Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(136,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.136");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.w (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.523596960000.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 136.3 | ||
Root | \(-0.336732 - 0.583237i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.136 |
Dual form | 315.3.w.a.271.3 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.336732 | + | 0.583237i | 0.168366 | + | 0.291618i | 0.937845 | − | 0.347053i | \(-0.112818\pi\) |
−0.769480 | + | 0.638671i | \(0.779484\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.77322 | − | 3.07131i | 0.443306 | − | 0.767828i | ||||
\(5\) | −1.93649 | + | 1.11803i | −0.387298 | + | 0.223607i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.82455 | − | 1.55742i | −0.974935 | − | 0.222489i | ||||
\(8\) | 5.08226 | 0.635282 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.30416 | − | 0.752955i | −0.130416 | − | 0.0752955i | ||||
\(11\) | −0.0223800 | + | 0.0387632i | −0.00203454 | + | 0.00352393i | −0.867041 | − | 0.498237i | \(-0.833981\pi\) |
0.865006 | + | 0.501761i | \(0.167314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 23.0010i | − | 1.76931i | −0.466246 | − | 0.884655i | \(-0.654394\pi\) | ||
0.466246 | − | 0.884655i | \(-0.345606\pi\) | |||||||
\(14\) | −1.38970 | − | 4.50476i | −0.0992641 | − | 0.321768i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.38154 | − | 9.32109i | −0.336346 | − | 0.582568i | ||||
\(17\) | 8.16292 | + | 4.71286i | 0.480172 | + | 0.277227i | 0.720488 | − | 0.693467i | \(-0.243918\pi\) |
−0.240316 | + | 0.970695i | \(0.577251\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.991050 | − | 0.572183i | 0.0521605 | − | 0.0301149i | −0.473693 | − | 0.880690i | \(-0.657079\pi\) |
0.525853 | + | 0.850575i | \(0.323746\pi\) | |||||||
\(20\) | 7.93010i | 0.396505i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0301442 | −0.00137019 | ||||||||
\(23\) | −22.1202 | − | 38.3133i | −0.961748 | − | 1.66580i | −0.718110 | − | 0.695929i | \(-0.754993\pi\) |
−0.243637 | − | 0.969866i | \(-0.578341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.100000 | − | 0.173205i | ||||
\(26\) | 13.4150 | − | 7.74518i | 0.515963 | − | 0.297891i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.8848 | + | 18.1987i | −0.603028 | + | 0.649952i | ||||
\(29\) | −53.0004 | −1.82760 | −0.913799 | − | 0.406166i | \(-0.866866\pi\) | ||||
−0.913799 | + | 0.406166i | \(0.866866\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.5690 | + | 11.2982i | 0.631258 | + | 0.364457i | 0.781239 | − | 0.624232i | \(-0.214588\pi\) |
−0.149981 | + | 0.988689i | \(0.547921\pi\) | |||||||
\(32\) | 13.7888 | − | 23.8829i | 0.430899 | − | 0.746340i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.34788i | 0.186702i | ||||||||
\(35\) | 14.9569 | − | 4.61414i | 0.427341 | − | 0.131833i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −21.1418 | − | 36.6186i | −0.571400 | − | 0.989693i | −0.996423 | − | 0.0845106i | \(-0.973067\pi\) |
0.425023 | − | 0.905183i | \(-0.360266\pi\) | |||||||
\(38\) | 0.667436 | + | 0.385344i | 0.0175641 | + | 0.0101406i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.84175 | + | 5.68214i | −0.246044 | + | 0.142053i | ||||
\(41\) | 38.2787i | 0.933628i | 0.884356 | + | 0.466814i | \(0.154598\pi\) | ||||
−0.884356 | + | 0.466814i | \(0.845402\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 76.5222 | 1.77959 | 0.889793 | − | 0.456365i | \(-0.150849\pi\) | ||||
0.889793 | + | 0.456365i | \(0.150849\pi\) | |||||||
\(44\) | 0.0793693 | + | 0.137472i | 0.00180385 | + | 0.00312436i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.8971 | − | 25.8026i | 0.323851 | − | 0.560926i | ||||
\(47\) | 23.5070 | − | 13.5718i | 0.500149 | − | 0.288761i | −0.228626 | − | 0.973514i | \(-0.573423\pi\) |
0.728775 | + | 0.684753i | \(0.240090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.1489 | + | 21.2574i | 0.900998 | + | 0.433824i | ||||
\(50\) | 3.36732 | 0.0673464 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −70.6434 | − | 40.7860i | −1.35853 | − | 0.784345i | ||||
\(53\) | 9.49388 | − | 16.4439i | 0.179130 | − | 0.310262i | −0.762453 | − | 0.647044i | \(-0.776005\pi\) |
0.941583 | + | 0.336782i | \(0.109338\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.100086i | − | 0.00181975i | ||||||
\(56\) | −34.6841 | − | 7.91521i | −0.619359 | − | 0.141343i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −17.8469 | − | 30.9118i | −0.307705 | − | 0.532961i | ||||
\(59\) | 4.21731 | + | 2.43486i | 0.0714798 | + | 0.0412689i | 0.535314 | − | 0.844653i | \(-0.320193\pi\) |
−0.463834 | + | 0.885922i | \(0.653527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33.6432 | + | 19.4239i | −0.551528 | + | 0.318425i | −0.749738 | − | 0.661735i | \(-0.769821\pi\) |
0.198210 | + | 0.980160i | \(0.436487\pi\) | |||||||
\(62\) | 15.2178i | 0.245449i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −24.4798 | −0.382497 | ||||||||
\(65\) | 25.7159 | + | 44.5413i | 0.395630 | + | 0.685251i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50439 | − | 6.06978i | 0.0523043 | − | 0.0905938i | −0.838688 | − | 0.544612i | \(-0.816677\pi\) |
0.890992 | + | 0.454019i | \(0.150010\pi\) | |||||||
\(68\) | 28.9494 | − | 16.7139i | 0.425726 | − | 0.245793i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.72761 | + | 7.16970i | 0.110394 | + | 0.102424i | ||||
\(71\) | 46.8735 | 0.660190 | 0.330095 | − | 0.943948i | \(-0.392919\pi\) | ||||
0.330095 | + | 0.943948i | \(0.392919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 72.3956 | + | 41.7976i | 0.991720 | + | 0.572570i | 0.905788 | − | 0.423731i | \(-0.139280\pi\) |
0.0859319 | + | 0.996301i | \(0.472613\pi\) | |||||||
\(74\) | 14.2382 | − | 24.6613i | 0.192408 | − | 0.333261i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.05843i | − | 0.0534004i | ||||||
\(77\) | 0.213104 | − | 0.229686i | 0.00276758 | − | 0.00298294i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2397 | − | 17.7357i | −0.129617 | − | 0.224502i | 0.793912 | − | 0.608033i | \(-0.208041\pi\) |
−0.923528 | + | 0.383531i | \(0.874708\pi\) | |||||||
\(80\) | 20.8426 | + | 12.0335i | 0.260533 | + | 0.150419i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −22.3256 | + | 12.8897i | −0.272263 | + | 0.157191i | ||||
\(83\) | 125.683i | 1.51425i | 0.653271 | + | 0.757124i | \(0.273396\pi\) | ||||
−0.653271 | + | 0.757124i | \(0.726604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.0766 | −0.247960 | ||||||||
\(86\) | 25.7674 | + | 44.6305i | 0.299621 | + | 0.518960i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.113741 | + | 0.197005i | −0.00129251 | + | 0.00223869i | ||||
\(89\) | −40.4455 | + | 23.3512i | −0.454444 | + | 0.262373i | −0.709705 | − | 0.704499i | \(-0.751172\pi\) |
0.255261 | + | 0.966872i | \(0.417838\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35.8223 | + | 156.972i | −0.393651 | + | 1.72496i | ||||
\(92\) | −156.896 | −1.70539 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.8311 | + | 9.14010i | 0.168416 | + | 0.0972351i | ||||
\(95\) | −1.27944 | + | 2.21606i | −0.0134678 | + | 0.0233269i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.11494i | − | 0.0321128i | −0.999871 | − | 0.0160564i | \(-0.994889\pi\) | ||
0.999871 | − | 0.0160564i | \(-0.00511112\pi\) | |||||||
\(98\) | 2.46826 | + | 32.9073i | 0.0251863 | + | 0.335789i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.86612 | − | 15.3566i | −0.0886612 | − | 0.153566i | ||||
\(101\) | 77.4555 | + | 44.7189i | 0.766886 | + | 0.442762i | 0.831763 | − | 0.555132i | \(-0.187332\pi\) |
−0.0648768 | + | 0.997893i | \(0.520665\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −79.1385 | + | 45.6906i | −0.768335 | + | 0.443598i | −0.832280 | − | 0.554355i | \(-0.812965\pi\) |
0.0639453 | + | 0.997953i | \(0.479632\pi\) | |||||||
\(104\) | − | 116.897i | − | 1.12401i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.7876 | 0.120637 | ||||||||
\(107\) | −52.5515 | − | 91.0219i | −0.491136 | − | 0.850672i | 0.508812 | − | 0.860877i | \(-0.330085\pi\) |
−0.999948 | + | 0.0102057i | \(0.996751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.8507 | + | 48.2388i | −0.255511 | + | 0.442558i | −0.965034 | − | 0.262124i | \(-0.915577\pi\) |
0.709523 | + | 0.704682i | \(0.248910\pi\) | |||||||
\(110\) | 0.0583739 | − | 0.0337022i | 0.000530672 | − | 0.000306384i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 22.2097 | + | 71.9936i | 0.198301 | + | 0.642800i | ||||
