Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(307,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.e (of order \(3\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 307.9 | ||
Character | \(\chi\) | \(=\) | 731.307 |
Dual form | 731.2.e.b.681.9 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32448 | −0.936550 | −0.468275 | − | 0.883583i | \(-0.655124\pi\) | ||||
−0.468275 | + | 0.883583i | \(0.655124\pi\) | |||||||
\(3\) | 1.04438 | − | 1.80892i | 0.602972 | − | 1.04438i | −0.389396 | − | 0.921070i | \(-0.627316\pi\) |
0.992368 | − | 0.123308i | \(-0.0393504\pi\) | |||||||
\(4\) | −0.245749 | −0.122874 | ||||||||
\(5\) | 1.40548 | − | 2.43436i | 0.628550 | − | 1.08868i | −0.359292 | − | 0.933225i | \(-0.616982\pi\) |
0.987843 | − | 0.155456i | \(-0.0496847\pi\) | |||||||
\(6\) | −1.38326 | + | 2.39588i | −0.564714 | + | 0.978113i | ||||
\(7\) | 0.178508 | + | 0.309184i | 0.0674696 | + | 0.116861i | 0.897787 | − | 0.440430i | \(-0.145174\pi\) |
−0.830317 | + | 0.557291i | \(0.811841\pi\) | |||||||
\(8\) | 2.97445 | 1.05163 | ||||||||
\(9\) | −0.681454 | − | 1.18031i | −0.227151 | − | 0.393438i | ||||
\(10\) | −1.86153 | + | 3.22427i | −0.588669 | + | 1.01960i | ||||
\(11\) | −3.97943 | −1.19984 | −0.599922 | − | 0.800059i | \(-0.704802\pi\) | ||||
−0.599922 | + | 0.800059i | \(0.704802\pi\) | |||||||
\(12\) | −0.256655 | + | 0.444539i | −0.0740898 | + | 0.128327i | ||||
\(13\) | −2.36455 | − | 4.09553i | −0.655809 | − | 1.13589i | −0.981690 | − | 0.190484i | \(-0.938994\pi\) |
0.325881 | − | 0.945411i | \(-0.394339\pi\) | |||||||
\(14\) | −0.236430 | − | 0.409509i | −0.0631886 | − | 0.109446i | ||||
\(15\) | −2.93571 | − | 5.08480i | −0.757997 | − | 1.31289i | ||||
\(16\) | −3.44811 | −0.862028 | ||||||||
\(17\) | −0.500000 | − | 0.866025i | −0.121268 | − | 0.210042i | ||||
\(18\) | 0.902573 | + | 1.56330i | 0.212739 | + | 0.368474i | ||||
\(19\) | 1.25318 | − | 2.17057i | 0.287500 | − | 0.497964i | −0.685713 | − | 0.727872i | \(-0.740509\pi\) |
0.973212 | + | 0.229909i | \(0.0738427\pi\) | |||||||
\(20\) | −0.345395 | + | 0.598242i | −0.0772327 | + | 0.133771i | ||||
\(21\) | 0.745719 | 0.162729 | ||||||||
\(22\) | 5.27068 | 1.12371 | ||||||||
\(23\) | 0.569368 | − | 0.986175i | 0.118721 | − | 0.205632i | −0.800540 | − | 0.599280i | \(-0.795454\pi\) |
0.919261 | + | 0.393648i | \(0.128787\pi\) | |||||||
\(24\) | 3.10646 | − | 5.38054i | 0.634103 | − | 1.09830i | ||||
\(25\) | −1.45076 | − | 2.51278i | −0.290151 | − | 0.502556i | ||||
\(26\) | 3.13181 | + | 5.42445i | 0.614198 | + | 1.06382i | ||||
\(27\) | 3.41949 | 0.658081 | ||||||||
\(28\) | −0.0438680 | − | 0.0759816i | −0.00829028 | − | 0.0143592i | ||||
\(29\) | 0.524106 | + | 0.907778i | 0.0973240 | + | 0.168570i | 0.910576 | − | 0.413341i | \(-0.135638\pi\) |
−0.813252 | + | 0.581911i | \(0.802305\pi\) | |||||||
\(30\) | 3.88829 | + | 6.73472i | 0.709902 | + | 1.22959i | ||||
\(31\) | 2.49198 | − | 4.31623i | 0.447572 | − | 0.775218i | −0.550655 | − | 0.834733i | \(-0.685622\pi\) |
0.998227 | + | 0.0595147i | \(0.0189553\pi\) | |||||||
\(32\) | −1.38195 | −0.244296 | ||||||||
\(33\) | −4.15603 | + | 7.19846i | −0.723473 | + | 1.25309i | ||||
\(34\) | 0.662241 | + | 1.14703i | 0.113573 | + | 0.196715i | ||||
\(35\) | 1.00356 | 0.169632 | ||||||||
\(36\) | 0.167466 | + | 0.290060i | 0.0279111 | + | 0.0483434i | ||||
\(37\) | −4.47170 | + | 7.74521i | −0.735142 | + | 1.27330i | 0.219518 | + | 0.975608i | \(0.429551\pi\) |
−0.954661 | + | 0.297696i | \(0.903782\pi\) | |||||||
\(38\) | −1.65982 | + | 2.87488i | −0.269258 | + | 0.466368i | ||||
\(39\) | −9.87796 | −1.58174 | ||||||||
\(40\) | 4.18054 | − | 7.24090i | 0.661001 | − | 1.14489i | ||||
\(41\) | −10.1140 | −1.57954 | −0.789771 | − | 0.613401i | \(-0.789801\pi\) | ||||
−0.789771 | + | 0.613401i | \(0.789801\pi\) | |||||||
\(42\) | −0.987690 | −0.152404 | ||||||||
\(43\) | 6.55501 | + | 0.178430i | 0.999630 | + | 0.0272103i | ||||
\(44\) | 0.977940 | 0.147430 | ||||||||
\(45\) | −3.83108 | −0.571104 | ||||||||
\(46\) | −0.754118 | + | 1.30617i | −0.111189 | + | 0.192584i | ||||
\(47\) | −13.0872 | −1.90896 | −0.954481 | − | 0.298271i | \(-0.903590\pi\) | ||||
−0.954481 | + | 0.298271i | \(0.903590\pi\) | |||||||
\(48\) | −3.60113 | + | 6.23735i | −0.519779 | + | 0.900283i | ||||
\(49\) | 3.43627 | − | 5.95179i | 0.490896 | − | 0.850256i | ||||
\(50\) | 1.92150 | + | 3.32813i | 0.271741 | + | 0.470669i | ||||
\(51\) | −2.08876 | −0.292485 | ||||||||
\(52\) | 0.581086 | + | 1.00647i | 0.0805821 | + | 0.139572i | ||||
\(53\) | 3.33610 | − | 5.77830i | 0.458249 | − | 0.793711i | −0.540619 | − | 0.841267i | \(-0.681810\pi\) |
0.998869 | + | 0.0475564i | \(0.0151434\pi\) | |||||||
\(54\) | −4.52905 | −0.616325 | ||||||||
\(55\) | −5.59302 | + | 9.68739i | −0.754162 | + | 1.30625i | ||||
\(56\) | 0.530963 | + | 0.919654i | 0.0709529 | + | 0.122894i | ||||
\(57\) | −2.61759 | − | 4.53380i | −0.346709 | − | 0.600517i | ||||
\(58\) | −0.694168 | − | 1.20233i | −0.0911488 | − | 0.157874i | ||||
\(59\) | 5.56077 | 0.723950 | 0.361975 | − | 0.932188i | \(-0.382102\pi\) | ||||
0.361975 | + | 0.932188i | \(0.382102\pi\) | |||||||
\(60\) | 0.721447 | + | 1.24958i | 0.0931384 | + | 0.161320i | ||||
\(61\) | 0.395036 | + | 0.684222i | 0.0505792 | + | 0.0876057i | 0.890207 | − | 0.455557i | \(-0.150560\pi\) |
−0.839627 | + | 0.543163i | \(0.817227\pi\) | |||||||
\(62\) | −3.30058 | + | 5.71677i | −0.419174 | + | 0.726031i | ||||
\(63\) | 0.243290 | − | 0.421390i | 0.0306516 | − | 0.0530901i | ||||
\(64\) | 8.72658 | 1.09082 | ||||||||
\(65\) | −13.2933 | −1.64884 | ||||||||
\(66\) | 5.50459 | − | 9.53423i | 0.677568 | − | 1.17358i | ||||
\(67\) | −7.02236 | + | 12.1631i | −0.857918 | + | 1.48596i | 0.0159938 | + | 0.999872i | \(0.494909\pi\) |
−0.873912 | + | 0.486085i | \(0.838425\pi\) | |||||||
\(68\) | 0.122874 | + | 0.212825i | 0.0149007 | + | 0.0258088i | ||||
\(69\) | −1.18927 | − | 2.05988i | −0.143172 | − | 0.247980i | ||||
\(70\) | −1.32919 | −0.158869 | ||||||||
\(71\) | −0.353987 | − | 0.613124i | −0.0420106 | − | 0.0727644i | 0.844256 | − | 0.535941i | \(-0.180043\pi\) |
−0.886266 | + | 0.463176i | \(0.846710\pi\) | |||||||
\(72\) | −2.02695 | − | 3.51079i | −0.238879 | − | 0.413750i | ||||
\(73\) | −1.13731 | − | 1.96987i | −0.133112 | − | 0.230556i | 0.791763 | − | 0.610829i | \(-0.209164\pi\) |
−0.924874 | + | 0.380273i | \(0.875830\pi\) | |||||||
\(74\) | 5.92268 | − | 10.2584i | 0.688498 | − | 1.19251i | ||||
\(75\) | −6.06055 | −0.699812 | ||||||||
\(76\) | −0.307968 | + | 0.533415i | −0.0353263 | + | 0.0611869i | ||||
\(77\) | −0.710359 | − | 1.23038i | −0.0809529 | − | 0.140215i | ||||
\(78\) | 13.0832 | 1.48138 | ||||||||
\(79\) | 0.704747 | + | 1.22066i | 0.0792902 | + | 0.137335i | 0.902944 | − | 0.429758i | \(-0.141401\pi\) |
−0.823654 | + | 0.567093i | \(0.808068\pi\) | |||||||
\(80\) | −4.84625 | + | 8.39396i | −0.541828 | + | 0.938473i | ||||
\(81\) | 5.61560 | − | 9.72651i | 0.623956 | − | 1.08072i | ||||
\(82\) | 13.3958 | 1.47932 | ||||||||
\(83\) | 4.87520 | − | 8.44409i | 0.535122 | − | 0.926859i | −0.464035 | − | 0.885817i | \(-0.653599\pi\) |
0.999157 | − | 0.0410421i | \(-0.0130678\pi\) | |||||||
\(84\) | −0.183259 | −0.0199952 | ||||||||
\(85\) | −2.81096 | −0.304892 | ||||||||
\(86\) | −8.68199 | − | 0.236327i | −0.936203 | − | 0.0254838i | ||||
\(87\) | 2.18946 | 0.234735 | ||||||||
\(88\) | −11.8366 | −1.26179 | ||||||||
\(89\) | 1.58885 | − | 2.75197i | 0.168418 | − | 0.291708i | −0.769446 | − | 0.638712i | \(-0.779468\pi\) |
0.937864 | + | 0.347004i | \(0.112801\pi\) | |||||||
\(90\) | 5.07420 | 0.534868 | ||||||||
\(91\) | 0.844182 | − | 1.46217i | 0.0884943 | − | 0.153277i | ||||
\(92\) | −0.139921 | + | 0.242351i | −0.0145878 | + | 0.0252668i | ||||
\(93\) | −5.20514 | − | 9.01556i | −0.539748 | − | 0.934870i | ||||
\(94\) | 17.3337 | 1.78784 | ||||||||
\(95\) | −3.52265 | − | 6.10140i | −0.361416 | − | 0.625991i | ||||
\(96\) | −1.44328 | + | 2.49983i | −0.147304 | + | 0.255138i | ||||
\(97\) | −7.36932 | −0.748241 | −0.374120 | − | 0.927380i | \(-0.622055\pi\) | ||||
−0.374120 | + | 0.927380i | \(0.622055\pi\) | |||||||
\(98\) | −4.55128 | + | 7.88304i | −0.459748 | + | 0.796307i | ||||
\(99\) | 2.71180 | + | 4.69698i | 0.272546 | + | 0.472064i | ||||
\(100\) | 0.356521 | + | 0.617513i | 0.0356521 | + | 0.0617513i | ||||
\(101\) | −1.55157 | − | 2.68739i | −0.154387 | − | 0.267406i | 0.778449 | − | 0.627708i | \(-0.216007\pi\) |
−0.932836 | + | 0.360302i | \(0.882674\pi\) | |||||||
\(102\) | 2.76652 | 0.273926 | ||||||||
\(103\) | 2.41493 | + | 4.18277i | 0.237950 | + | 0.412141i | 0.960126 | − | 0.279568i | \(-0.0901913\pi\) |
−0.722176 | + | 0.691709i | \(0.756858\pi\) | |||||||
\(104\) | −7.03325 | − | 12.1819i | −0.689667 | − | 1.19454i | ||||
\(105\) | 1.04809 | − | 1.81535i | 0.102283 | − | 0.177160i | ||||
\(106\) | −4.41861 | + | 7.65326i | −0.429173 | + | 0.743350i | ||||
\(107\) | 14.6213 | 1.41349 | 0.706747 | − | 0.707467i | \(-0.250162\pi\) | ||||
0.706747 | + | 0.707467i | \(0.250162\pi\) | |||||||
\(108\) | −0.840334 | −0.0808612 | ||||||||
\(109\) | −4.63683 | + | 8.03123i | −0.444128 | + | 0.769252i | −0.997991 | − | 0.0633558i | \(-0.979820\pi\) |
0.553863 | + | 0.832608i | \(0.313153\pi\) | |||||||
\(110\) | 7.40785 | − | 12.8308i | 0.706311 | − | 1.22337i | ||||
\(111\) | 9.34029 | + | 16.1779i | 0.886541 | + | 1.53553i | ||||
\(112\) | −0.615514 | − | 1.06610i | −0.0581606 | − | 0.100737i | ||||
