Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(166,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.166");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.s (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: | \(3.42558224671\) |
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 | 166.9 | ||
Character | \(\chi\) | \(=\) | 429.166 |
Dual form | 429.2.s.b.199.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.813989 | − | 0.469957i | 0.575577 | − | 0.332310i | −0.183797 | − | 0.982964i | \(-0.558839\pi\) |
0.759374 | + | 0.650655i | \(0.225505\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.558281 | + | 0.966972i | −0.279141 | + | 0.483486i | ||||
\(5\) | − | 0.163878i | − | 0.0732884i | −0.999328 | − | 0.0366442i | \(-0.988333\pi\) | ||
0.999328 | − | 0.0366442i | \(-0.0116668\pi\) | |||||||
\(6\) | −0.813989 | − | 0.469957i | −0.332310 | − | 0.191859i | ||||
\(7\) | 2.40248 | + | 1.38708i | 0.908054 | + | 0.524265i | 0.879804 | − | 0.475336i | \(-0.157673\pi\) |
0.0282494 | + | 0.999601i | \(0.491007\pi\) | |||||||
\(8\) | 2.92930i | 1.03566i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.0770155 | − | 0.133395i | −0.0243544 | − | 0.0421831i | ||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | 1.11656 | 0.322324 | ||||||||
\(13\) | 3.59344 | − | 0.295291i | 0.996641 | − | 0.0818989i | ||||
\(14\) | 2.60746 | 0.696873 | ||||||||
\(15\) | −0.141922 | + | 0.0819389i | −0.0366442 | + | 0.0211565i | ||||
\(16\) | 0.260081 | + | 0.450474i | 0.0650203 | + | 0.112619i | ||||
\(17\) | −1.03931 | + | 1.80013i | −0.252069 | + | 0.436596i | −0.964095 | − | 0.265556i | \(-0.914444\pi\) |
0.712026 | + | 0.702153i | \(0.247778\pi\) | |||||||
\(18\) | 0.939913i | 0.221540i | ||||||||
\(19\) | 2.48517 | + | 1.43482i | 0.570138 | + | 0.329169i | 0.757205 | − | 0.653178i | \(-0.226565\pi\) |
−0.187066 | + | 0.982347i | \(0.559898\pi\) | |||||||
\(20\) | 0.158465 | + | 0.0914899i | 0.0354339 | + | 0.0204578i | ||||
\(21\) | − | 2.77415i | − | 0.605369i | ||||||
\(22\) | 0.469957 | − | 0.813989i | 0.100195 | − | 0.173543i | ||||
\(23\) | 0.745923 | + | 1.29198i | 0.155536 | + | 0.269396i | 0.933254 | − | 0.359217i | \(-0.116956\pi\) |
−0.777718 | + | 0.628613i | \(0.783623\pi\) | |||||||
\(24\) | 2.53685 | − | 1.46465i | 0.517832 | − | 0.298970i | ||||
\(25\) | 4.97314 | 0.994629 | ||||||||
\(26\) | 2.78625 | − | 1.92912i | 0.546428 | − | 0.378332i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.68252 | + | 1.54876i | −0.506949 | + | 0.292687i | ||||
\(29\) | −0.213005 | − | 0.368936i | −0.0395540 | − | 0.0685096i | 0.845571 | − | 0.533864i | \(-0.179260\pi\) |
−0.885125 | + | 0.465354i | \(0.845927\pi\) | |||||||
\(30\) | −0.0770155 | + | 0.133395i | −0.0140610 | + | 0.0243544i | ||||
\(31\) | − | 6.48317i | − | 1.16441i | −0.813042 | − | 0.582205i | \(-0.802190\pi\) | ||
0.813042 | − | 0.582205i | \(-0.197810\pi\) | |||||||
\(32\) | −4.65029 | − | 2.68485i | −0.822063 | − | 0.474618i | ||||
\(33\) | −0.866025 | − | 0.500000i | −0.150756 | − | 0.0870388i | ||||
\(34\) | 1.95372i | 0.335060i | ||||||||
\(35\) | 0.227311 | − | 0.393714i | 0.0384226 | − | 0.0665498i | ||||
\(36\) | −0.558281 | − | 0.966972i | −0.0930469 | − | 0.161162i | ||||
\(37\) | 2.52192 | − | 1.45603i | 0.414601 | − | 0.239370i | −0.278164 | − | 0.960534i | \(-0.589726\pi\) |
0.692765 | + | 0.721164i | \(0.256392\pi\) | |||||||
\(38\) | 2.69721 | 0.437545 | ||||||||
\(39\) | −2.05245 | − | 2.96436i | −0.328655 | − | 0.474678i | ||||
\(40\) | 0.480047 | 0.0759021 | ||||||||
\(41\) | −3.97665 | + | 2.29592i | −0.621049 | + | 0.358563i | −0.777277 | − | 0.629158i | \(-0.783400\pi\) |
0.156228 | + | 0.987721i | \(0.450066\pi\) | |||||||
\(42\) | −1.30373 | − | 2.25813i | −0.201170 | − | 0.348437i | ||||
\(43\) | −3.72486 | + | 6.45165i | −0.568036 | + | 0.983867i | 0.428724 | + | 0.903435i | \(0.358963\pi\) |
−0.996760 | + | 0.0804316i | \(0.974370\pi\) | |||||||
\(44\) | 1.11656i | 0.168328i | ||||||||
\(45\) | 0.141922 | + | 0.0819389i | 0.0211565 | + | 0.0122147i | ||||
\(46\) | 1.21435 | + | 0.701103i | 0.179045 | + | 0.103372i | ||||
\(47\) | − | 2.71471i | − | 0.395981i | −0.980204 | − | 0.197990i | \(-0.936559\pi\) | ||
0.980204 | − | 0.197990i | \(-0.0634414\pi\) | |||||||
\(48\) | 0.260081 | − | 0.450474i | 0.0375395 | − | 0.0650203i | ||||
\(49\) | 0.347955 | + | 0.602676i | 0.0497079 | + | 0.0860966i | ||||
\(50\) | 4.04808 | − | 2.33716i | 0.572486 | − | 0.330525i | ||||
\(51\) | 2.07861 | 0.291064 | ||||||||
\(52\) | −1.72061 | + | 3.63961i | −0.238606 | + | 0.504723i | ||||
\(53\) | −5.71174 | −0.784568 | −0.392284 | − | 0.919844i | \(-0.628315\pi\) | ||||
−0.392284 | + | 0.919844i | \(0.628315\pi\) | |||||||
\(54\) | 0.813989 | − | 0.469957i | 0.110770 | − | 0.0639530i | ||||
\(55\) | −0.0819389 | − | 0.141922i | −0.0110486 | − | 0.0191368i | ||||
\(56\) | −4.06316 | + | 7.03760i | −0.542962 | + | 0.940438i | ||||
\(57\) | − | 2.86963i | − | 0.380092i | ||||||
\(58\) | −0.346767 | − | 0.200206i | −0.0455328 | − | 0.0262884i | ||||
\(59\) | 2.07066 | + | 1.19550i | 0.269578 | + | 0.155641i | 0.628696 | − | 0.777651i | \(-0.283589\pi\) |
−0.359118 | + | 0.933292i | \(0.616922\pi\) | |||||||
\(60\) | − | 0.182980i | − | 0.0236226i | ||||||
\(61\) | −2.65604 | + | 4.60039i | −0.340071 | + | 0.589020i | −0.984446 | − | 0.175690i | \(-0.943784\pi\) |
0.644375 | + | 0.764710i | \(0.277118\pi\) | |||||||
\(62\) | −3.04681 | − | 5.27723i | −0.386945 | − | 0.670208i | ||||
\(63\) | −2.40248 | + | 1.38708i | −0.302685 | + | 0.174755i | ||||
\(64\) | −6.08737 | −0.760921 | ||||||||
\(65\) | −0.0483916 | − | 0.588885i | −0.00600224 | − | 0.0730422i | ||||
\(66\) | −0.939913 | −0.115695 | ||||||||
\(67\) | −8.10306 | + | 4.67830i | −0.989946 | + | 0.571545i | −0.905258 | − | 0.424862i | \(-0.860323\pi\) |
−0.0846877 | + | 0.996408i | \(0.526989\pi\) | |||||||
\(68\) | −1.16045 | − | 2.00996i | −0.140725 | − | 0.243744i | ||||
\(69\) | 0.745923 | − | 1.29198i | 0.0897985 | − | 0.155536i | ||||
\(70\) | − | 0.427305i | − | 0.0510727i | ||||||
\(71\) | −11.3570 | − | 6.55696i | −1.34783 | − | 0.778167i | −0.359884 | − | 0.932997i | \(-0.617184\pi\) |
−0.987941 | + | 0.154830i | \(0.950517\pi\) | |||||||
\(72\) | −2.53685 | − | 1.46465i | −0.298970 | − | 0.172611i | ||||
\(73\) | − | 2.42783i | − | 0.284156i | −0.989855 | − | 0.142078i | \(-0.954622\pi\) | ||
0.989855 | − | 0.142078i | \(-0.0453783\pi\) | |||||||
\(74\) | 1.36854 | − | 2.37039i | 0.159090 | − | 0.275552i | ||||
\(75\) | −2.48657 | − | 4.30687i | −0.287125 | − | 0.497314i | ||||
\(76\) | −2.77485 | + | 1.60206i | −0.318298 | + | 0.183769i | ||||
\(77\) | 2.77415 | 0.316144 | ||||||||
\(78\) | −3.06379 | − | 1.44840i | −0.346906 | − | 0.163999i | ||||
\(79\) | 7.41437 | 0.834182 | 0.417091 | − | 0.908865i | \(-0.363050\pi\) | ||||
0.417091 | + | 0.908865i | \(0.363050\pi\) | |||||||
\(80\) | 0.0738227 | − | 0.0426216i | 0.00825363 | − | 0.00476524i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.15797 | + | 3.73771i | −0.238308 | + | 0.412761i | ||||
\(83\) | − | 7.48093i | − | 0.821139i | −0.911829 | − | 0.410570i | \(-0.865330\pi\) | ||
0.911829 | − | 0.410570i | \(-0.134670\pi\) | |||||||
\(84\) | 2.68252 | + | 1.54876i | 0.292687 | + | 0.168983i | ||||
\(85\) | 0.295002 | + | 0.170319i | 0.0319974 | + | 0.0184737i | ||||
\(86\) | 7.00209i | 0.755055i | ||||||||
\(87\) | −0.213005 | + | 0.368936i | −0.0228365 | + | 0.0395540i | ||||
\(88\) | 1.46465 | + | 2.53685i | 0.156132 | + | 0.270429i | ||||
\(89\) | 7.56642 | − | 4.36847i | 0.802039 | − | 0.463057i | −0.0421447 | − | 0.999112i | \(-0.513419\pi\) |
0.844184 | + | 0.536054i | \(0.180086\pi\) | |||||||
\(90\) | 0.154031 | 0.0162363 | ||||||||
\(91\) | 9.04277 | + | 4.27494i | 0.947940 | + | 0.448135i | ||||
\(92\) | −1.66574 | −0.173665 | ||||||||
\(93\) | −5.61459 | + | 3.24158i | −0.582205 | + | 0.336136i | ||||
\(94\) | −1.27579 | − | 2.20974i | −0.131588 | − | 0.227917i | ||||
\(95\) | 0.235135 | − | 0.407265i | 0.0241243 | − | 0.0417845i | ||||
\(96\) | 5.36969i | 0.548042i | ||||||||
\(97\) | 8.31993 | + | 4.80351i | 0.844761 | + | 0.487723i | 0.858880 | − | 0.512178i | \(-0.171161\pi\) |
−0.0141189 | + | 0.999900i | \(0.504494\pi\) | |||||||
\(98\) | 0.566463 | + | 0.327048i | 0.0572214 | + | 0.0330368i | ||||
\(99\) | 1.00000i | 0.100504i | ||||||||
\(100\) | −2.77641 | + | 4.80889i | −0.277641 | + | 0.480889i | ||||
\(101\) | −2.94671 | − | 5.10385i | −0.293208 | − | 0.507852i | 0.681358 | − | 0.731950i | \(-0.261390\pi\) |
−0.974567 | + | 0.224098i | \(0.928056\pi\) | |||||||
\(102\) | 1.69197 | − | 0.976859i | 0.167530 | − | 0.0967234i | ||||
\(103\) | −5.05671 | −0.498253 | −0.249126 | − | 0.968471i | \(-0.580143\pi\) | ||||
−0.249126 | + | 0.968471i | \(0.580143\pi\) | |||||||
\(104\) | 0.864994 | + | 10.5263i | 0.0848197 | + | 1.03218i | ||||
\(105\) | −0.454622 | −0.0443665 | ||||||||
\(106\) | −4.64930 | + | 2.68427i | −0.451580 | + | 0.260720i | ||||
\(107\) | −4.19490 | − | 7.26577i | −0.405536 | − | 0.702409i | 0.588848 | − | 0.808244i | \(-0.299582\pi\) |
−0.994384 | + | 0.105835i | \(0.966248\pi\) | |||||||
\(108\) | −0.558281 | + | 0.966972i | −0.0537206 | + | 0.0930469i | ||||
\(109\) | 11.4104i | 1.09292i | 0.837484 | + | 0.546461i | \(0.184025\pi\) | ||||
−0.837484 | + | 0.546461i | \(0.815975\pi\) | |||||||
\(110\) | −0.133395 | − | 0.0770155i | −0.0127187 | − | 0.00734314i | ||||
\(111\) | −2.52192 | − | 1.45603i | −0.239370 | − | 0.138200i | ||||
\(112\) | 1.44301i | 0.136352i | ||||||||
\(113\) | 4.67346 | − | 8.09467i | 0.439642 | − | 0.761483i | −0.558019 | − | 0.829828i | \(-0.688439\pi\) |
0.997662 | + | 0.0683451i | \(0.0217719\pi\) | |||||||
