Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(159,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.159");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.m (of order \(6\), degree \(2\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.8 | ||
Root | \(-2.90925i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.249 |
Dual form | 370.2.m.c.159.8 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 2.51948 | − | 1.45462i | 1.45462 | − | 0.839828i | 0.455886 | − | 0.890038i | \(-0.349322\pi\) |
0.998739 | + | 0.0502101i | \(0.0159891\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.19673 | + | 1.88887i | −0.535194 | + | 0.844729i | ||||
\(6\) | 2.90925i | 1.18770i | ||||||||
\(7\) | −0.191824 | + | 0.110750i | −0.0725026 | + | 0.0418594i | −0.535813 | − | 0.844337i | \(-0.679995\pi\) |
0.463310 | + | 0.886196i | \(0.346661\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.73187 | − | 4.73173i | 0.910622 | − | 1.57724i | ||||
\(10\) | −1.03745 | − | 1.98083i | −0.328069 | − | 0.626395i | ||||
\(11\) | 6.08400 | 1.83439 | 0.917197 | − | 0.398433i | \(-0.130446\pi\) | ||||
0.917197 | + | 0.398433i | \(0.130446\pi\) | |||||||
\(12\) | −2.51948 | − | 1.45462i | −0.727312 | − | 0.419914i | ||||
\(13\) | 0.0723701 | + | 0.125349i | 0.0200719 | + | 0.0347655i | 0.875887 | − | 0.482517i | \(-0.160277\pi\) |
−0.855815 | + | 0.517282i | \(0.826944\pi\) | |||||||
\(14\) | − | 0.221499i | − | 0.0591981i | ||||||
\(15\) | −0.267544 | + | 6.49978i | −0.0690795 | + | 1.67823i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.31013 | + | 2.26922i | −0.317754 | + | 0.550366i | −0.980019 | − | 0.198904i | \(-0.936262\pi\) |
0.662265 | + | 0.749270i | \(0.269595\pi\) | |||||||
\(18\) | 2.73187 | + | 4.73173i | 0.643907 | + | 1.11528i | ||||
\(19\) | 3.28333 | − | 1.89563i | 0.753249 | − | 0.434888i | −0.0736180 | − | 0.997287i | \(-0.523455\pi\) |
0.826866 | + | 0.562398i | \(0.190121\pi\) | |||||||
\(20\) | 2.23418 | + | 0.0919631i | 0.499577 | + | 0.0205636i | ||||
\(21\) | −0.322198 | + | 0.558064i | −0.0703094 | + | 0.121779i | ||||
\(22\) | −3.04200 | + | 5.26890i | −0.648557 | + | 1.12333i | ||||
\(23\) | −0.277470 | −0.0578565 | −0.0289282 | − | 0.999581i | \(-0.509209\pi\) | ||||
−0.0289282 | + | 0.999581i | \(0.509209\pi\) | |||||||
\(24\) | 2.51948 | − | 1.45462i | 0.514288 | − | 0.296924i | ||||
\(25\) | −2.13567 | − | 4.52094i | −0.427134 | − | 0.904188i | ||||
\(26\) | −0.144740 | −0.0283859 | ||||||||
\(27\) | − | 7.16761i | − | 1.37941i | ||||||
\(28\) | 0.191824 | + | 0.110750i | 0.0362513 | + | 0.0209297i | ||||
\(29\) | 1.60727i | 0.298463i | 0.988802 | + | 0.149231i | \(0.0476800\pi\) | ||||
−0.988802 | + | 0.149231i | \(0.952320\pi\) | |||||||
\(30\) | −5.49520 | − | 3.48159i | −1.00328 | − | 0.635648i | ||||
\(31\) | − | 0.776351i | − | 0.139437i | −0.997567 | − | 0.0697184i | \(-0.977790\pi\) | ||
0.997567 | − | 0.0697184i | \(-0.0222101\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 15.3285 | − | 8.84994i | 2.66836 | − | 1.54058i | ||||
\(34\) | −1.31013 | − | 2.26922i | −0.224686 | − | 0.389168i | ||||
\(35\) | 0.0203698 | − | 0.494868i | 0.00344312 | − | 0.0836480i | ||||
\(36\) | −5.46373 | −0.910622 | ||||||||
\(37\) | −5.49268 | − | 2.61351i | −0.902992 | − | 0.429658i | ||||
\(38\) | 3.79127i | 0.615025i | ||||||||
\(39\) | 0.364671 | + | 0.210543i | 0.0583940 | + | 0.0337138i | ||||
\(40\) | −1.19673 | + | 1.88887i | −0.189220 | + | 0.298657i | ||||
\(41\) | −5.07928 | − | 8.79757i | −0.793250 | − | 1.37395i | −0.923944 | − | 0.382527i | \(-0.875054\pi\) |
0.130694 | − | 0.991423i | \(-0.458279\pi\) | |||||||
\(42\) | −0.322198 | − | 0.558064i | −0.0497163 | − | 0.0861111i | ||||
\(43\) | −6.51449 | −0.993451 | −0.496726 | − | 0.867908i | \(-0.665464\pi\) | ||||
−0.496726 | + | 0.867908i | \(0.665464\pi\) | |||||||
\(44\) | −3.04200 | − | 5.26890i | −0.458599 | − | 0.794316i | ||||
\(45\) | 5.66833 | + | 10.8228i | 0.844984 | + | 1.61336i | ||||
\(46\) | 0.138735 | − | 0.240296i | 0.0204553 | − | 0.0354297i | ||||
\(47\) | 7.42616i | 1.08322i | 0.840631 | + | 0.541608i | \(0.182184\pi\) | ||||
−0.840631 | + | 0.541608i | \(0.817816\pi\) | |||||||
\(48\) | 2.90925i | 0.419914i | ||||||||
\(49\) | −3.47547 | + | 6.01969i | −0.496496 | + | 0.859956i | ||||
\(50\) | 4.98309 | + | 0.410924i | 0.704715 | + | 0.0581134i | ||||
\(51\) | 7.62301i | 1.06743i | ||||||||
\(52\) | 0.0723701 | − | 0.125349i | 0.0100359 | − | 0.0173827i | ||||
\(53\) | 3.13449 | + | 1.80970i | 0.430556 | + | 0.248582i | 0.699583 | − | 0.714551i | \(-0.253369\pi\) |
−0.269028 | + | 0.963132i | \(0.586702\pi\) | |||||||
\(54\) | 6.20734 | + | 3.58381i | 0.844711 | + | 0.487694i | ||||
\(55\) | −7.28091 | + | 11.4919i | −0.981757 | + | 1.54957i | ||||
\(56\) | −0.191824 | + | 0.110750i | −0.0256335 | + | 0.0147995i | ||||
\(57\) | 5.51487 | − | 9.55204i | 0.730463 | − | 1.26520i | ||||
\(58\) | −1.39194 | − | 0.803636i | −0.182770 | − | 0.105523i | ||||
\(59\) | 11.3301 | + | 6.54142i | 1.47505 | + | 0.851620i | 0.999604 | − | 0.0281258i | \(-0.00895390\pi\) |
0.475445 | + | 0.879746i | \(0.342287\pi\) | |||||||
\(60\) | 5.76274 | − | 3.01819i | 0.743967 | − | 0.389646i | ||||
\(61\) | −8.82479 | + | 5.09500i | −1.12990 | + | 0.652347i | −0.943909 | − | 0.330205i | \(-0.892882\pi\) |
−0.185989 | + | 0.982552i | \(0.559549\pi\) | |||||||
\(62\) | 0.672340 | + | 0.388176i | 0.0853873 | + | 0.0492984i | ||||
\(63\) | 1.21021i | 0.152472i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.323375 | − | 0.0133108i | −0.0401097 | − | 0.00165100i | ||||
\(66\) | 17.6999i | 2.17870i | ||||||||
\(67\) | −12.9680 | + | 7.48709i | −1.58429 | + | 0.914693i | −0.590073 | + | 0.807350i | \(0.700901\pi\) |
−0.994222 | + | 0.107343i | \(0.965766\pi\) | |||||||
\(68\) | 2.62027 | 0.317754 | ||||||||
\(69\) | −0.699081 | + | 0.403615i | −0.0841594 | + | 0.0485895i | ||||
\(70\) | 0.418383 | + | 0.265075i | 0.0500064 | + | 0.0316825i | ||||
\(71\) | −6.50051 | − | 11.2592i | −0.771468 | − | 1.33622i | −0.936758 | − | 0.349977i | \(-0.886189\pi\) |
0.165290 | − | 0.986245i | \(-0.447144\pi\) | |||||||
\(72\) | 2.73187 | − | 4.73173i | 0.321954 | − | 0.557640i | ||||
\(73\) | − | 5.99590i | − | 0.701767i | −0.936419 | − | 0.350884i | \(-0.885881\pi\) | ||
0.936419 | − | 0.350884i | \(-0.114119\pi\) | |||||||
\(74\) | 5.00970 | − | 3.45005i | 0.582366 | − | 0.401060i | ||||
\(75\) | −11.9571 | − | 8.28384i | −1.38068 | − | 0.956535i | ||||
\(76\) | −3.28333 | − | 1.89563i | −0.376624 | − | 0.217444i | ||||
\(77\) | −1.16706 | + | 0.673800i | −0.132998 | + | 0.0767867i | ||||
\(78\) | −0.364671 | + | 0.210543i | −0.0412908 | + | 0.0238393i | ||||
\(79\) | 5.73029 | − | 3.30838i | 0.644707 | − | 0.372222i | −0.141718 | − | 0.989907i | \(-0.545263\pi\) |
0.786426 | + | 0.617685i | \(0.211929\pi\) | |||||||
\(80\) | −1.03745 | − | 1.98083i | −0.115990 | − | 0.221464i | ||||
\(81\) | −2.23059 | − | 3.86349i | −0.247843 | − | 0.429277i | ||||
\(82\) | 10.1586 | 1.12183 | ||||||||
\(83\) | −3.52033 | − | 2.03246i | −0.386406 | − | 0.223092i | 0.294196 | − | 0.955745i | \(-0.404948\pi\) |
−0.680602 | + | 0.732654i | \(0.738282\pi\) | |||||||
\(84\) | 0.644396 | 0.0703094 | ||||||||
\(85\) | −2.71838 | − | 5.19032i | −0.294850 | − | 0.562969i | ||||
\(86\) | 3.25725 | − | 5.64172i | 0.351238 | − | 0.608362i | ||||
\(87\) | 2.33798 | + | 4.04950i | 0.250658 | + | 0.434152i | ||||
\(88\) | 6.08400 | 0.648557 | ||||||||
\(89\) | −10.8608 | − | 6.27049i | −1.15124 | − | 0.664671i | −0.202053 | − | 0.979375i | \(-0.564761\pi\) |
−0.949190 | + | 0.314704i | \(0.898095\pi\) | |||||||
\(90\) | −12.2069 | − | 0.502462i | −1.28672 | − | 0.0529641i | ||||
\(91\) | −0.0277646 | − | 0.0160299i | −0.00291052 | − | 0.00168039i | ||||
\(92\) | 0.138735 | + | 0.240296i | 0.0144641 | + | 0.0250526i | ||||
\(93\) | −1.12930 | − | 1.95600i | −0.117103 | − | 0.202828i | ||||
\(94\) | −6.43124 | − | 3.71308i | −0.663332 | − | 0.382975i | ||||
\(95\) | −0.348657 | + | 8.47036i | −0.0357714 | + | 0.869041i | ||||
\(96\) | −2.51948 | − | 1.45462i | −0.257144 | − | 0.148462i | ||||
\(97\) | −5.20777 | −0.528769 | −0.264385 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264385 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(98\) | −3.47547 | − | 6.01969i | −0.351075 | − | 0.608080i | ||||
\(99\) | 16.6207 | − | 28.7879i | 1.67044 | − | 2.89329i | ||||
\(100\) | −2.84741 | + | 4.11002i | −0.284741 | + | 0.411002i | ||||
\(101\) | 8.65668 | 0.861372 | 0.430686 | − | 0.902502i | \(-0.358272\pi\) | ||||
0.430686 | + | 0.902502i | \(0.358272\pi\) | |||||||
\(102\) | −6.60172 | − | 3.81150i | −0.653668 | − | 0.377395i | ||||
\(103\) | −11.1036 | −1.09407 | −0.547035 | − | 0.837109i | \(-0.684244\pi\) | ||||
−0.547035 | + | 0.837109i | \(0.684244\pi\) | |||||||
\(104\) | 0.0723701 | + | 0.125349i | 0.00709647 | + | 0.0122914i | ||||
\(105\) | −0.668526 | − | 1.27644i | −0.0652415 | − | 0.124568i | ||||
\(106\) | −3.13449 | + | 1.80970i | −0.304449 | + | 0.175774i | ||||
\(107\) | 15.5556 | − | 8.98104i | 1.50382 | − | 0.868230i | 0.503828 | − | 0.863804i | \(-0.331924\pi\) |
0.999990 | − | 0.00442608i | \(-0.00140887\pi\) | |||||||
\(108\) | −6.20734 | + | 3.58381i | −0.597301 | + | 0.344852i | ||||
\(109\) | 5.62967 | + | 3.25029i | 0.539224 | + | 0.311321i | 0.744764 | − | 0.667327i | \(-0.232562\pi\) |
−0.205540 | + | 0.978649i | \(0.565895\pi\) | |||||||
\(110\) | −6.31182 | − | 12.0514i | −0.601808 | − | 1.14906i | ||||
\(111\) | −17.6404 | + | 1.40511i | −1.67435 | + | 0.133367i | ||||
\(112\) | − | 0.221499i | − | 0.0209297i | ||||||
\(113\) | −4.08400 | + | 7.07369i | −0.384190 | + | 0.665437i | −0.991657 | − | 0.128908i | \(-0.958853\pi\) |
0.607466 | + | 0.794346i | \(0.292186\pi\) | |||||||
\(114\) | 5.51487 | + | 9.55204i | 0.516515 | + | 0.894630i | ||||
