Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(79,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.4 | ||
Root | \(0.550552 - 0.147520i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.79 |
Dual form | 735.2.q.f.214.4 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.167954 | + | 0.0969683i | 0.118761 | + | 0.0685669i | 0.558204 | − | 0.829704i | \(-0.311491\pi\) |
−0.439443 | + | 0.898271i | \(0.644824\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.981194 | − | 1.69948i | −0.490597 | − | 0.849739i | ||||
\(5\) | −2.19130 | + | 0.445186i | −0.979981 | + | 0.199093i | ||||
\(6\) | 0.193937 | 0.0791743 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.768452i | − | 0.271689i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.411207 | − | 0.137716i | −0.130035 | − | 0.0435496i | ||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | −1.69948 | − | 0.981194i | −0.490597 | − | 0.283246i | ||||
\(13\) | − | 1.35026i | − | 0.374495i | −0.982313 | − | 0.187248i | \(-0.940043\pi\) | ||
0.982313 | − | 0.187248i | \(-0.0599567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67513 | + | 1.48119i | −0.432517 | + | 0.382443i | ||||
\(16\) | −1.88787 | + | 3.26989i | −0.471968 | + | 0.817473i | ||||
\(17\) | −2.90141 | + | 1.67513i | −0.703696 | + | 0.406279i | −0.808722 | − | 0.588190i | \(-0.799841\pi\) |
0.105027 | + | 0.994469i | \(0.466507\pi\) | |||||||
\(18\) | 0.167954 | − | 0.0969683i | 0.0395871 | − | 0.0228556i | ||||
\(19\) | −2.67513 | + | 4.63346i | −0.613717 | + | 1.06299i | 0.376891 | + | 0.926258i | \(0.376993\pi\) |
−0.990608 | + | 0.136732i | \(0.956340\pi\) | |||||||
\(20\) | 2.90668 | + | 3.28726i | 0.649953 | + | 0.735053i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.387873i | − | 0.0826948i | ||||||
\(23\) | −4.29755 | − | 2.48119i | −0.896102 | − | 0.517365i | −0.0201686 | − | 0.999797i | \(-0.506420\pi\) |
−0.875934 | + | 0.482432i | \(0.839754\pi\) | |||||||
\(24\) | −0.384226 | − | 0.665499i | −0.0784298 | − | 0.135844i | ||||
\(25\) | 4.60362 | − | 1.95108i | 0.920724 | − | 0.390215i | ||||
\(26\) | 0.130933 | − | 0.226782i | 0.0256780 | − | 0.0444756i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.92478 | −1.47159 | −0.735797 | − | 0.677202i | \(-0.763192\pi\) | ||||
−0.735797 | + | 0.677202i | \(0.763192\pi\) | |||||||
\(30\) | −0.424974 | + | 0.0863379i | −0.0775892 | + | 0.0157631i | ||||
\(31\) | 2.28726 | + | 3.96165i | 0.410804 | + | 0.711533i | 0.994978 | − | 0.100096i | \(-0.0319149\pi\) |
−0.584174 | + | 0.811628i | \(0.698582\pi\) | |||||||
\(32\) | −1.96515 | + | 1.13458i | −0.347393 | + | 0.200567i | ||||
\(33\) | −1.73205 | − | 1.00000i | −0.301511 | − | 0.174078i | ||||
\(34\) | −0.649738 | −0.111429 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96239 | −0.327065 | ||||||||
\(37\) | −0.671816 | − | 0.387873i | −0.110446 | − | 0.0637660i | 0.443760 | − | 0.896146i | \(-0.353644\pi\) |
−0.554205 | + | 0.832380i | \(0.686978\pi\) | |||||||
\(38\) | −0.898598 | + | 0.518806i | −0.145772 | + | 0.0841614i | ||||
\(39\) | −0.675131 | − | 1.16936i | −0.108107 | − | 0.187248i | ||||
\(40\) | 0.342104 | + | 1.68391i | 0.0540915 | + | 0.266250i | ||||
\(41\) | −3.73813 | −0.583799 | −0.291899 | − | 0.956449i | \(-0.594287\pi\) | ||||
−0.291899 | + | 0.956449i | \(0.594287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.6253i | − | 1.92534i | −0.270677 | − | 0.962670i | \(-0.587248\pi\) | ||
0.270677 | − | 0.962670i | \(-0.412752\pi\) | |||||||
\(44\) | −1.96239 | + | 3.39896i | −0.295841 | + | 0.512412i | ||||
\(45\) | −0.710109 | + | 2.12032i | −0.105857 | + | 0.316078i | ||||
\(46\) | −0.481194 | − | 0.833453i | −0.0709482 | − | 0.122886i | ||||
\(47\) | −8.59511 | − | 4.96239i | −1.25373 | − | 0.723839i | −0.281878 | − | 0.959450i | \(-0.590957\pi\) |
−0.971847 | + | 0.235611i | \(0.924291\pi\) | |||||||
\(48\) | 3.77575i | 0.544982i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.962389 | + | 0.118714i | 0.136102 | + | 0.0167887i | ||||
\(51\) | −1.67513 | + | 2.90141i | −0.234565 | + | 0.406279i | ||||
\(52\) | −2.29474 | + | 1.32487i | −0.318223 | + | 0.183726i | ||||
\(53\) | 7.42575 | − | 4.28726i | 1.02000 | − | 0.588900i | 0.105900 | − | 0.994377i | \(-0.466228\pi\) |
0.914105 | + | 0.405477i | \(0.132894\pi\) | |||||||
\(54\) | 0.0969683 | − | 0.167954i | 0.0131957 | − | 0.0228556i | ||||
\(55\) | 2.96239 | + | 3.35026i | 0.399448 | + | 0.451749i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.35026i | 0.708659i | ||||||||
\(58\) | −1.33100 | − | 0.768452i | −0.174769 | − | 0.100903i | ||||
\(59\) | 4.31265 | + | 7.46973i | 0.561459 | + | 0.972476i | 0.997369 | + | 0.0724858i | \(0.0230932\pi\) |
−0.435910 | + | 0.899990i | \(0.643573\pi\) | |||||||
\(60\) | 4.16089 | + | 1.39351i | 0.537168 | + | 0.179901i | ||||
\(61\) | −4.35026 | + | 7.53487i | −0.556994 | + | 0.964742i | 0.440751 | + | 0.897629i | \(0.354712\pi\) |
−0.997745 | + | 0.0671126i | \(0.978621\pi\) | |||||||
\(62\) | 0.887166i | 0.112670i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.11142 | 0.888927 | ||||||||
\(65\) | 0.601118 | + | 2.95883i | 0.0745595 | + | 0.366998i | ||||
\(66\) | −0.193937 | − | 0.335908i | −0.0238719 | − | 0.0413474i | ||||
\(67\) | −8.59511 | + | 4.96239i | −1.05006 | + | 0.606252i | −0.922666 | − | 0.385600i | \(-0.873994\pi\) |
−0.127394 | + | 0.991852i | \(0.540661\pi\) | |||||||
\(68\) | 5.69370 | + | 3.28726i | 0.690462 | + | 0.398639i | ||||
\(69\) | −4.96239 | −0.597401 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −0.665499 | − | 0.384226i | −0.0784298 | − | 0.0452815i | ||||
\(73\) | 8.09756 | − | 4.67513i | 0.947748 | − | 0.547183i | 0.0553675 | − | 0.998466i | \(-0.482367\pi\) |
0.892381 | + | 0.451283i | \(0.149034\pi\) | |||||||
\(74\) | −0.0752228 | − | 0.130290i | −0.00874447 | − | 0.0151459i | ||||
\(75\) | 3.01131 | − | 3.99149i | 0.347716 | − | 0.460898i | ||||
\(76\) | 10.4993 | 1.20435 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 0.261865i | − | 0.0296504i | ||||||
\(79\) | 5.35026 | − | 9.26693i | 0.601951 | − | 1.04261i | −0.390574 | − | 0.920572i | \(-0.627723\pi\) |
0.992525 | − | 0.122039i | \(-0.0389433\pi\) | |||||||
\(80\) | 2.68119 | − | 8.00578i | 0.299766 | − | 0.895073i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.627835 | − | 0.362481i | −0.0693327 | − | 0.0400293i | ||||
\(83\) | − | 3.22425i | − | 0.353908i | −0.984219 | − | 0.176954i | \(-0.943376\pi\) | ||
0.984219 | − | 0.176954i | \(-0.0566244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.61213 | − | 4.96239i | 0.608721 | − | 0.538247i | ||||
\(86\) | 1.22425 | − | 2.12047i | 0.132015 | − | 0.228656i | ||||
\(87\) | −6.86306 | + | 3.96239i | −0.735797 | + | 0.424813i | ||||
\(88\) | −1.33100 | + | 0.768452i | −0.141885 | + | 0.0819173i | ||||
\(89\) | −0.518806 | + | 0.898598i | −0.0549933 | + | 0.0952512i | −0.892212 | − | 0.451618i | \(-0.850847\pi\) |
0.837218 | + | 0.546869i | \(0.184180\pi\) | |||||||
\(90\) | −0.324869 | + | 0.287258i | −0.0342442 | + | 0.0302796i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.73813i | 1.01527i | ||||||||
\(93\) | 3.96165 | + | 2.28726i | 0.410804 | + | 0.237178i | ||||
\(94\) | −0.962389 | − | 1.66691i | −0.0992628 | − | 0.171928i | ||||
\(95\) | 3.79927 | − | 11.3443i | 0.389797 | − | 1.16390i | ||||
\(96\) | −1.13458 | + | 1.96515i | −0.115798 | + | 0.200567i | ||||
\(97\) | − | 18.4993i | − | 1.87832i | −0.343482 | − | 0.939159i | \(-0.611606\pi\) | ||
0.343482 | − | 0.939159i | \(-0.388394\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −7.83286 | − | 5.90936i | −0.783286 | − | 0.590936i | ||||
\(101\) | −8.83146 | − | 15.2965i | −0.878763 | − | 1.52206i | −0.852700 | − | 0.522401i | \(-0.825036\pi\) |
−0.0260630 | − | 0.999660i | \(-0.508297\pi\) | |||||||
\(102\) | −0.562690 | + | 0.324869i | −0.0557146 | + | 0.0321668i | ||||
\(103\) | 5.80282 | + | 3.35026i | 0.571769 | + | 0.330111i | 0.757856 | − | 0.652422i | \(-0.226247\pi\) |
−0.186086 | + | 0.982533i | \(0.559580\pi\) | |||||||
\(104\) | −1.03761 | −0.101746 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.66291 | 0.161516 | ||||||||
\(107\) | 11.8976 | + | 6.86907i | 1.15018 | + | 0.664058i | 0.948932 | − | 0.315482i | \(-0.102166\pi\) |
0.201250 | + | 0.979540i | \(0.435500\pi\) | |||||||
\(108\) | −1.69948 | + | 0.981194i | −0.163532 | + | 0.0944155i | ||||
\(109\) | −1.38787 | − | 2.40387i | −0.132934 | − | 0.230249i | 0.791872 | − | 0.610687i | \(-0.209107\pi\) |
−0.924806 | + | 0.380438i | \(0.875773\pi\) | |||||||
\(110\) | 0.172676 | + | 0.849948i | 0.0164640 | + | 0.0810393i | ||||
\(111\) | −0.775746 | −0.0736306 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0508i | 1.13364i | 0.823841 | + | 0.566821i | \(0.191827\pi\) | ||||
−0.823841 | + | 0.566821i | \(0.808173\pi\) | |||||||
\(114\) | −0.518806 | + | 0.898598i | −0.0485906 | + | 0.0841614i | ||||
\(115\) | 10.5218 | + | 3.52384i | 0.981167 | + | 0.328599i | ||||
\(116\) | 7.77575 | + | 13.4680i | 0.721960 | + | 1.25047i | ||||
\(117\) | −1.16936 | − | 0.675131i | −0.108107 | − | 0.0624159i | ||||
\(118\) | 1.67276i | 0.153990i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.13823 | + | 1.28726i | 0.103905 | + | 0.117510i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | −1.46129 | + | 0.843675i | −0.132299 | + | 0.0763827i | ||||
\(123\) | −3.23732 | + | 1.86907i | −0.291899 | + | 0.168528i | ||||
\(124\) | 4.48849 | − | 7.77429i | 0.403078 | − | 0.698152i | ||||
