Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 6 x^{10} - 12 x^{9} + 43 x^{8} + 72 x^{7} + 155 x^{6} + 162 x^{5} + 541 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.3 | ||
Root | \(2.31880 - 1.68471i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.o.251.3 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.725848 | + | 2.23393i | 0.513252 | + | 1.57963i | 0.786440 | + | 0.617667i | \(0.211922\pi\) |
−0.273187 | + | 0.961961i | \(0.588078\pi\) | |||||||
\(3\) | −2.31880 | − | 1.68471i | −1.33876 | − | 0.972667i | −0.999489 | − | 0.0319793i | \(-0.989819\pi\) |
−0.339273 | − | 0.940688i | \(-0.610181\pi\) | |||||||
\(4\) | −2.84556 | + | 2.06742i | −1.42278 | + | 1.03371i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | 2.08042 | − | 6.40289i | 0.849330 | − | 2.61397i | ||||
\(7\) | 2.73731 | − | 1.98877i | 1.03461 | − | 0.751685i | 0.0653808 | − | 0.997860i | \(-0.479174\pi\) |
0.969225 | + | 0.246175i | \(0.0791738\pi\) | |||||||
\(8\) | −2.88333 | − | 2.09486i | −1.01941 | − | 0.740644i | ||||
\(9\) | 1.61155 | + | 4.95985i | 0.537184 | + | 1.65328i | ||||
\(10\) | −2.34889 | −0.742786 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 10.0813 | 2.91022 | ||||||||
\(13\) | 0.458178 | + | 1.41013i | 0.127076 | + | 0.391099i | 0.994274 | − | 0.106865i | \(-0.0340812\pi\) |
−0.867198 | + | 0.497964i | \(0.834081\pi\) | |||||||
\(14\) | 6.42965 | + | 4.67142i | 1.71840 | + | 1.24849i | ||||
\(15\) | 2.31880 | − | 1.68471i | 0.598712 | − | 0.434990i | ||||
\(16\) | 0.413100 | − | 1.27139i | 0.103275 | − | 0.317848i | ||||
\(17\) | −1.15337 | + | 3.54972i | −0.279734 | + | 0.860934i | 0.708194 | + | 0.706018i | \(0.249510\pi\) |
−0.987928 | + | 0.154915i | \(0.950490\pi\) | |||||||
\(18\) | −9.91022 | + | 7.20019i | −2.33586 | + | 1.69710i | ||||
\(19\) | 2.60106 | + | 1.88978i | 0.596725 | + | 0.433546i | 0.844715 | − | 0.535216i | \(-0.179770\pi\) |
−0.247990 | + | 0.968763i | \(0.579770\pi\) | |||||||
\(20\) | −1.08691 | − | 3.34515i | −0.243040 | − | 0.747999i | ||||
\(21\) | −9.69779 | −2.11623 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.51730 | −0.524894 | −0.262447 | − | 0.964946i | \(-0.584530\pi\) | ||||
−0.262447 | + | 0.964946i | \(0.584530\pi\) | |||||||
\(24\) | 3.15664 | + | 9.71513i | 0.644346 | + | 1.98309i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | −2.81756 | + | 2.04708i | −0.552569 | + | 0.401465i | ||||
\(27\) | 1.96192 | − | 6.03816i | 0.377571 | − | 1.16204i | ||||
\(28\) | −3.67755 | + | 11.3183i | −0.694992 | + | 2.13897i | ||||
\(29\) | −3.80059 | + | 2.76129i | −0.705752 | + | 0.512759i | −0.881800 | − | 0.471623i | \(-0.843668\pi\) |
0.176048 | + | 0.984381i | \(0.443668\pi\) | |||||||
\(30\) | 5.44662 | + | 3.95720i | 0.994413 | + | 0.722483i | ||||
\(31\) | 2.84762 | + | 8.76407i | 0.511448 | + | 1.57407i | 0.789654 | + | 0.613553i | \(0.210260\pi\) |
−0.278206 | + | 0.960521i | \(0.589740\pi\) | |||||||
\(32\) | −3.98793 | −0.704972 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.76700 | −1.50353 | ||||||||
\(35\) | 1.04556 | + | 3.21790i | 0.176732 | + | 0.543925i | ||||
\(36\) | −14.8399 | − | 10.7818i | −2.47331 | − | 1.79696i | ||||
\(37\) | 2.18256 | − | 1.58572i | 0.358810 | − | 0.260691i | −0.393746 | − | 0.919219i | \(-0.628821\pi\) |
0.752556 | + | 0.658529i | \(0.228821\pi\) | |||||||
\(38\) | −2.33367 | + | 7.18230i | −0.378571 | + | 1.16512i | ||||
\(39\) | 1.31323 | − | 4.04171i | 0.210285 | − | 0.647191i | ||||
\(40\) | 2.88333 | − | 2.09486i | 0.455894 | − | 0.331226i | ||||
\(41\) | −3.68257 | − | 2.67555i | −0.575121 | − | 0.417850i | 0.261841 | − | 0.965111i | \(-0.415671\pi\) |
−0.836962 | + | 0.547261i | \(0.815671\pi\) | |||||||
\(42\) | −7.03912 | − | 21.6642i | −1.08616 | − | 3.34286i | ||||
\(43\) | 5.38350 | 0.820976 | 0.410488 | − | 0.911866i | \(-0.365358\pi\) | ||||
0.410488 | + | 0.911866i | \(0.365358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.21509 | −0.777420 | ||||||||
\(46\) | −1.82718 | − | 5.62348i | −0.269403 | − | 0.829137i | ||||
\(47\) | 8.51845 | + | 6.18901i | 1.24254 | + | 0.902760i | 0.997765 | − | 0.0668188i | \(-0.0212849\pi\) |
0.244778 | + | 0.969579i | \(0.421285\pi\) | |||||||
\(48\) | −3.09982 | + | 2.25215i | −0.447421 | + | 0.325070i | ||||
\(49\) | 1.37453 | − | 4.23038i | 0.196362 | − | 0.604340i | ||||
\(50\) | 0.725848 | − | 2.23393i | 0.102650 | − | 0.315926i | ||||
\(51\) | 8.65469 | − | 6.28800i | 1.21190 | − | 0.880496i | ||||
\(52\) | −4.21910 | − | 3.06535i | −0.585084 | − | 0.425088i | ||||
\(53\) | −0.777890 | − | 2.39410i | −0.106851 | − | 0.328855i | 0.883309 | − | 0.468791i | \(-0.155310\pi\) |
−0.990161 | + | 0.139936i | \(0.955310\pi\) | |||||||
\(54\) | 14.9129 | 2.02939 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.0588 | −1.61142 | ||||||||
\(57\) | −2.84762 | − | 8.76407i | −0.377177 | − | 1.16083i | ||||
\(58\) | −8.92719 | − | 6.48598i | −1.17220 | − | 0.851651i | ||||
\(59\) | −9.63772 | + | 7.00222i | −1.25472 | + | 0.911611i | −0.998486 | − | 0.0550028i | \(-0.982483\pi\) |
−0.256238 | + | 0.966614i | \(0.582483\pi\) | |||||||
\(60\) | −3.11529 | + | 9.58788i | −0.402182 | + | 1.23779i | ||||
\(61\) | −4.22732 | + | 13.0103i | −0.541252 | + | 1.66580i | 0.188485 | + | 0.982076i | \(0.439642\pi\) |
−0.729737 | + | 0.683728i | \(0.760358\pi\) | |||||||
\(62\) | −17.5114 | + | 12.7228i | −2.22395 | + | 1.61579i | ||||
\(63\) | 14.2753 | + | 10.3716i | 1.79852 | + | 1.30670i | ||||
\(64\) | −3.72083 | − | 11.4515i | −0.465104 | − | 1.43144i | ||||
\(65\) | −1.48270 | −0.183906 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.83159 | 0.956781 | 0.478391 | − | 0.878147i | \(-0.341220\pi\) | ||||
0.478391 | + | 0.878147i | \(0.341220\pi\) | |||||||
\(68\) | −4.05677 | − | 12.4854i | −0.491955 | − | 1.51408i | ||||
\(69\) | 5.83713 | + | 4.24092i | 0.702708 | + | 0.510547i | ||||
\(70\) | −6.42965 | + | 4.67142i | −0.768491 | + | 0.558341i | ||||
\(71\) | 0.777890 | − | 2.39410i | 0.0923185 | − | 0.284127i | −0.894227 | − | 0.447614i | \(-0.852274\pi\) |
0.986546 | + | 0.163486i | \(0.0522740\pi\) | |||||||
\(72\) | 5.74355 | − | 17.6768i | 0.676884 | − | 2.08323i | ||||
\(73\) | 2.39905 | − | 1.74301i | 0.280788 | − | 0.204004i | −0.438473 | − | 0.898744i | \(-0.644481\pi\) |
0.719261 | + | 0.694740i | \(0.244481\pi\) | |||||||
\(74\) | 5.12659 | + | 3.72469i | 0.595955 | + | 0.432986i | ||||
\(75\) | 0.885704 | + | 2.72592i | 0.102272 | + | 0.314762i | ||||
\(76\) | −11.3085 | −1.29717 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.98210 | 1.13025 | ||||||||
\(79\) | 2.09112 | + | 6.43580i | 0.235269 | + | 0.724085i | 0.997086 | + | 0.0762913i | \(0.0243079\pi\) |
−0.761816 | + | 0.647793i | \(0.775692\pi\) | |||||||
\(80\) | 1.08151 | + | 0.785763i | 0.120916 | + | 0.0878510i | ||||
\(81\) | −2.06454 | + | 1.49998i | −0.229393 | + | 0.166664i | ||||
\(82\) | 3.30400 | − | 10.1687i | 0.364865 | − | 1.12294i | ||||
\(83\) | 2.33367 | − | 7.18230i | 0.256153 | − | 0.788359i | −0.737447 | − | 0.675405i | \(-0.763969\pi\) |
0.993600 | − | 0.112954i | \(-0.0360313\pi\) | |||||||
\(84\) | 27.5956 | − | 20.0494i | 3.01093 | − | 2.18757i | ||||
\(85\) | −3.01957 | − | 2.19385i | −0.327519 | − | 0.237956i | ||||
\(86\) | 3.90761 | + | 12.0264i | 0.421368 | + | 1.29684i | ||||
\(87\) | 13.4648 | 1.44358 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8016 | 1.14497 | 0.572484 | − | 0.819916i | \(-0.305980\pi\) | ||||
0.572484 | + | 0.819916i | \(0.305980\pi\) | |||||||
\(90\) | −3.78537 | − | 11.6502i | −0.399013 | − | 1.22803i | ||||
\(91\) | 4.05860 | + | 2.94875i | 0.425457 | + | 0.309113i | ||||
\(92\) | 7.16314 | − | 5.20432i | 0.746809 | − | 0.542588i | ||||
\(93\) | 8.16184 | − | 25.1196i | 0.846344 | − | 2.60478i | ||||
\(94\) | −7.64273 | + | 23.5219i | −0.788287 | + | 2.42610i | ||||
\(95\) | −2.60106 | + | 1.88978i | −0.266864 | + | 0.193888i | ||||
\(96\) | 9.24721 | + | 6.71849i | 0.943790 | + | 0.685703i | ||||
\(97\) | 3.40435 | + | 10.4775i | 0.345659 | + | 1.06383i | 0.961230 | + | 0.275748i | \(0.0889256\pi\) |
−0.615571 | + | 0.788082i | \(0.711074\pi\) | |||||||
\(98\) | 10.4481 | 1.05542 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.51730 | 0.351730 | ||||||||
\(101\) | −3.93453 | − | 12.1092i | −0.391500 | − | 1.20491i | −0.931654 | − | 0.363347i | \(-0.881634\pi\) |
0.540154 | − | 0.841566i | \(-0.318366\pi\) | |||||||
\(102\) | 20.3290 | + | 14.7699i | 2.01287 | + | 1.46243i | ||||
\(103\) | 14.8399 | − | 10.7818i | 1.46221 | − | 1.06236i | 0.479435 | − | 0.877578i | \(-0.340842\pi\) |
0.982779 | − | 0.184783i | \(-0.0591583\pi\) | |||||||
\(104\) | 1.63294 | − | 5.02568i | 0.160123 | − | 0.492808i | ||||
\(105\) | 2.99678 | − | 9.22314i | 0.292456 | − | 0.900087i | ||||
\(106\) | 4.78362 | − | 3.47550i | 0.464626 | − | 0.337571i | ||||
\(107\) | −5.77137 | − | 4.19314i | −0.557939 | − | 0.405366i | 0.272765 | − | 0.962081i | \(-0.412062\pi\) |
−0.830704 | + | 0.556714i | \(0.812062\pi\) | |||||||
\(108\) | 6.90066 | + | 21.2380i | 0.664016 | + | 2.04363i | ||||
\(109\) | 4.14588 | 0.397103 | 0.198551 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198551 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.73240 | −0.733927 | ||||||||
\(112\) | −1.39772 | − | 4.30175i | −0.132073 | − | 0.406478i | ||||
\(113\) | −1.18504 | − | 0.860984i | −0.111479 | − | 0.0809945i | 0.530649 | − | 0.847592i | \(-0.321948\pi\) |
−0.642128 | + | 0.766597i | \(0.721948\pi\) | |||||||
\(114\) | 17.5114 | − | 12.7228i | 1.64009 | − | 1.19160i | ||||
\(115\) | 0.777890 | − | 2.39410i | 0.0725386 | − | 0.223251i | ||||
