Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(13,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.7 | ||
Root | \(-0.944649 - 1.05244i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.13 |
Dual form | 105.2.m.a.97.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48838 | − | 1.48838i | 1.05244 | − | 1.05244i | 0.0538973 | − | 0.998546i | \(-0.482836\pi\) |
0.998546 | − | 0.0538973i | \(-0.0171644\pi\) | |||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 2.43055i | − | 1.21528i | ||||||
\(5\) | 1.28999 | − | 1.82645i | 0.576899 | − | 0.816815i | ||||
\(6\) | 2.10489i | 0.859317i | ||||||||
\(7\) | −1.75993 | + | 1.97552i | −0.665189 | + | 0.746675i | ||||
\(8\) | −0.640825 | − | 0.640825i | −0.226566 | − | 0.226566i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −0.798469 | − | 4.63845i | −0.252498 | − | 1.46681i | ||||
\(11\) | −2.67187 | −0.805600 | −0.402800 | − | 0.915288i | \(-0.631963\pi\) | ||||
−0.402800 | + | 0.915288i | \(0.631963\pi\) | |||||||
\(12\) | 1.71866 | + | 1.71866i | 0.496134 | + | 0.496134i | ||||
\(13\) | −1.22714 | + | 1.22714i | −0.340348 | + | 0.340348i | −0.856498 | − | 0.516150i | \(-0.827365\pi\) |
0.516150 | + | 0.856498i | \(0.327365\pi\) | |||||||
\(14\) | 0.320879 | + | 5.55976i | 0.0857585 | + | 1.48591i | ||||
\(15\) | 0.379340 | + | 2.20366i | 0.0979452 | + | 0.568982i | ||||
\(16\) | 2.95352 | 0.738380 | ||||||||
\(17\) | 4.74624 | + | 4.74624i | 1.15113 | + | 1.15113i | 0.986326 | + | 0.164807i | \(0.0527002\pi\) |
0.164807 | + | 0.986326i | \(0.447300\pi\) | |||||||
\(18\) | −1.48838 | − | 1.48838i | −0.350815 | − | 0.350815i | ||||
\(19\) | −6.01729 | −1.38046 | −0.690231 | − | 0.723589i | \(-0.742491\pi\) | ||||
−0.690231 | + | 0.723589i | \(0.742491\pi\) | |||||||
\(20\) | −4.43929 | − | 3.13538i | −0.992656 | − | 0.701092i | ||||
\(21\) | −0.152445 | − | 2.64136i | −0.0332662 | − | 0.576391i | ||||
\(22\) | −3.97676 | + | 3.97676i | −0.847848 | + | 0.847848i | ||||
\(23\) | −0.175684 | − | 0.175684i | −0.0366327 | − | 0.0366327i | 0.688553 | − | 0.725186i | \(-0.258246\pi\) |
−0.725186 | + | 0.688553i | \(0.758246\pi\) | |||||||
\(24\) | 0.906263 | 0.184990 | ||||||||
\(25\) | −1.67187 | − | 4.71220i | −0.334374 | − | 0.942440i | ||||
\(26\) | 3.65291i | 0.716394i | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 4.80159 | + | 4.27759i | 0.907416 | + | 0.808389i | ||||
\(29\) | 0.304889i | 0.0566165i | 0.999599 | + | 0.0283083i | \(0.00901200\pi\) | ||||
−0.999599 | + | 0.0283083i | \(0.990988\pi\) | |||||||
\(30\) | 3.84448 | + | 2.71528i | 0.701903 | + | 0.495739i | ||||
\(31\) | − | 7.25379i | − | 1.30282i | −0.758726 | − | 0.651410i | \(-0.774178\pi\) | ||
0.758726 | − | 0.651410i | \(-0.225822\pi\) | |||||||
\(32\) | 5.67761 | − | 5.67761i | 1.00367 | − | 1.00367i | ||||
\(33\) | 1.88930 | − | 1.88930i | 0.328885 | − | 0.328885i | ||||
\(34\) | 14.1284 | 2.42301 | ||||||||
\(35\) | 1.33791 | + | 5.76281i | 0.226148 | + | 0.974093i | ||||
\(36\) | −2.43055 | −0.405092 | ||||||||
\(37\) | −0.735441 | + | 0.735441i | −0.120906 | + | 0.120906i | −0.764971 | − | 0.644065i | \(-0.777247\pi\) |
0.644065 | + | 0.764971i | \(0.277247\pi\) | |||||||
\(38\) | −8.95602 | + | 8.95602i | −1.45286 | + | 1.45286i | ||||
\(39\) | − | 1.73544i | − | 0.277893i | ||||||
\(40\) | −1.99709 | + | 0.343782i | −0.315768 | + | 0.0543567i | ||||
\(41\) | − | 7.05736i | − | 1.10217i | −0.834447 | − | 0.551087i | \(-0.814213\pi\) | ||
0.834447 | − | 0.551087i | \(-0.185787\pi\) | |||||||
\(42\) | −4.15824 | − | 3.70445i | −0.641630 | − | 0.571608i | ||||
\(43\) | 0.304889 | + | 0.304889i | 0.0464952 | + | 0.0464952i | 0.729972 | − | 0.683477i | \(-0.239533\pi\) |
−0.683477 | + | 0.729972i | \(0.739533\pi\) | |||||||
\(44\) | 6.49412i | 0.979026i | ||||||||
\(45\) | −1.82645 | − | 1.28999i | −0.272272 | − | 0.192300i | ||||
\(46\) | −0.522969 | −0.0771076 | ||||||||
\(47\) | −0.556866 | − | 0.556866i | −0.0812273 | − | 0.0812273i | 0.665326 | − | 0.746553i | \(-0.268293\pi\) |
−0.746553 | + | 0.665326i | \(0.768293\pi\) | |||||||
\(48\) | −2.08845 | + | 2.08845i | −0.301442 | + | 0.301442i | ||||
\(49\) | −0.805321 | − | 6.95352i | −0.115046 | − | 0.993360i | ||||
\(50\) | −9.50193 | − | 4.52517i | −1.34378 | − | 0.639955i | ||||
\(51\) | −6.71220 | −0.939896 | ||||||||
\(52\) | 2.98263 | + | 2.98263i | 0.413617 | + | 0.413617i | ||||
\(53\) | −4.99031 | − | 4.99031i | −0.685472 | − | 0.685472i | 0.275756 | − | 0.961228i | \(-0.411072\pi\) |
−0.961228 | + | 0.275756i | \(0.911072\pi\) | |||||||
\(54\) | 2.10489 | 0.286439 | ||||||||
\(55\) | −3.44668 | + | 4.88005i | −0.464750 | + | 0.658026i | ||||
\(56\) | 2.39376 | − | 0.138155i | 0.319880 | − | 0.0184617i | ||||
\(57\) | 4.25487 | − | 4.25487i | 0.563571 | − | 0.563571i | ||||
\(58\) | 0.453791 | + | 0.453791i | 0.0595857 | + | 0.0595857i | ||||
\(59\) | 7.98837 | 1.04000 | 0.519999 | − | 0.854167i | \(-0.325932\pi\) | ||||
0.519999 | + | 0.854167i | \(0.325932\pi\) | |||||||
\(60\) | 5.35610 | − | 0.922006i | 0.691470 | − | 0.119031i | ||||
\(61\) | 5.53409i | 0.708567i | 0.935138 | + | 0.354284i | \(0.115275\pi\) | ||||
−0.935138 | + | 0.354284i | \(0.884725\pi\) | |||||||
\(62\) | −10.7964 | − | 10.7964i | −1.37114 | − | 1.37114i | ||||
\(63\) | 1.97552 | + | 1.75993i | 0.248892 | + | 0.221730i | ||||
\(64\) | − | 10.9939i | − | 1.37423i | ||||||
\(65\) | 0.658323 | + | 3.82432i | 0.0816549 | + | 0.474348i | ||||
\(66\) | − | 5.62399i | − | 0.692265i | ||||||
\(67\) | −3.43055 | + | 3.43055i | −0.419109 | + | 0.419109i | −0.884896 | − | 0.465788i | \(-0.845771\pi\) |
0.465788 | + | 0.884896i | \(0.345771\pi\) | |||||||
\(68\) | 11.5360 | − | 11.5360i | 1.39894 | − | 1.39894i | ||||
\(69\) | 0.248455 | 0.0299104 | ||||||||
\(70\) | 10.5686 | + | 6.58594i | 1.26319 | + | 0.787170i | ||||
\(71\) | 15.3087 | 1.81681 | 0.908407 | − | 0.418087i | \(-0.137299\pi\) | ||||
0.908407 | + | 0.418087i | \(0.137299\pi\) | |||||||
\(72\) | −0.640825 | + | 0.640825i | −0.0755219 | + | 0.0755219i | ||||
\(73\) | −10.0208 | + | 10.0208i | −1.17285 | + | 1.17285i | −0.191323 | + | 0.981527i | \(0.561278\pi\) |
−0.981527 | + | 0.191323i | \(0.938722\pi\) | |||||||
\(74\) | 2.18923i | 0.254493i | ||||||||
\(75\) | 4.51422 | + | 2.14984i | 0.521257 | + | 0.248242i | ||||
\(76\) | 14.6253i | 1.67764i | ||||||||
\(77\) | 4.70230 | − | 5.27832i | 0.535876 | − | 0.601521i | ||||
\(78\) | −2.58300 | − | 2.58300i | −0.292467 | − | 0.292467i | ||||
\(79\) | 11.2973i | 1.27104i | 0.772084 | + | 0.635521i | \(0.219215\pi\) | ||||
−0.772084 | + | 0.635521i | \(0.780785\pi\) | |||||||
\(80\) | 3.81000 | − | 5.39447i | 0.425971 | − | 0.603120i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −10.5040 | − | 10.5040i | −1.15998 | − | 1.15998i | ||||
\(83\) | 4.88941 | − | 4.88941i | 0.536682 | − | 0.536682i | −0.385871 | − | 0.922553i | \(-0.626099\pi\) |
0.922553 | + | 0.385871i | \(0.126099\pi\) | |||||||
\(84\) | −6.41995 | + | 0.370525i | −0.700474 | + | 0.0404276i | ||||
\(85\) | 14.7914 | − | 2.54621i | 1.60435 | − | 0.276175i | ||||
\(86\) | 0.907583 | 0.0978671 | ||||||||
\(87\) | −0.215589 | − | 0.215589i | −0.0231136 | − | 0.0231136i | ||||
\(88\) | 1.71220 | + | 1.71220i | 0.182521 | + | 0.182521i | ||||
\(89\) | −6.91251 | −0.732725 | −0.366363 | − | 0.930472i | \(-0.619397\pi\) | ||||
−0.366363 | + | 0.930472i | \(0.619397\pi\) | |||||||
\(90\) | −4.63845 | + | 0.798469i | −0.488935 | + | 0.0841660i | ||||
\(91\) | −0.264559 | − | 4.58392i | −0.0277333 | − | 0.480525i | ||||
\(92\) | −0.427009 | + | 0.427009i | −0.0445188 | + | 0.0445188i | ||||
\(93\) | 5.12921 | + | 5.12921i | 0.531874 | + | 0.531874i | ||||
\(94\) | −1.65766 | −0.170974 | ||||||||
\(95\) | −7.76222 | + | 10.9903i | −0.796387 | + | 1.12758i | ||||
\(96\) | 8.02936i | 0.819493i | ||||||||
\(97\) | 8.84137 | + | 8.84137i | 0.897705 | + | 0.897705i | 0.995233 | − | 0.0975276i | \(-0.0310934\pi\) |
−0.0975276 | + | 0.995233i | \(0.531093\pi\) | |||||||
\(98\) | −11.5481 | − | 9.15086i | −1.16654 | − | 0.924376i | ||||
\(99\) | 2.67187i | 0.268533i | ||||||||
\(100\) | −11.4533 | + | 4.06357i | −1.14533 | + | 0.406357i | ||||
\(101\) | − | 7.22962i | − | 0.719374i | −0.933073 | − | 0.359687i | \(-0.882883\pi\) | ||
0.933073 | − | 0.359687i | \(-0.117117\pi\) | |||||||
\(102\) | −9.99031 | + | 9.99031i | −0.989188 | + | 0.989188i | ||||
\(103\) | 6.94538 | − | 6.94538i | 0.684349 | − | 0.684349i | −0.276628 | − | 0.960977i | \(-0.589217\pi\) |
0.960977 | + | 0.276628i | \(0.0892171\pi\) | |||||||
\(104\) | 1.57277 | 0.154222 | ||||||||
\(105\) | −5.02097 | − | 3.12888i | −0.489996 | − | 0.305347i | ||||
\(106\) | −14.8550 | −1.44284 | ||||||||
\(107\) | −7.47295 | + | 7.47295i | −0.722437 | + | 0.722437i | −0.969101 | − | 0.246664i | \(-0.920666\pi\) |
0.246664 | + | 0.969101i | \(0.420666\pi\) | |||||||
\(108\) | 1.71866 | − | 1.71866i | 0.165378 | − | 0.165378i | ||||
\(109\) | 5.95352i | 0.570244i | 0.958491 | + | 0.285122i | \(0.0920341\pi\) | ||||
−0.958491 | + | 0.285122i | \(0.907966\pi\) | |||||||
\(110\) | 2.13341 | + | 12.3933i | 0.203412 | + | 1.18166i | ||||
\(111\) | − | 1.04007i | − | 0.0987192i | ||||||
\(112\) | −5.19798 | + | 5.83473i | −0.491163 | + | 0.551330i | ||||
\(113\) | 6.99031 | + | 6.99031i | 0.657593 | + | 0.657593i | 0.954810 | − | 0.297217i | \(-0.0960585\pi\) |
−0.297217 | + | 0.954810i | \(0.596058\pi\) | |||||||
\(114\) | − | 12.6657i | − | 1.18625i | ||||||
\(115\) | −0.547509 | + | 0.0942489i | −0.0510555 | + | 0.00878876i | ||||
\(116\) | 0.741049 | 0.0688047 | ||||||||
\(117\) | 1.22714 | + | 1.22714i | 0.113449 | + | 0.113449i | ||||
\(118\) | 11.8897 | − | 11.8897i | 1.09454 | − | 1.09454i | ||||
\(119\) | −17.7293 | + | 1.02324i | −1.62524 | + | 0.0938002i | ||||
