Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,2,Mod(49,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("176.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.m (of order \(5\), degree \(4\), 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: | \(1.40536707557\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.682515625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 88) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(2.51217 - 1.82520i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.97 |
Dual form | 176.2.m.d.49.2 |
$q$-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 \(\left(\mathbb{Z}/176\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(133\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.55261 | − | 1.12804i | 0.896399 | − | 0.651272i | −0.0411392 | − | 0.999153i | \(-0.513099\pi\) |
0.937539 | + | 0.347881i | \(0.113099\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.05261 | + | 3.23960i | 0.470741 | + | 1.44879i | 0.851616 | + | 0.524166i | \(0.175623\pi\) |
−0.380875 | + | 0.924627i | \(0.624377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.703158 | + | 0.510874i | 0.265769 | + | 0.193092i | 0.712686 | − | 0.701483i | \(-0.247478\pi\) |
−0.446918 | + | 0.894575i | \(0.647478\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.211078 | − | 0.649631i | 0.0703593 | − | 0.216544i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.16272 | − | 0.998590i | −0.953597 | − | 0.301086i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.866521 | − | 2.66688i | 0.240330 | − | 0.739659i | −0.756040 | − | 0.654526i | \(-0.772868\pi\) |
0.996370 | − | 0.0851334i | \(-0.0271316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.28868 | + | 3.84245i | 1.36553 | + | 0.992116i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.25314 | − | 6.93444i | −0.546466 | − | 1.68185i | −0.717478 | − | 0.696581i | \(-0.754704\pi\) |
0.171012 | − | 0.985269i | \(-0.445296\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.92705 | − | 1.40008i | 0.442096 | − | 0.321201i | −0.344371 | − | 0.938834i | \(-0.611908\pi\) |
0.786467 | + | 0.617632i | \(0.211908\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.66801 | 0.363990 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.44651 | −1.55270 | −0.776352 | − | 0.630300i | \(-0.782932\pi\) | ||||
−0.776352 | + | 0.630300i | \(0.782932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.34193 | + | 3.88114i | −1.06839 | + | 0.776227i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.37405 | + | 4.22888i | 0.264435 | + | 0.813848i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.93923 | + | 4.31510i | 1.10289 | + | 0.801294i | 0.981529 | − | 0.191315i | \(-0.0612752\pi\) |
0.121358 | + | 0.992609i | \(0.461275\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.816541 | − | 2.51306i | 0.146655 | − | 0.451358i | −0.850565 | − | 0.525870i | \(-0.823740\pi\) |
0.997220 | + | 0.0745118i | \(0.0237398\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.03692 | + | 2.01725i | −1.05089 | + | 0.351158i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.914876 | + | 2.81570i | −0.154642 | + | 0.475940i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.834007 | − | 0.605942i | −0.137110 | − | 0.0996162i | 0.517116 | − | 0.855915i | \(-0.327006\pi\) |
−0.654226 | + | 0.756299i | \(0.727006\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.66297 | − | 5.11809i | −0.266288 | − | 0.819550i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.34089 | + | 1.70076i | −0.365586 | + | 0.265614i | −0.755378 | − | 0.655289i | \(-0.772547\pi\) |
0.389792 | + | 0.920903i | \(0.372547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.18609 | −0.333375 | −0.166688 | − | 0.986010i | \(-0.553307\pi\) | ||||
−0.166688 | + | 0.986010i | \(0.553307\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.32673 | 0.346848 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.19034 | + | 2.31792i | −0.465359 | + | 0.338103i | −0.795630 | − | 0.605783i | \(-0.792860\pi\) |
0.330271 | + | 0.943886i | \(0.392860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.92968 | − | 5.93895i | −0.275669 | − | 0.848421i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.3206 | − | 8.22486i | −1.58519 | − | 1.15171i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.19851 | + | 6.76631i | −0.301988 | + | 0.929424i | 0.678796 | + | 0.734327i | \(0.262502\pi\) |
−0.980784 | + | 0.195097i | \(0.937498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0940804 | − | 11.2971i | −0.0126858 | − | 1.52330i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.41261 | − | 4.34757i | 0.187105 | − | 0.575850i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.54508 | + | 4.75528i | 0.852097 | + | 0.619085i | 0.925724 | − | 0.378201i | \(-0.123457\pi\) |
−0.0736261 | + | 0.997286i | \(0.523457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.832382 | − | 2.56181i | −0.106576 | − | 0.328006i | 0.883521 | − | 0.468391i | \(-0.155166\pi\) |
−0.990097 | + | 0.140385i | \(0.955166\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.480301 | − | 0.348959i | 0.0605122 | − | 0.0439647i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.55172 | 1.18475 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.7720 | 1.68251 | 0.841256 | − | 0.540637i | \(-0.181817\pi\) | ||||
0.841256 | + | 0.540637i | \(0.181817\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.5615 | + | 8.39993i | −1.39184 | + | 1.01123i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.596314 | + | 1.83527i | 0.0707694 | + | 0.217806i | 0.980186 | − | 0.198081i | \(-0.0634710\pi\) |
−0.909416 | + | 0.415887i | \(0.863471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.03979 | − | 2.93508i | −0.472822 | − | 0.343525i | 0.325718 | − | 0.945467i | \(-0.394394\pi\) |
−0.798540 | + | 0.601942i | \(0.794394\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.91586 | + | 12.0518i | −0.452165 | + | 1.39162i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.71374 | − | 2.31792i | −0.195299 | − | 0.264151i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.15783 | + | 12.7965i | −0.467792 | + | 1.43972i | 0.387644 | + | 0.921809i | \(0.373289\pi\) |
−0.855437 | + | 0.517907i | \(0.826711\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.56151 | + | 6.22030i | 0.951279 | + | 0.691145i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0601338 | + | 0.185073i | 0.00660054 | + | 0.0203144i | 0.954303 | − | 0.298842i | \(-0.0966004\pi\) |
−0.947702 | + | 0.319157i | \(0.896600\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.0931 | − | 14.5985i | 2.17941 | − | 1.58343i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.0889 | 1.51049 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.18609 | 0.443724 | 0.221862 | − | 0.975078i | \(-0.428786\pi\) | ||||
0.221862 | + | 0.975078i | \(0.428786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.97174 | − | 1.43255i | 0.206695 | − | 0.150172i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.56705 | − | 4.82288i | −0.162495 | − | 0.500110i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.56414 | + | 4.76913i | 0.673467 | + | 0.489302i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.54206 | − | 4.74597i | 0.156572 | − | 0.481880i | −0.841744 | − | 0.539876i | \(-0.818471\pi\) |
0.998317 | + | 0.0579959i | \(0.0184710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.31630 | + | 1.84382i | −0.132293 | + | 0.185311i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.55563 | + | 7.86543i | −0.254295 | + | 0.782640i | 0.739673 | + | 0.672967i | \(0.234980\pi\) |
−0.993968 | + | 0.109673i | \(0.965020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.663759 | + | 0.482249i | 0.0654022 | + | 0.0475175i | 0.620006 | − | 0.784597i | \(-0.287130\pi\) |
−0.554604 | + | 0.832115i | \(0.687130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.75577 | + | 5.40370i | 0.171345 | + | 0.527347i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.0247 | − | 7.28340i | 0.969129 | − | 0.704113i | 0.0138759 | − | 0.999904i | \(-0.495583\pi\) |
0.955253 | + | 0.295791i | \(0.0955830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.20439 | −0.690055 | −0.345028 | − | 0.938593i | \(-0.612130\pi\) | ||||
