Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(309,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.309");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 309.8 | ||
Character | \(\chi\) | \(=\) | 572.309 |
Dual form | 572.2.p.a.485.8 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.196667 | + | 0.340638i | 0.113546 | + | 0.196667i | 0.917198 | − | 0.398433i | \(-0.130446\pi\) |
−0.803652 | + | 0.595100i | \(0.797112\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.15244i | 1.85703i | 0.371299 | + | 0.928513i | \(0.378913\pi\) | ||||
−0.371299 | + | 0.928513i | \(0.621087\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.01581 | + | 1.16383i | 0.761906 | + | 0.439886i | 0.829980 | − | 0.557794i | \(-0.188352\pi\) |
−0.0680739 | + | 0.997680i | \(0.521685\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.42264 | − | 2.46409i | 0.474215 | − | 0.821364i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.866025 | + | 0.500000i | −0.261116 | + | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.74448 | + | 2.33834i | −0.761182 | + | 0.648538i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41448 | + | 0.816649i | −0.365216 | + | 0.210858i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0827699 | − | 0.143362i | 0.0200746 | − | 0.0347703i | −0.855814 | − | 0.517284i | \(-0.826943\pi\) |
0.875888 | + | 0.482514i | \(0.160276\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.59019 | + | 0.918097i | 0.364815 | + | 0.210626i | 0.671191 | − | 0.741285i | \(-0.265783\pi\) |
−0.306376 | + | 0.951911i | \(0.599116\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.915549i | 0.199789i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.418176 | − | 0.724302i | −0.0871958 | − | 0.151027i | 0.819129 | − | 0.573609i | \(-0.194457\pi\) |
−0.906325 | + | 0.422582i | \(0.861124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.2427 | −2.44855 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.29915 | 0.442472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.469194 | + | 0.812668i | 0.0871272 | + | 0.150909i | 0.906296 | − | 0.422644i | \(-0.138898\pi\) |
−0.819168 | + | 0.573553i | \(0.805565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.37801i | 0.247497i | 0.992314 | + | 0.123749i | \(0.0394916\pi\) | ||||
−0.992314 | + | 0.123749i | \(0.960508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.340638 | − | 0.196667i | −0.0592974 | − | 0.0342354i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.83273 | + | 8.37054i | −0.816881 | + | 1.41488i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.644128 | + | 0.371887i | −0.105894 | + | 0.0611379i | −0.552012 | − | 0.833836i | \(-0.686140\pi\) |
0.446118 | + | 0.894974i | \(0.352806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.33628 | − | 0.475000i | −0.213975 | − | 0.0760608i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.53339 | + | 4.34940i | −1.17652 | + | 0.679263i | −0.955206 | − | 0.295941i | \(-0.904367\pi\) |
−0.221311 | + | 0.975203i | \(0.571034\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.41962 | − | 7.65501i | 0.673986 | − | 1.16738i | −0.302778 | − | 0.953061i | \(-0.597914\pi\) |
0.976764 | − | 0.214317i | \(-0.0687527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.2320 | + | 5.90744i | 1.52529 | + | 0.880629i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.78488i | 1.42727i | 0.700517 | + | 0.713636i | \(0.252953\pi\) | ||||
−0.700517 | + | 0.713636i | \(0.747047\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.790999 | − | 1.37005i | −0.113000 | − | 0.195722i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0651125 | 0.00911757 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1251 | 1.80288 | 0.901439 | − | 0.432907i | \(-0.142512\pi\) | ||||
0.901439 | + | 0.432907i | \(0.142512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.07622 | − | 3.59612i | −0.279957 | − | 0.484900i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.722239i | 0.0956628i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.81016 | + | 3.93185i | 0.886607 | + | 0.511883i | 0.872831 | − | 0.488022i | \(-0.162281\pi\) |
0.0137761 | + | 0.999905i | \(0.495615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.13275 | + | 1.96197i | −0.145033 | + | 0.251205i | −0.929385 | − | 0.369111i | \(-0.879662\pi\) |
0.784352 | + | 0.620316i | \(0.212996\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.73557 | − | 3.31143i | 0.722614 | − | 0.417201i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.70980 | − | 11.3963i | −1.20435 | − | 1.41354i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7974 | − | 6.23386i | 1.31911 | − | 0.761587i | 0.335523 | − | 0.942032i | \(-0.391087\pi\) |
0.983585 | + | 0.180445i | \(0.0577537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.164483 | − | 0.284893i | 0.0198014 | − | 0.0342971i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.71084 | + | 4.45185i | 0.915108 | + | 0.528338i | 0.882071 | − | 0.471116i | \(-0.156149\pi\) |
0.0330368 | + | 0.999454i | \(0.489482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.7918i | − | 1.73125i | −0.500693 | − | 0.865625i | \(-0.666921\pi\) | ||
0.500693 | − | 0.865625i | \(-0.333079\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.40775 | − | 4.17034i | −0.278023 | − | 0.481549i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.32766 | −0.265261 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.93399 | −0.217591 | −0.108795 | − | 0.994064i | \(-0.534699\pi\) | ||||
−0.108795 | + | 0.994064i | \(0.534699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.81576 | − | 6.60910i | −0.423974 | − | 0.734344i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5351i | 1.37591i | 0.725753 | + | 0.687956i | \(0.241492\pi\) | ||||
−0.725753 | + | 0.687956i | \(0.758508\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.595300 | + | 0.343697i | 0.0645694 | + | 0.0372792i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.184550 | + | 0.319651i | −0.0197859 | + | 0.0342701i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.14413 | + | 1.23791i | −0.227277 | + | 0.131219i | −0.609315 | − | 0.792928i | \(-0.708556\pi\) |
0.382038 | + | 0.924147i | \(0.375222\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.25379 | + | 1.51954i | −0.865232 | + | 0.159291i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.469401 | + | 0.271009i | −0.0486746 | + | 0.0281023i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.81234 | + | 6.60317i | −0.391138 | + | 0.677471i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.09963 | − | 1.78957i | −0.314720 | − | 0.181704i | 0.334317 | − | 0.942461i | \(-0.391495\pi\) |
−0.649037 | + | 0.760757i | \(0.724828\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.84529i | 0.285962i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.52574 | − | 9.57087i | −0.549832 | − | 0.952337i | −0.998286 | − | 0.0585308i | \(-0.981358\pi\) |
0.448454 | − | 0.893806i | \(-0.351975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.64085 | −0.555809 | −0.277905 | − | 0.960609i | \(-0.589640\pi\) | ||||
−0.277905 | + | 0.960609i | \(0.589640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.80176 | −0.371014 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.06950 | − | 10.5127i | −0.586760 | − | 1.01630i | −0.994653 | − | 0.103269i | \(-0.967070\pi\) |
0.407893 | − | 0.913030i | \(-0.366264\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.58233i | − | 0.917821i | −0.888483 | − | 0.458910i | \(-0.848240\pi\) | ||
0.888483 | − | 0.458910i | \(-0.151760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.253358 | − | 0.146276i | −0.0240477 | − | 0.0138839i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.30405 | − | 9.18689i | 0.498963 | − | 0.864230i | −0.501036 | − | 0.865426i | \(-0.667048\pi\) |
