 | + | 0.763215i | −0.0227326 | + | 0.0699638i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.271378 | − | 0.835215i | −0.0246707 | − | 0.0759286i | ||||
\(122\) | −0.106118 | − | 0.326598i | −0.00960749 | − | 0.0295688i | ||||
\(123\) | 1.19098 | + | 0.865300i | 0.107387 | + | 0.0780215i | ||||
\(124\) | 28.9464 | 2.59946 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.27279 | 0.113389 | ||||||||
\(127\) | 1.43910 | + | 1.04557i | 0.127699 | + | 0.0927790i | 0.649801 | − | 0.760104i | \(-0.274852\pi\) |
−0.522102 | + | 0.852883i | \(0.674852\pi\) | |||||||
\(128\) | −8.48418 | − | 26.1116i | −0.749903 | − | 2.30796i | ||||
\(129\) | 2.07882 | + | 6.39796i | 0.183030 | + | 0.563309i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.82895 | + | 5.62892i | −0.159796 | + | 0.491801i | −0.998615 | − | 0.0526087i | \(-0.983246\pi\) |
0.838819 | + | 0.544410i | \(0.183246\pi\) | |||||||
\(132\) | 16.9395 | 1.47439 | ||||||||
\(133\) | −0.543545 | + | 1.67286i | −0.0471313 | + | 0.145055i | ||||
\(134\) | 6.11895 | − | 4.44568i | 0.528597 | − | 0.384048i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.4202 | + | 9.02378i | 1.06502 | + | 0.773783i | ||||
\(137\) | −4.13902 | + | 3.00717i | −0.353620 | + | 0.256920i | −0.750386 | − | 0.661000i | \(-0.770132\pi\) |
0.396766 | + | 0.917920i | \(0.370132\pi\) | |||||||
\(138\) | −4.96973 | + | 3.61072i | −0.423051 | + | 0.307365i | ||||
\(139\) | 6.66482 | + | 4.84228i | 0.565303 | + | 0.410717i | 0.833396 | − | 0.552676i | \(-0.186393\pi\) |
−0.268093 | + | 0.963393i | \(0.586393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.58684 | − | 2.60599i | 0.302066 | − | 0.219464i | ||||
\(142\) | −13.4192 | + | 41.3000i | −1.12611 | + | 3.46581i | ||||
\(143\) | 1.79259 | 0.149904 | ||||||||
\(144\) | 4.23366 | − | 13.0299i | 0.352805 | − | 1.08582i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.18643 | − | 25.1952i | −0.677514 | − | 2.08517i | ||||
\(147\) | 2.09477 | + | 6.44704i | 0.172774 | + | 0.531743i | ||||
\(148\) | 4.39735 | + | 3.19486i | 0.361460 | + | 0.262616i | ||||
\(149\) | −10.0585 | −0.824027 | −0.412014 | − | 0.911178i | \(-0.635174\pi\) | ||||
−0.412014 | + | 0.911178i | \(0.635174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9810 | −0.974999 | −0.487500 | − | 0.873123i | \(-0.662091\pi\) | ||||
−0.487500 | + | 0.873123i | \(0.662091\pi\) | |||||||
\(152\) | 27.2232 | + | 19.7788i | 2.20810 | + | 1.60428i | ||||
\(153\) | 0.527295 | + | 1.62285i | 0.0426293 | + | 0.131199i | ||||
\(154\) | −1.25132 | − | 3.85115i | −0.100834 | − | 0.310335i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.927051 | − | 2.85317i | 0.0742235 | − | 0.228436i | ||||
\(157\) | −19.5960 | −1.56393 | −0.781967 | − | 0.623319i | \(-0.785784\pi\) | ||||
−0.781967 | + | 0.623319i | \(0.785784\pi\) | |||||||
\(158\) | 3.97666 | − | 12.2389i | 0.316366 | − | 0.973674i | ||||
\(159\) | 5.70487 | − | 4.14483i | 0.452426 | − | 0.328707i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.863607 | + | 0.627447i | 0.0680618 | + | 0.0494498i | ||||
\(162\) | 2.18949 | − | 1.59076i | 0.172023 | − | 0.124982i | ||||
\(163\) | 9.62137 | − | 6.99033i | 0.753604 | − | 0.547525i | −0.143338 | − | 0.989674i | \(-0.545784\pi\) |
0.896942 | + | 0.442149i | \(0.145784\pi\) | |||||||
\(164\) | −6.34127 | − | 4.60720i | −0.495170 | − | 0.359762i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.5963 | + | 18.5968i | −1.98665 | + | 1.44339i | ||||
\(167\) | 1.85218 | − | 5.70042i | 0.143326 | − | 0.441112i | −0.853466 | − | 0.521149i | \(-0.825504\pi\) |
0.996792 | + | 0.0800367i | \(0.0255038\pi\) | |||||||
\(168\) | −4.23125 | −0.326448 | ||||||||
\(169\) | −3.91912 | + | 12.0618i | −0.301471 | + | 0.927831i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.15575 | + | 3.55705i | 0.0883828 | + | 0.272014i | ||||
\(172\) | −11.0685 | − | 34.0653i | −0.843964 | − | 2.59745i | ||||
\(173\) | 14.0157 | + | 10.1830i | 1.06560 | + | 0.774201i | 0.975116 | − | 0.221697i | \(-0.0711596\pi\) |
0.0904807 | + | 0.995898i | \(0.471160\pi\) | |||||||
\(174\) | −22.5288 | −1.70791 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −43.5875 | −3.28553 | ||||||||
\(177\) | −10.4136 | − | 7.56596i | −0.782738 | − | 0.568692i | ||||
\(178\) | 5.18554 | + | 15.9595i | 0.388673 | + | 1.19621i | ||||
\(179\) | 3.26832 | + | 10.0588i | 0.244285 | + | 0.751833i | 0.995753 | + | 0.0920634i | \(0.0293462\pi\) |
−0.751468 | + | 0.659770i | \(0.770654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.70198 | − | 11.3935i | 0.275166 | − | 0.846873i | −0.714010 | − | 0.700136i | \(-0.753123\pi\) |
0.989175 | − | 0.146738i | \(-0.0468773\pi\) | |||||||
\(182\) | −0.717144 | −0.0531583 | ||||||||
\(183\) | −0.0392107 | + | 0.120678i | −0.00289854 | + | 0.00892077i | ||||
\(184\) | 16.5213 | − | 12.0035i | 1.21797 | − | 0.884906i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.9033 | − | 8.64825i | −0.872792 | − | 0.634121i | ||||
\(187\) | 4.39195 | − | 3.19094i | 0.321172 | − | 0.233345i | ||||
\(188\) | −19.0977 | + | 13.8753i | −1.39285 | + | 1.01196i | ||||
\(189\) | −0.380476 | − | 0.276432i | −0.0276756 | − | 0.0201075i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7773 | + | 10.7363i | −1.06924 | + | 0.776852i | −0.975776 | − | 0.218771i | \(-0.929795\pi\) |
−0.0934681 | + | 0.995622i | \(0.529795\pi\) | |||||||
\(192\) | −7.49304 | + | 23.0612i | −0.540763 | + | 1.66430i | ||||
\(193\) | −25.2063 | −1.81439 | −0.907194 | − | 0.420713i | \(-0.861780\pi\) | ||||
−0.907194 | + | 0.420713i | \(0.861780\pi\) | |||||||
\(194\) | 7.07054 | − | 21.7609i | 0.507635 | − | 1.56234i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.1534 | − | 34.3266i | −0.796671 | − | 2.45190i | ||||
\(197\) | −3.73672 | − | 11.5004i | −0.266230 | − | 0.819372i | −0.991407 | − | 0.130810i | \(-0.958242\pi\) |
0.725177 | − | 0.688562i | \(-0.241758\pi\) | |||||||
\(198\) | −6.96582 | − | 5.06097i | −0.495040 | − | 0.359667i | ||||
\(199\) | −0.544434 | −0.0385939 | −0.0192970 | − | 0.999814i | \(-0.506143\pi\) | ||||
−0.0192970 | + | 0.999814i | \(0.506143\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.79469 | −0.197122 | ||||||||
\(202\) | −12.7719 | − | 9.27930i | −0.898625 | − | 0.652889i | ||||
\(203\) | 1.20978 | + | 3.72331i | 0.0849096 | + | 0.261325i | ||||
\(204\) | −2.80753 | − | 8.64068i | −0.196566 | − | 0.604969i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.7748 | + | 36.2390i | −0.820386 | + | 2.52489i | ||||
\(207\) | 2.26981 | 0.157762 | ||||||||
\(208\) | −2.38543 | + | 7.34160i | −0.165400 | + | 0.509048i | ||||
\(209\) | 9.62653 | − | 6.99409i | 0.665881 | − | 0.483791i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.52580 | + | 1.83510i | 0.173884 | + | 0.126334i | 0.671323 | − | 0.741165i | \(-0.265726\pi\) |
−0.497439 | + | 0.867499i | \(0.665726\pi\) | |||||||
\(212\) | −30.3750 | + | 22.0687i | −2.08616 | + | 1.51569i | ||||
\(213\) | 12.9812 | − | 9.43140i | 0.889457 | − | 0.646229i | ||||
\(214\) | 18.8561 | + | 13.6997i | 1.28897 | + | 0.936495i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.27874 | + | 5.28832i | −0.495256 | + | 0.359824i | ||||
\(217\) | −0.790089 | + | 2.43164i | −0.0536347 | + | 0.165071i | ||||
\(218\) | −45.1625 | −3.05879 | ||||||||
\(219\) | −3.02488 | + | 9.30964i | −0.204403 | + | 0.629087i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.297101 | − | 0.914384i | −0.0199852 | − | 0.0615081i | ||||
\(222\) | −0.853750 | − | 2.62757i | −0.0573000 | − | 0.176351i | ||||
\(223\) | 0.274358 | + | 0.199333i | 0.0183724 | + | 0.0133483i | 0.596934 | − | 0.802291i | \(-0.296386\pi\) |
−0.578561 | + | 0.815639i | \(0.696386\pi\) | |||||||
\(224\) | 8.97519 | 0.599680 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.8697 | 2.11994 | ||||||||
\(227\) | −1.44690 | − | 1.05123i | −0.0960341 | − | 0.0697729i | 0.538732 | − | 0.842477i | \(-0.318904\pi\) |
−0.634766 | + | 0.772704i | \(0.718904\pi\) | |||||||
\(228\) | −6.15370 | − | 18.9391i | −0.407538 | − | 1.25427i | ||||
