Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [430,2,Mod(221,430)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(430, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("430.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 430 = 2 \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 430.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: | \(3.43356728692\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.27870912.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 7x^{4} + 2x^{3} + 38x^{2} - 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 251.3 | ||
Root | \(-1.08870 - 1.88569i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 430.251 |
Dual form | 430.2.e.f.221.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).
\(n\) | \(87\) | \(261\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.58870 | + | 2.75172i | 0.917239 | + | 1.58870i | 0.803589 | + | 0.595184i | \(0.202921\pi\) |
0.113650 | + | 0.993521i | \(0.463746\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 1.58870 | + | 2.75172i | 0.648586 | + | 1.12338i | ||||
\(7\) | 1.00000 | − | 1.73205i | 0.377964 | − | 0.654654i | −0.612801 | − | 0.790237i | \(-0.709957\pi\) |
0.990766 | + | 0.135583i | \(0.0432908\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.54797 | + | 6.14526i | −1.18266 | + | 2.04842i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 2.17741 | 0.656514 | 0.328257 | − | 0.944588i | \(-0.393539\pi\) | ||||
0.328257 | + | 0.944588i | \(0.393539\pi\) | |||||||
\(12\) | 1.58870 | + | 2.75172i | 0.458620 | + | 0.794352i | ||||
\(13\) | −1.45926 | + | 2.52751i | −0.404726 | + | 0.701006i | −0.994290 | − | 0.106716i | \(-0.965967\pi\) |
0.589563 | + | 0.807722i | \(0.299300\pi\) | |||||||
\(14\) | 1.00000 | − | 1.73205i | 0.267261 | − | 0.462910i | ||||
\(15\) | 1.58870 | − | 2.75172i | 0.410202 | − | 0.710490i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.629444 | + | 1.09023i | −0.152662 | + | 0.264419i | −0.932205 | − | 0.361930i | \(-0.882118\pi\) |
0.779543 | + | 0.626349i | \(0.215451\pi\) | |||||||
\(18\) | −3.54797 | + | 6.14526i | −0.836264 | + | 1.44845i | ||||
\(19\) | −2.82982 | − | 4.90139i | −0.649205 | − | 1.12446i | −0.983313 | − | 0.181921i | \(-0.941769\pi\) |
0.334108 | − | 0.942535i | \(-0.391565\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 6.35482 | 1.38674 | ||||||||
\(22\) | 2.17741 | 0.464225 | ||||||||
\(23\) | −1.17741 | − | 2.03933i | −0.245507 | − | 0.425230i | 0.716767 | − | 0.697313i | \(-0.245621\pi\) |
−0.962274 | + | 0.272082i | \(0.912288\pi\) | |||||||
\(24\) | 1.58870 | + | 2.75172i | 0.324293 | + | 0.561692i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −1.45926 | + | 2.52751i | −0.286185 | + | 0.495686i | ||||
\(27\) | −13.0145 | −2.50463 | ||||||||
\(28\) | 1.00000 | − | 1.73205i | 0.188982 | − | 0.327327i | ||||
\(29\) | 3.32982 | − | 5.76741i | 0.618332 | − | 1.07098i | −0.371459 | − | 0.928450i | \(-0.621142\pi\) |
0.989790 | − | 0.142532i | \(-0.0455245\pi\) | |||||||
\(30\) | 1.58870 | − | 2.75172i | 0.290056 | − | 0.502393i | ||||
\(31\) | 0.459261 | + | 0.795464i | 0.0824858 | + | 0.142870i | 0.904317 | − | 0.426861i | \(-0.140381\pi\) |
−0.821831 | + | 0.569731i | \(0.807047\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.45926 | + | 5.99162i | 0.602180 | + | 1.04301i | ||||
\(34\) | −0.629444 | + | 1.09023i | −0.107949 | + | 0.186973i | ||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | −3.54797 | + | 6.14526i | −0.591328 | + | 1.02421i | ||||
\(37\) | −2.71815 | − | 4.70797i | −0.446861 | − | 0.773986i | 0.551319 | − | 0.834295i | \(-0.314125\pi\) |
−0.998180 | + | 0.0603089i | \(0.980791\pi\) | |||||||
\(38\) | −2.82982 | − | 4.90139i | −0.459057 | − | 0.795110i | ||||
\(39\) | −9.27334 | −1.48492 | ||||||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −11.7096 | −1.82874 | −0.914369 | − | 0.404882i | \(-0.867313\pi\) | ||||
−0.914369 | + | 0.404882i | \(0.867313\pi\) | |||||||
\(42\) | 6.35482 | 0.980570 | ||||||||
\(43\) | 5.31408 | + | 3.84195i | 0.810390 | + | 0.585891i | ||||
\(44\) | 2.17741 | 0.328257 | ||||||||
\(45\) | 7.09593 | 1.05780 | ||||||||
\(46\) | −1.17741 | − | 2.03933i | −0.173600 | − | 0.300683i | ||||
\(47\) | 1.74111 | 0.253967 | 0.126984 | − | 0.991905i | \(-0.459470\pi\) | ||||
0.126984 | + | 0.991905i | \(0.459470\pi\) | |||||||
\(48\) | 1.58870 | + | 2.75172i | 0.229310 | + | 0.397176i | ||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −1.45926 | + | 2.52751i | −0.202363 | + | 0.350503i | ||||
\(53\) | 1.74111 | + | 3.01570i | 0.239160 | + | 0.414238i | 0.960474 | − | 0.278371i | \(-0.0897945\pi\) |
−0.721313 | + | 0.692609i | \(0.756461\pi\) | |||||||
\(54\) | −13.0145 | −1.77104 | ||||||||
\(55\) | −1.08870 | − | 1.88569i | −0.146801 | − | 0.254267i | ||||
\(56\) | 1.00000 | − | 1.73205i | 0.133631 | − | 0.231455i | ||||
\(57\) | 8.99149 | − | 15.5737i | 1.19095 | − | 2.06279i | ||||
\(58\) | 3.32982 | − | 5.76741i | 0.437226 | − | 0.757298i | ||||
\(59\) | −9.45075 | −1.23038 | −0.615192 | − | 0.788378i | \(-0.710921\pi\) | ||||
−0.615192 | + | 0.788378i | \(0.710921\pi\) | |||||||
\(60\) | 1.58870 | − | 2.75172i | 0.205101 | − | 0.355245i | ||||
\(61\) | 7.27334 | − | 12.5978i | 0.931256 | − | 1.61298i | 0.150078 | − | 0.988674i | \(-0.452047\pi\) |
0.781178 | − | 0.624309i | \(-0.214619\pi\) | |||||||
\(62\) | 0.459261 | + | 0.795464i | 0.0583262 | + | 0.101024i | ||||
\(63\) | 7.09593 | + | 12.2905i | 0.894003 | + | 1.54846i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.91852 | 0.361998 | ||||||||
\(66\) | 3.45926 | + | 5.99162i | 0.425806 | + | 0.737517i | ||||
\(67\) | 5.87778 | + | 10.1806i | 0.718086 | + | 1.24376i | 0.961757 | + | 0.273903i | \(0.0883147\pi\) |
−0.243672 | + | 0.969858i | \(0.578352\pi\) | |||||||
\(68\) | −0.629444 | + | 1.09023i | −0.0763312 | + | 0.132210i | ||||
\(69\) | 3.74111 | − | 6.47980i | 0.450377 | − | 0.780076i | ||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | 4.63667 | − | 8.03095i | 0.550272 | − | 0.953098i | −0.447983 | − | 0.894042i | \(-0.647858\pi\) |
0.998255 | − | 0.0590563i | \(-0.0188092\pi\) | |||||||
\(72\) | −3.54797 | + | 6.14526i | −0.418132 | + | 0.724226i | ||||
\(73\) | 7.26611 | − | 12.5853i | 0.850434 | − | 1.47300i | −0.0303824 | − | 0.999538i | \(-0.509673\pi\) |
0.880817 | − | 0.473457i | \(-0.156994\pi\) | |||||||
\(74\) | −2.71815 | − | 4.70797i | −0.315978 | − | 0.547291i | ||||
\(75\) | −3.17741 | −0.366896 | ||||||||
\(76\) | −2.82982 | − | 4.90139i | −0.324602 | − | 0.562228i | ||||
\(77\) | 2.17741 | − | 3.77138i | 0.248139 | − | 0.429789i | ||||
\(78\) | −9.27334 | −1.05000 | ||||||||
\(79\) | −4.35482 | + | 7.54277i | −0.489955 | + | 0.848628i | −0.999933 | − | 0.0115599i | \(-0.996320\pi\) |
0.509978 | + | 0.860188i | \(0.329654\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −10.0322 | − | 17.3763i | −1.11469 | − | 1.93070i | ||||
\(82\) | −11.7096 | −1.29311 | ||||||||
\(83\) | −2.50723 | − | 4.34265i | −0.275204 | − | 0.476667i | 0.694983 | − | 0.719027i | \(-0.255412\pi\) |
−0.970187 | + | 0.242359i | \(0.922079\pi\) | |||||||
\(84\) | 6.35482 | 0.693368 | ||||||||
\(85\) | 1.25889 | 0.136545 | ||||||||
\(86\) | 5.31408 | + | 3.84195i | 0.573032 | + | 0.414288i | ||||
\(87\) | 21.1604 | 2.26863 | ||||||||
\(88\) | 2.17741 | 0.232113 | ||||||||
\(89\) | 0.758887 | + | 1.31443i | 0.0804419 | + | 0.139329i | 0.903440 | − | 0.428715i | \(-0.141034\pi\) |
−0.822998 | + | 0.568044i | \(0.807700\pi\) | |||||||
\(90\) | 7.09593 | 0.747977 | ||||||||
\(91\) | 2.91852 | + | 5.05503i | 0.305944 | + | 0.529911i | ||||
\(92\) | −1.17741 | − | 2.03933i | −0.122753 | − | 0.212615i | ||||
\(93\) | −1.45926 | + | 2.52751i | −0.151318 | + | 0.262091i | ||||
\(94\) | 1.74111 | 0.179582 | ||||||||
\(95\) | −2.82982 | + | 4.90139i | −0.290333 | + | 0.502872i | ||||
\(96\) | 1.58870 | + | 2.75172i | 0.162147 | + | 0.280846i | ||||
\(97\) | 12.9330 | 1.31314 | 0.656572 | − | 0.754263i | \(-0.272006\pi\) | ||||
0.656572 | + | 0.754263i | \(0.272006\pi\) | |||||||
\(98\) | 1.50000 | + | 2.59808i | 0.151523 | + | 0.262445i | ||||
\(99\) | −7.72538 | + | 13.3807i | −0.776429 | + | 1.34482i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −7.94352 | + | 13.7586i | −0.790410 | + | 1.36903i | 0.135303 | + | 0.990804i | \(0.456799\pi\) |
−0.925713 | + | 0.378226i | \(0.876534\pi\) | |||||||
\(102\) | −4.00000 | −0.396059 | ||||||||
\(103\) | −4.30685 | + | 7.45969i | −0.424367 | + | 0.735025i | −0.996361 | − | 0.0852327i | \(-0.972837\pi\) |
0.571994 | + | 0.820258i | \(0.306170\pi\) | |||||||
\(104\) | −1.45926 | + | 2.52751i | −0.143092 | + | 0.247843i | ||||
\(105\) | −3.17741 | − | 5.50344i | −0.310083 | − | 0.537080i | ||||
\(106\) | 1.74111 | + | 3.01570i | 0.169112 | + | 0.292910i | ||||
\(107\) | −2.27334 | −0.219772 | −0.109886 | − | 0.993944i | \(-0.535049\pi\) | ||||
−0.109886 | + | 0.993944i | \(0.535049\pi\) | |||||||
\(108\) | −13.0145 | −1.25232 | ||||||||
\(109\) | 4.15241 | + | 7.19218i | 0.397729 | + | 0.688886i | 0.993445 | − | 0.114309i | \(-0.0364652\pi\) |
−0.595717 | + | 0.803195i | \(0.703132\pi\) | |||||||
\(110\) | −1.08870 | − | 1.88569i | −0.103804 | − | 0.179794i | ||||
\(111\) | 8.63667 | − | 14.9592i | 0.819757 | − | 1.41986i | ||||
\(112\) | 1.00000 | − | 1.73205i | 0.0944911 | − | 0.163663i | ||||
\(113\) | −11.0500 | −1.03950 | −0.519748 | − | 0.854319i | \(-0.673974\pi\) | ||||
