Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(106,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.4 | ||
Root | \(-0.978148 - 0.207912i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.106 |
Dual form | 315.2.i.d.211.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.913545 | − | 1.58231i | 0.645974 | − | 1.11886i | −0.338101 | − | 0.941110i | \(-0.609785\pi\) |
0.984076 | − | 0.177750i | \(-0.0568820\pi\) | |||||||
\(3\) | 0.360114 | + | 1.69420i | 0.207912 | + | 0.978148i | ||||
\(4\) | −0.669131 | − | 1.15897i | −0.334565 | − | 0.579484i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 3.00973 | + | 0.977920i | 1.22872 | + | 0.399234i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 1.20906 | 0.427466 | ||||||||
\(9\) | −2.74064 | + | 1.22021i | −0.913545 | + | 0.406737i | ||||
\(10\) | 1.82709 | 0.577777 | ||||||||
\(11\) | −0.0864545 | + | 0.149744i | −0.0260670 | + | 0.0451494i | −0.878765 | − | 0.477255i | \(-0.841632\pi\) |
0.852698 | + | 0.522405i | \(0.174965\pi\) | |||||||
\(12\) | 1.72256 | − | 1.55100i | 0.497261 | − | 0.447736i | ||||
\(13\) | 1.87362 | + | 3.24520i | 0.519648 | + | 0.900058i | 0.999739 | + | 0.0228387i | \(0.00727041\pi\) |
−0.480091 | + | 0.877219i | \(0.659396\pi\) | |||||||
\(14\) | −0.913545 | − | 1.58231i | −0.244155 | − | 0.422889i | ||||
\(15\) | −1.28716 | + | 1.15897i | −0.332344 | + | 0.299244i | ||||
\(16\) | 2.44279 | − | 4.23104i | 0.610697 | − | 1.05776i | ||||
\(17\) | 1.82709 | 0.443135 | 0.221567 | − | 0.975145i | \(-0.428883\pi\) | ||||
0.221567 | + | 0.975145i | \(0.428883\pi\) | |||||||
\(18\) | −0.572949 | + | 5.45125i | −0.135045 | + | 1.28487i | ||||
\(19\) | −0.138341 | −0.0317376 | −0.0158688 | − | 0.999874i | \(-0.505051\pi\) | ||||
−0.0158688 | + | 0.999874i | \(0.505051\pi\) | |||||||
\(20\) | 0.669131 | − | 1.15897i | 0.149622 | − | 0.259153i | ||||
\(21\) | 1.64728 | + | 0.535233i | 0.359466 | + | 0.116797i | ||||
\(22\) | 0.157960 | + | 0.273595i | 0.0336773 | + | 0.0583307i | ||||
\(23\) | −3.90142 | − | 6.75746i | −0.813502 | − | 1.40903i | −0.910398 | − | 0.413733i | \(-0.864225\pi\) |
0.0968960 | − | 0.995295i | \(-0.469109\pi\) | |||||||
\(24\) | 0.435398 | + | 2.04839i | 0.0888752 | + | 0.418125i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 6.84655 | 1.34272 | ||||||||
\(27\) | −3.05422 | − | 4.20378i | −0.587785 | − | 0.809017i | ||||
\(28\) | −1.33826 | −0.252908 | ||||||||
\(29\) | 0.489318 | − | 0.847523i | 0.0908641 | − | 0.157381i | −0.817011 | − | 0.576622i | \(-0.804370\pi\) |
0.907875 | + | 0.419241i | \(0.137704\pi\) | |||||||
\(30\) | 0.657960 | + | 3.09546i | 0.120127 | + | 0.565151i | ||||
\(31\) | 1.36245 | + | 2.35983i | 0.244703 | + | 0.423838i | 0.962048 | − | 0.272880i | \(-0.0879762\pi\) |
−0.717345 | + | 0.696718i | \(0.754643\pi\) | |||||||
\(32\) | −3.25414 | − | 5.63634i | −0.575256 | − | 0.996373i | ||||
\(33\) | −0.284829 | − | 0.0925467i | −0.0495824 | − | 0.0161103i | ||||
\(34\) | 1.66913 | − | 2.89102i | 0.286254 | − | 0.495806i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 3.24803 | + | 2.35983i | 0.541338 | + | 0.393305i | ||||
\(37\) | −7.88558 | −1.29638 | −0.648191 | − | 0.761478i | \(-0.724474\pi\) | ||||
−0.648191 | + | 0.761478i | \(0.724474\pi\) | |||||||
\(38\) | −0.126381 | + | 0.218898i | −0.0205017 | + | 0.0355100i | ||||
\(39\) | −4.82331 | + | 4.34293i | −0.772348 | + | 0.695425i | ||||
\(40\) | 0.604528 | + | 1.04707i | 0.0955843 | + | 0.165557i | ||||
\(41\) | −5.02090 | − | 8.69645i | −0.784132 | − | 1.35816i | −0.929516 | − | 0.368782i | \(-0.879775\pi\) |
0.145384 | − | 0.989375i | \(-0.453558\pi\) | |||||||
\(42\) | 2.35177 | − | 2.11754i | 0.362885 | − | 0.326744i | ||||
\(43\) | −3.69693 | + | 6.40327i | −0.563777 | + | 0.976490i | 0.433386 | + | 0.901209i | \(0.357319\pi\) |
−0.997162 | + | 0.0752814i | \(0.976014\pi\) | |||||||
\(44\) | 0.231398 | 0.0348845 | ||||||||
\(45\) | −2.42705 | − | 1.76336i | −0.361803 | − | 0.262866i | ||||
\(46\) | −14.2565 | −2.10201 | ||||||||
\(47\) | 2.90063 | − | 5.02404i | 0.423100 | − | 0.732831i | −0.573141 | − | 0.819457i | \(-0.694275\pi\) |
0.996241 | + | 0.0866257i | \(0.0276084\pi\) | |||||||
\(48\) | 8.04791 | + | 2.61492i | 1.16162 | + | 0.377432i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0.913545 | + | 1.58231i | 0.129195 | + | 0.223772i | ||||
\(51\) | 0.657960 | + | 3.09546i | 0.0921329 | + | 0.433451i | ||||
\(52\) | 2.50739 | − | 4.34293i | 0.347713 | − | 0.602256i | ||||
\(53\) | −11.7139 | −1.60902 | −0.804511 | − | 0.593938i | \(-0.797572\pi\) | ||||
−0.804511 | + | 0.593938i | \(0.797572\pi\) | |||||||
\(54\) | −9.44183 | + | 0.992377i | −1.28487 | + | 0.135045i | ||||
\(55\) | −0.172909 | −0.0233151 | ||||||||
\(56\) | 0.604528 | − | 1.04707i | 0.0807835 | − | 0.139921i | ||||
\(57\) | −0.0498185 | − | 0.234378i | −0.00659862 | − | 0.0310441i | ||||
\(58\) | −0.894028 | − | 1.54850i | −0.117392 | − | 0.203328i | ||||
\(59\) | 0.590068 | + | 1.02203i | 0.0768203 | + | 0.133057i | 0.901876 | − | 0.431994i | \(-0.142190\pi\) |
−0.825056 | + | 0.565051i | \(0.808857\pi\) | |||||||
\(60\) | 2.20449 | + | 0.716282i | 0.284598 | + | 0.0924716i | ||||
\(61\) | −3.50138 | + | 6.06457i | −0.448306 | + | 0.776488i | −0.998276 | − | 0.0586959i | \(-0.981306\pi\) |
0.549970 | + | 0.835184i | \(0.314639\pi\) | |||||||
\(62\) | 4.97864 | 0.632287 | ||||||||
\(63\) | −0.313585 | + | 2.98357i | −0.0395080 | + | 0.375894i | ||||
\(64\) | −2.12007 | −0.265008 | ||||||||
\(65\) | −1.87362 | + | 3.24520i | −0.232394 | + | 0.402518i | ||||
\(66\) | −0.406642 | + | 0.366142i | −0.0500541 | + | 0.0450690i | ||||
\(67\) | 2.19098 | + | 3.79489i | 0.267671 | + | 0.463620i | 0.968260 | − | 0.249945i | \(-0.0804126\pi\) |
−0.700589 | + | 0.713565i | \(0.747079\pi\) | |||||||
\(68\) | −1.22256 | − | 2.11754i | −0.148257 | − | 0.256789i | ||||
\(69\) | 10.0435 | − | 9.04324i | 1.20910 | − | 1.08868i | ||||
\(70\) | 0.913545 | − | 1.58231i | 0.109190 | − | 0.189122i | ||||
\(71\) | 11.2163 | 1.33113 | 0.665564 | − | 0.746341i | \(-0.268191\pi\) | ||||
0.665564 | + | 0.746341i | \(0.268191\pi\) | |||||||
\(72\) | −3.31359 | + | 1.47530i | −0.390510 | + | 0.173866i | ||||
\(73\) | −1.60792 | −0.188193 | −0.0940964 | − | 0.995563i | \(-0.529996\pi\) | ||||
−0.0940964 | + | 0.995563i | \(0.529996\pi\) | |||||||
\(74\) | −7.20384 | + | 12.4774i | −0.837429 | + | 1.45047i | ||||
\(75\) | −1.64728 | − | 0.535233i | −0.190211 | − | 0.0618034i | ||||
\(76\) | 0.0925682 | + | 0.160333i | 0.0106183 | + | 0.0183914i | ||||
\(77\) | 0.0864545 | + | 0.149744i | 0.00985241 | + | 0.0170649i | ||||
\(78\) | 2.46553 | + | 11.5994i | 0.279167 | + | 1.31338i | ||||
\(79\) | 7.08327 | − | 12.2686i | 0.796930 | − | 1.38032i | −0.124677 | − | 0.992197i | \(-0.539789\pi\) |
0.921607 | − | 0.388125i | \(-0.126877\pi\) | |||||||
\(80\) | 4.88558 | 0.546224 | ||||||||
\(81\) | 6.02218 | − | 6.68830i | 0.669131 | − | 0.743145i | ||||
\(82\) | −18.3473 | −2.02612 | ||||||||
\(83\) | 4.63660 | − | 8.03082i | 0.508933 | − | 0.881497i | −0.491014 | − | 0.871152i | \(-0.663374\pi\) |
0.999946 | − | 0.0103453i | \(-0.00329307\pi\) | |||||||
\(84\) | −0.481926 | − | 2.26728i | −0.0525824 | − | 0.247381i | ||||
\(85\) | 0.913545 | + | 1.58231i | 0.0990879 | + | 0.171625i | ||||
\(86\) | 6.75463 | + | 11.6994i | 0.728370 | + | 1.26157i | ||||
\(87\) | 1.61209 | + | 0.523798i | 0.172834 | + | 0.0561571i | ||||
\(88\) | −0.104528 | + | 0.181049i | −0.0111428 | + | 0.0192998i | ||||
\(89\) | 11.8868 | 1.25999 | 0.629997 | − | 0.776598i | \(-0.283056\pi\) | ||||
0.629997 | + | 0.776598i | \(0.283056\pi\) | |||||||
\(90\) | −5.00739 | + | 2.22943i | −0.527825 | + | 0.235003i | ||||
\(91\) | 3.74724 | 0.392817 | ||||||||
\(92\) | −5.22112 | + | 9.04324i | −0.544339 | + | 0.942823i | ||||
\(93\) | −3.50739 | + | 3.15807i | −0.363700 | + | 0.327477i | ||||
\(94\) | −5.29972 | − | 9.17938i | −0.546624 | − | 0.946780i | ||||
\(95\) | −0.0691705 | − | 0.119807i | −0.00709675 | − | 0.0122919i | ||||
\(96\) | 8.37723 | − | 7.54289i | 0.854998 | − | 0.769843i | ||||
\(97\) | −5.18907 | + | 8.98774i | −0.526871 | + | 0.912567i | 0.472639 | + | 0.881256i | \(0.343301\pi\) |
−0.999510 | + | 0.0313105i | \(0.990032\pi\) | |||||||
\(98\) | −1.82709 | −0.184564 | ||||||||
\(99\) | 0.0542218 | − | 0.515886i | 0.00544949 | − | 0.0518485i | ||||
\(100\) | 1.33826 | 0.133826 | ||||||||
\(101\) | −8.85160 | + | 15.3314i | −0.880767 | + | 1.52553i | −0.0302779 | + | 0.999542i | \(0.509639\pi\) |
−0.850489 | + | 0.525992i | \(0.823694\pi\) | |||||||
\(102\) | 5.49904 | + | 1.78675i | 0.544487 | + | 0.176914i | ||||
\(103\) | 1.07860 | + | 1.86818i | 0.106277 | + | 0.184078i | 0.914259 | − | 0.405130i | \(-0.132774\pi\) |
−0.807982 | + | 0.589207i | \(0.799440\pi\) | |||||||
\(104\) | 2.26531 | + | 3.92364i | 0.222132 | + | 0.384744i | ||||
\(105\) | 0.360114 | + | 1.69420i | 0.0351435 | + | 0.165337i | ||||
\(106\) | −10.7011 | + | 18.5349i | −1.03939 | + | 1.80027i | ||||
\(107\) | −11.5229 | −1.11396 | −0.556979 | − | 0.830527i | \(-0.688039\pi\) | ||||
−0.556979 | + | 0.830527i | \(0.688039\pi\) | |||||||
\(108\) | −2.82837 | + | 6.35262i | −0.272160 | + | 0.611281i | ||||
\(109\) | 6.89492 | 0.660414 | 0.330207 | − | 0.943909i | \(-0.392882\pi\) | ||||
0.330207 | + | 0.943909i | \(0.392882\pi\) | |||||||
\(110\) | −0.157960 | + | 0.273595i | −0.0150609 | + | 0.0260863i | ||||
\(111\) | −2.83970 | − | 13.3598i | −0.269533 | − | 1.26805i | ||||
\(112\) | −2.44279 | − | 4.23104i | −0.230822 | − | 0.399795i | ||||
\(113\) | −3.34848 | − | 5.79973i | −0.314998 | − | 0.545593i | 0.664439 | − | 0.747343i | \(-0.268671\pi\) |
−0.979437 | + | 0.201750i | \(0.935337\pi\) | |||||||
\(114\) | −0.416369 | − | 0.135286i | −0.0389965 | − | 0.0126707i | ||||
\(115\) | 3.90142 | − | 6.75746i | 0.363809 | − | 0.630136i | ||||
\(116\) | −1.30967 | −0.121600 | ||||||||
