Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(324,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.b (of order \(2\), degree \(1\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} + 5x^{4} + 6x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 324.1 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.324 |
Dual form | 475.2.b.c.324.6 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.80194i | − 1.98127i | −0.136540 | − | 0.990635i | \(-0.543598\pi\) | ||||
0.136540 | − | 0.990635i | \(-0.456402\pi\) | |||||||
\(3\) | 0.554958i | 0.320405i | 0.987084 | + | 0.160203i | \(0.0512148\pi\) | ||||
−0.987084 | + | 0.160203i | \(0.948785\pi\) | |||||||
\(4\) | −5.85086 | −2.92543 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.55496 | 0.634809 | ||||||||
\(7\) | 3.04892i | 1.15238i | 0.817315 | + | 0.576191i | \(0.195462\pi\) | ||||
−0.817315 | + | 0.576191i | \(0.804538\pi\) | |||||||
\(8\) | 10.7899i | 3.81479i | ||||||||
\(9\) | 2.69202 | 0.897340 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.93900 | −0.886142 | −0.443071 | − | 0.896486i | \(-0.646111\pi\) | ||||
−0.443071 | + | 0.896486i | \(0.646111\pi\) | |||||||
\(12\) | − 3.24698i | − 0.937322i | ||||||||
\(13\) | 3.24698i | 0.900550i | 0.892890 | + | 0.450275i | \(0.148674\pi\) | ||||
−0.892890 | + | 0.450275i | \(0.851326\pi\) | |||||||
\(14\) | 8.54288 | 2.28318 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.5308 | 4.63270 | ||||||||
\(17\) | 2.15883i | 0.523594i | 0.965123 | + | 0.261797i | \(0.0843151\pi\) | ||||
−0.965123 | + | 0.261797i | \(0.915685\pi\) | |||||||
\(18\) | − 7.54288i | − 1.77787i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.69202 | −0.369229 | ||||||||
\(22\) | 8.23490i | 1.75569i | ||||||||
\(23\) | 1.19806i | 0.249813i | 0.992169 | + | 0.124907i | \(0.0398631\pi\) | ||||
−0.992169 | + | 0.124907i | \(0.960137\pi\) | |||||||
\(24\) | −5.98792 | −1.22228 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.09783 | 1.78423 | ||||||||
\(27\) | 3.15883i | 0.607918i | ||||||||
\(28\) | − 17.8388i | − 3.37121i | ||||||||
\(29\) | 1.77479 | 0.329570 | 0.164785 | − | 0.986329i | \(-0.447307\pi\) | ||||
0.164785 | + | 0.986329i | \(0.447307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.34481 | −1.67838 | −0.839189 | − | 0.543840i | \(-0.816970\pi\) | ||||
−0.839189 | + | 0.543840i | \(0.816970\pi\) | |||||||
\(32\) | − 30.3424i | − 5.36383i | ||||||||
\(33\) | − 1.63102i | − 0.283925i | ||||||||
\(34\) | 6.04892 | 1.03738 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15.7506 | −2.62510 | ||||||||
\(37\) | 1.15883i | 0.190511i | 0.995453 | + | 0.0952555i | \(0.0303668\pi\) | ||||
−0.995453 | + | 0.0952555i | \(0.969633\pi\) | |||||||
\(38\) | − 2.80194i | − 0.454534i | ||||||||
\(39\) | −1.80194 | −0.288541 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.57002 | 1.33841 | 0.669206 | − | 0.743077i | \(-0.266634\pi\) | ||||
0.669206 | + | 0.743077i | \(0.266634\pi\) | |||||||
\(42\) | 4.74094i | 0.731543i | ||||||||
\(43\) | 5.27413i | 0.804297i | 0.915575 | + | 0.402148i | \(0.131736\pi\) | ||||
−0.915575 | + | 0.402148i | \(0.868264\pi\) | |||||||
\(44\) | 17.1957 | 2.59234 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.35690 | 0.494947 | ||||||||
\(47\) | − 2.35690i | − 0.343789i | −0.985115 | − | 0.171894i | \(-0.945011\pi\) | ||||
0.985115 | − | 0.171894i | \(-0.0549888\pi\) | |||||||
\(48\) | 10.2838i | 1.48434i | ||||||||
\(49\) | −2.29590 | −0.327985 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.19806 | −0.167762 | ||||||||
\(52\) | − 18.9976i | − 2.63449i | ||||||||
\(53\) | 8.82371i | 1.21203i | 0.795453 | + | 0.606015i | \(0.207233\pi\) | ||||
−0.795453 | + | 0.606015i | \(0.792767\pi\) | |||||||
\(54\) | 8.85086 | 1.20445 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −32.8974 | −4.39610 | ||||||||
\(57\) | 0.554958i | 0.0735060i | ||||||||
\(58\) | − 4.97285i | − 0.652968i | ||||||||
\(59\) | 5.70171 | 0.742299 | 0.371150 | − | 0.928573i | \(-0.378964\pi\) | ||||
0.371150 | + | 0.928573i | \(0.378964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.96077 | −1.27535 | −0.637673 | − | 0.770307i | \(-0.720103\pi\) | ||||
−0.637673 | + | 0.770307i | \(0.720103\pi\) | |||||||
\(62\) | 26.1836i | 3.32532i | ||||||||
\(63\) | 8.20775i | 1.03408i | ||||||||
\(64\) | −47.9560 | −5.99450 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.57002 | −0.562531 | ||||||||
\(67\) | − 4.98254i | − 0.608714i | −0.952558 | − | 0.304357i | \(-0.901558\pi\) | ||||
0.952558 | − | 0.304357i | \(-0.0984416\pi\) | |||||||
\(68\) | − 12.6310i | − 1.53174i | ||||||||
\(69\) | −0.664874 | −0.0800415 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.70171 | 0.320634 | 0.160317 | − | 0.987066i | \(-0.448748\pi\) | ||||
0.160317 | + | 0.987066i | \(0.448748\pi\) | |||||||
\(72\) | 29.0465i | 3.42317i | ||||||||
\(73\) | 13.7778i | 1.61257i | 0.591530 | + | 0.806283i | \(0.298524\pi\) | ||||
−0.591530 | + | 0.806283i | \(0.701476\pi\) | |||||||
\(74\) | 3.24698 | 0.377454 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.85086 | −0.671139 | ||||||||
\(77\) | − 8.96077i | − 1.02117i | ||||||||
\(78\) | 5.04892i | 0.571677i | ||||||||
\(79\) | −5.66487 | −0.637348 | −0.318674 | − | 0.947864i | \(-0.603238\pi\) | ||||
−0.318674 | + | 0.947864i | \(0.603238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.32304 | 0.702560 | ||||||||
\(82\) | − 24.0127i | − 2.65176i | ||||||||
\(83\) | − 3.00969i | − 0.330356i | −0.986264 | − | 0.165178i | \(-0.947180\pi\) | ||||
0.986264 | − | 0.165178i | \(-0.0528199\pi\) | |||||||
\(84\) | 9.89977 | 1.08015 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.7778 | 1.59353 | ||||||||
\(87\) | 0.984935i | 0.105596i | ||||||||
\(88\) | − 31.7114i | − 3.38045i | ||||||||
\(89\) | 10.2838 | 1.09008 | 0.545041 | − | 0.838409i | \(-0.316514\pi\) | ||||
0.545041 | + | 0.838409i | \(0.316514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.89977 | −1.03778 | ||||||||
\(92\) | − 7.00969i | − 0.730811i | ||||||||
\(93\) | − 5.18598i | − 0.537761i | ||||||||
\(94\) | −6.60388 | −0.681138 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16.8388 | 1.71860 | ||||||||
\(97\) | − 3.24698i | − 0.329681i | −0.986320 | − | 0.164840i | \(-0.947289\pi\) | ||||
0.986320 | − | 0.164840i | \(-0.0527109\pi\) | |||||||
\(98\) | 6.43296i | 0.649827i | ||||||||
\(99\) | −7.91185 | −0.795171 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.09246 | 0.506718 | 0.253359 | − | 0.967372i | \(-0.418465\pi\) | ||||
0.253359 | + | 0.967372i | \(0.418465\pi\) | |||||||
\(102\) | 3.35690i | 0.332382i | ||||||||
\(103\) | − 14.3110i | − 1.41010i | −0.709157 | − | 0.705051i | \(-0.750924\pi\) | ||||
0.709157 | − | 0.705051i | \(-0.249076\pi\) | |||||||
\(104\) | −35.0344 | −3.43541 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.7235 | 2.40136 | ||||||||
\(107\) | 8.18598i | 0.791369i | 0.918387 | + | 0.395684i | \(0.129493\pi\) | ||||
−0.918387 | + | 0.395684i | \(0.870507\pi\) | |||||||
\(108\) | − 18.4819i | − 1.77842i | ||||||||
\(109\) | 11.3274 | 1.08496 | 0.542482 | − | 0.840067i | \(-0.317485\pi\) | ||||
