Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(143,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([2, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.q (of order \(12\), 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 368.4 | ||
Root | \(-0.347596 - 1.29724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.368 |
Dual form | 675.2.q.a.332.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.347596 | − | 1.29724i | 0.245787 | − | 0.917290i | −0.727199 | − | 0.686427i | \(-0.759178\pi\) |
0.972986 | − | 0.230863i | \(-0.0741551\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.170031 | + | 0.0981673i | 0.0850154 | + | 0.0490837i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.97869 | − | 0.530190i | −0.747876 | − | 0.200393i | −0.135300 | − | 0.990805i | \(-0.543200\pi\) |
−0.612576 | + | 0.790412i | \(0.709867\pi\) | |||||||
\(8\) | 2.08575 | − | 2.08575i | 0.737423 | − | 0.737423i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.762281 | − | 0.440103i | 0.229836 | − | 0.132696i | −0.380660 | − | 0.924715i | \(-0.624303\pi\) |
0.610497 | + | 0.792019i | \(0.290970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.36743 | − | 1.43820i | 1.48866 | − | 0.398885i | 0.579374 | − | 0.815062i | \(-0.303297\pi\) |
0.909283 | + | 0.416177i | \(0.136630\pi\) | |||||||
\(14\) | −1.37557 | + | 2.38256i | −0.367637 | + | 0.636766i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.78439 | − | 3.09066i | −0.446098 | − | 0.772664i | ||||
\(17\) | −1.13610 | − | 1.13610i | −0.275544 | − | 0.275544i | 0.555783 | − | 0.831327i | \(-0.312418\pi\) |
−0.831327 | + | 0.555783i | \(0.812418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.52456i | − | 0.349758i | −0.984590 | − | 0.174879i | \(-0.944047\pi\) | ||
0.984590 | − | 0.174879i | \(-0.0559535\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.305956 | − | 1.14184i | −0.0652300 | − | 0.243442i | ||||
\(23\) | 0.410850 | + | 1.53331i | 0.0856682 | + | 0.319718i | 0.995440 | − | 0.0953909i | \(-0.0304101\pi\) |
−0.909772 | + | 0.415109i | \(0.863743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 7.46278i | − | 1.46357i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.284392 | − | 0.284392i | −0.0537450 | − | 0.0537450i | ||||
\(29\) | −0.796583 | − | 1.37972i | −0.147922 | − | 0.256208i | 0.782537 | − | 0.622603i | \(-0.213925\pi\) |
−0.930459 | + | 0.366396i | \(0.880592\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.49518 | − | 6.05383i | 0.627752 | − | 1.08730i | −0.360249 | − | 0.932856i | \(-0.617308\pi\) |
0.988002 | − | 0.154443i | \(-0.0493583\pi\) | |||||||
\(32\) | 1.06878 | − | 0.286379i | 0.188936 | − | 0.0506251i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.86870 | + | 1.07889i | −0.320479 | + | 0.185029i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.25746 | − | 4.25746i | 0.699922 | − | 0.699922i | −0.264472 | − | 0.964393i | \(-0.585198\pi\) |
0.964393 | + | 0.264472i | \(0.0851975\pi\) | |||||||
\(38\) | −1.97773 | − | 0.529931i | −0.320830 | − | 0.0859661i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.11546 | − | 1.79871i | −0.486552 | − | 0.280911i | 0.236591 | − | 0.971609i | \(-0.423970\pi\) |
−0.723143 | + | 0.690698i | \(0.757303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.497959 | + | 1.85841i | −0.0759380 | + | 0.283404i | −0.993444 | − | 0.114317i | \(-0.963532\pi\) |
0.917506 | + | 0.397721i | \(0.130199\pi\) | |||||||
\(44\) | 0.172815 | 0.0260528 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.13189 | 0.314330 | ||||||||
\(47\) | −2.14344 | + | 7.99942i | −0.312652 | + | 1.16683i | 0.613503 | + | 0.789693i | \(0.289760\pi\) |
−0.926155 | + | 0.377142i | \(0.876907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.42805 | − | 1.40183i | −0.346864 | − | 0.200262i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.05381 | + | 0.282368i | 0.146137 | + | 0.0391574i | ||||
\(53\) | 4.65601 | − | 4.65601i | 0.639552 | − | 0.639552i | −0.310893 | − | 0.950445i | \(-0.600628\pi\) |
0.950445 | + | 0.310893i | \(0.100628\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.23290 | + | 3.02121i | −0.699275 | + | 0.403727i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.06672 | + | 0.553777i | −0.271374 | + | 0.0727145i | ||||
\(59\) | −3.81780 | + | 6.61262i | −0.497035 | + | 0.860890i | −0.999994 | − | 0.00342048i | \(-0.998911\pi\) |
0.502959 | + | 0.864310i | \(0.332245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.64002 | + | 11.5008i | 0.850167 | + | 1.47253i | 0.881057 | + | 0.473010i | \(0.156833\pi\) |
−0.0308900 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(62\) | −6.63838 | − | 6.63838i | −0.843075 | − | 0.843075i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.62358i | − | 1.07795i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.859733 | + | 3.20857i | 0.105033 | + | 0.391989i | 0.998349 | − | 0.0574406i | \(-0.0182940\pi\) |
−0.893316 | + | 0.449429i | \(0.851627\pi\) | |||||||
\(68\) | −0.0816439 | − | 0.304699i | −0.00990078 | − | 0.0369502i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.89798i | 0.699961i | 0.936757 | + | 0.349980i | \(0.113812\pi\) | ||||
−0.936757 | + | 0.349980i | \(0.886188\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.58900 | − | 1.58900i | −0.185979 | − | 0.185979i | 0.607976 | − | 0.793955i | \(-0.291982\pi\) |
−0.793955 | + | 0.607976i | \(0.791982\pi\) | |||||||
\(74\) | −4.04309 | − | 7.00284i | −0.470000 | − | 0.814063i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.149662 | − | 0.259222i | 0.0171674 | − | 0.0297348i | ||||
\(77\) | −1.74166 | + | 0.466676i | −0.198480 | + | 0.0531827i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.69401 | + | 3.86479i | −0.753135 | + | 0.434823i | −0.826826 | − | 0.562458i | \(-0.809856\pi\) |
0.0736905 | + | 0.997281i | \(0.476522\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.41628 | + | 3.41628i | −0.377265 | + | 0.377265i | ||||
\(83\) | −9.59770 | − | 2.57170i | −1.05348 | − | 0.282280i | −0.309794 | − | 0.950804i | \(-0.600260\pi\) |
−0.743691 | + | 0.668523i | \(0.766927\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.23772 | + | 1.29195i | 0.241299 | + | 0.139314i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.671981 | − | 2.50787i | 0.0716334 | − | 0.267340i | ||||
\(89\) | 4.62765 | 0.490530 | 0.245265 | − | 0.969456i | \(-0.421125\pi\) | ||||
0.245265 | + | 0.969456i | \(0.421125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3830 | −1.19327 | ||||||||
\(92\) | −0.0806641 | + | 0.301043i | −0.00840982 | + | 0.0313859i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.63215 | + | 5.56112i | 0.993480 | + | 0.573586i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.82988 | − | 1.02621i | −0.388865 | − | 0.104196i | 0.0590888 | − | 0.998253i | \(-0.481180\pi\) |
−0.447954 | + | 0.894057i | \(0.647847\pi\) | |||||||
\(98\) | −2.66250 | + | 2.66250i | −0.268953 | + | 0.268953i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.23195 | − | 1.28862i | 0.222087 | − | 0.128222i | −0.384829 | − | 0.922988i | \(-0.625740\pi\) |
0.606916 | + | 0.794766i | \(0.292406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.6183 | + | 3.38106i | −1.24332 | + | 0.333146i | −0.819752 | − | 0.572719i | \(-0.805889\pi\) |
−0.423566 | + | 0.905865i | \(0.639222\pi\) | |||||||
\(104\) | 8.19538 | − | 14.1948i | 0.803623 | − | 1.39192i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.42157 | − | 7.65839i | −0.429461 | − | 0.743848i | ||||
\(107\) | 9.23034 | + | 9.23034i | 0.892331 | + | 0.892331i | 0.994742 | − | 0.102411i | \(-0.0326557\pi\) |
−0.102411 | + | 0.994742i | \(0.532656\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.05480i | 0.771510i | 0.922601 | + | 0.385755i | \(0.126059\pi\) | ||||
−0.922601 | + | 0.385755i | \(0.873941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.89213 | + | 7.06153i | 0.178790 | + | 0.667252i | ||||