\(120\) | 1.16907 | − | 1.65525i | 0.106721 | − | 0.151103i | ||||
\(121\) | −3.86110 | −0.351009 | ||||||||
\(122\) | 8.23683 | + | 8.23683i | 0.745727 | + | 0.745727i | ||||
\(123\) | 4.99031 | + | 4.99031i | 0.449961 | + | 0.449961i | ||||
\(124\) | −17.6307 | −1.58329 | ||||||||
\(125\) | −10.7633 | − | 3.02508i | −0.962700 | − | 0.270571i | ||||
\(126\) | 5.55976 | − | 0.320879i | 0.495303 | − | 0.0285862i | ||||
\(127\) | 2.86110 | − | 2.86110i | 0.253882 | − | 0.253882i | −0.568678 | − | 0.822560i | \(-0.692545\pi\) |
0.822560 | + | 0.568678i | \(0.192545\pi\) | |||||||
\(128\) | −5.00781 | − | 5.00781i | −0.442632 | − | 0.442632i | ||||
\(129\) | −0.431179 | −0.0379632 | ||||||||
\(130\) | 6.67187 | + | 4.71220i | 0.585162 | + | 0.413287i | ||||
\(131\) | 9.34764i | 0.816707i | 0.912824 | + | 0.408353i | \(0.133897\pi\) | ||||
−0.912824 | + | 0.408353i | \(0.866103\pi\) | |||||||
\(132\) | −4.59204 | − | 4.59204i | −0.399686 | − | 0.399686i | ||||
\(133\) | 10.5900 | − | 11.8873i | 0.918268 | − | 1.03076i | ||||
\(134\) | 10.2119i | 0.882177i | ||||||||
\(135\) | 2.20366 | − | 0.379340i | 0.189661 | − | 0.0326484i | ||||
\(136\) | − | 6.08302i | − | 0.521615i | ||||||
\(137\) | 7.51943 | − | 7.51943i | 0.642428 | − | 0.642428i | −0.308724 | − | 0.951152i | \(-0.599902\pi\) |
0.951152 | + | 0.308724i | \(0.0999019\pi\) | |||||||
\(138\) | 0.369795 | − | 0.369795i | 0.0314791 | − | 0.0314791i | ||||
\(139\) | −7.78902 | −0.660656 | −0.330328 | − | 0.943866i | \(-0.607159\pi\) | ||||
−0.330328 | + | 0.943866i | \(0.607159\pi\) | |||||||
\(140\) | 14.0068 | − | 3.25186i | 1.18379 | − | 0.274832i | ||||
\(141\) | 0.787528 | 0.0663218 | ||||||||
\(142\) | 22.7852 | − | 22.7852i | 1.91209 | − | 1.91209i | ||||
\(143\) | 3.27877 | − | 3.27877i | 0.274184 | − | 0.274184i | ||||
\(144\) | − | 2.95352i | − | 0.246127i | ||||||
\(145\) | 0.556866 | + | 0.393303i | 0.0462452 | + | 0.0326620i | ||||
\(146\) | 29.8296i | 2.46872i | ||||||||
\(147\) | 5.48633 | + | 4.34743i | 0.452505 | + | 0.358570i | ||||
\(148\) | 1.78753 | + | 1.78753i | 0.146934 | + | 0.146934i | ||||
\(149\) | − | 14.2855i | − | 1.17031i | −0.810920 | − | 0.585157i | \(-0.801033\pi\) | ||
0.810920 | − | 0.585157i | \(-0.198967\pi\) | |||||||
\(150\) | 9.91866 | − | 3.51910i | 0.809855 | − | 0.287333i | ||||
\(151\) | 9.77990 | 0.795877 | 0.397939 | − | 0.917412i | \(-0.369726\pi\) | ||||
0.397939 | + | 0.917412i | \(0.369726\pi\) | |||||||
\(152\) | 3.85603 | + | 3.85603i | 0.312765 | + | 0.312765i | ||||
\(153\) | 4.74624 | − | 4.74624i | 0.383711 | − | 0.383711i | ||||
\(154\) | −0.857347 | − | 14.8550i | −0.0690870 | − | 1.19705i | ||||
\(155\) | −13.2487 | − | 9.35729i | −1.06416 | − | 0.751596i | ||||
\(156\) | −4.21808 | −0.337717 | ||||||||
\(157\) | −2.17731 | − | 2.17731i | −0.173768 | − | 0.173768i | 0.614864 | − | 0.788633i | \(-0.289211\pi\) |
−0.788633 | + | 0.614864i | \(0.789211\pi\) | |||||||
\(158\) | 16.8146 | + | 16.8146i | 1.33770 | + | 1.33770i | ||||
\(159\) | 7.05736 | 0.559685 | ||||||||
\(160\) | −3.04586 | − | 17.6939i | −0.240796 | − | 1.39883i | ||||
\(161\) | 0.656257 | − | 0.0378756i | 0.0517203 | − | 0.00298502i | ||||
\(162\) | −1.48838 | + | 1.48838i | −0.116938 | + | 0.116938i | ||||
\(163\) | −13.6757 | − | 13.6757i | −1.07117 | − | 1.07117i | −0.997266 | − | 0.0739001i | \(-0.976455\pi\) |
−0.0739001 | − | 0.997266i | \(-0.523545\pi\) | |||||||
\(164\) | −17.1533 | −1.33945 | ||||||||
\(165\) | −1.01355 | − | 5.88789i | −0.0789046 | − | 0.458371i | ||||
\(166\) | − | 14.5546i | − | 1.12966i | ||||||
\(167\) | 6.23288 | + | 6.23288i | 0.482315 | + | 0.482315i | 0.905870 | − | 0.423555i | \(-0.139218\pi\) |
−0.423555 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(168\) | −1.59496 | + | 1.79034i | −0.123054 | + | 0.138128i | ||||
\(169\) | 9.98824i | 0.768326i | ||||||||
\(170\) | 18.2255 | − | 25.8049i | 1.39783 | − | 1.97915i | ||||
\(171\) | 6.01729i | 0.460154i | ||||||||
\(172\) | 0.741049 | − | 0.741049i | 0.0565045 | − | 0.0565045i | ||||
\(173\) | −6.76935 | + | 6.76935i | −0.514664 | + | 0.514664i | −0.915952 | − | 0.401288i | \(-0.868563\pi\) |
0.401288 | + | 0.915952i | \(0.368563\pi\) | |||||||
\(174\) | −0.641758 | −0.0486515 | ||||||||
\(175\) | 12.2514 | + | 4.99032i | 0.926119 | + | 0.377233i | ||||
\(176\) | −7.89143 | −0.594839 | ||||||||
\(177\) | −5.64863 | + | 5.64863i | −0.424577 | + | 0.424577i | ||||
\(178\) | −10.2885 | + | 10.2885i | −0.771152 | + | 0.771152i | ||||
\(179\) | − | 1.30103i | − | 0.0972437i | −0.998817 | − | 0.0486218i | \(-0.984517\pi\) | ||
0.998817 | − | 0.0486218i | \(-0.0154829\pi\) | |||||||
\(180\) | −3.13538 | + | 4.43929i | −0.233697 | + | 0.330885i | ||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | −7.21638 | − | 6.42885i | −0.534913 | − | 0.476538i | ||||
\(183\) | −3.91319 | − | 3.91319i | −0.289271 | − | 0.289271i | ||||
\(184\) | 0.225165i | 0.0165994i | ||||||||
\(185\) | 0.394541 | + | 2.29196i | 0.0290072 | + | 0.168508i | ||||
\(186\) | 15.2684 | 1.11953 | ||||||||
\(187\) | −12.6814 | − | 12.6814i | −0.927352 | − | 0.927352i | ||||
\(188\) | −1.35349 | + | 1.35349i | −0.0987136 | + | 0.0987136i | ||||
\(189\) | −2.64136 | + | 0.152445i | −0.192130 | + | 0.0110887i | ||||
\(190\) | 4.80462 | + | 27.9109i | 0.348564 | + | 2.02487i | ||||
\(191\) | 1.93791 | 0.140222 | 0.0701110 | − | 0.997539i | \(-0.477665\pi\) | ||||
0.0701110 | + | 0.997539i | \(0.477665\pi\) | |||||||
\(192\) | 7.77383 | + | 7.77383i | 0.561028 | + | 0.561028i | ||||
\(193\) | −7.82786 | − | 7.82786i | −0.563462 | − | 0.563462i | 0.366827 | − | 0.930289i | \(-0.380444\pi\) |
−0.930289 | + | 0.366827i | \(0.880444\pi\) | |||||||
\(194\) | 26.3186 | 1.88957 | ||||||||
\(195\) | −3.16970 | − | 2.23870i | −0.226987 | − | 0.160316i | ||||
\(196\) | −16.9009 | + | 1.95738i | −1.20721 | + | 0.139813i | ||||
\(197\) | −8.50767 | + | 8.50767i | −0.606146 | + | 0.606146i | −0.941937 | − | 0.335790i | \(-0.890997\pi\) |
0.335790 | + | 0.941937i | \(0.390997\pi\) | |||||||
\(198\) | 3.97676 | + | 3.97676i | 0.282616 | + | 0.282616i | ||||
\(199\) | 3.25460 | 0.230712 | 0.115356 | − | 0.993324i | \(-0.463199\pi\) | ||||
0.115356 | + | 0.993324i | \(0.463199\pi\) | |||||||
\(200\) | −1.94832 | + | 4.09107i | −0.137767 | + | 0.289283i | ||||
\(201\) | − | 4.85153i | − | 0.342201i | ||||||
\(202\) | −10.7604 | − | 10.7604i | −0.757101 | − | 0.757101i | ||||
\(203\) | −0.602314 | − | 0.536583i | −0.0422741 | − | 0.0376607i | ||||
\(204\) | 16.3144i | 1.14223i | ||||||||
\(205\) | −12.8900 | − | 9.10390i | −0.900273 | − | 0.635844i | ||||
\(206\) | − | 20.6747i | − | 1.44048i | ||||||
\(207\) | −0.175684 | + | 0.175684i | −0.0122109 | + | 0.0122109i | ||||
\(208\) | −3.62439 | + | 3.62439i | −0.251306 | + | 0.251306i | ||||
\(209\) | 16.0774 | 1.11210 | ||||||||
\(210\) | −12.1301 | + | 2.81615i | −0.837054 | + | 0.194333i | ||||
\(211\) | −17.2508 | −1.18759 | −0.593797 | − | 0.804615i | \(-0.702372\pi\) | ||||
−0.593797 | + | 0.804615i | \(0.702372\pi\) | |||||||
\(212\) | −12.1292 | + | 12.1292i | −0.833037 | + | 0.833037i | ||||
\(213\) | −10.8249 | + | 10.8249i | −0.741711 | + | 0.741711i | ||||
\(214\) | 22.2452i | 1.52065i | ||||||||
\(215\) | 0.950169 | − | 0.163563i | 0.0648010 | − | 0.0111549i | ||||
\(216\) | − | 0.906263i | − | 0.0616634i | ||||||
\(217\) | 14.3300 | + | 12.7661i | 0.972782 | + | 0.866622i | ||||
\(218\) | 8.86110 | + | 8.86110i | 0.600150 | + | 0.600150i | ||||
\(219\) | − | 14.1716i | − | 0.957628i | ||||||
\(220\) | 11.8612 | + | 8.37733i | 0.799683 | + | 0.564799i | ||||
\(221\) | −11.6486 | −0.783572 | ||||||||
\(222\) | −1.54802 | − | 1.54802i | −0.103896 | − | 0.103896i | ||||
\(223\) | 4.58392 | − | 4.58392i | 0.306962 | − | 0.306962i | −0.536768 | − | 0.843730i | \(-0.680355\pi\) |
0.843730 | + | 0.536768i | \(0.180355\pi\) | |||||||
\(224\) | 1.22403 | + | 21.2084i | 0.0817841 | + | 1.41705i | ||||
\(225\) | −4.71220 | + | 1.67187i | −0.314147 | + | 0.111458i | ||||
\(226\) | 20.8085 | 1.38416 | ||||||||
\(227\) | −14.1613 | − | 14.1613i | −0.939918 | − | 0.939918i | 0.0583764 | − | 0.998295i | \(-0.481408\pi\) |
−0.998295 | + | 0.0583764i | \(0.981408\pi\) | |||||||
\(228\) | −10.3417 | − | 10.3417i | −0.684894 | − | 0.684894i | ||||
\(229\) | 28.9307 | 1.91180 | 0.955898 | − | 0.293699i | \(-0.0948864\pi\) | ||||
0.955898 | + | 0.293699i | \(0.0948864\pi\) | |||||||
\(230\) | −0.674623 | + | 0.955180i | −0.0444833 | + | 0.0629827i | ||||
\(231\) | 0.407313 | + | 7.05736i | 0.0267992 | + | 0.464340i | ||||
\(232\) | 0.195381 | − | 0.195381i | 0.0128274 | − | 0.0128274i | ||||
\(233\) | −4.78546 | − | 4.78546i | −0.313506 | − | 0.313506i | 0.532760 | − | 0.846266i | \(-0.321155\pi\) |
−0.846266 | + | 0.532760i | \(0.821155\pi\) | |||||||
\(234\) | 3.65291 | 0.238798 | ||||||||
\(235\) | −1.73544 | + | 0.298741i | −0.113208 | + | 0.0194877i | ||||
\(236\) | − | 19.4162i | − | 1.26388i | ||||||
\(237\) | −7.98837 | − | 7.98837i | −0.518901 | − | 0.518901i | ||||
\(238\) | −24.8650 | + | 27.9109i | −1.61176 | + | 1.80920i | ||||
\(239\) | − | 16.1769i | − | 1.04640i | −0.852210 | − | 0.523200i | \(-0.824738\pi\) | ||
0.852210 | − | 0.523200i | \(-0.175262\pi\) | |||||||
\(240\) | 1.12039 | + | 6.50855i | 0.0723208 | + | 0.420125i | ||||
\(241\) | − | 11.3707i | − | 0.732454i | −0.930526 | − | 0.366227i | \(-0.880649\pi\) | ||
0.930526 | − | 0.366227i | \(-0.119351\pi\) | |||||||
\(242\) | −5.74679 | + | 5.74679i | −0.369418 | + | 0.369418i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 13.4509 | 0.861105 | ||||||||
\(245\) | −13.7391 | − | 7.49906i | −0.877762 | − | 0.479098i | ||||
\(246\) | 14.8550 | 0.947117 | ||||||||