0.542482 | + | 0.840067i | \(0.317485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.643104 | −0.0610407 | ||||||||
\(112\) | 56.4989i | 5.33864i | ||||||||
\(113\) | 3.43535i | 0.323171i | 0.986859 | + | 0.161585i | \(0.0516607\pi\) | ||||
−0.986859 | + | 0.161585i | \(0.948339\pi\) | |||||||
\(114\) | 1.55496 | 0.145635 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.3840 | −0.964134 | ||||||||
\(117\) | 8.74094i | 0.808100i | ||||||||
\(118\) | − 15.9758i | − 1.47069i | ||||||||
\(119\) | −6.58211 | −0.603381 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.36227 | −0.214752 | ||||||||
\(122\) | 27.9095i | 2.52680i | ||||||||
\(123\) | 4.75600i | 0.428834i | ||||||||
\(124\) | 54.6752 | 4.90997 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 22.9976 | 2.04879 | ||||||||
\(127\) | − 1.46144i | − 0.129681i | −0.997896 | − | 0.0648407i | \(-0.979346\pi\) | ||||
0.997896 | − | 0.0648407i | \(-0.0206539\pi\) | |||||||
\(128\) | 73.6848i | 6.51288i | ||||||||
\(129\) | −2.92692 | −0.257701 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.2295 | −1.15587 | −0.577934 | − | 0.816083i | \(-0.696141\pi\) | ||||
−0.577934 | + | 0.816083i | \(0.696141\pi\) | |||||||
\(132\) | 9.54288i | 0.830601i | ||||||||
\(133\) | 3.04892i | 0.264375i | ||||||||
\(134\) | −13.9608 | −1.20603 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23.2935 | −1.99740 | ||||||||
\(137\) | − 16.1739i | − 1.38183i | −0.722936 | − | 0.690915i | \(-0.757208\pi\) | ||||
0.722936 | − | 0.690915i | \(-0.242792\pi\) | |||||||
\(138\) | 1.86294i | 0.158584i | ||||||||
\(139\) | −13.0978 | −1.11094 | −0.555472 | − | 0.831535i | \(-0.687462\pi\) | ||||
−0.555472 | + | 0.831535i | \(0.687462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.30798 | 0.110152 | ||||||||
\(142\) | − 7.57002i | − 0.635262i | ||||||||
\(143\) | − 9.54288i | − 0.798015i | ||||||||
\(144\) | 49.8853 | 4.15711 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 38.6045 | 3.19493 | ||||||||
\(147\) | − 1.27413i | − 0.105088i | ||||||||
\(148\) | − 6.78017i | − 0.557326i | ||||||||
\(149\) | −11.0640 | −0.906397 | −0.453198 | − | 0.891410i | \(-0.649717\pi\) | ||||
−0.453198 | + | 0.891410i | \(0.649717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4426 | 0.849811 | 0.424905 | − | 0.905238i | \(-0.360307\pi\) | ||||
0.424905 | + | 0.905238i | \(0.360307\pi\) | |||||||
\(152\) | 10.7899i | 0.875173i | ||||||||
\(153\) | 5.81163i | 0.469842i | ||||||||
\(154\) | −25.1075 | −2.02322 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.5429 | 0.844106 | ||||||||
\(157\) | − 2.48427i | − 0.198266i | −0.995074 | − | 0.0991332i | \(-0.968393\pi\) | ||||
0.995074 | − | 0.0991332i | \(-0.0316070\pi\) | |||||||
\(158\) | 15.8726i | 1.26276i | ||||||||
\(159\) | −4.89679 | −0.388341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.65279 | −0.287880 | ||||||||
\(162\) | − 17.7168i | − 1.39196i | ||||||||
\(163\) | 3.16852i | 0.248178i | 0.992271 | + | 0.124089i | \(0.0396008\pi\) | ||||
−0.992271 | + | 0.124089i | \(0.960399\pi\) | |||||||
\(164\) | −50.1420 | −3.91543 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.43296 | −0.654525 | ||||||||
\(167\) | − 4.74632i | − 0.367281i | −0.982993 | − | 0.183640i | \(-0.941212\pi\) | ||||
0.982993 | − | 0.183640i | \(-0.0587882\pi\) | |||||||
\(168\) | − 18.2567i | − 1.40853i | ||||||||
\(169\) | 2.45712 | 0.189009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.69202 | 0.205864 | ||||||||
\(172\) | − 30.8582i | − 2.35291i | ||||||||
\(173\) | 3.96316i | 0.301314i | 0.988586 | + | 0.150657i | \(0.0481389\pi\) | ||||
−0.988586 | + | 0.150657i | \(0.951861\pi\) | |||||||
\(174\) | 2.75973 | 0.209214 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −54.4620 | −4.10523 | ||||||||
\(177\) | 3.16421i | 0.237837i | ||||||||
\(178\) | − 28.8146i | − 2.15975i | ||||||||
\(179\) | 14.0858 | 1.05282 | 0.526409 | − | 0.850231i | \(-0.323538\pi\) | ||||
0.526409 | + | 0.850231i | \(0.323538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2513 | −0.910631 | −0.455316 | − | 0.890330i | \(-0.650474\pi\) | ||||
−0.455316 | + | 0.890330i | \(0.650474\pi\) | |||||||
\(182\) | 27.7385i | 2.05612i | ||||||||
\(183\) | − 5.52781i | − 0.408628i | ||||||||
\(184\) | −12.9269 | −0.952985 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −14.5308 | −1.06545 | ||||||||
\(187\) | − 6.34481i | − 0.463979i | ||||||||
\(188\) | 13.7899i | 1.00573i | ||||||||
\(189\) | −9.63102 | −0.700554 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.1468 | 1.45777 | 0.728884 | − | 0.684637i | \(-0.240039\pi\) | ||||
0.728884 | + | 0.684637i | \(0.240039\pi\) | |||||||
\(192\) | − 26.6136i | − 1.92067i | ||||||||
\(193\) | − 9.52781i | − 0.685827i | −0.939367 | − | 0.342913i | \(-0.888586\pi\) | ||||
0.939367 | − | 0.342913i | \(-0.111414\pi\) | |||||||
\(194\) | −9.09783 | −0.653186 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4330 | 0.959497 | ||||||||
\(197\) | − 4.96316i | − 0.353611i | −0.984246 | − | 0.176805i | \(-0.943424\pi\) | ||||
0.984246 | − | 0.176805i | \(-0.0565763\pi\) | |||||||
\(198\) | 22.1685i | 1.57545i | ||||||||
\(199\) | −5.42221 | −0.384370 | −0.192185 | − | 0.981359i | \(-0.561557\pi\) | ||||
−0.192185 | + | 0.981359i | \(0.561557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.76510 | 0.195035 | ||||||||
\(202\) | − 14.2687i | − 1.00395i | ||||||||
\(203\) | 5.41119i | 0.379791i | ||||||||
\(204\) | 7.00969 | 0.490776 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −40.0984 | −2.79379 | ||||||||
\(207\) | 3.22521i | 0.224168i | ||||||||
\(208\) | 60.1691i | 4.17198i | ||||||||
\(209\) | −2.93900 | −0.203295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9638 | 1.09899 | 0.549495 | − | 0.835497i | \(-0.314820\pi\) | ||||
0.549495 | + | 0.835497i | \(0.314820\pi\) | |||||||
\(212\) | − 51.6262i | − 3.54570i | ||||||||
\(213\) | 1.49934i | 0.102733i | ||||||||
\(214\) | 22.9366 | 1.56791 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −34.0834 | −2.31908 | ||||||||
\(217\) | − 28.4916i | − 1.93413i | ||||||||
\(218\) | − 31.7385i | − 2.14961i | ||||||||
\(219\) | −7.64609 | −0.516675 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.00969 | −0.471523 | ||||||||
\(222\) | 1.80194i | 0.120938i | ||||||||
\(223\) | − 23.2150i | − 1.55459i | −0.629134 | − | 0.777297i | \(-0.716590\pi\) | ||||
0.629134 | − | 0.777297i | \(-0.283410\pi\) | |||||||
\(224\) | 92.5115 | 6.18119 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.62565 | 0.640288 | ||||||||
\(227\) | 17.4795i | 1.16015i | 0.814562 | + | 0.580077i | \(0.196978\pi\) | ||||
−0.814562 | + | 0.580077i | \(0.803022\pi\) | |||||||
\(228\) | − 3.24698i | − 0.215036i | ||||||||
\(229\) | 2.32544 | 0.153669 | 0.0768346 | − | 0.997044i | \(-0.475519\pi\) | ||||
0.0768346 | + | 0.997044i | \(0.475519\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.97285 | 0.327190 | ||||||||
\(232\) | 19.1497i | 1.25724i | ||||||||
\(233\) | − 18.9342i | − 1.24042i | −0.784435 | − | 0.620211i | \(-0.787047\pi\) | ||||
0.784435 | − | 0.620211i | \(-0.212953\pi\) | |||||||
