Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.1 | ||
Root | \(-0.0272949 + 1.41395i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.301 |
Dual form | 375.2.g.b.76.1 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38048 | + | 1.00297i | −0.976144 | + | 0.709210i | −0.956844 | − | 0.290604i | \(-0.906144\pi\) |
−0.0193004 | + | 0.999814i | \(0.506144\pi\) | |||||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 0.281722 | − | 0.867051i | 0.140861 | − | 0.433526i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.527295 | − | 1.62285i | −0.215267 | − | 0.662524i | ||||
\(7\) | 3.94243 | 1.49010 | 0.745049 | − | 0.667009i | \(-0.232426\pi\) | ||||
0.745049 | + | 0.667009i | \(0.232426\pi\) | |||||||
\(8\) | −0.573870 | − | 1.76619i | −0.202894 | − | 0.624442i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.78023 | − | 3.47304i | 1.44129 | − | 1.04716i | 0.453524 | − | 0.891244i | \(-0.350167\pi\) |
0.987770 | − | 0.155918i | \(-0.0498334\pi\) | |||||||
\(12\) | 0.737558 | + | 0.535867i | 0.212915 | + | 0.154692i | ||||
\(13\) | 2.66220 | + | 1.93420i | 0.738361 | + | 0.536451i | 0.892197 | − | 0.451646i | \(-0.149163\pi\) |
−0.153836 | + | 0.988096i | \(0.549163\pi\) | |||||||
\(14\) | −5.44243 | + | 3.95416i | −1.45455 | + | 1.05679i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.03877 | + | 2.93434i | 1.00969 | + | 0.733585i | ||||
\(17\) | −0.836312 | − | 2.57390i | −0.202835 | − | 0.624263i | −0.999795 | − | 0.0202310i | \(-0.993560\pi\) |
0.796960 | − | 0.604032i | \(-0.206440\pi\) | |||||||
\(18\) | 1.70636 | 0.402193 | ||||||||
\(19\) | −0.728704 | − | 2.24272i | −0.167176 | − | 0.514515i | 0.832014 | − | 0.554755i | \(-0.187188\pi\) |
−0.999190 | + | 0.0402396i | \(0.987188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.21828 | + | 3.74947i | −0.265850 | + | 0.818202i | ||||
\(22\) | −3.11562 | + | 9.58890i | −0.664253 | + | 2.04436i | ||||
\(23\) | −0.472705 | + | 0.343440i | −0.0985658 | + | 0.0716123i | −0.635977 | − | 0.771708i | \(-0.719403\pi\) |
0.537411 | + | 0.843321i | \(0.319403\pi\) | |||||||
\(24\) | 1.85708 | 0.379075 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.61505 | −1.10120 | ||||||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | 1.11067 | − | 3.41829i | 0.209897 | − | 0.645996i | ||||
\(29\) | −1.20877 | + | 3.72022i | −0.224464 | + | 0.690828i | 0.773882 | + | 0.633330i | \(0.218312\pi\) |
−0.998346 | + | 0.0574980i | \(0.981688\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.837233 | + | 2.57674i | 0.150371 | + | 0.462796i | 0.997663 | − | 0.0683330i | \(-0.0217680\pi\) |
−0.847291 | + | 0.531129i | \(0.821768\pi\) | |||||||
\(32\) | −4.80433 | −0.849294 | ||||||||
\(33\) | 1.82589 | + | 5.61950i | 0.317846 | + | 0.978229i | ||||
\(34\) | 3.73607 | + | 2.71441i | 0.640730 | + | 0.465518i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.737558 | + | 0.535867i | −0.122926 | + | 0.0893112i | ||||
\(37\) | −0.0168692 | − | 0.0122562i | −0.00277328 | − | 0.00201490i | 0.586398 | − | 0.810023i | \(-0.300546\pi\) |
−0.589171 | + | 0.808008i | \(0.700546\pi\) | |||||||
\(38\) | 3.25535 | + | 2.36515i | 0.528087 | + | 0.383678i | ||||
\(39\) | −2.66220 | + | 1.93420i | −0.426293 | + | 0.309720i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.19098 | − | 0.865300i | −0.186000 | − | 0.135137i | 0.490889 | − | 0.871222i | \(-0.336672\pi\) |
−0.676889 | + | 0.736085i | \(0.736672\pi\) | |||||||
\(42\) | −2.07882 | − | 6.39796i | −0.320769 | − | 0.987227i | ||||
\(43\) | −1.27279 | −0.194098 | −0.0970491 | − | 0.995280i | \(-0.530940\pi\) | ||||
−0.0970491 | + | 0.995280i | \(0.530940\pi\) | |||||||
\(44\) | −1.66461 | − | 5.12314i | −0.250949 | − | 0.772342i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.308096 | − | 0.948222i | 0.0454263 | − | 0.139808i | ||||
\(47\) | −1.67907 | + | 5.16764i | −0.244917 | + | 0.753777i | 0.750733 | + | 0.660606i | \(0.229701\pi\) |
−0.995650 | + | 0.0931716i | \(0.970299\pi\) | |||||||
\(48\) | −4.03877 | + | 2.93434i | −0.582947 | + | 0.423536i | ||||
\(49\) | 8.54276 | 1.22039 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.70636 | 0.378967 | ||||||||
\(52\) | 2.42705 | − | 1.76336i | 0.336571 | − | 0.244533i | ||||
\(53\) | −0.870050 | + | 2.67774i | −0.119511 | + | 0.367816i | −0.992861 | − | 0.119277i | \(-0.961942\pi\) |
0.873350 | + | 0.487092i | \(0.161942\pi\) | |||||||
\(54\) | −0.527295 | + | 1.62285i | −0.0717557 | + | 0.220841i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.26244 | − | 6.96308i | −0.302332 | − | 0.930481i | ||||
\(57\) | 2.35813 | 0.312343 | ||||||||
\(58\) | −2.06260 | − | 6.34804i | −0.270833 | − | 0.833539i | ||||
\(59\) | 3.79456 | + | 2.75691i | 0.494009 | + | 0.358919i | 0.806724 | − | 0.590928i | \(-0.201238\pi\) |
−0.312715 | + | 0.949847i | \(0.601238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.51538 | + | 3.28061i | −0.578135 | + | 0.420040i | −0.838051 | − | 0.545591i | \(-0.816305\pi\) |
0.259916 | + | 0.965631i | \(0.416305\pi\) | |||||||
\(62\) | −3.74018 | − | 2.71740i | −0.475004 | − | 0.345110i | ||||
\(63\) | −3.18949 | − | 2.31730i | −0.401838 | − | 0.291953i | ||||
\(64\) | −1.44528 | + | 1.05006i | −0.180660 | + | 0.131257i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.15681 | − | 5.92627i | −1.00403 | − | 0.729473i | ||||
\(67\) | −1.86361 | − | 5.73559i | −0.227676 | − | 0.700714i | −0.998009 | − | 0.0630725i | \(-0.979910\pi\) |
0.770333 | − | 0.637642i | \(-0.220090\pi\) | |||||||
\(68\) | −2.46731 | −0.299206 | ||||||||
\(69\) | −0.180557 | − | 0.555698i | −0.0217365 | − | 0.0668982i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.50346 | + | 7.70487i | −0.297106 | + | 0.914400i | 0.685399 | + | 0.728167i | \(0.259628\pi\) |
−0.982506 | + | 0.186232i | \(0.940372\pi\) | |||||||
\(72\) | −0.573870 | + | 1.76619i | −0.0676312 | + | 0.208147i | ||||
\(73\) | 10.7734 | − | 7.82730i | 1.26093 | − | 0.916116i | 0.262123 | − | 0.965035i | \(-0.415578\pi\) |
0.998803 | + | 0.0489187i | \(0.0155775\pi\) | |||||||
\(74\) | 0.0355801 | 0.00413611 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.14984 | −0.246604 | ||||||||
\(77\) | 18.8457 | − | 13.6922i | 2.14767 | − | 1.56037i | ||||
\(78\) | 1.73515 | − | 5.34023i | 0.196467 | − | 0.604662i | ||||
\(79\) | 5.14971 | − | 15.8492i | 0.579388 | − | 1.78317i | −0.0413379 | − | 0.999145i | \(-0.513162\pi\) |
0.620726 | − | 0.784028i | \(-0.286838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 2.51200 | 0.277404 | ||||||||
\(83\) | −0.241540 | − | 0.743385i | −0.0265125 | − | 0.0815971i | 0.936925 | − | 0.349531i | \(-0.113659\pi\) |
−0.963437 | + | 0.267934i | \(0.913659\pi\) | |||||||
\(84\) | 2.90777 | + | 2.11262i | 0.317264 | + | 0.230506i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.75705 | − | 1.27657i | 0.189468 | − | 0.137656i | ||||
\(87\) | −3.16461 | − | 2.29922i | −0.339282 | − | 0.246503i | ||||
\(88\) | −8.87728 | − | 6.44972i | −0.946322 | − | 0.687543i | ||||
\(89\) | 2.80994 | − | 2.04154i | 0.297853 | − | 0.216403i | −0.428814 | − | 0.903393i | \(-0.641068\pi\) |
0.726667 | + | 0.686990i | \(0.241068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4955 | + | 7.62545i | 1.10023 | + | 0.799364i | ||||
\(92\) | 0.164609 | + | 0.506614i | 0.0171617 | + | 0.0528182i | ||||
\(93\) | −2.70934 | −0.280946 | ||||||||
\(94\) | −2.86510 | − | 8.81786i | −0.295512 | − | 0.909493i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.48462 | − | 4.56919i | 0.151523 | − | 0.466341i | ||||
\(97\) | 0.758460 | − | 2.33430i | 0.0770099 | − | 0.237012i | −0.905139 | − | 0.425115i | \(-0.860234\pi\) |
0.982149 | + | 0.188103i | \(0.0602337\pi\) | |||||||
\(98\) | −11.7931 | + | 8.56817i | −1.19128 | + | 0.865515i | ||||
\(99\) | −5.90869 | −0.593846 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.87495 | −0.684083 | −0.342042 | − | 0.939685i | \(-0.611118\pi\) | ||||
−0.342042 | + | 0.939685i | \(0.611118\pi\) | |||||||
\(102\) | −3.73607 | + | 2.71441i | −0.369926 | + | 0.268767i | ||||
\(103\) | −3.63192 | + | 11.1779i | −0.357864 | + | 1.10139i | 0.596466 | + | 0.802638i | \(0.296571\pi\) |
−0.954330 | + | 0.298754i | \(0.903429\pi\) | |||||||
\(104\) | 1.88841 | − | 5.81193i | 0.185174 | − | 0.569906i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.48462 | − | 4.56919i | −0.144199 | − | 0.443799i | ||||
\(107\) | −5.66780 | −0.547927 | −0.273964 | − | 0.961740i | \(-0.588335\pi\) | ||||
−0.273964 | + | 0.961740i | \(0.588335\pi\) | |||||||
\(108\) | −0.281722 | − | 0.867051i | −0.0271087 | − | 0.0834321i | ||||
\(109\) | 1.10130 | + | 0.800139i | 0.105485 | + | 0.0766394i | 0.639277 | − | 0.768976i | \(-0.279234\pi\) |
−0.533792 | + | 0.845616i | \(0.679234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0168692 | − | 0.0122562i | 0.00160115 | − | 0.00116330i | ||||
\(112\) | 15.9226 | + | 11.5684i | 1.50454 | + | 1.09311i | ||||
\(113\) | −8.64489 | − | 6.28088i | −0.813243 | − | 0.590856i | 0.101526 | − | 0.994833i | \(-0.467627\pi\) |
−0.914769 | + | 0.403977i | \(0.867627\pi\) | |||||||
\(114\) | −3.25535 | + | 2.36515i | −0.304891 | + | 0.221516i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.88508 | + | 2.09614i | 0.267873 | + | 0.194621i | ||||
