Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(155,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.s (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: | \(2.68297350792\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.323 |
Dual form | 336.2.s.a.155.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | ||||
\(3\) | −1.00000 | + | 1.41421i | −0.577350 | + | 0.816497i | ||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 0.414214 | + | 0.414214i | 0.185242 | + | 0.185242i | 0.793635 | − | 0.608394i | \(-0.208186\pi\) |
−0.608394 | + | 0.793635i | \(0.708186\pi\) | |||||||
\(6\) | −0.414214 | − | 2.41421i | −0.169102 | − | 0.985599i | ||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | −0.828427 | −0.261972 | ||||||||
\(11\) | −3.82843 | + | 3.82843i | −1.15431 | + | 1.15431i | −0.168636 | + | 0.985678i | \(0.553936\pi\) |
−0.985678 | + | 0.168636i | \(0.946064\pi\) | |||||||
\(12\) | 2.82843 | + | 2.00000i | 0.816497 | + | 0.577350i | ||||
\(13\) | −4.41421 | − | 4.41421i | −1.22428 | − | 1.22428i | −0.966095 | − | 0.258188i | \(-0.916875\pi\) |
−0.258188 | − | 0.966095i | \(-0.583125\pi\) | |||||||
\(14\) | 1.00000 | − | 1.00000i | 0.267261 | − | 0.267261i | ||||
\(15\) | −1.00000 | + | 0.171573i | −0.258199 | + | 0.0442999i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 1.17157i | 0.284148i | 0.989856 | + | 0.142074i | \(0.0453771\pi\) | ||||
−0.989856 | + | 0.142074i | \(0.954623\pi\) | |||||||
\(18\) | 3.82843 | + | 1.82843i | 0.902369 | + | 0.430964i | ||||
\(19\) | 0.414214 | − | 0.414214i | 0.0950271 | − | 0.0950271i | −0.657995 | − | 0.753022i | \(-0.728595\pi\) |
0.753022 | + | 0.657995i | \(0.228595\pi\) | |||||||
\(20\) | 0.828427 | − | 0.828427i | 0.185242 | − | 0.185242i | ||||
\(21\) | 1.00000 | − | 1.41421i | 0.218218 | − | 0.308607i | ||||
\(22\) | − | 7.65685i | − | 1.63245i | ||||||
\(23\) | − | 7.65685i | − | 1.59656i | −0.602284 | − | 0.798282i | \(-0.705742\pi\) | ||
0.602284 | − | 0.798282i | \(-0.294258\pi\) | |||||||
\(24\) | −4.82843 | + | 0.828427i | −0.985599 | + | 0.169102i | ||||
\(25\) | − | 4.65685i | − | 0.931371i | ||||||
\(26\) | 8.82843 | 1.73140 | ||||||||
\(27\) | 5.00000 | + | 1.41421i | 0.962250 | + | 0.272166i | ||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | −3.00000 | + | 3.00000i | −0.557086 | + | 0.557086i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0.828427 | − | 1.17157i | 0.151249 | − | 0.213899i | ||||
\(31\) | 6.48528i | 1.16479i | 0.812906 | + | 0.582395i | \(0.197884\pi\) | ||||
−0.812906 | + | 0.582395i | \(0.802116\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | −1.58579 | − | 9.24264i | −0.276050 | − | 1.60894i | ||||
\(34\) | −1.17157 | − | 1.17157i | −0.200923 | − | 0.200923i | ||||
\(35\) | −0.414214 | − | 0.414214i | −0.0700149 | − | 0.0700149i | ||||
\(36\) | −5.65685 | + | 2.00000i | −0.942809 | + | 0.333333i | ||||
\(37\) | 1.82843 | − | 1.82843i | 0.300592 | − | 0.300592i | −0.540654 | − | 0.841245i | \(-0.681823\pi\) |
0.841245 | + | 0.540654i | \(0.181823\pi\) | |||||||
\(38\) | 0.828427i | 0.134389i | ||||||||
\(39\) | 10.6569 | − | 1.82843i | 1.70646 | − | 0.292783i | ||||
\(40\) | 1.65685i | 0.261972i | ||||||||
\(41\) | −0.343146 | −0.0535904 | −0.0267952 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267952 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(42\) | 0.414214 | + | 2.41421i | 0.0639145 | + | 0.372521i | ||||
\(43\) | −3.82843 | − | 3.82843i | −0.583830 | − | 0.583830i | 0.352124 | − | 0.935953i | \(-0.385460\pi\) |
−0.935953 | + | 0.352124i | \(0.885460\pi\) | |||||||
\(44\) | 7.65685 | + | 7.65685i | 1.15431 | + | 1.15431i | ||||
\(45\) | 0.757359 | − | 1.58579i | 0.112900 | − | 0.236395i | ||||
\(46\) | 7.65685 | + | 7.65685i | 1.12894 | + | 1.12894i | ||||
\(47\) | −5.65685 | −0.825137 | −0.412568 | − | 0.910927i | \(-0.635368\pi\) | ||||
−0.412568 | + | 0.910927i | \(0.635368\pi\) | |||||||
\(48\) | 4.00000 | − | 5.65685i | 0.577350 | − | 0.816497i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.65685 | + | 4.65685i | 0.658579 | + | 0.658579i | ||||
\(51\) | −1.65685 | − | 1.17157i | −0.232006 | − | 0.164053i | ||||
\(52\) | −8.82843 | + | 8.82843i | −1.22428 | + | 1.22428i | ||||
\(53\) | −5.82843 | − | 5.82843i | −0.800596 | − | 0.800596i | 0.182593 | − | 0.983189i | \(-0.441551\pi\) |
−0.983189 | + | 0.182593i | \(0.941551\pi\) | |||||||
\(54\) | −6.41421 | + | 3.58579i | −0.872864 | + | 0.487964i | ||||
\(55\) | −3.17157 | −0.427655 | ||||||||
\(56\) | −2.00000 | − | 2.00000i | −0.267261 | − | 0.267261i | ||||
\(57\) | 0.171573 | + | 1.00000i | 0.0227254 | + | 0.132453i | ||||
\(58\) | − | 6.00000i | − | 0.787839i | ||||||
\(59\) | −10.0711 | + | 10.0711i | −1.31114 | + | 1.31114i | −0.390567 | + | 0.920575i | \(0.627721\pi\) |
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0.343146 | + | 2.00000i | 0.0442999 | + | 0.258199i | ||||
\(61\) | 2.41421 | + | 2.41421i | 0.309108 | + | 0.309108i | 0.844564 | − | 0.535455i | \(-0.179860\pi\) |
−0.535455 | + | 0.844564i | \(0.679860\pi\) | |||||||
\(62\) | −6.48528 | − | 6.48528i | −0.823632 | − | 0.823632i | ||||
\(63\) | 1.00000 | + | 2.82843i | 0.125988 | + | 0.356348i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | − | 3.65685i | − | 0.453577i | ||||||
\(66\) | 10.8284 | + | 7.65685i | 1.33289 | + | 0.942494i | ||||
\(67\) | −7.00000 | + | 7.00000i | −0.855186 | + | 0.855186i | −0.990766 | − | 0.135580i | \(-0.956710\pi\) |
0.135580 | + | 0.990766i | \(0.456710\pi\) | |||||||
\(68\) | 2.34315 | 0.284148 | ||||||||
\(69\) | 10.8284 | + | 7.65685i | 1.30359 | + | 0.921777i | ||||
\(70\) | 0.828427 | 0.0990160 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 3.65685 | − | 7.65685i | 0.430964 | − | 0.902369i | ||||
\(73\) | 5.17157i | 0.605287i | 0.953104 | + | 0.302643i | \(0.0978691\pi\) | ||||
−0.953104 | + | 0.302643i | \(0.902131\pi\) | |||||||
\(74\) | 3.65685i | 0.425101i | ||||||||
\(75\) | 6.58579 | + | 4.65685i | 0.760461 | + | 0.537727i | ||||
\(76\) | −0.828427 | − | 0.828427i | −0.0950271 | − | 0.0950271i | ||||
\(77\) | 3.82843 | − | 3.82843i | 0.436290 | − | 0.436290i | ||||
\(78\) | −8.82843 | + | 12.4853i | −0.999623 | + | 1.41368i | ||||
\(79\) | 2.00000i | 0.225018i | 0.993651 | + | 0.112509i | \(0.0358886\pi\) | ||||
−0.993651 | + | 0.112509i | \(0.964111\pi\) | |||||||
\(80\) | −1.65685 | − | 1.65685i | −0.185242 | − | 0.185242i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0.343146 | − | 0.343146i | 0.0378941 | − | 0.0378941i | ||||
\(83\) | 8.89949 | + | 8.89949i | 0.976846 | + | 0.976846i | 0.999738 | − | 0.0228915i | \(-0.00728722\pi\) |
−0.0228915 | + | 0.999738i | \(0.507287\pi\) | |||||||
\(84\) | −2.82843 | − | 2.00000i | −0.308607 | − | 0.218218i | ||||
\(85\) | −0.485281 | + | 0.485281i | −0.0526362 | + | 0.0526362i | ||||
\(86\) | 7.65685 | 0.825660 | ||||||||
\(87\) | −1.24264 | − | 7.24264i | −0.133225 | − | 0.776493i | ||||
\(88\) | −15.3137 | −1.63245 | ||||||||
\(89\) | −15.6569 | −1.65962 | −0.829812 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829812 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(90\) | 0.828427 | + | 2.34315i | 0.0873239 | + | 0.246989i | ||||
\(91\) | 4.41421 | + | 4.41421i | 0.462735 | + | 0.462735i | ||||
\(92\) | −15.3137 | −1.59656 | ||||||||
\(93\) | −9.17157 | − | 6.48528i | −0.951048 | − | 0.672492i | ||||
\(94\) | 5.65685 | − | 5.65685i | 0.583460 | − | 0.583460i | ||||
\(95\) | 0.343146 | 0.0352060 | ||||||||
\(96\) | 1.65685 | + | 9.65685i | 0.169102 | + | 0.985599i | ||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −1.00000 | + | 1.00000i | −0.101015 | + | 0.101015i | ||||
\(99\) | 14.6569 | + | 7.00000i | 1.47307 | + | 0.703526i | ||||
\(100\) | −9.31371 | −0.931371 | ||||||||
\(101\) | 10.0711 | + | 10.0711i | 1.00211 | + | 1.00211i | 0.999998 | + | 0.00211093i | \(0.000671930\pi\) |
0.00211093 | + | 0.999998i | \(0.499328\pi\) | |||||||
\(102\) | 2.82843 | − | 0.485281i | 0.280056 | − | 0.0480500i | ||||
\(103\) | 11.3137 | 1.11477 | 0.557386 | − | 0.830253i | \(-0.311804\pi\) | ||||
0.557386 | + | 0.830253i | \(0.311804\pi\) | |||||||
\(104\) | − | 17.6569i | − | 1.73140i | ||||||
\(105\) | 1.00000 | − | 0.171573i | 0.0975900 | − | 0.0167438i | ||||
\(106\) | 11.6569 | 1.13221 | ||||||||
\(107\) | −5.00000 | + | 5.00000i | −0.483368 | + | 0.483368i | −0.906206 | − | 0.422837i | \(-0.861034\pi\) |
0.422837 | + | 0.906206i | \(0.361034\pi\) | |||||||
\(108\) | 2.82843 | − | 10.0000i | 0.272166 | − | 0.962250i | ||||
\(109\) | 5.82843 | + | 5.82843i | 0.558262 | + | 0.558262i | 0.928812 | − | 0.370550i | \(-0.120831\pi\) |
−0.370550 | + | 0.928812i | \(0.620831\pi\) | |||||||
\(110\) | 3.17157 | − | 3.17157i | 0.302398 | − | 0.302398i | ||||
\(111\) | 0.757359 | + | 4.41421i | 0.0718854 | + | 0.418979i | ||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 1.65685i | 0.155864i | 0.996959 | + | 0.0779319i | \(0.0248317\pi\) | ||||
−0.996959 | + | 0.0779319i | \(0.975168\pi\) | |||||||
\(114\) | −1.17157 | − | 0.828427i | −0.109728 | − | 0.0775893i | ||||
\(115\) | 3.17157 | − | 3.17157i | 0.295751 | − | 0.295751i | ||||
\(116\) | 6.00000 | + | 6.00000i | 0.557086 | + | 0.557086i | ||||
\(117\) | −8.07107 | + | 16.8995i | −0.746170 | + | 1.56236i | ||||
\(118\) | − | 20.1421i | − | 1.85423i | ||||||
\(119\) | − | 1.17157i | − | 0.107398i | ||||||
\(120\) | −2.34315 | − | 1.65685i | −0.213899 | − | 0.151249i | ||||
