Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(101,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 11 x^{10} + 60 x^{9} - 120 x^{8} - 342 x^{7} + 2709 x^{6} - 3078 x^{5} - 9720 x^{4} + 43740 x^{3} - 72171 x^{2} - 118098 x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 401.5 | ||
Root | \(-2.85525 + 0.920635i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.401 |
Dual form | 900.3.p.c.101.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.85525 | − | 0.920635i | 0.951749 | − | 0.306878i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.594587 | − | 1.02985i | −0.0849410 | − | 0.147122i | 0.820425 | − | 0.571754i | \(-0.193737\pi\) |
−0.905366 | + | 0.424632i | \(0.860404\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.30486 | − | 5.25728i | 0.811651 | − | 0.584142i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.63473 | − | 2.09851i | 0.330430 | − | 0.190774i | −0.325602 | − | 0.945507i | \(-0.605567\pi\) |
0.656032 | + | 0.754733i | \(0.272234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.15614 | + | 12.3948i | −0.550473 | + | 0.953447i | 0.447768 | + | 0.894150i | \(0.352219\pi\) |
−0.998240 | + | 0.0592967i | \(0.981114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.7074i | 1.10044i | 0.835021 | + | 0.550218i | \(0.185455\pi\) | ||||
−0.835021 | + | 0.550218i | \(0.814545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33.8986 | 1.78414 | 0.892069 | − | 0.451899i | \(-0.149253\pi\) | ||||
0.892069 | + | 0.451899i | \(0.149253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64581 | − | 2.39309i | −0.125991 | − | 0.113957i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.6912 | + | 6.74989i | 0.508311 | + | 0.293474i | 0.732139 | − | 0.681155i | \(-0.238522\pi\) |
−0.223828 | + | 0.974629i | \(0.571855\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.0171 | − | 21.7359i | 0.593227 | − | 0.805035i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.6315 | − | 17.6851i | 1.05626 | − | 0.609831i | 0.131863 | − | 0.991268i | \(-0.457904\pi\) |
0.924395 | + | 0.381437i | \(0.124571\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.97816 | − | 8.62242i | 0.160586 | − | 0.278143i | −0.774493 | − | 0.632582i | \(-0.781995\pi\) |
0.935079 | + | 0.354440i | \(0.115328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.44607 | − | 9.33802i | 0.255942 | − | 0.282970i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.3047 | 0.521750 | 0.260875 | − | 0.965373i | \(-0.415989\pi\) | ||||
0.260875 | + | 0.965373i | \(0.415989\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.02146 | + | 41.9784i | −0.231319 | + | 1.07637i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −55.9648 | − | 32.3113i | −1.36499 | − | 0.788080i | −0.374711 | − | 0.927142i | \(-0.622258\pi\) |
−0.990284 | + | 0.139062i | \(0.955591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.7772 | − | 35.9872i | −0.483191 | − | 0.836911i | 0.516623 | − | 0.856213i | \(-0.327189\pi\) |
−0.999814 | + | 0.0193018i | \(0.993856\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.2068 | − | 33.6057i | 1.23844 | − | 0.715015i | 0.269667 | − | 0.962954i | \(-0.413087\pi\) |
0.968776 | + | 0.247939i | \(0.0797532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.7929 | − | 41.2106i | 0.485570 | − | 0.841032i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.2227 | + | 53.4143i | 0.337700 | + | 1.04734i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30.0712i | 0.567382i | 0.958916 | + | 0.283691i | \(0.0915589\pi\) | ||||
−0.958916 | + | 0.283691i | \(0.908441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 96.7889 | − | 31.2083i | 1.69805 | − | 0.547513i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.66554 | + | 2.11630i | 0.0621278 | + | 0.0358695i | 0.530742 | − | 0.847533i | \(-0.321913\pi\) |
−0.468614 | + | 0.883403i | \(0.655247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43.8210 | + | 75.9002i | 0.718377 | + | 1.24427i | 0.961643 | + | 0.274305i | \(0.0884479\pi\) |
−0.243266 | + | 0.969960i | \(0.578219\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.75761 | − | 4.39704i | −0.154883 | − | 0.0697942i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −17.9040 | + | 31.0106i | −0.267224 | + | 0.462845i | −0.968144 | − | 0.250395i | \(-0.919440\pi\) |
0.700920 | + | 0.713240i | \(0.252773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 39.5953 | + | 8.50932i | 0.573845 | + | 0.123323i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 24.5173i | − | 0.345314i | −0.984982 | − | 0.172657i | \(-0.944765\pi\) | ||
0.984982 | − | 0.172657i | \(-0.0552352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9305 | −0.163432 | −0.0817159 | − | 0.996656i | \(-0.526040\pi\) | ||||
−0.0817159 | + | 0.996656i | \(0.526040\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.32232 | − | 2.49549i | −0.0561340 | − | 0.0324090i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.0858 | + | 33.0575i | 0.241592 | + | 0.418449i | 0.961168 | − | 0.275964i | \(-0.0889971\pi\) |
−0.719576 | + | 0.694414i | \(0.755664\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.7220 | − | 76.8074i | 0.317556 | − | 0.948240i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −20.8692 | + | 12.0489i | −0.251436 | + | 0.145167i | −0.620422 | − | 0.784268i | \(-0.713039\pi\) |
0.368985 | + | 0.929435i | \(0.379705\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 71.1789 | − | 78.6957i | 0.818148 | − | 0.904548i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 44.4494i | − | 0.499431i | −0.968319 | − | 0.249716i | \(-0.919663\pi\) | ||
0.968319 | − | 0.249716i | \(-0.0803371\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.0198 | 0.187031 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.27576 | − | 29.2022i | 0.0674813 | − | 0.314002i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 31.9672 | + | 55.3688i | 0.329558 | + | 0.570812i | 0.982424 | − | 0.186662i | \(-0.0597668\pi\) |
−0.652866 | + | 0.757474i | \(0.726433\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.5187 | − | 34.4381i | 0.156755 | − | 0.347860i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3591 | − | 5.98084i | 0.102566 | − | 0.0592163i | −0.447840 | − | 0.894114i | \(-0.647807\pi\) |
0.550405 | + | 0.834898i | \(0.314473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −81.9841 | + | 142.001i | −0.795963 | + | 1.37865i | 0.126264 | + | 0.991997i | \(0.459701\pi\) |
−0.922226 | + | 0.386651i | \(0.873632\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 102.401i | − | 0.957019i | −0.878082 | − | 0.478509i | \(-0.841177\pi\) | ||
0.878082 | − | 0.478509i | \(-0.158823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −56.4485 | −0.517876 | −0.258938 | − | 0.965894i | \(-0.583373\pi\) | ||||
−0.258938 | + | 0.965894i | \(0.583373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 55.1198 | − | 17.7726i | 0.496575 | − | 0.160114i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −149.307 | − | 86.2022i | −1.32130 | − | 0.762852i | −0.337362 | − | 0.941375i | \(-0.609535\pi\) |