−0.519748 | + | 0.854319i | \(0.673974\pi\) | |||||||
\(114\) | 8.99149 | − | 15.5737i | 0.842130 | − | 1.45861i | ||||
\(115\) | −1.17741 | + | 2.03933i | −0.109794 | + | 0.190169i | ||||
\(116\) | 3.32982 | − | 5.76741i | 0.309166 | − | 0.535491i | ||||
\(117\) | −10.3548 | − | 17.9351i | −0.957303 | − | 1.65810i | ||||
\(118\) | −9.45075 | −0.870012 | ||||||||
\(119\) | 1.25889 | + | 2.18046i | 0.115402 | + | 0.199882i | ||||
\(120\) | 1.58870 | − | 2.75172i | 0.145028 | − | 0.251196i | ||||
\(121\) | −6.25889 | −0.568990 | ||||||||
\(122\) | 7.27334 | − | 12.5978i | 0.658497 | − | 1.14055i | ||||
\(123\) | −18.6032 | − | 32.2216i | −1.67739 | − | 2.90533i | ||||
\(124\) | 0.459261 | + | 0.795464i | 0.0412429 | + | 0.0714348i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.09593 | + | 12.2905i | 0.632156 | + | 1.09493i | ||||
\(127\) | 10.9685 | 0.973299 | 0.486650 | − | 0.873597i | \(-0.338219\pi\) | ||||
0.486650 | + | 0.873597i | \(0.338219\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.12944 | + | 20.7266i | −0.187487 | + | 1.82487i | ||||
\(130\) | 2.91852 | 0.255971 | ||||||||
\(131\) | −8.22334 | −0.718476 | −0.359238 | − | 0.933246i | \(-0.616963\pi\) | ||||
−0.359238 | + | 0.933246i | \(0.616963\pi\) | |||||||
\(132\) | 3.45926 | + | 5.99162i | 0.301090 | + | 0.521503i | ||||
\(133\) | −11.3193 | −0.981505 | ||||||||
\(134\) | 5.87778 | + | 10.1806i | 0.507763 | + | 0.879472i | ||||
\(135\) | 6.50723 | + | 11.2708i | 0.560053 | + | 0.970040i | ||||
\(136\) | −0.629444 | + | 1.09023i | −0.0539743 | + | 0.0934863i | ||||
\(137\) | −11.0815 | −0.946755 | −0.473377 | − | 0.880860i | \(-0.656965\pi\) | ||||
−0.473377 | + | 0.880860i | \(0.656965\pi\) | |||||||
\(138\) | 3.74111 | − | 6.47980i | 0.318465 | − | 0.551597i | ||||
\(139\) | −8.20760 | − | 14.2160i | −0.696160 | − | 1.20578i | −0.969788 | − | 0.243948i | \(-0.921557\pi\) |
0.273629 | − | 0.961835i | \(-0.411776\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | 2.76611 | + | 4.79105i | 0.232949 | + | 0.403479i | ||||
\(142\) | 4.63667 | − | 8.03095i | 0.389101 | − | 0.673942i | ||||
\(143\) | −3.17741 | + | 5.50344i | −0.265708 | + | 0.460220i | ||||
\(144\) | −3.54797 | + | 6.14526i | −0.295664 | + | 0.512105i | ||||
\(145\) | −6.65964 | −0.553053 | ||||||||
\(146\) | 7.26611 | − | 12.5853i | 0.601348 | − | 1.04157i | ||||
\(147\) | −4.76611 | + | 8.25515i | −0.393103 | + | 0.680874i | ||||
\(148\) | −2.71815 | − | 4.70797i | −0.223430 | − | 0.386993i | ||||
\(149\) | 11.0250 | + | 19.0959i | 0.903203 | + | 1.56439i | 0.823311 | + | 0.567591i | \(0.192124\pi\) |
0.0798923 | + | 0.996803i | \(0.474542\pi\) | |||||||
\(150\) | −3.17741 | −0.259434 | ||||||||
\(151\) | −9.88297 | −0.804265 | −0.402133 | − | 0.915581i | \(-0.631731\pi\) | ||||
−0.402133 | + | 0.915581i | \(0.631731\pi\) | |||||||
\(152\) | −2.82982 | − | 4.90139i | −0.229529 | − | 0.397555i | ||||
\(153\) | −4.46649 | − | 7.73619i | −0.361094 | − | 0.625434i | ||||
\(154\) | 2.17741 | − | 3.77138i | 0.175461 | − | 0.303907i | ||||
\(155\) | 0.459261 | − | 0.795464i | 0.0368888 | − | 0.0638932i | ||||
\(156\) | −9.27334 | −0.742462 | ||||||||
\(157\) | 0.718148 | − | 1.24387i | 0.0573145 | − | 0.0992716i | −0.835945 | − | 0.548814i | \(-0.815080\pi\) |
0.893259 | + | 0.449542i | \(0.148413\pi\) | |||||||
\(158\) | −4.35482 | + | 7.54277i | −0.346451 | + | 0.600070i | ||||
\(159\) | −5.53223 | + | 9.58210i | −0.438734 | + | 0.759910i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −4.70964 | −0.371172 | ||||||||
\(162\) | −10.0322 | − | 17.3763i | −0.788206 | − | 1.36521i | ||||
\(163\) | −12.1511 | + | 21.0464i | −0.951750 | + | 1.64848i | −0.210113 | + | 0.977677i | \(0.567383\pi\) |
−0.741637 | + | 0.670802i | \(0.765950\pi\) | |||||||
\(164\) | −11.7096 | −0.914369 | ||||||||
\(165\) | 3.45926 | − | 5.99162i | 0.269303 | − | 0.466447i | ||||
\(166\) | −2.50723 | − | 4.34265i | −0.194599 | − | 0.337055i | ||||
\(167\) | 0.789079 | + | 1.36673i | 0.0610608 | + | 0.105760i | 0.894940 | − | 0.446187i | \(-0.147218\pi\) |
−0.833879 | + | 0.551947i | \(0.813885\pi\) | |||||||
\(168\) | 6.35482 | 0.490285 | ||||||||
\(169\) | 2.24111 | + | 3.88172i | 0.172393 | + | 0.298594i | ||||
\(170\) | 1.25889 | 0.0965522 | ||||||||
\(171\) | 40.1604 | 3.07114 | ||||||||
\(172\) | 5.31408 | + | 3.84195i | 0.405195 | + | 0.292946i | ||||
\(173\) | −12.0000 | −0.912343 | −0.456172 | − | 0.889892i | \(-0.650780\pi\) | ||||
−0.456172 | + | 0.889892i | \(0.650780\pi\) | |||||||
\(174\) | 21.1604 | 1.60417 | ||||||||
\(175\) | 1.00000 | + | 1.73205i | 0.0755929 | + | 0.130931i | ||||
\(176\) | 2.17741 | 0.164128 | ||||||||
\(177\) | −15.0145 | − | 26.0058i | −1.12856 | − | 1.95472i | ||||
\(178\) | 0.758887 | + | 1.31443i | 0.0568810 | + | 0.0985208i | ||||
\(179\) | −4.64390 | + | 8.04347i | −0.347101 | + | 0.601197i | −0.985733 | − | 0.168315i | \(-0.946167\pi\) |
0.638632 | + | 0.769512i | \(0.279501\pi\) | |||||||
\(180\) | 7.09593 | 0.528900 | ||||||||
\(181\) | 5.91852 | − | 10.2512i | 0.439920 | − | 0.761964i | −0.557763 | − | 0.830001i | \(-0.688340\pi\) |
0.997683 | + | 0.0680362i | \(0.0216733\pi\) | |||||||
\(182\) | 2.91852 | + | 5.05503i | 0.216335 | + | 0.374704i | ||||
\(183\) | 46.2208 | 3.41674 | ||||||||
\(184\) | −1.17741 | − | 2.03933i | −0.0867998 | − | 0.150342i | ||||
\(185\) | −2.71815 | + | 4.70797i | −0.199842 | + | 0.346137i | ||||
\(186\) | −1.45926 | + | 2.52751i | −0.106998 | + | 0.185326i | ||||
\(187\) | −1.37056 | + | 2.37387i | −0.100225 | + | 0.173595i | ||||
\(188\) | 1.74111 | 0.126984 | ||||||||
\(189\) | −13.0145 | + | 22.5417i | −0.946662 | + | 1.63967i | ||||
\(190\) | −2.82982 | + | 4.90139i | −0.205297 | + | 0.355584i | ||||
\(191\) | 2.91852 | + | 5.05503i | 0.211177 | + | 0.365769i | 0.952083 | − | 0.305839i | \(-0.0989371\pi\) |
−0.740906 | + | 0.671608i | \(0.765604\pi\) | |||||||
\(192\) | 1.58870 | + | 2.75172i | 0.114655 | + | 0.198588i | ||||
\(193\) | 12.0289 | 0.865860 | 0.432930 | − | 0.901428i | \(-0.357480\pi\) | ||||
0.432930 | + | 0.901428i | \(0.357480\pi\) | |||||||
\(194\) | 12.9330 | 0.928534 | ||||||||
\(195\) | 4.63667 | + | 8.03095i | 0.332039 | + | 0.575108i | ||||
\(196\) | 1.50000 | + | 2.59808i | 0.107143 | + | 0.185577i | ||||
\(197\) | 6.25889 | − | 10.8407i | 0.445927 | − | 0.772369i | −0.552189 | − | 0.833719i | \(-0.686207\pi\) |
0.998116 | + | 0.0613503i | \(0.0195407\pi\) | |||||||
\(198\) | −7.72538 | + | 13.3807i | −0.549019 | + | 0.950928i | ||||
\(199\) | −3.27334 | −0.232041 | −0.116021 | − | 0.993247i | \(-0.537014\pi\) | ||||
−0.116021 | + | 0.993247i | \(0.537014\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −18.6761 | + | 32.3480i | −1.31731 | + | 2.28165i | ||||
\(202\) | −7.94352 | + | 13.7586i | −0.558904 | + | 0.968051i | ||||
\(203\) | −6.65964 | − | 11.5348i | −0.467415 | − | 0.809586i | ||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 5.85482 | + | 10.1408i | 0.408918 | + | 0.708267i | ||||
\(206\) | −4.30685 | + | 7.45969i | −0.300073 | + | 0.519741i | ||||
\(207\) | 16.7096 | 1.16140 | ||||||||
\(208\) | −1.45926 | + | 2.52751i | −0.101182 | + | 0.175252i | ||||
\(209\) | −6.16167 | − | 10.6723i | −0.426212 | − | 0.738221i | ||||
\(210\) | −3.17741 | − | 5.50344i | −0.219262 | − | 0.379773i | ||||
\(211\) | −21.7911 | −1.50016 | −0.750081 | − | 0.661346i | \(-0.769986\pi\) | ||||
−0.750081 | + | 0.661346i | \(0.769986\pi\) | |||||||
\(212\) | 1.74111 | + | 3.01570i | 0.119580 | + | 0.207119i | ||||
\(213\) | 29.4652 | 2.01892 | ||||||||
\(214\) | −2.27334 | −0.155402 | ||||||||
\(215\) | 0.670182 | − | 6.52310i | 0.0457060 | − | 0.444872i | ||||
\(216\) | −13.0145 | −0.885521 | ||||||||
\(217\) | 1.83705 | 0.124707 | ||||||||
\(218\) | 4.15241 | + | 7.19218i | 0.281237 | + | 0.487116i | ||||
\(219\) | 46.1748 | 3.12021 | ||||||||
\(220\) | −1.08870 | − | 1.88569i | −0.0734005 | − | 0.127133i | ||||
\(221\) | −1.83705 | − | 3.18186i | −0.123573 | − | 0.214035i | ||||
\(222\) | 8.63667 | − | 14.9592i | 0.579655 | − | 1.00399i | ||||
\(223\) | 25.3233 | 1.69578 | 0.847888 | − | 0.530175i | \(-0.177874\pi\) | ||||
0.847888 | + | 0.530175i | \(0.177874\pi\) | |||||||
\(224\) | 1.00000 | − | 1.73205i | 0.0668153 | − | 0.115728i | ||||
\(225\) | −3.54797 | − | 6.14526i | −0.236531 | − | 0.409684i | ||||
\(226\) | −11.0500 | −0.735035 | ||||||||
\(227\) | 3.60444 | + | 6.24308i | 0.239235 | + | 0.414368i | 0.960495 | − | 0.278297i | \(-0.0897700\pi\) |
−0.721260 | + | 0.692665i | \(0.756437\pi\) | |||||||
\(228\) | 8.99149 | − | 15.5737i | 0.595476 | − | 1.03139i | ||||
\(229\) | −2.68464 | + | 4.64993i | −0.177406 | + | 0.307276i | −0.940991 | − | 0.338431i | \(-0.890104\pi\) |
0.763585 | + | 0.645707i | \(0.223437\pi\) | |||||||
\(230\) | −1.17741 | + | 2.03933i | −0.0776361 | + | 0.134470i | ||||
\(231\) | 13.8370 | 0.910411 | ||||||||
\(232\) | 3.32982 | − | 5.76741i | 0.218613 | − | 0.378649i | ||||
\(233\) | 9.08020 | − | 15.7274i | 0.594863 | − | 1.03033i | −0.398703 | − | 0.917080i | \(-0.630539\pi\) |
0.993566 | − | 0.113253i | \(-0.0361272\pi\) | |||||||
\(234\) | −10.3548 | − | 17.9351i | −0.676916 | − | 1.17245i | ||||
\(235\) | −0.870556 | − | 1.50785i | −0.0567888 | − | 0.0983612i | ||||
\(236\) | −9.45075 | −0.615192 | ||||||||
\(237\) | −27.6741 | −1.79763 | ||||||||
\(238\) | 1.25889 | + | 2.18046i | 0.0816015 | + | 0.141338i | ||||