−0.345028 | + | 0.938593i | \(0.612130\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.97841 | −0.187782 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.66535 | + | 1.20995i | −0.156663 | + | 0.113822i | −0.663355 | − | 0.748305i | \(-0.730868\pi\) |
0.506692 | + | 0.862127i | \(0.330868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.83826 | − | 24.1237i | −0.730922 | − | 2.24955i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.54958 | − | 1.12584i | −0.143259 | − | 0.104084i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.95832 | − | 6.02708i | 0.179519 | − | 0.552501i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00563 | + | 6.31653i | 0.818694 | + | 0.574230i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.71597 | + | 5.28122i | −0.154724 | + | 0.476192i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.41745 | − | 3.20947i | −0.395109 | − | 0.287064i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.58652 | − | 7.96050i | −0.229517 | − | 0.706380i | −0.997802 | − | 0.0662721i | \(-0.978889\pi\) |
0.768285 | − | 0.640108i | \(-0.221111\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.39414 | + | 2.46599i | −0.298837 | + | 0.217118i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3511 | −1.16649 | −0.583244 | − | 0.812297i | \(-0.698217\pi\) | ||||
−0.583244 | + | 0.812297i | \(0.698217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.07029 | 0.179517 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.2535 | + | 8.90271i | −1.05462 | + | 0.766224i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.305992 | + | 0.941746i | 0.0261426 | + | 0.0804588i | 0.963277 | − | 0.268511i | \(-0.0865316\pi\) |
−0.937134 | + | 0.348970i | \(0.886532\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.84985 | + | 3.52362i | 0.411359 | + | 0.298870i | 0.774152 | − | 0.633000i | \(-0.218177\pi\) |
−0.362793 | + | 0.931870i | \(0.618177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.33866 | + | 7.19765i | −0.196950 | + | 0.606151i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.40369 | + | 7.56930i | −0.451879 | + | 0.632977i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.72751 | + | 23.7828i | −0.641735 | + | 1.97506i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.69539 | − | 7.04411i | −0.799662 | − | 0.580989i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.34392 | − | 16.4469i | −0.437791 | − | 1.34738i | −0.890200 | − | 0.455571i | \(-0.849435\pi\) |
0.452409 | − | 0.891811i | \(-0.350565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.639410 | + | 0.464559i | −0.0520344 | + | 0.0378052i | −0.613498 | − | 0.789696i | \(-0.710238\pi\) |
0.561464 | + | 0.827501i | \(0.310238\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.98042 | −0.402643 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.00079 | 0.722961 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3041 | − | 7.48635i | 0.822354 | − | 0.597475i | −0.0950316 | − | 0.995474i | \(-0.530295\pi\) |
0.917386 | + | 0.397999i | \(0.130295\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.21922 | + | 12.9854i | 0.334606 | + | 1.02981i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.23607 | − | 3.80423i | −0.412660 | − | 0.299815i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0512092 | − | 0.157606i | 0.00401101 | − | 0.0123446i | −0.949031 | − | 0.315183i | \(-0.897934\pi\) |
0.953042 | + | 0.302838i | \(0.0979342\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.8896 | − | 17.4338i | −1.00345 | − | 1.35722i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.70153 | − | 20.6252i | 0.518580 | − | 1.59603i | −0.258092 | − | 0.966120i | \(-0.583094\pi\) |
0.776672 | − | 0.629905i | \(-0.216906\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.15584 | + | 3.01939i | 0.319680 | + | 0.232261i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.502781 | − | 1.54740i | −0.0384486 | − | 0.118333i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5967 | + | 7.69892i | −0.805649 | + | 0.585338i | −0.912566 | − | 0.408930i | \(-0.865902\pi\) |
0.106917 | + | 0.994268i | \(0.465902\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.73899 | −0.433827 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.5261 | 1.16701 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.56943 | + | 6.22606i | −0.640510 | + | 0.465357i | −0.860025 | − | 0.510252i | \(-0.829552\pi\) |
0.219516 | + | 0.975609i | \(0.429552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.97828 | + | 6.08852i | 0.147044 | + | 0.452556i | 0.997268 | − | 0.0738652i | \(-0.0235335\pi\) |
−0.850224 | + | 0.526421i | \(0.823533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.18218 | − | 3.03853i | −0.309155 | − | 0.224615i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.08512 | − | 3.33967i | 0.0797799 | − | 0.245537i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.201381 | + | 24.1817i | 0.0147265 | + | 1.76834i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.19425 | + | 3.67553i | −0.0868691 | + | 0.267356i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.49144 | + | 3.98976i | 0.397347 | + | 0.288689i | 0.768459 | − | 0.639899i | \(-0.221024\pi\) |
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.51465 | − | 7.73931i | −0.181009 | − | 0.557087i | 0.818848 | − | 0.574010i | \(-0.194613\pi\) |
−0.999857 | + | 0.0169228i | \(0.994613\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.8301 | − | 10.7747i | 1.06201 | − | 0.771592i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4907 | −1.17492 | −0.587458 | − | 0.809255i | \(-0.699871\pi\) | ||||
−0.587458 | + | 0.809255i | \(0.699871\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.39781 | −0.240864 | −0.120432 | − | 0.992722i | \(-0.538428\pi\) | ||||
−0.120432 | + | 0.992722i | \(0.538428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3825 | − | 15.5353i | 1.50820 | − | 1.09577i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.97174 | + | 6.06839i | 0.138389 | + | 0.425918i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.97381 | − | 5.79331i | −0.556915 | − | 0.404623i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.57179 | + | 4.83748i | −0.109247 | + | 0.336228i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.49284 | + | 2.50375i | −0.518291 | + | 0.173188i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.93907 | + | 15.2009i | −0.340020 | + | 1.04647i | 0.624176 | + | 0.781284i | \(0.285435\pi\) |
−0.964196 | + | 0.265190i | \(0.914565\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.99609 | + | 2.17679i | 0.205289 | + | 0.149151i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.30110 | − | 7.08205i | −0.156933 | − | 0.482992i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.85801 | − | 1.34993i | 0.126130 | − | 0.0916389i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.58310 | −0.647566 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.4457 | −1.37533 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.13382 | − | 4.45648i | 0.410751 | − | 0.298428i | −0.363155 | − | 0.931729i | \(-0.618300\pi\) |
0.773906 | + | 0.633301i | \(0.218300\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.39374 | + | 4.28951i | 0.0929163 | + | 0.285967i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1460 | + | 8.82458i | 0.806158 | + | 0.585708i | 0.912714 | − | 0.408599i | \(-0.133982\pi\) |
−0.106556 | + | 0.994307i | \(0.533982\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.742212 | − | 2.28429i | 0.0490467 | − | 0.150950i | −0.923534 | − | 0.383518i | \(-0.874713\pi\) |
0.972580 | + | 0.232567i | \(0.0747126\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.27547 | − | 1.66566i | −0.347100 | − | 0.109593i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.92928 | − | 5.93773i | 0.126392 | − | 0.388993i | −0.867760 | − | 0.496983i | \(-0.834441\pi\) |
0.994152 | + | 0.107989i | \(0.0344412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.8673 | − | 7.89557i | −0.708905 | − | 0.515050i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.97942 | + | 24.5581i | 0.518319 | + | 1.59522i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8018 | + | 10.0276i | −0.892767 | + | 0.648633i | −0.936598 | − | 0.350406i | \(-0.886044\pi\) |
