Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(101,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\), degree \(6\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Character | \(\chi\) | \(=\) | 475.101 |
Dual form | 475.2.l.f.301.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05812 | + | 1.72697i | −1.45531 | + | 1.22115i | −0.526724 | + | 0.850036i | \(0.676580\pi\) |
−0.928587 | + | 0.371115i | \(0.878976\pi\) | |||||||
\(3\) | −2.01713 | − | 0.734175i | −1.16459 | − | 0.423876i | −0.313855 | − | 0.949471i | \(-0.601621\pi\) |
−0.850735 | + | 0.525595i | \(0.823843\pi\) | |||||||
\(4\) | 0.906145 | − | 5.13900i | 0.453073 | − | 2.56950i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.41939 | − | 1.97250i | 2.21246 | − | 0.805269i | ||||
\(7\) | 1.39152 | − | 2.41018i | 0.525944 | − | 0.910961i | −0.473600 | − | 0.880740i | \(-0.657046\pi\) |
0.999543 | − | 0.0302209i | \(-0.00962108\pi\) | |||||||
\(8\) | 4.32326 | + | 7.48810i | 1.52850 | + | 2.64744i | ||||
\(9\) | 1.23166 | + | 1.03349i | 0.410554 | + | 0.344496i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.19000 | + | 2.06113i | 0.358797 | + | 0.621455i | 0.987760 | − | 0.155980i | \(-0.0498536\pi\) |
−0.628963 | + | 0.777435i | \(0.716520\pi\) | |||||||
\(12\) | −5.60074 | + | 9.70076i | −1.61679 | + | 2.80037i | ||||
\(13\) | 0.0380504 | − | 0.0138492i | 0.0105533 | − | 0.00384108i | −0.336738 | − | 0.941598i | \(-0.609324\pi\) |
0.347291 | + | 0.937757i | \(0.387101\pi\) | |||||||
\(14\) | 1.29839 | + | 7.36354i | 0.347010 | + | 1.96799i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.0223 | − | 4.37577i | −3.00558 | − | 1.09394i | ||||
\(17\) | 1.39094 | − | 1.16714i | 0.337353 | − | 0.283073i | −0.458335 | − | 0.888780i | \(-0.651554\pi\) |
0.795688 | + | 0.605707i | \(0.207109\pi\) | |||||||
\(18\) | −4.31971 | −1.01816 | ||||||||
\(19\) | −4.07652 | − | 1.54336i | −0.935219 | − | 0.354071i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.57636 | + | 3.84002i | −0.998643 | + | 0.837961i | ||||
\(22\) | −6.00867 | − | 2.18698i | −1.28105 | − | 0.466265i | ||||
\(23\) | 0.441819 | − | 2.50568i | 0.0921257 | − | 0.522471i | −0.903465 | − | 0.428663i | \(-0.858985\pi\) |
0.995590 | − | 0.0938080i | \(-0.0299040\pi\) | |||||||
\(24\) | −3.22299 | − | 18.2785i | −0.657890 | − | 3.73108i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.0543952 | + | 0.0942153i | −0.0106678 | + | 0.0184771i | ||||
\(27\) | 1.49422 | + | 2.58806i | 0.287562 | + | 0.498072i | ||||
\(28\) | −11.1250 | − | 9.33498i | −2.10243 | − | 1.76414i | ||||
\(29\) | 2.25845 | + | 1.89507i | 0.419384 | + | 0.351905i | 0.827929 | − | 0.560833i | \(-0.189519\pi\) |
−0.408545 | + | 0.912738i | \(0.633964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.44307 | − | 2.49947i | 0.259183 | − | 0.448918i | −0.706840 | − | 0.707373i | \(-0.749880\pi\) |
0.966023 | + | 0.258455i | \(0.0832134\pi\) | |||||||
\(32\) | 16.0501 | − | 5.84176i | 2.83728 | − | 1.03269i | ||||
\(33\) | −0.887142 | − | 5.03123i | −0.154432 | − | 0.875826i | ||||
\(34\) | −0.847116 | + | 4.80423i | −0.145279 | + | 0.823919i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.42716 | − | 5.39302i | 1.07119 | − | 0.898837i | ||||
\(37\) | 0.227089 | 0.0373333 | 0.0186666 | − | 0.999826i | \(-0.494058\pi\) | ||||
0.0186666 | + | 0.999826i | \(0.494058\pi\) | |||||||
\(38\) | 11.0553 | − | 3.86361i | 1.79341 | − | 0.626761i | ||||
\(39\) | −0.0869204 | −0.0139184 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.55269 | − | 2.74896i | −1.17953 | − | 0.429315i | −0.323496 | − | 0.946230i | \(-0.604858\pi\) |
−0.856037 | + | 0.516915i | \(0.827080\pi\) | |||||||
\(42\) | 2.78710 | − | 15.8065i | 0.430059 | − | 2.43899i | ||||
\(43\) | −0.891282 | − | 5.05471i | −0.135919 | − | 0.770836i | −0.974215 | − | 0.225621i | \(-0.927559\pi\) |
0.838296 | − | 0.545215i | \(-0.183552\pi\) | |||||||
\(44\) | 11.6705 | − | 4.24771i | 1.75939 | − | 0.640366i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.41791 | + | 5.92000i | 0.503944 | + | 0.872857i | ||||
\(47\) | −8.48501 | − | 7.11977i | −1.23767 | − | 1.03853i | −0.997703 | − | 0.0677434i | \(-0.978420\pi\) |
−0.239964 | − | 0.970782i | \(-0.577135\pi\) | |||||||
\(48\) | 21.0380 | + | 17.6530i | 3.03657 | + | 2.54799i | ||||
\(49\) | −0.372635 | − | 0.645423i | −0.0532336 | − | 0.0922032i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.66260 | + | 1.33308i | −0.512866 | + | 0.186668i | ||||
\(52\) | −0.0366920 | − | 0.208091i | −0.00508827 | − | 0.0288570i | ||||
\(53\) | −0.992310 | + | 5.62767i | −0.136304 | + | 0.773020i | 0.837638 | + | 0.546225i | \(0.183936\pi\) |
−0.973943 | + | 0.226794i | \(0.927175\pi\) | |||||||
\(54\) | −7.54477 | − | 2.74607i | −1.02671 | − | 0.373693i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 24.0635 | 3.21562 | ||||||||
\(57\) | 7.08978 | + | 6.10603i | 0.939064 | + | 0.808764i | ||||
\(58\) | −7.92088 | −1.04006 | ||||||||
\(59\) | 8.89878 | − | 7.46696i | 1.15852 | − | 0.972116i | 0.158638 | − | 0.987337i | \(-0.449290\pi\) |
0.999884 | + | 0.0152208i | \(0.00484512\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.795974 | − | 4.51419i | 0.101914 | − | 0.577983i | −0.890494 | − | 0.454995i | \(-0.849641\pi\) |
0.992408 | − | 0.122988i | \(-0.0392477\pi\) | |||||||
\(62\) | 1.34649 | + | 7.63635i | 0.171005 | + | 0.969817i | ||||
\(63\) | 4.20476 | − | 1.53041i | 0.529750 | − | 0.192813i | ||||
\(64\) | −10.1506 | + | 17.5814i | −1.26883 | + | 2.19767i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.5146 | + | 8.82282i | 1.29426 | + | 1.08601i | ||||
\(67\) | −3.71745 | − | 3.11931i | −0.454159 | − | 0.381084i | 0.386818 | − | 0.922156i | \(-0.373574\pi\) |
−0.840976 | + | 0.541072i | \(0.818019\pi\) | |||||||
\(68\) | −4.73754 | − | 8.20566i | −0.574511 | − | 0.995083i | ||||
\(69\) | −2.73081 | + | 4.72991i | −0.328751 | + | 0.569414i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.34912 | − | 7.65124i | −0.160111 | − | 0.908035i | −0.953963 | − | 0.299924i | \(-0.903039\pi\) |
0.793852 | − | 0.608111i | \(-0.208072\pi\) | |||||||
\(72\) | −2.41406 | + | 13.6908i | −0.284500 | + | 1.61348i | ||||
\(73\) | −3.99151 | − | 1.45279i | −0.467171 | − | 0.170036i | 0.0976997 | − | 0.995216i | \(-0.468852\pi\) |
−0.564870 | + | 0.825180i | \(0.691074\pi\) | |||||||
\(74\) | −0.467377 | + | 0.392176i | −0.0543315 | + | 0.0455896i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.6252 | + | 19.5508i | −1.33351 | + | 2.24263i | ||||
\(77\) | 6.62359 | 0.754828 | ||||||||
\(78\) | 0.178893 | − | 0.150109i | 0.0202556 | − | 0.0169965i | ||||
\(79\) | −10.9102 | − | 3.97100i | −1.22750 | − | 0.446773i | −0.354758 | − | 0.934958i | \(-0.615437\pi\) |
−0.872740 | + | 0.488185i | \(0.837659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.95152 | − | 11.0676i | −0.216836 | − | 1.22974i | ||||
\(82\) | 20.2917 | − | 7.38558i | 2.24085 | − | 0.815601i | ||||
\(83\) | 2.23528 | − | 3.87161i | 0.245354 | − | 0.424965i | −0.716877 | − | 0.697199i | \(-0.754429\pi\) |
0.962231 | + | 0.272234i | \(0.0877626\pi\) | |||||||
\(84\) | 15.5870 | + | 26.9975i | 1.70069 | + | 2.94567i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.5637 | + | 8.86399i | 1.13911 | + | 0.955828i | ||||
\(87\) | −3.16428 | − | 5.48069i | −0.339246 | − | 0.587592i | ||||
\(88\) | −10.2893 | + | 17.8216i | −1.09684 | + | 1.89979i | ||||
\(89\) | −14.4648 | + | 5.26476i | −1.53327 | + | 0.558064i | −0.964419 | − | 0.264378i | \(-0.914833\pi\) |
−0.568849 | + | 0.822442i | \(0.692611\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0195687 | − | 0.110980i | 0.00205136 | − | 0.0116338i | ||||
\(92\) | −12.4764 | − | 4.54102i | −1.30075 | − | 0.473434i | ||||
\(93\) | −4.74590 | + | 3.98229i | −0.492127 | + | 0.412944i | ||||
\(94\) | 29.7588 | 3.06939 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −36.6640 | −3.74200 | ||||||||
\(97\) | −4.28633 | + | 3.59666i | −0.435211 | + | 0.365185i | −0.833914 | − | 0.551895i | \(-0.813905\pi\) |
0.398703 | + | 0.917080i | \(0.369460\pi\) | |||||||
\(98\) | 1.88155 | + | 0.684829i | 0.190066 | + | 0.0691782i | ||||
\(99\) | −0.664482 | + | 3.76846i | −0.0667829 | + | 0.378745i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2361 | + | 4.08961i | −1.11804 | + | 0.406932i | −0.833935 | − | 0.551863i | \(-0.813917\pi\) |
−0.284101 | + | 0.958794i | \(0.591695\pi\) | |||||||
\(102\) | 5.23589 | − | 9.06882i | 0.518430 | − | 0.897947i | ||||
\(103\) | −7.04702 | − | 12.2058i | −0.694363 | − | 1.20267i | −0.970395 | − | 0.241524i | \(-0.922353\pi\) |
0.276031 | − | 0.961149i | \(-0.410981\pi\) | |||||||
\(104\) | 0.268206 | + | 0.225052i | 0.0262998 | + | 0.0220681i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.67651 | − | 13.2961i | −0.745609 | − | 1.29143i | ||||
\(107\) | −5.86249 | + | 10.1541i | −0.566748 | + | 0.981637i | 0.430137 | + | 0.902764i | \(0.358465\pi\) |
−0.996885 | + | 0.0788727i | \(0.974868\pi\) | |||||||
\(108\) | 14.6540 | − | 5.33362i | 1.41008 | − | 0.513228i | ||||
\(109\) | −1.16558 | − | 6.61032i | −0.111642 | − | 0.633154i | −0.988358 | − | 0.152145i | \(-0.951382\pi\) |
0.876716 | − | 0.481008i | \(-0.159729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.458068 | − | 0.166723i | −0.0434779 | − | 0.0158247i | ||||
\(112\) | −27.2757 | + | 22.8870i | −2.57731 | + | 2.16262i | ||||
\(113\) | −2.46603 | −0.231985 | −0.115992 | − | 0.993250i | \(-0.537005\pi\) | ||||
−0.115992 | + | 0.993250i | \(0.537005\pi\) | |||||||