\(117\) | −1.01687 | − | 3.12960i | −0.0940096 | − | 0.289332i | ||||
\(118\) | −8.00341 | −0.736773 | ||||||||
\(119\) | −3.29710 | − | 10.1474i | −0.302245 | − | 0.930214i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.38941 | − | 22.7423i | 0.671765 | − | 2.06748i | ||||
\(122\) | 2.94300 | − | 9.05762i | 0.266447 | − | 0.820038i | ||||
\(123\) | 1.19098 | − | 0.865300i | 0.107387 | − | 0.0780215i | ||||
\(124\) | 2.47003 | 0.221815 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.72721 | 0.599308 | ||||||||
\(127\) | −10.9563 | + | 7.96023i | −0.972216 | + | 0.706356i | −0.955956 | − | 0.293511i | \(-0.905176\pi\) |
−0.0162606 | + | 0.999868i | \(0.505176\pi\) | |||||||
\(128\) | 3.91123 | − | 12.0375i | 0.345708 | − | 1.06398i | ||||
\(129\) | 0.393313 | − | 1.21049i | 0.0346292 | − | 0.106578i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.41912 | + | 4.36759i | 0.123989 | + | 0.381599i | 0.993716 | − | 0.111935i | \(-0.0357049\pi\) |
−0.869727 | + | 0.493534i | \(0.835705\pi\) | |||||||
\(132\) | 5.38679 | 0.468860 | ||||||||
\(133\) | −2.87286 | − | 8.84176i | −0.249109 | − | 0.766678i | ||||
\(134\) | 8.32532 | + | 6.04870i | 0.719198 | + | 0.522528i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.06607 | + | 2.95417i | −0.348662 | + | 0.253318i | ||||
\(137\) | 12.3472 | + | 8.97078i | 1.05489 | + | 0.766426i | 0.973137 | − | 0.230227i | \(-0.0739468\pi\) |
0.0817573 | + | 0.996652i | \(0.473947\pi\) | |||||||
\(138\) | 0.806606 | + | 0.586034i | 0.0686629 | + | 0.0498865i | ||||
\(139\) | −14.7550 | + | 10.7201i | −1.25150 | + | 0.909269i | −0.998308 | − | 0.0581460i | \(-0.981481\pi\) |
−0.253194 | + | 0.967416i | \(0.581481\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.39586 | − | 3.19378i | −0.370198 | − | 0.268964i | ||||
\(142\) | −4.27182 | − | 13.1473i | −0.358483 | − | 1.10330i | ||||
\(143\) | 19.4435 | 1.62595 | ||||||||
\(144\) | −1.54267 | − | 4.74786i | −0.128556 | − | 0.395655i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.02177 | + | 21.6108i | −0.581126 | + | 1.78852i | ||||
\(147\) | −2.63986 | + | 8.12464i | −0.217732 | + | 0.670109i | ||||
\(148\) | −0.0153792 | + | 0.0111736i | −0.00126416 | + | 0.000918465i | ||||
\(149\) | 14.7323 | 1.20692 | 0.603458 | − | 0.797394i | \(-0.293789\pi\) | ||||
0.603458 | + | 0.797394i | \(0.293789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.4354 | −1.41887 | −0.709437 | − | 0.704769i | \(-0.751051\pi\) | ||||
−0.709437 | + | 0.704769i | \(0.751051\pi\) | |||||||
\(152\) | −3.54289 | + | 2.57406i | −0.287366 | + | 0.208784i | ||||
\(153\) | −0.836312 | + | 2.57390i | −0.0676118 | + | 0.208088i | ||||
\(154\) | −12.2831 | + | 37.8036i | −0.989803 | + | 3.04630i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.927051 | + | 2.85317i | 0.0742235 | + | 0.228436i | ||||
\(157\) | −17.9105 | −1.42942 | −0.714708 | − | 0.699423i | \(-0.753440\pi\) | ||||
−0.714708 | + | 0.699423i | \(0.753440\pi\) | |||||||
\(158\) | 8.78728 | + | 27.0445i | 0.699078 | + | 2.15154i | ||||
\(159\) | −2.27782 | − | 1.65493i | −0.180643 | − | 0.131245i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.86361 | + | 1.35399i | −0.146873 | + | 0.106709i | ||||
\(162\) | −1.38048 | − | 1.00297i | −0.108460 | − | 0.0788011i | ||||
\(163\) | 17.6041 | + | 12.7901i | 1.37886 | + | 1.00180i | 0.996986 | + | 0.0775819i | \(0.0247199\pi\) |
0.381870 | + | 0.924216i | \(0.375280\pi\) | |||||||
\(164\) | −1.08579 | + | 0.788869i | −0.0847856 | + | 0.0616004i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.07904 | + | 0.783966i | 0.0837495 | + | 0.0608475i | ||||
\(167\) | 6.98470 | + | 21.4967i | 0.540492 | + | 1.66346i | 0.731473 | + | 0.681871i | \(0.238833\pi\) |
−0.190980 | + | 0.981594i | \(0.561167\pi\) | |||||||
\(168\) | 7.32142 | 0.564860 | ||||||||
\(169\) | −0.671052 | − | 2.06529i | −0.0516194 | − | 0.158868i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.728704 | + | 2.24272i | −0.0557254 | + | 0.171505i | ||||
\(172\) | −0.358572 | + | 1.10357i | −0.0273409 | + | 0.0841465i | ||||
\(173\) | 10.4458 | − | 7.58929i | 0.794177 | − | 0.577003i | −0.115023 | − | 0.993363i | \(-0.536694\pi\) |
0.909200 | + | 0.416360i | \(0.136694\pi\) | |||||||
\(174\) | 6.67473 | 0.506010 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 29.4974 | 2.22345 | ||||||||
\(177\) | −3.79456 | + | 2.75691i | −0.285216 | + | 0.207222i | ||||
\(178\) | −1.83144 | + | 5.63659i | −0.137272 | + | 0.422480i | ||||
\(179\) | −1.98716 | + | 6.11586i | −0.148528 | + | 0.457121i | −0.997448 | − | 0.0714002i | \(-0.977253\pi\) |
0.848920 | + | 0.528521i | \(0.177253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.54473 | + | 13.9873i | 0.337807 | + | 1.03966i | 0.965323 | + | 0.261060i | \(0.0840720\pi\) |
−0.627515 | + | 0.778604i | \(0.715928\pi\) | |||||||
\(182\) | −22.1370 | −1.64090 | ||||||||
\(183\) | −1.72472 | − | 5.30815i | −0.127495 | − | 0.392389i | ||||
\(184\) | 0.877852 | + | 0.637797i | 0.0647161 | + | 0.0470190i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.74018 | − | 2.71740i | 0.274243 | − | 0.199250i | ||||
\(187\) | −12.9370 | − | 9.39931i | −0.946050 | − | 0.687346i | ||||
\(188\) | 4.00758 | + | 2.91168i | 0.292283 | + | 0.212356i | ||||
\(189\) | 3.18949 | − | 2.31730i | 0.232001 | − | 0.168559i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.43095 | − | 3.94582i | −0.392970 | − | 0.285509i | 0.373702 | − | 0.927549i | \(-0.378088\pi\) |
−0.766671 | + | 0.642040i | \(0.778088\pi\) | |||||||
\(192\) | −0.552047 | − | 1.69903i | −0.0398406 | − | 0.122617i | ||||
\(193\) | −4.82817 | −0.347539 | −0.173769 | − | 0.984786i | \(-0.555595\pi\) | ||||
−0.173769 | + | 0.984786i | \(0.555595\pi\) | |||||||
\(194\) | 1.29421 | + | 3.98316i | 0.0929186 | + | 0.285974i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.40668 | − | 7.40701i | 0.171906 | − | 0.529072i | ||||
\(197\) | 4.44492 | − | 13.6801i | 0.316688 | − | 0.974664i | −0.658367 | − | 0.752697i | \(-0.728752\pi\) |
0.975054 | − | 0.221967i | \(-0.0712477\pi\) | |||||||
\(198\) | 8.15681 | − | 5.92627i | 0.579679 | − | 0.421161i | ||||
\(199\) | −8.72608 | −0.618575 | −0.309288 | − | 0.950969i | \(-0.600091\pi\) | ||||
−0.309288 | + | 0.950969i | \(0.600091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.03076 | 0.425377 | ||||||||
\(202\) | 9.49071 | − | 6.89540i | 0.667764 | − | 0.485159i | ||||
\(203\) | −4.76550 | + | 14.6667i | −0.334473 | + | 1.02940i | ||||
\(204\) | 0.762442 | − | 2.34656i | 0.0533816 | − | 0.164292i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.19738 | − | 19.0736i | −0.431792 | − | 1.32892i | ||||
\(207\) | 0.584296 | 0.0406114 | ||||||||
\(208\) | 5.07641 | + | 15.6236i | 0.351986 | + | 1.08330i | ||||
\(209\) | −11.2724 | − | 8.18990i | −0.779730 | − | 0.566507i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.40777 | + | 1.74935i | −0.165758 | + | 0.120430i | −0.667572 | − | 0.744546i | \(-0.732666\pi\) |
0.501814 | + | 0.864976i | \(0.332666\pi\) | |||||||
\(212\) | 2.07663 | + | 1.50876i | 0.142623 | + | 0.103622i | ||||
\(213\) | −6.55415 | − | 4.76187i | −0.449083 | − | 0.326278i | ||||
\(214\) | 7.82426 | − | 5.68466i | 0.534856 | − | 0.388595i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.50241 | − | 1.09157i | −0.102226 | − | 0.0742716i | ||||
\(217\) | 3.30073 | + | 10.1586i | 0.224068 | + | 0.689611i | ||||
\(218\) | −2.32283 | −0.157322 | ||||||||
\(219\) | 4.11505 | + | 12.6648i | 0.278070 | + | 0.855810i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.75202 | − | 8.46984i | 0.185121 | − | 0.569743i | ||||
\(222\) | −0.0109949 | + | 0.0338387i | −0.000737927 | + | 0.00227111i | ||||
\(223\) | −0.246494 | + | 0.179088i | −0.0165064 | + | 0.0119926i | −0.596008 | − | 0.802979i | \(-0.703247\pi\) |
0.579501 | + | 0.814971i | \(0.303247\pi\) | |||||||
\(224\) | −18.9408 | −1.26553 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.2336 | 1.21288 | ||||||||
\(227\) | −7.74408 | + | 5.62641i | −0.513993 | + | 0.373438i | −0.814336 | − | 0.580394i | \(-0.802899\pi\) |
0.300343 | + | 0.953831i | \(0.402899\pi\) | |||||||
\(228\) | 0.664339 | − | 2.04462i | 0.0439969 | − | 0.135409i | ||||
\(229\) | 3.74812 | − | 11.5355i | 0.247682 | − | 0.762288i | −0.747501 | − | 0.664260i | \(-0.768747\pi\) |
0.995184 | − | 0.0980277i | \(-0.0312534\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.19843 | + | 22.1545i | 0.473622 | + | 1.45766i | ||||
\(232\) | 7.26430 | 0.476924 | ||||||||
\(233\) | −6.21132 | − | 19.1165i | −0.406917 | − | 1.25236i | −0.919284 | − | 0.393595i | \(-0.871231\pi\) |
0.512367 | − | 0.858766i | \(-0.328769\pi\) | |||||||
\(234\) | 4.54267 | + | 3.30045i | 0.296964 | + | 0.215757i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.45939 | − | 2.51340i | 0.225187 | − | 0.163608i | ||||
\(237\) | 13.4821 | + | 9.79534i | 0.875758 | + | 0.636275i | ||||
\(238\) | 14.7292 | + | 10.7014i | 0.954751 | + | 0.693667i | ||||
\(239\) | −14.2902 | + | 10.3825i | −0.924358 | + | 0.671585i | −0.944605 | − | 0.328210i | \(-0.893555\pi\) |
0.0202473 | + | 0.999795i | \(0.493555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.8973 | − | 17.3624i | −1.53936 | − | 1.11841i | −0.950733 | − | 0.310010i | \(-0.899668\pi\) |
