Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.4 | ||
Root | \(-0.606661 - 1.05077i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.508 |
Dual form | 1183.2.e.f.170.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10666 | + | 1.91679i | 0.782527 | + | 1.35538i | 0.930465 | + | 0.366381i | \(0.119403\pi\) |
−0.147938 | + | 0.988997i | \(0.547263\pi\) | |||||||
\(3\) | −1.23721 | + | 2.14292i | −0.714306 | + | 1.23721i | 0.248921 | + | 0.968524i | \(0.419924\pi\) |
−0.963227 | + | 0.268690i | \(0.913409\pi\) | |||||||
\(4\) | −1.44940 | + | 2.51043i | −0.724699 | + | 1.25521i | ||||
\(5\) | −1.06140 | − | 1.83839i | −0.474671 | − | 0.822155i | 0.524908 | − | 0.851159i | \(-0.324100\pi\) |
−0.999579 | + | 0.0290040i | \(0.990766\pi\) | |||||||
\(6\) | −5.47671 | −2.23586 | ||||||||
\(7\) | −2.63169 | − | 0.272389i | −0.994686 | − | 0.102953i | ||||
\(8\) | −1.98932 | −0.703331 | ||||||||
\(9\) | −1.56140 | − | 2.70442i | −0.520466 | − | 0.901473i | ||||
\(10\) | 2.34921 | − | 4.06896i | 0.742887 | − | 1.28672i | ||||
\(11\) | 2.39448 | − | 4.14736i | 0.721962 | − | 1.25048i | −0.238250 | − | 0.971204i | \(-0.576574\pi\) |
0.960212 | − | 0.279272i | \(-0.0900930\pi\) | |||||||
\(12\) | −3.58643 | − | 6.21188i | −1.03531 | − | 1.79321i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.39028 | − | 5.34585i | −0.638829 | − | 1.42874i | ||||
\(15\) | 5.25271 | 1.35624 | ||||||||
\(16\) | 0.697291 | + | 1.20774i | 0.174323 | + | 0.301936i | ||||
\(17\) | 1.88914 | − | 3.27208i | 0.458183 | − | 0.793597i | −0.540682 | − | 0.841227i | \(-0.681834\pi\) |
0.998865 | + | 0.0476304i | \(0.0151670\pi\) | |||||||
\(18\) | 3.45588 | − | 5.98575i | 0.814558 | − | 1.41086i | ||||
\(19\) | −1.78362 | − | 3.08931i | −0.409190 | − | 0.708737i | 0.585609 | − | 0.810593i | \(-0.300855\pi\) |
−0.994799 | + | 0.101856i | \(0.967522\pi\) | |||||||
\(20\) | 6.15355 | 1.37597 | ||||||||
\(21\) | 3.83967 | − | 5.30250i | 0.837886 | − | 1.15710i | ||||
\(22\) | 10.5995 | 2.25982 | ||||||||
\(23\) | −2.23721 | − | 3.87497i | −0.466491 | − | 0.807987i | 0.532776 | − | 0.846256i | \(-0.321149\pi\) |
−0.999267 | + | 0.0382695i | \(0.987815\pi\) | |||||||
\(24\) | 2.46122 | − | 4.26295i | 0.502394 | − | 0.870171i | ||||
\(25\) | 0.246870 | − | 0.427591i | 0.0493740 | − | 0.0855182i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.303848 | 0.0584757 | ||||||||
\(28\) | 4.49818 | − | 6.21188i | 0.850076 | − | 1.17393i | ||||
\(29\) | −5.90107 | −1.09580 | −0.547901 | − | 0.836543i | \(-0.684573\pi\) | ||||
−0.547901 | + | 0.836543i | \(0.684573\pi\) | |||||||
\(30\) | 5.81296 | + | 10.0683i | 1.06130 | + | 1.83822i | ||||
\(31\) | −1.88558 | + | 3.26592i | −0.338660 | + | 0.586577i | −0.984181 | − | 0.177166i | \(-0.943307\pi\) |
0.645521 | + | 0.763743i | \(0.276640\pi\) | |||||||
\(32\) | −3.53265 | + | 6.11873i | −0.624490 | + | 1.08165i | ||||
\(33\) | 5.92496 | + | 10.2623i | 1.03140 | + | 1.78644i | ||||
\(34\) | 8.36254 | 1.43416 | ||||||||
\(35\) | 2.29251 | + | 5.12720i | 0.387505 | + | 0.866655i | ||||
\(36\) | 9.05234 | 1.50872 | ||||||||
\(37\) | 2.81285 | + | 4.87200i | 0.462429 | + | 0.800951i | 0.999081 | − | 0.0428524i | \(-0.0136445\pi\) |
−0.536652 | + | 0.843804i | \(0.680311\pi\) | |||||||
\(38\) | 3.94772 | − | 6.83765i | 0.640404 | − | 1.10921i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.11146 | + | 3.65716i | 0.333851 | + | 0.578247i | ||||
\(41\) | −10.3948 | −1.62340 | −0.811698 | − | 0.584077i | \(-0.801457\pi\) | ||||
−0.811698 | + | 0.584077i | \(0.801457\pi\) | |||||||
\(42\) | 14.4130 | + | 1.49180i | 2.22398 | + | 0.230189i | ||||
\(43\) | 3.40733 | 0.519613 | 0.259807 | − | 0.965661i | \(-0.416341\pi\) | ||||
0.259807 | + | 0.965661i | \(0.416341\pi\) | |||||||
\(44\) | 6.94110 | + | 12.0223i | 1.04641 | + | 1.81244i | ||||
\(45\) | −3.31453 | + | 5.74093i | −0.494101 | + | 0.855807i | ||||
\(46\) | 4.95168 | − | 8.57655i | 0.730085 | − | 1.26454i | ||||
\(47\) | −3.55438 | − | 6.15636i | −0.518459 | − | 0.897998i | −0.999770 | − | 0.0214479i | \(-0.993172\pi\) |
0.481311 | − | 0.876550i | \(-0.340161\pi\) | |||||||
\(48\) | −3.45079 | −0.498079 | ||||||||
\(49\) | 6.85161 | + | 1.43369i | 0.978801 | + | 0.204813i | ||||
\(50\) | 1.09280 | 0.154546 | ||||||||
\(51\) | 4.67454 | + | 8.09654i | 0.654566 | + | 1.13374i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.19003 | − | 10.7214i | 0.850266 | − | 1.47270i | −0.0307027 | − | 0.999529i | \(-0.509774\pi\) |
0.880968 | − | 0.473175i | \(-0.156892\pi\) | |||||||
\(54\) | 0.336257 | + | 0.582415i | 0.0457588 | + | 0.0792566i | ||||
\(55\) | −10.1660 | −1.37078 | ||||||||
\(56\) | 5.23528 | + | 0.541869i | 0.699594 | + | 0.0724103i | ||||
\(57\) | 8.82686 | 1.16915 | ||||||||
\(58\) | −6.53049 | − | 11.3111i | −0.857495 | − | 1.48522i | ||||
\(59\) | 2.39448 | − | 4.14736i | 0.311734 | − | 0.539940i | −0.667003 | − | 0.745055i | \(-0.732423\pi\) |
0.978738 | + | 0.205115i | \(0.0657567\pi\) | |||||||
\(60\) | −7.61326 | + | 13.1865i | −0.982867 | + | 1.70238i | ||||
\(61\) | −1.60348 | − | 2.77732i | −0.205305 | − | 0.355599i | 0.744925 | − | 0.667148i | \(-0.232485\pi\) |
−0.950230 | + | 0.311550i | \(0.899152\pi\) | |||||||
\(62\) | −8.34680 | −1.06004 | ||||||||
\(63\) | 3.37246 | + | 7.54251i | 0.424890 | + | 0.950267i | ||||
\(64\) | −12.8486 | −1.60608 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.1139 | + | 22.7139i | −1.61420 | + | 2.79588i | ||||
\(67\) | −1.44978 | + | 2.51109i | −0.177118 | + | 0.306778i | −0.940892 | − | 0.338706i | \(-0.890011\pi\) |
0.763774 | + | 0.645484i | \(0.223344\pi\) | |||||||
\(68\) | 5.47622 | + | 9.48510i | 0.664090 | + | 1.15024i | ||||
\(69\) | 11.0717 | 1.33287 | ||||||||
\(70\) | −7.29075 | + | 10.0683i | −0.871411 | + | 1.20340i | ||||
\(71\) | 2.53876 | 0.301295 | 0.150648 | − | 0.988588i | \(-0.451864\pi\) | ||||
0.150648 | + | 0.988588i | \(0.451864\pi\) | |||||||
\(72\) | 3.10612 | + | 5.37996i | 0.366060 | + | 0.634034i | ||||
\(73\) | 3.85035 | − | 6.66901i | 0.450650 | − | 0.780548i | −0.547777 | − | 0.836625i | \(-0.684526\pi\) |
0.998426 | + | 0.0560762i | \(0.0178590\pi\) | |||||||
\(74\) | −6.22574 | + | 10.7833i | −0.723727 | + | 1.25353i | ||||
\(75\) | 0.610862 | + | 1.05804i | 0.0705362 | + | 0.122172i | ||||
\(76\) | 10.3407 | 1.18616 | ||||||||
\(77\) | −7.43122 | + | 10.2623i | −0.846867 | + | 1.16950i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.58925 | + | 4.48471i | 0.291313 | + | 0.504569i | 0.974120 | − | 0.226029i | \(-0.0725745\pi\) |
−0.682807 | + | 0.730598i | \(0.739241\pi\) | |||||||
\(80\) | 1.48021 | − | 2.56379i | 0.165492 | − | 0.286641i | ||||
\(81\) | 4.30827 | − | 7.46214i | 0.478696 | − | 0.829126i | ||||
\(82\) | −11.5035 | − | 19.9247i | −1.27035 | − | 2.20032i | ||||
\(83\) | −3.46731 | −0.380587 | −0.190294 | − | 0.981727i | \(-0.560944\pi\) | ||||
−0.190294 | + | 0.981727i | \(0.560944\pi\) | |||||||
\(84\) | 7.74633 | + | 17.3247i | 0.845194 | + | 1.89027i | ||||
\(85\) | −8.02051 | −0.869946 | ||||||||
\(86\) | 3.77076 | + | 6.53115i | 0.406612 | + | 0.704272i | ||||
\(87\) | 7.30089 | − | 12.6455i | 0.782738 | − | 1.35574i | ||||
\(88\) | −4.76338 | + | 8.25042i | −0.507778 | + | 0.879498i | ||||
\(89\) | 1.83216 | + | 3.17339i | 0.194209 | + | 0.336379i | 0.946641 | − | 0.322291i | \(-0.104453\pi\) |
−0.752432 | + | 0.658670i | \(0.771119\pi\) | |||||||
\(90\) | −14.6722 | −1.54659 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.9704 | 1.35226 | ||||||||
\(93\) | −4.66574 | − | 8.08129i | −0.483814 | − | 0.837991i | ||||
\(94\) | 7.86698 | − | 13.6260i | 0.811417 | − | 1.40542i | ||||
\(95\) | −3.78625 | + | 6.55798i | −0.388461 | + | 0.672835i | ||||
\(96\) | −8.74129 | − | 15.1404i | −0.892154 | − | 1.54526i | ||||
\(97\) | 5.40733 | 0.549031 | 0.274516 | − | 0.961583i | \(-0.411482\pi\) | ||||
0.274516 | + | 0.961583i | \(0.411482\pi\) | |||||||
\(98\) | 4.83432 | + | 14.7197i | 0.488340 | + | 1.48692i | ||||
\(99\) | −14.9549 | −1.50303 | ||||||||
\(100\) | 0.715625 | + | 1.23950i | 0.0715625 | + | 0.123950i | ||||
\(101\) | −4.65862 | + | 8.06897i | −0.463550 | + | 0.802892i | −0.999135 | − | 0.0415891i | \(-0.986758\pi\) |
0.535585 | + | 0.844482i | \(0.320091\pi\) | |||||||
\(102\) | −10.3463 | + | 17.9202i | −1.02443 | + | 1.77437i | ||||
\(103\) | −3.65318 | − | 6.32749i | −0.359958 | − | 0.623466i | 0.627995 | − | 0.778217i | \(-0.283876\pi\) |
−0.987953 | + | 0.154751i | \(0.950542\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.8235 | − | 1.43078i | −1.34904 | − | 0.139630i | ||||
\(106\) | 27.4011 | 2.66143 | ||||||||
\(107\) | −3.37365 | − | 5.84333i | −0.326143 | − | 0.564896i | 0.655600 | − | 0.755108i | \(-0.272416\pi\) |
−0.981743 | + | 0.190212i | \(0.939082\pi\) | |||||||
\(108\) | −0.440397 | + | 0.762790i | −0.0423772 | + | 0.0733995i | ||||
\(109\) | 2.08822 | − | 3.61691i | 0.200016 | − | 0.346437i | −0.748518 | − | 0.663115i | \(-0.769234\pi\) |
0.948533 | + | 0.316678i | \(0.102567\pi\) | |||||||
\(110\) | −11.2503 | − | 19.4861i | −1.07267 | − | 1.85792i | ||||
\(111\) | −13.9204 | −1.32126 | ||||||||
\(112\) | −1.50608 | − | 3.36834i | −0.142311 | − | 0.318278i | ||||
\(113\) | 5.90107 | 0.555126 | 0.277563 | − | 0.960707i | \(-0.410473\pi\) | ||||
0.277563 | + | 0.960707i | \(0.410473\pi\) | |||||||
\(114\) | 9.76834 | + | 16.9193i | 0.914889 | + | 1.58463i | ||||