\(113\) | 3.10662 | + | 11.5941i | 0.292246 | + | 1.09068i | 0.943380 | + | 0.331714i | \(0.107627\pi\) |
−0.651134 | + | 0.758963i | \(0.725706\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 0.312794i | − | 0.0290422i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.25113 | + | 7.25113i | 0.667521 | + | 0.667521i | ||||
\(119\) | 1.64564 | + | 2.85034i | 0.150856 | + | 0.261290i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.11262 | + | 8.85532i | −0.464784 | + | 0.805029i | ||||
\(122\) | 17.2274 | − | 4.61608i | 1.55970 | − | 0.417920i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.18858 | − | 0.686224i | 0.106737 | − | 0.0616248i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.90230 | + | 1.90230i | −0.168802 | + | 0.168802i | −0.786452 | − | 0.617651i | \(-0.788085\pi\) |
0.617651 | + | 0.786452i | \(0.288085\pi\) | |||||||
\(128\) | −9.04933 | − | 2.42476i | −0.799855 | − | 0.214321i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.5109 | + | 10.6873i | 1.61731 | + | 0.933754i | 0.987613 | + | 0.156912i | \(0.0501541\pi\) |
0.629696 | + | 0.776841i | \(0.283179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.808307 | + | 3.01664i | −0.0700891 | + | 0.261576i | ||||
\(134\) | 4.46113 | 0.385383 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.73922 | −0.406385 | ||||||||
\(137\) | 1.77541 | − | 6.62594i | 0.151684 | − | 0.566092i | −0.847683 | − | 0.530504i | \(-0.822003\pi\) |
0.999367 | − | 0.0355883i | \(-0.0113305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.24863 | − | 0.720896i | −0.105907 | − | 0.0611456i | 0.446111 | − | 0.894978i | \(-0.352809\pi\) |
−0.552018 | + | 0.833832i | \(0.686142\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.65111 | + | 2.05011i | 0.642067 | + | 0.172041i | ||||
\(143\) | 3.45853 | − | 3.45853i | 0.289217 | − | 0.289217i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.61366 | + | 1.50900i | −0.216308 | + | 0.124885i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.14184 | − | 0.305956i | 0.0938589 | − | 0.0251494i | ||||
\(149\) | −8.28457 | + | 14.3493i | −0.678699 | + | 1.17554i | 0.296674 | + | 0.954979i | \(0.404122\pi\) |
−0.975373 | + | 0.220562i | \(0.929211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.00283730 | + | 0.00491435i | 0.000230896 | + | 0.000399924i | 0.866141 | − | 0.499800i | \(-0.166593\pi\) |
−0.865910 | + | 0.500200i | \(0.833260\pi\) | |||||||
\(152\) | −3.17985 | − | 3.17985i | −0.257920 | − | 0.257920i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.42157i | 0.195136i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.18944 | − | 8.17112i | −0.174737 | − | 0.652126i | −0.996596 | − | 0.0824362i | \(-0.973730\pi\) |
0.821860 | − | 0.569690i | \(-0.192937\pi\) | |||||||
\(158\) | 2.68677 | + | 10.0272i | 0.213748 | + | 0.797717i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.25179i | − | 0.256277i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.19302 | − | 4.19302i | −0.328422 | − | 0.328422i | 0.523564 | − | 0.851986i | \(-0.324602\pi\) |
−0.851986 | + | 0.523564i | \(0.824602\pi\) | |||||||
\(164\) | −0.353149 | − | 0.611672i | −0.0275763 | − | 0.0477635i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.67224 | + | 11.5567i | −0.517866 | + | 0.896970i | ||||
\(167\) | −5.76334 | + | 1.54428i | −0.445980 | + | 0.119500i | −0.474818 | − | 0.880084i | \(-0.657486\pi\) |
0.0288375 | + | 0.999584i | \(0.490819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.4826 | − | 8.93886i | 1.19097 | − | 0.687605i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.267103 | + | 0.267103i | −0.0203664 | + | 0.0203664i | ||||
\(173\) | 13.1994 | + | 3.53677i | 1.00353 | + | 0.268896i | 0.722925 | − | 0.690927i | \(-0.242797\pi\) |
0.280608 | + | 0.959822i | \(0.409464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.72042 | − | 1.57063i | −0.205059 | − | 0.118391i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.60855 | − | 6.00319i | 0.120566 | − | 0.449958i | ||||
\(179\) | 17.2370 | 1.28836 | 0.644178 | − | 0.764875i | \(-0.277199\pi\) | ||||
0.644178 | + | 0.764875i | \(0.277199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7708 | 1.09790 | 0.548952 | − | 0.835854i | \(-0.315027\pi\) | ||||
0.548952 | + | 0.835854i | \(0.315027\pi\) | |||||||
\(182\) | −3.95669 | + | 14.7666i | −0.293289 | + | 1.09457i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.05503 | + | 2.34117i | 0.298941 | + | 0.172594i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.36603 | − | 0.366025i | −0.0998937 | − | 0.0267664i | ||||
\(188\) | −1.14973 | + | 1.14973i | −0.0838528 | + | 0.0838528i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.56792 | + | 2.63729i | −0.330523 | + | 0.190827i | −0.656073 | − | 0.754697i | \(-0.727784\pi\) |
0.325550 | + | 0.945525i | \(0.394450\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.98952 | − | 2.40873i | 0.647080 | − | 0.173384i | 0.0796715 | − | 0.996821i | \(-0.474613\pi\) |
0.567408 | + | 0.823437i | \(0.307946\pi\) | |||||||
\(194\) | −2.66250 | + | 4.61158i | −0.191156 | + | 0.331092i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.275228 | − | 0.476709i | −0.0196592 | − | 0.0340507i | ||||
\(197\) | −9.49539 | − | 9.49539i | −0.676519 | − | 0.676519i | 0.282692 | − | 0.959211i | \(-0.408773\pi\) |
−0.959211 | + | 0.282692i | \(0.908773\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6342i | 1.25005i | 0.780604 | + | 0.625026i | \(0.214912\pi\) | ||||
−0.780604 | + | 0.625026i | \(0.785088\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.895835 | − | 3.34330i | −0.0630307 | − | 0.235234i | ||||
\(203\) | 0.844680 | + | 3.15239i | 0.0592849 | + | 0.221254i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.5443i | 1.22237i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.0226 | − | 14.0226i | −0.972291 | − | 0.972291i | ||||
\(209\) | −0.670964 | − | 1.16214i | −0.0464116 | − | 0.0803872i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0616050 | − | 0.106703i | 0.00424106 | − | 0.00734574i | −0.863897 | − | 0.503668i | \(-0.831983\pi\) |
0.868138 | + | 0.496323i | \(0.165317\pi\) | |||||||
\(212\) | 1.24873 | − | 0.334597i | 0.0857633 | − | 0.0229802i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.1824 | − | 8.76558i | 1.03785 | − | 0.599203i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1256 | + | 10.1256i | −0.687368 | + | 0.687368i | ||||
\(218\) | 10.4490 | + | 2.79981i | 0.707698 | + | 0.189627i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.73186 | − | 4.46399i | −0.520101 | − | 0.300281i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.648014 | + | 2.41842i | −0.0433942 | + | 0.161949i | −0.984223 | − | 0.176933i | \(-0.943382\pi\) |
0.940829 | + | 0.338883i | \(0.110049\pi\) | |||||||
\(224\) | −2.26663 | −0.151445 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.1202 | 1.07230 | ||||||||
\(227\) | 3.94671 | − | 14.7293i | 0.261952 | − | 0.977619i | −0.702137 | − | 0.712042i | \(-0.747771\pi\) |
0.964090 | − | 0.265577i | \(-0.0855626\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1083 | − | 11.0322i | −1.26271 | − | 0.729029i | −0.289116 | − | 0.957294i | \(-0.593361\pi\) |
−0.973599 | + | 0.228265i | \(0.926695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.53922 | − | 1.21628i | −0.298014 | − | 0.0798527i | ||||
\(233\) | −4.22173 | + | 4.22173i | −0.276575 | + | 0.276575i | −0.831740 | − | 0.555165i | \(-0.812655\pi\) |
0.555165 | + | 0.831740i | \(0.312655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.29829 | + | 0.749566i | −0.0845112 | + | 0.0487926i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.26960 | − | 1.14404i | 0.276757 | − | 0.0741569i | ||||
\(239\) | 6.79199 | − | 11.7641i | 0.439338 | − | 0.760955i | −0.558301 | − | 0.829639i | \(-0.688547\pi\) |