−0.588630 | − | 0.808403i | \(-0.700332\pi\) | |||||||
\(242\) | 12.6090 | + | 38.8066i | 0.810538 | + | 2.49458i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.57238 | + | 4.83929i | 0.100661 | + | 0.309804i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.776250 | + | 2.38905i | −0.0494919 | + | 0.152320i | ||||
\(247\) | 2.39791 | − | 7.38002i | 0.152576 | − | 0.469580i | ||||
\(248\) | 4.07055 | − | 2.95742i | 0.258480 | − | 0.187797i | ||||
\(249\) | 0.781641 | 0.0495345 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.89396 | 0.119546 | 0.0597729 | − | 0.998212i | \(-0.480962\pi\) | ||||
0.0597729 | + | 0.998212i | \(0.480962\pi\) | |||||||
\(252\) | −2.90777 | + | 2.11262i | −0.183172 | + | 0.133083i | ||||
\(253\) | −1.06686 | + | 3.28345i | −0.0670727 | + | 0.206429i | ||||
\(254\) | 7.14103 | − | 21.9778i | 0.448068 | − | 1.37901i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.56989 | + | 17.1424i | 0.348118 | + | 1.07140i | ||||
\(257\) | −22.1211 | −1.37988 | −0.689938 | − | 0.723869i | \(-0.742362\pi\) | ||||
−0.689938 | + | 0.723869i | \(0.742362\pi\) | |||||||
\(258\) | 0.671134 | + | 2.06554i | 0.0417830 | + | 0.128595i | ||||
\(259\) | −0.0665056 | − | 0.0483191i | −0.00413245 | − | 0.00300240i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.16461 | − | 2.29922i | 0.195884 | − | 0.142318i | ||||
\(262\) | −6.33964 | − | 4.60602i | −0.391664 | − | 0.284561i | ||||
\(263\) | −15.9500 | − | 11.5884i | −0.983520 | − | 0.714569i | −0.0250272 | − | 0.999687i | \(-0.507967\pi\) |
−0.958492 | + | 0.285118i | \(0.907967\pi\) | |||||||
\(264\) | 8.87728 | − | 6.44972i | 0.546359 | − | 0.396953i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.8340 | + | 9.32443i | 0.786902 | + | 0.571718i | ||||
\(267\) | 1.07330 | + | 3.30328i | 0.0656849 | + | 0.202157i | ||||
\(268\) | −5.49807 | −0.335848 | ||||||||
\(269\) | 5.61321 | + | 17.2757i | 0.342244 | + | 1.05332i | 0.963043 | + | 0.269348i | \(0.0868082\pi\) |
−0.620799 | + | 0.783970i | \(0.713192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.97436 | − | 21.4649i | 0.423662 | − | 1.30390i | −0.480608 | − | 0.876936i | \(-0.659584\pi\) |
0.904270 | − | 0.426962i | \(-0.140416\pi\) | |||||||
\(272\) | 4.17503 | − | 12.8494i | 0.253149 | − | 0.779111i | ||||
\(273\) | −10.4955 | + | 7.62545i | −0.635218 | + | 0.461513i | ||||
\(274\) | −26.0425 | −1.57329 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.532686 | −0.0320639 | ||||||||
\(277\) | 6.67837 | − | 4.85212i | 0.401264 | − | 0.291535i | −0.368792 | − | 0.929512i | \(-0.620228\pi\) |
0.770056 | + | 0.637977i | \(0.220228\pi\) | |||||||
\(278\) | 9.61690 | − | 29.5978i | 0.576783 | − | 1.77516i | ||||
\(279\) | 0.837233 | − | 2.57674i | 0.0501238 | − | 0.154265i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.395941 | + | 1.21858i | 0.0236199 | + | 0.0726944i | 0.962172 | − | 0.272444i | \(-0.0878320\pi\) |
−0.938552 | + | 0.345138i | \(0.887832\pi\) | |||||||
\(282\) | 9.27165 | 0.552119 | ||||||||
\(283\) | −0.825484 | − | 2.54058i | −0.0490699 | − | 0.151022i | 0.923519 | − | 0.383552i | \(-0.125299\pi\) |
−0.972589 | + | 0.232531i | \(0.925299\pi\) | |||||||
\(284\) | 5.97524 | + | 4.34126i | 0.354565 | + | 0.257607i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.8413 | + | 19.5013i | −1.58716 | + | 1.15314i | ||||
\(287\) | −4.69537 | − | 3.41138i | −0.277159 | − | 0.201368i | ||||
\(288\) | 3.88679 | + | 2.82392i | 0.229031 | + | 0.166401i | ||||
\(289\) | 7.82773 | − | 5.68718i | 0.460455 | − | 0.334540i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.98567 | + | 1.44268i | 0.116402 | + | 0.0845712i | ||||
\(292\) | −3.75158 | − | 11.5462i | −0.219545 | − | 0.675689i | ||||
\(293\) | −17.6605 | −1.03174 | −0.515870 | − | 0.856667i | \(-0.672531\pi\) | ||||
−0.515870 | + | 0.856667i | \(0.672531\pi\) | |||||||
\(294\) | −4.50455 | − | 13.8636i | −0.262711 | − | 0.808541i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.0119660 | + | 0.0368276i | −0.000695511 | + | 0.00214056i | ||||
\(297\) | 1.82589 | − | 5.61950i | 0.105949 | − | 0.326076i | ||||
\(298\) | −20.3376 | + | 14.7761i | −1.17812 | + | 0.855958i | ||||
\(299\) | −1.92272 | −0.111194 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.01787 | −0.289225 | ||||||||
\(302\) | 24.0692 | − | 17.4873i | 1.38503 | − | 1.00628i | ||||
\(303\) | 2.12448 | − | 6.53847i | 0.122048 | − | 0.375625i | ||||
\(304\) | 3.63783 | − | 11.1961i | 0.208644 | − | 0.642140i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.42705 | − | 4.39201i | −0.0815791 | − | 0.251075i | ||||
\(307\) | 28.5593 | 1.62997 | 0.814983 | − | 0.579484i | \(-0.196746\pi\) | ||||
0.814983 | + | 0.579484i | \(0.196746\pi\) | |||||||
\(308\) | −6.56260 | − | 20.1976i | −0.373939 | − | 1.15087i | ||||
\(309\) | −9.50850 | − | 6.90833i | −0.540920 | − | 0.393001i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7271 | − | 17.2388i | 1.34544 | − | 0.977521i | 0.346217 | − | 0.938154i | \(-0.387466\pi\) |
0.999225 | − | 0.0393664i | \(-0.0125340\pi\) | |||||||
\(312\) | 4.94392 | + | 3.59197i | 0.279894 | + | 0.203355i | ||||
\(313\) | −14.1523 | − | 10.2823i | −0.799937 | − | 0.581189i | 0.110958 | − | 0.993825i | \(-0.464608\pi\) |
−0.910896 | + | 0.412637i | \(0.864608\pi\) | |||||||
\(314\) | 24.7251 | − | 17.9638i | 1.39532 | − | 1.01376i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.2913 | − | 8.93013i | −0.691438 | − | 0.502359i | ||||
\(317\) | −1.21061 | − | 3.72589i | −0.0679949 | − | 0.209267i | 0.911286 | − | 0.411775i | \(-0.135091\pi\) |
−0.979281 | + | 0.202508i | \(0.935091\pi\) | |||||||
\(318\) | 4.80433 | 0.269414 | ||||||||
\(319\) | 7.14227 | + | 21.9816i | 0.399890 | + | 1.23074i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75145 | − | 5.39040i | 0.0977562 | − | 0.300863i | ||||
\(322\) | 1.21465 | − | 3.73830i | 0.0676897 | − | 0.208327i | ||||
\(323\) | −5.16312 | + | 3.75123i | −0.287284 | + | 0.208724i | ||||
\(324\) | 0.911672 | 0.0506484 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −37.1301 | −2.05645 | ||||||||
\(327\) | −1.10130 | + | 0.800139i | −0.0609018 | + | 0.0442478i | ||||
\(328\) | −0.844815 | + | 2.60007i | −0.0466471 | + | 0.143565i | ||||
\(329\) | −6.61961 | + | 20.3731i | −0.364951 | + | 1.12320i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.42429 | − | 16.6942i | −0.298146 | − | 0.917599i | −0.982147 | − | 0.188117i | \(-0.939762\pi\) |
0.684001 | − | 0.729481i | \(-0.260238\pi\) | |||||||
\(332\) | −0.712600 | −0.0391090 | ||||||||
\(333\) | 0.00644345 | + | 0.0198309i | 0.000353099 | + | 0.00108673i | ||||
\(334\) | −31.2029 | − | 22.6702i | −1.70734 | − | 1.24046i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.9226 | + | 11.5684i | −0.868648 | + | 0.631110i | ||||
\(337\) | −11.3647 | − | 8.25697i | −0.619077 | − | 0.449786i | 0.233522 | − | 0.972352i | \(-0.424975\pi\) |
−0.852599 | + | 0.522566i | \(0.824975\pi\) | |||||||
\(338\) | 2.99780 | + | 2.17803i | 0.163059 | + | 0.118469i | ||||
\(339\) | 8.64489 | − | 6.28088i | 0.469526 | − | 0.341131i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9513 | + | 9.40966i | 0.701351 | + | 0.509562i | ||||
\(342\) | −1.24343 | − | 3.82689i | −0.0672371 | − | 0.206935i | ||||
\(343\) | 6.08221 | 0.328408 | ||||||||
\(344\) | 0.730414 | + | 2.24798i | 0.0393813 | + | 0.121203i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.80826 | + | 20.9537i | −0.366014 | + | 1.12648i | ||||
\(347\) | 0.318440 | − | 0.980059i | 0.0170948 | − | 0.0526123i | −0.942145 | − | 0.335205i | \(-0.891194\pi\) |
0.959240 | + | 0.282593i | \(0.0911944\pi\) | |||||||
\(348\) | −2.88508 | + | 2.09614i | −0.154657 | + | 0.112365i | ||||
\(349\) | 21.5626 | 1.15422 | 0.577109 | − | 0.816667i | \(-0.304181\pi\) | ||||
0.577109 | + | 0.816667i | \(0.304181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.29066 | 0.175642 | ||||||||
\(352\) | −22.9658 | + | 16.6857i | −1.22408 | + | 0.889348i | ||||
\(353\) | −2.21140 | + | 6.80599i | −0.117701 | + | 0.362246i | −0.992501 | − | 0.122238i | \(-0.960993\pi\) |
0.874800 | + | 0.484485i | \(0.160993\pi\) | |||||||
\(354\) | 2.47319 | − | 7.61169i | 0.131448 | − | 0.404557i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.978498 | − | 3.01151i | −0.0518603 | − | 0.159610i | ||||
\(357\) | 10.6696 | 0.564697 | ||||||||
\(358\) | −3.39082 | − | 10.4359i | −0.179210 | − | 0.551553i | ||||
\(359\) | −21.9663 | − | 15.9595i | −1.15934 | − | 0.842308i | −0.169643 | − | 0.985506i | \(-0.554262\pi\) |
−0.989694 | + | 0.143198i | \(0.954262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8725 | − | 7.89936i | 0.572239 | − | 0.415756i | ||||
\(362\) | −20.3028 | − | 14.7508i | −1.06709 | − | 0.775285i | ||||
\(363\) | 19.3457 | + | 14.0555i | 1.01539 | + | 0.737722i | ||||
\(364\) | 9.56848 | − | 6.95191i | 0.501525 | − | 0.364379i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.70487 | + | 5.59792i | 0.402740 | + | 0.292608i | ||||
\(367\) | −6.62605 | − | 20.3929i | −0.345877 | − | 1.06450i | −0.961113 | − | 0.276157i | \(-0.910939\pi\) |
0.615236 | − | 0.788343i | \(-0.289061\pi\) | |||||||
\(368\) | −2.91692 | −0.152055 | ||||||||
\(369\) | 0.454915 | + | 1.40008i | 0.0236819 | + | 0.0728855i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.43011 | + | 10.5568i | −0.178083 | + | 0.548082i | ||||