\(121\) | − | 18.3137i | − | 1.66488i | ||||||
\(122\) | −4.82843 | −0.437145 | ||||||||
\(123\) | 0.343146 | − | 0.485281i | 0.0309404 | − | 0.0437563i | ||||
\(124\) | 12.9706 | 1.16479 | ||||||||
\(125\) | 4.00000 | − | 4.00000i | 0.357771 | − | 0.357771i | ||||
\(126\) | −3.82843 | − | 1.82843i | −0.341063 | − | 0.162889i | ||||
\(127\) | − | 15.6569i | − | 1.38932i | −0.719338 | − | 0.694661i | \(-0.755555\pi\) | ||
0.719338 | − | 0.694661i | \(-0.244445\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | 9.24264 | − | 1.58579i | 0.813769 | − | 0.139621i | ||||
\(130\) | 3.65685 | + | 3.65685i | 0.320727 | + | 0.320727i | ||||
\(131\) | −4.07107 | − | 4.07107i | −0.355691 | − | 0.355691i | 0.506531 | − | 0.862222i | \(-0.330928\pi\) |
−0.862222 | + | 0.506531i | \(0.830928\pi\) | |||||||
\(132\) | −18.4853 | + | 3.17157i | −1.60894 | + | 0.276050i | ||||
\(133\) | −0.414214 | + | 0.414214i | −0.0359169 | + | 0.0359169i | ||||
\(134\) | − | 14.0000i | − | 1.20942i | ||||||
\(135\) | 1.48528 | + | 2.65685i | 0.127833 | + | 0.228666i | ||||
\(136\) | −2.34315 | + | 2.34315i | −0.200923 | + | 0.200923i | ||||
\(137\) | −7.65685 | −0.654169 | −0.327085 | − | 0.944995i | \(-0.606066\pi\) | ||||
−0.327085 | + | 0.944995i | \(0.606066\pi\) | |||||||
\(138\) | −18.4853 | + | 3.17157i | −1.57357 | + | 0.269982i | ||||
\(139\) | −4.41421 | − | 4.41421i | −0.374409 | − | 0.374409i | 0.494671 | − | 0.869080i | \(-0.335288\pi\) |
−0.869080 | + | 0.494671i | \(0.835288\pi\) | |||||||
\(140\) | −0.828427 | + | 0.828427i | −0.0700149 | + | 0.0700149i | ||||
\(141\) | 5.65685 | − | 8.00000i | 0.476393 | − | 0.673722i | ||||
\(142\) | 6.00000 | + | 6.00000i | 0.503509 | + | 0.503509i | ||||
\(143\) | 33.7990 | 2.82641 | ||||||||
\(144\) | 4.00000 | + | 11.3137i | 0.333333 | + | 0.942809i | ||||
\(145\) | −2.48528 | −0.206391 | ||||||||
\(146\) | −5.17157 | − | 5.17157i | −0.428002 | − | 0.428002i | ||||
\(147\) | −1.00000 | + | 1.41421i | −0.0824786 | + | 0.116642i | ||||
\(148\) | −3.65685 | − | 3.65685i | −0.300592 | − | 0.300592i | ||||
\(149\) | 9.48528 | + | 9.48528i | 0.777065 | + | 0.777065i | 0.979331 | − | 0.202266i | \(-0.0648306\pi\) |
−0.202266 | + | 0.979331i | \(0.564831\pi\) | |||||||
\(150\) | −11.2426 | + | 1.92893i | −0.917958 | + | 0.157497i | ||||
\(151\) | −17.6569 | −1.43689 | −0.718447 | − | 0.695581i | \(-0.755147\pi\) | ||||
−0.718447 | + | 0.695581i | \(0.755147\pi\) | |||||||
\(152\) | 1.65685 | 0.134389 | ||||||||
\(153\) | 3.31371 | − | 1.17157i | 0.267897 | − | 0.0947161i | ||||
\(154\) | 7.65685i | 0.617007i | ||||||||
\(155\) | −2.68629 | + | 2.68629i | −0.215768 | + | 0.215768i | ||||
\(156\) | −3.65685 | − | 21.3137i | −0.292783 | − | 1.70646i | ||||
\(157\) | 2.89949 | + | 2.89949i | 0.231405 | + | 0.231405i | 0.813279 | − | 0.581874i | \(-0.197680\pi\) |
−0.581874 | + | 0.813279i | \(0.697680\pi\) | |||||||
\(158\) | −2.00000 | − | 2.00000i | −0.159111 | − | 0.159111i | ||||
\(159\) | 14.0711 | − | 2.41421i | 1.11591 | − | 0.191460i | ||||
\(160\) | 3.31371 | 0.261972 | ||||||||
\(161\) | 7.65685i | 0.603445i | ||||||||
\(162\) | 1.34315 | − | 12.6569i | 0.105527 | − | 0.994416i | ||||
\(163\) | −1.82843 | + | 1.82843i | −0.143213 | + | 0.143213i | −0.775078 | − | 0.631865i | \(-0.782290\pi\) |
0.631865 | + | 0.775078i | \(0.282290\pi\) | |||||||
\(164\) | 0.686292i | 0.0535904i | ||||||||
\(165\) | 3.17157 | − | 4.48528i | 0.246907 | − | 0.349179i | ||||
\(166\) | −17.7990 | −1.38147 | ||||||||
\(167\) | 7.17157i | 0.554953i | 0.960732 | + | 0.277476i | \(0.0894981\pi\) | ||||
−0.960732 | + | 0.277476i | \(0.910502\pi\) | |||||||
\(168\) | 4.82843 | − | 0.828427i | 0.372521 | − | 0.0639145i | ||||
\(169\) | 25.9706i | 1.99774i | ||||||||
\(170\) | − | 0.970563i | − | 0.0744388i | ||||||
\(171\) | −1.58579 | − | 0.757359i | −0.121268 | − | 0.0579167i | ||||
\(172\) | −7.65685 | + | 7.65685i | −0.583830 | + | 0.583830i | ||||
\(173\) | 4.89949 | − | 4.89949i | 0.372502 | − | 0.372502i | −0.495886 | − | 0.868388i | \(-0.665157\pi\) |
0.868388 | + | 0.495886i | \(0.165157\pi\) | |||||||
\(174\) | 8.48528 | + | 6.00000i | 0.643268 | + | 0.454859i | ||||
\(175\) | 4.65685i | 0.352025i | ||||||||
\(176\) | 15.3137 | − | 15.3137i | 1.15431 | − | 1.15431i | ||||
\(177\) | −4.17157 | − | 24.3137i | −0.313555 | − | 1.82753i | ||||
\(178\) | 15.6569 | − | 15.6569i | 1.17353 | − | 1.17353i | ||||
\(179\) | −15.0000 | − | 15.0000i | −1.12115 | − | 1.12115i | −0.991568 | − | 0.129584i | \(-0.958636\pi\) |
−0.129584 | − | 0.991568i | \(-0.541364\pi\) | |||||||
\(180\) | −3.17157 | − | 1.51472i | −0.236395 | − | 0.112900i | ||||
\(181\) | −2.07107 | + | 2.07107i | −0.153941 | + | 0.153941i | −0.779876 | − | 0.625934i | \(-0.784718\pi\) |
0.625934 | + | 0.779876i | \(0.284718\pi\) | |||||||
\(182\) | −8.82843 | −0.654407 | ||||||||
\(183\) | −5.82843 | + | 1.00000i | −0.430850 | + | 0.0739221i | ||||
\(184\) | 15.3137 | − | 15.3137i | 1.12894 | − | 1.12894i | ||||
\(185\) | 1.51472 | 0.111364 | ||||||||
\(186\) | 15.6569 | − | 2.68629i | 1.14802 | − | 0.196968i | ||||
\(187\) | −4.48528 | − | 4.48528i | −0.327996 | − | 0.327996i | ||||
\(188\) | 11.3137i | 0.825137i | ||||||||
\(189\) | −5.00000 | − | 1.41421i | −0.363696 | − | 0.102869i | ||||
\(190\) | −0.343146 | + | 0.343146i | −0.0248944 | + | 0.0248944i | ||||
\(191\) | −6.34315 | −0.458974 | −0.229487 | − | 0.973312i | \(-0.573705\pi\) | ||||
−0.229487 | + | 0.973312i | \(0.573705\pi\) | |||||||
\(192\) | −11.3137 | − | 8.00000i | −0.816497 | − | 0.577350i | ||||
\(193\) | 15.6569 | 1.12701 | 0.563503 | − | 0.826114i | \(-0.309454\pi\) | ||||
0.563503 | + | 0.826114i | \(0.309454\pi\) | |||||||
\(194\) | 2.00000 | − | 2.00000i | 0.143592 | − | 0.143592i | ||||
\(195\) | 5.17157 | + | 3.65685i | 0.370344 | + | 0.261873i | ||||
\(196\) | − | 2.00000i | − | 0.142857i | ||||||
\(197\) | −5.82843 | − | 5.82843i | −0.415258 | − | 0.415258i | 0.468307 | − | 0.883566i | \(-0.344864\pi\) |
−0.883566 | + | 0.468307i | \(0.844864\pi\) | |||||||
\(198\) | −21.6569 | + | 7.65685i | −1.53909 | + | 0.544149i | ||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 9.31371 | − | 9.31371i | 0.658579 | − | 0.658579i | ||||
\(201\) | −2.89949 | − | 16.8995i | −0.204515 | − | 1.19200i | ||||
\(202\) | −20.1421 | −1.41720 | ||||||||
\(203\) | 3.00000 | − | 3.00000i | 0.210559 | − | 0.210559i | ||||
\(204\) | −2.34315 | + | 3.31371i | −0.164053 | + | 0.232006i | ||||
\(205\) | −0.142136 | − | 0.142136i | −0.00992718 | − | 0.00992718i | ||||
\(206\) | −11.3137 | + | 11.3137i | −0.788263 | + | 0.788263i | ||||
\(207\) | −21.6569 | + | 7.65685i | −1.50526 | + | 0.532188i | ||||
\(208\) | 17.6569 | + | 17.6569i | 1.22428 | + | 1.22428i | ||||
\(209\) | 3.17157i | 0.219382i | ||||||||
\(210\) | −0.828427 | + | 1.17157i | −0.0571669 | + | 0.0808462i | ||||
\(211\) | 5.00000 | − | 5.00000i | 0.344214 | − | 0.344214i | −0.513735 | − | 0.857949i | \(-0.671738\pi\) |
0.857949 | + | 0.513735i | \(0.171738\pi\) | |||||||
\(212\) | −11.6569 | + | 11.6569i | −0.800596 | + | 0.800596i | ||||
\(213\) | 8.48528 | + | 6.00000i | 0.581402 | + | 0.411113i | ||||
\(214\) | − | 10.0000i | − | 0.683586i | ||||||
\(215\) | − | 3.17157i | − | 0.216299i | ||||||
\(216\) | 7.17157 | + | 12.8284i | 0.487964 | + | 0.872864i | ||||
\(217\) | − | 6.48528i | − | 0.440250i | ||||||
\(218\) | −11.6569 | −0.789502 | ||||||||
\(219\) | −7.31371 | − | 5.17157i | −0.494215 | − | 0.349463i | ||||
\(220\) | 6.34315i | 0.427655i | ||||||||
\(221\) | 5.17157 | − | 5.17157i | 0.347878 | − | 0.347878i | ||||
\(222\) | −5.17157 | − | 3.65685i | −0.347093 | − | 0.245432i | ||||
\(223\) | − | 7.17157i | − | 0.480244i | −0.970743 | − | 0.240122i | \(-0.922813\pi\) | ||
0.970743 | − | 0.240122i | \(-0.0771875\pi\) | |||||||
\(224\) | −4.00000 | + | 4.00000i | −0.267261 | + | 0.267261i | ||||
\(225\) | −13.1716 | + | 4.65685i | −0.878105 | + | 0.310457i | ||||
\(226\) | −1.65685 | − | 1.65685i | −0.110212 | − | 0.110212i | ||||
\(227\) | −8.07107 | − | 8.07107i | −0.535696 | − | 0.535696i | 0.386566 | − | 0.922262i | \(-0.373661\pi\) |
−0.922262 | + | 0.386566i | \(0.873661\pi\) | |||||||
\(228\) | 2.00000 | − | 0.343146i | 0.132453 | − | 0.0227254i | ||||
\(229\) | 10.8995 | − | 10.8995i | 0.720259 | − | 0.720259i | −0.248399 | − | 0.968658i | \(-0.579904\pi\) |
0.968658 | + | 0.248399i | \(0.0799044\pi\) | |||||||
\(230\) | 6.34315i | 0.418255i | ||||||||
\(231\) | 1.58579 | + | 9.24264i | 0.104337 | + | 0.608121i | ||||
\(232\) | −12.0000 | −0.787839 | ||||||||
\(233\) | −1.31371 | −0.0860639 | −0.0430320 | − | 0.999074i | \(-0.513702\pi\) | ||||
−0.0430320 | + | 0.999074i | \(0.513702\pi\) | |||||||
\(234\) | −8.82843 | − | 24.9706i | −0.577132 | − | 1.63238i | ||||
\(235\) | −2.34315 | − | 2.34315i | −0.152850 | − | 0.152850i | ||||
\(236\) | 20.1421 | + | 20.1421i | 1.31114 | + | 1.31114i | ||||
\(237\) | −2.82843 | − | 2.00000i | −0.183726 | − | 0.129914i | ||||
\(238\) | 1.17157 | + | 1.17157i | 0.0759418 | + | 0.0759418i | ||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 4.00000 | − | 0.686292i | 0.258199 | − | 0.0442999i | ||||
\(241\) | 0.343146 | 0.0221040 | 0.0110520 | − | 0.999939i | \(-0.496482\pi\) | ||||
0.0110520 | + | 0.999939i | \(0.496482\pi\) | |||||||
\(242\) | 18.3137 | + | 18.3137i | 1.17725 | + | 1.17725i | ||||
\(243\) | −1.00000 | − | 15.5563i | −0.0641500 | − | 0.997940i | ||||
\(244\) | 4.82843 | − | 4.82843i | 0.309108 | − | 0.309108i | ||||