\(234\) | 24.4916 | 1.60106 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −33.3599 | −2.17154 | ||||||||
\(237\) | − 3.14377i | − 0.204210i | ||||||||
\(238\) | 18.4426i | 1.19546i | ||||||||
\(239\) | −11.1685 | −0.722432 | −0.361216 | − | 0.932482i | \(-0.617638\pi\) | ||||
−0.361216 | + | 0.932482i | \(0.617638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.42998 | 0.478607 | 0.239303 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239303 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(242\) | 6.61894i | 0.425482i | ||||||||
\(243\) | 12.9855i | 0.833022i | ||||||||
\(244\) | 58.2790 | 3.73093 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.3260 | 0.849637 | ||||||||
\(247\) | 3.24698i | 0.206600i | ||||||||
\(248\) | − 100.829i | − 6.40266i | ||||||||
\(249\) | 1.67025 | 0.105848 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.7409 | −0.930440 | −0.465220 | − | 0.885195i | \(-0.654025\pi\) | ||||
−0.465220 | + | 0.885195i | \(0.654025\pi\) | |||||||
\(252\) | − 48.0224i | − 3.02512i | ||||||||
\(253\) | − 3.52111i | − 0.221370i | ||||||||
\(254\) | −4.09485 | −0.256934 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 110.548 | 6.90927 | ||||||||
\(257\) | − 3.34721i | − 0.208793i | −0.994536 | − | 0.104397i | \(-0.966709\pi\) | ||||
0.994536 | − | 0.104397i | \(-0.0332911\pi\) | |||||||
\(258\) | 8.20105i | 0.510575i | ||||||||
\(259\) | −3.53319 | −0.219542 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.77777 | 0.295737 | ||||||||
\(262\) | 37.0683i | 2.29009i | ||||||||
\(263\) | − 16.6853i | − 1.02886i | −0.857532 | − | 0.514430i | \(-0.828003\pi\) | ||||
0.857532 | − | 0.514430i | \(-0.171997\pi\) | |||||||
\(264\) | 17.5985 | 1.08311 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.54288 | 0.523797 | ||||||||
\(267\) | 5.70709i | 0.349268i | ||||||||
\(268\) | 29.1521i | 1.78075i | ||||||||
\(269\) | −15.5961 | −0.950911 | −0.475456 | − | 0.879740i | \(-0.657717\pi\) | ||||
−0.475456 | + | 0.879740i | \(0.657717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.2131 | −0.802640 | −0.401320 | − | 0.915938i | \(-0.631449\pi\) | ||||
−0.401320 | + | 0.915938i | \(0.631449\pi\) | |||||||
\(272\) | 40.0049i | 2.42565i | ||||||||
\(273\) | − 5.49396i | − 0.332510i | ||||||||
\(274\) | −45.3183 | −2.73778 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.89008 | 0.234156 | ||||||||
\(277\) | − 12.9758i | − 0.779642i | −0.920891 | − | 0.389821i | \(-0.872537\pi\) | ||||
0.920891 | − | 0.389821i | \(-0.127463\pi\) | |||||||
\(278\) | 36.6993i | 2.20108i | ||||||||
\(279\) | −25.1564 | −1.50608 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8901 | 1.48482 | 0.742409 | − | 0.669947i | \(-0.233683\pi\) | ||||
0.742409 | + | 0.669947i | \(0.233683\pi\) | |||||||
\(282\) | − 3.66487i | − 0.218240i | ||||||||
\(283\) | − 13.5821i | − 0.807372i | −0.914898 | − | 0.403686i | \(-0.867729\pi\) | ||||
0.914898 | − | 0.403686i | \(-0.132271\pi\) | |||||||
\(284\) | −15.8073 | −0.937992 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.7385 | −1.58108 | ||||||||
\(287\) | 26.1293i | 1.54236i | ||||||||
\(288\) | − 81.6824i | − 4.81318i | ||||||||
\(289\) | 12.3394 | 0.725849 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.80194 | 0.105631 | ||||||||
\(292\) | − 80.6118i | − 4.71745i | ||||||||
\(293\) | 1.27652i | 0.0745751i | 0.999305 | + | 0.0372875i | \(0.0118717\pi\) | ||||
−0.999305 | + | 0.0372875i | \(0.988128\pi\) | |||||||
\(294\) | −3.57002 | −0.208208 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.5036 | −0.726760 | ||||||||
\(297\) | − 9.28382i | − 0.538702i | ||||||||
\(298\) | 31.0006i | 1.79582i | ||||||||
\(299\) | −3.89008 | −0.224969 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0804 | −0.926857 | ||||||||
\(302\) | − 29.2597i | − 1.68370i | ||||||||
\(303\) | 2.82610i | 0.162355i | ||||||||
\(304\) | 18.5308 | 1.06281 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.2838 | 0.930884 | ||||||||
\(307\) | 32.2295i | 1.83944i | 0.392580 | + | 0.919718i | \(0.371583\pi\) | ||||
−0.392580 | + | 0.919718i | \(0.628417\pi\) | |||||||
\(308\) | 52.4282i | 2.98737i | ||||||||
\(309\) | 7.94198 | 0.451804 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4983 | 0.708712 | 0.354356 | − | 0.935111i | \(-0.384700\pi\) | ||||
0.354356 | + | 0.935111i | \(0.384700\pi\) | |||||||
\(312\) | − 19.4426i | − 1.10072i | ||||||||
\(313\) | − 20.9390i | − 1.18354i | −0.806106 | − | 0.591771i | \(-0.798429\pi\) | ||||
0.806106 | − | 0.591771i | \(-0.201571\pi\) | |||||||
\(314\) | −6.96077 | −0.392819 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.1444 | 1.86452 | ||||||||
\(317\) | − 15.8562i | − 0.890575i | −0.895388 | − | 0.445287i | \(-0.853102\pi\) | ||||
0.895388 | − | 0.445287i | \(-0.146898\pi\) | |||||||
\(318\) | 13.7205i | 0.769407i | ||||||||
\(319\) | −5.21611 | −0.292046 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.54288 | −0.253559 | ||||||||
\(322\) | 10.2349i | 0.570369i | ||||||||
\(323\) | 2.15883i | 0.120121i | ||||||||
\(324\) | −36.9952 | −2.05529 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.87800 | 0.491707 | ||||||||
\(327\) | 6.28621i | 0.347628i | ||||||||
\(328\) | 92.4693i | 5.10576i | ||||||||
\(329\) | 7.18598 | 0.396176 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2349 | −0.727456 | −0.363728 | − | 0.931505i | \(-0.618496\pi\) | ||||
−0.363728 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(332\) | 17.6093i | 0.966433i | ||||||||
\(333\) | 3.11960i | 0.170953i | ||||||||
\(334\) | −13.2989 | −0.727682 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −31.3545 | −1.71053 | ||||||||
\(337\) | 26.0780i | 1.42056i | 0.703920 | + | 0.710279i | \(0.251431\pi\) | ||||
−0.703920 | + | 0.710279i | \(0.748569\pi\) | |||||||
\(338\) | − 6.88471i | − 0.374479i | ||||||||
\(339\) | −1.90648 | −0.103546 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.4644 | 1.48728 | ||||||||
\(342\) | − 7.54288i | − 0.407872i | ||||||||
\(343\) | 14.3424i | 0.774418i | ||||||||
\(344\) | −56.9071 | −3.06822 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.1045 | 0.596984 | ||||||||
\(347\) | − 8.98254i | − 0.482208i | −0.970499 | − | 0.241104i | \(-0.922490\pi\) | ||||
0.970499 | − | 0.241104i | \(-0.0775095\pi\) | |||||||
\(348\) | − 5.76271i | − 0.308914i | ||||||||
\(349\) | −0.599564 | −0.0320939 | −0.0160470 | − | 0.999871i | \(-0.505108\pi\) | ||||
−0.0160470 | + | 0.999871i | \(0.505108\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.2567 | −0.547460 | ||||||||
\(352\) | 89.1764i | 4.75312i | ||||||||
\(353\) | 31.8896i | 1.69731i | 0.528945 | + | 0.848656i | \(0.322588\pi\) | ||||
−0.528945 | + | 0.848656i | \(0.677412\pi\) | |||||||
\(354\) | 8.86592 | 0.471218 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −60.1691 | −3.18896 | ||||||||
\(357\) | − 3.65279i | − 0.193326i | ||||||||
\(358\) | − 39.4674i | − 2.08592i | ||||||||
\(359\) | 18.3763 | 0.969863 | 0.484931 | − | 0.874552i | \(-0.338845\pi\) | ||||
0.484931 | + | 0.874552i | \(0.338845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 34.3274i | 1.80421i | ||||||||