−0.983936 | + | 0.178523i | \(0.942868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.8883 | + | 128.164i | 0.110157 | + | 1.09542i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.2659 | − | 11.1232i | 0.161899 | − | 0.0934722i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −51.6925 | + | 89.5341i | −0.427211 | + | 0.739951i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −189.540 | − | 40.7335i | −1.54098 | − | 0.331167i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 195.853 | 1.54215 | 0.771073 | − | 0.636746i | \(-0.219720\pi\) | ||||
0.771073 | + | 0.636746i | \(0.219720\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −92.4551 | − | 83.6240i | −0.716706 | − | 0.648248i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −98.5249 | − | 56.8834i | −0.752099 | − | 0.434224i | 0.0743530 | − | 0.997232i | \(-0.476311\pi\) |
−0.826452 | + | 0.563008i | \(0.809644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.1557 | − | 34.9107i | −0.151546 | − | 0.262486i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −156.773 | + | 90.5130i | −1.14433 | + | 0.660679i | −0.947499 | − | 0.319759i | \(-0.896398\pi\) |
−0.196830 | + | 0.980438i | \(0.563065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 114.555 | − | 198.414i | 0.824134 | − | 1.42744i | −0.0784454 | − | 0.996918i | \(-0.524996\pi\) |
0.902579 | − | 0.430524i | \(-0.141671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 135.256 | − | 149.540i | 0.959263 | − | 1.06057i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 60.0689i | 0.420063i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 29.9948 | − | 139.571i | 0.204046 | − | 0.949462i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 233.844 | + | 135.010i | 1.56942 | + | 0.906107i | 0.996236 | + | 0.0866818i | \(0.0276263\pi\) |
0.573187 | + | 0.819425i | \(0.305707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 81.5705 | + | 141.284i | 0.540202 | + | 0.935658i | 0.998892 | + | 0.0470612i | \(0.0149856\pi\) |
−0.458690 | + | 0.888596i | \(0.651681\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 98.3501 | + | 136.655i | 0.642811 | + | 0.893171i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −67.2998 | + | 116.567i | −0.428661 | + | 0.742463i | −0.996754 | − | 0.0805014i | \(-0.974348\pi\) |
0.568094 | + | 0.822964i | \(0.307681\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.6846 | + | 85.8607i | 0.174117 | + | 0.540005i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.0536i | − | 0.0997118i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 159.658 | 0.979500 | 0.489750 | − | 0.871863i | \(-0.337088\pi\) | ||||
0.489750 | + | 0.871863i | \(0.337088\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −96.2622 | − | 55.5770i | −0.576420 | − | 0.332796i | 0.183289 | − | 0.983059i | \(-0.441326\pi\) |
−0.759709 | + | 0.650263i | \(0.774659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.9208 | − | 31.0397i | −0.106040 | − | 0.183667i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 247.625 | − | 178.215i | 1.44810 | − | 1.04219i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 127.610 | − | 73.6755i | 0.737629 | − | 0.425870i | −0.0835778 | − | 0.996501i | \(-0.526635\pi\) |
0.821207 | + | 0.570631i | \(0.193301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.4144 | + | 2.66793i | 0.0701376 | + | 0.0150731i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 253.022i | 1.41353i | 0.707449 | + | 0.706765i | \(0.249846\pi\) | ||||
−0.707449 | + | 0.706765i | \(0.750154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −212.017 | −1.17136 | −0.585682 | − | 0.810541i | \(-0.699173\pi\) | ||||
−0.585682 | + | 0.810541i | \(0.699173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 194.996 | + | 176.371i | 1.06555 | + | 0.963773i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39.2577 | + | 67.9963i | 0.209934 | + | 0.363617i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −31.9084 | − | 3.57142i | −0.168828 | − | 0.0188964i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −287.027 | + | 165.715i | −1.50276 | + | 0.867619i | −0.502765 | + | 0.864423i | \(0.667684\pi\) |
−0.999995 | + | 0.00319548i | \(0.998983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 166.279 | − | 288.004i | 0.861549 | − | 1.49225i | −0.00888358 | − | 0.999961i | \(-0.502828\pi\) |
0.870433 | − | 0.492287i | \(-0.163839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 321.219i | − | 1.63056i | −0.579070 | − | 0.815278i | \(-0.696584\pi\) | ||
0.579070 | − | 0.815278i | \(-0.303416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −208.913 | −1.04981 | −0.524907 | − | 0.851160i | \(-0.675900\pi\) | ||||
−0.524907 | + | 0.851160i | \(0.675900\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.5708 | + | 105.026i | −0.112293 | + | 0.522518i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −36.4262 | − | 21.0307i | −0.179439 | − | 0.103599i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 120.888 | − | 12.1567i | 0.584002 | − | 0.0587278i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 123.212 | − | 71.1366i | 0.589532 | − | 0.340366i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −110.304 | + | 191.053i | −0.522769 | + | 0.905463i | 0.476880 | + | 0.878969i | \(0.341768\pi\) |
−0.999649 | + | 0.0264945i | \(0.991566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.5715 | − | 70.0028i | −0.105969 | − | 0.328652i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.8398 | −0.0545613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −34.0646 | + | 10.9837i | −0.155546 | + | 0.0501537i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −231.875 | − | 133.873i | −1.04921 | − | 0.605760i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 143.626 | + | 248.767i | 0.644062 | + | 1.11555i | 0.984517 | + | 0.175287i | \(0.0560855\pi\) |
−0.340455 | + | 0.940261i | \(0.610581\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −226.479 | + | 130.758i | −0.997704 | + | 0.576024i | −0.907568 | − | 0.419905i | \(-0.862063\pi\) |
−0.0901356 | + | 0.995930i | \(0.528730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −99.2244 | + | 171.862i | −0.433294 | + | 0.750488i | −0.997155 | − | 0.0753822i | \(-0.975982\pi\) |
0.563860 | + | 0.825870i | \(0.309316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.6387 | − | 3.14597i | −0.0633711 | − | 0.0136189i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 182.063i | − | 0.781387i | −0.920521 | − | 0.390693i | \(-0.872235\pi\) | ||
0.920521 | − | 0.390693i | \(-0.127765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 84.9284 | + | 76.8163i | 0.358348 | + | 0.324119i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −210.133 | − | 121.320i | −0.879218 | − | 0.507617i | −0.00881748 | − | 0.999961i | \(-0.502807\pi\) |
