Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (of order \(2\), degree \(1\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.12 | ||
Root | \(0.430324 + 1.60599i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.b.1077.5 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | 0.707107i | ||||||||
\(3\) | − | 1.02738i | − | 0.593160i | −0.955008 | − | 0.296580i | \(-0.904154\pi\) | ||
0.955008 | − | 0.296580i | \(-0.0958461\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.25868i | − | 0.562900i | −0.959576 | − | 0.281450i | \(-0.909185\pi\) | ||
0.959576 | − | 0.281450i | \(-0.0908153\pi\) | |||||||
\(6\) | 1.02738 | 0.419427 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.94448 | 0.648162 | ||||||||
\(10\) | 1.25868 | 0.398030 | ||||||||
\(11\) | −3.30824 | + | 0.235617i | −0.997473 | + | 0.0710412i | ||||
\(12\) | 1.02738i | 0.296580i | ||||||||
\(13\) | 4.08338 | 1.13253 | 0.566263 | − | 0.824224i | \(-0.308388\pi\) | ||||
0.566263 | + | 0.824224i | \(0.308388\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.29315 | −0.333890 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.20191 | −0.776578 | −0.388289 | − | 0.921538i | \(-0.626934\pi\) | ||||
−0.388289 | + | 0.921538i | \(0.626934\pi\) | |||||||
\(18\) | 1.94448i | 0.458319i | ||||||||
\(19\) | 7.62813 | 1.75001 | 0.875007 | − | 0.484111i | \(-0.160857\pi\) | ||||
0.875007 | + | 0.484111i | \(0.160857\pi\) | |||||||
\(20\) | 1.25868i | 0.281450i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.235617 | − | 3.30824i | −0.0502337 | − | 0.705320i | ||||
\(23\) | −8.25273 | −1.72081 | −0.860407 | − | 0.509608i | \(-0.829790\pi\) | ||||
−0.860407 | + | 0.509608i | \(0.829790\pi\) | |||||||
\(24\) | −1.02738 | −0.209714 | ||||||||
\(25\) | 3.41572 | 0.683144 | ||||||||
\(26\) | 4.08338i | 0.800817i | ||||||||
\(27\) | − | 5.07988i | − | 0.977623i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.54386i | − | 0.658079i | −0.944316 | − | 0.329039i | \(-0.893275\pi\) | ||
0.944316 | − | 0.329039i | \(-0.106725\pi\) | |||||||
\(30\) | − | 1.29315i | − | 0.236096i | ||||||
\(31\) | − | 9.18338i | − | 1.64938i | −0.565582 | − | 0.824692i | \(-0.691349\pi\) | ||
0.565582 | − | 0.824692i | \(-0.308651\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.242069 | + | 3.39883i | 0.0421388 | + | 0.591661i | ||||
\(34\) | − | 3.20191i | − | 0.549124i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.94448 | −0.324081 | ||||||||
\(37\) | −0.308245 | −0.0506752 | −0.0253376 | − | 0.999679i | \(-0.508066\pi\) | ||||
−0.0253376 | + | 0.999679i | \(0.508066\pi\) | |||||||
\(38\) | 7.62813i | 1.23745i | ||||||||
\(39\) | − | 4.19520i | − | 0.671769i | ||||||
\(40\) | −1.25868 | −0.199015 | ||||||||
\(41\) | 6.05276 | 0.945283 | 0.472641 | − | 0.881255i | \(-0.343301\pi\) | ||||
0.472641 | + | 0.881255i | \(0.343301\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.57607i | − | 1.15534i | −0.816270 | − | 0.577670i | \(-0.803962\pi\) | ||
0.816270 | − | 0.577670i | \(-0.196038\pi\) | |||||||
\(44\) | 3.30824 | − | 0.235617i | 0.498737 | − | 0.0355206i | ||||
\(45\) | − | 2.44749i | − | 0.364850i | ||||||
\(46\) | − | 8.25273i | − | 1.21680i | ||||||
\(47\) | − | 4.70267i | − | 0.685954i | −0.939344 | − | 0.342977i | \(-0.888565\pi\) | ||
0.939344 | − | 0.342977i | \(-0.111435\pi\) | |||||||
\(48\) | − | 1.02738i | − | 0.148290i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.41572i | 0.483056i | ||||||||
\(51\) | 3.28959i | 0.460635i | ||||||||
\(52\) | −4.08338 | −0.566263 | ||||||||
\(53\) | −4.79659 | −0.658863 | −0.329431 | − | 0.944180i | \(-0.606857\pi\) | ||||
−0.329431 | + | 0.944180i | \(0.606857\pi\) | |||||||
\(54\) | 5.07988 | 0.691284 | ||||||||
\(55\) | 0.296567 | + | 4.16403i | 0.0399891 | + | 0.561478i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.83701i | − | 1.03804i | ||||||
\(58\) | 3.54386 | 0.465332 | ||||||||
\(59\) | 2.73329i | 0.355844i | 0.984045 | + | 0.177922i | \(0.0569374\pi\) | ||||
−0.984045 | + | 0.177922i | \(0.943063\pi\) | |||||||
\(60\) | 1.29315 | 0.166945 | ||||||||
\(61\) | −1.51010 | −0.193349 | −0.0966743 | − | 0.995316i | \(-0.530821\pi\) | ||||
−0.0966743 | + | 0.995316i | \(0.530821\pi\) | |||||||
\(62\) | 9.18338 | 1.16629 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 5.13968i | − | 0.637499i | ||||||
\(66\) | −3.39883 | + | 0.242069i | −0.418368 | + | 0.0297966i | ||||
\(67\) | 3.38087 | 0.413039 | 0.206520 | − | 0.978442i | \(-0.433786\pi\) | ||||
0.206520 | + | 0.978442i | \(0.433786\pi\) | |||||||
\(68\) | 3.20191 | 0.388289 | ||||||||
\(69\) | 8.47871i | 1.02072i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.50810 | 0.416334 | 0.208167 | − | 0.978093i | \(-0.433250\pi\) | ||||
0.208167 | + | 0.978093i | \(0.433250\pi\) | |||||||
\(72\) | − | 1.94448i | − | 0.229160i | ||||||
\(73\) | 0.966855 | 0.113162 | 0.0565809 | − | 0.998398i | \(-0.481980\pi\) | ||||
0.0565809 | + | 0.998398i | \(0.481980\pi\) | |||||||
\(74\) | − | 0.308245i | − | 0.0358327i | ||||||
\(75\) | − | 3.50925i | − | 0.405213i | ||||||
\(76\) | −7.62813 | −0.875007 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.19520 | 0.475013 | ||||||||
\(79\) | − | 15.6129i | − | 1.75659i | −0.478117 | − | 0.878296i | \(-0.658681\pi\) | ||
0.478117 | − | 0.878296i | \(-0.341319\pi\) | |||||||
\(80\) | − | 1.25868i | − | 0.140725i | ||||||
\(81\) | 0.614474 | 0.0682749 | ||||||||
\(82\) | 6.05276i | 0.668416i | ||||||||
\(83\) | 1.32998 | 0.145984 | 0.0729921 | − | 0.997333i | \(-0.476745\pi\) | ||||
0.0729921 | + | 0.997333i | \(0.476745\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.03019i | 0.437136i | ||||||||
\(86\) | 7.57607 | 0.816949 | ||||||||
\(87\) | −3.64090 | −0.390346 | ||||||||
\(88\) | 0.235617 | + | 3.30824i | 0.0251169 | + | 0.352660i | ||||
\(89\) | − | 10.6498i | − | 1.12887i | −0.825477 | − | 0.564436i | \(-0.809094\pi\) | ||
0.825477 | − | 0.564436i | \(-0.190906\pi\) | |||||||
\(90\) | 2.44749 | 0.257988 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.25273 | 0.860407 | ||||||||
\(93\) | −9.43485 | −0.978348 | ||||||||
\(94\) | 4.70267 | 0.485043 | ||||||||
\(95\) | − | 9.60139i | − | 0.985082i | ||||||
\(96\) | 1.02738 | 0.104857 | ||||||||
\(97\) | 10.6748i | 1.08386i | 0.840424 | + | 0.541930i | \(0.182306\pi\) | ||||
−0.840424 | + | 0.541930i | \(0.817694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.43283 | + | 0.458154i | −0.646524 | + | 0.0460462i | ||||
\(100\) | −3.41572 | −0.341572 | ||||||||
\(101\) | 10.0648 | 1.00149 | 0.500745 | − | 0.865595i | \(-0.333059\pi\) | ||||
0.500745 | + | 0.865595i | \(0.333059\pi\) | |||||||
\(102\) | −3.28959 | −0.325718 | ||||||||
\(103\) | − | 2.88523i | − | 0.284290i | −0.989846 | − | 0.142145i | \(-0.954600\pi\) | ||
0.989846 | − | 0.142145i | \(-0.0453999\pi\) | |||||||
\(104\) | − | 4.08338i | − | 0.400409i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 4.79659i | − | 0.465886i | ||||||
\(107\) | 16.3000i | 1.57578i | 0.615814 | + | 0.787892i | \(0.288827\pi\) | ||||
−0.615814 | + | 0.787892i | \(0.711173\pi\) | |||||||
\(108\) | 5.07988i | 0.488812i | ||||||||
\(109\) | 11.5034i | 1.10183i | 0.834561 | + | 0.550915i | \(0.185721\pi\) | ||||
−0.834561 | + | 0.550915i | \(0.814279\pi\) | |||||||
\(110\) | −4.16403 | + | 0.296567i | −0.397025 | + | 0.0282766i | ||||
\(111\) | 0.316686i | 0.0300585i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.558958 | 0.0525824 | 0.0262912 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262912 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(114\) | 7.83701 | 0.734003 | ||||||||
\(115\) | 10.3876i | 0.968645i | ||||||||
