Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(218,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.r (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 218.8 | ||
Character | \(\chi\) | \(=\) | 403.218 |
Dual form | 403.2.r.a.342.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56202 | + | 0.901835i | −1.10452 | + | 0.637694i | −0.937404 | − | 0.348244i | \(-0.886778\pi\) |
−0.167114 | + | 0.985938i | \(0.553445\pi\) | |||||||
\(3\) | 0.553992 | + | 0.959542i | 0.319847 | + | 0.553992i | 0.980456 | − | 0.196739i | \(-0.0630351\pi\) |
−0.660609 | + | 0.750730i | \(0.729702\pi\) | |||||||
\(4\) | 0.626612 | − | 1.08532i | 0.313306 | − | 0.542662i | ||||
\(5\) | 0.771735i | 0.345130i | 0.984998 | + | 0.172565i | \(0.0552055\pi\) | ||||
−0.984998 | + | 0.172565i | \(0.944794\pi\) | |||||||
\(6\) | −1.73070 | − | 0.999218i | −0.706554 | − | 0.407929i | ||||
\(7\) | 3.80672 | + | 2.19781i | 1.43881 | + | 0.830695i | 0.997767 | − | 0.0667923i | \(-0.0212765\pi\) |
0.441040 | + | 0.897488i | \(0.354610\pi\) | |||||||
\(8\) | − | 1.34694i | − | 0.476214i | ||||||
\(9\) | 0.886187 | − | 1.53492i | 0.295396 | − | 0.511640i | ||||
\(10\) | −0.695977 | − | 1.20547i | −0.220087 | − | 0.381202i | ||||
\(11\) | 4.70330 | − | 2.71545i | 1.41810 | − | 0.818740i | 0.421967 | − | 0.906611i | \(-0.361340\pi\) |
0.996132 | + | 0.0878717i | \(0.0280066\pi\) | |||||||
\(12\) | 1.38855 | 0.400840 | ||||||||
\(13\) | 3.40753 | − | 1.17844i | 0.945080 | − | 0.326840i | ||||
\(14\) | −7.92826 | −2.11892 | ||||||||
\(15\) | −0.740511 | + | 0.427534i | −0.191199 | + | 0.110389i | ||||
\(16\) | 2.46794 | + | 4.27460i | 0.616985 | + | 1.06865i | ||||
\(17\) | −0.585633 | + | 1.01435i | −0.142037 | + | 0.246015i | −0.928263 | − | 0.371923i | \(-0.878698\pi\) |
0.786227 | + | 0.617938i | \(0.212032\pi\) | |||||||
\(18\) | 3.19678i | 0.753487i | ||||||||
\(19\) | −5.24197 | − | 3.02646i | −1.20259 | − | 0.694316i | −0.241461 | − | 0.970411i | \(-0.577626\pi\) |
−0.961131 | + | 0.276094i | \(0.910960\pi\) | |||||||
\(20\) | 0.837582 | + | 0.483578i | 0.187289 | + | 0.108131i | ||||
\(21\) | 4.87028i | 1.06278i | ||||||||
\(22\) | −4.89778 | + | 8.48320i | −1.04421 | + | 1.80862i | ||||
\(23\) | −0.575237 | − | 0.996341i | −0.119945 | − | 0.207751i | 0.799800 | − | 0.600266i | \(-0.204939\pi\) |
−0.919746 | + | 0.392515i | \(0.871605\pi\) | |||||||
\(24\) | 1.29244 | − | 0.746191i | 0.263819 | − | 0.152316i | ||||
\(25\) | 4.40443 | 0.880885 | ||||||||
\(26\) | −4.25989 | + | 4.91378i | −0.835433 | + | 0.963672i | ||||
\(27\) | 5.28771 | 1.01762 | ||||||||
\(28\) | 4.77068 | − | 2.75435i | 0.901574 | − | 0.520524i | ||||
\(29\) | −2.41217 | − | 4.17801i | −0.447929 | − | 0.775836i | 0.550322 | − | 0.834953i | \(-0.314505\pi\) |
−0.998251 | + | 0.0591165i | \(0.981172\pi\) | |||||||
\(30\) | 0.771131 | − | 1.33564i | 0.140789 | − | 0.243853i | ||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | −5.37700 | − | 3.10441i | −0.950528 | − | 0.548787i | ||||
\(33\) | 5.21118 | + | 3.00868i | 0.907150 | + | 0.523743i | ||||
\(34\) | − | 2.11258i | − | 0.362304i | ||||||
\(35\) | −1.69613 | + | 2.93778i | −0.286698 | + | 0.496576i | ||||
\(36\) | −1.11059 | − | 1.92360i | −0.185098 | − | 0.320600i | ||||
\(37\) | −5.52259 | + | 3.18847i | −0.907909 | + | 0.524181i | −0.879758 | − | 0.475422i | \(-0.842295\pi\) |
−0.0281510 | + | 0.999604i | \(0.508962\pi\) | |||||||
\(38\) | 10.9175 | 1.77104 | ||||||||
\(39\) | 3.01851 | + | 2.61682i | 0.483348 | + | 0.419027i | ||||
\(40\) | 1.03948 | 0.164356 | ||||||||
\(41\) | −10.1628 | + | 5.86751i | −1.58717 | + | 0.916350i | −0.593394 | + | 0.804912i | \(0.702212\pi\) |
−0.993771 | + | 0.111438i | \(0.964454\pi\) | |||||||
\(42\) | −4.39219 | − | 7.60749i | −0.677729 | − | 1.17386i | ||||
\(43\) | −2.82424 | + | 4.89172i | −0.430692 | + | 0.745981i | −0.996933 | − | 0.0782590i | \(-0.975064\pi\) |
0.566241 | + | 0.824240i | \(0.308397\pi\) | |||||||
\(44\) | − | 6.80614i | − | 1.02606i | ||||||
\(45\) | 1.18455 | + | 0.683901i | 0.176582 | + | 0.101950i | ||||
\(46\) | 1.79707 | + | 1.03754i | 0.264963 | + | 0.152977i | ||||
\(47\) | − | 4.06481i | − | 0.592914i | −0.955046 | − | 0.296457i | \(-0.904195\pi\) | ||
0.955046 | − | 0.296457i | \(-0.0958052\pi\) | |||||||
\(48\) | −2.73443 | + | 4.73618i | −0.394682 | + | 0.683609i | ||||
\(49\) | 6.16077 | + | 10.6708i | 0.880109 | + | 1.52439i | ||||
\(50\) | −6.87982 | + | 3.97206i | −0.972953 | + | 0.561735i | ||||
\(51\) | −1.29774 | −0.181720 | ||||||||
\(52\) | 0.856214 | − | 4.43670i | 0.118735 | − | 0.615260i | ||||
\(53\) | 1.26335 | 0.173535 | 0.0867674 | − | 0.996229i | \(-0.472346\pi\) | ||||
0.0867674 | + | 0.996229i | \(0.472346\pi\) | |||||||
\(54\) | −8.25953 | + | 4.76864i | −1.12398 | + | 0.648930i | ||||
\(55\) | 2.09561 | + | 3.62970i | 0.282572 | + | 0.489429i | ||||
\(56\) | 2.96031 | − | 5.12742i | 0.395589 | − | 0.685180i | ||||
\(57\) | − | 6.70652i | − | 0.888301i | ||||||
\(58\) | 7.53574 | + | 4.35076i | 0.989491 | + | 0.571283i | ||||
\(59\) | −7.47234 | − | 4.31416i | −0.972816 | − | 0.561656i | −0.0727223 | − | 0.997352i | \(-0.523169\pi\) |
−0.900094 | + | 0.435697i | \(0.856502\pi\) | |||||||
\(60\) | 1.07159i | 0.138342i | ||||||||
\(61\) | −0.487781 | + | 0.844861i | −0.0624540 | + | 0.108173i | −0.895562 | − | 0.444937i | \(-0.853226\pi\) |
0.833108 | + | 0.553111i | \(0.186559\pi\) | |||||||
\(62\) | −0.901835 | − | 1.56202i | −0.114533 | − | 0.198377i | ||||
\(63\) | 6.74694 | − | 3.89535i | 0.850034 | − | 0.490767i | ||||
\(64\) | 1.32691 | 0.165863 | ||||||||
\(65\) | 0.909442 | + | 2.62971i | 0.112802 | + | 0.326176i | ||||
\(66\) | −10.8533 | −1.33595 | ||||||||
\(67\) | −7.34983 | + | 4.24343i | −0.897925 | + | 0.518417i | −0.876526 | − | 0.481354i | \(-0.840145\pi\) |
−0.0213986 | + | 0.999771i | \(0.506812\pi\) | |||||||
\(68\) | 0.733929 | + | 1.27120i | 0.0890020 | + | 0.154156i | ||||
\(69\) | 0.637353 | − | 1.10393i | 0.0767283 | − | 0.132897i | ||||
\(70\) | − | 6.11851i | − | 0.731302i | ||||||
\(71\) | −3.32559 | − | 1.92003i | −0.394675 | − | 0.227866i | 0.289509 | − | 0.957175i | \(-0.406508\pi\) |
−0.684184 | + | 0.729309i | \(0.739841\pi\) | |||||||
\(72\) | −2.06744 | − | 1.19364i | −0.243650 | − | 0.140671i | ||||
\(73\) | 4.37422i | 0.511964i | 0.966682 | + | 0.255982i | \(0.0823988\pi\) | ||||
−0.966682 | + | 0.255982i | \(0.917601\pi\) | |||||||
\(74\) | 5.75095 | − | 9.96093i | 0.668534 | − | 1.15793i | ||||
\(75\) | 2.44001 | + | 4.22623i | 0.281749 | + | 0.488003i | ||||
\(76\) | −6.56937 | + | 3.79283i | −0.753558 | + | 0.435067i | ||||
\(77\) | 23.8722 | 2.72049 | ||||||||
\(78\) | −7.07492 | − | 1.36535i | −0.801077 | − | 0.154595i | ||||
\(79\) | 8.38024 | 0.942851 | 0.471425 | − | 0.881906i | \(-0.343740\pi\) | ||||
0.471425 | + | 0.881906i | \(0.343740\pi\) | |||||||
\(80\) | −3.29885 | + | 1.90459i | −0.368823 | + | 0.212940i | ||||
\(81\) | 0.270787 | + | 0.469016i | 0.0300874 | + | 0.0521129i | ||||
\(82\) | 10.5830 | − | 18.3304i | 1.16870 | − | 2.02425i | ||||
\(83\) | − | 12.8430i | − | 1.40971i | −0.709353 | − | 0.704853i | \(-0.751013\pi\) | ||
0.709353 | − | 0.704853i | \(-0.248987\pi\) | |||||||
\(84\) | 5.28583 | + | 3.05178i | 0.576732 | + | 0.332976i | ||||
\(85\) | −0.782805 | − | 0.451953i | −0.0849072 | − | 0.0490212i | ||||
\(86\) | − | 10.1880i | − | 1.09860i | ||||||
\(87\) | 2.67265 | − | 4.62916i | 0.286538 | − | 0.496298i | ||||
\(88\) | −3.65754 | − | 6.33505i | −0.389895 | − | 0.675318i | ||||
\(89\) | −9.37105 | + | 5.41038i | −0.993329 | + | 0.573499i | −0.906268 | − | 0.422704i | \(-0.861081\pi\) |
−0.0870612 | + | 0.996203i | \(0.527748\pi\) | |||||||
\(90\) | −2.46706 | −0.260051 | ||||||||
\(91\) | 15.5615 | + | 3.00313i | 1.63129 | + | 0.314814i | ||||
\(92\) | −1.44180 | −0.150318 | ||||||||
\(93\) | −0.959542 | + | 0.553992i | −0.0994998 | + | 0.0574463i | ||||
\(94\) | 3.66579 | + | 6.34934i | 0.378097 | + | 0.654884i | ||||
\(95\) | 2.33562 | − | 4.04541i | 0.239630 | − | 0.415051i | ||||
\(96\) | − | 6.87927i | − | 0.702112i | ||||||
\(97\) | 0.0599268 | + | 0.0345988i | 0.00608465 | + | 0.00351297i | 0.503039 | − | 0.864264i | \(-0.332215\pi\) |
−0.496955 | + | 0.867777i | \(0.665548\pi\) | |||||||
\(98\) | −19.2465 | − | 11.1120i | −1.94419 | − | 1.12248i | ||||
\(99\) | − | 9.62559i | − | 0.967408i | ||||||
\(100\) | 2.75987 | − | 4.78023i | 0.275987 | − | 0.478023i | ||||
\(101\) | 0.771499 | + | 1.33627i | 0.0767670 | + | 0.132964i | 0.901853 | − | 0.432042i | \(-0.142207\pi\) |
−0.825086 | + | 0.565007i | \(0.808874\pi\) | |||||||
\(102\) | 2.02710 | − | 1.17035i | 0.200713 | − | 0.115882i | ||||
\(103\) | −4.80271 | −0.473225 | −0.236612 | − | 0.971604i | \(-0.576037\pi\) | ||||
−0.236612 | + | 0.971604i | \(0.576037\pi\) | |||||||
\(104\) | −1.58728 | − | 4.58973i | −0.155646 | − | 0.450060i | ||||
\(105\) | −3.75856 | −0.366798 | ||||||||
\(106\) | −1.97339 | + | 1.13934i | −0.191672 | + | 0.110662i | ||||
\(107\) | 6.18532 | + | 10.7133i | 0.597957 | + | 1.03569i | 0.993122 | + | 0.117082i | \(0.0373541\pi\) |
−0.395165 | + | 0.918610i | \(0.629313\pi\) | |||||||
\(108\) | 3.31334 | − | 5.73888i | 0.318827 | − | 0.552224i | ||||
\(109\) | − | 6.83808i | − | 0.654970i | −0.944856 | − | 0.327485i | \(-0.893799\pi\) | ||
0.944856 | − | 0.327485i | \(-0.106201\pi\) | |||||||
\(110\) | −6.54678 | − | 3.77978i | −0.624211 | − | 0.360388i | ||||
\(111\) | −6.11894 | − | 3.53277i | −0.580784 | − | 0.335316i | ||||
\(112\) | 21.6963i | 2.05011i | ||||||||
\(113\) | 3.48893 | − | 6.04301i | 0.328211 | − | 0.568478i | −0.653946 | − | 0.756541i | \(-0.726888\pi\) |