\(125\) | −9.21933 | + | 6.32487i | −0.824602 | + | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.70052i | − | 0.239633i | −0.992796 | − | 0.119816i | \(-0.961769\pi\) | ||
0.992796 | − | 0.119816i | \(-0.0382306\pi\) | |||||||
\(128\) | 5.12469 | + | 2.95874i | 0.452963 | + | 0.261518i | ||||
\(129\) | −6.31265 | − | 10.9338i | −0.555798 | − | 0.962670i | ||||
\(130\) | −0.185953 | + | 0.555237i | −0.0163091 | + | 0.0486975i | ||||
\(131\) | 10.3127 | − | 17.8620i | 0.901020 | − | 1.56061i | 0.0748486 | − | 0.997195i | \(-0.476153\pi\) |
0.826172 | − | 0.563418i | \(-0.190514\pi\) | |||||||
\(132\) | 3.92478i | 0.341608i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.92478 | −0.166275 | ||||||||
\(135\) | 0.445186 | + | 2.19130i | 0.0383155 | + | 0.188597i | ||||
\(136\) | 1.28726 | + | 2.22960i | 0.110381 | + | 0.191186i | ||||
\(137\) | −19.4850 | + | 11.2496i | −1.66471 | + | 0.961122i | −0.694294 | + | 0.719691i | \(0.744283\pi\) |
−0.970418 | + | 0.241431i | \(0.922383\pi\) | |||||||
\(138\) | −0.833453 | − | 0.481194i | −0.0709482 | − | 0.0409620i | ||||
\(139\) | −3.27504 | −0.277785 | −0.138893 | − | 0.990307i | \(-0.544354\pi\) | ||||
−0.138893 | + | 0.990307i | \(0.544354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.92478 | −0.835817 | ||||||||
\(142\) | 0.335908 | + | 0.193937i | 0.0281888 | + | 0.0162748i | ||||
\(143\) | −2.33872 | + | 1.35026i | −0.195574 | + | 0.112915i | ||||
\(144\) | 1.88787 | + | 3.26989i | 0.157323 | + | 0.272491i | ||||
\(145\) | 17.3656 | − | 3.52800i | 1.44213 | − | 0.292985i | ||||
\(146\) | 1.81336 | 0.150075 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.52232i | 0.125134i | ||||||||
\(149\) | −2.22425 | + | 3.85252i | −0.182218 | + | 0.315611i | −0.942636 | − | 0.333824i | \(-0.891661\pi\) |
0.760418 | + | 0.649434i | \(0.224994\pi\) | |||||||
\(150\) | 0.892810 | − | 0.378385i | 0.0728976 | − | 0.0308950i | ||||
\(151\) | −0.649738 | − | 1.12538i | −0.0528749 | − | 0.0915821i | 0.838376 | − | 0.545092i | \(-0.183505\pi\) |
−0.891251 | + | 0.453510i | \(0.850172\pi\) | |||||||
\(152\) | 3.56059 | + | 2.05571i | 0.288802 | + | 0.166740i | ||||
\(153\) | 3.35026i | 0.270853i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.77575 | − | 7.66291i | −0.544241 | − | 0.615500i | ||||
\(156\) | −1.32487 | + | 2.29474i | −0.106074 | + | 0.183726i | ||||
\(157\) | −2.29474 | + | 1.32487i | −0.183140 | + | 0.105736i | −0.588767 | − | 0.808303i | \(-0.700387\pi\) |
0.405627 | + | 0.914039i | \(0.367053\pi\) | |||||||
\(158\) | 1.79720 | − | 1.03761i | 0.142977 | − | 0.0825479i | ||||
\(159\) | 4.28726 | − | 7.42575i | 0.340002 | − | 0.588900i | ||||
\(160\) | 3.80114 | − | 3.36107i | 0.300506 | − | 0.265716i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 0.193937i | − | 0.0152371i | ||||||
\(163\) | −4.58948 | − | 2.64974i | −0.359476 | − | 0.207544i | 0.309375 | − | 0.950940i | \(-0.399880\pi\) |
−0.668851 | + | 0.743397i | \(0.733214\pi\) | |||||||
\(164\) | 3.66784 | + | 6.35288i | 0.286410 | + | 0.496077i | ||||
\(165\) | 4.24063 | + | 1.42022i | 0.330133 | + | 0.110564i | ||||
\(166\) | 0.312650 | − | 0.541526i | 0.0242664 | − | 0.0420306i | ||||
\(167\) | − | 14.5501i | − | 1.12592i | −0.826485 | − | 0.562959i | \(-0.809663\pi\) | ||
0.826485 | − | 0.562959i | \(-0.190337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1768 | 0.859753 | ||||||||
\(170\) | 1.42377 | − | 0.289255i | 0.109198 | − | 0.0221848i | ||||
\(171\) | 2.67513 | + | 4.63346i | 0.204572 | + | 0.354330i | ||||
\(172\) | −21.4564 | + | 12.3879i | −1.63604 | + | 0.944566i | ||||
\(173\) | −3.89650 | − | 2.24965i | −0.296246 | − | 0.171037i | 0.344509 | − | 0.938783i | \(-0.388045\pi\) |
−0.640755 | + | 0.767745i | \(0.721379\pi\) | |||||||
\(174\) | −1.53690 | −0.116512 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.55149 | 0.569215 | ||||||||
\(177\) | 7.46973 | + | 4.31265i | 0.561459 | + | 0.324159i | ||||
\(178\) | −0.174271 | + | 0.100615i | −0.0130622 | + | 0.00754144i | ||||
\(179\) | 5.00000 | + | 8.66025i | 0.373718 | + | 0.647298i | 0.990134 | − | 0.140122i | \(-0.0447496\pi\) |
−0.616417 | + | 0.787420i | \(0.711416\pi\) | |||||||
\(180\) | 4.30019 | − | 0.873629i | 0.320517 | − | 0.0651164i | ||||
\(181\) | −10.6253 | −0.789772 | −0.394886 | − | 0.918730i | \(-0.629216\pi\) | ||||
−0.394886 | + | 0.918730i | \(0.629216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.70052i | 0.643161i | ||||||||
\(184\) | −1.90668 | + | 3.30246i | −0.140562 | + | 0.243461i | ||||
\(185\) | 1.64483 | + | 0.550864i | 0.120930 | + | 0.0405003i | ||||
\(186\) | 0.443583 | + | 0.768308i | 0.0325251 | + | 0.0563351i | ||||
\(187\) | 5.80282 | + | 3.35026i | 0.424344 | + | 0.244995i | ||||
\(188\) | 19.4763i | 1.42045i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.73813 | − | 1.53690i | 0.126098 | − | 0.111499i | ||||
\(191\) | 6.92478 | − | 11.9941i | 0.501059 | − | 0.867860i | −0.498940 | − | 0.866637i | \(-0.666277\pi\) |
0.999999 | − | 0.00122360i | \(-0.000389484\pi\) | |||||||
\(192\) | 6.15867 | − | 3.55571i | 0.444464 | − | 0.256611i | ||||
\(193\) | 13.2726 | − | 7.66291i | 0.955379 | − | 0.551588i | 0.0606314 | − | 0.998160i | \(-0.480689\pi\) |
0.894748 | + | 0.446572i | \(0.147355\pi\) | |||||||
\(194\) | 1.79384 | − | 3.10703i | 0.128791 | − | 0.223072i | ||||
\(195\) | 2.00000 | + | 2.26187i | 0.143223 | + | 0.161976i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.574515i | 0.0409325i | 0.999791 | + | 0.0204663i | \(0.00651507\pi\) | ||||
−0.999791 | + | 0.0204663i | \(0.993485\pi\) | |||||||
\(198\) | −0.335908 | − | 0.193937i | −0.0238719 | − | 0.0137825i | ||||
\(199\) | 0.100615 | + | 0.174271i | 0.00713244 | + | 0.0123537i | 0.869570 | − | 0.493810i | \(-0.164396\pi\) |
−0.862437 | + | 0.506164i | \(0.831063\pi\) | |||||||
\(200\) | −1.49931 | − | 3.53766i | −0.106017 | − | 0.250150i | ||||
\(201\) | −4.96239 | + | 8.59511i | −0.350020 | + | 0.606252i | ||||
\(202\) | − | 3.42548i | − | 0.241016i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.57452 | 0.460308 | ||||||||
\(205\) | 8.19139 | − | 1.66417i | 0.572111 | − | 0.116230i | ||||
\(206\) | 0.649738 | + | 1.12538i | 0.0452694 | + | 0.0784089i | ||||
\(207\) | −4.29755 | + | 2.48119i | −0.298701 | + | 0.172455i | ||||
\(208\) | 4.41521 | + | 2.54912i | 0.306140 | + | 0.176750i | ||||
\(209\) | 10.7005 | 0.740171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44851 | 0.443934 | 0.221967 | − | 0.975054i | \(-0.428752\pi\) | ||||
0.221967 | + | 0.975054i | \(0.428752\pi\) | |||||||
\(212\) | −14.5722 | − | 8.41327i | −1.00082 | − | 0.577825i | ||||
\(213\) | 1.73205 | − | 1.00000i | 0.118678 | − | 0.0685189i | ||||
\(214\) | 1.33216 | + | 2.30737i | 0.0910648 | + | 0.157729i | ||||
\(215\) | 5.62061 | + | 27.6659i | 0.383323 | + | 1.88680i | ||||
\(216\) | −0.768452 | −0.0522865 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 0.538319i | − | 0.0364595i | ||||||
\(219\) | 4.67513 | − | 8.09756i | 0.315916 | − | 0.547183i | ||||
\(220\) | 2.78702 | − | 8.32177i | 0.187901 | − | 0.561054i | ||||
\(221\) | 2.26187 | + | 3.91767i | 0.152150 | + | 0.263531i | ||||
\(222\) | −0.130290 | − | 0.0752228i | −0.00874447 | − | 0.00504862i | ||||
\(223\) | − | 1.55149i | − | 0.103896i | −0.998650 | − | 0.0519478i | \(-0.983457\pi\) | ||
0.998650 | − | 0.0519478i | \(-0.0165429\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.612127 | − | 4.96239i | 0.0408085 | − | 0.330826i | ||||
\(226\) | −1.16854 | + | 2.02398i | −0.0777304 | + | 0.134633i | ||||
\(227\) | −11.3874 | + | 6.57452i | −0.755808 | + | 0.436366i | −0.827789 | − | 0.561040i | \(-0.810401\pi\) |
0.0719807 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(228\) | 9.09265 | − | 5.24965i | 0.602176 | − | 0.347666i | ||||
\(229\) | −1.38787 | + | 2.40387i | −0.0917132 | + | 0.158852i | −0.908232 | − | 0.418467i | \(-0.862568\pi\) |
0.816519 | + | 0.577319i | \(0.195901\pi\) | |||||||
\(230\) | 1.42548 | + | 1.61213i | 0.0939937 | + | 0.106300i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.08981i | 0.399816i | ||||||||
\(233\) | 0.0439813 | + | 0.0253926i | 0.00288131 | + | 0.00166353i | 0.501440 | − | 0.865192i | \(-0.332804\pi\) |
−0.498559 | + | 0.866856i | \(0.666137\pi\) | |||||||
\(234\) | −0.130933 | − | 0.226782i | −0.00855933 | − | 0.0148252i | ||||
\(235\) | 21.0437 | + | 7.04767i | 1.37274 | + | 0.459739i | ||||
\(236\) | 8.46310 | − | 14.6585i | 0.550901 | − | 0.954188i | ||||
\(237\) | − | 10.7005i | − | 0.695074i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.84955 | −0.378376 | −0.189188 | − | 0.981941i | \(-0.560586\pi\) | ||||
−0.189188 | + | 0.981941i | \(0.560586\pi\) | |||||||
\(240\) | −1.68091 | − | 8.27380i | −0.108502 | − | 0.534072i | ||||
\(241\) | −0.0376114 | − | 0.0651448i | −0.00242276 | − | 0.00419635i | 0.864811 | − | 0.502097i | \(-0.167438\pi\) |
−0.867234 | + | 0.497900i | \(0.834105\pi\) | |||||||
\(242\) | 1.17568 | − | 0.678778i | 0.0755754 | − | 0.0436335i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 17.0738 | 1.09304 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.724961 | −0.0462218 | ||||||||
\(247\) | 6.25639 | + | 3.61213i | 0.398084 | + | 0.229834i | ||||
\(248\) | 3.04434 | − | 1.75765i | 0.193315 | − | 0.111611i | ||||
\(249\) | −1.61213 | − | 2.79229i | −0.102164 | − | 0.176954i | ||||
\(250\) | −2.16173 | + | 0.168305i | −0.136720 | + | 0.0106445i | ||||
