Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(9,605)]
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([5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.j (of order \(10\), 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: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.6879707136000000000000.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 124.1 | ||
Root | \(1.83730 - 0.596975i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.124 |
Dual form | 605.2.j.f.444.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13551 | − | 1.56290i | −0.802930 | − | 1.10514i | −0.992376 | − | 0.123247i | \(-0.960669\pi\) |
0.189446 | − | 0.981891i | \(-0.439331\pi\) | |||||||
\(3\) | −0.492303 | + | 0.159959i | −0.284231 | + | 0.0923524i | −0.447663 | − | 0.894202i | \(-0.647744\pi\) |
0.163432 | + | 0.986555i | \(0.447744\pi\) | |||||||
\(4\) | −0.535233 | + | 1.64728i | −0.267617 | + | 0.823639i | ||||
\(5\) | 2.23251 | − | 0.126049i | 0.998410 | − | 0.0563708i | ||||
\(6\) | 0.809017 | + | 0.587785i | 0.330280 | + | 0.239962i | ||||
\(7\) | 0.852694 | + | 0.277057i | 0.322288 | + | 0.104718i | 0.465693 | − | 0.884946i | \(-0.345805\pi\) |
−0.143405 | + | 0.989664i | \(0.545805\pi\) | |||||||
\(8\) | −0.492303 | + | 0.159959i | −0.174055 | + | 0.0565540i | ||||
\(9\) | −2.21028 | + | 1.60586i | −0.736759 | + | 0.535286i | ||||
\(10\) | −2.73205 | − | 3.34607i | −0.863950 | − | 1.05812i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 0.896575i | − | 0.258819i | ||||||
\(13\) | −2.49376 | − | 3.43237i | −0.691645 | − | 0.951968i | −1.00000 | 0.000696272i | \(-0.999778\pi\) | |
0.308355 | − | 0.951271i | \(-0.400222\pi\) | |||||||
\(14\) | −0.535233 | − | 1.64728i | −0.143047 | − | 0.440254i | ||||
\(15\) | −1.07891 | + | 0.419165i | −0.278573 | + | 0.108228i | ||||
\(16\) | 3.61153 | + | 2.62393i | 0.902884 | + | 0.655983i | ||||
\(17\) | 0.608520 | − | 0.837556i | 0.147588 | − | 0.203137i | −0.728822 | − | 0.684703i | \(-0.759932\pi\) |
0.876410 | + | 0.481566i | \(0.159932\pi\) | |||||||
\(18\) | 5.01960 | + | 1.63097i | 1.18313 | + | 0.384422i | ||||
\(19\) | −1.91472 | − | 5.89289i | −0.439266 | − | 1.35192i | −0.888651 | − | 0.458584i | \(-0.848357\pi\) |
0.449385 | − | 0.893338i | \(-0.351643\pi\) | |||||||
\(20\) | −0.987277 | + | 3.74503i | −0.220762 | + | 0.837415i | ||||
\(21\) | −0.464102 | −0.101275 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.31319i | − | 1.31639i | −0.752847 | − | 0.658196i | \(-0.771320\pi\) | ||
0.752847 | − | 0.658196i | \(-0.228680\pi\) | |||||||
\(24\) | 0.216775 | − | 0.157497i | 0.0442491 | − | 0.0321489i | ||||
\(25\) | 4.96822 | − | 0.562811i | 0.993645 | − | 0.112562i | ||||
\(26\) | −2.53275 | + | 7.79500i | −0.496713 | + | 1.52873i | ||||
\(27\) | 1.74403 | − | 2.40046i | 0.335639 | − | 0.461968i | ||||
\(28\) | −0.912780 | + | 1.25633i | −0.172499 | + | 0.237425i | ||||
\(29\) | 2.14093 | − | 6.58911i | 0.397561 | − | 1.22357i | −0.529388 | − | 0.848380i | \(-0.677578\pi\) |
0.926949 | − | 0.375188i | \(-0.122422\pi\) | |||||||
\(30\) | 1.88023 | + | 1.21026i | 0.343281 | + | 0.220963i | ||||
\(31\) | 4.26186 | − | 3.09642i | 0.765453 | − | 0.556134i | −0.135125 | − | 0.990829i | \(-0.543144\pi\) |
0.900578 | + | 0.434695i | \(0.143144\pi\) | |||||||
\(32\) | − | 7.58871i | − | 1.34151i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 1.93857 | + | 0.511052i | 0.327679 | + | 0.0863836i | ||||
\(36\) | −1.46228 | − | 4.50045i | −0.243714 | − | 0.750075i | ||||
\(37\) | −6.36459 | − | 2.06798i | −1.04633 | − | 0.339974i | −0.265105 | − | 0.964220i | \(-0.585406\pi\) |
−0.781228 | + | 0.624246i | \(0.785406\pi\) | |||||||
\(38\) | −7.03582 | + | 9.68397i | −1.14136 | + | 1.57095i | ||||
\(39\) | 1.77672 | + | 1.29087i | 0.284504 | + | 0.206704i | ||||
\(40\) | −1.07891 | + | 0.419165i | −0.170591 | + | 0.0662757i | ||||
\(41\) | −0.535233 | − | 1.64728i | −0.0835894 | − | 0.257262i | 0.900523 | − | 0.434808i | \(-0.143184\pi\) |
−0.984112 | + | 0.177547i | \(0.943184\pi\) | |||||||
\(42\) | 0.526994 | + | 0.725345i | 0.0813169 | + | 0.111923i | ||||
\(43\) | 10.6945i | 1.63090i | 0.578827 | + | 0.815451i | \(0.303511\pi\) | ||||
−0.578827 | + | 0.815451i | \(0.696489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.73205 | + | 3.86370i | −0.705412 | + | 0.575967i | ||||
\(46\) | −9.86689 | + | 7.16872i | −1.45479 | + | 1.05697i | ||||
\(47\) | 3.90308 | − | 1.26819i | 0.569323 | − | 0.184984i | −0.0101891 | − | 0.999948i | \(-0.503243\pi\) |
0.579512 | + | 0.814964i | \(0.303243\pi\) | |||||||
\(48\) | −2.19769 | − | 0.714073i | −0.317209 | − | 0.103068i | ||||
\(49\) | −5.01279 | − | 3.64201i | −0.716113 | − | 0.520287i | ||||
\(50\) | −6.52111 | − | 7.12576i | −0.922224 | − | 1.00773i | ||||
\(51\) | −0.165602 | + | 0.509670i | −0.0231889 | + | 0.0713680i | ||||
\(52\) | 6.98881 | − | 2.27080i | 0.969174 | − | 0.314904i | ||||
\(53\) | −7.03582 | − | 9.68397i | −0.966444 | − | 1.33020i | −0.943823 | − | 0.330452i | \(-0.892799\pi\) |
−0.0226209 | − | 0.999744i | \(-0.507201\pi\) | |||||||
\(54\) | −5.73205 | −0.780033 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.464102 | −0.0620182 | ||||||||
\(57\) | 1.88524 | + | 2.59481i | 0.249706 | + | 0.343691i | ||||
\(58\) | −12.7292 | + | 4.13596i | −1.67142 | + | 0.543079i | ||||
\(59\) | 1.46228 | − | 4.50045i | 0.190373 | − | 0.585908i | −0.809626 | − | 0.586946i | \(-0.800330\pi\) |
0.999999 | + | 0.00103733i | \(0.000330192\pi\) | |||||||
\(60\) | −0.113012 | − | 2.00162i | −0.0145898 | − | 0.258407i | ||||
\(61\) | 6.68891 | + | 4.85978i | 0.856427 | + | 0.622231i | 0.926911 | − | 0.375282i | \(-0.122454\pi\) |
−0.0704833 | + | 0.997513i | \(0.522454\pi\) | |||||||
\(62\) | −9.67880 | − | 3.14483i | −1.22921 | − | 0.399394i | ||||
\(63\) | −2.32960 | + | 0.756934i | −0.293502 | + | 0.0953647i | ||||
\(64\) | −4.63733 | + | 3.36921i | −0.579666 | + | 0.421152i | ||||
\(65\) | −6.00000 | − | 7.34847i | −0.744208 | − | 0.911465i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.9372i | 1.82487i | 0.409226 | + | 0.912433i | \(0.365799\pi\) | ||||
−0.409226 | + | 0.912433i | \(0.634201\pi\) | |||||||
\(68\) | 1.05399 | + | 1.45069i | 0.127815 | + | 0.175922i | ||||
\(69\) | 1.00985 | + | 3.10800i | 0.121572 | + | 0.374160i | ||||
\(70\) | −1.40255 | − | 3.61010i | −0.167637 | − | 0.431490i | ||||
\(71\) | −1.77672 | − | 1.29087i | −0.210858 | − | 0.153198i | 0.477344 | − | 0.878717i | \(-0.341600\pi\) |
−0.688202 | + | 0.725519i | \(0.741600\pi\) | |||||||
\(72\) | 0.831254 | − | 1.14412i | 0.0979642 | − | 0.134836i | ||||
\(73\) | 4.65921 | + | 1.51387i | 0.545319 | + | 0.177185i | 0.568705 | − | 0.822542i | \(-0.307445\pi\) |
−0.0233860 | + | 0.999727i | \(0.507445\pi\) | |||||||
\(74\) | 3.99503 | + | 12.2955i | 0.464413 | + | 1.42932i | ||||
\(75\) | −2.35584 | + | 1.07179i | −0.272030 | + | 0.123759i | ||||
\(76\) | 10.7321 | 1.23105 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 4.24264i | − | 0.480384i | ||||||
\(79\) | −4.42055 | + | 3.21172i | −0.497351 | + | 0.361347i | −0.808004 | − | 0.589177i | \(-0.799452\pi\) |
0.310653 | + | 0.950523i | \(0.399452\pi\) | |||||||
\(80\) | 8.39354 | + | 5.40273i | 0.938426 | + | 0.604044i | ||||
\(81\) | 2.05813 | − | 6.33428i | 0.228681 | − | 0.703809i | ||||
\(82\) | −1.96677 | + | 2.70702i | −0.217193 | + | 0.298941i | ||||
\(83\) | −5.81878 | + | 8.00886i | −0.638694 | + | 0.879087i | −0.998545 | − | 0.0539231i | \(-0.982827\pi\) |
0.359851 | + | 0.933010i | \(0.382827\pi\) | |||||||
\(84\) | 0.248403 | − | 0.764504i | 0.0271029 | − | 0.0834143i | ||||
\(85\) | 1.25296 | − | 1.94656i | 0.135902 | − | 0.211134i | ||||
\(86\) | 16.7145 | − | 12.1438i | 1.80237 | − | 1.30950i | ||||
\(87\) | 3.58630i | 0.384492i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.46410 | 0.685193 | 0.342597 | − | 0.939483i | \(-0.388694\pi\) | ||||
0.342597 | + | 0.939483i | \(0.388694\pi\) | |||||||
\(90\) | 11.4119 | + | 3.00844i | 1.20292 | + | 0.317117i | ||||
\(91\) | −1.17545 | − | 3.61767i | −0.123221 | − | 0.379235i | ||||
\(92\) | 10.3996 | + | 3.37903i | 1.08423 | + | 0.352288i | ||||
\(93\) | −1.60283 | + | 2.20610i | −0.166205 | + | 0.228762i | ||||
\(94\) | −6.41405 | − | 4.66008i | −0.661559 | − | 0.480651i | ||||
\(95\) | −5.01742 | − | 12.9146i | −0.514776 | − | 1.32501i | ||||
\(96\) | 1.21388 | + | 3.73594i | 0.123891 | + | 0.381298i | ||||
\(97\) | 0.385786 | + | 0.530989i | 0.0391707 | + | 0.0539138i | 0.828153 | − | 0.560502i | \(-0.189392\pi\) |
−0.788982 | + | 0.614416i | \(0.789392\pi\) | |||||||
\(98\) | 11.9700i | 1.20916i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.73205 | + | 8.48528i | −0.173205 | + | 0.848528i | ||||
\(101\) | 1.12640 | − | 0.818376i | 0.112081 | − | 0.0814315i | −0.530333 | − | 0.847789i | \(-0.677933\pi\) |
0.642414 | + | 0.766358i | \(0.277933\pi\) | |||||||
\(102\) | 0.984606 | − | 0.319918i | 0.0974905 | − | 0.0316766i | ||||
\(103\) | 4.03499 | + | 1.31105i | 0.397579 | + | 0.129181i | 0.500981 | − | 0.865458i | \(-0.332973\pi\) |
−0.103401 | + | 0.994640i | \(0.532973\pi\) | |||||||
\(104\) | 1.77672 | + | 1.29087i | 0.174222 | + | 0.126580i | ||||
\(105\) | −1.03611 | + | 0.0584995i | −0.101114 | + | 0.00570897i | ||||
\(106\) | −7.14582 | + | 21.9926i | −0.694063 | + | 2.13611i | ||||
\(107\) | −4.16690 | + | 1.35391i | −0.402830 | + | 0.130887i | −0.503423 | − | 0.864040i | \(-0.667926\pi\) |
0.100593 | + | 0.994928i | \(0.467926\pi\) | |||||||
\(108\) | 3.02076 | + | 4.15771i | 0.290672 | + | 0.400076i | ||||
\(109\) | 1.19615 | 0.114571 | 0.0572853 | − | 0.998358i | \(-0.481756\pi\) | ||||
0.0572853 | + | 0.998358i | \(0.481756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.46410 | 0.328798 | ||||||||
\(112\) | 2.35255 | + | 3.23801i | 0.222295 | + | 0.305963i | ||||
\(113\) | −2.68999 | + | 0.874032i | −0.253053 | + | 0.0822220i | −0.432797 | − | 0.901492i | \(-0.642473\pi\) |