\(229\) | −8.64730 | − | 26.6137i | −0.571430 | − | 1.75868i | −0.648026 | − | 0.761618i | \(-0.724405\pi\) |
0.0765965 | − | 0.997062i | \(-0.475595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.462361 | + | 1.42300i | −0.0304211 | + | 0.0936265i | ||||
\(232\) | 74.8948 | 4.91708 | ||||||||
\(233\) | 2.09328 | − | 6.44246i | 0.137135 | − | 0.422059i | −0.858781 | − | 0.512343i | \(-0.828777\pi\) |
0.995916 | + | 0.0902840i | \(0.0287775\pi\) | |||||||
\(234\) | −1.23366 | + | 0.896304i | −0.0806467 | + | 0.0585932i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 55.4464 | + | 40.2841i | 3.60925 | + | 2.62227i | ||||
\(237\) | −3.84687 | + | 2.79491i | −0.249881 | + | 0.181549i | ||||
\(238\) | −1.75705 | + | 1.27657i | −0.113893 | + | 0.0827479i | ||||
\(239\) | 5.24514 | + | 3.81081i | 0.339280 | + | 0.246501i | 0.744358 | − | 0.667781i | \(-0.232756\pi\) |
−0.405078 | + | 0.914282i | \(0.632756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.02602 | − | 4.37816i | 0.388170 | − | 0.282022i | −0.376535 | − | 0.926402i | \(-0.622885\pi\) |
0.764705 | + | 0.644380i | \(0.222885\pi\) | |||||||
\(242\) | 0.734446 | − | 2.26039i | 0.0472120 | − | 0.145304i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.208773 | − | 0.642537i | 0.0133653 | − | 0.0411342i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.23116 | + | 3.78914i | 0.0784962 | + | 0.241586i | ||||
\(247\) | −0.651203 | − | 2.00420i | −0.0414351 | − | 0.127524i | ||||
\(248\) | 39.5713 | + | 28.7502i | 2.51278 | + | 1.82564i | ||||
\(249\) | 11.6905 | 0.740855 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.60217 | −0.290486 | −0.145243 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145243 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(252\) | 2.02580 | + | 1.47183i | 0.127614 | + | 0.0927168i | ||||
\(253\) | −2.23152 | − | 6.86790i | −0.140294 | − | 0.431781i | ||||
\(254\) | 1.48765 | + | 4.57852i | 0.0933435 | + | 0.287282i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.97520 | − | 24.5451i | 0.498450 | − | 1.53407i | ||||
\(257\) | 5.79485 | 0.361473 | 0.180736 | − | 0.983532i | \(-0.442152\pi\) | ||||
0.180736 | + | 0.983532i | \(0.442152\pi\) | |||||||
\(258\) | −5.62605 | + | 17.3152i | −0.350262 | + | 1.07800i | ||||
\(259\) | −0.388409 | + | 0.282196i | −0.0241346 | + | 0.0175348i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.73458 | + | 4.89296i | 0.416860 | + | 0.302866i | ||||
\(262\) | −12.9587 | + | 9.41507i | −0.800593 | + | 0.581665i | ||||
\(263\) | 11.5680 | − | 8.40467i | 0.713316 | − | 0.518254i | −0.170926 | − | 0.985284i | \(-0.554676\pi\) |
0.884242 | + | 0.467030i | \(0.154676\pi\) | |||||||
\(264\) | 23.1572 | + | 16.8247i | 1.42522 | + | 1.03549i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.85120 | + | 2.79806i | −0.236132 | + | 0.171560i | ||||
\(267\) | 1.91606 | − | 5.89701i | 0.117261 | − | 0.360891i | ||||
\(268\) | 14.8800 | 0.908943 | ||||||||
\(269\) | −5.93945 | + | 18.2797i | −0.362135 | + | 1.11454i | 0.589621 | + | 0.807680i | \(0.299277\pi\) |
−0.951756 | + | 0.306856i | \(0.900723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.18256 | − | 22.1057i | −0.436310 | − | 1.34282i | −0.891739 | − | 0.452551i | \(-0.850514\pi\) |
0.455429 | − | 0.890272i | \(-0.349486\pi\) | |||||||
\(272\) | 7.22415 | + | 22.2337i | 0.438029 | + | 1.34811i | ||||
\(273\) | 0.214377 | + | 0.155754i | 0.0129747 | + | 0.00942666i | ||||
\(274\) | −13.8460 | −0.836470 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.0853 | −0.727452 | ||||||||
\(277\) | 17.7102 | + | 12.8672i | 1.06410 | + | 0.773115i | 0.974843 | − | 0.222894i | \(-0.0715502\pi\) |
0.0892586 | + | 0.996008i | \(0.471550\pi\) | |||||||
\(278\) | 6.88968 | + | 21.2043i | 0.413216 | + | 1.27175i | ||||
\(279\) | 1.67999 | + | 5.17047i | 0.100578 | + | 0.309548i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.37863 | − | 25.7868i | 0.499827 | − | 1.53831i | −0.309469 | − | 0.950910i | \(-0.600151\pi\) |
0.809296 | − | 0.587401i | \(-0.199849\pi\) | |||||||
\(282\) | 11.9989 | 0.714522 | ||||||||
\(283\) | −5.03926 | + | 15.5093i | −0.299553 | + | 0.921929i | 0.682101 | + | 0.731258i | \(0.261066\pi\) |
−0.981654 | + | 0.190671i | \(0.938934\pi\) | |||||||
\(284\) | −69.1171 | + | 50.2165i | −4.10134 | + | 2.97980i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.92485 | + | 2.85157i | 0.232081 | + | 0.168617i | ||||
\(287\) | 0.560112 | − | 0.406945i | 0.0330624 | − | 0.0240212i | ||||
\(288\) | 15.4395 | − | 11.2174i | 0.909778 | − | 0.660993i | ||||
\(289\) | 11.3977 | + | 8.28091i | 0.670453 | + | 0.487112i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.83978 | + | 4.96939i | −0.400955 | + | 0.291311i | ||||
\(292\) | 16.1057 | − | 49.5682i | 0.942514 | − | 2.90076i | ||||
\(293\) | −5.46407 | −0.319214 | −0.159607 | − | 0.987181i | \(-0.551023\pi\) | ||||
−0.159607 | + | 0.987181i | \(0.551023\pi\) | |||||||
\(294\) | −5.66921 | + | 17.4480i | −0.330635 | + | 1.01759i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.83820 | + | 8.73509i | 0.164967 | + | 0.507717i | ||||
\(297\) | 0.983131 | + | 3.02577i | 0.0570470 | + | 0.175573i | ||||
\(298\) | −22.0231 | − | 16.0007i | −1.27576 | − | 0.926897i | ||||
\(299\) | −1.27891 | −0.0739612 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.16377 | 0.182357 | ||||||||
\(302\) | −26.2323 | − | 19.0589i | −1.50950 | − | 1.09672i | ||||
\(303\) | 1.80257 | + | 5.54775i | 0.103555 | + | 0.318710i | ||||
\(304\) | 15.8343 | + | 48.7330i | 0.908160 | + | 2.79503i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.42705 | + | 4.39201i | −0.0815791 | + | 0.251075i | ||||
\(307\) | 21.4194 | 1.22247 | 0.611235 | − | 0.791450i | \(-0.290673\pi\) | ||||
0.611235 | + | 0.791450i | \(0.290673\pi\) | |||||||
\(308\) | 2.46179 | − | 7.57662i | 0.140274 | − | 0.431718i | ||||
\(309\) | 11.3905 | − | 8.27566i | 0.647981 | − | 0.470786i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.30731 | + | 1.67636i | 0.130836 | + | 0.0950578i | 0.651278 | − | 0.758839i | \(-0.274233\pi\) |
−0.520443 | + | 0.853897i | \(0.674233\pi\) | |||||||
\(312\) | 4.10116 | − | 2.97967i | 0.232183 | − | 0.168691i | ||||
\(313\) | 11.6802 | − | 8.48616i | 0.660204 | − | 0.479666i | −0.206528 | − | 0.978441i | \(-0.566216\pi\) |
0.866732 | + | 0.498774i | \(0.166216\pi\) | |||||||
\(314\) | −42.9054 | − | 31.1726i | −2.42129 | − | 1.75917i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.4823 | − | 14.8812i | 1.15222 | − | 0.837135i | ||||
\(317\) | −6.98695 | + | 21.5036i | −0.392426 | + | 1.20776i | 0.538522 | + | 0.842611i | \(0.318983\pi\) |
−0.930948 | + | 0.365152i | \(0.881017\pi\) | |||||||
\(318\) | 19.0842 | 1.07019 | ||||||||
\(319\) | 8.18397 | − | 25.1877i | 0.458214 | − | 1.41024i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.66128 | − | 8.19057i | −0.148538 | − | 0.457153i | ||||
\(322\) | 0.892743 | + | 2.74758i | 0.0497506 | + | 0.153117i | ||||
\(323\) | −5.16312 | − | 3.75123i | −0.287284 | − | 0.208724i | ||||
\(324\) | 5.32440 | 0.295800 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.1859 | 1.78261 | ||||||||
\(327\) | 13.5005 | + | 9.80868i | 0.746578 | + | 0.542421i | ||||
\(328\) | −4.09288 | − | 12.5966i | −0.225991 | − | 0.695530i | ||||
\(329\) | −0.644327 | − | 1.98303i | −0.0355229 | − | 0.109328i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.19480 | − | 3.67721i | 0.0656720 | − | 0.202118i | −0.912836 | − | 0.408326i | \(-0.866113\pi\) |
0.978508 | + | 0.206209i | \(0.0661125\pi\) | |||||||
\(332\) | −62.2448 | −3.41613 | ||||||||
\(333\) | −0.315460 | + | 0.970887i | −0.0172871 | + | 0.0532043i | ||||
\(334\) | 13.1233 | − | 9.53466i | 0.718077 | − | 0.521713i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.21267 | − | 3.78723i | −0.284375 | − | 0.206610i | ||||
\(337\) | 14.1459 | − | 10.2776i | 0.770576 | − | 0.559856i | −0.131560 | − | 0.991308i | \(-0.541999\pi\) |
0.902136 | + | 0.431452i | \(0.141999\pi\) | |||||||
\(338\) | −27.7683 | + | 20.1749i | −1.51040 | + | 1.09737i | ||||