\(115\) | 0.332057 | − | 0.524105i | 0.0309644 | − | 0.0488730i | ||||
\(116\) | 1.39194 | − | 0.803636i | 0.129238 | − | 0.0746157i | ||||
\(117\) | 0.790822 | 0.0731115 | ||||||||
\(118\) | −11.3301 | + | 6.54142i | −1.04302 | + | 0.602186i | ||||
\(119\) | − | 0.580387i | − | 0.0532040i | ||||||
\(120\) | −0.267544 | + | 6.49978i | −0.0244233 | + | 0.593346i | ||||
\(121\) | 26.0150 | 2.36500 | ||||||||
\(122\) | − | 10.1900i | − | 0.922558i | ||||||
\(123\) | −25.5943 | − | 14.7769i | −2.30776 | − | 1.33239i | ||||
\(124\) | −0.672340 | + | 0.388176i | −0.0603779 | + | 0.0348592i | ||||
\(125\) | 11.0953 | + | 1.37634i | 0.992394 | + | 0.123103i | ||||
\(126\) | −1.04807 | − | 0.605106i | −0.0933699 | − | 0.0539071i | ||||
\(127\) | −8.48756 | − | 4.90030i | −0.753150 | − | 0.434831i | 0.0736812 | − | 0.997282i | \(-0.476525\pi\) |
−0.826831 | + | 0.562451i | \(0.809859\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −16.4132 | + | 9.47614i | −1.44510 | + | 0.834328i | ||||
\(130\) | 0.173215 | − | 0.273396i | 0.0151920 | − | 0.0239784i | ||||
\(131\) | 1.84401 | + | 1.06464i | 0.161112 | + | 0.0930179i | 0.578388 | − | 0.815762i | \(-0.303682\pi\) |
−0.417276 | + | 0.908780i | \(0.637015\pi\) | |||||||
\(132\) | −15.3285 | − | 8.84994i | −1.33418 | − | 0.770288i | ||||
\(133\) | −0.419881 | + | 0.727256i | −0.0364083 | + | 0.0630611i | ||||
\(134\) | − | 14.9742i | − | 1.29357i | ||||||
\(135\) | 13.5387 | + | 8.57770i | 1.16523 | + | 0.738251i | ||||
\(136\) | −1.31013 | + | 2.26922i | −0.112343 | + | 0.194584i | ||||
\(137\) | 11.3683i | 0.971259i | 0.874165 | + | 0.485630i | \(0.161410\pi\) | ||||
−0.874165 | + | 0.485630i | \(0.838590\pi\) | |||||||
\(138\) | − | 0.807229i | − | 0.0687159i | ||||||
\(139\) | −3.73056 | + | 6.46151i | −0.316422 | + | 0.548058i | −0.979739 | − | 0.200280i | \(-0.935815\pi\) |
0.663317 | + | 0.748339i | \(0.269148\pi\) | |||||||
\(140\) | −0.438753 | + | 0.229793i | −0.0370814 | + | 0.0194211i | ||||
\(141\) | 10.8023 | + | 18.7101i | 0.909716 | + | 1.57567i | ||||
\(142\) | 13.0010 | 1.09102 | ||||||||
\(143\) | 0.440300 | + | 0.762621i | 0.0368197 | + | 0.0637736i | ||||
\(144\) | 2.73187 | + | 4.73173i | 0.227656 | + | 0.394311i | ||||
\(145\) | −3.03593 | − | 1.92347i | −0.252120 | − | 0.159736i | ||||
\(146\) | 5.19260 | + | 2.99795i | 0.429743 | + | 0.248112i | ||||
\(147\) | 20.2220i | 1.66788i | ||||||||
\(148\) | 0.482980 | + | 6.06356i | 0.0397007 | + | 0.498421i | ||||
\(149\) | −10.5731 | −0.866181 | −0.433091 | − | 0.901350i | \(-0.642577\pi\) | ||||
−0.433091 | + | 0.901350i | \(0.642577\pi\) | |||||||
\(150\) | 13.1525 | − | 6.21320i | 1.07390 | − | 0.507306i | ||||
\(151\) | −7.03678 | − | 12.1881i | −0.572645 | − | 0.991851i | −0.996293 | − | 0.0860237i | \(-0.972584\pi\) |
0.423648 | − | 0.905827i | \(-0.360749\pi\) | |||||||
\(152\) | 3.28333 | − | 1.89563i | 0.266314 | − | 0.153756i | ||||
\(153\) | 7.15822 | + | 12.3984i | 0.578708 | + | 1.00235i | ||||
\(154\) | − | 1.34760i | − | 0.108593i | ||||||
\(155\) | 1.46643 | + | 0.929083i | 0.117786 | + | 0.0746258i | ||||
\(156\) | − | 0.421085i | − | 0.0337138i | ||||||
\(157\) | 13.2368 | + | 7.64224i | 1.05641 | + | 0.609917i | 0.924436 | − | 0.381336i | \(-0.124536\pi\) |
0.131971 | + | 0.991254i | \(0.457869\pi\) | |||||||
\(158\) | 6.61676i | 0.526401i | ||||||||
\(159\) | 10.5297 | 0.835063 | ||||||||
\(160\) | 2.23418 | + | 0.0919631i | 0.176627 | + | 0.00727032i | ||||
\(161\) | 0.0532253 | − | 0.0307297i | 0.00419475 | − | 0.00242184i | ||||
\(162\) | 4.46118 | 0.350503 | ||||||||
\(163\) | 8.94061 | − | 15.4856i | 0.700283 | − | 1.21293i | −0.268084 | − | 0.963395i | \(-0.586391\pi\) |
0.968367 | − | 0.249530i | \(-0.0802761\pi\) | |||||||
\(164\) | −5.07928 | + | 8.79757i | −0.396625 | + | 0.686975i | ||||
\(165\) | −1.62774 | + | 39.5446i | −0.126719 | + | 3.07855i | ||||
\(166\) | 3.52033 | − | 2.03246i | 0.273230 | − | 0.157750i | ||||
\(167\) | −3.85790 | − | 6.68208i | −0.298533 | − | 0.517075i | 0.677267 | − | 0.735737i | \(-0.263164\pi\) |
−0.975801 | + | 0.218662i | \(0.929831\pi\) | |||||||
\(168\) | −0.322198 | + | 0.558064i | −0.0248581 | + | 0.0430555i | ||||
\(169\) | 6.48953 | − | 11.2402i | 0.499194 | − | 0.864630i | ||||
\(170\) | 5.85414 | + | 0.240968i | 0.448992 | + | 0.0184814i | ||||
\(171\) | − | 20.7145i | − | 1.58408i | ||||||
\(172\) | 3.25725 | + | 5.64172i | 0.248363 | + | 0.430177i | ||||
\(173\) | −8.22699 | − | 4.74986i | −0.625487 | − | 0.361125i | 0.153515 | − | 0.988146i | \(-0.450941\pi\) |
−0.779002 | + | 0.627021i | \(0.784274\pi\) | |||||||
\(174\) | −4.67596 | −0.354483 | ||||||||
\(175\) | 0.910365 | + | 0.630700i | 0.0688171 | + | 0.0476764i | ||||
\(176\) | −3.04200 | + | 5.26890i | −0.229299 | + | 0.397158i | ||||
\(177\) | 38.0612 | 2.86086 | ||||||||
\(178\) | 10.8608 | − | 6.27049i | 0.814052 | − | 0.469993i | ||||
\(179\) | − | 10.8474i | − | 0.810776i | −0.914145 | − | 0.405388i | \(-0.867136\pi\) | ||
0.914145 | − | 0.405388i | \(-0.132864\pi\) | |||||||
\(180\) | 6.53862 | − | 10.3203i | 0.487360 | − | 0.769229i | ||||
\(181\) | −8.45183 | − | 14.6390i | −0.628220 | − | 1.08811i | −0.987909 | − | 0.155036i | \(-0.950451\pi\) |
0.359689 | − | 0.933072i | \(-0.382883\pi\) | |||||||
\(182\) | 0.0277646 | − | 0.0160299i | 0.00205805 | − | 0.00118822i | ||||
\(183\) | −14.8226 | + | 25.6735i | −1.09572 | + | 1.89784i | ||||
\(184\) | −0.277470 | −0.0204553 | ||||||||
\(185\) | 11.5098 | − | 7.24731i | 0.846220 | − | 0.532833i | ||||
\(186\) | 2.25860 | 0.165609 | ||||||||
\(187\) | −7.97085 | + | 13.8059i | −0.582886 | + | 1.00959i | ||||
\(188\) | 6.43124 | − | 3.71308i | 0.469047 | − | 0.270804i | ||||
\(189\) | 0.793810 | + | 1.37492i | 0.0577412 | + | 0.100011i | ||||
\(190\) | −7.16122 | − | 4.53713i | −0.519529 | − | 0.329158i | ||||
\(191\) | 20.7156i | 1.49893i | 0.662044 | + | 0.749465i | \(0.269689\pi\) | ||||
−0.662044 | + | 0.749465i | \(0.730311\pi\) | |||||||
\(192\) | 2.51948 | − | 1.45462i | 0.181828 | − | 0.104979i | ||||
\(193\) | 14.7238 | 1.05984 | 0.529922 | − | 0.848047i | \(-0.322221\pi\) | ||||
0.529922 | + | 0.848047i | \(0.322221\pi\) | |||||||
\(194\) | 2.60389 | − | 4.51006i | 0.186948 | − | 0.323804i | ||||
\(195\) | −0.834101 | + | 0.436853i | −0.0597312 | + | 0.0312837i | ||||
\(196\) | 6.95094 | 0.496496 | ||||||||
\(197\) | 18.3664 | + | 10.6038i | 1.30855 | + | 0.755491i | 0.981854 | − | 0.189639i | \(-0.0607317\pi\) |
0.326695 | + | 0.945130i | \(0.394065\pi\) | |||||||
\(198\) | 16.6207 | + | 28.7879i | 1.18118 | + | 2.04586i | ||||
\(199\) | 14.0640i | 0.996972i | 0.866898 | + | 0.498486i | \(0.166110\pi\) | ||||
−0.866898 | + | 0.498486i | \(0.833890\pi\) | |||||||
\(200\) | −2.13567 | − | 4.52094i | −0.151015 | − | 0.319679i | ||||
\(201\) | −21.7818 | + | 37.7272i | −1.53637 | + | 2.66107i | ||||
\(202\) | −4.32834 | + | 7.49690i | −0.304541 | + | 0.527480i | ||||
\(203\) | −0.178005 | − | 0.308313i | −0.0124935 | − | 0.0216393i | ||||
\(204\) | 6.60172 | − | 3.81150i | 0.462213 | − | 0.266859i | ||||
\(205\) | 22.6960 | + | 0.934213i | 1.58516 | + | 0.0652483i | ||||
\(206\) | 5.55180 | − | 9.61601i | 0.386812 | − | 0.669979i | ||||
\(207\) | −0.758011 | + | 1.31291i | −0.0526854 | + | 0.0912538i | ||||
\(208\) | −0.144740 | −0.0100359 | ||||||||
\(209\) | 19.9758 | − | 11.5330i | 1.38176 | − | 0.797757i | ||||
\(210\) | 1.43969 | + | 0.0592607i | 0.0993484 | + | 0.00408938i | ||||
\(211\) | −4.44627 | −0.306094 | −0.153047 | − | 0.988219i | \(-0.548909\pi\) | ||||
−0.153047 | + | 0.988219i | \(0.548909\pi\) | |||||||
\(212\) | − | 3.61940i | − | 0.248582i | ||||||
\(213\) | −32.7558 | − | 18.9116i | −2.24439 | − | 1.29580i | ||||
\(214\) | 17.9621i | 1.22786i | ||||||||
\(215\) | 7.79609 | − | 12.3050i | 0.531689 | − | 0.839197i | ||||
\(216\) | − | 7.16761i | − | 0.487694i | ||||||
\(217\) | 0.0859806 | + | 0.148923i | 0.00583674 | + | 0.0101095i | ||||
\(218\) | −5.62967 | + | 3.25029i | −0.381289 | + | 0.220137i | ||||
\(219\) | −8.72179 | − | 15.1066i | −0.589364 | − | 1.02081i | ||||
\(220\) | 13.5927 | + | 0.559504i | 0.916421 | + | 0.0377217i | ||||
\(221\) | −0.379258 | −0.0255116 | ||||||||
\(222\) | 7.60334 | − | 15.9796i | 0.510303 | − | 1.07248i | ||||
\(223\) | − | 10.8958i | − | 0.729635i | −0.931079 | − | 0.364818i | \(-0.881131\pi\) | ||
0.931079 | − | 0.364818i | \(-0.118869\pi\) | |||||||
\(224\) | 0.191824 | + | 0.110750i | 0.0128168 | + | 0.00739977i | ||||
\(225\) | −27.2262 | − | 2.24518i | −1.81508 | − | 0.149678i | ||||
\(226\) | −4.08400 | − | 7.07369i | −0.271664 | − | 0.470535i | ||||
\(227\) | −1.84751 | − | 3.19999i | −0.122624 | − | 0.212391i | 0.798178 | − | 0.602422i | \(-0.205798\pi\) |
−0.920802 | + | 0.390031i | \(0.872464\pi\) | |||||||
\(228\) | −11.0297 | −0.730463 | ||||||||
\(229\) | 10.3979 | + | 18.0097i | 0.687113 | + | 1.19011i | 0.972768 | + | 0.231782i | \(0.0744556\pi\) |
−0.285655 | + | 0.958333i | \(0.592211\pi\) | |||||||
\(230\) | 0.287860 | + | 0.549622i | 0.0189809 | + | 0.0362410i | ||||
\(231\) | −1.96025 | + | 3.39526i | −0.128975 | + | 0.223392i | ||||
\(232\) | 1.60727i | 0.105523i | ||||||||
\(233\) | 9.94711i | 0.651657i | 0.945429 | + | 0.325828i | \(0.105643\pi\) | ||||
−0.945429 | + | 0.325828i | \(0.894357\pi\) | |||||||
\(234\) | −0.395411 | + | 0.684872i | −0.0258488 | + | 0.0447715i | ||||
\(235\) | −14.0271 | − | 8.88711i | −0.915025 | − | 0.579731i | ||||
\(236\) | − | 13.0828i | − | 0.851620i | ||||||
\(237\) | 9.62491 | − | 16.6708i | 0.625205 | − | 1.08289i | ||||
\(238\) | 0.502630 | + | 0.290193i | 0.0325806 | + | 0.0188104i | ||||
\(239\) | −10.2828 | − | 5.93680i | −0.665142 | − | 0.384020i | 0.129091 | − | 0.991633i | \(-0.458794\pi\) |
−0.794233 | + | 0.607613i | \(0.792127\pi\) | |||||||
