Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(1.79663404548\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(-0.0272949 + 1.41395i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.136 |
Dual form | 225.2.h.c.91.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | 0 | ||||||||
\(4\) | 0.281722 | − | 0.867051i | 0.140861 | − | 0.433526i | ||||
\(5\) | 1.02729 | − | 1.98612i | 0.459420 | − | 0.888219i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.94243 | −1.49010 | −0.745049 | − | 0.667009i | \(-0.767574\pi\) | ||||
−0.745049 | + | 0.667009i | \(0.767574\pi\) | |||||||
\(8\) | −0.573870 | − | 1.76619i | −0.202894 | − | 0.624442i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.573870 | + | 3.77214i | 0.181474 | + | 1.19286i | ||||
\(11\) | −4.78023 | + | 3.47304i | −1.44129 | + | 1.04716i | −0.453524 | + | 0.891244i | \(0.649833\pi\) |
−0.987770 | + | 0.155918i | \(0.950167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.66220 | − | 1.93420i | −0.738361 | − | 0.536451i | 0.153836 | − | 0.988096i | \(-0.450837\pi\) |
−0.892197 | + | 0.451646i | \(0.850837\pi\) | |||||||
\(14\) | 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 | \(-0.206440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.728704 | − | 2.24272i | −0.167176 | − | 0.514515i | 0.832014 | − | 0.554755i | \(-0.187188\pi\) |
−0.999190 | + | 0.0402396i | \(0.987188\pi\) | |||||||
\(20\) | −1.43265 | − | 1.45025i | −0.320351 | − | 0.324286i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | \(0.319403\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.88933 | − | 4.08066i | −0.577866 | − | 0.816132i | ||||
\(26\) | 5.61505 | 1.10120 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.11067 | + | 3.41829i | −0.209897 | + | 0.645996i | ||||
\(29\) | 1.20877 | − | 3.72022i | 0.224464 | − | 0.690828i | −0.773882 | − | 0.633330i | \(-0.781688\pi\) |
0.998346 | − | 0.0574980i | \(-0.0183123\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.73607 | + | 2.71441i | 0.640730 | + | 0.465518i | ||||
\(35\) | −4.05004 | + | 7.83013i | −0.684581 | + | 1.32353i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0168692 | + | 0.0122562i | 0.00277328 | + | 0.00201490i | 0.589171 | − | 0.808008i | \(-0.299454\pi\) |
−0.586398 | + | 0.810023i | \(0.699454\pi\) | |||||||
\(38\) | 3.25535 | + | 2.36515i | 0.528087 | + | 0.383678i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.09740 | − | 0.674625i | −0.647855 | − | 0.106668i | ||||
\(41\) | 1.19098 | + | 0.865300i | 0.186000 | + | 0.135137i | 0.676889 | − | 0.736085i | \(-0.263328\pi\) |
−0.490889 | + | 0.871222i | \(0.663328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.27279 | 0.194098 | 0.0970491 | − | 0.995280i | \(-0.469060\pi\) | ||||
0.0970491 | + | 0.995280i | \(0.469060\pi\) | |||||||
\(44\) | 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 | \(0.970299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.54276 | 1.22039 | ||||||||
\(50\) | 8.08145 | + | 2.73533i | 1.14289 | + | 0.386833i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −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 | 0 | ||||||||
\(55\) | 1.98716 | + | 13.0619i | 0.267949 | + | 1.76127i | ||||
\(56\) | 2.26244 | + | 6.96308i | 0.302332 | + | 0.930481i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.06260 | + | 6.34804i | 0.270833 | + | 0.833539i | ||||
\(59\) | −3.79456 | − | 2.75691i | −0.494009 | − | 0.358919i | 0.312715 | − | 0.949847i | \(-0.398762\pi\) |
−0.806724 | + | 0.590928i | \(0.798762\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.44528 | + | 1.05006i | −0.180660 | + | 0.131257i | ||||
\(65\) | −6.57641 | + | 3.30045i | −0.815704 | + | 0.409370i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.86361 | + | 5.73559i | 0.227676 | + | 0.700714i | 0.998009 | + | 0.0630725i | \(0.0200899\pi\) |
−0.770333 | + | 0.637642i | \(0.779910\pi\) | |||||||
\(68\) | −2.46731 | −0.299206 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.26244 | − | 14.8714i | −0.270414 | − | 1.77747i | ||||
\(71\) | 2.50346 | − | 7.70487i | 0.297106 | − | 0.914400i | −0.685399 | − | 0.728167i | \(-0.740372\pi\) |
0.982506 | − | 0.186232i | \(-0.0596277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7734 | + | 7.82730i | −1.26093 | + | 0.916116i | −0.998803 | − | 0.0489187i | \(-0.984422\pi\) |
−0.262123 | + | 0.965035i | \(0.584422\pi\) | |||||||
\(74\) | −0.0355801 | −0.00413611 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.14984 | −0.246604 | ||||||||
\(77\) | 18.8457 | − | 13.6922i | 2.14767 | − | 1.56037i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.14971 | − | 15.8492i | 0.579388 | − | 1.78317i | −0.0413379 | − | 0.999145i | \(-0.513162\pi\) |
0.620726 | − | 0.784028i | \(-0.286838\pi\) | |||||||
\(80\) | 9.97696 | − | 5.00705i | 1.11546 | − | 0.559805i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.51200 | −0.277404 | ||||||||
\(83\) | −0.241540 | − | 0.743385i | −0.0265125 | − | 0.0815971i | 0.936925 | − | 0.349531i | \(-0.113659\pi\) |
−0.963437 | + | 0.267934i | \(0.913659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.97122 | − | 0.983144i | −0.647669 | − | 0.106637i | ||||
\(86\) | −1.75705 | + | 1.27657i | −0.189468 | + | 0.137656i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.87728 | + | 6.44972i | 0.946322 | + | 0.687543i | ||||
\(89\) | −2.80994 | + | 2.04154i | −0.297853 | + | 0.216403i | −0.726667 | − | 0.686990i | \(-0.758932\pi\) |
0.428814 | + | 0.903393i | \(0.358932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4955 | + | 7.62545i | 1.10023 | + | 0.799364i | ||||
\(92\) | 0.164609 | + | 0.506614i | 0.0171617 | + | 0.0528182i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.86510 | − | 8.81786i | −0.295512 | − | 0.909493i | ||||
\(95\) | −5.20290 | − | 0.856643i | −0.533806 | − | 0.0878897i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.758460 | + | 2.33430i | −0.0770099 | + | 0.237012i | −0.982149 | − | 0.188103i | \(-0.939766\pi\) |
0.905139 | + | 0.425115i | \(0.139766\pi\) | |||||||
\(98\) | −11.7931 | + | 8.56817i | −1.19128 | + | 0.865515i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.35213 | + | 1.35559i | −0.435213 | + | 0.135559i | ||||
\(101\) | 6.87495 | 0.684083 | 0.342042 | − | 0.939685i | \(-0.388882\pi\) | ||||
0.342042 | + | 0.939685i | \(0.388882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.63192 | − | 11.1779i | 0.357864 | − | 1.10139i | −0.596466 | − | 0.802638i | \(-0.703429\pi\) |
0.954330 | − | 0.298754i | \(-0.0965710\pi\) | |||||||
\(104\) | −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 | 0 | ||||||||
\(109\) | 1.10130 | + | 0.800139i | 0.105485 | + | 0.0766394i | 0.639277 | − | 0.768976i | \(-0.279234\pi\) |
