Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 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("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.484000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 631.1 | ||
Root | \(-0.476925 - 1.46782i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.631 |
Dual form | 770.2.n.f.421.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | −0.785942 | + | 2.41888i | −0.453764 | + | 1.39654i | 0.418816 | + | 0.908071i | \(0.362445\pi\) |
−0.872580 | + | 0.488471i | \(0.837555\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | −0.809017 | + | 0.587785i | −0.361803 | + | 0.262866i | ||||
\(6\) | −2.05762 | + | 1.49495i | −0.840021 | + | 0.610311i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | −2.80623 | − | 2.03884i | −0.935410 | − | 0.679615i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.31504 | − | 2.37499i | −0.698012 | − | 0.716086i | ||||
\(12\) | −2.54336 | −0.734205 | ||||||||
\(13\) | −5.19594 | − | 3.77507i | −1.44110 | − | 1.04702i | −0.987812 | − | 0.155651i | \(-0.950253\pi\) |
−0.453283 | − | 0.891366i | \(-0.649747\pi\) | |||||||
\(14\) | 0.309017 | − | 0.951057i | 0.0825883 | − | 0.254181i | ||||
\(15\) | −0.785942 | − | 2.41888i | −0.202929 | − | 0.624552i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −3.19873 | + | 2.32401i | −0.775806 | + | 0.563656i | −0.903718 | − | 0.428129i | \(-0.859173\pi\) |
0.127911 | + | 0.991786i | \(0.459173\pi\) | |||||||
\(18\) | −1.07188 | − | 3.29892i | −0.252646 | − | 0.777563i | ||||
\(19\) | −0.762867 | + | 2.34786i | −0.175014 | + | 0.538637i | −0.999634 | − | 0.0270497i | \(-0.991389\pi\) |
0.824620 | + | 0.565687i | \(0.191389\pi\) | |||||||
\(20\) | −0.809017 | − | 0.587785i | −0.180902 | − | 0.131433i | ||||
\(21\) | 2.54336 | 0.555007 | ||||||||
\(22\) | −0.476925 | − | 3.28216i | −0.101681 | − | 0.699758i | ||||
\(23\) | 4.99442 | 1.04141 | 0.520705 | − | 0.853737i | \(-0.325669\pi\) | ||||
0.520705 | + | 0.853737i | \(0.325669\pi\) | |||||||
\(24\) | −2.05762 | − | 1.49495i | −0.420011 | − | 0.305156i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | −1.98467 | − | 6.10820i | −0.389227 | − | 1.19792i | ||||
\(27\) | 0.964387 | − | 0.700668i | 0.185596 | − | 0.134844i | ||||
\(28\) | 0.809017 | − | 0.587785i | 0.152890 | − | 0.111081i | ||||
\(29\) | 2.79476 | + | 8.60137i | 0.518973 | + | 1.59724i | 0.775935 | + | 0.630813i | \(0.217279\pi\) |
−0.256961 | + | 0.966422i | \(0.582721\pi\) | |||||||
\(30\) | 0.785942 | − | 2.41888i | 0.143493 | − | 0.441625i | ||||
\(31\) | −6.38242 | − | 4.63710i | −1.14632 | − | 0.832847i | −0.158329 | − | 0.987386i | \(-0.550611\pi\) |
−0.987987 | + | 0.154539i | \(0.950611\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.56431 | − | 3.73321i | 1.31678 | − | 0.649868i | ||||
\(34\) | −3.95385 | −0.678080 | ||||||||
\(35\) | 0.809017 | + | 0.587785i | 0.136749 | + | 0.0993538i | ||||
\(36\) | 1.07188 | − | 3.29892i | 0.178647 | − | 0.549820i | ||||
\(37\) | 3.41279 | + | 10.5035i | 0.561059 | + | 1.72676i | 0.679379 | + | 0.733787i | \(0.262249\pi\) |
−0.118320 | + | 0.992975i | \(0.537751\pi\) | |||||||
\(38\) | −1.99721 | + | 1.45106i | −0.323991 | + | 0.235393i | ||||
\(39\) | 13.2152 | − | 9.60138i | 2.11612 | − | 1.53745i | ||||
\(40\) | −0.309017 | − | 0.951057i | −0.0488599 | − | 0.150375i | ||||
\(41\) | 2.14886 | − | 6.61350i | 0.335595 | − | 1.03286i | −0.630833 | − | 0.775919i | \(-0.717287\pi\) |
0.966428 | − | 0.256937i | \(-0.0827133\pi\) | |||||||
\(42\) | 2.05762 | + | 1.49495i | 0.317498 | + | 0.230676i | ||||
\(43\) | −3.02295 | −0.460995 | −0.230497 | − | 0.973073i | \(-0.574035\pi\) | ||||
−0.230497 | + | 0.973073i | \(0.574035\pi\) | |||||||
\(44\) | 1.54336 | − | 2.93565i | 0.232671 | − | 0.442566i | ||||
\(45\) | 3.46869 | 0.517082 | ||||||||
\(46\) | 4.04057 | + | 2.93565i | 0.595750 | + | 0.432838i | ||||
\(47\) | −2.58951 | + | 7.96970i | −0.377719 | + | 1.16250i | 0.563907 | + | 0.825839i | \(0.309298\pi\) |
−0.941626 | + | 0.336661i | \(0.890702\pi\) | |||||||
\(48\) | −0.785942 | − | 2.41888i | −0.113441 | − | 0.349135i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0.809017 | − | 0.587785i | 0.114412 | − | 0.0831254i | ||||
\(51\) | −3.10750 | − | 9.56389i | −0.435137 | − | 1.33921i | ||||
\(52\) | 1.98467 | − | 6.10820i | 0.275225 | − | 0.847055i | ||||
\(53\) | −8.14004 | − | 5.91409i | −1.11812 | − | 0.812362i | −0.134198 | − | 0.990955i | \(-0.542846\pi\) |
−0.983923 | + | 0.178592i | \(0.942846\pi\) | |||||||
\(54\) | 1.19205 | 0.162217 | ||||||||
\(55\) | 3.26889 | + | 0.560659i | 0.440777 | + | 0.0755992i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −5.07963 | − | 3.69057i | −0.672814 | − | 0.488828i | ||||
\(58\) | −2.79476 | + | 8.60137i | −0.366969 | + | 1.12942i | ||||
\(59\) | −1.26566 | − | 3.89529i | −0.164774 | − | 0.507123i | 0.834245 | − | 0.551393i | \(-0.185904\pi\) |
−0.999020 | + | 0.0442704i | \(0.985904\pi\) | |||||||
\(60\) | 2.05762 | − | 1.49495i | 0.265638 | − | 0.192997i | ||||
\(61\) | −2.91000 | + | 2.11424i | −0.372588 | + | 0.270701i | −0.758283 | − | 0.651925i | \(-0.773962\pi\) |
0.385696 | + | 0.922626i | \(0.373962\pi\) | |||||||
\(62\) | −2.43787 | − | 7.50298i | −0.309609 | − | 0.952879i | ||||
\(63\) | −1.07188 | + | 3.29892i | −0.135045 | + | 0.415625i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 6.42254 | 0.796618 | ||||||||
\(66\) | 8.31398 | + | 1.42596i | 1.02338 | + | 0.175523i | ||||
\(67\) | −1.28222 | −0.156648 | −0.0783239 | − | 0.996928i | \(-0.524957\pi\) | ||||
−0.0783239 | + | 0.996928i | \(0.524957\pi\) | |||||||
\(68\) | −3.19873 | − | 2.32401i | −0.387903 | − | 0.281828i | ||||
\(69\) | −3.92533 | + | 12.0809i | −0.472554 | + | 1.45437i | ||||
\(70\) | 0.309017 | + | 0.951057i | 0.0369346 | + | 0.113673i | ||||
\(71\) | 4.77340 | − | 3.46808i | 0.566499 | − | 0.411585i | −0.267333 | − | 0.963604i | \(-0.586142\pi\) |
0.833832 | + | 0.552019i | \(0.186142\pi\) | |||||||
\(72\) | 2.80623 | − | 2.03884i | 0.330717 | − | 0.240280i | ||||
\(73\) | 3.16808 | + | 9.75035i | 0.370796 | + | 1.14119i | 0.946272 | + | 0.323373i | \(0.104817\pi\) |
−0.575476 | + | 0.817819i | \(0.695183\pi\) | |||||||
\(74\) | −3.41279 | + | 10.5035i | −0.396729 | + | 1.22101i | ||||
\(75\) | 2.05762 | + | 1.49495i | 0.237594 | + | 0.172622i | ||||
\(76\) | −2.46869 | −0.283178 | ||||||||
\(77\) | −1.54336 | + | 2.93565i | −0.175882 | + | 0.334548i | ||||
\(78\) | 16.3348 | 1.84956 | ||||||||
\(79\) | −5.02480 | − | 3.65073i | −0.565334 | − | 0.410739i | 0.268073 | − | 0.963399i | \(-0.413613\pi\) |
−0.833407 | + | 0.552659i | \(0.813613\pi\) | |||||||
\(80\) | 0.309017 | − | 0.951057i | 0.0345492 | − | 0.106331i | ||||
\(81\) | −2.27877 | − | 7.01334i | −0.253197 | − | 0.779260i | ||||
\(82\) | 5.62578 | − | 4.08737i | 0.621264 | − | 0.451375i | ||||
\(83\) | −10.7909 | + | 7.84005i | −1.18446 | + | 0.860557i | −0.992667 | − | 0.120879i | \(-0.961429\pi\) |
−0.191788 | + | 0.981436i | \(0.561429\pi\) | |||||||
\(84\) | 0.785942 | + | 2.41888i | 0.0857533 | + | 0.263922i | ||||
\(85\) | 1.22181 | − | 3.76033i | 0.132524 | − | 0.407866i | ||||
\(86\) | −2.44561 | − | 1.77684i | −0.263717 | − | 0.191602i | ||||
\(87\) | −23.0022 | −2.46610 | ||||||||
\(88\) | 2.97414 | − | 1.46782i | 0.317044 | − | 0.156471i | ||||
\(89\) | 14.7432 | 1.56278 | 0.781388 | − | 0.624045i | \(-0.214512\pi\) | ||||
0.781388 | + | 0.624045i | \(0.214512\pi\) | |||||||
\(90\) | 2.80623 | + | 2.03884i | 0.295803 | + | 0.214913i | ||||
\(91\) | −1.98467 | + | 6.10820i | −0.208050 | + | 0.640313i | ||||
\(92\) | 1.54336 | + | 4.74998i | 0.160907 | + | 0.495220i | ||||
\(93\) | 16.2328 | − | 11.7938i | 1.68326 | − | 1.22296i | ||||
\(94\) | −6.77943 | + | 4.92554i | −0.699245 | + | 0.508031i | ||||
\(95\) | −0.762867 | − | 2.34786i | −0.0782685 | − | 0.240886i | ||||
\(96\) | 0.785942 | − | 2.41888i | 0.0802149 | − | 0.246876i | ||||
\(97\) | 9.67611 | + | 7.03010i | 0.982460 | + | 0.713799i | 0.958257 | − | 0.285908i | \(-0.0922953\pi\) |
0.0242028 | + | 0.999707i | \(0.492295\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.65431 | + | 11.3848i | 0.166264 | + | 1.14421i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.82930 | + | 1.32907i | 0.182023 | + | 0.132247i | 0.675065 | − | 0.737758i | \(-0.264115\pi\) |
−0.493043 | + | 0.870005i | \(0.664115\pi\) | |||||||
\(102\) | 3.10750 | − | 9.56389i | 0.307688 | − | 0.946966i | ||||
\(103\) | 4.15192 | + | 12.7783i | 0.409101 | + | 1.25908i | 0.917422 | + | 0.397916i | \(0.130267\pi\) |
−0.508321 | + | 0.861168i | \(0.669733\pi\) | |||||||
\(104\) | 5.19594 | − | 3.77507i | 0.509504 | − | 0.370176i | ||||
\(105\) | −2.05762 | + | 1.49495i | −0.200803 | + | 0.145892i | ||||
\(106\) | −3.10922 | − | 9.56920i | −0.301994 | − | 0.929442i | ||||
\(107\) | 4.13708 | − | 12.7326i | 0.399947 | − | 1.23091i | −0.525094 | − | 0.851044i | \(-0.675970\pi\) |
0.925041 | − | 0.379866i | \(-0.124030\pi\) | |||||||
\(108\) | 0.964387 | + | 0.700668i | 0.0927982 | + | 0.0674218i | ||||
\(109\) | −8.67624 | −0.831033 | −0.415516 | − | 0.909586i | \(-0.636399\pi\) | ||||
−0.415516 | + | 0.909586i | \(0.636399\pi\) | |||||||
\(110\) | 2.31504 | + | 2.37499i | 0.220731 | + | 0.226446i | ||||
\(111\) | −28.0889 | −2.66608 | ||||||||
\(112\) | 0.809017 | + | 0.587785i | 0.0764449 | + | 0.0555405i | ||||
\(113\) | −2.83267 | + | 8.71806i | −0.266475 | + | 0.820126i | 0.724875 | + | 0.688881i | \(0.241898\pi\) |
−0.991350 | + | 0.131246i | \(0.958102\pi\) | |||||||
\(114\) | −1.94025 | − | 5.97147i | −0.181721 | − | 0.559279i | ||||
\(115\) | −4.04057 | + | 2.93565i | −0.376785 | + | 0.273751i | ||||
\(116\) | −7.31677 | + | 5.31594i | −0.679345 | + | 0.493573i | ||||
\(117\) | 6.88422 | + | 21.1874i | 0.636446 | + | 1.95878i | ||||
\(118\) | 1.26566 | − | 3.89529i | 0.116513 | − | 0.358590i | ||||
\(119\) | 3.19873 | + | 2.32401i | 0.293227 | + | 0.213042i | ||||
