Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1057 |
Dual form | 1200.3.bg.f.193.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.775255 | − | 0.775255i | −0.110751 | − | 0.110751i | 0.649560 | − | 0.760311i | \(-0.274953\pi\) |
−0.760311 | + | 0.649560i | \(0.774953\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.89898 | −0.263544 | −0.131772 | − | 0.991280i | \(-0.542067\pi\) | ||||
−0.131772 | + | 0.991280i | \(0.542067\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.87628 | − | 5.87628i | 0.452021 | − | 0.452021i | −0.444004 | − | 0.896025i | \(-0.646442\pi\) |
0.896025 | + | 0.444004i | \(0.146442\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.44949 | + | 4.44949i | 0.261735 | + | 0.261735i | 0.825759 | − | 0.564024i | \(-0.190747\pi\) |
−0.564024 | + | 0.825759i | \(0.690747\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.101021i | − | 0.00531687i | −0.999996 | − | 0.00265843i | \(-0.999154\pi\) | ||
0.999996 | − | 0.00265843i | \(-0.000846207\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.89898 | 0.0904276 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −25.3485 | + | 25.3485i | −1.10211 | + | 1.10211i | −0.107951 | + | 0.994156i | \(0.534429\pi\) |
−0.994156 | + | 0.107951i | \(0.965571\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 32.2929i | − | 1.11355i | −0.830664 | − | 0.556773i | \(-0.812039\pi\) | ||
0.830664 | − | 0.556773i | \(-0.187961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69694 | 0.119256 | 0.0596280 | − | 0.998221i | \(-0.481009\pi\) | ||||
0.0596280 | + | 0.998221i | \(0.481009\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.55051 | − | 3.55051i | 0.107591 | − | 0.107591i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 42.6969 | + | 42.6969i | 1.15397 | + | 1.15397i | 0.985749 | + | 0.168222i | \(0.0538026\pi\) |
0.168222 | + | 0.985749i | \(0.446197\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.3939i | 0.369074i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.8990 | −0.314609 | −0.157305 | − | 0.987550i | \(-0.550280\pi\) | ||||
−0.157305 | + | 0.987550i | \(0.550280\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −49.2702 | + | 49.2702i | −1.14582 | + | 1.14582i | −0.158451 | + | 0.987367i | \(0.550650\pi\) |
−0.987367 | + | 0.158451i | \(0.949350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.85357 | − | 2.85357i | −0.0607143 | − | 0.0607143i | 0.676098 | − | 0.736812i | \(-0.263670\pi\) |
−0.736812 | + | 0.676098i | \(0.763670\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 47.7980i | − | 0.975469i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.8990 | −0.213705 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1918 | + | 13.1918i | −0.248903 | + | 0.248903i | −0.820520 | − | 0.571618i | \(-0.806316\pi\) |
0.571618 | + | 0.820520i | \(0.306316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.123724 | + | 0.123724i | 0.00217060 | + | 0.00217060i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 76.3837i | 1.29464i | 0.762219 | + | 0.647319i | \(0.224110\pi\) | ||||
−0.762219 | + | 0.647319i | \(0.775890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −103.788 | −1.70144 | −0.850719 | − | 0.525620i | \(-0.823833\pi\) | ||||
−0.850719 | + | 0.525620i | \(0.823833\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.32577 | + | 2.32577i | −0.0369169 | + | 0.0369169i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47.6288 | − | 47.6288i | −0.710878 | − | 0.710878i | 0.255841 | − | 0.966719i | \(-0.417648\pi\) |
−0.966719 | + | 0.255841i | \(0.917648\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 62.0908i | − | 0.899867i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −29.7071 | −0.418410 | −0.209205 | − | 0.977872i | \(-0.567088\pi\) | ||||
−0.209205 | + | 0.977872i | \(0.567088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.50510 | − | 3.50510i | 0.0480151 | − | 0.0480151i | −0.682692 | − | 0.730707i | \(-0.739191\pi\) |
0.730707 | + | 0.682692i | \(0.239191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.24745 | + | 2.24745i | 0.0291876 | + | 0.0291876i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 87.7980i | − | 1.11137i | −0.831394 | − | 0.555683i | \(-0.812457\pi\) | ||
0.831394 | − | 0.555683i | \(-0.187543\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −81.7321 | + | 81.7321i | −0.984725 | + | 0.984725i | −0.999885 | − | 0.0151605i | \(-0.995174\pi\) |
0.0151605 | + | 0.999885i | \(0.495174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 39.5505 | + | 39.5505i | 0.454604 | + | 0.454604i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 96.5857i | − | 1.08523i | −0.839981 | − | 0.542616i | \(-0.817434\pi\) | ||
0.839981 | − | 0.542616i | \(-0.182566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.11123 | −0.100123 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.52781 | + | 4.52781i | −0.0486861 | + | 0.0486861i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 54.2804 | + | 54.2804i | 0.559591 | + | 0.559591i | 0.929191 | − | 0.369600i | \(-0.120505\pi\) |
−0.369600 | + | 0.929191i | \(0.620505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.69694i | 0.0878479i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.5153 | −0.500152 | −0.250076 | − | 0.968226i | \(-0.580456\pi\) | ||||
−0.250076 | + | 0.968226i | \(0.580456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −26.2020 | + | 26.2020i | −0.254389 | + | 0.254389i | −0.822767 | − | 0.568378i | \(-0.807571\pi\) |
0.568378 | + | 0.822767i | \(0.307571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.48469 | − | 7.48469i | −0.0699504 | − | 0.0699504i | 0.671266 | − | 0.741216i | \(-0.265751\pi\) |
−0.741216 | + | 0.671266i | \(0.765751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 94.5755i | 0.867665i | 0.900993 | + | 0.433833i | \(0.142839\pi\) | ||||
−0.900993 | + | 0.433833i | \(0.857161\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −104.586 | −0.942214 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −89.9796 | + | 89.9796i | −0.796280 | + | 0.796280i | −0.982507 | − | 0.186227i | \(-0.940374\pi\) |