\(372\) | −0.763282 | + | 2.34914i | −0.0395743 | + | 0.121797i | ||||
\(373\) | 5.17021 | − | 3.75638i | 0.267703 | − | 0.194498i | −0.445833 | − | 0.895116i | \(-0.647092\pi\) |
0.713536 | + | 0.700618i | \(0.247092\pi\) | |||||||
\(374\) | 27.2865 | 1.41095 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.0906 | 0.520383 | ||||||||
\(377\) | −10.4136 | + | 7.56596i | −0.536330 | + | 0.389667i | ||||
\(378\) | −2.07882 | + | 6.39796i | −0.106923 | + | 0.329076i | ||||
\(379\) | −0.0477946 | + | 0.147097i | −0.00245504 | + | 0.00755585i | −0.952277 | − | 0.305237i | \(-0.901264\pi\) |
0.949821 | + | 0.312792i | \(0.101264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.18494 | − | 12.8799i | −0.214401 | − | 0.659859i | ||||
\(382\) | 11.4549 | 0.586081 | ||||||||
\(383\) | 1.31489 | + | 4.04682i | 0.0671878 | + | 0.206783i | 0.979014 | − | 0.203794i | \(-0.0653273\pi\) |
−0.911826 | + | 0.410577i | \(0.865327\pi\) | |||||||
\(384\) | 10.2397 | + | 7.43961i | 0.522545 | + | 0.379651i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.66517 | − | 4.84253i | 0.339248 | − | 0.246478i | ||||
\(387\) | 1.02971 | + | 0.748125i | 0.0523429 | + | 0.0380293i | ||||
\(388\) | −1.81028 | − | 1.31525i | −0.0919032 | − | 0.0667716i | ||||
\(389\) | 16.4782 | − | 11.9721i | 0.835479 | − | 0.607011i | −0.0856250 | − | 0.996327i | \(-0.527289\pi\) |
0.921104 | + | 0.389316i | \(0.127289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.27931 | + | 0.929474i | 0.0646975 | + | 0.0470055i | ||||
\(392\) | −4.90243 | − | 15.0881i | −0.247610 | − | 0.762066i | ||||
\(393\) | −4.59236 | −0.231654 | ||||||||
\(394\) | 7.58465 | + | 23.3431i | 0.382109 | + | 1.17601i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.66461 | + | 5.12314i | −0.0836497 | + | 0.257447i | ||||
\(397\) | 0.604795 | − | 1.86137i | 0.0303538 | − | 0.0934194i | −0.934732 | − | 0.355354i | \(-0.884360\pi\) |
0.965086 | + | 0.261934i | \(0.0843604\pi\) | |||||||
\(398\) | 12.0461 | − | 8.75203i | 0.603818 | − | 0.438700i | ||||
\(399\) | 9.29678 | 0.465421 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.8337 | −1.63964 | −0.819818 | − | 0.572624i | \(-0.805925\pi\) | ||||
−0.819818 | + | 0.572624i | \(0.805925\pi\) | |||||||
\(402\) | −8.32532 | + | 6.04870i | −0.415229 | + | 0.301682i | ||||
\(403\) | −2.75505 | + | 8.47916i | −0.137239 | + | 0.422377i | ||||
\(404\) | −1.93683 | + | 5.96094i | −0.0963607 | + | 0.296568i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.13167 | − | 25.0267i | −0.403568 | − | 1.24206i | ||||
\(407\) | −0.123205 | −0.00610704 | ||||||||
\(408\) | −1.55310 | − | 4.77995i | −0.0768899 | − | 0.236643i | ||||
\(409\) | 32.0180 | + | 23.2624i | 1.58319 | + | 1.15025i | 0.912923 | + | 0.408132i | \(0.133820\pi\) |
0.670265 | + | 0.742122i | \(0.266180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3472 | + | 8.97078i | −0.609043 | + | 0.442496i | ||||
\(412\) | 8.66863 | + | 6.29813i | 0.427073 | + | 0.310287i | ||||
\(413\) | 14.9598 | + | 10.8689i | 0.736123 | + | 0.534825i | ||||
\(414\) | −0.806606 | + | 0.586034i | −0.0396425 | + | 0.0288020i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.7901 | − | 9.29254i | −0.627086 | − | 0.455604i | ||||
\(417\) | −5.63591 | − | 17.3455i | −0.275991 | − | 0.849414i | ||||
\(418\) | 23.7756 | 1.16290 | ||||||||
\(419\) | 6.04421 | + | 18.6022i | 0.295279 | + | 0.908776i | 0.983128 | + | 0.182921i | \(0.0585554\pi\) |
−0.687848 | + | 0.725854i | \(0.741445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4634 | + | 38.3584i | −0.607430 | + | 1.86948i | −0.128292 | + | 0.991736i | \(0.540949\pi\) |
−0.479138 | + | 0.877740i | \(0.659051\pi\) | |||||||
\(422\) | 1.56932 | − | 4.82987i | 0.0763932 | − | 0.235114i | ||||
\(423\) | 4.39586 | − | 3.19378i | 0.213734 | − | 0.155287i | ||||
\(424\) | 5.22869 | 0.253928 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.8239 | 0.669769 | ||||||||
\(427\) | −17.8016 | + | 12.9336i | −0.861478 | + | 0.625901i | ||||
\(428\) | −1.59675 | + | 4.91428i | −0.0771816 | + | 0.237540i | ||||
\(429\) | −6.00837 | + | 18.4919i | −0.290087 | + | 0.892795i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.24497 | + | 13.0647i | 0.204473 | + | 0.629304i | 0.999735 | + | 0.0230370i | \(0.00733356\pi\) |
−0.795261 | + | 0.606267i | \(0.792666\pi\) | |||||||
\(432\) | 4.99220 | 0.240187 | ||||||||
\(433\) | 3.83964 | + | 11.8172i | 0.184522 | + | 0.567899i | 0.999940 | − | 0.0109734i | \(-0.00349301\pi\) |
−0.815418 | + | 0.578872i | \(0.803493\pi\) | |||||||
\(434\) | −14.7454 | − | 10.7132i | −0.707802 | − | 0.514248i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00402 | − | 0.729464i | 0.0480839 | − | 0.0349350i | ||||
\(437\) | 1.11470 | + | 0.809879i | 0.0533234 | + | 0.0387417i | ||||
\(438\) | −18.3832 | − | 13.3562i | −0.878385 | − | 0.638184i | ||||
\(439\) | −8.87118 | + | 6.44529i | −0.423399 | + | 0.307617i | −0.779004 | − | 0.627019i | \(-0.784275\pi\) |
0.355605 | + | 0.934636i | \(0.384275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.91123 | − | 5.02131i | −0.329106 | − | 0.239110i | ||||
\(442\) | 4.69594 | + | 14.4526i | 0.223363 | + | 0.687440i | ||||
\(443\) | −8.13187 | −0.386357 | −0.193178 | − | 0.981164i | \(-0.561880\pi\) | ||||
−0.193178 | + | 0.981164i | \(0.561880\pi\) | |||||||
\(444\) | −0.00587431 | − | 0.0180793i | −0.000278783 | − | 0.000858005i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.160658 | − | 0.494454i | 0.00760737 | − | 0.0234131i | ||||
\(447\) | −4.55253 | + | 14.0112i | −0.215327 | + | 0.662709i | ||||
\(448\) | −5.69791 | + | 4.13977i | −0.269201 | + | 0.195586i | ||||
\(449\) | −32.9503 | −1.55502 | −0.777511 | − | 0.628869i | \(-0.783518\pi\) | ||||
−0.777511 | + | 0.628869i | \(0.783518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.69840 | −0.409592 | ||||||||
\(452\) | −7.88130 | + | 5.72610i | −0.370705 | + | 0.269333i | ||||
\(453\) | 5.38784 | − | 16.5821i | 0.253143 | − | 0.779093i | ||||
\(454\) | 5.04738 | − | 15.5342i | 0.236885 | − | 0.729058i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.35326 | − | 4.16491i | −0.0633723 | − | 0.195040i | ||||
\(457\) | 22.8800 | 1.07028 | 0.535142 | − | 0.844762i | \(-0.320258\pi\) | ||||
0.535142 | + | 0.844762i | \(0.320258\pi\) | |||||||
\(458\) | 6.39564 | + | 19.6838i | 0.298849 | + | 0.919762i | ||||
\(459\) | −2.18949 | − | 1.59076i | −0.102197 | − | 0.0742503i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.74259 | + | 7.07841i | −0.453758 | + | 0.329674i | −0.791078 | − | 0.611716i | \(-0.790480\pi\) |
0.337320 | + | 0.941390i | \(0.390480\pi\) | |||||||
\(462\) | −32.1576 | − | 23.3639i | −1.49611 | − | 1.08699i | ||||
\(463\) | −22.0054 | − | 15.9878i | −1.02268 | − | 0.743018i | −0.0558471 | − | 0.998439i | \(-0.517786\pi\) |
−0.966830 | + | 0.255421i | \(0.917786\pi\) | |||||||
\(464\) | −15.7984 | + | 11.4782i | −0.733420 | + | 0.532861i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.7479 | + | 20.1600i | 1.28540 | + | 0.933895i | ||||
\(467\) | 1.21828 | + | 3.74947i | 0.0563752 | + | 0.173505i | 0.975279 | − | 0.220976i | \(-0.0709243\pi\) |
−0.918904 | + | 0.394481i | \(0.870924\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −7.34714 | − | 22.6122i | −0.339259 | − | 1.04413i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.53466 | − | 17.0339i | 0.255024 | − | 0.784882i | ||||
\(472\) | 2.69164 | − | 8.28402i | 0.123893 | − | 0.381303i | ||||
\(473\) | −6.08421 | + | 4.42044i | −0.279752 | + | 0.203252i | ||||
\(474\) | −28.4362 | −1.30612 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.72721 | −0.445846 | ||||||||
\(477\) | 2.27782 | − | 1.65493i | 0.104294 | − | 0.0757742i | ||||
\(478\) | 9.31397 | − | 28.6655i | 0.426011 | − | 1.31113i | ||||
\(479\) | 6.16466 | − | 18.9729i | 0.281670 | − | 0.866893i | −0.705706 | − | 0.708504i | \(-0.749370\pi\) |
0.987377 | − | 0.158388i | \(-0.0506298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0212032 | − | 0.0652567i | −0.000966783 | − | 0.00297545i | ||||
\(482\) | 50.4038 | 2.29583 | ||||||||
\(483\) | −0.711834 | − | 2.19080i | −0.0323896 | − | 0.0996849i | ||||
\(484\) | −17.6370 | − | 12.8140i | −0.801680 | − | 0.582455i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.38048 | − | 1.00297i | 0.0626197 | − | 0.0454958i | ||||
\(487\) | −8.90102 | − | 6.46697i | −0.403344 | − | 0.293046i | 0.367558 | − | 0.930001i | \(-0.380194\pi\) |
−0.770902 | + | 0.636954i | \(0.780194\pi\) | |||||||
\(488\) | 8.38543 | + | 6.09237i | 0.379591 | + | 0.275789i | ||||
\(489\) | −17.6041 | + | 12.7901i | −0.796083 | + | 0.578388i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9348 | + | 19.5693i | 1.21555 | + | 0.883151i | 0.995723 | − | 0.0923876i | \(-0.0294499\pi\) |
0.219830 | + | 0.975538i | \(0.429450\pi\) | |||||||
\(492\) | −0.414733 | − | 1.27642i | −0.0186976 | − | 0.0575453i | ||||
\(493\) | 10.5864 | 0.476788 | ||||||||
\(494\) | 4.09171 | + | 12.5930i | 0.184095 | + | 0.566585i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.17963 | + | 12.8636i | −0.187671 | + | 0.577592i | ||||
\(497\) | −9.86973 | + | 30.3759i | −0.442718 | + | 1.36255i | ||||
