Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(107,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.7 | ||
Character | \(\chi\) | \(=\) | 756.107 |
Dual form | 756.2.be.c.431.7 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.109104 | + | 1.41000i | −0.0771483 | + | 0.997020i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.97619 | − | 0.307674i | −0.988096 | − | 0.153837i | ||||
\(5\) | 3.44992 | + | 1.99182i | 1.54285 | + | 0.890767i | 0.998657 | + | 0.0518089i | \(0.0164987\pi\) |
0.544196 | + | 0.838958i | \(0.316835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.212727 | − | 2.63719i | 0.0804033 | − | 0.996762i | ||||
\(8\) | 0.649430 | − | 2.75286i | 0.229608 | − | 0.973283i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.18486 | + | 4.64707i | −1.00714 | + | 1.46953i | ||||
\(11\) | 0.936467 | + | 1.62201i | 0.282356 | + | 0.489054i | 0.971964 | − | 0.235128i | \(-0.0755509\pi\) |
−0.689609 | + | 0.724182i | \(0.742218\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.05785 | 0.293394 | 0.146697 | − | 0.989182i | \(-0.453136\pi\) | ||||
0.146697 | + | 0.989182i | \(0.453136\pi\) | |||||||
\(14\) | 3.69522 | + | 0.587673i | 0.987589 | + | 0.157062i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.81067 | + | 1.21604i | 0.952668 | + | 0.304011i | ||||
\(17\) | 2.30404 | − | 1.33024i | 0.558811 | − | 0.322630i | −0.193857 | − | 0.981030i | \(-0.562100\pi\) |
0.752668 | + | 0.658400i | \(0.228766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.628053 | + | 0.362606i | 0.144085 | + | 0.0831876i | 0.570310 | − | 0.821430i | \(-0.306823\pi\) |
−0.426224 | + | 0.904617i | \(0.640157\pi\) | |||||||
\(20\) | −6.20489 | − | 4.99766i | −1.38745 | − | 1.11751i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.38920 | + | 1.14345i | −0.509380 | + | 0.243784i | ||||
\(23\) | 3.00404 | − | 5.20316i | 0.626387 | − | 1.08493i | −0.361884 | − | 0.932223i | \(-0.617866\pi\) |
0.988271 | − | 0.152711i | \(-0.0488002\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.43465 | + | 9.41310i | 1.08693 | + | 1.88262i | ||||
\(26\) | −0.115415 | + | 1.49156i | −0.0226348 | + | 0.292519i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.23178 | + | 5.14614i | −0.232785 | + | 0.972528i | ||||
\(29\) | 5.09494i | 0.946106i | 0.881034 | + | 0.473053i | \(0.156848\pi\) | ||||
−0.881034 | + | 0.473053i | \(0.843152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.48051 | + | 2.00948i | −0.625119 | + | 0.360912i | −0.778859 | − | 0.627199i | \(-0.784201\pi\) |
0.153741 | + | 0.988111i | \(0.450868\pi\) | |||||||
\(32\) | −2.13038 | + | 5.24037i | −0.376602 | + | 0.926375i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.62425 | + | 3.39382i | 0.278557 | + | 0.582036i | ||||
\(35\) | 5.98668 | − | 8.67438i | 1.01193 | − | 1.46624i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.48131 | − | 7.76185i | 0.736722 | − | 1.27604i | −0.217241 | − | 0.976118i | \(-0.569706\pi\) |
0.953963 | − | 0.299923i | \(-0.0969609\pi\) | |||||||
\(38\) | −0.579798 | + | 0.845992i | −0.0940556 | + | 0.137238i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.72367 | − | 8.20362i | 1.22122 | − | 1.29711i | ||||
\(41\) | − | 6.19225i | − | 0.967067i | −0.875326 | − | 0.483534i | \(-0.839353\pi\) | ||
0.875326 | − | 0.483534i | \(-0.160647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.3071i | 1.87681i | 0.345533 | + | 0.938407i | \(0.387698\pi\) | ||||
−0.345533 | + | 0.938407i | \(0.612302\pi\) | |||||||
\(44\) | −1.35159 | − | 3.49353i | −0.203760 | − | 0.526669i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.00869 | + | 4.80339i | 1.03338 | + | 0.708221i | ||||
\(47\) | 2.03670 | − | 3.52767i | 0.297084 | − | 0.514564i | −0.678384 | − | 0.734708i | \(-0.737319\pi\) |
0.975467 | + | 0.220144i | \(0.0706526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90949 | − | 1.12200i | −0.987071 | − | 0.160286i | ||||
\(50\) | −13.8654 | + | 6.63585i | −1.96086 | + | 0.938451i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.09051 | − | 0.325471i | −0.289901 | − | 0.0451347i | ||||
\(53\) | −11.2365 | + | 6.48742i | −1.54346 | + | 0.891116i | −0.544841 | + | 0.838539i | \(0.683410\pi\) |
−0.998617 | + | 0.0525765i | \(0.983257\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.46108i | 1.00605i | ||||||||
\(56\) | −7.12165 | − | 2.29828i | −0.951671 | − | 0.307120i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.18386 | − | 0.555879i | −0.943287 | − | 0.0729905i | ||||
\(59\) | 4.56454 | + | 7.90602i | 0.594253 | + | 1.02928i | 0.993652 | + | 0.112499i | \(0.0358856\pi\) |
−0.399399 | + | 0.916777i | \(0.630781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.21274 | + | 9.02873i | −0.667423 | + | 1.15601i | 0.311199 | + | 0.950345i | \(0.399269\pi\) |
−0.978622 | + | 0.205666i | \(0.934064\pi\) | |||||||
\(62\) | −2.45362 | − | 5.12676i | −0.311610 | − | 0.651099i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.15648 | − | 3.57558i | −0.894560 | − | 0.446948i | ||||
\(65\) | 3.64949 | + | 2.10703i | 0.452663 | + | 0.261345i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00193 | + | 2.88786i | −0.611083 | + | 0.352809i | −0.773389 | − | 0.633932i | \(-0.781440\pi\) |
0.162306 | + | 0.986740i | \(0.448107\pi\) | |||||||
\(68\) | −4.96250 | + | 1.91991i | −0.601792 | + | 0.232824i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.5777 | + | 9.38762i | 1.38380 | + | 1.12204i | ||||
\(71\) | 6.24090 | 0.740658 | 0.370329 | − | 0.928901i | \(-0.379245\pi\) | ||||
0.370329 | + | 0.928901i | \(0.379245\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.37051 | − | 12.7661i | −0.862653 | − | 1.49416i | −0.869359 | − | 0.494181i | \(-0.835468\pi\) |
0.00670577 | − | 0.999978i | \(-0.497865\pi\) | |||||||
\(74\) | 10.4553 | + | 7.16549i | 1.21540 | + | 0.832971i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.12959 | − | 0.909815i | −0.129573 | − | 0.104363i | ||||
\(77\) | 4.47675 | − | 2.12459i | 0.510173 | − | 0.242120i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.92434 | − | 2.84307i | −0.554031 | − | 0.319870i | 0.196715 | − | 0.980461i | \(-0.436973\pi\) |
−0.750746 | + | 0.660591i | \(0.770306\pi\) | |||||||
\(80\) | 10.7244 | + | 11.7854i | 1.19902 | + | 1.31765i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.73107 | + | 0.675601i | 0.964185 | + | 0.0746076i | ||||
\(83\) | 3.27295 | 0.359253 | 0.179626 | − | 0.983735i | \(-0.442511\pi\) | ||||
0.179626 | + | 0.983735i | \(0.442511\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.5983 | 1.14955 | ||||||||
\(86\) | −17.3530 | − | 1.34275i | −1.87122 | − | 0.144793i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.07333 | − | 1.52458i | 0.540819 | − | 0.162521i | ||||
\(89\) | 8.80546 | + | 5.08384i | 0.933377 | + | 0.538886i | 0.887878 | − | 0.460079i | \(-0.152179\pi\) |
0.0454992 | + | 0.998964i | \(0.485512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.225033 | − | 2.78973i | 0.0235898 | − | 0.292444i | ||||
\(92\) | −7.53745 | + | 9.35818i | −0.785833 | + | 0.975657i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.75180 | + | 3.25663i | 0.490111 | + | 0.335896i | ||||
\(95\) | 1.44449 | + | 2.50193i | 0.148202 | + | 0.256693i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.03772 | −0.206900 | −0.103450 | − | 0.994635i | \(-0.532988\pi\) | ||||
−0.103450 | + | 0.994635i | \(0.532988\pi\) | |||||||
\(98\) | 2.33588 | − | 9.61996i | 0.235959 | − | 0.971763i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.84376 | − | 20.2742i | −0.784376 | − | 2.02742i | ||||
\(101\) | −8.70650 | + | 5.02670i | −0.866330 | + | 0.500176i | −0.866127 | − | 0.499824i | \(-0.833398\pi\) |
−0.000202762 | 1.00000i | \(0.500065\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.29973 | − | 4.79185i | −0.817796 | − | 0.472155i | 0.0318595 | − | 0.999492i | \(-0.489857\pi\) |
−0.849656 | + | 0.527337i | \(0.823190\pi\) | |||||||
\(104\) | 0.686997 | − | 2.91210i | 0.0673656 | − | 0.285555i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.92130 | − | 16.5513i | −0.769385 | − | 1.60761i | ||||
\(107\) | 2.21486 | − | 3.83624i | 0.214118 | − | 0.370863i | −0.738881 | − | 0.673836i | \(-0.764646\pi\) |
0.952999 | + | 0.302972i | \(0.0979789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.40807 | + | 5.90294i | 0.326433 | + | 0.565399i | 0.981801 | − | 0.189910i | \(-0.0608198\pi\) |
−0.655368 | + | 0.755310i | \(0.727486\pi\) | |||||||
\(110\) | −10.5201 | − | 0.814035i | −1.00305 | − | 0.0776152i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.01757 | − | 9.79077i | 0.379625 | − | 0.925141i | ||||
\(113\) | − | 11.0586i | − | 1.04030i | −0.854074 | − | 0.520151i | \(-0.825875\pi\) | ||