\(247\) | 7.38407 | − | 7.38407i | 0.469837 | − | 0.469837i | ||||
\(248\) | −4.64841 | + | 4.64841i | −0.295174 | + | 0.295174i | ||||
\(249\) | 6.91467i | 0.438199i | ||||||||
\(250\) | −20.5224 | + | 11.5174i | −1.29795 | + | 0.728427i | ||||
\(251\) | 6.95039i | 0.438705i | 0.975646 | + | 0.219352i | \(0.0703944\pi\) | ||||
−0.975646 | + | 0.219352i | \(0.929606\pi\) | |||||||
\(252\) | 4.27759 | − | 4.80159i | 0.269463 | − | 0.302472i | ||||
\(253\) | 0.469405 | + | 0.469405i | 0.0295112 | + | 0.0295112i | ||||
\(254\) | − | 8.51682i | − | 0.534393i | ||||||
\(255\) | −8.65865 | + | 12.2595i | −0.542226 | + | 0.767722i | ||||
\(256\) | 7.08066 | 0.442541 | ||||||||
\(257\) | −10.0889 | − | 10.0889i | −0.629329 | − | 0.629329i | 0.318570 | − | 0.947899i | \(-0.396797\pi\) |
−0.947899 | + | 0.318570i | \(0.896797\pi\) | |||||||
\(258\) | −0.641758 | + | 0.641758i | −0.0399541 | + | 0.0399541i | ||||
\(259\) | −0.158553 | − | 2.74720i | −0.00985202 | − | 0.170703i | ||||
\(260\) | 9.29520 | − | 1.60009i | 0.576464 | − | 0.0992332i | ||||
\(261\) | 0.304889 | 0.0188722 | ||||||||
\(262\) | 13.9128 | + | 13.9128i | 0.859538 | + | 0.859538i | ||||
\(263\) | 18.1984 | + | 18.1984i | 1.12216 | + | 1.12216i | 0.991416 | + | 0.130744i | \(0.0417367\pi\) |
0.130744 | + | 0.991416i | \(0.458263\pi\) | |||||||
\(264\) | −2.42142 | −0.149028 | ||||||||
\(265\) | −15.5520 | + | 2.67714i | −0.955352 | + | 0.164456i | ||||
\(266\) | −1.93082 | − | 33.4547i | −0.118386 | − | 2.05124i | ||||
\(267\) | 4.88789 | − | 4.88789i | 0.299134 | − | 0.299134i | ||||
\(268\) | 8.33813 | + | 8.33813i | 0.509333 | + | 0.509333i | ||||
\(269\) | 15.5119 | 0.945775 | 0.472888 | − | 0.881123i | \(-0.343212\pi\) | ||||
0.472888 | + | 0.881123i | \(0.343212\pi\) | |||||||
\(270\) | 2.71528 | − | 3.84448i | 0.165246 | − | 0.233968i | ||||
\(271\) | 13.3418i | 0.810458i | 0.914215 | + | 0.405229i | \(0.132808\pi\) | ||||
−0.914215 | + | 0.405229i | \(0.867192\pi\) | |||||||
\(272\) | 14.0181 | + | 14.0181i | 0.849974 | + | 0.849974i | ||||
\(273\) | 3.42839 | + | 3.05425i | 0.207496 | + | 0.184852i | ||||
\(274\) | − | 22.3835i | − | 1.35224i | ||||||
\(275\) | 4.46702 | + | 12.5904i | 0.269372 | + | 0.759229i | ||||
\(276\) | − | 0.603882i | − | 0.0363494i | ||||||
\(277\) | −2.00561 | + | 2.00561i | −0.120505 | + | 0.120505i | −0.764788 | − | 0.644282i | \(-0.777156\pi\) |
0.644282 | + | 0.764788i | \(0.277156\pi\) | |||||||
\(278\) | −11.5930 | + | 11.5930i | −0.695304 | + | 0.695304i | ||||
\(279\) | −7.25379 | −0.434273 | ||||||||
\(280\) | 2.83559 | − | 4.55032i | 0.169459 | − | 0.271934i | ||||
\(281\) | 13.5557 | 0.808664 | 0.404332 | − | 0.914612i | \(-0.367504\pi\) | ||||
0.404332 | + | 0.914612i | \(0.367504\pi\) | |||||||
\(282\) | 1.17214 | − | 1.17214i | 0.0698000 | − | 0.0698000i | ||||
\(283\) | 16.2444 | − | 16.2444i | 0.965627 | − | 0.965627i | −0.0338017 | − | 0.999429i | \(-0.510761\pi\) |
0.999429 | + | 0.0338017i | \(0.0107615\pi\) | |||||||
\(284\) | − | 37.2087i | − | 2.20793i | ||||||
\(285\) | −2.28260 | − | 13.2600i | −0.135210 | − | 0.785457i | ||||
\(286\) | − | 9.76010i | − | 0.577127i | ||||||
\(287\) | 13.9419 | + | 12.4204i | 0.822966 | + | 0.733155i | ||||
\(288\) | −5.67761 | − | 5.67761i | −0.334557 | − | 0.334557i | ||||
\(289\) | 28.0537i | 1.65021i | ||||||||
\(290\) | 1.41421 | − | 0.243445i | 0.0830455 | − | 0.0142956i | ||||
\(291\) | −12.5036 | −0.732973 | ||||||||
\(292\) | 24.3562 | + | 24.3562i | 1.42534 | + | 1.42534i | ||||
\(293\) | 2.41765 | − | 2.41765i | 0.141240 | − | 0.141240i | −0.632951 | − | 0.774192i | \(-0.718157\pi\) |
0.774192 | + | 0.632951i | \(0.218157\pi\) | |||||||
\(294\) | 14.6364 | − | 1.69511i | 0.853611 | − | 0.0988609i | ||||
\(295\) | 10.3049 | − | 14.5904i | 0.599974 | − | 0.849486i | ||||
\(296\) | 0.942578 | 0.0547862 | ||||||||
\(297\) | −1.88930 | − | 1.88930i | −0.109628 | − | 0.109628i | ||||
\(298\) | −21.2623 | − | 21.2623i | −1.23169 | − | 1.23169i | ||||
\(299\) | 0.431179 | 0.0249357 | ||||||||
\(300\) | 5.22529 | − | 10.9720i | 0.301682 | − | 0.633472i | ||||
\(301\) | −1.13890 | + | 0.0657309i | −0.0656449 | + | 0.00378867i | ||||
\(302\) | 14.5562 | − | 14.5562i | 0.837616 | − | 0.837616i | ||||
\(303\) | 5.11211 | + | 5.11211i | 0.293683 | + | 0.293683i | ||||
\(304\) | −17.7722 | −1.01931 | ||||||||
\(305\) | 10.1078 | + | 7.13890i | 0.578769 | + | 0.408772i | ||||
\(306\) | − | 14.1284i | − | 0.807669i | ||||||
\(307\) | −7.21300 | − | 7.21300i | −0.411667 | − | 0.411667i | 0.470652 | − | 0.882319i | \(-0.344019\pi\) |
−0.882319 | + | 0.470652i | \(0.844019\pi\) | |||||||
\(308\) | −12.8292 | − | 11.4292i | −0.731014 | − | 0.651238i | ||||
\(309\) | 9.82225i | 0.558768i | ||||||||
\(310\) | −33.6463 | + | 5.79193i | −1.91098 | + | 0.328959i | ||||
\(311\) | 10.2542i | 0.581460i | 0.956805 | + | 0.290730i | \(0.0938981\pi\) | ||||
−0.956805 | + | 0.290730i | \(0.906102\pi\) | |||||||
\(312\) | −1.11211 | + | 1.11211i | −0.0629611 | + | 0.0629611i | ||||
\(313\) | −22.0904 | + | 22.0904i | −1.24862 | + | 1.24862i | −0.292293 | + | 0.956329i | \(0.594418\pi\) |
−0.956329 | + | 0.292293i | \(0.905582\pi\) | |||||||
\(314\) | −6.48134 | −0.365763 | ||||||||
\(315\) | 5.76281 | − | 1.33791i | 0.324698 | − | 0.0753826i | ||||
\(316\) | 27.4586 | 1.54467 | ||||||||
\(317\) | −12.2563 | + | 12.2563i | −0.688385 | + | 0.688385i | −0.961875 | − | 0.273490i | \(-0.911822\pi\) |
0.273490 | + | 0.961875i | \(0.411822\pi\) | |||||||
\(318\) | 10.5040 | − | 10.5040i | 0.589037 | − | 0.589037i | ||||
\(319\) | − | 0.814625i | − | 0.0456102i | ||||||
\(320\) | −20.0798 | − | 14.1819i | −1.12249 | − | 0.792793i | ||||
\(321\) | − | 10.5683i | − | 0.589867i | ||||||
\(322\) | 0.920387 | − | 1.03313i | 0.0512912 | − | 0.0575743i | ||||
\(323\) | −28.5595 | − | 28.5595i | −1.58909 | − | 1.58909i | ||||
\(324\) | 2.43055i | 0.135031i | ||||||||
\(325\) | 7.83417 | + | 3.73092i | 0.434561 | + | 0.206954i | ||||
\(326\) | −40.7094 | −2.25468 | ||||||||
\(327\) | −4.20978 | − | 4.20978i | −0.232801 | − | 0.232801i | ||||
\(328\) | −4.52253 | + | 4.52253i | −0.249715 | + | 0.249715i | ||||
\(329\) | 2.08014 | − | 0.120054i | 0.114682 | − | 0.00661882i | ||||
\(330\) | −10.2720 | − | 7.25487i | −0.565453 | − | 0.399367i | ||||
\(331\) | 1.26308 | 0.0694252 | 0.0347126 | − | 0.999397i | \(-0.488948\pi\) | ||||
0.0347126 | + | 0.999397i | \(0.488948\pi\) | |||||||
\(332\) | −11.8840 | − | 11.8840i | −0.652217 | − | 0.652217i | ||||
\(333\) | 0.735441 | + | 0.735441i | 0.0403019 | + | 0.0403019i | ||||
\(334\) | 18.5538 | 1.01522 | ||||||||
\(335\) | 1.84038 | + | 10.6911i | 0.100551 | + | 0.584118i | ||||
\(336\) | −0.450249 | − | 7.80130i | −0.0245631 | − | 0.425596i | ||||
\(337\) | −9.55621 | + | 9.55621i | −0.520560 | + | 0.520560i | −0.917741 | − | 0.397180i | \(-0.869989\pi\) |
0.397180 | + | 0.917741i | \(0.369989\pi\) | |||||||
\(338\) | 14.8663 | + | 14.8663i | 0.808620 | + | 0.808620i | ||||
\(339\) | −9.88579 | −0.536922 | ||||||||
\(340\) | −6.18869 | − | 35.9512i | −0.335629 | − | 1.94973i | ||||
\(341\) | 19.3812i | 1.04955i | ||||||||
\(342\) | 8.95602 | + | 8.95602i | 0.484286 | + | 0.484286i | ||||
\(343\) | 15.1541 | + | 10.6468i | 0.818244 | + | 0.574871i | ||||
\(344\) | − | 0.390761i | − | 0.0210684i | ||||||
\(345\) | 0.320503 | − | 0.453791i | 0.0172553 | − | 0.0244313i | ||||
\(346\) | 20.1507i | 1.08331i | ||||||||
\(347\) | 6.54975 | − | 6.54975i | 0.351609 | − | 0.351609i | −0.509099 | − | 0.860708i | \(-0.670021\pi\) |
0.860708 | + | 0.509099i | \(0.170021\pi\) | |||||||
\(348\) | −0.524001 | + | 0.524001i | −0.0280894 | + | 0.0280894i | ||||
\(349\) | 2.77139 | 0.148349 | 0.0741746 | − | 0.997245i | \(-0.476368\pi\) | ||||
0.0741746 | + | 0.997245i | \(0.476368\pi\) | |||||||
\(350\) | 25.6622 | − | 10.8072i | 1.37170 | − | 0.577672i | ||||
\(351\) | −1.73544 | −0.0926310 | ||||||||
\(352\) | −15.1699 | + | 15.1699i | −0.808556 | + | 0.808556i | ||||
\(353\) | 0.970568 | − | 0.970568i | 0.0516581 | − | 0.0516581i | −0.680806 | − | 0.732464i | \(-0.738370\pi\) |
0.732464 | + | 0.680806i | \(0.238370\pi\) | |||||||
\(354\) | 16.8146i | 0.893687i | ||||||||
\(355\) | 19.7481 | − | 27.9607i | 1.04812 | − | 1.48400i | ||||
\(356\) | 16.8012i | 0.890463i | ||||||||
\(357\) | 11.8130 | − | 13.2601i | 0.625209 | − | 0.701797i | ||||
\(358\) | −1.93643 | − | 1.93643i | −0.102344 | − | 0.102344i | ||||
\(359\) | 9.32813i | 0.492320i | 0.969229 | + | 0.246160i | \(0.0791688\pi\) | ||||
−0.969229 | + | 0.246160i | \(0.920831\pi\) | |||||||
\(360\) | 0.343782 | + | 1.99709i | 0.0181189 | + | 0.105256i | ||||
\(361\) | 17.2078 | 0.905674 | ||||||||
\(362\) | 12.6293 | + | 12.6293i | 0.663783 | + | 0.663783i | ||||
\(363\) | 2.73021 | − | 2.73021i | 0.143299 | − | 0.143299i | ||||
\(364\) | −11.1415 | + | 0.643024i | −0.583971 | + | 0.0337036i | ||||
\(365\) | 5.37586 | + | 31.2293i | 0.281385 | + | 1.63462i | ||||
\(366\) | −11.6486 | −0.608884 | ||||||||
\(367\) | −13.0035 | − | 13.0035i | −0.678776 | − | 0.678776i | 0.280948 | − | 0.959723i | \(-0.409351\pi\) |
−0.959723 | + | 0.280948i | \(0.909351\pi\) | |||||||
\(368\) | −0.518887 | − | 0.518887i | −0.0270488 | − | 0.0270488i | ||||
\(369\) | −7.05736 | −0.367392 | ||||||||
\(370\) | 3.99853 | + | 2.82408i | 0.207874 | + | 0.146817i | ||||
\(371\) | 18.6410 | − | 1.07586i | 0.967793 | − | 0.0558557i | ||||
\(372\) | 12.4668 | − | 12.4668i | 0.646373 | − | 0.646373i | ||||
\(373\) | 20.6757 | + | 20.6757i | 1.07055 | + | 1.07055i | 0.997315 | + | 0.0732339i | \(0.0233320\pi\) |
0.0732339 | + | 0.997315i | \(0.476668\pi\) | |||||||
\(374\) | −37.7493 | −1.95197 | ||||||||
\(375\) | 9.74986 | − | 5.47176i | 0.503481 | − | 0.282560i | ||||