\(113\) | 5.25425 | 0.0464978 | 0.0232489 | − | 0.999730i | \(-0.492599\pi\) | ||||
0.0232489 | + | 0.999730i | \(0.492599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 85.6711 | + | 49.4623i | 0.744967 | + | 0.430107i | ||||
\(116\) | −93.9815 | + | 162.781i | −0.810185 | + | 1.40328i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.27958i | 0.0277931i | ||||||||
\(119\) | −48.3683 | − | 44.8763i | −0.406457 | − | 0.377111i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.4990 | + | 104.787i | 0.499992 | + | 0.866011i | ||||
\(122\) | −22.6575 | − | 13.0813i | −0.185717 | − | 0.107224i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 69.4005 | − | 40.0684i | 0.559681 | − | 0.323132i | ||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.54989 | −0.0436999 | −0.0218500 | − | 0.999761i | \(-0.506956\pi\) | ||||
−0.0218500 | + | 0.999761i | \(0.506956\pi\) | |||||||
\(128\) | −63.3983 | − | 109.809i | −0.495299 | − | 0.857883i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −17.3187 | + | 29.9969i | −0.133221 | + | 0.230746i | ||||
\(131\) | 144.212 | − | 83.2606i | 1.10085 | − | 0.635577i | 0.164407 | − | 0.986393i | \(-0.447429\pi\) |
0.936445 | + | 0.350815i | \(0.114096\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.65460 | + | 2.36141i | −0.0575534 | + | 0.0177550i | ||||
\(134\) | 4.72016 | 0.0352251 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 41.4861 | + | 23.9520i | 0.305045 | + | 0.176118i | ||||
\(137\) | 36.4731 | − | 63.1733i | 0.266227 | − | 0.461119i | −0.701657 | − | 0.712515i | \(-0.747556\pi\) |
0.967884 | + | 0.251395i | \(0.0808895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 114.994i | − | 0.827292i | −0.910438 | − | 0.413646i | \(-0.864255\pi\) | ||
0.910438 | − | 0.413646i | \(-0.135745\pi\) | |||||||
\(140\) | 12.3505 | − | 54.1193i | 0.0882178 | − | 0.386567i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.7838 | + | 27.3383i | 0.111153 | + | 0.192523i | ||||
\(143\) | 0.891594 | + | 0.514762i | 0.00623492 | + | 0.00359973i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 102.635 | − | 59.2562i | 0.707826 | − | 0.408664i | ||||
\(146\) | 56.2983i | 0.385605i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −149.956 | −1.01322 | ||||||||
\(149\) | 36.3729 | + | 62.9997i | 0.244113 | + | 0.422817i | 0.961882 | − | 0.273465i | \(-0.0881698\pi\) |
−0.717769 | + | 0.696282i | \(0.754836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 63.5643 | − | 110.097i | 0.420956 | − | 0.729117i | −0.575078 | − | 0.818099i | \(-0.695028\pi\) |
0.996033 | + | 0.0889823i | \(0.0283615\pi\) | |||||||
\(152\) | 5.03677 | − | 2.90798i | 0.0331366 | − | 0.0191315i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.205720 | + | 0.0469471i | 0.00133585 | + | 0.000304851i | ||||
\(155\) | −50.5270 | −0.325980 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 130.826 | + | 75.5327i | 0.833290 | + | 0.481100i | 0.854978 | − | 0.518665i | \(-0.173571\pi\) |
−0.0216880 | + | 0.999765i | \(0.506904\pi\) | |||||||
\(158\) | 6.89607 | − | 11.9443i | 0.0436460 | − | 0.0755971i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 61.6653i | 0.385408i | ||||||||
\(161\) | 91.2904 | + | 295.921i | 0.567021 | + | 1.83802i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 29.9639 | + | 51.8990i | 0.183828 | + | 0.318399i | 0.943181 | − | 0.332280i | \(-0.107818\pi\) |
−0.759353 | + | 0.650679i | \(0.774485\pi\) | |||||||
\(164\) | 117.566 | + | 67.8768i | 0.716866 | + | 0.413883i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −73.3027 | + | 42.3213i | −0.441582 | + | 0.254948i | ||||
\(167\) | − | 224.089i | − | 1.34185i | −0.741526 | − | 0.670924i | \(-0.765898\pi\) | ||
0.741526 | − | 0.670924i | \(-0.234102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −360.047 | −2.13046 | ||||||||
\(170\) | −7.09715 | − | 12.2926i | −0.0417479 | − | 0.0723096i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 135.691 | − | 235.024i | 0.788901 | − | 1.36642i | ||||
\(173\) | −165.080 | + | 95.3092i | −0.954221 | + | 0.550920i | −0.894390 | − | 0.447288i | \(-0.852390\pi\) |
−0.0598317 | + | 0.998208i | \(0.519056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.8052 | + | 25.6576i | −0.136030 | + | 0.146615i | ||||
\(176\) | 0.481754 | 0.00273724 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.2386 | − | 15.7262i | −0.153026 | − | 0.0883494i | ||||
\(179\) | 108.931 | − | 188.674i | 0.608553 | − | 1.05404i | −0.382926 | − | 0.923779i | \(-0.625084\pi\) |
0.991479 | − | 0.130265i | \(-0.0415829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 39.0804i | − | 0.215914i | −0.994156 | − | 0.107957i | \(-0.965569\pi\) | ||
0.994156 | − | 0.107957i | \(-0.0344309\pi\) | |||||||
\(182\) | −103.614 | + | 31.9645i | −0.569308 | + | 0.175629i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −112.421 | − | 194.718i | −0.610981 | − | 1.05825i | ||||
\(185\) | 81.8818 | + | 47.2745i | 0.442604 | + | 0.255538i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.365372 | + | 0.210947i | −0.00195386 | + | 0.00112806i | ||||
\(188\) | − | 96.2632i | − | 0.512038i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.72331 | −0.00907006 | ||||||||
\(191\) | 94.7586 | + | 164.127i | 0.496118 | + | 0.859302i | 0.999990 | − | 0.00447651i | \(-0.00142492\pi\) |
−0.503872 | + | 0.863778i | \(0.668092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 136.570 | − | 236.547i | 0.707619 | − | 1.22563i | −0.258119 | − | 0.966113i | \(-0.583103\pi\) |
0.965738 | − | 0.259519i | \(-0.0835640\pi\) | |||||||
\(194\) | 1.81675 | − | 1.04890i | 0.00936467 | − | 0.00540669i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 143.574 | − | 97.9010i | 0.732520 | − | 0.499495i | ||||
\(197\) | −198.898 | −1.00963 | −0.504817 | − | 0.863226i | \(-0.668440\pi\) | ||||
−0.504817 | + | 0.863226i | \(0.668440\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 33.2334 | + | 19.1873i | 0.167002 | + | 0.0964185i | 0.581171 | − | 0.813781i | \(-0.302595\pi\) |
−0.414170 | + | 0.910200i | \(0.635928\pi\) | |||||||
\(200\) | 12.7056 | − | 22.0068i | 0.0635282 | − | 0.110034i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 60.2331i | 0.298184i | ||||||||
\(203\) | 361.704 | + | 82.5438i | 1.78179 | + | 0.406620i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −42.7969 | − | 74.1265i | −0.208766 | − | 0.361593i | ||||
\(206\) | −53.2969 | − | 30.7710i | −0.258723 | − | 0.149374i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −214.395 | + | 123.781i | −1.03074 | + | 0.595100i | ||||
\(209\) | 0.0512217i | 0.000245080i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −127.283 | −0.603238 | −0.301619 | − | 0.953429i | \(-0.597527\pi\) | ||||
−0.301619 | + | 0.953429i | \(0.597527\pi\) | |||||||
\(212\) | −33.6695 | − | 58.3173i | −0.158819 | − | 0.275082i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 35.3915 | − | 61.2999i | 0.165381 | − | 0.286448i | ||||
\(215\) | −148.185 | + | 85.5544i | −0.689230 | + | 0.397927i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −115.954 | − | 107.582i | −0.534349 | − | 0.495770i | ||||
\(218\) | −37.5129 | −0.172077 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.307396 | − | 0.177475i | −0.00139725 | − | 0.000806705i | ||||
\(221\) | 108.401 | − | 187.756i | 0.490501 | − | 0.849573i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 293.558i | − | 1.31641i | −0.752841 | − | 0.658203i | \(-0.771317\pi\) | ||
0.752841 | − | 0.658203i | \(-0.228683\pi\) | |||||||
\(224\) | −131.298 | + | 141.515i | −0.586151 | + | 0.631763i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.76927 | + | 3.06447i | 0.00782864 | + | 0.0135596i | ||||
\(227\) | −186.611 | − | 107.740i | −0.822077 | − | 0.474626i | 0.0290554 | − | 0.999578i | \(-0.490750\pi\) |
−0.851132 | + | 0.524952i | \(0.824083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 124.938 | − | 72.1332i | 0.545582 | − | 0.314992i | −0.201756 | − | 0.979436i | \(-0.564665\pi\) |
0.747338 | + | 0.664444i | \(0.231332\pi\) | |||||||
\(230\) | 66.6221i | 0.289661i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −269.361 | −1.16104 | ||||||||
\(233\) | −143.216 | − | 248.058i | −0.614662 | − | 1.06463i | −0.990444 | − | 0.137918i | \(-0.955959\pi\) |
0.375781 | − | 0.926708i | \(-0.377374\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.3474 | + | 52.5633i | −0.129138 | + | 0.223673i | ||||
\(236\) | 14.9565 | − | 8.63511i | 0.0633748 | − | 0.0365895i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.88632 | − | 43.3214i | 0.0415392 | − | 0.182023i | ||||