\(245\) | 0.414214 | + | 0.414214i | 0.0264631 | + | 0.0264631i | ||||
\(246\) | 0.142136 | + | 0.828427i | 0.00906224 | + | 0.0528186i | ||||
\(247\) | −3.65685 | −0.232680 | ||||||||
\(248\) | −12.9706 | + | 12.9706i | −0.823632 | + | 0.823632i | ||||
\(249\) | −21.4853 | + | 3.68629i | −1.36157 | + | 0.233609i | ||||
\(250\) | 8.00000i | 0.505964i | ||||||||
\(251\) | 2.41421 | − | 2.41421i | 0.152384 | − | 0.152384i | −0.626798 | − | 0.779182i | \(-0.715635\pi\) |
0.779182 | + | 0.626798i | \(0.215635\pi\) | |||||||
\(252\) | 5.65685 | − | 2.00000i | 0.356348 | − | 0.125988i | ||||
\(253\) | 29.3137 | + | 29.3137i | 1.84294 | + | 1.84294i | ||||
\(254\) | 15.6569 | + | 15.6569i | 0.982398 | + | 0.982398i | ||||
\(255\) | −0.201010 | − | 1.17157i | −0.0125877 | − | 0.0733667i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 26.8284i | 1.67351i | 0.547576 | + | 0.836756i | \(0.315551\pi\) | ||||
−0.547576 | + | 0.836756i | \(0.684449\pi\) | |||||||
\(258\) | −7.65685 | + | 10.8284i | −0.476695 | + | 0.674148i | ||||
\(259\) | −1.82843 | + | 1.82843i | −0.113613 | + | 0.113613i | ||||
\(260\) | −7.31371 | −0.453577 | ||||||||
\(261\) | 11.4853 | + | 5.48528i | 0.710921 | + | 0.339530i | ||||
\(262\) | 8.14214 | 0.503023 | ||||||||
\(263\) | − | 11.6569i | − | 0.718792i | −0.933185 | − | 0.359396i | \(-0.882983\pi\) | ||
0.933185 | − | 0.359396i | \(-0.117017\pi\) | |||||||
\(264\) | 15.3137 | − | 21.6569i | 0.942494 | − | 1.33289i | ||||
\(265\) | − | 4.82843i | − | 0.296608i | ||||||
\(266\) | − | 0.828427i | − | 0.0507941i | ||||||
\(267\) | 15.6569 | − | 22.1421i | 0.958184 | − | 1.35508i | ||||
\(268\) | 14.0000 | + | 14.0000i | 0.855186 | + | 0.855186i | ||||
\(269\) | 5.58579 | − | 5.58579i | 0.340571 | − | 0.340571i | −0.516011 | − | 0.856582i | \(-0.672584\pi\) |
0.856582 | + | 0.516011i | \(0.172584\pi\) | |||||||
\(270\) | −4.14214 | − | 1.17157i | −0.252082 | − | 0.0712997i | ||||
\(271\) | 16.8284i | 1.02225i | 0.859505 | + | 0.511127i | \(0.170772\pi\) | ||||
−0.859505 | + | 0.511127i | \(0.829228\pi\) | |||||||
\(272\) | − | 4.68629i | − | 0.284148i | ||||||
\(273\) | −10.6569 | + | 1.82843i | −0.644982 | + | 0.110661i | ||||
\(274\) | 7.65685 | − | 7.65685i | 0.462567 | − | 0.462567i | ||||
\(275\) | 17.8284 | + | 17.8284i | 1.07509 | + | 1.07509i | ||||
\(276\) | 15.3137 | − | 21.6569i | 0.921777 | − | 1.30359i | ||||
\(277\) | 6.31371 | − | 6.31371i | 0.379354 | − | 0.379354i | −0.491515 | − | 0.870869i | \(-0.663557\pi\) |
0.870869 | + | 0.491515i | \(0.163557\pi\) | |||||||
\(278\) | 8.82843 | 0.529494 | ||||||||
\(279\) | 18.3431 | − | 6.48528i | 1.09818 | − | 0.388264i | ||||
\(280\) | − | 1.65685i | − | 0.0990160i | ||||||
\(281\) | 6.68629 | 0.398871 | 0.199435 | − | 0.979911i | \(-0.436089\pi\) | ||||
0.199435 | + | 0.979911i | \(0.436089\pi\) | |||||||
\(282\) | 2.34315 | + | 13.6569i | 0.139532 | + | 0.813254i | ||||
\(283\) | −12.8995 | − | 12.8995i | −0.766795 | − | 0.766795i | 0.210746 | − | 0.977541i | \(-0.432411\pi\) |
−0.977541 | + | 0.210746i | \(0.932411\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | −0.343146 | + | 0.485281i | −0.0203262 | + | 0.0287456i | ||||
\(286\) | −33.7990 | + | 33.7990i | −1.99858 | + | 1.99858i | ||||
\(287\) | 0.343146 | 0.0202553 | ||||||||
\(288\) | −15.3137 | − | 7.31371i | −0.902369 | − | 0.430964i | ||||
\(289\) | 15.6274 | 0.919260 | ||||||||
\(290\) | 2.48528 | − | 2.48528i | 0.145941 | − | 0.145941i | ||||
\(291\) | 2.00000 | − | 2.82843i | 0.117242 | − | 0.165805i | ||||
\(292\) | 10.3431 | 0.605287 | ||||||||
\(293\) | −9.24264 | − | 9.24264i | −0.539961 | − | 0.539961i | 0.383557 | − | 0.923517i | \(-0.374699\pi\) |
−0.923517 | + | 0.383557i | \(0.874699\pi\) | |||||||
\(294\) | −0.414214 | − | 2.41421i | −0.0241574 | − | 0.140800i | ||||
\(295\) | −8.34315 | −0.485757 | ||||||||
\(296\) | 7.31371 | 0.425101 | ||||||||
\(297\) | −24.5563 | + | 13.7279i | −1.42490 | + | 0.796575i | ||||
\(298\) | −18.9706 | −1.09894 | ||||||||
\(299\) | −33.7990 | + | 33.7990i | −1.95465 | + | 1.95465i | ||||
\(300\) | 9.31371 | − | 13.1716i | 0.537727 | − | 0.760461i | ||||
\(301\) | 3.82843 | + | 3.82843i | 0.220667 | + | 0.220667i | ||||
\(302\) | 17.6569 | − | 17.6569i | 1.01604 | − | 1.01604i | ||||
\(303\) | −24.3137 | + | 4.17157i | −1.39679 | + | 0.239651i | ||||
\(304\) | −1.65685 | + | 1.65685i | −0.0950271 | + | 0.0950271i | ||||
\(305\) | 2.00000i | 0.114520i | ||||||||
\(306\) | −2.14214 | + | 4.48528i | −0.122458 | + | 0.256406i | ||||
\(307\) | −14.8995 | + | 14.8995i | −0.850359 | + | 0.850359i | −0.990177 | − | 0.139818i | \(-0.955348\pi\) |
0.139818 | + | 0.990177i | \(0.455348\pi\) | |||||||
\(308\) | −7.65685 | − | 7.65685i | −0.436290 | − | 0.436290i | ||||
\(309\) | −11.3137 | + | 16.0000i | −0.643614 | + | 0.910208i | ||||
\(310\) | − | 5.37258i | − | 0.305142i | ||||||
\(311\) | 1.51472i | 0.0858918i | 0.999077 | + | 0.0429459i | \(0.0136743\pi\) | ||||
−0.999077 | + | 0.0429459i | \(0.986326\pi\) | |||||||
\(312\) | 24.9706 | + | 17.6569i | 1.41368 | + | 0.999623i | ||||
\(313\) | 20.4853i | 1.15790i | 0.815364 | + | 0.578948i | \(0.196537\pi\) | ||||
−0.815364 | + | 0.578948i | \(0.803463\pi\) | |||||||
\(314\) | −5.79899 | −0.327256 | ||||||||
\(315\) | −0.757359 | + | 1.58579i | −0.0426724 | + | 0.0893489i | ||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −13.1421 | + | 13.1421i | −0.738136 | + | 0.738136i | −0.972217 | − | 0.234081i | \(-0.924792\pi\) |
0.234081 | + | 0.972217i | \(0.424792\pi\) | |||||||
\(318\) | −11.6569 | + | 16.4853i | −0.653684 | + | 0.924449i | ||||
\(319\) | − | 22.9706i | − | 1.28610i | ||||||
\(320\) | −3.31371 | + | 3.31371i | −0.185242 | + | 0.185242i | ||||
\(321\) | −2.07107 | − | 12.0711i | −0.115596 | − | 0.673741i | ||||
\(322\) | −7.65685 | − | 7.65685i | −0.426700 | − | 0.426700i | ||||
\(323\) | 0.485281 | + | 0.485281i | 0.0270018 | + | 0.0270018i | ||||
\(324\) | 11.3137 | + | 14.0000i | 0.628539 | + | 0.777778i | ||||
\(325\) | −20.5563 | + | 20.5563i | −1.14026 | + | 1.14026i | ||||
\(326\) | − | 3.65685i | − | 0.202534i | ||||||
\(327\) | −14.0711 | + | 2.41421i | −0.778132 | + | 0.133506i | ||||
\(328\) | −0.686292 | − | 0.686292i | −0.0378941 | − | 0.0378941i | ||||
\(329\) | 5.65685 | 0.311872 | ||||||||
\(330\) | 1.31371 | + | 7.65685i | 0.0723173 | + | 0.421496i | ||||
\(331\) | 17.1421 | + | 17.1421i | 0.942217 | + | 0.942217i | 0.998419 | − | 0.0562024i | \(-0.0178992\pi\) |
−0.0562024 | + | 0.998419i | \(0.517899\pi\) | |||||||
\(332\) | 17.7990 | − | 17.7990i | 0.976846 | − | 0.976846i | ||||
\(333\) | −7.00000 | − | 3.34315i | −0.383598 | − | 0.183203i | ||||
\(334\) | −7.17157 | − | 7.17157i | −0.392411 | − | 0.392411i | ||||
\(335\) | −5.79899 | −0.316833 | ||||||||
\(336\) | −4.00000 | + | 5.65685i | −0.218218 | + | 0.308607i | ||||
\(337\) | 25.3137 | 1.37893 | 0.689463 | − | 0.724321i | \(-0.257847\pi\) | ||||
0.689463 | + | 0.724321i | \(0.257847\pi\) | |||||||
\(338\) | −25.9706 | − | 25.9706i | −1.41261 | − | 1.41261i | ||||
\(339\) | −2.34315 | − | 1.65685i | −0.127262 | − | 0.0899880i | ||||
\(340\) | 0.970563 | + | 0.970563i | 0.0526362 | + | 0.0526362i | ||||
\(341\) | −24.8284 | − | 24.8284i | −1.34453 | − | 1.34453i | ||||
\(342\) | 2.34315 | − | 0.828427i | 0.126703 | − | 0.0447962i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | − | 15.3137i | − | 0.825660i | ||||||
\(345\) | 1.31371 | + | 7.65685i | 0.0707277 | + | 0.412231i | ||||
\(346\) | 9.79899i | 0.526797i | ||||||||
\(347\) | 13.1421 | − | 13.1421i | 0.705507 | − | 0.705507i | −0.260080 | − | 0.965587i | \(-0.583749\pi\) |
0.965587 | + | 0.260080i | \(0.0837490\pi\) | |||||||
\(348\) | −14.4853 | + | 2.48528i | −0.776493 | + | 0.133225i | ||||
\(349\) | −2.07107 | − | 2.07107i | −0.110862 | − | 0.110862i | 0.649500 | − | 0.760362i | \(-0.274978\pi\) |
−0.760362 | + | 0.649500i | \(0.774978\pi\) | |||||||
\(350\) | −4.65685 | − | 4.65685i | −0.248919 | − | 0.248919i | ||||
\(351\) | −15.8284 | − | 28.3137i | −0.844859 | − | 1.51127i | ||||
\(352\) | 30.6274i | 1.63245i | ||||||||
\(353\) | − | 8.48528i | − | 0.451626i | −0.974171 | − | 0.225813i | \(-0.927496\pi\) | ||
0.974171 | − | 0.225813i | \(-0.0725038\pi\) | |||||||
\(354\) | 28.4853 | + | 20.1421i | 1.51398 | + | 1.07054i | ||||
\(355\) | 2.48528 | − | 2.48528i | 0.131905 | − | 0.131905i | ||||
\(356\) | 31.3137i | 1.65962i | ||||||||
\(357\) | 1.65685 | + | 1.17157i | 0.0876900 | + | 0.0620062i | ||||
\(358\) | 30.0000 | 1.58555 | ||||||||
\(359\) | − | 20.3431i | − | 1.07367i | −0.843687 | − | 0.536835i | \(-0.819620\pi\) | ||
0.843687 | − | 0.536835i | \(-0.180380\pi\) | |||||||
\(360\) | 4.68629 | − | 1.65685i | 0.246989 | − | 0.0873239i | ||||
\(361\) | 18.6569i | 0.981940i | ||||||||
\(362\) | − | 4.14214i | − | 0.217706i | ||||||
\(363\) | 25.8995 | + | 18.3137i | 1.35937 | + | 0.961220i | ||||
\(364\) | 8.82843 | − | 8.82843i | 0.462735 | − | 0.462735i | ||||
\(365\) | −2.14214 | + | 2.14214i | −0.112125 | + | 0.112125i | ||||
\(366\) | 4.82843 | − | 6.82843i | 0.252386 | − | 0.356928i | ||||
\(367\) | − | 16.1421i | − | 0.842613i | −0.906918 | − | 0.421306i | \(-0.861572\pi\) | ||
0.906918 | − | 0.421306i | \(-0.138428\pi\) | |||||||
\(368\) | 30.6274i | 1.59656i | ||||||||
\(369\) | 0.343146 | + | 0.970563i | 0.0178635 | + | 0.0505255i | ||||
\(370\) | −1.51472 | + | 1.51472i | −0.0787465 | + | 0.0787465i | ||||
\(371\) | 5.82843 | + | 5.82843i | 0.302597 | + | 0.302597i | ||||
