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 | 444.1 | ||
Root | \(1.83730 + 0.596975i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.444 |
Dual form | 605.2.j.e.124.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 | 0.189446 | + | 0.981891i | \(0.439331\pi\) |
−0.992376 | + | 0.123247i | \(0.960669\pi\) | |||||||
\(3\) | 0.492303 | + | 0.159959i | 0.284231 | + | 0.0923524i | 0.447663 | − | 0.894202i | \(-0.352256\pi\) |
−0.163432 | + | 0.986555i | \(0.552256\pi\) | |||||||
\(4\) | −0.535233 | − | 1.64728i | −0.267617 | − | 0.823639i | ||||
\(5\) | 0.570005 | − | 2.16220i | 0.254914 | − | 0.966964i | ||||
\(6\) | −0.809017 | + | 0.587785i | −0.330280 | + | 0.239962i | ||||
\(7\) | 0.852694 | − | 0.277057i | 0.322288 | − | 0.104718i | −0.143405 | − | 0.989664i | \(-0.545805\pi\) |
0.465693 | + | 0.884946i | \(0.345805\pi\) | |||||||
\(8\) | −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 | 0.308355 | + | 0.951271i | \(0.400222\pi\) |
−1.00000 | 0.000696272i | \(0.999778\pi\) | ||||||||
\(14\) | −0.535233 | + | 1.64728i | −0.143047 | + | 0.440254i | ||||
\(15\) | 0.626478 | − | 0.973279i | 0.161756 | − | 0.251299i | ||||
\(16\) | 3.61153 | − | 2.62393i | 0.902884 | − | 0.655983i | ||||
\(17\) | 0.608520 | + | 0.837556i | 0.147588 | + | 0.203137i | 0.876410 | − | 0.481566i | \(-0.159932\pi\) |
−0.728822 | + | 0.684703i | \(0.759932\pi\) | |||||||
\(18\) | 5.01960 | − | 1.63097i | 1.18313 | − | 0.384422i | ||||
\(19\) | 1.91472 | − | 5.89289i | 0.439266 | − | 1.35192i | −0.449385 | − | 0.893338i | \(-0.648357\pi\) |
0.888651 | − | 0.458584i | \(-0.151643\pi\) | |||||||
\(20\) | −3.86682 | + | 0.218323i | −0.864648 | + | 0.0488185i | ||||
\(21\) | 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 | ||||
\(25\) | −4.35019 | − | 2.46492i | −0.870038 | − | 0.492985i | ||||
\(26\) | −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 | −0.926949 | − | 0.375188i | \(-0.877578\pi\) |
0.529388 | − | 0.848380i | \(-0.322422\pi\) | |||||||
\(30\) | 0.809764 | + | 2.08429i | 0.147842 | + | 0.380538i | ||||
\(31\) | 4.26186 | + | 3.09642i | 0.765453 | + | 0.556134i | 0.900578 | − | 0.434695i | \(-0.143144\pi\) |
−0.135125 | + | 0.990829i | \(0.543144\pi\) | |||||||
\(32\) | 7.58871i | 1.34151i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −0.113012 | − | 2.00162i | −0.0191026 | − | 0.338335i | ||||
\(36\) | −1.46228 | + | 4.50045i | −0.243714 | + | 0.750075i | ||||
\(37\) | 6.36459 | − | 2.06798i | 1.04633 | − | 0.339974i | 0.265105 | − | 0.964220i | \(-0.414594\pi\) |
0.781228 | + | 0.624246i | \(0.214594\pi\) | |||||||
\(38\) | 7.03582 | + | 9.68397i | 1.14136 | + | 1.57095i | ||||
\(39\) | −1.77672 | + | 1.29087i | −0.284504 | + | 0.206704i | ||||
\(40\) | −0.626478 | + | 0.973279i | −0.0990548 | + | 0.153889i | ||||
\(41\) | 0.535233 | − | 1.64728i | 0.0835894 | − | 0.257262i | −0.900523 | − | 0.434808i | \(-0.856816\pi\) |
0.984112 | + | 0.177547i | \(0.0568161\pi\) | |||||||
\(42\) | −0.526994 | + | 0.725345i | −0.0813169 | + | 0.111923i | ||||
\(43\) | − | 10.6945i | − | 1.63090i | −0.578827 | − | 0.815451i | \(-0.696489\pi\) | ||
0.578827 | − | 0.815451i | \(-0.303511\pi\) | |||||||
\(44\) | 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 | \(-0.496757\pi\) |
−0.579512 | + | 0.814964i | \(0.696757\pi\) | |||||||
\(48\) | 2.19769 | − | 0.714073i | 0.317209 | − | 0.103068i | ||||
\(49\) | −5.01279 | + | 3.64201i | −0.716113 | + | 0.520287i | ||||
\(50\) | 8.79213 | − | 3.99996i | 1.24340 | − | 0.565680i | ||||
\(51\) | 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 | 0.0226209 | − | 0.999744i | \(-0.492799\pi\) |
0.943823 | − | 0.330452i | \(-0.107201\pi\) | |||||||
\(54\) | 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 | 0.999999 | − | 0.00103733i | \(-0.000330192\pi\) |
−0.809626 | + | 0.586946i | \(0.800330\pi\) | |||||||
\(60\) | −1.93857 | − | 0.511052i | −0.250269 | − | 0.0659766i | ||||
\(61\) | −6.68891 | + | 4.85978i | −0.856427 | + | 0.622231i | −0.926911 | − | 0.375282i | \(-0.877546\pi\) |
0.0704833 | + | 0.997513i | \(0.477546\pi\) | |||||||
\(62\) | −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 | ||||
\(70\) | 3.25665 | + | 2.09624i | 0.389245 | + | 0.250548i | ||||
\(71\) | −1.77672 | + | 1.29087i | −0.210858 | + | 0.153198i | −0.688202 | − | 0.725519i | \(-0.741600\pi\) |
0.477344 | + | 0.878717i | \(0.341600\pi\) | |||||||
\(72\) | 0.831254 | + | 1.14412i | 0.0979642 | + | 0.134836i | ||||
\(73\) | 4.65921 | − | 1.51387i | 0.545319 | − | 0.177185i | −0.0233860 | − | 0.999727i | \(-0.507445\pi\) |
0.568705 | + | 0.822542i | \(0.307445\pi\) | |||||||
\(74\) | −3.99503 | + | 12.2955i | −0.464413 | + | 1.42932i | ||||
\(75\) | −1.74732 | − | 1.90934i | −0.201764 | − | 0.220472i | ||||
\(76\) | −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 | \(-0.200548\pi\) |
−0.310653 | + | 0.950523i | \(0.600548\pi\) | |||||||
\(80\) | −3.61487 | − | 9.30450i | −0.404155 | − | 1.04027i | ||||
\(81\) | 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 | 0.359851 | − | 0.933010i | \(-0.382827\pi\) |
−0.998545 | + | 0.0539231i | \(0.982827\pi\) | |||||||
\(84\) | −0.248403 | − | 0.764504i | −0.0271029 | − | 0.0834143i | ||||
\(85\) | 2.15782 | − | 0.838329i | 0.234048 | − | 0.0909296i | ||||
\(86\) | 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 | \(0.388694\pi\) | |||||||
\(90\) | −0.665276 | − | 11.7830i | −0.0701262 | − | 1.24204i | ||||
\(91\) | −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 | ||||
\(95\) | −11.6502 | − | 7.49897i | −1.19528 | − | 0.769378i | ||||
\(96\) | −1.21388 | + | 3.73594i | −0.123891 | + | 0.381298i | ||||
\(97\) | −0.385786 | + | 0.530989i | −0.0391707 | + | 0.0539138i | −0.828153 | − | 0.560502i | \(-0.810608\pi\) |
0.788982 | + | 0.614416i | \(0.210608\pi\) | |||||||
\(98\) | − | 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 | \(-0.322067\pi\) |
−0.642414 | + | 0.766358i | \(0.722067\pi\) | |||||||
\(102\) | −0.984606 | − | 0.319918i | −0.0974905 | − | 0.0316766i | ||||
\(103\) | −4.03499 | + | 1.31105i | −0.397579 | + | 0.129181i | −0.500981 | − | 0.865458i | \(-0.667027\pi\) |
0.103401 | + | 0.994640i | \(0.467027\pi\) | |||||||
\(104\) | 1.77672 | − | 1.29087i | 0.174222 | − | 0.126580i | ||||
\(105\) | 0.264540 | − | 1.00348i | 0.0258165 | − | 0.0979295i | ||||
\(106\) | 7.14582 | + | 21.9926i | 0.694063 | + | 2.13611i | ||||