\(240\) | −5.49520 | − | 3.48159i | −0.354714 | − | 0.224736i | ||||
\(241\) | 7.68274 | − | 4.43563i | 0.494889 | − | 0.285724i | −0.231712 | − | 0.972785i | \(-0.574433\pi\) |
0.726600 | + | 0.687060i | \(0.241099\pi\) | |||||||
\(242\) | −13.0075 | + | 22.5297i | −0.836155 | + | 1.44826i | ||||
\(243\) | 7.38214 | + | 4.26208i | 0.473564 | + | 0.273413i | ||||
\(244\) | 8.82479 | + | 5.09500i | 0.564949 | + | 0.326174i | ||||
\(245\) | −7.21122 | − | 13.7687i | −0.460708 | − | 0.879647i | ||||
\(246\) | 25.5943 | − | 14.7769i | 1.63183 | − | 0.942140i | ||||
\(247\) | 0.475230 | + | 0.274374i | 0.0302382 | + | 0.0174580i | ||||
\(248\) | − | 0.776351i | − | 0.0492984i | ||||||
\(249\) | −11.8259 | −0.749434 | ||||||||
\(250\) | −6.73959 | + | 8.92064i | −0.426249 | + | 0.564191i | ||||
\(251\) | 7.69687i | 0.485822i | 0.970049 | + | 0.242911i | \(0.0781023\pi\) | ||||
−0.970049 | + | 0.242911i | \(0.921898\pi\) | |||||||
\(252\) | 1.04807 | − | 0.605106i | 0.0660225 | − | 0.0381181i | ||||
\(253\) | −1.68813 | −0.106132 | ||||||||
\(254\) | 8.48756 | − | 4.90030i | 0.532557 | − | 0.307472i | ||||
\(255\) | −14.3989 | − | 9.12269i | −0.901693 | − | 0.571285i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −11.0691 | + | 19.1723i | −0.690472 | + | 1.19593i | 0.281212 | + | 0.959646i | \(0.409264\pi\) |
−0.971683 | + | 0.236287i | \(0.924070\pi\) | |||||||
\(258\) | − | 18.9523i | − | 1.17992i | ||||||
\(259\) | 1.34307 | − | 0.106980i | 0.0834545 | − | 0.00664739i | ||||
\(260\) | 0.150160 | + | 0.286706i | 0.00931253 | + | 0.0177808i | ||||
\(261\) | 7.60518 | + | 4.39085i | 0.470749 | + | 0.271787i | ||||
\(262\) | −1.84401 | + | 1.06464i | −0.113923 | + | 0.0657736i | ||||
\(263\) | 24.9793 | − | 14.4218i | 1.54029 | − | 0.889287i | 0.541469 | − | 0.840720i | \(-0.317868\pi\) |
0.998820 | − | 0.0485661i | \(-0.0154652\pi\) | |||||||
\(264\) | 15.3285 | − | 8.84994i | 0.943406 | − | 0.544676i | ||||
\(265\) | −7.16944 | + | 3.75493i | −0.440415 | + | 0.230664i | ||||
\(266\) | −0.419881 | − | 0.727256i | −0.0257446 | − | 0.0445909i | ||||
\(267\) | −36.4848 | −2.23284 | ||||||||
\(268\) | 12.9680 | + | 7.48709i | 0.792147 | + | 0.457347i | ||||
\(269\) | 9.51308 | 0.580023 | 0.290011 | − | 0.957023i | \(-0.406341\pi\) | ||||
0.290011 | + | 0.957023i | \(0.406341\pi\) | |||||||
\(270\) | −14.1979 | + | 7.43601i | −0.864054 | + | 0.452541i | ||||
\(271\) | −5.71516 | + | 9.89894i | −0.347171 | + | 0.601318i | −0.985746 | − | 0.168242i | \(-0.946191\pi\) |
0.638575 | + | 0.769560i | \(0.279524\pi\) | |||||||
\(272\) | −1.31013 | − | 2.26922i | −0.0794385 | − | 0.137592i | ||||
\(273\) | −0.0932700 | −0.00564496 | ||||||||
\(274\) | −9.84523 | − | 5.68415i | −0.594772 | − | 0.343392i | ||||
\(275\) | −12.9934 | − | 27.5054i | −0.783533 | − | 1.65864i | ||||
\(276\) | 0.699081 | + | 0.403615i | 0.0420797 | + | 0.0242947i | ||||
\(277\) | −15.7756 | − | 27.3242i | −0.947867 | − | 1.64175i | −0.749907 | − | 0.661544i | \(-0.769902\pi\) |
−0.197960 | − | 0.980210i | \(-0.563432\pi\) | |||||||
\(278\) | −3.73056 | − | 6.46151i | −0.223744 | − | 0.387536i | ||||
\(279\) | −3.67349 | − | 2.12089i | −0.219926 | − | 0.126974i | ||||
\(280\) | 0.0203698 | − | 0.494868i | 0.00121733 | − | 0.0295740i | ||||
\(281\) | 12.3570 | + | 7.13433i | 0.737158 | + | 0.425598i | 0.821035 | − | 0.570878i | \(-0.193397\pi\) |
−0.0838770 | + | 0.996476i | \(0.526730\pi\) | |||||||
\(282\) | −21.6045 | −1.28653 | ||||||||
\(283\) | −2.27949 | − | 3.94820i | −0.135502 | − | 0.234696i | 0.790287 | − | 0.612737i | \(-0.209931\pi\) |
−0.925789 | + | 0.378041i | \(0.876598\pi\) | |||||||
\(284\) | −6.50051 | + | 11.2592i | −0.385734 | + | 0.668111i | ||||
\(285\) | 11.4428 | + | 21.8481i | 0.677811 | + | 1.29417i | ||||
\(286\) | −0.880599 | −0.0520709 | ||||||||
\(287\) | 1.94865 | + | 1.12506i | 0.115025 | + | 0.0664100i | ||||
\(288\) | −5.46373 | −0.321954 | ||||||||
\(289\) | 5.06710 | + | 8.77648i | 0.298065 | + | 0.516263i | ||||
\(290\) | 3.18374 | − | 1.66746i | 0.186956 | − | 0.0979165i | ||||
\(291\) | −13.1209 | + | 7.57535i | −0.769161 | + | 0.444075i | ||||
\(292\) | −5.19260 | + | 2.99795i | −0.303874 | + | 0.175442i | ||||
\(293\) | 5.06215 | − | 2.92263i | 0.295734 | − | 0.170742i | −0.344791 | − | 0.938679i | \(-0.612050\pi\) |
0.640525 | + | 0.767938i | \(0.278717\pi\) | |||||||
\(294\) | −17.5128 | − | 10.1110i | −1.02137 | − | 0.589686i | ||||
\(295\) | −25.9149 | + | 13.5727i | −1.50883 | + | 0.790235i | ||||
\(296\) | −5.49268 | − | 2.61351i | −0.319256 | − | 0.151907i | ||||
\(297\) | − | 43.6078i | − | 2.53038i | ||||||
\(298\) | 5.28654 | − | 9.15656i | 0.306241 | − | 0.530425i | ||||
\(299\) | −0.0200805 | − | 0.0347805i | −0.00116129 | − | 0.00201141i | ||||
\(300\) | −1.19548 | + | 14.4970i | −0.0690210 | + | 0.836987i | ||||
\(301\) | 1.24964 | − | 0.721477i | 0.0720278 | − | 0.0415853i | ||||
\(302\) | 14.0736 | 0.809843 | ||||||||
\(303\) | 21.8104 | − | 12.5922i | 1.25297 | − | 0.723404i | ||||
\(304\) | 3.79127i | 0.217444i | ||||||||
\(305\) | 0.937103 | − | 22.7662i | 0.0536584 | − | 1.30359i | ||||
\(306\) | −14.3164 | −0.818416 | ||||||||
\(307\) | 33.1089i | 1.88962i | 0.327614 | + | 0.944812i | \(0.393756\pi\) | ||||
−0.327614 | + | 0.944812i | \(0.606244\pi\) | |||||||
\(308\) | 1.16706 | + | 0.673800i | 0.0664992 | + | 0.0383933i | ||||
\(309\) | −27.9754 | + | 16.1516i | −1.59146 | + | 0.918831i | ||||
\(310\) | −1.53782 | + | 0.805422i | −0.0873425 | + | 0.0457449i | ||||
\(311\) | 21.7793 | + | 12.5743i | 1.23499 | + | 0.713022i | 0.968066 | − | 0.250696i | \(-0.0806594\pi\) |
0.266924 | + | 0.963718i | \(0.413993\pi\) | |||||||
\(312\) | 0.364671 | + | 0.210543i | 0.0206454 | + | 0.0119196i | ||||
\(313\) | 5.97122 | − | 10.3425i | 0.337513 | − | 0.584590i | −0.646451 | − | 0.762955i | \(-0.723748\pi\) |
0.983964 | + | 0.178365i | \(0.0570809\pi\) | |||||||
\(314\) | −13.2368 | + | 7.64224i | −0.746993 | + | 0.431277i | ||||
\(315\) | −2.28594 | − | 1.44830i | −0.128798 | − | 0.0816023i | ||||
\(316\) | −5.73029 | − | 3.30838i | −0.322354 | − | 0.186111i | ||||
\(317\) | 0.692689 | + | 0.399924i | 0.0389053 | + | 0.0224620i | 0.519327 | − | 0.854576i | \(-0.326183\pi\) |
−0.480421 | + | 0.877038i | \(0.659516\pi\) | |||||||
\(318\) | −5.26487 | + | 9.11902i | −0.295239 | + | 0.511369i | ||||
\(319\) | 9.77864i | 0.547499i | ||||||||
\(320\) | −1.19673 | + | 1.88887i | −0.0668993 | + | 0.105591i | ||||
\(321\) | 26.1281 | − | 45.2552i | 1.45833 | − | 2.52590i | ||||
\(322\) | 0.0614593i | 0.00342500i | ||||||||
\(323\) | 9.93413i | 0.552750i | ||||||||
\(324\) | −2.23059 | + | 3.86349i | −0.123922 | + | 0.214639i | ||||
\(325\) | 0.412135 | − | 0.594885i | 0.0228611 | − | 0.0329983i | ||||
\(326\) | 8.94061 | + | 15.4856i | 0.495175 | + | 0.857668i | ||||
\(327\) | 18.9118 | 1.04583 | ||||||||
\(328\) | −5.07928 | − | 8.79757i | −0.280456 | − | 0.485765i | ||||
\(329\) | −0.822444 | − | 1.42451i | −0.0453428 | − | 0.0785360i | ||||
\(330\) | −33.4328 | − | 21.1820i | −1.84041 | − | 1.16603i | ||||
\(331\) | −8.83765 | − | 5.10242i | −0.485761 | − | 0.280454i | 0.237053 | − | 0.971497i | \(-0.423818\pi\) |
−0.722814 | + | 0.691042i | \(0.757152\pi\) | |||||||
\(332\) | 4.06492i | 0.223092i | ||||||||
\(333\) | −27.3717 | + | 18.8502i | −1.49996 | + | 1.03298i | ||||
\(334\) | 7.71580 | 0.422190 | ||||||||
\(335\) | 1.37707 | − | 33.4549i | 0.0752375 | − | 1.82784i | ||||
\(336\) | −0.322198 | − | 0.558064i | −0.0175774 | − | 0.0304449i | ||||
\(337\) | 16.4969 | − | 9.52449i | 0.898644 | − | 0.518832i | 0.0218837 | − | 0.999761i | \(-0.493034\pi\) |
0.876760 | + | 0.480928i | \(0.159700\pi\) | |||||||
\(338\) | 6.48953 | + | 11.2402i | 0.352984 | + | 0.611386i | ||||
\(339\) | 23.7627i | 1.29062i | ||||||||
\(340\) | −3.13575 | + | 4.94935i | −0.170060 | + | 0.268416i | ||||
\(341\) | − | 4.72332i | − | 0.255782i | ||||||
\(342\) | 17.9393 | + | 10.3572i | 0.970044 | + | 0.560055i | ||||
\(343\) | − | 3.09012i | − | 0.166851i | ||||||
\(344\) | −6.51449 | −0.351238 | ||||||||
\(345\) | 0.0742353 | − | 1.80349i | 0.00399669 | − | 0.0970967i | ||||
\(346\) | 8.22699 | − | 4.74986i | 0.442286 | − | 0.255354i | ||||
\(347\) | −13.8443 | −0.743199 | −0.371600 | − | 0.928393i | \(-0.621191\pi\) | ||||
−0.371600 | + | 0.928393i | \(0.621191\pi\) | |||||||
\(348\) | 2.33798 | − | 4.04950i | 0.125329 | − | 0.217076i | ||||
\(349\) | −4.07759 | + | 7.06260i | −0.218268 | + | 0.378052i | −0.954279 | − | 0.298918i | \(-0.903374\pi\) |
0.736010 | + | 0.676970i | \(0.236708\pi\) | |||||||
\(350\) | −1.00138 | + | 0.473050i | −0.0535263 | + | 0.0252856i | ||||
\(351\) | 0.898451 | − | 0.518721i | 0.0479558 | − | 0.0276873i | ||||
\(352\) | −3.04200 | − | 5.26890i | −0.162139 | − | 0.280833i | ||||
\(353\) | 9.11593 | − | 15.7892i | 0.485192 | − | 0.840377i | −0.514663 | − | 0.857392i | \(-0.672083\pi\) |
0.999855 | + | 0.0170155i | \(0.00541646\pi\) | |||||||
\(354\) | −19.0306 | + | 32.9620i | −1.01147 | + | 1.75191i | ||||
\(355\) | 29.0465 | + | 1.19561i | 1.54163 | + | 0.0634566i | ||||
\(356\) | 12.5410i | 0.664671i | ||||||||
\(357\) | −0.844245 | − | 1.46228i | −0.0446822 | − | 0.0773918i | ||||
\(358\) | 9.39416 | + | 5.42372i | 0.496497 | + | 0.286653i | ||||
\(359\) | 10.2372 | 0.540301 | 0.270150 | − | 0.962818i | \(-0.412927\pi\) | ||||
0.270150 | + | 0.962818i | \(0.412927\pi\) | |||||||
\(360\) | 5.66833 | + | 10.8228i | 0.298747 | + | 0.570409i | ||||
\(361\) | −2.31314 | + | 4.00648i | −0.121744 | + | 0.210868i | ||||
\(362\) | 16.9037 | 0.888437 | ||||||||
\(363\) | 65.5445 | − | 37.8421i | 3.44019 | − | 1.98620i | ||||
\(364\) | 0.0320598i | 0.00168039i | ||||||||
\(365\) | 11.3255 | + | 7.17548i | 0.592803 | + | 0.375582i | ||||
\(366\) | −14.8226 | − | 25.6735i | −0.774790 | − | 1.34198i | ||||
