Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,4,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (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: | \(26.5508595026\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.143 |
Dual form | 450.4.f.a.107.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | − | 1.41421i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.00000 | + | 9.00000i | −0.485954 | + | 0.485954i | −0.907027 | − | 0.421073i | \(-0.861654\pi\) |
0.421073 | + | 0.907027i | \(0.361654\pi\) | |||||||
\(8\) | 5.65685 | − | 5.65685i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 38.1838i | − | 1.04662i | −0.852142 | − | 0.523311i | \(-0.824697\pi\) | ||
0.852142 | − | 0.523311i | \(-0.175303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.00000 | + | 9.00000i | 0.192012 | + | 0.192012i | 0.796565 | − | 0.604553i | \(-0.206648\pi\) |
−0.604553 | + | 0.796565i | \(0.706648\pi\) | |||||||
\(14\) | 25.4558 | 0.485954 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | 55.1543 | + | 55.1543i | 0.786876 | + | 0.786876i | 0.980981 | − | 0.194105i | \(-0.0621802\pi\) |
−0.194105 | + | 0.980981i | \(0.562180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 38.0000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −54.0000 | + | 54.0000i | −0.523311 | + | 0.523311i | ||||
\(23\) | −29.6985 | + | 29.6985i | −0.269242 | + | 0.269242i | −0.828795 | − | 0.559553i | \(-0.810973\pi\) |
0.559553 | + | 0.828795i | \(0.310973\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 25.4558i | − | 0.192012i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −36.0000 | − | 36.0000i | −0.242977 | − | 0.242977i | ||||
\(29\) | 76.3675 | 0.489003 | 0.244502 | − | 0.969649i | \(-0.421376\pi\) | ||||
0.244502 | + | 0.969649i | \(0.421376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −236.000 | −1.36732 | −0.683659 | − | 0.729802i | \(-0.739612\pi\) | ||||
−0.683659 | + | 0.729802i | \(0.739612\pi\) | |||||||
\(32\) | 22.6274 | + | 22.6274i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 156.000i | − | 0.786876i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −279.000 | + | 279.000i | −1.23966 | + | 1.23966i | −0.279516 | + | 0.960141i | \(0.590174\pi\) |
−0.960141 | + | 0.279516i | \(0.909826\pi\) | |||||||
\(38\) | −53.7401 | + | 53.7401i | −0.229416 | + | 0.229416i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 343.654i | − | 1.30902i | −0.756054 | − | 0.654509i | \(-0.772875\pi\) | ||
0.756054 | − | 0.654509i | \(-0.227125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −360.000 | − | 360.000i | −1.27673 | − | 1.27673i | −0.942486 | − | 0.334247i | \(-0.891518\pi\) |
−0.334247 | − | 0.942486i | \(-0.608482\pi\) | |||||||
\(44\) | 152.735 | 0.523311 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 84.0000 | 0.269242 | ||||||||
\(47\) | 254.558 | + | 254.558i | 0.790025 | + | 0.790025i | 0.981498 | − | 0.191473i | \(-0.0613265\pi\) |
−0.191473 | + | 0.981498i | \(0.561326\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 181.000i | 0.527697i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −36.0000 | + | 36.0000i | −0.0960058 | + | 0.0960058i | ||||
\(53\) | −352.139 | + | 352.139i | −0.912642 | + | 0.912642i | −0.996479 | − | 0.0838373i | \(-0.973282\pi\) |
0.0838373 | + | 0.996479i | \(0.473282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 101.823i | 0.242977i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −108.000 | − | 108.000i | −0.244502 | − | 0.244502i | ||||
\(59\) | −343.654 | −0.758304 | −0.379152 | − | 0.925334i | \(-0.623784\pi\) | ||||
−0.379152 | + | 0.925334i | \(0.623784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 110.000 | 0.230886 | 0.115443 | − | 0.993314i | \(-0.463171\pi\) | ||||
0.115443 | + | 0.993314i | \(0.463171\pi\) | |||||||
\(62\) | 333.754 | + | 333.754i | 0.683659 | + | 0.683659i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 64.0000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −702.000 | + | 702.000i | −1.28004 | + | 1.28004i | −0.339403 | + | 0.940641i | \(0.610225\pi\) |
−0.940641 | + | 0.339403i | \(0.889775\pi\) | |||||||
\(68\) | −220.617 | + | 220.617i | −0.393438 | + | 0.393438i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 76.3675i | − | 0.127650i | −0.997961 | − | 0.0638251i | \(-0.979670\pi\) | ||
0.997961 | − | 0.0638251i | \(-0.0203300\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −378.000 | − | 378.000i | −0.606049 | − | 0.606049i | 0.335862 | − | 0.941911i | \(-0.390972\pi\) |
−0.941911 | + | 0.335862i | \(0.890972\pi\) | |||||||
\(74\) | 789.131 | 1.23966 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 152.000 | 0.229416 | ||||||||
\(77\) | 343.654 | + | 343.654i | 0.508610 | + | 0.508610i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 272.000i | 0.387372i | 0.981064 | + | 0.193686i | \(0.0620443\pi\) | ||||
−0.981064 | + | 0.193686i | \(0.937956\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −486.000 | + | 486.000i | −0.654509 | + | 0.654509i | ||||
\(83\) | 59.3970 | − | 59.3970i | 0.0785502 | − | 0.0785502i | −0.666740 | − | 0.745290i | \(-0.732311\pi\) |
0.745290 | + | 0.666740i | \(0.232311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1018.23i | 1.27673i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −216.000 | − | 216.000i | −0.261655 | − | 0.261655i | ||||
\(89\) | −1489.17 | −1.77361 | −0.886805 | − | 0.462143i | \(-0.847081\pi\) | ||||
−0.886805 | + | 0.462143i | \(0.847081\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −162.000 | −0.186618 | ||||||||
\(92\) | −118.794 | − | 118.794i | −0.134621 | − | 0.134621i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 720.000i | − | 0.790025i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −684.000 | + | 684.000i | −0.715976 | + | 0.715976i | −0.967779 | − | 0.251803i | \(-0.918977\pi\) |
0.251803 | + | 0.967779i | \(0.418977\pi\) | |||||||
\(98\) | 255.973 | − | 255.973i | 0.263848 | − | 0.263848i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 840.043i | 0.827598i | 0.910368 | + | 0.413799i | \(0.135798\pi\) | ||||
−0.910368 | + | 0.413799i | \(0.864202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 81.0000 | + | 81.0000i | 0.0774871 | + | 0.0774871i | 0.744788 | − | 0.667301i | \(-0.232551\pi\) |
−0.667301 | + | 0.744788i | \(0.732551\pi\) | |||||||
\(104\) | 101.823 | 0.0960058 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 996.000 | 0.912642 | ||||||||
\(107\) | 1018.23 | + | 1018.23i | 0.919966 | + | 0.919966i | 0.997026 | − | 0.0770603i | \(-0.0245534\pi\) |
−0.0770603 | + | 0.997026i | \(0.524553\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1658.00i | 1.45695i | 0.685072 | + | 0.728475i | \(0.259771\pi\) | ||||
−0.685072 | + | 0.728475i | \(0.740229\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 144.000 | − | 144.000i | 0.121489 | − | 0.121489i | ||||
\(113\) | −470.933 | + | 470.933i | −0.392050 | + | 0.392050i | −0.875418 | − | 0.483367i | \(-0.839414\pi\) |
