Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,3,Mod(174,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.174");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.c (of order \(2\), degree \(1\), not 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: | \(4.76840462631\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 174.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.174 |
Dual form | 175.3.c.d.174.4 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.500000i | −0.968246 | − | 0.250000i | \(-0.919569\pi\) | ||||
0.968246 | − | 0.250000i | \(-0.0804306\pi\) | |||||||
\(3\) | 4.47214 | 1.49071 | 0.745356 | − | 0.666667i | \(-0.232280\pi\) | ||||
0.745356 | + | 0.666667i | \(0.232280\pi\) | |||||||
\(4\) | 3.00000 | 0.750000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − 4.47214i | − 0.745356i | ||||||||
\(7\) | 7.00000i | 1.00000i | ||||||||
\(8\) | − 7.00000i | − 0.875000i | ||||||||
\(9\) | 11.0000 | 1.22222 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.181818 | 0.0909091 | − | 0.995859i | \(-0.471023\pi\) | ||||
0.0909091 | + | 0.995859i | \(0.471023\pi\) | |||||||
\(12\) | 13.4164 | 1.11803 | ||||||||
\(13\) | −13.4164 | −1.03203 | −0.516016 | − | 0.856579i | \(-0.672585\pi\) | ||||
−0.516016 | + | 0.856579i | \(0.672585\pi\) | |||||||
\(14\) | 7.00000 | 0.500000 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | −26.8328 | −1.57840 | −0.789200 | − | 0.614136i | \(-0.789505\pi\) | ||||
−0.789200 | + | 0.614136i | \(0.789505\pi\) | |||||||
\(18\) | − 11.0000i | − 0.611111i | ||||||||
\(19\) | 13.4164i | 0.706127i | 0.935599 | + | 0.353063i | \(0.114860\pi\) | ||||
−0.935599 | + | 0.353063i | \(0.885140\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 31.3050i | 1.49071i | ||||||||
\(22\) | − 2.00000i | − 0.0909091i | ||||||||
\(23\) | − 26.0000i | − 1.13043i | −0.824942 | − | 0.565217i | \(-0.808792\pi\) | ||||
0.824942 | − | 0.565217i | \(-0.191208\pi\) | |||||||
\(24\) | − 31.3050i | − 1.30437i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 13.4164i | 0.516016i | ||||||||
\(27\) | 8.94427 | 0.331269 | ||||||||
\(28\) | 21.0000i | 0.750000i | ||||||||
\(29\) | 22.0000 | 0.758621 | 0.379310 | − | 0.925270i | \(-0.376161\pi\) | ||||
0.379310 | + | 0.925270i | \(0.376161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 53.6656i | − 1.73115i | −0.500780 | − | 0.865575i | \(-0.666953\pi\) | ||||
0.500780 | − | 0.865575i | \(-0.333047\pi\) | |||||||
\(32\) | − 33.0000i | − 1.03125i | ||||||||
\(33\) | 8.94427 | 0.271039 | ||||||||
\(34\) | 26.8328i | 0.789200i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 33.0000 | 0.916667 | ||||||||
\(37\) | 14.0000i | 0.378378i | 0.981941 | + | 0.189189i | \(0.0605859\pi\) | ||||
−0.981941 | + | 0.189189i | \(0.939414\pi\) | |||||||
\(38\) | 13.4164 | 0.353063 | ||||||||
\(39\) | −60.0000 | −1.53846 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 26.8328i | − 0.654459i | −0.944945 | − | 0.327229i | \(-0.893885\pi\) | ||||
0.944945 | − | 0.327229i | \(-0.106115\pi\) | |||||||
\(42\) | 31.3050 | 0.745356 | ||||||||
\(43\) | 34.0000i | 0.790698i | 0.918531 | + | 0.395349i | \(0.129376\pi\) | ||||
−0.918531 | + | 0.395349i | \(0.870624\pi\) | |||||||
\(44\) | 6.00000 | 0.136364 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.0000 | −0.565217 | ||||||||
\(47\) | 26.8328 | 0.570911 | 0.285455 | − | 0.958392i | \(-0.407855\pi\) | ||||
0.285455 | + | 0.958392i | \(0.407855\pi\) | |||||||
\(48\) | 22.3607 | 0.465847 | ||||||||
\(49\) | −49.0000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −120.000 | −2.35294 | ||||||||
\(52\) | −40.2492 | −0.774024 | ||||||||
\(53\) | 34.0000i | 0.641509i | 0.947162 | + | 0.320755i | \(0.103937\pi\) | ||||
−0.947162 | + | 0.320755i | \(0.896063\pi\) | |||||||
\(54\) | − 8.94427i | − 0.165635i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 49.0000 | 0.875000 | ||||||||
\(57\) | 60.0000i | 1.05263i | ||||||||
\(58\) | − 22.0000i | − 0.379310i | ||||||||
\(59\) | 40.2492i | 0.682190i | 0.940029 | + | 0.341095i | \(0.110798\pi\) | ||||
−0.940029 | + | 0.341095i | \(0.889202\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 93.9149i | 1.53959i | 0.638293 | + | 0.769794i | \(0.279641\pi\) | ||||
−0.638293 | + | 0.769794i | \(0.720359\pi\) | |||||||
\(62\) | −53.6656 | −0.865575 | ||||||||
\(63\) | 77.0000i | 1.22222i | ||||||||
\(64\) | −13.0000 | −0.203125 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − 8.94427i | − 0.135519i | ||||||||
\(67\) | 14.0000i | 0.208955i | 0.994527 | + | 0.104478i | \(0.0333171\pi\) | ||||
−0.994527 | + | 0.104478i | \(0.966683\pi\) | |||||||
\(68\) | −80.4984 | −1.18380 | ||||||||
\(69\) | − 116.276i | − 1.68515i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 62.0000 | 0.873239 | 0.436620 | − | 0.899646i | \(-0.356176\pi\) | ||||
0.436620 | + | 0.899646i | \(0.356176\pi\) | |||||||
\(72\) | − 77.0000i | − 1.06944i | ||||||||
\(73\) | −53.6656 | −0.735146 | −0.367573 | − | 0.929995i | \(-0.619811\pi\) | ||||
−0.367573 | + | 0.929995i | \(0.619811\pi\) | |||||||
\(74\) | 14.0000 | 0.189189 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 40.2492i | 0.529595i | ||||||||
\(77\) | 14.0000i | 0.181818i | ||||||||
\(78\) | 60.0000i | 0.769231i | ||||||||
\(79\) | −38.0000 | −0.481013 | −0.240506 | − | 0.970648i | \(-0.577313\pi\) | ||||
−0.240506 | + | 0.970648i | \(0.577313\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59.0000 | −0.728395 | ||||||||
\(82\) | −26.8328 | −0.327229 | ||||||||
\(83\) | 40.2492 | 0.484930 | 0.242465 | − | 0.970160i | \(-0.422044\pi\) | ||||
0.242465 | + | 0.970160i | \(0.422044\pi\) | |||||||
\(84\) | 93.9149i | 1.11803i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 34.0000 | 0.395349 | ||||||||
\(87\) | 98.3870 | 1.13088 | ||||||||
\(88\) | − 14.0000i | − 0.159091i | ||||||||
\(89\) | 26.8328i | 0.301492i | 0.988573 | + | 0.150746i | \(0.0481676\pi\) | ||||
−0.988573 | + | 0.150746i | \(0.951832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 93.9149i | − 1.03203i | ||||||||
\(92\) | − 78.0000i | − 0.847826i | ||||||||
\(93\) | − 240.000i | − 2.58065i | ||||||||
\(94\) | − 26.8328i | − 0.285455i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − 147.580i | − 1.53730i | ||||||||
\(97\) | 26.8328 | 0.276627 | 0.138313 | − | 0.990388i | \(-0.455832\pi\) | ||||
0.138313 | + | 0.990388i | \(0.455832\pi\) | |||||||
\(98\) | 49.0000i | 0.500000i | ||||||||
\(99\) | 22.0000 | 0.222222 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 67.0820i | 0.664179i | 0.943248 | + | 0.332089i | \(0.107754\pi\) | ||||
−0.943248 | + | 0.332089i | \(0.892246\pi\) | |||||||
\(102\) | 120.000i | 1.17647i | ||||||||
\(103\) | 160.997 | 1.56308 | 0.781538 | − | 0.623857i | \(-0.214435\pi\) | ||||
0.781538 | + | 0.623857i | \(0.214435\pi\) | |||||||
\(104\) | 93.9149i | 0.903027i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 34.0000 | 0.320755 | ||||||||
\(107\) | − 106.000i | − 0.990654i | −0.868707 | − | 0.495327i | \(-0.835048\pi\) | ||||
0.868707 | − | 0.495327i | \(-0.164952\pi\) | |||||||
\(108\) | 26.8328 | 0.248452 | ||||||||
\(109\) | 142.000 | 1.30275 | 0.651376 | − | 0.758755i | \(-0.274192\pi\) | ||||