\(115\) | −4.74915 | + | 8.22577i | −0.442860 | + | 0.767057i | ||||
\(116\) | 8.55300 | − | 14.8142i | 0.794126 | − | 1.37547i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.5995 | 0.975763 | ||||||||
\(119\) | −5.86291 | + | 8.09654i | −0.537452 | + | 0.742208i | ||||
\(120\) | −10.4493 | −0.953888 | ||||||||
\(121\) | −5.96705 | − | 10.3352i | −0.542459 | − | 0.939567i | ||||
\(122\) | 3.54903 | − | 6.14709i | 0.321314 | − | 0.556532i | ||||
\(123\) | 12.8606 | − | 22.2752i | 1.15960 | − | 2.00849i | ||||
\(124\) | −5.46591 | − | 9.46724i | −0.490853 | − | 0.850183i | ||||
\(125\) | −11.6621 | −1.04309 | ||||||||
\(126\) | −10.7253 | + | 14.8113i | −0.955482 | + | 1.31950i | ||||
\(127\) | −10.5268 | −0.934100 | −0.467050 | − | 0.884231i | \(-0.654683\pi\) | ||||
−0.467050 | + | 0.884231i | \(0.654683\pi\) | |||||||
\(128\) | −7.15377 | − | 12.3907i | −0.632309 | − | 1.09519i | ||||
\(129\) | −4.21560 | + | 7.30163i | −0.371163 | + | 0.642873i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.71204 | − | 4.69740i | −0.236952 | − | 0.410413i | 0.722886 | − | 0.690967i | \(-0.242815\pi\) |
−0.959838 | + | 0.280554i | \(0.909482\pi\) | |||||||
\(132\) | −34.3505 | −2.98983 | ||||||||
\(133\) | 3.85243 | + | 8.61596i | 0.334048 | + | 0.747099i | ||||
\(134\) | −6.41765 | −0.554400 | ||||||||
\(135\) | −0.322504 | − | 0.558593i | −0.0277567 | − | 0.0480761i | ||||
\(136\) | −3.75810 | + | 6.50922i | −0.322255 | + | 0.558161i | ||||
\(137\) | 11.1224 | − | 19.2645i | 0.950248 | − | 1.64588i | 0.205363 | − | 0.978686i | \(-0.434163\pi\) |
0.744886 | − | 0.667192i | \(-0.232504\pi\) | |||||||
\(138\) | 12.2526 | + | 21.2221i | 1.04301 | + | 1.80654i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −16.1942 | − | 1.67616i | −1.36866 | − | 0.141661i | ||||
\(141\) | 17.5901 | 1.48135 | ||||||||
\(142\) | 2.80955 | + | 4.86628i | 0.235772 | + | 0.408369i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.17750 | − | 3.77153i | 0.181458 | − | 0.314294i | ||||
\(145\) | 6.26338 | + | 10.8485i | 0.520146 | + | 0.900919i | ||||
\(146\) | 17.0441 | 1.41058 | ||||||||
\(147\) | −11.5492 | + | 12.9087i | −0.952561 | + | 1.06469i | ||||
\(148\) | −16.3077 | −1.34049 | ||||||||
\(149\) | 1.47736 | + | 2.55887i | 0.121030 | + | 0.209630i | 0.920174 | − | 0.391509i | \(-0.128047\pi\) |
−0.799144 | + | 0.601140i | \(0.794714\pi\) | |||||||
\(150\) | −1.35203 | + | 2.34179i | −0.110393 | + | 0.191206i | ||||
\(151\) | −9.27736 | + | 16.0689i | −0.754981 | + | 1.30766i | 0.190403 | + | 0.981706i | \(0.439020\pi\) |
−0.945384 | + | 0.325959i | \(0.894313\pi\) | |||||||
\(152\) | 3.54818 | + | 6.14564i | 0.287796 | + | 0.498477i | ||||
\(153\) | −11.7988 | −0.953875 | ||||||||
\(154\) | −27.8946 | − | 2.88719i | −2.24781 | − | 0.232656i | ||||
\(155\) | 8.00541 | 0.643010 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.89982 | − | 8.48673i | 0.391048 | − | 0.677315i | −0.601540 | − | 0.798843i | \(-0.705446\pi\) |
0.992588 | + | 0.121528i | \(0.0387793\pi\) | |||||||
\(158\) | −5.73084 | + | 9.92610i | −0.455921 | + | 0.789678i | ||||
\(159\) | 15.3168 | + | 26.5294i | 1.21470 | + | 2.10392i | ||||
\(160\) | 14.9982 | 1.18571 | ||||||||
\(161\) | 4.83216 | + | 10.8071i | 0.380828 | + | 0.851720i | ||||
\(162\) | 19.0712 | 1.49837 | ||||||||
\(163\) | 6.91709 | + | 11.9808i | 0.541788 | + | 0.938405i | 0.998801 | + | 0.0489451i | \(0.0155859\pi\) |
−0.457013 | + | 0.889460i | \(0.651081\pi\) | |||||||
\(164\) | 15.0662 | − | 26.0954i | 1.17647 | − | 2.03771i | ||||
\(165\) | 12.5775 | − | 21.7848i | 0.979156 | − | 1.69595i | ||||
\(166\) | −3.83714 | − | 6.64612i | −0.297820 | − | 0.515839i | ||||
\(167\) | −17.3534 | −1.34285 | −0.671424 | − | 0.741073i | \(-0.734317\pi\) | ||||
−0.671424 | + | 0.741073i | \(0.734317\pi\) | |||||||
\(168\) | −7.63834 | + | 10.5484i | −0.589311 | + | 0.813824i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.87598 | − | 15.3737i | −0.680757 | − | 1.17911i | ||||
\(171\) | −5.56987 | + | 9.64730i | −0.425939 | + | 0.737747i | ||||
\(172\) | −4.93858 | + | 8.55387i | −0.376563 | + | 0.652226i | ||||
\(173\) | 1.48069 | + | 2.56463i | 0.112575 | + | 0.194985i | 0.916808 | − | 0.399329i | \(-0.130757\pi\) |
−0.804233 | + | 0.594314i | \(0.797424\pi\) | |||||||
\(174\) | 32.3184 | 2.45005 | ||||||||
\(175\) | −0.766156 | + | 1.05804i | −0.0579160 | + | 0.0799806i | ||||
\(176\) | 6.67859 | 0.503418 | ||||||||
\(177\) | 5.92496 | + | 10.2623i | 0.445348 | + | 0.771365i | ||||
\(178\) | −4.05516 | + | 7.02374i | −0.303947 | + | 0.526452i | ||||
\(179\) | 2.83444 | − | 4.90939i | 0.211856 | − | 0.366945i | −0.740440 | − | 0.672123i | \(-0.765383\pi\) |
0.952295 | + | 0.305178i | \(0.0987159\pi\) | |||||||
\(180\) | −9.60813 | − | 16.6418i | −0.716148 | − | 1.24040i | ||||
\(181\) | 7.17645 | 0.533421 | 0.266711 | − | 0.963777i | \(-0.414063\pi\) | ||||
0.266711 | + | 0.963777i | \(0.414063\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.93541 | 0.586603 | ||||||||
\(184\) | 4.45054 | + | 7.70855i | 0.328098 | + | 0.568282i | ||||
\(185\) | 5.97110 | − | 10.3423i | 0.439004 | − | 0.760377i | ||||
\(186\) | 10.3268 | − | 17.8865i | 0.757196 | − | 1.31150i | ||||
\(187\) | −9.04700 | − | 15.6699i | −0.661582 | − | 1.14589i | ||||
\(188\) | 20.6068 | 1.50291 | ||||||||
\(189\) | −0.799636 | − | 0.0827650i | −0.0581649 | − | 0.00602027i | ||||
\(190\) | −16.7604 | −1.21593 | ||||||||
\(191\) | −5.94088 | − | 10.2899i | −0.429867 | − | 0.744552i | 0.566994 | − | 0.823722i | \(-0.308106\pi\) |
−0.996861 | + | 0.0791703i | \(0.974773\pi\) | |||||||
\(192\) | 15.8965 | − | 27.5335i | 1.14723 | − | 1.98706i | ||||
\(193\) | 11.4851 | − | 19.8927i | 0.826714 | − | 1.43191i | −0.0738876 | − | 0.997267i | \(-0.523541\pi\) |
0.900602 | − | 0.434645i | \(-0.143126\pi\) | |||||||
\(194\) | 5.98408 | + | 10.3647i | 0.429632 | + | 0.744145i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.5299 | + | 15.1225i | −0.966420 | + | 1.08018i | ||||
\(197\) | −16.9216 | −1.20561 | −0.602806 | − | 0.797888i | \(-0.705951\pi\) | ||||
−0.602806 | + | 0.797888i | \(0.705951\pi\) | |||||||
\(198\) | −16.5500 | − | 28.6655i | −1.17616 | − | 2.03717i | ||||
\(199\) | −5.02953 | + | 8.71140i | −0.356534 | + | 0.617535i | −0.987379 | − | 0.158374i | \(-0.949375\pi\) |
0.630845 | + | 0.775909i | \(0.282708\pi\) | |||||||
\(200\) | −0.491103 | + | 0.850616i | −0.0347262 | + | 0.0601476i | ||||
\(201\) | −3.58737 | − | 6.21351i | −0.253034 | − | 0.438267i | ||||
\(202\) | −20.6221 | −1.45096 | ||||||||
\(203\) | 15.5298 | + | 1.60739i | 1.08998 | + | 0.112817i | ||||
\(204\) | −27.1010 | −1.89745 | ||||||||
\(205\) | 11.0330 | + | 19.1098i | 0.770580 | + | 1.33468i | ||||
\(206\) | 8.08566 | − | 14.0048i | 0.563355 | − | 0.975759i | ||||
\(207\) | −6.98636 | + | 12.1007i | −0.485586 | + | 0.841059i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.0833 | −1.18168 | ||||||||
\(210\) | −12.5554 | − | 28.0802i | −0.866406 | − | 1.93772i | ||||
\(211\) | −24.4609 | −1.68396 | −0.841978 | − | 0.539512i | \(-0.818609\pi\) | ||||
−0.841978 | + | 0.539512i | \(0.818609\pi\) | |||||||
\(212\) | 17.9436 | + | 31.0793i | 1.23237 | + | 2.13453i | ||||
\(213\) | −3.14099 | + | 5.44035i | −0.215217 | + | 0.372767i | ||||
\(214\) | 7.46697 | − | 12.9332i | 0.510431 | − | 0.884093i | ||||
\(215\) | −3.61654 | − | 6.26402i | −0.246646 | − | 0.427203i | ||||
\(216\) | −0.604452 | −0.0411277 | ||||||||
\(217\) | 5.85187 | − | 8.08129i | 0.397251 | − | 0.548594i | ||||
\(218\) | 9.24382 | 0.626071 | ||||||||
\(219\) | 9.52742 | + | 16.5020i | 0.643804 | + | 1.11510i | ||||
\(220\) | 14.7345 | − | 25.5210i | 0.993402 | − | 1.72062i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −15.4051 | − | 26.6825i | −1.03393 | − | 1.79081i | ||||
\(223\) | 29.2625 | 1.95956 | 0.979780 | − | 0.200076i | \(-0.0641188\pi\) | ||||
0.979780 | + | 0.200076i | \(0.0641188\pi\) | |||||||
\(224\) | 10.9635 | − | 15.1404i | 0.732531 | − | 1.01161i | ||||
\(225\) | −1.54185 | −0.102790 | ||||||||
\(226\) | 6.53049 | + | 11.3111i | 0.434401 | + | 0.752405i | ||||
\(227\) | −5.03685 | + | 8.72408i | −0.334307 | + | 0.579038i | −0.983352 | − | 0.181713i | \(-0.941836\pi\) |
0.649044 | + | 0.760751i | \(0.275169\pi\) | |||||||
\(228\) | −12.7936 | + | 22.1592i | −0.847279 | + | 1.46753i | ||||
\(229\) | −5.56997 | − | 9.64748i | −0.368074 | − | 0.637523i | 0.621190 | − | 0.783660i | \(-0.286649\pi\) |
−0.989264 | + | 0.146137i | \(0.953316\pi\) | |||||||
\(230\) | −21.0228 | −1.38620 | ||||||||
\(231\) | −12.7973 | − | 28.6212i | −0.842003 | − | 1.88314i | ||||
\(232\) | 11.7391 | 0.770711 | ||||||||
\(233\) | 8.54166 | + | 14.7946i | 0.559583 | + | 0.969226i | 0.997531 | + | 0.0702257i | \(0.0223720\pi\) |
−0.437948 | + | 0.899000i | \(0.644295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.54522 | + | 13.0687i | −0.492196 | + | 0.852508i | ||||
\(236\) | 6.94110 | + | 12.0223i | 0.451827 | + | 0.782587i | ||||
\(237\) | −12.8138 | −0.832347 | ||||||||
\(238\) | −22.0076 | − | 2.27787i | −1.42654 | − | 0.147652i | ||||
\(239\) | −6.92142 | −0.447710 | −0.223855 | − | 0.974622i | \(-0.571864\pi\) | ||||
−0.223855 | + | 0.974622i | \(0.571864\pi\) | |||||||
\(240\) | 3.66266 | + | 6.34392i | 0.236424 | + | 0.409498i | ||||
\(241\) | 3.24812 | − | 5.62592i | 0.209230 | − | 0.362397i | −0.742242 | − | 0.670132i | \(-0.766238\pi\) |