\(117\) | −9.09474 | − | 6.60771i | −0.840809 | − | 0.610883i | ||||
\(118\) | 2.15622 | 0.198496 | ||||||||
\(119\) | 0.913545 | − | 1.58231i | 0.0837446 | − | 0.145050i | ||||
\(120\) | −1.55626 | + | 1.40126i | −0.142066 | + | 0.127917i | ||||
\(121\) | 5.48505 | + | 9.50039i | 0.498641 | + | 0.863672i | ||||
\(122\) | 6.39734 | + | 11.0805i | 0.579188 | + | 1.00318i | ||||
\(123\) | 12.9254 | − | 11.6381i | 1.16545 | − | 1.04937i | ||||
\(124\) | 1.82331 | − | 3.15807i | 0.163738 | − | 0.283603i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.43444 | + | 3.22181i | 0.395052 | + | 0.287022i | ||||
\(127\) | −16.8604 | −1.49611 | −0.748057 | − | 0.663634i | \(-0.769013\pi\) | ||||
−0.748057 | + | 0.663634i | \(0.769013\pi\) | |||||||
\(128\) | 4.57151 | − | 7.91808i | 0.404068 | − | 0.699866i | ||||
\(129\) | −12.1797 | − | 3.95744i | −1.07237 | − | 0.348433i | ||||
\(130\) | 3.42327 | + | 5.92928i | 0.300241 | + | 0.520032i | ||||
\(131\) | 6.33458 | + | 10.9718i | 0.553455 | + | 0.958613i | 0.998022 | + | 0.0628668i | \(0.0200243\pi\) |
−0.444567 | + | 0.895746i | \(0.646642\pi\) | |||||||
\(132\) | 0.0833294 | + | 0.392034i | 0.00725289 | + | 0.0341222i | ||||
\(133\) | −0.0691705 | + | 0.119807i | −0.00599785 | + | 0.0103886i | ||||
\(134\) | 8.00625 | 0.691635 | ||||||||
\(135\) | 2.11347 | − | 4.74692i | 0.181898 | − | 0.408550i | ||||
\(136\) | 2.20906 | 0.189425 | ||||||||
\(137\) | 1.69555 | − | 2.93678i | 0.144861 | − | 0.250906i | −0.784460 | − | 0.620179i | \(-0.787060\pi\) |
0.929321 | + | 0.369273i | \(0.120393\pi\) | |||||||
\(138\) | −5.13396 | − | 24.1534i | −0.437032 | − | 2.05607i | ||||
\(139\) | −4.06773 | − | 7.04551i | −0.345020 | − | 0.597592i | 0.640337 | − | 0.768094i | \(-0.278795\pi\) |
−0.985357 | + | 0.170501i | \(0.945461\pi\) | |||||||
\(140\) | −0.669131 | − | 1.15897i | −0.0565519 | − | 0.0979507i | ||||
\(141\) | 9.55629 | + | 3.10503i | 0.804785 | + | 0.261490i | ||||
\(142\) | 10.2466 | − | 17.7476i | 0.859874 | − | 1.48935i | ||||
\(143\) | −0.647932 | −0.0541828 | ||||||||
\(144\) | −1.53205 | + | 14.5764i | −0.127671 | + | 1.21470i | ||||
\(145\) | 0.978636 | 0.0812713 | ||||||||
\(146\) | −1.46891 | + | 2.54422i | −0.121568 | + | 0.210562i | ||||
\(147\) | 1.28716 | − | 1.15897i | 0.106164 | − | 0.0955901i | ||||
\(148\) | 5.27648 | + | 9.13914i | 0.433724 | + | 0.751232i | ||||
\(149\) | 2.04131 | + | 3.53565i | 0.167230 | + | 0.289651i | 0.937445 | − | 0.348133i | \(-0.113184\pi\) |
−0.770215 | + | 0.637785i | \(0.779851\pi\) | |||||||
\(150\) | −2.35177 | + | 2.11754i | −0.192021 | + | 0.172896i | ||||
\(151\) | 7.85489 | − | 13.6051i | 0.639222 | − | 1.10717i | −0.346382 | − | 0.938094i | \(-0.612590\pi\) |
0.985604 | − | 0.169071i | \(-0.0540769\pi\) | |||||||
\(152\) | −0.167262 | −0.0135668 | ||||||||
\(153\) | −5.00739 | + | 2.22943i | −0.404824 | + | 0.180239i | ||||
\(154\) | 0.315921 | 0.0254576 | ||||||||
\(155\) | −1.36245 | + | 2.35983i | −0.109435 | + | 0.189546i | ||||
\(156\) | 8.26074 | + | 2.68408i | 0.661389 | + | 0.214898i | ||||
\(157\) | 1.15280 | + | 1.99671i | 0.0920036 | + | 0.159355i | 0.908354 | − | 0.418202i | \(-0.137340\pi\) |
−0.816351 | + | 0.577557i | \(0.804006\pi\) | |||||||
\(158\) | −12.9418 | − | 22.4158i | −1.02959 | − | 1.78331i | ||||
\(159\) | −4.21832 | − | 19.8456i | −0.334534 | − | 1.57386i | ||||
\(160\) | 3.25414 | − | 5.63634i | 0.257263 | − | 0.445592i | ||||
\(161\) | −7.80284 | −0.614950 | ||||||||
\(162\) | −5.08142 | − | 15.6390i | −0.399234 | − | 1.22872i | ||||
\(163\) | 18.7421 | 1.46800 | 0.733998 | − | 0.679152i | \(-0.237652\pi\) | ||||
0.733998 | + | 0.679152i | \(0.237652\pi\) | |||||||
\(164\) | −6.71927 | + | 11.6381i | −0.524687 | + | 0.908785i | ||||
\(165\) | −0.0622669 | − | 0.292943i | −0.00484747 | − | 0.0228056i | ||||
\(166\) | −8.47148 | − | 14.6730i | −0.657515 | − | 1.13885i | ||||
\(167\) | 2.85634 | + | 4.94732i | 0.221030 | + | 0.382835i | 0.955121 | − | 0.296216i | \(-0.0957248\pi\) |
−0.734091 | + | 0.679051i | \(0.762392\pi\) | |||||||
\(168\) | 1.99165 | + | 0.647127i | 0.153659 | + | 0.0499270i | ||||
\(169\) | −0.520897 | + | 0.902221i | −0.0400690 | + | 0.0694016i | ||||
\(170\) | 3.33826 | 0.256033 | ||||||||
\(171\) | 0.379143 | − | 0.168805i | 0.0289938 | − | 0.0129089i | ||||
\(172\) | 9.89492 | 0.754481 | ||||||||
\(173\) | 8.83149 | − | 15.2966i | 0.671446 | − | 1.16298i | −0.306048 | − | 0.952016i | \(-0.599007\pi\) |
0.977494 | − | 0.210963i | \(-0.0676598\pi\) | |||||||
\(174\) | 2.30152 | − | 2.07230i | 0.174478 | − | 0.157101i | ||||
\(175\) | 0.500000 | + | 0.866025i | 0.0377964 | + | 0.0654654i | ||||
\(176\) | 0.422381 | + | 0.731585i | 0.0318381 | + | 0.0551453i | ||||
\(177\) | −1.51903 | + | 1.36774i | −0.114177 | + | 0.102806i | ||||
\(178\) | 10.8591 | − | 18.8085i | 0.813924 | − | 1.40976i | ||||
\(179\) | 3.59700 | 0.268852 | 0.134426 | − | 0.990924i | \(-0.457081\pi\) | ||||
0.134426 | + | 0.990924i | \(0.457081\pi\) | |||||||
\(180\) | −0.419659 | + | 3.99279i | −0.0312795 | + | 0.297605i | ||||
\(181\) | −13.8362 | −1.02844 | −0.514219 | − | 0.857659i | \(-0.671918\pi\) | ||||
−0.514219 | + | 0.857659i | \(0.671918\pi\) | |||||||
\(182\) | 3.42327 | − | 5.92928i | 0.253750 | − | 0.439508i | ||||
\(183\) | −11.5355 | − | 3.74811i | −0.852728 | − | 0.277068i | ||||
\(184\) | −4.71704 | − | 8.17015i | −0.347745 | − | 0.602312i | ||||
\(185\) | −3.94279 | − | 6.82911i | −0.289880 | − | 0.502086i | ||||
\(186\) | 1.79287 | + | 8.43481i | 0.131460 | + | 0.618470i | ||||
\(187\) | −0.157960 | + | 0.273595i | −0.0115512 | + | 0.0200073i | ||||
\(188\) | −7.76360 | −0.566219 | ||||||||
\(189\) | −5.16769 | + | 0.543146i | −0.375894 | + | 0.0395080i | ||||
\(190\) | −0.252762 | −0.0183373 | ||||||||
\(191\) | 2.99212 | − | 5.18250i | 0.216502 | − | 0.374993i | −0.737234 | − | 0.675637i | \(-0.763868\pi\) |
0.953736 | + | 0.300645i | \(0.0972018\pi\) | |||||||
\(192\) | −0.763465 | − | 3.59182i | −0.0550984 | − | 0.259217i | ||||
\(193\) | 8.83948 | + | 15.3104i | 0.636279 | + | 1.10207i | 0.986243 | + | 0.165305i | \(0.0528608\pi\) |
−0.349963 | + | 0.936763i | \(0.613806\pi\) | |||||||
\(194\) | 9.48091 | + | 16.4214i | 0.680690 | + | 1.17899i | ||||
\(195\) | −6.17274 | − | 2.00565i | −0.442039 | − | 0.143627i | ||||
\(196\) | −0.669131 | + | 1.15897i | −0.0477950 | + | 0.0827834i | ||||
\(197\) | −20.1914 | −1.43858 | −0.719290 | − | 0.694710i | \(-0.755533\pi\) | ||||
−0.719290 | + | 0.694710i | \(0.755533\pi\) | |||||||
\(198\) | −0.766755 | − | 0.557080i | −0.0544909 | − | 0.0395900i | ||||
\(199\) | 18.0867 | 1.28214 | 0.641068 | − | 0.767484i | \(-0.278492\pi\) | ||||
0.641068 | + | 0.767484i | \(0.278492\pi\) | |||||||
\(200\) | −0.604528 | + | 1.04707i | −0.0427466 | + | 0.0740393i | ||||
\(201\) | −5.64031 | + | 5.07856i | −0.397837 | + | 0.358214i | ||||
\(202\) | 16.1727 | + | 28.0119i | 1.13791 | + | 1.97091i | ||||
\(203\) | −0.489318 | − | 0.847523i | −0.0343434 | − | 0.0594845i | ||||
\(204\) | 3.14728 | − | 2.83382i | 0.220354 | − | 0.198407i | ||||
\(205\) | 5.02090 | − | 8.69645i | 0.350675 | − | 0.607386i | ||||
\(206\) | 3.94139 | 0.274609 | ||||||||
\(207\) | 18.9379 | + | 13.7592i | 1.31627 | + | 0.956329i | ||||
\(208\) | 18.3074 | 1.26939 | ||||||||
\(209\) | 0.0119602 | − | 0.0207157i | 0.000827305 | − | 0.00143293i | ||||
\(210\) | 3.00973 | + | 0.977920i | 0.207691 | + | 0.0674829i | ||||
\(211\) | 11.9382 | + | 20.6775i | 0.821857 | + | 1.42350i | 0.904298 | + | 0.426902i | \(0.140395\pi\) |
−0.0824414 | + | 0.996596i | \(0.526272\pi\) | |||||||
\(212\) | 7.83810 | + | 13.5760i | 0.538323 | + | 0.932402i | ||||
\(213\) | 4.03914 | + | 19.0026i | 0.276757 | + | 1.30204i | ||||
\(214\) | −10.5267 | + | 18.2327i | −0.719588 | + | 1.24636i | ||||
\(215\) | −7.39386 | −0.504257 | ||||||||
\(216\) | −3.69273 | − | 5.08260i | −0.251258 | − | 0.345827i | ||||
\(217\) | 2.72490 | 0.184978 | ||||||||
\(218\) | 6.29882 | − | 10.9099i | 0.426610 | − | 0.738910i | ||||
\(219\) | −0.579034 | − | 2.72414i | −0.0391275 | − | 0.184080i | ||||
\(220\) | 0.115699 | + | 0.200396i | 0.00780041 | + | 0.0135107i | ||||
\(221\) | 3.42327 | + | 5.92928i | 0.230274 | + | 0.398847i | ||||
\(222\) | −23.7334 | − | 7.71146i | −1.59288 | − | 0.517559i | ||||
\(223\) | −3.81407 | + | 6.60617i | −0.255409 | + | 0.442382i | −0.965007 | − | 0.262226i | \(-0.915544\pi\) |
0.709597 | + | 0.704607i | \(0.248877\pi\) | |||||||
\(224\) | −6.50828 | −0.434853 | ||||||||
\(225\) | 0.313585 | − | 2.98357i | 0.0209057 | − | 0.198904i | ||||
\(226\) | −12.2359 | −0.813923 | ||||||||
\(227\) | −8.09650 | + | 14.0236i | −0.537384 | + | 0.930776i | 0.461660 | + | 0.887057i | \(0.347254\pi\) |
−0.999044 | + | 0.0437192i | \(0.986079\pi\) | |||||||
\(228\) | −0.238301 | + | 0.214567i | −0.0157819 | + | 0.0142101i | ||||
\(229\) | 12.5200 | + | 21.6854i | 0.827348 | + | 1.43301i | 0.900112 | + | 0.435659i | \(0.143485\pi\) |
−0.0727638 | + | 0.997349i | \(0.523182\pi\) | |||||||
\(230\) | −7.12825 | − | 12.3465i | −0.470023 | − | 0.814103i | ||||
\(231\) | −0.222562 | + | 0.200396i | −0.0146435 | + | 0.0131851i | ||||
\(232\) | 0.591613 | − | 1.02470i | 0.0388413 | − | 0.0672751i | ||||
\(233\) | −10.2963 | −0.674536 | −0.337268 | − | 0.941409i | \(-0.609503\pi\) | ||||
−0.337268 | + | 0.941409i | \(0.609503\pi\) | |||||||
\(234\) | −18.7639 | + | 8.35422i | −1.22663 | + | 0.546133i | ||||
\(235\) | 5.80126 | 0.378433 | ||||||||
\(236\) | 0.789665 | − | 1.36774i | 0.0514028 | − | 0.0890323i | ||||
\(237\) | 23.3362 | + | 7.58240i | 1.51585 | + | 0.492530i | ||||
\(238\) | −1.66913 | − | 2.89102i | −0.108194 | − | 0.187397i | ||||
\(239\) | −9.95235 | − | 17.2380i | −0.643764 | − | 1.11503i | −0.984585 | − | 0.174904i | \(-0.944038\pi\) |
0.340821 | − | 0.940128i | \(-0.389295\pi\) | |||||||
\(240\) | 1.75936 | + | 8.27716i | 0.113566 | + | 0.534288i | ||||
