Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.4 | ||
Root | \(-0.437442 - 0.757672i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.g.508.4 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.134063 | + | 0.232203i | −0.0947966 | + | 0.164193i | −0.909524 | − | 0.415652i | \(-0.863553\pi\) |
0.814727 | + | 0.579845i | \(0.196887\pi\) | |||||||
\(3\) | 0.571504 | + | 0.989875i | 0.329958 | + | 0.571504i | 0.982503 | − | 0.186246i | \(-0.0596320\pi\) |
−0.652545 | + | 0.757750i | \(0.726299\pi\) | |||||||
\(4\) | 0.964054 | + | 1.66979i | 0.482027 | + | 0.834896i | ||||
\(5\) | −1.28088 | + | 2.21854i | −0.572826 | + | 0.992163i | 0.423448 | + | 0.905920i | \(0.360820\pi\) |
−0.996274 | + | 0.0862431i | \(0.972514\pi\) | |||||||
\(6\) | −0.306470 | −0.125116 | ||||||||
\(7\) | 2.57801 | + | 0.594848i | 0.974398 | + | 0.224831i | ||||
\(8\) | −1.05323 | −0.372371 | ||||||||
\(9\) | 0.846765 | − | 1.46664i | 0.282255 | − | 0.488880i | ||||
\(10\) | −0.343436 | − | 0.594848i | −0.108604 | − | 0.188107i | ||||
\(11\) | 1.97300 | + | 3.41734i | 0.594882 | + | 1.03037i | 0.993563 | + | 0.113277i | \(0.0361346\pi\) |
−0.398681 | + | 0.917090i | \(0.630532\pi\) | |||||||
\(12\) | −1.10192 | + | 1.90859i | −0.318098 | + | 0.550961i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.483741 | + | 0.518876i | −0.129285 | + | 0.138676i | ||||
\(15\) | −2.92811 | −0.756034 | ||||||||
\(16\) | −1.78691 | + | 3.09502i | −0.446728 | + | 0.773755i | ||||
\(17\) | −0.392550 | − | 0.679916i | −0.0952073 | − | 0.164904i | 0.814488 | − | 0.580181i | \(-0.197018\pi\) |
−0.909695 | + | 0.415277i | \(0.863685\pi\) | |||||||
\(18\) | 0.227039 | + | 0.393243i | 0.0535136 | + | 0.0926883i | ||||
\(19\) | −3.74764 | + | 6.49110i | −0.859767 | + | 1.48916i | 0.0123849 | + | 0.999923i | \(0.496058\pi\) |
−0.872151 | + | 0.489236i | \(0.837276\pi\) | |||||||
\(20\) | −4.93934 | −1.10447 | ||||||||
\(21\) | 0.884522 | + | 2.89187i | 0.193018 | + | 0.631058i | ||||
\(22\) | −1.05802 | −0.225571 | ||||||||
\(23\) | 3.97759 | − | 6.88938i | 0.829384 | − | 1.43654i | −0.0691375 | − | 0.997607i | \(-0.522025\pi\) |
0.898522 | − | 0.438929i | \(-0.144642\pi\) | |||||||
\(24\) | −0.601923 | − | 1.04256i | −0.122867 | − | 0.212812i | ||||
\(25\) | −0.781294 | − | 1.35324i | −0.156259 | − | 0.270648i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.36475 | 1.03245 | ||||||||
\(28\) | 1.49207 | + | 4.87821i | 0.281975 | + | 0.921895i | ||||
\(29\) | 2.35173 | 0.436705 | 0.218353 | − | 0.975870i | \(-0.429932\pi\) | ||||
0.218353 | + | 0.975870i | \(0.429932\pi\) | |||||||
\(30\) | 0.392550 | − | 0.679916i | 0.0716695 | − | 0.124135i | ||||
\(31\) | −1.27718 | − | 2.21215i | −0.229389 | − | 0.397313i | 0.728238 | − | 0.685324i | \(-0.240339\pi\) |
−0.957627 | + | 0.288011i | \(0.907006\pi\) | |||||||
\(32\) | −1.53234 | − | 2.65409i | −0.270882 | − | 0.469182i | ||||
\(33\) | −2.25516 | + | 3.90605i | −0.392573 | + | 0.679956i | ||||
\(34\) | 0.210505 | 0.0361013 | ||||||||
\(35\) | −4.62182 | + | 4.95751i | −0.781230 | + | 0.837973i | ||||
\(36\) | 3.26531 | 0.544219 | ||||||||
\(37\) | 3.37858 | − | 5.85187i | 0.555435 | − | 0.962041i | −0.442435 | − | 0.896801i | \(-0.645885\pi\) |
0.997870 | − | 0.0652406i | \(-0.0207815\pi\) | |||||||
\(38\) | −1.00484 | − | 1.74043i | −0.163006 | − | 0.282334i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.34905 | − | 2.33663i | 0.213304 | − | 0.369453i | ||||
\(41\) | 2.43747 | 0.380669 | 0.190335 | − | 0.981719i | \(-0.439043\pi\) | ||||
0.190335 | + | 0.981719i | \(0.439043\pi\) | |||||||
\(42\) | −0.790083 | − | 0.182303i | −0.121912 | − | 0.0281299i | ||||
\(43\) | −2.24946 | −0.343039 | −0.171520 | − | 0.985181i | \(-0.554868\pi\) | ||||
−0.171520 | + | 0.985181i | \(0.554868\pi\) | |||||||
\(44\) | −3.80416 | + | 6.58900i | −0.573499 | + | 0.993329i | ||||
\(45\) | 2.16920 | + | 3.75717i | 0.323366 | + | 0.560086i | ||||
\(46\) | 1.06649 | + | 1.84722i | 0.157246 | + | 0.272357i | ||||
\(47\) | 0.658276 | − | 1.14017i | 0.0960195 | − | 0.166311i | −0.814014 | − | 0.580845i | \(-0.802722\pi\) |
0.910034 | + | 0.414534i | \(0.136056\pi\) | |||||||
\(48\) | −4.08491 | −0.589606 | ||||||||
\(49\) | 6.29231 | + | 3.06705i | 0.898902 | + | 0.438150i | ||||
\(50\) | 0.418969 | 0.0592512 | ||||||||
\(51\) | 0.448688 | − | 0.777151i | 0.0628289 | − | 0.108823i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.63977 | − | 8.03632i | −0.637321 | − | 1.10387i | −0.986018 | − | 0.166637i | \(-0.946709\pi\) |
0.348697 | − | 0.937236i | \(-0.386624\pi\) | |||||||
\(54\) | −0.719212 | + | 1.24571i | −0.0978724 | + | 0.169520i | ||||
\(55\) | −10.1087 | −1.36306 | ||||||||
\(56\) | −2.71523 | − | 0.626509i | −0.362838 | − | 0.0837207i | ||||
\(57\) | −8.56716 | −1.13475 | ||||||||
\(58\) | −0.315279 | + | 0.546079i | −0.0413981 | + | 0.0717037i | ||||
\(59\) | −4.48335 | − | 7.76540i | −0.583683 | − | 1.01097i | −0.995038 | − | 0.0994935i | \(-0.968278\pi\) |
0.411355 | − | 0.911475i | \(-0.365056\pi\) | |||||||
\(60\) | −2.82286 | − | 4.88933i | −0.364429 | − | 0.631210i | ||||
\(61\) | −4.72273 | + | 8.18002i | −0.604684 | + | 1.04734i | 0.387417 | + | 0.921905i | \(0.373367\pi\) |
−0.992101 | + | 0.125439i | \(0.959966\pi\) | |||||||
\(62\) | 0.684890 | 0.0869811 | ||||||||
\(63\) | 3.05540 | − | 3.27732i | 0.384944 | − | 0.412904i | ||||
\(64\) | −6.32592 | −0.790741 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.604665 | − | 1.04731i | −0.0744291 | − | 0.128915i | ||||
\(67\) | −0.676281 | − | 1.17135i | −0.0826209 | − | 0.143104i | 0.821754 | − | 0.569842i | \(-0.192996\pi\) |
−0.904375 | + | 0.426739i | \(0.859662\pi\) | |||||||
\(68\) | 0.756879 | − | 1.31095i | 0.0917851 | − | 0.158976i | ||||
\(69\) | 9.09284 | 1.09465 | ||||||||
\(70\) | −0.531538 | − | 1.73782i | −0.0635309 | − | 0.207709i | ||||
\(71\) | −12.3162 | −1.46166 | −0.730829 | − | 0.682560i | \(-0.760867\pi\) | ||||
−0.730829 | + | 0.682560i | \(0.760867\pi\) | |||||||
\(72\) | −0.891834 | + | 1.54470i | −0.105104 | + | 0.182045i | ||||
\(73\) | 0.384295 | + | 0.665619i | 0.0449783 | + | 0.0779048i | 0.887638 | − | 0.460542i | \(-0.152345\pi\) |
−0.842660 | + | 0.538446i | \(0.819011\pi\) | |||||||
\(74\) | 0.905882 | + | 1.56903i | 0.105307 | + | 0.182396i | ||||
\(75\) | 0.893026 | − | 1.54677i | 0.103118 | − | 0.178605i | ||||
\(76\) | −14.4517 | −1.65772 | ||||||||
\(77\) | 3.05363 | + | 9.98358i | 0.347993 | + | 1.13773i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.09642 | + | 5.36316i | −0.348375 | + | 0.603402i | −0.985961 | − | 0.166976i | \(-0.946600\pi\) |
0.637586 | + | 0.770379i | \(0.279933\pi\) | |||||||
\(80\) | −4.57763 | − | 7.92868i | −0.511794 | − | 0.886454i | ||||
\(81\) | 0.525682 | + | 0.910507i | 0.0584091 | + | 0.101167i | ||||
\(82\) | −0.326774 | + | 0.565989i | −0.0360861 | + | 0.0625030i | ||||
\(83\) | 1.07292 | 0.117768 | 0.0588841 | − | 0.998265i | \(-0.481246\pi\) | ||||
0.0588841 | + | 0.998265i | \(0.481246\pi\) | |||||||
\(84\) | −3.97609 | + | 4.26489i | −0.433827 | + | 0.465337i | ||||
\(85\) | 2.01123 | 0.218149 | ||||||||
\(86\) | 0.301568 | − | 0.522332i | 0.0325190 | − | 0.0563245i | ||||
\(87\) | 1.34402 | + | 2.32792i | 0.144094 | + | 0.249579i | ||||
\(88\) | −2.07801 | − | 3.59923i | −0.221517 | − | 0.383679i | ||||
\(89\) | 3.83149 | − | 6.63634i | 0.406138 | − | 0.703451i | −0.588316 | − | 0.808631i | \(-0.700209\pi\) |
0.994453 | + | 0.105180i | \(0.0335420\pi\) | |||||||
\(90\) | −1.16324 | −0.122616 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.3384 | 1.59914 | ||||||||
\(93\) | 1.45983 | − | 2.52850i | 0.151378 | − | 0.262194i | ||||
\(94\) | 0.176501 | + | 0.305708i | 0.0182046 | + | 0.0315314i | ||||
\(95\) | −9.60052 | − | 16.6286i | −0.984993 | − | 1.70606i | ||||
\(96\) | 1.75148 | − | 3.03365i | 0.178760 | − | 0.309621i | ||||
\(97\) | 2.37202 | 0.240842 | 0.120421 | − | 0.992723i | \(-0.461576\pi\) | ||||
0.120421 | + | 0.992723i | \(0.461576\pi\) | |||||||
\(98\) | −1.55574 | + | 1.04992i | −0.157154 | + | 0.106058i | ||||
\(99\) | 6.68267 | 0.671634 | ||||||||
\(100\) | 1.50642 | − | 2.60920i | 0.150642 | − | 0.260920i | ||||
\(101\) | 0.398665 | + | 0.690508i | 0.0396686 | + | 0.0687081i | 0.885178 | − | 0.465252i | \(-0.154036\pi\) |
−0.845509 | + | 0.533961i | \(0.820703\pi\) | |||||||
\(102\) | 0.120305 | + | 0.208374i | 0.0119119 | + | 0.0206321i | ||||
\(103\) | −1.08309 | + | 1.87597i | −0.106720 | + | 0.184844i | −0.914440 | − | 0.404722i | \(-0.867368\pi\) |
0.807720 | + | 0.589567i | \(0.200701\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.54871 | − | 1.74178i | −0.736678 | − | 0.169980i | ||||
\(106\) | 2.48808 | 0.241664 | ||||||||
\(107\) | 5.76311 | − | 9.98201i | 0.557141 | − | 0.964997i | −0.440592 | − | 0.897707i | \(-0.645232\pi\) |
0.997733 | − | 0.0672896i | \(-0.0214351\pi\) | |||||||
\(108\) | 5.17191 | + | 8.95801i | 0.497667 | + | 0.861985i | ||||
\(109\) | 4.03912 | + | 6.99595i | 0.386877 | + | 0.670091i | 0.992028 | − | 0.126020i | \(-0.0402204\pi\) |
−0.605151 | + | 0.796111i | \(0.706887\pi\) | |||||||
\(110\) | 1.35520 | − | 2.34727i | 0.129213 | − | 0.223803i | ||||
\(111\) | 7.72349 | 0.733081 | ||||||||
\(112\) | −6.44775 | + | 6.91607i | −0.609255 | + | 0.653507i | ||||
\(113\) | 8.04135 | 0.756467 | 0.378233 | − | 0.925710i | \(-0.376532\pi\) | ||||
0.378233 | + | 0.925710i | \(0.376532\pi\) | |||||||
\(114\) | 1.14854 | − | 1.98932i | 0.107570 | − | 0.186317i | ||||
\(115\) | 10.1896 | + | 17.6489i | 0.950186 | + | 1.64577i | ||||
\(116\) | 2.26719 | + | 3.92690i | 0.210504 | + | 0.364603i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.40420 | 0.221325 | ||||||||