\(367\) | 13.0111 | − | 7.51197i | 0.679175 | − | 0.392122i | −0.120369 | − | 0.992729i | \(-0.538408\pi\) |
0.799544 | + | 0.600607i | \(0.205075\pi\) | |||||||
\(368\) | 0.138735 | − | 0.240296i | 0.00723206 | − | 0.0125263i | ||||
\(369\) | −55.5037 | −2.88940 | ||||||||
\(370\) | 0.521439 | + | 13.5915i | 0.0271083 | + | 0.706587i | ||||
\(371\) | −0.801694 | −0.0416219 | ||||||||
\(372\) | −1.12930 | + | 1.95600i | −0.0585515 | + | 0.101414i | ||||
\(373\) | 7.24996 | − | 4.18576i | 0.375389 | − | 0.216731i | −0.300421 | − | 0.953807i | \(-0.597127\pi\) |
0.675810 | + | 0.737076i | \(0.263794\pi\) | |||||||
\(374\) | −7.97085 | − | 13.8059i | −0.412163 | − | 0.713887i | ||||
\(375\) | 29.9565 | − | 12.6718i | 1.54695 | − | 0.654371i | ||||
\(376\) | 7.42616i | 0.382975i | ||||||||
\(377\) | −0.201469 | + | 0.116318i | −0.0103762 | + | 0.00599070i | ||||
\(378\) | −1.58762 | −0.0816584 | ||||||||
\(379\) | −7.69375 | + | 13.3260i | −0.395201 | + | 0.684509i | −0.993127 | − | 0.117043i | \(-0.962658\pi\) |
0.597926 | + | 0.801552i | \(0.295992\pi\) | |||||||
\(380\) | 7.50987 | − | 3.93323i | 0.385248 | − | 0.201771i | ||||
\(381\) | −28.5124 | −1.46073 | ||||||||
\(382\) | −17.9402 | − | 10.3578i | −0.917903 | − | 0.529952i | ||||
\(383\) | 14.0817 | + | 24.3903i | 0.719543 | + | 1.24629i | 0.961181 | + | 0.275919i | \(0.0889822\pi\) |
−0.241637 | + | 0.970367i | \(0.577684\pi\) | |||||||
\(384\) | 2.90925i | 0.148462i | ||||||||
\(385\) | 0.123930 | − | 3.01078i | 0.00631604 | − | 0.153443i | ||||
\(386\) | −7.36191 | + | 12.7512i | −0.374711 | + | 0.649019i | ||||
\(387\) | −17.7967 | + | 30.8248i | −0.904659 | + | 1.56691i | ||||
\(388\) | 2.60389 | + | 4.51006i | 0.132192 | + | 0.228964i | ||||
\(389\) | −15.2311 | + | 8.79367i | −0.772246 | + | 0.445857i | −0.833675 | − | 0.552255i | \(-0.813768\pi\) |
0.0614289 | + | 0.998111i | \(0.480434\pi\) | |||||||
\(390\) | 0.0387243 | − | 0.940779i | 0.00196088 | − | 0.0476382i | ||||
\(391\) | 0.363522 | − | 0.629639i | 0.0183841 | − | 0.0318422i | ||||
\(392\) | −3.47547 | + | 6.01969i | −0.175538 | + | 0.304040i | ||||
\(393\) | 6.19460 | 0.312476 | ||||||||
\(394\) | −18.3664 | + | 10.6038i | −0.925284 | + | 0.534213i | ||||
\(395\) | −0.608498 | + | 14.7830i | −0.0306169 | + | 0.743814i | ||||
\(396\) | −33.2413 | −1.67044 | ||||||||
\(397\) | − | 8.29560i | − | 0.416344i | −0.978092 | − | 0.208172i | \(-0.933249\pi\) | ||
0.978092 | − | 0.208172i | \(-0.0667514\pi\) | |||||||
\(398\) | −12.1798 | − | 7.03201i | −0.610518 | − | 0.352483i | ||||
\(399\) | 2.44308i | 0.122307i | ||||||||
\(400\) | 4.98309 | + | 0.410924i | 0.249154 | + | 0.0205462i | ||||
\(401\) | 12.0757i | 0.603034i | 0.953461 | + | 0.301517i | \(0.0974930\pi\) | ||||
−0.953461 | + | 0.301517i | \(0.902507\pi\) | |||||||
\(402\) | −21.7818 | − | 37.7272i | −1.08638 | − | 1.88166i | ||||
\(403\) | 0.0973146 | − | 0.0561846i | 0.00484759 | − | 0.00279876i | ||||
\(404\) | −4.32834 | − | 7.49690i | −0.215343 | − | 0.372985i | ||||
\(405\) | 9.96706 | + | 0.410264i | 0.495267 | + | 0.0203862i | ||||
\(406\) | 0.356009 | 0.0176685 | ||||||||
\(407\) | −33.4175 | − | 15.9006i | −1.65644 | − | 0.788162i | ||||
\(408\) | 7.62301i | 0.377395i | ||||||||
\(409\) | −8.90476 | − | 5.14117i | −0.440312 | − | 0.254214i | 0.263418 | − | 0.964682i | \(-0.415150\pi\) |
−0.703730 | + | 0.710467i | \(0.748484\pi\) | |||||||
\(410\) | −12.1571 | + | 19.1882i | −0.600394 | + | 0.947638i | ||||
\(411\) | 16.5366 | + | 28.6422i | 0.815691 | + | 1.41282i | ||||
\(412\) | 5.55180 | + | 9.61601i | 0.273518 | + | 0.473747i | ||||
\(413\) | −2.89784 | −0.142593 | ||||||||
\(414\) | −0.758011 | − | 1.31291i | −0.0372542 | − | 0.0645261i | ||||
\(415\) | 8.05194 | − | 4.21714i | 0.395254 | − | 0.207011i | ||||
\(416\) | 0.0723701 | − | 0.125349i | 0.00354824 | − | 0.00614572i | ||||
\(417\) | 21.7062i | 1.06296i | ||||||||
\(418\) | 23.0661i | 1.12820i | ||||||||
\(419\) | −1.28468 | + | 2.22513i | −0.0627606 | + | 0.108704i | −0.895698 | − | 0.444662i | \(-0.853324\pi\) |
0.832938 | + | 0.553367i | \(0.186657\pi\) | |||||||
\(420\) | −0.771169 | + | 1.21718i | −0.0376292 | + | 0.0593924i | ||||
\(421\) | − | 36.5506i | − | 1.78137i | −0.454624 | − | 0.890683i | \(-0.650226\pi\) | ||
0.454624 | − | 0.890683i | \(-0.349774\pi\) | |||||||
\(422\) | 2.22314 | − | 3.85059i | 0.108221 | − | 0.187444i | ||||
\(423\) | 35.1386 | + | 20.2873i | 1.70850 | + | 0.986401i | ||||
\(424\) | 3.13449 | + | 1.80970i | 0.152224 | + | 0.0878868i | ||||
\(425\) | 13.0570 | + | 1.07673i | 0.633358 | + | 0.0522291i | ||||
\(426\) | 32.7558 | − | 18.9116i | 1.58703 | − | 0.916270i | ||||
\(427\) | 1.12854 | − | 1.95468i | 0.0546137 | − | 0.0945938i | ||||
\(428\) | −15.5556 | − | 8.98104i | −0.751909 | − | 0.434115i | ||||
\(429\) | 2.21866 | + | 1.28094i | 0.107118 | + | 0.0618444i | ||||
\(430\) | 6.75843 | + | 12.9041i | 0.325921 | + | 0.622293i | ||||
\(431\) | −12.9598 | + | 7.48236i | −0.624253 | + | 0.360413i | −0.778523 | − | 0.627616i | \(-0.784031\pi\) |
0.154270 | + | 0.988029i | \(0.450697\pi\) | |||||||
\(432\) | 6.20734 | + | 3.58381i | 0.298651 | + | 0.172426i | ||||
\(433\) | 26.7819i | 1.28706i | 0.765422 | + | 0.643528i | \(0.222530\pi\) | ||||
−0.765422 | + | 0.643528i | \(0.777470\pi\) | |||||||
\(434\) | −0.171961 | −0.00825440 | ||||||||
\(435\) | −10.4469 | − | 0.430016i | −0.500891 | − | 0.0206177i | ||||
\(436\) | − | 6.50058i | − | 0.311321i | ||||||
\(437\) | −0.911026 | + | 0.525981i | −0.0435803 | + | 0.0251611i | ||||
\(438\) | 17.4436 | 0.833486 | ||||||||
\(439\) | 27.5675 | − | 15.9161i | 1.31572 | − | 0.759634i | 0.332687 | − | 0.943037i | \(-0.392045\pi\) |
0.983038 | + | 0.183404i | \(0.0587116\pi\) | |||||||
\(440\) | −7.28091 | + | 11.4919i | −0.347104 | + | 0.547855i | ||||
\(441\) | 18.9890 | + | 32.8900i | 0.904240 | + | 1.56619i | ||||
\(442\) | 0.189629 | − | 0.328447i | 0.00901973 | − | 0.0156226i | ||||
\(443\) | 4.63532i | 0.220231i | 0.993919 | + | 0.110115i | \(0.0351220\pi\) | ||||
−0.993919 | + | 0.110115i | \(0.964878\pi\) | |||||||
\(444\) | 10.0371 | + | 14.5745i | 0.476338 | + | 0.691674i | ||||
\(445\) | 24.8416 | − | 13.0106i | 1.17761 | − | 0.616761i | ||||
\(446\) | 9.43602 | + | 5.44789i | 0.446808 | + | 0.257965i | ||||
\(447\) | −26.6387 | + | 15.3799i | −1.25997 | + | 0.727443i | ||||
\(448\) | −0.191824 | + | 0.110750i | −0.00906283 | + | 0.00523243i | ||||
\(449\) | −2.66572 | + | 1.53905i | −0.125803 | + | 0.0726324i | −0.561581 | − | 0.827422i | \(-0.689807\pi\) |
0.435778 | + | 0.900054i | \(0.356473\pi\) | |||||||
\(450\) | 15.5575 | − | 22.4560i | 0.733388 | − | 1.05859i | ||||
\(451\) | −30.9023 | − | 53.5244i | −1.45513 | − | 2.52037i | ||||
\(452\) | 8.16800 | 0.384190 | ||||||||
\(453\) | −35.4581 | − | 20.4718i | −1.66597 | − | 0.961847i | ||||
\(454\) | 3.69503 | 0.173416 | ||||||||
\(455\) | 0.0635052 | − | 0.0332603i | 0.00297717 | − | 0.00155927i | ||||
\(456\) | 5.51487 | − | 9.55204i | 0.258258 | − | 0.447315i | ||||
\(457\) | −5.97845 | − | 10.3550i | −0.279660 | − | 0.484386i | 0.691640 | − | 0.722242i | \(-0.256889\pi\) |
−0.971300 | + | 0.237857i | \(0.923555\pi\) | |||||||
\(458\) | −20.7958 | −0.971725 | ||||||||
\(459\) | 16.2649 | + | 9.39053i | 0.759179 | + | 0.438312i | ||||
\(460\) | −0.619917 | − | 0.0255170i | −0.0289038 | − | 0.00118974i | ||||
\(461\) | −20.8728 | − | 12.0509i | −0.972142 | − | 0.561266i | −0.0722531 | − | 0.997386i | \(-0.523019\pi\) |
−0.899888 | + | 0.436120i | \(0.856352\pi\) | |||||||
\(462\) | −1.96025 | − | 3.39526i | −0.0911992 | − | 0.157962i | ||||
\(463\) | −14.0877 | − | 24.4006i | −0.654712 | − | 1.13399i | −0.981966 | − | 0.189057i | \(-0.939457\pi\) |
0.327254 | − | 0.944936i | \(-0.393877\pi\) | |||||||
\(464\) | −1.39194 | − | 0.803636i | −0.0646191 | − | 0.0373079i | ||||
\(465\) | 5.04611 | + | 0.207708i | 0.234008 | + | 0.00963222i | ||||
\(466\) | −8.61445 | − | 4.97356i | −0.399057 | − | 0.230396i | ||||
\(467\) | −9.72748 | −0.450134 | −0.225067 | − | 0.974343i | \(-0.572260\pi\) | ||||
−0.225067 | + | 0.974343i | \(0.572260\pi\) | |||||||
\(468\) | −0.395411 | − | 0.684872i | −0.0182779 | − | 0.0316582i | ||||
\(469\) | 1.65838 | − | 2.87240i | 0.0765770 | − | 0.132635i | ||||
\(470\) | 14.7100 | − | 7.70424i | 0.678521 | − | 0.355370i | ||||
\(471\) | 44.4664 | 2.04890 | ||||||||
\(472\) | 11.3301 | + | 6.54142i | 0.521509 | + | 0.301093i | ||||
\(473\) | −39.6342 | −1.82238 | ||||||||
\(474\) | 9.62491 | + | 16.6708i | 0.442087 | + | 0.765717i | ||||
\(475\) | −15.5822 | − | 10.7953i | −0.714959 | − | 0.495323i | ||||
\(476\) | −0.502630 | + | 0.290193i | −0.0230380 | + | 0.0133010i | ||||
\(477\) | 17.1260 | − | 9.88772i | 0.784147 | − | 0.452728i | ||||
\(478\) | 10.2828 | − | 5.93680i | 0.470326 | − | 0.271543i | ||||
\(479\) | 12.3632 | + | 7.13788i | 0.564888 | + | 0.326138i | 0.755105 | − | 0.655604i | \(-0.227586\pi\) |
−0.190217 | + | 0.981742i | \(0.560919\pi\) | |||||||
\(480\) | 5.76274 | − | 3.01819i | 0.263032 | − | 0.137761i | ||||
\(481\) | −0.0699066 | − | 0.877641i | −0.00318747 | − | 0.0400170i | ||||
\(482\) | 8.87126i | 0.404075i | ||||||||
\(483\) | 0.0894003 | − | 0.154846i | 0.00406785 | − | 0.00704573i | ||||
\(484\) | −13.0075 | − | 22.5297i | −0.591251 | − | 1.02408i | ||||
\(485\) | 6.23230 | − | 9.83681i | 0.282994 | − | 0.446667i | ||||
\(486\) | −7.38214 | + | 4.26208i | −0.334861 | + | 0.193332i | ||||
\(487\) | 8.42422 | 0.381738 | 0.190869 | − | 0.981616i | \(-0.438869\pi\) | ||||
0.190869 | + | 0.981616i | \(0.438869\pi\) | |||||||
\(488\) | −8.82479 | + | 5.09500i | −0.399479 | + | 0.230640i | ||||
\(489\) | − | 52.0209i | − | 2.35247i | ||||||
\(490\) | 15.5296 | + | 0.639230i | 0.701557 | + | 0.0288775i | ||||