0.997639 | + | 0.0686835i | \(0.0218799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.56728 | − | 4.44666i | −0.165373 | − | 0.286434i | 0.771415 | − | 0.636333i | \(-0.219549\pi\) |
−0.936788 | + | 0.349898i | \(0.886216\pi\) | |||||||
\(242\) | 9.71038 | + | 9.71038i | 0.624207 | + | 0.624207i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.60733i | 0.166917i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.19262 | − | 8.18298i | −0.139513 | − | 0.520670i | ||||
\(248\) | −5.33669 | − | 19.9168i | −0.338880 | − | 1.26472i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.60221i | − | 0.164250i | −0.996622 | − | 0.0821251i | \(-0.973829\pi\) | ||
0.996622 | − | 0.0821251i | \(-0.0261707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.987999 | + | 0.987999i | 0.0621150 | + | 0.0621150i | ||||
\(254\) | 1.80652 | + | 3.12898i | 0.113351 | + | 0.196329i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.33257 | − | 4.04013i | 0.145786 | − | 0.252508i | ||||
\(257\) | −10.1958 | + | 2.73197i | −0.635999 | + | 0.170415i | −0.562390 | − | 0.826872i | \(-0.690118\pi\) |
−0.0736085 | + | 0.997287i | \(0.523452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6815 | + | 6.16695i | −0.663714 | + | 0.383196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.2984 | − | 20.2984i | 1.25404 | − | 1.25404i | ||||
\(263\) | −8.12541 | − | 2.17720i | −0.501034 | − | 0.134252i | −0.000554412 | − | 1.00000i | \(-0.500176\pi\) |
−0.500480 | + | 0.865748i | \(0.666843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.63236 | + | 2.09714i | 0.222714 | + | 0.128584i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.168795 | + | 0.629953i | −0.0103108 | + | 0.0384805i | ||||
\(269\) | −26.7708 | −1.63225 | −0.816123 | − | 0.577878i | \(-0.803881\pi\) | ||||
−0.816123 | + | 0.577878i | \(0.803881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.5850 | −1.12896 | −0.564480 | − | 0.825447i | \(-0.690923\pi\) | ||||
−0.564480 | + | 0.825447i | \(0.690923\pi\) | |||||||
\(272\) | −1.48405 | + | 5.53853i | −0.0899834 | + | 0.335823i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.97833 | − | 4.60629i | −0.481989 | − | 0.278276i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.3206 | + | 7.05259i | 1.58145 | + | 0.423749i | 0.939375 | − | 0.342891i | \(-0.111406\pi\) |
0.642078 | + | 0.766640i | \(0.278073\pi\) | |||||||
\(278\) | −1.36920 | + | 1.36920i | −0.0821189 | + | 0.0821189i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7050 | − | 13.1087i | 1.35447 | − | 0.782002i | 0.365595 | − | 0.930774i | \(-0.380865\pi\) |
0.988872 | + | 0.148772i | \(0.0475320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.44050 | + | 0.921880i | −0.204517 | + | 0.0548001i | −0.359623 | − | 0.933098i | \(-0.617095\pi\) |
0.155106 | + | 0.987898i | \(0.450428\pi\) | |||||||
\(284\) | −0.578988 | + | 1.00284i | −0.0343566 | + | 0.0595074i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.28439 | − | 5.68873i | −0.194210 | − | 0.336382i | ||||
\(287\) | 5.21088 | + | 5.21088i | 0.307589 | + | 0.307589i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.4186i | − | 0.848151i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.114191 | − | 0.426168i | −0.00668254 | − | 0.0249396i | ||||
\(293\) | 0.771199 | + | 2.87816i | 0.0450539 | + | 0.168144i | 0.984787 | − | 0.173765i | \(-0.0555933\pi\) |
−0.939733 | + | 0.341909i | \(0.888927\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 17.7600i | − | 1.03228i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.7349 | + | 15.7349i | 0.911496 | + | 0.911496i | ||||
\(299\) | 4.41042 | + | 7.63907i | 0.255061 | + | 0.441779i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.97062 | − | 3.41321i | 0.113584 | − | 0.196734i | ||||
\(302\) | 0.00736135 | − | 0.00197247i | 0.000423598 | − | 0.000113503i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.71190 | + | 2.72042i | −0.270246 | + | 0.156027i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.8017 | + | 21.8017i | −1.24429 | + | 1.24429i | −0.286081 | + | 0.958205i | \(0.592353\pi\) |
−0.958205 | + | 0.286081i | \(0.907647\pi\) | |||||||
\(308\) | −0.341948 | − | 0.0916247i | −0.0194843 | − | 0.00522080i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.3878 | − | 16.9671i | −1.66643 | − | 0.962114i | −0.969539 | − | 0.244939i | \(-0.921232\pi\) |
−0.696892 | − | 0.717176i | \(-0.745435\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00279 | + | 22.4027i | −0.339298 | + | 1.26628i | 0.559836 | + | 0.828603i | \(0.310864\pi\) |
−0.899134 | + | 0.437673i | \(0.855803\pi\) | |||||||
\(314\) | −11.3610 | −0.641137 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.51758 | −0.0853708 | ||||||||
\(317\) | −1.03536 | + | 3.86401i | −0.0581515 | + | 0.217024i | −0.988887 | − | 0.148669i | \(-0.952501\pi\) |
0.930736 | + | 0.365693i | \(0.119168\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.21444 | − | 0.701157i | −0.0679956 | − | 0.0392573i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.21836 | − | 1.13031i | −0.235080 | − | 0.0629896i | ||||
\(323\) | −1.73205 | + | 1.73205i | −0.0963739 | + | 0.0963739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.89684 | + | 3.98189i | −0.381981 | + | 0.220537i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.2497 | + | 2.74640i | −0.565945 | + | 0.151645i | ||||
\(329\) | 8.48242 | − | 14.6920i | 0.467651 | − | 0.809995i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.98175 | − | 5.16454i | −0.163892 | − | 0.283869i | 0.772369 | − | 0.635174i | \(-0.219071\pi\) |
−0.936261 | + | 0.351305i | \(0.885738\pi\) | |||||||
\(332\) | −1.37945 | − | 1.37945i | −0.0757071 | − | 0.0757071i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.01324i | 0.438465i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.56397 | + | 9.56887i | 0.139668 | + | 0.521250i | 0.999935 | + | 0.0114051i | \(0.00363044\pi\) |
−0.860267 | + | 0.509845i | \(0.829703\pi\) | |||||||
\(338\) | −6.21422 | − | 23.1918i | −0.338009 | − | 1.26147i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.15295i | − | 0.333201i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2007 | + | 14.2007i | 0.766764 | + | 0.766764i | ||||
\(344\) | 2.83755 | + | 4.91478i | 0.152990 | + | 0.264987i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.17611 | − | 15.8935i | 0.493311 | − | 0.854440i | ||||
\(347\) | −10.2471 | + | 2.74569i | −0.550091 | + | 0.147396i | −0.523150 | − | 0.852241i | \(-0.675243\pi\) |
−0.0269407 | + | 0.999637i | \(0.508577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.08831 | + | 4.66979i | −0.432957 | + | 0.249968i | −0.700606 | − | 0.713549i | \(-0.747087\pi\) |
0.267648 | + | 0.963517i | \(0.413753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.688675 | − | 0.688675i | 0.0367065 | − | 0.0367065i | ||||
\(353\) | −18.5470 | − | 4.96965i | −0.987156 | − | 0.264508i | −0.271100 | − | 0.962551i | \(-0.587388\pi\) |
−0.716055 | + | 0.698043i | \(0.754054\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.786842 | + | 0.454284i | 0.0417026 | + | 0.0240770i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.99152 | − | 22.3606i | 0.316662 | − | 1.18180i | ||||
\(359\) | −12.5944 | −0.664705 | −0.332352 | − | 0.943155i | \(-0.607842\pi\) | ||||
−0.332352 | + | 0.943155i | \(0.607842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.6757 | 0.877669 | ||||||||
\(362\) | 5.13426 | − | 19.1613i | 0.269851 | − | 1.00710i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.93546 | − | 1.11744i | −0.101446 | − | 0.0585698i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.3263 | − | 7.32206i | −1.42642 | − | 0.382209i | −0.538665 | − | 0.842520i | \(-0.681071\pi\) |
−0.887757 | + | 0.460312i | \(0.847738\pi\) | |||||||