−0.870400 | + | 0.492344i | \(0.836140\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 158.882 | + | 275.192i | 0.659263 | + | 1.14188i | 0.980807 | + | 0.194983i | \(0.0624650\pi\) |
−0.321544 | + | 0.946895i | \(0.604202\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.73105 | − | 242.985i | 0.0112389 | − | 0.999937i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −242.583 | + | 420.167i | −0.982119 | + | 1.70108i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −48.4942 | + | 53.6154i | −0.194756 | + | 0.215323i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 64.0280i | − | 0.255092i | −0.991833 | − | 0.127546i | \(-0.959290\pi\) | ||
0.991833 | − | 0.127546i | \(-0.0407100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 56.6589 | 0.223948 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −402.010 | − | 232.101i | −1.56424 | − | 0.903116i | −0.996820 | − | 0.0796896i | \(-0.974607\pi\) |
−0.567423 | − | 0.823426i | \(-0.692060\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4784 | − | 19.8811i | −0.0443180 | − | 0.0767610i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 130.783 | − | 290.225i | 0.501085 | − | 1.11197i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 48.5809 | − | 28.0482i | 0.184718 | − | 0.106647i | −0.404789 | − | 0.914410i | \(-0.632655\pi\) |
0.589508 | + | 0.807763i | \(0.299322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −40.9217 | − | 126.914i | −0.153265 | − | 0.475333i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 29.8910i | − | 0.111119i | −0.998455 | − | 0.0555594i | \(-0.982306\pi\) | ||
0.998455 | − | 0.0555594i | \(-0.0176942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −166.826 | −0.615594 | −0.307797 | − | 0.951452i | \(-0.599592\pi\) | ||||
−0.307797 | + | 0.951452i | \(0.599592\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 48.5957 | − | 15.6690i | 0.178006 | − | 0.0573957i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 98.4054 | + | 170.443i | 0.355254 | + | 0.615318i | 0.987161 | − | 0.159726i | \(-0.0510609\pi\) |
−0.631907 | + | 0.775044i | \(0.717728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.96574 | − | 89.1572i | −0.0321353 | − | 0.319560i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 288.196 | − | 166.390i | 1.02561 | − | 0.592136i | 0.109886 | − | 0.993944i | \(-0.464951\pi\) |
0.915724 | + | 0.401808i | \(0.131618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −233.467 | + | 404.376i | −0.824971 | + | 1.42889i | 0.0769712 | + | 0.997033i | \(0.475475\pi\) |
−0.901942 | + | 0.431858i | \(0.857858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 76.8474i | 0.267761i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −60.9675 | −0.210960 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 142.249 | + | 128.661i | 0.488827 | + | 0.442135i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.6397 | + | 10.7616i | 0.0636167 | + | 0.0367291i | 0.531471 | − | 0.847077i | \(-0.321639\pi\) |
−0.467854 | + | 0.883806i | \(0.654973\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.6048 | − | 112.616i | 0.0424405 | − | 0.379179i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −167.327 | + | 96.6064i | −0.559623 | + | 0.323098i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.7077 | + | 42.7950i | −0.0820854 | + | 0.142176i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.0717 | − | 26.6137i | 0.0794445 | − | 0.0878342i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −452.833 | −1.47503 | −0.737514 | − | 0.675332i | \(-0.764000\pi\) | ||||
−0.737514 | + | 0.675332i | \(0.764000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −103.354 | + | 480.924i | −0.334479 | + | 1.55639i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −488.695 | − | 282.148i | −1.57137 | − | 0.907229i | −0.996002 | − | 0.0893313i | \(-0.971527\pi\) |
−0.575364 | − | 0.817897i | \(-0.695140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −230.660 | − | 399.515i | −0.736933 | − | 1.27641i | −0.953870 | − | 0.300220i | \(-0.902940\pi\) |
0.216937 | − | 0.976186i | \(-0.430393\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −291.643 | + | 168.380i | −0.920008 | + | 0.531167i | −0.883638 | − | 0.468171i | \(-0.844913\pi\) |
−0.0363706 | + | 0.999338i | \(0.511580\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 74.2247 | − | 128.561i | 0.232679 | − | 0.403012i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −94.2740 | − | 292.380i | −0.293688 | − | 0.910841i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 634.156i | 1.96333i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −161.174 | + | 51.9684i | −0.492888 | + | 0.158925i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −69.2180 | − | 39.9630i | −0.210389 | − | 0.121468i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 210.896 | + | 365.283i | 0.637149 | + | 1.10357i | 0.986055 | + | 0.166417i | \(0.0532197\pi\) |
−0.348907 | + | 0.937158i | \(0.613447\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 141.019 | − | 101.490i | 0.423479 | − | 0.304776i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −59.2115 | + | 102.557i | −0.175702 | + | 0.304325i | −0.940404 | − | 0.340059i | \(-0.889553\pi\) |
0.764702 | + | 0.644384i | \(0.222886\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −505.668 | − | 108.672i | −1.49165 | − | 0.320565i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 41.7869i | − | 0.122542i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −114.857 | −0.334861 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −147.224 | − | 85.0001i | −0.424278 | − | 0.244957i | 0.272628 | − | 0.962120i | \(-0.412107\pi\) |
−0.696906 | + | 0.717163i | \(0.745441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −310.127 | − | 537.156i | −0.888617 | − | 1.53913i | −0.841511 | − | 0.540240i | \(-0.818333\pi\) |
−0.0471063 | − | 0.998890i | \(-0.515000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 154.792 | + | 354.075i | 0.441002 | + | 1.00876i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 354.557 | − | 204.704i | 1.00441 | − | 0.579897i | 0.0948611 | − | 0.995491i | \(-0.469759\pi\) |
0.909551 | + | 0.415593i | \(0.136426\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44.7686 | − | 49.4963i | 0.125402 | − | 0.138645i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 138.441i | 0.385630i | 0.981235 | + | 0.192815i | \(0.0617618\pi\) | ||||
−0.981235 | + | 0.192815i | \(0.938238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 788.116 | 2.18315 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −65.1666 | + | 303.232i | −0.179522 | + | 0.835349i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 39.5358 | + | 68.4781i | 0.107727 | + | 0.186589i | 0.914849 | − | 0.403796i | \(-0.132309\pi\) |
−0.807122 | + | 0.590385i | \(0.798976\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −578.684 | + | 58.1931i | −1.56825 | + | 0.157705i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.9690 | − | 17.8800i | 0.0834744 | − | 0.0481940i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 51.8849 | − | 89.8672i | 0.139102 | − | 0.240931i | −0.788055 | − | 0.615605i | \(-0.788912\pi\) |