\(363\) | − 1.31096i | − 0.0688077i | ||||||||
\(364\) | 57.9221 | 3.03594 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15.4886 | −0.809601 | ||||||||
\(367\) | 14.6377i | 0.764083i | 0.924145 | + | 0.382042i | \(0.124779\pi\) | ||||
−0.924145 | + | 0.382042i | \(0.875221\pi\) | |||||||
\(368\) | 22.2010i | 1.15731i | ||||||||
\(369\) | 23.0707 | 1.20101 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.9028 | −1.39672 | ||||||||
\(372\) | 30.3424i | 1.57318i | ||||||||
\(373\) | − 1.02715i | − 0.0531837i | −0.999646 | − | 0.0265918i | \(-0.991535\pi\) | ||||
0.999646 | − | 0.0265918i | \(-0.00846544\pi\) | |||||||
\(374\) | −17.7778 | −0.919267 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.4306 | 1.31148 | ||||||||
\(377\) | 5.76271i | 0.296795i | ||||||||
\(378\) | 26.9855i | 1.38799i | ||||||||
\(379\) | 22.5284 | 1.15721 | 0.578603 | − | 0.815609i | \(-0.303598\pi\) | ||||
0.578603 | + | 0.815609i | \(0.303598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.811035 | 0.0415506 | ||||||||
\(382\) | − 56.4499i | − 2.88823i | ||||||||
\(383\) | 32.6698i | 1.66935i | 0.550745 | + | 0.834674i | \(0.314344\pi\) | ||||
−0.550745 | + | 0.834674i | \(0.685656\pi\) | |||||||
\(384\) | −40.8920 | −2.08676 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.6963 | −1.35881 | ||||||||
\(387\) | 14.1981i | 0.721728i | ||||||||
\(388\) | 18.9976i | 0.964457i | ||||||||
\(389\) | 8.16421 | 0.413942 | 0.206971 | − | 0.978347i | \(-0.433639\pi\) | ||||
0.206971 | + | 0.978347i | \(0.433639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.58642 | −0.130801 | ||||||||
\(392\) | − 24.7724i | − 1.25120i | ||||||||
\(393\) | − 7.34183i | − 0.370346i | ||||||||
\(394\) | −13.9065 | −0.700598 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 46.2911 | 2.32622 | ||||||||
\(397\) | − 37.5478i | − 1.88447i | −0.334954 | − | 0.942235i | \(-0.608721\pi\) | ||||
0.334954 | − | 0.942235i | \(-0.391279\pi\) | |||||||
\(398\) | 15.1927i | 0.761541i | ||||||||
\(399\) | −1.69202 | −0.0847070 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.2519 | 1.61058 | 0.805291 | − | 0.592880i | \(-0.202009\pi\) | ||||
0.805291 | + | 0.592880i | \(0.202009\pi\) | |||||||
\(402\) | − 7.74764i | − 0.386417i | ||||||||
\(403\) | − 30.3424i | − 1.51146i | ||||||||
\(404\) | −29.7952 | −1.48237 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.1618 | 0.752468 | ||||||||
\(407\) | − 3.40581i | − 0.168820i | ||||||||
\(408\) | − 12.9269i | − 0.639978i | ||||||||
\(409\) | 31.5459 | 1.55984 | 0.779921 | − | 0.625878i | \(-0.215259\pi\) | ||||
0.779921 | + | 0.625878i | \(0.215259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.97584 | 0.442745 | ||||||||
\(412\) | 83.7314i | 4.12515i | ||||||||
\(413\) | 17.3840i | 0.855413i | ||||||||
\(414\) | 9.03684 | 0.444136 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 98.5212 | 4.83040 | ||||||||
\(417\) | − 7.26875i | − 0.355952i | ||||||||
\(418\) | 8.23490i | 0.402782i | ||||||||
\(419\) | 14.6866 | 0.717490 | 0.358745 | − | 0.933436i | \(-0.383205\pi\) | ||||
0.358745 | + | 0.933436i | \(0.383205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1142 | 0.736622 | 0.368311 | − | 0.929703i | \(-0.379936\pi\) | ||||
0.368311 | + | 0.929703i | \(0.379936\pi\) | |||||||
\(422\) | − 44.7294i | − 2.17740i | ||||||||
\(423\) | − 6.34481i | − 0.308495i | ||||||||
\(424\) | −95.2065 | −4.62364 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.20105 | 0.203541 | ||||||||
\(427\) | − 30.3696i | − 1.46969i | ||||||||
\(428\) | − 47.8950i | − 2.31509i | ||||||||
\(429\) | 5.29590 | 0.255688 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.67696 | 0.0807761 | 0.0403881 | − | 0.999184i | \(-0.487141\pi\) | ||||
0.0403881 | + | 0.999184i | \(0.487141\pi\) | |||||||
\(432\) | 58.5357i | 2.81630i | ||||||||
\(433\) | − 13.1545i | − 0.632166i | −0.948732 | − | 0.316083i | \(-0.897632\pi\) | ||||
0.948732 | − | 0.316083i | \(-0.102368\pi\) | |||||||
\(434\) | −79.8316 | −3.83204 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −66.2747 | −3.17398 | ||||||||
\(437\) | 1.19806i | 0.0573111i | ||||||||
\(438\) | 21.4239i | 1.02367i | ||||||||
\(439\) | −6.45580 | −0.308118 | −0.154059 | − | 0.988062i | \(-0.549235\pi\) | ||||
−0.154059 | + | 0.988062i | \(0.549235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.18060 | −0.294314 | ||||||||
\(442\) | 19.6407i | 0.934213i | ||||||||
\(443\) | − 25.3709i | − 1.20541i | −0.797965 | − | 0.602704i | \(-0.794090\pi\) | ||||
0.797965 | − | 0.602704i | \(-0.205910\pi\) | |||||||
\(444\) | 3.76271 | 0.178570 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −65.0471 | −3.08007 | ||||||||
\(447\) | − 6.14005i | − 0.290414i | ||||||||
\(448\) | − 146.214i | − 6.90795i | ||||||||
\(449\) | 3.59956 | 0.169874 | 0.0849370 | − | 0.996386i | \(-0.472931\pi\) | ||||
0.0849370 | + | 0.996386i | \(0.472931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.1873 | −1.18602 | ||||||||
\(452\) | − 20.0998i | − 0.945413i | ||||||||
\(453\) | 5.79523i | 0.272284i | ||||||||
\(454\) | 48.9764 | 2.29858 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.98792 | −0.280410 | ||||||||
\(457\) | 12.2784i | 0.574361i | 0.957876 | + | 0.287181i | \(0.0927180\pi\) | ||||
−0.957876 | + | 0.287181i | \(0.907282\pi\) | |||||||
\(458\) | − 6.51573i | − 0.304460i | ||||||||
\(459\) | −6.81940 | −0.318302 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.4935 | 1.83939 | 0.919697 | − | 0.392628i | \(-0.128434\pi\) | ||||
0.919697 | + | 0.392628i | \(0.128434\pi\) | |||||||
\(462\) | − 13.9336i | − 0.648251i | ||||||||
\(463\) | 18.3991i | 0.855079i | 0.903997 | + | 0.427540i | \(0.140620\pi\) | ||||
−0.903997 | + | 0.427540i | \(0.859380\pi\) | |||||||
\(464\) | 32.8883 | 1.52680 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −53.0525 | −2.45761 | ||||||||
\(467\) | 36.2282i | 1.67644i | 0.545332 | + | 0.838220i | \(0.316404\pi\) | ||||
−0.545332 | + | 0.838220i | \(0.683596\pi\) | |||||||
\(468\) | − 51.1420i | − 2.36404i | ||||||||
\(469\) | 15.1914 | 0.701472 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.37867 | 0.0635256 | ||||||||
\(472\) | 61.5206i | 2.83172i | ||||||||
\(473\) | − 15.5007i | − 0.712721i | ||||||||
\(474\) | −8.80864 | −0.404594 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 38.5109 | 1.76515 | ||||||||
\(477\) | 23.7536i | 1.08760i | ||||||||
\(478\) | 31.2935i | 1.43133i | ||||||||
\(479\) | 34.3129 | 1.56780 | 0.783898 | − | 0.620890i | \(-0.213229\pi\) | ||||
0.783898 | + | 0.620890i | \(0.213229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.76271 | −0.171565 | ||||||||
\(482\) | − 20.8183i | − 0.948249i | ||||||||
\(483\) | − 2.02715i | − 0.0922384i | ||||||||
\(484\) | 13.8213 | 0.628242 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 36.3846 | 1.65044 | ||||||||
\(487\) | 24.4722i | 1.10894i | 0.832203 | + | 0.554470i | \(0.187079\pi\) | ||||
−0.832203 | + | 0.554470i | \(0.812921\pi\) | |||||||
\(488\) | − 107.475i | − 4.86518i | ||||||||
\(489\) | −1.75840 | −0.0795175 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.3067 | 0.826168 | 0.413084 | − | 0.910693i | \(-0.364452\pi\) | ||||