\(113\) | −3.76954 | −0.354608 | −0.177304 | − | 0.984156i | \(-0.556738\pi\) | ||||
−0.177304 | + | 0.984156i | \(0.556738\pi\) | |||||||
\(114\) | 3.46695 | + | 6.00494i | 0.324710 | + | 0.562414i | ||||
\(115\) | −1.60047 | − | 2.77210i | −0.149245 | − | 0.258500i | ||||
\(116\) | −0.128798 | − | 0.223085i | −0.0119586 | − | 0.0207129i | ||||
\(117\) | −3.22267 | + | 5.58183i | −0.297936 | + | 0.516040i | ||||
\(118\) | −7.36514 | −0.678016 | ||||||||
\(119\) | 0.178508 | − | 0.309184i | 0.0163638 | − | 0.0283429i | ||||
\(120\) | −8.73213 | − | 15.1245i | −0.797131 | − | 1.38067i | ||||
\(121\) | 4.83588 | 0.439625 | ||||||||
\(122\) | −0.523218 | − | 0.906240i | −0.0473699 | − | 0.0820471i | ||||
\(123\) | −10.5629 | + | 18.2954i | −0.952421 | + | 1.64964i | ||||
\(124\) | −0.612400 | + | 1.06071i | −0.0549952 | + | 0.0952544i | ||||
\(125\) | 5.89878 | 0.527603 | ||||||||
\(126\) | −0.322233 | + | 0.558123i | −0.0287068 | + | 0.0497216i | ||||
\(127\) | −8.71353 | −0.773200 | −0.386600 | − | 0.922247i | \(-0.626351\pi\) | ||||
−0.386600 | + | 0.922247i | \(0.626351\pi\) | |||||||
\(128\) | −8.79431 | −0.777314 | ||||||||
\(129\) | 7.16868 | − | 11.6711i | 0.631167 | − | 1.02759i | ||||
\(130\) | 17.6068 | 1.54422 | ||||||||
\(131\) | −0.0278540 | −0.00243362 | −0.00121681 | − | 0.999999i | \(-0.500387\pi\) | ||||
−0.00121681 | + | 0.999999i | \(0.500387\pi\) | |||||||
\(132\) | 1.02134 | − | 1.76901i | 0.0888962 | − | 0.153973i | ||||
\(133\) | 0.894810 | 0.0775899 | ||||||||
\(134\) | 9.30099 | − | 16.1098i | 0.803483 | − | 1.39167i | ||||
\(135\) | 4.80603 | − | 8.32428i | 0.413637 | − | 0.716440i | ||||
\(136\) | −1.48723 | − | 2.57595i | −0.127529 | − | 0.220886i | ||||
\(137\) | 0.941787 | 0.0804623 | 0.0402311 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402311 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(138\) | 1.57517 | + | 2.72827i | 0.134087 | + | 0.232246i | ||||
\(139\) | 6.05172 | − | 10.4819i | 0.513300 | − | 0.889062i | −0.486581 | − | 0.873636i | \(-0.661756\pi\) |
0.999881 | − | 0.0154265i | \(-0.00491061\pi\) | |||||||
\(140\) | −0.246623 | −0.0208434 | ||||||||
\(141\) | −13.6680 | + | 23.6736i | −1.15105 | + | 1.99368i | ||||
\(142\) | 0.468850 | + | 0.812071i | 0.0393450 | + | 0.0681475i | ||||
\(143\) | 9.40958 | + | 16.2979i | 0.786868 | + | 1.36290i | ||||
\(144\) | 2.34973 | + | 4.06985i | 0.195811 | + | 0.339154i | ||||
\(145\) | 2.94648 | 0.244692 | ||||||||
\(146\) | 1.50634 | + | 2.60906i | 0.124666 | + | 0.215927i | ||||
\(147\) | −7.17754 | − | 12.4319i | −0.591993 | − | 1.02536i | ||||
\(148\) | 1.09891 | − | 1.90337i | 0.0903301 | − | 0.156456i | ||||
\(149\) | 7.50590 | − | 13.0006i | 0.614907 | − | 1.06505i | −0.375493 | − | 0.926825i | \(-0.622527\pi\) |
0.990401 | − | 0.138226i | \(-0.0441399\pi\) | |||||||
\(150\) | 8.02709 | 0.655409 | ||||||||
\(151\) | 14.5323 | 1.18262 | 0.591309 | − | 0.806445i | \(-0.298611\pi\) | ||||
0.591309 | + | 0.806445i | \(0.298611\pi\) | |||||||
\(152\) | 3.72753 | − | 6.45627i | 0.302342 | − | 0.523673i | ||||
\(153\) | −0.681454 | + | 1.18031i | −0.0550923 | + | 0.0954227i | ||||
\(154\) | 0.940858 | + | 1.62961i | 0.0758165 | + | 0.131318i | ||||
\(155\) | −7.00486 | − | 12.1328i | −0.562644 | − | 0.974527i | ||||
\(156\) | 2.42749 | 0.194355 | ||||||||
\(157\) | 1.79702 | + | 3.11253i | 0.143418 | + | 0.248407i | 0.928782 | − | 0.370628i | \(-0.120857\pi\) |
−0.785364 | + | 0.619035i | \(0.787524\pi\) | |||||||
\(158\) | −0.933424 | − | 1.61674i | −0.0742592 | − | 0.128621i | ||||
\(159\) | −6.96831 | − | 12.0695i | −0.552623 | − | 0.957172i | ||||
\(160\) | −1.94230 | + | 3.36416i | −0.153552 | + | 0.265960i | ||||
\(161\) | 0.406546 | 0.0320403 | ||||||||
\(162\) | −7.43776 | + | 12.8826i | −0.584366 | + | 1.01215i | ||||
\(163\) | 5.34492 | + | 9.25767i | 0.418646 | + | 0.725116i | 0.995804 | − | 0.0915166i | \(-0.0291714\pi\) |
−0.577157 | + | 0.816633i | \(0.695838\pi\) | |||||||
\(164\) | 2.48550 | 0.194085 | ||||||||
\(165\) | 11.6825 | + | 20.2346i | 0.909478 | + | 1.57526i | ||||
\(166\) | −6.45711 | + | 11.1840i | −0.501169 | + | 0.868050i | ||||
\(167\) | 8.21461 | − | 14.2281i | 0.635666 | − | 1.10101i | −0.350708 | − | 0.936485i | \(-0.614059\pi\) |
0.986374 | − | 0.164521i | \(-0.0526077\pi\) | |||||||
\(168\) | 2.21810 | 0.171130 | ||||||||
\(169\) | −4.68222 | + | 8.10985i | −0.360171 | + | 0.623834i | ||||
\(170\) | 3.72307 | 0.285546 | ||||||||
\(171\) | −3.41594 | −0.261224 | ||||||||
\(172\) | −1.61088 | − | 0.0438488i | −0.122829 | − | 0.00334344i | ||||
\(173\) | 4.44011 | 0.337575 | 0.168788 | − | 0.985652i | \(-0.446015\pi\) | ||||
0.168788 | + | 0.985652i | \(0.446015\pi\) | |||||||
\(174\) | −2.89990 | −0.219841 | ||||||||
\(175\) | 0.517942 | − | 0.897102i | 0.0391527 | − | 0.0678145i | ||||
\(176\) | 13.7215 | 1.03430 | ||||||||
\(177\) | 5.80755 | − | 10.0590i | 0.436522 | − | 0.756078i | ||||
\(178\) | −2.10440 | + | 3.64493i | −0.157731 | + | 0.273199i | ||||
\(179\) | −5.44729 | − | 9.43498i | −0.407150 | − | 0.705204i | 0.587419 | − | 0.809283i | \(-0.300144\pi\) |
−0.994569 | + | 0.104079i | \(0.966811\pi\) | |||||||
\(180\) | 0.941484 | 0.0701740 | ||||||||
\(181\) | −5.75467 | − | 9.96737i | −0.427741 | − | 0.740869i | 0.568931 | − | 0.822385i | \(-0.307357\pi\) |
−0.996672 | + | 0.0815161i | \(0.974024\pi\) | |||||||
\(182\) | −1.11810 | + | 1.93661i | −0.0828793 | + | 0.143551i | ||||
\(183\) | 1.65027 | 0.121991 | ||||||||
\(184\) | 1.69356 | − | 2.93333i | 0.124851 | − | 0.216248i | ||||
\(185\) | 12.5698 | + | 21.7715i | 0.924148 | + | 1.60067i | ||||
\(186\) | 6.89411 | + | 11.9409i | 0.505501 | + | 0.875553i | ||||
\(187\) | 1.98972 | + | 3.44629i | 0.145502 | + | 0.252018i | ||||
\(188\) | 3.21616 | 0.234562 | ||||||||
\(189\) | 0.610405 | + | 1.05725i | 0.0444004 | + | 0.0769038i | ||||
\(190\) | 4.66568 | + | 8.08119i | 0.338484 | + | 0.586271i | ||||
\(191\) | −9.82211 | + | 17.0124i | −0.710703 | + | 1.23097i | 0.253891 | + | 0.967233i | \(0.418290\pi\) |
−0.964594 | + | 0.263741i | \(0.915044\pi\) | |||||||
\(192\) | 9.11386 | − | 15.7857i | 0.657736 | − | 1.13923i | ||||
\(193\) | 16.6576 | 1.19904 | 0.599519 | − | 0.800361i | \(-0.295359\pi\) | ||||
0.599519 | + | 0.800361i | \(0.295359\pi\) | |||||||
\(194\) | 9.76053 | 0.700765 | ||||||||
\(195\) | −13.8833 | + | 24.0466i | −0.994203 | + | 1.72201i | ||||
\(196\) | −0.844459 | + | 1.46265i | −0.0603185 | + | 0.104475i | ||||
\(197\) | −4.23702 | − | 7.33873i | −0.301875 | − | 0.522863i | 0.674686 | − | 0.738105i | \(-0.264279\pi\) |
−0.976561 | + | 0.215242i | \(0.930946\pi\) | |||||||
\(198\) | −3.59173 | − | 6.22106i | −0.255253 | − | 0.442111i | ||||
\(199\) | 24.5628 | 1.74121 | 0.870605 | − | 0.491983i | \(-0.163728\pi\) | ||||
0.870605 | + | 0.491983i | \(0.163728\pi\) | |||||||
\(200\) | −4.31520 | − | 7.47415i | −0.305131 | − | 0.528502i | ||||
\(201\) | 14.6680 | + | 25.4057i | 1.03460 | + | 1.79198i | ||||
\(202\) | 2.05502 | + | 3.55940i | 0.144591 | + | 0.250439i | ||||
\(203\) | −0.187114 | + | 0.324091i | −0.0131328 | + | 0.0227467i | ||||
\(204\) | 0.513309 | 0.0359388 | ||||||||
\(205\) | −14.2151 | + | 24.6212i | −0.992822 | + | 1.71962i | ||||
\(206\) | −3.19852 | − | 5.54001i | −0.222852 | − | 0.385990i | ||||
\(207\) | −1.55199 | −0.107871 | ||||||||
\(208\) | 8.15324 | + | 14.1218i | 0.565325 | + | 0.979172i | ||||
\(209\) | −4.98695 | + | 8.63765i | −0.344954 | + | 0.597479i | ||||
\(210\) | −1.38818 | + | 2.40440i | −0.0957936 | + | 0.165919i | ||||
\(211\) | 25.1280 | 1.72988 | 0.864942 | − | 0.501872i | \(-0.167355\pi\) | ||||
0.864942 | + | 0.501872i | \(0.167355\pi\) | |||||||
\(212\) | −0.819843 | + | 1.42001i | −0.0563071 | + | 0.0975267i | ||||
\(213\) | −1.47879 | −0.101325 | ||||||||
\(214\) | −19.3656 | −1.32381 | ||||||||
\(215\) | 9.64731 | − | 15.7065i | 0.657941 | − | 1.07117i | ||||
\(216\) | 10.1711 | 0.692056 | ||||||||
\(217\) | 1.77935 | 0.120790 | ||||||||
\(218\) | 6.14140 | − | 10.6372i | 0.415948 | − | 0.720443i | ||||
\(219\) | −4.75111 | −0.321050 | ||||||||
\(220\) | 1.37448 | − | 2.38066i | 0.0926672 | − | 0.160504i | ||||
\(221\) | −2.36455 | + | 4.09553i | −0.159057 | + | 0.275495i | ||||
\(222\) | −12.3710 | − | 21.4273i | −0.830290 | − | 1.43810i | ||||
\(223\) | 3.74978 | 0.251104 | 0.125552 | − | 0.992087i | \(-0.459930\pi\) | ||||
0.125552 | + | 0.992087i | \(0.459930\pi\) | |||||||
\(224\) | −0.246688 | − | 0.427276i | −0.0164825 | − | 0.0285486i | ||||
\(225\) | −1.97725 | + | 3.42469i | −0.131816 | + | 0.228313i | ||||
\(226\) | 4.99269 | 0.332109 | ||||||||
\(227\) | 13.4759 | − | 23.3409i | 0.894424 | − | 1.54919i | 0.0599077 | − | 0.998204i | \(-0.480919\pi\) |
0.834516 | − | 0.550984i | \(-0.185747\pi\) | |||||||
\(228\) | 0.643270 | + | 1.11418i | 0.0426016 | + | 0.0737881i | ||||
\(229\) | 11.5732 | + | 20.0454i | 0.764780 | + | 1.32464i | 0.940363 | + | 0.340173i | \(0.110486\pi\) |
−0.175583 | + | 0.984465i | \(0.556181\pi\) | |||||||
\(230\) | 2.11980 | + | 3.67160i | 0.139775 | + | 0.242098i | ||||
\(231\) | −2.96754 | −0.195250 | ||||||||
\(232\) | 1.55893 | + | 2.70014i | 0.102349 | + | 0.177273i | ||||
\(233\) | 6.96795 | + | 12.0688i | 0.456486 | + | 0.790656i | 0.998772 | − | 0.0495373i | \(-0.0157747\pi\) |
−0.542287 | + | 0.840193i | \(0.682441\pi\) | |||||||
\(234\) | 4.26837 | − | 7.39303i | 0.279032 | − | 0.483297i | ||||
\(235\) | −18.3938 | + | 31.8590i | −1.19988 | + | 2.07825i | ||||
\(236\) | −1.36655 | −0.0889549 | ||||||||
\(237\) | 2.94409 | 0.191239 | ||||||||