\(239\) | 413.420 | 1.72979 | 0.864895 | − | 0.501954i | \(-0.167385\pi\) | ||||
0.864895 | + | 0.501954i | \(0.167385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 256.252 | + | 147.947i | 1.06329 | + | 0.613890i | 0.926340 | − | 0.376689i | \(-0.122937\pi\) |
0.136948 | + | 0.990578i | \(0.456271\pi\) | |||||||
\(242\) | −40.7439 | + | 70.5705i | −0.168363 | + | 0.291613i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 137.772i | 0.564639i | ||||||||
\(245\) | −109.260 | + | 8.19523i | −0.445961 | + | 0.0334499i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1608 | − | 22.7952i | −0.0532826 | − | 0.0922881i | ||||
\(248\) | 99.4547 | + | 57.4202i | 0.401027 | + | 0.231533i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.52078 | + | 3.76478i | −0.0260831 | + | 0.0150591i | ||||
\(251\) | − | 311.712i | − | 1.24188i | −0.783858 | − | 0.620940i | \(-0.786751\pi\) | ||
0.783858 | − | 0.620940i | \(-0.213249\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.98020 | 0.00782686 | ||||||||
\(254\) | −1.86882 | − | 3.23690i | −0.00735758 | − | 0.0127437i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.26320 | + | 10.8482i | −0.0244656 | + | 0.0423757i | ||||
\(257\) | 125.335 | − | 72.3619i | 0.487683 | − | 0.281564i | −0.235930 | − | 0.971770i | \(-0.575814\pi\) |
0.723613 | + | 0.690206i | \(0.242480\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 87.2525 | + | 282.832i | 0.336882 | + | 1.09202i | ||||
\(260\) | 182.400 | 0.701540 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 97.1213 | + | 56.0730i | 0.370692 | + | 0.214019i | ||||
\(263\) | −114.833 | + | 198.896i | −0.436626 | + | 0.756258i | −0.997427 | − | 0.0716928i | \(-0.977160\pi\) |
0.560801 | + | 0.827950i | \(0.310493\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 42.4579i | 0.160219i | ||||||||
\(266\) | −3.95481 | − | 3.66928i | −0.0148677 | − | 0.0137943i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.4281 | − | 21.5262i | −0.0463736 | − | 0.0803215i | ||||
\(269\) | −367.508 | − | 212.181i | −1.36620 | − | 0.788776i | −0.375760 | − | 0.926717i | \(-0.622618\pi\) |
−0.990440 | + | 0.137941i | \(0.955952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 252.710 | − | 145.902i | 0.932509 | − | 0.538385i | 0.0449051 | − | 0.998991i | \(-0.485701\pi\) |
0.887604 | + | 0.460607i | \(0.152368\pi\) | |||||||
\(272\) | − | 101.450i | − | 0.372977i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 49.1267 | 0.179294 | ||||||||
\(275\) | 0.111900 | + | 0.193816i | 0.000406908 | + | 0.000704786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 101.450 | − | 175.717i | 0.366247 | − | 0.634358i | −0.622729 | − | 0.782438i | \(-0.713976\pi\) |
0.988975 | + | 0.148080i | \(0.0473092\pi\) | |||||||
\(278\) | 67.0684 | − | 38.7220i | 0.241253 | − | 0.139288i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 76.0149 | − | 23.4503i | 0.271482 | − | 0.0837510i | ||||
\(281\) | −254.325 | −0.905071 | −0.452536 | − | 0.891746i | \(-0.649480\pi\) | ||||
−0.452536 | + | 0.891746i | \(0.649480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 384.259 | + | 221.852i | 1.35781 | + | 0.783930i | 0.989328 | − | 0.145706i | \(-0.0465455\pi\) |
0.368478 | + | 0.929636i | \(0.379879\pi\) | |||||||
\(284\) | 83.1172 | − | 143.963i | 0.292666 | − | 0.506912i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.693347i | 0.00242429i | ||||||||
\(287\) | 59.6161 | − | 261.235i | 0.207722 | − | 0.910227i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −100.078 | − | 173.340i | −0.346290 | − | 0.599792i | ||||
\(290\) | 69.1208 | + | 39.9069i | 0.238348 | + | 0.137610i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 256.747 | − | 148.233i | 0.879270 | − | 0.507647i | ||||
\(293\) | − | 223.513i | − | 0.762845i | −0.924401 | − | 0.381422i | \(-0.875434\pi\) | ||
0.924401 | − | 0.381422i | \(-0.124566\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.8890 | −0.0369120 | ||||||||
\(296\) | −107.448 | − | 186.105i | −0.363000 | − | 0.628734i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.4958 | + | 42.4280i | −0.0822007 | + | 0.142376i | ||||
\(299\) | −881.245 | + | 508.787i | −2.94731 | + | 1.70163i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −522.229 | − | 119.177i | −1.73498 | − | 0.395937i | ||||
\(302\) | 85.6165 | 0.283498 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.6667 | − | 6.15845i | −0.0350880 | − | 0.0202580i | ||||
\(305\) | 43.4332 | − | 75.2285i | 0.142404 | − | 0.246651i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 47.3887i | 0.154361i | 0.997017 | + | 0.0771803i | \(0.0245917\pi\) | ||||
−0.997017 | + | 0.0771803i | \(0.975408\pi\) | |||||||
\(308\) | −0.327559 | − | 1.06179i | −0.00106350 | − | 0.00344738i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.0140 | − | 29.4692i | −0.0548840 | − | 0.0950619i | ||||
\(311\) | 313.595 | + | 181.054i | 1.00834 | + | 0.582167i | 0.910706 | − | 0.413055i | \(-0.135538\pi\) |
0.0976367 | + | 0.995222i | \(0.468872\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −340.880 | + | 196.807i | −1.08907 | + | 0.628777i | −0.933330 | − | 0.359020i | \(-0.883111\pi\) |
−0.155744 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(314\) | 101.737i | 0.324003i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −72.6291 | −0.229839 | ||||||||
\(317\) | 288.788 | + | 500.196i | 0.911004 | + | 1.57791i | 0.812648 | + | 0.582754i | \(0.198025\pi\) |
0.0983557 | + | 0.995151i | \(0.468642\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.18615 | − | 2.05446i | 0.00371833 | − | 0.00644033i | ||||
\(320\) | 47.4049 | − | 27.3693i | 0.148140 | − | 0.0855289i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −141.852 | + | 152.890i | −0.440533 | + | 0.474814i | ||||
\(323\) | 10.7865 | 0.0333947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −99.5974 | − | 57.5026i | −0.306453 | − | 0.176931i | ||||
\(326\) | −20.1796 | + | 34.9521i | −0.0619006 | + | 0.107215i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 194.542i | 0.593117i | ||||||||
\(329\) | −181.562 | + | 56.0109i | −0.551859 | + | 0.170246i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 91.7974 | + | 158.998i | 0.277333 | + | 0.480356i | 0.970721 | − | 0.240209i | \(-0.0772160\pi\) |
−0.693388 | + | 0.720565i | \(0.743883\pi\) | |||||||
\(332\) | 386.011 | + | 222.863i | 1.16268 | + | 0.671275i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 130.697 | − | 75.4578i | 0.391307 | − | 0.225921i | ||||
\(335\) | 15.6721i | 0.0467824i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −205.885 | −0.610934 | −0.305467 | − | 0.952203i | \(-0.598813\pi\) | ||||
−0.305467 | + | 0.952203i | \(0.598813\pi\) | |||||||
\(338\) | −121.239 | − | 209.993i | −0.358696 | − | 0.621280i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −37.3735 | + | 64.7327i | −0.109922 | + | 0.190390i | ||||
\(341\) | −0.875907 | + | 0.505705i | −0.00256864 | + | 0.00148301i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −268.190 | − | 213.830i | −0.781894 | − | 0.623412i | ||||
\(344\) | 388.905 | 1.13054 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −111.176 | − | 64.1872i | −0.321317 | − | 0.185512i | ||||
\(347\) | 99.7256 | − | 172.730i | 0.287394 | − | 0.497780i | −0.685793 | − | 0.727796i | \(-0.740545\pi\) |
0.973187 | + | 0.230016i | \(0.0738779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 391.231i | 1.12101i | 0.828152 | + | 0.560503i | \(0.189392\pi\) | ||||
−0.828152 | + | 0.560503i | \(0.810608\pi\) | |||||||
\(350\) | −22.9804 | − | 5.24433i | −0.0656583 | − | 0.0149838i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.617185 | + | 1.06900i | 0.00175337 | + | 0.00303692i | ||||
\(353\) | 81.1020 | + | 46.8243i | 0.229751 | + | 0.132647i | 0.610457 | − | 0.792049i | \(-0.290986\pi\) |
−0.380706 | + | 0.924696i | \(0.624319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −90.7701 | + | 52.4061i | −0.255690 | + | 0.147623i | ||||
\(356\) | 165.628i | 0.465246i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 146.722 | 0.409838 | ||||||||
\(359\) | 73.8759 | + | 127.957i | 0.205782 | + | 0.356426i | 0.950382 | − | 0.311086i | \(-0.100693\pi\) |
−0.744599 | + | 0.667512i | \(0.767359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −179.845 | + | 311.501i | −0.498186 | + | 0.862884i | ||||
\(362\) | 22.7931 | − | 13.1596i | 0.0629644 | − | 0.0363525i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 418.588 | + | 388.367i | 1.14997 | + | 1.06694i | ||||
\(365\) | −186.925 | −0.512122 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −71.5485 | − | 41.3085i | −0.194955 | − | 0.112557i | 0.399345 | − | 0.916801i | \(-0.369238\pi\) |
