Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,2,Mod(16,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, 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("75.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.g (of order \(5\), degree \(4\), 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: | \(0.598878015160\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(1.33631 - 0.462894i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.61 |
Dual form | 75.2.g.b.16.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18949 | + | 1.59076i | −1.54821 | + | 1.12484i | −0.603290 | + | 0.797522i | \(0.706144\pi\) |
−0.944915 | + | 0.327315i | \(0.893856\pi\) | |||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 1.64533 | − | 5.06380i | 0.822664 | − | 2.53190i | ||||
\(5\) | 0.336312 | − | 2.21063i | 0.150403 | − | 0.988625i | ||||
\(6\) | 0.836312 | + | 2.57390i | 0.341423 | + | 1.05079i | ||||
\(7\) | 0.470294 | 0.177754 | 0.0888772 | − | 0.996043i | \(-0.471672\pi\) | ||||
0.0888772 | + | 0.996043i | \(0.471672\pi\) | |||||||
\(8\) | 2.78023 | + | 8.55667i | 0.982960 | + | 3.02524i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 2.78023 | + | 5.37515i | 0.879187 | + | 1.69977i | ||||
\(11\) | 2.57387 | − | 1.87003i | 0.776051 | − | 0.563834i | −0.127740 | − | 0.991808i | \(-0.540772\pi\) |
0.903791 | + | 0.427974i | \(0.140772\pi\) | |||||||
\(12\) | −4.30753 | − | 3.12960i | −1.24348 | − | 0.903438i | ||||
\(13\) | −0.455836 | − | 0.331184i | −0.126426 | − | 0.0918540i | 0.522775 | − | 0.852471i | \(-0.324897\pi\) |
−0.649201 | + | 0.760617i | \(0.724897\pi\) | |||||||
\(14\) | −1.02971 | + | 0.748125i | −0.275200 | + | 0.199945i | ||||
\(15\) | −1.99851 | − | 1.00297i | −0.516013 | − | 0.258967i | ||||
\(16\) | −11.0839 | − | 8.05289i | −2.77096 | − | 2.01322i | ||||
\(17\) | −0.527295 | − | 1.62285i | −0.127888 | − | 0.393598i | 0.866528 | − | 0.499128i | \(-0.166346\pi\) |
−0.994416 | + | 0.105530i | \(0.966346\pi\) | |||||||
\(18\) | 2.70636 | 0.637896 | ||||||||
\(19\) | 1.15575 | + | 3.55705i | 0.265148 | + | 0.816043i | 0.991659 | + | 0.128888i | \(0.0411406\pi\) |
−0.726511 | + | 0.687155i | \(0.758859\pi\) | |||||||
\(20\) | −10.6409 | − | 5.34023i | −2.37937 | − | 1.19411i | ||||
\(21\) | 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 | \(-0.623953\pi\) |
0.762539 | + | 0.646942i | \(0.223953\pi\) | |||||||
\(24\) | 8.99702 | 1.83651 | ||||||||
\(25\) | −4.77379 | − | 1.48692i | −0.954758 | − | 0.297385i | ||||
\(26\) | 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 | 0.364631 | + | 0.931152i | \(0.381195\pi\) |
−0.842310 | + | 0.538993i | \(0.818805\pi\) | |||||||
\(30\) | 5.97122 | − | 0.983144i | 1.09019 | − | 0.179497i | ||||
\(31\) | 1.67999 | + | 5.17047i | 0.301735 | + | 0.928644i | 0.980876 | + | 0.194636i | \(0.0623526\pi\) |
−0.679141 | + | 0.734008i | \(0.737647\pi\) | |||||||
\(32\) | 19.0842 | 3.37364 | ||||||||
\(33\) | −0.983131 | − | 3.02577i | −0.171141 | − | 0.526718i | ||||
\(34\) | 3.73607 | + | 2.71441i | 0.640730 | + | 0.465518i | ||||
\(35\) | 0.158166 | − | 1.03965i | 0.0267349 | − | 0.175732i | ||||
\(36\) | −4.30753 | + | 3.12960i | −0.717921 | + | 0.521600i | ||||
\(37\) | −0.825886 | − | 0.600041i | −0.135775 | − | 0.0986462i | 0.517825 | − | 0.855487i | \(-0.326742\pi\) |
−0.653600 | + | 0.756841i | \(0.726742\pi\) | |||||||
\(38\) | −8.18892 | − | 5.94960i | −1.32842 | − | 0.965153i | ||||
\(39\) | −0.455836 | + | 0.331184i | −0.0729922 | + | 0.0530319i | ||||
\(40\) | 19.8507 | − | 3.26836i | 3.13867 | − | 0.516773i | ||||
\(41\) | −1.19098 | − | 0.865300i | −0.186000 | − | 0.135137i | 0.490889 | − | 0.871222i | \(-0.336672\pi\) |
−0.676889 | + | 0.736085i | \(0.736672\pi\) | |||||||
\(42\) | 0.393313 | + | 1.21049i | 0.0606895 | + | 0.186783i | ||||
\(43\) | 6.72721 | 1.02589 | 0.512945 | − | 0.858421i | \(-0.328554\pi\) | ||||
0.512945 | + | 0.858421i | \(0.328554\pi\) | |||||||
\(44\) | −5.23458 | − | 16.1104i | −0.789142 | − | 2.42873i | ||||
\(45\) | −1.57146 | + | 1.59076i | −0.234259 | + | 0.237136i | ||||
\(46\) | −1.89827 | + | 5.84226i | −0.279884 | + | 0.861395i | ||||
\(47\) | −1.37005 | + | 4.21658i | −0.199842 | + | 0.615052i | 0.800043 | + | 0.599942i | \(0.204810\pi\) |
−0.999886 | + | 0.0151095i | \(0.995190\pi\) | |||||||
\(48\) | −11.0839 | + | 8.05289i | −1.59982 | + | 1.16234i | ||||
\(49\) | −6.77882 | −0.968403 | ||||||||
\(50\) | 12.8175 | − | 4.33834i | 1.81267 | − | 0.613534i | ||||
\(51\) | −1.70636 | −0.238938 | ||||||||
\(52\) | −2.42705 | + | 1.76336i | −0.336571 | + | 0.244533i | ||||
\(53\) | −2.17907 | + | 6.70648i | −0.299318 | + | 0.921206i | 0.682419 | + | 0.730961i | \(0.260928\pi\) |
−0.981737 | + | 0.190244i | \(0.939072\pi\) | |||||||
\(54\) | 0.836312 | − | 2.57390i | 0.113808 | − | 0.350264i | ||||
\(55\) | −3.26832 | − | 6.31879i | −0.440700 | − | 0.852026i | ||||
\(56\) | 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 | 0.998703 | + | 0.0509138i | \(0.0162134\pi\) |
0.357038 | + | 0.934090i | \(0.383787\pi\) | |||||||
\(60\) | −8.36707 | + | 8.46984i | −1.08018 | + | 1.09345i | ||||
\(61\) | −0.102655 | + | 0.0745831i | −0.0131436 | + | 0.00954939i | −0.594338 | − | 0.804216i | \(-0.702586\pi\) |
0.581194 | + | 0.813765i | \(0.302586\pi\) | |||||||
\(62\) | −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 | ||||
\(65\) | −0.885429 | + | 0.896304i | −0.109824 | + | 0.111173i | ||||
\(66\) | 6.96582 | + | 5.06097i | 0.857434 | + | 0.622962i | ||||
\(67\) | −0.863607 | − | 2.65791i | −0.105506 | − | 0.324715i | 0.884343 | − | 0.466838i | \(-0.154607\pi\) |
−0.989849 | + | 0.142123i | \(0.954607\pi\) | |||||||
\(68\) | −9.08535 | −1.10176 | ||||||||
\(69\) | −0.701409 | − | 2.15871i | −0.0844397 | − | 0.259879i | ||||
\(70\) | 1.30753 | + | 2.52790i | 0.156279 | + | 0.302142i | ||||
\(71\) | 4.95838 | − | 15.2603i | 0.588451 | − | 1.81107i | 0.00350617 | − | 0.999994i | \(-0.498884\pi\) |
0.584945 | − | 0.811073i | \(-0.301116\pi\) | |||||||
\(72\) | 2.78023 | − | 8.55667i | 0.327653 | − | 1.00841i | ||||
\(73\) | 7.91925 | − | 5.75367i | 0.926878 | − | 0.673416i | −0.0183484 | − | 0.999832i | \(-0.505841\pi\) |
0.945226 | + | 0.326415i | \(0.105841\pi\) | |||||||
\(74\) | 2.76279 | 0.321168 | ||||||||
\(75\) | −2.88933 | + | 4.08066i | −0.333631 | + | 0.471194i | ||||
\(76\) | 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 | −0.999060 | − | 0.0433593i | \(-0.986194\pi\) |
0.833742 | + | 0.552154i | \(0.186194\pi\) | |||||||
\(80\) | −21.5296 | + | 21.7940i | −2.40708 | + | 2.43665i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 3.98413 | 0.439974 | ||||||||
\(83\) | 3.61256 | + | 11.1183i | 0.396530 | + | 1.22039i | 0.927763 | + | 0.373169i | \(0.121729\pi\) |
−0.531233 | + | 0.847226i | \(0.678271\pi\) | |||||||
\(84\) | −2.02580 | − | 1.47183i | −0.221033 | − | 0.160590i | ||||
\(85\) | −3.76485 | + | 0.619872i | −0.408356 | + | 0.0672346i | ||||
\(86\) | −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 | −0.289277 | − | 0.957246i | \(-0.593415\pi\) |
0.821003 | + | 0.570923i | \(0.193415\pi\) | |||||||
\(90\) | 0.910182 | − | 5.98277i | 0.0959416 | − | 0.630639i | ||||
\(91\) | −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 | ||||
\(95\) | 8.25202 | − | 1.35867i | 0.846639 | − | 0.139397i | ||||
\(96\) | 5.89735 | − | 18.1502i | 0.601895 | − | 1.85244i | ||||
\(97\) | 2.61256 | − | 8.04064i | 0.265265 | − | 0.816403i | −0.726367 | − | 0.687307i | \(-0.758793\pi\) |
0.991632 | − | 0.129096i | \(-0.0412074\pi\) | |||||||