\(339\) | −9.52686 | − | 6.92167i | −0.517428 | − | 0.375933i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.9930 | − | 10.1665i | 0.757763 | − | 0.550547i | ||||
\(342\) | −3.12789 | + | 9.62666i | −0.169137 | + | 0.520550i | ||||
\(343\) | 6.48010 | 0.349893 | ||||||||
\(344\) | 18.7032 | − | 57.5626i | 1.00841 | − | 3.10357i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.4886 | + | 44.5913i | 0.778912 | + | 2.39724i | ||||
\(347\) | 7.13647 | + | 21.9638i | 0.383106 | + | 1.17908i | 0.937845 | + | 0.347055i | \(0.112818\pi\) |
−0.554739 | + | 0.832024i | \(0.687182\pi\) | |||||||
\(348\) | −35.8576 | − | 26.0520i | −1.92217 | − | 1.39654i | ||||
\(349\) | −9.32650 | −0.499236 | −0.249618 | − | 0.968344i | \(-0.580305\pi\) | ||||
−0.249618 | + | 0.968344i | \(0.580305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.563444 | 0.0300744 | ||||||||
\(352\) | −49.1203 | − | 35.6880i | −2.61812 | − | 1.90218i | ||||
\(353\) | −9.87219 | − | 30.3835i | −0.525444 | − | 1.61715i | −0.763437 | − | 0.645883i | \(-0.776490\pi\) |
0.237993 | − | 0.971267i | \(-0.423510\pi\) | |||||||
\(354\) | −10.7650 | − | 33.1312i | −0.572152 | − | 1.76090i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.2018 | + | 31.3980i | −0.540697 | + | 1.66409i | ||||
\(357\) | 0.802492 | 0.0424724 | ||||||||
\(358\) | −8.84525 | + | 27.2229i | −0.467486 | + | 1.43877i | ||||
\(359\) | 7.75810 | − | 5.63659i | 0.409457 | − | 0.297488i | −0.363925 | − | 0.931428i | \(-0.618564\pi\) |
0.773382 | + | 0.633940i | \(0.218564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.05451 | + | 2.94577i | 0.213395 | + | 0.155041i | ||||
\(362\) | 26.2298 | − | 19.0571i | 1.37861 | − | 1.00162i | ||||
\(363\) | −0.710476 | + | 0.516191i | −0.0372903 | + | 0.0270930i | ||||
\(364\) | −1.14143 | − | 0.829296i | −0.0598271 | − | 0.0434669i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.277821 | + | 0.201849i | −0.0145219 | + | 0.0105508i | ||||
\(367\) | −0.328866 | + | 1.01215i | −0.0171667 | + | 0.0528336i | −0.959273 | − | 0.282481i | \(-0.908843\pi\) |
0.942106 | + | 0.335315i | \(0.108843\pi\) | |||||||
\(368\) | 31.0973 | 1.62106 | ||||||||
\(369\) | 0.454915 | − | 1.40008i | 0.0236819 | − | 0.0728855i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.02480 | − | 3.15402i | −0.0532051 | − | 0.163748i | ||||
\(372\) | −8.94492 | − | 27.5296i | −0.463773 | − | 1.42735i | ||||
\(373\) | −3.33333 | − | 2.42181i | −0.172593 | − | 0.125396i | 0.498135 | − | 0.867099i | \(-0.334018\pi\) |
−0.670728 | + | 0.741703i | \(0.734018\pi\) | |||||||
\(374\) | 14.6922 | 0.759714 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −39.8890 | −2.05712 | ||||||||
\(377\) | −3.79456 | − | 2.75691i | −0.195430 | − | 0.141988i | ||||
\(378\) | −0.393313 | − | 1.21049i | −0.0202298 | − | 0.0622610i | ||||
\(379\) | 3.20027 | + | 9.84942i | 0.164387 | + | 0.505931i | 0.998991 | − | 0.0449201i | \(-0.0143033\pi\) |
−0.834604 | + | 0.550851i | \(0.814303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.549687 | − | 1.69176i | 0.0281613 | − | 0.0866716i | ||||
\(382\) | −49.4336 | −2.52924 | ||||||||
\(383\) | −0.370619 | + | 1.14065i | −0.0189378 | + | 0.0582845i | −0.960079 | − | 0.279730i | \(-0.909755\pi\) |
0.941141 | + | 0.338014i | \(0.109755\pi\) | |||||||
\(384\) | −22.2119 | + | 16.1379i | −1.13350 | + | 0.823533i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −55.1890 | − | 40.0971i | −2.80904 | − | 2.04089i | ||||
\(387\) | 5.44243 | − | 3.95416i | 0.276654 | − | 0.201001i | ||||
\(388\) | 36.4177 | − | 26.4590i | 1.84883 | − | 1.34325i | ||||
\(389\) | −10.1971 | − | 7.40861i | −0.517012 | − | 0.375631i | 0.298465 | − | 0.954421i | \(-0.403525\pi\) |
−0.815477 | + | 0.578789i | \(0.803525\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.13341 | + | 2.27656i | −0.158464 | + | 0.115130i | ||||
\(392\) | 18.8467 | − | 58.0042i | 0.951902 | − | 2.92965i | ||||
\(393\) | 5.91860 | 0.298554 | ||||||||
\(394\) | 10.1129 | − | 31.1243i | 0.509481 | − | 1.56802i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.23458 | − | 16.1104i | −0.263047 | − | 0.809577i | ||||
\(397\) | 0.405848 | + | 1.24907i | 0.0203689 | + | 0.0626891i | 0.960724 | − | 0.277505i | \(-0.0895074\pi\) |
−0.940355 | + | 0.340194i | \(0.889507\pi\) | |||||||
\(398\) | −1.19204 | − | 0.866064i | −0.0597513 | − | 0.0434119i | ||||
\(399\) | 1.75895 | 0.0880575 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.1042 | 0.804205 | 0.402102 | − | 0.915595i | \(-0.368280\pi\) | ||||
0.402102 | + | 0.915595i | \(0.368280\pi\) | |||||||
\(402\) | −6.11895 | − | 4.44568i | −0.305186 | − | 0.221730i | ||||
\(403\) | −0.946580 | − | 2.91327i | −0.0471525 | − | 0.145120i | ||||
\(404\) | −9.59762 | − | 29.5384i | −0.477499 | − | 1.46959i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.27409 | + | 10.0766i | −0.162490 | + | 0.500094i | ||||
\(407\) | 3.24782 | 0.160988 | ||||||||
\(408\) | 4.74408 | − | 14.6008i | 0.234867 | − | 0.722847i | ||||
\(409\) | −17.1188 | + | 12.4375i | −0.846471 | + | 0.614997i | −0.924171 | − | 0.381980i | \(-0.875242\pi\) |
0.0776999 | + | 0.996977i | \(0.475242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.13902 | + | 3.00717i | 0.204163 | + | 0.148333i | ||||
\(412\) | −60.6473 | + | 44.0629i | −2.98788 | + | 2.17082i | ||||
\(413\) | −4.89748 | + | 3.55823i | −0.240989 | + | 0.175089i | ||||
\(414\) | 4.96973 | + | 3.61072i | 0.244249 | + | 0.177457i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.69927 | + | 6.32039i | −0.426517 | + | 0.309883i | ||||
\(417\) | 2.54574 | − | 7.83497i | 0.124665 | − | 0.383680i | ||||
\(418\) | 32.2031 | 1.57511 | ||||||||
\(419\) | −2.06144 | + | 6.34445i | −0.100708 | + | 0.309946i | −0.988699 | − | 0.149914i | \(-0.952100\pi\) |
0.887991 | + | 0.459860i | \(0.152100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.43555 | + | 25.9620i | 0.411124 | + | 1.26531i | 0.915673 | + | 0.401925i | \(0.131659\pi\) |
−0.504549 | + | 0.863383i | \(0.668341\pi\) | |||||||
\(422\) | 2.61102 | + | 8.03590i | 0.127103 | + | 0.391181i | ||||
\(423\) | −3.58684 | − | 2.60599i | −0.174398 | − | 0.126708i | ||||
\(424\) | −63.4435 | −3.08109 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 43.4253 | 2.10396 | ||||||||
\(427\) | 0.0482780 | + | 0.0350760i | 0.00233633 | + | 0.00169745i | ||||
\(428\) | 14.1697 | + | 43.6098i | 0.684918 | + | 2.10796i | ||||
\(429\) | −0.553939 | − | 1.70485i | −0.0267444 | − | 0.0823109i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.80011 | − | 11.6955i | 0.183045 | − | 0.563354i | −0.816864 | − | 0.576830i | \(-0.804290\pi\) |
0.999909 | + | 0.0134755i | \(0.00428951\pi\) | |||||||
\(432\) | −13.7004 | −0.659161 | ||||||||
\(433\) | 10.4587 | − | 32.1887i | 0.502614 | − | 1.54689i | −0.302130 | − | 0.953267i | \(-0.597698\pi\) |
0.804744 | − | 0.593622i | \(-0.202302\pi\) | |||||||
\(434\) | −5.59805 | + | 4.06722i | −0.268715 | + | 0.195233i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −71.8819 | − | 52.2253i | −3.44252 | − | 2.50114i | ||||
\(437\) | −6.86799 | + | 4.98989i | −0.328541 | + | 0.238699i | ||||
\(438\) | −21.4324 | + | 15.5715i | −1.02408 | + | 0.744036i | ||||
\(439\) | 16.9614 | + | 12.3231i | 0.809521 | + | 0.588152i | 0.913692 | − | 0.406408i | \(-0.133219\pi\) |
−0.104171 | + | 0.994559i | \(0.533219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.48418 | − | 3.98449i | 0.261152 | − | 0.189738i | ||||
\(442\) | 0.804064 | − | 2.47465i | 0.0382454 | − | 0.117707i | ||||
\(443\) | −6.04847 | −0.287371 | −0.143686 | − | 0.989623i | \(-0.545895\pi\) | ||||
−0.143686 | + | 0.989623i | \(0.545895\pi\) | |||||||
\(444\) | 1.67964 | − | 5.16939i | 0.0797120 | − | 0.245328i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.283614 | + | 0.872875i | 0.0134295 | + | 0.0413318i | ||||
\(447\) | 3.10826 | + | 9.56624i | 0.147016 | + | 0.452467i | ||||
\(448\) | 9.22577 | + | 6.70292i | 0.435877 | + | 0.316683i | ||||
\(449\) | 15.5896 | 0.735721 | 0.367860 | − | 0.929881i | \(-0.380090\pi\) | ||||