0.186227 | + | 0.982507i | \(0.440374\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.6288 | − | 17.6288i | −0.150674 | − | 0.150674i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.89898i | − | 0.0579746i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −112.596 | −0.930545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.7980 | − | 15.7980i | 0.128439 | − | 0.128439i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −37.3031 | − | 37.3031i | −0.293725 | − | 0.293725i | 0.544825 | − | 0.838550i | \(-0.316596\pi\) |
−0.838550 | + | 0.544825i | \(0.816596\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 120.687i | − | 0.935556i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −192.677 | −1.47081 | −0.735407 | − | 0.677626i | \(-0.763009\pi\) | ||||
−0.735407 | + | 0.677626i | \(0.763009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0783167 | + | 0.0783167i | −0.000588847 | + | 0.000588847i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −165.328 | − | 165.328i | −1.20677 | − | 1.20677i | −0.972066 | − | 0.234708i | \(-0.924587\pi\) |
−0.234708 | − | 0.972066i | \(-0.575413\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 256.747i | − | 1.84710i | −0.383478 | − | 0.923550i | \(-0.625274\pi\) | ||
0.383478 | − | 0.923550i | \(-0.374726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.98979 | 0.0495730 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.0352 | + | 17.0352i | −0.119127 | + | 0.119127i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 58.5403 | + | 58.5403i | 0.398233 | + | 0.398233i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 192.788i | 1.29388i | 0.762542 | + | 0.646939i | \(0.223951\pi\) | ||||
−0.762542 | + | 0.646939i | \(0.776049\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −98.9092 | −0.655028 | −0.327514 | − | 0.944846i | \(-0.606211\pi\) | ||||
−0.327514 | + | 0.944846i | \(0.606211\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.3485 | − | 13.3485i | 0.0872449 | − | 0.0872449i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 103.452 | + | 103.452i | 0.658929 | + | 0.658929i | 0.955127 | − | 0.296198i | \(-0.0957188\pi\) |
−0.296198 | + | 0.955127i | \(0.595719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 32.3133i | − | 0.203228i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 39.3031 | 0.244118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.1339 | − | 19.1339i | 0.117386 | − | 0.117386i | −0.645974 | − | 0.763360i | \(-0.723548\pi\) |
0.763360 | + | 0.645974i | \(0.223548\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 96.6969 | + | 96.6969i | 0.579024 | + | 0.579024i | 0.934634 | − | 0.355611i | \(-0.115727\pi\) |
−0.355611 | + | 0.934634i | \(0.615727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 99.9388i | 0.591354i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.303062 | −0.00177229 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −180.136 | + | 180.136i | −1.04125 | + | 1.04125i | −0.0421380 | + | 0.999112i | \(0.513417\pi\) |
−0.999112 | + | 0.0421380i | \(0.986583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −93.5505 | − | 93.5505i | −0.528534 | − | 0.528534i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 134.000i | 0.748603i | 0.927307 | + | 0.374302i | \(0.122118\pi\) | ||||
−0.927307 | + | 0.374302i | \(0.877882\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −171.586 | −0.947987 | −0.473994 | − | 0.880528i | \(-0.657188\pi\) | ||||
−0.473994 | + | 0.880528i | \(0.657188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 127.114 | − | 127.114i | 0.694609 | − | 0.694609i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.8990 | − | 12.8990i | −0.0689785 | − | 0.0689785i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 5.69694i | − | 0.0301425i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.2724 | −0.137552 | −0.0687760 | − | 0.997632i | \(-0.521909\pi\) | ||||
−0.0687760 | + | 0.997632i | \(0.521909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −74.1237 | + | 74.1237i | −0.384061 | + | 0.384061i | −0.872563 | − | 0.488502i | \(-0.837543\pi\) |
0.488502 | + | 0.872563i | \(0.337543\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −47.7526 | − | 47.7526i | −0.242399 | − | 0.242399i | 0.575443 | − | 0.817842i | \(-0.304830\pi\) |
−0.817842 | + | 0.575443i | \(0.804830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 355.454i | − | 1.78620i | −0.449857 | − | 0.893101i | \(-0.648525\pi\) | ||
0.449857 | − | 0.893101i | \(-0.351475\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 116.666 | 0.580429 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.0352 | + | 25.0352i | −0.123326 | + | 0.123326i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 76.0454 | + | 76.0454i | 0.367369 | + | 0.367369i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.292856i | 0.00140123i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 145.474 | 0.689453 | 0.344726 | − | 0.938703i | \(-0.387972\pi\) | ||||
0.344726 | + | 0.938703i | \(0.387972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.3837 | − | 36.3837i | 0.170815 | − | 0.170815i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.86607 | − | 2.86607i | −0.0132077 | − | 0.0132077i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.58571i | 0.0392042i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 52.2929 | 0.236619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 230.351 | − | 230.351i | 1.03296 | − | 1.03296i | 0.0335252 | − | 0.999438i | \(-0.489327\pi\) |
0.999438 | − | 0.0335252i | \(-0.0106734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −40.4745 | − | 40.4745i | −0.178302 | − | 0.178302i | 0.612313 | − | 0.790615i | \(-0.290239\pi\) |
−0.790615 | + | 0.612313i | \(0.790239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 210.192i | 0.917868i | 0.888470 | + | 0.458934i | \(0.151769\pi\) | ||||
−0.888470 | + | 0.458934i | \(0.848231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.50510 | −0.0238316 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −296.384 | + | 296.384i | −1.27203 | + | 1.27203i | −0.327013 | + | 0.945020i | \(0.606042\pi\) |
−0.945020 | + | 0.327013i | \(0.893958\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 107.530 | + | 107.530i | 0.453714 | + | 0.453714i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 89.3031i | 0.373653i | 0.982393 | + | 0.186826i | \(0.0598202\pi\) | ||||
−0.982393 | + | 0.186826i | \(0.940180\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 120.616 | 0.500483 | 0.250241 | − | 0.968183i | \(-0.419490\pi\) | ||||