\(98\) | 14.8422 | − | 10.7835i | 1.49929 | − | 1.08930i | ||||
\(99\) | −3.18148 | −0.319751 | ||||||||
\(100\) | −15.3839 | + | 21.7270i | −1.53839 | + | 2.17270i | ||||
\(101\) | −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 | 0.470718 | + | 0.882284i | \(0.343995\pi\) |
−0.899412 | + | 0.437101i | \(0.856005\pi\) | |||||||
\(104\) | 1.56651 | − | 4.82121i | 0.153609 | − | 0.472758i | ||||
\(105\) | −0.939888 | − | 0.471693i | −0.0917236 | − | 0.0460325i | ||||
\(106\) | −5.89735 | − | 18.1502i | −0.572801 | − | 1.76290i | ||||
\(107\) | −8.61207 | −0.832561 | −0.416280 | − | 0.909236i | \(-0.636666\pi\) | ||||
−0.416280 | + | 0.909236i | \(0.636666\pi\) | |||||||
\(108\) | 1.64533 | + | 5.06380i | 0.158322 | + | 0.487265i | ||||
\(109\) | −13.5005 | − | 9.80868i | −1.29311 | − | 0.939501i | −0.293249 | − | 0.956036i | \(-0.594736\pi\) |
−0.999863 | + | 0.0165355i | \(0.994736\pi\) | |||||||
\(110\) | 17.2076 | + | 8.63584i | 1.64068 | + | 0.823395i | ||||
\(111\) | −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 | \(-0.486857\pi\) |
−0.937490 | + | 0.348012i | \(0.886857\pi\) | |||||||
\(114\) | −8.18892 | + | 5.94960i | −0.766963 | + | 0.557231i | ||||
\(115\) | −2.33176 | − | 4.50810i | −0.217438 | − | 0.420383i | ||||
\(116\) | 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 | ||||
\(120\) | 3.02580 | − | 19.8891i | 0.276217 | − | 1.81562i | ||||
\(121\) | −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 | ||||||||
\(125\) | −4.89252 | + | 10.0530i | −0.437601 | + | 0.899169i | ||||
\(126\) | 1.27279 | 0.113389 | ||||||||
\(127\) | −1.43910 | + | 1.04557i | −0.127699 | + | 0.0927790i | −0.649801 | − | 0.760104i | \(-0.725148\pi\) |
0.522102 | + | 0.852883i | \(0.325148\pi\) | |||||||
\(128\) | 8.48418 | − | 26.1116i | 0.749903 | − | 2.30796i | ||||
\(129\) | 2.07882 | − | 6.39796i | 0.183030 | − | 0.563309i | ||||
\(130\) | 0.512837 | − | 3.37096i | 0.0449787 | − | 0.295653i | ||||
\(131\) | −1.82895 | − | 5.62892i | −0.159796 | − | 0.491801i | 0.838819 | − | 0.544410i | \(-0.183246\pi\) |
−0.998615 | + | 0.0526087i | \(0.983246\pi\) | |||||||
\(132\) | −16.9395 | −1.47439 | ||||||||
\(133\) | 0.543545 | + | 1.67286i | 0.0471313 | + | 0.145055i | ||||
\(134\) | 6.11895 | + | 4.44568i | 0.528597 | + | 0.384048i | ||||
\(135\) | 1.02729 | + | 1.98612i | 0.0884155 | + | 0.170938i | ||||
\(136\) | 12.4202 | − | 9.02378i | 1.06502 | − | 0.773783i | ||||
\(137\) | 4.13902 | + | 3.00717i | 0.353620 | + | 0.256920i | 0.750386 | − | 0.661000i | \(-0.229868\pi\) |
−0.396766 | + | 0.917920i | \(0.629868\pi\) | |||||||
\(138\) | 4.96973 | + | 3.61072i | 0.423051 | + | 0.307365i | ||||
\(139\) | 6.66482 | − | 4.84228i | 0.565303 | − | 0.410717i | −0.268093 | − | 0.963393i | \(-0.586393\pi\) |
0.833396 | + | 0.552676i | \(0.186393\pi\) | |||||||
\(140\) | −5.00433 | − | 2.51148i | −0.422943 | − | 0.212259i | ||||
\(141\) | 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 | ||||
\(145\) | 16.6364 | + | 8.34916i | 1.38158 | + | 0.693360i | ||||
\(146\) | −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 | \(0.635174\pi\) | |||||||
\(150\) | −0.165178 | − | 13.5308i | −0.0134867 | − | 1.10479i | ||||
\(151\) | −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 | ||||
\(155\) | 11.9950 | − | 1.97494i | 0.963462 | − | 0.158631i | ||||
\(156\) | 0.927051 | + | 2.85317i | 0.0742235 | + | 0.228436i | ||||
\(157\) | 19.5960 | 1.56393 | 0.781967 | − | 0.623319i | \(-0.214216\pi\) | ||||
0.781967 | + | 0.623319i | \(0.214216\pi\) | |||||||
\(158\) | −3.97666 | − | 12.2389i | −0.316366 | − | 0.973674i | ||||
\(159\) | 5.70487 | + | 4.14483i | 0.452426 | + | 0.328707i | ||||
\(160\) | 6.41825 | − | 42.1882i | 0.507407 | − | 3.33527i | ||||
\(161\) | 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 | \(-0.454216\pi\) |
−0.896942 | + | 0.442149i | \(0.854216\pi\) | |||||||
\(164\) | −6.34127 | + | 4.60720i | −0.495170 | + | 0.359762i | ||||
\(165\) | −7.01949 | + | 1.15574i | −0.546467 | + | 0.0899742i | ||||
\(166\) | −25.5963 | − | 18.5968i | −1.98665 | − | 1.44339i | ||||
\(167\) | −1.85218 | − | 5.70042i | −0.143326 | − | 0.441112i | 0.853466 | − | 0.521149i | \(-0.174496\pi\) |
−0.996792 | + | 0.0800367i | \(0.974496\pi\) | |||||||
\(168\) | 4.23125 | 0.326448 | ||||||||
\(169\) | −3.91912 | − | 12.0618i | −0.301471 | − | 0.927831i | ||||
\(170\) | 7.25705 | − | 7.34618i | 0.556590 | − | 0.563426i | ||||
\(171\) | 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 | \(-0.928840\pi\) |
−0.0904807 | + | 0.995898i | \(0.528840\pi\) | |||||||
\(174\) | −22.5288 | −1.70791 | ||||||||
\(175\) | −2.24509 | − | 0.699292i | −0.169712 | − | 0.0528615i | ||||
\(176\) | −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 | −0.751468 | − | 0.659770i | \(-0.770654\pi\) |
0.995753 | − | 0.0920634i | \(-0.0293462\pi\) | |||||||
\(180\) | 5.46973 | + | 10.5749i | 0.407689 | + | 0.788205i | ||||
\(181\) | 3.70198 | + | 11.3935i | 0.275166 | + | 0.846873i | 0.989175 | + | 0.146738i | \(0.0468773\pi\) |
−0.714010 | + | 0.700136i | \(0.753123\pi\) | |||||||
\(182\) | 0.717144 | 0.0531583 | ||||||||
\(183\) | 0.0392107 | + | 0.120678i | 0.00289854 | + | 0.00892077i | ||||
\(184\) | 16.5213 | + | 12.0035i | 1.21797 | + | 0.884906i | ||||
\(185\) | −1.60423 | + | 1.62393i | −0.117945 | + | 0.119394i | ||||
\(186\) | −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 | ||||
\(190\) | −15.9064 | + | 16.1018i | −1.15397 | + | 1.16815i | ||||
\(191\) | −14.7773 | − | 10.7363i | −1.06924 | − | 0.776852i | −0.0934681 | − | 0.995622i | \(-0.529795\pi\) |
−0.975776 | + | 0.218771i | \(0.929795\pi\) | |||||||
\(192\) | 7.49304 | + | 23.0612i | 0.540763 | + | 1.66430i | ||||
\(193\) | 25.2063 | 1.81439 | 0.907194 | − | 0.420713i | \(-0.138220\pi\) | ||||
0.907194 | + | 0.420713i | \(0.138220\pi\) | |||||||
\(194\) | 7.07054 | + | 21.7609i | 0.507635 | + | 1.56234i | ||||
\(195\) | 0.578823 | + | 1.11907i | 0.0414504 | + | 0.0801380i | ||||
\(196\) | −11.1534 | + | 34.3266i | −0.796671 | + | 2.45190i | ||||
\(197\) | 3.73672 | − | 11.5004i | 0.266230 | − | 0.819372i | −0.725177 | − | 0.688562i | \(-0.758242\pi\) |
0.991407 | − | 0.130810i | \(-0.0417578\pi\) | |||||||
\(198\) | 6.96582 | − | 5.06097i | 0.495040 | − | 0.359667i | ||||
\(199\) | −0.544434 | −0.0385939 | −0.0192970 | − | 0.999814i | \(-0.506143\pi\) | ||||
−0.0192970 | + | 0.999814i | \(0.506143\pi\) | |||||||
\(200\) | −0.549118 | − | 44.9817i | −0.0388285 | − | 3.18069i | ||||
\(201\) | −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 | ||||
\(205\) | −2.31340 | + | 2.34181i | −0.161575 | + | 0.163559i | ||||
\(206\) | −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 | ||||
\(210\) | 2.80823 | − | 0.462367i | 0.193786 | − | 0.0319063i | ||||
\(211\) | 2.52580 | − | 1.83510i | 0.173884 | − | 0.126334i | −0.497439 | − | 0.867499i | \(-0.665726\pi\) |
0.671323 | + | 0.741165i | \(0.265726\pi\) | |||||||
\(212\) | 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 | ||||
\(215\) | 2.26244 | − | 14.8714i | 0.154297 | − | 1.01422i | ||||
\(216\) | −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 | ||||
\(220\) | −37.3746 | + | 6.15362i | −2.51979 | + | 0.414877i | ||||
\(221\) | −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 | \(-0.703614\pi\) |
0.578561 | + | 0.815639i | \(0.303614\pi\) | |||||||
\(224\) | 8.97519 | 0.599680 | ||||||||
\(225\) | 2.98808 | + | 4.00891i | 0.199206 | + | 0.267261i | ||||
\(226\) | 31.8697 | 2.11994 | ||||||||
