Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(551,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, 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("690.551");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.e (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: | \(5.50967773947\) |
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: | \( x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.10 | ||
Root | \(-1.14349 - 1.30094i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.551 |
Dual form | 690.2.e.b.551.2 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.30094 | + | 1.14349i | −0.751096 | + | 0.660193i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.14349 | − | 1.30094i | −0.466827 | − | 0.531105i | ||||
\(7\) | 1.02070i | 0.385789i | 0.981220 | + | 0.192894i | \(0.0617875\pi\) | ||||
−0.981220 | + | 0.192894i | \(0.938213\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.384868 | − | 2.97521i | 0.128289 | − | 0.991737i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | −0.336117 | −0.101343 | −0.0506716 | − | 0.998715i | \(-0.516136\pi\) | ||||
−0.0506716 | + | 0.998715i | \(0.516136\pi\) | |||||||
\(12\) | 1.30094 | − | 1.14349i | 0.375548 | − | 0.330097i | ||||
\(13\) | −4.92792 | −1.36676 | −0.683380 | − | 0.730063i | \(-0.739491\pi\) | ||||
−0.683380 | + | 0.730063i | \(0.739491\pi\) | |||||||
\(14\) | −1.02070 | −0.272794 | ||||||||
\(15\) | −1.30094 | + | 1.14349i | −0.335900 | + | 0.295247i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.57164 | −1.83639 | −0.918196 | − | 0.396127i | \(-0.870354\pi\) | ||||
−0.918196 | + | 0.396127i | \(0.870354\pi\) | |||||||
\(18\) | 2.97521 | + | 0.384868i | 0.701264 | + | 0.0907141i | ||||
\(19\) | 3.95042i | 0.906289i | 0.891437 | + | 0.453144i | \(0.149698\pi\) | ||||
−0.891437 | + | 0.453144i | \(0.850302\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.16716 | − | 1.32787i | −0.254695 | − | 0.289764i | ||||
\(22\) | − | 0.336117i | − | 0.0716604i | ||||||
\(23\) | −2.61089 | − | 4.02284i | −0.544408 | − | 0.838821i | ||||
\(24\) | 1.14349 | + | 1.30094i | 0.233414 | + | 0.265552i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | − | 4.92792i | − | 0.966445i | ||||||
\(27\) | 2.90143 | + | 4.31065i | 0.558381 | + | 0.829585i | ||||
\(28\) | − | 1.02070i | − | 0.192894i | ||||||
\(29\) | − | 2.20183i | − | 0.408869i | −0.978880 | − | 0.204434i | \(-0.934464\pi\) | ||
0.978880 | − | 0.204434i | \(-0.0655355\pi\) | |||||||
\(30\) | −1.14349 | − | 1.30094i | −0.208772 | − | 0.237517i | ||||
\(31\) | −1.27271 | −0.228586 | −0.114293 | − | 0.993447i | \(-0.536460\pi\) | ||||
−0.114293 | + | 0.993447i | \(0.536460\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.437267 | − | 0.384346i | 0.0761184 | − | 0.0669061i | ||||
\(34\) | − | 7.57164i | − | 1.29853i | ||||||
\(35\) | 1.02070i | 0.172530i | ||||||||
\(36\) | −0.384868 | + | 2.97521i | −0.0641446 | + | 0.495868i | ||||
\(37\) | − | 0.378822i | − | 0.0622779i | −0.999515 | − | 0.0311390i | \(-0.990087\pi\) | ||
0.999515 | − | 0.0311390i | \(-0.00991345\pi\) | |||||||
\(38\) | −3.95042 | −0.640843 | ||||||||
\(39\) | 6.41091 | − | 5.63502i | 1.02657 | − | 0.902326i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | − | 7.82260i | − | 1.22169i | −0.791752 | − | 0.610843i | \(-0.790831\pi\) | ||
0.791752 | − | 0.610843i | \(-0.209169\pi\) | |||||||
\(42\) | 1.32787 | − | 1.16716i | 0.204894 | − | 0.180097i | ||||
\(43\) | − | 10.0534i | − | 1.53313i | −0.642168 | − | 0.766564i | \(-0.721965\pi\) | ||
0.642168 | − | 0.766564i | \(-0.278035\pi\) | |||||||
\(44\) | 0.336117 | 0.0506716 | ||||||||
\(45\) | 0.384868 | − | 2.97521i | 0.0573727 | − | 0.443518i | ||||
\(46\) | 4.02284 | − | 2.61089i | 0.593136 | − | 0.384954i | ||||
\(47\) | 5.34859i | 0.780172i | 0.920778 | + | 0.390086i | \(0.127555\pi\) | ||||
−0.920778 | + | 0.390086i | \(0.872445\pi\) | |||||||
\(48\) | −1.30094 | + | 1.14349i | −0.187774 | + | 0.165048i | ||||
\(49\) | 5.95817 | 0.851167 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 9.85021 | − | 8.65808i | 1.37931 | − | 1.21237i | ||||
\(52\) | 4.92792 | 0.683380 | ||||||||
\(53\) | −13.2494 | −1.81995 | −0.909975 | − | 0.414664i | \(-0.863899\pi\) | ||||
−0.909975 | + | 0.414664i | \(0.863899\pi\) | |||||||
\(54\) | −4.31065 | + | 2.90143i | −0.586605 | + | 0.394835i | ||||
\(55\) | −0.336117 | −0.0453220 | ||||||||
\(56\) | 1.02070 | 0.136397 | ||||||||
\(57\) | −4.51726 | − | 5.13924i | −0.598326 | − | 0.680709i | ||||
\(58\) | 2.20183 | 0.289114 | ||||||||
\(59\) | 2.53151i | 0.329574i | 0.986329 | + | 0.164787i | \(0.0526937\pi\) | ||||
−0.986329 | + | 0.164787i | \(0.947306\pi\) | |||||||
\(60\) | 1.30094 | − | 1.14349i | 0.167950 | − | 0.147624i | ||||
\(61\) | 12.9663i | 1.66016i | 0.557644 | + | 0.830080i | \(0.311705\pi\) | ||||
−0.557644 | + | 0.830080i | \(0.688295\pi\) | |||||||
\(62\) | − | 1.27271i | − | 0.161634i | ||||||
\(63\) | 3.03680 | + | 0.392835i | 0.382601 | + | 0.0494925i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.92792 | −0.611234 | ||||||||
\(66\) | 0.384346 | + | 0.437267i | 0.0473097 | + | 0.0538238i | ||||
\(67\) | 3.67460i | 0.448924i | 0.974483 | + | 0.224462i | \(0.0720625\pi\) | ||||
−0.974483 | + | 0.224462i | \(0.927938\pi\) | |||||||
\(68\) | 7.57164 | 0.918196 | ||||||||
\(69\) | 7.99667 | + | 2.24794i | 0.962686 | + | 0.270620i | ||||
\(70\) | −1.02070 | −0.121997 | ||||||||
\(71\) | − | 10.8426i | − | 1.28677i | −0.765541 | − | 0.643387i | \(-0.777529\pi\) | ||
0.765541 | − | 0.643387i | \(-0.222471\pi\) | |||||||
\(72\) | −2.97521 | − | 0.384868i | −0.350632 | − | 0.0453571i | ||||
\(73\) | −7.22073 | −0.845123 | −0.422561 | − | 0.906334i | \(-0.638869\pi\) | ||||
−0.422561 | + | 0.906334i | \(0.638869\pi\) | |||||||
\(74\) | 0.378822 | 0.0440372 | ||||||||
\(75\) | −1.30094 | + | 1.14349i | −0.150219 | + | 0.132039i | ||||
\(76\) | − | 3.95042i | − | 0.453144i | ||||||
\(77\) | − | 0.343075i | − | 0.0390970i | ||||||
\(78\) | 5.63502 | + | 6.41091i | 0.638041 | + | 0.725893i | ||||
\(79\) | 4.78248i | 0.538070i | 0.963130 | + | 0.269035i | \(0.0867048\pi\) | ||||
−0.963130 | + | 0.269035i | \(0.913295\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −8.70375 | − | 2.29012i | −0.967084 | − | 0.254458i | ||||
\(82\) | 7.82260 | 0.863862 | ||||||||
\(83\) | 16.0711 | 1.76403 | 0.882017 | − | 0.471218i | \(-0.156186\pi\) | ||||
0.882017 | + | 0.471218i | \(0.156186\pi\) | |||||||
\(84\) | 1.16716 | + | 1.32787i | 0.127348 | + | 0.144882i | ||||
\(85\) | −7.57164 | −0.821259 | ||||||||
\(86\) | 10.0534 | 1.08408 | ||||||||
\(87\) | 2.51776 | + | 2.86443i | 0.269933 | + | 0.307100i | ||||
\(88\) | 0.336117i | 0.0358302i | ||||||||
\(89\) | −14.1373 | −1.49855 | −0.749274 | − | 0.662260i | \(-0.769597\pi\) | ||||
−0.749274 | + | 0.662260i | \(0.769597\pi\) | |||||||
\(90\) | 2.97521 | + | 0.384868i | 0.313615 | + | 0.0405686i | ||||
\(91\) | − | 5.02994i | − | 0.527281i | ||||||
\(92\) | 2.61089 | + | 4.02284i | 0.272204 | + | 0.419410i | ||||
\(93\) | 1.65571 | − | 1.45533i | 0.171690 | − | 0.150911i | ||||
\(94\) | −5.34859 | −0.551665 | ||||||||
\(95\) | 3.95042i | 0.405305i | ||||||||
\(96\) | −1.14349 | − | 1.30094i | −0.116707 | − | 0.132776i | ||||
\(97\) | 11.6476i | 1.18263i | 0.806441 | + | 0.591315i | \(0.201391\pi\) | ||||
−0.806441 | + | 0.591315i | \(0.798609\pi\) | |||||||
\(98\) | 5.95817i | 0.601866i | ||||||||
\(99\) | −0.129361 | + | 1.00002i | −0.0130012 | + | 0.100506i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | − | 12.2651i | − | 1.22042i | −0.792239 | − | 0.610211i | \(-0.791085\pi\) | ||
0.792239 | − | 0.610211i | \(-0.208915\pi\) | |||||||
\(102\) | 8.65808 | + | 9.85021i | 0.857278 | + | 0.975316i | ||||
\(103\) | 6.63946i | 0.654206i | 0.944989 | + | 0.327103i | \(0.106072\pi\) | ||||
−0.944989 | + | 0.327103i | \(0.893928\pi\) | |||||||
\(104\) | 4.92792i | 0.483223i | ||||||||
\(105\) | −1.16716 | − | 1.32787i | −0.113903 | − | 0.129587i | ||||
\(106\) | − | 13.2494i | − | 1.28690i | ||||||
\(107\) | −8.84979 | −0.855541 | −0.427771 | − | 0.903887i | \(-0.640701\pi\) | ||||
−0.427771 | + | 0.903887i | \(0.640701\pi\) | |||||||
\(108\) | −2.90143 | − | 4.31065i | −0.279190 | − | 0.414792i | ||||
\(109\) | 13.4015i | 1.28363i | 0.766858 | + | 0.641817i | \(0.221819\pi\) | ||||
−0.766858 | + | 0.641817i | \(0.778181\pi\) | |||||||
\(110\) | − | 0.336117i | − | 0.0320475i | ||||||
\(111\) | 0.433179 | + | 0.492823i | 0.0411155 | + | 0.0467767i | ||||
\(112\) | 1.02070i | 0.0964472i | ||||||||
\(113\) | −1.71841 | −0.161655 | −0.0808274 | − | 0.996728i | \(-0.525756\pi\) | ||||