0.927157 | + | 0.374674i | \(0.122245\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 506.228i | 1.34278i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 315.487 | 0.832419 | 0.416210 | − | 0.909269i | \(-0.363358\pi\) | ||||
0.416210 | + | 0.909269i | \(0.363358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 559.208 | − | 180.309i | 1.46774 | − | 0.473252i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −358.695 | − | 207.092i | −0.936540 | − | 0.540711i | −0.0476657 | − | 0.998863i | \(-0.515178\pi\) |
−0.888874 | + | 0.458152i | \(0.848512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −340.969 | − | 153.650i | −0.881058 | − | 0.397028i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −59.9057 | + | 34.5866i | −0.153999 | + | 0.0889115i | −0.575019 | − | 0.818140i | \(-0.695006\pi\) |
0.421020 | + | 0.907051i | \(0.361672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −126.273 | + | 218.711i | −0.322949 | + | 0.559364i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −333.682 | − | 71.7106i | −0.849063 | − | 0.182470i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −347.995 | −0.876562 | −0.438281 | − | 0.898838i | \(-0.644413\pi\) | ||||
−0.438281 | + | 0.898838i | \(0.644413\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −89.6894 | − | 81.1225i | −0.224785 | − | 0.203315i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −635.313 | − | 366.798i | −1.58432 | − | 0.914709i | −0.994218 | − | 0.107382i | \(-0.965753\pi\) |
−0.590104 | − | 0.807327i | \(-0.700913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 71.2488 | + | 123.407i | 0.176796 | + | 0.306220i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 70.1675 | − | 40.5112i | 0.172402 | − | 0.0995361i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −47.0727 | + | 81.5324i | −0.115092 | + | 0.199346i | −0.917817 | − | 0.397005i | \(-0.870050\pi\) |
0.802724 | + | 0.596350i | \(0.203383\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −364.296 | + | 402.768i | −0.886366 | + | 0.979970i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5.03330i | − | 0.0121872i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 144.414 | − | 671.985i | 0.346317 | − | 1.61147i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −90.6043 | − | 52.3104i | −0.216239 | − | 0.124846i | 0.387968 | − | 0.921673i | \(-0.373177\pi\) |
−0.604208 | + | 0.796827i | \(0.706510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −276.542 | − | 478.984i | −0.656868 | − | 1.13773i | −0.981422 | − | 0.191862i | \(-0.938547\pi\) |
0.324553 | − | 0.945867i | \(-0.394786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 248.518 | − | 551.494i | 0.587513 | − | 1.30377i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.1108 | − | 90.2585i | 0.122039 | − | 0.211378i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 55.3016 | + | 171.512i | 0.128908 | + | 0.399794i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 469.242i | 1.08873i | 0.838849 | + | 0.544364i | \(0.183229\pi\) | ||||
−0.838849 | + | 0.544364i | \(0.816771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −426.644 | −0.985321 | −0.492660 | − | 0.870222i | \(-0.663976\pi\) | ||||
−0.492660 | + | 0.870222i | \(0.663976\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 396.314 | + | 228.812i | 0.906898 | + | 0.523598i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 286.573 | + | 496.359i | 0.652786 | + | 1.13066i | 0.982444 | + | 0.186558i | \(0.0597332\pi\) |
−0.329658 | + | 0.944100i | \(0.606933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.8514 | − | 426.124i | −0.0971688 | − | 0.966267i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −90.5838 | + | 52.2986i | −0.204478 | + | 0.118055i | −0.598743 | − | 0.800942i | \(-0.704333\pi\) |
0.394264 | + | 0.918997i | \(0.370999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 791.977 | + | 170.201i | 1.77176 | + | 0.380764i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 401.878i | − | 0.895051i | −0.894271 | − | 0.447526i | \(-0.852305\pi\) | ||
0.894271 | − | 0.447526i | \(-0.147695\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −271.222 | −0.601379 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 362.975 | + | 328.305i | 0.801270 | + | 0.724735i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 48.1592 | + | 83.4142i | 0.105381 | + | 0.182526i | 0.913894 | − | 0.405953i | \(-0.133060\pi\) |
−0.808513 | + | 0.588479i | \(0.799727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 406.623 | + | 299.639i | 0.885890 | + | 0.652809i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −64.4588 | + | 37.2153i | −0.139824 | + | 0.0807274i | −0.568280 | − | 0.822835i | \(-0.692391\pi\) |
0.428456 | + | 0.903563i | \(0.359058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 198.930 | − | 344.558i | 0.429655 | − | 0.744185i | −0.567187 | − | 0.823589i | \(-0.691968\pi\) |
0.996843 | + | 0.0794042i | \(0.0253018\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 643.763i | − | 1.37851i | −0.724520 | − | 0.689254i | \(-0.757938\pi\) | ||
0.724520 | − | 0.689254i | \(-0.242062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.5819 | 0.0907931 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −84.8421 | + | 394.785i | −0.180132 | + | 0.838185i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −151.039 | − | 87.2024i | −0.319321 | − | 0.184360i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 158.093 | + | 219.666i | 0.331432 | + | 0.460516i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −152.770 | + | 88.2019i | −0.318936 | + | 0.184138i | −0.650918 | − | 0.759148i | \(-0.725616\pi\) |
0.331982 | + | 0.943286i | \(0.392283\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −138.148 | + | 239.279i | −0.287209 | + | 0.497461i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.7795 | − | 45.8370i | −0.0305994 | − | 0.0949006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 494.859 | 1.01614 | 0.508069 | − | 0.861317i | \(-0.330360\pi\) | ||||
0.508069 | + | 0.861317i | \(0.330360\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 455.864 | − | 146.987i | 0.932238 | − | 0.300587i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 159.777 | + | 92.2472i | 0.325411 | + | 0.187876i | 0.653802 | − | 0.756666i | \(-0.273173\pi\) |
−0.328391 | + | 0.944542i | \(0.606506\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 330.842 | + | 573.036i | 0.671080 | + | 1.16234i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.2492 | + | 14.5777i | −0.0508033 | + | 0.0293313i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −162.276 | + | 281.071i | −0.325203 | + | 0.563269i | −0.981553 | − | 0.191188i | \(-0.938766\pi\) |