\(241\) | −5.19868 | + | 9.00437i | −0.334876 | + | 0.580023i | −0.983461 | − | 0.181120i | \(-0.942028\pi\) |
0.648585 | + | 0.761142i | \(0.275361\pi\) | |||||||
\(242\) | 20.0434 | 1.28844 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 9.37152 | 0.599950 | ||||||||
\(245\) | 0.500000 | − | 0.866025i | 0.0319438 | − | 0.0553283i | ||||
\(246\) | −6.60710 | − | 31.0840i | −0.421253 | − | 1.98184i | ||||
\(247\) | −0.259198 | − | 0.448945i | −0.0164924 | − | 0.0285657i | ||||
\(248\) | 1.64728 | + | 2.85317i | 0.104602 | + | 0.181176i | ||||
\(249\) | 15.2755 | + | 4.96332i | 0.968047 | + | 0.314538i | ||||
\(250\) | −0.913545 | + | 1.58231i | −0.0577777 | + | 0.100074i | ||||
\(251\) | −24.0059 | −1.51524 | −0.757620 | − | 0.652696i | \(-0.773638\pi\) | ||||
−0.757620 | + | 0.652696i | \(0.773638\pi\) | |||||||
\(252\) | 3.66769 | − | 1.63296i | 0.231043 | − | 0.102867i | ||||
\(253\) | 1.34918 | 0.0848223 | ||||||||
\(254\) | −15.4027 | + | 26.6783i | −0.966451 | + | 1.67394i | ||||
\(255\) | −2.35177 | + | 2.11754i | −0.147273 | + | 0.132606i | ||||
\(256\) | −10.4726 | − | 18.1391i | −0.654539 | − | 1.13369i | ||||
\(257\) | 6.03395 | + | 10.4511i | 0.376387 | + | 0.651922i | 0.990534 | − | 0.137270i | \(-0.0438328\pi\) |
−0.614146 | + | 0.789192i | \(0.710500\pi\) | |||||||
\(258\) | −17.3886 | + | 15.6568i | −1.08257 | + | 0.974750i | ||||
\(259\) | −3.94279 | + | 6.82911i | −0.244993 | + | 0.424340i | ||||
\(260\) | 5.01478 | 0.311004 | ||||||||
\(261\) | −0.306886 | + | 2.91982i | −0.0189958 | + | 0.180733i | ||||
\(262\) | 23.1477 | 1.43007 | ||||||||
\(263\) | −1.93191 | + | 3.34616i | −0.119127 | + | 0.206333i | −0.919422 | − | 0.393273i | \(-0.871343\pi\) |
0.800295 | + | 0.599606i | \(0.204676\pi\) | |||||||
\(264\) | −0.344375 | − | 0.111894i | −0.0211948 | − | 0.00688661i | ||||
\(265\) | −5.85693 | − | 10.1445i | −0.359788 | − | 0.623171i | ||||
\(266\) | 0.126381 | + | 0.218898i | 0.00774891 | + | 0.0134215i | ||||
\(267\) | 4.28058 | + | 20.1386i | 0.261967 | + | 1.23246i | ||||
\(268\) | 2.93211 | − | 5.07856i | 0.179107 | − | 0.310222i | ||||
\(269\) | 8.48725 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(270\) | −5.58034 | − | 7.68068i | −0.339609 | − | 0.467431i | ||||
\(271\) | 11.8287 | 0.718541 | 0.359270 | − | 0.933234i | \(-0.383026\pi\) | ||||
0.359270 | + | 0.933234i | \(0.383026\pi\) | |||||||
\(272\) | 4.46320 | − | 7.73049i | 0.270621 | − | 0.468730i | ||||
\(273\) | 1.34943 | + | 6.34858i | 0.0816713 | + | 0.384233i | ||||
\(274\) | −3.09793 | − | 5.36577i | −0.187153 | − | 0.324158i | ||||
\(275\) | −0.0864545 | − | 0.149744i | −0.00521341 | − | 0.00902988i | ||||
\(276\) | −17.2013 | − | 5.58903i | −1.03539 | − | 0.336420i | ||||
\(277\) | 13.6581 | − | 23.6565i | 0.820636 | − | 1.42138i | −0.0845742 | − | 0.996417i | \(-0.526953\pi\) |
0.905210 | − | 0.424965i | \(-0.139714\pi\) | |||||||
\(278\) | −14.8642 | −0.891496 | ||||||||
\(279\) | −6.61347 | − | 4.80496i | −0.395938 | − | 0.287666i | ||||
\(280\) | 1.20906 | 0.0722550 | ||||||||
\(281\) | −7.94358 | + | 13.7587i | −0.473874 | + | 0.820774i | −0.999553 | − | 0.0299091i | \(-0.990478\pi\) |
0.525678 | + | 0.850683i | \(0.323812\pi\) | |||||||
\(282\) | 13.6432 | − | 12.2844i | 0.812441 | − | 0.731526i | ||||
\(283\) | −8.23065 | − | 14.2559i | −0.489261 | − | 0.847425i | 0.510663 | − | 0.859781i | \(-0.329400\pi\) |
−0.999924 | + | 0.0123561i | \(0.996067\pi\) | |||||||
\(284\) | −7.50516 | − | 12.9993i | −0.445349 | − | 0.771367i | ||||
\(285\) | 0.178068 | − | 0.160333i | 0.0105478 | − | 0.00949730i | ||||
\(286\) | −0.591915 | + | 1.02523i | −0.0350007 | + | 0.0606229i | ||||
\(287\) | −10.0418 | −0.592748 | ||||||||
\(288\) | 15.7959 | + | 11.4764i | 0.930784 | + | 0.676255i | ||||
\(289\) | −13.6617 | −0.803632 | ||||||||
\(290\) | 0.894028 | − | 1.54850i | 0.0524991 | − | 0.0909312i | ||||
\(291\) | −17.0957 | − | 5.55473i | −1.00217 | − | 0.325624i | ||||
\(292\) | 1.07591 | + | 1.86353i | 0.0629628 | + | 0.109055i | ||||
\(293\) | 11.9116 | + | 20.6315i | 0.695884 | + | 1.20531i | 0.969882 | + | 0.243576i | \(0.0783205\pi\) |
−0.273998 | + | 0.961730i | \(0.588346\pi\) | |||||||
\(294\) | −0.657960 | − | 3.09546i | −0.0383730 | − | 0.180531i | ||||
\(295\) | −0.590068 | + | 1.02203i | −0.0343551 | + | 0.0595047i | ||||
\(296\) | −9.53411 | −0.554159 | ||||||||
\(297\) | 0.893540 | − | 0.0939148i | 0.0518485 | − | 0.00544949i | ||||
\(298\) | 7.45931 | 0.432106 | ||||||||
\(299\) | 14.6196 | − | 25.3218i | 0.845470 | − | 1.46440i | ||||
\(300\) | 0.481926 | + | 2.26728i | 0.0278240 | + | 0.130902i | ||||
\(301\) | 3.69693 | + | 6.40327i | 0.213088 | + | 0.369079i | ||||
\(302\) | −14.3516 | − | 24.8577i | −0.825842 | − | 1.43040i | ||||
\(303\) | −29.1621 | − | 9.47534i | −1.67532 | − | 0.544344i | ||||
\(304\) | −0.337938 | + | 0.585326i | −0.0193821 | + | 0.0335708i | ||||
\(305\) | −7.00276 | −0.400977 | ||||||||
\(306\) | −1.04683 | + | 9.95992i | −0.0598433 | + | 0.569371i | ||||
\(307\) | −23.7097 | −1.35318 | −0.676591 | − | 0.736359i | \(-0.736543\pi\) | ||||
−0.676591 | + | 0.736359i | \(0.736543\pi\) | |||||||
\(308\) | 0.115699 | − | 0.200396i | 0.00659255 | − | 0.0114186i | ||||
\(309\) | −2.77666 | + | 2.50012i | −0.157959 | + | 0.142227i | ||||
\(310\) | 2.48932 | + | 4.31163i | 0.141384 | + | 0.244884i | ||||
\(311\) | 7.30983 | + | 12.6610i | 0.414502 | + | 0.717939i | 0.995376 | − | 0.0960546i | \(-0.0306223\pi\) |
−0.580874 | + | 0.813994i | \(0.697289\pi\) | |||||||
\(312\) | −5.83166 | + | 5.25085i | −0.330153 | + | 0.297271i | ||||
\(313\) | −5.34090 | + | 9.25071i | −0.301885 | + | 0.522881i | −0.976563 | − | 0.215232i | \(-0.930949\pi\) |
0.674678 | + | 0.738113i | \(0.264283\pi\) | |||||||
\(314\) | 4.21255 | 0.237728 | ||||||||
\(315\) | −2.74064 | + | 1.22021i | −0.154417 | + | 0.0687510i | ||||
\(316\) | −18.9585 | −1.06650 | ||||||||
\(317\) | 10.9564 | − | 18.9771i | 0.615375 | − | 1.06586i | −0.374944 | − | 0.927047i | \(-0.622338\pi\) |
0.990319 | − | 0.138813i | \(-0.0443285\pi\) | |||||||
\(318\) | −35.2555 | − | 11.4552i | −1.97703 | − | 0.642376i | ||||
\(319\) | 0.0846075 | + | 0.146545i | 0.00473711 | + | 0.00820492i | ||||
\(320\) | −1.06003 | − | 1.83603i | −0.0592577 | − | 0.102637i | ||||
\(321\) | −4.14954 | − | 19.5221i | −0.231605 | − | 1.08961i | ||||
\(322\) | −7.12825 | + | 12.3465i | −0.397242 | + | 0.688043i | ||||
\(323\) | −0.252762 | −0.0140640 | ||||||||
\(324\) | −11.7812 | − | 2.50416i | −0.654508 | − | 0.139120i | ||||
\(325\) | −3.74724 | −0.207859 | ||||||||
\(326\) | 17.1218 | − | 29.6558i | 0.948287 | − | 1.64248i | ||||
\(327\) | 2.48295 | + | 11.6814i | 0.137308 | + | 0.645982i | ||||
\(328\) | −6.07055 | − | 10.5145i | −0.335190 | − | 0.580566i | ||||
\(329\) | −2.90063 | − | 5.02404i | −0.159917 | − | 0.276984i | ||||
\(330\) | −0.520409 | − | 0.169091i | −0.0286476 | − | 0.00930816i | ||||
\(331\) | 11.2591 | − | 19.5014i | 0.618858 | − | 1.07189i | −0.370836 | − | 0.928698i | \(-0.620929\pi\) |
0.989694 | − | 0.143195i | \(-0.0457377\pi\) | |||||||
\(332\) | −12.4100 | −0.681085 | ||||||||
\(333\) | 21.6115 | − | 9.62206i | 1.18430 | − | 0.527286i | ||||
\(334\) | 10.4376 | 0.571118 | ||||||||
\(335\) | −2.19098 | + | 3.79489i | −0.119706 | + | 0.207337i | ||||
\(336\) | 6.28854 | − | 5.66223i | 0.343068 | − | 0.308900i | ||||
\(337\) | 3.70857 | + | 6.42343i | 0.202019 | + | 0.349906i | 0.949179 | − | 0.314738i | \(-0.101917\pi\) |
−0.747160 | + | 0.664644i | \(0.768583\pi\) | |||||||
\(338\) | 0.951727 | + | 1.64844i | 0.0517671 | + | 0.0896633i | ||||
\(339\) | 8.62008 | − | 7.76156i | 0.468179 | − | 0.421550i | ||||
\(340\) | 1.22256 | − | 2.11754i | 0.0663028 | − | 0.114840i | ||||
\(341\) | −0.471160 | −0.0255147 | ||||||||
\(342\) | 0.0792624 | − | 0.754131i | 0.00428602 | − | 0.0407787i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −4.46980 | + | 7.74192i | −0.240996 | + | 0.417416i | ||||
\(345\) | 12.8534 | + | 4.17634i | 0.692006 | + | 0.224847i | ||||
\(346\) | −16.1359 | − | 27.9483i | −0.867474 | − | 1.50251i | ||||
\(347\) | 12.0354 | + | 20.8459i | 0.646094 | + | 1.11907i | 0.984048 | + | 0.177905i | \(0.0569319\pi\) |
−0.337954 | + | 0.941163i | \(0.609735\pi\) | |||||||
\(348\) | −0.471630 | − | 2.21885i | −0.0252820 | − | 0.118943i | ||||
\(349\) | −7.74234 | + | 13.4101i | −0.414438 | + | 0.717828i | −0.995369 | − | 0.0961250i | \(-0.969355\pi\) |
0.580931 | + | 0.813953i | \(0.302688\pi\) | |||||||
\(350\) | 1.82709 | 0.0976621 | ||||||||
\(351\) | 7.91966 | − | 17.7878i | 0.422720 | − | 0.949445i | ||||
\(352\) | 1.12534 | 0.0599809 | ||||||||
\(353\) | −10.7716 | + | 18.6569i | −0.573312 | + | 0.993006i | 0.422910 | + | 0.906172i | \(0.361009\pi\) |
−0.996223 | + | 0.0868347i | \(0.972325\pi\) | |||||||
\(354\) | 0.776482 | + | 3.65306i | 0.0412696 | + | 0.194158i | ||||
\(355\) | 5.60814 | + | 9.71359i | 0.297649 | + | 0.515544i | ||||
\(356\) | −7.95379 | − | 13.7764i | −0.421550 | − | 0.730147i | ||||
\(357\) | 3.00973 | + | 0.977920i | 0.159292 | + | 0.0517570i | ||||
\(358\) | 3.28602 | − | 5.69156i | 0.173672 | − | 0.300808i | ||||
\(359\) | −18.2075 | −0.960954 | −0.480477 | − | 0.877007i | \(-0.659536\pi\) | ||||
−0.480477 | + | 0.877007i | \(0.659536\pi\) | |||||||
\(360\) | −2.93444 | − | 2.13200i | −0.154659 | − | 0.112366i | ||||
\(361\) | −18.9809 | −0.998993 | ||||||||
\(362\) | −12.6400 | + | 21.8932i | −0.664345 | + | 1.15068i | ||||
\(363\) | −14.1203 | + | 12.7140i | −0.741125 | + | 0.667312i | ||||
\(364\) | −2.50739 | − | 4.34293i | −0.131423 | − | 0.227631i | ||||
\(365\) | −0.803960 | − | 1.39250i | −0.0420812 | − | 0.0728868i | ||||
\(366\) | −16.4689 | + | 14.8286i | −0.860841 | + | 0.775105i | ||||
\(367\) | 12.5959 | − | 21.8167i | 0.657498 | − | 1.13882i | −0.323763 | − | 0.946138i | \(-0.604948\pi\) |