\(114\) | −1.34860 | − | 2.33585i | −0.126308 | − | 0.218772i | ||||
\(115\) | 0.211726 | − | 0.122240i | 0.0197436 | − | 0.0113990i | ||||
\(116\) | 0.475667 | 0.0441646 | ||||||||
\(117\) | −1.54099 | + | 3.25965i | −0.142465 | + | 0.301355i | ||||
\(118\) | 2.24733 | 0.206884 | ||||||||
\(119\) | −4.99384 | + | 2.88319i | −0.457784 | + | 0.264302i | ||||
\(120\) | −0.240024 | − | 0.415733i | −0.0219111 | − | 0.0379511i | ||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 4.99289i | 0.452035i | ||||||||
\(123\) | 3.97665 | + | 2.29592i | 0.358563 | + | 0.207016i | ||||
\(124\) | 6.26904 | + | 3.61943i | 0.562976 | + | 0.325034i | ||||
\(125\) | − | 1.63438i | − | 0.146183i | ||||||
\(126\) | −1.30373 | + | 2.25813i | −0.116146 | + | 0.201170i | ||||
\(127\) | −7.19603 | − | 12.4639i | −0.638545 | − | 1.10599i | −0.985752 | − | 0.168204i | \(-0.946203\pi\) |
0.347208 | − | 0.937788i | \(-0.387130\pi\) | |||||||
\(128\) | 4.34552 | − | 2.50889i | 0.384094 | − | 0.221757i | ||||
\(129\) | 7.44972 | 0.655911 | ||||||||
\(130\) | −0.316141 | − | 0.456604i | −0.0277274 | − | 0.0400468i | ||||
\(131\) | −8.12560 | −0.709937 | −0.354969 | − | 0.934878i | \(-0.615508\pi\) | ||||
−0.354969 | + | 0.934878i | \(0.615508\pi\) | |||||||
\(132\) | 0.966972 | − | 0.558281i | 0.0841641 | − | 0.0485922i | ||||
\(133\) | 3.98040 | + | 6.89425i | 0.345144 | + | 0.597807i | ||||
\(134\) | −4.39720 | + | 7.61617i | −0.379860 | + | 0.657937i | ||||
\(135\) | − | 0.163878i | − | 0.0141044i | ||||||
\(136\) | −5.27313 | − | 3.04444i | −0.452167 | − | 0.261059i | ||||
\(137\) | −15.7332 | − | 9.08356i | −1.34418 | − | 0.776061i | −0.356760 | − | 0.934196i | \(-0.616118\pi\) |
−0.987417 | + | 0.158135i | \(0.949452\pi\) | |||||||
\(138\) | − | 1.40221i | − | 0.119364i | ||||||
\(139\) | 5.46987 | − | 9.47409i | 0.463948 | − | 0.803582i | −0.535205 | − | 0.844722i | \(-0.679766\pi\) |
0.999153 | + | 0.0411403i | \(0.0130991\pi\) | |||||||
\(140\) | 0.253807 | + | 0.439606i | 0.0214506 | + | 0.0371535i | ||||
\(141\) | −2.35100 | + | 1.35735i | −0.197990 | + | 0.114310i | ||||
\(142\) | −12.3259 | −1.03437 | ||||||||
\(143\) | 2.96436 | − | 2.05245i | 0.247893 | − | 0.171634i | ||||
\(144\) | −0.520163 | −0.0433469 | ||||||||
\(145\) | −0.0604604 | + | 0.0349068i | −0.00502096 | + | 0.00289885i | ||||
\(146\) | −1.14097 | − | 1.97622i | −0.0944276 | − | 0.163553i | ||||
\(147\) | 0.347955 | − | 0.602676i | 0.0286989 | − | 0.0497079i | ||||
\(148\) | 3.25150i | 0.267272i | ||||||||
\(149\) | 13.8777 | + | 8.01230i | 1.13691 | + | 0.656394i | 0.945663 | − | 0.325149i | \(-0.105414\pi\) |
0.191244 | + | 0.981542i | \(0.438748\pi\) | |||||||
\(150\) | −4.04808 | − | 2.33716i | −0.330525 | − | 0.190829i | ||||
\(151\) | − | 16.5728i | − | 1.34868i | −0.738422 | − | 0.674339i | \(-0.764428\pi\) | ||
0.738422 | − | 0.674339i | \(-0.235572\pi\) | |||||||
\(152\) | −4.20301 | + | 7.27982i | −0.340909 | + | 0.590471i | ||||
\(153\) | −1.03931 | − | 1.80013i | −0.0840230 | − | 0.145532i | ||||
\(154\) | 2.25813 | − | 1.30373i | 0.181965 | − | 0.105058i | ||||
\(155\) | −1.06245 | −0.0853378 | ||||||||
\(156\) | 4.01230 | − | 0.329710i | 0.321241 | − | 0.0263980i | ||||
\(157\) | 21.1013 | 1.68407 | 0.842035 | − | 0.539423i | \(-0.181358\pi\) | ||||
0.842035 | + | 0.539423i | \(0.181358\pi\) | |||||||
\(158\) | 6.03521 | − | 3.48443i | 0.480136 | − | 0.277207i | ||||
\(159\) | 2.85587 | + | 4.94652i | 0.226485 | + | 0.392284i | ||||
\(160\) | −0.439987 | + | 0.762079i | −0.0347840 | + | 0.0602477i | ||||
\(161\) | 4.13860i | 0.326168i | ||||||||
\(162\) | −0.813989 | − | 0.469957i | −0.0639530 | − | 0.0369233i | ||||
\(163\) | −10.1609 | − | 5.86639i | −0.795863 | − | 0.459491i | 0.0461598 | − | 0.998934i | \(-0.485302\pi\) |
−0.842022 | + | 0.539443i | \(0.818635\pi\) | |||||||
\(164\) | − | 5.12708i | − | 0.400358i | ||||||
\(165\) | −0.0819389 | + | 0.141922i | −0.00637894 | + | 0.0110486i | ||||
\(166\) | −3.51572 | − | 6.08940i | −0.272872 | − | 0.472629i | ||||
\(167\) | 18.4503 | − | 10.6523i | 1.42772 | − | 0.824297i | 0.430783 | − | 0.902456i | \(-0.358237\pi\) |
0.996941 | + | 0.0781589i | \(0.0249042\pi\) | |||||||
\(168\) | 8.12632 | 0.626959 | ||||||||
\(169\) | 12.8256 | − | 2.12222i | 0.986585 | − | 0.163247i | ||||
\(170\) | 0.320171 | 0.0245560 | ||||||||
\(171\) | −2.48517 | + | 1.43482i | −0.190046 | + | 0.109723i | ||||
\(172\) | −4.15904 | − | 7.20367i | −0.317124 | − | 0.549275i | ||||
\(173\) | −1.17798 | + | 2.04032i | −0.0895600 | + | 0.155122i | −0.907325 | − | 0.420429i | \(-0.861879\pi\) |
0.817765 | + | 0.575552i | \(0.195213\pi\) | |||||||
\(174\) | 0.400413i | 0.0303552i | ||||||||
\(175\) | 11.9479 | + | 6.89812i | 0.903177 | + | 0.521449i | ||||
\(176\) | 0.450474 | + | 0.260081i | 0.0339558 | + | 0.0196044i | ||||
\(177\) | − | 2.39100i | − | 0.179718i | ||||||
\(178\) | 4.10599 | − | 7.11178i | 0.307757 | − | 0.533050i | ||||
\(179\) | −7.96439 | − | 13.7947i | −0.595286 | − | 1.03107i | −0.993506 | − | 0.113776i | \(-0.963705\pi\) |
0.398220 | − | 0.917290i | \(-0.369628\pi\) | |||||||
\(180\) | −0.158465 | + | 0.0914899i | −0.0118113 | + | 0.00681926i | ||||
\(181\) | −19.0296 | −1.41446 | −0.707230 | − | 0.706984i | \(-0.750055\pi\) | ||||
−0.707230 | + | 0.706984i | \(0.750055\pi\) | |||||||
\(182\) | 9.36975 | − | 0.769959i | 0.694532 | − | 0.0570731i | ||||
\(183\) | 5.31207 | 0.392680 | ||||||||
\(184\) | −3.78458 | + | 2.18503i | −0.279003 | + | 0.161083i | ||||
\(185\) | −0.238611 | − | 0.413287i | −0.0175431 | − | 0.0303855i | ||||
\(186\) | −3.04681 | + | 5.27723i | −0.223403 | + | 0.386945i | ||||
\(187\) | 2.07861i | 0.152003i | ||||||||
\(188\) | 2.62504 | + | 1.51557i | 0.191451 | + | 0.110534i | ||||
\(189\) | 2.40248 | + | 1.38708i | 0.174755 | + | 0.100895i | ||||
\(190\) | − | 0.442012i | − | 0.0320670i | ||||||
\(191\) | −4.53853 | + | 7.86097i | −0.328397 | + | 0.568800i | −0.982194 | − | 0.187870i | \(-0.939842\pi\) |
0.653797 | + | 0.756670i | \(0.273175\pi\) | |||||||
\(192\) | 3.04369 | + | 5.27182i | 0.219659 | + | 0.380461i | ||||
\(193\) | 0.989480 | − | 0.571277i | 0.0712243 | − | 0.0411214i | −0.463965 | − | 0.885854i | \(-0.653574\pi\) |
0.535189 | + | 0.844732i | \(0.320240\pi\) | |||||||
\(194\) | 9.02977 | 0.648300 | ||||||||
\(195\) | −0.485794 | + | 0.336351i | −0.0347884 | + | 0.0240866i | ||||
\(196\) | −0.777027 | −0.0555020 | ||||||||
\(197\) | −15.0212 | + | 8.67251i | −1.07022 | + | 0.617891i | −0.928241 | − | 0.371979i | \(-0.878679\pi\) |
−0.141977 | + | 0.989870i | \(0.545346\pi\) | |||||||
\(198\) | 0.469957 | + | 0.813989i | 0.0333984 | + | 0.0578477i | ||||
\(199\) | −0.475891 | + | 0.824267i | −0.0337350 | + | 0.0584307i | −0.882400 | − | 0.470500i | \(-0.844074\pi\) |
0.848665 | + | 0.528931i | \(0.177407\pi\) | |||||||
\(200\) | 14.5678i | 1.03010i | ||||||||
\(201\) | 8.10306 | + | 4.67830i | 0.571545 | + | 0.329982i | ||||
\(202\) | −4.79717 | − | 2.76965i | −0.337528 | − | 0.194872i | ||||
\(203\) | − | 1.18182i | − | 0.0829472i | ||||||
\(204\) | −1.16045 | + | 2.00996i | −0.0812478 | + | 0.140725i | ||||
\(205\) | 0.376251 | + | 0.651685i | 0.0262785 | + | 0.0455157i | ||||
\(206\) | −4.11611 | + | 2.37644i | −0.286783 | + | 0.165574i | ||||
\(207\) | −1.49185 | −0.103690 | ||||||||
\(208\) | 1.06761 | + | 1.54195i | 0.0740252 | + | 0.106915i | ||||
\(209\) | 2.86963 | 0.198497 | ||||||||
\(210\) | −0.370057 | + | 0.213653i | −0.0255364 | + | 0.0147434i | ||||
\(211\) | −4.98172 | − | 8.62859i | −0.342956 | − | 0.594017i | 0.642025 | − | 0.766684i | \(-0.278095\pi\) |
−0.984980 | + | 0.172667i | \(0.944761\pi\) | |||||||
\(212\) | 3.18876 | − | 5.52309i | 0.219005 | − | 0.379328i | ||||
\(213\) | 13.1139i | 0.898550i | ||||||||
\(214\) | −6.82920 | − | 3.94284i | −0.466834 | − | 0.269527i | ||||
\(215\) | 1.05728 | + | 0.610422i | 0.0721060 | + | 0.0416304i | ||||
\(216\) | 2.92930i | 0.199314i | ||||||||
\(217\) | 8.99264 | − | 15.5757i | 0.610460 | − | 1.05735i | ||||
\(218\) | 5.36241 | + | 9.28797i | 0.363189 | + | 0.629061i | ||||
\(219\) | −2.10256 | + | 1.21391i | −0.142078 | + | 0.0820286i | ||||
\(220\) | 0.182980 | 0.0123365 | ||||||||
\(221\) | −3.20312 | + | 6.77556i | −0.215465 | + | 0.455774i | ||||
\(222\) | −2.73709 | −0.183701 | ||||||||
\(223\) | −10.1997 | + | 5.88882i | −0.683025 | + | 0.394345i | −0.800994 | − | 0.598673i | \(-0.795695\pi\) |
0.117969 | + | 0.993017i | \(0.462362\pi\) | |||||||
\(224\) | −7.44816 | − | 12.9006i | −0.497651 | − | 0.861958i | ||||
\(225\) | −2.48657 | + | 4.30687i | −0.165771 | + | 0.287125i | ||||
\(226\) | − | 8.78530i | − | 0.584389i | ||||||
\(227\) | 11.7824 | + | 6.80259i | 0.782028 | + | 0.451504i | 0.837149 | − | 0.546976i | \(-0.184221\pi\) |
−0.0551205 | + | 0.998480i | \(0.517554\pi\) | |||||||
\(228\) | 2.77485 | + | 1.60206i | 0.183769 | + | 0.106099i | ||||
\(229\) | 19.3966i | 1.28176i | 0.767641 | + | 0.640881i | \(0.221431\pi\) | ||||
−0.767641 | + | 0.640881i | \(0.778569\pi\) | |||||||
\(230\) | 0.114895 | − | 0.199004i | 0.00757597 | − | 0.0131220i | ||||
\(231\) | −1.38708 | − | 2.40248i | −0.0912628 | − | 0.158072i | ||||
\(232\) | 1.08072 | − | 0.623955i | 0.0709529 | − | 0.0409647i | ||||
\(233\) | 28.5050 | 1.86742 | 0.933712 | − | 0.358026i | \(-0.116550\pi\) | ||||
0.933712 | + | 0.358026i | \(0.116550\pi\) | |||||||
\(234\) | 0.277548 | + | 3.37752i | 0.0181439 | + | 0.220796i | ||||
\(235\) | −0.444880 | −0.0290208 | ||||||||
\(236\) | −2.31203 | + | 1.33485i | −0.150500 | + | 0.0868913i | ||||
\(237\) | −3.70718 | − | 6.42103i | −0.240807 | − | 0.417091i | ||||
\(238\) | −2.70995 | + | 4.69378i | −0.175660 | + | 0.304252i | ||||
\(239\) | 2.55682i | 0.165387i | 0.996575 | + | 0.0826936i | \(0.0263523\pi\) | ||||