−0.0808274 | + | 0.996728i | \(0.525756\pi\) | |||||||
\(114\) | 5.13924 | − | 4.51726i | 0.481334 | − | 0.423080i | ||||
\(115\) | −2.61089 | − | 4.02284i | −0.243467 | − | 0.375132i | ||||
\(116\) | 2.20183i | 0.204434i | ||||||||
\(117\) | −1.89660 | + | 14.6616i | −0.175341 | + | 1.35547i | ||||
\(118\) | −2.53151 | −0.233044 | ||||||||
\(119\) | − | 7.72838i | − | 0.708460i | ||||||
\(120\) | 1.14349 | + | 1.30094i | 0.104386 | + | 0.118759i | ||||
\(121\) | −10.8870 | −0.989730 | ||||||||
\(122\) | −12.9663 | −1.17391 | ||||||||
\(123\) | 8.94506 | + | 10.1767i | 0.806549 | + | 0.917603i | ||||
\(124\) | 1.27271 | 0.114293 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.392835 | + | 3.03680i | −0.0349965 | + | 0.270540i | ||||
\(127\) | 17.6630 | 1.56733 | 0.783667 | − | 0.621181i | \(-0.213347\pi\) | ||||
0.783667 | + | 0.621181i | \(0.213347\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 11.4959 | + | 13.0788i | 1.01216 | + | 1.15153i | ||||
\(130\) | − | 4.92792i | − | 0.432207i | ||||||
\(131\) | 12.4875i | 1.09104i | 0.838098 | + | 0.545519i | \(0.183667\pi\) | ||||
−0.838098 | + | 0.545519i | \(0.816333\pi\) | |||||||
\(132\) | −0.437267 | + | 0.384346i | −0.0380592 | + | 0.0334530i | ||||
\(133\) | −4.03220 | −0.349636 | ||||||||
\(134\) | −3.67460 | −0.317437 | ||||||||
\(135\) | 2.90143 | + | 4.31065i | 0.249715 | + | 0.371002i | ||||
\(136\) | 7.57164i | 0.649263i | ||||||||
\(137\) | 0.245755 | 0.0209962 | 0.0104981 | − | 0.999945i | \(-0.496658\pi\) | ||||
0.0104981 | + | 0.999945i | \(0.496658\pi\) | |||||||
\(138\) | −2.24794 | + | 7.99667i | −0.191357 | + | 0.680722i | ||||
\(139\) | −5.22537 | −0.443210 | −0.221605 | − | 0.975137i | \(-0.571130\pi\) | ||||
−0.221605 | + | 0.975137i | \(0.571130\pi\) | |||||||
\(140\) | − | 1.02070i | − | 0.0862650i | ||||||
\(141\) | −6.11605 | − | 6.95817i | −0.515064 | − | 0.585984i | ||||
\(142\) | 10.8426 | 0.909887 | ||||||||
\(143\) | 1.65636 | 0.138512 | ||||||||
\(144\) | 0.384868 | − | 2.97521i | 0.0320723 | − | 0.247934i | ||||
\(145\) | − | 2.20183i | − | 0.182852i | ||||||
\(146\) | − | 7.22073i | − | 0.597592i | ||||||
\(147\) | −7.75119 | + | 6.81310i | −0.639308 | + | 0.561935i | ||||
\(148\) | 0.378822i | 0.0311390i | ||||||||
\(149\) | 3.43726 | 0.281591 | 0.140796 | − | 0.990039i | \(-0.455034\pi\) | ||||
0.140796 | + | 0.990039i | \(0.455034\pi\) | |||||||
\(150\) | −1.14349 | − | 1.30094i | −0.0933655 | − | 0.106221i | ||||
\(151\) | −19.8169 | −1.61268 | −0.806339 | − | 0.591454i | \(-0.798554\pi\) | ||||
−0.806339 | + | 0.591454i | \(0.798554\pi\) | |||||||
\(152\) | 3.95042 | 0.320421 | ||||||||
\(153\) | −2.91408 | + | 22.5272i | −0.235589 | + | 1.82122i | ||||
\(154\) | 0.343075 | 0.0276458 | ||||||||
\(155\) | −1.27271 | −0.102227 | ||||||||
\(156\) | −6.41091 | + | 5.63502i | −0.513284 | + | 0.451163i | ||||
\(157\) | 12.8500i | 1.02554i | 0.858525 | + | 0.512772i | \(0.171381\pi\) | ||||
−0.858525 | + | 0.512772i | \(0.828619\pi\) | |||||||
\(158\) | −4.78248 | −0.380473 | ||||||||
\(159\) | 17.2367 | − | 15.1506i | 1.36696 | − | 1.20152i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 4.10612 | − | 2.66494i | 0.323608 | − | 0.210026i | ||||
\(162\) | 2.29012 | − | 8.70375i | 0.179929 | − | 0.683831i | ||||
\(163\) | −7.48989 | −0.586654 | −0.293327 | − | 0.956012i | \(-0.594762\pi\) | ||||
−0.293327 | + | 0.956012i | \(0.594762\pi\) | |||||||
\(164\) | 7.82260i | 0.610843i | ||||||||
\(165\) | 0.437267 | − | 0.384346i | 0.0340412 | − | 0.0299213i | ||||
\(166\) | 16.0711i | 1.24736i | ||||||||
\(167\) | 10.1932i | 0.788776i | 0.918944 | + | 0.394388i | \(0.129043\pi\) | ||||
−0.918944 | + | 0.394388i | \(0.870957\pi\) | |||||||
\(168\) | −1.32787 | + | 1.16716i | −0.102447 | + | 0.0900484i | ||||
\(169\) | 11.2844 | 0.868033 | ||||||||
\(170\) | − | 7.57164i | − | 0.580718i | ||||||
\(171\) | 11.7533 | + | 1.52039i | 0.898800 | + | 0.116267i | ||||
\(172\) | 10.0534i | 0.766564i | ||||||||
\(173\) | − | 4.41012i | − | 0.335295i | −0.985847 | − | 0.167648i | \(-0.946383\pi\) | ||
0.985847 | − | 0.167648i | \(-0.0536171\pi\) | |||||||
\(174\) | −2.86443 | + | 2.51776i | −0.217152 | + | 0.190871i | ||||
\(175\) | 1.02070i | 0.0771578i | ||||||||
\(176\) | −0.336117 | −0.0253358 | ||||||||
\(177\) | −2.89475 | − | 3.29333i | −0.217583 | − | 0.247542i | ||||
\(178\) | − | 14.1373i | − | 1.05963i | ||||||
\(179\) | 7.99808i | 0.597804i | 0.954284 | + | 0.298902i | \(0.0966204\pi\) | ||||
−0.954284 | + | 0.298902i | \(0.903380\pi\) | |||||||
\(180\) | −0.384868 | + | 2.97521i | −0.0286863 | + | 0.221759i | ||||
\(181\) | − | 14.7941i | − | 1.09963i | −0.835285 | − | 0.549817i | \(-0.814698\pi\) | ||
0.835285 | − | 0.549817i | \(-0.185302\pi\) | |||||||
\(182\) | 5.02994 | 0.372844 | ||||||||
\(183\) | −14.8268 | − | 16.8683i | −1.09603 | − | 1.24694i | ||||
\(184\) | −4.02284 | + | 2.61089i | −0.296568 | + | 0.192477i | ||||
\(185\) | − | 0.378822i | − | 0.0278515i | ||||||
\(186\) | 1.45533 | + | 1.65571i | 0.106710 | + | 0.121403i | ||||
\(187\) | 2.54496 | 0.186106 | ||||||||
\(188\) | − | 5.34859i | − | 0.390086i | ||||||
\(189\) | −4.39989 | + | 2.96150i | −0.320045 | + | 0.215417i | ||||
\(190\) | −3.95042 | −0.286594 | ||||||||
\(191\) | −13.0642 | −0.945294 | −0.472647 | − | 0.881252i | \(-0.656701\pi\) | ||||
−0.472647 | + | 0.881252i | \(0.656701\pi\) | |||||||
\(192\) | 1.30094 | − | 1.14349i | 0.0938869 | − | 0.0825242i | ||||
\(193\) | −1.34388 | −0.0967343 | −0.0483672 | − | 0.998830i | \(-0.515402\pi\) | ||||
−0.0483672 | + | 0.998830i | \(0.515402\pi\) | |||||||
\(194\) | −11.6476 | −0.836245 | ||||||||
\(195\) | 6.41091 | − | 5.63502i | 0.459095 | − | 0.403532i | ||||
\(196\) | −5.95817 | −0.425583 | ||||||||
\(197\) | − | 6.30397i | − | 0.449139i | −0.974458 | − | 0.224570i | \(-0.927902\pi\) | ||
0.974458 | − | 0.224570i | \(-0.0720976\pi\) | |||||||
\(198\) | −1.00002 | − | 0.129361i | −0.0710683 | − | 0.00919325i | ||||
\(199\) | 7.67517i | 0.544078i | 0.962286 | + | 0.272039i | \(0.0876980\pi\) | ||||
−0.962286 | + | 0.272039i | \(0.912302\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | −4.20186 | − | 4.78042i | −0.296377 | − | 0.337185i | ||||
\(202\) | 12.2651 | 0.862969 | ||||||||
\(203\) | 2.24741 | 0.157737 | ||||||||
\(204\) | −9.85021 | + | 8.65808i | −0.689653 | + | 0.606187i | ||||
\(205\) | − | 7.82260i | − | 0.546354i | ||||||
\(206\) | −6.63946 | −0.462593 | ||||||||
\(207\) | −12.9737 | + | 6.21968i | −0.901731 | + | 0.432297i | ||||
\(208\) | −4.92792 | −0.341690 | ||||||||
\(209\) | − | 1.32780i | − | 0.0918461i | ||||||
\(210\) | 1.32787 | − | 1.16716i | 0.0916315 | − | 0.0805417i | ||||
\(211\) | 17.7592 | 1.22260 | 0.611298 | − | 0.791400i | \(-0.290648\pi\) | ||||
0.611298 | + | 0.791400i | \(0.290648\pi\) | |||||||
\(212\) | 13.2494 | 0.909975 | ||||||||
\(213\) | 12.3983 | + | 14.1055i | 0.849520 | + | 0.966490i | ||||
\(214\) | − | 8.84979i | − | 0.604959i | ||||||
\(215\) | − | 10.0534i | − | 0.685635i | ||||||
\(216\) | 4.31065 | − | 2.90143i | 0.293303 | − | 0.197417i | ||||
\(217\) | − | 1.29906i | − | 0.0881858i | ||||||
\(218\) | −13.4015 | −0.907667 | ||||||||
\(219\) | 9.39371 | − | 8.25682i | 0.634768 | − | 0.557945i | ||||
\(220\) | 0.336117 | 0.0226610 | ||||||||
\(221\) | 37.3124 | 2.50991 | ||||||||
\(222\) | −0.492823 | + | 0.433179i | −0.0330761 | + | 0.0290730i | ||||
\(223\) | −2.68511 | −0.179808 | −0.0899042 | − | 0.995950i | \(-0.528656\pi\) | ||||
−0.0899042 | + | 0.995950i | \(0.528656\pi\) | |||||||
\(224\) | −1.02070 | −0.0681985 | ||||||||
\(225\) | 0.384868 | − | 2.97521i | 0.0256578 | − | 0.198347i | ||||
\(226\) | − | 1.71841i | − | 0.114307i | ||||||
\(227\) | 4.16668 | 0.276552 | 0.138276 | − | 0.990394i | \(-0.455844\pi\) | ||||
0.138276 | + | 0.990394i | \(0.455844\pi\) | |||||||
\(228\) | 4.51726 | + | 5.13924i | 0.299163 | + | 0.340355i | ||||
\(229\) | − | 9.82184i | − | 0.649045i | −0.945878 | − | 0.324523i | \(-0.894796\pi\) | ||
0.945878 | − | 0.324523i | \(-0.105204\pi\) | |||||||
\(230\) | 4.02284 | − | 2.61089i | 0.265258 | − | 0.172157i | ||||
\(231\) | 0.392303 | + | 0.446319i | 0.0258116 | + | 0.0293656i | ||||
\(232\) | −2.20183 | −0.144557 | ||||||||
\(233\) | 20.4118i | 1.33722i | 0.743613 | + | 0.668610i | \(0.233110\pi\) | ||||
−0.743613 | + | 0.668610i | \(0.766890\pi\) | |||||||
\(234\) | −14.6616 | − | 1.89660i | −0.958459 | − | 0.123984i | ||||
\(235\) | 5.34859i | 0.348903i | ||||||||
\(236\) | − | 2.53151i | − | 0.164787i | ||||||
\(237\) | −5.46871 | − | 6.22169i | −0.355231 | − | 0.404142i | ||||