\(239\) | 11.4278 | + | 19.7935i | 0.739202 | + | 1.28034i | 0.952855 | + | 0.303426i | \(0.0981305\pi\) |
−0.213653 | + | 0.976910i | \(0.568536\pi\) | |||||||
\(240\) | 1.58870 | − | 2.75172i | 0.102550 | − | 0.177623i | ||||
\(241\) | 1.03351 | − | 1.79009i | 0.0665743 | − | 0.115310i | −0.830817 | − | 0.556546i | \(-0.812126\pi\) |
0.897391 | + | 0.441236i | \(0.145460\pi\) | |||||||
\(242\) | −6.25889 | −0.402336 | ||||||||
\(243\) | 12.3548 | − | 21.3992i | 0.792562 | − | 1.37276i | ||||
\(244\) | 7.27334 | − | 12.5978i | 0.465628 | − | 0.806491i | ||||
\(245\) | 1.50000 | − | 2.59808i | 0.0958315 | − | 0.165985i | ||||
\(246\) | −18.6032 | − | 32.2216i | −1.18609 | − | 2.05438i | ||||
\(247\) | 16.5178 | 1.05100 | ||||||||
\(248\) | 0.459261 | + | 0.795464i | 0.0291631 | + | 0.0505120i | ||||
\(249\) | 7.96649 | − | 13.7984i | 0.504856 | − | 0.874436i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −10.7024 | + | 18.5371i | −0.675530 | + | 1.17005i | 0.300783 | + | 0.953692i | \(0.402752\pi\) |
−0.976314 | + | 0.216360i | \(0.930581\pi\) | |||||||
\(252\) | 7.09593 | + | 12.2905i | 0.447002 | + | 0.774230i | ||||
\(253\) | −2.56370 | − | 4.44046i | −0.161179 | − | 0.279170i | ||||
\(254\) | 10.9685 | 0.688227 | ||||||||
\(255\) | 2.00000 | + | 3.46410i | 0.125245 | + | 0.216930i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.0145 | 0.749441 | 0.374721 | − | 0.927138i | \(-0.377739\pi\) | ||||
0.374721 | + | 0.927138i | \(0.377739\pi\) | |||||||
\(258\) | −2.12944 | + | 20.7266i | −0.132573 | + | 1.29038i | ||||
\(259\) | −10.8726 | −0.675590 | ||||||||
\(260\) | 2.91852 | 0.180999 | ||||||||
\(261\) | 23.6282 | + | 40.9252i | 1.46255 | + | 2.53320i | ||||
\(262\) | −8.22334 | −0.508040 | ||||||||
\(263\) | −12.9206 | − | 22.3791i | −0.796716 | − | 1.37995i | −0.921744 | − | 0.387799i | \(-0.873235\pi\) |
0.125028 | − | 0.992153i | \(-0.460098\pi\) | |||||||
\(264\) | 3.45926 | + | 5.99162i | 0.212903 | + | 0.368758i | ||||
\(265\) | 1.74111 | − | 3.01570i | 0.106956 | − | 0.185253i | ||||
\(266\) | −11.3193 | −0.694029 | ||||||||
\(267\) | −2.41130 | + | 4.17649i | −0.147569 | + | 0.255597i | ||||
\(268\) | 5.87778 | + | 10.1806i | 0.359043 | + | 0.621880i | ||||
\(269\) | −23.8160 | −1.45208 | −0.726042 | − | 0.687650i | \(-0.758642\pi\) | ||||
−0.726042 | + | 0.687650i | \(0.758642\pi\) | |||||||
\(270\) | 6.50723 | + | 11.2708i | 0.396017 | + | 0.685922i | ||||
\(271\) | 1.82259 | − | 3.15682i | 0.110714 | − | 0.191763i | −0.805344 | − | 0.592808i | \(-0.798019\pi\) |
0.916059 | + | 0.401045i | \(0.131353\pi\) | |||||||
\(272\) | −0.629444 | + | 1.09023i | −0.0381656 | + | 0.0661048i | ||||
\(273\) | −9.27334 | + | 16.0619i | −0.561248 | + | 0.972110i | ||||
\(274\) | −11.0815 | −0.669457 | ||||||||
\(275\) | −1.08870 | + | 1.88569i | −0.0656514 | + | 0.113712i | ||||
\(276\) | 3.74111 | − | 6.47980i | 0.225189 | − | 0.390038i | ||||
\(277\) | 8.53223 | + | 14.7783i | 0.512652 | + | 0.887939i | 0.999892 | + | 0.0146714i | \(0.00467021\pi\) |
−0.487240 | + | 0.873268i | \(0.661996\pi\) | |||||||
\(278\) | −8.20760 | − | 14.2160i | −0.492259 | − | 0.852618i | ||||
\(279\) | −6.51777 | −0.390209 | ||||||||
\(280\) | −2.00000 | −0.119523 | ||||||||
\(281\) | −11.8213 | − | 20.4751i | −0.705200 | − | 1.22144i | −0.966619 | − | 0.256217i | \(-0.917524\pi\) |
0.261419 | − | 0.965225i | \(-0.415810\pi\) | |||||||
\(282\) | 2.76611 | + | 4.79105i | 0.164720 | + | 0.285303i | ||||
\(283\) | −5.77130 | + | 9.99619i | −0.343068 | + | 0.594212i | −0.985001 | − | 0.172549i | \(-0.944800\pi\) |
0.641932 | + | 0.766761i | \(0.278133\pi\) | |||||||
\(284\) | 4.63667 | − | 8.03095i | 0.275136 | − | 0.476549i | ||||
\(285\) | −17.9830 | −1.06522 | ||||||||
\(286\) | −3.17741 | + | 5.50344i | −0.187884 | + | 0.325425i | ||||
\(287\) | −11.7096 | + | 20.2817i | −0.691198 | + | 1.19719i | ||||
\(288\) | −3.54797 | + | 6.14526i | −0.209066 | + | 0.362113i | ||||
\(289\) | 7.70760 | + | 13.3500i | 0.453388 | + | 0.785292i | ||||
\(290\) | −6.65964 | −0.391067 | ||||||||
\(291\) | 20.5467 | + | 35.5879i | 1.20447 | + | 2.08620i | ||||
\(292\) | 7.26611 | − | 12.5853i | 0.425217 | − | 0.736498i | ||||
\(293\) | −19.0645 | −1.11376 | −0.556879 | − | 0.830594i | \(-0.688001\pi\) | ||||
−0.556879 | + | 0.830594i | \(0.688001\pi\) | |||||||
\(294\) | −4.76611 | + | 8.25515i | −0.277965 | + | 0.481450i | ||||
\(295\) | 4.72538 | + | 8.18459i | 0.275122 | + | 0.476525i | ||||
\(296\) | −2.71815 | − | 4.70797i | −0.157989 | − | 0.273645i | ||||
\(297\) | −28.3378 | −1.64433 | ||||||||
\(298\) | 11.0250 | + | 19.0959i | 0.638661 | + | 1.10619i | ||||
\(299\) | 6.87259 | 0.397452 | ||||||||
\(300\) | −3.17741 | −0.183448 | ||||||||
\(301\) | 11.9685 | − | 5.36231i | 0.689854 | − | 0.309079i | ||||
\(302\) | −9.88297 | −0.568701 | ||||||||
\(303\) | −50.4797 | −2.89998 | ||||||||
\(304\) | −2.82982 | − | 4.90139i | −0.162301 | − | 0.281114i | ||||
\(305\) | −14.5467 | −0.832941 | ||||||||
\(306\) | −4.46649 | − | 7.73619i | −0.255332 | − | 0.442248i | ||||
\(307\) | 13.9278 | + | 24.1236i | 0.794901 | + | 1.37681i | 0.922902 | + | 0.385035i | \(0.125810\pi\) |
−0.128001 | + | 0.991774i | \(0.540856\pi\) | |||||||
\(308\) | 2.17741 | − | 3.77138i | 0.124069 | − | 0.214895i | ||||
\(309\) | −27.3693 | −1.55698 | ||||||||
\(310\) | 0.459261 | − | 0.795464i | 0.0260843 | − | 0.0451793i | ||||
\(311\) | −6.70964 | − | 11.6214i | −0.380469 | − | 0.658991i | 0.610661 | − | 0.791892i | \(-0.290904\pi\) |
−0.991129 | + | 0.132901i | \(0.957571\pi\) | |||||||
\(312\) | −9.27334 | −0.525000 | ||||||||
\(313\) | 5.07297 | + | 8.78664i | 0.286741 | + | 0.496650i | 0.973030 | − | 0.230679i | \(-0.0740947\pi\) |
−0.686289 | + | 0.727329i | \(0.740761\pi\) | |||||||
\(314\) | 0.718148 | − | 1.24387i | 0.0405275 | − | 0.0701956i | ||||
\(315\) | 7.09593 | − | 12.2905i | 0.399810 | − | 0.692492i | ||||
\(316\) | −4.35482 | + | 7.54277i | −0.244978 | + | 0.424314i | ||||
\(317\) | 14.4007 | 0.808827 | 0.404413 | − | 0.914576i | \(-0.367476\pi\) | ||||
0.404413 | + | 0.914576i | \(0.367476\pi\) | |||||||
\(318\) | −5.53223 | + | 9.58210i | −0.310232 | + | 0.537338i | ||||
\(319\) | 7.25038 | − | 12.5580i | 0.405943 | − | 0.703114i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −3.61167 | − | 6.25559i | −0.201584 | − | 0.349153i | ||||
\(322\) | −4.70964 | −0.262458 | ||||||||
\(323\) | 7.12484 | 0.396437 | ||||||||
\(324\) | −10.0322 | − | 17.3763i | −0.557346 | − | 0.965352i | ||||
\(325\) | −1.45926 | − | 2.52751i | −0.0809453 | − | 0.140201i | ||||
\(326\) | −12.1511 | + | 21.0464i | −0.672989 | + | 1.16565i | ||||
\(327\) | −13.1939 | + | 22.8525i | −0.729624 | + | 1.26375i | ||||
\(328\) | −11.7096 | −0.646557 | ||||||||
\(329\) | 1.74111 | − | 3.01570i | 0.0959907 | − | 0.166261i | ||||
\(330\) | 3.45926 | − | 5.99162i | 0.190426 | − | 0.329828i | ||||
\(331\) | 0.243150 | − | 0.421148i | 0.0133647 | − | 0.0231484i | −0.859266 | − | 0.511530i | \(-0.829079\pi\) |
0.872630 | + | 0.488381i | \(0.162412\pi\) | |||||||
\(332\) | −2.50723 | − | 4.34265i | −0.137602 | − | 0.238334i | ||||
\(333\) | 38.5756 | 2.11393 | ||||||||
\(334\) | 0.789079 | + | 1.36673i | 0.0431765 | + | 0.0747839i | ||||
\(335\) | 5.87778 | − | 10.1806i | 0.321138 | − | 0.556227i | ||||
\(336\) | 6.35482 | 0.346684 | ||||||||
\(337\) | 15.0572 | − | 26.0799i | 0.820220 | − | 1.42066i | −0.0852989 | − | 0.996355i | \(-0.527185\pi\) |
0.905519 | − | 0.424307i | \(-0.139482\pi\) | |||||||
\(338\) | 2.24111 | + | 3.88172i | 0.121900 | + | 0.211138i | ||||
\(339\) | −17.5552 | − | 30.4065i | −0.953467 | − | 1.65145i | ||||
\(340\) | 1.25889 | 0.0682727 | ||||||||
\(341\) | 1.00000 | + | 1.73205i | 0.0541530 | + | 0.0937958i | ||||
\(342\) | 40.1604 | 2.17163 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 5.31408 | + | 3.84195i | 0.286516 | + | 0.207144i | ||||
\(345\) | −7.48223 | −0.402829 | ||||||||
\(346\) | −12.0000 | −0.645124 | ||||||||
\(347\) | 8.87778 | + | 15.3768i | 0.476584 | + | 0.825468i | 0.999640 | − | 0.0268302i | \(-0.00854133\pi\) |
−0.523056 | + | 0.852299i | \(0.675208\pi\) | |||||||
\(348\) | 21.1604 | 1.13432 | ||||||||
\(349\) | −16.4258 | − | 28.4502i | −0.879250 | − | 1.52291i | −0.852165 | − | 0.523273i | \(-0.824711\pi\) |
−0.0270851 | − | 0.999633i | \(-0.508623\pi\) | |||||||
\(350\) | 1.00000 | + | 1.73205i | 0.0534522 | + | 0.0925820i | ||||
\(351\) | 18.9915 | − | 32.8942i | 1.01369 | − | 1.75576i | ||||
\(352\) | 2.17741 | 0.116056 | ||||||||
\(353\) | 6.53946 | − | 11.3267i | 0.348060 | − | 0.602858i | −0.637845 | − | 0.770165i | \(-0.720174\pi\) |
0.985905 | + | 0.167307i | \(0.0535072\pi\) | |||||||
\(354\) | −15.0145 | − | 26.0058i | −0.798009 | − | 1.38219i | ||||
\(355\) | −9.27334 | −0.492178 | ||||||||
\(356\) | 0.758887 | + | 1.31443i | 0.0402209 | + | 0.0696647i | ||||
\(357\) | −4.00000 | + | 6.92820i | −0.211702 | + | 0.366679i | ||||
\(358\) | −4.64390 | + | 8.04347i | −0.245438 | + | 0.425110i | ||||
\(359\) | 2.02296 | − | 3.50388i | 0.106768 | − | 0.184928i | −0.807691 | − | 0.589606i | \(-0.799283\pi\) |
0.914459 | + | 0.404678i | \(0.132616\pi\) | |||||||
\(360\) | 7.09593 | 0.373988 | ||||||||
\(361\) | −6.51574 | + | 11.2856i | −0.342934 | + | 0.593978i | ||||
\(362\) | 5.91852 | − | 10.2512i | 0.311071 | − | 0.538790i | ||||
\(363\) | −9.94352 | − | 17.2227i | −0.521900 | − | 0.903957i | ||||