\(227\) | 1.44690 | − | 1.05123i | 0.0960341 | − | 0.0697729i | −0.538732 | − | 0.842477i | \(-0.681096\pi\) |
0.634766 | + | 0.772704i | \(0.281096\pi\) | |||||||
\(228\) | 6.15370 | − | 18.9391i | 0.407538 | − | 1.25427i | ||||
\(229\) | −8.64730 | + | 26.6137i | −0.571430 | + | 1.75868i | 0.0765965 | + | 0.997062i | \(0.475595\pi\) |
−0.648026 | + | 0.761618i | \(0.724405\pi\) | |||||||
\(230\) | 12.2767 | + | 6.16119i | 0.809500 | + | 0.406257i | ||||
\(231\) | −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 | \(-0.171223\pi\) |
−0.995916 | + | 0.0902840i | \(0.971223\pi\) | |||||||
\(234\) | −1.23366 | − | 0.896304i | −0.0806467 | − | 0.0585932i | ||||
\(235\) | 8.86055 | + | 4.44676i | 0.577998 | + | 0.290075i | ||||
\(236\) | 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 | −0.405078 | − | 0.914282i | \(-0.632756\pi\) |
0.744358 | + | 0.667781i | \(0.232756\pi\) | |||||||
\(240\) | 14.0744 | + | 27.2106i | 0.908496 | + | 1.75644i | ||||
\(241\) | 6.02602 | + | 4.37816i | 0.388170 | + | 0.282022i | 0.764705 | − | 0.644380i | \(-0.222885\pi\) |
−0.376535 | + | 0.926402i | \(0.622885\pi\) | |||||||
\(242\) | −0.734446 | − | 2.26039i | −0.0472120 | − | 0.145304i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.208773 | + | 0.642537i | 0.0133653 | + | 0.0411342i | ||||
\(245\) | −2.27980 | + | 14.9855i | −0.145651 | + | 0.957387i | ||||
\(246\) | 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 | ||||||||
\(250\) | −5.27979 | − | 29.7938i | −0.333924 | − | 1.88433i | ||||
\(251\) | −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 | ||||
\(255\) | −0.573870 | + | 3.77214i | −0.0359371 | + | 0.236221i | ||||
\(256\) | 7.97520 | + | 24.5451i | 0.498450 | + | 1.53407i | ||||
\(257\) | −5.79485 | −0.361473 | −0.180736 | − | 0.983532i | \(-0.557848\pi\) | ||||
−0.180736 | + | 0.983532i | \(0.557848\pi\) | |||||||
\(258\) | 5.62605 | + | 17.3152i | 0.350262 | + | 1.07800i | ||||
\(259\) | −0.388409 | − | 0.282196i | −0.0241346 | − | 0.0175348i | ||||
\(260\) | 3.08188 | + | 5.95835i | 0.191130 | + | 0.369521i | ||||
\(261\) | 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 | \(-0.445324\pi\) |
−0.884242 | + | 0.467030i | \(0.845324\pi\) | |||||||
\(264\) | 23.1572 | − | 16.8247i | 1.42522 | − | 1.03549i | ||||
\(265\) | 14.0927 | + | 7.07258i | 0.865708 | + | 0.434465i | ||||
\(266\) | −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 | −0.951756 | − | 0.306856i | \(-0.900723\pi\) |
0.589621 | − | 0.807680i | \(-0.299277\pi\) | |||||||
\(270\) | −5.40869 | − | 2.71441i | −0.329162 | − | 0.165194i | ||||
\(271\) | −7.18256 | + | 22.1057i | −0.436310 | + | 1.34282i | 0.455429 | + | 0.890272i | \(0.349486\pi\) |
−0.891739 | + | 0.452551i | \(0.850514\pi\) | |||||||
\(272\) | −7.22415 | + | 22.2337i | −0.438029 | + | 1.34811i | ||||
\(273\) | −0.214377 | + | 0.155754i | −0.0129747 | + | 0.00942666i | ||||
\(274\) | −13.8460 | −0.836470 | ||||||||
\(275\) | −15.0677 | + | 5.09996i | −0.908616 | + | 0.307539i | ||||
\(276\) | −12.0853 | −0.727452 | ||||||||
\(277\) | −17.7102 | + | 12.8672i | −1.06410 | + | 0.773115i | −0.974843 | − | 0.222894i | \(-0.928450\pi\) |
−0.0892586 | + | 0.996008i | \(0.528450\pi\) | |||||||
\(278\) | −6.88968 | + | 21.2043i | −0.413216 | + | 1.27175i | ||||
\(279\) | 1.67999 | − | 5.17047i | 0.100578 | − | 0.309548i | ||||
\(280\) | 9.33566 | − | 1.53709i | 0.557912 | − | 0.0918587i | ||||
\(281\) | 8.37863 | + | 25.7868i | 0.499827 | + | 1.53831i | 0.809296 | + | 0.587401i | \(0.199849\pi\) |
−0.309469 | + | 0.950910i | \(0.600151\pi\) | |||||||
\(282\) | −11.9989 | −0.714522 | ||||||||
\(283\) | 5.03926 | + | 15.5093i | 0.299553 | + | 0.921929i | 0.981654 | + | 0.190671i | \(0.0610664\pi\) |
−0.682101 | + | 0.731258i | \(0.738934\pi\) | |||||||
\(284\) | −69.1171 | − | 50.2165i | −4.10134 | − | 2.97980i | ||||
\(285\) | 1.25784 | − | 8.26799i | 0.0745080 | − | 0.489753i | ||||
\(286\) | 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 | ||||
\(290\) | −49.7068 | + | 8.18408i | −2.91888 | + | 0.480586i | ||||
\(291\) | −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 | \(-0.448977\pi\) | ||||
0.159607 | + | 0.987181i | \(0.448977\pi\) | |||||||
\(294\) | −5.66921 | − | 17.4480i | −0.330635 | − | 1.01759i | ||||
\(295\) | 20.2278 | − | 20.4762i | 1.17771 | − | 1.19217i | ||||
\(296\) | 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 | ||||||||
\(300\) | 15.9097 | + | 21.3450i | 0.918550 | + | 1.23236i | ||||
\(301\) | 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 | ||||
\(305\) | 0.130352 | + | 0.252015i | 0.00746392 | + | 0.0144304i | ||||
\(306\) | −1.42705 | − | 4.39201i | −0.0815791 | − | 0.251075i | ||||
\(307\) | −21.4194 | −1.22247 | −0.611235 | − | 0.791450i | \(-0.709327\pi\) | ||||
−0.611235 | + | 0.791450i | \(0.709327\pi\) | |||||||
\(308\) | −2.46179 | − | 7.57662i | −0.140274 | − | 0.431718i | ||||
\(309\) | 11.3905 | + | 8.27566i | 0.647981 | + | 0.470786i | ||||
\(310\) | −23.1213 | + | 23.4053i | −1.31320 | + | 1.32933i | ||||
\(311\) | 2.30731 | − | 1.67636i | 0.130836 | − | 0.0950578i | −0.520443 | − | 0.853897i | \(-0.674233\pi\) |
0.651278 | + | 0.758839i | \(0.274233\pi\) | |||||||
\(312\) | −4.10116 | − | 2.97967i | −0.232183 | − | 0.168691i | ||||
\(313\) | −11.6802 | − | 8.48616i | −0.660204 | − | 0.479666i | 0.206528 | − | 0.978441i | \(-0.433784\pi\) |
−0.866732 | + | 0.498774i | \(0.833784\pi\) | |||||||
\(314\) | −42.9054 | + | 31.1726i | −2.42129 | + | 1.75917i | ||||
\(315\) | −0.739048 | + | 0.748125i | −0.0416406 | + | 0.0421521i | ||||
\(316\) | 20.4823 | + | 14.8812i | 1.15222 | + | 0.837135i | ||||
\(317\) | 6.98695 | + | 21.5036i | 0.392426 | + | 1.20776i | 0.930948 | + | 0.365152i | \(0.118983\pi\) |
−0.538522 | + | 0.842611i | \(0.681017\pi\) | |||||||
\(318\) | −19.0842 | −1.07019 | ||||||||
\(319\) | 8.18397 | + | 25.1877i | 0.458214 | + | 1.41024i | ||||
\(320\) | 24.9098 | + | 48.1594i | 1.39250 | + | 2.69219i | ||||
\(321\) | −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 | ||||||||
\(325\) | 1.68362 | + | 2.25880i | 0.0933904 | + | 0.125295i | ||||
\(326\) | 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 | ||||
\(330\) | 13.5306 | − | 13.6968i | 0.744836 | − | 0.753985i | ||||
\(331\) | 1.19480 | + | 3.67721i | 0.0656720 | + | 0.202118i | 0.978508 | − | 0.206209i | \(-0.0661125\pi\) |
−0.912836 | + | 0.408326i | \(0.866113\pi\) | |||||||
\(332\) | 62.2448 | 3.41613 | ||||||||
\(333\) | 0.315460 | + | 0.970887i | 0.0172871 | + | 0.0532043i | ||||
\(334\) | 13.1233 | + | 9.53466i | 0.718077 | + | 0.521713i | ||||
\(335\) | −6.16610 | + | 1.01523i | −0.336890 | + | 0.0554680i | ||||
\(336\) | −5.21267 | + | 3.78723i | −0.284375 | + | 0.206610i | ||||
\(337\) | −14.1459 | − | 10.2776i | −0.770576 | − | 0.559856i | 0.131560 | − | 0.991308i | \(-0.458001\pi\) |
−0.902136 | + | 0.431452i | \(0.858001\pi\) | |||||||
\(338\) | 27.7683 | + | 20.1749i | 1.51040 | + | 1.09737i | ||||
\(339\) | −9.52686 | + | 6.92167i | −0.517428 | + | 0.375933i | ||||
\(340\) | −3.05551 | + | 20.0844i | −0.165708 | + | 1.08923i | ||||
\(341\) | 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 | ||||
\(345\) | −5.00801 | + | 0.824555i | −0.269622 | + | 0.0443926i | ||||
\(346\) | 14.4886 | − | 44.5913i | 0.778912 | − | 2.39724i | ||||
\(347\) | −7.13647 | + | 21.9638i | −0.383106 | + | 1.17908i | 0.554739 | + | 0.832024i | \(0.312818\pi\) |
−0.937845 | + | 0.347055i | \(0.887182\pi\) | |||||||
\(348\) | 35.8576 | − | 26.0520i | 1.92217 | − | 1.39654i | ||||