0.651376 | + | 0.758755i | \(0.274192\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 62.6099i | 0.564053i | ||||||||
\(112\) | 35.0000i | 0.312500i | ||||||||
\(113\) | 34.0000i | 0.300885i | 0.988619 | + | 0.150442i | \(0.0480698\pi\) | ||||
−0.988619 | + | 0.150442i | \(0.951930\pi\) | |||||||
\(114\) | 60.0000 | 0.526316 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 66.0000 | 0.568966 | ||||||||
\(117\) | −147.580 | −1.26137 | ||||||||
\(118\) | 40.2492 | 0.341095 | ||||||||
\(119\) | − 187.830i | − 1.57840i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.000 | −0.966942 | ||||||||
\(122\) | 93.9149 | 0.769794 | ||||||||
\(123\) | − 120.000i | − 0.975610i | ||||||||
\(124\) | − 160.997i | − 1.29836i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 77.0000 | 0.611111 | ||||||||
\(127\) | 194.000i | 1.52756i | 0.645477 | + | 0.763780i | \(0.276659\pi\) | ||||
−0.645477 | + | 0.763780i | \(0.723341\pi\) | |||||||
\(128\) | − 119.000i | − 0.929688i | ||||||||
\(129\) | 152.053i | 1.17870i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 120.748i | − 0.921738i | −0.887468 | − | 0.460869i | \(-0.847538\pi\) | ||||
0.887468 | − | 0.460869i | \(-0.152462\pi\) | |||||||
\(132\) | 26.8328 | 0.203279 | ||||||||
\(133\) | −93.9149 | −0.706127 | ||||||||
\(134\) | 14.0000 | 0.104478 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 187.830i | 1.38110i | ||||||||
\(137\) | − 166.000i | − 1.21168i | −0.795587 | − | 0.605839i | \(-0.792837\pi\) | ||||
0.795587 | − | 0.605839i | \(-0.207163\pi\) | |||||||
\(138\) | −116.276 | −0.842576 | ||||||||
\(139\) | 93.9149i | 0.675646i | 0.941210 | + | 0.337823i | \(0.109691\pi\) | ||||
−0.941210 | + | 0.337823i | \(0.890309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 120.000 | 0.851064 | ||||||||
\(142\) | − 62.0000i | − 0.436620i | ||||||||
\(143\) | −26.8328 | −0.187642 | ||||||||
\(144\) | 55.0000 | 0.381944 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 53.6656i | 0.367573i | ||||||||
\(147\) | −219.135 | −1.49071 | ||||||||
\(148\) | 42.0000i | 0.283784i | ||||||||
\(149\) | 142.000 | 0.953020 | 0.476510 | − | 0.879169i | \(-0.341902\pi\) | ||||
0.476510 | + | 0.879169i | \(0.341902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | 0.0132450 | 0.00662252 | − | 0.999978i | \(-0.497892\pi\) | ||||
0.00662252 | + | 0.999978i | \(0.497892\pi\) | |||||||
\(152\) | 93.9149 | 0.617861 | ||||||||
\(153\) | −295.161 | −1.92916 | ||||||||
\(154\) | 14.0000 | 0.0909091 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −180.000 | −1.15385 | ||||||||
\(157\) | 67.0820 | 0.427274 | 0.213637 | − | 0.976913i | \(-0.431469\pi\) | ||||
0.213637 | + | 0.976913i | \(0.431469\pi\) | |||||||
\(158\) | 38.0000i | 0.240506i | ||||||||
\(159\) | 152.053i | 0.956306i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 182.000 | 1.13043 | ||||||||
\(162\) | 59.0000i | 0.364198i | ||||||||
\(163\) | 34.0000i | 0.208589i | 0.994546 | + | 0.104294i | \(0.0332584\pi\) | ||||
−0.994546 | + | 0.104294i | \(0.966742\pi\) | |||||||
\(164\) | − 80.4984i | − 0.490844i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 40.2492i | − 0.242465i | ||||||||
\(167\) | 107.331 | 0.642702 | 0.321351 | − | 0.946960i | \(-0.395863\pi\) | ||||
0.321351 | + | 0.946960i | \(0.395863\pi\) | |||||||
\(168\) | 219.135 | 1.30437 | ||||||||
\(169\) | 11.0000 | 0.0650888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 147.580i | 0.863044i | ||||||||
\(172\) | 102.000i | 0.593023i | ||||||||
\(173\) | 147.580 | 0.853066 | 0.426533 | − | 0.904472i | \(-0.359735\pi\) | ||||
0.426533 | + | 0.904472i | \(0.359735\pi\) | |||||||
\(174\) | − 98.3870i | − 0.565442i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.0000 | 0.0568182 | ||||||||
\(177\) | 180.000i | 1.01695i | ||||||||
\(178\) | 26.8328 | 0.150746 | ||||||||
\(179\) | −218.000 | −1.21788 | −0.608939 | − | 0.793217i | \(-0.708404\pi\) | ||||
−0.608939 | + | 0.793217i | \(0.708404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 254.912i | − 1.40835i | −0.710025 | − | 0.704176i | \(-0.751317\pi\) | ||||
0.710025 | − | 0.704176i | \(-0.248683\pi\) | |||||||
\(182\) | −93.9149 | −0.516016 | ||||||||
\(183\) | 420.000i | 2.29508i | ||||||||
\(184\) | −182.000 | −0.989130 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −240.000 | −1.29032 | ||||||||
\(187\) | −53.6656 | −0.286982 | ||||||||
\(188\) | 80.4984 | 0.428183 | ||||||||
\(189\) | 62.6099i | 0.331269i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −58.0000 | −0.303665 | −0.151832 | − | 0.988406i | \(-0.548517\pi\) | ||||
−0.151832 | + | 0.988406i | \(0.548517\pi\) | |||||||
\(192\) | −58.1378 | −0.302801 | ||||||||
\(193\) | − 206.000i | − 1.06736i | −0.845687 | − | 0.533679i | \(-0.820809\pi\) | ||||
0.845687 | − | 0.533679i | \(-0.179191\pi\) | |||||||
\(194\) | − 26.8328i | − 0.138313i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −147.000 | −0.750000 | ||||||||
\(197\) | − 226.000i | − 1.14721i | −0.819133 | − | 0.573604i | \(-0.805545\pi\) | ||||
0.819133 | − | 0.573604i | \(-0.194455\pi\) | |||||||
\(198\) | − 22.0000i | − 0.111111i | ||||||||
\(199\) | − 134.164i | − 0.674191i | −0.941470 | − | 0.337096i | \(-0.890555\pi\) | ||||
0.941470 | − | 0.337096i | \(-0.109445\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 62.6099i | 0.311492i | ||||||||
\(202\) | 67.0820 | 0.332089 | ||||||||
\(203\) | 154.000i | 0.758621i | ||||||||
\(204\) | −360.000 | −1.76471 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 160.997i | − 0.781538i | ||||||||
\(207\) | − 286.000i | − 1.38164i | ||||||||
\(208\) | −67.0820 | −0.322510 | ||||||||
\(209\) | 26.8328i | 0.128387i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −118.000 | −0.559242 | −0.279621 | − | 0.960111i | \(-0.590209\pi\) | ||||
−0.279621 | + | 0.960111i | \(0.590209\pi\) | |||||||
\(212\) | 102.000i | 0.481132i | ||||||||
\(213\) | 277.272 | 1.30175 | ||||||||
\(214\) | −106.000 | −0.495327 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − 62.6099i | − 0.289861i | ||||||||
\(217\) | 375.659 | 1.73115 | ||||||||
\(218\) | − 142.000i | − 0.651376i | ||||||||
\(219\) | −240.000 | −1.09589 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 360.000 | 1.62896 | ||||||||
\(222\) | 62.6099 | 0.282027 | ||||||||
\(223\) | 80.4984 | 0.360980 | 0.180490 | − | 0.983577i | \(-0.442232\pi\) | ||||
0.180490 | + | 0.983577i | \(0.442232\pi\) | |||||||
\(224\) | 231.000 | 1.03125 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 34.0000 | 0.150442 | ||||||||
\(227\) | −254.912 | −1.12296 | −0.561480 | − | 0.827491i | \(-0.689768\pi\) | ||||
−0.561480 | + | 0.827491i | \(0.689768\pi\) | |||||||
\(228\) | 180.000i | 0.789474i | ||||||||
\(229\) | − 13.4164i | − 0.0585869i | −0.999571 | − | 0.0292935i | \(-0.990674\pi\) | ||||
0.999571 | − | 0.0292935i | \(-0.00932573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 62.6099i | 0.271039i | ||||||||
\(232\) | − 154.000i | − 0.663793i | ||||||||
\(233\) | 214.000i | 0.918455i | 0.888319 | + | 0.459227i | \(0.151874\pi\) | ||||
−0.888319 | + | 0.459227i | \(0.848126\pi\) | |||||||
\(234\) | 147.580i | 0.630686i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 120.748i | 0.511643i | ||||||||