\(364\) | 2.91852 | + | 5.05503i | 0.152972 | + | 0.264956i | ||||
\(365\) | −14.5322 | −0.760652 | ||||||||
\(366\) | 46.2208 | 2.41600 | ||||||||
\(367\) | 2.38629 | + | 4.13318i | 0.124564 | + | 0.215750i | 0.921562 | − | 0.388231i | \(-0.126914\pi\) |
−0.796999 | + | 0.603981i | \(0.793580\pi\) | |||||||
\(368\) | −1.17741 | − | 2.03933i | −0.0613767 | − | 0.106308i | ||||
\(369\) | 41.5454 | − | 71.9587i | 2.16277 | − | 3.74602i | ||||
\(370\) | −2.71815 | + | 4.70797i | −0.141310 | + | 0.244756i | ||||
\(371\) | 6.96445 | 0.361576 | ||||||||
\(372\) | −1.45926 | + | 2.52751i | −0.0756592 | + | 0.131046i | ||||
\(373\) | −0.223339 | + | 0.386834i | −0.0115640 | + | 0.0200295i | −0.871750 | − | 0.489952i | \(-0.837014\pi\) |
0.860185 | + | 0.509981i | \(0.170348\pi\) | |||||||
\(374\) | −1.37056 | + | 2.37387i | −0.0708698 | + | 0.122750i | ||||
\(375\) | 1.58870 | + | 2.75172i | 0.0820404 | + | 0.142098i | ||||
\(376\) | 1.74111 | 0.0897910 | ||||||||
\(377\) | 9.71815 | + | 16.8323i | 0.500510 | + | 0.866909i | ||||
\(378\) | −13.0145 | + | 22.5417i | −0.669391 | + | 1.15942i | ||||
\(379\) | 13.0789 | 0.671819 | 0.335909 | − | 0.941894i | \(-0.390956\pi\) | ||||
0.335909 | + | 0.941894i | \(0.390956\pi\) | |||||||
\(380\) | −2.82982 | + | 4.90139i | −0.145167 | + | 0.251436i | ||||
\(381\) | 17.4258 | + | 30.1823i | 0.892748 | + | 1.54629i | ||||
\(382\) | 2.91852 | + | 5.05503i | 0.149325 | + | 0.258638i | ||||
\(383\) | −17.6782 | −0.903312 | −0.451656 | − | 0.892192i | \(-0.649167\pi\) | ||||
−0.451656 | + | 0.892192i | \(0.649167\pi\) | |||||||
\(384\) | 1.58870 | + | 2.75172i | 0.0810733 | + | 0.140423i | ||||
\(385\) | −4.35482 | −0.221942 | ||||||||
\(386\) | 12.0289 | 0.612255 | ||||||||
\(387\) | −42.4639 | + | 19.0253i | −2.15856 | + | 0.967110i | ||||
\(388\) | 12.9330 | 0.656572 | ||||||||
\(389\) | 11.1563 | 0.565648 | 0.282824 | − | 0.959172i | \(-0.408729\pi\) | ||||
0.282824 | + | 0.959172i | \(0.408729\pi\) | |||||||
\(390\) | 4.63667 | + | 8.03095i | 0.234787 | + | 0.406663i | ||||
\(391\) | 2.96445 | 0.149919 | ||||||||
\(392\) | 1.50000 | + | 2.59808i | 0.0757614 | + | 0.131223i | ||||
\(393\) | −13.0645 | − | 22.6283i | −0.659015 | − | 1.14145i | ||||
\(394\) | 6.25889 | − | 10.8407i | 0.315318 | − | 0.546147i | ||||
\(395\) | 8.70964 | 0.438229 | ||||||||
\(396\) | −7.72538 | + | 13.3807i | −0.388215 | + | 0.672408i | ||||
\(397\) | −10.4363 | − | 18.0762i | −0.523783 | − | 0.907218i | −0.999617 | − | 0.0276832i | \(-0.991187\pi\) |
0.475834 | − | 0.879535i | \(-0.342146\pi\) | |||||||
\(398\) | −3.27334 | −0.164078 | ||||||||
\(399\) | −17.9830 | − | 31.1474i | −0.900275 | − | 1.55932i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −1.82259 | + | 3.15682i | −0.0910158 | + | 0.157644i | −0.907939 | − | 0.419103i | \(-0.862345\pi\) |
0.816923 | + | 0.576747i | \(0.195678\pi\) | |||||||
\(402\) | −18.6761 | + | 32.3480i | −0.931481 | + | 1.61337i | ||||
\(403\) | −2.68073 | −0.133537 | ||||||||
\(404\) | −7.94352 | + | 13.7586i | −0.395205 | + | 0.684515i | ||||
\(405\) | −10.0322 | + | 17.3763i | −0.498505 | + | 0.863437i | ||||
\(406\) | −6.65964 | − | 11.5348i | −0.330512 | − | 0.572464i | ||||
\(407\) | −5.91852 | − | 10.2512i | −0.293370 | − | 0.508132i | ||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | 37.7675 | 1.86748 | 0.933740 | − | 0.357951i | \(-0.116525\pi\) | ||||
0.933740 | + | 0.357951i | \(0.116525\pi\) | |||||||
\(410\) | 5.85482 | + | 10.1408i | 0.289149 | + | 0.500821i | ||||
\(411\) | −17.6052 | − | 30.4931i | −0.868400 | − | 1.50411i | ||||
\(412\) | −4.30685 | + | 7.45969i | −0.212183 | + | 0.367512i | ||||
\(413\) | −9.45075 | + | 16.3692i | −0.465041 | + | 0.805475i | ||||
\(414\) | 16.7096 | 0.821234 | ||||||||
\(415\) | −2.50723 | + | 4.34265i | −0.123075 | + | 0.213172i | ||||
\(416\) | −1.45926 | + | 2.52751i | −0.0715462 | + | 0.123922i | ||||
\(417\) | 26.0789 | − | 45.1700i | 1.27709 | − | 2.21198i | ||||
\(418\) | −6.16167 | − | 10.6723i | −0.301377 | − | 0.522001i | ||||
\(419\) | −31.9660 | −1.56164 | −0.780820 | − | 0.624756i | \(-0.785198\pi\) | ||||
−0.780820 | + | 0.624756i | \(0.785198\pi\) | |||||||
\(420\) | −3.17741 | − | 5.50344i | −0.155042 | − | 0.268540i | ||||
\(421\) | −2.42575 | + | 4.20152i | −0.118224 | + | 0.204770i | −0.919064 | − | 0.394109i | \(-0.871053\pi\) |
0.800840 | + | 0.598878i | \(0.204387\pi\) | |||||||
\(422\) | −21.7911 | −1.06077 | ||||||||
\(423\) | −6.17741 | + | 10.6996i | −0.300356 | + | 0.520232i | ||||
\(424\) | 1.74111 | + | 3.01570i | 0.0845559 | + | 0.146455i | ||||
\(425\) | −0.629444 | − | 1.09023i | −0.0305325 | − | 0.0528838i | ||||
\(426\) | 29.4652 | 1.42759 | ||||||||
\(427\) | −14.5467 | − | 25.1956i | −0.703963 | − | 1.21930i | ||||
\(428\) | −2.27334 | −0.109886 | ||||||||
\(429\) | −20.1919 | −0.974872 | ||||||||
\(430\) | 0.670182 | − | 6.52310i | 0.0323191 | − | 0.314572i | ||||
\(431\) | −15.2444 | −0.734298 | −0.367149 | − | 0.930162i | \(-0.619666\pi\) | ||||
−0.367149 | + | 0.930162i | \(0.619666\pi\) | |||||||
\(432\) | −13.0145 | −0.626158 | ||||||||
\(433\) | −3.02296 | − | 5.23593i | −0.145274 | − | 0.251623i | 0.784201 | − | 0.620507i | \(-0.213073\pi\) |
−0.929475 | + | 0.368884i | \(0.879740\pi\) | |||||||
\(434\) | 1.83705 | 0.0881810 | ||||||||
\(435\) | −10.5802 | − | 18.3254i | −0.507282 | − | 0.878637i | ||||
\(436\) | 4.15241 | + | 7.19218i | 0.198864 | + | 0.344443i | ||||
\(437\) | −6.66371 | + | 11.5419i | −0.318768 | + | 0.552123i | ||||
\(438\) | 46.1748 | 2.20632 | ||||||||
\(439\) | 9.54668 | − | 16.5353i | 0.455638 | − | 0.789189i | −0.543086 | − | 0.839677i | \(-0.682744\pi\) |
0.998725 | + | 0.0504881i | \(0.0160777\pi\) | |||||||
\(440\) | −1.08870 | − | 1.88569i | −0.0519020 | − | 0.0898968i | ||||
\(441\) | −21.2878 | −1.01370 | ||||||||
\(442\) | −1.83705 | − | 3.18186i | −0.0873793 | − | 0.151345i | ||||
\(443\) | 10.1354 | − | 17.5550i | 0.481547 | − | 0.834064i | −0.518229 | − | 0.855242i | \(-0.673408\pi\) |
0.999776 | + | 0.0211784i | \(0.00674179\pi\) | |||||||
\(444\) | 8.63667 | − | 14.9592i | 0.409878 | − | 0.709930i | ||||
\(445\) | 0.758887 | − | 1.31443i | 0.0359747 | − | 0.0623100i | ||||
\(446\) | 25.3233 | 1.19910 | ||||||||
\(447\) | −35.0309 | + | 60.6754i | −1.65691 | + | 2.86985i | ||||
\(448\) | 1.00000 | − | 1.73205i | 0.0472456 | − | 0.0818317i | ||||
\(449\) | 2.15964 | + | 3.74060i | 0.101920 | + | 0.176530i | 0.912475 | − | 0.409131i | \(-0.134168\pi\) |
−0.810556 | + | 0.585661i | \(0.800835\pi\) | |||||||
\(450\) | −3.54797 | − | 6.14526i | −0.167253 | − | 0.289690i | ||||
\(451\) | −25.4967 | −1.20059 | ||||||||
\(452\) | −11.0500 | −0.519748 | ||||||||
\(453\) | −15.7011 | − | 27.1952i | −0.737703 | − | 1.27774i | ||||
\(454\) | 3.60444 | + | 6.24308i | 0.169165 | + | 0.293002i | ||||
\(455\) | 2.91852 | − | 5.05503i | 0.136822 | − | 0.236983i | ||||
\(456\) | 8.99149 | − | 15.5737i | 0.421065 | − | 0.729306i | ||||
\(457\) | 32.4152 | 1.51632 | 0.758160 | − | 0.652069i | \(-0.226099\pi\) | ||||
0.758160 | + | 0.652069i | \(0.226099\pi\) | |||||||
\(458\) | −2.68464 | + | 4.64993i | −0.125445 | + | 0.217277i | ||||
\(459\) | 8.19186 | − | 14.1887i | 0.382363 | − | 0.662273i | ||||
\(460\) | −1.17741 | + | 2.03933i | −0.0548970 | + | 0.0950844i | ||||
\(461\) | 3.78057 | + | 6.54814i | 0.176079 | + | 0.304977i | 0.940534 | − | 0.339699i | \(-0.110325\pi\) |
−0.764455 | + | 0.644677i | \(0.776992\pi\) | |||||||
\(462\) | 13.8370 | 0.643758 | ||||||||
\(463\) | 4.56574 | + | 7.90809i | 0.212188 | + | 0.367520i | 0.952399 | − | 0.304854i | \(-0.0986078\pi\) |
−0.740211 | + | 0.672375i | \(0.765274\pi\) | |||||||
\(464\) | 3.32982 | − | 5.76741i | 0.154583 | − | 0.267745i | ||||
\(465\) | 2.91852 | 0.135343 | ||||||||
\(466\) | 9.08020 | − | 15.7274i | 0.420632 | − | 0.728556i | ||||
\(467\) | 4.96981 | + | 8.60796i | 0.229975 | + | 0.398329i | 0.957801 | − | 0.287434i | \(-0.0928021\pi\) |
−0.727825 | + | 0.685763i | \(0.759469\pi\) | |||||||
\(468\) | −10.3548 | − | 17.9351i | −0.478652 | − | 0.829049i | ||||
\(469\) | 23.5111 | 1.08564 | ||||||||
\(470\) | −0.870556 | − | 1.50785i | −0.0401558 | − | 0.0695518i | ||||
\(471\) | 4.56370 | 0.210284 | ||||||||
\(472\) | −9.45075 | −0.435006 | ||||||||
\(473\) | 11.5709 | + | 8.36549i | 0.532032 | + | 0.384646i | ||||
\(474\) | −27.6741 | −1.27111 | ||||||||
\(475\) | 5.65964 | 0.259682 | ||||||||
\(476\) | 1.25889 | + | 2.18046i | 0.0577010 | + | 0.0999411i | ||||
\(477\) | −24.7096 | −1.13138 | ||||||||
\(478\) | 11.4278 | + | 19.7935i | 0.522695 | + | 0.905334i | ||||
\(479\) | 16.6741 | + | 28.8804i | 0.761859 | + | 1.31958i | 0.941891 | + | 0.335917i | \(0.109046\pi\) |
−0.180033 | + | 0.983661i | \(0.557620\pi\) | |||||||
\(480\) | 1.58870 | − | 2.75172i | 0.0725141 | − | 0.125598i | ||||
\(481\) | 15.8660 | 0.723425 | ||||||||
\(482\) | 1.03351 | − | 1.79009i | 0.0470751 | − | 0.0815365i | ||||
\(483\) | −7.48223 | − | 12.9596i | −0.340453 | − | 0.589682i | ||||
\(484\) | −6.25889 | −0.284495 | ||||||||
\(485\) | −6.46649 | − | 11.2003i | −0.293628 | − | 0.508579i | ||||
\(486\) | 12.3548 | − | 21.3992i | 0.560426 | − | 0.970686i | ||||
\(487\) | 2.61167 | − | 4.52354i | 0.118346 | − | 0.204981i | −0.800766 | − | 0.598977i | \(-0.795574\pi\) |
0.919112 | + | 0.393996i | \(0.128907\pi\) | |||||||
\(488\) | 7.27334 | − | 12.5978i | 0.329249 | − | 0.570276i | ||||