0.0438313 | + | 0.999039i | \(0.486044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0166322 | 0.00107138 | 0.000535688 | − | 1.00000i | \(-0.499829\pi\) | ||||
0.000535688 | 1.00000i | \(0.499829\pi\) | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.96990 | 0.447119 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.2086 | − | 12.5028i | 1.09942 | − | 0.798773i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.06402 | − | 6.35241i | −0.131331 | − | 0.404194i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.302133 | + | 0.219513i | 0.0191469 | + | 0.0139110i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.47477 | − | 23.0050i | 0.471803 | − | 1.45206i | −0.378418 | − | 0.925635i | \(-0.623532\pi\) |
0.850221 | − | 0.526426i | \(-0.176468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.5512 | + | 7.43601i | 1.48065 | + | 0.467498i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.7291 | − | 45.3316i | 0.922374 | − | 2.83878i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4041 | + | 17.0041i | 1.45991 | + | 1.06069i | 0.983386 | + | 0.181526i | \(0.0581037\pi\) |
0.476525 | + | 0.879161i | \(0.341896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.276879 | − | 0.852145i | −0.0172044 | − | 0.0529497i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.05686 | − | 2.94748i | 0.251114 | − | 0.182445i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.2531 | 1.06387 | 0.531935 | − | 0.846785i | \(-0.321465\pi\) | ||||
0.531935 | + | 0.846785i | \(0.321465\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.2343 | −1.48870 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.49936 | − | 4.72206i | 0.397754 | − | 0.288985i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.866521 | + | 2.66688i | 0.0528327 | + | 0.162602i | 0.973991 | − | 0.226585i | \(-0.0727560\pi\) |
−0.921159 | + | 0.389187i | \(0.872756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4114 | + | 13.3766i | 1.11841 | + | 0.812573i | 0.983967 | − | 0.178348i | \(-0.0570754\pi\) |
0.134443 | + | 0.990921i | \(0.457075\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.44537 | − | 4.44839i | 0.0874778 | − | 0.269229i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.7707 | − | 6.94057i | 1.25252 | − | 0.418532i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.02826 | − | 3.16466i | 0.0617821 | − | 0.190146i | −0.915401 | − | 0.402542i | \(-0.868127\pi\) |
0.977184 | + | 0.212396i | \(0.0681267\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.46021 | − | 1.06090i | −0.0874202 | − | 0.0635145i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.69322 | + | 8.28887i | 0.160664 | + | 0.494472i | 0.998691 | − | 0.0511566i | \(-0.0162908\pi\) |
−0.838027 | + | 0.545629i | \(0.816291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.5494 | + | 17.1097i | −1.39987 | + | 1.01706i | −0.405169 | + | 0.914242i | \(0.632787\pi\) |
−0.994700 | + | 0.102822i | \(0.967213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.5713 | 0.922364 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.51489 | −0.148449 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.2566 | + | 21.2562i | −1.72098 | + | 1.25036i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.95941 | − | 9.10814i | −0.173484 | − | 0.533929i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.7624 | + | 12.9052i | 1.03769 | + | 0.753928i | 0.969834 | − | 0.243767i | \(-0.0783832\pi\) |
0.0678589 | + | 0.997695i | \(0.478383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.51579 | + | 26.2089i | −0.495808 | + | 1.52594i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.122810 | − | 14.7469i | −0.00712615 | − | 0.855701i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.45256 | + | 19.8589i | −0.373161 | + | 1.14847i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.53716 | − | 1.11682i | −0.0886007 | − | 0.0643722i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.90460 | + | 15.0948i | 0.281762 | + | 0.867173i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.42306 | − | 5.39317i | 0.425043 | − | 0.308812i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1835 | 1.38023 | 0.690113 | − | 0.723701i | \(-0.257561\pi\) | ||||
0.690113 | + | 0.723701i | \(0.257561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.57455 | 0.0895733 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.88925 | + | 2.09916i | −0.163834 | + | 0.119032i | −0.666681 | − | 0.745343i | \(-0.732286\pi\) |
0.502847 | + | 0.864375i | \(0.332286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.69113 | + | 8.28246i | 0.152112 | + | 0.468152i | 0.997857 | − | 0.0654351i | \(-0.0208435\pi\) |
−0.845745 | + | 0.533587i | \(0.820844\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.63606 | + | 1.18866i | 0.0921813 | + | 0.0669737i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.80474 | − | 20.9428i | 0.382192 | − | 1.17627i | −0.556304 | − | 0.830979i | \(-0.687781\pi\) |
0.938497 | − | 0.345289i | \(-0.112219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.4751 | − | 19.5783i | −0.810451 | − | 1.09618i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.34857 | − | 22.6166i | 0.410157 | − | 1.26233i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.0507 | − | 10.2084i | −0.781803 | − | 0.568013i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.72163 | + | 17.6094i | 0.317379 | + | 0.976792i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.1856 | + | 8.12681i | −0.618565 | + | 0.449414i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.42748 | −0.188963 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.07719 | 0.114173 | 0.0570865 | − | 0.998369i | \(-0.481819\pi\) | ||||
0.0570865 | + | 0.998369i | \(0.481819\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.569679 | + | 0.413896i | −0.0312182 | + | 0.0226814i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.4965 | + | 44.6156i | 0.792028 | + | 2.43761i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4479 | − | 14.8563i | −1.11387 | − | 0.809272i | −0.130599 | − | 0.991435i | \(-0.541690\pi\) |
−0.983268 | + | 0.182163i | \(0.941690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.22077 | + | 3.75716i | −0.0663034 | + | 0.204061i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.09201 | + | 7.13271i | −0.275748 | + | 0.386258i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.55726 | − | 10.9481i | 0.192074 | − | 0.591143i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −39.3822 | − | 28.6128i | −2.12026 | − | 1.54046i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.50377 | − | 20.0165i | −0.349140 | − | 1.07454i | −0.959330 | − | 0.282288i | \(-0.908907\pi\) |
0.610189 | − | 0.792256i | \(-0.291093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.8164 | + | 13.6709i | −1.00722 | + | 0.731787i | −0.963624 | − | 0.267262i | \(-0.913881\pi\) |
−0.0435947 | + | 0.999049i | \(0.513881\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.4685 | 0.665522 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.6464 | −0.992446 | −0.496223 | − | 0.868195i | \(-0.665280\pi\) | ||||
−0.496223 | + | 0.868195i | \(0.665280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.31784 | + | 3.86364i | −0.282242 | + | 0.205060i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.75827 | − | 11.5668i | −0.198908 | − | 0.612177i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.4417 | − | 22.1172i | −1.60665 | − | 1.16730i | −0.872929 | − | 0.487847i | \(-0.837782\pi\) |
−0.733720 | − | 0.679452i | \(-0.762218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.11803 | + | 12.6740i | −0.216739 | + | 0.667053i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.1075 | − | 0.351585i | 1.10786 | − | 0.0184534i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.25616 | − | 16.1768i | 0.275120 | − | 0.846733i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.91280 | − | 5.02245i | −0.360845 | − | 0.262170i | 0.392559 | − | 0.919727i | \(-0.371590\pi\) |