0.367860 | + | 0.929881i | \(0.380090\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.68357 | −0.220541 | ||||||||
\(452\) | 50.7248 | + | 36.8537i | 2.38589 | + | 1.73345i | ||||
\(453\) | 3.70233 | + | 11.3946i | 0.173951 | + | 0.535365i | ||||
\(454\) | −1.49572 | − | 4.60334i | −0.0701974 | − | 0.216046i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.3983 | − | 32.0028i | 0.486947 | − | 1.49867i | ||||
\(457\) | 2.50193 | 0.117035 | 0.0585176 | − | 0.998286i | \(-0.481363\pi\) | ||||
0.0585176 | + | 0.998286i | \(0.481363\pi\) | |||||||
\(458\) | 23.4027 | − | 72.0262i | 1.09354 | − | 3.36556i | ||||
\(459\) | 1.38048 | − | 1.00297i | 0.0644351 | − | 0.0468148i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.124559 | + | 0.0904973i | 0.00580128 | + | 0.00421488i | 0.590682 | − | 0.806904i | \(-0.298859\pi\) |
−0.584881 | + | 0.811119i | \(0.698859\pi\) | |||||||
\(462\) | −3.27599 | + | 2.38014i | −0.152413 | + | 0.110734i | ||||
\(463\) | −9.41102 | + | 6.83751i | −0.437367 | + | 0.317766i | −0.784588 | − | 0.620018i | \(-0.787125\pi\) |
0.347221 | + | 0.937783i | \(0.387125\pi\) | |||||||
\(464\) | 92.2664 | + | 67.0355i | 4.28336 | + | 3.11204i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.8316 | − | 10.7758i | 0.687062 | − | 0.499180i | ||||
\(467\) | −0.145329 | + | 0.447276i | −0.00672502 | + | 0.0206975i | −0.954363 | − | 0.298650i | \(-0.903464\pi\) |
0.947638 | + | 0.319347i | \(0.103464\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −0.406149 | + | 1.25000i | −0.0187542 | + | 0.0577196i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.05551 | + | 18.6369i | 0.279023 | + | 0.858745i | ||||
\(472\) | 35.7871 | + | 110.141i | 1.64723 | + | 5.06966i | ||||
\(473\) | −17.3150 | − | 12.5801i | −0.796143 | − | 0.578432i | ||||
\(474\) | −12.8687 | −0.591080 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.27279 | −0.195843 | ||||||||
\(477\) | −5.70487 | − | 4.14483i | −0.261208 | − | 0.189779i | ||||
\(478\) | 5.42210 | + | 16.6875i | 0.248001 | + | 0.763269i | ||||
\(479\) | 3.83534 | + | 11.8040i | 0.175241 | + | 0.539337i | 0.999644 | − | 0.0266660i | \(-0.00848907\pi\) |
−0.824403 | + | 0.566003i | \(0.808489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.177744 | − | 0.547041i | 0.00810444 | − | 0.0249429i | ||||
\(482\) | 20.1585 | 0.918196 | ||||||||
\(483\) | 0.329868 | − | 1.01523i | 0.0150095 | − | 0.0461946i | ||||
\(484\) | 3.78286 | − | 2.74841i | 0.171948 | − | 0.124928i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.18949 | − | 1.59076i | −0.0993174 | − | 0.0721583i | ||||
\(487\) | 27.9633 | − | 20.3165i | 1.26714 | − | 0.920631i | 0.268055 | − | 0.963404i | \(-0.413619\pi\) |
0.999085 | + | 0.0427731i | \(0.0136193\pi\) | |||||||
\(488\) | 0.923588 | − | 0.671026i | 0.0418088 | − | 0.0303759i | ||||
\(489\) | −9.62137 | − | 6.99033i | −0.435093 | − | 0.316114i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.1168 | − | 14.6157i | 0.907859 | − | 0.659598i | −0.0326134 | − | 0.999468i | \(-0.510383\pi\) |
0.940473 | + | 0.339870i | \(0.110383\pi\) | |||||||
\(492\) | −2.42215 | + | 7.45460i | −0.109199 | + | 0.336080i | ||||
\(493\) | −14.2044 | −0.639736 | ||||||||
\(494\) | 1.76239 | − | 5.42408i | 0.0792938 | − | 0.244041i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.0165 | + | 70.8375i | 1.03347 | + | 3.18070i | ||||
\(497\) | −2.33190 | − | 7.17684i | −0.104600 | − | 0.321925i | ||||
\(498\) | 25.5963 | + | 18.5968i | 1.14700 | + | 0.833341i | ||||
\(499\) | 12.6037 | 0.564220 | 0.282110 | − | 0.959382i | \(-0.408966\pi\) | ||||
0.282110 | + | 0.959382i | \(0.408966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.99378 | −0.267782 | ||||||||
\(502\) | −10.0764 | − | 7.32094i | −0.449732 | − | 0.326750i | ||||
\(503\) | −9.26827 | − | 28.5248i | −0.413252 | − | 1.27186i | −0.913805 | − | 0.406152i | \(-0.866870\pi\) |
0.500554 | − | 0.865705i | \(-0.333130\pi\) | |||||||
\(504\) | 1.30753 | + | 4.02415i | 0.0582419 | + | 0.179250i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.03929 | − | 18.5870i | 0.268479 | − | 0.826294i | ||||
\(507\) | 12.6825 | 0.563251 | ||||||||
\(508\) | −2.92675 | + | 9.00761i | −0.129854 | + | 0.399648i | ||||
\(509\) | 0.377802 | − | 0.274489i | 0.0167458 | − | 0.0121665i | −0.579381 | − | 0.815057i | \(-0.696706\pi\) |
0.596127 | + | 0.802890i | \(0.296706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.72438 | + | 2.70592i | 0.164757 | + | 0.119703i | ||||
\(512\) | 12.0833 | − | 8.77902i | 0.534011 | − | 0.387982i | ||||
\(513\) | 3.02580 | − | 2.19838i | 0.133593 | − | 0.0970607i | ||||
\(514\) | 12.6878 | + | 9.21822i | 0.559634 | + | 0.406598i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −28.9777 | + | 21.0535i | −1.27567 | + | 0.926829i | ||||
\(517\) | −4.35878 | + | 13.4150i | −0.191699 | + | 0.589989i | ||||
\(518\) | −1.29933 | −0.0570891 | ||||||||
\(519\) | 5.35353 | − | 16.4765i | 0.234994 | − | 0.723237i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.34039 | − | 16.4360i | −0.233967 | − | 0.720076i | −0.997257 | − | 0.0740200i | \(-0.976417\pi\) |
0.763290 | − | 0.646056i | \(-0.223583\pi\) | |||||||
\(522\) | 6.96179 | + | 21.4262i | 0.304709 | + | 0.937799i | ||||
\(523\) | 32.8849 | + | 23.8922i | 1.43795 | + | 1.04473i | 0.988465 | + | 0.151449i | \(0.0483940\pi\) |
0.449489 | + | 0.893286i | \(0.351606\pi\) | |||||||
\(524\) | −31.5130 | −1.37665 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.6980 | 1.68731 | ||||||||
\(527\) | −7.50503 | − | 5.45273i | −0.326924 | − | 0.237525i | ||||
\(528\) | 13.4693 | + | 41.4542i | 0.586175 | + | 1.80406i | ||||
\(529\) | −5.51533 | − | 16.9744i | −0.239797 | − | 0.738019i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.97766 | + | 12.2420i | −0.172616 | + | 0.531256i | ||||
\(532\) | −9.36533 | −0.406039 | ||||||||
\(533\) | −0.256319 | + | 0.788869i | −0.0111024 | + | 0.0341697i | ||||
\(534\) | 13.5759 | − | 9.86349i | 0.587488 | − | 0.426835i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.3418 | + | 14.7792i | 0.878633 | + | 0.638364i | ||||
\(537\) | 8.55656 | − | 6.21671i | 0.369243 | − | 0.268271i | ||||
\(538\) | −42.0831 | + | 30.5751i | −1.81433 | + | 1.31819i | ||||
\(539\) | −17.4478 | − | 12.6766i | −0.751530 | − | 0.546019i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.60265 | − | 1.16440i | 0.0689035 | − | 0.0500613i | −0.552800 | − | 0.833314i | \(-0.686441\pi\) |
0.621704 | + | 0.783252i | \(0.286441\pi\) | |||||||
\(542\) | 19.4386 | − | 59.8259i | 0.834960 | − | 2.56974i | ||||
\(543\) | −11.9799 | −0.514105 | ||||||||
\(544\) | −10.0630 | + | 30.9707i | −0.431448 | + | 1.32786i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.221610 | + | 0.682045i | 0.00948402 | + | 0.0291888i | ||||
\(547\) | −10.8324 | − | 33.3386i | −0.463158 | − | 1.42545i | −0.861284 | − | 0.508124i | \(-0.830339\pi\) |
0.398126 | − | 0.917331i | \(-0.369661\pi\) | |||||||
\(548\) | −22.0378 | − | 16.0114i | −0.941407 | − | 0.683972i | ||||
\(549\) | 0.126888 | 0.00541546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.1341 | −1.32636 | ||||||||
\(552\) | −16.5213 | − | 12.0035i | −0.703195 | − | 0.510901i | ||||
\(553\) | 0.691038 | + | 2.12680i | 0.0293859 | + | 0.0904405i | ||||
\(554\) | 18.3077 | + | 56.3453i | 0.777819 | + | 2.39388i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.5545 | + | 41.7165i | −0.574839 | + | 1.76917i | ||||
\(557\) | −19.2383 | −0.815154 | −0.407577 | − | 0.913171i | \(-0.633626\pi\) | ||||
−0.407577 | + | 0.913171i | \(0.633626\pi\) | |||||||
\(558\) | −4.54666 | + | 13.9932i | −0.192475 | + | 0.592378i | ||||
\(559\) | −3.06651 | + | 2.22795i | −0.129699 | + | 0.0942321i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.39195 | − | 3.19094i | −0.185428 | − | 0.134722i | ||||
\(562\) | 59.3655 | − | 43.1316i | 2.50418 | − | 1.81940i | ||||
\(563\) | −23.6023 | + | 17.1481i | −0.994720 | + | 0.722707i | −0.960950 | − | 0.276723i | \(-0.910752\pi\) |
−0.0337705 | + | 0.999430i | \(0.510752\pi\) | |||||||