\(116\) | 5.10606 | − | 15.7148i | 0.474086 | − | 1.45909i | ||||
\(117\) | −6.25564 | + | 4.54499i | −0.578334 | + | 0.420184i | ||||
\(118\) | −22.6380 | − | 16.4475i | −2.08400 | − | 1.51411i | ||||
\(119\) | 3.90244 | + | 12.0105i | 0.357736 | + | 1.10100i | ||||
\(120\) | −10.2151 | −0.932506 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −32.1326 | −2.90915 | ||||||||
\(123\) | 4.03165 | + | 12.4081i | 0.363521 | + | 1.11880i | ||||
\(124\) | −26.2221 | − | 19.0515i | −2.35481 | − | 1.71087i | ||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | −12.8078 | + | 39.4183i | −1.14101 | + | 3.51166i | ||||
\(127\) | 3.49077 | − | 10.7435i | 0.309756 | − | 0.953331i | −0.668103 | − | 0.744069i | \(-0.732894\pi\) |
0.977859 | − | 0.209263i | \(-0.0671064\pi\) | |||||||
\(128\) | 16.4286 | − | 11.9361i | 1.45210 | − | 1.05501i | ||||
\(129\) | −12.4833 | − | 9.06964i | −1.09909 | − | 0.798537i | ||||
\(130\) | −1.07621 | − | 3.31224i | −0.0943901 | − | 0.290503i | ||||
\(131\) | −14.6799 | −1.28259 | −0.641294 | − | 0.767295i | \(-0.721602\pi\) | ||||
−0.641294 | + | 0.767295i | \(0.721602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8783 | 0.943266 | ||||||||
\(134\) | 5.68455 | + | 17.4952i | 0.491070 | + | 1.51136i | ||||
\(135\) | 5.13636 | + | 3.73179i | 0.442068 | + | 0.321181i | ||||
\(136\) | 10.7617 | − | 7.81884i | 0.922809 | − | 0.670460i | ||||
\(137\) | −4.83466 | + | 14.8795i | −0.413053 | + | 1.27125i | 0.500929 | + | 0.865489i | \(0.332992\pi\) |
−0.913981 | + | 0.405757i | \(0.867008\pi\) | |||||||
\(138\) | −5.23706 | + | 16.1180i | −0.445808 | + | 1.37206i | ||||
\(139\) | −6.18516 | + | 4.49378i | −0.524618 | + | 0.381158i | −0.818341 | − | 0.574733i | \(-0.805106\pi\) |
0.293722 | + | 0.955891i | \(0.405106\pi\) | |||||||
\(140\) | −9.62795 | − | 6.99512i | −0.813711 | − | 0.591195i | ||||
\(141\) | −9.32591 | − | 28.7022i | −0.785384 | − | 2.41716i | ||||
\(142\) | 5.91288 | 0.496198 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.97164 | 0.580970 | ||||||||
\(145\) | −1.45170 | − | 4.46786i | −0.120557 | − | 0.371036i | ||||
\(146\) | 5.63512 | + | 4.09415i | 0.466366 | + | 0.338835i | ||||
\(147\) | −10.3142 | + | 7.49373i | −0.850704 | + | 0.618073i | ||||
\(148\) | −2.93224 | + | 9.02452i | −0.241029 | + | 0.741811i | ||||
\(149\) | 2.00326 | − | 6.16541i | 0.164114 | − | 0.505090i | −0.834856 | − | 0.550468i | \(-0.814449\pi\) |
0.998970 | + | 0.0453781i | \(0.0144492\pi\) | |||||||
\(150\) | −5.44662 | + | 3.95720i | −0.444715 | + | 0.323104i | ||||
\(151\) | −8.80071 | − | 6.39409i | −0.716191 | − | 0.520344i | 0.168974 | − | 0.985621i | \(-0.445955\pi\) |
−0.885165 | + | 0.465277i | \(0.845955\pi\) | |||||||
\(152\) | −3.54089 | − | 10.8977i | −0.287204 | − | 0.883922i | ||||
\(153\) | −19.4648 | −1.57364 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.21509 | −0.740174 | ||||||||
\(156\) | 4.61903 | + | 14.2159i | 0.369818 | + | 1.13818i | ||||
\(157\) | −8.43820 | − | 6.13071i | −0.673441 | − | 0.489284i | 0.197734 | − | 0.980256i | \(-0.436642\pi\) |
−0.871175 | + | 0.490972i | \(0.836642\pi\) | |||||||
\(158\) | −12.8593 | + | 9.34283i | −1.02303 | + | 0.743276i | ||||
\(159\) | −2.22959 | + | 6.86196i | −0.176818 | + | 0.544189i | ||||
\(160\) | 1.23234 | − | 3.79274i | 0.0974248 | − | 0.299843i | ||||
\(161\) | −6.89064 | + | 5.00635i | −0.543059 | + | 0.394555i | ||||
\(162\) | −4.84939 | − | 3.52329i | −0.381004 | − | 0.276815i | ||||
\(163\) | −3.16553 | − | 9.74250i | −0.247943 | − | 0.763092i | −0.995138 | − | 0.0984866i | \(-0.968600\pi\) |
0.747195 | − | 0.664605i | \(-0.231400\pi\) | |||||||
\(164\) | 16.0105 | 1.25021 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.7386 | 1.37679 | ||||||||
\(167\) | −0.323443 | − | 0.995454i | −0.0250287 | − | 0.0770306i | 0.937762 | − | 0.347279i | \(-0.112894\pi\) |
−0.962791 | + | 0.270248i | \(0.912894\pi\) | |||||||
\(168\) | 27.9619 | + | 20.3155i | 2.15731 | + | 1.56737i | ||||
\(169\) | 8.73869 | − | 6.34903i | 0.672207 | − | 0.488387i | ||||
\(170\) | 2.70915 | − | 8.33792i | 0.207783 | − | 0.639489i | ||||
\(171\) | −5.18129 | + | 15.9464i | −0.396223 | + | 1.21945i | ||||
\(172\) | −15.3191 | + | 11.1300i | −1.16807 | + | 0.848651i | ||||
\(173\) | −9.63772 | − | 7.00222i | −0.732743 | − | 0.532369i | 0.157687 | − | 0.987489i | \(-0.449596\pi\) |
−0.890430 | + | 0.455120i | \(0.849596\pi\) | |||||||
\(174\) | 9.77340 | + | 30.0794i | 0.740919 | + | 2.28031i | ||||
\(175\) | −3.38350 | −0.255769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 34.1447 | 2.56647 | ||||||||
\(178\) | 7.84033 | + | 24.1301i | 0.587658 | + | 1.80862i | ||||
\(179\) | 2.74708 | + | 1.99587i | 0.205326 | + | 0.149178i | 0.685697 | − | 0.727887i | \(-0.259498\pi\) |
−0.480370 | + | 0.877066i | \(0.659498\pi\) | |||||||
\(180\) | 14.8399 | − | 10.7818i | 1.10610 | − | 0.803627i | ||||
\(181\) | −1.76071 | + | 5.41892i | −0.130873 | + | 0.402785i | −0.994925 | − | 0.100617i | \(-0.967918\pi\) |
0.864052 | + | 0.503402i | \(0.167918\pi\) | |||||||
\(182\) | −3.64137 | + | 11.2070i | −0.269916 | + | 0.830716i | ||||
\(183\) | 31.7210 | − | 23.0466i | 2.34488 | − | 1.70366i | ||||
\(184\) | 7.25821 | + | 5.27340i | 0.535082 | + | 0.388760i | ||||
\(185\) | 0.833662 | + | 2.56575i | 0.0612921 | + | 0.188638i | ||||
\(186\) | 62.0397 | 4.54897 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −37.0350 | −2.70106 | ||||||||
\(189\) | −6.63815 | − | 20.4301i | −0.482854 | − | 1.48607i | ||||
\(190\) | −6.10963 | − | 4.43890i | −0.443239 | − | 0.322032i | ||||
\(191\) | 7.29467 | − | 5.29989i | 0.527824 | − | 0.383486i | −0.291719 | − | 0.956504i | \(-0.594227\pi\) |
0.819543 | + | 0.573018i | \(0.194227\pi\) | |||||||
\(192\) | −10.6646 | + | 32.8224i | −0.769654 | + | 2.36875i | ||||
\(193\) | 8.10607 | − | 24.9479i | 0.583488 | − | 1.79579i | −0.0217723 | − | 0.999763i | \(-0.506931\pi\) |
0.605260 | − | 0.796028i | \(-0.293069\pi\) | |||||||
\(194\) | −20.9350 | + | 15.2102i | −1.50304 | + | 1.09203i | ||||
\(195\) | 3.43808 | + | 2.49791i | 0.246206 | + | 0.178879i | ||||
\(196\) | 4.83466 | + | 14.8795i | 0.345333 | + | 1.06282i | ||||
\(197\) | −16.6978 | −1.18967 | −0.594834 | − | 0.803849i | \(-0.702782\pi\) | ||||
−0.594834 | + | 0.803849i | \(0.702782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7912 | −1.19029 | −0.595147 | − | 0.803617i | \(-0.702906\pi\) | ||||
−0.595147 | + | 0.803617i | \(0.702906\pi\) | |||||||
\(200\) | 1.10133 | + | 3.38955i | 0.0778760 | + | 0.239678i | ||||
\(201\) | −18.1599 | − | 13.1940i | −1.28090 | − | 0.930630i | ||||
\(202\) | 24.1953 | − | 17.5789i | 1.70238 | − | 1.23685i | ||||
\(203\) | −4.91182 | + | 15.1170i | −0.344742 | + | 1.06101i | ||||
\(204\) | −11.6275 | + | 35.7858i | −0.814088 | + | 2.50550i | ||||
\(205\) | 3.68257 | − | 2.67555i | 0.257202 | − | 0.186868i | ||||
\(206\) | 34.8572 | + | 25.3253i | 2.42862 | + | 1.76450i | ||||
\(207\) | −4.05677 | − | 12.4854i | −0.281965 | − | 0.867798i | ||||
\(208\) | 1.98210 | 0.137434 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 22.7791 | 1.57191 | ||||||||
\(211\) | 2.36252 | + | 7.27109i | 0.162643 | + | 0.500563i | 0.998855 | − | 0.0478434i | \(-0.0152349\pi\) |
−0.836212 | + | 0.548406i | \(0.815235\pi\) | |||||||
\(212\) | 7.16314 | + | 5.20432i | 0.491966 | + | 0.357434i | ||||
\(213\) | −5.83713 | + | 4.24092i | −0.399954 | + | 0.290583i | ||||
\(214\) | 5.17806 | − | 15.9364i | 0.353965 | − | 1.08939i | ||||
\(215\) | −1.66359 | + | 5.12001i | −0.113456 | + | 0.349182i | ||||
\(216\) | −18.3059 | + | 13.3000i | −1.24556 | + | 0.904953i | ||||
\(217\) | 25.2246 | + | 18.3267i | 1.71236 | + | 1.24410i | ||||
\(218\) | 3.00928 | + | 9.26160i | 0.203814 | + | 0.627275i | ||||
\(219\) | −8.49940 | −0.574336 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.53401 | −0.372258 | ||||||||
\(222\) | −5.61255 | − | 17.2736i | −0.376689 | − | 1.15933i | ||||
\(223\) | 3.06580 | + | 2.22743i | 0.205301 | + | 0.149160i | 0.685685 | − | 0.727898i | \(-0.259503\pi\) |
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(224\) | −10.9162 | + | 7.93108i | −0.729369 | + | 0.529917i | ||||
\(225\) | 1.61155 | − | 4.95985i | 0.107437 | − | 0.330657i | ||||
\(226\) | 1.06322 | − | 3.27225i | 0.0707242 | − | 0.217667i | ||||
\(227\) | 15.8131 | − | 11.4889i | 1.04955 | − | 0.762545i | 0.0774258 | − | 0.996998i | \(-0.475330\pi\) |
0.972127 | + | 0.234453i | \(0.0753299\pi\) | |||||||
\(228\) | 26.2221 | + | 19.0515i | 1.73660 | + | 1.26171i | ||||
\(229\) | 1.59533 | + | 4.90991i | 0.105422 | + | 0.324456i | 0.989829 | − | 0.142260i | \(-0.0454370\pi\) |
−0.884407 | + | 0.466716i | \(0.845437\pi\) | |||||||
\(230\) | 5.91288 | 0.389884 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.7429 | 1.09922 | ||||||||
\(233\) | 1.93126 | + | 5.94382i | 0.126521 | + | 0.389392i | 0.994175 | − | 0.107776i | \(-0.0343730\pi\) |
−0.867654 | + | 0.497169i | \(0.834373\pi\) | |||||||
\(234\) | −14.6938 | − | 10.6757i | −0.960566 | − | 0.697892i | ||||
\(235\) | −8.51845 | + | 6.18901i | −0.555682 | + | 0.403727i | ||||
\(236\) | 12.9482 | − | 39.8504i | 0.842855 | − | 2.59404i | ||||
\(237\) | 5.99356 | − | 18.4463i | 0.389324 | − | 1.19822i | ||||
\(238\) | −23.9980 | + | 17.4356i | −1.55556 | + | 1.13018i | ||||
\(239\) | −3.73011 | − | 2.71008i | −0.241281 | − | 0.175301i | 0.460573 | − | 0.887622i | \(-0.347644\pi\) |
−0.701854 | + | 0.712321i | \(0.747644\pi\) | |||||||
\(240\) | −1.18403 | − | 3.64406i | −0.0764286 | − | 0.235223i | ||||
\(241\) | 7.87827 | 0.507484 | 0.253742 | − | 0.967272i | \(-0.418339\pi\) | ||||