−0.594300 | + | 0.804243i | \(0.702571\pi\) | |||||||
\(368\) | −238.081 | + | 412.369i | −0.646960 | + | 1.12057i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 63.6753i | 0.172095i | ||||||||
\(371\) | −90.4014 | + | 97.4361i | −0.243670 | + | 0.262631i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 171.325 | + | 296.744i | 0.459318 | + | 0.795561i | 0.998925 | − | 0.0463554i | \(-0.0147607\pi\) |
−0.539607 | + | 0.841917i | \(0.681427\pi\) | |||||||
\(374\) | −0.246064 | − | 0.142065i | −0.000657926 | − | 0.000379854i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 119.469 | − | 68.9752i | 0.317736 | − | 0.183445i | ||||
\(377\) | 1219.06i | 3.23359i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 355.679 | 0.938467 | 0.469233 | − | 0.883074i | \(-0.344530\pi\) | ||||
0.469233 | + | 0.883074i | \(0.344530\pi\) | |||||||
\(380\) | 4.53747 | + | 7.85912i | 0.0119407 | + | 0.0206819i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −63.8164 | + | 110.533i | −0.167059 | + | 0.289354i | ||||
\(383\) | 144.616 | − | 83.4939i | 0.377586 | − | 0.218000i | −0.299181 | − | 0.954196i | \(-0.596714\pi\) |
0.676768 | + | 0.736197i | \(0.263380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.155876 | + | 0.683043i | −0.000404873 | + | 0.00177414i | ||||
\(386\) | 183.950 | 0.476556 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.56695 | − | 5.52348i | −0.0246571 | − | 0.0142358i | ||||
\(389\) | 79.6452 | − | 137.950i | 0.204744 | − | 0.354626i | −0.745307 | − | 0.666721i | \(-0.767697\pi\) |
0.950051 | + | 0.312095i | \(0.101031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 416.998i | − | 1.06649i | ||||||
\(392\) | 224.376 | + | 108.035i | 0.572388 | + | 0.275601i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −66.9753 | − | 116.005i | −0.169988 | − | 0.294428i | ||||
\(395\) | 39.6582 | + | 22.8967i | 0.100401 | + | 0.0579663i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −510.352 | + | 294.652i | −1.28552 | + | 0.742196i | −0.977852 | − | 0.209298i | \(-0.932882\pi\) |
−0.307669 | + | 0.951494i | \(0.599549\pi\) | |||||||
\(398\) | 25.8439i | 0.0649344i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −53.8154 | −0.134538 | ||||||||
\(401\) | −83.1535 | − | 144.026i | −0.207365 | − | 0.359167i | 0.743518 | − | 0.668716i | \(-0.233156\pi\) |
−0.950884 | + | 0.309548i | \(0.899822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 259.870 | − | 450.107i | 0.644838 | − | 1.11689i | ||||
\(404\) | 274.692 | − | 158.593i | 0.679930 | − | 0.392558i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 73.6545 | + | 238.754i | 0.181415 | + | 0.588064i | ||||
\(407\) | 1.89261 | 0.00465014 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −189.742 | − | 109.548i | −0.463917 | − | 0.267843i | 0.249773 | − | 0.968304i | \(-0.419644\pi\) |
−0.713690 | + | 0.700462i | \(0.752977\pi\) | |||||||
\(410\) | 28.8222 | − | 49.9215i | 0.0702980 | − | 0.121760i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 324.079i | 0.786599i | ||||||||
\(413\) | −24.9891 | − | 23.1850i | −0.0605063 | − | 0.0561379i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −140.517 | − | 243.383i | −0.338596 | − | 0.586466i | ||||
\(416\) | −549.331 | − | 317.156i | −1.32051 | − | 0.762395i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0298744 | + | 0.0172480i | −7.14698e−5 | + | 4.12631e-5i | ||||
\(419\) | − | 554.704i | − | 1.32388i | −0.749558 | − | 0.661938i | \(-0.769734\pi\) | ||
0.749558 | − | 0.661938i | \(-0.230266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 642.342 | 1.52575 | 0.762876 | − | 0.646545i | \(-0.223787\pi\) | ||||
0.762876 | + | 0.646545i | \(0.223787\pi\) | |||||||
\(422\) | −42.8603 | − | 74.2362i | −0.101565 | − | 0.175915i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 48.2503 | − | 83.5720i | 0.113798 | − | 0.197104i | ||||
\(425\) | 40.8146 | − | 23.5643i | 0.0960344 | − | 0.0554455i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 259.851 | − | 80.1629i | 0.608550 | − | 0.187735i | ||||
\(428\) | −372.742 | −0.870893 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −99.7969 | − | 57.6178i | −0.232086 | − | 0.133995i | ||||
\(431\) | 37.6661 | − | 65.2395i | 0.0873923 | − | 0.151368i | −0.819016 | − | 0.573771i | \(-0.805480\pi\) |
0.906408 | + | 0.422403i | \(0.138813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 353.064i | 0.815391i | 0.913118 | + | 0.407695i | \(0.133667\pi\) | ||||
−0.913118 | + | 0.407695i | \(0.866333\pi\) | |||||||
\(434\) | 23.7005 | − | 103.855i | 0.0546095 | − | 0.239297i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 98.7710 | + | 171.076i | 0.226539 | + | 0.392377i | ||||
\(437\) | −43.8444 | − | 25.3136i | −0.100331 | − | 0.0579259i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −235.512 | + | 135.973i | −0.536473 | + | 0.309733i | −0.743648 | − | 0.668571i | \(-0.766906\pi\) |
0.207175 | + | 0.978304i | \(0.433573\pi\) | |||||||
\(440\) | − | 0.508664i | − | 0.00115605i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 146.008 | 0.330335 | ||||||||
\(443\) | −55.1204 | − | 95.4714i | −0.124425 | − | 0.215511i | 0.797083 | − | 0.603870i | \(-0.206375\pi\) |
−0.921508 | + | 0.388359i | \(0.873042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 52.2149 | − | 90.4389i | 0.117337 | − | 0.203233i | ||||
\(446\) | 171.214 | − | 98.8504i | 0.383888 | − | 0.221638i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 167.064 | + | 38.1253i | 0.372910 | + | 0.0851012i | ||||
\(449\) | −59.1007 | −0.131627 | −0.0658137 | − | 0.997832i | \(-0.520964\pi\) | ||||
−0.0658137 | + | 0.997832i | \(0.520964\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.48381 | − | 0.856677i | −0.00329004 | − | 0.00189950i | ||||
\(452\) | 9.31696 | − | 16.1375i | 0.0206127 | − | 0.0357023i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 145.118i | − | 0.319643i | ||||||
\(455\) | −106.130 | − | 344.025i | −0.233253 | − | 0.756098i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 102.638 | + | 177.775i | 0.224592 | + | 0.389004i | 0.956197 | − | 0.292724i | \(-0.0945618\pi\) |
−0.731605 | + | 0.681729i | \(0.761228\pi\) | |||||||
\(458\) | 84.1414 | + | 48.5791i | 0.183715 | + | 0.106068i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 303.828 | − | 175.415i | 0.660496 | − | 0.381338i | ||||
\(461\) | − | 466.172i | − | 1.01122i | −0.862762 | − | 0.505610i | \(-0.831268\pi\) | ||
0.862762 | − | 0.505610i | \(-0.168732\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 191.705 | 0.414051 | 0.207025 | − | 0.978336i | \(-0.433622\pi\) | ||||
0.207025 | + | 0.978336i | \(0.433622\pi\) | |||||||
\(464\) | 285.223 | + | 494.021i | 0.614706 | + | 1.06470i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 96.4510 | − | 167.058i | 0.206976 | − | 0.358493i | ||||
\(467\) | 730.261 | − | 421.617i | 1.56373 | − | 0.902819i | 0.566855 | − | 0.823818i | \(-0.308160\pi\) |
0.996874 | − | 0.0790015i | \(-0.0251732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.3691 | + | 35.9657i | −0.0711494 | + | 0.0766859i | ||||
\(470\) | −40.8758 | −0.0869697 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.4334 | + | 12.3746i | 0.0454098 | + | 0.0262174i | ||||
\(473\) | −1.71256 | + | 2.96625i | −0.00362064 | + | 0.00627113i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.72183i | − | 0.0120460i | ||||||
\(476\) | −223.597 | + | 68.9786i | −0.469741 | + | 0.144913i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 139.212 | + | 241.121i | 0.291237 | + | 0.504438i | ||||
\(479\) | 246.540 | + | 142.340i | 0.514698 | + | 0.297161i | 0.734763 | − | 0.678324i | \(-0.237293\pi\) |
−0.220065 | + | 0.975485i | \(0.570627\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −842.267 | + | 486.283i | −1.75107 | + | 1.01098i | ||||
\(482\) | 199.274i | 0.413432i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 429.113 | 0.886597 | ||||||||
\(485\) | 3.48261 | + | 6.03205i | 0.00718063 | + | 0.0124372i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 97.8228 | − | 169.434i | 0.200868 | − | 0.347914i | −0.747940 | − | 0.663766i | \(-0.768957\pi\) |
0.948808 | + | 0.315852i | \(0.102290\pi\) | |||||||
\(488\) | −170.984 | + | 98.7174i | −0.350376 | + | 0.202290i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −41.5712 | − | 60.9651i | −0.0848392 | − | 0.124419i | ||||
\(491\) | −745.464 | −1.51826 | −0.759128 | − | 0.650941i | \(-0.774375\pi\) | ||||
−0.759128 | + | 0.650941i | \(0.774375\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −432.638 | − | 249.784i | −0.877562 | − | 0.506660i | ||||
