Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(371,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.371");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.h (of order \(2\), degree \(1\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} + 10x^{12} - 42x^{10} + 82x^{8} - 378x^{6} + 810x^{4} - 1458x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 371.10 | ||
Root | \(-1.06195 - 1.36831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.371 |
Dual form | 930.2.h.c.371.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.36831 | + | 1.06195i | −0.789994 | + | 0.613115i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −1.06195 | − | 1.36831i | −0.433538 | − | 0.558610i | ||||
\(7\) | 1.28192 | 0.484520 | 0.242260 | − | 0.970211i | \(-0.422111\pi\) | ||||
0.242260 | + | 0.970211i | \(0.422111\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.744540 | − | 2.90614i | 0.248180 | − | 0.968714i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −0.392733 | −0.118413 | −0.0592067 | − | 0.998246i | \(-0.518857\pi\) | ||||
−0.0592067 | + | 0.998246i | \(0.518857\pi\) | |||||||
\(12\) | 1.36831 | − | 1.06195i | 0.394997 | − | 0.306557i | ||||
\(13\) | 4.84655i | 1.34419i | 0.740464 | + | 0.672096i | \(0.234606\pi\) | ||||
−0.740464 | + | 0.672096i | \(0.765394\pi\) | |||||||
\(14\) | 1.28192i | 0.342608i | ||||||||
\(15\) | −1.06195 | − | 1.36831i | −0.274193 | − | 0.353296i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.52820 | −1.58332 | −0.791661 | − | 0.610961i | \(-0.790783\pi\) | ||||
−0.791661 | + | 0.610961i | \(0.790783\pi\) | |||||||
\(18\) | 2.90614 | + | 0.744540i | 0.684984 | + | 0.175490i | ||||
\(19\) | −4.77100 | −1.09454 | −0.547271 | − | 0.836955i | \(-0.684333\pi\) | ||||
−0.547271 | + | 0.836955i | \(0.684333\pi\) | |||||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | −1.75406 | + | 1.36133i | −0.382768 | + | 0.297067i | ||||
\(22\) | − | 0.392733i | − | 0.0837309i | ||||||
\(23\) | −2.51663 | −0.524753 | −0.262376 | − | 0.964966i | \(-0.584506\pi\) | ||||
−0.262376 | + | 0.964966i | \(0.584506\pi\) | |||||||
\(24\) | 1.06195 | + | 1.36831i | 0.216769 | + | 0.279305i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −4.84655 | −0.950487 | ||||||||
\(27\) | 2.06741 | + | 4.76716i | 0.397872 | + | 0.917441i | ||||
\(28\) | −1.28192 | −0.242260 | ||||||||
\(29\) | −4.57705 | −0.849937 | −0.424969 | − | 0.905208i | \(-0.639715\pi\) | ||||
−0.424969 | + | 0.905208i | \(0.639715\pi\) | |||||||
\(30\) | 1.36831 | − | 1.06195i | 0.249818 | − | 0.193884i | ||||
\(31\) | 4.60512 | − | 3.12935i | 0.827105 | − | 0.562048i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.537380 | − | 0.417061i | 0.0935459 | − | 0.0726010i | ||||
\(34\) | − | 6.52820i | − | 1.11958i | ||||||
\(35\) | 1.28192i | 0.216684i | ||||||||
\(36\) | −0.744540 | + | 2.90614i | −0.124090 | + | 0.484357i | ||||
\(37\) | − | 2.12389i | − | 0.349166i | −0.984642 | − | 0.174583i | \(-0.944142\pi\) | ||
0.984642 | − | 0.174583i | \(-0.0558577\pi\) | |||||||
\(38\) | − | 4.77100i | − | 0.773959i | ||||||
\(39\) | −5.14678 | − | 6.63158i | −0.824144 | − | 1.06190i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − | 5.07476i | − | 0.792544i | −0.918133 | − | 0.396272i | \(-0.870304\pi\) | ||
0.918133 | − | 0.396272i | \(-0.129696\pi\) | |||||||
\(42\) | −1.36133 | − | 1.75406i | −0.210058 | − | 0.270658i | ||||
\(43\) | − | 3.28588i | − | 0.501092i | −0.968105 | − | 0.250546i | \(-0.919390\pi\) | ||
0.968105 | − | 0.250546i | \(-0.0806101\pi\) | |||||||
\(44\) | 0.392733 | 0.0592067 | ||||||||
\(45\) | 2.90614 | + | 0.744540i | 0.433222 | + | 0.110990i | ||||
\(46\) | − | 2.51663i | − | 0.371056i | ||||||
\(47\) | 0.834122i | 0.121669i | 0.998148 | + | 0.0608346i | \(0.0193762\pi\) | ||||
−0.998148 | + | 0.0608346i | \(0.980624\pi\) | |||||||
\(48\) | −1.36831 | + | 1.06195i | −0.197498 | + | 0.153279i | ||||
\(49\) | −5.35668 | −0.765240 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 8.93260 | − | 6.93260i | 1.25081 | − | 0.970758i | ||||
\(52\) | − | 4.84655i | − | 0.672096i | ||||||
\(53\) | −0.123231 | −0.0169271 | −0.00846355 | − | 0.999964i | \(-0.502694\pi\) | ||||
−0.00846355 | + | 0.999964i | \(0.502694\pi\) | |||||||
\(54\) | −4.76716 | + | 2.06741i | −0.648729 | + | 0.281338i | ||||
\(55\) | − | 0.392733i | − | 0.0529561i | ||||||
\(56\) | − | 1.28192i | − | 0.171304i | ||||||
\(57\) | 6.52820 | − | 5.06655i | 0.864682 | − | 0.671080i | ||||
\(58\) | − | 4.57705i | − | 0.600996i | ||||||
\(59\) | 5.86520i | 0.763585i | 0.924248 | + | 0.381792i | \(0.124693\pi\) | ||||
−0.924248 | + | 0.381792i | \(0.875307\pi\) | |||||||
\(60\) | 1.06195 | + | 1.36831i | 0.137097 | + | 0.176648i | ||||
\(61\) | − | 9.87755i | − | 1.26469i | −0.774687 | − | 0.632345i | \(-0.782092\pi\) | ||
0.774687 | − | 0.632345i | \(-0.217908\pi\) | |||||||
\(62\) | 3.12935 | + | 4.60512i | 0.397428 | + | 0.584851i | ||||
\(63\) | 0.954441 | − | 3.72544i | 0.120248 | − | 0.469362i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.84655 | −0.601141 | ||||||||
\(66\) | 0.417061 | + | 0.537380i | 0.0513367 | + | 0.0661469i | ||||
\(67\) | 10.9782 | 1.34120 | 0.670598 | − | 0.741821i | \(-0.266038\pi\) | ||||
0.670598 | + | 0.741821i | \(0.266038\pi\) | |||||||
\(68\) | 6.52820 | 0.791661 | ||||||||
\(69\) | 3.44352 | − | 2.67252i | 0.414551 | − | 0.321734i | ||||
\(70\) | −1.28192 | −0.153219 | ||||||||
\(71\) | − | 9.33484i | − | 1.10784i | −0.832569 | − | 0.553921i | \(-0.813131\pi\) | ||
0.832569 | − | 0.553921i | \(-0.186869\pi\) | |||||||
\(72\) | −2.90614 | − | 0.744540i | −0.342492 | − | 0.0877449i | ||||
\(73\) | 9.18740i | 1.07530i | 0.843167 | + | 0.537652i | \(0.180689\pi\) | ||||
−0.843167 | + | 0.537652i | \(0.819311\pi\) | |||||||
\(74\) | 2.12389 | 0.246897 | ||||||||
\(75\) | 1.36831 | − | 1.06195i | 0.157999 | − | 0.122623i | ||||
\(76\) | 4.77100 | 0.547271 | ||||||||
\(77\) | −0.503452 | −0.0573737 | ||||||||
\(78\) | 6.63158 | − | 5.14678i | 0.750879 | − | 0.582758i | ||||
\(79\) | 6.12151i | 0.688724i | 0.938837 | + | 0.344362i | \(0.111905\pi\) | ||||
−0.938837 | + | 0.344362i | \(0.888095\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | −7.89132 | − | 4.32748i | −0.876813 | − | 0.480831i | ||||
\(82\) | 5.07476 | 0.560413 | ||||||||
\(83\) | −2.73662 | −0.300383 | −0.150191 | − | 0.988657i | \(-0.547989\pi\) | ||||
−0.150191 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(84\) | 1.75406 | − | 1.36133i | 0.191384 | − | 0.148533i | ||||
\(85\) | − | 6.52820i | − | 0.708083i | ||||||
\(86\) | 3.28588 | 0.354325 | ||||||||
\(87\) | 6.26282 | − | 4.86058i | 0.671445 | − | 0.521109i | ||||
\(88\) | 0.392733i | 0.0418655i | ||||||||
\(89\) | −11.0557 | −1.17191 | −0.585953 | − | 0.810345i | \(-0.699280\pi\) | ||||
−0.585953 | + | 0.810345i | \(0.699280\pi\) | |||||||
\(90\) | −0.744540 | + | 2.90614i | −0.0784814 | + | 0.306334i | ||||
\(91\) | 6.21290i | 0.651288i | ||||||||
\(92\) | 2.51663 | 0.262376 | ||||||||
\(93\) | −2.97803 | + | 9.17231i | −0.308807 | + | 0.951125i | ||||
\(94\) | −0.834122 | −0.0860332 | ||||||||
\(95\) | − | 4.77100i | − | 0.489494i | ||||||
\(96\) | −1.06195 | − | 1.36831i | −0.108384 | − | 0.139652i | ||||
\(97\) | −17.9181 | −1.81931 | −0.909655 | − | 0.415365i | \(-0.863654\pi\) | ||||
−0.909655 | + | 0.415365i | \(0.863654\pi\) | |||||||
\(98\) | − | 5.35668i | − | 0.541106i | ||||||
\(99\) | −0.292405 | + | 1.14134i | −0.0293879 | + | 0.114709i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.01164i | 0.498677i | 0.968416 | + | 0.249338i | \(0.0802131\pi\) | ||||
−0.968416 | + | 0.249338i | \(0.919787\pi\) | |||||||
\(102\) | 6.93260 | + | 8.93260i | 0.686430 | + | 0.884459i | ||||
\(103\) | −6.96961 | −0.686736 | −0.343368 | − | 0.939201i | \(-0.611568\pi\) | ||||
−0.343368 | + | 0.939201i | \(0.611568\pi\) | |||||||
\(104\) | 4.84655 | 0.475244 | ||||||||
\(105\) | −1.36133 | − | 1.75406i | −0.132852 | − | 0.171179i | ||||
\(106\) | − | 0.123231i | − | 0.0119693i | ||||||
\(107\) | 13.7406i | 1.32835i | 0.747575 | + | 0.664177i | \(0.231218\pi\) | ||||
−0.747575 | + | 0.664177i | \(0.768782\pi\) | |||||||
\(108\) | −2.06741 | − | 4.76716i | −0.198936 | − | 0.458720i | ||||
\(109\) | −8.88704 | −0.851224 | −0.425612 | − | 0.904906i | \(-0.639941\pi\) | ||||
−0.425612 | + | 0.904906i | \(0.639941\pi\) | |||||||
\(110\) | 0.392733 | 0.0374456 | ||||||||
\(111\) | 2.25546 | + | 2.90614i | 0.214079 | + | 0.275839i | ||||
\(112\) | 1.28192 | 0.121130 | ||||||||
\(113\) | − | 4.34265i | − | 0.408522i | −0.978916 | − | 0.204261i | \(-0.934521\pi\) | ||