\(238\) | 7.72838 | 0.500957 | ||||||||
\(239\) | 8.99553i | 0.581873i | 0.956742 | + | 0.290936i | \(0.0939668\pi\) | ||||
−0.956742 | + | 0.290936i | \(0.906033\pi\) | |||||||
\(240\) | −1.30094 | + | 1.14349i | −0.0839750 | + | 0.0738119i | ||||
\(241\) | − | 9.97182i | − | 0.642341i | −0.947021 | − | 0.321171i | \(-0.895924\pi\) | ||
0.947021 | − | 0.321171i | \(-0.104076\pi\) | |||||||
\(242\) | − | 10.8870i | − | 0.699844i | ||||||
\(243\) | 13.9418 | − | 6.97334i | 0.894364 | − | 0.447340i | ||||
\(244\) | − | 12.9663i | − | 0.830080i | ||||||
\(245\) | 5.95817 | 0.380653 | ||||||||
\(246\) | −10.1767 | + | 8.94506i | −0.648843 | + | 0.570316i | ||||
\(247\) | − | 19.4674i | − | 1.23868i | ||||||
\(248\) | 1.27271i | 0.0808172i | ||||||||
\(249\) | −20.9075 | + | 18.3771i | −1.32496 | + | 1.16460i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | 13.0633 | 0.824550 | 0.412275 | − | 0.911059i | \(-0.364734\pi\) | ||||
0.412275 | + | 0.911059i | \(0.364734\pi\) | |||||||
\(252\) | −3.03680 | − | 0.392835i | −0.191301 | − | 0.0247463i | ||||
\(253\) | 0.877564 | + | 1.35215i | 0.0551720 | + | 0.0850087i | ||||
\(254\) | 17.6630i | 1.10827i | ||||||||
\(255\) | 9.85021 | − | 8.65808i | 0.616844 | − | 0.542190i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.77735i | − | 0.298003i | −0.988837 | − | 0.149001i | \(-0.952394\pi\) | ||
0.988837 | − | 0.149001i | \(-0.0476059\pi\) | |||||||
\(258\) | −13.0788 | + | 11.4959i | −0.814251 | + | 0.715706i | ||||
\(259\) | 0.386664 | 0.0240261 | ||||||||
\(260\) | 4.92792 | 0.305617 | ||||||||
\(261\) | −6.55090 | − | 0.847412i | −0.405490 | − | 0.0524535i | ||||
\(262\) | −12.4875 | −0.771480 | ||||||||
\(263\) | 3.18728 | 0.196536 | 0.0982680 | − | 0.995160i | \(-0.468670\pi\) | ||||
0.0982680 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(264\) | −0.384346 | − | 0.437267i | −0.0236549 | − | 0.0269119i | ||||
\(265\) | −13.2494 | −0.813906 | ||||||||
\(266\) | − | 4.03220i | − | 0.247230i | ||||||
\(267\) | 18.3917 | − | 16.1658i | 1.12555 | − | 0.989331i | ||||
\(268\) | − | 3.67460i | − | 0.224462i | ||||||
\(269\) | − | 6.77166i | − | 0.412876i | −0.978460 | − | 0.206438i | \(-0.933813\pi\) | ||
0.978460 | − | 0.206438i | \(-0.0661871\pi\) | |||||||
\(270\) | −4.31065 | + | 2.90143i | −0.262338 | + | 0.176575i | ||||
\(271\) | −6.43609 | −0.390965 | −0.195482 | − | 0.980707i | \(-0.562627\pi\) | ||||
−0.195482 | + | 0.980707i | \(0.562627\pi\) | |||||||
\(272\) | −7.57164 | −0.459098 | ||||||||
\(273\) | 5.75168 | + | 6.54363i | 0.348107 | + | 0.396038i | ||||
\(274\) | 0.245755i | 0.0148466i | ||||||||
\(275\) | −0.336117 | −0.0202686 | ||||||||
\(276\) | −7.99667 | − | 2.24794i | −0.481343 | − | 0.135310i | ||||
\(277\) | 4.47192 | 0.268692 | 0.134346 | − | 0.990934i | \(-0.457107\pi\) | ||||
0.134346 | + | 0.990934i | \(0.457107\pi\) | |||||||
\(278\) | − | 5.22537i | − | 0.313397i | ||||||
\(279\) | −0.489825 | + | 3.78658i | −0.0293251 | + | 0.226697i | ||||
\(280\) | 1.02070 | 0.0609986 | ||||||||
\(281\) | −30.8476 | −1.84021 | −0.920106 | − | 0.391669i | \(-0.871898\pi\) | ||||
−0.920106 | + | 0.391669i | \(0.871898\pi\) | |||||||
\(282\) | 6.95817 | − | 6.11605i | 0.414353 | − | 0.364205i | ||||
\(283\) | 12.4633i | 0.740868i | 0.928859 | + | 0.370434i | \(0.120791\pi\) | ||||
−0.928859 | + | 0.370434i | \(0.879209\pi\) | |||||||
\(284\) | 10.8426i | 0.643387i | ||||||||
\(285\) | −4.51726 | − | 5.13924i | −0.267579 | − | 0.304423i | ||||
\(286\) | 1.65636i | 0.0979426i | ||||||||
\(287\) | 7.98454 | 0.471313 | ||||||||
\(288\) | 2.97521 | + | 0.384868i | 0.175316 | + | 0.0226785i | ||||
\(289\) | 40.3297 | 2.37233 | ||||||||
\(290\) | 2.20183 | 0.129296 | ||||||||
\(291\) | −13.3188 | − | 15.1527i | −0.780764 | − | 0.888268i | ||||
\(292\) | 7.22073 | 0.422561 | ||||||||
\(293\) | 12.9662 | 0.757491 | 0.378745 | − | 0.925501i | \(-0.376356\pi\) | ||||
0.378745 | + | 0.925501i | \(0.376356\pi\) | |||||||
\(294\) | −6.81310 | − | 7.75119i | −0.397348 | − | 0.452059i | ||||
\(295\) | 2.53151i | 0.147390i | ||||||||
\(296\) | −0.378822 | −0.0220186 | ||||||||
\(297\) | −0.975221 | − | 1.44888i | −0.0565880 | − | 0.0840727i | ||||
\(298\) | 3.43726i | 0.199115i | ||||||||
\(299\) | 12.8663 | + | 19.8243i | 0.744075 | + | 1.14647i | ||||
\(300\) | 1.30094 | − | 1.14349i | 0.0751096 | − | 0.0660193i | ||||
\(301\) | 10.2615 | 0.591464 | ||||||||
\(302\) | − | 19.8169i | − | 1.14034i | ||||||
\(303\) | 14.0250 | + | 15.9561i | 0.805715 | + | 0.916654i | ||||
\(304\) | 3.95042i | 0.226572i | ||||||||
\(305\) | 12.9663i | 0.742446i | ||||||||
\(306\) | −22.5272 | − | 2.91408i | −1.28780 | − | 0.166587i | ||||
\(307\) | −24.4391 | −1.39481 | −0.697406 | − | 0.716676i | \(-0.745663\pi\) | ||||
−0.697406 | + | 0.716676i | \(0.745663\pi\) | |||||||
\(308\) | 0.343075i | 0.0195485i | ||||||||
\(309\) | −7.59215 | − | 8.63752i | −0.431902 | − | 0.491371i | ||||
\(310\) | − | 1.27271i | − | 0.0722851i | ||||||
\(311\) | 20.4152i | 1.15764i | 0.815455 | + | 0.578820i | \(0.196487\pi\) | ||||
−0.815455 | + | 0.578820i | \(0.803513\pi\) | |||||||
\(312\) | −5.63502 | − | 6.41091i | −0.319020 | − | 0.362946i | ||||
\(313\) | − | 27.4387i | − | 1.55093i | −0.631392 | − | 0.775464i | \(-0.717516\pi\) | ||
0.631392 | − | 0.775464i | \(-0.282484\pi\) | |||||||
\(314\) | −12.8500 | −0.725169 | ||||||||
\(315\) | 3.03680 | + | 0.392835i | 0.171104 | + | 0.0221337i | ||||
\(316\) | − | 4.78248i | − | 0.269035i | ||||||
\(317\) | 2.34160i | 0.131517i | 0.997836 | + | 0.0657587i | \(0.0209468\pi\) | ||||
−0.997836 | + | 0.0657587i | \(0.979053\pi\) | |||||||
\(318\) | 15.1506 | + | 17.2367i | 0.849602 | + | 0.966584i | ||||
\(319\) | 0.740072i | 0.0414361i | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 11.5130 | − | 10.1196i | 0.642593 | − | 0.564823i | ||||
\(322\) | 2.66494 | + | 4.10612i | 0.148511 | + | 0.228825i | ||||
\(323\) | − | 29.9112i | − | 1.66430i | ||||||
\(324\) | 8.70375 | + | 2.29012i | 0.483542 | + | 0.127229i | ||||
\(325\) | −4.92792 | −0.273352 | ||||||||
\(326\) | − | 7.48989i | − | 0.414827i | ||||||
\(327\) | −15.3245 | − | 17.4345i | −0.847447 | − | 0.964132i | ||||
\(328\) | −7.82260 | −0.431931 | ||||||||
\(329\) | −5.45931 | −0.300982 | ||||||||
\(330\) | 0.384346 | + | 0.437267i | 0.0211576 | + | 0.0240707i | ||||
\(331\) | 27.4881 | 1.51088 | 0.755442 | − | 0.655216i | \(-0.227422\pi\) | ||||
0.755442 | + | 0.655216i | \(0.227422\pi\) | |||||||
\(332\) | −16.0711 | −0.882017 | ||||||||
\(333\) | −1.12708 | − | 0.145796i | −0.0617633 | − | 0.00798959i | ||||
\(334\) | −10.1932 | −0.557749 | ||||||||
\(335\) | 3.67460i | 0.200765i | ||||||||
\(336\) | −1.16716 | − | 1.32787i | −0.0636738 | − | 0.0724411i | ||||
\(337\) | 22.1863i | 1.20857i | 0.796770 | + | 0.604283i | \(0.206540\pi\) | ||||
−0.796770 | + | 0.604283i | \(0.793460\pi\) | |||||||
\(338\) | 11.2844i | 0.613792i | ||||||||
\(339\) | 2.23555 | − | 1.96499i | 0.121418 | − | 0.106723i | ||||
\(340\) | 7.57164 | 0.410630 | ||||||||
\(341\) | 0.427780 | 0.0231656 | ||||||||
\(342\) | −1.52039 | + | 11.7533i | −0.0822132 | + | 0.635547i | ||||
\(343\) | 13.2264i | 0.714160i | ||||||||
\(344\) | −10.0534 | −0.542042 | ||||||||
\(345\) | 7.99667 | + | 2.24794i | 0.430526 | + | 0.121025i | ||||
\(346\) | 4.41012 | 0.237090 | ||||||||
\(347\) | 24.4010i | 1.30992i | 0.755665 | + | 0.654958i | \(0.227314\pi\) | ||||
−0.755665 | + | 0.654958i | \(0.772686\pi\) | |||||||
\(348\) | −2.51776 | − | 2.86443i | −0.134966 | − | 0.153550i | ||||
\(349\) | −11.9864 | −0.641618 | −0.320809 | − | 0.947144i | \(-0.603955\pi\) | ||||
−0.320809 | + | 0.947144i | \(0.603955\pi\) | |||||||
\(350\) | −1.02070 | −0.0545588 | ||||||||
\(351\) | −14.2980 | − | 21.2425i | −0.763172 | − | 1.13384i | ||||
\(352\) | − | 0.336117i | − | 0.0179151i | ||||||
\(353\) | − | 22.4575i | − | 1.19529i | −0.801761 | − | 0.597645i | \(-0.796103\pi\) | ||
0.801761 | − | 0.597645i | \(-0.203897\pi\) | |||||||
\(354\) | 3.29333 | − | 2.89475i | 0.175039 | − | 0.153854i | ||||
\(355\) | − | 10.8426i | − | 0.575463i | ||||||
\(356\) | 14.1373 | 0.749274 | ||||||||
\(357\) | 8.83732 | + | 10.0541i | 0.467720 | + | 0.532121i | ||||
\(358\) | −7.99808 | −0.422712 | ||||||||
\(359\) | 10.4831 | 0.553277 | 0.276638 | − | 0.960974i | \(-0.410780\pi\) | ||||
0.276638 | + | 0.960974i | \(0.410780\pi\) | |||||||
\(360\) | −2.97521 | − | 0.384868i | −0.156807 | − | 0.0202843i | ||||
\(361\) | 3.39418 | 0.178641 | ||||||||
\(362\) | 14.7941 | 0.777558 | ||||||||
\(363\) | 14.1633 | − | 12.4492i | 0.743382 | − | 0.653413i | ||||
\(364\) | 5.02994i | 0.263640i | ||||||||