\(376\) | 0.713708i | 0.0368067i | ||||||||
\(377\) | −0.374143 | − | 0.374143i | −0.0192693 | − | 0.0192693i | ||||
\(378\) | −3.70445 | + | 4.15824i | −0.190536 | + | 0.213877i | ||||
\(379\) | − | 22.0077i | − | 1.13046i | −0.824933 | − | 0.565230i | \(-0.808787\pi\) | ||
0.824933 | − | 0.565230i | \(-0.191213\pi\) | |||||||
\(380\) | 26.7125 | + | 18.8665i | 1.37032 | + | 0.967830i | ||||
\(381\) | 4.04621i | 0.207294i | ||||||||
\(382\) | 2.88434 | − | 2.88434i | 0.147576 | − | 0.147576i | ||||
\(383\) | 0.390382 | − | 0.390382i | 0.0199476 | − | 0.0199476i | −0.697063 | − | 0.717010i | \(-0.745510\pi\) |
0.717010 | + | 0.697063i | \(0.245510\pi\) | |||||||
\(384\) | 7.08211 | 0.361407 | ||||||||
\(385\) | −3.57472 | − | 15.3975i | −0.182185 | − | 0.784729i | ||||
\(386\) | −23.3017 | −1.18602 | ||||||||
\(387\) | 0.304889 | − | 0.304889i | 0.0154984 | − | 0.0154984i | ||||
\(388\) | 21.4894 | − | 21.4894i | 1.09096 | − | 1.09096i | ||||
\(389\) | − | 25.9300i | − | 1.31470i | −0.753584 | − | 0.657352i | \(-0.771677\pi\) | ||
0.753584 | − | 0.657352i | \(-0.228323\pi\) | |||||||
\(390\) | −8.04976 | + | 1.38570i | −0.407615 | + | 0.0701674i | ||||
\(391\) | − | 1.66768i | − | 0.0843381i | ||||||
\(392\) | −3.93992 | + | 4.97206i | −0.198996 | + | 0.251127i | ||||
\(393\) | −6.60978 | − | 6.60978i | −0.333419 | − | 0.333419i | ||||
\(394\) | 25.3253i | 1.27587i | ||||||||
\(395\) | 20.6339 | + | 14.5733i | 1.03821 | + | 0.733263i | ||||
\(396\) | 6.49412 | 0.326342 | ||||||||
\(397\) | 17.1631 | + | 17.1631i | 0.861391 | + | 0.861391i | 0.991500 | − | 0.130109i | \(-0.0415327\pi\) |
−0.130109 | + | 0.991500i | \(0.541533\pi\) | |||||||
\(398\) | 4.84408 | − | 4.84408i | 0.242812 | − | 0.242812i | ||||
\(399\) | 0.917304 | + | 15.8938i | 0.0459226 | + | 0.795686i | ||||
\(400\) | −4.93791 | − | 13.9176i | −0.246895 | − | 0.695879i | ||||
\(401\) | −12.9418 | −0.646281 | −0.323140 | − | 0.946351i | \(-0.604739\pi\) | ||||
−0.323140 | + | 0.946351i | \(0.604739\pi\) | |||||||
\(402\) | −7.22093 | − | 7.22093i | −0.360147 | − | 0.360147i | ||||
\(403\) | 8.90143 | + | 8.90143i | 0.443412 | + | 0.443412i | ||||
\(404\) | −17.5720 | −0.874238 | ||||||||
\(405\) | −1.28999 | + | 1.82645i | −0.0640999 | + | 0.0907572i | ||||
\(406\) | −1.69511 | + | 0.0978326i | −0.0841269 | + | 0.00485535i | ||||
\(407\) | 1.96500 | − | 1.96500i | 0.0974016 | − | 0.0974016i | ||||
\(408\) | 4.30135 | + | 4.30135i | 0.212948 | + | 0.212948i | ||||
\(409\) | 2.64278 | 0.130677 | 0.0653386 | − | 0.997863i | \(-0.479187\pi\) | ||||
0.0653386 | + | 0.997863i | \(0.479187\pi\) | |||||||
\(410\) | −32.7352 | + | 5.63508i | −1.61668 | + | 0.278297i | ||||
\(411\) | 10.6341i | 0.524540i | ||||||||
\(412\) | −16.8811 | − | 16.8811i | −0.831672 | − | 0.831672i | ||||
\(413\) | −14.0589 | + | 15.7812i | −0.691795 | + | 0.776540i | ||||
\(414\) | 0.522969i | 0.0257025i | ||||||||
\(415\) | −2.62301 | − | 15.2376i | −0.128759 | − | 0.747982i | ||||
\(416\) | 13.9345i | 0.683194i | ||||||||
\(417\) | 5.50767 | − | 5.50767i | 0.269712 | − | 0.269712i | ||||
\(418\) | 23.9293 | − | 23.9293i | 1.17042 | − | 1.17042i | ||||
\(419\) | −10.0302 | −0.490007 | −0.245003 | − | 0.969522i | \(-0.578789\pi\) | ||||
−0.245003 | + | 0.969522i | \(0.578789\pi\) | |||||||
\(420\) | −7.60490 | + | 12.2037i | −0.371081 | + | 0.595481i | ||||
\(421\) | −26.6440 | −1.29855 | −0.649274 | − | 0.760555i | \(-0.724927\pi\) | ||||
−0.649274 | + | 0.760555i | \(0.724927\pi\) | |||||||
\(422\) | −25.6757 | + | 25.6757i | −1.24987 | + | 1.24987i | ||||
\(423\) | −0.556866 | + | 0.556866i | −0.0270758 | + | 0.0270758i | ||||
\(424\) | 6.39583i | 0.310609i | ||||||||
\(425\) | 14.4301 | − | 30.3004i | 0.699965 | − | 1.46978i | ||||
\(426\) | 32.2232i | 1.56122i | ||||||||
\(427\) | −10.9327 | − | 9.73958i | −0.529069 | − | 0.471332i | ||||
\(428\) | 18.1634 | + | 18.1634i | 0.877960 | + | 0.877960i | ||||
\(429\) | 4.63688i | 0.223870i | ||||||||
\(430\) | 1.17077 | − | 1.65766i | 0.0564595 | − | 0.0799394i | ||||
\(431\) | 22.3747 | 1.07775 | 0.538876 | − | 0.842385i | \(-0.318849\pi\) | ||||
0.538876 | + | 0.842385i | \(0.318849\pi\) | |||||||
\(432\) | 2.08845 | + | 2.08845i | 0.100481 | + | 0.100481i | ||||
\(433\) | −13.4723 | + | 13.4723i | −0.647438 | + | 0.647438i | −0.952373 | − | 0.304935i | \(-0.901365\pi\) |
0.304935 | + | 0.952373i | \(0.401365\pi\) | |||||||
\(434\) | 40.3293 | − | 2.32759i | 1.93587 | − | 0.111728i | ||||
\(435\) | −0.671871 | + | 0.115657i | −0.0322138 | + | 0.00554532i | ||||
\(436\) | 14.4703 | 0.693004 | ||||||||
\(437\) | 1.05714 | + | 1.05714i | 0.0505700 | + | 0.0505700i | ||||
\(438\) | −21.0927 | − | 21.0927i | −1.00785 | − | 1.00785i | ||||
\(439\) | −25.6790 | −1.22559 | −0.612795 | − | 0.790242i | \(-0.709955\pi\) | ||||
−0.612795 | + | 0.790242i | \(0.709955\pi\) | |||||||
\(440\) | 5.33598 | − | 0.918542i | 0.254383 | − | 0.0437898i | ||||
\(441\) | −6.95352 | + | 0.805321i | −0.331120 | + | 0.0383486i | ||||
\(442\) | −17.3376 | + | 17.3376i | −0.824665 | + | 0.824665i | ||||
\(443\) | −15.6351 | − | 15.6351i | −0.742845 | − | 0.742845i | 0.230279 | − | 0.973125i | \(-0.426036\pi\) |
−0.973125 | + | 0.230279i | \(0.926036\pi\) | |||||||
\(444\) | −2.52795 | −0.119971 | ||||||||
\(445\) | −8.91705 | + | 12.6254i | −0.422709 | + | 0.598501i | ||||
\(446\) | − | 13.6452i | − | 0.646120i | ||||||
\(447\) | 10.1014 | + | 10.1014i | 0.477779 | + | 0.477779i | ||||
\(448\) | 21.7185 | + | 19.3484i | 1.02610 | + | 0.914124i | ||||
\(449\) | 7.01947i | 0.331269i | 0.986187 | + | 0.165635i | \(0.0529673\pi\) | ||||
−0.986187 | + | 0.165635i | \(0.947033\pi\) | |||||||
\(450\) | −4.52517 | + | 9.50193i | −0.213318 | + | 0.447925i | ||||
\(451\) | 18.8564i | 0.887912i | ||||||||
\(452\) | 16.9903 | − | 16.9903i | 0.799157 | − | 0.799157i | ||||
\(453\) | −6.91544 | + | 6.91544i | −0.324916 | + | 0.324916i | ||||
\(454\) | −42.1548 | −1.97842 | ||||||||
\(455\) | −8.71359 | − | 5.42999i | −0.408500 | − | 0.254562i | ||||
\(456\) | −5.45325 | −0.255372 | ||||||||
\(457\) | 11.2119 | − | 11.2119i | 0.524472 | − | 0.524472i | −0.394447 | − | 0.918919i | \(-0.629064\pi\) |
0.918919 | + | 0.394447i | \(0.129064\pi\) | |||||||
\(458\) | 43.0599 | − | 43.0599i | 2.01206 | − | 2.01206i | ||||
\(459\) | 6.71220i | 0.313299i | ||||||||
\(460\) | 0.229077 | + | 1.33075i | 0.0106808 | + | 0.0620465i | ||||
\(461\) | − | 29.9845i | − | 1.39652i | −0.715846 | − | 0.698259i | \(-0.753959\pi\) | ||
0.715846 | − | 0.698259i | \(-0.246041\pi\) | |||||||
\(462\) | 11.1103 | + | 9.89780i | 0.516897 | + | 0.460488i | ||||
\(463\) | 7.70220 | + | 7.70220i | 0.357951 | + | 0.357951i | 0.863057 | − | 0.505106i | \(-0.168547\pi\) |
−0.505106 | + | 0.863057i | \(0.668547\pi\) | |||||||
\(464\) | 0.900497i | 0.0418045i | ||||||||
\(465\) | 15.9849 | − | 2.75166i | 0.741280 | − | 0.127605i | ||||
\(466\) | −14.2452 | −0.659895 | ||||||||
\(467\) | −1.80961 | − | 1.80961i | −0.0837386 | − | 0.0837386i | 0.663997 | − | 0.747735i | \(-0.268859\pi\) |
−0.747735 | + | 0.663997i | \(0.768859\pi\) | |||||||
\(468\) | 2.98263 | − | 2.98263i | 0.137872 | − | 0.137872i | ||||
\(469\) | −0.739590 | − | 12.8146i | −0.0341511 | − | 0.591724i | ||||
\(470\) | −2.13836 | + | 3.02764i | −0.0986350 | + | 0.139654i | ||||
\(471\) | 3.07918 | 0.141881 | ||||||||
\(472\) | −5.11915 | − | 5.11915i | −0.235628 | − | 0.235628i | ||||
\(473\) | −0.814625 | − | 0.814625i | −0.0374565 | − | 0.0374565i | ||||
\(474\) | −23.7795 | −1.09223 | ||||||||
\(475\) | 10.0601 | + | 28.3547i | 0.461591 | + | 1.30100i | ||||
\(476\) | 2.48704 | + | 43.0920i | 0.113993 | + | 1.97512i | ||||
\(477\) | −4.99031 | + | 4.99031i | −0.228491 | + | 0.228491i | ||||
\(478\) | −24.0774 | − | 24.0774i | −1.10128 | − | 1.10128i | ||||
\(479\) | −4.09455 | −0.187085 | −0.0935425 | − | 0.995615i | \(-0.529819\pi\) | ||||
−0.0935425 | + | 0.995615i | \(0.529819\pi\) | |||||||
\(480\) | 14.6653 | + | 10.3578i | 0.669374 | + | 0.472765i | ||||
\(481\) | − | 1.80498i | − | 0.0823001i | ||||||
\(482\) | −16.9240 | − | 16.9240i | −0.770867 | − | 0.770867i | ||||
\(483\) | −0.437262 | + | 0.490826i | −0.0198961 | + | 0.0223334i | ||||
\(484\) | 9.38461i | 0.426573i | ||||||||
\(485\) | 27.5536 | − | 4.74311i | 1.25114 | − | 0.215374i | ||||
\(486\) | − | 2.10489i | − | 0.0954796i | ||||||
\(487\) | −10.3049 | + | 10.3049i | −0.466959 | + | 0.466959i | −0.900928 | − | 0.433969i | \(-0.857113\pi\) |
0.433969 | + | 0.900928i | \(0.357113\pi\) | |||||||
\(488\) | 3.54638 | − | 3.54638i | 0.160537 | − | 0.160537i | ||||
\(489\) | 19.3404 | 0.874603 | ||||||||
\(490\) | −31.6105 | + | 9.28761i | −1.42802 | + | 0.419571i | ||||
\(491\) | −8.55953 | −0.386286 | −0.193143 | − | 0.981171i | \(-0.561868\pi\) | ||||
−0.193143 | + | 0.981171i | \(0.561868\pi\) | |||||||
\(492\) | 12.1292 | − | 12.1292i | 0.546827 | − | 0.546827i | ||||
\(493\) | −1.44708 | + | 1.44708i | −0.0651732 | + | 0.0651732i | ||||
\(494\) | − | 21.9806i | − | 0.988955i | ||||||
\(495\) | 4.88005 | + | 3.44668i | 0.219342 | + | 0.154917i | ||||
\(496\) | − | 21.4242i | − | 0.961976i | ||||||
\(497\) | −26.9423 | + | 30.2427i | −1.20853 | + | 1.35657i | ||||
\(498\) | 10.2917 | + | 10.2917i | 0.461180 | + | 0.461180i | ||||
\(499\) | − | 23.7564i | − | 1.06348i | −0.846907 | − | 0.531741i | \(-0.821538\pi\) | ||
0.846907 | − | 0.531741i | \(-0.178462\pi\) | |||||||
\(500\) | −7.35261 | + | 26.1608i | −0.328819 | + | 1.16995i | ||||
\(501\) | −8.81463 | −0.393808 | ||||||||
\(502\) | 10.3448 | + | 10.3448i | 0.461712 | + | 0.461712i | ||||
\(503\) | 17.9504 | − | 17.9504i | 0.800367 | − | 0.800367i | −0.182786 | − | 0.983153i | \(-0.558511\pi\) |
0.983153 | + | 0.182786i | \(0.0585115\pi\) | |||||||