\(564\) | 19.0977 | + | 13.8753i | 0.804160 | + | 0.584257i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −35.7049 | + | 25.9411i | −1.50079 | + | 1.09039i | ||||
\(567\) | −0.145329 | + | 0.447276i | −0.00610324 | + | 0.0187838i | ||||
\(568\) | −144.363 | −6.05734 | ||||||||
\(569\) | −10.1701 | + | 31.3004i | −0.426354 | + | 1.31218i | 0.475338 | + | 0.879803i | \(0.342326\pi\) |
−0.901692 | + | 0.432380i | \(0.857674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.23065 | + | 25.3313i | 0.344442 | + | 1.06008i | 0.961882 | + | 0.273465i | \(0.0881698\pi\) |
−0.617440 | + | 0.786618i | \(0.711830\pi\) | |||||||
\(572\) | 2.94939 | + | 9.07730i | 0.123320 | + | 0.379541i | ||||
\(573\) | 14.7773 | + | 10.7363i | 0.617329 | + | 0.448515i | ||||
\(574\) | 1.87371 | 0.0782073 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.2480 | 1.01033 | ||||||||
\(577\) | 27.9237 | + | 20.2878i | 1.16248 | + | 0.844591i | 0.990089 | − | 0.140438i | \(-0.0448511\pi\) |
0.172390 | + | 0.985029i | \(0.444851\pi\) | |||||||
\(578\) | 11.7822 | + | 36.2620i | 0.490076 | + | 1.50830i | ||||
\(579\) | 7.78917 | + | 23.9726i | 0.323707 | + | 0.996267i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.69897 | − | 5.22888i | 0.0704850 | − | 0.216931i | ||||
\(582\) | −22.8807 | −0.948437 | ||||||||
\(583\) | −6.93265 | + | 21.3365i | −0.287121 | + | 0.883668i | ||||
\(584\) | 71.2496 | − | 51.7659i | 2.94833 | − | 2.14209i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.9635 | − | 8.69202i | −0.494209 | − | 0.359064i | ||||
\(587\) | −18.0213 | + | 13.0932i | −0.743817 | + | 0.540414i | −0.893904 | − | 0.448258i | \(-0.852045\pi\) |
0.150087 | + | 0.988673i | \(0.452045\pi\) | |||||||
\(588\) | −29.2000 | + | 21.2150i | −1.20419 | + | 0.874893i | ||||
\(589\) | −16.4500 | − | 11.9516i | −0.677809 | − | 0.492457i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.78286 | + | 7.10766i | −0.402413 | + | 0.292370i | ||||
\(592\) | −4.32193 | + | 13.3015i | −0.177630 | + | 0.546690i | ||||
\(593\) | 30.9158 | 1.26956 | 0.634779 | − | 0.772693i | \(-0.281091\pi\) | ||||
0.634779 | + | 0.772693i | \(0.281091\pi\) | |||||||
\(594\) | −2.66071 | + | 8.18882i | −0.109170 | + | 0.335991i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.5496 | − | 50.9344i | −0.677898 | − | 2.08636i | ||||
\(597\) | 0.168240 | + | 0.517788i | 0.00688558 | + | 0.0211917i | ||||
\(598\) | −2.80016 | − | 2.03444i | −0.114507 | − | 0.0831943i | ||||
\(599\) | −24.0276 | −0.981742 | −0.490871 | − | 0.871232i | \(-0.663321\pi\) | ||||
−0.490871 | + | 0.871232i | \(0.663321\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.0387 | −1.30688 | −0.653442 | − | 0.756977i | \(-0.726676\pi\) | ||||
−0.653442 | + | 0.756977i | \(0.726676\pi\) | |||||||
\(602\) | 6.92705 | + | 5.03280i | 0.282326 | + | 0.205121i | ||||
\(603\) | 0.863607 | + | 2.65791i | 0.0351688 | + | 0.108238i | ||||
\(604\) | −19.7127 | − | 60.6694i | −0.802097 | − | 2.46860i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.87842 | + | 15.0142i | −0.198172 | + | 0.609911i | ||||
\(607\) | −45.5915 | −1.85050 | −0.925251 | − | 0.379356i | \(-0.876145\pi\) | ||||
−0.925251 | + | 0.379356i | \(0.876145\pi\) | |||||||
\(608\) | −22.0567 | + | 67.8834i | −0.894516 | + | 2.75304i | ||||
\(609\) | 3.16723 | − | 2.30113i | 0.128343 | − | 0.0932465i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.02098 | + | 1.46833i | 0.0817602 | + | 0.0594023i | ||||
\(612\) | −7.35020 | + | 5.34023i | −0.297114 | + | 0.215866i | ||||
\(613\) | −8.78299 | + | 6.38121i | −0.354742 | + | 0.257735i | −0.750855 | − | 0.660467i | \(-0.770359\pi\) |
0.396114 | + | 0.918201i | \(0.370359\pi\) | |||||||
\(614\) | 46.8976 | + | 34.0731i | 1.89263 | + | 1.37508i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.8907 | − | 7.91254i | 0.438798 | − | 0.318805i | ||||
\(617\) | 4.97685 | − | 15.3172i | 0.200360 | − | 0.616646i | −0.799512 | − | 0.600651i | \(-0.794908\pi\) |
0.999872 | − | 0.0159954i | \(-0.00509171\pi\) | |||||||
\(618\) | 38.1039 | 1.53276 | ||||||||
\(619\) | 11.8533 | − | 36.4807i | 0.476425 | − | 1.46628i | −0.367602 | − | 0.929983i | \(-0.619821\pi\) |
0.844026 | − | 0.536302i | \(-0.180179\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.701409 | − | 2.15871i | −0.0281466 | − | 0.0866262i | ||||
\(622\) | 2.38516 | + | 7.34076i | 0.0956362 | + | 0.294338i | ||||
\(623\) | −2.35914 | − | 1.71401i | −0.0945168 | − | 0.0686705i | ||||
\(624\) | 7.71941 | 0.309024 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.0732 | 1.56168 | ||||||||
\(627\) | −9.62653 | − | 6.99409i | −0.384447 | − | 0.279317i | ||||
\(628\) | −32.2419 | − | 99.2305i | −1.28659 | − | 3.95973i | ||||
\(629\) | −0.538290 | − | 1.65669i | −0.0214630 | − | 0.0660564i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.02370 | − | 21.6167i | 0.279609 | − | 0.860548i | −0.708354 | − | 0.705857i | \(-0.750562\pi\) |
0.987963 | − | 0.154690i | \(-0.0494380\pi\) | |||||||
\(632\) | 42.7808 | 1.70173 | ||||||||
\(633\) | 0.964772 | − | 2.96926i | 0.0383462 | − | 0.118018i | ||||
\(634\) | −49.5049 | + | 35.9674i | −1.96609 | + | 1.42845i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 30.3750 | + | 22.0687i | 1.20445 | + | 0.875082i | ||||
\(637\) | −3.09003 | + | 2.24504i | −0.122431 | + | 0.0889517i | ||||
\(638\) | 57.9863 | − | 42.1295i | 2.29570 | − | 1.66792i | ||||
\(639\) | −12.9812 | − | 9.43140i | −0.513528 | − | 0.373100i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.8378 | + | 15.8661i | −0.862541 | + | 0.626673i | −0.928575 | − | 0.371145i | \(-0.878965\pi\) |
0.0660340 | + | 0.997817i | \(0.478965\pi\) | |||||||
\(642\) | 7.20238 | − | 22.1666i | 0.284255 | − | 0.874848i | ||||
\(643\) | 25.9062 | 1.02164 | 0.510821 | − | 0.859687i | \(-0.329341\pi\) | ||||
0.510821 | + | 0.859687i | \(0.329341\pi\) | |||||||
\(644\) | −1.75635 | + | 5.40549i | −0.0692099 | + | 0.213006i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.33731 | − | 16.4266i | −0.209994 | − | 0.646295i | ||||
\(647\) | 6.69401 | + | 20.6021i | 0.263169 | + | 0.809950i | 0.992110 | + | 0.125374i | \(0.0400129\pi\) |
−0.728941 | + | 0.684577i | \(0.759987\pi\) | |||||||
\(648\) | 7.27874 | + | 5.28832i | 0.285936 | + | 0.207745i | ||||
\(649\) | 40.9519 | 1.60750 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.55678 | 0.100208 | ||||||||
\(652\) | 51.2280 | + | 37.2193i | 2.00624 | + | 1.45762i | ||||
\(653\) | −3.45405 | − | 10.6305i | −0.135167 | − | 0.416002i | 0.860449 | − | 0.509537i | \(-0.170183\pi\) |
−0.995616 | + | 0.0935349i | \(0.970183\pi\) | |||||||
\(654\) | 13.9560 | + | 42.9521i | 0.545722 | + | 1.67956i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.23252 | − | 19.1817i | 0.243339 | − | 0.748920i | ||||
\(657\) | 9.78873 | 0.381895 | ||||||||
\(658\) | 1.74378 | − | 5.36681i | 0.0679797 | − | 0.209220i | ||||
\(659\) | −10.9010 | + | 7.92006i | −0.424644 | + | 0.308522i | −0.779503 | − | 0.626398i | \(-0.784529\pi\) |
0.354860 | + | 0.934919i | \(0.384529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8195 | + | 13.6732i | 0.731993 | + | 0.531824i | 0.890193 | − | 0.455583i | \(-0.150569\pi\) |
−0.158200 | + | 0.987407i | \(0.550569\pi\) | |||||||
\(662\) | 8.46556 | − | 6.15059i | 0.329023 | − | 0.239049i | ||||
\(663\) | −0.777821 | + | 0.565120i | −0.0302081 | + | 0.0219474i | ||||
\(664\) | −85.0921 | − | 61.8230i | −3.30221 | − | 2.39920i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.23515 | + | 1.62393i | −0.0866102 | + | 0.0629260i | ||||
\(667\) | −5.83880 | + | 17.9700i | −0.226079 | + | 0.695801i | ||||
\(668\) | 31.9132 | 1.23476 | ||||||||
\(669\) | 0.104795 | − | 0.322527i | 0.00405162 | − | 0.0124696i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.124748 | − | 0.383934i | −0.00481584 | − | 0.0148216i | ||||
\(672\) | −2.77349 | − | 8.53592i | −0.106990 | − | 0.329280i | ||||
\(673\) | 15.2412 | + | 11.0734i | 0.587507 | + | 0.426849i | 0.841423 | − | 0.540378i | \(-0.181719\pi\) |
−0.253916 | + | 0.967226i | \(0.581719\pi\) | |||||||
\(674\) | 47.3215 | 1.82276 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −67.5268 | −2.59719 | ||||||||