\(494\) | 8.86332 | − | 15.3517i | 0.0179419 | − | 0.0310763i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 243.206i | − | 0.490335i | ||||||
\(497\) | −319.890 | − | 73.0017i | −0.643642 | − | 0.146885i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −45.9747 | − | 79.6306i | −0.0921337 | − | 0.159580i | 0.816275 | − | 0.577663i | \(-0.196035\pi\) |
−0.908409 | + | 0.418083i | \(0.862702\pi\) | |||||||
\(500\) | 34.3383 | + | 19.8252i | 0.0686766 | + | 0.0396505i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 181.802 | − | 104.963i | 0.362155 | − | 0.209090i | ||||
\(503\) | 672.220i | 1.33642i | 0.743972 | + | 0.668211i | \(0.232940\pi\) | ||||
−0.743972 | + | 0.668211i | \(0.767060\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −199.989 | −0.396018 | ||||||||
\(506\) | 0.666795 | + | 1.15492i | 0.00131778 | + | 0.00228246i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.84119 | + | 17.0454i | −0.0193724 | + | 0.0335540i | ||||
\(509\) | −282.238 | + | 162.950i | −0.554495 | + | 0.320138i | −0.750933 | − | 0.660378i | \(-0.770396\pi\) |
0.196438 | + | 0.980516i | \(0.437063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −428.970 | − | 398.000i | −0.839473 | − | 0.778865i | ||||
\(512\) | −515.622 | −1.00707 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 84.4082 | + | 48.7331i | 0.164218 | + | 0.0948115i | ||||
\(515\) | 102.167 | − | 176.959i | 0.198383 | − | 0.343610i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.21494i | 0.00234999i | ||||||||
\(518\) | −135.577 | + | 146.127i | −0.261733 | + | 0.282099i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 130.695 | + | 226.370i | 0.251336 | + | 0.435328i | ||||
\(521\) | −515.449 | − | 297.595i | −0.989346 | − | 0.571199i | −0.0842672 | − | 0.996443i | \(-0.526855\pi\) |
−0.905079 | + | 0.425244i | \(0.860188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.6490 | + | 25.2007i | −0.0834588 | + | 0.0481850i | −0.541149 | − | 0.840927i | \(-0.682010\pi\) |
0.457690 | + | 0.889112i | \(0.348677\pi\) | |||||||
\(524\) | − | 590.559i | − | 1.12702i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −154.671 | −0.294051 | ||||||||
\(527\) | 106.494 | + | 184.452i | 0.202075 | + | 0.350004i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −714.106 | + | 1236.87i | −1.34992 | + | 2.33812i | ||||
\(530\) | −24.7630 | + | 14.2969i | −0.0467227 | + | 0.0269753i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.32068 | + | 27.6970i | −0.0118810 | + | 0.0520620i | ||||
\(533\) | 880.451 | 1.65188 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 203.531 | + | 117.509i | 0.380432 | + | 0.219642i | ||||
\(536\) | 17.8102 | − | 30.8482i | 0.0332280 | − | 0.0575526i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 285.792i | − | 0.531212i | ||||||
\(539\) | −1.81205 | + | 1.23561i | −0.00336188 | + | 0.00229242i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −468.381 | − | 811.260i | −0.865769 | − | 1.49956i | −0.866282 | − | 0.499556i | \(-0.833497\pi\) |
0.000512769 | − | 1.00000i | \(-0.499837\pi\) | |||||||
\(542\) | 170.191 | + | 98.2598i | 0.314006 | + | 0.181291i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 225.113 | − | 129.969i | 0.413812 | − | 0.238914i | ||||
\(545\) | − | 124.552i | − | 0.228536i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.89041 | −0.00711227 | −0.00355613 | − | 0.999994i | \(-0.501132\pi\) | ||||
−0.00355613 | + | 0.999994i | \(0.501132\pi\) | |||||||
\(548\) | −129.350 | − | 224.041i | −0.236040 | − | 0.408834i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0753604 | + | 0.130528i | −0.000137019 | + | 0.000237324i | ||||
\(551\) | −52.5260 | + | 30.3259i | −0.0953285 | + | 0.0550379i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.2594 | + | 136.986i | 0.0764185 | + | 0.247714i | ||||
\(554\) | 136.646 | 0.246654 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −353.181 | − | 203.909i | −0.635218 | − | 0.366743i | ||||
\(557\) | 193.381 | − | 334.945i | 0.347183 | − | 0.601338i | −0.638565 | − | 0.769568i | \(-0.720472\pi\) |
0.985748 | + | 0.168230i | \(0.0538051\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1760.09i | − | 3.14864i | ||||||
\(560\) | −123.500 | − | 114.584i | −0.220536 | − | 0.204614i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −85.6393 | − | 148.332i | −0.152383 | − | 0.263935i | ||||
\(563\) | 105.001 | + | 60.6226i | 0.186503 | + | 0.107678i | 0.590345 | − | 0.807151i | \(-0.298992\pi\) |
−0.403841 | + | 0.914829i | \(0.632325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1748 | + | 5.87443i | −0.0180085 | + | 0.0103972i | ||||
\(566\) | 298.819i | 0.527948i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 238.223 | 0.419407 | ||||||||
\(569\) | 204.955 | + | 354.993i | 0.360202 | + | 0.623889i | 0.987994 | − | 0.154493i | \(-0.0493743\pi\) |
−0.627792 | + | 0.778381i | \(0.716041\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 287.861 | − | 498.591i | 0.504136 | − | 0.873188i | −0.495853 | − | 0.868406i | \(-0.665145\pi\) |
0.999989 | − | 0.00478199i | \(-0.00152216\pi\) | |||||||
\(572\) | 3.16199 | − | 1.82558i | 0.00552796 | − | 0.00319157i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 172.436 | − | 53.1959i | 0.300412 | − | 0.0926758i | ||||
\(575\) | −221.202 | −0.384699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −202.254 | − | 116.772i | −0.350527 | − | 0.202377i | 0.314390 | − | 0.949294i | \(-0.398200\pi\) |
−0.664917 | + | 0.746917i | \(0.731533\pi\) | |||||||
\(578\) | 67.3988 | − | 116.738i | 0.116607 | − | 0.201969i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 420.298i | − | 0.724652i | ||||||
\(581\) | 195.741 | − | 857.727i | 0.336903 | − | 1.47629i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.424945 | + | 0.736027i | 0.000728894 | + | 0.00126248i | ||||
\(584\) | 367.933 | + | 212.426i | 0.630022 | + | 0.363743i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 130.361 | − | 75.2641i | 0.222459 | − | 0.128437i | ||||
\(587\) | 606.882i | 1.03387i | 0.856024 | + | 0.516935i | \(0.172927\pi\) | ||||
−0.856024 | + | 0.516935i | \(0.827073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.8585 | 0.0439024 | ||||||||
\(590\) | −3.66668 | − | 6.35088i | −0.00621472 | − | 0.0107642i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −227.551 | + | 394.129i | −0.384376 | + | 0.665759i | ||||
\(593\) | 701.998 | − | 405.299i | 1.18381 | − | 0.683472i | 0.226915 | − | 0.973914i | \(-0.427136\pi\) |
0.956892 | + | 0.290443i | \(0.0938026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 143.838 | + | 32.8251i | 0.241745 | + | 0.0551682i | ||||
\(596\) | 257.989 | 0.432867 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −593.487 | − | 342.650i | −0.992453 | − | 0.572993i | ||||
\(599\) | −511.389 | + | 885.752i | −0.853738 | + | 1.47872i | 0.0240732 | + | 0.999710i | \(0.492337\pi\) |
−0.877811 | + | 0.479007i | \(0.840997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 147.884i | − | 0.246063i | −0.992403 | − | 0.123032i | \(-0.960738\pi\) | ||
0.992403 | − | 0.123032i | \(-0.0392617\pi\) | |||||||
\(602\) | −106.343 | − | 344.714i | −0.176649 | − | 0.572614i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −225.427 | − | 390.452i | −0.373224 | − | 0.646443i | ||||
\(605\) | −234.312 | − | 135.280i | −0.387292 | − | 0.223603i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 815.490 | − | 470.823i | 1.34348 | − | 0.775656i | 0.356160 | − | 0.934425i | \(-0.384086\pi\) |
0.987316 | + | 0.158769i | \(0.0507524\pi\) | |||||||
\(608\) | − | 31.5588i | − | 0.0519060i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 58.5014 | 0.0959039 | ||||||||
\(611\) | −312.165 | − | 540.685i | −0.510908 | − | 0.884919i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −180.068 | + | 311.886i | −0.293748 | + | 0.508786i | −0.974693 | − | 0.223548i | \(-0.928236\pi\) |
0.680945 | + | 0.732335i | \(0.261569\pi\) | |||||||
\(614\) | −27.6388 | + | 15.9573i | −0.0450144 | + | 0.0259891i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.08305 | − | 1.16733i | 0.00175819 | − | 0.00189501i | ||||
\(617\) | −769.687 | −1.24747 | −0.623734 | − | 0.781637i | \(-0.714385\pi\) | ||||
−0.623734 | + | 0.781637i | \(0.714385\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −853.542 | − | 492.793i | −1.37890 | − | 0.796111i | −0.386877 | − | 0.922131i | \(-0.626446\pi\) |
−0.992028 | + | 0.126020i | \(0.959780\pi\) | |||||||
\(620\) | −89.5956 | + | 155.184i | −0.144509 | + | 0.250297i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 243.866i | 0.392068i | ||||||||