0.179743 | + | 0.983714i | \(0.442473\pi\) | |||||||
\(114\) | 1.91472 | − | 5.89289i | 0.179330 | − | 0.551920i | ||||
\(115\) | −0.795771 | − | 14.0943i | −0.0742060 | − | 1.31430i | ||||
\(116\) | 9.70820 | + | 7.05342i | 0.901384 | + | 0.654894i | ||||
\(117\) | 11.0238 | + | 3.58185i | 1.01915 | + | 0.331142i | ||||
\(118\) | −8.69420 | + | 2.82492i | −0.800366 | + | 0.260055i | ||||
\(119\) | 0.750932 | − | 0.545584i | 0.0688378 | − | 0.0500136i | ||||
\(120\) | 0.464102 | − | 0.378937i | 0.0423665 | − | 0.0345921i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 15.9725i | − | 1.44608i | ||||||
\(123\) | 0.526994 | + | 0.725345i | 0.0475174 | + | 0.0654021i | ||||
\(124\) | 2.81958 | + | 8.67778i | 0.253206 | + | 0.779287i | ||||
\(125\) | 11.0207 | − | 1.88272i | 0.985719 | − | 0.168396i | ||||
\(126\) | 3.82831 | + | 2.78143i | 0.341053 | + | 0.247789i | ||||
\(127\) | 1.96677 | − | 2.70702i | 0.174522 | − | 0.240210i | −0.712791 | − | 0.701377i | \(-0.752569\pi\) |
0.887313 | + | 0.461167i | \(0.152569\pi\) | |||||||
\(128\) | −3.90308 | − | 1.26819i | −0.344987 | − | 0.112093i | ||||
\(129\) | −1.71069 | − | 5.26495i | −0.150618 | − | 0.463553i | ||||
\(130\) | −4.67185 | + | 17.7217i | −0.409748 | + | 1.55430i | ||||
\(131\) | 21.1244 | 1.84564 | 0.922822 | − | 0.385227i | \(-0.125877\pi\) | ||||
0.922822 | + | 0.385227i | \(0.125877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.55532i | − | 0.481707i | ||||||
\(134\) | 23.3453 | − | 16.9614i | 2.01673 | − | 1.46524i | ||||
\(135\) | 3.59100 | − | 5.57888i | 0.309064 | − | 0.480154i | ||||
\(136\) | −0.165602 | + | 0.509670i | −0.0142002 | + | 0.0437038i | ||||
\(137\) | 8.08980 | − | 11.1347i | 0.691159 | − | 0.951298i | −0.308841 | − | 0.951114i | \(-0.599941\pi\) |
1.00000 | 0.000184728i | \(-5.88009e-5\pi\) | ||||||||
\(138\) | 3.71080 | − | 5.10748i | 0.315884 | − | 0.434778i | ||||
\(139\) | −5.12612 | + | 15.7766i | −0.434791 | + | 1.33815i | 0.458509 | + | 0.888690i | \(0.348384\pi\) |
−0.893300 | + | 0.449461i | \(0.851616\pi\) | |||||||
\(140\) | −1.87943 | + | 2.91984i | −0.158841 | + | 0.246771i | ||||
\(141\) | −1.71864 | + | 1.24866i | −0.144736 | + | 0.105157i | ||||
\(142\) | 4.24264i | 0.356034i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.1962 | −1.01635 | ||||||||
\(145\) | 3.94911 | − | 14.9801i | 0.327956 | − | 1.24403i | ||||
\(146\) | −2.92457 | − | 9.00090i | −0.242039 | − | 0.744919i | ||||
\(147\) | 3.05038 | + | 0.991130i | 0.251592 | + | 0.0817470i | ||||
\(148\) | 6.81308 | − | 9.37740i | 0.560032 | − | 0.770818i | ||||
\(149\) | −11.1095 | − | 8.07150i | −0.910123 | − | 0.661243i | 0.0309232 | − | 0.999522i | \(-0.490155\pi\) |
−0.941046 | + | 0.338279i | \(0.890155\pi\) | |||||||
\(150\) | 4.35019 | + | 2.46492i | 0.355191 | + | 0.201260i | ||||
\(151\) | −1.91472 | − | 5.89289i | −0.155817 | − | 0.479557i | 0.842425 | − | 0.538813i | \(-0.181127\pi\) |
−0.998243 | + | 0.0592563i | \(0.981127\pi\) | |||||||
\(152\) | 1.88524 | + | 2.59481i | 0.152913 | + | 0.210467i | ||||
\(153\) | 2.82843i | 0.228665i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.12436 | − | 7.45001i | 0.732886 | − | 0.598399i | ||||
\(156\) | −3.07738 | + | 2.23585i | −0.246387 | + | 0.179011i | ||||
\(157\) | −11.4808 | + | 3.73032i | −0.916264 | + | 0.297712i | −0.728933 | − | 0.684585i | \(-0.759984\pi\) |
−0.187331 | + | 0.982297i | \(0.559984\pi\) | |||||||
\(158\) | 10.0392 | + | 3.26193i | 0.798675 | + | 0.259505i | ||||
\(159\) | 5.01279 | + | 3.64201i | 0.397540 | + | 0.288830i | ||||
\(160\) | −0.956548 | − | 16.9419i | −0.0756218 | − | 1.33937i | ||||
\(161\) | 1.74911 | − | 5.38322i | 0.137850 | − | 0.424257i | ||||
\(162\) | −12.2369 | + | 3.97601i | −0.961421 | + | 0.312384i | ||||
\(163\) | 4.46053 | + | 6.13939i | 0.349376 | + | 0.480874i | 0.947150 | − | 0.320790i | \(-0.103948\pi\) |
−0.597775 | + | 0.801664i | \(0.703948\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.1244 | 1.48434 | ||||||||
\(167\) | −1.13551 | − | 1.56290i | −0.0878687 | − | 0.120941i | 0.762820 | − | 0.646611i | \(-0.223814\pi\) |
−0.850688 | + | 0.525671i | \(0.823814\pi\) | |||||||
\(168\) | 0.228479 | − | 0.0742372i | 0.0176275 | − | 0.00572753i | ||||
\(169\) | −1.54508 | + | 4.75528i | −0.118853 | + | 0.365791i | ||||
\(170\) | −4.46502 | + | 0.252098i | −0.342452 | + | 0.0193350i | ||||
\(171\) | 13.6952 | + | 9.95015i | 1.04730 | + | 0.760907i | ||||
\(172\) | −17.6169 | − | 5.72407i | −1.34327 | − | 0.436456i | ||||
\(173\) | 7.25263 | − | 2.35652i | 0.551408 | − | 0.179163i | −0.0200438 | − | 0.999799i | \(-0.506381\pi\) |
0.571451 | + | 0.820636i | \(0.306381\pi\) | |||||||
\(174\) | 5.60503 | − | 4.07230i | 0.424917 | − | 0.308720i | ||||
\(175\) | 4.39230 | + | 0.896575i | 0.332027 | + | 0.0677747i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.44949i | 0.184115i | ||||||||
\(178\) | −7.34008 | − | 10.1027i | −0.550162 | − | 0.757233i | ||||
\(179\) | 2.63774 | + | 8.11812i | 0.197154 | + | 0.606777i | 0.999945 | + | 0.0105163i | \(0.00334750\pi\) |
−0.802791 | + | 0.596261i | \(0.796652\pi\) | |||||||
\(180\) | −3.83184 | − | 9.86299i | −0.285609 | − | 0.735144i | ||||
\(181\) | −2.74443 | − | 1.99395i | −0.203992 | − | 0.148209i | 0.481099 | − | 0.876666i | \(-0.340238\pi\) |
−0.685091 | + | 0.728457i | \(0.740238\pi\) | |||||||
\(182\) | −4.31932 | + | 5.94504i | −0.320169 | + | 0.440675i | ||||
\(183\) | −4.07034 | − | 1.32253i | −0.300888 | − | 0.0977644i | ||||
\(184\) | 1.00985 | + | 3.10800i | 0.0744473 | + | 0.229125i | ||||
\(185\) | −14.4697 | − | 3.81455i | −1.06383 | − | 0.280451i | ||||
\(186\) | 5.26795 | 0.386265 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.10823i | 0.518421i | ||||||||
\(189\) | 2.15219 | − | 1.56366i | 0.156549 | − | 0.113739i | ||||
\(190\) | −14.4869 | + | 22.5064i | −1.05099 | + | 1.63279i | ||||
\(191\) | −3.31639 | + | 10.2068i | −0.239965 | + | 0.738537i | 0.756459 | + | 0.654042i | \(0.226928\pi\) |
−0.996424 | + | 0.0844956i | \(0.973072\pi\) | |||||||
\(192\) | 1.74403 | − | 2.40046i | 0.125865 | − | 0.173238i | ||||
\(193\) | 6.04151 | − | 8.31543i | 0.434877 | − | 0.598557i | −0.534187 | − | 0.845367i | \(-0.679382\pi\) |
0.969064 | + | 0.246809i | \(0.0793821\pi\) | |||||||
\(194\) | 0.391818 | − | 1.20589i | 0.0281309 | − | 0.0865780i | ||||
\(195\) | 4.12927 | + | 2.65792i | 0.295703 | + | 0.190338i | ||||
\(196\) | 8.68241 | − | 6.30814i | 0.620172 | − | 0.450582i | ||||
\(197\) | − | 2.55103i | − | 0.181753i | −0.995862 | − | 0.0908765i | \(-0.971033\pi\) | ||
0.995862 | − | 0.0908765i | \(-0.0289669\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | −2.35584 | + | 1.07179i | −0.166583 | + | 0.0757867i | ||||
\(201\) | −2.38934 | − | 7.35362i | −0.168531 | − | 0.518684i | ||||
\(202\) | −2.55808 | − | 0.831171i | −0.179986 | − | 0.0584810i | ||||
\(203\) | 3.65112 | − | 5.02534i | 0.256258 | − | 0.352709i | ||||
\(204\) | −0.750932 | − | 0.545584i | −0.0525758 | − | 0.0381985i | ||||
\(205\) | −1.40255 | − | 3.61010i | −0.0979585 | − | 0.252141i | ||||
\(206\) | −2.53275 | − | 7.79500i | −0.176465 | − | 0.543104i | ||||
\(207\) | 10.1381 | + | 13.9539i | 0.704647 | + | 0.969863i | ||||
\(208\) | − | 18.9396i | − | 1.31322i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.26795 | + | 1.55291i | 0.0874968 | + | 0.107161i | ||||
\(211\) | −8.99979 | + | 6.53873i | −0.619571 | + | 0.450145i | −0.852772 | − | 0.522284i | \(-0.825080\pi\) |
0.233200 | + | 0.972429i | \(0.425080\pi\) | |||||||
\(212\) | 19.7180 | − | 6.40677i | 1.35424 | − | 0.440018i | ||||
\(213\) | 1.08117 | + | 0.351294i | 0.0740807 | + | 0.0240703i | ||||
\(214\) | 6.84760 | + | 4.97507i | 0.468092 | + | 0.340089i | ||||
\(215\) | 1.34803 | + | 23.8757i | 0.0919352 | + | 1.62831i | ||||
\(216\) | −0.474619 | + | 1.46073i | −0.0322937 | + | 0.0993898i | ||||
\(217\) | 4.49195 | − | 1.45952i | 0.304933 | − | 0.0990788i | ||||
\(218\) | −1.35825 | − | 1.86947i | −0.0919921 | − | 0.126616i | ||||
\(219\) | −2.53590 | −0.171360 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.39230 | −0.295458 | ||||||||
\(222\) | −3.93354 | − | 5.41405i | −0.264002 | − | 0.363367i | ||||
\(223\) | 5.51190 | − | 1.79092i | 0.369104 | − | 0.119929i | −0.118591 | − | 0.992943i | \(-0.537838\pi\) |
0.487695 | + | 0.873014i | \(0.337838\pi\) | |||||||
\(224\) | 2.10250 | − | 6.47084i | 0.140479 | − | 0.432351i | ||||
\(225\) | −10.0773 | + | 9.22224i | −0.671823 | + | 0.614816i | ||||
\(226\) | 4.42055 | + | 3.21172i | 0.294051 | + | 0.213640i | ||||
\(227\) | 20.4741 | + | 6.65245i | 1.35892 | + | 0.441538i | 0.895681 | − | 0.444697i | \(-0.146689\pi\) |
0.463235 | + | 0.886236i | \(0.346689\pi\) | |||||||
\(228\) | −5.28342 | + | 1.71669i | −0.349903 | + | 0.113690i | ||||
\(229\) | −14.5042 | + | 10.5379i | −0.958466 | + | 0.696366i | −0.952794 | − | 0.303618i | \(-0.901805\pi\) |
−0.00567196 | + | 0.999984i | \(0.501805\pi\) | |||||||
\(230\) | −21.1244 | + | 17.2480i | −1.39290 | + | 1.13730i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.58630i | 0.235452i | ||||||||
\(233\) | 7.64434 | + | 10.5215i | 0.500797 | + | 0.689288i | 0.982334 | − | 0.187138i | \(-0.0599211\pi\) |
−0.481536 | + | 0.876426i | \(0.659921\pi\) | |||||||
\(234\) | −6.91960 | − | 21.2963i | −0.452349 | − | 1.39219i | ||||
\(235\) | 8.55382 | − | 3.32322i | 0.557990 | − | 0.216783i | ||||
\(236\) | 6.63083 | + | 4.81758i | 0.431630 | + | 0.313598i | ||||
\(237\) | 1.66251 | − | 2.28825i | 0.107991 | − | 0.148638i | ||||
\(238\) | −1.70539 | − | 0.554114i | −0.110544 | − | 0.0359179i | ||||
\(239\) | 3.60322 | + | 11.0896i | 0.233073 | + | 0.717324i | 0.997371 | + | 0.0724614i | \(0.0230854\pi\) |
−0.764299 | + | 0.644863i | \(0.776915\pi\) | |||||||
\(240\) | −4.99638 | − | 1.31716i | −0.322515 | − | 0.0850223i | ||||
\(241\) | −10.1244 | −0.652167 | −0.326084 | − | 0.945341i | \(-0.605729\pi\) | ||||