\(238\) | −0.236430 | + | 0.409509i | −0.0153255 | + | 0.0265445i | ||||
\(239\) | 13.9045 | − | 24.0833i | 0.899409 | − | 1.55782i | 0.0711579 | − | 0.997465i | \(-0.477331\pi\) |
0.828251 | − | 0.560357i | \(-0.189336\pi\) | |||||||
\(240\) | 10.1227 | + | 17.5329i | 0.653414 | + | 1.13175i | ||||
\(241\) | −3.74510 | − | 6.48671i | −0.241243 | − | 0.417846i | 0.719825 | − | 0.694155i | \(-0.244222\pi\) |
−0.961069 | + | 0.276310i | \(0.910889\pi\) | |||||||
\(242\) | −6.40503 | −0.411731 | ||||||||
\(243\) | −6.60040 | − | 11.4322i | −0.423416 | − | 0.733378i | ||||
\(244\) | −0.0970796 | − | 0.168147i | −0.00621488 | − | 0.0107645i | ||||
\(245\) | −9.65923 | − | 16.7303i | −0.617105 | − | 1.06886i | ||||
\(246\) | 13.9903 | − | 24.2319i | 0.891990 | − | 1.54497i | ||||
\(247\) | −11.8529 | −0.754179 | ||||||||
\(248\) | 7.41227 | − | 12.8384i | 0.470680 | − | 0.815241i | ||||
\(249\) | −10.1831 | − | 17.6376i | −0.645328 | − | 1.11774i | ||||
\(250\) | −7.81282 | −0.494126 | ||||||||
\(251\) | −13.4352 | − | 23.2704i | −0.848021 | − | 1.46882i | −0.882971 | − | 0.469427i | \(-0.844460\pi\) |
0.0349498 | − | 0.999389i | \(-0.488873\pi\) | |||||||
\(252\) | −0.0597881 | + | 0.103556i | −0.00376629 | + | 0.00652341i | ||||
\(253\) | −2.26576 | + | 3.92442i | −0.142447 | + | 0.246726i | ||||
\(254\) | 11.5409 | 0.724141 | ||||||||
\(255\) | −2.93571 | + | 5.08480i | −0.183841 | + | 0.318422i | ||||
\(256\) | −5.80527 | −0.362829 | ||||||||
\(257\) | −15.9810 | −0.996868 | −0.498434 | − | 0.866928i | \(-0.666091\pi\) | ||||
−0.498434 | + | 0.866928i | \(0.666091\pi\) | |||||||
\(258\) | −9.49478 | + | 15.4582i | −0.591119 | + | 0.962385i | ||||
\(259\) | −3.19293 | −0.198399 | ||||||||
\(260\) | 3.26682 | 0.202600 | ||||||||
\(261\) | 0.714308 | − | 1.23722i | 0.0442146 | − | 0.0765818i | ||||
\(262\) | 0.0368921 | 0.00227920 | ||||||||
\(263\) | −1.04702 | + | 1.81349i | −0.0645619 | + | 0.111824i | −0.896500 | − | 0.443045i | \(-0.853898\pi\) |
0.831938 | + | 0.554869i | \(0.187232\pi\) | |||||||
\(264\) | −12.3619 | + | 21.4115i | −0.760824 | + | 1.31779i | ||||
\(265\) | −9.37767 | − | 16.2426i | −0.576065 | − | 0.997775i | ||||
\(266\) | −1.18516 | −0.0726668 | ||||||||
\(267\) | −3.31872 | − | 5.74819i | −0.203102 | − | 0.351783i | ||||
\(268\) | 1.72574 | − | 2.98906i | 0.105416 | − | 0.182586i | ||||
\(269\) | 6.46541 | 0.394203 | 0.197102 | − | 0.980383i | \(-0.436847\pi\) | ||||
0.197102 | + | 0.980383i | \(0.436847\pi\) | |||||||
\(270\) | −6.36549 | + | 11.0254i | −0.387392 | + | 0.670982i | ||||
\(271\) | 7.27343 | + | 12.5979i | 0.441829 | + | 0.765270i | 0.997825 | − | 0.0659144i | \(-0.0209964\pi\) |
−0.555996 | + | 0.831185i | \(0.687663\pi\) | |||||||
\(272\) | 1.72406 | + | 2.98615i | 0.104536 | + | 0.181062i | ||||
\(273\) | −1.76329 | − | 3.05411i | −0.106719 | − | 0.184843i | ||||
\(274\) | −1.24738 | −0.0753570 | ||||||||
\(275\) | 5.77318 | + | 9.99944i | 0.348136 | + | 0.602989i | ||||
\(276\) | 0.292262 | + | 0.506213i | 0.0175921 | + | 0.0304704i | ||||
\(277\) | 9.82609 | − | 17.0193i | 0.590392 | − | 1.02259i | −0.403787 | − | 0.914853i | \(-0.632306\pi\) |
0.994179 | − | 0.107737i | \(-0.0343603\pi\) | |||||||
\(278\) | −8.01539 | + | 13.8831i | −0.480731 | + | 0.832651i | ||||
\(279\) | −6.79267 | −0.406667 | ||||||||
\(280\) | 2.98503 | 0.178390 | ||||||||
\(281\) | 1.49084 | − | 2.58221i | 0.0889359 | − | 0.154041i | −0.818126 | − | 0.575039i | \(-0.804987\pi\) |
0.907062 | + | 0.420998i | \(0.138320\pi\) | |||||||
\(282\) | 18.1030 | − | 31.3553i | 1.07802 | − | 1.86718i | ||||
\(283\) | −2.01758 | − | 3.49455i | −0.119933 | − | 0.207730i | 0.799808 | − | 0.600256i | \(-0.204935\pi\) |
−0.919741 | + | 0.392526i | \(0.871601\pi\) | |||||||
\(284\) | 0.0869919 | + | 0.150674i | 0.00516202 | + | 0.00894088i | ||||
\(285\) | −14.7159 | −0.871695 | ||||||||
\(286\) | −12.4628 | − | 21.5862i | −0.736942 | − | 1.27642i | ||||
\(287\) | −1.80543 | − | 3.12709i | −0.106571 | − | 0.184587i | ||||
\(288\) | 0.941733 | + | 1.63113i | 0.0554922 | + | 0.0961152i | ||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | −3.90256 | −0.229166 | ||||||||
\(291\) | −7.69636 | + | 13.3305i | −0.451169 | + | 0.781447i | ||||
\(292\) | 0.279491 | + | 0.484093i | 0.0163560 | + | 0.0283294i | ||||
\(293\) | −32.3236 | −1.88837 | −0.944183 | − | 0.329422i | \(-0.893146\pi\) | ||||
−0.944183 | + | 0.329422i | \(0.893146\pi\) | |||||||
\(294\) | 9.50651 | + | 16.4658i | 0.554431 | + | 0.960303i | ||||
\(295\) | 7.81556 | − | 13.5369i | 0.455039 | − | 0.788151i | ||||
\(296\) | −13.3009 | + | 23.0377i | −0.773096 | + | 1.33904i | ||||
\(297\) | −13.6076 | −0.789594 | ||||||||
\(298\) | −9.94143 | + | 17.2191i | −0.575891 | + | 0.997473i | ||||
\(299\) | −5.38521 | −0.311435 | ||||||||
\(300\) | 1.48937 | 0.0859889 | ||||||||
\(301\) | 1.11495 | + | 2.05856i | 0.0642648 | + | 0.118653i | ||||
\(302\) | −19.2477 | −1.10758 | ||||||||
\(303\) | −6.48170 | −0.372364 | ||||||||
\(304\) | −4.32111 | + | 7.48438i | −0.247833 | + | 0.429258i | ||||
\(305\) | 2.22086 | 0.127166 | ||||||||
\(306\) | 0.902573 | − | 1.56330i | 0.0515967 | − | 0.0893681i | ||||
\(307\) | 6.19107 | − | 10.7232i | 0.353343 | − | 0.612008i | −0.633490 | − | 0.773751i | \(-0.718378\pi\) |
0.986833 | + | 0.161743i | \(0.0517115\pi\) | |||||||
\(308\) | 0.174570 | + | 0.302364i | 0.00994704 | + | 0.0172288i | ||||
\(309\) | 10.0884 | 0.573908 | ||||||||
\(310\) | 9.27780 | + | 16.0696i | 0.526944 | + | 0.912693i | ||||
\(311\) | 7.11938 | − | 12.3311i | 0.403703 | − | 0.699234i | −0.590467 | − | 0.807062i | \(-0.701056\pi\) |
0.994170 | + | 0.107828i | \(0.0343897\pi\) | |||||||
\(312\) | −29.3815 | −1.66340 | ||||||||
\(313\) | 12.1823 | − | 21.1004i | 0.688587 | − | 1.19267i | −0.283709 | − | 0.958911i | \(-0.591565\pi\) |
0.972295 | − | 0.233756i | \(-0.0751018\pi\) | |||||||
\(314\) | −2.38012 | − | 4.12249i | −0.134318 | − | 0.232646i | ||||
\(315\) | −0.683878 | − | 1.18451i | −0.0385322 | − | 0.0667397i | ||||
\(316\) | −0.173191 | − | 0.299975i | −0.00974273 | − | 0.0168749i | ||||
\(317\) | 0.641654 | 0.0360389 | 0.0180194 | − | 0.999838i | \(-0.494264\pi\) | ||||
0.0180194 | + | 0.999838i | \(0.494264\pi\) | |||||||
\(318\) | 9.22940 | + | 15.9858i | 0.517559 | + | 0.896439i | ||||
\(319\) | −2.08564 | − | 3.61244i | −0.116774 | − | 0.202258i | ||||
\(320\) | 12.2650 | − | 21.2437i | 0.685637 | − | 1.18756i | ||||
\(321\) | 15.2702 | − | 26.4487i | 0.852298 | − | 1.47622i | ||||
\(322\) | −0.538463 | −0.0300074 | ||||||||
\(323\) | −2.50636 | −0.139458 | ||||||||
\(324\) | −1.38003 | + | 2.39028i | −0.0766681 | + | 0.132793i | ||||
\(325\) | −6.86078 | + | 11.8832i | −0.380567 | + | 0.659162i | ||||
\(326\) | −7.07924 | − | 12.2616i | −0.392083 | − | 0.679108i | ||||
\(327\) | 9.68521 | + | 16.7753i | 0.535594 | + | 0.927675i | ||||
\(328\) | −30.0836 | −1.66109 | ||||||||
\(329\) | −2.33616 | − | 4.04635i | −0.128797 | − | 0.223083i | ||||
\(330\) | −15.4732 | − | 26.8004i | −0.851771 | − | 1.47531i | ||||
\(331\) | 14.4327 | + | 24.9982i | 0.793294 | + | 1.37403i | 0.923917 | + | 0.382593i | \(0.124969\pi\) |
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(332\) | −1.19807 | + | 2.07512i | −0.0657528 | + | 0.113887i | ||||
\(333\) | 12.1890 | 0.667954 | ||||||||
\(334\) | −10.8801 | + | 18.8449i | −0.595333 | + | 1.03115i | ||||
\(335\) | 19.7396 | + | 34.1900i | 1.07849 | + | 1.86800i | ||||
\(336\) | −2.57132 | −0.140277 | ||||||||
\(337\) | −12.6770 | − | 21.9572i | −0.690560 | − | 1.19608i | −0.971655 | − | 0.236405i | \(-0.924031\pi\) |
0.281095 | − | 0.959680i | \(-0.409302\pi\) | |||||||
\(338\) | 6.20152 | − | 10.7413i | 0.337318 | − | 0.584252i | ||||
\(339\) | −3.93683 | + | 6.81879i | −0.213819 | + | 0.370346i | ||||
\(340\) | 0.690790 | 0.0374634 | ||||||||
\(341\) | −9.91666 | + | 17.1762i | −0.537017 | + | 0.930141i | ||||
\(342\) | 4.52435 | 0.244649 | ||||||||
\(343\) | 4.95271 | 0.267421 | ||||||||
\(344\) | 19.4976 | + | 0.530731i | 1.05124 | + | 0.0286151i | ||||
\(345\) | −6.68600 | −0.359962 | ||||||||
\(346\) | −5.88084 | −0.316156 | ||||||||
\(347\) | −0.224642 | + | 0.389091i | −0.0120594 | + | 0.0208875i | −0.871992 | − | 0.489520i | \(-0.837172\pi\) |
0.859933 | + | 0.510407i | \(0.170505\pi\) | |||||||
\(348\) | −0.538057 | −0.0288429 | ||||||||
\(349\) | −8.43559 | + | 14.6109i | −0.451547 | + | 0.782102i | −0.998482 | − | 0.0550729i | \(-0.982461\pi\) |
0.546936 | + | 0.837175i | \(0.315794\pi\) | |||||||
\(350\) | −0.686005 | + | 1.18819i | −0.0366685 | + | 0.0635117i | ||||
\(351\) | −8.08556 | − | 14.0046i | −0.431575 | − | 0.747510i | ||||
\(352\) | 5.49936 | 0.293117 | ||||||||
\(353\) | 6.06714 | + | 10.5086i | 0.322921 | + | 0.559316i | 0.981089 | − | 0.193555i | \(-0.0620018\pi\) |
−0.658168 | + | 0.752871i | \(0.728668\pi\) | |||||||
\(354\) | −7.69199 | + | 13.3229i | −0.408825 | + | 0.708105i | ||||
\(355\) | −1.99009 | −0.105623 | ||||||||
\(356\) | −0.390457 | + | 0.676292i | −0.0206942 | + | 0.0358434i | ||||
\(357\) | −0.372859 | − | 0.645811i | −0.0197338 | − | 0.0341800i | ||||
\(358\) | 7.21484 | + | 12.4965i | 0.381316 | + | 0.660459i | ||||
\(359\) | −17.3845 | − | 30.1109i | −0.917520 | − | 1.58919i | −0.803170 | − | 0.595750i | \(-0.796855\pi\) |
−0.114350 | − | 0.993441i | \(-0.536478\pi\) | |||||||
\(360\) | −11.3954 | −0.600589 | ||||||||
\(361\) | 6.35907 | + | 11.0142i | 0.334688 | + | 0.579697i | ||||
\(362\) | 7.62195 | + | 13.2016i | 0.400601 | + | 0.693861i | ||||