\(107\) | −4.16690 | − | 1.35391i | −0.402830 | − | 0.130887i | 0.100593 | − | 0.994928i | \(-0.467926\pi\) |
−0.503423 | + | 0.864040i | \(0.667926\pi\) | |||||||
\(108\) | −3.02076 | + | 4.15771i | −0.290672 | + | 0.400076i | ||||
\(109\) | −1.19615 | −0.114571 | −0.0572853 | − | 0.998358i | \(-0.518244\pi\) | ||||
−0.0572853 | + | 0.998358i | \(0.518244\pi\) | |||||||
\(110\) | 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 | \(-0.357527\pi\) |
−0.179743 | + | 0.983714i | \(0.557527\pi\) | |||||||
\(114\) | 1.91472 | + | 5.89289i | 0.179330 | + | 0.551920i | ||||
\(115\) | −13.6504 | − | 3.59855i | −1.27290 | − | 0.335566i | ||||
\(116\) | −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 | ||||
\(125\) | −7.80928 | + | 8.00095i | −0.698483 | + | 0.715626i | ||||
\(126\) | 3.82831 | − | 2.78143i | 0.341053 | − | 0.247789i | ||||
\(127\) | 1.96677 | + | 2.70702i | 0.174522 | + | 0.240210i | 0.887313 | − | 0.461167i | \(-0.152569\pi\) |
−0.712791 | + | 0.701377i | \(0.752569\pi\) | |||||||
\(128\) | −3.90308 | + | 1.26819i | −0.344987 | + | 0.112093i | ||||
\(129\) | 1.71069 | − | 5.26495i | 0.150618 | − | 0.463553i | ||||
\(130\) | −18.2980 | + | 1.03312i | −1.60484 | + | 0.0906103i | ||||
\(131\) | −21.1244 | −1.84564 | −0.922822 | − | 0.385227i | \(-0.874123\pi\) | ||||
−0.922822 | + | 0.385227i | \(0.874123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.55532i | − | 0.481707i | ||||||
\(134\) | −23.3453 | − | 16.9614i | −2.01673 | − | 1.46524i | ||||
\(135\) | −6.18437 | + | 2.40267i | −0.532266 | + | 0.206789i | ||||
\(136\) | −0.165602 | − | 0.509670i | −0.0142002 | − | 0.0437038i | ||||
\(137\) | −8.08980 | − | 11.1347i | −0.691159 | − | 0.951298i | −1.00000 | 0.000184728i | \(-0.999941\pi\) | |
0.308841 | − | 0.951114i | \(-0.400059\pi\) | |||||||
\(138\) | 3.71080 | + | 5.10748i | 0.315884 | + | 0.434778i | ||||
\(139\) | 5.12612 | + | 15.7766i | 0.434791 | + | 1.33815i | 0.893300 | + | 0.449461i | \(0.148384\pi\) |
−0.458509 | + | 0.888690i | \(0.651616\pi\) | |||||||
\(140\) | −3.23673 | + | 1.25749i | −0.273554 | + | 0.106278i | ||||
\(141\) | −1.71864 | − | 1.24866i | −0.144736 | − | 0.105157i | ||||
\(142\) | − | 4.24264i | − | 0.356034i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.1962 | −1.01635 | ||||||||
\(145\) | −15.4673 | + | 0.873292i | −1.28449 | + | 0.0725230i | ||||
\(146\) | −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 | \(-0.509845\pi\) |
0.941046 | + | 0.338279i | \(0.109845\pi\) | |||||||
\(150\) | 4.96822 | − | 0.562811i | 0.405654 | − | 0.0459534i | ||||
\(151\) | 1.91472 | − | 5.89289i | 0.155817 | − | 0.479557i | −0.842425 | − | 0.538813i | \(-0.818873\pi\) |
0.998243 | + | 0.0592563i | \(0.0188729\pi\) | |||||||
\(152\) | −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 | \(-0.240016\pi\) |
0.187331 | + | 0.982297i | \(0.440016\pi\) | |||||||
\(158\) | −10.0392 | + | 3.26193i | −0.798675 | + | 0.259505i | ||||
\(159\) | 5.01279 | − | 3.64201i | 0.397540 | − | 0.288830i | ||||
\(160\) | 16.4083 | + | 4.32560i | 1.29719 | + | 0.341969i | ||||
\(161\) | −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 | \(-0.896052\pi\) |
0.597775 | + | 0.801664i | \(0.296052\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.1244 | 1.48434 | ||||||||
\(167\) | −1.13551 | + | 1.56290i | −0.0878687 | + | 0.120941i | −0.850688 | − | 0.525671i | \(-0.823814\pi\) |
0.762820 | + | 0.646611i | \(0.223814\pi\) | |||||||
\(168\) | −0.228479 | − | 0.0742372i | −0.0176275 | − | 0.00572753i | ||||
\(169\) | −1.54508 | − | 4.75528i | −0.118853 | − | 0.365791i | ||||
\(170\) | −1.14001 | + | 4.32439i | −0.0874347 | + | 0.331666i | ||||
\(171\) | −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 | 0.571451 | − | 0.820636i | \(-0.306381\pi\) |
−0.0200438 | + | 0.999799i | \(0.506381\pi\) | |||||||
\(174\) | 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 | −0.802791 | − | 0.596261i | \(-0.796652\pi\) |
0.999945 | − | 0.0105163i | \(-0.00334750\pi\) | |||||||
\(180\) | 8.89734 | + | 5.72702i | 0.663169 | + | 0.426867i | ||||
\(181\) | −2.74443 | + | 1.99395i | −0.203992 | + | 0.148209i | −0.685091 | − | 0.728457i | \(-0.740238\pi\) |
0.481099 | + | 0.876666i | \(0.340238\pi\) | |||||||
\(182\) | −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 | ||||
\(185\) | −0.843536 | − | 14.9403i | −0.0620180 | − | 1.09843i | ||||
\(186\) | −5.26795 | −0.386265 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.10823i | 0.518421i | ||||||||
\(189\) | −2.15219 | − | 1.56366i | −0.156549 | − | 0.113739i | ||||
\(190\) | 24.9491 | − | 9.69291i | 1.81000 | − | 0.703198i | ||||
\(191\) | −3.31639 | − | 10.2068i | −0.239965 | − | 0.738537i | −0.996424 | − | 0.0844956i | \(-0.973072\pi\) |
0.756459 | − | 0.654042i | \(-0.226928\pi\) | |||||||
\(192\) | −1.74403 | − | 2.40046i | −0.125865 | − | 0.173238i | ||||
\(193\) | 6.04151 | + | 8.31543i | 0.434877 | + | 0.598557i | 0.969064 | − | 0.246809i | \(-0.0793821\pi\) |
−0.534187 | + | 0.845367i | \(0.679382\pi\) | |||||||
\(194\) | −0.391818 | − | 1.20589i | −0.0281309 | − | 0.0865780i | ||||
\(195\) | 1.77836 | + | 4.57743i | 0.127351 | + | 0.327796i | ||||
\(196\) | 8.68241 | + | 6.30814i | 0.620172 | + | 0.450582i | ||||
\(197\) | 2.55103i | 0.181753i | 0.995862 | + | 0.0908765i | \(0.0289669\pi\) | ||||
−0.995862 | + | 0.0908765i | \(0.971033\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 1.74732 | + | 1.90934i | 0.123555 | + | 0.135011i | ||||
\(201\) | −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 | ||||
\(205\) | −3.25665 | − | 2.09624i | −0.227455 | − | 0.146407i | ||||
\(206\) | 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 | \(-0.174920\pi\) |
−0.233200 | + | 0.972429i | \(0.574920\pi\) | |||||||
\(212\) | −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 | ||||
\(215\) | −23.1237 | − | 6.09593i | −1.57702 | − | 0.415739i | ||||
\(216\) | 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 | \(-0.462162\pi\) |
−0.487695 | + | 0.873014i | \(0.662162\pi\) | |||||||
\(224\) | 2.10250 | + | 6.47084i | 0.140479 | + | 0.432351i | ||||
\(225\) | 5.65680 | + | 12.4340i | 0.377120 | + | 0.828930i | ||||
\(226\) | −4.42055 | + | 3.21172i | −0.294051 | + | 0.213640i | ||||
\(227\) | 20.4741 | − | 6.65245i | 1.35892 | − | 0.441538i | 0.463235 | − | 0.886236i | \(-0.346689\pi\) |
0.895681 | + | 0.444697i | \(0.146689\pi\) | |||||||
\(228\) | −5.28342 | − | 1.71669i | −0.349903 | − | 0.113690i | ||||