−0.326084 | + | 0.945341i | \(0.605729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3490i | 0.792188i | ||||||||
\(244\) | −11.5855 | + | 8.41738i | −0.741688 | + | 0.538868i | ||||
\(245\) | −11.6502 | − | 7.49897i | −0.744304 | − | 0.479092i | ||||
\(246\) | 0.535233 | − | 1.64728i | 0.0341252 | − | 0.105027i | ||||
\(247\) | −15.4517 | + | 21.2675i | −0.983170 | + | 1.35322i | ||||
\(248\) | −1.60283 | + | 2.20610i | −0.101780 | + | 0.140088i | ||||
\(249\) | 1.58351 | − | 4.87355i | 0.100351 | − | 0.308849i | ||||
\(250\) | −15.4566 | − | 15.0864i | −0.977564 | − | 0.954146i | ||||
\(251\) | 11.4849 | − | 8.34429i | 0.724922 | − | 0.526687i | −0.163031 | − | 0.986621i | \(-0.552127\pi\) |
0.887953 | + | 0.459934i | \(0.152127\pi\) | |||||||
\(252\) | − | 4.24264i | − | 0.267261i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.46410 | −0.405594 | ||||||||
\(255\) | −0.305465 | + | 1.15872i | −0.0191289 | + | 0.0725617i | ||||
\(256\) | 5.99255 | + | 18.4432i | 0.374534 | + | 1.15270i | ||||
\(257\) | −4.75577 | − | 1.54524i | −0.296657 | − | 0.0963897i | 0.156907 | − | 0.987613i | \(-0.449848\pi\) |
−0.453564 | + | 0.891224i | \(0.649848\pi\) | |||||||
\(258\) | −6.28609 | + | 8.65206i | −0.391355 | + | 0.538654i | ||||
\(259\) | −4.85410 | − | 3.52671i | −0.301619 | − | 0.219139i | ||||
\(260\) | 15.3164 | − | 5.95053i | 0.949881 | − | 0.369036i | ||||
\(261\) | 5.84914 | + | 18.0018i | 0.362052 | + | 1.11428i | ||||
\(262\) | −23.9870 | − | 33.0153i | −1.48192 | − | 2.03969i | ||||
\(263\) | − | 21.4906i | − | 1.32517i | −0.748988 | − | 0.662584i | \(-0.769460\pi\) | ||
0.748988 | − | 0.662584i | \(-0.230540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.9282 | − | 20.7327i | −1.03989 | − | 1.27360i | ||||
\(266\) | −8.68241 | + | 6.30814i | −0.532353 | + | 0.386777i | ||||
\(267\) | −3.18230 | + | 1.03399i | −0.194753 | + | 0.0632792i | ||||
\(268\) | −24.6057 | − | 7.99487i | −1.50303 | − | 0.488364i | ||||
\(269\) | −15.9636 | − | 11.5982i | −0.973316 | − | 0.707155i | −0.0171109 | − | 0.999854i | \(-0.505447\pi\) |
−0.956205 | + | 0.292698i | \(0.905447\pi\) | |||||||
\(270\) | −12.7969 | + | 0.722519i | −0.778793 | + | 0.0439711i | ||||
\(271\) | 1.40167 | − | 4.31390i | 0.0851454 | − | 0.262051i | −0.899415 | − | 0.437096i | \(-0.856007\pi\) |
0.984560 | + | 0.175045i | \(0.0560071\pi\) | |||||||
\(272\) | 4.39538 | − | 1.42815i | 0.266509 | − | 0.0865941i | ||||
\(273\) | 1.15736 | + | 1.59297i | 0.0700465 | + | 0.0964108i | ||||
\(274\) | −26.5885 | −1.60627 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.66025 | −0.340707 | ||||||||
\(277\) | 13.3438 | + | 18.3661i | 0.801748 | + | 1.10351i | 0.992545 | + | 0.121882i | \(0.0388930\pi\) |
−0.190796 | + | 0.981630i | \(0.561107\pi\) | |||||||
\(278\) | 30.4780 | − | 9.90289i | 1.82795 | − | 0.593936i | ||||
\(279\) | −4.44747 | + | 13.6879i | −0.266263 | + | 0.819473i | ||||
\(280\) | −1.03611 | + | 0.0584995i | −0.0619196 | + | 0.00349601i | ||||
\(281\) | −14.0126 | − | 10.1807i | −0.835921 | − | 0.607332i | 0.0853074 | − | 0.996355i | \(-0.472813\pi\) |
−0.921228 | + | 0.389023i | \(0.872813\pi\) | |||||||
\(282\) | 3.90308 | + | 1.26819i | 0.232425 | + | 0.0755194i | ||||
\(283\) | 28.6407 | − | 9.30592i | 1.70251 | − | 0.553179i | 0.713453 | − | 0.700703i | \(-0.247130\pi\) |
0.989059 | + | 0.147524i | \(0.0471303\pi\) | |||||||
\(284\) | 3.07738 | − | 2.23585i | 0.182609 | − | 0.132673i | ||||
\(285\) | 4.53590 | + | 5.55532i | 0.268683 | + | 0.329069i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.55291i | − | 0.0916656i | ||||||
\(288\) | 12.1864 | + | 16.7731i | 0.718090 | + | 0.988366i | ||||
\(289\) | 4.92209 | + | 15.1486i | 0.289534 | + | 0.891095i | ||||
\(290\) | −27.8967 | + | 10.8381i | −1.63815 | + | 0.636435i | ||||
\(291\) | −0.274860 | − | 0.199698i | −0.0161126 | − | 0.0117065i | ||||
\(292\) | −4.98752 | + | 6.86474i | −0.291873 | + | 0.401728i | ||||
\(293\) | −8.95802 | − | 2.91064i | −0.523333 | − | 0.170041i | 0.0354243 | − | 0.999372i | \(-0.488722\pi\) |
−0.558757 | + | 0.829331i | \(0.688722\pi\) | |||||||
\(294\) | −1.91472 | − | 5.89289i | −0.111669 | − | 0.343680i | ||||
\(295\) | 2.69729 | − | 10.2316i | 0.157042 | − | 0.595708i | ||||
\(296\) | 3.46410 | 0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.5283i | 1.53674i | ||||||||
\(299\) | −21.6692 | + | 15.7436i | −1.25316 | + | 0.910476i | ||||
\(300\) | −0.504603 | − | 4.45439i | −0.0291333 | − | 0.257174i | ||||
\(301\) | −2.96300 | + | 9.11916i | −0.170784 | + | 0.525620i | ||||
\(302\) | −7.03582 | + | 9.68397i | −0.404866 | + | 0.557250i | ||||
\(303\) | −0.423623 | + | 0.583067i | −0.0243365 | + | 0.0334963i | ||||
\(304\) | 8.54749 | − | 26.3065i | 0.490232 | − | 1.50878i | ||||
\(305\) | 15.5456 | + | 10.0064i | 0.890141 | + | 0.572964i | ||||
\(306\) | 4.42055 | − | 3.21172i | 0.252706 | − | 0.183602i | ||||
\(307\) | 17.6269i | 1.00602i | 0.864280 | + | 0.503010i | \(0.167774\pi\) | ||||
−0.864280 | + | 0.503010i | \(0.832226\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.19615 | −0.124935 | ||||||||
\(310\) | −22.0045 | − | 5.80088i | −1.24977 | − | 0.329468i | ||||
\(311\) | −8.66872 | − | 26.6796i | −0.491558 | − | 1.51286i | −0.822253 | − | 0.569122i | \(-0.807283\pi\) |
0.330695 | − | 0.943738i | \(-0.392717\pi\) | |||||||
\(312\) | −1.08117 | − | 0.351294i | −0.0612093 | − | 0.0198881i | ||||
\(313\) | 10.0784 | − | 13.8718i | 0.569666 | − | 0.784078i | −0.422849 | − | 0.906200i | \(-0.638970\pi\) |
0.992515 | + | 0.122122i | \(0.0389700\pi\) | |||||||
\(314\) | 18.8667 | + | 13.7075i | 1.06471 | + | 0.773556i | ||||
\(315\) | −5.10546 | + | 1.98351i | −0.287660 | + | 0.111758i | ||||
\(316\) | −2.92457 | − | 9.00090i | −0.164520 | − | 0.506340i | ||||
\(317\) | 4.09659 | + | 5.63847i | 0.230087 | + | 0.316688i | 0.908413 | − | 0.418073i | \(-0.137294\pi\) |
−0.678326 | + | 0.734761i | \(0.737294\pi\) | |||||||
\(318\) | − | 11.9700i | − | 0.671247i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −9.92820 | + | 8.10634i | −0.555003 | + | 0.453158i | ||||
\(321\) | 1.83481 | − | 1.33307i | 0.102409 | − | 0.0744045i | ||||
\(322\) | −10.3996 | + | 3.37903i | −0.579546 | + | 0.188306i | ||||
\(323\) | −6.10077 | − | 1.98226i | −0.339456 | − | 0.110296i | ||||
\(324\) | 9.33274 | + | 6.78063i | 0.518485 | + | 0.376702i | ||||
\(325\) | −14.3213 | − | 15.6493i | −0.794405 | − | 0.868065i | ||||
\(326\) | 4.53027 | − | 13.9427i | 0.250908 | − | 0.772216i | ||||
\(327\) | −0.588870 | + | 0.191335i | −0.0325646 | + | 0.0105809i | ||||
\(328\) | 0.526994 | + | 0.725345i | 0.0290984 | + | 0.0400505i | ||||
\(329\) | 3.67949 | 0.202857 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.80385 | −0.428938 | −0.214469 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214469 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(332\) | −10.0784 | − | 13.8718i | −0.553125 | − | 0.761311i | ||||
\(333\) | 17.3884 | − | 5.64983i | 0.952878 | − | 0.309609i | ||||
\(334\) | −1.15327 | + | 3.54939i | −0.0631040 | + | 0.194214i | ||||
\(335\) | 1.88281 | + | 33.3474i | 0.102869 | + | 1.82196i | ||||
\(336\) | −1.67612 | − | 1.21777i | −0.0914398 | − | 0.0664349i | ||||
\(337\) | 7.44577 | + | 2.41928i | 0.405597 | + | 0.131786i | 0.504708 | − | 0.863290i | \(-0.331600\pi\) |
−0.0991115 | + | 0.995076i | \(0.531600\pi\) | |||||||
\(338\) | 9.18650 | − | 2.98487i | 0.499680 | − | 0.162356i | ||||
\(339\) | 1.18448 | − | 0.860577i | 0.0643323 | − | 0.0467401i | ||||
\(340\) | 2.53590 | + | 3.10583i | 0.137528 | + | 0.168437i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 32.7028i | − | 1.76836i | ||||||
\(343\) | −6.95429 | − | 9.57176i | −0.375496 | − | 0.516826i | ||||
\(344\) | −1.71069 | − | 5.26495i | −0.0922340 | − | 0.283867i | ||||
\(345\) | 2.64627 | + | 6.81137i | 0.142470 | + | 0.366712i | ||||
\(346\) | −11.9185 | − | 8.65928i | −0.640741 | − | 0.465526i | ||||
\(347\) | −1.74403 | + | 2.40046i | −0.0936246 | + | 0.128863i | −0.853260 | − | 0.521487i | \(-0.825378\pi\) |
0.759635 | + | 0.650350i | \(0.225378\pi\) | |||||||
\(348\) | −5.90764 | − | 1.91951i | −0.316683 | − | 0.102896i | ||||
\(349\) | −8.44250 | − | 25.9833i | −0.451917 | − | 1.39086i | −0.874717 | − | 0.484634i | \(-0.838953\pi\) |
0.422800 | − | 0.906223i | \(-0.361047\pi\) | |||||||
\(350\) | −3.58626 | − | 7.88281i | −0.191694 | − | 0.421354i | ||||
\(351\) | −12.5885 | −0.671922 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.69161i | 0.0900356i | 0.998986 | + | 0.0450178i | \(0.0143345\pi\) | ||||
−0.998986 | + | 0.0450178i | \(0.985666\pi\) | |||||||
\(354\) | 3.82831 | − | 2.78143i | 0.203472 | − | 0.147831i | ||||
\(355\) | −4.12927 | − | 2.65792i | −0.219159 | − | 0.141068i | ||||
\(356\) | −3.45980 | + | 10.6482i | −0.183369 | + | 0.564352i | ||||
\(357\) | −0.282415 | + | 0.388711i | −0.0149470 | + | 0.0205728i | ||||
\(358\) | 9.69263 | − | 13.3408i | 0.512271 | − | 0.705081i | ||||
\(359\) | −5.66729 | + | 17.4421i | −0.299108 | + | 0.920561i | 0.682702 | + | 0.730697i | \(0.260805\pi\) |
−0.981810 | + | 0.189864i | \(0.939195\pi\) | |||||||
\(360\) | 1.71157 | − | 2.65905i | 0.0902076 | − | 0.140144i | ||||
\(361\) | −15.6887 | + | 11.3985i | −0.825721 | + | 0.599922i | ||||
\(362\) | 6.55343i | 0.344441i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.58846 | 0.345329 | ||||||||
\(365\) | 10.5926 | + | 2.79244i | 0.554440 | + | 0.146163i | ||||
\(366\) | 2.55494 | + | 7.86329i | 0.133549 | + | 0.411021i | ||||
\(367\) | −28.1837 | − | 9.15744i | −1.47118 | − | 0.478015i | −0.539714 | − | 0.841848i | \(-0.681468\pi\) |
−0.931464 | + | 0.363834i | \(0.881468\pi\) | |||||||
\(368\) | 16.5654 | − | 22.8003i | 0.863531 | − | 1.18855i | ||||
\(369\) | 3.82831 | + | 2.78143i | 0.199294 | + | 0.144795i | ||||
\(370\) | 10.4688 | + | 26.9462i | 0.544247 | + | 1.40087i | ||||
\(371\) | −3.31639 | − | 10.2068i | −0.172178 | − | 0.529910i | ||||
\(372\) | −2.77618 | − | 3.82108i | −0.143938 | − | 0.198114i | ||||