0.951472 | + | 0.307735i | \(0.0995709\pi\) | |||||||
\(242\) | 13.2070 | − | 22.8752i | 0.848978 | − | 1.47047i | ||||
\(243\) | 11.1163 | + | 19.2539i | 0.713109 | + | 1.23514i | ||||
\(244\) | 9.29634 | 0.595137 | ||||||||
\(245\) | −4.63660 | − | 14.1177i | −0.296221 | − | 0.901945i | ||||
\(246\) | 56.9293 | 3.62968 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.75103 | − | 6.49697i | 0.238190 | − | 0.412558i | ||||
\(249\) | 4.28981 | − | 7.43017i | 0.271856 | − | 0.470868i | ||||
\(250\) | −12.9060 | − | 22.3538i | −0.816246 | − | 1.41378i | ||||
\(251\) | −9.86804 | −0.622865 | −0.311433 | − | 0.950268i | \(-0.600809\pi\) | ||||
−0.311433 | + | 0.950268i | \(0.600809\pi\) | |||||||
\(252\) | −23.8230 | − | 2.46576i | −1.50071 | − | 0.155328i | ||||
\(253\) | −21.4278 | −1.34716 | ||||||||
\(254\) | −11.6496 | − | 20.1776i | −0.730959 | − | 1.26606i | ||||
\(255\) | 9.92309 | − | 17.1873i | 0.621408 | − | 1.07631i | ||||
\(256\) | 2.98497 | − | 5.17012i | 0.186560 | − | 0.323132i | ||||
\(257\) | −3.43234 | − | 5.94499i | −0.214104 | − | 0.370838i | 0.738891 | − | 0.673825i | \(-0.235350\pi\) |
−0.952995 | + | 0.302986i | \(0.902016\pi\) | |||||||
\(258\) | −18.6610 | −1.16178 | ||||||||
\(259\) | −6.07547 | − | 13.5878i | −0.377511 | − | 0.844304i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.21392 | + | 15.9590i | 0.570327 | + | 0.987836i | ||||
\(262\) | 6.00262 | − | 10.3969i | 0.370843 | − | 0.642320i | ||||
\(263\) | 0.0632753 | − | 0.109596i | 0.00390172 | − | 0.00675798i | −0.864068 | − | 0.503375i | \(-0.832091\pi\) |
0.867970 | + | 0.496617i | \(0.165425\pi\) | |||||||
\(264\) | −11.7867 | − | 20.4151i | −0.725418 | − | 1.25646i | ||||
\(265\) | −26.2803 | −1.61439 | ||||||||
\(266\) | −12.2517 | + | 16.9193i | −0.751199 | + | 1.03739i | ||||
\(267\) | −9.06710 | −0.554897 | ||||||||
\(268\) | −4.20261 | − | 7.27913i | −0.256715 | − | 0.444643i | ||||
\(269\) | 2.12154 | − | 3.67462i | 0.129353 | − | 0.224045i | −0.794073 | − | 0.607822i | \(-0.792043\pi\) |
0.923426 | + | 0.383777i | \(0.125377\pi\) | |||||||
\(270\) | 0.713805 | − | 1.23635i | 0.0434408 | − | 0.0752417i | ||||
\(271\) | 0.783616 | + | 1.35726i | 0.0476013 | + | 0.0824479i | 0.888844 | − | 0.458209i | \(-0.151509\pi\) |
−0.841243 | + | 0.540657i | \(0.818176\pi\) | |||||||
\(272\) | 5.26911 | 0.319487 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 49.2348 | 2.97438 | ||||||||
\(275\) | −1.18225 | − | 2.04771i | −0.0712923 | − | 0.123482i | ||||
\(276\) | −16.0472 | + | 27.7946i | −0.965929 | + | 1.67304i | ||||
\(277\) | 6.37260 | − | 11.0377i | 0.382892 | − | 0.663189i | −0.608582 | − | 0.793491i | \(-0.708261\pi\) |
0.991474 | + | 0.130302i | \(0.0415947\pi\) | |||||||
\(278\) | −4.42664 | − | 7.66717i | −0.265492 | − | 0.459846i | ||||
\(279\) | 11.7766 | 0.705045 | ||||||||
\(280\) | −4.56054 | − | 10.1996i | −0.272545 | − | 0.609546i | ||||
\(281\) | −4.62986 | −0.276194 | −0.138097 | − | 0.990419i | \(-0.544099\pi\) | ||||
−0.138097 | + | 0.990419i | \(0.544099\pi\) | |||||||
\(282\) | 19.4663 | + | 33.7166i | 1.15920 | + | 2.00779i | ||||
\(283\) | −1.82416 | + | 3.15954i | −0.108435 | + | 0.187815i | −0.915136 | − | 0.403144i | \(-0.867917\pi\) |
0.806701 | + | 0.590959i | \(0.201251\pi\) | |||||||
\(284\) | −3.67967 | + | 6.37338i | −0.218348 | + | 0.378190i | ||||
\(285\) | −9.36881 | − | 16.2273i | −0.554960 | − | 0.961220i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.3559 | + | 2.83143i | 1.61477 | + | 0.167134i | ||||
\(288\) | 22.0635 | 1.30010 | ||||||||
\(289\) | 1.36231 | + | 2.35959i | 0.0801360 | + | 0.138800i | ||||
\(290\) | −13.8629 | + | 24.0112i | −0.814057 | + | 1.40999i | ||||
\(291\) | −6.69003 | + | 11.5875i | −0.392176 | + | 0.679269i | ||||
\(292\) | 11.1614 | + | 19.3321i | 0.653171 | + | 1.13132i | ||||
\(293\) | 21.0415 | 1.22926 | 0.614630 | − | 0.788816i | \(-0.289305\pi\) | ||||
0.614630 | + | 0.788816i | \(0.289305\pi\) | |||||||
\(294\) | −37.5242 | − | 7.85189i | −2.18846 | − | 0.457932i | ||||
\(295\) | −10.1660 | −0.591886 | ||||||||
\(296\) | −5.59566 | − | 9.69196i | −0.325241 | − | 0.563334i | ||||
\(297\) | 0.727559 | − | 1.26017i | 0.0422172 | − | 0.0731224i | ||||
\(298\) | −3.26988 | + | 5.66359i | −0.189419 | + | 0.328083i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.54152 | −0.204470 | ||||||||
\(301\) | −8.96705 | − | 0.928120i | −0.516852 | − | 0.0534960i | ||||
\(302\) | −41.0676 | −2.36317 | ||||||||
\(303\) | −11.5274 | − | 19.9661i | −0.662233 | − | 1.14702i | ||||
\(304\) | 2.48740 | − | 4.30830i | 0.142662 | − | 0.247098i | ||||
\(305\) | −3.40387 | + | 5.89567i | −0.194905 | + | 0.337585i | ||||
\(306\) | −13.0573 | − | 22.6158i | −0.746434 | − | 1.29286i | ||||
\(307\) | 4.95861 | 0.283003 | 0.141502 | − | 0.989938i | \(-0.454807\pi\) | ||||
0.141502 | + | 0.989938i | \(0.454807\pi\) | |||||||
\(308\) | −14.9921 | − | 33.5298i | −0.854253 | − | 1.91054i | ||||
\(309\) | 18.0791 | 1.02848 | ||||||||
\(310\) | 8.85927 | + | 15.3447i | 0.503173 | + | 0.871521i | ||||
\(311\) | 1.21079 | − | 2.09715i | 0.0686575 | − | 0.118918i | −0.829653 | − | 0.558279i | \(-0.811462\pi\) |
0.898311 | + | 0.439361i | \(0.144795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.98026 | − | 12.0902i | −0.394548 | − | 0.683377i | 0.598496 | − | 0.801126i | \(-0.295765\pi\) |
−0.993043 | + | 0.117749i | \(0.962432\pi\) | |||||||
\(314\) | 21.6897 | 1.22402 | ||||||||
\(315\) | 10.2866 | − | 14.2055i | 0.579583 | − | 0.800390i | ||||
\(316\) | −15.0114 | −0.844457 | ||||||||
\(317\) | 1.53431 | + | 2.65750i | 0.0861753 | + | 0.149260i | 0.905891 | − | 0.423510i | \(-0.139202\pi\) |
−0.819716 | + | 0.572770i | \(0.805869\pi\) | |||||||
\(318\) | −33.9010 | + | 58.7182i | −1.90107 | + | 3.29275i | ||||
\(319\) | −14.1300 | + | 24.4739i | −0.791127 | + | 1.37027i | ||||
\(320\) | 13.6375 | + | 23.6208i | 0.762359 | + | 1.32044i | ||||
\(321\) | 16.6957 | 0.931863 | ||||||||
\(322\) | −15.3674 | + | 21.2221i | −0.856394 | + | 1.18266i | ||||
\(323\) | −13.4780 | −0.749936 | ||||||||
\(324\) | 12.4888 | + | 21.6312i | 0.693821 | + | 1.20173i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.3098 | + | 26.5173i | −0.847929 | + | 1.46866i | ||||
\(327\) | 5.16716 | + | 8.94978i | 0.285745 | + | 0.494924i | ||||
\(328\) | 20.6786 | 1.14179 | ||||||||
\(329\) | 7.67710 | + | 17.1698i | 0.423252 | + | 0.946603i | ||||
\(330\) | 55.6761 | 3.06487 | ||||||||
\(331\) | 6.80261 | + | 11.7825i | 0.373905 | + | 0.647623i | 0.990162 | − | 0.139922i | \(-0.0446853\pi\) |
−0.616257 | + | 0.787545i | \(0.711352\pi\) | |||||||
\(332\) | 5.02551 | − | 8.70445i | 0.275811 | − | 0.477719i | ||||
\(333\) | 8.78395 | − | 15.2142i | 0.481358 | − | 0.833736i | ||||
\(334\) | −19.2044 | − | 33.2629i | −1.05082 | − | 1.82007i | ||||
\(335\) | 6.15516 | 0.336292 | ||||||||
\(336\) | 9.08142 | + | 0.939958i | 0.495432 | + | 0.0512789i | ||||
\(337\) | −35.1646 | −1.91554 | −0.957769 | − | 0.287538i | \(-0.907163\pi\) | ||||
−0.957769 | + | 0.287538i | \(0.907163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.30089 | + | 12.6455i | −0.396530 | + | 0.686810i | ||||
\(340\) | 11.6249 | − | 20.1349i | 0.630449 | − | 1.09197i | ||||
\(341\) | 9.02997 | + | 15.6404i | 0.489000 | + | 0.846973i | ||||
\(342\) | −24.6558 | −1.33323 | ||||||||
\(343\) | −17.6408 | − | 5.63933i | −0.952514 | − | 0.304495i | ||||
\(344\) | −6.77828 | −0.365460 | ||||||||
\(345\) | −11.7514 | − | 20.3541i | −0.632676 | − | 1.09583i | ||||
\(346\) | −3.27724 | + | 5.67635i | −0.176186 | + | 0.305162i | ||||
\(347\) | 2.73551 | − | 4.73804i | 0.146850 | − | 0.254351i | −0.783212 | − | 0.621755i | \(-0.786420\pi\) |
0.930062 | + | 0.367404i | \(0.119753\pi\) | |||||||
\(348\) | 21.1638 | + | 36.6567i | 1.13450 | + | 1.96501i | ||||
\(349\) | −4.34196 | −0.232420 | −0.116210 | − | 0.993225i | \(-0.537075\pi\) | ||||
−0.116210 | + | 0.993225i | \(0.537075\pi\) | |||||||
\(350\) | −2.87593 | − | 0.297668i | −0.153725 | − | 0.0159110i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9177 | + | 29.3023i | 0.901717 | + | 1.56182i | ||||
\(353\) | 13.7996 | − | 23.9016i | 0.734479 | − | 1.27216i | −0.220472 | − | 0.975393i | \(-0.570760\pi\) |
0.954951 | − | 0.296762i | \(-0.0959068\pi\) | |||||||
\(354\) | −13.1139 | + | 22.7139i | −0.696993 | + | 1.20723i | ||||
\(355\) | −2.69463 | − | 4.66724i | −0.143016 | − | 0.247712i | ||||
\(356\) | −10.6221 | −0.562971 | ||||||||
\(357\) | −10.0965 | − | 22.5809i | −0.534365 | − | 1.19511i | ||||
\(358\) | 12.5470 | 0.663132 | ||||||||
\(359\) | 3.31427 | + | 5.74049i | 0.174921 | + | 0.302971i | 0.940134 | − | 0.340806i | \(-0.110700\pi\) |
−0.765213 | + | 0.643777i | \(0.777366\pi\) | |||||||
\(360\) | 6.59366 | − | 11.4206i | 0.347516 | − | 0.601916i | ||||
\(361\) | 3.13742 | − | 5.43418i | 0.165128 | − | 0.286009i | ||||
\(362\) | 7.94189 | + | 13.7558i | 0.417417 | + | 0.722987i | ||||
\(363\) | 29.5301 | 1.54993 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3470 | −0.855643 | ||||||||
\(366\) | 8.78181 | + | 15.2105i | 0.459033 | + | 0.795068i | ||||
\(367\) | −15.6037 | + | 27.0264i | −0.814506 | + | 1.41077i | 0.0951768 | + | 0.995460i | \(0.469658\pi\) |
−0.909682 | + | 0.415305i | \(0.863675\pi\) | |||||||
\(368\) | 3.11998 | − | 5.40396i | 0.162640 | − | 0.281701i | ||||
\(369\) | 16.2304 | + | 28.1119i | 0.844923 | + | 1.46345i | ||||
\(370\) | 26.4319 | 1.37413 | ||||||||