−0.533792 | + | 0.845616i | \(0.679234\pi\) | |||||||
\(110\) | −15.8440 | − | 16.0386i | −1.51067 | − | 1.52922i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −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 | \(0.867627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.196506 | + | 1.29166i | 0.0183242 | + | 0.120448i | ||||
\(116\) | −2.88508 | − | 2.09614i | −0.267873 | − | 0.194621i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.47003 | 0.221815 | ||||||||
\(125\) | −11.0729 | + | 1.54651i | −0.990387 | + | 0.138324i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9563 | − | 7.96023i | 0.972216 | − | 0.706356i | 0.0162606 | − | 0.999868i | \(-0.494824\pi\) |
0.955956 | + | 0.293511i | \(0.0948239\pi\) | |||||||
\(128\) | 3.91123 | − | 12.0375i | 0.345708 | − | 1.06398i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.76832 | − | 11.1522i | 0.505915 | − | 0.978109i | ||||
\(131\) | −1.41912 | − | 4.36759i | −0.123989 | − | 0.381599i | 0.869727 | − | 0.493534i | \(-0.164295\pi\) |
−0.993716 | + | 0.111935i | \(0.964295\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 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 | 0 | ||||||||
\(139\) | −14.7550 | + | 10.7201i | −1.25150 | + | 0.909269i | −0.998308 | − | 0.0581460i | \(-0.981481\pi\) |
−0.253194 | + | 0.967416i | \(0.581481\pi\) | |||||||
\(140\) | 5.64814 | + | 5.71751i | 0.477355 | + | 0.483218i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.27182 | + | 13.1473i | 0.358483 | + | 1.10330i | ||||
\(143\) | 19.4435 | 1.62595 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.14703 | − | 6.22253i | −0.510483 | − | 0.516753i | ||||
\(146\) | 7.02177 | − | 21.6108i | 0.581126 | − | 1.78852i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0153792 | − | 0.0111736i | 0.00126416 | − | 0.000918465i | ||||
\(149\) | −14.7323 | −1.20692 | −0.603458 | − | 0.797394i | \(-0.706211\pi\) | ||||
−0.603458 | + | 0.797394i | \(0.706211\pi\) | |||||||
\(150\) | 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 | 0 | ||||||||
\(154\) | −12.2831 | + | 37.8036i | −0.989803 | + | 3.04630i | ||||
\(155\) | 5.97779 | + | 0.984226i | 0.480148 | + | 0.0790549i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.9105 | 1.42942 | 0.714708 | − | 0.699423i | \(-0.246560\pi\) | ||||
0.714708 | + | 0.699423i | \(0.246560\pi\) | |||||||
\(158\) | 8.78728 | + | 27.0445i | 0.699078 | + | 2.15154i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.93547 | + | 9.54197i | −0.390183 | + | 0.754359i | ||||
\(161\) | 1.86361 | − | 1.35399i | 0.146873 | − | 0.106709i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6041 | − | 12.7901i | −1.37886 | − | 1.00180i | −0.996986 | − | 0.0775819i | \(-0.975280\pi\) |
−0.381870 | − | 0.924216i | \(-0.624720\pi\) | |||||||
\(164\) | 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 | \(0.561167\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.671052 | − | 2.06529i | −0.0516194 | − | 0.158868i | ||||
\(170\) | 9.22919 | − | 4.63177i | 0.707846 | − | 0.355241i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | \(0.136694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.3910 | + | 16.0877i | 0.861077 | + | 1.21612i | ||||
\(176\) | −29.4974 | −2.22345 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.83144 | − | 5.63659i | 0.137272 | − | 0.422480i | ||||
\(179\) | 1.98716 | − | 6.11586i | 0.148528 | − | 0.457121i | −0.848920 | − | 0.528521i | \(-0.822747\pi\) |
0.997448 | + | 0.0714002i | \(0.0227468\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.877852 | + | 0.637797i | 0.0647161 | + | 0.0470190i | ||||
\(185\) | 0.0416718 | − | 0.0209135i | 0.00306377 | − | 0.00153759i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9370 | + | 9.39931i | 0.946050 | + | 0.687346i | ||||
\(188\) | 4.00758 | + | 2.91168i | 0.292283 | + | 0.212356i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.04167 | − | 4.03580i | 0.583404 | − | 0.292788i | ||||
\(191\) | 5.43095 | + | 3.94582i | 0.392970 | + | 0.285509i | 0.766671 | − | 0.642040i | \(-0.221912\pi\) |
−0.373702 | + | 0.927549i | \(0.621912\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.82817 | 0.347539 | 0.173769 | − | 0.984786i | \(-0.444405\pi\) | ||||
0.173769 | + | 0.984786i | \(0.444405\pi\) | |||||||
\(194\) | −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 | \(-0.0712477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.72608 | −0.618575 | −0.309288 | − | 0.950969i | \(-0.600091\pi\) | ||||
−0.309288 | + | 0.950969i | \(0.600091\pi\) | |||||||
\(200\) | −5.54912 | + | 7.44487i | −0.392382 | + | 0.526432i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.49071 | + | 6.89540i | −0.667764 | + | 0.485159i | ||||
\(203\) | −4.76550 | + | 14.6667i | −0.334473 | + | 1.02940i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.94208 | − | 1.47651i | 0.205484 | − | 0.103124i | ||||
\(206\) | 6.19738 | + | 19.0736i | 0.431792 | + | 1.32892i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.82426 | − | 5.68466i | 0.534856 | − | 0.388595i | ||||
\(215\) | 1.30753 | − | 2.52790i | 0.0891726 | − | 0.172402i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.30073 | − | 10.1586i | −0.224068 | − | 0.689611i | ||||
\(218\) | −2.32283 | −0.157322 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.8852 | + | 1.95687i | 0.801300 | + | 0.131932i | ||||
\(221\) | −2.75202 | + | 8.46984i | −0.185121 | + | 0.569743i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.246494 | − | 0.179088i | 0.0165064 | − | 0.0119926i | −0.579501 | − | 0.814971i | \(-0.696753\pi\) |
0.596008 | + | 0.802979i | \(0.296753\pi\) | |||||||
\(224\) | 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 | 0 | ||||||||
\(229\) | 3.74812 | − | 11.5355i | 0.247682 | − | 0.762288i | −0.747501 | − | 0.664260i | \(-0.768747\pi\) |
0.995184 | − | 0.0980277i | \(-0.0312534\pi\) | |||||||
\(230\) | −1.56678 | − | 1.58602i | −0.103310 | − | 0.104579i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.26430 | −0.476924 | ||||||||
\(233\) | −6.21132 | − | 19.1165i | −0.406917 | − | 1.25236i | −0.919284 | − | 0.393595i | \(-0.871231\pi\) |
0.512367 | − | 0.858766i | \(-0.328769\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.53864 | + | 8.64351i | 0.557000 | + | 0.563841i | ||||
\(236\) | −3.45939 | + | 2.51340i | −0.225187 | + | 0.163608i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.7292 | − | 10.7014i | −0.954751 | − | 0.693667i | ||||
\(239\) | 14.2902 | − | 10.3825i | 0.924358 | − | 0.671585i | −0.0202473 | − | 0.999795i | \(-0.506445\pi\) |
0.944605 | + | 0.328210i | \(0.106445\pi\) | |||||||