\(119\) | −0.607552 | − | 1.98634i | −0.0556942 | − | 0.182088i | ||||
\(120\) | 3.08396 | 0.281526 | ||||||||
\(121\) | −2.28546 | + | 3.95854i | −0.207769 | + | 0.359867i | ||||
\(122\) | −1.26628 | − | 2.19327i | −0.114644 | − | 0.198569i | ||||
\(123\) | 1.39303 | + | 2.41279i | 0.125605 | + | 0.217554i | ||||
\(124\) | 2.46255 | − | 4.26526i | 0.221143 | − | 0.383032i | ||||
\(125\) | −8.80581 | −0.787615 | ||||||||
\(126\) | 0.351390 | + | 1.14884i | 0.0313043 | + | 0.102347i | ||||
\(127\) | 1.78805 | 0.158663 | 0.0793317 | − | 0.996848i | \(-0.474721\pi\) | ||||
0.0793317 | + | 0.996848i | \(0.474721\pi\) | |||||||
\(128\) | 3.91275 | − | 6.77709i | 0.345842 | − | 0.599015i | ||||
\(129\) | −1.28558 | − | 2.22668i | −0.113189 | − | 0.196049i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.19545 | − | 5.53469i | 0.279188 | − | 0.483568i | −0.691995 | − | 0.721902i | \(-0.743268\pi\) |
0.971183 | + | 0.238334i | \(0.0766014\pi\) | |||||||
\(132\) | −8.69638 | −0.756923 | ||||||||
\(133\) | −13.5227 | + | 14.5049i | −1.17256 | + | 1.25773i | ||||
\(134\) | 0.362656 | 0.0313287 | ||||||||
\(135\) | −6.87158 | + | 11.9019i | −0.591412 | + | 1.02436i | ||||
\(136\) | 0.413443 | + | 0.716105i | 0.0354525 | + | 0.0614055i | ||||
\(137\) | 5.01827 | + | 8.69190i | 0.428740 | + | 0.742599i | 0.996762 | − | 0.0804144i | \(-0.0256244\pi\) |
−0.568022 | + | 0.823014i | \(0.692291\pi\) | |||||||
\(138\) | −1.21901 | + | 2.11139i | −0.103769 | + | 0.179733i | ||||
\(139\) | −5.54557 | −0.470369 | −0.235184 | − | 0.971951i | \(-0.575569\pi\) | ||||
−0.235184 | + | 0.971951i | \(0.575569\pi\) | |||||||
\(140\) | −12.7337 | − | 2.93816i | −1.07619 | − | 0.248320i | ||||
\(141\) | 1.50483 | 0.126730 | ||||||||
\(142\) | 1.65114 | − | 2.85985i | 0.138560 | − | 0.239993i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.02619 | + | 5.24151i | 0.252182 | + | 0.436793i | ||||
\(145\) | −3.01228 | + | 5.21742i | −0.250156 | + | 0.433283i | ||||
\(146\) | −0.206078 | −0.0170552 | ||||||||
\(147\) | 0.560087 | + | 7.98144i | 0.0461952 | + | 0.658298i | ||||
\(148\) | 13.0285 | 1.07094 | ||||||||
\(149\) | 9.23254 | − | 15.9912i | 0.756359 | − | 1.31005i | −0.188337 | − | 0.982104i | \(-0.560310\pi\) |
0.944696 | − | 0.327947i | \(-0.106357\pi\) | |||||||
\(150\) | 0.239443 | + | 0.414727i | 0.0195504 | + | 0.0338623i | ||||
\(151\) | 0.803678 | + | 1.39201i | 0.0654024 | + | 0.113280i | 0.896872 | − | 0.442289i | \(-0.145834\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(152\) | 3.94710 | − | 6.83658i | 0.320152 | − | 0.554520i | ||||
\(153\) | −1.32959 | −0.107491 | ||||||||
\(154\) | −2.72760 | − | 0.629362i | −0.219796 | − | 0.0507155i | ||||
\(155\) | 6.54366 | 0.525600 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.822967 | + | 1.42542i | 0.0656799 | + | 0.113761i | 0.896995 | − | 0.442040i | \(-0.145745\pi\) |
−0.831315 | + | 0.555801i | \(0.812412\pi\) | |||||||
\(158\) | −0.830229 | − | 1.43800i | −0.0660494 | − | 0.114401i | ||||
\(159\) | 5.30330 | − | 9.18558i | 0.420579 | − | 0.728464i | ||||
\(160\) | 7.85096 | 0.620673 | ||||||||
\(161\) | 14.3524 | − | 15.3949i | 1.13113 | − | 1.21329i | ||||
\(162\) | −0.281897 | −0.0221479 | ||||||||
\(163\) | −3.27409 | + | 5.67090i | −0.256447 | + | 0.444179i | −0.965287 | − | 0.261190i | \(-0.915885\pi\) |
0.708841 | + | 0.705369i | \(0.249218\pi\) | |||||||
\(164\) | 2.34986 | + | 4.07007i | 0.183493 | + | 0.317819i | ||||
\(165\) | −5.77716 | − | 10.0063i | −0.449751 | − | 0.778992i | ||||
\(166\) | −0.143838 | + | 0.249135i | −0.0111640 | + | 0.0193367i | ||||
\(167\) | −9.54880 | −0.738908 | −0.369454 | − | 0.929249i | \(-0.620455\pi\) | ||||
−0.369454 | + | 0.929249i | \(0.620455\pi\) | |||||||
\(168\) | −0.931600 | − | 3.04579i | −0.0718745 | − | 0.234988i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.269631 | + | 0.467015i | −0.0206798 | + | 0.0358184i | ||||
\(171\) | 6.34673 | + | 10.9929i | 0.485347 | + | 0.840646i | ||||
\(172\) | −2.16860 | − | 3.75613i | −0.165354 | − | 0.286402i | ||||
\(173\) | −5.56582 | + | 9.64028i | −0.423161 | + | 0.732937i | −0.996247 | − | 0.0865588i | \(-0.972413\pi\) |
0.573085 | + | 0.819496i | \(0.305746\pi\) | |||||||
\(174\) | −0.720733 | −0.0546386 | ||||||||
\(175\) | −1.20921 | − | 3.95343i | −0.0914080 | − | 0.298851i | ||||
\(176\) | −14.1023 | −1.06300 | ||||||||
\(177\) | 5.12451 | − | 8.87592i | 0.385182 | − | 0.667155i | ||||
\(178\) | 1.02732 | + | 1.77937i | 0.0770009 | + | 0.133369i | ||||
\(179\) | 6.32173 | + | 10.9496i | 0.472508 | + | 0.818409i | 0.999505 | − | 0.0314588i | \(-0.0100153\pi\) |
−0.526997 | + | 0.849867i | \(0.676682\pi\) | |||||||
\(180\) | −4.18246 | + | 7.24424i | −0.311742 | + | 0.539954i | ||||
\(181\) | 14.9158 | 1.10868 | 0.554341 | − | 0.832289i | \(-0.312970\pi\) | ||||
0.554341 | + | 0.832289i | \(0.312970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7963 | −0.798082 | ||||||||
\(184\) | −4.18930 | + | 7.25607i | −0.308839 | + | 0.534925i | ||||
\(185\) | 8.65509 | + | 14.9911i | 0.636335 | + | 1.10216i | ||||
\(186\) | 0.391418 | + | 0.677956i | 0.0287001 | + | 0.0497101i | ||||
\(187\) | 1.54900 | − | 2.68295i | 0.113274 | − | 0.196197i | ||||
\(188\) | 2.53846 | 0.185136 | ||||||||
\(189\) | 13.8304 | + | 3.19121i | 1.00601 | + | 0.232126i | ||||
\(190\) | 5.14829 | 0.373496 | ||||||||
\(191\) | 7.06528 | − | 12.2374i | 0.511226 | − | 0.885469i | −0.488690 | − | 0.872458i | \(-0.662525\pi\) |
0.999915 | − | 0.0130110i | \(-0.00414165\pi\) | |||||||
\(192\) | −3.61529 | − | 6.26187i | −0.260911 | − | 0.451912i | ||||
\(193\) | 1.94727 | + | 3.37277i | 0.140167 | + | 0.242777i | 0.927560 | − | 0.373675i | \(-0.121903\pi\) |
−0.787392 | + | 0.616452i | \(0.788569\pi\) | |||||||
\(194\) | −0.317999 | + | 0.550790i | −0.0228310 | + | 0.0395444i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.944795 | + | 13.4637i | 0.0674853 | + | 0.961689i | ||||
\(197\) | 11.7089 | 0.834224 | 0.417112 | − | 0.908855i | \(-0.363042\pi\) | ||||
0.417112 | + | 0.908855i | \(0.363042\pi\) | |||||||
\(198\) | −0.895897 | + | 1.55174i | −0.0636686 | + | 0.110277i | ||||
\(199\) | −1.74842 | − | 3.02835i | −0.123942 | − | 0.214674i | 0.797377 | − | 0.603482i | \(-0.206220\pi\) |
−0.921319 | + | 0.388808i | \(0.872887\pi\) | |||||||
\(200\) | 0.822878 | + | 1.42527i | 0.0581863 | + | 0.100782i | ||||
\(201\) | 0.772995 | − | 1.33887i | 0.0545229 | − | 0.0944364i | ||||
\(202\) | −0.213784 | −0.0150418 | ||||||||
\(203\) | 6.06279 | + | 1.39892i | 0.425524 | + | 0.0981850i | ||||
\(204\) | 1.73024 | 0.121141 | ||||||||
\(205\) | −3.12210 | + | 5.40764i | −0.218057 | + | 0.377686i | ||||
\(206\) | −0.290403 | − | 0.502994i | −0.0202334 | − | 0.0350452i | ||||
\(207\) | −6.73617 | − | 11.6674i | −0.468196 | − | 0.810939i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.5764 | −2.04584 | ||||||||
\(210\) | 1.41645 | − | 1.51933i | 0.0977441 | − | 0.104843i | ||||
\(211\) | 19.0052 | 1.30837 | 0.654184 | − | 0.756335i | \(-0.273012\pi\) | ||||
0.654184 | + | 0.756335i | \(0.273012\pi\) | |||||||
\(212\) | 8.94598 | − | 15.4949i | 0.614412 | − | 1.06419i | ||||
\(213\) | −7.03874 | − | 12.1915i | −0.482286 | − | 0.835345i | ||||
\(214\) | 1.54524 | + | 2.67643i | 0.105630 | + | 0.182957i | ||||
\(215\) | 2.88128 | − | 4.99053i | 0.196502 | − | 0.340351i | ||||
\(216\) | −5.65029 | −0.384453 | ||||||||
\(217\) | −1.97671 | − | 6.46267i | −0.134188 | − | 0.438715i | ||||
\(218\) | −2.16598 | −0.146698 | ||||||||
\(219\) | −0.439253 | + | 0.760808i | −0.0296820 | + | 0.0514106i | ||||
\(220\) | −9.74533 | − | 16.8794i | −0.657030 | − | 1.13801i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.03543 | + | 1.79342i | −0.0694936 | + | 0.120366i | ||||
\(223\) | 11.9662 | 0.801317 | 0.400658 | − | 0.916228i | \(-0.368781\pi\) | ||||
0.400658 | + | 0.916228i | \(0.368781\pi\) | |||||||
\(224\) | −2.37162 | − | 7.75380i | −0.158460 | − | 0.518072i | ||||
\(225\) | −2.64629 | −0.176419 | ||||||||
\(226\) | −1.07804 | + | 1.86723i | −0.0717104 | + | 0.124206i | ||||
\(227\) | 7.69209 | + | 13.3231i | 0.510542 | + | 0.884284i | 0.999925 | + | 0.0122157i | \(0.00388847\pi\) |
−0.489384 | + | 0.872069i | \(0.662778\pi\) | |||||||
\(228\) | −8.25921 | − | 14.3054i | −0.546980 | − | 0.947396i | ||||
\(229\) | 4.33084 | − | 7.50123i | 0.286190 | − | 0.495695i | −0.686707 | − | 0.726934i | \(-0.740945\pi\) |
0.972897 | + | 0.231239i | \(0.0742779\pi\) | |||||||
\(230\) | −5.46418 | −0.360297 | ||||||||
\(231\) | −8.13733 | + | 8.72837i | −0.535397 | + | 0.574285i | ||||
\(232\) | −2.47690 | −0.162616 | ||||||||
\(233\) | −10.1253 | + | 17.5376i | −0.663333 | + | 1.14893i | 0.316402 | + | 0.948625i | \(0.397525\pi\) |
−0.979734 | + | 0.200301i | \(0.935808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.68634 | + | 2.92083i | 0.110005 | + | 0.190534i | ||||
\(236\) | 8.64440 | − | 14.9725i | 0.562702 | − | 0.974629i | ||||
\(237\) | −7.07847 | −0.459796 | ||||||||
\(238\) | 0.542685 | + | 0.125218i | 0.0351770 | + | 0.00811671i | ||||
\(239\) | −16.5526 | −1.07070 | −0.535350 | − | 0.844630i | \(-0.679820\pi\) | ||||
−0.535350 | + | 0.844630i | \(0.679820\pi\) | |||||||
\(240\) | 5.23227 | − | 9.06256i | 0.337742 | − | 0.584985i | ||||
\(241\) | −8.20038 | − | 14.2035i | −0.528233 | − | 0.914926i | −0.999458 | − | 0.0329132i | \(-0.989522\pi\) |
0.471225 | − | 0.882013i | \(-0.343812\pi\) | |||||||
\(242\) | −0.612791 | − | 1.06138i | −0.0393917 | − | 0.0682284i | ||||
\(243\) | 7.44626 | − | 12.8973i | 0.477678 | − | 0.827362i | ||||