\(489\) | −77.2182 | −3.49193 | ||||||||
\(490\) | 1.50000 | − | 2.59808i | 0.0677631 | − | 0.117369i | ||||
\(491\) | 5.96130 | − | 10.3253i | 0.269030 | − | 0.465973i | −0.699582 | − | 0.714552i | \(-0.746630\pi\) |
0.968612 | + | 0.248579i | \(0.0799637\pi\) | |||||||
\(492\) | −18.6032 | − | 32.2216i | −0.838695 | − | 1.45266i | ||||
\(493\) | 4.19186 | + | 7.26052i | 0.188792 | + | 0.326997i | ||||
\(494\) | 16.5178 | 0.743170 | ||||||||
\(495\) | 15.4508 | 0.694460 | ||||||||
\(496\) | 0.459261 | + | 0.795464i | 0.0206214 | + | 0.0357174i | ||||
\(497\) | −9.27334 | − | 16.0619i | −0.415966 | − | 0.720475i | ||||
\(498\) | 7.96649 | − | 13.7984i | 0.356987 | − | 0.618319i | ||||
\(499\) | 5.60648 | − | 9.71071i | 0.250980 | − | 0.434711i | −0.712816 | − | 0.701352i | \(-0.752580\pi\) |
0.963796 | + | 0.266641i | \(0.0859137\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −2.50723 | + | 4.34265i | −0.112015 | + | 0.194015i | ||||
\(502\) | −10.7024 | + | 18.5371i | −0.477672 | + | 0.827352i | ||||
\(503\) | −1.43426 | + | 2.48421i | −0.0639505 | + | 0.110765i | −0.896228 | − | 0.443594i | \(-0.853703\pi\) |
0.832277 | + | 0.554359i | \(0.187037\pi\) | |||||||
\(504\) | 7.09593 | + | 12.2905i | 0.316078 | + | 0.547463i | ||||
\(505\) | 15.8870 | 0.706964 | ||||||||
\(506\) | −2.56370 | − | 4.44046i | −0.113971 | − | 0.197403i | ||||
\(507\) | −7.12093 | + | 12.3338i | −0.316252 | + | 0.547764i | ||||
\(508\) | 10.9685 | 0.486650 | ||||||||
\(509\) | −5.42575 | + | 9.39767i | −0.240492 | + | 0.416545i | −0.960855 | − | 0.277053i | \(-0.910642\pi\) |
0.720362 | + | 0.693598i | \(0.243975\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | −14.5322 | − | 25.1706i | −0.642868 | − | 1.11348i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 36.8285 | + | 63.7889i | 1.62602 | + | 2.81635i | ||||
\(514\) | 12.0145 | 0.529935 | ||||||||
\(515\) | 8.61371 | 0.379565 | ||||||||
\(516\) | −2.12944 | + | 20.7266i | −0.0937435 | + | 0.912436i | ||||
\(517\) | 3.79112 | 0.166733 | ||||||||
\(518\) | −10.8726 | −0.477714 | ||||||||
\(519\) | −19.0645 | − | 33.0206i | −0.836837 | − | 1.44944i | ||||
\(520\) | 2.91852 | 0.127986 | ||||||||
\(521\) | −10.2576 | − | 17.7667i | −0.449394 | − | 0.778373i | 0.548953 | − | 0.835853i | \(-0.315027\pi\) |
−0.998347 | + | 0.0574804i | \(0.981693\pi\) | |||||||
\(522\) | 23.6282 | + | 40.9252i | 1.03418 | + | 1.79125i | ||||
\(523\) | −12.1867 | + | 21.1079i | −0.532886 | + | 0.922986i | 0.466376 | + | 0.884586i | \(0.345559\pi\) |
−0.999262 | + | 0.0383994i | \(0.987774\pi\) | |||||||
\(524\) | −8.22334 | −0.359238 | ||||||||
\(525\) | −3.17741 | + | 5.50344i | −0.138674 | + | 0.240190i | ||||
\(526\) | −12.9206 | − | 22.3791i | −0.563363 | − | 0.975774i | ||||
\(527\) | −1.15632 | −0.0503699 | ||||||||
\(528\) | 3.45926 | + | 5.99162i | 0.150545 | + | 0.260752i | ||||
\(529\) | 8.72741 | − | 15.1163i | 0.379453 | − | 0.657231i | ||||
\(530\) | 1.74111 | − | 3.01570i | 0.0756291 | − | 0.130993i | ||||
\(531\) | 33.5309 | − | 58.0773i | 1.45512 | − | 2.52034i | ||||
\(532\) | −11.3193 | −0.490753 | ||||||||
\(533\) | 17.0874 | − | 29.5963i | 0.740138 | − | 1.28196i | ||||
\(534\) | −2.41130 | + | 4.17649i | −0.104347 | + | 0.180734i | ||||
\(535\) | 1.13667 | + | 1.96877i | 0.0491426 | + | 0.0851174i | ||||
\(536\) | 5.87778 | + | 10.1806i | 0.253882 | + | 0.439736i | ||||
\(537\) | −29.5111 | −1.27350 | ||||||||
\(538\) | −23.8160 | −1.02678 | ||||||||
\(539\) | 3.26611 | + | 5.65708i | 0.140682 | + | 0.243668i | ||||
\(540\) | 6.50723 | + | 11.2708i | 0.280026 | + | 0.485020i | ||||
\(541\) | 4.63463 | − | 8.02742i | 0.199258 | − | 0.345126i | −0.749030 | − | 0.662536i | \(-0.769480\pi\) |
0.948288 | + | 0.317411i | \(0.102813\pi\) | |||||||
\(542\) | 1.82259 | − | 3.15682i | 0.0782870 | − | 0.135597i | ||||
\(543\) | 37.6111 | 1.61405 | ||||||||
\(544\) | −0.629444 | + | 1.09023i | −0.0269872 | + | 0.0467431i | ||||
\(545\) | 4.15241 | − | 7.19218i | 0.177870 | − | 0.308079i | ||||
\(546\) | −9.27334 | + | 16.0619i | −0.396862 | + | 0.687386i | ||||
\(547\) | −11.4258 | − | 19.7900i | −0.488530 | − | 0.846158i | 0.511383 | − | 0.859353i | \(-0.329133\pi\) |
−0.999913 | + | 0.0131944i | \(0.995800\pi\) | |||||||
\(548\) | −11.0815 | −0.473377 | ||||||||
\(549\) | 51.6111 | + | 89.3931i | 2.20271 | + | 3.81521i | ||||
\(550\) | −1.08870 | + | 1.88569i | −0.0464225 | + | 0.0804062i | ||||
\(551\) | −37.6911 | −1.60570 | ||||||||
\(552\) | 3.74111 | − | 6.47980i | 0.159232 | − | 0.275799i | ||||
\(553\) | 8.70964 | + | 15.0855i | 0.370372 | + | 0.641502i | ||||
\(554\) | 8.53223 | + | 14.7783i | 0.362500 | + | 0.627868i | ||||
\(555\) | −17.2733 | −0.733213 | ||||||||
\(556\) | −8.20760 | − | 14.2160i | −0.348080 | − | 0.602892i | ||||
\(557\) | 33.5822 | 1.42292 | 0.711462 | − | 0.702724i | \(-0.248033\pi\) | ||||
0.711462 | + | 0.702724i | \(0.248033\pi\) | |||||||
\(558\) | −6.51777 | −0.275919 | ||||||||
\(559\) | −17.4652 | + | 7.82501i | −0.738700 | + | 0.330963i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | −8.70964 | −0.367721 | ||||||||
\(562\) | −11.8213 | − | 20.4751i | −0.498652 | − | 0.863690i | ||||
\(563\) | 19.3693 | 0.816318 | 0.408159 | − | 0.912911i | \(-0.366171\pi\) | ||||
0.408159 | + | 0.912911i | \(0.366171\pi\) | |||||||
\(564\) | 2.76611 | + | 4.79105i | 0.116474 | + | 0.201740i | ||||
\(565\) | 5.52500 | + | 9.56958i | 0.232439 | + | 0.402595i | ||||
\(566\) | −5.77130 | + | 9.99619i | −0.242586 | + | 0.420171i | ||||
\(567\) | −40.1289 | −1.68526 | ||||||||
\(568\) | 4.63667 | − | 8.03095i | 0.194550 | − | 0.336971i | ||||
\(569\) | 7.43298 | + | 12.8743i | 0.311607 | + | 0.539719i | 0.978710 | − | 0.205246i | \(-0.0657996\pi\) |
−0.667104 | + | 0.744965i | \(0.732466\pi\) | |||||||
\(570\) | −17.9830 | −0.753224 | ||||||||
\(571\) | 5.03742 | + | 8.72507i | 0.210809 | + | 0.365133i | 0.951968 | − | 0.306197i | \(-0.0990567\pi\) |
−0.741159 | + | 0.671330i | \(0.765723\pi\) | |||||||
\(572\) | −3.17741 | + | 5.50344i | −0.132854 | + | 0.230110i | ||||
\(573\) | −9.27334 | + | 16.0619i | −0.387399 | + | 0.670995i | ||||
\(574\) | −11.7096 | + | 20.2817i | −0.488751 | + | 0.846541i | ||||
\(575\) | 2.35482 | 0.0982028 | ||||||||
\(576\) | −3.54797 | + | 6.14526i | −0.147832 | + | 0.256052i | ||||
\(577\) | −19.5237 | + | 33.8161i | −0.812783 | + | 1.40778i | 0.0981258 | + | 0.995174i | \(0.468715\pi\) |
−0.910909 | + | 0.412608i | \(0.864618\pi\) | |||||||
\(578\) | 7.70760 | + | 13.3500i | 0.320594 | + | 0.555285i | ||||
\(579\) | 19.1104 | + | 33.1002i | 0.794201 | + | 1.37560i | ||||
\(580\) | −6.65964 | −0.276526 | ||||||||
\(581\) | −10.0289 | −0.416069 | ||||||||
\(582\) | 20.5467 | + | 35.5879i | 0.851687 | + | 1.47517i | ||||
\(583\) | 3.79112 | + | 6.56641i | 0.157012 | + | 0.271953i | ||||
\(584\) | 7.26611 | − | 12.5853i | 0.300674 | − | 0.520783i | ||||
\(585\) | −10.3548 | + | 17.9351i | −0.428119 | + | 0.741524i | ||||
\(586\) | −19.0645 | −0.787546 | ||||||||
\(587\) | 5.04074 | − | 8.73082i | 0.208054 | − | 0.360359i | −0.743048 | − | 0.669238i | \(-0.766621\pi\) |
0.951101 | + | 0.308879i | \(0.0999538\pi\) | |||||||
\(588\) | −4.76611 | + | 8.25515i | −0.196551 | + | 0.340437i | ||||
\(589\) | 2.59925 | − | 4.50204i | 0.107100 | − | 0.185503i | ||||
\(590\) | 4.72538 | + | 8.18459i | 0.194541 | + | 0.336954i | ||||
\(591\) | 39.7741 | 1.63609 | ||||||||
\(592\) | −2.71815 | − | 4.70797i | −0.111715 | − | 0.193496i | ||||
\(593\) | 18.8672 | − | 32.6790i | 0.774785 | − | 1.34197i | −0.160131 | − | 0.987096i | \(-0.551192\pi\) |
0.934915 | − | 0.354870i | \(-0.115475\pi\) | |||||||
\(594\) | −28.3378 | −1.16271 | ||||||||
\(595\) | 1.25889 | − | 2.18046i | 0.0516093 | − | 0.0893900i | ||||
\(596\) | 11.0250 | + | 19.0959i | 0.451602 | + | 0.782197i | ||||
\(597\) | −5.20037 | − | 9.00731i | −0.212837 | − | 0.368645i | ||||
\(598\) | 6.87259 | 0.281041 | ||||||||
\(599\) | −18.2963 | − | 31.6901i | −0.747567 | − | 1.29482i | −0.948986 | − | 0.315319i | \(-0.897889\pi\) |
0.201419 | − | 0.979505i | \(-0.435445\pi\) | |||||||
\(600\) | −3.17741 | −0.129717 | ||||||||
\(601\) | −25.5756 | −1.04325 | −0.521625 | − | 0.853175i | \(-0.674674\pi\) | ||||
−0.521625 | + | 0.853175i | \(0.674674\pi\) | |||||||
\(602\) | 11.9685 | − | 5.36231i | 0.487801 | − | 0.218552i | ||||
\(603\) | −83.4167 | −3.39699 | ||||||||
\(604\) | −9.88297 | −0.402133 | ||||||||
\(605\) | 3.12944 | + | 5.42036i | 0.127230 | + | 0.220369i | ||||
\(606\) | −50.4797 | −2.05060 | ||||||||
\(607\) | 4.58020 | + | 7.93313i | 0.185904 | + | 0.321996i | 0.943881 | − | 0.330286i | \(-0.107145\pi\) |
−0.757977 | + | 0.652282i | \(0.773812\pi\) | |||||||
\(608\) | −2.82982 | − | 4.90139i | −0.114764 | − | 0.198778i | ||||
\(609\) | 21.1604 | − | 36.6509i | 0.857462 | − | 1.48517i | ||||
\(610\) | −14.5467 | −0.588978 | ||||||||
\(611\) | −2.54074 | + | 4.40069i | −0.102787 | + | 0.178033i | ||||
\(612\) | −4.46649 | − | 7.73619i | −0.180547 | − | 0.312717i | ||||
\(613\) | 47.2274 | 1.90750 | 0.953749 | − | 0.300605i | \(-0.0971887\pi\) | ||||
0.953749 | + | 0.300605i | \(0.0971887\pi\) | |||||||
\(614\) | 13.9278 | + | 24.1236i | 0.562080 | + | 0.973551i | ||||
\(615\) | −18.6032 | + | 32.2216i | −0.750152 | + | 1.29930i | ||||
\(616\) | 2.17741 | − | 3.77138i | 0.0877303 | − | 0.151953i | ||||