−0.753405 | + | 0.657557i | \(0.771590\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.610754 | + | 1.87971i | 0.0317946 | + | 0.0978537i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.00263 | + | 3.63462i | −0.259724 | + | 0.188700i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.1461 | 0.939569 | 0.469785 | − | 0.882781i | \(-0.344332\pi\) | ||||
0.469785 | + | 0.882781i | \(0.344332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.4790 | −0.541132 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6543 | − | 12.1001i | 0.857741 | − | 0.623185i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.68422 | − | 26.7273i | −0.446078 | − | 1.37289i | −0.881297 | − | 0.472563i | \(-0.843329\pi\) |
0.435219 | − | 0.900325i | \(-0.356671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.9956 | − | 9.44186i | −0.665785 | − | 0.483721i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.47477 | − | 16.8496i | 0.279747 | − | 0.860974i | −0.708177 | − | 0.706035i | \(-0.750482\pi\) |
0.987924 | − | 0.154939i | \(-0.0495180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.70523 | − | 7.99169i | 0.290765 | − | 0.407294i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.461435 | + | 1.42015i | −0.0234561 | + | 0.0721903i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.06800 | + | 0.775949i | 0.0541499 | + | 0.0393422i | 0.614531 | − | 0.788893i | \(-0.289345\pi\) |
−0.560381 | + | 0.828235i | \(0.689345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7780 | + | 51.6374i | 0.848500 | + | 2.61141i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.7290 | + | 15.0605i | −1.04564 | + | 0.759702i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −45.8320 | −2.30606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.7700 | 0.691096 | 0.345548 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345548 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.21435 | − | 2.33536i | 0.160919 | − | 0.116914i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.30875 | − | 16.3387i | −0.265106 | − | 0.815914i | −0.991669 | − | 0.128813i | \(-0.958883\pi\) |
0.726562 | − | 0.687100i | \(-0.241117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.99446 | − | 4.35523i | −0.298606 | − | 0.216950i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.1394 | + | 34.2834i | −0.553519 | + | 1.70356i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.03265 | + | 2.74926i | 0.100755 | + | 0.136276i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.60935 | − | 8.03077i | 0.129024 | − | 0.397096i | −0.865589 | − | 0.500756i | \(-0.833055\pi\) |
0.994613 | + | 0.103660i | \(0.0330554\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.53741 | + | 1.11699i | 0.0758348 | + | 0.0550972i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.17288 | + | 6.68743i | 0.106920 | + | 0.329067i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.536264 | + | 0.389619i | −0.0263242 | + | 0.0191256i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.5047 | 0.563387 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.9791 | −1.51343 | −0.756715 | − | 0.653745i | \(-0.773197\pi\) | ||||
−0.756715 | + | 0.653745i | \(0.773197\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.6770 | + | 15.0227i | −1.00774 | + | 0.732164i | −0.963733 | − | 0.266867i | \(-0.914011\pi\) |
−0.0440039 | + | 0.999031i | \(0.514011\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.832382 | + | 2.56181i | 0.0404718 | + | 0.124559i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.9496 | + | 28.2986i | 1.88933 | + | 1.37268i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.723465 | − | 2.22660i | 0.0350109 | − | 0.107753i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.148633 | + | 17.8477i | 0.00717607 | + | 0.861696i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.57473 | − | 17.1572i | 0.268525 | − | 0.826435i | −0.722335 | − | 0.691543i | \(-0.756931\pi\) |
0.990860 | − | 0.134892i | \(-0.0430688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.4722 | − | 14.8739i | −0.983833 | − | 0.714796i | −0.0252709 | − | 0.999681i | \(-0.508045\pi\) |
−0.958562 | + | 0.284884i | \(0.908045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.8301 | + | 45.6423i | 0.711049 | + | 2.18838i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.3498 | + | 10.4257i | −0.686444 | + | 0.498731i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.5630 | 1.36324 | 0.681620 | − | 0.731707i | \(-0.261276\pi\) | ||||
0.681620 | + | 0.731707i | \(0.261276\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.26544 | −0.203116 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.0734 | − | 21.8496i | 1.42883 | − | 1.03811i | 0.438600 | − | 0.898682i | \(-0.355475\pi\) |
0.990233 | − | 0.139425i | \(-0.0445254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.40632 | + | 13.5612i | 0.208879 | + | 0.642865i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.8497 | − | 19.5075i | −1.26995 | − | 0.922671i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.22505 | − | 9.92568i | 0.152199 | − | 0.468422i | −0.845667 | − | 0.533711i | \(-0.820797\pi\) |
0.997866 | + | 0.0652892i | \(0.0207970\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.10195 | − | 3.04143i | 0.428594 | − | 0.143215i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.468715 | + | 1.44256i | −0.0220221 | + | 0.0677772i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.71637 | + | 4.87973i | 0.314868 | + | 0.228765i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.07597 | + | 24.8553i | 0.377778 | + | 1.16268i | 0.941585 | + | 0.336775i | \(0.109336\pi\) |
−0.563807 | + | 0.825907i | \(0.690664\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.2290 | − | 19.0565i | 1.22427 | − | 0.889481i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.1743 | 0.520439 | 0.260219 | − | 0.965550i | \(-0.416205\pi\) | ||||
0.260219 | + | 0.965550i | \(0.416205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.7695 | −1.80177 | −0.900885 | − | 0.434059i | \(-0.857081\pi\) | ||||
−0.900885 | + | 0.434059i | \(0.857081\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.9747 | − | 10.1532i | 0.648062 | − | 0.470844i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.717071 | + | 2.20692i | 0.0331821 | + | 0.102124i | 0.966276 | − | 0.257509i | \(-0.0829018\pi\) |
−0.933094 | + | 0.359633i | \(0.882902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.68385 | + | 7.03573i | 0.447159 | + | 0.324880i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.55332 | − | 23.2467i | 0.348039 | − | 1.07115i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.91399 | + | 2.18301i | 0.317906 | + | 0.100375i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.86025 | + | 14.9583i | −0.223003 | + | 0.686334i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.93155 | + | 2.85644i | 0.180013 | + | 0.130787i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.66660 | − | 23.5954i | −0.350296 | − | 1.07810i | −0.958687 | − | 0.284463i | \(-0.908185\pi\) |
0.608391 | − | 0.793637i | \(-0.291815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.33866 | + | 1.69913i | −0.106634 | + | 0.0774738i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.4209 | −0.565169 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.9982 | 0.771850 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.8506 | − | 10.7896i | 0.672947 | − | 0.488924i | −0.198064 | − | 0.980189i | \(-0.563465\pi\) |
0.871010 | + | 0.491265i | \(0.163465\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0982771 | − | 0.302466i | −0.00444424 | − | 0.0136780i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4798 | + | 12.6998i | 0.788851 | + | 0.573133i | 0.907622 | − | 0.419788i | \(-0.137896\pi\) |
−0.118772 | + | 0.992922i | \(0.537896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.5409 | − | 50.9077i | 0.744966 | − | 2.29277i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.35879 | − | 2.32345i | −0.330753 | − | 0.104431i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.518287 | + | 1.59512i | −0.0232483 | + | 0.0715510i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9657 | + | 18.1386i | 1.11762 | + | 0.811996i | 0.983846 | − | 0.179016i | \(-0.0572915\pi\) |