−0.996575 | + | 0.0826936i | \(0.973648\pi\) | |||||||
\(240\) | −0.0738227 | − | 0.0426216i | −0.00476524 | − | 0.00275121i | ||||
\(241\) | 6.57793 | + | 3.79777i | 0.423722 | + | 0.244636i | 0.696668 | − | 0.717393i | \(-0.254665\pi\) |
−0.272947 | + | 0.962029i | \(0.587998\pi\) | |||||||
\(242\) | − | 0.939913i | − | 0.0604199i | ||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.96563 | − | 5.13662i | −0.189855 | − | 0.328839i | ||||
\(245\) | 0.0987652 | − | 0.0570221i | 0.00630988 | − | 0.00364301i | ||||
\(246\) | 4.31593 | 0.275174 | ||||||||
\(247\) | 9.35401 | + | 4.42208i | 0.595182 | + | 0.281370i | ||||
\(248\) | 18.9911 | 1.20594 | ||||||||
\(249\) | −6.47868 | + | 3.74047i | −0.410570 | + | 0.237042i | ||||
\(250\) | −0.768087 | − | 1.33037i | −0.0485781 | − | 0.0841397i | ||||
\(251\) | −1.62987 | + | 2.82301i | −0.102876 | + | 0.178187i | −0.912869 | − | 0.408254i | \(-0.866138\pi\) |
0.809992 | + | 0.586441i | \(0.199471\pi\) | |||||||
\(252\) | − | 3.09751i | − | 0.195125i | ||||||
\(253\) | 1.29198 | + | 0.745923i | 0.0812258 | + | 0.0468957i | ||||
\(254\) | −11.7150 | − | 6.76365i | −0.735063 | − | 0.424389i | ||||
\(255\) | − | 0.340639i | − | 0.0213316i | ||||||
\(256\) | 8.44551 | − | 14.6281i | 0.527844 | − | 0.914253i | ||||
\(257\) | 11.0734 | + | 19.1798i | 0.690742 | + | 1.19640i | 0.971595 | + | 0.236650i | \(0.0760495\pi\) |
−0.280853 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(258\) | 6.06399 | − | 3.50105i | 0.377528 | − | 0.217966i | ||||
\(259\) | 8.07850 | 0.501974 | ||||||||
\(260\) | 0.596451 | + | 0.281970i | 0.0369903 | + | 0.0174871i | ||||
\(261\) | 0.426010 | 0.0263694 | ||||||||
\(262\) | −6.61415 | + | 3.81868i | −0.408624 | + | 0.235919i | ||||
\(263\) | −12.5479 | − | 21.7336i | −0.773738 | − | 1.34015i | −0.935501 | − | 0.353324i | \(-0.885051\pi\) |
0.161763 | − | 0.986830i | \(-0.448282\pi\) | |||||||
\(264\) | 1.46465 | − | 2.53685i | 0.0901430 | − | 0.156132i | ||||
\(265\) | 0.936028i | 0.0574998i | ||||||||
\(266\) | 6.48000 | + | 3.74123i | 0.397314 | + | 0.229389i | ||||
\(267\) | −7.56642 | − | 4.36847i | −0.463057 | − | 0.267346i | ||||
\(268\) | − | 10.4472i | − | 0.638166i | ||||||
\(269\) | −3.12969 | + | 5.42078i | −0.190820 | + | 0.330511i | −0.945522 | − | 0.325557i | \(-0.894448\pi\) |
0.754702 | + | 0.656068i | \(0.227781\pi\) | |||||||
\(270\) | −0.0770155 | − | 0.133395i | −0.00468701 | − | 0.00811815i | ||||
\(271\) | −7.51874 | + | 4.34095i | −0.456731 | + | 0.263694i | −0.710669 | − | 0.703527i | \(-0.751608\pi\) |
0.253938 | + | 0.967221i | \(0.418274\pi\) | |||||||
\(272\) | −1.08122 | −0.0655584 | ||||||||
\(273\) | −0.819180 | − | 9.96874i | −0.0495791 | − | 0.603336i | ||||
\(274\) | −17.0755 | −1.03157 | ||||||||
\(275\) | 4.30687 | − | 2.48657i | 0.259714 | − | 0.149946i | ||||
\(276\) | 0.832869 | + | 1.44257i | 0.0501328 | + | 0.0868326i | ||||
\(277\) | 15.0094 | − | 25.9971i | 0.901829 | − | 1.56201i | 0.0767120 | − | 0.997053i | \(-0.475558\pi\) |
0.825117 | − | 0.564961i | \(-0.191109\pi\) | |||||||
\(278\) | − | 10.2824i | − | 0.616698i | ||||||
\(279\) | 5.61459 | + | 3.24158i | 0.336136 | + | 0.194068i | ||||
\(280\) | 1.15331 | + | 0.665862i | 0.0689232 | + | 0.0397928i | ||||
\(281\) | 26.5273i | 1.58248i | 0.611503 | + | 0.791242i | \(0.290565\pi\) | ||||
−0.611503 | + | 0.791242i | \(0.709435\pi\) | |||||||
\(282\) | −1.27579 | + | 2.20974i | −0.0759724 | + | 0.131588i | ||||
\(283\) | 0.322563 | + | 0.558696i | 0.0191744 | + | 0.0332110i | 0.875453 | − | 0.483303i | \(-0.160563\pi\) |
−0.856279 | + | 0.516514i | \(0.827230\pi\) | |||||||
\(284\) | 12.6808 | − | 7.32125i | 0.752466 | − | 0.434436i | ||||
\(285\) | −0.470269 | −0.0278563 | ||||||||
\(286\) | 1.44840 | − | 3.06379i | 0.0856455 | − | 0.181166i | ||||
\(287\) | −12.7385 | −0.751928 | ||||||||
\(288\) | 4.65029 | − | 2.68485i | 0.274021 | − | 0.158206i | ||||
\(289\) | 6.33968 | + | 10.9807i | 0.372922 | + | 0.645921i | ||||
\(290\) | −0.0328094 | + | 0.0568275i | −0.00192663 | + | 0.00333703i | ||||
\(291\) | − | 9.60702i | − | 0.563174i | ||||||
\(292\) | 2.34764 | + | 1.35541i | 0.137385 | + | 0.0793194i | ||||
\(293\) | 15.0751 | + | 8.70364i | 0.880699 | + | 0.508472i | 0.870889 | − | 0.491480i | \(-0.163544\pi\) |
0.00981048 | + | 0.999952i | \(0.496877\pi\) | |||||||
\(294\) | − | 0.654095i | − | 0.0381476i | ||||||
\(295\) | 0.195916 | − | 0.339336i | 0.0114067 | − | 0.0197569i | ||||
\(296\) | 4.26515 | + | 7.38746i | 0.247907 | + | 0.429387i | ||||
\(297\) | 0.866025 | − | 0.500000i | 0.0502519 | − | 0.0290129i | ||||
\(298\) | 15.0617 | 0.872504 | ||||||||
\(299\) | 3.06194 | + | 4.42237i | 0.177076 | + | 0.255752i | ||||
\(300\) | 5.55283 | 0.320593 | ||||||||
\(301\) | −17.8978 | + | 10.3333i | −1.03161 | + | 0.595603i | ||||
\(302\) | −7.78852 | − | 13.4901i | −0.448179 | − | 0.776269i | ||||
\(303\) | −2.94671 | + | 5.10385i | −0.169284 | + | 0.293208i | ||||
\(304\) | 1.49268i | 0.0856108i | ||||||||
\(305\) | 0.753902 | + | 0.435266i | 0.0431683 | + | 0.0249232i | ||||
\(306\) | −1.69197 | − | 0.976859i | −0.0967234 | − | 0.0558433i | ||||
\(307\) | − | 7.60069i | − | 0.433794i | −0.976194 | − | 0.216897i | \(-0.930406\pi\) | ||
0.976194 | − | 0.216897i | \(-0.0695937\pi\) | |||||||
\(308\) | −1.54876 | + | 2.68252i | −0.0882486 | + | 0.152851i | ||||
\(309\) | 2.52836 | + | 4.37924i | 0.143833 | + | 0.249126i | ||||
\(310\) | −0.864820 | + | 0.499304i | −0.0491185 | + | 0.0283586i | ||||
\(311\) | −8.88702 | −0.503937 | −0.251968 | − | 0.967735i | \(-0.581078\pi\) | ||||
−0.251968 | + | 0.967735i | \(0.581078\pi\) | |||||||
\(312\) | 8.68351 | − | 6.01224i | 0.491607 | − | 0.340376i | ||||
\(313\) | 17.2887 | 0.977213 | 0.488606 | − | 0.872504i | \(-0.337505\pi\) | ||||
0.488606 | + | 0.872504i | \(0.337505\pi\) | |||||||
\(314\) | 17.1762 | − | 9.91671i | 0.969312 | − | 0.559632i | ||||
\(315\) | 0.227311 | + | 0.393714i | 0.0128075 | + | 0.0221833i | ||||
\(316\) | −4.13930 | + | 7.16948i | −0.232854 | + | 0.403315i | ||||
\(317\) | 10.7911i | 0.606086i | 0.952977 | + | 0.303043i | \(0.0980026\pi\) | ||||
−0.952977 | + | 0.303043i | \(0.901997\pi\) | |||||||
\(318\) | 4.64930 | + | 2.68427i | 0.260720 | + | 0.150527i | ||||
\(319\) | −0.368936 | − | 0.213005i | −0.0206564 | − | 0.0119260i | ||||
\(320\) | 0.997585i | 0.0557667i | ||||||||
\(321\) | −4.19490 | + | 7.26577i | −0.234136 | + | 0.405536i | ||||
\(322\) | 1.94496 | + | 3.36878i | 0.108389 | + | 0.187735i | ||||
\(323\) | −5.16572 | + | 2.98243i | −0.287428 | + | 0.165947i | ||||
\(324\) | 1.11656 | 0.0620313 | ||||||||
\(325\) | 17.8707 | − | 1.46852i | 0.991287 | − | 0.0814590i | ||||
\(326\) | −11.0278 | −0.610774 | ||||||||
\(327\) | 9.88173 | − | 5.70522i | 0.546461 | − | 0.315499i | ||||
\(328\) | −6.72544 | − | 11.6488i | −0.371350 | − | 0.643198i | ||||
\(329\) | 3.76550 | − | 6.52204i | 0.207599 | − | 0.359572i | ||||
\(330\) | 0.154031i | 0.00847913i | ||||||||
\(331\) | −20.5365 | − | 11.8568i | −1.12879 | − | 0.651706i | −0.185159 | − | 0.982709i | \(-0.559280\pi\) |
−0.943630 | + | 0.331002i | \(0.892613\pi\) | |||||||
\(332\) | 7.23385 | + | 4.17647i | 0.397009 | + | 0.229213i | ||||
\(333\) | 2.91206i | 0.159580i | ||||||||
\(334\) | 10.0122 | − | 17.3416i | 0.547843 | − | 0.948893i | ||||
\(335\) | 0.766670 | + | 1.32791i | 0.0418877 | + | 0.0725515i | ||||
\(336\) | 1.24968 | − | 0.721505i | 0.0681758 | − | 0.0393613i | ||||
\(337\) | −15.0119 | −0.817753 | −0.408876 | − | 0.912590i | \(-0.634079\pi\) | ||||
−0.408876 | + | 0.912590i | \(0.634079\pi\) | |||||||
\(338\) | 9.44255 | − | 7.75494i | 0.513607 | − | 0.421813i | ||||
\(339\) | −9.34692 | −0.507655 | ||||||||
\(340\) | −0.329388 | + | 0.190172i | −0.0178636 | + | 0.0103135i | ||||
\(341\) | −3.24158 | − | 5.61459i | −0.175542 | − | 0.304047i | ||||
\(342\) | −1.34860 | + | 2.33585i | −0.0729241 | + | 0.126308i | ||||
\(343\) | − | 17.4885i | − | 0.944290i | ||||||
\(344\) | −18.8988 | − | 10.9112i | −1.01896 | − | 0.588294i | ||||
\(345\) | −0.211726 | − | 0.122240i | −0.0113990 | − | 0.00658119i | ||||
\(346\) | 2.21440i | 0.119047i | ||||||||
\(347\) | −12.1188 | + | 20.9905i | −0.650574 | + | 1.12683i | 0.332410 | + | 0.943135i | \(0.392138\pi\) |
−0.982984 | + | 0.183692i | \(0.941195\pi\) | |||||||
\(348\) | −0.237833 | − | 0.411940i | −0.0127492 | − | 0.0220823i | ||||
\(349\) | −16.8523 | + | 9.72970i | −0.902085 | + | 0.520819i | −0.877876 | − | 0.478888i | \(-0.841040\pi\) |
−0.0242087 | + | 0.999707i | \(0.507707\pi\) | |||||||
\(350\) | 12.9673 | 0.693130 | ||||||||
\(351\) | 3.59344 | − | 0.295291i | 0.191804 | − | 0.0157614i | ||||
\(352\) | −5.36969 | −0.286205 | ||||||||
\(353\) | −28.4220 | + | 16.4094i | −1.51275 | + | 0.873386i | −0.512860 | + | 0.858472i | \(0.671414\pi\) |
−0.999889 | + | 0.0149134i | \(0.995253\pi\) | |||||||
\(354\) | −1.12367 | − | 1.94625i | −0.0597221 | − | 0.103442i | ||||
\(355\) | −1.07454 | + | 1.86116i | −0.0570307 | + | 0.0987800i | ||||
\(356\) | 9.75535i | 0.517033i | ||||||||
\(357\) | 4.99384 | + | 2.88319i | 0.264302 | + | 0.152595i | ||||
\(358\) | −12.9658 | − | 7.48584i | −0.685266 | − | 0.395639i | ||||
\(359\) | 26.5319i | 1.40030i | 0.713996 | + | 0.700149i | \(0.246883\pi\) | ||||
−0.713996 | + | 0.700149i | \(0.753117\pi\) | |||||||
\(360\) | −0.240024 | + | 0.415733i | −0.0126504 | + | 0.0219111i | ||||
\(361\) | −5.38260 | − | 9.32294i | −0.283295 | − | 0.490681i | ||||
\(362\) | −15.4899 | + | 8.94309i | −0.814131 | + | 0.470039i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −9.18216 | + | 6.35749i | −0.481276 | + | 0.333223i | ||||
\(365\) | −0.397867 | −0.0208253 | ||||||||