0.413084 | + | 0.910693i | \(0.364452\pi\) | |||||||
\(492\) | − 27.8267i | − 1.25452i | ||||||||
\(493\) | 3.83148i | 0.172561i | ||||||||
\(494\) | 9.09783 | 0.409331 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −173.167 | −7.77542 | ||||||||
\(497\) | 8.23729i | 0.369493i | ||||||||
\(498\) | − 4.67994i | − 0.209713i | ||||||||
\(499\) | 25.3424 | 1.13448 | 0.567241 | − | 0.823552i | \(-0.308011\pi\) | ||||
0.567241 | + | 0.823552i | \(0.308011\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.63401 | 0.117679 | ||||||||
\(502\) | 41.3032i | 1.84345i | ||||||||
\(503\) | 14.1105i | 0.629156i | 0.949232 | + | 0.314578i | \(0.101863\pi\) | ||||
−0.949232 | + | 0.314578i | \(0.898137\pi\) | |||||||
\(504\) | −88.5605 | −3.94480 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.86592 | −0.438594 | ||||||||
\(507\) | 1.36360i | 0.0605596i | ||||||||
\(508\) | 8.55065i | 0.379374i | ||||||||
\(509\) | 17.8019 | 0.789057 | 0.394529 | − | 0.918884i | \(-0.370908\pi\) | ||||
0.394529 | + | 0.918884i | \(0.370908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.0073 | −1.85829 | ||||||||
\(512\) | − 162.380i | − 7.17625i | ||||||||
\(513\) | 3.15883i | 0.139466i | ||||||||
\(514\) | −9.37867 | −0.413675 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 17.1250 | 0.753885 | ||||||||
\(517\) | 6.92692i | 0.304646i | ||||||||
\(518\) | 9.89977i | 0.434971i | ||||||||
\(519\) | −2.19939 | −0.0965425 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3948 | 0.586837 | 0.293418 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293418 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(522\) | − 13.3870i | − 0.585934i | ||||||||
\(523\) | − 1.46921i | − 0.0642439i | −0.999484 | − | 0.0321219i | \(-0.989774\pi\) | ||||
0.999484 | − | 0.0321219i | \(-0.0102265\pi\) | |||||||
\(524\) | 77.4040 | 3.38141 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.7512 | −2.03845 | ||||||||
\(527\) | − 20.1739i | − 0.878789i | ||||||||
\(528\) | − 30.2241i | − 1.31534i | ||||||||
\(529\) | 21.5646 | 0.937593 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.3491 | 0.666095 | ||||||||
\(532\) | − 17.8388i | − 0.773409i | ||||||||
\(533\) | 27.8267i | 1.20531i | ||||||||
\(534\) | 15.9909 | 0.691994 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 53.7609 | 2.32212 | ||||||||
\(537\) | 7.81700i | 0.337329i | ||||||||
\(538\) | 43.6993i | 1.88401i | ||||||||
\(539\) | 6.74764 | 0.290642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.7144 | −1.83643 | −0.918217 | − | 0.396077i | \(-0.870371\pi\) | ||||
−0.918217 | + | 0.396077i | \(0.870371\pi\) | |||||||
\(542\) | 37.0224i | 1.59025i | ||||||||
\(543\) | − 6.79895i | − 0.291771i | ||||||||
\(544\) | 65.5042 | 2.80847 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −15.3937 | −0.658791 | ||||||||
\(547\) | − 10.6866i | − 0.456928i | −0.973552 | − | 0.228464i | \(-0.926630\pi\) | ||||
0.973552 | − | 0.228464i | \(-0.0733703\pi\) | |||||||
\(548\) | 94.6311i | 4.04244i | ||||||||
\(549\) | −26.8146 | −1.14442 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.77479 | 0.0756086 | ||||||||
\(552\) | − 7.17390i | − 0.305341i | ||||||||
\(553\) | − 17.2717i | − 0.734469i | ||||||||
\(554\) | −36.3575 | −1.54468 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 76.6335 | 3.24999 | ||||||||
\(557\) | 34.2083i | 1.44945i | 0.689036 | + | 0.724727i | \(0.258034\pi\) | ||||
−0.689036 | + | 0.724727i | \(0.741966\pi\) | |||||||
\(558\) | 70.4868i | 2.98394i | ||||||||
\(559\) | −17.1250 | −0.724310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.52111 | 0.148661 | ||||||||
\(562\) | − 69.7405i | − 2.94182i | ||||||||
\(563\) | − 5.46788i | − 0.230444i | −0.993340 | − | 0.115222i | \(-0.963242\pi\) | ||||
0.993340 | − | 0.115222i | \(-0.0367579\pi\) | |||||||
\(564\) | −7.65279 | −0.322241 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −38.0562 | −1.59962 | ||||||||
\(567\) | 19.2784i | 0.809618i | ||||||||
\(568\) | 29.1511i | 1.22315i | ||||||||
\(569\) | 17.4819 | 0.732878 | 0.366439 | − | 0.930442i | \(-0.380577\pi\) | ||||
0.366439 | + | 0.930442i | \(0.380577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.21877 | −0.302096 | −0.151048 | − | 0.988526i | \(-0.548265\pi\) | ||||
−0.151048 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(572\) | 55.8340i | 2.33454i | ||||||||
\(573\) | 11.1806i | 0.467076i | ||||||||
\(574\) | 73.2127 | 3.05584 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −129.099 | −5.37911 | ||||||||
\(577\) | − 1.80625i | − 0.0751952i | −0.999293 | − | 0.0375976i | \(-0.988029\pi\) | ||||
0.999293 | − | 0.0375976i | \(-0.0119705\pi\) | |||||||
\(578\) | − 34.5743i | − 1.43810i | ||||||||
\(579\) | 5.28754 | 0.219743 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.17629 | 0.380697 | ||||||||
\(582\) | − 5.04892i | − 0.209284i | ||||||||
\(583\) | − 25.9329i | − 1.07403i | ||||||||
\(584\) | −148.660 | −6.15160 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.57673 | 0.147753 | ||||||||
\(587\) | − 2.39075i | − 0.0986767i | −0.998782 | − | 0.0493384i | \(-0.984289\pi\) | ||||
0.998782 | − | 0.0493384i | \(-0.0157113\pi\) | |||||||
\(588\) | 7.45473i | 0.307428i | ||||||||
\(589\) | −9.34481 | −0.385046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.75435 | 0.113299 | ||||||||
\(592\) | 21.4741i | 0.882580i | ||||||||
\(593\) | − 42.2650i | − 1.73562i | −0.496899 | − | 0.867808i | \(-0.665528\pi\) | ||||
0.496899 | − | 0.867808i | \(-0.334472\pi\) | |||||||
\(594\) | −26.0127 | −1.06731 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 64.7338 | 2.65160 | ||||||||
\(597\) | − 3.00910i | − 0.123154i | ||||||||
\(598\) | 10.8998i | 0.445725i | ||||||||
\(599\) | −8.95838 | −0.366029 | −0.183015 | − | 0.983110i | \(-0.558586\pi\) | ||||
−0.183015 | + | 0.983110i | \(0.558586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8998 | −0.811729 | −0.405864 | − | 0.913933i | \(-0.633029\pi\) | ||||
−0.405864 | + | 0.913933i | \(0.633029\pi\) | |||||||
\(602\) | 45.0562i | 1.83635i | ||||||||
\(603\) | − 13.4131i | − 0.546224i | ||||||||
\(604\) | −61.0984 | −2.48606 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.91856 | 0.321669 | ||||||||
\(607\) | − 26.0084i | − 1.05565i | −0.849354 | − | 0.527823i | \(-0.823008\pi\) | ||||
0.849354 | − | 0.527823i | \(-0.176992\pi\) | |||||||
\(608\) | − 30.3424i | − 1.23055i | ||||||||
\(609\) | −3.00298 | −0.121687 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.65279 | 0.309599 | ||||||||
\(612\) | − 34.0030i | − 1.37449i | ||||||||
\(613\) | 41.3763i | 1.67117i | 0.549360 | + | 0.835586i | \(0.314872\pi\) | ||||
−0.549360 | + | 0.835586i | \(0.685128\pi\) | |||||||
\(614\) | 90.3051 | 3.64442 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 96.6854 | 3.89557 | ||||||||
\(617\) | − 43.9845i | − 1.77075i | −0.464880 | − | 0.885374i | \(-0.653902\pi\) | ||||
0.464880 | − | 0.885374i | \(-0.346098\pi\) | |||||||
\(618\) | − 22.2529i | − 0.895145i | ||||||||
\(619\) | −23.4553 | −0.942749 | −0.471374 | − | 0.881933i | \(-0.656242\pi\) | ||||