0.133770 | + | 0.991012i | \(0.457292\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.8611 | − | 39.5824i | −0.574592 | − | 1.76841i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.62755 | + | 1.90902i | −0.117157 | + | 0.0851192i | −0.644821 | − | 0.764334i | \(-0.723068\pi\) |
0.527664 | + | 0.849453i | \(0.323068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.1709 | −1.25359 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.85838 | 0.437826 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.76819 | − | 2.73775i | 0.167022 | − | 0.121349i | −0.501134 | − | 0.865369i | \(-0.667084\pi\) |
0.668156 | + | 0.744021i | \(0.267084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.34116 | − | 4.12765i | −0.0593292 | − | 0.182597i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.56864 | + | 6.22548i | 0.378315 | + | 0.274862i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.863615 | + | 2.65793i | −0.0380554 | + | 0.117123i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4048 | − | 4.14509i | 0.545563 | − | 0.182301i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.76780 | + | 23.9068i | −0.340969 | + | 1.04939i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.2935 | − | 24.9157i | −1.50242 | − | 1.09158i | −0.969403 | − | 0.245474i | \(-0.921057\pi\) |
−0.533021 | − | 0.846102i | \(-0.678943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0934079 | − | 0.287480i | −0.00408444 | − | 0.0125706i | 0.948994 | − | 0.315296i | \(-0.102104\pi\) |
−0.953078 | + | 0.302725i | \(0.902104\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.91041 | + | 6.47379i | −0.388882 | + | 0.282539i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.2664 | −0.839259 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.4504 | 1.41089 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.47070 | − | 3.24816i | 0.194012 | − | 0.140958i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.50728 | + | 7.71661i | 0.108602 | + | 0.334244i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.1474 | + | 24.8096i | 1.47632 | + | 1.07261i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.28176 | + | 19.3333i | −0.271078 | + | 0.834292i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.172471 | + | 20.7102i | 0.00742887 | + | 0.892051i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.21912 | − | 16.0628i | 0.224387 | − | 0.690593i | −0.773966 | − | 0.633227i | \(-0.781730\pi\) |
0.998353 | − | 0.0573660i | \(-0.0182702\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.93957 | + | 7.22152i | 0.426548 | + | 0.309905i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.58341 | − | 23.3393i | −0.324837 | − | 0.999747i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0947 | + | 10.2404i | −0.602647 | + | 0.437849i | −0.846818 | − | 0.531883i | \(-0.821484\pi\) |
0.244170 | + | 0.969732i | \(0.421484\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.83993 | −0.0785262 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.4867 | 0.744958 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.46100 | + | 6.87382i | −0.402323 | + | 0.292304i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.08249 | − | 6.40926i | −0.0883970 | − | 0.272058i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.6848 | − | 12.1222i | −0.706956 | − | 0.513633i | 0.175234 | − | 0.984527i | \(-0.443932\pi\) |
−0.882190 | + | 0.470893i | \(0.843932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.89429 | + | 5.83003i | −0.0801200 | + | 0.246584i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.5905 | + | 37.3176i | 1.16487 | + | 1.57555i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.06369 | + | 18.6621i | −0.255554 | + | 0.786514i | 0.738166 | + | 0.674619i | \(0.235692\pi\) |
−0.993720 | + | 0.111895i | \(0.964308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.67272 | − | 4.12147i | −0.238653 | − | 0.173392i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.84230 | + | 8.74771i | 0.119366 | + | 0.367369i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.3007 | − | 19.8351i | 1.14451 | − | 0.831532i | 0.156765 | − | 0.987636i | \(-0.449894\pi\) |
0.987741 | + | 0.156104i | \(0.0498936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8373 | −0.830164 | −0.415082 | − | 0.909784i | \(-0.636247\pi\) | ||||
−0.415082 | + | 0.909784i | \(0.636247\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.0267 | 0.544197 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 39.7787 | − | 28.9009i | 1.65889 | − | 1.20525i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.80486 | + | 30.1763i | 0.408182 | + | 1.25625i | 0.918209 | + | 0.396096i | \(0.129635\pi\) |
−0.510027 | + | 0.860158i | \(0.670365\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6345 | − | 9.17950i | −0.525072 | − | 0.381487i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0522653 | + | 0.160856i | −0.00216833 | + | 0.00667344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.7100 | − | 19.2046i | 0.567812 | − | 0.795371i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.01616 | − | 6.20510i | 0.0833579 | − | 0.256549i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5596 | − | 11.3047i | −0.642215 | − | 0.466597i | 0.218395 | − | 0.975860i | \(-0.429918\pi\) |
−0.860611 | + | 0.509264i | \(0.829918\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.94497 | − | 5.98601i | −0.0801413 | − | 0.246649i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.6037 | + | 18.6022i | −1.05319 | + | 0.765191i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.8924 | −1.51499 | −0.757495 | − | 0.652841i | \(-0.773577\pi\) | ||||
−0.757495 | + | 0.652841i | \(0.773577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.5867 | 0.884967 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.27547 | + | 3.83285i | −0.215910 | + | 0.156868i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.26482 | + | 3.89271i | 0.0516790 | + | 0.159052i | 0.973565 | − | 0.228409i | \(-0.0733523\pi\) |
−0.921886 | + | 0.387461i | \(0.873352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1681 | + | 13.1999i | 0.741091 | + | 0.538434i | 0.893053 | − | 0.449952i | \(-0.148559\pi\) |
−0.151961 | + | 0.988386i | \(0.548559\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.90696 | − | 8.94669i | 0.118380 | − | 0.364337i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9836 | + | 35.8235i | −0.446547 | + | 1.45643i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.39764 | − | 13.5345i | 0.178495 | − | 0.549350i | −0.821281 | − | 0.570523i | \(-0.806740\pi\) |
0.999776 | + | 0.0211738i | \(0.00674035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.90671 | + | 7.19765i | 0.401440 | + | 0.291663i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.41711 | + | 10.5168i | 0.138241 | + | 0.425463i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4021 | − | 9.01062i | 0.500915 | − | 0.363936i | −0.308452 | − | 0.951240i | \(-0.599811\pi\) |
0.809366 | + | 0.587304i | \(0.199811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.9153 | −0.762738 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4466 | 0.501080 | 0.250540 | − | 0.968106i | \(-0.419392\pi\) | ||||
0.250540 | + | 0.968106i | \(0.419392\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.2349 | − | 19.0608i | 1.05447 | − | 0.766117i | 0.0814119 | − | 0.996681i | \(-0.474057\pi\) |
0.973057 | + | 0.230564i | \(0.0740571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.2318 | − | 31.4904i | −0.410590 | − | 1.26366i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.94348 | + | 2.13856i | 0.117928 | + | 0.0856797i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.45464 | + | 13.7100i | −0.178186 | + | 0.548399i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.80914 | + | 12.3395i | −0.351803 | + | 0.492794i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.32274 | + | 7.14865i | −0.0926135 | + | 0.285035i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4849 | − | 9.79735i | −0.536825 | − | 0.390026i | 0.286079 | − | 0.958206i | \(-0.407648\pi\) |