0.483367 | + | 0.875418i | \(0.339414\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 305.470i | 0.244502i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 486.000 | + | 486.000i | 0.379152 | + | 0.379152i | ||||
\(119\) | −992.778 | −0.764771 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −127.000 | −0.0954170 | ||||||||
\(122\) | −155.563 | − | 155.563i | −0.115443 | − | 0.115443i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 944.000i | − | 0.683659i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 747.000 | − | 747.000i | 0.521933 | − | 0.521933i | −0.396222 | − | 0.918155i | \(-0.629679\pi\) |
0.918155 | + | 0.396222i | \(0.129679\pi\) | |||||||
\(128\) | −90.5097 | + | 90.5097i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1718.27i | − | 1.14600i | −0.819556 | − | 0.573000i | \(-0.805780\pi\) | ||
0.819556 | − | 0.573000i | \(-0.194220\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 342.000 | + | 342.000i | 0.222971 | + | 0.222971i | ||||
\(134\) | 1985.56 | 1.28004 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 624.000 | 0.393438 | ||||||||
\(137\) | −963.079 | − | 963.079i | −0.600594 | − | 0.600594i | 0.339876 | − | 0.940470i | \(-0.389615\pi\) |
−0.940470 | + | 0.339876i | \(0.889615\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1636.00i | 0.998300i | 0.866516 | + | 0.499150i | \(0.166354\pi\) | ||||
−0.866516 | + | 0.499150i | \(0.833646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −108.000 | + | 108.000i | −0.0638251 | + | 0.0638251i | ||||
\(143\) | 343.654 | − | 343.654i | 0.200964 | − | 0.200964i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1069.15i | 0.606049i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1116.00 | − | 1116.00i | −0.619829 | − | 0.619829i | ||||
\(149\) | −1527.35 | −0.839768 | −0.419884 | − | 0.907578i | \(-0.637929\pi\) | ||||
−0.419884 | + | 0.907578i | \(0.637929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −128.000 | −0.0689834 | −0.0344917 | − | 0.999405i | \(-0.510981\pi\) | ||||
−0.0344917 | + | 0.999405i | \(0.510981\pi\) | |||||||
\(152\) | −214.960 | − | 214.960i | −0.114708 | − | 0.114708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 972.000i | − | 0.508610i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1683.00 | − | 1683.00i | 0.855529 | − | 0.855529i | −0.135279 | − | 0.990808i | \(-0.543193\pi\) |
0.990808 | + | 0.135279i | \(0.0431930\pi\) | |||||||
\(158\) | 384.666 | − | 384.666i | 0.193686 | − | 0.193686i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 534.573i | − | 0.261678i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 198.000 | + | 198.000i | 0.0951445 | + | 0.0951445i | 0.753077 | − | 0.657932i | \(-0.228569\pi\) |
−0.657932 | + | 0.753077i | \(0.728569\pi\) | |||||||
\(164\) | 1374.62 | 0.654509 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −168.000 | −0.0785502 | ||||||||
\(167\) | −2982.58 | − | 2982.58i | −1.38203 | − | 1.38203i | −0.841013 | − | 0.541015i | \(-0.818040\pi\) |
−0.541015 | − | 0.841013i | \(-0.681960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2035.00i | − | 0.926263i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1440.00 | − | 1440.00i | 0.638366 | − | 0.638366i | ||||
\(173\) | 1684.33 | − | 1684.33i | 0.740215 | − | 0.740215i | −0.232405 | − | 0.972619i | \(-0.574659\pi\) |
0.972619 | + | 0.232405i | \(0.0746594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 610.940i | 0.261655i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2106.00 | + | 2106.00i | 0.886805 | + | 0.886805i | ||||
\(179\) | 343.654 | 0.143497 | 0.0717483 | − | 0.997423i | \(-0.477142\pi\) | ||||
0.0717483 | + | 0.997423i | \(0.477142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2522.00 | −1.03568 | −0.517842 | − | 0.855476i | \(-0.673264\pi\) | ||||
−0.517842 | + | 0.855476i | \(0.673264\pi\) | |||||||
\(182\) | 229.103 | + | 229.103i | 0.0933089 | + | 0.0933089i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 336.000i | 0.134621i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2106.00 | − | 2106.00i | 0.823561 | − | 0.823561i | ||||
\(188\) | −1018.23 | + | 1018.23i | −0.395012 | + | 0.395012i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4505.68i | − | 1.70691i | −0.521166 | − | 0.853455i | \(-0.674503\pi\) | ||
0.521166 | − | 0.853455i | \(-0.325497\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1458.00 | + | 1458.00i | 0.543778 | + | 0.543778i | 0.924634 | − | 0.380856i | \(-0.124371\pi\) |
−0.380856 | + | 0.924634i | \(0.624371\pi\) | |||||||
\(194\) | 1934.64 | 0.715976 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −724.000 | −0.263848 | ||||||||
\(197\) | 110.309 | + | 110.309i | 0.0398942 | + | 0.0398942i | 0.726772 | − | 0.686878i | \(-0.241019\pi\) |
−0.686878 | + | 0.726772i | \(0.741019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 700.000i | − | 0.249355i | −0.992197 | − | 0.124678i | \(-0.960210\pi\) | ||
0.992197 | − | 0.124678i | \(-0.0397897\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1188.00 | − | 1188.00i | 0.413799 | − | 0.413799i | ||||
\(203\) | −687.308 | + | 687.308i | −0.237633 | + | 0.237633i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 229.103i | − | 0.0774871i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −144.000 | − | 144.000i | −0.0480029 | − | 0.0480029i | ||||
\(209\) | −1450.98 | −0.480223 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4084.00 | −1.33248 | −0.666242 | − | 0.745736i | \(-0.732098\pi\) | ||||
−0.666242 | + | 0.745736i | \(0.732098\pi\) | |||||||
\(212\) | −1408.56 | − | 1408.56i | −0.456321 | − | 0.456321i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 2880.00i | − | 0.919966i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2124.00 | − | 2124.00i | 0.664454 | − | 0.664454i | ||||
\(218\) | 2344.77 | − | 2344.77i | 0.728475 | − | 0.728475i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 992.778i | 0.302179i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2637.00 | + | 2637.00i | 0.791868 | + | 0.791868i | 0.981798 | − | 0.189930i | \(-0.0608260\pi\) |
−0.189930 | + | 0.981798i | \(0.560826\pi\) | |||||||
\(224\) | −407.294 | −0.121489 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1332.00 | 0.392050 | ||||||||
\(227\) | −1671.60 | − | 1671.60i | −0.488758 | − | 0.488758i | 0.419156 | − | 0.907914i | \(-0.362326\pi\) |
−0.907914 | + | 0.419156i | \(0.862326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5434.00i | 1.56807i | 0.620714 | + | 0.784037i | \(0.286843\pi\) | ||||
−0.620714 | + | 0.784037i | \(0.713157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 432.000 | − | 432.000i | 0.122251 | − | 0.122251i | ||||
\(233\) | 4034.75 | − | 4034.75i | 1.13444 | − | 1.13444i | 0.145014 | − | 0.989430i | \(-0.453677\pi\) |
0.989430 | − | 0.145014i | \(-0.0463227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1374.62i | − | 0.379152i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1404.00 | + | 1404.00i | 0.382386 | + | 0.382386i | ||||
\(239\) | 3589.27 | 0.971426 | 0.485713 | − | 0.874118i | \(-0.338560\pi\) | ||||