0.250241 | + | 0.968183i | \(0.419490\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.593624 | − | 0.593624i | −0.00240334 | − | 0.00240334i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 200.202i | − | 0.804024i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 197.576 | 0.787153 | 0.393577 | − | 0.919292i | \(-0.371238\pi\) | ||||
0.393577 | + | 0.919292i | \(0.371238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 73.4847 | − | 73.4847i | 0.290453 | − | 0.290453i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −223.868 | − | 223.868i | −0.871083 | − | 0.871083i | 0.121507 | − | 0.992591i | \(-0.461227\pi\) |
−0.992591 | + | 0.121507i | \(0.961227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 66.2020i | − | 0.255606i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −96.8786 | −0.371182 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −90.7673 | + | 90.7673i | −0.345123 | + | 0.345123i | −0.858289 | − | 0.513166i | \(-0.828472\pi\) |
0.513166 | + | 0.858289i | \(0.328472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 118.293 | + | 118.293i | 0.443044 | + | 0.443044i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 361.909i | 1.34539i | 0.739921 | + | 0.672694i | \(0.234863\pi\) | ||||
−0.739921 | + | 0.672694i | \(0.765137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 216.788 | 0.799955 | 0.399977 | − | 0.916525i | \(-0.369018\pi\) | ||||
0.399977 | + | 0.916525i | \(0.369018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.1589 | − | 11.1589i | 0.0408752 | − | 0.0408752i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 205.406 | + | 205.406i | 0.741539 | + | 0.741539i | 0.972874 | − | 0.231335i | \(-0.0743093\pi\) |
−0.231335 | + | 0.972874i | \(0.574309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 11.0908i | − | 0.0397520i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 334.899 | 1.19181 | 0.595906 | − | 0.803054i | \(-0.296793\pi\) | ||||
0.595906 | + | 0.803054i | \(0.296793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 74.3508 | − | 74.3508i | 0.262724 | − | 0.262724i | −0.563436 | − | 0.826160i | \(-0.690521\pi\) |
0.826160 | + | 0.563436i | \(0.190521\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | + | 10.0000i | 0.0348432 | + | 0.0348432i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 249.404i | − | 0.862990i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −132.959 | −0.456904 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 116.874 | − | 116.874i | 0.398887 | − | 0.398887i | −0.478953 | − | 0.877840i | \(-0.658984\pi\) |
0.877840 | + | 0.478953i | \(0.158984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.6515 | − | 10.6515i | −0.0358637 | − | 0.0358637i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 297.909i | 0.996352i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 76.3939 | 0.253800 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 61.8684 | − | 61.8684i | 0.204186 | − | 0.204186i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 135.250 | + | 135.250i | 0.440553 | + | 0.440553i | 0.892198 | − | 0.451645i | \(-0.149163\pi\) |
−0.451645 | + | 0.892198i | \(0.649163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 64.1816i | − | 0.207708i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 239.212 | 0.769171 | 0.384586 | − | 0.923089i | \(-0.374344\pi\) | ||||
0.384586 | + | 0.923089i | \(0.374344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 271.386 | − | 271.386i | 0.867048 | − | 0.867048i | −0.125097 | − | 0.992145i | \(-0.539924\pi\) |
0.992145 | + | 0.125097i | \(0.0399241\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 175.060 | + | 175.060i | 0.552240 | + | 0.552240i | 0.927087 | − | 0.374847i | \(-0.122305\pi\) |
−0.374847 | + | 0.927087i | \(0.622305\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 93.6163i | 0.293468i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.3337 | 0.0571143 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.449490 | − | 0.449490i | 0.00139161 | − | 0.00139161i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −115.831 | − | 115.831i | −0.354223 | − | 0.354223i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.42449i | 0.0134483i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 134.445 | 0.406178 | 0.203089 | − | 0.979160i | \(-0.434902\pi\) | ||||
0.203089 | + | 0.979160i | \(0.434902\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 128.091 | − | 128.091i | 0.384657 | − | 0.384657i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −137.654 | − | 137.654i | −0.408468 | − | 0.408468i | 0.472736 | − | 0.881204i | \(-0.343266\pi\) |
−0.881204 | + | 0.472736i | \(0.843266\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 220.404i | − | 0.650160i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.7173 | −0.0314292 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −75.0431 | + | 75.0431i | −0.218785 | + | 0.218785i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −365.823 | − | 365.823i | −1.05424 | − | 1.05424i | −0.998442 | − | 0.0558030i | \(-0.982228\pi\) |
−0.0558030 | − | 0.998442i | \(-0.517772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 140.020i | 0.401205i | 0.979673 | + | 0.200602i | \(0.0642899\pi\) | ||||
−0.979673 | + | 0.200602i | \(0.935710\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 43.1816 | 0.123025 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 208.672 | − | 208.672i | 0.591139 | − | 0.591139i | −0.346800 | − | 0.937939i | \(-0.612732\pi\) |
0.937939 | + | 0.346800i | \(0.112732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.44949 | + | 8.44949i | 0.0236680 | + | 0.0236680i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 583.019i | 1.62401i | 0.583651 | + | 0.812005i | \(0.301624\pi\) | ||||
−0.583651 | + | 0.812005i | \(0.698376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 360.990 | 0.999972 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 137.901 | − | 137.901i | 0.379893 | − | 0.379893i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −123.341 | − | 123.341i | −0.336078 | − | 0.336078i | 0.518811 | − | 0.854889i | \(-0.326375\pi\) |
−0.854889 | + | 0.518811i | \(0.826375\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 38.6969i | 0.104870i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.4541 | 0.0551323 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 345.052 | − | 345.052i | 0.925073 | − | 0.925073i | −0.0723091 | − | 0.997382i | \(-0.523037\pi\) |