\(114\) | −25.1365 | − | 0.323128i | −2.35425 | − | 0.0302637i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.7852 | − | 9.88899i | 1.09423 | − | 0.918169i | ||||
\(117\) | 0.0611783 | + | 0.0222671i | 0.00565593 | + | 0.00205859i | ||||
\(118\) | −5.41956 | + | 30.7358i | −0.498911 | + | 2.82946i | ||||
\(119\) | −0.877494 | − | 4.97651i | −0.0804397 | − | 0.456196i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.66782 | − | 4.62080i | 0.242529 | − | 0.420073i | ||||
\(122\) | 6.15765 | + | 10.6654i | 0.557488 | + | 0.965597i | ||||
\(123\) | 13.2165 | + | 11.0900i | 1.19170 | + | 0.999951i | ||||
\(124\) | −11.5372 | − | 9.68082i | −1.03607 | − | 0.869364i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.01094 | + | 10.4113i | −0.535497 | + | 0.927509i | ||||
\(127\) | 0.694456 | − | 0.252761i | 0.0616230 | − | 0.0224289i | −0.311025 | − | 0.950402i | \(-0.600672\pi\) |
0.372648 | + | 0.927973i | \(0.378450\pi\) | |||||||
\(128\) | −3.53942 | − | 20.0731i | −0.312844 | − | 1.77423i | ||||
\(129\) | −1.91321 | + | 10.8504i | −0.168449 | + | 0.955320i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.35925 | + | 7.01424i | −0.730351 | + | 0.612837i | −0.930227 | − | 0.366984i | \(-0.880390\pi\) |
0.199876 | + | 0.979821i | \(0.435946\pi\) | |||||||
\(132\) | −26.6594 | −2.32040 | ||||||||
\(133\) | −9.39231 | + | 7.67754i | −0.814417 | + | 0.665727i | ||||
\(134\) | 13.0379 | 1.12630 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.7531 | + | 5.36968i | 1.26506 | + | 0.460446i | ||||
\(137\) | −0.797114 | + | 4.52066i | −0.0681021 | + | 0.386226i | 0.931637 | + | 0.363390i | \(0.118381\pi\) |
−0.999739 | + | 0.0228361i | \(0.992730\pi\) | |||||||
\(138\) | −2.54806 | − | 14.4508i | −0.216905 | − | 1.23013i | ||||
\(139\) | 7.37217 | − | 2.68325i | 0.625299 | − | 0.227590i | −0.00988487 | − | 0.999951i | \(-0.503147\pi\) |
0.635184 | + | 0.772361i | \(0.280924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.8882 | + | 20.5910i | 1.00117 | + | 1.73407i | ||||
\(142\) | 15.9901 | + | 13.4173i | 1.34186 | + | 1.12595i | ||||
\(143\) | 0.0738250 | + | 0.0619465i | 0.00617355 | + | 0.00518023i | ||||
\(144\) | −10.2851 | − | 17.8144i | −0.857095 | − | 1.48453i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.7239 | − | 3.90319i | 0.887518 | − | 0.323030i | ||||
\(147\) | 0.277800 | + | 1.57548i | 0.0229125 | + | 0.129943i | ||||
\(148\) | 0.205776 | − | 1.16701i | 0.0169147 | − | 0.0959279i | ||||
\(149\) | 20.4289 | + | 7.43550i | 1.67360 | + | 0.609140i | 0.992411 | − | 0.122968i | \(-0.0392412\pi\) |
0.681188 | + | 0.732108i | \(0.261463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.68916 | 0.788493 | 0.394247 | − | 0.919005i | \(-0.371006\pi\) | ||||
0.394247 | + | 0.919005i | \(0.371006\pi\) | |||||||
\(152\) | −6.06704 | − | 37.1977i | −0.492102 | − | 3.01714i | ||||
\(153\) | 2.91940 | 0.236019 | ||||||||
\(154\) | −13.6322 | + | 11.4387i | −1.09851 | + | 0.921760i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0787625 | + | 0.446684i | −0.00630604 | + | 0.0357634i | ||||
\(157\) | −1.28145 | − | 7.26744i | −0.102271 | − | 0.580005i | −0.992275 | − | 0.124054i | \(-0.960410\pi\) |
0.890005 | − | 0.455951i | \(-0.150701\pi\) | |||||||
\(158\) | 29.3124 | − | 10.6688i | 2.33197 | − | 0.848767i | ||||
\(159\) | 6.13331 | − | 10.6232i | 0.486403 | − | 0.842474i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.42434 | − | 4.55156i | −0.427498 | − | 0.358713i | ||||
\(162\) | 23.1299 | + | 19.4083i | 1.81726 | + | 1.52486i | ||||
\(163\) | 2.45155 | + | 4.24622i | 0.192021 | + | 0.332589i | 0.945920 | − | 0.324401i | \(-0.105163\pi\) |
−0.753899 | + | 0.656990i | \(0.771829\pi\) | |||||||
\(164\) | −20.9707 | + | 36.3224i | −1.63754 | + | 2.83630i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.08568 | + | 11.8285i | 0.161880 | + | 0.918070i | ||||
\(167\) | 1.75241 | − | 9.93844i | 0.135606 | − | 0.769059i | −0.838830 | − | 0.544394i | \(-0.816760\pi\) |
0.974436 | − | 0.224666i | \(-0.0721290\pi\) | |||||||
\(168\) | −48.5392 | − | 17.6668i | −3.74488 | − | 1.36303i | ||||
\(169\) | −9.95732 | + | 8.35518i | −0.765948 | + | 0.642707i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.42586 | − | 6.11393i | −0.261982 | − | 0.467544i | ||||
\(172\) | −26.7838 | −2.04225 | ||||||||
\(173\) | 3.73777 | − | 3.13636i | 0.284177 | − | 0.238453i | −0.489545 | − | 0.871978i | \(-0.662837\pi\) |
0.773722 | + | 0.633525i | \(0.218393\pi\) | |||||||
\(174\) | 15.9774 | + | 5.81531i | 1.21125 | + | 0.440858i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.28748 | − | 29.9868i | −0.398559 | − | 2.26034i | ||||
\(177\) | −23.4320 | + | 8.52857i | −1.76126 | + | 0.641046i | ||||
\(178\) | 20.6783 | − | 35.8158i | 1.54990 | − | 2.68451i | ||||
\(179\) | −11.9422 | − | 20.6845i | −0.892604 | − | 1.54604i | −0.836743 | − | 0.547597i | \(-0.815543\pi\) |
−0.0558613 | − | 0.998439i | \(-0.517790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.96682 | + | 1.65036i | 0.146193 | + | 0.122670i | 0.712951 | − | 0.701214i | \(-0.247358\pi\) |
−0.566758 | + | 0.823884i | \(0.691803\pi\) | |||||||
\(182\) | 0.151384 | + | 0.262204i | 0.0112213 | + | 0.0194359i | ||||
\(183\) | −4.91979 | + | 8.52132i | −0.363681 | + | 0.629914i | ||||
\(184\) | 20.6729 | − | 7.52431i | 1.52403 | − | 0.554700i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.89036 | − | 16.3921i | 0.211932 | − | 1.20192i | ||||
\(187\) | 4.06085 | + | 1.47803i | 0.296959 | + | 0.108084i | ||||
\(188\) | −44.2772 | + | 37.1530i | −3.22925 | + | 2.70966i | ||||
\(189\) | 8.31690 | 0.604965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.28746 | 0.672017 | 0.336008 | − | 0.941859i | \(-0.390923\pi\) | ||||
0.336008 | + | 0.941859i | \(0.390923\pi\) | |||||||
\(192\) | 33.3829 | − | 28.0116i | 2.40920 | − | 2.02156i | ||||
\(193\) | 23.3341 | + | 8.49293i | 1.67963 | + | 0.611334i | 0.993259 | − | 0.115920i | \(-0.0369816\pi\) |
0.686368 | + | 0.727254i | \(0.259204\pi\) | |||||||
\(194\) | 2.61047 | − | 14.8047i | 0.187421 | − | 1.06292i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.65449 | + | 1.33013i | −0.261035 | + | 0.0950090i | ||||
\(197\) | −2.08658 | + | 3.61406i | −0.148663 | + | 0.257491i | −0.930733 | − | 0.365698i | \(-0.880830\pi\) |
0.782071 | + | 0.623190i | \(0.214164\pi\) | |||||||
\(198\) | −5.14043 | − | 8.90349i | −0.365315 | − | 0.632744i | ||||
\(199\) | 17.1492 | + | 14.3899i | 1.21567 | + | 1.02007i | 0.999039 | + | 0.0438194i | \(0.0139526\pi\) |
0.216635 | + | 0.976253i | \(0.430492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.20845 | + | 9.02131i | 0.367376 | + | 0.636314i | ||||
\(202\) | 16.0627 | − | 27.8213i | 1.13016 | − | 1.95750i | ||||
\(203\) | 7.71012 | − | 2.80625i | 0.541144 | − | 0.196960i | ||||
\(204\) | 3.53184 | + | 20.0301i | 0.247278 | + | 1.40238i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 35.5826 | + | 12.9510i | 2.47916 | + | 0.902340i | ||||
\(207\) | 3.13376 | − | 2.62954i | 0.217811 | − | 0.182765i | ||||
\(208\) | −0.518056 | −0.0359207 | ||||||||
\(209\) | −1.66998 | − | 10.2388i | −0.115515 | − | 0.708236i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.28817 | − | 1.08090i | 0.0886814 | − | 0.0744125i | −0.597369 | − | 0.801966i | \(-0.703787\pi\) |
0.686051 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(212\) | 28.0214 | + | 10.1990i | 1.92452 | + | 0.700468i | ||||
\(213\) | −2.89600 | + | 16.4240i | −0.198431 | + | 1.12536i | ||||
\(214\) | −5.47015 | − | 31.0228i | −0.373932 | − | 2.12067i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −12.9197 | + | 22.3777i | −0.879078 | + | 1.52261i | ||||
\(217\) | −4.01611 | − | 6.95611i | −0.272631 | − | 0.472211i | ||||
\(218\) | 13.8147 | + | 11.5919i | 0.935650 | + | 0.785104i | ||||
\(219\) | 6.98478 | + | 5.86093i | 0.471988 | + | 0.396045i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0367620 | − | 0.0636737i | 0.00247288 | − | 0.00428316i | ||||
\(222\) | 1.23069 | − | 0.447933i | 0.0825982 | − | 0.0300633i | ||||
\(223\) | −1.66903 | − | 9.46555i | −0.111767 | − | 0.633860i | −0.988300 | − | 0.152520i | \(-0.951261\pi\) |
0.876534 | − | 0.481340i | \(-0.159850\pi\) | |||||||
\(224\) | 8.25431 | − | 46.8125i | 0.551514 | − | 3.12779i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.07539 | − | 4.25876i | 0.337610 | − | 0.283288i | ||||
\(227\) | 23.4650 | 1.55743 | 0.778714 | − | 0.627379i | \(-0.215872\pi\) | ||||
0.778714 | + | 0.627379i | \(0.215872\pi\) | |||||||
\(228\) | 37.8033 | − | 30.9014i | 2.50358 | − | 2.04650i | ||||
\(229\) | −1.19088 | −0.0786952 | −0.0393476 | − | 0.999226i | \(-0.512528\pi\) | ||||
−0.0393476 | + | 0.999226i | \(0.512528\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.3606 | − | 4.86287i | −0.879065 | − | 0.319954i | ||||
\(232\) | −4.42658 | + | 25.1044i | −0.290619 | + | 1.64818i | ||||
\(233\) | 4.01831 | + | 22.7889i | 0.263248 | + | 1.49295i | 0.773978 | + | 0.633212i | \(0.218264\pi\) |
−0.510730 | + | 0.859741i | \(0.670625\pi\) | |||||||
\(234\) | −0.164367 | + | 0.0598246i | −0.0107450 | + | 0.00391086i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −30.3092 | − | 52.4970i | −1.97296 | − | 3.41727i | ||||
\(237\) | 19.0920 | + | 16.0200i | 1.24016 | + | 1.04061i | ||||
\(238\) | 10.4003 | + | 8.72686i | 0.674149 | + | 0.565679i | ||||
\(239\) | −4.84358 | − | 8.38932i | −0.313305 | − | 0.542660i | 0.665771 | − | 0.746156i | \(-0.268103\pi\) |
−0.979076 | + | 0.203496i | \(0.934770\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8334 | + | 5.39891i | −0.955503 | + | 0.347775i | −0.772270 | − | 0.635295i | \(-0.780879\pi\) |
−0.183233 | + | 0.983070i | \(0.558656\pi\) | |||||||