\(237\) | −169.941 | −0.717051 | ||||||||
\(238\) | −187.830 | −0.789200 | ||||||||
\(239\) | −98.0000 | −0.410042 | −0.205021 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205021 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 160.997i | − 0.668037i | −0.942567 | − | 0.334018i | \(-0.891595\pi\) | ||||
0.942567 | − | 0.334018i | \(-0.108405\pi\) | |||||||
\(242\) | 117.000i | 0.483471i | ||||||||
\(243\) | −344.354 | −1.41710 | ||||||||
\(244\) | 281.745i | 1.15469i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −120.000 | −0.487805 | ||||||||
\(247\) | − 180.000i | − 0.728745i | ||||||||
\(248\) | −375.659 | −1.51476 | ||||||||
\(249\) | 180.000 | 0.722892 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 335.410i | 1.33630i | 0.744029 | + | 0.668148i | \(0.232913\pi\) | ||||
−0.744029 | + | 0.668148i | \(0.767087\pi\) | |||||||
\(252\) | 231.000i | 0.916667i | ||||||||
\(253\) | − 52.0000i | − 0.205534i | ||||||||
\(254\) | 194.000 | 0.763780 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | 134.164 | 0.522039 | 0.261020 | − | 0.965333i | \(-0.415941\pi\) | ||||
0.261020 | + | 0.965333i | \(0.415941\pi\) | |||||||
\(258\) | 152.053 | 0.589351 | ||||||||
\(259\) | −98.0000 | −0.378378 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 242.000 | 0.927203 | ||||||||
\(262\) | −120.748 | −0.460869 | ||||||||
\(263\) | 34.0000i | 0.129278i | 0.997909 | + | 0.0646388i | \(0.0205895\pi\) | ||||
−0.997909 | + | 0.0646388i | \(0.979410\pi\) | |||||||
\(264\) | − 62.6099i | − 0.237159i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 93.9149i | 0.353063i | ||||||||
\(267\) | 120.000i | 0.449438i | ||||||||
\(268\) | 42.0000i | 0.156716i | ||||||||
\(269\) | − 254.912i | − 0.947627i | −0.880625 | − | 0.473814i | \(-0.842877\pi\) | ||||
0.880625 | − | 0.473814i | \(-0.157123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 321.994i | 1.18817i | 0.804403 | + | 0.594084i | \(0.202486\pi\) | ||||
−0.804403 | + | 0.594084i | \(0.797514\pi\) | |||||||
\(272\) | −134.164 | −0.493250 | ||||||||
\(273\) | − 420.000i | − 1.53846i | ||||||||
\(274\) | −166.000 | −0.605839 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − 348.827i | − 1.26386i | ||||||||
\(277\) | 14.0000i | 0.0505415i | 0.999681 | + | 0.0252708i | \(0.00804479\pi\) | ||||
−0.999681 | + | 0.0252708i | \(0.991955\pi\) | |||||||
\(278\) | 93.9149 | 0.337823 | ||||||||
\(279\) | − 590.322i | − 2.11585i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.00711744 | 0.00355872 | − | 0.999994i | \(-0.498867\pi\) | ||||
0.00355872 | + | 0.999994i | \(0.498867\pi\) | |||||||
\(282\) | − 120.000i | − 0.425532i | ||||||||
\(283\) | −93.9149 | −0.331855 | −0.165927 | − | 0.986138i | \(-0.553062\pi\) | ||||
−0.165927 | + | 0.986138i | \(0.553062\pi\) | |||||||
\(284\) | 186.000 | 0.654930 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.8328i | 0.0938210i | ||||||||
\(287\) | 187.830 | 0.654459 | ||||||||
\(288\) | − 363.000i | − 1.26042i | ||||||||
\(289\) | 431.000 | 1.49135 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 120.000 | 0.412371 | ||||||||
\(292\) | −160.997 | −0.551359 | ||||||||
\(293\) | 335.410 | 1.14474 | 0.572372 | − | 0.819994i | \(-0.306023\pi\) | ||||
0.572372 | + | 0.819994i | \(0.306023\pi\) | |||||||
\(294\) | 219.135i | 0.745356i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 98.0000 | 0.331081 | ||||||||
\(297\) | 17.8885 | 0.0602308 | ||||||||
\(298\) | − 142.000i | − 0.476510i | ||||||||
\(299\) | 348.827i | 1.16664i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −238.000 | −0.790698 | ||||||||
\(302\) | − 2.00000i | − 0.00662252i | ||||||||
\(303\) | 300.000i | 0.990099i | ||||||||
\(304\) | 67.0820i | 0.220665i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 295.161i | 0.964578i | ||||||||
\(307\) | −201.246 | −0.655525 | −0.327762 | − | 0.944760i | \(-0.606295\pi\) | ||||
−0.327762 | + | 0.944760i | \(0.606295\pi\) | |||||||
\(308\) | 42.0000i | 0.136364i | ||||||||
\(309\) | 720.000 | 2.33010 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 509.823i | − 1.63930i | −0.572862 | − | 0.819652i | \(-0.694167\pi\) | ||||
0.572862 | − | 0.819652i | \(-0.305833\pi\) | |||||||
\(312\) | 420.000i | 1.34615i | ||||||||
\(313\) | 321.994 | 1.02873 | 0.514367 | − | 0.857570i | \(-0.328027\pi\) | ||||
0.514367 | + | 0.857570i | \(0.328027\pi\) | |||||||
\(314\) | − 67.0820i | − 0.213637i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −114.000 | −0.360759 | ||||||||
\(317\) | 374.000i | 1.17981i | 0.807472 | + | 0.589905i | \(0.200835\pi\) | ||||
−0.807472 | + | 0.589905i | \(0.799165\pi\) | |||||||
\(318\) | 152.053 | 0.478153 | ||||||||
\(319\) | 44.0000 | 0.137931 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 474.046i | − 1.47678i | ||||||||
\(322\) | − 182.000i | − 0.565217i | ||||||||
\(323\) | − 360.000i | − 1.11455i | ||||||||
\(324\) | −177.000 | −0.546296 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 34.0000 | 0.104294 | ||||||||
\(327\) | 635.043 | 1.94203 | ||||||||
\(328\) | −187.830 | −0.572652 | ||||||||
\(329\) | 187.830i | 0.570911i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 482.000 | 1.45619 | 0.728097 | − | 0.685474i | \(-0.240405\pi\) | ||||
0.728097 | + | 0.685474i | \(0.240405\pi\) | |||||||
\(332\) | 120.748 | 0.363698 | ||||||||
\(333\) | 154.000i | 0.462462i | ||||||||
\(334\) | − 107.331i | − 0.321351i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 156.525i | 0.465847i | ||||||||
\(337\) | 494.000i | 1.46588i | 0.680296 | + | 0.732938i | \(0.261851\pi\) | ||||
−0.680296 | + | 0.732938i | \(0.738149\pi\) | |||||||
\(338\) | − 11.0000i | − 0.0325444i | ||||||||
\(339\) | 152.053i | 0.448533i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 107.331i | − 0.314754i | ||||||||
\(342\) | 147.580 | 0.431522 | ||||||||
\(343\) | − 343.000i | − 1.00000i | ||||||||
\(344\) | 238.000 | 0.691860 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 147.580i | − 0.426533i | ||||||||
\(347\) | − 346.000i | − 0.997118i | −0.866856 | − | 0.498559i | \(-0.833863\pi\) | ||||
0.866856 | − | 0.498559i | \(-0.166137\pi\) | |||||||
\(348\) | 295.161 | 0.848164 | ||||||||
\(349\) | 335.410i | 0.961061i | 0.876978 | + | 0.480530i | \(0.159556\pi\) | ||||
−0.876978 | + | 0.480530i | \(0.840444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −120.000 | −0.341880 | ||||||||
\(352\) | − 66.0000i | − 0.187500i | ||||||||
\(353\) | 26.8328 | 0.0760136 | 0.0380068 | − | 0.999277i | \(-0.487899\pi\) | ||||
0.0380068 | + | 0.999277i | \(0.487899\pi\) | |||||||
\(354\) | 180.000 | 0.508475 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 80.4984i | 0.226119i | ||||||||
\(357\) | − 840.000i | − 2.35294i | ||||||||
\(358\) | 218.000i | 0.608939i | ||||||||
\(359\) | −338.000 | −0.941504 | −0.470752 | − | 0.882266i | \(-0.656017\pi\) | ||||
−0.470752 | + | 0.882266i | \(0.656017\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 181.000 | 0.501385 | ||||||||
\(362\) | −254.912 | −0.704176 | ||||||||
\(363\) | −523.240 | −1.44143 | ||||||||
\(364\) | − 281.745i | − 0.774024i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 420.000 | 1.14754 | ||||||||
\(367\) | −295.161 | −0.804253 | −0.402127 | − | 0.915584i | \(-0.631729\pi\) | ||||
