Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(109,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.m (of order \(4\), 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 \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.3 | ||
Character | \(\chi\) | \(=\) | 429.307 |
Dual form | 429.2.m.a.109.3 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.12106 | + | 1.12106i | −0.792712 | + | 0.792712i | −0.981934 | − | 0.189222i | \(-0.939403\pi\) |
0.189222 | + | 0.981934i | \(0.439403\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | − | 0.513571i | − | 0.256786i | ||||||
\(5\) | 0.850971 | + | 0.850971i | 0.380566 | + | 0.380566i | 0.871306 | − | 0.490740i | \(-0.163274\pi\) |
−0.490740 | + | 0.871306i | \(0.663274\pi\) | |||||||
\(6\) | 1.12106 | − | 1.12106i | 0.457673 | − | 0.457673i | ||||
\(7\) | −0.675060 | − | 0.675060i | −0.255149 | − | 0.255149i | 0.567929 | − | 0.823078i | \(-0.307745\pi\) |
−0.823078 | + | 0.567929i | \(0.807745\pi\) | |||||||
\(8\) | −1.66638 | − | 1.66638i | −0.589155 | − | 0.589155i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.90799 | −0.603358 | ||||||||
\(11\) | −0.299521 | + | 3.30307i | −0.0903091 | + | 0.995914i | ||||
\(12\) | 0.513571i | 0.148255i | ||||||||
\(13\) | −3.60528 | − | 0.0438666i | −0.999926 | − | 0.0121664i | ||||
\(14\) | 1.51357 | 0.404519 | ||||||||
\(15\) | −0.850971 | − | 0.850971i | −0.219720 | − | 0.219720i | ||||
\(16\) | 4.76339 | 1.19085 | ||||||||
\(17\) | −7.43124 | −1.80234 | −0.901170 | − | 0.433466i | \(-0.857290\pi\) | ||||
−0.901170 | + | 0.433466i | \(0.857290\pi\) | |||||||
\(18\) | −1.12106 | + | 1.12106i | −0.264237 | + | 0.264237i | ||||
\(19\) | 2.00891 | − | 2.00891i | 0.460876 | − | 0.460876i | −0.438067 | − | 0.898943i | \(-0.644337\pi\) |
0.898943 | + | 0.438067i | \(0.144337\pi\) | |||||||
\(20\) | 0.437034 | − | 0.437034i | 0.0977239 | − | 0.0977239i | ||||
\(21\) | 0.675060 | + | 0.675060i | 0.147310 | + | 0.147310i | ||||
\(22\) | −3.36717 | − | 4.03874i | −0.717884 | − | 0.861062i | ||||
\(23\) | 3.77898i | 0.787971i | 0.919117 | + | 0.393986i | \(0.128904\pi\) | ||||
−0.919117 | + | 0.393986i | \(0.871096\pi\) | |||||||
\(24\) | 1.66638 | + | 1.66638i | 0.340149 | + | 0.340149i | ||||
\(25\) | − | 3.55170i | − | 0.710339i | ||||||
\(26\) | 4.09093 | − | 3.99258i | 0.802298 | − | 0.783009i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.346691 | + | 0.346691i | −0.0655185 | + | 0.0655185i | ||||
\(29\) | 0.246409i | 0.0457571i | 0.999738 | + | 0.0228785i | \(0.00728310\pi\) | ||||
−0.999738 | + | 0.0228785i | \(0.992717\pi\) | |||||||
\(30\) | 1.90799 | 0.348349 | ||||||||
\(31\) | −7.23254 | − | 7.23254i | −1.29900 | − | 1.29900i | −0.929051 | − | 0.369952i | \(-0.879374\pi\) |
−0.369952 | − | 0.929051i | \(-0.620626\pi\) | |||||||
\(32\) | −2.00730 | + | 2.00730i | −0.354844 | + | 0.354844i | ||||
\(33\) | 0.299521 | − | 3.30307i | 0.0521400 | − | 0.574991i | ||||
\(34\) | 8.33090 | − | 8.33090i | 1.42874 | − | 1.42874i | ||||
\(35\) | − | 1.14891i | − | 0.194202i | ||||||
\(36\) | − | 0.513571i | − | 0.0855952i | ||||||
\(37\) | 0.872788 | − | 0.872788i | 0.143486 | − | 0.143486i | −0.631715 | − | 0.775201i | \(-0.717649\pi\) |
0.775201 | + | 0.631715i | \(0.217649\pi\) | |||||||
\(38\) | 4.50424i | 0.730684i | ||||||||
\(39\) | 3.60528 | + | 0.0438666i | 0.577308 | + | 0.00702427i | ||||
\(40\) | − | 2.83609i | − | 0.448425i | ||||||
\(41\) | 2.78745 | − | 2.78745i | 0.435326 | − | 0.435326i | −0.455109 | − | 0.890436i | \(-0.650400\pi\) |
0.890436 | + | 0.455109i | \(0.150400\pi\) | |||||||
\(42\) | −1.51357 | −0.233549 | ||||||||
\(43\) | −4.52405 | −0.689911 | −0.344955 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344955 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(44\) | 1.69636 | + | 0.153826i | 0.255736 | + | 0.0231901i | ||||
\(45\) | 0.850971 | + | 0.850971i | 0.126855 | + | 0.126855i | ||||
\(46\) | −4.23648 | − | 4.23648i | −0.624635 | − | 0.624635i | ||||
\(47\) | 2.70266 | − | 2.70266i | 0.394224 | − | 0.394224i | −0.481966 | − | 0.876190i | \(-0.660077\pi\) |
0.876190 | + | 0.481966i | \(0.160077\pi\) | |||||||
\(48\) | −4.76339 | −0.687536 | ||||||||
\(49\) | − | 6.08859i | − | 0.869798i | ||||||
\(50\) | 3.98168 | + | 3.98168i | 0.563095 | + | 0.563095i | ||||
\(51\) | 7.43124 | 1.04058 | ||||||||
\(52\) | −0.0225286 | + | 1.85157i | −0.00312416 | + | 0.256767i | ||||
\(53\) | −12.4473 | −1.70976 | −0.854882 | − | 0.518822i | \(-0.826371\pi\) | ||||
−0.854882 | + | 0.518822i | \(0.826371\pi\) | |||||||
\(54\) | 1.12106 | − | 1.12106i | 0.152558 | − | 0.152558i | ||||
\(55\) | −3.06570 | + | 2.55593i | −0.413379 | + | 0.344642i | ||||
\(56\) | 2.24982i | 0.300644i | ||||||||
\(57\) | −2.00891 | + | 2.00891i | −0.266087 | + | 0.266087i | ||||
\(58\) | −0.276241 | − | 0.276241i | −0.0362722 | − | 0.0362722i | ||||
\(59\) | −6.27696 | + | 6.27696i | −0.817190 | + | 0.817190i | −0.985700 | − | 0.168510i | \(-0.946105\pi\) |
0.168510 | + | 0.985700i | \(0.446105\pi\) | |||||||
\(60\) | −0.437034 | + | 0.437034i | −0.0564209 | + | 0.0564209i | ||||
\(61\) | − | 3.96296i | − | 0.507405i | −0.967282 | − | 0.253702i | \(-0.918352\pi\) | ||
0.967282 | − | 0.253702i | \(-0.0816484\pi\) | |||||||
\(62\) | 16.2163 | 2.05947 | ||||||||
\(63\) | −0.675060 | − | 0.675060i | −0.0850496 | − | 0.0850496i | ||||
\(64\) | 5.02615i | 0.628269i | ||||||||
\(65\) | −3.03066 | − | 3.10532i | −0.375907 | − | 0.385168i | ||||
\(66\) | 3.36717 | + | 4.03874i | 0.414471 | + | 0.497135i | ||||
\(67\) | 6.55818 | + | 6.55818i | 0.801209 | + | 0.801209i | 0.983285 | − | 0.182076i | \(-0.0582816\pi\) |
−0.182076 | + | 0.983285i | \(0.558282\pi\) | |||||||
\(68\) | 3.81647i | 0.462815i | ||||||||
\(69\) | − | 3.77898i | − | 0.454935i | ||||||
\(70\) | 1.28801 | + | 1.28801i | 0.153946 | + | 0.153946i | ||||
\(71\) | 2.41976 | + | 2.41976i | 0.287173 | + | 0.287173i | 0.835961 | − | 0.548788i | \(-0.184911\pi\) |
−0.548788 | + | 0.835961i | \(0.684911\pi\) | |||||||
\(72\) | −1.66638 | − | 1.66638i | −0.196385 | − | 0.196385i | ||||
\(73\) | 5.88991 | + | 5.88991i | 0.689362 | + | 0.689362i | 0.962091 | − | 0.272729i | \(-0.0879263\pi\) |
−0.272729 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(74\) | 1.95690i | 0.227485i | ||||||||
\(75\) | 3.55170i | 0.410115i | ||||||||
\(76\) | −1.03172 | − | 1.03172i | −0.118346 | − | 0.118346i | ||||
\(77\) | 2.43197 | − | 2.02758i | 0.277148 | − | 0.231064i | ||||
\(78\) | −4.09093 | + | 3.99258i | −0.463207 | + | 0.452071i | ||||
\(79\) | 11.3349i | 1.27528i | 0.770334 | + | 0.637640i | \(0.220089\pi\) | ||||
−0.770334 | + | 0.637640i | \(0.779911\pi\) | |||||||
\(80\) | 4.05350 | + | 4.05350i | 0.453196 | + | 0.453196i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.24982i | 0.690177i | ||||||||
\(83\) | 2.61335 | − | 2.61335i | 0.286853 | − | 0.286853i | −0.548982 | − | 0.835834i | \(-0.684984\pi\) |
0.835834 | + | 0.548982i | \(0.184984\pi\) | |||||||
\(84\) | 0.346691 | − | 0.346691i | 0.0378271 | − | 0.0378271i | ||||
\(85\) | −6.32377 | − | 6.32377i | −0.685909 | − | 0.685909i | ||||
\(86\) | 5.07175 | − | 5.07175i | 0.546901 | − | 0.546901i | ||||
\(87\) | − | 0.246409i | − | 0.0264179i | ||||||
\(88\) | 6.00330 | − | 5.00506i | 0.639954 | − | 0.533542i | ||||
\(89\) | −5.39241 | + | 5.39241i | −0.571594 | + | 0.571594i | −0.932574 | − | 0.360980i | \(-0.882442\pi\) |
0.360980 | + | 0.932574i | \(0.382442\pi\) | |||||||
\(90\) | −1.90799 | −0.201119 | ||||||||
\(91\) | 2.40417 | + | 2.46340i | 0.252026 | + | 0.258234i | ||||
\(92\) | 1.94077 | 0.202340 | ||||||||
\(93\) | 7.23254 | + | 7.23254i | 0.749980 | + | 0.749980i | ||||
\(94\) | 6.05972i | 0.625012i | ||||||||
\(95\) | 3.41905 | 0.350787 | ||||||||
\(96\) | 2.00730 | − | 2.00730i | 0.204869 | − | 0.204869i | ||||
\(97\) | −10.7087 | − | 10.7087i | −1.08730 | − | 1.08730i | −0.995805 | − | 0.0914992i | \(-0.970834\pi\) |
−0.0914992 | − | 0.995805i | \(-0.529166\pi\) | |||||||
\(98\) | 6.82570 | + | 6.82570i | 0.689500 | + | 0.689500i | ||||
\(99\) | −0.299521 | + | 3.30307i | −0.0301030 | + | 0.331971i | ||||
\(100\) | −1.82405 | −0.182405 | ||||||||
\(101\) | −2.29024 | −0.227888 | −0.113944 | − | 0.993487i | \(-0.536348\pi\) | ||||
−0.113944 | + | 0.993487i | \(0.536348\pi\) | |||||||
\(102\) | −8.33090 | + | 8.33090i | −0.824882 | + | 0.824882i | ||||
\(103\) | 11.4308i | 1.12631i | 0.826352 | + | 0.563154i | \(0.190412\pi\) | ||||
−0.826352 | + | 0.563154i | \(0.809588\pi\) | |||||||
\(104\) | 5.93468 | + | 6.08088i | 0.581944 | + | 0.596279i | ||||
\(105\) | 1.14891i | 0.112122i | ||||||||
\(106\) | 13.9542 | − | 13.9542i | 1.35535 | − | 1.35535i | ||||
\(107\) | 19.5035i | 1.88548i | 0.333533 | + | 0.942738i | \(0.391759\pi\) | ||||
−0.333533 | + | 0.942738i | \(0.608241\pi\) | |||||||
\(108\) | 0.513571i | 0.0494184i | ||||||||
\(109\) | −12.9767 | + | 12.9767i | −1.24294 | + | 1.24294i | −0.284164 | + | 0.958776i | \(0.591716\pi\) |
−0.958776 | + | 0.284164i | \(0.908284\pi\) | |||||||
\(110\) | 0.571483 | − | 6.30222i | 0.0544887 | − | 0.600893i | ||||
\(111\) | −0.872788 | + | 0.872788i | −0.0828414 | + | 0.0828414i | ||||
\(112\) | −3.21557 | − | 3.21557i | −0.303843 | − | 0.303843i | ||||
\(113\) | −18.4795 | −1.73840 | −0.869201 | − | 0.494459i | \(-0.835366\pi\) | ||||