\(116\) | 3.54386i | 0.329039i | ||||||||
\(117\) | 7.94008 | 0.734060 | ||||||||
\(118\) | −2.73329 | −0.251619 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.29315i | 0.118048i | ||||||||
\(121\) | 10.8890 | − | 1.55896i | 0.989906 | − | 0.141723i | ||||
\(122\) | − | 1.51010i | − | 0.136718i | ||||||
\(123\) | − | 6.21850i | − | 0.560704i | ||||||
\(124\) | 9.18338i | 0.824692i | ||||||||
\(125\) | − | 10.5927i | − | 0.947441i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2829i | 1.00120i | 0.865679 | + | 0.500599i | \(0.166887\pi\) | ||||
−0.865679 | + | 0.500599i | \(0.833113\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −7.78352 | −0.685301 | ||||||||
\(130\) | 5.13968 | 0.450780 | ||||||||
\(131\) | −7.03388 | −0.614553 | −0.307276 | − | 0.951620i | \(-0.599418\pi\) | ||||
−0.307276 | + | 0.951620i | \(0.599418\pi\) | |||||||
\(132\) | −0.242069 | − | 3.39883i | −0.0210694 | − | 0.295831i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.38087i | 0.292063i | ||||||||
\(135\) | −6.39395 | −0.550304 | ||||||||
\(136\) | 3.20191i | 0.274562i | ||||||||
\(137\) | 9.08974 | 0.776589 | 0.388294 | − | 0.921535i | \(-0.373064\pi\) | ||||
0.388294 | + | 0.921535i | \(0.373064\pi\) | |||||||
\(138\) | −8.47871 | −0.721756 | ||||||||
\(139\) | −7.86546 | −0.667140 | −0.333570 | − | 0.942725i | \(-0.608253\pi\) | ||||
−0.333570 | + | 0.942725i | \(0.608253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.83144 | −0.406880 | ||||||||
\(142\) | 3.50810i | 0.294393i | ||||||||
\(143\) | −13.5088 | + | 0.962115i | −1.12967 | + | 0.0804561i | ||||
\(144\) | 1.94448 | 0.162040 | ||||||||
\(145\) | −4.46060 | −0.370432 | ||||||||
\(146\) | 0.966855i | 0.0800175i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.308245 | 0.0253376 | ||||||||
\(149\) | 6.23096i | 0.510460i | 0.966880 | + | 0.255230i | \(0.0821513\pi\) | ||||
−0.966880 | + | 0.255230i | \(0.917849\pi\) | |||||||
\(150\) | 3.50925 | 0.286529 | ||||||||
\(151\) | 17.5101i | 1.42495i | 0.701696 | + | 0.712476i | \(0.252426\pi\) | ||||
−0.701696 | + | 0.712476i | \(0.747574\pi\) | |||||||
\(152\) | − | 7.62813i | − | 0.618723i | ||||||
\(153\) | −6.22607 | −0.503348 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.5590 | −0.928438 | ||||||||
\(156\) | 4.19520i | 0.335885i | ||||||||
\(157\) | − | 7.77404i | − | 0.620436i | −0.950665 | − | 0.310218i | \(-0.899598\pi\) | ||
0.950665 | − | 0.310218i | \(-0.100402\pi\) | |||||||
\(158\) | 15.6129 | 1.24210 | ||||||||
\(159\) | 4.92794i | 0.390811i | ||||||||
\(160\) | 1.25868 | 0.0995076 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.614474i | 0.0482776i | ||||||||
\(163\) | −18.2123 | −1.42650 | −0.713249 | − | 0.700911i | \(-0.752777\pi\) | ||||
−0.713249 | + | 0.700911i | \(0.752777\pi\) | |||||||
\(164\) | −6.05276 | −0.472641 | ||||||||
\(165\) | 4.27805 | − | 0.304688i | 0.333046 | − | 0.0237199i | ||||
\(166\) | 1.32998i | 0.103226i | ||||||||
\(167\) | 14.3653 | 1.11162 | 0.555809 | − | 0.831310i | \(-0.312409\pi\) | ||||
0.555809 | + | 0.831310i | \(0.312409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67402 | 0.282617 | ||||||||
\(170\) | −4.03019 | −0.309102 | ||||||||
\(171\) | 14.8328 | 1.13429 | ||||||||
\(172\) | 7.57607i | 0.577670i | ||||||||
\(173\) | −4.76319 | −0.362139 | −0.181069 | − | 0.983470i | \(-0.557956\pi\) | ||||
−0.181069 | + | 0.983470i | \(0.557956\pi\) | |||||||
\(174\) | − | 3.64090i | − | 0.276016i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.30824 | + | 0.235617i | −0.249368 | + | 0.0177603i | ||||
\(177\) | 2.80813 | 0.211072 | ||||||||
\(178\) | 10.6498 | 0.798233 | ||||||||
\(179\) | −3.89051 | −0.290790 | −0.145395 | − | 0.989374i | \(-0.546445\pi\) | ||||
−0.145395 | + | 0.989374i | \(0.546445\pi\) | |||||||
\(180\) | 2.44749i | 0.182425i | ||||||||
\(181\) | 13.0698i | 0.971474i | 0.874105 | + | 0.485737i | \(0.161449\pi\) | ||||
−0.874105 | + | 0.485737i | \(0.838551\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.55145i | 0.114687i | ||||||||
\(184\) | 8.25273i | 0.608399i | ||||||||
\(185\) | 0.387982i | 0.0285250i | ||||||||
\(186\) | − | 9.43485i | − | 0.691797i | ||||||
\(187\) | 10.5927 | − | 0.754426i | 0.774616 | − | 0.0551691i | ||||
\(188\) | 4.70267i | 0.342977i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.60139 | 0.696558 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 1.02738i | 0.0741450i | ||||||||
\(193\) | − | 9.38289i | − | 0.675395i | −0.941255 | − | 0.337698i | \(-0.890352\pi\) | ||
0.941255 | − | 0.337698i | \(-0.109648\pi\) | |||||||
\(194\) | −10.6748 | −0.766405 | ||||||||
\(195\) | −5.28042 | −0.378139 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.3471i | 1.23593i | 0.786205 | + | 0.617966i | \(0.212043\pi\) | ||||
−0.786205 | + | 0.617966i | \(0.787957\pi\) | |||||||
\(198\) | −0.458154 | − | 6.43283i | −0.0325596 | − | 0.457161i | ||||
\(199\) | 2.92547i | 0.207381i | 0.994610 | + | 0.103690i | \(0.0330651\pi\) | ||||
−0.994610 | + | 0.103690i | \(0.966935\pi\) | |||||||
\(200\) | − | 3.41572i | − | 0.241528i | ||||||
\(201\) | − | 3.47345i | − | 0.244998i | ||||||
\(202\) | 10.0648i | 0.708160i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 3.28959i | − | 0.230317i | ||||||
\(205\) | − | 7.61851i | − | 0.532100i | ||||||
\(206\) | 2.88523 | 0.201023 | ||||||||
\(207\) | −16.0473 | −1.11536 | ||||||||
\(208\) | 4.08338 | 0.283132 | ||||||||
\(209\) | −25.2357 | + | 1.79732i | −1.74559 | + | 0.124323i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.252729i | 0.0173986i | 0.999962 | + | 0.00869931i | \(0.00276911\pi\) | ||||
−0.999962 | + | 0.00869931i | \(0.997231\pi\) | |||||||
\(212\) | 4.79659 | 0.329431 | ||||||||
\(213\) | − | 3.60416i | − | 0.246953i | ||||||
\(214\) | −16.3000 | −1.11425 | ||||||||
\(215\) | −9.53587 | −0.650341 | ||||||||
\(216\) | −5.07988 | −0.345642 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.5034 | −0.779111 | ||||||||
\(219\) | − | 0.993331i | − | 0.0671231i | ||||||
\(220\) | −0.296567 | − | 4.16403i | −0.0199946 | − | 0.280739i | ||||
\(221\) | −13.0746 | −0.879496 | ||||||||
\(222\) | −0.316686 | −0.0212545 | ||||||||
\(223\) | − | 19.0370i | − | 1.27482i | −0.770527 | − | 0.637408i | \(-0.780007\pi\) | ||
0.770527 | − | 0.637408i | \(-0.219993\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.64181 | 0.442788 | ||||||||
\(226\) | 0.558958i | 0.0371814i | ||||||||
\(227\) | 18.4070 | 1.22172 | 0.610858 | − | 0.791740i | \(-0.290825\pi\) | ||||
0.610858 | + | 0.791740i | \(0.290825\pi\) | |||||||
\(228\) | 7.83701i | 0.519019i | ||||||||
\(229\) | 5.30786i | 0.350753i | 0.984501 | + | 0.175377i | \(0.0561143\pi\) | ||||
−0.984501 | + | 0.175377i | \(0.943886\pi\) | |||||||
\(230\) | −10.3876 | −0.684936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.54386 | −0.232666 | ||||||||
\(233\) | 21.3192i | 1.39666i | 0.715774 | + | 0.698332i | \(0.246074\pi\) | ||||
−0.715774 | + | 0.698332i | \(0.753926\pi\) | |||||||
\(234\) | 7.94008i | 0.519059i | ||||||||
\(235\) | −5.91916 | −0.386124 | ||||||||
\(236\) | − | 2.73329i | − | 0.177922i | ||||||
\(237\) | −16.0405 | −1.04194 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.25163i | 0.469069i | 0.972108 | + | 0.234535i | \(0.0753566\pi\) | ||||
−0.972108 | + | 0.234535i | \(0.924643\pi\) | |||||||
\(240\) | −1.29315 | −0.0834724 | ||||||||
\(241\) | −3.55410 | −0.228939 | −0.114470 | − | 0.993427i | \(-0.536517\pi\) | ||||
−0.114470 | + | 0.993427i | \(0.536517\pi\) | |||||||
\(242\) | 1.55896 | + | 10.8890i | 0.100214 | + | 0.699969i | ||||
\(243\) | − | 15.8709i | − | 1.01812i | ||||||