0.997382 | + | 0.0723091i | \(0.0230368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −189.762 | − | 189.762i | −0.503347 | − | 0.503347i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 421.393i | 1.11185i | 0.831231 | + | 0.555927i | \(0.187637\pi\) | ||||
−0.831231 | + | 0.555927i | \(0.812363\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 91.3735 | 0.239825 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −344.586 | + | 344.586i | −0.899702 | + | 0.899702i | −0.995409 | − | 0.0957079i | \(-0.969489\pi\) |
0.0957079 | + | 0.995409i | \(0.469489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 147.810 | + | 147.810i | 0.381939 | + | 0.381939i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 486.111i | 1.24964i | 0.780768 | + | 0.624822i | \(0.214828\pi\) | ||||
−0.780768 | + | 0.624822i | \(0.785172\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −225.576 | −0.576919 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 235.980 | − | 235.980i | 0.600457 | − | 0.600457i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 312.062 | + | 312.062i | 0.786052 | + | 0.786052i | 0.980844 | − | 0.194793i | \(-0.0624034\pi\) |
−0.194793 | + | 0.980844i | \(0.562403\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.191836i | − | 0.000480792i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 590.252 | 1.47195 | 0.735975 | − | 0.677009i | \(-0.236724\pi\) | ||||
0.735975 | + | 0.677009i | \(0.236724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.7242 | − | 21.7242i | 0.0539063 | − | 0.0539063i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −123.778 | − | 123.778i | −0.304122 | − | 0.304122i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 736.696i | − | 1.80121i | −0.434636 | − | 0.900606i | \(-0.643123\pi\) | ||
0.434636 | − | 0.900606i | \(-0.356877\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 404.969 | 0.985327 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 59.2168 | − | 59.2168i | 0.143382 | − | 0.143382i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 314.449 | + | 314.449i | 0.754076 | + | 0.754076i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 38.0296i | − | 0.0907627i | −0.998970 | − | 0.0453814i | \(-0.985550\pi\) | ||
0.998970 | − | 0.0453814i | \(-0.0144503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −331.394 | −0.787159 | −0.393579 | − | 0.919291i | \(-0.628763\pi\) | ||||
−0.393579 | + | 0.919291i | \(0.628763\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.56072 | + | 8.56072i | −0.0202381 | + | 0.0202381i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 80.4620 | + | 80.4620i | 0.188436 | + | 0.188436i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 41.7276i | − | 0.0972670i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 843.040 | 1.95601 | 0.978004 | − | 0.208584i | \(-0.0668856\pi\) | ||||
0.978004 | + | 0.208584i | \(0.0668856\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 149.381 | − | 149.381i | 0.344992 | − | 0.344992i | −0.513248 | − | 0.858240i | \(-0.671558\pi\) |
0.858240 | + | 0.513248i | \(0.171558\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.56072 | + | 2.56072i | 0.00585976 | + | 0.00585976i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 545.999i | 1.24373i | 0.783123 | + | 0.621867i | \(0.213625\pi\) | ||||
−0.783123 | + | 0.621867i | \(0.786375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −143.394 | −0.325156 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 45.0398 | − | 45.0398i | 0.101670 | − | 0.101670i | −0.654442 | − | 0.756112i | \(-0.727096\pi\) |
0.756112 | + | 0.654442i | \(0.227096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −236.116 | − | 236.116i | −0.528223 | − | 0.528223i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 320.767i | − | 0.714404i | −0.934027 | − | 0.357202i | \(-0.883731\pi\) | ||
0.934027 | − | 0.357202i | \(-0.116269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.3939 | 0.0829133 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 121.139 | − | 121.139i | 0.267414 | − | 0.267414i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −599.918 | − | 599.918i | −1.31273 | − | 1.31273i | −0.919394 | − | 0.393337i | \(-0.871320\pi\) |
−0.393337 | − | 0.919394i | \(-0.628680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.6969i | 0.0712352i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −376.595 | −0.816909 | −0.408454 | − | 0.912779i | \(-0.633932\pi\) | ||||
−0.408454 | + | 0.912779i | \(0.633932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 214.838 | − | 214.838i | 0.464012 | − | 0.464012i | −0.435956 | − | 0.899968i | \(-0.643590\pi\) |
0.899968 | + | 0.435956i | \(0.143590\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −463.419 | − | 463.419i | −0.992332 | − | 0.992332i | 0.00763918 | − | 0.999971i | \(-0.497568\pi\) |
−0.999971 | + | 0.00763918i | \(0.997568\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 73.8490i | 0.157461i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −253.404 | −0.538013 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 142.833 | − | 142.833i | 0.301973 | − | 0.301973i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 39.5755 | + | 39.5755i | 0.0829675 | + | 0.0829675i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 415.394i | 0.867211i | 0.901103 | + | 0.433605i | \(0.142759\pi\) | ||||
−0.901103 | + | 0.433605i | \(0.857241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 501.798 | 1.04324 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −48.1362 | + | 48.1362i | −0.0996609 | + | 0.0996609i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.1033 | − | 38.1033i | −0.0782409 | − | 0.0782409i | 0.666903 | − | 0.745144i | \(-0.267619\pi\) |
−0.745144 | + | 0.666903i | \(0.767619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.8684i | 0.0958453i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −383.514 | −0.781088 | −0.390544 | − | 0.920584i | \(-0.627713\pi\) | ||||
−0.390544 | + | 0.920584i | \(0.627713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 143.687 | − | 143.687i | 0.291454 | − | 0.291454i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.0306 | + | 23.0306i | 0.0463393 | + | 0.0463393i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 81.4133i | 0.163153i | 0.996667 | + | 0.0815764i | \(0.0259955\pi\) | ||||