0.978916 | − | 0.204261i | \(-0.0654791\pi\) | |||||||
\(114\) | 5.06655 | + | 6.52820i | 0.474526 | + | 0.611422i | ||||
\(115\) | − | 2.51663i | − | 0.234677i | ||||||
\(116\) | 4.57705 | 0.424969 | ||||||||
\(117\) | 14.0848 | + | 3.60845i | 1.30214 | + | 0.333602i | ||||
\(118\) | −5.86520 | −0.539936 | ||||||||
\(119\) | −8.36864 | −0.767152 | ||||||||
\(120\) | −1.36831 | + | 1.06195i | −0.124909 | + | 0.0969420i | ||||
\(121\) | −10.8458 | −0.985978 | ||||||||
\(122\) | 9.87755 | 0.894271 | ||||||||
\(123\) | 5.38912 | + | 6.94384i | 0.485921 | + | 0.626105i | ||||
\(124\) | −4.60512 | + | 3.12935i | −0.413552 | + | 0.281024i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.72544 | + | 0.954441i | 0.331889 | + | 0.0850284i | ||||
\(127\) | − | 10.7481i | − | 0.953737i | −0.878975 | − | 0.476869i | \(-0.841772\pi\) | ||
0.878975 | − | 0.476869i | \(-0.158228\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 3.48943 | + | 4.49610i | 0.307227 | + | 0.395859i | ||||
\(130\) | − | 4.84655i | − | 0.425071i | ||||||
\(131\) | 14.9782i | 1.30865i | 0.756214 | + | 0.654324i | \(0.227047\pi\) | ||||
−0.756214 | + | 0.654324i | \(0.772953\pi\) | |||||||
\(132\) | −0.537380 | + | 0.417061i | −0.0467729 | + | 0.0363005i | ||||
\(133\) | −6.11604 | −0.530328 | ||||||||
\(134\) | 10.9782i | 0.948369i | ||||||||
\(135\) | −4.76716 | + | 2.06741i | −0.410292 | + | 0.177934i | ||||
\(136\) | 6.52820i | 0.559789i | ||||||||
\(137\) | 18.3592 | 1.56853 | 0.784265 | − | 0.620427i | \(-0.213041\pi\) | ||||
0.784265 | + | 0.620427i | \(0.213041\pi\) | |||||||
\(138\) | 2.67252 | + | 3.44352i | 0.227500 | + | 0.293132i | ||||
\(139\) | − | 5.31671i | − | 0.450957i | −0.974248 | − | 0.225479i | \(-0.927605\pi\) | ||
0.974248 | − | 0.225479i | \(-0.0723946\pi\) | |||||||
\(140\) | − | 1.28192i | − | 0.108342i | ||||||
\(141\) | −0.885793 | − | 1.14134i | −0.0745972 | − | 0.0961180i | ||||
\(142\) | 9.33484 | 0.783362 | ||||||||
\(143\) | − | 1.90340i | − | 0.159170i | ||||||
\(144\) | 0.744540 | − | 2.90614i | 0.0620450 | − | 0.242178i | ||||
\(145\) | − | 4.57705i | − | 0.380103i | ||||||
\(146\) | −9.18740 | −0.760355 | ||||||||
\(147\) | 7.32960 | − | 5.68851i | 0.604535 | − | 0.469180i | ||||
\(148\) | 2.12389i | 0.174583i | ||||||||
\(149\) | − | 5.26789i | − | 0.431562i | −0.976442 | − | 0.215781i | \(-0.930770\pi\) | ||
0.976442 | − | 0.215781i | \(-0.0692297\pi\) | |||||||
\(150\) | 1.06195 | + | 1.36831i | 0.0867075 | + | 0.111722i | ||||
\(151\) | 4.12085i | 0.335350i | 0.985842 | + | 0.167675i | \(0.0536260\pi\) | ||||
−0.985842 | + | 0.167675i | \(0.946374\pi\) | |||||||
\(152\) | 4.77100i | 0.386979i | ||||||||
\(153\) | −4.86051 | + | 18.9719i | −0.392949 | + | 1.53379i | ||||
\(154\) | − | 0.503452i | − | 0.0405693i | ||||||
\(155\) | 3.12935 | + | 4.60512i | 0.251356 | + | 0.369892i | ||||
\(156\) | 5.14678 | + | 6.63158i | 0.412072 | + | 0.530952i | ||||
\(157\) | −2.19861 | −0.175468 | −0.0877340 | − | 0.996144i | \(-0.527963\pi\) | ||||
−0.0877340 | + | 0.996144i | \(0.527963\pi\) | |||||||
\(158\) | −6.12151 | −0.487002 | ||||||||
\(159\) | 0.168618 | − | 0.130865i | 0.0133723 | − | 0.0103783i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −3.22611 | −0.254253 | ||||||||
\(162\) | 4.32748 | − | 7.89132i | 0.339999 | − | 0.620001i | ||||
\(163\) | 12.1058 | 0.948203 | 0.474101 | − | 0.880470i | \(-0.342773\pi\) | ||||
0.474101 | + | 0.880470i | \(0.342773\pi\) | |||||||
\(164\) | 5.07476i | 0.396272i | ||||||||
\(165\) | 0.417061 | + | 0.537380i | 0.0324682 | + | 0.0418350i | ||||
\(166\) | − | 2.73662i | − | 0.212403i | ||||||
\(167\) | 16.9254 | 1.30973 | 0.654864 | − | 0.755747i | \(-0.272726\pi\) | ||||
0.654864 | + | 0.755747i | \(0.272726\pi\) | |||||||
\(168\) | 1.36133 | + | 1.75406i | 0.105029 | + | 0.135329i | ||||
\(169\) | −10.4891 | −0.806852 | ||||||||
\(170\) | 6.52820 | 0.500690 | ||||||||
\(171\) | −3.55220 | + | 13.8652i | −0.271644 | + | 1.06030i | ||||
\(172\) | 3.28588i | 0.250546i | ||||||||
\(173\) | 18.7522i | 1.42571i | 0.701313 | + | 0.712854i | \(0.252598\pi\) | ||||
−0.701313 | + | 0.712854i | \(0.747402\pi\) | |||||||
\(174\) | 4.86058 | + | 6.26282i | 0.368480 | + | 0.474783i | ||||
\(175\) | −1.28192 | −0.0969041 | ||||||||
\(176\) | −0.392733 | −0.0296034 | ||||||||
\(177\) | −6.22853 | − | 8.02541i | −0.468165 | − | 0.603227i | ||||
\(178\) | − | 11.0557i | − | 0.828663i | ||||||
\(179\) | −2.59405 | −0.193888 | −0.0969442 | − | 0.995290i | \(-0.530907\pi\) | ||||
−0.0969442 | + | 0.995290i | \(0.530907\pi\) | |||||||
\(180\) | −2.90614 | − | 0.744540i | −0.216611 | − | 0.0554948i | ||||
\(181\) | 4.02779i | 0.299383i | 0.988733 | + | 0.149692i | \(0.0478281\pi\) | ||||
−0.988733 | + | 0.149692i | \(0.952172\pi\) | |||||||
\(182\) | −6.21290 | −0.460530 | ||||||||
\(183\) | 10.4894 | + | 13.5155i | 0.775401 | + | 0.999098i | ||||
\(184\) | 2.51663i | 0.185528i | ||||||||
\(185\) | 2.12389 | 0.156152 | ||||||||
\(186\) | −9.17231 | − | 2.97803i | −0.672547 | − | 0.218360i | ||||
\(187\) | 2.56384 | 0.187487 | ||||||||
\(188\) | − | 0.834122i | − | 0.0608346i | ||||||
\(189\) | 2.65025 | + | 6.11112i | 0.192777 | + | 0.444519i | ||||
\(190\) | 4.77100 | 0.346125 | ||||||||
\(191\) | − | 7.48908i | − | 0.541891i | −0.962595 | − | 0.270945i | \(-0.912664\pi\) | ||
0.962595 | − | 0.270945i | \(-0.0873363\pi\) | |||||||
\(192\) | 1.36831 | − | 1.06195i | 0.0987492 | − | 0.0766394i | ||||
\(193\) | −19.5334 | −1.40605 | −0.703024 | − | 0.711166i | \(-0.748167\pi\) | ||||
−0.703024 | + | 0.711166i | \(0.748167\pi\) | |||||||
\(194\) | − | 17.9181i | − | 1.28645i | ||||||
\(195\) | 6.63158 | − | 5.14678i | 0.474898 | − | 0.368569i | ||||
\(196\) | 5.35668 | 0.382620 | ||||||||
\(197\) | 0.598768 | 0.0426605 | 0.0213302 | − | 0.999772i | \(-0.493210\pi\) | ||||
0.0213302 | + | 0.999772i | \(0.493210\pi\) | |||||||
\(198\) | −1.14134 | − | 0.292405i | −0.0811113 | − | 0.0207804i | ||||
\(199\) | 12.0672i | 0.855419i | 0.903916 | + | 0.427709i | \(0.140679\pi\) | ||||
−0.903916 | + | 0.427709i | \(0.859321\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −15.0215 | + | 11.6582i | −1.05954 | + | 0.822307i | ||||
\(202\) | −5.01164 | −0.352618 | ||||||||
\(203\) | −5.86742 | −0.411812 | ||||||||
\(204\) | −8.93260 | + | 6.93260i | −0.625407 | + | 0.485379i | ||||
\(205\) | 5.07476 | 0.354437 | ||||||||
\(206\) | − | 6.96961i | − | 0.485596i | ||||||
\(207\) | −1.87373 | + | 7.31367i | −0.130233 | + | 0.508335i | ||||
\(208\) | 4.84655i | 0.336048i | ||||||||
\(209\) | 1.87373 | 0.129609 | ||||||||
\(210\) | 1.75406 | − | 1.36133i | 0.121042 | − | 0.0939407i | ||||
\(211\) | −15.3737 | −1.05837 | −0.529186 | − | 0.848506i | \(-0.677502\pi\) | ||||
−0.529186 | + | 0.848506i | \(0.677502\pi\) | |||||||
\(212\) | 0.123231 | 0.00846355 | ||||||||
\(213\) | 9.91310 | + | 12.7729i | 0.679234 | + | 0.875188i | ||||
\(214\) | −13.7406 | −0.939289 | ||||||||
\(215\) | 3.28588 | 0.224095 | ||||||||
\(216\) | 4.76716 | − | 2.06741i | 0.324364 | − | 0.140669i | ||||
\(217\) | 5.90340 | − | 4.01158i | 0.400749 | − | 0.272324i | ||||
\(218\) | − | 8.88704i | − | 0.601907i | ||||||
\(219\) | −9.75652 | − | 12.5712i | −0.659285 | − | 0.849483i | ||||
\(220\) | 0.392733i | 0.0264780i | ||||||||
\(221\) | − | 31.6393i | − | 2.12829i | ||||||
\(222\) | −2.90614 | + | 2.25546i | −0.195047 | + | 0.151377i | ||||
\(223\) | − | 18.0137i | − | 1.20629i | −0.797633 | − | 0.603143i | \(-0.793915\pi\) | ||
0.797633 | − | 0.603143i | \(-0.206085\pi\) | |||||||
\(224\) | 1.28192i | 0.0856519i | ||||||||
\(225\) | −0.744540 | + | 2.90614i | −0.0496360 | + | 0.193743i | ||||
\(226\) | 4.34265 | 0.288869 | ||||||||
\(227\) | 24.3045i | 1.61314i | 0.591137 | + | 0.806572i | \(0.298679\pi\) | ||||
−0.591137 | + | 0.806572i | \(0.701321\pi\) | |||||||
\(228\) | −6.52820 | + | 5.06655i | −0.432341 | + | 0.335540i | ||||
\(229\) | 16.4436i | 1.08662i | 0.839532 | + | 0.543311i | \(0.182829\pi\) | ||||
−0.839532 | + | 0.543311i | \(0.817171\pi\) | |||||||
\(230\) | 2.51663 | 0.165941 | ||||||||
\(231\) | 0.688878 | − | 0.534639i | 0.0453249 | − | 0.0351767i | ||||
\(232\) | 4.57705i | 0.300498i | ||||||||
\(233\) | 24.9298i | 1.63320i | 0.577202 | + | 0.816602i | \(0.304145\pi\) | ||||
−0.577202 | + | 0.816602i | \(0.695855\pi\) | |||||||
\(234\) | −3.60845 | + | 14.0848i | −0.235892 | + | 0.920750i | ||||
\(235\) | −0.834122 | −0.0544121 | ||||||||
\(236\) | − | 5.86520i | − | 0.381792i | ||||||
\(237\) | −6.50072 | − | 8.37612i | −0.422267 | − | 0.544088i | ||||
\(238\) | − | 8.36864i | − | 0.542458i | ||||||