\(368\) | 4.00583 | − | 4.00583i | 0.208818 | − | 0.208818i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6814 | + | 6.74425i | −0.606467 | + | 0.350144i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.25734 | − | 0.604851i | 0.116880 | − | 0.0313180i | −0.199905 | − | 0.979815i | \(-0.564063\pi\) |
0.316785 | + | 0.948497i | \(0.397397\pi\) | |||||||
\(374\) | −0.949649 | + | 1.64484i | −0.0491052 | + | 0.0850526i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.2141 | + | 21.1554i | 0.629894 | + | 1.09101i | ||||
\(377\) | −6.25992 | − | 6.25992i | −0.322402 | − | 0.322402i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 18.4618i | − | 0.948320i | −0.880439 | − | 0.474160i | \(-0.842752\pi\) | ||
0.880439 | − | 0.474160i | \(-0.157248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.83342 | + | 6.84241i | 0.0938059 | + | 0.350088i | ||||
\(383\) | −6.26481 | − | 23.3806i | −0.320117 | − | 1.19469i | −0.919131 | − | 0.393953i | \(-0.871107\pi\) |
0.599014 | − | 0.800739i | \(-0.295559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.4989i | − | 0.636176i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.550457 | − | 0.550457i | −0.0279452 | − | 0.0279452i | ||||
\(389\) | −13.5444 | − | 23.4596i | −0.686729 | − | 1.18945i | −0.972890 | − | 0.231268i | \(-0.925712\pi\) |
0.286161 | − | 0.958182i | \(-0.407621\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.27523 | − | 2.20876i | 0.0644911 | − | 0.111702i | ||||
\(392\) | −7.98815 | + | 2.14042i | −0.403463 | + | 0.108108i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.6184 | + | 9.01729i | −0.786844 | + | 0.454284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2252 | − | 18.2252i | 0.914698 | − | 0.914698i | −0.0819389 | − | 0.996637i | \(-0.526111\pi\) |
0.996637 | + | 0.0819389i | \(0.0261112\pi\) | |||||||
\(398\) | 22.8758 | + | 6.12955i | 1.14666 | + | 0.307247i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1294 | + | 6.42558i | 0.555777 | + | 0.320878i | 0.751449 | − | 0.659791i | \(-0.229355\pi\) |
−0.195672 | + | 0.980669i | \(0.562689\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0535 | − | 37.5202i | 0.500801 | − | 1.86902i | ||||
\(404\) | 0.506000 | 0.0251745 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.38302 | 0.217526 | ||||||||
\(407\) | 1.37166 | − | 5.11910i | 0.0679906 | − | 0.253744i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.2450 | + | 12.8431i | 1.09994 | + | 0.635053i | 0.936206 | − | 0.351451i | \(-0.114312\pi\) |
0.163737 | + | 0.986504i | \(0.447645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.47741 | − | 0.663820i | −0.122053 | − | 0.0327041i | ||||
\(413\) | 11.0602 | − | 11.0602i | 0.544237 | − | 0.544237i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.32474 | − | 3.07424i | 0.261067 | − | 0.150727i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.74081 | + | 0.466448i | −0.0851457 | + | 0.0228147i | ||||
\(419\) | −6.13243 | + | 10.6217i | −0.299589 | + | 0.518903i | −0.976042 | − | 0.217583i | \(-0.930183\pi\) |
0.676453 | + | 0.736486i | \(0.263516\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.24056 | − | 12.5410i | −0.352883 | − | 0.611212i | 0.633870 | − | 0.773439i | \(-0.281465\pi\) |
−0.986753 | + | 0.162228i | \(0.948132\pi\) | |||||||
\(422\) | −0.117006 | − | 0.117006i | −0.00569577 | − | 0.00569577i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 19.4225i | − | 0.943240i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.04094 | − | 26.2771i | −0.340735 | − | 1.27164i | ||||
\(428\) | 0.663324 | + | 2.47556i | 0.0320630 | + | 0.119661i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.9660i | 1.73242i | 0.499678 | + | 0.866211i | \(0.333452\pi\) | ||||
−0.499678 | + | 0.866211i | \(0.666548\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.331545 | + | 0.331545i | 0.0159331 | + | 0.0159331i | 0.715028 | − | 0.699095i | \(-0.246414\pi\) |
−0.699095 | + | 0.715028i | \(0.746414\pi\) | |||||||
\(434\) | 9.61573 | + | 16.6549i | 0.461570 | + | 0.799462i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.790718 | + | 1.36956i | −0.0378685 | + | 0.0655902i | ||||
\(437\) | 2.33763 | − | 0.626366i | 0.111824 | − | 0.0299632i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.28953 | + | 0.744511i | −0.0615459 | + | 0.0355336i | −0.530457 | − | 0.847712i | \(-0.677980\pi\) |
0.468911 | + | 0.883245i | \(0.344646\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.47845 | + | 8.47845i | −0.403279 | + | 0.403279i | ||||
\(443\) | 30.9468 | + | 8.29218i | 1.47033 | + | 0.393973i | 0.903044 | − | 0.429548i | \(-0.141327\pi\) |
0.567285 | + | 0.823522i | \(0.307994\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.91203 | + | 1.68126i | 0.137889 | + | 0.0796101i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.57213 | + | 17.0634i | −0.216013 | + | 0.806172i | ||||
\(449\) | 21.8283 | 1.03014 | 0.515071 | − | 0.857147i | \(-0.327766\pi\) | ||||
0.515071 | + | 0.857147i | \(0.327766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.16647 | −0.149103 | ||||||||
\(452\) | −0.609937 | + | 2.27631i | −0.0286890 | + | 0.107069i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.7357 | − | 10.2397i | −0.832376 | − | 0.480572i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.880339 | − | 0.235886i | −0.0411805 | − | 0.0110343i | 0.238170 | − | 0.971223i | \(-0.423452\pi\) |
−0.279351 | + | 0.960189i | \(0.590119\pi\) | |||||||
\(458\) | −20.9534 | + | 20.9534i | −0.979090 | + | 0.979090i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.7320 | − | 10.8149i | 0.872434 | − | 0.503700i | 0.00427761 | − | 0.999991i | \(-0.498638\pi\) |
0.868156 | + | 0.496291i | \(0.165305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1245 | − | 4.85644i | 0.842316 | − | 0.225698i | 0.188236 | − | 0.982124i | \(-0.439723\pi\) |
0.654079 | + | 0.756426i | \(0.273056\pi\) | |||||||
\(464\) | −2.84283 | + | 4.92393i | −0.131975 | + | 0.228588i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.00916 | + | 6.94407i | 0.185721 | + | 0.321678i | ||||
\(467\) | 16.8295 | + | 16.8295i | 0.778777 | + | 0.778777i | 0.979623 | − | 0.200846i | \(-0.0643691\pi\) |
−0.200846 | + | 0.979623i | \(0.564369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.80460i | − | 0.314207i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.82929 | + | 21.7552i | 0.268315 | + | 1.00136i | ||||
\(473\) | 0.438306 | + | 1.63578i | 0.0201533 | + | 0.0752133i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.646194i | 0.0296182i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.9000 | − | 12.9000i | −0.590033 | − | 0.590033i | ||||
\(479\) | 8.91724 | + | 15.4451i | 0.407439 | + | 0.705705i | 0.994602 | − | 0.103764i | \(-0.0330886\pi\) |
−0.587163 | + | 0.809469i | \(0.699755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7285 | − | 28.9747i | 0.762756 | − | 1.32113i | ||||
\(482\) | −6.66078 | + | 1.78475i | −0.303390 | + | 0.0812931i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73861 | + | 1.00378i | −0.0790275 | + | 0.0456265i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.8232 | − | 21.8232i | 0.988904 | − | 0.988904i | −0.0110354 | − | 0.999939i | \(-0.503513\pi\) |
0.999939 | + | 0.0110354i | \(0.00351274\pi\) | |||||||
\(488\) | 37.8372 | + | 10.1385i | 1.71281 | + | 0.458946i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.1670 | − | 20.3037i | −1.58707 | − | 0.916292i | −0.993787 | − | 0.111295i | \(-0.964500\pi\) |
−0.593278 | − | 0.804998i | \(-0.702166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.662503 | + | 2.47249i | −0.0298376 | + | 0.111356i | ||||
\(494\) | −11.3775 | −0.511896 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.9471 | −1.12016 | ||||||||
\(497\) | 3.12705 | − | 11.6703i | 0.140267 | − | 0.523484i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.3397 | + | 21.5581i | 1.67156 | + | 0.965073i | 0.966768 | + | 0.255655i | \(0.0822910\pi\) |
0.704788 | + | 0.709418i | \(0.251042\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.37571 | − | 0.904518i | −0.150665 | − | 0.0403706i | ||||