−0.996667 | + | 0.0815764i | \(0.974005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −236.858 | −0.472771 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −171.626 | + | 171.626i | −0.341204 | + | 0.341204i | −0.856820 | − | 0.515616i | \(-0.827563\pi\) |
0.515616 | + | 0.856820i | \(0.327563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −122.399 | − | 122.399i | −0.241419 | − | 0.241419i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 452.202i | 0.888413i | 0.895925 | + | 0.444206i | \(0.146514\pi\) | ||||
−0.895925 | + | 0.444206i | \(0.853486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.43470 | −0.0106354 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.371173 | − | 0.371173i | 0.000723534 | − | 0.000723534i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.27245 | + | 8.27245i | 0.0160009 | + | 0.0160009i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 441.242i | − | 0.850177i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −773.928 | −1.48547 | −0.742733 | − | 0.669588i | \(-0.766471\pi\) | ||||
−0.742733 | + | 0.669588i | \(0.766471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 474.507 | − | 474.507i | 0.907280 | − | 0.907280i | −0.0887721 | − | 0.996052i | \(-0.528294\pi\) |
0.996052 | + | 0.0887721i | \(0.0282943\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.4495 | + | 16.4495i | 0.0312135 | + | 0.0312135i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 756.090i | − | 1.42928i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 229.151 | 0.431546 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −75.7980 | + | 75.7980i | −0.142210 | + | 0.142210i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −164.116 | − | 164.116i | −0.305616 | − | 0.305616i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 138.565i | 0.257078i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 511.867 | 0.946150 | 0.473075 | − | 0.881022i | \(-0.343144\pi\) | ||||
0.473075 | + | 0.881022i | \(0.343144\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 210.149 | − | 210.149i | 0.387014 | − | 0.387014i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 373.980 | + | 373.980i | 0.683692 | + | 0.683692i | 0.960830 | − | 0.277138i | \(-0.0893859\pi\) |
−0.277138 | + | 0.960830i | \(0.589386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 311.363i | 0.567146i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.26224 | −0.00592058 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −68.0658 | + | 68.0658i | −0.123085 | + | 0.123085i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 421.015 | + | 421.015i | 0.755861 | + | 0.755861i | 0.975566 | − | 0.219705i | \(-0.0705095\pi\) |
−0.219705 | + | 0.975566i | \(0.570509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 579.050i | 1.03587i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.5959 | 0.0563207 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.77296 | + | 7.77296i | −0.0138063 | + | 0.0138063i | −0.713976 | − | 0.700170i | \(-0.753108\pi\) |
0.700170 | + | 0.713976i | \(0.253108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.97730 | + | 6.97730i | 0.0123056 | + | 0.0123056i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 473.787i | 0.832666i | 0.909212 | + | 0.416333i | \(0.136685\pi\) | ||||
−0.909212 | + | 0.416333i | \(0.863315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 120.344 | 0.210760 | 0.105380 | − | 0.994432i | \(-0.466394\pi\) | ||||
0.105380 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.1770 | − | 32.1770i | 0.0561554 | − | 0.0561554i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −266.033 | − | 266.033i | −0.461062 | − | 0.461062i | 0.437941 | − | 0.899004i | \(-0.355708\pi\) |
−0.899004 | + | 0.437941i | \(0.855708\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 181.565i | − | 0.313584i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 126.727 | 0.218118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.2429 | − | 38.2429i | 0.0655967 | − | 0.0655967i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −114.141 | − | 114.141i | −0.194448 | − | 0.194448i | 0.603167 | − | 0.797615i | \(-0.293905\pi\) |
−0.797615 | + | 0.603167i | \(0.793905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.373467i | − | 0.000634069i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 116.969 | 0.197918 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −566.636 | + | 566.636i | −0.955541 | + | 0.955541i | −0.999053 | − | 0.0435121i | \(-0.986145\pi\) |
0.0435121 | + | 0.999053i | \(0.486145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 435.341 | + | 435.341i | 0.729214 | + | 0.729214i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1002.44i | − | 1.67353i | −0.547564 | − | 0.836764i | \(-0.684445\pi\) | ||
0.547564 | − | 0.836764i | \(-0.315555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.8796 | −0.0347414 | −0.0173707 | − | 0.999849i | \(-0.505530\pi\) | ||||
−0.0173707 | + | 0.999849i | \(0.505530\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −142.886 | + | 142.886i | −0.236959 | + | 0.236959i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 305.748 | + | 305.748i | 0.503703 | + | 0.503703i | 0.912587 | − | 0.408883i | \(-0.134082\pi\) |
−0.408883 | + | 0.912587i | \(0.634082\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 61.3235i | − | 0.100695i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.5367 | −0.0548883 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −153.303 | + | 153.303i | −0.250087 | + | 0.250087i | −0.821006 | − | 0.570919i | \(-0.806587\pi\) |
0.570919 | + | 0.821006i | \(0.306587\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −276.879 | − | 276.879i | −0.448750 | − | 0.448750i | 0.446189 | − | 0.894939i | \(-0.352781\pi\) |
−0.894939 | + | 0.446189i | \(0.852781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 389.352i | − | 0.629002i | −0.949257 | − | 0.314501i | \(-0.898163\pi\) | ||
0.949257 | − | 0.314501i | \(-0.101837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −186.272 | −0.299956 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −74.8786 | + | 74.8786i | −0.120190 | + | 0.120190i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.358674 | − | 0.358674i | −0.000572048 | − | 0.000572048i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 379.959i | 0.604069i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −576.201 | −0.913155 | −0.456578 | − | 0.889684i | \(-0.650925\pi\) | ||||