\(239\) | −8.26962 | −0.534917 | −0.267459 | − | 0.963569i | \(-0.586184\pi\) | ||||
−0.267459 | + | 0.963569i | \(0.586184\pi\) | |||||||
\(240\) | −1.06195 | − | 1.36831i | −0.0685483 | − | 0.0883240i | ||||
\(241\) | 12.4895i | 0.804519i | 0.915526 | + | 0.402259i | \(0.131775\pi\) | ||||
−0.915526 | + | 0.402259i | \(0.868225\pi\) | |||||||
\(242\) | − | 10.8458i | − | 0.697192i | ||||||
\(243\) | 15.3933 | − | 2.45883i | 0.987482 | − | 0.157734i | ||||
\(244\) | 9.87755i | 0.632345i | ||||||||
\(245\) | − | 5.35668i | − | 0.342226i | ||||||
\(246\) | −6.94384 | + | 5.38912i | −0.442723 | + | 0.343598i | ||||
\(247\) | − | 23.1229i | − | 1.47128i | ||||||
\(248\) | −3.12935 | − | 4.60512i | −0.198714 | − | 0.292426i | ||||
\(249\) | 3.74454 | − | 2.90614i | 0.237301 | − | 0.184169i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 25.1708 | 1.58877 | 0.794384 | − | 0.607416i | \(-0.207794\pi\) | ||||
0.794384 | + | 0.607416i | \(0.207794\pi\) | |||||||
\(252\) | −0.954441 | + | 3.72544i | −0.0601241 | + | 0.234681i | ||||
\(253\) | 0.988362 | 0.0621378 | ||||||||
\(254\) | 10.7481 | 0.674394 | ||||||||
\(255\) | 6.93260 | + | 8.93260i | 0.434136 | + | 0.559381i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.3737i | 1.45801i | 0.684507 | + | 0.729007i | \(0.260018\pi\) | ||||
−0.684507 | + | 0.729007i | \(0.739982\pi\) | |||||||
\(258\) | −4.49610 | + | 3.48943i | −0.279915 | + | 0.217242i | ||||
\(259\) | − | 2.72266i | − | 0.169178i | ||||||
\(260\) | 4.84655 | 0.300570 | ||||||||
\(261\) | −3.40780 | + | 13.3016i | −0.210937 | + | 0.823346i | ||||
\(262\) | −14.9782 | −0.925354 | ||||||||
\(263\) | 10.4026 | 0.641451 | 0.320726 | − | 0.947172i | \(-0.396073\pi\) | ||||
0.320726 | + | 0.947172i | \(0.396073\pi\) | |||||||
\(264\) | −0.417061 | − | 0.537380i | −0.0256683 | − | 0.0330735i | ||||
\(265\) | − | 0.123231i | − | 0.00757003i | ||||||
\(266\) | − | 6.11604i | − | 0.374999i | ||||||
\(267\) | 15.1277 | − | 11.7406i | 0.925799 | − | 0.718514i | ||||
\(268\) | −10.9782 | −0.670598 | ||||||||
\(269\) | −23.5925 | −1.43846 | −0.719230 | − | 0.694772i | \(-0.755505\pi\) | ||||
−0.719230 | + | 0.694772i | \(0.755505\pi\) | |||||||
\(270\) | −2.06741 | − | 4.76716i | −0.125818 | − | 0.290120i | ||||
\(271\) | 24.7707i | 1.50471i | 0.658757 | + | 0.752356i | \(0.271083\pi\) | ||||
−0.658757 | + | 0.752356i | \(0.728917\pi\) | |||||||
\(272\) | −6.52820 | −0.395831 | ||||||||
\(273\) | −6.59776 | − | 8.50116i | −0.399315 | − | 0.514514i | ||||
\(274\) | 18.3592i | 1.10912i | ||||||||
\(275\) | 0.392733 | 0.0236827 | ||||||||
\(276\) | −3.44352 | + | 2.67252i | −0.207276 | + | 0.160867i | ||||
\(277\) | 20.0687i | 1.20581i | 0.797812 | + | 0.602906i | \(0.205991\pi\) | ||||
−0.797812 | + | 0.602906i | \(0.794009\pi\) | |||||||
\(278\) | 5.31671 | 0.318875 | ||||||||
\(279\) | −5.66564 | − | 15.7131i | −0.339193 | − | 0.940717i | ||||
\(280\) | 1.28192 | 0.0766094 | ||||||||
\(281\) | − | 10.6464i | − | 0.635111i | −0.948240 | − | 0.317556i | \(-0.897138\pi\) | ||
0.948240 | − | 0.317556i | \(-0.102862\pi\) | |||||||
\(282\) | 1.14134 | − | 0.885793i | 0.0679657 | − | 0.0527482i | ||||
\(283\) | −16.3379 | −0.971189 | −0.485594 | − | 0.874184i | \(-0.661397\pi\) | ||||
−0.485594 | + | 0.874184i | \(0.661397\pi\) | |||||||
\(284\) | 9.33484i | 0.553921i | ||||||||
\(285\) | 5.06655 | + | 6.52820i | 0.300116 | + | 0.386697i | ||||
\(286\) | 1.90340 | 0.112550 | ||||||||
\(287\) | − | 6.50544i | − | 0.384004i | ||||||
\(288\) | 2.90614 | + | 0.744540i | 0.171246 | + | 0.0438725i | ||||
\(289\) | 25.6175 | 1.50691 | ||||||||
\(290\) | 4.57705 | 0.268774 | ||||||||
\(291\) | 24.5175 | − | 19.0281i | 1.43724 | − | 1.11545i | ||||
\(292\) | − | 9.18740i | − | 0.537652i | ||||||
\(293\) | − | 23.8799i | − | 1.39508i | −0.716546 | − | 0.697540i | \(-0.754278\pi\) | ||
0.716546 | − | 0.697540i | \(-0.245722\pi\) | |||||||
\(294\) | 5.68851 | + | 7.32960i | 0.331760 | + | 0.427471i | ||||
\(295\) | −5.86520 | −0.341485 | ||||||||
\(296\) | −2.12389 | −0.123449 | ||||||||
\(297\) | −0.811938 | − | 1.87222i | −0.0471134 | − | 0.108637i | ||||
\(298\) | 5.26789 | 0.305160 | ||||||||
\(299\) | − | 12.1970i | − | 0.705368i | ||||||
\(300\) | −1.36831 | + | 1.06195i | −0.0789994 | + | 0.0613115i | ||||
\(301\) | − | 4.21223i | − | 0.242789i | ||||||
\(302\) | −4.12085 | −0.237128 | ||||||||
\(303\) | −5.32209 | − | 6.85747i | −0.305746 | − | 0.393951i | ||||
\(304\) | −4.77100 | −0.273636 | ||||||||
\(305\) | 9.87755 | 0.565587 | ||||||||
\(306\) | −18.9719 | − | 4.86051i | −1.08455 | − | 0.277857i | ||||
\(307\) | 8.71336 | 0.497298 | 0.248649 | − | 0.968594i | \(-0.420013\pi\) | ||||
0.248649 | + | 0.968594i | \(0.420013\pi\) | |||||||
\(308\) | 0.503452 | 0.0286869 | ||||||||
\(309\) | 9.53658 | − | 7.40135i | 0.542517 | − | 0.421048i | ||||
\(310\) | −4.60512 | + | 3.12935i | −0.261553 | + | 0.177735i | ||||
\(311\) | 6.24064i | 0.353874i | 0.984222 | + | 0.176937i | \(0.0566189\pi\) | ||||
−0.984222 | + | 0.176937i | \(0.943381\pi\) | |||||||
\(312\) | −6.63158 | + | 5.14678i | −0.375440 | + | 0.291379i | ||||
\(313\) | 7.88059i | 0.445437i | 0.974883 | + | 0.222719i | \(0.0714931\pi\) | ||||
−0.974883 | + | 0.222719i | \(0.928507\pi\) | |||||||
\(314\) | − | 2.19861i | − | 0.124075i | ||||||
\(315\) | 3.72544 | + | 0.954441i | 0.209905 | + | 0.0537767i | ||||
\(316\) | − | 6.12151i | − | 0.344362i | ||||||
\(317\) | 9.14329i | 0.513538i | 0.966473 | + | 0.256769i | \(0.0826580\pi\) | ||||
−0.966473 | + | 0.256769i | \(0.917342\pi\) | |||||||
\(318\) | 0.130865 | + | 0.168618i | 0.00733854 | + | 0.00945565i | ||||
\(319\) | 1.79756 | 0.100644 | ||||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | −14.5918 | − | 18.8014i | −0.814434 | − | 1.04939i | ||||
\(322\) | − | 3.22611i | − | 0.179784i | ||||||
\(323\) | 31.1461 | 1.73301 | ||||||||
\(324\) | 7.89132 | + | 4.32748i | 0.438407 | + | 0.240416i | ||||
\(325\) | − | 4.84655i | − | 0.268838i | ||||||
\(326\) | 12.1058i | 0.670481i | ||||||||
\(327\) | 12.1602 | − | 9.43756i | 0.672462 | − | 0.521898i | ||||
\(328\) | −5.07476 | −0.280207 | ||||||||
\(329\) | 1.06928i | 0.0589512i | ||||||||
\(330\) | −0.537380 | + | 0.417061i | −0.0295818 | + | 0.0229585i | ||||
\(331\) | − | 23.9175i | − | 1.31462i | −0.753619 | − | 0.657311i | \(-0.771694\pi\) | ||
0.753619 | − | 0.657311i | \(-0.228306\pi\) | |||||||
\(332\) | 2.73662 | 0.150191 | ||||||||
\(333\) | −6.17233 | − | 1.58132i | −0.338242 | − | 0.0866560i | ||||
\(334\) | 16.9254i | 0.926118i | ||||||||
\(335\) | 10.9782i | 0.599801i | ||||||||
\(336\) | −1.75406 | + | 1.36133i | −0.0956920 | + | 0.0742667i | ||||
\(337\) | − | 13.6435i | − | 0.743207i | −0.928391 | − | 0.371604i | \(-0.878808\pi\) | ||
0.928391 | − | 0.371604i | \(-0.121192\pi\) | |||||||
\(338\) | − | 10.4891i | − | 0.570531i | ||||||
\(339\) | 4.61166 | + | 5.94208i | 0.250471 | + | 0.322730i | ||||
\(340\) | 6.52820i | 0.354042i | ||||||||
\(341\) | −1.80858 | + | 1.22900i | −0.0979403 | + | 0.0665540i | ||||
\(342\) | −13.8652 | − | 3.55220i | −0.749744 | − | 0.192081i | ||||
\(343\) | −15.8403 | −0.855295 | ||||||||
\(344\) | −3.28588 | −0.177163 | ||||||||
\(345\) | 2.67252 | + | 3.44352i | 0.143884 | + | 0.185393i | ||||
\(346\) | −18.7522 | −1.00813 | ||||||||
\(347\) | −15.0787 | −0.809465 | −0.404733 | − | 0.914435i | \(-0.632635\pi\) | ||||
−0.404733 | + | 0.914435i | \(0.632635\pi\) | |||||||
\(348\) | −6.26282 | + | 4.86058i | −0.335723 | + | 0.260555i | ||||
\(349\) | 13.1714 | 0.705047 | 0.352523 | − | 0.935803i | \(-0.385324\pi\) | ||||
0.352523 | + | 0.935803i | \(0.385324\pi\) | |||||||
\(350\) | − | 1.28192i | − | 0.0685215i | ||||||
\(351\) | −23.1043 | + | 10.0198i | −1.23322 | + | 0.534817i | ||||
\(352\) | − | 0.392733i | − | 0.0209327i | ||||||
\(353\) | −1.46704 | −0.0780826 | −0.0390413 | − | 0.999238i | \(-0.512430\pi\) | ||||
−0.0390413 | + | 0.999238i | \(0.512430\pi\) | |||||||
\(354\) | 8.02541 | − | 6.22853i | 0.426546 | − | 0.331043i | ||||
\(355\) | 9.33484 | 0.495442 | ||||||||
\(356\) | 11.0557 | 0.585953 | ||||||||
\(357\) | 11.4509 | − | 8.88704i | 0.606045 | − | 0.470352i | ||||
\(358\) | − | 2.59405i | − | 0.137100i | ||||||
\(359\) | 4.42521i | 0.233554i | 0.993158 | + | 0.116777i | \(0.0372562\pi\) | ||||
−0.993158 | + | 0.116777i | \(0.962744\pi\) | |||||||
\(360\) | 0.744540 | − | 2.90614i | 0.0392407 | − | 0.153167i | ||||
\(361\) | 3.76245 | 0.198024 | ||||||||
\(362\) | −4.02779 | −0.211696 | ||||||||
\(363\) | 14.8404 | − | 11.5176i | 0.778917 | − | 0.604518i | ||||