\(623\) | 312.390 | − | 96.3709i | 0.501428 | − | 0.154688i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −229.570 | − | 132.542i | −0.366726 | − | 0.211729i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 463.969 | − | 267.873i | 0.738804 | − | 0.426549i | ||||
\(629\) | − | 398.554i | − | 0.633630i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −89.7688 | −0.142264 | −0.0711322 | − | 0.997467i | \(-0.522661\pi\) | ||||
−0.0711322 | + | 0.997467i | \(0.522661\pi\) | |||||||
\(632\) | −52.0408 | − | 90.1373i | −0.0823431 | − | 0.142622i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −194.488 | + | 336.864i | −0.306764 | + | 0.531331i | ||||
\(635\) | 10.7473 | − | 6.20497i | 0.0169249 | − | 0.00977160i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 488.941 | − | 1015.47i | 0.767569 | − | 1.59414i | ||||
\(638\) | 1.59765 | 0.00250416 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 245.540 | + | 141.763i | 0.383657 | + | 0.221504i | ||||
\(641\) | −214.166 | + | 370.947i | −0.334113 | + | 0.578701i | −0.983314 | − | 0.181916i | \(-0.941770\pi\) |
0.649201 | + | 0.760617i | \(0.275103\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 111.498i | − | 0.173403i | −0.996234 | − | 0.0867015i | \(-0.972367\pi\) | ||
0.996234 | − | 0.0867015i | \(-0.0276326\pi\) | |||||||
\(644\) | 1070.75 | + | 244.353i | 1.66265 | + | 0.379431i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.63215 | + | 6.29107i | 0.00562253 | + | 0.00973850i | ||||
\(647\) | 250.033 | + | 144.357i | 0.386450 | + | 0.223117i | 0.680621 | − | 0.732636i | \(-0.261710\pi\) |
−0.294171 | + | 0.955753i | \(0.595043\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.188766 | + | 0.108984i | −0.000290857 | + | 0.000167926i | ||||
\(650\) | − | 77.4518i | − | 0.119157i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 212.531 | 0.325967 | ||||||||
\(653\) | 426.848 | + | 739.322i | 0.653672 | + | 1.13219i | 0.982225 | + | 0.187707i | \(0.0601056\pi\) |
−0.328553 | + | 0.944485i | \(0.606561\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −186.176 | + | 322.467i | −0.284239 | + | 0.492316i | ||||
\(656\) | 356.800 | − | 205.998i | 0.543902 | − | 0.314022i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −93.8052 | − | 87.0327i | −0.142561 | − | 0.132269i | ||||
\(659\) | 288.693 | 0.438077 | 0.219039 | − | 0.975716i | \(-0.429708\pi\) | ||||
0.219039 | + | 0.975716i | \(0.429708\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 182.367 | + | 105.289i | 0.275895 | + | 0.159288i | 0.631564 | − | 0.775324i | \(-0.282413\pi\) |
−0.355668 | + | 0.934612i | \(0.615747\pi\) | |||||||
\(662\) | −61.8222 | + | 107.079i | −0.0933870 | + | 0.161751i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 638.751i | 0.961974i | ||||||||
\(665\) | 12.1829 | − | 13.1309i | 0.0183202 | − | 0.0197458i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1172.38 | + | 2030.62i | 1.75769 | + | 3.04441i | ||||
\(668\) | −688.246 | − | 397.359i | −1.03031 | − | 0.594849i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.14055 | + | 5.27730i | −0.0136426 | + | 0.00787656i | ||||
\(671\) | − | 1.73883i | − | 0.00259140i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 760.139 | 1.12948 | 0.564739 | − | 0.825269i | \(-0.308977\pi\) | ||||
0.564739 | + | 0.825269i | \(0.308977\pi\) | |||||||
\(674\) | −69.3279 | − | 120.080i | −0.102860 | − | 0.178160i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −638.444 | + | 1105.82i | −0.944444 | + | 1.63583i | ||||
\(677\) | −163.263 | + | 94.2600i | −0.241157 | + | 0.139232i | −0.615708 | − | 0.787974i | \(-0.711130\pi\) |
0.374552 | + | 0.927206i | \(0.377797\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.85126 | + | 21.2580i | −0.00714472 | + | 0.0313079i | ||||
\(680\) | −107.117 | −0.157524 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.589892 | − | 0.340574i | −0.000864944 | − | 0.000499375i | ||||
\(683\) | 260.243 | − | 450.754i | 0.381029 | − | 0.659962i | −0.610181 | − | 0.792262i | \(-0.708903\pi\) |
0.991210 | + | 0.132301i | \(0.0422364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 163.113i | 0.238121i | ||||||||
\(686\) | 34.4057 | − | 228.421i | 0.0501541 | − | 0.332976i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −411.807 | − | 713.270i | −0.598556 | − | 1.03673i | ||||
\(689\) | −378.226 | − | 218.369i | −0.548949 | − | 0.316936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 590.615 | − | 340.991i | 0.854724 | − | 0.493475i | −0.00751772 | − | 0.999972i | \(-0.502393\pi\) |
0.862242 | + | 0.506496i | \(0.169060\pi\) | |||||||
\(692\) | 676.018i | 0.976904i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 134.323 | 0.193549 | ||||||||
\(695\) | 128.567 | + | 222.684i | 0.184988 | + | 0.320409i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −180.403 | + | 312.466i | −0.258827 | + | 0.448302i | ||||
\(698\) | −228.180 | + | 131.740i | −0.326906 | + | 0.188739i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 36.5906 | + | 118.610i | 0.0522723 | + | 0.169443i | ||||
\(701\) | 946.473 | 1.35018 | 0.675088 | − | 0.737737i | \(-0.264106\pi\) | ||||
0.675088 | + | 0.737737i | \(0.264106\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.9051 | − | 24.1939i | −0.0596090 | − | 0.0344153i | ||||
\(704\) | 0.547857 | − | 0.948916i | 0.000778206 | − | 0.00134789i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 63.0689i | 0.0893327i | ||||||||
\(707\) | −458.952 | − | 425.817i | −0.649155 | − | 0.602287i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 504.785 | + | 874.313i | 0.711967 | + | 1.23316i | 0.964118 | + | 0.265475i | \(0.0855289\pi\) |
−0.252150 | + | 0.967688i | \(0.581138\pi\) | |||||||
\(710\) | −61.1304 | − | 35.2936i | −0.0860991 | − | 0.0497093i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −205.554 | + | 118.677i | −0.288700 | + | 0.166681i | ||||
\(713\) | − | 999.671i | − | 1.40206i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.30209 | −0.00321970 | ||||||||
\(716\) | −386.318 | − | 669.122i | −0.539550 | − | 0.934528i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −49.7527 | + | 86.1742i | −0.0692935 | + | 0.120020i | ||||
\(719\) | −783.382 | + | 452.286i | −1.08954 | + | 0.629049i | −0.933455 | − | 0.358694i | \(-0.883222\pi\) |
−0.156089 | + | 0.987743i | \(0.549889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 611.244 | − | 188.566i | 0.847773 | − | 0.261534i | ||||
\(722\) | −242.238 | −0.335510 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −120.028 | − | 69.2983i | −0.165785 | − | 0.0957159i | ||||
\(725\) | −132.501 | + | 229.498i | −0.182760 | + | 0.316549i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 535.515i | 0.736609i | 0.929705 | + | 0.368304i | \(0.120062\pi\) | ||||
−0.929705 | + | 0.368304i | \(0.879938\pi\) | |||||||
\(728\) | −182.058 | + | 797.770i | −0.250080 | + | 1.09584i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −62.9434 | − | 109.021i | −0.0862239 | − | 0.149344i | ||||
\(731\) | 624.644 | + | 360.639i | 0.854507 | + | 0.493350i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −652.583 | + | 376.769i | −0.890290 | + | 0.514009i | −0.874037 | − | 0.485859i | \(-0.838507\pi\) |
−0.0162527 | + | 0.999868i | \(0.505174\pi\) | |||||||
\(734\) | − | 55.6396i | − | 0.0758033i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1220.04 | −1.65767 | ||||||||
\(737\) | 0.156856 | + | 0.271683i | 0.000212831 | + | 0.000368634i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 546.157 | − | 945.972i | 0.739049 | − | 1.28007i | −0.213875 | − | 0.976861i | \(-0.568609\pi\) |
0.952924 | − | 0.303209i | \(-0.0980580\pi\) | |||||||
\(740\) | 290.389 | − | 167.656i | 0.392418 | − | 0.226563i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −87.2693 | − | 19.9156i | −0.117614 | − | 0.0268404i | ||||
\(743\) | 362.303 | 0.487622 | 0.243811 | − | 0.969823i | \(-0.421602\pi\) | ||||
0.243811 | + | 0.969823i | \(0.421602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −140.872 | − | 81.3322i | −0.189089 | − | 0.109171i | ||||
\(746\) | −115.381 | + | 199.847i | −0.154667 | + | 0.267891i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.49623i | 0.00200030i | ||||||||
\(749\) | 216.881 | + | 703.028i | 0.289561 | + | 0.938622i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 336.270 | + | 582.437i | 0.447763 | + | 0.775548i | 0.998240 | − | 0.0593020i | \(-0.0188875\pi\) |
−0.550477 | + | 0.834850i | \(0.685554\pi\) | |||||||
\(752\) | −253.008 | − | 146.074i | −0.336446 | − | 0.194247i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −711.002 | + | 410.497i | −0.942974 | + | 0.544426i | ||||