0.999999 | + | 0.00119673i | \(0.000380930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00762 | − | 1.73645i | 0.280462 | − | 0.161925i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.85746 | + | 10.0893i | 0.171722 | + | 0.932754i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.333697 | − | 0.192660i | 0.0305900 | − | 0.0176611i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.96314 | − | 1.71077i | −0.267177 | − | 0.154255i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 30.0750i | − | 2.68999i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.29257 | + | 3.97084i | 0.203432 | + | 0.352355i | 0.949632 | − | 0.313367i | \(-0.101457\pi\) |
−0.746200 | + | 0.665722i | \(0.768124\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.47678 | 0.306114 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.1080 | 1.66947 | 0.834736 | − | 0.550650i | \(-0.185620\pi\) | ||||
0.834736 | + | 0.550650i | \(0.185620\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.13702 | + | 3.70142i | 0.185303 | + | 0.320954i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.54709i | 0.821683i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.20502 | + | 3.58247i | 0.530130 | + | 0.306071i | 0.741070 | − | 0.671428i | \(-0.234319\pi\) |
−0.210939 | + | 0.977499i | \(0.567652\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.49453 | + | 6.05270i | −0.296402 | + | 0.513383i | −0.975310 | − | 0.220840i | \(-0.929120\pi\) |
0.678908 | + | 0.734223i | \(0.262453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.33310 | + | 1.92437i | −0.280698 | + | 0.162061i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.20762 | − | 3.39730i | 0.100986 | − | 0.284097i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.37455 | + | 1.94830i | −0.280242 | + | 0.161798i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.311127 | − | 0.538888i | 0.0256613 | − | 0.0444467i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.81034 | − | 1.62255i | −0.230232 | − | 0.132925i | 0.380447 | − | 0.924803i | \(-0.375770\pi\) |
−0.610679 | + | 0.791878i | \(0.709103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.7292i | − | 1.60554i | −0.596290 | − | 0.802769i | \(-0.703359\pi\) | ||
0.596290 | − | 0.802769i | \(-0.296641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.235504 | − | 0.407905i | −0.0190394 | − | 0.0329772i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.72208 | −0.459609 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8959 | 1.50806 | 0.754029 | − | 0.656841i | \(-0.228108\pi\) | ||||
0.754029 | + | 0.656841i | \(0.228108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.58129 | + | 4.47092i | 0.204709 | + | 0.354567i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.94674i | − | 0.153425i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.52129 | + | 0.878315i | 0.119156 | + | 0.0687949i | 0.558394 | − | 0.829576i | \(-0.311418\pi\) |
−0.439237 | + | 0.898371i | \(0.644751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.816649 | − | 1.41448i | 0.0635760 | − | 0.110117i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.0909 | − | 12.1769i | 1.63207 | − | 0.942274i | 0.648611 | − | 0.761120i | \(-0.275350\pi\) |
0.983455 | − | 0.181154i | \(-0.0579833\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.06436 | − | 12.8350i | 0.158797 | − | 0.987311i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.52455 | − | 2.61225i | 0.346001 | − | 0.199764i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.49079 | + | 11.2424i | −0.493485 | + | 0.854742i | −0.999972 | − | 0.00750605i | \(-0.997611\pi\) |
0.506486 | + | 0.862248i | \(0.330944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.6791 | − | 14.2485i | −1.86556 | − | 1.07708i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.09306i | 0.232489i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.12703 | + | 14.0764i | 0.607443 | + | 1.05212i | 0.991660 | + | 0.128879i | \(0.0411379\pi\) |
−0.384218 | + | 0.923243i | \(0.625529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.68869 | 0.125519 | 0.0627597 | − | 0.998029i | \(-0.480010\pi\) | ||||
0.0627597 | + | 0.998029i | \(0.480010\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.891096 | −0.0658717 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.54424 | − | 2.67470i | −0.113535 | − | 0.196648i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.165540i | 0.0121055i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.63466 | + | 2.67582i | 0.337122 | + | 0.194638i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.85529 | − | 6.67756i | 0.278959 | − | 0.483171i | −0.692167 | − | 0.721737i | \(-0.743344\pi\) |
0.971126 | + | 0.238566i | \(0.0766773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1602 | + | 7.02071i | −0.875312 | + | 0.505362i | −0.869110 | − | 0.494619i | \(-0.835308\pi\) |
−0.00620235 | + | 0.999981i | \(0.501974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.97241 | − | 5.54880i | 0.141247 | − | 0.397358i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.56309 | + | 3.78920i | −0.467601 | + | 0.269970i | −0.715235 | − | 0.698884i | \(-0.753680\pi\) |
0.247634 | + | 0.968854i | \(0.420347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0842 | + | 19.1983i | −0.785736 | + | 1.36093i | 0.142823 | + | 0.989748i | \(0.454382\pi\) |
−0.928558 | + | 0.371186i | \(0.878951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.24698 | + | 2.45199i | 0.299559 | + | 0.172950i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.18425i | 0.153304i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0606 | − | 31.2819i | −1.26141 | − | 2.18482i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.37966 | −0.165398 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.83619 | −0.127012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.58671 | + | 11.4085i | 0.453448 | + | 0.785394i | 0.998597 | − | 0.0529442i | \(-0.0168605\pi\) |
−0.545150 | + | 0.838339i | \(0.683527\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.50214i | 0.239962i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.7870 | + | 18.3522i | 2.16785 | + | 1.25161i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.60376 | + | 2.77780i | −0.108871 | + | 0.188570i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.03865 | − | 2.90906i | 0.340480 | − | 0.196576i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.108067 | + | 0.586997i | 0.00726940 | + | 0.0394857i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7194 | − | 11.9624i | 1.38747 | − | 0.801059i | 0.394445 | − | 0.918920i | \(-0.370937\pi\) |
0.993030 | + | 0.117861i | \(0.0376037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.4171 | + | 30.1672i | −1.16114 | + | 2.01115i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3710 | − | 5.98771i | −0.688349 | − | 0.397419i | 0.114644 | − | 0.993407i | \(-0.463427\pi\) |
−0.802993 | + | 0.595988i | \(0.796761\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.0257i | 1.25725i | 0.777707 | + | 0.628627i | \(0.216383\pi\) | ||||
−0.777707 | + | 0.628627i | \(0.783617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.457775 | − | 0.792889i | −0.0301194 | − | 0.0521683i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3767 | 0.941850 | 0.470925 | − | 0.882173i | \(-0.343920\pi\) | ||||
0.470925 | + | 0.882173i | \(0.343920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −40.6311 | −2.65048 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.380352 | − | 0.658789i | −0.0247065 | − | 0.0427930i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.6839i | − | 1.01450i | −0.861798 | − | 0.507252i | \(-0.830661\pi\) | ||
