Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(205,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.205");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 205.1 | ||
Root | \(2.55339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.205 |
Dual form | 546.2.bm.b.277.6 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.21130 | − | 1.27669i | −0.988923 | − | 0.570955i | −0.0839705 | − | 0.996468i | \(-0.526760\pi\) |
−0.904952 | + | 0.425513i | \(0.860093\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | 1.74192 | − | 1.99141i | 0.658384 | − | 0.752682i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.27669 | + | 2.21130i | −0.403726 | + | 0.699274i | ||||
\(11\) | −0.449678 | − | 0.259622i | −0.135583 | − | 0.0782788i | 0.430674 | − | 0.902507i | \(-0.358276\pi\) |
−0.566257 | + | 0.824229i | \(0.691609\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −1.57238 | + | 3.24463i | −0.436099 | + | 0.899899i | ||||
\(14\) | −1.99141 | − | 1.74192i | −0.532227 | − | 0.465548i | ||||
\(15\) | 2.21130 | − | 1.27669i | 0.570955 | − | 0.329641i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.868301 | −0.210594 | −0.105297 | − | 0.994441i | \(-0.533579\pi\) | ||||
−0.105297 | + | 0.994441i | \(0.533579\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −4.00705 | + | 2.31347i | −0.919281 | + | 0.530747i | −0.883406 | − | 0.468609i | \(-0.844755\pi\) |
−0.0358753 | + | 0.999356i | \(0.511422\pi\) | |||||||
\(20\) | 2.21130 | + | 1.27669i | 0.494461 | + | 0.285477i | ||||
\(21\) | 0.853651 | + | 2.50425i | 0.186282 | + | 0.546473i | ||||
\(22\) | −0.259622 | + | 0.449678i | −0.0553515 | + | 0.0958716i | ||||
\(23\) | −8.52091 | −1.77673 | −0.888367 | − | 0.459135i | \(-0.848159\pi\) | ||||
−0.888367 | + | 0.459135i | \(0.848159\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0.759893 | + | 1.31617i | 0.151979 | + | 0.263235i | ||||
\(26\) | 3.24463 | + | 1.57238i | 0.636324 | + | 0.308369i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.74192 | + | 1.99141i | −0.329192 | + | 0.376341i | ||||
\(29\) | −1.98376 | − | 3.43598i | −0.368375 | − | 0.638045i | 0.620936 | − | 0.783861i | \(-0.286753\pi\) |
−0.989312 | + | 0.145816i | \(0.953419\pi\) | |||||||
\(30\) | −1.27669 | − | 2.21130i | −0.233091 | − | 0.403726i | ||||
\(31\) | −3.49539 | + | 2.01806i | −0.627791 | + | 0.362455i | −0.779896 | − | 0.625909i | \(-0.784728\pi\) |
0.152105 | + | 0.988364i | \(0.451395\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0.449678 | − | 0.259622i | 0.0782788 | − | 0.0451943i | ||||
\(34\) | 0.868301i | 0.148912i | ||||||||
\(35\) | −6.39433 | + | 2.17970i | −1.08084 | + | 0.368437i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 5.92304i | 0.973741i | 0.873474 | + | 0.486871i | \(0.161862\pi\) | ||||
−0.873474 | + | 0.486871i | \(0.838138\pi\) | |||||||
\(38\) | 2.31347 | + | 4.00705i | 0.375295 | + | 0.650030i | ||||
\(39\) | −2.02374 | − | 2.98403i | −0.324058 | − | 0.477828i | ||||
\(40\) | 1.27669 | − | 2.21130i | 0.201863 | − | 0.349637i | ||||
\(41\) | −5.87598 | + | 3.39250i | −0.917674 | + | 0.529819i | −0.882892 | − | 0.469576i | \(-0.844407\pi\) |
−0.0347817 | + | 0.999395i | \(0.511074\pi\) | |||||||
\(42\) | 2.50425 | − | 0.853651i | 0.386415 | − | 0.131721i | ||||
\(43\) | 2.24805 | − | 3.89373i | 0.342824 | − | 0.593789i | −0.642132 | − | 0.766594i | \(-0.721950\pi\) |
0.984956 | + | 0.172805i | \(0.0552831\pi\) | |||||||
\(44\) | 0.449678 | + | 0.259622i | 0.0677915 | + | 0.0391394i | ||||
\(45\) | 2.55339i | 0.380636i | ||||||||
\(46\) | 8.52091i | 1.25634i | ||||||||
\(47\) | −2.81446 | − | 1.62493i | −0.410531 | − | 0.237020i | 0.280487 | − | 0.959858i | \(-0.409504\pi\) |
−0.691018 | + | 0.722838i | \(0.742837\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −0.931425 | − | 6.93776i | −0.133061 | − | 0.991108i | ||||
\(50\) | 1.31617 | − | 0.759893i | 0.186135 | − | 0.107465i | ||||
\(51\) | 0.434150 | − | 0.751971i | 0.0607932 | − | 0.105297i | ||||
\(52\) | 1.57238 | − | 3.24463i | 0.218050 | − | 0.449949i | ||||
\(53\) | −4.12845 | − | 7.15068i | −0.567086 | − | 0.982222i | −0.996852 | − | 0.0792817i | \(-0.974737\pi\) |
0.429766 | − | 0.902940i | \(-0.358596\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 0.662914 | + | 1.14820i | 0.0893873 | + | 0.154823i | ||||
\(56\) | 1.99141 | + | 1.74192i | 0.266113 | + | 0.232774i | ||||
\(57\) | − | 4.62695i | − | 0.612854i | ||||||
\(58\) | −3.43598 | + | 1.98376i | −0.451166 | + | 0.260481i | ||||
\(59\) | − | 1.40079i | − | 0.182368i | −0.995834 | − | 0.0911839i | \(-0.970935\pi\) | ||
0.995834 | − | 0.0911839i | \(-0.0290651\pi\) | |||||||
\(60\) | −2.21130 | + | 1.27669i | −0.285477 | + | 0.164820i | ||||
\(61\) | 3.01909 | + | 5.22921i | 0.386554 | + | 0.669532i | 0.991983 | − | 0.126368i | \(-0.0403319\pi\) |
−0.605429 | + | 0.795899i | \(0.706999\pi\) | |||||||
\(62\) | 2.01806 | + | 3.49539i | 0.256294 | + | 0.443915i | ||||
\(63\) | −2.59557 | − | 0.512843i | −0.327011 | − | 0.0646121i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 7.61939 | − | 5.16740i | 0.945070 | − | 0.640937i | ||||
\(66\) | −0.259622 | − | 0.449678i | −0.0319572 | − | 0.0553515i | ||||
\(67\) | 9.54619 | + | 5.51150i | 1.16625 | + | 0.673337i | 0.952795 | − | 0.303616i | \(-0.0981939\pi\) |
0.213458 | + | 0.976952i | \(0.431527\pi\) | |||||||
\(68\) | 0.868301 | 0.105297 | ||||||||
\(69\) | 4.26046 | − | 7.37933i | 0.512899 | − | 0.888367i | ||||
\(70\) | 2.17970 | + | 6.39433i | 0.260524 | + | 0.764268i | ||||
\(71\) | 4.47375 | + | 2.58292i | 0.530937 | + | 0.306536i | 0.741398 | − | 0.671066i | \(-0.234163\pi\) |
−0.210461 | + | 0.977602i | \(0.567497\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 10.3558 | − | 5.97895i | 1.21206 | − | 0.699783i | 0.248852 | − | 0.968542i | \(-0.419947\pi\) |
0.963208 | + | 0.268759i | \(0.0866134\pi\) | |||||||
\(74\) | 5.92304 | 0.688539 | ||||||||
\(75\) | −1.51979 | −0.175490 | ||||||||
\(76\) | 4.00705 | − | 2.31347i | 0.459640 | − | 0.265374i | ||||
\(77\) | −1.30032 | + | 0.443252i | −0.148185 | + | 0.0505133i | ||||
\(78\) | −2.98403 | + | 2.02374i | −0.337875 | + | 0.229144i | ||||
\(79\) | 5.47473 | − | 9.48251i | 0.615955 | − | 1.06687i | −0.374261 | − | 0.927323i | \(-0.622104\pi\) |
0.990216 | − | 0.139542i | \(-0.0445630\pi\) | |||||||
\(80\) | −2.21130 | − | 1.27669i | −0.247231 | − | 0.142739i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.39250 | + | 5.87598i | 0.374639 | + | 0.648894i | ||||
\(83\) | 12.9984i | 1.42676i | 0.700778 | + | 0.713379i | \(0.252836\pi\) | ||||
−0.700778 | + | 0.713379i | \(0.747164\pi\) | |||||||
\(84\) | −0.853651 | − | 2.50425i | −0.0931410 | − | 0.273236i | ||||
\(85\) | 1.92007 | + | 1.10855i | 0.208261 | + | 0.120240i | ||||
\(86\) | −3.89373 | − | 2.24805i | −0.419872 | − | 0.242413i | ||||
\(87\) | 3.96752 | 0.425363 | ||||||||
\(88\) | 0.259622 | − | 0.449678i | 0.0276757 | − | 0.0479358i | ||||
\(89\) | − | 8.02946i | − | 0.851121i | −0.904930 | − | 0.425560i | \(-0.860077\pi\) | ||
0.904930 | − | 0.425560i | \(-0.139923\pi\) | |||||||
\(90\) | 2.55339 | 0.269151 | ||||||||
\(91\) | 3.72243 | + | 8.78314i | 0.390217 | + | 0.920723i | ||||
\(92\) | 8.52091 | 0.888367 | ||||||||
\(93\) | − | 4.03613i | − | 0.418527i | ||||||
\(94\) | −1.62493 | + | 2.81446i | −0.167599 | + | 0.290290i | ||||
\(95\) | 11.8144 | 1.21213 | ||||||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | −13.0095 | − | 7.51106i | −1.32092 | − | 0.762632i | −0.337043 | − | 0.941489i | \(-0.609427\pi\) |
−0.983875 | + | 0.178857i | \(0.942760\pi\) | |||||||
\(98\) | −6.93776 | + | 0.931425i | −0.700819 | + | 0.0940881i | ||||
\(99\) | 0.519243i | 0.0521859i | ||||||||
\(100\) | −0.759893 | − | 1.31617i | −0.0759893 | − | 0.131617i | ||||
\(101\) | 4.25033 | − | 7.36178i | 0.422923 | − | 0.732525i | −0.573301 | − | 0.819345i | \(-0.694337\pi\) |
0.996224 | + | 0.0868203i | \(0.0276706\pi\) | |||||||
\(102\) | −0.751971 | − | 0.434150i | −0.0744562 | − | 0.0429873i | ||||
\(103\) | −7.78135 | + | 13.4777i | −0.766719 | + | 1.32800i | 0.172613 | + | 0.984990i | \(0.444779\pi\) |
−0.939333 | + | 0.343007i | \(0.888554\pi\) | |||||||
\(104\) | −3.24463 | − | 1.57238i | −0.318162 | − | 0.154184i | ||||
\(105\) | 1.30949 | − | 6.62750i | 0.127793 | − | 0.646778i | ||||
\(106\) | −7.15068 | + | 4.12845i | −0.694536 | + | 0.400990i | ||||
\(107\) | −2.74056 | −0.264940 | −0.132470 | − | 0.991187i | \(-0.542291\pi\) | ||||
−0.132470 | + | 0.991187i | \(0.542291\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −12.3004 | + | 7.10162i | −1.17816 | + | 0.680212i | −0.955588 | − | 0.294704i | \(-0.904779\pi\) |
−0.222573 | + | 0.974916i | \(0.571445\pi\) | |||||||
\(110\) | 1.14820 | − | 0.662914i | 0.109477 | − | 0.0632064i | ||||
\(111\) | −5.12950 | − | 2.96152i | −0.486871 | − | 0.281095i | ||||
\(112\) | 1.74192 | − | 1.99141i | 0.164596 | − | 0.188171i | ||||
\(113\) | 9.29913 | − | 16.1066i | 0.874788 | − | 1.51518i | 0.0178004 | − | 0.999842i | \(-0.494334\pi\) |
0.856988 | − | 0.515336i | \(-0.172333\pi\) | |||||||
\(114\) | −4.62695 | −0.433353 | ||||||||
\(115\) | 18.8423 | + | 10.8786i | 1.75705 | + | 1.01443i | ||||
\(116\) | 1.98376 | + | 3.43598i | 0.184188 | + | 0.319022i | ||||
\(117\) | 3.59612 | − | 0.260597i | 0.332462 | − | 0.0240922i | ||||
\(118\) | −1.40079 | −0.128954 | ||||||||
\(119\) | −1.51251 | + | 1.72914i | −0.138652 | + | 0.158510i | ||||
\(120\) | 1.27669 | + | 2.21130i | 0.116546 | + | 0.201863i | ||||
\(121\) | −5.36519 | − | 9.29279i | −0.487745 | − | 0.844799i | ||||
\(122\) | 5.22921 | − | 3.01909i | 0.473430 | − | 0.273335i | ||||
\(123\) | − | 6.78500i | − | 0.611783i | ||||||