\(677\) | −34.1761 | − | 24.8304i | −1.31350 | − | 0.954310i | −0.999989 | − | 0.00472433i | \(-0.998496\pi\) |
−0.313507 | − | 0.949586i | \(-0.601504\pi\) | |||||||
\(678\) | −9.84828 | − | 30.3099i | −0.378221 | − | 1.16404i | ||||
\(679\) | 1.22867 | + | 3.78147i | 0.0471521 | + | 0.145119i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.552667 | + | 1.70093i | −0.0211782 | + | 0.0651799i | ||||
\(682\) | 46.8100 | 1.79245 | ||||||||
\(683\) | −15.1264 | + | 46.5544i | −0.578797 | + | 1.78135i | 0.0440734 | + | 0.999028i | \(0.485966\pi\) |
−0.622870 | + | 0.782325i | \(0.714034\pi\) | |||||||
\(684\) | −16.1106 | + | 11.7050i | −0.616004 | + | 0.447553i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.1881 | + | 10.3083i | 0.541705 | + | 0.393572i | ||||
\(687\) | −22.6389 | + | 16.4481i | −0.863729 | + | 0.627536i | ||||
\(688\) | 74.5635 | − | 54.1735i | 2.84271 | − | 2.06535i | ||||
\(689\) | 3.21438 | + | 2.33538i | 0.122458 | + | 0.0889710i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.4813 | − | 8.34168i | 0.436771 | − | 0.317332i | −0.347580 | − | 0.937650i | \(-0.612996\pi\) |
0.784350 | + | 0.620318i | \(0.212996\pi\) | |||||||
\(692\) | −28.5043 | + | 87.7273i | −1.08357 | + | 3.33489i | ||||
\(693\) | 1.49623 | 0.0568371 | ||||||||
\(694\) | −19.3139 | + | 59.4420i | −0.733145 | + | 2.25639i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −23.1438 | − | 71.2291i | −0.877262 | − | 2.69993i | ||||
\(697\) | 0.776250 | + | 2.38905i | 0.0294026 | + | 0.0904918i | ||||
\(698\) | −20.4203 | − | 14.8362i | −0.772920 | − | 0.561559i | ||||
\(699\) | −6.77400 | −0.256216 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.00786 | −0.340222 | −0.170111 | − | 0.985425i | \(-0.554413\pi\) | ||||
−0.170111 | + | 0.985425i | \(0.554413\pi\) | |||||||
\(702\) | 1.23366 | + | 0.896304i | 0.0465614 | + | 0.0338288i | ||||
\(703\) | −1.17985 | − | 3.63122i | −0.0444990 | − | 0.136954i | ||||
\(704\) | −23.8389 | − | 73.3687i | −0.898464 | − | 2.76519i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.7177 | − | 82.2287i | 1.00553 | − | 3.09472i | ||||
\(707\) | 2.74334 | 0.103174 | ||||||||
\(708\) | 21.1786 | − | 65.1811i | 0.795942 | − | 2.44966i | ||||
\(709\) | −40.2076 | + | 29.2126i | −1.51003 | + | 1.09710i | −0.543865 | + | 0.839173i | \(0.683040\pi\) |
−0.966164 | + | 0.257928i | \(0.916960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.84687 | + | 2.79491i | 0.144269 | + | 0.104817i | ||||
\(712\) | −45.1318 | + | 32.7901i | −1.69138 | + | 1.22886i | ||||
\(713\) | −9.98321 | + | 7.25323i | −0.373874 | + | 0.271636i | ||||
\(714\) | 1.75705 | + | 1.27657i | 0.0657560 | + | 0.0477745i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −45.5585 | + | 33.1002i | −1.70260 | + | 1.23701i | ||||
\(717\) | 2.00346 | − | 6.16603i | 0.0748207 | − | 0.230274i | ||||
\(718\) | 25.9528 | 0.968549 | ||||||||
\(719\) | −0.660387 | + | 2.03246i | −0.0246283 | + | 0.0757981i | −0.962615 | − | 0.270872i | \(-0.912688\pi\) |
0.937987 | + | 0.346671i | \(0.112688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.04614 | − | 6.29738i | −0.0762023 | − | 0.234527i | ||||
\(722\) | 4.19130 | + | 12.8995i | 0.155984 | + | 0.480070i | ||||
\(723\) | −6.02602 | − | 4.37816i | −0.224110 | − | 0.162825i | ||||
\(724\) | 63.7855 | 2.37057 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.37672 | −0.0882083 | ||||||||
\(727\) | −33.5446 | − | 24.3716i | −1.24410 | − | 0.903891i | −0.246235 | − | 0.969210i | \(-0.579193\pi\) |
−0.997864 | + | 0.0653195i | \(0.979193\pi\) | |||||||
\(728\) | −0.736718 | − | 2.26739i | −0.0273046 | − | 0.0840349i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.54723 | + | 10.9172i | −0.131199 | + | 0.403789i | ||||
\(732\) | −0.675604 | −0.0249710 | ||||||||
\(733\) | −10.0496 | + | 30.9293i | −0.371189 | + | 1.14240i | 0.574826 | + | 0.818276i | \(0.305070\pi\) |
−0.946014 | + | 0.324125i | \(0.894930\pi\) | |||||||
\(734\) | −2.33013 | + | 1.69294i | −0.0860067 | + | 0.0624875i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.0446 | + | 25.4614i | 1.29176 | + | 0.938518i | ||||
\(737\) | 7.19317 | − | 5.22614i | 0.264964 | − | 0.192507i | ||||
\(738\) | 3.22323 | − | 2.34181i | 0.118649 | − | 0.0862034i | ||||
\(739\) | 28.5724 | + | 20.7591i | 1.05105 | + | 0.763635i | 0.972413 | − | 0.233268i | \(-0.0749419\pi\) |
0.0786411 | + | 0.996903i | \(0.474942\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.70487 | + | 1.23866i | −0.0626300 | + | 0.0455034i | ||||
\(742\) | 2.77349 | − | 8.53592i | 0.101818 | − | 0.313363i | ||||
\(743\) | 36.0897 | 1.32400 | 0.662001 | − | 0.749503i | \(-0.269708\pi\) | ||||
0.662001 | + | 0.749503i | \(0.269708\pi\) | |||||||
\(744\) | 15.1149 | − | 46.5188i | 0.554139 | − | 1.70546i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.44579 | − | 10.6051i | −0.126159 | − | 0.388279i | ||||
\(747\) | −3.61256 | − | 11.1183i | −0.132177 | − | 0.406798i | ||||
\(748\) | 23.3845 | + | 16.9898i | 0.855022 | + | 0.621210i | ||||
\(749\) | −4.05021 | −0.147991 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.62810 | −0.168882 | −0.0844409 | − | 0.996428i | \(-0.526910\pi\) | ||||
−0.0844409 | + | 0.996428i | \(0.526910\pi\) | |||||||
\(752\) | −49.1411 | − | 35.7031i | −1.79199 | − | 1.30196i | ||||
\(753\) | 1.42215 | + | 4.37692i | 0.0518259 | + | 0.159504i | ||||
\(754\) | −3.92258 | − | 12.0725i | −0.142852 | − | 0.439653i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.773789 | − | 2.38148i | 0.0281424 | − | 0.0866135i | ||||
\(757\) | −14.6243 | −0.531530 | −0.265765 | − | 0.964038i | \(-0.585625\pi\) | ||||
−0.265765 | + | 0.964038i | \(0.585625\pi\) | |||||||
\(758\) | −8.66109 | + | 26.6561i | −0.314585 | + | 0.968193i | ||||
\(759\) | −5.84219 | + | 4.24460i | −0.212058 | + | 0.154069i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.86133 | − | 7.16467i | −0.357473 | − | 0.259719i | 0.394524 | − | 0.918885i | \(-0.370909\pi\) |
−0.751997 | + | 0.659166i | \(0.770909\pi\) | |||||||
\(762\) | 3.89472 | − | 2.82968i | 0.141091 | − | 0.102509i | ||||
\(763\) | 6.34920 | − | 4.61296i | 0.229856 | − | 0.167000i | ||||
\(764\) | −78.6799 | − | 57.1643i | −2.84654 | − | 2.06813i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.62597 | + | 1.90788i | −0.0948801 | + | 0.0689344i | ||||
\(767\) | 2.24119 | − | 6.89767i | 0.0809246 | − | 0.249060i | ||||
\(768\) | −25.8083 | −0.931276 | ||||||||
\(769\) | 4.26323 | − | 13.1209i | 0.153736 | − | 0.473150i | −0.844295 | − | 0.535879i | \(-0.819980\pi\) |
0.998031 | + | 0.0627287i | \(0.0199803\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.79071 | − | 5.51123i | −0.0644908 | − | 0.198482i | ||||
\(772\) | −41.4726 | − | 127.640i | −1.49263 | − | 4.59385i | ||||
\(773\) | 18.3274 | + | 13.3156i | 0.659190 | + | 0.478929i | 0.866389 | − | 0.499369i | \(-0.166435\pi\) |
−0.207199 | + | 0.978299i | \(0.566435\pi\) | |||||||
\(774\) | 18.2063 | 0.654411 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 76.0647 | 2.73056 | ||||||||
\(777\) | 0.388409 | + | 0.282196i | 0.0139341 | + | 0.0101237i | ||||
\(778\) | −10.5411 | − | 32.4422i | −0.377917 | − | 1.16311i | ||||
\(779\) | 1.70143 | + | 5.23646i | 0.0609600 | + | 0.187616i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.7750 | + | 48.5504i | −0.564473 | + | 1.73727i | ||||
\(782\) | −10.4820 | −0.374837 | ||||||||
\(783\) | 2.57238 | − | 7.91697i | 0.0919294 | − | 0.282929i | ||||
\(784\) | 75.1355 | − | 54.5891i | 2.68341 | − | 1.94961i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.9587 | + | 9.41507i | 0.462223 | + | 0.335824i | ||||
\(787\) | −38.5785 | + | 28.0289i | −1.37518 | + | 0.999123i | −0.377863 | + | 0.925862i | \(0.623341\pi\) |
−0.997313 | + | 0.0732618i | \(0.976659\pi\) | |||||||
\(788\) | 52.0878 | − | 37.8440i | 1.85555 | − | 1.34814i | ||||
\(789\) | −11.5680 | − | 8.40467i | −0.411833 | − | 0.299214i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.48043 | + | 3.25522i | −0.159306 | + | 0.115742i | ||||