\(244\) | −18.2119 | −1.16590 | ||||||||
\(245\) | −14.8641 | + | 10.0313i | −0.949631 | + | 0.640874i | ||||
\(246\) | −0.747011 | −0.0476277 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.34516 | + | 2.32989i | 0.0854178 | + | 0.147948i | ||||
\(249\) | 0.613178 | + | 1.06206i | 0.0388586 | + | 0.0673051i | ||||
\(250\) | 1.18053 | − | 2.04474i | 0.0746632 | − | 0.129321i | ||||
\(251\) | −20.4307 | −1.28958 | −0.644788 | − | 0.764362i | \(-0.723054\pi\) | ||||
−0.644788 | + | 0.764362i | \(0.723054\pi\) | |||||||
\(252\) | 8.41802 | + | 1.94236i | 0.530285 | + | 0.122357i | ||||
\(253\) | 31.3911 | 1.97354 | ||||||||
\(254\) | −0.239710 | + | 0.415190i | −0.0150407 | + | 0.0260513i | ||||
\(255\) | 1.14943 | + | 1.99087i | 0.0719800 | + | 0.124673i | ||||
\(256\) | −5.27682 | − | 9.13972i | −0.329801 | − | 0.571232i | ||||
\(257\) | −6.88895 | + | 11.9320i | −0.429721 | + | 0.744299i | −0.996848 | − | 0.0793315i | \(-0.974721\pi\) |
0.567127 | + | 0.823630i | \(0.308055\pi\) | |||||||
\(258\) | 0.689391 | 0.0429196 | ||||||||
\(259\) | 12.1910 | − | 13.0765i | 0.757511 | − | 0.812532i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.99136 | − | 3.44914i | 0.123262 | − | 0.213496i | ||||
\(262\) | 0.856782 | + | 1.48399i | 0.0529321 | + | 0.0916812i | ||||
\(263\) | −12.9587 | − | 22.4451i | −0.799065 | − | 1.38402i | −0.920225 | − | 0.391389i | \(-0.871995\pi\) |
0.121160 | − | 0.992633i | \(-0.461338\pi\) | |||||||
\(264\) | 2.37519 | − | 4.11395i | 0.146183 | − | 0.253196i | ||||
\(265\) | 23.7719 | 1.46030 | ||||||||
\(266\) | −1.55519 | − | 5.08457i | −0.0953549 | − | 0.311755i | ||||
\(267\) | 8.75887 | 0.536034 | ||||||||
\(268\) | 1.30394 | − | 2.25850i | 0.0796510 | − | 0.137960i | ||||
\(269\) | 15.0333 | + | 26.0384i | 0.916596 | + | 1.58759i | 0.804547 | + | 0.593889i | \(0.202408\pi\) |
0.112050 | + | 0.993703i | \(0.464258\pi\) | |||||||
\(270\) | −1.84245 | − | 3.19121i | −0.112128 | − | 0.194211i | ||||
\(271\) | 7.22527 | − | 12.5145i | 0.438904 | − | 0.760204i | −0.558701 | − | 0.829369i | \(-0.688700\pi\) |
0.997605 | + | 0.0691651i | \(0.0220335\pi\) | |||||||
\(272\) | 2.80581 | 0.170127 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.69105 | −0.162572 | ||||||||
\(275\) | 3.08299 | − | 5.33989i | 0.185911 | − | 0.322008i | ||||
\(276\) | 8.76599 | + | 15.1831i | 0.527651 | + | 0.913918i | ||||
\(277\) | 7.66274 | + | 13.2723i | 0.460409 | + | 0.797452i | 0.998981 | − | 0.0451272i | \(-0.0143693\pi\) |
−0.538572 | + | 0.842580i | \(0.681036\pi\) | |||||||
\(278\) | 0.743453 | − | 1.28770i | 0.0445894 | − | 0.0772310i | ||||
\(279\) | −4.32590 | −0.258985 | ||||||||
\(280\) | 4.86781 | − | 5.22138i | 0.290907 | − | 0.312037i | ||||
\(281\) | −5.29279 | −0.315741 | −0.157871 | − | 0.987460i | \(-0.550463\pi\) | ||||
−0.157871 | + | 0.987460i | \(0.550463\pi\) | |||||||
\(282\) | −0.201742 | + | 0.349427i | −0.0120135 | + | 0.0208081i | ||||
\(283\) | 15.3923 | + | 26.6602i | 0.914975 | + | 1.58478i | 0.806938 | + | 0.590636i | \(0.201123\pi\) |
0.108036 | + | 0.994147i | \(0.465544\pi\) | |||||||
\(284\) | −11.8734 | − | 20.5654i | −0.704559 | − | 1.22033i | ||||
\(285\) | 10.9735 | − | 19.0066i | 0.650013 | − | 1.12586i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.28384 | + | 1.44992i | 0.370923 | + | 0.0855864i | ||||
\(288\) | −5.19013 | −0.305831 | ||||||||
\(289\) | 8.19181 | − | 14.1886i | 0.481871 | − | 0.834625i | ||||
\(290\) | −0.807667 | − | 1.39892i | −0.0474279 | − | 0.0821474i | ||||
\(291\) | 1.35562 | + | 2.34800i | 0.0794677 | + | 0.137642i | ||||
\(292\) | −0.740963 | + | 1.28339i | −0.0433616 | + | 0.0751044i | ||||
\(293\) | 17.5173 | 1.02337 | 0.511685 | − | 0.859173i | \(-0.329021\pi\) | ||||
0.511685 | + | 0.859173i | \(0.329021\pi\) | |||||||
\(294\) | −1.92840 | − | 0.939958i | −0.112467 | − | 0.0548195i | ||||
\(295\) | 22.9705 | 1.33739 | ||||||||
\(296\) | −3.55840 | + | 6.16333i | −0.206828 | + | 0.358237i | ||||
\(297\) | 10.5847 | + | 18.3332i | 0.614184 | + | 1.06380i | ||||
\(298\) | 2.47548 | + | 4.28765i | 0.143400 | + | 0.248377i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.44370 | 0.198822 | ||||||||
\(301\) | −5.79914 | − | 1.33809i | −0.334257 | − | 0.0771260i | ||||
\(302\) | −0.430973 | −0.0247997 | ||||||||
\(303\) | −0.455678 | + | 0.789257i | −0.0261780 | + | 0.0453416i | ||||
\(304\) | −13.3934 | − | 23.1980i | −0.768163 | − | 1.33050i | ||||
\(305\) | −12.0985 | − | 20.9552i | −0.692757 | − | 1.19989i | ||||
\(306\) | 0.178248 | − | 0.308735i | 0.0101898 | − | 0.0176492i | ||||
\(307\) | 8.63573 | 0.492867 | 0.246434 | − | 0.969160i | \(-0.420741\pi\) | ||||
0.246434 | + | 0.969160i | \(0.420741\pi\) | |||||||
\(308\) | −13.7266 | + | 14.7236i | −0.782147 | + | 0.838957i | ||||
\(309\) | −2.47596 | −0.140852 | ||||||||
\(310\) | −0.877260 | + | 1.51946i | −0.0498250 | + | 0.0862995i | ||||
\(311\) | 8.21130 | + | 14.2224i | 0.465620 | + | 0.806478i | 0.999229 | − | 0.0392535i | \(-0.0124980\pi\) |
−0.533609 | + | 0.845731i | \(0.679165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.02308 | + | 8.70024i | −0.283921 | + | 0.491766i | −0.972347 | − | 0.233541i | \(-0.924969\pi\) |
0.688426 | + | 0.725307i | \(0.258302\pi\) | |||||||
\(314\) | −0.441316 | −0.0249049 | ||||||||
\(315\) | 3.35729 | + | 10.9764i | 0.189162 | + | 0.618450i | ||||
\(316\) | −11.9405 | −0.671704 | ||||||||
\(317\) | 5.07249 | − | 8.78581i | 0.284899 | − | 0.493460i | −0.687685 | − | 0.726009i | \(-0.741373\pi\) |
0.972585 | + | 0.232549i | \(0.0747064\pi\) | |||||||
\(318\) | 1.42195 | + | 2.46289i | 0.0797389 | + | 0.138112i | ||||
\(319\) | 4.63996 | + | 8.03665i | 0.259788 | + | 0.449966i | ||||
\(320\) | 8.10273 | − | 14.0343i | 0.452957 | − | 0.784544i | ||||
\(321\) | 13.1746 | 0.735333 | ||||||||
\(322\) | 1.65062 | + | 5.39655i | 0.0919853 | + | 0.300738i | ||||
\(323\) | 5.88454 | 0.327424 | ||||||||
\(324\) | −1.01357 | + | 1.75556i | −0.0563095 | + | 0.0975310i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.877867 | − | 1.52051i | −0.0486206 | − | 0.0842133i | ||||
\(327\) | −4.61674 | + | 7.99644i | −0.255307 | + | 0.442204i | ||||
\(328\) | −2.56721 | −0.141750 | ||||||||
\(329\) | 2.37527 | − | 2.54780i | 0.130953 | − | 0.140464i | ||||
\(330\) | 3.09801 | 0.170540 | ||||||||
\(331\) | 1.15958 | − | 2.00845i | 0.0637363 | − | 0.110395i | −0.832396 | − | 0.554181i | \(-0.813032\pi\) |
0.896133 | + | 0.443786i | \(0.146365\pi\) | |||||||
\(332\) | 1.03435 | + | 1.79155i | 0.0567675 | + | 0.0983242i | ||||
\(333\) | −5.72172 | − | 9.91032i | −0.313549 | − | 0.543082i | ||||
\(334\) | 1.28014 | − | 2.21726i | 0.0700460 | − | 0.121323i | ||||
\(335\) | 3.46493 | 0.189309 | ||||||||
\(336\) | −10.5310 | − | 2.42990i | −0.574511 | − | 0.132562i | ||||
\(337\) | −15.9998 | −0.871565 | −0.435783 | − | 0.900052i | \(-0.643528\pi\) | ||||
−0.435783 | + | 0.900052i | \(0.643528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.59567 | + | 7.95993i | 0.249602 | + | 0.432324i | ||||
\(340\) | 1.93894 | + | 3.35834i | 0.105154 | + | 0.182132i | ||||
\(341\) | 5.03977 | − | 8.72913i | 0.272919 | − | 0.472709i | ||||
\(342\) | −3.40344 | −0.184037 | ||||||||
\(343\) | 14.3972 | + | 11.6499i | 0.777378 | + | 0.629034i | ||||
\(344\) | 2.36919 | 0.127738 | ||||||||
\(345\) | −11.6468 | + | 20.1729i | −0.627043 | + | 1.08607i | ||||
\(346\) | −1.49234 | − | 2.58480i | −0.0802285 | − | 0.138960i | ||||
\(347\) | 11.4104 | + | 19.7634i | 0.612543 | + | 1.06096i | 0.990810 | + | 0.135259i | \(0.0431867\pi\) |
−0.378267 | + | 0.925696i | \(0.623480\pi\) | |||||||
\(348\) | −2.59142 | + | 4.48848i | −0.138915 | + | 0.240608i | ||||
\(349\) | 22.7022 | 1.21522 | 0.607612 | − | 0.794234i | \(-0.292128\pi\) | ||||
0.607612 | + | 0.794234i | \(0.292128\pi\) | |||||||
\(350\) | 1.08011 | + | 0.249223i | 0.0577342 | + | 0.0133215i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.04662 | − | 10.4731i | 0.322286 | − | 0.558216i | ||||
\(353\) | −13.6322 | − | 23.6116i | −0.725568 | − | 1.25672i | −0.958740 | − | 0.284286i | \(-0.908244\pi\) |
0.233171 | − | 0.972436i | \(-0.425090\pi\) | |||||||
\(354\) | 1.37401 | + | 2.37986i | 0.0730279 | + | 0.126488i | ||||
\(355\) | 15.7755 | − | 27.3239i | 0.837276 | − | 1.45020i | ||||
\(356\) | 14.7751 | 0.783077 | ||||||||
\(357\) | 1.61901 | − | 1.73660i | 0.0856871 | − | 0.0919108i | ||||
\(358\) | −3.39003 | −0.179169 | ||||||||
\(359\) | −7.21309 | + | 12.4934i | −0.380692 | + | 0.659378i | −0.991161 | − | 0.132662i | \(-0.957648\pi\) |
0.610469 | + | 0.792040i | \(0.290981\pi\) | |||||||
\(360\) | −2.28466 | − | 3.95715i | −0.120412 | − | 0.208560i | ||||
\(361\) | −18.5895 | − | 32.1980i | −0.978397 | − | 1.69463i | ||||
\(362\) | −1.99965 | + | 3.46350i | −0.105099 | + | 0.182037i | ||||
\(363\) | −5.22461 | −0.274221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.96894 | −0.103059 | ||||||||
\(366\) | 1.44737 | − | 2.50693i | 0.0756555 | − | 0.131039i | ||||
\(367\) | 5.69586 | + | 9.86553i | 0.297322 | + | 0.514976i | 0.975522 | − | 0.219901i | \(-0.0705733\pi\) |
−0.678201 | + | 0.734877i | \(0.737240\pi\) | |||||||
\(368\) | 14.2152 | + | 24.6214i | 0.741018 | + | 1.28348i | ||||
\(369\) | 2.06397 | − | 3.57489i | 0.107446 | − | 0.186102i | ||||
\(370\) | −4.64130 | −0.241289 | ||||||||
\(371\) | −7.18100 | − | 23.4777i | −0.372819 | − | 1.21890i | ||||
\(372\) | 5.62943 | 0.291872 | ||||||||
\(373\) | 15.4815 | − | 26.8147i | 0.801599 | − | 1.38841i | −0.116964 | − | 0.993136i | \(-0.537316\pi\) |
0.918563 | − | 0.395274i | \(-0.129351\pi\) | |||||||
\(374\) | 0.415327 | + | 0.719367i | 0.0214760 | + | 0.0371976i | ||||