\(240\) | 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 | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.57238 | + | 4.83929i | 0.100661 | + | 0.309804i | ||||
\(245\) | 8.77593 | − | 16.9669i | 0.560674 | − | 1.08398i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.39791 | + | 7.38002i | −0.152576 | + | 0.469580i | ||||
\(248\) | 4.07055 | − | 2.95742i | 0.258480 | − | 0.187797i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.7347 | − | 13.2407i | 0.868659 | − | 0.837417i | ||||
\(251\) | −1.89396 | −0.119546 | −0.0597729 | − | 0.998212i | \(-0.519038\pi\) | ||||
−0.0597729 | + | 0.998212i | \(0.519038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | 0 | ||||||||
\(259\) | −0.0665056 | − | 0.0483191i | −0.00413245 | − | 0.00300240i | ||||
\(260\) | 1.00894 | + | 6.63190i | 0.0625715 | + | 0.411293i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | \(0.907967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.42451 | + | 4.47885i | 0.271795 | + | 0.275134i | ||||
\(266\) | −12.8340 | − | 9.32443i | −0.786902 | − | 0.571718i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.49807 | 0.335848 | ||||||||
\(269\) | −5.61321 | − | 17.2757i | −0.342244 | − | 1.05332i | −0.963043 | − | 0.269348i | \(-0.913192\pi\) |
0.620799 | − | 0.783970i | \(-0.286808\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.0425 | −1.57329 | ||||||||
\(275\) | 27.9840 | + | 9.47173i | 1.68750 | + | 0.571167i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.67837 | + | 4.85212i | −0.401264 | + | 0.291535i | −0.770056 | − | 0.637977i | \(-0.779772\pi\) |
0.368792 | + | 0.929512i | \(0.379772\pi\) | |||||||
\(278\) | 9.61690 | − | 29.5978i | 0.576783 | − | 1.77516i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 16.1537 | + | 2.65966i | 0.965368 | + | 0.158945i | ||||
\(281\) | −0.395941 | − | 1.21858i | −0.0236199 | − | 0.0726944i | 0.938552 | − | 0.345138i | \(-0.112168\pi\) |
−0.962172 | + | 0.272444i | \(0.912168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.825484 | + | 2.54058i | 0.0490699 | + | 0.151022i | 0.972589 | − | 0.232531i | \(-0.0747006\pi\) |
−0.923519 | + | 0.383552i | \(0.874701\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.82773 | − | 5.68718i | 0.460455 | − | 0.334540i | ||||
\(290\) | 14.7269 | + | 2.42474i | 0.864792 | + | 0.142385i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.75158 | + | 11.5462i | 0.219545 | + | 0.675689i | ||||
\(293\) | −17.6605 | −1.03174 | −0.515870 | − | 0.856667i | \(-0.672531\pi\) | ||||
−0.515870 | + | 0.856667i | \(0.672531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.37368 | + | 4.70428i | −0.545757 | + | 0.273894i | ||||
\(296\) | 0.0119660 | − | 0.0368276i | 0.000695511 | − | 0.00214056i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.63783 | − | 11.1961i | 0.208644 | − | 0.642140i | ||||
\(305\) | 1.87706 | + | 12.3382i | 0.107480 | + | 0.706485i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.5593 | −1.62997 | −0.814983 | − | 0.579484i | \(-0.803254\pi\) | ||||
−0.814983 | + | 0.579484i | \(0.803254\pi\) | |||||||
\(308\) | −6.56260 | − | 20.1976i | −0.373939 | − | 1.15087i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.23935 | + | 4.63687i | −0.524760 | + | 0.263357i | ||||
\(311\) | −23.7271 | + | 17.2388i | −1.34544 | + | 0.977521i | −0.346217 | + | 0.938154i | \(0.612534\pi\) |
−0.999225 | + | 0.0393664i | \(0.987466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1523 | + | 10.2823i | 0.799937 | + | 0.581189i | 0.910896 | − | 0.412637i | \(-0.135392\pi\) |
−0.110958 | + | 0.993825i | \(0.535392\pi\) | |||||||
\(314\) | −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 | \(0.935091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.14227 | + | 21.9816i | 0.399890 | + | 1.23074i | ||||
\(320\) | 0.600809 | + | 3.94921i | 0.0335862 | + | 0.220768i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.21465 | + | 3.73830i | −0.0676897 | + | 0.208327i | ||||
\(323\) | −5.16312 | + | 3.75123i | −0.287284 | + | 0.208724i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.200840 | + | 16.4521i | −0.0111406 | + | 0.912596i | ||||
\(326\) | 37.1301 | 2.05645 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | 0 | ||||||||
\(334\) | −31.2029 | − | 22.6702i | −1.70734 | − | 1.24046i | ||||
\(335\) | 13.3060 | + | 2.19080i | 0.726986 | + | 0.119696i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3647 | + | 8.25697i | 0.619077 | + | 0.449786i | 0.852599 | − | 0.522566i | \(-0.175025\pi\) |
−0.233522 | + | 0.972352i | \(0.575025\pi\) | |||||||
\(338\) | 2.99780 | + | 2.17803i | 0.163059 | + | 0.118469i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.53466 | + | 4.90038i | −0.137461 | + | 0.265760i | ||||
\(341\) | −12.9513 | − | 9.40966i | −0.701351 | − | 0.509562i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −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 | \(0.0911944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.5626 | 1.15422 | 0.577109 | − | 0.816667i | \(-0.304181\pi\) | ||||
0.577109 | + | 0.816667i | \(0.304181\pi\) | |||||||
\(350\) | −31.8605 | − | 10.7838i | −1.70302 | − | 0.576420i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 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 | \(0.160993\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7310 | − | 12.8873i | −0.675690 | − | 0.683989i | ||||
\(356\) | 0.978498 | + | 3.01151i | 0.0518603 | + | 0.159610i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.39082 | + | 10.4359i | 0.179210 | + | 0.551553i | ||||
\(359\) | 21.9663 | + | 15.9595i | 1.15934 | + | 0.842308i | 0.989694 | − | 0.143198i | \(-0.0457385\pi\) |
0.169643 | + | 0.985506i | \(0.445738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8725 | − | 7.89936i | 0.572239 | − | 0.415756i | ||||
\(362\) | −20.3028 | − | 14.7508i | −1.06709 | − | 0.775285i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.56848 | − | 6.95191i | 0.501525 | − | 0.364379i | ||||
\(365\) | 4.47853 | + | 29.4381i | 0.234417 | + | 1.54086i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.62605 | + | 20.3929i | 0.345877 | + | 1.06450i | 0.961113 | + | 0.276157i | \(0.0890608\pi\) |
−0.615236 | + | 0.788343i | \(0.710939\pi\) | |||||||
\(368\) | −2.91692 | −0.152055 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.0365513 | + | 0.0706663i | −0.00190021 | + | 0.00367377i | ||||
\(371\) | 3.43011 | − | 10.5568i | 0.178083 | − | 0.548082i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.17021 | + | 3.75638i | −0.267703 | + | 0.194498i | −0.713536 | − | 0.700618i | \(-0.752908\pi\) |
0.445833 | + | 0.895116i | \(0.352908\pi\) | |||||||