−0.869201 | + | 0.494459i | \(0.835366\pi\) | |||||||
\(114\) | − | 4.50424i | − | 0.421861i | ||||||
\(115\) | −3.21580 | + | 3.21580i | −0.299875 | + | 0.299875i | ||||
\(116\) | 0.126549 | 0.0117498 | ||||||||
\(117\) | −3.60528 | − | 0.0438666i | −0.333309 | − | 0.00405546i | ||||
\(118\) | − | 14.0738i | − | 1.29559i | ||||||
\(119\) | 5.01653 | + | 5.01653i | 0.459865 | + | 0.459865i | ||||
\(120\) | 2.83609i | 0.258898i | ||||||||
\(121\) | −10.8206 | − | 1.97868i | −0.983689 | − | 0.179880i | ||||
\(122\) | 4.44273 | + | 4.44273i | 0.402226 | + | 0.402226i | ||||
\(123\) | −2.78745 | + | 2.78745i | −0.251336 | + | 0.251336i | ||||
\(124\) | −3.71443 | + | 3.71443i | −0.333565 | + | 0.333565i | ||||
\(125\) | 7.27725 | − | 7.27725i | 0.650897 | − | 0.650897i | ||||
\(126\) | 1.51357 | 0.134840 | ||||||||
\(127\) | −4.89459 | −0.434324 | −0.217162 | − | 0.976136i | \(-0.569680\pi\) | ||||
−0.217162 | + | 0.976136i | \(0.569680\pi\) | |||||||
\(128\) | −9.64924 | − | 9.64924i | −0.852880 | − | 0.852880i | ||||
\(129\) | 4.52405 | 0.398320 | ||||||||
\(130\) | 6.87883 | + | 0.0836968i | 0.603314 | + | 0.00734069i | ||||
\(131\) | − | 1.84165i | − | 0.160906i | −0.996758 | − | 0.0804530i | \(-0.974363\pi\) | ||
0.996758 | − | 0.0804530i | \(-0.0256367\pi\) | |||||||
\(132\) | −1.69636 | − | 0.153826i | −0.147649 | − | 0.0133888i | ||||
\(133\) | −2.71227 | −0.235184 | ||||||||
\(134\) | −14.7043 | −1.27026 | ||||||||
\(135\) | −0.850971 | − | 0.850971i | −0.0732399 | − | 0.0732399i | ||||
\(136\) | 12.3833 | + | 12.3833i | 1.06186 | + | 1.06186i | ||||
\(137\) | 12.4192 | − | 12.4192i | 1.06104 | − | 1.06104i | 0.0630322 | − | 0.998011i | \(-0.479923\pi\) |
0.998011 | − | 0.0630322i | \(-0.0200771\pi\) | |||||||
\(138\) | 4.23648 | + | 4.23648i | 0.360633 | + | 0.360633i | ||||
\(139\) | 11.7143i | 0.993593i | 0.867867 | + | 0.496796i | \(0.165490\pi\) | ||||
−0.867867 | + | 0.496796i | \(0.834510\pi\) | |||||||
\(140\) | −0.590049 | −0.0498682 | ||||||||
\(141\) | −2.70266 | + | 2.70266i | −0.227605 | + | 0.227605i | ||||
\(142\) | −5.42542 | −0.455291 | ||||||||
\(143\) | 1.22475 | − | 11.8954i | 0.102419 | − | 0.994741i | ||||
\(144\) | 4.76339 | 0.396949 | ||||||||
\(145\) | −0.209687 | + | 0.209687i | −0.0174136 | + | 0.0174136i | ||||
\(146\) | −13.2059 | −1.09293 | ||||||||
\(147\) | 6.08859i | 0.502178i | ||||||||
\(148\) | −0.448239 | − | 0.448239i | −0.0368450 | − | 0.0368450i | ||||
\(149\) | 13.0754 | − | 13.0754i | 1.07118 | − | 1.07118i | 0.0739121 | − | 0.997265i | \(-0.476452\pi\) |
0.997265 | − | 0.0739121i | \(-0.0235484\pi\) | |||||||
\(150\) | −3.98168 | − | 3.98168i | −0.325103 | − | 0.325103i | ||||
\(151\) | 9.57308 | + | 9.57308i | 0.779047 | + | 0.779047i | 0.979669 | − | 0.200622i | \(-0.0642963\pi\) |
−0.200622 | + | 0.979669i | \(0.564296\pi\) | |||||||
\(152\) | −6.69523 | −0.543055 | ||||||||
\(153\) | −7.43124 | −0.600780 | ||||||||
\(154\) | −0.453347 | + | 4.99944i | −0.0365317 | + | 0.402866i | ||||
\(155\) | − | 12.3094i | − | 0.988712i | ||||||
\(156\) | 0.0225286 | − | 1.85157i | 0.00180373 | − | 0.148244i | ||||
\(157\) | 8.15572 | 0.650897 | 0.325449 | − | 0.945560i | \(-0.394485\pi\) | ||||
0.325449 | + | 0.945560i | \(0.394485\pi\) | |||||||
\(158\) | −12.7072 | − | 12.7072i | −1.01093 | − | 1.01093i | ||||
\(159\) | 12.4473 | 0.987133 | ||||||||
\(160\) | −3.41631 | −0.270083 | ||||||||
\(161\) | 2.55104 | − | 2.55104i | 0.201050 | − | 0.201050i | ||||
\(162\) | −1.12106 | + | 1.12106i | −0.0880791 | + | 0.0880791i | ||||
\(163\) | 5.54165 | − | 5.54165i | 0.434055 | − | 0.434055i | −0.455950 | − | 0.890005i | \(-0.650700\pi\) |
0.890005 | + | 0.455950i | \(0.150700\pi\) | |||||||
\(164\) | −1.43155 | − | 1.43155i | −0.111786 | − | 0.111786i | ||||
\(165\) | 3.06570 | − | 2.55593i | 0.238665 | − | 0.198979i | ||||
\(166\) | 5.85947i | 0.454783i | ||||||||
\(167\) | −0.229296 | − | 0.229296i | −0.0177435 | − | 0.0177435i | 0.698179 | − | 0.715923i | \(-0.253994\pi\) |
−0.715923 | + | 0.698179i | \(0.753994\pi\) | |||||||
\(168\) | − | 2.24982i | − | 0.173577i | ||||||
\(169\) | 12.9962 | + | 0.316303i | 0.999704 | + | 0.0243310i | ||||
\(170\) | 14.1787 | 1.08746 | ||||||||
\(171\) | 2.00891 | − | 2.00891i | 0.153625 | − | 0.153625i | ||||
\(172\) | 2.32342i | 0.177159i | ||||||||
\(173\) | −10.9234 | −0.830491 | −0.415245 | − | 0.909709i | \(-0.636304\pi\) | ||||
−0.415245 | + | 0.909709i | \(0.636304\pi\) | |||||||
\(174\) | 0.276241 | + | 0.276241i | 0.0209418 | + | 0.0209418i | ||||
\(175\) | −2.39761 | + | 2.39761i | −0.181242 | + | 0.181242i | ||||
\(176\) | −1.42674 | + | 15.7338i | −0.107544 | + | 1.18598i | ||||
\(177\) | 6.27696 | − | 6.27696i | 0.471805 | − | 0.471805i | ||||
\(178\) | − | 12.0905i | − | 0.906219i | ||||||
\(179\) | − | 10.3266i | − | 0.771847i | −0.922531 | − | 0.385923i | \(-0.873883\pi\) | ||
0.922531 | − | 0.385923i | \(-0.126117\pi\) | |||||||
\(180\) | 0.437034 | − | 0.437034i | 0.0325746 | − | 0.0325746i | ||||
\(181\) | 11.0278i | 0.819690i | 0.912155 | + | 0.409845i | \(0.134417\pi\) | ||||
−0.912155 | + | 0.409845i | \(0.865583\pi\) | |||||||
\(182\) | −5.45686 | − | 0.0663952i | −0.404489 | − | 0.00492154i | ||||
\(183\) | 3.96296i | 0.292950i | ||||||||
\(184\) | 6.29722 | − | 6.29722i | 0.464237 | − | 0.464237i | ||||
\(185\) | 1.48543 | 0.109211 | ||||||||
\(186\) | −16.2163 | −1.18904 | ||||||||
\(187\) | 2.22581 | − | 24.5459i | 0.162768 | − | 1.79498i | ||||
\(188\) | −1.38801 | − | 1.38801i | −0.101231 | − | 0.101231i | ||||
\(189\) | 0.675060 | + | 0.675060i | 0.0491034 | + | 0.0491034i | ||||
\(190\) | −3.83298 | + | 3.83298i | −0.278073 | + | 0.278073i | ||||
\(191\) | −13.1251 | −0.949697 | −0.474849 | − | 0.880067i | \(-0.657497\pi\) | ||||
−0.474849 | + | 0.880067i | \(0.657497\pi\) | |||||||
\(192\) | − | 5.02615i | − | 0.362731i | ||||||
\(193\) | 14.4855 | + | 14.4855i | 1.04269 | + | 1.04269i | 0.999047 | + | 0.0436394i | \(0.0138953\pi\) |
0.0436394 | + | 0.999047i | \(0.486105\pi\) | |||||||
\(194\) | 24.0103 | 1.72384 | ||||||||
\(195\) | 3.03066 | + | 3.10532i | 0.217030 | + | 0.222377i | ||||
\(196\) | −3.12692 | −0.223352 | ||||||||
\(197\) | 1.33757 | − | 1.33757i | 0.0952980 | − | 0.0952980i | −0.657851 | − | 0.753149i | \(-0.728534\pi\) |
0.753149 | + | 0.657851i | \(0.228534\pi\) | |||||||
\(198\) | −3.36717 | − | 4.03874i | −0.239295 | − | 0.287021i | ||||
\(199\) | − | 5.28728i | − | 0.374806i | −0.982283 | − | 0.187403i | \(-0.939993\pi\) | ||
0.982283 | − | 0.187403i | \(-0.0600070\pi\) | |||||||
\(200\) | −5.91849 | + | 5.91849i | −0.418500 | + | 0.418500i | ||||
\(201\) | −6.55818 | − | 6.55818i | −0.462578 | − | 0.462578i | ||||
\(202\) | 2.56751 | − | 2.56751i | 0.180649 | − | 0.180649i | ||||
\(203\) | 0.166341 | − | 0.166341i | 0.0116749 | − | 0.0116749i | ||||
\(204\) | − | 3.81647i | − | 0.267206i | ||||||
\(205\) | 4.74407 | 0.331340 | ||||||||
\(206\) | −12.8146 | − | 12.8146i | −0.892839 | − | 0.892839i | ||||
\(207\) | 3.77898i | 0.262657i | ||||||||
\(208\) | −17.1734 | − | 0.208953i | −1.19076 | − | 0.0144883i | ||||
\(209\) | 6.03387 | + | 7.23729i | 0.417371 | + | 0.500614i | ||||
\(210\) | −1.28801 | − | 1.28801i | −0.0888808 | − | 0.0888808i | ||||
\(211\) | − | 1.85803i | − | 0.127912i | −0.997953 | − | 0.0639562i | \(-0.979628\pi\) | ||
0.997953 | − | 0.0639562i | \(-0.0203718\pi\) | |||||||
\(212\) | 6.39256i | 0.439043i | ||||||||
\(213\) | −2.41976 | − | 2.41976i | −0.165799 | − | 0.165799i | ||||
\(214\) | −21.8647 | − | 21.8647i | −1.49464 | − | 1.49464i | ||||
\(215\) | −3.84983 | − | 3.84983i | −0.262556 | − | 0.262556i | ||||
\(216\) | 1.66638 | + | 1.66638i | 0.113383 | + | 0.113383i | ||||
\(217\) | 9.76480i | 0.662878i | ||||||||
\(218\) | − | 29.0954i | − | 1.97059i | ||||||
\(219\) | −5.88991 | − | 5.88991i | −0.398003 | − | 0.398003i | ||||
\(220\) | 1.31265 | + | 1.57446i | 0.0884992 | + | 0.106150i | ||||
\(221\) | 26.7917 | + | 0.325983i | 1.80221 | + | 0.0219280i | ||||
\(222\) | − | 1.95690i | − | 0.131339i | ||||||
\(223\) | −2.11012 | − | 2.11012i | −0.141304 | − | 0.141304i | 0.632916 | − | 0.774220i | \(-0.281858\pi\) |
−0.774220 | + | 0.632916i | \(0.781858\pi\) | |||||||
\(224\) | 2.71010 | 0.181076 | ||||||||
\(225\) | − | 3.55170i | − | 0.236780i | ||||||
\(226\) | 20.7167 | − | 20.7167i | 1.37805 | − | 1.37805i | ||||
\(227\) | 20.5713 | − | 20.5713i | 1.36537 | − | 1.36537i | 0.498448 | − | 0.866920i | \(-0.333904\pi\) |
0.866920 | − | 0.498448i | \(-0.166096\pi\) | |||||||
\(228\) | 1.03172 | + | 1.03172i | 0.0683273 | + | 0.0683273i | ||||
\(229\) | −7.75638 | + | 7.75638i | −0.512556 | + | 0.512556i | −0.915309 | − | 0.402753i | \(-0.868053\pi\) |
0.402753 | + | 0.915309i | \(0.368053\pi\) | |||||||
\(230\) | − | 7.21024i | − | 0.475429i | ||||||
\(231\) | −2.43197 | + | 2.02758i | −0.160012 | + | 0.133405i | ||||
\(232\) | 0.410612 | − | 0.410612i | 0.0269580 | − | 0.0269580i | ||||
\(233\) | −20.1032 | −1.31701 | −0.658503 | − | 0.752578i | \(-0.728810\pi\) | ||||
−0.658503 | + | 0.752578i | \(0.728810\pi\) | |||||||
\(234\) | 4.09093 | − | 3.99258i | 0.267433 | − | 0.261003i | ||||
\(235\) | 4.59977 | 0.300056 | ||||||||
\(236\) | 3.22367 | + | 3.22367i | 0.209843 | + | 0.209843i | ||||
\(237\) | − | 11.3349i | − | 0.736284i | ||||||
\(238\) | −11.2477 | −0.729081 | ||||||||