\(366\) | 4.32397 | − | 2.49644i | 0.226017 | − | 0.130491i | ||||
\(367\) | 6.99940 | + | 12.1233i | 0.365366 | + | 0.632832i | 0.988835 | − | 0.149016i | \(-0.0476107\pi\) |
−0.623469 | + | 0.781848i | \(0.714277\pi\) | |||||||
\(368\) | −0.388001 | + | 0.672038i | −0.0202260 | + | 0.0350324i | ||||
\(369\) | − | 4.59184i | − | 0.239042i | ||||||
\(370\) | −0.388454 | − | 0.224274i | −0.0201948 | − | 0.0116594i | ||||
\(371\) | −13.7224 | − | 7.92262i | −0.712430 | − | 0.411322i | ||||
\(372\) | − | 7.23886i | − | 0.375317i | ||||||
\(373\) | 16.6872 | − | 28.9031i | 0.864030 | − | 1.49654i | −0.00397769 | − | 0.999992i | \(-0.501266\pi\) |
0.868007 | − | 0.496551i | \(-0.165401\pi\) | |||||||
\(374\) | 0.976859 | + | 1.69197i | 0.0505122 | + | 0.0874896i | ||||
\(375\) | −1.41541 | + | 0.817189i | −0.0730916 | + | 0.0421994i | ||||
\(376\) | 7.95219 | 0.410103 | ||||||||
\(377\) | −0.874364 | − | 1.26285i | −0.0450320 | − | 0.0650400i | ||||
\(378\) | 2.60746 | 0.134113 | ||||||||
\(379\) | −10.9640 | + | 6.33009i | −0.563185 | + | 0.325155i | −0.754423 | − | 0.656389i | \(-0.772083\pi\) |
0.191238 | + | 0.981544i | \(0.438750\pi\) | |||||||
\(380\) | 0.262543 | + | 0.454737i | 0.0134681 | + | 0.0233275i | ||||
\(381\) | −7.19603 | + | 12.4639i | −0.368664 | + | 0.638545i | ||||
\(382\) | 8.53166i | 0.436518i | ||||||||
\(383\) | 24.9991 | + | 14.4332i | 1.27739 | + | 0.737504i | 0.976369 | − | 0.216112i | \(-0.0693375\pi\) |
0.301026 | + | 0.953616i | \(0.402671\pi\) | |||||||
\(384\) | −4.34552 | − | 2.50889i | −0.221757 | − | 0.128031i | ||||
\(385\) | − | 0.454622i | − | 0.0231697i | ||||||
\(386\) | 0.536951 | − | 0.930026i | 0.0273301 | − | 0.0473371i | ||||
\(387\) | −3.72486 | − | 6.45165i | −0.189345 | − | 0.327956i | ||||
\(388\) | −9.28972 | + | 5.36342i | −0.471614 | + | 0.272287i | ||||
\(389\) | −34.6650 | −1.75759 | −0.878793 | − | 0.477203i | \(-0.841651\pi\) | ||||
−0.878793 | + | 0.477203i | \(0.841651\pi\) | |||||||
\(390\) | −0.237360 | + | 0.502088i | −0.0120192 | + | 0.0254242i | ||||
\(391\) | −3.10097 | −0.156823 | ||||||||
\(392\) | −1.76542 | + | 1.01926i | −0.0891671 | + | 0.0514806i | ||||
\(393\) | 4.06280 | + | 7.03698i | 0.204941 | + | 0.354969i | ||||
\(394\) | −8.15141 | + | 14.1187i | −0.410662 | + | 0.711288i | ||||
\(395\) | − | 1.21505i | − | 0.0611358i | ||||||
\(396\) | −0.966972 | − | 0.558281i | −0.0485922 | − | 0.0280547i | ||||
\(397\) | −23.0989 | − | 13.3362i | −1.15930 | − | 0.669322i | −0.208164 | − | 0.978094i | \(-0.566749\pi\) |
−0.951136 | + | 0.308772i | \(0.900082\pi\) | |||||||
\(398\) | 0.894592i | 0.0448419i | ||||||||
\(399\) | 3.98040 | − | 6.89425i | 0.199269 | − | 0.345144i | ||||
\(400\) | 1.29342 | + | 2.24027i | 0.0646711 | + | 0.112014i | ||||
\(401\) | 14.5178 | − | 8.38188i | 0.724986 | − | 0.418571i | −0.0915990 | − | 0.995796i | \(-0.529198\pi\) |
0.816585 | + | 0.577225i | \(0.195864\pi\) | |||||||
\(402\) | 8.79440 | 0.438625 | ||||||||
\(403\) | −1.91442 | − | 23.2969i | −0.0953639 | − | 1.16050i | ||||
\(404\) | 6.58037 | 0.327386 | ||||||||
\(405\) | −0.141922 | + | 0.0819389i | −0.00705218 | + | 0.00407158i | ||||
\(406\) | −0.555402 | − | 0.961985i | −0.0275642 | − | 0.0477425i | ||||
\(407\) | 1.45603 | − | 2.52192i | 0.0721728 | − | 0.125007i | ||||
\(408\) | 6.08888i | 0.301445i | ||||||||
\(409\) | −20.6351 | − | 11.9137i | −1.02034 | − | 0.589095i | −0.106139 | − | 0.994351i | \(-0.533849\pi\) |
−0.914203 | + | 0.405256i | \(0.867182\pi\) | |||||||
\(410\) | 0.612528 | + | 0.353643i | 0.0302506 | + | 0.0174652i | ||||
\(411\) | 18.1671i | 0.896118i | ||||||||
\(412\) | 2.82307 | − | 4.88970i | 0.139083 | − | 0.240898i | ||||
\(413\) | 3.31649 | + | 5.74433i | 0.163194 | + | 0.282660i | ||||
\(414\) | −1.21435 | + | 0.701103i | −0.0596818 | + | 0.0344573i | ||||
\(415\) | −1.22596 | −0.0601800 | ||||||||
\(416\) | −17.5033 | − | 8.27464i | −0.858172 | − | 0.405698i | ||||
\(417\) | −10.9397 | −0.535721 | ||||||||
\(418\) | 2.33585 | − | 1.34860i | 0.114250 | − | 0.0659623i | ||||
\(419\) | −9.06959 | − | 15.7090i | −0.443078 | − | 0.767434i | 0.554838 | − | 0.831959i | \(-0.312780\pi\) |
−0.997916 | + | 0.0645244i | \(0.979447\pi\) | |||||||
\(420\) | 0.253807 | − | 0.439606i | 0.0123845 | − | 0.0214506i | ||||
\(421\) | 20.8542i | 1.01637i | 0.861247 | + | 0.508186i | \(0.169684\pi\) | ||||
−0.861247 | + | 0.508186i | \(0.830316\pi\) | |||||||
\(422\) | −8.11013 | − | 4.68238i | −0.394795 | − | 0.227935i | ||||
\(423\) | 2.35100 | + | 1.35735i | 0.114310 | + | 0.0659968i | ||||
\(424\) | − | 16.7314i | − | 0.812549i | ||||||
\(425\) | −5.16862 | + | 8.95232i | −0.250715 | + | 0.434251i | ||||
\(426\) | 6.16297 | + | 10.6746i | 0.298597 | + | 0.517185i | ||||
\(427\) | −12.7622 | + | 7.36825i | −0.617605 | + | 0.356574i | ||||
\(428\) | 9.36773 | 0.452806 | ||||||||
\(429\) | −3.25965 | − | 1.54099i | −0.157378 | − | 0.0743997i | ||||
\(430\) | 1.14749 | 0.0553368 | ||||||||
\(431\) | 11.0792 | − | 6.39656i | 0.533665 | − | 0.308112i | −0.208843 | − | 0.977949i | \(-0.566970\pi\) |
0.742508 | + | 0.669838i | \(0.233636\pi\) | |||||||
\(432\) | 0.260081 | + | 0.450474i | 0.0125132 | + | 0.0216734i | ||||
\(433\) | 2.25122 | − | 3.89923i | 0.108187 | − | 0.187385i | −0.806849 | − | 0.590758i | \(-0.798829\pi\) |
0.915036 | + | 0.403373i | \(0.132162\pi\) | |||||||
\(434\) | − | 16.9046i | − | 0.811447i | ||||||
\(435\) | 0.0604604 | + | 0.0349068i | 0.00289885 | + | 0.00167365i | ||||
\(436\) | −11.0336 | − | 6.37024i | −0.528412 | − | 0.305079i | ||||
\(437\) | 4.28105i | 0.204790i | ||||||||
\(438\) | −1.14097 | + | 1.97622i | −0.0545178 | + | 0.0944276i | ||||
\(439\) | 14.3923 | + | 24.9282i | 0.686908 | + | 1.18976i | 0.972833 | + | 0.231507i | \(0.0743657\pi\) |
−0.285925 | + | 0.958252i | \(0.592301\pi\) | |||||||
\(440\) | 0.415733 | − | 0.240024i | 0.0198193 | − | 0.0114427i | ||||
\(441\) | −0.695910 | −0.0331386 | ||||||||
\(442\) | 0.576914 | + | 7.02056i | 0.0274410 | + | 0.333934i | ||||
\(443\) | −8.71939 | −0.414271 | −0.207135 | − | 0.978312i | \(-0.566414\pi\) | ||||
−0.207135 | + | 0.978312i | \(0.566414\pi\) | |||||||
\(444\) | 2.81588 | − | 1.62575i | 0.133636 | − | 0.0771547i | ||||
\(445\) | −0.715896 | − | 1.23997i | −0.0339367 | − | 0.0587801i | ||||
\(446\) | −5.53498 | + | 9.58687i | −0.262089 | + | 0.453951i | ||||
\(447\) | − | 16.0246i | − | 0.757938i | ||||||
\(448\) | −14.6248 | − | 8.44364i | −0.690957 | − | 0.398924i | ||||
\(449\) | 16.2711 | + | 9.39411i | 0.767879 | + | 0.443335i | 0.832118 | − | 0.554599i | \(-0.187128\pi\) |
−0.0642383 | + | 0.997935i | \(0.520462\pi\) | |||||||
\(450\) | 4.67433i | 0.220350i | ||||||||
\(451\) | −2.29592 | + | 3.97665i | −0.108111 | + | 0.187253i | ||||
\(452\) | 5.21821 | + | 9.03821i | 0.245444 | + | 0.425122i | ||||
\(453\) | −14.3525 | + | 8.28642i | −0.674339 | + | 0.389330i | ||||
\(454\) | 12.7877 | 0.600157 | ||||||||
\(455\) | 0.700568 | − | 1.48191i | 0.0328431 | − | 0.0694730i | ||||
\(456\) | 8.40601 | 0.393648 | ||||||||
\(457\) | −11.1189 | + | 6.41951i | −0.520121 | + | 0.300292i | −0.736984 | − | 0.675910i | \(-0.763751\pi\) |
0.216863 | + | 0.976202i | \(0.430417\pi\) | |||||||
\(458\) | 9.11555 | + | 15.7886i | 0.425942 | + | 0.737752i | ||||
\(459\) | −1.03931 | + | 1.80013i | −0.0485107 | + | 0.0840230i | ||||
\(460\) | 0.272978i | 0.0127276i | ||||||||
\(461\) | 11.3477 | + | 6.55160i | 0.528515 | + | 0.305138i | 0.740412 | − | 0.672154i | \(-0.234631\pi\) |
−0.211897 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(462\) | −2.25813 | − | 1.30373i | −0.105058 | − | 0.0606550i | ||||
\(463\) | − | 5.97803i | − | 0.277823i | −0.990305 | − | 0.138911i | \(-0.955640\pi\) | ||
0.990305 | − | 0.138911i | \(-0.0443603\pi\) | |||||||
\(464\) | 0.110797 | − | 0.191906i | 0.00514363 | − | 0.00890903i | ||||
\(465\) | 0.531224 | + | 0.920106i | 0.0246349 | + | 0.0426689i | ||||
\(466\) | 23.2027 | − | 13.3961i | 1.07485 | − | 0.620563i | ||||
\(467\) | −29.5922 | −1.36936 | −0.684682 | − | 0.728842i | \(-0.740059\pi\) | ||||
−0.684682 | + | 0.728842i | \(0.740059\pi\) | |||||||
\(468\) | −2.29169 | − | 3.30990i | −0.105933 | − | 0.153000i | ||||
\(469\) | −25.9566 | −1.19857 | ||||||||
\(470\) | −0.362128 | + | 0.209074i | −0.0167037 | + | 0.00964388i | ||||
\(471\) | −10.5507 | − | 18.2743i | −0.486149 | − | 0.842035i | ||||
\(472\) | −3.50197 | + | 6.06560i | −0.161191 | + | 0.279192i | ||||
\(473\) | 7.44972i | 0.342539i | ||||||||
\(474\) | −6.03521 | − | 3.48443i | −0.277207 | − | 0.160045i | ||||
\(475\) | 12.3591 | + | 7.13555i | 0.567076 | + | 0.327401i | ||||
\(476\) | − | 6.43853i | − | 0.295110i | ||||||
\(477\) | 2.85587 | − | 4.94652i | 0.130761 | − | 0.226485i | ||||
\(478\) | 1.20160 | + | 2.08123i | 0.0549598 | + | 0.0951931i | ||||
\(479\) | 7.03802 | − | 4.06340i | 0.321575 | − | 0.185661i | −0.330519 | − | 0.943799i | \(-0.607224\pi\) |
0.652094 | + | 0.758138i | \(0.273891\pi\) | |||||||
\(480\) | 0.879973 | 0.0401651 | ||||||||
\(481\) | 8.63241 | − | 5.97686i | 0.393604 | − | 0.272521i | ||||
\(482\) | 7.13915 | 0.325179 | ||||||||
\(483\) | 3.58413 | − | 2.06930i | 0.163084 | − | 0.0941565i | ||||
\(484\) | 0.558281 | + | 0.966972i | 0.0253764 | + | 0.0439533i | ||||
\(485\) | 0.787189 | − | 1.36345i | 0.0357444 | − | 0.0619112i | ||||
\(486\) | 0.939913i | 0.0426353i | ||||||||
\(487\) | −3.72481 | − | 2.15052i | −0.168787 | − | 0.0974494i | 0.413227 | − | 0.910628i | \(-0.364402\pi\) |
−0.582014 | + | 0.813179i | \(0.697735\pi\) | |||||||
\(488\) | −13.4759 | − | 7.78033i | −0.610026 | − | 0.352199i | ||||
\(489\) | 11.7328i | 0.530575i | ||||||||
\(490\) | 0.0535959 | − | 0.0928308i | 0.00242122 | − | 0.00419367i | ||||