0.982157 | + | 0.188063i | \(0.0602209\pi\) | |||||||
\(114\) | 6.04818 | + | 10.4757i | 0.566464 | + | 0.981144i | ||||
\(115\) | 0.768910 | − | 0.443931i | 0.0717013 | − | 0.0413967i | ||||
\(116\) | −6.04599 | −0.561356 | ||||||||
\(117\) | 1.21090 | − | 6.27461i | 0.111948 | − | 0.580088i | ||||
\(118\) | 15.5626 | 1.43266 | ||||||||
\(119\) | −4.45868 | + | 2.57422i | −0.408727 | + | 0.235979i | ||||
\(120\) | 0.575862 | + | 0.997422i | 0.0525687 | + | 0.0910517i | ||||
\(121\) | 9.24736 | − | 16.0169i | 0.840669 | − | 1.45608i | ||||
\(122\) | − | 1.75959i | − | 0.159306i | ||||||
\(123\) | −11.2602 | − | 6.50110i | −1.01530 | − | 0.586184i | ||||
\(124\) | 1.08532 | + | 0.626612i | 0.0974650 | + | 0.0562714i | ||||
\(125\) | 7.25772i | 0.649150i | ||||||||
\(126\) | −7.02592 | + | 12.1692i | −0.625918 | + | 1.08412i | ||||
\(127\) | −7.37671 | − | 12.7768i | −0.654577 | − | 1.13376i | −0.982000 | − | 0.188883i | \(-0.939513\pi\) |
0.327423 | − | 0.944878i | \(-0.393820\pi\) | |||||||
\(128\) | 8.68133 | − | 5.01217i | 0.767329 | − | 0.443017i | ||||
\(129\) | −6.25842 | −0.551023 | ||||||||
\(130\) | −3.79214 | − | 3.28750i | −0.332592 | − | 0.288333i | ||||
\(131\) | −17.3028 | −1.51175 | −0.755875 | − | 0.654716i | \(-0.772788\pi\) | ||||
−0.755875 | + | 0.654716i | \(0.772788\pi\) | |||||||
\(132\) | 6.53078 | − | 3.77055i | 0.568431 | − | 0.328184i | ||||
\(133\) | −13.3032 | − | 23.0418i | −1.15353 | − | 1.99797i | ||||
\(134\) | 7.65374 | − | 13.2567i | 0.661183 | − | 1.14520i | ||||
\(135\) | 4.08071i | 0.351211i | ||||||||
\(136\) | 1.36626 | + | 0.788810i | 0.117156 | + | 0.0676399i | ||||
\(137\) | 1.33498 | + | 0.770749i | 0.114055 | + | 0.0658495i | 0.555942 | − | 0.831221i | \(-0.312358\pi\) |
−0.441887 | + | 0.897070i | \(0.645691\pi\) | |||||||
\(138\) | 2.29915i | 0.195717i | ||||||||
\(139\) | −8.46083 | + | 14.6546i | −0.717638 | + | 1.24299i | 0.244295 | + | 0.969701i | \(0.421444\pi\) |
−0.961933 | + | 0.273285i | \(0.911890\pi\) | |||||||
\(140\) | 2.12563 | + | 3.68170i | 0.179648 | + | 0.311160i | ||||
\(141\) | 3.90036 | − | 2.25187i | 0.328469 | − | 0.189642i | ||||
\(142\) | 6.92621 | 0.581235 | ||||||||
\(143\) | 12.8267 | − | 14.7955i | 1.07262 | − | 1.23727i | ||||
\(144\) | 8.74822 | 0.729018 | ||||||||
\(145\) | 3.22431 | − | 1.86156i | 0.267764 | − | 0.154594i | ||||
\(146\) | −3.94483 | − | 6.83264i | −0.326476 | − | 0.565474i | ||||
\(147\) | −6.82602 | + | 11.8230i | −0.563001 | + | 0.975146i | ||||
\(148\) | 7.99174i | 0.656917i | ||||||||
\(149\) | 7.99695 | + | 4.61704i | 0.655136 | + | 0.378243i | 0.790421 | − | 0.612564i | \(-0.209862\pi\) |
−0.135285 | + | 0.990807i | \(0.543195\pi\) | |||||||
\(150\) | −7.62272 | − | 4.40098i | −0.622393 | − | 0.359339i | ||||
\(151\) | 21.7043i | 1.76627i | 0.469119 | + | 0.883135i | \(0.344571\pi\) | ||||
−0.469119 | + | 0.883135i | \(0.655429\pi\) | |||||||
\(152\) | −4.07644 | + | 7.06061i | −0.330643 | + | 0.572691i | ||||
\(153\) | 1.03796 | + | 1.79780i | 0.0839141 | + | 0.145343i | ||||
\(154\) | −37.2890 | + | 21.5288i | −3.00483 | + | 1.73484i | ||||
\(155\) | −0.771735 | −0.0619872 | ||||||||
\(156\) | 4.73154 | − | 1.63632i | 0.378826 | − | 0.131011i | ||||
\(157\) | 22.7044 | 1.81201 | 0.906003 | − | 0.423272i | \(-0.139119\pi\) | ||||
0.906003 | + | 0.423272i | \(0.139119\pi\) | |||||||
\(158\) | −13.0901 | + | 7.55759i | −1.04140 | + | 0.601250i | ||||
\(159\) | 0.699887 | + | 1.21224i | 0.0555046 | + | 0.0961368i | ||||
\(160\) | 2.39578 | − | 4.14961i | 0.189403 | − | 0.328056i | ||||
\(161\) | − | 5.05706i | − | 0.398552i | ||||||
\(162\) | −0.845950 | − | 0.488410i | −0.0664641 | − | 0.0383731i | ||||
\(163\) | −3.16124 | − | 1.82514i | −0.247608 | − | 0.142956i | 0.371061 | − | 0.928609i | \(-0.378994\pi\) |
−0.618668 | + | 0.785652i | \(0.712328\pi\) | |||||||
\(164\) | 14.7066i | 1.14839i | ||||||||
\(165\) | −2.32190 | + | 4.02165i | −0.180760 | + | 0.313085i | ||||
\(166\) | 11.5823 | + | 20.0611i | 0.898961 | + | 1.55705i | ||||
\(167\) | −18.0767 | + | 10.4366i | −1.39882 | + | 0.807607i | −0.994269 | − | 0.106910i | \(-0.965904\pi\) |
−0.404548 | + | 0.914517i | \(0.632571\pi\) | |||||||
\(168\) | 6.55996 | 0.506112 | ||||||||
\(169\) | 10.2226 | − | 8.03114i | 0.786351 | − | 0.617780i | ||||
\(170\) | 1.63035 | 0.125042 | ||||||||
\(171\) | −9.29073 | + | 5.36401i | −0.710480 | + | 0.410196i | ||||
\(172\) | 3.53940 | + | 6.13043i | 0.269877 | + | 0.467441i | ||||
\(173\) | −4.05899 | + | 7.03037i | −0.308599 | + | 0.534509i | −0.978056 | − | 0.208341i | \(-0.933193\pi\) |
0.669457 | + | 0.742851i | \(0.266527\pi\) | |||||||
\(174\) | 9.64114i | 0.730893i | ||||||||
\(175\) | 16.7664 | + | 9.68011i | 1.26742 | + | 0.731747i | ||||
\(176\) | 23.2149 | + | 13.4031i | 1.74989 | + | 1.01030i | ||||
\(177\) | − | 9.56003i | − | 0.718576i | ||||||
\(178\) | 9.75853 | − | 16.9023i | 0.731433 | − | 1.26688i | ||||
\(179\) | 11.5613 | + | 20.0247i | 0.864132 | + | 1.49672i | 0.867907 | + | 0.496727i | \(0.165465\pi\) |
−0.00377519 | + | 0.999993i | \(0.501202\pi\) | |||||||
\(180\) | 1.48451 | − | 0.857081i | 0.110649 | − | 0.0638831i | ||||
\(181\) | −8.27560 | −0.615120 | −0.307560 | − | 0.951529i | \(-0.599513\pi\) | ||||
−0.307560 | + | 0.951529i | \(0.599513\pi\) | |||||||
\(182\) | −27.0158 | + | 9.34297i | −2.00254 | + | 0.692547i | ||||
\(183\) | −1.08091 | −0.0799029 | ||||||||
\(184\) | −1.34201 | + | 0.774808i | −0.0989341 | + | 0.0571196i | ||||
\(185\) | −2.46065 | − | 4.26198i | −0.180911 | − | 0.313347i | ||||
\(186\) | 0.999218 | − | 1.73070i | 0.0732662 | − | 0.126901i | ||||
\(187\) | 6.36103i | 0.465165i | ||||||||
\(188\) | −4.41164 | − | 2.54706i | −0.321752 | − | 0.185764i | ||||
\(189\) | 20.1289 | + | 11.6214i | 1.46416 | + | 0.845332i | ||||
\(190\) | 8.42537i | 0.611241i | ||||||||
\(191\) | −5.99143 | + | 10.3775i | −0.433524 | + | 0.750886i | −0.997174 | − | 0.0751277i | \(-0.976064\pi\) |
0.563649 | + | 0.826014i | \(0.309397\pi\) | |||||||
\(192\) | 0.735094 | + | 1.27322i | 0.0530509 | + | 0.0918868i | ||||
\(193\) | 5.88123 | − | 3.39553i | 0.423340 | − | 0.244416i | −0.273165 | − | 0.961967i | \(-0.588071\pi\) |
0.696505 | + | 0.717552i | \(0.254737\pi\) | |||||||
\(194\) | −0.124810 | −0.00896080 | ||||||||
\(195\) | −2.01949 | + | 2.32949i | −0.144619 | + | 0.166818i | ||||
\(196\) | 15.4416 | 1.10297 | ||||||||
\(197\) | 2.21397 | − | 1.27824i | 0.157739 | − | 0.0910707i | −0.419053 | − | 0.907962i | \(-0.637638\pi\) |
0.576792 | + | 0.816891i | \(0.304304\pi\) | |||||||
\(198\) | 8.68069 | + | 15.0354i | 0.616910 | + | 1.06852i | ||||
\(199\) | −2.52695 | + | 4.37681i | −0.179131 | + | 0.310264i | −0.941583 | − | 0.336781i | \(-0.890662\pi\) |
0.762452 | + | 0.647044i | \(0.223995\pi\) | |||||||
\(200\) | − | 5.93248i | − | 0.419490i | ||||||
\(201\) | −8.14349 | − | 4.70165i | −0.574398 | − | 0.331629i | ||||
\(202\) | −2.41020 | − | 1.39153i | −0.169581 | − | 0.0979076i | ||||
\(203\) | − | 21.2060i | − | 1.48837i | ||||||
\(204\) | −0.813181 | + | 1.40847i | −0.0569341 | + | 0.0986127i | ||||
\(205\) | −4.52816 | − | 7.84300i | −0.316260 | − | 0.547779i | ||||
\(206\) | 7.50194 | − | 4.33125i | 0.522685 | − | 0.301772i | ||||
\(207\) | −2.03907 | −0.141725 | ||||||||
\(208\) | 13.4469 | + | 11.6575i | 0.932377 | + | 0.808303i | ||||
\(209\) | −32.8728 | −2.27386 | ||||||||
\(210\) | 5.87097 | − | 3.38960i | 0.405135 | − | 0.233905i | ||||
\(211\) | −5.75706 | − | 9.97152i | −0.396332 | − | 0.686468i | 0.596938 | − | 0.802287i | \(-0.296384\pi\) |
−0.993270 | + | 0.115820i | \(0.963050\pi\) | |||||||
\(212\) | 0.791632 | − | 1.37115i | 0.0543695 | − | 0.0941708i | ||||
\(213\) | − | 4.25473i | − | 0.291529i | ||||||
\(214\) | −19.3232 | − | 11.1563i | −1.32091 | − | 0.762627i | ||||
\(215\) | −3.77511 | − | 2.17956i | −0.257461 | − | 0.148645i | ||||
\(216\) | − | 7.12221i | − | 0.484605i | ||||||
\(217\) | −2.19781 | + | 3.80672i | −0.149197 | + | 0.258417i | ||||
\(218\) | 6.16682 | + | 10.6812i | 0.417670 | + | 0.723425i | ||||
\(219\) | −4.19725 | + | 2.42328i | −0.283624 | + | 0.163750i | ||||
\(220\) | 5.25253 | 0.354126 | ||||||||
\(221\) | −0.800219 | + | 4.14655i | −0.0538285 | + | 0.278927i | ||||
\(222\) | 12.7439 | 0.855315 | ||||||||
\(223\) | −5.01462 | + | 2.89519i | −0.335804 | + | 0.193877i | −0.658415 | − | 0.752655i | \(-0.728773\pi\) |
0.322611 | + | 0.946532i | \(0.395439\pi\) | |||||||
\(224\) | −13.6458 | − | 23.6353i | −0.911750 | − | 1.57920i | ||||
\(225\) | 3.90314 | − | 6.76044i | 0.260210 | − | 0.450696i | ||||
\(226\) | 12.5858i | 0.837192i | ||||||||
\(227\) | 9.72159 | + | 5.61276i | 0.645245 | + | 0.372532i | 0.786632 | − | 0.617422i | \(-0.211823\pi\) |
−0.141387 | + | 0.989954i | \(0.545156\pi\) | |||||||
\(228\) | −7.27875 | − | 4.20239i | −0.482047 | − | 0.278310i | ||||
\(229\) | − | 26.0722i | − | 1.72290i | −0.507842 | − | 0.861450i | \(-0.669556\pi\) | ||
0.507842 | − | 0.861450i | \(-0.330444\pi\) | |||||||
\(230\) | −0.800704 | + | 1.38686i | −0.0527969 | + | 0.0914469i | ||||
\(231\) | 13.2250 | + | 22.9064i | 0.870142 | + | 1.50713i | ||||
\(232\) | −5.62751 | + | 3.24904i | −0.369464 | + | 0.213310i | ||||
\(233\) | 3.14064 | 0.205750 | 0.102875 | − | 0.994694i | \(-0.467196\pi\) | ||||
0.102875 | + | 0.994694i | \(0.467196\pi\) | |||||||
\(234\) | 3.76720 | + | 10.8931i | 0.246270 | + | 0.712106i | ||||
\(235\) | 3.13696 | 0.204633 | ||||||||
\(236\) | −9.36452 | + | 5.40661i | −0.609578 | + | 0.351940i | ||||
\(237\) | 4.64258 | + | 8.04119i | 0.301568 | + | 0.522331i | ||||
\(238\) | 4.64305 | − | 8.04199i | 0.300964 | − | 0.521285i | ||||