\(504\) | −0.138155 | − | 2.39376i | −0.00615391 | − | 0.106627i | ||||
\(505\) | −13.2046 | − | 9.32611i | −0.587596 | − | 0.415007i | ||||
\(506\) | 1.39731 | 0.0621179 | ||||||||
\(507\) | −7.06275 | − | 7.06275i | −0.313668 | − | 0.313668i | ||||
\(508\) | −6.95406 | − | 6.95406i | −0.308537 | − | 0.308537i | ||||
\(509\) | −16.8977 | −0.748979 | −0.374489 | − | 0.927231i | \(-0.622182\pi\) | ||||
−0.374489 | + | 0.927231i | \(0.622182\pi\) | |||||||
\(510\) | 5.35948 | + | 31.1342i | 0.237322 | + | 1.37865i | ||||
\(511\) | −2.16039 | − | 37.4322i | −0.0955698 | − | 1.65590i | ||||
\(512\) | 20.5543 | − | 20.5543i | 0.908382 | − | 0.908382i | ||||
\(513\) | −4.25487 | − | 4.25487i | −0.187857 | − | 0.187857i | ||||
\(514\) | −30.0323 | −1.32467 | ||||||||
\(515\) | −3.72598 | − | 21.6449i | −0.164186 | − | 0.953787i | ||||
\(516\) | 1.04800i | 0.0461357i | ||||||||
\(517\) | 1.48788 | + | 1.48788i | 0.0654367 | + | 0.0654367i | ||||
\(518\) | −4.32486 | − | 3.85289i | −0.190024 | − | 0.169286i | ||||
\(519\) | − | 9.57331i | − | 0.420221i | ||||||
\(520\) | 2.02885 | − | 2.87259i | 0.0889708 | − | 0.125971i | ||||
\(521\) | − | 7.88477i | − | 0.345438i | −0.984971 | − | 0.172719i | \(-0.944745\pi\) | ||
0.984971 | − | 0.172719i | \(-0.0552552\pi\) | |||||||
\(522\) | 0.453791 | − | 0.453791i | 0.0198619 | − | 0.0198619i | ||||
\(523\) | 1.23149 | − | 1.23149i | 0.0538493 | − | 0.0538493i | −0.679669 | − | 0.733519i | \(-0.737877\pi\) |
0.733519 | + | 0.679669i | \(0.237877\pi\) | |||||||
\(524\) | 22.7199 | 0.992524 | ||||||||
\(525\) | −12.1917 | + | 5.13436i | −0.532091 | + | 0.224082i | ||||
\(526\) | 54.1722 | 2.36202 | ||||||||
\(527\) | 34.4283 | − | 34.4283i | 1.49972 | − | 1.49972i | ||||
\(528\) | 5.58008 | − | 5.58008i | 0.242842 | − | 0.242842i | ||||
\(529\) | − | 22.9383i | − | 0.997316i | ||||||
\(530\) | −19.1627 | + | 27.1319i | −0.832374 | + | 1.17853i | ||||
\(531\) | − | 7.98837i | − | 0.346666i | ||||||
\(532\) | −28.8926 | − | 25.7395i | −1.25265 | − | 1.11595i | ||||
\(533\) | 8.66039 | + | 8.66039i | 0.375123 | + | 0.375123i | ||||
\(534\) | − | 14.5501i | − | 0.629643i | ||||||
\(535\) | 4.00900 | + | 23.2890i | 0.173324 | + | 1.00687i | ||||
\(536\) | 4.39677 | 0.189911 | ||||||||
\(537\) | 0.919968 | + | 0.919968i | 0.0396996 | + | 0.0396996i | ||||
\(538\) | 23.0876 | − | 23.0876i | 0.995375 | − | 0.995375i | ||||
\(539\) | 2.15171 | + | 18.5789i | 0.0926809 | + | 0.800250i | ||||
\(540\) | −0.922006 | − | 5.35610i | −0.0396768 | − | 0.230490i | ||||
\(541\) | 34.9495 | 1.50260 | 0.751298 | − | 0.659963i | \(-0.229428\pi\) | ||||
0.751298 | + | 0.659963i | \(0.229428\pi\) | |||||||
\(542\) | 19.8577 | + | 19.8577i | 0.852962 | + | 0.852962i | ||||
\(543\) | −6.00000 | − | 6.00000i | −0.257485 | − | 0.257485i | ||||
\(544\) | 53.8947 | 2.31071 | ||||||||
\(545\) | 10.8738 | + | 7.67996i | 0.465784 | + | 0.328973i | ||||
\(546\) | 9.64863 | − | 0.556866i | 0.412923 | − | 0.0238317i | ||||
\(547\) | 3.83548 | − | 3.83548i | 0.163993 | − | 0.163993i | −0.620340 | − | 0.784333i | \(-0.713005\pi\) |
0.784333 | + | 0.620340i | \(0.213005\pi\) | |||||||
\(548\) | −18.2764 | − | 18.2764i | −0.780727 | − | 0.780727i | ||||
\(549\) | 5.53409 | 0.236189 | ||||||||
\(550\) | 25.3879 | + | 12.0907i | 1.08255 | + | 0.515548i | ||||
\(551\) | − | 1.83461i | − | 0.0781569i | ||||||
\(552\) | −0.159216 | − | 0.159216i | −0.00677668 | − | 0.00677668i | ||||
\(553\) | −22.3179 | − | 19.8823i | −0.949054 | − | 0.845483i | ||||
\(554\) | 5.97022i | 0.253650i | ||||||||
\(555\) | −1.89964 | − | 1.34168i | −0.0806353 | − | 0.0569510i | ||||
\(556\) | 18.9316i | 0.802880i | ||||||||
\(557\) | −16.3147 | + | 16.3147i | −0.691275 | + | 0.691275i | −0.962512 | − | 0.271238i | \(-0.912567\pi\) |
0.271238 | + | 0.962512i | \(0.412567\pi\) | |||||||
\(558\) | −10.7964 | + | 10.7964i | −0.457048 | + | 0.457048i | ||||
\(559\) | −0.748285 | −0.0316491 | ||||||||
\(560\) | 3.95154 | + | 17.0206i | 0.166983 | + | 0.719251i | ||||
\(561\) | 17.9341 | 0.757180 | ||||||||
\(562\) | 20.1760 | − | 20.1760i | 0.851073 | − | 0.851073i | ||||
\(563\) | −23.7521 | + | 23.7521i | −1.00103 | + | 1.00103i | −0.00103054 | + | 0.999999i | \(0.500328\pi\) |
−0.999999 | + | 0.00103054i | \(0.999672\pi\) | |||||||
\(564\) | − | 1.91413i | − | 0.0805993i | ||||||
\(565\) | 21.7849 | − | 3.75008i | 0.916497 | − | 0.157767i | ||||
\(566\) | − | 48.3556i | − | 2.03254i | ||||||
\(567\) | 1.75993 | − | 1.97552i | 0.0739099 | − | 0.0829638i | ||||
\(568\) | −9.81023 | − | 9.81023i | −0.411628 | − | 0.411628i | ||||
\(569\) | 0.277792i | 0.0116457i | 0.999983 | + | 0.00582283i | \(0.00185348\pi\) | ||||
−0.999983 | + | 0.00582283i | \(0.998147\pi\) | |||||||
\(570\) | −23.1334 | − | 16.3386i | −0.968950 | − | 0.684349i | ||||
\(571\) | −3.11538 | −0.130375 | −0.0651874 | − | 0.997873i | \(-0.520765\pi\) | ||||
−0.0651874 | + | 0.997873i | \(0.520765\pi\) | |||||||
\(572\) | −7.96921 | − | 7.96921i | −0.333209 | − | 0.333209i | ||||
\(573\) | −1.37031 | + | 1.37031i | −0.0572454 | + | 0.0572454i | ||||
\(574\) | 39.2372 | − | 2.26456i | 1.63773 | − | 0.0945209i | ||||
\(575\) | −0.534138 | + | 1.12158i | −0.0222751 | + | 0.0467731i | ||||
\(576\) | −10.9939 | −0.458077 | ||||||||
\(577\) | −29.5905 | − | 29.5905i | −1.23187 | − | 1.23187i | −0.963245 | − | 0.268625i | \(-0.913431\pi\) |
−0.268625 | − | 0.963245i | \(-0.586569\pi\) | |||||||
\(578\) | 41.7545 | + | 41.7545i | 1.73676 | + | 1.73676i | ||||
\(579\) | 11.0703 | 0.460064 | ||||||||
\(580\) | 0.955943 | − | 1.35349i | 0.0396934 | − | 0.0562007i | ||||
\(581\) | 1.05410 | + | 18.2641i | 0.0437316 | + | 0.757722i | ||||
\(582\) | −18.6101 | + | 18.6101i | −0.771413 | + | 0.771413i | ||||
\(583\) | 13.3335 | + | 13.3335i | 0.552216 | + | 0.552216i | ||||
\(584\) | 12.8432 | 0.531456 | ||||||||
\(585\) | 3.82432 | − | 0.658323i | 0.158116 | − | 0.0272183i | ||||
\(586\) | − | 7.19676i | − | 0.297295i | ||||||
\(587\) | −26.6462 | − | 26.6462i | −1.09981 | − | 1.09981i | −0.994433 | − | 0.105375i | \(-0.966396\pi\) |
−0.105375 | − | 0.994433i | \(-0.533604\pi\) | |||||||
\(588\) | 10.5667 | − | 13.3348i | 0.435762 | − | 0.549918i | ||||
\(589\) | 43.6482i | 1.79849i | ||||||||
\(590\) | −6.37847 | − | 37.0537i | −0.262597 | − | 1.52547i | ||||
\(591\) | − | 12.0317i | − | 0.494916i | ||||||
\(592\) | −2.17214 | + | 2.17214i | −0.0892745 | + | 0.0892745i | ||||
\(593\) | −15.1889 | + | 15.1889i | −0.623733 | + | 0.623733i | −0.946484 | − | 0.322751i | \(-0.895392\pi\) |
0.322751 | + | 0.946484i | \(0.395392\pi\) | |||||||
\(594\) | −5.62399 | −0.230755 | ||||||||
\(595\) | −21.0017 | + | 33.7017i | −0.860985 | + | 1.38164i | ||||
\(596\) | −34.7217 | −1.42225 | ||||||||
\(597\) | −2.30135 | + | 2.30135i | −0.0941878 | + | 0.0941878i | ||||
\(598\) | 0.641758 | − | 0.641758i | 0.0262434 | − | 0.0262434i | ||||
\(599\) | 22.2776i | 0.910238i | 0.890431 | + | 0.455119i | \(0.150403\pi\) | ||||
−0.890431 | + | 0.455119i | \(0.849597\pi\) | |||||||
\(600\) | −1.51516 | − | 4.27050i | −0.0618560 | − | 0.174342i | ||||
\(601\) | 22.3458i | 0.911503i | 0.890107 | + | 0.455752i | \(0.150629\pi\) | ||||
−0.890107 | + | 0.455752i | \(0.849371\pi\) | |||||||
\(602\) | −1.59728 | + | 1.79294i | −0.0651002 | + | 0.0730749i | ||||
\(603\) | 3.43055 | + | 3.43055i | 0.139703 | + | 0.139703i | ||||
\(604\) | − | 23.7706i | − | 0.967210i | ||||||
\(605\) | −4.98077 | + | 7.05213i | −0.202497 | + | 0.286710i | ||||
\(606\) | 15.2175 | 0.618170 | ||||||||
\(607\) | 0.576027 | + | 0.576027i | 0.0233802 | + | 0.0233802i | 0.718700 | − | 0.695320i | \(-0.244737\pi\) |
−0.695320 | + | 0.718700i | \(0.744737\pi\) | |||||||
\(608\) | −34.1639 | + | 34.1639i | −1.38553 | + | 1.38553i | ||||
\(609\) | 0.805321 | − | 0.0464788i | 0.0326333 | − | 0.00188341i | ||||
\(610\) | 25.6696 | − | 4.41880i | 1.03933 | − | 0.178912i | ||||
\(611\) | 1.36671 | 0.0552911 | ||||||||
\(612\) | −11.5360 | − | 11.5360i | −0.466315 | − | 0.466315i | ||||
\(613\) | −16.4709 | − | 16.4709i | −0.665253 | − | 0.665253i | 0.291361 | − | 0.956613i | \(-0.405892\pi\) |
−0.956613 | + | 0.291361i | \(0.905892\pi\) | |||||||
\(614\) | −21.4714 | −0.866514 | ||||||||
\(615\) | 15.5520 | − | 2.67714i | 0.627117 | − | 0.107953i | ||||
\(616\) | −6.39583 | + | 0.369132i | −0.257695 | + | 0.0148728i | ||||
\(617\) | −3.70013 | + | 3.70013i | −0.148962 | + | 0.148962i | −0.777654 | − | 0.628692i | \(-0.783590\pi\) |
0.628692 | + | 0.777654i | \(0.283590\pi\) | |||||||
\(618\) | 14.6192 | + | 14.6192i | 0.588072 | + | 0.588072i | ||||
\(619\) | 39.8840 | 1.60307 | 0.801536 | − | 0.597946i | \(-0.204016\pi\) | ||||
0.801536 | + | 0.597946i | \(0.204016\pi\) | |||||||
\(620\) | −22.7434 | + | 32.2017i | −0.913396 | + | 1.29325i | ||||
\(621\) | − | 0.248455i | − | 0.00997015i | ||||||
\(622\) | 15.2621 | + | 15.2621i | 0.611954 | + | 0.611954i | ||||
\(623\) | 12.1655 | − | 13.6558i | 0.487401 | − | 0.547107i | ||||
\(624\) | − | 5.12566i | − | 0.205191i | ||||||
\(625\) | −19.4097 | + | 15.7564i | −0.776388 | + | 0.630256i | ||||
\(626\) | 65.7578i | 2.62821i | ||||||||
\(627\) | −11.3685 | + | 11.3685i | −0.454013 | + | 0.454013i | ||||
\(628\) | −5.29207 | + | 5.29207i | −0.211177 | + | 0.211177i | ||||
\(629\) | −6.98117 | −0.278357 | ||||||||
\(630\) | 6.58594 | − | 10.5686i | 0.262390 | − | 0.421062i | ||||
\(631\) | −33.9725 | −1.35242 | −0.676211 | − | 0.736708i | \(-0.736379\pi\) | ||||
−0.676211 | + | 0.736708i | \(0.736379\pi\) | |||||||
\(632\) | 7.23957 | − | 7.23957i | 0.287975 | − | 0.287975i | ||||
\(633\) | 12.1981 | − | 12.1981i | 0.484833 | − | 0.484833i | ||||
\(634\) | 36.4842i | 1.44897i | ||||||||