\(491\) | −10.9243 | − | 18.9214i | −0.493006 | − | 0.853911i | 0.506962 | − | 0.861969i | \(-0.330769\pi\) |
−0.999968 | + | 0.00805728i | \(0.997435\pi\) | |||||||
\(492\) | −4.44018 | + | 2.56354i | −0.200179 | + | 0.115573i | ||||
\(493\) | 0.885510 | 0.0398814 | ||||||||
\(494\) | 9.69225 | − | 0.796460i | 0.436075 | − | 0.0358344i | ||||
\(495\) | 0.163878 | 0.00736576 | ||||||||
\(496\) | 2.92050 | − | 1.68615i | 0.131134 | − | 0.0757104i | ||||
\(497\) | −18.1900 | − | 31.5060i | −0.815932 | − | 1.41324i | ||||
\(498\) | −3.51572 | + | 6.08940i | −0.157543 | + | 0.272872i | ||||
\(499\) | 33.9761i | 1.52098i | 0.649349 | + | 0.760490i | \(0.275041\pi\) | ||||
−0.649349 | + | 0.760490i | \(0.724959\pi\) | |||||||
\(500\) | 1.58040 | + | 0.912442i | 0.0706775 | + | 0.0408057i | ||||
\(501\) | −18.4503 | − | 10.6523i | −0.824297 | − | 0.475908i | ||||
\(502\) | 3.06387i | 0.136747i | ||||||||
\(503\) | 13.3026 | − | 23.0407i | 0.593132 | − | 1.02733i | −0.400676 | − | 0.916220i | \(-0.631225\pi\) |
0.993808 | − | 0.111115i | \(-0.0354420\pi\) | |||||||
\(504\) | −4.06316 | − | 7.03760i | −0.180987 | − | 0.313479i | ||||
\(505\) | −0.836408 | + | 0.482900i | −0.0372196 | + | 0.0214888i | ||||
\(506\) | 1.40221 | 0.0623356 | ||||||||
\(507\) | −8.25070 | − | 10.0462i | −0.366426 | − | 0.446167i | ||||
\(508\) | 16.0696 | 0.712975 | ||||||||
\(509\) | −15.3229 | + | 8.84669i | −0.679176 | + | 0.392123i | −0.799545 | − | 0.600607i | \(-0.794926\pi\) |
0.120368 | + | 0.992729i | \(0.461592\pi\) | |||||||
\(510\) | −0.160086 | − | 0.277276i | −0.00708871 | − | 0.0122780i | ||||
\(511\) | 3.36758 | − | 5.83282i | 0.148973 | − | 0.258029i | ||||
\(512\) | − | 5.84054i | − | 0.258118i | ||||||
\(513\) | 2.48517 | + | 1.43482i | 0.109723 | + | 0.0633487i | ||||
\(514\) | 18.0273 | + | 10.4081i | 0.795151 | + | 0.459081i | ||||
\(515\) | 0.828683i | 0.0365161i | ||||||||
\(516\) | −4.15904 | + | 7.20367i | −0.183092 | + | 0.317124i | ||||
\(517\) | −1.35735 | − | 2.35100i | −0.0596963 | − | 0.103397i | ||||
\(518\) | 6.57581 | − | 3.79655i | 0.288924 | − | 0.166811i | ||||
\(519\) | 2.35596 | 0.103415 | ||||||||
\(520\) | 1.72502 | − | 0.141753i | 0.0756472 | − | 0.00621630i | ||||
\(521\) | −33.6991 | −1.47638 | −0.738191 | − | 0.674591i | \(-0.764320\pi\) | ||||
−0.738191 | + | 0.674591i | \(0.764320\pi\) | |||||||
\(522\) | 0.346767 | − | 0.200206i | 0.0151776 | − | 0.00876279i | ||||
\(523\) | 7.65910 | + | 13.2660i | 0.334909 | + | 0.580080i | 0.983467 | − | 0.181085i | \(-0.0579610\pi\) |
−0.648558 | + | 0.761165i | \(0.724628\pi\) | |||||||
\(524\) | 4.53637 | − | 7.85723i | 0.198172 | − | 0.343245i | ||||
\(525\) | − | 13.7962i | − | 0.602118i | ||||||
\(526\) | −20.4277 | − | 11.7940i | −0.890692 | − | 0.514241i | ||||
\(527\) | 11.6706 | + | 6.73800i | 0.508377 | + | 0.293512i | ||||
\(528\) | − | 0.520163i | − | 0.0226372i | ||||||
\(529\) | 10.3872 | − | 17.9912i | 0.451617 | − | 0.782224i | ||||
\(530\) | 0.439893 | + | 0.761917i | 0.0191077 | + | 0.0330956i | ||||
\(531\) | −2.07066 | + | 1.19550i | −0.0898592 | + | 0.0518802i | ||||
\(532\) | −8.88872 | −0.385375 | ||||||||
\(533\) | −13.6119 | + | 9.42452i | −0.589597 | + | 0.408221i | ||||
\(534\) | −8.21198 | −0.355367 | ||||||||
\(535\) | −1.19070 | + | 0.687451i | −0.0514784 | + | 0.0297211i | ||||
\(536\) | −13.7041 | − | 23.7363i | −0.591929 | − | 1.02525i | ||||
\(537\) | −7.96439 | + | 13.7947i | −0.343689 | + | 0.595286i | ||||
\(538\) | 5.88327i | 0.253646i | ||||||||
\(539\) | 0.602676 | + | 0.347955i | 0.0259591 | + | 0.0149875i | ||||
\(540\) | 0.158465 | + | 0.0914899i | 0.00681926 | + | 0.00393710i | ||||
\(541\) | 24.9462i | 1.07252i | 0.844052 | + | 0.536261i | \(0.180164\pi\) | ||||
−0.844052 | + | 0.536261i | \(0.819836\pi\) | |||||||
\(542\) | −4.08011 | + | 7.06697i | −0.175256 | + | 0.303552i | ||||
\(543\) | 9.51481 | + | 16.4801i | 0.408319 | + | 0.707230i | ||||
\(544\) | 9.66615 | − | 5.58076i | 0.414433 | − | 0.239273i | ||||
\(545\) | 1.86992 | 0.0800985 | ||||||||
\(546\) | −5.35168 | − | 7.72946i | −0.229031 | − | 0.330791i | ||||
\(547\) | 25.6012 | 1.09463 | 0.547315 | − | 0.836927i | \(-0.315650\pi\) | ||||
0.547315 | + | 0.836927i | \(0.315650\pi\) | |||||||
\(548\) | 17.5671 | − | 10.1424i | 0.750429 | − | 0.433260i | ||||
\(549\) | −2.65604 | − | 4.60039i | −0.113357 | − | 0.196340i | ||||
\(550\) | 2.33716 | − | 4.04808i | 0.0996569 | − | 0.172611i | ||||
\(551\) | − | 1.22249i | − | 0.0520799i | ||||||
\(552\) | 3.78458 | + | 2.18503i | 0.161083 | + | 0.0930011i | ||||
\(553\) | 17.8129 | + | 10.2843i | 0.757482 | + | 0.437332i | ||||
\(554\) | − | 28.2151i | − | 1.19875i | ||||||
\(555\) | −0.238611 | + | 0.413287i | −0.0101285 | + | 0.0175431i | ||||
\(556\) | 6.10745 | + | 10.5784i | 0.259014 | + | 0.448625i | ||||
\(557\) | 7.86475 | − | 4.54072i | 0.333240 | − | 0.192396i | −0.324038 | − | 0.946044i | \(-0.605041\pi\) |
0.657279 | + | 0.753648i | \(0.271707\pi\) | |||||||
\(558\) | 6.09361 | 0.257963 | ||||||||
\(559\) | −11.4799 | + | 24.2835i | −0.485550 | + | 1.02708i | ||||
\(560\) | 0.236477 | 0.00999299 | ||||||||
\(561\) | 1.80013 | − | 1.03931i | 0.0760017 | − | 0.0438796i | ||||
\(562\) | 12.4667 | + | 21.5929i | 0.525875 | + | 0.910842i | ||||
\(563\) | 8.38486 | − | 14.5230i | 0.353380 | − | 0.612072i | −0.633459 | − | 0.773776i | \(-0.718366\pi\) |
0.986839 | + | 0.161704i | \(0.0516990\pi\) | |||||||
\(564\) | − | 3.03114i | − | 0.127634i | ||||||
\(565\) | −1.32654 | − | 0.765877i | −0.0558079 | − | 0.0322207i | ||||
\(566\) | 0.525126 | + | 0.303181i | 0.0220727 | + | 0.0127437i | ||||
\(567\) | − | 2.77415i | − | 0.116503i | ||||||
\(568\) | 19.2073 | − | 33.2680i | 0.805920 | − | 1.39589i | ||||
\(569\) | −12.5298 | − | 21.7023i | −0.525278 | − | 0.909807i | −0.999567 | − | 0.0294382i | \(-0.990628\pi\) |
0.474289 | − | 0.880369i | \(-0.342705\pi\) | |||||||
\(570\) | −0.382794 | + | 0.221006i | −0.0160335 | + | 0.00925693i | ||||
\(571\) | −8.44547 | −0.353432 | −0.176716 | − | 0.984262i | \(-0.556547\pi\) | ||||
−0.176716 | + | 0.984262i | \(0.556547\pi\) | |||||||
\(572\) | 0.329710 | + | 4.01230i | 0.0137859 | + | 0.167763i | ||||
\(573\) | 9.07707 | 0.379200 | ||||||||
\(574\) | −10.3690 | + | 5.98653i | −0.432792 | + | 0.249873i | ||||
\(575\) | 3.70958 | + | 6.42518i | 0.154700 | + | 0.267949i | ||||
\(576\) | 3.04369 | − | 5.27182i | 0.126820 | − | 0.219659i | ||||
\(577\) | 22.5888i | 0.940383i | 0.882564 | + | 0.470192i | \(0.155815\pi\) | ||||
−0.882564 | + | 0.470192i | \(0.844185\pi\) | |||||||
\(578\) | 10.3209 | + | 5.95875i | 0.429291 | + | 0.247851i | ||||
\(579\) | −0.989480 | − | 0.571277i | −0.0411214 | − | 0.0237414i | ||||
\(580\) | − | 0.0779513i | − | 0.00323675i | ||||||
\(581\) | 10.3766 | − | 17.9728i | 0.430495 | − | 0.745639i | ||||
\(582\) | −4.51489 | − | 7.82001i | −0.187148 | − | 0.324150i | ||||
\(583\) | −4.94652 | + | 2.85587i | −0.204864 | + | 0.118278i | ||||
\(584\) | 7.11183 | 0.294290 | ||||||||
\(585\) | 0.534185 | + | 0.252534i | 0.0220858 | + | 0.0104410i | ||||
\(586\) | 16.3613 | 0.675881 | ||||||||
\(587\) | 13.9083 | − | 8.02998i | 0.574058 | − | 0.331433i | −0.184710 | − | 0.982793i | \(-0.559135\pi\) |
0.758769 | + | 0.651360i | \(0.225801\pi\) | |||||||
\(588\) | 0.388514 | + | 0.672925i | 0.0160220 | + | 0.0277510i | ||||
\(589\) | 9.30215 | − | 16.1118i | 0.383288 | − | 0.663875i | ||||
\(590\) | − | 0.368288i | − | 0.0151622i | ||||||
\(591\) | 15.0212 | + | 8.67251i | 0.617891 | + | 0.356740i | ||||
\(592\) | 1.31181 | + | 0.757373i | 0.0539150 | + | 0.0311278i | ||||
\(593\) | 18.7915i | 0.771673i | 0.922567 | + | 0.385837i | \(0.126087\pi\) | ||||
−0.922567 | + | 0.385837i | \(0.873913\pi\) | |||||||
\(594\) | 0.469957 | − | 0.813989i | 0.0192826 | − | 0.0333984i | ||||
\(595\) | 0.472492 | + | 0.818380i | 0.0193703 | + | 0.0335503i | ||||
\(596\) | −15.4953 | + | 8.94624i | −0.634714 | + | 0.366452i | ||||
\(597\) | 0.951782 | 0.0389538 | ||||||||
\(598\) | 4.57071 | + | 2.16078i | 0.186910 | + | 0.0883611i | ||||
\(599\) | 29.3796 | 1.20042 | 0.600208 | − | 0.799844i | \(-0.295084\pi\) | ||||
0.600208 | + | 0.799844i | \(0.295084\pi\) | |||||||
\(600\) | 12.6161 | − | 7.28391i | 0.515050 | − | 0.297365i | ||||
\(601\) | −8.10907 | − | 14.0453i | −0.330776 | − | 0.572921i | 0.651888 | − | 0.758315i | \(-0.273977\pi\) |
−0.982664 | + | 0.185394i | \(0.940644\pi\) | |||||||
\(602\) | −9.71243 | + | 16.8224i | −0.395849 | + | 0.685631i | ||||
\(603\) | − | 9.35660i | − | 0.381030i | ||||||
\(604\) | 16.0255 | + | 9.25231i | 0.652067 | + | 0.376471i | ||||
\(605\) | −0.141922 | − | 0.0819389i | −0.00576997 | − | 0.00333129i | ||||
\(606\) | 5.53930i | 0.225019i | ||||||||
\(607\) | −3.67343 | + | 6.36256i | −0.149100 | + | 0.258249i | −0.930895 | − | 0.365287i | \(-0.880971\pi\) |
0.781795 | + | 0.623535i | \(0.214304\pi\) | |||||||
\(608\) | −7.70452 | − | 13.3446i | −0.312460 | − | 0.541196i | ||||
\(609\) | −1.02348 | + | 0.590908i | −0.0414736 | + | 0.0239448i | ||||
\(610\) | 0.818224 | 0.0331289 | ||||||||
\(611\) | −0.801627 | − | 9.75513i | −0.0324304 | − | 0.394650i | ||||
\(612\) | 2.32090 | 0.0938169 | ||||||||
\(613\) | 25.7402 | − | 14.8611i | 1.03964 | − | 0.600236i | 0.119908 | − | 0.992785i | \(-0.461740\pi\) |
0.919731 | + | 0.392549i | \(0.128407\pi\) | |||||||
\(614\) | −3.57200 | − | 6.18688i | −0.144154 | − | 0.249682i | ||||
\(615\) | 0.376251 | − | 0.651685i | 0.0151719 | − | 0.0262785i | ||||
\(616\) | 8.12632i | 0.327419i | ||||||||
\(617\) | 8.75194 | + | 5.05294i | 0.352340 | + | 0.203424i | 0.665715 | − | 0.746206i | \(-0.268127\pi\) |
−0.313375 | + | 0.949629i | \(0.601460\pi\) | |||||||
\(618\) | 4.11611 | + | 2.37644i | 0.165574 | + | 0.0955943i | ||||