\(374\) | −27.2865 | −1.41095 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.0906 | 0.520383 | ||||||||
\(377\) | −10.4136 | + | 7.56596i | −0.536330 | + | 0.389667i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0477946 | + | 0.147097i | −0.00245504 | + | 0.00755585i | −0.952277 | − | 0.305237i | \(-0.901264\pi\) |
0.949821 | + | 0.312792i | \(0.101264\pi\) | |||||||
\(380\) | −2.20852 | + | 4.26985i | −0.113295 | + | 0.219038i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.4549 | −0.586081 | ||||||||
\(383\) | 1.31489 | + | 4.04682i | 0.0671878 | + | 0.206783i | 0.979014 | − | 0.203794i | \(-0.0653273\pi\) |
−0.911826 | + | 0.410577i | \(0.865327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.83425 | − | 51.4958i | −0.399270 | − | 2.62447i | ||||
\(386\) | −6.66517 | + | 4.84253i | −0.339248 | + | 0.246478i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.81028 | + | 1.31525i | 0.0919032 | + | 0.0667716i | ||||
\(389\) | −16.4782 | + | 11.9721i | −0.835479 | + | 0.607011i | −0.921104 | − | 0.389316i | \(-0.872711\pi\) |
0.0856250 | + | 0.996327i | \(0.472711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.27931 | + | 0.929474i | 0.0646975 | + | 0.0470055i | ||||
\(392\) | −4.90243 | − | 15.0881i | −0.247610 | − | 0.762066i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.58465 | + | 23.3431i | 0.382109 | + | 1.17601i | ||||
\(395\) | −26.1881 | − | 26.5097i | −1.31767 | − | 1.33385i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.604795 | + | 1.86137i | −0.0303538 | + | 0.0934194i | −0.965086 | − | 0.261934i | \(-0.915640\pi\) |
0.934732 | + | 0.355354i | \(0.115640\pi\) | |||||||
\(398\) | 12.0461 | − | 8.75203i | 0.603818 | − | 0.438700i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.304690 | − | 24.9591i | 0.0152345 | − | 1.24796i | ||||
\(401\) | 32.8337 | 1.63964 | 0.819818 | − | 0.572624i | \(-0.194075\pi\) | ||||
0.819818 | + | 0.572624i | \(0.194075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 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 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.0180 | + | 23.2624i | 1.58319 | + | 1.15025i | 0.912923 | + | 0.408132i | \(0.133820\pi\) |
0.670265 | + | 0.742122i | \(0.266180\pi\) | |||||||
\(410\) | −2.58056 | + | 4.98912i | −0.127445 | + | 0.246395i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.66863 | − | 6.29813i | −0.427073 | − | 0.310287i | ||||
\(413\) | 14.9598 | + | 10.8689i | 0.736123 | + | 0.534825i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.72458 | − | 0.283948i | −0.0846564 | − | 0.0139384i | ||||
\(416\) | 12.7901 | + | 9.29254i | 0.627086 | + | 0.455604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.7756 | −1.16290 | ||||||||
\(419\) | −6.04421 | − | 18.6022i | −0.295279 | − | 0.908776i | −0.983128 | − | 0.182921i | \(-0.941445\pi\) |
0.687848 | − | 0.725854i | \(-0.258555\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.22869 | 0.253928 | ||||||||
\(425\) | −8.08684 | + | 10.8496i | −0.392269 | + | 0.526281i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.8016 | − | 12.9336i | 0.861478 | − | 0.625901i | ||||
\(428\) | −1.59675 | + | 4.91428i | −0.0771816 | + | 0.237540i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.730414 | + | 4.80113i | 0.0352237 | + | 0.231531i | ||||
\(431\) | −4.24497 | − | 13.0647i | −0.204473 | − | 0.629304i | −0.999735 | − | 0.0230370i | \(-0.992666\pi\) |
0.795261 | − | 0.606267i | \(-0.207334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.83964 | − | 11.8172i | −0.184522 | − | 0.567899i | 0.815418 | − | 0.578872i | \(-0.196507\pi\) |
−0.999940 | + | 0.0109734i | \(0.996507\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.87118 | + | 6.44529i | −0.423399 | + | 0.307617i | −0.779004 | − | 0.627019i | \(-0.784275\pi\) |
0.355605 | + | 0.934636i | \(0.384275\pi\) | |||||||
\(440\) | 21.9295 | − | 11.0056i | 1.04545 | − | 0.524670i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −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 | 0 | ||||||||
\(445\) | 1.16810 | + | 7.67813i | 0.0553734 | + | 0.363978i | ||||
\(446\) | −0.160658 | + | 0.494454i | −0.00760737 | + | 0.0234131i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.69791 | − | 4.13977i | 0.269201 | − | 0.195586i | ||||
\(449\) | 32.9503 | 1.55502 | 0.777511 | − | 0.628869i | \(-0.216482\pi\) | ||||
0.777511 | + | 0.628869i | \(0.216482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.69840 | −0.409592 | ||||||||
\(452\) | −7.88130 | + | 5.72610i | −0.370705 | + | 0.269333i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.04738 | − | 15.5342i | 0.236885 | − | 0.729058i | ||||
\(455\) | 25.9270 | − | 13.0118i | 1.21548 | − | 0.610002i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.8800 | −1.07028 | −0.535142 | − | 0.844762i | \(-0.679742\pi\) | ||||
−0.535142 | + | 0.844762i | \(0.679742\pi\) | |||||||
\(458\) | 6.39564 | + | 19.6838i | 0.298849 | + | 0.919762i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.17530 | + | 0.193509i | 0.0547985 | + | 0.00902243i | ||||
\(461\) | 9.74259 | − | 7.07841i | 0.453758 | − | 0.329674i | −0.337320 | − | 0.941390i | \(-0.609520\pi\) |
0.791078 | + | 0.611716i | \(0.209520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0054 | + | 15.9878i | 1.02268 | + | 0.743018i | 0.966830 | − | 0.255421i | \(-0.0822141\pi\) |
0.0558471 | + | 0.998439i | \(0.482214\pi\) | |||||||
\(464\) | 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 | \(0.870924\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.34714 | − | 22.6122i | −0.339259 | − | 1.04413i | ||||
\(470\) | −20.4566 | − | 3.36812i | −0.943593 | − | 0.155360i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.69164 | + | 8.28402i | −0.123893 | + | 0.381303i | ||||
\(473\) | −6.08421 | + | 4.42044i | −0.279752 | + | 0.203252i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.04630 | + | 9.45355i | −0.323307 | + | 0.433758i | ||||
\(476\) | 9.72721 | 0.445846 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.31397 | + | 28.6655i | −0.426011 | + | 1.31113i | ||||
\(479\) | −6.16466 | + | 18.9729i | −0.281670 | + | 0.866893i | 0.705706 | + | 0.708504i | \(0.250630\pi\) |
−0.987377 | + | 0.158388i | \(0.949370\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0212032 | − | 0.0652567i | −0.000966783 | − | 0.00297545i | ||||
\(482\) | 50.4038 | 2.29583 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.6370 | − | 12.8140i | −0.801680 | − | 0.582455i | ||||
\(485\) | 3.85703 | + | 3.90440i | 0.175139 | + | 0.177290i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.90102 | + | 6.46697i | 0.403344 | + | 0.293046i | 0.770902 | − | 0.636954i | \(-0.219806\pi\) |
