Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(419,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bq (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 503.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.503 |
Dual form | 546.2.bq.a.419.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −3.46410 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | −1.50000 | + | 0.866025i | −0.612372 | + | 0.353553i | ||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | −3.00000 | − | 1.73205i | −0.948683 | − | 0.547723i | ||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | −1.73205 | −0.500000 | ||||||||
\(13\) | −3.50000 | − | 0.866025i | −0.970725 | − | 0.240192i | ||||
\(14\) | 1.73205 | − | 2.00000i | 0.462910 | − | 0.534522i | ||||
\(15\) | 3.00000 | − | 5.19615i | 0.774597 | − | 1.34164i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.866025 | − | 1.50000i | −0.210042 | − | 0.363803i | 0.741685 | − | 0.670748i | \(-0.234027\pi\) |
−0.951727 | + | 0.306944i | \(0.900693\pi\) | |||||||
\(18\) | − | 3.00000i | − | 0.707107i | ||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | −1.73205 | − | 3.00000i | −0.387298 | − | 0.670820i | ||||
\(21\) | 3.46410 | + | 3.00000i | 0.755929 | + | 0.654654i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59808 | − | 1.50000i | −0.541736 | − | 0.312772i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | −1.50000 | − | 0.866025i | −0.306186 | − | 0.176777i | ||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | −2.59808 | − | 2.50000i | −0.509525 | − | 0.490290i | ||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 2.50000 | − | 0.866025i | 0.472456 | − | 0.163663i | ||||
\(29\) | −5.19615 | − | 3.00000i | −0.964901 | − | 0.557086i | −0.0672232 | − | 0.997738i | \(-0.521414\pi\) |
−0.897678 | + | 0.440652i | \(0.854747\pi\) | |||||||
\(30\) | 5.19615 | − | 3.00000i | 0.948683 | − | 0.547723i | ||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.73205i | − | 0.297044i | ||||||
\(35\) | −1.73205 | + | 9.00000i | −0.292770 | + | 1.52128i | ||||
\(36\) | 1.50000 | − | 2.59808i | 0.250000 | − | 0.433013i | ||||
\(37\) | −2.00000 | + | 3.46410i | −0.328798 | + | 0.569495i | −0.982274 | − | 0.187453i | \(-0.939977\pi\) |
0.653476 | + | 0.756948i | \(0.273310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.33013 | − | 4.50000i | 0.693375 | − | 0.720577i | ||||
\(40\) | − | 3.46410i | − | 0.547723i | ||||||
\(41\) | 3.46410 | − | 6.00000i | 0.541002 | − | 0.937043i | −0.457845 | − | 0.889032i | \(-0.651379\pi\) |
0.998847 | − | 0.0480106i | \(-0.0152881\pi\) | |||||||
\(42\) | 1.50000 | + | 4.33013i | 0.231455 | + | 0.668153i | ||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.19615 | + | 9.00000i | 0.774597 | + | 1.34164i | ||||
\(46\) | −1.50000 | − | 2.59808i | −0.221163 | − | 0.383065i | ||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | −0.866025 | − | 1.50000i | −0.125000 | − | 0.216506i | ||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 6.06218 | + | 3.50000i | 0.857321 | + | 0.494975i | ||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | −1.00000 | − | 3.46410i | −0.138675 | − | 0.480384i | ||||
\(53\) | 9.00000i | 1.23625i | 0.786082 | + | 0.618123i | \(0.212106\pi\) | ||||
−0.786082 | + | 0.618123i | \(0.787894\pi\) | |||||||
\(54\) | 4.50000 | + | 2.59808i | 0.612372 | + | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.59808 | + | 0.500000i | 0.347183 | + | 0.0668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | 0.866025 | + | 1.50000i | 0.112747 | + | 0.195283i | 0.916877 | − | 0.399170i | \(-0.130702\pi\) |
−0.804130 | + | 0.594454i | \(0.797368\pi\) | |||||||
\(60\) | 6.00000 | 0.774597 | ||||||||
\(61\) | −10.5000 | + | 6.06218i | −1.34439 | + | 0.776182i | −0.987448 | − | 0.157945i | \(-0.949513\pi\) |
−0.356939 | + | 0.934128i | \(0.616180\pi\) | |||||||
\(62\) | 0.866025 | − | 1.50000i | 0.109985 | − | 0.190500i | ||||