\(251\) | −19.2243 | −1.21342 | −0.606712 | − | 0.794922i | \(-0.707512\pi\) | ||||
−0.606712 | + | 0.794922i | \(0.707512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.92478i | 0.623965i | ||||||||
\(254\) | 0.261865 | − | 0.453564i | 0.0164309 | − | 0.0284591i | ||||
\(255\) | 2.37905 | − | 7.10362i | 0.148982 | − | 0.444846i | ||||
\(256\) | −6.53761 | − | 11.3235i | −0.408601 | − | 0.707717i | ||||
\(257\) | −6.36551 | − | 3.67513i | −0.397070 | − | 0.229248i | 0.288149 | − | 0.957586i | \(-0.406960\pi\) |
−0.685219 | + | 0.728337i | \(0.740293\pi\) | |||||||
\(258\) | − | 2.44851i | − | 0.152437i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.43866 | − | 3.92478i | 0.275274 | − | 0.243404i | ||||
\(261\) | −3.96239 | + | 6.86306i | −0.245266 | + | 0.424813i | ||||
\(262\) | 3.46410 | − | 2.00000i | 0.214013 | − | 0.123560i | ||||
\(263\) | −11.2258 | + | 6.48119i | −0.692210 | + | 0.399648i | −0.804439 | − | 0.594035i | \(-0.797534\pi\) |
0.112229 | + | 0.993682i | \(0.464201\pi\) | |||||||
\(264\) | −0.768452 | + | 1.33100i | −0.0472950 | + | 0.0819173i | ||||
\(265\) | −14.3634 | + | 12.7005i | −0.882339 | + | 0.780187i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.03761i | 0.0635008i | ||||||||
\(268\) | 16.8669 | + | 9.73813i | 1.03031 | + | 0.594851i | ||||
\(269\) | −2.05571 | − | 3.56059i | −0.125339 | − | 0.217093i | 0.796527 | − | 0.604604i | \(-0.206668\pi\) |
−0.921865 | + | 0.387510i | \(0.873335\pi\) | |||||||
\(270\) | −0.137716 | + | 0.411207i | −0.00838113 | + | 0.0250253i | ||||
\(271\) | −8.21203 | + | 14.2237i | −0.498846 | + | 0.864026i | −0.999999 | − | 0.00133248i | \(-0.999576\pi\) |
0.501154 | + | 0.865358i | \(0.332909\pi\) | |||||||
\(272\) | − | 12.6497i | − | 0.767003i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.36344 | −0.263605 | ||||||||
\(275\) | −7.98298 | − | 6.02262i | −0.481392 | − | 0.363178i | ||||
\(276\) | 4.86907 | + | 8.43347i | 0.293083 | + | 0.507635i | ||||
\(277\) | 9.59020 | − | 5.53690i | 0.576219 | − | 0.332680i | −0.183410 | − | 0.983036i | \(-0.558714\pi\) |
0.759629 | + | 0.650356i | \(0.225380\pi\) | |||||||
\(278\) | −0.550056 | − | 0.317575i | −0.0329902 | − | 0.0190469i | ||||
\(279\) | 4.57452 | 0.273869 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.3733 | 0.857438 | 0.428719 | − | 0.903438i | \(-0.358965\pi\) | ||||
0.428719 | + | 0.903438i | \(0.358965\pi\) | |||||||
\(282\) | −1.66691 | − | 0.962389i | −0.0992628 | − | 0.0573094i | ||||
\(283\) | −0.995090 | + | 0.574515i | −0.0591520 | + | 0.0341514i | −0.529284 | − | 0.848445i | \(-0.677540\pi\) |
0.470132 | + | 0.882596i | \(0.344206\pi\) | |||||||
\(284\) | −1.96239 | − | 3.39896i | −0.116446 | − | 0.201691i | ||||
\(285\) | −2.38186 | − | 11.7240i | −0.141089 | − | 0.694472i | ||||
\(286\) | −0.523730 | −0.0309688 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.26916i | 0.133711i | ||||||||
\(289\) | −2.88787 | + | 5.00194i | −0.169875 | + | 0.294232i | ||||
\(290\) | 3.25872 | + | 1.09137i | 0.191359 | + | 0.0640874i | ||||
\(291\) | −9.24965 | − | 16.0209i | −0.542224 | − | 0.939159i | ||||
\(292\) | −15.8906 | − | 9.17442i | −0.929925 | − | 0.536893i | ||||
\(293\) | − | 0.649738i | − | 0.0379581i | −0.999820 | − | 0.0189791i | \(-0.993958\pi\) | ||
0.999820 | − | 0.0189791i | \(-0.00604158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7757 | − | 14.4485i | −0.743833 | − | 0.841225i | ||||
\(296\) | −0.298062 | + | 0.516258i | −0.0173245 | + | 0.0300069i | ||||
\(297\) | −1.73205 | + | 1.00000i | −0.100504 | + | 0.0580259i | ||||
\(298\) | −0.747145 | + | 0.431364i | −0.0432809 | + | 0.0249883i | ||||
\(299\) | −3.35026 | + | 5.80282i | −0.193751 | + | 0.335586i | ||||
\(300\) | −9.73813 | − | 1.20123i | −0.562231 | − | 0.0693531i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 0.252016i | − | 0.0145019i | ||||||
\(303\) | −15.2965 | − | 8.83146i | −0.878763 | − | 0.507354i | ||||
\(304\) | −10.1006 | − | 17.4948i | −0.579310 | − | 1.00339i | ||||
\(305\) | 6.17832 | − | 18.4479i | 0.353769 | − | 1.05632i | ||||
\(306\) | −0.324869 | + | 0.562690i | −0.0185715 | + | 0.0321668i | ||||
\(307\) | 24.1016i | 1.37555i | 0.725924 | + | 0.687775i | \(0.241412\pi\) | ||||
−0.725924 | + | 0.687775i | \(0.758588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.70052 | 0.381179 | ||||||||
\(310\) | −0.394954 | − | 1.94405i | −0.0224319 | − | 0.110415i | ||||
\(311\) | 4.12601 | + | 7.14646i | 0.233964 | + | 0.405238i | 0.958971 | − | 0.283503i | \(-0.0914967\pi\) |
−0.725007 | + | 0.688742i | \(0.758163\pi\) | |||||||
\(312\) | −0.898598 | + | 0.518806i | −0.0508731 | + | 0.0293716i | ||||
\(313\) | −12.9053 | − | 7.45088i | −0.729451 | − | 0.421148i | 0.0887706 | − | 0.996052i | \(-0.471706\pi\) |
−0.818221 | + | 0.574904i | \(0.805040\pi\) | |||||||
\(314\) | −0.513881 | −0.0290000 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.9986 | −1.18126 | ||||||||
\(317\) | 8.76938 | + | 5.06300i | 0.492537 | + | 0.284367i | 0.725627 | − | 0.688089i | \(-0.241550\pi\) |
−0.233089 | + | 0.972455i | \(0.574883\pi\) | |||||||
\(318\) | 1.44012 | − | 0.831456i | 0.0807582 | − | 0.0466257i | ||||
\(319\) | 7.92478 | + | 13.7261i | 0.443702 | + | 0.768515i | ||||
\(320\) | −15.5833 | + | 3.16591i | −0.871132 | + | 0.176980i | ||||
\(321\) | 13.7381 | 0.766788 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 17.9248i | − | 0.997361i | ||||||
\(324\) | −0.981194 | + | 1.69948i | −0.0545108 | + | 0.0944155i | ||||
\(325\) | −2.63446 | − | 6.21609i | −0.146134 | − | 0.344807i | ||||
\(326\) | −0.513881 | − | 0.890068i | −0.0284612 | − | 0.0492963i | ||||
\(327\) | −2.40387 | − | 1.38787i | −0.132934 | − | 0.0767496i | ||||
\(328\) | 2.87258i | 0.158612i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.574515 | + | 0.649738i | 0.0316260 | + | 0.0357669i | ||||
\(331\) | −13.9248 | + | 24.1184i | −0.765375 | + | 1.32567i | 0.174673 | + | 0.984626i | \(0.444113\pi\) |
−0.940048 | + | 0.341042i | \(0.889220\pi\) | |||||||
\(332\) | −5.47955 | + | 3.16362i | −0.300729 | + | 0.173626i | ||||
\(333\) | −0.671816 | + | 0.387873i | −0.0368153 | + | 0.0212553i | ||||
\(334\) | 1.41090 | − | 2.44374i | 0.0772008 | − | 0.133716i | ||||
\(335\) | 16.6253 | − | 14.7005i | 0.908337 | − | 0.803175i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.84955i | 0.209699i | 0.994488 | + | 0.104849i | \(0.0334360\pi\) | ||||
−0.994488 | + | 0.104849i | \(0.966564\pi\) | |||||||
\(338\) | 1.87719 | + | 1.08379i | 0.102106 | + | 0.0589506i | ||||
\(339\) | 6.02539 | + | 10.4363i | 0.327254 | + | 0.566821i | ||||
\(340\) | −13.9401 | − | 4.66862i | −0.756006 | − | 0.253192i | ||||
\(341\) | 4.57452 | − | 7.92329i | 0.247724 | − | 0.429070i | ||||
\(342\) | 1.03761i | 0.0561076i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.70194 | −0.523093 | ||||||||
\(345\) | 10.8741 | − | 2.20919i | 0.585442 | − | 0.118939i | ||||
\(346\) | −0.436289 | − | 0.755674i | −0.0234550 | − | 0.0406253i | ||||
\(347\) | −8.30318 | + | 4.79384i | −0.445738 | + | 0.257347i | −0.706029 | − | 0.708183i | \(-0.749515\pi\) |
0.260290 | + | 0.965530i | \(0.416182\pi\) | |||||||
\(348\) | 13.4680 | + | 7.77575i | 0.721960 | + | 0.416824i | ||||
\(349\) | −15.1490 | −0.810909 | −0.405455 | − | 0.914115i | \(-0.632887\pi\) | ||||
−0.405455 | + | 0.914115i | \(0.632887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.35026 | −0.0720716 | ||||||||
\(352\) | 3.93030 | + | 2.26916i | 0.209486 | + | 0.120947i | ||||
\(353\) | 17.6226 | − | 10.1744i | 0.937957 | − | 0.541530i | 0.0486379 | − | 0.998816i | \(-0.484512\pi\) |
0.889319 | + | 0.457287i | \(0.151179\pi\) | |||||||
\(354\) | 0.836381 | + | 1.44865i | 0.0444531 | + | 0.0769951i | ||||
\(355\) | −4.38261 | + | 0.890373i | −0.232605 | + | 0.0472561i | ||||
\(356\) | 2.03620 | 0.107918 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.93937i | 0.102499i | ||||||||
\(359\) | −15.7005 | + | 27.1941i | −0.828642 | + | 1.43525i | 0.0704619 | + | 0.997514i | \(0.477553\pi\) |
−0.899104 | + | 0.437735i | \(0.855781\pi\) | |||||||
\(360\) | 1.62936 | + | 0.545685i | 0.0858749 | + | 0.0287601i | ||||
\(361\) | −4.81265 | − | 8.33575i | −0.253297 | − | 0.438724i | ||||
\(362\) | −1.78456 | − | 1.03032i | −0.0937945 | − | 0.0541523i | ||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6629 | + | 13.8496i | −0.819834 | + | 0.724919i | ||||
\(366\) | −0.843675 | + | 1.46129i | −0.0440996 | + | 0.0763827i | ||||
\(367\) | −25.4621 | + | 14.7005i | −1.32911 | + | 0.767361i | −0.985162 | − | 0.171628i | \(-0.945097\pi\) |
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(368\) | 16.2265 | − | 9.36836i | 0.845864 | − | 0.488360i | ||||
\(369\) | −1.86907 | + | 3.23732i | −0.0972998 | + | 0.168528i | ||||
\(370\) | 0.222839 | + | 0.252016i | 0.0115849 | + | 0.0131017i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 8.97698i | − | 0.465435i | ||||||
\(373\) | −13.8564 | − | 8.00000i | −0.717458 | − | 0.414224i | 0.0963587 | − | 0.995347i | \(-0.469280\pi\) |
−0.813816 | + | 0.581122i | \(0.802614\pi\) | |||||||
\(374\) | 0.649738 | + | 1.12538i | 0.0335972 | + | 0.0581920i | ||||
\(375\) | −4.82174 | + | 10.0872i | −0.248994 | + | 0.520899i | ||||
\(376\) | −3.81336 | + | 6.60493i | −0.196659 | + | 0.340623i | ||||
\(377\) | 10.7005i | 0.551105i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7005 | −0.549649 | −0.274824 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274824 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(380\) | −23.0071 | + | 4.67414i | −1.18024 | + | 0.239778i | ||||