−0.402127 | + | 0.915584i | \(0.631729\pi\) | |||||||
\(368\) | − 130.000i | − 0.353261i | ||||||||
\(369\) | − 295.161i | − 0.799894i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −238.000 | −0.641509 | ||||||||
\(372\) | − 720.000i | − 1.93548i | ||||||||
\(373\) | − 86.0000i | − 0.230563i | −0.993333 | − | 0.115282i | \(-0.963223\pi\) | ||||
0.993333 | − | 0.115282i | \(-0.0367770\pi\) | |||||||
\(374\) | 53.6656i | 0.143491i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 187.830i | − 0.499547i | ||||||||
\(377\) | −295.161 | −0.782920 | ||||||||
\(378\) | 62.6099 | 0.165635 | ||||||||
\(379\) | 262.000 | 0.691293 | 0.345646 | − | 0.938365i | \(-0.387660\pi\) | ||||
0.345646 | + | 0.938365i | \(0.387660\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 867.594i | 2.27715i | ||||||||
\(382\) | 58.0000i | 0.151832i | ||||||||
\(383\) | −563.489 | −1.47125 | −0.735625 | − | 0.677388i | \(-0.763112\pi\) | ||||
−0.735625 | + | 0.677388i | \(0.763112\pi\) | |||||||
\(384\) | − 532.184i | − 1.38590i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −206.000 | −0.533679 | ||||||||
\(387\) | 374.000i | 0.966408i | ||||||||
\(388\) | 80.4984 | 0.207470 | ||||||||
\(389\) | −698.000 | −1.79434 | −0.897172 | − | 0.441681i | \(-0.854382\pi\) | ||||
−0.897172 | + | 0.441681i | \(0.854382\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 697.653i | 1.78428i | ||||||||
\(392\) | 343.000i | 0.875000i | ||||||||
\(393\) | − 540.000i | − 1.37405i | ||||||||
\(394\) | −226.000 | −0.573604 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 66.0000 | 0.166667 | ||||||||
\(397\) | −308.577 | −0.777273 | −0.388636 | − | 0.921391i | \(-0.627054\pi\) | ||||
−0.388636 | + | 0.921391i | \(0.627054\pi\) | |||||||
\(398\) | −134.164 | −0.337096 | ||||||||
\(399\) | −420.000 | −1.05263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −538.000 | −1.34165 | −0.670823 | − | 0.741618i | \(-0.734059\pi\) | ||||
−0.670823 | + | 0.741618i | \(0.734059\pi\) | |||||||
\(402\) | 62.6099 | 0.155746 | ||||||||
\(403\) | 720.000i | 1.78660i | ||||||||
\(404\) | 201.246i | 0.498134i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 154.000 | 0.379310 | ||||||||
\(407\) | 28.0000i | 0.0687961i | ||||||||
\(408\) | 840.000i | 2.05882i | ||||||||
\(409\) | − 295.161i | − 0.721665i | −0.932631 | − | 0.360832i | \(-0.882493\pi\) | ||||
0.932631 | − | 0.360832i | \(-0.117507\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 742.375i | − 1.80626i | ||||||||
\(412\) | 482.991 | 1.17231 | ||||||||
\(413\) | −281.745 | −0.682190 | ||||||||
\(414\) | −286.000 | −0.690821 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 442.741i | 1.06428i | ||||||||
\(417\) | 420.000i | 1.00719i | ||||||||
\(418\) | 26.8328 | 0.0641933 | ||||||||
\(419\) | 818.401i | 1.95322i | 0.215009 | + | 0.976612i | \(0.431022\pi\) | ||||
−0.215009 | + | 0.976612i | \(0.568978\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −118.000 | −0.280285 | −0.140143 | − | 0.990131i | \(-0.544756\pi\) | ||||
−0.140143 | + | 0.990131i | \(0.544756\pi\) | |||||||
\(422\) | 118.000i | 0.279621i | ||||||||
\(423\) | 295.161 | 0.697780 | ||||||||
\(424\) | 238.000 | 0.561321 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − 277.272i | − 0.650874i | ||||||||
\(427\) | −657.404 | −1.53959 | ||||||||
\(428\) | − 318.000i | − 0.742991i | ||||||||
\(429\) | −120.000 | −0.279720 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −718.000 | −1.66589 | −0.832947 | − | 0.553353i | \(-0.813348\pi\) | ||||
−0.832947 | + | 0.553353i | \(0.813348\pi\) | |||||||
\(432\) | 44.7214 | 0.103522 | ||||||||
\(433\) | 509.823 | 1.17742 | 0.588711 | − | 0.808344i | \(-0.299636\pi\) | ||||
0.588711 | + | 0.808344i | \(0.299636\pi\) | |||||||
\(434\) | − 375.659i | − 0.865575i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 426.000 | 0.977064 | ||||||||
\(437\) | 348.827 | 0.798230 | ||||||||
\(438\) | 240.000i | 0.547945i | ||||||||
\(439\) | 26.8328i | 0.0611226i | 0.999533 | + | 0.0305613i | \(0.00972948\pi\) | ||||
−0.999533 | + | 0.0305613i | \(0.990271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −539.000 | −1.22222 | ||||||||
\(442\) | − 360.000i | − 0.814480i | ||||||||
\(443\) | 634.000i | 1.43115i | 0.698535 | + | 0.715576i | \(0.253836\pi\) | ||||
−0.698535 | + | 0.715576i | \(0.746164\pi\) | |||||||
\(444\) | 187.830i | 0.423040i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 80.4984i | − 0.180490i | ||||||||
\(447\) | 635.043 | 1.42068 | ||||||||
\(448\) | − 91.0000i | − 0.203125i | ||||||||
\(449\) | −338.000 | −0.752784 | −0.376392 | − | 0.926461i | \(-0.622835\pi\) | ||||
−0.376392 | + | 0.926461i | \(0.622835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 53.6656i | − 0.118993i | ||||||||
\(452\) | 102.000i | 0.225664i | ||||||||
\(453\) | 8.94427 | 0.0197445 | ||||||||
\(454\) | 254.912i | 0.561480i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 420.000 | 0.921053 | ||||||||
\(457\) | − 466.000i | − 1.01969i | −0.860265 | − | 0.509847i | \(-0.829702\pi\) | ||||
0.860265 | − | 0.509847i | \(-0.170298\pi\) | |||||||
\(458\) | −13.4164 | −0.0292935 | ||||||||
\(459\) | −240.000 | −0.522876 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 442.741i | − 0.960394i | −0.877161 | − | 0.480197i | \(-0.840565\pi\) | ||||
0.877161 | − | 0.480197i | \(-0.159435\pi\) | |||||||
\(462\) | 62.6099 | 0.135519 | ||||||||
\(463\) | − 206.000i | − 0.444924i | −0.974941 | − | 0.222462i | \(-0.928591\pi\) | ||||
0.974941 | − | 0.222462i | \(-0.0714094\pi\) | |||||||
\(464\) | 110.000 | 0.237069 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 214.000 | 0.459227 | ||||||||
\(467\) | −362.243 | −0.775681 | −0.387840 | − | 0.921727i | \(-0.626779\pi\) | ||||
−0.387840 | + | 0.921727i | \(0.626779\pi\) | |||||||
\(468\) | −442.741 | −0.946029 | ||||||||
\(469\) | −98.0000 | −0.208955 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 300.000 | 0.636943 | ||||||||
\(472\) | 281.745 | 0.596916 | ||||||||
\(473\) | 68.0000i | 0.143763i | ||||||||
\(474\) | 169.941i | 0.358526i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 563.489i | − 1.18380i | ||||||||
\(477\) | 374.000i | 0.784067i | ||||||||
\(478\) | 98.0000i | 0.205021i | ||||||||
\(479\) | − 214.663i | − 0.448147i | −0.974572 | − | 0.224074i | \(-0.928064\pi\) | ||||
0.974572 | − | 0.224074i | \(-0.0719356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 187.830i | − 0.390498i | ||||||||
\(482\) | −160.997 | −0.334018 | ||||||||
\(483\) | 813.929 | 1.68515 | ||||||||
\(484\) | −351.000 | −0.725207 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 344.354i | 0.708548i | ||||||||
\(487\) | − 166.000i | − 0.340862i | −0.985370 | − | 0.170431i | \(-0.945484\pi\) | ||||
0.985370 | − | 0.170431i | \(-0.0545161\pi\) | |||||||
\(488\) | 657.404 | 1.34714 | ||||||||
\(489\) | 152.053i | 0.310946i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −838.000 | −1.70672 | −0.853360 | − | 0.521321i | \(-0.825439\pi\) | ||||
−0.853360 | + | 0.521321i | \(0.825439\pi\) | |||||||
\(492\) | − 360.000i | − 0.731707i | ||||||||
\(493\) | −590.322 | −1.19741 | ||||||||