\(239\) | −10.8128 | + | 10.8128i | −0.699423 | + | 0.699423i | −0.964286 | − | 0.264863i | \(-0.914673\pi\) |
0.264863 | + | 0.964286i | \(0.414673\pi\) | |||||||
\(240\) | −4.05350 | − | 4.05350i | −0.261653 | − | 0.261653i | ||||
\(241\) | −8.92902 | − | 8.92902i | −0.575169 | − | 0.575169i | 0.358399 | − | 0.933568i | \(-0.383323\pi\) |
−0.933568 | + | 0.358399i | \(0.883323\pi\) | |||||||
\(242\) | 14.3488 | − | 9.91233i | 0.922375 | − | 0.637189i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.03526 | −0.130294 | ||||||||
\(245\) | 5.18121 | − | 5.18121i | 0.331015 | − | 0.331015i | ||||
\(246\) | − | 6.24982i | − | 0.398474i | ||||||
\(247\) | −7.33082 | + | 7.15457i | −0.466449 | + | 0.455235i | ||||
\(248\) | 24.1044i | 1.53063i | ||||||||
\(249\) | −2.61335 | + | 2.61335i | −0.165614 | + | 0.165614i | ||||
\(250\) | 16.3165i | 1.03195i | ||||||||
\(251\) | 23.1015i | 1.45816i | 0.684430 | + | 0.729078i | \(0.260051\pi\) | ||||
−0.684430 | + | 0.729078i | \(0.739949\pi\) | |||||||
\(252\) | −0.346691 | + | 0.346691i | −0.0218395 | + | 0.0218395i | ||||
\(253\) | −12.4822 | − | 1.13188i | −0.784751 | − | 0.0711610i | ||||
\(254\) | 5.48715 | − | 5.48715i | 0.344294 | − | 0.344294i | ||||
\(255\) | 6.32377 | + | 6.32377i | 0.396010 | + | 0.396010i | ||||
\(256\) | 11.5825 | 0.723909 | ||||||||
\(257\) | 11.2666i | 0.702793i | 0.936227 | + | 0.351397i | \(0.114293\pi\) | ||||
−0.936227 | + | 0.351397i | \(0.885707\pi\) | |||||||
\(258\) | −5.07175 | + | 5.07175i | −0.315753 | + | 0.315753i | ||||
\(259\) | −1.17837 | −0.0732203 | ||||||||
\(260\) | −1.59480 | + | 1.55646i | −0.0989056 | + | 0.0965277i | ||||
\(261\) | 0.246409i | 0.0152524i | ||||||||
\(262\) | 2.06461 | + | 2.06461i | 0.127552 | + | 0.127552i | ||||
\(263\) | 6.58637i | 0.406133i | 0.979165 | + | 0.203066i | \(0.0650907\pi\) | ||||
−0.979165 | + | 0.203066i | \(0.934909\pi\) | |||||||
\(264\) | −6.00330 | + | 5.00506i | −0.369477 | + | 0.308040i | ||||
\(265\) | −10.5923 | − | 10.5923i | −0.650678 | − | 0.650678i | ||||
\(266\) | 3.04063 | − | 3.04063i | 0.186433 | − | 0.186433i | ||||
\(267\) | 5.39241 | − | 5.39241i | 0.330010 | − | 0.330010i | ||||
\(268\) | 3.36809 | − | 3.36809i | 0.205739 | − | 0.205739i | ||||
\(269\) | 8.85053 | 0.539627 | 0.269813 | − | 0.962913i | \(-0.413038\pi\) | ||||
0.269813 | + | 0.962913i | \(0.413038\pi\) | |||||||
\(270\) | 1.90799 | 0.116116 | ||||||||
\(271\) | −9.40355 | − | 9.40355i | −0.571225 | − | 0.571225i | 0.361246 | − | 0.932471i | \(-0.382352\pi\) |
−0.932471 | + | 0.361246i | \(0.882352\pi\) | |||||||
\(272\) | −35.3979 | −2.14631 | ||||||||
\(273\) | −2.40417 | − | 2.46340i | −0.145507 | − | 0.149091i | ||||
\(274\) | 27.8454i | 1.68220i | ||||||||
\(275\) | 11.7315 | + | 1.06381i | 0.707437 | + | 0.0641501i | ||||
\(276\) | −1.94077 | −0.116821 | ||||||||
\(277\) | 11.5221 | 0.692296 | 0.346148 | − | 0.938180i | \(-0.387489\pi\) | ||||
0.346148 | + | 0.938180i | \(0.387489\pi\) | |||||||
\(278\) | −13.1325 | − | 13.1325i | −0.787633 | − | 0.787633i | ||||
\(279\) | −7.23254 | − | 7.23254i | −0.433001 | − | 0.433001i | ||||
\(280\) | −1.91453 | + | 1.91453i | −0.114415 | + | 0.114415i | ||||
\(281\) | −15.2681 | − | 15.2681i | −0.910819 | − | 0.910819i | 0.0855176 | − | 0.996337i | \(-0.472746\pi\) |
−0.996337 | + | 0.0855176i | \(0.972746\pi\) | |||||||
\(282\) | − | 6.05972i | − | 0.360851i | ||||||
\(283\) | 1.21751 | 0.0723737 | 0.0361869 | − | 0.999345i | \(-0.488479\pi\) | ||||
0.0361869 | + | 0.999345i | \(0.488479\pi\) | |||||||
\(284\) | 1.24272 | − | 1.24272i | 0.0737419 | − | 0.0737419i | ||||
\(285\) | −3.41905 | −0.202527 | ||||||||
\(286\) | 11.9625 | + | 14.7085i | 0.707355 | + | 0.869733i | ||||
\(287\) | −3.76339 | −0.222146 | ||||||||
\(288\) | −2.00730 | + | 2.00730i | −0.118281 | + | 0.118281i | ||||
\(289\) | 38.2233 | 2.24843 | ||||||||
\(290\) | − | 0.470146i | − | 0.0276079i | ||||||
\(291\) | 10.7087 | + | 10.7087i | 0.627755 | + | 0.627755i | ||||
\(292\) | 3.02489 | − | 3.02489i | 0.177018 | − | 0.177018i | ||||
\(293\) | −8.56257 | − | 8.56257i | −0.500231 | − | 0.500231i | 0.411279 | − | 0.911510i | \(-0.365082\pi\) |
−0.911510 | + | 0.411279i | \(0.865082\pi\) | |||||||
\(294\) | −6.82570 | − | 6.82570i | −0.398083 | − | 0.398083i | ||||
\(295\) | −10.6830 | −0.621989 | ||||||||
\(296\) | −2.90880 | −0.169070 | ||||||||
\(297\) | 0.299521 | − | 3.30307i | 0.0173800 | − | 0.191664i | ||||
\(298\) | 29.3167i | 1.69827i | ||||||||
\(299\) | 0.165771 | − | 13.6243i | 0.00958677 | − | 0.787913i | ||||
\(300\) | 1.82405 | 0.105312 | ||||||||
\(301\) | 3.05400 | + | 3.05400i | 0.176030 | + | 0.176030i | ||||
\(302\) | −21.4641 | −1.23512 | ||||||||
\(303\) | 2.29024 | 0.131571 | ||||||||
\(304\) | 9.56922 | − | 9.56922i | 0.548833 | − | 0.548833i | ||||
\(305\) | 3.37236 | − | 3.37236i | 0.193101 | − | 0.193101i | ||||
\(306\) | 8.33090 | − | 8.33090i | 0.476246 | − | 0.476246i | ||||
\(307\) | 3.18728 | + | 3.18728i | 0.181908 | + | 0.181908i | 0.792187 | − | 0.610279i | \(-0.208943\pi\) |
−0.610279 | + | 0.792187i | \(0.708943\pi\) | |||||||
\(308\) | −1.04131 | − | 1.24899i | −0.0593339 | − | 0.0711677i | ||||
\(309\) | − | 11.4308i | − | 0.650274i | ||||||
\(310\) | 13.7996 | + | 13.7996i | 0.783764 | + | 0.783764i | ||||
\(311\) | 6.59476i | 0.373954i | 0.982364 | + | 0.186977i | \(0.0598691\pi\) | ||||
−0.982364 | + | 0.186977i | \(0.940131\pi\) | |||||||
\(312\) | −5.93468 | − | 6.08088i | −0.335985 | − | 0.344262i | ||||
\(313\) | −24.4375 | −1.38129 | −0.690644 | − | 0.723195i | \(-0.742673\pi\) | ||||
−0.690644 | + | 0.723195i | \(0.742673\pi\) | |||||||
\(314\) | −9.14309 | + | 9.14309i | −0.515974 | + | 0.515974i | ||||
\(315\) | − | 1.14891i | − | 0.0647339i | ||||||
\(316\) | 5.82130 | 0.327474 | ||||||||
\(317\) | 21.5305 | + | 21.5305i | 1.20928 | + | 1.20928i | 0.971262 | + | 0.238014i | \(0.0764963\pi\) |
0.238014 | + | 0.971262i | \(0.423504\pi\) | |||||||
\(318\) | −13.9542 | + | 13.9542i | −0.782513 | + | 0.782513i | ||||
\(319\) | −0.813908 | − | 0.0738049i | −0.0455701 | − | 0.00413228i | ||||
\(320\) | −4.27711 | + | 4.27711i | −0.239098 | + | 0.239098i | ||||
\(321\) | − | 19.5035i | − | 1.08858i | ||||||
\(322\) | 5.71975i | 0.318749i | ||||||||
\(323\) | −14.9287 | + | 14.9287i | −0.830655 | + | 0.830655i | ||||
\(324\) | − | 0.513571i | − | 0.0285317i | ||||||
\(325\) | −0.155801 | + | 12.8049i | −0.00864227 | + | 0.710287i | ||||
\(326\) | 12.4251i | 0.688162i | ||||||||
\(327\) | 12.9767 | − | 12.9767i | 0.717612 | − | 0.717612i | ||||
\(328\) | −9.28990 | −0.512949 | ||||||||
\(329\) | −3.64892 | −0.201171 | ||||||||
\(330\) | −0.571483 | + | 6.30222i | −0.0314591 | + | 0.346926i | ||||
\(331\) | 5.84499 | + | 5.84499i | 0.321270 | + | 0.321270i | 0.849254 | − | 0.527984i | \(-0.177052\pi\) |
−0.527984 | + | 0.849254i | \(0.677052\pi\) | |||||||
\(332\) | −1.34214 | − | 1.34214i | −0.0736597 | − | 0.0736597i | ||||
\(333\) | 0.872788 | − | 0.872788i | 0.0478285 | − | 0.0478285i | ||||
\(334\) | 0.514111 | 0.0281309 | ||||||||
\(335\) | 11.1616i | 0.609825i | ||||||||
\(336\) | 3.21557 | + | 3.21557i | 0.175424 | + | 0.175424i | ||||
\(337\) | 4.57368 | 0.249144 | 0.124572 | − | 0.992211i | \(-0.460244\pi\) | ||||
0.124572 | + | 0.992211i | \(0.460244\pi\) | |||||||
\(338\) | −14.9241 | + | 14.2149i | −0.811765 | + | 0.773190i | ||||
\(339\) | 18.4795 | 1.00367 | ||||||||
\(340\) | −3.24771 | + | 3.24771i | −0.176132 | + | 0.176132i | ||||
\(341\) | 26.0559 | − | 21.7233i | 1.41101 | − | 1.17638i | ||||
\(342\) | 4.50424i | 0.243561i | ||||||||
\(343\) | −8.83558 | + | 8.83558i | −0.477077 | + | 0.477077i | ||||
\(344\) | 7.53879 | + | 7.53879i | 0.406464 | + | 0.406464i | ||||
\(345\) | 3.21580 | − | 3.21580i | 0.173133 | − | 0.173133i | ||||
\(346\) | 12.2458 | − | 12.2458i | 0.658340 | − | 0.658340i | ||||
\(347\) | 7.58514i | 0.407191i | 0.979055 | + | 0.203596i | \(0.0652628\pi\) | ||||
−0.979055 | + | 0.203596i | \(0.934737\pi\) | |||||||
\(348\) | −0.126549 | −0.00678373 | ||||||||
\(349\) | 6.09310 | + | 6.09310i | 0.326156 | + | 0.326156i | 0.851123 | − | 0.524967i | \(-0.175922\pi\) |
−0.524967 | + | 0.851123i | \(0.675922\pi\) | |||||||
\(350\) | − | 5.37575i | − | 0.287346i | ||||||
\(351\) | 3.60528 | + | 0.0438666i | 0.192436 | + | 0.00234142i | ||||
\(352\) | −6.02903 | − | 7.23149i | −0.321348 | − | 0.385439i | ||||
\(353\) | −9.88986 | − | 9.88986i | −0.526384 | − | 0.526384i | 0.393108 | − | 0.919492i | \(-0.371400\pi\) |
−0.919492 | + | 0.393108i | \(0.871400\pi\) | |||||||
\(354\) | 14.0738i | 0.748011i | ||||||||
\(355\) | 4.11829i | 0.218576i | ||||||||
\(356\) | 2.76939 | + | 2.76939i | 0.146777 | + | 0.146777i | ||||
\(357\) | −5.01653 | − | 5.01653i | −0.265503 | − | 0.265503i | ||||
\(358\) | 11.5768 | + | 11.5768i | 0.611852 | + | 0.611852i | ||||
\(359\) | 1.75029 | + | 1.75029i | 0.0923766 | + | 0.0923766i | 0.751785 | − | 0.659408i | \(-0.229193\pi\) |
−0.659408 | + | 0.751785i | \(0.729193\pi\) | |||||||
\(360\) | − | 2.83609i | − | 0.149475i | ||||||
\(361\) | 10.9285i | 0.575187i | ||||||||
\(362\) | −12.3629 | − | 12.3629i | −0.649778 | − | 0.649778i | ||||
\(363\) | 10.8206 | + | 1.97868i | 0.567933 | + | 0.103854i | ||||
\(364\) | 1.26513 | − | 1.23471i | 0.0663108 | − | 0.0647166i | ||||
\(365\) | 10.0243i | 0.524695i | ||||||||