\(381\) | −1.35026 | − | 2.33872i | −0.0691760 | − | 0.119816i | ||||
\(382\) | 2.32609 | − | 1.34297i | 0.119013 | − | 0.0687122i | ||||
\(383\) | −14.5282 | − | 8.38787i | −0.742357 | − | 0.428600i | 0.0805684 | − | 0.996749i | \(-0.474326\pi\) |
−0.822926 | + | 0.568149i | \(0.807660\pi\) | |||||||
\(384\) | 5.91748 | 0.301975 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.97224 | 0.151283 | ||||||||
\(387\) | −10.9338 | − | 6.31265i | −0.555798 | − | 0.320890i | ||||
\(388\) | −31.4391 | + | 18.1514i | −1.59608 | + | 0.921498i | ||||
\(389\) | −14.6629 | − | 25.3969i | −0.743439 | − | 1.28767i | −0.950920 | − | 0.309435i | \(-0.899860\pi\) |
0.207481 | − | 0.978239i | \(-0.433473\pi\) | |||||||
\(390\) | 0.116579 | + | 0.573826i | 0.00590320 | + | 0.0290568i | ||||
\(391\) | 16.6253 | 0.840778 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.6253i | − | 1.04041i | ||||||
\(394\) | −0.0557098 | + | 0.0964922i | −0.00280662 | + | 0.00486121i | ||||
\(395\) | −7.59854 | + | 22.6885i | −0.382324 | + | 1.14158i | ||||
\(396\) | 1.96239 | + | 3.39896i | 0.0986137 | + | 0.170804i | ||||
\(397\) | −15.8906 | − | 9.17442i | −0.797525 | − | 0.460451i | 0.0450802 | − | 0.998983i | \(-0.485646\pi\) |
−0.842605 | + | 0.538532i | \(0.818979\pi\) | |||||||
\(398\) | 0.0390260i | 0.00195620i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.31124 | + | 18.7367i | −0.115562 | + | 0.936836i | ||||
\(401\) | 18.6629 | − | 32.3251i | 0.931981 | − | 1.61424i | 0.152051 | − | 0.988373i | \(-0.451412\pi\) |
0.779930 | − | 0.625866i | \(-0.215254\pi\) | |||||||
\(402\) | −1.66691 | + | 0.962389i | −0.0831377 | + | 0.0479996i | ||||
\(403\) | 5.34926 | − | 3.08840i | 0.266466 | − | 0.153844i | ||||
\(404\) | −17.3307 | + | 30.0177i | −0.862237 | + | 1.49344i | ||||
\(405\) | 1.48119 | + | 1.67513i | 0.0736011 | + | 0.0832379i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.55149i | 0.0769046i | ||||||||
\(408\) | 2.22960 | + | 1.28726i | 0.110381 | + | 0.0637288i | ||||
\(409\) | 11.1866 | + | 19.3758i | 0.553144 | + | 0.958073i | 0.998045 | + | 0.0624938i | \(0.0199054\pi\) |
−0.444901 | + | 0.895580i | \(0.646761\pi\) | |||||||
\(410\) | 1.53715 | + | 0.514801i | 0.0759143 | + | 0.0254242i | ||||
\(411\) | −11.2496 | + | 19.4850i | −0.554904 | + | 0.961122i | ||||
\(412\) | − | 13.1490i | − | 0.647806i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.962389 | −0.0472988 | ||||||||
\(415\) | 1.43539 | + | 7.06532i | 0.0704607 | + | 0.346823i | ||||
\(416\) | 1.53198 | + | 2.65347i | 0.0751115 | + | 0.130097i | ||||
\(417\) | −2.83627 | + | 1.63752i | −0.138893 | + | 0.0801897i | ||||
\(418\) | 1.79720 | + | 1.03761i | 0.0879037 | + | 0.0507512i | ||||
\(419\) | 23.4763 | 1.14689 | 0.573445 | − | 0.819244i | \(-0.305606\pi\) | ||||
0.573445 | + | 0.819244i | \(0.305606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2243 | −1.22935 | −0.614677 | − | 0.788779i | \(-0.710714\pi\) | ||||
−0.614677 | + | 0.788779i | \(0.710714\pi\) | |||||||
\(422\) | 1.08305 | + | 0.625301i | 0.0527222 | + | 0.0304392i | ||||
\(423\) | −8.59511 | + | 4.96239i | −0.417909 | + | 0.241280i | ||||
\(424\) | −3.29455 | − | 5.70633i | −0.159998 | − | 0.277124i | ||||
\(425\) | −10.0887 | + | 13.3725i | −0.489373 | + | 0.648663i | ||||
\(426\) | 0.387873 | 0.0187925 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 26.9596i | − | 1.30314i | ||||||
\(429\) | −1.35026 | + | 2.33872i | −0.0651913 | + | 0.112915i | ||||
\(430\) | −1.73871 | + | 5.19161i | −0.0838479 | + | 0.250362i | ||||
\(431\) | 9.70052 | + | 16.8018i | 0.467258 | + | 0.809314i | 0.999300 | − | 0.0374035i | \(-0.0119087\pi\) |
−0.532042 | + | 0.846718i | \(0.678575\pi\) | |||||||
\(432\) | 3.26989 | + | 1.88787i | 0.157323 | + | 0.0908303i | ||||
\(433\) | − | 6.49929i | − | 0.312336i | −0.987731 | − | 0.156168i | \(-0.950086\pi\) | ||
0.987731 | − | 0.156168i | \(-0.0499141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.2750 | − | 11.7381i | 0.636489 | − | 0.562800i | ||||
\(436\) | −2.72355 | + | 4.71732i | −0.130434 | + | 0.225919i | ||||
\(437\) | 22.9930 | − | 13.2750i | 1.09991 | − | 0.635031i | ||||
\(438\) | 1.57041 | − | 0.906679i | 0.0750373 | − | 0.0433228i | ||||
\(439\) | 7.32487 | − | 12.6870i | 0.349597 | − | 0.605520i | −0.636581 | − | 0.771210i | \(-0.719652\pi\) |
0.986178 | + | 0.165690i | \(0.0529852\pi\) | |||||||
\(440\) | 2.57452 | − | 2.27645i | 0.122735 | − | 0.108526i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.877317i | 0.0417297i | ||||||||
\(443\) | −16.5750 | − | 9.56959i | −0.787503 | − | 0.454665i | 0.0515798 | − | 0.998669i | \(-0.483574\pi\) |
−0.839083 | + | 0.544004i | \(0.816908\pi\) | |||||||
\(444\) | 0.761158 | + | 1.31836i | 0.0361230 | + | 0.0625668i | ||||
\(445\) | 0.736817 | − | 2.20007i | 0.0349285 | − | 0.104293i | ||||
\(446\) | 0.150446 | − | 0.260579i | 0.00712380 | − | 0.0123388i | ||||
\(447\) | 4.44851i | 0.210407i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.8021 | 1.54803 | 0.774013 | − | 0.633169i | \(-0.218246\pi\) | ||||
0.774013 | + | 0.633169i | \(0.218246\pi\) | |||||||
\(450\) | 0.584003 | − | 0.774096i | 0.0275302 | − | 0.0364912i | ||||
\(451\) | 3.73813 | + | 6.47464i | 0.176022 | + | 0.304879i | ||||
\(452\) | 20.4800 | − | 11.8242i | 0.963300 | − | 0.556162i | ||||
\(453\) | −1.12538 | − | 0.649738i | −0.0528749 | − | 0.0305274i | ||||
\(454\) | −2.55008 | −0.119681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.11142 | 0.192535 | ||||||||
\(457\) | −16.1951 | − | 9.35026i | −0.757576 | − | 0.437387i | 0.0708487 | − | 0.997487i | \(-0.477429\pi\) |
−0.828425 | + | 0.560100i | \(0.810763\pi\) | |||||||
\(458\) | −0.466198 | + | 0.269159i | −0.0217840 | + | 0.0125770i | ||||
\(459\) | 1.67513 | + | 2.90141i | 0.0781884 | + | 0.135426i | ||||
\(460\) | −4.33529 | − | 21.3392i | −0.202134 | − | 0.994946i | ||||
\(461\) | 6.96239 | 0.324271 | 0.162135 | − | 0.986769i | \(-0.448162\pi\) | ||||
0.162135 | + | 0.986769i | \(0.448162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.29948i | 0.246288i | 0.992389 | + | 0.123144i | \(0.0392976\pi\) | ||||
−0.992389 | + | 0.123144i | \(0.960702\pi\) | |||||||
\(464\) | 14.9610 | − | 25.9132i | 0.694546 | − | 1.20299i | ||||
\(465\) | −9.69942 | − | 3.24840i | −0.449800 | − | 0.150641i | ||||
\(466\) | 0.00492456 | + | 0.00852958i | 0.000228126 | + | 0.000395125i | ||||
\(467\) | 11.3874 | + | 6.57452i | 0.526946 | + | 0.304232i | 0.739772 | − | 0.672858i | \(-0.234933\pi\) |
−0.212826 | + | 0.977090i | \(0.568267\pi\) | |||||||
\(468\) | 2.64974i | 0.122484i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.85097 | + | 3.22425i | 0.131505 | + | 0.148724i | ||||
\(471\) | −1.32487 | + | 2.29474i | −0.0610467 | + | 0.105736i | ||||
\(472\) | 5.74013 | − | 3.31406i | 0.264211 | − | 0.152542i | ||||
\(473\) | −21.8677 | + | 12.6253i | −1.00548 | + | 0.580512i | ||||
\(474\) | 1.03761 | − | 1.79720i | 0.0476591 | − | 0.0825479i | ||||
\(475\) | −3.27504 | + | 26.5501i | −0.150269 | + | 1.21820i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 8.57452i | − | 0.392600i | ||||||
\(478\) | −0.982456 | − | 0.567221i | −0.0449365 | − | 0.0259441i | ||||
\(479\) | −2.57452 | − | 4.45919i | −0.117633 | − | 0.203746i | 0.801196 | − | 0.598401i | \(-0.204197\pi\) |
−0.918829 | + | 0.394656i | \(0.870864\pi\) | |||||||
\(480\) | 1.61135 | − | 4.81134i | 0.0735477 | − | 0.219607i | ||||
\(481\) | −0.523730 | + | 0.907127i | −0.0238800 | + | 0.0413614i | ||||
\(482\) | − | 0.0145884i | − | 0.000664486i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.7367 | −0.624396 | ||||||||
\(485\) | 8.23563 | + | 40.5376i | 0.373961 | + | 1.84072i | ||||
\(486\) | −0.0969683 | − | 0.167954i | −0.00439857 | − | 0.00761855i | ||||
\(487\) | 19.2057 | − | 11.0884i | 0.870292 | − | 0.502463i | 0.00284661 | − | 0.999996i | \(-0.499094\pi\) |
0.867445 | + | 0.497533i | \(0.165761\pi\) | |||||||
\(488\) | 5.79019 | + | 3.34297i | 0.262110 | + | 0.151329i | ||||
\(489\) | −5.29948 | −0.239651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | 0.0902587 | 0.0451294 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451294 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(492\) | 6.35288 | + | 3.66784i | 0.286410 | + | 0.165359i | ||||
\(493\) | 22.9930 | − | 13.2750i | 1.03555 | − | 0.597878i | ||||
\(494\) | 0.700523 | + | 1.21334i | 0.0315180 | + | 0.0545908i | ||||
\(495\) | 4.38261 | − | 0.890373i | 0.196983 | − | 0.0400193i | ||||
\(496\) | −17.2722 | −0.775545 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 0.625301i | − | 0.0280204i | ||||||
\(499\) | −3.27504 | + | 5.67253i | −0.146611 | + | 0.253937i | −0.929973 | − | 0.367628i | \(-0.880170\pi\) |
0.783362 | + | 0.621566i | \(0.213503\pi\) | |||||||
\(500\) | 19.7949 | + | 9.46213i | 0.885256 | + | 0.423159i | ||||
\(501\) | −7.27504 | − | 12.6007i | −0.325025 | − | 0.562959i | ||||
\(502\) | −3.22879 | − | 1.86414i | −0.144108 | − | 0.0832008i | ||||
\(503\) | − | 8.77575i | − | 0.391291i | −0.980675 | − | 0.195646i | \(-0.937320\pi\) | ||
0.980675 | − | 0.195646i | \(-0.0626802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.1622 | + | 29.5877i | 1.16420 | + | 1.31663i | ||||
\(506\) | −0.962389 | + | 1.66691i | −0.0427834 | + | 0.0741030i | ||||
\(507\) | 9.67939 | − | 5.58840i | 0.429877 | − | 0.248189i | ||||