\(494\) | −180.000 | −0.364372 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 268.328i | − 0.540984i | ||||||||
\(497\) | 434.000i | 0.873239i | ||||||||
\(498\) | − 180.000i | − 0.361446i | ||||||||
\(499\) | 262.000 | 0.525050 | 0.262525 | − | 0.964925i | \(-0.415445\pi\) | ||||
0.262525 | + | 0.964925i | \(0.415445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 480.000 | 0.958084 | ||||||||
\(502\) | 335.410 | 0.668148 | ||||||||
\(503\) | 429.325 | 0.853529 | 0.426764 | − | 0.904363i | \(-0.359653\pi\) | ||||
0.426764 | + | 0.904363i | \(0.359653\pi\) | |||||||
\(504\) | 539.000 | 1.06944 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −52.0000 | −0.102767 | ||||||||
\(507\) | 49.1935 | 0.0970286 | ||||||||
\(508\) | 582.000i | 1.14567i | ||||||||
\(509\) | − 898.899i | − 1.76601i | −0.469363 | − | 0.883005i | \(-0.655516\pi\) | ||||
0.469363 | − | 0.883005i | \(-0.344484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 375.659i | − 0.735146i | ||||||||
\(512\) | − 305.000i | − 0.595703i | ||||||||
\(513\) | 120.000i | 0.233918i | ||||||||
\(514\) | − 134.164i | − 0.261020i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 456.158i | 0.884027i | ||||||||
\(517\) | 53.6656 | 0.103802 | ||||||||
\(518\) | 98.0000i | 0.189189i | ||||||||
\(519\) | 660.000 | 1.27168 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 724.486i | 1.39057i | 0.718735 | + | 0.695284i | \(0.244721\pi\) | ||||
−0.718735 | + | 0.695284i | \(0.755279\pi\) | |||||||
\(522\) | − 242.000i | − 0.463602i | ||||||||
\(523\) | −523.240 | −1.00046 | −0.500229 | − | 0.865893i | \(-0.666751\pi\) | ||||
−0.500229 | + | 0.865893i | \(0.666751\pi\) | |||||||
\(524\) | − 362.243i | − 0.691303i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.0000 | 0.0646388 | ||||||||
\(527\) | 1440.00i | 2.73245i | ||||||||
\(528\) | 44.7214 | 0.0846995 | ||||||||
\(529\) | −147.000 | −0.277883 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 442.741i | 0.833788i | ||||||||
\(532\) | −281.745 | −0.529595 | ||||||||
\(533\) | 360.000i | 0.675422i | ||||||||
\(534\) | 120.000 | 0.224719 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 98.0000 | 0.182836 | ||||||||
\(537\) | −974.926 | −1.81550 | ||||||||
\(538\) | −254.912 | −0.473814 | ||||||||
\(539\) | −98.0000 | −0.181818 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 842.000 | 1.55638 | 0.778189 | − | 0.628031i | \(-0.216139\pi\) | ||||
0.778189 | + | 0.628031i | \(0.216139\pi\) | |||||||
\(542\) | 321.994 | 0.594084 | ||||||||
\(543\) | − 1140.00i | − 2.09945i | ||||||||
\(544\) | 885.483i | 1.62773i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −420.000 | −0.769231 | ||||||||
\(547\) | 134.000i | 0.244973i | 0.992470 | + | 0.122486i | \(0.0390868\pi\) | ||||
−0.992470 | + | 0.122486i | \(0.960913\pi\) | |||||||
\(548\) | − 498.000i | − 0.908759i | ||||||||
\(549\) | 1033.06i | 1.88172i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 295.161i | 0.535682i | ||||||||
\(552\) | −813.929 | −1.47451 | ||||||||
\(553\) | − 266.000i | − 0.481013i | ||||||||
\(554\) | 14.0000 | 0.0252708 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 281.745i | 0.506735i | ||||||||
\(557\) | − 706.000i | − 1.26750i | −0.773536 | − | 0.633752i | \(-0.781514\pi\) | ||||
0.773536 | − | 0.633752i | \(-0.218486\pi\) | |||||||
\(558\) | −590.322 | −1.05792 | ||||||||
\(559\) | − 456.158i | − 0.816025i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −240.000 | −0.427807 | ||||||||
\(562\) | − 2.00000i | − 0.00355872i | ||||||||
\(563\) | −13.4164 | −0.0238302 | −0.0119151 | − | 0.999929i | \(-0.503793\pi\) | ||||
−0.0119151 | + | 0.999929i | \(0.503793\pi\) | |||||||
\(564\) | 360.000 | 0.638298 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 93.9149i | 0.165927i | ||||||||
\(567\) | − 413.000i | − 0.728395i | ||||||||
\(568\) | − 434.000i | − 0.764085i | ||||||||
\(569\) | 82.0000 | 0.144112 | 0.0720562 | − | 0.997401i | \(-0.477044\pi\) | ||||
0.0720562 | + | 0.997401i | \(0.477044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −118.000 | −0.206655 | −0.103327 | − | 0.994647i | \(-0.532949\pi\) | ||||
−0.103327 | + | 0.994647i | \(0.532949\pi\) | |||||||
\(572\) | −80.4984 | −0.140732 | ||||||||
\(573\) | −259.384 | −0.452677 | ||||||||
\(574\) | − 187.830i | − 0.327229i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −143.000 | −0.248264 | ||||||||
\(577\) | 885.483 | 1.53463 | 0.767316 | − | 0.641269i | \(-0.221592\pi\) | ||||
0.767316 | + | 0.641269i | \(0.221592\pi\) | |||||||
\(578\) | − 431.000i | − 0.745675i | ||||||||
\(579\) | − 921.260i | − 1.59112i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 281.745i | 0.484930i | ||||||||
\(582\) | − 120.000i | − 0.206186i | ||||||||
\(583\) | 68.0000i | 0.116638i | ||||||||
\(584\) | 375.659i | 0.643252i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 335.410i | − 0.572372i | ||||||||
\(587\) | 791.568 | 1.34850 | 0.674249 | − | 0.738504i | \(-0.264468\pi\) | ||||
0.674249 | + | 0.738504i | \(0.264468\pi\) | |||||||
\(588\) | −657.404 | −1.11803 | ||||||||
\(589\) | 720.000 | 1.22241 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 1010.70i | − 1.71016i | ||||||||
\(592\) | 70.0000i | 0.118243i | ||||||||
\(593\) | −134.164 | −0.226246 | −0.113123 | − | 0.993581i | \(-0.536085\pi\) | ||||
−0.113123 | + | 0.993581i | \(0.536085\pi\) | |||||||
\(594\) | − 17.8885i | − 0.0301154i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 426.000 | 0.714765 | ||||||||
\(597\) | − 600.000i | − 1.00503i | ||||||||
\(598\) | 348.827 | 0.583322 | ||||||||
\(599\) | −398.000 | −0.664441 | −0.332220 | − | 0.943202i | \(-0.607798\pi\) | ||||
−0.332220 | + | 0.943202i | \(0.607798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 134.164i | 0.223235i | 0.993751 | + | 0.111617i | \(0.0356031\pi\) | ||||
−0.993751 | + | 0.111617i | \(0.964397\pi\) | |||||||
\(602\) | 238.000i | 0.395349i | ||||||||
\(603\) | 154.000i | 0.255390i | ||||||||
\(604\) | 6.00000 | 0.00993377 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 300.000 | 0.495050 | ||||||||
\(607\) | 939.149 | 1.54720 | 0.773598 | − | 0.633676i | \(-0.218455\pi\) | ||||
0.773598 | + | 0.633676i | \(0.218455\pi\) | |||||||
\(608\) | 442.741 | 0.728193 | ||||||||
\(609\) | 688.709i | 1.13088i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −360.000 | −0.589198 | ||||||||
\(612\) | −885.483 | −1.44687 | ||||||||
\(613\) | − 206.000i | − 0.336052i | −0.985783 | − | 0.168026i | \(-0.946261\pi\) | ||||
0.985783 | − | 0.168026i | \(-0.0537393\pi\) | |||||||
\(614\) | 201.246i | 0.327762i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 98.0000 | 0.159091 | ||||||||
\(617\) | 494.000i | 0.800648i | 0.916374 | + | 0.400324i | \(0.131102\pi\) | ||||
−0.916374 | + | 0.400324i | \(0.868898\pi\) | |||||||
\(618\) | − 720.000i | − 1.16505i | ||||||||
\(619\) | − 120.748i | − 0.195069i | −0.995232 | − | 0.0975345i | \(-0.968904\pi\) | ||||
0.995232 | − | 0.0975345i | \(-0.0310956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 232.551i | − 0.374478i | ||||||||
\(622\) | −509.823 | −0.819652 | ||||||||
\(623\) | −187.830 | −0.301492 | ||||||||
\(624\) | −300.000 | −0.480769 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 321.994i | − 0.514367i | ||||||||