\(124\) | 3.49539 | − | 2.01806i | 0.313895 | − | 0.181228i | ||||
\(125\) | 8.88633i | 0.794818i | ||||||||
\(126\) | −0.512843 | + | 2.59557i | −0.0456877 | + | 0.231232i | ||||
\(127\) | −5.67318 | − | 9.82624i | −0.503413 | − | 0.871938i | −0.999992 | − | 0.00394597i | \(-0.998744\pi\) |
0.496579 | − | 0.867992i | \(-0.334589\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 2.24805 | + | 3.89373i | 0.197930 | + | 0.342824i | ||||
\(130\) | −5.16740 | − | 7.61939i | −0.453211 | − | 0.668265i | ||||
\(131\) | −1.43219 | + | 2.48062i | −0.125131 | + | 0.216733i | −0.921784 | − | 0.387704i | \(-0.873268\pi\) |
0.796653 | + | 0.604437i | \(0.206602\pi\) | |||||||
\(132\) | −0.449678 | + | 0.259622i | −0.0391394 | + | 0.0225972i | ||||
\(133\) | −2.37290 | + | 12.0096i | −0.205756 | + | 1.04136i | ||||
\(134\) | 5.51150 | − | 9.54619i | 0.476121 | − | 0.824665i | ||||
\(135\) | −2.21130 | − | 1.27669i | −0.190318 | − | 0.109880i | ||||
\(136\) | − | 0.868301i | − | 0.0744562i | ||||||
\(137\) | − | 9.80651i | − | 0.837827i | −0.908026 | − | 0.418913i | \(-0.862411\pi\) | ||
0.908026 | − | 0.418913i | \(-0.137589\pi\) | |||||||
\(138\) | −7.37933 | − | 4.26046i | −0.628170 | − | 0.362674i | ||||
\(139\) | −3.49317 | + | 6.05035i | −0.296287 | + | 0.513184i | −0.975283 | − | 0.220957i | \(-0.929082\pi\) |
0.678996 | + | 0.734142i | \(0.262415\pi\) | |||||||
\(140\) | 6.39433 | − | 2.17970i | 0.540419 | − | 0.184218i | ||||
\(141\) | 2.81446 | − | 1.62493i | 0.237020 | − | 0.136844i | ||||
\(142\) | 2.58292 | − | 4.47375i | 0.216754 | − | 0.375429i | ||||
\(143\) | 1.54944 | − | 1.05082i | 0.129571 | − | 0.0878736i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 10.1306i | 0.841303i | ||||||||
\(146\) | −5.97895 | − | 10.3558i | −0.494821 | − | 0.857055i | ||||
\(147\) | 6.47398 | + | 2.66224i | 0.533965 | + | 0.219578i | ||||
\(148\) | − | 5.92304i | − | 0.486871i | ||||||
\(149\) | 0.548493 | − | 0.316672i | 0.0449343 | − | 0.0259428i | −0.477365 | − | 0.878705i | \(-0.658408\pi\) |
0.522299 | + | 0.852763i | \(0.325075\pi\) | |||||||
\(150\) | 1.51979i | 0.124090i | ||||||||
\(151\) | −3.43434 | + | 1.98282i | −0.279483 | + | 0.161360i | −0.633189 | − | 0.773997i | \(-0.718255\pi\) |
0.353706 | + | 0.935357i | \(0.384921\pi\) | |||||||
\(152\) | −2.31347 | − | 4.00705i | −0.187647 | − | 0.325015i | ||||
\(153\) | 0.434150 | + | 0.751971i | 0.0350990 | + | 0.0607932i | ||||
\(154\) | 0.443252 | + | 1.30032i | 0.0357183 | + | 0.104782i | ||||
\(155\) | 10.3058 | 0.827782 | ||||||||
\(156\) | 2.02374 | + | 2.98403i | 0.162029 | + | 0.238914i | ||||
\(157\) | −4.83448 | − | 8.37356i | −0.385833 | − | 0.668283i | 0.606051 | − | 0.795426i | \(-0.292753\pi\) |
−0.991884 | + | 0.127143i | \(0.959419\pi\) | |||||||
\(158\) | −9.48251 | − | 5.47473i | −0.754388 | − | 0.435546i | ||||
\(159\) | 8.25690 | 0.654815 | ||||||||
\(160\) | −1.27669 | + | 2.21130i | −0.100931 | + | 0.174818i | ||||
\(161\) | −14.8428 | + | 16.9686i | −1.16977 | + | 1.33732i | ||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | 20.5444 | − | 11.8613i | 1.60917 | − | 0.929052i | 0.619608 | − | 0.784912i | \(-0.287292\pi\) |
0.989557 | − | 0.144140i | \(-0.0460417\pi\) | |||||||
\(164\) | 5.87598 | − | 3.39250i | 0.458837 | − | 0.264910i | ||||
\(165\) | −1.32583 | −0.103216 | ||||||||
\(166\) | 12.9984 | 1.00887 | ||||||||
\(167\) | 3.53346 | − | 2.04005i | 0.273428 | − | 0.157864i | −0.357017 | − | 0.934098i | \(-0.616206\pi\) |
0.630444 | + | 0.776234i | \(0.282873\pi\) | |||||||
\(168\) | −2.50425 | + | 0.853651i | −0.193207 | + | 0.0658606i | ||||
\(169\) | −8.05526 | − | 10.2036i | −0.619635 | − | 0.784890i | ||||
\(170\) | 1.10855 | − | 1.92007i | 0.0850222 | − | 0.147263i | ||||
\(171\) | 4.00705 | + | 2.31347i | 0.306427 | + | 0.176916i | ||||
\(172\) | −2.24805 | + | 3.89373i | −0.171412 | + | 0.296894i | ||||
\(173\) | −6.89043 | − | 11.9346i | −0.523869 | − | 0.907368i | −0.999614 | − | 0.0277848i | \(-0.991155\pi\) |
0.475745 | − | 0.879583i | \(-0.342179\pi\) | |||||||
\(174\) | − | 3.96752i | − | 0.300777i | ||||||
\(175\) | 3.94471 | + | 0.779411i | 0.298192 | + | 0.0589180i | ||||
\(176\) | −0.449678 | − | 0.259622i | −0.0338957 | − | 0.0195697i | ||||
\(177\) | 1.21312 | + | 0.700397i | 0.0911839 | + | 0.0526451i | ||||
\(178\) | −8.02946 | −0.601833 | ||||||||
\(179\) | −1.92793 | + | 3.33928i | −0.144100 | + | 0.249589i | −0.929037 | − | 0.369987i | \(-0.879362\pi\) |
0.784937 | + | 0.619576i | \(0.212696\pi\) | |||||||
\(180\) | − | 2.55339i | − | 0.190318i | ||||||
\(181\) | −3.18446 | −0.236699 | −0.118349 | − | 0.992972i | \(-0.537760\pi\) | ||||
−0.118349 | + | 0.992972i | \(0.537760\pi\) | |||||||
\(182\) | 8.78314 | − | 3.72243i | 0.651049 | − | 0.275925i | ||||
\(183\) | −6.03817 | −0.446354 | ||||||||
\(184\) | − | 8.52091i | − | 0.628170i | ||||||
\(185\) | 7.56190 | − | 13.0976i | 0.555962 | − | 0.962955i | ||||
\(186\) | −4.03613 | −0.295943 | ||||||||
\(187\) | 0.390455 | + | 0.225430i | 0.0285529 | + | 0.0164850i | ||||
\(188\) | 2.81446 | + | 1.62493i | 0.205266 | + | 0.118510i | ||||
\(189\) | 1.74192 | − | 1.99141i | 0.126706 | − | 0.144854i | ||||
\(190\) | − | 11.8144i | − | 0.857105i | ||||||
\(191\) | −6.70696 | − | 11.6168i | −0.485299 | − | 0.840562i | 0.514559 | − | 0.857455i | \(-0.327956\pi\) |
−0.999857 | + | 0.0168934i | \(0.994622\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 5.18745 | + | 2.99498i | 0.373401 | + | 0.215583i | 0.674943 | − | 0.737870i | \(-0.264168\pi\) |
−0.301542 | + | 0.953453i | \(0.597501\pi\) | |||||||
\(194\) | −7.51106 | + | 13.0095i | −0.539262 | + | 0.934030i | ||||
\(195\) | 0.665404 | + | 9.18229i | 0.0476506 | + | 0.657557i | ||||
\(196\) | 0.931425 | + | 6.93776i | 0.0665303 | + | 0.495554i | ||||
\(197\) | −3.78655 | + | 2.18617i | −0.269781 | + | 0.155758i | −0.628788 | − | 0.777577i | \(-0.716449\pi\) |
0.359007 | + | 0.933335i | \(0.383115\pi\) | |||||||
\(198\) | 0.519243 | 0.0369010 | ||||||||
\(199\) | 9.69511 | 0.687268 | 0.343634 | − | 0.939104i | \(-0.388342\pi\) | ||||
0.343634 | + | 0.939104i | \(0.388342\pi\) | |||||||
\(200\) | −1.31617 | + | 0.759893i | −0.0930675 | + | 0.0537326i | ||||
\(201\) | −9.54619 | + | 5.51150i | −0.673337 | + | 0.388751i | ||||
\(202\) | −7.36178 | − | 4.25033i | −0.517973 | − | 0.299052i | ||||
\(203\) | −10.2980 | − | 2.03472i | −0.722778 | − | 0.142809i | ||||
\(204\) | −0.434150 | + | 0.751971i | −0.0303966 | + | 0.0526485i | ||||
\(205\) | 17.3247 | 1.21001 | ||||||||
\(206\) | 13.4777 | + | 7.78135i | 0.939036 | + | 0.542153i | ||||
\(207\) | 4.26046 | + | 7.37933i | 0.296122 | + | 0.512899i | ||||
\(208\) | −1.57238 | + | 3.24463i | −0.109025 | + | 0.224975i | ||||
\(209\) | 2.40251 | 0.166185 | ||||||||
\(210\) | −6.62750 | − | 1.30949i | −0.457341 | − | 0.0903631i | ||||
\(211\) | 3.54943 | + | 6.14780i | 0.244353 | + | 0.423232i | 0.961950 | − | 0.273227i | \(-0.0880911\pi\) |
−0.717596 | + | 0.696459i | \(0.754758\pi\) | |||||||
\(212\) | 4.12845 | + | 7.15068i | 0.283543 | + | 0.491111i | ||||
\(213\) | −4.47375 | + | 2.58292i | −0.306536 | + | 0.176979i | ||||
\(214\) | 2.74056i | 0.187341i | ||||||||
\(215\) | −9.94221 | + | 5.74014i | −0.678053 | + | 0.391474i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −2.06990 | + | 10.4761i | −0.140514 | + | 0.711161i | ||||
\(218\) | 7.10162 | + | 12.3004i | 0.480982 | + | 0.833086i | ||||
\(219\) | 11.9579i | 0.808040i | ||||||||
\(220\) | −0.662914 | − | 1.14820i | −0.0446937 | − | 0.0774117i | ||||
\(221\) | 1.36530 | − | 2.81732i | 0.0918398 | − | 0.189513i | ||||
\(222\) | −2.96152 | + | 5.12950i | −0.198764 | + | 0.344269i | ||||
\(223\) | −5.20714 | + | 3.00634i | −0.348696 | + | 0.201320i | −0.664111 | − | 0.747634i | \(-0.731190\pi\) |
0.315415 | + | 0.948954i | \(0.397856\pi\) | |||||||
\(224\) | −1.99141 | − | 1.74192i | −0.133057 | − | 0.116387i | ||||
\(225\) | 0.759893 | − | 1.31617i | 0.0506595 | − | 0.0877449i | ||||
\(226\) | −16.1066 | − | 9.29913i | −1.07139 | − | 0.618569i | ||||
\(227\) | 3.60284i | 0.239129i | 0.992826 | + | 0.119564i | \(0.0381498\pi\) | ||||
−0.992826 | + | 0.119564i | \(0.961850\pi\) | |||||||
\(228\) | 4.62695i | 0.306427i | ||||||||
\(229\) | −23.8424 | − | 13.7654i | −1.57555 | − | 0.909644i | −0.995469 | − | 0.0950854i | \(-0.969688\pi\) |
−0.580081 | − | 0.814559i | \(-0.696979\pi\) | |||||||
\(230\) | 10.8786 | − | 18.8423i | 0.717313 | − | 1.24242i | ||||
\(231\) | 0.266290 | − | 1.34773i | 0.0175206 | − | 0.0886743i | ||||
\(232\) | 3.43598 | − | 1.98376i | 0.225583 | − | 0.130240i | ||||
\(233\) | −5.84917 | + | 10.1311i | −0.383192 | + | 0.663708i | −0.991517 | − | 0.129981i | \(-0.958509\pi\) |
0.608325 | + | 0.793688i | \(0.291842\pi\) | |||||||
\(234\) | −0.260597 | − | 3.59612i | −0.0170357 | − | 0.235086i | ||||
\(235\) | 4.14908 | + | 7.18641i | 0.270656 | + | 0.468790i | ||||
\(236\) | 1.40079i | 0.0911839i | ||||||||
\(237\) | 5.47473 | + | 9.48251i | 0.355622 | + | 0.615955i | ||||
\(238\) | 1.72914 | + | 1.51251i | 0.112084 | + | 0.0980415i | ||||
\(239\) | 16.4292i | 1.06272i | 0.847147 | + | 0.531359i | \(0.178318\pi\) | ||||
−0.847147 | + | 0.531359i | \(0.821682\pi\) | |||||||
\(240\) | 2.21130 | − | 1.27669i | 0.142739 | − | 0.0824102i | ||||
\(241\) | − | 14.3659i | − | 0.925392i | −0.886517 | − | 0.462696i | \(-0.846882\pi\) | ||
0.886517 | − | 0.462696i | \(-0.153118\pi\) | |||||||
\(242\) | −9.29279 | + | 5.36519i | −0.597363 | + | 0.344888i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −3.01909 | − | 5.22921i | −0.193277 | − | 0.334766i | ||||
\(245\) | −6.79773 | + | 16.5306i | −0.434291 | + | 1.05610i | ||||
\(246\) | −6.78500 | −0.432596 | ||||||||