\(508\) | −4.58948 | + | 2.64974i | −0.203625 | + | 0.117563i | ||||
\(509\) | −6.56959 | + | 11.3789i | −0.291192 | + | 0.504359i | −0.974092 | − | 0.226153i | \(-0.927385\pi\) |
0.682900 | + | 0.730512i | \(0.260719\pi\) | |||||||
\(510\) | 1.08840 | − | 0.962389i | 0.0481950 | − | 0.0426153i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 14.3707i | − | 0.635103i | ||||||
\(513\) | 4.63346 | + | 2.67513i | 0.204572 | + | 0.118110i | ||||
\(514\) | −0.712742 | − | 1.23451i | −0.0314377 | − | 0.0544517i | ||||
\(515\) | −14.2072 | − | 4.75810i | −0.626046 | − | 0.209667i | ||||
\(516\) | −12.3879 | + | 21.4564i | −0.545346 | + | 0.944566i | ||||
\(517\) | 19.8496i | 0.872982i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.49929 | −0.197497 | ||||||||
\(520\) | 2.27372 | − | 0.461931i | 0.0997093 | − | 0.0202570i | ||||
\(521\) | −18.8315 | − | 32.6170i | −0.825021 | − | 1.42898i | −0.901903 | − | 0.431938i | \(-0.857830\pi\) |
0.0768821 | − | 0.997040i | \(-0.475503\pi\) | |||||||
\(522\) | −1.33100 | + | 0.768452i | −0.0582562 | + | 0.0336342i | ||||
\(523\) | −3.46410 | − | 2.00000i | −0.151475 | − | 0.0874539i | 0.422347 | − | 0.906434i | \(-0.361206\pi\) |
−0.573822 | + | 0.818980i | \(0.694540\pi\) | |||||||
\(524\) | −40.4749 | −1.76815 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.51388 | −0.109610 | ||||||||
\(527\) | −13.2726 | − | 7.66291i | −0.578161 | − | 0.333802i | ||||
\(528\) | 6.53978 | − | 3.77575i | 0.284608 | − | 0.164318i | ||||
\(529\) | 0.812650 | + | 1.40755i | 0.0353326 | + | 0.0611979i | ||||
\(530\) | −3.64394 | + | 0.740306i | −0.158283 | + | 0.0321568i | ||||
\(531\) | 8.62530 | 0.374306 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.04746i | 0.218630i | ||||||||
\(534\) | −0.100615 | + | 0.174271i | −0.00435405 | + | 0.00754144i | ||||
\(535\) | −29.1292 | − | 9.75557i | −1.25937 | − | 0.421770i | ||||
\(536\) | 3.81336 | + | 6.60493i | 0.164712 | + | 0.285289i | ||||
\(537\) | 8.66025 | + | 5.00000i | 0.373718 | + | 0.215766i | ||||
\(538\) | − | 0.797355i | − | 0.0343764i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.28726 | − | 2.90668i | 0.141461 | − | 0.125084i | ||||
\(541\) | 11.2374 | − | 19.4638i | 0.483135 | − | 0.836814i | −0.516678 | − | 0.856180i | \(-0.672831\pi\) |
0.999812 | + | 0.0193660i | \(0.00616479\pi\) | |||||||
\(542\) | −2.75849 | + | 1.59261i | −0.118487 | + | 0.0684086i | ||||
\(543\) | −9.20178 | + | 5.31265i | −0.394886 | + | 0.227988i | ||||
\(544\) | 3.80114 | − | 6.58377i | 0.162972 | − | 0.282277i | ||||
\(545\) | 4.11142 | + | 4.64974i | 0.176114 | + | 0.199173i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9248i | 1.10846i | 0.832362 | + | 0.554232i | \(0.186988\pi\) | ||||
−0.832362 | + | 0.554232i | \(0.813012\pi\) | |||||||
\(548\) | 38.2371 | + | 22.0762i | 1.63341 | + | 0.943048i | ||||
\(549\) | 4.35026 | + | 7.53487i | 0.185665 | + | 0.321581i | ||||
\(550\) | −0.756770 | − | 1.78562i | −0.0322688 | − | 0.0761391i | ||||
\(551\) | 21.1998 | − | 36.7192i | 0.903143 | − | 1.56429i | ||||
\(552\) | 3.81336i | 0.162307i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.14762 | 0.0912435 | ||||||||
\(555\) | 1.69990 | − | 0.345352i | 0.0721565 | − | 0.0146594i | ||||
\(556\) | 3.21345 | + | 5.56586i | 0.136281 | + | 0.236045i | ||||
\(557\) | 24.7039 | − | 14.2628i | 1.04674 | − | 0.604335i | 0.125004 | − | 0.992156i | \(-0.460105\pi\) |
0.921735 | + | 0.387821i | \(0.126772\pi\) | |||||||
\(558\) | 0.768308 | + | 0.443583i | 0.0325251 | + | 0.0187784i | ||||
\(559\) | −17.0475 | −0.721031 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.70052 | 0.282896 | ||||||||
\(562\) | 2.41405 | + | 1.39375i | 0.101831 | + | 0.0587919i | ||||
\(563\) | 10.0690 | − | 5.81336i | 0.424359 | − | 0.245004i | −0.272582 | − | 0.962133i | \(-0.587877\pi\) |
0.696941 | + | 0.717129i | \(0.254544\pi\) | |||||||
\(564\) | 9.73813 | + | 16.8669i | 0.410049 | + | 0.710226i | ||||
\(565\) | −5.36485 | − | 26.4069i | −0.225701 | − | 1.11095i | ||||
\(566\) | −0.222839 | −0.00936663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.53690i | − | 0.0644871i | ||||||
\(569\) | 4.66291 | − | 8.07640i | 0.195479 | − | 0.338580i | −0.751578 | − | 0.659644i | \(-0.770707\pi\) |
0.947058 | + | 0.321064i | \(0.104040\pi\) | |||||||
\(570\) | 0.736817 | − | 2.20007i | 0.0308619 | − | 0.0921506i | ||||
\(571\) | 9.84955 | + | 17.0599i | 0.412191 | + | 0.713936i | 0.995129 | − | 0.0985808i | \(-0.0314303\pi\) |
−0.582938 | + | 0.812517i | \(0.698097\pi\) | |||||||
\(572\) | 4.58948 | + | 2.64974i | 0.191896 | + | 0.110791i | ||||
\(573\) | − | 13.8496i | − | 0.578573i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.6253 | − | 3.03761i | −1.02695 | − | 0.126677i | ||||
\(576\) | 3.55571 | − | 6.15867i | 0.148155 | − | 0.256611i | ||||
\(577\) | 28.4033 | − | 16.3987i | 1.18245 | − | 0.682686i | 0.225867 | − | 0.974158i | \(-0.427478\pi\) |
0.956579 | + | 0.291472i | \(0.0941451\pi\) | |||||||
\(578\) | −0.970060 | + | 0.560064i | −0.0403492 | + | 0.0232956i | ||||
\(579\) | 7.66291 | − | 13.2726i | 0.318460 | − | 0.551588i | ||||
\(580\) | −23.0348 | − | 26.0508i | −0.956467 | − | 1.08170i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 3.58769i | − | 0.148715i | ||||||
\(583\) | −14.8515 | − | 8.57452i | −0.615086 | − | 0.355120i | ||||
\(584\) | −3.59261 | − | 6.22259i | −0.148663 | − | 0.257493i | ||||
\(585\) | 2.86298 | + | 0.958833i | 0.118370 | + | 0.0396429i | ||||
\(586\) | 0.0630040 | − | 0.109126i | 0.00260267 | − | 0.00450796i | ||||
\(587\) | 18.8218i | 0.776859i | 0.921479 | + | 0.388429i | \(0.126982\pi\) | ||||
−0.921479 | + | 0.388429i | \(0.873018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.4749 | −1.00847 | ||||||||
\(590\) | −0.744691 | − | 3.66553i | −0.0306584 | − | 0.150907i | ||||
\(591\) | 0.287258 | + | 0.497545i | 0.0118162 | + | 0.0204663i | ||||
\(592\) | 2.53661 | − | 1.46451i | 0.104254 | − | 0.0601910i | ||||
\(593\) | 29.2283 | + | 16.8749i | 1.20026 | + | 0.692971i | 0.960613 | − | 0.277889i | \(-0.0896347\pi\) |
0.239648 | + | 0.970860i | \(0.422968\pi\) | |||||||
\(594\) | −0.387873 | −0.0159146 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.72970 | 0.357582 | ||||||||
\(597\) | 0.174271 | + | 0.100615i | 0.00713244 | + | 0.00411791i | ||||
\(598\) | −1.12538 | + | 0.649738i | −0.0460202 | + | 0.0265698i | ||||
\(599\) | −10.1490 | − | 17.5786i | −0.414678 | − | 0.718244i | 0.580716 | − | 0.814106i | \(-0.302773\pi\) |
−0.995395 | + | 0.0958622i | \(0.969439\pi\) | |||||||
\(600\) | −3.06727 | − | 2.31405i | −0.125221 | − | 0.0944706i | ||||
\(601\) | 13.8496 | 0.564935 | 0.282468 | − | 0.959277i | \(-0.408847\pi\) | ||||
0.282468 | + | 0.959277i | \(0.408847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.92478i | 0.404168i | ||||||||
\(604\) | −1.27504 | + | 2.20843i | −0.0518806 | + | 0.0898598i | ||||
\(605\) | −4.97076 | + | 14.8422i | −0.202090 | + | 0.603422i | ||||
\(606\) | −1.71274 | − | 2.96656i | −0.0695754 | − | 0.120508i | ||||
\(607\) | 21.8677 | + | 12.6253i | 0.887581 | + | 0.512445i | 0.873150 | − | 0.487451i | \(-0.162073\pi\) |
0.0144305 | + | 0.999896i | \(0.495406\pi\) | |||||||
\(608\) | − | 12.1406i | − | 0.492366i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.82653 | − | 2.49929i | 0.114443 | − | 0.101193i | ||||
\(611\) | −6.70052 | + | 11.6056i | −0.271074 | + | 0.469514i | ||||
\(612\) | 5.69370 | − | 3.28726i | 0.230154 | − | 0.132880i | ||||
\(613\) | −7.92329 | + | 4.57452i | −0.320019 | + | 0.184763i | −0.651401 | − | 0.758734i | \(-0.725818\pi\) |
0.331382 | + | 0.943497i | \(0.392485\pi\) | |||||||
\(614\) | −2.33709 | + | 4.04796i | −0.0943172 | + | 0.163362i | ||||
\(615\) | 6.26187 | − | 5.53690i | 0.252503 | − | 0.223270i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.9492i | − | 0.642091i | −0.947064 | − | 0.321046i | \(-0.895966\pi\) | ||
0.947064 | − | 0.321046i | \(-0.104034\pi\) | |||||||
\(618\) | 1.12538 | + | 0.649738i | 0.0452694 | + | 0.0261363i | ||||
\(619\) | −5.58673 | − | 9.67651i | −0.224550 | − | 0.388932i | 0.731634 | − | 0.681697i | \(-0.238758\pi\) |
−0.956184 | + | 0.292765i | \(0.905424\pi\) | |||||||
\(620\) | −6.37463 | + | 19.0340i | −0.256011 | + | 0.764425i | ||||
\(621\) | −2.48119 | + | 4.29755i | −0.0995669 | + | 0.172455i | ||||
\(622\) | 1.60037i | 0.0641689i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.09825 | 0.204093 | ||||||||
\(625\) | 17.3866 | − | 17.9640i | 0.695464 | − | 0.718561i | ||||
\(626\) | −1.44500 | − | 2.50281i | −0.0577537 | − | 0.100032i | ||||
\(627\) | 9.26693 | − | 5.35026i | 0.370085 | − | 0.213669i | ||||
\(628\) | 4.50317 | + | 2.59991i | 0.179696 | + | 0.103748i | ||||
\(629\) | 2.59895 | 0.103627 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5501 | −0.579229 | −0.289615 | − | 0.957143i | \(-0.593527\pi\) | ||||
−0.289615 | + | 0.957143i | \(0.593527\pi\) | |||||||
\(632\) | −7.12119 | − | 4.11142i | −0.283266 | − | 0.163543i | ||||
\(633\) | 5.58457 | − | 3.22425i | 0.221967 | − | 0.128153i | ||||
\(634\) | 0.981902 | + | 1.70070i | 0.0389963 | + | 0.0675436i | ||||
\(635\) | 1.20224 | + | 5.91767i | 0.0477093 | + | 0.234835i | ||||
\(636\) | −16.8265 | −0.667215 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.07381i | 0.121693i | ||||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | −12.5469 | − | 4.20206i | −0.495961 | − | 0.166101i | ||||