\(366\) | −4.44273 | − | 4.44273i | −0.232225 | − | 0.232225i | ||||
\(367\) | 4.27025 | 0.222905 | 0.111453 | − | 0.993770i | \(-0.464450\pi\) | ||||
0.111453 | + | 0.993770i | \(0.464450\pi\) | |||||||
\(368\) | 18.0007i | 0.938353i | ||||||||
\(369\) | 2.78745 | − | 2.78745i | 0.145109 | − | 0.145109i | ||||
\(370\) | −1.66527 | + | 1.66527i | −0.0865732 | + | 0.0865732i | ||||
\(371\) | 8.40266 | + | 8.40266i | 0.436244 | + | 0.436244i | ||||
\(372\) | 3.71443 | − | 3.71443i | 0.192584 | − | 0.192584i | ||||
\(373\) | − | 25.9516i | − | 1.34372i | −0.740676 | − | 0.671862i | \(-0.765495\pi\) | ||
0.740676 | − | 0.671862i | \(-0.234505\pi\) | |||||||
\(374\) | 25.0223 | + | 30.0128i | 1.29387 | + | 1.55193i | ||||
\(375\) | −7.27725 | + | 7.27725i | −0.375795 | + | 0.375795i | ||||
\(376\) | −9.00734 | −0.464518 | ||||||||
\(377\) | 0.0108091 | − | 0.888376i | 0.000556698 | − | 0.0457537i | ||||
\(378\) | −1.51357 | −0.0778497 | ||||||||
\(379\) | −14.4270 | − | 14.4270i | −0.741066 | − | 0.741066i | 0.231717 | − | 0.972783i | \(-0.425566\pi\) |
−0.972783 | + | 0.231717i | \(0.925566\pi\) | |||||||
\(380\) | − | 1.75593i | − | 0.0900771i | ||||||
\(381\) | 4.89459 | 0.250757 | ||||||||
\(382\) | 14.7141 | − | 14.7141i | 0.752837 | − | 0.752837i | ||||
\(383\) | 3.27449 | + | 3.27449i | 0.167319 | + | 0.167319i | 0.785800 | − | 0.618481i | \(-0.212252\pi\) |
−0.618481 | + | 0.785800i | \(0.712252\pi\) | |||||||
\(384\) | 9.64924 | + | 9.64924i | 0.492411 | + | 0.492411i | ||||
\(385\) | 3.79494 | + | 0.344124i | 0.193408 | + | 0.0175382i | ||||
\(386\) | −32.4783 | −1.65310 | ||||||||
\(387\) | −4.52405 | −0.229970 | ||||||||
\(388\) | −5.49969 | + | 5.49969i | −0.279204 | + | 0.279204i | ||||
\(389\) | − | 34.6092i | − | 1.75475i | −0.479802 | − | 0.877377i | \(-0.659291\pi\) | ||
0.479802 | − | 0.877377i | \(-0.340709\pi\) | |||||||
\(390\) | −6.87883 | − | 0.0836968i | −0.348323 | − | 0.00423815i | ||||
\(391\) | − | 28.0825i | − | 1.42019i | ||||||
\(392\) | −10.1459 | + | 10.1459i | −0.512446 | + | 0.512446i | ||||
\(393\) | 1.84165i | 0.0928991i | ||||||||
\(394\) | 2.99901i | 0.151088i | ||||||||
\(395\) | −9.64571 | + | 9.64571i | −0.485328 | + | 0.485328i | ||||
\(396\) | 1.69636 | + | 0.153826i | 0.0852455 | + | 0.00773003i | ||||
\(397\) | −18.8071 | + | 18.8071i | −0.943899 | + | 0.943899i | −0.998508 | − | 0.0546085i | \(-0.982609\pi\) |
0.0546085 | + | 0.998508i | \(0.482609\pi\) | |||||||
\(398\) | 5.92739 | + | 5.92739i | 0.297113 | + | 0.297113i | ||||
\(399\) | 2.71227 | 0.135783 | ||||||||
\(400\) | − | 16.9181i | − | 0.845905i | ||||||
\(401\) | −10.3747 | + | 10.3747i | −0.518086 | + | 0.518086i | −0.916992 | − | 0.398906i | \(-0.869390\pi\) |
0.398906 | + | 0.916992i | \(0.369390\pi\) | |||||||
\(402\) | 14.7043 | 0.733383 | ||||||||
\(403\) | 25.7581 | + | 26.3926i | 1.28310 | + | 1.31471i | ||||
\(404\) | 1.17620i | 0.0585183i | ||||||||
\(405\) | 0.850971 | + | 0.850971i | 0.0422851 | + | 0.0422851i | ||||
\(406\) | 0.372958i | 0.0185096i | ||||||||
\(407\) | 2.62146 | + | 3.14430i | 0.129941 | + | 0.155857i | ||||
\(408\) | −12.3833 | − | 12.3833i | −0.613064 | − | 0.613064i | ||||
\(409\) | 12.5400 | − | 12.5400i | 0.620065 | − | 0.620065i | −0.325483 | − | 0.945548i | \(-0.605527\pi\) |
0.945548 | + | 0.325483i | \(0.105527\pi\) | |||||||
\(410\) | −5.31841 | + | 5.31841i | −0.262658 | + | 0.262658i | ||||
\(411\) | −12.4192 | + | 12.4192i | −0.612594 | + | 0.612594i | ||||
\(412\) | 5.87052 | 0.289220 | ||||||||
\(413\) | 8.47465 | 0.417010 | ||||||||
\(414\) | −4.23648 | − | 4.23648i | −0.208212 | − | 0.208212i | ||||
\(415\) | 4.44777 | 0.218333 | ||||||||
\(416\) | 7.32494 | − | 7.14883i | 0.359135 | − | 0.350500i | ||||
\(417\) | − | 11.7143i | − | 0.573651i | ||||||
\(418\) | −14.8778 | − | 1.34912i | −0.727698 | − | 0.0659874i | ||||
\(419\) | −0.0491403 | −0.00240066 | −0.00120033 | − | 0.999999i | \(-0.500382\pi\) | ||||
−0.00120033 | + | 0.999999i | \(0.500382\pi\) | |||||||
\(420\) | 0.590049 | 0.0287914 | ||||||||
\(421\) | −7.93330 | − | 7.93330i | −0.386646 | − | 0.386646i | 0.486844 | − | 0.873489i | \(-0.338148\pi\) |
−0.873489 | + | 0.486844i | \(0.838148\pi\) | |||||||
\(422\) | 2.08298 | + | 2.08298i | 0.101398 | + | 0.101398i | ||||
\(423\) | 2.70266 | − | 2.70266i | 0.131408 | − | 0.131408i | ||||
\(424\) | 20.7419 | + | 20.7419i | 1.00732 | + | 1.00732i | ||||
\(425\) | 26.3935i | 1.28027i | ||||||||
\(426\) | 5.42542 | 0.262862 | ||||||||
\(427\) | −2.67523 | + | 2.67523i | −0.129464 | + | 0.129464i | ||||
\(428\) | 10.0165 | 0.484164 | ||||||||
\(429\) | −1.22475 | + | 11.8954i | −0.0591317 | + | 0.574314i | ||||
\(430\) | 8.63182 | 0.416263 | ||||||||
\(431\) | −4.16310 | + | 4.16310i | −0.200530 | + | 0.200530i | −0.800227 | − | 0.599697i | \(-0.795288\pi\) |
0.599697 | + | 0.800227i | \(0.295288\pi\) | |||||||
\(432\) | −4.76339 | −0.229179 | ||||||||
\(433\) | 29.3722i | 1.41154i | 0.708442 | + | 0.705769i | \(0.249398\pi\) | ||||
−0.708442 | + | 0.705769i | \(0.750602\pi\) | |||||||
\(434\) | −10.9470 | − | 10.9470i | −0.525471 | − | 0.525471i | ||||
\(435\) | 0.209687 | − | 0.209687i | 0.0100537 | − | 0.0100537i | ||||
\(436\) | 6.66445 | + | 6.66445i | 0.319169 | + | 0.319169i | ||||
\(437\) | 7.59163 | + | 7.59163i | 0.363157 | + | 0.363157i | ||||
\(438\) | 13.2059 | 0.631004 | ||||||||
\(439\) | −11.4725 | −0.547551 | −0.273776 | − | 0.961794i | \(-0.588273\pi\) | ||||
−0.273776 | + | 0.961794i | \(0.588273\pi\) | |||||||
\(440\) | 9.36780 | + | 0.849468i | 0.446592 | + | 0.0404968i | ||||
\(441\) | − | 6.08859i | − | 0.289933i | ||||||
\(442\) | −30.4007 | + | 29.6698i | −1.44601 | + | 1.41125i | ||||
\(443\) | 22.7420 | 1.08051 | 0.540253 | − | 0.841502i | \(-0.318328\pi\) | ||||
0.540253 | + | 0.841502i | \(0.318328\pi\) | |||||||
\(444\) | 0.448239 | + | 0.448239i | 0.0212725 | + | 0.0212725i | ||||
\(445\) | −9.17756 | −0.435058 | ||||||||
\(446\) | 4.73116 | 0.224027 | ||||||||
\(447\) | −13.0754 | + | 13.0754i | −0.618444 | + | 0.618444i | ||||
\(448\) | 3.39295 | − | 3.39295i | 0.160302 | − | 0.160302i | ||||
\(449\) | −5.03844 | + | 5.03844i | −0.237779 | + | 0.237779i | −0.815930 | − | 0.578151i | \(-0.803774\pi\) |
0.578151 | + | 0.815930i | \(0.303774\pi\) | |||||||
\(450\) | 3.98168 | + | 3.98168i | 0.187698 | + | 0.187698i | ||||
\(451\) | 8.37224 | + | 10.0420i | 0.394233 | + | 0.472861i | ||||
\(452\) | 9.49053i | 0.446397i | ||||||||
\(453\) | −9.57308 | − | 9.57308i | −0.449783 | − | 0.449783i | ||||
\(454\) | 46.1236i | 2.16469i | ||||||||
\(455\) | −0.0503988 | + | 4.14216i | −0.00236273 | + | 0.194187i | ||||
\(456\) | 6.69523 | 0.313533 | ||||||||
\(457\) | 24.1395 | − | 24.1395i | 1.12920 | − | 1.12920i | 0.138892 | − | 0.990308i | \(-0.455646\pi\) |
0.990308 | − | 0.138892i | \(-0.0443541\pi\) | |||||||
\(458\) | − | 17.3908i | − | 0.812619i | ||||||
\(459\) | 7.43124 | 0.346860 | ||||||||
\(460\) | 1.65154 | + | 1.65154i | 0.0770036 | + | 0.0770036i | ||||
\(461\) | 19.5166 | − | 19.5166i | 0.908977 | − | 0.908977i | −0.0872123 | − | 0.996190i | \(-0.527796\pi\) |
0.996190 | + | 0.0872123i | \(0.0277959\pi\) | |||||||
\(462\) | 0.453347 | − | 4.99944i | 0.0210916 | − | 0.232595i | ||||
\(463\) | 1.92897 | − | 1.92897i | 0.0896469 | − | 0.0896469i | −0.660861 | − | 0.750508i | \(-0.729809\pi\) |
0.750508 | + | 0.660861i | \(0.229809\pi\) | |||||||
\(464\) | 1.17374i | 0.0544897i | ||||||||
\(465\) | 12.3094i | 0.570833i | ||||||||
\(466\) | 22.5370 | − | 22.5370i | 1.04401 | − | 1.04401i | ||||
\(467\) | − | 31.1406i | − | 1.44102i | −0.693447 | − | 0.720508i | \(-0.743909\pi\) | ||
0.693447 | − | 0.720508i | \(-0.256091\pi\) | |||||||
\(468\) | −0.0225286 | + | 1.85157i | −0.00104139 | + | 0.0855889i | ||||
\(469\) | − | 8.85432i | − | 0.408855i | ||||||
\(470\) | −5.15664 | + | 5.15664i | −0.237858 | + | 0.237858i | ||||
\(471\) | −8.15572 | −0.375796 | ||||||||
\(472\) | 20.9196 | 0.962904 | ||||||||
\(473\) | 1.35505 | − | 14.9433i | 0.0623052 | − | 0.687092i | ||||
\(474\) | 12.7072 | + | 12.7072i | 0.583661 | + | 0.583661i | ||||
\(475\) | −7.13505 | − | 7.13505i | −0.327378 | − | 0.327378i | ||||
\(476\) | 2.57635 | − | 2.57635i | 0.118087 | − | 0.118087i | ||||
\(477\) | −12.4473 | −0.569922 | ||||||||
\(478\) | − | 24.2437i | − | 1.10888i | ||||||
\(479\) | −12.5135 | − | 12.5135i | −0.571756 | − | 0.571756i | 0.360863 | − | 0.932619i | \(-0.382482\pi\) |
−0.932619 | + | 0.360863i | \(0.882482\pi\) | |||||||
\(480\) | 3.41631 | 0.155932 | ||||||||
\(481\) | −3.18494 | + | 3.10836i | −0.145221 | + | 0.141729i | ||||
\(482\) | 20.0200 | 0.911887 | ||||||||
\(483\) | −2.55104 | + | 2.55104i | −0.116076 | + | 0.116076i | ||||
\(484\) | −1.01619 | + | 5.55714i | −0.0461906 | + | 0.252597i | ||||
\(485\) | − | 18.2256i | − | 0.827582i | ||||||
\(486\) | 1.12106 | − | 1.12106i | 0.0508525 | − | 0.0508525i | ||||
\(487\) | −11.2499 | − | 11.2499i | −0.509781 | − | 0.509781i | 0.404678 | − | 0.914459i | \(-0.367384\pi\) |
−0.914459 | + | 0.404678i | \(0.867384\pi\) | |||||||
\(488\) | −6.60380 | + | 6.60380i | −0.298940 | + | 0.298940i | ||||
\(489\) | −5.54165 | + | 5.54165i | −0.250602 | + | 0.250602i | ||||
\(490\) | 11.6169i | 0.524800i | ||||||||
\(491\) | 2.39305 | 0.107997 | 0.0539985 | − | 0.998541i | \(-0.482803\pi\) | ||||