\(239\) | 10.9723i | 0.709737i | 0.934916 | + | 0.354868i | \(0.115474\pi\) | ||||
−0.934916 | + | 0.354868i | \(0.884526\pi\) | |||||||
\(240\) | −3.65507 | − | 2.11026i | −0.235934 | − | 0.136217i | ||||
\(241\) | −5.75097 | − | 3.32032i | −0.370453 | − | 0.213881i | 0.303204 | − | 0.952926i | \(-0.401944\pi\) |
−0.673656 | + | 0.739045i | \(0.735277\pi\) | |||||||
\(242\) | 33.3584i | 2.14436i | ||||||||
\(243\) | 7.63154 | − | 13.2182i | 0.489563 | − | 0.847949i | ||||
\(244\) | 0.611299 | + | 1.05880i | 0.0391344 | + | 0.0677828i | ||||
\(245\) | −8.23499 | + | 4.75448i | −0.526114 | + | 0.303752i | ||||
\(246\) | 23.4517 | 1.49522 | ||||||||
\(247\) | −21.4287 | − | 4.13540i | −1.36347 | − | 0.263129i | ||||
\(248\) | 1.34694 | 0.0855305 | ||||||||
\(249\) | 12.3234 | − | 7.11493i | 0.780966 | − | 0.450891i | ||||
\(250\) | −6.54527 | − | 11.3367i | −0.413959 | − | 0.716998i | ||||
\(251\) | −6.09671 | + | 10.5598i | −0.384821 | + | 0.666529i | −0.991744 | − | 0.128231i | \(-0.959070\pi\) |
0.606923 | + | 0.794760i | \(0.292403\pi\) | |||||||
\(252\) | − | 9.76348i | − | 0.615042i | ||||||
\(253\) | −5.41103 | − | 3.12406i | −0.340189 | − | 0.196408i | ||||
\(254\) | 23.0452 | + | 13.3051i | 1.44598 | + | 0.834839i | ||||
\(255\) | − | 1.00151i | − | 0.0627171i | ||||||
\(256\) | −10.3672 | + | 17.9565i | −0.647950 | + | 1.12228i | ||||
\(257\) | 9.43664 | + | 16.3447i | 0.588641 | + | 1.01956i | 0.994411 | + | 0.105581i | \(0.0336703\pi\) |
−0.405769 | + | 0.913976i | \(0.632996\pi\) | |||||||
\(258\) | 9.77580 | − | 5.64406i | 0.608614 | − | 0.351384i | ||||
\(259\) | −28.0306 | −1.74174 | ||||||||
\(260\) | 3.42396 | + | 0.660770i | 0.212345 | + | 0.0409792i | ||||
\(261\) | −8.55054 | −0.529265 | ||||||||
\(262\) | 27.0273 | − | 15.6042i | 1.66976 | − | 0.964034i | ||||
\(263\) | 3.64200 | + | 6.30813i | 0.224576 | + | 0.388976i | 0.956192 | − | 0.292740i | \(-0.0945671\pi\) |
−0.731616 | + | 0.681716i | \(0.761234\pi\) | |||||||
\(264\) | 4.05249 | − | 7.01913i | 0.249414 | − | 0.431997i | ||||
\(265\) | 0.974973i | 0.0598921i | ||||||||
\(266\) | 41.5597 | + | 23.9945i | 2.54819 | + | 1.47120i | ||||
\(267\) | −10.3830 | − | 5.99461i | −0.635427 | − | 0.366864i | ||||
\(268\) | 10.6359i | 0.649693i | ||||||||
\(269\) | 9.02400 | − | 15.6300i | 0.550203 | − | 0.952980i | −0.448056 | − | 0.894005i | \(-0.647884\pi\) |
0.998259 | − | 0.0589746i | \(-0.0187831\pi\) | |||||||
\(270\) | −3.68012 | − | 6.37416i | −0.223965 | − | 0.387919i | ||||
\(271\) | 0.762776 | − | 0.440389i | 0.0463353 | − | 0.0267517i | −0.476653 | − | 0.879091i | \(-0.658150\pi\) |
0.522989 | + | 0.852340i | \(0.324817\pi\) | |||||||
\(272\) | −5.78122 | −0.350538 | ||||||||
\(273\) | 5.73933 | + | 16.5956i | 0.347360 | + | 1.00441i | ||||
\(274\) | −2.78035 | −0.167967 | ||||||||
\(275\) | 20.7153 | − | 11.9600i | 1.24918 | − | 0.721216i | ||||
\(276\) | −0.798747 | − | 1.38347i | −0.0480789 | − | 0.0832751i | ||||
\(277\) | 10.6773 | − | 18.4936i | 0.641534 | − | 1.11117i | −0.343556 | − | 0.939132i | \(-0.611631\pi\) |
0.985090 | − | 0.172038i | \(-0.0550352\pi\) | |||||||
\(278\) | − | 30.5211i | − | 1.83053i | ||||||
\(279\) | 1.53492 | + | 0.886187i | 0.0918933 | + | 0.0530546i | ||||
\(280\) | 3.95700 | + | 2.28458i | 0.236476 | + | 0.136530i | ||||
\(281\) | 16.9935i | 1.01374i | 0.862021 | + | 0.506872i | \(0.169198\pi\) | ||||
−0.862021 | + | 0.506872i | \(0.830802\pi\) | |||||||
\(282\) | −4.06163 | + | 7.03496i | −0.241867 | + | 0.418926i | ||||
\(283\) | −10.0096 | − | 17.3371i | −0.595006 | − | 1.03058i | −0.993546 | − | 0.113430i | \(-0.963816\pi\) |
0.398540 | − | 0.917151i | \(-0.369517\pi\) | |||||||
\(284\) | −4.16772 | + | 2.40623i | −0.247308 | + | 0.142784i | ||||
\(285\) | 5.17566 | 0.306579 | ||||||||
\(286\) | −6.69241 | + | 34.6785i | −0.395730 | + | 2.05058i | ||||
\(287\) | −51.5827 | −3.04483 | ||||||||
\(288\) | −9.53004 | + | 5.50217i | −0.561563 | + | 0.324219i | ||||
\(289\) | 7.81407 | + | 13.5344i | 0.459651 | + | 0.796139i | ||||
\(290\) | −3.35763 | + | 5.81559i | −0.197167 | + | 0.341503i | ||||
\(291\) | 0.0766697i | 0.00449446i | ||||||||
\(292\) | 4.74745 | + | 2.74094i | 0.277824 | + | 0.160402i | ||||
\(293\) | −23.1301 | − | 13.3542i | −1.35127 | − | 0.780158i | −0.362845 | − | 0.931849i | \(-0.618195\pi\) |
−0.988428 | + | 0.151692i | \(0.951528\pi\) | |||||||
\(294\) | − | 24.6238i | − | 1.43609i | ||||||
\(295\) | 3.32938 | − | 5.76666i | 0.193844 | − | 0.335748i | ||||
\(296\) | 4.29467 | + | 7.43858i | 0.249622 | + | 0.432359i | ||||
\(297\) | 24.8697 | − | 14.3585i | 1.44309 | − | 0.833166i | ||||
\(298\) | −16.6552 | −0.964812 | ||||||||
\(299\) | −3.13427 | − | 2.71718i | −0.181259 | − | 0.157139i | ||||
\(300\) | 6.11577 | 0.353094 | ||||||||
\(301\) | −21.5022 | + | 12.4143i | −1.23937 | + | 0.715548i | ||||
\(302\) | −19.5737 | − | 33.9026i | −1.12634 | − | 1.95088i | ||||
\(303\) | −0.854808 | + | 1.48057i | −0.0491074 | + | 0.0850565i | ||||
\(304\) | − | 29.8764i | − | 1.71353i | ||||||
\(305\) | −0.652009 | − | 0.376437i | −0.0373339 | − | 0.0215547i | ||||
\(306\) | −3.24264 | − | 1.87214i | −0.185369 | − | 0.107023i | ||||
\(307\) | − | 26.9507i | − | 1.53816i | −0.639152 | − | 0.769080i | \(-0.720715\pi\) | ||
0.639152 | − | 0.769080i | \(-0.279285\pi\) | |||||||
\(308\) | 14.9586 | − | 25.9091i | 0.852347 | − | 1.47631i | ||||
\(309\) | −2.66066 | − | 4.60840i | −0.151360 | − | 0.262162i | ||||
\(310\) | 1.20547 | − | 0.695977i | 0.0684660 | − | 0.0395288i | ||||
\(311\) | 17.1492 | 0.972443 | 0.486222 | − | 0.873836i | \(-0.338375\pi\) | ||||
0.486222 | + | 0.873836i | \(0.338375\pi\) | |||||||
\(312\) | 3.52470 | − | 4.06574i | 0.199547 | − | 0.230177i | ||||
\(313\) | −18.2964 | −1.03417 | −0.517087 | − | 0.855933i | \(-0.672984\pi\) | ||||
−0.517087 | + | 0.855933i | \(0.672984\pi\) | |||||||
\(314\) | −35.4648 | + | 20.4756i | −2.00139 | + | 1.15550i | ||||
\(315\) | 3.00617 | + | 5.20684i | 0.169379 | + | 0.293372i | ||||
\(316\) | 5.25116 | − | 9.09528i | 0.295401 | − | 0.511649i | ||||
\(317\) | − | 20.2800i | − | 1.13904i | −0.821978 | − | 0.569519i | \(-0.807130\pi\) | ||
0.821978 | − | 0.569519i | \(-0.192870\pi\) | |||||||
\(318\) | −2.18648 | − | 1.26236i | −0.122612 | − | 0.0707899i | ||||
\(319\) | −22.6903 | − | 13.1003i | −1.27042 | − | 0.733475i | ||||
\(320\) | 1.02402i | 0.0572444i | ||||||||
\(321\) | −6.85323 | + | 11.8701i | −0.382510 | + | 0.662527i | ||||
\(322\) | 4.56063 | + | 7.89924i | 0.254154 | + | 0.440208i | ||||
\(323\) | 6.13974 | − | 3.54478i | 0.341624 | − | 0.197237i | ||||
\(324\) | 0.678713 | 0.0377063 | ||||||||
\(325\) | 15.0082 | − | 5.19035i | 0.832507 | − | 0.287909i | ||||
\(326\) | 6.58391 | 0.364649 | ||||||||
\(327\) | 6.56143 | − | 3.78824i | 0.362848 | − | 0.209490i | ||||
\(328\) | 7.90316 | + | 13.6887i | 0.436379 | + | 0.755830i | ||||
\(329\) | 8.93370 | − | 15.4736i | 0.492531 | − | 0.853089i | ||||
\(330\) | − | 8.37588i | − | 0.461077i | ||||||
\(331\) | 25.8655 | + | 14.9335i | 1.42170 | + | 0.820817i | 0.996444 | − | 0.0842572i | \(-0.0268517\pi\) |
0.425253 | + | 0.905074i | \(0.360185\pi\) | |||||||
\(332\) | −13.9389 | − | 8.04760i | −0.764994 | − | 0.441670i | ||||
\(333\) | 11.3023i | 0.619363i | ||||||||
\(334\) | 18.8242 | − | 32.6044i | 1.03001 | − | 1.78403i | ||||
\(335\) | −3.27480 | − | 5.67212i | −0.178921 | − | 0.309901i | ||||
\(336\) | −20.8185 | + | 12.0196i | −1.13574 | + | 0.655720i | ||||
\(337\) | 25.6842 | 1.39911 | 0.699555 | − | 0.714579i | \(-0.253382\pi\) | ||||
0.699555 | + | 0.714579i | \(0.253382\pi\) | |||||||
\(338\) | −8.72513 | + | 21.7639i | −0.474584 | + | 1.18380i | ||||
\(339\) | 7.73136 | 0.419910 | ||||||||
\(340\) | −0.981031 | + | 0.566398i | −0.0532039 | + | 0.0307173i | ||||
\(341\) | 2.71545 | + | 4.70330i | 0.147050 | + | 0.254698i | ||||
\(342\) | 9.67490 | − | 16.7574i | 0.523159 | − | 0.906137i | ||||
\(343\) | 23.3915i | 1.26302i | ||||||||
\(344\) | 6.58884 | + | 3.80407i | 0.355247 | + | 0.205102i | ||||
\(345\) | 0.851940 | + | 0.491868i | 0.0458669 | + | 0.0264813i | ||||
\(346\) | − | 14.6421i | − | 0.787167i | ||||||
\(347\) | −2.17506 | + | 3.76732i | −0.116763 | + | 0.202240i | −0.918483 | − | 0.395460i | \(-0.870585\pi\) |
0.801720 | + | 0.597700i | \(0.203919\pi\) | |||||||
\(348\) | −3.34943 | − | 5.80138i | −0.179548 | − | 0.310986i | ||||
\(349\) | 4.31619 | − | 2.49195i | 0.231040 | − | 0.133391i | −0.380012 | − | 0.924982i | \(-0.624080\pi\) |
0.611052 | + | 0.791591i | \(0.290747\pi\) | |||||||
\(350\) | −34.9194 | −1.86652 | ||||||||
\(351\) | 18.0180 | − | 6.23124i | 0.961732 | − | 0.332599i | ||||
\(352\) | −33.7195 | −1.79726 | ||||||||
\(353\) | −8.34116 | + | 4.81577i | −0.443955 | + | 0.256318i | −0.705274 | − | 0.708935i | \(-0.749176\pi\) |
0.261319 | + | 0.965253i | \(0.415843\pi\) | |||||||
\(354\) | 8.62157 | + | 14.9330i | 0.458231 | + | 0.793680i | ||||
\(355\) | 1.48176 | − | 2.56648i | 0.0786434 | − | 0.136214i | ||||
\(356\) | 13.5608i | 0.718723i | ||||||||
\(357\) | −4.94015 | − | 2.85219i | −0.261460 | − | 0.150954i | ||||
\(358\) | −36.1180 | − | 20.8528i | −1.90890 | − | 1.10210i | ||||
\(359\) | − | 36.8886i | − | 1.94691i | −0.228887 | − | 0.973453i | \(-0.573509\pi\) | ||
0.228887 | − | 0.973453i | \(-0.426491\pi\) | |||||||
\(360\) | 0.921171 | − | 1.59551i | 0.0485500 | − | 0.0840910i | ||||
\(361\) | 8.81886 | + | 15.2747i | 0.464151 | + | 0.803932i | ||||
\(362\) | 12.9267 | − | 7.46322i | 0.679411 | − | 0.392258i | ||||
\(363\) | 20.4918 | 1.07554 | ||||||||
\(364\) | 13.0104 | − | 15.0075i | 0.681931 | − | 0.786607i | ||||