\(503\) | −28.0936 | + | 28.0936i | −1.25263 | + | 1.25263i | −0.298093 | + | 0.954537i | \(0.596351\pi\) |
−0.954537 | + | 0.298093i | \(0.903649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.62510 | − | 0.938252i | 0.0722445 | − | 0.0417104i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.510193 | + | 0.136706i | −0.0226361 | + | 0.00606534i | ||||
\(509\) | −7.39188 | + | 12.8031i | −0.327639 | + | 0.567488i | −0.982043 | − | 0.188658i | \(-0.939586\pi\) |
0.654404 | + | 0.756145i | \(0.272920\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.30168 | + | 3.98663i | 0.101820 | + | 0.176358i | ||||
\(512\) | −17.6794 | − | 17.6794i | −0.781325 | − | 0.781325i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.1761i | 0.625282i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.88667 | + | 7.04114i | 0.0829755 | + | 0.309669i | ||||
\(518\) | 4.28721 | + | 16.0001i | 0.188369 | + | 0.703003i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.4812i | − | 1.24778i | −0.781511 | − | 0.623892i | \(-0.785551\pi\) | ||
0.781511 | − | 0.623892i | \(-0.214449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.4076 | − | 15.4076i | −0.673726 | − | 0.673726i | 0.284847 | − | 0.958573i | \(-0.408057\pi\) |
−0.958573 | + | 0.284847i | \(0.908057\pi\) | |||||||
\(524\) | 2.09829 | + | 3.63434i | 0.0916641 | + | 0.158767i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.64872 | + | 9.78386i | −0.246296 | + | 0.426597i | ||||
\(527\) | −10.8486 | + | 2.90687i | −0.472572 | + | 0.126625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.7363 | − | 10.2401i | 0.771145 | − | 0.445221i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.433573 | + | 0.433573i | −0.0187978 | + | 0.0187978i | ||||
\(533\) | −19.3089 | − | 5.17380i | −0.836361 | − | 0.224102i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.48544 | + | 4.89907i | 0.366515 | + | 0.211608i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.30542 | + | 34.7283i | −0.401185 | + | 1.49724i | ||||
\(539\) | −2.46780 | −0.106296 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.11754 | −0.0480466 | −0.0240233 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240233 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(542\) | −6.46008 | + | 24.1093i | −0.277484 | + | 1.03558i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.53959 | − | 0.888885i | −0.0660096 | − | 0.0381106i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1213 | + | 8.33894i | 1.33065 | + | 0.356547i | 0.852958 | − | 0.521979i | \(-0.174806\pi\) |
0.477694 | + | 0.878526i | \(0.341473\pi\) | |||||||
\(548\) | 0.952326 | − | 0.952326i | 0.0406813 | − | 0.0406813i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.10347 | + | 1.21444i | −0.0896109 | + | 0.0517369i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2945 | − | 4.09814i | 0.650387 | − | 0.174271i | ||||
\(554\) | 18.2979 | − | 31.6928i | 0.777402 | − | 1.34650i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.141537 | − | 0.245149i | −0.00600250 | − | 0.0103966i | ||||
\(557\) | 30.4033 | + | 30.4033i | 1.28823 | + | 1.28823i | 0.935862 | + | 0.352366i | \(0.114623\pi\) |
0.352366 | + | 0.935862i | \(0.385377\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6910i | 0.452182i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.11308 | − | 34.0105i | −0.384412 | − | 1.43465i | ||||
\(563\) | 0.300692 | + | 1.12220i | 0.0126727 | + | 0.0472950i | 0.971973 | − | 0.235094i | \(-0.0755398\pi\) |
−0.959300 | + | 0.282389i | \(0.908873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.78361i | 0.201070i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.3017 | + | 12.3017i | 0.516167 | + | 0.516167i | ||||
\(569\) | 0.145367 | + | 0.251784i | 0.00609412 | + | 0.0105553i | 0.869056 | − | 0.494713i | \(-0.164727\pi\) |
−0.862962 | + | 0.505268i | \(0.831394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.0283 | + | 22.5656i | −0.545215 | + | 0.944341i | 0.453378 | + | 0.891318i | \(0.350219\pi\) |
−0.998593 | + | 0.0530223i | \(0.983115\pi\) | |||||||
\(572\) | 0.927572 | − | 0.248542i | 0.0387837 | − | 0.0103921i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.57106 | − | 4.94851i | 0.357749 | − | 0.206547i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.52834 | − | 2.52834i | 0.105256 | − | 0.105256i | −0.652517 | − | 0.757774i | \(-0.726287\pi\) |
0.757774 | + | 0.652517i | \(0.226287\pi\) | |||||||
\(578\) | −18.7044 | − | 5.01183i | −0.778000 | − | 0.208465i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.6274 | + | 10.1772i | 0.731309 | + | 0.422222i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.50006 | − | 5.59831i | 0.0621262 | − | 0.231858i | ||||
\(584\) | −6.62852 | −0.274290 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.00174 | 0.165310 | ||||||||
\(587\) | 10.7212 | − | 40.0121i | 0.442511 | − | 1.65147i | −0.279914 | − | 0.960025i | \(-0.590306\pi\) |
0.722425 | − | 0.691449i | \(-0.243027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.22943 | − | 5.32861i | −0.380292 | − | 0.219562i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.7553 | − | 5.56137i | −0.853038 | − | 0.228571i | ||||
\(593\) | 26.6583 | − | 26.6583i | 1.09473 | − | 1.09473i | 0.0997087 | − | 0.995017i | \(-0.468209\pi\) |
0.995017 | − | 0.0997087i | \(-0.0317911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.81726 | + | 1.62655i | −0.115400 | + | 0.0666260i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.4428 | − | 3.06608i | 0.467930 | − | 0.125382i | ||||
\(599\) | 13.2427 | − | 22.9370i | 0.541080 | − | 0.937178i | −0.457762 | − | 0.889075i | \(-0.651349\pi\) |
0.998842 | − | 0.0481037i | \(-0.0153178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.26710 | + | 7.39084i | 0.174059 | + | 0.301479i | 0.939835 | − | 0.341628i | \(-0.110978\pi\) |
−0.765776 | + | 0.643107i | \(0.777645\pi\) | |||||||
\(602\) | −3.74279 | − | 3.74279i | −0.152545 | − | 0.152545i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.00111412i | 4.53329e-5i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.9000 | + | 44.4113i | 0.483005 | + | 1.80260i | 0.588881 | + | 0.808220i | \(0.299569\pi\) |
−0.105876 | + | 0.994379i | \(0.533765\pi\) | |||||||
\(608\) | −0.436602 | − | 1.62942i | −0.0177066 | − | 0.0660818i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.0190i | 1.86173i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3219 | − | 17.3219i | −0.699625 | − | 0.699625i | 0.264705 | − | 0.964330i | \(-0.414726\pi\) |
−0.964330 | + | 0.264705i | \(0.914726\pi\) | |||||||
\(614\) | 20.7039 | + | 35.8602i | 0.835542 | + | 1.44720i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.65929 | + | 4.60603i | −0.107146 | + | 0.185582i | ||||
\(617\) | 36.3708 | − | 9.74553i | 1.46423 | − | 0.392340i | 0.563284 | − | 0.826263i | \(-0.309538\pi\) |
0.900950 | + | 0.433923i | \(0.142871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.57434 | − | 4.95040i | 0.344632 | − | 0.198973i | −0.317687 | − | 0.948196i | \(-0.602906\pi\) |
0.662318 | + | 0.749223i | \(0.269573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.2255 | + | 32.2255i | −1.29213 | + | 1.29213i | ||||
\(623\) | −9.15670 | − | 2.45353i | −0.366855 | − | 0.0982986i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.9753 | + | 15.5742i | 1.07815 | + | 0.622469i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.429864 | − | 1.60427i | 0.0171534 | − | 0.0640175i | ||||
\(629\) | −9.67378 | −0.385719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0279 | −0.876918 | −0.438459 | − | 0.898751i | \(-0.644476\pi\) | ||||
−0.438459 | + | 0.898751i | \(0.644476\pi\) | |||||||
\(632\) | −5.90104 | + | 22.0230i | −0.234731 | + | 0.876027i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.65268 | + | 2.68622i | 0.184781 | + | 0.106684i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0485 | − | 4.03223i | −0.596242 | − | 0.159763i | ||||