\(491\) | −16.2253 | −0.732237 | −0.366119 | − | 0.930568i | \(-0.619314\pi\) | ||||
−0.366119 | + | 0.930568i | \(0.619314\pi\) | |||||||
\(492\) | 29.5538i | 1.33239i | ||||||||
\(493\) | −3.64725 | − | 2.10574i | −0.164264 | − | 0.0948378i | ||||
\(494\) | −0.475230 | + | 0.274374i | −0.0213816 | + | 0.0123447i | ||||
\(495\) | 34.4861 | + | 65.8456i | 1.55003 | + | 2.95954i | ||||
\(496\) | 0.672340 | + | 0.388176i | 0.0301890 | + | 0.0174296i | ||||
\(497\) | 2.49390 | + | 1.43986i | 0.111867 | + | 0.0645864i | ||||
\(498\) | 5.91294 | − | 10.2415i | 0.264965 | − | 0.458933i | ||||
\(499\) | 18.3628 | − | 10.6018i | 0.822033 | − | 0.474601i | −0.0290841 | − | 0.999577i | \(-0.509259\pi\) |
0.851117 | + | 0.524976i | \(0.175926\pi\) | |||||||
\(500\) | −4.35571 | − | 10.2970i | −0.194793 | − | 0.460495i | ||||
\(501\) | −19.4398 | − | 11.2236i | −0.868507 | − | 0.501433i | ||||
\(502\) | −6.66569 | − | 3.84844i | −0.297504 | − | 0.171764i | ||||
\(503\) | −21.0542 | + | 36.4669i | −0.938760 | + | 1.62598i | −0.170972 | + | 0.985276i | \(0.554691\pi\) |
−0.767788 | + | 0.640704i | \(0.778642\pi\) | |||||||
\(504\) | 1.21021i | 0.0539071i | ||||||||
\(505\) | −10.3597 | + | 16.3514i | −0.461001 | + | 0.727626i | ||||
\(506\) | 0.844063 | − | 1.46196i | 0.0375232 | − | 0.0649921i | ||||
\(507\) | − | 37.7593i | − | 1.67695i | ||||||
\(508\) | 9.80060i | 0.434831i | ||||||||
\(509\) | 1.65619 | − | 2.86861i | 0.0734095 | − | 0.127149i | −0.826984 | − | 0.562225i | \(-0.809945\pi\) |
0.900393 | + | 0.435076i | \(0.143279\pi\) | |||||||
\(510\) | 15.0999 | − | 7.90846i | 0.668636 | − | 0.350192i | ||||
\(511\) | 0.664044 | + | 1.15016i | 0.0293756 | + | 0.0508800i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.5872 | − | 23.5337i | −0.599888 | − | 1.03904i | ||||
\(514\) | −11.0691 | − | 19.1723i | −0.488237 | − | 0.845652i | ||||
\(515\) | 13.2880 | − | 20.9733i | 0.585540 | − | 0.924194i | ||||
\(516\) | 16.4132 | + | 9.47614i | 0.722549 | + | 0.417164i | ||||
\(517\) | 45.1807i | 1.98705i | ||||||||
\(518\) | −0.578889 | + | 1.21663i | −0.0254349 | + | 0.0534554i | ||||
\(519\) | −27.6370 | −1.21313 | ||||||||
\(520\) | −0.323375 | − | 0.0133108i | −0.0141809 | − | 0.000583716i | ||||
\(521\) | 2.68321 | + | 4.64745i | 0.117554 | + | 0.203609i | 0.918798 | − | 0.394729i | \(-0.129161\pi\) |
−0.801244 | + | 0.598338i | \(0.795828\pi\) | |||||||
\(522\) | −7.60518 | + | 4.39085i | −0.332870 | + | 0.192182i | ||||
\(523\) | −17.5017 | − | 30.3138i | −0.765294 | − | 1.32553i | −0.940091 | − | 0.340924i | \(-0.889260\pi\) |
0.174796 | − | 0.984605i | \(-0.444073\pi\) | |||||||
\(524\) | − | 2.12928i | − | 0.0930179i | ||||||
\(525\) | 3.21108 | + | 0.264798i | 0.140143 | + | 0.0115567i | ||||
\(526\) | 28.8436i | 1.25764i | ||||||||
\(527\) | 1.76171 | + | 1.01712i | 0.0767413 | + | 0.0443066i | ||||
\(528\) | 17.6999i | 0.770288i | ||||||||
\(529\) | −22.9230 | −0.996653 | ||||||||
\(530\) | 0.332851 | − | 8.08638i | 0.0144581 | − | 0.351250i | ||||
\(531\) | 61.9045 | − | 35.7406i | 2.68642 | − | 1.55101i | ||||
\(532\) | 0.839763 | 0.0364083 | ||||||||
\(533\) | 0.735176 | − | 1.27336i | 0.0318440 | − | 0.0551554i | ||||
\(534\) | 18.2424 | − | 31.5968i | 0.789427 | − | 1.36733i | ||||
\(535\) | −1.65185 | + | 40.1305i | −0.0714157 | + | 1.73499i | ||||
\(536\) | −12.9680 | + | 7.48709i | −0.560133 | + | 0.323393i | ||||
\(537\) | −15.7790 | − | 27.3300i | −0.680912 | − | 1.17937i | ||||
\(538\) | −4.75654 | + | 8.23857i | −0.205069 | + | 0.355190i | ||||
\(539\) | −21.1448 | + | 36.6238i | −0.910769 | + | 1.57750i | ||||
\(540\) | 0.659156 | − | 16.0137i | 0.0283656 | − | 0.689120i | ||||
\(541\) | − | 30.8147i | − | 1.32483i | −0.749138 | − | 0.662414i | \(-0.769532\pi\) | ||
0.749138 | − | 0.662414i | \(-0.230468\pi\) | |||||||
\(542\) | −5.71516 | − | 9.89894i | −0.245487 | − | 0.425196i | ||||
\(543\) | −42.5885 | − | 24.5885i | −1.82765 | − | 1.05519i | ||||
\(544\) | 2.62027 | 0.112343 | ||||||||
\(545\) | −12.8766 | + | 6.74400i | −0.551572 | + | 0.288881i | ||||
\(546\) | 0.0466350 | − | 0.0807742i | 0.00199579 | − | 0.00345682i | ||||
\(547\) | 1.96309 | 0.0839356 | 0.0419678 | − | 0.999119i | \(-0.486637\pi\) | ||||
0.0419678 | + | 0.999119i | \(0.486637\pi\) | |||||||
\(548\) | 9.84523 | − | 5.68415i | 0.420568 | − | 0.242815i | ||||
\(549\) | 55.6754i | 2.37617i | ||||||||
\(550\) | 30.3171 | + | 2.50006i | 1.29273 | + | 0.106603i | ||||
\(551\) | 3.04680 | + | 5.27721i | 0.129798 | + | 0.224817i | ||||
\(552\) | −0.699081 | + | 0.403615i | −0.0297549 | + | 0.0171790i | ||||
\(553\) | −0.732804 | + | 1.26925i | −0.0311620 | + | 0.0539741i | ||||
\(554\) | 31.5513 | 1.34049 | ||||||||
\(555\) | 18.4567 | − | 35.0020i | 0.783445 | − | 1.48575i | ||||
\(556\) | 7.46111 | 0.316422 | ||||||||
\(557\) | 11.0114 | − | 19.0723i | 0.466567 | − | 0.808118i | −0.532704 | − | 0.846302i | \(-0.678824\pi\) |
0.999271 | + | 0.0381841i | \(0.0121573\pi\) | |||||||
\(558\) | 3.67349 | − | 2.12089i | 0.155511 | − | 0.0897843i | ||||
\(559\) | −0.471455 | − | 0.816583i | −0.0199404 | − | 0.0345378i | ||||
\(560\) | 0.418383 | + | 0.265075i | 0.0176799 | + | 0.0112015i | ||||
\(561\) | 46.3784i | 1.95810i | ||||||||
\(562\) | −12.3570 | + | 7.13433i | −0.521250 | + | 0.300944i | ||||
\(563\) | −15.7065 | −0.661950 | −0.330975 | − | 0.943639i | \(-0.607378\pi\) | ||||
−0.330975 | + | 0.943639i | \(0.607378\pi\) | |||||||
\(564\) | 10.8023 | − | 18.7101i | 0.454858 | − | 0.787837i | ||||
\(565\) | −8.47385 | − | 16.1795i | −0.356498 | − | 0.680675i | ||||
\(566\) | 4.55899 | 0.191629 | ||||||||
\(567\) | 0.855761 | + | 0.494074i | 0.0359386 | + | 0.0207491i | ||||
\(568\) | −6.50051 | − | 11.2592i | −0.272755 | − | 0.472426i | ||||
\(569\) | 4.82994i | 0.202482i | 0.994862 | + | 0.101241i | \(0.0322813\pi\) | ||||
−0.994862 | + | 0.101241i | \(0.967719\pi\) | |||||||
\(570\) | −24.6424 | − | 1.01433i | −1.03216 | − | 0.0424856i | ||||
\(571\) | −0.111370 | + | 0.192898i | −0.00466068 | + | 0.00807253i | −0.868346 | − | 0.495958i | \(-0.834817\pi\) |
0.863686 | + | 0.504031i | \(0.168150\pi\) | |||||||
\(572\) | 0.440300 | − | 0.762621i | 0.0184099 | − | 0.0318868i | ||||
\(573\) | 30.1334 | + | 52.1927i | 1.25884 | + | 2.18038i | ||||
\(574\) | −1.94865 | + | 1.12506i | −0.0813353 | + | 0.0469589i | ||||
\(575\) | 0.592585 | + | 1.25442i | 0.0247125 | + | 0.0523131i | ||||
\(576\) | 2.73187 | − | 4.73173i | 0.113828 | − | 0.197155i | ||||
\(577\) | 18.5090 | − | 32.0586i | 0.770541 | − | 1.33462i | −0.166725 | − | 0.986003i | \(-0.553319\pi\) |
0.937267 | − | 0.348614i | \(-0.113347\pi\) | |||||||
\(578\) | −10.1342 | −0.421527 | ||||||||
\(579\) | 37.0964 | − | 21.4176i | 1.54167 | − | 0.890086i | ||||
\(580\) | −0.147810 | + | 3.59093i | −0.00613747 | + | 0.149105i | ||||
\(581\) | 0.900377 | 0.0373539 | ||||||||
\(582\) | − | 15.1507i | − | 0.628017i | ||||||
\(583\) | 19.0703 | + | 11.0102i | 0.789809 | + | 0.455997i | ||||
\(584\) | − | 5.99590i | − | 0.248112i | ||||||
\(585\) | −0.946400 | + | 1.49376i | −0.0391288 | + | 0.0617594i | ||||
\(586\) | 5.84526i | 0.241466i | ||||||||
\(587\) | 4.12294 | + | 7.14114i | 0.170172 | + | 0.294746i | 0.938480 | − | 0.345334i | \(-0.112234\pi\) |
−0.768308 | + | 0.640080i | \(0.778901\pi\) | |||||||
\(588\) | 17.5128 | − | 10.1110i | 0.722215 | − | 0.416971i | ||||
\(589\) | −1.47168 | − | 2.54902i | −0.0606394 | − | 0.105031i | ||||
\(590\) | 1.20314 | − | 29.2294i | 0.0495324 | − | 1.20335i | ||||
\(591\) | 61.6983 | 2.53793 | ||||||||
\(592\) | 5.00970 | − | 3.45005i | 0.205898 | − | 0.141796i | ||||
\(593\) | 17.9870i | 0.738639i | 0.929302 | + | 0.369320i | \(0.120409\pi\) | ||||
−0.929302 | + | 0.369320i | \(0.879591\pi\) | |||||||
\(594\) | 37.7654 | + | 21.8039i | 1.54953 | + | 0.894624i | ||||
\(595\) | 1.09628 | + | 0.694567i | 0.0449429 | + | 0.0284745i | ||||
\(596\) | 5.28654 | + | 9.15656i | 0.216545 | + | 0.375067i | ||||
\(597\) | 20.4579 | + | 35.4341i | 0.837285 | + | 1.45022i | ||||
\(598\) | 0.0401610 | 0.00164231 | ||||||||
\(599\) | 12.8394 | + | 22.2385i | 0.524604 | + | 0.908640i | 0.999590 | + | 0.0286469i | \(0.00911982\pi\) |
−0.474986 | + | 0.879993i | \(0.657547\pi\) | |||||||
\(600\) | −11.9571 | − | 8.28384i | −0.488145 | − | 0.338186i | ||||
\(601\) | 12.2173 | − | 21.1611i | 0.498356 | − | 0.863178i | −0.501642 | − | 0.865075i | \(-0.667271\pi\) |
0.999998 | + | 0.00189748i | \(0.000603988\pi\) | |||||||
\(602\) | 1.44295i | 0.0588105i | ||||||||
\(603\) | 81.8149i | 3.33176i | ||||||||
\(604\) | −7.03678 | + | 12.1881i | −0.286323 | + | 0.495925i | ||||
\(605\) | −31.1330 | + | 49.1391i | −1.26574 | + | 1.99779i | ||||
\(606\) | 25.1844i | 1.02305i | ||||||||
\(607\) | −8.34623 | + | 14.4561i | −0.338763 | + | 0.586755i | −0.984200 | − | 0.177059i | \(-0.943342\pi\) |
0.645437 | + | 0.763813i | \(0.276675\pi\) | |||||||
\(608\) | −3.28333 | − | 1.89563i | −0.133157 | − | 0.0768781i | ||||
\(609\) | −0.896960 | − | 0.517860i | −0.0363467 | − | 0.0209848i | ||||
\(610\) | 19.2476 | + | 12.1947i | 0.779312 | + | 0.493748i | ||||
\(611\) | −0.930859 | + | 0.537432i | −0.0376585 | + | 0.0217422i | ||||
\(612\) | 7.15822 | − | 12.3984i | 0.289354 | − | 0.501176i | ||||
\(613\) | 28.6684 | + | 16.5517i | 1.15791 | + | 0.668517i | 0.950801 | − | 0.309801i | \(-0.100263\pi\) |
0.207105 | + | 0.978319i | \(0.433596\pi\) | |||||||
\(614\) | −28.6731 | − | 16.5544i | −1.15715 | − | 0.668083i | ||||
\(615\) | 58.5412 | − | 30.6604i | 2.36061 | − | 1.23635i | ||||
\(616\) | −1.16706 | + | 0.673800i | −0.0470220 | + | 0.0271482i | ||||
\(617\) | −4.91286 | − | 2.83644i | −0.197784 | − | 0.114191i | 0.397837 | − | 0.917456i | \(-0.369761\pi\) |
−0.595622 | + | 0.803265i | \(0.703094\pi\) | |||||||
\(618\) | − | 32.3032i | − | 1.29942i | ||||||