0.253742 | + | 0.967272i | \(0.418339\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7324 | −0.752634 | ||||||||
\(244\) | −14.8688 | − | 45.7613i | −0.951875 | − | 2.92957i | ||||
\(245\) | 3.59858 | + | 2.61452i | 0.229905 | + | 0.167036i | ||||
\(246\) | −24.7926 | + | 18.0128i | −1.58072 | + | 1.14846i | ||||
\(247\) | −1.47309 | + | 4.53369i | −0.0937302 | + | 0.288472i | ||||
\(248\) | 10.1489 | − | 31.2350i | 0.644455 | − | 1.98343i | ||||
\(249\) | −17.5114 | + | 12.7228i | −1.10974 | + | 0.806273i | ||||
\(250\) | 1.90030 | + | 1.38065i | 0.120185 | + | 0.0873197i | ||||
\(251\) | 3.29280 | + | 10.1342i | 0.207840 | + | 0.639666i | 0.999585 | + | 0.0288136i | \(0.00917293\pi\) |
−0.791745 | + | 0.610852i | \(0.790827\pi\) | |||||||
\(252\) | −62.0638 | −3.90965 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 26.5340 | 1.66489 | ||||||||
\(255\) | 3.30580 | + | 10.1742i | 0.207017 | + | 0.637133i | ||||
\(256\) | 19.1065 | + | 13.8817i | 1.19416 | + | 0.867605i | ||||
\(257\) | −2.27257 | + | 1.65112i | −0.141759 | + | 0.102994i | −0.656405 | − | 0.754409i | \(-0.727924\pi\) |
0.514645 | + | 0.857403i | \(0.327924\pi\) | |||||||
\(258\) | 11.2000 | − | 34.4700i | 0.697280 | − | 2.14601i | ||||
\(259\) | 2.82070 | − | 8.68122i | 0.175270 | − | 0.539425i | ||||
\(260\) | 4.21910 | − | 3.06535i | 0.261657 | − | 0.190105i | ||||
\(261\) | −19.8204 | − | 14.4004i | −1.22685 | − | 0.891362i | ||||
\(262\) | −10.6554 | − | 32.7939i | −0.658291 | − | 2.02601i | ||||
\(263\) | 27.6453 | 1.70468 | 0.852340 | − | 0.522987i | \(-0.175183\pi\) | ||||
0.852340 | + | 0.522987i | \(0.175183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.51730 | 0.154637 | ||||||||
\(266\) | 7.89598 | + | 24.3013i | 0.484133 | + | 1.49001i | ||||
\(267\) | −25.0468 | − | 18.1976i | −1.53284 | − | 1.11367i | ||||
\(268\) | −22.2852 | + | 16.1912i | −1.36129 | + | 0.989034i | ||||
\(269\) | −4.50425 | + | 13.8627i | −0.274629 | + | 0.845221i | 0.714688 | + | 0.699443i | \(0.246569\pi\) |
−0.989317 | + | 0.145778i | \(0.953431\pi\) | |||||||
\(270\) | −4.60833 | + | 14.1830i | −0.280454 | + | 0.863149i | ||||
\(271\) | 1.74957 | − | 1.27113i | 0.106279 | − | 0.0772159i | −0.533377 | − | 0.845878i | \(-0.679077\pi\) |
0.639655 | + | 0.768662i | \(0.279077\pi\) | |||||||
\(272\) | 4.03662 | + | 2.93278i | 0.244756 | + | 0.177826i | ||||
\(273\) | −4.44332 | − | 13.6751i | −0.268922 | − | 0.827656i | ||||
\(274\) | −36.7491 | −2.22009 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −25.3777 | −1.52756 | ||||||||
\(277\) | −4.72864 | − | 14.5533i | −0.284117 | − | 0.874421i | −0.986662 | − | 0.162782i | \(-0.947953\pi\) |
0.702545 | − | 0.711639i | \(-0.252047\pi\) | |||||||
\(278\) | −14.5283 | − | 10.5554i | −0.871349 | − | 0.633072i | ||||
\(279\) | −38.8794 | + | 28.2475i | −2.32765 | + | 1.69114i | ||||
\(280\) | 3.72636 | − | 11.4686i | 0.222693 | − | 0.685378i | ||||
\(281\) | 0.660812 | − | 2.03377i | 0.0394207 | − | 0.121325i | −0.929410 | − | 0.369050i | \(-0.879683\pi\) |
0.968830 | + | 0.247725i | \(0.0796831\pi\) | |||||||
\(282\) | 57.3496 | − | 41.6669i | 3.41512 | − | 2.48123i | ||||
\(283\) | −3.50385 | − | 2.54569i | −0.208282 | − | 0.151326i | 0.478754 | − | 0.877949i | \(-0.341089\pi\) |
−0.687036 | + | 0.726623i | \(0.741089\pi\) | |||||||
\(284\) | 2.73607 | + | 8.42077i | 0.162356 | + | 0.499681i | ||||
\(285\) | 9.21509 | 0.545855 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.4014 | −0.909116 | ||||||||
\(288\) | −6.42675 | − | 19.7795i | −0.378700 | − | 1.16552i | ||||
\(289\) | 2.48305 | + | 1.80404i | 0.146062 | + | 0.106120i | ||||
\(290\) | 8.92719 | − | 6.48598i | 0.524222 | − | 0.380870i | ||||
\(291\) | 9.75754 | − | 30.0306i | 0.571997 | − | 1.76043i | ||||
\(292\) | −3.22310 | + | 9.91970i | −0.188618 | + | 0.580506i | ||||
\(293\) | 10.9273 | − | 7.93912i | 0.638378 | − | 0.463809i | −0.220915 | − | 0.975293i | \(-0.570904\pi\) |
0.859292 | + | 0.511485i | \(0.170904\pi\) | |||||||
\(294\) | −24.2271 | − | 17.6020i | −1.41295 | − | 1.02657i | ||||
\(295\) | −3.68128 | − | 11.3298i | −0.214333 | − | 0.659648i | ||||
\(296\) | −9.61488 | −0.558854 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2272 | 0.882086 | ||||||||
\(299\) | −1.15337 | − | 3.54972i | −0.0667013 | − | 0.205286i | ||||
\(300\) | −8.15594 | − | 5.92563i | −0.470883 | − | 0.342117i | ||||
\(301\) | 14.7363 | − | 10.7066i | 0.849387 | − | 0.617116i | ||||
\(302\) | 7.89598 | − | 24.3013i | 0.454362 | − | 1.39838i | ||||
\(303\) | −11.2771 | + | 34.7075i | −0.647854 | + | 1.99389i | ||||
\(304\) | 3.47715 | − | 2.52630i | 0.199428 | − | 0.144893i | ||||
\(305\) | −11.0673 | − | 8.04083i | −0.633709 | − | 0.460417i | ||||
\(306\) | −14.1285 | − | 43.4830i | −0.807672 | − | 2.48576i | ||||
\(307\) | −2.37887 | −0.135769 | −0.0678847 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678847 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −52.5749 | −2.99088 | ||||||||
\(310\) | −6.68876 | − | 20.5859i | −0.379896 | − | 1.16920i | ||||
\(311\) | 17.9154 | + | 13.0163i | 1.01589 | + | 0.738088i | 0.965436 | − | 0.260639i | \(-0.0839332\pi\) |
0.0504540 | + | 0.998726i | \(0.483933\pi\) | |||||||
\(312\) | −12.2533 | + | 8.90252i | −0.693705 | + | 0.504006i | ||||
\(313\) | −8.43132 | + | 25.9489i | −0.476566 | + | 1.46672i | 0.367268 | + | 0.930115i | \(0.380293\pi\) |
−0.843834 | + | 0.536604i | \(0.819707\pi\) | |||||||
\(314\) | 7.57073 | − | 23.3003i | 0.427241 | − | 1.31491i | ||||
\(315\) | −14.2753 | + | 10.3716i | −0.804324 | + | 0.584375i | ||||
\(316\) | −19.2559 | − | 13.9902i | −1.08323 | − | 0.787012i | ||||
\(317\) | −4.75749 | − | 14.6421i | −0.267208 | − | 0.822380i | −0.991177 | − | 0.132548i | \(-0.957684\pi\) |
0.723969 | − | 0.689832i | \(-0.242316\pi\) | |||||||
\(318\) | −16.9475 | −0.950368 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 12.0409 | 0.673104 | ||||||||
\(321\) | 6.31844 | + | 19.4461i | 0.352661 | + | 1.08538i | ||||
\(322\) | −16.1854 | − | 11.7594i | −0.901977 | − | 0.655324i | ||||
\(323\) | −9.70820 | + | 7.05342i | −0.540179 | + | 0.392463i | ||||
\(324\) | 2.77369 | − | 8.53654i | 0.154094 | − | 0.474252i | ||||
\(325\) | 0.458178 | − | 1.41013i | 0.0254152 | − | 0.0782198i | ||||
\(326\) | 19.4664 | − | 14.1432i | 1.07814 | − | 0.783317i | ||||
\(327\) | −9.61347 | − | 6.98460i | −0.531626 | − | 0.386249i | ||||
\(328\) | 5.01317 | + | 15.4289i | 0.276806 | + | 0.851921i | ||||
\(329\) | 35.6262 | 1.96413 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9129 | 1.42430 | 0.712150 | − | 0.702027i | \(-0.247721\pi\) | ||||
0.712150 | + | 0.702027i | \(0.247721\pi\) | |||||||
\(332\) | 8.20822 | + | 25.2623i | 0.450485 | + | 1.38645i | ||||
\(333\) | 11.3822 | + | 8.26968i | 0.623743 | + | 0.453176i | ||||
\(334\) | 1.98901 | − | 1.44510i | 0.108834 | − | 0.0790722i | ||||
\(335\) | −2.42009 | + | 7.44828i | −0.132224 | + | 0.406943i | ||||
\(336\) | −4.00616 | + | 12.3297i | −0.218554 | + | 0.672639i | ||||
\(337\) | −11.3118 | + | 8.21847i | −0.616191 | + | 0.447689i | −0.851589 | − | 0.524210i | \(-0.824361\pi\) |
0.235398 | + | 0.971899i | \(0.424361\pi\) | |||||||
\(338\) | 20.5263 | + | 14.9132i | 1.11648 | + | 0.811171i | ||||
\(339\) | 1.29737 | + | 3.99290i | 0.0704636 | + | 0.216865i | ||||
\(340\) | 13.1280 | 0.711964 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −39.3839 | −2.12964 | ||||||||
\(343\) | 2.66818 | + | 8.21180i | 0.144068 | + | 0.443396i | ||||
\(344\) | −15.5224 | − | 11.2777i | −0.836911 | − | 0.608052i | ||||
\(345\) | −5.83713 | + | 4.24092i | −0.314261 | + | 0.228324i | ||||
\(346\) | 8.64694 | − | 26.6126i | 0.464863 | − | 1.43070i | ||||
\(347\) | −9.59395 | + | 29.5271i | −0.515030 | + | 1.58510i | 0.268196 | + | 0.963364i | \(0.413572\pi\) |
−0.783227 | + | 0.621736i | \(0.786428\pi\) | |||||||
\(348\) | −38.3149 | + | 27.8374i | −2.05389 | + | 1.49224i | ||||
\(349\) | −2.96358 | − | 2.15316i | −0.158637 | − | 0.115256i | 0.505635 | − | 0.862747i | \(-0.331258\pi\) |
−0.664272 | + | 0.747491i | \(0.731258\pi\) | |||||||
\(350\) | −2.45591 | − | 7.55851i | −0.131274 | − | 0.404019i | ||||
\(351\) | 9.41348 | 0.502454 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.5749 | 1.30799 | 0.653994 | − | 0.756500i | \(-0.273092\pi\) | ||||
0.653994 | + | 0.756500i | \(0.273092\pi\) | |||||||
\(354\) | 24.7839 | + | 76.2769i | 1.31725 | + | 4.05407i | ||||
\(355\) | 2.03654 | + | 1.47963i | 0.108088 | + | 0.0785308i | ||||
\(356\) | −30.7366 | + | 22.3315i | −1.62904 | + | 1.18357i | ||||
\(357\) | 11.1852 | − | 34.4244i | 0.591982 | − | 1.82193i | ||||
\(358\) | −2.46467 | + | 7.58548i | −0.130262 | + | 0.400905i | ||||
\(359\) | 5.32861 | − | 3.87146i | 0.281233 | − | 0.204328i | −0.438222 | − | 0.898867i | \(-0.644392\pi\) |
0.719455 | + | 0.694539i | \(0.244392\pi\) | |||||||
\(360\) | 15.0368 | + | 10.9249i | 0.792510 | + | 0.575792i | ||||
\(361\) | −2.67707 | − | 8.23917i | −0.140898 | − | 0.433641i | ||||
\(362\) | −13.3835 | −0.703421 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.6453 | −0.924864 | ||||||||
\(365\) | 0.916356 | + | 2.82026i | 0.0479643 | + | 0.147619i | ||||
\(366\) | 74.5092 | + | 54.1341i | 3.89466 | + | 2.82963i | ||||
\(367\) | −6.60838 | + | 4.80127i | −0.344955 | + | 0.250624i | −0.746749 | − | 0.665105i | \(-0.768387\pi\) |
0.401795 | + | 0.915730i | \(0.368387\pi\) | |||||||
\(368\) | −1.03990 | + | 3.20048i | −0.0542084 | + | 0.166836i | ||||
\(369\) | 7.33564 | − | 22.5768i | 0.381878 | − | 1.17530i | ||||
\(370\) | −5.12659 | + | 3.72469i | −0.266519 | + | 0.193637i | ||||