\(229\) | −14.5042 | − | 10.5379i | −0.958466 | − | 0.696366i | −0.00567196 | − | 0.999984i | \(-0.501805\pi\) |
−0.952794 | + | 0.303618i | \(0.901805\pi\) | |||||||
\(230\) | 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 | −0.481536 | − | 0.876426i | \(-0.659921\pi\) |
0.982334 | + | 0.187138i | \(0.0599211\pi\) | |||||||
\(234\) | −6.91960 | + | 21.2963i | −0.452349 | + | 1.39219i | ||||
\(235\) | −4.96684 | + | 7.71635i | −0.324001 | + | 0.503359i | ||||
\(236\) | 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 | 0.764299 | + | 0.644863i | \(0.223085\pi\) |
−0.997371 | + | 0.0724614i | \(0.976915\pi\) | |||||||
\(240\) | −0.291272 | − | 5.15887i | −0.0188016 | − | 0.333003i | ||||
\(241\) | 10.1244 | 0.652167 | 0.326084 | − | 0.945341i | \(-0.394271\pi\) | ||||
0.326084 | + | 0.945341i | \(0.394271\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3490i | 0.792188i | ||||||||
\(244\) | 11.5855 | + | 8.41738i | 0.741688 | + | 0.538868i | ||||
\(245\) | 5.01742 | + | 12.9146i | 0.320551 | + | 0.825084i | ||||
\(246\) | 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 | ||||
\(250\) | −3.63714 | − | 21.2903i | −0.230033 | − | 1.34652i | ||||
\(251\) | 11.4849 | + | 8.34429i | 0.724922 | + | 0.526687i | 0.887953 | − | 0.459934i | \(-0.152127\pi\) |
−0.163031 | + | 0.986621i | \(0.552127\pi\) | |||||||
\(252\) | 4.24264i | 0.267261i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.46410 | −0.405594 | ||||||||
\(255\) | 1.19640 | − | 0.0675494i | 0.0749215 | − | 0.00423011i | ||||
\(256\) | 5.99255 | − | 18.4432i | 0.374534 | − | 1.15270i | ||||
\(257\) | 4.75577 | − | 1.54524i | 0.296657 | − | 0.0963897i | −0.156907 | − | 0.987613i | \(-0.550152\pi\) |
0.453564 | + | 0.891224i | \(0.350152\pi\) | |||||||
\(258\) | 6.28609 | + | 8.65206i | 0.391355 | + | 0.538654i | ||||
\(259\) | 4.85410 | − | 3.52671i | 0.301619 | − | 0.219139i | ||||
\(260\) | 8.89357 | − | 13.8168i | 0.551556 | − | 0.856882i | ||||
\(261\) | −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 | \(0.230540\pi\) | ||||
−0.748988 | + | 0.662584i | \(0.769460\pi\) | |||||||
\(264\) | 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 | −0.956205 | − | 0.292698i | \(-0.905447\pi\) |
−0.0171109 | + | 0.999854i | \(0.505447\pi\) | |||||||
\(270\) | 3.26730 | − | 12.3938i | 0.198841 | − | 0.754264i | ||||
\(271\) | −1.40167 | − | 4.31390i | −0.0851454 | − | 0.262051i | 0.899415 | − | 0.437096i | \(-0.143993\pi\) |
−0.984560 | + | 0.175045i | \(0.943993\pi\) | |||||||
\(272\) | 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 | −0.190796 | − | 0.981630i | \(-0.561107\pi\) |
0.992545 | − | 0.121882i | \(-0.0388930\pi\) | |||||||
\(278\) | −30.4780 | − | 9.90289i | −1.82795 | − | 0.593936i | ||||
\(279\) | −4.44747 | − | 13.6879i | −0.266263 | − | 0.819473i | ||||
\(280\) | −0.264540 | + | 1.00348i | −0.0158093 | + | 0.0599693i | ||||
\(281\) | 14.0126 | − | 10.1807i | 0.835921 | − | 0.607332i | −0.0853074 | − | 0.996355i | \(-0.527187\pi\) |
0.921228 | + | 0.389023i | \(0.127187\pi\) | |||||||
\(282\) | 3.90308 | − | 1.26819i | 0.232425 | − | 0.0755194i | ||||
\(283\) | 28.6407 | + | 9.30592i | 1.70251 | + | 0.553179i | 0.989059 | − | 0.147524i | \(-0.0471303\pi\) |
0.713453 | + | 0.700703i | \(0.247130\pi\) | |||||||
\(284\) | 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 | ||||
\(290\) | 16.1985 | − | 25.1655i | 0.951207 | − | 1.47777i | ||||
\(291\) | −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 | −0.558757 | − | 0.829331i | \(-0.688722\pi\) |
0.0354243 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(294\) | 1.91472 | − | 5.89289i | 0.111669 | − | 0.343680i | ||||
\(295\) | 10.5644 | − | 0.596470i | 0.615081 | − | 0.0347278i | ||||
\(296\) | −3.46410 | −0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.5283i | 1.53674i | ||||||||
\(299\) | 21.6692 | + | 15.7436i | 1.25316 | + | 0.910476i | ||||
\(300\) | −2.20999 | + | 3.90027i | −0.127594 | + | 0.225182i | ||||
\(301\) | −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 | ||||
\(305\) | 6.69509 | + | 17.2328i | 0.383360 | + | 0.986749i | ||||
\(306\) | 4.42055 | + | 3.21172i | 0.252706 | + | 0.183602i | ||||
\(307\) | − | 17.6269i | − | 1.00602i | −0.864280 | − | 0.503010i | \(-0.832226\pi\) | ||
0.864280 | − | 0.503010i | \(-0.167774\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.19615 | −0.124935 | ||||||||
\(310\) | 1.28279 | + | 22.7200i | 0.0728574 | + | 1.29041i | ||||
\(311\) | −8.66872 | + | 26.6796i | −0.491558 | + | 1.51286i | 0.330695 | + | 0.943738i | \(0.392717\pi\) |
−0.822253 | + | 0.569122i | \(0.807283\pi\) | |||||||
\(312\) | 1.08117 | − | 0.351294i | 0.0612093 | − | 0.0198881i | ||||
\(313\) | −10.0784 | − | 13.8718i | −0.569666 | − | 0.784078i | 0.422849 | − | 0.906200i | \(-0.361030\pi\) |
−0.992515 | + | 0.122122i | \(0.961030\pi\) | |||||||
\(314\) | −18.8667 | + | 13.7075i | −1.06471 | + | 0.773556i | ||||
\(315\) | −2.96452 | + | 4.60560i | −0.167032 | + | 0.259496i | ||||
\(316\) | 2.92457 | − | 9.00090i | 0.164520 | − | 0.506340i | ||||
\(317\) | −4.09659 | + | 5.63847i | −0.230087 | + | 0.316688i | −0.908413 | − | 0.418073i | \(-0.862706\pi\) |
0.678326 | + | 0.734761i | \(0.262706\pi\) | |||||||
\(318\) | 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 | ||||
\(325\) | 19.3089 | − | 8.78452i | 1.07106 | − | 0.487277i | ||||
\(326\) | −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 | ||||
\(335\) | 32.2971 | + | 8.51426i | 1.76458 | + | 0.465184i | ||||
\(336\) | 1.67612 | − | 1.21777i | 0.0914398 | − | 0.0664349i | ||||
\(337\) | 7.44577 | − | 2.41928i | 0.405597 | − | 0.131786i | −0.0991115 | − | 0.995076i | \(-0.531600\pi\) |
0.504708 | + | 0.863290i | \(0.331600\pi\) | |||||||
\(338\) | 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 | ||||
\(345\) | −6.14450 | − | 3.95508i | −0.330809 | − | 0.212934i | ||||
\(346\) | −11.9185 | + | 8.65928i | −0.640741 | + | 0.465526i | ||||
\(347\) | −1.74403 | − | 2.40046i | −0.0936246 | − | 0.128863i | 0.759635 | − | 0.650350i | \(-0.225378\pi\) |
−0.853260 | + | 0.521487i | \(0.825378\pi\) | |||||||
\(348\) | −5.90764 | + | 1.91951i | −0.316683 | + | 0.102896i | ||||
\(349\) | 8.44250 | − | 25.9833i | 0.451917 | − | 1.39086i | −0.422800 | − | 0.906223i | \(-0.638953\pi\) |
0.874717 | − | 0.484634i | \(-0.161047\pi\) | |||||||
\(350\) | 6.38878 | − | 5.84666i | 0.341495 | − | 0.312517i | ||||