\(375\) | −5.03256 | − | 8.71665i | −0.259880 | − | 0.450126i | ||||
\(376\) | −0.693313 | + | 1.20085i | −0.0357549 | + | 0.0619293i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.59515 | + | 2.78364i | −0.133480 | + | 0.143175i | ||||
\(379\) | −10.5866 | −0.543797 | −0.271898 | − | 0.962326i | \(-0.587651\pi\) | ||||
−0.271898 | + | 0.962326i | \(0.587651\pi\) | |||||||
\(380\) | 18.5109 | − | 32.0617i | 0.949587 | − | 1.64473i | ||||
\(381\) | 1.02188 | + | 1.76994i | 0.0523523 | + | 0.0906768i | ||||
\(382\) | 1.89438 | + | 3.28116i | 0.0969249 | + | 0.167879i | ||||
\(383\) | 15.3758 | − | 26.6317i | 0.785668 | − | 1.36082i | −0.142931 | − | 0.989733i | \(-0.545653\pi\) |
0.928599 | − | 0.371084i | \(-0.121014\pi\) | |||||||
\(384\) | 8.94462 | 0.456453 | ||||||||
\(385\) | −26.0603 | − | 6.01313i | −1.32816 | − | 0.306458i | ||||
\(386\) | −1.04422 | −0.0531496 | ||||||||
\(387\) | −1.90476 | + | 3.29915i | −0.0968246 | + | 0.167705i | ||||
\(388\) | 2.28675 | + | 3.96077i | 0.116092 | + | 0.201078i | ||||
\(389\) | 8.18978 | + | 14.1851i | 0.415239 | + | 0.719214i | 0.995453 | − | 0.0952492i | \(-0.0303648\pi\) |
−0.580215 | + | 0.814463i | \(0.697031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.24561 | −0.315854 | ||||||||
\(392\) | −6.62722 | − | 3.23030i | −0.334725 | − | 0.163155i | ||||
\(393\) | 7.30486 | 0.368482 | ||||||||
\(394\) | −1.56972 | + | 2.71884i | −0.0790816 | + | 0.136973i | ||||
\(395\) | −7.93227 | − | 13.7391i | −0.399116 | − | 0.691289i | ||||
\(396\) | 6.44246 | + | 11.1587i | 0.323746 | + | 0.560744i | ||||
\(397\) | −7.94133 | + | 13.7548i | −0.398564 | + | 0.690333i | −0.993549 | − | 0.113404i | \(-0.963825\pi\) |
0.594985 | + | 0.803737i | \(0.297158\pi\) | |||||||
\(398\) | 0.937591 | 0.0469972 | ||||||||
\(399\) | −22.0863 | − | 5.09616i | −1.10570 | − | 0.255127i | ||||
\(400\) | 5.58441 | 0.279221 | ||||||||
\(401\) | 3.31787 | − | 5.74671i | 0.165686 | − | 0.286977i | −0.771212 | − | 0.636578i | \(-0.780349\pi\) |
0.936899 | + | 0.349601i | \(0.113683\pi\) | |||||||
\(402\) | 0.207259 | + | 0.358984i | 0.0103372 | + | 0.0179045i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.768670 | + | 1.33137i | −0.0382427 | + | 0.0662384i | ||||
\(405\) | −2.69334 | −0.133833 | ||||||||
\(406\) | −1.13763 | + | 1.22026i | −0.0564595 | + | 0.0605603i | ||||
\(407\) | 26.6637 | 1.32167 | ||||||||
\(408\) | −0.472570 | + | 0.818515i | −0.0233957 | + | 0.0405225i | ||||
\(409\) | 2.93617 | + | 5.08560i | 0.145184 | + | 0.251467i | 0.929442 | − | 0.368969i | \(-0.120289\pi\) |
−0.784257 | + | 0.620436i | \(0.786956\pi\) | |||||||
\(410\) | −0.837115 | − | 1.44992i | −0.0413421 | − | 0.0716067i | ||||
\(411\) | −5.73593 | + | 9.93492i | −0.282933 | + | 0.490053i | ||||
\(412\) | −4.17663 | −0.205768 | ||||||||
\(413\) | −6.93892 | − | 22.6862i | −0.341442 | − | 1.11632i | ||||
\(414\) | 3.61227 | 0.177533 | ||||||||
\(415\) | −1.37428 | + | 2.38032i | −0.0674607 | + | 0.116845i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.16932 | − | 5.48942i | −0.155202 | − | 0.268818i | ||||
\(418\) | 3.96508 | − | 6.86773i | 0.193939 | − | 0.335911i | ||||
\(419\) | −30.1423 | −1.47255 | −0.736274 | − | 0.676683i | \(-0.763417\pi\) | ||||
−0.736274 | + | 0.676683i | \(0.763417\pi\) | |||||||
\(420\) | −4.36896 | − | 14.2839i | −0.213183 | − | 0.696985i | ||||
\(421\) | −40.0580 | −1.95231 | −0.976153 | − | 0.217083i | \(-0.930346\pi\) | ||||
−0.976153 | + | 0.217083i | \(0.930346\pi\) | |||||||
\(422\) | −2.54788 | + | 4.41306i | −0.124029 | + | 0.214824i | ||||
\(423\) | −1.11481 | − | 1.93091i | −0.0542040 | − | 0.0938840i | ||||
\(424\) | 4.88672 | + | 8.46405i | 0.237320 | + | 0.411051i | ||||
\(425\) | −0.613394 | + | 1.06243i | −0.0297540 | + | 0.0515354i | ||||
\(426\) | 3.77453 | 0.182876 | ||||||||
\(427\) | −17.0411 | + | 18.2789i | −0.824679 | + | 0.884577i | ||||
\(428\) | 22.2238 | 1.07423 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.772544 | + | 1.33809i | 0.0372554 | + | 0.0645282i | ||||
\(431\) | −1.95793 | − | 3.39124i | −0.0943104 | − | 0.163350i | 0.815010 | − | 0.579447i | \(-0.196731\pi\) |
−0.909321 | + | 0.416096i | \(0.863398\pi\) | |||||||
\(432\) | −9.58632 | + | 16.6040i | −0.461222 | + | 0.798860i | ||||
\(433\) | −40.7925 | −1.96036 | −0.980182 | − | 0.198100i | \(-0.936523\pi\) | ||||
−0.980182 | + | 0.198100i | \(0.936523\pi\) | |||||||
\(434\) | 1.76566 | + | 0.407405i | 0.0847542 | + | 0.0195561i | ||||
\(435\) | −6.88612 | −0.330164 | ||||||||
\(436\) | −7.78785 | + | 13.4890i | −0.372971 | + | 0.646004i | ||||
\(437\) | 29.8131 | + | 51.6378i | 1.42615 | + | 2.47017i | ||||
\(438\) | −0.117775 | − | 0.203992i | −0.00562750 | − | 0.00974711i | ||||
\(439\) | 12.7811 | − | 22.1376i | 0.610010 | − | 1.05657i | −0.381228 | − | 0.924481i | \(-0.624499\pi\) |
0.991238 | − | 0.132087i | \(-0.0421680\pi\) | |||||||
\(440\) | 10.6467 | 0.507563 | ||||||||
\(441\) | 9.82637 | − | 6.63149i | 0.467923 | − | 0.315785i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7282 | − | 23.7779i | 0.652247 | − | 1.12972i | −0.330330 | − | 0.943866i | \(-0.607160\pi\) |
0.982576 | − | 0.185859i | \(-0.0595067\pi\) | |||||||
\(444\) | 7.44586 | + | 12.8966i | 0.353365 | + | 0.612046i | ||||
\(445\) | 9.81535 | + | 17.0007i | 0.465292 | + | 0.805910i | ||||
\(446\) | −1.60422 | + | 2.77859i | −0.0759621 | + | 0.131570i | ||||
\(447\) | 21.1057 | 0.998267 | ||||||||
\(448\) | −16.3083 | − | 3.76296i | −0.770496 | − | 0.177783i | ||||
\(449\) | 14.8036 | 0.698626 | 0.349313 | − | 0.937006i | \(-0.386415\pi\) | ||||
0.349313 | + | 0.937006i | \(0.386415\pi\) | |||||||
\(450\) | 0.354769 | − | 0.614477i | 0.0167240 | − | 0.0289667i | ||||
\(451\) | 4.80913 | + | 8.32966i | 0.226453 | + | 0.392229i | ||||
\(452\) | 7.75230 | + | 13.4274i | 0.364637 | + | 0.631571i | ||||
\(453\) | −0.918611 | + | 1.59108i | −0.0431601 | + | 0.0747555i | ||||
\(454\) | −4.12489 | −0.193590 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.02315 | 0.422548 | ||||||||
\(457\) | −0.325975 | + | 0.564606i | −0.0152485 | + | 0.0264112i | −0.873549 | − | 0.486736i | \(-0.838187\pi\) |
0.858300 | + | 0.513147i | \(0.171521\pi\) | |||||||
\(458\) | 1.16121 | + | 2.01127i | 0.0542596 | + | 0.0939805i | ||||
\(459\) | −2.10593 | − | 3.64758i | −0.0982965 | − | 0.170254i | ||||
\(460\) | −19.6467 | + | 34.0290i | −0.916031 | + | 1.58661i | ||||
\(461\) | −12.4955 | −0.581972 | −0.290986 | − | 0.956727i | \(-0.593983\pi\) | ||||
−0.290986 | + | 0.956727i | \(0.593983\pi\) | |||||||
\(462\) | −0.935844 | − | 3.05966i | −0.0435394 | − | 0.142348i | ||||
\(463\) | 0.309503 | 0.0143838 | 0.00719190 | − | 0.999974i | \(-0.497711\pi\) | ||||
0.00719190 | + | 0.999974i | \(0.497711\pi\) | |||||||
\(464\) | −4.20233 | + | 7.27865i | −0.195088 | + | 0.337903i | ||||
\(465\) | 3.73973 | + | 6.47741i | 0.173426 | + | 0.300382i | ||||
\(466\) | −2.71486 | − | 4.70227i | −0.125763 | − | 0.217829i | ||||
\(467\) | −12.2387 | + | 21.1980i | −0.566338 | + | 0.980926i | 0.430586 | + | 0.902549i | \(0.358307\pi\) |
−0.996924 | + | 0.0783762i | \(0.975026\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.04668 | − | 3.42205i | −0.0483314 | − | 0.158016i | ||||
\(470\) | −0.904302 | −0.0417123 | ||||||||
\(471\) | −0.940659 | + | 1.62927i | −0.0433433 | + | 0.0750727i | ||||
\(472\) | 4.72198 | + | 8.17871i | 0.217347 | + | 0.376456i | ||||
\(473\) | −4.43818 | − | 7.68716i | −0.204068 | − | 0.353456i | ||||
\(474\) | 0.948959 | − | 1.64364i | 0.0435871 | − | 0.0754951i | ||||
\(475\) | 11.7120 | 0.537384 | ||||||||
\(476\) | 2.73106 | − | 2.92943i | 0.125178 | − | 0.134270i | ||||
\(477\) | −15.7152 | −0.719549 | ||||||||
\(478\) | 2.21909 | − | 3.84357i | 0.101499 | − | 0.175801i | ||||
\(479\) | 4.06925 | + | 7.04815i | 0.185929 | + | 0.322038i | 0.943889 | − | 0.330262i | \(-0.107137\pi\) |
−0.757960 | + | 0.652301i | \(0.773804\pi\) | |||||||
\(480\) | 4.48686 | + | 7.77147i | 0.204796 | + | 0.354718i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.39746 | 0.200299 | ||||||||
\(483\) | 23.4415 | + | 5.40885i | 1.06662 | + | 0.246111i | ||||
\(484\) | −8.81325 | −0.400602 | ||||||||
\(485\) | −3.03826 | + | 5.26243i | −0.137960 | + | 0.238954i | ||||
\(486\) | 1.99653 | + | 3.45809i | 0.0905645 | + | 0.156862i | ||||
\(487\) | 2.30480 | + | 3.99203i | 0.104440 | + | 0.180896i | 0.913509 | − | 0.406817i | \(-0.133362\pi\) |
−0.809069 | + | 0.587714i | \(0.800028\pi\) | |||||||
\(488\) | 4.97410 | − | 8.61540i | 0.225167 | − | 0.390001i | ||||
\(489\) | −7.48464 | −0.338467 | ||||||||
\(490\) | −0.336574 | − | 4.79630i | −0.0152049 | − | 0.216675i | ||||
\(491\) | 13.0189 | 0.587537 | 0.293768 | − | 0.955877i | \(-0.405091\pi\) | ||||
0.293768 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(492\) | −2.68591 | + | 4.65213i | −0.121090 | + | 0.209734i | ||||
\(493\) | −0.923171 | − | 1.59898i | −0.0415775 | − | 0.0720144i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.55969 | + | 14.8258i | −0.384729 | + | 0.666371i | ||||
\(496\) | 9.12885 | 0.409897 | ||||||||
\(497\) | −31.7512 | − | 7.32624i | −1.42424 | − | 0.328627i | ||||
\(498\) | −0.328817 | −0.0147347 | ||||||||
\(499\) | −16.1603 | + | 27.9905i | −0.723436 | + | 1.25303i | 0.236178 | + | 0.971710i | \(0.424105\pi\) |
−0.959614 | + | 0.281319i | \(0.909228\pi\) | |||||||
\(500\) | −8.48928 | − | 14.7039i | −0.379652 | − | 0.657577i | ||||
\(501\) | −5.45718 | − | 9.45211i | −0.243809 | − | 0.422289i | ||||
\(502\) | 2.73900 | − | 4.74408i | 0.122247 | − | 0.211739i | ||||