\(365\) | −3.37574 | −0.176694 | ||||||||
\(366\) | 1.68840 | − | 0.974799i | 0.0882541 | − | 0.0509536i | ||||
\(367\) | 1.56657 | + | 2.71338i | 0.0817743 | + | 0.141637i | 0.904012 | − | 0.427507i | \(-0.140608\pi\) |
−0.822238 | + | 0.569144i | \(0.807275\pi\) | |||||||
\(368\) | 2.83930 | − | 4.91781i | 0.148009 | − | 0.256359i | ||||
\(369\) | 20.7988i | 1.08274i | ||||||||
\(370\) | 7.68720 | + | 4.43820i | 0.399638 | + | 0.230731i | ||||
\(371\) | 4.80923 | + | 2.77661i | 0.249683 | + | 0.144155i | ||||
\(372\) | 1.38855i | 0.0719930i | ||||||||
\(373\) | 8.77281 | − | 15.1950i | 0.454239 | − | 0.786765i | −0.544405 | − | 0.838822i | \(-0.683245\pi\) |
0.998644 | + | 0.0520574i | \(0.0165779\pi\) | |||||||
\(374\) | −5.73660 | − | 9.93608i | −0.296632 | − | 0.513782i | ||||
\(375\) | −6.96408 | + | 4.02072i | −0.359624 | + | 0.207629i | ||||
\(376\) | −5.47505 | −0.282354 | ||||||||
\(377\) | −13.1431 | − | 11.3941i | −0.676903 | − | 0.586826i | ||||
\(378\) | −41.9223 | −2.15625 | ||||||||
\(379\) | −24.6650 | + | 14.2403i | −1.26695 | + | 0.731476i | −0.974410 | − | 0.224776i | \(-0.927835\pi\) |
−0.292544 | + | 0.956252i | \(0.594502\pi\) | |||||||
\(380\) | −2.92706 | − | 5.06981i | −0.150155 | − | 0.260076i | ||||
\(381\) | 8.17327 | − | 14.1565i | 0.418729 | − | 0.725260i | ||||
\(382\) | − | 21.6131i | − | 1.10582i | ||||||
\(383\) | −9.24097 | − | 5.33528i | −0.472191 | − | 0.272620i | 0.244965 | − | 0.969532i | \(-0.421223\pi\) |
−0.717157 | + | 0.696912i | \(0.754557\pi\) | |||||||
\(384\) | 9.61877 | + | 5.55340i | 0.490856 | + | 0.283396i | ||||
\(385\) | 18.4230i | 0.938924i | ||||||||
\(386\) | −6.12441 | + | 10.6078i | −0.311724 | + | 0.539923i | ||||
\(387\) | 5.00560 | + | 8.66996i | 0.254449 | + | 0.440719i | ||||
\(388\) | 0.0751018 | − | 0.0433600i | 0.00381271 | − | 0.00220127i | ||||
\(389\) | −14.5072 | −0.735545 | −0.367773 | − | 0.929916i | \(-0.619880\pi\) | ||||
−0.367773 | + | 0.929916i | \(0.619880\pi\) | |||||||
\(390\) | 1.05369 | − | 5.45996i | 0.0533555 | − | 0.276476i | ||||
\(391\) | 1.34751 | 0.0681466 | ||||||||
\(392\) | 14.3728 | − | 8.29816i | 0.725938 | − | 0.419120i | ||||
\(393\) | −9.58559 | − | 16.6027i | −0.483529 | − | 0.837497i | ||||
\(394\) | −2.30552 | + | 3.99328i | −0.116150 | + | 0.201178i | ||||
\(395\) | 6.46732i | 0.325406i | ||||||||
\(396\) | −10.4469 | − | 6.03151i | −0.524976 | − | 0.303095i | ||||
\(397\) | 26.6092 | + | 15.3628i | 1.33548 | + | 0.771037i | 0.986133 | − | 0.165958i | \(-0.0530717\pi\) |
0.349342 | + | 0.936995i | \(0.386405\pi\) | |||||||
\(398\) | − | 9.11557i | − | 0.456922i | ||||||
\(399\) | 14.7397 | − | 25.5299i | 0.737907 | − | 1.27809i | ||||
\(400\) | 10.8699 | + | 18.8271i | 0.543493 | + | 0.941357i | ||||
\(401\) | 26.8763 | − | 15.5171i | 1.34214 | − | 0.774885i | 0.355020 | − | 0.934859i | \(-0.384474\pi\) |
0.987121 | + | 0.159973i | \(0.0511409\pi\) | |||||||
\(402\) | 16.9604 | 0.845910 | ||||||||
\(403\) | 1.17844 | + | 3.40753i | 0.0587022 | + | 0.169741i | ||||
\(404\) | 1.93372 | 0.0962063 | ||||||||
\(405\) | −0.361956 | + | 0.208975i | −0.0179857 | + | 0.0103841i | ||||
\(406\) | 19.1243 | + | 33.1243i | 0.949124 | + | 1.64393i | ||||
\(407\) | −17.3163 | + | 29.9927i | −0.858336 | + | 1.48668i | ||||
\(408\) | 1.74798i | 0.0865377i | ||||||||
\(409\) | 1.56955 | + | 0.906182i | 0.0776094 | + | 0.0448078i | 0.538303 | − | 0.842752i | \(-0.319066\pi\) |
−0.460693 | + | 0.887559i | \(0.652399\pi\) | |||||||
\(410\) | 14.1462 | + | 8.16730i | 0.698630 | + | 0.403354i | ||||
\(411\) | 1.70795i | 0.0842471i | ||||||||
\(412\) | −3.00943 | + | 5.21249i | −0.148264 | + | 0.256801i | ||||
\(413\) | −18.9634 | − | 32.8456i | −0.933129 | − | 1.61623i | ||||
\(414\) | 3.18508 | − | 1.83891i | 0.156538 | − | 0.0903773i | ||||
\(415\) | 9.91142 | 0.486532 | ||||||||
\(416\) | −21.9806 | − | 4.24192i | −1.07769 | − | 0.207977i | ||||
\(417\) | −18.7489 | −0.918139 | ||||||||
\(418\) | 51.3481 | − | 29.6458i | 2.51152 | − | 1.45002i | ||||
\(419\) | 9.29506 | + | 16.0995i | 0.454094 | + | 0.786513i | 0.998636 | − | 0.0522205i | \(-0.0166299\pi\) |
−0.544542 | + | 0.838734i | \(0.683297\pi\) | |||||||
\(420\) | −2.35516 | + | 4.07926i | −0.114920 | + | 0.199048i | ||||
\(421\) | − | 5.36839i | − | 0.261639i | −0.991406 | − | 0.130820i | \(-0.958239\pi\) | ||
0.991406 | − | 0.130820i | \(-0.0417609\pi\) | |||||||
\(422\) | 17.9853 | + | 10.3838i | 0.875512 | + | 0.505477i | ||||
\(423\) | −6.23917 | − | 3.60218i | −0.303359 | − | 0.175144i | ||||
\(424\) | − | 1.70166i | − | 0.0826397i | ||||||
\(425\) | −2.57938 | + | 4.46761i | −0.125118 | + | 0.216711i | ||||
\(426\) | 3.83706 | + | 6.64599i | 0.185906 | + | 0.321999i | ||||
\(427\) | −3.71370 | + | 2.14410i | −0.179718 | + | 0.103760i | ||||
\(428\) | 15.5032 | 0.749375 | ||||||||
\(429\) | 21.3028 | + | 4.11111i | 1.02851 | + | 0.198486i | ||||
\(430\) | 7.86242 | 0.379160 | ||||||||
\(431\) | −19.4215 | + | 11.2130i | −0.935500 | + | 0.540111i | −0.888547 | − | 0.458786i | \(-0.848285\pi\) |
−0.0469534 | + | 0.998897i | \(0.514951\pi\) | |||||||
\(432\) | 13.0497 | + | 22.6028i | 0.627856 | + | 1.08748i | ||||
\(433\) | −6.64763 | + | 11.5140i | −0.319465 | + | 0.553329i | −0.980376 | − | 0.197134i | \(-0.936836\pi\) |
0.660912 | + | 0.750464i | \(0.270170\pi\) | |||||||
\(434\) | − | 7.92826i | − | 0.380569i | ||||||
\(435\) | 3.57248 | + | 2.06257i | 0.171287 | + | 0.0988928i | ||||
\(436\) | −7.42154 | − | 4.28483i | −0.355427 | − | 0.205206i | ||||
\(437\) | 6.96372i | 0.333120i | ||||||||
\(438\) | 4.37080 | − | 7.57045i | 0.208845 | − | 0.361730i | ||||
\(439\) | −15.8070 | − | 27.3785i | −0.754426 | − | 1.30670i | −0.945659 | − | 0.325160i | \(-0.894582\pi\) |
0.191233 | − | 0.981545i | \(-0.438751\pi\) | |||||||
\(440\) | 4.88897 | − | 2.82265i | 0.233073 | − | 0.134565i | ||||
\(441\) | 21.8384 | 1.03992 | ||||||||
\(442\) | −2.48954 | − | 7.19867i | −0.118415 | − | 0.342406i | ||||
\(443\) | 26.6865 | 1.26791 | 0.633957 | − | 0.773368i | \(-0.281430\pi\) | ||||
0.633957 | + | 0.773368i | \(0.281430\pi\) | |||||||
\(444\) | −7.66841 | + | 4.42736i | −0.363926 | + | 0.210113i | ||||
\(445\) | −4.17537 | − | 7.23196i | −0.197932 | − | 0.342828i | ||||
\(446\) | 5.22198 | − | 9.04473i | 0.247268 | − | 0.428280i | ||||
\(447\) | 10.2312i | 0.483920i | ||||||||
\(448\) | 5.05116 | + | 2.91629i | 0.238645 | + | 0.137782i | ||||
\(449\) | 17.1490 | + | 9.90098i | 0.809311 | + | 0.467256i | 0.846717 | − | 0.532044i | \(-0.178576\pi\) |
−0.0374054 | + | 0.999300i | \(0.511909\pi\) | |||||||
\(450\) | 14.0800i | 0.663736i | ||||||||
\(451\) | −31.8659 | + | 55.1933i | −1.50050 | + | 2.59895i | ||||
\(452\) | −4.37242 | − | 7.57325i | −0.205661 | − | 0.356215i | ||||
\(453\) | −20.8262 | + | 12.0240i | −0.978499 | + | 0.564936i | ||||
\(454\) | −20.2471 | −0.950246 | ||||||||
\(455\) | −2.31762 | + | 12.0094i | −0.108652 | + | 0.563008i | ||||
\(456\) | −9.03326 | −0.423021 | ||||||||
\(457\) | −19.2636 | + | 11.1219i | −0.901114 | + | 0.520258i | −0.877561 | − | 0.479464i | \(-0.840831\pi\) |
−0.0235524 | + | 0.999723i | \(0.507498\pi\) | |||||||
\(458\) | 23.5128 | + | 40.7254i | 1.09868 | + | 1.90297i | ||||
\(459\) | −3.09665 | + | 5.36356i | −0.144539 | + | 0.250350i | ||||
\(460\) | − | 1.11269i | − | 0.0518794i | ||||||
\(461\) | 4.55219 | + | 2.62821i | 0.212017 | + | 0.122408i | 0.602248 | − | 0.798309i | \(-0.294272\pi\) |
−0.390232 | + | 0.920717i | \(0.627605\pi\) | |||||||
\(462\) | −41.3156 | − | 23.8536i | −1.92217 | − | 1.10977i | ||||
\(463\) | 1.95426i | 0.0908223i | 0.998968 | + | 0.0454112i | \(0.0144598\pi\) | ||||
−0.998968 | + | 0.0454112i | \(0.985540\pi\) | |||||||
\(464\) | 11.9062 | − | 20.6221i | 0.552731 | − | 0.957358i | ||||
\(465\) | −0.427534 | − | 0.740511i | −0.0198264 | − | 0.0343404i | ||||
\(466\) | −4.90575 | + | 2.83234i | −0.227255 | + | 0.131206i | ||||
\(467\) | 32.8358 | 1.51946 | 0.759730 | − | 0.650239i | \(-0.225331\pi\) | ||||
0.759730 | + | 0.650239i | \(0.225331\pi\) | |||||||
\(468\) | −6.05122 | − | 5.24597i | −0.279718 | − | 0.242495i | ||||
\(469\) | −37.3051 | −1.72259 | ||||||||
\(470\) | −4.90000 | + | 2.82902i | −0.226020 | + | 0.130493i | ||||
\(471\) | 12.5780 | + | 21.7858i | 0.579565 | + | 1.00384i | ||||
\(472\) | −5.81090 | + | 10.0648i | −0.267468 | + | 0.463268i | ||||
\(473\) | 30.6763i | 1.41050i | ||||||||
\(474\) | −14.5037 | − | 8.37369i | −0.666175 | − | 0.384616i | ||||
\(475\) | −23.0879 | − | 13.3298i | −1.05934 | − | 0.611613i | ||||
\(476\) | 6.45216i | 0.295734i | ||||||||
\(477\) | 1.11957 | − | 1.93915i | 0.0512614 | − | 0.0887874i | ||||
\(478\) | −9.89517 | − | 17.1389i | −0.452595 | − | 0.783917i | ||||
\(479\) | −12.1735 | + | 7.02839i | −0.556222 | + | 0.321135i | −0.751628 | − | 0.659587i | \(-0.770731\pi\) |
0.195405 | + | 0.980723i | \(0.437398\pi\) | |||||||
\(480\) | 5.30897 | 0.242320 | ||||||||
\(481\) | −15.0610 | + | 17.3729i | −0.686723 | + | 0.792134i | ||||
\(482\) | 11.9775 | 0.545562 | ||||||||
\(483\) | 4.85246 | − | 2.80157i | 0.220794 | − | 0.127476i | ||||
\(484\) | −11.5890 | − | 20.0728i | −0.526773 | − | 0.912398i | ||||
\(485\) | −0.0267011 | + | 0.0462476i | −0.00121243 | + | 0.00210000i | ||||
\(486\) | 27.5295i | 1.24877i | ||||||||
\(487\) | −6.63768 | − | 3.83227i | −0.300782 | − | 0.173657i | 0.342012 | − | 0.939696i | \(-0.388892\pi\) |
−0.642794 | + | 0.766039i | \(0.722225\pi\) | |||||||
\(488\) | 1.13797 | + | 0.657010i | 0.0515137 | + | 0.0297414i | ||||
\(489\) | − | 4.04446i | − | 0.182897i | ||||||
\(490\) | 8.57550 | − | 14.8532i | 0.387402 | − | 0.671000i | ||||