\(619\) | 32.8446i | 1.32014i | 0.751205 | + | 0.660069i | \(0.229473\pi\) | ||||
−0.751205 | + | 0.660069i | \(0.770527\pi\) | |||||||
\(620\) | 0.593144 | − | 1.02736i | 0.0238213 | − | 0.0412596i | ||||
\(621\) | 0.745923 | + | 1.29198i | 0.0299328 | + | 0.0518452i | ||||
\(622\) | −7.23394 | + | 4.17652i | −0.290054 | + | 0.167463i | ||||
\(623\) | 24.2376 | 0.971059 | ||||||||
\(624\) | 0.801566 | − | 1.69555i | 0.0320883 | − | 0.0678764i | ||||
\(625\) | 24.5979 | 0.983915 | ||||||||
\(626\) | 14.0728 | − | 8.12492i | 0.562461 | − | 0.324737i | ||||
\(627\) | −1.43482 | − | 2.48517i | −0.0573010 | − | 0.0992483i | ||||
\(628\) | −11.7805 | + | 20.4044i | −0.470092 | + | 0.814224i | ||||
\(629\) | 6.05305i | 0.241351i | ||||||||
\(630\) | 0.370057 | + | 0.213653i | 0.0147434 | + | 0.00851212i | ||||
\(631\) | 4.96406 | + | 2.86600i | 0.197616 | + | 0.114094i | 0.595543 | − | 0.803323i | \(-0.296937\pi\) |
−0.397927 | + | 0.917417i | \(0.630270\pi\) | |||||||
\(632\) | 21.7189i | 0.863932i | ||||||||
\(633\) | −4.98172 | + | 8.62859i | −0.198006 | + | 0.342956i | ||||
\(634\) | 5.07133 | + | 8.78380i | 0.201408 | + | 0.348849i | ||||
\(635\) | −2.04256 | + | 1.17927i | −0.0810564 | + | 0.0467979i | ||||
\(636\) | −6.37752 | −0.252885 | ||||||||
\(637\) | 1.42832 | + | 2.06293i | 0.0565921 | + | 0.0817363i | ||||
\(638\) | −0.400413 | −0.0158525 | ||||||||
\(639\) | 11.3570 | − | 6.55696i | 0.449275 | − | 0.259389i | ||||
\(640\) | −0.411152 | − | 0.712135i | −0.0162522 | − | 0.0281496i | ||||
\(641\) | 12.1383 | − | 21.0242i | 0.479436 | − | 0.830407i | −0.520286 | − | 0.853992i | \(-0.674175\pi\) |
0.999722 | + | 0.0235847i | \(0.00750794\pi\) | |||||||
\(642\) | 7.88568i | 0.311223i | ||||||||
\(643\) | 7.88538 | + | 4.55263i | 0.310969 | + | 0.179538i | 0.647360 | − | 0.762184i | \(-0.275873\pi\) |
−0.336391 | + | 0.941722i | \(0.609206\pi\) | |||||||
\(644\) | −4.00191 | − | 2.31050i | −0.157697 | − | 0.0910466i | ||||
\(645\) | − | 1.22084i | − | 0.0480707i | ||||||
\(646\) | −2.80323 | + | 4.85533i | −0.110291 | + | 0.191030i | ||||
\(647\) | 19.6739 | + | 34.0761i | 0.773459 | + | 1.33967i | 0.935657 | + | 0.352912i | \(0.114808\pi\) |
−0.162198 | + | 0.986758i | \(0.551858\pi\) | |||||||
\(648\) | 2.53685 | − | 1.46465i | 0.0996568 | − | 0.0575369i | ||||
\(649\) | 2.39100 | 0.0938548 | ||||||||
\(650\) | 13.8564 | − | 9.59381i | 0.543493 | − | 0.376300i | ||||
\(651\) | −17.9853 | −0.704899 | ||||||||
\(652\) | 11.3453 | − | 6.55020i | 0.444315 | − | 0.256525i | ||||
\(653\) | 12.8895 | + | 22.3253i | 0.504406 | + | 0.873657i | 0.999987 | + | 0.00509498i | \(0.00162179\pi\) |
−0.495581 | + | 0.868562i | \(0.665045\pi\) | |||||||
\(654\) | 5.36241 | − | 9.28797i | 0.209687 | − | 0.363189i | ||||
\(655\) | 1.33161i | 0.0520302i | ||||||||
\(656\) | −2.06851 | − | 1.19425i | −0.0807616 | − | 0.0466277i | ||||
\(657\) | 2.10256 | + | 1.21391i | 0.0820286 | + | 0.0473593i | ||||
\(658\) | − | 7.07849i | − | 0.275948i | ||||||
\(659\) | 5.08437 | − | 8.80639i | 0.198059 | − | 0.343048i | −0.749840 | − | 0.661619i | \(-0.769870\pi\) |
0.947899 | + | 0.318571i | \(0.103203\pi\) | |||||||
\(660\) | −0.0914899 | − | 0.158465i | −0.00356124 | − | 0.00616825i | ||||
\(661\) | 26.3447 | − | 15.2101i | 1.02469 | − | 0.591605i | 0.109231 | − | 0.994016i | \(-0.465161\pi\) |
0.915459 | + | 0.402411i | \(0.131828\pi\) | |||||||
\(662\) | −22.2887 | −0.866273 | ||||||||
\(663\) | 7.46937 | − | 0.613795i | 0.290086 | − | 0.0238378i | ||||
\(664\) | 21.9139 | 0.850424 | ||||||||
\(665\) | 1.12981 | − | 0.652299i | 0.0438123 | − | 0.0252951i | ||||
\(666\) | 1.36854 | + | 2.37039i | 0.0530300 | + | 0.0918506i | ||||
\(667\) | 0.317770 | − | 0.550395i | 0.0123041 | − | 0.0213114i | ||||
\(668\) | 23.7878i | 0.920379i | ||||||||
\(669\) | 10.1997 | + | 5.88882i | 0.394345 | + | 0.227675i | ||||
\(670\) | 1.24812 | + | 0.720603i | 0.0482192 | + | 0.0278393i | ||||
\(671\) | 5.31207i | 0.205070i | ||||||||
\(672\) | −7.44816 | + | 12.9006i | −0.287319 | + | 0.497651i | ||||
\(673\) | −8.09316 | − | 14.0178i | −0.311968 | − | 0.540345i | 0.666820 | − | 0.745219i | \(-0.267655\pi\) |
−0.978788 | + | 0.204874i | \(0.934322\pi\) | |||||||
\(674\) | −12.2196 | + | 7.05497i | −0.470680 | + | 0.271747i | ||||
\(675\) | 4.97314 | 0.191416 | ||||||||
\(676\) | −5.10817 | + | 13.5868i | −0.196468 | + | 0.522569i | ||||
\(677\) | 37.7024 | 1.44902 | 0.724511 | − | 0.689263i | \(-0.242066\pi\) | ||||
0.724511 | + | 0.689263i | \(0.242066\pi\) | |||||||
\(678\) | −7.60829 | + | 4.39265i | −0.292195 | + | 0.168699i | ||||
\(679\) | 13.3257 | + | 23.0807i | 0.511392 | + | 0.885757i | ||||
\(680\) | −0.498917 | + | 0.864149i | −0.0191326 | + | 0.0331386i | ||||
\(681\) | − | 13.6052i | − | 0.521352i | ||||||
\(682\) | −5.27723 | − | 3.04681i | −0.202075 | − | 0.116668i | ||||
\(683\) | −22.8738 | − | 13.2062i | −0.875240 | − | 0.505320i | −0.00615421 | − | 0.999981i | \(-0.501959\pi\) |
−0.869086 | + | 0.494661i | \(0.835292\pi\) | |||||||
\(684\) | − | 3.20412i | − | 0.122513i | ||||||
\(685\) | −1.48859 | + | 2.57832i | −0.0568763 | + | 0.0985126i | ||||
\(686\) | −8.21884 | − | 14.2354i | −0.313797 | − | 0.543512i | ||||
\(687\) | 16.7979 | − | 9.69828i | 0.640881 | − | 0.370013i | ||||
\(688\) | −3.87507 | −0.147736 | ||||||||
\(689\) | −20.5248 | + | 1.68662i | −0.781933 | + | 0.0642553i | ||||
\(690\) | −0.229790 | −0.00874797 | ||||||||
\(691\) | −7.30038 | + | 4.21488i | −0.277720 | + | 0.160341i | −0.632391 | − | 0.774650i | \(-0.717926\pi\) |
0.354671 | + | 0.934991i | \(0.384593\pi\) | |||||||
\(692\) | −1.31529 | − | 2.27814i | −0.0499997 | − | 0.0866020i | ||||
\(693\) | −1.38708 | + | 2.40248i | −0.0526906 | + | 0.0912628i | ||||
\(694\) | 22.7813i | 0.864768i | ||||||||
\(695\) | −1.55259 | − | 0.896390i | −0.0588932 | − | 0.0340020i | ||||
\(696\) | −1.08072 | − | 0.623955i | −0.0409647 | − | 0.0236510i | ||||
\(697\) | − | 9.54467i | − | 0.361530i | ||||||
\(698\) | −9.14507 | + | 15.8397i | −0.346146 | + | 0.599543i | ||||
\(699\) | −14.2525 | − | 24.6860i | −0.539079 | − | 0.933712i | ||||
\(700\) | −13.3406 | + | 7.70219i | −0.504227 | + | 0.291115i | ||||
\(701\) | −22.6008 | −0.853622 | −0.426811 | − | 0.904341i | \(-0.640363\pi\) | ||||
−0.426811 | + | 0.904341i | \(0.640363\pi\) | |||||||
\(702\) | 2.78625 | − | 1.92912i | 0.105160 | − | 0.0728101i | ||||
\(703\) | 8.35655 | 0.315173 | ||||||||
\(704\) | −5.27182 | + | 3.04369i | −0.198689 | + | 0.114713i | ||||
\(705\) | 0.222440 | + | 0.385278i | 0.00837758 | + | 0.0145104i | ||||
\(706\) | −15.4234 | + | 26.7142i | −0.580469 | + | 1.00540i | ||||
\(707\) | − | 16.3492i | − | 0.614876i | ||||||
\(708\) | 2.31203 | + | 1.33485i | 0.0868913 | + | 0.0501667i | ||||
\(709\) | 39.1916 | + | 22.6273i | 1.47187 | + | 0.849786i | 0.999500 | − | 0.0316131i | \(-0.0100645\pi\) |
0.472372 | + | 0.881399i | \(0.343398\pi\) | |||||||
\(710\) | 2.01995i | 0.0758073i | ||||||||
\(711\) | −3.70718 | + | 6.42103i | −0.139030 | + | 0.240807i | ||||
\(712\) | 12.7966 | + | 22.1643i | 0.479572 | + | 0.830643i | ||||
\(713\) | 8.37609 | − | 4.83594i | 0.313687 | − | 0.181107i | ||||
\(714\) | 5.41991 | 0.202835 | ||||||||
\(715\) | −0.336351 | − | 0.485794i | −0.0125788 | − | 0.0181677i | ||||
\(716\) | 17.7855 | 0.664675 | ||||||||
\(717\) | 2.21427 | − | 1.27841i | 0.0826936 | − | 0.0477432i | ||||
\(718\) | 12.4688 | + | 21.5967i | 0.465333 | + | 0.805980i | ||||
\(719\) | 23.0880 | − | 39.9896i | 0.861037 | − | 1.49136i | −0.00989249 | − | 0.999951i | \(-0.503149\pi\) |
0.870929 | − | 0.491408i | \(-0.163518\pi\) | |||||||
\(720\) | 0.0852431i | 0.00317682i | ||||||||
\(721\) | −12.1487 | − | 7.01404i | −0.452440 | − | 0.261217i | ||||
\(722\) | −8.76276 | − | 5.05918i | −0.326116 | − | 0.188283i | ||||
\(723\) | − | 7.59554i | − | 0.282481i | ||||||
\(724\) | 10.6239 | − | 18.4011i | 0.394833 | − | 0.683871i | ||||
\(725\) | −1.05930 | − | 1.83477i | −0.0393416 | − | 0.0681416i | ||||
\(726\) | −0.813989 | + | 0.469957i | −0.0302100 | + | 0.0174417i | ||||
\(727\) | −35.2721 | −1.30817 | −0.654086 | − | 0.756420i | \(-0.726946\pi\) | ||||
−0.654086 | + | 0.756420i | \(0.726946\pi\) | |||||||
\(728\) | −12.5226 | + | 26.4890i | −0.464118 | + | 0.981747i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.323859 | + | 0.186980i | −0.0119866 | + | 0.00692045i | ||||
\(731\) | −7.74255 | − | 13.4105i | −0.286368 | − | 0.496005i | ||||
\(732\) | −2.96563 | + | 5.13662i | −0.109613 | + | 0.189855i | ||||
\(733\) | 31.3865i | 1.15929i | 0.814870 | + | 0.579644i | \(0.196808\pi\) | ||||
−0.814870 | + | 0.579644i | \(0.803192\pi\) | |||||||
\(734\) | 11.3949 | + | 6.57883i | 0.420592 | + | 0.242829i | ||||
\(735\) | −0.0987652 | − | 0.0570221i | −0.00364301 | − | 0.00210329i | ||||
\(736\) | − | 8.01075i | − | 0.295280i | ||||||
\(737\) | −4.67830 | + | 8.10306i | −0.172327 | + | 0.298480i | ||||
\(738\) | −2.15797 | − | 3.73771i | −0.0794359 | − | 0.137587i | ||||
\(739\) | −36.6626 | + | 21.1672i | −1.34866 | + | 0.778647i | −0.988059 | − | 0.154075i | \(-0.950760\pi\) |
−0.360596 | + | 0.932722i | \(0.617427\pi\) | |||||||
\(740\) | 0.532849 | 0.0195879 | ||||||||
\(741\) | −0.847375 | − | 10.3118i | −0.0311291 | − | 0.378815i | ||||
\(742\) | −14.8932 | −0.546745 | ||||||||
\(743\) | 40.2960 | − | 23.2649i | 1.47832 | − | 0.853507i | 0.478618 | − | 0.878023i | \(-0.341138\pi\) |
0.999699 | + | 0.0245164i | \(0.00780459\pi\) | |||||||
\(744\) | −9.49557 | − | 16.4468i | −0.348124 | − | 0.602969i | ||||
\(745\) | 1.31304 | − | 2.27425i | 0.0481060 | − | 0.0833221i | ||||
\(746\) | − | 31.3690i | − | 1.14850i | ||||||
\(747\) | 6.47868 | + | 3.74047i | 0.237042 | + | 0.136857i | ||||