\(617\) | 2.10444 | − | 3.64500i | 0.0847216 | − | 0.146742i | −0.820551 | − | 0.571573i | \(-0.806333\pi\) |
0.905273 | + | 0.424831i | \(0.139667\pi\) | |||||||
\(618\) | −27.3693 | −1.10095 | ||||||||
\(619\) | −1.36333 | + | 2.36136i | −0.0547968 | + | 0.0949109i | −0.892123 | − | 0.451793i | \(-0.850784\pi\) |
0.837326 | + | 0.546704i | \(0.184118\pi\) | |||||||
\(620\) | 0.459261 | − | 0.795464i | 0.0184444 | − | 0.0319466i | ||||
\(621\) | 15.3233 | + | 26.5408i | 0.614905 | + | 1.06505i | ||||
\(622\) | −6.70964 | − | 11.6214i | −0.269032 | − | 0.465977i | ||||
\(623\) | 3.03555 | 0.121617 | ||||||||
\(624\) | −9.27334 | −0.371231 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 5.07297 | + | 8.78664i | 0.202757 | + | 0.351185i | ||||
\(627\) | 19.5782 | − | 33.9104i | 0.781876 | − | 1.35425i | ||||
\(628\) | 0.718148 | − | 1.24387i | 0.0286572 | − | 0.0496358i | ||||
\(629\) | 6.84368 | 0.272876 | ||||||||
\(630\) | 7.09593 | − | 12.2905i | 0.282709 | − | 0.489666i | ||||
\(631\) | 10.2878 | − | 17.8190i | 0.409551 | − | 0.709363i | −0.585289 | − | 0.810825i | \(-0.699019\pi\) |
0.994839 | + | 0.101462i | \(0.0323521\pi\) | |||||||
\(632\) | −4.35482 | + | 7.54277i | −0.173225 | + | 0.300035i | ||||
\(633\) | −34.6197 | − | 59.9630i | −1.37601 | − | 2.38332i | ||||
\(634\) | 14.4007 | 0.571927 | ||||||||
\(635\) | −5.48426 | − | 9.49902i | −0.217636 | − | 0.376957i | ||||
\(636\) | −5.53223 | + | 9.58210i | −0.219367 | + | 0.379955i | ||||
\(637\) | −8.75557 | −0.346908 | ||||||||
\(638\) | 7.25038 | − | 12.5580i | 0.287045 | − | 0.497177i | ||||
\(639\) | 32.9015 | + | 56.9871i | 1.30156 | + | 2.25437i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 24.5822 | 0.970940 | 0.485470 | − | 0.874253i | \(-0.338649\pi\) | ||||
0.485470 | + | 0.874253i | \(0.338649\pi\) | |||||||
\(642\) | −3.61167 | − | 6.25559i | −0.142541 | − | 0.246889i | ||||
\(643\) | 6.24443 | 0.246256 | 0.123128 | − | 0.992391i | \(-0.460707\pi\) | ||||
0.123128 | + | 0.992391i | \(0.460707\pi\) | |||||||
\(644\) | −4.70964 | −0.185586 | ||||||||
\(645\) | 19.0145 | − | 8.51913i | 0.748693 | − | 0.335440i | ||||
\(646\) | 7.12484 | 0.280323 | ||||||||
\(647\) | 15.3233 | 0.602423 | 0.301211 | − | 0.953557i | \(-0.402609\pi\) | ||||
0.301211 | + | 0.953557i | \(0.402609\pi\) | |||||||
\(648\) | −10.0322 | − | 17.3763i | −0.394103 | − | 0.682607i | ||||
\(649\) | −20.5782 | −0.807763 | ||||||||
\(650\) | −1.45926 | − | 2.52751i | −0.0572369 | − | 0.0991373i | ||||
\(651\) | 2.91852 | + | 5.05503i | 0.114386 | + | 0.198122i | ||||
\(652\) | −12.1511 | + | 21.0464i | −0.475875 | + | 0.824239i | ||||
\(653\) | −35.0934 | −1.37331 | −0.686655 | − | 0.726984i | \(-0.740922\pi\) | ||||
−0.686655 | + | 0.726984i | \(0.740922\pi\) | |||||||
\(654\) | −13.1939 | + | 22.8525i | −0.515922 | + | 0.893604i | ||||
\(655\) | 4.11167 | + | 7.12162i | 0.160656 | + | 0.278265i | ||||
\(656\) | −11.7096 | −0.457185 | ||||||||
\(657\) | 51.5599 | + | 89.3043i | 2.01154 | + | 3.48409i | ||||
\(658\) | 1.74111 | − | 3.01570i | 0.0678756 | − | 0.117564i | ||||
\(659\) | −1.74111 | + | 3.01570i | −0.0678241 | + | 0.117475i | −0.897943 | − | 0.440111i | \(-0.854939\pi\) |
0.830119 | + | 0.557586i | \(0.188272\pi\) | |||||||
\(660\) | 3.45926 | − | 5.99162i | 0.134652 | − | 0.233223i | ||||
\(661\) | 14.5467 | 0.565800 | 0.282900 | − | 0.959149i | \(-0.408703\pi\) | ||||
0.282900 | + | 0.959149i | \(0.408703\pi\) | |||||||
\(662\) | 0.243150 | − | 0.421148i | 0.00945029 | − | 0.0163684i | ||||
\(663\) | 5.83705 | − | 10.1101i | 0.226692 | − | 0.392642i | ||||
\(664\) | −2.50723 | − | 4.34265i | −0.0972993 | − | 0.168527i | ||||
\(665\) | 5.65964 | + | 9.80278i | 0.219471 | + | 0.380135i | ||||
\(666\) | 38.5756 | 1.49477 | ||||||||
\(667\) | −15.6822 | −0.607219 | ||||||||
\(668\) | 0.789079 | + | 1.36673i | 0.0305304 | + | 0.0528802i | ||||
\(669\) | 40.2313 | + | 69.6827i | 1.55543 | + | 2.69409i | ||||
\(670\) | 5.87778 | − | 10.1806i | 0.227079 | − | 0.393312i | ||||
\(671\) | 15.8370 | − | 27.4306i | 0.611382 | − | 1.05895i | ||||
\(672\) | 6.35482 | 0.245142 | ||||||||
\(673\) | −18.4495 | + | 31.9554i | −0.711175 | + | 1.23179i | 0.253242 | + | 0.967403i | \(0.418503\pi\) |
−0.964416 | + | 0.264388i | \(0.914830\pi\) | |||||||
\(674\) | 15.0572 | − | 26.0799i | 0.579983 | − | 1.00456i | ||||
\(675\) | 6.50723 | − | 11.2708i | 0.250463 | − | 0.433815i | ||||
\(676\) | 2.24111 | + | 3.88172i | 0.0861967 | + | 0.149297i | ||||
\(677\) | 26.2459 | 1.00871 | 0.504357 | − | 0.863495i | \(-0.331730\pi\) | ||||
0.504357 | + | 0.863495i | \(0.331730\pi\) | |||||||
\(678\) | −17.5552 | − | 30.4065i | −0.674203 | − | 1.16775i | ||||
\(679\) | 12.9330 | − | 22.4006i | 0.496322 | − | 0.859655i | ||||
\(680\) | 1.25889 | 0.0482761 | ||||||||
\(681\) | −11.4528 | + | 19.8368i | −0.438872 | + | 0.760148i | ||||
\(682\) | 1.00000 | + | 1.73205i | 0.0382920 | + | 0.0663237i | ||||
\(683\) | 2.75557 | + | 4.77278i | 0.105439 | + | 0.182625i | 0.913917 | − | 0.405900i | \(-0.133042\pi\) |
−0.808479 | + | 0.588526i | \(0.799709\pi\) | |||||||
\(684\) | 40.1604 | 1.53557 | ||||||||
\(685\) | 5.54074 | + | 9.59684i | 0.211701 | + | 0.366676i | ||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | −17.0604 | −0.650894 | ||||||||
\(688\) | 5.31408 | + | 3.84195i | 0.202597 | + | 0.146473i | ||||
\(689\) | −10.1630 | −0.387178 | ||||||||
\(690\) | −7.48223 | −0.284843 | ||||||||
\(691\) | 25.2661 | + | 43.7622i | 0.961168 | + | 1.66479i | 0.719575 | + | 0.694415i | \(0.244337\pi\) |
0.241593 | + | 0.970378i | \(0.422330\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 15.4508 | + | 26.7615i | 0.586926 | + | 1.01658i | ||||
\(694\) | 8.87778 | + | 15.3768i | 0.336996 | + | 0.583694i | ||||
\(695\) | −8.20760 | + | 14.2160i | −0.311332 | + | 0.539243i | ||||
\(696\) | 21.1604 | 0.802083 | ||||||||
\(697\) | 7.37056 | − | 12.7662i | 0.279180 | − | 0.483553i | ||||
\(698\) | −16.4258 | − | 28.4502i | −0.621724 | − | 1.07686i | ||||
\(699\) | 57.7030 | 2.18253 | ||||||||
\(700\) | 1.00000 | + | 1.73205i | 0.0377964 | + | 0.0654654i | ||||
\(701\) | 18.9895 | − | 32.8907i | 0.717222 | − | 1.24226i | −0.244875 | − | 0.969555i | \(-0.578747\pi\) |
0.962096 | − | 0.272710i | \(-0.0879199\pi\) | |||||||
\(702\) | 18.9915 | − | 32.8942i | 0.716788 | − | 1.24151i | ||||
\(703\) | −15.3837 | + | 26.6454i | −0.580208 | + | 1.00495i | ||||
\(704\) | 2.17741 | 0.0820642 | ||||||||
\(705\) | 2.76611 | − | 4.79105i | 0.104178 | − | 0.180441i | ||||
\(706\) | 6.53946 | − | 11.3267i | 0.246116 | − | 0.426285i | ||||
\(707\) | 15.8870 | + | 27.5172i | 0.597494 | + | 1.03489i | ||||
\(708\) | −15.0145 | − | 26.0058i | −0.564278 | − | 0.977358i | ||||
\(709\) | −38.5967 | −1.44953 | −0.724765 | − | 0.688997i | \(-0.758051\pi\) | ||||
−0.724765 | + | 0.688997i | \(0.758051\pi\) | |||||||
\(710\) | −9.27334 | −0.348022 | ||||||||
\(711\) | −30.9015 | − | 53.5230i | −1.15890 | − | 2.00727i | ||||
\(712\) | 0.758887 | + | 1.31443i | 0.0284405 | + | 0.0492604i | ||||
\(713\) | 1.08148 | − | 1.87317i | 0.0405016 | − | 0.0701509i | ||||
\(714\) | −4.00000 | + | 6.92820i | −0.149696 | + | 0.259281i | ||||
\(715\) | 6.35482 | 0.237657 | ||||||||
\(716\) | −4.64390 | + | 8.04347i | −0.173551 | + | 0.300599i | ||||
\(717\) | −36.3108 | + | 62.8921i | −1.35605 | + | 2.34875i | ||||
\(718\) | 2.02296 | − | 3.50388i | 0.0754964 | − | 0.130764i | ||||
\(719\) | −11.3548 | − | 19.6671i | −0.423463 | − | 0.733460i | 0.572812 | − | 0.819687i | \(-0.305852\pi\) |
−0.996276 | + | 0.0862266i | \(0.972519\pi\) | |||||||
\(720\) | 7.09593 | 0.264450 | ||||||||
\(721\) | 8.61371 | + | 14.9194i | 0.320791 | + | 0.555627i | ||||
\(722\) | −6.51574 | + | 11.2856i | −0.242491 | + | 0.420006i | ||||
\(723\) | 6.56778 | 0.244258 | ||||||||
\(724\) | 5.91852 | − | 10.2512i | 0.219960 | − | 0.380982i | ||||
\(725\) | 3.32982 | + | 5.76741i | 0.123666 | + | 0.214196i | ||||
\(726\) | −9.94352 | − | 17.2227i | −0.369039 | − | 0.639194i | ||||
\(727\) | −29.9371 | −1.11030 | −0.555152 | − | 0.831749i | \(-0.687340\pi\) | ||||
−0.555152 | + | 0.831749i | \(0.687340\pi\) | |||||||
\(728\) | 2.91852 | + | 5.05503i | 0.108168 | + | 0.187352i | ||||
\(729\) | 18.3193 | 0.678492 | ||||||||
\(730\) | −14.5322 | −0.537862 | ||||||||
\(731\) | −7.53351 | + | 3.37527i | −0.278637 | + | 0.124839i | ||||
\(732\) | 46.2208 | 1.70837 | ||||||||
\(733\) | 6.30889 | 0.233024 | 0.116512 | − | 0.993189i | \(-0.462829\pi\) | ||||
0.116512 | + | 0.993189i | \(0.462829\pi\) | |||||||
\(734\) | 2.38629 | + | 4.13318i | 0.0880797 | + | 0.152559i | ||||
\(735\) | 9.53223 | 0.351602 | ||||||||
\(736\) | −1.17741 | − | 2.03933i | −0.0433999 | − | 0.0751708i | ||||
\(737\) | 12.7983 | + | 22.1674i | 0.471433 | + | 0.816546i | ||||
\(738\) | 41.5454 | − | 71.9587i | 1.52931 | − | 2.64884i | ||||
\(739\) | −37.1393 | −1.36619 | −0.683096 | − | 0.730329i | \(-0.739367\pi\) | ||||
−0.683096 | + | 0.730329i | \(0.739367\pi\) | |||||||
\(740\) | −2.71815 | + | 4.70797i | −0.0999211 | + | 0.173068i | ||||
\(741\) | 26.2419 | + | 45.4522i | 0.964019 | + | 1.66973i | ||||
\(742\) | 6.96445 | 0.255673 | ||||||||
\(743\) | −8.32335 | − | 14.4165i | −0.305354 | − | 0.528889i | 0.671986 | − | 0.740564i | \(-0.265441\pi\) |
−0.977340 | + | 0.211675i | \(0.932108\pi\) | |||||||
\(744\) | −1.45926 | + | 2.52751i | −0.0534991 | + | 0.0926632i | ||||
\(745\) | 11.0250 | − | 19.0959i | 0.403925 | − | 0.699618i | ||||