\(242\) | 2.48928 | + | 14.1174i | 0.160017 | + | 0.907502i | ||||
\(243\) | −2.63230 | + | 14.9285i | −0.168862 | + | 0.957665i | ||||
\(244\) | −22.4772 | − | 8.18102i | −1.43895 | − | 0.523736i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −46.3533 | −2.95538 | ||||||||
\(247\) | −0.176488 | − | 0.00226874i | −0.0112297 | − | 0.000144356i | ||||
\(248\) | 24.9550 | 1.58465 | ||||||||
\(249\) | −7.35128 | + | 6.16846i | −0.465869 | + | 0.390910i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.951469 | − | 5.39605i | 0.0600562 | − | 0.340596i | −0.939944 | − | 0.341330i | \(-0.889123\pi\) |
1.00000 | 0.000734411i | \(0.000233770\pi\) | ||||||||
\(252\) | −4.05465 | − | 22.9951i | −0.255419 | − | 1.44855i | ||||
\(253\) | 5.69030 | − | 2.07110i | 0.357746 | − | 0.130209i | ||||
\(254\) | −0.992764 | + | 1.71952i | −0.0622915 | + | 0.107892i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.8468 | + | 9.10155i | 0.677926 | + | 0.568847i | ||||
\(257\) | 2.71792 | + | 2.28060i | 0.169539 | + | 0.142260i | 0.723609 | − | 0.690210i | \(-0.242482\pi\) |
−0.554070 | + | 0.832470i | \(0.686926\pi\) | |||||||
\(258\) | −14.8006 | − | 25.6354i | −0.921445 | − | 1.59599i | ||||
\(259\) | 0.315999 | − | 0.547326i | 0.0196352 | − | 0.0340092i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.823122 | + | 4.66816i | 0.0509500 | + | 0.288952i | ||||
\(262\) | 5.09097 | − | 28.8723i | 0.314521 | − | 1.78374i | ||||
\(263\) | −24.7587 | − | 9.01141i | −1.52668 | − | 0.555668i | −0.563877 | − | 0.825858i | \(-0.690691\pi\) |
−0.962807 | + | 0.270191i | \(0.912913\pi\) | |||||||
\(264\) | 33.8390 | − | 28.3943i | 2.08265 | − | 1.74755i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.07166 | − | 32.0215i | 0.372277 | − | 1.96337i | ||||
\(267\) | 33.0427 | 2.02218 | ||||||||
\(268\) | −19.3987 | + | 16.2774i | −1.18496 | + | 0.994303i | ||||
\(269\) | −21.7224 | − | 7.90629i | −1.32444 | − | 0.482055i | −0.419559 | − | 0.907728i | \(-0.637815\pi\) |
−0.904877 | + | 0.425673i | \(0.860037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.20656 | + | 18.1853i | 0.194785 | + | 1.10468i | 0.912725 | + | 0.408574i | \(0.133974\pi\) |
−0.717941 | + | 0.696104i | \(0.754915\pi\) | |||||||
\(272\) | −21.8295 | + | 7.94530i | −1.32361 | + | 0.481754i | ||||
\(273\) | −0.120951 | + | 0.209493i | −0.00732029 | + | 0.0126791i | ||||
\(274\) | −6.16648 | − | 10.6807i | −0.372531 | − | 0.645242i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 21.8325 | + | 18.3196i | 1.31416 | + | 1.10271i | ||||
\(277\) | −14.9854 | − | 25.9554i | −0.900384 | − | 1.55951i | −0.826996 | − | 0.562208i | \(-0.809952\pi\) |
−0.0733885 | − | 0.997303i | \(-0.523381\pi\) | |||||||
\(278\) | −10.5389 | + | 18.2540i | −0.632083 | + | 1.09480i | ||||
\(279\) | 4.36054 | − | 1.58711i | 0.261059 | − | 0.0950177i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.690977 | + | 3.91872i | −0.0412202 | + | 0.233771i | −0.998457 | − | 0.0555351i | \(-0.982314\pi\) |
0.957237 | + | 0.289306i | \(0.0934247\pi\) | |||||||
\(282\) | −60.0273 | − | 21.8482i | −3.57458 | − | 1.30104i | ||||
\(283\) | 6.93217 | − | 5.81678i | 0.412075 | − | 0.345772i | −0.413064 | − | 0.910702i | \(-0.635541\pi\) |
0.825139 | + | 0.564930i | \(0.191097\pi\) | |||||||
\(284\) | −40.5423 | −2.40574 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.258920 | −0.0153103 | ||||||||
\(287\) | −17.1352 | + | 14.3781i | −1.01146 | + | 0.848713i | ||||
\(288\) | 25.8057 | + | 9.39250i | 1.52061 | + | 0.553458i | ||||
\(289\) | −2.37951 | + | 13.4949i | −0.139971 | + | 0.793816i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.2867 | − | 4.10800i | 0.661635 | − | 0.240816i | ||||
\(292\) | −11.0828 | + | 19.1959i | −0.648570 | + | 1.12336i | ||||
\(293\) | 1.16822 | + | 2.02341i | 0.0682479 | + | 0.118209i | 0.898130 | − | 0.439730i | \(-0.144926\pi\) |
−0.829882 | + | 0.557939i | \(0.811592\pi\) | |||||||
\(294\) | −3.29255 | − | 2.76278i | −0.192025 | − | 0.161128i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.981765 | + | 1.70047i | 0.0570640 | + | 0.0988377i | ||||
\(297\) | −3.55622 | + | 6.15955i | −0.206353 | + | 0.357413i | ||||
\(298\) | −54.8860 | + | 19.9769i | −3.17946 | + | 1.15723i | ||||
\(299\) | −0.0178903 | − | 0.101461i | −0.00103462 | − | 0.00586765i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4230 | − | 4.88556i | −0.773687 | − | 0.281599i | ||||
\(302\) | −19.9415 | + | 16.7329i | −1.14750 | + | 0.962869i | ||||
\(303\) | 25.6672 | 1.47454 | ||||||||
\(304\) | 42.2559 | + | 36.3927i | 2.42354 | + | 2.08726i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.00847 | + | 5.04170i | −0.343481 | + | 0.288215i | ||||
\(307\) | 7.14274 | + | 2.59974i | 0.407658 | + | 0.148375i | 0.537706 | − | 0.843132i | \(-0.319291\pi\) |
−0.130048 | + | 0.991508i | \(0.541513\pi\) | |||||||
\(308\) | 6.00194 | − | 34.0387i | 0.341992 | − | 1.93953i | ||||
\(309\) | 5.25356 | + | 29.7944i | 0.298864 | + | 1.69494i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.41207 | − | 16.3022i | 0.533709 | − | 0.924412i | −0.465515 | − | 0.885040i | \(-0.654131\pi\) |
0.999225 | − | 0.0393720i | \(-0.0125357\pi\) | |||||||
\(312\) | −0.375779 | − | 0.650868i | −0.0212743 | − | 0.0368482i | ||||
\(313\) | −17.0147 | − | 14.2771i | −0.961729 | − | 0.806987i | 0.0195042 | − | 0.999810i | \(-0.493791\pi\) |
−0.981234 | + | 0.192823i | \(0.938236\pi\) | |||||||
\(314\) | 15.1880 | + | 12.7443i | 0.857109 | + | 0.719200i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.2933 | + | 52.4695i | −1.70413 | + | 2.95164i | ||||
\(317\) | 3.82711 | − | 1.39295i | 0.214952 | − | 0.0782360i | −0.232300 | − | 0.972644i | \(-0.574625\pi\) |
0.447252 | + | 0.894408i | \(0.352403\pi\) | |||||||
\(318\) | 5.72284 | + | 32.4559i | 0.320921 | + | 1.82003i | ||||
\(319\) | −1.21843 | + | 6.91009i | −0.0682193 | + | 0.386891i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.2803 | − | 16.1781i | 1.07612 | − | 0.902973i | ||||
\(322\) | 19.0243 | 1.06018 | ||||||||
\(323\) | −7.47153 | + | 2.61115i | −0.415727 | + | 0.145288i | ||||
\(324\) | −58.6450 | −3.25806 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.3787 | − | 4.50547i | −0.685591 | − | 0.249535i | ||||
\(327\) | −2.50201 | + | 14.1896i | −0.138361 | + | 0.784687i | ||||
\(328\) | −12.0678 | − | 68.4398i | −0.666331 | − | 3.77895i | ||||
\(329\) | −28.9669 | + | 10.5431i | −1.59700 | + | 0.581260i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3939 | − | 18.0028i | −0.571301 | − | 0.989523i | −0.996433 | − | 0.0843910i | \(-0.973106\pi\) |
0.425132 | − | 0.905132i | \(-0.360228\pi\) | |||||||
\(332\) | −17.8708 | − | 14.9953i | −0.980785 | − | 0.822976i | ||||
\(333\) | 0.279697 | + | 0.234694i | 0.0153273 | + | 0.0128611i | ||||
\(334\) | 13.5567 | + | 23.4809i | 0.741789 | + | 1.28482i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 71.8215 | − | 26.1409i | 3.91819 | − | 1.42610i | ||||
\(337\) | −4.54476 | − | 25.7746i | −0.247569 | − | 1.40403i | −0.814450 | − | 0.580234i | \(-0.802961\pi\) |
0.566881 | − | 0.823800i | \(-0.308150\pi\) | |||||||
\(338\) | 6.06423 | − | 34.3920i | 0.329851 | − | 1.87068i | ||||
\(339\) | 4.97430 | + | 1.81050i | 0.270167 | + | 0.0983328i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.86899 | 0.371976 | ||||||||
\(342\) | 17.6094 | + | 6.66685i | 0.952207 | + | 0.360502i | ||||
\(343\) | 17.4071 | 0.939896 | ||||||||
\(344\) | 33.9969 | − | 28.5268i | 1.83299 | − | 1.53806i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.27639 | + | 12.9100i | −0.122379 | + | 0.694047i | ||||
\(347\) | 3.57695 | + | 20.2859i | 0.192021 | + | 1.08901i | 0.916598 | + | 0.399811i | \(0.130924\pi\) |
−0.724577 | + | 0.689194i | \(0.757965\pi\) | |||||||
\(348\) | −31.0326 | + | 11.2949i | −1.66352 | + | 0.605472i | ||||
\(349\) | 12.5153 | − | 21.6772i | 0.669929 | − | 1.16035i | −0.307994 | − | 0.951388i | \(-0.599658\pi\) |
0.977924 | − | 0.208963i | \(-0.0670089\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0926981 | + | 0.0777830i | 0.00494786 | + | 0.00415175i | ||||
\(352\) | 31.1402 | + | 26.1297i | 1.65978 | + | 1.39272i | ||||
\(353\) | 3.60628 | + | 6.24627i | 0.191943 | + | 0.332455i | 0.945894 | − | 0.324475i | \(-0.105188\pi\) |
−0.753951 | + | 0.656931i | \(0.771854\pi\) | |||||||
\(354\) | 33.4974 | − | 58.0192i | 1.78037 | − | 3.08369i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.9484 | + | 79.1054i | 0.739265 | + | 4.19258i | ||||
\(357\) | −1.88361 | + | 10.6825i | −0.0996914 | + | 0.565378i | ||||
\(358\) | 60.3001 | + | 21.9474i | 3.18696 | + | 1.15996i | ||||
\(359\) | 12.1097 | − | 10.1613i | 0.639128 | − | 0.536292i | −0.264622 | − | 0.964352i | \(-0.585247\pi\) |
0.903750 | + | 0.428060i | \(0.140803\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.2361 | + | 12.5831i | 0.749268 | + | 0.662267i | ||||
\(362\) | −6.89807 | −0.362554 | ||||||||
\(363\) | −8.77381 | + | 7.36210i | −0.460506 | + | 0.386410i | ||||
\(364\) | −0.552593 | − | 0.201127i | −0.0289637 | − | 0.0105419i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.59053 | − | 26.0342i | −0.239951 | − | 1.36083i | ||||
\(367\) | 2.48326 | − | 0.903831i | 0.129625 | − | 0.0471796i | −0.276393 | − | 0.961045i | \(-0.589139\pi\) |
0.406018 | + | 0.913865i | \(0.366917\pi\) | |||||||
\(368\) | −16.2760 | + | 28.1908i | −0.848444 | + | 1.46955i | ||||
\(369\) | −6.46135 | − | 11.1914i | −0.336365 | − | 0.582601i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.1829 | + | 10.2226i | 0.632502 | + | 0.530733i | ||||