\(247\) | −1.20577 | − | 16.6391i | −0.0767211 | − | 1.05872i | ||||
\(248\) | −2.01806 | − | 3.49539i | −0.128147 | − | 0.221958i | ||||
\(249\) | −11.2569 | − | 6.49919i | −0.713379 | − | 0.411870i | ||||
\(250\) | 8.88633 | 0.562021 | ||||||||
\(251\) | −9.52013 | + | 16.4893i | −0.600905 | + | 1.04080i | 0.391779 | + | 0.920059i | \(0.371860\pi\) |
−0.992684 | + | 0.120739i | \(0.961474\pi\) | |||||||
\(252\) | 2.59557 | + | 0.512843i | 0.163506 | + | 0.0323061i | ||||
\(253\) | 3.83166 | + | 2.21221i | 0.240895 | + | 0.139081i | ||||
\(254\) | −9.82624 | + | 5.67318i | −0.616553 | + | 0.355967i | ||||
\(255\) | −1.92007 | + | 1.10855i | −0.120240 | + | 0.0694203i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.3332 | 1.45548 | 0.727742 | − | 0.685851i | \(-0.240570\pi\) | ||||
0.727742 | + | 0.685851i | \(0.240570\pi\) | |||||||
\(258\) | 3.89373 | − | 2.24805i | 0.242413 | − | 0.139957i | ||||
\(259\) | 11.7952 | + | 10.3175i | 0.732918 | + | 0.641096i | ||||
\(260\) | −7.61939 | + | 5.16740i | −0.472535 | + | 0.320469i | ||||
\(261\) | −1.98376 | + | 3.43598i | −0.122792 | + | 0.212682i | ||||
\(262\) | 2.48062 | + | 1.43219i | 0.153253 | + | 0.0884809i | ||||
\(263\) | −10.3167 | + | 17.8690i | −0.636152 | + | 1.10185i | 0.350118 | + | 0.936706i | \(0.386142\pi\) |
−0.986270 | + | 0.165142i | \(0.947192\pi\) | |||||||
\(264\) | 0.259622 | + | 0.449678i | 0.0159786 | + | 0.0276757i | ||||
\(265\) | 21.0831i | 1.29512i | ||||||||
\(266\) | 12.0096 | + | 2.37290i | 0.736354 | + | 0.145492i | ||||
\(267\) | 6.95371 | + | 4.01473i | 0.425560 | + | 0.245697i | ||||
\(268\) | −9.54619 | − | 5.51150i | −0.583127 | − | 0.336668i | ||||
\(269\) | −8.74233 | −0.533029 | −0.266515 | − | 0.963831i | \(-0.585872\pi\) | ||||
−0.266515 | + | 0.963831i | \(0.585872\pi\) | |||||||
\(270\) | −1.27669 | + | 2.21130i | −0.0776971 | + | 0.134575i | ||||
\(271\) | − | 10.1211i | − | 0.614811i | −0.951579 | − | 0.307406i | \(-0.900539\pi\) | ||
0.951579 | − | 0.307406i | \(-0.0994608\pi\) | |||||||
\(272\) | −0.868301 | −0.0526485 | ||||||||
\(273\) | −9.46764 | − | 1.16785i | −0.573007 | − | 0.0706813i | ||||
\(274\) | −9.80651 | −0.592433 | ||||||||
\(275\) | − | 0.789139i | − | 0.0475868i | ||||||
\(276\) | −4.26046 | + | 7.37933i | −0.256449 | + | 0.444183i | ||||
\(277\) | −4.97733 | −0.299059 | −0.149529 | − | 0.988757i | \(-0.547776\pi\) | ||||
−0.149529 | + | 0.988757i | \(0.547776\pi\) | |||||||
\(278\) | 6.05035 | + | 3.49317i | 0.362876 | + | 0.209507i | ||||
\(279\) | 3.49539 | + | 2.01806i | 0.209264 | + | 0.120818i | ||||
\(280\) | −2.17970 | − | 6.39433i | −0.130262 | − | 0.382134i | ||||
\(281\) | 27.2729i | 1.62696i | 0.581591 | + | 0.813481i | \(0.302430\pi\) | ||||
−0.581591 | + | 0.813481i | \(0.697570\pi\) | |||||||
\(282\) | −1.62493 | − | 2.81446i | −0.0967632 | − | 0.167599i | ||||
\(283\) | 4.90256 | − | 8.49149i | 0.291427 | − | 0.504767i | −0.682720 | − | 0.730680i | \(-0.739203\pi\) |
0.974147 | + | 0.225913i | \(0.0725366\pi\) | |||||||
\(284\) | −4.47375 | − | 2.58292i | −0.265468 | − | 0.153268i | ||||
\(285\) | −5.90719 | + | 10.2316i | −0.349912 | + | 0.606065i | ||||
\(286\) | −1.05082 | − | 1.54944i | −0.0621360 | − | 0.0916202i | ||||
\(287\) | −3.47964 | + | 17.6109i | −0.205396 | + | 1.03954i | ||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −16.2461 | −0.955650 | ||||||||
\(290\) | 10.1306 | 0.594891 | ||||||||
\(291\) | 13.0095 | − | 7.51106i | 0.762632 | − | 0.440306i | ||||
\(292\) | −10.3558 | + | 5.97895i | −0.606030 | + | 0.349891i | ||||
\(293\) | 24.3101 | + | 14.0354i | 1.42021 | + | 0.819959i | 0.996317 | − | 0.0857521i | \(-0.0273293\pi\) |
0.423895 | + | 0.905711i | \(0.360663\pi\) | |||||||
\(294\) | 2.66224 | − | 6.47398i | 0.155265 | − | 0.377570i | ||||
\(295\) | −1.78838 | + | 3.09757i | −0.104124 | + | 0.180348i | ||||
\(296\) | −5.92304 | −0.344269 | ||||||||
\(297\) | −0.449678 | − | 0.259622i | −0.0260929 | − | 0.0150648i | ||||
\(298\) | −0.316672 | − | 0.548493i | −0.0183443 | − | 0.0317733i | ||||
\(299\) | 13.3981 | − | 27.6472i | 0.774832 | − | 1.59888i | ||||
\(300\) | 1.51979 | 0.0877449 | ||||||||
\(301\) | −3.83810 | − | 11.2594i | −0.221224 | − | 0.648979i | ||||
\(302\) | 1.98282 | + | 3.43434i | 0.114098 | + | 0.197624i | ||||
\(303\) | 4.25033 | + | 7.36178i | 0.244175 | + | 0.422923i | ||||
\(304\) | −4.00705 | + | 2.31347i | −0.229820 | + | 0.132687i | ||||
\(305\) | − | 15.4178i | − | 0.882820i | ||||||
\(306\) | 0.751971 | − | 0.434150i | 0.0429873 | − | 0.0248187i | ||||
\(307\) | 27.0072i | 1.54139i | 0.637207 | + | 0.770693i | \(0.280090\pi\) | ||||
−0.637207 | + | 0.770693i | \(0.719910\pi\) | |||||||
\(308\) | 1.30032 | − | 0.443252i | 0.0740924 | − | 0.0252566i | ||||
\(309\) | −7.78135 | − | 13.4777i | −0.442666 | − | 0.766719i | ||||
\(310\) | − | 10.3058i | − | 0.585330i | ||||||
\(311\) | 12.0954 | + | 20.9499i | 0.685869 | + | 1.18796i | 0.973163 | + | 0.230118i | \(0.0739111\pi\) |
−0.287294 | + | 0.957843i | \(0.592756\pi\) | |||||||
\(312\) | 2.98403 | − | 2.02374i | 0.168938 | − | 0.114572i | ||||
\(313\) | 11.8941 | − | 20.6011i | 0.672293 | − | 1.16444i | −0.304960 | − | 0.952365i | \(-0.598643\pi\) |
0.977252 | − | 0.212080i | \(-0.0680236\pi\) | |||||||
\(314\) | −8.37356 | + | 4.83448i | −0.472548 | + | 0.272825i | ||||
\(315\) | 5.08484 | + | 4.44780i | 0.286498 | + | 0.250605i | ||||
\(316\) | −5.47473 | + | 9.48251i | −0.307977 | + | 0.533433i | ||||
\(317\) | 7.55286 | + | 4.36064i | 0.424211 | + | 0.244918i | 0.696877 | − | 0.717190i | \(-0.254572\pi\) |
−0.272667 | + | 0.962109i | \(0.587906\pi\) | |||||||
\(318\) | − | 8.25690i | − | 0.463024i | ||||||
\(319\) | 2.06011i | 0.115344i | ||||||||
\(320\) | 2.21130 | + | 1.27669i | 0.123615 | + | 0.0713693i | ||||
\(321\) | 1.37028 | − | 2.37339i | 0.0764814 | − | 0.132470i | ||||
\(322\) | 16.9686 | + | 14.8428i | 0.945625 | + | 0.827154i | ||||
\(323\) | 3.47933 | − | 2.00879i | 0.193595 | − | 0.111772i | ||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −5.46534 | + | 0.396051i | −0.303162 | + | 0.0219690i | ||||
\(326\) | −11.8613 | − | 20.5444i | −0.656939 | − | 1.13785i | ||||
\(327\) | − | 14.2032i | − | 0.785441i | ||||||
\(328\) | −3.39250 | − | 5.87598i | −0.187319 | − | 0.324447i | ||||
\(329\) | −8.13847 | + | 2.77425i | −0.448688 | + | 0.152949i | ||||
\(330\) | 1.32583i | 0.0729845i | ||||||||
\(331\) | 10.3972 | − | 6.00281i | 0.571480 | − | 0.329944i | −0.186260 | − | 0.982500i | \(-0.559637\pi\) |
0.757740 | + | 0.652556i | \(0.226303\pi\) | |||||||
\(332\) | − | 12.9984i | − | 0.713379i | ||||||
\(333\) | 5.12950 | − | 2.96152i | 0.281095 | − | 0.162290i | ||||
\(334\) | −2.04005 | − | 3.53346i | −0.111626 | − | 0.193343i | ||||
\(335\) | −14.0730 | − | 24.3751i | −0.768889 | − | 1.33176i | ||||
\(336\) | 0.853651 | + | 2.50425i | 0.0465705 | + | 0.136618i | ||||
\(337\) | 22.4347 | 1.22210 | 0.611049 | − | 0.791593i | \(-0.290748\pi\) | ||||
0.611049 | + | 0.791593i | \(0.290748\pi\) | |||||||
\(338\) | −10.2036 | + | 8.05526i | −0.555001 | + | 0.438148i | ||||
\(339\) | 9.29913 | + | 16.1066i | 0.505059 | + | 0.874788i | ||||
\(340\) | −1.92007 | − | 1.10855i | −0.104131 | − | 0.0601198i | ||||
\(341\) | 2.09573 | 0.113490 | ||||||||
\(342\) | 2.31347 | − | 4.00705i | 0.125098 | − | 0.216677i | ||||
\(343\) | −15.4384 | − | 10.2302i | −0.833594 | − | 0.552377i | ||||
\(344\) | 3.89373 | + | 2.24805i | 0.209936 | + | 0.121207i | ||||
\(345\) | −18.8423 | + | 10.8786i | −1.01443 | + | 0.585684i | ||||
\(346\) | −11.9346 | + | 6.89043i | −0.641606 | + | 0.370432i | ||||
\(347\) | 29.2720 | 1.57140 | 0.785701 | − | 0.618606i | \(-0.212302\pi\) | ||||
0.785701 | + | 0.618606i | \(0.212302\pi\) | |||||||
\(348\) | −3.96752 | −0.212682 | ||||||||
\(349\) | −22.1028 | + | 12.7610i | −1.18313 | + | 0.683083i | −0.956738 | − | 0.290952i | \(-0.906028\pi\) |
−0.226397 | + | 0.974035i | \(0.572695\pi\) | |||||||
\(350\) | 0.779411 | − | 3.94471i | 0.0416613 | − | 0.210854i | ||||
\(351\) | −1.57238 | + | 3.24463i | −0.0839273 | + | 0.173186i | ||||
\(352\) | −0.259622 | + | 0.449678i | −0.0138379 | + | 0.0239679i | ||||
\(353\) | 3.16688 | + | 1.82840i | 0.168556 | + | 0.0973158i | 0.581905 | − | 0.813257i | \(-0.302308\pi\) |
−0.413349 | + | 0.910573i | \(0.635641\pi\) | |||||||
\(354\) | 0.700397 | − | 1.21312i | 0.0372257 | − | 0.0644768i | ||||
\(355\) | −6.59520 | − | 11.4232i | −0.350037 | − | 0.606282i | ||||
\(356\) | 8.02946i | 0.425560i | ||||||||
\(357\) | −0.741226 | − | 2.17444i | −0.0392298 | − | 0.115084i | ||||
\(358\) | 3.33928 | + | 1.92793i | 0.176486 | + | 0.101894i | ||||
\(359\) | −29.7911 | − | 17.1999i | −1.57231 | − | 0.907775i | −0.995885 | − | 0.0906276i | \(-0.971113\pi\) |
−0.576428 | − | 0.817148i | \(-0.695554\pi\) | |||||||
\(360\) | −2.55339 | −0.134575 | ||||||||
\(361\) | 1.20431 | − | 2.08593i | 0.0633849 | − | 0.109786i | ||||
\(362\) | 3.18446i | 0.167371i | ||||||||
\(363\) | 10.7304 | 0.563199 | ||||||||
\(364\) | −3.72243 | − | 8.78314i | −0.195108 | − | 0.460361i | ||||
\(365\) | −30.5331 | −1.59818 | ||||||||
\(366\) | 6.03817i | 0.315620i | ||||||||
\(367\) | −3.19602 | + | 5.53566i | −0.166831 | + | 0.288959i | −0.937304 | − | 0.348513i | \(-0.886687\pi\) |
0.770473 | + | 0.637472i | \(0.220020\pi\) | |||||||
\(368\) | −8.52091 | −0.444183 | ||||||||
\(369\) | 5.87598 | + | 3.39250i | 0.305891 | + | 0.176606i | ||||
\(370\) | −13.0976 | − | 7.56190i | −0.680912 | − | 0.393125i | ||||
\(371\) | −21.4314 | − | 4.23449i | −1.11266 | − | 0.219844i | ||||
\(372\) | 4.03613i | 0.209264i | ||||||||
\(373\) | −9.11185 | − | 15.7822i | −0.471794 | − | 0.817171i | 0.527685 | − | 0.849440i | \(-0.323060\pi\) |