\(363\) | 5.05049 | − | 8.74770i | 0.265082 | − | 0.459135i | ||||
\(364\) | −0.207457 | + | 0.359325i | −0.0108737 | + | 0.0188338i | ||||
\(365\) | −6.39385 | −0.334669 | ||||||||
\(366\) | −2.18575 | −0.114251 | ||||||||
\(367\) | −5.03134 | + | 8.71453i | −0.262634 | + | 0.454895i | −0.966941 | − | 0.255000i | \(-0.917924\pi\) |
0.704307 | + | 0.709895i | \(0.251258\pi\) | |||||||
\(368\) | −1.96324 | + | 3.40044i | −0.102341 | + | 0.177260i | ||||
\(369\) | 6.89223 | + | 11.9377i | 0.358795 | + | 0.621452i | ||||
\(370\) | −16.6484 | − | 28.8359i | −0.865511 | − | 1.49911i | ||||
\(371\) | 2.38208 | 0.123671 | ||||||||
\(372\) | 1.27916 | + | 2.21556i | 0.0663211 | + | 0.114872i | ||||
\(373\) | −8.03969 | − | 13.9251i | −0.416279 | − | 0.721017i | 0.579283 | − | 0.815127i | \(-0.303333\pi\) |
−0.995562 | + | 0.0941101i | \(0.969999\pi\) | |||||||
\(374\) | −2.63534 | − | 4.56455i | −0.136270 | − | 0.236027i | ||||
\(375\) | 6.16056 | − | 10.6704i | 0.318130 | − | 0.551017i | ||||
\(376\) | −38.9272 | −2.00752 | ||||||||
\(377\) | 2.47855 | − | 4.29298i | 0.127652 | − | 0.221100i | ||||
\(378\) | −0.808470 | − | 1.40031i | −0.0415832 | − | 0.0720242i | ||||
\(379\) | 23.1774 | 1.19054 | 0.595272 | − | 0.803525i | \(-0.297044\pi\) | ||||
0.595272 | + | 0.803525i | \(0.297044\pi\) | |||||||
\(380\) | 0.865685 | + | 1.49941i | 0.0444087 | + | 0.0769182i | ||||
\(381\) | −9.10022 | + | 15.7620i | −0.466219 | + | 0.807514i | ||||
\(382\) | 13.0092 | − | 22.5326i | 0.665609 | − | 1.15287i | ||||
\(383\) | 16.4355 | 0.839814 | 0.419907 | − | 0.907567i | \(-0.362063\pi\) | ||||
0.419907 | + | 0.907567i | \(0.362063\pi\) | |||||||
\(384\) | −9.18459 | + | 15.9082i | −0.468699 | + | 0.811810i | ||||
\(385\) | −3.99359 | −0.203532 | ||||||||
\(386\) | −22.0626 | −1.12296 | ||||||||
\(387\) | −4.25634 | − | 7.85856i | −0.216362 | − | 0.399473i | ||||
\(388\) | 1.81100 | 0.0919396 | ||||||||
\(389\) | −33.9128 | −1.71945 | −0.859724 | − | 0.510760i | \(-0.829364\pi\) | ||||
−0.859724 | + | 0.510760i | \(0.829364\pi\) | |||||||
\(390\) | 18.3882 | − | 31.8492i | 0.931120 | − | 1.61275i | ||||
\(391\) | −1.13874 | −0.0575884 | ||||||||
\(392\) | 10.2210 | − | 17.7033i | 0.516240 | − | 0.894153i | ||||
\(393\) | −0.0290902 | + | 0.0503856i | −0.00146740 | + | 0.00254162i | ||||
\(394\) | 5.61185 | + | 9.72001i | 0.282721 | + | 0.489687i | ||||
\(395\) | 3.96203 | 0.199352 | ||||||||
\(396\) | −0.666421 | − | 1.15428i | −0.0334889 | − | 0.0580045i | ||||
\(397\) | −5.49988 | + | 9.52607i | −0.276031 | + | 0.478100i | −0.970395 | − | 0.241524i | \(-0.922353\pi\) |
0.694364 | + | 0.719624i | \(0.255686\pi\) | |||||||
\(398\) | −32.5330 | −1.63073 | ||||||||
\(399\) | 0.934521 | − | 1.61864i | 0.0467845 | − | 0.0810332i | ||||
\(400\) | 5.00236 | + | 8.66435i | 0.250118 | + | 0.433217i | ||||
\(401\) | 16.4027 | + | 28.4102i | 0.819109 | + | 1.41874i | 0.906339 | + | 0.422551i | \(0.138865\pi\) |
−0.0872299 | + | 0.996188i | \(0.527801\pi\) | |||||||
\(402\) | −19.4275 | − | 33.6494i | −0.968956 | − | 1.67828i | ||||
\(403\) | −23.5697 | −1.17409 | ||||||||
\(404\) | 0.381296 | + | 0.660423i | 0.0189702 | + | 0.0328573i | ||||
\(405\) | −15.7852 | − | 27.3409i | −0.784375 | − | 1.35858i | ||||
\(406\) | 0.247829 | − | 0.429252i | 0.0122995 | − | 0.0213034i | ||||
\(407\) | 17.7948 | − | 30.8215i | 0.882056 | − | 1.52777i | ||||
\(408\) | −6.21291 | −0.307585 | ||||||||
\(409\) | −11.8274 | −0.584825 | −0.292412 | − | 0.956292i | \(-0.594458\pi\) | ||||
−0.292412 | + | 0.956292i | \(0.594458\pi\) | |||||||
\(410\) | 18.8276 | − | 32.6103i | 0.929828 | − | 1.61051i | ||||
\(411\) | 0.983582 | − | 1.70361i | 0.0485165 | − | 0.0840331i | ||||
\(412\) | −0.593464 | − | 1.02791i | −0.0292379 | − | 0.0506415i | ||||
\(413\) | 0.992640 | + | 1.71930i | 0.0488446 | + | 0.0846014i | ||||
\(414\) | 2.05559 | 0.101027 | ||||||||
\(415\) | −13.7040 | − | 23.7360i | −0.672702 | − | 1.16515i | ||||
\(416\) | 3.26769 | + | 5.65980i | 0.160211 | + | 0.277494i | ||||
\(417\) | −12.6406 | − | 21.8941i | −0.619012 | − | 1.07216i | ||||
\(418\) | 6.60512 | − | 11.4404i | 0.323067 | − | 0.559569i | ||||
\(419\) | 5.84162 | 0.285382 | 0.142691 | − | 0.989767i | \(-0.454425\pi\) | ||||
0.142691 | + | 0.989767i | \(0.454425\pi\) | |||||||
\(420\) | −0.257568 | + | 0.446120i | −0.0125680 | + | 0.0217684i | ||||
\(421\) | 7.70598 | + | 13.3472i | 0.375567 | + | 0.650501i | 0.990412 | − | 0.138147i | \(-0.0441148\pi\) |
−0.614845 | + | 0.788648i | \(0.710781\pi\) | |||||||
\(422\) | −33.2816 | −1.62012 | ||||||||
\(423\) | 8.91832 | + | 15.4470i | 0.433623 | + | 0.751058i | ||||
\(424\) | 9.92309 | − | 17.1873i | 0.481908 | − | 0.834688i | ||||
\(425\) | −1.45076 | + | 2.51278i | −0.0703720 | + | 0.121888i | ||||
\(426\) | 1.95863 | 0.0948958 | ||||||||
\(427\) | −0.141034 | + | 0.244278i | −0.00682511 | + | 0.0118214i | ||||
\(428\) | −3.59316 | −0.173682 | ||||||||
\(429\) | 39.3087 | 1.89784 | ||||||||
\(430\) | −12.7777 | + | 20.8030i | −0.616194 | + | 1.00321i | ||||
\(431\) | −17.5524 | −0.845470 | −0.422735 | − | 0.906253i | \(-0.638930\pi\) | ||||
−0.422735 | + | 0.906253i | \(0.638930\pi\) | |||||||
\(432\) | −11.7908 | −0.567284 | ||||||||
\(433\) | 10.5919 | − | 18.3456i | 0.509012 | − | 0.881635i | −0.490934 | − | 0.871197i | \(-0.663344\pi\) |
0.999946 | − | 0.0104375i | \(-0.00332243\pi\) | |||||||
\(434\) | −2.35671 | −0.113126 | ||||||||
\(435\) | 3.07724 | − | 5.32994i | 0.147543 | − | 0.255551i | ||||
\(436\) | 1.13949 | − | 1.97366i | 0.0545719 | − | 0.0945213i | ||||
\(437\) | −1.42704 | − | 2.47171i | −0.0682647 | − | 0.118238i | ||||
\(438\) | 6.29276 | 0.300680 | ||||||||
\(439\) | 15.3257 | + | 26.5449i | 0.731457 | + | 1.26692i | 0.956260 | + | 0.292516i | \(0.0944926\pi\) |
−0.224804 | + | 0.974404i | \(0.572174\pi\) | |||||||
\(440\) | −16.6362 | + | 28.8147i | −0.793098 | + | 1.37369i | ||||
\(441\) | −9.36664 | −0.446031 | ||||||||
\(442\) | 3.13181 | − | 5.42445i | 0.148965 | − | 0.258015i | ||||
\(443\) | −4.32851 | − | 7.49720i | −0.205654 | − | 0.356203i | 0.744687 | − | 0.667414i | \(-0.232599\pi\) |
−0.950341 | + | 0.311211i | \(0.899265\pi\) | |||||||
\(444\) | −2.29536 | − | 3.97569i | −0.108933 | − | 0.188678i | ||||
\(445\) | −4.46619 | − | 7.73567i | −0.211718 | − | 0.366706i | ||||
\(446\) | −4.96651 | −0.235171 | ||||||||
\(447\) | −15.6780 | − | 27.1551i | −0.741544 | − | 1.28439i | ||||
\(448\) | 1.55776 | + | 2.69812i | 0.0735973 | + | 0.127474i | ||||
\(449\) | −14.8605 | + | 25.7391i | −0.701309 | + | 1.21470i | 0.266698 | + | 0.963780i | \(0.414067\pi\) |
−0.968007 | + | 0.250923i | \(0.919266\pi\) | |||||||
\(450\) | 2.61883 | − | 4.53594i | 0.123453 | − | 0.213826i | ||||
\(451\) | 40.2480 | 1.89520 | ||||||||
\(452\) | 0.926359 | 0.0435723 | ||||||||
\(453\) | 15.1772 | − | 26.2876i | 0.713086 | − | 1.23510i | ||||
\(454\) | −17.8485 | + | 30.9145i | −0.837673 | + | 1.45089i | ||||
\(455\) | −2.37296 | − | 4.11009i | −0.111246 | − | 0.192684i | ||||
\(456\) | −7.78590 | − | 13.4856i | −0.364608 | − | 0.631520i | ||||
\(457\) | −38.3052 | −1.79184 | −0.895922 | − | 0.444212i | \(-0.853484\pi\) | ||||
−0.895922 | + | 0.444212i | \(0.853484\pi\) | |||||||
\(458\) | −15.3285 | − | 26.5498i | −0.716255 | − | 1.24059i | ||||
\(459\) | −1.70974 | − | 2.96136i | −0.0798040 | − | 0.138225i | ||||
\(460\) | 0.393314 | + | 0.681240i | 0.0183384 | + | 0.0317630i | ||||
\(461\) | −2.89850 | + | 5.02035i | −0.134997 | + | 0.233821i | −0.925596 | − | 0.378513i | \(-0.876436\pi\) |
0.790600 | + | 0.612334i | \(0.209769\pi\) | |||||||
\(462\) | 3.93045 | 0.182861 | ||||||||
\(463\) | −0.701480 | + | 1.21500i | −0.0326006 | + | 0.0564658i | −0.881865 | − | 0.471501i | \(-0.843712\pi\) |
0.849265 | + | 0.527967i | \(0.177046\pi\) | |||||||
\(464\) | −1.80717 | − | 3.13012i | −0.0838960 | − | 0.145312i | ||||
\(465\) | −29.2629 | −1.35703 | ||||||||
\(466\) | −9.22892 | − | 15.9850i | −0.427521 | − | 0.740489i | ||||
\(467\) | −10.1240 | + | 17.5352i | −0.468482 | + | 0.811434i | −0.999351 | − | 0.0360196i | \(-0.988532\pi\) |
0.530869 | + | 0.847454i | \(0.321865\pi\) | |||||||
\(468\) | 0.791966 | − | 1.37173i | 0.0366087 | − | 0.0634081i | ||||
\(469\) | −5.01418 | −0.231533 | ||||||||
\(470\) | 24.3622 | − | 42.1966i | 1.12375 | − | 1.94639i | ||||
\(471\) | 7.50708 | 0.345908 | ||||||||
\(472\) | 16.5402 | 0.761326 | ||||||||
\(473\) | −26.0852 | − | 0.710049i | −1.19940 | − | 0.0326481i | ||||
\(474\) | −3.89939 | −0.179105 | ||||||||
\(475\) | −7.27224 | −0.333673 | ||||||||
\(476\) | −0.0438680 | + | 0.0759816i | −0.00201069 | + | 0.00348261i | ||||
\(477\) | −9.09361 | −0.416368 | ||||||||
\(478\) | −18.4163 | + | 31.8979i | −0.842341 | + | 1.45898i | ||||
\(479\) | 11.6743 | − | 20.2205i | 0.533413 | − | 0.923898i | −0.465825 | − | 0.884877i | \(-0.654243\pi\) |
0.999238 | − | 0.0390216i | \(-0.0124241\pi\) | |||||||
\(480\) | 4.05699 | + | 7.02692i | 0.185176 | + | 0.320734i | ||||
\(481\) | 42.2943 | 1.92845 | ||||||||
\(482\) | 4.96032 | + | 8.59153i | 0.225936 | + | 0.391333i | ||||
\(483\) | 0.424588 | − | 0.735409i | 0.0193194 | − | 0.0334623i | ||||
\(484\) | −1.18841 | −0.0540186 | ||||||||
\(485\) | −10.3574 | + | 17.9396i | −0.470307 | + | 0.814596i | ||||
\(486\) | 8.74211 | + | 15.1418i | 0.396550 | + | 0.686845i | ||||
\(487\) | −10.2567 | − | 17.7651i | −0.464776 | − | 0.805015i | 0.534416 | − | 0.845222i | \(-0.320532\pi\) |
−0.999191 | + | 0.0402068i | \(0.987198\pi\) | |||||||