0.656350 | + | 0.754456i | \(0.272099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −326.018 | − | 70.0636i | −0.650735 | − | 0.139848i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 626.131i | 1.24479i | 0.782702 | + | 0.622397i | \(0.213841\pi\) | ||||
−0.782702 | + | 0.622397i | \(0.786159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −79.7446 | − | 72.1276i | −0.157287 | − | 0.142263i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 387.634 | + | 223.800i | 0.761559 | + | 0.439686i | 0.829855 | − | 0.557979i | \(-0.188423\pi\) |
−0.0682960 | + | 0.997665i | \(0.521756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.09374 | + | 12.2867i | 0.0138821 | + | 0.0240444i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 542.959 | − | 736.818i | 1.05840 | − | 1.43629i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 141.044 | − | 244.295i | 0.272812 | − | 0.472524i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 296.529 | − | 327.844i | 0.571347 | − | 0.631684i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 181.821i | 0.348984i | 0.984659 | + | 0.174492i | \(0.0558284\pi\) | ||||
−0.984659 | + | 0.174492i | \(0.944172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 293.719 | 0.561604 | 0.280802 | − | 0.959766i | \(-0.409400\pi\) | ||||
0.280802 | + | 0.959766i | \(0.409400\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 161.303 | + | 93.1285i | 0.306078 | + | 0.176714i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −173.378 | − | 300.299i | −0.327746 | − | 0.567673i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 37.9022 | − | 3.81149i | 0.0713790 | − | 0.00717795i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 800.984 | − | 462.448i | 1.50278 | − | 0.867633i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 232.941 | + | 722.439i | 0.433782 | + | 1.34532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 199.719i | − | 0.370536i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 343.593 | 0.635107 | 0.317553 | − | 0.948240i | \(-0.397139\pi\) | ||||
0.317553 | + | 0.948240i | \(0.397139\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −605.360 | + | 195.190i | −1.11484 | + | 0.359466i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.5788 | − | 35.6434i | −0.0376211 | − | 0.0651617i | 0.846602 | − | 0.532227i | \(-0.178645\pi\) |
−0.884223 | + | 0.467065i | \(0.845311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 719.135 | + | 324.061i | 1.30990 | + | 0.590275i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1038.36 | − | 599.500i | 1.88451 | − | 1.08802i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.6963 | − | 39.3111i | 0.0410421 | − | 0.0710870i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 976.675i | − | 1.75346i | −0.480986 | − | 0.876728i | \(-0.659721\pi\) | ||
0.480986 | − | 0.876728i | \(-0.340279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 594.739 | 1.06393 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 174.690 | + | 158.004i | 0.311391 | + | 0.281647i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −383.325 | − | 221.313i | −0.680862 | − | 0.393096i | 0.119318 | − | 0.992856i | \(-0.461929\pi\) |
−0.800180 | + | 0.599760i | \(0.795263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −94.3945 | + | 19.1788i | −0.166481 | + | 0.0338250i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 681.591 | − | 393.517i | 1.19788 | − | 0.691594i | 0.237795 | − | 0.971315i | \(-0.423575\pi\) |
0.960081 | + | 0.279721i | \(0.0902421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.41373 | − | 5.91275i | 0.00597851 | − | 0.0103551i | −0.863021 | − | 0.505169i | \(-0.831430\pi\) |
0.868999 | + | 0.494814i | \(0.164764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −666.970 | + | 737.405i | −1.16400 | + | 1.28692i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.4328 | 0.0787396 | 0.0393698 | − | 0.999225i | \(-0.487465\pi\) | ||||
0.0393698 | + | 0.999225i | \(0.487465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 209.621 | − | 975.404i | 0.362040 | − | 1.68464i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.8171 | + | 14.3282i | 0.0427145 | + | 0.0246612i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 63.1048 | + | 109.301i | 0.108241 | + | 0.187480i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −85.9520 | + | 49.6244i | −0.146426 | + | 0.0845391i | −0.571423 | − | 0.820656i | \(-0.693608\pi\) |
0.424997 | + | 0.905195i | \(0.360275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 168.753 | − | 292.288i | 0.286507 | − | 0.496245i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −295.726 | − | 917.161i | −0.500382 | − | 1.55188i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 226.897i | 0.382626i | 0.981529 | + | 0.191313i | \(0.0612745\pi\) | ||||
−0.981529 | + | 0.191313i | \(0.938726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −596.498 | + | 192.333i | −0.999159 | + | 0.322165i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 652.129 | + | 376.507i | 1.08870 | + | 0.628559i | 0.933229 | − | 0.359282i | \(-0.116978\pi\) |
0.155467 | + | 0.987841i | \(0.450312\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −342.525 | − | 593.270i | −0.569924 | − | 0.987138i | −0.996573 | − | 0.0827206i | \(-0.973639\pi\) |
0.426648 | − | 0.904418i | \(-0.359694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.2454 | + | 320.655i | 0.0534749 | + | 0.531766i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 454.475 | − | 787.174i | 0.748724 | − | 1.29683i | −0.199711 | − | 0.979855i | \(-0.564000\pi\) |
0.948435 | − | 0.316973i | \(-0.102666\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −123.367 | − | 26.5125i | −0.202573 | − | 0.0435345i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 961.949i | 1.57438i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −514.234 | −0.838881 | −0.419441 | − | 0.907783i | \(-0.637774\pi\) | ||||
−0.419441 | + | 0.907783i | \(0.637774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 996.159 | + | 575.133i | 1.61452 | + | 0.932144i | 0.988304 | + | 0.152494i | \(0.0487304\pi\) |
0.626216 | + | 0.779650i | \(0.284603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 69.9937 | + | 121.233i | 0.113076 | + | 0.195853i | 0.917009 | − | 0.398867i | \(-0.130596\pi\) |
−0.803933 | + | 0.594719i | \(0.797263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 333.974 | − | 146.004i | 0.537801 | − | 0.235112i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.7764 | + | 26.4290i | −0.0734774 | + | 0.0424222i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 286.310 | − | 316.546i | 0.456635 | − | 0.504858i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 361.142i | 0.574153i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −369.971 | −0.586325 | −0.293163 | − | 0.956063i | \(-0.594708\pi\) | ||||