\(503\) | −31.8253 | −1.41902 | −0.709509 | − | 0.704696i | \(-0.751083\pi\) | ||||
−0.709509 | + | 0.704696i | \(0.751083\pi\) | |||||||
\(504\) | −3.21802 | + | 3.45176i | −0.143342 | + | 0.153754i | ||||
\(505\) | −2.04256 | −0.0908929 | ||||||||
\(506\) | −4.20838 | + | 7.28912i | −0.187085 | + | 0.324041i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.72377 | + | 2.98566i | 0.0764801 | + | 0.132467i | ||||
\(509\) | 1.12788 | − | 1.95354i | 0.0499922 | − | 0.0865891i | −0.839946 | − | 0.542669i | \(-0.817414\pi\) |
0.889939 | + | 0.456080i | \(0.150747\pi\) | |||||||
\(510\) | −0.616382 | −0.0272938 | ||||||||
\(511\) | 0.594776 | + | 1.94457i | 0.0263114 | + | 0.0860228i | ||||
\(512\) | 18.4807 | 0.816739 | ||||||||
\(513\) | −20.1051 | + | 34.8231i | −0.887663 | + | 1.53748i | ||||
\(514\) | −1.84710 | − | 3.19927i | −0.0814722 | − | 0.141114i | ||||
\(515\) | −2.77461 | − | 4.80576i | −0.122264 | − | 0.211767i | ||||
\(516\) | 2.47873 | − | 4.29329i | 0.109120 | − | 0.189001i | ||||
\(517\) | 5.19512 | 0.228481 | ||||||||
\(518\) | 1.40204 | + | 4.58385i | 0.0616021 | + | 0.201403i | ||||
\(519\) | −12.7236 | −0.558502 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.38562 | − | 9.32817i | −0.235948 | − | 0.408675i | 0.723600 | − | 0.690220i | \(-0.242486\pi\) |
−0.959548 | + | 0.281546i | \(0.909153\pi\) | |||||||
\(522\) | 0.533934 | + | 0.924801i | 0.0233697 | + | 0.0404775i | ||||
\(523\) | −3.70397 | + | 6.41546i | −0.161963 | + | 0.280528i | −0.935573 | − | 0.353134i | \(-0.885116\pi\) |
0.773610 | + | 0.633663i | \(0.218449\pi\) | |||||||
\(524\) | 12.3224 | 0.538305 | ||||||||
\(525\) | 3.22232 | − | 3.45637i | 0.140634 | − | 0.150848i | ||||
\(526\) | 6.94909 | 0.302995 | ||||||||
\(527\) | −1.00272 | + | 1.73676i | −0.0436790 | + | 0.0756543i | ||||
\(528\) | −8.05953 | − | 13.9595i | −0.350746 | − | 0.607510i | ||||
\(529\) | −20.1424 | − | 34.8877i | −0.875757 | − | 1.51686i | ||||
\(530\) | −3.18692 | + | 5.51991i | −0.138431 | + | 0.239770i | ||||
\(531\) | −15.1854 | −0.658990 | ||||||||
\(532\) | −37.2567 | − | 8.59656i | −1.61528 | − | 0.372708i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.17424 | + | 2.03384i | −0.0508142 | + | 0.0880127i | ||||
\(535\) | 14.7637 | + | 25.5715i | 0.638290 | + | 1.10555i | ||||
\(536\) | 0.712276 | + | 1.23370i | 0.0307656 | + | 0.0532876i | ||||
\(537\) | −7.22580 | + | 12.5154i | −0.311816 | + | 0.540081i | ||||
\(538\) | −8.06161 | −0.347561 | ||||||||
\(539\) | 1.93358 | + | 27.5543i | 0.0832854 | + | 1.18685i | ||||
\(540\) | −26.4983 | −1.14031 | ||||||||
\(541\) | 16.2741 | − | 28.1875i | 0.699676 | − | 1.21188i | −0.268902 | − | 0.963168i | \(-0.586661\pi\) |
0.968579 | − | 0.248708i | \(-0.0800058\pi\) | |||||||
\(542\) | 1.93728 | + | 3.35546i | 0.0832132 | + | 0.144129i | ||||
\(543\) | 8.52445 | + | 14.7648i | 0.365819 | + | 0.633617i | ||||
\(544\) | −1.20304 | + | 2.08373i | −0.0515799 | + | 0.0893391i | ||||
\(545\) | −20.6944 | −0.886453 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4997 | −0.577206 | −0.288603 | − | 0.957449i | \(-0.593191\pi\) | ||||
−0.288603 | + | 0.957449i | \(0.593191\pi\) | |||||||
\(548\) | −9.67577 | + | 16.7589i | −0.413329 | + | 0.715906i | ||||
\(549\) | 7.99810 | + | 13.8531i | 0.341350 | + | 0.591236i | ||||
\(550\) | 0.826627 | + | 1.43176i | 0.0352475 | + | 0.0610504i | ||||
\(551\) | −8.81342 | + | 15.2653i | −0.375464 | + | 0.650323i | ||||
\(552\) | −9.57680 | −0.407616 | ||||||||
\(553\) | −11.1729 | + | 11.9844i | −0.475119 | + | 0.509628i | ||||
\(554\) | −4.10915 | −0.174581 | ||||||||
\(555\) | −9.89284 | + | 17.1349i | −0.419928 | + | 0.727336i | ||||
\(556\) | −5.34623 | − | 9.25994i | −0.226731 | − | 0.392709i | ||||
\(557\) | −14.8851 | − | 25.7818i | −0.630703 | − | 1.09241i | −0.987408 | − | 0.158193i | \(-0.949433\pi\) |
0.356705 | − | 0.934217i | \(-0.383900\pi\) | |||||||
\(558\) | 0.579941 | − | 1.00449i | 0.0245509 | − | 0.0425233i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.08483 | − | 23.1632i | −0.299389 | − | 0.978826i | ||||
\(561\) | 3.54105 | 0.149503 | ||||||||
\(562\) | 0.709566 | − | 1.22900i | 0.0299312 | − | 0.0518424i | ||||
\(563\) | −7.06629 | − | 12.2392i | −0.297809 | − | 0.515819i | 0.677826 | − | 0.735223i | \(-0.262922\pi\) |
−0.975634 | + | 0.219403i | \(0.929589\pi\) | |||||||
\(564\) | 1.45074 | + | 2.51275i | 0.0610872 | + | 0.105806i | ||||
\(565\) | −10.3000 | + | 17.8401i | −0.433324 | + | 0.750538i | ||||
\(566\) | −8.25410 | −0.346946 | ||||||||
\(567\) | 0.813601 | + | 2.66000i | 0.0341680 | + | 0.111710i | ||||
\(568\) | 12.9717 | 0.544280 | ||||||||
\(569\) | 12.1270 | − | 21.0046i | 0.508391 | − | 0.880558i | −0.491562 | − | 0.870842i | \(-0.663574\pi\) |
0.999953 | − | 0.00971585i | \(-0.00309270\pi\) | |||||||
\(570\) | 2.94227 | + | 5.09616i | 0.123238 | + | 0.213455i | ||||
\(571\) | −0.604159 | − | 1.04643i | −0.0252832 | − | 0.0437919i | 0.853107 | − | 0.521736i | \(-0.174715\pi\) |
−0.878390 | + | 0.477944i | \(0.841382\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.1514 | 0.674732 | ||||||||
\(574\) | −1.17910 | + | 1.26475i | −0.0492149 | + | 0.0527895i | ||||
\(575\) | −12.4307 | −0.518394 | ||||||||
\(576\) | −5.35657 | + | 9.27786i | −0.223191 | + | 0.386577i | ||||
\(577\) | −7.30518 | − | 12.6529i | −0.304119 | − | 0.526749i | 0.672946 | − | 0.739692i | \(-0.265029\pi\) |
−0.977065 | + | 0.212943i | \(0.931695\pi\) | |||||||
\(578\) | 2.19643 | + | 3.80433i | 0.0913595 | + | 0.158239i | ||||
\(579\) | −2.22575 | + | 3.85510i | −0.0924988 | + | 0.160213i | ||||
\(580\) | −11.6160 | −0.482328 | ||||||||
\(581\) | 2.76600 | + | 0.638224i | 0.114753 | + | 0.0264780i | ||||
\(582\) | −0.726951 | −0.0301331 | ||||||||
\(583\) | 18.3085 | − | 31.7113i | 0.758262 | − | 1.31335i | ||||
\(584\) | −0.404749 | − | 0.701046i | −0.0167486 | − | 0.0290095i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.34841 | + | 4.06757i | −0.0970120 | + | 0.168030i | ||||
\(587\) | −21.5095 | −0.887793 | −0.443897 | − | 0.896078i | \(-0.646404\pi\) | ||||
−0.443897 | + | 0.896078i | \(0.646404\pi\) | |||||||
\(588\) | −12.7874 | + | 8.62977i | −0.527343 | + | 0.355886i | ||||
\(589\) | 19.1457 | 0.788884 | ||||||||
\(590\) | −3.07949 | + | 5.33383i | −0.126780 | + | 0.219590i | ||||
\(591\) | 6.69168 | + | 11.5903i | 0.275259 | + | 0.476763i | ||||
\(592\) | 12.0744 | + | 20.9135i | 0.496256 | + | 0.859541i | ||||
\(593\) | −1.32429 | + | 2.29373i | −0.0543820 | + | 0.0941923i | −0.891935 | − | 0.452164i | \(-0.850652\pi\) |
0.837553 | + | 0.546356i | \(0.183986\pi\) | |||||||
\(594\) | −5.67602 | −0.232890 | ||||||||
\(595\) | 5.18499 | + | 1.19638i | 0.212564 | + | 0.0490467i | ||||
\(596\) | 35.6027 | 1.45834 | ||||||||
\(597\) | 1.99846 | − | 3.46143i | 0.0817915 | − | 0.141667i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.1250 | + | 34.8576i | 0.822287 | + | 1.42424i | 0.903975 | + | 0.427584i | \(0.140635\pi\) |
−0.0816889 | + | 0.996658i | \(0.526031\pi\) | |||||||
\(600\) | −0.940558 | + | 1.62909i | −0.0383981 | + | 0.0665075i | ||||
\(601\) | 38.3449 | 1.56412 | 0.782061 | − | 0.623202i | \(-0.214169\pi\) | ||||
0.782061 | + | 0.623202i | \(0.214169\pi\) | |||||||
\(602\) | 1.08816 | − | 1.16719i | 0.0443499 | − | 0.0475712i | ||||
\(603\) | −2.29060 | −0.0932806 | ||||||||
\(604\) | −1.54958 | + | 2.68395i | −0.0630515 | + | 0.109208i | ||||
\(605\) | −5.85480 | − | 10.1408i | −0.238031 | − | 0.412283i | ||||
\(606\) | −0.122179 | − | 0.211620i | −0.00496317 | − | 0.00859646i | ||||
\(607\) | −21.2773 | + | 36.8534i | −0.863620 | + | 1.49583i | 0.00479063 | + | 0.999989i | \(0.498475\pi\) |
−0.868411 | + | 0.495845i | \(0.834858\pi\) | |||||||
\(608\) | 22.9706 | 0.931582 | ||||||||
\(609\) | 2.08015 | + | 6.80089i | 0.0842921 | + | 0.275586i | ||||
\(610\) | 6.48782 | 0.262684 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.28180 | − | 2.22014i | −0.0518136 | − | 0.0897438i | ||||
\(613\) | 7.63261 | + | 13.2201i | 0.308278 | + | 0.533953i | 0.977986 | − | 0.208672i | \(-0.0669140\pi\) |
−0.669708 | + | 0.742625i | \(0.733581\pi\) | |||||||
\(614\) | −1.15773 | + | 2.00524i | −0.0467221 | + | 0.0809251i | ||||
\(615\) | −7.13718 | −0.287799 | ||||||||
\(616\) | −3.21616 | − | 10.5150i | −0.129583 | − | 0.423660i | ||||
\(617\) | −13.9812 | −0.562863 | −0.281431 | − | 0.959581i | \(-0.590809\pi\) | ||||
−0.281431 | + | 0.959581i | \(0.590809\pi\) | |||||||
\(618\) | 0.331934 | − | 0.574926i | 0.0133523 | − | 0.0231269i | ||||
\(619\) | −4.25792 | − | 7.37494i | −0.171140 | − | 0.296424i | 0.767678 | − | 0.640835i | \(-0.221412\pi\) |
−0.938819 | + | 0.344411i | \(0.888079\pi\) | |||||||
\(620\) | 6.30845 | + | 10.9265i | 0.253353 | + | 0.438821i | ||||
\(621\) | 21.3388 | − | 36.9598i | 0.856295 | − | 1.48315i | ||||
\(622\) | −4.40331 | −0.176557 | ||||||||
\(623\) | 13.8253 | − | 14.8294i | 0.553897 | − | 0.594129i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.1856 | − | 26.3023i | 0.607425 | − | 1.05209i | ||||
\(626\) | −1.34682 | − | 2.33275i | −0.0538296 | − | 0.0932356i | ||||
\(627\) | −16.9030 | − | 29.2769i | −0.675042 | − | 1.16921i | ||||
\(628\) | −1.58677 | + | 2.74837i | −0.0633190 | + | 0.109672i | ||||
\(629\) | −5.30504 | −0.211526 | ||||||||
\(630\) | −2.99884 | − | 0.691949i | −0.119477 | − | 0.0275679i | ||||
\(631\) | −36.8292 | −1.46615 | −0.733074 | − | 0.680149i | \(-0.761915\pi\) | ||||
−0.733074 | + | 0.680149i | \(0.761915\pi\) | |||||||
\(632\) | 3.26123 | − | 5.64861i | 0.129725 | − | 0.224690i | ||||
\(633\) | 10.8615 | + | 18.8127i | 0.431707 | + | 0.747739i | ||||