\(755\) | 284.268i | 0.376514i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −368.166 | −0.486349 | −0.243174 | − | 0.969983i | \(-0.578189\pi\) | ||||
−0.243174 | + | 0.969983i | \(0.578189\pi\) | |||||||
\(758\) | 119.768 | + | 207.445i | 0.158006 | + | 0.273674i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.50244 | + | 11.2626i | −0.00855585 | + | 0.0148192i | ||||
\(761\) | −565.660 | + | 326.584i | −0.743312 | + | 0.429151i | −0.823272 | − | 0.567647i | \(-0.807854\pi\) |
0.0799606 | + | 0.996798i | \(0.474521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 265.197 | − | 285.833i | 0.347571 | − | 0.374617i | ||||
\(764\) | 672.113 | 0.879728 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 97.3933 | + | 56.2301i | 0.127145 | + | 0.0734074i | ||||
\(767\) | 56.0043 | − | 97.0024i | 0.0730174 | − | 0.126470i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1393.19i | 1.81170i | 0.423602 | + | 0.905848i | \(0.360765\pi\) | ||||
−0.423602 | + | 0.905848i | \(0.639235\pi\) | |||||||
\(770\) | −0.450864 | + | 0.139090i | −0.000585538 | + | 0.000180636i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −484.340 | − | 838.901i | −0.627383 | − | 1.08666i | ||||
\(773\) | −1129.82 | − | 652.302i | −1.46160 | − | 0.843858i | −0.462519 | − | 0.886609i | \(-0.653054\pi\) |
−0.999086 | + | 0.0427514i | \(0.986388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 97.8451 | − | 56.4909i | 0.126252 | − | 0.0728914i | ||||
\(776\) | − | 15.8309i | − | 0.0204007i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 107.276 | 0.137887 | ||||||||
\(779\) | 21.9024 | + | 37.9362i | 0.0281161 | + | 0.0486985i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04903 | + | 1.81697i | −0.00134318 | + | 0.00232646i | ||||
\(782\) | 243.208 | − | 140.416i | 0.311008 | − | 0.179561i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −39.4469 | − | 525.913i | −0.0503149 | − | 0.670808i | ||||
\(785\) | −337.793 | −0.430309 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 182.275 | + | 105.237i | 0.231607 | + | 0.133719i | 0.611313 | − | 0.791389i | \(-0.290642\pi\) |
−0.379706 | + | 0.925107i | \(0.623975\pi\) | |||||||
\(788\) | −352.691 | + | 610.878i | −0.447577 | + | 0.775226i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 30.8402i | 0.0390382i | ||||||||
\(791\) | −35.8579 | − | 8.18308i | −0.0453323 | − | 0.0103452i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 446.770 | + | 773.829i | 0.563393 | + | 0.975825i | ||||
\(794\) | −343.703 | − | 198.437i | −0.432876 | − | 0.249921i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 117.860 | − | 68.0467i | 0.148066 | − | 0.0854858i | ||||
\(797\) | 254.794i | 0.319691i | 0.987142 | + | 0.159845i | \(0.0510996\pi\) | ||||
−0.987142 | + | 0.159845i | \(0.948900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 255.848 | 0.320210 | ||||||||
\(800\) | −68.9439 | − | 119.414i | −0.0861799 | − | 0.149268i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 56.0009 | − | 96.9964i | 0.0698265 | − | 0.120943i | ||||
\(803\) | −3.24042 | + | 1.87086i | −0.00403539 | + | 0.00232983i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −507.633 | − | 470.983i | −0.630600 | − | 0.585073i | ||||
\(806\) | 350.025 | 0.434275 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 393.649 | + | 227.273i | 0.487189 | + | 0.281279i | ||||
\(809\) | −114.683 | + | 198.637i | −0.141759 | + | 0.245533i | −0.928159 | − | 0.372184i | \(-0.878609\pi\) |
0.786400 | + | 0.617717i | \(0.211942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1108.59i | 1.36694i | 0.729978 | + | 0.683470i | \(0.239530\pi\) | ||||
−0.729978 | + | 0.683470i | \(0.760470\pi\) | |||||||
\(812\) | 894.899 | − | 964.536i | 1.10209 | − | 1.18785i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.637302 | + | 1.10384i | 0.000782926 | + | 0.00135607i | ||||
\(815\) | −116.050 | − | 67.0013i | −0.142392 | − | 0.0822102i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 75.8373 | − | 43.7847i | 0.0928241 | − | 0.0535920i | ||||
\(818\) | − | 147.553i | − | 0.180382i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −303.554 | −0.370188 | ||||||||
\(821\) | 433.762 | + | 751.297i | 0.528333 | + | 0.915100i | 0.999454 | + | 0.0330318i | \(0.0105162\pi\) |
−0.471121 | + | 0.882069i | \(0.656150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −492.440 | + | 852.931i | −0.598348 | + | 1.03637i | 0.394718 | + | 0.918802i | \(0.370842\pi\) |
−0.993065 | + | 0.117566i | \(0.962491\pi\) | |||||||
\(824\) | −402.202 | + | 232.212i | −0.488110 | + | 0.281810i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.10769 | − | 22.3817i | 0.00618364 | − | 0.0270964i | ||||
\(827\) | 767.641 | 0.928224 | 0.464112 | − | 0.885777i | \(-0.346374\pi\) | ||||
0.464112 | + | 0.885777i | \(0.346374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −153.578 | − | 88.6684i | −0.185257 | − | 0.106958i | 0.404503 | − | 0.914537i | \(-0.367444\pi\) |
−0.589760 | + | 0.807578i | \(0.700778\pi\) | |||||||
\(830\) | 94.6333 | − | 163.910i | 0.114016 | − | 0.197482i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 563.061i | 0.676756i | ||||||||
\(833\) | 260.201 | + | 381.590i | 0.312366 | + | 0.458091i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 250.539 | + | 433.946i | 0.300046 | + | 0.519696i | ||||
\(836\) | 0.157318 | + | 0.0908275i | 0.000188179 | + | 0.000108645i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 323.524 | − | 186.787i | 0.386067 | − | 0.222896i | ||||
\(839\) | − | 15.9176i | − | 0.0189721i | −0.999955 | − | 0.00948606i | \(-0.996980\pi\) | ||
0.999955 | − | 0.00948606i | \(-0.00301955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1968.04 | 2.34012 | ||||||||
\(842\) | 216.297 | + | 374.637i | 0.256885 | + | 0.444937i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −225.701 | + | 390.926i | −0.267419 | + | 0.463183i | ||||
\(845\) | 697.229 | − | 402.545i | 0.825123 | − | 0.476385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −249.680 | − | 809.348i | −0.294782 | − | 0.955547i | ||||
\(848\) | −204.367 | −0.240998 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 27.4871 | + | 15.8697i | 0.0323378 | + | 0.0186702i | ||||
\(851\) | −935.321 | + | 1620.02i | −1.09908 | + | 1.90367i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 694.629i | − | 0.814336i | −0.913353 | − | 0.407168i | \(-0.866516\pi\) | ||
0.913353 | − | 0.407168i | \(-0.133484\pi\) | |||||||
\(854\) | 134.254 | + | 124.561i | 0.157206 | + | 0.145856i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −267.080 | − | 462.597i | −0.312010 | − | 0.540417i | ||||
\(857\) | 1301.17 | + | 751.232i | 1.51829 | + | 0.876583i | 0.999769 | + | 0.0215161i | \(0.00684933\pi\) |
0.518518 | + | 0.855067i | \(0.326484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −254.436 | + | 146.898i | −0.296200 | + | 0.171011i | −0.640734 | − | 0.767763i | \(-0.721370\pi\) |
0.344535 | + | 0.938774i | \(0.388037\pi\) | |||||||
\(860\) | 606.828i | 0.705614i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 50.7334 | 0.0588555 | ||||||||
\(863\) | −129.059 | − | 223.537i | −0.149547 | − | 0.259023i | 0.781513 | − | 0.623889i | \(-0.214448\pi\) |
−0.931060 | + | 0.364866i | \(0.881115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 213.118 | − | 369.131i | 0.246379 | − | 0.426741i | ||||
\(866\) | −205.920 | + | 118.888i | −0.237783 | + | 0.137284i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −536.030 | + | 165.363i | −0.617546 | + | 0.190510i | ||||
\(869\) | 0.916657 | 0.00105484 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −139.611 | − | 80.6046i | −0.160288 | − | 0.0925426i | ||||
\(872\) | −141.544 | + | 245.162i | −0.162322 | + | 0.281149i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 34.0956i | − | 0.0390109i | ||||||
\(875\) | 17.4125 | − | 76.3008i | 0.0199000 | − | 0.0872009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −668.747 | − | 1158.30i | −0.762539 | − | 1.32076i | −0.941538 | − | 0.336907i | \(-0.890619\pi\) |
0.178999 | − | 0.983849i | \(-0.442714\pi\) | |||||||
\(878\) | −158.609 | − | 91.5727i | −0.180648 | − | 0.104297i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.932913 | + | 0.538618i | −0.00106013 | + | 0.000612065i | ||||
\(881\) | − | 606.188i | − | 0.688069i | −0.938957 | − | 0.344034i | \(-0.888206\pi\) | ||
0.938957 | − | 0.344034i | \(-0.111794\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −862.650 | −0.976953 | −0.488477 | − | 0.872577i | \(-0.662447\pi\) | ||||