−0.822905 | + | 0.568179i | \(0.807648\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.47873 | + | 29.1725i | 0.376746 | + | 1.15950i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.0662 | − | 16.7586i | 0.915355 | − | 0.665045i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.5106 | −0.693793 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.31811 | 0.0521438 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8138 | − | 10.7629i | 0.585111 | − | 0.425108i | −0.255452 | − | 0.966822i | \(-0.582224\pi\) |
0.840563 | + | 0.541714i | \(0.182224\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.58274 | − | 4.87117i | −0.0624171 | − | 0.192100i | 0.914985 | − | 0.403487i | \(-0.132202\pi\) |
−0.977402 | + | 0.211387i | \(0.932202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.5615 | − | 8.39993i | −0.455234 | − | 0.330747i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.1774 | + | 37.4782i | −0.478743 | + | 1.47342i | 0.362099 | + | 0.932140i | \(0.382060\pi\) |
−0.840842 | + | 0.541281i | \(0.817940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.9517 | − | 21.5755i | −0.626159 | − | 0.846912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.36200 | − | 4.19181i | 0.0533811 | − | 0.164290i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.45332 | + | 1.78244i | 0.0960059 | + | 0.0697524i | 0.634753 | − | 0.772715i | \(-0.281102\pi\) |
−0.538747 | + | 0.842468i | \(0.681102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.0535 | − | 43.2521i | −0.549114 | − | 1.69000i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.75943 | + | 2.00485i | −0.107656 | + | 0.0782165i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.09096 | 0.0424978 | 0.0212489 | − | 0.999774i | \(-0.493236\pi\) | ||||
0.0212489 | + | 0.999774i | \(0.493236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1346 | −1.79443 | −0.897214 | − | 0.441596i | \(-0.854412\pi\) | ||||
−0.897214 | + | 0.441596i | \(0.854412\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.7442 | + | 23.0635i | −1.23284 | + | 0.895713i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.17920 | + | 6.70690i | 0.0845059 | + | 0.260082i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.2265 | − | 32.1324i | −1.71246 | − | 1.24417i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.49635 | − | 13.8384i | 0.173839 | − | 0.535022i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0743968 | + | 8.93350i | 0.00287206 | + | 0.344874i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.10596 | − | 18.7922i | 0.235367 | − | 0.724386i | −0.761705 | − | 0.647924i | \(-0.775637\pi\) |
0.997072 | − | 0.0764625i | \(-0.0243625\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.7529 | − | 17.2575i | −0.914250 | − | 0.664241i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.84542 | + | 24.1457i | 0.301524 | + | 0.927996i | 0.980951 | + | 0.194253i | \(0.0622282\pi\) |
−0.679427 | + | 0.733743i | \(0.737772\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50890 | − | 2.54937i | 0.134659 | − | 0.0978358i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.8124 | 1.10410 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.69756 | 0.141483 | 0.0707416 | − | 0.997495i | \(-0.477463\pi\) | ||||
0.0707416 | + | 0.997495i | \(0.477463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.72879 | + | 1.98258i | −0.104262 | + | 0.0757505i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.42440 | − | 4.38386i | −0.0543443 | − | 0.167255i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.1399 | + | 11.7263i | 0.614880 | + | 0.446737i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.790302 | + | 2.43230i | −0.0300645 | + | 0.0925291i | −0.964963 | − | 0.262387i | \(-0.915490\pi\) |
0.934898 | + | 0.354916i | \(0.115490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.86753 | + | 0.624037i | −0.0709414 | + | 0.0237052i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.31012 | + | 19.4206i | −0.239357 | + | 0.736664i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.0682 | + | 12.4007i | 0.646502 | + | 0.469711i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.70255 | − | 11.3953i | −0.140043 | − | 0.431009i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9131 | + | 21.7331i | −1.12980 | + | 0.820850i | −0.985666 | − | 0.168708i | \(-0.946040\pi\) |
−0.144136 | + | 0.989558i | \(0.546040\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.45554 | −0.0926126 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.7792 | −0.970900 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.81526 | + | 4.22503i | −0.218705 | + | 0.158899i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.3529 | − | 31.8630i | −0.388812 | − | 1.19664i | −0.933677 | − | 0.358116i | \(-0.883419\pi\) |
0.544865 | − | 0.838524i | \(-0.316581\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.43537 | + | 5.40211i | 0.278848 | + | 0.202595i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.08038 | + | 18.7135i | −0.227712 | + | 0.700826i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.2095 | − | 9.53826i | −1.12977 | − | 0.356711i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.1173 | + | 31.1380i | −0.377839 | + | 1.16287i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.3134 | + | 17.6647i | 0.906736 | + | 0.658782i | 0.940187 | − | 0.340658i | \(-0.110650\pi\) |
−0.0334515 | + | 0.999440i | \(0.510650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.220359 | + | 0.678195i | 0.00820659 | + | 0.0252573i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0258233 | − | 0.0187618i | 0.000960380 | − | 0.000697757i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −48.4744 | −1.80029 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.4183 | −0.831449 | −0.415725 | − | 0.909491i | \(-0.636472\pi\) | ||||
−0.415725 | + | 0.909491i | \(0.636472\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.8630 | + | 10.7986i | −0.550482 | + | 0.399948i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.92556 | + | 15.1593i | 0.182178 | + | 0.560687i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.8494 | − | 14.4214i | −0.733153 | − | 0.532667i | 0.157406 | − | 0.987534i | \(-0.449687\pi\) |
−0.890559 | + | 0.454867i | \(0.849687\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.6146 | − | 38.8239i | 0.465298 | − | 1.43204i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.5569 | − | 13.7525i | −1.60444 | − | 0.506581i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.04270 | + | 3.20910i | −0.0383563 | + | 0.118049i | −0.968401 | − | 0.249397i | \(-0.919768\pi\) |
0.930045 | + | 0.367446i | \(0.119768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.3704 | − | 7.53452i | −0.380965 | − | 0.276788i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.88683 | + | 5.80706i | 0.0692210 | + | 0.213040i | 0.979683 | − | 0.200552i | \(-0.0642737\pi\) |
−0.910462 | + | 0.413593i | \(0.864274\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.6562 | − | 34.6243i | 1.74599 | − | 1.26854i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.132922 | 0.00486336 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.7699 | 0.393523 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.5404 | + | 29.4544i | −1.47934 | + | 1.07480i | −0.501574 | + | 0.865115i | \(0.667245\pi\) |
−0.977768 | + | 0.209690i | \(0.932755\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.3451 | − | 44.1495i | −0.522763 | − | 1.60890i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.17803 | − | 1.58243i | −0.0792667 | − | 0.0575906i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.88482 | − | 5.80088i | 0.0685050 | − | 0.210837i | −0.910944 | − | 0.412531i | \(-0.864645\pi\) |
0.979448 | + | 0.201695i | \(0.0646448\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44.9540 | − | 15.0214i | 1.63173 | − | 0.545244i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.6183 | + | 41.9128i | −0.493662 | + | 1.51934i | 0.325368 | + | 0.945587i | \(0.394512\pi\) |
−0.819031 | + | 0.573749i | \(0.805488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.06582 | − | 3.68053i | −0.183395 | − | 0.133244i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.24244 | − | 16.1346i | −0.189541 | − | 0.583346i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.3532 | − | 13.3344i | 0.662696 | − | 0.481477i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.7688 | 1.93895 | 0.969476 | − | 0.245185i | \(-0.0788488\pi\) | ||||