\(120\) | 2.54336 | 0.232176 | ||||||||
\(121\) | −0.281153 | + | 10.9964i | −0.0255594 | + | 0.999673i | ||||
\(122\) | −3.59696 | −0.325653 | ||||||||
\(123\) | 14.3084 | + | 10.3957i | 1.29015 | + | 0.937345i | ||||
\(124\) | 2.43787 | − | 7.50298i | 0.218927 | − | 0.673787i | ||||
\(125\) | 0.309017 | + | 0.951057i | 0.0276393 | + | 0.0850651i | ||||
\(126\) | −2.80623 | + | 2.03884i | −0.249999 | + | 0.181635i | ||||
\(127\) | −12.3615 | + | 8.98117i | −1.09691 | + | 0.796950i | −0.980552 | − | 0.196258i | \(-0.937121\pi\) |
−0.116355 | + | 0.993208i | \(0.537121\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 2.37586 | − | 7.31215i | 0.209183 | − | 0.643799i | ||||
\(130\) | 5.19594 | + | 3.77507i | 0.455714 | + | 0.331096i | ||||
\(131\) | −5.65461 | −0.494045 | −0.247023 | − | 0.969010i | \(-0.579452\pi\) | ||||
−0.247023 | + | 0.969010i | \(0.579452\pi\) | |||||||
\(132\) | 5.88799 | + | 6.04046i | 0.512484 | + | 0.525754i | ||||
\(133\) | 2.46869 | 0.214063 | ||||||||
\(134\) | −1.03734 | − | 0.753669i | −0.0896122 | − | 0.0651071i | ||||
\(135\) | −0.368363 | + | 1.13370i | −0.0317036 | + | 0.0975738i | ||||
\(136\) | −1.22181 | − | 3.76033i | −0.104769 | − | 0.322446i | ||||
\(137\) | 3.19795 | − | 2.32344i | 0.273219 | − | 0.198505i | −0.442735 | − | 0.896652i | \(-0.645992\pi\) |
0.715954 | + | 0.698147i | \(0.245992\pi\) | |||||||
\(138\) | −10.2766 | + | 7.46642i | −0.874806 | + | 0.635584i | ||||
\(139\) | −6.49721 | − | 19.9964i | −0.551086 | − | 1.69607i | −0.706061 | − | 0.708151i | \(-0.749530\pi\) |
0.154975 | − | 0.987918i | \(-0.450470\pi\) | |||||||
\(140\) | −0.309017 | + | 0.951057i | −0.0261167 | + | 0.0803789i | ||||
\(141\) | −17.2425 | − | 12.5274i | −1.45208 | − | 1.05500i | ||||
\(142\) | 5.90025 | 0.495138 | ||||||||
\(143\) | 3.06307 | + | 21.0798i | 0.256147 | + | 1.76278i | ||||
\(144\) | 3.46869 | 0.289057 | ||||||||
\(145\) | −7.31677 | − | 5.31594i | −0.607624 | − | 0.441465i | ||||
\(146\) | −3.16808 | + | 9.75035i | −0.262192 | + | 0.806944i | ||||
\(147\) | −0.785942 | − | 2.41888i | −0.0648234 | − | 0.199506i | ||||
\(148\) | −8.93480 | + | 6.49151i | −0.734436 | + | 0.533599i | ||||
\(149\) | 6.91975 | − | 5.02749i | 0.566888 | − | 0.411868i | −0.267085 | − | 0.963673i | \(-0.586061\pi\) |
0.833973 | + | 0.551805i | \(0.186061\pi\) | |||||||
\(150\) | 0.785942 | + | 2.41888i | 0.0641719 | + | 0.197501i | ||||
\(151\) | −0.683406 | + | 2.10331i | −0.0556148 | + | 0.171165i | −0.975005 | − | 0.222181i | \(-0.928682\pi\) |
0.919391 | + | 0.393346i | \(0.128682\pi\) | |||||||
\(152\) | −1.99721 | − | 1.45106i | −0.161995 | − | 0.117696i | ||||
\(153\) | 13.7147 | 1.10877 | ||||||||
\(154\) | −2.97414 | + | 1.46782i | −0.239663 | + | 0.118281i | ||||
\(155\) | 7.88910 | 0.633668 | ||||||||
\(156\) | 13.2152 | + | 9.60138i | 1.05806 | + | 0.768726i | ||||
\(157\) | −4.13660 | + | 12.7311i | −0.330136 | + | 1.01606i | 0.638932 | + | 0.769263i | \(0.279377\pi\) |
−0.969068 | + | 0.246792i | \(0.920623\pi\) | |||||||
\(158\) | −1.91930 | − | 5.90700i | −0.152691 | − | 0.469936i | ||||
\(159\) | 20.7031 | − | 15.0417i | 1.64186 | − | 1.19288i | ||||
\(160\) | 0.809017 | − | 0.587785i | 0.0639584 | − | 0.0464685i | ||||
\(161\) | −1.54336 | − | 4.74998i | −0.121634 | − | 0.374351i | ||||
\(162\) | 2.27877 | − | 7.01334i | 0.179037 | − | 0.551020i | ||||
\(163\) | −1.66095 | − | 1.20675i | −0.130095 | − | 0.0945198i | 0.520835 | − | 0.853658i | \(-0.325621\pi\) |
−0.650930 | + | 0.759138i | \(0.725621\pi\) | |||||||
\(164\) | 6.95385 | 0.543004 | ||||||||
\(165\) | −3.92533 | + | 7.46642i | −0.305586 | + | 0.581260i | ||||
\(166\) | −13.3383 | −1.03525 | ||||||||
\(167\) | −17.1525 | − | 12.4621i | −1.32730 | − | 0.964343i | −0.999810 | − | 0.0194894i | \(-0.993796\pi\) |
−0.327494 | − | 0.944853i | \(-0.606204\pi\) | |||||||
\(168\) | −0.785942 | + | 2.41888i | −0.0606367 | + | 0.186621i | ||||
\(169\) | 8.72943 | + | 26.8664i | 0.671494 | + | 2.06665i | ||||
\(170\) | 3.19873 | − | 2.32401i | 0.245332 | − | 0.178244i | ||||
\(171\) | 6.92771 | − | 5.03328i | 0.529775 | − | 0.384904i | ||||
\(172\) | −0.934142 | − | 2.87499i | −0.0712276 | − | 0.219216i | ||||
\(173\) | −1.82700 | + | 5.62293i | −0.138904 | + | 0.427504i | −0.996177 | − | 0.0873592i | \(-0.972157\pi\) |
0.857272 | + | 0.514863i | \(0.172157\pi\) | |||||||
\(174\) | −18.6092 | − | 13.5204i | −1.41076 | − | 1.02498i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 3.26889 | + | 0.560659i | 0.246402 | + | 0.0422613i | ||||
\(177\) | 10.4170 | 0.782987 | ||||||||
\(178\) | 11.9275 | + | 8.66584i | 0.894004 | + | 0.649532i | ||||
\(179\) | −5.52768 | + | 17.0124i | −0.413158 | + | 1.27157i | 0.500730 | + | 0.865604i | \(0.333065\pi\) |
−0.913888 | + | 0.405966i | \(0.866935\pi\) | |||||||
\(180\) | 1.07188 | + | 3.29892i | 0.0798935 | + | 0.245887i | ||||
\(181\) | −8.95660 | + | 6.50735i | −0.665739 | + | 0.483688i | −0.868596 | − | 0.495521i | \(-0.834977\pi\) |
0.202857 | + | 0.979208i | \(0.434977\pi\) | |||||||
\(182\) | −5.19594 | + | 3.77507i | −0.385149 | + | 0.279827i | ||||
\(183\) | −2.82700 | − | 8.70062i | −0.208978 | − | 0.643168i | ||||
\(184\) | −1.54336 | + | 4.74998i | −0.113778 | + | 0.350173i | ||||
\(185\) | −8.93480 | − | 6.49151i | −0.656900 | − | 0.477265i | ||||
\(186\) | 20.0648 | 1.47123 | ||||||||
\(187\) | 12.9247 | + | 2.21676i | 0.945149 | + | 0.162106i | ||||
\(188\) | −8.37984 | −0.611162 | ||||||||
\(189\) | −0.964387 | − | 0.700668i | −0.0701488 | − | 0.0509661i | ||||
\(190\) | 0.762867 | − | 2.34786i | 0.0553442 | − | 0.170332i | ||||
\(191\) | −2.95413 | − | 9.09187i | −0.213753 | − | 0.657865i | −0.999240 | − | 0.0389860i | \(-0.987587\pi\) |
0.785487 | − | 0.618879i | \(-0.212413\pi\) | |||||||
\(192\) | 2.05762 | − | 1.49495i | 0.148496 | − | 0.107889i | ||||
\(193\) | 13.4981 | − | 9.80695i | 0.971615 | − | 0.705920i | 0.0157962 | − | 0.999875i | \(-0.494972\pi\) |
0.955819 | + | 0.293955i | \(0.0949717\pi\) | |||||||
\(194\) | 3.69594 | + | 11.3749i | 0.265353 | + | 0.816674i | ||||
\(195\) | −5.04774 | + | 15.5354i | −0.361476 | + | 1.11251i | ||||
\(196\) | −0.809017 | − | 0.587785i | −0.0577869 | − | 0.0419847i | ||||
\(197\) | 0.533440 | 0.0380060 | 0.0190030 | − | 0.999819i | \(-0.493951\pi\) | ||||
0.0190030 | + | 0.999819i | \(0.493951\pi\) | |||||||
\(198\) | −5.35344 | + | 10.1829i | −0.380453 | + | 0.723664i | ||||
\(199\) | −2.81443 | −0.199510 | −0.0997548 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997548 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(200\) | 0.809017 | + | 0.587785i | 0.0572061 | + | 0.0415627i | ||||
\(201\) | 1.00775 | − | 3.10153i | 0.0710811 | − | 0.218765i | ||||
\(202\) | 0.698732 | + | 2.15048i | 0.0491626 | + | 0.151307i | ||||
\(203\) | 7.31677 | − | 5.31594i | 0.513536 | − | 0.373106i | ||||
\(204\) | 8.13553 | − | 5.91081i | 0.569601 | − | 0.413840i | ||||
\(205\) | 2.14886 | + | 6.61350i | 0.150083 | + | 0.461907i | ||||
\(206\) | −4.15192 | + | 12.7783i | −0.289278 | + | 0.890307i | ||||
\(207\) | −14.0155 | − | 10.1829i | −0.974144 | − | 0.707757i | ||||
\(208\) | 6.42254 | 0.445323 | ||||||||
\(209\) | 7.34222 | − | 3.62360i | 0.507872 | − | 0.250650i | ||||
\(210\) | −2.54336 | −0.175509 | ||||||||
\(211\) | 2.59078 | + | 1.88232i | 0.178357 | + | 0.129584i | 0.673382 | − | 0.739295i | \(-0.264841\pi\) |
−0.495025 | + | 0.868879i | \(0.664841\pi\) | |||||||
\(212\) | 3.10922 | − | 9.56920i | 0.213542 | − | 0.657215i | ||||
\(213\) | 4.63726 | + | 14.2720i | 0.317740 | + | 0.977902i | ||||
\(214\) | 10.8310 | − | 7.86920i | 0.740394 | − | 0.537928i | ||||
\(215\) | 2.44561 | − | 1.77684i | 0.166790 | − | 0.121180i | ||||
\(216\) | 0.368363 | + | 1.13370i | 0.0250639 | + | 0.0771389i | ||||
\(217\) | −2.43787 | + | 7.50298i | −0.165493 | + | 0.509335i | ||||
\(218\) | −7.01922 | − | 5.09976i | −0.475402 | − | 0.345400i | ||||
\(219\) | −26.0749 | −1.76198 | ||||||||
\(220\) | 0.476925 | + | 3.28216i | 0.0321543 | + | 0.221283i | ||||
\(221\) | 25.3938 | 1.70817 | ||||||||
\(222\) | −22.7244 | − | 16.5103i | −1.52516 | − | 1.10810i | ||||
\(223\) | −0.237490 | + | 0.730921i | −0.0159035 | + | 0.0489461i | −0.958693 | − | 0.284442i | \(-0.908192\pi\) |
0.942790 | + | 0.333388i | \(0.108192\pi\) | |||||||
\(224\) | 0.309017 | + | 0.951057i | 0.0206471 | + | 0.0635451i | ||||
\(225\) | −2.80623 | + | 2.03884i | −0.187082 | + | 0.135923i | ||||
\(226\) | −7.41603 | + | 5.38806i | −0.493307 | + | 0.358408i | ||||
\(227\) | 2.03561 | + | 6.26497i | 0.135108 | + | 0.415821i | 0.995607 | − | 0.0936322i | \(-0.0298478\pi\) |
−0.860498 | + | 0.509453i | \(0.829848\pi\) | |||||||
\(228\) | 1.94025 | − | 5.97147i | 0.128496 | − | 0.395470i | ||||
\(229\) | 18.8362 | + | 13.6853i | 1.24473 | + | 0.904352i | 0.997904 | − | 0.0647076i | \(-0.0206115\pi\) |
0.246829 | + | 0.969059i | \(0.420611\pi\) | |||||||
\(230\) | −4.99442 | −0.329323 | ||||||||
\(231\) | −5.88799 | − | 6.04046i | −0.387401 | − | 0.397433i | ||||
\(232\) | −9.04402 | −0.593769 | ||||||||
\(233\) | 1.39344 | + | 1.01239i | 0.0912872 | + | 0.0663241i | 0.632493 | − | 0.774566i | \(-0.282032\pi\) |
−0.541205 | + | 0.840890i | \(0.682032\pi\) | |||||||
\(234\) | −6.88422 | + | 21.1874i | −0.450035 | + | 1.38507i | ||||
\(235\) | −2.58951 | − | 7.96970i | −0.168921 | − | 0.519886i | ||||
\(236\) | 3.31353 | − | 2.40742i | 0.215692 | − | 0.156710i | ||||
\(237\) | 12.7799 | − | 9.28513i | 0.830142 | − | 0.603134i | ||||
\(238\) | 1.22181 | + | 3.76033i | 0.0791980 | + | 0.243746i | ||||
\(239\) | 3.59810 | − | 11.0738i | 0.232742 | − | 0.716306i | −0.764671 | − | 0.644421i | \(-0.777098\pi\) |
0.997413 | − | 0.0718853i | \(-0.0229016\pi\) | |||||||
\(240\) | 2.05762 | + | 1.49495i | 0.132819 | + | 0.0964986i | ||||
\(241\) | −9.58236 | −0.617254 | −0.308627 | − | 0.951183i | \(-0.599870\pi\) | ||||
−0.308627 | + | 0.951183i | \(0.599870\pi\) | |||||||