\(244\) | 1.51010 | 0.0966743 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.21850 | 0.396477 | ||||||||
\(247\) | 31.1486 | 1.98194 | ||||||||
\(248\) | −9.18338 | −0.583145 | ||||||||
\(249\) | − | 1.36640i | − | 0.0865919i | ||||||
\(250\) | 10.5927 | 0.669942 | ||||||||
\(251\) | − | 0.735728i | − | 0.0464387i | −0.999730 | − | 0.0232194i | \(-0.992608\pi\) | ||
0.999730 | − | 0.0232194i | \(-0.00739162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.3021 | − | 1.94448i | 1.71647 | − | 0.122249i | ||||
\(254\) | −11.2829 | −0.707954 | ||||||||
\(255\) | 4.14055 | 0.259291 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.2065i | 1.01093i | 0.862846 | + | 0.505467i | \(0.168680\pi\) | ||||
−0.862846 | + | 0.505467i | \(0.831320\pi\) | |||||||
\(258\) | − | 7.78352i | − | 0.484581i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.13968i | 0.318750i | ||||||||
\(261\) | − | 6.89099i | − | 0.426541i | ||||||
\(262\) | − | 7.03388i | − | 0.434555i | ||||||
\(263\) | 24.3021i | 1.49853i | 0.662271 | + | 0.749264i | \(0.269593\pi\) | ||||
−0.662271 | + | 0.749264i | \(0.730407\pi\) | |||||||
\(264\) | 3.39883 | − | 0.242069i | 0.209184 | − | 0.0148983i | ||||
\(265\) | 6.03738i | 0.370874i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9414 | −0.669601 | ||||||||
\(268\) | −3.38087 | −0.206520 | ||||||||
\(269\) | − | 27.0484i | − | 1.64917i | −0.565737 | − | 0.824586i | \(-0.691408\pi\) | ||
0.565737 | − | 0.824586i | \(-0.308592\pi\) | |||||||
\(270\) | − | 6.39395i | − | 0.389124i | ||||||
\(271\) | −10.4433 | −0.634386 | −0.317193 | − | 0.948361i | \(-0.602740\pi\) | ||||
−0.317193 | + | 0.948361i | \(0.602740\pi\) | |||||||
\(272\) | −3.20191 | −0.194145 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.08974i | 0.549131i | ||||||||
\(275\) | −11.3000 | + | 0.804802i | −0.681418 | + | 0.0485314i | ||||
\(276\) | − | 8.47871i | − | 0.510359i | ||||||
\(277\) | − | 20.4006i | − | 1.22575i | −0.790178 | − | 0.612877i | \(-0.790012\pi\) | ||
0.790178 | − | 0.612877i | \(-0.209988\pi\) | |||||||
\(278\) | − | 7.86546i | − | 0.471739i | ||||||
\(279\) | − | 17.8569i | − | 1.06907i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.99535i | 0.596272i | 0.954523 | + | 0.298136i | \(0.0963650\pi\) | ||||
−0.954523 | + | 0.298136i | \(0.903635\pi\) | |||||||
\(282\) | − | 4.83144i | − | 0.287708i | ||||||
\(283\) | −3.48896 | −0.207397 | −0.103699 | − | 0.994609i | \(-0.533068\pi\) | ||||
−0.103699 | + | 0.994609i | \(0.533068\pi\) | |||||||
\(284\) | −3.50810 | −0.208167 | ||||||||
\(285\) | −9.86431 | −0.584311 | ||||||||
\(286\) | −0.962115 | − | 13.5088i | −0.0568911 | − | 0.798794i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.94448i | 0.114580i | ||||||||
\(289\) | −6.74775 | −0.396926 | ||||||||
\(290\) | − | 4.46060i | − | 0.261935i | ||||||
\(291\) | 10.9671 | 0.642902 | ||||||||
\(292\) | −0.966855 | −0.0565809 | ||||||||
\(293\) | 17.3549 | 1.01388 | 0.506942 | − | 0.861980i | \(-0.330776\pi\) | ||||
0.506942 | + | 0.861980i | \(0.330776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.44034 | 0.200304 | ||||||||
\(296\) | 0.308245i | 0.0179164i | ||||||||
\(297\) | 1.19691 | + | 16.8055i | 0.0694516 | + | 0.975153i | ||||
\(298\) | −6.23096 | −0.360950 | ||||||||
\(299\) | −33.6991 | −1.94887 | ||||||||
\(300\) | 3.50925i | 0.202607i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −17.5101 | −1.00759 | ||||||||
\(303\) | − | 10.3405i | − | 0.594044i | ||||||
\(304\) | 7.62813 | 0.437503 | ||||||||
\(305\) | 1.90074i | 0.108836i | ||||||||
\(306\) | − | 6.22607i | − | 0.355921i | ||||||
\(307\) | −22.6829 | −1.29458 | −0.647290 | − | 0.762244i | \(-0.724098\pi\) | ||||
−0.647290 | + | 0.762244i | \(0.724098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.96423 | −0.168629 | ||||||||
\(310\) | − | 11.5590i | − | 0.656505i | ||||||
\(311\) | 6.64116i | 0.376585i | 0.982113 | + | 0.188293i | \(0.0602954\pi\) | ||||
−0.982113 | + | 0.188293i | \(0.939705\pi\) | |||||||
\(312\) | −4.19520 | −0.237506 | ||||||||
\(313\) | 0.502967i | 0.0284294i | 0.999899 | + | 0.0142147i | \(0.00452483\pi\) | ||||
−0.999899 | + | 0.0142147i | \(0.995475\pi\) | |||||||
\(314\) | 7.77404 | 0.438715 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.6129i | 0.878296i | ||||||||
\(317\) | −10.5487 | −0.592476 | −0.296238 | − | 0.955114i | \(-0.595732\pi\) | ||||
−0.296238 | + | 0.955114i | \(0.595732\pi\) | |||||||
\(318\) | −4.92794 | −0.276345 | ||||||||
\(319\) | 0.834995 | + | 11.7240i | 0.0467507 | + | 0.656416i | ||||
\(320\) | 1.25868i | 0.0703625i | ||||||||
\(321\) | 16.7464 | 0.934692 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.4246 | −1.35902 | ||||||||
\(324\) | −0.614474 | −0.0341374 | ||||||||
\(325\) | 13.9477 | 0.773679 | ||||||||
\(326\) | − | 18.2123i | − | 1.00869i | ||||||
\(327\) | 11.8184 | 0.653561 | ||||||||
\(328\) | − | 6.05276i | − | 0.334208i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.304688 | + | 4.27805i | 0.0167725 | + | 0.235499i | ||||
\(331\) | −5.78058 | −0.317729 | −0.158865 | − | 0.987300i | \(-0.550783\pi\) | ||||
−0.158865 | + | 0.987300i | \(0.550783\pi\) | |||||||
\(332\) | −1.32998 | −0.0729921 | ||||||||
\(333\) | −0.599378 | −0.0328457 | ||||||||
\(334\) | 14.3653i | 0.786033i | ||||||||
\(335\) | − | 4.25544i | − | 0.232500i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1226i | 0.605885i | 0.953009 | + | 0.302943i | \(0.0979690\pi\) | ||||
−0.953009 | + | 0.302943i | \(0.902031\pi\) | |||||||
\(338\) | 3.67402i | 0.199840i | ||||||||
\(339\) | − | 0.574264i | − | 0.0311898i | ||||||
\(340\) | − | 4.03019i | − | 0.218568i | ||||||
\(341\) | 2.16376 | + | 30.3809i | 0.117174 | + | 1.64522i | ||||
\(342\) | 14.8328i | 0.802065i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.57607 | −0.408474 | ||||||||
\(345\) | 10.6720 | 0.574561 | ||||||||
\(346\) | − | 4.76319i | − | 0.256071i | ||||||
\(347\) | 14.6714i | 0.787601i | 0.919196 | + | 0.393801i | \(0.128840\pi\) | ||||
−0.919196 | + | 0.393801i | \(0.871160\pi\) | |||||||
\(348\) | 3.64090 | 0.195173 | ||||||||
\(349\) | −24.6769 | −1.32093 | −0.660463 | − | 0.750859i | \(-0.729640\pi\) | ||||
−0.660463 | + | 0.750859i | \(0.729640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 20.7431i | − | 1.10718i | ||||||
\(352\) | −0.235617 | − | 3.30824i | −0.0125584 | − | 0.176330i | ||||
\(353\) | − | 19.2447i | − | 1.02429i | −0.858898 | − | 0.512147i | \(-0.828850\pi\) | ||
0.858898 | − | 0.512147i | \(-0.171150\pi\) | |||||||
\(354\) | 2.80813i | 0.149250i | ||||||||
\(355\) | − | 4.41558i | − | 0.234355i | ||||||
\(356\) | 10.6498i | 0.564436i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.89051i | − | 0.205620i | ||||||
\(359\) | 3.29407i | 0.173854i | 0.996215 | + | 0.0869271i | \(0.0277047\pi\) | ||||
−0.996215 | + | 0.0869271i | \(0.972295\pi\) | |||||||
\(360\) | −2.44749 | −0.128994 | ||||||||
\(361\) | 39.1884 | 2.06255 | ||||||||
\(362\) | −13.0698 | −0.686936 | ||||||||
\(363\) | −1.60165 | − | 11.1871i | −0.0840647 | − | 0.587173i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.21696i | − | 0.0636988i | ||||||
\(366\) | −1.55145 | −0.0810956 | ||||||||
\(367\) | 30.9410i | 1.61511i | 0.589793 | + | 0.807555i | \(0.299209\pi\) | ||||
−0.589793 | + | 0.807555i | \(0.700791\pi\) | |||||||
\(368\) | −8.25273 | −0.430203 | ||||||||
\(369\) | 11.7695 | 0.612696 | ||||||||
\(370\) | −0.387982 | −0.0201702 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.43485 | 0.489174 | ||||||||
\(373\) | 0.961597i | 0.0497896i | 0.999690 | + | 0.0248948i | \(0.00792508\pi\) | ||||
−0.999690 | + | 0.0248948i | \(0.992075\pi\) | |||||||