0.861798 | − | 0.507252i | \(-0.169339\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3417 | − | 8.28018i | −0.923830 | − | 0.533373i | −0.0389750 | − | 0.999240i | \(-0.512409\pi\) |
−0.884855 | + | 0.465867i | \(0.845743\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.94960 | − | 8.57296i | 0.317517 | − | 0.549956i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.68905 | − | 3.28457i | 0.363460 | − | 0.209844i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.51107 | + | 1.19870i | −0.414290 | + | 0.0762716i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.26994 | + | 2.46525i | −0.270597 | + | 0.156229i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.82612 | + | 10.0911i | −0.367741 | + | 0.636947i | −0.989212 | − | 0.146491i | \(-0.953202\pi\) |
0.621471 | + | 0.783437i | \(0.286535\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.724302 | + | 0.418176i | 0.0455365 | + | 0.0262905i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.270376i | 0.0169316i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.92113 | + | 6.79159i | 0.244593 | + | 0.423648i | 0.962017 | − | 0.272989i | \(-0.0880122\pi\) |
−0.717424 | + | 0.696637i | \(0.754679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.73126 | −0.107575 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.66999 | 0.165268 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.95584 | − | 15.5120i | −0.552241 | − | 0.956509i | −0.998112 | − | 0.0614125i | \(-0.980439\pi\) |
0.445871 | − | 0.895097i | \(-0.352894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 54.5013i | 3.34799i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.843360 | − | 0.486914i | −0.0516128 | − | 0.0297986i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5579 | + | 18.2868i | −0.643727 | + | 1.11497i | 0.340867 | + | 0.940111i | \(0.389279\pi\) |
−0.984594 | + | 0.174856i | \(0.944054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.6463 | − | 12.4975i | 1.31492 | − | 0.759169i | 0.332013 | − | 0.943275i | \(-0.392272\pi\) |
0.982906 | + | 0.184106i | \(0.0589390\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.14086 | − | 2.51271i | −0.129571 | − | 0.152076i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.6025 | − | 6.12137i | 0.639356 | − | 0.369133i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5789 | + | 20.0552i | −0.695708 | + | 1.20500i | 0.274233 | + | 0.961663i | \(0.411576\pi\) |
−0.969941 | + | 0.243339i | \(0.921757\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.39553 | + | 1.96041i | 0.203285 | + | 0.117367i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.30130i | 0.256594i | 0.991736 | + | 0.128297i | \(0.0409511\pi\) | ||||
−0.991736 | + | 0.128297i | \(0.959049\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.53163 | − | 2.65286i | −0.0910459 | − | 0.157696i | 0.816906 | − | 0.576771i | \(-0.195688\pi\) |
−0.907951 | + | 0.419075i | \(0.862354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.99905 | −0.177648 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.2479 | −1.19519 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.48630 | + | 14.6987i | 0.499194 | + | 0.864629i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.40780i | − | 0.0825268i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.45792 | − | 0.841730i | −0.0851726 | − | 0.0491744i | 0.456809 | − | 0.889565i | \(-0.348992\pi\) |
−0.541981 | + | 0.840390i | \(0.682326\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.3268 | + | 28.2788i | −0.950581 | + | 1.64645i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.99113 | + | 1.14958i | −0.115537 | + | 0.0667052i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.84134 | + | 1.01000i | 0.164319 | + | 0.0584097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.8183 | − | 10.2874i | 1.02703 | − | 0.592955i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.17347 | − | 3.76455i | 0.124862 | − | 0.216268i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.14698 | − | 4.70366i | −0.466494 | − | 0.269331i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.06839i | − | 0.175122i | −0.996159 | − | 0.0875611i | \(-0.972093\pi\) | ||
0.996159 | − | 0.0875611i | \(-0.0279073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.10937 | − | 1.92148i | −0.0631098 | − | 0.109309i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.2084 | 0.692273 | 0.346136 | − | 0.938184i | \(-0.387493\pi\) | ||||
0.346136 | + | 0.938184i | \(0.387493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.42766 | −0.306789 | −0.153395 | − | 0.988165i | \(-0.549021\pi\) | ||||
−0.153395 | + | 0.988165i | \(0.549021\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.7505 | + | 23.8166i | 0.774754 | + | 1.34191i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 28.6945i | − | 1.61164i | −0.592160 | − | 0.805821i | \(-0.701725\pi\) | ||
0.592160 | − | 0.805821i | \(-0.298275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.812668 | − | 0.469194i | −0.0455007 | − | 0.0262698i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.38734 | − | 4.13500i | 0.133248 | − | 0.230793i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.263240 | − | 0.151982i | 0.0146471 | − | 0.00845648i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.6000 | − | 28.6277i | 1.86379 | − | 1.58798i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.26410 | − | 1.88453i | 0.180505 | − | 0.104215i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3879 | + | 19.7245i | −0.627837 | + | 1.08745i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3596 | − | 10.5999i | −1.00913 | − | 0.582624i | −0.0981962 | − | 0.995167i | \(-0.531307\pi\) |
−0.910938 | + | 0.412543i | \(0.864641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.11625i | 0.115970i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.8857 | + | 44.8354i | 1.41429 | + | 2.44962i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.84607 | −0.155035 | −0.0775177 | − | 0.996991i | \(-0.524699\pi\) | ||||
−0.0775177 | + | 0.996991i | \(0.524699\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.17253 | 0.226621 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.689003 | − | 1.19339i | −0.0373116 | − | 0.0646256i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.9760i | − | 1.07860i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.18300 | + | 0.683006i | 0.0636906 | + | 0.0367718i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.10902 | + | 3.65293i | −0.113218 | + | 0.196099i | −0.917066 | − | 0.398735i | \(-0.869449\pi\) |
0.803848 | + | 0.594835i | \(0.202783\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.47314 | + | 1.42787i | −0.132384 | + | 0.0764320i | −0.564729 | − | 0.825276i | \(-0.691019\pi\) |
0.432345 | + | 0.901708i | \(0.357686\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.30998 | + | 5.37620i | −0.336802 | + | 0.286960i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.38074 | + | 2.52922i | −0.233163 | + | 0.134617i | −0.612030 | − | 0.790834i | \(-0.709647\pi\) |
0.378867 | + | 0.925451i | \(0.376314\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.4860 | + | 32.0188i | −0.981137 | + | 1.69938i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.131255 | + | 0.0757799i | 0.00694673 | + | 0.00401070i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8849i | 1.63004i | 0.579431 | + | 0.815021i | \(0.303275\pi\) | ||||