\(634\) | 1.36006 | + | 2.35570i | 0.0540150 | + | 0.0935567i | ||||
\(635\) | −2.29027 | + | 3.96686i | −0.0908865 | + | 0.157420i | ||||
\(636\) | 20.4507 | 0.810922 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.48818 | −0.0985081 | ||||||||
\(639\) | −10.4289 | + | 18.0634i | −0.412561 | + | 0.714576i | ||||
\(640\) | 10.0235 | + | 17.3612i | 0.396214 | + | 0.686263i | ||||
\(641\) | −12.9374 | − | 22.4082i | −0.510996 | − | 0.885070i | −0.999919 | − | 0.0127435i | \(-0.995944\pi\) |
0.488923 | − | 0.872327i | \(-0.337390\pi\) | |||||||
\(642\) | −1.76622 | + | 3.05918i | −0.0697071 | + | 0.120736i | ||||
\(643\) | −40.5252 | −1.59816 | −0.799078 | − | 0.601227i | \(-0.794679\pi\) | ||||
−0.799078 | + | 0.601227i | \(0.794679\pi\) | |||||||
\(644\) | 39.5427 | + | 9.12404i | 1.55820 | + | 0.359538i | ||||
\(645\) | 6.58666 | 0.259350 | ||||||||
\(646\) | −0.788896 | + | 1.36641i | −0.0310387 | + | 0.0537606i | ||||
\(647\) | −0.892002 | − | 1.54499i | −0.0350682 | − | 0.0607399i | 0.847959 | − | 0.530062i | \(-0.177832\pi\) |
−0.883027 | + | 0.469322i | \(0.844498\pi\) | |||||||
\(648\) | −0.553661 | − | 0.958969i | −0.0217499 | − | 0.0376719i | ||||
\(649\) | 17.6913 | − | 30.6423i | 0.694445 | − | 1.20281i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.26754 | − | 5.65014i | 0.206451 | − | 0.221446i | ||||
\(652\) | −12.6256 | −0.494457 | ||||||||
\(653\) | −6.20210 | + | 10.7424i | −0.242707 | + | 0.420381i | −0.961484 | − | 0.274860i | \(-0.911369\pi\) |
0.718778 | + | 0.695240i | \(0.244702\pi\) | |||||||
\(654\) | −1.23787 | − | 2.14405i | −0.0484044 | − | 0.0838389i | ||||
\(655\) | 8.18597 | + | 14.1785i | 0.319852 | + | 0.554000i | ||||
\(656\) | −4.35554 | + | 7.54402i | −0.170055 | + | 0.294545i | ||||
\(657\) | 1.30163 | 0.0507815 | ||||||||
\(658\) | 0.273171 | + | 0.893110i | 0.0106493 | + | 0.0348171i | ||||
\(659\) | −1.12867 | −0.0439668 | −0.0219834 | − | 0.999758i | \(-0.506998\pi\) | ||||
−0.0219834 | + | 0.999758i | \(0.506998\pi\) | |||||||
\(660\) | 11.1390 | − | 19.2933i | 0.433585 | − | 0.750991i | ||||
\(661\) | −14.4627 | − | 25.0502i | −0.562534 | − | 0.974338i | −0.997274 | − | 0.0737821i | \(-0.976493\pi\) |
0.434740 | − | 0.900556i | \(-0.356840\pi\) | |||||||
\(662\) | 0.310913 | + | 0.538517i | 0.0120840 | + | 0.0209301i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.13003 | −0.0438535 | ||||||||
\(665\) | −14.8588 | − | 48.5796i | −0.576200 | − | 1.88384i | ||||
\(666\) | 3.06828 | 0.118893 | ||||||||
\(667\) | 9.35421 | − | 16.2020i | 0.362196 | − | 0.627342i | ||||
\(668\) | −9.20556 | − | 15.9445i | −0.356174 | − | 0.616911i | ||||
\(669\) | 6.83874 | + | 11.8451i | 0.264401 | + | 0.457956i | ||||
\(670\) | −0.464518 | + | 0.804568i | −0.0179459 | + | 0.0310832i | ||||
\(671\) | −37.2718 | −1.43886 | ||||||||
\(672\) | 6.31990 | − | 6.77893i | 0.243795 | − | 0.261503i | ||||
\(673\) | −7.09960 | −0.273669 | −0.136835 | − | 0.990594i | \(-0.543693\pi\) | ||||
−0.136835 | + | 0.990594i | \(0.543693\pi\) | |||||||
\(674\) | 2.14498 | − | 3.71521i | 0.0826214 | − | 0.143104i | ||||
\(675\) | −4.19145 | − | 7.25980i | −0.161329 | − | 0.279430i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.2010 | − | 43.6494i | 0.968552 | − | 1.67758i | 0.268800 | − | 0.963196i | \(-0.413373\pi\) |
0.699752 | − | 0.714386i | \(-0.253294\pi\) | |||||||
\(678\) | −2.46443 | −0.0946458 | ||||||||
\(679\) | 6.11509 | + | 1.41099i | 0.234676 | + | 0.0541488i | ||||
\(680\) | −2.11828 | −0.0812324 | ||||||||
\(681\) | −8.79213 | + | 15.2284i | −0.336915 | + | 0.583554i | ||||
\(682\) | 1.35129 | + | 2.34050i | 0.0517435 | + | 0.0896224i | ||||
\(683\) | 13.7641 | + | 23.8401i | 0.526669 | + | 0.912217i | 0.999517 | + | 0.0310735i | \(0.00989259\pi\) |
−0.472848 | + | 0.881144i | \(0.656774\pi\) | |||||||
\(684\) | −12.2372 | + | 21.1954i | −0.467901 | + | 0.810428i | ||||
\(685\) | −25.7112 | −0.982373 | ||||||||
\(686\) | −4.63527 | + | 1.78127i | −0.176975 | + | 0.0680093i | ||||
\(687\) | 9.90037 | 0.377723 | ||||||||
\(688\) | 4.01958 | − | 6.96212i | 0.153245 | − | 0.265428i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.12280 | − | 5.40885i | −0.118883 | − | 0.205912i | ||||
\(691\) | −12.1669 | + | 21.0737i | −0.462851 | + | 0.801682i | −0.999102 | − | 0.0423772i | \(-0.986507\pi\) |
0.536251 | + | 0.844059i | \(0.319840\pi\) | |||||||
\(692\) | −21.4630 | −0.815901 | ||||||||
\(693\) | 17.2280 | + | 3.97517i | 0.654439 | + | 0.151004i | ||||
\(694\) | −6.11884 | −0.232268 | ||||||||
\(695\) | 7.10319 | − | 12.3031i | 0.269439 | − | 0.466683i | ||||
\(696\) | −1.41556 | − | 2.45182i | −0.0536566 | − | 0.0929360i | ||||
\(697\) | −0.956829 | − | 1.65728i | −0.0362425 | − | 0.0627738i | ||||
\(698\) | −3.04352 | + | 5.27153i | −0.115199 | + | 0.199531i | ||||
\(699\) | −23.1467 | −0.875488 | ||||||||
\(700\) | 5.43565 | − | 5.83045i | 0.205448 | − | 0.220370i | ||||
\(701\) | −20.5588 | −0.776495 | −0.388248 | − | 0.921555i | \(-0.626919\pi\) | ||||
−0.388248 | + | 0.921555i | \(0.626919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.3234 | + | 43.8613i | 0.955088 | + | 1.65426i | ||||
\(704\) | −12.4811 | − | 21.6178i | −0.470397 | − | 0.814752i | ||||
\(705\) | −1.92751 | + | 3.33854i | −0.0725940 | + | 0.125737i | ||||
\(706\) | 7.31027 | 0.275126 | ||||||||
\(707\) | 0.617017 | + | 2.01728i | 0.0232053 | + | 0.0758678i | ||||
\(708\) | 19.7612 | 0.742673 | ||||||||
\(709\) | 20.4544 | − | 35.4281i | 0.768183 | − | 1.33053i | −0.170364 | − | 0.985381i | \(-0.554494\pi\) |
0.938547 | − | 0.345151i | \(-0.112172\pi\) | |||||||
\(710\) | 4.22981 | + | 7.32624i | 0.158742 | + | 0.274949i | ||||
\(711\) | 5.24388 | + | 9.08267i | 0.196661 | + | 0.340627i | ||||
\(712\) | −4.03543 | + | 6.98956i | −0.151234 | + | 0.261945i | ||||
\(713\) | −20.3204 | −0.761006 | ||||||||
\(714\) | 0.186196 | + | 0.608753i | 0.00696822 | + | 0.0227820i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.1890 | + | 21.1119i | −0.455524 | + | 0.788990i | ||||
\(717\) | −9.45989 | − | 16.3850i | −0.353286 | − | 0.611910i | ||||
\(718\) | −1.93401 | − | 3.34981i | −0.0721767 | − | 0.125014i | ||||
\(719\) | 0.599734 | − | 1.03877i | 0.0223663 | − | 0.0387396i | −0.854626 | − | 0.519245i | \(-0.826213\pi\) |
0.876992 | + | 0.480505i | \(0.159547\pi\) | |||||||
\(720\) | −15.5047 | −0.577826 | ||||||||
\(721\) | −3.90813 | + | 4.19199i | −0.145546 | + | 0.156118i | ||||
\(722\) | 9.96865 | 0.370995 | ||||||||
\(723\) | 9.37311 | − | 16.2347i | 0.348590 | − | 0.603775i | ||||
\(724\) | 14.3796 | + | 24.9063i | 0.534415 | + | 0.925634i | ||||
\(725\) | −1.83739 | − | 3.18246i | −0.0682390 | − | 0.118193i | ||||
\(726\) | 0.700425 | − | 1.21317i | 0.0259952 | − | 0.0450250i | ||||
\(727\) | −2.06230 | −0.0764865 | −0.0382433 | − | 0.999268i | \(-0.512176\pi\) | ||||
−0.0382433 | + | 0.999268i | \(0.512176\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1764 | 0.747273 | ||||||||
\(730\) | 0.263961 | − | 0.457194i | 0.00976964 | − | 0.0169215i | ||||
\(731\) | 0.883025 | + | 1.52944i | 0.0326599 | + | 0.0565685i | ||||
\(732\) | −10.4082 | − | 18.0275i | −0.384697 | − | 0.666315i | ||||
\(733\) | 15.0310 | − | 26.0345i | 0.555184 | − | 0.961606i | −0.442706 | − | 0.896667i | \(-0.645981\pi\) |
0.997889 | − | 0.0649392i | \(-0.0206853\pi\) | |||||||
\(734\) | −3.05441 | −0.112740 | ||||||||
\(735\) | −18.4246 | − | 8.98066i | −0.679601 | − | 0.331257i | ||||
\(736\) | −24.3801 | −0.898662 | ||||||||
\(737\) | 2.66861 | − | 4.62216i | 0.0982993 | − | 0.170259i | ||||
\(738\) | 0.553401 | + | 0.958519i | 0.0203710 | + | 0.0352836i | ||||
\(739\) | 22.1274 | + | 38.3257i | 0.813969 | + | 1.40984i | 0.910066 | + | 0.414464i | \(0.136031\pi\) |
−0.0960970 | + | 0.995372i | \(0.530636\pi\) | |||||||
\(740\) | −16.6880 | + | 28.9044i | −0.613461 | + | 1.06255i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.41430 | + | 1.48003i | 0.235476 | + | 0.0543335i | ||||
\(743\) | 8.62651 | 0.316476 | 0.158238 | − | 0.987401i | \(-0.449419\pi\) | ||||
0.158238 | + | 0.987401i | \(0.449419\pi\) | |||||||
\(744\) | −1.53753 | + | 2.66308i | −0.0563686 | + | 0.0976334i | ||||
\(745\) | 23.6515 | + | 40.9656i | 0.866524 | + | 1.50086i | ||||
\(746\) | 4.15097 | + | 7.18969i | 0.151978 | + | 0.263233i | ||||
\(747\) | 0.908511 | − | 1.57359i | 0.0332407 | − | 0.0575746i | ||||
\(748\) | 5.97329 | 0.218405 | ||||||||
\(749\) | 20.7952 | − | 22.3056i | 0.759839 | − | 0.815028i | ||||
\(750\) | 2.69871 | 0.0985430 | ||||||||
\(751\) | −2.86105 | + | 4.95549i | −0.104401 | + | 0.180828i | −0.913493 | − | 0.406853i | \(-0.866626\pi\) |
0.809092 | + | 0.587682i | \(0.199959\pi\) | |||||||
\(752\) | 2.35256 | + | 4.07476i | 0.0857891 | + | 0.148591i | ||||
\(753\) | −11.6763 | − | 20.2239i | −0.425506 | − | 0.736998i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.11765 | −0.149857 | ||||||||
\(756\) | 8.00460 | + | 26.1704i | 0.291125 | + | 0.951807i | ||||
\(757\) | −34.7222 | −1.26200 | −0.631000 | − | 0.775783i | \(-0.717355\pi\) | ||||
−0.631000 | + | 0.775783i | \(0.717355\pi\) | |||||||
\(758\) | 1.41927 | − | 2.45824i | 0.0515501 | − | 0.0892873i | ||||
\(759\) | 17.9402 | + | 31.0733i | 0.651187 | + | 1.12789i | ||||
\(760\) | 10.1115 | + | 17.5137i | 0.366783 | + | 0.635287i | ||||
\(761\) | −26.5867 | + | 46.0496i | −0.963768 | + | 1.66930i | −0.250880 | + | 0.968018i | \(0.580720\pi\) |
−0.712888 | + | 0.701278i | \(0.752613\pi\) | |||||||
\(762\) | −0.547981 | −0.0198513 | ||||||||
\(763\) | 6.25137 | + | 20.4383i | 0.226315 | + | 0.739917i | ||||
\(764\) | 27.2452 | 0.985699 | ||||||||
\(765\) | 1.70304 | − | 2.94976i | 0.0615736 | − | 0.106649i | ||||