\(372\) | −12.9706 | + | 18.3431i | −0.672492 | + | 0.951048i | ||||
\(373\) | −8.31371 | + | 8.31371i | −0.430468 | + | 0.430468i | −0.888787 | − | 0.458320i | \(-0.848451\pi\) |
0.458320 | + | 0.888787i | \(0.348451\pi\) | |||||||
\(374\) | 8.97056 | 0.463857 | ||||||||
\(375\) | 1.65685 | + | 9.65685i | 0.0855596 | + | 0.498678i | ||||
\(376\) | −11.3137 | − | 11.3137i | −0.583460 | − | 0.583460i | ||||
\(377\) | 26.4853 | 1.36406 | ||||||||
\(378\) | 6.41421 | − | 3.58579i | 0.329912 | − | 0.184433i | ||||
\(379\) | −27.1421 | − | 27.1421i | −1.39420 | − | 1.39420i | −0.815645 | − | 0.578553i | \(-0.803618\pi\) |
−0.578553 | − | 0.815645i | \(-0.696382\pi\) | |||||||
\(380\) | − | 0.686292i | − | 0.0352060i | ||||||
\(381\) | 22.1421 | + | 15.6569i | 1.13438 | + | 0.802125i | ||||
\(382\) | 6.34315 | − | 6.34315i | 0.324544 | − | 0.324544i | ||||
\(383\) | 19.3137 | 0.986884 | 0.493442 | − | 0.869779i | \(-0.335738\pi\) | ||||
0.493442 | + | 0.869779i | \(0.335738\pi\) | |||||||
\(384\) | 19.3137 | − | 3.31371i | 0.985599 | − | 0.169102i | ||||
\(385\) | 3.17157 | 0.161638 | ||||||||
\(386\) | −15.6569 | + | 15.6569i | −0.796913 | + | 0.796913i | ||||
\(387\) | −7.00000 | + | 14.6569i | −0.355830 | + | 0.745050i | ||||
\(388\) | 4.00000i | 0.203069i | ||||||||
\(389\) | −19.9706 | − | 19.9706i | −1.01255 | − | 1.01255i | −0.999920 | − | 0.0126275i | \(-0.995980\pi\) |
−0.0126275 | − | 0.999920i | \(-0.504020\pi\) | |||||||
\(390\) | −8.82843 | + | 1.51472i | −0.447045 | + | 0.0767008i | ||||
\(391\) | 8.97056 | 0.453661 | ||||||||
\(392\) | 2.00000 | + | 2.00000i | 0.101015 | + | 0.101015i | ||||
\(393\) | 9.82843 | − | 1.68629i | 0.495779 | − | 0.0850622i | ||||
\(394\) | 11.6569 | 0.587264 | ||||||||
\(395\) | −0.828427 | + | 0.828427i | −0.0416827 | + | 0.0416827i | ||||
\(396\) | 14.0000 | − | 29.3137i | 0.703526 | − | 1.47307i | ||||
\(397\) | −23.7279 | − | 23.7279i | −1.19087 | − | 1.19087i | −0.976823 | − | 0.214047i | \(-0.931335\pi\) |
−0.214047 | − | 0.976823i | \(-0.568665\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.171573 | − | 1.00000i | −0.00858939 | − | 0.0500626i | ||||
\(400\) | 18.6274i | 0.931371i | ||||||||
\(401\) | − | 19.3137i | − | 0.964481i | −0.876039 | − | 0.482240i | \(-0.839823\pi\) | ||
0.876039 | − | 0.482240i | \(-0.160177\pi\) | |||||||
\(402\) | 19.7990 | + | 14.0000i | 0.987484 | + | 0.698257i | ||||
\(403\) | 28.6274 | − | 28.6274i | 1.42603 | − | 1.42603i | ||||
\(404\) | 20.1421 | − | 20.1421i | 1.00211 | − | 1.00211i | ||||
\(405\) | −5.24264 | − | 0.556349i | −0.260509 | − | 0.0276452i | ||||
\(406\) | 6.00000i | 0.297775i | ||||||||
\(407\) | 14.0000i | 0.693954i | ||||||||
\(408\) | −0.970563 | − | 5.65685i | −0.0480500 | − | 0.280056i | ||||
\(409\) | − | 25.1716i | − | 1.24465i | −0.782757 | − | 0.622327i | \(-0.786187\pi\) | ||
0.782757 | − | 0.622327i | \(-0.213813\pi\) | |||||||
\(410\) | 0.284271 | 0.0140392 | ||||||||
\(411\) | 7.65685 | − | 10.8284i | 0.377685 | − | 0.534127i | ||||
\(412\) | − | 22.6274i | − | 1.11477i | ||||||
\(413\) | 10.0711 | − | 10.0711i | 0.495565 | − | 0.495565i | ||||
\(414\) | 14.0000 | − | 29.3137i | 0.688062 | − | 1.44069i | ||||
\(415\) | 7.37258i | 0.361906i | ||||||||
\(416\) | −35.3137 | −1.73140 | ||||||||
\(417\) | 10.6569 | − | 1.82843i | 0.521868 | − | 0.0895385i | ||||
\(418\) | −3.17157 | − | 3.17157i | −0.155127 | − | 0.155127i | ||||
\(419\) | −13.2426 | − | 13.2426i | −0.646945 | − | 0.646945i | 0.305308 | − | 0.952254i | \(-0.401241\pi\) |
−0.952254 | + | 0.305308i | \(0.901241\pi\) | |||||||
\(420\) | −0.343146 | − | 2.00000i | −0.0167438 | − | 0.0975900i | ||||
\(421\) | −1.68629 | + | 1.68629i | −0.0821848 | + | 0.0821848i | −0.747004 | − | 0.664819i | \(-0.768509\pi\) |
0.664819 | + | 0.747004i | \(0.268509\pi\) | |||||||
\(422\) | 10.0000i | 0.486792i | ||||||||
\(423\) | 5.65685 | + | 16.0000i | 0.275046 | + | 0.777947i | ||||
\(424\) | − | 23.3137i | − | 1.13221i | ||||||
\(425\) | 5.45584 | 0.264647 | ||||||||
\(426\) | −14.4853 | + | 2.48528i | −0.701814 | + | 0.120412i | ||||
\(427\) | −2.41421 | − | 2.41421i | −0.116832 | − | 0.116832i | ||||
\(428\) | 10.0000 | + | 10.0000i | 0.483368 | + | 0.483368i | ||||
\(429\) | −33.7990 | + | 47.7990i | −1.63183 | + | 2.30776i | ||||
\(430\) | 3.17157 | + | 3.17157i | 0.152947 | + | 0.152947i | ||||
\(431\) | −3.31371 | −0.159616 | −0.0798079 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798079 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(432\) | −20.0000 | − | 5.65685i | −0.962250 | − | 0.272166i | ||||
\(433\) | −14.6863 | −0.705778 | −0.352889 | − | 0.935665i | \(-0.614801\pi\) | ||||
−0.352889 | + | 0.935665i | \(0.614801\pi\) | |||||||
\(434\) | 6.48528 | + | 6.48528i | 0.311303 | + | 0.311303i | ||||
\(435\) | 2.48528 | − | 3.51472i | 0.119160 | − | 0.168518i | ||||
\(436\) | 11.6569 | − | 11.6569i | 0.558262 | − | 0.558262i | ||||
\(437\) | −3.17157 | − | 3.17157i | −0.151717 | − | 0.151717i | ||||
\(438\) | 12.4853 | − | 2.14214i | 0.596570 | − | 0.102355i | ||||
\(439\) | −0.970563 | −0.0463224 | −0.0231612 | − | 0.999732i | \(-0.507373\pi\) | ||||
−0.0231612 | + | 0.999732i | \(0.507373\pi\) | |||||||
\(440\) | −6.34315 | − | 6.34315i | −0.302398 | − | 0.302398i | ||||
\(441\) | −1.00000 | − | 2.82843i | −0.0476190 | − | 0.134687i | ||||
\(442\) | 10.3431i | 0.491973i | ||||||||
\(443\) | 16.6569 | − | 16.6569i | 0.791391 | − | 0.791391i | −0.190329 | − | 0.981720i | \(-0.560956\pi\) |
0.981720 | + | 0.190329i | \(0.0609556\pi\) | |||||||
\(444\) | 8.82843 | − | 1.51472i | 0.418979 | − | 0.0718854i | ||||
\(445\) | −6.48528 | − | 6.48528i | −0.307432 | − | 0.307432i | ||||
\(446\) | 7.17157 | + | 7.17157i | 0.339584 | + | 0.339584i | ||||
\(447\) | −22.8995 | + | 3.92893i | −1.08311 | + | 0.185832i | ||||
\(448\) | − | 8.00000i | − | 0.377964i | ||||||
\(449\) | 12.9706i | 0.612119i | 0.952012 | + | 0.306059i | \(0.0990106\pi\) | ||||
−0.952012 | + | 0.306059i | \(0.900989\pi\) | |||||||
\(450\) | 8.51472 | − | 17.8284i | 0.401388 | − | 0.840440i | ||||
\(451\) | 1.31371 | − | 1.31371i | 0.0618601 | − | 0.0618601i | ||||
\(452\) | 3.31371 | 0.155864 | ||||||||
\(453\) | 17.6569 | − | 24.9706i | 0.829591 | − | 1.17322i | ||||
\(454\) | 16.1421 | 0.757588 | ||||||||
\(455\) | 3.65685i | 0.171436i | ||||||||
\(456\) | −1.65685 | + | 2.34315i | −0.0775893 | + | 0.109728i | ||||
\(457\) | 29.9411i | 1.40059i | 0.713855 | + | 0.700293i | \(0.246947\pi\) | ||||
−0.713855 | + | 0.700293i | \(0.753053\pi\) | |||||||
\(458\) | 21.7990i | 1.01860i | ||||||||
\(459\) | −1.65685 | + | 5.85786i | −0.0773353 | + | 0.273422i | ||||
\(460\) | −6.34315 | − | 6.34315i | −0.295751 | − | 0.295751i | ||||
\(461\) | −22.4142 | + | 22.4142i | −1.04393 | + | 1.04393i | −0.0449445 | + | 0.998989i | \(0.514311\pi\) |
−0.998989 | + | 0.0449445i | \(0.985689\pi\) | |||||||
\(462\) | −10.8284 | − | 7.65685i | −0.503784 | − | 0.356229i | ||||
\(463\) | − | 11.6569i | − | 0.541740i | −0.962616 | − | 0.270870i | \(-0.912689\pi\) | ||
0.962616 | − | 0.270870i | \(-0.0873113\pi\) | |||||||
\(464\) | 12.0000 | − | 12.0000i | 0.557086 | − | 0.557086i | ||||
\(465\) | −1.11270 | − | 6.48528i | −0.0516002 | − | 0.300748i | ||||
\(466\) | 1.31371 | − | 1.31371i | 0.0608564 | − | 0.0608564i | ||||
\(467\) | −14.4142 | − | 14.4142i | −0.667010 | − | 0.667010i | 0.290013 | − | 0.957023i | \(-0.406341\pi\) |
−0.957023 | + | 0.290013i | \(0.906341\pi\) | |||||||
\(468\) | 33.7990 | + | 16.1421i | 1.56236 | + | 0.746170i | ||||
\(469\) | 7.00000 | − | 7.00000i | 0.323230 | − | 0.323230i | ||||
\(470\) | 4.68629 | 0.216163 | ||||||||
\(471\) | −7.00000 | + | 1.20101i | −0.322543 | + | 0.0553396i | ||||
\(472\) | −40.2843 | −1.85423 | ||||||||
\(473\) | 29.3137 | 1.34785 | ||||||||
\(474\) | 4.82843 | − | 0.828427i | 0.221777 | − | 0.0380509i | ||||
\(475\) | −1.92893 | − | 1.92893i | −0.0885055 | − | 0.0885055i | ||||
\(476\) | −2.34315 | −0.107398 | ||||||||
\(477\) | −10.6569 | + | 22.3137i | −0.487944 | + | 1.02167i | ||||
\(478\) | −11.3137 | + | 11.3137i | −0.517477 | + | 0.517477i | ||||
\(479\) | 27.3137 | 1.24800 | 0.623998 | − | 0.781426i | \(-0.285507\pi\) | ||||
0.623998 | + | 0.781426i | \(0.285507\pi\) | |||||||
\(480\) | −3.31371 | + | 4.68629i | −0.151249 | + | 0.213899i | ||||
\(481\) | −16.1421 | −0.736018 | ||||||||
\(482\) | −0.343146 | + | 0.343146i | −0.0156299 | + | 0.0156299i | ||||
\(483\) | −10.8284 | − | 7.65685i | −0.492710 | − | 0.348399i | ||||
\(484\) | −36.6274 | −1.66488 | ||||||||
\(485\) | −0.828427 | − | 0.828427i | −0.0376169 | − | 0.0376169i | ||||
\(486\) | 16.5563 | + | 14.5563i | 0.751011 | + | 0.660289i | ||||
\(487\) | −16.2843 | −0.737911 | −0.368955 | − | 0.929447i | \(-0.620284\pi\) | ||||
−0.368955 | + | 0.929447i | \(0.620284\pi\) | |||||||
\(488\) | 9.65685i | 0.437145i | ||||||||
\(489\) | −0.757359 | − | 4.41421i | −0.0342490 | − | 0.199618i | ||||
\(490\) | −0.828427 | −0.0374245 | ||||||||
\(491\) | 10.3137 | − | 10.3137i | 0.465451 | − | 0.465451i | −0.434986 | − | 0.900437i | \(-0.643247\pi\) |
0.900437 | + | 0.434986i | \(0.143247\pi\) | |||||||
\(492\) | −0.970563 | − | 0.686292i | −0.0437563 | − | 0.0309404i | ||||
\(493\) | −3.51472 | − | 3.51472i | −0.158295 | − | 0.158295i | ||||
\(494\) | 3.65685 | − | 3.65685i | 0.164530 | − | 0.164530i | ||||
\(495\) | 3.17157 | + | 8.97056i | 0.142552 | + | 0.403197i | ||||