0.0539985 | + | 0.998541i | \(0.482803\pi\) | |||||||
\(492\) | 1.43155 | + | 1.43155i | 0.0645394 | + | 0.0645394i | ||||
\(493\) | − | 1.83113i | − | 0.0824698i | ||||||
\(494\) | 0.197585 | − | 16.2391i | 0.00888979 | − | 0.730630i | ||||
\(495\) | −3.06570 | + | 2.55593i | −0.137793 | + | 0.114881i | ||||
\(496\) | −34.4514 | − | 34.4514i | −1.54691 | − | 1.54691i | ||||
\(497\) | − | 3.26697i | − | 0.146543i | ||||||
\(498\) | − | 5.85947i | − | 0.262569i | ||||||
\(499\) | 12.0345 | + | 12.0345i | 0.538739 | + | 0.538739i | 0.923158 | − | 0.384420i | \(-0.125598\pi\) |
−0.384420 | + | 0.923158i | \(0.625598\pi\) | |||||||
\(500\) | −3.73739 | − | 3.73739i | −0.167141 | − | 0.167141i | ||||
\(501\) | 0.229296 | + | 0.229296i | 0.0102442 | + | 0.0102442i | ||||
\(502\) | −25.8983 | − | 25.8983i | −1.15590 | − | 1.15590i | ||||
\(503\) | − | 4.93436i | − | 0.220012i | −0.993931 | − | 0.110006i | \(-0.964913\pi\) | ||
0.993931 | − | 0.110006i | \(-0.0350870\pi\) | |||||||
\(504\) | 2.24982i | 0.100215i | ||||||||
\(505\) | −1.94893 | − | 1.94893i | −0.0867262 | − | 0.0867262i | ||||
\(506\) | 15.2623 | − | 12.7245i | 0.678492 | − | 0.565672i | ||||
\(507\) | −12.9962 | − | 0.316303i | −0.577179 | − | 0.0140475i | ||||
\(508\) | 2.51372i | 0.111528i | ||||||||
\(509\) | −14.6289 | − | 14.6289i | −0.648413 | − | 0.648413i | 0.304197 | − | 0.952609i | \(-0.401612\pi\) |
−0.952609 | + | 0.304197i | \(0.901612\pi\) | |||||||
\(510\) | −14.1787 | −0.627843 | ||||||||
\(511\) | − | 7.95208i | − | 0.351779i | ||||||
\(512\) | 6.31370 | − | 6.31370i | 0.279029 | − | 0.279029i | ||||
\(513\) | −2.00891 | + | 2.00891i | −0.0886956 | + | 0.0886956i | ||||
\(514\) | −12.6306 | − | 12.6306i | −0.557113 | − | 0.557113i | ||||
\(515\) | −9.72726 | + | 9.72726i | −0.428634 | + | 0.428634i | ||||
\(516\) | − | 2.32342i | − | 0.102283i | ||||||
\(517\) | 8.11758 | + | 9.73659i | 0.357011 | + | 0.428215i | ||||
\(518\) | 1.32103 | − | 1.32103i | 0.0580426 | − | 0.0580426i | ||||
\(519\) | 10.9234 | 0.479484 | ||||||||
\(520\) | −0.124409 | + | 10.2249i | −0.00545571 | + | 0.448391i | ||||
\(521\) | 5.03014 | 0.220375 | 0.110187 | − | 0.993911i | \(-0.464855\pi\) | ||||
0.110187 | + | 0.993911i | \(0.464855\pi\) | |||||||
\(522\) | −0.276241 | − | 0.276241i | −0.0120907 | − | 0.0120907i | ||||
\(523\) | − | 28.7479i | − | 1.25706i | −0.777786 | − | 0.628529i | \(-0.783657\pi\) | ||
0.777786 | − | 0.628529i | \(-0.216343\pi\) | |||||||
\(524\) | −0.945820 | −0.0413183 | ||||||||
\(525\) | 2.39761 | − | 2.39761i | 0.104640 | − | 0.104640i | ||||
\(526\) | −7.38374 | − | 7.38374i | −0.321947 | − | 0.321947i | ||||
\(527\) | 53.7467 | + | 53.7467i | 2.34124 | + | 2.34124i | ||||
\(528\) | 1.42674 | − | 15.7338i | 0.0620907 | − | 0.684726i | ||||
\(529\) | 8.71933 | 0.379101 | ||||||||
\(530\) | 23.7492 | 1.03160 | ||||||||
\(531\) | −6.27696 | + | 6.27696i | −0.272397 | + | 0.272397i | ||||
\(532\) | 1.39295i | 0.0603918i | ||||||||
\(533\) | −10.1718 | + | 9.92726i | −0.440590 | + | 0.429998i | ||||
\(534\) | 12.0905i | 0.523206i | ||||||||
\(535\) | −16.5969 | + | 16.5969i | −0.717548 | + | 0.717548i | ||||
\(536\) | − | 21.8569i | − | 0.944073i | ||||||
\(537\) | 10.3266i | 0.445626i | ||||||||
\(538\) | −9.92202 | + | 9.92202i | −0.427769 | + | 0.427769i | ||||
\(539\) | 20.1110 | + | 1.82366i | 0.866244 | + | 0.0785507i | ||||
\(540\) | −0.437034 | + | 0.437034i | −0.0188070 | + | 0.0188070i | ||||
\(541\) | 4.07167 | + | 4.07167i | 0.175055 | + | 0.175055i | 0.789196 | − | 0.614141i | \(-0.210498\pi\) |
−0.614141 | + | 0.789196i | \(0.710498\pi\) | |||||||
\(542\) | 21.0840 | 0.905635 | ||||||||
\(543\) | − | 11.0278i | − | 0.473248i | ||||||
\(544\) | 14.9167 | − | 14.9167i | 0.639549 | − | 0.639549i | ||||
\(545\) | −22.0855 | −0.946041 | ||||||||
\(546\) | 5.45686 | + | 0.0663952i | 0.233532 | + | 0.00284145i | ||||
\(547\) | − | 31.7760i | − | 1.35864i | −0.733840 | − | 0.679322i | \(-0.762274\pi\) | ||
0.733840 | − | 0.679322i | \(-0.237726\pi\) | |||||||
\(548\) | −6.37815 | − | 6.37815i | −0.272461 | − | 0.272461i | ||||
\(549\) | − | 3.96296i | − | 0.169135i | ||||||
\(550\) | −14.3444 | + | 11.9592i | −0.611646 | + | 0.509941i | ||||
\(551\) | 0.495015 | + | 0.495015i | 0.0210883 | + | 0.0210883i | ||||
\(552\) | −6.29722 | + | 6.29722i | −0.268028 | + | 0.268028i | ||||
\(553\) | 7.65177 | − | 7.65177i | 0.325386 | − | 0.325386i | ||||
\(554\) | −12.9170 | + | 12.9170i | −0.548792 | + | 0.548792i | ||||
\(555\) | −1.48543 | −0.0630532 | ||||||||
\(556\) | 6.01612 | 0.255140 | ||||||||
\(557\) | −2.45042 | − | 2.45042i | −0.103828 | − | 0.103828i | 0.653285 | − | 0.757112i | \(-0.273391\pi\) |
−0.757112 | + | 0.653285i | \(0.773391\pi\) | |||||||
\(558\) | 16.2163 | 0.686490 | ||||||||
\(559\) | 16.3105 | + | 0.198454i | 0.689860 | + | 0.00839372i | ||||
\(560\) | − | 5.47272i | − | 0.231264i | ||||||
\(561\) | −2.22581 | + | 24.5459i | −0.0939739 | + | 1.03633i | ||||
\(562\) | 34.2331 | 1.44404 | ||||||||
\(563\) | 17.9163 | 0.755083 | 0.377541 | − | 0.925993i | \(-0.376770\pi\) | ||||
0.377541 | + | 0.925993i | \(0.376770\pi\) | |||||||
\(564\) | 1.38801 | + | 1.38801i | 0.0584458 | + | 0.0584458i | ||||
\(565\) | −15.7255 | − | 15.7255i | −0.661576 | − | 0.661576i | ||||
\(566\) | −1.36491 | + | 1.36491i | −0.0573716 | + | 0.0573716i | ||||
\(567\) | −0.675060 | − | 0.675060i | −0.0283499 | − | 0.0283499i | ||||
\(568\) | − | 8.06449i | − | 0.338379i | ||||||
\(569\) | −35.6567 | −1.49481 | −0.747403 | − | 0.664371i | \(-0.768699\pi\) | ||||
−0.747403 | + | 0.664371i | \(0.768699\pi\) | |||||||
\(570\) | 3.83298 | − | 3.83298i | 0.160546 | − | 0.160546i | ||||
\(571\) | −33.2072 | −1.38968 | −0.694838 | − | 0.719166i | \(-0.744524\pi\) | ||||
−0.694838 | + | 0.719166i | \(0.744524\pi\) | |||||||
\(572\) | −6.10913 | − | 0.628999i | −0.255435 | − | 0.0262998i | ||||
\(573\) | 13.1251 | 0.548308 | ||||||||
\(574\) | 4.21900 | − | 4.21900i | 0.176098 | − | 0.176098i | ||||
\(575\) | 13.4218 | 0.559727 | ||||||||
\(576\) | 5.02615i | 0.209423i | ||||||||
\(577\) | −7.21344 | − | 7.21344i | −0.300300 | − | 0.300300i | 0.540831 | − | 0.841131i | \(-0.318110\pi\) |
−0.841131 | + | 0.540831i | \(0.818110\pi\) | |||||||
\(578\) | −42.8508 | + | 42.8508i | −1.78236 | + | 1.78236i | ||||
\(579\) | −14.4855 | − | 14.4855i | −0.601995 | − | 0.601995i | ||||
\(580\) | 0.107689 | + | 0.107689i | 0.00447156 | + | 0.00447156i | ||||
\(581\) | −3.52834 | −0.146380 | ||||||||
\(582\) | −24.0103 | −0.995259 | ||||||||
\(583\) | 3.72822 | − | 41.1142i | 0.154407 | − | 1.70278i | ||||
\(584\) | − | 19.6297i | − | 0.812282i | ||||||
\(585\) | −3.03066 | − | 3.10532i | −0.125302 | − | 0.128389i | ||||
\(586\) | 19.1984 | 0.793079 | ||||||||
\(587\) | 0.242345 | + | 0.242345i | 0.0100026 | + | 0.0100026i | 0.712090 | − | 0.702088i | \(-0.247749\pi\) |
−0.702088 | + | 0.712090i | \(0.747749\pi\) | |||||||
\(588\) | 3.12692 | 0.128952 | ||||||||
\(589\) | −29.0591 | −1.19736 | ||||||||
\(590\) | 11.9764 | − | 11.9764i | 0.493059 | − | 0.493059i | ||||
\(591\) | −1.33757 | + | 1.33757i | −0.0550203 | + | 0.0550203i | ||||
\(592\) | 4.15743 | − | 4.15743i | 0.170869 | − | 0.170869i | ||||
\(593\) | 13.8714 | + | 13.8714i | 0.569629 | + | 0.569629i | 0.932025 | − | 0.362395i | \(-0.118041\pi\) |
−0.362395 | + | 0.932025i | \(0.618041\pi\) | |||||||
\(594\) | 3.36717 | + | 4.03874i | 0.138157 | + | 0.165712i | ||||
\(595\) | 8.53784i | 0.350017i | ||||||||
\(596\) | −6.71514 | − | 6.71514i | −0.275063 | − | 0.275063i | ||||
\(597\) | 5.28728i | 0.216394i | ||||||||
\(598\) | 15.0879 | + | 15.4595i | 0.616989 | + | 0.632188i | ||||
\(599\) | −33.2979 | −1.36051 | −0.680257 | − | 0.732973i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732973i | \(0.738132\pi\) | |||||||
\(600\) | 5.91849 | − | 5.91849i | 0.241621 | − | 0.241621i | ||||
\(601\) | 25.1042i | 1.02402i | 0.858978 | + | 0.512012i | \(0.171100\pi\) | ||||
−0.858978 | + | 0.512012i | \(0.828900\pi\) | |||||||
\(602\) | −6.84747 | −0.279082 | ||||||||
\(603\) | 6.55818 | + | 6.55818i | 0.267070 | + | 0.267070i | ||||
\(604\) | 4.91646 | − | 4.91646i | 0.200048 | − | 0.200048i | ||||
\(605\) | −7.52419 | − | 10.8918i | −0.305902 | − | 0.442814i | ||||
\(606\) | −2.56751 | + | 2.56751i | −0.104298 | + | 0.104298i | ||||
\(607\) | − | 2.79022i | − | 0.113251i | −0.998395 | − | 0.0566257i | \(-0.981966\pi\) | ||
0.998395 | − | 0.0566257i | \(-0.0180342\pi\) | |||||||
\(608\) | 8.06498i | 0.327078i | ||||||||
\(609\) | −0.166341 | + | 0.166341i | −0.00674048 | + | 0.00674048i | ||||
\(610\) | 7.56127i | 0.306147i | ||||||||
\(611\) | −9.86242 | + | 9.62531i | −0.398991 | + | 0.389398i | ||||
\(612\) | 3.81647i | 0.154272i | ||||||||
\(613\) | −32.3984 | + | 32.3984i | −1.30856 | + | 1.30856i | −0.386102 | + | 0.922456i | \(0.626179\pi\) |
−0.922456 | + | 0.386102i | \(0.873821\pi\) | |||||||
\(614\) | −7.14629 | −0.288401 | ||||||||
\(615\) | −4.74407 | −0.191299 | ||||||||
\(616\) | −7.43130 | − | 0.673868i | −0.299416 | − | 0.0271509i | ||||
\(617\) | 10.8226 | + | 10.8226i | 0.435700 | + | 0.435700i | 0.890562 | − | 0.454862i | \(-0.150311\pi\) |
−0.454862 | + | 0.890562i | \(0.650311\pi\) | |||||||
\(618\) | 12.8146 | + | 12.8146i | 0.515481 | + | 0.515481i | ||||