\(365\) | −7.22073 | −0.377950 | ||||||||
\(366\) | 16.8683 | − | 14.8268i | 0.881719 | − | 0.775008i | ||||
\(367\) | − | 22.8694i | − | 1.19377i | −0.802326 | − | 0.596886i | \(-0.796404\pi\) | ||
0.802326 | − | 0.596886i | \(-0.203596\pi\) | |||||||
\(368\) | −2.61089 | − | 4.02284i | −0.136102 | − | 0.209705i | ||||
\(369\) | −23.2739 | − | 3.01067i | −1.21159 | − | 0.156729i | ||||
\(370\) | 0.378822 | 0.0196940 | ||||||||
\(371\) | − | 13.5237i | − | 0.702116i | ||||||
\(372\) | −1.65571 | + | 1.45533i | −0.0858448 | + | 0.0754554i | ||||
\(373\) | − | 5.47431i | − | 0.283449i | −0.989906 | − | 0.141725i | \(-0.954735\pi\) | ||
0.989906 | − | 0.141725i | \(-0.0452647\pi\) | |||||||
\(374\) | 2.54496i | 0.131597i | ||||||||
\(375\) | −1.30094 | + | 1.14349i | −0.0671800 | + | 0.0590495i | ||||
\(376\) | 5.34859 | 0.275832 | ||||||||
\(377\) | 10.8504i | 0.558826i | ||||||||
\(378\) | −2.96150 | − | 4.39989i | −0.152323 | − | 0.226306i | ||||
\(379\) | − | 30.3390i | − | 1.55841i | −0.626768 | − | 0.779206i | \(-0.715623\pi\) | ||
0.626768 | − | 0.779206i | \(-0.284377\pi\) | |||||||
\(380\) | − | 3.95042i | − | 0.202652i | ||||||
\(381\) | −22.9784 | + | 20.1974i | −1.17722 | + | 1.03474i | ||||
\(382\) | − | 13.0642i | − | 0.668424i | ||||||
\(383\) | 14.8764 | 0.760149 | 0.380075 | − | 0.924956i | \(-0.375898\pi\) | ||||
0.380075 | + | 0.924956i | \(0.375898\pi\) | |||||||
\(384\) | 1.14349 | + | 1.30094i | 0.0583534 | + | 0.0663881i | ||||
\(385\) | − | 0.343075i | − | 0.0174847i | ||||||
\(386\) | − | 1.34388i | − | 0.0684015i | ||||||
\(387\) | −29.9110 | − | 3.86922i | −1.52046 | − | 0.196684i | ||||
\(388\) | − | 11.6476i | − | 0.591315i | ||||||
\(389\) | 12.5719 | 0.637422 | 0.318711 | − | 0.947852i | \(-0.396750\pi\) | ||||
0.318711 | + | 0.947852i | \(0.396750\pi\) | |||||||
\(390\) | 5.63502 | + | 6.41091i | 0.285341 | + | 0.324629i | ||||
\(391\) | 19.7687 | + | 30.4595i | 0.999746 | + | 1.54040i | ||||
\(392\) | − | 5.95817i | − | 0.300933i | ||||||
\(393\) | −14.2793 | − | 16.2454i | −0.720296 | − | 0.819474i | ||||
\(394\) | 6.30397 | 0.317589 | ||||||||
\(395\) | 4.78248i | 0.240632i | ||||||||
\(396\) | 0.129361 | − | 1.00002i | 0.00650061 | − | 0.0502528i | ||||
\(397\) | 24.1720 | 1.21316 | 0.606579 | − | 0.795023i | \(-0.292542\pi\) | ||||
0.606579 | + | 0.795023i | \(0.292542\pi\) | |||||||
\(398\) | −7.67517 | −0.384721 | ||||||||
\(399\) | 5.24563 | − | 4.61078i | 0.262610 | − | 0.230827i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −21.4707 | −1.07220 | −0.536098 | − | 0.844155i | \(-0.680102\pi\) | ||||
−0.536098 | + | 0.844155i | \(0.680102\pi\) | |||||||
\(402\) | 4.78042 | − | 4.20186i | 0.238426 | − | 0.209570i | ||||
\(403\) | 6.27182 | 0.312422 | ||||||||
\(404\) | 12.2651i | 0.610211i | ||||||||
\(405\) | −8.70375 | − | 2.29012i | −0.432493 | − | 0.113797i | ||||
\(406\) | 2.24741i | 0.111537i | ||||||||
\(407\) | 0.127329i | 0.00631144i | ||||||||
\(408\) | −8.65808 | − | 9.85021i | −0.428639 | − | 0.487658i | ||||
\(409\) | −13.5579 | −0.670397 | −0.335198 | − | 0.942148i | \(-0.608803\pi\) | ||||
−0.335198 | + | 0.942148i | \(0.608803\pi\) | |||||||
\(410\) | 7.82260 | 0.386331 | ||||||||
\(411\) | −0.319711 | + | 0.281018i | −0.0157702 | + | 0.0138616i | ||||
\(412\) | − | 6.63946i | − | 0.327103i | ||||||
\(413\) | −2.58391 | −0.127146 | ||||||||
\(414\) | −6.21968 | − | 12.9737i | −0.305680 | − | 0.637620i | ||||
\(415\) | 16.0711 | 0.788900 | ||||||||
\(416\) | − | 4.92792i | − | 0.241611i | ||||||
\(417\) | 6.79787 | − | 5.97515i | 0.332893 | − | 0.292604i | ||||
\(418\) | 1.32780 | 0.0649450 | ||||||||
\(419\) | 3.19459 | 0.156066 | 0.0780330 | − | 0.996951i | \(-0.475136\pi\) | ||||
0.0780330 | + | 0.996951i | \(0.475136\pi\) | |||||||
\(420\) | 1.16716 | + | 1.32787i | 0.0569516 | + | 0.0647933i | ||||
\(421\) | 23.8342i | 1.16161i | 0.814043 | + | 0.580805i | \(0.197262\pi\) | ||||
−0.814043 | + | 0.580805i | \(0.802738\pi\) | |||||||
\(422\) | 17.7592i | 0.864506i | ||||||||
\(423\) | 15.9132 | + | 2.05850i | 0.773725 | + | 0.100088i | ||||
\(424\) | 13.2494i | 0.643449i | ||||||||
\(425\) | −7.57164 | −0.367278 | ||||||||
\(426\) | −14.1055 | + | 12.3983i | −0.683412 | + | 0.600701i | ||||
\(427\) | −13.2347 | −0.640471 | ||||||||
\(428\) | 8.84979 | 0.427771 | ||||||||
\(429\) | −2.15482 | + | 1.89403i | −0.104036 | + | 0.0914445i | ||||
\(430\) | 10.0534 | 0.484818 | ||||||||
\(431\) | −14.0920 | −0.678787 | −0.339394 | − | 0.940644i | \(-0.610222\pi\) | ||||
−0.339394 | + | 0.940644i | \(0.610222\pi\) | |||||||
\(432\) | 2.90143 | + | 4.31065i | 0.139595 | + | 0.207396i | ||||
\(433\) | − | 24.3424i | − | 1.16982i | −0.811098 | − | 0.584910i | \(-0.801130\pi\) | ||
0.811098 | − | 0.584910i | \(-0.198870\pi\) | |||||||
\(434\) | 1.29906 | 0.0623568 | ||||||||
\(435\) | 2.51776 | + | 2.86443i | 0.120718 | + | 0.137339i | ||||
\(436\) | − | 13.4015i | − | 0.641817i | ||||||
\(437\) | 15.8919 | − | 10.3141i | 0.760214 | − | 0.493391i | ||||
\(438\) | 8.25682 | + | 9.39371i | 0.394526 | + | 0.448849i | ||||
\(439\) | −1.40497 | −0.0670555 | −0.0335277 | − | 0.999438i | \(-0.510674\pi\) | ||||
−0.0335277 | + | 0.999438i | \(0.510674\pi\) | |||||||
\(440\) | 0.336117i | 0.0160238i | ||||||||
\(441\) | 2.29311 | − | 17.7268i | 0.109196 | − | 0.844134i | ||||
\(442\) | 37.3124i | 1.77477i | ||||||||
\(443\) | − | 39.5844i | − | 1.88071i | −0.340195 | − | 0.940355i | \(-0.610493\pi\) | ||
0.340195 | − | 0.940355i | \(-0.389507\pi\) | |||||||
\(444\) | −0.433179 | − | 0.492823i | −0.0205577 | − | 0.0233883i | ||||
\(445\) | −14.1373 | −0.670171 | ||||||||
\(446\) | − | 2.68511i | − | 0.127144i | ||||||
\(447\) | −4.47165 | + | 3.93047i | −0.211502 | + | 0.185905i | ||||
\(448\) | − | 1.02070i | − | 0.0482236i | ||||||
\(449\) | − | 29.0379i | − | 1.37038i | −0.728364 | − | 0.685191i | \(-0.759719\pi\) | ||
0.728364 | − | 0.685191i | \(-0.240281\pi\) | |||||||
\(450\) | 2.97521 | + | 0.384868i | 0.140253 | + | 0.0181428i | ||||
\(451\) | 2.62931i | 0.123809i | ||||||||
\(452\) | 1.71841 | 0.0808274 | ||||||||
\(453\) | 25.7805 | − | 22.6604i | 1.21128 | − | 1.06468i | ||||
\(454\) | 4.16668i | 0.195552i | ||||||||
\(455\) | − | 5.02994i | − | 0.235807i | ||||||
\(456\) | −5.13924 | + | 4.51726i | −0.240667 | + | 0.211540i | ||||
\(457\) | − | 35.5772i | − | 1.66423i | −0.554603 | − | 0.832115i | \(-0.687130\pi\) | ||
0.554603 | − | 0.832115i | \(-0.312870\pi\) | |||||||
\(458\) | 9.82184 | 0.458944 | ||||||||
\(459\) | −21.9686 | − | 32.6387i | −1.02541 | − | 1.52344i | ||||
\(460\) | 2.61089 | + | 4.02284i | 0.121733 | + | 0.187566i | ||||
\(461\) | 29.4329i | 1.37083i | 0.728153 | + | 0.685415i | \(0.240379\pi\) | ||||
−0.728153 | + | 0.685415i | \(0.759621\pi\) | |||||||
\(462\) | −0.446319 | + | 0.392303i | −0.0207646 | + | 0.0182516i | ||||
\(463\) | −12.4050 | −0.576508 | −0.288254 | − | 0.957554i | \(-0.593075\pi\) | ||||
−0.288254 | + | 0.957554i | \(0.593075\pi\) | |||||||
\(464\) | − | 2.20183i | − | 0.102217i | ||||||
\(465\) | 1.65571 | − | 1.45533i | 0.0767819 | − | 0.0674893i | ||||
\(466\) | −20.4118 | −0.945557 | ||||||||
\(467\) | −37.4350 | −1.73229 | −0.866143 | − | 0.499796i | \(-0.833408\pi\) | ||||
−0.866143 | + | 0.499796i | \(0.833408\pi\) | |||||||
\(468\) | 1.89660 | − | 14.6616i | 0.0876703 | − | 0.677733i | ||||
\(469\) | −3.75067 | −0.173190 | ||||||||
\(470\) | −5.34859 | −0.246712 | ||||||||
\(471\) | −14.6939 | − | 16.7171i | −0.677057 | − | 0.770281i | ||||
\(472\) | 2.53151 | 0.116522 | ||||||||
\(473\) | 3.37912i | 0.155372i | ||||||||
\(474\) | 6.22169 | − | 5.46871i | 0.285772 | − | 0.251186i | ||||
\(475\) | 3.95042i | 0.181258i | ||||||||
\(476\) | 7.72838i | 0.354230i | ||||||||
\(477\) | −5.09927 | + | 39.4198i | −0.233480 | + | 1.80491i | ||||
\(478\) | −8.99553 | −0.411446 | ||||||||
\(479\) | −18.9516 | −0.865920 | −0.432960 | − | 0.901413i | \(-0.642531\pi\) | ||||
−0.432960 | + | 0.901413i | \(0.642531\pi\) | |||||||
\(480\) | −1.14349 | − | 1.30094i | −0.0521929 | − | 0.0593793i | ||||
\(481\) | 1.86681i | 0.0851190i | ||||||||
\(482\) | 9.97182 | 0.454204 | ||||||||
\(483\) | −2.29448 | + | 8.16221i | −0.104402 | + | 0.371394i | ||||
\(484\) | 10.8870 | 0.494865 | ||||||||
\(485\) | 11.6476i | 0.528888i | ||||||||
\(486\) | 6.97334 | + | 13.9418i | 0.316317 | + | 0.632411i | ||||
\(487\) | −41.8360 | −1.89577 | −0.947885 | − | 0.318612i | \(-0.896783\pi\) | ||||
−0.947885 | + | 0.318612i | \(0.896783\pi\) | |||||||
\(488\) | 12.9663 | 0.586955 | ||||||||
\(489\) | 9.74387 | − | 8.56461i | 0.440633 | − | 0.387305i | ||||