\(351\) | 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 | ||||
\(355\) | 1.77836 | + | 4.57743i | 0.0943858 | + | 0.242945i | ||||
\(356\) | −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 | 0.981810 | + | 0.189864i | \(0.0608047\pi\) |
−0.682702 | + | 0.730697i | \(0.739195\pi\) | |||||||
\(360\) | 2.94764 | − | 1.14518i | 0.155354 | − | 0.0603562i | ||||
\(361\) | −15.6887 | − | 11.3985i | −0.825721 | − | 0.599922i | ||||
\(362\) | − | 6.55343i | − | 0.344441i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.58846 | 0.345329 | ||||||||
\(365\) | −0.617511 | − | 10.9370i | −0.0323220 | − | 0.572470i | ||||
\(366\) | 2.55494 | − | 7.86329i | 0.133549 | − | 0.411021i | ||||
\(367\) | 28.1837 | − | 9.15744i | 1.47118 | − | 0.478015i | 0.539714 | − | 0.841848i | \(-0.318532\pi\) |
0.931464 | + | 0.363834i | \(0.118532\pi\) | |||||||
\(368\) | −16.5654 | − | 22.8003i | −0.863531 | − | 1.18855i | ||||
\(369\) | −3.82831 | + | 2.78143i | −0.199294 | + | 0.144795i | ||||
\(370\) | 24.3080 | + | 15.6465i | 1.26371 | + | 0.813424i | ||||
\(371\) | 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 | \(0.344653\pi\) | ||||
−0.468892 | + | 0.883255i | \(0.655347\pi\) | |||||||
\(374\) | 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 | −0.695503 | − | 0.718523i | \(-0.744818\pi\) |
0.468434 | + | 0.883498i | \(0.344818\pi\) | |||||||
\(380\) | −6.11732 | + | 23.2048i | −0.313812 | + | 1.19038i | ||||
\(381\) | 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 | 0.285964 | + | 0.958240i | \(0.407686\pi\) |
−0.999708 | + | 0.0241451i | \(0.992314\pi\) | |||||||
\(384\) | −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 | 0.986706 | + | 0.162516i | \(0.0519609\pi\) |
−0.702737 | + | 0.711449i | \(0.748039\pi\) | |||||||
\(390\) | −9.17342 | − | 2.41832i | −0.464514 | − | 0.122457i | ||||
\(391\) | 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 | ||||
\(400\) | −22.1787 | + | 2.51245i | −1.10893 | + | 0.125622i | ||||
\(401\) | 26.1478 | − | 18.9975i | 1.30576 | − | 0.948691i | 0.305767 | − | 0.952106i | \(-0.401087\pi\) |
0.999994 | + | 0.00341570i | \(0.00108725\pi\) | |||||||
\(402\) | −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 | ||||
\(405\) | 14.8691 | − | 0.839518i | 0.738852 | − | 0.0417160i | ||||
\(406\) | 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 | \(-0.285234\pi\) |
−0.549637 | + | 0.835404i | \(0.685234\pi\) | |||||||
\(410\) | 6.97418 | − | 2.70952i | 0.344430 | − | 0.133814i | ||||
\(411\) | −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 | ||||
\(415\) | −20.6335 | + | 8.01625i | −1.01286 | + | 0.393502i | ||||
\(416\) | −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 | \(0.242071\pi\) | |||||||
\(420\) | −1.79460 | + | 0.101324i | −0.0875675 | + | 0.00494411i | ||||
\(421\) | 6.50560 | − | 20.0222i | 0.317063 | − | 0.975821i | −0.657833 | − | 0.753164i | \(-0.728527\pi\) |
0.974897 | − | 0.222657i | \(-0.0714731\pi\) | |||||||
\(422\) | −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 | ||||
\(425\) | −0.582665 | − | 5.14348i | −0.0282634 | − | 0.249496i | ||||
\(426\) | 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 | \(-0.450672\pi\) |
−0.891963 | + | 0.452109i | \(0.850672\pi\) | |||||||
\(432\) | −12.5973 | − | 4.09310i | −0.606087 | − | 0.196930i | ||||
\(433\) | −19.2610 | + | 6.25829i | −0.925627 | + | 0.300754i | −0.732773 | − | 0.680473i | \(-0.761774\pi\) |
−0.192854 | + | 0.981228i | \(0.561774\pi\) | |||||||
\(434\) | −7.38176 | + | 5.36316i | −0.354336 | + | 0.257440i | ||||
\(435\) | −7.75429 | − | 2.04421i | −0.371790 | − | 0.0980123i | ||||
\(436\) | 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 | \(-0.660529\pi\) | ||||
−0.483209 | + | 0.875505i | \(0.660529\pi\) | |||||||
\(440\) | 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 | \(-0.469969\pi\) |
−0.508958 | + | 0.860791i | \(0.669969\pi\) | |||||||
\(444\) | −1.85410 | − | 5.70634i | −0.0879918 | − | 0.270811i | ||||
\(445\) | 3.68457 | − | 13.9767i | 0.174665 | − | 0.662557i | ||||
\(446\) | 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 | 0.368637 | − | 0.929573i | \(-0.379825\pi\) |
−0.770162 | + | 0.637849i | \(0.779825\pi\) | |||||||
\(450\) | −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 | ||||
\(455\) | 7.15211 | + | 4.60365i | 0.335296 | + | 0.215823i | ||||
\(456\) | −1.34317 | + | 0.975873i | −0.0628999 | + | 0.0456994i | ||||
\(457\) | 12.4688 | + | 17.1618i | 0.583266 | + | 0.802797i | 0.994049 | − | 0.108936i | \(-0.0347444\pi\) |
−0.410782 | + | 0.911733i | \(0.634744\pi\) | |||||||
\(458\) | 32.9395 | − | 10.7027i | 1.53916 | − | 0.500104i | ||||
\(459\) | 0.949237 | − | 2.92145i | 0.0443066 | − | 0.136362i | ||||
\(460\) | 1.37832 | + | 24.4120i | 0.0642643 | + | 1.13822i | ||||
\(461\) | 33.0000 | 1.53696 | 0.768482 | − | 0.639872i | \(-0.221013\pi\) | ||||
0.768482 | + | 0.639872i | \(0.221013\pi\) | |||||||
\(462\) | 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 | ||||
\(465\) | 5.68364 | − | 2.20814i | 0.263573 | − | 0.102400i | ||||
\(466\) | 7.76385 | + | 23.8947i | 0.359654 | + | 1.10690i | ||||
\(467\) | −10.4424 | − | 14.3727i | −0.483215 | − | 0.665088i | 0.495904 | − | 0.868377i | \(-0.334837\pi\) |
−0.979119 | + | 0.203289i | \(0.934837\pi\) | |||||||
\(468\) | −11.8006 | − | 16.2421i | −0.545483 | − | 0.750793i | ||||
\(469\) | 4.13845 | + | 12.7368i | 0.191096 | + | 0.588133i | ||||
\(470\) | −6.41997 | − | 16.5247i | −0.296131 | − | 0.762228i | ||||
\(471\) | 5.05531 | + | 3.67290i | 0.232937 | + | 0.169238i | ||||
\(472\) | − | 2.44949i | − | 0.112747i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.46410 | −0.250974 | ||||||||
\(475\) | −22.8549 | + | 20.9156i | −1.04866 | + | 0.959672i | ||||
\(476\) | 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 | \(-0.769371\pi\) |
0.398962 | + | 0.916967i | \(0.369371\pi\) | |||||||
\(480\) | 7.38593 | + | 4.75416i | 0.337120 | + | 0.216997i | ||||
\(481\) | −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 | \(-0.493116\pi\) |
−0.570153 | + | 0.821538i | \(0.693116\pi\) | |||||||
\(488\) | 4.07034 | − | 1.32253i | 0.184255 | − | 0.0598682i | ||||
\(489\) | −3.17798 | + | 2.30894i | −0.143713 | + | 0.104414i | ||||
\(490\) | −25.8816 | − | 6.82298i | −1.16921 | − | 0.308231i | ||||
\(491\) | 4.85553 | + | 14.9438i | 0.219127 | + | 0.674403i | 0.998835 | + | 0.0482597i | \(0.0153675\pi\) |