0.854074 | − | 0.520151i | \(-0.174125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.7275 | − | 11.9670i | 1.93285 | − | 1.11593i | ||||
\(116\) | 1.56758 | − | 10.0686i | 0.145546 | − | 0.934844i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.6455 | + | 5.57342i | −1.07205 | + | 0.513075i | ||||
\(119\) | −3.01795 | − | 6.35915i | −0.276655 | − | 0.582943i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.74606 | − | 6.48836i | 0.340551 | − | 0.589851i | ||||
\(122\) | −12.1618 | − | 8.33503i | −1.10107 | − | 0.754618i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.49643 | − | 2.90025i | 0.673199 | − | 0.260450i | ||||
\(125\) | 23.3812i | 2.09127i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.8137i | − | 1.31450i | −0.753670 | − | 0.657252i | \(-0.771719\pi\) | ||
0.753670 | − | 0.657252i | \(-0.228281\pi\) | |||||||
\(128\) | 5.82237 | − | 9.70052i | 0.514629 | − | 0.857413i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.36909 | + | 4.91589i | −0.295489 | + | 0.431152i | ||||
\(131\) | 1.22561 | − | 2.12281i | 0.107082 | − | 0.185471i | −0.807505 | − | 0.589861i | \(-0.799183\pi\) |
0.914587 | + | 0.404390i | \(0.132516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.08986 | − | 1.57916i | 0.0945032 | − | 0.136930i | ||||
\(134\) | −3.52615 | − | 7.36779i | −0.304613 | − | 0.636480i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.16564 | − | 7.20659i | −0.185702 | − | 0.617960i | ||||
\(137\) | 0.536858 | − | 0.309955i | 0.0458669 | − | 0.0264812i | −0.476891 | − | 0.878962i | \(-0.658236\pi\) |
0.522758 | + | 0.852481i | \(0.324903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00673i | 0.170209i | 0.996372 | + | 0.0851044i | \(0.0271224\pi\) | ||||
−0.996372 | + | 0.0851044i | \(0.972878\pi\) | |||||||
\(140\) | −14.4997 | + | 15.3003i | −1.22545 | + | 1.29311i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.680908 | + | 8.79966i | −0.0571405 | + | 0.738451i | ||||
\(143\) | 0.990638 | + | 1.71583i | 0.0828413 | + | 0.143485i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.1482 | + | 17.5772i | −0.842760 | + | 1.45970i | ||||
\(146\) | 18.8043 | − | 8.99958i | 1.55626 | − | 0.744810i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.2440 | + | 13.9601i | −0.924255 | + | 1.14752i | ||||
\(149\) | −6.01927 | − | 3.47523i | −0.493118 | − | 0.284702i | 0.232749 | − | 0.972537i | \(-0.425228\pi\) |
−0.725867 | + | 0.687835i | \(0.758561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9420 | − | 7.47207i | 1.05320 | − | 0.608068i | 0.129660 | − | 0.991559i | \(-0.458611\pi\) |
0.923545 | + | 0.383490i | \(0.125278\pi\) | |||||||
\(152\) | 1.40608 | − | 1.49345i | 0.114048 | − | 0.121135i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.50724 | + | 6.54401i | 0.202039 | + | 0.527332i | ||||
\(155\) | −16.0100 | −1.28596 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.82313 | − | 13.5501i | −0.624354 | − | 1.08141i | −0.988665 | − | 0.150135i | \(-0.952029\pi\) |
0.364312 | − | 0.931277i | \(-0.381304\pi\) | |||||||
\(158\) | 4.54599 | − | 6.63312i | 0.361659 | − | 0.527702i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −17.7875 | + | 13.8356i | −1.40623 | + | 1.09380i | ||||
\(161\) | −13.0827 | − | 9.02908i | −1.03106 | − | 0.711591i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.27734 | − | 3.62422i | −0.491679 | − | 0.283871i | 0.233592 | − | 0.972335i | \(-0.424952\pi\) |
−0.725271 | + | 0.688464i | \(0.758285\pi\) | |||||||
\(164\) | −1.90519 | + | 12.2371i | −0.148770 | + | 0.955555i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.357092 | + | 4.61485i | −0.0277157 | + | 0.358182i | ||||
\(167\) | 18.1132 | 1.40164 | 0.700822 | − | 0.713337i | \(-0.252817\pi\) | ||||
0.700822 | + | 0.713337i | \(0.252817\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8810 | −0.913920 | ||||||||
\(170\) | −1.15632 | + | 14.9437i | −0.0886860 | + | 1.14613i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.78657 | − | 24.3212i | 0.288723 | − | 1.85447i | ||||
\(173\) | 9.26339 | + | 5.34822i | 0.704283 | + | 0.406618i | 0.808941 | − | 0.587890i | \(-0.200041\pi\) |
−0.104658 | + | 0.994508i | \(0.533375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 25.9802 | − | 12.3298i | 1.96392 | − | 0.932043i | ||||
\(176\) | 1.59614 | + | 7.31973i | 0.120313 | + | 0.551746i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.12892 | + | 11.8610i | −0.609288 | + | 0.889021i | ||||
\(179\) | −11.6609 | − | 20.1973i | −0.871578 | − | 1.50962i | −0.860364 | − | 0.509681i | \(-0.829764\pi\) |
−0.0112146 | − | 0.999937i | \(-0.503570\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.90143 | −0.215662 | −0.107831 | − | 0.994169i | \(-0.534391\pi\) | ||||
−0.107831 | + | 0.994169i | \(0.534391\pi\) | |||||||
\(182\) | 3.90897 | + | 0.621667i | 0.289752 | + | 0.0460811i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.3727 | − | 11.6488i | −0.912124 | − | 0.858761i | ||||
\(185\) | 30.9204 | − | 17.8519i | 2.27331 | − | 1.31250i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.31531 | + | 2.49145i | 0.315567 | + | 0.182193i | ||||
\(188\) | −5.11029 | + | 6.34472i | −0.372706 | + | 0.462736i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.68532 | + | 1.76376i | −0.267361 | + | 0.127956i | ||||
\(191\) | 4.64881 | − | 8.05197i | 0.336376 | − | 0.582620i | −0.647372 | − | 0.762174i | \(-0.724132\pi\) |
0.983748 | + | 0.179554i | \(0.0574654\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.54336 | + | 6.13728i | 0.255056 | + | 0.441771i | 0.964911 | − | 0.262578i | \(-0.0845726\pi\) |
−0.709854 | + | 0.704348i | \(0.751239\pi\) | |||||||
\(194\) | 0.222324 | − | 2.87319i | 0.0159620 | − | 0.206283i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.3093 | + | 4.34316i | 0.950663 | + | 0.310226i | ||||
\(197\) | − | 4.03120i | − | 0.287211i | −0.989635 | − | 0.143606i | \(-0.954130\pi\) | ||
0.989635 | − | 0.143606i | \(-0.0458697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.5689 | + | 11.2981i | −1.38720 | + | 0.800900i | −0.992999 | − | 0.118124i | \(-0.962312\pi\) |
−0.394201 | + | 0.919024i | \(0.628979\pi\) | |||||||
\(200\) | 29.4424 | − | 8.84770i | 2.08189 | − | 0.625627i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.13773 | − | 12.8246i | −0.431849 | − | 0.902335i | ||||
\(203\) | 13.4363 | + | 1.08383i | 0.943043 | + | 0.0760701i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3338 | − | 21.3628i | 0.861431 | − | 1.49204i | ||||
\(206\) | 7.66204 | − | 11.1798i | 0.533839 | − | 0.778933i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.03110 | + | 1.28639i | 0.279507 | + | 0.0891949i | ||||
\(209\) | 1.35828i | 0.0939539i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.52953i | − | 0.242983i | −0.992592 | − | 0.121491i | \(-0.961232\pi\) | ||
0.992592 | − | 0.121491i | \(-0.0387676\pi\) | |||||||
\(212\) | 24.2016 | − | 9.36321i | 1.66217 | − | 0.643068i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.16745 | + | 3.54149i | 0.353239 | + | 0.242091i | ||||
\(215\) | −24.5134 | + | 42.4585i | −1.67180 | + | 2.89565i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.55896 | + | 9.60623i | 0.309482 | + | 0.652113i | ||||
\(218\) | −8.69497 | + | 4.16133i | −0.588898 | + | 0.281841i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.29558 | − | 14.7445i | 0.154768 | − | 0.994076i | ||||
\(221\) | 2.43732 | − | 1.40719i | 0.163952 | − | 0.0946575i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.17037i | 0.346234i | 0.984901 | + | 0.173117i | \(0.0553839\pi\) | ||||
−0.984901 | + | 0.173117i | \(0.944616\pi\) | |||||||
\(224\) | 13.3666 | + | 6.73298i | 0.893096 | + | 0.449866i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.5926 | + | 1.20654i | 1.03720 | + | 0.0802576i | ||||
\(227\) | 10.2679 | + | 17.7846i | 0.681507 | + | 1.18040i | 0.974521 | + | 0.224296i | \(0.0720084\pi\) |
−0.293014 | + | 0.956108i | \(0.594658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.10463 | − | 8.84148i | 0.337323 | − | 0.584261i | −0.646605 | − | 0.762825i | \(-0.723812\pi\) |
0.983928 | + | 0.178564i | \(0.0571451\pi\) | |||||||
\(230\) | 14.6120 | + | 30.5313i | 0.963487 | + | 2.01318i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.0257 | + | 3.30881i | 0.920829 | + | 0.217234i | ||||
\(233\) | 5.42215 | + | 3.13048i | 0.355217 | + | 0.205085i | 0.666981 | − | 0.745075i | \(-0.267586\pi\) |
−0.311764 | + | 0.950160i | \(0.600920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0529 | − | 8.11347i | 0.916713 | − | 0.529265i | ||||
\(236\) | −6.58794 | − | 17.0282i | −0.428839 | − | 1.10844i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.29567 | − | 3.56149i | 0.602549 | − | 0.230857i | ||||
\(239\) | −4.99283 | −0.322959 | −0.161480 | − | 0.986876i | \(-0.551627\pi\) | ||||