\(490\) | 5.95817i | 0.269163i | ||||||||
\(491\) | 35.6738i | 1.60994i | 0.593318 | + | 0.804968i | \(0.297818\pi\) | ||||
−0.593318 | + | 0.804968i | \(0.702182\pi\) | |||||||
\(492\) | −8.94506 | − | 10.1767i | −0.403274 | − | 0.458801i | ||||
\(493\) | 16.6714i | 0.750844i | ||||||||
\(494\) | 19.4674 | 0.875878 | ||||||||
\(495\) | −0.129361 | + | 1.00002i | −0.00581432 | + | 0.0449475i | ||||
\(496\) | −1.27271 | −0.0571464 | ||||||||
\(497\) | 11.0670 | 0.496423 | ||||||||
\(498\) | −18.3771 | − | 20.9075i | −0.823499 | − | 0.936887i | ||||
\(499\) | 3.39015 | 0.151764 | 0.0758821 | − | 0.997117i | \(-0.475823\pi\) | ||||
0.0758821 | + | 0.997117i | \(0.475823\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −11.6558 | − | 13.2607i | −0.520745 | − | 0.592446i | ||||
\(502\) | 13.0633i | 0.583045i | ||||||||
\(503\) | 2.86791 | 0.127874 | 0.0639369 | − | 0.997954i | \(-0.479634\pi\) | ||||
0.0639369 | + | 0.997954i | \(0.479634\pi\) | |||||||
\(504\) | 0.392835 | − | 3.03680i | 0.0174983 | − | 0.135270i | ||||
\(505\) | − | 12.2651i | − | 0.545790i | ||||||
\(506\) | −1.35215 | + | 0.877564i | −0.0601102 | + | 0.0390125i | ||||
\(507\) | −14.6803 | + | 12.9036i | −0.651976 | + | 0.573070i | ||||
\(508\) | −17.6630 | −0.783667 | ||||||||
\(509\) | − | 4.03161i | − | 0.178698i | −0.996000 | − | 0.0893491i | \(-0.971521\pi\) | ||
0.996000 | − | 0.0893491i | \(-0.0284787\pi\) | |||||||
\(510\) | 8.65808 | + | 9.85021i | 0.383386 | + | 0.436175i | ||||
\(511\) | − | 7.37021i | − | 0.326039i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −17.0289 | + | 11.4619i | −0.751843 | + | 0.506054i | ||||
\(514\) | 4.77735 | 0.210720 | ||||||||
\(515\) | 6.63946i | 0.292570i | ||||||||
\(516\) | −11.4959 | − | 13.0788i | −0.506080 | − | 0.575763i | ||||
\(517\) | − | 1.79775i | − | 0.0790650i | ||||||
\(518\) | 0.386664i | 0.0169890i | ||||||||
\(519\) | 5.04292 | + | 5.73728i | 0.221360 | + | 0.251839i | ||||
\(520\) | 4.92792i | 0.216104i | ||||||||
\(521\) | 14.2955 | 0.626296 | 0.313148 | − | 0.949704i | \(-0.398616\pi\) | ||||
0.313148 | + | 0.949704i | \(0.398616\pi\) | |||||||
\(522\) | 0.847412 | − | 6.55090i | 0.0370902 | − | 0.286725i | ||||
\(523\) | 8.12221i | 0.355159i | 0.984106 | + | 0.177580i | \(0.0568267\pi\) | ||||
−0.984106 | + | 0.177580i | \(0.943173\pi\) | |||||||
\(524\) | − | 12.4875i | − | 0.545519i | ||||||
\(525\) | −1.16716 | − | 1.32787i | −0.0509391 | − | 0.0579529i | ||||
\(526\) | 3.18728i | 0.138972i | ||||||||
\(527\) | 9.63650 | 0.419773 | ||||||||
\(528\) | 0.437267 | − | 0.384346i | 0.0190296 | − | 0.0167265i | ||||
\(529\) | −9.36653 | + | 21.0064i | −0.407241 | + | 0.913321i | ||||
\(530\) | − | 13.2494i | − | 0.575518i | ||||||
\(531\) | 7.53177 | + | 0.974295i | 0.326851 | + | 0.0422808i | ||||
\(532\) | 4.03220 | 0.174818 | ||||||||
\(533\) | 38.5492i | 1.66975i | ||||||||
\(534\) | 16.1658 | + | 18.3917i | 0.699563 | + | 0.795886i | ||||
\(535\) | −8.84979 | −0.382610 | ||||||||
\(536\) | 3.67460 | 0.158719 | ||||||||
\(537\) | −9.14571 | − | 10.4050i | −0.394667 | − | 0.449008i | ||||
\(538\) | 6.77166 | 0.291947 | ||||||||
\(539\) | −2.00264 | −0.0862599 | ||||||||
\(540\) | −2.90143 | − | 4.31065i | −0.124858 | − | 0.185501i | ||||
\(541\) | −1.95561 | −0.0840783 | −0.0420391 | − | 0.999116i | \(-0.513385\pi\) | ||||
−0.0420391 | + | 0.999116i | \(0.513385\pi\) | |||||||
\(542\) | − | 6.43609i | − | 0.276454i | ||||||
\(543\) | 16.9168 | + | 19.2461i | 0.725971 | + | 0.825930i | ||||
\(544\) | − | 7.57164i | − | 0.324631i | ||||||
\(545\) | 13.4015i | 0.574059i | ||||||||
\(546\) | −6.54363 | + | 5.75168i | −0.280041 | + | 0.246149i | ||||
\(547\) | 33.2009 | 1.41957 | 0.709784 | − | 0.704420i | \(-0.248793\pi\) | ||||
0.709784 | + | 0.704420i | \(0.248793\pi\) | |||||||
\(548\) | −0.245755 | −0.0104981 | ||||||||
\(549\) | 38.5774 | + | 4.99029i | 1.64644 | + | 0.212981i | ||||
\(550\) | − | 0.336117i | − | 0.0143321i | ||||||
\(551\) | 8.69814 | 0.370553 | ||||||||
\(552\) | 2.24794 | − | 7.99667i | 0.0956787 | − | 0.340361i | ||||
\(553\) | −4.88148 | −0.207582 | ||||||||
\(554\) | 4.47192i | 0.189994i | ||||||||
\(555\) | 0.433179 | + | 0.492823i | 0.0183874 | + | 0.0209192i | ||||
\(556\) | 5.22537 | 0.221605 | ||||||||
\(557\) | −5.11839 | −0.216873 | −0.108437 | − | 0.994103i | \(-0.534584\pi\) | ||||
−0.108437 | + | 0.994103i | \(0.534584\pi\) | |||||||
\(558\) | −3.78658 | − | 0.489825i | −0.160299 | − | 0.0207359i | ||||
\(559\) | 49.5423i | 2.09542i | ||||||||
\(560\) | 1.02070i | 0.0431325i | ||||||||
\(561\) | −3.31082 | + | 2.91013i | −0.139783 | + | 0.122866i | ||||
\(562\) | − | 30.8476i | − | 1.30123i | ||||||
\(563\) | 34.6454 | 1.46013 | 0.730065 | − | 0.683378i | \(-0.239490\pi\) | ||||
0.730065 | + | 0.683378i | \(0.239490\pi\) | |||||||
\(564\) | 6.11605 | + | 6.95817i | 0.257532 | + | 0.292992i | ||||
\(565\) | −1.71841 | −0.0722943 | ||||||||
\(566\) | −12.4633 | −0.523873 | ||||||||
\(567\) | 2.33753 | − | 8.88393i | 0.0981671 | − | 0.373090i | ||||
\(568\) | −10.8426 | −0.454943 | ||||||||
\(569\) | 2.79385 | 0.117124 | 0.0585621 | − | 0.998284i | \(-0.481348\pi\) | ||||
0.0585621 | + | 0.998284i | \(0.481348\pi\) | |||||||
\(570\) | 5.13924 | − | 4.51726i | 0.215259 | − | 0.189207i | ||||
\(571\) | 18.8564i | 0.789118i | 0.918871 | + | 0.394559i | \(0.129103\pi\) | ||||
−0.918871 | + | 0.394559i | \(0.870897\pi\) | |||||||
\(572\) | −1.65636 | −0.0692559 | ||||||||
\(573\) | 16.9957 | − | 14.9388i | 0.710006 | − | 0.624077i | ||||
\(574\) | 7.98454i | 0.333268i | ||||||||
\(575\) | −2.61089 | − | 4.02284i | −0.108882 | − | 0.167764i | ||||
\(576\) | −0.384868 | + | 2.97521i | −0.0160361 | + | 0.123967i | ||||
\(577\) | 12.8591 | 0.535331 | 0.267665 | − | 0.963512i | \(-0.413748\pi\) | ||||
0.267665 | + | 0.963512i | \(0.413748\pi\) | |||||||
\(578\) | 40.3297i | 1.67749i | ||||||||
\(579\) | 1.74830 | − | 1.53671i | 0.0726567 | − | 0.0638634i | ||||
\(580\) | 2.20183i | 0.0914259i | ||||||||
\(581\) | 16.4038i | 0.680545i | ||||||||
\(582\) | 15.1527 | − | 13.3188i | 0.628100 | − | 0.552084i | ||||
\(583\) | 4.45336 | 0.184439 | ||||||||
\(584\) | 7.22073i | 0.298796i | ||||||||
\(585\) | −1.89660 | + | 14.6616i | −0.0784147 | + | 0.606183i | ||||
\(586\) | 12.9662i | 0.535627i | ||||||||
\(587\) | 4.49967i | 0.185721i | 0.995679 | + | 0.0928607i | \(0.0296011\pi\) | ||||
−0.995679 | + | 0.0928607i | \(0.970399\pi\) | |||||||
\(588\) | 7.75119 | − | 6.81310i | 0.319654 | − | 0.280967i | ||||
\(589\) | − | 5.02774i | − | 0.207165i | ||||||
\(590\) | −2.53151 | −0.104221 | ||||||||
\(591\) | 7.20851 | + | 8.20106i | 0.296519 | + | 0.337346i | ||||
\(592\) | − | 0.378822i | − | 0.0155695i | ||||||
\(593\) | 6.11300i | 0.251031i | 0.992092 | + | 0.125515i | \(0.0400584\pi\) | ||||
−0.992092 | + | 0.125515i | \(0.959942\pi\) | |||||||
\(594\) | 1.44888 | − | 0.975221i | 0.0594484 | − | 0.0400138i | ||||
\(595\) | − | 7.72838i | − | 0.316833i | ||||||
\(596\) | −3.43726 | −0.140796 | ||||||||
\(597\) | −8.77647 | − | 9.98490i | −0.359197 | − | 0.408655i | ||||
\(598\) | −19.8243 | + | 12.8663i | −0.810674 | + | 0.526140i | ||||
\(599\) | − | 30.8437i | − | 1.26024i | −0.776498 | − | 0.630120i | \(-0.783006\pi\) | ||
0.776498 | − | 0.630120i | \(-0.216994\pi\) | |||||||
\(600\) | 1.14349 | + | 1.30094i | 0.0466827 | + | 0.0531105i | ||||
\(601\) | 20.6559 | 0.842574 | 0.421287 | − | 0.906927i | \(-0.361579\pi\) | ||||
0.421287 | + | 0.906927i | \(0.361579\pi\) | |||||||
\(602\) | 10.2615i | 0.418228i | ||||||||
\(603\) | 10.9327 | + | 1.41423i | 0.445214 | + | 0.0575921i | ||||
\(604\) | 19.8169 | 0.806339 | ||||||||
\(605\) | −10.8870 | −0.442621 | ||||||||
\(606\) | −15.9561 | + | 14.0250i | −0.648172 | + | 0.569727i | ||||
\(607\) | −37.9955 | −1.54219 | −0.771095 | − | 0.636720i | \(-0.780291\pi\) | ||||
−0.771095 | + | 0.636720i | \(0.780291\pi\) | |||||||
\(608\) | −3.95042 | −0.160211 | ||||||||
\(609\) | −2.92373 | + | 2.56989i | −0.118476 | + | 0.104137i | ||||
\(610\) | −12.9663 | −0.524989 | ||||||||
\(611\) | − | 26.3574i | − | 1.06631i | ||||||
\(612\) | 2.91408 | − | 22.5272i | 0.117795 | − | 0.910609i | ||||
\(613\) | 38.5259i | 1.55604i | 0.628237 | + | 0.778022i | \(0.283777\pi\) | ||||
−0.628237 | + | 0.778022i | \(0.716223\pi\) | |||||||
\(614\) | − | 24.4391i | − | 0.986281i | ||||||
\(615\) | 8.94506 | + | 10.1767i | 0.360700 | + | 0.410364i | ||||
\(616\) | −0.343075 | −0.0138229 | ||||||||
\(617\) | 18.7768 | 0.755925 | 0.377963 | − | 0.925821i | \(-0.376625\pi\) | ||||
0.377963 | + | 0.925821i | \(0.376625\pi\) | |||||||
\(618\) | 8.63752 | − | 7.59215i | 0.347452 | − | 0.305401i | ||||