\(63\) | −7.50000 | + | 2.59808i | −0.944911 | + | 0.327327i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 12.1244 | + | 3.00000i | 1.50384 | + | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0.866025 | − | 1.50000i | 0.105021 | − | 0.181902i | ||||
\(69\) | 4.50000 | − | 2.59808i | 0.541736 | − | 0.312772i | ||||
\(70\) | −6.00000 | + | 6.92820i | −0.717137 | + | 0.828079i | ||||
\(71\) | −12.9904 | + | 7.50000i | −1.54167 | + | 0.890086i | −0.542941 | + | 0.839771i | \(0.682689\pi\) |
−0.998733 | + | 0.0503155i | \(0.983977\pi\) | |||||||
\(72\) | 2.59808 | − | 1.50000i | 0.306186 | − | 0.176777i | ||||
\(73\) | 13.8564i | 1.62177i | 0.585206 | + | 0.810885i | \(0.301014\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | −3.46410 | + | 2.00000i | −0.402694 | + | 0.232495i | ||||
\(75\) | −6.06218 | + | 10.5000i | −0.700000 | + | 1.21244i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.00000 | − | 1.73205i | 0.679366 | − | 0.196116i | ||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 1.73205 | − | 3.00000i | 0.193649 | − | 0.335410i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 6.00000 | − | 3.46410i | 0.662589 | − | 0.382546i | ||||
\(83\) | −12.1244 | −1.33082 | −0.665410 | − | 0.746478i | \(-0.731743\pi\) | ||||
−0.665410 | + | 0.746478i | \(0.731743\pi\) | |||||||
\(84\) | −0.866025 | + | 4.50000i | −0.0944911 | + | 0.490990i | ||||
\(85\) | 3.00000 | + | 5.19615i | 0.325396 | + | 0.563602i | ||||
\(86\) | − | 1.00000i | − | 0.107833i | ||||||
\(87\) | 9.00000 | − | 5.19615i | 0.964901 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.79423 | − | 13.5000i | 0.826187 | − | 1.43100i | −0.0748225 | − | 0.997197i | \(-0.523839\pi\) |
0.901009 | − | 0.433800i | \(-0.142828\pi\) | |||||||
\(90\) | 10.3923i | 1.09545i | ||||||||
\(91\) | −4.00000 | + | 8.66025i | −0.419314 | + | 0.907841i | ||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | 2.59808 | + | 1.50000i | 0.269408 | + | 0.155543i | ||||
\(94\) | −3.00000 | − | 1.73205i | −0.309426 | − | 0.178647i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | 15.0000 | − | 8.66025i | 1.52302 | − | 0.879316i | 0.523390 | − | 0.852093i | \(-0.324667\pi\) |
0.999629 | − | 0.0272222i | \(-0.00866617\pi\) | |||||||
\(98\) | −4.33013 | − | 5.50000i | −0.437409 | − | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.50000 | + | 6.06218i | 0.350000 | + | 0.606218i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 2.59808 | + | 1.50000i | 0.257248 | + | 0.148522i | ||||
\(103\) | − | 8.66025i | − | 0.853320i | −0.904412 | − | 0.426660i | \(-0.859690\pi\) | ||
0.904412 | − | 0.426660i | \(-0.140310\pi\) | |||||||
\(104\) | 0.866025 | − | 3.50000i | 0.0849208 | − | 0.343203i | ||||
\(105\) | −12.0000 | − | 10.3923i | −1.17108 | − | 1.01419i | ||||
\(106\) | −4.50000 | + | 7.79423i | −0.437079 | + | 0.757042i | ||||
\(107\) | −15.5885 | − | 9.00000i | −1.50699 | − | 0.870063i | −0.999967 | − | 0.00813215i | \(-0.997411\pi\) |
−0.507026 | − | 0.861931i | \(-0.669255\pi\) | |||||||
\(108\) | 2.59808 | + | 4.50000i | 0.250000 | + | 0.433013i | ||||
\(109\) | 16.0000 | 1.53252 | 0.766261 | − | 0.642529i | \(-0.222115\pi\) | ||||
0.766261 | + | 0.642529i | \(0.222115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46410 | − | 6.00000i | −0.328798 | − | 0.569495i | ||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | −5.19615 | + | 3.00000i | −0.488813 | + | 0.282216i | −0.724082 | − | 0.689714i | \(-0.757736\pi\) |
0.235269 | + | 0.971930i | \(0.424403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | + | 5.19615i | 0.839254 | + | 0.484544i | ||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | 3.00000 | + | 10.3923i | 0.277350 | + | 0.960769i | ||||
\(118\) | 1.73205i | 0.159448i | ||||||||
\(119\) | −4.33013 | + | 1.50000i | −0.396942 | + | 0.137505i | ||||
\(120\) | 5.19615 | + | 3.00000i | 0.474342 | + | 0.273861i | ||||
\(121\) | −5.50000 | − | 9.52628i | −0.500000 | − | 0.866025i | ||||