\(496\) | − | 25.9411i | − | 1.16479i | ||||||
\(497\) | 6.00000i | 0.269137i | ||||||||
\(498\) | 17.7990 | − | 25.1716i | 0.797592 | − | 1.12797i | ||||
\(499\) | 5.68629 | − | 5.68629i | 0.254553 | − | 0.254553i | −0.568281 | − | 0.822834i | \(-0.692391\pi\) |
0.822834 | + | 0.568281i | \(0.192391\pi\) | |||||||
\(500\) | −8.00000 | − | 8.00000i | −0.357771 | − | 0.357771i | ||||
\(501\) | −10.1421 | − | 7.17157i | −0.453117 | − | 0.320402i | ||||
\(502\) | 4.82843i | 0.215503i | ||||||||
\(503\) | − | 16.8284i | − | 0.750342i | −0.926956 | − | 0.375171i | \(-0.877584\pi\) | ||
0.926956 | − | 0.375171i | \(-0.122416\pi\) | |||||||
\(504\) | −3.65685 | + | 7.65685i | −0.162889 | + | 0.341063i | ||||
\(505\) | 8.34315i | 0.371265i | ||||||||
\(506\) | −58.6274 | −2.60631 | ||||||||
\(507\) | −36.7279 | − | 25.9706i | −1.63114 | − | 1.15339i | ||||
\(508\) | −31.3137 | −1.38932 | ||||||||
\(509\) | 7.24264 | − | 7.24264i | 0.321024 | − | 0.321024i | −0.528136 | − | 0.849160i | \(-0.677109\pi\) |
0.849160 | + | 0.528136i | \(0.177109\pi\) | |||||||
\(510\) | 1.37258 | + | 0.970563i | 0.0607790 | + | 0.0429772i | ||||
\(511\) | − | 5.17157i | − | 0.228777i | ||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 2.65685 | − | 1.48528i | 0.117303 | − | 0.0655768i | ||||
\(514\) | −26.8284 | − | 26.8284i | −1.18335 | − | 1.18335i | ||||
\(515\) | 4.68629 | + | 4.68629i | 0.206503 | + | 0.206503i | ||||
\(516\) | −3.17157 | − | 18.4853i | −0.139621 | − | 0.813769i | ||||
\(517\) | 21.6569 | − | 21.6569i | 0.952467 | − | 0.952467i | ||||
\(518\) | − | 3.65685i | − | 0.160673i | ||||||
\(519\) | 2.02944 | + | 11.8284i | 0.0890824 | + | 0.519210i | ||||
\(520\) | 7.31371 | − | 7.31371i | 0.320727 | − | 0.320727i | ||||
\(521\) | 13.3137 | 0.583284 | 0.291642 | − | 0.956528i | \(-0.405798\pi\) | ||||
0.291642 | + | 0.956528i | \(0.405798\pi\) | |||||||
\(522\) | −16.9706 | + | 6.00000i | −0.742781 | + | 0.262613i | ||||
\(523\) | 21.0416 | + | 21.0416i | 0.920086 | + | 0.920086i | 0.997035 | − | 0.0769488i | \(-0.0245178\pi\) |
−0.0769488 | + | 0.997035i | \(0.524518\pi\) | |||||||
\(524\) | −8.14214 | + | 8.14214i | −0.355691 | + | 0.355691i | ||||
\(525\) | −6.58579 | − | 4.65685i | −0.287427 | − | 0.203242i | ||||
\(526\) | 11.6569 | + | 11.6569i | 0.508263 | + | 0.508263i | ||||
\(527\) | −7.59798 | −0.330973 | ||||||||
\(528\) | 6.34315 | + | 36.9706i | 0.276050 | + | 1.60894i | ||||
\(529\) | −35.6274 | −1.54902 | ||||||||
\(530\) | 4.82843 | + | 4.82843i | 0.209733 | + | 0.209733i | ||||
\(531\) | 38.5563 | + | 18.4142i | 1.67320 | + | 0.799109i | ||||
\(532\) | 0.828427 | + | 0.828427i | 0.0359169 | + | 0.0359169i | ||||
\(533\) | 1.51472 | + | 1.51472i | 0.0656097 | + | 0.0656097i | ||||
\(534\) | 6.48528 | + | 37.7990i | 0.280646 | + | 1.63572i | ||||
\(535\) | −4.14214 | −0.179080 | ||||||||
\(536\) | −28.0000 | −1.20942 | ||||||||
\(537\) | 36.2132 | − | 6.21320i | 1.56272 | − | 0.268120i | ||||
\(538\) | 11.1716i | 0.481641i | ||||||||
\(539\) | −3.82843 | + | 3.82843i | −0.164902 | + | 0.164902i | ||||
\(540\) | 5.31371 | − | 2.97056i | 0.228666 | − | 0.127833i | ||||
\(541\) | −21.0000 | − | 21.0000i | −0.902861 | − | 0.902861i | 0.0928222 | − | 0.995683i | \(-0.470411\pi\) |
−0.995683 | + | 0.0928222i | \(0.970411\pi\) | |||||||
\(542\) | −16.8284 | − | 16.8284i | −0.722843 | − | 0.722843i | ||||
\(543\) | −0.857864 | − | 5.00000i | −0.0368145 | − | 0.214571i | ||||
\(544\) | 4.68629 | + | 4.68629i | 0.200923 | + | 0.200923i | ||||
\(545\) | 4.82843i | 0.206827i | ||||||||
\(546\) | 8.82843 | − | 12.4853i | 0.377822 | − | 0.534321i | ||||
\(547\) | −17.1421 | + | 17.1421i | −0.732945 | + | 0.732945i | −0.971202 | − | 0.238257i | \(-0.923424\pi\) |
0.238257 | + | 0.971202i | \(0.423424\pi\) | |||||||
\(548\) | 15.3137i | 0.654169i | ||||||||
\(549\) | 4.41421 | − | 9.24264i | 0.188394 | − | 0.394466i | ||||
\(550\) | −35.6569 | −1.52041 | ||||||||
\(551\) | 2.48528i | 0.105877i | ||||||||
\(552\) | 6.34315 | + | 36.9706i | 0.269982 | + | 1.57357i | ||||
\(553\) | − | 2.00000i | − | 0.0850487i | ||||||
\(554\) | 12.6274i | 0.536488i | ||||||||
\(555\) | −1.51472 | + | 2.14214i | −0.0642962 | + | 0.0909286i | ||||
\(556\) | −8.82843 | + | 8.82843i | −0.374409 | + | 0.374409i | ||||
\(557\) | 15.1421 | − | 15.1421i | 0.641593 | − | 0.641593i | −0.309354 | − | 0.950947i | \(-0.600113\pi\) |
0.950947 | + | 0.309354i | \(0.100113\pi\) | |||||||
\(558\) | −11.8579 | + | 24.8284i | −0.501983 | + | 1.05107i | ||||
\(559\) | 33.7990i | 1.42954i | ||||||||
\(560\) | 1.65685 | + | 1.65685i | 0.0700149 | + | 0.0700149i | ||||
\(561\) | 10.8284 | − | 1.85786i | 0.457177 | − | 0.0784391i | ||||
\(562\) | −6.68629 | + | 6.68629i | −0.282044 | + | 0.282044i | ||||
\(563\) | −19.5858 | − | 19.5858i | −0.825442 | − | 0.825442i | 0.161440 | − | 0.986883i | \(-0.448386\pi\) |
−0.986883 | + | 0.161440i | \(0.948386\pi\) | |||||||
\(564\) | −16.0000 | − | 11.3137i | −0.673722 | − | 0.476393i | ||||
\(565\) | −0.686292 | + | 0.686292i | −0.0288725 | + | 0.0288725i | ||||
\(566\) | 25.7990 | 1.08441 | ||||||||
\(567\) | 7.00000 | − | 5.65685i | 0.293972 | − | 0.237566i | ||||
\(568\) | 12.0000 | − | 12.0000i | 0.503509 | − | 0.503509i | ||||
\(569\) | 32.6274 | 1.36781 | 0.683906 | − | 0.729570i | \(-0.260280\pi\) | ||||
0.683906 | + | 0.729570i | \(0.260280\pi\) | |||||||
\(570\) | −0.142136 | − | 0.828427i | −0.00595341 | − | 0.0346990i | ||||
\(571\) | −6.17157 | − | 6.17157i | −0.258272 | − | 0.258272i | 0.566079 | − | 0.824351i | \(-0.308460\pi\) |
−0.824351 | + | 0.566079i | \(0.808460\pi\) | |||||||
\(572\) | − | 67.5980i | − | 2.82641i | ||||||
\(573\) | 6.34315 | − | 8.97056i | 0.264989 | − | 0.374751i | ||||
\(574\) | −0.343146 | + | 0.343146i | −0.0143226 | + | 0.0143226i | ||||
\(575\) | −35.6569 | −1.48699 | ||||||||
\(576\) | 22.6274 | − | 8.00000i | 0.942809 | − | 0.333333i | ||||
\(577\) | −0.343146 | −0.0142853 | −0.00714267 | − | 0.999974i | \(-0.502274\pi\) | ||||
−0.00714267 | + | 0.999974i | \(0.502274\pi\) | |||||||
\(578\) | −15.6274 | + | 15.6274i | −0.650015 | + | 0.650015i | ||||
\(579\) | −15.6569 | + | 22.1421i | −0.650677 | + | 0.920196i | ||||
\(580\) | 4.97056i | 0.206391i | ||||||||
\(581\) | −8.89949 | − | 8.89949i | −0.369213 | − | 0.369213i | ||||
\(582\) | 0.828427 | + | 4.82843i | 0.0343394 | + | 0.200145i | ||||
\(583\) | 44.6274 | 1.84828 | ||||||||
\(584\) | −10.3431 | + | 10.3431i | −0.428002 | + | 0.428002i | ||||
\(585\) | −10.3431 | + | 3.65685i | −0.427636 | + | 0.151192i | ||||
\(586\) | 18.4853 | 0.763620 | ||||||||
\(587\) | 16.0711 | − | 16.0711i | 0.663324 | − | 0.663324i | −0.292838 | − | 0.956162i | \(-0.594600\pi\) |
0.956162 | + | 0.292838i | \(0.0945997\pi\) | |||||||
\(588\) | 2.82843 | + | 2.00000i | 0.116642 | + | 0.0824786i | ||||
\(589\) | 2.68629 | + | 2.68629i | 0.110687 | + | 0.110687i | ||||
\(590\) | 8.34315 | − | 8.34315i | 0.343482 | − | 0.343482i | ||||
\(591\) | 14.0711 | − | 2.41421i | 0.578806 | − | 0.0993075i | ||||
\(592\) | −7.31371 | + | 7.31371i | −0.300592 | + | 0.300592i | ||||
\(593\) | 1.85786i | 0.0762933i | 0.999272 | + | 0.0381467i | \(0.0121454\pi\) | ||||
−0.999272 | + | 0.0381467i | \(0.987855\pi\) | |||||||
\(594\) | 10.8284 | − | 38.2843i | 0.444296 | − | 1.57082i | ||||
\(595\) | 0.485281 | − | 0.485281i | 0.0198946 | − | 0.0198946i | ||||
\(596\) | 18.9706 | − | 18.9706i | 0.777065 | − | 0.777065i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 67.5980i | − | 2.76429i | ||||||
\(599\) | 42.9706i | 1.75573i | 0.478909 | + | 0.877865i | \(0.341033\pi\) | ||||
−0.478909 | + | 0.877865i | \(0.658967\pi\) | |||||||
\(600\) | 3.85786 | + | 22.4853i | 0.157497 | + | 0.917958i | ||||
\(601\) | − | 16.4853i | − | 0.672449i | −0.941782 | − | 0.336224i | \(-0.890850\pi\) | ||
0.941782 | − | 0.336224i | \(-0.109150\pi\) | |||||||
\(602\) | −7.65685 | −0.312070 | ||||||||
\(603\) | 26.7990 | + | 12.7990i | 1.09134 | + | 0.521215i | ||||
\(604\) | 35.3137i | 1.43689i | ||||||||
\(605\) | 7.58579 | − | 7.58579i | 0.308406 | − | 0.308406i | ||||
\(606\) | 20.1421 | − | 28.4853i | 0.818218 | − | 1.15714i | ||||
\(607\) | 21.1127i | 0.856938i | 0.903556 | + | 0.428469i | \(0.140947\pi\) | ||||
−0.903556 | + | 0.428469i | \(0.859053\pi\) | |||||||
\(608\) | − | 3.31371i | − | 0.134389i | ||||||
\(609\) | 1.24264 | + | 7.24264i | 0.0503543 | + | 0.293487i | ||||
\(610\) | −2.00000 | − | 2.00000i | −0.0809776 | − | 0.0809776i | ||||
\(611\) | 24.9706 | + | 24.9706i | 1.01020 | + | 1.01020i | ||||
\(612\) | −2.34315 | − | 6.62742i | −0.0947161 | − | 0.267897i | ||||
\(613\) | −14.1716 | + | 14.1716i | −0.572384 | + | 0.572384i | −0.932794 | − | 0.360410i | \(-0.882637\pi\) |
0.360410 | + | 0.932794i | \(0.382637\pi\) | |||||||
\(614\) | − | 29.7990i | − | 1.20259i | ||||||
\(615\) | 0.343146 | − | 0.0588745i | 0.0138370 | − | 0.00237405i | ||||
\(616\) | 15.3137 | 0.617007 | ||||||||
\(617\) | −26.0000 | −1.04672 | −0.523360 | − | 0.852111i | \(-0.675322\pi\) | ||||
−0.523360 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(618\) | −4.68629 | − | 27.3137i | −0.188510 | − | 1.09872i | ||||
\(619\) | 26.4142 | + | 26.4142i | 1.06168 | + | 1.06168i | 0.997969 | + | 0.0637083i | \(0.0202927\pi\) |
0.0637083 | + | 0.997969i | \(0.479707\pi\) | |||||||
\(620\) | 5.37258 | + | 5.37258i | 0.215768 | + | 0.215768i | ||||
\(621\) | 10.8284 | − | 38.2843i | 0.434530 | − | 1.53629i | ||||