\(374\) | 0.754426 | + | 10.5927i | 0.0390104 | + | 0.547736i | ||||
\(375\) | −10.8828 | −0.561984 | ||||||||
\(376\) | −4.70267 | −0.242521 | ||||||||
\(377\) | − | 14.4709i | − | 0.745292i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.41216 | −0.0725379 | −0.0362689 | − | 0.999342i | \(-0.511547\pi\) | ||||
−0.0362689 | + | 0.999342i | \(0.511547\pi\) | |||||||
\(380\) | 9.60139i | 0.492541i | ||||||||
\(381\) | 11.5919 | 0.593870 | ||||||||
\(382\) | 6.00000i | 0.306987i | ||||||||
\(383\) | − | 3.78079i | − | 0.193189i | −0.995324 | − | 0.0965946i | \(-0.969205\pi\) | ||
0.995324 | − | 0.0965946i | \(-0.0307950\pi\) | |||||||
\(384\) | −1.02738 | −0.0524284 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.38289 | 0.477576 | ||||||||
\(387\) | − | 14.7316i | − | 0.748847i | ||||||
\(388\) | − | 10.6748i | − | 0.541930i | ||||||
\(389\) | −3.37886 | −0.171315 | −0.0856574 | − | 0.996325i | \(-0.527299\pi\) | ||||
−0.0856574 | + | 0.996325i | \(0.527299\pi\) | |||||||
\(390\) | − | 5.28042i | − | 0.267385i | ||||||
\(391\) | 26.4245 | 1.33635 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.22649i | 0.364528i | ||||||||
\(394\) | −17.3471 | −0.873935 | ||||||||
\(395\) | −19.6517 | −0.988785 | ||||||||
\(396\) | 6.43283 | − | 0.458154i | 0.323262 | − | 0.0230231i | ||||
\(397\) | 11.5300i | 0.578673i | 0.957227 | + | 0.289336i | \(0.0934346\pi\) | ||||
−0.957227 | + | 0.289336i | \(0.906565\pi\) | |||||||
\(398\) | −2.92547 | −0.146640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.41572 | 0.170786 | ||||||||
\(401\) | 26.0523 | 1.30099 | 0.650494 | − | 0.759512i | \(-0.274562\pi\) | ||||
0.650494 | + | 0.759512i | \(0.274562\pi\) | |||||||
\(402\) | 3.47345 | 0.173240 | ||||||||
\(403\) | − | 37.4993i | − | 1.86797i | ||||||
\(404\) | −10.0648 | −0.500745 | ||||||||
\(405\) | − | 0.773427i | − | 0.0384319i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.01975 | − | 0.0726278i | 0.0505471 | − | 0.00360003i | ||||
\(408\) | 3.28959 | 0.162859 | ||||||||
\(409\) | 35.0217 | 1.73171 | 0.865856 | − | 0.500293i | \(-0.166774\pi\) | ||||
0.865856 | + | 0.500293i | \(0.166774\pi\) | |||||||
\(410\) | 7.61851 | 0.376251 | ||||||||
\(411\) | − | 9.33864i | − | 0.460641i | ||||||
\(412\) | 2.88523i | 0.142145i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 16.0473i | − | 0.788682i | ||||||
\(415\) | − | 1.67402i | − | 0.0821745i | ||||||
\(416\) | 4.08338i | 0.200204i | ||||||||
\(417\) | 8.08084i | 0.395720i | ||||||||
\(418\) | −1.79732 | − | 25.2357i | −0.0879097 | − | 1.23432i | ||||
\(419\) | 12.1242i | 0.592307i | 0.955140 | + | 0.296154i | \(0.0957040\pi\) | ||||
−0.955140 | + | 0.296154i | \(0.904296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6940 | 0.911089 | 0.455545 | − | 0.890213i | \(-0.349445\pi\) | ||||
0.455545 | + | 0.890213i | \(0.349445\pi\) | |||||||
\(422\) | −0.252729 | −0.0123027 | ||||||||
\(423\) | − | 9.14426i | − | 0.444609i | ||||||
\(424\) | 4.79659i | 0.232943i | ||||||||
\(425\) | −10.9368 | −0.530515 | ||||||||
\(426\) | 3.60416 | 0.174622 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 16.3000i | − | 0.787892i | ||||||
\(429\) | 0.988461 | + | 13.8787i | 0.0477233 | + | 0.670072i | ||||
\(430\) | − | 9.53587i | − | 0.459860i | ||||||
\(431\) | − | 33.9418i | − | 1.63492i | −0.575984 | − | 0.817461i | \(-0.695381\pi\) | ||
0.575984 | − | 0.817461i | \(-0.304619\pi\) | |||||||
\(432\) | − | 5.07988i | − | 0.244406i | ||||||
\(433\) | 27.0949i | 1.30210i | 0.759037 | + | 0.651048i | \(0.225670\pi\) | ||||
−0.759037 | + | 0.651048i | \(0.774330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.58274i | 0.219726i | ||||||||
\(436\) | − | 11.5034i | − | 0.550915i | ||||||
\(437\) | −62.9529 | −3.01145 | ||||||||
\(438\) | 0.993331 | 0.0474632 | ||||||||
\(439\) | 20.4538 | 0.976208 | 0.488104 | − | 0.872785i | \(-0.337689\pi\) | ||||
0.488104 | + | 0.872785i | \(0.337689\pi\) | |||||||
\(440\) | 4.16403 | − | 0.296567i | 0.198512 | − | 0.0141383i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 13.0746i | − | 0.621897i | ||||||
\(443\) | −3.59736 | −0.170916 | −0.0854579 | − | 0.996342i | \(-0.527235\pi\) | ||||
−0.0854579 | + | 0.996342i | \(0.527235\pi\) | |||||||
\(444\) | − | 0.316686i | − | 0.0150292i | ||||||
\(445\) | −13.4047 | −0.635442 | ||||||||
\(446\) | 19.0370 | 0.901430 | ||||||||
\(447\) | 6.40159 | 0.302785 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.0664 | 1.74927 | 0.874637 | − | 0.484779i | \(-0.161100\pi\) | ||||
0.874637 | + | 0.484779i | \(0.161100\pi\) | |||||||
\(450\) | 6.64181i | 0.313098i | ||||||||
\(451\) | −20.0240 | + | 1.42613i | −0.942894 | + | 0.0671541i | ||||
\(452\) | −0.558958 | −0.0262912 | ||||||||
\(453\) | 17.9896 | 0.845225 | ||||||||
\(454\) | 18.4070i | 0.863883i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.83701 | −0.367002 | ||||||||
\(457\) | 18.1512i | 0.849078i | 0.905410 | + | 0.424539i | \(0.139564\pi\) | ||||
−0.905410 | + | 0.424539i | \(0.860436\pi\) | |||||||
\(458\) | −5.30786 | −0.248020 | ||||||||
\(459\) | 16.2653i | 0.759201i | ||||||||
\(460\) | − | 10.3876i | − | 0.484323i | ||||||
\(461\) | 22.4278 | 1.04457 | 0.522284 | − | 0.852772i | \(-0.325080\pi\) | ||||
0.522284 | + | 0.852772i | \(0.325080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.6274 | −0.726267 | −0.363134 | − | 0.931737i | \(-0.618293\pi\) | ||||
−0.363134 | + | 0.931737i | \(0.618293\pi\) | |||||||
\(464\) | − | 3.54386i | − | 0.164520i | ||||||
\(465\) | 11.8755i | 0.550712i | ||||||||
\(466\) | −21.3192 | −0.987591 | ||||||||
\(467\) | 6.09520i | 0.282052i | 0.990006 | + | 0.141026i | \(0.0450402\pi\) | ||||
−0.990006 | + | 0.141026i | \(0.954960\pi\) | |||||||
\(468\) | −7.94008 | −0.367030 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 5.91916i | − | 0.273031i | ||||||
\(471\) | −7.98692 | −0.368018 | ||||||||
\(472\) | 2.73329 | 0.125810 | ||||||||
\(473\) | 1.78505 | + | 25.0635i | 0.0820768 | + | 1.15242i | ||||
\(474\) | − | 16.0405i | − | 0.736763i | ||||||
\(475\) | 26.0556 | 1.19551 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.32690 | −0.427049 | ||||||||
\(478\) | −7.25163 | −0.331682 | ||||||||
\(479\) | −30.6275 | −1.39941 | −0.699704 | − | 0.714433i | \(-0.746685\pi\) | ||||
−0.699704 | + | 0.714433i | \(0.746685\pi\) | |||||||
\(480\) | − | 1.29315i | − | 0.0590239i | ||||||
\(481\) | −1.25868 | −0.0573910 | ||||||||
\(482\) | − | 3.55410i | − | 0.161885i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8890 | + | 1.55896i | −0.494953 | + | 0.0708617i | ||||
\(485\) | 13.4362 | 0.610105 | ||||||||
\(486\) | 15.8709 | 0.719920 | ||||||||
\(487\) | −3.17453 | −0.143852 | −0.0719258 | − | 0.997410i | \(-0.522914\pi\) | ||||
−0.0719258 | + | 0.997410i | \(0.522914\pi\) | |||||||
\(488\) | 1.51010i | 0.0683590i | ||||||||
\(489\) | 18.7110i | 0.846141i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.6507i | − | 1.47351i | −0.676162 | − | 0.736753i | \(-0.736358\pi\) | ||
0.676162 | − | 0.736753i | \(-0.263642\pi\) | |||||||
\(492\) | 6.21850i | 0.280352i | ||||||||
\(493\) | 11.3471i | 0.511050i | ||||||||
\(494\) | 31.1486i | 1.40144i | ||||||||
\(495\) | 0.576670 | + | 8.09689i | 0.0259194 | + | 0.363928i | ||||
\(496\) | − | 9.18338i | − | 0.412346i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.36640 | 0.0612297 | ||||||||
\(499\) | 28.4548 | 1.27381 | 0.636906 | − | 0.770941i | \(-0.280214\pi\) | ||||
0.636906 | + | 0.770941i | \(0.280214\pi\) | |||||||
\(500\) | 10.5927i | 0.473721i | ||||||||
\(501\) | − | 14.7586i | − | 0.659367i | ||||||
\(502\) | 0.735728 | 0.0328372 | ||||||||