\(122\) | −12.1244 | −1.09769 | ||||||||
\(123\) | 6.00000 | + | 10.3923i | 0.541002 | + | 0.937043i | ||||
\(124\) | 1.50000 | − | 0.866025i | 0.134704 | − | 0.0777714i | ||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | −7.79423 | − | 1.50000i | −0.694365 | − | 0.133631i | ||||
\(127\) | −10.0000 | + | 17.3205i | −0.887357 | + | 1.53695i | −0.0443678 | + | 0.999015i | \(0.514127\pi\) |
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 1.73205 | 0.152499 | ||||||||
\(130\) | 9.00000 | + | 8.66025i | 0.789352 | + | 0.759555i | ||||
\(131\) | 15.5885 | 1.36197 | 0.680985 | − | 0.732297i | \(-0.261552\pi\) | ||||
0.680985 | + | 0.732297i | \(0.261552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.06218 | − | 3.50000i | 0.523692 | − | 0.302354i | ||||
\(135\) | −18.0000 | −1.54919 | ||||||||
\(136\) | 1.50000 | − | 0.866025i | 0.128624 | − | 0.0742611i | ||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 5.19615 | 0.442326 | ||||||||
\(139\) | −6.00000 | + | 3.46410i | −0.508913 | + | 0.293821i | −0.732387 | − | 0.680889i | \(-0.761594\pi\) |
0.223474 | + | 0.974710i | \(0.428260\pi\) | |||||||
\(140\) | −8.66025 | + | 3.00000i | −0.731925 | + | 0.253546i | ||||
\(141\) | 3.00000 | − | 5.19615i | 0.252646 | − | 0.437595i | ||||
\(142\) | −15.0000 | −1.25877 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 18.0000 | + | 10.3923i | 1.49482 | + | 0.863034i | ||||
\(146\) | −6.92820 | + | 12.0000i | −0.573382 | + | 0.993127i | ||||
\(147\) | 9.52628 | − | 7.50000i | 0.785714 | − | 0.618590i | ||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 18.1865 | − | 10.5000i | 1.48990 | − | 0.860194i | 0.489966 | − | 0.871742i | \(-0.337009\pi\) |
0.999933 | + | 0.0115483i | \(0.00367601\pi\) | |||||||
\(150\) | −10.5000 | + | 6.06218i | −0.857321 | + | 0.494975i | ||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.59808 | + | 4.50000i | −0.210042 | + | 0.363803i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | 6.06218 | + | 1.50000i | 0.485363 | + | 0.120096i | ||||
\(157\) | 13.8564i | 1.10586i | 0.833227 | + | 0.552931i | \(0.186491\pi\) | ||||
−0.833227 | + | 0.552931i | \(0.813509\pi\) | |||||||
\(158\) | −8.66025 | − | 5.00000i | −0.688973 | − | 0.397779i | ||||
\(159\) | −13.5000 | − | 7.79423i | −1.07062 | − | 0.618123i | ||||
\(160\) | 3.00000 | − | 1.73205i | 0.237171 | − | 0.136931i | ||||
\(161\) | −5.19615 | + | 6.00000i | −0.409514 | + | 0.472866i | ||||
\(162\) | −7.79423 | + | 4.50000i | −0.612372 | + | 0.353553i | ||||
\(163\) | 3.50000 | + | 6.06218i | 0.274141 | + | 0.474826i | 0.969918 | − | 0.243432i | \(-0.0782731\pi\) |
−0.695777 | + | 0.718258i | \(0.744940\pi\) | |||||||
\(164\) | 6.92820 | 0.541002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.5000 | − | 6.06218i | −0.814958 | − | 0.470516i | ||||
\(167\) | −3.46410 | + | 6.00000i | −0.268060 | + | 0.464294i | −0.968361 | − | 0.249554i | \(-0.919716\pi\) |
0.700301 | + | 0.713848i | \(0.253049\pi\) | |||||||
\(168\) | −3.00000 | + | 3.46410i | −0.231455 | + | 0.267261i | ||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 6.00000i | 0.460179i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 10.3923 | 0.787839 | ||||||||
\(175\) | 3.50000 | − | 18.1865i | 0.264575 | − | 1.37477i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00000 | −0.225494 | ||||||||
\(178\) | 13.5000 | − | 7.79423i | 1.01187 | − | 0.584202i | ||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | −5.19615 | + | 9.00000i | −0.387298 | + | 0.670820i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | −7.79423 | + | 5.50000i | −0.577747 | + | 0.407687i | ||||
\(183\) | − | 21.0000i | − | 1.55236i | ||||||
\(184\) | 1.50000 | − | 2.59808i | 0.110581 | − | 0.191533i | ||||
\(185\) | 6.92820 | − | 12.0000i | 0.509372 | − | 0.882258i | ||||
\(186\) | 1.50000 | + | 2.59808i | 0.109985 | + | 0.190500i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.73205 | − | 3.00000i | −0.126323 | − | 0.218797i | ||||