\(372\) | 16.1645 | + | 27.9978i | 0.838091 | + | 1.45162i | ||||
\(373\) | 3.08220 | − | 5.33853i | 0.159590 | − | 0.276419i | −0.775131 | − | 0.631801i | \(-0.782316\pi\) |
0.934721 | + | 0.355382i | \(0.115649\pi\) | |||||||
\(374\) | −10.9102 | + | 3.97100i | −0.564154 | + | 0.205335i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.6307 | − | 94.3172i | 0.857661 | − | 4.86404i | ||||
\(377\) | 0.112180 | + | 0.0408303i | 0.00577758 | + | 0.00210287i | ||||
\(378\) | −17.1172 | + | 14.3630i | −0.880413 | + | 0.738754i | ||||
\(379\) | 0.156142 | 0.00802047 | 0.00401024 | − | 0.999992i | \(-0.498723\pi\) | ||||
0.00401024 | + | 0.999992i | \(0.498723\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.58638 | −0.0812726 | ||||||||
\(382\) | −19.1147 | + | 16.0391i | −0.977993 | + | 0.820634i | ||||
\(383\) | −15.1497 | − | 5.51405i | −0.774115 | − | 0.281755i | −0.0753983 | − | 0.997153i | \(-0.524023\pi\) |
−0.698716 | + | 0.715399i | \(0.746245\pi\) | |||||||
\(384\) | −7.59767 | + | 43.0885i | −0.387717 | + | 2.19885i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −62.6915 | + | 22.8178i | −3.19091 | + | 1.16140i | ||||
\(387\) | 4.12622 | − | 7.14682i | 0.209747 | − | 0.363293i | ||||
\(388\) | 14.5992 | + | 25.2866i | 0.741162 | + | 1.28373i | ||||
\(389\) | 2.07987 | + | 1.74521i | 0.105453 | + | 0.0884859i | 0.693990 | − | 0.719985i | \(-0.255851\pi\) |
−0.588537 | + | 0.808471i | \(0.700296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.30994 | − | 4.00093i | −0.116818 | − | 0.202336i | ||||
\(392\) | 3.22199 | − | 5.58065i | 0.162735 | − | 0.281866i | ||||
\(393\) | 22.0114 | − | 8.01148i | 1.11033 | − | 0.404126i | ||||
\(394\) | −1.94694 | − | 11.0416i | −0.0980854 | − | 0.556270i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 18.7640 | + | 6.82955i | 0.942928 | + | 0.343198i | ||||
\(397\) | 12.1440 | − | 10.1900i | 0.609488 | − | 0.511422i | −0.284991 | − | 0.958530i | \(-0.591991\pi\) |
0.894480 | + | 0.447109i | \(0.147546\pi\) | |||||||
\(398\) | −60.1460 | −3.01485 | ||||||||
\(399\) | 24.5822 | − | 8.59098i | 1.23065 | − | 0.430087i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.54746 | + | 2.13757i | −0.127214 | + | 0.106745i | −0.704175 | − | 0.710026i | \(-0.748683\pi\) |
0.576961 | + | 0.816772i | \(0.304239\pi\) | |||||||
\(402\) | −26.2991 | − | 9.57210i | −1.31168 | − | 0.477413i | ||||
\(403\) | 0.0202937 | − | 0.115091i | 0.00101090 | − | 0.00573311i | ||||
\(404\) | 10.8350 | + | 61.4483i | 0.539061 | + | 3.05717i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.0220 | + | 19.0907i | −0.547015 | + | 0.947457i | ||||
\(407\) | 0.270235 | + | 0.468061i | 0.0133951 | + | 0.0232009i | ||||
\(408\) | −25.8165 | − | 21.6627i | −1.27811 | − | 1.07246i | ||||
\(409\) | 5.73789 | + | 4.81466i | 0.283720 | + | 0.238070i | 0.773530 | − | 0.633760i | \(-0.218489\pi\) |
−0.489809 | + | 0.871830i | \(0.662934\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.92684 | − | 8.53353i | 0.243023 | − | 0.420928i | ||||
\(412\) | −69.1113 | + | 25.1544i | −3.40487 | + | 1.23927i | ||||
\(413\) | −5.61391 | − | 31.8380i | −0.276242 | − | 1.56665i | ||||
\(414\) | −1.90853 | + | 10.8238i | −0.0937991 | + | 0.531961i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.529810 | − | 0.444563i | 0.0259761 | − | 0.0217965i | ||||
\(417\) | −16.8406 | −0.824687 | ||||||||
\(418\) | 21.1192 | + | 18.1888i | 1.03297 | + | 0.889642i | ||||
\(419\) | 14.4108 | 0.704012 | 0.352006 | − | 0.935998i | \(-0.385500\pi\) | ||||
0.352006 | + | 0.935998i | \(0.385500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.6092 | + | 12.2327i | 1.63801 | + | 0.596187i | 0.986690 | − | 0.162614i | \(-0.0519927\pi\) |
0.651322 | + | 0.758802i | \(0.274215\pi\) | |||||||
\(422\) | −0.784525 | + | 4.44926i | −0.0381901 | + | 0.216587i | ||||
\(423\) | −3.09247 | − | 17.5383i | −0.150361 | − | 0.852741i | ||||
\(424\) | −46.4305 | + | 16.8993i | −2.25487 | + | 0.820704i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.4035 | − | 38.8039i | −1.08545 | − | 1.88006i | ||||
\(427\) | −9.77239 | − | 8.20001i | −0.472919 | − | 0.396826i | ||||
\(428\) | 46.8698 | + | 39.3285i | 2.26554 | + | 1.90101i | ||||
\(429\) | −0.103435 | − | 0.179154i | −0.00499388 | − | 0.00864966i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.76286 | + | 3.55339i | −0.470260 | + | 0.171161i | −0.566270 | − | 0.824220i | \(-0.691614\pi\) |
0.0960100 | + | 0.995380i | \(0.469392\pi\) | |||||||
\(432\) | −6.63921 | − | 37.6528i | −0.319429 | − | 1.81157i | ||||
\(433\) | 6.09178 | − | 34.5482i | 0.292752 | − | 1.66028i | −0.383448 | − | 0.923563i | \(-0.625263\pi\) |
0.676200 | − | 0.736718i | \(-0.263626\pi\) | |||||||
\(434\) | 20.2786 | + | 7.38081i | 0.973405 | + | 0.354290i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.0266 | −1.67747 | ||||||||
\(437\) | −5.66825 | + | 9.53258i | −0.271149 | + | 0.456005i | ||||
\(438\) | −24.4972 | −1.17052 | ||||||||
\(439\) | 14.6520 | − | 12.2945i | 0.699303 | − | 0.586785i | −0.222272 | − | 0.974985i | \(-0.571347\pi\) |
0.921575 | + | 0.388199i | \(0.126903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.208076 | − | 1.18006i | 0.00990836 | − | 0.0561931i | ||||
\(442\) | 0.0343018 | + | 0.194535i | 0.00163157 | + | 0.00925309i | ||||
\(443\) | −21.6050 | + | 7.86358i | −1.02649 | + | 0.373610i | −0.799742 | − | 0.600344i | \(-0.795030\pi\) |
−0.226744 | + | 0.973954i | \(0.572808\pi\) | |||||||
\(444\) | −1.27187 | + | 2.20294i | −0.0603602 | + | 0.104547i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.7818 | + | 16.5989i | 0.936694 | + | 0.785980i | ||||
\(447\) | −35.7487 | − | 29.9967i | −1.69086 | − | 1.41880i | ||||
\(448\) | 28.2495 | + | 48.9296i | 1.33466 | + | 2.31171i | ||||
\(449\) | −7.88692 | + | 13.6605i | −0.372207 | + | 0.644681i | −0.989905 | − | 0.141734i | \(-0.954732\pi\) |
0.617698 | + | 0.786415i | \(0.288065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.32171 | − | 18.8384i | −0.156413 | − | 0.887063i | ||||
\(452\) | −2.23458 | + | 12.6729i | −0.105106 | + | 0.596085i | ||||
\(453\) | −19.5443 | − | 7.11354i | −0.918271 | − | 0.334223i | ||||
\(454\) | −48.2939 | + | 40.5234i | −2.26654 | + | 1.90186i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.0716 | + | 79.4869i | −0.705794 | + | 3.72231i | ||||
\(457\) | 34.6414 | 1.62046 | 0.810229 | − | 0.586114i | \(-0.199343\pi\) | ||||
0.810229 | + | 0.586114i | \(0.199343\pi\) | |||||||
\(458\) | 2.45096 | − | 2.05660i | 0.114526 | − | 0.0960988i | ||||
\(459\) | 5.09899 | + | 1.85588i | 0.238001 | + | 0.0866252i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.26528 | + | 24.1896i | 0.198654 | + | 1.12662i | 0.907119 | + | 0.420875i | \(0.138277\pi\) |
−0.708465 | + | 0.705746i | \(0.750612\pi\) | |||||||
\(462\) | 35.8958 | − | 13.0650i | 1.67003 | − | 0.607840i | ||||
\(463\) | −3.85305 | + | 6.67368i | −0.179067 | + | 0.310152i | −0.941561 | − | 0.336842i | \(-0.890641\pi\) |
0.762495 | + | 0.646995i | \(0.223974\pi\) | |||||||
\(464\) | −18.8595 | − | 32.6656i | −0.875529 | − | 1.51646i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.6260 | − | 39.9629i | −2.20623 | − | 1.85125i | ||||
\(467\) | −3.25944 | − | 5.64552i | −0.150829 | − | 0.261243i | 0.780704 | − | 0.624902i | \(-0.214861\pi\) |
−0.931532 | + | 0.363658i | \(0.881528\pi\) | |||||||
\(468\) | 0.169867 | − | 0.294218i | 0.00785210 | − | 0.0136002i | ||||
\(469\) | −12.6910 | + | 4.61914i | −0.586015 | + | 0.213292i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.75073 | + | 15.6002i | −0.126747 | + | 0.718818i | ||||
\(472\) | 94.3851 | + | 34.3534i | 4.34442 | + | 1.58124i | ||||
\(473\) | 9.35781 | − | 7.85213i | 0.430272 | − | 0.361041i | ||||
\(474\) | −66.9597 | −3.07556 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −26.3695 | −1.20864 | ||||||||
\(477\) | −7.03831 | + | 5.90584i | −0.322262 | + | 0.270410i | ||||
\(478\) | 24.4568 | + | 8.90153i | 1.11863 | + | 0.407147i | ||||
\(479\) | 2.14887 | − | 12.1868i | 0.0981842 | − | 0.556830i | −0.895541 | − | 0.444979i | \(-0.853211\pi\) |
0.993725 | − | 0.111851i | \(-0.0356779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.00864085 | − | 0.00314501i | 0.000393989 | − | 0.000143400i | ||||
\(482\) | 21.2052 | − | 36.7284i | 0.965868 | − | 1.67293i | ||||
\(483\) | 7.59994 | + | 13.1635i | 0.345809 | + | 0.598959i | ||||
\(484\) | −21.3289 | − | 17.8971i | −0.969495 | − | 0.813503i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −20.3635 | − | 35.2706i | −0.923707 | − | 1.59991i | ||||
\(487\) | −19.3605 | + | 33.5333i | −0.877306 | + | 1.51954i | −0.0230209 | + | 0.999735i | \(0.507328\pi\) |
−0.854285 | + | 0.519804i | \(0.826005\pi\) | |||||||
\(488\) | 37.2439 | − | 13.5557i | 1.68595 | − | 0.613636i | ||||
\(489\) | −1.82763 | − | 10.3650i | −0.0826485 | − | 0.468723i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.5147 | + | 10.7425i | 1.33198 | + | 0.484802i | 0.907278 | − | 0.420531i | \(-0.138156\pi\) |
0.424704 | + | 0.905332i | \(0.360378\pi\) | |||||||
\(492\) | 68.9676 | − | 57.8707i | 3.10930 | − | 2.60901i | ||||
\(493\) | 5.35319 | 0.241095 | ||||||||
\(494\) | 0.367151 | − | 0.300120i | 0.0165189 | − | 0.0135030i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.2862 | + | 23.7349i | −1.27009 | + | 1.06573i | ||||
\(497\) | −20.3182 | − | 7.39521i | −0.911394 | − | 0.331720i | ||||
\(498\) | 4.47709 | − | 25.3909i | 0.200623 | − | 1.13779i | ||||
\(499\) | 3.37331 | + | 19.1310i | 0.151010 | + | 0.856422i | 0.962343 | + | 0.271837i | \(0.0876312\pi\) |