−0.161480 | + | 0.986876i | \(0.551627\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.48576 | + | 6.03752i | 0.224538 | + | 0.388911i | 0.956181 | − | 0.292777i | \(-0.0945795\pi\) |
−0.731643 | + | 0.681688i | \(0.761246\pi\) | |||||||
\(242\) | 8.73987 | + | 5.98984i | 0.561820 | + | 0.385042i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.0793 | − | 16.2387i | 0.837315 | − | 1.03958i | ||||
\(245\) | −21.6024 | − | 17.6333i | −1.38013 | − | 1.12655i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.664383 | + | 0.383582i | 0.0422737 | + | 0.0244067i | ||||
\(248\) | 3.27145 | + | 10.8864i | 0.207738 | + | 0.691286i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −32.9674 | − | 2.55098i | −2.08504 | − | 0.161338i | ||||
\(251\) | −18.9350 | −1.19516 | −0.597582 | − | 0.801808i | \(-0.703872\pi\) | ||||
−0.597582 | + | 0.801808i | \(0.703872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.2528 | 0.707455 | ||||||||
\(254\) | 20.8873 | + | 1.61624i | 1.31059 | + | 0.101412i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.0425 | + | 9.26790i | 0.815155 | + | 0.579244i | ||||
\(257\) | −0.662857 | − | 0.382701i | −0.0413479 | − | 0.0238722i | 0.479184 | − | 0.877715i | \(-0.340933\pi\) |
−0.520531 | + | 0.853842i | \(0.674266\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.5161 | − | 13.4692i | −1.21267 | − | 0.836935i | ||||
\(260\) | −6.56381 | − | 5.28675i | −0.407070 | − | 0.327871i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.85944 | + | 1.95971i | 0.176657 | + | 0.121071i | ||||
\(263\) | −7.12695 | − | 12.3442i | −0.439466 | − | 0.761178i | 0.558182 | − | 0.829719i | \(-0.311499\pi\) |
−0.997648 | + | 0.0685403i | \(0.978166\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −51.6870 | −3.17511 | ||||||||
\(266\) | 2.10770 | + | 1.70900i | 0.129231 | + | 0.104785i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.7733 | − | 4.16801i | 0.658083 | − | 0.254602i | ||||
\(269\) | 8.25667 | − | 4.76699i | 0.503418 | − | 0.290649i | −0.226706 | − | 0.973963i | \(-0.572796\pi\) |
0.730124 | + | 0.683315i | \(0.239462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.98753 | + | 1.72485i | 0.181479 | + | 0.104777i | 0.587988 | − | 0.808870i | \(-0.299920\pi\) |
−0.406508 | + | 0.913647i | \(0.633254\pi\) | |||||||
\(272\) | 10.3976 | − | 2.26729i | 0.630445 | − | 0.137474i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.378463 | + | 0.790786i | 0.0228638 | + | 0.0477731i | ||||
\(275\) | −10.1788 | + | 17.6301i | −0.613802 | + | 1.06314i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.78023 | − | 13.4757i | −0.467469 | − | 0.809679i | 0.531841 | − | 0.846844i | \(-0.321501\pi\) |
−0.999309 | + | 0.0371652i | \(0.988167\pi\) | |||||||
\(278\) | −2.82949 | − | 0.218943i | −0.169701 | − | 0.0131313i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.9914 | − | 22.1139i | −1.19472 | − | 1.32156i | ||||
\(281\) | − | 7.65968i | − | 0.456938i | −0.973551 | − | 0.228469i | \(-0.926628\pi\) | ||
0.973551 | − | 0.228469i | \(-0.0733720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.5108 | + | 15.8834i | −1.63535 | + | 0.944167i | −0.652940 | + | 0.757410i | \(0.726465\pi\) |
−0.982406 | + | 0.186758i | \(0.940202\pi\) | |||||||
\(284\) | −12.3332 | − | 1.92016i | −0.731842 | − | 0.113940i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.52741 | + | 1.20959i | −0.149449 | + | 0.0715247i | ||||
\(287\) | −16.3301 | − | 1.31726i | −0.963936 | − | 0.0777554i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.96094 | + | 8.59260i | −0.291820 | + | 0.505447i | ||||
\(290\) | −23.6766 | − | 16.2267i | −1.39034 | − | 0.952862i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.6378 | + | 27.4960i | 0.622528 | + | 1.60908i | ||||
\(293\) | 8.77681i | 0.512747i | 0.966578 | + | 0.256373i | \(0.0825277\pi\) | ||||
−0.966578 | + | 0.256373i | \(0.917472\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.3669i | 2.11736i | ||||||||
\(296\) | −18.4570 | − | 17.3772i | −1.07279 | − | 1.01003i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.55679 | − | 8.10800i | 0.321896 | − | 0.469684i | ||||
\(299\) | 3.17782 | − | 5.50414i | 0.183778 | − | 0.318313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.4561 | + | 2.61805i | 1.87074 | + | 0.150902i | ||||
\(302\) | 9.12358 | + | 19.0634i | 0.525003 | + | 1.09698i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.95236 | + | 2.14551i | 0.111975 | + | 0.123054i | ||||
\(305\) | −35.9671 | + | 20.7656i | −2.05947 | + | 1.18904i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7116i | 0.896709i | 0.893856 | + | 0.448355i | \(0.147990\pi\) | ||||
−0.893856 | + | 0.448355i | \(0.852010\pi\) | |||||||
\(308\) | −9.50060 | + | 2.82123i | −0.541347 | + | 0.160754i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.74676 | − | 22.5741i | 0.0992093 | − | 1.28212i | ||||
\(311\) | −6.73255 | − | 11.6611i | −0.381768 | − | 0.661241i | 0.609547 | − | 0.792750i | \(-0.291351\pi\) |
−0.991315 | + | 0.131508i | \(0.958018\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.18899 | + | 10.7196i | −0.349822 | + | 0.605910i | −0.986218 | − | 0.165453i | \(-0.947091\pi\) |
0.636395 | + | 0.771363i | \(0.280425\pi\) | |||||||
\(314\) | 19.9591 | − | 9.55224i | 1.12636 | − | 0.539064i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.85670 | + | 7.13354i | 0.498228 | + | 0.401293i | ||||
\(317\) | 15.9748 | + | 9.22303i | 0.897232 | + | 0.518017i | 0.876301 | − | 0.481764i | \(-0.160004\pi\) |
0.0209310 | + | 0.999781i | \(0.493337\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.26404 | + | 4.77124i | −0.462697 | + | 0.267138i | ||||
\(320\) | −17.5674 | − | 26.5899i | −0.982049 | − | 1.48642i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.1584 | − | 17.4614i | 0.789014 | − | 0.973086i | ||||
\(323\) | 1.92941 | 0.107355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.74903 | + | 9.95760i | 0.318899 | + | 0.552348i | ||||
\(326\) | 5.79503 | − | 8.45562i | 0.320957 | − | 0.468314i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.0464 | − | 4.02144i | −0.941230 | − | 0.222047i | ||||
\(329\) | −8.86987 | − | 6.12160i | −0.489012 | − | 0.337495i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2310 | − | 12.8351i | −1.22193 | − | 0.705480i | −0.256599 | − | 0.966518i | \(-0.582602\pi\) |
−0.965329 | + | 0.261037i | \(0.915935\pi\) | |||||||
\(332\) | −6.46798 | − | 1.00700i | −0.354976 | − | 0.0552663i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.97623 | + | 25.5396i | −0.108134 | + | 1.39747i | ||||
\(335\) | −23.0084 | −1.25708 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.12521 | 0.0612942 | 0.0306471 | − | 0.999530i | \(-0.490243\pi\) | ||||
0.0306471 | + | 0.999530i | \(0.490243\pi\) | |||||||
\(338\) | 1.29626 | − | 16.7521i | 0.0705074 | − | 0.911196i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.9444 | − | 3.26083i | −1.13587 | − | 0.176843i | ||||
\(341\) | −6.51877 | − | 3.76362i | −0.353011 | − | 0.203811i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.42877 | + | 17.9829i | −0.239131 | + | 0.970987i | ||||
\(344\) | 33.8797 | + | 7.99259i | 1.82667 | + | 0.430932i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.55166 | + | 12.4779i | −0.459740 | + | 0.670814i | ||||
\(347\) | 1.10428 | + | 1.91268i | 0.0592811 | + | 0.102678i | 0.894143 | − | 0.447782i | \(-0.147786\pi\) |
−0.834862 | + | 0.550460i | \(0.814453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3373 | 0.820986 | 0.410493 | − | 0.911864i | \(-0.365357\pi\) | ||||
0.410493 | + | 0.911864i | \(0.365357\pi\) | |||||||
\(350\) | 14.5504 | + | 37.9773i | 0.777752 | + | 2.02997i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.4950 | + | 1.45194i | −0.559383 | + | 0.0773885i | ||||
\(353\) | −29.3810 | + | 16.9631i | −1.56379 | + | 0.902855i | −0.566922 | + | 0.823771i | \(0.691866\pi\) |
−0.996868 | + | 0.0790836i | \(0.974801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.5306 | + | 12.4307i | 1.14273 | + | 0.659754i | ||||
\(356\) | −15.8371 | − | 12.7558i | −0.839366 | − | 0.676059i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 29.7504 | − | 14.2383i | 1.57236 | − | 0.752516i | ||||
\(359\) | −3.48440 | + | 6.03516i | −0.183900 | + | 0.318523i | −0.943205 | − | 0.332211i | \(-0.892205\pi\) |
0.759306 | + | 0.650734i | \(0.225539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.23703 | − | 15.9990i | −0.486160 | − | 0.842053i | ||||
\(362\) | 0.316559 | − | 4.09102i | 0.0166379 | − | 0.215019i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.30304 | + | 5.44382i | −0.0682976 | + | 0.285334i | ||||
\(365\) | − | 58.7228i | − | 3.07369i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.65689 | − | 0.956605i | 0.0864889 | − | 0.0499344i | −0.456132 | − | 0.889912i | \(-0.650765\pi\) |