\(622\) | −1.51472 | − | 1.51472i | −0.0607347 | − | 0.0607347i | ||||
\(623\) | 15.6569 | 0.627279 | ||||||||
\(624\) | −42.6274 | + | 7.31371i | −1.70646 | + | 0.292783i | ||||
\(625\) | −19.9706 | −0.798823 | ||||||||
\(626\) | −20.4853 | − | 20.4853i | −0.818757 | − | 0.818757i | ||||
\(627\) | −4.48528 | − | 3.17157i | −0.179125 | − | 0.126660i | ||||
\(628\) | 5.79899 | − | 5.79899i | 0.231405 | − | 0.231405i | ||||
\(629\) | 2.14214 | + | 2.14214i | 0.0854125 | + | 0.0854125i | ||||
\(630\) | −0.828427 | − | 2.34315i | −0.0330053 | − | 0.0933532i | ||||
\(631\) | −13.6569 | −0.543671 | −0.271835 | − | 0.962344i | \(-0.587631\pi\) | ||||
−0.271835 | + | 0.962344i | \(0.587631\pi\) | |||||||
\(632\) | −4.00000 | + | 4.00000i | −0.159111 | + | 0.159111i | ||||
\(633\) | 2.07107 | + | 12.0711i | 0.0823176 | + | 0.479782i | ||||
\(634\) | − | 26.2843i | − | 1.04388i | ||||||
\(635\) | 6.48528 | − | 6.48528i | 0.257361 | − | 0.257361i | ||||
\(636\) | −4.82843 | − | 28.1421i | −0.191460 | − | 1.11591i | ||||
\(637\) | −4.41421 | − | 4.41421i | −0.174898 | − | 0.174898i | ||||
\(638\) | 22.9706 | + | 22.9706i | 0.909413 | + | 0.909413i | ||||
\(639\) | −16.9706 | + | 6.00000i | −0.671345 | + | 0.237356i | ||||
\(640\) | − | 6.62742i | − | 0.261972i | ||||||
\(641\) | 45.2548i | 1.78746i | 0.448607 | + | 0.893729i | \(0.351920\pi\) | ||||
−0.448607 | + | 0.893729i | \(0.648080\pi\) | |||||||
\(642\) | 14.1421 | + | 10.0000i | 0.558146 | + | 0.394669i | ||||
\(643\) | −21.0416 | + | 21.0416i | −0.829801 | + | 0.829801i | −0.987489 | − | 0.157688i | \(-0.949596\pi\) |
0.157688 | + | 0.987489i | \(0.449596\pi\) | |||||||
\(644\) | 15.3137 | 0.603445 | ||||||||
\(645\) | 4.48528 | + | 3.17157i | 0.176608 | + | 0.124881i | ||||
\(646\) | −0.970563 | −0.0381863 | ||||||||
\(647\) | 16.1421i | 0.634613i | 0.948323 | + | 0.317306i | \(0.102778\pi\) | ||||
−0.948323 | + | 0.317306i | \(0.897222\pi\) | |||||||
\(648\) | −25.3137 | − | 2.68629i | −0.994416 | − | 0.105527i | ||||
\(649\) | − | 77.1127i | − | 3.02694i | ||||||
\(650\) | − | 41.1127i | − | 1.61257i | ||||||
\(651\) | 9.17157 | + | 6.48528i | 0.359462 | + | 0.254178i | ||||
\(652\) | 3.65685 | + | 3.65685i | 0.143213 | + | 0.143213i | ||||
\(653\) | 11.3431 | − | 11.3431i | 0.443892 | − | 0.443892i | −0.449426 | − | 0.893318i | \(-0.648371\pi\) |
0.893318 | + | 0.449426i | \(0.148371\pi\) | |||||||
\(654\) | 11.6569 | − | 16.4853i | 0.455819 | − | 0.644626i | ||||
\(655\) | − | 3.37258i | − | 0.131778i | ||||||
\(656\) | 1.37258 | 0.0535904 | ||||||||
\(657\) | 14.6274 | − | 5.17157i | 0.570670 | − | 0.201762i | ||||
\(658\) | −5.65685 | + | 5.65685i | −0.220527 | + | 0.220527i | ||||
\(659\) | 25.4853 | + | 25.4853i | 0.992766 | + | 0.992766i | 0.999974 | − | 0.00720841i | \(-0.00229453\pi\) |
−0.00720841 | + | 0.999974i | \(0.502295\pi\) | |||||||
\(660\) | −8.97056 | − | 6.34315i | −0.349179 | − | 0.246907i | ||||
\(661\) | 11.3848 | − | 11.3848i | 0.442816 | − | 0.442816i | −0.450141 | − | 0.892957i | \(-0.648626\pi\) |
0.892957 | + | 0.450141i | \(0.148626\pi\) | |||||||
\(662\) | −34.2843 | −1.33250 | ||||||||
\(663\) | 2.14214 | + | 12.4853i | 0.0831937 | + | 0.484888i | ||||
\(664\) | 35.5980i | 1.38147i | ||||||||
\(665\) | −0.343146 | −0.0133066 | ||||||||
\(666\) | 10.3431 | − | 3.65685i | 0.400789 | − | 0.141700i | ||||
\(667\) | 22.9706 | + | 22.9706i | 0.889424 | + | 0.889424i | ||||
\(668\) | 14.3431 | 0.554953 | ||||||||
\(669\) | 10.1421 | + | 7.17157i | 0.392118 | + | 0.277269i | ||||
\(670\) | 5.79899 | − | 5.79899i | 0.224035 | − | 0.224035i | ||||
\(671\) | −18.4853 | −0.713616 | ||||||||
\(672\) | −1.65685 | − | 9.65685i | −0.0639145 | − | 0.372521i | ||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | −25.3137 | + | 25.3137i | −0.975048 | + | 0.975048i | ||||
\(675\) | 6.58579 | − | 23.2843i | 0.253487 | − | 0.896212i | ||||
\(676\) | 51.9411 | 1.99774 | ||||||||
\(677\) | 20.8995 | + | 20.8995i | 0.803233 | + | 0.803233i | 0.983599 | − | 0.180367i | \(-0.0577284\pi\) |
−0.180367 | + | 0.983599i | \(0.557728\pi\) | |||||||
\(678\) | 4.00000 | − | 0.686292i | 0.153619 | − | 0.0263569i | ||||
\(679\) | 2.00000 | 0.0767530 | ||||||||
\(680\) | −1.94113 | −0.0744388 | ||||||||
\(681\) | 19.4853 | − | 3.34315i | 0.746678 | − | 0.128110i | ||||
\(682\) | 49.6569 | 1.90146 | ||||||||
\(683\) | −0.313708 | + | 0.313708i | −0.0120037 | + | 0.0120037i | −0.713083 | − | 0.701079i | \(-0.752702\pi\) |
0.701079 | + | 0.713083i | \(0.252702\pi\) | |||||||
\(684\) | −1.51472 | + | 3.17157i | −0.0579167 | + | 0.121268i | ||||
\(685\) | −3.17157 | − | 3.17157i | −0.121180 | − | 0.121180i | ||||
\(686\) | 1.00000 | − | 1.00000i | 0.0381802 | − | 0.0381802i | ||||
\(687\) | 4.51472 | + | 26.3137i | 0.172247 | + | 1.00393i | ||||
\(688\) | 15.3137 | + | 15.3137i | 0.583830 | + | 0.583830i | ||||
\(689\) | 51.4558i | 1.96031i | ||||||||
\(690\) | −8.97056 | − | 6.34315i | −0.341503 | − | 0.241479i | ||||
\(691\) | −14.8995 | + | 14.8995i | −0.566803 | + | 0.566803i | −0.931232 | − | 0.364428i | \(-0.881265\pi\) |
0.364428 | + | 0.931232i | \(0.381265\pi\) | |||||||
\(692\) | −9.79899 | − | 9.79899i | −0.372502 | − | 0.372502i | ||||
\(693\) | −14.6569 | − | 7.00000i | −0.556768 | − | 0.265908i | ||||
\(694\) | 26.2843i | 0.997737i | ||||||||
\(695\) | − | 3.65685i | − | 0.138712i | ||||||
\(696\) | 12.0000 | − | 16.9706i | 0.454859 | − | 0.643268i | ||||
\(697\) | − | 0.402020i | − | 0.0152276i | ||||||
\(698\) | 4.14214 | 0.156782 | ||||||||
\(699\) | 1.31371 | − | 1.85786i | 0.0496890 | − | 0.0702709i | ||||
\(700\) | 9.31371 | 0.352025 | ||||||||
\(701\) | −0.656854 | + | 0.656854i | −0.0248090 | + | 0.0248090i | −0.719402 | − | 0.694593i | \(-0.755584\pi\) |
0.694593 | + | 0.719402i | \(0.255584\pi\) | |||||||
\(702\) | 44.1421 | + | 12.4853i | 1.66604 | + | 0.471227i | ||||
\(703\) | − | 1.51472i | − | 0.0571287i | ||||||
\(704\) | −30.6274 | − | 30.6274i | −1.15431 | − | 1.15431i | ||||
\(705\) | 5.65685 | − | 0.970563i | 0.213049 | − | 0.0365535i | ||||
\(706\) | 8.48528 | + | 8.48528i | 0.319348 | + | 0.319348i | ||||
\(707\) | −10.0711 | − | 10.0711i | −0.378761 | − | 0.378761i | ||||
\(708\) | −48.6274 | + | 8.34315i | −1.82753 | + | 0.313555i | ||||
\(709\) | −2.17157 | + | 2.17157i | −0.0815551 | + | 0.0815551i | −0.746708 | − | 0.665152i | \(-0.768367\pi\) |
0.665152 | + | 0.746708i | \(0.268367\pi\) | |||||||
\(710\) | 4.97056i | 0.186542i | ||||||||
\(711\) | 5.65685 | − | 2.00000i | 0.212149 | − | 0.0750059i | ||||
\(712\) | −31.3137 | − | 31.3137i | −1.17353 | − | 1.17353i | ||||
\(713\) | 49.6569 | 1.85966 | ||||||||
\(714\) | −2.82843 | + | 0.485281i | −0.105851 | + | 0.0181612i | ||||
\(715\) | 14.0000 | + | 14.0000i | 0.523570 | + | 0.523570i | ||||
\(716\) | −30.0000 | + | 30.0000i | −1.12115 | + | 1.12115i | ||||
\(717\) | −11.3137 | + | 16.0000i | −0.422518 | + | 0.597531i | ||||
\(718\) | 20.3431 | + | 20.3431i | 0.759199 | + | 0.759199i | ||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | −3.02944 | + | 6.34315i | −0.112900 | + | 0.236395i | ||||
\(721\) | −11.3137 | −0.421345 | ||||||||
\(722\) | −18.6569 | − | 18.6569i | −0.694336 | − | 0.694336i | ||||
\(723\) | −0.343146 | + | 0.485281i | −0.0127617 | + | 0.0180478i | ||||
\(724\) | 4.14214 | + | 4.14214i | 0.153941 | + | 0.153941i | ||||
\(725\) | 13.9706 | + | 13.9706i | 0.518854 | + | 0.518854i | ||||
\(726\) | −44.2132 | + | 7.58579i | −1.64091 | + | 0.281535i | ||||
\(727\) | −35.3137 | −1.30971 | −0.654856 | − | 0.755753i | \(-0.727271\pi\) | ||||
−0.654856 | + | 0.755753i | \(0.727271\pi\) | |||||||
\(728\) | 17.6569i | 0.654407i | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | − | 4.28427i | − | 0.158568i | ||||||
\(731\) | 4.48528 | − | 4.48528i | 0.165894 | − | 0.165894i | ||||
\(732\) | 2.00000 | + | 11.6569i | 0.0739221 | + | 0.430850i | ||||
\(733\) | −2.27208 | − | 2.27208i | −0.0839211 | − | 0.0839211i | 0.663900 | − | 0.747821i | \(-0.268900\pi\) |
−0.747821 | + | 0.663900i | \(0.768900\pi\) | |||||||
\(734\) | 16.1421 | + | 16.1421i | 0.595817 | + | 0.595817i | ||||
\(735\) | −1.00000 | + | 0.171573i | −0.0368856 | + | 0.00632856i | ||||
\(736\) | −30.6274 | − | 30.6274i | −1.12894 | − | 1.12894i | ||||
\(737\) | − | 53.5980i | − | 1.97431i | ||||||
\(738\) | −1.31371 | − | 0.627417i | −0.0483583 | − | 0.0230955i | ||||
\(739\) | −21.8284 | + | 21.8284i | −0.802972 | + | 0.802972i | −0.983559 | − | 0.180587i | \(-0.942200\pi\) |
0.180587 | + | 0.983559i | \(0.442200\pi\) | |||||||
\(740\) | − | 3.02944i | − | 0.111364i | ||||||
\(741\) | 3.65685 | − | 5.17157i | 0.134338 | − | 0.189982i | ||||
\(742\) | −11.6569 | −0.427937 | ||||||||
\(743\) | − | 4.34315i | − | 0.159335i | −0.996822 | − | 0.0796673i | \(-0.974614\pi\) | ||
0.996822 | − | 0.0796673i | \(-0.0253858\pi\) | |||||||
\(744\) | −5.37258 | − | 31.3137i | −0.196968 | − | 1.14802i | ||||
\(745\) | 7.85786i | 0.287890i | ||||||||
\(746\) | − | 16.6274i | − | 0.608773i | ||||||
\(747\) | 16.2721 | − | 34.0711i | 0.595364 | − | 1.24660i | ||||
\(748\) | −8.97056 | + | 8.97056i | −0.327996 | + | 0.327996i | ||||
\(749\) | 5.00000 | − | 5.00000i | 0.182696 | − | 0.182696i | ||||
\(750\) | −11.3137 | − | 8.00000i | −0.413118 | − | 0.292119i | ||||
\(751\) | 18.6863i | 0.681872i | 0.940086 | + | 0.340936i | \(0.110744\pi\) | ||||
−0.940086 | + | 0.340936i | \(0.889256\pi\) | |||||||
\(752\) | 22.6274 | 0.825137 | ||||||||
\(753\) | 1.00000 | + | 5.82843i | 0.0364420 | + | 0.212400i | ||||