\(498\) | −1.07904 | + | 0.783966i | −0.0483528 | + | 0.0351303i | ||||
\(499\) | −41.1448 | −1.84189 | −0.920946 | − | 0.389690i | \(-0.872582\pi\) | ||||
−0.920946 | + | 0.389690i | \(0.872582\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.6030 | −1.00983 | ||||||||
\(502\) | −2.61457 | + | 1.89960i | −0.116694 | + | 0.0847832i | ||||
\(503\) | −9.91207 | + | 30.5062i | −0.441958 | + | 1.36021i | 0.443829 | + | 0.896112i | \(0.353620\pi\) |
−0.885786 | + | 0.464094i | \(0.846380\pi\) | |||||||
\(504\) | −2.26244 | + | 6.96308i | −0.100777 | + | 0.310160i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.82044 | − | 5.60275i | −0.0809286 | − | 0.249073i | ||||
\(507\) | 2.17157 | 0.0964429 | ||||||||
\(508\) | 3.81529 | + | 11.7423i | 0.169276 | + | 0.520979i | ||||
\(509\) | 21.9206 | + | 15.9262i | 0.971612 | + | 0.705918i | 0.955818 | − | 0.293958i | \(-0.0949725\pi\) |
0.0157938 | + | 0.999875i | \(0.494972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.4732 | − | 30.8586i | 1.87890 | − | 1.36510i | ||||
\(512\) | −4.40295 | − | 3.19893i | −0.194585 | − | 0.141374i | ||||
\(513\) | −1.90777 | − | 1.38608i | −0.0842301 | − | 0.0611968i | ||||
\(514\) | 30.5376 | − | 22.1869i | 1.34696 | − | 0.978622i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.938754 | − | 0.682045i | −0.0413263 | − | 0.0300253i | ||||
\(517\) | 9.92109 | + | 30.5340i | 0.436329 | + | 1.34288i | ||||
\(518\) | 0.140272 | 0.00616321 | ||||||||
\(519\) | 3.98993 | + | 12.2797i | 0.175138 | + | 0.539020i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.02073 | − | 24.6853i | 0.351395 | − | 1.08148i | −0.606676 | − | 0.794949i | \(-0.707497\pi\) |
0.958071 | − | 0.286532i | \(-0.0925026\pi\) | |||||||
\(522\) | −2.06260 | + | 6.34804i | −0.0902778 | + | 0.277846i | ||||
\(523\) | −1.45123 | + | 1.05438i | −0.0634577 | + | 0.0461047i | −0.619062 | − | 0.785342i | \(-0.712487\pi\) |
0.555604 | + | 0.831447i | \(0.312487\pi\) | |||||||
\(524\) | 4.18673 | 0.182898 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.6414 | 1.46684 | ||||||||
\(527\) | 5.93209 | − | 4.30991i | 0.258406 | − | 0.187743i | ||||
\(528\) | −9.11519 | + | 28.0537i | −0.396688 | + | 1.22088i | ||||
\(529\) | −7.00189 | + | 21.5496i | −0.304430 | + | 0.936939i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.44939 | − | 4.46077i | −0.0628983 | − | 0.193581i | ||||
\(532\) | −8.47561 | −0.367464 | ||||||||
\(533\) | −1.49697 | − | 4.60720i | −0.0648410 | − | 0.199560i | ||||
\(534\) | −4.79477 | − | 3.48361i | −0.207490 | − | 0.150750i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.06068 | + | 6.58297i | −0.391362 | + | 0.284341i | ||||
\(537\) | −5.20246 | − | 3.77981i | −0.224503 | − | 0.163111i | ||||
\(538\) | −25.0760 | − | 18.2188i | −1.08110 | − | 0.785467i | ||||
\(539\) | 40.8364 | − | 29.6693i | 1.75895 | − | 1.27795i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.01538 | + | 4.37043i | 0.258621 | + | 0.187899i | 0.709539 | − | 0.704666i | \(-0.248903\pi\) |
−0.450918 | + | 0.892566i | \(0.648903\pi\) | |||||||
\(542\) | 11.9008 | + | 36.6268i | 0.511182 | + | 1.57326i | ||||
\(543\) | −14.7071 | −0.631141 | ||||||||
\(544\) | 4.01792 | + | 12.3659i | 0.172267 | + | 0.530183i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.84070 | − | 21.0535i | 0.292755 | − | 0.901007i | ||||
\(547\) | −6.02174 | + | 18.5330i | −0.257471 | + | 0.792414i | 0.735862 | + | 0.677132i | \(0.236777\pi\) |
−0.993333 | + | 0.115283i | \(0.963223\pi\) | |||||||
\(548\) | 11.2566 | − | 8.17841i | 0.480859 | − | 0.349364i | ||||
\(549\) | 5.58132 | 0.238205 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.22425 | 0.392966 | ||||||||
\(552\) | −0.877852 | + | 0.637797i | −0.0373639 | + | 0.0271464i | ||||
\(553\) | 20.3024 | − | 62.4843i | 0.863345 | − | 2.65710i | ||||
\(554\) | −4.35277 | + | 13.3965i | −0.184932 | + | 0.569161i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.13810 | + | 15.8134i | 0.217904 | + | 0.670639i | ||||
\(557\) | 26.3285 | 1.11557 | 0.557787 | − | 0.829984i | \(-0.311650\pi\) | ||||
0.557787 | + | 0.829984i | \(0.311650\pi\) | |||||||
\(558\) | 1.42862 | + | 4.39685i | 0.0604784 | + | 0.186133i | ||||
\(559\) | −3.38841 | − | 2.46182i | −0.143314 | − | 0.104124i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9370 | − | 9.39931i | 0.546202 | − | 0.396839i | ||||
\(562\) | −1.76879 | − | 1.28510i | −0.0746120 | − | 0.0542088i | ||||
\(563\) | 29.7482 | + | 21.6134i | 1.25374 | + | 0.910895i | 0.998433 | − | 0.0559656i | \(-0.0178237\pi\) |
0.255306 | + | 0.966860i | \(0.417824\pi\) | |||||||
\(564\) | −4.00758 | + | 2.91168i | −0.168749 | + | 0.122604i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.68770 | + | 2.67927i | 0.155005 | + | 0.112618i | ||||
\(567\) | 1.21828 | + | 3.74947i | 0.0511629 | + | 0.157463i | ||||
\(568\) | 15.0449 | 0.631271 | ||||||||
\(569\) | −11.2118 | − | 34.5065i | −0.470025 | − | 1.44659i | −0.852552 | − | 0.522643i | \(-0.824946\pi\) |
0.382527 | − | 0.923944i | \(-0.375054\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.03966 | + | 3.19975i | −0.0435085 | + | 0.133906i | −0.970451 | − | 0.241298i | \(-0.922427\pi\) |
0.926943 | + | 0.375203i | \(0.122427\pi\) | |||||||
\(572\) | 5.47766 | − | 16.8585i | 0.229032 | − | 0.704889i | ||||
\(573\) | 5.43095 | − | 3.94582i | 0.226881 | − | 0.164839i | ||||
\(574\) | 9.90337 | 0.413359 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.78646 | 0.0744359 | ||||||||
\(577\) | −5.56961 | + | 4.04656i | −0.231866 | + | 0.168461i | −0.697652 | − | 0.716437i | \(-0.745772\pi\) |
0.465786 | + | 0.884898i | \(0.345772\pi\) | |||||||
\(578\) | −5.10190 | + | 15.7020i | −0.212211 | + | 0.653118i | ||||
\(579\) | 1.49199 | − | 4.59186i | 0.0620048 | − | 0.190831i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.952256 | − | 2.93074i | −0.0395062 | − | 0.121588i | ||||
\(582\) | −4.18814 | −0.173604 | ||||||||
\(583\) | 5.14086 | + | 15.8219i | 0.212913 | + | 0.655278i | ||||
\(584\) | −20.0070 | − | 14.5359i | −0.827895 | − | 0.601501i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.3800 | − | 17.7131i | 1.00713 | − | 0.731720i | ||||
\(587\) | −11.9230 | − | 8.66258i | −0.492116 | − | 0.357543i | 0.313882 | − | 0.949462i | \(-0.398370\pi\) |
−0.805997 | + | 0.591919i | \(0.798370\pi\) | |||||||
\(588\) | 6.30078 | + | 4.57778i | 0.259840 | + | 0.188785i | ||||
\(589\) | 5.16880 | − | 3.75536i | 0.212977 | − | 0.154737i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.6370 | + | 8.45474i | 0.478680 | + | 0.347782i | ||||
\(592\) | −0.0321670 | − | 0.0989998i | −0.00132206 | − | 0.00406887i | ||||
\(593\) | −5.82561 | −0.239229 | −0.119615 | − | 0.992820i | \(-0.538166\pi\) | ||||
−0.119615 | + | 0.992820i | \(0.538166\pi\) | |||||||
\(594\) | 3.11562 | + | 9.58890i | 0.127836 | + | 0.393437i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.15041 | − | 12.7737i | 0.170008 | − | 0.523230i | ||||
\(597\) | 2.69651 | − | 8.29899i | 0.110361 | − | 0.339655i | ||||
\(598\) | 2.65426 | − | 1.92844i | 0.108541 | − | 0.0788596i | ||||
\(599\) | −27.1527 | −1.10943 | −0.554715 | − | 0.832040i | \(-0.687173\pi\) | ||||
−0.554715 | + | 0.832040i | \(0.687173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.9140 | 0.853101 | 0.426551 | − | 0.904464i | \(-0.359729\pi\) | ||||
0.426551 | + | 0.904464i | \(0.359729\pi\) | |||||||
\(602\) | 6.92705 | − | 5.03280i | 0.282326 | − | 0.205121i | ||||
\(603\) | −1.86361 | + | 5.73559i | −0.0758919 | + | 0.233571i | ||||
\(604\) | −4.91194 | + | 15.1174i | −0.199864 | + | 0.615118i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.62513 | + | 11.1570i | 0.147261 | + | 0.453222i | ||||
\(607\) | −1.46424 | −0.0594318 | −0.0297159 | − | 0.999558i | \(-0.509460\pi\) | ||||
−0.0297159 | + | 0.999558i | \(0.509460\pi\) | |||||||
\(608\) | 3.50094 | + | 10.7748i | 0.141982 | + | 0.436975i | ||||
\(609\) | −12.4762 | − | 9.06453i | −0.505563 | − | 0.367313i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.4653 | + | 10.5096i | −0.585202 | + | 0.425174i | ||||
\(612\) | 1.99610 | + | 1.45025i | 0.0806875 | + | 0.0586229i | ||||
\(613\) | 28.0814 | + | 20.4023i | 1.13420 | + | 0.824041i | 0.986300 | − | 0.164962i | \(-0.0527501\pi\) |
0.147896 | + | 0.989003i | \(0.452750\pi\) | |||||||
\(614\) | −39.4255 | + | 28.6443i | −1.59108 | + | 1.15599i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −34.9981 | − | 25.4276i | −1.41011 | − | 1.02451i | ||||
\(617\) | −12.9490 | − | 39.8529i | −0.521307 | − | 1.60442i | −0.771506 | − | 0.636222i | \(-0.780496\pi\) |
0.250199 | − | 0.968194i | \(-0.419504\pi\) | |||||||
\(618\) | 20.0551 | 0.806736 | ||||||||
\(619\) | −5.79758 | − | 17.8431i | −0.233025 | − | 0.717176i | −0.997377 | − | 0.0723776i | \(-0.976941\pi\) |
0.764353 | − | 0.644798i | \(-0.223059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.180557 | + | 0.555698i | −0.00724551 | + | 0.0222994i | ||||
\(622\) | −15.4647 | + | 47.5954i | −0.620077 | + | 1.90840i | ||||
\(623\) | 11.0780 | − | 8.04863i | 0.443830 | − | 0.322461i | ||||
\(624\) | −16.4276 | −0.657631 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 29.8498 | 1.19304 | ||||||||
\(627\) | 11.2724 | − | 8.18990i | 0.450177 | − | 0.327073i | ||||