\(371\) | −6.89064 | − | 5.00635i | −0.357744 | − | 0.259917i | ||||
\(372\) | 28.7077 | + | 88.3532i | 1.48842 | + | 4.58090i | ||||
\(373\) | −27.0409 | −1.40012 | −0.700061 | − | 0.714083i | \(-0.746844\pi\) | ||||
−0.700061 | + | 0.714083i | \(0.746844\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.86620 | −0.148010 | ||||||||
\(376\) | −11.5963 | − | 35.6899i | −0.598036 | − | 1.84057i | ||||
\(377\) | −5.63512 | − | 4.09415i | −0.290223 | − | 0.210860i | ||||
\(378\) | 40.8212 | − | 29.6583i | 2.09962 | − | 1.52546i | ||||
\(379\) | 10.0931 | − | 31.0634i | 0.518448 | − | 1.59562i | −0.258471 | − | 0.966019i | \(-0.583219\pi\) |
0.776919 | − | 0.629600i | \(-0.216781\pi\) | |||||||
\(380\) | 3.49451 | − | 10.7550i | 0.179264 | − | 0.551719i | ||||
\(381\) | −26.1941 | + | 19.0311i | −1.34196 | + | 0.974994i | ||||
\(382\) | 17.1344 | + | 12.4489i | 0.876672 | + | 0.636940i | ||||
\(383\) | −0.817806 | − | 2.51695i | −0.0417879 | − | 0.128610i | 0.927986 | − | 0.372615i | \(-0.121539\pi\) |
−0.969774 | + | 0.244005i | \(0.921539\pi\) | |||||||
\(384\) | −58.2034 | −2.97018 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 61.6157 | 3.13616 | ||||||||
\(387\) | 8.67580 | + | 26.7014i | 0.441015 | + | 1.35731i | ||||
\(388\) | −31.3487 | − | 22.7762i | −1.59149 | − | 1.15628i | ||||
\(389\) | 23.5030 | − | 17.0759i | 1.19165 | − | 0.865784i | 0.198212 | − | 0.980159i | \(-0.436487\pi\) |
0.993438 | + | 0.114375i | \(0.0364865\pi\) | |||||||
\(390\) | −3.08464 | + | 9.49354i | −0.156197 | + | 0.480724i | ||||
\(391\) | 2.90339 | − | 8.93572i | 0.146831 | − | 0.451899i | ||||
\(392\) | −12.8253 | + | 9.31812i | −0.647775 | + | 0.470636i | ||||
\(393\) | 34.0398 | + | 24.7313i | 1.71708 | + | 1.24753i | ||||
\(394\) | −12.1201 | − | 37.3017i | −0.610600 | − | 1.87923i | ||||
\(395\) | −6.76700 | −0.340485 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.35977 | −0.469753 | −0.234877 | − | 0.972025i | \(-0.575469\pi\) | ||||
−0.234877 | + | 0.972025i | \(0.575469\pi\) | |||||||
\(398\) | −12.1878 | − | 37.5103i | −0.610921 | − | 1.88022i | ||||
\(399\) | −25.2246 | − | 18.3267i | −1.26281 | − | 0.917484i | ||||
\(400\) | −1.08151 | + | 0.785763i | −0.0540755 | + | 0.0392881i | ||||
\(401\) | 1.52370 | − | 4.68945i | 0.0760897 | − | 0.234180i | −0.905776 | − | 0.423756i | \(-0.860711\pi\) |
0.981866 | + | 0.189576i | \(0.0607113\pi\) | |||||||
\(402\) | 16.2930 | − | 50.1448i | 0.812623 | − | 2.50100i | ||||
\(403\) | −11.0537 | + | 8.03102i | −0.550626 | + | 0.400053i | ||||
\(404\) | 36.2308 | + | 26.3232i | 1.80255 | + | 1.30963i | ||||
\(405\) | −0.788584 | − | 2.42701i | −0.0391851 | − | 0.120599i | ||||
\(406\) | −37.3356 | −1.85294 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −38.1268 | −1.88756 | ||||||||
\(409\) | −11.8380 | − | 36.4335i | −0.585350 | − | 1.80152i | −0.597862 | − | 0.801599i | \(-0.703983\pi\) |
0.0125120 | − | 0.999922i | \(-0.496017\pi\) | |||||||
\(410\) | 8.64998 | + | 6.28458i | 0.427192 | + | 0.310373i | ||||
\(411\) | 36.2783 | − | 26.3577i | 1.78948 | − | 1.30013i | ||||
\(412\) | −19.9372 | + | 61.3604i | −0.982235 | + | 3.02301i | ||||
\(413\) | −12.4556 | + | 38.3345i | −0.612901 | + | 1.88632i | ||||
\(414\) | 24.9470 | − | 18.1251i | 1.22608 | − | 0.890799i | ||||
\(415\) | 6.10963 | + | 4.43890i | 0.299910 | + | 0.217897i | ||||
\(416\) | −1.82718 | − | 5.62348i | −0.0895849 | − | 0.275714i | ||||
\(417\) | 21.9129 | 1.07308 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.3777 | 1.82602 | 0.913009 | − | 0.407938i | \(-0.133752\pi\) | ||||
0.913009 | + | 0.407938i | \(0.133752\pi\) | |||||||
\(420\) | 10.5406 | + | 32.4406i | 0.514328 | + | 1.58294i | ||||
\(421\) | −23.7950 | − | 17.2881i | −1.15970 | − | 0.842571i | −0.169959 | − | 0.985451i | \(-0.554364\pi\) |
−0.989740 | + | 0.142880i | \(0.954364\pi\) | |||||||
\(422\) | −14.5283 | + | 10.5554i | −0.707226 | + | 0.513830i | ||||
\(423\) | −16.9686 | + | 52.2241i | −0.825044 | + | 2.53922i | ||||
\(424\) | −2.77239 | + | 8.53253i | −0.134639 | + | 0.414377i | ||||
\(425\) | 3.01957 | − | 2.19385i | 0.146471 | − | 0.106417i | ||||
\(426\) | −13.7108 | − | 9.96148i | −0.664291 | − | 0.482635i | ||||
\(427\) | 14.3031 | + | 44.0205i | 0.692177 | + | 2.13030i | ||||
\(428\) | 25.0917 | 1.21286 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.6453 | −0.609809 | ||||||||
\(431\) | 0.546405 | + | 1.68166i | 0.0263194 | + | 0.0810027i | 0.963353 | − | 0.268235i | \(-0.0864405\pi\) |
−0.937034 | + | 0.349238i | \(0.886440\pi\) | |||||||
\(432\) | −6.86639 | − | 4.98873i | −0.330359 | − | 0.240020i | ||||
\(433\) | −8.13168 | + | 5.90801i | −0.390784 | + | 0.283921i | −0.765777 | − | 0.643107i | \(-0.777645\pi\) |
0.374993 | + | 0.927028i | \(0.377645\pi\) | |||||||
\(434\) | −22.6314 | + | 69.6524i | −1.08634 | + | 3.34342i | ||||
\(435\) | −4.16085 | + | 12.8058i | −0.199497 | + | 0.613990i | ||||
\(436\) | −11.7973 | + | 8.57127i | −0.564990 | + | 0.410489i | ||||
\(437\) | −6.54767 | − | 4.75716i | −0.313218 | − | 0.227566i | ||||
\(438\) | −6.16928 | − | 18.9871i | −0.294779 | − | 0.907238i | ||||
\(439\) | 39.1972 | 1.87078 | 0.935390 | − | 0.353618i | \(-0.115049\pi\) | ||||
0.935390 | + | 0.353618i | \(0.115049\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.1972 | 1.10463 | ||||||||
\(442\) | −4.01685 | − | 12.3626i | −0.191062 | − | 0.588029i | ||||
\(443\) | 11.3360 | + | 8.23609i | 0.538590 | + | 0.391308i | 0.823561 | − | 0.567228i | \(-0.191984\pi\) |
−0.284971 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(444\) | 22.0030 | − | 15.9861i | 1.04422 | − | 0.758667i | ||||
\(445\) | −3.33788 | + | 10.2729i | −0.158231 | + | 0.486984i | ||||
\(446\) | −2.75063 | + | 8.46557i | −0.130246 | + | 0.400856i | ||||
\(447\) | −15.0321 | + | 10.9215i | −0.710994 | + | 0.516567i | ||||
\(448\) | −32.9596 | − | 23.9465i | −1.55719 | − | 1.13137i | ||||
\(449\) | 0.796047 | + | 2.44998i | 0.0375678 | + | 0.115622i | 0.968082 | − | 0.250635i | \(-0.0806393\pi\) |
−0.930514 | + | 0.366256i | \(0.880639\pi\) | |||||||
\(450\) | 12.2497 | 0.577456 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5.15212 | 0.242335 | ||||||||
\(453\) | 9.63493 | + | 29.6533i | 0.452688 | + | 1.39323i | ||||
\(454\) | 37.1433 | + | 26.9862i | 1.74322 | + | 1.26653i | ||||
\(455\) | −4.05860 | + | 2.94875i | −0.190270 | + | 0.138239i | ||||
\(456\) | −10.1489 | + | 31.2350i | −0.475265 | + | 1.46271i | ||||
\(457\) | 4.67287 | − | 14.3816i | 0.218588 | − | 0.672744i | −0.780292 | − | 0.625416i | \(-0.784929\pi\) |
0.998879 | − | 0.0473280i | \(-0.0150706\pi\) | |||||||
\(458\) | −9.81043 | + | 7.12769i | −0.458411 | + | 0.333055i | ||||
\(459\) | 19.1709 | + | 13.9285i | 0.894823 | + | 0.650127i | ||||
\(460\) | 2.73607 | + | 8.42077i | 0.127570 | + | 0.392621i | ||||
\(461\) | 9.83622 | 0.458118 | 0.229059 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229059 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2093 | 0.985678 | 0.492839 | − | 0.870120i | \(-0.335959\pi\) | ||||
0.492839 | + | 0.870120i | \(0.335959\pi\) | |||||||
\(464\) | 1.94066 | + | 5.97273i | 0.0900927 | + | 0.277277i | ||||
\(465\) | 21.3680 | + | 15.5247i | 0.990917 | + | 0.719943i | ||||
\(466\) | −11.8763 | + | 8.62862i | −0.550158 | + | 0.399713i | ||||
\(467\) | −2.95543 | + | 9.09589i | −0.136761 | + | 0.420908i | −0.995860 | − | 0.0909024i | \(-0.971025\pi\) |
0.859099 | + | 0.511810i | \(0.171025\pi\) | |||||||
\(468\) | 8.40439 | − | 25.8661i | 0.388493 | − | 1.19566i | ||||
\(469\) | 21.4375 | − | 15.5753i | 0.989892 | − | 0.719198i | ||||
\(470\) | −20.0089 | − | 14.5373i | −0.922943 | − | 0.670557i | ||||
\(471\) | 9.23806 | + | 28.4318i | 0.425667 | + | 1.31007i | ||||
\(472\) | 42.4573 | 1.95426 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 45.5582 | 2.09256 | ||||||||
\(475\) | −0.993518 | − | 3.05773i | −0.0455857 | − | 0.140298i | ||||
\(476\) | −35.9353 | − | 26.1086i | −1.64709 | − | 1.19668i | ||||
\(477\) | 10.6208 | − | 7.71643i | 0.486291 | − | 0.353311i | ||||
\(478\) | 3.34665 | − | 10.2999i | 0.153072 | − | 0.471107i | ||||
\(479\) | −5.31422 | + | 16.3555i | −0.242813 | + | 0.747302i | 0.753175 | + | 0.657820i | \(0.228521\pi\) |
−0.995988 | + | 0.0894820i | \(0.971479\pi\) | |||||||
\(480\) | −9.24721 | + | 6.71849i | −0.422076 | + | 0.306656i | ||||
\(481\) | 3.23607 | + | 2.35114i | 0.147552 | + | 0.107203i | ||||
\(482\) | 5.71843 | + | 17.5995i | 0.260467 | + | 0.801636i | ||||
\(483\) | 24.4123 | 1.11080 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.0167 | −0.500243 | ||||||||
\(486\) | −8.51594 | − | 26.2094i | −0.386291 | − | 1.18888i | ||||
\(487\) | −12.5818 | − | 9.14118i | −0.570134 | − | 0.414227i | 0.265020 | − | 0.964243i | \(-0.414621\pi\) |
−0.835154 | + | 0.550016i | \(0.814621\pi\) | |||||||
\(488\) | 39.4436 | − | 28.6574i | 1.78553 | − | 1.29726i | ||||
\(489\) | −9.07304 | + | 27.9239i | −0.410297 | + | 1.26276i | ||||
\(490\) | −3.22864 | + | 9.93672i | −0.145855 | + | 0.448895i | ||||
\(491\) | 7.32869 | − | 5.32460i | 0.330739 | − | 0.240296i | −0.410005 | − | 0.912083i | \(-0.634473\pi\) |
0.740744 | + | 0.671787i | \(0.234473\pi\) | |||||||
\(492\) | −37.1251 | − | 26.9730i | −1.67373 | − | 1.21604i | ||||
\(493\) | −5.41831 | − | 16.6758i | −0.244028 | − | 0.751042i | ||||
\(494\) | −11.1972 | −0.503785 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.3189 | 0.553136 | ||||||||
\(497\) | −2.63199 | − | 8.10044i | −0.118061 | − | 0.363354i | ||||
\(498\) | −41.1324 | − | 29.8845i | −1.84319 | − | 1.33915i | ||||