\(619\) | −34.6316 | −1.39196 | −0.695980 | − | 0.718061i | \(-0.745030\pi\) | ||||
−0.695980 | + | 0.718061i | \(0.745030\pi\) | |||||||
\(620\) | 0.0713957 | − | 1.73451i | 0.00286732 | − | 0.0696594i | ||||
\(621\) | 1.98880i | 0.0798077i | ||||||||
\(622\) | −21.7793 | + | 12.5743i | −0.873270 | + | 0.504183i | ||||
\(623\) | 2.77782 | 0.111291 | ||||||||
\(624\) | −0.364671 | + | 0.210543i | −0.0145985 | + | 0.00842845i | ||||
\(625\) | −15.8778 | + | 19.3105i | −0.635112 | + | 0.772420i | ||||
\(626\) | 5.97122 | + | 10.3425i | 0.238658 | + | 0.413368i | ||||
\(627\) | 33.5525 | − | 58.1146i | 1.33996 | − | 2.32087i | ||||
\(628\) | − | 15.2845i | − | 0.609917i | ||||||
\(629\) | 13.1268 | − | 9.04005i | 0.523398 | − | 0.360451i | ||||
\(630\) | 2.39723 | − | 1.25553i | 0.0955079 | − | 0.0500215i | ||||
\(631\) | −10.4928 | − | 6.05801i | −0.417711 | − | 0.241165i | 0.276387 | − | 0.961047i | \(-0.410863\pi\) |
−0.694097 | + | 0.719881i | \(0.744196\pi\) | |||||||
\(632\) | 5.73029 | − | 3.30838i | 0.227939 | − | 0.131600i | ||||
\(633\) | −11.2023 | + | 6.46766i | −0.445252 | + | 0.257066i | ||||
\(634\) | −0.692689 | + | 0.399924i | −0.0275102 | + | 0.0158830i | ||||
\(635\) | 19.4134 | − | 10.1676i | 0.770396 | − | 0.403488i | ||||
\(636\) | −5.26487 | − | 9.11902i | −0.208766 | − | 0.361593i | ||||
\(637\) | −1.00608 | −0.0398623 | ||||||||
\(638\) | −8.46855 | − | 4.88932i | −0.335273 | − | 0.193570i | ||||
\(639\) | −71.0341 | −2.81006 | ||||||||
\(640\) | −1.03745 | − | 1.98083i | −0.0410086 | − | 0.0782994i | ||||
\(641\) | −0.0554737 | + | 0.0960833i | −0.00219108 | + | 0.00379506i | −0.867119 | − | 0.498101i | \(-0.834031\pi\) |
0.864928 | + | 0.501896i | \(0.167364\pi\) | |||||||
\(642\) | 26.1281 | + | 45.2552i | 1.03119 | + | 1.78608i | ||||
\(643\) | 13.5510 | 0.534401 | 0.267200 | − | 0.963641i | \(-0.413901\pi\) | ||||
0.267200 | + | 0.963641i | \(0.413901\pi\) | |||||||
\(644\) | −0.0532253 | − | 0.0307297i | −0.00209737 | − | 0.00121092i | ||||
\(645\) | 1.74291 | − | 42.3428i | 0.0686271 | − | 1.66724i | ||||
\(646\) | −8.60321 | − | 4.96707i | −0.338489 | − | 0.195427i | ||||
\(647\) | 11.6638 | + | 20.2022i | 0.458549 | + | 0.794231i | 0.998885 | − | 0.0472191i | \(-0.0150359\pi\) |
−0.540335 | + | 0.841450i | \(0.681703\pi\) | |||||||
\(648\) | −2.23059 | − | 3.86349i | −0.0876258 | − | 0.151772i | ||||
\(649\) | 68.9321 | + | 39.7980i | 2.70582 | + | 1.56221i | ||||
\(650\) | 0.309118 | + | 0.654362i | 0.0121246 | + | 0.0256662i | ||||
\(651\) | 0.433253 | + | 0.250139i | 0.0169805 | + | 0.00980372i | ||||
\(652\) | −17.8812 | −0.700283 | ||||||||
\(653\) | −6.35214 | − | 11.0022i | −0.248578 | − | 0.430551i | 0.714553 | − | 0.699581i | \(-0.246630\pi\) |
−0.963132 | + | 0.269031i | \(0.913297\pi\) | |||||||
\(654\) | −9.45590 | + | 16.3781i | −0.369755 | + | 0.640435i | ||||
\(655\) | −4.21775 | + | 2.20901i | −0.164801 | + | 0.0863131i | ||||
\(656\) | 10.1586 | 0.396625 | ||||||||
\(657\) | −28.3710 | − | 16.3800i | −1.10686 | − | 0.639045i | ||||
\(658\) | 1.64489 | 0.0641244 | ||||||||
\(659\) | −4.80410 | − | 8.32095i | −0.187141 | − | 0.324138i | 0.757155 | − | 0.653236i | \(-0.226589\pi\) |
−0.944296 | + | 0.329097i | \(0.893256\pi\) | |||||||
\(660\) | 35.0605 | − | 18.3627i | 1.36473 | − | 0.714765i | ||||
\(661\) | 7.07993 | − | 4.08760i | 0.275377 | − | 0.158989i | −0.355951 | − | 0.934504i | \(-0.615843\pi\) |
0.631329 | + | 0.775515i | \(0.282510\pi\) | |||||||
\(662\) | 8.83765 | − | 5.10242i | 0.343485 | − | 0.198311i | ||||
\(663\) | −0.955534 | + | 0.551678i | −0.0371099 | + | 0.0214254i | ||||
\(664\) | −3.52033 | − | 2.03246i | −0.136615 | − | 0.0788748i | ||||
\(665\) | −0.871208 | − | 1.66343i | −0.0337840 | − | 0.0645051i | ||||
\(666\) | −2.63887 | − | 33.1297i | −0.102254 | − | 1.28375i | ||||
\(667\) | − | 0.445970i | − | 0.0172680i | ||||||
\(668\) | −3.85790 | + | 6.68208i | −0.149267 | + | 0.258537i | ||||
\(669\) | −15.8493 | − | 27.4517i | −0.612768 | − | 1.06135i | ||||
\(670\) | 28.2843 | + | 17.9200i | 1.09272 | + | 0.692312i | ||||
\(671\) | −53.6900 | + | 30.9979i | −2.07268 | + | 1.19666i | ||||
\(672\) | 0.644396 | 0.0248581 | ||||||||
\(673\) | −24.0589 | + | 13.8904i | −0.927401 | + | 0.535435i | −0.885989 | − | 0.463707i | \(-0.846519\pi\) |
−0.0414126 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(674\) | 19.0490i | 0.733739i | ||||||||
\(675\) | −32.4044 | + | 15.3077i | −1.24724 | + | 0.589193i | ||||
\(676\) | −12.9791 | −0.499194 | ||||||||
\(677\) | − | 25.9326i | − | 0.996672i | −0.866984 | − | 0.498336i | \(-0.833945\pi\) | ||
0.866984 | − | 0.498336i | \(-0.166055\pi\) | |||||||
\(678\) | −20.5791 | − | 11.8814i | −0.790337 | − | 0.456301i | ||||
\(679\) | 0.998975 | − | 0.576759i | 0.0383371 | − | 0.0221340i | ||||
\(680\) | −2.71838 | − | 5.19032i | −0.104245 | − | 0.199039i | ||||
\(681\) | −9.30956 | − | 5.37488i | −0.356743 | − | 0.205966i | ||||
\(682\) | 4.09052 | + | 2.36166i | 0.156634 | + | 0.0904326i | ||||
\(683\) | −11.0153 | + | 19.0791i | −0.421490 | + | 0.730041i | −0.996085 | − | 0.0883959i | \(-0.971826\pi\) |
0.574596 | + | 0.818437i | \(0.305159\pi\) | |||||||
\(684\) | −17.9393 | + | 10.3572i | −0.685925 | + | 0.396019i | ||||
\(685\) | −21.4733 | − | 13.6048i | −0.820451 | − | 0.519812i | ||||
\(686\) | 2.67612 | + | 1.54506i | 0.102175 | + | 0.0589907i | ||||
\(687\) | 52.3947 | + | 30.2501i | 1.99898 | + | 1.15411i | ||||
\(688\) | 3.25725 | − | 5.64172i | 0.124181 | − | 0.215088i | ||||
\(689\) | 0.523873i | 0.0199580i | ||||||||
\(690\) | 1.52475 | + | 0.966036i | 0.0580463 | + | 0.0367763i | ||||
\(691\) | 1.38776 | − | 2.40367i | 0.0527929 | − | 0.0914401i | −0.838421 | − | 0.545023i | \(-0.816521\pi\) |
0.891214 | + | 0.453583i | \(0.149854\pi\) | |||||||
\(692\) | 9.49971i | 0.361125i | ||||||||
\(693\) | 7.36293i | 0.279695i | ||||||||
\(694\) | 6.92213 | − | 11.9895i | 0.262761 | − | 0.455115i | ||||
\(695\) | −7.74050 | − | 14.7792i | −0.293614 | − | 0.560608i | ||||
\(696\) | 2.33798 | + | 4.04950i | 0.0886208 | + | 0.153496i | ||||
\(697\) | 26.6181 | 1.00823 | ||||||||
\(698\) | −4.07759 | − | 7.06260i | −0.154339 | − | 0.267323i | ||||
\(699\) | 14.4693 | + | 25.0616i | 0.547280 | + | 0.947916i | ||||
\(700\) | 0.0910192 | − | 1.10375i | 0.00344020 | − | 0.0417178i | ||||
\(701\) | 2.68900 | + | 1.55249i | 0.101562 | + | 0.0586369i | 0.549921 | − | 0.835217i | \(-0.314658\pi\) |
−0.448359 | + | 0.893854i | \(0.647991\pi\) | |||||||
\(702\) | 1.03744i | 0.0391557i | ||||||||
\(703\) | −22.9886 | + | 1.83111i | −0.867030 | + | 0.0690615i | ||||
\(704\) | 6.08400 | 0.229299 | ||||||||
\(705\) | −48.2684 | − | 1.98682i | −1.81789 | − | 0.0748280i | ||||
\(706\) | 9.11593 | + | 15.7892i | 0.343082 | + | 0.594236i | ||||
\(707\) | −1.66056 | + | 0.958724i | −0.0624517 | + | 0.0360565i | ||||
\(708\) | −19.0306 | − | 32.9620i | −0.715214 | − | 1.23879i | ||||
\(709\) | − | 23.0858i | − | 0.867006i | −0.901152 | − | 0.433503i | \(-0.857277\pi\) | ||
0.901152 | − | 0.433503i | \(-0.142723\pi\) | |||||||
\(710\) | −15.5587 | + | 24.5572i | −0.583908 | + | 0.921617i | ||||
\(711\) | − | 36.1522i | − | 1.35581i | ||||||
\(712\) | −10.8608 | − | 6.27049i | −0.407026 | − | 0.234997i | ||||
\(713\) | 0.215414i | 0.00806732i | ||||||||
\(714\) | 1.68849 | 0.0631902 | ||||||||
\(715\) | −1.96741 | − | 0.0809827i | −0.0735771 | − | 0.00302858i | ||||
\(716\) | −9.39416 | + | 5.42372i | −0.351076 | + | 0.202694i | ||||
\(717\) | −34.5433 | −1.29004 | ||||||||
\(718\) | −5.11862 | + | 8.86571i | −0.191025 | + | 0.330865i | ||||
\(719\) | −6.87917 | + | 11.9151i | −0.256550 | + | 0.444357i | −0.965315 | − | 0.261087i | \(-0.915919\pi\) |
0.708766 | + | 0.705444i | \(0.249252\pi\) | |||||||
\(720\) | −12.2069 | − | 0.502462i | −0.454926 | − | 0.0187257i | ||||
\(721\) | 2.12994 | − | 1.22972i | 0.0793230 | − | 0.0457972i | ||||
\(722\) | −2.31314 | − | 4.00648i | −0.0860863 | − | 0.149106i | ||||
\(723\) | 12.9044 | − | 22.3510i | 0.479918 | − | 0.831243i | ||||
\(724\) | −8.45183 | + | 14.6390i | −0.314110 | + | 0.544054i | ||||
\(725\) | 7.26638 | − | 3.43261i | 0.269867 | − | 0.127484i | ||||
\(726\) | 75.6843i | 2.80891i | ||||||||
\(727\) | 24.4548 | + | 42.3570i | 0.906980 | + | 1.57094i | 0.818237 | + | 0.574881i | \(0.194952\pi\) |
0.0887430 | + | 0.996055i | \(0.471715\pi\) | |||||||
\(728\) | −0.0277646 | − | 0.0160299i | −0.00102903 | − | 0.000594108i | ||||
\(729\) | 38.1824 | 1.41416 | ||||||||
\(730\) | −11.8769 | + | 6.22042i | −0.439584 | + | 0.230228i | ||||
\(731\) | 8.53486 | − | 14.7828i | 0.315673 | − | 0.546762i | ||||
\(732\) | 29.6452 | 1.09572 | ||||||||
\(733\) | −30.1463 | + | 17.4049i | −1.11348 | + | 0.642866i | −0.939728 | − | 0.341924i | \(-0.888922\pi\) |
−0.173749 | + | 0.984790i | \(0.555588\pi\) | |||||||
\(734\) | 15.0239i | 0.554544i | ||||||||
\(735\) | −38.1968 | − | 24.2003i | −1.40891 | − | 0.892641i | ||||
\(736\) | 0.138735 | + | 0.240296i | 0.00511384 | + | 0.00885743i | ||||
\(737\) | −78.8974 | + | 45.5514i | −2.90622 | + | 1.67791i | ||||
\(738\) | 27.7518 | − | 48.0676i | 1.02156 | − | 1.76939i | ||||
\(739\) | 24.3924 | 0.897288 | 0.448644 | − | 0.893711i | \(-0.351907\pi\) | ||||
0.448644 | + | 0.893711i | \(0.351907\pi\) | |||||||
\(740\) | −12.0313 | − | 6.34416i | −0.442279 | − | 0.233216i | ||||
\(741\) | 1.59645 | 0.0586470 | ||||||||
\(742\) | 0.400847 | − | 0.694288i | 0.0147156 | − | 0.0254881i | ||||
\(743\) | −9.95998 | + | 5.75040i | −0.365396 | + | 0.210962i | −0.671445 | − | 0.741054i | \(-0.734326\pi\) |
0.306049 | + | 0.952016i | \(0.400993\pi\) | |||||||
\(744\) | −1.12930 | − | 1.95600i | −0.0414021 | − | 0.0717106i | ||||
\(745\) | 12.6531 | − | 19.9712i | 0.463575 | − | 0.731688i | ||||
\(746\) | 8.37153i | 0.306503i | ||||||||