0.542621 | + | 0.839978i | \(0.317432\pi\) | |||||||
\(368\) | 17.7747 | − | 16.1745i | 0.926571 | − | 0.843153i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.7976 | + | 45.5454i | 1.13320 | + | 2.36779i | ||||
\(371\) | 14.7182 | + | 31.0129i | 0.764132 | + | 1.61011i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.08938 | + | 7.08301i | −0.211740 | + | 0.366745i | −0.952259 | − | 0.305291i | \(-0.901246\pi\) |
0.740519 | + | 0.672035i | \(0.234580\pi\) | |||||||
\(374\) | −3.98376 | + | 5.81276i | −0.205995 | + | 0.300571i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.38850 | − | 7.89774i | −0.432604 | − | 0.407295i | ||||
\(377\) | 5.38966i | 0.277582i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.1764i | − | 0.882295i | −0.897435 | − | 0.441147i | \(-0.854572\pi\) | ||
0.897435 | − | 0.441147i | \(-0.145428\pi\) | |||||||
\(380\) | −2.08481 | − | 5.38873i | −0.106949 | − | 0.276436i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.8461 | + | 7.43332i | 0.554933 | + | 0.380322i | ||||
\(383\) | −11.5136 | + | 19.9422i | −0.588320 | + | 1.01900i | 0.406133 | + | 0.913814i | \(0.366877\pi\) |
−0.994453 | + | 0.105186i | \(0.966456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.6762 | + | 1.58717i | 1.00279 | + | 0.0808899i | ||||
\(386\) | −9.04015 | + | 4.32653i | −0.460131 | + | 0.220214i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.02694 | + | 0.626954i | 0.204437 | + | 0.0318288i | ||||
\(389\) | −16.4368 | + | 9.48980i | −0.833380 | + | 0.481152i | −0.855009 | − | 0.518614i | \(-0.826448\pi\) |
0.0216286 | + | 0.999766i | \(0.493115\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.9844i | − | 0.808364i | ||||||
\(392\) | −7.57595 | + | 18.2922i | −0.382643 | + | 0.923896i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.68399 | + | 0.439821i | 0.286355 | + | 0.0221579i | ||||
\(395\) | −11.3257 | − | 19.6167i | −0.569859 | − | 0.987025i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.0876 | − | 29.5966i | 0.857603 | − | 1.48541i | −0.0166054 | − | 0.999862i | \(-0.505286\pi\) |
0.874209 | − | 0.485550i | \(-0.161381\pi\) | |||||||
\(398\) | −13.7952 | − | 28.8247i | −0.691493 | − | 1.44485i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.26295 | + | 42.4790i | 0.463148 | + | 2.12395i | ||||
\(401\) | −11.4019 | − | 6.58287i | −0.569382 | − | 0.328733i | 0.187521 | − | 0.982261i | \(-0.439955\pi\) |
−0.756902 | + | 0.653528i | \(0.773288\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.68184 | + | 2.12571i | −0.183406 | + | 0.105889i | ||||
\(404\) | 18.7523 | − | 7.25497i | 0.932962 | − | 0.360948i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.99416 | + | 18.8269i | −0.148598 | + | 0.934364i | ||||
\(407\) | 16.7864 | 0.832071 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9583 | + | 24.1765i | 0.690193 | + | 1.19545i | 0.971774 | + | 0.235912i | \(0.0758076\pi\) |
−0.281582 | + | 0.959537i | \(0.590859\pi\) | |||||||
\(410\) | 28.7759 | + | 19.7214i | 1.42114 | + | 0.973973i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.9275 | + | 12.0232i | 0.735427 | + | 0.592342i | ||||
\(413\) | 21.8206 | − | 10.3557i | 1.07372 | − | 0.509572i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2914 | + | 6.51911i | 0.554274 | + | 0.320010i | ||||
\(416\) | −2.25361 | + | 5.54350i | −0.110493 | + | 0.271793i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.91517 | − | 0.148194i | −0.0936739 | − | 0.00724839i | ||||
\(419\) | −32.2539 | −1.57571 | −0.787854 | − | 0.615863i | \(-0.788808\pi\) | ||||
−0.787854 | + | 0.615863i | \(0.788808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.3473 | −0.991667 | −0.495833 | − | 0.868418i | \(-0.665137\pi\) | ||||
−0.495833 | + | 0.868418i | \(0.665137\pi\) | |||||||
\(422\) | 4.97663 | + | 0.385086i | 0.242258 | + | 0.0187457i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.5616 | + | 35.1458i | 0.512917 | + | 1.70683i | ||||
\(425\) | 25.0433 | + | 14.4588i | 1.21478 | + | 0.701353i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.7015 | + | 15.6676i | 1.09860 | + | 0.758209i | ||||
\(428\) | −5.55729 | + | 6.89970i | −0.268622 | + | 0.333510i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −57.1920 | − | 39.1963i | −2.75804 | − | 1.89021i | ||||
\(431\) | 11.8556 | + | 20.5344i | 0.571062 | + | 0.989108i | 0.996457 | + | 0.0841006i | \(0.0268017\pi\) |
−0.425395 | + | 0.905008i | \(0.639865\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4523 | 0.598417 | 0.299209 | − | 0.954188i | \(-0.403277\pi\) | ||||
0.299209 | + | 0.954188i | \(0.403277\pi\) | |||||||
\(434\) | −14.0422 | + | 5.38005i | −0.674046 | + | 0.258250i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.91881 | − | 12.7139i | −0.235568 | − | 0.608886i | ||||
\(437\) | 3.77340 | − | 2.17857i | 0.180506 | − | 0.104215i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.32885 | + | 0.767212i | 0.0634225 | + | 0.0366170i | 0.531376 | − | 0.847136i | \(-0.321675\pi\) |
−0.467953 | + | 0.883753i | \(0.655008\pi\) | |||||||
\(440\) | 20.5393 | + | 4.84545i | 0.979173 | + | 0.230998i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.71821 | + | 3.59014i | 0.0817268 | + | 0.170766i | ||||
\(443\) | −14.6601 | + | 25.3921i | −0.696523 | + | 1.20641i | 0.273141 | + | 0.961974i | \(0.411937\pi\) |
−0.969664 | + | 0.244440i | \(0.921396\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.2521 | + | 35.0777i | 0.960043 | + | 1.66284i | ||||
\(446\) | −7.29022 | − | 0.564110i | −0.345202 | − | 0.0267114i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.9518 | + | 18.1123i | −0.517426 | + | 0.855728i | ||||
\(449\) | 4.29939i | 0.202901i | 0.994841 | + | 0.101450i | \(0.0323483\pi\) | ||||
−0.994841 | + | 0.101450i | \(0.967652\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0439 | − | 5.79884i | 0.472948 | − | 0.273057i | ||||
\(452\) | −3.40243 | + | 21.8539i | −0.160037 | + | 1.02792i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.1965 | + | 12.5374i | −1.22946 | + | 0.588409i | ||||
\(455\) | 6.33298 | − | 9.17615i | 0.296895 | − | 0.430185i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.32454 | + | 4.02622i | −0.108737 | + | 0.188339i | −0.915259 | − | 0.402866i | \(-0.868014\pi\) |
0.806522 | + | 0.591205i | \(0.201347\pi\) | |||||||
\(458\) | 11.9095 | + | 8.16216i | 0.556496 | + | 0.381393i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −44.6434 | + | 17.2718i | −2.08151 | + | 0.805302i | ||||
\(461\) | − | 24.2351i | − | 1.12874i | −0.825521 | − | 0.564371i | \(-0.809119\pi\) | ||
0.825521 | − | 0.564371i | \(-0.190881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.7274i | − | 0.870335i | −0.900349 | − | 0.435168i | \(-0.856689\pi\) | ||
0.900349 | − | 0.435168i | \(-0.143311\pi\) | |||||||
\(464\) | −6.19567 | + | 19.4152i | −0.287627 | + | 0.901326i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.00555 | + | 7.30368i | −0.231878 | + | 0.338336i | ||||
\(467\) | 9.28665 | − | 16.0849i | 0.429735 | − | 0.744323i | −0.567115 | − | 0.823639i | \(-0.691940\pi\) |
0.996850 | + | 0.0793162i | \(0.0252737\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.55179 | + | 13.8053i | 0.302533 | + | 0.637471i | ||||
\(470\) | 9.90675 | + | 20.6999i | 0.456964 | + | 0.954813i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.7285 | − | 7.43114i | 1.13822 | − | 0.342046i | ||||
\(473\) | −19.9622 | + | 11.5252i | −0.917863 | + | 0.529929i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.88256i | 0.361677i | ||||||||
\(476\) | 4.00751 | + | 13.4955i | 0.183684 | + | 0.618563i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.544739 | − | 7.03989i | 0.0249158 | − | 0.321997i | ||||
\(479\) | −5.24836 | − | 9.09043i | −0.239804 | − | 0.415352i | 0.720854 | − | 0.693087i | \(-0.243750\pi\) |
−0.960658 | + | 0.277734i | \(0.910416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.74053 | − | 8.21084i | 0.216150 | − | 0.374382i | ||||
\(482\) | −8.89321 | + | 4.25620i | −0.405074 | + | 0.193865i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.39923 | + | 11.6697i | −0.427238 | + | 0.530441i | ||||
\(485\) | −7.03000 | − | 4.05877i | −0.319216 | − | 0.184299i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.4523 | − | 13.5402i | 1.06273 | − | 0.613565i | 0.136540 | − | 0.990635i | \(-0.456402\pi\) |
0.926185 | + | 0.377070i | \(0.123068\pi\) | |||||||
\(488\) | 21.4695 | + | 20.2135i | 0.971880 | + | 0.915021i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 27.2198 | − | 28.5355i | 1.22966 | − | 1.28910i | ||||
\(491\) | 8.39226 | 0.378737 | 0.189369 | − | 0.981906i | \(-0.439356\pi\) | ||||
0.189369 | + | 0.981906i | \(0.439356\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.77748 | + | 11.7389i | 0.305242 | + | 0.528695i | ||||