\(488\) | 1.17502 | + | 2.03519i | 0.0531905 | + | 0.0921286i | ||||
\(489\) | 22.3285 | 1.00973 | ||||||||
\(490\) | 12.7935 | + | 22.1589i | 0.577950 | + | 1.00104i | ||||
\(491\) | 14.5516 | + | 25.2042i | 0.656706 | + | 1.13745i | 0.981463 | + | 0.191651i | \(0.0613843\pi\) |
−0.324757 | + | 0.945798i | \(0.605282\pi\) | |||||||
\(492\) | 2.59581 | − | 4.49607i | 0.117028 | − | 0.202699i | ||||
\(493\) | 0.524106 | − | 0.907778i | 0.0236045 | − | 0.0408842i | ||||
\(494\) | 15.6989 | 0.706326 | ||||||||
\(495\) | 15.2455 | 0.685236 | ||||||||
\(496\) | −8.59262 | + | 14.8828i | −0.385820 | + | 0.668260i | ||||
\(497\) | 0.126379 | − | 0.218895i | 0.00566887 | − | 0.00981877i | ||||
\(498\) | 13.4873 | + | 23.3607i | 0.604382 | + | 1.04682i | ||||
\(499\) | 12.6818 | + | 21.9655i | 0.567714 | + | 0.983310i | 0.996791 | + | 0.0800420i | \(0.0255054\pi\) |
−0.429077 | + | 0.903268i | \(0.641161\pi\) | |||||||
\(500\) | −1.44962 | −0.0648288 | ||||||||
\(501\) | −17.1583 | − | 29.7191i | −0.766578 | − | 1.32775i | ||||
\(502\) | 17.7947 | + | 30.8212i | 0.794214 | + | 1.37562i | ||||
\(503\) | 13.8934 | + | 24.0641i | 0.619476 | + | 1.07296i | 0.989581 | + | 0.143974i | \(0.0459883\pi\) |
−0.370105 | + | 0.928990i | \(0.620678\pi\) | |||||||
\(504\) | 0.723653 | − | 1.25340i | 0.0322341 | − | 0.0558311i | ||||
\(505\) | −8.72280 | −0.388159 | ||||||||
\(506\) | 3.00096 | − | 5.19782i | 0.133409 | − | 0.231071i | ||||
\(507\) | 9.78003 | + | 16.9395i | 0.434346 | + | 0.752310i | ||||
\(508\) | 2.14134 | 0.0950065 | ||||||||
\(509\) | 4.48123 | + | 7.76171i | 0.198627 | + | 0.344032i | 0.948083 | − | 0.318022i | \(-0.103018\pi\) |
−0.749457 | + | 0.662054i | \(0.769685\pi\) | |||||||
\(510\) | 3.88829 | − | 6.73472i | 0.172177 | − | 0.298218i | ||||
\(511\) | 0.406036 | − | 0.703274i | 0.0179620 | − | 0.0311110i | ||||
\(512\) | 25.2776 | 1.11712 | ||||||||
\(513\) | 4.28524 | − | 7.42225i | 0.189198 | − | 0.327700i | ||||
\(514\) | 21.1665 | 0.933616 | ||||||||
\(515\) | 13.5765 | 0.598253 | ||||||||
\(516\) | −1.76169 | + | 2.86816i | −0.0775542 | + | 0.126264i | ||||
\(517\) | 52.0796 | 2.29046 | ||||||||
\(518\) | 4.22898 | 0.185811 | ||||||||
\(519\) | 4.63715 | − | 8.03179i | 0.203548 | − | 0.352556i | ||||
\(520\) | −39.5404 | −1.73396 | ||||||||
\(521\) | 6.60683 | − | 11.4434i | 0.289450 | − | 0.501343i | −0.684228 | − | 0.729268i | \(-0.739861\pi\) |
0.973679 | + | 0.227925i | \(0.0731941\pi\) | |||||||
\(522\) | −0.946088 | + | 1.63867i | −0.0414091 | + | 0.0717227i | ||||
\(523\) | −6.26508 | − | 10.8514i | −0.273953 | − | 0.474500i | 0.695918 | − | 0.718122i | \(-0.254998\pi\) |
−0.969870 | + | 0.243621i | \(0.921665\pi\) | |||||||
\(524\) | 0.00684509 | 0.000299029 | ||||||||
\(525\) | −1.08186 | − | 1.87383i | −0.0472160 | − | 0.0817806i | ||||
\(526\) | 1.38676 | − | 2.40193i | 0.0604654 | − | 0.104729i | ||||
\(527\) | −4.98396 | −0.217105 | ||||||||
\(528\) | 14.3305 | − | 24.8211i | 0.623653 | − | 1.08020i | ||||
\(529\) | 10.8516 | + | 18.7956i | 0.471810 | + | 0.817200i | ||||
\(530\) | 12.4205 | + | 21.5130i | 0.539514 | + | 0.934466i | ||||
\(531\) | −3.78941 | − | 6.56345i | −0.164446 | − | 0.284829i | ||||
\(532\) | −0.219898 | −0.00953380 | ||||||||
\(533\) | 23.9151 | + | 41.4222i | 1.03588 | + | 1.79419i | ||||
\(534\) | 4.39558 | + | 7.61337i | 0.190215 | + | 0.329463i | ||||
\(535\) | 20.5500 | − | 35.5936i | 0.888452 | − | 1.53884i | ||||
\(536\) | −20.8877 | + | 36.1785i | −0.902210 | + | 1.56267i | ||||
\(537\) | −22.7561 | −0.982000 | ||||||||
\(538\) | −8.56332 | −0.369191 | ||||||||
\(539\) | −13.6744 | + | 23.6848i | −0.588998 | + | 1.02017i | ||||
\(540\) | −1.18107 | + | 2.04568i | −0.0508253 | + | 0.0880321i | ||||
\(541\) | 15.2447 | + | 26.4046i | 0.655420 | + | 1.13522i | 0.981788 | + | 0.189978i | \(0.0608418\pi\) |
−0.326368 | + | 0.945243i | \(0.605825\pi\) | |||||||
\(542\) | −9.63352 | − | 16.6857i | −0.413795 | − | 0.716714i | ||||
\(543\) | −24.0402 | −1.03166 | ||||||||
\(544\) | 0.690973 | + | 1.19680i | 0.0296252 | + | 0.0513124i | ||||
\(545\) | 13.0340 | + | 22.5755i | 0.558313 | + | 0.967027i | ||||
\(546\) | 2.33545 | + | 4.04511i | 0.0999479 | + | 0.173115i | ||||
\(547\) | −6.54873 | + | 11.3427i | −0.280003 | + | 0.484980i | −0.971385 | − | 0.237510i | \(-0.923669\pi\) |
0.691382 | + | 0.722489i | \(0.257002\pi\) | |||||||
\(548\) | −0.231443 | −0.00988675 | ||||||||
\(549\) | 0.538398 | − | 0.932532i | 0.0229783 | − | 0.0397995i | ||||
\(550\) | −7.64647 | − | 13.2441i | −0.326047 | − | 0.564729i | ||||
\(551\) | 2.62720 | 0.111922 | ||||||||
\(552\) | −3.53743 | − | 6.12702i | −0.150563 | − | 0.260783i | ||||
\(553\) | −0.251605 | + | 0.435793i | −0.0106994 | + | 0.0185318i | ||||
\(554\) | −13.0145 | + | 22.5417i | −0.552932 | + | 0.957706i | ||||
\(555\) | 52.5104 | 2.22894 | ||||||||
\(556\) | −1.48720 | + | 2.57591i | −0.0630714 | + | 0.109243i | ||||
\(557\) | −15.3484 | −0.650333 | −0.325167 | − | 0.945657i | \(-0.605420\pi\) | ||||
−0.325167 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(558\) | 8.99677 | 0.380864 | ||||||||
\(559\) | −14.7689 | − | 27.2681i | −0.624658 | − | 1.15332i | ||||
\(560\) | −3.46037 | −0.146228 | ||||||||
\(561\) | 8.31207 | 0.350936 | ||||||||
\(562\) | −1.97459 | + | 3.42008i | −0.0832929 | + | 0.144268i | ||||
\(563\) | −20.8536 | −0.878875 | −0.439438 | − | 0.898273i | \(-0.644822\pi\) | ||||
−0.439438 | + | 0.898273i | \(0.644822\pi\) | |||||||
\(564\) | 3.35889 | − | 5.81776i | 0.141435 | − | 0.244972i | ||||
\(565\) | −5.29802 | + | 9.17644i | −0.222889 | + | 0.386056i | ||||
\(566\) | 2.67225 | + | 4.62847i | 0.112323 | + | 0.194549i | ||||
\(567\) | 4.00971 | 0.168392 | ||||||||
\(568\) | −1.05292 | − | 1.82371i | −0.0441795 | − | 0.0765211i | ||||
\(569\) | −3.51989 | + | 6.09663i | −0.147562 | + | 0.255584i | −0.930326 | − | 0.366734i | \(-0.880476\pi\) |
0.782764 | + | 0.622318i | \(0.213809\pi\) | |||||||
\(570\) | 19.4909 | 0.816386 | ||||||||
\(571\) | −10.3376 | + | 17.9053i | −0.432617 | + | 0.749315i | −0.997098 | − | 0.0761315i | \(-0.975743\pi\) |
0.564481 | + | 0.825446i | \(0.309076\pi\) | |||||||
\(572\) | −2.31239 | − | 4.00518i | −0.0966859 | − | 0.167465i | ||||
\(573\) | 20.5160 | + | 35.5348i | 0.857068 | + | 1.48449i | ||||
\(574\) | 2.39126 | + | 4.14178i | 0.0998091 | + | 0.172874i | ||||
\(575\) | −3.30406 | −0.137789 | ||||||||
\(576\) | −5.94677 | − | 10.3001i | −0.247782 | − | 0.429171i | ||||
\(577\) | 21.0641 | + | 36.4841i | 0.876910 | + | 1.51885i | 0.854714 | + | 0.519100i | \(0.173733\pi\) |
0.0221966 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(578\) | 0.662241 | − | 1.14703i | 0.0275456 | − | 0.0477104i | ||||
\(579\) | 17.3968 | − | 30.1322i | 0.722987 | − | 1.25225i | ||||
\(580\) | −0.724094 | −0.0300664 | ||||||||
\(581\) | 3.48104 | 0.144418 | ||||||||
\(582\) | 10.1937 | − | 17.6560i | 0.422542 | − | 0.731864i | ||||
\(583\) | −13.2758 | + | 22.9944i | −0.549827 | + | 0.952329i | ||||
\(584\) | −3.38286 | − | 5.85929i | −0.139984 | − | 0.242459i | ||||
\(585\) | 9.05880 | + | 15.6903i | 0.374535 | + | 0.648714i | ||||
\(586\) | 42.8120 | 1.76855 | ||||||||
\(587\) | 17.5169 | + | 30.3401i | 0.722998 | + | 1.25227i | 0.959793 | + | 0.280710i | \(0.0905700\pi\) |
−0.236794 | + | 0.971560i | \(0.576097\pi\) | |||||||
\(588\) | 1.76387 | + | 3.05511i | 0.0727407 | + | 0.125991i | ||||
\(589\) | −6.24580 | − | 10.8180i | −0.257354 | − | 0.445750i | ||||
\(590\) | −10.3516 | + | 17.9294i | −0.426167 | + | 0.738143i | ||||
\(591\) | −17.7002 | −0.728089 | ||||||||
\(592\) | 15.4189 | − | 26.7063i | 0.633713 | − | 1.09762i | ||||
\(593\) | 1.72507 | + | 2.98791i | 0.0708401 | + | 0.122699i | 0.899270 | − | 0.437395i | \(-0.144099\pi\) |
−0.828430 | + | 0.560093i | \(0.810765\pi\) | |||||||
\(594\) | 18.0230 | 0.739494 | ||||||||
\(595\) | −0.501778 | − | 0.869106i | −0.0205709 | − | 0.0356299i | ||||
\(596\) | −1.84456 | + | 3.19488i | −0.0755563 | + | 0.130867i | ||||
\(597\) | 25.6529 | − | 44.4321i | 1.04990 | − | 1.81848i | ||||
\(598\) | 7.13261 | 0.291674 | ||||||||
\(599\) | −13.3331 | + | 23.0935i | −0.544774 | + | 0.943577i | 0.453847 | + | 0.891080i | \(0.350051\pi\) |
−0.998621 | + | 0.0524969i | \(0.983282\pi\) | |||||||
\(600\) | −18.0268 | −0.735942 | ||||||||
\(601\) | 5.40057 | 0.220294 | 0.110147 | − | 0.993915i | \(-0.464868\pi\) | ||||
0.110147 | + | 0.993915i | \(0.464868\pi\) | |||||||
\(602\) | −1.47673 | − | 2.72652i | −0.0601872 | − | 0.111125i | ||||
\(603\) | 19.1417 | 0.779509 | ||||||||
\(604\) | −3.57128 | −0.145313 | ||||||||
\(605\) | 6.79673 | − | 11.7723i | 0.276327 | − | 0.478612i | ||||
\(606\) | 8.58489 | 0.348737 | ||||||||
\(607\) | 8.84568 | − | 15.3212i | 0.359035 | − | 0.621867i | −0.628765 | − | 0.777595i | \(-0.716439\pi\) |
0.987800 | + | 0.155729i | \(0.0497726\pi\) | |||||||
\(608\) | −1.73183 | + | 2.99962i | −0.0702350 | + | 0.121651i | ||||
\(609\) | 0.390835 | + | 0.676947i | 0.0158374 | + | 0.0274313i | ||||
\(610\) | −2.94149 | −0.119098 | ||||||||
\(611\) | 30.9453 | + | 53.5989i | 1.25191 | + | 2.16838i | ||||
\(612\) | 0.167466 | − | 0.290060i | 0.00676943 | − | 0.0117250i | ||||
\(613\) | −36.3494 | −1.46814 | −0.734070 | − | 0.679074i | \(-0.762381\pi\) | ||||
−0.734070 | + | 0.679074i | \(0.762381\pi\) | |||||||
\(614\) | −8.19996 | + | 14.2027i | −0.330923 | + | 0.573176i | ||||
\(615\) | 29.6918 | + | 51.4277i | 1.19729 | + | 2.07376i | ||||
\(616\) | −2.11293 | − | 3.65970i | −0.0851324 | − | 0.147454i | ||||