−0.488477 | + | 0.872577i | \(0.662447\pi\) | |||||||
\(884\) | −384.437 | − | 665.865i | −0.434884 | − | 0.753241i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 37.1216 | − | 64.2965i | 0.0418980 | − | 0.0725694i | ||||
\(887\) | 799.662 | − | 461.685i | 0.901536 | − | 0.520502i | 0.0238378 | − | 0.999716i | \(-0.492411\pi\) |
0.877698 | + | 0.479214i | \(0.159078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.8755 | + | 8.64351i | 0.0426046 | + | 0.00972273i | ||||
\(890\) | 70.3297 | 0.0790221 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −901.610 | − | 520.545i | −1.01077 | − | 0.583570i | ||||
\(893\) | 15.5311 | − | 26.9006i | 0.0173920 | − | 0.0301239i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 487.154i | 0.544306i | ||||||||
\(896\) | 261.646 | + | 848.134i | 0.292015 | + | 0.946579i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.9011 | − | 34.4697i | −0.0221616 | − | 0.0383850i | ||||
\(899\) | −1037.16 | − | 598.807i | −1.15369 | − | 0.666082i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 154.996 | − | 89.4867i | 0.172026 | − | 0.0993193i | ||||
\(902\) | − | 1.15388i | − | 0.00127925i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.7035 | 0.0295392 | ||||||||
\(905\) | 43.6932 | + | 75.6789i | 0.0482798 | + | 0.0836231i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.3567 | − | 82.0242i | 0.0522125 | − | 0.0904346i | −0.838738 | − | 0.544535i | \(-0.816706\pi\) |
0.890950 | + | 0.454101i | \(0.150039\pi\) | |||||||
\(908\) | −661.807 | + | 382.095i | −0.728863 | + | 0.420809i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 164.910 | − | 177.743i | 0.181220 | − | 0.195322i | ||||
\(911\) | 556.948 | 0.611359 | 0.305679 | − | 0.952134i | \(-0.401116\pi\) | ||||
0.305679 | + | 0.952134i | \(0.401116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.87186 | − | 2.81277i | −0.00533610 | − | 0.00308080i | ||||
\(914\) | −69.1233 | + | 119.725i | −0.0756272 | + | 0.130990i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 511.633i | − | 0.558551i | ||||||
\(917\) | −1113.85 | + | 343.618i | −1.21467 | + | 0.374720i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 478.581 | + | 828.926i | 0.520762 | + | 0.901987i | 0.999709 | + | 0.0241428i | \(0.00768562\pi\) |
−0.478946 | + | 0.877844i | \(0.658981\pi\) | |||||||
\(920\) | 435.403 | + | 251.380i | 0.473264 | + | 0.273239i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 271.889 | − | 156.975i | 0.294890 | − | 0.170255i | ||||
\(923\) | − | 1078.14i | − | 1.16808i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −211.418 | −0.228560 | ||||||||
\(926\) | 64.5533 | + | 111.810i | 0.0697120 | + | 0.120745i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −730.811 | + | 1265.80i | −0.787511 | + | 1.36401i | ||||
\(929\) | 990.414 | − | 571.816i | 1.06611 | − | 0.615517i | 0.138992 | − | 0.990294i | \(-0.455614\pi\) |
0.927115 | + | 0.374776i | \(0.122280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 55.9169 | − | 4.19412i | 0.0600611 | − | 0.00450497i | ||||
\(932\) | −1015.82 | −1.08993 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 491.804 | + | 283.943i | 0.526557 | + | 0.304008i | ||||
\(935\) | 0.471693 | − | 0.816996i | 0.000504484 | − | 0.000873792i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 578.660i | 0.617567i | 0.951132 | + | 0.308783i | \(0.0999218\pi\) | ||||
−0.951132 | + | 0.308783i | \(0.900078\pi\) | |||||||
\(938\) | −32.2129 | − | 7.35127i | −0.0343422 | − | 0.00783717i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 107.625 | + | 186.413i | 0.114495 | + | 0.198312i | ||||
\(941\) | 1086.18 | + | 627.108i | 1.15428 | + | 0.666427i | 0.949928 | − | 0.312470i | \(-0.101156\pi\) |
0.204357 | + | 0.978896i | \(0.434490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1466.59 | − | 846.733i | 1.55523 | − | 0.897915i | ||||
\(944\) | − | 52.4132i | − | 0.0555225i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.30670 | −0.00243837 | ||||||||
\(947\) | −878.012 | − | 1520.76i | −0.927151 | − | 1.60587i | −0.788065 | − | 0.615592i | \(-0.788917\pi\) |
−0.139086 | − | 0.990280i | \(-0.544417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 961.388 | − | 1665.17i | 1.01305 | − | 1.75466i | ||||
\(950\) | 3.33718 | − | 1.92672i | 0.00351282 | − | 0.00202813i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −245.820 | − | 228.073i | −0.258215 | − | 0.239572i | ||||
\(953\) | 1048.32 | 1.10002 | 0.550011 | − | 0.835157i | \(-0.314624\pi\) | ||||
0.550011 | + | 0.835157i | \(0.314624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −366.998 | − | 211.887i | −0.384292 | − | 0.221871i | ||||
\(956\) | 733.085 | − | 1269.74i | 0.766826 | − | 1.32818i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 191.722i | 0.200127i | ||||||||
\(959\) | −347.300 | + | 374.325i | −0.362148 | + | 0.390329i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −225.203 | − | 390.062i | −0.234342 | − | 0.405892i | ||||
\(962\) | −567.236 | − | 327.494i | −0.589642 | − | 0.340430i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 908.785 | − | 524.688i | 0.942723 | − | 0.544282i | ||||
\(965\) | 610.762i | 0.632914i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1770.86 | −1.83130 | −0.915648 | − | 0.401982i | \(-0.868321\pi\) | ||||
−0.915648 | + | 0.401982i | \(0.868321\pi\) | |||||||
\(968\) | 307.471 | + | 532.556i | 0.317636 | + | 0.550161i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.34541 | + | 4.06237i | −0.00241795 | + | 0.00418801i | ||||
\(971\) | −834.000 | + | 481.510i | −0.858908 | + | 0.495891i | −0.863646 | − | 0.504098i | \(-0.831825\pi\) |
0.00473848 | + | 0.999989i | \(0.498492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −179.093 | + | 784.779i | −0.184063 | + | 0.806556i | ||||
\(974\) | 131.760 | 0.135277 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 362.105 | + | 209.061i | 0.371009 | + | 0.214202i | ||||
\(977\) | −269.150 | + | 466.182i | −0.275487 | + | 0.477157i | −0.970258 | − | 0.242074i | \(-0.922172\pi\) |
0.694771 | + | 0.719231i | \(0.255506\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.09040i | − | 0.00213524i | ||||||
\(980\) | −168.573 | + | 350.105i | −0.172013 | + | 0.357250i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −251.021 | − | 434.782i | −0.255623 | − | 0.442751i | ||||
\(983\) | 586.233 | + | 338.462i | 0.596371 | + | 0.344315i | 0.767613 | − | 0.640914i | \(-0.221444\pi\) |
−0.171241 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 385.164 | − | 222.375i | 0.391030 | − | 0.225761i | ||||
\(986\) | − | 336.440i | − | 0.341217i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −93.3481 | −0.0944819 | ||||||||
\(989\) | −1692.69 | − | 2931.82i | −1.71151 | − | 2.96443i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −584.900 | + | 1013.08i | −0.590212 | + | 1.02228i | 0.403992 | + | 0.914763i | \(0.367622\pi\) |
−0.994204 | + | 0.107514i | \(0.965711\pi\) | |||||||
\(992\) | 539.666 | − | 311.576i | 0.544018 | − | 0.314089i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −65.1400 | − | 211.154i | −0.0655332 | − | 0.212428i | ||||
\(995\) | −85.8082 | −0.0862394 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 523.016 | + | 301.963i | 0.524590 | + | 0.302872i | 0.738810 | − | 0.673913i | \(-0.235388\pi\) |
−0.214221 | + | 0.976785i | \(0.568721\pi\) | |||||||
\(998\) | 30.9623 | − | 53.6283i | 0.0310244 | − | 0.0537358i | ||||
\(999\) | 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 | 315.3.w.a.136.3 | 8 | ||
3.2 | odd | 2 | 105.3.n.a.31.2 | ✓ | 8 | ||
7.5 | odd | 6 | inner | 315.3.w.a.271.3 | 8 | ||
15.2 | even | 4 | 525.3.s.h.199.5 | 16 | |||
15.8 | even | 4 | 525.3.s.h.199.4 | 16 | |||
15.14 | odd | 2 | 525.3.o.l.451.3 | 8 | |||
21.5 | even | 6 | 105.3.n.a.61.2 | yes | 8 | ||
21.11 | odd | 6 | 735.3.h.a.391.6 | 8 | |||
21.17 | even | 6 | 735.3.h.a.391.5 | 8 | |||
105.47 | odd | 12 | 525.3.s.h.124.4 | 16 | |||
105.68 | odd | 12 | 525.3.s.h.124.5 | 16 | |||
105.89 | even | 6 | 525.3.o.l.376.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.n.a.31.2 | ✓ | 8 | 3.2 | odd | 2 | ||
105.3.n.a.61.2 | yes | 8 | 21.5 | even | 6 | ||
315.3.w.a.136.3 | 8 | 1.1 | even | 1 | trivial | ||
315.3.w.a.271.3 | 8 | 7.5 | odd | 6 | inner | ||
525.3.o.l.376.3 | 8 | 105.89 | even | 6 | |||
525.3.o.l.451.3 | 8 | 15.14 | odd | 2 | |||
525.3.s.h.124.4 | 16 | 105.47 | odd | 12 | |||
525.3.s.h.124.5 | 16 | 105.68 | odd | 12 | |||
525.3.s.h.199.4 | 16 | 15.8 | even | 4 | |||
525.3.s.h.199.5 | 16 | 15.2 | even | 4 | |||
735.3.h.a.391.5 | 8 | 21.17 | even | 6 | |||
735.3.h.a.391.6 | 8 | 21.11 | odd | 6 |