\(364\) | − | 6.21290i | − | 0.325644i | ||||||
\(365\) | −9.18740 | −0.480890 | ||||||||
\(366\) | −13.5155 | + | 10.4894i | −0.706469 | + | 0.548291i | ||||
\(367\) | 6.28174i | 0.327904i | 0.986468 | + | 0.163952i | \(0.0524243\pi\) | ||||
−0.986468 | + | 0.163952i | \(0.947576\pi\) | |||||||
\(368\) | −2.51663 | −0.131188 | ||||||||
\(369\) | −14.7480 | − | 3.77836i | −0.767749 | − | 0.196694i | ||||
\(370\) | 2.12389i | 0.110416i | ||||||||
\(371\) | −0.157973 | −0.00820152 | ||||||||
\(372\) | 2.97803 | − | 9.17231i | 0.154404 | − | 0.475562i | ||||
\(373\) | −30.4103 | −1.57459 | −0.787293 | − | 0.616580i | \(-0.788518\pi\) | ||||
−0.787293 | + | 0.616580i | \(0.788518\pi\) | |||||||
\(374\) | 2.56384i | 0.132573i | ||||||||
\(375\) | 1.06195 | + | 1.36831i | 0.0548387 | + | 0.0706592i | ||||
\(376\) | 0.834122 | 0.0430166 | ||||||||
\(377\) | − | 22.1829i | − | 1.14248i | ||||||
\(378\) | −6.11112 | + | 2.65025i | −0.314322 | + | 0.136314i | ||||
\(379\) | 30.4929 | 1.56631 | 0.783156 | − | 0.621825i | \(-0.213608\pi\) | ||||
0.783156 | + | 0.621825i | \(0.213608\pi\) | |||||||
\(380\) | 4.77100i | 0.244747i | ||||||||
\(381\) | 11.4139 | + | 14.7067i | 0.584751 | + | 0.753447i | ||||
\(382\) | 7.48908 | 0.383175 | ||||||||
\(383\) | −34.4055 | −1.75804 | −0.879019 | − | 0.476787i | \(-0.841801\pi\) | ||||
−0.879019 | + | 0.476787i | \(0.841801\pi\) | |||||||
\(384\) | 1.06195 | + | 1.36831i | 0.0541922 | + | 0.0698262i | ||||
\(385\) | − | 0.503452i | − | 0.0256583i | ||||||
\(386\) | − | 19.5334i | − | 0.994226i | ||||||
\(387\) | −9.54923 | − | 2.44647i | −0.485415 | − | 0.124361i | ||||
\(388\) | 17.9181 | 0.909655 | ||||||||
\(389\) | −7.32763 | −0.371525 | −0.185763 | − | 0.982595i | \(-0.559476\pi\) | ||||
−0.185763 | + | 0.982595i | \(0.559476\pi\) | |||||||
\(390\) | 5.14678 | + | 6.63158i | 0.260617 | + | 0.335803i | ||||
\(391\) | 16.4290 | 0.830853 | ||||||||
\(392\) | 5.35668i | 0.270553i | ||||||||
\(393\) | −15.9060 | − | 20.4948i | −0.802352 | − | 1.03382i | ||||
\(394\) | 0.598768i | 0.0301655i | ||||||||
\(395\) | −6.12151 | −0.308007 | ||||||||
\(396\) | 0.292405 | − | 1.14134i | 0.0146939 | − | 0.0573544i | ||||
\(397\) | 26.7188 | 1.34098 | 0.670488 | − | 0.741920i | \(-0.266085\pi\) | ||||
0.670488 | + | 0.741920i | \(0.266085\pi\) | |||||||
\(398\) | −12.0672 | −0.604872 | ||||||||
\(399\) | 8.36864 | − | 6.49491i | 0.418956 | − | 0.325152i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 27.1300 | 1.35481 | 0.677403 | − | 0.735612i | \(-0.263105\pi\) | ||||
0.677403 | + | 0.735612i | \(0.263105\pi\) | |||||||
\(402\) | −11.6582 | − | 15.0215i | −0.581459 | − | 0.749205i | ||||
\(403\) | 15.1666 | + | 22.3190i | 0.755501 | + | 1.11179i | ||||
\(404\) | − | 5.01164i | − | 0.249338i | ||||||
\(405\) | 4.32748 | − | 7.89132i | 0.215034 | − | 0.392123i | ||||
\(406\) | − | 5.86742i | − | 0.291195i | ||||||
\(407\) | 0.834122i | 0.0413459i | ||||||||
\(408\) | −6.93260 | − | 8.93260i | −0.343215 | − | 0.442230i | ||||
\(409\) | − | 3.23637i | − | 0.160028i | −0.996794 | − | 0.0800141i | \(-0.974503\pi\) | ||
0.996794 | − | 0.0800141i | \(-0.0254965\pi\) | |||||||
\(410\) | 5.07476i | 0.250625i | ||||||||
\(411\) | −25.1210 | + | 19.4964i | −1.23913 | + | 0.961689i | ||||
\(412\) | 6.96961 | 0.343368 | ||||||||
\(413\) | 7.51872i | 0.369972i | ||||||||
\(414\) | −7.31367 | − | 1.87373i | −0.359447 | − | 0.0920888i | ||||
\(415\) | − | 2.73662i | − | 0.134335i | ||||||
\(416\) | −4.84655 | −0.237622 | ||||||||
\(417\) | 5.64606 | + | 7.27490i | 0.276489 | + | 0.356254i | ||||
\(418\) | 1.87373i | 0.0916471i | ||||||||
\(419\) | − | 15.8496i | − | 0.774303i | −0.922016 | − | 0.387152i | \(-0.873459\pi\) | ||
0.922016 | − | 0.387152i | \(-0.126541\pi\) | |||||||
\(420\) | 1.36133 | + | 1.75406i | 0.0664261 | + | 0.0855895i | ||||
\(421\) | 24.7086 | 1.20422 | 0.602111 | − | 0.798412i | \(-0.294326\pi\) | ||||
0.602111 | + | 0.798412i | \(0.294326\pi\) | |||||||
\(422\) | − | 15.3737i | − | 0.748381i | ||||||
\(423\) | 2.42408 | + | 0.621038i | 0.117863 | + | 0.0301959i | ||||
\(424\) | 0.123231i | 0.00598463i | ||||||||
\(425\) | 6.52820 | 0.316664 | ||||||||
\(426\) | −12.7729 | + | 9.91310i | −0.618851 | + | 0.480291i | ||||
\(427\) | − | 12.6622i | − | 0.612768i | ||||||
\(428\) | − | 13.7406i | − | 0.664177i | ||||||
\(429\) | 2.02131 | + | 2.60444i | 0.0975897 | + | 0.125744i | ||||
\(430\) | 3.28588i | 0.158459i | ||||||||
\(431\) | − | 1.24844i | − | 0.0601354i | −0.999548 | − | 0.0300677i | \(-0.990428\pi\) | ||
0.999548 | − | 0.0300677i | \(-0.00957229\pi\) | |||||||
\(432\) | 2.06741 | + | 4.76716i | 0.0994681 | + | 0.229360i | ||||
\(433\) | − | 23.2831i | − | 1.11892i | −0.828859 | − | 0.559458i | \(-0.811009\pi\) | ||
0.828859 | − | 0.559458i | \(-0.188991\pi\) | |||||||
\(434\) | 4.01158 | + | 5.90340i | 0.192562 | + | 0.283372i | ||||
\(435\) | 4.86058 | + | 6.26282i | 0.233047 | + | 0.300279i | ||||
\(436\) | 8.88704 | 0.425612 | ||||||||
\(437\) | 12.0068 | 0.574364 | ||||||||
\(438\) | 12.5712 | − | 9.75652i | 0.600675 | − | 0.466185i | ||||
\(439\) | 37.2109 | 1.77598 | 0.887991 | − | 0.459862i | \(-0.152101\pi\) | ||||
0.887991 | + | 0.459862i | \(0.152101\pi\) | |||||||
\(440\) | −0.392733 | −0.0187228 | ||||||||
\(441\) | −3.98826 | + | 15.5673i | −0.189917 | + | 0.741299i | ||||
\(442\) | 31.6393 | 1.50493 | ||||||||
\(443\) | 18.8683i | 0.896460i | 0.893918 | + | 0.448230i | \(0.147945\pi\) | ||||
−0.893918 | + | 0.448230i | \(0.852055\pi\) | |||||||
\(444\) | −2.25546 | − | 2.90614i | −0.107039 | − | 0.137919i | ||||
\(445\) | − | 11.0557i | − | 0.524093i | ||||||
\(446\) | 18.0137 | 0.852973 | ||||||||
\(447\) | 5.59421 | + | 7.20810i | 0.264597 | + | 0.340931i | ||||
\(448\) | −1.28192 | −0.0605650 | ||||||||
\(449\) | −30.0196 | −1.41671 | −0.708357 | − | 0.705854i | \(-0.750563\pi\) | ||||
−0.708357 | + | 0.705854i | \(0.750563\pi\) | |||||||
\(450\) | −2.90614 | − | 0.744540i | −0.136997 | − | 0.0350980i | ||||
\(451\) | 1.99303i | 0.0938479i | ||||||||
\(452\) | 4.34265i | 0.204261i | ||||||||
\(453\) | −4.37612 | − | 5.63860i | −0.205608 | − | 0.264925i | ||||
\(454\) | −24.3045 | −1.14066 | ||||||||
\(455\) | −6.21290 | −0.291265 | ||||||||
\(456\) | −5.06655 | − | 6.52820i | −0.237263 | − | 0.305711i | ||||
\(457\) | 16.6613i | 0.779383i | 0.920946 | + | 0.389691i | \(0.127418\pi\) | ||||
−0.920946 | + | 0.389691i | \(0.872582\pi\) | |||||||
\(458\) | −16.4436 | −0.768357 | ||||||||
\(459\) | −13.4964 | − | 31.1210i | −0.629960 | − | 1.45260i | ||||
\(460\) | 2.51663i | 0.117338i | ||||||||
\(461\) | −25.1429 | −1.17102 | −0.585511 | − | 0.810664i | \(-0.699106\pi\) | ||||
−0.585511 | + | 0.810664i | \(0.699106\pi\) | |||||||
\(462\) | 0.534639 | + | 0.688878i | 0.0248737 | + | 0.0320495i | ||||
\(463\) | 10.9029i | 0.506702i | 0.967374 | + | 0.253351i | \(0.0815327\pi\) | ||||
−0.967374 | + | 0.253351i | \(0.918467\pi\) | |||||||
\(464\) | −4.57705 | −0.212484 | ||||||||
\(465\) | −9.17231 | − | 2.97803i | −0.425356 | − | 0.138103i | ||||
\(466\) | −24.9298 | −1.15485 | ||||||||
\(467\) | 38.5263i | 1.78279i | 0.453231 | + | 0.891393i | \(0.350271\pi\) | ||||
−0.453231 | + | 0.891393i | \(0.649729\pi\) | |||||||
\(468\) | −14.0848 | − | 3.60845i | −0.651069 | − | 0.166801i | ||||
\(469\) | 14.0731 | 0.649837 | ||||||||
\(470\) | − | 0.834122i | − | 0.0384752i | ||||||
\(471\) | 3.00838 | − | 2.33480i | 0.138619 | − | 0.107582i | ||||
\(472\) | 5.86520 | 0.269968 | ||||||||
\(473\) | 1.29047i | 0.0593360i | ||||||||
\(474\) | 8.37612 | − | 6.50072i | 0.384728 | − | 0.298588i | ||||
\(475\) | 4.77100 | 0.218909 | ||||||||
\(476\) | 8.36864 | 0.383576 | ||||||||
\(477\) | −0.0917506 | + | 0.358127i | −0.00420097 | + | 0.0163975i | ||||
\(478\) | − | 8.26962i | − | 0.378244i | ||||||
\(479\) | − | 0.704046i | − | 0.0321687i | −0.999871 | − | 0.0160843i | \(-0.994880\pi\) | ||
0.999871 | − | 0.0160843i | \(-0.00512003\pi\) | |||||||
\(480\) | 1.36831 | − | 1.06195i | 0.0624545 | − | 0.0484710i | ||||
\(481\) | 10.2936 | 0.469346 | ||||||||
\(482\) | −12.4895 | −0.568881 | ||||||||
\(483\) | 4.41432 | − | 3.42596i | 0.200859 | − | 0.155887i | ||||
\(484\) | 10.8458 | 0.492989 | ||||||||
\(485\) | − | 17.9181i | − | 0.813620i | ||||||
\(486\) | 2.45883 | + | 15.3933i | 0.111535 | + | 0.698255i | ||||
\(487\) | − | 39.3676i | − | 1.78392i | −0.452117 | − | 0.891959i | \(-0.649331\pi\) | ||
0.452117 | − | 0.891959i | \(-0.350669\pi\) | |||||||
\(488\) | −9.87755 | −0.447136 | ||||||||
\(489\) | −16.5645 | + | 12.8558i | −0.749074 | + | 0.581357i | ||||