\(349\) | −9.32650 | −0.499236 | −0.249618 | − | 0.968344i | \(-0.580305\pi\) | ||||
−0.249618 | + | 0.968344i | \(0.580305\pi\) | |||||||
\(350\) | 6.02800 | − | 2.04030i | 0.322210 | − | 0.109058i | ||||
\(351\) | 0.563444 | 0.0300744 | ||||||||
\(352\) | 49.1203 | − | 35.6880i | 2.61812 | − | 1.90218i | ||||
\(353\) | 9.87219 | − | 30.3835i | 0.525444 | − | 1.61715i | −0.237993 | − | 0.971267i | \(-0.576490\pi\) |
0.763437 | − | 0.645883i | \(-0.223510\pi\) | |||||||
\(354\) | −10.7650 | + | 33.1312i | −0.572152 | + | 1.76090i | ||||
\(355\) | −32.0674 | − | 16.0934i | −1.70196 | − | 0.854148i | ||||
\(356\) | −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 | 0.773382 | − | 0.633940i | \(-0.218564\pi\) |
−0.363925 | + | 0.931428i | \(0.618564\pi\) | |||||||
\(360\) | −17.9806 | − | 9.02378i | −0.947663 | − | 0.475595i | ||||
\(361\) | 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 | ||||
\(365\) | −10.0559 | − | 19.4416i | −0.526351 | − | 1.01762i | ||||
\(366\) | −0.277821 | − | 0.201849i | −0.0145219 | − | 0.0105508i | ||||
\(367\) | 0.328866 | + | 1.01215i | 0.0171667 | + | 0.0528336i | 0.959273 | − | 0.282481i | \(-0.0911574\pi\) |
−0.942106 | + | 0.335315i | \(0.891157\pi\) | |||||||
\(368\) | −31.0973 | −1.62106 | ||||||||
\(369\) | 0.454915 | + | 1.40008i | 0.0236819 | + | 0.0728855i | ||||
\(370\) | 0.929160 | − | 6.10752i | 0.0483047 | − | 0.317515i | ||||
\(371\) | −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 | \(-0.665982\pi\) |
0.670728 | + | 0.741703i | \(0.265982\pi\) | |||||||
\(374\) | 14.6922 | 0.759714 | ||||||||
\(375\) | 8.04912 | + | 7.75962i | 0.415655 | + | 0.400705i | ||||
\(376\) | −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 | −0.834604 | − | 0.550851i | \(-0.814303\pi\) |
0.998991 | + | 0.0449201i | \(0.0143033\pi\) | |||||||
\(380\) | 6.69724 | − | 44.0220i | 0.343561 | − | 2.25828i | ||||
\(381\) | 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 | \(-0.0902448\pi\) |
−0.941141 | + | 0.338014i | \(0.890245\pi\) | |||||||
\(384\) | −22.2119 | − | 16.1379i | −1.13350 | − | 0.823533i | ||||
\(385\) | −1.53707 | − | 2.97169i | −0.0783363 | − | 0.151451i | ||||
\(386\) | −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 | −0.815477 | − | 0.578789i | \(-0.803525\pi\) |
0.298465 | + | 0.954421i | \(0.403525\pi\) | |||||||
\(390\) | −3.04750 | − | 1.52942i | −0.154316 | − | 0.0774452i | ||||
\(391\) | −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 | ||||
\(395\) | 9.50290 | + | 4.76914i | 0.478143 | + | 0.239961i | ||||
\(396\) | −5.23458 | + | 16.1104i | −0.263047 | + | 0.809577i | ||||
\(397\) | −0.405848 | + | 1.24907i | −0.0203689 | + | 0.0626891i | −0.960724 | − | 0.277505i | \(-0.910493\pi\) |
0.940355 | + | 0.340194i | \(0.110493\pi\) | |||||||
\(398\) | 1.19204 | − | 0.866064i | 0.0597513 | − | 0.0434119i | ||||
\(399\) | 1.75895 | 0.0880575 | ||||||||
\(400\) | 40.9380 | + | 54.9237i | 2.04690 | + | 2.74618i | ||||
\(401\) | 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 | ||||
\(405\) | 2.20636 | − | 0.363271i | 0.109635 | − | 0.0180511i | ||||
\(406\) | −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 | 0.0776999 | − | 0.996977i | \(-0.475242\pi\) |
−0.924171 | + | 0.381980i | \(0.875242\pi\) | |||||||
\(410\) | 1.33991 | − | 8.80745i | 0.0661735 | − | 0.434969i | ||||
\(411\) | 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 | ||||
\(415\) | 25.7935 | − | 4.24682i | 1.26615 | − | 0.208468i | ||||
\(416\) | −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 | 0.887991 | − | 0.459860i | \(-0.152100\pi\) |
−0.988699 | + | 0.149914i | \(0.952100\pi\) | |||||||
\(420\) | −3.93498 | + | 3.98331i | −0.192008 | + | 0.194366i | ||||
\(421\) | 8.43555 | − | 25.9620i | 0.411124 | − | 1.26531i | −0.504549 | − | 0.863383i | \(-0.668341\pi\) |
0.915673 | − | 0.401925i | \(-0.131659\pi\) | |||||||
\(422\) | −2.61102 | + | 8.03590i | −0.127103 | + | 0.391181i | ||||
\(423\) | 3.58684 | − | 2.60599i | 0.174398 | − | 0.126708i | ||||
\(424\) | −63.4435 | −3.08109 | ||||||||
\(425\) | 0.104145 | + | 8.53118i | 0.00505177 | + | 0.413823i | ||||
\(426\) | 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 | ||||
\(430\) | 18.7032 | + | 36.1598i | 0.901949 | + | 1.74378i | ||||
\(431\) | 3.80011 | + | 11.6955i | 0.183045 | + | 0.563354i | 0.999909 | − | 0.0134755i | \(-0.00428951\pi\) |
−0.816864 | + | 0.576830i | \(0.804290\pi\) | |||||||
\(432\) | 13.7004 | 0.659161 | ||||||||
\(433\) | −10.4587 | − | 32.1887i | −0.502614 | − | 1.54689i | −0.804744 | − | 0.593622i | \(-0.797698\pi\) |
0.302130 | − | 0.953267i | \(-0.402302\pi\) | |||||||
\(434\) | −5.59805 | − | 4.06722i | −0.268715 | − | 0.195233i | ||||
\(435\) | 13.0814 | − | 13.2421i | 0.627207 | − | 0.634911i | ||||
\(436\) | −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 | −0.104171 | − | 0.994559i | \(-0.533219\pi\) |
0.913692 | + | 0.406408i | \(0.133219\pi\) | |||||||
\(440\) | 44.9812 | − | 45.5336i | 2.14439 | − | 2.17073i | ||||
\(441\) | 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 | \(-0.454105\pi\) | ||||
0.143686 | + | 0.989623i | \(0.454105\pi\) | |||||||
\(444\) | 1.67964 | + | 5.16939i | 0.0797120 | + | 0.245328i | ||||
\(445\) | −6.36973 | − | 12.3149i | −0.301954 | − | 0.583782i | ||||
\(446\) | 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 | \(0.380090\pi\) | |||||||
\(450\) | −12.9196 | − | 4.02415i | −0.609036 | − | 0.189700i | ||||
\(451\) | −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 | ||||
\(455\) | −0.416412 | + | 0.421527i | −0.0195217 | + | 0.0197615i | ||||
\(456\) | 10.3983 | + | 32.0028i | 0.486947 | + | 1.49867i | ||||
\(457\) | −2.50193 | −0.117035 | −0.0585176 | − | 0.998286i | \(-0.518637\pi\) | ||||
−0.0585176 | + | 0.998286i | \(0.518637\pi\) | |||||||
\(458\) | −23.4027 | − | 72.0262i | −1.09354 | − | 3.36556i | ||||
\(459\) | 1.38048 | + | 1.00297i | 0.0644351 | + | 0.0468148i | ||||
\(460\) | −26.6647 | + | 4.39026i | −1.24325 | + | 0.204697i | ||||
\(461\) | 0.124559 | − | 0.0904973i | 0.00580128 | − | 0.00421488i | −0.584881 | − | 0.811119i | \(-0.698859\pi\) |
0.590682 | + | 0.806904i | \(0.298859\pi\) | |||||||
\(462\) | 3.27599 | + | 2.38014i | 0.152413 | + | 0.110734i | ||||
\(463\) | 9.41102 | + | 6.83751i | 0.437367 | + | 0.317766i | 0.784588 | − | 0.620018i | \(-0.212875\pi\) |
−0.347221 | + | 0.937783i | \(0.612875\pi\) | |||||||
\(464\) | 92.2664 | − | 67.0355i | 4.28336 | − | 3.11204i | ||||
\(465\) | 1.82838 | − | 12.0182i | 0.0847890 | − | 0.557332i | ||||
\(466\) | 14.8316 | + | 10.7758i | 0.687062 | + | 0.499180i | ||||
\(467\) | 0.145329 | + | 0.447276i | 0.00672502 | + | 0.0206975i | 0.954363 | − | 0.298650i | \(-0.0965363\pi\) |
−0.947638 | + | 0.319347i | \(0.896536\pi\) | |||||||
\(468\) | 3.00000 | 0.138675 | ||||||||
\(469\) | −0.406149 | − | 1.25000i | −0.0187542 | − | 0.0577196i | ||||
\(470\) | −26.4738 | + | 4.35884i | −1.22115 | + | 0.201058i | ||||
\(471\) | 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 | ||||||||
\(475\) | −0.228271 | − | 18.6991i | −0.0104738 | − | 0.857974i | ||||
\(476\) | −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 | −0.824403 | − | 0.566003i | \(-0.808489\pi\) |
0.999644 | + | 0.0266660i | \(0.00848907\pi\) | |||||||
\(480\) | −38.1400 | − | 19.1410i | −1.74084 | − | 0.873662i | ||||
\(481\) | 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 | ||||
\(485\) | −16.8963 | − | 8.47958i | −0.767220 | − | 0.385038i | ||||
\(486\) | −2.18949 | + | 1.59076i | −0.0993174 | + | 0.0721583i | ||||