0.969476 | + | 0.245185i | \(0.0788488\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.5188 | 1.99946 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.5645 | − | 18.5737i | 0.919491 | − | 0.668049i | −0.0239065 | − | 0.999714i | \(-0.507610\pi\) |
0.943397 | + | 0.331665i | \(0.107610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.39161 | + | 16.5937i | 0.193672 | + | 0.596062i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.39114 | − | 1.01072i | −0.0499067 | − | 0.0362593i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.12981 | + | 6.55489i | −0.0763085 | + | 0.234853i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0532975 | − | 6.39991i | −0.00190713 | − | 0.229007i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.0873 | + | 31.0454i | −0.360489 | + | 1.10947i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.0989 | + | 25.5009i | 1.25273 | + | 0.910164i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.00679045 | + | 0.0208988i | 0.000242053 | + | 0.000744964i | 0.951177 | − | 0.308644i | \(-0.0998753\pi\) |
−0.950935 | + | 0.309389i | \(0.899875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.7873 | − | 19.4621i | 0.953653 | − | 0.692870i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.78914 | −0.0636144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.55331 | −0.268226 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −37.6264 | + | 27.3372i | −1.33447 | + | 0.969550i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.33212 | − | 7.17752i | −0.0826078 | − | 0.254241i | 0.901219 | − | 0.433365i | \(-0.142674\pi\) |
−0.983827 | + | 0.179124i | \(0.942674\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.2618 | + | 16.9007i | 0.822942 | + | 0.597902i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.883591 | − | 2.71941i | 0.0312202 | − | 0.0960858i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.84581 | + | 13.3170i | 0.347451 | + | 0.469945i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.81263 | − | 20.9671i | 0.240114 | − | 0.738994i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.35371 | + | 3.16315i | 0.153258 | + | 0.111348i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.0296 | − | 43.1787i | −0.493255 | − | 1.51808i | −0.819658 | − | 0.572853i | \(-0.805837\pi\) |
0.326403 | − | 0.945231i | \(-0.394163\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.4192 | + | 8.29653i | −0.400982 | + | 0.291331i | −0.769941 | − | 0.638115i | \(-0.779714\pi\) |
0.368959 | + | 0.929446i | \(0.379714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.6750 | 1.53175 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.564482 | 0.0197729 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.21270 | + | 3.06071i | −0.147384 | + | 0.107081i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.514440 | − | 1.58328i | −0.0179760 | − | 0.0553244i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.291583 | + | 0.211848i | 0.0101763 | + | 0.00739354i | 0.592862 | − | 0.805304i | \(-0.297998\pi\) |
−0.582685 | + | 0.812698i | \(0.697998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.52800 | − | 10.8581i | 0.122978 | − | 0.378488i | −0.870549 | − | 0.492082i | \(-0.836236\pi\) |
0.993527 | + | 0.113594i | \(0.0362362\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.4196 | − | 34.2061i | 0.850180 | − | 1.19090i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.1120 | − | 37.2769i | 0.421176 | − | 1.29625i | −0.485433 | − | 0.874274i | \(-0.661338\pi\) |
0.906609 | − | 0.421972i | \(-0.138662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9729 | + | 17.4173i | 0.832612 | + | 0.604928i | 0.920297 | − | 0.391220i | \(-0.127947\pi\) |
−0.0876848 | + | 0.996148i | \(0.527947\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.97337 | − | 6.07339i | −0.0684553 | − | 0.210684i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.8355 | + | 26.7625i | −1.27627 | + | 0.927267i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 73.8715 | 2.55643 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.7494 | 0.406118 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.6388 | + | 16.4481i | −0.781579 | + | 0.567850i | −0.905452 | − | 0.424448i | \(-0.860468\pi\) |
0.123874 | + | 0.992298i | \(0.460468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.69282 | + | 23.6761i | 0.265270 | + | 0.816416i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.5317 | + | 9.83133i | 0.466055 | + | 0.338609i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.40715 | + | 16.6415i | −0.186012 | + | 0.572485i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.10543 | + | 9.04226i | 0.106704 | + | 0.310696i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.2627 | + | 53.1293i | −0.592456 | + | 1.82339i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.21044 | + | 4.51215i | 0.212891 | + | 0.154674i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6246 | + | 38.8547i | 0.432259 | + | 1.33036i | 0.895869 | + | 0.444318i | \(0.146554\pi\) |
−0.463610 | + | 0.886040i | \(0.653446\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.48372 | − | 3.25761i | 0.153340 | − | 0.111408i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.8702 | −0.986189 | −0.493094 | − | 0.869976i | \(-0.664134\pi\) | ||||
−0.493094 | + | 0.869976i | \(0.664134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.76432 | 0.299035 | 0.149517 | − | 0.988759i | \(-0.452228\pi\) | ||||
0.149517 | + | 0.988759i | \(0.452228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.90464 | + | 2.83689i | −0.133070 | + | 0.0966808i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.4027 | − | 35.0939i | −0.388153 | − | 1.19461i | −0.934167 | − | 0.356835i | \(-0.883856\pi\) |
0.546015 | − | 0.837776i | \(-0.316144\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.0956 | − | 26.2250i | −1.22729 | − | 0.891675i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.4463 | + | 66.0051i | −0.728356 | + | 2.24165i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.9285 | − | 36.3198i | 0.879564 | − | 1.23206i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9337 | − | 36.7281i | 0.404358 | − | 1.24448i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.75764 | − | 2.00354i | −0.0933319 | − | 0.0678096i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.46653 | − | 4.51352i | −0.0495779 | − | 0.152585i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.1655 | + | 14.6511i | −0.680941 | + | 0.494732i | −0.873670 | − | 0.486520i | \(-0.838266\pi\) |
0.192729 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.1356 | 1.42120 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.1252 | 0.846491 | 0.423245 | − | 0.906015i | \(-0.360891\pi\) | ||||
0.423245 | + | 0.906015i | \(0.360891\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.69532 | + | 2.68481i | −0.124357 | + | 0.0903510i | −0.648225 | − | 0.761449i | \(-0.724489\pi\) |
0.523868 | + | 0.851800i | \(0.324489\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.3429 | + | 50.2983i | 0.549361 | + | 1.69076i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.45848 | + | 1.78619i | 0.0825476 | + | 0.0599743i | 0.628294 | − | 0.777976i | \(-0.283754\pi\) |
−0.545746 | + | 0.837951i | \(0.683754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.24808 | − | 6.91888i | 0.0753982 | − | 0.232052i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.8662 | − | 28.2225i | −0.699043 | − | 0.945491i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.90267 | + | 8.93350i | −0.0971341 | + | 0.298948i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.1902 | − | 21.2079i | −0.975721 | − | 0.708903i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.3833 | + | 38.1119i | 0.413466 | + | 1.27252i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.6937 | − | 11.4021i | 0.523415 | − | 0.380283i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.8741 | 1.72818 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.64643 | −0.121345 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.6420 | + | 12.8177i | −0.586440 | + | 0.426074i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.33775 | + | 13.3502i | 0.144033 | + | 0.443286i | 0.996885 | − | 0.0788649i | \(-0.0251296\pi\) |