−0.579431 | + | 0.815021i | \(0.696725\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.81420 | − | 13.5346i | −0.411273 | − | 0.712346i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.393335 | 0.0206447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 61.4221 | 3.21498 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.24324 | − | 16.0098i | −0.482493 | − | 0.835703i | 0.517305 | − | 0.855801i | \(-0.326935\pi\) |
−0.999798 | + | 0.0200985i | \(0.993602\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.7506i | 1.28847i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.4578 | + | 15.2754i | 1.37362 | + | 0.793061i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.68112 | − | 15.0361i | 0.449491 | − | 0.778541i | −0.548862 | − | 0.835913i | \(-0.684939\pi\) |
0.998353 | + | 0.0573717i | \(0.0182720\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2447 | − | 5.91478i | 0.529034 | − | 0.305438i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.18799 | − | 1.13322i | −0.164190 | − | 0.0583637i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.69614 | + | 0.979265i | −0.0871247 | + | 0.0503015i | −0.542929 | − | 0.839778i | \(-0.682685\pi\) |
0.455805 | + | 0.890080i | \(0.349352\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.901746 | + | 1.56187i | −0.0461978 | + | 0.0800170i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.2399 | − | 15.1496i | −1.34080 | − | 0.774109i | −0.353871 | − | 0.935294i | \(-0.615135\pi\) |
−0.986924 | + | 0.161185i | \(0.948468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 9.66546i | − | 0.492598i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.5751 | − | 21.7807i | −0.639228 | − | 1.10718i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.7855 | −0.901763 | −0.450882 | − | 0.892584i | \(-0.648890\pi\) | ||||
−0.450882 | + | 0.892584i | \(0.648890\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.138450 | −0.00700170 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.75791 | + | 6.50890i | 0.189562 | + | 0.328330i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 8.03076i | − | 0.404072i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0539 | + | 6.38194i | 0.554777 | + | 0.320301i | 0.751046 | − | 0.660249i | \(-0.229549\pi\) |
−0.196270 | + | 0.980550i | \(0.562883\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.840563 | + | 1.45590i | −0.0420808 | + | 0.0728861i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.62185 | − | 1.51372i | 0.130929 | − | 0.0755917i | −0.433105 | − | 0.901343i | \(-0.642582\pi\) |
0.564034 | + | 0.825752i | \(0.309249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.22224 | − | 3.78191i | −0.160511 | − | 0.188390i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.4439 | − | 15.8447i | 1.36370 | − | 0.787331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.371887 | − | 0.644128i | 0.0184338 | − | 0.0319282i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5147 | − | 6.07065i | −0.519917 | − | 0.300174i | 0.216983 | − | 0.976175i | \(-0.430378\pi\) |
−0.736901 | + | 0.676001i | \(0.763712\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.81822i | 0.139012i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.15201 | + | 15.8517i | 0.450341 | + | 0.780013i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −52.0514 | −2.55510 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.74904 | −0.134621 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.45520 | + | 2.52048i | 0.0710913 | + | 0.123134i | 0.899380 | − | 0.437168i | \(-0.144019\pi\) |
−0.828289 | + | 0.560302i | \(0.810685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.6503i | − | 0.567800i | −0.958854 | − | 0.283900i | \(-0.908372\pi\) | ||
0.958854 | − | 0.283900i | \(-0.0916284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.1108 | + | 13.9204i | 1.17231 | + | 0.676833i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.01333 | + | 1.75514i | −0.0491537 | + | 0.0851368i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.56681 | + | 2.63665i | −0.221003 | + | 0.127596i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.39475 | − | 0.256776i | 0.0673391 | − | 0.0123973i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.6602 | + | 11.9282i | −0.995167 | + | 0.574560i | −0.906815 | − | 0.421530i | \(-0.861493\pi\) |
−0.0883520 | + | 0.996089i | \(0.528160\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.46406 | + | 5.99992i | −0.166472 | + | 0.288338i | −0.937177 | − | 0.348854i | \(-0.886571\pi\) |
0.770705 | + | 0.637192i | \(0.219904\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.32733 | − | 0.766334i | −0.0636406 | − | 0.0367429i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.53571i | − | 0.0734628i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.1741 | − | 34.9425i | −0.962856 | − | 1.66771i | −0.715269 | − | 0.698849i | \(-0.753696\pi\) |
−0.247586 | − | 0.968866i | \(-0.579637\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.50124 | −0.214345 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.1853 | −0.721476 | −0.360738 | − | 0.932667i | \(-0.617475\pi\) | ||||
−0.360738 | + | 0.932667i | \(0.617475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.14036 | − | 8.90336i | −0.243676 | − | 0.422060i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.27641i | − | 0.0603721i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0286 | + | 5.79004i | 0.473281 | + | 0.273249i | 0.717612 | − | 0.696443i | \(-0.245235\pi\) |
−0.244331 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.34940 | − | 7.53339i | 0.204805 | − | 0.354733i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.72050 | − | 3.88008i | 0.315757 | − | 0.182302i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.30979 | − | 34.2733i | −0.295808 | − | 1.60676i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.05179 | + | 4.64870i | −0.376647 | + | 0.217457i | −0.676358 | − | 0.736573i | \(-0.736443\pi\) |
0.299712 | + | 0.954030i | \(0.403110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.190301 | − | 0.329610i | 0.00888247 | − | 0.0153849i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8146 | − | 13.1720i | −1.06258 | − | 0.613481i | −0.136435 | − | 0.990649i | \(-0.543564\pi\) |
−0.926145 | + | 0.377168i | \(0.876898\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2989i | 0.478630i | 0.970942 | + | 0.239315i | \(0.0769228\pi\) | ||||
−0.970942 | + | 0.239315i | \(0.923077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.12535 | − | 1.94916i | −0.0521867 | − | 0.0903900i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.9502 | −0.738085 | −0.369043 | − | 0.929413i | \(-0.620314\pi\) | ||||
−0.369043 | + | 0.929413i | \(0.620314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.0206 | 1.34005 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.71621 | + | 6.43666i | 0.171234 | + | 0.296586i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.83925i | 0.406429i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.4683 | − | 11.2400i | −0.893267 | − | 0.515728i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.6724 | − | 32.3416i | 0.854951 | − | 1.48082i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.9498 | + | 19.0236i | −1.50552 | + | 0.869210i | −0.505536 | + | 0.862805i | \(0.668705\pi\) |
−0.999979 | + | 0.00640464i | \(0.997961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.898199 | − | 2.52683i | 0.0409544 | − | 0.115213i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.663134 | − | 0.382861i | 0.0301737 | − | 0.0174208i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.43110 | − | 12.8710i | 0.337429 | − | 0.584444i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0666 | − | 6.38928i | −0.501474 | − | 0.289526i | 0.227848 | − | 0.973697i | \(-0.426831\pi\) |