−0.471374 | + | 0.881933i | \(0.656242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.78448 | −0.151866 | ||||||||
\(622\) | − 35.0194i | − 1.40415i | ||||||||
\(623\) | 31.3545i | 1.25619i | ||||||||
\(624\) | −33.3913 | −1.33672 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −58.6698 | −2.34492 | ||||||||
\(627\) | − 1.63102i | − 0.0651368i | ||||||||
\(628\) | 14.5351i | 0.580014i | ||||||||
\(629\) | −2.50173 | −0.0997505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.8877 | −1.38886 | −0.694429 | − | 0.719562i | \(-0.744343\pi\) | ||||
−0.694429 | + | 0.719562i | \(0.744343\pi\) | |||||||
\(632\) | − 61.1232i | − 2.43135i | ||||||||
\(633\) | 8.85922i | 0.352122i | ||||||||
\(634\) | −44.4282 | −1.76447 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 28.6504 | 1.13606 | ||||||||
\(637\) | − 7.45473i | − 0.295367i | ||||||||
\(638\) | 14.6152i | 0.578622i | ||||||||
\(639\) | 7.27306 | 0.287718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.5314 | −1.52190 | −0.760949 | − | 0.648812i | \(-0.775266\pi\) | ||||
−0.760949 | + | 0.648812i | \(0.775266\pi\) | |||||||
\(642\) | 12.7289i | 0.502368i | ||||||||
\(643\) | − 18.6353i | − 0.734906i | −0.930042 | − | 0.367453i | \(-0.880230\pi\) | ||||
0.930042 | − | 0.367453i | \(-0.119770\pi\) | |||||||
\(644\) | 21.3720 | 0.842173 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.04892 | 0.237991 | ||||||||
\(647\) | − 19.2282i | − 0.755938i | −0.925818 | − | 0.377969i | \(-0.876623\pi\) | ||||
0.925818 | − | 0.377969i | \(-0.123377\pi\) | |||||||
\(648\) | 68.2247i | 2.68012i | ||||||||
\(649\) | −16.7573 | −0.657783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.8116 | 0.619706 | ||||||||
\(652\) | − 18.5386i | − 0.726026i | ||||||||
\(653\) | − 3.98553i | − 0.155966i | −0.996955 | − | 0.0779828i | \(-0.975152\pi\) | ||||
0.996955 | − | 0.0779828i | \(-0.0248479\pi\) | |||||||
\(654\) | 17.6136 | 0.688745 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 158.809 | 6.20046 | ||||||||
\(657\) | 37.0901i | 1.44702i | ||||||||
\(658\) | − 20.1347i | − 0.784931i | ||||||||
\(659\) | −33.5719 | −1.30778 | −0.653889 | − | 0.756591i | \(-0.726864\pi\) | ||||
−0.653889 | + | 0.756591i | \(0.726864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.9909 | 1.43878 | 0.719390 | − | 0.694607i | \(-0.244422\pi\) | ||||
0.719390 | + | 0.694607i | \(0.244422\pi\) | |||||||
\(662\) | 37.0834i | 1.44129i | ||||||||
\(663\) | − 3.89008i | − 0.151078i | ||||||||
\(664\) | 32.4741 | 1.26024 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.74094 | 0.338704 | ||||||||
\(667\) | 2.12631i | 0.0823310i | ||||||||
\(668\) | 27.7700i | 1.07445i | ||||||||
\(669\) | 12.8834 | 0.498100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.2747 | 1.13014 | ||||||||
\(672\) | 51.3400i | 1.98048i | ||||||||
\(673\) | 12.0747i | 0.465447i | 0.972543 | + | 0.232723i | \(0.0747637\pi\) | ||||
−0.972543 | + | 0.232723i | \(0.925236\pi\) | |||||||
\(674\) | 73.0689 | 2.81451 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.3763 | −0.552934 | ||||||||
\(677\) | − 41.9135i | − 1.61087i | −0.592686 | − | 0.805434i | \(-0.701933\pi\) | ||||
0.592686 | − | 0.805434i | \(-0.298067\pi\) | |||||||
\(678\) | 5.34183i | 0.205152i | ||||||||
\(679\) | 9.89977 | 0.379918 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.70038 | −0.371719 | ||||||||
\(682\) | − 76.9536i | − 2.94671i | ||||||||
\(683\) | 9.17092i | 0.350915i | 0.984487 | + | 0.175458i | \(0.0561405\pi\) | ||||
−0.984487 | + | 0.175458i | \(0.943859\pi\) | |||||||
\(684\) | −15.7506 | −0.602240 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 40.1866 | 1.53433 | ||||||||
\(687\) | 1.29052i | 0.0492364i | ||||||||
\(688\) | 97.7338i | 3.72606i | ||||||||
\(689\) | −28.6504 | −1.09149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.111244 | −0.00423193 | −0.00211596 | − | 0.999998i | \(-0.500674\pi\) | ||||
−0.00211596 | + | 0.999998i | \(0.500674\pi\) | |||||||
\(692\) | − 23.1879i | − 0.881472i | ||||||||
\(693\) | − 24.1226i | − 0.916341i | ||||||||
\(694\) | −25.1685 | −0.955384 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.6273 | −0.402827 | ||||||||
\(697\) | 18.5013i | 0.700785i | ||||||||
\(698\) | 1.67994i | 0.0635867i | ||||||||
\(699\) | 10.5077 | 0.397438 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.7832 | −1.04936 | −0.524678 | − | 0.851301i | \(-0.675814\pi\) | ||||
−0.524678 | + | 0.851301i | \(0.675814\pi\) | |||||||
\(702\) | 28.7385i | 1.08467i | ||||||||
\(703\) | 1.15883i | 0.0437062i | ||||||||
\(704\) | 140.943 | 5.31198 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 89.3527 | 3.36283 | ||||||||
\(707\) | 15.5265i | 0.583933i | ||||||||
\(708\) | − 18.5133i | − 0.695774i | ||||||||
\(709\) | −37.4668 | −1.40710 | −0.703548 | − | 0.710648i | \(-0.748402\pi\) | ||||
−0.703548 | + | 0.710648i | \(0.748402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.2500 | −0.571918 | ||||||||
\(712\) | 110.961i | 4.15844i | ||||||||
\(713\) | − 11.1957i | − 0.419281i | ||||||||
\(714\) | −10.2349 | −0.383031 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −82.4137 | −3.07994 | ||||||||
\(717\) | − 6.19806i | − 0.231471i | ||||||||
\(718\) | − 51.4892i | − 1.92156i | ||||||||
\(719\) | 21.0513 | 0.785081 | 0.392541 | − | 0.919735i | \(-0.371596\pi\) | ||||
0.392541 | + | 0.919735i | \(0.371596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.6329 | 1.62498 | ||||||||
\(722\) | − 2.80194i | − 0.104277i | ||||||||
\(723\) | 4.12333i | 0.153348i | ||||||||
\(724\) | 71.6805 | 2.66399 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.67324 | −0.136327 | ||||||||
\(727\) | 44.7023i | 1.65792i | 0.559310 | + | 0.828958i | \(0.311066\pi\) | ||||
−0.559310 | + | 0.828958i | \(0.688934\pi\) | |||||||
\(728\) | − 106.817i | − 3.95891i | ||||||||
\(729\) | 11.7627 | 0.435656 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.3860 | −0.421125 | ||||||||
\(732\) | 32.3424i | 1.19541i | ||||||||
\(733\) | 25.0301i | 0.924509i | 0.886747 | + | 0.462254i | \(0.152959\pi\) | ||||
−0.886747 | + | 0.462254i | \(0.847041\pi\) | |||||||
\(734\) | 41.0140 | 1.51385 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.3521 | 1.33996 | ||||||||
\(737\) | 14.6437i | 0.539407i | ||||||||
\(738\) | − 64.6426i | − 2.37953i | ||||||||
\(739\) | 23.9982 | 0.882788 | 0.441394 | − | 0.897313i | \(-0.354484\pi\) | ||||
0.441394 | + | 0.897313i | \(0.354484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.80194 | −0.0661958 | ||||||||
\(742\) | 75.3798i | 2.76728i | ||||||||
\(743\) | 10.4601i | 0.383744i | 0.981420 | + | 0.191872i | \(0.0614559\pi\) | ||||
−0.981420 | + | 0.191872i | \(0.938544\pi\) | |||||||
\(744\) | 55.9560 | 2.05145 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.87800 | −0.105371 | ||||||||
\(747\) | − 8.10215i | − 0.296442i | ||||||||
\(748\) | 37.1226i | 1.35734i | ||||||||
\(749\) | −24.9584 | −0.911959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.9420 | −1.09260 | −0.546299 | − | 0.837590i | \(-0.683964\pi\) | ||||
−0.546299 | + | 0.837590i | \(0.683964\pi\) | |||||||