\(641\) | 19.3634 | + | 33.5385i | 0.764810 | + | 1.32469i | 0.940347 | + | 0.340217i | \(0.110500\pi\) |
−0.175537 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(642\) | 2.30737 | + | 1.33216i | 0.0910648 | + | 0.0525763i | ||||
\(643\) | 11.9511i | 0.471306i | 0.971837 | + | 0.235653i | \(0.0757229\pi\) | ||||
−0.971837 | + | 0.235653i | \(0.924277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.7005 | + | 21.1490i | 0.736332 | + | 0.832742i | ||||
\(646\) | 1.73813 | − | 3.01054i | 0.0683860 | − | 0.118448i | ||||
\(647\) | −12.6007 | + | 7.27504i | −0.495386 | + | 0.286011i | −0.726806 | − | 0.686843i | \(-0.758996\pi\) |
0.231420 | + | 0.972854i | \(0.425663\pi\) | |||||||
\(648\) | −0.665499 | + | 0.384226i | −0.0261433 | + | 0.0150938i | ||||
\(649\) | 8.62530 | − | 14.9395i | 0.338573 | − | 0.586425i | ||||
\(650\) | 0.160295 | − | 1.29948i | 0.00628727 | − | 0.0509697i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.3996i | 0.407281i | ||||||||
\(653\) | −43.2801 | − | 24.9878i | −1.69368 | − | 0.977847i | −0.951500 | − | 0.307648i | \(-0.900458\pi\) |
−0.742181 | − | 0.670199i | \(-0.766209\pi\) | |||||||
\(654\) | −0.269159 | − | 0.466198i | −0.0105250 | − | 0.0182298i | ||||
\(655\) | −14.6462 | + | 43.7322i | −0.572275 | + | 1.70876i | ||||
\(656\) | 7.05712 | − | 12.2233i | 0.275534 | − | 0.477240i | ||||
\(657\) | − | 9.35026i | − | 0.364788i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9525 | 0.660377 | 0.330189 | − | 0.943915i | \(-0.392888\pi\) | ||||
0.330189 | + | 0.943915i | \(0.392888\pi\) | |||||||
\(660\) | −1.74726 | − | 8.60038i | −0.0680119 | − | 0.334769i | ||||
\(661\) | −7.82653 | − | 13.5560i | −0.304417 | − | 0.527265i | 0.672715 | − | 0.739902i | \(-0.265128\pi\) |
−0.977131 | + | 0.212637i | \(0.931795\pi\) | |||||||
\(662\) | −4.67744 | + | 2.70052i | −0.181794 | + | 0.104959i | ||||
\(663\) | 3.91767 | + | 2.26187i | 0.152150 | + | 0.0878436i | ||||
\(664\) | −2.47768 | −0.0961528 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.150446 | −0.00582965 | ||||||||
\(667\) | 34.0572 | + | 19.6629i | 1.31870 | + | 0.761351i | ||||
\(668\) | −24.7275 | + | 14.2765i | −0.956737 | + | 0.552373i | ||||
\(669\) | −0.775746 | − | 1.34363i | −0.0299921 | − | 0.0519478i | ||||
\(670\) | 4.21777 | − | 0.856885i | 0.162947 | − | 0.0331043i | ||||
\(671\) | 17.4010 | 0.671760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0263i | 1.00324i | 0.865088 | + | 0.501621i | \(0.167263\pi\) | ||||
−0.865088 | + | 0.501621i | \(0.832737\pi\) | |||||||
\(674\) | −0.373285 | + | 0.646548i | −0.0143784 | + | 0.0249041i | ||||
\(675\) | −1.95108 | − | 4.60362i | −0.0750970 | − | 0.177193i | ||||
\(676\) | −10.9666 | − | 18.9947i | −0.421793 | − | 0.730566i | ||||
\(677\) | 30.7022 | + | 17.7259i | 1.17998 | + | 0.681262i | 0.956010 | − | 0.293334i | \(-0.0947647\pi\) |
0.223971 | + | 0.974596i | \(0.428098\pi\) | |||||||
\(678\) | 2.33709i | 0.0897553i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.81336 | − | 4.31265i | −0.146236 | − | 0.165383i | ||||
\(681\) | −6.57452 | + | 11.3874i | −0.251936 | + | 0.436366i | ||||
\(682\) | 1.53662 | − | 0.887166i | 0.0588401 | − | 0.0339713i | ||||
\(683\) | −20.4927 | + | 11.8315i | −0.784131 | + | 0.452718i | −0.837892 | − | 0.545836i | \(-0.816212\pi\) |
0.0537615 | + | 0.998554i | \(0.482879\pi\) | |||||||
\(684\) | 5.24965 | − | 9.09265i | 0.200725 | − | 0.347666i | ||||
\(685\) | 37.6893 | − | 33.3258i | 1.44003 | − | 1.27331i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.77575i | 0.105901i | ||||||||
\(688\) | 41.2834 | + | 23.8350i | 1.57391 | + | 0.908700i | ||||
\(689\) | −5.78892 | − | 10.0267i | −0.220540 | − | 0.381987i | ||||
\(690\) | 2.04057 | + | 0.683401i | 0.0776831 | + | 0.0260166i | ||||
\(691\) | −0.287258 | + | 0.497545i | −0.0109278 | + | 0.0189275i | −0.871438 | − | 0.490506i | \(-0.836812\pi\) |
0.860510 | + | 0.509434i | \(0.170145\pi\) | |||||||
\(692\) | 8.82936i | 0.335642i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.85940 | −0.0705820 | ||||||||
\(695\) | 7.17660 | − | 1.45800i | 0.272224 | − | 0.0553052i | ||||
\(696\) | 3.04491 | + | 5.27393i | 0.115417 | + | 0.199908i | ||||
\(697\) | 10.8459 | − | 6.26187i | 0.410817 | − | 0.237185i | ||||
\(698\) | −2.54434 | − | 1.46898i | −0.0963047 | − | 0.0556015i | ||||
\(699\) | 0.0507852 | 0.00192087 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7269 | 1.61377 | 0.806886 | − | 0.590707i | \(-0.201151\pi\) | ||||
0.806886 | + | 0.590707i | \(0.201151\pi\) | |||||||
\(702\) | −0.226782 | − | 0.130933i | −0.00855933 | − | 0.00494173i | ||||
\(703\) | 3.59439 | − | 2.07522i | 0.135565 | − | 0.0782685i | ||||
\(704\) | −7.11142 | − | 12.3173i | −0.268022 | − | 0.464227i | ||||
\(705\) | 21.7482 | − | 4.41838i | 0.819084 | − | 0.166406i | ||||
\(706\) | 3.94639 | 0.148524 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 16.9262i | − | 0.636125i | ||||||
\(709\) | 13.6253 | − | 23.5997i | 0.511709 | − | 0.886306i | −0.488199 | − | 0.872732i | \(-0.662346\pi\) |
0.999908 | − | 0.0135735i | \(-0.00432070\pi\) | |||||||
\(710\) | −0.822414 | − | 0.275432i | −0.0308647 | − | 0.0103368i | ||||
\(711\) | −5.35026 | − | 9.26693i | −0.200650 | − | 0.347537i | ||||
\(712\) | 0.690529 | + | 0.398677i | 0.0258787 | + | 0.0149411i | ||||
\(713\) | − | 22.7005i | − | 0.850141i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.52373 | − | 4.00000i | 0.169178 | − | 0.149592i | ||||
\(716\) | 9.81194 | − | 16.9948i | 0.366690 | − | 0.635125i | ||||
\(717\) | −5.06586 | + | 2.92478i | −0.189188 | + | 0.109228i | ||||
\(718\) | −5.27393 | + | 3.04491i | −0.196821 | + | 0.113635i | ||||
\(719\) | 5.35026 | − | 9.26693i | 0.199531 | − | 0.345598i | −0.748845 | − | 0.662745i | \(-0.769391\pi\) |
0.948376 | + | 0.317147i | \(0.102725\pi\) | |||||||
\(720\) | −5.59261 | − | 6.32487i | −0.208424 | − | 0.235714i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.86670i | − | 0.0694713i | ||||||
\(723\) | −0.0651448 | − | 0.0376114i | −0.00242276 | − | 0.00139878i | ||||
\(724\) | 10.4255 | + | 18.0575i | 0.387460 | + | 0.671101i | ||||
\(725\) | −36.4826 | + | 15.4618i | −1.35493 | + | 0.574239i | ||||
\(726\) | 0.678778 | − | 1.17568i | 0.0251918 | − | 0.0436335i | ||||
\(727\) | 39.9511i | 1.48171i | 0.671668 | + | 0.740853i | \(0.265578\pi\) | ||||
−0.671668 | + | 0.740853i | \(0.734422\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −3.97362 | + | 0.807282i | −0.147070 | + | 0.0298789i | ||||
\(731\) | 21.1490 | + | 36.6312i | 0.782225 | + | 1.35485i | ||||
\(732\) | 14.7864 | − | 8.53690i | 0.546519 | − | 0.315533i | ||||
\(733\) | −26.2829 | − | 15.1744i | −0.970780 | − | 0.560480i | −0.0713061 | − | 0.997454i | \(-0.522717\pi\) |
−0.899474 | + | 0.436974i | \(0.856050\pi\) | |||||||
\(734\) | −5.70194 | −0.210462 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.2605 | 0.415066 | ||||||||
\(737\) | 17.1902 | + | 9.92478i | 0.633210 | + | 0.365584i | ||||
\(738\) | −0.627835 | + | 0.362481i | −0.0231109 | + | 0.0133431i | ||||
\(739\) | 18.6253 | + | 32.2600i | 0.685143 | + | 1.18670i | 0.973392 | + | 0.229147i | \(0.0735935\pi\) |
−0.288249 | + | 0.957555i | \(0.593073\pi\) | |||||||
\(740\) | −0.677714 | − | 3.33585i | −0.0249133 | − | 0.122628i | ||||
\(741\) | 7.22425 | 0.265390 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.3634i | 0.967181i | 0.875294 | + | 0.483590i | \(0.160668\pi\) | ||||
−0.875294 | + | 0.483590i | \(0.839332\pi\) | |||||||
\(744\) | 1.75765 | − | 3.04434i | 0.0644385 | − | 0.111611i | ||||
\(745\) | 3.15892 | − | 9.43225i | 0.115734 | − | 0.345571i | ||||
\(746\) | −1.55149 | − | 2.68726i | −0.0568042 | − | 0.0983877i | ||||
\(747\) | −2.79229 | − | 1.61213i | −0.102164 | − | 0.0589846i | ||||
\(748\) | − | 13.1490i | − | 0.480776i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.78797 | + | 1.22662i | −0.0652873 | + | 0.0447900i | ||||
\(751\) | −25.3258 | + | 43.8656i | −0.924152 | + | 1.60068i | −0.131234 | + | 0.991351i | \(0.541894\pi\) |
−0.792919 | + | 0.609328i | \(0.791439\pi\) | |||||||
\(752\) | 32.4530 | − | 18.7367i | 1.18344 | − | 0.683258i | ||||
\(753\) | −16.6487 | + | 9.61213i | −0.606712 | + | 0.350285i | ||||
\(754\) | −1.03761 | + | 1.79720i | −0.0377876 | + | 0.0654500i | ||||
\(755\) | 1.92478 | + | 2.17679i | 0.0700498 | + | 0.0792216i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 38.9525i | − | 1.41575i | −0.706336 | − | 0.707877i | \(-0.749653\pi\) | ||
0.706336 | − | 0.707877i | \(-0.250347\pi\) | |||||||
\(758\) | −1.79720 | − | 1.03761i | −0.0652771 | − | 0.0376877i | ||||
\(759\) | 4.96239 | + | 8.59511i | 0.180123 | + | 0.311983i | ||||
\(760\) | −8.71751 | − | 2.91955i | −0.316217 | − | 0.105903i | ||||
\(761\) | 24.1065 | − | 41.7537i | 0.873860 | − | 1.51357i | 0.0158873 | − | 0.999874i | \(-0.494943\pi\) |
0.857972 | − | 0.513696i | \(-0.171724\pi\) | |||||||
\(762\) | − | 0.523730i | − | 0.0189727i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −27.1782 | −0.983273 | ||||||||
\(765\) | −1.49149 | − | 7.34144i | −0.0539250 | − | 0.265430i | ||||
\(766\) | −1.62672 | − | 2.81755i | −0.0587756 | − | 0.101802i | ||||
\(767\) | 10.0861 | − | 5.82321i | 0.364188 | − | 0.210264i | ||||
\(768\) | −11.3235 | − | 6.53761i | −0.408601 | − | 0.235906i | ||||
\(769\) | 4.44851 | 0.160417 | 0.0802086 | − | 0.996778i | \(-0.474441\pi\) | ||||
0.0802086 | + | 0.996778i | \(0.474441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.35026 | −0.264713 | ||||||||