0.485713 | + | 0.874118i | \(0.338560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6212.00 | 1.66037 | 0.830187 | − | 0.557485i | \(-0.188234\pi\) | ||||
0.830187 | + | 0.557485i | \(0.188234\pi\) | |||||||
\(242\) | 179.605 | + | 179.605i | 0.0477085 | + | 0.0477085i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 440.000i | 0.115443i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 342.000 | − | 342.000i | 0.0881010 | − | 0.0881010i | ||||
\(248\) | −1335.02 | + | 1335.02i | −0.341829 | + | 0.341829i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1641.90i | − | 0.412892i | −0.978458 | − | 0.206446i | \(-0.933810\pi\) | ||
0.978458 | − | 0.206446i | \(-0.0661898\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1134.00 | + | 1134.00i | 0.281794 | + | 0.281794i | ||||
\(254\) | −2112.84 | −0.521933 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1981.31 | − | 1981.31i | −0.480899 | − | 0.480899i | 0.424520 | − | 0.905419i | \(-0.360443\pi\) |
−0.905419 | + | 0.424520i | \(0.860443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5022.00i | − | 1.20483i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2430.00 | + | 2430.00i | −0.573000 | + | 0.573000i | ||||
\(263\) | 420.021 | − | 420.021i | 0.0984777 | − | 0.0984777i | −0.656152 | − | 0.754629i | \(-0.727817\pi\) |
0.754629 | + | 0.656152i | \(0.227817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 967.322i | − | 0.222971i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2808.00 | − | 2808.00i | −0.640022 | − | 0.640022i | ||||
\(269\) | −76.3675 | −0.0173093 | −0.00865467 | − | 0.999963i | \(-0.502755\pi\) | ||||
−0.00865467 | + | 0.999963i | \(0.502755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3580.00 | −0.802471 | −0.401235 | − | 0.915975i | \(-0.631419\pi\) | ||||
−0.401235 | + | 0.915975i | \(0.631419\pi\) | |||||||
\(272\) | −882.469 | − | 882.469i | −0.196719 | − | 0.196719i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2724.00i | 0.600594i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2277.00 | − | 2277.00i | 0.493905 | − | 0.493905i | −0.415629 | − | 0.909534i | \(-0.636439\pi\) |
0.909534 | + | 0.415629i | \(0.136439\pi\) | |||||||
\(278\) | 2313.65 | − | 2313.65i | 0.499150 | − | 0.499150i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5613.01i | 1.19162i | 0.803127 | + | 0.595808i | \(0.203168\pi\) | ||||
−0.803127 | + | 0.595808i | \(0.796832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1206.00 | + | 1206.00i | 0.253319 | + | 0.253319i | 0.822330 | − | 0.569011i | \(-0.192674\pi\) |
−0.569011 | + | 0.822330i | \(0.692674\pi\) | |||||||
\(284\) | 305.470 | 0.0638251 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −972.000 | −0.200964 | ||||||||
\(287\) | 3092.89 | + | 3092.89i | 0.636123 | + | 0.636123i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1171.00i | 0.238347i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1512.00 | − | 1512.00i | 0.303024 | − | 0.303024i | ||||
\(293\) | −6932.47 | + | 6932.47i | −1.38225 | + | 1.38225i | −0.541641 | + | 0.840610i | \(0.682197\pi\) |
−0.840610 | + | 0.541641i | \(0.817803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3156.52i | 0.619829i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2160.00 | + | 2160.00i | 0.419884 | + | 0.419884i | ||||
\(299\) | −534.573 | −0.103395 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6480.00 | 1.24087 | ||||||||
\(302\) | 181.019 | + | 181.019i | 0.0344917 | + | 0.0344917i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 608.000i | 0.114708i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2160.00 | + | 2160.00i | −0.401556 | + | 0.401556i | −0.878781 | − | 0.477225i | \(-0.841643\pi\) |
0.477225 | + | 0.878781i | \(0.341643\pi\) | |||||||
\(308\) | −1374.62 | + | 1374.62i | −0.254305 | + | 0.254305i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4658.42i | 0.849372i | 0.905341 | + | 0.424686i | \(0.139616\pi\) | ||||
−0.905341 | + | 0.424686i | \(0.860384\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5742.00 | − | 5742.00i | −1.03692 | − | 1.03692i | −0.999292 | − | 0.0376317i | \(-0.988019\pi\) |
−0.0376317 | − | 0.999292i | \(-0.511981\pi\) | |||||||
\(314\) | −4760.24 | −0.855529 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1088.00 | −0.193686 | ||||||||
\(317\) | 4183.24 | + | 4183.24i | 0.741181 | + | 0.741181i | 0.972805 | − | 0.231624i | \(-0.0744040\pi\) |
−0.231624 | + | 0.972805i | \(0.574404\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2916.00i | − | 0.511801i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −756.000 | + | 756.000i | −0.130839 | + | 0.130839i | ||||
\(323\) | 2095.86 | − | 2095.86i | 0.361043 | − | 0.361043i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 560.029i | − | 0.0951445i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1944.00 | − | 1944.00i | −0.327254 | − | 0.327254i | ||||
\(329\) | −4582.05 | −0.767832 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2126.00 | 0.353038 | 0.176519 | − | 0.984297i | \(-0.443516\pi\) | ||||
0.176519 | + | 0.984297i | \(0.443516\pi\) | |||||||
\(332\) | 237.588 | + | 237.588i | 0.0392751 | + | 0.0392751i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8436.00i | 1.38203i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5958.00 | + | 5958.00i | −0.963065 | + | 0.963065i | −0.999342 | − | 0.0362767i | \(-0.988450\pi\) |
0.0362767 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(338\) | −2877.92 | + | 2877.92i | −0.463132 | + | 0.463132i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9011.37i | 1.43106i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4716.00 | − | 4716.00i | −0.742391 | − | 0.742391i | ||||
\(344\) | −4072.94 | −0.638366 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4764.00 | −0.740215 | ||||||||
\(347\) | −2112.84 | − | 2112.84i | −0.326867 | − | 0.326867i | 0.524527 | − | 0.851394i | \(-0.324242\pi\) |
−0.851394 | + | 0.524527i | \(0.824242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2594.00i | − | 0.397861i | −0.980014 | − | 0.198931i | \(-0.936253\pi\) | ||
0.980014 | − | 0.198931i | \(-0.0637469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 864.000 | − | 864.000i | 0.130828 | − | 0.130828i | ||||
\(353\) | 980.050 | − | 980.050i | 0.147770 | − | 0.147770i | −0.629351 | − | 0.777121i | \(-0.716679\pi\) |
0.777121 | + | 0.629351i | \(0.216679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 5956.67i | − | 0.886805i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −486.000 | − | 486.000i | −0.0717483 | − | 0.0717483i | ||||
\(359\) | 9011.37 | 1.32480 | 0.662398 | − | 0.749152i | \(-0.269539\pi\) | ||||
0.662398 | + | 0.749152i | \(0.269539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5415.00 | 0.789474 | ||||||||
\(362\) | 3566.65 | + | 3566.65i | 0.517842 | + | 0.517842i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 648.000i | − | 0.0933089i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5751.00 | + | 5751.00i | −0.817983 | + | 0.817983i | −0.985816 | − | 0.167833i | \(-0.946323\pi\) |