\(371\) | −19.2107 | + | 26.5294i | −0.997368 | + | 1.37734i | ||||
\(372\) | 27.0500 | 1.40248 | ||||||||
\(373\) | 7.88730 | + | 13.6612i | 0.408389 | + | 0.707350i | 0.994709 | − | 0.102729i | \(-0.0327574\pi\) |
−0.586321 | + | 0.810079i | \(0.699424\pi\) | |||||||
\(374\) | 20.0239 | − | 34.6825i | 1.03541 | − | 1.79339i | ||||
\(375\) | 14.4285 | − | 24.9909i | 0.745084 | − | 1.29052i | ||||
\(376\) | 7.07080 | + | 12.2470i | 0.364649 | + | 0.631590i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.726282 | − | 1.62433i | −0.0373559 | − | 0.0835465i | ||||
\(379\) | −31.6512 | −1.62581 | −0.812907 | − | 0.582393i | \(-0.802116\pi\) | ||||
−0.812907 | + | 0.582393i | \(0.802116\pi\) | |||||||
\(380\) | −10.9756 | − | 19.0102i | −0.563035 | − | 0.975205i | ||||
\(381\) | 13.0239 | − | 22.5580i | 0.667233 | − | 1.15568i | ||||
\(382\) | 13.1491 | − | 22.7749i | 0.672766 | − | 1.16526i | ||||
\(383\) | 6.19675 | + | 10.7331i | 0.316639 | + | 0.548435i | 0.979785 | − | 0.200055i | \(-0.0641122\pi\) |
−0.663145 | + | 0.748491i | \(0.730779\pi\) | |||||||
\(384\) | 35.4030 | 1.80665 | ||||||||
\(385\) | 26.7537 | + | 2.76910i | 1.36350 | + | 0.141126i | ||||
\(386\) | 50.8404 | 2.58771 | ||||||||
\(387\) | −5.32020 | − | 9.21486i | −0.270441 | − | 0.468418i | ||||
\(388\) | −7.83737 | + | 13.5747i | −0.397882 | + | 0.689152i | ||||
\(389\) | 7.03705 | − | 12.1885i | 0.356792 | − | 0.617983i | −0.630631 | − | 0.776083i | \(-0.717204\pi\) |
0.987423 | + | 0.158100i | \(0.0505370\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.9056 | −0.854954 | ||||||||
\(392\) | −13.6300 | − | 2.85207i | −0.688421 | − | 0.144051i | ||||
\(393\) | 13.4215 | 0.677026 | ||||||||
\(394\) | −18.7265 | − | 32.4352i | −0.943425 | − | 1.63406i | ||||
\(395\) | 5.49644 | − | 9.52012i | 0.276556 | − | 0.479009i | ||||
\(396\) | 21.6756 | − | 37.5433i | 1.08924 | − | 1.88662i | ||||
\(397\) | −3.48652 | − | 6.03884i | −0.174984 | − | 0.303081i | 0.765172 | − | 0.643826i | \(-0.222654\pi\) |
−0.940156 | + | 0.340745i | \(0.889321\pi\) | |||||||
\(398\) | −22.2639 | −1.11599 | ||||||||
\(399\) | −23.2296 | − | 2.40434i | −1.16293 | − | 0.120368i | ||||
\(400\) | 0.688560 | 0.0344280 | ||||||||
\(401\) | 1.36841 | + | 2.37016i | 0.0683352 | + | 0.118360i | 0.898169 | − | 0.439651i | \(-0.144898\pi\) |
−0.829833 | + | 0.558011i | \(0.811565\pi\) | |||||||
\(402\) | 7.94000 | − | 13.7525i | 0.396011 | − | 0.685912i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −13.5044 | − | 23.3903i | −0.671868 | − | 1.16371i | ||||
\(405\) | −18.2911 | −0.908894 | ||||||||
\(406\) | 14.1052 | + | 31.5463i | 0.700029 | + | 1.56561i | ||||
\(407\) | 26.9412 | 1.33543 | ||||||||
\(408\) | −9.29915 | − | 16.1066i | −0.460377 | − | 0.797396i | ||||
\(409\) | −12.2577 | + | 21.2309i | −0.606104 | + | 1.04980i | 0.385772 | + | 0.922594i | \(0.373935\pi\) |
−0.991876 | + | 0.127208i | \(0.959398\pi\) | |||||||
\(410\) | −24.4196 | + | 42.2961i | −1.20600 | + | 2.08885i | ||||
\(411\) | 27.5215 | + | 47.6686i | 1.35754 | + | 2.35132i | ||||
\(412\) | 21.1796 | 1.04345 | ||||||||
\(413\) | −7.43122 | + | 10.2623i | −0.365667 | + | 0.504977i | ||||
\(414\) | −30.9261 | −1.51994 | ||||||||
\(415\) | 3.68020 | + | 6.37429i | 0.180654 | + | 0.312902i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.94886 | − | 8.57167i | 0.242347 | − | 0.419757i | ||||
\(418\) | −18.9054 | − | 32.7452i | −0.924696 | − | 1.60162i | ||||
\(419\) | −3.01252 | −0.147171 | −0.0735856 | − | 0.997289i | \(-0.523444\pi\) | ||||
−0.0735856 | + | 0.997289i | \(0.523444\pi\) | |||||||
\(420\) | 23.6276 | − | 32.6292i | 1.15291 | − | 1.59214i | ||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | −27.0699 | − | 46.8864i | −1.31774 | − | 2.28240i | ||||
\(423\) | −11.0996 | + | 19.2251i | −0.539681 | + | 0.934755i | ||||
\(424\) | −12.3140 | + | 21.3284i | −0.598018 | + | 1.03580i | ||||
\(425\) | −0.932742 | − | 1.61556i | −0.0452447 | − | 0.0783660i | ||||
\(426\) | −13.9040 | −0.673653 | ||||||||
\(427\) | 3.46337 | + | 7.74581i | 0.167604 | + | 0.374846i | ||||
\(428\) | 19.5590 | 0.945421 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00456 | − | 13.8643i | 0.386014 | − | 0.668596i | ||||
\(431\) | −9.39711 | + | 16.2763i | −0.452643 | + | 0.784001i | −0.998549 | − | 0.0538455i | \(-0.982852\pi\) |
0.545906 | + | 0.837846i | \(0.316185\pi\) | |||||||
\(432\) | 0.211871 | + | 0.366971i | 0.0101936 | + | 0.0176559i | ||||
\(433\) | −7.76911 | −0.373360 | −0.186680 | − | 0.982421i | \(-0.559773\pi\) | ||||
−0.186680 | + | 0.982421i | \(0.559773\pi\) | |||||||
\(434\) | 21.9662 | + | 2.27358i | 1.05441 | + | 0.109135i | ||||
\(435\) | −30.9966 | −1.48617 | ||||||||
\(436\) | 6.05333 | + | 10.4847i | 0.289902 | + | 0.502125i | ||||
\(437\) | −7.98066 | + | 13.8229i | −0.381767 | + | 0.661240i | ||||
\(438\) | −21.0873 | + | 36.5242i | −1.00759 | + | 1.74519i | ||||
\(439\) | 18.9841 | + | 32.8814i | 0.906060 | + | 1.56934i | 0.819488 | + | 0.573096i | \(0.194258\pi\) |
0.0865713 | + | 0.996246i | \(0.472409\pi\) | |||||||
\(440\) | 20.2234 | 0.964112 | ||||||||
\(441\) | −6.82079 | − | 20.7682i | −0.324799 | − | 0.988961i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.8135 | − | 30.8539i | −0.846344 | − | 1.46591i | −0.884449 | − | 0.466637i | \(-0.845465\pi\) |
0.0381050 | − | 0.999274i | \(-0.487868\pi\) | |||||||
\(444\) | 20.1762 | − | 34.9461i | 0.957518 | − | 1.65847i | ||||
\(445\) | 3.88930 | − | 6.73647i | 0.184371 | − | 0.319339i | ||||
\(446\) | 32.3837 | + | 56.0901i | 1.53341 | + | 2.65594i | ||||
\(447\) | −7.31125 | −0.345810 | ||||||||
\(448\) | 33.8136 | + | 3.49982i | 1.59754 | + | 0.165351i | ||||
\(449\) | 8.05285 | 0.380038 | 0.190019 | − | 0.981780i | \(-0.439145\pi\) | ||||
0.190019 | + | 0.981780i | \(0.439145\pi\) | |||||||
\(450\) | −1.70630 | − | 2.95540i | −0.0804359 | − | 0.139319i | ||||
\(451\) | −24.8901 | + | 43.1110i | −1.17203 | + | 2.03002i | ||||
\(452\) | −8.55300 | + | 14.8142i | −0.402299 | + | 0.696803i | ||||
\(453\) | −22.9562 | − | 39.7612i | −1.07857 | − | 1.86815i | ||||
\(454\) | −22.2963 | −1.04642 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.5595 | −0.822297 | ||||||||
\(457\) | 7.79881 | + | 13.5079i | 0.364813 | + | 0.631875i | 0.988746 | − | 0.149603i | \(-0.0477996\pi\) |
−0.623933 | + | 0.781478i | \(0.714466\pi\) | |||||||
\(458\) | 12.3281 | − | 21.3530i | 0.576056 | − | 0.997759i | ||||
\(459\) | 0.574012 | − | 0.994218i | 0.0267926 | − | 0.0464061i | ||||
\(460\) | −13.7668 | − | 23.8448i | −0.641880 | − | 1.11177i | ||||
\(461\) | 25.6991 | 1.19692 | 0.598462 | − | 0.801151i | \(-0.295779\pi\) | ||||
0.598462 | + | 0.801151i | \(0.295779\pi\) | |||||||
\(462\) | 40.6986 | − | 56.2038i | 1.89347 | − | 2.61484i | ||||
\(463\) | 20.5209 | 0.953685 | 0.476842 | − | 0.878989i | \(-0.341781\pi\) | ||||
0.476842 | + | 0.878989i | \(0.341781\pi\) | |||||||
\(464\) | −4.11476 | − | 7.12698i | −0.191023 | − | 0.330862i | ||||
\(465\) | −9.90440 | + | 17.1549i | −0.459306 | + | 0.795541i | ||||
\(466\) | −18.9054 | + | 32.7452i | −0.875778 | + | 1.51689i | ||||
\(467\) | −5.91241 | − | 10.2406i | −0.273594 | − | 0.473878i | 0.696186 | − | 0.717862i | \(-0.254879\pi\) |
−0.969779 | + | 0.243984i | \(0.921546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.49936 | − | 6.21351i | 0.207761 | − | 0.286913i | ||||
\(470\) | −33.4000 | −1.54063 | ||||||||
\(471\) | 12.1242 | + | 20.9998i | 0.558656 | + | 0.967620i | ||||
\(472\) | −4.76338 | + | 8.25042i | −0.219253 | + | 0.379757i | ||||
\(473\) | 8.15878 | − | 14.1314i | 0.375141 | − | 0.649764i | ||||
\(474\) | −14.1805 | − | 24.5614i | −0.651334 | − | 1.12814i | ||||
\(475\) | −1.76128 | −0.0808133 | ||||||||
\(476\) | −11.8281 | − | 26.4535i | −0.542140 | − | 1.21250i | ||||
\(477\) | −38.6604 | −1.77014 | ||||||||
\(478\) | −7.65967 | − | 13.2669i | −0.350345 | − | 0.606816i | ||||
\(479\) | 11.3276 | − | 19.6200i | 0.517571 | − | 0.896459i | −0.482221 | − | 0.876050i | \(-0.660170\pi\) |
0.999792 | − | 0.0204092i | \(-0.00649690\pi\) | |||||||
\(480\) | −18.5560 | + | 32.1399i | −0.846960 | + | 1.46698i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.3783 | 0.654913 | ||||||||
\(483\) | −29.1372 | − | 3.01580i | −1.32579 | − | 0.137224i | ||||
\(484\) | 34.5945 | 1.57248 | ||||||||
\(485\) | −5.73933 | − | 9.94081i | −0.260610 | − | 0.451389i | ||||
\(486\) | −24.6039 | + | 42.6152i | −1.11606 | + | 1.93306i | ||||
\(487\) | −16.3584 | + | 28.3335i | −0.741268 | + | 1.28391i | 0.210650 | + | 0.977562i | \(0.432442\pi\) |
−0.951918 | + | 0.306353i | \(0.900891\pi\) | |||||||
\(488\) | 3.18984 | + | 5.52497i | 0.144397 | + | 0.250104i | ||||
\(489\) | −34.2317 | −1.54801 | ||||||||
\(490\) | 21.9295 | − | 24.5109i | 0.990675 | − | 1.10729i | ||||
\(491\) | 6.17281 | 0.278575 | 0.139288 | − | 0.990252i | \(-0.455519\pi\) | ||||
0.139288 | + | 0.990252i | \(0.455519\pi\) | |||||||
\(492\) | 37.2803 | + | 64.5713i | 1.68072 | + | 2.91110i | ||||
\(493\) | −11.1479 | + | 19.3088i | −0.502078 | + | 0.869625i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.8731 | + | 27.4931i | 0.713444 | + | 1.23572i | ||||
\(496\) | −5.25919 | −0.236145 | ||||||||
\(497\) | −6.68123 | − | 0.691531i | −0.299694 | − | 0.0310194i | ||||
\(498\) | 18.9895 | 0.850938 | ||||||||
\(499\) | −7.31934 | − | 12.6775i | −0.327659 | − | 0.567521i | 0.654388 | − | 0.756159i | \(-0.272926\pi\) |