\(628\) | −5.04579 | + | 15.5294i | −0.201349 | + | 0.619689i | ||||
\(629\) | −0.0174383 | + | 0.0536696i | −0.000695311 | + | 0.00213995i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.05583 | + | 9.40488i | 0.121651 | + | 0.374402i | 0.993276 | − | 0.115770i | \(-0.0369337\pi\) |
−0.871625 | + | 0.490173i | \(0.836934\pi\) | |||||||
\(632\) | −30.9479 | −1.23104 | ||||||||
\(633\) | −0.919687 | − | 2.83050i | −0.0365543 | − | 0.112502i | ||||
\(634\) | 5.40820 | + | 3.92928i | 0.214787 | + | 0.156052i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.07663 | + | 1.50876i | −0.0823436 | + | 0.0598261i | ||||
\(637\) | 22.7425 | + | 16.5234i | 0.901091 | + | 0.654681i | ||||
\(638\) | −31.9068 | − | 23.1816i | −1.26320 | − | 0.917769i | ||||
\(639\) | 6.55415 | − | 4.76187i | 0.259278 | − | 0.188377i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.46647 | + | 1.06546i | 0.0579223 | + | 0.0420830i | 0.616370 | − | 0.787457i | \(-0.288603\pi\) |
−0.558447 | + | 0.829540i | \(0.688603\pi\) | |||||||
\(642\) | 2.98860 | + | 9.19797i | 0.117951 | + | 0.363015i | ||||
\(643\) | −45.7391 | −1.80377 | −0.901886 | − | 0.431974i | \(-0.857817\pi\) | ||||
−0.901886 | + | 0.431974i | \(0.857817\pi\) | |||||||
\(644\) | 0.648959 | + | 1.99729i | 0.0255726 | + | 0.0787043i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.36518 | − | 10.3570i | 0.132401 | − | 0.407489i | ||||
\(647\) | 7.93466 | − | 24.4204i | 0.311944 | − | 0.960064i | −0.665050 | − | 0.746798i | \(-0.731590\pi\) |
0.976994 | − | 0.213266i | \(-0.0684101\pi\) | |||||||
\(648\) | 1.50241 | − | 1.09157i | 0.0590203 | − | 0.0428807i | ||||
\(649\) | 27.7137 | 1.08786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6814 | −0.418637 | ||||||||
\(652\) | 16.0491 | − | 11.6604i | 0.628532 | − | 0.456655i | ||||
\(653\) | −11.1148 | + | 34.2079i | −0.434957 | + | 1.33866i | 0.458173 | + | 0.888863i | \(0.348504\pi\) |
−0.893130 | + | 0.449798i | \(0.851496\pi\) | |||||||
\(654\) | 0.717795 | − | 2.20914i | 0.0280680 | − | 0.0863844i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.27103 | − | 6.98950i | −0.0886687 | − | 0.272894i | ||||
\(657\) | −13.3166 | −0.519530 | ||||||||
\(658\) | −11.2954 | − | 34.7638i | −0.440342 | − | 1.35523i | ||||
\(659\) | 25.9633 | + | 18.8635i | 1.01139 | + | 0.734816i | 0.964500 | − | 0.264084i | \(-0.0850696\pi\) |
0.0468880 | + | 0.998900i | \(0.485070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.1113 | + | 9.52591i | −0.509970 | + | 0.370515i | −0.812812 | − | 0.582526i | \(-0.802064\pi\) |
0.302842 | + | 0.953041i | \(0.402064\pi\) | |||||||
\(662\) | 24.2320 | + | 17.6056i | 0.941803 | + | 0.684260i | ||||
\(663\) | 7.20487 | + | 5.23465i | 0.279814 | + | 0.203297i | ||||
\(664\) | −1.17435 | + | 0.853212i | −0.0455734 | + | 0.0331110i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0287849 | − | 0.0209135i | −0.00111539 | − | 0.000810381i | ||||
\(667\) | −0.706281 | − | 2.17371i | −0.0273473 | − | 0.0841663i | ||||
\(668\) | 20.6065 | 0.797289 | ||||||||
\(669\) | −0.0941522 | − | 0.289771i | −0.00364014 | − | 0.0112032i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.1908 | + | 31.3642i | −0.393413 | + | 1.21080i | ||||
\(672\) | 5.85301 | − | 18.0137i | 0.225785 | − | 0.694895i | ||||
\(673\) | 27.6367 | − | 20.0792i | 1.06531 | − | 0.773997i | 0.0902506 | − | 0.995919i | \(-0.471233\pi\) |
0.975064 | + | 0.221922i | \(0.0712332\pi\) | |||||||
\(674\) | 23.9703 | 0.923301 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.97976 | −0.0761446 | ||||||||
\(677\) | 7.42284 | − | 5.39301i | 0.285283 | − | 0.207270i | −0.435935 | − | 0.899978i | \(-0.643582\pi\) |
0.721218 | + | 0.692708i | \(0.243582\pi\) | |||||||
\(678\) | −5.63450 | + | 17.3412i | −0.216392 | + | 0.665985i | ||||
\(679\) | 2.99017 | − | 9.20281i | 0.114752 | − | 0.353171i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.95798 | − | 9.10372i | −0.113350 | − | 0.348855i | ||||
\(682\) | −27.3166 | −1.04601 | ||||||||
\(683\) | −6.02604 | − | 18.5463i | −0.230580 | − | 0.709653i | −0.997677 | − | 0.0681215i | \(-0.978299\pi\) |
0.767097 | − | 0.641531i | \(-0.221701\pi\) | |||||||
\(684\) | 1.73926 | + | 1.26365i | 0.0665023 | + | 0.0483168i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.39634 | + | 6.10030i | −0.320574 | + | 0.232910i | ||||
\(687\) | 9.81269 | + | 7.12934i | 0.374378 | + | 0.272001i | ||||
\(688\) | −5.14050 | − | 3.73479i | −0.195980 | − | 0.142387i | ||||
\(689\) | −7.49553 | + | 5.44582i | −0.285557 | + | 0.207469i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.4986 | − | 17.0727i | −0.893927 | − | 0.649476i | 0.0429718 | − | 0.999076i | \(-0.486317\pi\) |
−0.936899 | + | 0.349600i | \(0.886317\pi\) | |||||||
\(692\) | −3.63750 | − | 11.1951i | −0.138277 | − | 0.425573i | ||||
\(693\) | −23.2946 | −0.884889 | ||||||||
\(694\) | 0.543375 | + | 1.67234i | 0.0206262 | + | 0.0634810i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.24479 | + | 6.90876i | −0.0850886 | + | 0.261876i | ||||
\(697\) | −1.23116 | + | 3.78914i | −0.0466337 | + | 0.143524i | ||||
\(698\) | −29.7666 | + | 21.6267i | −1.12668 | + | 0.818583i | ||||
\(699\) | 20.1002 | 0.760261 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4085 | −0.770820 | −0.385410 | − | 0.922745i | \(-0.625940\pi\) | ||||
−0.385410 | + | 0.922745i | \(0.625940\pi\) | |||||||
\(702\) | −4.54267 | + | 3.30045i | −0.171452 | + | 0.124567i | ||||
\(703\) | −0.0151945 | + | 0.0467640i | −0.000573073 | + | 0.00176374i | ||||
\(704\) | −3.26188 | + | 10.0390i | −0.122937 | + | 0.378360i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.77345 | − | 11.6135i | −0.142016 | − | 0.437079i | ||||
\(707\) | −27.1040 | −1.01935 | ||||||||
\(708\) | 1.32137 | + | 4.06676i | 0.0496601 | + | 0.152838i | ||||
\(709\) | −13.3334 | − | 9.68727i | −0.500746 | − | 0.363813i | 0.308556 | − | 0.951206i | \(-0.400154\pi\) |
−0.809302 | + | 0.587393i | \(0.800154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.4821 | + | 9.79534i | −0.505619 | + | 0.367354i | ||||
\(712\) | −5.21829 | − | 3.79131i | −0.195564 | − | 0.142085i | ||||
\(713\) | −1.28072 | − | 0.930497i | −0.0479633 | − | 0.0348474i | ||||
\(714\) | −14.7292 | + | 10.7014i | −0.551226 | + | 0.400489i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.74294 | + | 3.44595i | 0.177252 | + | 0.128781i | ||||
\(717\) | −5.45838 | − | 16.7992i | −0.203847 | − | 0.627376i | ||||
\(718\) | 46.3309 | 1.72905 | ||||||||
\(719\) | 9.60466 | + | 29.5601i | 0.358193 | + | 1.10241i | 0.954135 | + | 0.299378i | \(0.0967791\pi\) |
−0.595941 | + | 0.803028i | \(0.703221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.3186 | + | 44.0681i | −0.533253 | + | 1.64118i | ||||
\(722\) | −7.08642 | + | 21.8098i | −0.263729 | + | 0.811675i | ||||
\(723\) | 23.8973 | − | 17.3624i | 0.888752 | − | 0.645716i | ||||
\(724\) | 13.4080 | 0.498305 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −40.8036 | −1.51436 | ||||||||
\(727\) | −0.771033 | + | 0.560188i | −0.0285960 | + | 0.0207762i | −0.601991 | − | 0.798503i | \(-0.705626\pi\) |
0.573395 | + | 0.819279i | \(0.305626\pi\) | |||||||
\(728\) | 7.44492 | − | 22.9131i | 0.275927 | − | 0.849217i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.06445 | + | 3.27603i | 0.0393700 | + | 0.121168i | ||||
\(732\) | −5.08833 | −0.188070 | ||||||||
\(733\) | 4.75118 | + | 14.6226i | 0.175489 | + | 0.540099i | 0.999655 | − | 0.0262485i | \(-0.00835612\pi\) |
−0.824167 | + | 0.566347i | \(0.808356\pi\) | |||||||
\(734\) | 29.6006 | + | 21.5061i | 1.09258 | + | 0.793806i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.27103 | − | 1.65000i | 0.0837114 | − | 0.0608199i | ||||
\(737\) | −28.8284 | − | 20.9451i | −1.06191 | − | 0.771522i | ||||
\(738\) | −2.03225 | − | 1.47651i | −0.0748081 | − | 0.0543513i | ||||
\(739\) | −4.20110 | + | 3.05228i | −0.154540 | + | 0.112280i | −0.662368 | − | 0.749179i | \(-0.730449\pi\) |
0.507828 | + | 0.861458i | \(0.330449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.27782 | + | 4.56110i | 0.230622 | + | 0.167556i | ||||
\(742\) | −5.85301 | − | 18.0137i | −0.214871 | − | 0.661305i | ||||
\(743\) | 42.3399 | 1.55330 | 0.776650 | − | 0.629932i | \(-0.216917\pi\) | ||||
0.776650 | + | 0.629932i | \(0.216917\pi\) | |||||||
\(744\) | 1.55481 | + | 4.78521i | 0.0570021 | + | 0.175434i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.36980 | + | 10.3712i | −0.123377 | + | 0.379716i | ||||
\(747\) | −0.241540 | + | 0.743385i | −0.00883750 | + | 0.0271990i | ||||
\(748\) | −11.7943 | + | 8.56909i | −0.431244 | + | 0.313317i | ||||
\(749\) | −22.3449 | −0.816465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2461 | 0.811773 | 0.405887 | − | 0.913923i | \(-0.366963\pi\) | ||||
0.405887 | + | 0.913923i | \(0.366963\pi\) | |||||||
\(752\) | −21.9450 | + | 15.9440i | −0.800251 | + | 0.581416i | ||||
\(753\) | −0.585267 | + | 1.80127i | −0.0213283 | + | 0.0656418i | ||||
\(754\) | 6.78733 | − | 20.8892i | 0.247180 | − | 0.760741i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.11067 | − | 3.41829i | −0.0403947 | − | 0.124322i | ||||
\(757\) | 9.27680 | 0.337171 | 0.168585 | − | 0.985687i | \(-0.446080\pi\) | ||||
0.168585 | + | 0.985687i | \(0.446080\pi\) | |||||||