0.167833 | + | 0.985816i | \(0.446323\pi\) | |||||||
\(368\) | 475.176 | − | 475.176i | 0.0673105 | − | 0.0673105i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6338.51i | − | 0.887005i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2205.00 | − | 2205.00i | −0.306087 | − | 0.306087i | 0.537302 | − | 0.843390i | \(-0.319443\pi\) |
−0.843390 | + | 0.537302i | \(0.819443\pi\) | |||||||
\(374\) | −5956.67 | −0.823561 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2880.00 | 0.395012 | ||||||||
\(377\) | 687.308 | + | 687.308i | 0.0938943 | + | 0.0938943i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 740.000i | − | 0.100294i | −0.998742 | − | 0.0501468i | \(-0.984031\pi\) | ||
0.998742 | − | 0.0501468i | \(-0.0159689\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6372.00 | + | 6372.00i | −0.853455 | + | 0.853455i | ||||
\(383\) | −8281.63 | + | 8281.63i | −1.10489 | + | 1.10489i | −0.111075 | + | 0.993812i | \(0.535429\pi\) |
−0.993812 | + | 0.111075i | \(0.964571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4123.85i | − | 0.543778i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2736.00 | − | 2736.00i | −0.357988 | − | 0.357988i | ||||
\(389\) | 6109.40 | 0.796296 | 0.398148 | − | 0.917321i | \(-0.369653\pi\) | ||||
0.398148 | + | 0.917321i | \(0.369653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3276.00 | −0.423720 | ||||||||
\(392\) | 1023.89 | + | 1023.89i | 0.131924 | + | 0.131924i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 312.000i | − | 0.0398942i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6849.00 | + | 6849.00i | −0.865847 | + | 0.865847i | −0.992010 | − | 0.126162i | \(-0.959734\pi\) |
0.126162 | + | 0.992010i | \(0.459734\pi\) | |||||||
\(398\) | −989.949 | + | 989.949i | −0.124678 | + | 0.124678i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11722.4i | 1.45982i | 0.683541 | + | 0.729912i | \(0.260439\pi\) | ||||
−0.683541 | + | 0.729912i | \(0.739561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2124.00 | − | 2124.00i | −0.262541 | − | 0.262541i | ||||
\(404\) | −3360.17 | −0.413799 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1944.00 | 0.237633 | ||||||||
\(407\) | 10653.3 | + | 10653.3i | 1.29745 | + | 1.29745i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4354.00i | 0.526385i | 0.964743 | + | 0.263192i | \(0.0847754\pi\) | ||||
−0.964743 | + | 0.263192i | \(0.915225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −324.000 | + | 324.000i | −0.0387435 | + | 0.0387435i | ||||
\(413\) | 3092.89 | − | 3092.89i | 0.368501 | − | 0.368501i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 407.294i | 0.0480029i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2052.00 | + | 2052.00i | 0.240111 | + | 0.240111i | ||||
\(419\) | 13708.0 | 1.59828 | 0.799139 | − | 0.601147i | \(-0.205289\pi\) | ||||
0.799139 | + | 0.601147i | \(0.205289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8530.00 | 0.987474 | 0.493737 | − | 0.869611i | \(-0.335630\pi\) | ||||
0.493737 | + | 0.869611i | \(0.335630\pi\) | |||||||
\(422\) | 5775.65 | + | 5775.65i | 0.666242 | + | 0.666242i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3984.00i | 0.456321i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −990.000 | + | 990.000i | −0.112200 | + | 0.112200i | ||||
\(428\) | −4072.94 | + | 4072.94i | −0.459983 | + | 0.459983i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13593.4i | − | 1.51919i | −0.650395 | − | 0.759596i | \(-0.725397\pi\) | ||
0.650395 | − | 0.759596i | \(-0.274603\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4626.00 | + | 4626.00i | 0.513421 | + | 0.513421i | 0.915573 | − | 0.402152i | \(-0.131738\pi\) |
−0.402152 | + | 0.915573i | \(0.631738\pi\) | |||||||
\(434\) | −6007.58 | −0.664454 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6632.00 | −0.728475 | ||||||||
\(437\) | 1128.54 | + | 1128.54i | 0.123537 | + | 0.123537i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14092.0i | − | 1.53206i | −0.642805 | − | 0.766030i | \(-0.722229\pi\) | ||
0.642805 | − | 0.766030i | \(-0.277771\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1404.00 | − | 1404.00i | 0.151089 | − | 0.151089i | ||||
\(443\) | 2664.38 | − | 2664.38i | 0.285753 | − | 0.285753i | −0.549645 | − | 0.835398i | \(-0.685237\pi\) |
0.835398 | + | 0.549645i | \(0.185237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 7458.56i | − | 0.791868i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 576.000 | + | 576.000i | 0.0607443 | + | 0.0607443i | ||||
\(449\) | −1260.06 | −0.132441 | −0.0662206 | − | 0.997805i | \(-0.521094\pi\) | ||||
−0.0662206 | + | 0.997805i | \(0.521094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13122.0 | −1.37005 | ||||||||
\(452\) | −1883.73 | − | 1883.73i | −0.196025 | − | 0.196025i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4728.00i | 0.488758i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8280.00 | + | 8280.00i | −0.847532 | + | 0.847532i | −0.989825 | − | 0.142293i | \(-0.954553\pi\) |
0.142293 | + | 0.989825i | \(0.454553\pi\) | |||||||
\(458\) | 7684.84 | − | 7684.84i | 0.784037 | − | 0.784037i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12371.5i | 1.24989i | 0.780668 | + | 0.624946i | \(0.214879\pi\) | ||||
−0.780668 | + | 0.624946i | \(0.785121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8847.00 | − | 8847.00i | −0.888024 | − | 0.888024i | 0.106309 | − | 0.994333i | \(-0.466097\pi\) |
−0.994333 | + | 0.106309i | \(0.966097\pi\) | |||||||
\(464\) | −1221.88 | −0.122251 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11412.0 | −1.13444 | ||||||||
\(467\) | 4946.92 | + | 4946.92i | 0.490184 | + | 0.490184i | 0.908364 | − | 0.418180i | \(-0.137332\pi\) |
−0.418180 | + | 0.908364i | \(0.637332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12636.0i | − | 1.24409i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1944.00 | + | 1944.00i | −0.189576 | + | 0.189576i | ||||
\(473\) | −13746.2 | + | 13746.2i | −1.33626 | + | 1.33626i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 3971.11i | − | 0.382386i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5076.00 | − | 5076.00i | −0.485713 | − | 0.485713i | ||||
\(479\) | 12906.1 | 1.23110 | 0.615548 | − | 0.788099i | \(-0.288935\pi\) | ||||
0.615548 | + | 0.788099i | \(0.288935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5022.00 | −0.476057 | ||||||||
\(482\) | −8785.09 | − | 8785.09i | −0.830187 | − | 0.830187i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 508.000i | − | 0.0477085i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −369.000 | + | 369.000i | −0.0343347 | + | 0.0343347i | −0.724066 | − | 0.689731i | \(-0.757729\pi\) |
0.689731 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(488\) | 622.254 | − | 622.254i | 0.0577215 | − | 0.0577215i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19817.4i | − | 1.82148i | −0.412983 | − | 0.910739i | \(-0.635513\pi\) | ||
0.412983 | − | 0.910739i | \(-0.364487\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4212.00 | + | 4212.00i | 0.384785 | + | 0.384785i | ||||