−0.999479 | + | 0.0322690i | \(0.989727\pi\) | |||||||
\(374\) | 0.225430 | − | 0.390455i | 0.0116567 | − | 0.0201900i | ||||
\(375\) | −7.69579 | − | 4.44317i | −0.397409 | − | 0.229444i | ||||
\(376\) | 1.62493 | − | 2.81446i | 0.0837994 | − | 0.145145i | ||||
\(377\) | 14.2677 | − | 1.03392i | 0.734824 | − | 0.0532498i | ||||
\(378\) | −1.99141 | − | 1.74192i | −0.102427 | − | 0.0895947i | ||||
\(379\) | −6.69334 | + | 3.86440i | −0.343814 | + | 0.198501i | −0.661957 | − | 0.749542i | \(-0.730274\pi\) |
0.318143 | + | 0.948043i | \(0.396941\pi\) | |||||||
\(380\) | −11.8144 | −0.606065 | ||||||||
\(381\) | 11.3464 | 0.581292 | ||||||||
\(382\) | −11.6168 | + | 6.70696i | −0.594367 | + | 0.343158i | ||||
\(383\) | 8.50425 | − | 4.90993i | 0.434547 | − | 0.250886i | −0.266735 | − | 0.963770i | \(-0.585945\pi\) |
0.701282 | + | 0.712884i | \(0.252612\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 3.44128 | + | 0.679942i | 0.175384 | + | 0.0346530i | ||||
\(386\) | 2.99498 | − | 5.18745i | 0.152440 | − | 0.264034i | ||||
\(387\) | −4.49610 | −0.228549 | ||||||||
\(388\) | 13.0095 | + | 7.51106i | 0.660459 | + | 0.381316i | ||||
\(389\) | 4.70287 | + | 8.14562i | 0.238445 | + | 0.412999i | 0.960268 | − | 0.279078i | \(-0.0900289\pi\) |
−0.721823 | + | 0.692078i | \(0.756696\pi\) | |||||||
\(390\) | 9.18229 | − | 0.665404i | 0.464963 | − | 0.0336941i | ||||
\(391\) | 7.39871 | 0.374169 | ||||||||
\(392\) | 6.93776 | − | 0.931425i | 0.350410 | − | 0.0470440i | ||||
\(393\) | −1.43219 | − | 2.48062i | −0.0722444 | − | 0.125131i | ||||
\(394\) | 2.18617 | + | 3.78655i | 0.110138 | + | 0.190764i | ||||
\(395\) | −24.2125 | + | 13.9791i | −1.21826 | + | 0.703365i | ||||
\(396\) | − | 0.519243i | − | 0.0260929i | ||||||
\(397\) | 9.99586 | − | 5.77112i | 0.501678 | − | 0.289644i | −0.227728 | − | 0.973725i | \(-0.573130\pi\) |
0.729406 | + | 0.684081i | \(0.239796\pi\) | |||||||
\(398\) | − | 9.69511i | − | 0.485972i | ||||||
\(399\) | −9.21414 | − | 8.05977i | −0.461284 | − | 0.403493i | ||||
\(400\) | 0.759893 | + | 1.31617i | 0.0379947 | + | 0.0658087i | ||||
\(401\) | 33.5631i | 1.67606i | 0.545623 | + | 0.838030i | \(0.316293\pi\) | ||||
−0.545623 | + | 0.838030i | \(0.683707\pi\) | |||||||
\(402\) | 5.51150 | + | 9.54619i | 0.274888 | + | 0.476121i | ||||
\(403\) | −1.05180 | − | 14.5144i | −0.0523940 | − | 0.723014i | ||||
\(404\) | −4.25033 | + | 7.36178i | −0.211462 | + | 0.366262i | ||||
\(405\) | 2.21130 | − | 1.27669i | 0.109880 | − | 0.0634394i | ||||
\(406\) | −2.03472 | + | 10.2980i | −0.100981 | + | 0.511081i | ||||
\(407\) | 1.53775 | − | 2.66346i | 0.0762233 | − | 0.132023i | ||||
\(408\) | 0.751971 | + | 0.434150i | 0.0372281 | + | 0.0214936i | ||||
\(409\) | − | 18.3070i | − | 0.905221i | −0.891708 | − | 0.452611i | \(-0.850493\pi\) | ||
0.891708 | − | 0.452611i | \(-0.149507\pi\) | |||||||
\(410\) | − | 17.3247i | − | 0.855607i | ||||||
\(411\) | 8.49269 | + | 4.90326i | 0.418913 | + | 0.241860i | ||||
\(412\) | 7.78135 | − | 13.4777i | 0.383360 | − | 0.663999i | ||||
\(413\) | −2.78955 | − | 2.44007i | −0.137265 | − | 0.120068i | ||||
\(414\) | 7.37933 | − | 4.26046i | 0.362674 | − | 0.209390i | ||||
\(415\) | 16.5950 | − | 28.7433i | 0.814614 | − | 1.41095i | ||||
\(416\) | 3.24463 | + | 1.57238i | 0.159081 | + | 0.0770921i | ||||
\(417\) | −3.49317 | − | 6.05035i | −0.171061 | − | 0.296287i | ||||
\(418\) | − | 2.40251i | − | 0.117511i | ||||||
\(419\) | −8.13046 | − | 14.0824i | −0.397199 | − | 0.687969i | 0.596180 | − | 0.802851i | \(-0.296684\pi\) |
−0.993379 | + | 0.114882i | \(0.963351\pi\) | |||||||
\(420\) | −1.30949 | + | 6.62750i | −0.0638964 | + | 0.323389i | ||||
\(421\) | − | 20.7347i | − | 1.01055i | −0.862959 | − | 0.505274i | \(-0.831392\pi\) | ||
0.862959 | − | 0.505274i | \(-0.168608\pi\) | |||||||
\(422\) | 6.14780 | − | 3.54943i | 0.299270 | − | 0.172784i | ||||
\(423\) | 3.24986i | 0.158014i | ||||||||
\(424\) | 7.15068 | − | 4.12845i | 0.347268 | − | 0.200495i | ||||
\(425\) | −0.659816 | − | 1.14283i | −0.0320058 | − | 0.0554356i | ||||
\(426\) | 2.58292 | + | 4.47375i | 0.125143 | + | 0.216754i | ||||
\(427\) | 15.6725 | + | 3.09663i | 0.758446 | + | 0.149857i | ||||
\(428\) | 2.74056 | 0.132470 | ||||||||
\(429\) | 0.135313 | + | 1.86726i | 0.00653297 | + | 0.0901522i | ||||
\(430\) | 5.74014 | + | 9.94221i | 0.276814 | + | 0.479456i | ||||
\(431\) | −23.4819 | − | 13.5573i | −1.13108 | − | 0.653030i | −0.186875 | − | 0.982384i | \(-0.559836\pi\) |
−0.944207 | + | 0.329353i | \(0.893169\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 9.82893 | − | 17.0242i | 0.472348 | − | 0.818131i | −0.527151 | − | 0.849772i | \(-0.676740\pi\) |
0.999499 | + | 0.0316404i | \(0.0100731\pi\) | |||||||
\(434\) | 10.4761 | + | 2.06990i | 0.502867 | + | 0.0993584i | ||||
\(435\) | −8.77338 | − | 5.06531i | −0.420651 | − | 0.242863i | ||||
\(436\) | 12.3004 | − | 7.10162i | 0.589081 | − | 0.340106i | ||||
\(437\) | 34.1437 | − | 19.7129i | 1.63332 | − | 0.942996i | ||||
\(438\) | 11.9579 | 0.571370 | ||||||||
\(439\) | −17.5185 | −0.836111 | −0.418055 | − | 0.908422i | \(-0.637288\pi\) | ||||
−0.418055 | + | 0.908422i | \(0.637288\pi\) | |||||||
\(440\) | −1.14820 | + | 0.662914i | −0.0547383 | + | 0.0316032i | ||||
\(441\) | −5.54256 | + | 4.27552i | −0.263931 | + | 0.203596i | ||||
\(442\) | −2.81732 | − | 1.36530i | −0.134006 | − | 0.0649405i | ||||
\(443\) | −17.0463 | + | 29.5250i | −0.809894 | + | 1.40278i | 0.103044 | + | 0.994677i | \(0.467142\pi\) |
−0.912937 | + | 0.408100i | \(0.866191\pi\) | |||||||
\(444\) | 5.12950 | + | 2.96152i | 0.243435 | + | 0.140547i | ||||
\(445\) | −10.2512 | + | 17.7555i | −0.485951 | + | 0.841692i | ||||
\(446\) | 3.00634 | + | 5.20714i | 0.142355 | + | 0.246565i | ||||
\(447\) | 0.633345i | 0.0299562i | ||||||||
\(448\) | −1.74192 | + | 1.99141i | −0.0822980 | + | 0.0940853i | ||||
\(449\) | 24.4229 | + | 14.1006i | 1.15259 | + | 0.665447i | 0.949517 | − | 0.313716i | \(-0.101574\pi\) |
0.203072 | + | 0.979164i | \(0.434907\pi\) | |||||||
\(450\) | −1.31617 | − | 0.759893i | −0.0620450 | − | 0.0358217i | ||||
\(451\) | 3.52306 | 0.165895 | ||||||||
\(452\) | −9.29913 | + | 16.1066i | −0.437394 | + | 0.757589i | ||||
\(453\) | − | 3.96564i | − | 0.186322i | ||||||
\(454\) | 3.60284 | 0.169090 | ||||||||
\(455\) | 2.98197 | − | 24.1745i | 0.139797 | − | 1.13332i | ||||
\(456\) | 4.62695 | 0.216677 | ||||||||
\(457\) | 22.8685i | 1.06974i | 0.844934 | + | 0.534871i | \(0.179640\pi\) | ||||
−0.844934 | + | 0.534871i | \(0.820360\pi\) | |||||||
\(458\) | −13.7654 | + | 23.8424i | −0.643216 | + | 1.11408i | ||||
\(459\) | −0.868301 | −0.0405288 | ||||||||
\(460\) | −18.8423 | − | 10.8786i | −0.878526 | − | 0.507217i | ||||
\(461\) | −20.8622 | − | 12.0448i | −0.971648 | − | 0.560981i | −0.0719098 | − | 0.997411i | \(-0.522909\pi\) |
−0.899738 | + | 0.436430i | \(0.856243\pi\) | |||||||
\(462\) | −1.34773 | − | 0.266290i | −0.0627022 | − | 0.0123889i | ||||
\(463\) | 12.2189i | 0.567860i | 0.958845 | + | 0.283930i | \(0.0916384\pi\) | ||||
−0.958845 | + | 0.283930i | \(0.908362\pi\) | |||||||
\(464\) | −1.98376 | − | 3.43598i | −0.0920939 | − | 0.159511i | ||||
\(465\) | −5.15290 | + | 8.92509i | −0.238960 | + | 0.413891i | ||||
\(466\) | 10.1311 | + | 5.84917i | 0.469312 | + | 0.270958i | ||||
\(467\) | −7.51520 | + | 13.0167i | −0.347762 | + | 0.602341i | −0.985852 | − | 0.167621i | \(-0.946392\pi\) |
0.638090 | + | 0.769962i | \(0.279725\pi\) | |||||||
\(468\) | −3.59612 | + | 0.260597i | −0.166231 | + | 0.0120461i | ||||
\(469\) | 27.6044 | − | 9.40979i | 1.27465 | − | 0.434504i | ||||
\(470\) | 7.18641 | − | 4.14908i | 0.331484 | − | 0.191383i | ||||
\(471\) | 9.66896 | 0.445522 | ||||||||
\(472\) | 1.40079 | 0.0644768 | ||||||||
\(473\) | −2.02179 | + | 1.16728i | −0.0929622 | + | 0.0536718i | ||||
\(474\) | 9.48251 | − | 5.47473i | 0.435546 | − | 0.251463i | ||||
\(475\) | −6.08986 | − | 3.51598i | −0.279422 | − | 0.161324i | ||||
\(476\) | 1.51251 | − | 1.72914i | 0.0693258 | − | 0.0792551i | ||||
\(477\) | −4.12845 | + | 7.15068i | −0.189029 | + | 0.327407i | ||||
\(478\) | 16.4292 | 0.751455 | ||||||||
\(479\) | −0.784884 | − | 0.453153i | −0.0358623 | − | 0.0207051i | 0.481962 | − | 0.876192i | \(-0.339924\pi\) |
−0.517824 | + | 0.855487i | \(0.673258\pi\) | |||||||
\(480\) | −1.27669 | − | 2.21130i | −0.0582728 | − | 0.100931i | ||||
\(481\) | −19.2181 | − | 9.31325i | −0.876268 | − | 0.424648i | ||||
\(482\) | −14.3659 | −0.654351 | ||||||||
\(483\) | −7.27389 | − | 21.3385i | −0.330973 | − | 0.970936i | ||||
\(484\) | 5.36519 | + | 9.29279i | 0.243872 | + | 0.422399i | ||||
\(485\) | 19.1786 | + | 33.2184i | 0.870857 | + | 1.50837i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | − | 28.7559i | − | 1.30305i | −0.758625 | − | 0.651527i | \(-0.774129\pi\) | ||
0.758625 | − | 0.651527i | \(-0.225871\pi\) | |||||||
\(488\) | −5.22921 | + | 3.01909i | −0.236715 | + | 0.136668i | ||||
\(489\) | 23.7227i | 1.07278i | ||||||||
\(490\) | 16.5306 | + | 6.79773i | 0.746776 | + | 0.307090i | ||||
\(491\) | −13.8621 | − | 24.0099i | −0.625589 | − | 1.08355i | −0.988427 | − | 0.151700i | \(-0.951525\pi\) |
0.362838 | − | 0.931852i | \(-0.381808\pi\) | |||||||
\(492\) | 6.78500i | 0.305891i | ||||||||
\(493\) | 1.72250 | + | 2.98346i | 0.0775776 | + | 0.134368i | ||||
\(494\) | −16.6391 | + | 1.20577i | −0.748627 | + | 0.0542500i | ||||
\(495\) | 0.662914 | − | 1.14820i | 0.0297958 | − | 0.0516078i | ||||
\(496\) | −3.49539 | + | 2.01806i | −0.156948 | + | 0.0906138i | ||||
\(497\) | 12.9366 | − | 4.40983i | 0.580285 | − | 0.197808i | ||||
\(498\) | −6.49919 | + | 11.2569i | −0.291236 | + | 0.504435i | ||||