\(373\) | − | 34.1170i | − | 1.76651i | −0.468892 | − | 0.883255i | \(-0.655347\pi\) | ||
0.468892 | − | 0.883255i | \(-0.344653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.12436 | + | 2.68973i | −0.264621 | + | 0.138897i | ||||
\(376\) | −1.71864 | + | 1.24866i | −0.0886321 | + | 0.0643950i | ||||
\(377\) | −27.9552 | + | 9.08321i | −1.43977 | + | 0.467809i | ||||
\(378\) | −4.88769 | − | 1.58811i | −0.251395 | − | 0.0816833i | ||||
\(379\) | −4.42055 | − | 3.21172i | −0.227068 | − | 0.164975i | 0.468434 | − | 0.883498i | \(-0.344818\pi\) |
−0.695503 | + | 0.718523i | \(0.744818\pi\) | |||||||
\(380\) | 23.9594 | − | 1.35276i | 1.22909 | − | 0.0693953i | ||||
\(381\) | −0.535233 | + | 1.64728i | −0.0274208 | + | 0.0843926i | ||||
\(382\) | 19.7180 | − | 6.40677i | 1.00886 | − | 0.327799i | ||||
\(383\) | 13.9683 | + | 19.2257i | 0.713745 | + | 0.982386i | 0.999708 | + | 0.0241451i | \(0.00768637\pi\) |
−0.285964 | + | 0.958240i | \(0.592314\pi\) | |||||||
\(384\) | 2.12436 | 0.108408 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.8564 | −1.01066 | ||||||||
\(387\) | −17.1739 | − | 23.6379i | −0.872999 | − | 1.20158i | ||||
\(388\) | −1.08117 | + | 0.351294i | −0.0548882 | + | 0.0178343i | ||||
\(389\) | 5.60073 | − | 17.2373i | 0.283968 | − | 0.873965i | −0.702737 | − | 0.711449i | \(-0.748039\pi\) |
0.986706 | − | 0.162516i | \(-0.0519609\pi\) | |||||||
\(390\) | −0.534780 | − | 9.47175i | −0.0270796 | − | 0.479621i | ||||
\(391\) | −5.28765 | − | 3.84170i | −0.267408 | − | 0.194283i | ||||
\(392\) | 3.05038 | + | 0.991130i | 0.154068 | + | 0.0500596i | ||||
\(393\) | −10.3996 | + | 3.37903i | −0.524590 | + | 0.170450i | ||||
\(394\) | −3.98700 | + | 2.89673i | −0.200862 | + | 0.145935i | ||||
\(395\) | −9.46410 | + | 7.72741i | −0.476191 | + | 0.388808i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.0096i | 0.803500i | 0.915749 | + | 0.401750i | \(0.131598\pi\) | ||||
−0.915749 | + | 0.401750i | \(0.868402\pi\) | |||||||
\(398\) | −2.27103 | − | 3.12580i | −0.113836 | − | 0.156682i | ||||
\(399\) | 0.888623 | + | 2.73490i | 0.0444868 | + | 0.136916i | ||||
\(400\) | 19.4197 | + | 11.0037i | 0.970984 | + | 0.550184i | ||||
\(401\) | 26.1478 | + | 18.9975i | 1.30576 | + | 0.948691i | 0.999994 | − | 0.00341570i | \(-0.00108725\pi\) |
0.305767 | + | 0.952106i | \(0.401087\pi\) | |||||||
\(402\) | −8.77985 | + | 12.0844i | −0.437899 | + | 0.602717i | ||||
\(403\) | −21.2561 | − | 6.90653i | −1.05884 | − | 0.344039i | ||||
\(404\) | 0.745208 | + | 2.29351i | 0.0370755 | + | 0.114107i | ||||
\(405\) | 3.79638 | − | 14.4008i | 0.188643 | − | 0.715580i | ||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 0.277401i | − | 0.0137334i | ||||||
\(409\) | −1.51743 | + | 1.10248i | −0.0750320 | + | 0.0545139i | −0.624669 | − | 0.780890i | \(-0.714766\pi\) |
0.549637 | + | 0.835404i | \(0.314766\pi\) | |||||||
\(410\) | −4.04962 | + | 6.29137i | −0.199996 | + | 0.310709i | ||||
\(411\) | −2.20155 | + | 6.77566i | −0.108594 | + | 0.334219i | ||||
\(412\) | −4.31932 | + | 5.94504i | −0.212798 | + | 0.292891i | ||||
\(413\) | 2.49376 | − | 3.43237i | 0.122710 | − | 0.168896i | ||||
\(414\) | 10.2966 | − | 31.6897i | 0.506050 | − | 1.55746i | ||||
\(415\) | −11.9810 | + | 18.6133i | −0.588123 | + | 0.913692i | ||||
\(416\) | −26.0472 | + | 18.9244i | −1.27707 | + | 0.927846i | ||||
\(417\) | − | 8.58682i | − | 0.420498i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.6603 | 1.44900 | 0.724499 | − | 0.689276i | \(-0.242071\pi\) | ||||
0.724499 | + | 0.689276i | \(0.242071\pi\) | |||||||
\(420\) | 0.458197 | − | 1.73808i | 0.0223577 | − | 0.0848095i | ||||
\(421\) | 6.50560 | + | 20.0222i | 0.317063 | + | 0.975821i | 0.974897 | + | 0.222657i | \(0.0714731\pi\) |
−0.657833 | + | 0.753164i | \(0.728527\pi\) | |||||||
\(422\) | 20.4388 | + | 6.64096i | 0.994944 | + | 0.323277i | ||||
\(423\) | −6.59035 | + | 9.07084i | −0.320434 | + | 0.441039i | ||||
\(424\) | 5.01279 | + | 3.64201i | 0.243443 | + | 0.176871i | ||||
\(425\) | 2.55188 | − | 4.50365i | 0.123784 | − | 0.218459i | ||||
\(426\) | −0.678648 | − | 2.08867i | −0.0328806 | − | 0.101196i | ||||
\(427\) | 4.35716 | + | 5.99711i | 0.210858 | + | 0.290221i | ||||
\(428\) | − | 7.58871i | − | 0.366814i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 35.7846 | − | 29.2180i | 1.72569 | − | 1.40902i | ||||
\(431\) | 15.3132 | − | 11.1257i | 0.737613 | − | 0.535907i | −0.154350 | − | 0.988016i | \(-0.549328\pi\) |
0.891963 | + | 0.452109i | \(0.149328\pi\) | |||||||
\(432\) | 12.5973 | − | 4.09310i | 0.606087 | − | 0.196930i | ||||
\(433\) | 19.2610 | + | 6.25829i | 0.925627 | + | 0.300754i | 0.732773 | − | 0.680473i | \(-0.238226\pi\) |
0.192854 | + | 0.981228i | \(0.438226\pi\) | |||||||
\(434\) | −7.38176 | − | 5.36316i | −0.354336 | − | 0.257440i | ||||
\(435\) | 0.452049 | + | 8.00646i | 0.0216741 | + | 0.383881i | ||||
\(436\) | −0.640220 | + | 1.97040i | −0.0306610 | + | 0.0943648i | ||||
\(437\) | −37.2030 | + | 12.0880i | −1.77966 | + | 0.578246i | ||||
\(438\) | 2.87955 | + | 3.96336i | 0.137590 | + | 0.189377i | ||||
\(439\) | 20.2487 | 0.966418 | 0.483209 | − | 0.875505i | \(-0.339471\pi\) | ||||
0.483209 | + | 0.875505i | \(0.339471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.9282 | 0.806105 | ||||||||
\(442\) | 4.98752 | + | 6.86474i | 0.237232 | + | 0.326522i | ||||
\(443\) | 8.72954 | − | 2.83640i | 0.414753 | − | 0.134761i | −0.0942048 | − | 0.995553i | \(-0.530031\pi\) |
0.508958 | + | 0.860791i | \(0.330031\pi\) | |||||||
\(444\) | −1.85410 | + | 5.70634i | −0.0879918 | + | 0.270811i | ||||
\(445\) | 14.4312 | − | 0.814793i | 0.684104 | − | 0.0386249i | ||||
\(446\) | −9.05788 | − | 6.58093i | −0.428903 | − | 0.311616i | ||||
\(447\) | 6.76033 | + | 2.19656i | 0.319753 | + | 0.103894i | ||||
\(448\) | −4.88769 | + | 1.58811i | −0.230921 | + | 0.0750309i | ||||
\(449\) | −8.50816 | + | 6.18154i | −0.401525 | + | 0.291725i | −0.770162 | − | 0.637849i | \(-0.779825\pi\) |
0.368637 | + | 0.929573i | \(0.379825\pi\) | |||||||
\(450\) | 25.8564 | + | 5.27792i | 1.21888 | + | 0.248803i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 4.89898i | − | 0.230429i | ||||||
\(453\) | 1.88524 | + | 2.59481i | 0.0885764 | + | 0.121915i | ||||
\(454\) | −12.8515 | − | 39.5530i | −0.603153 | − | 1.85631i | ||||
\(455\) | −3.08022 | − | 7.92834i | −0.144403 | − | 0.371686i | ||||
\(456\) | −1.34317 | − | 0.975873i | −0.0628999 | − | 0.0456994i | ||||
\(457\) | 12.4688 | − | 17.1618i | 0.583266 | − | 0.802797i | −0.410782 | − | 0.911733i | \(-0.634744\pi\) |
0.994049 | + | 0.108936i | \(0.0347444\pi\) | |||||||
\(458\) | 32.9395 | + | 10.7027i | 1.53916 | + | 0.500104i | ||||
\(459\) | −0.949237 | − | 2.92145i | −0.0443066 | − | 0.136362i | ||||
\(460\) | 23.6431 | + | 6.23287i | 1.10237 | + | 0.290609i | ||||
\(461\) | −33.0000 | −1.53696 | −0.768482 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768482 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.8671i | − | 0.830356i | −0.909740 | − | 0.415178i | \(-0.863719\pi\) | ||
0.909740 | − | 0.415178i | \(-0.136281\pi\) | |||||||
\(464\) | 25.0214 | − | 18.1791i | 1.16159 | − | 0.843945i | ||||
\(465\) | −3.30025 | + | 5.12718i | −0.153046 | + | 0.237767i | ||||
\(466\) | 7.76385 | − | 23.8947i | 0.359654 | − | 1.10690i | ||||
\(467\) | 10.4424 | − | 14.3727i | 0.483215 | − | 0.665088i | −0.495904 | − | 0.868377i | \(-0.665163\pi\) |
0.979119 | + | 0.203289i | \(0.0651632\pi\) | |||||||
\(468\) | −11.8006 | + | 16.2421i | −0.545483 | + | 0.750793i | ||||
\(469\) | −4.13845 | + | 12.7368i | −0.191096 | + | 0.588133i | ||||
\(470\) | −14.9068 | − | 9.59520i | −0.687602 | − | 0.442594i | ||||
\(471\) | 5.05531 | − | 3.67290i | 0.232937 | − | 0.169238i | ||||
\(472\) | 2.44949i | 0.112747i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.46410 | −0.250974 | ||||||||
\(475\) | −12.8293 | − | 28.1996i | −0.588650 | − | 1.29389i | ||||
\(476\) | 0.496805 | + | 1.52901i | 0.0227710 | + | 0.0700820i | ||||
\(477\) | 31.1022 | + | 10.1057i | 1.42407 | + | 0.462709i | ||||
\(478\) | 13.2404 | − | 18.2238i | 0.605601 | − | 0.833538i | ||||
\(479\) | 7.65662 | + | 5.56286i | 0.349840 | + | 0.254174i | 0.748802 | − | 0.662794i | \(-0.230629\pi\) |
−0.398962 | + | 0.916967i | \(0.630629\pi\) | |||||||
\(480\) | 3.18092 | + | 8.18753i | 0.145188 | + | 0.373708i | ||||
\(481\) | 8.77370 | + | 27.0027i | 0.400047 | + | 1.23122i | ||||
\(482\) | 11.4963 | + | 15.8234i | 0.523644 | + | 0.720734i | ||||
\(483\) | 2.92996i | 0.133318i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.928203 | + | 1.13681i | 0.0421475 | + | 0.0516200i | ||||
\(486\) | 19.3002 | − | 14.0224i | 0.875477 | − | 0.636071i | ||||
\(487\) | 12.1050 | − | 3.93314i | 0.548529 | − | 0.178228i | −0.0216245 | − | 0.999766i | \(-0.506884\pi\) |
0.570153 | + | 0.821538i | \(0.306884\pi\) | |||||||
\(488\) | −4.07034 | − | 1.32253i | −0.184255 | − | 0.0598682i | ||||
\(489\) | −3.17798 | − | 2.30894i | −0.143713 | − | 0.104414i | ||||
\(490\) | 1.50881 | + | 26.7233i | 0.0681611 | + | 1.20723i | ||||
\(491\) | −4.85553 | + | 14.9438i | −0.219127 | + | 0.674403i | 0.779708 | + | 0.626143i | \(0.215368\pi\) |
−0.998835 | + | 0.0482597i | \(0.984632\pi\) | |||||||
\(492\) | −1.47691 | + | 0.479877i | −0.0665842 | + | 0.0216345i | ||||
\(493\) | −4.21595 | − | 5.80276i | −0.189877 | − | 0.261343i | ||||
\(494\) | 50.7846 | 2.28491 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.5167 | 1.05593 | ||||||||
\(497\) | −1.15736 | − | 1.59297i | −0.0519146 | − | 0.0714544i | ||||
\(498\) | −9.41498 | + | 3.05911i | −0.421895 | + | 0.137082i | ||||
\(499\) | −11.8639 | + | 36.5133i | −0.531100 | + | 1.63456i | 0.220828 | + | 0.975313i | \(0.429124\pi\) |
−0.751928 | + | 0.659245i | \(0.770876\pi\) | |||||||
\(500\) | −2.79726 | + | 19.1618i | −0.125097 | + | 0.856943i | ||||
\(501\) | 0.809017 | + | 0.587785i | 0.0361442 | + | 0.0262603i | ||||