\(494\) | −967.322 | −0.0881010 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3776.00 | 0.341829 | ||||||||
\(497\) | 687.308 | + | 687.308i | 0.0620321 | + | 0.0620321i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3058.00i | − | 0.274338i | −0.990548 | − | 0.137169i | \(-0.956200\pi\) | ||
0.990548 | − | 0.137169i | \(-0.0438004\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2322.00 | + | 2322.00i | −0.206446 | + | 0.206446i | ||||
\(503\) | 11336.3 | − | 11336.3i | 1.00490 | − | 1.00490i | 0.00490714 | − | 0.999988i | \(-0.498438\pi\) |
0.999988 | − | 0.00490714i | \(-0.00156200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 3207.44i | − | 0.281794i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2988.00 | + | 2988.00i | 0.260967 | + | 0.260967i | ||||
\(509\) | −13517.1 | −1.17708 | −0.588539 | − | 0.808469i | \(-0.700297\pi\) | ||||
−0.588539 | + | 0.808469i | \(0.700297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6804.00 | 0.589024 | ||||||||
\(512\) | −362.039 | − | 362.039i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5604.00i | 0.480899i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9720.00 | − | 9720.00i | 0.826857 | − | 0.826857i | ||||
\(518\) | −7102.18 | + | 7102.18i | −0.602417 | + | 0.602417i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8667.71i | 0.728867i | 0.931229 | + | 0.364433i | \(0.118737\pi\) | ||||
−0.931229 | + | 0.364433i | \(0.881263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1242.00 | + | 1242.00i | 0.103841 | + | 0.103841i | 0.757119 | − | 0.653278i | \(-0.226606\pi\) |
−0.653278 | + | 0.757119i | \(0.726606\pi\) | |||||||
\(524\) | 6873.08 | 0.573000 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1188.00 | −0.0984777 | ||||||||
\(527\) | −13016.4 | − | 13016.4i | −1.07591 | − | 1.07591i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10403.0i | 0.855018i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1368.00 | + | 1368.00i | −0.111486 | + | 0.111486i | ||||
\(533\) | 3092.89 | − | 3092.89i | 0.251347 | − | 0.251347i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7942.22i | 0.640022i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 108.000 | + | 108.000i | 0.00865467 | + | 0.00865467i | ||||
\(539\) | 6911.26 | 0.552299 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3242.00 | 0.257642 | 0.128821 | − | 0.991668i | \(-0.458881\pi\) | ||||
0.128821 | + | 0.991668i | \(0.458881\pi\) | |||||||
\(542\) | 5062.88 | + | 5062.88i | 0.401235 | + | 0.401235i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2496.00i | 0.196719i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10476.0 | − | 10476.0i | 0.818869 | − | 0.818869i | −0.167075 | − | 0.985944i | \(-0.553432\pi\) |
0.985944 | + | 0.167075i | \(0.0534322\pi\) | |||||||
\(548\) | 3852.32 | − | 3852.32i | 0.300297 | − | 0.300297i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2901.97i | − | 0.224370i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2448.00 | − | 2448.00i | −0.188245 | − | 0.188245i | ||||
\(554\) | −6440.33 | −0.493905 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6544.00 | −0.499150 | ||||||||
\(557\) | 165.463 | + | 165.463i | 0.0125869 | + | 0.0125869i | 0.713372 | − | 0.700785i | \(-0.247167\pi\) |
−0.700785 | + | 0.713372i | \(0.747167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6480.00i | − | 0.490295i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7938.00 | − | 7938.00i | 0.595808 | − | 0.595808i | ||||
\(563\) | −14586.2 | + | 14586.2i | −1.09189 | + | 1.09189i | −0.0965649 | + | 0.995327i | \(0.530786\pi\) |
−0.995327 | + | 0.0965649i | \(0.969214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 3411.08i | − | 0.253319i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −432.000 | − | 432.000i | −0.0319125 | − | 0.0319125i | ||||
\(569\) | 7216.73 | 0.531707 | 0.265853 | − | 0.964013i | \(-0.414346\pi\) | ||||
0.265853 | + | 0.964013i | \(0.414346\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1762.00 | −0.129137 | −0.0645687 | − | 0.997913i | \(-0.520567\pi\) | ||||
−0.0645687 | + | 0.997913i | \(0.520567\pi\) | |||||||
\(572\) | 1374.62 | + | 1374.62i | 0.100482 | + | 0.100482i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8748.00i | − | 0.636123i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14688.0 | − | 14688.0i | 1.05974 | − | 1.05974i | 0.0616407 | − | 0.998098i | \(-0.480367\pi\) |
0.998098 | − | 0.0616407i | \(-0.0196333\pi\) | |||||||
\(578\) | 1656.04 | − | 1656.04i | 0.119174 | − | 0.119174i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1069.15i | 0.0763436i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13446.0 | + | 13446.0i | 0.955191 | + | 0.955191i | ||||
\(584\) | −4276.58 | −0.303024 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19608.0 | 1.38225 | ||||||||
\(587\) | −2324.97 | − | 2324.97i | −0.163478 | − | 0.163478i | 0.620627 | − | 0.784106i | \(-0.286878\pi\) |
−0.784106 | + | 0.620627i | \(0.786878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8968.00i | 0.627368i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4464.00 | − | 4464.00i | 0.309914 | − | 0.309914i | ||||
\(593\) | 15625.6 | − | 15625.6i | 1.08207 | − | 1.08207i | 0.0857552 | − | 0.996316i | \(-0.472670\pi\) |
0.996316 | − | 0.0857552i | \(-0.0273303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6109.40i | − | 0.419884i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 756.000 | + | 756.000i | 0.0516976 | + | 0.0516976i | ||||
\(599\) | 9011.37 | 0.614682 | 0.307341 | − | 0.951599i | \(-0.400561\pi\) | ||||
0.307341 | + | 0.951599i | \(0.400561\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15388.0 | 1.04441 | 0.522204 | − | 0.852820i | \(-0.325110\pi\) | ||||
0.522204 | + | 0.852820i | \(0.325110\pi\) | |||||||
\(602\) | −9164.10 | − | 9164.10i | −0.620434 | − | 0.620434i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 512.000i | − | 0.0344917i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3177.00 | − | 3177.00i | 0.212439 | − | 0.212439i | −0.592864 | − | 0.805303i | \(-0.702003\pi\) |
0.805303 | + | 0.592864i | \(0.202003\pi\) | |||||||
\(608\) | 859.842 | − | 859.842i | 0.0573539 | − | 0.0573539i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4582.05i | 0.303388i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1701.00 | − | 1701.00i | −0.112076 | − | 0.112076i | 0.648845 | − | 0.760921i | \(-0.275253\pi\) |
−0.760921 | + | 0.648845i | \(0.775253\pi\) | |||||||
\(614\) | 6109.40 | 0.401556 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3888.00 | 0.254305 | ||||||||
\(617\) | −18782.2 | − | 18782.2i | −1.22551 | − | 1.22551i | −0.965644 | − | 0.259870i | \(-0.916320\pi\) |
−0.259870 | − | 0.965644i | \(-0.583680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12548.0i | 0.814777i | 0.913255 | + | 0.407388i | \(0.133560\pi\) | ||||
−0.913255 | + | 0.407388i | \(0.866440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6588.00 | − | 6588.00i | 0.424686 | − | 0.424686i | ||||