−0.456578 | + | 0.889684i | \(0.650925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −178.169 | + | 178.169i | −0.281468 | + | 0.281468i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −280.874 | − | 280.874i | −0.440932 | − | 0.440932i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 89.1214i | 0.139470i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 780.827 | 1.21814 | 0.609069 | − | 0.793117i | \(-0.291543\pi\) | ||||
0.609069 | + | 0.793117i | \(0.291543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −403.787 | + | 403.787i | −0.627973 | + | 0.627973i | −0.947558 | − | 0.319585i | \(-0.896457\pi\) |
0.319585 | + | 0.947558i | \(0.396457\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 381.898 | + | 381.898i | 0.590260 | + | 0.590260i | 0.937702 | − | 0.347442i | \(-0.112950\pi\) |
−0.347442 | + | 0.937702i | \(0.612950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 221.435i | − | 0.341194i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.02041 | 0.0107840 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 149.864 | − | 149.864i | 0.229500 | − | 0.229500i | −0.582984 | − | 0.812484i | \(-0.698115\pi\) |
0.812484 | + | 0.582984i | \(0.198115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.5153 | − | 10.5153i | −0.0160050 | − | 0.0160050i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 552.495i | − | 0.838384i | −0.907898 | − | 0.419192i | \(-0.862313\pi\) | ||
0.907898 | − | 0.419192i | \(-0.137687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −274.767 | −0.415684 | −0.207842 | − | 0.978162i | \(-0.566644\pi\) | ||||
−0.207842 | + | 0.978162i | \(0.566644\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −64.0454 | + | 64.0454i | −0.0965994 | + | 0.0965994i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 818.574 | + | 818.574i | 1.22725 | + | 1.22725i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 564.242i | 0.843411i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 300.879 | 0.448403 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −624.272 | + | 624.272i | −0.927597 | + | 0.927597i | −0.997550 | − | 0.0699537i | \(-0.977715\pi\) |
0.0699537 | + | 0.997550i | \(0.477715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.04541 | − | 4.04541i | −0.00597549 | − | 0.00597549i | 0.704113 | − | 0.710088i | \(-0.251345\pi\) |
−0.710088 | + | 0.704113i | \(0.751345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 84.1623i | − | 0.123950i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 99.1418 | 0.145583 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 913.757 | − | 913.757i | 1.33786 | − | 1.33786i | 0.439726 | − | 0.898132i | \(-0.355075\pi\) |
0.898132 | − | 0.439726i | \(-0.144925\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −257.431 | − | 257.431i | −0.374718 | − | 0.374718i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 155.038i | 0.225018i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1286.24 | −1.86142 | −0.930710 | − | 0.365759i | \(-0.880810\pi\) | ||||
−0.930710 | + | 0.365759i | \(0.880810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.74235 | − | 6.74235i | 0.00972922 | − | 0.00972922i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −57.3939 | − | 57.3939i | −0.0823442 | − | 0.0823442i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 725.989i | − | 1.03861i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −527.181 | −0.752041 | −0.376020 | − | 0.926611i | \(-0.622708\pi\) | ||||
−0.376020 | + | 0.926611i | \(0.622708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.31327 | − | 4.31327i | 0.00613551 | − | 0.00613551i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.1623 | + | 39.1623i | 0.0553922 | + | 0.0553922i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 204.514i | − | 0.288455i | −0.989545 | − | 0.144227i | \(-0.953930\pi\) | ||
0.989545 | − | 0.144227i | \(-0.0460696\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −263.394 | −0.370456 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −93.7117 | + | 93.7117i | −0.131433 | + | 0.131433i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −109.373 | − | 109.373i | −0.152543 | − | 0.152543i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 511.989i | − | 0.712085i | −0.934470 | − | 0.356042i | \(-0.884126\pi\) | ||
0.934470 | − | 0.356042i | \(-0.115874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.6265 | 0.0563475 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −147.724 | + | 147.724i | −0.204321 | + | 0.204321i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −211.992 | − | 211.992i | −0.291598 | − | 0.291598i | 0.546113 | − | 0.837712i | \(-0.316107\pi\) |
−0.837712 | + | 0.546113i | \(0.816107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −438.454 | −0.599800 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −702.979 | + | 702.979i | −0.959043 | + | 0.959043i | −0.999194 | − | 0.0401506i | \(-0.987216\pi\) |
0.0401506 | + | 0.999194i | \(0.487216\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 138.075 | + | 138.075i | 0.187347 | + | 0.187347i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 838.586i | − | 1.13476i | −0.823457 | − | 0.567379i | \(-0.807958\pi\) | ||
0.823457 | − | 0.567379i | \(-0.192042\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.45408 | 0.00196232 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −962.534 | + | 962.534i | −1.29547 | + | 1.29547i | −0.364115 | + | 0.931354i | \(0.618629\pi\) |
−0.931354 | + | 0.364115i | \(0.881371\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 245.196 | + | 245.196i | 0.328242 | + | 0.328242i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6051i | 0.0154941i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −594.241 | −0.791266 | −0.395633 | − | 0.918409i | \(-0.629475\pi\) | ||||
−0.395633 | + | 0.918409i | \(0.629475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −241.980 | + | 241.980i | −0.321354 | + | 0.321354i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −399.402 | − | 399.402i | −0.527611 | − | 0.527611i | 0.392248 | − | 0.919859i | \(-0.371697\pi\) |
−0.919859 | + | 0.392248i | \(0.871697\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 180.000i | 0.237154i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 127.292 | 0.167269 | 0.0836346 | − | 0.996496i | \(-0.473347\pi\) | ||||