\(638\) | −1.33171 | + | 1.33171i | −0.0527227 | + | 0.0527227i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.8054 | + | 12.5894i | −0.861263 | + | 0.497251i | −0.864435 | − | 0.502744i | \(-0.832324\pi\) |
0.00317173 | + | 0.999995i | \(0.498990\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.0492 | + | 8.05166i | −1.18502 | + | 0.317526i | −0.796918 | − | 0.604088i | \(-0.793538\pi\) |
−0.388107 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(644\) | 0.319219 | − | 0.552904i | 0.0125790 | − | 0.0217875i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.64484 | + | 2.84895i | 0.0647154 | + | 0.112090i | ||||
\(647\) | −7.86580 | − | 7.86580i | −0.309237 | − | 0.309237i | 0.535377 | − | 0.844613i | \(-0.320170\pi\) |
−0.844613 | + | 0.535377i | \(0.820170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.72090i | 0.263818i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.301325 | − | 1.12456i | −0.0118008 | − | 0.0440411i | ||||
\(653\) | 0.0749391 | + | 0.279676i | 0.00293259 | + | 0.0109446i | 0.967377 | − | 0.253343i | \(-0.0815300\pi\) |
−0.964444 | + | 0.264287i | \(0.914863\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.8384i | 0.501256i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.1106 | − | 16.1106i | −0.628058 | − | 0.628058i | ||||
\(659\) | −13.4009 | − | 23.2111i | −0.522026 | − | 0.904175i | −0.999672 | − | 0.0256228i | \(-0.991843\pi\) |
0.477646 | − | 0.878552i | \(-0.341490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6438 | + | 21.8997i | −0.491787 | + | 0.851800i | −0.999955 | − | 0.00945786i | \(-0.996989\pi\) |
0.508168 | + | 0.861258i | \(0.330323\pi\) | |||||||
\(662\) | −7.73611 | + | 2.07289i | −0.300673 | + | 0.0805650i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25.3823 | + | 14.6545i | −0.985024 | + | 0.568704i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.78827 | − | 1.78827i | 0.0692421 | − | 0.0692421i | ||||
\(668\) | −1.13154 | − | 0.303196i | −0.0437807 | − | 0.0117310i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1231 | + | 5.84458i | 0.390799 | + | 0.225628i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.30290 | + | 23.5227i | −0.242959 | + | 0.906735i | 0.731439 | + | 0.681906i | \(0.238849\pi\) |
−0.974398 | + | 0.224829i | \(0.927818\pi\) | |||||||
\(674\) | 13.3044 | 0.512466 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.51002 | 0.135001 | ||||||||
\(677\) | −0.240265 | + | 0.896681i | −0.00923414 | + | 0.0344623i | −0.970389 | − | 0.241547i | \(-0.922345\pi\) |
0.961155 | + | 0.276009i | \(0.0890120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.03407 | + | 4.06112i | 0.269943 | + | 0.155852i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.98188 | − | 2.13874i | −0.305642 | − | 0.0818966i | ||||
\(683\) | −22.2024 | + | 22.2024i | −0.849550 | + | 0.849550i | −0.990077 | − | 0.140526i | \(-0.955120\pi\) |
0.140526 | + | 0.990077i | \(0.455120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.3578 | − | 13.4856i | 0.891805 | − | 0.514884i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.63225 | − | 1.77711i | 0.252852 | − | 0.0677515i | ||||
\(689\) | 18.2945 | − | 31.6871i | 0.696966 | − | 1.20718i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.05877 | − | 7.02999i | −0.154403 | − | 0.267433i | 0.778439 | − | 0.627721i | \(-0.216012\pi\) |
−0.932841 | + | 0.360287i | \(0.882679\pi\) | |||||||
\(692\) | 1.89711 | + | 1.89711i | 0.0721173 | + | 0.0721173i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2473i | 0.540821i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.49595 | + | 5.58297i | 0.0566633 | + | 0.211470i | ||||
\(698\) | 3.24640 | + | 12.1157i | 0.122878 | + | 0.458586i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6359i | 0.741637i | 0.928705 | + | 0.370819i | \(0.120923\pi\) | ||||
−0.928705 | + | 0.370819i | \(0.879077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.49076 | − | 6.49076i | −0.244804 | − | 0.244804i | ||||
\(704\) | −3.79526 | − | 6.57359i | −0.143039 | − | 0.247752i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.8937 | + | 22.3325i | −0.485260 | + | 0.840496i | ||||
\(707\) | −5.09956 | + | 1.36642i | −0.191789 | + | 0.0513896i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.68383 | + | 1.54951i | −0.100793 | + | 0.0581931i | −0.549549 | − | 0.835461i | \(-0.685201\pi\) |
0.448756 | + | 0.893654i | \(0.351867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.65210 | − | 9.65210i | 0.361728 | − | 0.361728i | ||||
\(713\) | 10.7184 | + | 2.87199i | 0.401408 | + | 0.107557i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.93083 | + | 1.69211i | 0.109530 | + | 0.0632373i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.37774 | + | 16.3380i | −0.163376 | + | 0.609727i | ||||
\(719\) | 20.3126 | 0.757533 | 0.378767 | − | 0.925492i | \(-0.376348\pi\) | ||||
0.378767 | + | 0.925492i | \(0.376348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.7604 | 0.996608 | ||||||||
\(722\) | 5.79640 | − | 21.6325i | 0.215720 | − | 0.805077i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.51149 | + | 1.45001i | 0.0933388 | + | 0.0538892i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0647 | + | 4.57247i | 0.632895 | + | 0.169584i | 0.560983 | − | 0.827827i | \(-0.310423\pi\) |
0.0719119 | + | 0.997411i | \(0.477090\pi\) | |||||||
\(728\) | −23.7421 | + | 23.7421i | −0.879941 | + | 0.879941i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.67706 | − | 1.54560i | 0.0990147 | − | 0.0571662i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4785 | + | 6.82693i | −0.941068 | + | 0.252158i | −0.696568 | − | 0.717491i | \(-0.745291\pi\) |
−0.244500 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(734\) | −18.9970 | + | 32.9038i | −0.701192 | + | 1.21450i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.878218 | + | 1.52112i | 0.0323715 | + | 0.0560692i | ||||
\(737\) | 2.06746 | + | 2.06746i | 0.0761558 | + | 0.0761558i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.41459i | − | 0.235965i | −0.993016 | − | 0.117982i | \(-0.962357\pi\) | ||
0.993016 | − | 0.117982i | \(-0.0376426\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.68854 | + | 17.4979i | 0.172122 | + | 0.642368i | ||||
\(743\) | −4.95625 | − | 18.4970i | −0.181827 | − | 0.678588i | −0.995288 | − | 0.0969677i | \(-0.969086\pi\) |
0.813460 | − | 0.581620i | \(-0.197581\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 3.13856i | − | 0.114911i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.196335 | − | 0.196335i | −0.00717870 | − | 0.00717870i | ||||
\(749\) | −13.3702 | − | 23.1579i | −0.488536 | − | 0.846170i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.96958 | + | 3.41141i | −0.0718709 | + | 0.124484i | −0.899721 | − | 0.436465i | \(-0.856230\pi\) |
0.827850 | + | 0.560949i | \(0.189564\pi\) | |||||||
\(752\) | 28.5482 | − | 7.64946i | 1.04105 | − | 0.278947i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.2966 | + | 5.94472i | −0.374979 | + | 0.216494i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3710 | + | 17.3710i | −0.631361 | + | 0.631361i | −0.948409 | − | 0.317049i | \(-0.897308\pi\) |
0.317049 | + | 0.948409i | \(0.397308\pi\) | |||||||
\(758\) | −23.9495 | − | 6.41725i | −0.869885 | − | 0.233085i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.11860 | − | 4.10993i | −0.258049 | − | 0.148985i | 0.365395 | − | 0.930853i | \(-0.380934\pi\) |
−0.623444 | + | 0.781868i | \(0.714267\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.27057 | − | 15.9380i | 0.154605 | − | 0.576994i | ||||
\(764\) | −1.03558 | −0.0374660 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.5079 | −1.17456 | ||||||||