\(772\) | −26.0459 | − | 15.0376i | −0.937413 | − | 0.541215i | ||||
\(773\) | −34.0360 | + | 19.6507i | −1.22419 | + | 0.706786i | −0.965808 | − | 0.259257i | \(-0.916522\pi\) |
−0.258381 | + | 0.966043i | \(0.583189\pi\) | |||||||
\(774\) | −1.22425 | − | 2.12047i | −0.0440049 | − | 0.0762187i | ||||
\(775\) | 18.2591 | + | 13.7753i | 0.655888 | + | 0.494823i | ||||
\(776\) | −14.2158 | −0.510318 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 5.68735i | − | 0.203901i | ||||||
\(779\) | 10.0000 | − | 17.3205i | 0.358287 | − | 0.620572i | ||||
\(780\) | 1.88160 | − | 5.61829i | 0.0673722 | − | 0.201167i | ||||
\(781\) | −2.00000 | − | 3.46410i | −0.0715656 | − | 0.123955i | ||||
\(782\) | 2.79229 | + | 1.61213i | 0.0998519 | + | 0.0576495i | ||||
\(783\) | 7.92478i | 0.283208i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.43866 | − | 3.92478i | 0.158423 | − | 0.140081i | ||||
\(786\) | 2.00000 | − | 3.46410i | 0.0713376 | − | 0.123560i | ||||
\(787\) | 0.776838 | − | 0.448507i | 0.0276913 | − | 0.0159876i | −0.486090 | − | 0.873909i | \(-0.661577\pi\) |
0.513782 | + | 0.857921i | \(0.328244\pi\) | |||||||
\(788\) | 0.976377 | − | 0.563711i | 0.0347820 | − | 0.0200814i | ||||
\(789\) | −6.48119 | + | 11.2258i | −0.230737 | + | 0.399648i | ||||
\(790\) | −3.47627 | + | 3.07381i | −0.123680 | + | 0.109361i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.53690i | 0.0546115i | ||||||||
\(793\) | 10.1741 | + | 5.87399i | 0.361291 | + | 0.208592i | ||||
\(794\) | −1.77926 | − | 3.08176i | −0.0631434 | − | 0.109368i | ||||
\(795\) | −6.08884 | + | 18.1807i | −0.215949 | + | 0.644803i | ||||
\(796\) | 0.197447 | − | 0.341987i | 0.00699831 | − | 0.0121214i | ||||
\(797\) | 3.19982i | 0.113343i | 0.998393 | + | 0.0566717i | \(0.0180488\pi\) | ||||
−0.998393 | + | 0.0566717i | \(0.981951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.2506 | 1.17632 | ||||||||
\(800\) | −6.83315 | + | 9.05733i | −0.241588 | + | 0.320225i | ||||
\(801\) | 0.518806 | + | 0.898598i | 0.0183311 | + | 0.0317504i | ||||
\(802\) | 6.26902 | − | 3.61942i | 0.221367 | − | 0.127806i | ||||
\(803\) | −16.1951 | − | 9.35026i | −0.571514 | − | 0.329964i | ||||
\(804\) | 19.4763 | 0.686875 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.19791 | 0.0421944 | ||||||||
\(807\) | −3.56059 | − | 2.05571i | −0.125339 | − | 0.0723644i | ||||
\(808\) | −11.7547 | + | 6.78655i | −0.413527 | + | 0.238750i | ||||
\(809\) | 2.22425 | + | 3.85252i | 0.0782006 | + | 0.135447i | 0.902474 | − | 0.430745i | \(-0.141749\pi\) |
−0.824273 | + | 0.566193i | \(0.808416\pi\) | |||||||
\(810\) | 0.0863379 | + | 0.424974i | 0.00303361 | + | 0.0149321i | ||||
\(811\) | −37.6747 | −1.32294 | −0.661468 | − | 0.749973i | \(-0.730066\pi\) | ||||
−0.661468 | + | 0.749973i | \(0.730066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.4241i | 0.576017i | ||||||||
\(814\) | −0.150446 | + | 0.260579i | −0.00527311 | + | 0.00913330i | ||||
\(815\) | 11.2366 | + | 3.76320i | 0.393600 | + | 0.131819i | ||||
\(816\) | −6.32487 | − | 10.9550i | −0.221415 | − | 0.383502i | ||||
\(817\) | 58.4989 | + | 33.7743i | 2.04662 | + | 1.18161i | ||||
\(818\) | 4.33900i | 0.151710i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.8656 | − | 12.2882i | −0.379442 | − | 0.429123i | ||||
\(821\) | 0.374699 | − | 0.648998i | 0.0130771 | − | 0.0226502i | −0.859413 | − | 0.511282i | \(-0.829171\pi\) |
0.872490 | + | 0.488632i | \(0.162504\pi\) | |||||||
\(822\) | −3.77885 | + | 2.18172i | −0.131802 | + | 0.0760961i | ||||
\(823\) | −22.8628 | + | 13.1998i | −0.796945 | + | 0.460117i | −0.842402 | − | 0.538850i | \(-0.818859\pi\) |
0.0454565 | + | 0.998966i | \(0.485526\pi\) | |||||||
\(824\) | 2.57452 | − | 4.45919i | 0.0896875 | − | 0.155343i | ||||
\(825\) | −9.92478 | − | 1.22425i | −0.345536 | − | 0.0426230i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.43724i | − | 0.189071i | −0.995521 | − | 0.0945357i | \(-0.969863\pi\) | ||
0.995521 | − | 0.0945357i | \(-0.0301367\pi\) | |||||||
\(828\) | 8.43347 | + | 4.86907i | 0.293083 | + | 0.169212i | ||||
\(829\) | −11.3879 | − | 19.7244i | −0.395517 | − | 0.685056i | 0.597650 | − | 0.801757i | \(-0.296101\pi\) |
−0.993167 | + | 0.116701i | \(0.962768\pi\) | |||||||
\(830\) | −0.444031 | + | 1.32584i | −0.0154126 | + | 0.0460204i | ||||
\(831\) | 5.53690 | − | 9.59020i | 0.192073 | − | 0.332680i | ||||
\(832\) | − | 9.60228i | − | 0.332899i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.635150 | −0.0219934 | ||||||||
\(835\) | 6.47750 | + | 31.8836i | 0.224163 | + | 1.10338i | ||||
\(836\) | −10.4993 | − | 18.1853i | −0.363126 | − | 0.628952i | ||||
\(837\) | 3.96165 | − | 2.28726i | 0.136935 | − | 0.0790592i | ||||
\(838\) | 3.94293 | + | 2.27645i | 0.136206 | + | 0.0786388i | ||||
\(839\) | 15.8496 | 0.547187 | 0.273594 | − | 0.961845i | \(-0.411788\pi\) | ||||
0.273594 | + | 0.961845i | \(0.411788\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8021 | 1.16559 | ||||||||
\(842\) | −4.23651 | − | 2.44595i | −0.146000 | − | 0.0842931i | ||||
\(843\) | 12.4476 | − | 7.18664i | 0.428719 | − | 0.247521i | ||||
\(844\) | −6.32724 | − | 10.9591i | −0.217793 | − | 0.377228i | ||||
\(845\) | −24.4917 | + | 4.97576i | −0.842542 | + | 0.171171i | ||||
\(846\) | −1.92478 | −0.0661752 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 32.3752i | 1.11177i | ||||||||
\(849\) | −0.574515 | + | 0.995090i | −0.0197173 | + | 0.0341514i | ||||
\(850\) | −2.99115 | + | 1.26769i | −0.102595 | + | 0.0434814i | ||||
\(851\) | 1.92478 | + | 3.33381i | 0.0659805 | + | 0.114282i | ||||
\(852\) | −3.39896 | − | 1.96239i | −0.116446 | − | 0.0672303i | ||||
\(853\) | 21.0494i | 0.720717i | 0.932814 | + | 0.360358i | \(0.117346\pi\) | ||||
−0.932814 | + | 0.360358i | \(0.882654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.92478 | − | 8.96239i | −0.271022 | − | 0.306507i | ||||
\(856\) | 5.27855 | − | 9.14271i | 0.180417 | − | 0.312492i | ||||
\(857\) | 43.4332 | − | 25.0762i | 1.48365 | − | 0.856586i | 0.483823 | − | 0.875166i | \(-0.339248\pi\) |
0.999827 | + | 0.0185800i | \(0.00591453\pi\) | |||||||
\(858\) | −0.453564 | + | 0.261865i | −0.0154844 | + | 0.00893993i | ||||
\(859\) | 2.67513 | − | 4.63346i | 0.0912743 | − | 0.158092i | −0.816773 | − | 0.576959i | \(-0.804239\pi\) |
0.908048 | + | 0.418867i | \(0.137573\pi\) | |||||||
\(860\) | 41.5026 | − | 36.6977i | 1.41523 | − | 1.25138i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.76257i | 0.128154i | ||||||||
\(863\) | 29.1758 | + | 16.8446i | 0.993154 | + | 0.573398i | 0.906216 | − | 0.422816i | \(-0.138958\pi\) |
0.0869386 | + | 0.996214i | \(0.472292\pi\) | |||||||
\(864\) | 1.13458 | + | 1.96515i | 0.0385992 | + | 0.0668557i | ||||
\(865\) | 9.53993 | + | 3.19499i | 0.324367 | + | 0.108633i | ||||
\(866\) | 0.630225 | − | 1.09158i | 0.0214159 | − | 0.0370935i | ||||
\(867\) | 5.77575i | 0.196155i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.4010 | −0.725981 | ||||||||
\(870\) | 3.36782 | − | 0.684209i | 0.114180 | − | 0.0231969i | ||||
\(871\) | 6.70052 | + | 11.6056i | 0.227039 | + | 0.393242i | ||||
\(872\) | −1.84726 | + | 1.06651i | −0.0625560 | + | 0.0361167i | ||||
\(873\) | −16.0209 | − | 9.24965i | −0.542224 | − | 0.313053i | ||||
\(874\) | 5.14903 | 0.174169 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.3488 | −0.619950 | ||||||||
\(877\) | −18.6218 | − | 10.7513i | −0.628814 | − | 0.363046i | 0.151479 | − | 0.988461i | \(-0.451597\pi\) |
−0.780293 | + | 0.625415i | \(0.784930\pi\) | |||||||
\(878\) | 2.46048 | − | 1.42056i | 0.0830372 | − | 0.0479416i | ||||
\(879\) | −0.324869 | − | 0.562690i | −0.0109576 | − | 0.0189791i | ||||
\(880\) | −16.5476 | + | 3.36182i | −0.557820 | + | 0.113327i | ||||
\(881\) | −32.3634 | −1.09035 | −0.545176 | − | 0.838322i | \(-0.683537\pi\) | ||||
−0.545176 | + | 0.838322i | \(0.683537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.59895i | − | 0.0874617i | −0.999043 | − | 0.0437309i | \(-0.986076\pi\) | ||
0.999043 | − | 0.0437309i | \(-0.0139244\pi\) | |||||||
\(884\) | 4.43866 | − | 7.68798i | 0.149288 | − | 0.258575i | ||||
\(885\) | −18.2884 | − | 6.12490i | −0.614757 | − | 0.205886i | ||||
\(886\) | −1.85589 | − | 3.21450i | −0.0623500 | − | 0.107993i | ||||
\(887\) | −33.1500 | − | 19.1392i | −1.11307 | − | 0.642631i | −0.173447 | − | 0.984843i | \(-0.555490\pi\) |
−0.939623 | + | 0.342212i | \(0.888824\pi\) | |||||||
\(888\) | 0.596124i | 0.0200046i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.337088 | − | 0.298062i | 0.0112992 | − | 0.00999106i | ||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | −2.63673 | + | 1.52232i | −0.0882842 | + | 0.0509709i | ||||
\(893\) | 45.9861 | − | 26.5501i | 1.53887 | − | 0.888464i | ||||
\(894\) | −0.431364 | + | 0.747145i | −0.0144270 | + | 0.0249883i | ||||
\(895\) | −14.8119 | − | 16.7513i | −0.495109 | − | 0.559934i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.70052i | 0.223724i | ||||||||
\(898\) | 5.50924 | + | 3.18076i | 0.183846 | + | 0.106143i | ||||
\(899\) | −18.1260 | − | 31.3952i | −0.604536 | − | 1.04709i | ||||
\(900\) | −9.03409 | + | 3.82877i | −0.301136 | + | 0.127626i | ||||
\(901\) | −14.3634 | + | 24.8782i | −0.478515 | + | 0.828813i | ||||
\(902\) | 1.44992i | 0.0482771i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.26045 | 0.307998 | ||||||||
\(905\) | 23.2833 | − | 4.73024i | 0.773962 | − | 0.157238i | ||||