0.981261 | − | 0.192682i | \(-0.0617186\pi\) | |||||||
\(368\) | −38.1214 | −1.98722 | ||||||||
\(369\) | 24.3719 | + | 17.7073i | 1.26875 | + | 0.921803i | ||||
\(370\) | −14.4077 | −0.749019 | ||||||||
\(371\) | −5.85693 | + | 10.1445i | −0.304076 | + | 0.526676i | ||||
\(372\) | 6.00701 | + | 1.95179i | 0.311449 | + | 0.101196i | ||||
\(373\) | 16.3150 | + | 28.2583i | 0.844757 | + | 1.46316i | 0.885832 | + | 0.464006i | \(0.153588\pi\) |
−0.0410753 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(374\) | 0.288608 | + | 0.499883i | 0.0149236 | + | 0.0258484i | ||||
\(375\) | −0.360114 | − | 1.69420i | −0.0185962 | − | 0.0874882i | ||||
\(376\) | 3.50703 | − | 6.07435i | 0.180861 | − | 0.313261i | ||||
\(377\) | 3.66718 | 0.188869 | ||||||||
\(378\) | −3.86149 | + | 8.67306i | −0.198614 | + | 0.446094i | ||||
\(379\) | −2.59358 | −0.133223 | −0.0666116 | − | 0.997779i | \(-0.521219\pi\) | ||||
−0.0666116 | + | 0.997779i | \(0.521219\pi\) | |||||||
\(380\) | −0.0925682 | + | 0.160333i | −0.00474865 | + | 0.00822490i | ||||
\(381\) | −6.07164 | − | 28.5648i | −0.311060 | − | 1.46342i | ||||
\(382\) | −5.46688 | − | 9.46891i | −0.279710 | − | 0.484471i | ||||
\(383\) | 10.8790 | + | 18.8429i | 0.555890 | + | 0.962829i | 0.997834 | + | 0.0657867i | \(0.0209557\pi\) |
−0.441944 | + | 0.897043i | \(0.645711\pi\) | |||||||
\(384\) | 15.0611 | + | 4.89364i | 0.768583 | + | 0.249728i | ||||
\(385\) | −0.0864545 | + | 0.149744i | −0.00440613 | + | 0.00763164i | ||||
\(386\) | 32.3011 | 1.64408 | ||||||||
\(387\) | 2.31861 | − | 22.0601i | 0.117861 | − | 1.12138i | ||||
\(388\) | 13.8887 | 0.705090 | ||||||||
\(389\) | 6.03881 | − | 10.4595i | 0.306180 | − | 0.530319i | −0.671344 | − | 0.741146i | \(-0.734283\pi\) |
0.977523 | + | 0.210828i | \(0.0676158\pi\) | |||||||
\(390\) | −8.81263 | + | 7.93493i | −0.446245 | + | 0.401801i | ||||
\(391\) | −7.12825 | − | 12.3465i | −0.360491 | − | 0.624389i | ||||
\(392\) | −0.604528 | − | 1.04707i | −0.0305333 | − | 0.0528852i | ||||
\(393\) | −16.3073 | + | 14.6832i | −0.822595 | + | 0.740668i | ||||
\(394\) | −18.4458 | + | 31.9490i | −0.929285 | + | 1.60957i | ||||
\(395\) | 14.1665 | 0.712796 | ||||||||
\(396\) | −0.634176 | + | 0.282354i | −0.0318686 | + | 0.0141888i | ||||
\(397\) | −33.2451 | −1.66852 | −0.834262 | − | 0.551368i | \(-0.814106\pi\) | ||||
−0.834262 | + | 0.551368i | \(0.814106\pi\) | |||||||
\(398\) | 16.5231 | − | 28.6188i | 0.828227 | − | 1.43453i | ||||
\(399\) | −0.227886 | − | 0.0740447i | −0.0114086 | − | 0.00370687i | ||||
\(400\) | 2.44279 | + | 4.23104i | 0.122139 | + | 0.211552i | ||||
\(401\) | 8.81576 | + | 15.2693i | 0.440238 | + | 0.762514i | 0.997707 | − | 0.0676835i | \(-0.0215608\pi\) |
−0.557469 | + | 0.830198i | \(0.688227\pi\) | |||||||
\(402\) | 2.88316 | + | 13.5642i | 0.143799 | + | 0.676521i | ||||
\(403\) | −5.10542 | + | 8.84285i | −0.254319 | + | 0.440494i | ||||
\(404\) | 23.6915 | 1.17870 | ||||||||
\(405\) | 8.80333 | + | 1.87121i | 0.437441 | + | 0.0929809i | ||||
\(406\) | −1.78806 | −0.0887398 | ||||||||
\(407\) | 0.681744 | − | 1.18082i | 0.0337928 | − | 0.0585309i | ||||
\(408\) | 0.795511 | + | 3.74259i | 0.0393837 | + | 0.185286i | ||||
\(409\) | −6.99886 | − | 12.1224i | −0.346071 | − | 0.599413i | 0.639477 | − | 0.768811i | \(-0.279151\pi\) |
−0.985548 | + | 0.169398i | \(0.945818\pi\) | |||||||
\(410\) | −9.17364 | − | 15.8892i | −0.453054 | − | 0.784712i | ||||
\(411\) | 5.58609 | + | 1.81503i | 0.275541 | + | 0.0895289i | ||||
\(412\) | 1.44344 | − | 2.50012i | 0.0711133 | − | 0.123172i | ||||
\(413\) | 1.18014 | 0.0580707 | ||||||||
\(414\) | 39.0719 | − | 17.3959i | 1.92028 | − | 0.854963i | ||||
\(415\) | 9.27319 | 0.455203 | ||||||||
\(416\) | 12.1940 | − | 21.1207i | 0.597862 | − | 1.03553i | ||||
\(417\) | 10.4717 | − | 9.42873i | 0.512800 | − | 0.461727i | ||||
\(418\) | −0.0218524 | − | 0.0378495i | −0.00106884 | − | 0.00185128i | ||||
\(419\) | 9.20103 | + | 15.9367i | 0.449500 | + | 0.778557i | 0.998353 | − | 0.0573619i | \(-0.0182689\pi\) |
−0.548854 | + | 0.835919i | \(0.684936\pi\) | |||||||
\(420\) | 1.72256 | − | 1.55100i | 0.0840524 | − | 0.0756812i | ||||
\(421\) | −1.38600 | + | 2.40063i | −0.0675497 | + | 0.117000i | −0.897822 | − | 0.440358i | \(-0.854851\pi\) |
0.830272 | + | 0.557358i | \(0.188185\pi\) | |||||||
\(422\) | 43.6242 | 2.12359 | ||||||||
\(423\) | −1.81919 | + | 17.3084i | −0.0884521 | + | 0.841565i | ||||
\(424\) | −14.1627 | −0.687802 | ||||||||
\(425\) | −0.913545 | + | 1.58231i | −0.0443135 | + | 0.0767532i | ||||
\(426\) | 33.7580 | + | 10.9686i | 1.63558 | + | 0.531432i | ||||
\(427\) | 3.50138 | + | 6.06457i | 0.169444 | + | 0.293485i | ||||
\(428\) | 7.71030 | + | 13.3546i | 0.372691 | + | 0.645521i | ||||
\(429\) | −0.233329 | − | 1.09773i | −0.0112652 | − | 0.0529987i | ||||
\(430\) | −6.75463 | + | 11.6994i | −0.325737 | + | 0.564193i | ||||
\(431\) | 6.55882 | 0.315927 | 0.157964 | − | 0.987445i | \(-0.449507\pi\) | ||||
0.157964 | + | 0.987445i | \(0.449507\pi\) | |||||||
\(432\) | −25.2471 | + | 2.65358i | −1.21470 | + | 0.127671i | ||||
\(433\) | 3.44922 | 0.165759 | 0.0828794 | − | 0.996560i | \(-0.473588\pi\) | ||||
0.0828794 | + | 0.996560i | \(0.473588\pi\) | |||||||
\(434\) | 2.48932 | − | 4.31163i | 0.119491 | − | 0.206965i | ||||
\(435\) | 0.352420 | + | 1.65801i | 0.0168972 | + | 0.0794953i | ||||
\(436\) | −4.61360 | − | 7.99099i | −0.220951 | − | 0.382699i | ||||
\(437\) | 0.539727 | + | 0.934834i | 0.0258186 | + | 0.0447192i | ||||
\(438\) | −4.83940 | − | 1.57242i | −0.231236 | − | 0.0751330i | ||||
\(439\) | 5.45818 | − | 9.45384i | 0.260505 | − | 0.451207i | −0.705872 | − | 0.708340i | \(-0.749444\pi\) |
0.966376 | + | 0.257133i | \(0.0827778\pi\) | |||||||
\(440\) | −0.209057 | −0.00996640 | ||||||||
\(441\) | 2.42705 | + | 1.76336i | 0.115574 | + | 0.0839693i | ||||
\(442\) | 12.5093 | 0.595005 | ||||||||
\(443\) | −6.96293 | + | 12.0602i | −0.330819 | + | 0.572995i | −0.982673 | − | 0.185350i | \(-0.940658\pi\) |
0.651854 | + | 0.758345i | \(0.273992\pi\) | |||||||
\(444\) | −13.5834 | + | 12.2306i | −0.644640 | + | 0.580436i | ||||
\(445\) | 5.94338 | + | 10.2942i | 0.281743 | + | 0.487994i | ||||
\(446\) | 6.96866 | + | 12.0701i | 0.329976 | + | 0.571534i | ||||
\(447\) | −5.25499 | + | 4.73162i | −0.248553 | + | 0.223798i | ||||
\(448\) | −1.06003 | + | 1.83603i | −0.0500819 | + | 0.0867444i | ||||
\(449\) | 8.71051 | 0.411075 | 0.205537 | − | 0.978649i | \(-0.434106\pi\) | ||||
0.205537 | + | 0.978649i | \(0.434106\pi\) | |||||||
\(450\) | −4.43444 | − | 3.22181i | −0.209042 | − | 0.151878i | ||||
\(451\) | 1.73632 | 0.0817600 | ||||||||
\(452\) | −4.48114 | + | 7.76156i | −0.210775 | + | 0.365073i | ||||
\(453\) | 25.8784 | + | 8.40840i | 1.21587 | + | 0.395061i | ||||
\(454\) | 14.7931 | + | 25.6223i | 0.694272 | + | 1.20251i | ||||
\(455\) | 1.87362 | + | 3.24520i | 0.0878366 | + | 0.152137i | ||||
\(456\) | −0.0602334 | − | 0.283376i | −0.00282069 | − | 0.0132703i | ||||
\(457\) | 0.824467 | − | 1.42802i | 0.0385669 | − | 0.0667999i | −0.846098 | − | 0.533028i | \(-0.821054\pi\) |
0.884665 | + | 0.466228i | \(0.154387\pi\) | |||||||
\(458\) | 45.7505 | 2.13778 | ||||||||
\(459\) | −5.58034 | − | 7.68068i | −0.260468 | − | 0.358503i | ||||
\(460\) | −10.4422 | −0.486872 | ||||||||
\(461\) | −3.17896 | + | 5.50612i | −0.148059 | + | 0.256446i | −0.930510 | − | 0.366266i | \(-0.880636\pi\) |
0.782451 | + | 0.622712i | \(0.213969\pi\) | |||||||
\(462\) | 0.113767 | + | 0.535233i | 0.00529293 | + | 0.0249013i | ||||
\(463\) | −18.5298 | − | 32.0946i | −0.861153 | − | 1.49156i | −0.870817 | − | 0.491608i | \(-0.836409\pi\) |
0.00966371 | − | 0.999953i | \(-0.496924\pi\) | |||||||
\(464\) | −2.39060 | − | 4.14064i | −0.110981 | − | 0.192225i | ||||
\(465\) | −4.48866 | − | 1.45846i | −0.208157 | − | 0.0676343i | ||||
\(466\) | −9.40617 | + | 16.2920i | −0.435733 | + | 0.754711i | ||||
\(467\) | −11.7091 | −0.541834 | −0.270917 | − | 0.962603i | \(-0.587327\pi\) | ||||
−0.270917 | + | 0.962603i | \(0.587327\pi\) | |||||||
\(468\) | −1.57256 | + | 14.9619i | −0.0726917 | + | 0.691616i | ||||
\(469\) | 4.38197 | 0.202340 | ||||||||
\(470\) | 5.29972 | − | 9.17938i | 0.244458 | − | 0.423413i | ||||
\(471\) | −2.96769 | + | 2.67212i | −0.136744 | + | 0.123125i | ||||
\(472\) | 0.713426 | + | 1.23569i | 0.0328381 | + | 0.0568772i | ||||
\(473\) | −0.639233 | − | 1.10718i | −0.0293920 | − | 0.0509084i | ||||
\(474\) | 33.3164 | − | 29.9982i | 1.53027 | − | 1.37786i | ||||
\(475\) | 0.0691705 | − | 0.119807i | 0.00317376 | − | 0.00549712i | ||||
\(476\) | −2.44512 | −0.112072 | ||||||||
\(477\) | 32.1034 | − | 14.2934i | 1.46991 | − | 0.654448i | ||||
\(478\) | −36.3677 | −1.66342 | ||||||||
\(479\) | 12.8295 | − | 22.2214i | 0.586197 | − | 1.01532i | −0.408528 | − | 0.912746i | \(-0.633958\pi\) |
0.994725 | − | 0.102577i | \(-0.0327089\pi\) | |||||||
\(480\) | 10.7210 | + | 3.48345i | 0.489342 | + | 0.158997i | ||||
\(481\) | −14.7746 | − | 25.5903i | −0.673663 | − | 1.16682i | ||||
\(482\) | 9.49845 | + | 16.4518i | 0.432643 | + | 0.749359i | ||||
\(483\) | −2.80991 | − | 13.2196i | −0.127855 | − | 0.601512i | ||||
\(484\) | 7.34043 | − | 12.7140i | 0.333656 | − | 0.577909i | ||||
\(485\) | −10.3781 | −0.471247 | ||||||||
\(486\) | 24.6657 | − | 14.2408i | 1.11886 | − | 0.645974i | ||||
\(487\) | −22.1058 | −1.00171 | −0.500855 | − | 0.865531i | \(-0.666981\pi\) | ||||
−0.500855 | + | 0.865531i | \(0.666981\pi\) | |||||||
\(488\) | −4.23337 | + | 7.33241i | −0.191636 | + | 0.331923i | ||||
\(489\) | 6.74929 | + | 31.7529i | 0.305213 | + | 1.43592i | ||||
\(490\) | −0.913545 | − | 1.58231i | −0.0412698 | − | 0.0714814i | ||||
\(491\) | −12.1665 | − | 21.0731i | −0.549069 | − | 0.951015i | −0.998339 | − | 0.0576186i | \(-0.981649\pi\) |
0.449270 | − | 0.893396i | \(-0.351684\pi\) | |||||||