\(242\) | −6.69098 | + | 8.73102i | −0.430113 | + | 0.561251i | ||||
\(243\) | 22.3316 | 1.43257 | ||||||||
\(244\) | −2.91000 | − | 2.11424i | −0.186294 | − | 0.135350i | ||||
\(245\) | 0.309017 | − | 0.951057i | 0.0197424 | − | 0.0607608i | ||||
\(246\) | 5.46532 | + | 16.8205i | 0.348456 | + | 1.07244i | ||||
\(247\) | 12.8272 | − | 9.31949i | 0.816174 | − | 0.592985i | ||||
\(248\) | 6.38242 | − | 4.63710i | 0.405284 | − | 0.294456i | ||||
\(249\) | −10.4831 | − | 32.2637i | −0.664341 | − | 2.04463i | ||||
\(250\) | −0.309017 | + | 0.951057i | −0.0195440 | + | 0.0601501i | ||||
\(251\) | 6.83950 | + | 4.96919i | 0.431706 | + | 0.313653i | 0.782331 | − | 0.622863i | \(-0.214031\pi\) |
−0.350625 | + | 0.936516i | \(0.614031\pi\) | |||||||
\(252\) | −3.46869 | −0.218507 | ||||||||
\(253\) | −11.5623 | − | 11.8617i | −0.726916 | − | 0.745739i | ||||
\(254\) | −15.2797 | −0.958732 | ||||||||
\(255\) | 8.13553 | + | 5.91081i | 0.509467 | + | 0.370149i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −6.29635 | − | 19.3782i | −0.392756 | − | 1.20878i | −0.930696 | − | 0.365794i | \(-0.880797\pi\) |
0.537940 | − | 0.842983i | \(-0.319203\pi\) | |||||||
\(258\) | 6.22008 | − | 4.51916i | 0.387246 | − | 0.281350i | ||||
\(259\) | 8.93480 | − | 6.49151i | 0.555181 | − | 0.403363i | ||||
\(260\) | 1.98467 | + | 6.10820i | 0.123084 | + | 0.378814i | ||||
\(261\) | 9.69414 | − | 29.8355i | 0.600052 | − | 1.84677i | ||||
\(262\) | −4.57467 | − | 3.32369i | −0.282624 | − | 0.205338i | ||||
\(263\) | 16.1920 | 0.998444 | 0.499222 | − | 0.866474i | \(-0.333619\pi\) | ||||
0.499222 | + | 0.866474i | \(0.333619\pi\) | |||||||
\(264\) | 1.21299 | + | 8.34771i | 0.0746546 | + | 0.513766i | ||||
\(265\) | 10.0616 | 0.618082 | ||||||||
\(266\) | 1.99721 | + | 1.45106i | 0.122457 | + | 0.0889702i | ||||
\(267\) | −11.5873 | + | 35.6621i | −0.709131 | + | 2.18248i | ||||
\(268\) | −0.396227 | − | 1.21946i | −0.0242034 | − | 0.0744905i | ||||
\(269\) | 21.6933 | − | 15.7611i | 1.32267 | − | 0.960973i | 0.322771 | − | 0.946477i | \(-0.395386\pi\) |
0.999895 | − | 0.0144955i | \(-0.00461424\pi\) | |||||||
\(270\) | −0.964387 | + | 0.700668i | −0.0586907 | + | 0.0426413i | ||||
\(271\) | −6.93163 | − | 21.3334i | −0.421067 | − | 1.29591i | −0.906711 | − | 0.421753i | \(-0.861415\pi\) |
0.485644 | − | 0.874157i | \(-0.338585\pi\) | |||||||
\(272\) | 1.22181 | − | 3.76033i | 0.0740829 | − | 0.228004i | ||||
\(273\) | −13.2152 | − | 9.60138i | −0.799818 | − | 0.581102i | ||||
\(274\) | 3.95288 | 0.238802 | ||||||||
\(275\) | −2.97414 | + | 1.46782i | −0.179347 | + | 0.0885131i | ||||
\(276\) | −12.7026 | −0.764608 | ||||||||
\(277\) | −17.8914 | − | 12.9989i | −1.07499 | − | 0.781026i | −0.0981876 | − | 0.995168i | \(-0.531305\pi\) |
−0.976803 | + | 0.214142i | \(0.931305\pi\) | |||||||
\(278\) | 6.49721 | − | 19.9964i | 0.389677 | − | 1.19930i | ||||
\(279\) | 8.45620 | + | 26.0255i | 0.506260 | + | 1.55811i | ||||
\(280\) | −0.809017 | + | 0.587785i | −0.0483480 | + | 0.0351269i | ||||
\(281\) | 10.1696 | − | 7.38864i | 0.606667 | − | 0.440769i | −0.241572 | − | 0.970383i | \(-0.577663\pi\) |
0.848239 | + | 0.529613i | \(0.177663\pi\) | |||||||
\(282\) | −6.58607 | − | 20.2698i | −0.392195 | − | 1.20705i | ||||
\(283\) | 1.57746 | − | 4.85492i | 0.0937703 | − | 0.288595i | −0.893161 | − | 0.449737i | \(-0.851518\pi\) |
0.986931 | + | 0.161142i | \(0.0515177\pi\) | |||||||
\(284\) | 4.77340 | + | 3.46808i | 0.283249 | + | 0.205793i | ||||
\(285\) | 6.27877 | 0.371922 | ||||||||
\(286\) | −9.91230 | + | 18.8543i | −0.586127 | + | 1.11488i | ||||
\(287\) | −6.95385 | −0.410473 | ||||||||
\(288\) | 2.80623 | + | 2.03884i | 0.165359 | + | 0.120140i | ||||
\(289\) | −0.422448 | + | 1.30016i | −0.0248499 | + | 0.0764800i | ||||
\(290\) | −2.79476 | − | 8.60137i | −0.164114 | − | 0.505090i | ||||
\(291\) | −24.6098 | + | 17.8801i | −1.44265 | + | 1.04815i | ||||
\(292\) | −8.29414 | + | 6.02605i | −0.485378 | + | 0.352648i | ||||
\(293\) | 5.33226 | + | 16.4110i | 0.311514 | + | 0.958742i | 0.977166 | + | 0.212479i | \(0.0681538\pi\) |
−0.665651 | + | 0.746263i | \(0.731846\pi\) | |||||||
\(294\) | 0.785942 | − | 2.41888i | 0.0458371 | − | 0.141072i | ||||
\(295\) | 3.31353 | + | 2.40742i | 0.192921 | + | 0.140165i | ||||
\(296\) | −11.0440 | −0.641921 | ||||||||
\(297\) | −3.89668 | − | 0.668332i | −0.226108 | − | 0.0387806i | ||||
\(298\) | 8.55328 | 0.495478 | ||||||||
\(299\) | −25.9507 | − | 18.8543i | −1.50077 | − | 1.09037i | ||||
\(300\) | −0.785942 | + | 2.41888i | −0.0453764 | + | 0.139654i | ||||
\(301\) | 0.934142 | + | 2.87499i | 0.0538430 | + | 0.165712i | ||||
\(302\) | −1.78918 | + | 1.29992i | −0.102956 | + | 0.0748017i | ||||
\(303\) | −4.65258 | + | 3.38030i | −0.267284 | + | 0.194193i | ||||
\(304\) | −0.762867 | − | 2.34786i | −0.0437534 | − | 0.134659i | ||||
\(305\) | 1.11152 | − | 3.42091i | 0.0636456 | − | 0.195881i | ||||
\(306\) | 11.0954 | + | 8.06129i | 0.634282 | + | 0.460833i | ||||
\(307\) | 24.8048 | 1.41569 | 0.707844 | − | 0.706369i | \(-0.249668\pi\) | ||||
0.707844 | + | 0.706369i | \(0.249668\pi\) | |||||||
\(308\) | −3.26889 | − | 0.560659i | −0.186262 | − | 0.0319465i | ||||
\(309\) | −34.1724 | −1.94400 | ||||||||
\(310\) | 6.38242 | + | 4.63710i | 0.362497 | + | 0.263369i | ||||
\(311\) | −4.65745 | + | 14.3342i | −0.264100 | + | 0.812816i | 0.727800 | + | 0.685790i | \(0.240543\pi\) |
−0.991899 | + | 0.127026i | \(0.959457\pi\) | |||||||
\(312\) | 5.04774 | + | 15.5354i | 0.285772 | + | 0.879517i | ||||
\(313\) | 11.8713 | − | 8.62498i | 0.671004 | − | 0.487513i | −0.199357 | − | 0.979927i | \(-0.563885\pi\) |
0.870361 | + | 0.492414i | \(0.163885\pi\) | |||||||
\(314\) | −10.8298 | + | 7.86828i | −0.611158 | + | 0.444033i | ||||
\(315\) | −1.07188 | − | 3.29892i | −0.0603938 | − | 0.185873i | ||||
\(316\) | 1.91930 | − | 5.90700i | 0.107969 | − | 0.332295i | ||||
\(317\) | 11.5438 | + | 8.38707i | 0.648365 | + | 0.471065i | 0.862714 | − | 0.505692i | \(-0.168763\pi\) |
−0.214349 | + | 0.976757i | \(0.568763\pi\) | |||||||
\(318\) | 25.5904 | 1.43504 | ||||||||
\(319\) | 13.9582 | − | 26.5501i | 0.781509 | − | 1.48652i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 27.5472 | + | 20.0142i | 1.53754 | + | 1.11709i | ||||
\(322\) | 1.54336 | − | 4.74998i | 0.0860082 | − | 0.264706i | ||||
\(323\) | −3.01626 | − | 9.28310i | −0.167829 | − | 0.516526i | ||||
\(324\) | 5.96590 | − | 4.33448i | 0.331439 | − | 0.240805i | ||||
\(325\) | −5.19594 | + | 3.77507i | −0.288219 | + | 0.209403i | ||||
\(326\) | −0.634425 | − | 1.95256i | −0.0351375 | − | 0.108142i | ||||
\(327\) | 6.81902 | − | 20.9868i | 0.377093 | − | 1.16057i | ||||
\(328\) | 5.62578 | + | 4.08737i | 0.310632 | + | 0.225687i | ||||
\(329\) | 8.37984 | 0.461995 | ||||||||
\(330\) | −7.56431 | + | 3.73321i | −0.416401 | + | 0.205506i | ||||
\(331\) | −12.9209 | −0.710197 | −0.355099 | − | 0.934829i | \(-0.615553\pi\) | ||||
−0.355099 | + | 0.934829i | \(0.615553\pi\) | |||||||
\(332\) | −10.7909 | − | 7.84005i | −0.592228 | − | 0.430279i | ||||
\(333\) | 11.8379 | − | 36.4333i | 0.648713 | − | 1.99653i | ||||
\(334\) | −6.55169 | − | 20.1640i | −0.358492 | − | 1.10333i | ||||
\(335\) | 1.03734 | − | 0.753669i | 0.0566757 | − | 0.0411773i | ||||
\(336\) | −2.05762 | + | 1.49495i | −0.112253 | + | 0.0815562i | ||||
\(337\) | 6.36585 | + | 19.5921i | 0.346770 | + | 1.06725i | 0.960629 | + | 0.277833i | \(0.0896162\pi\) |
−0.613859 | + | 0.789416i | \(0.710384\pi\) | |||||||
\(338\) | −8.72943 | + | 26.8664i | −0.474818 | + | 1.46134i | ||||
\(339\) | −18.8616 | − | 13.7038i | −1.02442 | − | 0.744287i | ||||
\(340\) | 3.95385 | 0.214428 | ||||||||
\(341\) | 3.76251 | + | 25.8933i | 0.203751 | + | 1.40220i | ||||
\(342\) | 8.56312 | 0.463040 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 0.934142 | − | 2.87499i | 0.0503655 | − | 0.155009i | ||||
\(345\) | −3.92533 | − | 12.0809i | −0.211333 | − | 0.650415i | ||||
\(346\) | −4.78315 | + | 3.47516i | −0.257144 | + | 0.186826i | ||||
\(347\) | 3.08349 | − | 2.24028i | 0.165530 | − | 0.120265i | −0.501936 | − | 0.864905i | \(-0.667379\pi\) |
0.667466 | + | 0.744640i | \(0.267379\pi\) | |||||||
\(348\) | −7.10808 | − | 21.8764i | −0.381033 | − | 1.17270i | ||||
\(349\) | −6.11180 | + | 18.8102i | −0.327157 | + | 1.00689i | 0.643300 | + | 0.765614i | \(0.277565\pi\) |
−0.970457 | + | 0.241272i | \(0.922435\pi\) | |||||||
\(350\) | −0.809017 | − | 0.587785i | −0.0432438 | − | 0.0314184i | ||||
\(351\) | −7.65598 | −0.408646 | ||||||||
\(352\) | 2.31504 | + | 2.37499i | 0.123392 | + | 0.126587i | ||||
\(353\) | −2.85223 | −0.151809 | −0.0759044 | − | 0.997115i | \(-0.524184\pi\) | ||||
−0.0759044 | + | 0.997115i | \(0.524184\pi\) | |||||||
\(354\) | 8.42750 | + | 6.12294i | 0.447917 | + | 0.325430i | ||||
\(355\) | −1.82328 | + | 5.61147i | −0.0967696 | + | 0.297826i | ||||
\(356\) | 4.55590 | + | 14.0216i | 0.241462 | + | 0.743144i | ||||
\(357\) | −8.13553 | + | 5.91081i | −0.430578 | + | 0.312833i | ||||
\(358\) | −14.4716 | + | 10.5143i | −0.764850 | + | 0.555696i | ||||
\(359\) | 5.23394 | + | 16.1084i | 0.276237 | + | 0.850169i | 0.988890 | + | 0.148652i | \(0.0474935\pi\) |
−0.712653 | + | 0.701517i | \(0.752506\pi\) | |||||||
\(360\) | −1.07188 | + | 3.29892i | −0.0564933 | + | 0.173868i | ||||
\(361\) | 10.4408 | + | 7.58570i | 0.549517 | + | 0.399248i | ||||
\(362\) | −11.0710 | −0.581877 | ||||||||
\(363\) | −26.3780 | − | 9.32261i | −1.38449 | − | 0.489310i | ||||
\(364\) | −6.42254 | −0.336633 | ||||||||
\(365\) | −8.29414 | − | 6.02605i | −0.434135 | − | 0.315418i | ||||
\(366\) | 2.82700 | − | 8.70062i | 0.147770 | − | 0.454789i | ||||
\(367\) | −6.18204 | − | 19.0264i | −0.322700 | − | 0.993168i | −0.972468 | − | 0.233036i | \(-0.925134\pi\) |
0.649768 | − | 0.760132i | \(-0.274866\pi\) | |||||||
\(368\) | −4.04057 | + | 2.93565i | −0.210629 | + | 0.153031i | ||||