−0.811333 | + | 0.584584i | \(0.801258\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.8314 | + | 18.7605i | −0.483911 | + | 0.838158i | ||||
\(502\) | 7.36057 | + | 12.7489i | 0.328518 | + | 0.569010i | ||||
\(503\) | −3.26190 | − | 2.73706i | −0.145441 | − | 0.122039i | 0.567164 | − | 0.823605i | \(-0.308040\pi\) |
−0.712605 | + | 0.701565i | \(0.752485\pi\) | |||||||
\(504\) | 29.6381 | + | 24.8693i | 1.32019 | + | 1.10777i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.13461 | + | 14.0896i | −0.361627 | + | 0.626357i | ||||
\(507\) | 26.2194 | − | 9.54307i | 1.16444 | − | 0.423823i | ||||
\(508\) | −0.669664 | − | 3.79785i | −0.0297115 | − | 0.168502i | ||||
\(509\) | −1.27413 | + | 7.22597i | −0.0564750 | + | 0.320286i | −0.999937 | − | 0.0111941i | \(-0.996437\pi\) |
0.943462 | + | 0.331480i | \(0.107548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.05573 | + | 7.59866i | −0.400602 | + | 0.336145i | ||||
\(512\) | 2.72331 | 0.120354 | ||||||||
\(513\) | −2.09691 | − | 12.8564i | −0.0925807 | − | 0.567623i | ||||
\(514\) | −9.53234 | −0.420453 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 54.0264 | + | 19.6640i | 2.37838 | + | 0.865659i | ||||
\(517\) | 4.57767 | − | 25.9612i | 0.201326 | − | 1.14177i | ||||
\(518\) | 0.294851 | + | 1.67218i | 0.0129550 | + | 0.0734714i | ||||
\(519\) | −9.84220 | + | 3.58227i | −0.432025 | + | 0.157244i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.98404 | + | 6.90057i | 0.174544 | + | 0.302319i | 0.940003 | − | 0.341165i | \(-0.110822\pi\) |
−0.765459 | + | 0.643484i | \(0.777488\pi\) | |||||||
\(522\) | −9.75585 | − | 8.18613i | −0.427002 | − | 0.358297i | ||||
\(523\) | −12.0080 | − | 10.0759i | −0.525075 | − | 0.440590i | 0.341322 | − | 0.939946i | \(-0.389125\pi\) |
−0.866397 | + | 0.499357i | \(0.833570\pi\) | |||||||
\(524\) | 28.4715 | + | 49.3141i | 1.24378 | + | 2.15430i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 66.5187 | − | 24.2108i | 2.90035 | − | 1.05564i | ||||
\(527\) | −0.910003 | − | 5.16089i | −0.0396404 | − | 0.224812i | ||||
\(528\) | −11.3500 | + | 64.3691i | −0.493946 | + | 2.80131i | ||||
\(529\) | 15.5297 | + | 5.65235i | 0.675204 | + | 0.245754i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.6773 | 0.810526 | ||||||||
\(532\) | 30.9441 | + | 55.2241i | 1.34160 | + | 2.39427i | ||||
\(533\) | −0.325454 | −0.0140970 | ||||||||
\(534\) | −68.0058 | + | 57.0636i | −2.94290 | + | 2.46938i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.28622 | − | 41.3222i | 0.314717 | − | 1.78485i | ||||
\(537\) | 8.90294 | + | 50.4911i | 0.384190 | + | 2.17885i | ||||
\(538\) | 58.3612 | − | 21.2417i | 2.51613 | − | 0.915796i | ||||
\(539\) | 0.886868 | − | 1.53610i | 0.0382001 | − | 0.0661645i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3123 | + | 18.7223i | 0.959283 | + | 0.804934i | 0.980836 | − | 0.194834i | \(-0.0624168\pi\) |
−0.0215537 | + | 0.999768i | \(0.506861\pi\) | |||||||
\(542\) | −38.0049 | − | 31.8899i | −1.63245 | − | 1.36979i | ||||
\(543\) | −2.75568 | − | 4.77297i | −0.118257 | − | 0.204828i | ||||
\(544\) | 15.5066 | − | 26.8583i | 0.664841 | − | 1.15154i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.112857 | − | 0.640042i | −0.00482982 | − | 0.0273913i | ||||
\(547\) | 2.51214 | − | 14.2470i | 0.107411 | − | 0.609160i | −0.882818 | − | 0.469714i | \(-0.844357\pi\) |
0.990230 | − | 0.139445i | \(-0.0445320\pi\) | |||||||
\(548\) | 22.5094 | + | 8.19275i | 0.961553 | + | 0.349977i | ||||
\(549\) | 5.64573 | − | 4.73733i | 0.240954 | − | 0.202184i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.28187 | − | 11.2109i | −0.267617 | − | 0.477599i | ||||
\(552\) | −47.2240 | −2.00999 | ||||||||
\(553\) | −24.7526 | + | 20.7699i | −1.05259 | + | 0.883226i | ||||
\(554\) | 75.6660 | + | 27.5402i | 3.21474 | + | 1.17007i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.10898 | − | 40.3170i | −0.301488 | − | 1.70982i | ||||
\(557\) | 31.6465 | − | 11.5184i | 1.34090 | − | 0.488049i | 0.430807 | − | 0.902444i | \(-0.358229\pi\) |
0.910097 | + | 0.414395i | \(0.136007\pi\) | |||||||
\(558\) | −6.23364 | + | 10.7970i | −0.263891 | + | 0.457073i | ||||
\(559\) | −0.103917 | − | 0.179990i | −0.00439524 | − | 0.00761278i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.10612 | − | 5.96274i | −0.300021 | − | 0.251747i | ||||
\(562\) | −5.34540 | − | 9.25850i | −0.225482 | − | 0.390546i | ||||
\(563\) | −12.4577 | + | 21.5774i | −0.525030 | + | 0.909378i | 0.474545 | + | 0.880231i | \(0.342613\pi\) |
−0.999575 | + | 0.0291473i | \(0.990721\pi\) | |||||||
\(564\) | 116.590 | − | 42.4351i | 4.90931 | − | 1.78684i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.22185 | + | 23.9433i | −0.177457 | + | 1.00641i | ||||
\(567\) | −29.3905 | − | 10.6973i | −1.23429 | − | 0.449244i | ||||
\(568\) | 51.4607 | − | 43.1806i | 2.15924 | − | 1.81182i | ||||
\(569\) | 19.7304 | 0.827141 | 0.413571 | − | 0.910472i | \(-0.364281\pi\) | ||||
0.413571 | + | 0.910472i | \(0.364281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8463 | −0.579452 | −0.289726 | − | 0.957110i | \(-0.593564\pi\) | ||||
−0.289726 | + | 0.957110i | \(0.593564\pi\) | |||||||
\(572\) | 0.385239 | − | 0.323254i | 0.0161077 | − | 0.0135159i | ||||
\(573\) | −18.7340 | − | 6.81862i | −0.782624 | − | 0.284852i | ||||
\(574\) | 10.4357 | − | 59.1838i | 0.435578 | − | 2.47028i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −30.6723 | + | 11.1638i | −1.27801 | + | 0.465158i | ||||
\(577\) | 20.8327 | − | 36.0832i | 0.867275 | − | 1.50216i | 0.00250405 | − | 0.999997i | \(-0.499203\pi\) |
0.864771 | − | 0.502167i | \(-0.167464\pi\) | |||||||
\(578\) | −18.4079 | − | 31.8834i | −0.765668 | − | 1.32618i | ||||
\(579\) | −40.8326 | − | 34.2626i | −1.69695 | − | 1.42391i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.22085 | − | 10.7748i | −0.258084 | − | 0.447015i | ||||
\(582\) | −16.1349 | + | 27.9465i | −0.668813 | + | 1.15842i | ||||
\(583\) | −12.7802 | + | 4.65162i | −0.529302 | + | 0.192650i | ||||
\(584\) | −6.37767 | − | 36.1696i | −0.263910 | − | 1.49671i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.89869 | − | 2.14695i | −0.243673 | − | 0.0886896i | ||||
\(587\) | −12.3875 | + | 10.3943i | −0.511286 | + | 0.429020i | −0.861581 | − | 0.507619i | \(-0.830526\pi\) |
0.350296 | + | 0.936639i | \(0.386081\pi\) | |||||||
\(588\) | 8.34812 | 0.344271 | ||||||||
\(589\) | −9.74028 | + | 7.96198i | −0.401341 | + | 0.328068i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.86226 | − | 5.75812i | 0.282276 | − | 0.236857i | ||||
\(592\) | −2.73014 | − | 0.993691i | −0.112208 | − | 0.0408405i | ||||
\(593\) | 3.90122 | − | 22.1249i | 0.160204 | − | 0.908562i | −0.793669 | − | 0.608350i | \(-0.791832\pi\) |
0.953873 | − | 0.300212i | \(-0.0970573\pi\) | |||||||
\(594\) | −3.31822 | − | 18.8186i | −0.136148 | − | 0.772136i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 56.7226 | − | 98.2464i | 2.32345 | − | 4.02433i | ||||
\(597\) | −24.0274 | − | 41.6168i | −0.983378 | − | 1.70326i | ||||
\(598\) | 0.212041 | + | 0.177923i | 0.00867099 | + | 0.00727582i | ||||
\(599\) | 1.65472 | + | 1.38847i | 0.0676099 | + | 0.0567314i | 0.675966 | − | 0.736932i | \(-0.263726\pi\) |
−0.608356 | + | 0.793664i | \(0.708171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.52974 | − | 14.7739i | 0.347935 | − | 0.602641i | −0.637947 | − | 0.770080i | \(-0.720216\pi\) |
0.985883 | + | 0.167439i | \(0.0535496\pi\) | |||||||
\(602\) | 36.0633 | − | 13.1260i | 1.46983 | − | 0.534975i | ||||
\(603\) | −1.35487 | − | 7.68387i | −0.0551747 | − | 0.312911i | ||||
\(604\) | 8.77979 | − | 49.7927i | 0.357245 | − | 2.02603i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −52.8262 | + | 44.3264i | −2.14592 | + | 1.80064i | ||||
\(607\) | 3.47625 | 0.141097 | 0.0705483 | − | 0.997508i | \(-0.477525\pi\) | ||||
0.0705483 | + | 0.997508i | \(0.477525\pi\) | |||||||
\(608\) | −74.4446 | − | 0.956978i | −3.01913 | − | 0.0388106i | ||||
\(609\) | −17.6126 | −0.713697 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.421462 | − | 0.153400i | −0.0170505 | − | 0.00620588i | ||||
\(612\) | 2.64540 | − | 15.0028i | 0.106934 | − | 0.606452i | ||||
\(613\) | 3.22691 | + | 18.3007i | 0.130334 | + | 0.739159i | 0.977996 | + | 0.208623i | \(0.0668981\pi\) |
−0.847663 | + | 0.530536i | \(0.821991\pi\) | |||||||
\(614\) | −19.1903 | + | 6.98470i | −0.774457 | + | 0.281879i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.6355 | + | 49.5981i | 1.15376 | + | 1.99837i | ||||
\(617\) | 15.2199 | + | 12.7710i | 0.612729 | + | 0.514141i | 0.895509 | − | 0.445044i | \(-0.146812\pi\) |
−0.282779 | + | 0.959185i | \(0.591256\pi\) | |||||||
\(618\) | −62.2664 | − | 52.2478i | −2.50472 | − | 2.10171i | ||||
\(619\) | 4.21208 | + | 7.29553i | 0.169298 | + | 0.293232i | 0.938173 | − | 0.346166i | \(-0.112517\pi\) |
−0.768875 | + | 0.639399i | \(0.779183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.14502 | − | 2.60057i | 0.286720 | − | 0.104357i | ||||
\(622\) | 8.78218 | + | 49.8062i | 0.352133 | + | 1.99705i | ||||
\(623\) | −7.43902 | + | 42.1888i | −0.298038 | + | 1.69026i | ||||
\(624\) | 1.04499 | + | 0.380344i | 0.0418329 | + | 0.0152259i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 59.6744 | 2.38507 | ||||||||
\(627\) | −4.14854 | + | 21.8791i | −0.165677 | + | 0.873768i | ||||
\(628\) | −38.5086 | −1.53666 | ||||||||
\(629\) | 0.315868 | − | 0.265045i | 0.0125945 | − | 0.0105680i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.278838 | − | 1.58137i | 0.0111004 | − | 0.0629534i | −0.978754 | − | 0.205036i | \(-0.934269\pi\) |
0.989855 | + | 0.142083i | \(0.0453799\pi\) | |||||||