\(635\) | −1.53489 | − | 8.91646i | −0.0609103 | − | 0.353839i | ||||
\(636\) | − | 17.1533i | − | 0.680172i | ||||||
\(637\) | 9.52120 | + | 7.54472i | 0.377244 | + | 0.298933i | ||||
\(638\) | −1.21247 | − | 1.21247i | −0.0480022 | − | 0.0480022i | ||||
\(639\) | − | 15.3087i | − | 0.605605i | ||||||
\(640\) | −15.6065 | + | 2.68653i | −0.616902 | + | 0.106194i | ||||
\(641\) | −18.1113 | −0.715352 | −0.357676 | − | 0.933846i | \(-0.616431\pi\) | ||||
−0.357676 | + | 0.933846i | \(0.616431\pi\) | |||||||
\(642\) | −15.7297 | − | 15.7297i | −0.620802 | − | 0.620802i | ||||
\(643\) | −32.1062 | + | 32.1062i | −1.26614 | + | 1.26614i | −0.318082 | + | 0.948063i | \(0.603039\pi\) |
−0.948063 | + | 0.318082i | \(0.896961\pi\) | |||||||
\(644\) | −0.0920586 | − | 1.59507i | −0.00362762 | − | 0.0628545i | ||||
\(645\) | −0.556214 | + | 0.787528i | −0.0219009 | + | 0.0310089i | ||||
\(646\) | −85.0149 | −3.34487 | ||||||||
\(647\) | −12.9277 | − | 12.9277i | −0.508241 | − | 0.508241i | 0.405745 | − | 0.913986i | \(-0.367012\pi\) |
−0.913986 | + | 0.405745i | \(0.867012\pi\) | |||||||
\(648\) | 0.640825 | + | 0.640825i | 0.0251740 | + | 0.0251740i | ||||
\(649\) | −21.3439 | −0.837821 | ||||||||
\(650\) | 17.2132 | − | 6.10719i | 0.675159 | − | 0.239544i | ||||
\(651\) | −19.1598 | + | 1.10580i | −0.750934 | + | 0.0433398i | ||||
\(652\) | −33.2396 | + | 33.2396i | −1.30176 | + | 1.30176i | ||||
\(653\) | −9.39937 | − | 9.39937i | −0.367826 | − | 0.367826i | 0.498858 | − | 0.866684i | \(-0.333753\pi\) |
−0.866684 | + | 0.498858i | \(0.833753\pi\) | |||||||
\(654\) | −12.5315 | −0.490020 | ||||||||
\(655\) | 17.0730 | + | 12.0583i | 0.667099 | + | 0.471158i | ||||
\(656\) | − | 20.8441i | − | 0.813824i | ||||||
\(657\) | 10.0208 | + | 10.0208i | 0.390950 | + | 0.390950i | ||||
\(658\) | 2.91736 | − | 3.27473i | 0.113730 | − | 0.127662i | ||||
\(659\) | 9.13808i | 0.355969i | 0.984033 | + | 0.177985i | \(0.0569577\pi\) | ||||
−0.984033 | + | 0.177985i | \(0.943042\pi\) | |||||||
\(660\) | −14.3108 | + | 2.46348i | −0.557048 | + | 0.0958909i | ||||
\(661\) | − | 28.4837i | − | 1.10789i | −0.832554 | − | 0.553943i | \(-0.813122\pi\) | ||
0.832554 | − | 0.553943i | \(-0.186878\pi\) | |||||||
\(662\) | 1.87995 | − | 1.87995i | 0.0730662 | − | 0.0730662i | ||||
\(663\) | 8.23683 | − | 8.23683i | 0.319892 | − | 0.319892i | ||||
\(664\) | −6.26651 | −0.243188 | ||||||||
\(665\) | −8.05059 | − | 34.6765i | −0.312188 | − | 1.34470i | ||||
\(666\) | 2.18923 | 0.0848310 | ||||||||
\(667\) | 0.0535642 | − | 0.0535642i | 0.00207401 | − | 0.00207401i | ||||
\(668\) | 15.1493 | − | 15.1493i | 0.586146 | − | 0.586146i | ||||
\(669\) | 6.48264i | 0.250633i | ||||||||
\(670\) | 18.6516 | + | 13.1733i | 0.720575 | + | 0.508927i | ||||
\(671\) | − | 14.7864i | − | 0.570821i | ||||||
\(672\) | −15.8621 | − | 14.1311i | −0.611894 | − | 0.545118i | ||||
\(673\) | 26.8815 | + | 26.8815i | 1.03621 | + | 1.03621i | 0.999319 | + | 0.0368867i | \(0.0117441\pi\) |
0.0368867 | + | 0.999319i | \(0.488256\pi\) | |||||||
\(674\) | 28.4466i | 1.09572i | ||||||||
\(675\) | 2.14984 | − | 4.51422i | 0.0827473 | − | 0.173752i | ||||
\(676\) | 24.2769 | 0.933729 | ||||||||
\(677\) | 1.19694 | + | 1.19694i | 0.0460022 | + | 0.0460022i | 0.729734 | − | 0.683731i | \(-0.239644\pi\) |
−0.683731 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(678\) | −14.7138 | + | 14.7138i | −0.565081 | + | 0.565081i | ||||
\(679\) | −33.0264 | + | 1.90611i | −1.26744 | + | 0.0731496i | ||||
\(680\) | −11.1104 | − | 7.84702i | −0.426063 | − | 0.300919i | ||||
\(681\) | 20.0271 | 0.767440 | ||||||||
\(682\) | 28.8466 | + | 28.8466i | 1.10459 | + | 1.10459i | ||||
\(683\) | 2.41553 | + | 2.41553i | 0.0924275 | + | 0.0924275i | 0.751809 | − | 0.659381i | \(-0.229182\pi\) |
−0.659381 | + | 0.751809i | \(0.729182\pi\) | |||||||
\(684\) | 14.6253 | 0.559214 | ||||||||
\(685\) | −4.03393 | − | 23.4338i | −0.154129 | − | 0.895361i | ||||
\(686\) | 38.4015 | − | 6.70863i | 1.46618 | − | 0.256137i | ||||
\(687\) | −20.4571 | + | 20.4571i | −0.780487 | + | 0.780487i | ||||
\(688\) | 0.900497 | + | 0.900497i | 0.0343311 | + | 0.0343311i | ||||
\(689\) | 12.2476 | 0.466598 | ||||||||
\(690\) | −0.198383 | − | 1.15244i | −0.00755233 | − | 0.0438728i | ||||
\(691\) | 41.6703i | 1.58521i | 0.609735 | + | 0.792606i | \(0.291276\pi\) | ||||
−0.609735 | + | 0.792606i | \(0.708724\pi\) | |||||||
\(692\) | 16.4533 | + | 16.4533i | 0.625459 | + | 0.625459i | ||||
\(693\) | −5.27832 | − | 4.70230i | −0.200507 | − | 0.178625i | ||||
\(694\) | − | 19.4970i | − | 0.740098i | ||||||
\(695\) | −10.0477 | + | 14.2263i | −0.381132 | + | 0.539634i | ||||
\(696\) | 0.276310i | 0.0104735i | ||||||||
\(697\) | 33.4960 | − | 33.4960i | 1.26875 | − | 1.26875i | ||||
\(698\) | 4.12488 | − | 4.12488i | 0.156129 | − | 0.156129i | ||||
\(699\) | 6.76767 | 0.255977 | ||||||||
\(700\) | 12.1292 | − | 29.7777i | 0.458442 | − | 1.12549i | ||||
\(701\) | 13.7870 | 0.520727 | 0.260364 | − | 0.965511i | \(-0.416158\pi\) | ||||
0.260364 | + | 0.965511i | \(0.416158\pi\) | |||||||
\(702\) | −2.58300 | + | 2.58300i | −0.0974889 | + | 0.0974889i | ||||
\(703\) | 4.42536 | − | 4.42536i | 0.166906 | − | 0.166906i | ||||
\(704\) | 29.3742i | 1.10708i | ||||||||
\(705\) | 1.01590 | − | 1.43838i | 0.0382610 | − | 0.0541727i | ||||
\(706\) | − | 2.88915i | − | 0.108735i | ||||||
\(707\) | 14.2822 | + | 12.7236i | 0.537138 | + | 0.478520i | ||||
\(708\) | 13.7293 | + | 13.7293i | 0.515978 | + | 0.515978i | ||||
\(709\) | − | 24.6722i | − | 0.926585i | −0.886205 | − | 0.463293i | \(-0.846668\pi\) | ||
0.886205 | − | 0.463293i | \(-0.153332\pi\) | |||||||
\(710\) | −12.2236 | − | 71.0088i | −0.458742 | − | 2.66491i | ||||
\(711\) | 11.2973 | 0.423680 | ||||||||
\(712\) | 4.42971 | + | 4.42971i | 0.166010 | + | 0.166010i | ||||
\(713\) | −1.27438 | + | 1.27438i | −0.0477257 | + | 0.0477257i | ||||
\(714\) | −2.15380 | − | 37.3182i | −0.0806041 | − | 1.39660i | ||||
\(715\) | −1.75895 | − | 10.2181i | −0.0657811 | − | 0.382135i | ||||
\(716\) | −3.16223 | −0.118178 | ||||||||
\(717\) | 11.4388 | + | 11.4388i | 0.427191 | + | 0.427191i | ||||
\(718\) | 13.8838 | + | 13.8838i | 0.518139 | + | 0.518139i | ||||
\(719\) | 29.9117 | 1.11552 | 0.557758 | − | 0.830003i | \(-0.311662\pi\) | ||||
0.557758 | + | 0.830003i | \(0.311662\pi\) | |||||||
\(720\) | −5.39447 | − | 3.81000i | −0.201040 | − | 0.141990i | ||||
\(721\) | 1.49735 | + | 25.9441i | 0.0557642 | + | 0.966207i | ||||
\(722\) | 25.6118 | − | 25.6118i | 0.953171 | − | 0.953171i | ||||
\(723\) | 8.04033 | + | 8.04033i | 0.299023 | + | 0.299023i | ||||
\(724\) | 20.6239 | 0.766482 | ||||||||
\(725\) | 1.43670 | − | 0.509736i | 0.0533577 | − | 0.0189311i | ||||
\(726\) | − | 8.12719i | − | 0.301628i | ||||||
\(727\) | 29.8488 | + | 29.8488i | 1.10703 | + | 1.10703i | 0.993539 | + | 0.113491i | \(0.0362034\pi\) |
0.113491 | + | 0.993539i | \(0.463797\pi\) | |||||||
\(728\) | −2.76795 | + | 3.10702i | −0.102587 | + | 0.115154i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 54.4825 | + | 38.4798i | 2.01649 | + | 1.42420i | ||||
\(731\) | 2.89416i | 0.107044i | ||||||||
\(732\) | −9.51121 | + | 9.51121i | −0.351545 | + | 0.351545i | ||||
\(733\) | 3.86707 | − | 3.86707i | 0.142834 | − | 0.142834i | −0.632074 | − | 0.774908i | \(-0.717796\pi\) |
0.774908 | + | 0.632074i | \(0.217796\pi\) | |||||||
\(734\) | −38.7082 | −1.42875 | ||||||||
\(735\) | 15.0177 | − | 4.41240i | 0.553935 | − | 0.162754i | ||||
\(736\) | −1.99493 | −0.0735342 | ||||||||
\(737\) | 9.16599 | − | 9.16599i | 0.337634 | − | 0.337634i | ||||
\(738\) | −10.5040 | + | 10.5040i | −0.386659 | + | 0.386659i | ||||
\(739\) | 11.9735i | 0.440454i | 0.975449 | + | 0.220227i | \(0.0706797\pi\) | ||||
−0.975449 | + | 0.220227i | \(0.929320\pi\) | |||||||
\(740\) | 5.57073 | − | 0.958952i | 0.204784 | − | 0.0352518i | ||||
\(741\) | 10.4427i | 0.383621i | ||||||||
\(742\) | 26.1436 | − | 29.3462i | 0.959763 | − | 1.07733i | ||||
\(743\) | −12.0406 | − | 12.0406i | −0.441728 | − | 0.441728i | 0.450864 | − | 0.892593i | \(-0.351116\pi\) |
−0.892593 | + | 0.450864i | \(0.851116\pi\) | |||||||
\(744\) | − | 6.57385i | − | 0.241009i | ||||||
\(745\) | −26.0918 | − | 18.4281i | −0.955931 | − | 0.675154i | ||||
\(746\) | 61.5467 | 2.25338 | ||||||||
\(747\) | −4.88941 | − | 4.88941i | −0.178894 | − | 0.178894i | ||||
\(748\) | −30.8227 | + | 30.8227i | −1.12699 | + | 1.12699i | ||||
\(749\) | −1.61109 | − | 27.9148i | −0.0588679 | − | 1.01998i | ||||
\(750\) | 6.36745 | − | 22.6556i | 0.232506 | − | 0.827264i | ||||
\(751\) | −24.1119 | −0.879855 | −0.439928 | − | 0.898033i | \(-0.644996\pi\) | ||||
−0.439928 | + | 0.898033i | \(0.644996\pi\) | |||||||
\(752\) | −1.64472 | − | 1.64472i | −0.0599767 | − | 0.0599767i | ||||
\(753\) | −4.91467 | − | 4.91467i | −0.179100 | − | 0.179100i | ||||
\(754\) | −1.11373 | −0.0405598 | ||||||||
\(755\) | 12.6159 | − | 17.8625i | 0.459141 | − | 0.650085i | ||||
\(756\) | 0.370525 | + | 6.41995i | 0.0134759 | + | 0.233491i | ||||
\(757\) | 29.2896 | − | 29.2896i | 1.06455 | − | 1.06455i | 0.0667825 | − | 0.997768i | \(-0.478727\pi\) |
0.997768 | − | 0.0667825i | \(-0.0212733\pi\) | |||||||
\(758\) | −32.7558 | − | 32.7558i | −1.18975 | − | 1.18975i | ||||
\(759\) | −0.663839 | −0.0240958 | ||||||||
\(760\) | 12.0171 | − | 2.06864i | 0.435906 | − | 0.0750374i | ||||
\(761\) | − | 32.3002i | − | 1.17088i | −0.810716 | − | 0.585440i | \(-0.800922\pi\) | ||
0.810716 | − | 0.585440i | \(-0.199078\pi\) | |||||||
\(762\) | 6.02230 | + | 6.02230i | 0.218165 | + | 0.218165i | ||||
\(763\) | −11.7613 | − | 10.4778i | −0.425787 | − | 0.379320i | ||||
\(764\) | − | 4.71018i | − | 0.170408i | ||||||
\(765\) | −2.54621 | − | 14.7914i | −0.0920584 | − | 0.534784i | ||||