−0.779708 | + | 0.626143i | \(0.784632\pi\) | |||||||
\(492\) | −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 | −0.751928 | − | 0.659245i | \(-0.770876\pi\) |
0.220828 | − | 0.975313i | \(-0.429124\pi\) | |||||||
\(500\) | 17.3596 | + | 8.58168i | 0.776344 | + | 0.383785i | ||||
\(501\) | −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 | −0.526820 | − | 0.849977i | \(-0.676616\pi\) |
−0.925810 | + | 0.377989i | \(0.876616\pi\) | |||||||
\(504\) | 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 | −0.681023 | − | 0.732262i | \(-0.738465\pi\) |
0.981372 | − | 0.192118i | \(-0.0615355\pi\) | |||||||
\(510\) | −1.25296 | + | 1.94656i | −0.0554818 | + | 0.0861950i | ||||
\(511\) | 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 | ||||
\(515\) | 0.534780 | + | 9.47175i | 0.0235652 | + | 0.417375i | ||||
\(516\) | −9.58846 | −0.422108 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.5911i | 0.509284i | ||||||||
\(519\) | 3.19355 | + | 2.32025i | 0.140181 | + | 0.101848i | ||||
\(520\) | −1.77836 | − | 4.57743i | −0.0779865 | − | 0.200733i | ||||
\(521\) | 12.1285 | + | 37.3277i | 0.531360 | + | 1.63536i | 0.751385 | + | 0.659864i | \(0.229386\pi\) |
−0.220025 | + | 0.975494i | \(0.570614\pi\) | |||||||
\(522\) | −21.4932 | − | 29.5829i | −0.940733 | − | 1.29481i | ||||
\(523\) | −5.09089 | − | 7.00701i | −0.222609 | − | 0.306395i | 0.683075 | − | 0.730348i | \(-0.260642\pi\) |
−0.905684 | + | 0.423953i | \(0.860642\pi\) | |||||||
\(524\) | 11.3065 | + | 34.7977i | 0.493925 | + | 1.52014i | ||||
\(525\) | −2.01893 | − | 1.14398i | −0.0881133 | − | 0.0499272i | ||||
\(526\) | −33.5877 | − | 24.4029i | −1.46449 | − | 1.06402i | ||||
\(527\) | 5.45378i | 0.237570i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8564 | −0.732887 | ||||||||
\(530\) | 51.6254 | − | 2.91480i | 2.24246 | − | 0.126611i | ||||
\(531\) | 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 | ||||
\(535\) | −5.30257 | + | 8.23793i | −0.229250 | + | 0.356157i | ||||
\(536\) | 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 | \(-0.467718\pi\) |
−0.914884 | + | 0.403718i | \(0.867718\pi\) | |||||||
\(542\) | 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 | ||||
\(545\) | −0.681812 | + | 2.58632i | −0.0292056 | + | 0.110786i | ||||
\(546\) | −1.17545 | − | 3.61767i | −0.0503048 | − | 0.154822i | ||||
\(547\) | 19.2610 | + | 6.25829i | 0.823543 | + | 0.267585i | 0.690323 | − | 0.723501i | \(-0.257468\pi\) |
0.133220 | + | 0.991087i | \(0.457468\pi\) | |||||||
\(548\) | −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 | ||||
\(555\) | 1.97455 | − | 7.49007i | 0.0838152 | − | 0.317936i | ||||
\(556\) | 23.2447 | − | 16.8883i | 0.985796 | − | 0.716222i | ||||
\(557\) | −6.17146 | + | 2.00523i | −0.261493 | + | 0.0849643i | −0.436830 | − | 0.899544i | \(-0.643899\pi\) |
0.175336 | + | 0.984509i | \(0.443899\pi\) | |||||||
\(558\) | 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 | −0.727145 | − | 0.686484i | \(-0.759153\pi\) |
0.877585 | + | 0.479421i | \(0.159153\pi\) | |||||||
\(564\) | −1.13703 | + | 3.49940i | −0.0478774 | + | 0.147352i | ||||
\(565\) | 3.42314 | − | 5.31809i | 0.144013 | − | 0.223734i | ||||
\(566\) | −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 | \(-0.860697\pi\) |
0.981874 | + | 0.189532i | \(0.0606972\pi\) | |||||||
\(570\) | 13.8330 | − | 0.781018i | 0.579400 | − | 0.0327132i | ||||
\(571\) | −35.7128 | −1.49453 | −0.747267 | − | 0.664524i | \(-0.768635\pi\) | ||||
−0.747267 | + | 0.664524i | \(0.768635\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.55532i | − | 0.232077i | ||||||
\(574\) | 2.42705 | + | 1.76336i | 0.101303 | + | 0.0736010i | ||||
\(575\) | −15.5615 | + | 27.4636i | −0.648961 | + | 1.14531i | ||||
\(576\) | 4.83928 | + | 14.8938i | 0.201637 | + | 0.620574i | ||||
\(577\) | 12.1864 | + | 16.7731i | 0.507326 | + | 0.698275i | 0.983466 | − | 0.181095i | \(-0.0579642\pi\) |
−0.476139 | + | 0.879370i | \(0.657964\pi\) | |||||||
\(578\) | 18.0867 | + | 24.8942i | 0.752307 | + | 1.03546i | ||||
\(579\) | 1.64413 | + | 5.06010i | 0.0683276 | + | 0.210291i | ||||
\(580\) | 9.71717 | + | 25.0115i | 0.403483 | + | 1.03855i | ||||
\(581\) | −7.18055 | − | 5.21697i | −0.297899 | − | 0.216437i | ||||
\(582\) | − | 0.656339i | − | 0.0272061i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.53590 | −0.104936 | ||||||||
\(585\) | −1.46105 | − | 25.8773i | −0.0604068 | − | 1.06989i | ||||
\(586\) | 5.62292 | − | 17.3056i | 0.232281 | − | 0.714886i | ||||
\(587\) | 34.1879 | − | 11.1083i | 1.41109 | − | 0.458490i | 0.498328 | − | 0.866989i | \(-0.333948\pi\) |
0.912759 | + | 0.408499i | \(0.133948\pi\) | |||||||
\(588\) | 3.26533 | + | 4.49435i | 0.134660 | + | 0.185344i | ||||
\(589\) | 26.4071 | − | 19.1859i | 1.08809 | − | 0.790542i | ||||
\(590\) | −11.0638 | + | 17.1883i | −0.455488 | + | 0.707633i | ||||
\(591\) | −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 | \(-0.786655\pi\) | ||
0.783670 | − | 0.621177i | \(-0.213345\pi\) | |||||||
\(594\) | 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 | −0.196151 | − | 0.980574i | \(-0.562844\pi\) |
0.871967 | + | 0.489565i | \(0.162844\pi\) | |||||||
\(600\) | 0.554797 | + | 1.21948i | 0.0226495 | + | 0.0497849i | ||||
\(601\) | −6.18034 | − | 19.0211i | −0.252101 | − | 0.775888i | −0.994387 | − | 0.105804i | \(-0.966258\pi\) |
0.742286 | − | 0.670084i | \(-0.233742\pi\) | |||||||
\(602\) | 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 | −0.246577 | − | 0.969123i | \(-0.579306\pi\) |
0.997887 | − | 0.0649672i | \(-0.0206943\pi\) | |||||||
\(608\) | 44.7194 | + | 14.5302i | 1.81361 | + | 0.589278i | ||||
\(609\) | −0.993610 | − | 3.05802i | −0.0402631 | − | 0.123917i | ||||
\(610\) | −34.5356 | − | 9.10437i | −1.39830 | − | 0.368625i | ||||
\(611\) | 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 | 0.177650 | − | 0.984094i | \(-0.443150\pi\) |
−0.434714 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(614\) | 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 | −0.597018 | − | 0.802228i | \(-0.703648\pi\) |
0.954535 | − | 0.298098i | \(-0.0963522\pi\) | |||||||
\(620\) | −17.1559 | − | 11.0429i | −0.688997 | − | 0.443492i | ||||
\(621\) | −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 | ||||
\(625\) | 12.8483 | + | 21.4458i | 0.513932 | + | 0.857831i | ||||
\(626\) | 33.1244 | 1.32392 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 20.9086i | − | 0.834344i | ||||||