\(502\) | −26.0826 | − | 8.47475i | −1.16412 | − | 0.378247i | ||||
\(503\) | −32.5791 | + | 10.5856i | −1.45263 | + | 0.471988i | −0.925810 | − | 0.377989i | \(-0.876616\pi\) |
−0.526820 | + | 0.849977i | \(0.676616\pi\) | |||||||
\(504\) | 1.02579 | − | 0.745282i | 0.0456924 | − | 0.0331975i | ||||
\(505\) | 2.41154 | − | 1.96902i | 0.107312 | − | 0.0876201i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 2.58819i | − | 0.114946i | ||||||
\(508\) | 3.40654 | + | 4.68870i | 0.151141 | + | 0.208028i | ||||
\(509\) | 6.77619 | + | 20.8550i | 0.300349 | + | 0.924380i | 0.981372 | + | 0.192118i | \(0.0615355\pi\) |
−0.681023 | + | 0.732262i | \(0.738465\pi\) | |||||||
\(510\) | 2.15782 | − | 0.838329i | 0.0955499 | − | 0.0371218i | ||||
\(511\) | 3.55345 | + | 2.58173i | 0.157195 | + | 0.114209i | ||||
\(512\) | 17.1958 | − | 23.6679i | 0.759952 | − | 1.04598i | ||||
\(513\) | −17.4850 | − | 5.68121i | −0.771980 | − | 0.250831i | ||||
\(514\) | 2.98518 | + | 9.18745i | 0.131671 | + | 0.405241i | ||||
\(515\) | 9.17342 | + | 2.41832i | 0.404229 | + | 0.106564i | ||||
\(516\) | 9.58846 | 0.422108 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.5911i | 0.509284i | ||||||||
\(519\) | −3.19355 | + | 2.32025i | −0.140181 | + | 0.101848i | ||||
\(520\) | 4.12927 | + | 2.65792i | 0.181081 | + | 0.116558i | ||||
\(521\) | 12.1285 | − | 37.3277i | 0.531360 | − | 1.63536i | −0.220025 | − | 0.975494i | \(-0.570614\pi\) |
0.751385 | − | 0.659864i | \(-0.229386\pi\) | |||||||
\(522\) | 21.4932 | − | 29.5829i | 0.940733 | − | 1.29481i | ||||
\(523\) | −5.09089 | + | 7.00701i | −0.222609 | + | 0.306395i | −0.905684 | − | 0.423953i | \(-0.860642\pi\) |
0.683075 | + | 0.730348i | \(0.260642\pi\) | |||||||
\(524\) | −11.3065 | + | 34.7977i | −0.493925 | + | 1.52014i | ||||
\(525\) | −2.30576 | + | 0.261202i | −0.100632 | + | 0.0113998i | ||||
\(526\) | −33.5877 | + | 24.4029i | −1.46449 | + | 1.06402i | ||||
\(527\) | − | 5.45378i | − | 0.237570i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8564 | −0.732887 | ||||||||
\(530\) | −13.1810 | + | 49.9994i | −0.572546 | + | 2.17184i | ||||
\(531\) | 3.99503 | + | 12.2955i | 0.173370 | + | 0.533577i | ||||
\(532\) | 9.15115 | + | 2.97339i | 0.396753 | + | 0.128913i | ||||
\(533\) | −4.31932 | + | 5.94504i | −0.187091 | + | 0.257508i | ||||
\(534\) | 5.22957 | + | 3.79950i | 0.226306 | + | 0.164421i | ||||
\(535\) | −9.13200 | + | 3.54785i | −0.394811 | + | 0.153387i | ||||
\(536\) | −2.38934 | − | 7.35362i | −0.103204 | − | 0.317628i | ||||
\(537\) | −2.59713 | − | 3.57465i | −0.112075 | − | 0.154257i | ||||
\(538\) | 38.1194i | 1.64344i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.26795 | + | 8.90138i | 0.312763 | + | 0.383055i | ||||
\(541\) | 18.9248 | − | 13.7497i | 0.813640 | − | 0.591144i | −0.101244 | − | 0.994862i | \(-0.532282\pi\) |
0.914884 | + | 0.403718i | \(0.132282\pi\) | |||||||
\(542\) | −8.33381 | + | 2.70782i | −0.357968 | + | 0.116311i | ||||
\(543\) | 1.67004 | + | 0.542630i | 0.0716684 | + | 0.0232865i | ||||
\(544\) | −6.35597 | − | 4.61788i | −0.272510 | − | 0.197990i | ||||
\(545\) | 2.67043 | − | 0.150774i | 0.114388 | − | 0.00645843i | ||||
\(546\) | 1.17545 | − | 3.61767i | 0.0503048 | − | 0.154822i | ||||
\(547\) | 19.2610 | − | 6.25829i | 0.823543 | − | 0.267585i | 0.133220 | − | 0.991087i | \(-0.457468\pi\) |
0.690323 | + | 0.723501i | \(0.257468\pi\) | |||||||
\(548\) | 14.0120 | + | 19.2858i | 0.598561 | + | 0.823849i | ||||
\(549\) | −22.5885 | −0.964052 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.9282 | −1.82880 | ||||||||
\(552\) | −0.994306 | − | 1.36855i | −0.0423205 | − | 0.0582492i | ||||
\(553\) | −4.65921 | + | 1.51387i | −0.198130 | + | 0.0643762i | ||||
\(554\) | 13.5524 | − | 41.7099i | 0.575785 | − | 1.77208i | ||||
\(555\) | 7.73365 | − | 0.436646i | 0.328275 | − | 0.0185346i | ||||
\(556\) | −23.2447 | − | 16.8883i | −0.985796 | − | 0.716222i | ||||
\(557\) | −6.17146 | − | 2.00523i | −0.261493 | − | 0.0849643i | 0.175336 | − | 0.984509i | \(-0.443899\pi\) |
−0.436830 | + | 0.899544i | \(0.643899\pi\) | |||||||
\(558\) | 26.4430 | − | 8.59185i | 1.11942 | − | 0.363722i | ||||
\(559\) | 36.7076 | − | 26.6696i | 1.55257 | − | 1.12800i | ||||
\(560\) | 5.66025 | + | 6.93237i | 0.239189 | + | 0.292946i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.4607i | 1.41145i | ||||||||
\(563\) | 3.56959 | + | 4.91312i | 0.150440 | + | 0.207064i | 0.877585 | − | 0.479421i | \(-0.159153\pi\) |
−0.727145 | + | 0.686484i | \(0.759153\pi\) | |||||||
\(564\) | −1.13703 | − | 3.49940i | −0.0478774 | − | 0.147352i | ||||
\(565\) | −5.89527 | + | 2.29036i | −0.248016 | + | 0.0963561i | ||||
\(566\) | −47.0661 | − | 34.1955i | −1.97834 | − | 1.43735i | ||||
\(567\) | 3.50991 | − | 4.83098i | 0.147402 | − | 0.202882i | ||||
\(568\) | 1.08117 | + | 0.351294i | 0.0453650 | + | 0.0147400i | ||||
\(569\) | −1.81567 | − | 5.58807i | −0.0761170 | − | 0.234264i | 0.905757 | − | 0.423796i | \(-0.139303\pi\) |
−0.981874 | + | 0.189532i | \(0.939303\pi\) | |||||||
\(570\) | 3.53184 | − | 13.3973i | 0.147932 | − | 0.561151i | ||||
\(571\) | 35.7128 | 1.49453 | 0.747267 | − | 0.664524i | \(-0.231365\pi\) | ||||
0.747267 | + | 0.664524i | \(0.231365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.55532i | − | 0.232077i | ||||||
\(574\) | −2.42705 | + | 1.76336i | −0.101303 | + | 0.0736010i | ||||
\(575\) | −3.55314 | − | 31.3654i | −0.148176 | − | 1.30803i | ||||
\(576\) | 4.83928 | − | 14.8938i | 0.201637 | − | 0.620574i | ||||
\(577\) | −12.1864 | + | 16.7731i | −0.507326 | + | 0.698275i | −0.983466 | − | 0.181095i | \(-0.942036\pi\) |
0.476139 | + | 0.879370i | \(0.342036\pi\) | |||||||
\(578\) | 18.0867 | − | 24.8942i | 0.752307 | − | 1.03546i | ||||
\(579\) | −1.64413 | + | 5.06010i | −0.0683276 | + | 0.210291i | ||||
\(580\) | 22.5628 | + | 14.5231i | 0.936868 | + | 0.603041i | ||||
\(581\) | −7.18055 | + | 5.21697i | −0.297899 | + | 0.216437i | ||||
\(582\) | 0.656339i | 0.0272061i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.53590 | −0.104936 | ||||||||
\(585\) | 25.0623 | + | 6.60699i | 1.03620 | + | 0.273165i | ||||
\(586\) | 5.62292 | + | 17.3056i | 0.232281 | + | 0.714886i | ||||
\(587\) | −34.1879 | − | 11.1083i | −1.41109 | − | 0.458490i | −0.498328 | − | 0.866989i | \(-0.666052\pi\) |
−0.912759 | + | 0.408499i | \(0.866052\pi\) | |||||||
\(588\) | −3.26533 | + | 4.49435i | −0.134660 | + | 0.185344i | ||||
\(589\) | −26.4071 | − | 19.1859i | −1.08809 | − | 0.790542i | ||||
\(590\) | −19.0538 | + | 7.40255i | −0.784434 | + | 0.304758i | ||||
\(591\) | 0.408059 | + | 1.25588i | 0.0167853 | + | 0.0516599i | ||||
\(592\) | −17.5597 | − | 24.1689i | −0.721699 | − | 0.993334i | ||||
\(593\) | 30.2533i | 1.24235i | 0.783670 | + | 0.621177i | \(0.213345\pi\) | ||||
−0.783670 | + | 0.621177i | \(0.786655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.60770 | − | 1.31268i | 0.0659091 | − | 0.0538145i | ||||
\(596\) | 19.2422 | − | 13.9802i | 0.788189 | − | 0.572653i | ||||
\(597\) | −0.984606 | + | 0.319918i | −0.0402972 | + | 0.0130934i | ||||
\(598\) | 49.2114 | + | 15.9897i | 2.01240 | + | 0.653869i | ||||
\(599\) | 16.5402 | + | 12.0172i | 0.675816 | + | 0.491009i | 0.871967 | − | 0.489565i | \(-0.162844\pi\) |
−0.196151 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(600\) | 0.988348 | − | 0.904482i | 0.0403491 | − | 0.0369253i | ||||
\(601\) | 6.18034 | − | 19.0211i | 0.252101 | − | 0.775888i | −0.742286 | − | 0.670084i | \(-0.766258\pi\) |
0.994387 | − | 0.105804i | \(-0.0337418\pi\) | |||||||
\(602\) | 17.6169 | − | 5.72407i | 0.718010 | − | 0.233296i | ||||
\(603\) | −23.9870 | − | 33.0153i | −0.976826 | − | 1.34449i | ||||
\(604\) | 10.7321 | 0.436681 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.39230 | 0.0565585 | ||||||||
\(607\) | 18.5103 | + | 25.4773i | 0.751311 | + | 1.03409i | 0.997887 | + | 0.0649672i | \(0.0206943\pi\) |
−0.246577 | + | 0.969123i | \(0.579306\pi\) | |||||||
\(608\) | −44.7194 | + | 14.5302i | −1.81361 | + | 0.589278i | ||||
\(609\) | −0.993610 | + | 3.05802i | −0.0402631 | + | 0.123917i | ||||
\(610\) | −2.01331 | − | 35.6587i | −0.0815165 | − | 1.44378i | ||||
\(611\) | −14.0862 | − | 10.2342i | −0.569868 | − | 0.414033i | ||||
\(612\) | −4.65921 | − | 1.51387i | −0.188337 | − | 0.0611945i | ||||
\(613\) | −6.36459 | + | 2.06798i | −0.257064 | + | 0.0835250i | −0.434714 | − | 0.900569i | \(-0.643150\pi\) |
0.177650 | + | 0.984094i | \(0.443150\pi\) | |||||||
\(614\) | 27.5491 | − | 20.0156i | 1.11179 | − | 0.807764i | ||||
\(615\) | 1.26795 | + | 1.55291i | 0.0511286 | + | 0.0626195i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.69161i | 0.0681019i | 0.999420 | + | 0.0340509i | \(0.0108408\pi\) | ||||
−0.999420 | + | 0.0340509i | \(0.989159\pi\) | |||||||
\(618\) | 2.49376 | + | 3.43237i | 0.100314 | + | 0.138070i | ||||
\(619\) | 8.89493 | + | 27.3758i | 0.357518 | + | 1.10033i | 0.954535 | + | 0.298098i | \(0.0963522\pi\) |
−0.597018 | + | 0.802228i | \(0.703648\pi\) | |||||||
\(620\) | 7.38857 | + | 19.0178i | 0.296732 | + | 0.763775i | ||||
\(621\) | −15.1545 | − | 11.0104i | −0.608131 | − | 0.441833i | ||||
\(622\) | −31.8541 | + | 43.8434i | −1.27723 | + | 1.75796i | ||||
\(623\) | 5.51190 | + | 1.79092i | 0.220830 | + | 0.0717519i | ||||
\(624\) | 3.02956 | + | 9.32401i | 0.121279 | + | 0.373259i | ||||
\(625\) | 24.3665 | − | 5.59235i | 0.974659 | − | 0.223694i | ||||
\(626\) | −33.1244 | −1.32392 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 20.9086i | − | 0.834344i | ||||||
\(629\) | −5.60503 | + | 4.07230i | −0.223487 | + | 0.162373i | ||||
\(630\) | 8.89734 | + | 5.72702i | 0.354479 | + | 0.228170i | ||||
\(631\) | 5.97037 | − | 18.3749i | 0.237676 | − | 0.731493i | −0.759079 | − | 0.650999i | \(-0.774350\pi\) |
0.996755 | − | 0.0804940i | \(-0.0256498\pi\) | |||||||
\(632\) | 1.66251 | − | 2.28825i | 0.0661310 | − | 0.0910215i | ||||