−0.982047 | + | 0.188637i | \(0.939593\pi\) | |||||||
\(500\) | 16.9030 | − | 29.2768i | 0.755925 | − | 1.30930i | ||||
\(501\) | 21.4699 | − | 37.1870i | 0.959205 | − | 1.66139i | ||||
\(502\) | −10.9206 | − | 18.9150i | −0.487409 | − | 0.844218i | ||||
\(503\) | 12.7787 | 0.569774 | 0.284887 | − | 0.958561i | \(-0.408044\pi\) | ||||
0.284887 | + | 0.958561i | \(0.408044\pi\) | |||||||
\(504\) | −6.70891 | − | 15.0045i | −0.298839 | − | 0.668352i | ||||
\(505\) | 19.7786 | 0.880136 | ||||||||
\(506\) | −23.7134 | − | 41.0727i | −1.05419 | − | 1.82591i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.2575 | − | 26.4267i | 0.676941 | − | 1.17250i | ||||
\(509\) | 5.84263 | + | 10.1197i | 0.258970 | + | 0.448549i | 0.965966 | − | 0.258668i | \(-0.0832835\pi\) |
−0.706996 | + | 0.707217i | \(0.749950\pi\) | |||||||
\(510\) | 43.9260 | 1.94507 | ||||||||
\(511\) | −11.9495 | + | 16.5020i | −0.528615 | + | 0.730005i | ||||
\(512\) | −15.4017 | −0.680664 | ||||||||
\(513\) | −0.541949 | − | 0.938683i | −0.0239276 | − | 0.0414439i | ||||
\(514\) | 7.59688 | − | 13.1582i | 0.335084 | − | 0.580382i | ||||
\(515\) | −7.75495 | + | 13.4320i | −0.341724 | + | 0.591883i | ||||
\(516\) | −12.2202 | − | 21.1659i | −0.537962 | − | 0.931778i | ||||
\(517\) | −34.0435 | −1.49723 | ||||||||
\(518\) | 19.3215 | − | 26.6825i | 0.848937 | − | 1.17236i | ||||
\(519\) | −7.32772 | −0.321651 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.23838 | + | 7.34108i | −0.185687 | + | 0.321619i | −0.943808 | − | 0.330495i | \(-0.892784\pi\) |
0.758121 | + | 0.652114i | \(0.226118\pi\) | |||||||
\(522\) | −20.3934 | + | 35.3224i | −0.892594 | + | 1.54602i | ||||
\(523\) | −16.3554 | − | 28.3284i | −0.715172 | − | 1.23871i | −0.962893 | − | 0.269883i | \(-0.913015\pi\) |
0.247721 | − | 0.968831i | \(-0.420318\pi\) | |||||||
\(524\) | 15.7233 | 0.686876 | ||||||||
\(525\) | −1.31940 | − | 2.95084i | −0.0575833 | − | 0.128785i | ||||
\(526\) | 0.280097 | 0.0122128 | ||||||||
\(527\) | 7.12425 | + | 12.3396i | 0.310337 | + | 0.537520i | ||||
\(528\) | −8.26284 | + | 14.3117i | −0.359594 | + | 0.622835i | ||||
\(529\) | 1.48975 | − | 2.58032i | 0.0647716 | − | 0.112188i | ||||
\(530\) | −29.0834 | − | 50.3739i | −1.26330 | − | 2.18810i | ||||
\(531\) | −14.9549 | −0.648989 | ||||||||
\(532\) | −27.2135 | − | 2.81669i | −1.17985 | − | 0.122119i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −10.0342 | − | 17.3797i | −0.434222 | − | 0.752095i | ||||
\(535\) | −7.16156 | + | 12.4042i | −0.309621 | + | 0.536280i | ||||
\(536\) | 2.88407 | − | 4.99536i | 0.124573 | − | 0.215767i | ||||
\(537\) | 7.01361 | + | 12.1479i | 0.302660 | + | 0.524222i | ||||
\(538\) | 9.39131 | 0.404888 | ||||||||
\(539\) | 22.3520 | − | 24.9831i | 0.962771 | − | 1.07610i | ||||
\(540\) | 1.86975 | 0.0804610 | ||||||||
\(541\) | −14.0853 | − | 24.3964i | −0.605573 | − | 1.04888i | −0.991961 | − | 0.126547i | \(-0.959611\pi\) |
0.386388 | − | 0.922336i | \(-0.373723\pi\) | |||||||
\(542\) | −1.73440 | + | 3.00406i | −0.0744987 | + | 0.129035i | ||||
\(543\) | −8.87880 | + | 15.3785i | −0.381026 | + | 0.659956i | ||||
\(544\) | 13.3473 | + | 23.1182i | 0.572262 | + | 0.991187i | ||||
\(545\) | −8.86574 | −0.379767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.5377 | −0.792615 | −0.396307 | − | 0.918118i | \(-0.629709\pi\) | ||||
−0.396307 | + | 0.918118i | \(0.629709\pi\) | |||||||
\(548\) | 32.2415 | + | 55.8438i | 1.37729 | + | 2.38553i | ||||
\(549\) | −5.00735 | + | 8.67299i | −0.213709 | + | 0.370154i | ||||
\(550\) | 2.61670 | − | 4.53225i | 0.111576 | − | 0.193256i | ||||
\(551\) | 10.5252 | + | 18.2303i | 0.448391 | + | 0.776635i | ||||
\(552\) | −22.0251 | −0.937449 | ||||||||
\(553\) | −5.59252 | − | 12.5077i | −0.237818 | − | 0.531880i | ||||
\(554\) | 28.2092 | 1.19850 | ||||||||
\(555\) | 14.7751 | + | 25.5912i | 0.627167 | + | 1.08628i | ||||
\(556\) | 5.79759 | − | 10.0417i | 0.245873 | − | 0.425864i | ||||
\(557\) | 2.00142 | − | 3.46655i | 0.0848027 | − | 0.146883i | −0.820504 | − | 0.571640i | \(-0.806307\pi\) |
0.905307 | + | 0.424758i | \(0.139641\pi\) | |||||||
\(558\) | 13.0327 | + | 22.5732i | 0.551717 | + | 0.955602i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.59379 | + | 6.34392i | −0.194123 | + | 0.268079i | ||||
\(561\) | 44.7723 | 1.89029 | ||||||||
\(562\) | −5.12368 | − | 8.87448i | −0.216129 | − | 0.374347i | ||||
\(563\) | 8.93100 | − | 15.4689i | 0.376397 | − | 0.651938i | −0.614138 | − | 0.789199i | \(-0.710496\pi\) |
0.990535 | + | 0.137260i | \(0.0438296\pi\) | |||||||
\(564\) | −25.4951 | + | 44.1587i | −1.07354 | + | 1.85942i | ||||
\(565\) | −6.26338 | − | 10.8485i | −0.263503 | − | 0.456400i | ||||
\(566\) | −8.07490 | −0.339413 | ||||||||
\(567\) | −13.3706 | + | 18.4645i | −0.561514 | + | 0.775437i | ||||
\(568\) | −5.05041 | −0.211910 | ||||||||
\(569\) | 18.7336 | + | 32.4475i | 0.785353 | + | 1.36027i | 0.928788 | + | 0.370612i | \(0.120852\pi\) |
−0.143434 | + | 0.989660i | \(0.545815\pi\) | |||||||
\(570\) | 20.7362 | − | 35.9161i | 0.868544 | − | 1.50436i | ||||
\(571\) | −8.78514 | + | 15.2163i | −0.367646 | + | 0.636782i | −0.989197 | − | 0.146592i | \(-0.953170\pi\) |
0.621551 | + | 0.783374i | \(0.286503\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.4006 | 1.22823 | ||||||||
\(574\) | 24.8465 | + | 55.5691i | 1.03707 | + | 2.31941i | ||||
\(575\) | −2.20920 | −0.0921301 | ||||||||
\(576\) | 20.0618 | + | 34.7481i | 0.835908 | + | 1.44784i | ||||
\(577\) | −17.1247 | + | 29.6608i | −0.712910 | + | 1.23480i | 0.250850 | + | 0.968026i | \(0.419290\pi\) |
−0.963760 | + | 0.266770i | \(0.914043\pi\) | |||||||
\(578\) | −3.01524 | + | 5.22254i | −0.125417 | + | 0.217229i | ||||
\(579\) | 28.4190 | + | 49.2232i | 1.18105 | + | 2.04565i | ||||
\(580\) | −36.3125 | −1.50780 | ||||||||
\(581\) | 9.12490 | + | 0.944459i | 0.378565 | + | 0.0391828i | ||||
\(582\) | −29.6144 | −1.22756 | ||||||||
\(583\) | −29.6438 | − | 51.3445i | −1.22772 | − | 2.12647i | ||||
\(584\) | −7.65959 | + | 13.2668i | −0.316956 | + | 0.548984i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.2859 | + | 40.3323i | 0.961930 | + | 1.66611i | ||||
\(587\) | 29.4494 | 1.21551 | 0.607754 | − | 0.794126i | \(-0.292071\pi\) | ||||
0.607754 | + | 0.794126i | \(0.292071\pi\) | |||||||
\(588\) | −15.6669 | − | 47.7032i | −0.646092 | − | 1.96725i | ||||
\(589\) | 13.4526 | 0.554305 | ||||||||
\(590\) | −11.2503 | − | 19.4861i | −0.463167 | − | 0.802229i | ||||
\(591\) | 20.9356 | − | 36.2616i | 0.861176 | − | 1.49160i | ||||
\(592\) | −3.92275 | + | 6.79439i | −0.161224 | + | 0.279248i | ||||
\(593\) | −17.0001 | − | 29.4450i | −0.698109 | − | 1.20916i | −0.969121 | − | 0.246584i | \(-0.920692\pi\) |
0.271013 | − | 0.962576i | \(-0.412641\pi\) | |||||||
\(594\) | 3.22064 | 0.132145 | ||||||||
\(595\) | 21.1075 | + | 2.18470i | 0.865324 | + | 0.0895640i | ||||
\(596\) | −8.56514 | −0.350842 | ||||||||
\(597\) | −12.4452 | − | 21.5557i | −0.509349 | − | 0.882218i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.7209 | + | 18.5691i | −0.438043 | + | 0.758713i | −0.997539 | − | 0.0701203i | \(-0.977662\pi\) |
0.559495 | + | 0.828834i | \(0.310995\pi\) | |||||||
\(600\) | −1.21520 | − | 2.10479i | −0.0496103 | − | 0.0859276i | ||||
\(601\) | 40.4039 | 1.64811 | 0.824054 | − | 0.566511i | \(-0.191707\pi\) | ||||
0.824054 | + | 0.566511i | \(0.191707\pi\) | |||||||
\(602\) | −8.14447 | − | 18.2151i | −0.331944 | − | 0.742392i | ||||
\(603\) | 9.05472 | 0.368737 | ||||||||
\(604\) | −26.8931 | − | 46.5803i | −1.09427 | − | 1.89533i | ||||
\(605\) | −12.6668 | + | 21.9396i | −0.514980 | + | 0.891971i | ||||
\(606\) | 25.5139 | − | 44.1914i | 1.03643 | − | 1.79515i | ||||
\(607\) | 21.9456 | + | 38.0110i | 0.890746 | + | 1.54282i | 0.838983 | + | 0.544158i | \(0.183151\pi\) |
0.0517636 | + | 0.998659i | \(0.483516\pi\) | |||||||
\(608\) | 25.2036 | 1.02214 | ||||||||
\(609\) | −22.6582 | + | 31.2904i | −0.918156 | + | 1.26795i | ||||
\(610\) | −15.0677 | −0.610074 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 17.1011 | − | 29.6200i | 0.691272 | − | 1.19732i | ||||
\(613\) | −7.15777 | + | 12.3976i | −0.289100 | + | 0.500735i | −0.973595 | − | 0.228282i | \(-0.926689\pi\) |
0.684496 | + | 0.729017i | \(0.260023\pi\) | |||||||
\(614\) | 5.48750 | + | 9.50464i | 0.221458 | + | 0.383576i | ||||
\(615\) | −54.6009 | −2.20172 | ||||||||
\(616\) | 14.7831 | − | 20.4151i | 0.595628 | − | 0.822547i | ||||
\(617\) | 36.9097 | 1.48593 | 0.742965 | − | 0.669330i | \(-0.233419\pi\) | ||||
0.742965 | + | 0.669330i | \(0.233419\pi\) | |||||||
\(618\) | 20.0074 | + | 34.6538i | 0.804815 | + | 1.39398i | ||||
\(619\) | 7.14646 | − | 12.3780i | 0.287240 | − | 0.497515i | −0.685910 | − | 0.727687i | \(-0.740595\pi\) |
0.973150 | + | 0.230172i | \(0.0739288\pi\) | |||||||
\(620\) | −11.6030 | + | 20.0970i | −0.465988 | + | 0.807115i | ||||
\(621\) | −0.679774 | − | 1.17740i | −0.0272784 | − | 0.0472476i | ||||
\(622\) | 5.35973 | 0.214906 | ||||||||
\(623\) | −3.95728 | − | 8.85046i | −0.158545 | − | 0.354586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1438 | + | 19.3016i | 0.445750 | + | 0.772062i | ||||
\(626\) | 15.4496 | − | 26.7594i | 0.617489 | − | 1.06952i | ||||
\(627\) | 21.1357 | − | 36.6082i | 0.844080 | − | 1.46199i | ||||
\(628\) | 14.2036 | + | 24.6013i | 0.566784 | + | 0.981698i | ||||