\(499\) | −19.8764 | + | 14.4411i | −0.889791 | + | 0.646471i | −0.935824 | − | 0.352469i | \(-0.885342\pi\) |
0.0460324 | + | 0.998940i | \(0.485342\pi\) | |||||||
\(500\) | −1.08691 | + | 3.34515i | −0.0486079 | + | 0.149600i | ||||
\(501\) | −0.927051 | + | 2.85317i | −0.0414176 | + | 0.127470i | ||||
\(502\) | −20.2490 | + | 14.7118i | −0.903759 | + | 0.656619i | ||||
\(503\) | 9.16793 | + | 6.66089i | 0.408778 | + | 0.296995i | 0.773107 | − | 0.634276i | \(-0.218702\pi\) |
−0.364329 | + | 0.931270i | \(0.618702\pi\) | |||||||
\(504\) | −19.4333 | − | 59.8096i | −0.865629 | − | 2.66413i | ||||
\(505\) | 12.7324 | 0.566584 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.9596 | −1.37496 | ||||||||
\(508\) | 12.2781 | + | 37.7882i | 0.544753 | + | 1.67658i | ||||
\(509\) | 21.4300 | + | 15.5698i | 0.949868 | + | 0.690120i | 0.950776 | − | 0.309880i | \(-0.100289\pi\) |
−0.000907460 | 1.00000i | \(0.500289\pi\) | ||||||||
\(510\) | −20.3290 | + | 14.7699i | −0.900181 | + | 0.654020i | ||||
\(511\) | 3.10049 | − | 9.54234i | 0.137158 | − | 0.422128i | ||||
\(512\) | −4.59198 | + | 14.1327i | −0.202939 | + | 0.624581i | ||||
\(513\) | 16.5139 | − | 11.9980i | 0.729106 | − | 0.529726i | ||||
\(514\) | −5.33804 | − | 3.87831i | −0.235451 | − | 0.171065i | ||||
\(515\) | 5.66832 | + | 17.4453i | 0.249776 | + | 0.768731i | ||||
\(516\) | 54.2727 | 2.38922 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 21.4406 | 0.942048 | ||||||||
\(519\) | 10.5513 | + | 32.4735i | 0.463150 | + | 1.42543i | ||||
\(520\) | 4.27510 | + | 3.10604i | 0.187475 | + | 0.136209i | ||||
\(521\) | −21.5980 | + | 15.6919i | −0.946225 | + | 0.687473i | −0.949911 | − | 0.312520i | \(-0.898827\pi\) |
0.00368574 | + | 0.999993i | \(0.498827\pi\) | |||||||
\(522\) | 17.7828 | − | 54.7300i | 0.778334 | − | 2.39547i | ||||
\(523\) | −1.50001 | + | 4.61655i | −0.0655907 | + | 0.201867i | −0.978481 | − | 0.206338i | \(-0.933845\pi\) |
0.912890 | + | 0.408206i | \(0.133845\pi\) | |||||||
\(524\) | 41.7725 | − | 30.3495i | 1.82484 | − | 1.32582i | ||||
\(525\) | 7.84568 | + | 5.70022i | 0.342413 | + | 0.248778i | ||||
\(526\) | 20.0663 | + | 61.7576i | 0.874931 | + | 2.69276i | ||||
\(527\) | −34.3944 | −1.49824 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6632 | −0.724486 | ||||||||
\(530\) | 1.82718 | + | 5.62348i | 0.0793677 | + | 0.244269i | ||||
\(531\) | −50.2616 | − | 36.5172i | −2.18117 | − | 1.58471i | ||||
\(532\) | −30.9548 | + | 22.4900i | −1.34206 | + | 0.975063i | ||||
\(533\) | 2.08559 | − | 6.41878i | 0.0903368 | − | 0.278028i | ||||
\(534\) | 22.4719 | − | 69.1615i | 0.972456 | − | 2.99291i | ||||
\(535\) | 5.77137 | − | 4.19314i | 0.249518 | − | 0.181285i | ||||
\(536\) | −22.5810 | − | 16.4061i | −0.975352 | − | 0.708635i | ||||
\(537\) | −3.00748 | − | 9.25606i | −0.129782 | − | 0.399428i | ||||
\(538\) | −34.2376 | −1.47609 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −22.3310 | −0.960973 | ||||||||
\(541\) | 6.12613 | + | 18.8543i | 0.263383 | + | 0.810609i | 0.992062 | + | 0.125753i | \(0.0401347\pi\) |
−0.728679 | + | 0.684856i | \(0.759865\pi\) | |||||||
\(542\) | 4.10954 | + | 2.98576i | 0.176520 | + | 0.128249i | ||||
\(543\) | 13.2120 | − | 9.59912i | 0.566983 | − | 0.411937i | ||||
\(544\) | 4.59957 | − | 14.1560i | 0.197205 | − | 0.606934i | ||||
\(545\) | −1.28115 | + | 3.94296i | −0.0548783 | + | 0.168898i | ||||
\(546\) | 27.3241 | − | 19.8521i | 1.16936 | − | 0.849592i | ||||
\(547\) | −11.8567 | − | 8.61443i | −0.506958 | − | 0.368326i | 0.304711 | − | 0.952445i | \(-0.401440\pi\) |
−0.811668 | + | 0.584119i | \(0.801440\pi\) | |||||||
\(548\) | −17.0050 | − | 52.3359i | −0.726416 | − | 2.23568i | ||||
\(549\) | −71.3419 | −3.04480 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.1038 | −0.643445 | ||||||||
\(552\) | −7.94622 | − | 24.4559i | −0.338213 | − | 1.04091i | ||||
\(553\) | 18.5234 | + | 13.4580i | 0.787695 | + | 0.572294i | ||||
\(554\) | 29.0787 | − | 21.1269i | 1.23544 | − | 0.897597i | ||||
\(555\) | 2.38944 | − | 7.35395i | 0.101426 | − | 0.312158i | ||||
\(556\) | 8.30970 | − | 25.5746i | 0.352410 | − | 1.08461i | ||||
\(557\) | −4.72257 | + | 3.43115i | −0.200102 | + | 0.145382i | −0.683324 | − | 0.730115i | \(-0.739466\pi\) |
0.483222 | + | 0.875498i | \(0.339466\pi\) | |||||||
\(558\) | −91.3236 | − | 66.3504i | −3.86603 | − | 2.80884i | ||||
\(559\) | 2.46660 | + | 7.59143i | 0.104326 | + | 0.321083i | ||||
\(560\) | 4.52313 | 0.191137 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.02295 | 0.211880 | ||||||||
\(563\) | −12.1452 | − | 37.3790i | −0.511858 | − | 1.57534i | −0.788926 | − | 0.614488i | \(-0.789363\pi\) |
0.277068 | − | 0.960850i | \(-0.410637\pi\) | |||||||
\(564\) | 85.8769 | + | 62.3932i | 3.61607 | + | 2.62723i | ||||
\(565\) | 1.18504 | − | 0.860984i | 0.0498551 | − | 0.0362219i | ||||
\(566\) | 3.14364 | − | 9.67514i | 0.132137 | − | 0.406676i | ||||
\(567\) | −2.66818 | + | 8.21180i | −0.112053 | + | 0.344863i | ||||
\(568\) | −7.25821 | + | 5.27340i | −0.304548 | + | 0.221267i | ||||
\(569\) | 6.56118 | + | 4.76698i | 0.275059 | + | 0.199842i | 0.716759 | − | 0.697320i | \(-0.245625\pi\) |
−0.441700 | + | 0.897163i | \(0.645625\pi\) | |||||||
\(570\) | 6.68876 | + | 20.5859i | 0.280161 | + | 0.862248i | ||||
\(571\) | 35.6274 | 1.49096 | 0.745480 | − | 0.666528i | \(-0.232220\pi\) | ||||
0.745480 | + | 0.666528i | \(0.232220\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.8437 | −1.07963 | ||||||||
\(574\) | −11.1791 | − | 34.4057i | −0.466606 | − | 1.43607i | ||||
\(575\) | 2.03654 | + | 1.47963i | 0.0849297 | + | 0.0617050i | ||||
\(576\) | 50.8015 | − | 36.9095i | 2.11673 | − | 1.53790i | ||||
\(577\) | −9.84310 | + | 30.2939i | −0.409773 | + | 1.26115i | 0.507070 | + | 0.861905i | \(0.330729\pi\) |
−0.916843 | + | 0.399248i | \(0.869271\pi\) | |||||||
\(578\) | −2.22779 | + | 6.85642i | −0.0926636 | + | 0.285189i | ||||
\(579\) | −60.8264 | + | 44.1929i | −2.52786 | + | 1.83660i | ||||
\(580\) | 13.3678 | + | 9.71230i | 0.555069 | + | 0.403281i | ||||
\(581\) | −7.89598 | − | 24.3013i | −0.327580 | − | 1.00819i | ||||
\(582\) | 74.1688 | 3.07440 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.5686 | −0.437332 | ||||||||
\(585\) | −2.38944 | − | 7.35395i | −0.0987913 | − | 0.304048i | ||||
\(586\) | 25.6670 | + | 18.6482i | 1.06029 | + | 0.770349i | ||||
\(587\) | 35.9060 | − | 26.0873i | 1.48200 | − | 1.07674i | 0.505096 | − | 0.863063i | \(-0.331457\pi\) |
0.976905 | − | 0.213673i | \(-0.0685428\pi\) | |||||||
\(588\) | 13.8571 | − | 42.6477i | 0.571457 | − | 1.75876i | ||||
\(589\) | −9.15536 | + | 28.1773i | −0.377240 | + | 1.16103i | ||||
\(590\) | 22.6380 | − | 16.4475i | 0.931991 | − | 0.677131i | ||||
\(591\) | 38.7189 | + | 28.1309i | 1.59268 | + | 1.15715i | ||||
\(592\) | −1.11446 | − | 3.42994i | −0.0458039 | − | 0.140970i | ||||
\(593\) | −41.9463 | −1.72253 | −0.861264 | − | 0.508158i | \(-0.830327\pi\) | ||||
−0.861264 | + | 0.508158i | \(0.830327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.6286 | −0.517721 | ||||||||
\(596\) | 7.04609 | + | 21.6856i | 0.288619 | + | 0.888278i | ||||
\(597\) | 38.9354 | + | 28.2882i | 1.59352 | + | 1.15776i | ||||
\(598\) | 7.09266 | − | 5.15312i | 0.290040 | − | 0.210727i | ||||
\(599\) | 5.13298 | − | 15.7977i | 0.209728 | − | 0.645476i | −0.789758 | − | 0.613418i | \(-0.789794\pi\) |
0.999486 | − | 0.0320576i | \(-0.0102060\pi\) | |||||||
\(600\) | 3.15664 | − | 9.71513i | 0.128869 | − | 0.396619i | ||||
\(601\) | 10.6768 | − | 7.75711i | 0.435514 | − | 0.316419i | −0.348336 | − | 0.937370i | \(-0.613253\pi\) |
0.783850 | + | 0.620950i | \(0.213253\pi\) | |||||||
\(602\) | 34.6141 | + | 25.1486i | 1.41076 | + | 1.02498i | ||||
\(603\) | 12.6210 | + | 38.8435i | 0.513968 | + | 1.58183i | ||||
\(604\) | 38.2622 | 1.55687 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −85.7195 | −3.48212 | ||||||||
\(607\) | −2.79378 | − | 8.59836i | −0.113396 | − | 0.348997i | 0.878213 | − | 0.478269i | \(-0.158736\pi\) |
−0.991609 | + | 0.129273i | \(0.958736\pi\) | |||||||
\(608\) | −10.3729 | − | 7.53632i | −0.420675 | − | 0.305638i | ||||
\(609\) | 36.8573 | − | 26.7784i | 1.49353 | − | 1.08512i | ||||
\(610\) | 9.92952 | − | 30.5599i | 0.402035 | − | 1.23734i | ||||
\(611\) | −4.82433 | + | 14.8478i | −0.195172 | + | 0.600676i | ||||
\(612\) | 55.3882 | − | 40.2419i | 2.23894 | − | 1.62668i | ||||
\(613\) | 6.19964 | + | 4.50430i | 0.250401 | + | 0.181927i | 0.705905 | − | 0.708307i | \(-0.250541\pi\) |
−0.455503 | + | 0.890234i | \(0.650541\pi\) | |||||||
\(614\) | −1.72670 | − | 5.31424i | −0.0696839 | − | 0.214465i | ||||
\(615\) | −13.0467 | −0.526093 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.67989 | −0.107888 | −0.0539441 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539441 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(618\) | −38.1614 | − | 117.449i | −1.53508 | − | 4.72448i | ||||
\(619\) | −6.61310 | − | 4.80470i | −0.265803 | − | 0.193117i | 0.446899 | − | 0.894585i | \(-0.352529\pi\) |
−0.712701 | + | 0.701468i | \(0.752529\pi\) | |||||||
\(620\) | 26.2221 | − | 19.0515i | 1.05310 | − | 0.765125i | ||||
\(621\) | −4.93874 | + | 15.1999i | −0.198185 | + | 0.609950i | ||||
\(622\) | −16.0737 | + | 49.4697i | −0.644496 | + | 1.98355i | ||||
\(623\) | 29.5674 | − | 21.4820i | 1.18459 | − | 0.860656i | ||||
\(624\) | −4.59609 | − | 3.33926i | −0.183991 | − | 0.133677i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | −64.0880 | −2.56147 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.6861 | 1.46394 | ||||||||