\(748\) | −2.00996 | − | 1.16045i | −0.0734914 | − | 0.0424303i | ||||
\(749\) | − | 23.2745i | − | 0.850433i | ||||||
\(750\) | −0.768087 | + | 1.33037i | −0.0280466 | + | 0.0485781i | ||||
\(751\) | −16.5675 | − | 28.6958i | −0.604558 | − | 1.04713i | −0.992121 | − | 0.125282i | \(-0.960016\pi\) |
0.387563 | − | 0.921843i | \(-0.373317\pi\) | |||||||
\(752\) | 1.22290 | − | 0.706044i | 0.0445947 | − | 0.0257468i | ||||
\(753\) | 3.25973 | 0.118791 | ||||||||
\(754\) | −1.30521 | − | 0.617032i | −0.0475328 | − | 0.0224710i | ||||
\(755\) | −2.71592 | −0.0988425 | ||||||||
\(756\) | −2.68252 | + | 1.54876i | −0.0975625 | + | 0.0563277i | ||||
\(757\) | 5.57461 | + | 9.65551i | 0.202613 | + | 0.350935i | 0.949369 | − | 0.314162i | \(-0.101723\pi\) |
−0.746757 | + | 0.665097i | \(0.768390\pi\) | |||||||
\(758\) | −5.94974 | + | 10.3053i | −0.216104 | + | 0.374304i | ||||
\(759\) | − | 1.49185i | − | 0.0541505i | ||||||
\(760\) | 1.19300 | + | 0.688780i | 0.0432747 | + | 0.0249847i | ||||
\(761\) | 34.9378 | + | 20.1713i | 1.26649 | + | 0.731210i | 0.974323 | − | 0.225156i | \(-0.0722891\pi\) |
0.292171 | + | 0.956366i | \(0.405622\pi\) | |||||||
\(762\) | 13.5273i | 0.490042i | ||||||||
\(763\) | −15.8271 | + | 27.4134i | −0.572981 | + | 0.992432i | ||||
\(764\) | −5.06756 | − | 8.77727i | −0.183338 | − | 0.317550i | ||||
\(765\) | −0.295002 | + | 0.170319i | −0.0106658 | + | 0.00615791i | ||||
\(766\) | 27.1320 | 0.980319 | ||||||||
\(767\) | 7.79383 | + | 3.68450i | 0.281419 | + | 0.133040i | ||||
\(768\) | −16.8910 | −0.609502 | ||||||||
\(769\) | 2.87354 | − | 1.65904i | 0.103623 | − | 0.0598265i | −0.447293 | − | 0.894387i | \(-0.647612\pi\) |
0.550916 | + | 0.834561i | \(0.314279\pi\) | |||||||
\(770\) | −0.213653 | − | 0.370057i | −0.00769950 | − | 0.0133359i | ||||
\(771\) | 11.0734 | − | 19.1798i | 0.398800 | − | 0.690742i | ||||
\(772\) | 1.27573i | 0.0459146i | ||||||||
\(773\) | −22.3406 | − | 12.8983i | −0.803535 | − | 0.463921i | 0.0411707 | − | 0.999152i | \(-0.486891\pi\) |
−0.844706 | + | 0.535231i | \(0.820225\pi\) | |||||||
\(774\) | −6.06399 | − | 3.50105i | −0.217966 | − | 0.125843i | ||||
\(775\) | − | 32.2417i | − | 1.15816i | ||||||
\(776\) | −14.0709 | + | 24.3716i | −0.505117 | + | 0.874888i | ||||
\(777\) | −4.03925 | − | 6.99619i | −0.144907 | − | 0.250987i | ||||
\(778\) | −28.2169 | + | 16.2911i | −1.01163 | + | 0.584063i | ||||
\(779\) | −13.1769 | −0.472112 | ||||||||
\(780\) | −0.0540322 | − | 0.657527i | −0.00193466 | − | 0.0235432i | ||||
\(781\) | −13.1139 | −0.469253 | ||||||||
\(782\) | −2.52416 | + | 1.45732i | −0.0902636 | + | 0.0521137i | ||||
\(783\) | −0.213005 | − | 0.368936i | −0.00761218 | − | 0.0131847i | ||||
\(784\) | −0.180993 | + | 0.313490i | −0.00646405 | + | 0.0111961i | ||||
\(785\) | − | 3.45804i | − | 0.123423i | ||||||
\(786\) | 6.61415 | + | 3.81868i | 0.235919 | + | 0.136208i | ||||
\(787\) | −29.0089 | − | 16.7483i | −1.03406 | − | 0.597012i | −0.115912 | − | 0.993259i | \(-0.536979\pi\) |
−0.918144 | + | 0.396247i | \(0.870312\pi\) | |||||||
\(788\) | − | 19.3668i | − | 0.689914i | ||||||
\(789\) | −12.5479 | + | 21.7336i | −0.446718 | + | 0.773738i | ||||
\(790\) | −0.571021 | − | 0.989038i | −0.0203160 | − | 0.0351884i | ||||
\(791\) | 22.4558 | − | 12.9649i | 0.798438 | − | 0.460978i | ||||
\(792\) | −2.92930 | −0.104088 | ||||||||
\(793\) | −8.18585 | + | 17.3155i | −0.290688 | + | 0.614892i | ||||
\(794\) | −25.0697 | −0.889689 | ||||||||
\(795\) | 0.810624 | − | 0.468014i | 0.0287499 | − | 0.0165988i | ||||
\(796\) | −0.531362 | − | 0.920346i | −0.0188336 | − | 0.0326208i | ||||
\(797\) | 2.69109 | − | 4.66111i | 0.0953234 | − | 0.165105i | −0.814420 | − | 0.580276i | \(-0.802945\pi\) |
0.909744 | + | 0.415171i | \(0.136278\pi\) | |||||||
\(798\) | − | 7.48246i | − | 0.264876i | ||||||
\(799\) | 4.88683 | + | 2.82141i | 0.172884 | + | 0.0998144i | ||||
\(800\) | −23.1266 | − | 13.3521i | −0.817647 | − | 0.472069i | ||||
\(801\) | 8.73695i | 0.308705i | ||||||||
\(802\) | 7.87824 | − | 13.6455i | 0.278190 | − | 0.481840i | ||||
\(803\) | −1.21391 | − | 2.10256i | −0.0428381 | − | 0.0741977i | ||||
\(804\) | −9.04757 | + | 5.22362i | −0.319083 | + | 0.184223i | ||||
\(805\) | 0.678225 | 0.0239043 | ||||||||
\(806\) | −12.5068 | − | 18.0637i | −0.440534 | − | 0.636266i | ||||
\(807\) | 6.25938 | 0.220341 | ||||||||
\(808\) | 14.9507 | − | 8.63179i | 0.525964 | − | 0.303665i | ||||
\(809\) | 10.8061 | + | 18.7168i | 0.379924 | + | 0.658048i | 0.991051 | − | 0.133485i | \(-0.0426168\pi\) |
−0.611127 | + | 0.791533i | \(0.709284\pi\) | |||||||
\(810\) | −0.0770155 | + | 0.133395i | −0.00270605 | + | 0.00468701i | ||||
\(811\) | − | 19.2028i | − | 0.674301i | −0.941451 | − | 0.337151i | \(-0.890537\pi\) | ||
0.941451 | − | 0.337151i | \(-0.109463\pi\) | |||||||
\(812\) | 1.14278 | + | 0.659786i | 0.0401038 | + | 0.0231539i | ||||
\(813\) | 7.51874 | + | 4.34095i | 0.263694 | + | 0.152244i | ||||
\(814\) | − | 2.73709i | − | 0.0959348i | ||||||
\(815\) | −0.961372 | + | 1.66515i | −0.0336754 | + | 0.0583275i | ||||
\(816\) | 0.540609 | + | 0.936362i | 0.0189251 | + | 0.0327792i | ||||
\(817\) | −18.5139 | + | 10.6890i | −0.647718 | + | 0.373960i | ||||
\(818\) | −22.3957 | −0.783048 | ||||||||
\(819\) | −8.22359 | + | 5.69380i | −0.287356 | + | 0.198958i | ||||
\(820\) | −0.840215 | −0.0293416 | ||||||||
\(821\) | 9.85527 | − | 5.68994i | 0.343951 | − | 0.198580i | −0.318067 | − | 0.948068i | \(-0.603034\pi\) |
0.662018 | + | 0.749488i | \(0.269700\pi\) | |||||||
\(822\) | 8.53776 | + | 14.7878i | 0.297789 | + | 0.515785i | ||||
\(823\) | 16.8531 | − | 29.1903i | 0.587460 | − | 1.01751i | −0.407103 | − | 0.913382i | \(-0.633461\pi\) |
0.994564 | − | 0.104129i | \(-0.0332056\pi\) | |||||||
\(824\) | − | 14.8126i | − | 0.516022i | ||||||
\(825\) | −4.30687 | − | 2.48657i | −0.149946 | − | 0.0865713i | ||||
\(826\) | 5.39918 | + | 3.11722i | 0.187861 | + | 0.108462i | ||||
\(827\) | 31.2953i | 1.08824i | 0.839006 | + | 0.544122i | \(0.183137\pi\) | ||||
−0.839006 | + | 0.544122i | \(0.816863\pi\) | |||||||
\(828\) | 0.832869 | − | 1.44257i | 0.0289442 | − | 0.0501328i | ||||
\(829\) | −3.68138 | − | 6.37633i | −0.127859 | − | 0.221459i | 0.794988 | − | 0.606626i | \(-0.207477\pi\) |
−0.922847 | + | 0.385167i | \(0.874144\pi\) | |||||||
\(830\) | −0.997917 | + | 0.576148i | −0.0346382 | + | 0.0199984i | ||||
\(831\) | −30.0189 | −1.04134 | ||||||||
\(832\) | −21.8746 | + | 1.79754i | −0.758365 | + | 0.0623186i | ||||
\(833\) | −1.44653 | −0.0501193 | ||||||||
\(834\) | −8.90482 | + | 5.14120i | −0.308349 | + | 0.178025i | ||||
\(835\) | −1.74567 | − | 3.02359i | −0.0604114 | − | 0.104636i | ||||
\(836\) | −1.60206 | + | 2.77485i | −0.0554085 | + | 0.0959703i | ||||
\(837\) | − | 6.48317i | − | 0.224091i | ||||||
\(838\) | −14.7651 | − | 8.52463i | −0.510051 | − | 0.294478i | ||||
\(839\) | −7.04747 | − | 4.06886i | −0.243306 | − | 0.140473i | 0.373389 | − | 0.927675i | \(-0.378196\pi\) |
−0.616695 | + | 0.787202i | \(0.711529\pi\) | |||||||
\(840\) | − | 1.33172i | − | 0.0459488i | ||||||
\(841\) | 14.4093 | − | 24.9576i | 0.496871 | − | 0.860606i | ||||
\(842\) | 9.80057 | + | 16.9751i | 0.337750 | + | 0.585000i | ||||
\(843\) | 22.9733 | − | 13.2636i | 0.791242 | − | 0.456824i | ||||
\(844\) | 11.1248 | 0.382931 | ||||||||
\(845\) | −0.347784 | − | 2.10183i | −0.0119641 | − | 0.0723053i | ||||
\(846\) | 2.55159 | 0.0877254 | ||||||||
\(847\) | 2.40248 | − | 1.38708i | 0.0825504 | − | 0.0476605i | ||||
\(848\) | −1.48552 | − | 2.57299i | −0.0510129 | − | 0.0883569i | ||||
\(849\) | 0.322563 | − | 0.558696i | 0.0110703 | − | 0.0191744i | ||||
\(850\) | 9.71612i | 0.333260i | ||||||||
\(851\) | 3.76231 | + | 2.17217i | 0.128970 | + | 0.0744611i | ||||
\(852\) | −12.6808 | − | 7.32125i | −0.434436 | − | 0.250822i | ||||
\(853\) | − | 31.8425i | − | 1.09027i | −0.838349 | − | 0.545134i | \(-0.816479\pi\) | ||
0.838349 | − | 0.545134i | \(-0.183521\pi\) | |||||||
\(854\) | −6.92551 | + | 11.9953i | −0.236986 | + | 0.410472i | ||||
\(855\) | 0.235135 | + | 0.407265i | 0.00804143 | + | 0.0139282i | ||||
\(856\) | 21.2836 | − | 12.2881i | 0.727459 | − | 0.419999i | ||||
\(857\) | −10.4553 | −0.357146 | −0.178573 | − | 0.983927i | \(-0.557148\pi\) | ||||
−0.178573 | + | 0.983927i | \(0.557148\pi\) | |||||||
\(858\) | −3.37752 | + | 0.277548i | −0.115307 | + | 0.00947532i | ||||
\(859\) | 38.4561 | 1.31210 | 0.656052 | − | 0.754715i | \(-0.272225\pi\) | ||||
0.656052 | + | 0.754715i | \(0.272225\pi\) | |||||||
\(860\) | −1.18052 | + | 0.681575i | −0.0402555 | + | 0.0232415i | ||||
\(861\) | 6.36923 | + | 11.0318i | 0.217063 | + | 0.375964i | ||||
\(862\) | 6.01221 | − | 10.4135i | 0.204777 | − | 0.354684i | ||||
\(863\) | − | 22.3930i | − | 0.762266i | −0.924520 | − | 0.381133i | \(-0.875534\pi\) | ||
0.924520 | − | 0.381133i | \(-0.124466\pi\) | |||||||
\(864\) | −4.65029 | − | 2.68485i | −0.158206 | − | 0.0913403i | ||||
\(865\) | 0.334363 | + | 0.193045i | 0.0113687 | + | 0.00656371i | ||||
\(866\) | − | 4.23191i | − | 0.143806i | ||||||
\(867\) | 6.33968 | − | 10.9807i | 0.215307 | − | 0.372922i | ||||
\(868\) | 10.0408 | + | 17.3913i | 0.340808 | + | 0.590298i | ||||
\(869\) | 6.42103 | − | 3.70718i | 0.217819 | − | 0.125758i | ||||
\(870\) | 0.0656188 | 0.00222468 | ||||||||
\(871\) | −27.7364 | + | 19.2039i | −0.939811 | + | 0.650701i | ||||
\(872\) | −33.4246 | −1.13190 | ||||||||
\(873\) | −8.31993 | + | 4.80351i | −0.281587 | + | 0.162574i | ||||
\(874\) | 2.01191 | + | 3.48473i | 0.0680538 | + | 0.117873i | ||||
\(875\) | 2.26700 | − | 3.92657i | 0.0766387 | − | 0.132742i | ||||
\(876\) | − | 2.71082i | − | 0.0915901i | ||||||