\(619\) | 9.07149 | − | 9.07149i | 0.364614 | − | 0.364614i | −0.500895 | − | 0.865508i | \(-0.666996\pi\) |
0.865508 | + | 0.500895i | \(0.166996\pi\) | |||||||
\(620\) | −6.32174 | −0.253887 | ||||||||
\(621\) | − | 3.77898i | − | 0.151645i | ||||||
\(622\) | −7.39315 | − | 7.39315i | −0.296438 | − | 0.296438i | ||||
\(623\) | 7.28039 | 0.291683 | ||||||||
\(624\) | 17.1734 | + | 0.208953i | 0.687485 | + | 0.00836483i | ||||
\(625\) | −5.37304 | −0.214921 | ||||||||
\(626\) | 27.3960 | − | 27.3960i | 1.09496 | − | 1.09496i | ||||
\(627\) | −6.03387 | − | 7.23729i | −0.240970 | − | 0.289030i | ||||
\(628\) | − | 4.18854i | − | 0.167141i | ||||||
\(629\) | −6.48590 | + | 6.48590i | −0.258610 | + | 0.258610i | ||||
\(630\) | 1.28801 | + | 1.28801i | 0.0513154 | + | 0.0513154i | ||||
\(631\) | 0.717627 | − | 0.717627i | 0.0285683 | − | 0.0285683i | −0.692678 | − | 0.721247i | \(-0.743569\pi\) |
0.721247 | + | 0.692678i | \(0.243569\pi\) | |||||||
\(632\) | 18.8884 | − | 18.8884i | 0.751338 | − | 0.751338i | ||||
\(633\) | 1.85803i | 0.0738502i | ||||||||
\(634\) | −48.2742 | −1.91722 | ||||||||
\(635\) | −4.16515 | − | 4.16515i | −0.165289 | − | 0.165289i | ||||
\(636\) | − | 6.39256i | − | 0.253482i | ||||||
\(637\) | −0.267085 | + | 21.9511i | −0.0105823 | + | 0.869734i | ||||
\(638\) | 0.995183 | − | 0.829703i | 0.0393997 | − | 0.0328483i | ||||
\(639\) | 2.41976 | + | 2.41976i | 0.0957243 | + | 0.0957243i | ||||
\(640\) | − | 16.4224i | − | 0.649154i | ||||||
\(641\) | − | 3.01763i | − | 0.119189i | −0.998223 | − | 0.0595946i | \(-0.981019\pi\) | ||
0.998223 | − | 0.0595946i | \(-0.0189808\pi\) | |||||||
\(642\) | 21.8647 | + | 21.8647i | 0.862931 | + | 0.862931i | ||||
\(643\) | −7.27088 | − | 7.27088i | −0.286736 | − | 0.286736i | 0.549052 | − | 0.835788i | \(-0.314989\pi\) |
−0.835788 | + | 0.549052i | \(0.814989\pi\) | |||||||
\(644\) | −1.31014 | − | 1.31014i | −0.0516267 | − | 0.0516267i | ||||
\(645\) | 3.84983 | + | 3.84983i | 0.151587 | + | 0.151587i | ||||
\(646\) | − | 33.4721i | − | 1.31694i | ||||||
\(647\) | 6.96565i | 0.273848i | 0.990582 | + | 0.136924i | \(0.0437216\pi\) | ||||
−0.990582 | + | 0.136924i | \(0.956278\pi\) | |||||||
\(648\) | −1.66638 | − | 1.66638i | −0.0654617 | − | 0.0654617i | ||||
\(649\) | −18.8532 | − | 22.6133i | −0.740051 | − | 0.887651i | ||||
\(650\) | −14.1804 | − | 14.5298i | −0.556202 | − | 0.569904i | ||||
\(651\) | − | 9.76480i | − | 0.382713i | ||||||
\(652\) | −2.84603 | − | 2.84603i | −0.111459 | − | 0.111459i | ||||
\(653\) | −3.51009 | −0.137360 | −0.0686802 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686802 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(654\) | 29.0954i | 1.13772i | ||||||||
\(655\) | 1.56719 | − | 1.56719i | 0.0612353 | − | 0.0612353i | ||||
\(656\) | 13.2777 | − | 13.2777i | 0.518407 | − | 0.518407i | ||||
\(657\) | 5.88991 | + | 5.88991i | 0.229787 | + | 0.229787i | ||||
\(658\) | 4.09067 | − | 4.09067i | 0.159471 | − | 0.159471i | ||||
\(659\) | − | 38.2738i | − | 1.49094i | −0.666541 | − | 0.745468i | \(-0.732226\pi\) | ||
0.666541 | − | 0.745468i | \(-0.267774\pi\) | |||||||
\(660\) | −1.31265 | − | 1.57446i | −0.0510950 | − | 0.0612857i | ||||
\(661\) | −5.90612 | + | 5.90612i | −0.229722 | + | 0.229722i | −0.812576 | − | 0.582855i | \(-0.801936\pi\) |
0.582855 | + | 0.812576i | \(0.301936\pi\) | |||||||
\(662\) | −13.1052 | −0.509349 | ||||||||
\(663\) | −26.7917 | − | 0.325983i | −1.04050 | − | 0.0126601i | ||||
\(664\) | −8.70969 | −0.338001 | ||||||||
\(665\) | −2.30806 | − | 2.30806i | −0.0895029 | − | 0.0895029i | ||||
\(666\) | 1.95690i | 0.0758285i | ||||||||
\(667\) | −0.931175 | −0.0360553 | ||||||||
\(668\) | −0.117760 | + | 0.117760i | −0.00455627 | + | 0.00455627i | ||||
\(669\) | 2.11012 | + | 2.11012i | 0.0815819 | + | 0.0815819i | ||||
\(670\) | −12.5129 | − | 12.5129i | −0.483416 | − | 0.483416i | ||||
\(671\) | 13.0899 | + | 1.18699i | 0.505331 | + | 0.0458232i | ||||
\(672\) | −2.71010 | −0.104544 | ||||||||
\(673\) | −25.6800 | −0.989890 | −0.494945 | − | 0.868924i | \(-0.664812\pi\) | ||||
−0.494945 | + | 0.868924i | \(0.664812\pi\) | |||||||
\(674\) | −5.12739 | + | 5.12739i | −0.197500 | + | 0.197500i | ||||
\(675\) | 3.55170i | 0.136705i | ||||||||
\(676\) | 0.162444 | − | 6.67445i | 0.00624785 | − | 0.256710i | ||||
\(677\) | − | 16.6812i | − | 0.641111i | −0.947230 | − | 0.320555i | \(-0.896130\pi\) | ||
0.947230 | − | 0.320555i | \(-0.103870\pi\) | |||||||
\(678\) | −20.7167 | + | 20.7167i | −0.795619 | + | 0.795619i | ||||
\(679\) | 14.4580i | 0.554848i | ||||||||
\(680\) | 21.0756i | 0.808213i | ||||||||
\(681\) | −20.5713 | + | 20.5713i | −0.788295 | + | 0.788295i | ||||
\(682\) | −4.85713 | + | 53.5636i | −0.185989 | + | 2.05106i | ||||
\(683\) | −13.1925 | + | 13.1925i | −0.504796 | + | 0.504796i | −0.912925 | − | 0.408128i | \(-0.866182\pi\) |
0.408128 | + | 0.912925i | \(0.366182\pi\) | |||||||
\(684\) | −1.03172 | − | 1.03172i | −0.0394488 | − | 0.0394488i | ||||
\(685\) | 21.1368 | 0.807594 | ||||||||
\(686\) | − | 19.8105i | − | 0.756369i | ||||||
\(687\) | 7.75638 | − | 7.75638i | 0.295924 | − | 0.295924i | ||||
\(688\) | −21.5498 | −0.821578 | ||||||||
\(689\) | 44.8760 | + | 0.546019i | 1.70964 | + | 0.0208017i | ||||
\(690\) | 7.21024i | 0.274489i | ||||||||
\(691\) | 26.0272 | + | 26.0272i | 0.990121 | + | 0.990121i | 0.999952 | − | 0.00983101i | \(-0.00312936\pi\) |
−0.00983101 | + | 0.999952i | \(0.503129\pi\) | |||||||
\(692\) | 5.60995i | 0.213258i | ||||||||
\(693\) | 2.43197 | − | 2.02758i | 0.0923828 | − | 0.0770213i | ||||
\(694\) | −8.50343 | − | 8.50343i | −0.322786 | − | 0.322786i | ||||
\(695\) | −9.96852 | + | 9.96852i | −0.378127 | + | 0.378127i | ||||
\(696\) | −0.410612 | + | 0.410612i | −0.0155642 | + | 0.0155642i | ||||
\(697\) | −20.7142 | + | 20.7142i | −0.784605 | + | 0.784605i | ||||
\(698\) | −13.6615 | −0.517096 | ||||||||
\(699\) | 20.1032 | 0.760374 | ||||||||
\(700\) | 1.23134 | + | 1.23134i | 0.0465404 | + | 0.0465404i | ||||
\(701\) | −25.5094 | −0.963478 | −0.481739 | − | 0.876315i | \(-0.659995\pi\) | ||||
−0.481739 | + | 0.876315i | \(0.659995\pi\) | |||||||
\(702\) | −4.09093 | + | 3.99258i | −0.154402 | + | 0.150690i | ||||
\(703\) | − | 3.50671i | − | 0.132258i | ||||||
\(704\) | −16.6017 | − | 1.50544i | −0.625701 | − | 0.0567384i | ||||
\(705\) | −4.59977 | −0.173238 | ||||||||
\(706\) | 22.1743 | 0.834542 | ||||||||
\(707\) | 1.54605 | + | 1.54605i | 0.0581452 | + | 0.0581452i | ||||
\(708\) | −3.22367 | − | 3.22367i | −0.121153 | − | 0.121153i | ||||
\(709\) | −21.5724 | + | 21.5724i | −0.810169 | + | 0.810169i | −0.984659 | − | 0.174490i | \(-0.944172\pi\) |
0.174490 | + | 0.984659i | \(0.444172\pi\) | |||||||
\(710\) | −4.61687 | − | 4.61687i | −0.173268 | − | 0.173268i | ||||
\(711\) | 11.3349i | 0.425094i | ||||||||
\(712\) | 17.9716 | 0.673515 | ||||||||
\(713\) | 27.3316 | − | 27.3316i | 1.02358 | − | 1.02358i | ||||
\(714\) | 11.2477 | 0.420935 | ||||||||
\(715\) | 11.1648 | − | 9.08039i | 0.417542 | − | 0.339587i | ||||
\(716\) | −5.30345 | −0.198199 | ||||||||
\(717\) | 10.8128 | − | 10.8128i | 0.403812 | − | 0.403812i | ||||
\(718\) | −3.92437 | −0.146456 | ||||||||
\(719\) | − | 17.3939i | − | 0.648682i | −0.945940 | − | 0.324341i | \(-0.894857\pi\) | ||
0.945940 | − | 0.324341i | \(-0.105143\pi\) | |||||||
\(720\) | 4.05350 | + | 4.05350i | 0.151065 | + | 0.151065i | ||||
\(721\) | 7.71646 | − | 7.71646i | 0.287376 | − | 0.287376i | ||||
\(722\) | −12.2516 | − | 12.2516i | −0.455958 | − | 0.455958i | ||||
\(723\) | 8.92902 | + | 8.92902i | 0.332074 | + | 0.332074i | ||||
\(724\) | 5.66356 | 0.210485 | ||||||||
\(725\) | 0.875171 | 0.0325030 | ||||||||
\(726\) | −14.3488 | + | 9.91233i | −0.532534 | + | 0.367881i | ||||
\(727\) | − | 52.6079i | − | 1.95112i | −0.219737 | − | 0.975559i | \(-0.570520\pi\) | ||
0.219737 | − | 0.975559i | \(-0.429480\pi\) | |||||||
\(728\) | 0.0986917 | − | 8.11123i | 0.00365776 | − | 0.300622i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.2379 | − | 11.2379i | −0.415932 | − | 0.415932i | ||||
\(731\) | 33.6193 | 1.24345 | ||||||||
\(732\) | 2.03526 | 0.0752254 | ||||||||
\(733\) | 24.6461 | − | 24.6461i | 0.910323 | − | 0.910323i | −0.0859740 | − | 0.996297i | \(-0.527400\pi\) |
0.996297 | + | 0.0859740i | \(0.0274002\pi\) | |||||||
\(734\) | −4.78722 | + | 4.78722i | −0.176700 | + | 0.176700i | ||||
\(735\) | −5.18121 | + | 5.18121i | −0.191112 | + | 0.191112i | ||||
\(736\) | −7.58554 | − | 7.58554i | −0.279607 | − | 0.279607i | ||||
\(737\) | −23.6264 | + | 19.6978i | −0.870291 | + | 0.725579i | ||||
\(738\) | 6.24982i | 0.230059i | ||||||||
\(739\) | 1.30403 | + | 1.30403i | 0.0479696 | + | 0.0479696i | 0.730685 | − | 0.682715i | \(-0.239201\pi\) |
−0.682715 | + | 0.730685i | \(0.739201\pi\) | |||||||
\(740\) | − | 0.762877i | − | 0.0280439i | ||||||
\(741\) | 7.33082 | − | 7.15457i | 0.269304 | − | 0.262830i | ||||
\(742\) | −18.8398 | −0.691632 | ||||||||
\(743\) | −20.7321 | + | 20.7321i | −0.760586 | + | 0.760586i | −0.976428 | − | 0.215842i | \(-0.930750\pi\) |
0.215842 | + | 0.976428i | \(0.430750\pi\) | |||||||
\(744\) | − | 24.1044i | − | 0.883709i | ||||||
\(745\) | 22.2535 | 0.815306 | ||||||||
\(746\) | 29.0935 | + | 29.0935i | 1.06519 | + | 1.06519i | ||||
\(747\) | 2.61335 | − | 2.61335i | 0.0956175 | − | 0.0956175i | ||||