\(629\) | 3.11156 | + | 9.57639i | 0.124066 | + | 0.381836i | ||||
\(630\) | −33.5312 | − | 24.3619i | −1.33592 | − | 0.970600i | ||||
\(631\) | −4.50608 | + | 3.27386i | −0.179384 | + | 0.130330i | −0.673854 | − | 0.738865i | \(-0.735362\pi\) |
0.494470 | + | 0.869195i | \(0.335362\pi\) | |||||||
\(632\) | 7.45272 | − | 22.9371i | 0.296453 | − | 0.912390i | ||||
\(633\) | 6.77145 | − | 20.8404i | 0.269141 | − | 0.828331i | ||||
\(634\) | 29.2561 | − | 21.2558i | 1.16191 | − | 0.844177i | ||||
\(635\) | 9.13897 | + | 6.63985i | 0.362669 | + | 0.263494i | ||||
\(636\) | −7.84213 | − | 24.1356i | −0.310961 | − | 0.957039i | ||||
\(637\) | 6.59516 | 0.261310 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1280 | 0.519335 | ||||||||
\(640\) | 6.27516 | + | 19.3130i | 0.248047 | + | 0.763412i | ||||
\(641\) | 10.7523 | + | 7.81199i | 0.424690 | + | 0.308555i | 0.779522 | − | 0.626375i | \(-0.215462\pi\) |
−0.354832 | + | 0.934930i | \(0.615462\pi\) | |||||||
\(642\) | −38.8551 | + | 28.2299i | −1.53349 | + | 1.11415i | ||||
\(643\) | 5.50473 | − | 16.9418i | 0.217085 | − | 0.668120i | −0.781914 | − | 0.623387i | \(-0.785756\pi\) |
0.998999 | − | 0.0447334i | \(-0.0142438\pi\) | |||||||
\(644\) | 9.25752 | − | 28.4917i | 0.364797 | − | 1.12273i | ||||
\(645\) | 12.4833 | − | 9.06964i | 0.491529 | − | 0.357117i | ||||
\(646\) | −22.8035 | − | 16.5677i | −0.897193 | − | 0.651849i | ||||
\(647\) | −7.99826 | − | 24.6161i | −0.314444 | − | 0.967759i | −0.975983 | − | 0.217848i | \(-0.930096\pi\) |
0.661539 | − | 0.749911i | \(-0.269904\pi\) | |||||||
\(648\) | 9.09498 | 0.357285 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.48270 | 0.136603 | ||||||||
\(651\) | −27.6156 | − | 84.9921i | −1.08234 | − | 3.33110i | ||||
\(652\) | 29.1495 | + | 21.1784i | 1.14158 | + | 0.829409i | ||||
\(653\) | −10.7887 | + | 7.83848i | −0.422196 | + | 0.306744i | −0.778521 | − | 0.627619i | \(-0.784030\pi\) |
0.356325 | + | 0.934362i | \(0.384030\pi\) | |||||||
\(654\) | 8.62518 | − | 26.5456i | 0.337271 | − | 1.03801i | ||||
\(655\) | 4.53633 | − | 13.9614i | 0.177249 | − | 0.545517i | ||||
\(656\) | −4.92294 | + | 3.57672i | −0.192208 | + | 0.139648i | ||||
\(657\) | 12.5113 | + | 9.08998i | 0.488112 | + | 0.354634i | ||||
\(658\) | 25.8592 | + | 79.5864i | 1.00810 | + | 3.10260i | ||||
\(659\) | −24.4877 | −0.953907 | −0.476954 | − | 0.878929i | \(-0.658259\pi\) | ||||
−0.476954 | + | 0.878929i | \(0.658259\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2738 | −0.905248 | −0.452624 | − | 0.891702i | \(-0.649512\pi\) | ||||
−0.452624 | + | 0.891702i | \(0.649512\pi\) | |||||||
\(662\) | 18.8088 | + | 57.8876i | 0.731026 | + | 2.24987i | ||||
\(663\) | 12.8323 | + | 9.32320i | 0.498364 | + | 0.362083i | ||||
\(664\) | −21.7746 | + | 15.8202i | −0.845019 | + | 0.613942i | ||||
\(665\) | −3.36157 | + | 10.3459i | −0.130356 | + | 0.401195i | ||||
\(666\) | −10.2121 | + | 31.4297i | −0.395711 | + | 1.21787i | ||||
\(667\) | 9.56724 | − | 6.95101i | 0.370445 | − | 0.269144i | ||||
\(668\) | 2.97840 | + | 2.16393i | 0.115238 | + | 0.0837250i | ||||
\(669\) | −3.35641 | − | 10.3300i | −0.129766 | − | 0.399380i | ||||
\(670\) | −18.3956 | −0.710683 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 38.6741 | 1.49188 | ||||||||
\(673\) | 3.50557 | + | 10.7890i | 0.135130 | + | 0.415887i | 0.995610 | − | 0.0935968i | \(-0.0298365\pi\) |
−0.860480 | + | 0.509484i | \(0.829836\pi\) | |||||||
\(674\) | −26.5701 | − | 19.3043i | −1.02344 | − | 0.743575i | ||||
\(675\) | −5.13636 | + | 3.73179i | −0.197699 | + | 0.143637i | ||||
\(676\) | −11.7403 | + | 36.1331i | −0.451552 | + | 1.38973i | ||||
\(677\) | −6.61160 | + | 20.3484i | −0.254104 | + | 0.782053i | 0.739901 | + | 0.672716i | \(0.234873\pi\) |
−0.994005 | + | 0.109336i | \(0.965127\pi\) | |||||||
\(678\) | −7.97818 | + | 5.79648i | −0.306400 | + | 0.222613i | ||||
\(679\) | 30.1561 | + | 21.9097i | 1.15729 | + | 0.840818i | ||||
\(680\) | 4.11061 | + | 12.6512i | 0.157635 | + | 0.485150i | ||||
\(681\) | −56.0230 | −2.14680 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.11590 | −0.195754 | −0.0978772 | − | 0.995198i | \(-0.531205\pi\) | ||||
−0.0978772 | + | 0.995198i | \(0.531205\pi\) | |||||||
\(684\) | −18.2242 | − | 56.0882i | −0.696819 | − | 2.14459i | ||||
\(685\) | −12.6573 | − | 9.19606i | −0.483610 | − | 0.351364i | ||||
\(686\) | −16.4079 | + | 11.9210i | −0.626457 | + | 0.455148i | ||||
\(687\) | 4.57252 | − | 14.0728i | 0.174452 | − | 0.536910i | ||||
\(688\) | 2.22392 | − | 6.84454i | 0.0847863 | − | 0.260946i | ||||
\(689\) | 3.01957 | − | 2.19385i | 0.115037 | − | 0.0835789i | ||||
\(690\) | −13.7108 | − | 9.96148i | −0.521961 | − | 0.379227i | ||||
\(691\) | −7.08010 | − | 21.7903i | −0.269340 | − | 0.828942i | −0.990662 | − | 0.136343i | \(-0.956465\pi\) |
0.721322 | − | 0.692600i | \(-0.243535\pi\) | |||||||
\(692\) | 41.9012 | 1.59285 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −72.9254 | −2.76821 | ||||||||
\(695\) | −2.36252 | − | 7.27109i | −0.0896155 | − | 0.275808i | ||||
\(696\) | −38.8234 | − | 28.2068i | −1.47160 | − | 1.06918i | ||||
\(697\) | 13.7448 | − | 9.98620i | 0.520622 | − | 0.378254i | ||||
\(698\) | 2.65891 | − | 8.18329i | 0.100641 | − | 0.309742i | ||||
\(699\) | 5.53538 | − | 17.0362i | 0.209367 | − | 0.644367i | ||||
\(700\) | 9.62795 | − | 6.99512i | 0.363902 | − | 0.264391i | ||||
\(701\) | 30.6772 | + | 22.2883i | 1.15866 | + | 0.841818i | 0.989608 | − | 0.143789i | \(-0.0459287\pi\) |
0.169054 | + | 0.985607i | \(0.445929\pi\) | |||||||
\(702\) | 6.83276 | + | 21.0291i | 0.257886 | + | 0.793691i | ||||
\(703\) | 8.67364 | 0.327133 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.1793 | 1.13662 | ||||||||
\(706\) | 17.8376 | + | 54.8986i | 0.671328 | + | 2.06613i | ||||
\(707\) | −34.8525 | − | 25.3218i | −1.31076 | − | 0.952326i | ||||
\(708\) | −97.1607 | + | 70.5914i | −3.65152 | + | 2.65299i | ||||
\(709\) | −1.63064 | + | 5.01860i | −0.0612400 | + | 0.188477i | −0.976996 | − | 0.213258i | \(-0.931593\pi\) |
0.915756 | + | 0.401735i | \(0.131593\pi\) | |||||||
\(710\) | −1.82718 | + | 5.62348i | −0.0685729 | + | 0.211046i | ||||
\(711\) | −28.5507 | + | 20.7433i | −1.07073 | + | 0.777933i | ||||
\(712\) | −31.1446 | − | 22.6279i | −1.16719 | − | 0.848015i | ||||
\(713\) | −7.16833 | − | 22.0618i | −0.268456 | − | 0.826222i | ||||
\(714\) | 85.0206 | 3.18181 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.9433 | −0.446341 | ||||||||
\(717\) | 4.08369 | + | 12.5683i | 0.152508 | + | 0.469372i | ||||
\(718\) | 12.5163 | + | 9.09365i | 0.467105 | + | 0.339372i | ||||
\(719\) | −25.0081 | + | 18.1694i | −0.932644 | + | 0.677605i | −0.946639 | − | 0.322297i | \(-0.895545\pi\) |
0.0139948 | + | 0.999902i | \(0.495545\pi\) | |||||||
\(720\) | −2.15435 | + | 6.63042i | −0.0802881 | + | 0.247101i | ||||
\(721\) | 19.1788 | − | 59.0262i | 0.714255 | − | 2.19825i | ||||
\(722\) | 16.4626 | − | 11.9608i | 0.612675 | − | 0.445134i | ||||
\(723\) | −18.2682 | − | 13.2726i | −0.679400 | − | 0.493613i | ||||
\(724\) | −6.19296 | − | 19.0600i | −0.230160 | − | 0.708359i | ||||
\(725\) | 4.69779 | 0.174471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.24387 | 0.305748 | 0.152874 | − | 0.988246i | \(-0.451147\pi\) | ||||
0.152874 | + | 0.988246i | \(0.451147\pi\) | |||||||
\(728\) | −5.52506 | − | 17.0044i | −0.204772 | − | 0.630225i | ||||
\(729\) | 33.3987 | + | 24.2656i | 1.23699 | + | 0.898726i | ||||
\(730\) | −5.63512 | + | 4.09415i | −0.208565 | + | 0.151531i | ||||
\(731\) | −6.20919 | + | 19.1099i | −0.229655 | + | 0.706806i | ||||
\(732\) | −42.6168 | + | 131.161i | −1.57516 | + | 4.84785i | ||||
\(733\) | −35.0983 | + | 25.5004i | −1.29639 | + | 0.941880i | −0.999913 | − | 0.0131614i | \(-0.995810\pi\) |
−0.296473 | + | 0.955041i | \(0.595810\pi\) | |||||||
\(734\) | −15.5224 | − | 11.2777i | −0.572942 | − | 0.416267i | ||||
\(735\) | −3.93969 | − | 12.1251i | −0.145318 | − | 0.447242i | ||||
\(736\) | 10.0388 | 0.370036 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 55.7596 | 2.05254 | ||||||||
\(739\) | 0.0930184 | + | 0.286281i | 0.00342174 | + | 0.0105310i | 0.952753 | − | 0.303747i | \(-0.0982377\pi\) |
−0.949331 | + | 0.314278i | \(0.898238\pi\) | |||||||
\(740\) | −7.67672 | − | 5.57746i | −0.282202 | − | 0.205032i | ||||
\(741\) | 11.0537 | − | 8.03102i | 0.406069 | − | 0.295027i | ||||
\(742\) | 6.18227 | − | 19.0271i | 0.226958 | − | 0.698506i | ||||
\(743\) | 9.73528 | − | 29.9621i | 0.357153 | − | 1.09920i | −0.597598 | − | 0.801796i | \(-0.703878\pi\) |
0.954751 | − | 0.297407i | \(-0.0961220\pi\) | |||||||
\(744\) | −76.1552 | + | 55.3300i | −2.79199 | + | 2.02850i | ||||
\(745\) | 5.24461 | + | 3.81043i | 0.192148 | + | 0.139603i | ||||
\(746\) | −19.6276 | − | 60.4074i | −0.718616 | − | 2.21167i | ||||
\(747\) | 39.3839 | 1.44098 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.1372 | −0.881955 | ||||||||
\(750\) | −2.08042 | − | 6.40289i | −0.0759664 | − | 0.233800i | ||||
\(751\) | −26.9326 | − | 19.5677i | −0.982785 | − | 0.714035i | −0.0244560 | − | 0.999701i | \(-0.507785\pi\) |
−0.958329 | + | 0.285665i | \(0.907785\pi\) | |||||||
\(752\) | 11.3876 | − | 8.27359i | 0.415264 | − | 0.301707i | ||||
\(753\) | 9.43783 | − | 29.0466i | 0.343934 | − | 1.05852i | ||||
\(754\) | 5.05582 | − | 15.5602i | 0.184122 | − | 0.566669i | ||||
\(755\) | 8.80071 | − | 6.39409i | 0.320291 | − | 0.232705i | ||||
\(756\) | 61.1269 | + | 44.4113i | 2.22316 | + | 1.61522i | ||||
\(757\) | 4.79188 | + | 14.7479i | 0.174164 | + | 0.536021i | 0.999594 | − | 0.0284827i | \(-0.00906756\pi\) |