\(629\) | 21.2554 | 0.847510 | ||||||||
\(630\) | 38.6128 | + | 3.99656i | 1.53837 | + | 0.159227i | ||||
\(631\) | 0.0431064 | 0.00171604 | 0.000858019 | − | 1.00000i | \(-0.499727\pi\) | ||||
0.000858019 | 1.00000i | \(0.499727\pi\) | ||||||||
\(632\) | −5.15084 | − | 8.92152i | −0.204890 | − | 0.354879i | ||||
\(633\) | 30.2633 | − | 52.4176i | 1.20286 | − | 2.08341i | ||||
\(634\) | −3.39592 | + | 5.88190i | −0.134869 | + | 0.233600i | ||||
\(635\) | 11.1731 | + | 19.3524i | 0.443390 | + | 0.767975i | ||||
\(636\) | −88.8004 | −3.52116 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −62.5484 | −2.47632 | ||||||||
\(639\) | −3.96401 | − | 6.86587i | −0.156814 | − | 0.271610i | ||||
\(640\) | −15.1860 | + | 26.3029i | −0.600279 | + | 1.03971i | ||||
\(641\) | −21.3328 | + | 36.9494i | −0.842594 | + | 1.45942i | 0.0451008 | + | 0.998982i | \(0.485639\pi\) |
−0.887695 | + | 0.460433i | \(0.847694\pi\) | |||||||
\(642\) | 18.4765 | + | 32.0022i | 0.729208 | + | 1.26303i | ||||
\(643\) | 5.49737 | 0.216795 | 0.108398 | − | 0.994108i | \(-0.465428\pi\) | ||||
0.108398 | + | 0.994108i | \(0.465428\pi\) | |||||||
\(644\) | −34.1342 | − | 3.53301i | −1.34508 | − | 0.139220i | ||||
\(645\) | 17.8977 | 0.704722 | ||||||||
\(646\) | −14.9156 | − | 25.8345i | −0.586845 | − | 1.01645i | ||||
\(647\) | 19.0933 | − | 33.0706i | 0.750637 | − | 1.30014i | −0.196877 | − | 0.980428i | \(-0.563080\pi\) |
0.947514 | − | 0.319713i | \(-0.103587\pi\) | |||||||
\(648\) | −8.57053 | + | 14.8446i | −0.336682 | + | 0.583150i | ||||
\(649\) | −11.4671 | − | 19.8615i | −0.450121 | − | 0.779633i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0775 | + | 22.5384i | 0.394969 | + | 0.883348i | ||||
\(652\) | −40.1024 | −1.57053 | ||||||||
\(653\) | −19.2510 | − | 33.3437i | −0.753349 | − | 1.30484i | −0.946191 | − | 0.323608i | \(-0.895104\pi\) |
0.192843 | − | 0.981230i | \(-0.438229\pi\) | |||||||
\(654\) | −11.4366 | + | 19.8088i | −0.447206 | + | 0.774584i | ||||
\(655\) | −5.75711 | + | 9.97161i | −0.224949 | + | 0.389623i | ||||
\(656\) | −7.24820 | − | 12.5543i | −0.282995 | − | 0.490161i | ||||
\(657\) | −24.0477 | −0.938192 | ||||||||
\(658\) | −24.4151 | + | 33.7166i | −0.951798 | + | 1.31441i | ||||
\(659\) | 19.4843 | 0.759002 | 0.379501 | − | 0.925191i | \(-0.376096\pi\) | ||||
0.379501 | + | 0.925191i | \(0.376096\pi\) | |||||||
\(660\) | 36.4595 | + | 63.1498i | 1.41919 | + | 2.45810i | ||||
\(661\) | −20.8334 | + | 36.0844i | −0.810324 | + | 1.40352i | 0.102314 | + | 0.994752i | \(0.467375\pi\) |
−0.912638 | + | 0.408770i | \(0.865958\pi\) | |||||||
\(662\) | −15.0564 | + | 26.0784i | −0.585182 | + | 1.01356i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.89760 | 0.267679 | ||||||||
\(665\) | 11.7506 | − | 16.2273i | 0.455668 | − | 0.629266i | ||||
\(666\) | 38.8834 | 1.50670 | ||||||||
\(667\) | 13.2020 | + | 22.8665i | 0.511182 | + | 0.885393i | ||||
\(668\) | 25.1520 | − | 43.5645i | 0.973160 | − | 1.68556i | ||||
\(669\) | −36.2040 | + | 62.7071i | −1.39973 | + | 2.42440i | ||||
\(670\) | 6.81168 | + | 11.7982i | 0.263158 | + | 0.455803i | ||||
\(671\) | −15.3580 | −0.592890 | ||||||||
\(672\) | 18.8803 | + | 42.2258i | 0.728324 | + | 1.62889i | ||||
\(673\) | −14.3157 | −0.551830 | −0.275915 | − | 0.961182i | \(-0.588981\pi\) | ||||
−0.275915 | + | 0.961182i | \(0.588981\pi\) | |||||||
\(674\) | −38.9153 | − | 67.4033i | −1.49896 | − | 2.59628i | ||||
\(675\) | 0.0750110 | − | 0.129923i | 0.00288718 | − | 0.00500073i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.7641 | + | 25.5721i | 0.567429 | + | 0.982815i | 0.996819 | + | 0.0796963i | \(0.0253950\pi\) |
−0.429391 | + | 0.903119i | \(0.641272\pi\) | |||||||
\(678\) | −32.3184 | −1.24118 | ||||||||
\(679\) | −14.2304 | − | 1.47290i | −0.546114 | − | 0.0565247i | ||||
\(680\) | 15.9554 | 0.611860 | ||||||||
\(681\) | −12.4633 | − | 21.5871i | −0.477596 | − | 0.827220i | ||||
\(682\) | −19.9862 | + | 34.6172i | −0.765312 | + | 1.32556i | ||||
\(683\) | 23.5349 | − | 40.7637i | 0.900539 | − | 1.55978i | 0.0737441 | − | 0.997277i | \(-0.476505\pi\) |
0.826795 | − | 0.562503i | \(-0.190161\pi\) | |||||||
\(684\) | −16.1459 | − | 27.9655i | −0.617354 | − | 1.06929i | ||||
\(685\) | −47.2210 | −1.80422 | ||||||||
\(686\) | −8.71296 | − | 40.0546i | −0.332662 | − | 1.52929i | ||||
\(687\) | 27.5650 | 1.05167 | ||||||||
\(688\) | 2.37590 | + | 4.11518i | 0.0905804 | + | 0.156890i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 26.0097 | − | 45.0501i | 0.990172 | − | 1.71503i | ||||
\(691\) | −15.4334 | − | 26.7314i | −0.587113 | − | 1.01691i | −0.994608 | − | 0.103703i | \(-0.966931\pi\) |
0.407495 | − | 0.913207i | \(-0.366402\pi\) | |||||||
\(692\) | −8.58442 | −0.326331 | ||||||||
\(693\) | 39.3568 | + | 4.07356i | 1.49504 | + | 0.154742i | ||||
\(694\) | 12.1091 | 0.459656 | ||||||||
\(695\) | 4.24559 | + | 7.35358i | 0.161044 | + | 0.278937i | ||||
\(696\) | −14.5238 | + | 25.1560i | −0.550524 | + | 0.953535i | ||||
\(697\) | −19.6372 | + | 34.0127i | −0.743813 | + | 1.28832i | ||||
\(698\) | −4.80508 | − | 8.32264i | −0.181875 | − | 0.315017i | ||||
\(699\) | −42.2715 | −1.59885 | ||||||||
\(700\) | −1.54568 | − | 3.45691i | −0.0584211 | − | 0.130659i | ||||
\(701\) | 6.48958 | 0.245108 | 0.122554 | − | 0.992462i | \(-0.460892\pi\) | ||||
0.122554 | + | 0.992462i | \(0.460892\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0341 | − | 17.3795i | 0.378443 | − | 0.655482i | ||||
\(704\) | −30.7657 | + | 53.2878i | −1.15953 | + | 2.00836i | ||||
\(705\) | −18.6701 | − | 32.3376i | −0.703157 | − | 1.21790i | ||||
\(706\) | 61.0860 | 2.29900 | ||||||||
\(707\) | 14.4580 | − | 19.9661i | 0.543747 | − | 0.750902i | ||||
\(708\) | −34.3505 | −1.29097 | ||||||||
\(709\) | −6.68689 | − | 11.5820i | −0.251131 | − | 0.434972i | 0.712706 | − | 0.701463i | \(-0.247469\pi\) |
−0.963838 | + | 0.266490i | \(0.914136\pi\) | |||||||
\(710\) | 5.96409 | − | 10.3301i | 0.223828 | − | 0.387682i | ||||
\(711\) | 8.08569 | − | 14.0048i | 0.303237 | − | 0.525222i | ||||
\(712\) | −3.64475 | − | 6.31290i | −0.136593 | − | 0.236586i | ||||
\(713\) | 16.8738 | 0.631929 | ||||||||
\(714\) | 32.1094 | − | 44.3424i | 1.20167 | − | 1.65947i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.21645 | + | 14.2313i | 0.307063 | + | 0.531849i | ||||
\(717\) | 8.56328 | − | 14.8320i | 0.319802 | − | 0.553913i | ||||
\(718\) | −7.33555 | + | 12.7055i | −0.273760 | + | 0.474167i | ||||
\(719\) | 8.37048 | + | 14.4981i | 0.312166 | + | 0.540688i | 0.978831 | − | 0.204670i | \(-0.0656120\pi\) |
−0.666665 | + | 0.745358i | \(0.732279\pi\) | |||||||
\(720\) | −9.24476 | −0.344532 | ||||||||
\(721\) | 7.89050 | + | 17.6471i | 0.293858 | + | 0.657212i | ||||
\(722\) | 13.8883 | 0.516868 | ||||||||
\(723\) | 8.03725 | + | 13.9209i | 0.298909 | + | 0.517725i | ||||
\(724\) | −10.4015 | + | 18.0160i | −0.386570 | + | 0.669558i | ||||
\(725\) | −1.45680 | + | 2.52325i | −0.0541041 | + | 0.0937110i | ||||
\(726\) | 32.6798 | + | 56.6030i | 1.21286 | + | 2.10074i | ||||
\(727\) | 38.8138 | 1.43952 | 0.719761 | − | 0.694221i | \(-0.244251\pi\) | ||||
0.719761 | + | 0.694221i | \(0.244251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.1632 | −1.08012 | ||||||||
\(730\) | −18.0906 | − | 31.3339i | −0.669564 | − | 1.15972i | ||||
\(731\) | 6.43692 | − | 11.1491i | 0.238078 | − | 0.412364i | ||||
\(732\) | −11.5016 | + | 19.9213i | −0.425110 | + | 0.736312i | ||||
\(733\) | 18.8639 | + | 32.6733i | 0.696756 | + | 1.20682i | 0.969585 | + | 0.244754i | \(0.0787071\pi\) |
−0.272830 | + | 0.962062i | \(0.587960\pi\) | |||||||
\(734\) | −69.0719 | −2.54949 | ||||||||
\(735\) | 35.9895 | + | 7.53074i | 1.32749 | + | 0.277776i | ||||
\(736\) | 31.6132 | 1.16528 | ||||||||
\(737\) | 6.94292 | + | 12.0255i | 0.255746 | + | 0.442965i | ||||
\(738\) | −35.9232 | + | 62.2208i | −1.32235 | + | 2.29038i | ||||
\(739\) | −4.61476 | + | 7.99300i | −0.169757 | + | 0.294027i | −0.938334 | − | 0.345729i | \(-0.887632\pi\) |
0.768578 | + | 0.639757i | \(0.220965\pi\) | |||||||
\(740\) | 17.3090 | + | 29.9801i | 0.636291 | + | 1.10209i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −72.1111 | − | 7.46375i | −2.64728 | − | 0.274003i | ||||
\(743\) | 3.56327 | 0.130724 | 0.0653619 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653619 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(744\) | 9.28164 | + | 16.0763i | 0.340282 | + | 0.589385i | ||||
\(745\) | 3.13614 | − | 5.43195i | 0.114899 | − | 0.199011i | ||||
\(746\) | −17.4571 | + | 30.2366i | −0.639151 | + | 1.10704i | ||||
\(747\) | 5.41386 | + | 9.37707i | 0.198083 | + | 0.343089i | ||||
\(748\) | 52.4508 | 1.91779 | ||||||||
\(749\) | 7.28674 | + | 16.2968i | 0.266252 | + | 0.595472i | ||||
\(750\) | 63.8698 | 2.33220 | ||||||||
\(751\) | −25.6053 | − | 44.3496i | −0.934350 | − | 1.61834i | −0.775789 | − | 0.630992i | \(-0.782648\pi\) |
−0.158561 | − | 0.987349i | \(-0.550685\pi\) | |||||||
\(752\) | 4.95687 | − | 8.58555i | 0.180758 | − | 0.313083i | ||||
\(753\) | 12.2089 | − | 21.1464i | 0.444916 | − | 0.770618i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.3879 | 1.43347 | ||||||||
\(756\) | 1.36677 | − | 1.88747i | 0.0497088 | − | 0.0686466i | ||||
\(757\) | 25.2305 | 0.917019 | 0.458509 | − | 0.888690i | \(-0.348384\pi\) | ||||
0.458509 | + | 0.888690i | \(0.348384\pi\) | |||||||
\(758\) | −35.0272 | − | 60.6688i | −1.27224 | − | 2.20359i | ||||