\(491\) | −16.9491 | − | 29.3567i | −0.764901 | − | 1.32485i | −0.940299 | − | 0.340350i | \(-0.889455\pi\) |
0.175398 | − | 0.984498i | \(-0.443879\pi\) | |||||||
\(492\) | −14.1116 | + | 8.14733i | −0.636200 | + | 0.367310i | ||||
\(493\) | 5.65059 | 0.254490 | ||||||||
\(494\) | 37.2016 | − | 12.8655i | 1.67378 | − | 0.578848i | ||||
\(495\) | 7.42840 | 0.333882 | ||||||||
\(496\) | −4.27460 | + | 2.46794i | −0.191935 | + | 0.110814i | ||||
\(497\) | −8.43975 | − | 14.6181i | −0.378574 | − | 0.655710i | ||||
\(498\) | −12.8330 | + | 22.2274i | −0.575060 | + | 0.996033i | ||||
\(499\) | − | 31.4186i | − | 1.40649i | −0.710947 | − | 0.703245i | \(-0.751734\pi\) | ||
0.710947 | − | 0.703245i | \(-0.248266\pi\) | |||||||
\(500\) | 7.87698 | + | 4.54778i | 0.352269 | + | 0.203383i | ||||
\(501\) | −20.0287 | − | 11.5636i | −0.894815 | − | 0.516622i | ||||
\(502\) | − | 21.9929i | − | 0.981591i | ||||||
\(503\) | 8.42508 | − | 14.5927i | 0.375656 | − | 0.650654i | −0.614769 | − | 0.788707i | \(-0.710751\pi\) |
0.990425 | + | 0.138052i | \(0.0440842\pi\) | |||||||
\(504\) | −5.24678 | − | 9.08769i | −0.233710 | − | 0.404798i | ||||
\(505\) | −1.03125 | + | 0.595392i | −0.0458900 | + | 0.0264946i | ||||
\(506\) | 11.2695 | 0.500992 | ||||||||
\(507\) | 13.3694 | + | 5.35979i | 0.593757 | + | 0.238037i | ||||
\(508\) | −18.4893 | −0.820332 | ||||||||
\(509\) | 20.5415 | − | 11.8596i | 0.910484 | − | 0.525668i | 0.0298971 | − | 0.999553i | \(-0.490482\pi\) |
0.880587 | + | 0.473885i | \(0.157149\pi\) | |||||||
\(510\) | 0.903199 | + | 1.56439i | 0.0399943 | + | 0.0692722i | ||||
\(511\) | −9.61373 | + | 16.6515i | −0.425286 | + | 0.736617i | ||||
\(512\) | − | 17.3493i | − | 0.766740i | ||||||
\(513\) | −27.7180 | − | 16.0030i | −1.22378 | − | 0.706550i | ||||
\(514\) | −29.4805 | − | 17.0206i | −1.30033 | − | 0.750746i | ||||
\(515\) | − | 3.70641i | − | 0.163324i | ||||||
\(516\) | −3.92160 | + | 6.79241i | −0.172639 | + | 0.299019i | ||||
\(517\) | −11.0378 | − | 19.1180i | −0.485442 | − | 0.840811i | ||||
\(518\) | 43.7845 | − | 25.2790i | 1.92378 | − | 1.11070i | ||||
\(519\) | −8.99458 | −0.394818 | ||||||||
\(520\) | 3.54205 | − | 1.22496i | 0.155329 | − | 0.0537181i | ||||
\(521\) | 8.07286 | 0.353678 | 0.176839 | − | 0.984240i | \(-0.443413\pi\) | ||||
0.176839 | + | 0.984240i | \(0.443413\pi\) | |||||||
\(522\) | 13.3561 | − | 7.71117i | 0.584583 | − | 0.337509i | ||||
\(523\) | −16.4687 | − | 28.5247i | −0.720128 | − | 1.24730i | −0.960948 | − | 0.276728i | \(-0.910750\pi\) |
0.240820 | − | 0.970570i | \(-0.422584\pi\) | |||||||
\(524\) | −10.8421 | + | 18.7791i | −0.473641 | + | 0.820370i | ||||
\(525\) | 21.4508i | 0.936189i | ||||||||
\(526\) | −11.3778 | − | 6.56897i | −0.496095 | − | 0.286421i | ||||
\(527\) | −1.01435 | − | 0.585633i | −0.0441856 | − | 0.0255106i | ||||
\(528\) | 29.7009i | 1.29257i | ||||||||
\(529\) | 10.8382 | − | 18.7723i | 0.471226 | − | 0.816188i | ||||
\(530\) | −0.879264 | − | 1.52293i | −0.0381928 | − | 0.0661519i | ||||
\(531\) | −13.2438 | + | 7.64630i | −0.574731 | + | 0.331821i | ||||
\(532\) | −33.3437 | −1.44563 | ||||||||
\(533\) | −27.7156 | + | 31.9700i | −1.20050 | + | 1.38477i | ||||
\(534\) | 21.6246 | 0.935787 | ||||||||
\(535\) | −8.26781 | + | 4.77342i | −0.357449 | + | 0.206373i | ||||
\(536\) | 5.71563 | + | 9.89976i | 0.246878 | + | 0.427604i | ||||
\(537\) | −12.8097 | + | 22.1871i | −0.552780 | + | 0.957443i | ||||
\(538\) | 32.5526i | 1.40344i | ||||||||
\(539\) | 57.9519 | + | 33.4585i | 2.49616 | + | 1.44116i | ||||
\(540\) | 4.42889 | + | 2.55702i | 0.190589 | + | 0.110037i | ||||
\(541\) | − | 22.2562i | − | 0.956871i | −0.878123 | − | 0.478435i | \(-0.841204\pi\) | ||
0.878123 | − | 0.478435i | \(-0.158796\pi\) | |||||||
\(542\) | −0.794316 | + | 1.37580i | −0.0341188 | + | 0.0590955i | ||||
\(543\) | −4.58461 | − | 7.94078i | −0.196744 | − | 0.340771i | ||||
\(544\) | 6.29789 | − | 3.63609i | 0.270020 | − | 0.155896i | ||||
\(545\) | 5.27718 | 0.226050 | ||||||||
\(546\) | −23.9315 | − | 20.7469i | −1.02417 | − | 0.887884i | ||||
\(547\) | −0.321415 | −0.0137427 | −0.00687136 | − | 0.999976i | \(-0.502187\pi\) | ||||
−0.00687136 | + | 0.999976i | \(0.502187\pi\) | |||||||
\(548\) | 1.67302 | − | 0.965921i | 0.0714680 | − | 0.0412621i | ||||
\(549\) | 0.864530 | + | 1.49741i | 0.0368972 | + | 0.0639079i | ||||
\(550\) | −21.5719 | + | 37.3636i | −0.919829 | + | 1.59319i | ||||
\(551\) | 29.2013i | 1.24402i | ||||||||
\(552\) | −1.48692 | − | 0.858475i | −0.0632876 | − | 0.0365391i | ||||
\(553\) | 31.9013 | + | 18.4182i | 1.35658 | + | 0.783222i | ||||
\(554\) | 38.5165i | 1.63641i | ||||||||
\(555\) | 2.72636 | − | 4.72220i | 0.115728 | − | 0.200446i | ||||
\(556\) | 10.6033 | + | 18.3655i | 0.449681 | + | 0.778870i | ||||
\(557\) | 28.4115 | − | 16.4034i | 1.20383 | − | 0.695034i | 0.242428 | − | 0.970169i | \(-0.422056\pi\) |
0.961405 | + | 0.275136i | \(0.0887228\pi\) | |||||||
\(558\) | −3.19678 | −0.135330 | ||||||||
\(559\) | −3.85909 | + | 19.9969i | −0.163222 | + | 0.845779i | ||||
\(560\) | −16.7438 | −0.707553 | ||||||||
\(561\) | −6.10367 | + | 3.52396i | −0.257697 | + | 0.148782i | ||||
\(562\) | −15.3253 | − | 26.5442i | −0.646458 | − | 1.11970i | ||||
\(563\) | 6.55543 | − | 11.3543i | 0.276278 | − | 0.478528i | −0.694178 | − | 0.719803i | \(-0.744232\pi\) |
0.970457 | + | 0.241275i | \(0.0775655\pi\) | |||||||
\(564\) | − | 5.64420i | − | 0.237664i | ||||||
\(565\) | 4.66360 | + | 2.69253i | 0.196199 | + | 0.113276i | ||||
\(566\) | 31.2703 | + | 18.0539i | 1.31439 | + | 0.758863i | ||||
\(567\) | 2.38055i | 0.0999738i | ||||||||
\(568\) | −2.58616 | + | 4.47936i | −0.108513 | + | 0.187950i | ||||
\(569\) | −3.96039 | − | 6.85959i | −0.166028 | − | 0.287569i | 0.770992 | − | 0.636845i | \(-0.219761\pi\) |
−0.937020 | + | 0.349276i | \(0.886428\pi\) | |||||||
\(570\) | −8.08450 | + | 4.66759i | −0.338622 | + | 0.195504i | ||||
\(571\) | −25.1527 | −1.05261 | −0.526304 | − | 0.850297i | \(-0.676422\pi\) | ||||
−0.526304 | + | 0.850297i | \(0.676422\pi\) | |||||||
\(572\) | −8.02062 | − | 23.1922i | −0.335359 | − | 0.969713i | ||||
\(573\) | −13.2768 | −0.554646 | ||||||||
\(574\) | 80.5734 | − | 46.5191i | 3.36307 | − | 1.94167i | ||||
\(575\) | −2.53359 | − | 4.38831i | −0.105658 | − | 0.183005i | ||||
\(576\) | 1.17589 | − | 2.03669i | 0.0489952 | − | 0.0848623i | ||||
\(577\) | − | 8.99328i | − | 0.374395i | −0.982322 | − | 0.187198i | \(-0.940060\pi\) | ||
0.982322 | − | 0.187198i | \(-0.0599404\pi\) | |||||||
\(578\) | −24.4115 | − | 14.0940i | −1.01539 | − | 0.586233i | ||||
\(579\) | 6.51630 | + | 3.76219i | 0.270808 | + | 0.156351i | ||||
\(580\) | − | 4.66590i | − | 0.193741i | ||||||
\(581\) | 28.2266 | − | 48.8899i | 1.17104 | − | 2.02829i | ||||
\(582\) | −0.0691434 | − | 0.119760i | −0.00286609 | − | 0.00496421i | ||||
\(583\) | 5.94193 | − | 3.43057i | 0.246089 | − | 0.142080i | ||||
\(584\) | 5.89180 | 0.243804 | ||||||||
\(585\) | 4.84233 | + | 0.934494i | 0.200206 | + | 0.0386366i | ||||
\(586\) | 48.1730 | 1.99001 | ||||||||
\(587\) | −4.64202 | + | 2.68007i | −0.191597 | + | 0.110618i | −0.592730 | − | 0.805401i | \(-0.701950\pi\) |
0.401133 | + | 0.916020i | \(0.368616\pi\) | |||||||
\(588\) | 8.55454 | + | 14.8169i | 0.352783 | + | 0.611039i | ||||
\(589\) | 3.02646 | − | 5.24197i | 0.124703 | − | 0.215992i | ||||
\(590\) | 12.0102i | 0.494453i | ||||||||
\(591\) | 2.45304 | + | 1.41627i | 0.100905 | + | 0.0582574i | ||||
\(592\) | −27.2588 | − | 15.7379i | −1.12033 | − | 0.646824i | ||||
\(593\) | 15.8227i | 0.649759i | 0.945755 | + | 0.324879i | \(0.105324\pi\) | ||||
−0.945755 | + | 0.324879i | \(0.894676\pi\) | |||||||
\(594\) | −25.8980 | + | 44.8567i | −1.06261 | + | 1.84049i | ||||
\(595\) | −1.98662 | − | 3.44092i | −0.0814433 | − | 0.141064i | ||||
\(596\) | 10.0220 | − | 5.78619i | 0.410516 | − | 0.237012i | ||||
\(597\) | −5.59964 | −0.229178 | ||||||||
\(598\) | 7.34625 | + | 1.41771i | 0.300410 | + | 0.0579745i | ||||
\(599\) | 22.5066 | 0.919593 | 0.459797 | − | 0.888024i | \(-0.347922\pi\) | ||||
0.459797 | + | 0.888024i | \(0.347922\pi\) | |||||||
\(600\) | 5.69246 | − | 3.28654i | 0.232394 | − | 0.134173i | ||||
\(601\) | 4.61763 | + | 7.99798i | 0.188357 | + | 0.326244i | 0.944703 | − | 0.327928i | \(-0.106350\pi\) |
−0.756345 | + | 0.654172i | \(0.773017\pi\) | |||||||
\(602\) | 22.3913 | − | 38.7829i | 0.912601 | − | 1.58067i | ||||
\(603\) | 15.0419i | 0.612553i | ||||||||
\(604\) | 23.5562 | + | 13.6002i | 0.958488 | + | 0.553383i | ||||
\(605\) | 12.3608 | + | 7.13651i | 0.502538 | + | 0.290140i | ||||
\(606\) | − | 3.08358i | − | 0.125262i | ||||||
\(607\) | −4.11052 | + | 7.11962i | −0.166841 | + | 0.288977i | −0.937307 | − | 0.348504i | \(-0.886690\pi\) |
0.770467 | + | 0.637480i | \(0.220023\pi\) | |||||||
\(608\) | 18.7907 | + | 32.5465i | 0.762064 | + | 1.31993i | ||||
\(609\) | 20.3481 | − | 11.7480i | 0.824545 | − | 0.476051i | ||||
\(610\) | 1.35794 | 0.0549813 | ||||||||
\(611\) | −4.79013 | − | 13.8510i | −0.193788 | − | 0.560351i | ||||
\(612\) | 2.60159 | 0.105163 | ||||||||
\(613\) | 5.74587 | − | 3.31738i | 0.232074 | − | 0.133988i | −0.379455 | − | 0.925210i | \(-0.623888\pi\) |
0.611528 | + | 0.791223i | \(0.290555\pi\) | |||||||
\(614\) | 24.3051 | + | 42.0977i | 0.980875 | + | 1.69893i | ||||
\(615\) | 5.01712 | − | 8.68991i | 0.202310 | − | 0.350411i | ||||
\(616\) | − | 32.1544i | − | 1.29554i | ||||||
\(617\) | 21.0292 | + | 12.1412i | 0.846605 | + | 0.488788i | 0.859504 | − | 0.511129i | \(-0.170773\pi\) |
−0.0128986 | + | 0.999917i | \(0.504106\pi\) | |||||||