\(490\) | 5.35668 | 0.241990 | ||||||||
\(491\) | 24.0294 | 1.08443 | 0.542215 | − | 0.840240i | \(-0.317586\pi\) | ||||
0.542215 | + | 0.840240i | \(0.317586\pi\) | |||||||
\(492\) | −5.38912 | − | 6.94384i | −0.242960 | − | 0.313053i | ||||
\(493\) | 29.8799 | 1.34572 | ||||||||
\(494\) | 23.1229 | 1.04035 | ||||||||
\(495\) | −1.14134 | − | 0.292405i | −0.0512993 | − | 0.0131426i | ||||
\(496\) | 4.60512 | − | 3.12935i | 0.206776 | − | 0.140512i | ||||
\(497\) | − | 11.9665i | − | 0.536772i | ||||||
\(498\) | 2.90614 | + | 3.74454i | 0.130227 | + | 0.167797i | ||||
\(499\) | − | 31.8208i | − | 1.42450i | −0.701928 | − | 0.712248i | \(-0.747677\pi\) | ||
0.701928 | − | 0.712248i | \(-0.252323\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −23.1592 | + | 17.9739i | −1.03468 | + | 0.803014i | ||||
\(502\) | 25.1708i | 1.12343i | ||||||||
\(503\) | 18.8823i | 0.841918i | 0.907080 | + | 0.420959i | \(0.138306\pi\) | ||||
−0.907080 | + | 0.420959i | \(0.861694\pi\) | |||||||
\(504\) | −3.72544 | − | 0.954441i | −0.165944 | − | 0.0425142i | ||||
\(505\) | −5.01164 | −0.223015 | ||||||||
\(506\) | 0.988362i | 0.0439380i | ||||||||
\(507\) | 14.3523 | − | 11.1388i | 0.637408 | − | 0.494693i | ||||
\(508\) | 10.7481i | 0.476869i | ||||||||
\(509\) | 24.1873 | 1.07208 | 0.536042 | − | 0.844191i | \(-0.319919\pi\) | ||||
0.536042 | + | 0.844191i | \(0.319919\pi\) | |||||||
\(510\) | −8.93260 | + | 6.93260i | −0.395542 | + | 0.306981i | ||||
\(511\) | 11.7775i | 0.521007i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −9.86359 | − | 22.7441i | −0.435488 | − | 1.00418i | ||||
\(514\) | −23.3737 | −1.03097 | ||||||||
\(515\) | − | 6.96961i | − | 0.307118i | ||||||
\(516\) | −3.48943 | − | 4.49610i | −0.153613 | − | 0.197930i | ||||
\(517\) | − | 0.327587i | − | 0.0144073i | ||||||
\(518\) | 2.72266 | 0.119627 | ||||||||
\(519\) | −19.9139 | − | 25.6589i | −0.874122 | − | 1.12630i | ||||
\(520\) | 4.84655i | 0.212535i | ||||||||
\(521\) | 0.707188i | 0.0309825i | 0.999880 | + | 0.0154912i | \(0.00493121\pi\) | ||||
−0.999880 | + | 0.0154912i | \(0.995069\pi\) | |||||||
\(522\) | −13.3016 | − | 3.40780i | −0.582194 | − | 0.149155i | ||||
\(523\) | − | 9.65100i | − | 0.422009i | −0.977485 | − | 0.211004i | \(-0.932327\pi\) | ||
0.977485 | − | 0.211004i | \(-0.0676734\pi\) | |||||||
\(524\) | − | 14.9782i | − | 0.654324i | ||||||
\(525\) | 1.75406 | − | 1.36133i | 0.0765536 | − | 0.0594133i | ||||
\(526\) | 10.4026i | 0.453575i | ||||||||
\(527\) | −30.0632 | + | 20.4290i | −1.30957 | + | 0.889903i | ||||
\(528\) | 0.537380 | − | 0.417061i | 0.0233865 | − | 0.0181503i | ||||
\(529\) | −16.6666 | −0.724635 | ||||||||
\(530\) | 0.123231 | 0.00535282 | ||||||||
\(531\) | 17.0451 | + | 4.36688i | 0.739695 | + | 0.189506i | ||||
\(532\) | 6.11604 | 0.265164 | ||||||||
\(533\) | 24.5951 | 1.06533 | ||||||||
\(534\) | 11.7406 | + | 15.1277i | 0.508066 | + | 0.654639i | ||||
\(535\) | −13.7406 | −0.594058 | ||||||||
\(536\) | − | 10.9782i | − | 0.474184i | ||||||
\(537\) | 3.54946 | − | 2.75474i | 0.153171 | − | 0.118876i | ||||
\(538\) | − | 23.5925i | − | 1.01714i | ||||||
\(539\) | 2.10374 | 0.0906147 | ||||||||
\(540\) | 4.76716 | − | 2.06741i | 0.205146 | − | 0.0889669i | ||||
\(541\) | 19.0755 | 0.820118 | 0.410059 | − | 0.912059i | \(-0.365508\pi\) | ||||
0.410059 | + | 0.912059i | \(0.365508\pi\) | |||||||
\(542\) | −24.7707 | −1.06399 | ||||||||
\(543\) | −4.27730 | − | 5.51126i | −0.183556 | − | 0.236511i | ||||
\(544\) | − | 6.52820i | − | 0.279894i | ||||||
\(545\) | − | 8.88704i | − | 0.380679i | ||||||
\(546\) | 8.50116 | − | 6.59776i | 0.363816 | − | 0.282358i | ||||
\(547\) | −16.2881 | −0.696428 | −0.348214 | − | 0.937415i | \(-0.613212\pi\) | ||||
−0.348214 | + | 0.937415i | \(0.613212\pi\) | |||||||
\(548\) | −18.3592 | −0.784265 | ||||||||
\(549\) | −28.7056 | − | 7.35423i | −1.22512 | − | 0.313871i | ||||
\(550\) | 0.392733i | 0.0167462i | ||||||||
\(551\) | 21.8371 | 0.930292 | ||||||||
\(552\) | −2.67252 | − | 3.44352i | −0.113750 | − | 0.146566i | ||||
\(553\) | 7.84729i | 0.333701i | ||||||||
\(554\) | −20.0687 | −0.852639 | ||||||||
\(555\) | −2.90614 | + | 2.25546i | −0.123359 | + | 0.0957389i | ||||
\(556\) | 5.31671i | 0.225479i | ||||||||
\(557\) | −15.4857 | −0.656151 | −0.328075 | − | 0.944652i | \(-0.606400\pi\) | ||||
−0.328075 | + | 0.944652i | \(0.606400\pi\) | |||||||
\(558\) | 15.7131 | − | 5.66564i | 0.665187 | − | 0.239846i | ||||
\(559\) | 15.9252 | 0.673564 | ||||||||
\(560\) | 1.28192i | 0.0541710i | ||||||||
\(561\) | −3.50813 | + | 2.72266i | −0.148113 | + | 0.114951i | ||||
\(562\) | 10.6464 | 0.449092 | ||||||||
\(563\) | − | 16.5871i | − | 0.699064i | −0.936924 | − | 0.349532i | \(-0.886341\pi\) | ||
0.936924 | − | 0.349532i | \(-0.113659\pi\) | |||||||
\(564\) | 0.885793 | + | 1.14134i | 0.0372986 | + | 0.0480590i | ||||
\(565\) | 4.34265 | 0.182697 | ||||||||
\(566\) | − | 16.3379i | − | 0.686734i | ||||||
\(567\) | −10.1160 | − | 5.54748i | −0.424834 | − | 0.232972i | ||||
\(568\) | −9.33484 | −0.391681 | ||||||||
\(569\) | −5.90748 | −0.247654 | −0.123827 | − | 0.992304i | \(-0.539517\pi\) | ||||
−0.123827 | + | 0.992304i | \(0.539517\pi\) | |||||||
\(570\) | −6.52820 | + | 5.06655i | −0.273436 | + | 0.212214i | ||||
\(571\) | − | 11.5683i | − | 0.484118i | −0.970262 | − | 0.242059i | \(-0.922177\pi\) | ||
0.970262 | − | 0.242059i | \(-0.0778227\pi\) | |||||||
\(572\) | 1.90340i | 0.0795852i | ||||||||
\(573\) | 7.95300 | + | 10.2474i | 0.332241 | + | 0.428090i | ||||
\(574\) | 6.50544 | 0.271532 | ||||||||
\(575\) | 2.51663 | 0.104951 | ||||||||
\(576\) | −0.744540 | + | 2.90614i | −0.0310225 | + | 0.121089i | ||||
\(577\) | −33.5427 | −1.39640 | −0.698200 | − | 0.715902i | \(-0.746016\pi\) | ||||
−0.698200 | + | 0.715902i | \(0.746016\pi\) | |||||||
\(578\) | 25.6175i | 1.06555i | ||||||||
\(579\) | 26.7278 | − | 20.7435i | 1.11077 | − | 0.862069i | ||||
\(580\) | 4.57705i | 0.190052i | ||||||||
\(581\) | −3.50813 | −0.145542 | ||||||||
\(582\) | 19.0281 | + | 24.5175i | 0.788740 | + | 1.01628i | ||||
\(583\) | 0.0483969 | 0.00200440 | ||||||||
\(584\) | 9.18740 | 0.380177 | ||||||||
\(585\) | −3.60845 | + | 14.0848i | −0.149191 | + | 0.582334i | ||||
\(586\) | 23.8799 | 0.986471 | ||||||||
\(587\) | −42.6221 | −1.75920 | −0.879601 | − | 0.475712i | \(-0.842190\pi\) | ||||
−0.879601 | + | 0.475712i | \(0.842190\pi\) | |||||||
\(588\) | −7.32960 | + | 5.68851i | −0.302267 | + | 0.234590i | ||||
\(589\) | −21.9710 | + | 14.9301i | −0.905301 | + | 0.615186i | ||||
\(590\) | − | 5.86520i | − | 0.241467i | ||||||
\(591\) | −0.819300 | + | 0.635860i | −0.0337015 | + | 0.0261558i | ||||
\(592\) | − | 2.12389i | − | 0.0872914i | ||||||
\(593\) | − | 30.3324i | − | 1.24560i | −0.782379 | − | 0.622802i | \(-0.785994\pi\) | ||
0.782379 | − | 0.622802i | \(-0.214006\pi\) | |||||||
\(594\) | 1.87222 | − | 0.811938i | 0.0768182 | − | 0.0333142i | ||||
\(595\) | − | 8.36864i | − | 0.343081i | ||||||
\(596\) | 5.26789i | 0.215781i | ||||||||
\(597\) | −12.8147 | − | 16.5116i | −0.524470 | − | 0.675775i | ||||
\(598\) | 12.1970 | 0.498771 | ||||||||
\(599\) | 39.2007i | 1.60170i | 0.598866 | + | 0.800849i | \(0.295618\pi\) | ||||
−0.598866 | + | 0.800849i | \(0.704382\pi\) | |||||||
\(600\) | −1.06195 | − | 1.36831i | −0.0433538 | − | 0.0558610i | ||||
\(601\) | − | 7.23029i | − | 0.294930i | −0.989067 | − | 0.147465i | \(-0.952889\pi\) | ||
0.989067 | − | 0.147465i | \(-0.0471113\pi\) | |||||||
\(602\) | 4.21223 | 0.171678 | ||||||||
\(603\) | 8.17368 | − | 31.9041i | 0.332858 | − | 1.29924i | ||||
\(604\) | − | 4.12085i | − | 0.167675i | ||||||
\(605\) | − | 10.8458i | − | 0.440943i | ||||||
\(606\) | 6.85747 | − | 5.32209i | 0.278566 | − | 0.216195i | ||||
\(607\) | −6.11604 | −0.248243 | −0.124121 | − | 0.992267i | \(-0.539611\pi\) | ||||
−0.124121 | + | 0.992267i | \(0.539611\pi\) | |||||||
\(608\) | − | 4.77100i | − | 0.193490i | ||||||
\(609\) | 8.02844 | − | 6.23088i | 0.325329 | − | 0.252488i | ||||
\(610\) | 9.87755i | 0.399930i | ||||||||
\(611\) | −4.04262 | −0.163547 | ||||||||
\(612\) | 4.86051 | − | 18.9719i | 0.196475 | − | 0.766893i | ||||
\(613\) | 32.3900i | 1.30822i | 0.756400 | + | 0.654110i | \(0.226957\pi\) | ||||
−0.756400 | + | 0.654110i | \(0.773043\pi\) | |||||||
\(614\) | 8.71336i | 0.351643i | ||||||||
\(615\) | −6.94384 | + | 5.38912i | −0.280003 | + | 0.217310i | ||||
\(616\) | 0.503452i | 0.0202847i | ||||||||
\(617\) | − | 33.7250i | − | 1.35772i | −0.734269 | − | 0.678859i | \(-0.762475\pi\) | ||
0.734269 | − | 0.678859i | \(-0.237525\pi\) | |||||||