\(766\) | 4.12265 | + | 7.14063i | 0.148957 | + | 0.258002i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 6.03145 | − | 10.4468i | 0.217641 | − | 0.376966i | ||||
\(769\) | −4.91157 | −0.177116 | −0.0885578 | − | 0.996071i | \(-0.528226\pi\) | ||||
−0.0885578 | + | 0.996071i | \(0.528226\pi\) | |||||||
\(770\) | 4.88999 | − | 5.24516i | 0.176223 | − | 0.189022i | ||||
\(771\) | −15.7483 | −0.567160 | ||||||||
\(772\) | −3.75455 | + | 6.50306i | −0.135129 | + | 0.234050i | ||||
\(773\) | −11.4903 | − | 19.9018i | −0.413279 | − | 0.715819i | 0.581967 | − | 0.813212i | \(-0.302283\pi\) |
−0.995246 | + | 0.0973926i | \(0.968950\pi\) | |||||||
\(774\) | −0.510715 | − | 0.884585i | −0.0183573 | − | 0.0317957i | ||||
\(775\) | −1.99571 | + | 3.45667i | −0.0716881 | + | 0.124167i | ||||
\(776\) | −2.49827 | −0.0896826 | ||||||||
\(777\) | 19.9113 | + | 4.59430i | 0.714313 | + | 0.164820i | ||||
\(778\) | −4.39178 | −0.157453 | ||||||||
\(779\) | −9.13476 | + | 15.8219i | −0.327287 | + | 0.566877i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.2998 | − | 42.0885i | −0.869515 | − | 1.50604i | ||||
\(782\) | 0.837302 | − | 1.45025i | 0.0299419 | − | 0.0518608i | ||||
\(783\) | 12.6164 | 0.450874 | ||||||||
\(784\) | −20.7364 | + | 13.9943i | −0.740585 | + | 0.499796i | ||||
\(785\) | −4.21648 | −0.150493 | ||||||||
\(786\) | −0.979309 | + | 1.69621i | −0.0349308 | + | 0.0605019i | ||||
\(787\) | −1.59387 | − | 2.76067i | −0.0568154 | − | 0.0984071i | 0.836219 | − | 0.548396i | \(-0.184761\pi\) |
−0.893034 | + | 0.449989i | \(0.851428\pi\) | |||||||
\(788\) | 11.2880 | + | 19.5514i | 0.402119 | + | 0.696490i | ||||
\(789\) | 14.8119 | − | 25.6549i | 0.527316 | − | 0.913339i | ||||
\(790\) | 4.25368 | 0.151339 | ||||||||
\(791\) | 20.7307 | + | 4.78338i | 0.737099 | + | 0.170077i | ||||
\(792\) | −7.03836 | −0.250097 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2.12927 | − | 3.68800i | −0.0755650 | − | 0.130882i | ||||
\(795\) | 13.5857 | + | 23.5312i | 0.481837 | + | 0.834566i | ||||
\(796\) | 3.37114 | − | 5.83899i | 0.119487 | − | 0.206958i | ||||
\(797\) | 54.6509 | 1.93584 | 0.967918 | − | 0.251267i | \(-0.0808472\pi\) | ||||
0.967918 | + | 0.251267i | \(0.0808472\pi\) | |||||||
\(798\) | 4.14429 | − | 4.44530i | 0.146706 | − | 0.157362i | ||||
\(799\) | −1.03363 | −0.0365670 | ||||||||
\(800\) | −2.39442 | + | 4.14725i | −0.0846554 | + | 0.146628i | ||||
\(801\) | −6.48875 | − | 11.2388i | −0.229269 | − | 0.397105i | ||||
\(802\) | 0.889604 | + | 1.54084i | 0.0314130 | + | 0.0544089i | ||||
\(803\) | −1.51643 | + | 2.62653i | −0.0535136 | + | 0.0926883i | ||||
\(804\) | 2.98084 | 0.105126 | ||||||||
\(805\) | 15.7705 | + | 51.5604i | 0.555838 | + | 1.81727i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.1832 | + | 29.7622i | −0.604877 | + | 1.04768i | ||||
\(808\) | −0.419884 | − | 0.727260i | −0.0147715 | − | 0.0255849i | ||||
\(809\) | 10.1498 | + | 17.5799i | 0.356847 | + | 0.618077i | 0.987432 | − | 0.158043i | \(-0.0505185\pi\) |
−0.630585 | + | 0.776120i | \(0.717185\pi\) | |||||||
\(810\) | 0.361076 | − | 0.625401i | 0.0126869 | − | 0.0219744i | ||||
\(811\) | −2.43587 | −0.0855350 | −0.0427675 | − | 0.999085i | \(-0.513617\pi\) | ||||
−0.0427675 | + | 0.999085i | \(0.513617\pi\) | |||||||
\(812\) | 3.50895 | + | 11.4722i | 0.123140 | + | 0.402596i | ||||
\(813\) | 16.5171 | 0.579280 | ||||||||
\(814\) | −3.57461 | + | 6.19141i | −0.125290 | + | 0.217009i | ||||
\(815\) | −8.38742 | − | 14.5274i | −0.293799 | − | 0.508874i | ||||
\(816\) | 1.60353 | + | 2.77740i | 0.0561348 | + | 0.0972284i | ||||
\(817\) | 8.43015 | − | 14.6015i | 0.294934 | − | 0.510840i | ||||
\(818\) | −1.57452 | −0.0550519 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0395 | −0.420438 | ||||||||
\(821\) | 22.6762 | − | 39.2763i | 0.791405 | − | 1.37075i | −0.133692 | − | 0.991023i | \(-0.542683\pi\) |
0.925097 | − | 0.379731i | \(-0.123983\pi\) | |||||||
\(822\) | −1.53795 | − | 2.66380i | −0.0536421 | − | 0.0929108i | ||||
\(823\) | 1.37871 | + | 2.38800i | 0.0480588 | + | 0.0832403i | 0.889054 | − | 0.457802i | \(-0.151363\pi\) |
−0.840995 | + | 0.541042i | \(0.818030\pi\) | |||||||
\(824\) | 1.14074 | − | 1.97581i | 0.0397394 | − | 0.0688307i | ||||
\(825\) | 7.04776 | 0.245372 | ||||||||
\(826\) | 6.19806 | + | 1.43013i | 0.215658 | + | 0.0497607i | ||||
\(827\) | 8.64504 | 0.300618 | 0.150309 | − | 0.988639i | \(-0.451973\pi\) | ||||
0.150309 | + | 0.988639i | \(0.451973\pi\) | |||||||
\(828\) | 12.9881 | − | 22.4960i | 0.451366 | − | 0.781789i | ||||
\(829\) | 14.7871 | + | 25.6119i | 0.513576 | + | 0.889540i | 0.999876 | + | 0.0157478i | \(0.00501289\pi\) |
−0.486300 | + | 0.873792i | \(0.661654\pi\) | |||||||
\(830\) | −0.368479 | − | 0.638224i | −0.0127901 | − | 0.0221531i | ||||
\(831\) | −8.75858 | + | 15.1703i | −0.303832 | + | 0.526252i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.384708 | − | 5.48222i | −0.0133293 | − | 0.189948i | ||||
\(834\) | 1.69955 | 0.0588505 | ||||||||
\(835\) | 12.2308 | − | 21.1844i | 0.423266 | − | 0.733117i | ||||
\(836\) | −28.5132 | − | 49.3863i | −0.986150 | − | 1.70806i | ||||
\(837\) | −6.85177 | − | 11.8676i | −0.236832 | − | 0.410204i | ||||
\(838\) | 4.04096 | − | 6.99914i | 0.139593 | − | 0.241781i | ||||
\(839\) | −25.2473 | −0.871633 | −0.435817 | − | 0.900035i | \(-0.643540\pi\) | ||||
−0.435817 | + | 0.900035i | \(0.643540\pi\) | |||||||
\(840\) | 7.95049 | + | 1.83449i | 0.274318 | + | 0.0632958i | ||||
\(841\) | −23.4694 | −0.809289 | ||||||||
\(842\) | 5.37028 | − | 9.30159i | 0.185072 | − | 0.320554i | ||||
\(843\) | −3.02485 | − | 5.23920i | −0.104182 | − | 0.180448i | ||||
\(844\) | 18.3220 | + | 31.7346i | 0.630669 | + | 1.09235i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.597818 | 0.0205534 | ||||||||
\(847\) | −8.24669 | + | 8.84567i | −0.283360 | + | 0.303941i | ||||
\(848\) | 33.1634 | 1.13884 | ||||||||
\(849\) | −17.5935 | + | 30.4728i | −0.603807 | + | 1.04582i | ||||
\(850\) | −0.164466 | − | 0.284864i | −0.00564115 | − | 0.00977076i | ||||
\(851\) | −26.8772 | − | 46.5526i | −0.921338 | − | 1.59580i | ||||
\(852\) | 13.5715 | − | 23.5064i | 0.464950 | − | 0.805318i | ||||
\(853\) | 35.1368 | 1.20306 | 0.601531 | − | 0.798850i | \(-0.294558\pi\) | ||||
0.601531 | + | 0.798850i | \(0.294558\pi\) | |||||||
\(854\) | −1.95984 | − | 6.40752i | −0.0670643 | − | 0.219261i | ||||
\(855\) | −32.5176 | −1.11208 | ||||||||
\(856\) | −6.06986 | + | 10.5133i | −0.207463 | + | 0.359337i | ||||
\(857\) | 0.671345 | + | 1.16280i | 0.0229327 | + | 0.0397206i | 0.877264 | − | 0.480008i | \(-0.159366\pi\) |
−0.854331 | + | 0.519729i | \(0.826033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.38386 | + | 4.12897i | −0.0813363 | + | 0.140879i | −0.903824 | − | 0.427904i | \(-0.859252\pi\) |
0.822488 | + | 0.568783i | \(0.192585\pi\) | |||||||
\(860\) | 11.1108 | 0.378877 | ||||||||
\(861\) | 2.15600 | + | 7.04885i | 0.0734762 | + | 0.240224i | ||||
\(862\) | 1.04994 | 0.0357612 | ||||||||
\(863\) | −13.3052 | + | 23.0453i | −0.452915 | + | 0.784472i | −0.998566 | − | 0.0535407i | \(-0.982949\pi\) |
0.545650 | + | 0.838013i | \(0.316283\pi\) | |||||||
\(864\) | −8.22062 | − | 14.2385i | −0.279671 | − | 0.484405i | ||||
\(865\) | −14.2583 | − | 24.6960i | −0.484795 | − | 0.839690i | ||||
\(866\) | 5.46875 | − | 9.47216i | 0.185836 | − | 0.321877i | ||||
\(867\) | 18.7266 | 0.635989 | ||||||||
\(868\) | 8.88566 | − | 9.53106i | 0.301599 | − | 0.323505i | ||||
\(869\) | −24.4370 | −0.828967 | ||||||||
\(870\) | 0.923171 | − | 1.59898i | 0.0312984 | − | 0.0542105i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.25410 | − | 7.36831i | −0.144062 | − | 0.249523i | ||||
\(873\) | 2.00854 | − | 3.47890i | 0.0679788 | − | 0.117743i | ||||
\(874\) | −15.9873 | −0.540778 | ||||||||
\(875\) | −22.7015 | − | 5.23812i | −0.767451 | − | 0.177081i | ||||
\(876\) | −1.69385 | −0.0572300 | ||||||||
\(877\) | 4.01848 | − | 6.96022i | 0.135695 | − | 0.235030i | −0.790168 | − | 0.612890i | \(-0.790007\pi\) |
0.925863 | + | 0.377860i | \(0.123340\pi\) | |||||||
\(878\) | 3.42694 | + | 5.93564i | 0.115654 | + | 0.200318i | ||||
\(879\) | 10.0112 | + | 17.3399i | 0.337670 | + | 0.584861i | ||||
\(880\) | 18.0633 | − | 31.2866i | 0.608915 | − | 1.05467i | ||||
\(881\) | −54.6697 | −1.84187 | −0.920935 | − | 0.389716i | \(-0.872573\pi\) | ||||
−0.920935 | + | 0.389716i | \(0.872573\pi\) | |||||||
\(882\) | 0.222503 | + | 3.17075i | 0.00749208 | + | 0.106765i | ||||
\(883\) | −8.45085 | −0.284394 | −0.142197 | − | 0.989838i | \(-0.545417\pi\) | ||||
−0.142197 | + | 0.989838i | \(0.545417\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.1277 | + | 22.7379i | 0.441284 | + | 0.764327i | ||||
\(886\) | 3.68088 | + | 6.37547i | 0.123662 | + | 0.214188i | ||||
\(887\) | 5.17784 | − | 8.96829i | 0.173855 | − | 0.301126i | −0.765909 | − | 0.642948i | \(-0.777711\pi\) |
0.939764 | + | 0.341823i | \(0.111044\pi\) | |||||||
\(888\) | −8.13457 | −0.272978 | ||||||||
\(889\) | 4.60961 | + | 1.06361i | 0.154601 | + | 0.0356725i | ||||
\(890\) | −5.26349 | −0.176432 | ||||||||
\(891\) | −2.07434 | + | 3.59286i | −0.0694930 | + | 0.120365i | ||||
\(892\) | 11.5361 | + | 19.9811i | 0.386256 | + | 0.669016i | ||||
\(893\) | 4.93396 | + | 8.54587i | 0.165109 | + | 0.285977i | ||||
\(894\) | −2.82949 | + | 4.90082i | −0.0946323 | + | 0.163908i | ||||
\(895\) | −32.3895 | −1.08266 | ||||||||
\(896\) | 14.1185 | − | 15.1439i | 0.471665 | − | 0.505923i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.98461 | + | 3.43745i | −0.0662274 | + | 0.114709i | ||||