\(746\) | −0.223339 | + | 0.386834i | −0.00817701 | + | 0.0141630i | ||||
\(747\) | 35.5822 | 1.30189 | ||||||||
\(748\) | −1.37056 | + | 2.37387i | −0.0501125 | + | 0.0867974i | ||||
\(749\) | −2.27334 | + | 3.93754i | −0.0830661 | + | 0.143875i | ||||
\(750\) | 1.58870 | + | 2.75172i | 0.0580113 | + | 0.100479i | ||||
\(751\) | −17.4737 | − | 30.2654i | −0.637625 | − | 1.10440i | −0.985953 | − | 0.167026i | \(-0.946584\pi\) |
0.348328 | − | 0.937373i | \(-0.386750\pi\) | |||||||
\(752\) | 1.74111 | 0.0634919 | ||||||||
\(753\) | −68.0119 | −2.47849 | ||||||||
\(754\) | 9.71815 | + | 16.8323i | 0.353914 | + | 0.612997i | ||||
\(755\) | 4.94149 | + | 8.55891i | 0.179839 | + | 0.311491i | ||||
\(756\) | −13.0145 | + | 22.5417i | −0.473331 | + | 0.819834i | ||||
\(757\) | 14.2819 | − | 24.7369i | 0.519083 | − | 0.899078i | −0.480671 | − | 0.876901i | \(-0.659607\pi\) |
0.999754 | − | 0.0221768i | \(-0.00705968\pi\) | |||||||
\(758\) | 13.0789 | 0.475048 | ||||||||
\(759\) | 8.14594 | − | 14.1092i | 0.295679 | − | 0.512131i | ||||
\(760\) | −2.82982 | + | 4.90139i | −0.102648 | + | 0.177792i | ||||
\(761\) | 3.99796 | − | 6.92467i | 0.144926 | − | 0.251019i | −0.784419 | − | 0.620231i | \(-0.787039\pi\) |
0.929345 | + | 0.369212i | \(0.120372\pi\) | |||||||
\(762\) | 17.4258 | + | 30.1823i | 0.631268 | + | 1.09339i | ||||
\(763\) | 16.6096 | 0.601309 | ||||||||
\(764\) | 2.91852 | + | 5.05503i | 0.105588 | + | 0.182885i | ||||
\(765\) | −4.46649 | + | 7.73619i | −0.161486 | + | 0.279702i | ||||
\(766\) | −17.6782 | −0.638738 | ||||||||
\(767\) | 13.7911 | − | 23.8869i | 0.497968 | − | 0.862506i | ||||
\(768\) | 1.58870 | + | 2.75172i | 0.0573274 | + | 0.0992941i | ||||
\(769\) | 4.64390 | + | 8.04347i | 0.167463 | + | 0.290055i | 0.937527 | − | 0.347912i | \(-0.113109\pi\) |
−0.770064 | + | 0.637967i | \(0.779776\pi\) | |||||||
\(770\) | −4.35482 | −0.156937 | ||||||||
\(771\) | 19.0874 | + | 33.0604i | 0.687417 | + | 1.19064i | ||||
\(772\) | 12.0289 | 0.432930 | ||||||||
\(773\) | −2.88961 | −0.103932 | −0.0519661 | − | 0.998649i | \(-0.516549\pi\) | ||||
−0.0519661 | + | 0.998649i | \(0.516549\pi\) | |||||||
\(774\) | −42.4639 | + | 19.0253i | −1.52633 | + | 0.683850i | ||||
\(775\) | −0.918523 | −0.0329943 | ||||||||
\(776\) | 12.9330 | 0.464267 | ||||||||
\(777\) | −17.2733 | − | 29.9183i | −0.619678 | − | 1.07331i | ||||
\(778\) | 11.1563 | 0.399973 | ||||||||
\(779\) | 33.1361 | + | 57.3935i | 1.18723 | + | 2.05633i | ||||
\(780\) | 4.63667 | + | 8.03095i | 0.166019 | + | 0.287554i | ||||
\(781\) | 10.0959 | − | 17.4867i | 0.361261 | − | 0.625722i | ||||
\(782\) | 2.96445 | 0.106009 | ||||||||
\(783\) | −43.3358 | + | 75.0597i | −1.54869 | + | 2.68242i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | −1.43630 | −0.0512636 | ||||||||
\(786\) | −13.0645 | − | 22.6283i | −0.465994 | − | 0.807125i | ||||
\(787\) | −3.04202 | + | 5.26893i | −0.108436 | + | 0.187817i | −0.915137 | − | 0.403143i | \(-0.867918\pi\) |
0.806701 | + | 0.590960i | \(0.201251\pi\) | |||||||
\(788\) | 6.25889 | − | 10.8407i | 0.222964 | − | 0.386184i | ||||
\(789\) | 41.0539 | − | 71.1075i | 1.46156 | − | 2.53149i | ||||
\(790\) | 8.70964 | 0.309875 | ||||||||
\(791\) | −11.0500 | + | 19.1392i | −0.392893 | + | 0.680510i | ||||
\(792\) | −7.72538 | + | 13.3807i | −0.274509 | + | 0.475464i | ||||
\(793\) | 21.2274 | + | 36.7670i | 0.753808 | + | 1.30563i | ||||
\(794\) | −10.4363 | − | 18.0762i | −0.370370 | − | 0.641500i | ||||
\(795\) | 11.0645 | 0.392416 | ||||||||
\(796\) | −3.27334 | −0.116021 | ||||||||
\(797\) | 8.93111 | + | 15.4691i | 0.316356 | + | 0.547945i | 0.979725 | − | 0.200348i | \(-0.0642073\pi\) |
−0.663369 | + | 0.748293i | \(0.730874\pi\) | |||||||
\(798\) | −17.9830 | − | 31.1474i | −0.636591 | − | 1.10261i | ||||
\(799\) | −1.09593 | + | 1.89821i | −0.0387713 | + | 0.0671539i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −10.7700 | −0.380540 | ||||||||
\(802\) | −1.82259 | + | 3.15682i | −0.0643579 | + | 0.111471i | ||||
\(803\) | 15.8213 | − | 27.4033i | 0.558322 | − | 0.967042i | ||||
\(804\) | −18.6761 | + | 32.3480i | −0.658656 | + | 1.14083i | ||||
\(805\) | 2.35482 | + | 4.07867i | 0.0829965 | + | 0.143754i | ||||
\(806\) | −2.68073 | −0.0944247 | ||||||||
\(807\) | −37.8365 | − | 65.5348i | −1.33191 | − | 2.30693i | ||||
\(808\) | −7.94352 | + | 13.7586i | −0.279452 | + | 0.484025i | ||||
\(809\) | 29.8989 | 1.05119 | 0.525595 | − | 0.850735i | \(-0.323843\pi\) | ||||
0.525595 | + | 0.850735i | \(0.323843\pi\) | |||||||
\(810\) | −10.0322 | + | 17.3763i | −0.352497 | + | 0.610542i | ||||
\(811\) | −21.6269 | − | 37.4589i | −0.759422 | − | 1.31536i | −0.943145 | − | 0.332380i | \(-0.892148\pi\) |
0.183723 | − | 0.982978i | \(-0.441185\pi\) | |||||||
\(812\) | −6.65964 | − | 11.5348i | −0.233707 | − | 0.404793i | ||||
\(813\) | 11.5822 | 0.406207 | ||||||||
\(814\) | −5.91852 | − | 10.2512i | −0.207444 | − | 0.359304i | ||||
\(815\) | 24.3023 | 0.851271 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 3.79299 | − | 36.9184i | 0.132700 | − | 1.29161i | ||||
\(818\) | 37.7675 | 1.32051 | ||||||||
\(819\) | −41.4193 | −1.44731 | ||||||||
\(820\) | 5.85482 | + | 10.1408i | 0.204459 | + | 0.354134i | ||||
\(821\) | 0.134045 | 0.00467820 | 0.00233910 | − | 0.999997i | \(-0.499255\pi\) | ||||
0.00233910 | + | 0.999997i | \(0.499255\pi\) | |||||||
\(822\) | −17.6052 | − | 30.4931i | −0.614052 | − | 1.06357i | ||||
\(823\) | −19.2398 | − | 33.3244i | −0.670658 | − | 1.16161i | −0.977718 | − | 0.209924i | \(-0.932678\pi\) |
0.307059 | − | 0.951690i | \(-0.400655\pi\) | |||||||
\(824\) | −4.30685 | + | 7.45969i | −0.150036 | + | 0.259871i | ||||
\(825\) | −6.91852 | −0.240872 | ||||||||
\(826\) | −9.45075 | + | 16.3692i | −0.328834 | + | 0.569557i | ||||
\(827\) | −1.43758 | − | 2.48996i | −0.0499895 | − | 0.0865844i | 0.839948 | − | 0.542667i | \(-0.182585\pi\) |
−0.889937 | + | 0.456083i | \(0.849252\pi\) | |||||||
\(828\) | 16.7096 | 0.580700 | ||||||||
\(829\) | −21.7135 | − | 37.6090i | −0.754143 | − | 1.30621i | −0.945799 | − | 0.324751i | \(-0.894719\pi\) |
0.191657 | − | 0.981462i | \(-0.438614\pi\) | |||||||
\(830\) | −2.50723 | + | 4.34265i | −0.0870271 | + | 0.150735i | ||||
\(831\) | −27.1104 | + | 46.9566i | −0.940449 | + | 1.62891i | ||||
\(832\) | −1.45926 | + | 2.52751i | −0.0505908 | + | 0.0876258i | ||||
\(833\) | −3.77666 | −0.130854 | ||||||||
\(834\) | 26.0789 | − | 45.1700i | 0.903039 | − | 1.56411i | ||||
\(835\) | 0.789079 | − | 1.36673i | 0.0273072 | − | 0.0472975i | ||||
\(836\) | −6.16167 | − | 10.6723i | −0.213106 | − | 0.369110i | ||||
\(837\) | −5.97704 | − | 10.3525i | −0.206597 | − | 0.357836i | ||||
\(838\) | −31.9660 | −1.10425 | ||||||||
\(839\) | −4.84743 | −0.167352 | −0.0836759 | − | 0.996493i | \(-0.526666\pi\) | ||||
−0.0836759 | + | 0.996493i | \(0.526666\pi\) | |||||||
\(840\) | −3.17741 | − | 5.50344i | −0.109631 | − | 0.189887i | ||||
\(841\) | −7.67537 | − | 13.2941i | −0.264668 | − | 0.458418i | ||||
\(842\) | −2.42575 | + | 4.20152i | −0.0835969 | + | 0.144794i | ||||
\(843\) | 37.5611 | − | 65.0578i | 1.29367 | − | 2.24071i | ||||
\(844\) | −21.7911 | −0.750081 | ||||||||
\(845\) | 2.24111 | − | 3.88172i | 0.0770966 | − | 0.133535i | ||||
\(846\) | −6.17741 | + | 10.6996i | −0.212384 | + | 0.367859i | ||||
\(847\) | −6.25889 | + | 10.8407i | −0.215058 | + | 0.372491i | ||||
\(848\) | 1.74111 | + | 3.01570i | 0.0597901 | + | 0.103559i | ||||
\(849\) | −36.6756 | −1.25870 | ||||||||
\(850\) | −0.629444 | − | 1.09023i | −0.0215897 | − | 0.0373945i | ||||
\(851\) | −6.40075 | + | 11.0864i | −0.219415 | + | 0.380038i | ||||
\(852\) | 29.4652 | 1.00946 | ||||||||
\(853\) | 9.03742 | − | 15.6533i | 0.309435 | − | 0.535958i | −0.668804 | − | 0.743439i | \(-0.733193\pi\) |
0.978239 | + | 0.207481i | \(0.0665266\pi\) | |||||||
\(854\) | −14.5467 | − | 25.1956i | −0.497777 | − | 0.862176i | ||||
\(855\) | −20.0802 | − | 34.7799i | −0.686728 | − | 1.18945i | ||||
\(856\) | −2.27334 | −0.0777012 | ||||||||
\(857\) | −19.3819 | − | 33.5704i | −0.662072 | − | 1.14674i | −0.980070 | − | 0.198651i | \(-0.936344\pi\) |
0.317999 | − | 0.948091i | \(-0.396989\pi\) | |||||||
\(858\) | −20.1919 | −0.689339 | ||||||||
\(859\) | −13.5218 | −0.461360 | −0.230680 | − | 0.973030i | \(-0.574095\pi\) | ||||
−0.230680 | + | 0.973030i | \(0.574095\pi\) | |||||||
\(860\) | 0.670182 | − | 6.52310i | 0.0228530 | − | 0.222436i | ||||
\(861\) | −74.4126 | −2.53598 | ||||||||
\(862\) | −15.2444 | −0.519227 | ||||||||
\(863\) | 14.7911 | + | 25.6190i | 0.503495 | + | 0.872080i | 0.999992 | + | 0.00404091i | \(0.00128627\pi\) |
−0.496496 | + | 0.868039i | \(0.665380\pi\) | |||||||
\(864\) | −13.0145 | −0.442761 | ||||||||
\(865\) | 6.00000 | + | 10.3923i | 0.204006 | + | 0.353349i | ||||
\(866\) | −3.02296 | − | 5.23593i | −0.102725 | − | 0.177924i | ||||
\(867\) | −24.4902 | + | 42.4183i | −0.831731 | + | 1.44060i | ||||
\(868\) | 1.83705 | 0.0623534 | ||||||||
\(869\) | −9.48223 | + | 16.4237i | −0.321662 | + | 0.557136i | ||||
\(870\) | −10.5802 | − | 18.3254i | −0.358702 | − | 0.621290i | ||||
\(871\) | −34.3089 | −1.16251 | ||||||||
\(872\) | 4.15241 | + | 7.19218i | 0.140618 | + | 0.243558i | ||||
\(873\) | −45.8858 | + | 79.4765i | −1.55300 | + | 2.68987i | ||||
\(874\) | −6.66371 | + | 11.5419i | −0.225403 | + | 0.390410i | ||||