\(766\) | − | 1.16207i | − | 0.0419874i | ||||||
\(767\) | −9.80287 | + | 9.80287i | −0.353961 | + | 0.353961i | ||||
\(768\) | −5.00678 | + | 5.00678i | −0.180667 | + | 0.180667i | ||||
\(769\) | −18.4310 | −0.664640 | −0.332320 | − | 0.943167i | \(-0.607831\pi\) | ||||
−0.332320 | + | 0.943167i | \(0.607831\pi\) | |||||||
\(770\) | −28.2379 | − | 17.5968i | −1.01762 | − | 0.634144i | ||||
\(771\) | 14.2679 | 0.513845 | ||||||||
\(772\) | −19.0260 | + | 19.0260i | −0.684761 | + | 0.684761i | ||||
\(773\) | −17.7963 | + | 17.7963i | −0.640088 | + | 0.640088i | −0.950577 | − | 0.310489i | \(-0.899507\pi\) |
0.310489 | + | 0.950577i | \(0.399507\pi\) | |||||||
\(774\) | − | 0.907583i | − | 0.0326224i | ||||||
\(775\) | −34.1813 | + | 12.1274i | −1.22783 | + | 0.435629i | ||||
\(776\) | − | 11.3315i | − | 0.406779i | ||||||
\(777\) | 2.05468 | + | 1.83045i | 0.0737111 | + | 0.0656670i | ||||
\(778\) | −38.5937 | − | 38.5937i | −1.38365 | − | 1.38365i | ||||
\(779\) | 42.4662i | 1.52151i | ||||||||
\(780\) | −5.44126 | + | 7.70413i | −0.194829 | + | 0.275852i | ||||
\(781\) | −40.9030 | −1.46362 | ||||||||
\(782\) | −2.48214 | − | 2.48214i | −0.0887611 | − | 0.0887611i | ||||
\(783\) | −0.215589 | + | 0.215589i | −0.00770453 | + | 0.00770453i | ||||
\(784\) | −2.37853 | − | 20.5374i | −0.0849476 | − | 0.733478i | ||||
\(785\) | −6.78546 | + | 1.16806i | −0.242184 | + | 0.0416898i | ||||
\(786\) | −19.6757 | −0.701810 | ||||||||
\(787\) | 16.0671 | + | 16.0671i | 0.572730 | + | 0.572730i | 0.932890 | − | 0.360160i | \(-0.117278\pi\) |
−0.360160 | + | 0.932890i | \(0.617278\pi\) | |||||||
\(788\) | 20.6783 | + | 20.6783i | 0.736635 | + | 0.736635i | ||||
\(789\) | −25.7364 | −0.916240 | ||||||||
\(790\) | 52.4018 | − | 9.02051i | 1.86437 | − | 0.320935i | ||||
\(791\) | −26.1119 | + | 1.50704i | −0.928432 | + | 0.0535840i | ||||
\(792\) | 1.71220 | − | 1.71220i | 0.0608404 | − | 0.0608404i | ||||
\(793\) | −6.79111 | − | 6.79111i | −0.241159 | − | 0.241159i | ||||
\(794\) | 51.0904 | 1.81313 | ||||||||
\(795\) | 9.10390 | − | 12.8900i | 0.322882 | − | 0.457159i | ||||
\(796\) | − | 7.91046i | − | 0.280379i | ||||||
\(797\) | 25.5337 | + | 25.5337i | 0.904451 | + | 0.904451i | 0.995817 | − | 0.0913664i | \(-0.0291235\pi\) |
−0.0913664 | + | 0.995817i | \(0.529123\pi\) | |||||||
\(798\) | 25.0213 | + | 22.2907i | 0.885745 | + | 0.789083i | ||||
\(799\) | − | 5.28605i | − | 0.187007i | ||||||
\(800\) | −36.2463 | − | 17.2618i | −1.28150 | − | 0.610297i | ||||
\(801\) | 6.91251i | 0.244242i | ||||||||
\(802\) | −19.2623 | + | 19.2623i | −0.680174 | + | 0.680174i | ||||
\(803\) | 26.7744 | − | 26.7744i | 0.944847 | − | 0.944847i | ||||
\(804\) | −11.7919 | −0.415868 | ||||||||
\(805\) | 0.777385 | − | 1.24748i | 0.0273992 | − | 0.0439680i | ||||
\(806\) | 26.4974 | 0.933332 | ||||||||
\(807\) | −10.9685 | + | 10.9685i | −0.386111 | + | 0.386111i | ||||
\(808\) | −4.63292 | + | 4.63292i | −0.162986 | + | 0.162986i | ||||
\(809\) | − | 27.5404i | − | 0.968270i | −0.874993 | − | 0.484135i | \(-0.839134\pi\) | ||
0.874993 | − | 0.484135i | \(-0.160866\pi\) | |||||||
\(810\) | 0.798469 | + | 4.63845i | 0.0280553 | + | 0.162978i | ||||
\(811\) | − | 34.2545i | − | 1.20284i | −0.798933 | − | 0.601420i | \(-0.794602\pi\) | ||
0.798933 | − | 0.601420i | \(-0.205398\pi\) | |||||||
\(812\) | −1.30419 | + | 1.46395i | −0.0457682 | + | 0.0513747i | ||||
\(813\) | −9.43409 | − | 9.43409i | −0.330868 | − | 0.330868i | ||||
\(814\) | − | 5.84935i | − | 0.205020i | ||||||
\(815\) | −42.6196 | + | 7.33659i | −1.49290 | + | 0.256990i | ||||
\(816\) | −19.8246 | −0.694001 | ||||||||
\(817\) | −1.83461 | − | 1.83461i | −0.0641848 | − | 0.0641848i | ||||
\(818\) | 3.93347 | − | 3.93347i | 0.137530 | − | 0.137530i | ||||
\(819\) | −4.58392 | + | 0.264559i | −0.160175 | + | 0.00924443i | ||||
\(820\) | −22.1275 | + | 31.3297i | −0.772726 | + | 1.09408i | ||||
\(821\) | 49.7482 | 1.73623 | 0.868113 | − | 0.496367i | \(-0.165333\pi\) | ||||
0.868113 | + | 0.496367i | \(0.165333\pi\) | |||||||
\(822\) | 15.8275 | + | 15.8275i | 0.552049 | + | 0.552049i | ||||
\(823\) | −6.10417 | − | 6.10417i | −0.212778 | − | 0.212778i | 0.592668 | − | 0.805447i | \(-0.298074\pi\) |
−0.805447 | + | 0.592668i | \(0.798074\pi\) | |||||||
\(824\) | −8.90155 | −0.310100 | ||||||||
\(825\) | −12.0614 | − | 5.74409i | −0.419925 | − | 0.199984i | ||||
\(826\) | 2.56330 | + | 44.4134i | 0.0891886 | + | 1.54534i | ||||
\(827\) | −4.96734 | + | 4.96734i | −0.172731 | + | 0.172731i | −0.788178 | − | 0.615447i | \(-0.788976\pi\) |
0.615447 | + | 0.788178i | \(0.288976\pi\) | |||||||
\(828\) | 0.427009 | + | 0.427009i | 0.0148396 | + | 0.0148396i | ||||
\(829\) | 28.3500 | 0.984636 | 0.492318 | − | 0.870415i | \(-0.336150\pi\) | ||||
0.492318 | + | 0.870415i | \(0.336150\pi\) | |||||||
\(830\) | −26.5833 | − | 18.7752i | −0.922720 | − | 0.651698i | ||||
\(831\) | − | 2.83636i | − | 0.0983922i | ||||||
\(832\) | 13.4910 | + | 13.4910i | 0.467717 | + | 0.467717i | ||||
\(833\) | 29.1809 | − | 36.8254i | 1.01106 | − | 1.27592i | ||||
\(834\) | − | 16.3950i | − | 0.567713i | ||||||
\(835\) | 19.4244 | − | 3.34374i | 0.672209 | − | 0.115715i | ||||
\(836\) | − | 39.0770i | − | 1.35151i | ||||||
\(837\) | 5.12921 | − | 5.12921i | 0.177291 | − | 0.177291i | ||||
\(838\) | −14.9287 | + | 14.9287i | −0.515705 | + | 0.515705i | ||||
\(839\) | −32.8100 | −1.13273 | −0.566364 | − | 0.824156i | \(-0.691650\pi\) | ||||
−0.566364 | + | 0.824156i | \(0.691650\pi\) | |||||||
\(840\) | 1.21250 | + | 5.22263i | 0.0418351 | + | 0.180198i | ||||
\(841\) | 28.9070 | 0.996795 | ||||||||
\(842\) | −39.6563 | + | 39.6563i | −1.36665 | + | 1.36665i | ||||
\(843\) | −9.58531 | + | 9.58531i | −0.330136 | + | 0.330136i | ||||
\(844\) | 41.9289i | 1.44325i | ||||||||
\(845\) | 18.2431 | + | 12.8847i | 0.627581 | + | 0.443247i | ||||
\(846\) | 1.65766i | 0.0569915i | ||||||||
\(847\) | 6.79526 | − | 7.62767i | 0.233488 | − | 0.262090i | ||||
\(848\) | −14.7390 | − | 14.7390i | −0.506139 | − | 0.506139i | ||||
\(849\) | 22.9730i | 0.788431i | ||||||||
\(850\) | −23.6209 | − | 66.5760i | −0.810191 | − | 2.28354i | ||||
\(851\) | 0.258411 | 0.00885820 | ||||||||
\(852\) | 26.3105 | + | 26.3105i | 0.901384 | + | 0.901384i | ||||
\(853\) | 15.4954 | − | 15.4954i | 0.530553 | − | 0.530553i | −0.390184 | − | 0.920737i | \(-0.627589\pi\) |
0.920737 | + | 0.390184i | \(0.127589\pi\) | |||||||
\(854\) | −30.7682 | + | 1.77577i | −1.05287 | + | 0.0607657i | ||||
\(855\) | 10.9903 | + | 7.76222i | 0.375861 | + | 0.265462i | ||||
\(856\) | 9.57770 | 0.327359 | ||||||||
\(857\) | 17.8346 | + | 17.8346i | 0.609218 | + | 0.609218i | 0.942742 | − | 0.333523i | \(-0.108238\pi\) |
−0.333523 | + | 0.942742i | \(0.608238\pi\) | |||||||
\(858\) | 6.90143 | + | 6.90143i | 0.235611 | + | 0.235611i | ||||
\(859\) | −17.2711 | −0.589283 | −0.294641 | − | 0.955608i | \(-0.595200\pi\) | ||||
−0.294641 | + | 0.955608i | \(0.595200\pi\) | |||||||
\(860\) | −0.397549 | − | 2.30944i | −0.0135563 | − | 0.0787511i | ||||
\(861\) | −18.6410 | + | 1.07586i | −0.635284 | + | 0.0366651i | ||||
\(862\) | 33.3021 | − | 33.3021i | 1.13427 | − | 1.13427i | ||||
\(863\) | 2.94383 | + | 2.94383i | 0.100209 | + | 0.100209i | 0.755434 | − | 0.655225i | \(-0.227426\pi\) |
−0.655225 | + | 0.755434i | \(0.727426\pi\) | |||||||
\(864\) | 8.02936 | 0.273164 | ||||||||
\(865\) | 3.63154 | + | 21.0963i | 0.123476 | + | 0.717295i | ||||
\(866\) | 40.1038i | 1.36278i | ||||||||
\(867\) | −19.8369 | − | 19.8369i | −0.673697 | − | 0.673697i | ||||
\(868\) | 31.0288 | − | 34.8298i | 1.05318 | − | 1.18220i | ||||
\(869\) | − | 30.1848i | − | 1.02395i | ||||||
\(870\) | −0.827859 | + | 1.17214i | −0.0280670 | + | 0.0397393i | ||||
\(871\) | − | 8.41955i | − | 0.285286i | ||||||
\(872\) | 3.81517 | − | 3.81517i | 0.129198 | − | 0.129198i | ||||
\(873\) | 8.84137 | − | 8.84137i | 0.299235 | − | 0.299235i | ||||
\(874\) | 3.14686 | 0.106444 | ||||||||
\(875\) | 24.9187 | − | 15.9392i | 0.842407 | − | 0.538842i | ||||
\(876\) | −34.4448 | −1.16378 | ||||||||
\(877\) | −8.49735 | + | 8.49735i | −0.286935 | + | 0.286935i | −0.835867 | − | 0.548932i | \(-0.815035\pi\) |
0.548932 | + | 0.835867i | \(0.315035\pi\) | |||||||
\(878\) | −38.2201 | + | 38.2201i | −1.28987 | + | 1.28987i | ||||
\(879\) | 3.41907i | 0.115322i | ||||||||
\(880\) | −10.1798 | + | 14.4133i | −0.343162 | + | 0.485873i | ||||
\(881\) | 35.7762i | 1.20533i | 0.797994 | + | 0.602665i | \(0.205894\pi\) | ||||
−0.797994 | + | 0.602665i | \(0.794106\pi\) | |||||||
\(882\) | −9.15086 | + | 11.5481i | −0.308125 | + | 0.388845i | ||||
\(883\) | 24.6278 | + | 24.6278i | 0.828791 | + | 0.828791i | 0.987350 | − | 0.158559i | \(-0.0506848\pi\) |
−0.158559 | + | 0.987350i | \(0.550685\pi\) | |||||||
\(884\) | 28.3126i | 0.952256i | ||||||||
\(885\) | 3.03031 | + | 17.6036i | 0.101863 | + | 0.591739i | ||||
\(886\) | −46.5419 | −1.56361 | ||||||||
\(887\) | −0.732491 | − | 0.732491i | −0.0245946 | − | 0.0245946i | 0.694703 | − | 0.719297i | \(-0.255536\pi\) |
−0.719297 | + | 0.694703i | \(0.755536\pi\) | |||||||
\(888\) | −0.666503 | + | 0.666503i | −0.0223664 | + | 0.0223664i | ||||
\(889\) | 0.616823 | + | 10.6875i | 0.0206876 | + | 0.358447i | ||||
\(890\) | 5.51943 | + | 32.0633i | 0.185012 | + | 1.07477i | ||||
\(891\) | 2.67187 | 0.0895111 | ||||||||
\(892\) | −11.1415 | − | 11.1415i | −0.373043 | − | 0.373043i | ||||
\(893\) | 3.35083 | + | 3.35083i | 0.112131 | + | 0.112131i | ||||
\(894\) | 30.0694 | 1.00567 | ||||||||
\(895\) | −2.37628 | − | 1.67831i | −0.0794301 | − | 0.0560998i | ||||
\(896\) | 18.7064 | − | 1.07963i | 0.624936 | − | 0.0360679i | ||||