\(487\) | −27.9633 | − | 20.3165i | −1.26714 | − | 0.920631i | −0.268055 | − | 0.963404i | \(-0.586381\pi\) |
−0.999085 | + | 0.0427731i | \(0.986381\pi\) | |||||||
\(488\) | −0.923588 | − | 0.671026i | −0.0418088 | − | 0.0303759i | ||||
\(489\) | −9.62137 | + | 6.99033i | −0.435093 | + | 0.316114i | ||||
\(490\) | −18.8467 | − | 36.4372i | −0.851407 | − | 1.64607i | ||||
\(491\) | 20.1168 | + | 14.6157i | 0.907859 | + | 0.659598i | 0.940473 | − | 0.339870i | \(-0.110383\pi\) |
−0.0326134 | + | 0.999468i | \(0.510383\pi\) | |||||||
\(492\) | 2.42215 | + | 7.45460i | 0.109199 | + | 0.336080i | ||||
\(493\) | 14.2044 | 0.639736 | ||||||||
\(494\) | 1.76239 | + | 5.42408i | 0.0792938 | + | 0.244041i | ||||
\(495\) | −1.06997 | + | 7.03308i | −0.0480915 | + | 0.316113i | ||||
\(496\) | 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 | \(0.408966\pi\) | |||||||
\(500\) | 42.8567 | + | 41.3153i | 1.91661 | + | 1.84768i | ||||
\(501\) | −5.99378 | −0.267782 | ||||||||
\(502\) | 10.0764 | − | 7.32094i | 0.449732 | − | 0.326750i | ||||
\(503\) | 9.26827 | − | 28.5248i | 0.413252 | − | 1.27186i | −0.500554 | − | 0.865705i | \(-0.666870\pi\) |
0.913805 | − | 0.406152i | \(-0.133130\pi\) | |||||||
\(504\) | 1.30753 | − | 4.02415i | 0.0582419 | − | 0.179250i | ||||
\(505\) | −1.96179 | + | 12.8952i | −0.0872986 | + | 0.573828i | ||||
\(506\) | 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 | 0.596127 | − | 0.802890i | \(-0.296706\pi\) |
−0.579381 | + | 0.815057i | \(0.696706\pi\) | |||||||
\(510\) | −4.74408 | − | 9.17196i | −0.210072 | − | 0.406141i | ||||
\(511\) | 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 | ||||
\(515\) | 28.1378 | + | 14.1213i | 1.23990 | + | 0.622257i | ||||
\(516\) | −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 | ||||
\(520\) | −10.1311 | − | 5.08440i | −0.444277 | − | 0.222966i | ||||
\(521\) | −5.34039 | + | 16.4360i | −0.233967 | + | 0.720076i | 0.763290 | + | 0.646056i | \(0.223583\pi\) |
−0.997257 | + | 0.0740200i | \(0.976417\pi\) | |||||||
\(522\) | −6.96179 | + | 21.4262i | −0.304709 | + | 0.937799i | ||||
\(523\) | −32.8849 | + | 23.8922i | −1.43795 | + | 1.04473i | −0.449489 | + | 0.893286i | \(0.648394\pi\) |
−0.988465 | + | 0.151449i | \(0.951606\pi\) | |||||||
\(524\) | −31.5130 | −1.37665 | ||||||||
\(525\) | −1.35884 | + | 1.91911i | −0.0593044 | + | 0.0837568i | ||||
\(526\) | 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 | ||||
\(530\) | −42.1067 | + | 6.93275i | −1.82900 | + | 0.301139i | ||||
\(531\) | −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 | ||||
\(535\) | −2.89634 | + | 19.0381i | −0.125220 | + | 0.823090i | ||||
\(536\) | 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 | ||||
\(540\) | 11.7475 | − | 1.93420i | 0.505534 | − | 0.0832347i | ||||
\(541\) | 1.60265 | + | 1.16440i | 0.0689035 | + | 0.0500613i | 0.621704 | − | 0.783252i | \(-0.286441\pi\) |
−0.552800 | + | 0.833314i | \(0.686441\pi\) | |||||||
\(542\) | −19.4386 | − | 59.8259i | −0.834960 | − | 2.56974i | ||||
\(543\) | 11.9799 | 0.514105 | ||||||||
\(544\) | −10.0630 | − | 30.9707i | −0.431448 | − | 1.32786i | ||||
\(545\) | −26.2237 | + | 26.5458i | −1.12330 | + | 1.13710i | ||||
\(546\) | 0.221610 | − | 0.682045i | 0.00948402 | − | 0.0291888i | ||||
\(547\) | 10.8324 | − | 33.3386i | 0.463158 | − | 1.42545i | −0.398126 | − | 0.917331i | \(-0.630339\pi\) |
0.861284 | − | 0.508124i | \(-0.169661\pi\) | |||||||
\(548\) | 22.0378 | − | 16.0114i | 0.941407 | − | 0.683972i | ||||
\(549\) | 0.126888 | 0.00541546 | ||||||||
\(550\) | 24.8778 | − | 35.1354i | 1.06079 | − | 1.49818i | ||||
\(551\) | −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 | ||||
\(555\) | 1.04872 | + | 2.02753i | 0.0445155 | + | 0.0860639i | ||||
\(556\) | −13.5545 | − | 41.7165i | −0.574839 | − | 1.76917i | ||||
\(557\) | 19.2383 | 0.815154 | 0.407577 | − | 0.913171i | \(-0.366374\pi\) | ||||
0.407577 | + | 0.913171i | \(0.366374\pi\) | |||||||
\(558\) | 4.54666 | + | 13.9932i | 0.192475 | + | 0.592378i | ||||
\(559\) | −3.06651 | − | 2.22795i | −0.129699 | − | 0.0942321i | ||||
\(560\) | −10.1253 | + | 10.2496i | −0.427870 | + | 0.433125i | ||||
\(561\) | −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 | \(-0.0892485\pi\) |
0.0337705 | + | 0.999430i | \(0.489248\pi\) | |||||||
\(564\) | 19.0977 | − | 13.8753i | 0.804160 | − | 0.584257i | ||||
\(565\) | −18.5053 | + | 18.7325i | −0.778522 | + | 0.788084i | ||||
\(566\) | −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 | −0.901692 | − | 0.432380i | \(-0.857674\pi\) |
0.475338 | − | 0.879803i | \(-0.342326\pi\) | |||||||
\(570\) | 10.3983 | + | 20.1036i | 0.435539 | + | 0.842048i | ||||
\(571\) | 8.23065 | − | 25.3313i | 0.344442 | − | 1.06008i | −0.617440 | − | 0.786618i | \(-0.711830\pi\) |
0.961882 | − | 0.273465i | \(-0.0881698\pi\) | |||||||
\(572\) | −2.94939 | + | 9.07730i | −0.123320 | + | 0.379541i | ||||
\(573\) | −14.7773 | + | 10.7363i | −0.617329 | + | 0.448515i | ||||
\(574\) | 1.87371 | 0.0782073 | ||||||||
\(575\) | −10.7500 | + | 3.63854i | −0.448304 | + | 0.151737i | ||||
\(576\) | 24.2480 | 1.01033 | ||||||||
\(577\) | −27.9237 | + | 20.2878i | −1.16248 | + | 0.844591i | −0.990089 | − | 0.140438i | \(-0.955149\pi\) |
−0.172390 | + | 0.985029i | \(0.555149\pi\) | |||||||
\(578\) | −11.7822 | + | 36.2620i | −0.490076 | + | 1.50830i | ||||
\(579\) | 7.78917 | − | 23.9726i | 0.323707 | − | 0.996267i | ||||
\(580\) | 69.6508 | − | 70.5063i | 2.89209 | − | 2.92761i | ||||
\(581\) | 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 | ||||
\(585\) | 1.24316 | − | 0.204683i | 0.0513984 | − | 0.00846260i | ||||
\(586\) | −11.9635 | + | 8.69202i | −0.494209 | + | 0.359064i | ||||
\(587\) | 18.0213 | + | 13.0932i | 0.743817 | + | 0.540414i | 0.893904 | − | 0.448258i | \(-0.147955\pi\) |
−0.150087 | + | 0.988673i | \(0.547955\pi\) | |||||||
\(588\) | 29.2000 | + | 21.2150i | 1.20419 | + | 0.874893i | ||||
\(589\) | −16.4500 | + | 11.9516i | −0.677809 | + | 0.492457i | ||||
\(590\) | −11.7158 | + | 77.0101i | −0.482333 | + | 3.17045i | ||||
\(591\) | −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 | \(-0.718909\pi\) | ||||
−0.634779 | + | 0.772693i | \(0.718909\pi\) | |||||||
\(594\) | −2.66071 | − | 8.18882i | −0.109170 | − | 0.335991i | ||||
\(595\) | −1.77059 | + | 0.291522i | −0.0725870 | + | 0.0119513i | ||||
\(596\) | −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 | \(0.663321\pi\) | |||||||
\(600\) | −42.9499 | − | 13.3779i | −1.75342 | − | 0.546150i | ||||
\(601\) | −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 | ||||
\(605\) | 1.75508 | + | 0.880809i | 0.0713543 | + | 0.0358100i | ||||
\(606\) | −4.87842 | − | 15.0142i | −0.198172 | − | 0.609911i | ||||
\(607\) | 45.5915 | 1.85050 | 0.925251 | − | 0.379356i | \(-0.123855\pi\) | ||||
0.925251 | + | 0.379356i | \(0.123855\pi\) | |||||||
\(608\) | 22.0567 | + | 67.8834i | 0.894516 | + | 2.75304i | ||||
\(609\) | 3.16723 | + | 2.30113i | 0.128343 | + | 0.0932465i | ||||
\(610\) | −0.686300 | − | 0.344427i | −0.0277875 | − | 0.0139455i | ||||
\(611\) | 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 | \(-0.229641\pi\) |
−0.396114 | + | 0.918201i | \(0.629641\pi\) | |||||||
\(614\) | 46.8976 | − | 34.0731i | 1.89263 | − | 1.37508i | ||||
\(615\) | 1.51232 | + | 2.92384i | 0.0609825 | + | 0.117900i | ||||
\(616\) | 10.8907 | + | 7.91254i | 0.438798 | + | 0.318805i | ||||
\(617\) | −4.97685 | − | 15.3172i | −0.200360 | − | 0.616646i | −0.999872 | − | 0.0159954i | \(-0.994908\pi\) |