\(618\) | 7.40135 | + | 9.53658i | 0.297726 | + | 0.383618i | ||||
\(619\) | − | 27.5804i | − | 1.10855i | −0.832333 | − | 0.554276i | \(-0.812995\pi\) | ||
0.832333 | − | 0.554276i | \(-0.187005\pi\) | |||||||
\(620\) | −3.12935 | − | 4.60512i | −0.125678 | − | 0.184946i | ||||
\(621\) | −5.20288 | − | 11.9972i | −0.208785 | − | 0.481430i | ||||
\(622\) | −6.24064 | −0.250227 | ||||||||
\(623\) | −14.1726 | −0.567813 | ||||||||
\(624\) | −5.14678 | − | 6.63158i | −0.206036 | − | 0.265476i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.88059 | −0.314972 | ||||||||
\(627\) | −2.56384 | + | 1.98980i | −0.102390 | + | 0.0794649i | ||||
\(628\) | 2.19861 | 0.0877340 | ||||||||
\(629\) | 13.8652i | 0.552842i | ||||||||
\(630\) | −0.954441 | + | 3.72544i | −0.0380259 | + | 0.148425i | ||||
\(631\) | 49.0587i | 1.95300i | 0.215525 | + | 0.976498i | \(0.430854\pi\) | ||||
−0.215525 | + | 0.976498i | \(0.569146\pi\) | |||||||
\(632\) | 6.12151 | 0.243501 | ||||||||
\(633\) | 21.0360 | − | 16.3261i | 0.836107 | − | 0.648903i | ||||
\(634\) | −9.14329 | −0.363127 | ||||||||
\(635\) | 10.7481 | 0.426524 | ||||||||
\(636\) | −0.168618 | + | 0.130865i | −0.00668615 | + | 0.00518913i | ||||
\(637\) | − | 25.9614i | − | 1.02863i | ||||||
\(638\) | 1.79756i | 0.0711660i | ||||||||
\(639\) | −27.1284 | − | 6.95017i | −1.07318 | − | 0.274944i | ||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 18.5342 | 0.732055 | 0.366028 | − | 0.930604i | \(-0.380718\pi\) | ||||
0.366028 | + | 0.930604i | \(0.380718\pi\) | |||||||
\(642\) | 18.8014 | − | 14.5918i | 0.742032 | − | 0.575892i | ||||
\(643\) | − | 29.4769i | − | 1.16246i | −0.813741 | − | 0.581228i | \(-0.802572\pi\) | ||
0.813741 | − | 0.581228i | \(-0.197428\pi\) | |||||||
\(644\) | 3.22611 | 0.127127 | ||||||||
\(645\) | −4.49610 | + | 3.48943i | −0.177034 | + | 0.137396i | ||||
\(646\) | 31.1461i | 1.22543i | ||||||||
\(647\) | −36.1460 | −1.42105 | −0.710523 | − | 0.703674i | \(-0.751542\pi\) | ||||
−0.710523 | + | 0.703674i | \(0.751542\pi\) | |||||||
\(648\) | −4.32748 | + | 7.89132i | −0.169999 | + | 0.310000i | ||||
\(649\) | − | 2.30346i | − | 0.0904187i | ||||||
\(650\) | 4.84655 | 0.190097 | ||||||||
\(651\) | −3.81760 | + | 11.7582i | −0.149623 | + | 0.460839i | ||||
\(652\) | −12.1058 | −0.474101 | ||||||||
\(653\) | 0.398710i | 0.0156027i | 0.999970 | + | 0.00780136i | \(0.00248328\pi\) | ||||
−0.999970 | + | 0.00780136i | \(0.997517\pi\) | |||||||
\(654\) | 9.43756 | + | 12.1602i | 0.369038 | + | 0.475502i | ||||
\(655\) | −14.9782 | −0.585245 | ||||||||
\(656\) | − | 5.07476i | − | 0.198136i | ||||||
\(657\) | 26.6999 | + | 6.84039i | 1.04166 | + | 0.266869i | ||||
\(658\) | −1.06928 | −0.0416848 | ||||||||
\(659\) | − | 33.1277i | − | 1.29047i | −0.763984 | − | 0.645236i | \(-0.776759\pi\) | ||
0.763984 | − | 0.645236i | \(-0.223241\pi\) | |||||||
\(660\) | −0.417061 | − | 0.537380i | −0.0162341 | − | 0.0209175i | ||||
\(661\) | −7.45088 | −0.289806 | −0.144903 | − | 0.989446i | \(-0.546287\pi\) | ||||
−0.144903 | + | 0.989446i | \(0.546287\pi\) | |||||||
\(662\) | 23.9175 | 0.929578 | ||||||||
\(663\) | 33.5992 | + | 43.2923i | 1.30489 | + | 1.68133i | ||||
\(664\) | 2.73662i | 0.106201i | ||||||||
\(665\) | − | 6.11604i | − | 0.237170i | ||||||
\(666\) | 1.58132 | − | 6.17233i | 0.0612750 | − | 0.239173i | ||||
\(667\) | 11.5187 | 0.446007 | ||||||||
\(668\) | −16.9254 | −0.654864 | ||||||||
\(669\) | 19.1296 | + | 24.6483i | 0.739592 | + | 0.952958i | ||||
\(670\) | −10.9782 | −0.424123 | ||||||||
\(671\) | 3.87924i | 0.149756i | ||||||||
\(672\) | −1.36133 | − | 1.75406i | −0.0525145 | − | 0.0676645i | ||||
\(673\) | 46.6024i | 1.79639i | 0.439596 | + | 0.898196i | \(0.355122\pi\) | ||||
−0.439596 | + | 0.898196i | \(0.644878\pi\) | |||||||
\(674\) | 13.6435 | 0.525527 | ||||||||
\(675\) | −2.06741 | − | 4.76716i | −0.0795745 | − | 0.183488i | ||||
\(676\) | 10.4891 | 0.403426 | ||||||||
\(677\) | 14.1352 | 0.543261 | 0.271630 | − | 0.962402i | \(-0.412437\pi\) | ||||
0.271630 | + | 0.962402i | \(0.412437\pi\) | |||||||
\(678\) | −5.94208 | + | 4.61166i | −0.228204 | + | 0.177110i | ||||
\(679\) | −22.9696 | −0.881493 | ||||||||
\(680\) | −6.52820 | −0.250345 | ||||||||
\(681\) | −25.8100 | − | 33.2560i | −0.989042 | − | 1.27437i | ||||
\(682\) | −1.22900 | − | 1.80858i | −0.0470608 | − | 0.0692542i | ||||
\(683\) | 20.8246i | 0.796832i | 0.917205 | + | 0.398416i | \(0.130440\pi\) | ||||
−0.917205 | + | 0.398416i | \(0.869560\pi\) | |||||||
\(684\) | 3.55220 | − | 13.8652i | 0.135822 | − | 0.530149i | ||||
\(685\) | 18.3592i | 0.701467i | ||||||||
\(686\) | − | 15.8403i | − | 0.604785i | ||||||
\(687\) | −17.4622 | − | 22.4999i | −0.666224 | − | 0.858424i | ||||
\(688\) | − | 3.28588i | − | 0.125273i | ||||||
\(689\) | − | 0.597246i | − | 0.0227533i | ||||||
\(690\) | −3.44352 | + | 2.67252i | −0.131093 | + | 0.101741i | ||||
\(691\) | −10.0491 | −0.382285 | −0.191143 | − | 0.981562i | \(-0.561219\pi\) | ||||
−0.191143 | + | 0.981562i | \(0.561219\pi\) | |||||||
\(692\) | − | 18.7522i | − | 0.712854i | ||||||
\(693\) | −0.374840 | + | 1.46310i | −0.0142390 | + | 0.0555787i | ||||
\(694\) | − | 15.0787i | − | 0.572378i | ||||||
\(695\) | 5.31671 | 0.201674 | ||||||||
\(696\) | −4.86058 | − | 6.26282i | −0.184240 | − | 0.237392i | ||||
\(697\) | 33.1291i | 1.25485i | ||||||||
\(698\) | 13.1714i | 0.498543i | ||||||||
\(699\) | −26.4741 | − | 34.1116i | −1.00134 | − | 1.29022i | ||||
\(700\) | 1.28192 | 0.0484520 | ||||||||
\(701\) | − | 5.98125i | − | 0.225909i | −0.993600 | − | 0.112954i | \(-0.963969\pi\) | ||
0.993600 | − | 0.112954i | \(-0.0360314\pi\) | |||||||
\(702\) | −10.0198 | − | 23.1043i | −0.378173 | − | 0.872016i | ||||
\(703\) | 10.1331i | 0.382177i | ||||||||
\(704\) | 0.392733 | 0.0148017 | ||||||||
\(705\) | 1.14134 | − | 0.885793i | 0.0429853 | − | 0.0333609i | ||||
\(706\) | − | 1.46704i | − | 0.0552127i | ||||||
\(707\) | 6.42452i | 0.241619i | ||||||||
\(708\) | 6.22853 | + | 8.02541i | 0.234083 | + | 0.301614i | ||||
\(709\) | − | 10.5995i | − | 0.398074i | −0.979992 | − | 0.199037i | \(-0.936219\pi\) | ||
0.979992 | − | 0.199037i | \(-0.0637815\pi\) | |||||||
\(710\) | 9.33484i | 0.350330i | ||||||||
\(711\) | 17.7900 | + | 4.55771i | 0.667177 | + | 0.170928i | ||||
\(712\) | 11.0557i | 0.414332i | ||||||||
\(713\) | −11.5894 | + | 7.87541i | −0.434025 | + | 0.294936i | ||||
\(714\) | 8.88704 | + | 11.4509i | 0.332589 | + | 0.428539i | ||||
\(715\) | 1.90340 | 0.0711832 | ||||||||
\(716\) | 2.59405 | 0.0969442 | ||||||||
\(717\) | 11.3154 | − | 8.78189i | 0.422581 | − | 0.327966i | ||||
\(718\) | −4.42521 | −0.165147 | ||||||||
\(719\) | 10.7883 | 0.402334 | 0.201167 | − | 0.979557i | \(-0.435527\pi\) | ||||
0.201167 | + | 0.979557i | \(0.435527\pi\) | |||||||
\(720\) | 2.90614 | + | 0.744540i | 0.108306 | + | 0.0277474i | ||||
\(721\) | −8.93448 | −0.332738 | ||||||||
\(722\) | 3.76245i | 0.140024i | ||||||||
\(723\) | −13.2632 | − | 17.0895i | −0.493263 | − | 0.635565i | ||||
\(724\) | − | 4.02779i | − | 0.149692i | ||||||
\(725\) | 4.57705 | 0.169987 | ||||||||
\(726\) | 11.5176 | + | 14.8404i | 0.427459 | + | 0.550777i | ||||
\(727\) | 24.6314 | 0.913529 | 0.456764 | − | 0.889588i | \(-0.349008\pi\) | ||||
0.456764 | + | 0.889588i | \(0.349008\pi\) | |||||||
\(728\) | 6.21290 | 0.230265 | ||||||||
\(729\) | −18.4517 | + | 19.7113i | −0.683395 | + | 0.730049i | ||||
\(730\) | − | 9.18740i | − | 0.340041i | ||||||
\(731\) | 21.4509i | 0.793390i | ||||||||
\(732\) | −10.4894 | − | 13.5155i | −0.387700 | − | 0.499549i | ||||
\(733\) | 18.5871 | 0.686531 | 0.343265 | − | 0.939238i | \(-0.388467\pi\) | ||||
0.343265 | + | 0.939238i | \(0.388467\pi\) | |||||||
\(734\) | −6.28174 | −0.231863 | ||||||||
\(735\) | 5.68851 | + | 7.32960i | 0.209824 | + | 0.270356i | ||||
\(736\) | − | 2.51663i | − | 0.0927640i | ||||||
\(737\) | −4.31148 | −0.158816 | ||||||||
\(738\) | 3.77836 | − | 14.7480i | 0.139083 | − | 0.542880i | ||||
\(739\) | 42.0629i | 1.54731i | 0.633607 | + | 0.773655i | \(0.281574\pi\) | ||||
−0.633607 | + | 0.773655i | \(0.718426\pi\) | |||||||
\(740\) | −2.12389 | −0.0780758 | ||||||||
\(741\) | 24.5553 | + | 31.6393i | 0.902061 | + | 1.16230i | ||||
\(742\) | − | 0.157973i | − | 0.00579935i | ||||||
\(743\) | −3.32260 | −0.121895 | −0.0609473 | − | 0.998141i | \(-0.519412\pi\) | ||||
−0.0609473 | + | 0.998141i | \(0.519412\pi\) | |||||||
\(744\) | 9.17231 | + | 2.97803i | 0.336273 | + | 0.109180i | ||||
\(745\) | 5.26789 | 0.193000 | ||||||||
\(746\) | − | 30.4103i | − | 1.11340i | ||||||