\(499\) | 3.50306 | + | 2.02249i | 0.156818 | + | 0.0905392i | 0.576356 | − | 0.817199i | \(-0.304474\pi\) |
−0.419537 | + | 0.907738i | \(0.637808\pi\) | |||||||
\(500\) | − | 8.88633i | − | 0.397409i | ||||||
\(501\) | 4.08009i | 0.182285i | ||||||||
\(502\) | 16.4893 | + | 9.52013i | 0.735955 | + | 0.424904i | ||||
\(503\) | −0.861181 | + | 1.49161i | −0.0383982 | + | 0.0665076i | −0.884586 | − | 0.466377i | \(-0.845559\pi\) |
0.846188 | + | 0.532885i | \(0.178892\pi\) | |||||||
\(504\) | 0.512843 | − | 2.59557i | 0.0228438 | − | 0.115616i | ||||
\(505\) | −18.7975 | + | 10.8527i | −0.836477 | + | 0.482940i | ||||
\(506\) | 2.21221 | − | 3.83166i | 0.0983448 | − | 0.170338i | ||||
\(507\) | 12.8642 | − | 1.87427i | 0.571318 | − | 0.0832395i | ||||
\(508\) | 5.67318 | + | 9.82624i | 0.251707 | + | 0.435969i | ||||
\(509\) | − | 41.8260i | − | 1.85391i | −0.375178 | − | 0.926953i | \(-0.622418\pi\) | ||
0.375178 | − | 0.926953i | \(-0.377582\pi\) | |||||||
\(510\) | 1.10855 | + | 1.92007i | 0.0490876 | + | 0.0850222i | ||||
\(511\) | 6.13252 | − | 31.0376i | 0.271287 | − | 1.37302i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −4.00705 | + | 2.31347i | −0.176916 | + | 0.102142i | ||||
\(514\) | − | 23.3332i | − | 1.02918i | ||||||
\(515\) | 34.4138 | − | 19.8688i | 1.51645 | − | 0.875524i | ||||
\(516\) | −2.24805 | − | 3.89373i | −0.0989648 | − | 0.171412i | ||||
\(517\) | 0.843734 | + | 1.46139i | 0.0371074 | + | 0.0642718i | ||||
\(518\) | 10.3175 | − | 11.7952i | 0.453323 | − | 0.518251i | ||||
\(519\) | 13.7809 | 0.604912 | ||||||||
\(520\) | 5.16740 | + | 7.61939i | 0.226606 | + | 0.334133i | ||||
\(521\) | −14.7751 | − | 25.5912i | −0.647308 | − | 1.12117i | −0.983763 | − | 0.179471i | \(-0.942561\pi\) |
0.336455 | − | 0.941700i | \(-0.390772\pi\) | |||||||
\(522\) | 3.43598 | + | 1.98376i | 0.150389 | + | 0.0868269i | ||||
\(523\) | 10.8626 | 0.474989 | 0.237495 | − | 0.971389i | \(-0.423674\pi\) | ||||
0.237495 | + | 0.971389i | \(0.423674\pi\) | |||||||
\(524\) | 1.43219 | − | 2.48062i | 0.0625655 | − | 0.108367i | ||||
\(525\) | −2.64735 | + | 3.02652i | −0.115540 | + | 0.132088i | ||||
\(526\) | 17.8690 | + | 10.3167i | 0.779124 | + | 0.449828i | ||||
\(527\) | 3.03505 | − | 1.75229i | 0.132209 | − | 0.0763308i | ||||
\(528\) | 0.449678 | − | 0.259622i | 0.0195697 | − | 0.0112986i | ||||
\(529\) | 49.6059 | 2.15678 | ||||||||
\(530\) | 21.0831 | 0.915790 | ||||||||
\(531\) | −1.21312 | + | 0.700397i | −0.0526451 | + | 0.0303946i | ||||
\(532\) | 2.37290 | − | 12.0096i | 0.102878 | − | 0.520681i | ||||
\(533\) | −1.76815 | − | 24.3997i | −0.0765870 | − | 1.05687i | ||||
\(534\) | 4.01473 | − | 6.95371i | 0.173734 | − | 0.300917i | ||||
\(535\) | 6.06019 | + | 3.49885i | 0.262005 | + | 0.151268i | ||||
\(536\) | −5.51150 | + | 9.54619i | −0.238060 | + | 0.412333i | ||||
\(537\) | −1.92793 | − | 3.33928i | −0.0831965 | − | 0.144100i | ||||
\(538\) | 8.74233i | 0.376909i | ||||||||
\(539\) | −1.38235 | + | 3.36157i | −0.0595420 | + | 0.144793i | ||||
\(540\) | 2.21130 | + | 1.27669i | 0.0951591 | + | 0.0549401i | ||||
\(541\) | 9.53428 | + | 5.50462i | 0.409911 | + | 0.236662i | 0.690751 | − | 0.723092i | \(-0.257280\pi\) |
−0.280841 | + | 0.959754i | \(0.590613\pi\) | |||||||
\(542\) | −10.1211 | −0.434737 | ||||||||
\(543\) | 1.59223 | − | 2.75782i | 0.0683291 | − | 0.118349i | ||||
\(544\) | 0.868301i | 0.0372281i | ||||||||
\(545\) | 36.2664 | 1.55348 | ||||||||
\(546\) | −1.16785 | + | 9.46764i | −0.0499793 | + | 0.405177i | ||||
\(547\) | −36.2418 | −1.54959 | −0.774793 | − | 0.632215i | \(-0.782146\pi\) | ||||
−0.774793 | + | 0.632215i | \(0.782146\pi\) | |||||||
\(548\) | 9.80651i | 0.418913i | ||||||||
\(549\) | 3.01909 | − | 5.22921i | 0.128851 | − | 0.223177i | ||||
\(550\) | −0.789139 | −0.0336490 | ||||||||
\(551\) | 15.8981 | + | 9.17876i | 0.677281 | + | 0.391028i | ||||
\(552\) | 7.37933 | + | 4.26046i | 0.314085 | + | 0.181337i | ||||
\(553\) | −9.34701 | − | 27.4202i | −0.397475 | − | 1.16603i | ||||
\(554\) | 4.97733i | 0.211466i | ||||||||
\(555\) | 7.56190 | + | 13.0976i | 0.320985 | + | 0.555962i | ||||
\(556\) | 3.49317 | − | 6.05035i | 0.148144 | − | 0.256592i | ||||
\(557\) | −9.61691 | − | 5.55232i | −0.407481 | − | 0.235260i | 0.282226 | − | 0.959348i | \(-0.408927\pi\) |
−0.689707 | + | 0.724089i | \(0.742261\pi\) | |||||||
\(558\) | 2.01806 | − | 3.49539i | 0.0854315 | − | 0.147972i | ||||
\(559\) | 9.09895 | + | 13.4165i | 0.384845 | + | 0.567458i | ||||
\(560\) | −6.39433 | + | 2.17970i | −0.270210 | + | 0.0921092i | ||||
\(561\) | −0.390455 | + | 0.225430i | −0.0164850 | + | 0.00951764i | ||||
\(562\) | 27.2729 | 1.15044 | ||||||||
\(563\) | 10.3121 | 0.434604 | 0.217302 | − | 0.976104i | \(-0.430274\pi\) | ||||
0.217302 | + | 0.976104i | \(0.430274\pi\) | |||||||
\(564\) | −2.81446 | + | 1.62493i | −0.118510 | + | 0.0684219i | ||||
\(565\) | −41.1263 | + | 23.7443i | −1.73020 | + | 0.998929i | ||||
\(566\) | −8.49149 | − | 4.90256i | −0.356924 | − | 0.206070i | ||||
\(567\) | 0.853651 | + | 2.50425i | 0.0358500 | + | 0.105169i | ||||
\(568\) | −2.58292 | + | 4.47375i | −0.108377 | + | 0.187714i | ||||
\(569\) | −33.8195 | −1.41779 | −0.708894 | − | 0.705315i | \(-0.750806\pi\) | ||||
−0.708894 | + | 0.705315i | \(0.750806\pi\) | |||||||
\(570\) | 10.2316 | + | 5.90719i | 0.428553 | + | 0.247425i | ||||
\(571\) | 6.09944 | + | 10.5645i | 0.255254 | + | 0.442112i | 0.964964 | − | 0.262381i | \(-0.0845077\pi\) |
−0.709711 | + | 0.704493i | \(0.751174\pi\) | |||||||
\(572\) | −1.54944 | + | 1.05082i | −0.0647853 | + | 0.0439368i | ||||
\(573\) | 13.4139 | 0.560374 | ||||||||
\(574\) | 17.6109 | + | 3.47964i | 0.735067 | + | 0.145237i | ||||
\(575\) | −6.47498 | − | 11.2150i | −0.270025 | − | 0.467698i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −22.1116 | + | 12.7661i | −0.920517 | + | 0.531460i | −0.883800 | − | 0.467865i | \(-0.845023\pi\) |
−0.0367167 | + | 0.999326i | \(0.511690\pi\) | |||||||
\(578\) | 16.2461i | 0.675747i | ||||||||
\(579\) | −5.18745 | + | 2.99498i | −0.215583 | + | 0.124467i | ||||
\(580\) | − | 10.1306i | − | 0.420651i | ||||||
\(581\) | 25.8851 | + | 22.6422i | 1.07390 | + | 0.939355i | ||||
\(582\) | −7.51106 | − | 13.0095i | −0.311343 | − | 0.539262i | ||||
\(583\) | 4.28734i | 0.177563i | ||||||||
\(584\) | 5.97895 | + | 10.3558i | 0.247411 | + | 0.428528i | ||||
\(585\) | −8.28480 | − | 4.01489i | −0.342534 | − | 0.165995i | ||||
\(586\) | 14.0354 | − | 24.3101i | 0.579799 | − | 1.00424i | ||||
\(587\) | 17.3456 | − | 10.0145i | 0.715928 | − | 0.413341i | −0.0973243 | − | 0.995253i | \(-0.531028\pi\) |
0.813252 | + | 0.581912i | \(0.197695\pi\) | |||||||
\(588\) | −6.47398 | − | 2.66224i | −0.266983 | − | 0.109789i | ||||
\(589\) | 9.33747 | − | 16.1730i | 0.384744 | − | 0.666396i | ||||
\(590\) | 3.09757 | + | 1.78838i | 0.127525 | + | 0.0736266i | ||||
\(591\) | − | 4.37233i | − | 0.179854i | ||||||
\(592\) | 5.92304i | 0.243435i | ||||||||
\(593\) | 3.62655 | + | 2.09379i | 0.148924 | + | 0.0859816i | 0.572611 | − | 0.819827i | \(-0.305931\pi\) |
−0.423686 | + | 0.905809i | \(0.639264\pi\) | |||||||
\(594\) | −0.259622 | + | 0.449678i | −0.0106524 | + | 0.0184505i | ||||
\(595\) | 5.55220 | − | 1.89264i | 0.227618 | − | 0.0775905i | ||||
\(596\) | −0.548493 | + | 0.316672i | −0.0224671 | + | 0.0129714i | ||||
\(597\) | −4.84755 | + | 8.39621i | −0.198397 | + | 0.343634i | ||||
\(598\) | −27.6472 | − | 13.3981i | −1.13058 | − | 0.547889i | ||||
\(599\) | 13.7033 | + | 23.7348i | 0.559900 | + | 0.969776i | 0.997504 | + | 0.0706079i | \(0.0224939\pi\) |
−0.437604 | + | 0.899168i | \(0.644173\pi\) | |||||||
\(600\) | − | 1.51979i | − | 0.0620450i | ||||||
\(601\) | −12.7864 | − | 22.1467i | −0.521569 | − | 0.903383i | −0.999685 | − | 0.0250869i | \(-0.992014\pi\) |
0.478117 | − | 0.878296i | \(-0.341320\pi\) | |||||||
\(602\) | −11.2594 | + | 3.83810i | −0.458897 | + | 0.156429i | ||||
\(603\) | − | 11.0230i | − | 0.448891i | ||||||
\(604\) | 3.43434 | − | 1.98282i | 0.139741 | − | 0.0806798i | ||||
\(605\) | 27.3988i | 1.11392i | ||||||||
\(606\) | 7.36178 | − | 4.25033i | 0.299052 | − | 0.172658i | ||||
\(607\) | 18.1780 | + | 31.4852i | 0.737822 | + | 1.27795i | 0.953474 | + | 0.301475i | \(0.0974791\pi\) |
−0.215652 | + | 0.976470i | \(0.569188\pi\) | |||||||
\(608\) | 2.31347 | + | 4.00705i | 0.0938237 | + | 0.162507i | ||||
\(609\) | 6.91111 | − | 7.90097i | 0.280052 | − | 0.320163i | ||||
\(610\) | −15.4178 | −0.624248 | ||||||||
\(611\) | 9.69769 | − | 6.57688i | 0.392327 | − | 0.266072i | ||||
\(612\) | −0.434150 | − | 0.751971i | −0.0175495 | − | 0.0303966i | ||||
\(613\) | 19.4132 | + | 11.2082i | 0.784092 | + | 0.452696i | 0.837878 | − | 0.545857i | \(-0.183796\pi\) |
−0.0537867 | + | 0.998552i | \(0.517129\pi\) | |||||||
\(614\) | 27.0072 | 1.08992 | ||||||||
\(615\) | −8.66236 | + | 15.0037i | −0.349300 | + | 0.605006i | ||||
\(616\) | −0.443252 | − | 1.30032i | −0.0178591 | − | 0.0523912i | ||||
\(617\) | −9.38150 | − | 5.41641i | −0.377685 | − | 0.218056i | 0.299126 | − | 0.954214i | \(-0.403305\pi\) |
−0.676810 | + | 0.736157i | \(0.736638\pi\) | |||||||
\(618\) | −13.4777 | + | 7.78135i | −0.542153 | + | 0.313012i | ||||
\(619\) | −35.7658 | + | 20.6494i | −1.43755 | + | 0.829969i | −0.997679 | − | 0.0680933i | \(-0.978308\pi\) |
−0.439869 | + | 0.898062i | \(0.644975\pi\) | |||||||
\(620\) | −10.3058 | −0.413891 | ||||||||
\(621\) | −8.52091 | −0.341932 | ||||||||
\(622\) | 20.9499 | − | 12.0954i | 0.840015 | − | 0.484983i | ||||
\(623\) | −15.9899 | − | 13.9867i | −0.640623 | − | 0.560364i | ||||
\(624\) | −2.02374 | − | 2.98403i | −0.0810146 | − | 0.119457i | ||||
\(625\) | 15.1446 | − | 26.2312i | 0.605784 | − | 1.04925i | ||||