\(494\) | −0.613336 | + | 0.894928i | −0.0275953 | + | 0.0402647i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.7067 | + | 3.42500i | −0.705252 | + | 0.153787i | ||||
\(497\) | 1.32761 | − | 16.4584i | 0.0595514 | − | 0.738260i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.4658 | − | 8.92917i | −0.692343 | − | 0.399724i | 0.112146 | − | 0.993692i | \(-0.464228\pi\) |
−0.804489 | + | 0.593967i | \(0.797561\pi\) | |||||||
\(500\) | 7.19376 | − | 46.2057i | 0.321715 | − | 2.06638i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.06588 | − | 26.6983i | 0.0922049 | − | 1.19160i | ||||
\(503\) | 15.3493 | 0.684392 | 0.342196 | − | 0.939629i | \(-0.388829\pi\) | ||||
0.342196 | + | 0.939629i | \(0.388829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.0490 | −1.78216 | ||||||||
\(506\) | −1.22772 | + | 15.8664i | −0.0545790 | + | 0.705346i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.55779 | + | 29.2748i | −0.202219 | + | 1.29886i | ||||
\(509\) | 25.2937 | + | 14.6033i | 1.12112 | + | 0.647281i | 0.941687 | − | 0.336489i | \(-0.109240\pi\) |
0.179436 | + | 0.983770i | \(0.442573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.2345 | + | 16.7217i | −1.55868 | + | 0.739725i | ||||
\(512\) | −14.4907 | + | 17.3787i | −0.640405 | + | 0.768037i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.611928 | − | 0.892873i | 0.0269910 | − | 0.0393829i | ||||
\(515\) | −19.0890 | − | 33.0630i | −0.841160 | − | 1.45693i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.62922 | 0.335533 | ||||||||
\(518\) | 21.1208 | − | 26.0482i | 0.927997 | − | 1.14449i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.17045 | − | 8.67816i | 0.358298 | − | 0.380562i | ||||
\(521\) | 12.9936 | − | 7.50183i | 0.569258 | − | 0.328661i | −0.187595 | − | 0.982246i | \(-0.560069\pi\) |
0.756853 | + | 0.653585i | \(0.226736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6638 | − | 6.15676i | −0.466296 | − | 0.269216i | 0.248392 | − | 0.968660i | \(-0.420098\pi\) |
−0.714688 | + | 0.699443i | \(0.753431\pi\) | |||||||
\(524\) | −3.07517 | + | 3.81800i | −0.134339 | + | 0.166790i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.1829 | − | 8.70218i | 0.792814 | − | 0.379433i | ||||
\(527\) | −5.34616 | + | 9.25981i | −0.232882 | + | 0.403364i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.54857 | − | 11.3425i | −0.284720 | − | 0.493150i | ||||
\(530\) | 5.63927 | − | 72.8786i | 0.244954 | − | 3.16564i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.63965 | + | 2.78539i | −0.114443 | + | 0.120762i | ||||
\(533\) | − | 6.55045i | − | 0.283731i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2822 | − | 8.82316i | 0.660706 | − | 0.381459i | ||||
\(536\) | 4.70148 | + | 15.6451i | 0.203073 | + | 0.675764i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.82061 | + | 12.1620i | 0.250944 | + | 0.524341i | ||||
\(539\) | −4.65062 | − | 12.2580i | −0.200316 | − | 0.527989i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1895 | − | 21.1128i | 0.524066 | − | 0.907708i | −0.475542 | − | 0.879693i | \(-0.657748\pi\) |
0.999608 | − | 0.0280151i | \(-0.00891864\pi\) | |||||||
\(542\) | −2.75799 | + | 4.02422i | −0.118466 | + | 0.172855i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.06245 | + | 14.9079i | 0.0884270 | + | 0.639172i | ||||
\(545\) | 27.1529i | 1.16310i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.9284i | − | 1.15138i | −0.817669 | − | 0.575688i | \(-0.804734\pi\) | ||
0.817669 | − | 0.575688i | \(-0.195266\pi\) | |||||||
\(548\) | −1.15630 | + | 0.447354i | −0.0493947 | + | 0.0191100i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.7479 | − | 16.2755i | −1.01261 | − | 0.693992i | ||||
\(551\) | −1.84746 | + | 3.19989i | −0.0787043 | + | 0.136320i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.54523 | + | 12.3816i | −0.363380 | + | 0.526519i | ||||
\(554\) | 19.8496 | − | 9.49985i | 0.843331 | − | 0.403610i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.617418 | − | 3.96569i | 0.0261844 | − | 0.168183i | ||||
\(557\) | −3.35873 | + | 1.93917i | −0.142314 | + | 0.0821651i | −0.569466 | − | 0.822015i | \(-0.692850\pi\) |
0.427152 | + | 0.904180i | \(0.359517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.0190i | 0.550645i | ||||||||
\(560\) | 33.3617 | − | 25.7752i | 1.40979 | − | 1.08920i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.8001 | + | 0.835704i | 0.455577 | + | 0.0352520i | ||||
\(563\) | 20.6486 | + | 35.7644i | 0.870234 | + | 1.50729i | 0.861755 | + | 0.507325i | \(0.169366\pi\) |
0.00847940 | + | 0.999964i | \(0.497301\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.0266 | − | 38.1512i | 0.926667 | − | 1.60503i | ||||
\(566\) | −19.3940 | − | 40.5231i | −0.815189 | − | 1.70331i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.05303 | − | 17.1803i | 0.170061 | − | 0.720870i | ||||
\(569\) | 8.24961 | + | 4.76292i | 0.345842 | + | 0.199672i | 0.662852 | − | 0.748750i | \(-0.269346\pi\) |
−0.317011 | + | 0.948422i | \(0.602679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0822 | + | 12.7492i | −0.924111 | + | 0.533536i | −0.884944 | − | 0.465697i | \(-0.845804\pi\) |
−0.0391670 | + | 0.999233i | \(0.512470\pi\) | |||||||
\(572\) | −1.42977 | − | 3.69561i | −0.0597819 | − | 0.154521i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.63902 | − | 22.8817i | 0.151890 | − | 0.955065i | ||||
\(575\) | 65.3038 | 2.72336 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.94249 | − | 5.09654i | −0.122498 | − | 0.212172i | 0.798254 | − | 0.602320i | \(-0.205757\pi\) |
−0.920752 | + | 0.390148i | \(0.872424\pi\) | |||||||
\(578\) | −11.5743 | − | 7.93241i | −0.481427 | − | 0.329945i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.4628 | − | 31.6135i | 1.05728 | − | 1.31268i | ||||
\(581\) | 0.696245 | − | 8.63137i | 0.0288851 | − | 0.358090i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.0453 | − | 12.1505i | −0.871608 | − | 0.503223i | ||||
\(584\) | −39.9299 | + | 11.9993i | −1.65231 | + | 0.496534i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.3753 | − | 0.957587i | −0.511219 | − | 0.0395576i | ||||
\(587\) | −16.1329 | −0.665878 | −0.332939 | − | 0.942948i | \(-0.608040\pi\) | ||||
−0.332939 | + | 0.942948i | \(0.608040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.91459 | −0.120094 | ||||||||
\(590\) | −51.2773 | − | 3.96778i | −2.11105 | − | 0.163351i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26.5156 | − | 24.1284i | 1.08978 | − | 0.991672i | ||||
\(593\) | 7.56550 | + | 4.36794i | 0.310678 | + | 0.179370i | 0.647230 | − | 0.762295i | \(-0.275927\pi\) |
−0.336552 | + | 0.941665i | \(0.609261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.25456 | − | 27.9498i | 0.0924278 | − | 1.14583i | ||||
\(596\) | 10.8260 | + | 8.71968i | 0.443450 | + | 0.357172i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.41411 | + | 5.08124i | 0.303186 | + | 0.207787i | ||||
\(599\) | −17.0745 | − | 29.5738i | −0.697644 | − | 1.20835i | −0.969281 | − | 0.245955i | \(-0.920899\pi\) |
0.271638 | − | 0.962400i | \(-0.412435\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.8371 | −0.564426 | −0.282213 | − | 0.959352i | \(-0.591068\pi\) | ||||
−0.282213 | + | 0.959352i | \(0.591068\pi\) | |||||||
\(602\) | −7.23254 | + | 45.4774i | −0.294777 | + | 1.85352i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.8748 | + | 10.7843i | −1.13421 | + | 0.438808i | ||||
\(605\) | 25.8472 | − | 14.9229i | 1.05084 | − | 0.606703i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.7444 | + | 14.2862i | 1.00434 | + | 0.579858i | 0.909530 | − | 0.415638i | \(-0.136442\pi\) |
0.0948125 | + | 0.995495i | \(0.469775\pi\) | |||||||
\(608\) | −3.23818 | + | 2.51874i | −0.131326 | + | 0.102148i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25.3553 | − | 52.9792i | −1.02661 | − | 2.14507i | ||||
\(611\) | 2.15452 | − | 3.73173i | 0.0871624 | − | 0.150970i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5641 | − | 18.2976i | −0.426680 | − | 0.739032i | 0.569895 | − | 0.821717i | \(-0.306984\pi\) |
−0.996576 | + | 0.0826853i | \(0.973650\pi\) | |||||||
\(614\) | −22.1534 | − | 1.71420i | −0.894037 | − | 0.0691796i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.94137 | − | 13.7036i | −0.118511 | − | 0.552136i | ||||
\(617\) | 43.3809i | 1.74645i | 0.487319 | + | 0.873224i | \(0.337975\pi\) | ||||
−0.487319 | + | 0.873224i | \(0.662025\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8607 | + | 6.84777i | −0.476721 | + | 0.275235i | −0.719049 | − | 0.694959i | \(-0.755422\pi\) |
0.242328 | + | 0.970194i | \(0.422089\pi\) | |||||||
\(620\) | 31.6389 | + | 4.92586i | 1.27065 | + | 0.197827i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.1767 | − | 8.22061i | 0.688723 | − | 0.329616i | ||||