0.0836346 | + | 0.996496i | \(0.473347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 73.3201 | − | 73.3201i | 0.0960946 | − | 0.0960946i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 448.852 | + | 448.852i | 0.585204 | + | 0.585204i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 699.847i | 0.910074i | 0.890473 | + | 0.455037i | \(0.150374\pi\) | ||||
−0.890473 | + | 0.455037i | \(0.849626\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 548.363 | 0.711236 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −627.485 | + | 627.485i | −0.811753 | + | 0.811753i | −0.984897 | − | 0.173144i | \(-0.944607\pi\) |
0.173144 | + | 0.984897i | \(0.444607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 81.0806 | + | 81.0806i | 0.104351 | + | 0.104351i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.30306i | 0.00167274i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 86.1204 | 0.110269 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 118.652 | − | 118.652i | 0.151535 | − | 0.151535i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 363.992 | + | 363.992i | 0.462506 | + | 0.462506i | 0.899476 | − | 0.436970i | \(-0.143948\pi\) |
−0.436970 | + | 0.899476i | \(0.643948\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 222.334i | − | 0.281792i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 139.514 | 0.176377 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −609.885 | + | 609.885i | −0.769086 | + | 0.769086i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 506.080 | + | 506.080i | 0.634981 | + | 0.634981i | 0.949313 | − | 0.314332i | \(-0.101781\pi\) |
−0.314332 | + | 0.949313i | \(0.601781\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 25.3939i | − | 0.0317821i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −289.757 | −0.361744 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.1612 | + | 10.1612i | −0.0126541 | + | 0.0126541i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −443.246 | − | 443.246i | −0.549252 | − | 0.549252i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1165.28i | − | 1.44040i | −0.693768 | − | 0.720198i | \(-0.744051\pi\) | ||
0.693768 | − | 0.720198i | \(-0.255949\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1507.67 | 1.85903 | 0.929516 | − | 0.368783i | \(-0.120225\pi\) | ||||
0.929516 | + | 0.368783i | \(0.120225\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −265.510 | + | 265.510i | −0.326580 | + | 0.326580i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.97730 | + | 4.97730i | 0.00609216 | + | 0.00609216i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.3337i | 0.0333745i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −965.959 | −1.17656 | −0.588282 | − | 0.808656i | \(-0.700196\pi\) | ||||
−0.588282 | + | 0.808656i | \(0.700196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 88.9727 | − | 88.9727i | 0.108108 | − | 0.108108i | −0.650984 | − | 0.759092i | \(-0.725643\pi\) |
0.759092 | + | 0.650984i | \(0.225643\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −275.271 | − | 275.271i | −0.332855 | − | 0.332855i | 0.520814 | − | 0.853670i | \(-0.325628\pi\) |
−0.853670 | + | 0.520814i | \(0.825628\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 351.980i | − | 0.424583i | −0.977206 | − | 0.212292i | \(-0.931907\pi\) | ||
0.977206 | − | 0.212292i | \(-0.0680927\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −503.141 | −0.605464 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 212.677 | − | 212.677i | 0.255314 | − | 0.255314i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.5834 | + | 13.5834i | 0.0162287 | + | 0.0162287i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1408.43i | − | 1.67871i | −0.543587 | − | 0.839353i | \(-0.682934\pi\) | ||
0.543587 | − | 0.839353i | \(-0.317066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −201.829 | −0.239986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −410.166 | + | 410.166i | −0.486555 | + | 0.486555i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 87.2906 | + | 87.2906i | 0.103059 | + | 0.103059i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 182.121i | 0.214513i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2164.60 | −2.54360 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.5528 | − | 50.5528i | 0.0592647 | − | 0.0592647i | −0.676853 | − | 0.736118i | \(-0.736657\pi\) |
0.736118 | + | 0.676853i | \(0.236657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −210.434 | − | 210.434i | −0.245547 | − | 0.245547i | 0.573593 | − | 0.819140i | \(-0.305549\pi\) |
−0.819140 | + | 0.573593i | \(0.805549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1255.45i | 1.46153i | 0.682630 | + | 0.730764i | \(0.260836\pi\) | ||||
−0.682630 | + | 0.730764i | \(0.739164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.4949 | −0.0284494 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1007.70 | − | 1007.70i | 1.16767 | − | 1.16767i | 0.184911 | − | 0.982755i | \(-0.440800\pi\) |
0.982755 | − | 0.184911i | \(-0.0591996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 305.456 | + | 305.456i | 0.352314 | + | 0.352314i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 254.524i | 0.292894i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −559.760 | −0.642664 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 162.841 | − | 162.841i | 0.186530 | − | 0.186530i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 282.346 | + | 282.346i | 0.321945 | + | 0.321945i | 0.849513 | − | 0.527568i | \(-0.176896\pi\) |
−0.527568 | + | 0.849513i | \(0.676896\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 286.282i | 0.325690i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1420.34 | −1.61219 | −0.806096 | − | 0.591785i | \(-0.798423\pi\) | ||||
−0.806096 | + | 0.591785i | \(0.798423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1170.15 | + | 1170.15i | −1.32519 | + | 1.32519i | −0.415686 | + | 0.909508i | \(0.636459\pi\) |
−0.909508 | + | 0.415686i | \(0.863541\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 756.711 | + | 756.711i | 0.853112 | + | 0.853112i | 0.990515 | − | 0.137403i | \(-0.0438755\pi\) |