−0.367558 | + | 0.930001i | \(0.619806\pi\) | |||||||
\(488\) | 8.38543 | + | 6.09237i | 0.379591 | + | 0.275789i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.90243 | + | 32.2245i | 0.221469 | + | 1.45575i | ||||
\(491\) | −26.9348 | − | 19.5693i | −1.21555 | − | 0.883151i | −0.219830 | − | 0.975538i | \(-0.570550\pi\) |
−0.995723 | + | 0.0923876i | \(0.970550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −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 | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.1448 | −1.84189 | −0.920946 | − | 0.389690i | \(-0.872582\pi\) | ||||
−0.920946 | + | 0.389690i | \(0.872582\pi\) | |||||||
\(500\) | −1.77856 | + | 10.0364i | −0.0795398 | + | 0.448843i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | \(0.846380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.06260 | − | 13.6545i | 0.314282 | − | 0.607616i | ||||
\(506\) | 1.82044 | + | 5.60275i | 0.0809286 | + | 0.249073i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.81529 | − | 11.7423i | −0.169276 | − | 0.520979i | ||||
\(509\) | −21.9206 | − | 15.9262i | −0.971612 | − | 0.705918i | −0.0157938 | − | 0.999875i | \(-0.505028\pi\) |
−0.955818 | + | 0.293958i | \(0.905028\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.4732 | − | 30.8586i | 1.87890 | − | 1.36510i | ||||
\(512\) | −4.40295 | − | 3.19893i | −0.194585 | − | 0.141374i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.5376 | − | 22.1869i | 1.34696 | − | 0.978622i | ||||
\(515\) | −18.4696 | − | 18.6964i | −0.813868 | − | 0.823864i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.92109 | − | 30.5340i | −0.436329 | − | 1.34288i | ||||
\(518\) | 0.140272 | 0.00616321 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.60322 | + | 9.72117i | 0.421129 | + | 0.426301i | ||||
\(521\) | −8.02073 | + | 24.6853i | −0.351395 | + | 1.08148i | 0.606676 | + | 0.794949i | \(0.292503\pi\) |
−0.958071 | + | 0.286532i | \(0.907497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.45123 | − | 1.05438i | 0.0634577 | − | 0.0461047i | −0.555604 | − | 0.831447i | \(-0.687513\pi\) |
0.619062 | + | 0.785342i | \(0.287513\pi\) | |||||||
\(524\) | −4.18673 | −0.182898 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.6414 | 1.46684 | ||||||||
\(527\) | 5.93209 | − | 4.30991i | 0.258406 | − | 0.187743i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00189 | + | 21.5496i | −0.304430 | + | 0.936939i | ||||
\(530\) | −10.6001 | − | 1.74528i | −0.460439 | − | 0.0758100i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.47561 | 0.367464 | ||||||||
\(533\) | −1.49697 | − | 4.60720i | −0.0648410 | − | 0.199560i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.82250 | + | 11.2569i | −0.251729 | + | 0.486679i | ||||
\(536\) | 9.06068 | − | 6.58297i | 0.391362 | − | 0.284341i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.01792 | + | 12.3659i | 0.172267 | + | 0.530183i | ||||
\(545\) | 2.72053 | − | 1.36533i | 0.116535 | − | 0.0584842i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.02174 | − | 18.5330i | 0.257471 | − | 0.792414i | −0.735862 | − | 0.677132i | \(-0.763223\pi\) |
0.993333 | − | 0.115283i | \(-0.0367774\pi\) | |||||||
\(548\) | 11.2566 | − | 8.17841i | 0.480859 | − | 0.349364i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −48.1311 | + | 14.9917i | −2.05232 | + | 0.639249i | ||||
\(551\) | −9.22425 | −0.392966 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −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 | \(0.311650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.38841 | − | 2.46182i | −0.143314 | − | 0.104124i | ||||
\(560\) | −39.3335 | + | 19.7399i | −1.66214 | + | 0.834165i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | \(0.417824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.3554 | + | 10.7175i | −0.898429 | + | 0.450887i | ||||
\(566\) | −3.68770 | − | 2.67927i | −0.155005 | − | 0.112618i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.0449 | −0.631271 | ||||||||
\(569\) | 11.2118 | + | 34.5065i | 0.470025 | + | 1.44659i | 0.852552 | + | 0.522643i | \(0.175054\pi\) |
−0.382527 | + | 0.923944i | \(0.624946\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.90337 | 0.413359 | ||||||||
\(575\) | 2.76726 | + | 0.936635i | 0.115403 | + | 0.0390604i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.56961 | − | 4.04656i | 0.231866 | − | 0.168461i | −0.465786 | − | 0.884898i | \(-0.654228\pi\) |
0.697652 | + | 0.716437i | \(0.254228\pi\) | |||||||
\(578\) | −5.10190 | + | 15.7020i | −0.212211 | + | 0.653118i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.12701 | + | 3.57677i | −0.295933 | + | 0.148517i | ||||
\(581\) | 0.952256 | + | 2.93074i | 0.0395062 | + | 0.121588i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −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 | \(0.798370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.16880 | − | 3.75536i | 0.212977 | − | 0.154737i | ||||
\(590\) | 8.22186 | − | 15.8957i | 0.338489 | − | 0.654416i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0321670 | + | 0.0989998i | 0.00132206 | + | 0.00406887i | ||||
\(593\) | −5.82561 | −0.239229 | −0.119615 | − | 0.992820i | \(-0.538166\pi\) | ||||
−0.119615 | + | 0.992820i | \(0.538166\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.5411 | + | 3.87597i | 0.965091 | + | 0.158899i | ||||
\(596\) | −4.15041 | + | 12.7737i | −0.170008 | + | 0.523230i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.65426 | + | 1.92844i | −0.108541 | + | 0.0788596i | ||||
\(599\) | 27.1527 | 1.10943 | 0.554715 | − | 0.832040i | \(-0.312827\pi\) | ||||
0.554715 | + | 0.832040i | \(0.312827\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.91194 | + | 15.1174i | −0.199864 | + | 0.615118i | ||||
\(605\) | −37.5777 | − | 38.0393i | −1.52775 | − | 1.54652i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.46424 | 0.0594318 | 0.0297159 | − | 0.999558i | \(-0.490540\pi\) | ||||
0.0297159 | + | 0.999558i | \(0.490540\pi\) | |||||||
\(608\) | 3.50094 | + | 10.7748i | 0.141982 | + | 0.436975i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.9662 | − | 15.1500i | −0.605963 | − | 0.613405i | ||||
\(611\) | 14.4653 | − | 10.5096i | 0.585202 | − | 0.425174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.0814 | − | 20.4023i | −1.13420 | − | 0.824041i | −0.147896 | − | 0.989003i | \(-0.547250\pi\) |
−0.986300 | + | 0.164962i | \(0.947250\pi\) | |||||||
\(614\) | 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 | \(-0.419504\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.79758 | − | 17.8431i | −0.233025 | − | 0.717176i | −0.997377 | − | 0.0723776i | \(-0.976941\pi\) |
0.764353 | − | 0.644798i | \(-0.223059\pi\) | |||||||