\(623\) | 13402.5 | − | 13402.5i | 0.861894 | − | 0.861894i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16240.8i | 1.03692i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6732.00 | + | 6732.00i | 0.427764 | + | 0.427764i | ||||
\(629\) | −30776.1 | −1.95091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27340.0 | −1.72486 | −0.862431 | − | 0.506174i | \(-0.831059\pi\) | ||||
−0.862431 | + | 0.506174i | \(0.831059\pi\) | |||||||
\(632\) | 1538.66 | + | 1538.66i | 0.0968430 | + | 0.0968430i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 11832.0i | − | 0.741181i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1629.00 | + | 1629.00i | −0.101324 | + | 0.101324i | ||||
\(638\) | −4123.85 | + | 4123.85i | −0.255901 | + | 0.255901i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21039.3i | 1.29641i | 0.761465 | + | 0.648206i | \(0.224481\pi\) | ||||
−0.761465 | + | 0.648206i | \(0.775519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11394.0 | + | 11394.0i | 0.698811 | + | 0.698811i | 0.964154 | − | 0.265343i | \(-0.0854852\pi\) |
−0.265343 | + | 0.964154i | \(0.585485\pi\) | |||||||
\(644\) | 2138.29 | 0.130839 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5928.00 | −0.361043 | ||||||||
\(647\) | −6584.58 | − | 6584.58i | −0.400103 | − | 0.400103i | 0.478166 | − | 0.878269i | \(-0.341302\pi\) |
−0.878269 | + | 0.478166i | \(0.841302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13122.0i | 0.793657i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −792.000 | + | 792.000i | −0.0475723 | + | 0.0475723i | ||||
\(653\) | −7008.84 | + | 7008.84i | −0.420026 | + | 0.420026i | −0.885213 | − | 0.465186i | \(-0.845987\pi\) |
0.465186 | + | 0.885213i | \(0.345987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5498.46i | 0.327254i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6480.00 | + | 6480.00i | 0.383916 | + | 0.383916i | ||||
\(659\) | −32112.5 | −1.89822 | −0.949110 | − | 0.314944i | \(-0.898014\pi\) | ||||
−0.949110 | + | 0.314944i | \(0.898014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31822.0 | 1.87251 | 0.936257 | − | 0.351315i | \(-0.114265\pi\) | ||||
0.936257 | + | 0.351315i | \(0.114265\pi\) | |||||||
\(662\) | −3006.62 | − | 3006.62i | −0.176519 | − | 0.176519i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 672.000i | − | 0.0392751i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2268.00 | + | 2268.00i | −0.131660 | + | 0.131660i | ||||
\(668\) | 11930.3 | − | 11930.3i | 0.691014 | − | 0.691014i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4200.21i | − | 0.241650i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3330.00 | + | 3330.00i | 0.190731 | + | 0.190731i | 0.796012 | − | 0.605281i | \(-0.206939\pi\) |
−0.605281 | + | 0.796012i | \(0.706939\pi\) | |||||||
\(674\) | 16851.8 | 0.963065 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8140.00 | 0.463132 | ||||||||
\(677\) | −5600.29 | − | 5600.29i | −0.317927 | − | 0.317927i | 0.530044 | − | 0.847970i | \(-0.322176\pi\) |
−0.847970 | + | 0.530044i | \(0.822176\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12312.0i | − | 0.695863i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12744.0 | − | 12744.0i | 0.715532 | − | 0.715532i | ||||
\(683\) | 17581.5 | − | 17581.5i | 0.984974 | − | 0.984974i | −0.0149144 | − | 0.999889i | \(-0.504748\pi\) |
0.999889 | + | 0.0149144i | \(0.00474757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13338.9i | 0.742391i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5760.00 | + | 5760.00i | 0.319183 | + | 0.319183i | ||||
\(689\) | −6338.51 | −0.350476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23330.0 | −1.28439 | −0.642196 | − | 0.766540i | \(-0.721977\pi\) | ||||
−0.642196 | + | 0.766540i | \(0.721977\pi\) | |||||||
\(692\) | 6737.31 | + | 6737.31i | 0.370107 | + | 0.370107i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5976.00i | 0.326867i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18954.0 | − | 18954.0i | 1.03003 | − | 1.03003i | ||||
\(698\) | −3668.47 | + | 3668.47i | −0.198931 | + | 0.198931i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8018.59i | 0.432037i | 0.976389 | + | 0.216019i | \(0.0693072\pi\) | ||||
−0.976389 | + | 0.216019i | \(0.930693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10602.0 | + | 10602.0i | 0.568794 | + | 0.568794i | ||||
\(704\) | −2443.76 | −0.130828 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2772.00 | −0.147770 | ||||||||
\(707\) | −7560.39 | − | 7560.39i | −0.402175 | − | 0.402175i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25414.0i | 1.34618i | 0.739560 | + | 0.673091i | \(0.235034\pi\) | ||||
−0.739560 | + | 0.673091i | \(0.764966\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8424.00 | + | 8424.00i | −0.443403 | + | 0.443403i | ||||
\(713\) | 7008.84 | − | 7008.84i | 0.368139 | − | 0.368139i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1374.62i | 0.0717483i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12744.0 | − | 12744.0i | −0.662398 | − | 0.662398i | ||||
\(719\) | 10386.0 | 0.538709 | 0.269355 | − | 0.963041i | \(-0.413190\pi\) | ||||
0.269355 | + | 0.963041i | \(0.413190\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1458.00 | −0.0753103 | ||||||||
\(722\) | −7657.97 | − | 7657.97i | −0.394737 | − | 0.394737i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10088.0i | − | 0.517842i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22707.0 | − | 22707.0i | 1.15840 | − | 1.15840i | 0.173579 | − | 0.984820i | \(-0.444467\pi\) |
0.984820 | − | 0.173579i | \(-0.0555332\pi\) | |||||||
\(728\) | −916.410 | + | 916.410i | −0.0466544 | + | 0.0466544i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 39711.1i | − | 2.00926i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12573.0 | + | 12573.0i | 0.633553 | + | 0.633553i | 0.948957 | − | 0.315404i | \(-0.102140\pi\) |
−0.315404 | + | 0.948957i | \(0.602140\pi\) | |||||||
\(734\) | 16266.3 | 0.817983 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1344.00 | −0.0673105 | ||||||||
\(737\) | 26805.0 | + | 26805.0i | 1.33972 | + | 1.33972i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 14402.0i | − | 0.716896i | −0.933550 | − | 0.358448i | \(-0.883306\pi\) | ||
0.933550 | − | 0.358448i | \(-0.116694\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8964.00 | + | 8964.00i | −0.443502 | + | 0.443502i | ||||
\(743\) | −22146.6 | + | 22146.6i | −1.09351 | + | 1.09351i | −0.0983612 | + | 0.995151i | \(0.531360\pi\) |
−0.995151 | + | 0.0983612i | \(0.968640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6236.68i | 0.306087i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8424.00 | + | 8424.00i | 0.411781 | + | 0.411781i | ||||
\(749\) | −18328.2 | −0.894123 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15208.0 | 0.738945 | 0.369473 | − | 0.929242i | \(-0.379538\pi\) | ||||
0.369473 | + | 0.929242i | \(0.379538\pi\) | |||||||