\(492\) | −22.1370 | − | 7.19275i | −0.998014 | − | 0.324274i | ||||
\(493\) | 0.894028 | − | 1.54850i | 0.0402650 | − | 0.0697410i | ||||
\(494\) | −0.947158 | −0.0426147 | ||||||||
\(495\) | 0.473881 | − | 0.210985i | 0.0212994 | − | 0.00948309i | ||||
\(496\) | 13.3127 | 0.597758 | ||||||||
\(497\) | 5.60814 | − | 9.71359i | 0.251560 | − | 0.435714i | ||||
\(498\) | 21.8084 | − | 19.6364i | 0.977257 | − | 0.879926i | ||||
\(499\) | −11.5859 | − | 20.0674i | −0.518656 | − | 0.898339i | −0.999765 | − | 0.0216781i | \(-0.993099\pi\) |
0.481109 | − | 0.876661i | \(-0.340234\pi\) | |||||||
\(500\) | 0.669131 | + | 1.15897i | 0.0299244 | + | 0.0518306i | ||||
\(501\) | −7.35315 | + | 6.62080i | −0.328514 | + | 0.295796i | ||||
\(502\) | −21.9305 | + | 37.9847i | −0.978806 | + | 1.69534i | ||||
\(503\) | 34.4400 | 1.53561 | 0.767803 | − | 0.640686i | \(-0.221350\pi\) | ||||
0.767803 | + | 0.640686i | \(0.221350\pi\) | |||||||
\(504\) | −0.379143 | + | 3.60730i | −0.0168884 | + | 0.160682i | ||||
\(505\) | −17.7032 | −0.787782 | ||||||||
\(506\) | 1.23254 | − | 2.13482i | 0.0547930 | − | 0.0949043i | ||||
\(507\) | −1.71613 | − | 0.557603i | −0.0762158 | − | 0.0247640i | ||||
\(508\) | 11.2818 | + | 19.5406i | 0.500548 | + | 0.866974i | ||||
\(509\) | −20.0258 | − | 34.6858i | −0.887629 | − | 1.53742i | −0.842670 | − | 0.538430i | \(-0.819018\pi\) |
−0.0449590 | − | 0.998989i | \(-0.514316\pi\) | |||||||
\(510\) | 1.20215 | + | 5.65569i | 0.0532322 | + | 0.250438i | ||||
\(511\) | −0.803960 | + | 1.39250i | −0.0355651 | + | 0.0616006i | ||||
\(512\) | −19.9828 | −0.883126 | ||||||||
\(513\) | 0.422524 | + | 0.581555i | 0.0186549 | + | 0.0256763i | ||||
\(514\) | 22.0491 | 0.972546 | ||||||||
\(515\) | −1.07860 | + | 1.86818i | −0.0475286 | + | 0.0823220i | ||||
\(516\) | 3.56330 | + | 16.7640i | 0.156865 | + | 0.737993i | ||||
\(517\) | 0.501545 | + | 0.868702i | 0.0220579 | + | 0.0382055i | ||||
\(518\) | 7.20384 | + | 12.4774i | 0.316518 | + | 0.548226i | ||||
\(519\) | 29.0959 | + | 9.45382i | 1.27717 | + | 0.414976i | ||||
\(520\) | −2.26531 | + | 3.92364i | −0.0993405 | + | 0.172063i | ||||
\(521\) | −17.2174 | −0.754309 | −0.377154 | − | 0.926150i | \(-0.623097\pi\) | ||||
−0.377154 | + | 0.926150i | \(0.623097\pi\) | |||||||
\(522\) | 4.33970 | + | 3.15298i | 0.189944 | + | 0.138002i | ||||
\(523\) | 27.1363 | 1.18659 | 0.593293 | − | 0.804987i | \(-0.297828\pi\) | ||||
0.593293 | + | 0.804987i | \(0.297828\pi\) | |||||||
\(524\) | 8.47733 | − | 14.6832i | 0.370334 | − | 0.641437i | ||||
\(525\) | −1.28716 | + | 1.15897i | −0.0561765 | + | 0.0505815i | ||||
\(526\) | 3.52977 | + | 6.11374i | 0.153905 | + | 0.266572i | ||||
\(527\) | 2.48932 | + | 4.31163i | 0.108436 | + | 0.187817i | ||||
\(528\) | −1.08735 | + | 0.979051i | −0.0473207 | + | 0.0426077i | ||||
\(529\) | −18.9422 | + | 32.8088i | −0.823572 | + | 1.42647i | ||||
\(530\) | −21.4023 | −0.929655 | ||||||||
\(531\) | −2.86425 | − | 2.08100i | −0.124298 | − | 0.0903077i | ||||
\(532\) | 0.185136 | 0.00802669 | ||||||||
\(533\) | 18.8145 | − | 32.5877i | 0.814946 | − | 1.41153i | ||||
\(534\) | 35.7759 | + | 11.6243i | 1.54817 | + | 0.503032i | ||||
\(535\) | −5.76143 | − | 9.97909i | −0.249088 | − | 0.431434i | ||||
\(536\) | 2.64902 | + | 4.58824i | 0.114420 | + | 0.198182i | ||||
\(537\) | 1.29533 | + | 6.09404i | 0.0558976 | + | 0.262977i | ||||
\(538\) | 7.75349 | − | 13.4294i | 0.334277 | − | 0.578984i | ||||
\(539\) | 0.172909 | 0.00744772 | ||||||||
\(540\) | −6.91572 | + | 0.726871i | −0.297605 | + | 0.0312795i | ||||
\(541\) | 16.6450 | 0.715624 | 0.357812 | − | 0.933794i | \(-0.383523\pi\) | ||||
0.357812 | + | 0.933794i | \(0.383523\pi\) | |||||||
\(542\) | 10.8060 | − | 18.7166i | 0.464159 | − | 0.803946i | ||||
\(543\) | −4.98261 | − | 23.4414i | −0.213824 | − | 1.00596i | ||||
\(544\) | −5.94561 | − | 10.2981i | −0.254916 | − | 0.441528i | ||||
\(545\) | 3.44746 | + | 5.97118i | 0.147673 | + | 0.255777i | ||||
\(546\) | 11.2782 | + | 3.66450i | 0.482661 | + | 0.156826i | ||||
\(547\) | 11.8219 | − | 20.4761i | 0.505468 | − | 0.875495i | −0.494512 | − | 0.869171i | \(-0.664653\pi\) |
0.999980 | − | 0.00632492i | \(-0.00201330\pi\) | |||||||
\(548\) | −4.53818 | −0.193861 | ||||||||
\(549\) | 2.19596 | − | 20.8932i | 0.0937214 | − | 0.891700i | ||||
\(550\) | −0.315921 | −0.0134709 | ||||||||
\(551\) | −0.0676928 | + | 0.117247i | −0.00288381 | + | 0.00499490i | ||||
\(552\) | 12.1432 | − | 10.9338i | 0.516849 | − | 0.465373i | ||||
\(553\) | −7.08327 | − | 12.2686i | −0.301211 | − | 0.521713i | ||||
\(554\) | −24.9546 | − | 43.2226i | −1.06022 | − | 1.83635i | ||||
\(555\) | 10.1500 | − | 9.13914i | 0.430845 | − | 0.387935i | ||||
\(556\) | −5.44368 | + | 9.42873i | −0.230864 | + | 0.399867i | ||||
\(557\) | 37.1981 | 1.57613 | 0.788067 | − | 0.615590i | \(-0.211082\pi\) | ||||
0.788067 | + | 0.615590i | \(0.211082\pi\) | |||||||
\(558\) | −13.6446 | + | 6.07498i | −0.577623 | + | 0.257174i | ||||
\(559\) | −27.7066 | −1.17186 | ||||||||
\(560\) | 2.44279 | − | 4.23104i | 0.103227 | − | 0.178794i | ||||
\(561\) | −0.520409 | − | 0.169091i | −0.0219717 | − | 0.00713904i | ||||
\(562\) | 14.5136 | + | 25.1384i | 0.612221 | + | 1.06040i | ||||
\(563\) | 12.8803 | + | 22.3093i | 0.542840 | + | 0.940226i | 0.998739 | + | 0.0501948i | \(0.0159842\pi\) |
−0.455900 | + | 0.890031i | \(0.650682\pi\) | |||||||
\(564\) | −2.79578 | − | 13.1531i | −0.117724 | − | 0.553846i | ||||
\(565\) | 3.34848 | − | 5.79973i | 0.140871 | − | 0.243997i | ||||
\(566\) | −30.0763 | −1.26420 | ||||||||
\(567\) | −2.78115 | − | 8.55951i | −0.116797 | − | 0.359466i | ||||
\(568\) | 13.5611 | 0.569012 | ||||||||
\(569\) | −2.32571 | + | 4.02825i | −0.0974989 | + | 0.168873i | −0.910649 | − | 0.413181i | \(-0.864418\pi\) |
0.813150 | + | 0.582054i | \(0.197751\pi\) | |||||||
\(570\) | −0.0910229 | − | 0.428229i | −0.00381253 | − | 0.0179365i | ||||
\(571\) | −13.9779 | − | 24.2105i | −0.584958 | − | 1.01318i | −0.994881 | − | 0.101056i | \(-0.967778\pi\) |
0.409923 | − | 0.912120i | \(-0.365556\pi\) | |||||||
\(572\) | 0.433551 | + | 0.750932i | 0.0181277 | + | 0.0313980i | ||||
\(573\) | 9.85771 | + | 3.20296i | 0.411812 | + | 0.133806i | ||||
\(574\) | −9.17364 | + | 15.8892i | −0.382900 | + | 0.663203i | ||||
\(575\) | 7.80284 | 0.325401 | ||||||||
\(576\) | 5.81033 | − | 2.58693i | 0.242097 | − | 0.107789i | ||||
\(577\) | −5.63651 | −0.234651 | −0.117326 | − | 0.993094i | \(-0.537432\pi\) | ||||
−0.117326 | + | 0.993094i | \(0.537432\pi\) | |||||||
\(578\) | −12.4806 | + | 21.6171i | −0.519125 | + | 0.899151i | ||||
\(579\) | −22.7557 | + | 20.4893i | −0.945696 | + | 0.851508i | ||||
\(580\) | −0.654835 | − | 1.13421i | −0.0271906 | − | 0.0470954i | ||||
\(581\) | −4.63660 | − | 8.03082i | −0.192358 | − | 0.333175i | ||||
\(582\) | −24.4070 | + | 21.9761i | −1.01170 | + | 0.910940i | ||||
\(583\) | 1.01272 | − | 1.75407i | 0.0419424 | − | 0.0726464i | ||||
\(584\) | −1.94407 | −0.0804461 | ||||||||
\(585\) | 1.17508 | − | 11.1801i | 0.0485835 | − | 0.462242i | ||||
\(586\) | 43.5272 | 1.79809 | ||||||||
\(587\) | −14.8898 | + | 25.7899i | −0.614569 | + | 1.06446i | 0.375892 | + | 0.926664i | \(0.377337\pi\) |
−0.990460 | + | 0.137800i | \(0.955997\pi\) | |||||||
\(588\) | −2.20449 | − | 0.716282i | −0.0909116 | − | 0.0295390i | ||||
\(589\) | −0.188483 | − | 0.326462i | −0.00776629 | − | 0.0134516i | ||||
\(590\) | 1.07811 | + | 1.86734i | 0.0443850 | + | 0.0768771i | ||||
\(591\) | −7.27121 | − | 34.2083i | −0.299098 | − | 1.40714i | ||||
\(592\) | −19.2628 | + | 33.3642i | −0.791697 | + | 1.37126i | ||||
\(593\) | −46.0749 | −1.89207 | −0.946035 | − | 0.324064i | \(-0.894951\pi\) | ||||
−0.946035 | + | 0.324064i | \(0.894951\pi\) | |||||||
\(594\) | 0.667687 | − | 1.49965i | 0.0273955 | − | 0.0615314i | ||||
\(595\) | 1.82709 | 0.0749034 | ||||||||
\(596\) | 2.73180 | − | 4.73162i | 0.111899 | − | 0.193815i | ||||
\(597\) | 6.51328 | + | 30.6426i | 0.266571 | + | 1.25412i | ||||
\(598\) | −26.7112 | − | 46.2652i | −1.09230 | − | 1.89193i | ||||
\(599\) | −6.41929 | − | 11.1185i | −0.262285 | − | 0.454291i | 0.704564 | − | 0.709641i | \(-0.251143\pi\) |
−0.966849 | + | 0.255349i | \(0.917809\pi\) | |||||||
\(600\) | −1.99165 | − | 0.647127i | −0.0813089 | − | 0.0264189i | ||||
\(601\) | 0.326789 | − | 0.566015i | 0.0133300 | − | 0.0230883i | −0.859283 | − | 0.511500i | \(-0.829090\pi\) |
0.872613 | + | 0.488411i | \(0.162423\pi\) | |||||||
\(602\) | 13.5093 | 0.550596 | ||||||||
\(603\) | −10.6353 | − | 7.72696i | −0.433101 | − | 0.314666i | ||||
\(604\) | −21.0238 | −0.855446 | ||||||||
\(605\) | −5.48505 | + | 9.50039i | −0.222999 | + | 0.386246i | ||||
\(606\) | −41.6338 | + | 37.4872i | −1.69126 | + | 1.52282i | ||||
\(607\) | −16.0765 | − | 27.8453i | −0.652524 | − | 1.13021i | −0.982508 | − | 0.186219i | \(-0.940377\pi\) |
0.329984 | − | 0.943987i | \(-0.392957\pi\) | |||||||
\(608\) | 0.450181 | + | 0.779737i | 0.0182573 | + | 0.0316225i | ||||
\(609\) | 1.25967 | − | 1.13421i | 0.0510442 | − | 0.0459604i | ||||
\(610\) | −6.39734 | + | 11.0805i | −0.259021 | + | 0.448637i | ||||
\(611\) | 21.7387 | 0.879454 | ||||||||
\(612\) | 5.93444 | + | 4.31163i | 0.239886 | + | 0.174287i | ||||
\(613\) | 7.74782 | 0.312931 | 0.156466 | − | 0.987683i | \(-0.449990\pi\) | ||||
0.156466 | + | 0.987683i | \(0.449990\pi\) | |||||||
\(614\) | −21.6599 | + | 37.5160i | −0.874120 | + | 1.51402i | ||||
\(615\) | 16.5416 | + | 5.37470i | 0.667023 | + | 0.216729i | ||||
\(616\) | 0.104528 | + | 0.181049i | 0.00421157 | + | 0.00729466i | ||||
\(617\) | −15.3193 | − | 26.5338i | −0.616732 | − | 1.06821i | −0.990078 | − | 0.140519i | \(-0.955123\pi\) |
0.373346 | − | 0.927692i | \(-0.378210\pi\) | |||||||
\(618\) | 1.41935 | + | 6.67750i | 0.0570945 | + | 0.268608i | ||||
\(619\) | −15.9913 | + | 27.6977i | −0.642745 | + | 1.11327i | 0.342073 | + | 0.939673i | \(0.388871\pi\) |