\(620\) | 2.53745 | − | 4.90577i | 0.101906 | − | 0.197021i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.4647 | − | 47.5954i | 0.620077 | − | 1.90840i | ||||
\(623\) | 11.0780 | − | 8.04863i | 0.443830 | − | 0.322461i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.30354 | + | 23.5807i | −0.332142 | + | 0.943230i | ||||
\(626\) | −29.8498 | −1.19304 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | 0 | ||||||||
\(634\) | 5.40820 | + | 3.92928i | 0.214787 | + | 0.156052i | ||||
\(635\) | −4.55459 | − | 29.9380i | −0.180743 | − | 1.18806i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.7425 | − | 16.5234i | −0.901091 | − | 0.654681i | ||||
\(638\) | −31.9068 | − | 23.1816i | −1.26320 | − | 0.917769i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.8900 | − | 20.1343i | −0.786221 | − | 0.795877i | ||||
\(641\) | −1.46647 | − | 1.06546i | −0.0579223 | − | 0.0420830i | 0.558447 | − | 0.829540i | \(-0.311397\pi\) |
−0.616370 | + | 0.787457i | \(0.711397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.7391 | 1.80377 | 0.901886 | − | 0.431974i | \(-0.142183\pi\) | ||||
0.901886 | + | 0.431974i | \(0.142183\pi\) | |||||||
\(644\) | −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 | \(-0.0684101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.7137 | 1.08786 | ||||||||
\(650\) | −16.2237 | − | 22.9131i | −0.636348 | − | 0.898726i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −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 | 0 | ||||||||
\(655\) | −10.1324 | − | 1.66827i | −0.395906 | − | 0.0651848i | ||||
\(656\) | 2.27103 | + | 6.98950i | 0.0886687 | + | 0.272894i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.2954 | + | 34.7638i | 0.440342 | + | 1.35523i | ||||
\(659\) | −25.9633 | − | 18.8635i | −1.01139 | − | 0.734816i | −0.0468880 | − | 0.998900i | \(-0.514930\pi\) |
−0.964500 | + | 0.264084i | \(0.914930\pi\) | |||||||
\(660\) | 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 | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.17435 | + | 0.853212i | −0.0455734 | + | 0.0331110i | ||||
\(665\) | 20.5121 | + | 3.37725i | 0.795424 | + | 0.130964i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.706281 | + | 2.17371i | 0.0273473 | + | 0.0841663i | ||||
\(668\) | 20.6065 | 0.797289 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.5660 | + | 10.3213i | −0.794533 | + | 0.398745i | ||||
\(671\) | 10.1908 | − | 31.3642i | 0.393413 | − | 1.21080i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.6367 | + | 20.0792i | −1.06531 | + | 0.773997i | −0.975064 | − | 0.221922i | \(-0.928767\pi\) |
−0.0902506 | + | 0.995919i | \(0.528767\pi\) | |||||||
\(674\) | −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 | \(0.243582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.99017 | − | 9.20281i | 0.114752 | − | 0.353171i | ||||
\(680\) | 1.69028 | + | 11.1105i | 0.0648194 | + | 0.426068i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.3166 | 1.04601 | ||||||||
\(683\) | −6.02604 | − | 18.5463i | −0.230580 | − | 0.709653i | −0.997677 | − | 0.0681215i | \(-0.978299\pi\) |
0.767097 | − | 0.641531i | \(-0.221701\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.5013 | − | 15.3074i | 1.16539 | − | 0.584866i | ||||
\(686\) | 8.39634 | − | 6.10030i | 0.320574 | − | 0.232910i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.543375 | + | 1.67234i | 0.0206262 | + | 0.0634810i | ||||
\(695\) | 6.13371 | + | 40.3179i | 0.232665 | + | 1.52934i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.23116 | − | 3.78914i | 0.0466337 | − | 0.143524i | ||||
\(698\) | −29.7666 | + | 21.6267i | −1.12668 | + | 0.818583i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.1580 | − | 5.34431i | 0.648510 | − | 0.201996i | ||||
\(701\) | 20.4085 | 0.770820 | 0.385410 | − | 0.922745i | \(-0.374060\pi\) | ||||
0.385410 | + | 0.922745i | \(0.374060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 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 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.3334 | − | 9.68727i | −0.500746 | − | 0.363813i | 0.308556 | − | 0.951206i | \(-0.400154\pi\) |
−0.809302 | + | 0.587393i | \(0.800154\pi\) | |||||||
\(710\) | 30.5005 | + | 5.02182i | 1.14466 | + | 0.188466i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.21829 | + | 3.79131i | 0.195564 | + | 0.142085i | ||||
\(713\) | −1.28072 | − | 0.930497i | −0.0479633 | − | 0.0348474i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.9742 | − | 38.6171i | 0.746992 | − | 1.44420i | ||||
\(716\) | −4.74294 | − | 3.44595i | −0.177252 | − | 0.128781i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −46.3309 | −1.72905 | ||||||||
\(719\) | −9.60466 | − | 29.5601i | −0.358193 | − | 1.10241i | −0.954135 | − | 0.299378i | \(-0.903221\pi\) |
0.595941 | − | 0.803028i | \(-0.296779\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.3186 | + | 44.0681i | −0.533253 | + | 1.64118i | ||||
\(722\) | −7.08642 | + | 21.8098i | −0.263729 | + | 0.811675i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.4080 | 0.498305 | ||||||||
\(725\) | −18.6735 | + | 5.81636i | −0.693516 | + | 0.216014i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.771033 | − | 0.560188i | 0.0285960 | − | 0.0207762i | −0.573395 | − | 0.819279i | \(-0.694374\pi\) |
0.601991 | + | 0.798503i | \(0.294374\pi\) | |||||||
\(728\) | 7.44492 | − | 22.9131i | 0.275927 | − | 0.849217i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −35.7082 | − | 36.1467i | −1.32162 | − | 1.33785i | ||||
\(731\) | −1.06445 | − | 3.27603i | −0.0393700 | − | 0.121168i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.75118 | − | 14.6226i | −0.175489 | − | 0.540099i | 0.824167 | − | 0.566347i | \(-0.191644\pi\) |
−0.999655 | + | 0.0262485i | \(0.991644\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.20110 | + | 3.05228i | −0.154540 | + | 0.112280i | −0.662368 | − | 0.749179i | \(-0.730449\pi\) |
0.507828 | + | 0.861458i | \(0.330449\pi\) | |||||||
\(740\) | −0.00639318 | − | 0.0420234i | −0.000235018 | − | 0.00154481i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.85301 | + | 18.0137i | 0.214871 | + | 0.661305i | ||||
\(743\) | 42.3399 | 1.55330 | 0.776650 | − | 0.629932i | \(-0.216917\pi\) | ||||
0.776650 | + | 0.629932i | \(0.216917\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1344 | + | 29.2601i | −0.554482 | + | 1.07201i | ||||
\(746\) | 3.36980 | − | 10.3712i | 0.123377 | − | 0.379716i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | 0 | ||||||||
\(754\) | 6.78733 | − | 20.8892i | 0.247180 | − | 0.760741i | ||||