\(754\) | −26.4853 | + | 26.4853i | −0.964537 | + | 0.964537i | ||||
\(755\) | −7.31371 | − | 7.31371i | −0.266173 | − | 0.266173i | ||||
\(756\) | −2.82843 | + | 10.0000i | −0.102869 | + | 0.363696i | ||||
\(757\) | 14.5147 | − | 14.5147i | 0.527546 | − | 0.527546i | −0.392294 | − | 0.919840i | \(-0.628318\pi\) |
0.919840 | + | 0.392294i | \(0.128318\pi\) | |||||||
\(758\) | 54.2843 | 1.97169 | ||||||||
\(759\) | −70.7696 | + | 12.1421i | −2.56877 | + | 0.440732i | ||||
\(760\) | 0.686292 | + | 0.686292i | 0.0248944 | + | 0.0248944i | ||||
\(761\) | −36.6274 | −1.32774 | −0.663871 | − | 0.747847i | \(-0.731088\pi\) | ||||
−0.663871 | + | 0.747847i | \(0.731088\pi\) | |||||||
\(762\) | −37.7990 | + | 6.48528i | −1.36931 | + | 0.234937i | ||||
\(763\) | −5.82843 | − | 5.82843i | −0.211003 | − | 0.211003i | ||||
\(764\) | 12.6863i | 0.458974i | ||||||||
\(765\) | 1.85786 | + | 0.887302i | 0.0671712 | + | 0.0320805i | ||||
\(766\) | −19.3137 | + | 19.3137i | −0.697833 | + | 0.697833i | ||||
\(767\) | 88.9117 | 3.21041 | ||||||||
\(768\) | −16.0000 | + | 22.6274i | −0.577350 | + | 0.816497i | ||||
\(769\) | 24.3431 | 0.877836 | 0.438918 | − | 0.898527i | \(-0.355362\pi\) | ||||
0.438918 | + | 0.898527i | \(0.355362\pi\) | |||||||
\(770\) | −3.17157 | + | 3.17157i | −0.114296 | + | 0.114296i | ||||
\(771\) | −37.9411 | − | 26.8284i | −1.36642 | − | 0.966202i | ||||
\(772\) | − | 31.3137i | − | 1.12701i | ||||||
\(773\) | −36.5563 | − | 36.5563i | −1.31484 | − | 1.31484i | −0.917802 | − | 0.397039i | \(-0.870038\pi\) |
−0.397039 | − | 0.917802i | \(-0.629962\pi\) | |||||||
\(774\) | −7.65685 | − | 21.6569i | −0.275220 | − | 0.778440i | ||||
\(775\) | 30.2010 | 1.08485 | ||||||||
\(776\) | −4.00000 | − | 4.00000i | −0.143592 | − | 0.143592i | ||||
\(777\) | −0.757359 | − | 4.41421i | −0.0271701 | − | 0.158359i | ||||
\(778\) | 39.9411 | 1.43196 | ||||||||
\(779\) | −0.142136 | + | 0.142136i | −0.00509254 | + | 0.00509254i | ||||
\(780\) | 7.31371 | − | 10.3431i | 0.261873 | − | 0.370344i | ||||
\(781\) | 22.9706 | + | 22.9706i | 0.821951 | + | 0.821951i | ||||
\(782\) | −8.97056 | + | 8.97056i | −0.320787 | + | 0.320787i | ||||
\(783\) | −19.2426 | + | 10.7574i | −0.687676 | + | 0.384437i | ||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | 2.40202i | 0.0857318i | ||||||||
\(786\) | −8.14214 | + | 11.5147i | −0.290420 | + | 0.410716i | ||||
\(787\) | 23.0416 | − | 23.0416i | 0.821345 | − | 0.821345i | −0.164956 | − | 0.986301i | \(-0.552748\pi\) |
0.986301 | + | 0.164956i | \(0.0527481\pi\) | |||||||
\(788\) | −11.6569 | + | 11.6569i | −0.415258 | + | 0.415258i | ||||
\(789\) | 16.4853 | + | 11.6569i | 0.586892 | + | 0.414995i | ||||
\(790\) | − | 1.65685i | − | 0.0589482i | ||||||
\(791\) | − | 1.65685i | − | 0.0589110i | ||||||
\(792\) | 15.3137 | + | 43.3137i | 0.544149 | + | 1.53909i | ||||
\(793\) | − | 21.3137i | − | 0.756872i | ||||||
\(794\) | 47.4558 | 1.68414 | ||||||||
\(795\) | 6.82843 | + | 4.82843i | 0.242179 | + | 0.171247i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.4142 | + | 34.4142i | −1.21901 | + | 1.21901i | −0.251036 | + | 0.967978i | \(0.580771\pi\) |
−0.967978 | + | 0.251036i | \(0.919229\pi\) | |||||||
\(798\) | 1.17157 | + | 0.828427i | 0.0414732 | + | 0.0293260i | ||||
\(799\) | − | 6.62742i | − | 0.234461i | ||||||
\(800\) | −18.6274 | − | 18.6274i | −0.658579 | − | 0.658579i | ||||
\(801\) | 15.6569 | + | 44.2843i | 0.553208 | + | 1.56471i | ||||
\(802\) | 19.3137 | + | 19.3137i | 0.681991 | + | 0.681991i | ||||
\(803\) | −19.7990 | − | 19.7990i | −0.698691 | − | 0.698691i | ||||
\(804\) | −33.7990 | + | 5.79899i | −1.19200 | + | 0.204515i | ||||
\(805\) | −3.17157 | + | 3.17157i | −0.111783 | + | 0.111783i | ||||
\(806\) | 57.2548i | 2.01672i | ||||||||
\(807\) | 2.31371 | + | 13.4853i | 0.0814464 | + | 0.474704i | ||||
\(808\) | 40.2843i | 1.41720i | ||||||||
\(809\) | 22.6863 | 0.797608 | 0.398804 | − | 0.917036i | \(-0.369425\pi\) | ||||
0.398804 | + | 0.917036i | \(0.369425\pi\) | |||||||
\(810\) | 5.79899 | − | 4.68629i | 0.203756 | − | 0.164659i | ||||
\(811\) | 16.0711 | + | 16.0711i | 0.564332 | + | 0.564332i | 0.930535 | − | 0.366203i | \(-0.119343\pi\) |
−0.366203 | + | 0.930535i | \(0.619343\pi\) | |||||||
\(812\) | −6.00000 | − | 6.00000i | −0.210559 | − | 0.210559i | ||||
\(813\) | −23.7990 | − | 16.8284i | −0.834667 | − | 0.590199i | ||||
\(814\) | −14.0000 | − | 14.0000i | −0.490700 | − | 0.490700i | ||||
\(815\) | −1.51472 | −0.0530583 | ||||||||
\(816\) | 6.62742 | + | 4.68629i | 0.232006 | + | 0.164053i | ||||
\(817\) | −3.17157 | −0.110959 | ||||||||
\(818\) | 25.1716 | + | 25.1716i | 0.880103 | + | 0.880103i | ||||
\(819\) | 8.07107 | − | 16.8995i | 0.282026 | − | 0.590516i | ||||
\(820\) | −0.284271 | + | 0.284271i | −0.00992718 | + | 0.00992718i | ||||
\(821\) | −15.4853 | − | 15.4853i | −0.540440 | − | 0.540440i | 0.383218 | − | 0.923658i | \(-0.374816\pi\) |
−0.923658 | + | 0.383218i | \(0.874816\pi\) | |||||||
\(822\) | 3.17157 | + | 18.4853i | 0.110621 | + | 0.644748i | ||||
\(823\) | 24.9706 | 0.870419 | 0.435210 | − | 0.900329i | \(-0.356674\pi\) | ||||
0.435210 | + | 0.900329i | \(0.356674\pi\) | |||||||
\(824\) | 22.6274 | + | 22.6274i | 0.788263 | + | 0.788263i | ||||
\(825\) | −43.0416 | + | 7.38478i | −1.49852 | + | 0.257105i | ||||
\(826\) | 20.1421i | 0.700835i | ||||||||
\(827\) | −9.00000 | + | 9.00000i | −0.312961 | + | 0.312961i | −0.846055 | − | 0.533095i | \(-0.821029\pi\) |
0.533095 | + | 0.846055i | \(0.321029\pi\) | |||||||
\(828\) | 15.3137 | + | 43.3137i | 0.532188 | + | 1.50526i | ||||
\(829\) | −24.8995 | − | 24.8995i | −0.864795 | − | 0.864795i | 0.127095 | − | 0.991891i | \(-0.459435\pi\) |
−0.991891 | + | 0.127095i | \(0.959435\pi\) | |||||||
\(830\) | −7.37258 | − | 7.37258i | −0.255906 | − | 0.255906i | ||||
\(831\) | 2.61522 | + | 15.2426i | 0.0907211 | + | 0.528761i | ||||
\(832\) | 35.3137 | − | 35.3137i | 1.22428 | − | 1.22428i | ||||
\(833\) | 1.17157i | 0.0405926i | ||||||||
\(834\) | −8.82843 | + | 12.4853i | −0.305703 | + | 0.432330i | ||||
\(835\) | −2.97056 | + | 2.97056i | −0.102801 | + | 0.102801i | ||||
\(836\) | 6.34315 | 0.219382 | ||||||||
\(837\) | −9.17157 | + | 32.4264i | −0.317016 | + | 1.12082i | ||||
\(838\) | 26.4853 | 0.914919 | ||||||||
\(839\) | 51.4558i | 1.77645i | 0.459406 | + | 0.888227i | \(0.348062\pi\) | ||||
−0.459406 | + | 0.888227i | \(0.651938\pi\) | |||||||
\(840\) | 2.34315 | + | 1.65685i | 0.0808462 | + | 0.0571669i | ||||
\(841\) | 11.0000i | 0.379310i | ||||||||
\(842\) | − | 3.37258i | − | 0.116227i | ||||||
\(843\) | −6.68629 | + | 9.45584i | −0.230288 | + | 0.325677i | ||||
\(844\) | −10.0000 | − | 10.0000i | −0.344214 | − | 0.344214i | ||||
\(845\) | −10.7574 | + | 10.7574i | −0.370064 | + | 0.370064i | ||||
\(846\) | −21.6569 | − | 10.3431i | −0.744578 | − | 0.355605i | ||||
\(847\) | 18.3137i | 0.629266i | ||||||||
\(848\) | 23.3137 | + | 23.3137i | 0.800596 | + | 0.800596i | ||||
\(849\) | 31.1421 | − | 5.34315i | 1.06880 | − | 0.183376i | ||||
\(850\) | −5.45584 | + | 5.45584i | −0.187134 | + | 0.187134i | ||||
\(851\) | −14.0000 | − | 14.0000i | −0.479914 | − | 0.479914i | ||||
\(852\) | 12.0000 | − | 16.9706i | 0.411113 | − | 0.581402i | ||||
\(853\) | −28.4142 | + | 28.4142i | −0.972884 | + | 0.972884i | −0.999642 | − | 0.0267578i | \(-0.991482\pi\) |
0.0267578 | + | 0.999642i | \(0.491482\pi\) | |||||||
\(854\) | 4.82843 | 0.165225 | ||||||||
\(855\) | −0.343146 | − | 0.970563i | −0.0117353 | − | 0.0331925i | ||||
\(856\) | −20.0000 | −0.683586 | ||||||||
\(857\) | −31.9411 | −1.09109 | −0.545544 | − | 0.838082i | \(-0.683677\pi\) | ||||
−0.545544 | + | 0.838082i | \(0.683677\pi\) | |||||||
\(858\) | −14.0000 | − | 81.5980i | −0.477952 | − | 2.78571i | ||||
\(859\) | 22.8995 | + | 22.8995i | 0.781321 | + | 0.781321i | 0.980054 | − | 0.198733i | \(-0.0636827\pi\) |
−0.198733 | + | 0.980054i | \(0.563683\pi\) | |||||||
\(860\) | −6.34315 | −0.216299 | ||||||||
\(861\) | −0.343146 | + | 0.485281i | −0.0116944 | + | 0.0165383i | ||||
\(862\) | 3.31371 | − | 3.31371i | 0.112865 | − | 0.112865i | ||||
\(863\) | −39.3137 | −1.33825 | −0.669127 | − | 0.743148i | \(-0.733332\pi\) | ||||
−0.669127 | + | 0.743148i | \(0.733332\pi\) | |||||||
\(864\) | 25.6569 | − | 14.3431i | 0.872864 | − | 0.487964i | ||||
\(865\) | 4.05887 | 0.138006 | ||||||||
\(866\) | 14.6863 | − | 14.6863i | 0.499061 | − | 0.499061i | ||||
\(867\) | −15.6274 | + | 22.1005i | −0.530735 | + | 0.750573i | ||||
\(868\) | −12.9706 | −0.440250 | ||||||||
\(869\) | −7.65685 | − | 7.65685i | −0.259741 | − | 0.259741i | ||||
\(870\) | 1.02944 | + | 6.00000i | 0.0349012 | + | 0.203419i | ||||
\(871\) | 61.7990 | 2.09398 | ||||||||
\(872\) | 23.3137i | 0.789502i | ||||||||
\(873\) | 2.00000 | + | 5.65685i | 0.0676897 | + | 0.191456i | ||||
\(874\) | 6.34315 | 0.214560 | ||||||||
\(875\) | −4.00000 | + | 4.00000i | −0.135225 | + | 0.135225i | ||||
\(876\) | −10.3431 | + | 14.6274i | −0.349463 | + | 0.494215i | ||||
\(877\) | 6.51472 | + | 6.51472i | 0.219986 | + | 0.219986i | 0.808493 | − | 0.588506i | \(-0.200284\pi\) |
−0.588506 | + | 0.808493i | \(0.700284\pi\) | |||||||
\(878\) | 0.970563 | − | 0.970563i | 0.0327549 | − | 0.0327549i | ||||
\(879\) | 22.3137 | − | 3.82843i | 0.752623 | − | 0.129130i | ||||
\(880\) | 12.6863 | 0.427655 | ||||||||
\(881\) | − | 48.4853i | − | 1.63351i | −0.576984 | − | 0.816755i | \(-0.695771\pi\) | ||