\(619\) | 10.9690i | 0.440881i | 0.975400 | + | 0.220441i | \(0.0707496\pi\) | ||||
−0.975400 | + | 0.220441i | \(0.929250\pi\) | |||||||
\(620\) | 1.27271 | 0.0511133 | ||||||||
\(621\) | 9.76575 | − | 22.9266i | 0.391886 | − | 0.920014i | ||||
\(622\) | −20.4152 | −0.818575 | ||||||||
\(623\) | − | 14.4299i | − | 0.578123i | ||||||
\(624\) | 6.41091 | − | 5.63502i | 0.256642 | − | 0.225582i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 27.4387 | 1.09667 | ||||||||
\(627\) | 1.51833 | + | 1.72739i | 0.0606362 | + | 0.0689852i | ||||
\(628\) | − | 12.8500i | − | 0.512772i | ||||||
\(629\) | 2.86830i | 0.114367i | ||||||||
\(630\) | −0.392835 | + | 3.03680i | −0.0156509 | + | 0.120989i | ||||
\(631\) | 22.4999i | 0.895709i | 0.894107 | + | 0.447854i | \(0.147812\pi\) | ||||
−0.894107 | + | 0.447854i | \(0.852188\pi\) | |||||||
\(632\) | 4.78248 | 0.190237 | ||||||||
\(633\) | −23.1036 | + | 20.3075i | −0.918287 | + | 0.807150i | ||||
\(634\) | −2.34160 | −0.0929969 | ||||||||
\(635\) | 17.6630 | 0.700933 | ||||||||
\(636\) | −17.2367 | + | 15.1506i | −0.683478 | + | 0.600759i | ||||
\(637\) | −29.3614 | −1.16334 | ||||||||
\(638\) | −0.740072 | −0.0292997 | ||||||||
\(639\) | −32.2589 | − | 4.17295i | −1.27614 | − | 0.165079i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 10.2836 | 0.406178 | 0.203089 | − | 0.979160i | \(-0.434902\pi\) | ||||
0.203089 | + | 0.979160i | \(0.434902\pi\) | |||||||
\(642\) | 10.1196 | + | 11.5130i | 0.399390 | + | 0.454382i | ||||
\(643\) | − | 37.6763i | − | 1.48581i | −0.669399 | − | 0.742903i | \(-0.733448\pi\) | ||
0.669399 | − | 0.742903i | \(-0.266552\pi\) | |||||||
\(644\) | −4.10612 | + | 2.66494i | −0.161804 | + | 0.105013i | ||||
\(645\) | 11.4959 | + | 13.0788i | 0.452652 | + | 0.514978i | ||||
\(646\) | 29.9112 | 1.17684 | ||||||||
\(647\) | − | 27.6384i | − | 1.08658i | −0.839546 | − | 0.543289i | \(-0.817179\pi\) | ||
0.839546 | − | 0.543289i | \(-0.182821\pi\) | |||||||
\(648\) | −2.29012 | + | 8.70375i | −0.0899646 | + | 0.341916i | ||||
\(649\) | − | 0.850883i | − | 0.0334001i | ||||||
\(650\) | − | 4.92792i | − | 0.193289i | ||||||
\(651\) | 1.48546 | + | 1.68999i | 0.0582197 | + | 0.0662360i | ||||
\(652\) | 7.48989 | 0.293327 | ||||||||
\(653\) | 23.6302i | 0.924720i | 0.886692 | + | 0.462360i | \(0.152997\pi\) | ||||
−0.886692 | + | 0.462360i | \(0.847003\pi\) | |||||||
\(654\) | 17.4345 | − | 15.3245i | 0.681744 | − | 0.599236i | ||||
\(655\) | 12.4875i | 0.487927i | ||||||||
\(656\) | − | 7.82260i | − | 0.305421i | ||||||
\(657\) | −2.77903 | + | 21.4832i | −0.108420 | + | 0.838139i | ||||
\(658\) | − | 5.45931i | − | 0.212826i | ||||||
\(659\) | 4.24256 | 0.165267 | 0.0826333 | − | 0.996580i | \(-0.473667\pi\) | ||||
0.0826333 | + | 0.996580i | \(0.473667\pi\) | |||||||
\(660\) | −0.437267 | + | 0.384346i | −0.0170206 | + | 0.0149607i | ||||
\(661\) | − | 1.60933i | − | 0.0625956i | −0.999510 | − | 0.0312978i | \(-0.990036\pi\) | ||
0.999510 | − | 0.0312978i | \(-0.00996402\pi\) | |||||||
\(662\) | 27.4881i | 1.06836i | ||||||||
\(663\) | −48.5411 | + | 42.6664i | −1.88518 | + | 1.65702i | ||||
\(664\) | − | 16.0711i | − | 0.623680i | ||||||
\(665\) | −4.03220 | −0.156362 | ||||||||
\(666\) | 0.145796 | − | 1.12708i | 0.00564949 | − | 0.0436733i | ||||
\(667\) | −8.85760 | + | 5.74872i | −0.342968 | + | 0.222591i | ||||
\(668\) | − | 10.1932i | − | 0.394388i | ||||||
\(669\) | 3.49316 | − | 3.07039i | 0.135053 | − | 0.118708i | ||||
\(670\) | −3.67460 | −0.141962 | ||||||||
\(671\) | − | 4.35818i | − | 0.168246i | ||||||
\(672\) | 1.32787 | − | 1.16716i | 0.0512236 | − | 0.0450242i | ||||
\(673\) | −25.6047 | −0.986988 | −0.493494 | − | 0.869749i | \(-0.664280\pi\) | ||||
−0.493494 | + | 0.869749i | \(0.664280\pi\) | |||||||
\(674\) | −22.1863 | −0.854586 | ||||||||
\(675\) | 2.90143 | + | 4.31065i | 0.111676 | + | 0.165917i | ||||
\(676\) | −11.2844 | −0.434016 | ||||||||
\(677\) | −19.9065 | −0.765071 | −0.382535 | − | 0.923941i | \(-0.624949\pi\) | ||||
−0.382535 | + | 0.923941i | \(0.624949\pi\) | |||||||
\(678\) | 1.96499 | + | 2.23555i | 0.0754649 | + | 0.0858557i | ||||
\(679\) | −11.8887 | −0.456245 | ||||||||
\(680\) | 7.57164i | 0.290359i | ||||||||
\(681\) | −5.42058 | + | 4.76455i | −0.207717 | + | 0.182578i | ||||
\(682\) | 0.427780i | 0.0163805i | ||||||||
\(683\) | − | 14.5455i | − | 0.556569i | −0.960499 | − | 0.278284i | \(-0.910234\pi\) | ||
0.960499 | − | 0.278284i | \(-0.0897657\pi\) | |||||||
\(684\) | −11.7533 | − | 1.52039i | −0.449400 | − | 0.0581335i | ||||
\(685\) | 0.245755 | 0.00938980 | ||||||||
\(686\) | −13.2264 | −0.504987 | ||||||||
\(687\) | 11.2312 | + | 12.7776i | 0.428495 | + | 0.487495i | ||||
\(688\) | − | 10.0534i | − | 0.383282i | ||||||
\(689\) | 65.2922 | 2.48743 | ||||||||
\(690\) | −2.24794 | + | 7.99667i | −0.0855776 | + | 0.304428i | ||||
\(691\) | 12.9697 | 0.493391 | 0.246696 | − | 0.969093i | \(-0.420655\pi\) | ||||
0.246696 | + | 0.969093i | \(0.420655\pi\) | |||||||
\(692\) | 4.41012i | 0.167648i | ||||||||
\(693\) | −1.02072 | − | 0.132038i | −0.0387740 | − | 0.00501573i | ||||
\(694\) | −24.4010 | −0.926250 | ||||||||
\(695\) | −5.22537 | −0.198209 | ||||||||
\(696\) | 2.86443 | − | 2.51776i | 0.108576 | − | 0.0954356i | ||||
\(697\) | 59.2299i | 2.24349i | ||||||||
\(698\) | − | 11.9864i | − | 0.453693i | ||||||
\(699\) | −23.3406 | − | 26.5544i | −0.882824 | − | 1.00438i | ||||
\(700\) | − | 1.02070i | − | 0.0385789i | ||||||
\(701\) | −18.3901 | −0.694586 | −0.347293 | − | 0.937757i | \(-0.612899\pi\) | ||||
−0.347293 | + | 0.937757i | \(0.612899\pi\) | |||||||
\(702\) | 21.2425 | − | 14.2980i | 0.801748 | − | 0.539644i | ||||
\(703\) | 1.49651 | 0.0564418 | ||||||||
\(704\) | 0.336117 | 0.0126679 | ||||||||
\(705\) | −6.11605 | − | 6.95817i | −0.230344 | − | 0.262060i | ||||
\(706\) | 22.4575 | 0.845197 | ||||||||
\(707\) | 12.5190 | 0.470825 | ||||||||
\(708\) | 2.89475 | + | 3.29333i | 0.108791 | + | 0.123771i | ||||
\(709\) | − | 52.2675i | − | 1.96295i | −0.191596 | − | 0.981474i | \(-0.561366\pi\) | ||
0.191596 | − | 0.981474i | \(-0.438634\pi\) | |||||||
\(710\) | 10.8426 | 0.406914 | ||||||||
\(711\) | 14.2289 | + | 1.84062i | 0.533624 | + | 0.0690286i | ||||
\(712\) | 14.1373i | 0.529817i | ||||||||
\(713\) | 3.32290 | + | 5.11992i | 0.124444 | + | 0.191742i | ||||
\(714\) | −10.0541 | + | 8.83732i | −0.376266 | + | 0.330728i | ||||
\(715\) | 1.65636 | 0.0619443 | ||||||||
\(716\) | − | 7.99808i | − | 0.298902i | ||||||
\(717\) | −10.2863 | − | 11.7026i | −0.384149 | − | 0.437042i | ||||
\(718\) | 10.4831i | 0.391226i | ||||||||
\(719\) | 10.1289i | 0.377743i | 0.982002 | + | 0.188872i | \(0.0604830\pi\) | ||||
−0.982002 | + | 0.188872i | \(0.939517\pi\) | |||||||
\(720\) | 0.384868 | − | 2.97521i | 0.0143432 | − | 0.110880i | ||||
\(721\) | −6.77691 | −0.252385 | ||||||||
\(722\) | 3.39418i | 0.126318i | ||||||||
\(723\) | 11.4027 | + | 12.9727i | 0.424070 | + | 0.482460i | ||||
\(724\) | 14.7941i | 0.549817i | ||||||||
\(725\) | − | 2.20183i | − | 0.0817738i | ||||||
\(726\) | 12.4492 | + | 14.1633i | 0.462033 | + | 0.525650i | ||||
\(727\) | 50.8542i | 1.88608i | 0.332680 | + | 0.943040i | \(0.392047\pi\) | ||||
−0.332680 | + | 0.943040i | \(0.607953\pi\) | |||||||
\(728\) | −5.02994 | −0.186422 | ||||||||
\(729\) | −10.1634 | + | 25.0141i | −0.376422 | + | 0.926448i | ||||
\(730\) | − | 7.22073i | − | 0.267251i | ||||||
\(731\) | 76.1206i | 2.81542i | ||||||||
\(732\) | 14.8268 | + | 16.8683i | 0.548013 | + | 0.623469i | ||||
\(733\) | − | 6.58068i | − | 0.243063i | −0.992588 | − | 0.121531i | \(-0.961219\pi\) | ||
0.992588 | − | 0.121531i | \(-0.0387805\pi\) | |||||||
\(734\) | 22.8694 | 0.844124 | ||||||||
\(735\) | −7.75119 | + | 6.81310i | −0.285907 | + | 0.251305i | ||||
\(736\) | 4.02284 | − | 2.61089i | 0.148284 | − | 0.0962386i | ||||
\(737\) | − | 1.23510i | − | 0.0454954i | ||||||
\(738\) | 3.01067 | − | 23.2739i | 0.110824 | − | 0.856724i | ||||
\(739\) | −12.4255 | −0.457080 | −0.228540 | − | 0.973535i | \(-0.573395\pi\) | ||||
−0.228540 | + | 0.973535i | \(0.573395\pi\) | |||||||
\(740\) | 0.378822i | 0.0139258i | ||||||||
\(741\) | 22.2607 | + | 25.3258i | 0.817768 | + | 0.930366i | ||||
\(742\) | 13.5237 | 0.496471 | ||||||||
\(743\) | −17.8783 | −0.655890 | −0.327945 | − | 0.944697i | \(-0.606356\pi\) | ||||
−0.327945 | + | 0.944697i | \(0.606356\pi\) | |||||||
\(744\) | −1.45533 | − | 1.65571i | −0.0533550 | − | 0.0607015i | ||||
\(745\) | 3.43726 | 0.125931 | ||||||||
\(746\) | 5.47431 | 0.200429 | ||||||||
\(747\) | 6.18525 | − | 47.8149i | 0.226306 | − | 1.74946i | ||||