\(617\) | −7.04369 | − | 12.2000i | −0.283568 | − | 0.491155i | 0.688693 | − | 0.725053i | \(-0.258185\pi\) |
−0.972261 | + | 0.233899i | \(0.924852\pi\) | |||||||
\(618\) | −13.3619 | −0.537494 | ||||||||
\(619\) | −5.74484 | − | 9.95035i | −0.230905 | − | 0.399938i | 0.727170 | − | 0.686457i | \(-0.240835\pi\) |
−0.958075 | + | 0.286519i | \(0.907502\pi\) | |||||||
\(620\) | 1.72143 | + | 2.98161i | 0.0691344 | + | 0.119744i | ||||
\(621\) | 1.94695 | − | 3.37221i | 0.0781283 | − | 0.135322i | ||||
\(622\) | −9.42948 | + | 16.3323i | −0.378088 | + | 0.654867i | ||||
\(623\) | 1.13449 | 0.0454522 | ||||||||
\(624\) | 34.0603 | 1.36350 | ||||||||
\(625\) | 15.5444 | − | 26.9237i | 0.621776 | − | 1.07695i | ||||
\(626\) | −16.1353 | + | 27.9471i | −0.644896 | + | 1.11699i | ||||
\(627\) | 10.4165 | + | 18.0420i | 0.415996 | + | 0.720526i | ||||
\(628\) | −0.441615 | − | 0.764900i | −0.0176224 | − | 0.0305229i | ||||
\(629\) | 8.94339 | 0.356596 | ||||||||
\(630\) | 0.905784 | + | 1.56886i | 0.0360873 | + | 0.0625050i | ||||
\(631\) | −14.9497 | − | 25.8936i | −0.595137 | − | 1.03081i | −0.993528 | − | 0.113591i | \(-0.963765\pi\) |
0.398391 | − | 0.917216i | \(-0.369569\pi\) | |||||||
\(632\) | 2.09624 | + | 3.63079i | 0.0833838 | + | 0.144425i | ||||
\(633\) | 26.2432 | − | 45.4545i | 1.04307 | − | 1.80665i | ||||
\(634\) | −0.849859 | −0.0337522 | ||||||||
\(635\) | −12.2467 | + | 21.2119i | −0.485995 | + | 0.841769i | ||||
\(636\) | 1.71245 | + | 2.96606i | 0.0679032 | + | 0.117612i | ||||
\(637\) | −32.5010 | −1.28774 | ||||||||
\(638\) | 2.76240 | + | 4.78461i | 0.109364 | + | 0.189424i | ||||
\(639\) | −0.482452 | + | 0.835632i | −0.0190855 | + | 0.0330571i | ||||
\(640\) | −12.3602 | + | 21.4086i | −0.488581 | + | 0.846247i | ||||
\(641\) | 38.3573 | 1.51502 | 0.757512 | − | 0.652821i | \(-0.226415\pi\) | ||||
0.757512 | + | 0.652821i | \(0.226415\pi\) | |||||||
\(642\) | −20.2251 | + | 35.0308i | −0.798219 | + | 1.38256i | ||||
\(643\) | 27.8773 | 1.09937 | 0.549686 | − | 0.835371i | \(-0.314747\pi\) | ||||
0.549686 | + | 0.835371i | \(0.314747\pi\) | |||||||
\(644\) | −0.0999082 | −0.00393694 | ||||||||
\(645\) | −18.3363 | − | 33.8547i | −0.721992 | − | 1.33303i | ||||
\(646\) | 3.31963 | 0.130609 | ||||||||
\(647\) | −4.71992 | −0.185559 | −0.0927796 | − | 0.995687i | \(-0.529575\pi\) | ||||
−0.0927796 | + | 0.995687i | \(0.529575\pi\) | |||||||
\(648\) | 16.7033 | − | 28.9310i | 0.656169 | − | 1.13652i | ||||
\(649\) | −22.1287 | −0.868627 | ||||||||
\(650\) | 9.08697 | − | 15.7391i | 0.356420 | − | 0.617338i | ||||
\(651\) | 1.85831 | − | 3.21869i | 0.0728331 | − | 0.126151i | ||||
\(652\) | −1.31351 | − | 2.27506i | −0.0514408 | − | 0.0890982i | ||||
\(653\) | −19.0543 | −0.745653 | −0.372827 | − | 0.927901i | \(-0.621611\pi\) | ||||
−0.372827 | + | 0.927901i | \(0.621611\pi\) | |||||||
\(654\) | −12.8279 | − | 22.2186i | −0.501610 | − | 0.868814i | ||||
\(655\) | −0.0391483 | + | 0.0678069i | −0.00152965 | + | 0.00264943i | ||||
\(656\) | 34.8742 | 1.36161 | ||||||||
\(657\) | −1.55004 | + | 2.68475i | −0.0604729 | + | 0.104742i | ||||
\(658\) | 3.09421 | + | 5.35932i | 0.120625 | + | 0.208928i | ||||
\(659\) | 6.88143 | + | 11.9190i | 0.268063 | + | 0.464298i | 0.968361 | − | 0.249552i | \(-0.0802833\pi\) |
−0.700299 | + | 0.713850i | \(0.746950\pi\) | |||||||
\(660\) | −2.87095 | − | 4.97263i | −0.111751 | − | 0.193559i | ||||
\(661\) | −6.32246 | −0.245915 | −0.122958 | − | 0.992412i | \(-0.539238\pi\) | ||||
−0.122958 | + | 0.992412i | \(0.539238\pi\) | |||||||
\(662\) | −19.1159 | − | 33.1096i | −0.742959 | − | 1.28684i | ||||
\(663\) | 4.93898 | + | 8.55456i | 0.191814 | + | 0.332232i | ||||
\(664\) | 14.5010 | − | 25.1165i | 0.562749 | − | 0.974711i | ||||
\(665\) | 1.25764 | − | 2.17829i | 0.0487691 | − | 0.0844706i | ||||
\(666\) | −16.1441 | −0.625573 | ||||||||
\(667\) | 1.19364 | 0.0462178 | ||||||||
\(668\) | −2.01873 | + | 3.49654i | −0.0781070 | + | 0.135285i | ||||
\(669\) | 3.91619 | − | 6.78304i | 0.151409 | − | 0.262247i | ||||
\(670\) | −26.1447 | − | 45.2840i | −1.01006 | − | 1.74947i | ||||
\(671\) | −1.57202 | − | 2.72282i | −0.0606871 | − | 0.105113i | ||||
\(672\) | −1.03054 | −0.0397541 | ||||||||
\(673\) | −12.3506 | − | 21.3919i | −0.476081 | − | 0.824596i | 0.523544 | − | 0.851999i | \(-0.324610\pi\) |
−0.999624 | + | 0.0274028i | \(0.991276\pi\) | |||||||
\(674\) | 16.7904 | + | 29.0819i | 0.646744 | + | 1.12019i | ||||
\(675\) | −4.96084 | − | 8.59243i | −0.190943 | − | 0.330723i | ||||
\(676\) | 1.15065 | − | 1.99298i | 0.0442558 | − | 0.0766532i | ||||
\(677\) | 20.9415 | 0.804846 | 0.402423 | − | 0.915454i | \(-0.368168\pi\) | ||||
0.402423 | + | 0.915454i | \(0.368168\pi\) | |||||||
\(678\) | 5.21426 | − | 9.03136i | 0.200252 | − | 0.346847i | ||||
\(679\) | −1.31548 | − | 2.27848i | −0.0504835 | − | 0.0874400i | ||||
\(680\) | −8.36107 | −0.320633 | ||||||||
\(681\) | −28.1478 | − | 48.7534i | −1.07863 | − | 1.86823i | ||||
\(682\) | 13.1344 | − | 22.7495i | 0.502943 | − | 0.871123i | ||||
\(683\) | 0.611462 | − | 1.05908i | 0.0233969 | − | 0.0405247i | −0.854090 | − | 0.520125i | \(-0.825885\pi\) |
0.877487 | + | 0.479601i | \(0.159219\pi\) | |||||||
\(684\) | 0.839463 | 0.0320977 | ||||||||
\(685\) | 1.32366 | − | 2.29265i | 0.0505746 | − | 0.0875978i | ||||
\(686\) | −6.55977 | −0.250453 | ||||||||
\(687\) | 48.3473 | 1.84456 | ||||||||
\(688\) | −22.6024 | − | 0.615245i | −0.861708 | − | 0.0234560i | ||||
\(689\) | −31.5536 | −1.20210 | ||||||||
\(690\) | 8.85548 | 0.337122 | ||||||||
\(691\) | −2.04517 | + | 3.54233i | −0.0778018 | + | 0.134757i | −0.902301 | − | 0.431106i | \(-0.858123\pi\) |
0.824499 | + | 0.565863i | \(0.191457\pi\) | |||||||
\(692\) | −1.09115 | −0.0414793 | ||||||||
\(693\) | −0.968154 | + | 1.67689i | −0.0367771 | + | 0.0636999i | ||||
\(694\) | 0.297534 | − | 0.515344i | 0.0112942 | − | 0.0195622i | ||||
\(695\) | −17.0112 | − | 29.4642i | −0.645270 | − | 1.11764i | ||||
\(696\) | 6.51244 | 0.246854 | ||||||||
\(697\) | 5.05700 | + | 8.75899i | 0.191548 | + | 0.331770i | ||||
\(698\) | 11.1728 | − | 19.3518i | 0.422896 | − | 0.732477i | ||||
\(699\) | 29.1087 | 1.10099 | ||||||||
\(700\) | −0.127284 | + | 0.220462i | −0.00481086 | + | 0.00833266i | ||||
\(701\) | −13.3092 | − | 23.0521i | −0.502680 | − | 0.870667i | −0.999995 | − | 0.00309698i | \(-0.999014\pi\) |
0.497316 | − | 0.867570i | \(-0.334319\pi\) | |||||||
\(702\) | 10.7092 | + | 18.5488i | 0.404192 | + | 0.700081i | ||||
\(703\) | 11.2077 | + | 19.4123i | 0.422706 | + | 0.732149i | ||||
\(704\) | −34.7268 | −1.30882 | ||||||||
\(705\) | 38.4202 | + | 66.5457i | 1.44699 | + | 2.50626i | ||||
\(706\) | −8.03581 | − | 13.9184i | −0.302432 | − | 0.523827i | ||||
\(707\) | 0.553934 | − | 0.959441i | 0.0208328 | − | 0.0360835i | ||||
\(708\) | −1.42720 | + | 2.47198i | −0.0536374 | + | 0.0929026i | ||||
\(709\) | −45.0283 | −1.69107 | −0.845536 | − | 0.533918i | \(-0.820719\pi\) | ||||
−0.845536 | + | 0.533918i | \(0.820719\pi\) | |||||||
\(710\) | 2.63584 | 0.0989212 | ||||||||
\(711\) | 0.960505 | − | 1.66364i | 0.0360218 | − | 0.0623915i | ||||
\(712\) | 4.72595 | − | 8.18559i | 0.177113 | − | 0.306768i | ||||
\(713\) | −2.83771 | − | 4.91505i | −0.106273 | − | 0.184070i | ||||
\(714\) | 0.493845 | + | 0.855365i | 0.0184817 | + | 0.0320112i | ||||
\(715\) | 52.8999 | 1.97835 | ||||||||
\(716\) | 1.33866 | + | 2.31863i | 0.0500282 | + | 0.0866514i | ||||
\(717\) | −29.0432 | − | 50.3043i | −1.08464 | − | 1.87865i | ||||
\(718\) | 23.0255 | + | 39.8813i | 0.859303 | + | 1.48836i | ||||
\(719\) | −0.252554 | + | 0.437436i | −0.00941868 | + | 0.0163136i | −0.870696 | − | 0.491821i | \(-0.836331\pi\) |
0.861278 | + | 0.508135i | \(0.169665\pi\) | |||||||
\(720\) | 13.2100 | 0.492308 | ||||||||
\(721\) | −0.862165 | + | 1.49331i | −0.0321087 | + | 0.0556139i | ||||
\(722\) | −8.42248 | − | 14.5882i | −0.313452 | − | 0.542915i | ||||
\(723\) | −15.6452 | −0.581852 | ||||||||
\(724\) | 1.41420 | + | 2.44947i | 0.0525584 | + | 0.0910338i | ||||
\(725\) | 1.52070 | − | 2.63393i | 0.0564773 | − | 0.0978216i | ||||
\(726\) | −6.68928 | + | 11.5862i | −0.248262 | + | 0.430003i | ||||
\(727\) | 6.17679 | 0.229084 | 0.114542 | − | 0.993418i | \(-0.463460\pi\) | ||||
0.114542 | + | 0.993418i | \(0.463460\pi\) | |||||||
\(728\) | 2.51098 | − | 4.34914i | 0.0930631 | − | 0.161190i | ||||
\(729\) | 6.12034 | 0.226679 | ||||||||
\(730\) | 8.46853 | 0.313434 | ||||||||
\(731\) | −3.12298 | − | 5.76602i | −0.115508 | − | 0.213264i | ||||
\(732\) | −0.405551 | −0.0149896 | ||||||||
\(733\) | −6.44519 | −0.238059 | −0.119029 | − | 0.992891i | \(-0.537978\pi\) | ||||
−0.119029 | + | 0.992891i | \(0.537978\pi\) | |||||||
\(734\) | 6.66391 | − | 11.5422i | 0.245970 | − | 0.426032i | ||||
\(735\) | −40.3516 | −1.48839 | ||||||||
\(736\) | −0.786837 | + | 1.36284i | −0.0290032 | + | 0.0502350i | ||||
\(737\) | 27.9450 | − | 48.4022i | 1.02937 | − | 1.78292i | ||||
\(738\) | −9.12864 | − | 15.8113i | −0.336030 | − | 0.582021i | ||||
\(739\) | −24.6756 | −0.907708 | −0.453854 | − | 0.891076i | \(-0.649951\pi\) | ||||
−0.453854 | + | 0.891076i | \(0.649951\pi\) | |||||||
\(740\) | −3.08900 | − | 5.35031i | −0.113554 | − | 0.196681i | ||||
\(741\) | −12.3789 | + | 21.4408i | −0.454749 | + | 0.787649i | ||||
\(742\) | −3.15502 | −0.115825 | ||||||||
\(743\) | −8.18646 | + | 14.1794i | −0.300332 | + | 0.520190i | −0.976211 | − | 0.216822i | \(-0.930431\pi\) |
0.675879 | + | 0.737012i | \(0.263764\pi\) | |||||||