−0.729322 | + | 0.684171i | \(0.760164\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.690943i | 0.0312455i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.64322 | − | 14.9705i | −0.390063 | − | 0.675609i | 0.602394 | − | 0.798199i | \(-0.294214\pi\) |
−0.992457 | + | 0.122589i | \(0.960880\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.155341 | 0.00699619 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.8149 | −0.531039 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3624 | + | 17.9482i | 0.464817 | + | 0.805087i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.3670i | 1.80708i | 0.428508 | + | 0.903538i | \(0.359039\pi\) | ||||
−0.428508 | + | 0.903538i | \(0.640961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.29580 | + | 4.78958i | 0.370629 | + | 0.213983i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.63045 | − | 16.6804i | 0.429401 | − | 0.743744i | −0.567419 | − | 0.823429i | \(-0.692058\pi\) |
0.996820 | + | 0.0796851i | \(0.0253915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.7424 | − | 22.9453i | 1.76852 | − | 1.02105i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.77809 | − | 1.82104i | 0.212203 | − | 0.0808750i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.0826 | + | 15.6361i | −1.20041 | + | 0.693059i | −0.960647 | − | 0.277771i | \(-0.910404\pi\) |
−0.239767 | + | 0.970831i | \(0.577071\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.2152 | − | 29.8175i | 0.761554 | − | 1.31905i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.65609 | + | 2.11085i | 0.161420 | + | 0.0931961i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 23.4233i | − | 1.03215i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.89244 | − | 8.47395i | −0.215169 | − | 0.372684i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.10610 | −0.224133 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.6133 | −1.07833 | −0.539165 | − | 0.842200i | \(-0.681260\pi\) | ||||
−0.539165 | + | 0.842200i | \(0.681260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.1978 | − | 34.9836i | −0.883187 | − | 1.52973i | −0.847777 | − | 0.530353i | \(-0.822060\pi\) |
−0.0354102 | − | 0.999373i | \(-0.511274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 11.2088i | − | 0.489194i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.197553 | + | 0.114057i | 0.00860555 | + | 0.00496842i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1503 | − | 19.3128i | 0.484794 | − | 0.839687i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.3769 | − | 11.1872i | 0.840884 | − | 0.485485i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5049 | − | 29.5525i | 0.455016 | − | 1.28006i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.6532 | − | 25.2032i | 1.88729 | − | 1.08963i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.19664 | + | 5.53675i | −0.137945 | + | 0.238928i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.37005 | + | 0.790999i | 0.0590123 | + | 0.0340707i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.8068i | 1.92639i | 0.268797 | + | 0.963197i | \(0.413374\pi\) | ||||
−0.268797 | + | 0.963197i | \(0.586626\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.332110 | + | 0.575232i | 0.0142522 | + | 0.0246856i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.7900 | 1.70442 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.7801 | 1.14503 | 0.572517 | − | 0.819893i | \(-0.305967\pi\) | ||||
0.572517 | + | 0.819893i | \(0.305967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.22299 | + | 5.58238i | 0.137554 | + | 0.238250i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.72306i | 0.0734050i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.89856 | − | 2.25083i | −0.165784 | − | 0.0957152i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.607403 | − | 1.05205i | 0.0257828 | − | 0.0446571i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.9164 | + | 9.76666i | −0.716769 | + | 0.413827i | −0.813562 | − | 0.581478i | \(-0.802475\pi\) |
0.0967934 | + | 0.995304i | \(0.469141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.77042 | + | 31.3436i | 0.244063 | + | 1.32569i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0563891 | + | 0.0325563i | −0.00238075 | + | 0.00137453i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.32028 | − | 14.4111i | 0.350658 | − | 0.607357i | −0.635707 | − | 0.771930i | \(-0.719291\pi\) |
0.986365 | + | 0.164573i | \(0.0526247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.1480 | + | 22.0247i | 1.60490 | + | 0.926588i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 17.7636i | − | 0.746001i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.7339 | + | 27.2518i | 0.659597 | + | 1.14246i | 0.980720 | + | 0.195419i | \(0.0626065\pi\) |
−0.321123 | + | 0.947038i | \(0.604060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.8120 | 1.20574 | 0.602871 | − | 0.797838i | \(-0.294023\pi\) | ||||
0.602871 | + | 0.797838i | \(0.294023\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.03284 | 0.126699 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.11962 | + | 8.86745i | 0.213503 | + | 0.369798i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.99850i | − | 0.166460i | −0.996530 | − | 0.0832299i | \(-0.973476\pi\) | ||
0.996530 | − | 0.0832299i | \(-0.0265236\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.78304 | − | 2.76149i | −0.198776 | − | 0.114764i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.5888 | + | 25.2685i | −0.605245 | + | 1.04831i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3667 | + | 6.56257i | −0.470761 | + | 0.271794i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −41.8951 | + | 7.71297i | −1.73215 | + | 0.318892i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.6537 | − | 12.5018i | 0.893743 | − | 0.516003i | 0.0185782 | − | 0.999827i | \(-0.494086\pi\) |
0.875165 | + | 0.483825i | \(0.160753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.26514 | + | 2.19129i | −0.0521293 | + | 0.0902906i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.58149 | − | 1.49042i | −0.106188 | − | 0.0613079i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10.2878i | − | 0.422468i | −0.977436 | − | 0.211234i | \(-0.932252\pi\) | ||
0.977436 | − | 0.211234i | \(-0.0677481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.800009 | + | 1.38566i | 0.0327972 | + | 0.0568064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.71957 | −0.356868 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.4134 | 1.28352 | 0.641759 | − | 0.766906i | \(-0.278205\pi\) | ||||
0.641759 | + | 0.766906i | \(0.278205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.4959 | − | 26.8398i | −0.632093 | − | 1.09482i | −0.987123 | − | 0.159962i | \(-0.948863\pi\) |
0.355030 | − | 0.934855i | \(-0.384471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 35.4743i | − | 1.44462i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.59612 | + | 2.07622i | 0.146203 | + | 0.0844103i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.4065 | + | 31.8811i | −0.747099 | + | 1.29401i | 0.202109 | + | 0.979363i | \(0.435220\pi\) |
−0.949208 | + | 0.314650i | \(0.898113\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.744038 | + | 0.429570i | −0.0301499 | + | 0.0174071i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.8803 | − | 26.8544i | −0.925640 | − | 1.08641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0921 | − | 7.55872i | 0.528784 | − | 0.305294i | −0.211737 | − | 0.977327i | \(-0.567912\pi\) |
0.740521 | + | 0.672033i | \(0.234579\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.10387 | − | 12.3043i | 0.286456 | − | 0.496156i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.9492 | + | 17.2912i | 1.20571 | + | 0.696117i | 0.961819 | − | 0.273686i | \(-0.0882428\pi\) |