\(748\) | −12.6061 | − | 1.14311i | −0.460924 | − | 0.0417964i | ||||
\(749\) | 13.1660 | − | 13.1660i | 0.481077 | − | 0.481077i | ||||
\(750\) | − | 16.3165i | − | 0.595795i | ||||||
\(751\) | 9.40675i | 0.343257i | 0.985162 | + | 0.171629i | \(0.0549029\pi\) | ||||
−0.985162 | + | 0.171629i | \(0.945097\pi\) | |||||||
\(752\) | 12.8738 | − | 12.8738i | 0.469460 | − | 0.469460i | ||||
\(753\) | − | 23.1015i | − | 0.841867i | ||||||
\(754\) | 0.983809 | + | 1.00804i | 0.0358282 | + | 0.0367108i | ||||
\(755\) | 16.2928i | 0.592957i | ||||||||
\(756\) | 0.346691 | − | 0.346691i | 0.0126090 | − | 0.0126090i | ||||
\(757\) | 40.3458 | 1.46639 | 0.733197 | − | 0.680017i | \(-0.238028\pi\) | ||||
0.733197 | + | 0.680017i | \(0.238028\pi\) | |||||||
\(758\) | 32.3472 | 1.17490 | ||||||||
\(759\) | 12.4822 | + | 1.13188i | 0.453076 | + | 0.0410848i | ||||
\(760\) | −5.69745 | − | 5.69745i | −0.206668 | − | 0.206668i | ||||
\(761\) | 21.5979 | + | 21.5979i | 0.782922 | + | 0.782922i | 0.980323 | − | 0.197401i | \(-0.0632501\pi\) |
−0.197401 | + | 0.980323i | \(0.563250\pi\) | |||||||
\(762\) | −5.48715 | + | 5.48715i | −0.198778 | + | 0.198778i | ||||
\(763\) | 17.5201 | 0.634269 | ||||||||
\(764\) | 6.74066i | 0.243869i | ||||||||
\(765\) | −6.32377 | − | 6.32377i | −0.228636 | − | 0.228636i | ||||
\(766\) | −7.34184 | −0.265271 | ||||||||
\(767\) | 22.9056 | − | 22.3549i | 0.827072 | − | 0.807188i | ||||
\(768\) | −11.5825 | −0.417949 | ||||||||
\(769\) | 15.9879 | − | 15.9879i | 0.576538 | − | 0.576538i | −0.357410 | − | 0.933948i | \(-0.616340\pi\) |
0.933948 | + | 0.357410i | \(0.116340\pi\) | |||||||
\(770\) | −4.64016 | + | 3.86859i | −0.167220 | + | 0.139414i | ||||
\(771\) | − | 11.2666i | − | 0.405758i | ||||||
\(772\) | 7.43932 | − | 7.43932i | 0.267747 | − | 0.267747i | ||||
\(773\) | −8.50452 | − | 8.50452i | −0.305886 | − | 0.305886i | 0.537425 | − | 0.843312i | \(-0.319397\pi\) |
−0.843312 | + | 0.537425i | \(0.819397\pi\) | |||||||
\(774\) | 5.07175 | − | 5.07175i | 0.182300 | − | 0.182300i | ||||
\(775\) | −25.6878 | + | 25.6878i | −0.922733 | + | 0.922733i | ||||
\(776\) | 35.6896i | 1.28118i | ||||||||
\(777\) | 1.17837 | 0.0422737 | ||||||||
\(778\) | 38.7991 | + | 38.7991i | 1.39102 | + | 1.39102i | ||||
\(779\) | − | 11.1995i | − | 0.401263i | ||||||
\(780\) | 1.59480 | − | 1.55646i | 0.0571032 | − | 0.0557303i | ||||
\(781\) | −8.71741 | + | 7.26787i | −0.311934 | + | 0.260065i | ||||
\(782\) | 31.4823 | + | 31.4823i | 1.12580 | + | 1.12580i | ||||
\(783\) | − | 0.246409i | − | 0.00880595i | ||||||
\(784\) | − | 29.0023i | − | 1.03580i | ||||||
\(785\) | 6.94028 | + | 6.94028i | 0.247709 | + | 0.247709i | ||||
\(786\) | −2.06461 | − | 2.06461i | −0.0736423 | − | 0.0736423i | ||||
\(787\) | −26.7297 | − | 26.7297i | −0.952810 | − | 0.952810i | 0.0461256 | − | 0.998936i | \(-0.485313\pi\) |
−0.998936 | + | 0.0461256i | \(0.985313\pi\) | |||||||
\(788\) | −0.686938 | − | 0.686938i | −0.0244712 | − | 0.0244712i | ||||
\(789\) | − | 6.58637i | − | 0.234481i | ||||||
\(790\) | − | 21.6269i | − | 0.769451i | ||||||
\(791\) | 12.4747 | + | 12.4747i | 0.443551 | + | 0.443551i | ||||
\(792\) | 6.00330 | − | 5.00506i | 0.213318 | − | 0.177847i | ||||
\(793\) | −0.173841 | + | 14.2876i | −0.00617328 | + | 0.507367i | ||||
\(794\) | − | 42.1679i | − | 1.49648i | ||||||
\(795\) | 10.5923 | + | 10.5923i | 0.375669 | + | 0.375669i | ||||
\(796\) | −2.71540 | −0.0962447 | ||||||||
\(797\) | − | 17.1251i | − | 0.606601i | −0.952895 | − | 0.303301i | \(-0.901911\pi\) | ||
0.952895 | − | 0.303301i | \(-0.0980887\pi\) | |||||||
\(798\) | −3.04063 | + | 3.04063i | −0.107637 | + | 0.107637i | ||||
\(799\) | −20.0841 | + | 20.0841i | −0.710525 | + | 0.710525i | ||||
\(800\) | 7.12932 | + | 7.12932i | 0.252060 | + | 0.252060i | ||||
\(801\) | −5.39241 | + | 5.39241i | −0.190531 | + | 0.190531i | ||||
\(802\) | − | 23.2613i | − | 0.821387i | ||||||
\(803\) | −21.2189 | + | 17.6906i | −0.748800 | + | 0.624289i | ||||
\(804\) | −3.36809 | + | 3.36809i | −0.118783 | + | 0.118783i | ||||
\(805\) | 4.34172 | 0.153025 | ||||||||
\(806\) | −58.4643 | − | 0.711353i | −2.05932 | − | 0.0250563i | ||||
\(807\) | −8.85053 | −0.311554 | ||||||||
\(808\) | 3.81642 | + | 3.81642i | 0.134261 | + | 0.134261i | ||||
\(809\) | − | 13.4600i | − | 0.473228i | −0.971604 | − | 0.236614i | \(-0.923962\pi\) | ||
0.971604 | − | 0.236614i | \(-0.0760377\pi\) | |||||||
\(810\) | −1.90799 | −0.0670398 | ||||||||
\(811\) | 7.51966 | − | 7.51966i | 0.264051 | − | 0.264051i | −0.562646 | − | 0.826698i | \(-0.690217\pi\) |
0.826698 | + | 0.562646i | \(0.190217\pi\) | |||||||
\(812\) | −0.0854280 | − | 0.0854280i | −0.00299794 | − | 0.00299794i | ||||
\(813\) | 9.40355 | + | 9.40355i | 0.329797 | + | 0.329797i | ||||
\(814\) | −6.46380 | − | 0.586135i | −0.226556 | − | 0.0205440i | ||||
\(815\) | 9.43156 | 0.330373 | ||||||||
\(816\) | 35.3979 | 1.23917 | ||||||||
\(817\) | −9.08841 | + | 9.08841i | −0.317963 | + | 0.317963i | ||||
\(818\) | 28.1164i | 0.983066i | ||||||||
\(819\) | 2.40417 | + | 2.46340i | 0.0840085 | + | 0.0860780i | ||||
\(820\) | − | 2.43642i | − | 0.0850835i | ||||||
\(821\) | −27.3995 | + | 27.3995i | −0.956249 | + | 0.956249i | −0.999082 | − | 0.0428337i | \(-0.986361\pi\) |
0.0428337 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(822\) | − | 27.8454i | − | 0.971221i | ||||||
\(823\) | − | 36.7296i | − | 1.28031i | −0.768244 | − | 0.640157i | \(-0.778869\pi\) | ||
0.768244 | − | 0.640157i | \(-0.221131\pi\) | |||||||
\(824\) | 19.0481 | − | 19.0481i | 0.663570 | − | 0.663570i | ||||
\(825\) | −11.7315 | − | 1.06381i | −0.408439 | − | 0.0370371i | ||||
\(826\) | −9.50063 | + | 9.50063i | −0.330569 | + | 0.330569i | ||||
\(827\) | 21.2708 | + | 21.2708i | 0.739658 | + | 0.739658i | 0.972512 | − | 0.232854i | \(-0.0748064\pi\) |
−0.232854 | + | 0.972512i | \(0.574806\pi\) | |||||||
\(828\) | 1.94077 | 0.0674466 | ||||||||
\(829\) | − | 27.5482i | − | 0.956790i | −0.878145 | − | 0.478395i | \(-0.841219\pi\) | ||
0.878145 | − | 0.478395i | \(-0.158781\pi\) | |||||||
\(830\) | −4.98624 | + | 4.98624i | −0.173075 | + | 0.173075i | ||||
\(831\) | −11.5221 | −0.399697 | ||||||||
\(832\) | 0.220480 | − | 18.1207i | 0.00764376 | − | 0.628222i | ||||
\(833\) | 45.2457i | 1.56767i | ||||||||
\(834\) | 13.1325 | + | 13.1325i | 0.454740 | + | 0.454740i | ||||
\(835\) | − | 0.390248i | − | 0.0135051i | ||||||
\(836\) | 3.71687 | − | 3.09882i | 0.128551 | − | 0.107175i | ||||
\(837\) | 7.23254 | + | 7.23254i | 0.249993 | + | 0.249993i | ||||
\(838\) | 0.0550895 | − | 0.0550895i | 0.00190303 | − | 0.00190303i | ||||
\(839\) | 3.05505 | − | 3.05505i | 0.105472 | − | 0.105472i | −0.652401 | − | 0.757874i | \(-0.726238\pi\) |
0.757874 | + | 0.652401i | \(0.226238\pi\) | |||||||
\(840\) | 1.91453 | − | 1.91453i | 0.0660575 | − | 0.0660575i | ||||
\(841\) | 28.9393 | 0.997906 | ||||||||
\(842\) | 17.7875 | 0.612997 | ||||||||
\(843\) | 15.2681 | + | 15.2681i | 0.525862 | + | 0.525862i | ||||
\(844\) | −0.954233 | −0.0328461 | ||||||||
\(845\) | 10.7902 | + | 11.3285i | 0.371194 | + | 0.389713i | ||||
\(846\) | 6.05972i | 0.208337i | ||||||||
\(847\) | 5.96881 | + | 8.64026i | 0.205091 | + | 0.296883i | ||||
\(848\) | −59.2912 | −2.03607 | ||||||||
\(849\) | −1.21751 | −0.0417850 | ||||||||
\(850\) | −29.5888 | − | 29.5888i | −1.01489 | − | 1.01489i | ||||
\(851\) | 3.29825 | + | 3.29825i | 0.113062 | + | 0.113062i | ||||
\(852\) | −1.24272 | + | 1.24272i | −0.0425749 | + | 0.0425749i | ||||
\(853\) | −3.27233 | − | 3.27233i | −0.112043 | − | 0.112043i | 0.648863 | − | 0.760905i | \(-0.275245\pi\) |
−0.760905 | + | 0.648863i | \(0.775245\pi\) | |||||||
\(854\) | − | 5.99822i | − | 0.205255i | ||||||
\(855\) | 3.41905 | 0.116929 | ||||||||
\(856\) | 32.5003 | − | 32.5003i | 1.11084 | − | 1.11084i | ||||
\(857\) | 19.4140 | 0.663170 | 0.331585 | − | 0.943425i | \(-0.392417\pi\) | ||||
0.331585 | + | 0.943425i | \(0.392417\pi\) | |||||||
\(858\) | −11.9625 | − | 14.7085i | −0.408392 | − | 0.502140i | ||||
\(859\) | −27.1641 | −0.926826 | −0.463413 | − | 0.886142i | \(-0.653375\pi\) | ||||
−0.463413 | + | 0.886142i | \(0.653375\pi\) | |||||||
\(860\) | −1.97716 | + | 1.97716i | −0.0674207 | + | 0.0674207i | ||||
\(861\) | 3.76339 | 0.128256 | ||||||||
\(862\) | − | 9.33421i | − | 0.317924i | ||||||
\(863\) | 9.88657 | + | 9.88657i | 0.336543 | + | 0.336543i | 0.855064 | − | 0.518522i | \(-0.173517\pi\) |
−0.518522 | + | 0.855064i | \(0.673517\pi\) | |||||||
\(864\) | 2.00730 | − | 2.00730i | 0.0682897 | − | 0.0682897i | ||||
\(865\) | −9.29550 | − | 9.29550i | −0.316056 | − | 0.316056i | ||||
\(866\) | −32.9281 | − | 32.9281i | −1.11894 | − | 1.11894i | ||||
\(867\) | −38.2233 | −1.29813 | ||||||||
\(868\) | 5.01492 | 0.170218 | ||||||||
\(869\) | −37.4401 | − | 3.39506i | −1.27007 | − | 0.115169i | ||||
\(870\) | 0.470146i | 0.0159394i | ||||||||
\(871\) | −23.3564 | − | 23.9318i | −0.791402 | − | 0.810897i | ||||
\(872\) | 43.2482 | 1.46457 | ||||||||
\(873\) | −10.7087 | − | 10.7087i | −0.362435 | − | 0.362435i | ||||
\(874\) | −17.0214 | −0.575758 | ||||||||
\(875\) | −9.82515 | −0.332151 | ||||||||
\(876\) | −3.02489 | + | 3.02489i | −0.102202 | + | 0.102202i | ||||
\(877\) | 23.9980 | − | 23.9980i | 0.810356 | − | 0.810356i | −0.174331 | − | 0.984687i | \(-0.555776\pi\) |