\(906\) | −0.126008 | − | 0.218252i | −0.00418634 | − | 0.00725095i | ||||
\(907\) | 43.2988 | − | 24.9986i | 1.43771 | − | 0.830064i | 0.440023 | − | 0.897986i | \(-0.354970\pi\) |
0.997691 | + | 0.0679221i | \(0.0216369\pi\) | |||||||
\(908\) | 22.3465 | + | 12.9018i | 0.741594 | + | 0.428160i | ||||
\(909\) | −17.6629 | −0.585842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9525 | −0.826715 | −0.413357 | − | 0.910569i | \(-0.635644\pi\) | ||||
−0.413357 | + | 0.910569i | \(0.635644\pi\) | |||||||
\(912\) | −17.4948 | − | 10.1006i | −0.579310 | − | 0.334465i | ||||
\(913\) | −5.58457 | + | 3.22425i | −0.184822 | + | 0.106707i | ||||
\(914\) | −1.81336 | − | 3.14083i | −0.0599805 | − | 0.103889i | ||||
\(915\) | −3.87336 | − | 19.0655i | −0.128049 | − | 0.630285i | ||||
\(916\) | 5.44709 | 0.179977 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.649738i | 0.0214446i | ||||||||
\(919\) | −5.84955 | + | 10.1317i | −0.192959 | + | 0.334215i | −0.946230 | − | 0.323496i | \(-0.895142\pi\) |
0.753271 | + | 0.657711i | \(0.228475\pi\) | |||||||
\(920\) | 2.70790 | − | 8.08553i | 0.0892768 | − | 0.266572i | ||||
\(921\) | 12.0508 | + | 20.8726i | 0.397087 | + | 0.687775i | ||||
\(922\) | 1.16936 | + | 0.675131i | 0.0385109 | + | 0.0222343i | ||||
\(923\) | − | 2.70052i | − | 0.0888888i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.84955 | − | 0.474855i | −0.126573 | − | 0.0156131i | ||||
\(926\) | −0.513881 | + | 0.890068i | −0.0168872 | + | 0.0292495i | ||||
\(927\) | 5.80282 | − | 3.35026i | 0.190590 | − | 0.110037i | ||||
\(928\) | 15.5734 | − | 8.99129i | 0.511221 | − | 0.295154i | ||||
\(929\) | −11.8545 | + | 20.5326i | −0.388933 | + | 0.673651i | −0.992306 | − | 0.123807i | \(-0.960490\pi\) |
0.603373 | + | 0.797459i | \(0.293823\pi\) | |||||||
\(930\) | −1.31406 | − | 1.48612i | −0.0430899 | − | 0.0487318i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 0.0996603i | − | 0.00326448i | ||||||
\(933\) | 7.14646 | + | 4.12601i | 0.233964 | + | 0.135079i | ||||
\(934\) | 1.27504 | + | 2.20843i | 0.0417205 | + | 0.0722621i | ||||
\(935\) | −14.2072 | − | 4.75810i | −0.464626 | − | 0.155607i | ||||
\(936\) | −0.518806 | + | 0.898598i | −0.0169577 | + | 0.0293716i | ||||
\(937\) | − | 19.9003i | − | 0.650116i | −0.945694 | − | 0.325058i | \(-0.894616\pi\) | ||
0.945694 | − | 0.325058i | \(-0.105384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.9018 | −0.486300 | ||||||||
\(940\) | −8.67057 | − | 42.6784i | −0.282803 | − | 1.39202i | ||||
\(941\) | −3.14411 | − | 5.44575i | −0.102495 | − | 0.177526i | 0.810217 | − | 0.586130i | \(-0.199349\pi\) |
−0.912712 | + | 0.408604i | \(0.866016\pi\) | |||||||
\(942\) | −0.445034 | + | 0.256941i | −0.0145000 | + | 0.00837158i | ||||
\(943\) | 16.0648 | + | 9.27504i | 0.523143 | + | 0.302037i | ||||
\(944\) | −32.5669 | −1.05996 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.89701 | −0.159216 | ||||||||
\(947\) | −34.6724 | − | 20.0181i | −1.12670 | − | 0.650501i | −0.183597 | − | 0.983002i | \(-0.558774\pi\) |
−0.943103 | + | 0.332501i | \(0.892108\pi\) | |||||||
\(948\) | −18.1853 | + | 10.4993i | −0.590631 | + | 0.341001i | ||||
\(949\) | −6.31265 | − | 10.9338i | −0.204917 | − | 0.354927i | ||||
\(950\) | −3.12457 | + | 4.14162i | −0.101374 | + | 0.134372i | ||||
\(951\) | 10.1260 | 0.328358 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.9478i | 1.32643i | 0.748429 | + | 0.663215i | \(0.230808\pi\) | ||||
−0.748429 | + | 0.663215i | \(0.769192\pi\) | |||||||
\(954\) | 0.831456 | − | 1.44012i | 0.0269194 | − | 0.0466257i | ||||
\(955\) | −9.83469 | + | 29.3655i | −0.318243 | + | 0.950244i | ||||
\(956\) | 5.73955 | + | 9.94119i | 0.185630 | + | 0.321521i | ||||
\(957\) | 13.7261 | + | 7.92478i | 0.443702 | + | 0.256172i | ||||
\(958\) | − | 0.998585i | − | 0.0322628i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −11.9126 | + | 10.5334i | −0.384476 | + | 0.339964i | ||||
\(961\) | 5.03690 | − | 8.72417i | 0.162481 | − | 0.281425i | ||||
\(962\) | −0.175925 | + | 0.101570i | −0.00567206 | + | 0.00327476i | ||||
\(963\) | 11.8976 | − | 6.86907i | 0.383394 | − | 0.221353i | ||||
\(964\) | −0.0738082 | + | 0.127839i | −0.00237720 | + | 0.00411743i | ||||
\(965\) | −25.6728 | + | 22.7005i | −0.826435 | + | 0.730756i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.2784i | − | 1.23095i | −0.788157 | − | 0.615475i | \(-0.788964\pi\) | ||
0.788157 | − | 0.615475i | \(-0.211036\pi\) | |||||||
\(968\) | −4.65849 | − | 2.68958i | −0.149730 | − | 0.0864464i | ||||
\(969\) | −8.96239 | − | 15.5233i | −0.287913 | − | 0.498681i | ||||
\(970\) | −2.54765 | + | 7.60704i | −0.0818001 | + | 0.244247i | ||||
\(971\) | −14.3634 | + | 24.8782i | −0.460945 | + | 0.798379i | −0.999008 | − | 0.0445247i | \(-0.985823\pi\) |
0.538064 | + | 0.842904i | \(0.319156\pi\) | |||||||
\(972\) | 1.96239i | 0.0629436i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.30089 | 0.137809 | ||||||||
\(975\) | −5.38956 | − | 4.06606i | −0.172604 | − | 0.130218i | ||||
\(976\) | −16.4255 | − | 28.4498i | −0.525767 | − | 0.910655i | ||||
\(977\) | 35.7681 | − | 20.6507i | 1.14432 | − | 0.660674i | 0.196824 | − | 0.980439i | \(-0.436937\pi\) |
0.947497 | + | 0.319765i | \(0.103604\pi\) | |||||||
\(978\) | −0.890068 | − | 0.513881i | −0.0284612 | − | 0.0164321i | ||||
\(979\) | 2.07522 | 0.0663244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.77575 | −0.0886228 | ||||||||
\(982\) | 0.335908 | + | 0.193937i | 0.0107193 | + | 0.00618876i | ||||
\(983\) | 20.7846 | − | 12.0000i | 0.662926 | − | 0.382741i | −0.130465 | − | 0.991453i | \(-0.541647\pi\) |
0.793391 | + | 0.608712i | \(0.208314\pi\) | |||||||
\(984\) | 1.43629 | + | 2.48772i | 0.0457872 | + | 0.0793058i | ||||
\(985\) | −0.255767 | − | 1.25894i | −0.00814940 | − | 0.0401131i | ||||
\(986\) | 5.14903 | 0.163979 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 14.1768i | − | 0.451024i | ||||||
\(989\) | −31.3258 | + | 54.2579i | −0.996103 | + | 1.72530i | ||||
\(990\) | 0.822414 | + | 0.275432i | 0.0261380 | + | 0.00875381i | ||||
\(991\) | −12.5501 | − | 21.7374i | −0.398666 | − | 0.690510i | 0.594895 | − | 0.803803i | \(-0.297194\pi\) |
−0.993562 | + | 0.113293i | \(0.963860\pi\) | |||||||
\(992\) | −8.98961 | − | 5.19015i | −0.285420 | − | 0.164787i | ||||
\(993\) | 27.8496i | 0.883779i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.298062 | − | 0.337088i | −0.00944920 | − | 0.0106864i | ||||
\(996\) | −3.16362 | + | 5.47955i | −0.100243 | + | 0.173626i | ||||
\(997\) | 28.4033 | − | 16.3987i | 0.899543 | − | 0.519351i | 0.0224910 | − | 0.999747i | \(-0.492840\pi\) |
0.877052 | + | 0.480396i | \(0.159507\pi\) | |||||||
\(998\) | −1.10011 | + | 0.635150i | −0.0348234 | + | 0.0201053i | ||||
\(999\) | −0.387873 | + | 0.671816i | −0.0122718 | + | 0.0212553i |
(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 | 735.2.q.f.79.4 | 12 | ||
5.4 | even | 2 | inner | 735.2.q.f.79.3 | 12 | ||
7.2 | even | 3 | 735.2.d.b.589.3 | 6 | |||
7.3 | odd | 6 | 735.2.q.e.214.3 | 12 | |||
7.4 | even | 3 | inner | 735.2.q.f.214.3 | 12 | ||
7.5 | odd | 6 | 105.2.d.b.64.3 | ✓ | 6 | ||
7.6 | odd | 2 | 735.2.q.e.79.4 | 12 | |||
21.2 | odd | 6 | 2205.2.d.l.1324.4 | 6 | |||
21.5 | even | 6 | 315.2.d.e.64.4 | 6 | |||
28.19 | even | 6 | 1680.2.t.k.1009.4 | 6 | |||
35.2 | odd | 12 | 3675.2.a.bj.1.2 | 3 | |||
35.4 | even | 6 | inner | 735.2.q.f.214.4 | 12 | ||
35.9 | even | 6 | 735.2.d.b.589.4 | 6 | |||
35.12 | even | 12 | 525.2.a.k.1.2 | 3 | |||
35.19 | odd | 6 | 105.2.d.b.64.4 | yes | 6 | ||
35.23 | odd | 12 | 3675.2.a.bi.1.2 | 3 | |||
35.24 | odd | 6 | 735.2.q.e.214.4 | 12 | |||
35.33 | even | 12 | 525.2.a.j.1.2 | 3 | |||
35.34 | odd | 2 | 735.2.q.e.79.3 | 12 | |||
84.47 | odd | 6 | 5040.2.t.v.1009.6 | 6 | |||
105.44 | odd | 6 | 2205.2.d.l.1324.3 | 6 | |||
105.47 | odd | 12 | 1575.2.a.w.1.2 | 3 | |||
105.68 | odd | 12 | 1575.2.a.x.1.2 | 3 | |||
105.89 | even | 6 | 315.2.d.e.64.3 | 6 | |||
140.19 | even | 6 | 1680.2.t.k.1009.1 | 6 | |||
140.47 | odd | 12 | 8400.2.a.dj.1.3 | 3 | |||
140.103 | odd | 12 | 8400.2.a.dg.1.1 | 3 | |||
420.299 | odd | 6 | 5040.2.t.v.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.3 | ✓ | 6 | 7.5 | odd | 6 | ||
105.2.d.b.64.4 | yes | 6 | 35.19 | odd | 6 | ||
315.2.d.e.64.3 | 6 | 105.89 | even | 6 | |||
315.2.d.e.64.4 | 6 | 21.5 | even | 6 | |||
525.2.a.j.1.2 | 3 | 35.33 | even | 12 | |||
525.2.a.k.1.2 | 3 | 35.12 | even | 12 | |||
735.2.d.b.589.3 | 6 | 7.2 | even | 3 | |||
735.2.d.b.589.4 | 6 | 35.9 | even | 6 | |||
735.2.q.e.79.3 | 12 | 35.34 | odd | 2 | |||
735.2.q.e.79.4 | 12 | 7.6 | odd | 2 | |||
735.2.q.e.214.3 | 12 | 7.3 | odd | 6 | |||
735.2.q.e.214.4 | 12 | 35.24 | odd | 6 | |||
735.2.q.f.79.3 | 12 | 5.4 | even | 2 | inner | ||
735.2.q.f.79.4 | 12 | 1.1 | even | 1 | trivial | ||
735.2.q.f.214.3 | 12 | 7.4 | even | 3 | inner | ||
735.2.q.f.214.4 | 12 | 35.4 | even | 6 | inner | ||
1575.2.a.w.1.2 | 3 | 105.47 | odd | 12 | |||
1575.2.a.x.1.2 | 3 | 105.68 | odd | 12 | |||
1680.2.t.k.1009.1 | 6 | 140.19 | even | 6 | |||
1680.2.t.k.1009.4 | 6 | 28.19 | even | 6 | |||
2205.2.d.l.1324.3 | 6 | 105.44 | odd | 6 | |||
2205.2.d.l.1324.4 | 6 | 21.2 | odd | 6 | |||
3675.2.a.bi.1.2 | 3 | 35.23 | odd | 12 | |||
3675.2.a.bj.1.2 | 3 | 35.2 | odd | 12 | |||
5040.2.t.v.1009.5 | 6 | 420.299 | odd | 6 | |||
5040.2.t.v.1009.6 | 6 | 84.47 | odd | 6 | |||
8400.2.a.dg.1.1 | 3 | 140.103 | odd | 12 | |||
8400.2.a.dj.1.3 | 3 | 140.47 | odd | 12 |