\(748\) | −2.54496 | −0.0930528 | ||||||||
\(749\) | − | 9.03299i | − | 0.330058i | ||||||
\(750\) | −1.14349 | − | 1.30094i | −0.0417543 | − | 0.0475035i | ||||
\(751\) | 14.4641i | 0.527802i | 0.964550 | + | 0.263901i | \(0.0850093\pi\) | ||||
−0.964550 | + | 0.263901i | \(0.914991\pi\) | |||||||
\(752\) | 5.34859i | 0.195043i | ||||||||
\(753\) | −16.9946 | + | 14.9378i | −0.619316 | + | 0.544363i | ||||
\(754\) | −10.8504 | −0.395149 | ||||||||
\(755\) | −19.8169 | −0.721211 | ||||||||
\(756\) | 4.39989 | − | 2.96150i | 0.160022 | − | 0.107709i | ||||
\(757\) | − | 44.8565i | − | 1.63034i | −0.579224 | − | 0.815169i | \(-0.696644\pi\) | ||
0.579224 | − | 0.815169i | \(-0.303356\pi\) | |||||||
\(758\) | 30.3390 | 1.10196 | ||||||||
\(759\) | −2.68782 | − | 0.755571i | −0.0975616 | − | 0.0274255i | ||||
\(760\) | 3.95042 | 0.143297 | ||||||||
\(761\) | 8.43284i | 0.305690i | 0.988250 | + | 0.152845i | \(0.0488435\pi\) | ||||
−0.988250 | + | 0.152845i | \(0.951156\pi\) | |||||||
\(762\) | −20.1974 | − | 22.9784i | −0.731674 | − | 0.832419i | ||||
\(763\) | −13.6790 | −0.495212 | ||||||||
\(764\) | 13.0642 | 0.472647 | ||||||||
\(765\) | −2.91408 | + | 22.5272i | −0.105359 | + | 0.814473i | ||||
\(766\) | 14.8764i | 0.537507i | ||||||||
\(767\) | − | 12.4751i | − | 0.450449i | ||||||
\(768\) | −1.30094 | + | 1.14349i | −0.0469435 | + | 0.0412621i | ||||
\(769\) | 12.1869i | 0.439472i | 0.975559 | + | 0.219736i | \(0.0705196\pi\) | ||||
−0.975559 | + | 0.219736i | \(0.929480\pi\) | |||||||
\(770\) | 0.343075 | 0.0123636 | ||||||||
\(771\) | 5.46284 | + | 6.21502i | 0.196739 | + | 0.223829i | ||||
\(772\) | 1.34388 | 0.0483672 | ||||||||
\(773\) | −10.4195 | −0.374764 | −0.187382 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187382 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(774\) | 3.86922 | − | 29.9110i | 0.139076 | − | 1.07513i | ||||
\(775\) | −1.27271 | −0.0457171 | ||||||||
\(776\) | 11.6476 | 0.418123 | ||||||||
\(777\) | −0.503025 | + | 0.442146i | −0.0180459 | + | 0.0158619i | ||||
\(778\) | 12.5719i | 0.450726i | ||||||||
\(779\) | 30.9026 | 1.10720 | ||||||||
\(780\) | −6.41091 | + | 5.63502i | −0.229547 | + | 0.201766i | ||||
\(781\) | 3.64437i | 0.130406i | ||||||||
\(782\) | −30.4595 | + | 19.7687i | −1.08923 | + | 0.706927i | ||||
\(783\) | 9.49130 | − | 6.38845i | 0.339191 | − | 0.228305i | ||||
\(784\) | 5.95817 | 0.212792 | ||||||||
\(785\) | 12.8500i | 0.458637i | ||||||||
\(786\) | 16.2454 | − | 14.2793i | 0.579456 | − | 0.509326i | ||||
\(787\) | − | 27.8222i | − | 0.991756i | −0.868392 | − | 0.495878i | \(-0.834846\pi\) | ||
0.868392 | − | 0.495878i | \(-0.165154\pi\) | |||||||
\(788\) | 6.30397i | 0.224570i | ||||||||
\(789\) | −4.14645 | + | 3.64462i | −0.147617 | + | 0.129752i | ||||
\(790\) | −4.78248 | −0.170153 | ||||||||
\(791\) | − | 1.75399i | − | 0.0623647i | ||||||
\(792\) | 1.00002 | + | 0.129361i | 0.0355341 | + | 0.00459663i | ||||
\(793\) | − | 63.8967i | − | 2.26904i | ||||||
\(794\) | 24.1720i | 0.857832i | ||||||||
\(795\) | 17.2367 | − | 15.1506i | 0.611321 | − | 0.537335i | ||||
\(796\) | − | 7.67517i | − | 0.272039i | ||||||
\(797\) | 43.0453 | 1.52474 | 0.762372 | − | 0.647139i | \(-0.224035\pi\) | ||||
0.762372 | + | 0.647139i | \(0.224035\pi\) | |||||||
\(798\) | 4.61078 | + | 5.24563i | 0.163220 | + | 0.185693i | ||||
\(799\) | − | 40.4976i | − | 1.43270i | ||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | −5.44098 | + | 42.0614i | −0.192247 | + | 1.48617i | ||||
\(802\) | − | 21.4707i | − | 0.758158i | ||||||
\(803\) | 2.42701 | 0.0856474 | ||||||||
\(804\) | 4.20186 | + | 4.78042i | 0.148188 | + | 0.168592i | ||||
\(805\) | 4.10612 | − | 2.66494i | 0.144722 | − | 0.0939267i | ||||
\(806\) | 6.27182i | 0.220915i | ||||||||
\(807\) | 7.74332 | + | 8.80950i | 0.272578 | + | 0.310109i | ||||
\(808\) | −12.2651 | −0.431485 | ||||||||
\(809\) | − | 31.2888i | − | 1.10006i | −0.835146 | − | 0.550028i | \(-0.814617\pi\) | ||
0.835146 | − | 0.550028i | \(-0.185383\pi\) | |||||||
\(810\) | 2.29012 | − | 8.70375i | 0.0804667 | − | 0.305819i | ||||
\(811\) | 7.67811 | 0.269615 | 0.134807 | − | 0.990872i | \(-0.456958\pi\) | ||||
0.134807 | + | 0.990872i | \(0.456958\pi\) | |||||||
\(812\) | −2.24741 | −0.0788685 | ||||||||
\(813\) | 8.37294 | − | 7.35960i | 0.293652 | − | 0.258112i | ||||
\(814\) | −0.127329 | −0.00446286 | ||||||||
\(815\) | −7.48989 | −0.262359 | ||||||||
\(816\) | 9.85021 | − | 8.65808i | 0.344826 | − | 0.303093i | ||||
\(817\) | 39.7151 | 1.38946 | ||||||||
\(818\) | − | 13.5579i | − | 0.474042i | ||||||
\(819\) | −14.9651 | − | 1.93586i | −0.522924 | − | 0.0676444i | ||||
\(820\) | 7.82260i | 0.273177i | ||||||||
\(821\) | − | 20.6930i | − | 0.722191i | −0.932529 | − | 0.361095i | \(-0.882403\pi\) | ||
0.932529 | − | 0.361095i | \(-0.117597\pi\) | |||||||
\(822\) | −0.281018 | − | 0.319711i | −0.00980162 | − | 0.0111512i | ||||
\(823\) | 26.1496 | 0.911519 | 0.455760 | − | 0.890103i | \(-0.349368\pi\) | ||||
0.455760 | + | 0.890103i | \(0.349368\pi\) | |||||||
\(824\) | 6.63946 | 0.231297 | ||||||||
\(825\) | 0.437267 | − | 0.384346i | 0.0152237 | − | 0.0133812i | ||||
\(826\) | − | 2.58391i | − | 0.0899059i | ||||||
\(827\) | 35.5900 | 1.23759 | 0.618793 | − | 0.785554i | \(-0.287622\pi\) | ||||
0.618793 | + | 0.785554i | \(0.287622\pi\) | |||||||
\(828\) | 12.9737 | − | 6.21968i | 0.450866 | − | 0.216149i | ||||
\(829\) | −27.5242 | −0.955954 | −0.477977 | − | 0.878372i | \(-0.658630\pi\) | ||||
−0.477977 | + | 0.878372i | \(0.658630\pi\) | |||||||
\(830\) | 16.0711i | 0.557836i | ||||||||
\(831\) | −5.81768 | + | 5.11359i | −0.201813 | + | 0.177389i | ||||
\(832\) | 4.92792 | 0.170845 | ||||||||
\(833\) | −45.1131 | −1.56308 | ||||||||
\(834\) | 5.97515 | + | 6.79787i | 0.206902 | + | 0.235391i | ||||
\(835\) | 10.1932i | 0.352751i | ||||||||
\(836\) | 1.32780i | 0.0459231i | ||||||||
\(837\) | −3.69268 | − | 5.48621i | −0.127638 | − | 0.189631i | ||||
\(838\) | 3.19459i | 0.110355i | ||||||||
\(839\) | −30.4186 | −1.05017 | −0.525083 | − | 0.851051i | \(-0.675966\pi\) | ||||
−0.525083 | + | 0.851051i | \(0.675966\pi\) | |||||||
\(840\) | −1.32787 | + | 1.16716i | −0.0458158 | + | 0.0402709i | ||||
\(841\) | 24.1520 | 0.832826 | ||||||||
\(842\) | −23.8342 | −0.821382 | ||||||||
\(843\) | 40.1307 | − | 35.2739i | 1.38218 | − | 1.21490i | ||||
\(844\) | −17.7592 | −0.611298 | ||||||||
\(845\) | 11.2844 | 0.388196 | ||||||||
\(846\) | −2.05850 | + | 15.9132i | −0.0707726 | + | 0.547106i | ||||
\(847\) | − | 11.1124i | − | 0.381827i | ||||||
\(848\) | −13.2494 | −0.454987 | ||||||||
\(849\) | −14.2517 | − | 16.2140i | −0.489116 | − | 0.556463i | ||||
\(850\) | − | 7.57164i | − | 0.259705i | ||||||
\(851\) | −1.52394 | + | 0.989061i | −0.0522400 | + | 0.0339046i | ||||
\(852\) | −12.3983 | − | 14.1055i | −0.424760 | − | 0.483245i | ||||
\(853\) | −17.8266 | −0.610370 | −0.305185 | − | 0.952293i | \(-0.598718\pi\) | ||||
−0.305185 | + | 0.952293i | \(0.598718\pi\) | |||||||
\(854\) | − | 13.2347i | − | 0.452882i | ||||||
\(855\) | 11.7533 | + | 1.52039i | 0.401956 | + | 0.0519962i | ||||
\(856\) | 8.84979i | 0.302479i | ||||||||
\(857\) | − | 29.7593i | − | 1.01656i | −0.861192 | − | 0.508279i | \(-0.830282\pi\) | ||
0.861192 | − | 0.508279i | \(-0.169718\pi\) | |||||||
\(858\) | −1.89403 | − | 2.15482i | −0.0646610 | − | 0.0735642i | ||||
\(859\) | 22.5038 | 0.767819 | 0.383910 | − | 0.923371i | \(-0.374577\pi\) | ||||
0.383910 | + | 0.923371i | \(0.374577\pi\) | |||||||
\(860\) | 10.0534i | 0.342818i | ||||||||
\(861\) | −10.3874 | + | 9.13023i | −0.354001 | + | 0.311158i | ||||
\(862\) | − | 14.0920i | − | 0.479975i | ||||||
\(863\) | 9.58024i | 0.326115i | 0.986617 | + | 0.163058i | \(0.0521356\pi\) | ||||
−0.986617 | + | 0.163058i | \(0.947864\pi\) | |||||||
\(864\) | −4.31065 | + | 2.90143i | −0.146651 | + | 0.0987087i | ||||
\(865\) | − | 4.41012i | − | 0.149949i | ||||||
\(866\) | 24.3424 | 0.827188 | ||||||||
\(867\) | −52.4663 | + | 46.1165i | −1.78185 | + | 1.56620i | ||||
\(868\) | 1.29906i | 0.0440929i | ||||||||
\(869\) | − | 1.60747i | − | 0.0545297i | ||||||
\(870\) | −2.86443 | + | 2.51776i | −0.0971134 | + | 0.0853602i | ||||
\(871\) | − | 18.1082i | − | 0.613571i | ||||||
\(872\) | 13.4015 | 0.453833 | ||||||||
\(873\) | 34.6539 | + | 4.48276i | 1.17286 | + | 0.151719i | ||||
\(874\) | 10.3141 | + | 15.8919i | 0.348880 | + | 0.537552i | ||||
\(875\) | 1.02070i | 0.0345060i | ||||||||
\(876\) | −9.39371 | + | 8.25682i | −0.317384 | + | 0.278972i | ||||
\(877\) | 13.9728 | 0.471827 | 0.235914 | − | 0.971774i | \(-0.424192\pi\) | ||||