−0.984817 | + | 0.173593i | \(0.944462\pi\) | |||||||
\(620\) | 3.64662 | 0.146452 | ||||||||
\(621\) | −16.4910 | + | 37.0395i | −0.661762 | + | 1.48634i | ||||
\(622\) | 26.7114 | 1.07103 | ||||||||
\(623\) | 5.94338 | − | 10.2942i | 0.238116 | − | 0.412430i | ||||
\(624\) | 6.59275 | + | 31.0165i | 0.263921 | + | 1.24165i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 9.75831 | + | 16.9019i | 0.390020 | + | 0.675535i | ||||
\(627\) | 0.0394036 | + | 0.0128030i | 0.00157363 | + | 0.000511303i | ||||
\(628\) | 1.54275 | − | 2.67212i | 0.0615624 | − | 0.106629i | ||||
\(629\) | −14.4077 | −0.574471 | ||||||||
\(630\) | −0.572949 | + | 5.45125i | −0.0228268 | + | 0.217183i | ||||
\(631\) | 8.65557 | 0.344573 | 0.172286 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172286 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(632\) | 8.56407 | − | 14.8334i | 0.340661 | − | 0.590041i | ||||
\(633\) | −30.7327 | + | 27.6719i | −1.22152 | + | 1.09986i | ||||
\(634\) | −20.0184 | − | 34.6729i | −0.795032 | − | 1.37704i | ||||
\(635\) | −8.43018 | − | 14.6015i | −0.334541 | − | 0.579443i | ||||
\(636\) | −20.1778 | + | 18.1682i | −0.800103 | + | 0.720416i | ||||
\(637\) | 1.87362 | − | 3.24520i | 0.0742355 | − | 0.128580i | ||||
\(638\) | 0.309171 | 0.0122402 | ||||||||
\(639\) | −30.7398 | + | 13.6862i | −1.21605 | + | 0.541419i | ||||
\(640\) | 9.14301 | 0.361409 | ||||||||
\(641\) | 2.06538 | − | 3.57734i | 0.0815776 | − | 0.141296i | −0.822350 | − | 0.568982i | \(-0.807338\pi\) |
0.903928 | + | 0.427685i | \(0.140671\pi\) | |||||||
\(642\) | −34.6807 | − | 11.2684i | −1.36874 | − | 0.444730i | ||||
\(643\) | −7.21704 | − | 12.5003i | −0.284612 | − | 0.492963i | 0.687903 | − | 0.725803i | \(-0.258532\pi\) |
−0.972515 | + | 0.232840i | \(0.925198\pi\) | |||||||
\(644\) | 5.22112 | + | 9.04324i | 0.205741 | + | 0.356354i | ||||
\(645\) | −2.66263 | − | 12.5267i | −0.104841 | − | 0.493238i | ||||
\(646\) | −0.230909 | + | 0.399947i | −0.00908501 | + | 0.0157357i | ||||
\(647\) | 28.1790 | 1.10783 | 0.553916 | − | 0.832573i | \(-0.313133\pi\) | ||||
0.553916 | + | 0.832573i | \(0.313133\pi\) | |||||||
\(648\) | 7.28115 | − | 8.08654i | 0.286031 | − | 0.317669i | ||||
\(649\) | −0.204056 | −0.00800991 | ||||||||
\(650\) | −3.42327 | + | 5.92928i | −0.134272 | + | 0.232566i | ||||
\(651\) | 0.981273 | + | 4.61653i | 0.0384591 | + | 0.180936i | ||||
\(652\) | −12.5409 | − | 21.7215i | −0.491140 | − | 0.850680i | ||||
\(653\) | 2.96698 | + | 5.13896i | 0.116107 | + | 0.201103i | 0.918222 | − | 0.396067i | \(-0.129625\pi\) |
−0.802115 | + | 0.597170i | \(0.796292\pi\) | |||||||
\(654\) | 20.7518 | + | 6.74268i | 0.811461 | + | 0.263660i | ||||
\(655\) | −6.33458 | + | 10.9718i | −0.247513 | + | 0.428705i | ||||
\(656\) | −49.0600 | −1.91547 | ||||||||
\(657\) | 4.40673 | − | 1.96200i | 0.171923 | − | 0.0765449i | ||||
\(658\) | −10.5994 | −0.413209 | ||||||||
\(659\) | −19.7763 | + | 34.2536i | −0.770376 | + | 1.33433i | 0.166981 | + | 0.985960i | \(0.446598\pi\) |
−0.937357 | + | 0.348370i | \(0.886735\pi\) | |||||||
\(660\) | −0.297847 | + | 0.268182i | −0.0115937 | + | 0.0104390i | ||||
\(661\) | 20.8000 | + | 36.0266i | 0.809025 | + | 1.40127i | 0.913540 | + | 0.406749i | \(0.133338\pi\) |
−0.104514 | + | 0.994523i | \(0.533329\pi\) | |||||||
\(662\) | −20.5715 | − | 35.6308i | −0.799533 | − | 1.38483i | ||||
\(663\) | −8.81263 | + | 7.93493i | −0.342254 | + | 0.308167i | ||||
\(664\) | 5.60591 | − | 9.70972i | 0.217551 | − | 0.376810i | ||||
\(665\) | −0.138341 | −0.00536464 | ||||||||
\(666\) | 4.51803 | − | 42.9862i | 0.175070 | − | 1.66568i | ||||
\(667\) | −7.63614 | −0.295672 | ||||||||
\(668\) | 3.82252 | − | 6.62080i | 0.147898 | − | 0.256167i | ||||
\(669\) | −12.5657 | − | 4.08284i | −0.485817 | − | 0.157852i | ||||
\(670\) | 4.00313 | + | 6.93362i | 0.154654 | + | 0.267869i | ||||
\(671\) | −0.605420 | − | 1.04862i | −0.0233720 | − | 0.0404815i | ||||
\(672\) | −2.34372 | − | 11.0263i | −0.0904110 | − | 0.425350i | ||||
\(673\) | 16.6716 | − | 28.8760i | 0.642643 | − | 1.11309i | −0.342198 | − | 0.939628i | \(-0.611171\pi\) |
0.984841 | − | 0.173462i | \(-0.0554953\pi\) | |||||||
\(674\) | 13.5518 | 0.521995 | ||||||||
\(675\) | 5.16769 | − | 0.543146i | 0.198904 | − | 0.0209057i | ||||
\(676\) | 1.39419 | 0.0536228 | ||||||||
\(677\) | 9.09786 | − | 15.7580i | 0.349659 | − | 0.605628i | −0.636530 | − | 0.771252i | \(-0.719631\pi\) |
0.986189 | + | 0.165625i | \(0.0529640\pi\) | |||||||
\(678\) | −4.40633 | − | 20.7301i | −0.169224 | − | 0.796137i | ||||
\(679\) | 5.18907 | + | 8.98774i | 0.199138 | + | 0.344918i | ||||
\(680\) | 1.10453 | + | 1.91310i | 0.0423567 | + | 0.0733640i | ||||
\(681\) | −26.6744 | − | 8.66704i | −1.02216 | − | 0.332122i | ||||
\(682\) | −0.430426 | + | 0.745519i | −0.0164819 | + | 0.0285474i | ||||
\(683\) | −14.0903 | −0.539150 | −0.269575 | − | 0.962979i | \(-0.586883\pi\) | ||||
−0.269575 | + | 0.962979i | \(0.586883\pi\) | |||||||
\(684\) | −0.449336 | − | 0.326462i | −0.0171808 | − | 0.0124826i | ||||
\(685\) | 3.39110 | 0.129567 | ||||||||
\(686\) | −0.913545 | + | 1.58231i | −0.0348793 | + | 0.0604128i | ||||
\(687\) | −32.2307 | + | 29.0207i | −1.22968 | + | 1.10721i | ||||
\(688\) | 18.0617 | + | 31.2837i | 0.688594 | + | 1.19268i | ||||
\(689\) | −21.9473 | − | 38.0138i | −0.836125 | − | 1.44821i | ||||
\(690\) | 18.3505 | − | 16.5228i | 0.698590 | − | 0.629013i | ||||
\(691\) | 16.1752 | − | 28.0162i | 0.615333 | − | 1.06579i | −0.374993 | − | 0.927027i | \(-0.622355\pi\) |
0.990326 | − | 0.138760i | \(-0.0443116\pi\) | |||||||
\(692\) | −23.6377 | −0.898570 | ||||||||
\(693\) | −0.419659 | − | 0.304900i | −0.0159415 | − | 0.0115822i | ||||
\(694\) | 43.9795 | 1.66944 | ||||||||
\(695\) | 4.06773 | − | 7.04551i | 0.154298 | − | 0.267251i | ||||
\(696\) | 1.94910 | + | 0.633302i | 0.0738806 | + | 0.0240052i | ||||
\(697\) | −9.17364 | − | 15.8892i | −0.347476 | − | 0.601846i | ||||
\(698\) | 14.1460 | + | 24.5015i | 0.535432 | + | 0.927396i | ||||
\(699\) | −3.70785 | − | 17.4441i | −0.140244 | − | 0.659795i | ||||
\(700\) | 0.669131 | − | 1.15897i | 0.0252908 | − | 0.0438049i | ||||
\(701\) | 26.0054 | 0.982210 | 0.491105 | − | 0.871100i | \(-0.336593\pi\) | ||||
0.491105 | + | 0.871100i | \(0.336593\pi\) | |||||||
\(702\) | −20.9109 | − | 28.7813i | −0.789230 | − | 1.08628i | ||||
\(703\) | 1.09090 | 0.0411441 | ||||||||
\(704\) | 0.183289 | − | 0.317467i | 0.00690798 | − | 0.0119650i | ||||
\(705\) | 2.08911 | + | 9.82850i | 0.0786805 | + | 0.370163i | ||||
\(706\) | 19.6806 | + | 34.0878i | 0.740690 | + | 1.28291i | ||||
\(707\) | 8.85160 | + | 15.3314i | 0.332899 | + | 0.576598i | ||||
\(708\) | 2.60160 | + | 0.845310i | 0.0977740 | + | 0.0317687i | ||||
\(709\) | 8.55973 | − | 14.8259i | 0.321467 | − | 0.556798i | −0.659324 | − | 0.751859i | \(-0.729157\pi\) |
0.980791 | + | 0.195061i | \(0.0624906\pi\) | |||||||
\(710\) | 20.4932 | 0.769095 | ||||||||
\(711\) | −4.44242 | + | 42.2668i | −0.166604 | + | 1.58513i | ||||
\(712\) | 14.3718 | 0.538605 | ||||||||
\(713\) | 10.6310 | − | 18.4134i | 0.398133 | − | 0.689587i | ||||
\(714\) | 4.29689 | − | 3.86894i | 0.160807 | − | 0.144791i | ||||
\(715\) | −0.323966 | − | 0.561125i | −0.0121156 | − | 0.0209849i | ||||
\(716\) | −2.40686 | − | 4.16881i | −0.0899487 | − | 0.155796i | ||||
\(717\) | 25.6206 | − | 23.0689i | 0.956820 | − | 0.861525i | ||||
\(718\) | −16.6334 | + | 28.8098i | −0.620751 | + | 1.07517i | ||||
\(719\) | 21.1007 | 0.786923 | 0.393461 | − | 0.919341i | \(-0.371278\pi\) | ||||
0.393461 | + | 0.919341i | \(0.371278\pi\) | |||||||
\(720\) | −13.3896 | + | 5.96143i | −0.499001 | + | 0.222169i | ||||
\(721\) | 2.15719 | 0.0803380 | ||||||||
\(722\) | −17.3399 | + | 30.0336i | −0.645324 | + | 1.11773i | ||||
\(723\) | −17.1273 | − | 5.56501i | −0.636972 | − | 0.206965i | ||||
\(724\) | 9.25824 | + | 16.0357i | 0.344080 | + | 0.595964i | ||||
\(725\) | 0.489318 | + | 0.847523i | 0.0181728 | + | 0.0314762i | ||||
\(726\) | 7.21789 | + | 33.9575i | 0.267881 | + | 1.26028i | ||||
\(727\) | −7.34228 | + | 12.7172i | −0.272310 | + | 0.471655i | −0.969453 | − | 0.245277i | \(-0.921121\pi\) |
0.697143 | + | 0.716932i | \(0.254454\pi\) | |||||||
\(728\) | 4.53062 | 0.167916 | ||||||||
\(729\) | −8.34346 | + | 25.6785i | −0.309017 | + | 0.951057i | ||||
\(730\) | −2.93782 | −0.108734 | ||||||||
\(731\) | −6.75463 | + | 11.6994i | −0.249829 | + | 0.432717i | ||||
\(732\) | 3.37481 | + | 15.8772i | 0.124737 | + | 0.586840i | ||||
\(733\) | −21.2290 | − | 36.7698i | −0.784112 | − | 1.35812i | −0.929528 | − | 0.368752i | \(-0.879785\pi\) |
0.145416 | − | 0.989371i | \(-0.453548\pi\) | |||||||
\(734\) | −23.0138 | − | 39.8610i | −0.849454 | − | 1.47130i | ||||
\(735\) | 1.64728 | + | 0.535233i | 0.0607608 | + | 0.0197424i | ||||
\(736\) | −25.3915 | + | 43.9795i | −0.935945 | + | 1.62110i | ||||
\(737\) | −0.757682 | −0.0279096 | ||||||||
\(738\) | 50.2832 | − | 22.3875i | 1.85095 | − | 0.824096i | ||||
\(739\) | 28.5354 | 1.04969 | 0.524846 | − | 0.851197i | \(-0.324123\pi\) | ||||
0.524846 | + | 0.851197i | \(0.324123\pi\) | |||||||
\(740\) | −5.27648 | + | 9.13914i | −0.193967 | + | 0.335961i | ||||
\(741\) | 0.667262 | − | 0.600806i | 0.0245125 | − | 0.0220711i | ||||
\(742\) | 10.7011 | + | 18.5349i | 0.392851 | + | 0.680438i | ||||
\(743\) | −16.1206 | − | 27.9217i | −0.591408 | − | 1.02435i | −0.994043 | − | 0.108988i | \(-0.965239\pi\) |
0.402635 | − | 0.915360i | \(-0.368094\pi\) | |||||||
\(744\) | −4.24064 | + | 3.81829i | −0.155469 | + | 0.139985i | ||||
\(745\) | −2.04131 | + | 3.53565i | −0.0747877 | + | 0.129536i | ||||
\(746\) | 59.6179 | 2.18276 | ||||||||
\(747\) | −2.90794 | + | 27.6672i | −0.106396 | + | 1.01229i | ||||
\(748\) | 0.422784 | 0.0154585 | ||||||||
\(749\) | −5.76143 | + | 9.97909i | −0.210518 | + | 0.364628i | ||||