\(369\) | −19.5141 | + | 14.1778i | −1.01586 | + | 0.738068i | ||||
\(370\) | −3.41279 | − | 10.5035i | −0.177422 | − | 0.546050i | ||||
\(371\) | −3.10922 | + | 9.56920i | −0.161423 | + | 0.496808i | ||||
\(372\) | 16.2328 | + | 11.7938i | 0.841631 | + | 0.611481i | ||||
\(373\) | −23.1627 | −1.19932 | −0.599660 | − | 0.800255i | \(-0.704697\pi\) | ||||
−0.599660 | + | 0.800255i | \(0.704697\pi\) | |||||||
\(374\) | 9.15333 | + | 9.39035i | 0.473308 | + | 0.485564i | ||||
\(375\) | −2.54336 | −0.131339 | ||||||||
\(376\) | −6.77943 | − | 4.92554i | −0.349622 | − | 0.254016i | ||||
\(377\) | 17.9494 | − | 55.2427i | 0.924443 | − | 2.84514i | ||||
\(378\) | −0.368363 | − | 1.13370i | −0.0189466 | − | 0.0583115i | ||||
\(379\) | −26.3795 | + | 19.1658i | −1.35502 | + | 0.984481i | −0.356278 | + | 0.934380i | \(0.615954\pi\) |
−0.998744 | + | 0.0501010i | \(0.984046\pi\) | |||||||
\(380\) | 1.99721 | − | 1.45106i | 0.102455 | − | 0.0744378i | ||||
\(381\) | −12.0089 | − | 36.9597i | −0.615236 | − | 1.89350i | ||||
\(382\) | 2.95413 | − | 9.09187i | 0.151146 | − | 0.465181i | ||||
\(383\) | −4.18202 | − | 3.03842i | −0.213691 | − | 0.155256i | 0.475791 | − | 0.879558i | \(-0.342162\pi\) |
−0.689482 | + | 0.724303i | \(0.742162\pi\) | |||||||
\(384\) | 2.54336 | 0.129790 | ||||||||
\(385\) | −0.476925 | − | 3.28216i | −0.0243064 | − | 0.167274i | ||||
\(386\) | 16.6846 | 0.849223 | ||||||||
\(387\) | 8.48308 | + | 6.16332i | 0.431219 | + | 0.313299i | ||||
\(388\) | −3.69594 | + | 11.3749i | −0.187633 | + | 0.577475i | ||||
\(389\) | −0.268314 | − | 0.825787i | −0.0136041 | − | 0.0418690i | 0.944024 | − | 0.329877i | \(-0.107007\pi\) |
−0.957628 | + | 0.288008i | \(0.907007\pi\) | |||||||
\(390\) | −13.2152 | + | 9.60138i | −0.669176 | + | 0.486185i | ||||
\(391\) | −15.9758 | + | 11.6071i | −0.807932 | + | 0.586997i | ||||
\(392\) | −0.309017 | − | 0.951057i | −0.0156077 | − | 0.0480356i | ||||
\(393\) | 4.44419 | − | 13.6778i | 0.224180 | − | 0.689955i | ||||
\(394\) | 0.431562 | + | 0.313548i | 0.0217418 | + | 0.0157963i | ||||
\(395\) | 6.21099 | 0.312509 | ||||||||
\(396\) | −10.3164 | + | 5.09143i | −0.518417 | + | 0.255854i | ||||
\(397\) | −16.7823 | −0.842280 | −0.421140 | − | 0.906996i | \(-0.638370\pi\) | ||||
−0.421140 | + | 0.906996i | \(0.638370\pi\) | |||||||
\(398\) | −2.27692 | − | 1.65428i | −0.114132 | − | 0.0829215i | ||||
\(399\) | −1.94025 | + | 5.97147i | −0.0971339 | + | 0.298947i | ||||
\(400\) | 0.309017 | + | 0.951057i | 0.0154508 | + | 0.0475528i | ||||
\(401\) | 1.34614 | − | 0.978031i | 0.0672233 | − | 0.0488406i | −0.553666 | − | 0.832739i | \(-0.686772\pi\) |
0.620889 | + | 0.783898i | \(0.286772\pi\) | |||||||
\(402\) | 2.63832 | − | 1.91685i | 0.131587 | − | 0.0956039i | ||||
\(403\) | 15.6573 | + | 48.1882i | 0.779945 | + | 2.40042i | ||||
\(404\) | −0.698732 | + | 2.15048i | −0.0347632 | + | 0.106990i | ||||
\(405\) | 5.96590 | + | 4.33448i | 0.296448 | + | 0.215382i | ||||
\(406\) | 9.04402 | 0.448847 | ||||||||
\(407\) | 17.0449 | − | 32.4214i | 0.844885 | − | 1.60707i | ||||
\(408\) | 10.0561 | 0.497850 | ||||||||
\(409\) | 16.5468 | + | 12.0220i | 0.818187 | + | 0.594448i | 0.916193 | − | 0.400738i | \(-0.131246\pi\) |
−0.0980056 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(410\) | −2.14886 | + | 6.61350i | −0.106125 | + | 0.326618i | ||||
\(411\) | 3.10673 | + | 9.56154i | 0.153244 | + | 0.471636i | ||||
\(412\) | −10.8699 | + | 7.89743i | −0.535520 | + | 0.389078i | ||||
\(413\) | −3.31353 | + | 2.40742i | −0.163048 | + | 0.118461i | ||||
\(414\) | −5.35344 | − | 16.4762i | −0.263107 | − | 0.809761i | ||||
\(415\) | 4.12176 | − | 12.6855i | 0.202329 | − | 0.622705i | ||||
\(416\) | 5.19594 | + | 3.77507i | 0.254752 | + | 0.185088i | ||||
\(417\) | 53.4753 | 2.61869 | ||||||||
\(418\) | 8.06988 | + | 1.38409i | 0.394711 | + | 0.0676982i | ||||
\(419\) | 18.0870 | 0.883609 | 0.441804 | − | 0.897111i | \(-0.354339\pi\) | ||||
0.441804 | + | 0.897111i | \(0.354339\pi\) | |||||||
\(420\) | −2.05762 | − | 1.49495i | −0.100402 | − | 0.0729461i | ||||
\(421\) | −4.52289 | + | 13.9200i | −0.220432 | + | 0.678420i | 0.778291 | + | 0.627904i | \(0.216087\pi\) |
−0.998723 | + | 0.0505167i | \(0.983913\pi\) | |||||||
\(422\) | 0.989592 | + | 3.04565i | 0.0481726 | + | 0.148260i | ||||
\(423\) | 23.5157 | − | 17.0852i | 1.14337 | − | 0.830710i | ||||
\(424\) | 8.14004 | − | 5.91409i | 0.395315 | − | 0.287214i | ||||
\(425\) | 1.22181 | + | 3.76033i | 0.0592663 | + | 0.182403i | ||||
\(426\) | −4.63726 | + | 14.2720i | −0.224676 | + | 0.691481i | ||||
\(427\) | 2.91000 | + | 2.11424i | 0.140825 | + | 0.102315i | ||||
\(428\) | 13.3879 | 0.647128 | ||||||||
\(429\) | −53.3969 | − | 9.15828i | −2.57802 | − | 0.442166i | ||||
\(430\) | 3.02295 | 0.145779 | ||||||||
\(431\) | 0.509264 | + | 0.370002i | 0.0245304 | + | 0.0178224i | 0.599983 | − | 0.800013i | \(-0.295174\pi\) |
−0.575453 | + | 0.817835i | \(0.695174\pi\) | |||||||
\(432\) | −0.368363 | + | 1.13370i | −0.0177229 | + | 0.0545454i | ||||
\(433\) | −4.69050 | − | 14.4359i | −0.225411 | − | 0.693743i | −0.998250 | − | 0.0591409i | \(-0.981164\pi\) |
0.772839 | − | 0.634602i | \(-0.218836\pi\) | |||||||
\(434\) | −6.38242 | + | 4.63710i | −0.306366 | + | 0.222588i | ||||
\(435\) | 18.6092 | − | 13.5204i | 0.892242 | − | 0.648252i | ||||
\(436\) | −2.68110 | − | 8.25159i | −0.128402 | − | 0.395180i | ||||
\(437\) | −3.81008 | + | 11.7262i | −0.182261 | + | 0.560941i | ||||
\(438\) | −21.0950 | − | 15.3264i | −1.00796 | − | 0.732324i | ||||
\(439\) | 12.5690 | 0.599888 | 0.299944 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299944 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(440\) | −1.54336 | + | 2.93565i | −0.0735769 | + | 0.139952i | ||||
\(441\) | 3.46869 | 0.165176 | ||||||||
\(442\) | 20.5440 | + | 14.9261i | 0.977178 | + | 0.709961i | ||||
\(443\) | −0.883389 | + | 2.71879i | −0.0419711 | + | 0.129174i | −0.969846 | − | 0.243717i | \(-0.921633\pi\) |
0.927875 | + | 0.372890i | \(0.121633\pi\) | |||||||
\(444\) | −8.67996 | − | 26.7142i | −0.411933 | − | 1.26780i | ||||
\(445\) | −11.9275 | + | 8.66584i | −0.565418 | + | 0.410800i | ||||
\(446\) | −0.621758 | + | 0.451734i | −0.0294411 | + | 0.0213902i | ||||
\(447\) | 6.72239 | + | 20.6894i | 0.317958 | + | 0.978574i | ||||
\(448\) | −0.309017 | + | 0.951057i | −0.0145997 | + | 0.0449332i | ||||
\(449\) | −23.0357 | − | 16.7364i | −1.08712 | − | 0.789839i | −0.108209 | − | 0.994128i | \(-0.534512\pi\) |
−0.978911 | + | 0.204289i | \(0.934512\pi\) | |||||||
\(450\) | −3.46869 | −0.163516 | ||||||||
\(451\) | −20.6817 | + | 10.2070i | −0.973863 | + | 0.480630i | ||||
\(452\) | −9.16671 | −0.431166 | ||||||||
\(453\) | −4.55053 | − | 3.30616i | −0.213803 | − | 0.155337i | ||||
\(454\) | −2.03561 | + | 6.26497i | −0.0955361 | + | 0.294030i | ||||
\(455\) | −1.98467 | − | 6.10820i | −0.0930430 | − | 0.286357i | ||||
\(456\) | 5.07963 | − | 3.69057i | 0.237876 | − | 0.172827i | ||||
\(457\) | −6.17590 | + | 4.48705i | −0.288896 | + | 0.209895i | −0.722788 | − | 0.691069i | \(-0.757140\pi\) |
0.433892 | + | 0.900965i | \(0.357140\pi\) | |||||||
\(458\) | 7.19480 | + | 22.1433i | 0.336191 | + | 1.03469i | ||||
\(459\) | −1.45645 | + | 4.48250i | −0.0679814 | + | 0.209225i | ||||
\(460\) | −4.04057 | − | 2.93565i | −0.188393 | − | 0.136875i | ||||
\(461\) | −4.72213 | −0.219931 | −0.109966 | − | 0.993935i | \(-0.535074\pi\) | ||||
−0.109966 | + | 0.993935i | \(0.535074\pi\) | |||||||
\(462\) | −1.21299 | − | 8.34771i | −0.0564335 | − | 0.388371i | ||||
\(463\) | −19.4328 | −0.903117 | −0.451558 | − | 0.892242i | \(-0.649132\pi\) | ||||
−0.451558 | + | 0.892242i | \(0.649132\pi\) | |||||||
\(464\) | −7.31677 | − | 5.31594i | −0.339672 | − | 0.246786i | ||||
\(465\) | −6.20038 | + | 19.0828i | −0.287536 | + | 0.884943i | ||||
\(466\) | 0.532246 | + | 1.63809i | 0.0246558 | + | 0.0758829i | ||||
\(467\) | 10.9573 | − | 7.96094i | 0.507043 | − | 0.368388i | −0.304658 | − | 0.952462i | \(-0.598542\pi\) |
0.811701 | + | 0.584073i | \(0.198542\pi\) | |||||||
\(468\) | −18.0231 | + | 13.0946i | −0.833119 | + | 0.605296i | ||||
\(469\) | 0.396227 | + | 1.21946i | 0.0182961 | + | 0.0563095i | ||||
\(470\) | 2.58951 | − | 7.96970i | 0.119445 | − | 0.367615i | ||||
\(471\) | −27.5440 | − | 20.0119i | −1.26916 | − | 0.922099i | ||||
\(472\) | 4.09575 | 0.188522 | ||||||||
\(473\) | 6.99825 | + | 7.17947i | 0.321780 | + | 0.330112i | ||||
\(474\) | 15.7968 | 0.725571 | ||||||||
\(475\) | 1.99721 | + | 1.45106i | 0.0916384 | + | 0.0665792i | ||||
\(476\) | −1.22181 | + | 3.76033i | −0.0560014 | + | 0.172355i | ||||
\(477\) | 10.7849 | + | 33.1926i | 0.493808 | + | 1.51978i | ||||
\(478\) | 9.41996 | − | 6.84400i | 0.430859 | − | 0.313037i | ||||
\(479\) | −3.50324 | + | 2.54525i | −0.160067 | + | 0.116296i | −0.664936 | − | 0.746901i | \(-0.731541\pi\) |
0.504868 | + | 0.863196i | \(0.331541\pi\) | |||||||
\(480\) | 0.785942 | + | 2.41888i | 0.0358732 | + | 0.110406i | ||||
\(481\) | 21.9188 | − | 67.4591i | 0.999410 | − | 3.07587i | ||||
\(482\) | −7.75229 | − | 5.63237i | −0.353107 | − | 0.256547i | ||||
\(483\) | 12.7026 | 0.577990 | ||||||||
\(484\) | −10.5451 | + | 3.13068i | −0.479322 | + | 0.142304i | ||||
\(485\) | −11.9603 | −0.543090 | ||||||||
\(486\) | 18.0666 | + | 13.1262i | 0.819518 | + | 0.595415i | ||||
\(487\) | −11.3026 | + | 34.7858i | −0.512170 | + | 1.57630i | 0.276204 | + | 0.961099i | \(0.410923\pi\) |
−0.788374 | + | 0.615197i | \(0.789077\pi\) | |||||||
\(488\) | −1.11152 | − | 3.42091i | −0.0503162 | − | 0.154857i | ||||
\(489\) | 4.22439 | − | 3.06920i | 0.191033 | − | 0.138794i | ||||
\(490\) | 0.809017 | − | 0.587785i | 0.0365477 | − | 0.0265534i | ||||
\(491\) | −9.80286 | − | 30.1701i | −0.442397 | − | 1.36156i | −0.885313 | − | 0.464995i | \(-0.846056\pi\) |
0.442916 | − | 0.896563i | \(-0.353944\pi\) | |||||||
\(492\) | −5.46532 | + | 16.8205i | −0.246396 | + | 0.758328i | ||||