0.243891 | + | 0.969803i | \(0.421576\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 45.0400i | − | 1.81031i | −0.425083 | − | 0.905154i | \(-0.639755\pi\) | ||
0.425083 | − | 0.905154i | \(-0.360245\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.961451 | − | 1.66528i | −0.0385817 | − | 0.0668255i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.76288 | −0.230885 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 63.6710 | 2.54684 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.361119 | − | 0.625477i | −0.0144217 | − | 0.0249791i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.123124i | 0.00490929i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.78431 | − | 3.91692i | −0.270079 | − | 0.155930i | 0.358845 | − | 0.933397i | \(-0.383171\pi\) |
−0.628924 | + | 0.777467i | \(0.716504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.59078 | + | 4.48736i | −0.102974 | + | 0.178357i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.4887 | + | 9.51974i | −0.654333 | + | 0.377780i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.37452 | + | 1.91046i | 0.212946 | + | 0.0756950i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.9395 | − | 12.6668i | 0.867915 | − | 0.501091i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2601 | + | 17.7710i | −0.405250 | + | 0.701914i | −0.994351 | − | 0.106146i | \(-0.966149\pi\) |
0.589100 | + | 0.808060i | \(0.299482\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0680 | + | 10.4315i | 0.712531 | + | 0.411380i | 0.811998 | − | 0.583661i | \(-0.198380\pi\) |
−0.0994663 | + | 0.995041i | \(0.531714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4371i | 0.568461i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.3504 | − | 28.3197i | −0.642801 | − | 1.11336i | −0.984805 | − | 0.173665i | \(-0.944439\pi\) |
0.342004 | − | 0.939698i | \(-0.388894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.86370 | −0.308677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.26163 | −0.0494473 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.6070 | − | 30.4962i | −0.689016 | − | 1.19341i | −0.972157 | − | 0.234332i | \(-0.924710\pi\) |
0.283141 | − | 0.959078i | \(-0.408624\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 79.3447i | 3.10025i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.4484 | − | 21.0435i | −1.42199 | − | 0.820984i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.3910 | + | 24.9259i | −0.560594 | + | 0.970977i | 0.436851 | + | 0.899534i | \(0.356094\pi\) |
−0.997445 | + | 0.0714427i | \(0.977240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.68713 | − | 3.28346i | 0.221204 | − | 0.127712i | −0.385304 | − | 0.922790i | \(-0.625903\pi\) |
0.606507 | + | 0.795078i | \(0.292570\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.178700 | + | 0.152255i | −0.00694014 | + | 0.00591309i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.3699 | + | 8.87384i | −0.596020 | + | 0.344113i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.392412 | − | 0.679677i | 0.0151942 | − | 0.0263172i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.14966 | + | 4.70521i | 0.315084 | + | 0.181914i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.26549i | − | 0.0874584i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.2655 | − | 26.4406i | −0.588442 | − | 1.01921i | −0.994437 | − | 0.105336i | \(-0.966408\pi\) |
0.405995 | − | 0.913875i | \(-0.366925\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −28.1479 | −1.08341 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −51.0976 | −1.96384 | −0.981919 | − | 0.189300i | \(-0.939378\pi\) | ||||
−0.981919 | + | 0.189300i | \(0.939378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.16552 | − | 7.21489i | −0.159858 | − | 0.276882i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.71035i | − | 0.180501i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.18785 | + | 4.14991i | 0.275036 | + | 0.158792i | 0.631174 | − | 0.775641i | \(-0.282573\pi\) |
−0.356138 | + | 0.934433i | \(0.615907\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8760 | + | 25.7660i | −0.568382 | + | 0.984466i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.48087 | + | 3.74173i | −0.247261 | + | 0.142756i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0217 | + | 30.6910i | −1.37232 | + | 1.16923i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.6477 | + | 11.9209i | −0.785474 | + | 0.453494i | −0.838367 | − | 0.545107i | \(-0.816489\pi\) |
0.0528928 | + | 0.998600i | \(0.483156\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.31143 | + | 5.73557i | −0.125791 | + | 0.217876i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.1335 | − | 14.5108i | −0.953366 | − | 0.550426i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.44000i | 0.0545438i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.82743 | + | 4.89725i | 0.106943 | + | 0.185231i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.86402 | 0.259250 | 0.129625 | − | 0.991563i | \(-0.458623\pi\) | ||||
0.129625 | + | 0.991563i | \(0.458623\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.36572 | −0.0515089 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.99081 | − | 13.8405i | −0.300951 | − | 0.521263i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 25.7241i | − | 0.967454i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.6102 | + | 12.4767i | 0.811589 | + | 0.468571i | 0.847508 | − | 0.530783i | \(-0.178102\pi\) |
−0.0359182 | + | 0.999355i | \(0.511436\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.75138 | + | 4.76552i | −0.103185 | + | 0.178721i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.998093 | − | 0.576249i | 0.0373789 | − | 0.0215807i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.1071 | + | 5.01458i | 0.527575 | + | 0.187535i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.34251 | − | 3.08450i | 0.199520 | − | 0.115193i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.3833 | − | 26.6446i | 0.573700 | − | 0.993678i | −0.422481 | − | 0.906372i | \(-0.638841\pi\) |
0.996182 | − | 0.0873061i | \(-0.0278258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.3709 | − | 6.56499i | −0.423474 | − | 0.244493i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 6.51376i | − | 0.242249i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.74422 | − | 9.94929i | −0.213335 | − | 0.369507i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.4796 | 0.944986 | 0.472493 | − | 0.881335i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881335i | \(0.343354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.0009 | −0.703736 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.731623 | − | 1.26721i | −0.0270601 | − | 0.0468694i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 8.13794i | − | 0.300582i | −0.988642 | − | 0.150291i | \(-0.951979\pi\) | ||
0.988642 | − | 0.150291i | \(-0.0480210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.23770 | + | 1.29194i | 0.0825388 | + | 0.0476538i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.23386 | + | 10.7974i | −0.229627 | + | 0.397726i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.4183 | + | 18.1394i | −1.15574 | + | 0.667267i | −0.950280 | − | 0.311398i | \(-0.899203\pi\) |
−0.205461 | + | 0.978665i | \(0.565869\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.68884 | − | 1.98217i | −0.0620410 | − | 0.0728169i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.32307 | + | 1.91857i | −0.121911 | + | 0.0703856i | −0.559716 | − | 0.828685i | \(-0.689090\pi\) |