\(755\) | −17.9113 | + | 34.6288i | −0.651860 | + | 1.26027i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.27680 | −0.337171 | −0.168585 | − | 0.985687i | \(-0.553920\pi\) | ||||
−0.168585 | + | 0.985687i | \(0.553920\pi\) | |||||||
\(758\) | −0.0815549 | − | 0.251000i | −0.00296221 | − | 0.00911674i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.47279 | + | 9.68091i | 0.0534238 | + | 0.351163i | ||||
\(761\) | −14.0868 | + | 10.2346i | −0.510644 | + | 0.371005i | −0.813068 | − | 0.582169i | \(-0.802204\pi\) |
0.302424 | + | 0.953174i | \(0.402204\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −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 | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.16648 | − | 22.0562i | −0.258430 | − | 0.795365i | −0.993134 | − | 0.116978i | \(-0.962679\pi\) |
0.734705 | − | 0.678387i | \(-0.237321\pi\) | |||||||
\(770\) | 62.4640 | + | 63.2312i | 2.25105 | + | 2.27869i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | \(0.331582\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.09574 | − | 10.8615i | 0.290808 | − | 0.390157i | ||||
\(776\) | 4.55807 | 0.163625 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 34.5023 | + | 25.0674i | 1.23222 | + | 0.895263i | ||||
\(785\) | 18.3994 | − | 35.5724i | 0.656703 | − | 1.26963i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.8703 | − | 15.1632i | −0.743946 | − | 0.540509i | 0.149998 | − | 0.988686i | \(-0.452073\pi\) |
−0.893944 | + | 0.448178i | \(0.852073\pi\) | |||||||
\(788\) | −10.6091 | − | 7.70795i | −0.377933 | − | 0.274584i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 62.7406 | + | 10.3301i | 2.23221 | + | 0.367527i | ||||
\(791\) | 34.0819 | + | 24.7619i | 1.21181 | + | 0.880433i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(0.120930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.7052 | 0.520233 | ||||||||
\(800\) | 13.8813 | + | 19.6048i | 0.490778 | + | 0.693136i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −45.3261 | + | 32.9313i | −1.60052 | + | 1.16285i | ||||
\(803\) | 24.3146 | − | 74.8326i | 0.858043 | − | 2.64079i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.774709 | − | 5.09229i | −0.0273049 | − | 0.179480i | ||||
\(806\) | 4.70111 | + | 14.4685i | 0.165589 | + | 0.509632i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.94533 | − | 12.1425i | −0.138796 | − | 0.427171i | ||||
\(809\) | 30.3414 | + | 22.0443i | 1.06675 | + | 0.775037i | 0.975325 | − | 0.220776i | \(-0.0708588\pi\) |
0.0914219 | + | 0.995812i | \(0.470859\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.170081 | − | 0.123571i | 0.00596135 | − | 0.00433117i | ||||
\(815\) | −43.4872 | + | 21.8245i | −1.52329 | + | 0.764480i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.927484 | − | 2.85450i | −0.0324486 | − | 0.0998664i | ||||
\(818\) | −67.5317 | −2.36119 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.451366 | − | 2.96690i | −0.0157624 | − | 0.103609i | ||||
\(821\) | −13.9216 | + | 42.8462i | −0.485866 | + | 1.49534i | 0.344857 | + | 0.938655i | \(0.387927\pi\) |
−0.830723 | + | 0.556686i | \(0.812073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.5397 | − | 24.3680i | 1.16912 | − | 0.849415i | 0.178217 | − | 0.983991i | \(-0.442967\pi\) |
0.990903 | + | 0.134576i | \(0.0429672\pi\) | |||||||
\(824\) | −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 | 0 | ||||||||
\(829\) | 7.45527 | − | 22.9450i | 0.258932 | − | 0.796911i | −0.734097 | − | 0.679044i | \(-0.762394\pi\) |
0.993029 | − | 0.117867i | \(-0.0376056\pi\) | |||||||
\(830\) | 2.66554 | − | 1.33773i | 0.0925221 | − | 0.0464333i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.87864 | 0.203805 | ||||||||
\(833\) | −7.14441 | − | 21.9882i | −0.247539 | − | 0.761847i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.8703 | + | 8.21101i | 1.72583 | + | 0.284154i | ||||
\(836\) | 10.2768 | − | 7.46650i | 0.355429 | − | 0.258234i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.0014 | + | 19.6177i | 0.932748 | + | 0.677681i | ||||
\(839\) | −14.3890 | + | 10.4542i | −0.496763 | + | 0.360919i | −0.807779 | − | 0.589485i | \(-0.799331\pi\) |
0.311016 | + | 0.950405i | \(0.399331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0826 | + | 8.05197i | 0.382158 | + | 0.277654i | ||||
\(842\) | −21.2671 | − | 65.4534i | −0.732913 | − | 2.25567i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.838452 | + | 2.58049i | 0.0288607 | + | 0.0888242i | ||||
\(845\) | −4.79127 | − | 0.788869i | −0.164825 | − | 0.0271379i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.1322 | + | 89.6598i | −1.00100 | + | 3.08075i | ||||
\(848\) | −11.3713 | + | 8.26176i | −0.390493 | + | 0.283710i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.281854 | − | 23.0884i | 0.00966750 | − | 0.791927i | ||||
\(851\) | −0.0121834 | −0.000417642 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.96878 | − | 12.2147i | 0.135889 | − | 0.418222i | −0.859839 | − | 0.510566i | \(-0.829436\pi\) |
0.995727 | + | 0.0923439i | \(0.0294359\pi\) | |||||||
\(854\) | −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 | \(0.414143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.90628 | − | 2.83808i | −0.133281 | − | 0.0968340i | 0.519147 | − | 0.854685i | \(-0.326250\pi\) |
−0.652428 | + | 0.757851i | \(0.726250\pi\) | |||||||
\(860\) | −1.82346 | − | 1.84586i | −0.0621796 | − | 0.0629433i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | \(0.771878\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.34235 | − | 28.5430i | −0.147644 | − | 0.970490i | ||||
\(866\) | 17.1529 | + | 12.4623i | 0.582879 | + | 0.423486i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −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 | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.35111 | −0.0795274 | ||||||||
\(875\) | 43.6540 | − | 6.09702i | 1.47577 | − | 0.206117i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.05840 | + | 3.67515i | −0.170810 | + | 0.124101i | −0.669906 | − | 0.742446i | \(-0.733666\pi\) |
0.499096 | + | 0.866547i | \(0.333666\pi\) | |||||||
\(878\) | 5.78199 | − | 17.7951i | 0.195133 | − | 0.600557i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30.3025 | + | 58.5852i | −1.02150 | + | 1.97491i | ||||
\(881\) | 5.18532 | + | 15.9588i | 0.174698 | + | 0.537665i | 0.999620 | − | 0.0275821i | \(-0.00878076\pi\) |
−0.824922 | + | 0.565247i | \(0.808781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.01740 | + | 15.4420i | 0.168849 | + | 0.519664i | 0.999299 | − | 0.0374289i | \(-0.0119168\pi\) |
−0.830450 | + | 0.557093i | \(0.811917\pi\) | |||||||
\(884\) | 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 | 0 | ||||||||
\(889\) | −43.1945 | + | 31.3827i | −1.44870 | + | 1.05254i | ||||