\(626\) | −20.6011 | − | 11.8941i | −0.823387 | − | 0.475383i | ||||
\(627\) | −1.20125 | + | 2.08063i | −0.0479735 | + | 0.0830925i | ||||
\(628\) | 4.83448 | + | 8.37356i | 0.192917 | + | 0.334142i | ||||
\(629\) | − | 5.14298i | − | 0.205064i | ||||||
\(630\) | 4.44780 | − | 5.08484i | 0.177205 | − | 0.202585i | ||||
\(631\) | 4.11495 | + | 2.37577i | 0.163814 | + | 0.0945779i | 0.579666 | − | 0.814854i | \(-0.303183\pi\) |
−0.415852 | + | 0.909432i | \(0.636517\pi\) | |||||||
\(632\) | 9.48251 | + | 5.47473i | 0.377194 | + | 0.217773i | ||||
\(633\) | −7.09887 | −0.282155 | ||||||||
\(634\) | 4.36064 | − | 7.55286i | 0.173183 | − | 0.299962i | ||||
\(635\) | 28.9717i | 1.14971i | ||||||||
\(636\) | −8.25690 | −0.327407 | ||||||||
\(637\) | 23.9750 | + | 7.88664i | 0.949924 | + | 0.312480i | ||||
\(638\) | 2.06011 | 0.0815605 | ||||||||
\(639\) | − | 5.16584i | − | 0.204358i | ||||||
\(640\) | 1.27669 | − | 2.21130i | 0.0504657 | − | 0.0874092i | ||||
\(641\) | 8.01307 | 0.316497 | 0.158249 | − | 0.987399i | \(-0.449415\pi\) | ||||
0.158249 | + | 0.987399i | \(0.449415\pi\) | |||||||
\(642\) | −2.37339 | − | 1.37028i | −0.0936703 | − | 0.0540806i | ||||
\(643\) | −41.7271 | − | 24.0911i | −1.64556 | − | 0.950062i | −0.978809 | − | 0.204777i | \(-0.934353\pi\) |
−0.666747 | − | 0.745284i | \(-0.732314\pi\) | |||||||
\(644\) | 14.8428 | − | 16.9686i | 0.584886 | − | 0.668658i | ||||
\(645\) | − | 11.4803i | − | 0.452035i | ||||||
\(646\) | −2.00879 | − | 3.47933i | −0.0790348 | − | 0.136892i | ||||
\(647\) | −13.1082 | + | 22.7041i | −0.515337 | + | 0.892590i | 0.484504 | + | 0.874789i | \(0.339000\pi\) |
−0.999842 | + | 0.0178012i | \(0.994333\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | −0.363676 | + | 0.629906i | −0.0142755 | + | 0.0247260i | ||||
\(650\) | 0.396051 | + | 5.46534i | 0.0155344 | + | 0.214368i | ||||
\(651\) | −8.03759 | − | 7.03062i | −0.315018 | − | 0.275552i | ||||
\(652\) | −20.5444 | + | 11.8613i | −0.804583 | + | 0.464526i | ||||
\(653\) | 27.1318 | 1.06175 | 0.530874 | − | 0.847451i | \(-0.321864\pi\) | ||||
0.530874 | + | 0.847451i | \(0.321864\pi\) | |||||||
\(654\) | −14.2032 | −0.555391 | ||||||||
\(655\) | 6.33399 | − | 3.65693i | 0.247490 | − | 0.142888i | ||||
\(656\) | −5.87598 | + | 3.39250i | −0.229419 | + | 0.132455i | ||||
\(657\) | −10.3558 | − | 5.97895i | −0.404020 | − | 0.233261i | ||||
\(658\) | 2.77425 | + | 8.13847i | 0.108151 | + | 0.317271i | ||||
\(659\) | −18.6795 | + | 32.3538i | −0.727649 | + | 1.26033i | 0.230225 | + | 0.973137i | \(0.426054\pi\) |
−0.957874 | + | 0.287188i | \(0.907279\pi\) | |||||||
\(660\) | 1.32583 | 0.0516078 | ||||||||
\(661\) | −10.8466 | − | 6.26227i | −0.421882 | − | 0.243574i | 0.274000 | − | 0.961730i | \(-0.411653\pi\) |
−0.695882 | + | 0.718156i | \(0.744987\pi\) | |||||||
\(662\) | −6.00281 | − | 10.3972i | −0.233306 | − | 0.404097i | ||||
\(663\) | 1.75722 | + | 2.59104i | 0.0682447 | + | 0.100628i | ||||
\(664\) | −12.9984 | −0.504435 | ||||||||
\(665\) | 20.5797 | − | 23.5273i | 0.798047 | − | 0.912349i | ||||
\(666\) | −2.96152 | − | 5.12950i | −0.114756 | − | 0.198764i | ||||
\(667\) | 16.9035 | + | 29.2777i | 0.654505 | + | 1.13364i | ||||
\(668\) | −3.53346 | + | 2.04005i | −0.136714 | + | 0.0789318i | ||||
\(669\) | − | 6.01269i | − | 0.232464i | ||||||
\(670\) | −24.3751 | + | 14.0730i | −0.941693 | + | 0.543687i | ||||
\(671\) | − | 3.13528i | − | 0.121036i | ||||||
\(672\) | 2.50425 | − | 0.853651i | 0.0966036 | − | 0.0329303i | ||||
\(673\) | −0.488082 | − | 0.845383i | −0.0188142 | − | 0.0325871i | 0.856465 | − | 0.516205i | \(-0.172656\pi\) |
−0.875279 | + | 0.483618i | \(0.839322\pi\) | |||||||
\(674\) | − | 22.4347i | − | 0.864154i | ||||||
\(675\) | 0.759893 | + | 1.31617i | 0.0292483 | + | 0.0506595i | ||||
\(676\) | 8.05526 | + | 10.2036i | 0.309818 | + | 0.392445i | ||||
\(677\) | 11.9057 | − | 20.6213i | 0.457574 | − | 0.792541i | −0.541258 | − | 0.840856i | \(-0.682052\pi\) |
0.998832 | + | 0.0483154i | \(0.0153853\pi\) | |||||||
\(678\) | 16.1066 | − | 9.29913i | 0.618569 | − | 0.357131i | ||||
\(679\) | −37.6192 | + | 12.8236i | −1.44369 | + | 0.492126i | ||||
\(680\) | −1.10855 | + | 1.92007i | −0.0425111 | + | 0.0736314i | ||||
\(681\) | −3.12015 | − | 1.80142i | −0.119564 | − | 0.0690306i | ||||
\(682\) | − | 2.09573i | − | 0.0802497i | ||||||
\(683\) | 42.6064i | 1.63029i | 0.579258 | + | 0.815144i | \(0.303342\pi\) | ||||
−0.579258 | + | 0.815144i | \(0.696658\pi\) | |||||||
\(684\) | −4.00705 | − | 2.31347i | −0.153213 | − | 0.0884578i | ||||
\(685\) | −12.5199 | + | 21.6851i | −0.478361 | + | 0.828546i | ||||
\(686\) | −10.2302 | + | 15.4384i | −0.390590 | + | 0.589440i | ||||
\(687\) | 23.8424 | − | 13.7654i | 0.909644 | − | 0.525183i | ||||
\(688\) | 2.24805 | − | 3.89373i | 0.0857061 | − | 0.148447i | ||||
\(689\) | 29.6928 | − | 2.15172i | 1.13121 | − | 0.0819740i | ||||
\(690\) | 10.8786 | + | 18.8423i | 0.414141 | + | 0.717313i | ||||
\(691\) | 38.6569i | 1.47058i | 0.677753 | + | 0.735289i | \(0.262954\pi\) | ||||
−0.677753 | + | 0.735289i | \(0.737046\pi\) | |||||||
\(692\) | 6.89043 | + | 11.9346i | 0.261935 | + | 0.453684i | ||||
\(693\) | 1.03403 | + | 0.904480i | 0.0392794 | + | 0.0343584i | ||||
\(694\) | − | 29.2720i | − | 1.11115i | ||||||
\(695\) | 15.4489 | − | 8.91942i | 0.586010 | − | 0.338333i | ||||
\(696\) | 3.96752i | 0.150389i | ||||||||
\(697\) | 5.10212 | − | 2.94571i | 0.193257 | − | 0.111577i | ||||
\(698\) | 12.7610 | + | 22.1028i | 0.483013 | + | 0.836603i | ||||
\(699\) | −5.84917 | − | 10.1311i | −0.221236 | − | 0.383192i | ||||
\(700\) | −3.94471 | − | 0.779411i | −0.149096 | − | 0.0294590i | ||||
\(701\) | −12.0226 | −0.454087 | −0.227044 | − | 0.973885i | \(-0.572906\pi\) | ||||
−0.227044 | + | 0.973885i | \(0.572906\pi\) | |||||||
\(702\) | 3.24463 | + | 1.57238i | 0.122461 | + | 0.0593456i | ||||
\(703\) | −13.7028 | − | 23.7339i | −0.516810 | − | 0.895142i | ||||
\(704\) | 0.449678 | + | 0.259622i | 0.0169479 | + | 0.00978485i | ||||
\(705\) | −8.29815 | −0.312526 | ||||||||
\(706\) | 1.82840 | − | 3.16688i | 0.0688127 | − | 0.119187i | ||||
\(707\) | −7.25659 | − | 21.2878i | −0.272912 | − | 0.800610i | ||||
\(708\) | −1.21312 | − | 0.700397i | −0.0455920 | − | 0.0263225i | ||||
\(709\) | −27.2218 | + | 15.7165i | −1.02233 | + | 0.590245i | −0.914779 | − | 0.403954i | \(-0.867636\pi\) |
−0.107555 | + | 0.994199i | \(0.534302\pi\) | |||||||
\(710\) | −11.4232 | + | 6.59520i | −0.428706 | + | 0.247513i | ||||
\(711\) | −10.9495 | −0.410637 | ||||||||
\(712\) | 8.02946 | 0.300917 | ||||||||
\(713\) | 29.7839 | − | 17.1958i | 1.11542 | − | 0.643986i | ||||
\(714\) | −2.17444 | + | 0.741226i | −0.0813765 | + | 0.0277397i | ||||
\(715\) | −4.76784 | + | 0.345507i | −0.178307 | + | 0.0129212i | ||||
\(716\) | 1.92793 | − | 3.33928i | 0.0720502 | − | 0.124795i | ||||
\(717\) | −14.2281 | − | 8.21461i | −0.531359 | − | 0.306780i | ||||
\(718\) | −17.1999 | + | 29.7911i | −0.641894 | + | 1.11179i | ||||
\(719\) | −25.6676 | − | 44.4577i | −0.957241 | − | 1.65799i | −0.729154 | − | 0.684350i | \(-0.760086\pi\) |
−0.228088 | − | 0.973641i | \(-0.573247\pi\) | |||||||
\(720\) | 2.55339i | 0.0951591i | ||||||||
\(721\) | 13.2851 | + | 38.9729i | 0.494764 | + | 1.45143i | ||||
\(722\) | −2.08593 | − | 1.20431i | −0.0776303 | − | 0.0448199i | ||||
\(723\) | 12.4413 | + | 7.18297i | 0.462696 | + | 0.267138i | ||||
\(724\) | 3.18446 | 0.118349 | ||||||||
\(725\) | 3.01490 | − | 5.22195i | 0.111970 | − | 0.193938i | ||||
\(726\) | − | 10.7304i | − | 0.398242i | ||||||
\(727\) | −10.6652 | −0.395549 | −0.197774 | − | 0.980248i | \(-0.563371\pi\) | ||||
−0.197774 | + | 0.980248i | \(0.563371\pi\) | |||||||
\(728\) | −8.78314 | + | 3.72243i | −0.325525 | + | 0.137963i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.5331i | 1.13008i | ||||||||
\(731\) | −1.95198 | + | 3.38093i | −0.0721967 | + | 0.125048i | ||||
\(732\) | 6.03817 | 0.223177 | ||||||||
\(733\) | −1.58513 | − | 0.915174i | −0.0585481 | − | 0.0338027i | 0.470440 | − | 0.882432i | \(-0.344095\pi\) |
−0.528988 | + | 0.848629i | \(0.677428\pi\) | |||||||
\(734\) | 5.53566 | + | 3.19602i | 0.204325 | + | 0.117967i | ||||
\(735\) | −10.9170 | − | 14.1523i | −0.402681 | − | 0.522016i | ||||
\(736\) | 8.52091i | 0.314085i | ||||||||
\(737\) | −2.86181 | − | 4.95679i | −0.105416 | − | 0.182586i | ||||
\(738\) | 3.39250 | − | 5.87598i | 0.124880 | − | 0.216298i | ||||
\(739\) | −38.8381 | − | 22.4232i | −1.42868 | − | 0.824849i | −0.431664 | − | 0.902034i | \(-0.642073\pi\) |
−0.997017 | + | 0.0771851i | \(0.975407\pi\) | |||||||
\(740\) | −7.56190 | + | 13.0976i | −0.277981 | + | 0.481477i | ||||
\(741\) | 15.0127 | + | 7.27530i | 0.551506 | + | 0.267265i | ||||
\(742\) | −4.23449 | + | 21.4314i | −0.155453 | + | 0.786770i | ||||
\(743\) | 31.7298 | − | 18.3192i | 1.16405 | − | 0.672066i | 0.211781 | − | 0.977317i | \(-0.432074\pi\) |
0.952272 | + | 0.305251i | \(0.0987405\pi\) | |||||||
\(744\) | 4.03613 | 0.147972 | ||||||||
\(745\) | −1.61717 | −0.0592487 | ||||||||
\(746\) | −15.7822 | + | 9.11185i | −0.577827 | + | 0.333609i | ||||
\(747\) | 11.2569 | − | 6.49919i | 0.411870 | − | 0.237793i | ||||
\(748\) | −0.390455 | − | 0.225430i | −0.0142765 | − | 0.00824252i | ||||
\(749\) | −4.77383 | + | 5.45757i | −0.174432 | + | 0.199415i | ||||
\(750\) | −4.44317 | + | 7.69579i | −0.162242 | + | 0.281011i | ||||
\(751\) | 37.6469 | 1.37375 | 0.686877 | − | 0.726774i | \(-0.258981\pi\) | ||||
0.686877 | + | 0.726774i | \(0.258981\pi\) | |||||||
\(752\) | −2.81446 | − | 1.62493i | −0.102633 | − | 0.0592551i | ||||
\(753\) | −9.52013 | − | 16.4893i | −0.346933 | − | 0.600905i | ||||