\(632\) | −17.4325 | − | 98.8646i | −0.693428 | − | 3.93262i | ||||
\(633\) | −3.39198 | + | 1.23458i | −0.134819 | + | 0.0490701i | ||||
\(634\) | −5.47106 | + | 9.47616i | −0.217284 | + | 0.376346i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −49.0350 | − | 41.1452i | −1.94436 | − | 1.63152i | ||||
\(637\) | −0.0231175 | − | 0.0193979i | −0.000915950 | − | 0.000768573i | ||||
\(638\) | −9.42582 | − | 16.3260i | −0.373172 | − | 0.646352i | ||||
\(639\) | 6.24580 | − | 10.8180i | 0.247080 | − | 0.427955i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.96102 | − | 45.1492i | −0.314442 | − | 1.78329i | −0.575334 | − | 0.817919i | \(-0.695128\pi\) |
0.260892 | − | 0.965368i | \(-0.415983\pi\) | |||||||
\(642\) | −11.7421 | + | 66.5929i | −0.463425 | + | 2.62821i | ||||
\(643\) | 17.2221 | + | 6.26834i | 0.679175 | + | 0.247199i | 0.658493 | − | 0.752587i | \(-0.271194\pi\) |
0.0206816 | + | 0.999786i | \(0.493416\pi\) | |||||||
\(644\) | −28.3057 | + | 23.7513i | −1.11540 | + | 0.935933i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.8679 | − | 18.2772i | 0.427593 | − | 0.719105i | ||||
\(647\) | −25.1770 | −0.989808 | −0.494904 | − | 0.868948i | \(-0.664797\pi\) | ||||
−0.494904 | + | 0.868948i | \(0.664797\pi\) | |||||||
\(648\) | 74.4386 | − | 62.4614i | 2.92423 | − | 2.45372i | ||||
\(649\) | 25.9799 | + | 9.45592i | 1.01980 | + | 0.371177i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.99401 | + | 16.9799i | 0.117345 | + | 0.665494i | ||||
\(652\) | 24.0428 | − | 8.75086i | 0.941588 | − | 0.342710i | ||||
\(653\) | 0.349290 | − | 0.604989i | 0.0136688 | − | 0.0236750i | −0.859110 | − | 0.511791i | \(-0.828982\pi\) |
0.872779 | + | 0.488116i | \(0.162316\pi\) | |||||||
\(654\) | −19.3556 | − | 33.5248i | −0.756862 | − | 1.31092i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 78.7722 | + | 66.0977i | 3.07554 | + | 2.58068i | ||||
\(657\) | −3.41475 | − | 5.91451i | −0.133222 | − | 0.230747i | ||||
\(658\) | 41.4099 | − | 71.7240i | 1.61432 | − | 2.79609i | ||||
\(659\) | −19.1350 | + | 6.96458i | −0.745395 | + | 0.271301i | −0.686667 | − | 0.726973i | \(-0.740927\pi\) |
−0.0587281 | + | 0.998274i | \(0.518705\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.03199 | + | 34.2091i | −0.234617 | + | 1.33058i | 0.608801 | + | 0.793323i | \(0.291651\pi\) |
−0.843418 | + | 0.537258i | \(0.819460\pi\) | |||||||
\(662\) | 52.4822 | + | 19.1019i | 2.03978 | + | 0.742418i | ||||
\(663\) | −0.120901 | + | 0.101448i | −0.00469542 | + | 0.00393992i | ||||
\(664\) | 38.6547 | 1.50009 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.980960 | −0.0380114 | ||||||||
\(667\) | 5.74626 | − | 4.82168i | 0.222496 | − | 0.186696i | ||||
\(668\) | −49.4857 | − | 18.0113i | −1.91466 | − | 0.696879i | ||||
\(669\) | −3.58272 | + | 20.3186i | −0.138516 | + | 0.785562i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2516 | − | 3.73126i | 0.395757 | − | 0.144044i | ||||
\(672\) | −51.0185 | + | 88.3667i | −1.96808 | + | 3.40882i | ||||
\(673\) | −12.7767 | − | 22.1298i | −0.492505 | − | 0.853043i | 0.507458 | − | 0.861676i | \(-0.330585\pi\) |
−0.999963 | + | 0.00863342i | \(0.997252\pi\) | |||||||
\(674\) | 53.8656 | + | 45.1986i | 2.07483 | + | 1.74099i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.9146 | + | 58.7417i | 1.30441 | + | 2.25930i | ||||
\(677\) | −19.0216 | + | 32.9463i | −0.731058 | + | 1.26623i | 0.225373 | + | 0.974273i | \(0.427640\pi\) |
−0.956431 | + | 0.291957i | \(0.905693\pi\) | |||||||
\(678\) | −13.3644 | + | 4.86424i | −0.513256 | + | 0.186810i | ||||
\(679\) | 2.70408 | + | 15.3356i | 0.103773 | + | 0.588527i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.3320 | − | 17.2274i | −1.81376 | − | 0.660156i | ||||
\(682\) | −14.1372 | + | 11.8625i | −0.541342 | + | 0.454239i | ||||
\(683\) | 31.7070 | 1.21324 | 0.606618 | − | 0.794994i | \(-0.292526\pi\) | ||||
0.606618 | + | 0.794994i | \(0.292526\pi\) | |||||||
\(684\) | −34.5238 | + | 12.0654i | −1.32005 | + | 0.461332i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −35.8260 | + | 30.0615i | −1.36784 | + | 1.14775i | ||||
\(687\) | 2.40215 | + | 0.874310i | 0.0916477 | + | 0.0333570i | ||||
\(688\) | −11.4030 | + | 64.6694i | −0.434734 | + | 2.46550i | ||||
\(689\) | 0.0401810 | + | 0.227878i | 0.00153078 | + | 0.00868146i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.05528 | + | 3.55984i | −0.0781864 | + | 0.135423i | −0.902467 | − | 0.430758i | \(-0.858246\pi\) |
0.824281 | + | 0.566181i | \(0.191580\pi\) | |||||||
\(692\) | −12.7308 | − | 22.0504i | −0.483953 | − | 0.838231i | ||||
\(693\) | 8.15802 | + | 6.84540i | 0.309898 | + | 0.260035i | ||||
\(694\) | −42.3949 | − | 35.5736i | −1.60929 | − | 1.35035i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 27.3600 | − | 47.3888i | 1.03708 | − | 1.79627i | ||||
\(697\) | −13.7138 | + | 4.99141i | −0.519447 | + | 0.189063i | ||||
\(698\) | 11.6777 | + | 66.2277i | 0.442009 | + | 2.50676i | ||||
\(699\) | 8.62563 | − | 48.9184i | 0.326251 | − | 1.85026i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.40592 | + | 2.85791i | −0.128640 | + | 0.107942i | −0.704838 | − | 0.709369i | \(-0.748980\pi\) |
0.576198 | + | 0.817310i | \(0.304536\pi\) | |||||||
\(702\) | −0.325113 | −0.0122706 | ||||||||
\(703\) | −0.925735 | − | 0.350480i | −0.0349148 | − | 0.0132186i | ||||
\(704\) | −48.3168 | −1.82101 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.2093 | − | 6.62763i | −0.685315 | − | 0.249434i | ||||
\(707\) | −5.77855 | + | 32.7718i | −0.217325 | + | 1.23251i | ||||
\(708\) | 22.5955 | + | 128.145i | 0.849191 | + | 4.81600i | ||||
\(709\) | −3.15334 | + | 1.14772i | −0.118426 | + | 0.0431036i | −0.400554 | − | 0.916273i | \(-0.631182\pi\) |
0.282127 | + | 0.959377i | \(0.408960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.33375 | − | 16.1665i | −0.350043 | − | 0.606292i | ||||
\(712\) | −101.958 | − | 85.5531i | −3.82104 | − | 3.20624i | ||||
\(713\) | −5.62530 | − | 4.72019i | −0.210669 | − | 0.176772i | ||||
\(714\) | −14.5716 | − | 25.2388i | −0.545330 | − | 0.944539i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −117.119 | + | 42.6279i | −4.37695 | + | 1.59308i | ||||
\(717\) | 3.61089 | + | 20.4784i | 0.134851 | + | 0.764779i | ||||
\(718\) | −7.37510 | + | 41.8263i | −0.275236 | + | 1.56094i | ||||
\(719\) | −38.6145 | − | 14.0545i | −1.44008 | − | 0.524145i | −0.500275 | − | 0.865866i | \(-0.666768\pi\) |
−0.939801 | + | 0.341721i | \(0.888990\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.2242 | −1.46078 | ||||||||
\(722\) | −51.0302 | − | 1.31219i | −1.89915 | − | 0.0488348i | ||||
\(723\) | 33.8846 | 1.26018 | ||||||||
\(724\) | 10.2634 | − | 8.61203i | 0.381437 | − | 0.320064i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.34345 | − | 30.3042i | 0.198314 | − | 1.12469i | ||||
\(727\) | −2.09533 | − | 11.8832i | −0.0777114 | − | 0.440723i | −0.998693 | − | 0.0511164i | \(-0.983722\pi\) |
0.920981 | − | 0.389607i | \(-0.127389\pi\) | |||||||
\(728\) | 0.915628 | − | 0.333261i | 0.0339354 | − | 0.0123515i | ||||
\(729\) | −0.587731 | + | 1.01798i | −0.0217678 | + | 0.0377029i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.13928 | − | 5.99056i | −0.264056 | − | 0.221569i | ||||
\(732\) | 39.3330 | + | 33.0043i | 1.45379 | + | 1.21988i | ||||
\(733\) | 6.81748 | + | 11.8082i | 0.251809 | + | 0.436147i | 0.964024 | − | 0.265815i | \(-0.0856410\pi\) |
−0.712215 | + | 0.701962i | \(0.752308\pi\) | |||||||
\(734\) | −3.54995 | + | 6.14870i | −0.131031 | + | 0.226953i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.54634 | − | 42.7974i | −0.278162 | − | 1.57753i | ||||
\(737\) | 2.00556 | − | 11.3741i | 0.0738759 | − | 0.418971i | ||||
\(738\) | 32.6254 | + | 11.8747i | 1.20096 | + | 0.437113i | ||||
\(739\) | 29.2757 | − | 24.5652i | 1.07692 | − | 0.903645i | 0.0812609 | − | 0.996693i | \(-0.474105\pi\) |
0.995662 | + | 0.0930476i | \(0.0296609\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.354333 | + | 0.134149i | 0.0130167 | + | 0.00492810i | ||||
\(742\) | −42.7280 | −1.56859 | ||||||||
\(743\) | 4.65236 | − | 3.90379i | 0.170679 | − | 0.143216i | −0.553447 | − | 0.832884i | \(-0.686688\pi\) |
0.724126 | + | 0.689668i | \(0.242243\pi\) | |||||||
\(744\) | −50.3375 | − | 18.3214i | −1.84546 | − | 0.671694i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.87593 | + | 16.3102i | 0.105295 | + | 0.597159i | ||||
\(747\) | 6.75437 | − | 2.45839i | 0.247129 | − | 0.0899477i | ||||
\(748\) | 11.2753 | − | 19.5294i | 0.412266 | − | 0.714066i | ||||
\(749\) | 16.3155 | + | 28.2593i | 0.596155 | + | 1.03257i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.156655 | + | 0.131449i | 0.00571641 | + | 0.00479664i | 0.645641 | − | 0.763641i | \(-0.276590\pi\) |
−0.639925 | + | 0.768437i | \(0.721035\pi\) | |||||||
\(752\) | 70.8551 | + | 122.725i | 2.58382 | + | 4.47531i | ||||
\(753\) | −5.88088 | + | 10.1860i | −0.214311 | + | 0.371198i | ||||
\(754\) | −0.301393 | + | 0.109698i | −0.0109761 | + | 0.00399497i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.53632 | − | 42.7406i | 0.274093 | − | 1.55446i | ||||
\(757\) | −17.2765 | − | 6.28814i | −0.627926 | − | 0.228546i | 0.00840229 | − | 0.999965i | \(-0.497325\pi\) |
−0.636328 | + | 0.771418i | \(0.719548\pi\) | |||||||
\(758\) | −0.321359 | + | 0.269652i | −0.0116723 | + | 0.00979421i | ||||
\(759\) | −12.9986 | −0.471820 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.4304 | −1.13935 | −0.569675 | − | 0.821870i | \(-0.692931\pi\) | ||||
−0.569675 | + | 0.821870i | \(0.692931\pi\) | |||||||