\(618\) | 8.31202 | + | 4.79895i | 0.334359 | + | 0.193042i | ||||
\(619\) | 6.89786i | 0.277248i | 0.990345 | + | 0.138624i | \(0.0442680\pi\) | ||||
−0.990345 | + | 0.138624i | \(0.955732\pi\) | |||||||
\(620\) | −0.483578 | + | 0.837582i | −0.0194210 | + | 0.0336381i | ||||
\(621\) | −3.04169 | − | 5.26836i | −0.122059 | − | 0.211412i | ||||
\(622\) | −26.7875 | + | 15.4658i | −1.07408 | + | 0.620121i | ||||
\(623\) | −47.5640 | −1.90561 | ||||||||
\(624\) | −3.73638 | + | 19.3611i | −0.149575 | + | 0.775062i | ||||
\(625\) | 16.4211 | 0.656844 | ||||||||
\(626\) | 28.5794 | − | 16.5003i | 1.14226 | − | 0.659486i | ||||
\(627\) | −18.2112 | − | 31.5428i | −0.727287 | − | 1.25970i | ||||
\(628\) | 14.2268 | − | 24.6416i | 0.567712 | − | 0.983307i | ||||
\(629\) | − | 7.46909i | − | 0.297812i | ||||||
\(630\) | −9.39143 | − | 5.42214i | −0.374163 | − | 0.216023i | ||||
\(631\) | −6.94561 | − | 4.01005i | −0.276500 | − | 0.159638i | 0.355338 | − | 0.934738i | \(-0.384366\pi\) |
−0.631838 | + | 0.775100i | \(0.717699\pi\) | |||||||
\(632\) | − | 11.2877i | − | 0.448999i | ||||||
\(633\) | 6.37872 | − | 11.0483i | 0.253532 | − | 0.439129i | ||||
\(634\) | 18.2892 | + | 31.6778i | 0.726357 | + | 1.25809i | ||||
\(635\) | 9.86033 | − | 5.69286i | 0.391295 | − | 0.225914i | ||||
\(636\) | 1.75423 | 0.0695597 | ||||||||
\(637\) | 33.5679 | + | 29.1009i | 1.33001 | + | 1.15302i | ||||
\(638\) | 47.2571 | 1.87093 | ||||||||
\(639\) | −5.89420 | + | 3.40302i | −0.233171 | + | 0.134621i | ||||
\(640\) | 3.86806 | + | 6.69968i | 0.152899 | + | 0.264828i | ||||
\(641\) | −15.5726 | + | 26.9726i | −0.615082 | + | 1.06535i | 0.375288 | + | 0.926908i | \(0.377544\pi\) |
−0.990370 | + | 0.138445i | \(0.955790\pi\) | |||||||
\(642\) | − | 24.7219i | − | 0.975697i | ||||||
\(643\) | 23.0748 | + | 13.3222i | 0.909981 | + | 0.525378i | 0.880425 | − | 0.474185i | \(-0.157257\pi\) |
0.0295560 | + | 0.999563i | \(0.490591\pi\) | |||||||
\(644\) | −5.48855 | − | 3.16881i | −0.216279 | − | 0.124869i | ||||
\(645\) | − | 4.82984i | − | 0.190175i | ||||||
\(646\) | −6.39362 | + | 11.0741i | −0.251553 | + | 0.435703i | ||||
\(647\) | −0.622426 | − | 1.07807i | −0.0244701 | − | 0.0423835i | 0.853531 | − | 0.521042i | \(-0.174457\pi\) |
−0.878001 | + | 0.478659i | \(0.841123\pi\) | |||||||
\(648\) | 0.631735 | − | 0.364732i | 0.0248169 | − | 0.0143280i | ||||
\(649\) | −46.8596 | −1.83940 | ||||||||
\(650\) | −18.7624 | + | 21.6424i | −0.735921 | + | 0.848884i | ||||
\(651\) | −4.87028 | −0.190881 | ||||||||
\(652\) | −3.96175 | + | 2.28732i | −0.155154 | + | 0.0895782i | ||||
\(653\) | −9.17302 | − | 15.8881i | −0.358968 | − | 0.621751i | 0.628821 | − | 0.777550i | \(-0.283538\pi\) |
−0.987789 | + | 0.155800i | \(0.950205\pi\) | |||||||
\(654\) | −6.83273 | + | 11.8346i | −0.267181 | + | 0.462771i | ||||
\(655\) | − | 13.3531i | − | 0.521751i | ||||||
\(656\) | −50.1624 | − | 28.9613i | −1.95851 | − | 1.13075i | ||||
\(657\) | 6.71409 | + | 3.87638i | 0.261941 | + | 0.151232i | ||||
\(658\) | 32.2269i | 1.25634i | ||||||||
\(659\) | −8.18629 | + | 14.1791i | −0.318893 | + | 0.552338i | −0.980257 | − | 0.197726i | \(-0.936644\pi\) |
0.661365 | + | 0.750065i | \(0.269978\pi\) | |||||||
\(660\) | 2.90986 | + | 5.04003i | 0.113266 | + | 0.196183i | ||||
\(661\) | 17.9932 | − | 10.3884i | 0.699853 | − | 0.404060i | −0.107440 | − | 0.994212i | \(-0.534265\pi\) |
0.807293 | + | 0.590151i | \(0.200932\pi\) | |||||||
\(662\) | −53.8701 | −2.09372 | ||||||||
\(663\) | −4.42210 | + | 1.52931i | −0.171740 | + | 0.0593935i | ||||
\(664\) | −17.2988 | −0.671322 | ||||||||
\(665\) | 17.7821 | − | 10.2665i | 0.689561 | − | 0.398118i | ||||
\(666\) | −10.1928 | − | 17.6545i | −0.394964 | − | 0.684098i | ||||
\(667\) | −2.77514 | + | 4.80669i | −0.107454 | + | 0.186116i | ||||
\(668\) | 26.1588i | 1.01211i | ||||||||
\(669\) | −5.55612 | − | 3.20783i | −0.214812 | − | 0.124022i | ||||
\(670\) | 10.2306 | + | 5.90666i | 0.395244 | + | 0.228194i | ||||
\(671\) | 5.29818i | 0.204534i | ||||||||
\(672\) | 15.1193 | − | 26.1875i | 0.583241 | − | 1.01020i | ||||
\(673\) | 6.65698 | + | 11.5302i | 0.256608 | + | 0.444458i | 0.965331 | − | 0.261029i | \(-0.0840618\pi\) |
−0.708723 | + | 0.705487i | \(0.750728\pi\) | |||||||
\(674\) | −40.1194 | + | 23.1629i | −1.54534 | + | 0.892203i | ||||
\(675\) | 23.2893 | 0.896406 | ||||||||
\(676\) | −2.31081 | − | 16.1272i | −0.0888771 | − | 0.620277i | ||||
\(677\) | 9.58632 | 0.368432 | 0.184216 | − | 0.982886i | \(-0.441025\pi\) | ||||
0.184216 | + | 0.982886i | \(0.441025\pi\) | |||||||
\(678\) | −12.0766 | + | 6.97241i | −0.463798 | + | 0.267774i | ||||
\(679\) | 0.152083 | + | 0.263416i | 0.00583642 | + | 0.0101090i | ||||
\(680\) | −0.608752 | + | 1.05439i | −0.0233446 | + | 0.0404340i | ||||
\(681\) | 12.4377i | 0.476614i | ||||||||
\(682\) | −8.48320 | − | 4.89778i | −0.324839 | − | 0.187546i | ||||
\(683\) | 20.2327 | + | 11.6813i | 0.774181 | + | 0.446974i | 0.834364 | − | 0.551214i | \(-0.185835\pi\) |
−0.0601829 | + | 0.998187i | \(0.519168\pi\) | |||||||
\(684\) | 13.4446i | 0.514068i | ||||||||
\(685\) | −0.594813 | + | 1.03025i | −0.0227266 | + | 0.0393637i | ||||
\(686\) | −21.0952 | − | 36.5380i | −0.805420 | − | 1.39503i | ||||
\(687\) | 25.0174 | − | 14.4438i | 0.954473 | − | 0.551065i | ||||
\(688\) | −27.8802 | −1.06292 | ||||||||
\(689\) | 4.30492 | − | 1.48878i | 0.164004 | − | 0.0567181i | ||||
\(690\) | −1.77433 | −0.0675477 | ||||||||
\(691\) | 4.75944 | − | 2.74786i | 0.181057 | − | 0.104534i | −0.406732 | − | 0.913548i | \(-0.633332\pi\) |
0.587789 | + | 0.809014i | \(0.299998\pi\) | |||||||
\(692\) | 5.08682 | + | 8.81064i | 0.193372 | + | 0.334930i | ||||
\(693\) | 21.1552 | − | 36.6420i | 0.803621 | − | 1.39191i | ||||
\(694\) | − | 7.84618i | − | 0.297837i | ||||||
\(695\) | −11.3095 | − | 6.52952i | −0.428992 | − | 0.247679i | ||||
\(696\) | −6.23518 | − | 3.59988i | −0.236344 | − | 0.136453i | ||||
\(697\) | − | 13.7448i | − | 0.520622i | ||||||
\(698\) | −4.49466 | + | 7.78498i | −0.170125 | + | 0.294666i | ||||
\(699\) | 1.73989 | + | 3.01357i | 0.0658086 | + | 0.113984i | ||||
\(700\) | 21.0121 | − | 12.1313i | 0.794183 | − | 0.458522i | ||||
\(701\) | −43.4482 | −1.64101 | −0.820507 | − | 0.571636i | \(-0.806309\pi\) | ||||
−0.820507 | + | 0.571636i | \(0.806309\pi\) | |||||||
\(702\) | −22.5251 | + | 25.9826i | −0.850154 | + | 0.980652i | ||||
\(703\) | 38.5990 | 1.45579 | ||||||||
\(704\) | 6.24084 | − | 3.60315i | 0.235210 | − | 0.135799i | ||||
\(705\) | 1.73785 | + | 3.01004i | 0.0654511 | + | 0.113365i | ||||
\(706\) | 8.68606 | − | 15.0447i | 0.326904 | − | 0.566215i | ||||
\(707\) | 6.78244i | 0.255080i | ||||||||
\(708\) | −10.3757 | − | 5.99043i | −0.389944 | − | 0.225134i | ||||
\(709\) | −2.58897 | − | 1.49474i | −0.0972307 | − | 0.0561361i | 0.450596 | − | 0.892728i | \(-0.351211\pi\) |
−0.547827 | + | 0.836592i | \(0.684545\pi\) | |||||||
\(710\) | 5.34520i | 0.200602i | ||||||||
\(711\) | 7.42646 | − | 12.8630i | 0.278514 | − | 0.482400i | ||||
\(712\) | 7.28743 | + | 12.6222i | 0.273108 | + | 0.473037i | ||||
\(713\) | 0.996341 | − | 0.575237i | 0.0373132 | − | 0.0215428i | ||||
\(714\) | 10.2888 | 0.385050 | ||||||||
\(715\) | 11.4182 | + | 9.89878i | 0.427018 | + | 0.370193i | ||||
\(716\) | 28.9778 | 1.08295 | ||||||||
\(717\) | −10.5283 | + | 6.07854i | −0.393188 | + | 0.227007i | ||||
\(718\) | 33.2674 | + | 57.6209i | 1.24153 | + | 2.15039i | ||||
\(719\) | −4.33930 | + | 7.51590i | −0.161829 | + | 0.280296i | −0.935525 | − | 0.353262i | \(-0.885073\pi\) |
0.773696 | + | 0.633557i | \(0.218406\pi\) | |||||||
\(720\) | 6.75130i | 0.251606i | ||||||||
\(721\) | −18.2826 | − | 10.5555i | −0.680879 | − | 0.393106i | ||||
\(722\) | −27.5505 | − | 15.9063i | −1.02532 | − | 0.591972i | ||||
\(723\) | − | 7.35773i | − | 0.273637i | ||||||
\(724\) | −5.18559 | + | 8.98170i | −0.192721 | + | 0.333802i | ||||
\(725\) | −10.6242 | − | 18.4017i | −0.394574 | − | 0.683422i | ||||
\(726\) | −32.0087 | + | 18.4803i | −1.18796 | + | 0.685867i | ||||
\(727\) | 3.15935 | 0.117174 | 0.0585869 | − | 0.998282i | \(-0.481341\pi\) | ||||
0.0585869 | + | 0.998282i | \(0.481341\pi\) | |||||||
\(728\) | 4.04503 | − | 20.9604i | 0.149919 | − | 0.776844i | ||||
\(729\) | 18.5359 | 0.686517 | ||||||||
\(730\) | 5.27299 | − | 3.04436i | 0.195162 | − | 0.112677i | ||||
\(731\) | −3.30793 | − | 5.72951i | −0.122348 | − | 0.211913i | ||||
\(732\) | −0.677309 | + | 1.17313i | −0.0250341 | + | 0.0433603i | ||||
\(733\) | − | 28.0004i | − | 1.03422i | −0.855920 | − | 0.517109i | \(-0.827008\pi\) | ||
0.855920 | − | 0.517109i | \(-0.172992\pi\) | |||||||
\(734\) | −4.89404 | − | 2.82557i | −0.180642 | − | 0.104294i | ||||
\(735\) | −9.12423 | − | 5.26788i | −0.336552 | − | 0.194309i | ||||
\(736\) | 7.14309i | 0.263298i | ||||||||
\(737\) | −23.0457 | + | 39.9162i | −0.848897 | + | 1.47033i | ||||
\(738\) | −18.7571 | − | 32.4883i | −0.690458 | − | 1.19591i | ||||
\(739\) | −42.3817 | + | 24.4691i | −1.55903 | + | 0.900109i | −0.561685 | + | 0.827351i | \(0.689847\pi\) |
−0.997350 | + | 0.0727582i | \(0.976820\pi\) | |||||||
\(740\) | −6.16750 | −0.226722 | ||||||||
\(741\) | −7.90323 | − | 22.8527i | −0.290332 | − | 0.839515i | ||||
\(742\) | −10.0162 | −0.367706 | ||||||||
\(743\) | −13.1491 | + | 7.59161i | −0.482392 | + | 0.278509i | −0.721413 | − | 0.692505i | \(-0.756507\pi\) |
0.239021 | + | 0.971014i | \(0.423174\pi\) | |||||||
\(744\) | 0.746191 | + | 1.29244i | 0.0273567 | + | 0.0473832i | ||||
\(745\) | −3.56313 | + | 6.17152i | −0.130543 | + | 0.226107i | ||||
\(746\) | 31.6465i | 1.15866i | ||||||||