\(899\) | −3.00359 | − | 5.20237i | −0.100175 | − | 0.173509i | ||||
\(900\) | −2.55117 | − | 4.41875i | −0.0850389 | − | 0.147292i | ||||
\(901\) | −3.64268 | + | 6.30931i | −0.121355 | + | 0.210194i | ||||
\(902\) | −2.57890 | −0.0858680 | ||||||||
\(903\) | −1.98970 | − | 6.50514i | −0.0662129 | − | 0.216478i | ||||
\(904\) | −8.46935 | −0.281686 | ||||||||
\(905\) | −19.1053 | + | 33.0914i | −0.635082 | + | 1.09999i | ||||
\(906\) | −0.246303 | − | 0.426609i | −0.00818287 | − | 0.0141731i | ||||
\(907\) | −9.24019 | − | 16.0045i | −0.306815 | − | 0.531420i | 0.670849 | − | 0.741594i | \(-0.265930\pi\) |
−0.977664 | + | 0.210175i | \(0.932597\pi\) | |||||||
\(908\) | −14.8312 | + | 25.6884i | −0.492190 | + | 0.852498i | ||||
\(909\) | 1.35030 | 0.0447867 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.6282 | −0.882230 | −0.441115 | − | 0.897451i | \(-0.645417\pi\) | ||||
−0.441115 | + | 0.897451i | \(0.645417\pi\) | |||||||
\(912\) | 15.3088 | − | 26.5155i | 0.506924 | − | 0.878017i | ||||
\(913\) | 2.11687 | + | 3.66653i | 0.0700582 | + | 0.121344i | ||||
\(914\) | −0.0874022 | − | 0.151385i | −0.00289101 | − | 0.00500737i | ||||
\(915\) | 13.8287 | − | 23.9520i | 0.457162 | − | 0.791828i | ||||
\(916\) | 16.7007 | 0.551805 | ||||||||
\(917\) | 11.5302 | − | 12.3677i | 0.380761 | − | 0.408417i | ||||
\(918\) | 1.12931 | 0.0372727 | ||||||||
\(919\) | 5.57467 | − | 9.65561i | 0.183891 | − | 0.318509i | −0.759311 | − | 0.650728i | \(-0.774464\pi\) |
0.943202 | + | 0.332219i | \(0.107797\pi\) | |||||||
\(920\) | −10.7319 | − | 18.5883i | −0.353822 | − | 0.612837i | ||||
\(921\) | 4.93536 | + | 8.54829i | 0.162626 | + | 0.281676i | ||||
\(922\) | 1.67518 | − | 2.90149i | 0.0551690 | − | 0.0955555i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −22.4194 | − | 5.17302i | −0.737544 | − | 0.170180i | ||||
\(925\) | −10.5587 | −0.347166 | ||||||||
\(926\) | −0.0414927 | + | 0.0718675i | −0.00136354 | + | 0.00236171i | ||||
\(927\) | 1.83424 | + | 3.17700i | 0.0602445 | + | 0.104347i | ||||
\(928\) | −3.60365 | − | 6.24170i | −0.118296 | − | 0.204894i | ||||
\(929\) | 3.87255 | − | 6.70745i | 0.127054 | − | 0.220064i | −0.795480 | − | 0.605980i | \(-0.792781\pi\) |
0.922534 | + | 0.385916i | \(0.126114\pi\) | |||||||
\(930\) | −2.00543 | −0.0657607 | ||||||||
\(931\) | −43.4898 | + | 29.3498i | −1.42532 | + | 0.961901i | ||||
\(932\) | −39.0455 | −1.27898 | ||||||||
\(933\) | −9.38559 | + | 16.2563i | −0.307270 | + | 0.532208i | ||||
\(934\) | −3.28149 | − | 5.68371i | −0.107374 | − | 0.185977i | ||||
\(935\) | 3.96817 | + | 6.87306i | 0.129773 | + | 0.224773i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.4239 | 1.18992 | 0.594959 | − | 0.803756i | \(-0.297168\pi\) | ||||
0.594959 | + | 0.803756i | \(0.297168\pi\) | |||||||
\(938\) | 0.934932 | + | 0.215725i | 0.0305266 | + | 0.00704367i | ||||
\(939\) | −11.4829 | −0.374729 | ||||||||
\(940\) | −3.25145 | + | 5.63168i | −0.106051 | + | 0.183685i | ||||
\(941\) | −9.89466 | − | 17.1381i | −0.322557 | − | 0.558685i | 0.658458 | − | 0.752617i | \(-0.271209\pi\) |
−0.981015 | + | 0.193933i | \(0.937876\pi\) | |||||||
\(942\) | −0.252214 | − | 0.436848i | −0.00821759 | − | 0.0142333i | ||||
\(943\) | 9.69526 | − | 16.7927i | 0.315721 | − | 0.546845i | ||||
\(944\) | 32.0454 | 1.04299 | ||||||||
\(945\) | −24.7949 | + | 26.5958i | −0.806577 | + | 0.865161i | ||||
\(946\) | 2.37998 | 0.0773798 | ||||||||
\(947\) | 4.97398 | − | 8.61519i | 0.161633 | − | 0.279956i | −0.773822 | − | 0.633403i | \(-0.781657\pi\) |
0.935454 | + | 0.353448i | \(0.114991\pi\) | |||||||
\(948\) | −6.82403 | − | 11.8196i | −0.221634 | − | 0.383882i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.57014 | + | 2.71957i | −0.0509422 | + | 0.0882345i | ||||
\(951\) | 11.5958 | 0.376020 | ||||||||
\(952\) | 0.639889 | + | 2.09206i | 0.0207389 | + | 0.0678042i | ||||
\(953\) | 0.0211134 | 0.000683929 | 0.000341965 | − | 1.00000i | \(-0.499891\pi\) | ||||
0.000341965 | 1.00000i | \(0.499891\pi\) | ||||||||
\(954\) | 2.10682 | − | 3.64912i | 0.0682108 | − | 0.118144i | ||||
\(955\) | 18.0995 | + | 31.3493i | 0.585686 | + | 1.01444i | ||||
\(956\) | −15.9576 | − | 27.6394i | −0.516106 | − | 0.893922i | ||||
\(957\) | −5.30352 | + | 9.18596i | −0.171438 | + | 0.296940i | ||||
\(958\) | −2.18214 | −0.0705017 | ||||||||
\(959\) | 7.76681 | + | 25.3929i | 0.250804 | + | 0.819981i | ||||
\(960\) | 18.5230 | 0.597827 | ||||||||
\(961\) | 12.2376 | − | 21.1962i | 0.394761 | − | 0.683747i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.76001 | − | 16.9048i | −0.314512 | − | 0.544751i | ||||
\(964\) | 15.8112 | − | 27.3858i | 0.509245 | − | 0.882039i | ||||
\(965\) | −9.97685 | −0.321166 | ||||||||
\(966\) | −4.39858 | + | 4.71806i | −0.141522 | + | 0.151801i | ||||
\(967\) | 19.8102 | 0.637053 | 0.318526 | − | 0.947914i | \(-0.396812\pi\) | ||||
0.318526 | + | 0.947914i | \(0.396812\pi\) | |||||||
\(968\) | 2.40711 | − | 4.16923i | 0.0773674 | − | 0.134004i | ||||
\(969\) | 3.36304 | + | 5.82495i | 0.108036 | + | 0.187124i | ||||
\(970\) | −0.814635 | − | 1.41099i | −0.0261563 | − | 0.0453041i | ||||
\(971\) | 1.80887 | − | 3.13305i | 0.0580493 | − | 0.100544i | −0.835540 | − | 0.549429i | \(-0.814845\pi\) |
0.893590 | + | 0.448885i | \(0.148179\pi\) | |||||||
\(972\) | 28.7144 | 0.921015 | ||||||||
\(973\) | −14.2966 | − | 3.29877i | −0.458326 | − | 0.105754i | ||||
\(974\) | −1.23595 | −0.0396024 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.8782 | − | 29.2339i | −0.540258 | − | 0.935755i | ||||
\(977\) | 1.08085 | + | 1.87208i | 0.0345793 | + | 0.0598931i | 0.882797 | − | 0.469754i | \(-0.155658\pi\) |
−0.848218 | + | 0.529648i | \(0.822324\pi\) | |||||||
\(978\) | 1.00341 | − | 1.73796i | 0.0320855 | − | 0.0555737i | ||||
\(979\) | 30.2382 | 0.966416 | ||||||||
\(980\) | −31.0799 | − | 15.1492i | −0.992810 | − | 0.483924i | ||||
\(981\) | 13.6807 | 0.436792 | ||||||||
\(982\) | −1.74535 | + | 3.02304i | −0.0556965 | + | 0.0964692i | ||||
\(983\) | −15.0545 | − | 26.0752i | −0.480165 | − | 0.831671i | 0.519576 | − | 0.854424i | \(-0.326090\pi\) |
−0.999741 | + | 0.0227535i | \(0.992757\pi\) | |||||||
\(984\) | −1.46717 | − | 2.54121i | −0.0467717 | − | 0.0810109i | ||||
\(985\) | −14.9977 | + | 25.9767i | −0.477865 | + | 0.827687i | ||||
\(986\) | 0.495051 | 0.0157656 | ||||||||
\(987\) | 3.87948 | + | 0.895146i | 0.123485 | + | 0.0284928i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.94742 | + | 15.4974i | −0.284511 | + | 0.492788i | ||||
\(990\) | −2.29507 | − | 3.97517i | −0.0729420 | − | 0.126339i | ||||
\(991\) | 13.5730 | + | 23.5092i | 0.431161 | + | 0.746793i | 0.996974 | − | 0.0777408i | \(-0.0247706\pi\) |
−0.565812 | + | 0.824534i | \(0.691437\pi\) | |||||||
\(992\) | −3.91416 | + | 6.77953i | −0.124275 | + | 0.215250i | ||||
\(993\) | 2.65082 | 0.0841213 | ||||||||
\(994\) | 5.95783 | − | 6.39056i | 0.188971 | − | 0.202696i | ||||
\(995\) | 8.95805 | 0.283989 | ||||||||
\(996\) | −1.18227 | + | 2.04776i | −0.0374618 | + | 0.0648858i | ||||
\(997\) | −25.4005 | − | 43.9949i | −0.804441 | − | 1.39333i | −0.916668 | − | 0.399650i | \(-0.869132\pi\) |
0.112227 | − | 0.993683i | \(-0.464202\pi\) | |||||||
\(998\) | −4.33300 | − | 7.50497i | −0.137159 | − | 0.237566i | ||||
\(999\) | 18.1252 | − | 31.3938i | 0.573456 | − | 0.993256i |
(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 | 1183.2.e.g.170.4 | 12 | ||
7.2 | even | 3 | 8281.2.a.ce.1.3 | 6 | |||
7.4 | even | 3 | inner | 1183.2.e.g.508.4 | 12 | ||
7.5 | odd | 6 | 8281.2.a.cf.1.3 | 6 | |||
13.4 | even | 6 | 91.2.h.b.16.4 | yes | 12 | ||
13.10 | even | 6 | 91.2.g.b.9.3 | ✓ | 12 | ||
13.12 | even | 2 | 1183.2.e.h.170.3 | 12 | |||
39.17 | odd | 6 | 819.2.s.d.289.3 | 12 | |||
39.23 | odd | 6 | 819.2.n.d.100.4 | 12 | |||
91.4 | even | 6 | 91.2.g.b.81.3 | yes | 12 | ||
91.10 | odd | 6 | 637.2.h.l.165.4 | 12 | |||
91.12 | odd | 6 | 8281.2.a.ca.1.4 | 6 | |||
91.17 | odd | 6 | 637.2.g.l.263.3 | 12 | |||
91.23 | even | 6 | 637.2.f.k.295.3 | 12 | |||
91.25 | even | 6 | 1183.2.e.h.508.3 | 12 | |||
91.30 | even | 6 | 637.2.f.k.393.3 | 12 | |||
91.51 | even | 6 | 8281.2.a.bz.1.4 | 6 | |||
91.62 | odd | 6 | 637.2.g.l.373.3 | 12 | |||
91.69 | odd | 6 | 637.2.h.l.471.4 | 12 | |||
91.75 | odd | 6 | 637.2.f.j.295.3 | 12 | |||
91.82 | odd | 6 | 637.2.f.j.393.3 | 12 | |||
91.88 | even | 6 | 91.2.h.b.74.4 | yes | 12 | ||
273.95 | odd | 6 | 819.2.n.d.172.4 | 12 | |||
273.179 | odd | 6 | 819.2.s.d.802.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.3 | ✓ | 12 | 13.10 | even | 6 | ||
91.2.g.b.81.3 | yes | 12 | 91.4 | even | 6 | ||
91.2.h.b.16.4 | yes | 12 | 13.4 | even | 6 | ||
91.2.h.b.74.4 | yes | 12 | 91.88 | even | 6 | ||
637.2.f.j.295.3 | 12 | 91.75 | odd | 6 | |||
637.2.f.j.393.3 | 12 | 91.82 | odd | 6 | |||
637.2.f.k.295.3 | 12 | 91.23 | even | 6 | |||
637.2.f.k.393.3 | 12 | 91.30 | even | 6 | |||
637.2.g.l.263.3 | 12 | 91.17 | odd | 6 | |||
637.2.g.l.373.3 | 12 | 91.62 | odd | 6 | |||
637.2.h.l.165.4 | 12 | 91.10 | odd | 6 | |||
637.2.h.l.471.4 | 12 | 91.69 | odd | 6 | |||
819.2.n.d.100.4 | 12 | 39.23 | odd | 6 | |||
819.2.n.d.172.4 | 12 | 273.95 | odd | 6 | |||
819.2.s.d.289.3 | 12 | 39.17 | odd | 6 | |||
819.2.s.d.802.3 | 12 | 273.179 | odd | 6 | |||
1183.2.e.g.170.4 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.g.508.4 | 12 | 7.4 | even | 3 | inner | ||
1183.2.e.h.170.3 | 12 | 13.12 | even | 2 | |||
1183.2.e.h.508.3 | 12 | 91.25 | even | 6 | |||
8281.2.a.bz.1.4 | 6 | 91.51 | even | 6 | |||
8281.2.a.ca.1.4 | 6 | 91.12 | odd | 6 | |||
8281.2.a.ce.1.3 | 6 | 7.2 | even | 3 | |||
8281.2.a.cf.1.3 | 6 | 7.5 | odd | 6 |