\(762\) | 3.26496 | − | 2.73963i | 0.118277 | − | 0.0992461i | ||||
\(763\) | −17.5540 | − | 6.38912i | −0.635496 | − | 0.231302i | ||||
\(764\) | 8.41578 | − | 47.7283i | 0.304472 | − | 1.72675i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.7026 | − | 14.8145i | 1.47064 | − | 0.535270i | ||||
\(767\) | 0.235191 | − | 0.407363i | 0.00849225 | − | 0.0147090i | ||||
\(768\) | −15.1973 | − | 26.3225i | −0.548385 | − | 0.949830i | ||||
\(769\) | −16.5419 | − | 13.8803i | −0.596516 | − | 0.500537i | 0.293807 | − | 0.955865i | \(-0.405078\pi\) |
−0.890324 | + | 0.455328i | \(0.849522\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.80803 | − | 6.59570i | −0.137143 | − | 0.237538i | ||||
\(772\) | 64.7893 | − | 112.218i | 2.33182 | − | 4.03883i | ||||
\(773\) | 34.8529 | − | 12.6854i | 1.25357 | − | 0.456263i | 0.371965 | − | 0.928247i | \(-0.378684\pi\) |
0.881607 | + | 0.471983i | \(0.156462\pi\) | |||||||
\(774\) | 3.85008 | + | 21.8349i | 0.138388 | + | 0.784838i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −45.4630 | − | 16.5472i | −1.63203 | − | 0.594009i | ||||
\(777\) | −1.03924 | + | 0.872028i | −0.0372826 | + | 0.0312838i | ||||
\(778\) | −7.29454 | −0.261522 | ||||||||
\(779\) | 26.5461 | + | 22.8627i | 0.951113 | + | 0.819141i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.1648 | − | 11.8857i | 0.506856 | − | 0.425302i | ||||
\(782\) | 11.6636 | + | 4.24520i | 0.417089 | + | 0.151808i | ||||
\(783\) | −1.52993 | + | 8.67664i | −0.0546751 | + | 0.310078i | ||||
\(784\) | 1.65572 | + | 9.39005i | 0.0591328 | + | 0.335359i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −31.4665 | + | 54.5015i | −1.12237 | + | 1.94401i | ||||
\(787\) | −1.00158 | − | 1.73479i | −0.0357025 | − | 0.0618385i | 0.847622 | − | 0.530600i | \(-0.178034\pi\) |
−0.883325 | + | 0.468762i | \(0.844700\pi\) | |||||||
\(788\) | 16.6819 | + | 13.9978i | 0.594270 | + | 0.498652i | ||||
\(789\) | 43.3254 | + | 36.3544i | 1.54243 | + | 1.29425i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.43152 | + | 5.94357i | −0.122011 | + | 0.211329i | ||||
\(792\) | −31.0913 | + | 11.3163i | −1.10478 | + | 0.402108i | ||||
\(793\) | −0.0322309 | − | 0.182791i | −0.00114455 | − | 0.00649108i | ||||
\(794\) | −7.39595 | + | 41.9445i | −0.262472 | + | 1.48856i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 89.4894 | − | 75.0905i | 3.17187 | − | 2.66151i | ||||
\(797\) | 12.8587 | 0.455480 | 0.227740 | − | 0.973722i | \(-0.426866\pi\) | ||||
0.227740 | + | 0.973722i | \(0.426866\pi\) | |||||||
\(798\) | −35.7567 | + | 60.1339i | −1.26577 | + | 2.12872i | ||||
\(799\) | −20.1119 | −0.711509 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.2568 | − | 8.46479i | −0.821739 | − | 0.299089i | ||||
\(802\) | 1.55146 | − | 8.79877i | 0.0547840 | − | 0.310695i | ||||
\(803\) | −1.75548 | − | 9.95584i | −0.0619496 | − | 0.351334i | ||||
\(804\) | 51.0801 | − | 18.5917i | 1.80146 | − | 0.655677i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.156992 | + | 0.271918i | 0.00552981 | + | 0.00957792i | ||||
\(807\) | 38.0122 | + | 31.8960i | 1.33809 | + | 1.12279i | ||||
\(808\) | −79.2001 | − | 66.4567i | −2.78625 | − | 2.33794i | ||||
\(809\) | −10.5986 | − | 18.3573i | −0.372627 | − | 0.645410i | 0.617341 | − | 0.786695i | \(-0.288210\pi\) |
−0.989969 | + | 0.141286i | \(0.954876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.40909 | − | 3.06066i | 0.295283 | − | 0.107474i | −0.190131 | − | 0.981759i | \(-0.560891\pi\) |
0.485414 | + | 0.874284i | \(0.338669\pi\) | |||||||
\(812\) | −7.43486 | − | 42.1652i | −0.260912 | − | 1.47971i | ||||
\(813\) | 6.88314 | − | 39.0362i | 0.241402 | − | 1.36906i | ||||
\(814\) | −1.36450 | − | 0.496639i | −0.0478258 | − | 0.0174072i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 49.8662 | 1.74567 | ||||||||
\(817\) | −4.16789 | + | 21.9812i | −0.145816 | + | 0.769025i | ||||
\(818\) | −20.1240 | −0.703621 | ||||||||
\(819\) | 0.138798 | − | 0.116465i | 0.00485000 | − | 0.00406963i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.600509 | + | 3.40566i | −0.0209579 | + | 0.118858i | −0.993492 | − | 0.113903i | \(-0.963665\pi\) |
0.972534 | + | 0.232761i | \(0.0747759\pi\) | |||||||
\(822\) | 4.59711 | + | 26.0715i | 0.160343 | + | 0.909349i | ||||
\(823\) | −17.0350 | + | 6.20022i | −0.593801 | + | 0.216126i | −0.621401 | − | 0.783493i | \(-0.713436\pi\) |
0.0275992 | + | 0.999619i | \(0.491214\pi\) | |||||||
\(824\) | 60.9321 | − | 105.538i | 2.12267 | − | 3.67657i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 66.5374 | + | 55.8315i | 2.31513 | + | 1.94263i | ||||
\(827\) | −22.5132 | − | 18.8909i | −0.782862 | − | 0.656899i | 0.161105 | − | 0.986937i | \(-0.448494\pi\) |
−0.943968 | + | 0.330038i | \(0.892939\pi\) | |||||||
\(828\) | −10.6736 | − | 18.4871i | −0.370932 | − | 0.642473i | ||||
\(829\) | 1.73389 | − | 3.00318i | 0.0602204 | − | 0.104305i | −0.834343 | − | 0.551245i | \(-0.814153\pi\) |
0.894564 | + | 0.446940i | \(0.147486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.1716 | + | 63.3574i | 0.387539 | + | 2.19784i | ||||
\(832\) | −0.142747 | + | 0.809558i | −0.00494886 | + | 0.0280664i | ||||
\(833\) | −1.27161 | − | 0.462829i | −0.0440588 | − | 0.0160361i | ||||
\(834\) | 34.6600 | − | 29.0832i | 1.20018 | − | 1.00707i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −54.1307 | − | 0.695845i | −1.87215 | − | 0.0240663i | ||||
\(837\) | 8.62503 | 0.298125 | ||||||||
\(838\) | −29.6591 | + | 24.8869i | −1.02456 | + | 0.859705i | ||||
\(839\) | −37.4283 | − | 13.6228i | −1.29217 | − | 0.470311i | −0.397730 | − | 0.917503i | \(-0.630202\pi\) |
−0.894438 | + | 0.447192i | \(0.852424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.52647 | − | 19.9996i | −0.121602 | − | 0.689641i | ||||
\(842\) | −90.2973 | + | 32.8655i | −3.11185 | + | 1.13262i | ||||
\(843\) | 4.27082 | − | 7.39727i | 0.147095 | − | 0.254775i | ||||
\(844\) | −4.38750 | − | 7.59938i | −0.151024 | − | 0.261581i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 36.6528 | + | 30.7553i | 1.26015 | + | 1.05739i | ||||
\(847\) | −7.42463 | − | 12.8598i | −0.255113 | − | 0.441869i | ||||
\(848\) | 36.5553 | − | 63.3156i | 1.25531 | − | 2.17427i | ||||
\(849\) | −18.2536 | + | 6.64377i | −0.626462 | + | 0.228014i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.100332 | − | 0.569014i | 0.00343935 | − | 0.0195055i | ||||
\(852\) | 81.7789 | + | 29.7651i | 2.80170 | + | 1.01974i | ||||
\(853\) | 12.2652 | − | 10.2917i | 0.419953 | − | 0.352383i | −0.408192 | − | 0.912896i | \(-0.633841\pi\) |
0.828145 | + | 0.560513i | \(0.189396\pi\) | |||||||
\(854\) | 34.2739 | 1.17283 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −101.380 | −3.46510 | ||||||||
\(857\) | −12.4439 | + | 10.4417i | −0.425075 | + | 0.356680i | −0.830090 | − | 0.557630i | \(-0.811711\pi\) |
0.405015 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(858\) | 0.522276 | + | 0.190093i | 0.0178302 | + | 0.00648966i | ||||
\(859\) | −9.76555 | + | 55.3832i | −0.333196 | + | 1.88965i | 0.111163 | + | 0.993802i | \(0.464542\pi\) |
−0.444360 | + | 0.895849i | \(0.646569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 45.1199 | − | 16.4223i | 1.53768 | − | 0.559670i | ||||
\(862\) | 13.9565 | − | 24.1734i | 0.475362 | − | 0.823351i | ||||
\(863\) | 7.07944 | + | 12.2619i | 0.240987 | + | 0.417402i | 0.960996 | − | 0.276563i | \(-0.0891956\pi\) |
−0.720009 | + | 0.693965i | \(0.755862\pi\) | |||||||
\(864\) | 39.1011 | + | 32.8097i | 1.33025 | + | 1.11621i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 47.1260 | + | 81.6247i | 1.60141 | + | 2.77372i | ||||
\(867\) | 14.7074 | − | 25.4739i | 0.499489 | − | 0.865140i | ||||
\(868\) | −39.3866 | + | 14.3356i | −1.33687 | + | 0.486581i | ||||
\(869\) | −4.79838 | − | 27.2129i | −0.162774 | − | 0.923136i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.184651 | − | 0.0672073i | −0.00625665 | − | 0.00227723i | ||||
\(872\) | 44.4596 | − | 37.3061i | 1.50559 | − | 1.26334i | ||||
\(873\) | −8.99640 | −0.304482 | ||||||||
\(874\) | −4.79653 | − | 29.4081i | −0.162245 | − | 0.994744i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 36.4485 | − | 30.5840i | 1.23148 | − | 1.03334i | ||||
\(877\) | 6.02143 | + | 2.19162i | 0.203329 | + | 0.0740058i | 0.441677 | − | 0.897174i | \(-0.354384\pi\) |
−0.238348 | + | 0.971180i | \(0.576606\pi\) | |||||||
\(878\) | −8.92342 | + | 50.6072i | −0.301151 | + | 1.70791i | ||||
\(879\) | −0.870905 | − | 4.93915i | −0.0293749 | − | 0.166593i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.80585 | − | 10.0560i | 0.195604 | − | 0.338796i | −0.751494 | − | 0.659740i | \(-0.770667\pi\) |
0.947098 | + | 0.320943i | \(0.104000\pi\) | |||||||
\(882\) | 1.60967 | + | 2.78804i | 0.0542005 | + | 0.0938781i | ||||
\(883\) | 20.2430 | + | 16.9859i | 0.681231 | + | 0.571620i | 0.916366 | − | 0.400342i | \(-0.131109\pi\) |
−0.235135 | + | 0.971963i | \(0.575553\pi\) | |||||||
\(884\) | −0.293908 | − | 0.246618i | −0.00988518 | − | 0.00829465i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.8856 | − | 53.4954i | 1.03762 | − | 1.79721i | ||||
\(887\) | 36.7051 | − | 13.3596i | 1.23244 | − | 0.448570i | 0.358005 | − | 0.933720i | \(-0.383457\pi\) |
0.874431 | + | 0.485149i | \(0.161235\pi\) | |||||||
\(888\) | −0.731907 | − | 4.15085i | −0.0245612 | − | 0.139293i | ||||
\(889\) | 0.357147 | − | 2.02548i | 0.0119783 | − | 0.0679325i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.4896 | − | 17.1928i | 0.686426 | − | 0.575980i | ||||
\(892\) | −50.1559 | −1.67934 | ||||||||