0.235914 | + | 0.971774i | \(0.424192\pi\) | |||||||
\(878\) | − | 1.40497i | − | 0.0474154i | ||||||
\(879\) | −16.8681 | + | 14.8266i | −0.568948 | + | 0.500090i | ||||
\(880\) | −0.336117 | −0.0113305 | ||||||||
\(881\) | 0.000653309 | 0 | 2.20105e−5 | 0 | 1.10053e−5 | − | 1.00000i | \(-0.499996\pi\) | ||
1.10053e−5 | 1.00000i | \(0.499996\pi\) | ||||||||
\(882\) | 17.7268 | + | 2.29311i | 0.596893 | + | 0.0772129i | ||||
\(883\) | 28.3523 | 0.954131 | 0.477066 | − | 0.878868i | \(-0.341700\pi\) | ||||
0.477066 | + | 0.878868i | \(0.341700\pi\) | |||||||
\(884\) | −37.3124 | −1.25495 | ||||||||
\(885\) | −2.89475 | − | 3.29333i | −0.0973060 | − | 0.110704i | ||||
\(886\) | 39.5844 | 1.32986 | ||||||||
\(887\) | − | 7.93986i | − | 0.266594i | −0.991076 | − | 0.133297i | \(-0.957444\pi\) | ||
0.991076 | − | 0.133297i | \(-0.0425565\pi\) | |||||||
\(888\) | 0.492823 | − | 0.433179i | 0.0165381 | − | 0.0145365i | ||||
\(889\) | 18.0286i | 0.604660i | ||||||||
\(890\) | − | 14.1373i | − | 0.473882i | ||||||
\(891\) | 2.92548 | + | 0.769750i | 0.0980073 | + | 0.0257876i | ||||
\(892\) | 2.68511 | 0.0899042 | ||||||||
\(893\) | −21.1292 | −0.707061 | ||||||||
\(894\) | −3.93047 | − | 4.47165i | −0.131454 | − | 0.149554i | ||||
\(895\) | 7.99808i | 0.267346i | ||||||||
\(896\) | 1.02070 | 0.0340992 | ||||||||
\(897\) | −39.4070 | − | 11.0777i | −1.31576 | − | 0.369873i | ||||
\(898\) | 29.0379 | 0.969006 | ||||||||
\(899\) | 2.80229i | 0.0934616i | ||||||||
\(900\) | −0.384868 | + | 2.97521i | −0.0128289 | + | 0.0991737i | ||||
\(901\) | 100.320 | 3.34214 | ||||||||
\(902\) | −2.62931 | −0.0875465 | ||||||||
\(903\) | −13.3496 | + | 11.7339i | −0.444246 | + | 0.390480i | ||||
\(904\) | 1.71841i | 0.0571536i | ||||||||
\(905\) | − | 14.7941i | − | 0.491771i | ||||||
\(906\) | 22.6604 | + | 25.7805i | 0.752842 | + | 0.856501i | ||||
\(907\) | 18.1858i | 0.603849i | 0.953332 | + | 0.301924i | \(0.0976290\pi\) | ||||
−0.953332 | + | 0.301924i | \(0.902371\pi\) | |||||||
\(908\) | −4.16668 | −0.138276 | ||||||||
\(909\) | −36.4912 | − | 4.72044i | −1.21034 | − | 0.156567i | ||||
\(910\) | 5.02994 | 0.166741 | ||||||||
\(911\) | −18.7950 | −0.622707 | −0.311354 | − | 0.950294i | \(-0.600782\pi\) | ||||
−0.311354 | + | 0.950294i | \(0.600782\pi\) | |||||||
\(912\) | −4.51726 | − | 5.13924i | −0.149581 | − | 0.170177i | ||||
\(913\) | −5.40177 | −0.178773 | ||||||||
\(914\) | 35.5772 | 1.17679 | ||||||||
\(915\) | −14.8268 | − | 16.8683i | −0.490158 | − | 0.557648i | ||||
\(916\) | 9.82184i | 0.324523i | ||||||||
\(917\) | −12.7460 | −0.420910 | ||||||||
\(918\) | 32.6387 | − | 21.9686i | 1.07724 | − | 0.725071i | ||||
\(919\) | − | 2.72538i | − | 0.0899019i | −0.998989 | − | 0.0449510i | \(-0.985687\pi\) | ||
0.998989 | − | 0.0449510i | \(-0.0143132\pi\) | |||||||
\(920\) | −4.02284 | + | 2.61089i | −0.132629 | + | 0.0860784i | ||||
\(921\) | 31.7937 | − | 27.9458i | 1.04764 | − | 0.920846i | ||||
\(922\) | −29.4329 | −0.969323 | ||||||||
\(923\) | 53.4313i | 1.75871i | ||||||||
\(924\) | −0.392303 | − | 0.446319i | −0.0129058 | − | 0.0146828i | ||||
\(925\) | − | 0.378822i | − | 0.0124556i | ||||||
\(926\) | − | 12.4050i | − | 0.407652i | ||||||
\(927\) | 19.7538 | + | 2.55531i | 0.648800 | + | 0.0839275i | ||||
\(928\) | 2.20183 | 0.0722785 | ||||||||
\(929\) | − | 27.8642i | − | 0.914196i | −0.889416 | − | 0.457098i | \(-0.848889\pi\) | ||
0.889416 | − | 0.457098i | \(-0.151111\pi\) | |||||||
\(930\) | 1.45533 | + | 1.65571i | 0.0477222 | + | 0.0542930i | ||||
\(931\) | 23.5373i | 0.771403i | ||||||||
\(932\) | − | 20.4118i | − | 0.668610i | ||||||
\(933\) | −23.3446 | − | 26.5589i | −0.764267 | − | 0.869499i | ||||
\(934\) | − | 37.4350i | − | 1.22491i | ||||||
\(935\) | 2.54496 | 0.0832290 | ||||||||
\(936\) | 14.6616 | + | 1.89660i | 0.479230 | + | 0.0619922i | ||||
\(937\) | − | 58.4892i | − | 1.91076i | −0.295379 | − | 0.955380i | \(-0.595446\pi\) | ||
0.295379 | − | 0.955380i | \(-0.404554\pi\) | |||||||
\(938\) | − | 3.75067i | − | 0.122464i | ||||||
\(939\) | 31.3759 | + | 35.6960i | 1.02391 | + | 1.16490i | ||||
\(940\) | − | 5.34859i | − | 0.174452i | ||||||
\(941\) | −48.4064 | −1.57800 | −0.789001 | − | 0.614392i | \(-0.789402\pi\) | ||||
−0.789001 | + | 0.614392i | \(0.789402\pi\) | |||||||
\(942\) | 16.7171 | − | 14.6939i | 0.544671 | − | 0.478752i | ||||
\(943\) | −31.4691 | + | 20.4239i | −1.02478 | + | 0.665095i | ||||
\(944\) | 2.53151i | 0.0823936i | ||||||||
\(945\) | −4.39989 | + | 2.96150i | −0.143128 | + | 0.0963374i | ||||
\(946\) | −3.37912 | −0.109865 | ||||||||
\(947\) | − | 35.0021i | − | 1.13742i | −0.822539 | − | 0.568708i | \(-0.807443\pi\) | ||
0.822539 | − | 0.568708i | \(-0.192557\pi\) | |||||||
\(948\) | 5.46871 | + | 6.22169i | 0.177615 | + | 0.202071i | ||||
\(949\) | 35.5832 | 1.15508 | ||||||||
\(950\) | −3.95042 | −0.128169 | ||||||||
\(951\) | −2.67759 | − | 3.04627i | −0.0868270 | − | 0.0987822i | ||||
\(952\) | −7.72838 | −0.250478 | ||||||||
\(953\) | −54.6907 | −1.77160 | −0.885802 | − | 0.464063i | \(-0.846391\pi\) | ||||
−0.885802 | + | 0.464063i | \(0.846391\pi\) | |||||||
\(954\) | −39.4198 | − | 5.09927i | −1.27626 | − | 0.165095i | ||||
\(955\) | −13.0642 | −0.422748 | ||||||||
\(956\) | − | 8.99553i | − | 0.290936i | ||||||
\(957\) | −0.846263 | − | 0.962786i | −0.0273558 | − | 0.0311224i | ||||
\(958\) | − | 18.9516i | − | 0.612298i | ||||||
\(959\) | 0.250842i | 0.00810011i | ||||||||
\(960\) | 1.30094 | − | 1.14349i | 0.0419875 | − | 0.0369059i | ||||
\(961\) | −29.3802 | −0.947749 | ||||||||
\(962\) | −1.86681 | −0.0601882 | ||||||||
\(963\) | −3.40599 | + | 26.3300i | −0.109757 | + | 0.848472i | ||||
\(964\) | 9.97182i | 0.321171i | ||||||||
\(965\) | −1.34388 | −0.0432609 | ||||||||
\(966\) | −8.16221 | − | 2.29448i | −0.262615 | − | 0.0738236i | ||||
\(967\) | −41.7162 | −1.34150 | −0.670751 | − | 0.741683i | \(-0.734028\pi\) | ||||
−0.670751 | + | 0.741683i | \(0.734028\pi\) | |||||||
\(968\) | 10.8870i | 0.349922i | ||||||||
\(969\) | 34.2031 | + | 38.9125i | 1.09876 | + | 1.25005i | ||||
\(970\) | −11.6476 | −0.373980 | ||||||||
\(971\) | −33.7924 | −1.08445 | −0.542226 | − | 0.840233i | \(-0.682418\pi\) | ||||
−0.542226 | + | 0.840233i | \(0.682418\pi\) | |||||||
\(972\) | −13.9418 | + | 6.97334i | −0.447182 | + | 0.223670i | ||||
\(973\) | − | 5.33354i | − | 0.170985i | ||||||
\(974\) | − | 41.8360i | − | 1.34051i | ||||||
\(975\) | 6.41091 | − | 5.63502i | 0.205313 | − | 0.180465i | ||||
\(976\) | 12.9663i | 0.415040i | ||||||||
\(977\) | −36.3672 | −1.16349 | −0.581746 | − | 0.813371i | \(-0.697630\pi\) | ||||
−0.581746 | + | 0.813371i | \(0.697630\pi\) | |||||||
\(978\) | 8.56461 | + | 9.74387i | 0.273866 | + | 0.311574i | ||||
\(979\) | 4.75178 | 0.151868 | ||||||||
\(980\) | −5.95817 | −0.190327 | ||||||||
\(981\) | 39.8724 | + | 5.15782i | 1.27303 | + | 0.164676i | ||||
\(982\) | −35.6738 | −1.13840 | ||||||||
\(983\) | −21.7604 | −0.694050 | −0.347025 | − | 0.937856i | \(-0.612808\pi\) | ||||
−0.347025 | + | 0.937856i | \(0.612808\pi\) | |||||||
\(984\) | 10.1767 | − | 8.94506i | 0.324421 | − | 0.285158i | ||||
\(985\) | − | 6.30397i | − | 0.200861i | ||||||
\(986\) | −16.6714 | −0.530927 | ||||||||
\(987\) | 7.10221 | − | 6.24266i | 0.226066 | − | 0.198706i | ||||
\(988\) | 19.4674i | 0.619340i | ||||||||
\(989\) | −40.4432 | + | 26.2483i | −1.28602 | + | 0.834646i | ||||
\(990\) | −1.00002 | − | 0.129361i | −0.0317827 | − | 0.00411135i | ||||
\(991\) | −39.6331 | −1.25899 | −0.629493 | − | 0.777006i | \(-0.716738\pi\) | ||||
−0.629493 | + | 0.777006i | \(0.716738\pi\) | |||||||
\(992\) | − | 1.27271i | − | 0.0404086i | ||||||
\(993\) | −35.7603 | + | 31.4323i | −1.13482 | + | 0.997475i | ||||
\(994\) | 11.0670i | 0.351024i | ||||||||
\(995\) | 7.67517i | 0.243319i | ||||||||
\(996\) | 20.9075 | − | 18.3771i | 0.662479 | − | 0.582302i | ||||
\(997\) | 51.0995 | 1.61834 | 0.809169 | − | 0.587576i | \(-0.199918\pi\) | ||||
0.809169 | + | 0.587576i | \(0.199918\pi\) | |||||||
\(998\) | 3.39015i | 0.107313i | ||||||||
\(999\) | 1.63297 | − | 1.09913i | 0.0516648 | − | 0.0347748i |
(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 | 690.2.e.b.551.10 | yes | 16 | |
3.2 | odd | 2 | 690.2.e.a.551.2 | ✓ | 16 | ||
23.22 | odd | 2 | 690.2.e.a.551.10 | yes | 16 | ||
69.68 | even | 2 | inner | 690.2.e.b.551.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.e.a.551.2 | ✓ | 16 | 3.2 | odd | 2 | ||
690.2.e.a.551.10 | yes | 16 | 23.22 | odd | 2 | ||
690.2.e.b.551.2 | yes | 16 | 69.68 | even | 2 | inner | |
690.2.e.b.551.10 | yes | 16 | 1.1 | even | 1 | trivial |