\(629\) | 5.60503 | + | 4.07230i | 0.223487 | + | 0.162373i | ||||
\(630\) | −3.83184 | − | 9.86299i | −0.152664 | − | 0.392951i | ||||
\(631\) | 5.97037 | + | 18.3749i | 0.237676 | + | 0.731493i | 0.996755 | + | 0.0804940i | \(0.0256498\pi\) |
−0.759079 | + | 0.650999i | \(0.774350\pi\) | |||||||
\(632\) | −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 | ||||
\(635\) | 6.97418 | − | 2.70952i | 0.276762 | − | 0.107524i | ||||
\(636\) | −8.68241 | − | 6.30814i | −0.344280 | − | 0.250134i | ||||
\(637\) | − | 26.2880i | − | 1.04157i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0.517297 | + | 9.16210i | 0.0204480 | + | 0.362164i | ||||
\(641\) | 6.13597 | − | 18.8846i | 0.242356 | − | 0.745895i | −0.753704 | − | 0.657214i | \(-0.771735\pi\) |
0.996060 | − | 0.0886813i | \(-0.0282653\pi\) | |||||||
\(642\) | 4.16690 | − | 1.35391i | 0.164455 | − | 0.0534345i | ||||
\(643\) | 16.2611 | + | 22.3815i | 0.641277 | + | 0.882642i | 0.998683 | − | 0.0513075i | \(-0.0163388\pi\) |
−0.357406 | + | 0.933949i | \(0.616339\pi\) | |||||||
\(644\) | −7.93148 | + | 5.76256i | −0.312544 | + | 0.227077i | ||||
\(645\) | −10.4088 | − | 6.69989i | −0.409845 | − | 0.263808i | ||||
\(646\) | −3.82943 | + | 11.7858i | −0.150667 | + | 0.463705i | ||||
\(647\) | −11.1543 | + | 15.3525i | −0.438519 | + | 0.603569i | −0.969882 | − | 0.243575i | \(-0.921680\pi\) |
0.531363 | + | 0.847144i | \(0.321680\pi\) | |||||||
\(648\) | − | 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 | \(-0.385078\pi\) |
0.835672 | + | 0.549229i | \(0.185078\pi\) | |||||||
\(654\) | 0.967708 | − | 0.703081i | 0.0378404 | − | 0.0274926i | ||||
\(655\) | −12.0410 | + | 45.6750i | −0.470480 | + | 1.78467i | ||||
\(656\) | −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 | \(-0.429234\pi\) | ||||
0.220492 | + | 0.975389i | \(0.429234\pi\) | |||||||
\(660\) | 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 | ||||
\(665\) | −12.0117 | − | 3.16656i | −0.465793 | − | 0.122794i | ||||
\(666\) | 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 | −0.790302 | − | 0.612717i | \(-0.790076\pi\) |
0.826946 | + | 0.562282i | \(0.190076\pi\) | |||||||
\(674\) | −4.67368 | + | 14.3841i | −0.180024 | + | 0.554055i | ||||
\(675\) | 1.66993 | + | 14.7414i | 0.0642758 | + | 0.567395i | ||||
\(676\) | −7.00629 | + | 5.09037i | −0.269473 | + | 0.195783i | ||||
\(677\) | 5.31363 | + | 7.31358i | 0.204219 | + | 0.281084i | 0.898826 | − | 0.438306i | \(-0.144421\pi\) |
−0.694606 | + | 0.719390i | \(0.744421\pi\) | |||||||
\(678\) | −2.68999 | + | 0.874032i | −0.103309 | + | 0.0335670i | ||||
\(679\) | −0.181843 | + | 0.559656i | −0.00697851 | + | 0.0214776i | ||||
\(680\) | −1.19640 | + | 0.0675494i | −0.0458798 | + | 0.00259040i | ||||
\(681\) | 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 | ||||
\(685\) | −28.6866 | + | 11.1449i | −1.09606 | + | 0.425826i | ||||
\(686\) | −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 | ||||
\(690\) | 13.1586 | − | 5.11220i | 0.500938 | − | 0.194618i | ||||
\(691\) | 22.5788 | + | 16.4045i | 0.858939 | + | 0.624056i | 0.927596 | − | 0.373585i | \(-0.121871\pi\) |
−0.0686571 | + | 0.997640i | \(0.521871\pi\) | |||||||
\(692\) | − | 13.2084i | − | 0.502108i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.73205 | 0.217586 | ||||||||
\(695\) | 37.0339 | − | 2.09096i | 1.40478 | − | 0.0793145i | ||||
\(696\) | −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 | ||||
\(700\) | 0.873998 | + | 7.71522i | 0.0330340 | + | 0.291608i | ||||
\(701\) | −3.13454 | + | 9.64713i | −0.118390 | + | 0.364367i | −0.992639 | − | 0.121111i | \(-0.961354\pi\) |
0.874249 | + | 0.485478i | \(0.161354\pi\) | |||||||
\(702\) | −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 | −0.172676 | − | 0.984979i | \(-0.555241\pi\) |
0.883411 | + | 0.468600i | \(0.155241\pi\) | |||||||
\(710\) | −9.17342 | − | 2.41832i | −0.344272 | − | 0.0907581i | ||||
\(711\) | −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 | 0.866718 | + | 0.498799i | \(0.166225\pi\) |
−0.408003 | + | 0.912981i | \(0.633775\pi\) | |||||||
\(720\) | −6.95186 | + | 26.3705i | −0.259081 | + | 0.982770i | ||||
\(721\) | −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 | ||||
\(730\) | 17.7947 | + | 11.4540i | 0.658611 | + | 0.423933i | ||||
\(731\) | 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 | 0.373885 | − | 0.927475i | \(-0.378026\pi\) |
0.847635 | + | 0.530579i | \(0.178026\pi\) | |||||||
\(734\) | −17.6908 | + | 54.4468i | −0.652980 | + | 2.00967i | ||||
\(735\) | 0.404285 | + | 7.16048i | 0.0149123 | + | 0.264118i | ||||
\(736\) | 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 | \(-0.147440\pi\) |
−0.148487 | + | 0.988914i | \(0.547440\pi\) | |||||||
\(740\) | −24.1593 | + | 9.38606i | −0.888113 | + | 0.345039i | ||||
\(741\) | 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 | 0.713459 | − | 0.700697i | \(-0.247128\pi\) |
−0.886874 | + | 0.462012i | \(0.847128\pi\) | |||||||
\(744\) | −0.436191 | − | 1.34246i | −0.0159915 | − | 0.0492169i | ||||
\(745\) | −11.1197 | − | 28.6216i | −0.407395 | − | 1.04862i | ||||
\(746\) | −53.3215 | − | 38.7403i | −1.95224 | − | 1.41838i | ||||
\(747\) | 27.0459i | 0.989559i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.92820 | −0.143533 | ||||||||
\(750\) | 1.61500 | − | 11.0631i | 0.0589715 | − | 0.403967i | ||||
\(751\) | −6.37842 | + | 19.6308i | −0.232752 | + | 0.716337i | 0.764660 | + | 0.644434i | \(0.222907\pi\) |
−0.997412 | + | 0.0719027i | \(0.977093\pi\) | |||||||
\(752\) | −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 | ||||
\(755\) | −11.6502 | − | 7.49897i | −0.423994 | − | 0.272915i | ||||
\(756\) | −1.42386 | + | 4.38218i | −0.0517851 | + | 0.159378i | ||||
\(757\) | 20.6183 | − | 28.3786i | 0.749385 | − | 1.03144i | −0.248639 | − | 0.968596i | \(-0.579983\pi\) |
0.998023 | − | 0.0628432i | \(-0.0200168\pi\) | |||||||
\(758\) | − | 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 | \(-0.254519\pi\) |
−0.466594 | + | 0.884472i | \(0.654519\pi\) | |||||||
\(762\) | −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 | ||||
\(765\) | −6.11562 | − | 1.61222i | −0.221111 | − | 0.0582898i | ||||
\(766\) | −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 | \(-0.395659\pi\) | ||||
0.321959 | + | 0.946754i | \(0.395659\pi\) | |||||||