−0.293163 | + | 0.956063i | \(0.594708\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −139.056 | + | 647.053i | −0.219678 | + | 1.02220i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 340.531 | + | 589.818i | 0.534586 | + | 0.925930i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −128.894 | − | 179.095i | −0.201712 | − | 0.280274i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 67.0156 | − | 38.6914i | 0.104548 | − | 0.0603611i | −0.446814 | − | 0.894627i | \(-0.647441\pi\) |
0.551363 | + | 0.834266i | \(0.314108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 130.904 | − | 226.733i | 0.203583 | − | 0.352617i | −0.746097 | − | 0.665837i | \(-0.768075\pi\) |
0.949680 | + | 0.313220i | \(0.101408\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 617.428i | 0.954293i | 0.878824 | + | 0.477147i | \(0.158329\pi\) | ||||
−0.878824 | + | 0.477147i | \(0.841671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.7643 | 0.0273718 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −33.8055 | + | 10.9001i | −0.0519286 | + | 0.0167437i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −584.115 | − | 337.239i | −0.894510 | − | 0.516446i | −0.0190951 | − | 0.999818i | \(-0.506079\pi\) |
−0.875415 | + | 0.483372i | \(0.839412\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −87.1508 | + | 62.7221i | −0.132650 | + | 0.0954675i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 332.973 | − | 192.242i | 0.505271 | − | 0.291718i | −0.225617 | − | 0.974216i | \(-0.572440\pi\) |
0.730888 | + | 0.682498i | \(0.239106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 151.713 | − | 262.775i | 0.229520 | − | 0.397541i | −0.728146 | − | 0.685422i | \(-0.759618\pi\) |
0.957666 | + | 0.287882i | \(0.0929509\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −785.308 | − | 168.768i | −1.18448 | − | 0.254552i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 477.490 | 0.715877 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 639.111 | + | 578.065i | 0.955323 | + | 0.864073i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 318.554 | + | 183.918i | 0.474746 | + | 0.274095i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −280.062 | − | 485.081i | −0.416139 | − | 0.720775i | 0.579408 | − | 0.815038i | \(-0.303284\pi\) |
−0.995547 | + | 0.0942631i | \(0.969951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 880.370 | − | 508.282i | 1.30040 | − | 0.750786i | 0.319927 | − | 0.947442i | \(-0.396342\pi\) |
0.980472 | + | 0.196656i | \(0.0630083\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.0145 | − | 65.8431i | 0.0559860 | − | 0.0969707i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −526.273 | + | 581.849i | −0.772794 | + | 0.854404i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 88.7713i | 0.129973i | 0.997886 | + | 0.0649863i | \(0.0207004\pi\) | ||||
−0.997886 | + | 0.0649863i | \(0.979300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −125.088 | + | 582.057i | −0.182079 | + | 0.847245i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −372.727 | − | 215.194i | −0.540968 | − | 0.312328i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −403.626 | − | 699.101i | −0.584119 | − | 1.01172i | −0.994985 | − | 0.100027i | \(-0.968107\pi\) |
0.410866 | − | 0.911696i | \(-0.365226\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −44.6935 | + | 4.49442i | −0.0644927 | + | 0.00648546i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 604.460 | − | 1046.96i | 0.867232 | − | 1.50209i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −167.614 | − | 519.835i | −0.239791 | − | 0.743684i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 201.018i | 0.286758i | 0.989668 | + | 0.143379i | \(0.0457968\pi\) | ||||
−0.989668 | + | 0.143379i | \(0.954203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 654.404 | 0.930874 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.3188 | − | 7.11226i | −0.0174240 | − | 0.0100598i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −195.660 | − | 338.894i | −0.275967 | − | 0.477989i | 0.694412 | − | 0.719578i | \(-0.255665\pi\) |
−0.970379 | + | 0.241589i | \(0.922331\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 313.211 | + | 141.141i | 0.440522 | + | 0.198511i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 116.401 | − | 67.2041i | 0.163255 | − | 0.0942554i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −711.674 | − | 152.944i | −0.992571 | − | 0.213311i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1241.75i | 1.72705i | 0.504308 | + | 0.863524i | \(0.331747\pi\) | ||||
−0.504308 | + | 0.863524i | \(0.668253\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 194.987 | 0.270439 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 707.000 | + | 639.469i | 0.977870 | + | 0.884467i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −100.212 | − | 173.571i | −0.137843 | − | 0.238750i | 0.788837 | − | 0.614602i | \(-0.210683\pi\) |
−0.926680 | + | 0.375852i | \(0.877350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −215.902 | − | 696.295i | −0.296162 | − | 0.955138i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 673.227 | − | 388.688i | 0.920968 | − | 0.531721i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −60.3607 | + | 104.548i | −0.0823475 | + | 0.142630i | −0.904258 | − | 0.426987i | \(-0.859575\pi\) |
0.821910 | + | 0.569617i | \(0.192908\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 150.287i | 0.203917i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −471.461 | −0.637972 | −0.318986 | − | 0.947759i | \(-0.603342\pi\) | ||||
−0.318986 | + | 0.947759i | \(0.603342\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −305.815 | + | 1423.01i | −0.412706 | + | 1.92039i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1128.15 | − | 651.339i | −1.51837 | − | 0.876634i | −0.999766 | − | 0.0216220i | \(-0.993117\pi\) |
−0.518608 | − | 0.855012i | \(-0.673550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −89.1026 | + | 197.731i | −0.119281 | + | 0.264700i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −105.458 | + | 60.8863i | −0.140799 | + | 0.0812901i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 439.726 | − | 761.629i | 0.585521 | − | 1.01415i | −0.409289 | − | 0.912405i | \(-0.634223\pi\) |
0.994810 | − | 0.101748i | \(-0.0324435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −58.9464 | − | 182.816i | −0.0782821 | − | 0.242783i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.1814 | 0.0464748 | 0.0232374 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232374 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 161.775 | − | 52.1622i | 0.213142 | − | 0.0687248i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1102.94 | + | 636.785i | 1.44933 | + | 0.836774i | 0.998442 | − | 0.0558046i | \(-0.0177724\pi\) |
0.450893 | + | 0.892578i | \(0.351106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.5635 | + | 58.1337i | 0.0439889 | + | 0.0761910i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −52.4623 | + | 30.2891i | −0.0683993 | + | 0.0394903i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −379.742 | + | 657.733i | −0.493813 | + | 0.855310i | −0.999975 | − | 0.00712921i | \(-0.997731\pi\) |