\(792\) | 8.84525 | − | 27.2229i | 0.314302 | − | 0.967323i | ||||
\(793\) | −0.0714945 | −0.00253884 | ||||||||
\(794\) | −1.09837 | + | 3.38044i | −0.0389797 | + | 0.119967i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.895774 | − | 2.75691i | −0.0317499 | − | 0.0977160i | ||||
\(797\) | −8.40931 | − | 25.8812i | −0.297873 | − | 0.916759i | −0.982241 | − | 0.187622i | \(-0.939922\pi\) |
0.684368 | − | 0.729137i | \(-0.260078\pi\) | |||||||
\(798\) | 3.85120 | + | 2.79806i | 0.136331 | + | 0.0990504i | ||||
\(799\) | 7.56529 | 0.267641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.20049 | −0.219083 | ||||||||
\(802\) | 35.2600 | + | 25.6179i | 1.24507 | + | 0.904599i | ||||
\(803\) | −9.62360 | − | 29.6184i | −0.339610 | − | 1.04521i | ||||
\(804\) | −4.59818 | − | 14.1518i | −0.162165 | − | 0.499094i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.56179 | − | 7.88437i | 0.0902351 | − | 0.277715i | ||||
\(807\) | 19.2205 | 0.676592 | ||||||||
\(808\) | 16.2178 | − | 49.9132i | 0.570540 | − | 1.75594i | ||||
\(809\) | 15.8693 | − | 11.5297i | 0.557933 | − | 0.405362i | −0.272769 | − | 0.962080i | \(-0.587939\pi\) |
0.830702 | + | 0.556717i | \(0.187939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0468 | − | 12.3852i | −0.598594 | − | 0.434904i | 0.246786 | − | 0.969070i | \(-0.420626\pi\) |
−0.845380 | + | 0.534166i | \(0.820626\pi\) | |||||||
\(812\) | −16.8636 | + | 12.2521i | −0.591796 | + | 0.429965i | ||||
\(813\) | −18.8042 | + | 13.6620i | −0.659492 | + | 0.479149i | ||||
\(814\) | 7.11107 | + | 5.16650i | 0.249243 | + | 0.181086i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18.9131 | − | 13.7412i | 0.662090 | − | 0.481037i | ||||
\(817\) | −7.77501 | + | 23.9290i | −0.272013 | + | 0.837170i | ||||
\(818\) | −57.2667 | −2.00228 | ||||||||
\(819\) | 0.0818847 | − | 0.252015i | 0.00286128 | − | 0.00880613i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.8039 | + | 39.4062i | 0.446858 | + | 1.37529i | 0.880433 | + | 0.474170i | \(0.157252\pi\) |
−0.433575 | + | 0.901117i | \(0.642748\pi\) | |||||||
\(822\) | 4.27866 | + | 13.1684i | 0.149235 | + | 0.459299i | ||||
\(823\) | 4.88721 | + | 3.55077i | 0.170358 | + | 0.123772i | 0.669697 | − | 0.742634i | \(-0.266424\pi\) |
−0.499340 | + | 0.866406i | \(0.666424\pi\) | |||||||
\(824\) | −126.673 | −4.41285 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3833 | −0.570047 | ||||||||
\(827\) | −2.42188 | − | 1.75960i | −0.0842172 | − | 0.0611874i | 0.544880 | − | 0.838514i | \(-0.316575\pi\) |
−0.629097 | + | 0.777327i | \(0.716575\pi\) | |||||||
\(828\) | 3.73458 | + | 11.4938i | 0.129786 | + | 0.399439i | ||||
\(829\) | 8.29802 | + | 25.5387i | 0.288202 | + | 0.886995i | 0.985421 | + | 0.170136i | \(0.0544208\pi\) |
−0.697218 | + | 0.716859i | \(0.745579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.76469 | − | 20.8196i | 0.234664 | − | 0.722223i | ||||
\(832\) | −13.6624 | −0.473658 | ||||||||
\(833\) | −3.57444 | + | 11.0010i | −0.123847 | + | 0.381162i | ||||
\(834\) | 18.0374 | − | 13.1050i | 0.624585 | − | 0.453787i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 51.2555 | + | 37.2393i | 1.77271 | + | 1.28795i | ||||
\(837\) | 4.39827 | − | 3.19553i | 0.152026 | − | 0.110454i | ||||
\(838\) | −14.6060 | + | 10.6119i | −0.504555 | + | 0.366581i | ||||
\(839\) | −10.0800 | − | 7.32352i | −0.347999 | − | 0.252836i | 0.400030 | − | 0.916502i | \(-0.369000\pi\) |
−0.748029 | + | 0.663666i | \(0.769000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32.5998 | + | 23.6851i | −1.12413 | + | 0.816729i | ||||
\(842\) | −22.8297 | + | 70.2624i | −0.786762 | + | 2.42140i | ||||
\(843\) | −27.1138 | −0.933850 | ||||||||
\(844\) | −5.13683 | + | 15.8095i | −0.176817 | + | 0.544186i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.70785 | − | 11.4116i | −0.127479 | − | 0.392339i | ||||
\(847\) | 0.127627 | + | 0.392797i | 0.00438533 | + | 0.0134967i | ||||
\(848\) | −78.1590 | − | 56.7859i | −2.68399 | − | 1.95003i | ||||
\(849\) | 16.3074 | 0.559668 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.31714 | −0.0794304 | ||||||||
\(852\) | 69.1171 | + | 50.2165i | 2.36791 | + | 1.72039i | ||||
\(853\) | 1.76058 | + | 5.41851i | 0.0602811 | + | 0.185526i | 0.976662 | − | 0.214780i | \(-0.0689036\pi\) |
−0.916381 | + | 0.400307i | \(0.868904\pi\) | |||||||
\(854\) | 0.0499068 | + | 0.153597i | 0.00170778 | + | 0.00525599i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.9436 | + | 73.6907i | −0.818374 | + | 2.51870i | ||||
\(857\) | 7.41982 | 0.253456 | 0.126728 | − | 0.991937i | \(-0.459552\pi\) | ||||
0.126728 | + | 0.991937i | \(0.459552\pi\) | |||||||
\(858\) | 1.49916 | − | 4.61394i | 0.0511805 | − | 0.157517i | ||||
\(859\) | 4.59726 | − | 3.34011i | 0.156857 | − | 0.113963i | −0.506588 | − | 0.862188i | \(-0.669094\pi\) |
0.663445 | + | 0.748225i | \(0.269094\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.560112 | − | 0.406945i | −0.0190886 | − | 0.0138687i | ||||
\(862\) | 26.9251 | − | 19.5622i | 0.917073 | − | 0.666293i | ||||
\(863\) | −27.9715 | + | 20.3225i | −0.952160 | + | 0.691785i | −0.951317 | − | 0.308215i | \(-0.900268\pi\) |
−0.000843465 | 1.00000i | \(0.500268\pi\) | ||||||||
\(864\) | −15.4395 | − | 11.2174i | −0.525261 | − | 0.381624i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 74.1037 | − | 53.8395i | 2.51815 | − | 1.82954i | ||||
\(867\) | 4.35353 | − | 13.3988i | 0.147854 | − | 0.455047i | ||||
\(868\) | −13.6133 | −0.462066 | ||||||||
\(869\) | 4.67478 | − | 14.3875i | 0.158581 | − | 0.488062i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.486594 | − | 1.49758i | −0.0164876 | − | 0.0507437i | ||||
\(872\) | −46.3952 | − | 142.790i | −1.57114 | − | 4.83547i | ||||
\(873\) | 6.83978 | + | 4.96939i | 0.231491 | + | 0.168188i | ||||
\(874\) | −22.9751 | −0.777145 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −52.1191 | −1.76094 | ||||||||
\(877\) | −4.28790 | − | 3.11534i | −0.144792 | − | 0.105197i | 0.513031 | − | 0.858370i | \(-0.328523\pi\) |
−0.657823 | + | 0.753173i | \(0.728523\pi\) | |||||||
\(878\) | 17.5336 | + | 53.9629i | 0.591730 | + | 1.82116i | ||||
\(879\) | 1.68849 | + | 5.19664i | 0.0569514 | + | 0.175278i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.35251 | − | 7.24028i | 0.0792580 | − | 0.243931i | −0.903575 | − | 0.428431i | \(-0.859067\pi\) |
0.982833 | + | 0.184500i | \(0.0590665\pi\) | |||||||
\(882\) | 18.3460 | 0.617740 | ||||||||
\(883\) | 16.3264 | − | 50.2476i | 0.549428 | − | 1.69096i | −0.160795 | − | 0.986988i | \(-0.551406\pi\) |
0.710223 | − | 0.703977i | \(-0.248594\pi\) | |||||||
\(884\) | 4.14143 | − | 3.00892i | 0.139291 | − | 0.101201i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.2431 | − | 9.62166i | −0.444910 | − | 0.323246i | ||||
\(887\) | 6.23572 | − | 4.53052i | 0.209375 | − | 0.152120i | −0.478156 | − | 0.878275i | \(-0.658695\pi\) |
0.687531 | + | 0.726155i | \(0.258695\pi\) | |||||||
\(888\) | 7.43051 | − | 5.39858i | 0.249352 | − | 0.181165i | ||||
\(889\) | −0.676800 | − | 0.491724i | −0.0226991 | − | 0.0164919i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.57387 | − | 1.87003i | 0.0862279 | − | 0.0626482i | ||||
\(892\) | −0.557972 | + | 1.71726i | −0.0186823 | + | 0.0574981i | ||||
\(893\) | 16.5820 | 0.554896 | ||||||||
\(894\) | −8.41207 | + | 25.8897i | −0.281342 | + | 0.865881i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.99006 | + | 12.2801i | 0.133299 | + | 0.410251i | ||||
\(897\) | 0.395205 | + | 1.21631i | 0.0131955 | + | 0.0406116i | ||||
\(898\) | 34.1334 | + | 24.7994i | 1.13905 | + | 0.827566i | ||||
\(899\) | −45.2560 | −1.50937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0326 | 0.400864 | ||||||||
\(902\) | −10.2546 | − | 7.45043i | −0.341442 | − | 0.248072i | ||||
\(903\) | −0.977659 | − | 3.00892i | −0.0325344 | − | 0.100131i | ||||
\(904\) | 32.7396 | + | 100.762i | 1.08890 | + | 3.35130i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.0198 | + | 30.8379i | −0.332887 | + | 1.02452i | ||||
\(907\) | 11.3735 | 0.377650 | 0.188825 | − | 0.982011i | \(-0.439532\pi\) | ||||