\(747\) | −2.03752 | + | 7.95300i | −0.0745491 | + | 0.290985i | ||||
\(748\) | −2.56384 | −0.0937433 | ||||||||
\(749\) | 17.6144i | 0.643615i | ||||||||
\(750\) | −1.36831 | + | 1.06195i | −0.0499636 | + | 0.0387768i | ||||
\(751\) | −39.1525 | −1.42870 | −0.714348 | − | 0.699790i | \(-0.753277\pi\) | ||||
−0.714348 | + | 0.699790i | \(0.753277\pi\) | |||||||
\(752\) | 0.834122i | 0.0304173i | ||||||||
\(753\) | −34.4415 | + | 26.7301i | −1.25512 | + | 0.974098i | ||||
\(754\) | 22.1829 | 0.807855 | ||||||||
\(755\) | −4.12085 | −0.149973 | ||||||||
\(756\) | −2.65025 | − | 6.11112i | −0.0963886 | − | 0.222259i | ||||
\(757\) | 33.9683i | 1.23460i | 0.786728 | + | 0.617300i | \(0.211773\pi\) | ||||
−0.786728 | + | 0.617300i | \(0.788227\pi\) | |||||||
\(758\) | 30.4929i | 1.10755i | ||||||||
\(759\) | −1.35238 | + | 1.04959i | −0.0490884 | + | 0.0380976i | ||||
\(760\) | −4.77100 | −0.173062 | ||||||||
\(761\) | 50.8630 | 1.84378 | 0.921891 | − | 0.387449i | \(-0.126644\pi\) | ||||
0.921891 | + | 0.387449i | \(0.126644\pi\) | |||||||
\(762\) | −14.7067 | + | 11.4139i | −0.532767 | + | 0.413481i | ||||
\(763\) | −11.3925 | −0.412436 | ||||||||
\(764\) | 7.48908i | 0.270945i | ||||||||
\(765\) | −18.9719 | − | 4.86051i | −0.685930 | − | 0.175732i | ||||
\(766\) | − | 34.4055i | − | 1.24312i | ||||||
\(767\) | −28.4260 | −1.02640 | ||||||||
\(768\) | −1.36831 | + | 1.06195i | −0.0493746 | + | 0.0383197i | ||||
\(769\) | 37.4703 | 1.35121 | 0.675607 | − | 0.737262i | \(-0.263882\pi\) | ||||
0.675607 | + | 0.737262i | \(0.263882\pi\) | |||||||
\(770\) | 0.503452 | 0.0181432 | ||||||||
\(771\) | −24.8216 | − | 31.9825i | −0.893930 | − | 1.15182i | ||||
\(772\) | 19.5334 | 0.703024 | ||||||||
\(773\) | 43.2585 | 1.55590 | 0.777949 | − | 0.628327i | \(-0.216260\pi\) | ||||
0.777949 | + | 0.628327i | \(0.216260\pi\) | |||||||
\(774\) | 2.44647 | − | 9.54923i | 0.0879365 | − | 0.343240i | ||||
\(775\) | −4.60512 | + | 3.12935i | −0.165421 | + | 0.112410i | ||||
\(776\) | 17.9181i | 0.643223i | ||||||||
\(777\) | 2.89132 | + | 3.72544i | 0.103726 | + | 0.133649i | ||||
\(778\) | − | 7.32763i | − | 0.262708i | ||||||
\(779\) | 24.2117i | 0.867474i | ||||||||
\(780\) | −6.63158 | + | 5.14678i | −0.237449 | + | 0.184284i | ||||
\(781\) | 3.66610i | 0.131183i | ||||||||
\(782\) | 16.4290i | 0.587501i | ||||||||
\(783\) | −9.46262 | − | 21.8195i | −0.338166 | − | 0.779767i | ||||
\(784\) | −5.35668 | −0.191310 | ||||||||
\(785\) | − | 2.19861i | − | 0.0784717i | ||||||
\(786\) | 20.4948 | − | 15.9060i | 0.731024 | − | 0.567348i | ||||
\(787\) | 15.8331i | 0.564389i | 0.959357 | + | 0.282194i | \(0.0910623\pi\) | ||||
−0.959357 | + | 0.282194i | \(0.908938\pi\) | |||||||
\(788\) | −0.598768 | −0.0213302 | ||||||||
\(789\) | −14.2340 | + | 11.0470i | −0.506743 | + | 0.393283i | ||||
\(790\) | − | 6.12151i | − | 0.217794i | ||||||
\(791\) | − | 5.56693i | − | 0.197937i | ||||||
\(792\) | 1.14134 | + | 0.292405i | 0.0405557 | + | 0.0103902i | ||||
\(793\) | 47.8721 | 1.69999 | ||||||||
\(794\) | 26.7188i | 0.948214i | ||||||||
\(795\) | 0.130865 | + | 0.168618i | 0.00464130 | + | 0.00598028i | ||||
\(796\) | − | 12.0672i | − | 0.427709i | ||||||
\(797\) | 19.1608 | 0.678712 | 0.339356 | − | 0.940658i | \(-0.389791\pi\) | ||||
0.339356 | + | 0.940658i | \(0.389791\pi\) | |||||||
\(798\) | 6.49491 | + | 8.36864i | 0.229917 | + | 0.296247i | ||||
\(799\) | − | 5.44532i | − | 0.192642i | ||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | −8.23145 | + | 32.1296i | −0.290844 | + | 1.13524i | ||||
\(802\) | 27.1300i | 0.957993i | ||||||||
\(803\) | − | 3.60819i | − | 0.127330i | ||||||
\(804\) | 15.0215 | − | 11.6582i | 0.529768 | − | 0.411154i | ||||
\(805\) | − | 3.22611i | − | 0.113706i | ||||||
\(806\) | −22.3190 | + | 15.1666i | −0.786152 | + | 0.534220i | ||||
\(807\) | 32.2818 | − | 25.0540i | 1.13637 | − | 0.881941i | ||||
\(808\) | 5.01164 | 0.176309 | ||||||||
\(809\) | 13.6102 | 0.478508 | 0.239254 | − | 0.970957i | \(-0.423097\pi\) | ||||
0.239254 | + | 0.970957i | \(0.423097\pi\) | |||||||
\(810\) | 7.89132 | + | 4.32748i | 0.277273 | + | 0.152052i | ||||
\(811\) | 19.3201 | 0.678421 | 0.339211 | − | 0.940710i | \(-0.389840\pi\) | ||||
0.339211 | + | 0.940710i | \(0.389840\pi\) | |||||||
\(812\) | 5.86742 | 0.205906 | ||||||||
\(813\) | −26.3051 | − | 33.8940i | −0.922562 | − | 1.18871i | ||||
\(814\) | −0.834122 | −0.0292360 | ||||||||
\(815\) | 12.1058i | 0.424049i | ||||||||
\(816\) | 8.93260 | − | 6.93260i | 0.312704 | − | 0.242690i | ||||
\(817\) | 15.6769i | 0.548466i | ||||||||
\(818\) | 3.23637 | 0.113157 | ||||||||
\(819\) | 18.0556 | + | 4.62575i | 0.630912 | + | 0.161637i | ||||
\(820\) | −5.07476 | −0.177218 | ||||||||
\(821\) | −55.7366 | −1.94522 | −0.972610 | − | 0.232442i | \(-0.925328\pi\) | ||||
−0.972610 | + | 0.232442i | \(0.925328\pi\) | |||||||
\(822\) | −19.4964 | − | 25.1210i | −0.680017 | − | 0.876196i | ||||
\(823\) | − | 37.2577i | − | 1.29872i | −0.760481 | − | 0.649361i | \(-0.775037\pi\) | ||
0.760481 | − | 0.649361i | \(-0.224963\pi\) | |||||||
\(824\) | 6.96961i | 0.242798i | ||||||||
\(825\) | −0.537380 | + | 0.417061i | −0.0187092 | + | 0.0145202i | ||||
\(826\) | −7.51872 | −0.261610 | ||||||||
\(827\) | 16.8889 | 0.587286 | 0.293643 | − | 0.955915i | \(-0.405132\pi\) | ||||
0.293643 | + | 0.955915i | \(0.405132\pi\) | |||||||
\(828\) | 1.87373 | − | 7.31367i | 0.0651166 | − | 0.254168i | ||||
\(829\) | 17.3927i | 0.604075i | 0.953296 | + | 0.302037i | \(0.0976668\pi\) | ||||
−0.953296 | + | 0.302037i | \(0.902333\pi\) | |||||||
\(830\) | 2.73662 | 0.0949894 | ||||||||
\(831\) | −21.3119 | − | 27.4602i | −0.739302 | − | 0.952585i | ||||
\(832\) | − | 4.84655i | − | 0.168024i | ||||||
\(833\) | 34.9695 | 1.21162 | ||||||||
\(834\) | −7.27490 | + | 5.64606i | −0.251909 | + | 0.195507i | ||||
\(835\) | 16.9254i | 0.585728i | ||||||||
\(836\) | −1.87373 | −0.0648043 | ||||||||
\(837\) | 24.4388 | + | 15.4837i | 0.844728 | + | 0.535196i | ||||
\(838\) | 15.8496 | 0.547515 | ||||||||
\(839\) | − | 29.5325i | − | 1.01957i | −0.860300 | − | 0.509787i | \(-0.829724\pi\) | ||
0.860300 | − | 0.509787i | \(-0.170276\pi\) | |||||||
\(840\) | −1.75406 | + | 1.36133i | −0.0605209 | + | 0.0469704i | ||||
\(841\) | −8.05060 | −0.277607 | ||||||||
\(842\) | 24.7086i | 0.851514i | ||||||||
\(843\) | 11.3059 | + | 14.5676i | 0.389396 | + | 0.501734i | ||||
\(844\) | 15.3737 | 0.529186 | ||||||||
\(845\) | − | 10.4891i | − | 0.360835i | ||||||
\(846\) | −0.621038 | + | 2.42408i | −0.0213517 | + | 0.0833415i | ||||
\(847\) | −13.9034 | −0.477727 | ||||||||
\(848\) | −0.123231 | −0.00423178 | ||||||||
\(849\) | 22.3553 | − | 17.3500i | 0.767233 | − | 0.595451i | ||||
\(850\) | 6.52820i | 0.223916i | ||||||||
\(851\) | 5.34504i | 0.183226i | ||||||||
\(852\) | −9.91310 | − | 12.7729i | −0.339617 | − | 0.437594i | ||||
\(853\) | 12.5693 | 0.430363 | 0.215181 | − | 0.976574i | \(-0.430966\pi\) | ||||
0.215181 | + | 0.976574i | \(0.430966\pi\) | |||||||
\(854\) | 12.6622 | 0.433293 | ||||||||
\(855\) | −13.8652 | − | 3.55220i | −0.474180 | − | 0.121483i | ||||
\(856\) | 13.7406 | 0.469644 | ||||||||
\(857\) | − | 3.29281i | − | 0.112480i | −0.998417 | − | 0.0562402i | \(-0.982089\pi\) | ||
0.998417 | − | 0.0562402i | \(-0.0179112\pi\) | |||||||
\(858\) | −2.60444 | + | 2.02131i | −0.0889142 | + | 0.0690064i | ||||
\(859\) | − | 50.1085i | − | 1.70968i | −0.518891 | − | 0.854840i | \(-0.673655\pi\) | ||
0.518891 | − | 0.854840i | \(-0.326345\pi\) | |||||||
\(860\) | −3.28588 | −0.112048 | ||||||||
\(861\) | 6.90843 | + | 8.90145i | 0.235439 | + | 0.303361i | ||||
\(862\) | 1.24844 | 0.0425221 | ||||||||
\(863\) | −4.65899 | −0.158594 | −0.0792969 | − | 0.996851i | \(-0.525268\pi\) | ||||
−0.0792969 | + | 0.996851i | \(0.525268\pi\) | |||||||
\(864\) | −4.76716 | + | 2.06741i | −0.162182 | + | 0.0703345i | ||||
\(865\) | −18.7522 | −0.637596 | ||||||||
\(866\) | 23.2831 | 0.791193 | ||||||||
\(867\) | −35.0526 | + | 27.2044i | −1.19045 | + | 0.923908i | ||||
\(868\) | −5.90340 | + | 4.01158i | −0.200374 | + | 0.136162i | ||||
\(869\) | − | 2.40412i | − | 0.0815542i | ||||||
\(870\) | −6.26282 | + | 4.86058i | −0.212330 | + | 0.164789i | ||||
\(871\) | 53.2062i | 1.80282i | ||||||||
\(872\) | 8.88704i | 0.300953i | ||||||||
\(873\) | −13.3408 | + | 52.0726i | −0.451517 | + | 1.76239i | ||||
\(874\) | 12.0068i | 0.406137i | ||||||||
\(875\) | − | 1.28192i | − | 0.0433368i | ||||||
\(876\) | 9.75652 | + | 12.5712i | 0.329642 | + | 0.424742i | ||||
\(877\) | −31.3987 | −1.06026 | −0.530129 | − | 0.847917i | \(-0.677856\pi\) | ||||