\(633\) | 3.38470 | − | 4.65864i | 0.134530 | − | 0.185164i | ||||
\(634\) | 4.16064 | − | 12.8051i | 0.165240 | − | 0.508556i | ||||
\(635\) | 4.04962 | − | 6.29137i | 0.160704 | − | 0.249666i | ||||
\(636\) | −8.68241 | + | 6.30814i | −0.344280 | + | 0.250134i | ||||
\(637\) | 26.2880i | 1.04157i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | −8.87353 | − | 2.33926i | −0.350757 | − | 0.0924676i | ||||
\(641\) | 6.13597 | + | 18.8846i | 0.242356 | + | 0.745895i | 0.996060 | + | 0.0886813i | \(0.0282653\pi\) |
−0.753704 | + | 0.657214i | \(0.771735\pi\) | |||||||
\(642\) | −4.16690 | − | 1.35391i | −0.164455 | − | 0.0534345i | ||||
\(643\) | −16.2611 | + | 22.3815i | −0.641277 | + | 0.882642i | −0.998683 | − | 0.0513075i | \(-0.983661\pi\) |
0.357406 | + | 0.933949i | \(0.383661\pi\) | |||||||
\(644\) | 7.93148 | + | 5.76256i | 0.312544 | + | 0.227077i | ||||
\(645\) | −4.48277 | − | 11.5384i | −0.176509 | − | 0.454326i | ||||
\(646\) | 3.82943 | + | 11.7858i | 0.150667 | + | 0.463705i | ||||
\(647\) | 11.1543 | + | 15.3525i | 0.438519 | + | 0.603569i | 0.969882 | − | 0.243575i | \(-0.0783201\pi\) |
−0.531363 | + | 0.847144i | \(0.678320\pi\) | |||||||
\(648\) | 3.44760i | 0.135435i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −8.19615 | + | 40.1528i | −0.321480 | + | 1.57492i | ||||
\(651\) | −1.97794 | + | 1.43705i | −0.0775214 | + | 0.0563226i | ||||
\(652\) | −12.5007 | + | 4.06173i | −0.489566 | + | 0.159069i | ||||
\(653\) | −30.3814 | − | 9.87152i | −1.18892 | − | 0.386302i | −0.353244 | − | 0.935531i | \(-0.614922\pi\) |
−0.835672 | + | 0.549229i | \(0.814922\pi\) | |||||||
\(654\) | 0.967708 | + | 0.703081i | 0.0378404 | + | 0.0274926i | ||||
\(655\) | 47.1604 | − | 2.66270i | 1.84271 | − | 0.104040i | ||||
\(656\) | 2.38934 | − | 7.35362i | 0.0932879 | − | 0.287111i | ||||
\(657\) | −12.7292 | + | 4.13596i | −0.496613 | + | 0.161359i | ||||
\(658\) | −4.17811 | − | 5.75068i | −0.162880 | − | 0.224185i | ||||
\(659\) | −11.3205 | −0.440984 | −0.220492 | − | 0.975389i | \(-0.570766\pi\) | ||||
−0.220492 | + | 0.975389i | \(0.570766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.58846 | −0.0617838 | −0.0308919 | − | 0.999523i | \(-0.509835\pi\) | ||||
−0.0308919 | + | 0.999523i | \(0.509835\pi\) | |||||||
\(662\) | 8.86138 | + | 12.1966i | 0.344407 | + | 0.474036i | ||||
\(663\) | 2.16235 | − | 0.702589i | 0.0839785 | − | 0.0272863i | ||||
\(664\) | 1.58351 | − | 4.87355i | 0.0614522 | − | 0.189130i | ||||
\(665\) | −0.700242 | − | 12.4023i | −0.0271542 | − | 0.480941i | ||||
\(666\) | −28.5749 | − | 20.7609i | −1.10725 | − | 0.804468i | ||||
\(667\) | −41.5983 | − | 13.5161i | −1.61069 | − | 0.523346i | ||||
\(668\) | 3.18230 | − | 1.03399i | 0.123127 | − | 0.0400063i | ||||
\(669\) | −2.42705 | + | 1.76336i | −0.0938352 | + | 0.0681753i | ||||
\(670\) | 49.9808 | − | 40.8091i | 1.93093 | − | 1.57659i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.52193i | 0.135861i | ||||||||
\(673\) | 0.950617 | + | 1.30841i | 0.0366436 | + | 0.0504356i | 0.826946 | − | 0.562282i | \(-0.190076\pi\) |
−0.790302 | + | 0.612717i | \(0.790076\pi\) | |||||||
\(674\) | −4.67368 | − | 14.3841i | −0.180024 | − | 0.554055i | ||||
\(675\) | 7.31375 | − | 12.9076i | 0.281506 | − | 0.496813i | ||||
\(676\) | −7.00629 | − | 5.09037i | −0.269473 | − | 0.195783i | ||||
\(677\) | 5.31363 | − | 7.31358i | 0.204219 | − | 0.281084i | −0.694606 | − | 0.719390i | \(-0.744421\pi\) |
0.898826 | + | 0.438306i | \(0.144421\pi\) | |||||||
\(678\) | −2.68999 | − | 0.874032i | −0.103309 | − | 0.0335670i | ||||
\(679\) | 0.181843 | + | 0.559656i | 0.00697851 | + | 0.0214776i | ||||
\(680\) | −0.305465 | + | 1.15872i | −0.0117140 | + | 0.0444348i | ||||
\(681\) | −11.1436 | −0.427023 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.4887i | 0.860507i | 0.902708 | + | 0.430253i | \(0.141576\pi\) | ||||
−0.902708 | + | 0.430253i | \(0.858424\pi\) | |||||||
\(684\) | −23.7208 | + | 17.2342i | −0.906987 | + | 0.658965i | ||||
\(685\) | 16.6571 | − | 25.8780i | 0.636434 | − | 0.988747i | ||||
\(686\) | −7.06302 | + | 21.7377i | −0.269667 | + | 0.829951i | ||||
\(687\) | 5.45484 | − | 7.50794i | 0.208115 | − | 0.286446i | ||||
\(688\) | −28.0617 | + | 38.6237i | −1.06984 | + | 1.47251i | ||||
\(689\) | −15.6933 | + | 48.2990i | −0.597867 | + | 1.84005i | ||||
\(690\) | 7.64062 | − | 11.8703i | 0.290873 | − | 0.451893i | ||||
\(691\) | 22.5788 | − | 16.4045i | 0.858939 | − | 0.624056i | −0.0686571 | − | 0.997640i | \(-0.521871\pi\) |
0.927596 | + | 0.373585i | \(0.121871\pi\) | |||||||
\(692\) | 13.2084i | 0.502108i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.73205 | 0.217586 | ||||||||
\(695\) | −9.45550 | + | 35.8675i | −0.358667 | + | 1.36053i | ||||
\(696\) | −0.573661 | − | 1.76555i | −0.0217446 | − | 0.0669229i | ||||
\(697\) | −1.70539 | − | 0.554114i | −0.0645962 | − | 0.0209886i | ||||
\(698\) | −31.0228 | + | 42.6992i | −1.17423 | + | 1.61619i | ||||
\(699\) | −5.44634 | − | 3.95700i | −0.206000 | − | 0.149667i | ||||
\(700\) | −3.82782 | + | 6.75547i | −0.144678 | + | 0.255333i | ||||
\(701\) | 3.13454 | + | 9.64713i | 0.118390 | + | 0.364367i | 0.992639 | − | 0.121111i | \(-0.0386456\pi\) |
−0.874249 | + | 0.485478i | \(0.838646\pi\) | |||||||
\(702\) | 14.2944 | + | 19.6745i | 0.539506 | + | 0.742567i | ||||
\(703\) | 41.4655i | 1.56390i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.67949 | + | 3.00429i | −0.138578 | + | 0.113148i | ||||
\(706\) | 2.64383 | − | 1.92085i | 0.0995017 | − | 0.0722922i | ||||
\(707\) | 1.18721 | − | 0.385748i | 0.0446496 | − | 0.0145075i | ||||
\(708\) | −4.03499 | − | 1.31105i | −0.151644 | − | 0.0492722i | ||||
\(709\) | 18.9248 | + | 13.7497i | 0.710735 | + | 0.516379i | 0.883411 | − | 0.468600i | \(-0.155241\pi\) |
−0.172676 | + | 0.984979i | \(0.555241\pi\) | |||||||
\(710\) | 0.534780 | + | 9.47175i | 0.0200699 | + | 0.355468i | ||||
\(711\) | 4.61307 | − | 14.1976i | 0.173004 | − | 0.532450i | ||||
\(712\) | −3.18230 | + | 1.03399i | −0.119262 | + | 0.0387505i | ||||
\(713\) | −19.5483 | − | 26.9059i | −0.732090 | − | 1.00764i | ||||
\(714\) | 0.928203 | 0.0347371 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.7846 | −0.552527 | ||||||||
\(717\) | −3.54775 | − | 4.88306i | −0.132493 | − | 0.182361i | ||||
\(718\) | 33.6956 | − | 10.9484i | 1.25751 | − | 0.408590i | ||||
\(719\) | 12.3001 | − | 37.8557i | 0.458715 | − | 1.41178i | −0.408003 | − | 0.912981i | \(-0.633775\pi\) |
0.866718 | − | 0.498799i | \(-0.166225\pi\) | |||||||
\(720\) | −27.2281 | + | 1.53731i | −1.01473 | + | 0.0572922i | ||||
\(721\) | 3.07738 | + | 2.23585i | 0.114608 | + | 0.0832672i | ||||
\(722\) | 35.6295 | + | 11.5767i | 1.32599 | + | 0.430841i | ||||
\(723\) | 4.98425 | − | 1.61948i | 0.185366 | − | 0.0602292i | ||||
\(724\) | 4.75350 | − | 3.45362i | 0.176662 | − | 0.128353i | ||||
\(725\) | 6.92820 | − | 33.9411i | 0.257307 | − | 1.26054i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.00240i | − | 0.148441i | −0.997242 | − | 0.0742205i | \(-0.976353\pi\) | ||
0.997242 | − | 0.0742205i | \(-0.0236469\pi\) | |||||||
\(728\) | 1.15736 | + | 1.59297i | 0.0428946 | + | 0.0590393i | ||||
\(729\) | 4.19906 | + | 12.9234i | 0.155521 | + | 0.478644i | ||||
\(730\) | −7.66369 | − | 19.7260i | −0.283646 | − | 0.730091i | ||||
\(731\) | 8.95727 | + | 6.50784i | 0.331297 | + | 0.240701i | ||||
\(732\) | 4.35716 | − | 5.99711i | 0.161045 | − | 0.221660i | ||||
\(733\) | 33.0714 | + | 10.7455i | 1.22152 | + | 0.396896i | 0.847635 | − | 0.530579i | \(-0.178026\pi\) |
0.373885 | + | 0.927475i | \(0.378026\pi\) | |||||||
\(734\) | 17.6908 | + | 54.4468i | 0.652980 | + | 2.00967i | ||||
\(735\) | 6.93495 | + | 1.82821i | 0.255800 | + | 0.0674346i | ||||
\(736\) | −47.9090 | −1.76595 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 9.14162i | − | 0.336508i | ||||||
\(739\) | −20.2835 | + | 14.7368i | −0.746141 | + | 0.542103i | −0.894628 | − | 0.446811i | \(-0.852560\pi\) |
0.148487 | + | 0.988914i | \(0.452560\pi\) | |||||||
\(740\) | 14.0283 | − | 21.7940i | 0.515690 | − | 0.801162i | ||||
\(741\) | 4.20501 | − | 12.9417i | 0.154475 | − | 0.475425i | ||||
\(742\) | −12.1864 | + | 16.7731i | −0.447377 | + | 0.615761i | ||||
\(743\) | −4.72695 | + | 6.50609i | −0.173415 | + | 0.238685i | −0.886874 | − | 0.462012i | \(-0.847128\pi\) |
0.713459 | + | 0.700697i | \(0.247128\pi\) | |||||||
\(744\) | 0.436191 | − | 1.34246i | 0.0159915 | − | 0.0492169i | ||||
\(745\) | −25.8194 | − | 16.6194i | −0.945950 | − | 0.608887i | ||||
\(746\) | −53.3215 | + | 38.7403i | −1.95224 | + | 1.41838i | ||||
\(747\) | − | 27.0459i | − | 0.989559i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.92820 | −0.143533 | ||||||||
\(750\) | 10.0226 | + | 4.95464i | 0.365972 | + | 0.180918i | ||||
\(751\) | −6.37842 | − | 19.6308i | −0.232752 | − | 0.716337i | −0.997412 | − | 0.0719027i | \(-0.977093\pi\) |
0.764660 | − | 0.644434i | \(-0.222907\pi\) | |||||||
\(752\) | 17.4237 | + | 5.66132i | 0.635378 | + | 0.206447i | ||||
\(753\) | −4.31932 | + | 5.94504i | −0.157405 | + | 0.216649i | ||||
\(754\) | 45.9397 | + | 33.3772i | 1.67303 | + | 1.21552i | ||||
\(755\) | −5.01742 | − | 12.9146i | −0.182603 | − | 0.470011i | ||||
\(756\) | 1.42386 | + | 4.38218i | 0.0517851 | + | 0.159378i | ||||
\(757\) | −20.6183 | − | 28.3786i | −0.749385 | − | 1.03144i | −0.998023 | − | 0.0628432i | \(-0.979983\pi\) |
0.248639 | − | 0.968596i | \(-0.420017\pi\) | |||||||
\(758\) | 10.5558i | 0.383405i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.53590 | + | 5.55532i | 0.164534 | + | 0.201513i | ||||
\(761\) | −6.35597 | + | 4.61788i | −0.230404 | + | 0.167398i | −0.696997 | − | 0.717074i | \(-0.745481\pi\) |
0.466594 | + | 0.884472i | \(0.345481\pi\) | |||||||
\(762\) | 3.18230 | − | 1.03399i | 0.115282 | − | 0.0374575i | ||||
\(763\) | 1.01995 | + | 0.331402i | 0.0369247 | + | 0.0119976i | ||||
\(764\) | −15.0384 | − | 10.9260i | −0.544069 | − | 0.395290i | ||||