\(750\) | −3.00973 | − | 0.977920i | −0.109900 | − | 0.0357086i | ||||
\(751\) | 13.1046 | + | 22.6978i | 0.478192 | + | 0.828253i | 0.999687 | − | 0.0250009i | \(-0.00795886\pi\) |
−0.521495 | + | 0.853254i | \(0.674626\pi\) | |||||||
\(752\) | −14.1713 | − | 24.5453i | −0.516773 | − | 0.895076i | ||||
\(753\) | −8.64486 | − | 40.6709i | −0.315036 | − | 1.48213i | ||||
\(754\) | 3.35014 | − | 5.80261i | 0.122005 | − | 0.211319i | ||||
\(755\) | 15.7098 | 0.571738 | ||||||||
\(756\) | 4.08735 | + | 5.62575i | 0.148655 | + | 0.204607i | ||||
\(757\) | 15.1032 | 0.548937 | 0.274468 | − | 0.961596i | \(-0.411498\pi\) | ||||
0.274468 | + | 0.961596i | \(0.411498\pi\) | |||||||
\(758\) | −2.36935 | + | 4.10384i | −0.0860588 | + | 0.149058i | ||||
\(759\) | 0.485859 | + | 2.28579i | 0.0176356 | + | 0.0829688i | ||||
\(760\) | −0.0836311 | − | 0.144853i | −0.00303362 | − | 0.00525438i | ||||
\(761\) | −4.76604 | − | 8.25502i | −0.172769 | − | 0.299244i | 0.766618 | − | 0.642103i | \(-0.221938\pi\) |
−0.939387 | + | 0.342859i | \(0.888605\pi\) | |||||||
\(762\) | −50.7451 | − | 16.4881i | −1.83830 | − | 0.597300i | ||||
\(763\) | 3.44746 | − | 5.97118i | 0.124806 | − | 0.216171i | ||||
\(764\) | −8.00848 | −0.289737 | ||||||||
\(765\) | −4.43444 | − | 3.22181i | −0.160328 | − | 0.116485i | ||||
\(766\) | 39.7538 | 1.43636 | ||||||||
\(767\) | −2.21112 | + | 3.82978i | −0.0798391 | + | 0.138285i | ||||
\(768\) | 26.9600 | − | 24.2749i | 0.972835 | − | 0.875944i | ||||
\(769\) | 14.5886 | + | 25.2682i | 0.526079 | + | 0.911196i | 0.999538 | + | 0.0303802i | \(0.00967182\pi\) |
−0.473459 | + | 0.880816i | \(0.656995\pi\) | |||||||
\(770\) | 0.157960 | + | 0.273595i | 0.00569249 | + | 0.00985969i | ||||
\(771\) | −15.5334 | + | 13.9863i | −0.559421 | + | 0.503705i | ||||
\(772\) | 11.8295 | − | 20.4893i | 0.425754 | − | 0.737428i | ||||
\(773\) | −2.52384 | −0.0907762 | −0.0453881 | − | 0.998969i | \(-0.514452\pi\) | ||||
−0.0453881 | + | 0.998969i | \(0.514452\pi\) | |||||||
\(774\) | −32.7877 | − | 23.8216i | −1.17853 | − | 0.856251i | ||||
\(775\) | −2.72490 | −0.0978812 | ||||||||
\(776\) | −6.27388 | + | 10.8667i | −0.225219 | + | 0.390091i | ||||
\(777\) | −12.9897 | − | 4.22062i | −0.466004 | − | 0.151414i | ||||
\(778\) | −11.0334 | − | 19.1105i | −0.395568 | − | 0.685144i | ||||
\(779\) | 0.694596 | + | 1.20308i | 0.0248865 | + | 0.0431047i | ||||
\(780\) | 1.80589 | + | 8.49605i | 0.0646613 | + | 0.304208i | ||||
\(781\) | −0.969699 | + | 1.67957i | −0.0346985 | + | 0.0600996i | ||||
\(782\) | −26.0479 | −0.931472 | ||||||||
\(783\) | −5.05728 | + | 0.531542i | −0.180733 | + | 0.0189958i | ||||
\(784\) | −4.88558 | −0.174485 | ||||||||
\(785\) | −1.15280 | + | 1.99671i | −0.0411453 | + | 0.0712657i | ||||
\(786\) | 8.33581 | + | 39.2169i | 0.297329 | + | 1.39882i | ||||
\(787\) | −4.55935 | − | 7.89702i | −0.162523 | − | 0.281498i | 0.773250 | − | 0.634102i | \(-0.218630\pi\) |
−0.935773 | + | 0.352603i | \(0.885297\pi\) | |||||||
\(788\) | 13.5107 | + | 23.4012i | 0.481299 | + | 0.833634i | ||||
\(789\) | −6.36478 | − | 2.06804i | −0.226592 | − | 0.0736243i | ||||
\(790\) | 12.9418 | − | 22.4158i | 0.460448 | − | 0.797519i | ||||
\(791\) | −6.69695 | −0.238116 | ||||||||
\(792\) | 0.0655572 | − | 0.623735i | 0.00232947 | − | 0.0221635i | ||||
\(793\) | −26.2410 | −0.931846 | ||||||||
\(794\) | −30.3709 | + | 52.6040i | −1.07782 | + | 1.86685i | ||||
\(795\) | 15.0777 | − | 13.5760i | 0.534749 | − | 0.481490i | ||||
\(796\) | −12.1024 | − | 20.9620i | −0.428958 | − | 0.742977i | ||||
\(797\) | −21.3529 | − | 36.9843i | −0.756358 | − | 1.31005i | −0.944696 | − | 0.327946i | \(-0.893644\pi\) |
0.188339 | − | 0.982104i | \(-0.439690\pi\) | |||||||
\(798\) | −0.325346 | + | 0.292943i | −0.0115171 | + | 0.0103701i | ||||
\(799\) | 5.29972 | − | 9.17938i | 0.187490 | − | 0.324743i | ||||
\(800\) | 6.50828 | 0.230103 | ||||||||
\(801\) | −32.5773 | + | 14.5043i | −1.15106 | + | 0.512486i | ||||
\(802\) | 32.2144 | 1.13753 | ||||||||
\(803\) | 0.139012 | − | 0.240776i | 0.00490563 | − | 0.00849680i | ||||
\(804\) | 9.65999 | + | 3.13872i | 0.340682 | + | 0.110694i | ||||
\(805\) | −3.90142 | − | 6.75746i | −0.137507 | − | 0.238169i | ||||
\(806\) | 9.32807 | + | 16.1567i | 0.328567 | + | 0.569095i | ||||
\(807\) | 3.05637 | + | 14.3791i | 0.107589 | + | 0.506169i | ||||
\(808\) | −10.7021 | + | 18.5366i | −0.376498 | + | 0.652114i | ||||
\(809\) | −4.68059 | −0.164561 | −0.0822804 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822804 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(810\) | 11.0031 | − | 12.2201i | 0.386608 | − | 0.429372i | ||||
\(811\) | 33.6854 | 1.18285 | 0.591427 | − | 0.806359i | \(-0.298565\pi\) | ||||
0.591427 | + | 0.806359i | \(0.298565\pi\) | |||||||
\(812\) | −0.654835 | + | 1.13421i | −0.0229802 | + | 0.0398029i | ||||
\(813\) | 4.25967 | + | 20.0401i | 0.149393 | + | 0.702839i | ||||
\(814\) | −1.24561 | − | 2.15746i | −0.0436586 | − | 0.0756188i | ||||
\(815\) | 9.37106 | + | 16.2311i | 0.328254 | + | 0.568552i | ||||
\(816\) | 14.7043 | + | 4.77770i | 0.514752 | + | 0.167253i | ||||
\(817\) | 0.511437 | − | 0.885836i | 0.0178929 | − | 0.0309915i | ||||
\(818\) | −25.5751 | −0.894212 | ||||||||
\(819\) | −10.2698 | + | 4.57242i | −0.358856 | + | 0.159773i | ||||
\(820\) | −13.4385 | −0.469294 | ||||||||
\(821\) | 3.95458 | − | 6.84954i | 0.138016 | − | 0.239051i | −0.788730 | − | 0.614740i | \(-0.789261\pi\) |
0.926746 | + | 0.375690i | \(0.122594\pi\) | |||||||
\(822\) | 7.97508 | − | 7.18080i | 0.278163 | − | 0.250459i | ||||
\(823\) | 21.8538 | + | 37.8519i | 0.761775 | + | 1.31943i | 0.941935 | + | 0.335795i | \(0.109005\pi\) |
−0.180160 | + | 0.983637i | \(0.557662\pi\) | |||||||
\(824\) | 1.30408 | + | 2.25874i | 0.0454299 | + | 0.0786869i | ||||
\(825\) | 0.222562 | − | 0.200396i | 0.00774863 | − | 0.00697690i | ||||
\(826\) | 1.07811 | − | 1.86734i | 0.0375122 | − | 0.0649730i | ||||
\(827\) | −23.5601 | −0.819265 | −0.409633 | − | 0.912251i | \(-0.634343\pi\) | ||||
−0.409633 | + | 0.912251i | \(0.634343\pi\) | |||||||
\(828\) | 3.27453 | − | 31.1551i | 0.113798 | − | 1.08271i | ||||
\(829\) | −27.9043 | −0.969156 | −0.484578 | − | 0.874748i | \(-0.661027\pi\) | ||||
−0.484578 | + | 0.874748i | \(0.661027\pi\) | |||||||
\(830\) | 8.47148 | − | 14.6730i | 0.294049 | − | 0.509309i | ||||
\(831\) | 44.9974 | + | 14.6205i | 1.56094 | + | 0.507181i | ||||
\(832\) | −3.97220 | − | 6.88005i | −0.137711 | − | 0.238523i | ||||
\(833\) | −0.913545 | − | 1.58231i | −0.0316525 | − | 0.0548237i | ||||
\(834\) | −5.35281 | − | 25.1830i | −0.185353 | − | 0.872015i | ||||
\(835\) | −2.85634 | + | 4.94732i | −0.0988476 | + | 0.171209i | ||||
\(836\) | −0.0320118 | −0.00110715 | ||||||||
\(837\) | 5.75898 | − | 12.9349i | 0.199059 | − | 0.447095i | ||||
\(838\) | 33.6222 | 1.16146 | ||||||||
\(839\) | −2.51039 | + | 4.34813i | −0.0866684 | + | 0.150114i | −0.906101 | − | 0.423062i | \(-0.860955\pi\) |
0.819433 | + | 0.573176i | \(0.194289\pi\) | |||||||
\(840\) | 0.435398 | + | 2.04839i | 0.0150227 | + | 0.0706760i | ||||
\(841\) | 14.0211 | + | 24.2853i | 0.483487 | + | 0.837425i | ||||
\(842\) | 2.53236 | + | 4.38617i | 0.0872708 | + | 0.151157i | ||||
\(843\) | −26.1706 | − | 8.50333i | −0.901362 | − | 0.292870i | ||||
\(844\) | 15.9764 | − | 27.6719i | 0.549929 | − | 0.952506i | ||||
\(845\) | −1.04179 | −0.0358388 | ||||||||
\(846\) | 25.7254 | + | 18.6906i | 0.884456 | + | 0.642595i | ||||
\(847\) | 10.9701 | 0.376937 | ||||||||
\(848\) | −28.6145 | + | 49.5617i | −0.982625 | + | 1.70196i | ||||
\(849\) | 21.1884 | − | 19.0781i | 0.727184 | − | 0.654759i | ||||
\(850\) | 1.66913 | + | 2.89102i | 0.0572507 | + | 0.0991611i | ||||
\(851\) | 30.7650 | + | 53.2865i | 1.05461 | + | 1.82664i | ||||
\(852\) | 19.3207 | − | 17.3965i | 0.661918 | − | 0.595994i | ||||
\(853\) | 8.91069 | − | 15.4338i | 0.305096 | − | 0.528442i | −0.672186 | − | 0.740382i | \(-0.734645\pi\) |
0.977283 | + | 0.211940i | \(0.0679780\pi\) | |||||||
\(854\) | 12.7947 | 0.437825 | ||||||||
\(855\) | 0.335761 | + | 0.243945i | 0.0114828 | + | 0.00834273i | ||||
\(856\) | −13.9318 | −0.476179 | ||||||||
\(857\) | −12.9518 | + | 22.4332i | −0.442425 | + | 0.766303i | −0.997869 | − | 0.0652514i | \(-0.979215\pi\) |
0.555444 | + | 0.831554i | \(0.312548\pi\) | |||||||
\(858\) | −1.95010 | − | 0.633625i | −0.0665752 | − | 0.0216316i | ||||
\(859\) | −9.01087 | − | 15.6073i | −0.307447 | − | 0.532514i | 0.670356 | − | 0.742039i | \(-0.266141\pi\) |
−0.977803 | + | 0.209526i | \(0.932808\pi\) | |||||||
\(860\) | 4.94746 | + | 8.56925i | 0.168707 | + | 0.292209i | ||||
\(861\) | −3.61619 | − | 17.0128i | −0.123239 | − | 0.579795i | ||||
\(862\) | 5.99178 | − | 10.3781i | 0.204081 | − | 0.353478i | ||||
\(863\) | 24.3762 | 0.829774 | 0.414887 | − | 0.909873i | \(-0.363821\pi\) | ||||
0.414887 | + | 0.909873i | \(0.363821\pi\) | |||||||
\(864\) | −13.7550 | + | 30.8943i | −0.467956 | + | 1.05105i | ||||
\(865\) | 17.6630 | 0.600560 | ||||||||
\(866\) | 3.15102 | − | 5.45772i | 0.107076 | − | 0.185461i | ||||
\(867\) | −4.91978 | − | 23.1457i | −0.167084 | − | 0.786070i | ||||
\(868\) | −1.82331 | − | 3.15807i | −0.0618873 | − | 0.107192i | ||||
\(869\) | 1.22476 | + | 2.12135i | 0.0415472 | + | 0.0719618i | ||||
\(870\) | 2.94543 | + | 0.957027i | 0.0998593 | + | 0.0324463i | ||||
\(871\) | −8.21014 | + | 14.2204i | −0.278190 | + | 0.481839i | ||||
\(872\) | 8.33635 | 0.282304 | ||||||||
\(873\) | 3.25443 | − | 30.9639i | 0.110146 | − | 1.04797i | ||||
\(874\) | 1.97226 | 0.0667127 | ||||||||
\(875\) | −0.500000 | + | 0.866025i | −0.0169031 | + | 0.0292770i | ||||
\(876\) | −2.76974 | + | 2.49389i | −0.0935810 | + | 0.0842607i | ||||
\(877\) | 16.4715 | + | 28.5294i | 0.556202 | + | 0.963370i | 0.997809 | + | 0.0661615i | \(0.0210753\pi\) |
−0.441607 | + | 0.897209i | \(0.645591\pi\) | |||||||