\(493\) | −28.9294 | − | 21.0184i | −1.30291 | − | 0.946623i | ||||
\(494\) | 15.8553 | 0.713362 | ||||||||
\(495\) | −8.03017 | − | 8.23810i | −0.360929 | − | 0.370275i | ||||
\(496\) | 7.88910 | 0.354231 | ||||||||
\(497\) | −4.77340 | − | 3.46808i | −0.214116 | − | 0.155565i | ||||
\(498\) | 10.4831 | − | 32.2637i | 0.469760 | − | 1.44577i | ||||
\(499\) | 11.3713 | + | 34.9973i | 0.509049 | + | 1.56669i | 0.793855 | + | 0.608107i | \(0.208071\pi\) |
−0.284805 | + | 0.958585i | \(0.591929\pi\) | |||||||
\(500\) | −0.809017 | + | 0.587785i | −0.0361803 | + | 0.0262866i | ||||
\(501\) | 43.6251 | − | 31.6955i | 1.94903 | − | 1.41605i | ||||
\(502\) | 2.61246 | + | 8.04032i | 0.116600 | + | 0.358857i | ||||
\(503\) | 2.83090 | − | 8.71261i | 0.126224 | − | 0.388476i | −0.867898 | − | 0.496742i | \(-0.834530\pi\) |
0.994122 | + | 0.108266i | \(0.0345297\pi\) | |||||||
\(504\) | −2.80623 | − | 2.03884i | −0.124999 | − | 0.0908174i | ||||
\(505\) | −2.26114 | −0.100620 | ||||||||
\(506\) | −2.38197 | − | 16.3925i | −0.105891 | − | 0.728734i | ||||
\(507\) | −71.8475 | −3.19086 | ||||||||
\(508\) | −12.3615 | − | 8.98117i | −0.548453 | − | 0.398475i | ||||
\(509\) | 4.63523 | − | 14.2658i | 0.205453 | − | 0.632320i | −0.794241 | − | 0.607602i | \(-0.792131\pi\) |
0.999694 | − | 0.0247172i | \(-0.00786853\pi\) | |||||||
\(510\) | 3.10750 | + | 9.56389i | 0.137602 | + | 0.423496i | ||||
\(511\) | 8.29414 | − | 6.02605i | 0.366911 | − | 0.266577i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 0.909374 | + | 2.79877i | 0.0401498 | + | 0.123569i | ||||
\(514\) | 6.29635 | − | 19.3782i | 0.277720 | − | 0.854735i | ||||
\(515\) | −10.8699 | − | 7.89743i | −0.478984 | − | 0.348002i | ||||
\(516\) | 7.68845 | 0.338465 | ||||||||
\(517\) | 24.9228 | − | 12.3001i | 1.09610 | − | 0.540959i | ||||
\(518\) | 11.0440 | 0.485246 | ||||||||
\(519\) | −12.1653 | − | 8.83860i | −0.533997 | − | 0.387972i | ||||
\(520\) | −1.98467 | + | 6.10820i | −0.0870337 | + | 0.267862i | ||||
\(521\) | −5.19586 | − | 15.9912i | −0.227635 | − | 0.700588i | −0.998013 | − | 0.0630015i | \(-0.979933\pi\) |
0.770378 | − | 0.637587i | \(-0.220067\pi\) | |||||||
\(522\) | 25.3796 | − | 18.4394i | 1.11083 | − | 0.807069i | ||||
\(523\) | −0.977990 | + | 0.710551i | −0.0427645 | + | 0.0310702i | −0.608962 | − | 0.793199i | \(-0.708414\pi\) |
0.566198 | + | 0.824269i | \(0.308414\pi\) | |||||||
\(524\) | −1.74737 | − | 5.37785i | −0.0763342 | − | 0.234932i | ||||
\(525\) | 0.785942 | − | 2.41888i | 0.0343013 | − | 0.105569i | ||||
\(526\) | 13.0996 | + | 9.51745i | 0.571172 | + | 0.414980i | ||||
\(527\) | 31.1923 | 1.35876 | ||||||||
\(528\) | −3.92533 | + | 7.46642i | −0.170828 | + | 0.324934i | ||||
\(529\) | 1.94427 | 0.0845336 | ||||||||
\(530\) | 8.14004 | + | 5.91409i | 0.353581 | + | 0.256892i | ||||
\(531\) | −4.39016 | + | 13.5115i | −0.190517 | + | 0.586351i | ||||
\(532\) | 0.762867 | + | 2.34786i | 0.0330745 | + | 0.101793i | ||||
\(533\) | −36.1318 | + | 26.2513i | −1.56504 | + | 1.13707i | ||||
\(534\) | −30.3360 | + | 22.0404i | −1.31277 | + | 0.953780i | ||||
\(535\) | 4.13708 | + | 12.7326i | 0.178862 | + | 0.550480i | ||||
\(536\) | 0.396227 | − | 1.21946i | 0.0171144 | − | 0.0526727i | ||||
\(537\) | −36.8066 | − | 26.7416i | −1.58832 | − | 1.15398i | ||||
\(538\) | 26.8144 | 1.15605 | ||||||||
\(539\) | 3.26889 | + | 0.560659i | 0.140801 | + | 0.0241493i | ||||
\(540\) | −1.19205 | −0.0512976 | ||||||||
\(541\) | 3.77643 | + | 2.74374i | 0.162362 | + | 0.117963i | 0.665999 | − | 0.745952i | \(-0.268005\pi\) |
−0.503638 | + | 0.863915i | \(0.668005\pi\) | |||||||
\(542\) | 6.93163 | − | 21.3334i | 0.297739 | − | 0.916347i | ||||
\(543\) | −8.70114 | − | 26.7794i | −0.373402 | − | 1.14921i | ||||
\(544\) | 3.19873 | − | 2.32401i | 0.137145 | − | 0.0996413i | ||||
\(545\) | 7.01922 | − | 5.09976i | 0.300670 | − | 0.218450i | ||||
\(546\) | −5.04774 | − | 15.5354i | −0.216024 | − | 0.664852i | ||||
\(547\) | 6.84613 | − | 21.0702i | 0.292719 | − | 0.900898i | −0.691258 | − | 0.722608i | \(-0.742943\pi\) |
0.983978 | − | 0.178290i | \(-0.0570566\pi\) | |||||||
\(548\) | 3.19795 | + | 2.32344i | 0.136609 | + | 0.0992526i | ||||
\(549\) | 12.4767 | 0.532494 | ||||||||
\(550\) | −3.26889 | − | 0.560659i | −0.139386 | − | 0.0239066i | ||||
\(551\) | −22.3269 | −0.951157 | ||||||||
\(552\) | −10.2766 | − | 7.46642i | −0.437403 | − | 0.317792i | ||||
\(553\) | −1.91930 | + | 5.90700i | −0.0816170 | + | 0.251191i | ||||
\(554\) | −6.83391 | − | 21.0326i | −0.290345 | − | 0.893590i | ||||
\(555\) | 22.7244 | − | 16.5103i | 0.964598 | − | 0.700822i | ||||
\(556\) | 17.0099 | − | 12.3584i | 0.721381 | − | 0.524114i | ||||
\(557\) | −11.6817 | − | 35.9525i | −0.494968 | − | 1.52335i | −0.817007 | − | 0.576628i | \(-0.804368\pi\) |
0.322039 | − | 0.946726i | \(-0.395632\pi\) | |||||||
\(558\) | −8.45620 | + | 26.0255i | −0.357980 | + | 1.10175i | ||||
\(559\) | 15.7071 | + | 11.4118i | 0.664338 | + | 0.482670i | ||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | −15.5202 | + | 29.5211i | −0.655262 | + | 1.24638i | ||||
\(562\) | 12.5703 | 0.530247 | ||||||||
\(563\) | 8.00803 | + | 5.81817i | 0.337498 | + | 0.245207i | 0.743605 | − | 0.668619i | \(-0.233114\pi\) |
−0.406107 | + | 0.913825i | \(0.633114\pi\) | |||||||
\(564\) | 6.58607 | − | 20.2698i | 0.277323 | − | 0.853514i | ||||
\(565\) | −2.83267 | − | 8.71806i | −0.119171 | − | 0.366772i | ||||
\(566\) | 4.12984 | − | 3.00051i | 0.173590 | − | 0.126121i | ||||
\(567\) | −5.96590 | + | 4.33448i | −0.250544 | + | 0.182031i | ||||
\(568\) | 1.82328 | + | 5.61147i | 0.0765030 | + | 0.235452i | ||||
\(569\) | 1.53025 | − | 4.70961i | 0.0641512 | − | 0.197437i | −0.913844 | − | 0.406066i | \(-0.866900\pi\) |
0.977995 | + | 0.208629i | \(0.0669002\pi\) | |||||||
\(570\) | 5.07963 | + | 3.69057i | 0.212762 | + | 0.154581i | ||||
\(571\) | 8.53293 | 0.357092 | 0.178546 | − | 0.983932i | \(-0.442861\pi\) | ||||
0.178546 | + | 0.983932i | \(0.442861\pi\) | |||||||
\(572\) | −19.1015 | + | 9.42716i | −0.798674 | + | 0.394169i | ||||
\(573\) | 24.3139 | 1.01573 | ||||||||
\(574\) | −5.62578 | − | 4.08737i | −0.234816 | − | 0.170604i | ||||
\(575\) | 1.54336 | − | 4.74998i | 0.0643626 | − | 0.198088i | ||||
\(576\) | 1.07188 | + | 3.29892i | 0.0446618 | + | 0.137455i | ||||
\(577\) | 7.95151 | − | 5.77711i | 0.331026 | − | 0.240504i | −0.409840 | − | 0.912157i | \(-0.634415\pi\) |
0.740866 | + | 0.671653i | \(0.234415\pi\) | |||||||
\(578\) | −1.10598 | + | 0.803543i | −0.0460028 | + | 0.0334230i | ||||
\(579\) | 13.1131 | + | 40.3580i | 0.544963 | + | 1.67722i | ||||
\(580\) | 2.79476 | − | 8.60137i | 0.116046 | − | 0.357153i | ||||
\(581\) | 10.7909 | + | 7.84005i | 0.447682 | + | 0.325260i | ||||
\(582\) | −30.4194 | −1.26093 | ||||||||
\(583\) | 4.79865 | + | 33.0239i | 0.198740 | + | 1.36771i | ||||
\(584\) | −10.2521 | −0.424236 | ||||||||
\(585\) | −18.0231 | − | 13.0946i | −0.745164 | − | 0.541393i | ||||
\(586\) | −5.33226 | + | 16.4110i | −0.220274 | + | 0.677933i | ||||
\(587\) | 6.20045 | + | 19.0830i | 0.255920 | + | 0.787641i | 0.993647 | + | 0.112542i | \(0.0358993\pi\) |
−0.737727 | + | 0.675099i | \(0.764101\pi\) | |||||||
\(588\) | 2.05762 | − | 1.49495i | 0.0848549 | − | 0.0616507i | ||||
\(589\) | 15.7562 | − | 11.4476i | 0.649223 | − | 0.471688i | ||||
\(590\) | 1.26566 | + | 3.89529i | 0.0521062 | + | 0.160366i | ||||
\(591\) | −0.419253 | + | 1.29033i | −0.0172458 | + | 0.0530770i | ||||
\(592\) | −8.93480 | − | 6.49151i | −0.367218 | − | 0.266800i | ||||
\(593\) | 3.85286 | 0.158218 | 0.0791090 | − | 0.996866i | \(-0.474792\pi\) | ||||
0.0791090 | + | 0.996866i | \(0.474792\pi\) | |||||||
\(594\) | −2.75964 | − | 2.83110i | −0.113229 | − | 0.116162i | ||||
\(595\) | −3.95385 | −0.162092 | ||||||||
\(596\) | 6.91975 | + | 5.02749i | 0.283444 | + | 0.205934i | ||||
\(597\) | 2.21198 | − | 6.80777i | 0.0905302 | − | 0.278623i | ||||
\(598\) | −9.91230 | − | 30.5069i | −0.405344 | − | 1.24752i | ||||
\(599\) | −5.97520 | + | 4.34124i | −0.244140 | + | 0.177378i | −0.703126 | − | 0.711065i | \(-0.748213\pi\) |
0.458986 | + | 0.888444i | \(0.348213\pi\) | |||||||
\(600\) | −2.05762 | + | 1.49495i | −0.0840021 | + | 0.0610311i | ||||
\(601\) | 7.94779 | + | 24.4608i | 0.324197 | + | 0.997776i | 0.971802 | + | 0.235799i | \(0.0757708\pi\) |
−0.647605 | + | 0.761976i | \(0.724229\pi\) | |||||||
\(602\) | −0.934142 | + | 2.87499i | −0.0380728 | + | 0.117176i | ||||
\(603\) | 3.59820 | + | 2.61424i | 0.146530 | + | 0.106460i | ||||
\(604\) | −2.21155 | −0.0899866 | ||||||||
\(605\) | −6.23607 | − | 9.06154i | −0.253532 | − | 0.368404i | ||||
\(606\) | −5.75091 | −0.233615 | ||||||||
\(607\) | −2.44661 | − | 1.77757i | −0.0993048 | − | 0.0721492i | 0.537025 | − | 0.843566i | \(-0.319548\pi\) |
−0.636330 | + | 0.771417i | \(0.719548\pi\) | |||||||
\(608\) | 0.762867 | − | 2.34786i | 0.0309383 | − | 0.0952184i | ||||
\(609\) | 7.10808 | + | 21.8764i | 0.288034 | + | 0.886477i | ||||
\(610\) | 2.91000 | − | 2.11424i | 0.117823 | − | 0.0856031i | ||||
\(611\) | 43.5412 | − | 31.6345i | 1.76149 | − | 1.27980i | ||||
\(612\) | 4.23807 | + | 13.0434i | 0.171314 | + | 0.527250i | ||||
\(613\) | −6.39757 | + | 19.6897i | −0.258395 | + | 0.795259i | 0.734746 | + | 0.678342i | \(0.237301\pi\) |
−0.993142 | + | 0.116917i | \(0.962699\pi\) | |||||||
\(614\) | 20.0675 | + | 14.5799i | 0.809860 | + | 0.588398i | ||||
\(615\) | −17.6862 | −0.713175 | ||||||||
\(616\) | −2.31504 | − | 2.37499i | −0.0932757 | − | 0.0956911i | ||||
\(617\) | 16.2405 | 0.653817 | 0.326909 | − | 0.945056i | \(-0.393993\pi\) | ||||
0.326909 | + | 0.945056i | \(0.393993\pi\) | |||||||
\(618\) | −27.6460 | − | 20.0860i | −1.11209 | − | 0.807978i | ||||
\(619\) | −11.1089 | + | 34.1896i | −0.446503 | + | 1.37419i | 0.434324 | + | 0.900757i | \(0.356987\pi\) |
−0.880827 | + | 0.473438i | \(0.843013\pi\) | |||||||