\(875\) | 1.00000 | − | 1.73205i | 0.0338062 | − | 0.0585540i | ||||
\(876\) | 46.1748 | 1.56010 | ||||||||
\(877\) | 16.3378 | − | 28.2979i | 0.551688 | − | 0.955552i | −0.446465 | − | 0.894801i | \(-0.647317\pi\) |
0.998153 | − | 0.0607509i | \(-0.0193495\pi\) | |||||||
\(878\) | 9.54668 | − | 16.5353i | 0.322185 | − | 0.558041i | ||||
\(879\) | −30.2878 | − | 52.4600i | −1.02158 | − | 1.76943i | ||||
\(880\) | −1.08870 | − | 1.88569i | −0.0367002 | − | 0.0635667i | ||||
\(881\) | 30.3482 | 1.02246 | 0.511228 | − | 0.859445i | \(-0.329191\pi\) | ||||
0.511228 | + | 0.859445i | \(0.329191\pi\) | |||||||
\(882\) | −21.2878 | −0.716797 | ||||||||
\(883\) | 6.10648 | + | 10.5767i | 0.205499 | + | 0.355935i | 0.950292 | − | 0.311361i | \(-0.100785\pi\) |
−0.744792 | + | 0.667296i | \(0.767451\pi\) | |||||||
\(884\) | −1.83705 | − | 3.18186i | −0.0617865 | − | 0.107017i | ||||
\(885\) | −15.0145 | + | 26.0058i | −0.504705 | + | 0.874175i | ||||
\(886\) | 10.1354 | − | 17.5550i | 0.340505 | − | 0.589772i | ||||
\(887\) | 10.2630 | 0.344597 | 0.172298 | − | 0.985045i | \(-0.444881\pi\) | ||||
0.172298 | + | 0.985045i | \(0.444881\pi\) | |||||||
\(888\) | 8.63667 | − | 14.9592i | 0.289828 | − | 0.501996i | ||||
\(889\) | 10.9685 | − | 18.9980i | 0.367873 | − | 0.637174i | ||||
\(890\) | 0.758887 | − | 1.31443i | 0.0254380 | − | 0.0440598i | ||||
\(891\) | −21.8443 | − | 37.8354i | −0.731811 | − | 1.26753i | ||||
\(892\) | 25.3233 | 0.847888 | ||||||||
\(893\) | −4.92703 | − | 8.53387i | −0.164877 | − | 0.285575i | ||||
\(894\) | −35.0309 | + | 60.6754i | −1.17161 | + | 2.02929i | ||||
\(895\) | 9.28780 | 0.310457 | ||||||||
\(896\) | 1.00000 | − | 1.73205i | 0.0334077 | − | 0.0578638i | ||||
\(897\) | 10.9185 | + | 18.9114i | 0.364559 | + | 0.631434i | ||||
\(898\) | 2.15964 | + | 3.74060i | 0.0720680 | + | 0.124825i | ||||
\(899\) | 6.11703 | 0.204014 | ||||||||
\(900\) | −3.54797 | − | 6.14526i | −0.118266 | − | 0.204842i | ||||
\(901\) | −4.38373 | −0.146043 | ||||||||
\(902\) | −25.4967 | −0.848947 | ||||||||
\(903\) | 33.7700 | + | 24.4149i | 1.12380 | + | 0.812476i | ||||
\(904\) | −11.0500 | −0.367518 | ||||||||
\(905\) | −11.8370 | −0.393477 | ||||||||
\(906\) | −15.7011 | − | 27.1952i | −0.521635 | − | 0.903498i | ||||
\(907\) | −34.6152 | −1.14938 | −0.574690 | − | 0.818371i | \(-0.694877\pi\) | ||||
−0.574690 | + | 0.818371i | \(0.694877\pi\) | |||||||
\(908\) | 3.60444 | + | 6.24308i | 0.119618 | + | 0.207184i | ||||
\(909\) | −56.3667 | − | 97.6300i | −1.86957 | − | 3.23818i | ||||
\(910\) | 2.91852 | − | 5.05503i | 0.0967481 | − | 0.167573i | ||||
\(911\) | 40.9134 | 1.35552 | 0.677761 | − | 0.735283i | \(-0.262951\pi\) | ||||
0.677761 | + | 0.735283i | \(0.262951\pi\) | |||||||
\(912\) | 8.99149 | − | 15.5737i | 0.297738 | − | 0.515697i | ||||
\(913\) | −5.45926 | − | 9.45572i | −0.180675 | − | 0.312939i | ||||
\(914\) | 32.4152 | 1.07220 | ||||||||
\(915\) | −23.1104 | − | 40.0284i | −0.764006 | − | 1.32330i | ||||
\(916\) | −2.68464 | + | 4.64993i | −0.0887029 | + | 0.153638i | ||||
\(917\) | −8.22334 | + | 14.2432i | −0.271559 | + | 0.470353i | ||||
\(918\) | 8.19186 | − | 14.1887i | 0.270372 | − | 0.468298i | ||||
\(919\) | −33.8452 | −1.11645 | −0.558225 | − | 0.829690i | \(-0.688517\pi\) | ||||
−0.558225 | + | 0.829690i | \(0.688517\pi\) | |||||||
\(920\) | −1.17741 | + | 2.03933i | −0.0388180 | + | 0.0672348i | ||||
\(921\) | −44.2543 | + | 76.6507i | −1.45823 | + | 2.52573i | ||||
\(922\) | 3.78057 | + | 6.54814i | 0.124506 | + | 0.215651i | ||||
\(923\) | 13.5322 | + | 23.4385i | 0.445419 | + | 0.771488i | ||||
\(924\) | 13.8370 | 0.455205 | ||||||||
\(925\) | 5.43630 | 0.178744 | ||||||||
\(926\) | 4.56574 | + | 7.90809i | 0.150040 | + | 0.259876i | ||||
\(927\) | −30.5611 | − | 52.9334i | −1.00376 | − | 1.73856i | ||||
\(928\) | 3.32982 | − | 5.76741i | 0.109307 | − | 0.189325i | ||||
\(929\) | 27.3076 | − | 47.2982i | 0.895934 | − | 1.55180i | 0.0632886 | − | 0.997995i | \(-0.479841\pi\) |
0.832645 | − | 0.553807i | \(-0.186826\pi\) | |||||||
\(930\) | 2.91852 | 0.0957021 | ||||||||
\(931\) | 8.48945 | − | 14.7042i | 0.278231 | − | 0.481910i | ||||
\(932\) | 9.08020 | − | 15.7274i | 0.297432 | − | 0.515167i | ||||
\(933\) | 21.3193 | − | 36.9261i | 0.697962 | − | 1.20890i | ||||
\(934\) | 4.96981 | + | 8.60796i | 0.162617 | + | 0.281661i | ||||
\(935\) | 2.74111 | 0.0896440 | ||||||||
\(936\) | −10.3548 | − | 17.9351i | −0.338458 | − | 0.586226i | ||||
\(937\) | −0.143144 | + | 0.247932i | −0.00467630 | + | 0.00809958i | −0.868354 | − | 0.495945i | \(-0.834822\pi\) |
0.863678 | + | 0.504044i | \(0.168155\pi\) | |||||||
\(938\) | 23.5111 | 0.767666 | ||||||||
\(939\) | −16.1189 | + | 27.9187i | −0.526020 | + | 0.911094i | ||||
\(940\) | −0.870556 | − | 1.50785i | −0.0283944 | − | 0.0491806i | ||||
\(941\) | −25.4652 | − | 44.1070i | −0.830142 | − | 1.43785i | −0.897925 | − | 0.440148i | \(-0.854926\pi\) |
0.0677832 | − | 0.997700i | \(-0.478407\pi\) | |||||||
\(942\) | 4.56370 | 0.148693 | ||||||||
\(943\) | 13.7870 | + | 23.8799i | 0.448968 | + | 0.777635i | ||||
\(944\) | −9.45075 | −0.307596 | ||||||||
\(945\) | 26.0289 | 0.846720 | ||||||||
\(946\) | 11.5709 | + | 8.36549i | 0.376203 | + | 0.271986i | ||||
\(947\) | −27.7767 | −0.902620 | −0.451310 | − | 0.892367i | \(-0.649043\pi\) | ||||
−0.451310 | + | 0.892367i | \(0.649043\pi\) | |||||||
\(948\) | −27.6741 | −0.898813 | ||||||||
\(949\) | 21.2063 | + | 36.7304i | 0.688386 | + | 1.19232i | ||||
\(950\) | 5.65964 | 0.183623 | ||||||||
\(951\) | 22.8785 | + | 39.6268i | 0.741887 | + | 1.28499i | ||||
\(952\) | 1.25889 | + | 2.18046i | 0.0408008 | + | 0.0706690i | ||||
\(953\) | −11.6826 | + | 20.2349i | −0.378437 | + | 0.655471i | −0.990835 | − | 0.135078i | \(-0.956872\pi\) |
0.612398 | + | 0.790549i | \(0.290205\pi\) | |||||||
\(954\) | −24.7096 | −0.800004 | ||||||||
\(955\) | 2.91852 | − | 5.05503i | 0.0944412 | − | 0.163577i | ||||
\(956\) | 11.4278 | + | 19.7935i | 0.369601 | + | 0.640168i | ||||
\(957\) | 46.0748 | 1.48939 | ||||||||
\(958\) | 16.6741 | + | 28.8804i | 0.538715 | + | 0.933082i | ||||
\(959\) | −11.0815 | + | 19.1937i | −0.357840 | + | 0.619796i | ||||
\(960\) | 1.58870 | − | 2.75172i | 0.0512752 | − | 0.0888113i | ||||
\(961\) | 15.0782 | − | 26.1161i | 0.486392 | − | 0.842456i | ||||
\(962\) | 15.8660 | 0.511539 | ||||||||
\(963\) | 8.06574 | − | 13.9703i | 0.259915 | − | 0.450186i | ||||
\(964\) | 1.03351 | − | 1.79009i | 0.0332872 | − | 0.0576550i | ||||
\(965\) | −6.01445 | − | 10.4173i | −0.193612 | − | 0.335346i | ||||
\(966\) | −7.48223 | − | 12.9596i | −0.240737 | − | 0.416968i | ||||
\(967\) | −10.2341 | −0.329105 | −0.164552 | − | 0.986368i | \(-0.552618\pi\) | ||||
−0.164552 | + | 0.986368i | \(0.552618\pi\) | |||||||
\(968\) | −6.25889 | −0.201168 | ||||||||
\(969\) | 11.3193 | + | 19.6056i | 0.363627 | + | 0.629821i | ||||
\(970\) | −6.46649 | − | 11.2003i | −0.207626 | − | 0.359620i | ||||
\(971\) | −6.51965 | + | 11.2924i | −0.209225 | + | 0.362389i | −0.951471 | − | 0.307739i | \(-0.900428\pi\) |
0.742245 | + | 0.670128i | \(0.233761\pi\) | |||||||
\(972\) | 12.3548 | − | 21.3992i | 0.396281 | − | 0.686379i | ||||
\(973\) | −32.8304 | −1.05249 | ||||||||
\(974\) | 2.61167 | − | 4.52354i | 0.0836833 | − | 0.144944i | ||||
\(975\) | 4.63667 | − | 8.03095i | 0.148492 | − | 0.257196i | ||||
\(976\) | 7.27334 | − | 12.5978i | 0.232814 | − | 0.403246i | ||||
\(977\) | 14.9087 | + | 25.8227i | 0.476973 | + | 0.826141i | 0.999652 | − | 0.0263887i | \(-0.00840077\pi\) |
−0.522679 | + | 0.852529i | \(0.675067\pi\) | |||||||
\(978\) | −77.2182 | −2.46917 | ||||||||
\(979\) | 1.65241 | + | 2.86205i | 0.0528112 | + | 0.0914717i | ||||
\(980\) | 1.50000 | − | 2.59808i | 0.0479157 | − | 0.0829925i | ||||
\(981\) | −58.9304 | −1.88150 | ||||||||
\(982\) | 5.96130 | − | 10.3253i | 0.190233 | − | 0.329493i | ||||
\(983\) | 4.65760 | + | 8.06720i | 0.148554 | + | 0.257304i | 0.930693 | − | 0.365800i | \(-0.119205\pi\) |
−0.782139 | + | 0.623104i | \(0.785871\pi\) | |||||||
\(984\) | −18.6032 | − | 32.2216i | −0.593047 | − | 1.02719i | ||||
\(985\) | −12.5178 | −0.398849 | ||||||||
\(986\) | 4.19186 | + | 7.26052i | 0.133496 | + | 0.231222i | ||||
\(987\) | 11.0645 | 0.352186 | ||||||||
\(988\) | 16.5178 | 0.525500 | ||||||||
\(989\) | 1.57816 | − | 15.3607i | 0.0501825 | − | 0.488443i | ||||
\(990\) | 15.4508 | 0.491057 | ||||||||
\(991\) | −48.4837 | −1.54014 | −0.770068 | − | 0.637961i | \(-0.779778\pi\) | ||||
−0.770068 | + | 0.637961i | \(0.779778\pi\) | |||||||
\(992\) | 0.459261 | + | 0.795464i | 0.0145816 | + | 0.0252560i | ||||
\(993\) | 1.54517 | 0.0490346 | ||||||||
\(994\) | −9.27334 | − | 16.0619i | −0.294133 | − | 0.509453i | ||||
\(995\) | 1.63667 | + | 2.83480i | 0.0518860 | + | 0.0898691i | ||||
\(996\) | 7.96649 | − | 13.7984i | 0.252428 | − | 0.437218i | ||||
\(997\) | 21.8660 | 0.692502 | 0.346251 | − | 0.938142i | \(-0.387455\pi\) | ||||
0.346251 | + | 0.938142i | \(0.387455\pi\) | |||||||
\(998\) | 5.60648 | − | 9.71071i | 0.177470 | − | 0.307387i | ||||
\(999\) | 35.3752 | + | 61.2717i | 1.11922 | + | 1.93855i |
(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 | 430.2.e.f.251.3 | yes | 6 | |
43.6 | even | 3 | inner | 430.2.e.f.221.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
430.2.e.f.221.3 | ✓ | 6 | 43.6 | even | 3 | inner | |
430.2.e.f.251.3 | yes | 6 | 1.1 | even | 1 | trivial |