0.506161 | + | 0.862439i | \(0.331064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1361.52 | − | 292.600i | −1.76591 | − | 0.379507i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 165.240i | 0.213765i | 0.994272 | + | 0.106883i | \(0.0340869\pi\) | ||||
−0.994272 | + | 0.106883i | \(0.965913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −51.0767 | − | 46.1980i | −0.0657358 | − | 0.0594569i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1897.13 | − | 1095.31i | −2.43534 | − | 1.40604i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.4497 | − | 89.1135i | −0.0658767 | − | 0.114102i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 106.227 | − | 949.069i | 0.135666 | − | 1.21209i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 287.752 | − | 498.401i | 0.365632 | − | 0.633293i | −0.623246 | − | 0.782026i | \(-0.714186\pi\) |
0.988877 | + | 0.148733i | \(0.0475197\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 112.888 | − | 124.810i | 0.143078 | − | 0.158187i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 205.019i | 0.259190i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1254.36 | −1.58179 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 526.210 | + | 303.808i | 0.660238 | + | 0.381189i | 0.792368 | − | 0.610044i | \(-0.208848\pi\) |
−0.132129 | + | 0.991232i | \(0.542181\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 628.676 | + | 1088.90i | 0.786828 | + | 1.36283i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −233.683 | − | 324.696i | −0.291739 | − | 0.405364i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −43.3642 | + | 25.0363i | −0.0540027 | + | 0.0311785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.5187 | − | 85.3460i | −0.0341000 | − | 0.105757i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 962.401i | − | 1.18962i | −0.803867 | − | 0.594809i | \(-0.797228\pi\) | ||
0.803867 | − | 0.594809i | \(-0.202772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −140.096 | −0.172745 | −0.0863723 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863723 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −476.329 | + | 153.586i | −0.585891 | + | 0.188913i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −704.319 | − | 1219.92i | −0.862079 | − | 1.49317i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 124.327 | − | 89.4779i | 0.151804 | − | 0.109253i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −280.294 | + | 161.828i | −0.341406 | + | 0.197111i | −0.660894 | − | 0.750480i | \(-0.729823\pi\) |
0.319488 | + | 0.947590i | \(0.396489\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −96.6061 | + | 167.327i | −0.117383 | + | 0.203313i | −0.918730 | − | 0.394887i | \(-0.870784\pi\) |
0.801347 | + | 0.598200i | \(0.204117\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7916i | 0.0190951i | 0.999954 | + | 0.00954754i | \(0.00303912\pi\) | ||||
−0.999954 | + | 0.00954754i | \(0.996961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −265.576 | −0.320357 | −0.160178 | − | 0.987088i | \(-0.551207\pi\) | ||||
−0.160178 | + | 0.987088i | \(0.551207\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 437.888 | + | 396.062i | 0.526941 | + | 0.476609i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 770.943 | + | 445.104i | 0.925502 | + | 0.534339i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −107.681 | − | 246.312i | −0.128651 | − | 0.294279i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −761.943 | + | 439.908i | −0.908156 | + | 0.524324i | −0.879838 | − | 0.475275i | \(-0.842349\pi\) |
−0.0283189 | + | 0.999599i | \(0.509015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 205.025 | − | 355.114i | 0.243787 | − | 0.422252i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 669.687 | − | 740.409i | 0.794409 | − | 0.878303i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 122.943 | 0.145151 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −294.322 | + | 1369.53i | −0.346669 | + | 1.61311i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 225.695 | + | 130.305i | 0.265211 | + | 0.153120i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 102.073 | + | 176.795i | 0.119663 | + | 0.207263i | 0.919634 | − | 0.392776i | \(-0.128485\pi\) |
−0.799971 | + | 0.600039i | \(0.795152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −184.859 | + | 106.729i | −0.215705 | + | 0.124537i | −0.603960 | − | 0.797015i | \(-0.706411\pi\) |
0.388255 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −323.677 | + | 560.625i | −0.376806 | + | 0.652648i | −0.990596 | − | 0.136822i | \(-0.956311\pi\) |
0.613789 | + | 0.789470i | \(0.289644\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 70.7485 | + | 219.418i | 0.0821701 | + | 0.254841i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 699.772i | 0.810859i | 0.914126 | + | 0.405430i | \(0.132878\pi\) | ||||
−0.914126 | + | 0.405430i | \(0.867122\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −174.077 | + | 56.1288i | −0.200781 | + | 0.0647391i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 138.743 | + | 80.1033i | 0.159658 | + | 0.0921787i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −256.247 | − | 443.833i | −0.294199 | − | 0.509567i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 524.605 | + | 236.401i | 0.600922 | + | 0.270791i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −712.480 | + | 1234.05i | −0.812406 | + | 1.40713i | 0.0987694 | + | 0.995110i | \(0.468509\pi\) |
−0.911176 | + | 0.412018i | \(0.864824\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 63.1285 | + | 13.5668i | 0.0718185 | + | 0.0154343i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1598.97i | 1.81495i | 0.420102 | + | 0.907477i | \(0.361994\pi\) | ||||
−0.420102 | + | 0.907477i | \(0.638006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1117.03 | 1.26504 | 0.632522 | − | 0.774542i | \(-0.282020\pi\) | ||||
0.632522 | + | 0.774542i | \(0.282020\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1009.79 | + | 583.003i | 1.13843 | + | 0.657275i | 0.946042 | − | 0.324044i | \(-0.105042\pi\) |
0.192391 | + | 0.981318i | \(0.438376\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −116.451 | − | 201.700i | −0.130992 | − | 0.226884i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −67.6887 | − | 333.152i | −0.0759693 | − | 0.373908i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1973.13 | − | 1139.19i | 2.20955 | − | 1.27569i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −388.821 | + | 429.883i | −0.433468 | + | 0.479245i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 352.157i | − | 0.391721i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −562.555 | −0.624367 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.1480 | + | 144.937i | −0.0344939 | + | 0.160506i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −881.243 | − | 1526.36i | −0.971602 | − | 1.68286i | −0.690720 | − | 0.723122i | \(-0.742706\pi\) |