\(620\) | 2.43787 | + | 7.50298i | 0.0979071 | + | 0.301327i | ||||
\(621\) | 4.81656 | − | 3.49943i | 0.193282 | − | 0.140427i | ||||
\(622\) | −12.1934 | + | 8.85900i | −0.488909 | + | 0.355213i | ||||
\(623\) | −4.55590 | − | 14.0216i | −0.182528 | − | 0.561764i | ||||
\(624\) | −5.04774 | + | 15.5354i | −0.202071 | + | 0.621912i | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | 14.6737 | 0.586479 | ||||||||
\(627\) | 2.99450 | + | 20.6079i | 0.119589 | + | 0.823000i | ||||
\(628\) | −13.3863 | −0.534172 | ||||||||
\(629\) | −35.3269 | − | 25.6665i | −1.40857 | − | 1.02339i | ||||
\(630\) | 1.07188 | − | 3.29892i | 0.0427049 | − | 0.131432i | ||||
\(631\) | −12.8157 | − | 39.4428i | −0.510187 | − | 1.57019i | −0.791872 | − | 0.610687i | \(-0.790894\pi\) |
0.281686 | − | 0.959507i | \(-0.409106\pi\) | |||||||
\(632\) | 5.02480 | − | 3.65073i | 0.199876 | − | 0.145218i | ||||
\(633\) | −6.58930 | + | 4.78741i | −0.261901 | + | 0.190282i | ||||
\(634\) | 4.40934 | + | 13.5706i | 0.175117 | + | 0.538956i | ||||
\(635\) | 4.72168 | − | 14.5318i | 0.187374 | − | 0.576678i | ||||
\(636\) | 20.7031 | + | 15.0417i | 0.820930 | + | 0.596441i | ||||
\(637\) | 6.42254 | 0.254470 | ||||||||
\(638\) | 26.8982 | − | 13.2750i | 1.06491 | − | 0.525564i | ||||
\(639\) | −20.4661 | −0.809628 | ||||||||
\(640\) | 0.809017 | + | 0.587785i | 0.0319792 | + | 0.0232343i | ||||
\(641\) | 0.982315 | − | 3.02326i | 0.0387991 | − | 0.119411i | −0.929781 | − | 0.368113i | \(-0.880004\pi\) |
0.968580 | + | 0.248702i | \(0.0800039\pi\) | |||||||
\(642\) | 10.5221 | + | 32.3837i | 0.415274 | + | 1.27808i | ||||
\(643\) | −16.2410 | + | 11.7998i | −0.640482 | + | 0.465338i | −0.860016 | − | 0.510267i | \(-0.829546\pi\) |
0.219534 | + | 0.975605i | \(0.429546\pi\) | |||||||
\(644\) | 4.04057 | − | 2.93565i | 0.159221 | − | 0.115681i | ||||
\(645\) | 2.37586 | + | 7.31215i | 0.0935494 | + | 0.287916i | ||||
\(646\) | 3.01626 | − | 9.28310i | 0.118673 | − | 0.365239i | ||||
\(647\) | 30.8832 | + | 22.4380i | 1.21415 | + | 0.882128i | 0.995601 | − | 0.0936984i | \(-0.0298689\pi\) |
0.218545 | + | 0.975827i | \(0.429869\pi\) | |||||||
\(648\) | 7.37426 | 0.289688 | ||||||||
\(649\) | −6.32122 | + | 12.0237i | −0.248130 | + | 0.471970i | ||||
\(650\) | −6.42254 | −0.251913 | ||||||||
\(651\) | −16.2328 | − | 11.7938i | −0.636213 | − | 0.462236i | ||||
\(652\) | 0.634425 | − | 1.95256i | 0.0248460 | − | 0.0764681i | ||||
\(653\) | 13.6863 | + | 42.1219i | 0.535584 | + | 1.64836i | 0.742383 | + | 0.669976i | \(0.233696\pi\) |
−0.206799 | + | 0.978384i | \(0.566304\pi\) | |||||||
\(654\) | 17.8524 | − | 12.9705i | 0.698085 | − | 0.507188i | ||||
\(655\) | 4.57467 | − | 3.32369i | 0.178747 | − | 0.129867i | ||||
\(656\) | 2.14886 | + | 6.61350i | 0.0838988 | + | 0.258214i | ||||
\(657\) | 10.9891 | − | 33.8209i | 0.428725 | − | 1.31948i | ||||
\(658\) | 6.77943 | + | 4.92554i | 0.264290 | + | 0.192018i | ||||
\(659\) | 30.2781 | 1.17947 | 0.589734 | − | 0.807598i | \(-0.299233\pi\) | ||||
0.589734 | + | 0.807598i | \(0.299233\pi\) | |||||||
\(660\) | −8.31398 | − | 1.42596i | −0.323621 | − | 0.0555054i | ||||
\(661\) | 7.16382 | 0.278640 | 0.139320 | − | 0.990247i | \(-0.455508\pi\) | ||||
0.139320 | + | 0.990247i | \(0.455508\pi\) | |||||||
\(662\) | −10.4532 | − | 7.59472i | −0.406277 | − | 0.295177i | ||||
\(663\) | −19.9580 | + | 61.4245i | −0.775105 | + | 2.38553i | ||||
\(664\) | −4.12176 | − | 12.6855i | −0.159955 | − | 0.492292i | ||||
\(665\) | −1.99721 | + | 1.45106i | −0.0774486 | + | 0.0562697i | ||||
\(666\) | 30.9920 | − | 22.5170i | 1.20092 | − | 0.872518i | ||||
\(667\) | 13.9582 | + | 42.9589i | 0.540464 | + | 1.66338i | ||||
\(668\) | 6.55169 | − | 20.1640i | 0.253492 | − | 0.780170i | ||||
\(669\) | −1.58136 | − | 1.14892i | −0.0611388 | − | 0.0444199i | ||||
\(670\) | 1.28222 | 0.0495364 | ||||||||
\(671\) | 11.7581 | + | 2.01667i | 0.453916 | + | 0.0778526i | ||||
\(672\) | −2.54336 | −0.0981123 | ||||||||
\(673\) | −17.8339 | − | 12.9571i | −0.687446 | − | 0.499459i | 0.188374 | − | 0.982097i | \(-0.439678\pi\) |
−0.875820 | + | 0.482639i | \(0.839678\pi\) | |||||||
\(674\) | −6.36585 | + | 19.5921i | −0.245204 | + | 0.754659i | ||||
\(675\) | −0.368363 | − | 1.13370i | −0.0141783 | − | 0.0436363i | ||||
\(676\) | −22.8539 | + | 16.6044i | −0.878998 | + | 0.638629i | ||||
\(677\) | −28.1578 | + | 20.4579i | −1.08219 | + | 0.786260i | −0.978064 | − | 0.208304i | \(-0.933206\pi\) |
−0.104130 | + | 0.994564i | \(0.533206\pi\) | |||||||
\(678\) | −7.20451 | − | 22.1732i | −0.276687 | − | 0.851556i | ||||
\(679\) | 3.69594 | − | 11.3749i | 0.141837 | − | 0.436530i | ||||
\(680\) | 3.19873 | + | 2.32401i | 0.122666 | + | 0.0891219i | ||||
\(681\) | −16.7541 | −0.642018 | ||||||||
\(682\) | −12.1757 | + | 23.1596i | −0.466233 | + | 0.886828i | ||||
\(683\) | 35.0185 | 1.33995 | 0.669973 | − | 0.742385i | \(-0.266306\pi\) | ||||
0.669973 | + | 0.742385i | \(0.266306\pi\) | |||||||
\(684\) | 6.92771 | + | 5.03328i | 0.264888 | + | 0.192452i | ||||
\(685\) | −1.22151 | + | 3.75941i | −0.0466714 | + | 0.143640i | ||||
\(686\) | 0.309017 | + | 0.951057i | 0.0117983 | + | 0.0363115i | ||||
\(687\) | −47.9073 | + | 34.8067i | −1.82778 | + | 1.32796i | ||||
\(688\) | 2.44561 | − | 1.77684i | 0.0932382 | − | 0.0677415i | ||||
\(689\) | 19.9691 | + | 61.4585i | 0.760762 | + | 2.34138i | ||||
\(690\) | 3.92533 | − | 12.0809i | 0.149435 | − | 0.459913i | ||||
\(691\) | 15.8191 | + | 11.4932i | 0.601786 | + | 0.437223i | 0.846513 | − | 0.532369i | \(-0.178698\pi\) |
−0.244726 | + | 0.969592i | \(0.578698\pi\) | |||||||
\(692\) | −5.91230 | −0.224752 | ||||||||
\(693\) | 10.3164 | − | 5.09143i | 0.391886 | − | 0.193407i | ||||
\(694\) | 3.81140 | 0.144679 | ||||||||
\(695\) | 17.0099 | + | 12.3584i | 0.645223 | + | 0.468782i | ||||
\(696\) | 7.10808 | − | 21.8764i | 0.269431 | − | 0.829223i | ||||
\(697\) | 8.49626 | + | 26.1488i | 0.321819 | + | 0.990457i | ||||
\(698\) | −16.0009 | + | 11.6253i | −0.605643 | + | 0.440025i | ||||
\(699\) | −3.54402 | + | 2.57488i | −0.134047 | + | 0.0973910i | ||||
\(700\) | −0.309017 | − | 0.951057i | −0.0116797 | − | 0.0359466i | ||||
\(701\) | −4.30949 | + | 13.2632i | −0.162767 | + | 0.500946i | −0.998865 | − | 0.0476348i | \(-0.984832\pi\) |
0.836098 | + | 0.548581i | \(0.184832\pi\) | |||||||
\(702\) | −6.19381 | − | 4.50007i | −0.233770 | − | 0.169844i | ||||
\(703\) | −27.2643 | −1.02829 | ||||||||
\(704\) | 0.476925 | + | 3.28216i | 0.0179748 | + | 0.123701i | ||||
\(705\) | 21.3130 | 0.802692 | ||||||||
\(706\) | −2.30750 | − | 1.67650i | −0.0868440 | − | 0.0630959i | ||||
\(707\) | 0.698732 | − | 2.15048i | 0.0262785 | − | 0.0808770i | ||||
\(708\) | 3.21902 | + | 9.90712i | 0.120978 | + | 0.372332i | ||||
\(709\) | 0.444308 | − | 0.322809i | 0.0166863 | − | 0.0121233i | −0.579411 | − | 0.815036i | \(-0.696717\pi\) |
0.596097 | + | 0.802912i | \(0.296717\pi\) | |||||||
\(710\) | −4.77340 | + | 3.46808i | −0.179143 | + | 0.130155i | ||||
\(711\) | 6.65746 | + | 20.4896i | 0.249674 | + | 0.768419i | ||||
\(712\) | −4.55590 | + | 14.0216i | −0.170740 | + | 0.525482i | ||||
\(713\) | −31.8765 | − | 23.1596i | −1.19378 | − | 0.867335i | ||||
\(714\) | −10.0561 | −0.376339 | ||||||||
\(715\) | −14.8685 | − | 15.2535i | −0.556049 | − | 0.570447i | ||||
\(716\) | −17.8879 | −0.668504 | ||||||||
\(717\) | 23.9584 | + | 17.4068i | 0.894742 | + | 0.650068i | ||||
\(718\) | −5.23394 | + | 16.1084i | −0.195329 | + | 0.601160i | ||||
\(719\) | −8.00088 | − | 24.6242i | −0.298382 | − | 0.918327i | −0.982064 | − | 0.188547i | \(-0.939622\pi\) |
0.683682 | − | 0.729780i | \(-0.260378\pi\) | |||||||
\(720\) | −2.80623 | + | 2.03884i | −0.104582 | + | 0.0759833i | ||||
\(721\) | 10.8699 | − | 7.89743i | 0.404815 | − | 0.294116i | ||||
\(722\) | 3.98804 | + | 12.2739i | 0.148420 | + | 0.456788i | ||||
\(723\) | 7.53118 | − | 23.1786i | 0.280088 | − | 0.862021i | ||||
\(724\) | −8.95660 | − | 6.50735i | −0.332869 | − | 0.241844i | ||||
\(725\) | 9.04402 | 0.335886 | ||||||||
\(726\) | −15.8606 | − | 23.0468i | −0.588641 | − | 0.855346i | ||||
\(727\) | −41.6185 | −1.54355 | −0.771773 | − | 0.635898i | \(-0.780630\pi\) | ||||
−0.771773 | + | 0.635898i | \(0.780630\pi\) | |||||||
\(728\) | −5.19594 | − | 3.77507i | −0.192574 | − | 0.139914i | ||||
\(729\) | −10.7150 | + | 32.9774i | −0.396852 | + | 1.22138i | ||||
\(730\) | −3.16808 | − | 9.75035i | −0.117256 | − | 0.360877i | ||||
\(731\) | 9.66959 | − | 7.02537i | 0.357643 | − | 0.259843i | ||||
\(732\) | 7.40119 | − | 5.37728i | 0.273556 | − | 0.198750i | ||||
\(733\) | −0.670104 | − | 2.06237i | −0.0247508 | − | 0.0761752i | 0.937918 | − | 0.346857i | \(-0.112751\pi\) |
−0.962669 | + | 0.270681i | \(0.912751\pi\) | |||||||
\(734\) | 6.18204 | − | 19.0264i | 0.228183 | − | 0.702276i | ||||
\(735\) | 2.05762 | + | 1.49495i | 0.0758966 | + | 0.0551421i | ||||
\(736\) | −4.99442 | −0.184097 | ||||||||
\(737\) | 2.96839 | + | 3.04525i | 0.109342 | + | 0.112173i | ||||
\(738\) | −24.1207 | −0.887897 | ||||||||
\(739\) | −2.48164 | − | 1.80302i | −0.0912888 | − | 0.0663252i | 0.541205 | − | 0.840891i | \(-0.317968\pi\) |
−0.632493 | + | 0.774566i | \(0.717968\pi\) | |||||||
\(740\) | 3.41279 | − | 10.5035i | 0.125457 | − | 0.386116i | ||||
\(741\) | 12.4613 | + | 38.3520i | 0.457778 | + | 1.40890i | ||||
\(742\) | −8.14004 | + | 5.91409i | −0.298830 | + | 0.217113i | ||||
\(743\) | −31.5381 | + | 22.9138i | −1.15702 | + | 0.840626i | −0.989399 | − | 0.145226i | \(-0.953609\pi\) |
−0.167623 | + | 0.985851i | \(0.553609\pi\) | |||||||
\(744\) | 6.20038 | + | 19.0828i | 0.227317 | + | 0.699609i | ||||
\(745\) | −2.64311 | + | 8.13466i | −0.0968361 | + | 0.298031i | ||||
\(746\) | −18.7390 | − | 13.6147i | −0.686085 | − | 0.498470i | ||||
\(747\) | 46.2664 | 1.69280 | ||||||||
\(748\) | 1.88569 | + | 12.9771i | 0.0689477 | + | 0.474492i | ||||
\(749\) | −13.3879 | −0.489183 | ||||||||