0.437804 | + | 0.899070i | \(0.355756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.73754 | − | 11.6698i | 0.246844 | − | 0.427547i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.8878 | + | 17.8331i | 1.13012 | + | 0.652477i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 28.2555i | − | 1.03243i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.99922 | − | 8.65891i | −0.182424 | − | 0.315968i | 0.760281 | − | 0.649594i | \(-0.225061\pi\) |
−0.942706 | + | 0.333626i | \(0.891728\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.58323 | −0.167022 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 81.9242 | 2.98153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.97749 | − | 10.3533i | −0.217256 | − | 0.376298i | 0.736712 | − | 0.676206i | \(-0.236377\pi\) |
−0.953968 | + | 0.299908i | \(0.903044\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.328966i | 0.0119407i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.6310 | − | 8.44722i | −0.530374 | − | 0.306212i | 0.210795 | − | 0.977530i | \(-0.432395\pi\) |
−0.741169 | + | 0.671319i | \(0.765728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1522 | − | 19.3162i | 0.403737 | − | 0.699293i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.69380 | − | 0.977916i | 0.0612395 | − | 0.0353566i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.8843 | + | 5.13357i | −1.00685 | + | 0.185362i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.3755 | + | 16.3826i | −1.02325 | + | 0.590772i | −0.915043 | − | 0.403357i | \(-0.867843\pi\) |
−0.108204 | + | 0.994129i | \(0.534510\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.54232 | + | 2.67137i | −0.0555451 | + | 0.0962070i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.9048 | + | 17.2655i | 1.07560 | + | 0.620997i | 0.929706 | − | 0.368303i | \(-0.120061\pi\) |
0.145893 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 16.8706i | − | 0.606009i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.340481 | − | 0.589731i | −0.0122147 | − | 0.0211565i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.9727 | −0.572281 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.90371 | −0.318600 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.07875 | + | 1.86845i | 0.0385514 | + | 0.0667729i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 78.4641i | 2.80051i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0764 | + | 13.3232i | 0.822586 | + | 0.474920i | 0.851307 | − | 0.524667i | \(-0.175810\pi\) |
−0.0287213 | + | 0.999587i | \(0.509144\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.52264 | − | 6.10140i | 0.125409 | − | 0.217215i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.3840 | − | 12.3460i | 0.760326 | − | 0.438974i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.47896 | − | 8.03334i | −0.0525193 | − | 0.285272i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.5652 | + | 10.7186i | −0.658440 | + | 0.380151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.59793 | + | 16.6241i | −0.339976 | + | 0.588856i | −0.984428 | − | 0.175789i | \(-0.943752\pi\) |
0.644452 | + | 0.764645i | \(0.277086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.40278 | + | 0.809893i | 0.0496266 | + | 0.0286520i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.04444i | 0.248903i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.39590 | + | 12.8101i | 0.260996 | + | 0.452058i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.08373 | 0.284914 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.30558 | −0.292370 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.98755 | − | 3.44254i | −0.0698787 | − | 0.121033i | 0.828969 | − | 0.559294i | \(-0.188928\pi\) |
−0.898848 | + | 0.438261i | \(0.855595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0060i | 0.562046i | 0.959701 | + | 0.281023i | \(0.0906738\pi\) | ||||
−0.959701 | + | 0.281023i | \(0.909326\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.51424 | + | 4.91570i | 0.298607 | + | 0.172401i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.64715 | + | 6.31704i | −0.127754 | + | 0.221276i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0561 | − | 8.11529i | 0.491760 | − | 0.283918i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.99792 | + | 22.4999i | −0.279470 | + | 0.786209i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.4599 | + | 15.2766i | −0.923457 | + | 0.533158i | −0.884736 | − | 0.466092i | \(-0.845662\pi\) |
−0.0387209 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.51382 | + | 4.35406i | −0.0876262 | + | 0.151773i | −0.906507 | − | 0.422190i | \(-0.861261\pi\) |
0.818881 | + | 0.573963i | \(0.194595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.17034 | + | 2.40775i | 0.145193 | + | 0.0838270i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.8249i | − | 0.515513i | −0.966210 | − | 0.257757i | \(-0.917017\pi\) | ||
0.966210 | − | 0.257757i | \(-0.0829833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.1458 | + | 33.1615i | 0.664962 | + | 1.15175i | 0.979296 | + | 0.202436i | \(0.0648857\pi\) |
−0.314334 | + | 0.949313i | \(0.601781\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.10876 | −0.315979 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.261884 | −0.00907373 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 50.5637 | + | 87.5788i | 1.74983 | + | 3.03079i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.16825i | 0.109511i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.6753 | + | 21.7518i | 1.30069 | + | 0.750956i | 0.980523 | − | 0.196404i | \(-0.0629262\pi\) |
0.320171 | + | 0.947360i | \(0.396260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0597 | − | 24.3521i | 0.484818 | − | 0.839729i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.46519 | + | 0.845926i | −0.0504637 | + | 0.0291352i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 53.2967 | + | 8.57212i | 1.83346 | + | 0.294890i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.01581 | − | 1.16383i | 0.0692641 | − | 0.0399897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.602442 | − | 1.04346i | 0.0206758 | − | 0.0358115i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.538718 | + | 0.311029i | 0.0184670 | + | 0.0106619i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.229155i | − | 0.00784612i | −0.999992 | − | 0.00392306i | \(-0.998751\pi\) | ||
0.999992 | − | 0.00392306i | \(-0.00124875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.8472 | + | 18.7879i | 0.370967 | + | 0.642533i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.2958 | 1.27400 | 0.636999 | − | 0.770864i | \(-0.280175\pi\) | ||||
0.636999 | + | 0.770864i | \(0.280175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.4892 | −1.21088 | −0.605438 | − | 0.795893i | \(-0.707002\pi\) | ||||
−0.605438 | + | 0.795893i | \(0.707002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.98209 | − | 6.89719i | −0.135709 | − | 0.235055i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.81967i | − | 0.130023i | −0.997885 | − | 0.0650115i | \(-0.979292\pi\) | ||
0.997885 | − | 0.0650115i | \(-0.0207084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.6833 | − | 26.9526i | −1.58728 | − | 0.916416i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.33795 | + | 5.78151i | −0.113363 | + | 0.196350i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.67488 | − | 0.966994i | 0.0568165 | − | 0.0328030i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0563 | + | 42.3566i | −0.510163 | + | 1.43520i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.81935 | + | 5.09185i | −0.298490 | + | 0.172333i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.0022 | − | 60.6256i | 1.18329 | − | 2.04952i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.4636 | + | 25.6710i | 1.50143 | + | 0.866850i | 0.999999 | + | 0.00165085i | \(0.000525482\pi\) |