0.799512 | − | 0.600651i | \(-0.205092\pi\) | |||||||
\(618\) | −38.1039 | −1.53276 | ||||||||
\(619\) | 11.8533 | + | 36.4807i | 0.476425 | + | 1.46628i | 0.844026 | + | 0.536302i | \(0.180179\pi\) |
−0.367602 | + | 0.929983i | \(0.619821\pi\) | |||||||
\(620\) | 9.73501 | − | 63.9898i | 0.390967 | − | 2.56989i | ||||
\(621\) | −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 | ||||||||
\(625\) | 20.5781 | + | 14.1965i | 0.823125 | + | 0.567861i | ||||
\(626\) | 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 | ||||
\(630\) | 0.428053 | − | 2.81366i | 0.0170540 | − | 0.112099i | ||||
\(631\) | 7.02370 | + | 21.6167i | 0.279609 | + | 0.860548i | 0.987963 | + | 0.154690i | \(0.0494380\pi\) |
−0.708354 | + | 0.705857i | \(0.750562\pi\) | |||||||
\(632\) | −42.7808 | −1.70173 | ||||||||
\(633\) | −0.964772 | − | 2.96926i | −0.0383462 | − | 0.118018i | ||||
\(634\) | −49.5049 | − | 35.9674i | −1.96609 | − | 1.42845i | ||||
\(635\) | 1.82738 | + | 3.53295i | 0.0725172 | + | 0.140201i | ||||
\(636\) | 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 | ||||
\(640\) | −54.8699 | − | 27.5371i | −2.16892 | − | 1.08850i | ||||
\(641\) | −21.8378 | − | 15.8661i | −0.862541 | − | 0.626673i | 0.0660340 | − | 0.997817i | \(-0.478965\pi\) |
−0.928575 | + | 0.371145i | \(0.878965\pi\) | |||||||
\(642\) | −7.20238 | − | 22.1666i | −0.284255 | − | 0.874848i | ||||
\(643\) | −25.9062 | −1.02164 | −0.510821 | − | 0.859687i | \(-0.670659\pi\) | ||||
−0.510821 | + | 0.859687i | \(0.670659\pi\) | |||||||
\(644\) | −1.75635 | − | 5.40549i | −0.0692099 | − | 0.213006i | ||||
\(645\) | −13.4444 | − | 6.74722i | −0.529373 | − | 0.265672i | ||||
\(646\) | −5.33731 | + | 16.4266i | −0.209994 | + | 0.646295i | ||||
\(647\) | −6.69401 | + | 20.6021i | −0.263169 | + | 0.809950i | 0.728941 | + | 0.684577i | \(0.240013\pi\) |
−0.992110 | + | 0.125374i | \(0.959987\pi\) | |||||||
\(648\) | −7.27874 | + | 5.28832i | −0.285936 | + | 0.207745i | ||||
\(649\) | 40.9519 | 1.60750 | ||||||||
\(650\) | −7.27947 | − | 2.26739i | −0.285524 | − | 0.0889342i | ||||
\(651\) | 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 | \(-0.829817\pi\) |
0.995616 | + | 0.0935349i | \(0.0298167\pi\) | |||||||
\(654\) | 13.9560 | − | 42.9521i | 0.545722 | − | 1.67956i | ||||
\(655\) | −13.0586 | + | 2.15006i | −0.510241 | + | 0.0840097i | ||||
\(656\) | 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 | 0.354860 | − | 0.934919i | \(-0.384529\pi\) |
−0.779503 | + | 0.626398i | \(0.784529\pi\) | |||||||
\(660\) | −5.69694 | + | 37.4469i | −0.221753 | + | 1.45762i | ||||
\(661\) | 18.8195 | − | 13.6732i | 0.731993 | − | 0.531824i | −0.158200 | − | 0.987407i | \(-0.550569\pi\) |
0.890193 | + | 0.455583i | \(0.150569\pi\) | |||||||
\(662\) | −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 | ||||
\(665\) | 3.88088 | − | 0.638975i | 0.150494 | − | 0.0247784i | ||||
\(666\) | −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 | ||||
\(670\) | 11.8856 | − | 12.0316i | 0.459182 | − | 0.464822i | ||||
\(671\) | −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 | \(-0.818281\pi\) |
0.253916 | + | 0.967226i | \(0.418281\pi\) | |||||||
\(674\) | 47.3215 | 1.82276 | ||||||||
\(675\) | 4.73607 | − | 1.60302i | 0.182291 | − | 0.0617001i | ||||
\(676\) | −67.5268 | −2.59719 | ||||||||
\(677\) | 34.1761 | − | 24.8304i | 1.31350 | − | 0.954310i | 0.313507 | − | 0.949586i | \(-0.398496\pi\) |
0.999989 | − | 0.00472433i | \(-0.00150381\pi\) | |||||||
\(678\) | 9.84828 | − | 30.3099i | 0.378221 | − | 1.16404i | ||||
\(679\) | 1.22867 | − | 3.78147i | 0.0471521 | − | 0.145119i | ||||
\(680\) | −15.7712 | − | 30.4912i | −0.604798 | − | 1.16929i | ||||
\(681\) | −0.552667 | − | 1.70093i | −0.0211782 | − | 0.0651799i | ||||
\(682\) | −46.8100 | −1.79245 | ||||||||
\(683\) | 15.1264 | + | 46.5544i | 0.578797 | + | 1.78135i | 0.622870 | + | 0.782325i | \(0.285966\pi\) |
−0.0440734 | + | 0.999028i | \(0.514034\pi\) | |||||||
\(684\) | −16.1106 | − | 11.7050i | −0.616004 | − | 0.447553i | ||||
\(685\) | 8.03975 | − | 8.13850i | 0.307183 | − | 0.310956i | ||||
\(686\) | 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 | ||||
\(690\) | 9.65334 | − | 9.77191i | 0.367497 | − | 0.372010i | ||||
\(691\) | 11.4813 | + | 8.34168i | 0.436771 | + | 0.317332i | 0.784350 | − | 0.620318i | \(-0.212996\pi\) |
−0.347580 | + | 0.937650i | \(0.612996\pi\) | |||||||
\(692\) | 28.5043 | + | 87.7273i | 1.08357 | + | 3.33489i | ||||
\(693\) | −1.49623 | −0.0568371 | ||||||||
\(694\) | −19.3139 | − | 59.4420i | −0.733145 | − | 2.25639i | ||||
\(695\) | −8.46303 | − | 16.3620i | −0.321021 | − | 0.620645i | ||||
\(696\) | −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 | ||||||||
\(700\) | −7.23498 | + | 10.2181i | −0.273456 | + | 0.386208i | ||||
\(701\) | −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 | ||||
\(705\) | 6.96718 | − | 7.05275i | 0.262399 | − | 0.265622i | ||||
\(706\) | 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 | −0.966164 | − | 0.257928i | \(-0.916960\pi\) |
−0.543865 | − | 0.839173i | \(-0.683040\pi\) | |||||||
\(710\) | 95.8120 | − | 15.7752i | 3.59576 | − | 0.592032i | ||||
\(711\) | 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 | ||||
\(715\) | −0.602868 | + | 3.96275i | −0.0225460 | + | 0.148198i | ||||
\(716\) | −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 | 0.937987 | − | 0.346671i | \(-0.112688\pi\) |
−0.962615 | + | 0.270872i | \(0.912688\pi\) | |||||||
\(720\) | 30.2280 | − | 4.97696i | 1.12653 | − | 0.185480i | ||||
\(721\) | −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 | ||||||||
\(725\) | 24.0519 | − | 33.9690i | 0.893266 | − | 1.26158i | ||||
\(726\) | −2.37672 | −0.0882083 | ||||||||
\(727\) | 33.5446 | − | 24.3716i | 1.24410 | − | 0.903891i | 0.246235 | − | 0.969210i | \(-0.420807\pi\) |
0.997864 | + | 0.0653195i | \(0.0208067\pi\) | |||||||
\(728\) | 0.736718 | − | 2.26739i | 0.0273046 | − | 0.0840349i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 52.9442 | + | 26.5706i | 1.95955 | + | 0.983424i | ||||
\(731\) | −3.54723 | − | 10.9172i | −0.131199 | − | 0.403789i | ||||
\(732\) | 0.675604 | 0.0249710 | ||||||||
\(733\) | 10.0496 | + | 30.9293i | 0.371189 | + | 1.14240i | 0.946014 | + | 0.324125i | \(0.105070\pi\) |
−0.574826 | + | 0.818276i | \(0.694930\pi\) | |||||||
\(734\) | −2.33013 | − | 1.69294i | −0.0860067 | − | 0.0624875i | ||||
\(735\) | 13.5475 | + | 6.79899i | 0.499709 | + | 0.250784i | ||||
\(736\) | 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 | 0.0786411 | − | 0.996903i | \(-0.474942\pi\) |
0.972413 | + | 0.233268i | \(0.0749419\pi\) | |||||||
\(740\) | 5.58378 | + | 10.7954i | 0.205264 | + | 0.396846i | ||||
\(741\) | −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 | \(-0.730292\pi\) | ||||
−0.662001 | + | 0.749503i | \(0.730292\pi\) | |||||||
\(744\) | 15.1149 | + | 46.5188i | 0.554139 | + | 1.70546i | ||||
\(745\) | −3.38281 | + | 22.2357i | −0.123936 | + | 0.814654i | ||||
\(746\) | −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 | ||||||||
\(750\) | −29.9672 | − | 4.18542i | −1.09425 | − | 0.152830i | ||||
\(751\) | −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 | ||||
\(755\) | −4.02935 | + | 26.4856i | −0.146643 | + | 0.963908i | ||||
\(756\) | 0.773789 | + | 2.38148i | 0.0281424 | + | 0.0866135i | ||||
\(757\) | 14.6243 | 0.531530 | 0.265765 | − | 0.964038i | \(-0.414375\pi\) | ||||
0.265765 | + | 0.964038i | \(0.414375\pi\) | |||||||
\(758\) | 8.66109 | + | 26.6561i | 0.314585 | + | 0.968193i | ||||