\(744\) | −15.4824 | − | 26.8164i | −0.567614 | − | 0.983136i | ||||
\(745\) | −21.0988 | − | 36.5442i | −0.773000 | − | 1.33888i | ||||
\(746\) | 10.6484 | + | 18.4436i | 0.389866 | + | 0.675268i | ||||
\(747\) | −13.2889 | −0.486215 | ||||||||
\(748\) | −0.488970 | − | 0.846921i | −0.0178785 | − | 0.0309665i | ||||
\(749\) | 2.61001 | + | 4.52067i | 0.0953678 | + | 0.165182i | ||||
\(750\) | −8.15954 | + | 14.1327i | −0.297944 | + | 0.516055i | ||||
\(751\) | −3.88963 | + | 6.73704i | −0.141935 | + | 0.245838i | −0.928225 | − | 0.372019i | \(-0.878666\pi\) |
0.786290 | + | 0.617857i | \(0.211999\pi\) | |||||||
\(752\) | 45.1261 | 1.64558 | ||||||||
\(753\) | −56.1257 | −2.04533 | ||||||||
\(754\) | −3.28280 | + | 5.68597i | −0.119552 | + | 0.207071i | ||||
\(755\) | 20.4248 | − | 35.3768i | 0.743335 | − | 1.28749i | ||||
\(756\) | −0.150006 | − | 0.259818i | −0.00545567 | − | 0.00944950i | ||||
\(757\) | −0.341751 | − | 0.591930i | −0.0124211 | − | 0.0215140i | 0.859748 | − | 0.510718i | \(-0.170621\pi\) |
−0.872169 | + | 0.489204i | \(0.837287\pi\) | |||||||
\(758\) | −30.6980 | −1.11500 | ||||||||
\(759\) | 4.73263 | + | 8.19715i | 0.171784 | + | 0.297538i | ||||
\(760\) | −10.4779 | − | 18.1483i | −0.380075 | − | 0.658309i | ||||
\(761\) | 7.68022 | + | 13.3025i | 0.278408 | + | 0.482216i | 0.970989 | − | 0.239123i | \(-0.0768600\pi\) |
−0.692581 | + | 0.721340i | \(0.743527\pi\) | |||||||
\(762\) | 12.0531 | − | 20.8765i | 0.436637 | − | 0.756277i | ||||
\(763\) | −3.31084 | −0.119860 | ||||||||
\(764\) | 2.41377 | − | 4.18077i | 0.0873271 | − | 0.151255i | ||||
\(765\) | 1.91554 | + | 3.31782i | 0.0692566 | + | 0.119956i | ||||
\(766\) | −21.7685 | −0.786528 | ||||||||
\(767\) | −13.1487 | − | 22.7743i | −0.474773 | − | 0.822331i | ||||
\(768\) | −6.06290 | + | 10.5013i | −0.218776 | + | 0.378931i | ||||
\(769\) | 8.17314 | − | 14.1563i | 0.294731 | − | 0.510489i | −0.680191 | − | 0.733035i | \(-0.738103\pi\) |
0.974922 | + | 0.222546i | \(0.0714366\pi\) | |||||||
\(770\) | 5.28943 | 0.190618 | ||||||||
\(771\) | −16.6902 | + | 28.9083i | −0.601084 | + | 1.04111i | ||||
\(772\) | −4.09357 | −0.147331 | ||||||||
\(773\) | −10.0417 | −0.361176 | −0.180588 | − | 0.983559i | \(-0.557800\pi\) | ||||
−0.180588 | + | 0.983559i | \(0.557800\pi\) | |||||||
\(774\) | 5.63744 | + | 10.4085i | 0.202634 | + | 0.374126i | ||||
\(775\) | −14.4610 | −0.519454 | ||||||||
\(776\) | −21.9197 | −0.786871 | ||||||||
\(777\) | −3.33463 | + | 5.77574i | −0.119629 | + | 0.207204i | ||||
\(778\) | 44.9169 | 1.61035 | ||||||||
\(779\) | −12.6747 | + | 21.9532i | −0.454118 | + | 0.786555i | ||||
\(780\) | 3.41180 | − | 5.90941i | 0.122162 | − | 0.211591i | ||||
\(781\) | 1.40867 | + | 2.43989i | 0.0504061 | + | 0.0873060i | ||||
\(782\) | 1.50824 | 0.0539344 | ||||||||
\(783\) | 1.79217 | + | 3.10413i | 0.0640470 | + | 0.110933i | ||||
\(784\) | −11.8486 | + | 20.5224i | −0.423166 | + | 0.732944i | ||||
\(785\) | 10.1027 | 0.360582 | ||||||||
\(786\) | 0.0385294 | − | 0.0667348i | 0.00137430 | − | 0.00238035i | ||||
\(787\) | 26.4315 | + | 45.7807i | 0.942182 | + | 1.63191i | 0.761298 | + | 0.648402i | \(0.224563\pi\) |
0.180884 | + | 0.983504i | \(0.442104\pi\) | |||||||
\(788\) | 1.04124 | + | 1.80348i | 0.0370927 | + | 0.0642464i | ||||
\(789\) | 2.18697 | + | 3.78794i | 0.0778580 | + | 0.134854i | ||||
\(790\) | −5.24764 | −0.186703 | ||||||||
\(791\) | −0.672892 | − | 1.16548i | −0.0239253 | − | 0.0414398i | ||||
\(792\) | 8.06612 | + | 13.9709i | 0.286617 | + | 0.496435i | ||||
\(793\) | 1.86817 | − | 3.23576i | 0.0663406 | − | 0.114905i | ||||
\(794\) | 7.28449 | − | 12.6171i | 0.258517 | − | 0.447764i | ||||
\(795\) | −39.1753 | −1.38941 | ||||||||
\(796\) | −6.03627 | −0.213950 | ||||||||
\(797\) | 24.2486 | − | 41.9998i | 0.858928 | − | 1.48771i | −0.0140235 | − | 0.999902i | \(-0.504464\pi\) |
0.872952 | − | 0.487806i | \(-0.162203\pi\) | |||||||
\(798\) | −1.23776 | + | 2.14385i | −0.0438161 | + | 0.0758916i | ||||
\(799\) | 6.54359 | + | 11.3338i | 0.231496 | + | 0.400962i | ||||
\(800\) | 2.00487 | + | 3.47253i | 0.0708827 | + | 0.122772i | ||||
\(801\) | −4.33091 | −0.153025 | ||||||||
\(802\) | −21.7250 | − | 37.6288i | −0.767137 | − | 1.32872i | ||||
\(803\) | 4.52583 | + | 7.83897i | 0.159713 | + | 0.276631i | ||||
\(804\) | −3.60464 | − | 6.24342i | −0.127126 | − | 0.220189i | ||||
\(805\) | 0.571393 | − | 0.989682i | 0.0201390 | − | 0.0348817i | ||||
\(806\) | 31.2176 | 1.09959 | ||||||||
\(807\) | 6.75234 | − | 11.6954i | 0.237694 | − | 0.411697i | ||||
\(808\) | −4.61507 | − | 7.99353i | −0.162357 | − | 0.281211i | ||||
\(809\) | 19.7172 | 0.693219 | 0.346610 | − | 0.938009i | \(-0.387333\pi\) | ||||
0.346610 | + | 0.938009i | \(0.387333\pi\) | |||||||
\(810\) | 20.9073 | + | 36.2125i | 0.734607 | + | 1.27238i | ||||
\(811\) | 20.1546 | − | 34.9088i | 0.707724 | − | 1.22581i | −0.257976 | − | 0.966151i | \(-0.583055\pi\) |
0.965699 | − | 0.259662i | \(-0.0836112\pi\) | |||||||
\(812\) | 0.0459830 | − | 0.0796448i | 0.00161369 | − | 0.00279498i | ||||
\(813\) | 30.3848 | 1.06564 | ||||||||
\(814\) | −23.5689 | + | 40.8225i | −0.826090 | + | 1.43083i | ||||
\(815\) | 30.0487 | 1.05256 | ||||||||
\(816\) | 7.20227 | 0.252130 | ||||||||
\(817\) | 8.60191 | − | 14.0045i | 0.300943 | − | 0.489956i | ||||
\(818\) | 15.6651 | 0.547718 | ||||||||
\(819\) | −2.30108 | −0.0804064 | ||||||||
\(820\) | 3.49333 | − | 6.05062i | 0.121992 | − | 0.211297i | ||||
\(821\) | −13.3494 | −0.465897 | −0.232949 | − | 0.972489i | \(-0.574837\pi\) | ||||
−0.232949 | + | 0.972489i | \(0.574837\pi\) | |||||||
\(822\) | −1.30274 | + | 2.25641i | −0.0454382 | + | 0.0787012i | ||||
\(823\) | 7.12218 | − | 12.3360i | 0.248264 | − | 0.430005i | −0.714780 | − | 0.699349i | \(-0.753473\pi\) |
0.963044 | + | 0.269344i | \(0.0868067\pi\) | |||||||
\(824\) | 7.18308 | + | 12.4415i | 0.250234 | + | 0.433419i | ||||
\(825\) | 24.1176 | 0.839665 | ||||||||
\(826\) | −1.31473 | − | 2.27718i | −0.0457454 | − | 0.0792334i | ||||
\(827\) | −10.0694 | + | 17.4407i | −0.350148 | + | 0.606474i | −0.986275 | − | 0.165110i | \(-0.947202\pi\) |
0.636127 | + | 0.771584i | \(0.280535\pi\) | |||||||
\(828\) | 0.381400 | 0.0132546 | ||||||||
\(829\) | −10.5418 | + | 18.2590i | −0.366133 | + | 0.634161i | −0.988957 | − | 0.148201i | \(-0.952652\pi\) |
0.622824 | + | 0.782362i | \(0.285985\pi\) | |||||||
\(830\) | 18.1507 | + | 31.4379i | 0.630019 | + | 1.09123i | ||||
\(831\) | −20.5243 | − | 35.5492i | −0.711981 | − | 1.23319i | ||||
\(832\) | −20.6345 | − | 35.7400i | −0.715372 | − | 1.23906i | ||||
\(833\) | −6.87254 | −0.238119 | ||||||||
\(834\) | 16.7422 | + | 28.9984i | 0.579735 | + | 1.00413i | ||||
\(835\) | −23.0910 | − | 39.9947i | −0.799096 | − | 1.38407i | ||||
\(836\) | 1.22554 | − | 2.12269i | 0.0423860 | − | 0.0734148i | ||||
\(837\) | 8.52129 | − | 14.7593i | 0.294539 | − | 0.510156i | ||||
\(838\) | −7.73712 | −0.267274 | ||||||||
\(839\) | −24.2961 | −0.838796 | −0.419398 | − | 0.907802i | \(-0.637759\pi\) | ||||
−0.419398 | + | 0.907802i | \(0.637759\pi\) | |||||||
\(840\) | 3.11750 | − | 5.39968i | 0.107564 | − | 0.186307i | ||||
\(841\) | 13.9506 | − | 24.1632i | 0.481056 | − | 0.833214i | ||||
\(842\) | −10.2064 | − | 17.6781i | −0.351737 | − | 0.609226i | ||||
\(843\) | −3.11400 | − | 5.39360i | −0.107252 | − | 0.185766i | ||||
\(844\) | −6.17517 | −0.212558 | ||||||||
\(845\) | 13.1616 | + | 22.7965i | 0.452771 | + | 0.784223i | ||||
\(846\) | −11.8121 | − | 20.4592i | −0.406110 | − | 0.703403i | ||||
\(847\) | 0.863241 | + | 1.49518i | 0.0296613 | + | 0.0513749i | ||||
\(848\) | −11.5033 | + | 19.9242i | −0.395023 | + | 0.684201i | ||||
\(849\) | −8.42848 | −0.289265 | ||||||||
\(850\) | 1.92150 | − | 3.32813i | 0.0659069 | − | 0.114154i | ||||
\(851\) | 5.09208 | + | 8.81975i | 0.174554 | + | 0.302337i | ||||
\(852\) | 0.363410 | 0.0124502 | ||||||||
\(853\) | 17.3422 | + | 30.0376i | 0.593786 | + | 1.02847i | 0.993717 | + | 0.111923i | \(0.0357009\pi\) |
−0.399931 | + | 0.916545i | \(0.630966\pi\) | |||||||
\(854\) | 0.186797 | − | 0.323542i | 0.00639206 | − | 0.0110714i | ||||
\(855\) | −4.80104 | + | 8.31565i | −0.164192 | + | 0.284389i | ||||
\(856\) | 43.4903 | 1.48647 | ||||||||
\(857\) | −0.501912 | + | 0.869336i | −0.0171450 | + | 0.0296960i | −0.874471 | − | 0.485079i | \(-0.838791\pi\) |
0.857326 | + | 0.514774i | \(0.172124\pi\) | |||||||
\(858\) | −52.0636 | −1.77742 | ||||||||
\(859\) | 31.4412 | 1.07276 | 0.536379 | − | 0.843977i | \(-0.319792\pi\) | ||||
0.536379 | + | 0.843977i | \(0.319792\pi\) | |||||||
\(860\) | −2.37081 | + | 3.85985i | −0.0808440 | + | 0.131620i | ||||
\(861\) | −7.54220 | −0.257038 | ||||||||
\(862\) | 23.2478 | 0.791825 | ||||||||
\(863\) | 12.6616 | − | 21.9305i | 0.431006 | − | 0.746523i | −0.565955 | − | 0.824436i | \(-0.691492\pi\) |
0.996960 | + | 0.0779129i | \(0.0248256\pi\) | |||||||
\(864\) | −4.72555 | −0.160766 | ||||||||
\(865\) | 6.24049 | − | 10.8088i | 0.212183 | − | 0.367512i | ||||
\(866\) | −14.0287 | + | 24.2984i | −0.476715 | + | 0.825695i | ||||
\(867\) | 1.04438 | + | 1.80892i | 0.0354690 | + | 0.0614340i | ||||
\(868\) | −0.437273 | −0.0148420 | ||||||||
\(869\) | −2.80449 | − | 4.85752i | −0.0951359 | − | 0.164780i | ||||
\(870\) | −4.07575 | + | 7.05941i | −0.138181 | + | 0.239336i | ||||
\(871\) | 66.4190 | 2.25052 | ||||||||
\(872\) | −13.7920 | + | 23.8885i | −0.467057 | + | 0.808967i | ||||
\(873\) | 5.02185 | + | 8.69810i | 0.169964 | + | 0.294386i | ||||
\(874\) | 1.89009 | + | 3.27374i | 0.0639333 | + | 0.110736i | ||||