0.501429 | + | 0.865199i | \(0.332808\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 0.662163i | − | 0.0223342i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.86059 | − | 11.8829i | −0.231139 | − | 0.400345i | 0.727004 | − | 0.686633i | \(-0.240912\pi\) |
−0.958144 | + | 0.286288i | \(0.907579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.0437 | −1.28027 | −0.640136 | − | 0.768261i | \(-0.721122\pi\) | ||||
−0.640136 | + | 0.768261i | \(0.721122\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.8438 | −0.431738 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.78761 | + | 6.56034i | 0.127176 | + | 0.220275i | 0.922581 | − | 0.385803i | \(-0.126076\pi\) |
−0.795406 | + | 0.606077i | \(0.792742\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.6726i | 0.357949i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.60910 | + | 3.81576i | 0.221413 | + | 0.127833i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.98347 | + | 15.5598i | −0.300620 | + | 0.520690i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −58.4515 | + | 33.7470i | −1.95382 | + | 1.12804i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.214755 | + | 1.16650i | 0.00717047 | + | 0.0389483i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.11986 | + | 0.646553i | −0.0373495 | + | 0.0215637i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.08637 | − | 1.88164i | 0.0361921 | − | 0.0626866i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.00854 | + | 4.04638i | 0.233230 | + | 0.134655i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.01219i | 0.233093i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.98922 | − | 10.3736i | −0.198869 | − | 0.344451i | 0.749293 | − | 0.662239i | \(-0.230393\pi\) |
−0.948162 | + | 0.317788i | \(0.897060\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.4447 | −1.04295 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.982872 | −0.0325640 | −0.0162820 | − | 0.999867i | \(-0.505183\pi\) | ||||
−0.0162820 | + | 0.999867i | \(0.505183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.26757 | − | 10.8558i | −0.207426 | − | 0.359273i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 3.70022i | − | 0.122326i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.5181 | + | 22.2384i | 1.27198 | + | 0.734378i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1135 | − | 17.5172i | 0.333615 | − | 0.577838i | −0.649603 | − | 0.760274i | \(-0.725065\pi\) |
0.983218 | + | 0.182436i | \(0.0583982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.04521 | − | 0.603452i | 0.0344408 | − | 0.0198844i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.5722 | + | 5.81250i | −1.03921 | + | 0.191321i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.88589 | − | 4.55292i | 0.259287 | − | 0.149699i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.02491 | + | 13.8996i | −0.263573 | + | 0.456521i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.9575 | − | 17.2960i | −0.982874 | − | 0.567463i | −0.0797377 | − | 0.996816i | \(-0.525408\pi\) |
−0.903137 | + | 0.429353i | \(0.858742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.90486i | − | 0.0952028i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.40099 | + | 4.15863i | 0.0786047 | + | 0.136147i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.687394 | −0.0224802 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.2497 | 1.83760 | 0.918798 | − | 0.394728i | \(-0.129161\pi\) | ||||
0.918798 | + | 0.394728i | \(0.129161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.06744 | − | 1.84887i | −0.0348347 | − | 0.0603354i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 5.03747i | − | 0.164217i | −0.996623 | − | 0.0821083i | \(-0.973835\pi\) | ||
0.996623 | − | 0.0821083i | \(-0.0261654\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.30057 | + | 3.63763i | 0.205175 | + | 0.118458i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.1112 | + | 19.2452i | −0.361447 | + | 0.626045i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.7612 | + | 19.4921i | −1.09709 | + | 0.633407i | −0.935456 | − | 0.353444i | \(-0.885011\pi\) |
−0.161637 | + | 0.986850i | \(0.551677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.5882 | + | 40.5958i | 1.12278 | + | 1.31780i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.77441 | − | 5.64326i | 0.316957 | − | 0.182995i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.68128 | − | 13.3044i | 0.248821 | − | 0.430970i | −0.714378 | − | 0.699760i | \(-0.753290\pi\) |
0.963199 | + | 0.268790i | \(0.0866236\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.7281 | + | 16.0088i | 0.897262 | + | 0.518034i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.369101i | − | 0.0119313i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.33877 | + | 14.4432i | 0.269273 | + | 0.466394i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.1011 | 0.938745 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.5389 | −1.11300 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.1531 | − | 50.4946i | −0.938470 | − | 1.62548i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.8969i | 0.350420i | 0.984531 | + | 0.175210i | \(0.0560604\pi\) | ||||
−0.984531 | + | 0.175210i | \(0.943940\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.103541 | + | 0.0597796i | 0.00332623 | + | 0.00192040i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.0861 | − | 33.0581i | 0.612502 | − | 1.06088i | −0.378315 | − | 0.925677i | \(-0.623496\pi\) |
0.990817 | − | 0.135208i | \(-0.0431702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0886 | + | 8.13407i | −0.451660 | + | 0.260766i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.3597 | + | 5.81530i | 0.523929 | + | 0.186239i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.7803 | + | 9.68811i | −0.536849 | + | 0.309950i | −0.743801 | − | 0.668401i | \(-0.766979\pi\) |
0.206952 | + | 0.978351i | \(0.433646\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.23791 | − | 2.14413i | 0.0395639 | − | 0.0685266i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.6117 | − | 13.6322i | −0.753865 | − | 0.435244i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 42.9882i | − | 1.37111i | −0.728021 | − | 0.685555i | \(-0.759560\pi\) | ||
0.728021 | − | 0.685555i | \(-0.240440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.7344 | − | 27.2528i | −0.501341 | − | 0.868348i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.95854 | −0.285153 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.39273 | −0.235075 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.5387 | + | 42.5022i | 0.779496 | + | 1.35013i | 0.932233 | + | 0.361860i | \(0.117858\pi\) |
−0.152737 | + | 0.988267i | \(0.548809\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.33862i | − | 0.264618i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −79.7199 | − | 46.0263i | −2.52729 | − | 1.45913i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4390 | + | 28.4733i | −0.520630 | + | 0.901757i | 0.479082 | + | 0.877770i | \(0.340969\pi\) |
−0.999712 | + | 0.0239873i | \(0.992364\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.48095 | + | 0.855027i | −0.0468552 | + | 0.0270518i |
(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 | 572.2.p.a.309.8 | ✓ | 24 | |
13.2 | odd | 12 | 7436.2.a.v.1.5 | 12 | |||
13.4 | even | 6 | inner | 572.2.p.a.485.8 | yes | 24 | |
13.11 | odd | 12 | 7436.2.a.u.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.p.a.309.8 | ✓ | 24 | 1.1 | even | 1 | trivial | |
572.2.p.a.485.8 | yes | 24 | 13.4 | even | 6 | inner | |
7436.2.a.u.1.5 | 12 | 13.11 | odd | 12 | |||
7436.2.a.v.1.5 | 12 | 13.2 | odd | 12 |