−0.852853 | + | 0.522151i | \(0.825130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.57019 | + | 3.32044i | 0.151584 | + | 0.110132i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.29223 | − | 28.5985i | 0.307865 | − | 0.947512i | −0.670727 | − | 0.741704i | \(-0.734018\pi\) |
0.978592 | − | 0.205808i | \(-0.0659822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.00537465 | − | 0.645383i | −0.000177875 | − | 0.0213591i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.44142 | − | 16.7470i | 0.179888 | − | 0.553637i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.38791 | − | 6.82072i | −0.310016 | − | 0.225240i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.9047 | − | 36.6389i | −0.392700 | − | 1.20861i | −0.930738 | − | 0.365686i | \(-0.880834\pi\) |
0.538038 | − | 0.842920i | \(-0.319166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37.5476 | − | 27.2799i | 1.23723 | − | 0.898903i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.41115 | 0.178110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.80695 | 0.223811 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.453389 | − | 0.329407i | 0.0148913 | − | 0.0108191i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.58354 | + | 29.4951i | 0.314426 | + | 0.967703i | 0.975990 | + | 0.217815i | \(0.0698928\pi\) |
−0.661564 | + | 0.749888i | \(0.730107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.0336 | − | 8.74294i | −0.394386 | − | 0.286538i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.11794 | + | 6.51835i | −0.0693383 | + | 0.213401i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −78.1270 | + | 26.1063i | −2.55503 | + | 0.853766i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.7606 | − | 33.1178i | 0.351534 | − | 1.08191i | −0.606457 | − | 0.795116i | \(-0.707410\pi\) |
0.957992 | − | 0.286796i | \(-0.0925901\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.5212 | + | 9.82373i | 0.441248 | + | 0.320585i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5435 | − | 32.4497i | −0.343709 | − | 1.05783i | −0.962271 | − | 0.272092i | \(-0.912284\pi\) |
0.618562 | − | 0.785736i | \(-0.287716\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.4315 | − | 12.6647i | 0.567646 | − | 0.412419i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.1643 | −0.428236 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.3465 | −0.466198 | −0.233099 | − | 0.972453i | \(-0.574887\pi\) | ||||
−0.233099 | + | 0.972453i | \(0.574887\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.3281 | + | 8.23033i | −0.367725 | + | 0.267168i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.0592 | − | 40.1921i | −0.423473 | − | 1.30332i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.4915 | − | 21.4268i | −0.955322 | − | 0.694082i | −0.00326235 | − | 0.999995i | \(-0.501038\pi\) |
−0.952060 | + | 0.305913i | \(0.901038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.14489 | + | 21.9897i | −0.231203 | + | 0.711571i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −44.5593 | − | 14.0690i | −1.44040 | − | 0.454787i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.265953 | + | 0.818519i | −0.00858807 | + | 0.0264314i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.4308 | + | 14.1173i | 0.626801 | + | 0.455397i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.61552 | − | 8.04975i | −0.0842841 | − | 0.259400i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.4253 | − | 16.2929i | 0.721896 | − | 0.524488i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0950 | 1.54663 | 0.773315 | − | 0.634022i | \(-0.218597\pi\) | ||||
0.773315 | + | 0.634022i | \(0.218597\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.3308 | −1.07074 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2115 | + | 13.9580i | −0.616527 | + | 0.447933i | −0.851707 | − | 0.524019i | \(-0.824432\pi\) |
0.235180 | + | 0.971952i | \(0.424432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.61008 | + | 4.95532i | 0.0516169 | + | 0.158860i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.7475 | + | 20.8863i | 0.920655 | + | 0.668895i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.34018 | − | 25.6684i | 0.266826 | − | 0.821206i | −0.724441 | − | 0.689337i | \(-0.757902\pi\) |
0.991267 | − | 0.131869i | \(-0.0420979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.2394 | − | 4.18019i | −0.423134 | − | 0.133599i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.52069 | + | 4.68020i | −0.0485518 | + | 0.149427i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.2858 | + | 14.0119i | 0.615121 | + | 0.446911i | 0.851214 | − | 0.524819i | \(-0.175867\pi\) |
−0.236093 | + | 0.971730i | \(0.575867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.3583 | − | 53.4234i | −0.553082 | − | 1.70221i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.32154 | + | 3.86632i | −0.169386 | + | 0.123066i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.2787 | 0.517633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.6048 | 0.336871 | 0.168436 | − | 0.985713i | \(-0.446128\pi\) | ||||
0.168436 | + | 0.985713i | \(0.446128\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.22507 | − | 2.34315i | 0.102345 | − | 0.0743576i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.57656 | − | 11.0075i | −0.113385 | − | 0.348962i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.18311 | − | 1.58613i | −0.0691399 | − | 0.0502331i | 0.552678 | − | 0.833395i | \(-0.313606\pi\) |
−0.621818 | + | 0.783162i | \(0.713606\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.41649 | − | 4.35951i | 0.0448157 | − | 0.137929i |
(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 | 176.2.m.d.97.2 | 8 | ||
4.3 | odd | 2 | 88.2.i.b.9.1 | ✓ | 8 | ||
8.3 | odd | 2 | 704.2.m.l.449.2 | 8 | |||
8.5 | even | 2 | 704.2.m.i.449.1 | 8 | |||
11.4 | even | 5 | 1936.2.a.bb.1.2 | 4 | |||
11.5 | even | 5 | inner | 176.2.m.d.49.2 | 8 | ||
11.7 | odd | 10 | 1936.2.a.bc.1.2 | 4 | |||
12.11 | even | 2 | 792.2.r.g.361.1 | 8 | |||
44.3 | odd | 10 | 968.2.i.s.81.2 | 8 | |||
44.7 | even | 10 | 968.2.a.m.1.3 | 4 | |||
44.15 | odd | 10 | 968.2.a.n.1.3 | 4 | |||
44.19 | even | 10 | 968.2.i.t.81.2 | 8 | |||
44.27 | odd | 10 | 88.2.i.b.49.1 | yes | 8 | ||
44.31 | odd | 10 | 968.2.i.s.729.2 | 8 | |||
44.35 | even | 10 | 968.2.i.t.729.2 | 8 | |||
44.39 | even | 10 | 968.2.i.p.753.1 | 8 | |||
44.43 | even | 2 | 968.2.i.p.9.1 | 8 | |||
88.5 | even | 10 | 704.2.m.i.577.1 | 8 | |||
88.27 | odd | 10 | 704.2.m.l.577.2 | 8 | |||
88.29 | odd | 10 | 7744.2.a.ds.1.3 | 4 | |||
88.37 | even | 10 | 7744.2.a.dr.1.3 | 4 | |||
88.51 | even | 10 | 7744.2.a.dh.1.2 | 4 | |||
88.59 | odd | 10 | 7744.2.a.di.1.2 | 4 | |||
132.59 | even | 10 | 8712.2.a.ce.1.1 | 4 | |||
132.71 | even | 10 | 792.2.r.g.577.1 | 8 | |||
132.95 | odd | 10 | 8712.2.a.cd.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
88.2.i.b.9.1 | ✓ | 8 | 4.3 | odd | 2 | ||
88.2.i.b.49.1 | yes | 8 | 44.27 | odd | 10 | ||
176.2.m.d.49.2 | 8 | 11.5 | even | 5 | inner | ||
176.2.m.d.97.2 | 8 | 1.1 | even | 1 | trivial | ||
704.2.m.i.449.1 | 8 | 8.5 | even | 2 | |||
704.2.m.i.577.1 | 8 | 88.5 | even | 10 | |||
704.2.m.l.449.2 | 8 | 8.3 | odd | 2 | |||
704.2.m.l.577.2 | 8 | 88.27 | odd | 10 | |||
792.2.r.g.361.1 | 8 | 12.11 | even | 2 | |||
792.2.r.g.577.1 | 8 | 132.71 | even | 10 | |||
968.2.a.m.1.3 | 4 | 44.7 | even | 10 | |||
968.2.a.n.1.3 | 4 | 44.15 | odd | 10 | |||
968.2.i.p.9.1 | 8 | 44.43 | even | 2 | |||
968.2.i.p.753.1 | 8 | 44.39 | even | 10 | |||
968.2.i.s.81.2 | 8 | 44.3 | odd | 10 | |||
968.2.i.s.729.2 | 8 | 44.31 | odd | 10 | |||
968.2.i.t.81.2 | 8 | 44.19 | even | 10 | |||
968.2.i.t.729.2 | 8 | 44.35 | even | 10 | |||
1936.2.a.bb.1.2 | 4 | 11.4 | even | 5 | |||
1936.2.a.bc.1.2 | 4 | 11.7 | odd | 10 | |||
7744.2.a.dh.1.2 | 4 | 88.51 | even | 10 | |||
7744.2.a.di.1.2 | 4 | 88.59 | odd | 10 | |||
7744.2.a.dr.1.3 | 4 | 88.37 | even | 10 | |||
7744.2.a.ds.1.3 | 4 | 88.29 | odd | 10 | |||
8712.2.a.cd.1.1 | 4 | 132.95 | odd | 10 | |||
8712.2.a.ce.1.1 | 4 | 132.59 | even | 10 |