\(750\) | −2.05762 | − | 1.49495i | −0.0751338 | − | 0.0545879i | ||||
\(751\) | 7.48994 | − | 23.0517i | 0.273312 | − | 0.841167i | −0.716350 | − | 0.697742i | \(-0.754188\pi\) |
0.989661 | − | 0.143425i | \(-0.0458116\pi\) | |||||||
\(752\) | −2.58951 | − | 7.96970i | −0.0944298 | − | 0.290625i | ||||
\(753\) | −17.3953 | + | 12.6384i | −0.633921 | + | 0.460571i | ||||
\(754\) | 46.9922 | − | 34.1418i | 1.71136 | − | 1.24337i | ||||
\(755\) | −0.683406 | − | 2.10331i | −0.0248717 | − | 0.0765472i | ||||
\(756\) | 0.368363 | − | 1.13370i | 0.0133972 | − | 0.0412324i | ||||
\(757\) | 19.5909 | + | 14.2336i | 0.712042 | + | 0.517329i | 0.883832 | − | 0.467805i | \(-0.154955\pi\) |
−0.171790 | + | 0.985134i | \(0.554955\pi\) | |||||||
\(758\) | −32.6068 | −1.18433 | ||||||||
\(759\) | 37.7794 | − | 18.6452i | 1.37130 | − | 0.676779i | ||||
\(760\) | 2.46869 | 0.0895488 | ||||||||
\(761\) | 1.68162 | + | 1.22177i | 0.0609588 | + | 0.0442892i | 0.617847 | − | 0.786298i | \(-0.288005\pi\) |
−0.556889 | + | 0.830587i | \(0.688005\pi\) | |||||||
\(762\) | 12.0089 | − | 36.9597i | 0.435038 | − | 1.33891i | ||||
\(763\) | 2.68110 | + | 8.25159i | 0.0970625 | + | 0.298728i | ||||
\(764\) | 7.73401 | − | 5.61909i | 0.279807 | − | 0.203291i | ||||
\(765\) | −11.0954 | + | 8.06129i | −0.401155 | + | 0.291456i | ||||
\(766\) | −1.59739 | − | 4.91626i | −0.0577160 | − | 0.177632i | ||||
\(767\) | −8.12872 | + | 25.0176i | −0.293511 | + | 0.903334i | ||||
\(768\) | 2.05762 | + | 1.49495i | 0.0742481 | + | 0.0539444i | ||||
\(769\) | 14.7508 | 0.531929 | 0.265964 | − | 0.963983i | \(-0.414310\pi\) | ||||
0.265964 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(770\) | 1.54336 | − | 2.93565i | 0.0556189 | − | 0.105793i | ||||
\(771\) | 51.8221 | 1.86633 | ||||||||
\(772\) | 13.4981 | + | 9.80695i | 0.485808 | + | 0.352960i | ||||
\(773\) | 15.3140 | − | 47.1318i | 0.550808 | − | 1.69521i | −0.155958 | − | 0.987764i | \(-0.549847\pi\) |
0.706766 | − | 0.707448i | \(-0.250153\pi\) | |||||||
\(774\) | 3.24025 | + | 9.97246i | 0.116468 | + | 0.358453i | ||||
\(775\) | −6.38242 | + | 4.63710i | −0.229263 | + | 0.166569i | ||||
\(776\) | −9.67611 | + | 7.03010i | −0.347352 | + | 0.252366i | ||||
\(777\) | 8.67996 | + | 26.7142i | 0.311392 | + | 0.958365i | ||||
\(778\) | 0.268314 | − | 0.825787i | 0.00961954 | − | 0.0296059i | ||||
\(779\) | 13.8883 | + | 10.0905i | 0.497600 | + | 0.361528i | ||||
\(780\) | −16.3348 | −0.584881 | ||||||||
\(781\) | −19.2873 | − | 3.30803i | −0.690154 | − | 0.118371i | ||||
\(782\) | −19.7472 | −0.706159 | ||||||||
\(783\) | 8.72194 | + | 6.33686i | 0.311697 | + | 0.226461i | ||||
\(784\) | 0.309017 | − | 0.951057i | 0.0110363 | − | 0.0339663i | ||||
\(785\) | −4.13660 | − | 12.7311i | −0.147642 | − | 0.454394i | ||||
\(786\) | 11.6350 | − | 8.45336i | 0.415008 | − | 0.301521i | ||||
\(787\) | 25.1397 | − | 18.2651i | 0.896135 | − | 0.651080i | −0.0413357 | − | 0.999145i | \(-0.513161\pi\) |
0.937470 | + | 0.348065i | \(0.113161\pi\) | |||||||
\(788\) | 0.164842 | + | 0.507332i | 0.00587225 | + | 0.0180729i | ||||
\(789\) | −12.7260 | + | 39.1666i | −0.453058 | + | 1.39437i | ||||
\(790\) | 5.02480 | + | 3.65073i | 0.178774 | + | 0.129887i | ||||
\(791\) | 9.16671 | 0.325931 | ||||||||
\(792\) | −11.3388 | − | 1.94475i | −0.402906 | − | 0.0691038i | ||||
\(793\) | 23.1016 | 0.820363 | ||||||||
\(794\) | −13.5772 | − | 9.86440i | −0.481836 | − | 0.350074i | ||||
\(795\) | −7.90787 | + | 24.3379i | −0.280463 | + | 0.863177i | ||||
\(796\) | −0.869706 | − | 2.67668i | −0.0308259 | − | 0.0948724i | ||||
\(797\) | −14.8729 | + | 10.8058i | −0.526824 | + | 0.382760i | −0.819168 | − | 0.573553i | \(-0.805565\pi\) |
0.292344 | + | 0.956313i | \(0.405565\pi\) | |||||||
\(798\) | −5.07963 | + | 3.69057i | −0.179817 | + | 0.130645i | ||||
\(799\) | −10.2385 | − | 31.5110i | −0.362214 | − | 1.11478i | ||||
\(800\) | −0.309017 | + | 0.951057i | −0.0109254 | + | 0.0336249i | ||||
\(801\) | −41.3728 | − | 30.0591i | −1.46184 | − | 1.06209i | ||||
\(802\) | 1.66393 | 0.0587553 | ||||||||
\(803\) | 15.8227 | − | 30.0966i | 0.558372 | − | 1.06209i | ||||
\(804\) | 3.26114 | 0.115012 | ||||||||
\(805\) | 4.04057 | + | 2.93565i | 0.142412 | + | 0.103468i | ||||
\(806\) | −15.6573 | + | 48.1882i | −0.551505 | + | 1.69736i | ||||
\(807\) | 21.0746 | + | 64.8609i | 0.741861 | + | 2.28321i | ||||
\(808\) | −1.82930 | + | 1.32907i | −0.0643547 | + | 0.0467564i | ||||
\(809\) | −33.5303 | + | 24.3612i | −1.17886 | + | 0.856494i | −0.992043 | − | 0.125900i | \(-0.959818\pi\) |
−0.186820 | + | 0.982394i | \(0.559818\pi\) | |||||||
\(810\) | 2.27877 | + | 7.01334i | 0.0800679 | + | 0.246424i | ||||
\(811\) | −2.37989 | + | 7.32456i | −0.0835694 | + | 0.257200i | −0.984107 | − | 0.177579i | \(-0.943173\pi\) |
0.900537 | + | 0.434779i | \(0.143173\pi\) | |||||||
\(812\) | 7.31677 | + | 5.31594i | 0.256768 | + | 0.186553i | ||||
\(813\) | 57.0507 | 2.00086 | ||||||||
\(814\) | 32.8464 | − | 16.2107i | 1.15127 | − | 0.568184i | ||||
\(815\) | 2.05304 | 0.0719149 | ||||||||
\(816\) | 8.13553 | + | 5.91081i | 0.284801 | + | 0.206920i | ||||
\(817\) | 2.30611 | − | 7.09747i | 0.0806804 | − | 0.248309i | ||||
\(818\) | 6.32032 | + | 19.4519i | 0.220985 | + | 0.680121i | ||||
\(819\) | 18.0231 | − | 13.0946i | 0.629779 | − | 0.457561i | ||||
\(820\) | −5.62578 | + | 4.08737i | −0.196461 | + | 0.142737i | ||||
\(821\) | 14.9242 | + | 45.9321i | 0.520860 | + | 1.60304i | 0.772360 | + | 0.635185i | \(0.219076\pi\) |
−0.251500 | + | 0.967857i | \(0.580924\pi\) | |||||||
\(822\) | −3.10673 | + | 9.56154i | −0.108360 | + | 0.333497i | ||||
\(823\) | −29.7402 | − | 21.6075i | −1.03668 | − | 0.753191i | −0.0670440 | − | 0.997750i | \(-0.521357\pi\) |
−0.969634 | + | 0.244559i | \(0.921357\pi\) | |||||||
\(824\) | −13.4359 | −0.468062 | ||||||||
\(825\) | −1.21299 | − | 8.34771i | −0.0422310 | − | 0.290630i | ||||
\(826\) | −4.09575 | −0.142509 | ||||||||
\(827\) | −24.1910 | − | 17.5758i | −0.841204 | − | 0.611171i | 0.0815024 | − | 0.996673i | \(-0.474028\pi\) |
−0.922707 | + | 0.385502i | \(0.874028\pi\) | |||||||
\(828\) | 5.35344 | − | 16.4762i | 0.186045 | − | 0.572588i | ||||
\(829\) | 5.81983 | + | 17.9116i | 0.202131 | + | 0.622096i | 0.999819 | + | 0.0190251i | \(0.00605625\pi\) |
−0.797688 | + | 0.603071i | \(0.793944\pi\) | |||||||
\(830\) | 10.7909 | − | 7.84005i | 0.374558 | − | 0.272132i | ||||
\(831\) | 45.5043 | − | 33.0608i | 1.57853 | − | 1.14687i | ||||
\(832\) | 1.98467 | + | 6.10820i | 0.0688062 | + | 0.211764i | ||||
\(833\) | 1.22181 | − | 3.76033i | 0.0423331 | − | 0.130288i | ||||
\(834\) | 43.2624 | + | 31.4320i | 1.49805 | + | 1.08840i | ||||
\(835\) | 21.2017 | 0.733716 | ||||||||
\(836\) | 5.71512 | + | 5.86311i | 0.197662 | + | 0.202780i | ||||
\(837\) | −9.40419 | −0.325056 | ||||||||
\(838\) | 14.6327 | + | 10.6313i | 0.505479 | + | 0.367252i | ||||
\(839\) | 2.40048 | − | 7.38792i | 0.0828738 | − | 0.255059i | −0.901030 | − | 0.433756i | \(-0.857188\pi\) |
0.983904 | + | 0.178697i | \(0.0571880\pi\) | |||||||
\(840\) | −0.785942 | − | 2.41888i | −0.0271176 | − | 0.0834593i | ||||
\(841\) | −42.7115 | + | 31.0317i | −1.47281 | + | 1.07006i | ||||
\(842\) | −11.8411 | + | 8.60305i | −0.408070 | + | 0.296481i | ||||
\(843\) | 9.87954 | + | 30.4061i | 0.340269 | + | 1.04724i | ||||
\(844\) | −0.989592 | + | 3.04565i | −0.0340632 | + | 0.104836i | ||||
\(845\) | −22.8539 | − | 16.6044i | −0.786199 | − | 0.571207i | ||||
\(846\) | 29.0671 | 0.999346 | ||||||||
\(847\) | 10.5451 | − | 3.13068i | 0.362333 | − | 0.107572i | ||||
\(848\) | 10.0616 | 0.345518 | ||||||||
\(849\) | 10.5037 | + | 7.63138i | 0.360486 | + | 0.261908i | ||||
\(850\) | −1.22181 | + | 3.76033i | −0.0419076 | + | 0.128978i | ||||
\(851\) | 17.0449 | + | 52.4589i | 0.584292 | + | 1.79827i | ||||
\(852\) | −12.1405 | + | 8.82059i | −0.415926 | + | 0.302188i | ||||
\(853\) | −19.5194 | + | 14.1817i | −0.668333 | + | 0.485572i | −0.869467 | − | 0.493992i | \(-0.835537\pi\) |
0.201134 | + | 0.979564i | \(0.435537\pi\) | |||||||
\(854\) | 1.11152 | + | 3.42091i | 0.0380355 | + | 0.117061i | ||||
\(855\) | −2.64615 | + | 8.14401i | −0.0904964 | + | 0.278519i | ||||
\(856\) | 10.8310 | + | 7.86920i | 0.370197 | + | 0.268964i | ||||
\(857\) | −22.2559 | −0.760246 | −0.380123 | − | 0.924936i | \(-0.624118\pi\) | ||||
−0.380123 | + | 0.924936i | \(0.624118\pi\) | |||||||
\(858\) | −37.8159 | − | 38.7951i | −1.29101 | − | 1.32444i | ||||
\(859\) | 5.09623 | 0.173881 | 0.0869406 | − | 0.996214i | \(-0.472291\pi\) | ||||
0.0869406 | + | 0.996214i | \(0.472291\pi\) | |||||||
\(860\) | 2.44561 | + | 1.77684i | 0.0833948 | + | 0.0605899i | ||||
\(861\) | 5.46532 | − | 16.8205i | 0.186258 | − | 0.573242i | ||||
\(862\) | 0.194521 | + | 0.598676i | 0.00662543 | + | 0.0203910i | ||||
\(863\) | −11.9162 | + | 8.65763i | −0.405632 | + | 0.294709i | −0.771831 | − | 0.635828i | \(-0.780659\pi\) |
0.366199 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(864\) | −0.964387 | + | 0.700668i | −0.0328091 | + | 0.0238372i | ||||
\(865\) | −1.82700 | − | 5.62293i | −0.0621199 | − | 0.191186i | ||||
\(866\) | 4.69050 | − | 14.4359i | 0.159390 | − | 0.490551i | ||||
\(867\) | −2.81291 | − | 2.04370i | −0.0955315 | − | 0.0694077i | ||||
\(868\) | −7.88910 | −0.267774 | ||||||||
\(869\) | 2.96218 | + | 20.3854i | 0.100485 | + | 0.691529i | ||||
\(870\) | 23.0022 | 0.779848 | ||||||||
\(871\) | 6.66233 | + | 4.84047i | 0.225745 | + | 0.164013i | ||||
\(872\) | 2.68110 | − | 8.25159i | 0.0907936 | − | 0.279434i | ||||
\(873\) | −12.8201 | − | 39.4562i | −0.433894 | − | 1.33539i | ||||
\(874\) | −9.97492 | + | 7.24721i | −0.337407 | + | 0.245140i | ||||
\(875\) | 0.809017 | − | 0.587785i | 0.0273498 | − | 0.0198708i | ||||
\(876\) | −8.05757 | − | 24.7987i | −0.272240 | − | 0.837869i | ||||
\(877\) | −15.5169 | + | 47.7561i | −0.523968 | + | 1.61261i | 0.242380 | + | 0.970181i | \(0.422072\pi\) |