\(623\) | 15.2802 | − | 22.1402i | 0.612188 | − | 0.887027i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.3977 | + | 33.5978i | −0.775907 | + | 1.34391i | ||||
\(626\) | −14.4394 | − | 9.89602i | −0.577116 | − | 0.395524i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.2910 | + | 29.1845i | 0.450561 | + | 1.16459i | ||||
\(629\) | − | 23.8448i | − | 0.950755i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.5175i | 1.13526i | 0.823283 | + | 0.567631i | \(0.192140\pi\) | ||||
−0.823283 | + | 0.567631i | \(0.807860\pi\) | |||||||
\(632\) | −11.0246 | + | 11.7096i | −0.438534 | + | 0.465784i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.7474 | + | 21.5181i | −0.585693 | + | 0.854594i | ||||
\(635\) | 29.5062 | − | 51.1062i | 1.17092 | − | 2.02809i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.30918 | − | 1.18691i | −0.289600 | − | 0.0470269i | ||||
\(638\) | −5.82581 | − | 12.1728i | −0.230646 | − | 0.481928i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.4084 | − | 21.8690i | 1.55775 | − | 0.864447i | ||||
\(641\) | −19.9029 | + | 11.4909i | −0.786116 | + | 0.453864i | −0.838593 | − | 0.544758i | \(-0.816622\pi\) |
0.0524773 | + | 0.998622i | \(0.483288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.79085i | − | 0.110060i | −0.998485 | − | 0.0550302i | \(-0.982474\pi\) | ||
0.998485 | − | 0.0550302i | \(-0.0175255\pi\) | |||||||
\(644\) | 23.0758 | + | 21.8684i | 0.909315 | + | 0.861735i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.210507 | + | 2.72046i | −0.00828227 | + | 0.107035i | ||||
\(647\) | −20.5616 | − | 35.6137i | −0.808359 | − | 1.40012i | −0.914000 | − | 0.405715i | \(-0.867023\pi\) |
0.105640 | − | 0.994404i | \(-0.466311\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.54909 | + | 14.8075i | −0.335581 | + | 0.581244i | ||||
\(650\) | −14.6675 | + | 7.01970i | −0.575305 | + | 0.275335i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.2902 | + | 9.09353i | 0.442156 | + | 0.356130i | ||||
\(653\) | 20.8186 | + | 12.0196i | 0.814694 | + | 0.470364i | 0.848583 | − | 0.529062i | \(-0.177456\pi\) |
−0.0338892 | + | 0.999426i | \(0.510789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.45650 | − | 4.88236i | 0.330423 | − | 0.190770i | ||||
\(656\) | 7.53005 | − | 23.5967i | 0.293999 | − | 0.921294i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.59918 | − | 11.8386i | 0.374215 | − | 0.461517i | ||||
\(659\) | −15.0431 | −0.585995 | −0.292997 | − | 0.956113i | \(-0.594653\pi\) | ||||
−0.292997 | + | 0.956113i | \(0.594653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7083 | − | 18.5474i | −0.416506 | − | 0.721409i | 0.579079 | − | 0.815271i | \(-0.303412\pi\) |
−0.995585 | + | 0.0938618i | \(0.970079\pi\) | |||||||
\(662\) | 20.5230 | − | 29.9454i | 0.797648 | − | 1.16386i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.12555 | − | 9.00997i | 0.0824874 | − | 0.349655i | ||||
\(665\) | 6.90533 | − | 3.27716i | 0.267777 | − | 0.127083i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.5098 | + | 15.3054i | 1.02646 | + | 0.592628i | ||||
\(668\) | −35.7952 | − | 5.57296i | −1.38496 | − | 0.215624i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.51031 | − | 32.4418i | 0.0969817 | − | 1.25333i | ||||
\(671\) | −19.5262 | −0.753802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.0940 | −1.04440 | −0.522198 | − | 0.852824i | \(-0.674888\pi\) | ||||
−0.522198 | + | 0.852824i | \(0.674888\pi\) | |||||||
\(674\) | −0.122765 | + | 1.58655i | −0.00472874 | + | 0.0611115i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.4791 | + | 3.65546i | 0.903041 | + | 0.140595i | ||||
\(677\) | 40.0846 | + | 23.1429i | 1.54058 | + | 0.889453i | 0.998802 | + | 0.0489293i | \(0.0155809\pi\) |
0.541775 | + | 0.840523i | \(0.317752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.433479 | + | 5.37386i | −0.0166354 | + | 0.206230i | ||||
\(680\) | 6.88288 | − | 29.1758i | 0.263947 | − | 1.11884i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.01792 | − | 8.78084i | 0.230438 | − | 0.336236i | ||||
\(683\) | 17.3257 | + | 30.0090i | 0.662949 | + | 1.14826i | 0.979837 | + | 0.199799i | \(0.0640288\pi\) |
−0.316888 | + | 0.948463i | \(0.602638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.46949 | 0.0943544 | ||||||||
\(686\) | −24.8727 | − | 8.20657i | −0.949645 | − | 0.313328i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.9660 | + | 46.8983i | −0.570572 | + | 1.78798i | ||||
\(689\) | −11.8865 | + | 6.86269i | −0.452841 | + | 0.261448i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5595 | + | 8.98330i | 0.591913 | + | 0.341741i | 0.765853 | − | 0.643015i | \(-0.222317\pi\) |
−0.173941 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(692\) | −16.6607 | − | 13.4192i | −0.633346 | − | 0.510122i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.81735 | + | 1.34836i | −0.106945 | + | 0.0511830i | ||||
\(695\) | −3.99704 | + | 6.92307i | −0.151616 | + | 0.262607i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.23716 | − | 14.2672i | −0.312005 | − | 0.540408i | ||||
\(698\) | −1.67336 | + | 21.6255i | −0.0633377 | + | 0.818539i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −55.1354 | + | 16.3726i | −2.08392 | + | 0.618826i | ||||
\(701\) | − | 2.58336i | − | 0.0975721i | −0.998809 | − | 0.0487861i | \(-0.984465\pi\) | ||
0.998809 | − | 0.0487861i | \(-0.0155353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.62899 | − | 3.24990i | 0.212302 | − | 0.122572i | ||||
\(704\) | −0.902185 | − | 14.9563i | −0.0340024 | − | 0.563686i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.7124 | − | 43.2779i | −0.779520 | − | 1.62878i | ||||
\(707\) | 11.4042 | + | 24.0300i | 0.428900 | + | 0.903740i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.03512 | − | 13.9172i | 0.301765 | − | 0.522673i | −0.674771 | − | 0.738027i | \(-0.735757\pi\) |
0.976536 | + | 0.215355i | \(0.0690908\pi\) | |||||||
\(710\) | −19.8764 | + | 29.0019i | −0.745947 | + | 1.08842i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.7136 | − | 20.9386i | 0.738799 | − | 0.784708i | ||||
\(713\) | 24.1462i | 0.904283i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.89267i | 0.295169i | ||||||||
\(716\) | 16.8300 | + | 43.5015i | 0.628968 | + | 1.62573i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.12940 | − | 5.57146i | −0.303386 | − | 0.207925i | ||||
\(719\) | −12.9613 | + | 22.4496i | −0.483374 | + | 0.837229i | −0.999818 | − | 0.0190926i | \(-0.993922\pi\) |
0.516444 | + | 0.856321i | \(0.327256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4026 | + | 20.8686i | −0.536380 | + | 0.777186i | ||||
\(722\) | 23.5664 | − | 11.2786i | 0.877050 | − | 0.419748i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.73379 | + | 0.892694i | 0.213095 | + | 0.0331767i | ||||
\(725\) | −47.9592 | + | 27.6892i | −1.78116 | + | 1.02835i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.7464i | − | 0.880706i | −0.897825 | − | 0.440353i | \(-0.854853\pi\) | ||
0.897825 | − | 0.440353i | \(-0.145147\pi\) | |||||||
\(728\) | −7.53361 | − | 2.43122i | −0.279214 | − | 0.0901071i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 82.7990 | + | 6.40690i | 3.06453 | + | 0.237130i | ||||
\(731\) | 16.3713 | + | 28.3560i | 0.605516 | + | 1.04878i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.21172 | − | 15.9552i | 0.340243 | − | 0.589318i | −0.644235 | − | 0.764828i | \(-0.722824\pi\) |
0.984478 | + | 0.175510i | \(0.0561574\pi\) | |||||||
\(734\) | 1.16804 | + | 2.44058i | 0.0431131 | + | 0.0900835i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8667 | + | 26.8270i | 0.769157 | + | 0.988857i | ||||
\(737\) | −9.36828 | − | 5.40878i | −0.345085 | − | 0.199235i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.1438 | + | 7.01125i | −0.446718 | + | 0.257913i | −0.706443 | − | 0.707770i | \(-0.749701\pi\) |
0.259725 | + | 0.965683i | \(0.416368\pi\) | |||||||
\(740\) | −66.5971 | + | 25.7654i | −2.44816 | + | 0.947154i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −45.3340 | + | 17.3690i | −1.66426 | + | 0.637637i | ||||
\(743\) | 49.8064 | 1.82722 | 0.913610 | − | 0.406592i | \(-0.133283\pi\) | ||||
0.913610 | + | 0.406592i | \(0.133283\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.8440 | − | 23.9785i | −0.507205 | − | 0.878506i | ||||
\(746\) | −9.54087 | − | 6.53881i | −0.349316 | − | 0.239403i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.76134 | − | 6.25129i | −0.283783 | − | 0.228570i | ||||
\(749\) | −9.64572 | − | 6.65706i | −0.352447 | − | 0.243244i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.68526 | − | 0.972983i | −0.0614959 | − | 0.0355047i | 0.468937 | − | 0.883232i | \(-0.344637\pi\) |