0.984687 | + | 0.174331i | \(0.0557763\pi\) | |||||||
\(878\) | 12.8614 | − | 12.8614i | 0.434050 | − | 0.434050i | ||||
\(879\) | 8.56257 | + | 8.56257i | 0.288808 | + | 0.288808i | ||||
\(880\) | −14.6031 | + | 12.1749i | −0.492271 | + | 0.410416i | ||||
\(881\) | − | 32.7833i | − | 1.10450i | −0.833679 | − | 0.552249i | \(-0.813770\pi\) | ||
0.833679 | − | 0.552249i | \(-0.186230\pi\) | |||||||
\(882\) | 6.82570 | + | 6.82570i | 0.229833 | + | 0.229833i | ||||
\(883\) | 0.187257i | 0.00630171i | 0.999995 | + | 0.00315085i | \(0.00100295\pi\) | ||||
−0.999995 | + | 0.00315085i | \(0.998997\pi\) | |||||||
\(884\) | 0.167415 | − | 13.7595i | 0.00563079 | − | 0.462781i | ||||
\(885\) | 10.6830 | 0.359106 | ||||||||
\(886\) | −25.4953 | + | 25.4953i | −0.856531 | + | 0.856531i | ||||
\(887\) | 20.7436i | 0.696501i | 0.937401 | + | 0.348251i | \(0.113224\pi\) | ||||
−0.937401 | + | 0.348251i | \(0.886776\pi\) | |||||||
\(888\) | 2.90880 | 0.0976129 | ||||||||
\(889\) | 3.30414 | + | 3.30414i | 0.110817 | + | 0.110817i | ||||
\(890\) | 10.2886 | − | 10.2886i | 0.344876 | − | 0.344876i | ||||
\(891\) | −0.299521 | + | 3.30307i | −0.0100343 | + | 0.110657i | ||||
\(892\) | −1.08370 | + | 1.08370i | −0.0362849 | + | 0.0362849i | ||||
\(893\) | − | 10.8588i | − | 0.363377i | ||||||
\(894\) | − | 29.3167i | − | 0.980497i | ||||||
\(895\) | 8.78764 | − | 8.78764i | 0.293738 | − | 0.293738i | ||||
\(896\) | 13.0276i | 0.435222i | ||||||||
\(897\) | −0.165771 | + | 13.6243i | −0.00553492 | + | 0.454902i | ||||
\(898\) | − | 11.2968i | − | 0.376980i | ||||||
\(899\) | 1.78217 | − | 1.78217i | 0.0594386 | − | 0.0594386i | ||||
\(900\) | −1.82405 | −0.0608017 | ||||||||
\(901\) | 92.4986 | 3.08158 | ||||||||
\(902\) | −20.6436 | − | 1.87195i | −0.687356 | − | 0.0623292i | ||||
\(903\) | −3.05400 | − | 3.05400i | −0.101631 | − | 0.101631i | ||||
\(904\) | 30.7939 | + | 30.7939i | 1.02419 | + | 1.02419i | ||||
\(905\) | −9.38434 | + | 9.38434i | −0.311946 | + | 0.311946i | ||||
\(906\) | 21.4641 | 0.713097 | ||||||||
\(907\) | 31.3448i | 1.04079i | 0.853926 | + | 0.520394i | \(0.174215\pi\) | ||||
−0.853926 | + | 0.520394i | \(0.825785\pi\) | |||||||
\(908\) | −10.5648 | − | 10.5648i | −0.350607 | − | 0.350607i | ||||
\(909\) | −2.29024 | −0.0759625 | ||||||||
\(910\) | −4.58712 | − | 4.70013i | −0.152062 | − | 0.155808i | ||||
\(911\) | −60.2940 | −1.99763 | −0.998815 | − | 0.0486660i | \(-0.984503\pi\) | ||||
−0.998815 | + | 0.0486660i | \(0.984503\pi\) | |||||||
\(912\) | −9.56922 | + | 9.56922i | −0.316869 | + | 0.316869i | ||||
\(913\) | 7.84934 | + | 9.41484i | 0.259775 | + | 0.311586i | ||||
\(914\) | 54.1239i | 1.79026i | ||||||||
\(915\) | −3.37236 | + | 3.37236i | −0.111487 | + | 0.111487i | ||||
\(916\) | 3.98345 | + | 3.98345i | 0.131617 | + | 0.131617i | ||||
\(917\) | −1.24323 | + | 1.24323i | −0.0410549 | + | 0.0410549i | ||||
\(918\) | −8.33090 | + | 8.33090i | −0.274961 | + | 0.274961i | ||||
\(919\) | 57.7808i | 1.90601i | 0.302948 | + | 0.953007i | \(0.402029\pi\) | ||||
−0.302948 | + | 0.953007i | \(0.597971\pi\) | |||||||
\(920\) | 10.7175 | 0.353346 | ||||||||
\(921\) | −3.18728 | − | 3.18728i | −0.105024 | − | 0.105024i | ||||
\(922\) | 43.7587i | 1.44112i | ||||||||
\(923\) | −8.61778 | − | 8.83007i | −0.283658 | − | 0.290645i | ||||
\(924\) | 1.04131 | + | 1.24899i | 0.0342564 | + | 0.0410887i | ||||
\(925\) | −3.09988 | − | 3.09988i | −0.101923 | − | 0.101923i | ||||
\(926\) | 4.32500i | 0.142128i | ||||||||
\(927\) | 11.4308i | 0.375436i | ||||||||
\(928\) | −0.494617 | − | 0.494617i | −0.0162366 | − | 0.0162366i | ||||
\(929\) | 22.2721 | + | 22.2721i | 0.730723 | + | 0.730723i | 0.970763 | − | 0.240040i | \(-0.0771607\pi\) |
−0.240040 | + | 0.970763i | \(0.577161\pi\) | |||||||
\(930\) | −13.7996 | − | 13.7996i | −0.452507 | − | 0.452507i | ||||
\(931\) | −12.2314 | − | 12.2314i | −0.400869 | − | 0.400869i | ||||
\(932\) | 10.3244i | 0.338188i | ||||||||
\(933\) | − | 6.59476i | − | 0.215903i | ||||||
\(934\) | 34.9106 | + | 34.9106i | 1.14231 | + | 1.14231i | ||||
\(935\) | 22.7820 | − | 18.9938i | 0.745050 | − | 0.621162i | ||||
\(936\) | 5.93468 | + | 6.08088i | 0.193981 | + | 0.198760i | ||||
\(937\) | − | 29.1339i | − | 0.951763i | −0.879510 | − | 0.475881i | \(-0.842129\pi\) | ||
0.879510 | − | 0.475881i | \(-0.157871\pi\) | |||||||
\(938\) | 9.92627 | + | 9.92627i | 0.324104 | + | 0.324104i | ||||
\(939\) | 24.4375 | 0.797487 | ||||||||
\(940\) | − | 2.36231i | − | 0.0770501i | ||||||
\(941\) | 0.967107 | − | 0.967107i | 0.0315268 | − | 0.0315268i | −0.691168 | − | 0.722694i | \(-0.742903\pi\) |
0.722694 | + | 0.691168i | \(0.242903\pi\) | |||||||
\(942\) | 9.14309 | − | 9.14309i | 0.297898 | − | 0.297898i | ||||
\(943\) | 10.5337 | + | 10.5337i | 0.343024 | + | 0.343024i | ||||
\(944\) | −29.8996 | + | 29.8996i | −0.973149 | + | 0.973149i | ||||
\(945\) | 1.14891i | 0.0373741i | ||||||||
\(946\) | 15.2333 | + | 18.2714i | 0.495276 | + | 0.594056i | ||||
\(947\) | 1.96456 | − | 1.96456i | 0.0638395 | − | 0.0638395i | −0.674466 | − | 0.738306i | \(-0.735626\pi\) |
0.738306 | + | 0.674466i | \(0.235626\pi\) | |||||||
\(948\) | −5.82130 | −0.189067 | ||||||||
\(949\) | −20.9764 | − | 21.4932i | −0.680924 | − | 0.697698i | ||||
\(950\) | 15.9977 | 0.519034 | ||||||||
\(951\) | −21.5305 | − | 21.5305i | −0.698175 | − | 0.698175i | ||||
\(952\) | − | 16.7189i | − | 0.541863i | ||||||
\(953\) | −37.6571 | −1.21983 | −0.609917 | − | 0.792465i | \(-0.708797\pi\) | ||||
−0.609917 | + | 0.792465i | \(0.708797\pi\) | |||||||
\(954\) | 13.9542 | − | 13.9542i | 0.451784 | − | 0.451784i | ||||
\(955\) | −11.1691 | − | 11.1691i | −0.361422 | − | 0.361422i | ||||
\(956\) | 5.55315 | + | 5.55315i | 0.179602 | + | 0.179602i | ||||
\(957\) | 0.813908 | + | 0.0738049i | 0.0263099 | + | 0.00238577i | ||||
\(958\) | 28.0568 | 0.906476 | ||||||||
\(959\) | −16.7674 | −0.541448 | ||||||||
\(960\) | 4.27711 | − | 4.27711i | 0.138043 | − | 0.138043i | ||||
\(961\) | 73.6193i | 2.37482i | ||||||||
\(962\) | 0.0858426 | − | 7.05520i | 0.00276768 | − | 0.227469i | ||||
\(963\) | 19.5035i | 0.628492i | ||||||||
\(964\) | −4.58569 | + | 4.58569i | −0.147695 | + | 0.147695i | ||||
\(965\) | 24.6534i | 0.793622i | ||||||||
\(966\) | − | 5.71975i | − | 0.184030i | ||||||
\(967\) | −27.9252 | + | 27.9252i | −0.898014 | + | 0.898014i | −0.995260 | − | 0.0972465i | \(-0.968996\pi\) |
0.0972465 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(968\) | 14.7340 | + | 21.3285i | 0.473568 | + | 0.685522i | ||||
\(969\) | 14.9287 | − | 14.9287i | 0.479579 | − | 0.479579i | ||||
\(970\) | 20.4321 | + | 20.4321i | 0.656034 | + | 0.656034i | ||||
\(971\) | 19.4007 | 0.622597 | 0.311299 | − | 0.950312i | \(-0.399236\pi\) | ||||
0.311299 | + | 0.950312i | \(0.399236\pi\) | |||||||
\(972\) | 0.513571i | 0.0164728i | ||||||||
\(973\) | 7.90785 | − | 7.90785i | 0.253514 | − | 0.253514i | ||||
\(974\) | 25.2237 | 0.808220 | ||||||||
\(975\) | 0.155801 | − | 12.8049i | 0.00498962 | − | 0.410084i | ||||
\(976\) | − | 18.8771i | − | 0.604241i | ||||||
\(977\) | −24.7208 | − | 24.7208i | −0.790887 | − | 0.790887i | 0.190751 | − | 0.981638i | \(-0.438908\pi\) |
−0.981638 | + | 0.190751i | \(0.938908\pi\) | |||||||
\(978\) | − | 12.4251i | − | 0.397310i | ||||||
\(979\) | −16.1964 | − | 19.4266i | −0.517638 | − | 0.620878i | ||||
\(980\) | −2.66092 | − | 2.66092i | −0.0850000 | − | 0.0850000i | ||||
\(981\) | −12.9767 | + | 12.9767i | −0.414313 | + | 0.414313i | ||||
\(982\) | −2.68277 | + | 2.68277i | −0.0856105 | + | 0.0856105i | ||||
\(983\) | −14.5113 | + | 14.5113i | −0.462838 | + | 0.462838i | −0.899585 | − | 0.436746i | \(-0.856131\pi\) |
0.436746 | + | 0.899585i | \(0.356131\pi\) | |||||||
\(984\) | 9.28990 | 0.296151 | ||||||||
\(985\) | 2.27647 | 0.0725343 | ||||||||
\(986\) | 2.05281 | + | 2.05281i | 0.0653748 | + | 0.0653748i | ||||
\(987\) | 3.64892 | 0.116146 | ||||||||
\(988\) | 3.67438 | + | 3.76490i | 0.116898 | + | 0.119777i | ||||
\(989\) | − | 17.0963i | − | 0.543630i | ||||||
\(990\) | 0.571483 | − | 6.30222i | 0.0181629 | − | 0.200298i | ||||
\(991\) | 30.6304 | 0.973007 | 0.486504 | − | 0.873679i | \(-0.338272\pi\) | ||||
0.486504 | + | 0.873679i | \(0.338272\pi\) | |||||||
\(992\) | 29.0358 | 0.921886 | ||||||||
\(993\) | −5.84499 | − | 5.84499i | −0.185485 | − | 0.185485i | ||||
\(994\) | 3.66248 | + | 3.66248i | 0.116167 | + | 0.116167i | ||||
\(995\) | 4.49933 | − | 4.49933i | 0.142638 | − | 0.142638i | ||||
\(996\) | 1.34214 | + | 1.34214i | 0.0425274 | + | 0.0425274i | ||||
\(997\) | 62.8288i | 1.98981i | 0.100834 | + | 0.994903i | \(0.467849\pi\) | ||||
−0.100834 | + | 0.994903i | \(0.532151\pi\) | |||||||
\(998\) | −26.9829 | −0.854130 | ||||||||
\(999\) | −0.872788 | + | 0.872788i | −0.0276138 | + | 0.0276138i |
(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.m.a.307.3 | yes | 28 | |
11.10 | odd | 2 | inner | 429.2.m.a.307.12 | yes | 28 | |
13.5 | odd | 4 | inner | 429.2.m.a.109.12 | yes | 28 | |
143.109 | even | 4 | inner | 429.2.m.a.109.3 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.m.a.109.3 | ✓ | 28 | 143.109 | even | 4 | inner | |
429.2.m.a.109.12 | yes | 28 | 13.5 | odd | 4 | inner | |
429.2.m.a.307.3 | yes | 28 | 1.1 | even | 1 | trivial | |
429.2.m.a.307.12 | yes | 28 | 11.10 | odd | 2 | inner |