\(758\) | −0.0815549 | − | 0.251000i | −0.00296221 | − | 0.00911674i | ||||
\(759\) | −2.79307 | − | 2.02928i | −0.101382 | − | 0.0736583i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0868 | − | 10.2346i | 0.510644 | − | 0.371005i | −0.302424 | − | 0.953174i | \(-0.597796\pi\) |
0.813068 | + | 0.582169i | \(0.197796\pi\) | |||||||
\(762\) | 18.6954 | + | 13.5830i | 0.677265 | + | 0.492062i | ||||
\(763\) | 4.34178 | + | 3.15449i | 0.157183 | + | 0.114200i | ||||
\(764\) | −4.95125 | + | 3.59729i | −0.179130 | + | 0.130145i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.87403 | − | 4.26773i | −0.212237 | − | 0.154200i | ||||
\(767\) | 4.76945 | + | 14.6789i | 0.172215 | + | 0.530023i | ||||
\(768\) | −18.0245 | −0.650404 | ||||||||
\(769\) | −7.16648 | − | 22.0562i | −0.258430 | − | 0.795365i | −0.993134 | − | 0.116978i | \(-0.962679\pi\) |
0.734705 | − | 0.678387i | \(-0.237321\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.83579 | − | 21.0384i | 0.246185 | − | 0.757680i | ||||
\(772\) | −1.36020 | + | 4.18627i | −0.0489547 | + | 0.150667i | ||||
\(773\) | −4.45605 | + | 3.23751i | −0.160273 | + | 0.116445i | −0.665031 | − | 0.746816i | \(-0.731582\pi\) |
0.504758 | + | 0.863261i | \(0.331582\pi\) | |||||||
\(774\) | −2.17183 | −0.0780650 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.55807 | −0.163625 | ||||||||
\(777\) | 0.0665056 | − | 0.0483191i | 0.00238587 | − | 0.00173344i | ||||
\(778\) | −10.7401 | + | 33.0545i | −0.385049 | + | 1.18506i | ||||
\(779\) | −1.07275 | + | 3.30159i | −0.0384353 | + | 0.118292i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.7922 | + | 45.5257i | 0.529306 | + | 1.62904i | ||||
\(782\) | −2.69830 | −0.0964909 | ||||||||
\(783\) | 1.20877 | + | 3.72022i | 0.0431980 | + | 0.132950i | ||||
\(784\) | 34.5023 | + | 25.0674i | 1.23222 | + | 0.895263i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.33964 | − | 4.60602i | 0.226128 | − | 0.164291i | ||||
\(787\) | 20.8703 | + | 15.1632i | 0.743946 | + | 0.540509i | 0.893944 | − | 0.448178i | \(-0.147927\pi\) |
−0.149998 | + | 0.988686i | \(0.547927\pi\) | |||||||
\(788\) | −10.6091 | − | 7.70795i | −0.377933 | − | 0.274584i | ||||
\(789\) | 15.9500 | − | 11.5884i | 0.567835 | − | 0.412556i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.0819 | − | 24.7619i | −1.21181 | − | 0.880433i | ||||
\(792\) | 3.39082 | + | 10.4359i | 0.120488 | + | 0.370823i | ||||
\(793\) | −18.3662 | −0.652203 | ||||||||
\(794\) | 1.03200 | + | 3.17617i | 0.0366243 | + | 0.112718i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.45833 | + | 7.56596i | −0.0871331 | + | 0.268168i | ||||
\(797\) | −1.14642 | + | 3.52831i | −0.0406082 | + | 0.124979i | −0.969305 | − | 0.245860i | \(-0.920930\pi\) |
0.928697 | + | 0.370839i | \(0.120930\pi\) | |||||||
\(798\) | −12.8340 | + | 9.32443i | −0.454318 | + | 0.330081i | ||||
\(799\) | 14.7052 | 0.520233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.47327 | −0.122722 | ||||||||
\(802\) | 45.3261 | − | 32.9313i | 1.60052 | − | 1.16285i | ||||
\(803\) | 24.3146 | − | 74.8326i | 0.858043 | − | 2.64079i | ||||
\(804\) | 1.69900 | − | 5.22898i | 0.0599190 | − | 0.184412i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.70111 | − | 14.4685i | −0.165589 | − | 0.509632i | ||||
\(807\) | −18.1647 | −0.639429 | ||||||||
\(808\) | 3.94533 | + | 12.1425i | 0.138796 | + | 0.427171i | ||||
\(809\) | −30.3414 | − | 22.0443i | −1.06675 | − | 0.775037i | −0.0914219 | − | 0.995812i | \(-0.529141\pi\) |
−0.975325 | + | 0.220776i | \(0.929141\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.9041 | + | 26.8124i | −1.29588 | + | 0.941509i | −0.999906 | − | 0.0136877i | \(-0.995643\pi\) |
−0.295970 | + | 0.955197i | \(0.595643\pi\) | |||||||
\(812\) | 11.3742 | + | 8.26387i | 0.399158 | + | 0.290005i | ||||
\(813\) | 18.2591 | + | 13.2660i | 0.640375 | + | 0.465260i | ||||
\(814\) | 0.170081 | − | 0.123571i | 0.00596135 | − | 0.00433117i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 10.9304 | + | 7.94139i | 0.382640 | + | 0.278004i | ||||
\(817\) | 0.927484 | + | 2.85450i | 0.0324486 | + | 0.0998664i | ||||
\(818\) | −67.5317 | −2.36119 | ||||||||
\(819\) | −4.00894 | − | 12.3382i | −0.140084 | − | 0.431133i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9216 | − | 42.8462i | 0.485866 | − | 1.49534i | −0.344857 | − | 0.938655i | \(-0.612073\pi\) |
0.830723 | − | 0.556686i | \(-0.187927\pi\) | |||||||
\(822\) | 8.04758 | − | 24.7679i | 0.280691 | − | 0.863880i | ||||
\(823\) | −33.5397 | + | 24.3680i | −1.16912 | + | 0.849415i | −0.990903 | − | 0.134576i | \(-0.957033\pi\) |
−0.178217 | + | 0.983991i | \(0.557033\pi\) | |||||||
\(824\) | 21.8266 | 0.760364 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.5529 | −1.09786 | ||||||||
\(827\) | −31.3035 | + | 22.7434i | −1.08853 | + | 0.790864i | −0.979151 | − | 0.203136i | \(-0.934887\pi\) |
−0.109380 | + | 0.994000i | \(0.534887\pi\) | |||||||
\(828\) | 0.164609 | − | 0.506614i | 0.00572056 | − | 0.0176061i | ||||
\(829\) | 7.45527 | − | 22.9450i | 0.258932 | − | 0.796911i | −0.734097 | − | 0.679044i | \(-0.762394\pi\) |
0.993029 | − | 0.117867i | \(-0.0376056\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.55091 | + | 7.85089i | 0.0884901 | + | 0.272344i | ||||
\(832\) | −5.87864 | −0.203805 | ||||||||
\(833\) | −7.14441 | − | 21.9882i | −0.247539 | − | 0.761847i | ||||
\(834\) | 25.1774 | + | 18.2924i | 0.871821 | + | 0.633415i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.2768 | + | 7.46650i | −0.355429 | + | 0.258234i | ||||
\(837\) | 2.19190 | + | 1.59251i | 0.0757633 | + | 0.0550452i | ||||
\(838\) | −27.0014 | − | 19.6177i | −0.932748 | − | 0.677681i | ||||
\(839\) | 14.3890 | − | 10.4542i | 0.496763 | − | 0.360919i | −0.311016 | − | 0.950405i | \(-0.600669\pi\) |
0.807779 | + | 0.589485i | \(0.200669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0826 | + | 8.05197i | 0.382158 | + | 0.277654i | ||||
\(842\) | −21.2671 | − | 65.4534i | −0.732913 | − | 2.25567i | ||||
\(843\) | −1.28129 | −0.0441300 | ||||||||
\(844\) | 0.838452 | + | 2.58049i | 0.0288607 | + | 0.0888242i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.86510 | + | 8.81786i | −0.0985041 | + | 0.303164i | ||||
\(847\) | 29.1322 | − | 89.6598i | 1.00100 | − | 3.08075i | ||||
\(848\) | −11.3713 | + | 8.26176i | −0.390493 | + | 0.283710i | ||||
\(849\) | 2.67132 | 0.0916796 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0121834 | 0.000417642 | ||||||||
\(852\) | −5.97524 | + | 4.34126i | −0.204708 | + | 0.148729i | ||||
\(853\) | −3.96878 | + | 12.2147i | −0.135889 | + | 0.418222i | −0.995727 | − | 0.0923439i | \(-0.970564\pi\) |
0.859839 | + | 0.510566i | \(0.170564\pi\) | |||||||
\(854\) | 11.6026 | − | 35.7090i | 0.397032 | − | 1.22194i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.25258 | + | 10.0104i | 0.111171 | + | 0.342149i | ||||
\(857\) | 15.6015 | 0.532936 | 0.266468 | − | 0.963844i | \(-0.414143\pi\) | ||||
0.266468 | + | 0.963844i | \(0.414143\pi\) | |||||||
\(858\) | −10.2524 | − | 31.5538i | −0.350013 | − | 1.07723i | ||||
\(859\) | −3.90628 | − | 2.83808i | −0.133281 | − | 0.0968340i | 0.519147 | − | 0.854685i | \(-0.326250\pi\) |
−0.652428 | + | 0.757851i | \(0.726250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.69537 | − | 3.41138i | 0.160018 | − | 0.116260i | ||||
\(862\) | −18.9636 | − | 13.7779i | −0.645904 | − | 0.469276i | ||||
\(863\) | −10.6425 | − | 7.73222i | −0.362274 | − | 0.263208i | 0.391726 | − | 0.920082i | \(-0.371878\pi\) |
−0.754000 | + | 0.656874i | \(0.771878\pi\) | |||||||
\(864\) | −3.88679 | + | 2.82392i | −0.132231 | + | 0.0960716i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.1529 | − | 12.4623i | −0.582879 | − | 0.423486i | ||||
\(867\) | 2.98993 | + | 9.20205i | 0.101543 | + | 0.312518i | ||||
\(868\) | 9.73792 | 0.330527 | ||||||||
\(869\) | −30.4281 | − | 93.6480i | −1.03220 | − | 3.17679i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.13249 | − | 18.8739i | 0.207792 | − | 0.639517i | ||||
\(872\) | 0.781196 | − | 2.40427i | 0.0264546 | − | 0.0814190i | ||||
\(873\) | −1.98567 | + | 1.44268i | −0.0672049 | + | 0.0488272i | ||||
\(874\) | −2.35111 | −0.0795274 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.1404 | 0.410185 | ||||||||
\(877\) | 5.05840 | − | 3.67515i | 0.170810 | − | 0.124101i | −0.499096 | − | 0.866547i | \(-0.666334\pi\) |
0.669906 | + | 0.742446i | \(0.266334\pi\) | |||||||
\(878\) | 5.78199 | − | 17.7951i | 0.195133 | − | 0.600557i | ||||
\(879\) | 5.45741 | − | 16.7962i | 0.184074 | − | 0.566521i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.18532 | − | 15.9588i | −0.174698 | − | 0.537665i | 0.824922 | − | 0.565247i | \(-0.191219\pi\) |
−0.999620 | + | 0.0275821i | \(0.991219\pi\) | |||||||
\(882\) | 14.5770 | 0.490834 | ||||||||
\(883\) | −5.01740 | − | 15.4420i | −0.168849 | − | 0.519664i | 0.830450 | − | 0.557093i | \(-0.188083\pi\) |
−0.999299 | + | 0.0374289i | \(0.988083\pi\) | |||||||
\(884\) | −6.56848 | − | 4.77228i | −0.220922 | − | 0.160509i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.2259 | − | 8.15606i | 0.377140 | − | 0.274008i | ||||
\(887\) | 46.6700 | + | 33.9078i | 1.56703 | + | 1.13851i | 0.929935 | + | 0.367723i | \(0.119863\pi\) |
0.637091 | + | 0.770788i | \(0.280137\pi\) | |||||||