\(747\) | −19.7130 | − | 11.3813i | −0.721262 | − | 0.416421i | ||||
\(748\) | 6.90378 | + | 3.98590i | 0.252427 | + | 0.145739i | ||||
\(749\) | 54.3767i | 1.98688i | ||||||||
\(750\) | 7.25204 | − | 12.5609i | 0.264807 | − | 0.458660i | ||||
\(751\) | 7.95992 | + | 13.7870i | 0.290462 | + | 0.503094i | 0.973919 | − | 0.226896i | \(-0.0728578\pi\) |
−0.683457 | + | 0.729990i | \(0.739525\pi\) | |||||||
\(752\) | 17.3754 | − | 10.0317i | 0.633617 | − | 0.365819i | ||||
\(753\) | −13.5101 | −0.492335 | ||||||||
\(754\) | 30.8054 | + | 5.94496i | 1.12187 | + | 0.216503i | ||||
\(755\) | −16.7499 | −0.609593 | ||||||||
\(756\) | 25.2260 | − | 14.5642i | 0.917460 | − | 0.529696i | ||||
\(757\) | 11.2728 | + | 19.5250i | 0.409715 | + | 0.709648i | 0.994858 | − | 0.101283i | \(-0.0322947\pi\) |
−0.585142 | + | 0.810931i | \(0.698961\pi\) | |||||||
\(758\) | 25.6848 | − | 44.4874i | 0.932915 | − | 1.61586i | ||||
\(759\) | − | 6.92281i | − | 0.251282i | ||||||
\(760\) | −5.44891 | − | 3.14593i | −0.197653 | − | 0.114115i | ||||
\(761\) | −17.0671 | − | 9.85369i | −0.618682 | − | 0.357196i | 0.157674 | − | 0.987491i | \(-0.449601\pi\) |
−0.776356 | + | 0.630295i | \(0.782934\pi\) | |||||||
\(762\) | 29.4838i | 1.06808i | ||||||||
\(763\) | 15.0288 | − | 26.0307i | 0.544080 | − | 0.942374i | ||||
\(764\) | 7.50860 | + | 13.0053i | 0.271652 | + | 0.470515i | ||||
\(765\) | −1.38742 | + | 0.801029i | −0.0501624 | + | 0.0289613i | ||||
\(766\) | 19.2462 | 0.695392 | ||||||||
\(767\) | −30.5462 | − | 5.89494i | −1.10296 | − | 0.212854i | ||||
\(768\) | −22.9734 | −0.828980 | ||||||||
\(769\) | −4.23795 | + | 2.44678i | −0.152824 | + | 0.0882332i | −0.574462 | − | 0.818531i | \(-0.694789\pi\) |
0.421638 | + | 0.906764i | \(0.361455\pi\) | |||||||
\(770\) | −16.6145 | − | 28.7772i | −0.598746 | − | 1.03706i | ||||
\(771\) | −10.4556 | + | 18.1097i | −0.376551 | + | 0.652205i | ||||
\(772\) | − | 8.51072i | − | 0.306308i | ||||||
\(773\) | 34.4908 | + | 19.9133i | 1.24055 | + | 0.716231i | 0.969206 | − | 0.246252i | \(-0.0791992\pi\) |
0.271342 | + | 0.962483i | \(0.412533\pi\) | |||||||
\(774\) | −15.6377 | − | 9.02846i | −0.562087 | − | 0.324521i | ||||
\(775\) | 4.40443i | 0.158212i | ||||||||
\(776\) | 0.0466023 | − | 0.0807176i | 0.00167293 | − | 0.00289759i | ||||
\(777\) | −15.5287 | − | 26.8966i | −0.557091 | − | 0.964909i | ||||
\(778\) | 22.6606 | − | 13.0831i | 0.812423 | − | 0.469052i | ||||
\(779\) | 71.0310 | 2.54495 | ||||||||
\(780\) | 1.26281 | + | 3.65149i | 0.0452157 | + | 0.130744i | ||||
\(781\) | −20.8550 | −0.746252 | ||||||||
\(782\) | −2.10484 | + | 1.21523i | −0.0752691 | + | 0.0434566i | ||||
\(783\) | −12.7549 | − | 22.0921i | −0.455822 | − | 0.789506i | ||||
\(784\) | −30.4088 | + | 52.6696i | −1.08603 | + | 1.88106i | ||||
\(785\) | 17.5217i | 0.625378i | ||||||||
\(786\) | 29.9458 | + | 17.2892i | 1.06813 | + | 0.616687i | ||||
\(787\) | 22.7376 | + | 13.1276i | 0.810510 | + | 0.467948i | 0.847133 | − | 0.531381i | \(-0.178327\pi\) |
−0.0366233 | + | 0.999329i | \(0.511660\pi\) | |||||||
\(788\) | − | 3.20384i | − | 0.114132i | ||||||
\(789\) | −4.03528 | + | 6.98931i | −0.143660 | + | 0.248826i | ||||
\(790\) | −5.83246 | − | 10.1021i | −0.207509 | − | 0.359417i | ||||
\(791\) | 26.5628 | − | 15.3360i | 0.944465 | − | 0.545287i | ||||
\(792\) | −12.9651 | −0.460693 | ||||||||
\(793\) | −0.666512 | + | 3.45371i | −0.0236685 | + | 0.122645i | ||||
\(794\) | −55.4188 | −1.96674 | ||||||||
\(795\) | −0.935527 | + | 0.540127i | −0.0331797 | + | 0.0191563i | ||||
\(796\) | 3.16684 | + | 5.48512i | 0.112246 | + | 0.194415i | ||||
\(797\) | −8.19833 | + | 14.1999i | −0.290400 | + | 0.502987i | −0.973904 | − | 0.226959i | \(-0.927122\pi\) |
0.683505 | + | 0.729946i | \(0.260455\pi\) | |||||||
\(798\) | 53.1710i | 1.88223i | ||||||||
\(799\) | 4.12313 | + | 2.38049i | 0.145866 | + | 0.0842156i | ||||
\(800\) | −23.6826 | − | 13.6731i | −0.837306 | − | 0.483419i | ||||
\(801\) | 19.1784i | 0.677636i | ||||||||
\(802\) | −27.9877 | + | 48.4761i | −0.988279 | + | 1.71175i | ||||
\(803\) | 11.8780 | + | 20.5733i | 0.419165 | + | 0.726016i | ||||
\(804\) | −10.2056 | + | 5.89222i | −0.359925 | + | 0.207803i | ||||
\(805\) | 3.90271 | 0.137552 | ||||||||
\(806\) | −4.91378 | − | 4.25989i | −0.173081 | − | 0.150048i | ||||
\(807\) | 19.9969 | 0.703924 | ||||||||
\(808\) | 1.79988 | − | 1.03916i | 0.0633195 | − | 0.0365575i | ||||
\(809\) | 7.07958 | + | 12.2622i | 0.248905 | + | 0.431116i | 0.963222 | − | 0.268706i | \(-0.0865961\pi\) |
−0.714317 | + | 0.699822i | \(0.753263\pi\) | |||||||
\(810\) | 0.376923 | − | 0.652849i | 0.0132437 | − | 0.0229388i | ||||
\(811\) | − | 20.7922i | − | 0.730114i | −0.930985 | − | 0.365057i | \(-0.881049\pi\) | ||
0.930985 | − | 0.365057i | \(-0.118951\pi\) | |||||||
\(812\) | −23.0154 | − | 13.2880i | −0.807682 | − | 0.466316i | ||||
\(813\) | 0.845143 | + | 0.487944i | 0.0296405 | + | 0.0171129i | ||||
\(814\) | − | 62.4657i | − | 2.18942i | ||||||
\(815\) | 1.40853 | − | 2.43964i | 0.0493385 | − | 0.0854569i | ||||
\(816\) | −3.20275 | − | 5.54732i | −0.112119 | − | 0.194195i | ||||
\(817\) | 29.6092 | − | 17.0949i | 1.03589 | − | 0.598073i | ||||
\(818\) | −3.26891 | −0.114295 | ||||||||
\(819\) | 18.4000 | − | 21.2244i | 0.642947 | − | 0.741639i | ||||
\(820\) | −11.3496 | −0.396345 | ||||||||
\(821\) | −23.2386 | + | 13.4168i | −0.811034 | + | 0.468251i | −0.847315 | − | 0.531091i | \(-0.821782\pi\) |
0.0362805 | + | 0.999342i | \(0.488449\pi\) | |||||||
\(822\) | −1.54029 | − | 2.66786i | −0.0537238 | − | 0.0930524i | ||||
\(823\) | 0.596052 | − | 1.03239i | 0.0207771 | − | 0.0359870i | −0.855450 | − | 0.517886i | \(-0.826719\pi\) |
0.876227 | + | 0.481899i | \(0.160053\pi\) | |||||||
\(824\) | 6.46894i | 0.225356i | ||||||||
\(825\) | 22.9522 | + | 13.2515i | 0.799095 | + | 0.461358i | ||||
\(826\) | 59.2426 | + | 34.2038i | 2.06132 | + | 1.19010i | ||||
\(827\) | 8.94631i | 0.311094i | 0.987829 | + | 0.155547i | \(0.0497140\pi\) | ||||
−0.987829 | + | 0.155547i | \(0.950286\pi\) | |||||||
\(828\) | −1.27771 | + | 2.21305i | −0.0444034 | + | 0.0769089i | ||||
\(829\) | −23.8676 | − | 41.3398i | −0.828955 | − | 1.43579i | −0.898859 | − | 0.438238i | \(-0.855603\pi\) |
0.0699039 | − | 0.997554i | \(-0.477731\pi\) | |||||||
\(830\) | −15.4819 | + | 8.93846i | −0.537383 | + | 0.310258i | ||||
\(831\) | 23.6605 | 0.820772 | ||||||||
\(832\) | 4.52147 | − | 1.56368i | 0.156754 | − | 0.0542107i | ||||
\(833\) | −14.4318 | −0.500032 | ||||||||
\(834\) | 29.2863 | − | 16.9084i | 1.01410 | − | 0.585491i | ||||
\(835\) | −8.05427 | − | 13.9504i | −0.278730 | − | 0.482774i | ||||
\(836\) | −20.5985 | + | 35.6776i | −0.712413 | + | 1.23394i | ||||
\(837\) | 5.28771i | 0.182770i | ||||||||
\(838\) | −29.0382 | − | 16.7652i | −1.00311 | − | 0.579145i | ||||
\(839\) | −42.6237 | − | 24.6088i | −1.47153 | − | 0.849591i | −0.472046 | − | 0.881574i | \(-0.656484\pi\) |
−0.999488 | + | 0.0319829i | \(0.989818\pi\) | |||||||
\(840\) | 5.06255i | 0.174674i | ||||||||
\(841\) | 2.86285 | − | 4.95860i | 0.0987189 | − | 0.170986i | ||||
\(842\) | 4.84140 | + | 8.38556i | 0.166846 | + | 0.288985i | ||||
\(843\) | −16.3059 | + | 9.41423i | −0.561606 | + | 0.324243i | ||||
\(844\) | −14.4298 | −0.496693 | ||||||||
\(845\) | 6.19791 | + | 7.88911i | 0.213214 | + | 0.271393i | ||||
\(846\) | 12.9943 | 0.446753 | ||||||||
\(847\) | 70.4043 | − | 40.6479i | 2.41912 | − | 1.39668i | ||||
\(848\) | 3.11788 | + | 5.40032i | 0.107068 | + | 0.185448i | ||||
\(849\) | 11.0904 | − | 19.2092i | 0.380622 | − | 0.659257i | ||||
\(850\) | − | 9.30468i | − | 0.319148i | ||||||
\(851\) | 6.35360 | + | 3.66826i | 0.217799 | + | 0.125746i | ||||
\(852\) | −4.61776 | − | 2.66607i | −0.158202 | − | 0.0913379i | ||||
\(853\) | 46.8047i | 1.60256i | 0.598288 | + | 0.801281i | \(0.295848\pi\) | ||||
−0.598288 | + | 0.801281i | \(0.704152\pi\) | |||||||
\(854\) | 3.86725 | − | 6.69828i | 0.132335 | − | 0.229210i | ||||
\(855\) | −4.13959 | − | 7.16998i | −0.141571 | − | 0.245208i | ||||
\(856\) | 14.4301 | − | 8.33123i | 0.493211 | − | 0.284756i | ||||
\(857\) | 26.2083 | 0.895257 | 0.447629 | − | 0.894220i | \(-0.352269\pi\) | ||||
0.447629 | + | 0.894220i | \(0.352269\pi\) | |||||||
\(858\) | −36.9830 | + | 12.7900i | −1.26258 | + | 0.436642i | ||||
\(859\) | 39.6143 | 1.35162 | 0.675812 | − | 0.737074i | \(-0.263793\pi\) | ||||
0.675812 | + | 0.737074i | \(0.263793\pi\) | |||||||
\(860\) | −4.73106 | + | 2.73148i | −0.161328 | + | 0.0931427i | ||||
\(861\) | −28.5764 | − | 49.4958i | −0.973881 | − | 1.68681i | ||||
\(862\) | 20.2246 | − | 35.0300i | 0.688851 | − | 1.19313i | ||||
\(863\) | 57.2856i | 1.95003i | 0.222149 | + | 0.975013i | \(0.428693\pi\) | ||||
−0.222149 | + | 0.975013i | \(0.571307\pi\) | |||||||
\(864\) | −28.4320 | − | 16.4152i | −0.967276 | − | 0.558457i | ||||
\(865\) | −5.42558 | − | 3.13246i | −0.184475 | − | 0.106507i | ||||
\(866\) | − | 23.9803i | − | 0.814883i | ||||||
\(867\) | −8.65786 | + | 14.9958i | −0.294036 | + | 0.509286i | ||||
\(868\) | 2.75435 | + | 4.77068i | 0.0934888 | + | 0.161927i | ||||
\(869\) | 39.4148 | − | 22.7561i | 1.33706 | − | 0.771949i | ||||
\(870\) | −7.44040 | −0.252253 | ||||||||
\(871\) | −20.0442 | + | 23.1210i | −0.679171 | + | 0.783424i | ||||
\(872\) | −9.21046 | −0.311906 | ||||||||
\(873\) | 0.106213 | − | 0.0613219i | 0.00359476 | − | 0.00207543i | ||||
\(874\) | −6.28013 | − | 10.8775i | −0.212428 | − | 0.367937i | ||||
\(875\) | −15.9511 | + | 27.6281i | −0.539246 | + | 0.934002i | ||||
\(876\) | 6.07384i | 0.205216i | ||||||||