\(759\) | −5.84219 | − | 4.24460i | −0.212058 | − | 0.154069i | ||||
\(760\) | 34.5682 | + | 66.8324i | 1.25392 | + | 2.42427i | ||||
\(761\) | −9.86133 | + | 7.16467i | −0.357473 | + | 0.259719i | −0.751997 | − | 0.659166i | \(-0.770909\pi\) |
0.394524 | + | 0.918885i | \(0.370909\pi\) | |||||||
\(762\) | −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 | ||||
\(765\) | 3.41018 | + | 1.71144i | 0.123295 | + | 0.0618772i | ||||
\(766\) | −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 | 0.998031 | − | 0.0627287i | \(-0.0199803\pi\) |
−0.844295 | + | 0.535879i | \(0.819980\pi\) | |||||||
\(770\) | 8.09265 | + | 4.06139i | 0.291639 | + | 0.146362i | ||||
\(771\) | −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 | \(-0.833565\pi\) |
0.207199 | + | 0.978299i | \(0.433565\pi\) | |||||||
\(774\) | 18.2063 | 0.654411 | ||||||||
\(775\) | −0.331811 | − | 27.1808i | −0.0119190 | − | 0.976362i | ||||
\(776\) | 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 | ||||
\(780\) | 6.61909 | − | 1.08981i | 0.237001 | − | 0.0390216i | ||||
\(781\) | −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 | ||||
\(785\) | 6.59038 | − | 43.3196i | 0.235221 | − | 1.54614i | ||||
\(786\) | 12.9587 | − | 9.41507i | 0.462223 | − | 0.335824i | ||||
\(787\) | 38.5785 | + | 28.0289i | 1.37518 | + | 0.999123i | 0.997313 | + | 0.0732618i | \(0.0233409\pi\) |
0.377863 | + | 0.925862i | \(0.376659\pi\) | |||||||
\(788\) | −52.0878 | − | 37.8440i | −1.85555 | − | 1.34814i | ||||
\(789\) | −11.5680 | + | 8.40467i | −0.411833 | + | 0.299214i | ||||
\(790\) | −28.3931 | + | 4.67484i | −1.01018 | + | 0.166323i | ||||
\(791\) | −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 | ||||
\(795\) | 11.0813 | − | 11.2174i | 0.393014 | − | 0.397841i | ||||
\(796\) | −0.895774 | + | 2.75691i | −0.0317499 | + | 0.0977160i | ||||
\(797\) | 8.40931 | − | 25.8812i | 0.297873 | − | 0.916759i | −0.684368 | − | 0.729137i | \(-0.739922\pi\) |
0.982241 | − | 0.187622i | \(-0.0600781\pi\) | |||||||
\(798\) | −3.85120 | + | 2.79806i | −0.136331 | + | 0.0990504i | ||||
\(799\) | 7.56529 | 0.267641 | ||||||||
\(800\) | −91.1040 | − | 28.3768i | −3.22101 | − | 1.00327i | ||||
\(801\) | −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 | ||||
\(805\) | −1.09661 | − | 2.12013i | −0.0386505 | − | 0.0747249i | ||||
\(806\) | 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 | 0.830702 | − | 0.556717i | \(-0.187939\pi\) |
−0.272769 | + | 0.962080i | \(0.587939\pi\) | |||||||
\(810\) | −4.25294 | + | 4.30517i | −0.149433 | + | 0.151268i | ||||
\(811\) | −17.0468 | + | 12.3852i | −0.598594 | + | 0.434904i | −0.845380 | − | 0.534166i | \(-0.820626\pi\) |
0.246786 | + | 0.969070i | \(0.420626\pi\) | |||||||
\(812\) | 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 | ||||
\(815\) | −18.6888 | + | 18.9184i | −0.654641 | + | 0.662682i | ||||
\(816\) | 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 | ||||
\(820\) | 8.05218 | + | 15.5677i | 0.281194 | + | 0.543646i | ||||
\(821\) | 12.8039 | − | 39.4062i | 0.446858 | − | 1.37529i | −0.433575 | − | 0.901117i | \(-0.642748\pi\) |
0.880433 | − | 0.474170i | \(-0.157252\pi\) | |||||||
\(822\) | −4.27866 | + | 13.1684i | −0.149235 | + | 0.459299i | ||||
\(823\) | −4.88721 | + | 3.55077i | −0.170358 | + | 0.123772i | −0.669697 | − | 0.742634i | \(-0.733576\pi\) |
0.499340 | + | 0.866406i | \(0.333576\pi\) | |||||||
\(824\) | −126.673 | −4.41285 | ||||||||
\(825\) | 0.194176 | + | 15.9062i | 0.00676034 | + | 0.553783i | ||||
\(826\) | −16.3833 | −0.570047 | ||||||||
\(827\) | 2.42188 | − | 1.75960i | 0.0842172 | − | 0.0611874i | −0.544880 | − | 0.838514i | \(-0.683425\pi\) |
0.629097 | + | 0.777327i | \(0.283425\pi\) | |||||||
\(828\) | −3.73458 | + | 11.4938i | −0.129786 | + | 0.399439i | ||||
\(829\) | 8.29802 | − | 25.5387i | 0.288202 | − | 0.886995i | −0.697218 | − | 0.716859i | \(-0.745579\pi\) |
0.985421 | − | 0.170136i | \(-0.0544208\pi\) | |||||||
\(830\) | −49.7189 | + | 50.3296i | −1.72577 | + | 1.74697i | ||||
\(831\) | 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 | ||||
\(835\) | −13.2244 | + | 2.17737i | −0.457651 | + | 0.0753509i | ||||
\(836\) | 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 | −0.748029 | − | 0.663666i | \(-0.769000\pi\) |
0.400030 | + | 0.916502i | \(0.369000\pi\) | |||||||
\(840\) | 1.42302 | − | 9.35373i | 0.0490988 | − | 0.322734i | ||||
\(841\) | −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 | ||||
\(845\) | −27.9823 | + | 4.60720i | −0.962619 | + | 0.158492i | ||||
\(846\) | −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 | ||||||||
\(850\) | −13.7991 | − | 18.5133i | −0.473304 | − | 0.635000i | ||||
\(851\) | −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 | \(-0.931096\pi\) |
0.916381 | + | 0.400307i | \(0.131096\pi\) | |||||||
\(854\) | 0.0499068 | − | 0.153597i | 0.00170778 | − | 0.00525599i | ||||
\(855\) | −7.47463 | − | 3.75123i | −0.255627 | − | 0.128289i | ||||
\(856\) | −23.9436 | − | 73.6907i | −0.818374 | − | 2.51870i | ||||
\(857\) | −7.41982 | −0.253456 | −0.126728 | − | 0.991937i | \(-0.540448\pi\) | ||||
−0.126728 | + | 0.991937i | \(0.540448\pi\) | |||||||
\(858\) | −1.49916 | − | 4.61394i | −0.0511805 | − | 0.157517i | ||||
\(859\) | 4.59726 | + | 3.34011i | 0.156857 | + | 0.113963i | 0.663445 | − | 0.748225i | \(-0.269094\pi\) |
−0.506588 | + | 0.862188i | \(0.669094\pi\) | |||||||
\(860\) | −71.5833 | − | 35.9249i | −2.44097 | − | 1.22503i | ||||
\(861\) | −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 | \(-0.0997315\pi\) |
0.000843465 | 1.00000i | \(0.499732\pi\) | ||||||||
\(864\) | −15.4395 | + | 11.2174i | −0.525261 | + | 0.381624i | ||||
\(865\) | 17.7973 | + | 34.4083i | 0.605125 | + | 1.16992i | ||||
\(866\) | 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 | ||||
\(870\) | −7.57671 | + | 49.8030i | −0.256875 | + | 1.68848i | ||||
\(871\) | −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 | ||||||||
\(875\) | −2.30093 | + | 4.72788i | −0.0777855 | + | 0.159831i | ||||
\(876\) | −52.1191 | −1.76094 | ||||||||
\(877\) | 4.28790 | − | 3.11534i | 0.144792 | − | 0.105197i | −0.513031 | − | 0.858370i | \(-0.671477\pi\) |
0.657823 | + | 0.753173i | \(0.271477\pi\) | |||||||
\(878\) | −17.5336 | + | 53.9629i | −0.591730 | + | 1.82116i | ||||
\(879\) | 1.68849 | − | 5.19664i | 0.0569514 | − | 0.175278i | ||||
\(880\) | −14.6590 | + | 96.3560i | −0.494155 | + | 3.24816i | ||||
\(881\) | 2.35251 | + | 7.24028i | 0.0792580 | + | 0.243931i | 0.982833 | − | 0.184500i | \(-0.0590665\pi\) |
−0.903575 | + | 0.428431i | \(0.859067\pi\) | |||||||
\(882\) | −18.3460 | −0.617740 | ||||||||
\(883\) | −16.3264 | − | 50.2476i | −0.549428 | − | 1.69096i | −0.710223 | − | 0.703977i | \(-0.751406\pi\) |
0.160795 | − | 0.986988i | \(-0.448594\pi\) | |||||||
\(884\) | 4.14143 | + | 3.00892i | 0.139291 | + | 0.101201i | ||||
\(885\) | −13.2233 | − | 25.5653i | −0.444497 | − | 0.859367i | ||||
\(886\) | −13.2431 | + | 9.62166i | −0.444910 | + | 0.323246i | ||||
\(887\) | −6.23572 | − | 4.53052i | −0.209375 | − | 0.152120i | 0.478156 | − | 0.878275i | \(-0.341305\pi\) |
−0.687531 | + | 0.726155i | \(0.741305\pi\) | |||||||
\(888\) | −7.43051 | − | 5.39858i | −0.249352 | − | 0.181165i | ||||
\(889\) | −0.676800 | + | 0.491724i | −0.0226991 | + | 0.0164919i | ||||
\(890\) | 33.5365 | + | 16.8307i | 1.12415 | + | 0.564166i | ||||
\(891\) | 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 | ||||
\(895\) | −21.1372 | − | 10.6080i | −0.706540 | − | 0.354585i | ||||