\(897\) | −0.304889 | + | 0.304889i | −0.0101800 | + | 0.0101800i | ||||
\(898\) | 10.4476 | + | 10.4476i | 0.348642 | + | 0.348642i | ||||
\(899\) | 2.21160 | 0.0737611 | ||||||||
\(900\) | 4.06357 | + | 11.4533i | 0.135452 | + | 0.381775i | ||||
\(901\) | − | 47.3704i | − | 1.57814i | ||||||
\(902\) | 28.0654 | + | 28.0654i | 0.934477 | + | 0.934477i | ||||
\(903\) | 0.758842 | − | 0.851800i | 0.0252527 | − | 0.0283461i | ||||
\(904\) | − | 8.95913i | − | 0.297976i | ||||||
\(905\) | 15.4980 | + | 10.9459i | 0.515170 | + | 0.363854i | ||||
\(906\) | 20.5856i | 0.683911i | ||||||||
\(907\) | −22.8743 | + | 22.8743i | −0.759530 | + | 0.759530i | −0.976237 | − | 0.216707i | \(-0.930468\pi\) |
0.216707 | + | 0.976237i | \(0.430468\pi\) | |||||||
\(908\) | −34.4198 | + | 34.4198i | −1.14226 | + | 1.14226i | ||||
\(909\) | −7.22962 | −0.239791 | ||||||||
\(910\) | −21.0510 | + | 4.88726i | −0.697835 | + | 0.162011i | ||||
\(911\) | 24.7867 | 0.821220 | 0.410610 | − | 0.911811i | \(-0.365316\pi\) | ||||
0.410610 | + | 0.911811i | \(0.365316\pi\) | |||||||
\(912\) | 12.5668 | − | 12.5668i | 0.416130 | − | 0.416130i | ||||
\(913\) | −13.0639 | + | 13.0639i | −0.432351 | + | 0.432351i | ||||
\(914\) | − | 33.3752i | − | 1.10395i | ||||||
\(915\) | −12.1952 | + | 2.09930i | −0.403162 | + | 0.0694008i | ||||
\(916\) | − | 70.3176i | − | 2.32336i | ||||||
\(917\) | −18.4664 | − | 16.4512i | −0.609814 | − | 0.543265i | ||||
\(918\) | 9.99031 | + | 9.99031i | 0.329729 | + | 0.329729i | ||||
\(919\) | − | 14.5898i | − | 0.481272i | −0.970615 | − | 0.240636i | \(-0.922644\pi\) | ||
0.970615 | − | 0.240636i | \(-0.0773560\pi\) | |||||||
\(920\) | 0.411254 | + | 0.290460i | 0.0135587 | + | 0.00957619i | ||||
\(921\) | 10.2007 | 0.336125 | ||||||||
\(922\) | −44.6283 | − | 44.6283i | −1.46976 | − | 1.46976i | ||||
\(923\) | −18.7860 | + | 18.7860i | −0.618349 | + | 0.618349i | ||||
\(924\) | 17.1533 | − | 0.989994i | 0.564302 | − | 0.0325684i | ||||
\(925\) | 4.69511 | + | 2.23598i | 0.154374 | + | 0.0735187i | ||||
\(926\) | 22.9276 | 0.753447 | ||||||||
\(927\) | −6.94538 | − | 6.94538i | −0.228116 | − | 0.228116i | ||||
\(928\) | 1.73104 | + | 1.73104i | 0.0568243 | + | 0.0568243i | ||||
\(929\) | 25.1526 | 0.825229 | 0.412615 | − | 0.910906i | \(-0.364616\pi\) | ||||
0.412615 | + | 0.910906i | \(0.364616\pi\) | |||||||
\(930\) | 19.6960 | − | 27.8871i | 0.645859 | − | 0.914453i | ||||
\(931\) | 4.84585 | + | 41.8414i | 0.158816 | + | 1.37130i | ||||
\(932\) | −11.6313 | + | 11.6313i | −0.380996 | + | 0.380996i | ||||
\(933\) | −7.25079 | − | 7.25079i | −0.237380 | − | 0.237380i | ||||
\(934\) | −5.38676 | −0.176260 | ||||||||
\(935\) | −39.5207 | + | 6.80314i | −1.29246 | + | 0.222487i | ||||
\(936\) | − | 1.57277i | − | 0.0514075i | ||||||
\(937\) | −28.3540 | − | 28.3540i | −0.926286 | − | 0.926286i | 0.0711778 | − | 0.997464i | \(-0.477324\pi\) |
−0.997464 | + | 0.0711778i | \(0.977324\pi\) | |||||||
\(938\) | −20.1738 | − | 17.9722i | −0.658699 | − | 0.586815i | ||||
\(939\) | − | 31.2405i | − | 1.01950i | ||||||
\(940\) | 0.726106 | + | 4.21808i | 0.0236830 | + | 0.137579i | ||||
\(941\) | 0.106973i | 0.00348721i | 0.999998 | + | 0.00174360i | \(0.000555007\pi\) | ||||
−0.999998 | + | 0.00174360i | \(0.999445\pi\) | |||||||
\(942\) | 4.58300 | − | 4.58300i | 0.149322 | − | 0.149322i | ||||
\(943\) | −1.23987 | + | 1.23987i | −0.0403756 | + | 0.0403756i | ||||
\(944\) | 23.5938 | 0.767914 | ||||||||
\(945\) | −3.12888 | + | 5.02097i | −0.101782 | + | 0.163332i | ||||
\(946\) | −2.42494 | −0.0788417 | ||||||||
\(947\) | 17.9671 | − | 17.9671i | 0.583851 | − | 0.583851i | −0.352108 | − | 0.935959i | \(-0.614535\pi\) |
0.935959 | + | 0.352108i | \(0.114535\pi\) | |||||||
\(948\) | −19.4162 | + | 19.4162i | −0.630607 | + | 0.630607i | ||||
\(949\) | − | 24.5940i | − | 0.798354i | ||||||
\(950\) | 57.1759 | + | 27.2293i | 1.85503 | + | 0.883434i | ||||
\(951\) | − | 17.3331i | − | 0.562064i | ||||||
\(952\) | 12.0171 | + | 10.7057i | 0.389477 | + | 0.346973i | ||||
\(953\) | 31.8008 | + | 31.8008i | 1.03013 | + | 1.03013i | 0.999532 | + | 0.0305973i | \(0.00974093\pi\) |
0.0305973 | + | 0.999532i | \(0.490259\pi\) | |||||||
\(954\) | 14.8550i | 0.480947i | ||||||||
\(955\) | 2.49987 | − | 3.53950i | 0.0808940 | − | 0.114536i | ||||
\(956\) | −39.3189 | −1.27166 | ||||||||
\(957\) | 0.576027 | + | 0.576027i | 0.0186203 | + | 0.0186203i | ||||
\(958\) | −6.09425 | + | 6.09425i | −0.196896 | + | 0.196896i | ||||
\(959\) | 1.62111 | + | 28.0884i | 0.0523483 | + | 0.907021i | ||||
\(960\) | 24.2267 | − | 4.17041i | 0.781912 | − | 0.134599i | ||||
\(961\) | −21.6175 | −0.697339 | ||||||||
\(962\) | −2.68650 | − | 2.68650i | −0.0866162 | − | 0.0866162i | ||||
\(963\) | 7.47295 | + | 7.47295i | 0.240812 | + | 0.240812i | ||||
\(964\) | −27.6372 | −0.890134 | ||||||||
\(965\) | −24.3951 | + | 4.19940i | −0.785305 | + | 0.135183i | ||||
\(966\) | 0.0797239 | + | 1.38135i | 0.00256507 | + | 0.0444441i | ||||
\(967\) | 0.210995 | − | 0.210995i | 0.00678513 | − | 0.00678513i | −0.703706 | − | 0.710491i | \(-0.748473\pi\) |
0.710491 | + | 0.703706i | \(0.248473\pi\) | |||||||
\(968\) | 2.47429 | + | 2.47429i | 0.0795267 | + | 0.0795267i | ||||
\(969\) | 40.3893 | 1.29749 | ||||||||
\(970\) | 33.9507 | − | 48.0698i | 1.09009 | − | 1.54343i | ||||
\(971\) | 54.1165i | 1.73668i | 0.495969 | + | 0.868340i | \(0.334813\pi\) | ||||
−0.495969 | + | 0.868340i | \(0.665187\pi\) | |||||||
\(972\) | −1.71866 | − | 1.71866i | −0.0551260 | − | 0.0551260i | ||||
\(973\) | 13.7081 | − | 15.3873i | 0.439462 | − | 0.493295i | ||||
\(974\) | 30.6752i | 0.982896i | ||||||||
\(975\) | −8.17775 | + | 2.90143i | −0.261898 | + | 0.0929203i | ||||
\(976\) | 16.3450i | 0.523192i | ||||||||
\(977\) | 25.0981 | − | 25.0981i | 0.802958 | − | 0.802958i | −0.180599 | − | 0.983557i | \(-0.557803\pi\) |
0.983557 | + | 0.180599i | \(0.0578035\pi\) | |||||||
\(978\) | 28.7859 | − | 28.7859i | 0.920471 | − | 0.920471i | ||||
\(979\) | 18.4693 | 0.590283 | ||||||||
\(980\) | −18.2269 | + | 33.3937i | −0.582236 | + | 1.06672i | ||||
\(981\) | 5.95352 | 0.190081 | ||||||||
\(982\) | −12.7398 | + | 12.7398i | −0.406545 | + | 0.406545i | ||||
\(983\) | 1.23358 | − | 1.23358i | 0.0393451 | − | 0.0393451i | −0.687161 | − | 0.726506i | \(-0.741143\pi\) |
0.726506 | + | 0.687161i | \(0.241143\pi\) | |||||||
\(984\) | − | 6.39583i | − | 0.203892i | ||||||
\(985\) | 4.56409 | + | 26.5136i | 0.145424 | + | 0.844795i | ||||
\(986\) | 4.30761i | 0.137182i | ||||||||
\(987\) | −1.38599 | + | 1.55577i | −0.0441166 | + | 0.0495208i | ||||
\(988\) | −17.9474 | − | 17.9474i | −0.570982 | − | 0.570982i | ||||
\(989\) | − | 0.107128i | − | 0.00340648i | ||||||
\(990\) | 12.3933 | − | 2.13341i | 0.393886 | − | 0.0678041i | ||||
\(991\) | 48.9637 | 1.55538 | 0.777691 | − | 0.628647i | \(-0.216391\pi\) | ||||
0.777691 | + | 0.628647i | \(0.216391\pi\) | |||||||
\(992\) | −41.1842 | − | 41.1842i | −1.30760 | − | 1.30760i | ||||
\(993\) | −0.893133 | + | 0.893133i | −0.0283427 | + | 0.0283427i | ||||
\(994\) | 4.91225 | + | 85.1129i | 0.155807 | + | 2.69962i | ||||
\(995\) | 4.19838 | − | 5.94437i | 0.133098 | − | 0.188449i | ||||
\(996\) | 16.8065 | 0.532533 | ||||||||
\(997\) | −11.9844 | − | 11.9844i | −0.379551 | − | 0.379551i | 0.491389 | − | 0.870940i | \(-0.336489\pi\) |
−0.870940 | + | 0.491389i | \(0.836489\pi\) | |||||||
\(998\) | −35.3585 | − | 35.3585i | −1.11926 | − | 1.11926i | ||||
\(999\) | −1.04007 | −0.0329064 |
(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 | 105.2.m.a.13.7 | ✓ | 16 | |
3.2 | odd | 2 | 315.2.p.e.118.1 | 16 | |||
4.3 | odd | 2 | 1680.2.cz.d.433.8 | 16 | |||
5.2 | odd | 4 | inner | 105.2.m.a.97.8 | yes | 16 | |
5.3 | odd | 4 | 525.2.m.b.307.1 | 16 | |||
5.4 | even | 2 | 525.2.m.b.118.2 | 16 | |||
7.2 | even | 3 | 735.2.v.a.178.1 | 32 | |||
7.3 | odd | 6 | 735.2.v.a.313.7 | 32 | |||
7.4 | even | 3 | 735.2.v.a.313.8 | 32 | |||
7.5 | odd | 6 | 735.2.v.a.178.2 | 32 | |||
7.6 | odd | 2 | inner | 105.2.m.a.13.8 | yes | 16 | |
15.2 | even | 4 | 315.2.p.e.307.2 | 16 | |||
20.7 | even | 4 | 1680.2.cz.d.97.1 | 16 | |||
21.20 | even | 2 | 315.2.p.e.118.2 | 16 | |||
28.27 | even | 2 | 1680.2.cz.d.433.1 | 16 | |||
35.2 | odd | 12 | 735.2.v.a.472.7 | 32 | |||
35.12 | even | 12 | 735.2.v.a.472.8 | 32 | |||
35.13 | even | 4 | 525.2.m.b.307.2 | 16 | |||
35.17 | even | 12 | 735.2.v.a.607.1 | 32 | |||
35.27 | even | 4 | inner | 105.2.m.a.97.7 | yes | 16 | |
35.32 | odd | 12 | 735.2.v.a.607.2 | 32 | |||
35.34 | odd | 2 | 525.2.m.b.118.1 | 16 | |||
105.62 | odd | 4 | 315.2.p.e.307.1 | 16 | |||
140.27 | odd | 4 | 1680.2.cz.d.97.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
105.2.m.a.13.8 | yes | 16 | 7.6 | odd | 2 | inner | |
105.2.m.a.97.7 | yes | 16 | 35.27 | even | 4 | inner | |
105.2.m.a.97.8 | yes | 16 | 5.2 | odd | 4 | inner | |
315.2.p.e.118.1 | 16 | 3.2 | odd | 2 | |||
315.2.p.e.118.2 | 16 | 21.20 | even | 2 | |||
315.2.p.e.307.1 | 16 | 105.62 | odd | 4 | |||
315.2.p.e.307.2 | 16 | 15.2 | even | 4 | |||
525.2.m.b.118.1 | 16 | 35.34 | odd | 2 | |||
525.2.m.b.118.2 | 16 | 5.4 | even | 2 | |||
525.2.m.b.307.1 | 16 | 5.3 | odd | 4 | |||
525.2.m.b.307.2 | 16 | 35.13 | even | 4 | |||
735.2.v.a.178.1 | 32 | 7.2 | even | 3 | |||
735.2.v.a.178.2 | 32 | 7.5 | odd | 6 | |||
735.2.v.a.313.7 | 32 | 7.3 | odd | 6 | |||
735.2.v.a.313.8 | 32 | 7.4 | even | 3 | |||
735.2.v.a.472.7 | 32 | 35.2 | odd | 12 | |||
735.2.v.a.472.8 | 32 | 35.12 | even | 12 | |||
735.2.v.a.607.1 | 32 | 35.17 | even | 12 | |||
735.2.v.a.607.2 | 32 | 35.32 | odd | 12 | |||
1680.2.cz.d.97.1 | 16 | 20.7 | even | 4 | |||
1680.2.cz.d.97.8 | 16 | 140.27 | odd | 4 | |||
1680.2.cz.d.433.1 | 16 | 28.27 | even | 2 | |||
1680.2.cz.d.433.8 | 16 | 4.3 | odd | 2 |