−0.530129 | + | 0.847917i | \(0.677856\pi\) | |||||||
\(878\) | 37.2109i | 1.25581i | ||||||||
\(879\) | 25.3592 | + | 32.6751i | 0.855345 | + | 1.10210i | ||||
\(880\) | − | 0.392733i | − | 0.0132390i | ||||||
\(881\) | 0.742278 | 0.0250080 | 0.0125040 | − | 0.999922i | \(-0.496020\pi\) | ||||
0.0125040 | + | 0.999922i | \(0.496020\pi\) | |||||||
\(882\) | −15.5673 | − | 3.98826i | −0.524177 | − | 0.134292i | ||||
\(883\) | 34.0936i | 1.14734i | 0.819086 | + | 0.573670i | \(0.194481\pi\) | ||||
−0.819086 | + | 0.573670i | \(0.805519\pi\) | |||||||
\(884\) | 31.6393i | 1.06414i | ||||||||
\(885\) | 8.02541 | − | 6.22853i | 0.269771 | − | 0.209370i | ||||
\(886\) | −18.8683 | −0.633893 | ||||||||
\(887\) | − | 7.22517i | − | 0.242597i | −0.992616 | − | 0.121299i | \(-0.961294\pi\) | ||
0.992616 | − | 0.121299i | \(-0.0387059\pi\) | |||||||
\(888\) | 2.90614 | − | 2.25546i | 0.0975237 | − | 0.0756883i | ||||
\(889\) | − | 13.7782i | − | 0.462105i | ||||||
\(890\) | 11.0557 | 0.370589 | ||||||||
\(891\) | 3.09918 | + | 1.69954i | 0.103826 | + | 0.0569368i | ||||
\(892\) | 18.0137i | 0.603143i | ||||||||
\(893\) | − | 3.97960i | − | 0.133172i | ||||||
\(894\) | −7.20810 | + | 5.59421i | −0.241075 | + | 0.187098i | ||||
\(895\) | − | 2.59405i | − | 0.0867095i | ||||||
\(896\) | − | 1.28192i | − | 0.0428260i | ||||||
\(897\) | 12.9525 | + | 16.6892i | 0.432472 | + | 0.557237i | ||||
\(898\) | − | 30.0196i | − | 1.00177i | ||||||
\(899\) | −21.0779 | + | 14.3232i | −0.702987 | + | 0.477706i | ||||
\(900\) | 0.744540 | − | 2.90614i | 0.0248180 | − | 0.0968714i | ||||
\(901\) | 0.804478 | 0.0268011 | ||||||||
\(902\) | −1.99303 | −0.0663605 | ||||||||
\(903\) | 4.47317 | + | 5.76364i | 0.148858 | + | 0.191802i | ||||
\(904\) | −4.34265 | −0.144434 | ||||||||
\(905\) | −4.02779 | −0.133888 | ||||||||
\(906\) | 5.63860 | − | 4.37612i | 0.187330 | − | 0.145387i | ||||
\(907\) | 2.18703 | 0.0726190 | 0.0363095 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363095 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(908\) | − | 24.3045i | − | 0.806572i | ||||||
\(909\) | 14.5645 | + | 3.73137i | 0.483075 | + | 0.123762i | ||||
\(910\) | − | 6.21290i | − | 0.205955i | ||||||
\(911\) | 27.3383 | 0.905757 | 0.452879 | − | 0.891572i | \(-0.350397\pi\) | ||||
0.452879 | + | 0.891572i | \(0.350397\pi\) | |||||||
\(912\) | 6.52820 | − | 5.06655i | 0.216170 | − | 0.167770i | ||||
\(913\) | 1.07476 | 0.0355694 | ||||||||
\(914\) | −16.6613 | −0.551107 | ||||||||
\(915\) | −13.5155 | + | 10.4894i | −0.446810 | + | 0.346770i | ||||
\(916\) | − | 16.4436i | − | 0.543311i | ||||||
\(917\) | 19.2008i | 0.634067i | ||||||||
\(918\) | 31.1210 | − | 13.4964i | 1.02715 | − | 0.445449i | ||||
\(919\) | 36.8059 | 1.21411 | 0.607057 | − | 0.794659i | \(-0.292350\pi\) | ||||
0.607057 | + | 0.794659i | \(0.292350\pi\) | |||||||
\(920\) | −2.51663 | −0.0829707 | ||||||||
\(921\) | −11.9226 | + | 9.25312i | −0.392862 | + | 0.304901i | ||||
\(922\) | − | 25.1429i | − | 0.828038i | ||||||
\(923\) | 45.2418 | 1.48915 | ||||||||
\(924\) | −0.688878 | + | 0.534639i | −0.0226624 | + | 0.0175883i | ||||
\(925\) | 2.12389i | 0.0698332i | ||||||||
\(926\) | −10.9029 | −0.358292 | ||||||||
\(927\) | −5.18915 | + | 20.2547i | −0.170434 | + | 0.665251i | ||||
\(928\) | − | 4.57705i | − | 0.150249i | ||||||
\(929\) | −37.6751 | −1.23608 | −0.618041 | − | 0.786146i | \(-0.712073\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(930\) | 2.97803 | − | 9.17231i | 0.0976534 | − | 0.300772i | ||||
\(931\) | 25.5567 | 0.837588 | ||||||||
\(932\) | − | 24.9298i | − | 0.816602i | ||||||
\(933\) | −6.62722 | − | 8.53912i | −0.216966 | − | 0.279558i | ||||
\(934\) | −38.5263 | −1.26062 | ||||||||
\(935\) | 2.56384i | 0.0838466i | ||||||||
\(936\) | 3.60845 | − | 14.0848i | 0.117946 | − | 0.460375i | ||||
\(937\) | −45.9539 | −1.50125 | −0.750625 | − | 0.660729i | \(-0.770247\pi\) | ||||
−0.750625 | + | 0.660729i | \(0.770247\pi\) | |||||||
\(938\) | 14.0731i | 0.459504i | ||||||||
\(939\) | −8.36876 | − | 10.7831i | −0.273104 | − | 0.351893i | ||||
\(940\) | 0.834122 | 0.0272061 | ||||||||
\(941\) | −40.3651 | −1.31586 | −0.657932 | − | 0.753077i | \(-0.728569\pi\) | ||||
−0.657932 | + | 0.753077i | \(0.728569\pi\) | |||||||
\(942\) | 2.33480 | + | 3.00838i | 0.0760720 | + | 0.0980182i | ||||
\(943\) | 12.7713i | 0.415890i | ||||||||
\(944\) | 5.86520i | 0.190896i | ||||||||
\(945\) | −6.11112 | + | 2.65025i | −0.198795 | + | 0.0862126i | ||||
\(946\) | −1.29047 | −0.0419569 | ||||||||
\(947\) | −52.5426 | −1.70741 | −0.853703 | − | 0.520760i | \(-0.825649\pi\) | ||||
−0.853703 | + | 0.520760i | \(0.825649\pi\) | |||||||
\(948\) | 6.50072 | + | 8.37612i | 0.211134 | + | 0.272044i | ||||
\(949\) | −44.5272 | −1.44541 | ||||||||
\(950\) | 4.77100i | 0.154792i | ||||||||
\(951\) | −9.70968 | − | 12.5109i | −0.314858 | − | 0.405692i | ||||
\(952\) | 8.36864i | 0.271229i | ||||||||
\(953\) | −53.3751 | −1.72899 | −0.864495 | − | 0.502642i | \(-0.832361\pi\) | ||||
−0.864495 | + | 0.502642i | \(0.832361\pi\) | |||||||
\(954\) | −0.358127 | − | 0.0917506i | −0.0115948 | − | 0.00297053i | ||||
\(955\) | 7.48908 | 0.242341 | ||||||||
\(956\) | 8.26962 | 0.267459 | ||||||||
\(957\) | −2.45962 | + | 1.90891i | −0.0795081 | + | 0.0617063i | ||||
\(958\) | 0.704046 | 0.0227467 | ||||||||
\(959\) | 23.5350 | 0.759984 | ||||||||
\(960\) | 1.06195 | + | 1.36831i | 0.0342742 | + | 0.0441620i | ||||
\(961\) | 11.4143 | − | 28.8221i | 0.368204 | − | 0.929745i | ||||
\(962\) | 10.2936i | 0.331878i | ||||||||
\(963\) | 39.9322 | + | 10.2304i | 1.28680 | + | 0.329671i | ||||
\(964\) | − | 12.4895i | − | 0.402259i | ||||||
\(965\) | − | 19.5334i | − | 0.628804i | ||||||
\(966\) | 3.42596 | + | 4.41432i | 0.110228 | + | 0.142028i | ||||
\(967\) | 47.8830i | 1.53981i | 0.638157 | + | 0.769906i | \(0.279697\pi\) | ||||
−0.638157 | + | 0.769906i | \(0.720303\pi\) | |||||||
\(968\) | 10.8458i | 0.348596i | ||||||||
\(969\) | −42.6175 | + | 33.0755i | −1.36907 | + | 1.06254i | ||||
\(970\) | 17.9181 | 0.575316 | ||||||||
\(971\) | 17.2188i | 0.552578i | 0.961075 | + | 0.276289i | \(0.0891046\pi\) | ||||
−0.961075 | + | 0.276289i | \(0.910895\pi\) | |||||||
\(972\) | −15.3933 | + | 2.45883i | −0.493741 | + | 0.0788669i | ||||
\(973\) | − | 6.81560i | − | 0.218498i | ||||||
\(974\) | 39.3676 | 1.26142 | ||||||||
\(975\) | 5.14678 | + | 6.63158i | 0.164829 | + | 0.212381i | ||||
\(976\) | − | 9.87755i | − | 0.316173i | ||||||
\(977\) | − | 8.41194i | − | 0.269122i | −0.990905 | − | 0.134561i | \(-0.957038\pi\) | ||
0.990905 | − | 0.134561i | \(-0.0429624\pi\) | |||||||
\(978\) | −12.8558 | − | 16.5645i | −0.411082 | − | 0.529675i | ||||
\(979\) | 4.34196 | 0.138770 | ||||||||
\(980\) | 5.35668i | 0.171113i | ||||||||
\(981\) | −6.61676 | + | 25.8270i | −0.211257 | + | 0.824593i | ||||
\(982\) | 24.0294i | 0.766807i | ||||||||
\(983\) | 3.47796 | 0.110930 | 0.0554648 | − | 0.998461i | \(-0.482336\pi\) | ||||
0.0554648 | + | 0.998461i | \(0.482336\pi\) | |||||||
\(984\) | 6.94384 | − | 5.38912i | 0.221362 | − | 0.171799i | ||||
\(985\) | 0.598768i | 0.0190783i | ||||||||
\(986\) | 29.8799i | 0.951571i | ||||||||
\(987\) | −1.13552 | − | 1.46310i | −0.0361439 | − | 0.0465711i | ||||
\(988\) | 23.1229i | 0.735638i | ||||||||
\(989\) | 8.26932i | 0.262949i | ||||||||
\(990\) | 0.292405 | − | 1.14134i | 0.00929326 | − | 0.0362741i | ||||
\(991\) | − | 6.14943i | − | 0.195343i | −0.995219 | − | 0.0976715i | \(-0.968861\pi\) | ||
0.995219 | − | 0.0976715i | \(-0.0311395\pi\) | |||||||
\(992\) | 3.12935 | + | 4.60512i | 0.0993570 | + | 0.146213i | ||||
\(993\) | 25.3991 | + | 32.7265i | 0.806015 | + | 1.03854i | ||||
\(994\) | 11.9665 | 0.379555 | ||||||||
\(995\) | −12.0672 | −0.382555 | ||||||||
\(996\) | −3.74454 | + | 2.90614i | −0.118650 | + | 0.0920846i | ||||
\(997\) | 0.524953 | 0.0166254 | 0.00831272 | − | 0.999965i | \(-0.497354\pi\) | ||||
0.00831272 | + | 0.999965i | \(0.497354\pi\) | |||||||
\(998\) | 31.8208 | 1.00727 | ||||||||
\(999\) | 10.1249 | − | 4.39095i | 0.320339 | − | 0.138923i |
(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 | 930.2.h.c.371.10 | yes | 16 | |
3.2 | odd | 2 | inner | 930.2.h.c.371.7 | yes | 16 | |
31.30 | odd | 2 | inner | 930.2.h.c.371.15 | yes | 16 | |
93.92 | even | 2 | inner | 930.2.h.c.371.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.h.c.371.2 | ✓ | 16 | 93.92 | even | 2 | inner | |
930.2.h.c.371.7 | yes | 16 | 3.2 | odd | 2 | inner | |
930.2.h.c.371.10 | yes | 16 | 1.1 | even | 1 | trivial | |
930.2.h.c.371.15 | yes | 16 | 31.30 | odd | 2 | inner |