\(770\) | 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 | \(-0.0209075\pi\) |
0.768693 | + | 0.639618i | \(0.220907\pi\) | |||||||
\(774\) | −17.4424 | − | 53.6823i | −0.626955 | − | 1.92957i | ||||
\(775\) | −10.9075 | − | 23.9752i | −0.391807 | − | 0.861214i | ||||
\(776\) | 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 | ||||
\(785\) | 14.6098 | − | 22.6974i | 0.521445 | − | 0.810103i | ||||
\(786\) | 17.0900 | − | 12.4166i | 0.609579 | − | 0.442885i | ||||
\(787\) | −2.73834 | − | 3.76900i | −0.0976113 | − | 0.134350i | 0.757418 | − | 0.652931i | \(-0.226461\pi\) |
−0.855029 | + | 0.518580i | \(0.826461\pi\) | |||||||
\(788\) | 4.20225 | − | 1.36539i | 0.149699 | − | 0.0486401i | ||||
\(789\) | −3.43761 | + | 10.5799i | −0.122382 | + | 0.376654i | ||||
\(790\) | 1.33055 | + | 23.5660i | 0.0473389 | + | 0.838442i | ||||
\(791\) | 2.53590 | 0.0901662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.0779i | − | 1.24565i | ||||||
\(794\) | −25.0214 | − | 18.1791i | −0.887978 | − | 0.645154i | ||||
\(795\) | −5.01742 | − | 12.9146i | −0.177950 | − | 0.458034i | ||||
\(796\) | −1.07047 | − | 3.29456i | −0.0379417 | − | 0.116772i | ||||
\(797\) | −4.64543 | − | 6.39388i | −0.164549 | − | 0.226483i | 0.718778 | − | 0.695240i | \(-0.244702\pi\) |
−0.883327 | + | 0.468757i | \(0.844702\pi\) | |||||||
\(798\) | 3.26533 | + | 4.49435i | 0.115592 | + | 0.159098i | ||||
\(799\) | −1.31292 | − | 4.04076i | −0.0464479 | − | 0.142952i | ||||
\(800\) | 18.7056 | − | 33.0123i | 0.661342 | − | 1.16716i | ||||
\(801\) | −14.2874 | − | 10.3804i | −0.504822 | − | 0.366775i | ||||
\(802\) | 62.4384i | 2.20478i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.3923 | 0.472310 | ||||||||
\(805\) | −12.6366 | + | 0.713469i | −0.445381 | + | 0.0251465i | ||||
\(806\) | 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 | \(-0.576846\pi\) |
0.849596 | + | 0.527435i | \(0.176846\pi\) | |||||||
\(810\) | −15.5720 | + | 24.1922i | −0.547144 | + | 0.850028i | ||||
\(811\) | 10.1916 | − | 31.3666i | 0.357876 | − | 1.10143i | −0.596447 | − | 0.802652i | \(-0.703421\pi\) |
0.954323 | − | 0.298777i | \(-0.0965786\pi\) | |||||||
\(812\) | −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 | ||||
\(820\) | −1.71001 | + | 6.48659i | −0.0597163 | + | 0.226522i | ||||
\(821\) | −5.81071 | − | 17.8835i | −0.202795 | − | 0.624139i | −0.999797 | − | 0.0201620i | \(-0.993582\pi\) |
0.797002 | − | 0.603977i | \(-0.206418\pi\) | |||||||
\(822\) | 13.0896 | + | 4.25306i | 0.456552 | + | 0.148343i | ||||
\(823\) | −28.4475 | + | 39.1547i | −0.991619 | + | 1.36485i | −0.0612894 | + | 0.998120i | \(0.519521\pi\) |
−0.930329 | + | 0.366726i | \(0.880479\pi\) | |||||||
\(824\) | 2.19615 | 0.0765066 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.19615 | −0.285181 | ||||||||
\(827\) | −15.7123 | + | 21.6261i | −0.546370 | + | 0.752014i | −0.989514 | − | 0.144437i | \(-0.953863\pi\) |
0.443144 | + | 0.896450i | \(0.353863\pi\) | |||||||
\(828\) | 28.4122 | + | 9.23168i | 0.987392 | + | 0.320823i | ||||
\(829\) | −12.9728 | − | 39.9261i | −0.450563 | − | 1.38669i | −0.876266 | − | 0.481827i | \(-0.839973\pi\) |
0.425703 | − | 0.904863i | \(-0.360027\pi\) | |||||||
\(830\) | 10.9010 | − | 41.3506i | 0.378378 | − | 1.43530i | ||||
\(831\) | 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 | −0.964811 | − | 0.262945i | \(-0.915306\pi\) |
0.935103 | + | 0.354375i | \(0.115306\pi\) | |||||||
\(840\) | −0.290749 | + | 0.451700i | −0.0100318 | + | 0.0155851i | ||||
\(841\) | −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 | ||||
\(845\) | −11.1626 | + | 0.630244i | −0.384004 | + | 0.0216811i | ||||
\(846\) | −21.6603 | −0.744695 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 53.4355i | − | 1.83498i | ||||||
\(849\) | 12.6113 | + | 9.16267i | 0.432820 | + | 0.314462i | ||||
\(850\) | 8.70038 | + | 4.92985i | 0.298421 | + | 0.169092i | ||||
\(851\) | −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 | 0.915520 | − | 0.402273i | \(-0.131780\pi\) |
−0.665496 | + | 0.746402i | \(0.731780\pi\) | |||||||
\(854\) | −4.42528 | − | 13.6196i | −0.151430 | − | 0.466054i | ||||
\(855\) | 13.7078 | + | 35.2834i | 0.468798 | + | 1.20667i | ||||
\(856\) | 1.83481 | + | 1.33307i | 0.0627125 | + | 0.0455633i | ||||
\(857\) | 24.4206i | 0.834191i | 0.908863 | + | 0.417095i | \(0.136952\pi\) | ||||
−0.908863 | + | 0.417095i | \(0.863048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8038 | 0.402742 | 0.201371 | − | 0.979515i | \(-0.435460\pi\) | ||||
0.201371 | + | 0.979515i | \(0.435460\pi\) | |||||||
\(860\) | 2.33486 | + | 41.3539i | 0.0796182 | + | 1.41016i | ||||
\(861\) | 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 | \(-0.253127\pi\) |
−0.895424 | + | 0.445215i | \(0.853127\pi\) | |||||||
\(864\) | 18.2164 | − | 13.2350i | 0.619733 | − | 0.450263i | ||||
\(865\) | 9.22930 | − | 14.3384i | 0.313806 | − | 0.487520i | ||||
\(866\) | 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 | ||||
\(875\) | −4.44221 | + | 8.98597i | −0.150174 | + | 0.303781i | ||||
\(876\) | −1.35730 | − | 4.17733i | −0.0458588 | − | 0.141139i | ||||
\(877\) | 53.2464 | + | 17.3008i | 1.79800 | + | 0.584206i | 0.999834 | − | 0.0182289i | \(-0.00580276\pi\) |
0.798168 | + | 0.602435i | \(0.205803\pi\) | |||||||
\(878\) | 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 | \(-0.109463\pi\) |
0.563477 | + | 0.826131i | \(0.309463\pi\) | |||||||
\(884\) | 2.35091 | + | 7.23535i | 0.0790696 | + | 0.243351i | ||||
\(885\) | 5.29628 | + | 1.39622i | 0.178032 | + | 0.0469334i | ||||
\(886\) | 14.3455 | − | 10.4226i | 0.481948 | − | 0.350155i | ||||
\(887\) | −7.93807 | + | 2.57924i | −0.266534 | + | 0.0866022i | −0.439235 | − | 0.898372i | \(-0.644751\pi\) |
0.172701 | + | 0.984974i | \(0.444751\pi\) | |||||||
\(888\) | −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 | ||||
\(895\) | −16.0495 | − | 10.3307i | −0.536474 | − | 0.345316i | ||||
\(896\) | −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 | ||||
\(900\) | 17.4545 | − | 15.9734i | 0.581816 | − | 0.532446i | ||||
\(901\) | 12.3923 | 0.412848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.96335i | − | 0.165170i | ||||||
\(904\) | −1.18448 | − | 0.860577i | −0.0393953 | − | 0.0286224i | ||||
\(905\) | 2.74697 | + | 7.07056i | 0.0913122 | + | 0.235033i | ||||
\(906\) | 1.91472 | + | 5.89289i | 0.0636122 | + | 0.195778i | ||||