\(888\) | −0.0313275 | − | 0.0227607i | −0.00105128 | − | 0.000763800i | ||||
\(889\) | −43.1945 | + | 31.3827i | −1.44870 | + | 1.05254i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.78023 | + | 3.47304i | 0.160144 | + | 0.116351i | ||||
\(892\) | 0.0858359 | + | 0.264176i | 0.00287400 | + | 0.00884526i | ||||
\(893\) | 12.8131 | 0.428774 | ||||||||
\(894\) | −7.76827 | − | 23.9083i | −0.259810 | − | 0.799612i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.4198 | − | 47.4572i | 0.515138 | − | 1.58543i | ||||
\(897\) | 0.594152 | − | 1.82861i | 0.0198382 | − | 0.0610556i | ||||
\(898\) | 45.4871 | − | 33.0483i | 1.51793 | − | 1.10284i | ||||
\(899\) | −10.5981 | −0.353465 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.61988 | 0.253855 | ||||||||
\(902\) | 12.0079 | − | 8.72427i | 0.399820 | − | 0.290486i | ||||
\(903\) | 1.55061 | − | 4.77228i | 0.0516010 | − | 0.158812i | ||||
\(904\) | −6.13219 | + | 18.8729i | −0.203953 | + | 0.627704i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.19361 | + | 28.2950i | 0.305437 | + | 0.940039i | ||||
\(907\) | −9.00465 | −0.298995 | −0.149497 | − | 0.988762i | \(-0.547766\pi\) | ||||
−0.149497 | + | 0.988762i | \(0.547766\pi\) | |||||||
\(908\) | 2.69670 | + | 8.29960i | 0.0894933 | + | 0.275432i | ||||
\(909\) | 5.56195 | + | 4.04100i | 0.184478 | + | 0.134031i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2303 | + | 17.6044i | −0.802786 | + | 0.583258i | −0.911730 | − | 0.410789i | \(-0.865253\pi\) |
0.108944 | + | 0.994048i | \(0.465253\pi\) | |||||||
\(912\) | 9.52397 | + | 6.91957i | 0.315370 | + | 0.229130i | ||||
\(913\) | −3.73642 | − | 2.71467i | −0.123658 | − | 0.0898425i | ||||
\(914\) | −31.5853 | + | 22.9481i | −1.04475 | + | 0.759056i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.94596 | − | 6.49962i | −0.295583 | − | 0.214753i | ||||
\(917\) | 5.59477 | + | 17.2189i | 0.184756 | + | 0.568619i | ||||
\(918\) | 4.61803 | 0.152418 | ||||||||
\(919\) | 2.76125 | + | 8.49826i | 0.0910853 | + | 0.280332i | 0.986214 | − | 0.165477i | \(-0.0529162\pi\) |
−0.895128 | + | 0.445808i | \(0.852916\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.82532 | + | 27.1615i | −0.290804 | + | 0.895003i | ||||
\(922\) | 6.34995 | − | 19.5431i | 0.209125 | − | 0.643619i | ||||
\(923\) | −21.5675 | + | 15.6697i | −0.709902 | + | 0.515774i | ||||
\(924\) | 21.2370 | 0.698647 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 46.4133 | 1.52524 | ||||||||
\(927\) | 9.50850 | − | 6.90833i | 0.312300 | − | 0.226899i | ||||
\(928\) | 5.80735 | − | 17.8732i | 0.190636 | − | 0.586716i | ||||
\(929\) | −12.8117 | + | 39.4304i | −0.420339 | + | 1.29367i | 0.487048 | + | 0.873375i | \(0.338074\pi\) |
−0.907387 | + | 0.420296i | \(0.861926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.22514 | − | 19.1590i | −0.204021 | − | 0.627911i | ||||
\(932\) | −18.3248 | −0.600250 | ||||||||
\(933\) | 9.06296 | + | 27.8929i | 0.296708 | + | 0.913173i | ||||
\(934\) | −5.44243 | − | 3.95416i | −0.178082 | − | 0.129384i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.94392 | + | 3.59197i | −0.161597 | + | 0.117407i | ||||
\(937\) | 16.8749 | + | 12.2603i | 0.551278 | + | 0.400527i | 0.828256 | − | 0.560349i | \(-0.189333\pi\) |
−0.276978 | + | 0.960876i | \(0.589333\pi\) | |||||||
\(938\) | 32.8220 | + | 23.8466i | 1.07168 | + | 0.778618i | ||||
\(939\) | 14.1523 | − | 10.2823i | 0.461844 | − | 0.335549i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.97219 | − | 2.15942i | −0.0968905 | − | 0.0703951i | 0.538285 | − | 0.842763i | \(-0.319072\pi\) |
−0.635176 | + | 0.772368i | \(0.719072\pi\) | |||||||
\(942\) | 9.44413 | + | 29.0661i | 0.307706 | + | 0.947023i | ||||
\(943\) | 0.860163 | 0.0280107 | ||||||||
\(944\) | 7.23565 | + | 22.2691i | 0.235500 | + | 0.724796i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.96552 | − | 12.2046i | 0.128930 | − | 0.396807i | ||||
\(947\) | 9.79575 | − | 30.1482i | 0.318319 | − | 0.979685i | −0.656048 | − | 0.754719i | \(-0.727773\pi\) |
0.974367 | − | 0.224966i | \(-0.0722270\pi\) | |||||||
\(948\) | 12.2913 | − | 8.93013i | 0.399202 | − | 0.290037i | ||||
\(949\) | 43.8204 | 1.42247 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.91763 | 0.127038 | ||||||||
\(952\) | −16.0302 | + | 11.6466i | −0.519541 | + | 0.377469i | ||||
\(953\) | −7.91746 | + | 24.3674i | −0.256472 | + | 0.789339i | 0.737064 | + | 0.675822i | \(0.236211\pi\) |
−0.993536 | + | 0.113516i | \(0.963789\pi\) | |||||||
\(954\) | −1.48462 | + | 4.56919i | −0.0480664 | + | 0.147933i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.97625 | + | 15.3153i | 0.160943 | + | 0.495333i | ||||
\(957\) | −23.1129 | −0.747133 | ||||||||
\(958\) | 10.5191 | + | 32.3746i | 0.339858 | + | 1.04598i | ||||
\(959\) | 48.6781 | + | 35.3667i | 1.57190 | + | 1.14205i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.1409 | − | 13.9067i | 0.617449 | − | 0.448603i | ||||
\(962\) | 0.0947214 | + | 0.0688191i | 0.00305394 | + | 0.00221882i | ||||
\(963\) | 4.58535 | + | 3.33145i | 0.147761 | + | 0.107354i | ||||
\(964\) | −21.7865 | + | 15.8288i | −0.701697 | + | 0.509813i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.17999 | + | 2.31040i | 0.102314 | + | 0.0743358i | ||||
\(967\) | 8.96663 | + | 27.5965i | 0.288347 | + | 0.887442i | 0.985375 | + | 0.170398i | \(0.0545054\pi\) |
−0.697028 | + | 0.717044i | \(0.745495\pi\) | |||||||
\(968\) | −44.4077 | −1.42732 | ||||||||
\(969\) | −1.97214 | − | 6.06961i | −0.0633541 | − | 0.194984i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.16588 | + | 3.58821i | −0.0374149 | + | 0.115151i | −0.968020 | − | 0.250875i | \(-0.919282\pi\) |
0.930605 | + | 0.366026i | \(0.119282\pi\) | |||||||
\(972\) | −0.281722 | + | 0.867051i | −0.00903624 | + | 0.0278107i | ||||
\(973\) | −58.1705 | + | 42.2634i | −1.86486 | + | 1.35490i | ||||
\(974\) | 18.7739 | 0.601553 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.8630 | −0.891874 | ||||||||
\(977\) | 29.7044 | − | 21.5815i | 0.950329 | − | 0.690455i | −0.000555441 | − | 1.00000i | \(-0.500177\pi\) |
0.950885 | + | 0.309545i | \(0.100177\pi\) | |||||||
\(978\) | 11.4738 | − | 35.3128i | 0.366893 | − | 1.12918i | ||||
\(979\) | 6.34180 | − | 19.5181i | 0.202685 | − | 0.623800i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.420658 | − | 1.29465i | −0.0134306 | − | 0.0413350i | ||||
\(982\) | −56.8104 | −1.81289 | ||||||||
\(983\) | −7.28128 | − | 22.4095i | −0.232237 | − | 0.714752i | −0.997476 | − | 0.0710055i | \(-0.977379\pi\) |
0.765239 | − | 0.643746i | \(-0.222621\pi\) | |||||||
\(984\) | −2.21175 | − | 1.60693i | −0.0705081 | − | 0.0512271i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −14.6143 | + | 10.6179i | −0.465413 | + | 0.338143i | ||||
\(987\) | −17.3304 | − | 12.5912i | −0.551631 | − | 0.400784i | ||||
\(988\) | −5.72331 | − | 4.15823i | −0.182083 | − | 0.132291i | ||||
\(989\) | 0.601653 | − | 0.437126i | 0.0191314 | − | 0.0138998i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5727 | − | 17.1266i | −0.748812 | − | 0.544044i | 0.146646 | − | 0.989189i | \(-0.453152\pi\) |
−0.895458 | + | 0.445145i | \(0.853152\pi\) | |||||||
\(992\) | −4.02235 | − | 12.3795i | −0.127710 | − | 0.393050i | ||||
\(993\) | 17.5534 | 0.557039 | ||||||||
\(994\) | −16.8413 | − | 51.8323i | −0.534175 | − | 1.64402i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.220205 | − | 0.677723i | 0.00697748 | − | 0.0214745i | ||||
\(997\) | −13.5733 | + | 41.7742i | −0.429870 | + | 1.32300i | 0.468384 | + | 0.883525i | \(0.344836\pi\) |
−0.898254 | + | 0.439478i | \(0.855164\pi\) | |||||||
\(998\) | 56.7993 | − | 41.2671i | 1.79795 | − | 1.30629i | ||||
\(999\) | −0.0208515 | −0.000659711 |
(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 | 375.2.g.b.301.1 | 8 | ||
5.2 | odd | 4 | 375.2.i.b.199.2 | 16 | |||
5.3 | odd | 4 | 375.2.i.b.199.3 | 16 | |||
5.4 | even | 2 | 75.2.g.b.61.2 | yes | 8 | ||
15.14 | odd | 2 | 225.2.h.c.136.1 | 8 | |||
25.3 | odd | 20 | 1875.2.b.c.1249.3 | 8 | |||
25.4 | even | 10 | 1875.2.a.h.1.1 | 4 | |||
25.9 | even | 10 | 75.2.g.b.16.2 | ✓ | 8 | ||
25.12 | odd | 20 | 375.2.i.b.49.3 | 16 | |||
25.13 | odd | 20 | 375.2.i.b.49.2 | 16 | |||
25.16 | even | 5 | inner | 375.2.g.b.76.1 | 8 | ||
25.21 | even | 5 | 1875.2.a.e.1.4 | 4 | |||
25.22 | odd | 20 | 1875.2.b.c.1249.6 | 8 | |||
75.29 | odd | 10 | 5625.2.a.i.1.4 | 4 | |||
75.59 | odd | 10 | 225.2.h.c.91.1 | 8 | |||
75.71 | odd | 10 | 5625.2.a.n.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.16.2 | ✓ | 8 | 25.9 | even | 10 | ||
75.2.g.b.61.2 | yes | 8 | 5.4 | even | 2 | ||
225.2.h.c.91.1 | 8 | 75.59 | odd | 10 | |||
225.2.h.c.136.1 | 8 | 15.14 | odd | 2 | |||
375.2.g.b.76.1 | 8 | 25.16 | even | 5 | inner | ||
375.2.g.b.301.1 | 8 | 1.1 | even | 1 | trivial | ||
375.2.i.b.49.2 | 16 | 25.13 | odd | 20 | |||
375.2.i.b.49.3 | 16 | 25.12 | odd | 20 | |||
375.2.i.b.199.2 | 16 | 5.2 | odd | 4 | |||
375.2.i.b.199.3 | 16 | 5.3 | odd | 4 | |||
1875.2.a.e.1.4 | 4 | 25.21 | even | 5 | |||
1875.2.a.h.1.1 | 4 | 25.4 | even | 10 | |||
1875.2.b.c.1249.3 | 8 | 25.3 | odd | 20 | |||
1875.2.b.c.1249.6 | 8 | 25.22 | odd | 20 | |||
5625.2.a.i.1.4 | 4 | 75.29 | odd | 10 | |||
5625.2.a.n.1.1 | 4 | 75.71 | odd | 10 |