\(754\) | −1.03392 | − | 14.2677i | −0.0376533 | − | 0.519599i | ||||
\(755\) | 10.1258 | 0.368516 | ||||||||
\(756\) | −1.74192 | + | 1.99141i | −0.0633530 | + | 0.0724269i | ||||
\(757\) | −0.733508 | − | 1.27047i | −0.0266598 | − | 0.0461761i | 0.852388 | − | 0.522910i | \(-0.175154\pi\) |
−0.879047 | + | 0.476734i | \(0.841820\pi\) | |||||||
\(758\) | 3.86440 | + | 6.69334i | 0.140361 | + | 0.243113i | ||||
\(759\) | −3.83166 | + | 2.21221i | −0.139081 | + | 0.0802982i | ||||
\(760\) | 11.8144i | 0.428553i | ||||||||
\(761\) | −12.5091 | + | 7.22215i | −0.453455 | + | 0.261803i | −0.709288 | − | 0.704918i | \(-0.750984\pi\) |
0.255833 | + | 0.966721i | \(0.417650\pi\) | |||||||
\(762\) | − | 11.3464i | − | 0.411035i | ||||||
\(763\) | −7.28403 | + | 36.8655i | −0.263699 | + | 1.33462i | ||||
\(764\) | 6.70696 | + | 11.6168i | 0.242649 | + | 0.420281i | ||||
\(765\) | − | 2.21711i | − | 0.0801597i | ||||||
\(766\) | −4.90993 | − | 8.50425i | −0.177403 | − | 0.307271i | ||||
\(767\) | 4.54506 | + | 2.20258i | 0.164113 | + | 0.0795304i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −36.5814 | + | 21.1203i | −1.31916 | + | 0.761617i | −0.983593 | − | 0.180400i | \(-0.942261\pi\) |
−0.335566 | + | 0.942017i | \(0.608928\pi\) | |||||||
\(770\) | 0.679942 | − | 3.44128i | 0.0245034 | − | 0.124015i | ||||
\(771\) | −11.6666 | + | 20.2071i | −0.420162 | + | 0.727742i | ||||
\(772\) | −5.18745 | − | 2.99498i | −0.186700 | − | 0.107792i | ||||
\(773\) | − | 6.87947i | − | 0.247437i | −0.992317 | − | 0.123719i | \(-0.960518\pi\) | ||
0.992317 | − | 0.123719i | \(-0.0394821\pi\) | |||||||
\(774\) | 4.49610i | 0.161609i | ||||||||
\(775\) | −5.31225 | − | 3.06703i | −0.190822 | − | 0.110171i | ||||
\(776\) | 7.51106 | − | 13.0095i | 0.269631 | − | 0.467015i | ||||
\(777\) | −14.8328 | + | 5.05621i | −0.532123 | + | 0.181390i | ||||
\(778\) | 8.14562 | − | 4.70287i | 0.292035 | − | 0.168606i | ||||
\(779\) | 15.6969 | − | 27.1878i | 0.562400 | − | 0.974106i | ||||
\(780\) | −0.665404 | − | 9.18229i | −0.0238253 | − | 0.328779i | ||||
\(781\) | −1.34116 | − | 2.32296i | −0.0479906 | − | 0.0831222i | ||||
\(782\) | − | 7.39871i | − | 0.264577i | ||||||
\(783\) | −1.98376 | − | 3.43598i | −0.0708939 | − | 0.122792i | ||||
\(784\) | −0.931425 | − | 6.93776i | −0.0332652 | − | 0.247777i | ||||
\(785\) | 24.6886i | 0.881174i | ||||||||
\(786\) | −2.48062 | + | 1.43219i | −0.0884809 | + | 0.0510845i | ||||
\(787\) | − | 30.4132i | − | 1.08411i | −0.840342 | − | 0.542057i | \(-0.817646\pi\) | ||
0.840342 | − | 0.542057i | \(-0.182354\pi\) | |||||||
\(788\) | 3.78655 | − | 2.18617i | 0.134890 | − | 0.0778790i | ||||
\(789\) | −10.3167 | − | 17.8690i | −0.367283 | − | 0.636152i | ||||
\(790\) | 13.9791 | + | 24.2125i | 0.497354 | + | 0.861442i | ||||
\(791\) | −15.8764 | − | 46.5747i | −0.564501 | − | 1.65601i | ||||
\(792\) | −0.519243 | −0.0184505 | ||||||||
\(793\) | −21.7140 | + | 1.57353i | −0.771087 | + | 0.0558776i | ||||
\(794\) | −5.77112 | − | 9.99586i | −0.204809 | − | 0.354740i | ||||
\(795\) | −18.2585 | − | 10.5415i | −0.647561 | − | 0.373870i | ||||
\(796\) | −9.69511 | −0.343634 | ||||||||
\(797\) | 8.31093 | − | 14.3949i | 0.294388 | − | 0.509895i | −0.680454 | − | 0.732791i | \(-0.738218\pi\) |
0.974842 | + | 0.222895i | \(0.0715508\pi\) | |||||||
\(798\) | −8.05977 | + | 9.21414i | −0.285313 | + | 0.326177i | ||||
\(799\) | 2.44380 | + | 1.41093i | 0.0864554 | + | 0.0499150i | ||||
\(800\) | 1.31617 | − | 0.759893i | 0.0465338 | − | 0.0268663i | ||||
\(801\) | −6.95371 | + | 4.01473i | −0.245697 | + | 0.141853i | ||||
\(802\) | 33.5631 | 1.18515 | ||||||||
\(803\) | −6.20905 | −0.219113 | ||||||||
\(804\) | 9.54619 | − | 5.51150i | 0.336668 | − | 0.194376i | ||||
\(805\) | 54.4855 | − | 18.5730i | 1.92036 | − | 0.654614i | ||||
\(806\) | −14.5144 | + | 1.05180i | −0.511248 | + | 0.0370481i | ||||
\(807\) | 4.37116 | − | 7.57108i | 0.153872 | − | 0.266515i | ||||
\(808\) | 7.36178 | + | 4.25033i | 0.258987 | + | 0.149526i | ||||
\(809\) | −16.9058 | + | 29.2817i | −0.594376 | + | 1.02949i | 0.399258 | + | 0.916839i | \(0.369268\pi\) |
−0.993635 | + | 0.112652i | \(0.964066\pi\) | |||||||
\(810\) | −1.27669 | − | 2.21130i | −0.0448584 | − | 0.0776971i | ||||
\(811\) | − | 34.4041i | − | 1.20809i | −0.796950 | − | 0.604045i | \(-0.793555\pi\) | ||
0.796950 | − | 0.604045i | \(-0.206445\pi\) | |||||||
\(812\) | 10.2980 | + | 2.03472i | 0.361389 | + | 0.0714045i | ||||
\(813\) | 8.76510 | + | 5.06054i | 0.307406 | + | 0.177481i | ||||
\(814\) | −2.66346 | − | 1.53775i | −0.0933541 | − | 0.0538980i | ||||
\(815\) | −60.5732 | −2.12179 | ||||||||
\(816\) | 0.434150 | − | 0.751971i | 0.0151983 | − | 0.0263242i | ||||
\(817\) | 20.8032i | 0.727812i | ||||||||
\(818\) | −18.3070 | −0.640088 | ||||||||
\(819\) | 5.74520 | − | 7.61529i | 0.200754 | − | 0.266100i | ||||
\(820\) | −17.3247 | −0.605006 | ||||||||
\(821\) | − | 15.2913i | − | 0.533671i | −0.963742 | − | 0.266836i | \(-0.914022\pi\) | ||
0.963742 | − | 0.266836i | \(-0.0859781\pi\) | |||||||
\(822\) | 4.90326 | − | 8.49269i | 0.171021 | − | 0.296216i | ||||
\(823\) | −14.2969 | −0.498360 | −0.249180 | − | 0.968457i | \(-0.580161\pi\) | ||||
−0.249180 | + | 0.968457i | \(0.580161\pi\) | |||||||
\(824\) | −13.4777 | − | 7.78135i | −0.469518 | − | 0.271076i | ||||
\(825\) | 0.683414 | + | 0.394569i | 0.0237934 | + | 0.0137371i | ||||
\(826\) | −2.44007 | + | 2.78955i | −0.0849010 | + | 0.0970610i | ||||
\(827\) | 40.6945i | 1.41509i | 0.706670 | + | 0.707543i | \(0.250196\pi\) | ||||
−0.706670 | + | 0.707543i | \(0.749804\pi\) | |||||||
\(828\) | −4.26046 | − | 7.37933i | −0.148061 | − | 0.256449i | ||||
\(829\) | −15.9598 | + | 27.6432i | −0.554306 | + | 0.960087i | 0.443651 | + | 0.896200i | \(0.353683\pi\) |
−0.997957 | + | 0.0638871i | \(0.979650\pi\) | |||||||
\(830\) | −28.7433 | − | 16.5950i | −0.997695 | − | 0.576019i | ||||
\(831\) | 2.48866 | − | 4.31049i | 0.0863308 | − | 0.149529i | ||||
\(832\) | 1.57238 | − | 3.24463i | 0.0545124 | − | 0.112487i | ||||
\(833\) | 0.808757 | + | 6.02406i | 0.0280218 | + | 0.208721i | ||||
\(834\) | −6.05035 | + | 3.49317i | −0.209507 | + | 0.120959i | ||||
\(835\) | −10.4181 | −0.360532 | ||||||||
\(836\) | −2.40251 | −0.0830925 | ||||||||
\(837\) | −3.49539 | + | 2.01806i | −0.120818 | + | 0.0697545i | ||||
\(838\) | −14.0824 | + | 8.13046i | −0.486468 | + | 0.280862i | ||||
\(839\) | 13.8203 | + | 7.97917i | 0.477131 | + | 0.275471i | 0.719220 | − | 0.694782i | \(-0.244499\pi\) |
−0.242089 | + | 0.970254i | \(0.577833\pi\) | |||||||
\(840\) | 6.62750 | + | 1.30949i | 0.228670 | + | 0.0451816i | ||||
\(841\) | 6.62937 | − | 11.4824i | 0.228599 | − | 0.395945i | ||||
\(842\) | −20.7347 | −0.714565 | ||||||||
\(843\) | −23.6190 | − | 13.6364i | −0.813481 | − | 0.469664i | ||||
\(844\) | −3.54943 | − | 6.14780i | −0.122177 | − | 0.211616i | ||||
\(845\) | 4.78575 | + | 32.8472i | 0.164635 | + | 1.12998i | ||||
\(846\) | 3.24986 | 0.111732 | ||||||||
\(847\) | −27.8515 | − | 5.50300i | −0.956988 | − | 0.189085i | ||||
\(848\) | −4.12845 | − | 7.15068i | −0.141772 | − | 0.245555i | ||||
\(849\) | 4.90256 | + | 8.49149i | 0.168256 | + | 0.291427i | ||||
\(850\) | −1.14283 | + | 0.659816i | −0.0391989 | + | 0.0226315i | ||||
\(851\) | − | 50.4697i | − | 1.73008i | ||||||
\(852\) | 4.47375 | − | 2.58292i | 0.153268 | − | 0.0884894i | ||||
\(853\) | − | 21.8333i | − | 0.747559i | −0.927518 | − | 0.373779i | \(-0.878062\pi\) | ||
0.927518 | − | 0.373779i | \(-0.121938\pi\) | |||||||
\(854\) | 3.09663 | − | 15.6725i | 0.105965 | − | 0.536302i | ||||
\(855\) | −5.90719 | − | 10.2316i | −0.202022 | − | 0.349912i | ||||
\(856\) | − | 2.74056i | − | 0.0936703i | ||||||
\(857\) | −27.3267 | − | 47.3312i | −0.933461 | − | 1.61680i | −0.777355 | − | 0.629062i | \(-0.783439\pi\) |
−0.156106 | − | 0.987740i | \(-0.549894\pi\) | |||||||
\(858\) | 1.86726 | − | 0.135313i | 0.0637472 | − | 0.00461951i | ||||
\(859\) | −19.0946 | + | 33.0728i | −0.651500 | + | 1.12843i | 0.331259 | + | 0.943540i | \(0.392527\pi\) |
−0.982759 | + | 0.184891i | \(0.940807\pi\) | |||||||
\(860\) | 9.94221 | − | 5.74014i | 0.339027 | − | 0.195737i | ||||
\(861\) | −13.5117 | − | 11.8189i | −0.460478 | − | 0.402788i | ||||
\(862\) | −13.5573 | + | 23.4819i | −0.461762 | + | 0.799796i | ||||
\(863\) | −5.85315 | − | 3.37932i | −0.199244 | − | 0.115033i | 0.397059 | − | 0.917793i | \(-0.370031\pi\) |
−0.596303 | + | 0.802760i | \(0.703364\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 35.1878i | 1.19642i | ||||||||
\(866\) | −17.0242 | − | 9.82893i | −0.578506 | − | 0.334001i | ||||
\(867\) | 8.12303 | − | 14.0695i | 0.275872 | − | 0.477825i | ||||
\(868\) | 2.06990 | − | 10.4761i | 0.0702570 | − | 0.355581i | ||||
\(869\) | −4.92372 | + | 2.84271i | −0.167026 | + | 0.0964325i | ||||
\(870\) | −5.06531 | + | 8.77338i | −0.171730 | + | 0.297445i | ||||
\(871\) | −32.8930 | + | 22.3077i | −1.11454 | + | 0.755868i | ||||
\(872\) | −7.10162 | − | 12.3004i | −0.240491 | − | 0.416543i | ||||
\(873\) | 15.0221i | 0.508421i | ||||||||
\(874\) | −19.7129 | − | 34.1437i | −0.666799 | − | 1.15493i | ||||
\(875\) | 17.6963 | + | 15.4793i | 0.598245 | + | 0.523295i | ||||
\(876\) | − | 11.9579i | − | 0.404020i | ||||||
\(877\) | 16.7929 | − | 9.69540i | 0.567057 | − | 0.327390i | −0.188916 | − | 0.981993i | \(-0.560497\pi\) |
0.755973 | + | 0.654603i | \(0.227164\pi\) | |||||||
\(878\) | 17.5185i | 0.591220i | ||||||||
\(879\) | −24.3101 | + | 14.0354i | −0.819959 | + | 0.473404i | ||||
\(880\) | 0.662914 | + | 1.14820i | 0.0223468 | + | 0.0387059i | ||||
\(881\) | 28.6313 | + | 49.5909i | 0.964615 | + | 1.67076i | 0.710647 | + | 0.703549i | \(0.248402\pi\) |