\(747\) | −19.2341 | + | 11.1048i | −0.703740 | + | 0.406304i | ||||
\(748\) | 15.9417 | 0.582886 | ||||||||
\(749\) | −1.98929 | + | 3.44556i | −0.0726872 | + | 0.125898i | ||||
\(750\) | −4.00410 | + | 32.2790i | −0.146209 | + | 1.17866i | ||||
\(751\) | −14.1263 | −0.515477 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(752\) | −6.43124 | − | 3.71308i | −0.234523 | − | 0.135402i | ||||
\(753\) | 11.1961 | + | 19.3921i | 0.408007 | + | 0.706689i | ||||
\(754\) | − | 0.232637i | − | 0.00847214i | ||||||
\(755\) | 31.4428 | + | 1.29425i | 1.14432 | + | 0.0471025i | ||||
\(756\) | 0.793810 | − | 1.37492i | 0.0288706 | − | 0.0500053i | ||||
\(757\) | 9.97530 | − | 17.2777i | 0.362558 | − | 0.627970i | −0.625823 | − | 0.779965i | \(-0.715237\pi\) |
0.988381 | + | 0.151996i | \(0.0485700\pi\) | |||||||
\(758\) | −7.69375 | − | 13.3260i | −0.279449 | − | 0.484021i | ||||
\(759\) | −4.25321 | + | 2.45559i | −0.154382 | + | 0.0891323i | ||||
\(760\) | −0.348657 | + | 8.47036i | −0.0126471 | + | 0.307252i | ||||
\(761\) | 10.8594 | − | 18.8091i | 0.393654 | − | 0.681829i | −0.599274 | − | 0.800544i | \(-0.704544\pi\) |
0.992928 | + | 0.118715i | \(0.0378775\pi\) | |||||||
\(762\) | 14.2562 | − | 24.6924i | 0.516447 | − | 0.894513i | ||||
\(763\) | −1.43987 | −0.0521269 | ||||||||
\(764\) | 17.9402 | − | 10.3578i | 0.649055 | − | 0.374732i | ||||
\(765\) | −31.9854 | − | 1.31658i | −1.15644 | − | 0.0476012i | ||||
\(766\) | −28.1635 | −1.01759 | ||||||||
\(767\) | 1.89361i | 0.0683744i | ||||||||
\(768\) | −2.51948 | − | 1.45462i | −0.0909140 | − | 0.0524893i | ||||
\(769\) | − | 0.619597i | − | 0.0223432i | −0.999938 | − | 0.0111716i | \(-0.996444\pi\) | ||
0.999938 | − | 0.0111716i | \(-0.00355611\pi\) | |||||||
\(770\) | 2.54544 | + | 1.61271i | 0.0917315 | + | 0.0581182i | ||||
\(771\) | 64.4056i | 2.31951i | ||||||||
\(772\) | −7.36191 | − | 12.7512i | −0.264961 | − | 0.458926i | ||||
\(773\) | 42.5741 | − | 24.5802i | 1.53128 | − | 0.884087i | 0.531981 | − | 0.846756i | \(-0.321448\pi\) |
0.999303 | − | 0.0373311i | \(-0.0118856\pi\) | |||||||
\(774\) | −17.7967 | − | 30.8248i | −0.639690 | − | 1.10798i | ||||
\(775\) | −3.50984 | + | 1.65803i | −0.126077 | + | 0.0595583i | ||||
\(776\) | −5.20777 | −0.186948 | ||||||||
\(777\) | 3.22824 | − | 2.22320i | 0.115812 | − | 0.0797569i | ||||
\(778\) | − | 17.5873i | − | 0.630537i | ||||||
\(779\) | −33.3539 | − | 19.2569i | −1.19503 | − | 0.689950i | ||||
\(780\) | 0.795376 | + | 0.503926i | 0.0284790 | + | 0.0180434i | ||||
\(781\) | −39.5491 | − | 68.5010i | −1.41518 | − | 2.45116i | ||||
\(782\) | 0.363522 | + | 0.629639i | 0.0129995 | + | 0.0225159i | ||||
\(783\) | 11.5203 | 0.411702 | ||||||||
\(784\) | −3.47547 | − | 6.01969i | −0.124124 | − | 0.214989i | ||||
\(785\) | −30.2760 | + | 15.8568i | −1.08060 | + | 0.565954i | ||||
\(786\) | −3.09730 | + | 5.36468i | −0.110477 | + | 0.191352i | ||||
\(787\) | 17.0706i | 0.608501i | 0.952592 | + | 0.304250i | \(0.0984060\pi\) | ||||
−0.952592 | + | 0.304250i | \(0.901594\pi\) | |||||||
\(788\) | − | 21.2076i | − | 0.755491i | ||||||
\(789\) | 41.9566 | − | 72.6710i | 1.49370 | − | 2.58716i | ||||
\(790\) | −12.4982 | − | 7.91848i | −0.444667 | − | 0.281727i | ||||
\(791\) | − | 1.80920i | − | 0.0643279i | ||||||
\(792\) | 16.6207 | − | 28.7879i | 0.590590 | − | 1.02293i | ||||
\(793\) | −1.27730 | − | 0.737451i | −0.0453583 | − | 0.0261876i | ||||
\(794\) | 7.18420 | + | 4.14780i | 0.254958 | + | 0.147200i | ||||
\(795\) | −12.6013 | + | 19.8893i | −0.446921 | + | 0.705402i | ||||
\(796\) | 12.1798 | − | 7.03201i | 0.431701 | − | 0.249243i | ||||
\(797\) | 3.34890 | − | 5.80047i | 0.118624 | − | 0.205463i | −0.800599 | − | 0.599201i | \(-0.795485\pi\) |
0.919223 | + | 0.393738i | \(0.128818\pi\) | |||||||
\(798\) | −2.11577 | − | 1.22154i | −0.0748974 | − | 0.0432420i | ||||
\(799\) | −16.8516 | − | 9.72926i | −0.596166 | − | 0.344196i | ||||
\(800\) | −2.84741 | + | 4.11002i | −0.100671 | + | 0.145311i | ||||
\(801\) | −59.3405 | + | 34.2603i | −2.09670 | + | 1.21053i | ||||
\(802\) | −10.4579 | − | 6.03787i | −0.369281 | − | 0.213205i | ||||
\(803\) | − | 36.4791i | − | 1.28732i | ||||||
\(804\) | 43.5636 | 1.53637 | ||||||||
\(805\) | −0.00565199 | + | 0.137311i | −0.000199207 | + | 0.00483958i | ||||
\(806\) | 0.112369i | 0.00395804i | ||||||||
\(807\) | 23.9681 | − | 13.8380i | 0.843716 | − | 0.487120i | ||||
\(808\) | 8.65668 | 0.304541 | ||||||||
\(809\) | −15.2207 | + | 8.78766i | −0.535130 | + | 0.308958i | −0.743103 | − | 0.669177i | \(-0.766647\pi\) |
0.207973 | + | 0.978135i | \(0.433313\pi\) | |||||||
\(810\) | −5.33883 | + | 8.42659i | −0.187587 | + | 0.296080i | ||||
\(811\) | 23.3915 | + | 40.5153i | 0.821386 | + | 1.42268i | 0.904650 | + | 0.426155i | \(0.140132\pi\) |
−0.0832636 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(812\) | −0.178005 | + | 0.308313i | −0.00624674 | + | 0.0108197i | ||||
\(813\) | 33.2536i | 1.16626i | ||||||||
\(814\) | 30.4790 | − | 20.9901i | 1.06829 | − | 0.735703i | ||||
\(815\) | 18.5508 | + | 35.4197i | 0.649806 | + | 1.24070i | ||||
\(816\) | −6.60172 | − | 3.81150i | −0.231106 | − | 0.133429i | ||||
\(817\) | −21.3893 | + | 12.3491i | −0.748316 | + | 0.432040i | ||||
\(818\) | 8.90476 | − | 5.14117i | 0.311348 | − | 0.179757i | ||||
\(819\) | −0.151699 | + | 0.0875832i | −0.00530077 | + | 0.00306040i | ||||
\(820\) | −10.5390 | − | 20.1224i | −0.368036 | − | 0.702706i | ||||
\(821\) | −24.8327 | − | 43.0115i | −0.866667 | − | 1.50111i | −0.865383 | − | 0.501111i | \(-0.832925\pi\) |
−0.00128385 | − | 0.999999i | \(-0.500409\pi\) | |||||||
\(822\) | −33.0732 | −1.15356 | ||||||||
\(823\) | 24.3430 | + | 14.0545i | 0.848545 | + | 0.489907i | 0.860160 | − | 0.510025i | \(-0.170364\pi\) |
−0.0116149 | + | 0.999933i | \(0.503697\pi\) | |||||||
\(824\) | −11.1036 | −0.386812 | ||||||||
\(825\) | −72.7468 | − | 50.3988i | −2.53272 | − | 1.75466i | ||||
\(826\) | 1.44892 | − | 2.50960i | 0.0504143 | − | 0.0873202i | ||||
\(827\) | −28.2038 | − | 48.8503i | −0.980741 | − | 1.69869i | −0.659518 | − | 0.751689i | \(-0.729240\pi\) |
−0.321223 | − | 0.947004i | \(-0.604094\pi\) | |||||||
\(828\) | 1.51602 | 0.0526854 | ||||||||
\(829\) | −10.8431 | − | 6.26029i | −0.376598 | − | 0.217429i | 0.299739 | − | 0.954021i | \(-0.403100\pi\) |
−0.676337 | + | 0.736592i | \(0.736434\pi\) | |||||||
\(830\) | −0.373823 | + | 9.08175i | −0.0129756 | + | 0.315232i | ||||
\(831\) | −79.4930 | − | 45.8953i | −2.75758 | − | 1.59209i | ||||
\(832\) | 0.0723701 | + | 0.125349i | 0.00250898 | + | 0.00434568i | ||||
\(833\) | −9.10666 | − | 15.7732i | −0.315527 | − | 0.546509i | ||||
\(834\) | −18.7982 | − | 10.8531i | −0.650927 | − | 0.375813i | ||||
\(835\) | 17.2385 | + | 0.709569i | 0.596561 | + | 0.0245556i | ||||
\(836\) | −19.9758 | − | 11.5330i | −0.690878 | − | 0.398878i | ||||
\(837\) | −5.56459 | −0.192340 | ||||||||
\(838\) | −1.28468 | − | 2.22513i | −0.0443784 | − | 0.0768657i | ||||
\(839\) | 6.73506 | − | 11.6655i | 0.232520 | − | 0.402737i | −0.726029 | − | 0.687664i | \(-0.758636\pi\) |
0.958549 | + | 0.284927i | \(0.0919695\pi\) | |||||||
\(840\) | −0.668526 | − | 1.27644i | −0.0230663 | − | 0.0440415i | ||||
\(841\) | 26.4167 | 0.910920 | ||||||||
\(842\) | 31.6537 | + | 18.2753i | 1.09086 | + | 0.629808i | ||||
\(843\) | 41.5111 | 1.42972 | ||||||||
\(844\) | 2.22314 | + | 3.85059i | 0.0765235 | + | 0.132543i | ||||
\(845\) | 13.4651 | + | 25.7094i | 0.463212 | + | 0.884429i | ||||
\(846\) | −35.1386 | + | 20.2873i | −1.20809 | + | 0.697491i | ||||
\(847\) | −4.99031 | + | 2.88116i | −0.171469 | + | 0.0989977i | ||||
\(848\) | −3.13449 | + | 1.80970i | −0.107639 | + | 0.0621454i | ||||
\(849\) | −11.4863 | − | 6.63162i | −0.394209 | − | 0.227596i | ||||
\(850\) | −7.46098 | + | 10.7693i | −0.255910 | + | 0.369385i | ||||
\(851\) | 1.52405 | + | 0.725169i | 0.0522439 | + | 0.0248585i | ||||
\(852\) | 37.8232i | 1.29580i | ||||||||
\(853\) | 15.6089 | − | 27.0354i | 0.534439 | − | 0.925675i | −0.464752 | − | 0.885441i | \(-0.653856\pi\) |
0.999190 | − | 0.0402339i | \(-0.0128103\pi\) | |||||||
\(854\) | 1.12854 | + | 1.95468i | 0.0386177 | + | 0.0668879i | ||||
\(855\) | 39.1270 | + | 24.7896i | 1.33811 | + | 0.847788i | ||||
\(856\) | 15.5556 | − | 8.98104i | 0.531680 | − | 0.306966i | ||||
\(857\) | 22.0143 | 0.751994 | 0.375997 | − | 0.926621i | \(-0.377300\pi\) | ||||
0.375997 | + | 0.926621i | \(0.377300\pi\) | |||||||
\(858\) | −2.21866 | + | 1.28094i | −0.0757437 | + | 0.0437306i | ||||
\(859\) | 32.2800i | 1.10138i | 0.834710 | + | 0.550690i | \(0.185635\pi\) | ||||
−0.834710 | + | 0.550690i | \(0.814365\pi\) | |||||||
\(860\) | −14.5545 | − | 0.599093i | −0.496305 | − | 0.0204289i | ||||
\(861\) | 6.54614 | 0.223092 | ||||||||
\(862\) | − | 14.9647i | − | 0.509700i | ||||||
\(863\) | 2.05241 | + | 1.18496i | 0.0698649 | + | 0.0403365i | 0.534526 | − | 0.845152i | \(-0.320490\pi\) |
−0.464661 | + | 0.885489i | \(0.653824\pi\) | |||||||
\(864\) | −6.20734 | + | 3.58381i | −0.211178 | + | 0.121924i | ||||
\(865\) | 18.8174 | − | 9.85543i | 0.639809 | − | 0.335095i | ||||
\(866\) | −23.1938 | − | 13.3910i | −0.788158 | − | 0.455043i | ||||
\(867\) | 25.5330 | + | 14.7415i | 0.867145 | + | 0.500646i | ||||
\(868\) | 0.0859806 | − | 0.148923i | 0.00291837 | − | 0.00505477i | ||||
\(869\) | 34.8631 | − | 20.1282i | 1.18265 | − | 0.682802i | ||||
\(870\) | 5.59586 | − | 8.83228i | 0.189717 | − | 0.299442i | ||||
\(871\) | −1.87699 | − | 1.08368i | −0.0635995 | − | 0.0367192i | ||||
\(872\) | 5.62967 | + | 3.25029i | 0.190645 | + | 0.110069i | ||||
\(873\) | −14.2269 | + | 24.6418i | −0.481509 | + | 0.833998i | ||||
\(874\) | − | 1.05196i | − | 0.0355832i | ||||||
\(875\) | −2.28077 | + | 0.964786i | −0.0771042 | + | 0.0326157i | ||||
\(876\) | −8.72179 | + | 15.1066i | −0.294682 | + | 0.510404i | ||||