\(759\) | 26.5108 | − | 45.9181i | 0.962282 | − | 1.66672i | ||||
\(760\) | 7.53207 | − | 13.0459i | 0.273217 | − | 0.473226i | ||||
\(761\) | 1.82372 | + | 3.15878i | 0.0661099 | + | 0.114506i | 0.897186 | − | 0.441653i | \(-0.145608\pi\) |
−0.831076 | + | 0.556159i | \(0.812275\pi\) | |||||||
\(762\) | 57.6520 | 2.08851 | ||||||||
\(763\) | −6.48077 | + | 8.94978i | −0.234620 | + | 0.324004i | ||||
\(764\) | 34.4428 | 1.24610 | ||||||||
\(765\) | 12.5232 | + | 21.6908i | 0.452777 | + | 0.784233i | ||||
\(766\) | −13.7154 | + | 23.7558i | −0.495558 | + | 0.858331i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 7.38609 | + | 12.7931i | 0.266523 | + | 0.461631i | ||||
\(769\) | −21.9882 | −0.792914 | −0.396457 | − | 0.918053i | \(-0.629760\pi\) | ||||
−0.396457 | + | 0.918053i | \(0.629760\pi\) | |||||||
\(770\) | 24.2995 | + | 54.3458i | 0.875693 | + | 1.95849i | ||||
\(771\) | 16.9862 | 0.611742 | ||||||||
\(772\) | 33.2929 | + | 57.6650i | 1.19824 | + | 2.07541i | ||||
\(773\) | 10.9295 | − | 18.9305i | 0.393108 | − | 0.680882i | −0.599750 | − | 0.800187i | \(-0.704733\pi\) |
0.992858 | + | 0.119305i | \(0.0380667\pi\) | |||||||
\(774\) | 11.7753 | − | 20.3954i | 0.423255 | − | 0.733099i | ||||
\(775\) | 0.930986 | + | 1.61252i | 0.0334420 | + | 0.0579233i | ||||
\(776\) | −10.7569 | −0.386151 | ||||||||
\(777\) | 36.6342 | + | 3.79176i | 1.31424 | + | 0.136029i | ||||
\(778\) | 31.1505 | 1.11680 | ||||||||
\(779\) | 18.5404 | + | 32.1128i | 0.664277 | + | 1.15056i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.07900 | − | 10.5291i | 0.217524 | − | 0.376762i | ||||
\(782\) | −18.7088 | − | 32.4046i | −0.669025 | − | 1.15879i | ||||
\(783\) | −1.79303 | −0.0640777 | ||||||||
\(784\) | 3.04603 | + | 9.27468i | 0.108787 | + | 0.331239i | ||||
\(785\) | −20.8026 | −0.742477 | ||||||||
\(786\) | 14.8531 | + | 25.7263i | 0.529791 | + | 0.917625i | ||||
\(787\) | 19.9336 | − | 34.5261i | 0.710557 | − | 1.23072i | −0.254091 | − | 0.967180i | \(-0.581776\pi\) |
0.964648 | − | 0.263541i | \(-0.0848905\pi\) | |||||||
\(788\) | 24.5261 | − | 42.4804i | 0.873706 | − | 1.51330i | ||||
\(789\) | 0.156570 | + | 0.271188i | 0.00557405 | + | 0.00965454i | ||||
\(790\) | 24.3308 | 0.865651 | ||||||||
\(791\) | −15.5298 | − | 1.60739i | −0.552176 | − | 0.0571521i | ||||
\(792\) | 29.7502 | 1.05713 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.71680 | − | 13.3659i | 0.273859 | − | 0.474338i | ||||
\(795\) | 32.5144 | − | 56.3166i | 1.15317 | − | 1.99734i | ||||
\(796\) | −14.5796 | − | 25.2526i | −0.516759 | − | 0.895053i | ||||
\(797\) | −40.1971 | −1.42385 | −0.711927 | − | 0.702253i | \(-0.752178\pi\) | ||||
−0.711927 | + | 0.702253i | \(0.752178\pi\) | |||||||
\(798\) | −21.0986 | − | 47.1871i | −0.746884 | − | 1.67041i | ||||
\(799\) | −26.8589 | −0.950198 | ||||||||
\(800\) | 1.74421 | + | 3.02106i | 0.0616671 | + | 0.106811i | ||||
\(801\) | 5.72146 | − | 9.90986i | 0.202158 | − | 0.350148i | ||||
\(802\) | −3.02873 | + | 5.24592i | −0.106948 | + | 0.185240i | ||||
\(803\) | −18.4392 | − | 31.9376i | −0.650704 | − | 1.12705i | ||||
\(804\) | 20.7981 | 0.733492 | ||||||||
\(805\) | 14.7389 | − | 20.3541i | 0.519478 | − | 0.717387i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.24960 | + | 9.09258i | 0.184795 | + | 0.320074i | ||||
\(808\) | 9.26749 | − | 16.0518i | 0.326029 | − | 0.564699i | ||||
\(809\) | −1.26924 | + | 2.19840i | −0.0446243 | + | 0.0772915i | −0.887475 | − | 0.460856i | \(-0.847542\pi\) |
0.842851 | + | 0.538148i | \(0.180876\pi\) | |||||||
\(810\) | −20.2421 | − | 35.0603i | −0.711235 | − | 1.23189i | ||||
\(811\) | 41.7062 | 1.46450 | 0.732251 | − | 0.681035i | \(-0.238470\pi\) | ||||
0.732251 | + | 0.681035i | \(0.238470\pi\) | |||||||
\(812\) | −26.5441 | + | 36.6567i | −0.931515 | + | 1.28640i | ||||
\(813\) | −3.87801 | −0.136008 | ||||||||
\(814\) | 29.8148 | + | 51.6407i | 1.04501 | + | 1.81001i | ||||
\(815\) | 14.6836 | − | 25.4327i | 0.514343 | − | 0.890868i | ||||
\(816\) | −6.51902 | + | 11.2913i | −0.228211 | + | 0.395274i | ||||
\(817\) | −6.07737 | − | 10.5263i | −0.212620 | − | 0.368269i | ||||
\(818\) | −54.2604 | −1.89717 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −63.9650 | −2.23375 | ||||||||
\(821\) | 15.9652 | + | 27.6525i | 0.557189 | + | 0.965079i | 0.997730 | + | 0.0673467i | \(0.0214534\pi\) |
−0.440541 | + | 0.897733i | \(0.645213\pi\) | |||||||
\(822\) | −60.9140 | + | 105.506i | −2.12462 | + | 3.67995i | ||||
\(823\) | 17.1266 | − | 29.6641i | 0.596995 | − | 1.03402i | −0.396267 | − | 0.918135i | \(-0.629695\pi\) |
0.993262 | − | 0.115890i | \(-0.0369720\pi\) | |||||||
\(824\) | 7.26734 | + | 12.5874i | 0.253170 | + | 0.438503i | ||||
\(825\) | 5.85078 | 0.203698 | ||||||||
\(826\) | −27.8946 | − | 2.88719i | −0.970578 | − | 0.100458i | ||||
\(827\) | −36.9755 | −1.28576 | −0.642882 | − | 0.765965i | \(-0.722261\pi\) | ||||
−0.642882 | + | 0.765965i | \(0.722261\pi\) | |||||||
\(828\) | −20.2520 | − | 35.0775i | −0.703807 | − | 1.21903i | ||||
\(829\) | 9.99473 | − | 17.3114i | 0.347131 | − | 0.601249i | −0.638607 | − | 0.769533i | \(-0.720489\pi\) |
0.985739 | + | 0.168284i | \(0.0538225\pi\) | |||||||
\(830\) | −8.14547 | + | 14.1084i | −0.282733 | + | 0.489708i | ||||
\(831\) | 15.7685 | + | 27.3119i | 0.547005 | + | 0.947440i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.6348 | − | 19.7106i | 0.611009 | − | 0.682932i | ||||
\(834\) | 21.9068 | 0.758571 | ||||||||
\(835\) | 18.4189 | + | 31.9024i | 0.637412 | + | 1.10403i | ||||
\(836\) | 24.7605 | − | 42.8865i | 0.856360 | − | 1.48326i | ||||
\(837\) | −0.572931 | + | 0.992346i | −0.0198034 | + | 0.0343005i | ||||
\(838\) | −3.33384 | − | 5.77438i | −0.115166 | − | 0.199473i | ||||
\(839\) | −12.8147 | −0.442411 | −0.221206 | − | 0.975227i | \(-0.570999\pi\) | ||||
−0.221206 | + | 0.975227i | \(0.570999\pi\) | |||||||
\(840\) | 27.4994 | + | 2.84628i | 0.948819 | + | 0.0982060i | ||||
\(841\) | 5.82265 | 0.200781 | ||||||||
\(842\) | 11.0666 | + | 19.1679i | 0.381381 | + | 0.660571i | ||||
\(843\) | 5.72812 | − | 9.92140i | 0.197287 | − | 0.341711i | ||||
\(844\) | 35.4535 | − | 61.4073i | 1.22036 | − | 2.11373i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −49.1340 | −1.68926 | ||||||||
\(847\) | 12.8882 | + | 28.8245i | 0.442845 | + | 0.990422i | ||||
\(848\) | 17.2650 | 0.592882 | ||||||||
\(849\) | −4.51375 | − | 7.81805i | −0.154912 | − | 0.268315i | ||||
\(850\) | 2.06446 | − | 3.57575i | 0.0708104 | − | 0.122647i | ||||
\(851\) | 12.5859 | − | 21.7994i | 0.431439 | − | 0.747274i | ||||
\(852\) | −9.10508 | − | 15.7705i | −0.311935 | − | 0.540287i | ||||
\(853\) | 30.1839 | 1.03348 | 0.516739 | − | 0.856143i | \(-0.327146\pi\) | ||||
0.516739 | + | 0.856143i | \(0.327146\pi\) | |||||||
\(854\) | −11.0143 | + | 15.2105i | −0.376903 | + | 0.520494i | ||||
\(855\) | 23.6474 | 0.808724 | ||||||||
\(856\) | 6.71127 | + | 11.6243i | 0.229386 | + | 0.397309i | ||||
\(857\) | 26.6164 | − | 46.1009i | 0.909197 | − | 1.57478i | 0.0940154 | − | 0.995571i | \(-0.470030\pi\) |
0.815182 | − | 0.579205i | \(-0.196637\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.13597 | + | 10.6278i | 0.209357 | + | 0.362616i | 0.951512 | − | 0.307611i | \(-0.0995297\pi\) |
−0.742155 | + | 0.670228i | \(0.766196\pi\) | |||||||
\(860\) | 20.9672 | 0.714975 | ||||||||
\(861\) | −39.9127 | + | 55.1185i | −1.36022 | + | 1.87843i | ||||
\(862\) | −41.5977 | −1.41682 | ||||||||
\(863\) | 12.2226 | + | 21.1702i | 0.416064 | + | 0.720643i | 0.995539 | − | 0.0943460i | \(-0.0300760\pi\) |
−0.579476 | + | 0.814989i | \(0.696743\pi\) | |||||||
\(864\) | −1.07339 | + | 1.85917i | −0.0365175 | + | 0.0632501i | ||||
\(865\) | 3.14320 | − | 5.44418i | 0.106872 | − | 0.185108i | ||||
\(866\) | −8.59778 | − | 14.8918i | −0.292164 | − | 0.506043i | ||||
\(867\) | −6.74189 | −0.228967 | ||||||||
\(868\) | 11.8058 | + | 26.4037i | 0.400716 | + | 0.896200i | ||||
\(869\) | 24.7996 | 0.841268 | ||||||||
\(870\) | −34.3027 | − | 59.4141i | −1.16297 | − | 2.01432i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.15415 | + | 7.19519i | −0.140677 | + | 0.243660i | ||||
\(873\) | −8.44300 | − | 14.6237i | −0.285752 | − | 0.494937i | ||||
\(874\) | −35.3276 | −1.19497 | ||||||||
\(875\) | 30.6910 | + | 3.17663i | 1.03755 | + | 0.107390i | ||||
\(876\) | −55.2361 | −1.86625 | ||||||||
\(877\) | −26.4376 | − | 45.7913i | −0.892736 | − | 1.54626i | −0.836582 | − | 0.547842i | \(-0.815450\pi\) |
−0.0561539 | − | 0.998422i | \(-0.517884\pi\) | |||||||
\(878\) | −42.0178 | + | 72.7770i | −1.41803 | + | 2.45611i | ||||
\(879\) | −26.0329 | + | 45.0903i | −0.878068 | + | 1.52086i | ||||
\(880\) | −7.08864 | − | 12.2779i | −0.238958 | − | 0.413887i | ||||
\(881\) | 55.0118 | 1.85339 | 0.926697 | − | 0.375809i | \(-0.122635\pi\) | ||||
0.926697 | + | 0.375809i | \(0.122635\pi\) | |||||||
\(882\) | 32.2600 | − | 36.0574i | 1.08625 | − | 1.21412i | ||||
\(883\) | 44.1730 | 1.48654 | 0.743269 | − | 0.668992i | \(-0.233274\pi\) | ||||
0.743269 | + | 0.668992i | \(0.233274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.5775 | − | 21.7848i | 0.422788 | − | 0.732290i | ||||
\(886\) | 39.4270 | − | 68.2895i | 1.32457 | − | 2.29423i | ||||
\(887\) | 2.54330 | + | 4.40512i | 0.0853955 | + | 0.147909i | 0.905560 | − | 0.424219i | \(-0.139451\pi\) |
−0.820164 | + | 0.572128i | \(0.806118\pi\) | |||||||