\(503\) | −22.5058 | −1.00348 | −0.501741 | − | 0.865018i | \(-0.667307\pi\) | ||||
−0.501741 | + | 0.865018i | \(0.667307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12.6684i | − | 0.563739i | ||||||
\(506\) | 1.94448 | + | 27.3021i | 0.0864429 | + | 1.21372i | ||||
\(507\) | − | 3.77463i | − | 0.167637i | ||||||
\(508\) | − | 11.2829i | − | 0.500599i | ||||||
\(509\) | 13.4450i | 0.595939i | 0.954575 | + | 0.297969i | \(0.0963093\pi\) | ||||
−0.954575 | + | 0.297969i | \(0.903691\pi\) | |||||||
\(510\) | 4.14055i | 0.183347i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 38.7500i | − | 1.71085i | ||||||
\(514\) | −16.2065 | −0.714838 | ||||||||
\(515\) | −3.63159 | −0.160027 | ||||||||
\(516\) | 7.78352 | 0.342651 | ||||||||
\(517\) | 1.10803 | + | 15.5576i | 0.0487310 | + | 0.684221i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.89362i | 0.214806i | ||||||||
\(520\) | −5.13968 | −0.225390 | ||||||||
\(521\) | 39.5299i | 1.73184i | 0.500187 | + | 0.865918i | \(0.333265\pi\) | ||||
−0.500187 | + | 0.865918i | \(0.666735\pi\) | |||||||
\(522\) | 6.89099 | 0.301610 | ||||||||
\(523\) | 29.6122 | 1.29485 | 0.647425 | − | 0.762129i | \(-0.275846\pi\) | ||||
0.647425 | + | 0.762129i | \(0.275846\pi\) | |||||||
\(524\) | 7.03388 | 0.307276 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.3021 | −1.05962 | ||||||||
\(527\) | 29.4044i | 1.28088i | ||||||||
\(528\) | 0.242069 | + | 3.39883i | 0.0105347 | + | 0.147915i | ||||
\(529\) | 45.1075 | 1.96120 | ||||||||
\(530\) | −6.03738 | −0.262247 | ||||||||
\(531\) | 5.31483i | 0.230644i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.7158 | 1.07056 | ||||||||
\(534\) | − | 10.9414i | − | 0.473479i | ||||||
\(535\) | 20.5166 | 0.887008 | ||||||||
\(536\) | − | 3.38087i | − | 0.146031i | ||||||
\(537\) | 3.99704i | 0.172485i | ||||||||
\(538\) | 27.0484 | 1.16614 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.39395 | 0.275152 | ||||||||
\(541\) | − | 17.4488i | − | 0.750185i | −0.926987 | − | 0.375092i | \(-0.877611\pi\) | ||
0.926987 | − | 0.375092i | \(-0.122389\pi\) | |||||||
\(542\) | − | 10.4433i | − | 0.448579i | ||||||
\(543\) | 13.4277 | 0.576239 | ||||||||
\(544\) | − | 3.20191i | − | 0.137281i | ||||||
\(545\) | 14.4792 | 0.620220 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.16878i | − | 0.0499734i | −0.999688 | − | 0.0249867i | \(-0.992046\pi\) | ||
0.999688 | − | 0.0249867i | \(-0.00795434\pi\) | |||||||
\(548\) | −9.08974 | −0.388294 | ||||||||
\(549\) | −2.93637 | −0.125321 | ||||||||
\(550\) | −0.804802 | − | 11.3000i | −0.0343169 | − | 0.481835i | ||||
\(551\) | − | 27.0330i | − | 1.15165i | ||||||
\(552\) | 8.47871 | 0.360878 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.4006 | 0.866739 | ||||||||
\(555\) | 0.398606 | 0.0169199 | ||||||||
\(556\) | 7.86546 | 0.333570 | ||||||||
\(557\) | 4.85149i | 0.205564i | 0.994704 | + | 0.102782i | \(0.0327744\pi\) | ||||
−0.994704 | + | 0.102782i | \(0.967226\pi\) | |||||||
\(558\) | 17.8569 | 0.755945 | ||||||||
\(559\) | − | 30.9360i | − | 1.30845i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.775084 | − | 10.8828i | −0.0327241 | − | 0.459471i | ||||
\(562\) | −9.99535 | −0.421628 | ||||||||
\(563\) | 26.1145 | 1.10059 | 0.550297 | − | 0.834969i | \(-0.314514\pi\) | ||||
0.550297 | + | 0.834969i | \(0.314514\pi\) | |||||||
\(564\) | 4.83144 | 0.203440 | ||||||||
\(565\) | − | 0.703551i | − | 0.0295986i | ||||||
\(566\) | − | 3.48896i | − | 0.146652i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 3.50810i | − | 0.147196i | ||||||
\(569\) | 7.48146i | 0.313639i | 0.987627 | + | 0.156820i | \(0.0501241\pi\) | ||||
−0.987627 | + | 0.156820i | \(0.949876\pi\) | |||||||
\(570\) | − | 9.86431i | − | 0.413170i | ||||||
\(571\) | − | 32.9377i | − | 1.37840i | −0.724572 | − | 0.689199i | \(-0.757962\pi\) | ||
0.724572 | − | 0.689199i | \(-0.242038\pi\) | |||||||
\(572\) | 13.5088 | − | 0.962115i | 0.564833 | − | 0.0402281i | ||||
\(573\) | − | 6.16430i | − | 0.257517i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.1890 | −1.17556 | ||||||||
\(576\) | −1.94448 | −0.0810202 | ||||||||
\(577\) | 1.55542i | 0.0647530i | 0.999476 | + | 0.0323765i | \(0.0103076\pi\) | ||||
−0.999476 | + | 0.0323765i | \(0.989692\pi\) | |||||||
\(578\) | − | 6.74775i | − | 0.280669i | ||||||
\(579\) | −9.63982 | −0.400617 | ||||||||
\(580\) | 4.46060 | 0.185216 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.9671i | 0.454600i | ||||||||
\(583\) | 15.8683 | − | 1.13016i | 0.657198 | − | 0.0468064i | ||||
\(584\) | − | 0.966855i | − | 0.0400088i | ||||||
\(585\) | − | 9.99403i | − | 0.413202i | ||||||
\(586\) | 17.3549i | 0.716924i | ||||||||
\(587\) | − | 42.8124i | − | 1.76706i | −0.468376 | − | 0.883529i | \(-0.655161\pi\) | ||
0.468376 | − | 0.883529i | \(-0.344839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 70.0520i | − | 2.88644i | ||||||
\(590\) | 3.44034i | 0.141637i | ||||||||
\(591\) | 17.8221 | 0.733105 | ||||||||
\(592\) | −0.308245 | −0.0126688 | ||||||||
\(593\) | 33.5422 | 1.37741 | 0.688707 | − | 0.725039i | \(-0.258178\pi\) | ||||
0.688707 | + | 0.725039i | \(0.258178\pi\) | |||||||
\(594\) | −16.8055 | + | 1.19691i | −0.689537 | + | 0.0491097i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.23096i | − | 0.255230i | ||||||
\(597\) | 3.00557 | 0.123010 | ||||||||
\(598\) | − | 33.6991i | − | 1.37806i | ||||||
\(599\) | 14.0171 | 0.572724 | 0.286362 | − | 0.958122i | \(-0.407554\pi\) | ||||
0.286362 | + | 0.958122i | \(0.407554\pi\) | |||||||
\(600\) | −3.50925 | −0.143265 | ||||||||
\(601\) | 36.1513 | 1.47464 | 0.737322 | − | 0.675542i | \(-0.236090\pi\) | ||||
0.737322 | + | 0.675542i | \(0.236090\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.57405 | 0.267716 | ||||||||
\(604\) | − | 17.5101i | − | 0.712476i | ||||||
\(605\) | −1.96223 | − | 13.7058i | −0.0797761 | − | 0.557218i | ||||
\(606\) | 10.3405 | 0.420052 | ||||||||
\(607\) | 29.6393 | 1.20302 | 0.601511 | − | 0.798865i | \(-0.294566\pi\) | ||||
0.601511 | + | 0.798865i | \(0.294566\pi\) | |||||||
\(608\) | 7.62813i | 0.309362i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.90074 | −0.0769586 | ||||||||
\(611\) | − | 19.2028i | − | 0.776862i | ||||||
\(612\) | 6.22607 | 0.251674 | ||||||||
\(613\) | 33.4822i | 1.35233i | 0.736750 | + | 0.676166i | \(0.236360\pi\) | ||||
−0.736750 | + | 0.676166i | \(0.763640\pi\) | |||||||
\(614\) | − | 22.6829i | − | 0.915406i | ||||||
\(615\) | −7.82712 | −0.315620 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.79395 | 0.354031 | 0.177016 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177016 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(618\) | − | 2.96423i | − | 0.119239i | ||||||
\(619\) | 27.9952i | 1.12522i | 0.826722 | + | 0.562610i | \(0.190203\pi\) | ||||
−0.826722 | + | 0.562610i | \(0.809797\pi\) | |||||||
\(620\) | 11.5590 | 0.464219 | ||||||||
\(621\) | 41.9229i | 1.68231i | ||||||||
\(622\) | −6.64116 | −0.266286 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.19520i | − | 0.167942i | ||||||
\(625\) | 3.74573 | 0.149829 | ||||||||
\(626\) | −0.502967 | −0.0201026 | ||||||||
\(627\) | 1.84653 | + | 25.9268i | 0.0737435 | + | 1.03541i | ||||
\(628\) | 7.77404i | 0.310218i | ||||||||
\(629\) | 0.986974 | 0.0393532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.154087 | −0.00613412 | −0.00306706 | − | 0.999995i | \(-0.500976\pi\) | ||||
−0.00306706 | + | 0.999995i | \(0.500976\pi\) | |||||||
\(632\) | −15.6129 | −0.621049 | ||||||||
\(633\) | 0.259650 | 0.0103202 | ||||||||
\(634\) | − | 10.5487i | − | 0.418944i | ||||||
\(635\) | 14.2016 | 0.563574 | ||||||||