\(877\) | −10.3935 | − | 6.00070i | −0.350964 | − | 0.202629i | 0.314146 | − | 0.949375i | \(-0.398282\pi\) |
−0.665110 | + | 0.746745i | \(0.731615\pi\) | |||||||
\(878\) | 23.4304 | + | 13.5275i | 0.790737 | + | 0.456532i | ||||
\(879\) | − | 17.4073i | − | 0.587133i | ||||||
\(880\) | 0.0426216 | − | 0.0738227i | 0.00143677 | − | 0.00248856i | ||||
\(881\) | 5.32032 | + | 9.21506i | 0.179246 | + | 0.310463i | 0.941622 | − | 0.336671i | \(-0.109301\pi\) |
−0.762377 | + | 0.647134i | \(0.775968\pi\) | |||||||
\(882\) | −0.566463 | + | 0.327048i | −0.0190738 | + | 0.0110123i | ||||
\(883\) | −36.8559 | −1.24030 | −0.620149 | − | 0.784484i | \(-0.712928\pi\) | ||||
−0.620149 | + | 0.784484i | \(0.712928\pi\) | |||||||
\(884\) | −4.76353 | − | 6.88000i | −0.160215 | − | 0.231399i | ||||
\(885\) | −0.391831 | −0.0131713 | ||||||||
\(886\) | −7.09749 | + | 4.09774i | −0.238445 | + | 0.137666i | ||||
\(887\) | 24.6627 | + | 42.7171i | 0.828093 | + | 1.43430i | 0.899532 | + | 0.436854i | \(0.143908\pi\) |
−0.0714390 | + | 0.997445i | \(0.522759\pi\) | |||||||
\(888\) | 4.26515 | − | 7.38746i | 0.143129 | − | 0.247907i | ||||
\(889\) | − | 39.9258i | − | 1.33907i | ||||||
\(890\) | −1.16546 | − | 0.672880i | −0.0390664 | − | 0.0225550i | ||||
\(891\) | −0.866025 | − | 0.500000i | −0.0290129 | − | 0.0167506i | ||||
\(892\) | − | 13.1505i | − | 0.440310i | ||||||
\(893\) | 3.89510 | − | 6.74652i | 0.130345 | − | 0.225764i | ||||
\(894\) | −7.53087 | − | 13.0439i | −0.251870 | − | 0.436252i | ||||
\(895\) | −2.26065 | + | 1.30519i | −0.0755652 | + | 0.0436276i | ||||
\(896\) | 13.9201 | 0.465037 | ||||||||
\(897\) | 2.29892 | − | 4.86290i | 0.0767587 | − | 0.162367i | ||||
\(898\) | 17.6593 | 0.589298 | ||||||||
\(899\) | −2.39187 | + | 1.38095i | −0.0797733 | + | 0.0460572i | ||||
\(900\) | −2.77641 | − | 4.80889i | −0.0925471 | − | 0.160296i | ||||
\(901\) | 5.93626 | − | 10.2819i | 0.197765 | − | 0.342540i | ||||
\(902\) | 4.31593i | 0.143705i | ||||||||
\(903\) | 17.8978 | + | 10.3333i | 0.595603 | + | 0.343871i | ||||
\(904\) | 23.7117 | + | 13.6900i | 0.788640 | + | 0.455322i | ||||
\(905\) | 3.11853i | 0.103664i | ||||||||
\(906\) | −7.78852 | + | 13.4901i | −0.258756 | + | 0.448179i | ||||
\(907\) | 12.9497 | + | 22.4295i | 0.429986 | + | 0.744758i | 0.996872 | − | 0.0790386i | \(-0.0251850\pi\) |
−0.566885 | + | 0.823797i | \(0.691852\pi\) | |||||||
\(908\) | −13.1558 | + | 7.59552i | −0.436592 | + | 0.252066i | ||||
\(909\) | 5.89342 | 0.195472 | ||||||||
\(910\) | −0.126179 | − | 1.53550i | −0.00418280 | − | 0.0509012i | ||||
\(911\) | −30.9025 | −1.02385 | −0.511923 | − | 0.859031i | \(-0.671067\pi\) | ||||
−0.511923 | + | 0.859031i | \(0.671067\pi\) | |||||||
\(912\) | 1.29270 | − | 0.746338i | 0.0428054 | − | 0.0247137i | ||||
\(913\) | −3.74047 | − | 6.47868i | −0.123791 | − | 0.214413i | ||||
\(914\) | −6.03378 | + | 10.4508i | −0.199580 | + | 0.345682i | ||||
\(915\) | − | 0.870531i | − | 0.0287789i | ||||||
\(916\) | −18.7559 | − | 10.8287i | −0.619713 | − | 0.357792i | ||||
\(917\) | −19.5216 | − | 11.2708i | −0.644661 | − | 0.372195i | ||||
\(918\) | 1.95372i | 0.0644823i | ||||||||
\(919\) | −26.3110 | + | 45.5719i | −0.867918 | + | 1.50328i | −0.00379808 | + | 0.999993i | \(0.501209\pi\) |
−0.864120 | + | 0.503286i | \(0.832124\pi\) | |||||||
\(920\) | 0.358078 | + | 0.620209i | 0.0118055 | + | 0.0204477i | ||||
\(921\) | −6.58239 | + | 3.80035i | −0.216897 | + | 0.125226i | ||||
\(922\) | 12.3159 | 0.405601 | ||||||||
\(923\) | −42.7468 | − | 20.2084i | −1.40703 | − | 0.665168i | ||||
\(924\) | 3.09751 | 0.101901 | ||||||||
\(925\) | 12.5419 | − | 7.24105i | 0.412374 | − | 0.238084i | ||||
\(926\) | −2.80942 | − | 4.86605i | −0.0923232 | − | 0.159908i | ||||
\(927\) | 2.52836 | − | 4.37924i | 0.0830421 | − | 0.143833i | ||||
\(928\) | 2.28754i | 0.0750922i | ||||||||
\(929\) | −23.7545 | − | 13.7147i | −0.779360 | − | 0.449963i | 0.0568437 | − | 0.998383i | \(-0.481896\pi\) |
−0.836203 | + | 0.548420i | \(0.815230\pi\) | |||||||
\(930\) | 0.864820 | + | 0.499304i | 0.0283586 | + | 0.0163728i | ||||
\(931\) | 1.99701i | 0.0654493i | ||||||||
\(932\) | −15.9138 | + | 27.5635i | −0.521274 | + | 0.902873i | ||||
\(933\) | 4.44351 | + | 7.69639i | 0.145474 | + | 0.251968i | ||||
\(934\) | −24.0877 | + | 13.9071i | −0.788175 | + | 0.455053i | ||||
\(935\) | 0.340639 | 0.0111401 | ||||||||
\(936\) | −9.54850 | − | 4.51402i | −0.312103 | − | 0.147545i | ||||
\(937\) | −3.29578 | −0.107668 | −0.0538342 | − | 0.998550i | \(-0.517144\pi\) | ||||
−0.0538342 | + | 0.998550i | \(0.517144\pi\) | |||||||
\(938\) | −21.1284 | + | 12.1985i | −0.689867 | + | 0.398295i | ||||
\(939\) | −8.64433 | − | 14.9724i | −0.282097 | − | 0.488606i | ||||
\(940\) | 0.248368 | − | 0.430186i | 0.00810088 | − | 0.0140311i | ||||
\(941\) | 52.3176i | 1.70550i | 0.522316 | + | 0.852752i | \(0.325068\pi\) | ||||
−0.522316 | + | 0.852752i | \(0.674932\pi\) | |||||||
\(942\) | −17.1762 | − | 9.91671i | −0.559632 | − | 0.323104i | ||||
\(943\) | −5.93255 | − | 3.42516i | −0.193190 | − | 0.111539i | ||||
\(944\) | 1.24371i | 0.0404792i | ||||||||
\(945\) | 0.227311 | − | 0.393714i | 0.00739442 | − | 0.0128075i | ||||
\(946\) | 3.50105 | + | 6.06399i | 0.113829 | + | 0.197157i | ||||
\(947\) | 46.9640 | − | 27.1147i | 1.52612 | − | 0.881108i | 0.526605 | − | 0.850110i | \(-0.323465\pi\) |
0.999519 | − | 0.0309981i | \(-0.00986859\pi\) | |||||||
\(948\) | 8.27861 | 0.268877 | ||||||||
\(949\) | −0.716914 | − | 8.72425i | −0.0232720 | − | 0.283201i | ||||
\(950\) | 13.4136 | 0.435195 | ||||||||
\(951\) | 9.34533 | − | 5.39553i | 0.303043 | − | 0.174962i | ||||
\(952\) | −8.44574 | − | 14.6284i | −0.273728 | − | 0.474111i | ||||
\(953\) | −19.8929 | + | 34.4554i | −0.644393 | + | 1.11612i | 0.340048 | + | 0.940408i | \(0.389557\pi\) |
−0.984441 | + | 0.175713i | \(0.943777\pi\) | |||||||
\(954\) | − | 5.36855i | − | 0.173813i | ||||||
\(955\) | 1.28824 | + | 0.743765i | 0.0416864 | + | 0.0240677i | ||||
\(956\) | −2.47238 | − | 1.42743i | −0.0799624 | − | 0.0461663i | ||||
\(957\) | 0.426010i | 0.0137709i | ||||||||
\(958\) | 3.81924 | − | 6.61513i | 0.123394 | − | 0.213725i | ||||
\(959\) | −25.1992 | − | 43.6462i | −0.813723 | − | 1.40941i | ||||
\(960\) | 0.863934 | − | 0.498793i | 0.0278834 | − | 0.0160985i | ||||
\(961\) | −11.0314 | −0.355853 | ||||||||
\(962\) | 4.21782 | − | 8.92196i | 0.135988 | − | 0.287655i | ||||
\(963\) | 8.38979 | 0.270357 | ||||||||
\(964\) | −7.34467 | + | 4.24045i | −0.236556 | + | 0.136576i | ||||
\(965\) | −0.0936196 | − | 0.162154i | −0.00301372 | − | 0.00521992i | ||||
\(966\) | 1.94496 | − | 3.36878i | 0.0625782 | − | 0.108389i | ||||
\(967\) | − | 26.4697i | − | 0.851207i | −0.904910 | − | 0.425603i | \(-0.860062\pi\) | ||
0.904910 | − | 0.425603i | \(-0.139938\pi\) | |||||||
\(968\) | 2.53685 | + | 1.46465i | 0.0815374 | + | 0.0470756i | ||||
\(969\) | 5.16572 | + | 2.98243i | 0.165947 | + | 0.0958094i | ||||
\(970\) | − | 1.47978i | − | 0.0475129i | ||||||
\(971\) | −26.8047 | + | 46.4272i | −0.860205 | + | 1.48992i | 0.0115258 | + | 0.999934i | \(0.496331\pi\) |
−0.871731 | + | 0.489985i | \(0.837002\pi\) | |||||||
\(972\) | −0.558281 | − | 0.966972i | −0.0179069 | − | 0.0310156i | ||||
\(973\) | 26.2825 | − | 15.1742i | 0.842580 | − | 0.486464i | ||||
\(974\) | −4.04261 | −0.129533 | ||||||||
\(975\) | −10.2071 | − | 14.7422i | −0.326890 | − | 0.472129i | ||||
\(976\) | −2.76314 | −0.0884460 | ||||||||
\(977\) | 5.53223 | − | 3.19404i | 0.176992 | − | 0.102186i | −0.408887 | − | 0.912585i | \(-0.634083\pi\) |
0.585879 | + | 0.810399i | \(0.300750\pi\) | |||||||
\(978\) | 5.51390 | + | 9.55036i | 0.176315 | + | 0.305387i | ||||
\(979\) | 4.36847 | − | 7.56642i | 0.139617 | − | 0.241824i | ||||
\(980\) | 0.127338i | 0.00406765i | ||||||||
\(981\) | −9.88173 | − | 5.70522i | −0.315499 | − | 0.182154i | ||||
\(982\) | −17.7845 | − | 10.2679i | −0.567526 | − | 0.327661i | ||||
\(983\) | 33.0630i | 1.05455i | 0.849696 | + | 0.527273i | \(0.176786\pi\) | ||||
−0.849696 | + | 0.527273i | \(0.823214\pi\) | |||||||
\(984\) | −6.72544 | + | 11.6488i | −0.214399 | + | 0.371350i | ||||
\(985\) | 1.42123 | + | 2.46165i | 0.0452842 | + | 0.0784346i | ||||
\(986\) | 0.720796 | − | 0.416152i | 0.0229548 | − | 0.0132530i | ||||
\(987\) | −7.53100 | −0.239714 | ||||||||
\(988\) | −9.49819 | + | 6.57630i | −0.302178 | + | 0.209220i | ||||
\(989\) | −11.1138 | −0.353399 | ||||||||
\(990\) | 0.133395 | − | 0.0770155i | 0.00423956 | − | 0.00244771i | ||||
\(991\) | 21.8087 | + | 37.7738i | 0.692777 | + | 1.19992i | 0.970924 | + | 0.239386i | \(0.0769463\pi\) |
−0.278147 | + | 0.960538i | \(0.589720\pi\) | |||||||
\(992\) | −17.4063 | + | 30.1486i | −0.552650 | + | 0.957219i | ||||
\(993\) | 23.7135i | 0.752526i | ||||||||
\(994\) | −29.6129 | − | 17.0970i | −0.939264 | − | 0.542284i | ||||
\(995\) | 0.135079 | + | 0.0779880i | 0.00428230 | + | 0.00247238i | ||||
\(996\) | − | 8.35293i | − | 0.264673i | ||||||
\(997\) | 18.1905 | − | 31.5069i | 0.576100 | − | 0.997834i | −0.419821 | − | 0.907607i | \(-0.637907\pi\) |
0.995921 | − | 0.0902275i | \(-0.0287594\pi\) | |||||||
\(998\) | 15.9673 | + | 27.6562i | 0.505436 | + | 0.875442i | ||||
\(999\) | 2.52192 | − | 1.45603i | 0.0797900 | − | 0.0460668i |
(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 | 429.2.s.b.166.9 | ✓ | 28 | |
13.2 | odd | 12 | 5577.2.a.bf.1.11 | 14 | |||
13.4 | even | 6 | inner | 429.2.s.b.199.9 | yes | 28 | |
13.11 | odd | 12 | 5577.2.a.bg.1.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.s.b.166.9 | ✓ | 28 | 1.1 | even | 1 | trivial | |
429.2.s.b.199.9 | yes | 28 | 13.4 | even | 6 | inner | |
5577.2.a.bf.1.11 | 14 | 13.2 | odd | 12 | |||
5577.2.a.bg.1.4 | 14 | 13.11 | odd | 12 |