\(907\) | −4.74294 | − | 6.52810i | −0.157487 | − | 0.216762i | 0.722981 | − | 0.690868i | \(-0.242771\pi\) |
−0.880468 | + | 0.474106i | \(0.842771\pi\) | |||||||
\(908\) | −21.9169 | − | 30.1660i | −0.727337 | − | 1.00109i | ||||
\(909\) | 1.17545 | + | 3.61767i | 0.0389873 | + | 0.119991i | ||||
\(910\) | −15.3164 | + | 5.95053i | −0.507733 | + | 0.197258i | ||||
\(911\) | −14.7635 | − | 10.7263i | −0.489137 | − | 0.355379i | 0.315715 | − | 0.948854i | \(-0.397756\pi\) |
−0.804852 | + | 0.593475i | \(0.797756\pi\) | |||||||
\(912\) | − | 14.3180i | − | 0.474116i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.9808 | −1.35552 | ||||||||
\(915\) | 0.539465 | + | 9.55472i | 0.0178342 | + | 0.315869i | ||||
\(916\) | −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 | \(-0.883079\pi\) |
0.0531354 | + | 0.998587i | \(0.483079\pi\) | |||||||
\(920\) | 6.14450 | + | 3.95508i | 0.202578 | + | 0.130395i | ||||
\(921\) | 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 | −0.781049 | − | 0.624470i | \(-0.785315\pi\) |
0.352549 | + | 0.935793i | \(0.385315\pi\) | |||||||
\(930\) | −3.00276 | + | 11.3903i | −0.0984642 | + | 0.373504i | ||||
\(931\) | 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 | −0.533378 | − | 0.845877i | \(-0.679078\pi\) |
0.969300 | + | 0.245883i | \(0.0790778\pi\) | |||||||
\(938\) | −24.6057 | − | 7.99487i | −0.803404 | − | 0.261042i | ||||
\(939\) | −2.74272 | − | 8.44124i | −0.0895054 | − | 0.275469i | ||||
\(940\) | 15.3694 | + | 4.05173i | 0.501294 | + | 0.132153i | ||||
\(941\) | −21.8435 | + | 15.8702i | −0.712076 | + | 0.517354i | −0.883843 | − | 0.467784i | \(-0.845053\pi\) |
0.171766 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(942\) | −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 | ||||
\(950\) | −6.73688 | − | 59.4699i | −0.218573 | − | 1.92946i | ||||
\(951\) | −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 | 0.217430 | − | 0.976076i | \(-0.430233\pi\) |
0.749628 | + | 0.661860i | \(0.230233\pi\) | |||||||
\(954\) | 19.5227 | − | 60.0848i | 0.632072 | − | 1.94532i | ||||
\(955\) | −23.9594 | + | 1.35276i | −0.775309 | + | 0.0437744i | ||||
\(956\) | 20.1962 | 0.653190 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 18.2832i | − | 0.590705i | ||||||
\(959\) | −9.98306 | − | 7.25312i | −0.322370 | − | 0.234215i | ||||
\(960\) | −6.18437 | + | 2.40267i | −0.199600 | + | 0.0775459i | ||||
\(961\) | −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 | ||||
\(965\) | 21.4233 | − | 8.32310i | 0.689640 | − | 0.267930i | ||||
\(966\) | 4.57924 | + | 3.32701i | 0.147335 | + | 0.107045i | ||||
\(967\) | 4.24264i | 0.136434i | 0.997671 | + | 0.0682171i | \(0.0217310\pi\) | ||||
−0.997671 | + | 0.0682171i | \(0.978269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.32051 | 0.106670 | ||||||||
\(970\) | −2.83071 | + | 0.159824i | −0.0908887 | + | 0.00513163i | ||||
\(971\) | −3.42137 | + | 10.5299i | −0.109797 | + | 0.337921i | −0.990826 | − | 0.135141i | \(-0.956851\pi\) |
0.881029 | + | 0.473062i | \(0.156851\pi\) | |||||||
\(972\) | 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 | ||||
\(975\) | 10.9110 | − | 1.23602i | 0.349431 | − | 0.0395843i | ||||
\(976\) | −11.4055 | + | 35.1025i | −0.365081 | + | 1.12360i | ||||
\(977\) | −8.80170 | + | 12.1145i | −0.281591 | + | 0.387577i | −0.926260 | − | 0.376885i | \(-0.876995\pi\) |
0.644669 | + | 0.764462i | \(0.276995\pi\) | |||||||
\(978\) | − | 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 | \(-0.676950\pi\) |
0.0723519 | + | 0.997379i | \(0.476950\pi\) | |||||||
\(984\) | −0.375466 | + | 0.272792i | −0.0119694 | + | 0.00869629i | ||||
\(985\) | 5.51582 | + | 1.45410i | 0.175749 | + | 0.0463314i | ||||
\(986\) | 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 | ||||
\(995\) | 1.14001 | − | 4.32439i | 0.0361407 | − | 0.137092i | ||||
\(996\) | −7.18055 | + | 5.21697i | −0.227524 | + | 0.165306i | ||||
\(997\) | −0.167258 | + | 0.0543454i | −0.00529711 | + | 0.00172114i | −0.311664 | − | 0.950192i | \(-0.600886\pi\) |
0.306367 | + | 0.951913i | \(0.400886\pi\) | |||||||
\(998\) | 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.e.444.1 | 16 | ||
5.4 | even | 2 | inner | 605.2.j.e.444.4 | 16 | ||
11.2 | odd | 10 | 605.2.j.f.269.1 | 16 | |||
11.3 | even | 5 | inner | 605.2.j.e.124.4 | 16 | ||
11.4 | even | 5 | inner | 605.2.j.e.9.1 | 16 | ||
11.5 | even | 5 | 605.2.b.e.364.1 | yes | 4 | ||
11.6 | odd | 10 | 605.2.b.d.364.4 | yes | 4 | ||
11.7 | odd | 10 | 605.2.j.f.9.4 | 16 | |||
11.8 | odd | 10 | 605.2.j.f.124.1 | 16 | |||
11.9 | even | 5 | inner | 605.2.j.e.269.4 | 16 | ||
11.10 | odd | 2 | 605.2.j.f.444.4 | 16 | |||
55.4 | even | 10 | inner | 605.2.j.e.9.4 | 16 | ||
55.9 | even | 10 | inner | 605.2.j.e.269.1 | 16 | ||
55.14 | even | 10 | inner | 605.2.j.e.124.1 | 16 | ||
55.17 | even | 20 | 3025.2.a.y.1.1 | 4 | |||
55.19 | odd | 10 | 605.2.j.f.124.4 | 16 | |||
55.24 | odd | 10 | 605.2.j.f.269.4 | 16 | |||
55.27 | odd | 20 | 3025.2.a.z.1.4 | 4 | |||
55.28 | even | 20 | 3025.2.a.y.1.4 | 4 | |||
55.29 | odd | 10 | 605.2.j.f.9.1 | 16 | |||
55.38 | odd | 20 | 3025.2.a.z.1.1 | 4 | |||
55.39 | odd | 10 | 605.2.b.d.364.1 | ✓ | 4 | ||
55.49 | even | 10 | 605.2.b.e.364.4 | yes | 4 | ||
55.54 | odd | 2 | 605.2.j.f.444.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.d.364.1 | ✓ | 4 | 55.39 | odd | 10 | ||
605.2.b.d.364.4 | yes | 4 | 11.6 | odd | 10 | ||
605.2.b.e.364.1 | yes | 4 | 11.5 | even | 5 | ||
605.2.b.e.364.4 | yes | 4 | 55.49 | even | 10 | ||
605.2.j.e.9.1 | 16 | 11.4 | even | 5 | inner | ||
605.2.j.e.9.4 | 16 | 55.4 | even | 10 | inner | ||
605.2.j.e.124.1 | 16 | 55.14 | even | 10 | inner | ||
605.2.j.e.124.4 | 16 | 11.3 | even | 5 | inner | ||
605.2.j.e.269.1 | 16 | 55.9 | even | 10 | inner | ||
605.2.j.e.269.4 | 16 | 11.9 | even | 5 | inner | ||
605.2.j.e.444.1 | 16 | 1.1 | even | 1 | trivial | ||
605.2.j.e.444.4 | 16 | 5.4 | even | 2 | inner | ||
605.2.j.f.9.1 | 16 | 55.29 | odd | 10 | |||
605.2.j.f.9.4 | 16 | 11.7 | odd | 10 | |||
605.2.j.f.124.1 | 16 | 11.8 | odd | 10 | |||
605.2.j.f.124.4 | 16 | 55.19 | odd | 10 | |||
605.2.j.f.269.1 | 16 | 11.2 | odd | 10 | |||
605.2.j.f.269.4 | 16 | 55.24 | odd | 10 | |||
605.2.j.f.444.1 | 16 | 55.54 | odd | 2 | |||
605.2.j.f.444.4 | 16 | 11.10 | odd | 2 | |||
3025.2.a.y.1.1 | 4 | 55.17 | even | 20 | |||
3025.2.a.y.1.4 | 4 | 55.28 | even | 20 | |||
3025.2.a.z.1.1 | 4 | 55.38 | odd | 20 | |||
3025.2.a.z.1.4 | 4 | 55.27 | odd | 20 |