\(627\) | 120.000i | 0.191388i | ||||||||
\(628\) | 201.246 | 0.320456 | ||||||||
\(629\) | − 375.659i | − 0.597233i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 542.000 | 0.858954 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(632\) | 266.000i | 0.420886i | ||||||||
\(633\) | −527.712 | −0.833668 | ||||||||
\(634\) | 374.000 | 0.589905 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 456.158i | 0.717229i | ||||||||
\(637\) | 657.404 | 1.03203 | ||||||||
\(638\) | − 44.0000i | − 0.0689655i | ||||||||
\(639\) | 682.000 | 1.06729 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −298.000 | −0.464899 | −0.232449 | − | 0.972609i | \(-0.574674\pi\) | ||||
−0.232449 | + | 0.972609i | \(0.574674\pi\) | |||||||
\(642\) | −474.046 | −0.738390 | ||||||||
\(643\) | 1006.23 | 1.56490 | 0.782450 | − | 0.622714i | \(-0.213970\pi\) | ||||
0.782450 | + | 0.622714i | \(0.213970\pi\) | |||||||
\(644\) | 546.000 | 0.847826 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −360.000 | −0.557276 | ||||||||
\(647\) | −643.988 | −0.995344 | −0.497672 | − | 0.867365i | \(-0.665812\pi\) | ||||
−0.497672 | + | 0.867365i | \(0.665812\pi\) | |||||||
\(648\) | 413.000i | 0.637346i | ||||||||
\(649\) | 80.4984i | 0.124035i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1680.00 | 2.58065 | ||||||||
\(652\) | 102.000i | 0.156442i | ||||||||
\(653\) | 154.000i | 0.235835i | 0.993023 | + | 0.117917i | \(0.0376218\pi\) | ||||
−0.993023 | + | 0.117917i | \(0.962378\pi\) | |||||||
\(654\) | − 635.043i | − 0.971014i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 134.164i | − 0.204518i | ||||||||
\(657\) | −590.322 | −0.898511 | ||||||||
\(658\) | 187.830 | 0.285455 | ||||||||
\(659\) | −338.000 | −0.512898 | −0.256449 | − | 0.966558i | \(-0.582553\pi\) | ||||
−0.256449 | + | 0.966558i | \(0.582553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 576.906i | − 0.872777i | −0.899758 | − | 0.436388i | \(-0.856257\pi\) | ||||
0.899758 | − | 0.436388i | \(-0.143743\pi\) | |||||||
\(662\) | − 482.000i | − 0.728097i | ||||||||
\(663\) | 1609.97 | 2.42831 | ||||||||
\(664\) | − 281.745i | − 0.424314i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 154.000 | 0.231231 | ||||||||
\(667\) | − 572.000i | − 0.857571i | ||||||||
\(668\) | 321.994 | 0.482027 | ||||||||
\(669\) | 360.000 | 0.538117 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 187.830i | 0.279925i | ||||||||
\(672\) | 1033.06 | 1.53730 | ||||||||
\(673\) | 814.000i | 1.20951i | 0.796412 | + | 0.604755i | \(0.206729\pi\) | ||||
−0.796412 | + | 0.604755i | \(0.793271\pi\) | |||||||
\(674\) | 494.000 | 0.732938 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.0000 | 0.0488166 | ||||||||
\(677\) | 684.237 | 1.01069 | 0.505345 | − | 0.862918i | \(-0.331365\pi\) | ||||
0.505345 | + | 0.862918i | \(0.331365\pi\) | |||||||
\(678\) | 152.053 | 0.224266 | ||||||||
\(679\) | 187.830i | 0.276627i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1140.00 | −1.67401 | ||||||||
\(682\) | −107.331 | −0.157377 | ||||||||
\(683\) | − 926.000i | − 1.35578i | −0.735162 | − | 0.677892i | \(-0.762894\pi\) | ||||
0.735162 | − | 0.677892i | \(-0.237106\pi\) | |||||||
\(684\) | 442.741i | 0.647283i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −343.000 | −0.500000 | ||||||||
\(687\) | − 60.0000i | − 0.0873362i | ||||||||
\(688\) | 170.000i | 0.247093i | ||||||||
\(689\) | − 456.158i | − 0.662058i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 576.906i | 0.834885i | 0.908703 | + | 0.417443i | \(0.137073\pi\) | ||||
−0.908703 | + | 0.417443i | \(0.862927\pi\) | |||||||
\(692\) | 442.741 | 0.639800 | ||||||||
\(693\) | 154.000i | 0.222222i | ||||||||
\(694\) | −346.000 | −0.498559 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − 688.709i | − 0.989524i | ||||||||
\(697\) | 720.000i | 1.03300i | ||||||||
\(698\) | 335.410 | 0.480530 | ||||||||
\(699\) | 957.037i | 1.36915i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 362.000 | 0.516405 | 0.258203 | − | 0.966091i | \(-0.416870\pi\) | ||||
0.258203 | + | 0.966091i | \(0.416870\pi\) | |||||||
\(702\) | 120.000i | 0.170940i | ||||||||
\(703\) | −187.830 | −0.267183 | ||||||||
\(704\) | −26.0000 | −0.0369318 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 26.8328i | − 0.0380068i | ||||||||
\(707\) | −469.574 | −0.664179 | ||||||||
\(708\) | 540.000i | 0.762712i | ||||||||
\(709\) | −1058.00 | −1.49224 | −0.746121 | − | 0.665810i | \(-0.768086\pi\) | ||||
−0.746121 | + | 0.665810i | \(0.768086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −418.000 | −0.587904 | ||||||||
\(712\) | 187.830 | 0.263806 | ||||||||
\(713\) | −1395.31 | −1.95695 | ||||||||
\(714\) | −840.000 | −1.17647 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −654.000 | −0.913408 | ||||||||
\(717\) | −438.269 | −0.611254 | ||||||||
\(718\) | 338.000i | 0.470752i | ||||||||
\(719\) | 482.991i | 0.671753i | 0.941906 | + | 0.335877i | \(0.109033\pi\) | ||||
−0.941906 | + | 0.335877i | \(0.890967\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1126.98i | 1.56308i | ||||||||
\(722\) | − 181.000i | − 0.250693i | ||||||||
\(723\) | − 720.000i | − 0.995851i | ||||||||
\(724\) | − 764.735i | − 1.05626i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 523.240i | 0.720716i | ||||||||
\(727\) | −1126.98 | −1.55018 | −0.775088 | − | 0.631853i | \(-0.782295\pi\) | ||||
−0.775088 | + | 0.631853i | \(0.782295\pi\) | |||||||
\(728\) | −657.404 | −0.903027 | ||||||||
\(729\) | −1009.00 | −1.38409 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 912.316i | − 1.24804i | ||||||||
\(732\) | 1260.00i | 1.72131i | ||||||||
\(733\) | −1301.39 | −1.77543 | −0.887716 | − | 0.460392i | \(-0.847709\pi\) | ||||
−0.887716 | + | 0.460392i | \(0.847709\pi\) | |||||||
\(734\) | 295.161i | 0.402127i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −858.000 | −1.16576 | ||||||||
\(737\) | 28.0000i | 0.0379919i | ||||||||
\(738\) | −295.161 | −0.399947 | ||||||||
\(739\) | 982.000 | 1.32882 | 0.664411 | − | 0.747367i | \(-0.268682\pi\) | ||||
0.664411 | + | 0.747367i | \(0.268682\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 804.984i | − 1.08635i | ||||||||
\(742\) | 238.000i | 0.320755i | ||||||||
\(743\) | 694.000i | 0.934051i | 0.884244 | + | 0.467026i | \(0.154674\pi\) | ||||
−0.884244 | + | 0.467026i | \(0.845326\pi\) | |||||||
\(744\) | −1680.00 | −2.25806 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −86.0000 | −0.115282 | ||||||||
\(747\) | 442.741 | 0.592693 | ||||||||
\(748\) | −160.997 | −0.215236 | ||||||||
\(749\) | 742.000 | 0.990654 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 242.000 | 0.322237 | 0.161119 | − | 0.986935i | \(-0.448490\pi\) | ||||
0.161119 | + | 0.986935i | \(0.448490\pi\) | |||||||
\(752\) | 134.164 | 0.178410 | ||||||||
\(753\) | 1500.00i | 1.99203i | ||||||||
\(754\) | 295.161i | 0.391460i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 187.830i | 0.248452i | ||||||||
\(757\) | − 106.000i | − 0.140026i | −0.997546 | − | 0.0700132i | \(-0.977696\pi\) | ||||
0.997546 | − | 0.0700132i | \(-0.0223041\pi\) | |||||||
\(758\) | − 262.000i | − 0.345646i | ||||||||