−0.825430 | + | 0.564504i | \(0.809068\pi\) | |||||||
\(758\) | 76.7195 | 2.78658 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.4585 | 0.415645 | ||||||||
\(761\) | −16.1908 | − | 49.8300i | −0.586914 | − | 1.80634i | −0.591443 | − | 0.806347i | \(-0.701441\pi\) |
0.00452850 | − | 0.999990i | \(-0.498559\pi\) | |||||||
\(762\) | −61.5271 | − | 44.7021i | −2.22889 | − | 1.61939i | ||||
\(763\) | 11.3486 | − | 8.24521i | 0.410845 | − | 0.298496i | ||||
\(764\) | −9.80032 | + | 30.1623i | −0.354563 | + | 1.09123i | ||||
\(765\) | 6.01495 | − | 18.5121i | 0.217471 | − | 0.669307i | ||||
\(766\) | 5.02908 | − | 3.65384i | 0.181708 | − | 0.132019i | ||||
\(767\) | −14.2898 | − | 10.3822i | −0.515975 | − | 0.374878i | ||||
\(768\) | −20.9176 | − | 64.3777i | −0.754799 | − | 2.32303i | ||||
\(769\) | 44.2652 | 1.59624 | 0.798122 | − | 0.602496i | \(-0.205827\pi\) | ||||
0.798122 | + | 0.602496i | \(0.205827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.05131 | 0.289961 | ||||||||
\(772\) | 28.5115 | + | 87.7494i | 1.02615 | + | 3.15817i | ||||
\(773\) | 28.5726 | + | 20.7592i | 1.02769 | + | 0.746658i | 0.967844 | − | 0.251550i | \(-0.0809403\pi\) |
0.0598420 | + | 0.998208i | \(0.480940\pi\) | |||||||
\(774\) | −53.3517 | + | 38.7623i | −1.91769 | + | 1.39328i | ||||
\(775\) | 2.84762 | − | 8.76407i | 0.102290 | − | 0.314815i | ||||
\(776\) | 12.1331 | − | 37.3417i | 0.435551 | − | 1.34049i | ||||
\(777\) | −21.1660 | + | 15.3780i | −0.759325 | + | 0.551682i | ||||
\(778\) | 55.2061 | + | 40.1096i | 1.97923 | + | 1.43800i | ||||
\(779\) | −4.52241 | − | 13.9185i | −0.162032 | − | 0.498683i | ||||
\(780\) | −14.9475 | −0.535206 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 22.0692 | 0.789194 | ||||||||
\(783\) | 9.21667 | + | 28.3660i | 0.329377 | + | 1.01372i | ||||
\(784\) | −4.81065 | − | 3.49514i | −0.171809 | − | 0.124827i | ||||
\(785\) | 8.43820 | − | 6.13071i | 0.301172 | − | 0.218814i | ||||
\(786\) | −30.5404 | + | 93.9937i | −1.08934 | + | 3.35264i | ||||
\(787\) | −11.3384 | + | 34.8961i | −0.404172 | + | 1.24391i | 0.517413 | + | 0.855736i | \(0.326895\pi\) |
−0.921585 | + | 0.388177i | \(0.873105\pi\) | |||||||
\(788\) | 47.5145 | − | 34.5213i | 1.69264 | − | 1.22977i | ||||
\(789\) | −64.1040 | − | 46.5742i | −2.28216 | − | 1.65809i | ||||
\(790\) | −4.91182 | − | 15.1170i | −0.174755 | − | 0.537840i | ||||
\(791\) | −4.95613 | −0.176220 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2831 | −0.720274 | ||||||||
\(794\) | −6.79377 | − | 20.9091i | −0.241102 | − | 0.742036i | ||||
\(795\) | −5.83713 | − | 4.24092i | −0.207022 | − | 0.150410i | ||||
\(796\) | 47.7802 | − | 34.7144i | 1.69352 | − | 1.23042i | ||||
\(797\) | −0.881973 | + | 2.71443i | −0.0312411 | + | 0.0961501i | −0.965461 | − | 0.260547i | \(-0.916097\pi\) |
0.934220 | + | 0.356697i | \(0.116097\pi\) | |||||||
\(798\) | 22.6314 | − | 69.6524i | 0.801144 | − | 2.46567i | ||||
\(799\) | −31.7942 | + | 23.0999i | −1.12480 | + | 0.817214i | ||||
\(800\) | 3.22630 | + | 2.34404i | 0.114067 | + | 0.0828745i | ||||
\(801\) | 17.4074 | + | 53.5744i | 0.615059 | + | 1.89296i | ||||
\(802\) | 11.5819 | 0.408971 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 78.9525 | 2.78444 | ||||||||
\(805\) | −2.63199 | − | 8.10044i | −0.0927655 | − | 0.285503i | ||||
\(806\) | −25.9641 | − | 18.8640i | −0.914546 | − | 0.664456i | ||||
\(807\) | 33.7990 | − | 24.5564i | 1.18978 | − | 0.864427i | ||||
\(808\) | −14.0226 | + | 43.1571i | −0.493313 | + | 1.51826i | ||||
\(809\) | −8.06329 | + | 24.8163i | −0.283490 | + | 0.872493i | 0.703357 | + | 0.710837i | \(0.251684\pi\) |
−0.986847 | + | 0.161656i | \(0.948316\pi\) | |||||||
\(810\) | 4.84939 | − | 3.52329i | 0.170390 | − | 0.123796i | ||||
\(811\) | −15.8934 | − | 11.5472i | −0.558091 | − | 0.405477i | 0.272668 | − | 0.962108i | \(-0.412094\pi\) |
−0.830760 | + | 0.556631i | \(0.812094\pi\) | |||||||
\(812\) | −17.2764 | − | 53.1712i | −0.606281 | − | 1.86594i | ||||
\(813\) | −6.19839 | −0.217387 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.2439 | 0.358827 | ||||||||
\(816\) | −4.41926 | − | 13.6011i | −0.154705 | − | 0.476133i | ||||
\(817\) | 14.0028 | + | 10.1737i | 0.489897 | + | 0.355931i | ||||
\(818\) | 72.7974 | − | 52.8904i | 2.54530 | − | 1.84927i | ||||
\(819\) | −8.08468 | + | 24.8821i | −0.282502 | + | 0.869451i | ||||
\(820\) | −4.94750 | + | 15.2269i | −0.172774 | + | 0.531745i | ||||
\(821\) | −41.9974 | + | 30.5129i | −1.46572 | + | 1.06491i | −0.483894 | + | 0.875126i | \(0.660778\pi\) |
−0.981826 | + | 0.189782i | \(0.939222\pi\) | |||||||
\(822\) | 85.2139 | + | 61.9115i | 2.97218 | + | 2.15941i | ||||
\(823\) | 4.92108 | + | 15.1455i | 0.171538 | + | 0.527940i | 0.999458 | − | 0.0329056i | \(-0.0104761\pi\) |
−0.827920 | + | 0.560846i | \(0.810476\pi\) | |||||||
\(824\) | −65.3744 | −2.27743 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −94.6775 | −3.29425 | ||||||||
\(827\) | −3.01960 | − | 9.29338i | −0.105002 | − | 0.323162i | 0.884729 | − | 0.466106i | \(-0.154343\pi\) |
−0.989731 | + | 0.142943i | \(0.954343\pi\) | |||||||
\(828\) | 37.3564 | + | 27.1410i | 1.29823 | + | 0.943216i | ||||
\(829\) | −0.823501 | + | 0.598308i | −0.0286014 | + | 0.0207801i | −0.601994 | − | 0.798501i | \(-0.705627\pi\) |
0.573393 | + | 0.819281i | \(0.305627\pi\) | |||||||
\(830\) | −5.48154 | + | 16.8705i | −0.190267 | + | 0.585582i | ||||
\(831\) | −13.5532 | + | 41.7126i | −0.470156 | + | 1.44699i | ||||
\(832\) | 14.4433 | − | 10.4937i | 0.500732 | − | 0.363803i | ||||
\(833\) | 13.4313 | + | 9.75843i | 0.465368 | + | 0.338109i | ||||
\(834\) | 15.9054 | + | 48.9519i | 0.550760 | + | 1.69506i | ||||
\(835\) | 1.04668 | 0.0362219 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 58.5056 | 2.02225 | ||||||||
\(838\) | 27.1305 | + | 83.4992i | 0.937208 | + | 2.88443i | ||||
\(839\) | −11.1563 | − | 8.10553i | −0.385159 | − | 0.279834i | 0.378310 | − | 0.925679i | \(-0.376505\pi\) |
−0.763469 | + | 0.645845i | \(0.776505\pi\) | |||||||
\(840\) | −27.9619 | + | 20.3155i | −0.964777 | + | 0.700951i | ||||
\(841\) | −2.14173 | + | 6.59157i | −0.0738528 | + | 0.227295i | ||||
\(842\) | 21.3489 | − | 65.7050i | 0.735730 | − | 2.26434i | ||||
\(843\) | −4.95860 | + | 3.60264i | −0.170783 | + | 0.124081i | ||||
\(844\) | −21.7551 | − | 15.8060i | −0.748841 | − | 0.544065i | ||||
\(845\) | 3.33788 | + | 10.2729i | 0.114827 | + | 0.353400i | ||||
\(846\) | −128.982 | −4.43448 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.36518 | −0.115561 | ||||||||
\(849\) | 3.83598 | + | 11.8059i | 0.131650 | + | 0.405178i | ||||
\(850\) | 7.09266 | + | 5.15312i | 0.243276 | + | 0.176750i | ||||
\(851\) | −5.49416 | + | 3.99174i | −0.188337 | + | 0.136835i | ||||
\(852\) | 7.84213 | − | 24.1356i | 0.268667 | − | 0.826872i | ||||
\(853\) | 8.44431 | − | 25.9889i | 0.289128 | − | 0.889843i | −0.696003 | − | 0.718039i | \(-0.745040\pi\) |
0.985131 | − | 0.171805i | \(-0.0549599\pi\) | |||||||
\(854\) | −87.9569 | + | 63.9044i | −3.00982 | + | 2.18677i | ||||
\(855\) | −13.5648 | − | 9.85540i | −0.463906 | − | 0.337048i | ||||
\(856\) | 7.85669 | + | 24.1804i | 0.268536 | + | 0.826469i | ||||
\(857\) | 22.2318 | 0.759424 | 0.379712 | − | 0.925105i | \(-0.376023\pi\) | ||||
0.379712 | + | 0.925105i | \(0.376023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5173 | 0.972998 | 0.486499 | − | 0.873681i | \(-0.338274\pi\) | ||||
0.486499 | + | 0.873681i | \(0.338274\pi\) | |||||||
\(860\) | −5.85136 | − | 18.0086i | −0.199530 | − | 0.614090i | ||||
\(861\) | 35.7128 | + | 25.9469i | 1.21709 | + | 0.884268i | ||||
\(862\) | −3.36011 | + | 2.44126i | −0.114446 | + | 0.0831497i | ||||
\(863\) | 16.1490 | − | 49.7016i | 0.549720 | − | 1.69186i | −0.159776 | − | 0.987153i | \(-0.551077\pi\) |
0.709496 | − | 0.704710i | \(-0.248923\pi\) | |||||||
\(864\) | −7.82398 | + | 24.0797i | −0.266177 | + | 0.819209i | ||||
\(865\) | 9.63772 | − | 7.00222i | 0.327692 | − | 0.238082i | ||||
\(866\) | −19.1005 | − | 13.8773i | −0.649060 | − | 0.471570i | ||||
\(867\) | −2.71842 | − | 8.36643i | −0.0923223 | − | 0.284139i | ||||
\(868\) | −109.667 | −3.72234 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −31.6274 | −1.07227 | ||||||||
\(871\) | 3.58826 | + | 11.0435i | 0.121584 | + | 0.374196i | ||||
\(872\) | −11.9539 | − | 8.68503i | −0.404811 | − | 0.294112i | ||||
\(873\) | −46.4806 | + | 33.7701i | −1.57313 | + | 1.14294i | ||||
\(874\) | 5.87455 | − | 18.0800i | 0.198710 | − | 0.611566i | ||||
\(875\) | 1.04556 | − | 3.21790i | 0.0353464 | − | 0.108785i | ||||
\(876\) | 24.1855 | − | 17.5718i | 0.817154 | − | 0.593697i | ||||
\(877\) | 16.9954 | + | 12.3479i | 0.573893 | + | 0.416958i | 0.836517 | − | 0.547940i | \(-0.184588\pi\) |
−0.262624 | + | 0.964898i | \(0.584588\pi\) | |||||||
\(878\) | 28.4512 | + | 87.5638i | 0.960182 | + | 2.95514i | ||||
\(879\) | −38.7133 | −1.30577 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0743 | 1.55228 | 0.776141 | − | 0.630560i | \(-0.217175\pi\) | ||||
0.776141 | + | 0.630560i | \(0.217175\pi\) | |||||||
\(882\) | 16.8376 | + | 51.8209i | 0.566953 | + | 1.74490i | ||||
\(883\) | −0.503472 | − | 0.365794i | −0.0169432 | − | 0.0123100i | 0.579281 | − | 0.815128i | \(-0.303333\pi\) |
−0.596225 | + | 0.802818i | \(0.703333\pi\) | |||||||
\(884\) | 15.7473 | − | 11.4411i | 0.529641 | − | 0.384806i | ||||
\(885\) | −10.5513 | + | 32.4735i | −0.354678 | + | 1.09159i | ||||
\(886\) | −10.1706 | + | 31.3020i | −0.341689 | + | 1.05161i | ||||
\(887\) | −9.22898 | + | 6.70525i | −0.309879 | + | 0.225140i | −0.731845 | − | 0.681472i | \(-0.761340\pi\) |