−0.530433 | + | 0.847727i | \(0.677971\pi\) | |||||||
\(752\) | 12.0510 | − | 10.9661i | 0.439455 | − | 0.399892i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.59941 | − | 0.588034i | −0.276754 | − | 0.0214149i | ||||
\(755\) | 59.5319 | 2.16659 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.74999 | 0.245333 | 0.122666 | − | 0.992448i | \(-0.460855\pi\) | ||||
0.122666 | + | 0.992448i | \(0.460855\pi\) | |||||||
\(758\) | 24.2188 | + | 1.87402i | 0.879665 | + | 0.0680675i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.82556 | − | 2.35165i | 0.283863 | − | 0.0853033i | ||||
\(761\) | 29.0741 | + | 16.7859i | 1.05393 | + | 0.608489i | 0.923748 | − | 0.383000i | \(-0.125109\pi\) |
0.130186 | + | 0.991490i | \(0.458443\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.2921 | − | 7.73198i | 0.589815 | − | 0.279917i | ||||
\(764\) | −11.6643 | + | 14.4819i | −0.422000 | + | 0.523938i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.8623 | − | 18.4100i | −0.970575 | − | 0.665180i | ||||
\(767\) | 4.82858 | + | 8.36335i | 0.174350 | + | 0.301983i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.09355 | 0.327922 | 0.163961 | − | 0.986467i | \(-0.447573\pi\) | ||||
0.163961 | + | 0.986467i | \(0.447573\pi\) | |||||||
\(770\) | −4.38468 | + | 27.5703i | −0.158013 | + | 0.993565i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.11408 | − | 13.2186i | −0.184060 | − | 0.475749i | ||||
\(773\) | 9.08272 | − | 5.24391i | 0.326683 | − | 0.188610i | −0.327685 | − | 0.944787i | \(-0.606268\pi\) |
0.654367 | + | 0.756177i | \(0.272935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.8308 | − | 21.8416i | −1.35892 | − | 0.784574i | ||||
\(776\) | −1.32336 | + | 5.60957i | −0.0475058 | + | 0.201372i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.5873 | − | 24.2113i | −0.415424 | − | 0.868016i | ||||
\(779\) | 2.24535 | − | 3.88906i | 0.0804480 | − | 0.139340i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.84440 | + | 10.1228i | 0.209129 | + | 0.362222i | ||||
\(782\) | 22.5379 | + | 1.74396i | 0.805955 | + | 0.0623639i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.9654 | − | 12.6778i | −0.891622 | − | 0.452780i | ||||
\(785\) | − | 62.3289i | − | 2.22461i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.11401 | + | 4.10728i | −0.253587 | + | 0.146409i | −0.621406 | − | 0.783489i | \(-0.713438\pi\) |
0.367819 | + | 0.929898i | \(0.380105\pi\) | |||||||
\(788\) | −1.24029 | + | 7.96643i | −0.0441836 | + | 0.283792i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 28.8953 | − | 13.8290i | 1.02805 | − | 0.492013i | ||||
\(791\) | −29.1635 | − | 2.35246i | −1.03693 | − | 0.0836438i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.51427 | + | 9.55100i | −0.195818 | + | 0.339166i | ||||
\(794\) | 39.8669 | + | 27.3226i | 1.41482 | + | 0.969644i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 42.1480 | − | 16.3064i | 1.49390 | − | 0.577964i | ||||
\(797\) | 27.6583i | 0.979709i | 0.871804 | + | 0.489854i | \(0.162950\pi\) | ||||
−0.871804 | + | 0.489854i | \(0.837050\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.8372i | − | 0.383392i | ||||||
\(800\) | −60.9060 | + | 8.42611i | −2.15335 | + | 0.297908i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.5258 | − | 15.3584i | 0.371680 | − | 0.542323i | ||||
\(803\) | 13.8045 | − | 23.9101i | 0.487150 | − | 0.843768i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.1499 | − | 57.2079i | −0.956909 | − | 2.01631i | ||||
\(806\) | −2.59555 | − | 5.42332i | −0.0914243 | − | 0.191028i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.18354 | + | 27.2323i | 0.287896 | + | 0.958028i | ||||
\(809\) | 30.5781 | − | 17.6543i | 1.07507 | − | 0.620691i | 0.145507 | − | 0.989357i | \(-0.453519\pi\) |
0.929562 | + | 0.368666i | \(0.120185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.31379i | 0.116363i | 0.998306 | + | 0.0581815i | \(0.0185302\pi\) | ||||
−0.998306 | + | 0.0581815i | \(0.981470\pi\) | |||||||
\(812\) | −26.2192 | − | 6.27586i | −0.920115 | − | 0.220239i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.83147 | + | 23.6688i | −0.0641928 | + | 0.829591i | ||||
\(815\) | −14.4376 | − | 25.0066i | −0.505726 | − | 0.875943i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.46263 | + | 7.72950i | −0.156128 | + | 0.270421i | ||||
\(818\) | −35.6117 | + | 17.0434i | −1.24513 | + | 0.595909i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −30.9468 | + | 38.4222i | −1.08071 | + | 1.34176i | ||||
\(821\) | −9.83140 | − | 5.67616i | −0.343118 | − | 0.198099i | 0.318532 | − | 0.947912i | \(-0.396810\pi\) |
−0.661650 | + | 0.749813i | \(0.730144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.0277 | − | 19.0685i | 1.15127 | − | 0.664687i | 0.202075 | − | 0.979370i | \(-0.435231\pi\) |
0.949197 | + | 0.314682i | \(0.101898\pi\) | |||||||
\(824\) | −18.5814 | + | 19.7360i | −0.647313 | + | 0.687537i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.2208 | + | 31.8969i | 0.425217 | + | 1.10984i | ||||
\(827\) | 9.51543 | 0.330884 | 0.165442 | − | 0.986220i | \(-0.447095\pi\) | ||||
0.165442 | + | 0.986220i | \(0.447095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.5375 | + | 25.1798i | 0.504910 | + | 0.874529i | 0.999984 | + | 0.00567849i | \(0.00180753\pi\) |
−0.495074 | + | 0.868851i | \(0.664859\pi\) | |||||||
\(830\) | −10.4239 | + | 15.2096i | −0.361818 | + | 0.527934i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.57045 | − | 3.78241i | −0.262458 | − | 0.131132i | ||||
\(833\) | −17.4123 | + | 6.60613i | −0.603299 | + | 0.228889i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 62.4893 | + | 36.0782i | 2.16253 | + | 1.24854i | ||||
\(836\) | 0.417906 | − | 2.68422i | 0.0144536 | − | 0.0928355i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.51904 | − | 45.4780i | 0.121563 | − | 1.57101i | ||||
\(839\) | 1.01793 | 0.0351429 | 0.0175715 | − | 0.999846i | \(-0.494407\pi\) | ||||
0.0175715 | + | 0.999846i | \(0.494407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.04159 | 0.104883 | ||||||||
\(842\) | 2.21998 | − | 28.6897i | 0.0765054 | − | 0.988711i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.08594 | + | 6.97502i | −0.0373797 | + | 0.240090i | ||||
\(845\) | −40.9884 | − | 23.6647i | −1.41004 | − | 0.814090i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.3141 | − | 11.2593i | −0.560560 | − | 0.386874i | ||||
\(848\) | −50.7078 | + | 11.0573i | −1.74131 | + | 0.379710i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23.1192 | + | 33.7335i | −0.792981 | + | 1.15705i | ||||
\(851\) | −26.9241 | − | 46.6339i | −0.922946 | − | 1.59859i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2563 | 0.453887 | 0.226944 | − | 0.973908i | \(-0.427127\pi\) | ||||
0.226944 | + | 0.973908i | \(0.427127\pi\) | |||||||
\(854\) | −24.5682 | + | 30.2997i | −0.840705 | + | 1.03684i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.12224 | − | 8.58856i | −0.311792 | − | 0.293551i | ||||
\(857\) | −20.4031 | + | 11.7797i | −0.696956 | + | 0.402388i | −0.806213 | − | 0.591626i | \(-0.798486\pi\) |
0.109257 | + | 0.994014i | \(0.465153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.285175 | + | 0.164646i | 0.00973004 | + | 0.00561764i | 0.504857 | − | 0.863203i | \(-0.331545\pi\) |
−0.495127 | + | 0.868821i | \(0.664879\pi\) | |||||||
\(860\) | 61.5067 | − | 76.3641i | 2.09736 | − | 2.60399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.2470 | + | 14.4759i | −1.03022 | + | 0.493052i | ||||
\(863\) | 25.0532 | − | 43.3934i | 0.852820 | − | 1.47713i | −0.0258325 | − | 0.999666i | \(-0.508224\pi\) |
0.878653 | − | 0.477462i | \(-0.158443\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.3053 | + | 36.9019i | 0.724403 | + | 1.25470i | ||||
\(866\) | −1.35859 | + | 17.5577i | −0.0461669 | + | 0.596634i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.05380 | − | 20.3864i | −0.205479 | − | 0.691960i | ||||
\(869\) | − | 10.6498i | − | 0.361268i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.29127 | + | 3.05491i | −0.179288 | + | 0.103512i | ||||
\(872\) | 18.4633 | − | 5.54838i | 0.625245 | − | 0.187892i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.66009 | + | 5.55818i | 0.0899789 | + | 0.188008i | ||||
\(875\) | 61.6605 | + | 4.97381i | 2.08450 | + | 0.168145i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.33001 | + | 12.6959i | −0.247517 | + | 0.428712i | −0.962836 | − | 0.270086i | \(-0.912948\pi\) |
0.715319 | + | 0.698798i | \(0.246281\pi\) | |||||||
\(878\) | −1.22675 | + | 1.78997i | −0.0414008 | + | 0.0604086i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.07300 | + | 28.4317i | −0.305851 | + | 0.958434i | ||||
\(881\) | 37.4296i | 1.26104i | 0.776174 | + | 0.630518i | \(0.217158\pi\) | ||||