\(759\) | − 232.551i | − 0.306391i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1100.15i | 1.44566i | 0.691027 | + | 0.722829i | \(0.257158\pi\) | ||||
−0.691027 | + | 0.722829i | \(0.742842\pi\) | |||||||
\(762\) | 867.594 | 1.13858 | ||||||||
\(763\) | 994.000i | 1.30275i | ||||||||
\(764\) | −174.000 | −0.227749 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 563.489i | 0.735625i | ||||||||
\(767\) | − 540.000i | − 0.704042i | ||||||||
\(768\) | −764.735 | −0.995749 | ||||||||
\(769\) | − 1126.98i | − 1.46551i | −0.680492 | − | 0.732756i | \(-0.738234\pi\) | ||||
0.680492 | − | 0.732756i | \(-0.261766\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 600.000 | 0.778210 | ||||||||
\(772\) | − 618.000i | − 0.800518i | ||||||||
\(773\) | 818.401 | 1.05873 | 0.529367 | − | 0.848393i | \(-0.322430\pi\) | ||||
0.529367 | + | 0.848393i | \(0.322430\pi\) | |||||||
\(774\) | 374.000 | 0.483204 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 187.830i | − 0.242049i | ||||||||
\(777\) | −438.269 | −0.564053 | ||||||||
\(778\) | 698.000i | 0.897172i | ||||||||
\(779\) | 360.000 | 0.462131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 124.000 | 0.158771 | ||||||||
\(782\) | 697.653 | 0.892140 | ||||||||
\(783\) | 196.774 | 0.251308 | ||||||||
\(784\) | −245.000 | −0.312500 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −540.000 | −0.687023 | ||||||||
\(787\) | −684.237 | −0.869424 | −0.434712 | − | 0.900569i | \(-0.643150\pi\) | ||||
−0.434712 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(788\) | − 678.000i | − 0.860406i | ||||||||
\(789\) | 152.053i | 0.192716i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −238.000 | −0.300885 | ||||||||
\(792\) | − 154.000i | − 0.194444i | ||||||||
\(793\) | − 1260.00i | − 1.58890i | ||||||||
\(794\) | 308.577i | 0.388636i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 402.492i | − 0.505644i | ||||||||
\(797\) | −308.577 | −0.387174 | −0.193587 | − | 0.981083i | \(-0.562012\pi\) | ||||
−0.193587 | + | 0.981083i | \(0.562012\pi\) | |||||||
\(798\) | 420.000i | 0.526316i | ||||||||
\(799\) | −720.000 | −0.901126 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 295.161i | 0.368491i | ||||||||
\(802\) | 538.000i | 0.670823i | ||||||||
\(803\) | −107.331 | −0.133663 | ||||||||
\(804\) | 187.830i | 0.233619i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 720.000 | 0.893300 | ||||||||
\(807\) | − 1140.00i | − 1.41264i | ||||||||
\(808\) | 469.574 | 0.581156 | ||||||||
\(809\) | −1358.00 | −1.67862 | −0.839308 | − | 0.543657i | \(-0.817039\pi\) | ||||
−0.839308 | + | 0.543657i | \(0.817039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 308.577i | − 0.380490i | −0.981737 | − | 0.190245i | \(-0.939072\pi\) | ||||
0.981737 | − | 0.190245i | \(-0.0609282\pi\) | |||||||
\(812\) | 462.000i | 0.568966i | ||||||||
\(813\) | 1440.00i | 1.77122i | ||||||||
\(814\) | 28.0000 | 0.0343980 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −600.000 | −0.735294 | ||||||||
\(817\) | −456.158 | −0.558333 | ||||||||
\(818\) | −295.161 | −0.360832 | ||||||||
\(819\) | − 1033.06i | − 1.26137i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 482.000 | 0.587089 | 0.293544 | − | 0.955945i | \(-0.405165\pi\) | ||||
0.293544 | + | 0.955945i | \(0.405165\pi\) | |||||||
\(822\) | −742.375 | −0.903132 | ||||||||
\(823\) | − 926.000i | − 1.12515i | −0.826746 | − | 0.562576i | \(-0.809810\pi\) | ||||
0.826746 | − | 0.562576i | \(-0.190190\pi\) | |||||||
\(824\) | − 1126.98i | − 1.36769i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 281.745i | 0.341095i | ||||||||
\(827\) | − 226.000i | − 0.273277i | −0.990621 | − | 0.136638i | \(-0.956370\pi\) | ||||
0.990621 | − | 0.136638i | \(-0.0436299\pi\) | |||||||
\(828\) | − 858.000i | − 1.03623i | ||||||||
\(829\) | 1462.39i | 1.76404i | 0.471213 | + | 0.882020i | \(0.343816\pi\) | ||||
−0.471213 | + | 0.882020i | \(0.656184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 62.6099i | 0.0753428i | ||||||||
\(832\) | 174.413 | 0.209631 | ||||||||
\(833\) | 1314.81 | 1.57840 | ||||||||
\(834\) | 420.000 | 0.503597 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 80.4984i | 0.0962900i | ||||||||
\(837\) | − 480.000i | − 0.573477i | ||||||||
\(838\) | 818.401 | 0.976612 | ||||||||
\(839\) | 831.817i | 0.991439i | 0.868483 | + | 0.495719i | \(0.165096\pi\) | ||||
−0.868483 | + | 0.495719i | \(0.834904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −357.000 | −0.424495 | ||||||||
\(842\) | 118.000i | 0.140143i | ||||||||
\(843\) | 8.94427 | 0.0106100 | ||||||||
\(844\) | −354.000 | −0.419431 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − 295.161i | − 0.348890i | ||||||||
\(847\) | − 819.000i | − 0.966942i | ||||||||
\(848\) | 170.000i | 0.200472i | ||||||||
\(849\) | −420.000 | −0.494700 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 364.000 | 0.427732 | ||||||||
\(852\) | 831.817 | 0.976311 | ||||||||
\(853\) | −40.2492 | −0.0471855 | −0.0235927 | − | 0.999722i | \(-0.507511\pi\) | ||||
−0.0235927 | + | 0.999722i | \(0.507511\pi\) | |||||||
\(854\) | 657.404i | 0.769794i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −742.000 | −0.866822 | ||||||||
\(857\) | −268.328 | −0.313102 | −0.156551 | − | 0.987670i | \(-0.550038\pi\) | ||||
−0.156551 | + | 0.987670i | \(0.550038\pi\) | |||||||
\(858\) | 120.000i | 0.139860i | ||||||||
\(859\) | 308.577i | 0.359229i | 0.983737 | + | 0.179614i | \(0.0574850\pi\) | ||||
−0.983737 | + | 0.179614i | \(0.942515\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 840.000 | 0.975610 | ||||||||
\(862\) | 718.000i | 0.832947i | ||||||||
\(863\) | 514.000i | 0.595597i | 0.954629 | + | 0.297798i | \(0.0962523\pi\) | ||||
−0.954629 | + | 0.297798i | \(0.903748\pi\) | |||||||
\(864\) | − 295.161i | − 0.341621i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 509.823i | − 0.588711i | ||||||||
\(867\) | 1927.49 | 2.22317 | ||||||||
\(868\) | 1126.98 | 1.29836 | ||||||||
\(869\) | −76.0000 | −0.0874568 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 187.830i | − 0.215648i | ||||||||
\(872\) | − 994.000i | − 1.13991i | ||||||||
\(873\) | 295.161 | 0.338100 | ||||||||
\(874\) | − 348.827i | − 0.399115i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −720.000 | −0.821918 | ||||||||
\(877\) | − 1306.00i | − 1.48917i | −0.667529 | − | 0.744584i | \(-0.732648\pi\) | ||||
0.667529 | − | 0.744584i | \(-0.267352\pi\) | |||||||
\(878\) | 26.8328 | 0.0305613 | ||||||||
\(879\) | 1500.00 | 1.70648 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1126.98i | − 1.27920i | −0.768706 | − | 0.639602i | \(-0.779099\pi\) | ||||
0.768706 | − | 0.639602i | \(-0.220901\pi\) | |||||||
\(882\) | 539.000i | 0.611111i | ||||||||
\(883\) | − 1526.00i | − 1.72820i | −0.503321 | − | 0.864100i | \(-0.667889\pi\) | ||||
0.503321 | − | 0.864100i | \(-0.332111\pi\) | |||||||
\(884\) | 1080.00 | 1.22172 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 634.000 | 0.715576 | ||||||||
\(887\) | −1556.30 | −1.75457 | −0.877285 | − | 0.479970i | \(-0.840648\pi\) | ||||
−0.877285 | + | 0.479970i | \(0.840648\pi\) | |||||||
\(888\) | 438.269 | 0.493547 | ||||||||
\(889\) | −1358.00 | −1.52756 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −118.000 | −0.132435 | ||||||||