\(765\) | 0.356520 | + | 6.31450i | 0.0128900 | + | 0.228301i | ||||
\(766\) | 14.1867 | − | 43.6620i | 0.512585 | − | 1.57757i | ||||
\(767\) | −19.0938 | + | 6.20395i | −0.689437 | + | 0.224012i | ||||
\(768\) | −5.90030 | − | 8.12107i | −0.212909 | − | 0.293044i | ||||
\(769\) | −17.8564 | −0.643918 | −0.321959 | − | 0.946754i | \(-0.604341\pi\) | ||||
−0.321959 | + | 0.946754i | \(0.604341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.58846 | 0.0932210 | ||||||||
\(772\) | 10.4642 | + | 14.4027i | 0.376615 | + | 0.518366i | ||||
\(773\) | −49.1148 | + | 15.9584i | −1.76654 | + | 0.573983i | −0.997844 | − | 0.0656355i | \(-0.979093\pi\) |
−0.768693 | + | 0.639618i | \(0.779093\pi\) | |||||||
\(774\) | −17.4424 | + | 53.6823i | −0.626955 | + | 1.92957i | ||||
\(775\) | 19.4312 | − | 17.7823i | 0.697988 | − | 0.638761i | ||||
\(776\) | −0.274860 | − | 0.199698i | −0.00986691 | − | 0.00716873i | ||||
\(777\) | 2.95382 | + | 0.959754i | 0.105968 | + | 0.0344310i | ||||
\(778\) | −33.2999 | + | 10.8198i | −1.19386 | + | 0.387908i | ||||
\(779\) | −8.68241 | + | 6.30814i | −0.311080 | + | 0.226013i | ||||
\(780\) | −6.58846 | + | 5.37945i | −0.235905 | + | 0.192615i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.6264i | 0.451519i | ||||||||
\(783\) | −12.0830 | − | 16.6309i | −0.431812 | − | 0.594338i | ||||
\(784\) | −8.54749 | − | 26.3065i | −0.305267 | − | 0.939517i | ||||
\(785\) | −25.1607 | + | 9.77513i | −0.898025 | + | 0.348889i | ||||
\(786\) | 17.0900 | + | 12.4166i | 0.609579 | + | 0.442885i | ||||
\(787\) | −2.73834 | + | 3.76900i | −0.0976113 | + | 0.134350i | −0.855029 | − | 0.518580i | \(-0.826461\pi\) |
0.757418 | + | 0.652931i | \(0.226461\pi\) | |||||||
\(788\) | 4.20225 | + | 1.36539i | 0.149699 | + | 0.0486401i | ||||
\(789\) | 3.43761 | + | 10.5799i | 0.122382 | + | 0.376654i | ||||
\(790\) | 22.8238 | + | 6.01687i | 0.812034 | + | 0.214071i | ||||
\(791\) | −2.53590 | −0.0901662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.0779i | − | 1.24565i | ||||||
\(794\) | 25.0214 | − | 18.1791i | 0.887978 | − | 0.645154i | ||||
\(795\) | 11.6502 | + | 7.49897i | 0.413190 | + | 0.265961i | ||||
\(796\) | −1.07047 | + | 3.29456i | −0.0379417 | + | 0.116772i | ||||
\(797\) | 4.64543 | − | 6.39388i | 0.164549 | − | 0.226483i | −0.718778 | − | 0.695240i | \(-0.755298\pi\) |
0.883327 | + | 0.468757i | \(0.155298\pi\) | |||||||
\(798\) | 3.26533 | − | 4.49435i | 0.115592 | − | 0.159098i | ||||
\(799\) | 1.31292 | − | 4.04076i | 0.0464479 | − | 0.142952i | ||||
\(800\) | −4.27101 | − | 37.7024i | −0.151003 | − | 1.33298i | ||||
\(801\) | −14.2874 | + | 10.3804i | −0.504822 | + | 0.366775i | ||||
\(802\) | − | 62.4384i | − | 2.20478i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.3923 | 0.472310 | ||||||||
\(805\) | 3.22637 | − | 12.2386i | 0.113715 | − | 0.431353i | ||||
\(806\) | 13.3424 | + | 41.0637i | 0.469966 | + | 1.44641i | ||||
\(807\) | 9.71415 | + | 3.15632i | 0.341954 | + | 0.111108i | ||||
\(808\) | −0.423623 | + | 0.583067i | −0.0149030 | + | 0.0205122i | ||||
\(809\) | −17.3648 | − | 12.6163i | −0.610515 | − | 0.443565i | 0.239081 | − | 0.971000i | \(-0.423154\pi\) |
−0.849596 | + | 0.527435i | \(0.823154\pi\) | |||||||
\(810\) | −26.8178 | + | 10.4189i | −0.942282 | + | 0.366084i | ||||
\(811\) | −10.1916 | − | 31.3666i | −0.357876 | − | 1.10143i | −0.954323 | − | 0.298777i | \(-0.903421\pi\) |
0.596447 | − | 0.802652i | \(-0.296579\pi\) | |||||||
\(812\) | 6.32393 | + | 8.70414i | 0.221926 | + | 0.305455i | ||||
\(813\) | 2.34795i | 0.0823463i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.7321 | + | 13.1440i | 0.375927 | + | 0.460415i | ||||
\(816\) | −1.93542 | + | 1.40616i | −0.0677531 | + | 0.0492255i | ||||
\(817\) | 63.0217 | − | 20.4770i | 2.20485 | − | 0.716400i | ||||
\(818\) | 3.44612 | + | 1.11971i | 0.120491 | + | 0.0391498i | ||||
\(819\) | 8.40755 | + | 6.10844i | 0.293784 | + | 0.213446i | ||||
\(820\) | 6.69754 | − | 0.378147i | 0.233888 | − | 0.0132055i | ||||
\(821\) | 5.81071 | − | 17.8835i | 0.202795 | − | 0.624139i | −0.797002 | − | 0.603977i | \(-0.793582\pi\) |
0.999797 | − | 0.0201620i | \(-0.00641821\pi\) | |||||||
\(822\) | 13.0896 | − | 4.25306i | 0.456552 | − | 0.148343i | ||||
\(823\) | 28.4475 | + | 39.1547i | 0.991619 | + | 1.36485i | 0.930329 | + | 0.366726i | \(0.119521\pi\) |
0.0612894 | + | 0.998120i | \(0.480479\pi\) | |||||||
\(824\) | −2.19615 | −0.0765066 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.19615 | −0.285181 | ||||||||
\(827\) | −15.7123 | − | 21.6261i | −0.546370 | − | 0.752014i | 0.443144 | − | 0.896450i | \(-0.353863\pi\) |
−0.989514 | + | 0.144437i | \(0.953863\pi\) | |||||||
\(828\) | −28.4122 | + | 9.23168i | −0.987392 | + | 0.320823i | ||||
\(829\) | −12.9728 | + | 39.9261i | −0.450563 | + | 1.38669i | 0.425703 | + | 0.904863i | \(0.360027\pi\) |
−0.876266 | + | 0.481827i | \(0.839973\pi\) | |||||||
\(830\) | 42.6954 | − | 2.41060i | 1.48198 | − | 0.0836733i | ||||
\(831\) | −9.50699 | − | 6.90723i | −0.329794 | − | 0.239609i | ||||
\(832\) | 23.1288 | + | 7.51499i | 0.801846 | + | 0.260536i | ||||
\(833\) | −6.10077 | + | 1.98226i | −0.211379 | + | 0.0686812i | ||||
\(834\) | −13.4203 | + | 9.75045i | −0.464709 | + | 0.337630i | ||||
\(835\) | −2.73205 | − | 3.34607i | −0.0945465 | − | 0.115795i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 15.6307i | − | 0.540275i | ||||||
\(838\) | −33.6796 | − | 46.3560i | −1.16344 | − | 1.60134i | ||||
\(839\) | −0.860492 | − | 2.64832i | −0.0297075 | − | 0.0914302i | 0.935103 | − | 0.354375i | \(-0.115306\pi\) |
−0.964811 | + | 0.262945i | \(0.915306\pi\) | |||||||
\(840\) | 0.500724 | − | 0.194535i | 0.0172766 | − | 0.00671209i | ||||
\(841\) | −15.3713 | − | 11.1679i | −0.530046 | − | 0.385101i | ||||
\(842\) | 23.9055 | − | 32.9031i | 0.823837 | − | 1.13391i | ||||
\(843\) | 8.52694 | + | 2.77057i | 0.293683 | + | 0.0954235i | ||||
\(844\) | −5.95412 | − | 18.3249i | −0.204949 | − | 0.630769i | ||||
\(845\) | −2.85002 | + | 10.8110i | −0.0980438 | + | 0.371909i | ||||
\(846\) | 21.6603 | 0.744695 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 53.4355i | − | 1.83498i | ||||||
\(849\) | −12.6113 | + | 9.16267i | −0.432820 | + | 0.314462i | ||||
\(850\) | −9.93645 | + | 1.12562i | −0.340817 | + | 0.0386085i | ||||
\(851\) | −13.0556 | + | 40.1809i | −0.447539 | + | 1.37738i | ||||
\(852\) | −1.15736 | + | 1.59297i | −0.0396505 | + | 0.0545742i | ||||
\(853\) | 7.30224 | − | 10.0507i | 0.250024 | − | 0.344128i | −0.665496 | − | 0.746402i | \(-0.731780\pi\) |
0.915520 | + | 0.402273i | \(0.131780\pi\) | |||||||
\(854\) | 4.42528 | − | 13.6196i | 0.151430 | − | 0.466054i | ||||
\(855\) | 31.8289 | + | 20.4876i | 1.08853 | + | 0.700660i | ||||
\(856\) | 1.83481 | − | 1.33307i | 0.0627125 | − | 0.0455633i | ||||
\(857\) | − | 24.4206i | − | 0.834191i | −0.908863 | − | 0.417095i | \(-0.863048\pi\) | ||
0.908863 | − | 0.417095i | \(-0.136952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8038 | 0.402742 | 0.201371 | − | 0.979515i | \(-0.435460\pi\) | ||||
0.201371 | + | 0.979515i | \(0.435460\pi\) | |||||||
\(860\) | −40.0514 | − | 10.5585i | −1.36574 | − | 0.360041i | ||||
\(861\) | 0.248403 | + | 0.764504i | 0.00846554 | + | 0.0260542i | ||||
\(862\) | −34.7768 | − | 11.2997i | −1.18450 | − | 0.384868i | ||||
\(863\) | 5.73725 | − | 7.89665i | 0.195298 | − | 0.268805i | −0.700126 | − | 0.714020i | \(-0.746873\pi\) |
0.895424 | + | 0.445215i | \(0.146873\pi\) | |||||||
\(864\) | −18.2164 | − | 13.2350i | −0.619733 | − | 0.450263i | ||||
\(865\) | 15.8946 | − | 6.17515i | 0.540431 | − | 0.209962i | ||||
\(866\) | −12.0901 | − | 37.2095i | −0.410838 | − | 1.26443i | ||||
\(867\) | −4.84632 | − | 6.67038i | −0.164590 | − | 0.226538i | ||||
\(868\) | 8.18067i | 0.277670i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.0000 | − | 9.79796i | 0.406838 | − | 0.332182i | ||||
\(871\) | 51.2699 | − | 37.2498i | 1.73721 | − | 1.26216i | ||||
\(872\) | −0.588870 | + | 0.191335i | −0.0199416 | + | 0.00647943i | ||||
\(873\) | −1.70539 | − | 0.554114i | −0.0577186 | − | 0.0187539i | ||||
\(874\) | 61.1368 | + | 44.4185i | 2.06798 | + | 1.50248i | ||||
\(875\) | 9.91889 | + | 1.44797i | 0.335320 | + | 0.0489503i | ||||
\(876\) | 1.35730 | − | 4.17733i | 0.0458588 | − | 0.141139i | ||||
\(877\) | 53.2464 | − | 17.3008i | 1.79800 | − | 0.584206i | 0.798168 | − | 0.602435i | \(-0.205803\pi\) |
0.999834 | + | 0.0182289i | \(0.00580276\pi\) | |||||||
\(878\) | −22.9927 | − | 31.6467i | −0.775966 | − | 1.06803i | ||||
\(879\) | 4.87564 | 0.164451 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.9090 | 1.31088 | 0.655438 | − | 0.755249i | \(-0.272484\pi\) | ||||
0.655438 | + | 0.755249i | \(0.272484\pi\) | |||||||
\(882\) | −19.2222 | − | 26.4571i | −0.647245 | − | 0.890857i | ||||
\(883\) | −44.7194 | + | 14.5302i | −1.50493 | + | 0.488981i | −0.941451 | − | 0.337151i | \(-0.890537\pi\) |
−0.563477 | + | 0.826131i | \(0.690537\pi\) | |||||||
\(884\) | 2.35091 | − | 7.23535i | 0.0790696 | − | 0.243351i | ||||
\(885\) | 0.308755 | + | 5.46852i | 0.0103787 | + | 0.183822i | ||||
\(886\) | −14.3455 | − | 10.4226i | −0.481948 | − | 0.350155i | ||||
\(887\) | −7.93807 | − | 2.57924i | −0.266534 | − | 0.0866022i | 0.172701 | − | 0.984974i | \(-0.444751\pi\) |
−0.439235 | + | 0.898372i | \(0.644751\pi\) | |||||||
\(888\) | −1.70539 | + | 0.554114i | −0.0572291 | + | 0.0185949i | ||||
\(889\) | 2.42705 | − | 1.76336i | 0.0814007 | − | 0.0591411i | ||||
\(890\) | −17.6603 | − | 21.6293i | −0.591973 | − | 0.725016i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.0382i | 0.336104i | ||||||||
\(893\) | −14.9466 | − | 20.5722i | −0.500168 | − | 0.688422i | ||||
\(894\) | −4.24344 | − | 13.0600i | −0.141922 | − | 0.436790i | ||||
\(895\) | 6.91206 | + | 17.7913i | 0.231045 | + | 0.594698i | ||||
\(896\) | −2.97677 | − | 2.16275i | −0.0994470 | − | 0.0722524i | ||||
\(897\) | 8.14949 | − | 11.2168i | 0.272103 | − | 0.374518i | ||||