0.576984 | − | 0.816755i | \(-0.304229\pi\) | |||||||
\(882\) | 3.82843 | + | 1.82843i | 0.128910 | + | 0.0615663i | ||||
\(883\) | 38.9411 | − | 38.9411i | 1.31047 | − | 1.31047i | 0.389408 | − | 0.921065i | \(-0.372680\pi\) |
0.921065 | − | 0.389408i | \(-0.127320\pi\) | |||||||
\(884\) | −10.3431 | − | 10.3431i | −0.347878 | − | 0.347878i | ||||
\(885\) | 8.34315 | − | 11.7990i | 0.280452 | − | 0.396619i | ||||
\(886\) | 33.3137i | 1.11920i | ||||||||
\(887\) | 39.1716i | 1.31525i | 0.753344 | + | 0.657626i | \(0.228439\pi\) | ||||
−0.753344 | + | 0.657626i | \(0.771561\pi\) | |||||||
\(888\) | −7.31371 | + | 10.3431i | −0.245432 | + | 0.347093i | ||||
\(889\) | 15.6569i | 0.525114i | ||||||||
\(890\) | 12.9706 | 0.434774 | ||||||||
\(891\) | 5.14214 | − | 48.4558i | 0.172268 | − | 1.62333i | ||||
\(892\) | −14.3431 | −0.480244 | ||||||||
\(893\) | −2.34315 | + | 2.34315i | −0.0784104 | + | 0.0784104i | ||||
\(894\) | 18.9706 | − | 26.8284i | 0.634471 | − | 0.897277i | ||||
\(895\) | − | 12.4264i | − | 0.415369i | ||||||
\(896\) | 8.00000 | + | 8.00000i | 0.267261 | + | 0.267261i | ||||
\(897\) | −14.0000 | − | 81.5980i | −0.467446 | − | 2.72448i | ||||
\(898\) | −12.9706 | − | 12.9706i | −0.432833 | − | 0.432833i | ||||
\(899\) | −19.4558 | − | 19.4558i | −0.648889 | − | 0.648889i | ||||
\(900\) | 9.31371 | + | 26.3431i | 0.310457 | + | 0.878105i | ||||
\(901\) | 6.82843 | − | 6.82843i | 0.227488 | − | 0.227488i | ||||
\(902\) | 2.62742i | 0.0874834i | ||||||||
\(903\) | −9.24264 | + | 1.58579i | −0.307576 | + | 0.0527717i | ||||
\(904\) | −3.31371 | + | 3.31371i | −0.110212 | + | 0.110212i | ||||
\(905\) | −1.71573 | −0.0570328 | ||||||||
\(906\) | 7.31371 | + | 42.6274i | 0.242982 | + | 1.41620i | ||||
\(907\) | −20.3137 | − | 20.3137i | −0.674506 | − | 0.674506i | 0.284246 | − | 0.958751i | \(-0.408257\pi\) |
−0.958751 | + | 0.284246i | \(0.908257\pi\) | |||||||
\(908\) | −16.1421 | + | 16.1421i | −0.535696 | + | 0.535696i | ||||
\(909\) | 18.4142 | − | 38.5563i | 0.610761 | − | 1.27883i | ||||
\(910\) | −3.65685 | − | 3.65685i | −0.121224 | − | 0.121224i | ||||
\(911\) | −44.2843 | −1.46720 | −0.733602 | − | 0.679580i | \(-0.762162\pi\) | ||||
−0.733602 | + | 0.679580i | \(0.762162\pi\) | |||||||
\(912\) | −0.686292 | − | 4.00000i | −0.0227254 | − | 0.132453i | ||||
\(913\) | −68.1421 | −2.25518 | ||||||||
\(914\) | −29.9411 | − | 29.9411i | −0.990364 | − | 0.990364i | ||||
\(915\) | −2.82843 | − | 2.00000i | −0.0935049 | − | 0.0661180i | ||||
\(916\) | −21.7990 | − | 21.7990i | −0.720259 | − | 0.720259i | ||||
\(917\) | 4.07107 | + | 4.07107i | 0.134439 | + | 0.134439i | ||||
\(918\) | −4.20101 | − | 7.51472i | −0.138654 | − | 0.248023i | ||||
\(919\) | −2.34315 | −0.0772932 | −0.0386466 | − | 0.999253i | \(-0.512305\pi\) | ||||
−0.0386466 | + | 0.999253i | \(0.512305\pi\) | |||||||
\(920\) | 12.6863 | 0.418255 | ||||||||
\(921\) | −6.17157 | − | 35.9706i | −0.203360 | − | 1.18527i | ||||
\(922\) | − | 44.8284i | − | 1.47635i | ||||||
\(923\) | −26.4853 | + | 26.4853i | −0.871774 | + | 0.871774i | ||||
\(924\) | 18.4853 | − | 3.17157i | 0.608121 | − | 0.104337i | ||||
\(925\) | −8.51472 | − | 8.51472i | −0.279962 | − | 0.279962i | ||||
\(926\) | 11.6569 | + | 11.6569i | 0.383068 | + | 0.383068i | ||||
\(927\) | −11.3137 | − | 32.0000i | −0.371591 | − | 1.05102i | ||||
\(928\) | 24.0000i | 0.787839i | ||||||||
\(929\) | 19.1127i | 0.627067i | 0.949577 | + | 0.313534i | \(0.101513\pi\) | ||||
−0.949577 | + | 0.313534i | \(0.898487\pi\) | |||||||
\(930\) | 7.59798 | + | 5.37258i | 0.249148 | + | 0.176174i | ||||
\(931\) | 0.414214 | − | 0.414214i | 0.0135753 | − | 0.0135753i | ||||
\(932\) | 2.62742i | 0.0860639i | ||||||||
\(933\) | −2.14214 | − | 1.51472i | −0.0701304 | − | 0.0495897i | ||||
\(934\) | 28.8284 | 0.943295 | ||||||||
\(935\) | − | 3.71573i | − | 0.121517i | ||||||
\(936\) | −49.9411 | + | 17.6569i | −1.63238 | + | 0.577132i | ||||
\(937\) | 1.85786i | 0.0606938i | 0.999539 | + | 0.0303469i | \(0.00966120\pi\) | ||||
−0.999539 | + | 0.0303469i | \(0.990339\pi\) | |||||||
\(938\) | 14.0000i | 0.457116i | ||||||||
\(939\) | −28.9706 | − | 20.4853i | −0.945419 | − | 0.668512i | ||||
\(940\) | −4.68629 | + | 4.68629i | −0.152850 | + | 0.152850i | ||||
\(941\) | 42.3553 | − | 42.3553i | 1.38074 | − | 1.38074i | 0.537447 | − | 0.843297i | \(-0.319389\pi\) |
0.843297 | − | 0.537447i | \(-0.180611\pi\) | |||||||
\(942\) | 5.79899 | − | 8.20101i | 0.188941 | − | 0.267203i | ||||
\(943\) | 2.62742i | 0.0855605i | ||||||||
\(944\) | 40.2843 | − | 40.2843i | 1.31114 | − | 1.31114i | ||||
\(945\) | −1.48528 | − | 2.65685i | −0.0483162 | − | 0.0864275i | ||||
\(946\) | −29.3137 | + | 29.3137i | −0.953071 | + | 0.953071i | ||||
\(947\) | 19.1421 | + | 19.1421i | 0.622036 | + | 0.622036i | 0.946052 | − | 0.324016i | \(-0.105033\pi\) |
−0.324016 | + | 0.946052i | \(0.605033\pi\) | |||||||
\(948\) | −4.00000 | + | 5.65685i | −0.129914 | + | 0.183726i | ||||
\(949\) | 22.8284 | − | 22.8284i | 0.741042 | − | 0.741042i | ||||
\(950\) | 3.85786 | 0.125166 | ||||||||
\(951\) | −5.44365 | − | 31.7279i | −0.176522 | − | 1.02885i | ||||
\(952\) | 2.34315 | − | 2.34315i | 0.0759418 | − | 0.0759418i | ||||
\(953\) | −20.3431 | −0.658979 | −0.329490 | − | 0.944159i | \(-0.606877\pi\) | ||||
−0.329490 | + | 0.944159i | \(0.606877\pi\) | |||||||
\(954\) | −11.6569 | − | 32.9706i | −0.377405 | − | 1.06746i | ||||
\(955\) | −2.62742 | − | 2.62742i | −0.0850212 | − | 0.0850212i | ||||
\(956\) | − | 22.6274i | − | 0.731823i | ||||||
\(957\) | 32.4853 | + | 22.9706i | 1.05010 | + | 0.742533i | ||||
\(958\) | −27.3137 | + | 27.3137i | −0.882466 | + | 0.882466i | ||||
\(959\) | 7.65685 | 0.247253 | ||||||||
\(960\) | −1.37258 | − | 8.00000i | −0.0442999 | − | 0.258199i | ||||
\(961\) | −11.0589 | −0.356738 | ||||||||
\(962\) | 16.1421 | − | 16.1421i | 0.520443 | − | 0.520443i | ||||
\(963\) | 19.1421 | + | 9.14214i | 0.616847 | + | 0.294601i | ||||
\(964\) | − | 0.686292i | − | 0.0221040i | ||||||
\(965\) | 6.48528 | + | 6.48528i | 0.208769 | + | 0.208769i | ||||
\(966\) | 18.4853 | − | 3.17157i | 0.594754 | − | 0.102044i | ||||
\(967\) | −23.3137 | −0.749718 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(968\) | 36.6274 | − | 36.6274i | 1.17725 | − | 1.17725i | ||||
\(969\) | −1.17157 | + | 0.201010i | −0.0376363 | + | 0.00645738i | ||||
\(970\) | 1.65685 | 0.0531984 | ||||||||
\(971\) | 2.89949 | − | 2.89949i | 0.0930492 | − | 0.0930492i | −0.659050 | − | 0.752099i | \(-0.729041\pi\) |
0.752099 | + | 0.659050i | \(0.229041\pi\) | |||||||
\(972\) | −31.1127 | + | 2.00000i | −0.997940 | + | 0.0641500i | ||||
\(973\) | 4.41421 | + | 4.41421i | 0.141513 | + | 0.141513i | ||||
\(974\) | 16.2843 | − | 16.2843i | 0.521782 | − | 0.521782i | ||||
\(975\) | −8.51472 | − | 49.6274i | −0.272689 | − | 1.58935i | ||||
\(976\) | −9.65685 | − | 9.65685i | −0.309108 | − | 0.309108i | ||||
\(977\) | 8.68629i | 0.277899i | 0.990299 | + | 0.138950i | \(0.0443726\pi\) | ||||
−0.990299 | + | 0.138950i | \(0.955627\pi\) | |||||||
\(978\) | 5.17157 | + | 3.65685i | 0.165369 | + | 0.116933i | ||||
\(979\) | 59.9411 | − | 59.9411i | 1.91573 | − | 1.91573i | ||||
\(980\) | 0.828427 | − | 0.828427i | 0.0264631 | − | 0.0264631i | ||||
\(981\) | 10.6569 | − | 22.3137i | 0.340247 | − | 0.712422i | ||||
\(982\) | 20.6274i | 0.658247i | ||||||||
\(983\) | − | 37.5147i | − | 1.19653i | −0.801297 | − | 0.598267i | \(-0.795856\pi\) | ||
0.801297 | − | 0.598267i | \(-0.204144\pi\) | |||||||
\(984\) | 1.65685 | − | 0.284271i | 0.0528186 | − | 0.00906224i | ||||
\(985\) | − | 4.82843i | − | 0.153846i | ||||||
\(986\) | 7.02944 | 0.223863 | ||||||||
\(987\) | −5.65685 | + | 8.00000i | −0.180060 | + | 0.254643i | ||||
\(988\) | 7.31371i | 0.232680i | ||||||||
\(989\) | −29.3137 | + | 29.3137i | −0.932122 | + | 0.932122i | ||||
\(990\) | −12.1421 | − | 5.79899i | −0.385902 | − | 0.184304i | ||||
\(991\) | 22.6863i | 0.720654i | 0.932826 | + | 0.360327i | \(0.117335\pi\) | ||||
−0.932826 | + | 0.360327i | \(0.882665\pi\) | |||||||
\(992\) | 25.9411 | + | 25.9411i | 0.823632 | + | 0.823632i | ||||
\(993\) | −41.3848 | + | 7.10051i | −1.31331 | + | 0.225328i | ||||
\(994\) | −6.00000 | − | 6.00000i | −0.190308 | − | 0.190308i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.37258 | + | 42.9706i | 0.233609 | + | 1.36157i | ||||
\(997\) | −19.9289 | + | 19.9289i | −0.631156 | + | 0.631156i | −0.948358 | − | 0.317202i | \(-0.897257\pi\) |
0.317202 | + | 0.948358i | \(0.397257\pi\) | |||||||
\(998\) | 11.3726i | 0.359993i | ||||||||
\(999\) | 11.7279 | − | 6.55635i | 0.371055 | − | 0.207434i |
(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 | 336.2.s.a.323.2 | yes | 4 | |
3.2 | odd | 2 | 336.2.s.b.323.1 | yes | 4 | ||
4.3 | odd | 2 | 1344.2.s.b.239.1 | 4 | |||
12.11 | even | 2 | 1344.2.s.a.239.2 | 4 | |||
16.5 | even | 4 | 1344.2.s.a.911.2 | 4 | |||
16.11 | odd | 4 | 336.2.s.b.155.1 | yes | 4 | ||
48.5 | odd | 4 | 1344.2.s.b.911.2 | 4 | |||
48.11 | even | 4 | inner | 336.2.s.a.155.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.a.155.1 | ✓ | 4 | 48.11 | even | 4 | inner | |
336.2.s.a.323.2 | yes | 4 | 1.1 | even | 1 | trivial | |
336.2.s.b.155.1 | yes | 4 | 16.11 | odd | 4 | ||
336.2.s.b.323.1 | yes | 4 | 3.2 | odd | 2 | ||
1344.2.s.a.239.2 | 4 | 12.11 | even | 2 | |||
1344.2.s.a.911.2 | 4 | 16.5 | even | 4 | |||
1344.2.s.b.239.1 | 4 | 4.3 | odd | 2 | |||
1344.2.s.b.911.2 | 4 | 48.5 | odd | 4 |