\(752\) | − 43.6752i | − 1.59267i | ||||||||
\(753\) | − 8.18060i | − 0.298118i | ||||||||
\(754\) | 16.1468 | 0.588030 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 56.3497 | 2.04942 | ||||||||
\(757\) | − 27.2174i | − 0.989235i | −0.869111 | − | 0.494617i | \(-0.835308\pi\) | ||||
0.869111 | − | 0.494617i | \(-0.164692\pi\) | |||||||
\(758\) | − 63.1232i | − 2.29274i | ||||||||
\(759\) | 1.95407 | 0.0709281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.6813 | 0.677195 | 0.338598 | − | 0.940931i | \(-0.390047\pi\) | ||||
0.338598 | + | 0.940931i | \(0.390047\pi\) | |||||||
\(762\) | − 2.27247i | − 0.0823229i | ||||||||
\(763\) | 34.5362i | 1.25029i | ||||||||
\(764\) | −117.876 | −4.26459 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 91.5387 | 3.30743 | ||||||||
\(767\) | 18.5133i | 0.668478i | ||||||||
\(768\) | 61.3497i | 2.21377i | ||||||||
\(769\) | −6.34780 | −0.228907 | −0.114454 | − | 0.993429i | \(-0.536512\pi\) | ||||
−0.114454 | + | 0.993429i | \(0.536512\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.85756 | 0.0668984 | ||||||||
\(772\) | 55.7458i | 2.00634i | ||||||||
\(773\) | 49.7851i | 1.79064i | 0.445419 | + | 0.895322i | \(0.353055\pi\) | ||||
−0.445419 | + | 0.895322i | \(0.646945\pi\) | |||||||
\(774\) | 39.7821 | 1.42994 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 35.0344 | 1.25766 | ||||||||
\(777\) | − 1.96077i | − 0.0703423i | ||||||||
\(778\) | − 22.8756i | − 0.820130i | ||||||||
\(779\) | 8.57002 | 0.307053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.94033 | −0.284127 | ||||||||
\(782\) | 7.24698i | 0.259151i | ||||||||
\(783\) | 5.60627i | 0.200352i | ||||||||
\(784\) | −42.5448 | −1.51946 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −20.5714 | −0.733756 | ||||||||
\(787\) | 9.19865i | 0.327897i | 0.986469 | + | 0.163948i | \(0.0524230\pi\) | ||||
−0.986469 | + | 0.163948i | \(0.947577\pi\) | |||||||
\(788\) | 29.0388i | 1.03446i | ||||||||
\(789\) | 9.25965 | 0.329652 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.4741 | −0.372416 | ||||||||
\(792\) | − 85.3678i | − 3.03341i | ||||||||
\(793\) | − 32.3424i | − 1.14851i | ||||||||
\(794\) | −105.207 | −3.73364 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.7245 | 1.12445 | ||||||||
\(797\) | − 13.5084i | − 0.478493i | −0.970959 | − | 0.239247i | \(-0.923100\pi\) | ||||
0.970959 | − | 0.239247i | \(-0.0769004\pi\) | |||||||
\(798\) | 4.74094i | 0.167827i | ||||||||
\(799\) | 5.08815 | 0.180006 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.6843 | 0.978175 | ||||||||
\(802\) | − 90.3678i | − 3.19100i | ||||||||
\(803\) | − 40.4929i | − 1.42896i | ||||||||
\(804\) | −16.1782 | −0.570562 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −85.0176 | −2.99462 | ||||||||
\(807\) | − 8.65519i | − 0.304677i | ||||||||
\(808\) | 54.9469i | 1.93302i | ||||||||
\(809\) | −31.9560 | −1.12351 | −0.561756 | − | 0.827303i | \(-0.689874\pi\) | ||||
−0.561756 | + | 0.827303i | \(0.689874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7012 | 1.42921 | 0.714607 | − | 0.699526i | \(-0.246606\pi\) | ||||
0.714607 | + | 0.699526i | \(0.246606\pi\) | |||||||
\(812\) | − 31.6601i | − 1.11105i | ||||||||
\(813\) | − 7.33273i | − 0.257170i | ||||||||
\(814\) | −9.54288 | −0.334478 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −22.2010 | −0.777192 | ||||||||
\(817\) | 5.27413i | 0.184518i | ||||||||
\(818\) | − 88.3895i | − 3.09047i | ||||||||
\(819\) | −26.6504 | −0.931240 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4300 | −0.468709 | −0.234355 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234355 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(822\) | − 25.1497i | − 0.877198i | ||||||||
\(823\) | − 26.7275i | − 0.931663i | −0.884873 | − | 0.465832i | \(-0.845755\pi\) | ||||
0.884873 | − | 0.465832i | \(-0.154245\pi\) | |||||||
\(824\) | 154.413 | 5.37924 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 48.7090 | 1.69480 | ||||||||
\(827\) | − 33.3435i | − 1.15947i | −0.814806 | − | 0.579733i | \(-0.803157\pi\) | ||||
0.814806 | − | 0.579733i | \(-0.196843\pi\) | |||||||
\(828\) | − 18.8702i | − 0.655786i | ||||||||
\(829\) | −12.2849 | −0.426672 | −0.213336 | − | 0.976979i | \(-0.568433\pi\) | ||||
−0.213336 | + | 0.976979i | \(0.568433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.20105 | 0.249802 | ||||||||
\(832\) | − 155.712i | − 5.39835i | ||||||||
\(833\) | − 4.95646i | − 0.171731i | ||||||||
\(834\) | −20.3666 | −0.705237 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.1957 | 0.594725 | ||||||||
\(837\) | − 29.5187i | − 1.02032i | ||||||||
\(838\) | − 41.1511i | − 1.42154i | ||||||||
\(839\) | −36.9922 | −1.27711 | −0.638557 | − | 0.769575i | \(-0.720468\pi\) | ||||
−0.638557 | + | 0.769575i | \(0.720468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8501 | −0.891383 | ||||||||
\(842\) | − 42.3491i | − 1.45945i | ||||||||
\(843\) | 13.8130i | 0.475743i | ||||||||
\(844\) | −93.4016 | −3.21502 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17.7778 | −0.611212 | ||||||||
\(847\) | − 7.20237i | − 0.247477i | ||||||||
\(848\) | 163.510i | 5.61497i | ||||||||
\(849\) | 7.53750 | 0.258686 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.38835 | −0.0475922 | ||||||||
\(852\) | − 8.77240i | − 0.300537i | ||||||||
\(853\) | 7.16959i | 0.245482i | 0.992439 | + | 0.122741i | \(0.0391684\pi\) | ||||
−0.992439 | + | 0.122741i | \(0.960832\pi\) | |||||||
\(854\) | −85.0936 | −2.91184 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −88.3256 | −3.01891 | ||||||||
\(857\) | − 2.55124i | − 0.0871486i | −0.999050 | − | 0.0435743i | \(-0.986125\pi\) | ||||
0.999050 | − | 0.0435743i | \(-0.0138745\pi\) | |||||||
\(858\) | − 14.8388i | − 0.506587i | ||||||||
\(859\) | −53.9493 | −1.84073 | −0.920363 | − | 0.391065i | \(-0.872107\pi\) | ||||
−0.920363 | + | 0.391065i | \(0.872107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.5007 | −0.494181 | ||||||||
\(862\) | − 4.69873i | − 0.160039i | ||||||||
\(863\) | 21.4698i | 0.730840i | 0.930843 | + | 0.365420i | \(0.119075\pi\) | ||||
−0.930843 | + | 0.365420i | \(0.880925\pi\) | |||||||
\(864\) | 95.8467 | 3.26077 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −36.8582 | −1.25249 | ||||||||
\(867\) | 6.84787i | 0.232566i | ||||||||
\(868\) | 166.700i | 5.65817i | ||||||||
\(869\) | 16.6491 | 0.564781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1782 | 0.548178 | ||||||||
\(872\) | 122.221i | 4.13891i | ||||||||
\(873\) | − 8.74094i | − 0.295836i | ||||||||
\(874\) | 3.35690 | 0.113549 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.7362 | 1.51149 | ||||||||
\(877\) | 38.9638i | 1.31571i | 0.753144 | + | 0.657856i | \(0.228537\pi\) | ||||
−0.753144 | + | 0.657856i | \(0.771463\pi\) | |||||||
\(878\) | 18.0887i | 0.610465i | ||||||||
\(879\) | −0.708415 | −0.0238942 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.4373 | −0.452713 | −0.226357 | − | 0.974045i | \(-0.572681\pi\) | ||||
−0.226357 | + | 0.974045i | \(0.572681\pi\) | |||||||
\(882\) | 17.3177i | 0.583116i | ||||||||