\(752\) | −4072.94 | − | 4072.94i | −0.197506 | − | 0.197506i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1944.00i | − | 0.0938943i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1485.00 | + | 1485.00i | −0.0712989 | + | 0.0712989i | −0.741857 | − | 0.670558i | \(-0.766055\pi\) |
0.670558 | + | 0.741857i | \(0.266055\pi\) | |||||||
\(758\) | −1046.52 | + | 1046.52i | −0.0501468 | + | 0.0501468i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2176.47i | − | 0.103676i | −0.998656 | − | 0.0518378i | \(-0.983492\pi\) | ||
0.998656 | − | 0.0518378i | \(-0.0165079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14922.0 | − | 14922.0i | −0.708011 | − | 0.708011i | ||||
\(764\) | 18022.7 | 0.853455 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23424.0 | 1.10489 | ||||||||
\(767\) | −3092.89 | − | 3092.89i | −0.145603 | − | 0.145603i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5960.00i | 0.279484i | 0.990188 | + | 0.139742i | \(0.0446273\pi\) | ||||
−0.990188 | + | 0.139742i | \(0.955373\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5832.00 | + | 5832.00i | −0.271889 | + | 0.271889i | ||||
\(773\) | 14569.2 | − | 14569.2i | 0.677903 | − | 0.677903i | −0.281623 | − | 0.959525i | \(-0.590873\pi\) |
0.959525 | + | 0.281623i | \(0.0908726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7738.58i | 0.357988i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8640.00 | − | 8640.00i | −0.398148 | − | 0.398148i | ||||
\(779\) | −13058.8 | −0.600618 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2916.00 | −0.133601 | ||||||||
\(782\) | 4632.96 | + | 4632.96i | 0.211860 | + | 0.211860i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 2896.00i | − | 0.131924i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21330.0 | + | 21330.0i | −0.966115 | + | 0.966115i | −0.999444 | − | 0.0333296i | \(-0.989389\pi\) |
0.0333296 | + | 0.999444i | \(0.489389\pi\) | |||||||
\(788\) | −441.235 | + | 441.235i | −0.0199471 | + | 0.0199471i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8476.80i | − | 0.381037i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 990.000 | + | 990.000i | 0.0443328 | + | 0.0443328i | ||||
\(794\) | 19371.9 | 0.865847 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2800.00 | 0.124678 | ||||||||
\(797\) | −21107.1 | − | 21107.1i | −0.938084 | − | 0.938084i | 0.0601076 | − | 0.998192i | \(-0.480856\pi\) |
−0.998192 | + | 0.0601076i | \(0.980856\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28080.0i | 1.24330i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16578.0 | − | 16578.0i | 0.729912 | − | 0.729912i | ||||
\(803\) | −14433.5 | + | 14433.5i | −0.634304 | + | 0.634304i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6007.58i | 0.262541i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4752.00 | + | 4752.00i | 0.206899 | + | 0.206899i | ||||
\(809\) | −3321.99 | −0.144369 | −0.0721847 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721847 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27380.0 | −1.18550 | −0.592751 | − | 0.805386i | \(-0.701958\pi\) | ||||
−0.592751 | + | 0.805386i | \(0.701958\pi\) | |||||||
\(812\) | −2749.23 | − | 2749.23i | −0.118817 | − | 0.118817i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 30132.0i | − | 1.29745i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13680.0 | + | 13680.0i | −0.585805 | + | 0.585805i | ||||
\(818\) | 6157.49 | − | 6157.49i | 0.263192 | − | 0.263192i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 14586.2i | − | 0.620051i | −0.950728 | − | 0.310025i | \(-0.899662\pi\) | ||
0.950728 | − | 0.310025i | \(-0.100338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11079.0 | − | 11079.0i | −0.469246 | − | 0.469246i | 0.432424 | − | 0.901670i | \(-0.357658\pi\) |
−0.901670 | + | 0.432424i | \(0.857658\pi\) | |||||||
\(824\) | 916.410 | 0.0387435 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8748.00 | −0.368501 | ||||||||
\(827\) | 12286.7 | + | 12286.7i | 0.516626 | + | 0.516626i | 0.916549 | − | 0.399923i | \(-0.130963\pi\) |
−0.399923 | + | 0.916549i | \(0.630963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 12854.0i | − | 0.538526i | −0.963067 | − | 0.269263i | \(-0.913220\pi\) | ||
0.963067 | − | 0.269263i | \(-0.0867801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 576.000 | − | 576.000i | 0.0240015 | − | 0.0240015i | ||||
\(833\) | −9982.93 | + | 9982.93i | −0.415232 | + | 0.415232i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 5803.93i | − | 0.240111i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19386.0 | − | 19386.0i | −0.799139 | − | 0.799139i | ||||
\(839\) | 18480.9 | 0.760468 | 0.380234 | − | 0.924890i | \(-0.375843\pi\) | ||||
0.380234 | + | 0.924890i | \(0.375843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18557.0 | −0.760876 | ||||||||
\(842\) | −12063.2 | − | 12063.2i | −0.493737 | − | 0.493737i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 16336.0i | − | 0.666242i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1143.00 | − | 1143.00i | 0.0463683 | − | 0.0463683i | ||||
\(848\) | 5634.23 | − | 5634.23i | 0.228161 | − | 0.228161i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16571.8i | − | 0.667535i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28377.0 | − | 28377.0i | −1.13905 | − | 1.13905i | −0.988621 | − | 0.150430i | \(-0.951934\pi\) |
−0.150430 | − | 0.988621i | \(-0.548066\pi\) | |||||||
\(854\) | 2800.14 | 0.112200 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11520.0 | 0.459983 | ||||||||
\(857\) | 19732.5 | + | 19732.5i | 0.786523 | + | 0.786523i | 0.980922 | − | 0.194400i | \(-0.0622758\pi\) |
−0.194400 | + | 0.980922i | \(0.562276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17084.0i | 0.678578i | 0.940682 | + | 0.339289i | \(0.110186\pi\) | ||||
−0.940682 | + | 0.339289i | \(0.889814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19224.0 | + | 19224.0i | −0.759596 | + | 0.759596i | ||||
\(863\) | −17280.3 | + | 17280.3i | −0.681608 | + | 0.681608i | −0.960362 | − | 0.278755i | \(-0.910078\pi\) |
0.278755 | + | 0.960362i | \(0.410078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 13084.3i | − | 0.513421i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8496.00 | + | 8496.00i | 0.332227 | + | 0.332227i | ||||
\(869\) | 10386.0 | 0.405432 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12636.0 | −0.491567 | ||||||||
\(872\) | 9379.06 | + | 9379.06i | 0.364238 | + | 0.364238i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3192.00i | − | 0.123537i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14805.0 | + | 14805.0i | −0.570045 | + | 0.570045i | −0.932141 | − | 0.362096i | \(-0.882061\pi\) |
0.362096 | + | 0.932141i | \(0.382061\pi\) | |||||||
\(878\) | −19929.1 | + | 19929.1i | −0.766030 | + | 0.766030i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23635.8i | − | 0.903869i | −0.892051 | − | 0.451935i | \(-0.850734\pi\) | ||
0.892051 | − | 0.451935i | \(-0.149266\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5958.00 | − | 5958.00i | −0.227070 | − | 0.227070i | 0.584398 | − | 0.811467i | \(-0.301331\pi\) |