\(636\) | − | 4.92794i | − | 0.195405i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.7240 | + | 0.834995i | −0.464156 | + | 0.0330578i | ||||
\(639\) | 6.82144 | 0.269852 | ||||||||
\(640\) | −1.25868 | −0.0497538 | ||||||||
\(641\) | −19.8403 | −0.783646 | −0.391823 | − | 0.920041i | \(-0.628155\pi\) | ||||
−0.391823 | + | 0.920041i | \(0.628155\pi\) | |||||||
\(642\) | 16.7464i | 0.660927i | ||||||||
\(643\) | 25.2948i | 0.997529i | 0.866737 | + | 0.498765i | \(0.166213\pi\) | ||||
−0.866737 | + | 0.498765i | \(0.833787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.79699i | 0.385756i | ||||||||
\(646\) | − | 24.4246i | − | 0.960974i | ||||||
\(647\) | 0.939459i | 0.0369340i | 0.999829 | + | 0.0184670i | \(0.00587856\pi\) | ||||
−0.999829 | + | 0.0184670i | \(0.994121\pi\) | |||||||
\(648\) | − | 0.614474i | − | 0.0241388i | ||||||
\(649\) | −0.644009 | − | 9.04238i | −0.0252796 | − | 0.354944i | ||||
\(650\) | 13.9477i | 0.547073i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.2123 | 0.713249 | ||||||||
\(653\) | −11.0075 | −0.430757 | −0.215379 | − | 0.976531i | \(-0.569099\pi\) | ||||
−0.215379 | + | 0.976531i | \(0.569099\pi\) | |||||||
\(654\) | 11.8184i | 0.462138i | ||||||||
\(655\) | 8.85342i | 0.345932i | ||||||||
\(656\) | 6.05276 | 0.236321 | ||||||||
\(657\) | 1.88004 | 0.0733472 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.9068i | 1.16500i | 0.812830 | + | 0.582501i | \(0.197926\pi\) | ||||
−0.812830 | + | 0.582501i | \(0.802074\pi\) | |||||||
\(660\) | −4.27805 | + | 0.304688i | −0.166523 | + | 0.0118600i | ||||
\(661\) | 2.68925i | 0.104600i | 0.998631 | + | 0.0522999i | \(0.0166552\pi\) | ||||
−0.998631 | + | 0.0522999i | \(0.983345\pi\) | |||||||
\(662\) | − | 5.78058i | − | 0.224668i | ||||||
\(663\) | 13.4327i | 0.521681i | ||||||||
\(664\) | − | 1.32998i | − | 0.0516132i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 0.599378i | − | 0.0232254i | ||||||
\(667\) | 29.2465i | 1.13243i | ||||||||
\(668\) | −14.3653 | −0.555809 | ||||||||
\(669\) | −19.5583 | −0.756169 | ||||||||
\(670\) | 4.25544 | 0.164402 | ||||||||
\(671\) | 4.99578 | − | 0.355806i | 0.192860 | − | 0.0137357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.56361i | − | 0.137367i | −0.997638 | − | 0.0686836i | \(-0.978120\pi\) | ||
0.997638 | − | 0.0686836i | \(-0.0218799\pi\) | |||||||
\(674\) | −11.1226 | −0.428425 | ||||||||
\(675\) | − | 17.3514i | − | 0.667857i | ||||||
\(676\) | −3.67402 | −0.141309 | ||||||||
\(677\) | −31.1803 | −1.19836 | −0.599178 | − | 0.800616i | \(-0.704506\pi\) | ||||
−0.599178 | + | 0.800616i | \(0.704506\pi\) | |||||||
\(678\) | 0.574264 | 0.0220545 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.03019 | 0.154551 | ||||||||
\(681\) | − | 18.9110i | − | 0.724672i | ||||||
\(682\) | −30.3809 | + | 2.16376i | −1.16334 | + | 0.0828547i | ||||
\(683\) | −15.5999 | −0.596912 | −0.298456 | − | 0.954423i | \(-0.596472\pi\) | ||||
−0.298456 | + | 0.954423i | \(0.596472\pi\) | |||||||
\(684\) | −14.8328 | −0.567146 | ||||||||
\(685\) | − | 11.4411i | − | 0.437142i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.45320 | 0.208053 | ||||||||
\(688\) | − | 7.57607i | − | 0.288835i | ||||||
\(689\) | −19.5863 | −0.746179 | ||||||||
\(690\) | 10.6720i | 0.406276i | ||||||||
\(691\) | 36.8236i | 1.40084i | 0.713732 | + | 0.700419i | \(0.247003\pi\) | ||||
−0.713732 | + | 0.700419i | \(0.752997\pi\) | |||||||
\(692\) | 4.76319 | 0.181069 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6714 | −0.556918 | ||||||||
\(695\) | 9.90012i | 0.375533i | ||||||||
\(696\) | 3.64090i | 0.138008i | ||||||||
\(697\) | −19.3804 | −0.734086 | ||||||||
\(698\) | − | 24.6769i | − | 0.934036i | ||||||
\(699\) | 21.9029 | 0.828445 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.6940i | − | 0.592754i | −0.955071 | − | 0.296377i | \(-0.904222\pi\) | ||
0.955071 | − | 0.296377i | \(-0.0957784\pi\) | |||||||
\(702\) | 20.7431 | 0.782898 | ||||||||
\(703\) | −2.35133 | −0.0886822 | ||||||||
\(704\) | 3.30824 | − | 0.235617i | 0.124684 | − | 0.00888016i | ||||
\(705\) | 6.08125i | 0.229033i | ||||||||
\(706\) | 19.2447 | 0.724285 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.80813 | −0.105536 | ||||||||
\(709\) | −24.3465 | −0.914352 | −0.457176 | − | 0.889376i | \(-0.651139\pi\) | ||||
−0.457176 | + | 0.889376i | \(0.651139\pi\) | |||||||
\(710\) | 4.41558 | 0.165714 | ||||||||
\(711\) | − | 30.3591i | − | 1.13856i | ||||||
\(712\) | −10.6498 | −0.399116 | ||||||||
\(713\) | 75.7880i | 2.83828i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.21100 | + | 17.0033i | 0.0452887 | + | 0.635888i | ||||
\(716\) | 3.89051 | 0.145395 | ||||||||
\(717\) | 7.45020 | 0.278233 | ||||||||
\(718\) | −3.29407 | −0.122934 | ||||||||
\(719\) | − | 42.6166i | − | 1.58933i | −0.607048 | − | 0.794665i | \(-0.707646\pi\) | ||
0.607048 | − | 0.794665i | \(-0.292354\pi\) | |||||||
\(720\) | − | 2.44749i | − | 0.0912125i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 39.1884i | 1.45844i | ||||||||
\(723\) | 3.65142i | 0.135798i | ||||||||
\(724\) | − | 13.0698i | − | 0.485737i | ||||||
\(725\) | − | 12.1048i | − | 0.449562i | ||||||
\(726\) | 11.1871 | − | 1.60165i | 0.415194 | − | 0.0594427i | ||||
\(727\) | − | 23.2698i | − | 0.863031i | −0.902106 | − | 0.431515i | \(-0.857979\pi\) | ||
0.902106 | − | 0.431515i | \(-0.142021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.4621 | −0.535633 | ||||||||
\(730\) | 1.21696 | 0.0450419 | ||||||||
\(731\) | 24.2579i | 0.897212i | ||||||||
\(732\) | − | 1.55145i | − | 0.0573433i | ||||||
\(733\) | −37.6757 | −1.39158 | −0.695791 | − | 0.718244i | \(-0.744946\pi\) | ||||
−0.695791 | + | 0.718244i | \(0.744946\pi\) | |||||||
\(734\) | −30.9410 | −1.14205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 8.25273i | − | 0.304200i | ||||||
\(737\) | −11.1848 | + | 0.796592i | −0.411996 | + | 0.0293428i | ||||
\(738\) | 11.7695i | 0.433241i | ||||||||
\(739\) | − | 0.554007i | − | 0.0203795i | −0.999948 | − | 0.0101897i | \(-0.996756\pi\) | ||
0.999948 | − | 0.0101897i | \(-0.00324355\pi\) | |||||||
\(740\) | − | 0.387982i | − | 0.0142625i | ||||||
\(741\) | − | 32.0015i | − | 1.17561i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 20.1974i | − | 0.740972i | −0.928838 | − | 0.370486i | \(-0.879191\pi\) | ||
0.928838 | − | 0.370486i | \(-0.120809\pi\) | |||||||
\(744\) | 9.43485i | 0.345898i | ||||||||
\(745\) | 7.84280 | 0.287338 | ||||||||
\(746\) | −0.961597 | −0.0352066 | ||||||||
\(747\) | 2.58612 | 0.0946213 | ||||||||
\(748\) | −10.5927 | + | 0.754426i | −0.387308 | + | 0.0275845i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 10.8828i | − | 0.397383i | ||||||
\(751\) | 7.40062 | 0.270053 | 0.135026 | − | 0.990842i | \(-0.456888\pi\) | ||||
0.135026 | + | 0.990842i | \(0.456888\pi\) | |||||||
\(752\) | − | 4.70267i | − | 0.171489i | ||||||
\(753\) | −0.755874 | −0.0275456 | ||||||||
\(754\) | 14.4709 | 0.527001 | ||||||||
\(755\) | 22.0397 | 0.802106 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1994 | −1.06127 | −0.530636 | − | 0.847600i | \(-0.678047\pi\) | ||||
−0.530636 | + | 0.847600i | \(0.678047\pi\) | |||||||
\(758\) | − | 1.41216i | − | 0.0512920i | ||||||
\(759\) | −1.99773 | − | 28.0497i | −0.0725130 | − | 1.01814i | ||||
\(760\) | −9.60139 | −0.348279 | ||||||||
\(761\) | −50.9662 | −1.84752 | −0.923761 | − | 0.382968i | \(-0.874902\pi\) | ||||
−0.923761 | + | 0.382968i | \(0.874902\pi\) | |||||||
\(762\) | 11.5919i | 0.419930i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 7.83665i | 0.283335i | ||||||||
\(766\) | 3.78079 | 0.136605 | ||||||||
\(767\) | 11.1611i | 0.403002i | ||||||||