\(883\) | − 27.8799i | − 0.938234i | −0.883136 | − | 0.469117i | \(-0.844572\pi\) | ||||
0.883136 | − | 0.469117i | \(-0.155428\pi\) | |||||||
\(884\) | 41.0127 | 1.37941 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −71.0877 | −2.38824 | ||||||||
\(887\) | 28.9135i | 0.970821i | 0.874286 | + | 0.485410i | \(0.161330\pi\) | ||||
−0.874286 | + | 0.485410i | \(0.838670\pi\) | |||||||
\(888\) | − 6.93900i | − 0.232858i | ||||||||
\(889\) | 4.45580 | 0.149443 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.5834 | −0.622568 | ||||||||
\(892\) | 135.828i | 4.54785i | ||||||||
\(893\) | − 2.35690i | − 0.0788705i | ||||||||
\(894\) | −17.2040 | −0.575389 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −224.659 | −7.50533 | ||||||||
\(897\) | − 2.15883i | − 0.0720814i | ||||||||
\(898\) | − 10.0858i | − 0.336566i | ||||||||
\(899\) | −16.5851 | −0.553144 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.0489 | −0.634611 | ||||||||
\(902\) | 70.5733i | 2.34983i | ||||||||
\(903\) | − 8.92394i | − 0.296970i | ||||||||
\(904\) | −37.0670 | −1.23283 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16.2379 | 0.539467 | ||||||||
\(907\) | − 30.7127i | − 1.01980i | −0.860234 | − | 0.509900i | \(-0.829683\pi\) | ||||
0.860234 | − | 0.509900i | \(-0.170317\pi\) | |||||||
\(908\) | − 102.270i | − 3.39395i | ||||||||
\(909\) | 13.7090 | 0.454699 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.3690 | 1.30435 | 0.652176 | − | 0.758067i | \(-0.273856\pi\) | ||||
0.652176 | + | 0.758067i | \(0.273856\pi\) | |||||||
\(912\) | 10.2838i | 0.340531i | ||||||||
\(913\) | 8.84548i | 0.292743i | ||||||||
\(914\) | 34.4034 | 1.13796 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.6058 | −0.449548 | ||||||||
\(917\) | − 40.3357i | − 1.33200i | ||||||||
\(918\) | 19.1075i | 0.630642i | ||||||||
\(919\) | 7.87023 | 0.259615 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.8860 | −0.589365 | ||||||||
\(922\) | − 110.658i | − 3.64434i | ||||||||
\(923\) | 8.77240i | 0.288747i | ||||||||
\(924\) | −29.0954 | −0.957170 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.5532 | 1.69414 | ||||||||
\(927\) | − 38.5254i | − 1.26534i | ||||||||
\(928\) | − 53.8514i | − 1.76776i | ||||||||
\(929\) | −39.2924 | −1.28914 | −0.644572 | − | 0.764544i | \(-0.722964\pi\) | ||||
−0.644572 | + | 0.764544i | \(0.722964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.29590 | −0.0752450 | ||||||||
\(932\) | 110.781i | 3.62876i | ||||||||
\(933\) | 6.93602i | 0.227075i | ||||||||
\(934\) | 101.509 | 3.32148 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −94.3135 | −3.08273 | ||||||||
\(937\) | 26.7554i | 0.874061i | 0.899447 | + | 0.437031i | \(0.143970\pi\) | ||||
−0.899447 | + | 0.437031i | \(0.856030\pi\) | |||||||
\(938\) | − 42.5652i | − 1.38980i | ||||||||
\(939\) | 11.6203 | 0.379213 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.9191 | −1.36653 | −0.683263 | − | 0.730173i | \(-0.739440\pi\) | ||||
−0.683263 | + | 0.730173i | \(0.739440\pi\) | |||||||
\(942\) | − 3.86294i | − 0.125861i | ||||||||
\(943\) | 10.2674i | 0.334353i | ||||||||
\(944\) | 105.657 | 3.43885 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.4319 | −1.41209 | ||||||||
\(947\) | − 55.4868i | − 1.80308i | −0.432698 | − | 0.901539i | \(-0.642438\pi\) | ||||
0.432698 | − | 0.901539i | \(-0.357562\pi\) | |||||||
\(948\) | 18.3937i | 0.597401i | ||||||||
\(949\) | −44.7362 | −1.45220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.79954 | 0.285345 | ||||||||
\(952\) | − 71.0200i | − 2.30177i | ||||||||
\(953\) | 8.48081i | 0.274720i | 0.990521 | + | 0.137360i | \(0.0438618\pi\) | ||||
−0.990521 | + | 0.137360i | \(0.956138\pi\) | |||||||
\(954\) | 66.5561 | 2.15483 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 65.3454 | 2.11342 | ||||||||
\(957\) | − 2.89472i | − 0.0935731i | ||||||||
\(958\) | − 96.1426i | − 3.10623i | ||||||||
\(959\) | 49.3129 | 1.59240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.3256 | 1.81695 | ||||||||
\(962\) | 10.5429i | 0.339916i | ||||||||
\(963\) | 22.0368i | 0.710127i | ||||||||
\(964\) | −43.4717 | −1.40013 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.67994 | −0.182749 | ||||||||
\(967\) | 7.63102i | 0.245397i | 0.992444 | + | 0.122699i | \(0.0391548\pi\) | ||||
−0.992444 | + | 0.122699i | \(0.960845\pi\) | |||||||
\(968\) | − 25.4886i | − 0.819234i | ||||||||
\(969\) | −1.19806 | −0.0384873 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.3599 | −0.621288 | −0.310644 | − | 0.950526i | \(-0.600545\pi\) | ||||
−0.310644 | + | 0.950526i | \(0.600545\pi\) | |||||||
\(972\) | − 75.9764i | − 2.43695i | ||||||||
\(973\) | − 39.9342i | − 1.28023i | ||||||||
\(974\) | 68.5695 | 2.19711 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −184.581 | −5.90829 | ||||||||
\(977\) | − 55.8883i | − 1.78802i | −0.448042 | − | 0.894012i | \(-0.647879\pi\) | ||||
0.448042 | − | 0.894012i | \(-0.352121\pi\) | |||||||
\(978\) | 4.92692i | 0.157546i | ||||||||
\(979\) | −30.2241 | −0.965968 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.4935 | 0.973582 | ||||||||
\(982\) | − 51.2941i | − 1.63686i | ||||||||
\(983\) | − 4.58450i | − 0.146223i | −0.997324 | − | 0.0731114i | \(-0.976707\pi\) | ||||
0.997324 | − | 0.0731114i | \(-0.0232929\pi\) | |||||||
\(984\) | −51.3166 | −1.63591 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.7356 | 0.341890 | ||||||||
\(987\) | 3.98792i | 0.126937i | ||||||||
\(988\) | − 18.9976i | − 0.604394i | ||||||||
\(989\) | −6.31873 | −0.200924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5666 | 0.875681 | 0.437840 | − | 0.899053i | \(-0.355743\pi\) | ||||
0.437840 | + | 0.899053i | \(0.355743\pi\) | |||||||
\(992\) | 283.544i | 9.00254i | ||||||||
\(993\) | − 7.34481i | − 0.233081i | ||||||||
\(994\) | 23.0804 | 0.732065 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.77240 | −0.309650 | ||||||||
\(997\) | − 15.9119i | − 0.503933i | −0.967736 | − | 0.251967i | \(-0.918923\pi\) | ||||
0.967736 | − | 0.251967i | \(-0.0810774\pi\) | |||||||
\(998\) | − 71.0079i | − 2.24772i | ||||||||
\(999\) | −3.66056 | −0.115815 |
(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 | 475.2.b.c.324.1 | 6 | ||
5.2 | odd | 4 | 475.2.a.h.1.3 | yes | 3 | ||
5.3 | odd | 4 | 475.2.a.d.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 475.2.b.c.324.6 | 6 | ||
15.2 | even | 4 | 4275.2.a.z.1.1 | 3 | |||
15.8 | even | 4 | 4275.2.a.bn.1.3 | 3 | |||
20.3 | even | 4 | 7600.2.a.bw.1.2 | 3 | |||
20.7 | even | 4 | 7600.2.a.bn.1.2 | 3 | |||
95.18 | even | 4 | 9025.2.a.be.1.3 | 3 | |||
95.37 | even | 4 | 9025.2.a.w.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.d.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
475.2.a.h.1.3 | yes | 3 | 5.2 | odd | 4 | ||
475.2.b.c.324.1 | 6 | 1.1 | even | 1 | trivial | ||
475.2.b.c.324.6 | 6 | 5.4 | even | 2 | inner | ||
4275.2.a.z.1.1 | 3 | 15.2 | even | 4 | |||
4275.2.a.bn.1.3 | 3 | 15.8 | even | 4 | |||
7600.2.a.bn.1.2 | 3 | 20.7 | even | 4 | |||
7600.2.a.bw.1.2 | 3 | 20.3 | even | 4 | |||
9025.2.a.w.1.1 | 3 | 95.37 | even | 4 | |||
9025.2.a.be.1.3 | 3 | 95.18 | even | 4 |