−0.766348 | + | 0.642426i | \(0.777928\pi\) | |||||||
\(878\) | 10.1686 | + | 7.38790i | 0.343172 | + | 0.249329i | ||||
\(879\) | −43.8872 | −1.48028 | ||||||||
\(880\) | −2.97414 | + | 1.46782i | −0.100258 | + | 0.0494804i | ||||
\(881\) | 11.6181 | 0.391423 | 0.195711 | − | 0.980662i | \(-0.437298\pi\) | ||||
0.195711 | + | 0.980662i | \(0.437298\pi\) | |||||||
\(882\) | 2.80623 | + | 2.03884i | 0.0944906 | + | 0.0686515i | ||||
\(883\) | 0.852737 | − | 2.62445i | 0.0286969 | − | 0.0883199i | −0.935682 | − | 0.352844i | \(-0.885215\pi\) |
0.964379 | + | 0.264524i | \(0.0852148\pi\) | |||||||
\(884\) | 7.84710 | + | 24.1509i | 0.263927 | + | 0.812283i | ||||
\(885\) | −8.42750 | + | 6.12294i | −0.283287 | + | 0.205820i | ||||
\(886\) | −2.31274 | + | 1.68030i | −0.0776981 | + | 0.0564509i | ||||
\(887\) | −10.7701 | − | 33.1471i | −0.361626 | − | 1.11297i | −0.952067 | − | 0.305889i | \(-0.901046\pi\) |
0.590442 | − | 0.807080i | \(-0.298954\pi\) | |||||||
\(888\) | 8.67996 | − | 26.7142i | 0.291280 | − | 0.896469i | ||||
\(889\) | 12.3615 | + | 8.98117i | 0.414592 | + | 0.301219i | ||||
\(890\) | −14.7432 | −0.494193 | ||||||||
\(891\) | −11.3812 | + | 21.6482i | −0.381283 | + | 0.725243i | ||||
\(892\) | −0.768535 | −0.0257325 | ||||||||
\(893\) | −16.7363 | − | 12.1596i | −0.560059 | − | 0.406907i | ||||
\(894\) | −6.72239 | + | 20.6894i | −0.224830 | + | 0.691956i | ||||
\(895\) | −5.52768 | − | 17.0124i | −0.184770 | − | 0.568663i | ||||
\(896\) | −0.809017 | + | 0.587785i | −0.0270274 | + | 0.0196365i | ||||
\(897\) | 66.0021 | − | 47.9534i | 2.20375 | − | 1.60112i | ||||
\(898\) | −8.79884 | − | 27.0800i | −0.293621 | − | 0.903673i | ||||
\(899\) | 22.0481 | − | 67.8571i | 0.735346 | − | 2.26316i | ||||
\(900\) | −2.80623 | − | 2.03884i | −0.0935410 | − | 0.0679615i | ||||
\(901\) | 39.7822 | 1.32534 | ||||||||
\(902\) | −22.7314 | − | 3.89874i | −0.756873 | − | 0.129814i | ||||
\(903\) | −7.68845 | −0.255855 | ||||||||
\(904\) | −7.41603 | − | 5.38806i | −0.246653 | − | 0.179204i | ||||
\(905\) | 3.42112 | − | 10.5291i | 0.113722 | − | 0.350000i | ||||
\(906\) | −1.73815 | − | 5.34947i | −0.0577461 | − | 0.177724i | ||||
\(907\) | 4.25136 | − | 3.08879i | 0.141164 | − | 0.102562i | −0.514962 | − | 0.857213i | \(-0.672194\pi\) |
0.656126 | + | 0.754651i | \(0.272194\pi\) | |||||||
\(908\) | −5.32930 | + | 3.87197i | −0.176859 | + | 0.128496i | ||||
\(909\) | −2.42368 | − | 7.45933i | −0.0803885 | − | 0.247410i | ||||
\(910\) | 1.98467 | − | 6.10820i | 0.0657913 | − | 0.202485i | ||||
\(911\) | 9.04475 | + | 6.57139i | 0.299666 | + | 0.217720i | 0.727450 | − | 0.686161i | \(-0.240706\pi\) |
−0.427784 | + | 0.903881i | \(0.640706\pi\) | |||||||
\(912\) | 6.27877 | 0.207911 | ||||||||
\(913\) | 43.6014 | + | 7.47823i | 1.44300 | + | 0.247493i | ||||
\(914\) | −7.63383 | −0.252505 | ||||||||
\(915\) | 7.40119 | + | 5.37728i | 0.244676 | + | 0.177767i | ||||
\(916\) | −7.19480 | + | 22.1433i | −0.237723 | + | 0.731636i | ||||
\(917\) | 1.74737 | + | 5.37785i | 0.0577032 | + | 0.177592i | ||||
\(918\) | −3.81304 | + | 2.77034i | −0.125849 | + | 0.0914347i | ||||
\(919\) | 19.7289 | − | 14.3339i | 0.650796 | − | 0.472831i | −0.212746 | − | 0.977107i | \(-0.568241\pi\) |
0.863542 | + | 0.504277i | \(0.168241\pi\) | |||||||
\(920\) | −1.54336 | − | 4.74998i | −0.0508831 | − | 0.156602i | ||||
\(921\) | −19.4952 | + | 60.0000i | −0.642388 | + | 1.97707i | ||||
\(922\) | −3.82028 | − | 2.77560i | −0.125814 | − | 0.0914094i | ||||
\(923\) | −37.8946 | −1.24732 | ||||||||
\(924\) | 3.92533 | − | 7.46642i | 0.129134 | − | 0.245627i | ||||
\(925\) | 11.0440 | 0.363125 | ||||||||
\(926\) | −15.7214 | − | 11.4223i | −0.516638 | − | 0.375360i | ||||
\(927\) | 14.4017 | − | 44.3240i | 0.473015 | − | 1.45579i | ||||
\(928\) | −2.79476 | − | 8.60137i | −0.0917424 | − | 0.282354i | ||||
\(929\) | −16.1197 | + | 11.7116i | −0.528869 | + | 0.384246i | −0.819935 | − | 0.572457i | \(-0.805990\pi\) |
0.291066 | + | 0.956703i | \(0.405990\pi\) | |||||||
\(930\) | −16.2328 | + | 11.7938i | −0.532294 | + | 0.386734i | ||||
\(931\) | −0.762867 | − | 2.34786i | −0.0250020 | − | 0.0769481i | ||||
\(932\) | −0.532246 | + | 1.63809i | −0.0174343 | + | 0.0536573i | ||||
\(933\) | −31.0121 | − | 22.5316i | −1.01529 | − | 0.737653i | ||||
\(934\) | 13.5440 | 0.443172 | ||||||||
\(935\) | −11.7593 | + | 5.80356i | −0.384570 | + | 0.189797i | ||||
\(936\) | −22.2778 | −0.728173 | ||||||||
\(937\) | 38.8069 | + | 28.1949i | 1.26777 | + | 0.921087i | 0.999111 | − | 0.0421495i | \(-0.0134206\pi\) |
0.268656 | + | 0.963236i | \(0.413421\pi\) | |||||||
\(938\) | −0.396227 | + | 1.21946i | −0.0129373 | + | 0.0398168i | ||||
\(939\) | 11.5327 | + | 35.4939i | 0.376354 | + | 1.15830i | ||||
\(940\) | 6.77943 | − | 4.92554i | 0.221121 | − | 0.160654i | ||||
\(941\) | 35.4739 | − | 25.7733i | 1.15642 | − | 0.840186i | 0.167095 | − | 0.985941i | \(-0.446561\pi\) |
0.989321 | + | 0.145755i | \(0.0465612\pi\) | |||||||
\(942\) | −10.5209 | − | 32.3799i | −0.342788 | − | 1.05499i | ||||
\(943\) | 10.7323 | − | 33.0306i | 0.349492 | − | 1.07563i | ||||
\(944\) | 3.31353 | + | 2.40742i | 0.107846 | + | 0.0783548i | ||||
\(945\) | 1.19205 | 0.0387773 | ||||||||
\(946\) | 1.44172 | + | 9.92178i | 0.0468743 | + | 0.322585i | ||||
\(947\) | −27.0791 | −0.879951 | −0.439976 | − | 0.898010i | \(-0.645013\pi\) | ||||
−0.439976 | + | 0.898010i | \(0.645013\pi\) | |||||||
\(948\) | 12.7799 | + | 9.28513i | 0.415071 | + | 0.301567i | ||||
\(949\) | 20.3471 | − | 62.6220i | 0.660495 | − | 2.03280i | ||||
\(950\) | 0.762867 | + | 2.34786i | 0.0247507 | + | 0.0761748i | ||||
\(951\) | −29.3601 | + | 21.3314i | −0.952066 | + | 0.691717i | ||||
\(952\) | −3.19873 | + | 2.32401i | −0.103671 | + | 0.0753218i | ||||
\(953\) | −9.54793 | − | 29.3855i | −0.309288 | − | 0.951890i | −0.978042 | − | 0.208407i | \(-0.933172\pi\) |
0.668755 | − | 0.743483i | \(-0.266828\pi\) | |||||||
\(954\) | −10.7849 | + | 33.1926i | −0.349175 | + | 1.07465i | ||||
\(955\) | 7.73401 | + | 5.61909i | 0.250267 | + | 0.181829i | ||||
\(956\) | 11.6437 | 0.376585 | ||||||||
\(957\) | 53.2511 | + | 54.6300i | 1.72136 | + | 1.76594i | ||||
\(958\) | −4.33024 | −0.139904 | ||||||||
\(959\) | −3.19795 | − | 2.32344i | −0.103267 | − | 0.0750279i | ||||
\(960\) | −0.785942 | + | 2.41888i | −0.0253662 | + | 0.0780690i | ||||
\(961\) | 9.65304 | + | 29.7090i | 0.311388 | + | 0.958355i | ||||
\(962\) | 57.3841 | − | 41.6920i | 1.85014 | − | 1.34420i | ||||
\(963\) | −37.5695 | + | 27.2958i | −1.21066 | + | 0.879596i | ||||
\(964\) | −2.96111 | − | 9.11337i | −0.0953710 | − | 0.293522i | ||||
\(965\) | −5.15582 | + | 15.8680i | −0.165972 | + | 0.510808i | ||||
\(966\) | 10.2766 | + | 7.46642i | 0.330646 | + | 0.240228i | ||||
\(967\) | 33.0146 | 1.06168 | 0.530839 | − | 0.847473i | \(-0.321877\pi\) | ||||
0.530839 | + | 0.847473i | \(0.321877\pi\) | |||||||
\(968\) | −10.3713 | − | 3.66547i | −0.333347 | − | 0.117813i | ||||
\(969\) | 24.8253 | 0.797504 | ||||||||
\(970\) | −9.67611 | − | 7.03010i | −0.310681 | − | 0.225723i | ||||
\(971\) | 5.47214 | − | 16.8415i | 0.175609 | − | 0.540470i | −0.824052 | − | 0.566515i | \(-0.808291\pi\) |
0.999661 | + | 0.0260453i | \(0.00829140\pi\) | |||||||
\(972\) | 6.90083 | + | 21.2386i | 0.221344 | + | 0.681228i | ||||
\(973\) | −17.0099 | + | 12.3584i | −0.545313 | + | 0.396193i | ||||
\(974\) | −29.5906 | + | 21.4988i | −0.948143 | + | 0.688867i | ||||
\(975\) | −5.04774 | − | 15.5354i | −0.161657 | − | 0.497530i | ||||
\(976\) | 1.11152 | − | 3.42091i | 0.0355789 | − | 0.109501i | ||||
\(977\) | −11.7011 | − | 8.50131i | −0.374350 | − | 0.271981i | 0.384663 | − | 0.923057i | \(-0.374318\pi\) |
−0.759012 | + | 0.651076i | \(0.774318\pi\) | |||||||
\(978\) | 5.22163 | 0.166969 | ||||||||
\(979\) | −34.1311 | − | 35.0150i | −1.09084 | − | 1.11908i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 24.3475 | + | 17.6895i | 0.777356 | + | 0.564782i | ||||
\(982\) | 9.80286 | − | 30.1701i | 0.312822 | − | 0.962767i | ||||
\(983\) | −3.82743 | − | 11.7796i | −0.122076 | − | 0.375712i | 0.871281 | − | 0.490785i | \(-0.163290\pi\) |
−0.993357 | + | 0.115073i | \(0.963290\pi\) | |||||||
\(984\) | −14.3084 | + | 10.3957i | −0.456135 | + | 0.331402i | ||||
\(985\) | −0.431562 | + | 0.313548i | −0.0137507 | + | 0.00999047i | ||||
\(986\) | −11.0500 | − | 34.0085i | −0.351905 | − | 1.08305i | ||||
\(987\) | −6.58607 | + | 20.2698i | −0.209637 | + | 0.645196i | ||||
\(988\) | 12.8272 | + | 9.31949i | 0.408087 | + | 0.296492i | ||||
\(989\) | −15.0979 | −0.480085 | ||||||||
\(990\) | −1.65431 | − | 11.3848i | −0.0525773 | − | 0.361832i | ||||
\(991\) | −48.6112 | −1.54419 | −0.772093 | − | 0.635509i | \(-0.780790\pi\) | ||||
−0.772093 | + | 0.635509i | \(0.780790\pi\) | |||||||
\(992\) | 6.38242 | + | 4.63710i | 0.202642 | + | 0.147228i | ||||
\(993\) | 10.1551 | − | 31.2541i | 0.322262 | − | 0.991820i | ||||
\(994\) | −1.82328 | − | 5.61147i | −0.0578309 | − | 0.177985i | ||||
\(995\) | 2.27692 | − | 1.65428i | 0.0721832 | − | 0.0524442i | ||||
\(996\) | 27.4452 | − | 19.9401i | 0.869634 | − | 0.631826i | ||||
\(997\) | −10.9005 | − | 33.5484i | −0.345223 | − | 1.06249i | −0.961464 | − | 0.274930i | \(-0.911345\pi\) |
0.616241 | − | 0.787558i | \(-0.288655\pi\) | |||||||
\(998\) | −11.3713 | + | 34.9973i | −0.359952 | + | 1.10782i | ||||
\(999\) | 10.6507 | + | 7.73819i | 0.336974 | + | 0.244826i |
(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 | 770.2.n.f.631.1 | yes | 8 | |
11.3 | even | 5 | inner | 770.2.n.f.421.1 | ✓ | 8 | |
11.5 | even | 5 | 8470.2.a.co.1.2 | 4 | |||
11.6 | odd | 10 | 8470.2.a.cs.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.f.421.1 | ✓ | 8 | 11.3 | even | 5 | inner | |
770.2.n.f.631.1 | yes | 8 | 1.1 | even | 1 | trivial | |
8470.2.a.co.1.2 | 4 | 11.5 | even | 5 | |||
8470.2.a.cs.1.2 | 4 | 11.6 | odd | 10 |