\(767\) | −10.9815 | + | 40.9835i | −0.396519 | + | 1.47983i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.91615 | − | 1.10629i | −0.0690983 | − | 0.0398939i | 0.465053 | − | 0.885283i | \(-0.346035\pi\) |
−0.534151 | + | 0.845389i | \(0.679369\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.76495 | + | 0.472918i | 0.0635221 | + | 0.0170207i | ||||
\(773\) | 8.23173 | − | 8.23173i | 0.296075 | − | 0.296075i | −0.543400 | − | 0.839474i | \(-0.682863\pi\) |
0.839474 | + | 0.543400i | \(0.182863\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.1286 | + | 5.84773i | −0.363595 | + | 0.209921i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.1408 | + | 9.41596i | −1.25986 | + | 0.337579i | ||||
\(779\) | −2.74224 | + | 4.74970i | −0.0982511 | + | 0.170176i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.59572 | + | 4.49591i | 0.0928820 | + | 0.160876i | ||||
\(782\) | −2.42204 | − | 2.42204i | −0.0866119 | − | 0.0866119i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.0057i | 0.357346i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.07119 | + | 33.8541i | 0.323353 | + | 1.20677i | 0.915957 | + | 0.401276i | \(0.131433\pi\) |
−0.592604 | + | 0.805494i | \(0.701900\pi\) | |||||||
\(788\) | −0.682372 | − | 2.54665i | −0.0243085 | − | 0.0907205i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 24.5882i | − | 0.874256i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.1803 | + | 52.1803i | 1.85298 | + | 1.85298i | ||||
\(794\) | −17.3076 | − | 29.9776i | −0.614223 | − | 1.06387i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.73110 | + | 2.99835i | −0.0613571 | + | 0.106274i | ||||
\(797\) | −25.2788 | + | 6.77343i | −0.895421 | + | 0.239927i | −0.677049 | − | 0.735938i | \(-0.736741\pi\) |
−0.218372 | + | 0.975866i | \(0.570075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.5233 | − | 6.65297i | 0.407664 | − | 0.235365i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.2041 | − | 12.2041i | 0.430941 | − | 0.430941i | ||||
\(803\) | −1.91059 | − | 0.511942i | −0.0674233 | − | 0.0180660i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −45.1784 | − | 26.0837i | −1.59134 | − | 0.918761i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.96755 | − | 7.34301i | 0.0692183 | − | 0.258326i | ||||
\(809\) | 40.3389 | 1.41824 | 0.709120 | − | 0.705088i | \(-0.249092\pi\) | ||||
0.709120 | + | 0.705088i | \(0.249092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.50040 | −0.158030 | −0.0790152 | − | 0.996873i | \(-0.525178\pi\) | ||||
−0.0790152 | + | 0.996873i | \(0.525178\pi\) | |||||||
\(812\) | −0.165840 | + | 0.618923i | −0.00581984 | + | 0.0217199i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.16394 | − | 3.55875i | −0.216046 | − | 0.124734i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.83326 | + | 0.759168i | 0.0991231 | + | 0.0265599i | ||||
\(818\) | 24.3930 | − | 24.3930i | 0.852880 | − | 0.852880i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.3109 | + | 7.68503i | −0.464552 | + | 0.268209i | −0.713956 | − | 0.700190i | \(-0.753099\pi\) |
0.249404 | + | 0.968399i | \(0.419765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.0723 | − | 3.77065i | 0.490528 | − | 0.131437i | −0.00507263 | − | 0.999987i | \(-0.501615\pi\) |
0.495601 | + | 0.868551i | \(0.334948\pi\) | |||||||
\(824\) | −19.2665 | + | 33.3706i | −0.671182 | + | 1.16252i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.5033 | − | 18.1923i | −0.365457 | − | 0.632989i | ||||
\(827\) | 3.31824 | + | 3.31824i | 0.115387 | + | 0.115387i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
−0.647056 | + | 0.762443i | \(0.724000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 33.9539i | − | 1.17927i | −0.807671 | − | 0.589633i | \(-0.799272\pi\) | ||
0.807671 | − | 0.589633i | \(-0.200728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.4024 | − | 46.2865i | −0.429977 | − | 1.60469i | ||||
\(833\) | 1.16588 | + | 4.35112i | 0.0403953 | + | 0.150757i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 0.263467i | − | 0.00911220i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.6473 | + | 11.6473i | 0.402349 | + | 0.402349i | ||||
\(839\) | 5.71824 | + | 9.90428i | 0.197416 | + | 0.341934i | 0.947690 | − | 0.319193i | \(-0.103412\pi\) |
−0.750274 | + | 0.661127i | \(0.770079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.2309 | − | 22.9166i | 0.456238 | − | 0.790228i | ||||
\(842\) | −18.7855 | + | 5.03357i | −0.647392 | + | 0.173468i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0209495 | − | 0.0120952i | 0.000721111 | − | 0.000416334i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.8113 | − | 14.8113i | 0.508923 | − | 0.508923i | ||||
\(848\) | −22.6983 | − | 6.08198i | −0.779462 | − | 0.208856i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.27720 | + | 4.77884i | 0.283739 | + | 0.163817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.18947 | − | 23.0994i | 0.211923 | − | 0.790909i | −0.775304 | − | 0.631589i | \(-0.782403\pi\) |
0.987227 | − | 0.159320i | \(-0.0509302\pi\) | |||||||
\(854\) | −36.5353 | −1.25021 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 38.5043 | 1.31605 | ||||||||
\(857\) | −3.88189 | + | 14.4874i | −0.132603 | + | 0.494881i | −0.999996 | − | 0.00274224i | \(-0.999127\pi\) |
0.867393 | + | 0.497623i | \(0.165794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.5983 | − | 21.7074i | −1.28284 | − | 0.740646i | −0.305471 | − | 0.952201i | \(-0.598814\pi\) |
−0.977366 | + | 0.211555i | \(0.932147\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.6567 | + | 12.5016i | 1.58913 | + | 0.425807i | ||||
\(863\) | 2.78648 | − | 2.78648i | 0.0948527 | − | 0.0948527i | −0.658088 | − | 0.752941i | \(-0.728635\pi\) |
0.752941 | + | 0.658088i | \(0.228635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.545339 | − | 0.314852i | 0.0185314 | − | 0.0106991i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.71566 | + | 0.727658i | −0.0921754 | + | 0.0246983i | ||||
\(869\) | −3.40181 | + | 5.89211i | −0.115399 | + | 0.199876i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.22911 | + | 15.9853i | 0.312717 | + | 0.541641i | ||||
\(872\) | 16.8003 | + | 16.8003i | 0.568929 | + | 0.568929i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.25020i | − | 0.109940i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.1359 | − | 41.5598i | −0.376033 | − | 1.40338i | −0.851829 | − | 0.523820i | \(-0.824507\pi\) |
0.475796 | − | 0.879556i | \(-0.342160\pi\) | |||||||
\(878\) | 0.517577 | + | 1.93163i | 0.0174674 | + | 0.0651892i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 47.0487i | − | 1.58511i | −0.609801 | − | 0.792555i | \(-0.708751\pi\) | ||
0.609801 | − | 0.792555i | \(-0.291249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.0669 | − | 21.0669i | −0.708957 | − | 0.708957i | 0.257359 | − | 0.966316i | \(-0.417148\pi\) |
−0.966316 | + | 0.257359i | \(0.917148\pi\) | |||||||
\(884\) | −0.876436 | − | 1.51803i | −0.0294777 | − | 0.0510569i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.5140 | − | 37.2633i | 0.722776 | − | 1.25188i | ||||
\(887\) | 3.50739 | − | 0.939801i | 0.117766 | − | 0.0315554i | −0.199454 | − | 0.979907i | \(-0.563917\pi\) |
0.317221 | + | 0.948352i | \(0.397250\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.77265 | − | 2.75549i | 0.160069 | − | 0.0924161i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.347592 | + | 0.347592i | −0.0116382 | + | 0.0116382i | ||||
\(893\) | 12.1956 | + | 3.26780i | 0.408110 | + | 0.109353i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.6203 | + | 9.59572i | 0.555245 | + | 0.320571i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.58743 | − | 28.3167i | 0.253196 | − | 0.944939i | ||||
\(899\) | −11.1368 | −0.371433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.5794 | −0.352450 | ||||||||