\(898\) | 19.3223 | + | 6.27818i | 0.644792 | + | 0.209506i | ||||
\(899\) | −11.2783 | − | 34.7111i | −0.376153 | − | 1.15768i | ||||
\(900\) | −9.79786 | − | 21.5362i | −0.326595 | − | 0.717875i | ||||
\(901\) | −12.3923 | −0.412848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.96335i | − | 0.165170i | ||||||
\(904\) | 1.18448 | − | 0.860577i | 0.0393953 | − | 0.0286224i | ||||
\(905\) | −6.37831 | − | 4.10558i | −0.212022 | − | 0.136474i | ||||
\(906\) | 1.91472 | − | 5.89289i | 0.0636122 | − | 0.195778i | ||||
\(907\) | 4.74294 | − | 6.52810i | 0.157487 | − | 0.216762i | −0.722981 | − | 0.690868i | \(-0.757229\pi\) |
0.880468 | + | 0.474106i | \(0.157229\pi\) | |||||||
\(908\) | −21.9169 | + | 30.1660i | −0.727337 | + | 1.00109i | ||||
\(909\) | −1.17545 | + | 3.61767i | −0.0389873 | + | 0.119991i | ||||
\(910\) | −8.89357 | + | 13.8168i | −0.294819 | + | 0.458023i | ||||
\(911\) | −14.7635 | + | 10.7263i | −0.489137 | + | 0.355379i | −0.804852 | − | 0.593475i | \(-0.797756\pi\) |
0.315715 | + | 0.948854i | \(0.397756\pi\) | |||||||
\(912\) | 14.3180i | 0.474116i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.9808 | −1.35552 | ||||||||
\(915\) | −9.25378 | − | 2.43951i | −0.305921 | − | 0.0806477i | ||||
\(916\) | −9.59577 | − | 29.5327i | −0.317053 | − | 0.975789i | ||||
\(917\) | 18.0126 | + | 5.85265i | 0.594829 | + | 0.193272i | ||||
\(918\) | −3.48807 | + | 4.80091i | −0.115123 | + | 0.158454i | ||||
\(919\) | 26.6820 | + | 19.3856i | 0.880158 | + | 0.639472i | 0.933293 | − | 0.359115i | \(-0.116921\pi\) |
−0.0531354 | + | 0.998587i | \(0.516921\pi\) | |||||||
\(920\) | 2.64627 | + | 6.81137i | 0.0872448 | + | 0.224564i | ||||
\(921\) | −2.81958 | − | 8.67778i | −0.0929084 | − | 0.285943i | ||||
\(922\) | 37.4720 | + | 51.5757i | 1.23407 | + | 1.69856i | ||||
\(923\) | 9.31749i | 0.306689i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.7846 | − | 6.69213i | −1.07795 | − | 0.220036i | ||||
\(926\) | −27.9246 | + | 20.2884i | −0.917658 | + | 0.666718i | ||||
\(927\) | −11.0238 | + | 3.58185i | −0.362069 | + | 0.117643i | ||||
\(928\) | −50.0028 | − | 16.2469i | −1.64142 | − | 0.533331i | ||||
\(929\) | −13.0604 | − | 9.48897i | −0.428499 | − | 0.311323i | 0.352549 | − | 0.935793i | \(-0.385315\pi\) |
−0.781049 | + | 0.624470i | \(0.785315\pi\) | |||||||
\(930\) | 11.7608 | − | 0.664019i | 0.385651 | − | 0.0217740i | ||||
\(931\) | −11.8639 | + | 36.5133i | −0.388823 | + | 1.19667i | ||||
\(932\) | −21.4234 | + | 6.96088i | −0.701746 | + | 0.228011i | ||||
\(933\) | 8.53527 | + | 11.7478i | 0.279432 | + | 0.384606i | ||||
\(934\) | −34.3205 | −1.12300 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 13.3438 | + | 18.3661i | 0.435921 | + | 0.599994i | 0.969300 | − | 0.245883i | \(-0.0790778\pi\) |
−0.533378 | + | 0.845877i | \(0.679078\pi\) | |||||||
\(938\) | 24.6057 | − | 7.99487i | 0.803404 | − | 0.261042i | ||||
\(939\) | −2.74272 | + | 8.44124i | −0.0895054 | + | 0.275469i | ||||
\(940\) | 0.895985 | + | 15.8692i | 0.0292238 | + | 0.517597i | ||||
\(941\) | 21.8435 | + | 15.8702i | 0.712076 | + | 0.517354i | 0.883843 | − | 0.467784i | \(-0.154947\pi\) |
−0.171766 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(942\) | −11.4808 | − | 3.73032i | −0.374063 | − | 0.121541i | ||||
\(943\) | −10.3996 | + | 3.37903i | −0.338657 | + | 0.110036i | ||||
\(944\) | 17.0900 | − | 12.4166i | 0.556231 | − | 0.404125i | ||||
\(945\) | 4.60770 | − | 3.76217i | 0.149888 | − | 0.122383i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.3180i | − | 0.465273i | −0.972564 | − | 0.232636i | \(-0.925265\pi\) | ||
0.972564 | − | 0.232636i | \(-0.0747352\pi\) | |||||||
\(948\) | 2.87955 | + | 3.96336i | 0.0935234 | + | 0.128724i | ||||
\(949\) | −6.42280 | − | 19.7673i | −0.208493 | − | 0.641675i | ||||
\(950\) | −29.5053 | + | 52.0720i | −0.957277 | + | 1.68944i | ||||
\(951\) | −2.91869 | − | 2.12055i | −0.0946449 | − | 0.0687635i | ||||
\(952\) | −0.282415 | + | 0.388711i | −0.00915313 | + | 0.0125982i | ||||
\(953\) | 29.8538 | + | 9.70007i | 0.967058 | + | 0.314216i | 0.749628 | − | 0.661860i | \(-0.230233\pi\) |
0.217430 | + | 0.976076i | \(0.430233\pi\) | |||||||
\(954\) | −19.5227 | − | 60.0848i | −0.632072 | − | 1.94532i | ||||
\(955\) | −6.11732 | + | 23.2048i | −0.197952 | + | 0.750890i | ||||
\(956\) | −20.1962 | −0.653190 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 18.2832i | − | 0.590705i | ||||||
\(959\) | 9.98306 | − | 7.25312i | 0.322370 | − | 0.234215i | ||||
\(960\) | 3.59100 | − | 5.57888i | 0.115899 | − | 0.180058i | ||||
\(961\) | −1.00391 | + | 3.08971i | −0.0323841 | + | 0.0996680i | ||||
\(962\) | 32.2399 | − | 44.3744i | 1.03945 | − | 1.43069i | ||||
\(963\) | 7.03582 | − | 9.68397i | 0.226726 | − | 0.312062i | ||||
\(964\) | 5.41889 | − | 16.6776i | 0.174531 | − | 0.537150i | ||||
\(965\) | 12.4396 | − | 19.3258i | 0.400445 | − | 0.622120i | ||||
\(966\) | 4.57924 | − | 3.32701i | 0.147335 | − | 0.107045i | ||||
\(967\) | − | 4.24264i | − | 0.136434i | −0.997671 | − | 0.0682171i | \(-0.978269\pi\) | ||
0.997671 | − | 0.0682171i | \(-0.0217310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.32051 | 0.106670 | ||||||||
\(970\) | 0.722737 | − | 2.74156i | 0.0232057 | − | 0.0880260i | ||||
\(971\) | −3.42137 | − | 10.5299i | −0.109797 | − | 0.337921i | 0.881029 | − | 0.473062i | \(-0.156851\pi\) |
−0.990826 | + | 0.135141i | \(0.956851\pi\) | |||||||
\(972\) | −20.3422 | − | 6.60959i | −0.652477 | − | 0.212003i | ||||
\(973\) | −8.74201 | + | 12.0324i | −0.280256 | + | 0.385739i | ||||
\(974\) | −19.8925 | − | 14.4527i | −0.637396 | − | 0.463095i | ||||
\(975\) | 9.55368 | + | 5.41335i | 0.305963 | + | 0.173366i | ||||
\(976\) | 11.4055 | + | 35.1025i | 0.365081 | + | 1.12360i | ||||
\(977\) | 8.80170 | + | 12.1145i | 0.281591 | + | 0.387577i | 0.926260 | − | 0.376885i | \(-0.123005\pi\) |
−0.644669 | + | 0.764462i | \(0.723005\pi\) | |||||||
\(978\) | 7.58871i | 0.242660i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 18.5885 | − | 15.1774i | 0.593786 | − | 0.484825i | ||||
\(981\) | −2.64383 | + | 1.92085i | −0.0844109 | + | 0.0613281i | ||||
\(982\) | 28.8692 | − | 9.38016i | 0.921252 | − | 0.299333i | ||||
\(983\) | 14.2768 | + | 4.63881i | 0.455359 | + | 0.147955i | 0.527711 | − | 0.849424i | \(-0.323050\pi\) |
−0.0723519 | + | 0.997379i | \(0.523050\pi\) | |||||||
\(984\) | −0.375466 | − | 0.272792i | −0.0119694 | − | 0.00869629i | ||||
\(985\) | −0.321554 | − | 5.69520i | −0.0102456 | − | 0.181464i | ||||
\(986\) | −4.28187 | + | 13.1782i | −0.136362 | + | 0.419680i | ||||
\(987\) | −1.81143 | + | 0.588568i | −0.0576583 | + | 0.0187343i | ||||
\(988\) | −26.7632 | − | 36.8364i | −0.851450 | − | 1.17192i | ||||
\(989\) | 67.5167 | 2.14690 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.9090 | −1.45835 | −0.729173 | − | 0.684329i | \(-0.760095\pi\) | ||||
−0.729173 | + | 0.684329i | \(0.760095\pi\) | |||||||
\(992\) | −23.4978 | − | 32.3420i | −0.746057 | − | 1.02686i | ||||
\(993\) | 3.84186 | − | 1.24830i | 0.121918 | − | 0.0396135i | ||||
\(994\) | −1.17545 | + | 3.61767i | −0.0372831 | + | 0.114746i | ||||
\(995\) | 4.46502 | − | 0.252098i | 0.141551 | − | 0.00799204i | ||||
\(996\) | 7.18055 | + | 5.21697i | 0.227524 | + | 0.165306i | ||||
\(997\) | −0.167258 | − | 0.0543454i | −0.00529711 | − | 0.00172114i | 0.306367 | − | 0.951913i | \(-0.400886\pi\) |
−0.311664 | + | 0.950192i | \(0.600886\pi\) | |||||||
\(998\) | 70.5382 | − | 22.9192i | 2.23285 | − | 0.725496i | ||||
\(999\) | −16.0642 | + | 11.6713i | −0.508248 | + | 0.369264i |
(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.j.f.124.1 | 16 | ||
5.4 | even | 2 | inner | 605.2.j.f.124.4 | 16 | ||
11.2 | odd | 10 | 605.2.b.e.364.1 | yes | 4 | ||
11.3 | even | 5 | inner | 605.2.j.f.269.1 | 16 | ||
11.4 | even | 5 | inner | 605.2.j.f.444.4 | 16 | ||
11.5 | even | 5 | inner | 605.2.j.f.9.4 | 16 | ||
11.6 | odd | 10 | 605.2.j.e.9.1 | 16 | |||
11.7 | odd | 10 | 605.2.j.e.444.1 | 16 | |||
11.8 | odd | 10 | 605.2.j.e.269.4 | 16 | |||
11.9 | even | 5 | 605.2.b.d.364.4 | yes | 4 | ||
11.10 | odd | 2 | 605.2.j.e.124.4 | 16 | |||
55.2 | even | 20 | 3025.2.a.z.1.4 | 4 | |||
55.4 | even | 10 | inner | 605.2.j.f.444.1 | 16 | ||
55.9 | even | 10 | 605.2.b.d.364.1 | ✓ | 4 | ||
55.13 | even | 20 | 3025.2.a.z.1.1 | 4 | |||
55.14 | even | 10 | inner | 605.2.j.f.269.4 | 16 | ||
55.19 | odd | 10 | 605.2.j.e.269.1 | 16 | |||
55.24 | odd | 10 | 605.2.b.e.364.4 | yes | 4 | ||
55.29 | odd | 10 | 605.2.j.e.444.4 | 16 | |||
55.39 | odd | 10 | 605.2.j.e.9.4 | 16 | |||
55.42 | odd | 20 | 3025.2.a.y.1.1 | 4 | |||
55.49 | even | 10 | inner | 605.2.j.f.9.1 | 16 | ||
55.53 | odd | 20 | 3025.2.a.y.1.4 | 4 | |||
55.54 | odd | 2 | 605.2.j.e.124.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.d.364.1 | ✓ | 4 | 55.9 | even | 10 | ||
605.2.b.d.364.4 | yes | 4 | 11.9 | even | 5 | ||
605.2.b.e.364.1 | yes | 4 | 11.2 | odd | 10 | ||
605.2.b.e.364.4 | yes | 4 | 55.24 | odd | 10 | ||
605.2.j.e.9.1 | 16 | 11.6 | odd | 10 | |||
605.2.j.e.9.4 | 16 | 55.39 | odd | 10 | |||
605.2.j.e.124.1 | 16 | 55.54 | odd | 2 | |||
605.2.j.e.124.4 | 16 | 11.10 | odd | 2 | |||
605.2.j.e.269.1 | 16 | 55.19 | odd | 10 | |||
605.2.j.e.269.4 | 16 | 11.8 | odd | 10 | |||
605.2.j.e.444.1 | 16 | 11.7 | odd | 10 | |||
605.2.j.e.444.4 | 16 | 55.29 | odd | 10 | |||
605.2.j.f.9.1 | 16 | 55.49 | even | 10 | inner | ||
605.2.j.f.9.4 | 16 | 11.5 | even | 5 | inner | ||
605.2.j.f.124.1 | 16 | 1.1 | even | 1 | trivial | ||
605.2.j.f.124.4 | 16 | 5.4 | even | 2 | inner | ||
605.2.j.f.269.1 | 16 | 11.3 | even | 5 | inner | ||
605.2.j.f.269.4 | 16 | 55.14 | even | 10 | inner | ||
605.2.j.f.444.1 | 16 | 55.4 | even | 10 | inner | ||
605.2.j.f.444.4 | 16 | 11.4 | even | 5 | inner | ||
3025.2.a.y.1.1 | 4 | 55.42 | odd | 20 | |||
3025.2.a.y.1.4 | 4 | 55.53 | odd | 20 | |||
3025.2.a.z.1.1 | 4 | 55.13 | even | 20 | |||
3025.2.a.z.1.4 | 4 | 55.2 | even | 20 |