0.253968 | + | 0.967213i | \(0.418264\pi\) | |||||||
\(882\) | 4.27552 | + | 5.54256i | 0.143964 | + | 0.186628i | ||||
\(883\) | 27.5353 | 0.926637 | 0.463318 | − | 0.886192i | \(-0.346659\pi\) | ||||
0.463318 | + | 0.886192i | \(0.346659\pi\) | |||||||
\(884\) | −1.36530 | + | 2.81732i | −0.0459199 | + | 0.0947566i | ||||
\(885\) | −1.78838 | − | 3.09757i | −0.0601159 | − | 0.104124i | ||||
\(886\) | 29.5250 | + | 17.0463i | 0.991913 | + | 0.572681i | ||||
\(887\) | 6.32268 | 0.212295 | 0.106147 | − | 0.994350i | \(-0.466148\pi\) | ||||
0.106147 | + | 0.994350i | \(0.466148\pi\) | |||||||
\(888\) | 2.96152 | − | 5.12950i | 0.0993820 | − | 0.172135i | ||||
\(889\) | −29.4503 | − | 5.81890i | −0.987731 | − | 0.195160i | ||||
\(890\) | 17.7555 | + | 10.2512i | 0.595166 | + | 0.343620i | ||||
\(891\) | 0.449678 | − | 0.259622i | 0.0150648 | − | 0.00869765i | ||||
\(892\) | 5.20714 | − | 3.00634i | 0.174348 | − | 0.100660i | ||||
\(893\) | 15.0369 | 0.503192 | ||||||||
\(894\) | 0.633345 | 0.0211822 | ||||||||
\(895\) | 8.52647 | − | 4.92276i | 0.285008 | − | 0.164550i | ||||
\(896\) | 1.99141 | + | 1.74192i | 0.0665283 | + | 0.0581935i | ||||
\(897\) | 17.2441 | + | 25.4267i | 0.575765 | + | 0.848973i | ||||
\(898\) | 14.1006 | − | 24.4229i | 0.470542 | − | 0.815003i | ||||
\(899\) | 13.8680 | + | 8.00672i | 0.462525 | + | 0.267039i | ||||
\(900\) | −0.759893 | + | 1.31617i | −0.0253298 | + | 0.0438725i | ||||
\(901\) | 3.58474 | + | 6.20894i | 0.119425 | + | 0.206850i | ||||
\(902\) | − | 3.52306i | − | 0.117305i | ||||||
\(903\) | 11.6699 | + | 2.30579i | 0.388351 | + | 0.0767319i | ||||
\(904\) | 16.1066 | + | 9.29913i | 0.535696 | + | 0.309284i | ||||
\(905\) | 7.04179 | + | 4.06558i | 0.234077 | + | 0.135144i | ||||
\(906\) | −3.96564 | −0.131750 | ||||||||
\(907\) | 21.5270 | − | 37.2859i | 0.714793 | − | 1.23806i | −0.248247 | − | 0.968697i | \(-0.579854\pi\) |
0.963039 | − | 0.269360i | \(-0.0868122\pi\) | |||||||
\(908\) | − | 3.60284i | − | 0.119564i | ||||||
\(909\) | −8.50066 | −0.281949 | ||||||||
\(910\) | −24.1745 | − | 2.98197i | −0.801378 | − | 0.0988512i | ||||
\(911\) | 21.4332 | 0.710114 | 0.355057 | − | 0.934845i | \(-0.384461\pi\) | ||||
0.355057 | + | 0.934845i | \(0.384461\pi\) | |||||||
\(912\) | − | 4.62695i | − | 0.153213i | ||||||
\(913\) | 3.37466 | − | 5.84508i | 0.111685 | − | 0.193444i | ||||
\(914\) | 22.8685 | 0.756422 | ||||||||
\(915\) | 13.3522 | + | 7.70889i | 0.441410 | + | 0.254848i | ||||
\(916\) | 23.8424 | + | 13.7654i | 0.787775 | + | 0.454822i | ||||
\(917\) | 2.44518 | + | 7.17313i | 0.0807469 | + | 0.236877i | ||||
\(918\) | 0.868301i | 0.0286582i | ||||||||
\(919\) | 22.9191 | + | 39.6970i | 0.756030 | + | 1.30948i | 0.944861 | + | 0.327473i | \(0.106197\pi\) |
−0.188831 | + | 0.982010i | \(0.560470\pi\) | |||||||
\(920\) | −10.8786 | + | 18.8423i | −0.358657 | + | 0.621212i | ||||
\(921\) | −23.3890 | − | 13.5036i | −0.770693 | − | 0.444960i | ||||
\(922\) | −12.0448 | + | 20.8622i | −0.396674 | + | 0.687059i | ||||
\(923\) | −15.4151 | + | 10.4543i | −0.507393 | + | 0.344109i | ||||
\(924\) | −0.266290 | + | 1.34773i | −0.00876030 | + | 0.0443371i | ||||
\(925\) | −7.79574 | + | 4.50088i | −0.256322 | + | 0.147988i | ||||
\(926\) | 12.2189 | 0.401538 | ||||||||
\(927\) | 15.5627 | 0.511146 | ||||||||
\(928\) | −3.43598 | + | 1.98376i | −0.112791 | + | 0.0651202i | ||||
\(929\) | −16.4490 | + | 9.49685i | −0.539675 | + | 0.311581i | −0.744947 | − | 0.667123i | \(-0.767525\pi\) |
0.205272 | + | 0.978705i | \(0.434192\pi\) | |||||||
\(930\) | 8.92509 | + | 5.15290i | 0.292665 | + | 0.168970i | ||||
\(931\) | 19.7826 | + | 25.6451i | 0.648348 | + | 0.840485i | ||||
\(932\) | 5.84917 | − | 10.1311i | 0.191596 | − | 0.331854i | ||||
\(933\) | −24.1909 | −0.791973 | ||||||||
\(934\) | 13.0167 | + | 7.51520i | 0.425920 | + | 0.245905i | ||||
\(935\) | −0.575609 | − | 0.996984i | −0.0188244 | − | 0.0326049i | ||||
\(936\) | 0.260597 | + | 3.59612i | 0.00851787 | + | 0.117543i | ||||
\(937\) | 30.7500 | 1.00456 | 0.502280 | − | 0.864705i | \(-0.332495\pi\) | ||||
0.502280 | + | 0.864705i | \(0.332495\pi\) | |||||||
\(938\) | −9.40979 | − | 27.6044i | −0.307241 | − | 0.901314i | ||||
\(939\) | 11.8941 | + | 20.6011i | 0.388148 | + | 0.672293i | ||||
\(940\) | −4.14908 | − | 7.18641i | −0.135328 | − | 0.234395i | ||||
\(941\) | −19.1978 | + | 11.0838i | −0.625830 | + | 0.361323i | −0.779135 | − | 0.626856i | \(-0.784341\pi\) |
0.153305 | + | 0.988179i | \(0.451008\pi\) | |||||||
\(942\) | − | 9.66896i | − | 0.315032i | ||||||
\(943\) | 50.0687 | − | 28.9072i | 1.63046 | − | 0.941348i | ||||
\(944\) | − | 1.40079i | − | 0.0455920i | ||||||
\(945\) | −6.39433 | + | 2.17970i | −0.208007 | + | 0.0709057i | ||||
\(946\) | 1.16728 | + | 2.02179i | 0.0379517 | + | 0.0657342i | ||||
\(947\) | 42.2814i | 1.37396i | 0.726676 | + | 0.686981i | \(0.241064\pi\) | ||||
−0.726676 | + | 0.686981i | \(0.758936\pi\) | |||||||
\(948\) | −5.47473 | − | 9.48251i | −0.177811 | − | 0.307977i | ||||
\(949\) | 3.11619 | + | 43.0020i | 0.101156 | + | 1.39591i | ||||
\(950\) | −3.51598 | + | 6.08986i | −0.114074 | + | 0.197581i | ||||
\(951\) | −7.55286 | + | 4.36064i | −0.244918 | + | 0.141404i | ||||
\(952\) | −1.72914 | − | 1.51251i | −0.0560418 | − | 0.0490208i | ||||
\(953\) | 11.3076 | − | 19.5853i | 0.366289 | − | 0.634431i | −0.622693 | − | 0.782466i | \(-0.713961\pi\) |
0.988982 | + | 0.148035i | \(0.0472948\pi\) | |||||||
\(954\) | 7.15068 | + | 4.12845i | 0.231512 | + | 0.133663i | ||||
\(955\) | 34.2509i | 1.10833i | ||||||||
\(956\) | − | 16.4292i | − | 0.531359i | ||||||
\(957\) | −1.78411 | − | 1.03005i | −0.0576720 | − | 0.0332969i | ||||
\(958\) | −0.453153 | + | 0.784884i | −0.0146407 | + | 0.0253585i | ||||
\(959\) | −19.5288 | − | 17.0822i | −0.630617 | − | 0.551612i | ||||
\(960\) | −2.21130 | + | 1.27669i | −0.0713693 | + | 0.0412051i | ||||
\(961\) | −7.35483 | + | 12.7389i | −0.237253 | + | 0.410934i | ||||
\(962\) | −9.31325 | + | 19.2181i | −0.300271 | + | 0.619615i | ||||
\(963\) | 1.37028 | + | 2.37339i | 0.0441566 | + | 0.0764814i | ||||
\(964\) | 14.3659i | 0.462696i | ||||||||
\(965\) | −7.64733 | − | 13.2456i | −0.246176 | − | 0.426390i | ||||
\(966\) | −21.3385 | + | 7.27389i | −0.686555 | + | 0.234033i | ||||
\(967\) | 24.8036i | 0.797629i | 0.917032 | + | 0.398815i | \(0.130578\pi\) | ||||
−0.917032 | + | 0.398815i | \(0.869422\pi\) | |||||||
\(968\) | 9.29279 | − | 5.36519i | 0.298682 | − | 0.172444i | ||||
\(969\) | 4.01758i | 0.129063i | ||||||||
\(970\) | 33.2184 | − | 19.1786i | 1.06658 | − | 0.615789i | ||||
\(971\) | −20.7015 | − | 35.8560i | −0.664342 | − | 1.15067i | −0.979463 | − | 0.201623i | \(-0.935379\pi\) |
0.315121 | − | 0.949051i | \(-0.397955\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 5.96390 | + | 17.4956i | 0.191194 | + | 0.560882i | ||||
\(974\) | −28.7559 | −0.921398 | ||||||||
\(975\) | 2.38968 | − | 4.93115i | 0.0765309 | − | 0.157923i | ||||
\(976\) | 3.01909 | + | 5.22921i | 0.0966386 | + | 0.167383i | ||||
\(977\) | 16.7244 | + | 9.65585i | 0.535062 | + | 0.308918i | 0.743075 | − | 0.669208i | \(-0.233366\pi\) |
−0.208013 | + | 0.978126i | \(0.566700\pi\) | |||||||
\(978\) | 23.7227 | 0.758568 | ||||||||
\(979\) | −2.08462 | + | 3.61067i | −0.0666247 | + | 0.115397i | ||||
\(980\) | 6.79773 | − | 16.5306i | 0.217146 | − | 0.528050i | ||||
\(981\) | 12.3004 | + | 7.10162i | 0.392720 | + | 0.226737i | ||||
\(982\) | −24.0099 | + | 13.8621i | −0.766187 | + | 0.442358i | ||||
\(983\) | 9.97803 | − | 5.76082i | 0.318250 | − | 0.183742i | −0.332362 | − | 0.943152i | \(-0.607846\pi\) |
0.650612 | + | 0.759410i | \(0.274512\pi\) | |||||||
\(984\) | 6.78500 | 0.216298 | ||||||||
\(985\) | 11.1643 | 0.355723 | ||||||||
\(986\) | 2.98346 | − | 1.72250i | 0.0950128 | − | 0.0548557i | ||||
\(987\) | 1.66667 | − | 8.43524i | 0.0530506 | − | 0.268497i | ||||
\(988\) | 1.20577 | + | 16.6391i | 0.0383605 | + | 0.529359i | ||||
\(989\) | −19.1554 | + | 33.1782i | −0.609107 | + | 1.05500i | ||||
\(990\) | −1.14820 | − | 0.662914i | −0.0364922 | − | 0.0210688i | ||||
\(991\) | 5.63816 | − | 9.76558i | 0.179102 | − | 0.310214i | −0.762471 | − | 0.647022i | \(-0.776014\pi\) |
0.941573 | + | 0.336808i | \(0.109347\pi\) | |||||||
\(992\) | 2.01806 | + | 3.49539i | 0.0640736 | + | 0.110979i | ||||
\(993\) | 12.0056i | 0.380987i | ||||||||
\(994\) | −4.40983 | − | 12.9366i | −0.139871 | − | 0.410323i | ||||
\(995\) | −21.4388 | − | 12.3777i | −0.679655 | − | 0.392399i | ||||
\(996\) | 11.2569 | + | 6.49919i | 0.356689 | + | 0.205935i | ||||
\(997\) | −21.3658 | −0.676663 | −0.338332 | − | 0.941027i | \(-0.609863\pi\) | ||||
−0.338332 | + | 0.941027i | \(0.609863\pi\) | |||||||
\(998\) | 2.02249 | − | 3.50306i | 0.0640209 | − | 0.110887i | ||||
\(999\) | 5.92304i | 0.187397i |
(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 | 546.2.bm.b.205.1 | yes | 20 | |
3.2 | odd | 2 | 1638.2.dt.b.1297.10 | 20 | |||
7.4 | even | 3 | 546.2.bd.b.361.10 | yes | 20 | ||
13.4 | even | 6 | 546.2.bd.b.121.10 | ✓ | 20 | ||
21.11 | odd | 6 | 1638.2.cr.b.361.1 | 20 | |||
39.17 | odd | 6 | 1638.2.cr.b.667.1 | 20 | |||
91.4 | even | 6 | inner | 546.2.bm.b.277.6 | yes | 20 | |
273.95 | odd | 6 | 1638.2.dt.b.1369.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bd.b.121.10 | ✓ | 20 | 13.4 | even | 6 | ||
546.2.bd.b.361.10 | yes | 20 | 7.4 | even | 3 | ||
546.2.bm.b.205.1 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.bm.b.277.6 | yes | 20 | 91.4 | even | 6 | inner | |
1638.2.cr.b.361.1 | 20 | 21.11 | odd | 6 | |||
1638.2.cr.b.667.1 | 20 | 39.17 | odd | 6 | |||
1638.2.dt.b.1297.10 | 20 | 3.2 | odd | 2 | |||
1638.2.dt.b.1369.5 | 20 | 273.95 | odd | 6 |