\(893\) | 23.6010 | + | 42.1193i | 0.789777 | + | 1.40947i | ||||
\(894\) | 125.379 | 4.19329 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −53.3048 | − | 19.4014i | −1.78079 | − | 0.648154i | ||||
\(897\) | −0.0384031 | + | 0.217795i | −0.00128224 | + | 0.00727196i | ||||
\(898\) | −7.35910 | − | 41.7355i | −0.245576 | − | 1.39273i | ||||
\(899\) | 7.99576 | − | 2.91022i | 0.266674 | − | 0.0970613i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.18803 | + | 8.98593i | 0.172838 | + | 0.299365i | ||||
\(902\) | 39.3697 | + | 33.0351i | 1.31087 | + | 1.09995i | ||||
\(903\) | 23.4890 | + | 19.7096i | 0.781665 | + | 0.655895i | ||||
\(904\) | −10.6613 | − | 18.4659i | −0.354589 | − | 0.614166i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 52.5094 | − | 19.1118i | 1.74451 | − | 0.634949i | ||||
\(907\) | 9.95684 | + | 56.4681i | 0.330612 | + | 1.87499i | 0.466882 | + | 0.884320i | \(0.345377\pi\) |
−0.136270 | + | 0.990672i | \(0.543511\pi\) | |||||||
\(908\) | 21.2627 | − | 120.587i | 0.705628 | − | 4.00182i | ||||
\(909\) | −18.0657 | − | 6.57536i | −0.599200 | − | 0.218091i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.2118 | 0.735909 | 0.367954 | − | 0.929844i | \(-0.380058\pi\) | ||||
0.367954 | + | 0.929844i | \(0.380058\pi\) | |||||||
\(912\) | −58.5171 | − | 104.432i | −1.93769 | − | 3.45809i | ||||
\(913\) | 10.6399 | 0.352129 | ||||||||
\(914\) | −71.2962 | + | 59.8247i | −2.35827 | + | 1.97882i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.07911 | + | 6.11991i | −0.0356546 | + | 0.202208i | ||||
\(917\) | 5.27354 | + | 29.9077i | 0.174148 | + | 0.987640i | ||||
\(918\) | −13.6994 | + | 4.98617i | −0.452147 | + | 0.164568i | ||||
\(919\) | −24.0265 | + | 41.6150i | −0.792560 | + | 1.37275i | 0.131817 | + | 0.991274i | \(0.457919\pi\) |
−0.924377 | + | 0.381480i | \(0.875415\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.4992 | − | 10.4880i | −0.411861 | − | 0.345593i | ||||
\(922\) | −50.5531 | − | 42.4191i | −1.66488 | − | 1.39700i | ||||
\(923\) | −0.157298 | − | 0.272449i | −0.00517754 | − | 0.00896776i | ||||
\(924\) | −37.0970 | + | 64.2539i | −1.22040 | + | 2.11380i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.59519 | − | 20.3893i | −0.118145 | − | 0.670035i | ||||
\(927\) | 3.93499 | − | 22.3164i | 0.129242 | − | 0.732967i | ||||
\(928\) | 47.3189 | + | 17.2227i | 1.55332 | + | 0.565362i | ||||
\(929\) | 6.24472 | − | 5.23994i | 0.204883 | − | 0.171917i | −0.534573 | − | 0.845122i | \(-0.679528\pi\) |
0.739455 | + | 0.673205i | \(0.235083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.522937 | + | 3.20619i | 0.0171386 | + | 0.105079i | ||||
\(932\) | 120.754 | 3.95542 | ||||||||
\(933\) | −30.9540 | + | 25.9735i | −1.01339 | + | 0.850334i | ||||
\(934\) | 16.4579 | + | 5.99020i | 0.538521 | + | 0.196005i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0977513 | + | 0.554375i | 0.00319510 | + | 0.0181203i | ||||
\(937\) | 33.0325 | − | 12.0229i | 1.07913 | − | 0.392770i | 0.259544 | − | 0.965731i | \(-0.416428\pi\) |
0.819582 | + | 0.572962i | \(0.194206\pi\) | |||||||
\(938\) | 18.1425 | − | 31.4237i | 0.592372 | − | 1.02602i | ||||
\(939\) | 23.8390 | + | 41.2904i | 0.777958 | + | 1.34746i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.4837 | − | 9.63598i | −0.374358 | − | 0.314124i | 0.436124 | − | 0.899886i | \(-0.356351\pi\) |
−0.810483 | + | 0.585762i | \(0.800795\pi\) | |||||||
\(942\) | −21.2797 | − | 36.8575i | −0.693329 | − | 1.20088i | ||||
\(943\) | −10.2249 | + | 17.7101i | −0.332970 | + | 0.576720i | ||||
\(944\) | −139.658 | + | 50.8313i | −4.54547 | + | 1.65442i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.69911 | + | 32.3213i | −0.185294 | + | 1.05086i | ||||
\(947\) | −30.9978 | − | 11.2823i | −1.00729 | − | 0.366625i | −0.214901 | − | 0.976636i | \(-0.568943\pi\) |
−0.792393 | + | 0.610011i | \(0.791165\pi\) | |||||||
\(948\) | 99.6272 | − | 83.5971i | 3.23574 | − | 2.71511i | ||||
\(949\) | −0.171999 | −0.00558331 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.74244 | −0.283493 | ||||||||
\(952\) | 33.4710 | − | 28.0855i | 1.08480 | − | 0.910256i | ||||
\(953\) | 27.2039 | + | 9.90142i | 0.881222 | + | 0.320739i | 0.742703 | − | 0.669621i | \(-0.233544\pi\) |
0.138519 | + | 0.990360i | \(0.455766\pi\) | |||||||
\(954\) | 4.28649 | − | 24.3099i | 0.138780 | − | 0.787061i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −47.5017 | + | 17.2892i | −1.53632 | + | 0.559173i | ||||
\(957\) | 7.53095 | − | 13.0440i | 0.243441 | − | 0.421652i | ||||
\(958\) | 16.6236 | + | 28.7930i | 0.537085 | + | 0.930259i | ||||
\(959\) | 9.78639 | + | 8.21176i | 0.316019 | + | 0.265171i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.3351 | + | 19.6330i | 0.365648 | + | 0.633322i | ||||
\(962\) | −0.0123526 | + | 0.0213953i | −0.000398263 | + | 0.000689812i | ||||
\(963\) | −17.7148 | + | 6.44764i | −0.570850 | + | 0.207772i | ||||
\(964\) | 14.3038 | + | 81.1210i | 0.460695 | + | 2.61273i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −38.3745 | − | 13.9672i | −1.23468 | − | 0.449387i | ||||
\(967\) | 25.5597 | − | 21.4472i | 0.821945 | − | 0.689694i | −0.131481 | − | 0.991319i | \(-0.541973\pi\) |
0.953427 | + | 0.301625i | \(0.0975289\pi\) | |||||||
\(968\) | 46.1347 | 1.48283 | ||||||||
\(969\) | 16.9881 | + | 0.218380i | 0.545736 | + | 0.00701538i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.21562 | + | 4.37643i | −0.167377 | + | 0.140446i | −0.722629 | − | 0.691236i | \(-0.757066\pi\) |
0.555252 | + | 0.831682i | \(0.312622\pi\) | |||||||
\(972\) | 74.3325 | + | 27.0548i | 2.38422 | + | 0.867783i | ||||
\(973\) | 3.79138 | − | 21.5020i | 0.121546 | − | 0.689323i | ||||
\(974\) | −18.0648 | − | 102.451i | −0.578833 | − | 3.28273i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.3225 | + | 50.7881i | −0.938591 | + | 1.62569i | ||||
\(977\) | 0.0334665 | + | 0.0579657i | 0.00107069 | + | 0.00185449i | 0.866560 | − | 0.499072i | \(-0.166326\pi\) |
−0.865490 | + | 0.500927i | \(0.832993\pi\) | |||||||
\(978\) | 21.6616 | + | 18.1762i | 0.692661 | + | 0.581211i | ||||
\(979\) | −28.0644 | − | 23.5489i | −0.896944 | − | 0.752625i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.39608 | − | 9.34629i | 0.172284 | − | 0.298404i | ||||
\(982\) | −79.2969 | + | 28.8617i | −2.53046 | + | 0.921014i | ||||
\(983\) | 8.73556 | + | 49.5418i | 0.278621 | + | 1.58014i | 0.727220 | + | 0.686405i | \(0.240812\pi\) |
−0.448599 | + | 0.893733i | \(0.648077\pi\) | |||||||
\(984\) | −25.9045 | + | 146.912i | −0.825805 | + | 4.68337i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.0175 | + | 9.24478i | −0.350869 | + | 0.294414i | ||||
\(987\) | 66.1705 | 2.10623 | ||||||||
\(988\) | −0.171583 | + | 0.904916i | −0.00545877 | + | 0.0287892i | ||||
\(989\) | −13.0593 | −0.415261 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.99186 | − | 1.45292i | −0.126806 | − | 0.0461534i | 0.277838 | − | 0.960628i | \(-0.410382\pi\) |
−0.404644 | + | 0.914475i | \(0.632604\pi\) | |||||||
\(992\) | 8.56011 | − | 48.5468i | 0.271784 | − | 1.54136i | ||||
\(993\) | 7.74867 | + | 43.9449i | 0.245897 | + | 1.39455i | ||||
\(994\) | 54.5885 | − | 19.8686i | 1.73144 | − | 0.630194i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 25.0384 | + | 43.3678i | 0.793372 | + | 1.37416i | ||||
\(997\) | 35.2540 | + | 29.5816i | 1.11650 | + | 0.936858i | 0.998423 | − | 0.0561457i | \(-0.0178811\pi\) |
0.118082 | + | 0.993004i | \(0.462326\pi\) | |||||||
\(998\) | −39.9813 | − | 33.5483i | −1.26559 | − | 1.06195i | ||||
\(999\) | 0.339320 | + | 0.587720i | 0.0107356 | + | 0.0185946i |
(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 | 475.2.l.f.101.1 | 48 | ||
5.2 | odd | 4 | 95.2.p.a.44.1 | ✓ | 48 | ||
5.3 | odd | 4 | 95.2.p.a.44.8 | yes | 48 | ||
5.4 | even | 2 | inner | 475.2.l.f.101.8 | 48 | ||
15.2 | even | 4 | 855.2.da.b.424.8 | 48 | |||
15.8 | even | 4 | 855.2.da.b.424.1 | 48 | |||
19.4 | even | 9 | 9025.2.a.cu.1.1 | 24 | |||
19.15 | odd | 18 | 9025.2.a.ct.1.24 | 24 | |||
19.16 | even | 9 | inner | 475.2.l.f.301.1 | 48 | ||
95.4 | even | 18 | 9025.2.a.cu.1.24 | 24 | |||
95.23 | odd | 36 | 1805.2.b.k.1084.24 | 24 | |||
95.34 | odd | 18 | 9025.2.a.ct.1.1 | 24 | |||
95.42 | odd | 36 | 1805.2.b.k.1084.1 | 24 | |||
95.53 | even | 36 | 1805.2.b.l.1084.1 | 24 | |||
95.54 | even | 18 | inner | 475.2.l.f.301.8 | 48 | ||
95.72 | even | 36 | 1805.2.b.l.1084.24 | 24 | |||
95.73 | odd | 36 | 95.2.p.a.54.1 | yes | 48 | ||
95.92 | odd | 36 | 95.2.p.a.54.8 | yes | 48 | ||
285.92 | even | 36 | 855.2.da.b.244.1 | 48 | |||
285.263 | even | 36 | 855.2.da.b.244.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.44.1 | ✓ | 48 | 5.2 | odd | 4 | ||
95.2.p.a.44.8 | yes | 48 | 5.3 | odd | 4 | ||
95.2.p.a.54.1 | yes | 48 | 95.73 | odd | 36 | ||
95.2.p.a.54.8 | yes | 48 | 95.92 | odd | 36 | ||
475.2.l.f.101.1 | 48 | 1.1 | even | 1 | trivial | ||
475.2.l.f.101.8 | 48 | 5.4 | even | 2 | inner | ||
475.2.l.f.301.1 | 48 | 19.16 | even | 9 | inner | ||
475.2.l.f.301.8 | 48 | 95.54 | even | 18 | inner | ||
855.2.da.b.244.1 | 48 | 285.92 | even | 36 | |||
855.2.da.b.244.8 | 48 | 285.263 | even | 36 | |||
855.2.da.b.424.1 | 48 | 15.8 | even | 4 | |||
855.2.da.b.424.8 | 48 | 15.2 | even | 4 | |||
1805.2.b.k.1084.1 | 24 | 95.42 | odd | 36 | |||
1805.2.b.k.1084.24 | 24 | 95.23 | odd | 36 | |||
1805.2.b.l.1084.1 | 24 | 95.53 | even | 36 | |||
1805.2.b.l.1084.24 | 24 | 95.72 | even | 36 | |||
9025.2.a.ct.1.1 | 24 | 95.34 | odd | 18 | |||
9025.2.a.ct.1.24 | 24 | 19.15 | odd | 18 | |||
9025.2.a.cu.1.1 | 24 | 19.4 | even | 9 | |||
9025.2.a.cu.1.24 | 24 | 95.4 | even | 18 |