\(890\) | −9.31351 | − | 9.42790i | −0.312190 | − | 0.316024i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.0858359 | − | 0.264176i | −0.00287400 | − | 0.00884526i | ||||
\(893\) | 12.8131 | 0.428774 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.1054 | − | 10.2295i | −0.337787 | − | 0.341936i | ||||
\(896\) | −15.4198 | + | 47.4572i | −0.515138 | + | 1.58543i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.13219 | + | 18.8729i | −0.203953 | + | 0.627704i | ||||
\(905\) | 32.4491 | + | 5.34265i | 1.07865 | + | 0.177596i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.00465 | 0.298995 | 0.149497 | − | 0.988762i | \(-0.452234\pi\) | ||||
0.149497 | + | 0.988762i | \(0.452234\pi\) | |||||||
\(908\) | 2.69670 | + | 8.29960i | 0.0894933 | + | 0.275432i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.7412 | + | 43.9666i | −0.753863 | + | 1.45748i | ||||
\(911\) | 24.2303 | − | 17.6044i | 0.802786 | − | 0.583258i | −0.108944 | − | 0.994048i | \(-0.534747\pi\) |
0.911730 | + | 0.410789i | \(0.134747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 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 | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.76125 | + | 8.49826i | 0.0910853 | + | 0.280332i | 0.986214 | − | 0.165477i | \(-0.0529162\pi\) |
−0.895128 | + | 0.445808i | \(0.852916\pi\) | |||||||
\(920\) | 2.16855 | − | 1.08831i | 0.0714951 | − | 0.0358806i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.34995 | + | 19.5431i | −0.209125 | + | 0.643619i | ||||
\(923\) | −21.5675 | + | 15.6697i | −0.709902 | + | 0.515774i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.00127263 | − | 0.104249i | 4.18439e−5 | − | 0.00342770i | ||||
\(926\) | −46.4133 | −1.52524 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.80735 | + | 17.8732i | −0.190636 | + | 0.586716i | ||||
\(929\) | 12.8117 | − | 39.4304i | 0.420339 | − | 1.29367i | −0.487048 | − | 0.873375i | \(-0.661926\pi\) |
0.907387 | − | 0.420296i | \(-0.138074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.22514 | − | 19.1590i | −0.204021 | − | 0.627911i | ||||
\(932\) | −18.3248 | −0.600250 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.44243 | − | 3.95416i | −0.178082 | − | 0.129384i | ||||
\(935\) | 31.9583 | − | 16.0386i | 1.04515 | − | 0.524519i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.8749 | − | 12.2603i | −0.551278 | − | 0.400527i | 0.276978 | − | 0.960876i | \(-0.410667\pi\) |
−0.828256 | + | 0.560349i | \(0.810667\pi\) | |||||||
\(938\) | 32.8220 | + | 23.8466i | 1.07168 | + | 0.778618i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.89989 | − | 4.96837i | 0.322899 | − | 0.162050i | ||||
\(941\) | 2.97219 | + | 2.15942i | 0.0968905 | + | 0.0703951i | 0.635176 | − | 0.772368i | \(-0.280928\pi\) |
−0.538285 | + | 0.842763i | \(0.680928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | \(-0.0722270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.8204 | 1.42247 | ||||||||
\(950\) | 0.245588 | − | 20.1177i | 0.00796791 | − | 0.652703i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | \(0.963789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.4160 | − | 6.73299i | 0.434133 | − | 0.217875i | ||||
\(956\) | −4.97625 | − | 15.3153i | −0.160943 | − | 0.495333i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −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 | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.7865 | + | 15.8288i | −0.701697 | + | 0.509813i | ||||
\(965\) | 4.95995 | − | 9.58931i | 0.159666 | − | 0.308691i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.96663 | − | 27.5965i | −0.288347 | − | 0.887442i | −0.985375 | − | 0.170398i | \(-0.945495\pi\) |
0.697028 | − | 0.717044i | \(-0.254505\pi\) | |||||||
\(968\) | −44.4077 | −1.42732 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.24056 | − | 1.52143i | −0.296696 | − | 0.0488502i | ||||
\(971\) | 1.16588 | − | 3.58821i | 0.0374149 | − | 0.115151i | −0.930605 | − | 0.366026i | \(-0.880718\pi\) |
0.968020 | + | 0.250875i | \(0.0807182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | \(0.100177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.34180 | − | 19.5181i | 0.202685 | − | 0.623800i | ||||
\(980\) | −12.2388 | − | 12.3891i | −0.390955 | − | 0.395757i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.8104 | 1.81289 | ||||||||
\(983\) | −7.28128 | − | 22.4095i | −0.232237 | − | 0.714752i | −0.997476 | − | 0.0710055i | \(-0.977379\pi\) |
0.765239 | − | 0.643746i | \(-0.222621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.6040 | − | 22.8816i | −0.720223 | − | 0.729068i | ||||
\(986\) | 14.6143 | − | 10.6179i | 0.465413 | − | 0.338143i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.8413 | − | 51.8323i | −0.534175 | − | 1.64402i | ||||
\(995\) | −8.96425 | + | 17.3310i | −0.284186 | + | 0.549430i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.5733 | − | 41.7742i | 0.429870 | − | 1.32300i | −0.468384 | − | 0.883525i | \(-0.655164\pi\) |
0.898254 | − | 0.439478i | \(-0.144836\pi\) | |||||||
\(998\) | 56.7993 | − | 41.2671i | 1.79795 | − | 1.30629i | ||||
\(999\) | 0 | 0 |
(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 | 225.2.h.c.136.1 | 8 | ||
3.2 | odd | 2 | 75.2.g.b.61.2 | yes | 8 | ||
15.2 | even | 4 | 375.2.i.b.199.3 | 16 | |||
15.8 | even | 4 | 375.2.i.b.199.2 | 16 | |||
15.14 | odd | 2 | 375.2.g.b.301.1 | 8 | |||
25.4 | even | 10 | 5625.2.a.n.1.1 | 4 | |||
25.16 | even | 5 | inner | 225.2.h.c.91.1 | 8 | ||
25.21 | even | 5 | 5625.2.a.i.1.4 | 4 | |||
75.29 | odd | 10 | 1875.2.a.e.1.4 | 4 | |||
75.38 | even | 20 | 375.2.i.b.49.3 | 16 | |||
75.41 | odd | 10 | 75.2.g.b.16.2 | ✓ | 8 | ||
75.47 | even | 20 | 1875.2.b.c.1249.3 | 8 | |||
75.53 | even | 20 | 1875.2.b.c.1249.6 | 8 | |||
75.59 | odd | 10 | 375.2.g.b.76.1 | 8 | |||
75.62 | even | 20 | 375.2.i.b.49.2 | 16 | |||
75.71 | odd | 10 | 1875.2.a.h.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.16.2 | ✓ | 8 | 75.41 | odd | 10 | ||
75.2.g.b.61.2 | yes | 8 | 3.2 | odd | 2 | ||
225.2.h.c.91.1 | 8 | 25.16 | even | 5 | inner | ||
225.2.h.c.136.1 | 8 | 1.1 | even | 1 | trivial | ||
375.2.g.b.76.1 | 8 | 75.59 | odd | 10 | |||
375.2.g.b.301.1 | 8 | 15.14 | odd | 2 | |||
375.2.i.b.49.2 | 16 | 75.62 | even | 20 | |||
375.2.i.b.49.3 | 16 | 75.38 | even | 20 | |||
375.2.i.b.199.2 | 16 | 15.8 | even | 4 | |||
375.2.i.b.199.3 | 16 | 15.2 | even | 4 | |||
1875.2.a.e.1.4 | 4 | 75.29 | odd | 10 | |||
1875.2.a.h.1.1 | 4 | 75.71 | odd | 10 | |||
1875.2.b.c.1249.3 | 8 | 75.47 | even | 20 | |||
1875.2.b.c.1249.6 | 8 | 75.53 | even | 20 | |||
5625.2.a.i.1.4 | 4 | 25.21 | even | 5 | |||
5625.2.a.n.1.1 | 4 | 25.4 | even | 10 |