−0.137403 | + | 0.990515i | \(0.543875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57.8388i | 0.0650605i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.0908 | 0.0292826 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.288269 | + | 0.288269i | −0.000322810 | + | 0.000322810i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −364.863 | − | 364.863i | −0.406759 | − | 0.406759i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 119.385i | − | 0.132797i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −117.394 | −0.130293 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −93.5630 | + | 93.5630i | −0.103614 | + | 0.103614i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −942.979 | − | 942.979i | −1.03967 | − | 1.03967i | −0.999180 | − | 0.0404876i | \(-0.987109\pi\) |
−0.0404876 | − | 0.999180i | \(-0.512891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 151.546i | 0.166717i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1181.15 | 1.29654 | 0.648272 | − | 0.761409i | \(-0.275492\pi\) | ||||
0.648272 | + | 0.761409i | \(0.275492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 236.940 | − | 236.940i | 0.259518 | − | 0.259518i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 149.373 | + | 149.373i | 0.162894 | + | 0.162894i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 473.595i | − | 0.515337i | −0.966233 | − | 0.257669i | \(-0.917046\pi\) | ||
0.966233 | − | 0.257669i | \(-0.0829543\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −331.293 | −0.359710 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −174.567 | + | 174.567i | −0.189130 | + | 0.189130i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 78.6061 | + | 78.6061i | 0.0847962 | + | 0.0847962i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1094.43i | − | 1.17807i | −0.808106 | − | 0.589037i | \(-0.799507\pi\) | ||
0.808106 | − | 0.589037i | \(-0.200493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.82857 | −0.00518644 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −292.974 | + | 292.974i | −0.314013 | + | 0.314013i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 654.891 | + | 654.891i | 0.698923 | + | 0.698923i | 0.964178 | − | 0.265255i | \(-0.0854562\pi\) |
−0.265255 | + | 0.964178i | \(0.585456\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 664.757i | 0.707942i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 766.382 | 0.814433 | 0.407217 | − | 0.913332i | \(-0.366499\pi\) | ||||
0.407217 | + | 0.913332i | \(0.366499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 326.969 | − | 326.969i | 0.346733 | − | 0.346733i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −325.348 | − | 325.348i | −0.343557 | − | 0.343557i | 0.514146 | − | 0.857703i | \(-0.328109\pi\) |
−0.857703 | + | 0.514146i | \(0.828109\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 41.1939i | − | 0.0434077i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −428.808 | −0.450902 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.1010 | + | 31.1010i | −0.0326349 | + | 0.0326349i | −0.723236 | − | 0.690601i | \(-0.757346\pi\) |
0.690601 | + | 0.723236i | \(0.257346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −114.656 | − | 114.656i | −0.119808 | − | 0.119808i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 256.343i | 0.267302i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −947.333 | −0.985778 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.4541 | + | 22.4541i | −0.0233168 | + | 0.0233168i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −314.656 | − | 314.656i | −0.325394 | − | 0.325394i | 0.525438 | − | 0.850832i | \(-0.323902\pi\) |
−0.850832 | + | 0.525438i | \(0.823902\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.10102i | 0.00113624i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 253.614 | 0.261189 | 0.130594 | − | 0.991436i | \(-0.458311\pi\) | ||||
0.130594 | + | 0.991436i | \(0.458311\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −199.044 | + | 199.044i | −0.204568 | + | 0.204568i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 580.974 | + | 580.974i | 0.594651 | + | 0.594651i | 0.938884 | − | 0.344233i | \(-0.111861\pi\) |
−0.344233 | + | 0.938884i | \(0.611861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 280.000i | 0.286006i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 283.727 | 0.289222 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −734.070 | + | 734.070i | −0.746765 | + | 0.746765i | −0.973870 | − | 0.227105i | \(-0.927074\pi\) |
0.227105 | + | 0.973870i | \(0.427074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.41887 | − | 5.41887i | −0.00549025 | − | 0.00549025i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2497.85i | − | 2.52563i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −616.887 | −0.622489 | −0.311245 | − | 0.950330i | \(-0.600746\pi\) | ||||
−0.311245 | + | 0.950330i | \(0.600746\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −164.661 | + | 164.661i | −0.165821 | + | 0.165821i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −460.191 | − | 460.191i | −0.461576 | − | 0.461576i | 0.437596 | − | 0.899172i | \(-0.355830\pi\) |
−0.899172 | + | 0.437596i | \(0.855830\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 313.757i | 0.314071i |
(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 | 1200.3.bg.f.1057.1 | 4 | ||
4.3 | odd | 2 | 600.3.u.d.457.2 | yes | 4 | ||
5.2 | odd | 4 | 1200.3.bg.l.193.2 | 4 | |||
5.3 | odd | 4 | inner | 1200.3.bg.f.193.1 | 4 | ||
5.4 | even | 2 | 1200.3.bg.l.1057.2 | 4 | |||
12.11 | even | 2 | 1800.3.v.m.1657.1 | 4 | |||
20.3 | even | 4 | 600.3.u.d.193.2 | yes | 4 | ||
20.7 | even | 4 | 600.3.u.c.193.1 | ✓ | 4 | ||
20.19 | odd | 2 | 600.3.u.c.457.1 | yes | 4 | ||
60.23 | odd | 4 | 1800.3.v.m.793.1 | 4 | |||
60.47 | odd | 4 | 1800.3.v.l.793.2 | 4 | |||
60.59 | even | 2 | 1800.3.v.l.1657.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.3.u.c.193.1 | ✓ | 4 | 20.7 | even | 4 | ||
600.3.u.c.457.1 | yes | 4 | 20.19 | odd | 2 | ||
600.3.u.d.193.2 | yes | 4 | 20.3 | even | 4 | ||
600.3.u.d.457.2 | yes | 4 | 4.3 | odd | 2 | ||
1200.3.bg.f.193.1 | 4 | 5.3 | odd | 4 | inner | ||
1200.3.bg.f.1057.1 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.l.193.2 | 4 | 5.2 | odd | 4 | |||
1200.3.bg.l.1057.2 | 4 | 5.4 | even | 2 | |||
1800.3.v.l.793.2 | 4 | 60.47 | odd | 4 | |||
1800.3.v.l.1657.2 | 4 | 60.59 | even | 2 | |||
1800.3.v.m.793.1 | 4 | 60.23 | odd | 4 | |||
1800.3.v.m.1657.1 | 4 | 12.11 | even | 2 |