\(768\) | − | 1.02738i | − | 0.0370725i | ||||||
\(769\) | −32.9963 | −1.18988 | −0.594938 | − | 0.803771i | \(-0.702824\pi\) | ||||
−0.594938 | + | 0.803771i | \(0.702824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6503 | 0.599645 | ||||||||
\(772\) | 9.38289i | 0.337698i | ||||||||
\(773\) | − | 32.5391i | − | 1.17035i | −0.810907 | − | 0.585175i | \(-0.801026\pi\) | ||
0.810907 | − | 0.585175i | \(-0.198974\pi\) | |||||||
\(774\) | 14.7316 | 0.529515 | ||||||||
\(775\) | − | 31.3678i | − | 1.12677i | ||||||
\(776\) | 10.6748 | 0.383202 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 3.37886i | − | 0.121138i | ||||||
\(779\) | 46.1713 | 1.65426 | ||||||||
\(780\) | 5.28042 | 0.189069 | ||||||||
\(781\) | −11.6056 | + | 0.826568i | −0.415283 | + | 0.0295769i | ||||
\(782\) | 26.4245i | 0.944939i | ||||||||
\(783\) | −18.0024 | −0.643353 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.78505 | −0.349243 | ||||||||
\(786\) | −7.22649 | −0.257760 | ||||||||
\(787\) | −20.1154 | −0.717038 | −0.358519 | − | 0.933522i | \(-0.616718\pi\) | ||||
−0.358519 | + | 0.933522i | \(0.616718\pi\) | |||||||
\(788\) | − | 17.3471i | − | 0.617966i | ||||||
\(789\) | 24.9675 | 0.888867 | ||||||||
\(790\) | − | 19.6517i | − | 0.699177i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.458154 | + | 6.43283i | 0.0162798 | + | 0.228581i | ||||
\(793\) | −6.16632 | −0.218972 | ||||||||
\(794\) | −11.5300 | −0.409183 | ||||||||
\(795\) | 6.20271 | 0.219987 | ||||||||
\(796\) | − | 2.92547i | − | 0.103690i | ||||||
\(797\) | − | 31.1568i | − | 1.10363i | −0.833966 | − | 0.551816i | \(-0.813935\pi\) | ||
0.833966 | − | 0.551816i | \(-0.186065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0575i | 0.532697i | ||||||||
\(800\) | 3.41572i | 0.120764i | ||||||||
\(801\) | − | 20.7083i | − | 0.731691i | ||||||
\(802\) | 26.0523i | 0.919937i | ||||||||
\(803\) | −3.19859 | + | 0.227808i | −0.112876 | + | 0.00803916i | ||||
\(804\) | 3.47345i | 0.122499i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 37.4993 | 1.32086 | ||||||||
\(807\) | −27.7891 | −0.978222 | ||||||||
\(808\) | − | 10.0648i | − | 0.354080i | ||||||
\(809\) | − | 14.6600i | − | 0.515419i | −0.966222 | − | 0.257709i | \(-0.917032\pi\) | ||
0.966222 | − | 0.257709i | \(-0.0829677\pi\) | |||||||
\(810\) | 0.773427 | 0.0271755 | ||||||||
\(811\) | −45.7501 | −1.60650 | −0.803251 | − | 0.595640i | \(-0.796898\pi\) | ||||
−0.803251 | + | 0.595640i | \(0.796898\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.7293i | 0.376292i | ||||||||
\(814\) | 0.0726278 | + | 1.01975i | 0.00254560 | + | 0.0357422i | ||||
\(815\) | 22.9235i | 0.802976i | ||||||||
\(816\) | 3.28959i | 0.115159i | ||||||||
\(817\) | − | 57.7913i | − | 2.02186i | ||||||
\(818\) | 35.0217i | 1.22451i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.61851i | 0.266050i | ||||||||
\(821\) | − | 7.05661i | − | 0.246277i | −0.992389 | − | 0.123139i | \(-0.960704\pi\) | ||
0.992389 | − | 0.123139i | \(-0.0392960\pi\) | |||||||
\(822\) | 9.33864 | 0.325723 | ||||||||
\(823\) | −28.4075 | −0.990223 | −0.495112 | − | 0.868829i | \(-0.664873\pi\) | ||||
−0.495112 | + | 0.868829i | \(0.664873\pi\) | |||||||
\(824\) | −2.88523 | −0.100512 | ||||||||
\(825\) | 0.826840 | + | 11.6095i | 0.0287869 | + | 0.404190i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.161893i | 0.00562957i | 0.999996 | + | 0.00281478i | \(0.000895975\pi\) | ||||
−0.999996 | + | 0.00281478i | \(0.999104\pi\) | |||||||
\(828\) | 16.0473 | 0.557682 | ||||||||
\(829\) | − | 24.3602i | − | 0.846066i | −0.906114 | − | 0.423033i | \(-0.860965\pi\) | ||
0.906114 | − | 0.423033i | \(-0.139035\pi\) | |||||||
\(830\) | 1.67402 | 0.0581061 | ||||||||
\(831\) | −20.9592 | −0.727068 | ||||||||
\(832\) | −4.08338 | −0.141566 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.08084 | −0.279817 | ||||||||
\(835\) | − | 18.0813i | − | 0.625730i | ||||||
\(836\) | 25.2357 | − | 1.79732i | 0.872796 | − | 0.0621616i | ||||
\(837\) | −46.6505 | −1.61248 | ||||||||
\(838\) | −12.1242 | −0.418824 | ||||||||
\(839\) | − | 3.31341i | − | 0.114392i | −0.998363 | − | 0.0571958i | \(-0.981784\pi\) | ||
0.998363 | − | 0.0571958i | \(-0.0182159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4410 | 0.566932 | ||||||||
\(842\) | 18.6940i | 0.644237i | ||||||||
\(843\) | 10.2690 | 0.353685 | ||||||||
\(844\) | − | 0.252729i | − | 0.00869931i | ||||||
\(845\) | − | 4.62443i | − | 0.159085i | ||||||
\(846\) | 9.14426 | 0.314386 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.79659 | −0.164716 | ||||||||
\(849\) | 3.58450i | 0.123020i | ||||||||
\(850\) | − | 10.9368i | − | 0.375130i | ||||||
\(851\) | 2.54386 | 0.0872025 | ||||||||
\(852\) | 3.60416i | 0.123476i | ||||||||
\(853\) | −17.0905 | −0.585169 | −0.292584 | − | 0.956240i | \(-0.594515\pi\) | ||||
−0.292584 | + | 0.956240i | \(0.594515\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 18.6698i | − | 0.638492i | ||||||
\(856\) | 16.3000 | 0.557124 | ||||||||
\(857\) | −22.4967 | −0.768473 | −0.384237 | − | 0.923235i | \(-0.625535\pi\) | ||||
−0.384237 | + | 0.923235i | \(0.625535\pi\) | |||||||
\(858\) | −13.8787 | + | 0.988461i | −0.473812 | + | 0.0337455i | ||||
\(859\) | 38.5321i | 1.31470i | 0.753586 | + | 0.657350i | \(0.228323\pi\) | ||||
−0.753586 | + | 0.657350i | \(0.771677\pi\) | |||||||
\(860\) | 9.53587 | 0.325170 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.9418 | 1.15606 | ||||||||
\(863\) | −25.7460 | −0.876405 | −0.438202 | − | 0.898876i | \(-0.644385\pi\) | ||||
−0.438202 | + | 0.898876i | \(0.644385\pi\) | |||||||
\(864\) | 5.07988 | 0.172821 | ||||||||
\(865\) | 5.99535i | 0.203848i | ||||||||
\(866\) | −27.0949 | −0.920721 | ||||||||
\(867\) | 6.93252i | 0.235441i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.67867 | + | 51.6514i | 0.124790 | + | 1.75215i | ||||
\(870\) | −4.58274 | −0.155369 | ||||||||
\(871\) | 13.8054 | 0.467778 | ||||||||
\(872\) | 11.5034 | 0.389556 | ||||||||
\(873\) | 20.7570i | 0.702516i | ||||||||
\(874\) | − | 62.9529i | − | 2.12941i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.993331i | 0.0335615i | ||||||||
\(877\) | − | 17.0522i | − | 0.575811i | −0.957659 | − | 0.287906i | \(-0.907041\pi\) | ||
0.957659 | − | 0.287906i | \(-0.0929589\pi\) | |||||||
\(878\) | 20.4538i | 0.690283i | ||||||||
\(879\) | − | 17.8301i | − | 0.601395i | ||||||
\(880\) | 0.296567 | + | 4.16403i | 0.00999728 | + | 0.140369i | ||||
\(881\) | − | 38.3968i | − | 1.29362i | −0.762651 | − | 0.646811i | \(-0.776102\pi\) | ||
0.762651 | − | 0.646811i | \(-0.223898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.3727 | −1.19038 | −0.595192 | − | 0.803583i | \(-0.702924\pi\) | ||||
−0.595192 | + | 0.803583i | \(0.702924\pi\) | |||||||
\(884\) | 13.0746 | 0.439748 | ||||||||
\(885\) | − | 3.53454i | − | 0.118812i | ||||||
\(886\) | − | 3.59736i | − | 0.120856i | ||||||
\(887\) | 2.10577 | 0.0707049 | 0.0353525 | − | 0.999375i | \(-0.488745\pi\) | ||||
0.0353525 | + | 0.999375i | \(0.488745\pi\) | |||||||
\(888\) | 0.316686 | 0.0106273 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 13.4047i | − | 0.449325i | ||||||
\(891\) | −2.03283 | + | 0.144781i | −0.0681024 | + | 0.00485033i | ||||
\(892\) | 19.0370i | 0.637408i | ||||||||
\(893\) | − | 35.8725i | − | 1.20043i | ||||||
\(894\) | 6.40159i | 0.214101i | ||||||||
\(895\) | 4.89692i | 0.163686i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.6218i | 1.15599i | ||||||||
\(898\) | 37.0664i | 1.23692i | ||||||||
\(899\) | −32.5446 | −1.08542 | ||||||||
\(900\) | −6.64181 | −0.221394 | ||||||||
\(901\) | 15.3583 | 0.511658 | ||||||||