\(896\) | 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 | ||||||||
\(900\) | 25.2167 | − | 8.53509i | 0.840557 | − | 0.284503i | ||||
\(901\) | 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 | ||||
\(905\) | 26.4319 | − | 4.35194i | 0.878626 | − | 0.144663i | ||||
\(906\) | −10.0198 | − | 30.8379i | −0.332887 | − | 1.02452i | ||||
\(907\) | −11.3735 | −0.377650 | −0.188825 | − | 0.982011i | \(-0.560468\pi\) | ||||
−0.188825 | + | 0.982011i | \(0.560468\pi\) | |||||||
\(908\) | −2.94262 | − | 9.05644i | −0.0976542 | − | 0.300549i | ||||
\(909\) | 4.71920 | + | 3.42870i | 0.156526 | + | 0.113723i | ||||
\(910\) | 0.241184 | − | 1.58534i | 0.00799517 | − | 0.0525536i | ||||
\(911\) | 15.0393 | − | 10.9267i | 0.498275 | − | 0.362018i | −0.310082 | − | 0.950710i | \(-0.600357\pi\) |
0.808358 | + | 0.588691i | \(0.200357\pi\) | |||||||
\(912\) | −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 | ||||
\(915\) | 0.279962 | − | 0.0460949i | 0.00925525 | − | 0.00152385i | ||||
\(916\) | 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 | 0.982440 | − | 0.186581i | \(-0.0597405\pi\) |
−0.904480 | + | 0.426517i | \(0.859741\pi\) | |||||||
\(920\) | 32.0915 | − | 32.4857i | 1.05803 | − | 1.07102i | ||||
\(921\) | −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 | ||||||||
\(925\) | 3.05039 | + | 4.09250i | 0.100296 | + | 0.134561i | ||||
\(926\) | −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 | 0.662483 | + | 0.749077i | \(0.269503\pi\) |
−0.976256 | + | 0.216619i | \(0.930497\pi\) | |||||||
\(930\) | 15.1149 | + | 29.2223i | 0.495637 | + | 0.958238i | ||||
\(931\) | −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 | ||||
\(935\) | −8.53106 | + | 8.63584i | −0.278996 | + | 0.282422i | ||||
\(936\) | −4.10116 | + | 2.97967i | −0.134051 | + | 0.0973936i | ||||
\(937\) | −25.3784 | − | 18.4385i | −0.829077 | − | 0.602360i | 0.0902212 | − | 0.995922i | \(-0.471243\pi\) |
−0.919298 | + | 0.393562i | \(0.871243\pi\) | |||||||
\(938\) | 2.87771 | + | 2.09078i | 0.0939605 | + | 0.0682663i | ||||
\(939\) | −11.6802 | + | 8.48616i | −0.381169 | + | 0.276935i | ||||
\(940\) | 37.0960 | − | 37.5517i | 1.20994 | − | 1.22480i | ||||
\(941\) | 2.92710 | + | 2.12666i | 0.0954208 | + | 0.0693273i | 0.634473 | − | 0.772945i | \(-0.281217\pi\) |
−0.539052 | + | 0.842273i | \(0.681217\pi\) | |||||||
\(942\) | 16.3884 | + | 50.4383i | 0.533963 | + | 1.64337i | ||||
\(943\) | −3.34146 | −0.108813 | ||||||||
\(944\) | −54.4955 | − | 167.720i | −1.77368 | − | 5.45882i | ||||
\(945\) | 0.483131 | + | 0.934060i | 0.0157162 | + | 0.0303850i | ||||
\(946\) | −17.8992 | + | 55.0879i | −0.581952 | + | 1.79106i | ||||
\(947\) | −3.49856 | + | 10.7675i | −0.113688 | + | 0.349896i | −0.991671 | − | 0.128796i | \(-0.958889\pi\) |
0.877983 | + | 0.478692i | \(0.158889\pi\) | |||||||
\(948\) | 20.4823 | − | 14.8812i | 0.665233 | − | 0.483320i | ||||
\(949\) | −5.51540 | −0.179038 | ||||||||
\(950\) | 30.2456 | + | 40.5784i | 0.981296 | + | 1.31654i | ||||
\(951\) | 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 | \(-0.989962\pi\) |
0.827148 | + | 0.561984i | \(0.189962\pi\) | |||||||
\(954\) | −5.89735 | + | 18.1502i | −0.190934 | + | 0.587633i | ||||
\(955\) | −28.7038 | + | 29.0563i | −0.928832 | + | 0.940240i | ||||
\(956\) | −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 | ||||
\(960\) | 53.4998 | − | 8.80859i | 1.72670 | − | 0.284296i | ||||
\(961\) | 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 | ||||
\(965\) | 8.47717 | − | 55.7218i | 0.272890 | − | 1.79375i | ||||
\(966\) | 2.33723 | + | 1.69810i | 0.0751992 | + | 0.0546354i | ||||
\(967\) | −9.24157 | − | 28.4426i | −0.297189 | − | 0.914653i | −0.982477 | − | 0.186382i | \(-0.940324\pi\) |
0.685289 | − | 0.728272i | \(-0.259676\pi\) | |||||||
\(968\) | −7.90115 | −0.253953 | ||||||||
\(969\) | −1.97214 | − | 6.06961i | −0.0633541 | − | 0.194984i | ||||
\(970\) | 50.4832 | − | 8.31192i | 1.62092 | − | 0.266880i | ||||
\(971\) | −7.78497 | + | 23.9597i | −0.249832 | + | 0.768902i | 0.744973 | + | 0.667095i | \(0.232463\pi\) |
−0.994804 | + | 0.101807i | \(0.967537\pi\) | |||||||
\(972\) | 1.64533 | − | 5.06380i | 0.0527739 | − | 0.162422i | ||||
\(973\) | 3.13443 | − | 2.27729i | 0.100485 | − | 0.0730067i | ||||
\(974\) | 93.5443 | 2.99735 | ||||||||
\(975\) | 2.66851 | − | 0.903210i | 0.0854607 | − | 0.0289259i | ||||
\(976\) | 1.73842 | 0.0556455 | ||||||||
\(977\) | −46.1907 | + | 33.5595i | −1.47777 | + | 1.07366i | −0.499504 | + | 0.866311i | \(0.666485\pi\) |
−0.978266 | + | 0.207352i | \(0.933515\pi\) | |||||||
\(978\) | 9.94597 | − | 30.6106i | 0.318037 | − | 0.978818i | ||||
\(979\) | 6.09589 | − | 18.7612i | 0.194826 | − | 0.599611i | ||||
\(980\) | 72.1325 | + | 36.2005i | 2.30419 | + | 1.15638i | ||||
\(981\) | 5.15673 | + | 15.8708i | 0.164642 | + | 0.506715i | ||||
\(982\) | −67.2957 | −2.14749 | ||||||||
\(983\) | −8.16325 | − | 25.1239i | −0.260367 | − | 0.801328i | −0.992725 | − | 0.120407i | \(-0.961580\pi\) |
0.732357 | − | 0.680921i | \(-0.238420\pi\) | |||||||
\(984\) | −10.7153 | − | 7.78512i | −0.341591 | − | 0.248181i | ||||
\(985\) | −24.1665 | − | 12.1282i | −0.770010 | − | 0.386438i | ||||
\(986\) | −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 | ||||
\(990\) | −8.84525 | − | 17.1009i | −0.281120 | − | 0.543503i | ||||
\(991\) | 18.2252 | + | 13.2414i | 0.578943 | + | 0.420626i | 0.838343 | − | 0.545144i | \(-0.183525\pi\) |
−0.259400 | + | 0.965770i | \(0.583525\pi\) | |||||||
\(992\) | 32.0612 | + | 98.6744i | 1.01795 | + | 3.13291i | ||||
\(993\) | 3.86645 | 0.122698 | ||||||||
\(994\) | 6.31096 | + | 19.4231i | 0.200171 | + | 0.616064i | ||||
\(995\) | −0.183100 | + | 1.20354i | −0.00580465 | + | 0.0381549i | ||||
\(996\) | 19.2347 | − | 59.1983i | 0.609475 | − | 1.87577i | ||||
\(997\) | −7.44865 | + | 22.9246i | −0.235901 | + | 0.726029i | 0.761099 | + | 0.648635i | \(0.224660\pi\) |
−0.997001 | + | 0.0773940i | \(0.975340\pi\) | |||||||
\(998\) | −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 | 75.2.g.b.61.1 | yes | 8 | |
3.2 | odd | 2 | 225.2.h.c.136.2 | 8 | |||
5.2 | odd | 4 | 375.2.i.b.199.1 | 16 | |||
5.3 | odd | 4 | 375.2.i.b.199.4 | 16 | |||
5.4 | even | 2 | 375.2.g.b.301.2 | 8 | |||
25.3 | odd | 20 | 1875.2.b.c.1249.1 | 8 | |||
25.4 | even | 10 | 1875.2.a.e.1.1 | 4 | |||
25.9 | even | 10 | 375.2.g.b.76.2 | 8 | |||
25.12 | odd | 20 | 375.2.i.b.49.4 | 16 | |||
25.13 | odd | 20 | 375.2.i.b.49.1 | 16 | |||
25.16 | even | 5 | inner | 75.2.g.b.16.1 | ✓ | 8 | |
25.21 | even | 5 | 1875.2.a.h.1.4 | 4 | |||
25.22 | odd | 20 | 1875.2.b.c.1249.8 | 8 | |||
75.29 | odd | 10 | 5625.2.a.n.1.4 | 4 | |||
75.41 | odd | 10 | 225.2.h.c.91.2 | 8 | |||
75.71 | odd | 10 | 5625.2.a.i.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.16.1 | ✓ | 8 | 25.16 | even | 5 | inner | |
75.2.g.b.61.1 | yes | 8 | 1.1 | even | 1 | trivial | |
225.2.h.c.91.2 | 8 | 75.41 | odd | 10 | |||
225.2.h.c.136.2 | 8 | 3.2 | odd | 2 | |||
375.2.g.b.76.2 | 8 | 25.9 | even | 10 | |||
375.2.g.b.301.2 | 8 | 5.4 | even | 2 | |||
375.2.i.b.49.1 | 16 | 25.13 | odd | 20 | |||
375.2.i.b.49.4 | 16 | 25.12 | odd | 20 | |||
375.2.i.b.199.1 | 16 | 5.2 | odd | 4 | |||
375.2.i.b.199.4 | 16 | 5.3 | odd | 4 | |||
1875.2.a.e.1.1 | 4 | 25.4 | even | 10 | |||
1875.2.a.h.1.4 | 4 | 25.21 | even | 5 | |||
1875.2.b.c.1249.1 | 8 | 25.3 | odd | 20 | |||
1875.2.b.c.1249.8 | 8 | 25.22 | odd | 20 | |||
5625.2.a.i.1.1 | 4 | 75.71 | odd | 10 | |||
5625.2.a.n.1.4 | 4 | 75.29 | odd | 10 |