\(892\) | 241.495 | 0.270735 | ||||||||
\(893\) | 360.000i | 0.403135i | ||||||||
\(894\) | − 635.043i | − 0.710339i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 833.000 | 0.929688 | ||||||||
\(897\) | 1560.00i | 1.73913i | ||||||||
\(898\) | 338.000i | 0.376392i | ||||||||
\(899\) | − 1180.64i | − 1.31329i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 912.316i | − 1.01256i | ||||||||
\(902\) | −53.6656 | −0.0594963 | ||||||||
\(903\) | −1064.37 | −1.17870 | ||||||||
\(904\) | 238.000 | 0.263274 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − 8.94427i | − 0.00987226i | ||||||||
\(907\) | 734.000i | 0.809261i | 0.914480 | + | 0.404631i | \(0.132600\pi\) | ||||
−0.914480 | + | 0.404631i | \(0.867400\pi\) | |||||||
\(908\) | −764.735 | −0.842219 | ||||||||
\(909\) | 737.902i | 0.811774i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1202.00 | 1.31943 | 0.659715 | − | 0.751516i | \(-0.270677\pi\) | ||||
0.659715 | + | 0.751516i | \(0.270677\pi\) | |||||||
\(912\) | 300.000i | 0.328947i | ||||||||
\(913\) | 80.4984 | 0.0881692 | ||||||||
\(914\) | −466.000 | −0.509847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 40.2492i | − 0.0439402i | ||||||||
\(917\) | 845.234 | 0.921738 | ||||||||
\(918\) | 240.000i | 0.261438i | ||||||||
\(919\) | 1282.00 | 1.39499 | 0.697497 | − | 0.716587i | \(-0.254297\pi\) | ||||
0.697497 | + | 0.716587i | \(0.254297\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −900.000 | −0.977199 | ||||||||
\(922\) | −442.741 | −0.480197 | ||||||||
\(923\) | −831.817 | −0.901210 | ||||||||
\(924\) | 187.830i | 0.203279i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −206.000 | −0.222462 | ||||||||
\(927\) | 1770.97 | 1.91043 | ||||||||
\(928\) | − 726.000i | − 0.782328i | ||||||||
\(929\) | 1126.98i | 1.21311i | 0.795042 | + | 0.606554i | \(0.207449\pi\) | ||||
−0.795042 | + | 0.606554i | \(0.792551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 657.404i | − 0.706127i | ||||||||
\(932\) | 642.000i | 0.688841i | ||||||||
\(933\) | − 2280.00i | − 2.44373i | ||||||||
\(934\) | 362.243i | 0.387840i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1033.06i | 1.10370i | ||||||||
\(937\) | −214.663 | −0.229096 | −0.114548 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114548 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(938\) | 98.0000i | 0.104478i | ||||||||
\(939\) | 1440.00 | 1.53355 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 845.234i | 0.898229i | 0.893474 | + | 0.449115i | \(0.148261\pi\) | ||||
−0.893474 | + | 0.449115i | \(0.851739\pi\) | |||||||
\(942\) | − 300.000i | − 0.318471i | ||||||||
\(943\) | −697.653 | −0.739823 | ||||||||
\(944\) | 201.246i | 0.213184i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 68.0000 | 0.0718816 | ||||||||
\(947\) | 734.000i | 0.775079i | 0.921853 | + | 0.387540i | \(0.126675\pi\) | ||||
−0.921853 | + | 0.387540i | \(0.873325\pi\) | |||||||
\(948\) | −509.823 | −0.537789 | ||||||||
\(949\) | 720.000 | 0.758693 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1672.58i | 1.75876i | ||||||||
\(952\) | −1314.81 | −1.38110 | ||||||||
\(953\) | 934.000i | 0.980063i | 0.871705 | + | 0.490031i | \(0.163015\pi\) | ||||
−0.871705 | + | 0.490031i | \(0.836985\pi\) | |||||||
\(954\) | 374.000 | 0.392034 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −294.000 | −0.307531 | ||||||||
\(957\) | 196.774 | 0.205615 | ||||||||
\(958\) | −214.663 | −0.224074 | ||||||||
\(959\) | 1162.00 | 1.21168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1919.00 | −1.99688 | ||||||||
\(962\) | −187.830 | −0.195249 | ||||||||
\(963\) | − 1166.00i | − 1.21080i | ||||||||
\(964\) | − 482.991i | − 0.501028i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | − 813.929i | − 0.842576i | ||||||||
\(967\) | 314.000i | 0.324716i | 0.986732 | + | 0.162358i | \(0.0519099\pi\) | ||||
−0.986732 | + | 0.162358i | \(0.948090\pi\) | |||||||
\(968\) | 819.000i | 0.846074i | ||||||||
\(969\) | − 1609.97i | − 1.66147i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 147.580i | − 0.151988i | −0.997108 | − | 0.0759941i | \(-0.975787\pi\) | ||||
0.997108 | − | 0.0759941i | \(-0.0242130\pi\) | |||||||
\(972\) | −1033.06 | −1.06282 | ||||||||
\(973\) | −657.404 | −0.675646 | ||||||||
\(974\) | −166.000 | −0.170431 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 469.574i | 0.481121i | ||||||||
\(977\) | − 1486.00i | − 1.52098i | −0.649348 | − | 0.760491i | \(-0.724958\pi\) | ||||
0.649348 | − | 0.760491i | \(-0.275042\pi\) | |||||||
\(978\) | 152.053 | 0.155473 | ||||||||
\(979\) | 53.6656i | 0.0548168i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1562.00 | 1.59225 | ||||||||
\(982\) | 838.000i | 0.853360i | ||||||||
\(983\) | −965.981 | −0.982687 | −0.491344 | − | 0.870966i | \(-0.663494\pi\) | ||||
−0.491344 | + | 0.870966i | \(0.663494\pi\) | |||||||
\(984\) | −840.000 | −0.853659 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 590.322i | 0.598704i | ||||||||
\(987\) | 840.000i | 0.851064i | ||||||||
\(988\) | − 540.000i | − 0.546559i | ||||||||
\(989\) | 884.000 | 0.893832 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.0000 | −0.0585267 | −0.0292634 | − | 0.999572i | \(-0.509316\pi\) | ||||
−0.0292634 | + | 0.999572i | \(0.509316\pi\) | |||||||
\(992\) | −1770.97 | −1.78525 | ||||||||
\(993\) | 2155.57 | 2.17076 | ||||||||
\(994\) | 434.000 | 0.436620 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 540.000 | 0.542169 | ||||||||
\(997\) | 630.571 | 0.632469 | 0.316234 | − | 0.948681i | \(-0.397581\pi\) | ||||
0.316234 | + | 0.948681i | \(0.397581\pi\) | |||||||
\(998\) | − 262.000i | − 0.262525i | ||||||||
\(999\) | 125.220i | 0.125345i |
(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 | 175.3.c.d.174.2 | 4 | ||
5.2 | odd | 4 | 175.3.d.f.76.1 | 2 | |||
5.3 | odd | 4 | 35.3.d.a.6.2 | yes | 2 | ||
5.4 | even | 2 | inner | 175.3.c.d.174.3 | 4 | ||
7.6 | odd | 2 | inner | 175.3.c.d.174.1 | 4 | ||
15.8 | even | 4 | 315.3.h.b.181.1 | 2 | |||
20.3 | even | 4 | 560.3.f.a.321.1 | 2 | |||
35.3 | even | 12 | 245.3.h.b.166.1 | 4 | |||
35.13 | even | 4 | 35.3.d.a.6.1 | ✓ | 2 | ||
35.18 | odd | 12 | 245.3.h.b.166.2 | 4 | |||
35.23 | odd | 12 | 245.3.h.b.31.1 | 4 | |||
35.27 | even | 4 | 175.3.d.f.76.2 | 2 | |||
35.33 | even | 12 | 245.3.h.b.31.2 | 4 | |||
35.34 | odd | 2 | inner | 175.3.c.d.174.4 | 4 | ||
105.83 | odd | 4 | 315.3.h.b.181.2 | 2 | |||
140.83 | odd | 4 | 560.3.f.a.321.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.3.d.a.6.1 | ✓ | 2 | 35.13 | even | 4 | ||
35.3.d.a.6.2 | yes | 2 | 5.3 | odd | 4 | ||
175.3.c.d.174.1 | 4 | 7.6 | odd | 2 | inner | ||
175.3.c.d.174.2 | 4 | 1.1 | even | 1 | trivial | ||
175.3.c.d.174.3 | 4 | 5.4 | even | 2 | inner | ||
175.3.c.d.174.4 | 4 | 35.34 | odd | 2 | inner | ||
175.3.d.f.76.1 | 2 | 5.2 | odd | 4 | |||
175.3.d.f.76.2 | 2 | 35.27 | even | 4 | |||
245.3.h.b.31.1 | 4 | 35.23 | odd | 12 | |||
245.3.h.b.31.2 | 4 | 35.33 | even | 12 | |||
245.3.h.b.166.1 | 4 | 35.3 | even | 12 | |||
245.3.h.b.166.2 | 4 | 35.18 | odd | 12 | |||
315.3.h.b.181.1 | 2 | 15.8 | even | 4 | |||
315.3.h.b.181.2 | 2 | 105.83 | odd | 4 | |||
560.3.f.a.321.1 | 2 | 20.3 | even | 4 | |||
560.3.f.a.321.2 | 2 | 140.83 | odd | 4 |