\(902\) | −1.42613 | − | 20.0240i | −0.0474851 | − | 0.666727i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.558958i | − | 0.0185907i | ||||||
\(905\) | 16.4508 | 0.546842 | ||||||||
\(906\) | 17.9896i | 0.597664i | ||||||||
\(907\) | 50.4409 | 1.67486 | 0.837431 | − | 0.546543i | \(-0.184056\pi\) | ||||
0.837431 | + | 0.546543i | \(0.184056\pi\) | |||||||
\(908\) | −18.4070 | −0.610858 | ||||||||
\(909\) | 19.5709 | 0.649127 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.24825 | −0.0413565 | −0.0206782 | − | 0.999786i | \(-0.506583\pi\) | ||||
−0.0206782 | + | 0.999786i | \(0.506583\pi\) | |||||||
\(912\) | − | 7.83701i | − | 0.259509i | ||||||
\(913\) | −4.39990 | + | 0.313366i | −0.145615 | + | 0.0103709i | ||||
\(914\) | −18.1512 | −0.600389 | ||||||||
\(915\) | 1.95278 | 0.0645570 | ||||||||
\(916\) | − | 5.30786i | − | 0.175377i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.2653 | −0.536836 | ||||||||
\(919\) | − | 16.2421i | − | 0.535776i | −0.963450 | − | 0.267888i | \(-0.913674\pi\) | ||
0.963450 | − | 0.267888i | \(-0.0863257\pi\) | |||||||
\(920\) | 10.3876 | 0.342468 | ||||||||
\(921\) | 23.3040i | 0.767892i | ||||||||
\(922\) | 22.4278i | 0.738621i | ||||||||
\(923\) | 14.3249 | 0.471510 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05288 | −0.0346184 | ||||||||
\(926\) | − | 15.6274i | − | 0.513548i | ||||||
\(927\) | − | 5.61028i | − | 0.184266i | ||||||
\(928\) | 3.54386 | 0.116333 | ||||||||
\(929\) | 23.9107i | 0.784483i | 0.919862 | + | 0.392242i | \(0.128300\pi\) | ||||
−0.919862 | + | 0.392242i | \(0.871700\pi\) | |||||||
\(930\) | −11.8755 | −0.389412 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 21.3192i | − | 0.698332i | ||||||
\(933\) | 6.82301 | 0.223375 | ||||||||
\(934\) | −6.09520 | −0.199441 | ||||||||
\(935\) | −0.949583 | − | 13.3329i | −0.0310547 | − | 0.436031i | ||||
\(936\) | − | 7.94008i | − | 0.259530i | ||||||
\(937\) | −28.2482 | −0.922827 | −0.461414 | − | 0.887185i | \(-0.652658\pi\) | ||||
−0.461414 | + | 0.887185i | \(0.652658\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.516740 | 0.0168632 | ||||||||
\(940\) | 5.91916 | 0.193062 | ||||||||
\(941\) | 58.7024 | 1.91364 | 0.956821 | − | 0.290677i | \(-0.0938805\pi\) | ||||
0.956821 | + | 0.290677i | \(0.0938805\pi\) | |||||||
\(942\) | − | 7.98692i | − | 0.260228i | ||||||
\(943\) | −49.9518 | −1.62665 | ||||||||
\(944\) | 2.73329i | 0.0889609i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.0635 | + | 1.78505i | −0.814885 | + | 0.0580371i | ||||
\(947\) | −44.3345 | −1.44068 | −0.720338 | − | 0.693623i | \(-0.756014\pi\) | ||||
−0.720338 | + | 0.693623i | \(0.756014\pi\) | |||||||
\(948\) | 16.0405 | 0.520970 | ||||||||
\(949\) | 3.94804 | 0.128159 | ||||||||
\(950\) | 26.0556i | 0.845354i | ||||||||
\(951\) | 10.8376i | 0.351433i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.9238i | − | 0.451037i | −0.974239 | − | 0.225518i | \(-0.927592\pi\) | ||
0.974239 | − | 0.225518i | \(-0.0724075\pi\) | |||||||
\(954\) | − | 9.32690i | − | 0.301969i | ||||||
\(955\) | − | 7.55209i | − | 0.244380i | ||||||
\(956\) | − | 7.25163i | − | 0.234535i | ||||||
\(957\) | 12.0450 | − | 0.857859i | 0.389360 | − | 0.0277306i | ||||
\(958\) | − | 30.6275i | − | 0.989531i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.29315 | 0.0417362 | ||||||||
\(961\) | −53.3345 | −1.72047 | ||||||||
\(962\) | − | 1.25868i | − | 0.0405815i | ||||||
\(963\) | 31.6952i | 1.02136i | ||||||||
\(964\) | 3.55410 | 0.114470 | ||||||||
\(965\) | −11.8101 | −0.380180 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3085i | 0.942499i | 0.882000 | + | 0.471250i | \(0.156197\pi\) | ||||
−0.882000 | + | 0.471250i | \(0.843803\pi\) | |||||||
\(968\) | −1.55896 | − | 10.8890i | −0.0501068 | − | 0.349985i | ||||
\(969\) | 25.0934i | 0.806117i | ||||||||
\(970\) | 13.4362i | 0.431409i | ||||||||
\(971\) | 0.0330907i | 0.00106193i | 1.00000 | 0.000530965i | \(0.000169012\pi\) | |||||
−1.00000 | 0.000530965i | \(0.999831\pi\) | ||||||||
\(972\) | 15.8709i | 0.509060i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 3.17453i | − | 0.101718i | ||||||
\(975\) | − | 14.3296i | − | 0.458915i | ||||||
\(976\) | −1.51010 | −0.0483371 | ||||||||
\(977\) | 42.1896 | 1.34977 | 0.674883 | − | 0.737925i | \(-0.264194\pi\) | ||||
0.674883 | + | 0.737925i | \(0.264194\pi\) | |||||||
\(978\) | −18.7110 | −0.598312 | ||||||||
\(979\) | 2.50926 | + | 35.2320i | 0.0801964 | + | 1.12602i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.3683i | 0.714164i | ||||||||
\(982\) | 32.6507 | 1.04193 | ||||||||
\(983\) | − | 50.8133i | − | 1.62069i | −0.585950 | − | 0.810347i | \(-0.699279\pi\) | ||
0.585950 | − | 0.810347i | \(-0.300721\pi\) | |||||||
\(984\) | −6.21850 | −0.198239 | ||||||||
\(985\) | 21.8345 | 0.695706 | ||||||||
\(986\) | −11.3471 | −0.361367 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.1486 | −0.990968 | ||||||||
\(989\) | 62.5233i | 1.98812i | ||||||||
\(990\) | −8.09689 | + | 0.576670i | −0.257336 | + | 0.0183278i | ||||
\(991\) | 46.5228 | 1.47785 | 0.738923 | − | 0.673790i | \(-0.235335\pi\) | ||||
0.738923 | + | 0.673790i | \(0.235335\pi\) | |||||||
\(992\) | 9.18338 | 0.291573 | ||||||||
\(993\) | 5.93886i | 0.188464i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.68223 | 0.116735 | ||||||||
\(996\) | 1.36640i | 0.0432960i | ||||||||
\(997\) | 4.53775 | 0.143712 | 0.0718560 | − | 0.997415i | \(-0.477108\pi\) | ||||
0.0718560 | + | 0.997415i | \(0.477108\pi\) | |||||||
\(998\) | 28.4548i | 0.900721i | ||||||||
\(999\) | 1.56585i | 0.0495412i |
(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 | 1078.2.c.b.1077.12 | 16 | ||
7.2 | even | 3 | 1078.2.i.c.1011.7 | 16 | |||
7.3 | odd | 6 | 1078.2.i.c.901.3 | 16 | |||
7.4 | even | 3 | 154.2.i.a.131.2 | yes | 16 | ||
7.5 | odd | 6 | 154.2.i.a.87.6 | yes | 16 | ||
7.6 | odd | 2 | inner | 1078.2.c.b.1077.13 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.c.b.1077.4 | 16 | ||
21.5 | even | 6 | 1386.2.bk.c.703.1 | 16 | |||
21.11 | odd | 6 | 1386.2.bk.c.901.5 | 16 | |||
28.11 | odd | 6 | 1232.2.bn.b.593.6 | 16 | |||
28.19 | even | 6 | 1232.2.bn.b.241.5 | 16 | |||
77.10 | even | 6 | 1078.2.i.c.901.7 | 16 | |||
77.32 | odd | 6 | 154.2.i.a.131.6 | yes | 16 | ||
77.54 | even | 6 | 154.2.i.a.87.2 | ✓ | 16 | ||
77.65 | odd | 6 | 1078.2.i.c.1011.3 | 16 | |||
77.76 | even | 2 | inner | 1078.2.c.b.1077.5 | 16 | ||
231.32 | even | 6 | 1386.2.bk.c.901.1 | 16 | |||
231.131 | odd | 6 | 1386.2.bk.c.703.5 | 16 | |||
308.131 | odd | 6 | 1232.2.bn.b.241.6 | 16 | |||
308.263 | even | 6 | 1232.2.bn.b.593.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.2 | ✓ | 16 | 77.54 | even | 6 | ||
154.2.i.a.87.6 | yes | 16 | 7.5 | odd | 6 | ||
154.2.i.a.131.2 | yes | 16 | 7.4 | even | 3 | ||
154.2.i.a.131.6 | yes | 16 | 77.32 | odd | 6 | ||
1078.2.c.b.1077.4 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.c.b.1077.5 | 16 | 77.76 | even | 2 | inner | ||
1078.2.c.b.1077.12 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.c.b.1077.13 | 16 | 7.6 | odd | 2 | inner | ||
1078.2.i.c.901.3 | 16 | 7.3 | odd | 6 | |||
1078.2.i.c.901.7 | 16 | 77.10 | even | 6 | |||
1078.2.i.c.1011.3 | 16 | 77.65 | odd | 6 | |||
1078.2.i.c.1011.7 | 16 | 7.2 | even | 3 | |||
1232.2.bn.b.241.5 | 16 | 28.19 | even | 6 | |||
1232.2.bn.b.241.6 | 16 | 308.131 | odd | 6 | |||
1232.2.bn.b.593.5 | 16 | 308.263 | even | 6 | |||
1232.2.bn.b.593.6 | 16 | 28.11 | odd | 6 | |||
1386.2.bk.c.703.1 | 16 | 21.5 | even | 6 | |||
1386.2.bk.c.703.5 | 16 | 231.131 | odd | 6 | |||
1386.2.bk.c.901.1 | 16 | 231.32 | even | 6 | |||
1386.2.bk.c.901.5 | 16 | 21.11 | odd | 6 |