\(875\) | 1.05298 | + | 1.82381i | 0.0355971 | + | 0.0616560i | ||||
\(876\) | 1.16758 | 0.0394488 | ||||||||
\(877\) | 3.06721 | + | 5.31256i | 0.103572 | + | 0.179392i | 0.913154 | − | 0.407615i | \(-0.133639\pi\) |
−0.809582 | + | 0.587007i | \(0.800306\pi\) | |||||||
\(878\) | −20.2986 | − | 35.1583i | −0.685046 | − | 1.18653i | ||||
\(879\) | −33.7581 | + | 58.4707i | −1.13863 | + | 1.97217i | ||||
\(880\) | 19.2853 | − | 33.4032i | 0.650109 | − | 1.12602i | ||||
\(881\) | −36.8129 | −1.24026 | −0.620130 | − | 0.784499i | \(-0.712920\pi\) | ||||
−0.620130 | + | 0.784499i | \(0.712920\pi\) | |||||||
\(882\) | 12.4059 | 0.417730 | ||||||||
\(883\) | −15.3041 | + | 26.5075i | −0.515025 | + | 0.892049i | 0.484823 | + | 0.874612i | \(0.338884\pi\) |
−0.999848 | + | 0.0174367i | \(0.994449\pi\) | |||||||
\(884\) | 0.581086 | − | 1.00647i | 0.0195440 | − | 0.0338512i | ||||
\(885\) | −16.3248 | − | 28.2754i | −0.548752 | − | 0.950467i | ||||
\(886\) | 5.73303 | + | 9.92990i | 0.192605 | + | 0.333601i | ||||
\(887\) | 13.7973 | 0.463268 | 0.231634 | − | 0.972803i | \(-0.425593\pi\) | ||||
0.231634 | + | 0.972803i | \(0.425593\pi\) | |||||||
\(888\) | 27.7823 | + | 48.1203i | 0.932311 | + | 1.61481i | ||||
\(889\) | −1.55543 | − | 2.69409i | −0.0521675 | − | 0.0903568i | ||||
\(890\) | 5.91539 | + | 10.2458i | 0.198284 | + | 0.343438i | ||||
\(891\) | −22.3469 | + | 38.7060i | −0.748650 | + | 1.29670i | ||||
\(892\) | −0.921503 | −0.0308542 | ||||||||
\(893\) | −16.4006 | + | 28.4067i | −0.548826 | + | 0.950594i | ||||
\(894\) | 20.7652 | + | 35.9664i | 0.694493 | + | 1.20290i | ||||
\(895\) | −30.6243 | −1.02366 | ||||||||
\(896\) | −1.56985 | − | 2.71906i | −0.0524450 | − | 0.0908375i | ||||
\(897\) | −5.62419 | + | 9.74139i | −0.187786 | + | 0.325256i | ||||
\(898\) | 19.6824 | − | 34.0910i | 0.656811 | − | 1.13763i | ||||
\(899\) | 5.22424 | 0.174238 | ||||||||
\(900\) | 0.485906 | − | 0.841613i | 0.0161969 | − | 0.0280538i | ||||
\(901\) | −6.67221 | −0.222284 | ||||||||
\(902\) | −53.3077 | −1.77495 | ||||||||
\(903\) | 4.88819 | + | 0.133058i | 0.162669 | + | 0.00442790i | ||||
\(904\) | −11.2123 | −0.372916 | ||||||||
\(905\) | −32.3523 | −1.07543 | ||||||||
\(906\) | −20.1019 | + | 34.8175i | −0.667841 | + | 1.15673i | ||||
\(907\) | −53.1994 | −1.76646 | −0.883229 | − | 0.468941i | \(-0.844636\pi\) | ||||
−0.883229 | + | 0.468941i | \(0.844636\pi\) | |||||||
\(908\) | −3.31167 | + | 5.73598i | −0.109902 | + | 0.190355i | ||||
\(909\) | −2.11464 | + | 3.66267i | −0.0701383 | + | 0.121483i | ||||
\(910\) | 3.14295 | + | 5.44374i | 0.104188 | + | 0.180458i | ||||
\(911\) | 13.0310 | 0.431735 | 0.215868 | − | 0.976423i | \(-0.430742\pi\) | ||||
0.215868 | + | 0.976423i | \(0.430742\pi\) | |||||||
\(912\) | 9.02575 | + | 15.6331i | 0.298872 | + | 0.517662i | ||||
\(913\) | −19.4005 | + | 33.6027i | −0.642063 | + | 1.11209i | ||||
\(914\) | 50.7346 | 1.67815 | ||||||||
\(915\) | 2.31942 | − | 4.01736i | 0.0766777 | − | 0.132810i | ||||
\(916\) | −2.84410 | − | 4.92613i | −0.0939718 | − | 0.162764i | ||||
\(917\) | −0.00497216 | − | 0.00861203i | −0.000164195 | − | 0.000284394i | ||||
\(918\) | 2.26452 | + | 3.92227i | 0.0747404 | + | 0.129454i | ||||
\(919\) | −20.4333 | −0.674031 | −0.337015 | − | 0.941499i | \(-0.609417\pi\) | ||||
−0.337015 | + | 0.941499i | \(0.609417\pi\) | |||||||
\(920\) | −4.76053 | − | 8.24548i | −0.156950 | − | 0.271845i | ||||
\(921\) | −12.9316 | − | 22.3983i | −0.426112 | − | 0.738048i | ||||
\(922\) | 3.83901 | − | 6.64936i | 0.126431 | − | 0.218985i | ||||
\(923\) | −1.67404 | + | 2.89953i | −0.0551018 | + | 0.0954391i | ||||
\(924\) | 0.729268 | 0.0239912 | ||||||||
\(925\) | 25.9494 | 0.853209 | ||||||||
\(926\) | 0.929098 | − | 1.60924i | 0.0305321 | − | 0.0528831i | ||||
\(927\) | 3.29132 | − | 5.70074i | 0.108101 | − | 0.187237i | ||||
\(928\) | −0.724286 | − | 1.25450i | −0.0237759 | − | 0.0411810i | ||||
\(929\) | 27.9368 | + | 48.3880i | 0.916577 | + | 1.58756i | 0.804576 | + | 0.593850i | \(0.202393\pi\) |
0.112001 | + | 0.993708i | \(0.464274\pi\) | |||||||
\(930\) | 38.7582 | 1.27093 | ||||||||
\(931\) | −8.61254 | − | 14.9174i | −0.282265 | − | 0.488897i | ||||
\(932\) | −1.71236 | − | 2.96590i | −0.0560903 | − | 0.0971513i | ||||
\(933\) | −14.8707 | − | 25.7567i | −0.486843 | − | 0.843237i | ||||
\(934\) | 13.4090 | − | 23.2251i | 0.438756 | − | 0.759948i | ||||
\(935\) | 11.1860 | 0.365822 | ||||||||
\(936\) | −9.58568 | + | 16.6029i | −0.313318 | + | 0.542682i | ||||
\(937\) | 25.8992 | + | 44.8587i | 0.846090 | + | 1.46547i | 0.884671 | + | 0.466216i | \(0.154383\pi\) |
−0.0385810 | + | 0.999255i | \(0.512284\pi\) | |||||||
\(938\) | 6.64119 | 0.216843 | ||||||||
\(939\) | −25.4460 | − | 44.0737i | −0.830397 | − | 1.43829i | ||||
\(940\) | 4.52025 | − | 7.82930i | 0.147434 | − | 0.255364i | ||||
\(941\) | −27.8664 | + | 48.2660i | −0.908418 | + | 1.57343i | −0.0921550 | + | 0.995745i | \(0.529376\pi\) |
−0.816263 | + | 0.577681i | \(0.803958\pi\) | |||||||
\(942\) | −9.94299 | −0.323960 | ||||||||
\(943\) | −5.75860 | + | 9.97418i | −0.187526 | + | 0.324804i | ||||
\(944\) | −19.1741 | −0.624065 | ||||||||
\(945\) | 3.43165 | 0.111632 | ||||||||
\(946\) | 34.5494 | + | 0.940446i | 1.12330 | + | 0.0305765i | ||||
\(947\) | 2.64708 | 0.0860185 | 0.0430093 | − | 0.999075i | \(-0.486305\pi\) | ||||
0.0430093 | + | 0.999075i | \(0.486305\pi\) | |||||||
\(948\) | −0.723506 | −0.0234984 | ||||||||
\(949\) | −5.37844 | + | 9.31573i | −0.174592 | + | 0.302401i | ||||
\(950\) | 9.63194 | 0.312502 | ||||||||
\(951\) | 0.670130 | − | 1.16070i | 0.0217304 | − | 0.0376382i | ||||
\(952\) | 0.530963 | − | 0.919654i | 0.0172086 | − | 0.0298062i | ||||
\(953\) | −15.7864 | − | 27.3428i | −0.511371 | − | 0.885720i | −0.999913 | − | 0.0131800i | \(-0.995805\pi\) |
0.488542 | − | 0.872540i | \(-0.337529\pi\) | |||||||
\(954\) | 12.0443 | 0.389949 | ||||||||
\(955\) | 27.6096 | + | 47.8212i | 0.893425 | + | 1.54746i | ||||
\(956\) | −3.41702 | + | 5.91845i | −0.110514 | + | 0.191416i | ||||
\(957\) | −8.71280 | −0.281645 | ||||||||
\(958\) | −15.4624 | + | 26.7817i | −0.499568 | + | 0.865277i | ||||
\(959\) | 0.168116 | + | 0.291186i | 0.00542876 | + | 0.00940288i | ||||
\(960\) | −25.6187 | − | 44.3729i | −0.826840 | − | 1.43213i | ||||
\(961\) | 3.08009 | + | 5.33488i | 0.0993578 | + | 0.172093i | ||||
\(962\) | −56.0180 | −1.80609 | ||||||||
\(963\) | −9.96374 | − | 17.2577i | −0.321077 | − | 0.556122i | ||||
\(964\) | 0.920354 | + | 1.59410i | 0.0296426 | + | 0.0513425i | ||||
\(965\) | 23.4119 | − | 40.5506i | 0.753656 | − | 1.30537i | ||||
\(966\) | −0.562360 | + | 0.974035i | −0.0180936 | + | 0.0313391i | ||||
\(967\) | 13.8022 | 0.443848 | 0.221924 | − | 0.975064i | \(-0.428766\pi\) | ||||
0.221924 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(968\) | 14.3841 | 0.462322 | ||||||||
\(969\) | −2.61759 | + | 4.53380i | −0.0840892 | + | 0.145647i | ||||
\(970\) | 13.7182 | − | 23.7607i | 0.440466 | − | 0.762910i | ||||
\(971\) | 23.9605 | + | 41.5007i | 0.768928 | + | 1.33182i | 0.938145 | + | 0.346243i | \(0.112543\pi\) |
−0.169217 | + | 0.985579i | \(0.554124\pi\) | |||||||
\(972\) | 1.62204 | + | 2.80945i | 0.0520269 | + | 0.0901133i | ||||
\(973\) | 4.32111 | 0.138529 | ||||||||
\(974\) | 13.5848 | + | 23.5296i | 0.435285 | + | 0.753937i | ||||
\(975\) | 14.3305 | + | 24.8211i | 0.458943 | + | 0.794913i | ||||
\(976\) | −1.36213 | − | 2.35927i | −0.0436006 | − | 0.0755185i | ||||
\(977\) | −18.9377 | + | 32.8011i | −0.605871 | + | 1.04940i | 0.386042 | + | 0.922481i | \(0.373842\pi\) |
−0.991913 | + | 0.126918i | \(0.959491\pi\) | |||||||
\(978\) | −29.5736 | −0.945661 | ||||||||
\(979\) | −6.32271 | + | 10.9513i | −0.202075 | + | 0.350004i | ||||
\(980\) | 2.37374 | + | 4.11144i | 0.0758264 | + | 0.131335i | ||||
\(981\) | 12.6391 | 0.403537 | ||||||||
\(982\) | −19.2734 | − | 33.3825i | −0.615038 | − | 1.06528i | ||||
\(983\) | 14.8151 | − | 25.6606i | 0.472530 | − | 0.818445i | −0.526976 | − | 0.849880i | \(-0.676674\pi\) |
0.999506 | + | 0.0314347i | \(0.0100076\pi\) | |||||||
\(984\) | −31.4187 | + | 54.4188i | −1.00159 | + | 1.73481i | ||||
\(985\) | −23.8202 | −0.758974 | ||||||||
\(986\) | −0.694168 | + | 1.20233i | −0.0221068 | + | 0.0382901i | ||||
\(987\) | −9.75936 | −0.310644 | ||||||||
\(988\) | 2.91282 | 0.0926692 | ||||||||
\(989\) | 3.90818 | − | 6.36279i | 0.124273 | − | 0.202325i | ||||
\(990\) | −20.1924 | −0.641758 | ||||||||
\(991\) | 29.5593 | 0.938984 | 0.469492 | − | 0.882937i | \(-0.344437\pi\) | ||||
0.469492 | + | 0.882937i | \(0.344437\pi\) | |||||||
\(992\) | −3.44378 | + | 5.96480i | −0.109340 | + | 0.189383i | ||||
\(993\) | 60.2929 | 1.91334 | ||||||||
\(994\) | −0.167387 | + | 0.289922i | −0.00530918 | + | 0.00919577i | ||||
\(995\) | 34.5225 | − | 59.7948i | 1.09444 | − | 1.89562i | ||||
\(996\) | 2.50248 | + | 4.33443i | 0.0792942 | + | 0.137342i | ||||
\(997\) | −42.3784 | −1.34214 | −0.671068 | − | 0.741396i | \(-0.734164\pi\) | ||||
−0.671068 | + | 0.741396i | \(0.734164\pi\) | |||||||
\(998\) | −16.7968 | − | 29.0929i | −0.531693 | − | 0.920919i | ||||
\(999\) | −15.2909 | + | 26.4846i | −0.483783 | + | 0.837937i |
(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 | 731.2.e.b.307.9 | ✓ | 58 | |
43.36 | even | 3 | inner | 731.2.e.b.681.9 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.e.b.307.9 | ✓ | 58 | 1.1 | even | 1 | trivial | |
731.2.e.b.681.9 | yes | 58 | 43.36 | even | 3 | inner |