−0.280882 | − | 0.959742i | \(-0.590627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.2290 | − | 98.1500i | 0.0486568 | − | 0.107976i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1449.90 | − | 837.098i | 1.59154 | − | 0.918878i | 0.598501 | − | 0.801122i | \(-0.295763\pi\) |
0.993043 | − | 0.117755i | \(-0.0375699\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.5693 | + | 87.5885i | −0.0553880 | + | 0.0959349i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 135.289i | 0.147534i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1136.29 | 1.23644 | 0.618221 | − | 0.786004i | \(-0.287854\pi\) | ||||
0.618221 | + | 0.786004i | \(0.287854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1292.95 | + | 416.894i | −1.40386 | + | 0.452654i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 303.887 | + | 175.449i | 0.329238 | + | 0.190086i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 147.655 | + | 1468.31i | 0.159282 | + | 1.58394i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 932.936 | − | 538.631i | 1.00424 | − | 0.579796i | 0.0947376 | − | 0.995502i | \(-0.469799\pi\) |
0.909499 | + | 0.415706i | \(0.136465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 806.548 | − | 1396.98i | 0.866324 | − | 1.50052i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1655.10 | − | 355.693i | −1.77395 | − | 0.381235i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1063.87 | −1.13540 | −0.567702 | − | 0.823234i | \(-0.692167\pi\) | ||||
−0.567702 | + | 0.823234i | \(0.692167\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1026.40 | − | 928.360i | −1.09308 | − | 0.988668i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −994.783 | − | 574.338i | −1.05716 | − | 0.610349i | −0.132511 | − | 0.991182i | \(-0.542304\pi\) |
−0.924644 | + | 0.380833i | \(0.875637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −436.195 | − | 755.513i | −0.462561 | − | 0.801180i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 100.366 | − | 57.9461i | 0.105983 | − | 0.0611891i | −0.446072 | − | 0.894997i | \(-0.647177\pi\) |
0.552054 | + | 0.833808i | \(0.313844\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 85.3766 | − | 147.877i | 0.0899648 | − | 0.155824i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −677.695 | + | 749.263i | −0.712613 | + | 0.787868i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1854.05i | 1.94549i | 0.231881 | + | 0.972744i | \(0.425512\pi\) | ||||
−0.231881 | + | 0.972744i | \(0.574488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 93.5720 | − | 435.407i | 0.0977764 | − | 0.454971i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 186.431 | + | 107.636i | 0.194401 | + | 0.112237i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 430.936 | + | 746.403i | 0.448424 | + | 0.776694i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −538.351 | − | 748.025i | −0.559035 | − | 0.776766i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −456.447 | + | 790.590i | −0.472024 | + | 0.817569i | −0.999488 | − | 0.0320081i | \(-0.989810\pi\) |
0.527464 | + | 0.849578i | \(0.323143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 583.826 | + | 1810.67i | 0.602504 | + | 1.86860i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1732.32i | − | 1.78405i | −0.451982 | − | 0.892027i | \(-0.649283\pi\) | ||
0.451982 | − | 0.892027i | \(-0.350717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −272.451 | −0.280011 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 200.352 | + | 115.673i | 0.205069 | + | 0.118396i | 0.599018 | − | 0.800736i | \(-0.295558\pi\) |
−0.393949 | + | 0.919132i | \(0.628891\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −93.2774 | − | 161.561i | −0.0952783 | − | 0.165027i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −412.348 | + | 296.765i | −0.420335 | + | 0.302513i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −674.808 | + | 389.601i | −0.686478 | + | 0.396338i | −0.802291 | − | 0.596933i | \(-0.796386\pi\) |
0.115813 | + | 0.993271i | \(0.463053\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −234.426 | − | 50.3798i | −0.237513 | − | 0.0510433i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 560.976i | − | 0.567215i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 222.470 | 0.224490 | 0.112245 | − | 0.993681i | \(-0.464196\pi\) | ||||
0.112245 | + | 0.993681i | \(0.464196\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 938.453 | + | 848.815i | 0.945069 | + | 0.854798i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −226.712 | − | 392.676i | −0.227394 | − | 0.393858i | 0.729641 | − | 0.683830i | \(-0.239687\pi\) |
−0.957035 | + | 0.289972i | \(0.906354\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 309.207 | − | 419.607i | 0.309516 | − | 0.420027i |
(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 | 900.3.p.c.401.5 | 12 | ||
3.2 | odd | 2 | 2700.3.p.c.2501.3 | 12 | |||
5.2 | odd | 4 | 900.3.u.c.149.4 | 24 | |||
5.3 | odd | 4 | 900.3.u.c.149.9 | 24 | |||
5.4 | even | 2 | 180.3.o.b.41.2 | ✓ | 12 | ||
9.2 | odd | 6 | inner | 900.3.p.c.101.5 | 12 | ||
9.7 | even | 3 | 2700.3.p.c.1601.3 | 12 | |||
15.2 | even | 4 | 2700.3.u.c.449.7 | 24 | |||
15.8 | even | 4 | 2700.3.u.c.449.6 | 24 | |||
15.14 | odd | 2 | 540.3.o.b.341.5 | 12 | |||
20.19 | odd | 2 | 720.3.bs.b.401.5 | 12 | |||
45.2 | even | 12 | 900.3.u.c.749.9 | 24 | |||
45.4 | even | 6 | 1620.3.g.b.161.9 | 12 | |||
45.7 | odd | 12 | 2700.3.u.c.2249.6 | 24 | |||
45.14 | odd | 6 | 1620.3.g.b.161.3 | 12 | |||
45.29 | odd | 6 | 180.3.o.b.101.2 | yes | 12 | ||
45.34 | even | 6 | 540.3.o.b.521.5 | 12 | |||
45.38 | even | 12 | 900.3.u.c.749.4 | 24 | |||
45.43 | odd | 12 | 2700.3.u.c.2249.7 | 24 | |||
60.59 | even | 2 | 2160.3.bs.b.881.5 | 12 | |||
180.79 | odd | 6 | 2160.3.bs.b.1601.5 | 12 | |||
180.119 | even | 6 | 720.3.bs.b.641.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.o.b.41.2 | ✓ | 12 | 5.4 | even | 2 | ||
180.3.o.b.101.2 | yes | 12 | 45.29 | odd | 6 | ||
540.3.o.b.341.5 | 12 | 15.14 | odd | 2 | |||
540.3.o.b.521.5 | 12 | 45.34 | even | 6 | |||
720.3.bs.b.401.5 | 12 | 20.19 | odd | 2 | |||
720.3.bs.b.641.5 | 12 | 180.119 | even | 6 | |||
900.3.p.c.101.5 | 12 | 9.2 | odd | 6 | inner | ||
900.3.p.c.401.5 | 12 | 1.1 | even | 1 | trivial | ||
900.3.u.c.149.4 | 24 | 5.2 | odd | 4 | |||
900.3.u.c.149.9 | 24 | 5.3 | odd | 4 | |||
900.3.u.c.749.4 | 24 | 45.38 | even | 12 | |||
900.3.u.c.749.9 | 24 | 45.2 | even | 12 | |||
1620.3.g.b.161.3 | 12 | 45.14 | odd | 6 | |||
1620.3.g.b.161.9 | 12 | 45.4 | even | 6 | |||
2160.3.bs.b.881.5 | 12 | 60.59 | even | 2 | |||
2160.3.bs.b.1601.5 | 12 | 180.79 | odd | 6 | |||
2700.3.p.c.1601.3 | 12 | 9.7 | even | 3 | |||
2700.3.p.c.2501.3 | 12 | 3.2 | odd | 2 | |||
2700.3.u.c.449.6 | 24 | 15.8 | even | 4 | |||
2700.3.u.c.449.7 | 24 | 15.2 | even | 4 | |||
2700.3.u.c.2249.6 | 24 | 45.7 | odd | 12 | |||
2700.3.u.c.2249.7 | 24 | 45.43 | odd | 12 |