\(877\) | − | 10.1611i | − | 0.343117i | −0.985174 | − | 0.171558i | \(-0.945120\pi\) | ||
0.985174 | − | 0.171558i | \(-0.0548802\pi\) | |||||||
\(878\) | 31.8322i | 1.07428i | ||||||||
\(879\) | 8.50266 | − | 14.7270i | 0.286788 | − | 0.496731i | ||||
\(880\) | −6.31182 | − | 12.0514i | −0.212771 | − | 0.406253i | ||||
\(881\) | 14.8099 | + | 25.6516i | 0.498959 | + | 0.864223i | 0.999999 | − | 0.00120108i | \(-0.000382314\pi\) |
−0.501040 | + | 0.865424i | \(0.667049\pi\) | |||||||
\(882\) | −37.9781 | −1.27879 | ||||||||
\(883\) | 7.92250 | + | 13.7222i | 0.266613 | + | 0.461788i | 0.967985 | − | 0.251008i | \(-0.0807620\pi\) |
−0.701372 | + | 0.712796i | \(0.747429\pi\) | |||||||
\(884\) | 0.189629 | + | 0.328447i | 0.00637791 | + | 0.0110469i | ||||
\(885\) | −45.5490 | + | 71.8928i | −1.53111 | + | 2.41665i | ||||
\(886\) | −4.01430 | − | 2.31766i | −0.134863 | − | 0.0778633i | ||||
\(887\) | − | 40.5502i | − | 1.36154i | −0.732496 | − | 0.680771i | \(-0.761645\pi\) | ||
0.732496 | − | 0.680771i | \(-0.238355\pi\) | |||||||
\(888\) | −17.6404 | + | 1.40511i | −0.591973 | + | 0.0471524i | ||||
\(889\) | 2.17082 | 0.0728071 | ||||||||
\(890\) | −1.15331 | + | 28.0188i | −0.0386590 | + | 0.939191i | ||||
\(891\) | −13.5709 | − | 23.5055i | −0.454642 | − | 0.787464i | ||||
\(892\) | −9.43602 | + | 5.44789i | −0.315941 | + | 0.182409i | ||||
\(893\) | 14.0773 | + | 24.3826i | 0.471078 | + | 0.815931i | ||||
\(894\) | − | 30.7598i | − | 1.02876i | ||||||
\(895\) | 20.4894 | + | 12.9815i | 0.684886 | + | 0.433923i | ||||
\(896\) | − | 0.221499i | − | 0.00739977i | ||||||
\(897\) | −0.101185 | − | 0.0584192i | −0.00337847 | − | 0.00195056i | ||||
\(898\) | − | 3.07810i | − | 0.102718i | ||||||
\(899\) | 1.24781 | 0.0416167 | ||||||||
\(900\) | 11.6687 | + | 24.7012i | 0.388958 | + | 0.823374i | ||||
\(901\) | −8.21321 | + | 4.74190i | −0.273622 | + | 0.157976i | ||||
\(902\) | 61.8047 | 2.05787 | ||||||||
\(903\) | 2.09896 | − | 3.63550i | 0.0698489 | − | 0.120982i | ||||
\(904\) | −4.08400 | + | 7.07369i | −0.135832 | + | 0.235268i | ||||
\(905\) | 37.7658 | + | 1.55451i | 1.25538 | + | 0.0516738i | ||||
\(906\) | 35.4581 | − | 20.4718i | 1.17802 | − | 0.680129i | ||||
\(907\) | −10.4477 | − | 18.0960i | −0.346911 | − | 0.600868i | 0.638788 | − | 0.769383i | \(-0.279436\pi\) |
−0.985699 | + | 0.168515i | \(0.946103\pi\) | |||||||
\(908\) | −1.84751 | + | 3.19999i | −0.0613119 | + | 0.106195i | ||||
\(909\) | 23.6489 | − | 40.9611i | 0.784384 | − | 1.35859i | ||||
\(910\) | −0.00294832 | + | 0.0716273i | −9.77359e−5 | + | 0.00237442i | ||||
\(911\) | 58.1026i | 1.92503i | 0.271236 | + | 0.962513i | \(0.412568\pi\) | ||||
−0.271236 | + | 0.962513i | \(0.587432\pi\) | |||||||
\(912\) | 5.51487 | + | 9.55204i | 0.182616 | + | 0.316300i | ||||
\(913\) | −21.4177 | − | 12.3655i | −0.708821 | − | 0.409238i | ||||
\(914\) | 11.9569 | 0.395499 | ||||||||
\(915\) | −30.7553 | − | 58.7223i | −1.01674 | − | 1.94130i | ||||
\(916\) | 10.3979 | − | 18.0097i | 0.343557 | − | 0.595057i | ||||
\(917\) | −0.471633 | −0.0155747 | ||||||||
\(918\) | −16.2649 | + | 9.39053i | −0.536821 | + | 0.309934i | ||||
\(919\) | − | 19.8144i | − | 0.653616i | −0.945091 | − | 0.326808i | \(-0.894027\pi\) | ||
0.945091 | − | 0.326808i | \(-0.105973\pi\) | |||||||
\(920\) | 0.332057 | − | 0.524105i | 0.0109476 | − | 0.0172792i | ||||
\(921\) | 48.1610 | + | 83.4173i | 1.58696 | + | 2.74869i | ||||
\(922\) | 20.8728 | − | 12.0509i | 0.687408 | − | 0.396875i | ||||
\(923\) | 0.940884 | − | 1.62966i | 0.0309696 | − | 0.0536409i | ||||
\(924\) | 3.92051 | 0.128975 | ||||||||
\(925\) | −0.0849288 | + | 30.4137i | −0.00279244 | + | 0.999996i | ||||
\(926\) | 28.1754 | 0.925902 | ||||||||
\(927\) | −30.3336 | + | 52.5393i | −0.996285 | + | 1.72562i | ||||
\(928\) | 1.39194 | − | 0.803636i | 0.0456926 | − | 0.0263806i | ||||
\(929\) | 27.0154 | + | 46.7921i | 0.886347 | + | 1.53520i | 0.844162 | + | 0.536088i | \(0.180098\pi\) |
0.0421844 | + | 0.999110i | \(0.486568\pi\) | |||||||
\(930\) | −2.70293 | + | 4.26620i | −0.0886327 | + | 0.139894i | ||||
\(931\) | 26.3529i | 0.863680i | ||||||||
\(932\) | 8.61445 | − | 4.97356i | 0.282176 | − | 0.162914i | ||||
\(933\) | 73.1634 | 2.39526 | ||||||||
\(934\) | 4.86374 | − | 8.42425i | 0.159147 | − | 0.275650i | ||||
\(935\) | −16.5386 | − | 31.5779i | −0.540872 | − | 1.03271i | ||||
\(936\) | 0.790822 | 0.0258488 | ||||||||
\(937\) | 12.6396 | + | 7.29747i | 0.412917 | + | 0.238398i | 0.692042 | − | 0.721857i | \(-0.256711\pi\) |
−0.279125 | + | 0.960255i | \(0.590044\pi\) | |||||||
\(938\) | 1.65838 | + | 2.87240i | 0.0541481 | + | 0.0937873i | ||||
\(939\) | − | 34.7435i | − | 1.13381i | ||||||
\(940\) | −0.682933 | + | 16.5913i | −0.0222748 | + | 0.541150i | ||||
\(941\) | −18.8735 | + | 32.6899i | −0.615260 | + | 1.06566i | 0.375079 | + | 0.926993i | \(0.377615\pi\) |
−0.990339 | + | 0.138668i | \(0.955718\pi\) | |||||||
\(942\) | −22.2332 | + | 38.5090i | −0.724397 | + | 1.25469i | ||||
\(943\) | 1.40935 | + | 2.44106i | 0.0458947 | + | 0.0794919i | ||||
\(944\) | −11.3301 | + | 6.54142i | −0.368762 | + | 0.212905i | ||||
\(945\) | −3.54702 | − | 0.146003i | −0.115385 | − | 0.00474946i | ||||
\(946\) | 19.8171 | − | 34.3242i | 0.644309 | − | 1.11598i | ||||
\(947\) | 3.85463 | − | 6.67642i | 0.125259 | − | 0.216955i | −0.796575 | − | 0.604539i | \(-0.793357\pi\) |
0.921834 | + | 0.387585i | \(0.126691\pi\) | |||||||
\(948\) | −19.2498 | −0.625205 | ||||||||
\(949\) | 0.751579 | − | 0.433924i | 0.0243973 | − | 0.0140858i | ||||
\(950\) | 17.1401 | − | 8.09691i | 0.556098 | − | 0.262698i | ||||
\(951\) | 2.32696 | 0.0754568 | ||||||||
\(952\) | − | 0.580387i | − | 0.0188104i | ||||||
\(953\) | 35.7363 | + | 20.6324i | 1.15761 | + | 0.668348i | 0.950731 | − | 0.310018i | \(-0.100335\pi\) |
0.206882 | + | 0.978366i | \(0.433668\pi\) | |||||||
\(954\) | 19.7754i | 0.640254i | ||||||||
\(955\) | −39.1291 | − | 24.7910i | −1.26619 | − | 0.802218i | ||||
\(956\) | 11.8736i | 0.384020i | ||||||||
\(957\) | 14.2243 | + | 24.6371i | 0.459805 | + | 0.796405i | ||||
\(958\) | −12.3632 | + | 7.13788i | −0.399436 | + | 0.230615i | ||||
\(959\) | −1.25903 | − | 2.18071i | −0.0406563 | − | 0.0704188i | ||||
\(960\) | −0.267544 | + | 6.49978i | −0.00863494 | + | 0.209779i | ||||
\(961\) | 30.3973 | 0.980557 | ||||||||
\(962\) | 0.795012 | + | 0.378279i | 0.0256322 | + | 0.0121962i | ||||
\(963\) | − | 98.1400i | − | 3.16252i | ||||||
\(964\) | −7.68274 | − | 4.43563i | −0.247444 | − | 0.142862i | ||||
\(965\) | −17.6204 | + | 27.8114i | −0.567222 | + | 0.895281i | ||||
\(966\) | 0.0894003 | + | 0.154846i | 0.00287641 | + | 0.00498208i | ||||
\(967\) | −20.2368 | − | 35.0512i | −0.650773 | − | 1.12717i | −0.982936 | − | 0.183950i | \(-0.941112\pi\) |
0.332163 | − | 0.943222i | \(-0.392222\pi\) | |||||||
\(968\) | 26.0150 | 0.836155 | ||||||||
\(969\) | 14.4504 | + | 25.0289i | 0.464215 | + | 0.804044i | ||||
\(970\) | 5.40278 | + | 10.3157i | 0.173473 | + | 0.331218i | ||||
\(971\) | −10.5662 | + | 18.3012i | −0.339086 | + | 0.587314i | −0.984261 | − | 0.176721i | \(-0.943451\pi\) |
0.645175 | + | 0.764035i | \(0.276784\pi\) | |||||||
\(972\) | − | 8.52416i | − | 0.273413i | ||||||
\(973\) | − | 1.65263i | − | 0.0529809i | ||||||
\(974\) | −4.21211 | + | 7.29559i | −0.134965 | + | 0.233766i | ||||
\(975\) | 0.173034 | − | 2.09830i | 0.00554152 | − | 0.0671995i | ||||
\(976\) | − | 10.1900i | − | 0.326174i | ||||||
\(977\) | 5.43288 | − | 9.41002i | 0.173813 | − | 0.301053i | −0.765937 | − | 0.642916i | \(-0.777724\pi\) |
0.939750 | + | 0.341863i | \(0.111058\pi\) | |||||||
\(978\) | 45.0515 | + | 26.0105i | 1.44059 | + | 0.831723i | ||||
\(979\) | −66.0771 | − | 38.1497i | −2.11183 | − | 1.21927i | ||||
\(980\) | −8.31840 | + | 13.1294i | −0.265722 | + | 0.419404i | ||||
\(981\) | 30.7590 | − | 17.7587i | 0.982059 | − | 0.566992i | ||||
\(982\) | 8.11265 | − | 14.0515i | 0.258885 | − | 0.448402i | ||||
\(983\) | −9.33874 | − | 5.39172i | −0.297860 | − | 0.171969i | 0.343621 | − | 0.939108i | \(-0.388346\pi\) |
−0.641481 | + | 0.767139i | \(0.721680\pi\) | |||||||
\(984\) | −25.5943 | − | 14.7769i | −0.815917 | − | 0.471070i | ||||
\(985\) | −42.0088 | + | 22.0018i | −1.33851 | + | 0.701035i | ||||
\(986\) | 3.64725 | − | 2.10574i | 0.116152 | − | 0.0670604i | ||||
\(987\) | −4.14427 | − | 2.39269i | −0.131914 | − | 0.0761603i | ||||
\(988\) | − | 0.548749i | − | 0.0174580i | ||||||
\(989\) | 1.80758 | 0.0574776 | ||||||||
\(990\) | −74.2670 | − | 3.05698i | −2.36036 | − | 0.0971571i | ||||
\(991\) | − | 5.98300i | − | 0.190056i | −0.995475 | − | 0.0950282i | \(-0.969706\pi\) | ||
0.995475 | − | 0.0950282i | \(-0.0302941\pi\) | |||||||
\(992\) | −0.672340 | + | 0.388176i | −0.0213468 | + | 0.0123246i | ||||
\(993\) | −29.6884 | −0.942134 | ||||||||
\(994\) | −2.49390 | + | 1.43986i | −0.0791019 | + | 0.0456695i | ||||
\(995\) | −26.5651 | − | 16.8308i | −0.842171 | − | 0.533573i | ||||
\(996\) | 5.91294 | + | 10.2415i | 0.187359 | + | 0.324515i | ||||
\(997\) | 11.8896 | − | 20.5935i | 0.376549 | − | 0.652202i | −0.614009 | − | 0.789299i | \(-0.710444\pi\) |
0.990558 | + | 0.137097i | \(0.0437773\pi\) | |||||||
\(998\) | 21.2036i | 0.671187i | ||||||||
\(999\) | −18.7326 | + | 39.3694i | −0.592673 | + | 1.24559i |
(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 | 370.2.m.c.249.8 | yes | 16 | |
5.4 | even | 2 | 370.2.m.d.249.1 | yes | 16 | ||
37.11 | even | 6 | 370.2.m.d.159.1 | yes | 16 | ||
185.159 | even | 6 | inner | 370.2.m.c.159.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.m.c.159.8 | ✓ | 16 | 185.159 | even | 6 | inner | |
370.2.m.c.249.8 | yes | 16 | 1.1 | even | 1 | trivial | |
370.2.m.d.159.1 | yes | 16 | 37.11 | even | 6 | ||
370.2.m.d.249.1 | yes | 16 | 5.4 | even | 2 |