−0.811467 | + | 0.584398i | \(0.801331\pi\) | |||||||
\(884\) | −3971.11 | −0.151089 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7536.00 | −0.285753 | ||||||||
\(887\) | 13164.9 | + | 13164.9i | 0.498348 | + | 0.498348i | 0.910923 | − | 0.412576i | \(-0.135371\pi\) |
−0.412576 | + | 0.910923i | \(0.635371\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13446.0i | 0.507272i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10548.0 | + | 10548.0i | −0.395934 | + | 0.395934i | ||||
\(893\) | 9673.22 | − | 9673.22i | 0.362488 | − | 0.362488i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1629.17i | − | 0.0607443i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1782.00 | + | 1782.00i | 0.0662206 | + | 0.0662206i | ||||
\(899\) | −18022.7 | −0.668623 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38844.0 | −1.43627 | ||||||||
\(902\) | 18557.3 | + | 18557.3i | 0.685023 | + | 0.685023i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5328.00i | 0.196025i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11088.0 | + | 11088.0i | −0.405922 | + | 0.405922i | −0.880314 | − | 0.474392i | \(-0.842668\pi\) |
0.474392 | + | 0.880314i | \(0.342668\pi\) | |||||||
\(908\) | 6686.40 | − | 6686.40i | 0.244379 | − | 0.244379i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3207.44i | 0.116649i | 0.998298 | + | 0.0583244i | \(0.0185758\pi\) | ||||
−0.998298 | + | 0.0583244i | \(0.981424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2268.00 | − | 2268.00i | −0.0822123 | − | 0.0822123i | ||||
\(914\) | 23419.4 | 0.847532 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21736.0 | −0.784037 | ||||||||
\(917\) | 15464.4 | + | 15464.4i | 0.556903 | + | 0.556903i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 46820.0i | − | 1.68058i | −0.542140 | − | 0.840288i | \(-0.682386\pi\) | ||
0.542140 | − | 0.840288i | \(-0.317614\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17496.0 | − | 17496.0i | 0.624946 | − | 0.624946i | ||||
\(923\) | 687.308 | − | 687.308i | 0.0245103 | − | 0.0245103i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25023.1i | 0.888024i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1728.00 | + | 1728.00i | 0.0611254 | + | 0.0611254i | ||||
\(929\) | −44331.4 | −1.56562 | −0.782812 | − | 0.622258i | \(-0.786215\pi\) | ||||
−0.782812 | + | 0.622258i | \(0.786215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6878.00 | 0.242124 | ||||||||
\(932\) | 16139.0 | + | 16139.0i | 0.567222 | + | 0.567222i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 13992.0i | − | 0.490184i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23688.0 | + | 23688.0i | −0.825884 | + | 0.825884i | −0.986945 | − | 0.161061i | \(-0.948509\pi\) |
0.161061 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(938\) | −17870.0 | + | 17870.0i | −0.622043 | + | 0.622043i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17259.1i | 0.597906i | 0.954268 | + | 0.298953i | \(0.0966373\pi\) | ||||
−0.954268 | + | 0.298953i | \(0.903363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10206.0 | + | 10206.0i | 0.352442 | + | 0.352442i | ||||
\(944\) | 5498.46 | 0.189576 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38880.0 | 1.33626 | ||||||||
\(947\) | −441.235 | − | 441.235i | −0.0151407 | − | 0.0151407i | 0.699496 | − | 0.714637i | \(-0.253408\pi\) |
−0.714637 | + | 0.699496i | \(0.753408\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6804.00i | − | 0.232737i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5616.00 | + | 5616.00i | −0.191193 | + | 0.191193i | ||||
\(953\) | −29414.2 | + | 29414.2i | −0.999811 | + | 0.999811i | −1.00000 | 0.000188542i | \(-0.999940\pi\) | |
0.000188542 | 1.00000i | \(0.499940\pi\) | ||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14357.1i | 0.485713i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18252.0 | − | 18252.0i | −0.615548 | − | 0.615548i | ||||
\(959\) | 17335.4 | 0.583723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25905.0 | 0.869558 | ||||||||
\(962\) | 7102.18 | + | 7102.18i | 0.238029 | + | 0.238029i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24848.0i | 0.830187i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33075.0 | + | 33075.0i | −1.09992 | + | 1.09992i | −0.105498 | + | 0.994420i | \(0.533644\pi\) |
−0.994420 | + | 0.105498i | \(0.966356\pi\) | |||||||
\(968\) | −718.420 | + | 718.420i | −0.0238542 | + | 0.0238542i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 35396.4i | − | 1.16985i | −0.811088 | − | 0.584924i | \(-0.801124\pi\) | ||
0.811088 | − | 0.584924i | \(-0.198876\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14724.0 | − | 14724.0i | −0.485128 | − | 0.485128i | ||||
\(974\) | 1043.69 | 0.0343347 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1760.00 | −0.0577215 | ||||||||
\(977\) | −2711.05 | − | 2711.05i | −0.0887759 | − | 0.0887759i | 0.661324 | − | 0.750100i | \(-0.269995\pi\) |
−0.750100 | + | 0.661324i | \(0.769995\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56862.0i | 1.85630i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28026.0 | + | 28026.0i | −0.910739 | + | 0.910739i | ||||
\(983\) | 38166.8 | − | 38166.8i | 1.23838 | − | 1.23838i | 0.277723 | − | 0.960661i | \(-0.410420\pi\) |
0.960661 | − | 0.277723i | \(-0.0895798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 11913.3i | − | 0.384785i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1368.00 | + | 1368.00i | 0.0440505 | + | 0.0440505i | ||||
\(989\) | 21382.9 | 0.687499 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27308.0 | 0.875345 | 0.437673 | − | 0.899134i | \(-0.355803\pi\) | ||||
0.437673 | + | 0.899134i | \(0.355803\pi\) | |||||||
\(992\) | −5340.07 | − | 5340.07i | −0.170915 | − | 0.170915i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 1944.00i | − | 0.0620321i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14391.0 | + | 14391.0i | −0.457139 | + | 0.457139i | −0.897715 | − | 0.440576i | \(-0.854774\pi\) |
0.440576 | + | 0.897715i | \(0.354774\pi\) | |||||||
\(998\) | −4324.67 | + | 4324.67i | −0.137169 | + | 0.137169i | ||||
\(999\) | 0 | 0 |
(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 | 450.4.f.a.143.1 | yes | 4 | |
3.2 | odd | 2 | inner | 450.4.f.a.143.2 | yes | 4 | |
5.2 | odd | 4 | inner | 450.4.f.a.107.2 | yes | 4 | |
5.3 | odd | 4 | 450.4.f.c.107.1 | yes | 4 | ||
5.4 | even | 2 | 450.4.f.c.143.2 | yes | 4 | ||
15.2 | even | 4 | inner | 450.4.f.a.107.1 | ✓ | 4 | |
15.8 | even | 4 | 450.4.f.c.107.2 | yes | 4 | ||
15.14 | odd | 2 | 450.4.f.c.143.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.4.f.a.107.1 | ✓ | 4 | 15.2 | even | 4 | inner | |
450.4.f.a.107.2 | yes | 4 | 5.2 | odd | 4 | inner | |
450.4.f.a.143.1 | yes | 4 | 1.1 | even | 1 | trivial | |
450.4.f.a.143.2 | yes | 4 | 3.2 | odd | 2 | inner | |
450.4.f.c.107.1 | yes | 4 | 5.3 | odd | 4 | ||
450.4.f.c.107.2 | yes | 4 | 15.8 | even | 4 | ||
450.4.f.c.143.1 | yes | 4 | 15.14 | odd | 2 | ||
450.4.f.c.143.2 | yes | 4 | 5.4 | even | 2 |