0.188825 | + | 0.982011i | \(0.439532\pi\) | |||||||
\(908\) | 2.94262 | − | 9.05644i | 0.0976542 | − | 0.300549i | ||||
\(909\) | 4.71920 | − | 3.42870i | 0.156526 | − | 0.113723i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0393 | + | 10.9267i | 0.498275 | + | 0.362018i | 0.808358 | − | 0.588691i | \(-0.200357\pi\) |
−0.310082 | + | 0.950710i | \(0.600357\pi\) | |||||||
\(912\) | 41.4547 | − | 30.1186i | 1.37270 | − | 0.997328i | ||||
\(913\) | −30.0898 | + | 21.8615i | −0.995827 | + | 0.723511i | ||||
\(914\) | 5.47795 | + | 3.97997i | 0.181195 | + | 0.131646i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 120.539 | − | 87.5764i | 3.98271 | − | 2.89361i | ||||
\(917\) | 0.860143 | − | 2.64725i | 0.0284044 | − | 0.0874199i | ||||
\(918\) | 4.61803 | 0.152418 | ||||||||
\(919\) | 2.36336 | − | 7.27367i | 0.0779600 | − | 0.239936i | −0.904480 | − | 0.426517i | \(-0.859741\pi\) |
0.982440 | + | 0.186581i | \(0.0597405\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.61895 | − | 20.3710i | −0.218102 | − | 0.671249i | ||||
\(922\) | 0.128761 | + | 0.396286i | 0.00424052 | + | 0.0130510i | ||||
\(923\) | 7.31418 | + | 5.31407i | 0.240749 | + | 0.174915i | ||||
\(924\) | −7.96652 | −0.262079 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.4822 | −1.03457 | ||||||||
\(927\) | −11.3905 | − | 8.27566i | −0.374112 | − | 0.271808i | ||||
\(928\) | 49.0918 | + | 151.089i | 1.61152 | + | 4.95974i | ||||
\(929\) | −9.56366 | − | 29.4339i | −0.313774 | − | 0.965696i | −0.976256 | − | 0.216619i | \(-0.930497\pi\) |
0.662483 | − | 0.749077i | \(-0.269503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.83466 | + | 24.1126i | −0.256770 | + | 0.790258i | ||||
\(932\) | 36.0675 | 1.18143 | ||||||||
\(933\) | 0.881316 | − | 2.71241i | 0.0288530 | − | 0.0888003i | ||||
\(934\) | −1.02971 | + | 0.748125i | −0.0336930 | + | 0.0244794i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.10116 | − | 2.97967i | −0.134051 | − | 0.0973936i | ||||
\(937\) | 25.3784 | − | 18.4385i | 0.829077 | − | 0.602360i | −0.0902212 | − | 0.995922i | \(-0.528757\pi\) |
0.919298 | + | 0.393562i | \(0.128757\pi\) | |||||||
\(938\) | −2.87771 | + | 2.09078i | −0.0939605 | + | 0.0682663i | ||||
\(939\) | −11.6802 | − | 8.48616i | −0.381169 | − | 0.276935i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.92710 | − | 2.12666i | 0.0954208 | − | 0.0693273i | −0.539052 | − | 0.842273i | \(-0.681217\pi\) |
0.634473 | + | 0.772945i | \(0.281217\pi\) | |||||||
\(942\) | −16.3884 | + | 50.4383i | −0.533963 | + | 1.64337i | ||||
\(943\) | 3.34146 | 0.108813 | ||||||||
\(944\) | −54.4955 | + | 167.720i | −1.77368 | + | 5.45882i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.8992 | − | 55.0879i | −0.581952 | − | 1.79106i | ||||
\(947\) | 3.49856 | + | 10.7675i | 0.113688 | + | 0.349896i | 0.991671 | − | 0.128796i | \(-0.0411112\pi\) |
−0.877983 | + | 0.478692i | \(0.841111\pi\) | |||||||
\(948\) | −20.4823 | − | 14.8812i | −0.665233 | − | 0.483320i | ||||
\(949\) | −5.51540 | −0.179038 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.6102 | 0.733187 | ||||||||
\(952\) | −5.84113 | − | 4.24383i | −0.189312 | − | 0.137543i | ||||
\(953\) | 5.32071 | + | 16.3755i | 0.172355 | + | 0.530453i | 0.999503 | − | 0.0315307i | \(-0.0100382\pi\) |
−0.827148 | + | 0.561984i | \(0.810038\pi\) | |||||||
\(954\) | −5.89735 | − | 18.1502i | −0.190934 | − | 0.587633i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.6672 | + | 32.8304i | −0.345003 | + | 1.06181i | ||||
\(957\) | −26.4839 | −0.856102 | ||||||||
\(958\) | −10.3798 | + | 31.9458i | −0.335357 | + | 1.03212i | ||||
\(959\) | 1.94656 | − | 1.41426i | 0.0628576 | − | 0.0456687i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.16811 | + | 0.848680i | 0.0376809 | + | 0.0273768i | ||||
\(962\) | 1.25938 | − | 0.914994i | 0.0406041 | − | 0.0295006i | ||||
\(963\) | −6.96731 | + | 5.06205i | −0.224519 | + | 0.163122i | ||||
\(964\) | 32.0849 | + | 23.3110i | 1.03339 | + | 0.750798i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.33723 | − | 1.69810i | 0.0751992 | − | 0.0546354i | ||||
\(967\) | 9.24157 | − | 28.4426i | 0.297189 | − | 0.914653i | −0.685289 | − | 0.728272i | \(-0.740324\pi\) |
0.982477 | − | 0.186382i | \(-0.0596761\pi\) | |||||||
\(968\) | 7.90115 | 0.253953 | ||||||||
\(969\) | −1.97214 | + | 6.06961i | −0.0633541 | + | 0.194984i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.78497 | − | 23.9597i | −0.249832 | − | 0.768902i | −0.994804 | − | 0.101807i | \(-0.967537\pi\) |
0.744973 | − | 0.667095i | \(-0.232463\pi\) | |||||||
\(972\) | −1.64533 | − | 5.06380i | −0.0527739 | − | 0.162422i | ||||
\(973\) | −3.13443 | − | 2.27729i | −0.100485 | − | 0.0730067i | ||||
\(974\) | 93.5443 | 2.99735 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.73842 | 0.0556455 | ||||||||
\(977\) | 46.1907 | + | 33.5595i | 1.47777 | + | 1.07366i | 0.978266 | + | 0.207352i | \(0.0664845\pi\) |
0.499504 | + | 0.866311i | \(0.333515\pi\) | |||||||
\(978\) | −9.94597 | − | 30.6106i | −0.318037 | − | 0.978818i | ||||
\(979\) | 6.09589 | + | 18.7612i | 0.194826 | + | 0.599611i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.15673 | − | 15.8708i | 0.164642 | − | 0.506715i | ||||
\(982\) | 67.2957 | 2.14749 | ||||||||
\(983\) | 8.16325 | − | 25.1239i | 0.260367 | − | 0.801328i | −0.732357 | − | 0.680921i | \(-0.761580\pi\) |
0.992725 | − | 0.120407i | \(-0.0384201\pi\) | |||||||
\(984\) | −10.7153 | + | 7.78512i | −0.341591 | + | 0.248181i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.1005 | − | 22.5958i | −0.990442 | − | 0.719598i | ||||
\(987\) | −1.68687 | + | 1.22558i | −0.0536936 | + | 0.0390107i | ||||
\(988\) | 9.07741 | − | 6.59513i | 0.288791 | − | 0.209819i | ||||
\(989\) | 12.3533 | + | 8.97517i | 0.392811 | + | 0.285394i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2252 | − | 13.2414i | 0.578943 | − | 0.420626i | −0.259400 | − | 0.965770i | \(-0.583525\pi\) |
0.838343 | + | 0.545144i | \(0.183525\pi\) | |||||||
\(992\) | −32.0612 | + | 98.6744i | −1.01795 | + | 3.13291i | ||||
\(993\) | −3.86645 | −0.122698 | ||||||||
\(994\) | 6.31096 | − | 19.4231i | 0.200171 | − | 0.616064i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19.2347 | + | 59.1983i | 0.609475 | + | 1.87577i | ||||
\(997\) | 7.44865 | + | 22.9246i | 0.235901 | + | 0.726029i | 0.997001 | + | 0.0773940i | \(0.0246599\pi\) |
−0.761099 | + | 0.648635i | \(0.775340\pi\) | |||||||
\(998\) | 27.5958 | + | 20.0495i | 0.873529 | + | 0.634656i | ||||
\(999\) | 1.02085 | 0.0322983 |
(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 | 375.2.g.b.76.2 | 8 | ||
5.2 | odd | 4 | 375.2.i.b.49.1 | 16 | |||
5.3 | odd | 4 | 375.2.i.b.49.4 | 16 | |||
5.4 | even | 2 | 75.2.g.b.16.1 | ✓ | 8 | ||
15.14 | odd | 2 | 225.2.h.c.91.2 | 8 | |||
25.2 | odd | 20 | 375.2.i.b.199.4 | 16 | |||
25.6 | even | 5 | 1875.2.a.e.1.1 | 4 | |||
25.8 | odd | 20 | 1875.2.b.c.1249.8 | 8 | |||
25.11 | even | 5 | inner | 375.2.g.b.301.2 | 8 | ||
25.14 | even | 10 | 75.2.g.b.61.1 | yes | 8 | ||
25.17 | odd | 20 | 1875.2.b.c.1249.1 | 8 | |||
25.19 | even | 10 | 1875.2.a.h.1.4 | 4 | |||
25.23 | odd | 20 | 375.2.i.b.199.1 | 16 | |||
75.14 | odd | 10 | 225.2.h.c.136.2 | 8 | |||
75.44 | odd | 10 | 5625.2.a.i.1.1 | 4 | |||
75.56 | odd | 10 | 5625.2.a.n.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.16.1 | ✓ | 8 | 5.4 | even | 2 | ||
75.2.g.b.61.1 | yes | 8 | 25.14 | even | 10 | ||
225.2.h.c.91.2 | 8 | 15.14 | odd | 2 | |||
225.2.h.c.136.2 | 8 | 75.14 | odd | 10 | |||
375.2.g.b.76.2 | 8 | 1.1 | even | 1 | trivial | ||
375.2.g.b.301.2 | 8 | 25.11 | even | 5 | inner | ||
375.2.i.b.49.1 | 16 | 5.2 | odd | 4 | |||
375.2.i.b.49.4 | 16 | 5.3 | odd | 4 | |||
375.2.i.b.199.1 | 16 | 25.23 | odd | 20 | |||
375.2.i.b.199.4 | 16 | 25.2 | odd | 20 | |||
1875.2.a.e.1.1 | 4 | 25.6 | even | 5 | |||
1875.2.a.h.1.4 | 4 | 25.19 | even | 10 | |||
1875.2.b.c.1249.1 | 8 | 25.17 | odd | 20 | |||
1875.2.b.c.1249.8 | 8 | 25.8 | odd | 20 | |||
5625.2.a.i.1.1 | 4 | 75.44 | odd | 10 | |||
5625.2.a.n.1.4 | 4 | 75.56 | odd | 10 |