\(902\) | −1.10065 | + | 4.10768i | −0.0366477 | + | 0.136771i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30.6619 | + | 17.7026i | 1.01980 | + | 0.588781i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.1363 | − | 2.71600i | −0.336569 | − | 0.0901833i | 0.0865764 | − | 0.996245i | \(-0.472407\pi\) |
−0.423145 | + | 0.906062i | \(0.639074\pi\) | |||||||
\(908\) | 2.11700 | − | 2.11700i | 0.0702551 | − | 0.0702551i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.77512 | + | 3.91162i | −0.224470 | + | 0.129598i | −0.608018 | − | 0.793923i | \(-0.708035\pi\) |
0.383548 | + | 0.923521i | \(0.374702\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.44796 | + | 2.26362i | −0.279587 | + | 0.0749150i | ||||
\(914\) | −0.612004 | + | 1.06002i | −0.0202433 | + | 0.0350624i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.16600 | − | 3.75163i | −0.0715668 | − | 0.123957i | ||||
\(917\) | −30.9612 | − | 30.9612i | −1.02243 | − | 1.02243i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.61000i | 0.152070i | 0.997105 | + | 0.0760349i | \(0.0242260\pi\) | ||||
−0.997105 | + | 0.0760349i | \(0.975774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.51842 | − | 28.0591i | −0.247606 | − | 0.924078i | ||||
\(923\) | 8.48246 | + | 31.6570i | 0.279204 | + | 1.04200i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 25.1999i | − | 0.828122i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.24650 | − | 1.24650i | −0.0409182 | − | 0.0409182i | ||||
\(929\) | 15.7062 | + | 27.2039i | 0.515302 | + | 0.892530i | 0.999842 | + | 0.0177609i | \(0.00565375\pi\) |
−0.484540 | + | 0.874769i | \(0.661013\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.13718 | + | 3.70170i | −0.0700433 | + | 0.121318i | ||||
\(932\) | −1.13226 | + | 0.303388i | −0.0370884 | + | 0.00993782i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.6818 | − | 15.9821i | 0.905778 | − | 0.522951i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3617 | − | 21.3617i | 0.697856 | − | 0.697856i | −0.266092 | − | 0.963948i | \(-0.585732\pi\) |
0.963948 | + | 0.266092i | \(0.0857324\pi\) | |||||||
\(938\) | −8.82722 | − | 2.36525i | −0.288219 | − | 0.0772281i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.77035 | + | 3.33151i | 0.188108 | + | 0.108604i | 0.591096 | − | 0.806601i | \(-0.298695\pi\) |
−0.402989 | + | 0.915205i | \(0.632029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.47800 | − | 5.51597i | 0.0481303 | − | 0.179625i | ||||
\(944\) | 27.2498 | 0.886905 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.27436 | 0.0739458 | ||||||||
\(947\) | 0.867814 | − | 3.23873i | 0.0282002 | − | 0.105245i | −0.950391 | − | 0.311057i | \(-0.899317\pi\) |
0.978591 | + | 0.205812i | \(0.0659837\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.8142 | − | 6.24356i | −0.351043 | − | 0.202675i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.37748 | + | 2.51269i | 0.303926 | + | 0.0814367i | ||||
\(953\) | 30.7161 | − | 30.7161i | 0.994992 | − | 0.994992i | −0.00499525 | − | 0.999988i | \(-0.501590\pi\) |
0.999988 | + | 0.00499525i | \(0.00159004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.30970 | − | 1.33350i | 0.0747009 | − | 0.0431286i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.1357 | − | 6.19919i | 0.747480 | − | 0.200287i | ||||
\(959\) | −7.02601 | + | 12.1694i | −0.226882 | + | 0.392970i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.93253 | − | 15.4716i | −0.288146 | − | 0.499084i | ||||
\(962\) | −31.7725 | − | 31.7725i | −1.02439 | − | 1.02439i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.00809i | − | 0.0324684i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.48419 | + | 5.53906i | 0.0477282 | + | 0.178124i | 0.985675 | − | 0.168654i | \(-0.0539422\pi\) |
−0.937947 | + | 0.346779i | \(0.887276\pi\) | |||||||
\(968\) | 7.80632 | + | 29.1336i | 0.250904 | + | 0.936388i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 14.2248i | − | 0.456496i | −0.973603 | − | 0.228248i | \(-0.926700\pi\) | ||
0.973603 | − | 0.228248i | \(-0.0732998\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.08844 | + | 2.08844i | 0.0669524 | + | 0.0669524i | ||||
\(974\) | −20.7244 | − | 35.8957i | −0.664052 | − | 1.15017i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.6968 | − | 41.0440i | 0.758516 | − | 1.31379i | ||||
\(977\) | 30.1529 | − | 8.07944i | 0.964676 | − | 0.258484i | 0.258097 | − | 0.966119i | \(-0.416904\pi\) |
0.706578 | + | 0.707635i | \(0.250238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.52757 | − | 2.03664i | 0.112742 | − | 0.0650913i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −38.5627 | + | 38.5627i | −1.23059 | + | 1.23059i | ||||
\(983\) | 9.94750 | + | 2.66543i | 0.317276 | + | 0.0850139i | 0.413943 | − | 0.910303i | \(-0.364151\pi\) |
−0.0966666 | + | 0.995317i | \(0.530818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.97715 | + | 1.71886i | 0.0948116 | + | 0.0547395i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.430488 | − | 1.60660i | 0.0136956 | − | 0.0511128i | ||||
\(989\) | −3.05411 | −0.0971150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.9180 | 1.20450 | 0.602252 | − | 0.798306i | \(-0.294270\pi\) | ||||
0.602252 | + | 0.798306i | \(0.294270\pi\) | |||||||
\(992\) | 2.00189 | − | 7.47116i | 0.0635601 | − | 0.237210i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.0523 | − | 8.11308i | −0.445711 | − | 0.257331i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.1153 | − | 8.06937i | −0.953761 | − | 0.255559i | −0.251804 | − | 0.967778i | \(-0.581024\pi\) |
−0.701957 | + | 0.712219i | \(0.747690\pi\) | |||||||
\(998\) | 40.9452 | − | 40.9452i | 1.29610 | − | 1.29610i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 675.2.q.a.368.4 | 16 | ||
3.2 | odd | 2 | 225.2.p.b.68.1 | 16 | |||
5.2 | odd | 4 | inner | 675.2.q.a.557.4 | 16 | ||
5.3 | odd | 4 | 135.2.m.a.17.1 | 16 | |||
5.4 | even | 2 | 135.2.m.a.98.1 | 16 | |||
9.2 | odd | 6 | inner | 675.2.q.a.143.4 | 16 | ||
9.7 | even | 3 | 225.2.p.b.218.1 | 16 | |||
15.2 | even | 4 | 225.2.p.b.32.1 | 16 | |||
15.8 | even | 4 | 45.2.l.a.32.4 | yes | 16 | ||
15.14 | odd | 2 | 45.2.l.a.23.4 | yes | 16 | ||
45.2 | even | 12 | inner | 675.2.q.a.332.4 | 16 | ||
45.4 | even | 6 | 405.2.f.a.323.3 | 16 | |||
45.7 | odd | 12 | 225.2.p.b.182.1 | 16 | |||
45.13 | odd | 12 | 405.2.f.a.242.6 | 16 | |||
45.14 | odd | 6 | 405.2.f.a.323.6 | 16 | |||
45.23 | even | 12 | 405.2.f.a.242.3 | 16 | |||
45.29 | odd | 6 | 135.2.m.a.8.1 | 16 | |||
45.34 | even | 6 | 45.2.l.a.38.4 | yes | 16 | ||
45.38 | even | 12 | 135.2.m.a.62.1 | 16 | |||
45.43 | odd | 12 | 45.2.l.a.2.4 | ✓ | 16 | ||
60.23 | odd | 4 | 720.2.cu.c.257.4 | 16 | |||
60.59 | even | 2 | 720.2.cu.c.113.3 | 16 | |||
180.43 | even | 12 | 720.2.cu.c.497.3 | 16 | |||
180.79 | odd | 6 | 720.2.cu.c.353.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.l.a.2.4 | ✓ | 16 | 45.43 | odd | 12 | ||
45.2.l.a.23.4 | yes | 16 | 15.14 | odd | 2 | ||
45.2.l.a.32.4 | yes | 16 | 15.8 | even | 4 | ||
45.2.l.a.38.4 | yes | 16 | 45.34 | even | 6 | ||
135.2.m.a.8.1 | 16 | 45.29 | odd | 6 | |||
135.2.m.a.17.1 | 16 | 5.3 | odd | 4 | |||
135.2.m.a.62.1 | 16 | 45.38 | even | 12 | |||
135.2.m.a.98.1 | 16 | 5.4 | even | 2 | |||
225.2.p.b.32.1 | 16 | 15.2 | even | 4 | |||
225.2.p.b.68.1 | 16 | 3.2 | odd | 2 | |||
225.2.p.b.182.1 | 16 | 45.7 | odd | 12 | |||
225.2.p.b.218.1 | 16 | 9.7 | even | 3 | |||
405.2.f.a.242.3 | 16 | 45.23 | even | 12 | |||
405.2.f.a.242.6 | 16 | 45.13 | odd | 12 | |||
405.2.f.a.323.3 | 16 | 45.4 | even | 6 | |||
405.2.f.a.323.6 | 16 | 45.14 | odd | 6 | |||
675.2.q.a.143.4 | 16 | 9.2 | odd | 6 | inner | ||
675.2.q.a.332.4 | 16 | 45.2 | even | 12 | inner | ||
675.2.q.a.368.4 | 16 | 1.1 | even | 1 | trivial | ||
675.2.q.a.557.4 | 16 | 5.2 | odd | 4 | inner | ||
720.2.cu.c.113.3 | 16 | 60.59 | even | 2 | |||
720.2.cu.c.257.4 | 16 | 60.23 | odd | 4 | |||
720.2.cu.c.353.4 | 16 | 180.79 | odd | 6 | |||
720.2.cu.c.497.3 | 16 | 180.43 | even | 12 |