\(877\) | 42.2980 | + | 24.4207i | 1.42830 | + | 0.824630i | 0.996987 | − | 0.0775716i | \(-0.0247166\pi\) |
0.431314 | + | 0.902202i | \(0.358050\pi\) | |||||||
\(878\) | 49.3818 | + | 28.5106i | 1.66655 | + | 0.962185i | ||||
\(879\) | − | 29.5923i | − | 0.998125i | ||||||
\(880\) | −10.3437 | + | 17.9158i | −0.348685 | + | 0.603940i | ||||
\(881\) | −15.5523 | − | 26.9374i | −0.523971 | − | 0.907544i | −0.999611 | − | 0.0279039i | \(-0.991117\pi\) |
0.475640 | − | 0.879640i | \(-0.342217\pi\) | |||||||
\(882\) | −34.1120 | + | 19.6946i | −1.14861 | + | 0.663151i | ||||
\(883\) | −32.2081 | −1.08389 | −0.541945 | − | 0.840414i | \(-0.682312\pi\) | ||||
−0.541945 | + | 0.840414i | \(0.682312\pi\) | |||||||
\(884\) | 3.99892 | + | 3.46677i | 0.134498 | + | 0.116600i | ||||
\(885\) | 7.37780 | 0.248002 | ||||||||
\(886\) | −41.6849 | + | 24.0668i | −1.40043 | + | 0.808540i | ||||
\(887\) | 9.87609 | + | 17.1059i | 0.331607 | + | 0.574360i | 0.982827 | − | 0.184529i | \(-0.0590760\pi\) |
−0.651220 | + | 0.758889i | \(0.725743\pi\) | |||||||
\(888\) | −4.75842 | + | 8.24182i | −0.159682 | + | 0.276577i | ||||
\(889\) | − | 64.8505i | − | 2.17502i | ||||||
\(890\) | 13.0441 | + | 7.53100i | 0.437238 | + | 0.252440i | ||||
\(891\) | 2.54718 | + | 1.47062i | 0.0853338 | + | 0.0492675i | ||||
\(892\) | 7.25666i | 0.242971i | ||||||||
\(893\) | −12.3020 | + | 21.3076i | −0.411670 | + | 0.713033i | ||||
\(894\) | −9.22686 | − | 15.9814i | −0.308592 | − | 0.534498i | ||||
\(895\) | −15.4538 | + | 8.92225i | −0.516563 | + | 0.298238i | ||||
\(896\) | 44.0633 | 1.47205 | ||||||||
\(897\) | 0.870891 | − | 4.51276i | 0.0290782 | − | 0.150677i | ||||
\(898\) | −35.7162 | −1.19186 | ||||||||
\(899\) | 4.17801 | − | 2.41217i | 0.139344 | − | 0.0804505i | ||||
\(900\) | −4.89151 | − | 8.47235i | −0.163050 | − | 0.282412i | ||||
\(901\) | −0.739860 | + | 1.28148i | −0.0246483 | + | 0.0426921i | ||||
\(902\) | − | 114.951i | − | 3.82745i | ||||||
\(903\) | −23.8241 | − | 13.7548i | −0.792815 | − | 0.457732i | ||||
\(904\) | −8.13955 | − | 4.69937i | −0.270717 | − | 0.156299i | ||||
\(905\) | − | 6.38656i | − | 0.212297i | ||||||
\(906\) | 21.6873 | − | 37.5635i | 0.720513 | − | 1.24796i | ||||
\(907\) | 22.4903 | + | 38.9544i | 0.746778 | + | 1.29346i | 0.949359 | + | 0.314193i | \(0.101734\pi\) |
−0.202581 | + | 0.979266i | \(0.564933\pi\) | |||||||
\(908\) | 12.1833 | − | 7.03405i | 0.404318 | − | 0.233433i | ||||
\(909\) | 2.73477 | 0.0907065 | ||||||||
\(910\) | −7.21029 | − | 20.8490i | −0.239019 | − | 0.691139i | ||||
\(911\) | −24.7942 | −0.821469 | −0.410735 | − | 0.911755i | \(-0.634728\pi\) | ||||
−0.410735 | + | 0.911755i | \(0.634728\pi\) | |||||||
\(912\) | 28.6677 | − | 16.5513i | 0.949281 | − | 0.548068i | ||||
\(913\) | −34.8746 | − | 60.4047i | −1.15418 | − | 1.99910i | ||||
\(914\) | 20.0601 | − | 34.7452i | 0.663531 | − | 1.14927i | ||||
\(915\) | − | 0.834173i | − | 0.0275769i | ||||||
\(916\) | −28.2968 | − | 16.3372i | −0.934953 | − | 0.539795i | ||||
\(917\) | −65.8669 | − | 38.0283i | −2.17512 | − | 1.25580i | ||||
\(918\) | − | 11.1707i | − | 0.368688i | ||||||
\(919\) | 25.8933 | − | 44.8484i | 0.854140 | − | 1.47941i | −0.0233014 | − | 0.999728i | \(-0.507418\pi\) |
0.877441 | − | 0.479685i | \(-0.159249\pi\) | |||||||
\(920\) | −0.597946 | − | 1.03567i | −0.0197137 | − | 0.0341451i | ||||
\(921\) | 25.8604 | − | 14.9305i | 0.852128 | − | 0.491976i | ||||
\(922\) | −9.48084 | −0.312235 | ||||||||
\(923\) | −13.5947 | − | 2.62357i | −0.447476 | − | 0.0863557i | ||||
\(924\) | 33.1478 | 1.09048 | ||||||||
\(925\) | −24.3239 | + | 14.0434i | −0.799763 | + | 0.461744i | ||||
\(926\) | −1.76242 | − | 3.05261i | −0.0579168 | − | 0.100315i | ||||
\(927\) | −4.25609 | + | 7.37177i | −0.139788 | + | 0.242121i | ||||
\(928\) | 29.9535i | 0.983271i | ||||||||
\(929\) | 24.5508 | + | 14.1744i | 0.805487 | + | 0.465048i | 0.845386 | − | 0.534156i | \(-0.179370\pi\) |
−0.0398993 | + | 0.999204i | \(0.512704\pi\) | |||||||
\(930\) | 1.33564 | + | 0.771131i | 0.0437973 | + | 0.0252864i | ||||
\(931\) | − | 74.5811i | − | 2.44430i | ||||||
\(932\) | 1.96796 | − | 3.40861i | 0.0644628 | − | 0.111653i | ||||
\(933\) | 9.50052 | + | 16.4554i | 0.311033 | + | 0.538725i | ||||
\(934\) | −51.2903 | + | 29.6125i | −1.67827 | + | 0.968949i | ||||
\(935\) | −4.90903 | −0.160542 | ||||||||
\(936\) | −8.45150 | − | 1.63101i | −0.276246 | − | 0.0533111i | ||||
\(937\) | 2.21095 | 0.0722287 | 0.0361143 | − | 0.999348i | \(-0.488502\pi\) | ||||
0.0361143 | + | 0.999348i | \(0.488502\pi\) | |||||||
\(938\) | 58.2714 | − | 33.6430i | 1.90263 | − | 1.09848i | ||||
\(939\) | −10.1361 | − | 17.5562i | −0.330778 | − | 0.572924i | ||||
\(940\) | 1.96566 | − | 3.40462i | 0.0641126 | − | 0.111046i | ||||
\(941\) | − | 22.2919i | − | 0.726694i | −0.931654 | − | 0.363347i | \(-0.881634\pi\) | ||
0.931654 | − | 0.363347i | \(-0.118366\pi\) | |||||||
\(942\) | −39.2943 | − | 22.6866i | −1.28028 | − | 0.739169i | ||||
\(943\) | 11.6921 | + | 6.75042i | 0.380746 | + | 0.219824i | ||||
\(944\) | − | 42.5883i | − | 1.38613i | ||||||
\(945\) | −8.96863 | + | 15.5341i | −0.291750 | + | 0.505325i | ||||
\(946\) | −27.6650 | − | 47.9172i | −0.899466 | − | 1.55792i | ||||
\(947\) | −12.3416 | + | 7.12545i | −0.401050 | + | 0.231546i | −0.686937 | − | 0.726717i | \(-0.741045\pi\) |
0.285887 | + | 0.958263i | \(0.407712\pi\) | |||||||
\(948\) | 11.6364 | 0.377933 | ||||||||
\(949\) | 5.15476 | + | 14.9053i | 0.167330 | + | 0.483847i | ||||
\(950\) | 48.0851 | 1.56009 | ||||||||
\(951\) | 19.4595 | − | 11.2349i | 0.631017 | − | 0.364318i | ||||
\(952\) | 3.46731 | + | 6.00556i | 0.112376 | + | 0.194641i | ||||
\(953\) | 19.8078 | − | 34.3082i | 0.641639 | − | 1.11135i | −0.343428 | − | 0.939179i | \(-0.611588\pi\) |
0.985067 | − | 0.172173i | \(-0.0550787\pi\) | |||||||
\(954\) | 4.03865i | 0.130756i | ||||||||
\(955\) | −8.00864 | − | 4.62379i | −0.259154 | − | 0.149622i | ||||
\(956\) | 11.9085 | + | 6.87536i | 0.385147 | + | 0.222365i | ||||
\(957\) | − | 29.0298i | − | 0.938399i | ||||||
\(958\) | 12.6769 | − | 21.9570i | 0.409572 | − | 0.709399i | ||||
\(959\) | 3.38792 | + | 5.86805i | 0.109402 | + | 0.189489i | ||||
\(960\) | −0.982589 | + | 0.567298i | −0.0317129 | + | 0.0183095i | ||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 7.85819 | − | 40.7194i | 0.253358 | − | 1.31284i | ||||
\(963\) | 21.9254 | 0.706536 | ||||||||
\(964\) | −7.20726 | + | 4.16111i | −0.232130 | + | 0.134020i | ||||
\(965\) | 2.62045 | + | 4.53875i | 0.0843552 | + | 0.146107i | ||||
\(966\) | −5.05310 | + | 8.75223i | −0.162581 | + | 0.281598i | ||||
\(967\) | 35.4974i | 1.14152i | 0.821117 | + | 0.570760i | \(0.193351\pi\) | ||||
−0.821117 | + | 0.570760i | \(0.806649\pi\) | |||||||
\(968\) | −21.5737 | − | 12.4556i | −0.693406 | − | 0.400338i | ||||
\(969\) | 6.80273 | + | 3.92756i | 0.218535 | + | 0.126171i | ||||
\(970\) | − | 0.0963198i | − | 0.00309264i | ||||||
\(971\) | 2.96522 | − | 5.13591i | 0.0951584 | − | 0.164819i | −0.814516 | − | 0.580141i | \(-0.802998\pi\) |
0.909675 | + | 0.415321i | \(0.136331\pi\) | |||||||
\(972\) | −9.56403 | − | 16.5654i | −0.306766 | − | 0.531335i | ||||
\(973\) | −64.4161 | + | 37.1907i | −2.06509 | + | 1.19228i | ||||
\(974\) | 13.8243 | 0.442959 | ||||||||
\(975\) | 13.2948 | + | 11.5256i | 0.425774 | + | 0.369115i | ||||
\(976\) | −4.81525 | −0.154133 | ||||||||
\(977\) | −9.00755 | + | 5.20051i | −0.288177 | + | 0.166379i | −0.637119 | − | 0.770765i | \(-0.719874\pi\) |
0.348942 | + | 0.937144i | \(0.386541\pi\) | |||||||
\(978\) | 3.64743 | + | 6.31754i | 0.116632 | + | 0.202013i | ||||
\(979\) | −29.3832 | + | 50.8932i | −0.939092 | + | 1.62656i | ||||
\(980\) | 11.9169i | 0.380670i | ||||||||
\(981\) | −10.4959 | − | 6.05982i | −0.335109 | − | 0.193475i | ||||
\(982\) | 52.9497 | + | 30.5705i | 1.68969 | + | 0.975545i | ||||
\(983\) | 21.6354i | 0.690062i | 0.938591 | + | 0.345031i | \(0.112132\pi\) | ||||
−0.938591 | + | 0.345031i | \(0.887868\pi\) | |||||||
\(984\) | −8.75657 | + | 15.1668i | −0.279149 | + | 0.483500i | ||||
\(985\) | 0.986460 | + | 1.70860i | 0.0314312 | + | 0.0544405i | ||||
\(986\) | −8.82635 | + | 5.09590i | −0.281088 | + | 0.162286i | ||||
\(987\) | 19.7968 | 0.630139 | ||||||||
\(988\) | −17.9157 | + | 20.6658i | −0.569975 | + | 0.657466i | ||||
\(989\) | 6.49843 | 0.206638 | ||||||||
\(990\) | −11.6033 | + | 6.69919i | −0.368778 | + | 0.212914i | ||||
\(991\) | −13.2496 | − | 22.9489i | −0.420886 | − | 0.728996i | 0.575141 | − | 0.818055i | \(-0.304947\pi\) |
−0.996026 | + | 0.0890590i | \(0.971614\pi\) | |||||||
\(992\) | 3.10441 | − | 5.37700i | 0.0985651 | − | 0.170720i | ||||
\(993\) | 33.0920i | 1.05014i | ||||||||
\(994\) | 26.3662 | + | 15.2225i | 0.836284 | + | 0.482829i | ||||
\(995\) | −3.37773 | − | 1.95014i | −0.107081 | − | 0.0618235i | ||||
\(996\) | − | 17.8332i | − | 0.565067i | ||||||
\(997\) | −7.64585 | + | 13.2430i | −0.242147 | + | 0.419410i | −0.961325 | − | 0.275415i | \(-0.911185\pi\) |
0.719179 | + | 0.694825i | \(0.244518\pi\) | |||||||
\(998\) | 28.3344 | + | 49.0766i | 0.896910 | + | 1.55349i | ||||
\(999\) | −29.2019 | + | 16.8597i | −0.923906 | + | 0.533417i |
(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 | 403.2.r.a.218.8 | ✓ | 68 | |
13.2 | odd | 12 | 5239.2.a.q.1.10 | 34 | |||
13.4 | even | 6 | inner | 403.2.r.a.342.8 | yes | 68 | |
13.11 | odd | 12 | 5239.2.a.r.1.25 | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.r.a.218.8 | ✓ | 68 | 1.1 | even | 1 | trivial | |
403.2.r.a.342.8 | yes | 68 | 13.4 | even | 6 | inner | |
5239.2.a.q.1.10 | 34 | 13.2 | odd | 12 | |||
5239.2.a.r.1.25 | 34 | 13.11 | odd | 12 |