\(888\) | 27.6921 | 0.929286 | ||||||||
\(889\) | 27.7032 | + | 2.86738i | 0.929136 | + | 0.0961688i | ||||
\(890\) | 17.2165 | 0.577100 | ||||||||
\(891\) | −20.6321 | − | 35.7359i | −0.691202 | − | 1.19720i | ||||
\(892\) | −42.4130 | + | 73.4614i | −1.42009 | + | 2.45967i | ||||
\(893\) | −12.6793 | + | 21.9612i | −0.424296 | + | 0.734903i | ||||
\(894\) | −8.09108 | − | 14.0142i | −0.270606 | − | 0.468704i | ||||
\(895\) | −12.0339 | −0.402248 | ||||||||
\(896\) | 15.4514 | + | 34.5571i | 0.516196 | + | 1.15447i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.91178 | + | 15.4356i | 0.297390 | + | 0.515094i | ||||
\(899\) | 11.1270 | − | 19.2724i | 0.371105 | − | 0.642772i | ||||
\(900\) | 2.23475 | − | 3.87070i | 0.0744917 | − | 0.129023i | ||||
\(901\) | −23.3876 | − | 40.5086i | −0.779155 | − | 1.34954i | ||||
\(902\) | −110.180 | −3.66859 | ||||||||
\(903\) | 13.0830 | − | 18.0674i | 0.435377 | − | 0.601244i | ||||
\(904\) | −11.7391 | −0.390437 | ||||||||
\(905\) | −7.61706 | − | 13.1931i | −0.253200 | − | 0.438555i | ||||
\(906\) | 50.8094 | − | 88.0044i | 1.68803 | − | 2.92375i | ||||
\(907\) | 9.06264 | − | 15.6969i | 0.300920 | − | 0.521209i | −0.675425 | − | 0.737429i | \(-0.736040\pi\) |
0.976345 | + | 0.216220i | \(0.0693730\pi\) | |||||||
\(908\) | −14.6008 | − | 25.2893i | −0.484544 | − | 0.839255i | ||||
\(909\) | 29.0958 | 0.965048 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.65804 | −0.319985 | −0.159993 | − | 0.987118i | \(-0.551147\pi\) | ||||
−0.159993 | + | 0.987118i | \(0.551147\pi\) | |||||||
\(912\) | 6.15489 | + | 10.6606i | 0.203809 | + | 0.353007i | ||||
\(913\) | −8.30241 | + | 14.3802i | −0.274770 | + | 0.475915i | ||||
\(914\) | −17.2613 | + | 29.8974i | −0.570952 | + | 0.988918i | ||||
\(915\) | −8.42263 | − | 14.5884i | −0.278444 | − | 0.482278i | ||||
\(916\) | 32.2924 | 1.06697 | ||||||||
\(917\) | 5.85774 | + | 13.1008i | 0.193440 | + | 0.432628i | ||||
\(918\) | 2.54095 | 0.0838637 | ||||||||
\(919\) | −23.8801 | − | 41.3616i | −0.787733 | − | 1.36439i | −0.927353 | − | 0.374188i | \(-0.877922\pi\) |
0.139620 | − | 0.990205i | \(-0.455412\pi\) | |||||||
\(920\) | 9.44758 | − | 16.3637i | 0.311477 | − | 0.539495i | ||||
\(921\) | −6.13487 | + | 10.6259i | −0.202151 | + | 0.350135i | ||||
\(922\) | 28.4401 | + | 49.2598i | 0.936626 | + | 1.62228i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 90.4000 | + | 9.35670i | 2.97394 | + | 0.307813i | ||||
\(925\) | 2.77763 | 0.0913279 | ||||||||
\(926\) | 22.7096 | + | 39.3342i | 0.746285 | + | 1.29260i | ||||
\(927\) | −11.4081 | + | 19.7595i | −0.374692 | + | 0.648986i | ||||
\(928\) | 20.8464 | − | 36.1071i | 0.684317 | − | 1.18527i | ||||
\(929\) | 16.9905 | + | 29.4285i | 0.557442 | + | 0.965517i | 0.997709 | + | 0.0676505i | \(0.0215503\pi\) |
−0.440267 | + | 0.897867i | \(0.645116\pi\) | |||||||
\(930\) | −43.8433 | −1.43768 | ||||||||
\(931\) | −7.79153 | − | 23.7239i | −0.255357 | − | 0.777520i | ||||
\(932\) | −49.5210 | −1.62212 | ||||||||
\(933\) | 2.99601 | + | 5.18924i | 0.0980850 | + | 0.169888i | ||||
\(934\) | 13.0861 | − | 22.6657i | 0.428189 | − | 0.741645i | ||||
\(935\) | −19.2049 | + | 33.2639i | −0.628068 | + | 1.08785i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.7948 | −0.810012 | −0.405006 | − | 0.914314i | \(-0.632731\pi\) | ||||
−0.405006 | + | 0.914314i | \(0.632731\pi\) | |||||||
\(938\) | 16.8893 | + | 1.74810i | 0.551454 | + | 0.0570774i | ||||
\(939\) | 34.5443 | 1.12731 | ||||||||
\(940\) | −21.8720 | − | 37.8835i | −0.713387 | − | 1.23562i | ||||
\(941\) | −4.12098 | + | 7.13774i | −0.134340 | + | 0.232684i | −0.925345 | − | 0.379126i | \(-0.876225\pi\) |
0.791005 | + | 0.611810i | \(0.209558\pi\) | |||||||
\(942\) | −26.8349 | + | 46.4793i | −0.874327 | + | 1.51438i | ||||
\(943\) | 23.2554 | + | 40.2796i | 0.757301 | + | 1.31168i | ||||
\(944\) | 6.67859 | 0.217370 | ||||||||
\(945\) | 0.696577 | + | 1.55789i | 0.0226596 | + | 0.0506783i | ||||
\(946\) | 36.1160 | 1.17423 | ||||||||
\(947\) | 9.98643 | + | 17.2970i | 0.324515 | + | 0.562077i | 0.981414 | − | 0.191902i | \(-0.0614655\pi\) |
−0.656899 | + | 0.753979i | \(0.728132\pi\) | |||||||
\(948\) | 18.5723 | − | 32.1682i | 0.603200 | − | 1.04477i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.94914 | − | 3.37602i | −0.0632386 | − | 0.109532i | ||||
\(951\) | −7.59307 | −0.246222 | ||||||||
\(952\) | 11.6632 | − | 16.1066i | 0.378007 | − | 0.522018i | ||||
\(953\) | −21.5341 | −0.697557 | −0.348778 | − | 0.937205i | \(-0.613403\pi\) | ||||
−0.348778 | + | 0.937205i | \(0.613403\pi\) | |||||||
\(954\) | −42.7839 | − | 74.1040i | −1.38518 | − | 2.39920i | ||||
\(955\) | −12.6113 | + | 21.8434i | −0.408091 | + | 0.706835i | ||||
\(956\) | 10.0319 | − | 17.3757i | 0.324455 | − | 0.561972i | ||||
\(957\) | −34.9636 | − | 60.5588i | −1.13021 | − | 1.95759i | ||||
\(958\) | 50.1432 | 1.62005 | ||||||||
\(959\) | −34.5181 | + | 47.6686i | −1.11465 | + | 1.53930i | ||||
\(960\) | −67.4900 | −2.17823 | ||||||||
\(961\) | 8.38917 | + | 14.5305i | 0.270618 | + | 0.468725i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.5352 | + | 18.2475i | −0.339492 | + | 0.588018i | ||||
\(964\) | 9.41564 | + | 16.3084i | 0.303257 | + | 0.525257i | ||||
\(965\) | −48.7610 | −1.56967 | ||||||||
\(966\) | −26.4643 | − | 59.1874i | −0.851476 | − | 1.90432i | ||||
\(967\) | −43.2887 | −1.39207 | −0.696036 | − | 0.718007i | \(-0.745055\pi\) | ||||
−0.696036 | + | 0.718007i | \(0.745055\pi\) | |||||||
\(968\) | 11.8704 | + | 20.5601i | 0.381528 | + | 0.660827i | ||||
\(969\) | 16.6752 | − | 28.8822i | 0.535683 | − | 0.927831i | ||||
\(970\) | 12.7030 | − | 22.0022i | 0.407868 | − | 0.706449i | ||||
\(971\) | 26.3356 | + | 45.6147i | 0.845151 | + | 1.46384i | 0.885490 | + | 0.464658i | \(0.153823\pi\) |
−0.0403390 | + | 0.999186i | \(0.512844\pi\) | |||||||
\(972\) | −64.4476 | −2.06716 | ||||||||
\(973\) | 10.5268 | + | 1.08956i | 0.337473 | + | 0.0349296i | ||||
\(974\) | −72.4127 | −2.32025 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.23619 | − | 3.87319i | 0.0715787 | − | 0.123978i | ||||
\(977\) | 7.70305 | − | 13.3421i | 0.246442 | − | 0.426851i | −0.716094 | − | 0.698004i | \(-0.754072\pi\) |
0.962536 | + | 0.271153i | \(0.0874051\pi\) | |||||||
\(978\) | −37.8829 | − | 65.6151i | −1.21136 | − | 2.09814i | ||||
\(979\) | 17.5483 | 0.560845 | ||||||||
\(980\) | 42.1617 | + | 8.82227i | 1.34681 | + | 0.281817i | ||||
\(981\) | −13.0422 | −0.416405 | ||||||||
\(982\) | 6.83121 | + | 11.8320i | 0.217993 | + | 0.377575i | ||||
\(983\) | 3.79073 | − | 6.56574i | 0.120906 | − | 0.209415i | −0.799219 | − | 0.601039i | \(-0.794754\pi\) |
0.920125 | + | 0.391625i | \(0.128087\pi\) | |||||||
\(984\) | −25.5839 | + | 44.3126i | −0.815584 | + | 1.41263i | ||||
\(985\) | 17.9605 | + | 31.1085i | 0.572270 | + | 0.991201i | ||||
\(986\) | −49.3480 | −1.57156 | ||||||||
\(987\) | −46.2918 | − | 4.79136i | −1.47348 | − | 0.152511i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.62293 | − | 13.2033i | −0.242395 | − | 0.419841i | ||||
\(990\) | −35.1323 | + | 60.8510i | −1.11658 | + | 1.93397i | ||||
\(991\) | 9.50923 | − | 16.4705i | 0.302071 | − | 0.523202i | −0.674534 | − | 0.738244i | \(-0.735655\pi\) |
0.976605 | + | 0.215042i | \(0.0689888\pi\) | |||||||
\(992\) | −13.3222 | − | 23.0747i | −0.422980 | − | 0.732623i | ||||
\(993\) | −33.6651 | −1.06833 | ||||||||
\(994\) | −6.06834 | − | 13.5718i | −0.192476 | − | 0.430472i | ||||
\(995\) | 21.3533 | 0.676946 | ||||||||
\(996\) | 12.4353 | + | 21.5385i | 0.394027 | + | 0.682474i | ||||
\(997\) | −23.0499 | + | 39.9236i | −0.729998 | + | 1.26439i | 0.226885 | + | 0.973922i | \(0.427146\pi\) |
−0.956883 | + | 0.290473i | \(0.906187\pi\) | |||||||
\(998\) | 16.2001 | − | 28.0593i | 0.512804 | − | 0.888202i | ||||
\(999\) | 0.854680 | + | 1.48035i | 0.0270409 | + | 0.0468362i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1183.2.e.f.508.4 | 10 | ||
7.2 | even | 3 | inner | 1183.2.e.f.170.4 | 10 | ||
7.3 | odd | 6 | 8281.2.a.bx.1.2 | 5 | |||
7.4 | even | 3 | 8281.2.a.bw.1.2 | 5 | |||
13.12 | even | 2 | 91.2.e.c.53.2 | ✓ | 10 | ||
39.38 | odd | 2 | 819.2.j.h.235.4 | 10 | |||
52.51 | odd | 2 | 1456.2.r.p.417.5 | 10 | |||
91.12 | odd | 6 | 637.2.e.m.79.2 | 10 | |||
91.25 | even | 6 | 637.2.a.l.1.4 | 5 | |||
91.38 | odd | 6 | 637.2.a.k.1.4 | 5 | |||
91.51 | even | 6 | 91.2.e.c.79.2 | yes | 10 | ||
91.90 | odd | 2 | 637.2.e.m.508.2 | 10 | |||
273.38 | even | 6 | 5733.2.a.bm.1.2 | 5 | |||
273.116 | odd | 6 | 5733.2.a.bl.1.2 | 5 | |||
273.233 | odd | 6 | 819.2.j.h.352.4 | 10 | |||
364.51 | odd | 6 | 1456.2.r.p.625.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.2 | ✓ | 10 | 13.12 | even | 2 | ||
91.2.e.c.79.2 | yes | 10 | 91.51 | even | 6 | ||
637.2.a.k.1.4 | 5 | 91.38 | odd | 6 | |||
637.2.a.l.1.4 | 5 | 91.25 | even | 6 | |||
637.2.e.m.79.2 | 10 | 91.12 | odd | 6 | |||
637.2.e.m.508.2 | 10 | 91.90 | odd | 2 | |||
819.2.j.h.235.4 | 10 | 39.38 | odd | 2 | |||
819.2.j.h.352.4 | 10 | 273.233 | odd | 6 | |||
1183.2.e.f.170.4 | 10 | 7.2 | even | 3 | inner | ||
1183.2.e.f.508.4 | 10 | 1.1 | even | 1 | trivial | ||
1456.2.r.p.417.5 | 10 | 52.51 | odd | 2 | |||
1456.2.r.p.625.5 | 10 | 364.51 | odd | 6 | |||
5733.2.a.bl.1.2 | 5 | 273.116 | odd | 6 | |||
5733.2.a.bm.1.2 | 5 | 273.38 | even | 6 | |||
8281.2.a.bw.1.2 | 5 | 7.4 | even | 3 | |||
8281.2.a.bx.1.2 | 5 | 7.3 | odd | 6 |