\(878\) | −9.97259 | − | 17.2730i | −0.336558 | − | 0.582936i | ||||
\(879\) | −30.6644 | + | 27.6104i | −1.03429 | + | 0.931274i | ||||
\(880\) | −0.422381 | + | 0.731585i | −0.0142384 | + | 0.0246617i | ||||
\(881\) | −22.2765 | −0.750513 | −0.375257 | − | 0.926921i | \(-0.622445\pi\) | ||||
−0.375257 | + | 0.926921i | \(0.622445\pi\) | |||||||
\(882\) | 5.00739 | − | 2.22943i | 0.168608 | − | 0.0750690i | ||||
\(883\) | −5.07478 | −0.170780 | −0.0853900 | − | 0.996348i | \(-0.527214\pi\) | ||||
−0.0853900 | + | 0.996348i | \(0.527214\pi\) | |||||||
\(884\) | 4.58123 | − | 7.93493i | 0.154084 | − | 0.266881i | ||||
\(885\) | −1.94401 | − | 0.631648i | −0.0653472 | − | 0.0212326i | ||||
\(886\) | 12.7219 | + | 22.0350i | 0.427401 | + | 0.740280i | ||||
\(887\) | 4.30954 | + | 7.46434i | 0.144700 | + | 0.250628i | 0.929261 | − | 0.369424i | \(-0.120445\pi\) |
−0.784561 | + | 0.620052i | \(0.787112\pi\) | |||||||
\(888\) | −3.43336 | − | 16.1527i | −0.115216 | − | 0.542049i | ||||
\(889\) | −8.43018 | + | 14.6015i | −0.282739 | + | 0.489718i | ||||
\(890\) | 21.7182 | 0.727995 | ||||||||
\(891\) | 0.480887 | + | 1.48002i | 0.0161103 | + | 0.0495824i | ||||
\(892\) | 10.2085 | 0.341804 | ||||||||
\(893\) | −0.401276 | + | 0.695031i | −0.0134282 | + | 0.0232583i | ||||
\(894\) | 2.68620 | + | 12.6376i | 0.0898399 | + | 0.422663i | ||||
\(895\) | 1.79850 | + | 3.11509i | 0.0601172 | + | 0.104126i | ||||
\(896\) | −4.57151 | − | 7.91808i | −0.152723 | − | 0.264524i | ||||
\(897\) | 48.1649 | + | 15.6497i | 1.60818 | + | 0.522529i | ||||
\(898\) | 7.95745 | − | 13.7827i | 0.265544 | − | 0.459935i | ||||
\(899\) | 2.66668 | 0.0889388 | ||||||||
\(900\) | −3.66769 | + | 1.63296i | −0.122256 | + | 0.0544320i | ||||
\(901\) | −21.4023 | −0.713013 | ||||||||
\(902\) | 1.58620 | − | 2.74739i | 0.0528148 | − | 0.0914780i | ||||
\(903\) | −9.51712 | + | 8.56925i | −0.316710 | + | 0.285167i | ||||
\(904\) | −4.04850 | − | 7.01221i | −0.134651 | − | 0.233222i | ||||
\(905\) | −6.91811 | − | 11.9825i | −0.229966 | − | 0.398313i | ||||
\(906\) | 36.9457 | − | 33.2661i | 1.22744 | − | 1.10519i | ||||
\(907\) | 24.1539 | − | 41.8358i | 0.802017 | − | 1.38914i | −0.116269 | − | 0.993218i | \(-0.537093\pi\) |
0.918286 | − | 0.395917i | \(-0.129573\pi\) | |||||||
\(908\) | 21.6705 | 0.719160 | ||||||||
\(909\) | 5.55147 | − | 52.8187i | 0.184131 | − | 1.75188i | ||||
\(910\) | 6.84655 | 0.226961 | ||||||||
\(911\) | 8.60304 | − | 14.9009i | 0.285032 | − | 0.493689i | −0.687585 | − | 0.726104i | \(-0.741329\pi\) |
0.972617 | + | 0.232415i | \(0.0746626\pi\) | |||||||
\(912\) | −1.11336 | − | 0.361751i | −0.0368669 | − | 0.0119788i | ||||
\(913\) | 0.801710 | + | 1.38860i | 0.0265327 | + | 0.0459560i | ||||
\(914\) | −1.50638 | − | 2.60912i | −0.0498265 | − | 0.0863020i | ||||
\(915\) | −2.52179 | − | 11.8641i | −0.0833678 | − | 0.392215i | ||||
\(916\) | 16.7551 | − | 29.0207i | 0.553604 | − | 0.958870i | ||||
\(917\) | 12.6692 | 0.418373 | ||||||||
\(918\) | −17.2511 | + | 1.81316i | −0.569371 | + | 0.0598433i | ||||
\(919\) | 32.7547 | 1.08048 | 0.540240 | − | 0.841511i | \(-0.318334\pi\) | ||||
0.540240 | + | 0.841511i | \(0.318334\pi\) | |||||||
\(920\) | 4.71704 | − | 8.17015i | 0.155516 | − | 0.269362i | ||||
\(921\) | −8.53817 | − | 40.1689i | −0.281342 | − | 1.32361i | ||||
\(922\) | 5.80825 | + | 10.0602i | 0.191284 | + | 0.331314i | ||||
\(923\) | 21.0150 | + | 36.3991i | 0.691719 | + | 1.19809i | ||||
\(924\) | 0.381176 | + | 0.123852i | 0.0125398 | + | 0.00407442i | ||||
\(925\) | 3.94279 | − | 6.82911i | 0.129638 | − | 0.224540i | ||||
\(926\) | −67.7113 | −2.22513 | ||||||||
\(927\) | −5.23561 | − | 3.80390i | −0.171960 | − | 0.124936i | ||||
\(928\) | −6.36924 | −0.209081 | ||||||||
\(929\) | 19.9714 | − | 34.5916i | 0.655242 | − | 1.13491i | −0.326591 | − | 0.945166i | \(-0.605900\pi\) |
0.981833 | − | 0.189746i | \(-0.0607666\pi\) | |||||||
\(930\) | −6.40832 | + | 5.77008i | −0.210137 | + | 0.189208i | ||||
\(931\) | 0.0691705 | + | 0.119807i | 0.00226697 | + | 0.00392651i | ||||
\(932\) | 6.88960 | + | 11.9331i | 0.225676 | + | 0.390883i | ||||
\(933\) | −18.8179 | + | 16.9437i | −0.616071 | + | 0.554712i | ||||
\(934\) | −10.6968 | + | 18.5275i | −0.350011 | + | 0.606237i | ||||
\(935\) | −0.315921 | −0.0103317 | ||||||||
\(936\) | −10.9961 | − | 7.98910i | −0.359417 | − | 0.261132i | ||||
\(937\) | −44.0780 | −1.43997 | −0.719983 | − | 0.693992i | \(-0.755850\pi\) | ||||
−0.719983 | + | 0.693992i | \(0.755850\pi\) | |||||||
\(938\) | 4.00313 | − | 6.93362i | 0.130707 | − | 0.226391i | ||||
\(939\) | −17.5959 | − | 5.71725i | −0.574220 | − | 0.186575i | ||||
\(940\) | −3.88180 | − | 6.72348i | −0.126610 | − | 0.219296i | ||||
\(941\) | −11.8989 | − | 20.6094i | −0.387892 | − | 0.671848i | 0.604274 | − | 0.796777i | \(-0.293463\pi\) |
−0.992166 | + | 0.124928i | \(0.960130\pi\) | |||||||
\(942\) | 1.51700 | + | 7.13690i | 0.0494264 | + | 0.232533i | ||||
\(943\) | −39.1773 | + | 67.8570i | −1.27579 | + | 2.20973i | ||||
\(944\) | 5.76565 | 0.187656 | ||||||||
\(945\) | −3.05422 | − | 4.20378i | −0.0993538 | − | 0.136749i | ||||
\(946\) | −2.33587 | −0.0759458 | ||||||||
\(947\) | 1.69901 | − | 2.94277i | 0.0552103 | − | 0.0956271i | −0.837099 | − | 0.547051i | \(-0.815750\pi\) |
0.892310 | + | 0.451424i | \(0.149084\pi\) | |||||||
\(948\) | −6.82722 | − | 32.1196i | −0.221738 | − | 1.04319i | ||||
\(949\) | −3.01263 | − | 5.21803i | −0.0977941 | − | 0.169384i | ||||
\(950\) | −0.126381 | − | 0.218898i | −0.00410034 | − | 0.00710199i | ||||
\(951\) | 36.0966 | + | 11.7285i | 1.17051 | + | 0.380322i | ||||
\(952\) | 1.10453 | − | 1.91310i | 0.0357980 | − | 0.0620039i | ||||
\(953\) | 43.2045 | 1.39953 | 0.699765 | − | 0.714373i | \(-0.253288\pi\) | ||||
0.699765 | + | 0.714373i | \(0.253288\pi\) | |||||||
\(954\) | 6.71144 | − | 63.8551i | 0.217291 | − | 2.06738i | ||||
\(955\) | 5.98424 | 0.193645 | ||||||||
\(956\) | −13.3188 | + | 23.0689i | −0.430762 | + | 0.746102i | ||||
\(957\) | −0.217808 | + | 0.196115i | −0.00704072 | + | 0.00633949i | ||||
\(958\) | −23.4408 | − | 40.6006i | −0.757336 | − | 1.31175i | ||||
\(959\) | −1.69555 | − | 2.93678i | −0.0547522 | − | 0.0948336i | ||||
\(960\) | 2.72888 | − | 2.45709i | 0.0880741 | − | 0.0793023i | ||||
\(961\) | 11.7875 | − | 20.4165i | 0.380241 | − | 0.658596i | ||||
\(962\) | −53.9890 | −1.74067 | ||||||||
\(963\) | 31.5800 | − | 14.0603i | 1.01765 | − | 0.453087i | ||||
\(964\) | 13.9144 | 0.448152 | ||||||||
\(965\) | −8.83948 | + | 15.3104i | −0.284553 | + | 0.492860i | ||||
\(966\) | −23.4844 | − | 7.63055i | −0.755599 | − | 0.245509i | ||||
\(967\) | −3.85325 | − | 6.67402i | −0.123912 | − | 0.214622i | 0.797395 | − | 0.603458i | \(-0.206211\pi\) |
−0.921307 | + | 0.388836i | \(0.872877\pi\) | |||||||
\(968\) | 6.63174 | + | 11.4865i | 0.213152 | + | 0.369190i | ||||
\(969\) | −0.0910229 | − | 0.428229i | −0.00292408 | − | 0.0137567i | ||||
\(970\) | −9.48091 | + | 16.4214i | −0.304414 | + | 0.527260i | ||||
\(971\) | −3.89455 | −0.124982 | −0.0624911 | − | 0.998046i | \(-0.519905\pi\) | ||||
−0.0624911 | + | 0.998046i | \(0.519905\pi\) | |||||||
\(972\) | − | 20.8614i | − | 0.669131i | ||||||
\(973\) | −8.13545 | −0.260811 | ||||||||
\(974\) | −20.1947 | + | 34.9782i | −0.647079 | + | 1.12077i | ||||
\(975\) | −1.34943 | − | 6.34858i | −0.0432164 | − | 0.203317i | ||||
\(976\) | 17.1063 | + | 29.6289i | 0.547558 | + | 0.948399i | ||||
\(977\) | −3.89947 | − | 6.75408i | −0.124755 | − | 0.216082i | 0.796882 | − | 0.604135i | \(-0.206481\pi\) |
−0.921637 | + | 0.388053i | \(0.873148\pi\) | |||||||
\(978\) | 56.4086 | + | 18.3283i | 1.80375 | + | 0.586074i | ||||
\(979\) | −1.02766 | + | 1.77997i | −0.0328443 | + | 0.0568880i | ||||
\(980\) | −1.33826 | −0.0427492 | ||||||||
\(981\) | −18.8965 | + | 8.41325i | −0.603318 | + | 0.268614i | ||||
\(982\) | −44.4588 | −1.41874 | ||||||||
\(983\) | −2.19529 | + | 3.80236i | −0.0700189 | + | 0.121276i | −0.898909 | − | 0.438135i | \(-0.855639\pi\) |
0.828890 | + | 0.559411i | \(0.188973\pi\) | |||||||
\(984\) | 15.6276 | − | 14.0712i | 0.498190 | − | 0.448572i | ||||
\(985\) | −10.0957 | − | 17.4863i | −0.321676 | − | 0.557160i | ||||
\(986\) | −1.63347 | − | 2.82925i | −0.0520203 | − | 0.0901018i | ||||
\(987\) | 7.46718 | − | 6.72348i | 0.237683 | − | 0.214011i | ||||
\(988\) | −0.346875 | + | 0.600806i | −0.0110356 | + | 0.0191142i | ||||
\(989\) | 57.6931 | 1.83453 | ||||||||
\(990\) | 0.0990681 | − | 0.942570i | 0.00314859 | − | 0.0299568i | ||||
\(991\) | 4.07623 | 0.129486 | 0.0647428 | − | 0.997902i | \(-0.479377\pi\) | ||||
0.0647428 | + | 0.997902i | \(0.479377\pi\) | |||||||
\(992\) | 8.86720 | − | 15.3584i | 0.281534 | − | 0.487631i | ||||
\(993\) | 37.0939 | + | 12.0525i | 1.17714 | + | 0.382475i | ||||
\(994\) | −10.2466 | − | 17.7476i | −0.325002 | − | 0.562920i | ||||
\(995\) | 9.04337 | + | 15.6636i | 0.286694 | + | 0.496569i | ||||
\(996\) | −4.46899 | − | 21.0250i | −0.141605 | − | 0.666201i | ||||
\(997\) | 11.8064 | − | 20.4492i | 0.373911 | − | 0.647633i | −0.616252 | − | 0.787549i | \(-0.711350\pi\) |
0.990163 | + | 0.139916i | \(0.0446832\pi\) | |||||||
\(998\) | −42.3370 | −1.34015 | ||||||||
\(999\) | 24.0843 | + | 33.1492i | 0.761994 | + | 1.04879i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.i.d.106.4 | ✓ | 8 | |
3.2 | odd | 2 | 945.2.i.c.316.1 | 8 | |||
9.2 | odd | 6 | 2835.2.a.q.1.4 | 4 | |||
9.4 | even | 3 | inner | 315.2.i.d.211.4 | yes | 8 | |
9.5 | odd | 6 | 945.2.i.c.631.1 | 8 | |||
9.7 | even | 3 | 2835.2.a.l.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.d.106.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
315.2.i.d.211.4 | yes | 8 | 9.4 | even | 3 | inner | |
945.2.i.c.316.1 | 8 | 3.2 | odd | 2 | |||
945.2.i.c.631.1 | 8 | 9.5 | odd | 6 | |||
2835.2.a.l.1.1 | 4 | 9.7 | even | 3 | |||
2835.2.a.q.1.4 | 4 | 9.2 | odd | 6 |