0.421966 | + | 0.906612i | \(0.361340\pi\) | |||||||
\(888\) | 22.2950 | + | 16.1983i | 0.748172 | + | 0.543579i | ||||
\(889\) | −11.8110 | − | 36.3507i | −0.396130 | − | 1.21916i | ||||
\(890\) | −25.3718 | −0.850466 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.3290 | −0.446287 | ||||||||
\(893\) | 10.4611 | + | 32.1960i | 0.350068 | + | 1.07740i | ||||
\(894\) | −35.3088 | − | 25.6533i | −1.18090 | − | 0.857976i | ||||
\(895\) | −2.74708 | + | 1.99587i | −0.0918247 | + | 0.0667146i | ||||
\(896\) | 21.2320 | − | 65.3454i | 0.709312 | − | 2.18304i | ||||
\(897\) | −3.30580 | + | 10.1742i | −0.110377 | + | 0.339707i | ||||
\(898\) | −4.89528 | + | 3.55663i | −0.163358 | + | 0.118686i | ||||
\(899\) | −35.0228 | − | 25.4455i | −1.16808 | − | 0.848657i | ||||
\(900\) | 5.66832 | + | 17.4453i | 0.188944 | + | 0.581510i | ||||
\(901\) | 9.39558 | 0.313012 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −52.2081 | −1.73738 | ||||||||
\(904\) | 1.61322 | + | 4.96499i | 0.0536550 | + | 0.165133i | ||||
\(905\) | −4.60961 | − | 3.34908i | −0.153229 | − | 0.111327i | ||||
\(906\) | −59.2499 | + | 43.0475i | −1.96844 | + | 1.43016i | ||||
\(907\) | 12.0262 | − | 37.0128i | 0.399323 | − | 1.22899i | −0.526221 | − | 0.850348i | \(-0.676392\pi\) |
0.925544 | − | 0.378641i | \(-0.123608\pi\) | |||||||
\(908\) | −21.2448 | + | 65.3847i | −0.705032 | + | 2.16987i | ||||
\(909\) | 53.7192 | − | 39.0293i | 1.78175 | − | 1.29452i | ||||
\(910\) | −9.53322 | − | 6.92629i | −0.316023 | − | 0.229604i | ||||
\(911\) | 11.7715 | + | 36.2289i | 0.390007 | + | 1.20032i | 0.932782 | + | 0.360440i | \(0.117374\pi\) |
−0.542775 | + | 0.839878i | \(0.682626\pi\) | |||||||
\(912\) | −12.3189 | −0.407920 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 35.5193 | 1.17488 | ||||||||
\(915\) | 12.1163 | + | 37.2902i | 0.400553 | + | 1.23278i | ||||
\(916\) | −14.6904 | − | 10.6732i | −0.485385 | − | 0.352653i | ||||
\(917\) | −40.1834 | + | 29.1950i | −1.32697 | + | 0.964102i | ||||
\(918\) | −17.2001 | + | 52.9366i | −0.567689 | + | 1.74717i | ||||
\(919\) | −5.95558 | + | 18.3294i | −0.196456 | + | 0.604630i | 0.803500 | + | 0.595305i | \(0.202969\pi\) |
−0.999957 | + | 0.00932595i | \(0.997031\pi\) | |||||||
\(920\) | −7.25821 | + | 5.27340i | −0.239296 | + | 0.173859i | ||||
\(921\) | 5.51614 | + | 4.00771i | 0.181763 | + | 0.132058i | ||||
\(922\) | 7.13960 | + | 21.9734i | 0.235130 | + | 0.723657i | ||||
\(923\) | 3.73240 | 0.122853 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.69779 | −0.0887027 | ||||||||
\(926\) | 15.3947 | + | 47.3800i | 0.505901 | + | 1.55700i | ||||
\(927\) | 77.3912 | + | 56.2280i | 2.54186 | + | 1.84677i | ||||
\(928\) | 15.1565 | − | 11.0118i | 0.497536 | − | 0.361481i | ||||
\(929\) | 9.63300 | − | 29.6473i | 0.316048 | − | 0.972697i | −0.659272 | − | 0.751904i | \(-0.729136\pi\) |
0.975321 | − | 0.220793i | \(-0.0708645\pi\) | |||||||
\(930\) | −19.1713 | + | 59.0032i | −0.628652 | + | 1.93479i | ||||
\(931\) | 11.5698 | − | 8.40593i | 0.379184 | − | 0.275493i | ||||
\(932\) | −17.7839 | − | 12.9208i | −0.582531 | − | 0.423233i | ||||
\(933\) | −19.6136 | − | 60.3645i | −0.642121 | − | 1.97625i | ||||
\(934\) | −22.4648 | −0.735070 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 27.5582 | 0.900767 | ||||||||
\(937\) | −7.99453 | − | 24.6046i | −0.261170 | − | 0.803798i | −0.992551 | − | 0.121829i | \(-0.961124\pi\) |
0.731381 | − | 0.681969i | \(-0.238876\pi\) | |||||||
\(938\) | 50.3544 | + | 36.5846i | 1.64413 | + | 1.19453i | ||||
\(939\) | 63.2669 | − | 45.9661i | 2.06464 | − | 1.50005i | ||||
\(940\) | 11.4445 | − | 35.2224i | 0.373277 | − | 1.14883i | ||||
\(941\) | −9.10475 | + | 28.0215i | −0.296806 | + | 0.913476i | 0.685802 | + | 0.727788i | \(0.259451\pi\) |
−0.982609 | + | 0.185688i | \(0.940549\pi\) | |||||||
\(942\) | −56.8093 | + | 41.2744i | −1.85095 | + | 1.34479i | ||||
\(943\) | 9.27016 | + | 6.73516i | 0.301878 | + | 0.219327i | ||||
\(944\) | 4.92121 | + | 15.1459i | 0.160172 | + | 0.492958i | ||||
\(945\) | 21.4815 | 0.698793 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.3881 | −0.467551 | −0.233776 | − | 0.972291i | \(-0.575108\pi\) | ||||
−0.233776 | + | 0.972291i | \(0.575108\pi\) | |||||||
\(948\) | 21.0812 | + | 64.8812i | 0.684685 | + | 2.10724i | ||||
\(949\) | 3.55707 | + | 2.58436i | 0.115467 | + | 0.0838919i | ||||
\(950\) | 6.10963 | − | 4.43890i | 0.198222 | − | 0.144017i | ||||
\(951\) | −13.6359 | + | 41.9671i | −0.442175 | + | 1.36088i | ||||
\(952\) | 13.9083 | − | 42.8052i | 0.450769 | − | 1.38732i | ||||
\(953\) | −25.8231 | + | 18.7616i | −0.836493 | + | 0.607748i | −0.921389 | − | 0.388642i | \(-0.872944\pi\) |
0.0848960 | + | 0.996390i | \(0.472944\pi\) | |||||||
\(954\) | 24.9470 | + | 18.1251i | 0.807690 | + | 0.586821i | ||||
\(955\) | 2.78632 | + | 8.57540i | 0.0901630 | + | 0.277493i | ||||
\(956\) | 16.2171 | 0.524499 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −40.3944 | −1.30508 | ||||||||
\(959\) | 16.3581 | + | 50.3450i | 0.528230 | + | 1.62572i | ||||
\(960\) | −27.9204 | − | 20.2853i | −0.901126 | − | 0.654706i | ||||
\(961\) | −43.6205 | + | 31.6922i | −1.40711 | + | 1.02233i | ||||
\(962\) | −2.90339 | + | 8.93572i | −0.0936091 | + | 0.288099i | ||||
\(963\) | 11.4965 | − | 35.3826i | 0.370469 | − | 1.14019i | ||||
\(964\) | −22.4181 | + | 16.2877i | −0.722038 | + | 0.524591i | ||||
\(965\) | 21.2220 | + | 15.4187i | 0.683159 | + | 0.496344i | ||||
\(966\) | 17.7196 | + | 54.5354i | 0.570119 | + | 1.75465i | ||||
\(967\) | −46.8425 | −1.50635 | −0.753176 | − | 0.657819i | \(-0.771479\pi\) | ||||
−0.753176 | + | 0.657819i | \(0.771479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.3944 | 1.10491 | ||||||||
\(970\) | −7.99646 | − | 24.6106i | −0.256751 | − | 0.790197i | ||||
\(971\) | 5.38966 | + | 3.91582i | 0.172962 | + | 0.125664i | 0.670898 | − | 0.741549i | \(-0.265909\pi\) |
−0.497936 | + | 0.867214i | \(0.665909\pi\) | |||||||
\(972\) | 33.3852 | − | 24.2558i | 1.07083 | − | 0.778005i | ||||
\(973\) | −7.99359 | + | 24.6018i | −0.256263 | + | 0.788696i | ||||
\(974\) | 11.2883 | − | 34.7419i | 0.361701 | − | 1.11320i | ||||
\(975\) | −3.43808 | + | 2.49791i | −0.110107 | + | 0.0799972i | ||||
\(976\) | 14.7949 | + | 10.7491i | 0.473574 | + | 0.344072i | ||||
\(977\) | −7.47697 | − | 23.0118i | −0.239210 | − | 0.736211i | −0.996535 | − | 0.0831737i | \(-0.973494\pi\) |
0.757326 | − | 0.653038i | \(-0.226506\pi\) | |||||||
\(978\) | −68.9658 | −2.20528 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −15.6453 | −0.499770 | ||||||||
\(981\) | 6.68130 | + | 20.5629i | 0.213317 | + | 0.656523i | ||||
\(982\) | 17.2143 | + | 12.5069i | 0.549331 | + | 0.399112i | ||||
\(983\) | 22.4677 | − | 16.3238i | 0.716609 | − | 0.520647i | −0.168690 | − | 0.985669i | \(-0.553954\pi\) |
0.885299 | + | 0.465022i | \(0.153954\pi\) | |||||||
\(984\) | 14.3687 | − | 44.2224i | 0.458059 | − | 1.40976i | ||||
\(985\) | 5.15990 | − | 15.8805i | 0.164408 | − | 0.505996i | ||||
\(986\) | 33.3198 | − | 24.2082i | 1.06112 | − | 0.770948i | ||||
\(987\) | −82.6101 | − | 60.0197i | −2.62951 | − | 1.91045i | ||||
\(988\) | −5.18129 | − | 15.9464i | −0.164839 | − | 0.507322i | ||||
\(989\) | −13.5519 | −0.430926 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.4227 | 1.44290 | 0.721450 | − | 0.692466i | \(-0.243476\pi\) | ||||
0.721450 | + | 0.692466i | \(0.243476\pi\) | |||||||
\(992\) | −11.3561 | − | 34.9505i | −0.360556 | − | 1.10968i | ||||
\(993\) | −60.0869 | − | 43.6557i | −1.90680 | − | 1.38537i | ||||
\(994\) | 16.1854 | − | 11.7594i | 0.513369 | − | 0.372985i | ||||
\(995\) | 5.18875 | − | 15.9693i | 0.164494 | − | 0.506262i | ||||
\(996\) | 23.5264 | − | 72.4068i | 0.745462 | − | 2.29430i | ||||
\(997\) | 41.0569 | − | 29.8296i | 1.30028 | − | 0.944712i | 0.300326 | − | 0.953837i | \(-0.402904\pi\) |
0.999958 | + | 0.00912447i | \(0.00290445\pi\) | |||||||
\(998\) | −46.6876 | − | 33.9205i | −1.47787 | − | 1.07374i | ||||
\(999\) | −5.29283 | − | 16.2897i | −0.167458 | − | 0.515382i |
(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 | 605.2.g.o.511.3 | 12 | ||
11.2 | odd | 10 | 605.2.g.p.251.1 | 12 | |||
11.3 | even | 5 | 605.2.a.h.1.3 | yes | 3 | ||
11.4 | even | 5 | inner | 605.2.g.o.366.1 | 12 | ||
11.5 | even | 5 | inner | 605.2.g.o.81.1 | 12 | ||
11.6 | odd | 10 | 605.2.g.p.81.3 | 12 | |||
11.7 | odd | 10 | 605.2.g.p.366.3 | 12 | |||
11.8 | odd | 10 | 605.2.a.g.1.1 | ✓ | 3 | ||
11.9 | even | 5 | inner | 605.2.g.o.251.3 | 12 | ||
11.10 | odd | 2 | 605.2.g.p.511.1 | 12 | |||
33.8 | even | 10 | 5445.2.a.bd.1.3 | 3 | |||
33.14 | odd | 10 | 5445.2.a.bb.1.1 | 3 | |||
44.3 | odd | 10 | 9680.2.a.cb.1.1 | 3 | |||
44.19 | even | 10 | 9680.2.a.bz.1.1 | 3 | |||
55.14 | even | 10 | 3025.2.a.p.1.1 | 3 | |||
55.19 | odd | 10 | 3025.2.a.u.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.g.1.1 | ✓ | 3 | 11.8 | odd | 10 | ||
605.2.a.h.1.3 | yes | 3 | 11.3 | even | 5 | ||
605.2.g.o.81.1 | 12 | 11.5 | even | 5 | inner | ||
605.2.g.o.251.3 | 12 | 11.9 | even | 5 | inner | ||
605.2.g.o.366.1 | 12 | 11.4 | even | 5 | inner | ||
605.2.g.o.511.3 | 12 | 1.1 | even | 1 | trivial | ||
605.2.g.p.81.3 | 12 | 11.6 | odd | 10 | |||
605.2.g.p.251.1 | 12 | 11.2 | odd | 10 | |||
605.2.g.p.366.3 | 12 | 11.7 | odd | 10 | |||
605.2.g.p.511.1 | 12 | 11.10 | odd | 2 | |||
3025.2.a.p.1.1 | 3 | 55.14 | even | 10 | |||
3025.2.a.u.1.3 | 3 | 55.19 | odd | 10 | |||
5445.2.a.bb.1.1 | 3 | 33.14 | odd | 10 | |||
5445.2.a.bd.1.3 | 3 | 33.8 | even | 10 | |||
9680.2.a.bz.1.1 | 3 | 44.19 | even | 10 | |||
9680.2.a.cb.1.1 | 3 | 44.3 | odd | 10 |