−0.776174 | + | 0.630518i | \(0.782842\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.1664i | − | 1.11614i | −0.829794 | − | 0.558070i | \(-0.811542\pi\) | ||
0.829794 | − | 0.558070i | \(-0.188458\pi\) | |||||||
\(884\) | −5.24956 | + | 2.03097i | −0.176562 | + | 0.0683089i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.2033 | − | 23.4411i | −1.14908 | − | 0.787520i | ||||
\(887\) | −10.7263 | + | 18.5785i | −0.360154 | + | 0.623804i | −0.987986 | − | 0.154544i | \(-0.950609\pi\) |
0.627832 | + | 0.778349i | \(0.283942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.0665 | − | 3.15128i | −1.31025 | − | 0.105691i | ||||
\(890\) | −51.6691 | + | 24.7283i | −1.73195 | + | 0.828896i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.59079 | − | 10.2177i | 0.0532635 | − | 0.342112i | ||||
\(893\) | 2.55831 | − | 1.47704i | 0.0856107 | − | 0.0494274i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 92.9056i | − | 3.10549i | ||||||
\(896\) | −24.3435 | − | 17.4182i | −0.813259 | − | 0.581902i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.06213 | − | 0.469081i | −0.202296 | − | 0.0156535i | ||||
\(899\) | −10.2382 | − | 17.7330i | −0.341462 | − | 0.591429i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.2596 | + | 29.8945i | −0.575001 | + | 0.995931i | ||||
\(902\) | 7.08053 | + | 14.7945i | 0.235756 | + | 0.492604i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.4427 | − | 7.18177i | −1.01251 | − | 0.238862i | ||||
\(905\) | −10.0097 | − | 5.77912i | −0.332735 | − | 0.192104i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.53272 | − | 2.61697i | 0.150507 | − | 0.0868951i | −0.422855 | − | 0.906197i | \(-0.638972\pi\) |
0.573362 | + | 0.819302i | \(0.305639\pi\) | |||||||
\(908\) | −14.8196 | − | 38.3049i | −0.491805 | − | 1.27119i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.2474 | + | 9.93065i | 0.405998 | + | 0.329198i | ||||
\(911\) | 43.4199 | 1.43857 | 0.719283 | − | 0.694717i | \(-0.244471\pi\) | ||||
0.719283 | + | 0.694717i | \(0.244471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.06501 | + | 5.30875i | 0.101437 | + | 0.175694i | ||||
\(914\) | −5.42334 | − | 3.71687i | −0.179388 | − | 0.122943i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.8080 | + | 15.9019i | −0.423189 | + | 0.525414i | ||||
\(917\) | −5.33753 | − | 3.68373i | −0.176261 | − | 0.121648i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3771 | − | 8.30065i | −0.474258 | − | 0.273813i | 0.243762 | − | 0.969835i | \(-0.421618\pi\) |
−0.718021 | + | 0.696022i | \(0.754952\pi\) | |||||||
\(920\) | −19.4825 | − | 64.8315i | −0.642317 | − | 2.13743i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.1715 | + | 2.64415i | 1.12538 | + | 0.0870806i | ||||
\(923\) | 6.60190 | 0.217304 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 97.4174 | 3.20307 | ||||||||
\(926\) | 26.4056 | + | 2.04324i | 0.867741 | + | 0.0671449i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.6994 | − | 10.8542i | −0.876450 | − | 0.356305i | ||||
\(929\) | −19.1671 | − | 11.0661i | −0.628851 | − | 0.363067i | 0.151456 | − | 0.988464i | \(-0.451604\pi\) |
−0.780307 | + | 0.625397i | \(0.784937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.93268 | − | 3.21010i | −0.128888 | − | 0.105207i | ||||
\(932\) | −9.75205 | − | 7.85469i | −0.319439 | − | 0.257289i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.6665 | + | 14.8491i | 0.708951 | + | 0.485877i | ||||
\(935\) | 9.92500 | + | 17.1906i | 0.324582 | + | 0.562193i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.3303 | 0.762167 | 0.381083 | − | 0.924541i | \(-0.375551\pi\) | ||||
0.381083 | + | 0.924541i | \(0.375551\pi\) | |||||||
\(938\) | −20.1803 | + | 7.73179i | −0.658911 | + | 0.252452i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.2676 | + | 11.7101i | −0.987221 | + | 0.381940i | ||||
\(941\) | −37.7784 | + | 21.8114i | −1.23154 | + | 0.711030i | −0.967351 | − | 0.253441i | \(-0.918438\pi\) |
−0.264190 | + | 0.964471i | \(0.585104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.2193 | − | 18.6018i | −1.04920 | − | 0.605758i | ||||
\(944\) | 7.77992 | + | 35.6780i | 0.253215 | + | 1.16122i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.0725 | − | 29.4041i | −0.457538 | − | 0.956011i | ||||
\(947\) | 12.6981 | − | 21.9938i | 0.412634 | − | 0.714702i | −0.582543 | − | 0.812800i | \(-0.697942\pi\) |
0.995177 | + | 0.0980973i | \(0.0312756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.79686 | − | 13.5046i | −0.253097 | − | 0.438377i | ||||
\(950\) | −11.1144 | − | 0.860021i | −0.360599 | − | 0.0279028i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.4658 | + | 4.17817i | −0.630890 | + | 0.135415i | ||||
\(953\) | − | 1.61704i | − | 0.0523809i | −0.999657 | − | 0.0261905i | \(-0.991662\pi\) | ||
0.999657 | − | 0.0261905i | \(-0.00833763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.0761 | − | 18.5191i | 1.03796 | − | 0.599265i | ||||
\(956\) | 9.86680 | + | 1.53616i | 0.319115 | + | 0.0496830i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.3901 | − | 6.40838i | 0.432615 | − | 0.207045i | ||||
\(959\) | −0.703204 | − | 1.48173i | −0.0227077 | − | 0.0478475i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.42402 | + | 12.8588i | −0.239485 | + | 0.414799i | ||||
\(962\) | 11.0601 | + | 7.57998i | 0.356591 | + | 0.244388i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.03095 | − | 13.0038i | −0.162036 | − | 0.418823i | ||||
\(965\) | 28.2309i | 0.908783i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.8714i | 0.896282i | 0.893963 | + | 0.448141i | \(0.147914\pi\) | ||||
−0.893963 | + | 0.448141i | \(0.852086\pi\) | |||||||
\(968\) | −15.4288 | − | 14.5261i | −0.495899 | − | 0.466887i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.48986 | − | 9.46946i | 0.208377 | − | 0.304046i | ||||
\(971\) | −14.9960 | + | 25.9738i | −0.481243 | + | 0.833538i | −0.999768 | − | 0.0215245i | \(-0.993148\pi\) |
0.518525 | + | 0.855062i | \(0.326481\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.29212 | + | 0.426886i | 0.169658 | + | 0.0136853i | ||||
\(974\) | 16.5329 | + | 34.5450i | 0.529748 | + | 1.10689i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.8434 | + | 28.0666i | −0.987273 | + | 0.898391i | ||||
\(977\) | 2.90454 | − | 1.67694i | 0.0929246 | − | 0.0536500i | −0.452818 | − | 0.891603i | \(-0.649581\pi\) |
0.545742 | + | 0.837953i | \(0.316248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.0434i | 0.608629i | ||||||||
\(980\) | 37.2652 | + | 41.4932i | 1.19039 | + | 1.32545i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.915631 | + | 11.8331i | −0.0292190 | + | 0.377609i | ||||
\(983\) | 13.4540 | + | 23.3029i | 0.429115 | + | 0.743249i | 0.996795 | − | 0.0800007i | \(-0.0254923\pi\) |
−0.567680 | + | 0.823249i | \(0.692159\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.02941 | − | 13.9073i | 0.255838 | − | 0.443125i | ||||
\(986\) | −17.2913 | + | 8.27547i | −0.550668 | + | 0.263545i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.19493 | − | 0.962444i | −0.0380158 | − | 0.0306194i | ||||
\(989\) | 64.0357 | + | 36.9710i | 2.03622 | + | 1.17561i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.8246 | + | 20.6834i | −1.13801 | + | 0.657029i | −0.945936 | − | 0.324352i | \(-0.894854\pi\) |
−0.192071 | + | 0.981381i | \(0.561520\pi\) | |||||||
\(992\) | −3.11557 | − | 22.5201i | −0.0989195 | − | 0.715015i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 23.0615 | + | 3.66761i | 0.731466 | + | 0.116329i | ||||
\(995\) | −90.0148 | −2.85366 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.74005 | − | 13.4062i | −0.245130 | − | 0.424577i | 0.717038 | − | 0.697034i | \(-0.245497\pi\) |
−0.962168 | + | 0.272457i | \(0.912164\pi\) | |||||||
\(998\) | 14.2775 | − | 20.8325i | 0.451946 | − | 0.659441i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.be.c.107.7 | ✓ | 28 | |
3.2 | odd | 2 | inner | 756.2.be.c.107.8 | yes | 28 | |
4.3 | odd | 2 | 756.2.be.d.107.12 | yes | 28 | ||
7.4 | even | 3 | 756.2.be.d.431.3 | yes | 28 | ||
12.11 | even | 2 | 756.2.be.d.107.3 | yes | 28 | ||
21.11 | odd | 6 | 756.2.be.d.431.12 | yes | 28 | ||
28.11 | odd | 6 | inner | 756.2.be.c.431.8 | yes | 28 | |
84.11 | even | 6 | inner | 756.2.be.c.431.7 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.be.c.107.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
756.2.be.c.107.8 | yes | 28 | 3.2 | odd | 2 | inner | |
756.2.be.c.431.7 | yes | 28 | 84.11 | even | 6 | inner | |
756.2.be.c.431.8 | yes | 28 | 28.11 | odd | 6 | inner | |
756.2.be.d.107.3 | yes | 28 | 12.11 | even | 2 | ||
756.2.be.d.107.12 | yes | 28 | 4.3 | odd | 2 | ||
756.2.be.d.431.3 | yes | 28 | 7.4 | even | 3 | ||
756.2.be.d.431.12 | yes | 28 | 21.11 | odd | 6 |