\(189\) | 2.59808 | − | 13.5000i | 0.188982 | − | 0.981981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9904 | − | 7.50000i | 0.939951 | − | 0.542681i | 0.0500060 | − | 0.998749i | \(-0.484076\pi\) |
0.889945 | + | 0.456068i | \(0.150743\pi\) | |||||||
\(192\) | 0.866025 | − | 1.50000i | 0.0625000 | − | 0.108253i | ||||
\(193\) | 7.00000 | − | 12.1244i | 0.503871 | − | 0.872730i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | 17.3205 | 1.24354 | ||||||||
\(195\) | −15.0000 | + | 15.5885i | −1.07417 | + | 1.11631i | ||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | −12.9904 | − | 7.50000i | −0.925526 | − | 0.534353i | −0.0401324 | − | 0.999194i | \(-0.512778\pi\) |
−0.885394 | + | 0.464841i | \(0.846111\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | − | 0.866025i | 0.106332 | − | 0.0613909i | −0.445891 | − | 0.895087i | \(-0.647113\pi\) |
0.552223 | + | 0.833696i | \(0.313780\pi\) | |||||||
\(200\) | 7.00000i | 0.494975i | ||||||||
\(201\) | 6.06218 | + | 10.5000i | 0.427593 | + | 0.740613i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.3923 | + | 12.0000i | −0.729397 | + | 0.842235i | ||||
\(204\) | 1.50000 | + | 2.59808i | 0.105021 | + | 0.181902i | ||||
\(205\) | −12.0000 | + | 20.7846i | −0.838116 | + | 1.45166i | ||||
\(206\) | 4.33013 | − | 7.50000i | 0.301694 | − | 0.522550i | ||||
\(207\) | 9.00000i | 0.625543i | ||||||||
\(208\) | 2.50000 | − | 2.59808i | 0.173344 | − | 0.180144i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −5.19615 | − | 15.0000i | −0.358569 | − | 1.03510i | ||||
\(211\) | 10.0000 | − | 17.3205i | 0.688428 | − | 1.19239i | −0.283918 | − | 0.958849i | \(-0.591634\pi\) |
0.972346 | − | 0.233544i | \(-0.0750324\pi\) | |||||||
\(212\) | −7.79423 | + | 4.50000i | −0.535310 | + | 0.309061i | ||||
\(213\) | − | 25.9808i | − | 1.78017i | ||||||
\(214\) | −9.00000 | − | 15.5885i | −0.615227 | − | 1.06561i | ||||
\(215\) | 1.73205 | + | 3.00000i | 0.118125 | + | 0.204598i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −4.50000 | − | 0.866025i | −0.305480 | − | 0.0587896i | ||||
\(218\) | 13.8564 | + | 8.00000i | 0.938474 | + | 0.541828i | ||||
\(219\) | −20.7846 | − | 12.0000i | −1.40449 | − | 0.810885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.73205 | + | 6.00000i | 0.116510 | + | 0.403604i | ||||
\(222\) | − | 6.92820i | − | 0.464991i | ||||||
\(223\) | −4.50000 | − | 2.59808i | −0.301342 | − | 0.173980i | 0.341703 | − | 0.939808i | \(-0.388996\pi\) |
−0.643046 | + | 0.765828i | \(0.722329\pi\) | |||||||
\(224\) | 0.866025 | + | 2.50000i | 0.0578638 | + | 0.167038i | ||||
\(225\) | −10.5000 | − | 18.1865i | −0.700000 | − | 1.21244i | ||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −5.19615 | − | 9.00000i | −0.344881 | − | 0.597351i | 0.640451 | − | 0.767999i | \(-0.278747\pi\) |
−0.985332 | + | 0.170648i | \(0.945414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5885i | 1.03011i | 0.857156 | + | 0.515057i | \(0.172229\pi\) | ||||
−0.857156 | + | 0.515057i | \(0.827771\pi\) | |||||||
\(230\) | 5.19615 | + | 9.00000i | 0.342624 | + | 0.593442i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | − | 5.19615i | 0.196960 | − | 0.341144i | ||||
\(233\) | 18.0000i | 1.17922i | 0.807688 | + | 0.589610i | \(0.200718\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799282\pi\) | |||||||
\(234\) | −2.59808 | + | 10.5000i | −0.169842 | + | 0.686406i | ||||
\(235\) | 12.0000 | 0.782794 | ||||||||
\(236\) | −0.866025 | + | 1.50000i | −0.0563735 | + | 0.0976417i | ||||
\(237\) | 8.66025 | − | 15.0000i | 0.562544 | − | 0.974355i | ||||
\(238\) | −4.50000 | − | 0.866025i | −0.291692 | − | 0.0561361i | ||||
\(239\) | − | 21.0000i | − | 1.35838i | −0.733964 | − | 0.679189i | \(-0.762332\pi\) | ||
0.733964 | − | 0.679189i | \(-0.237668\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | −9.00000 | + | 5.19615i | −0.579741 | + | 0.334714i | −0.761030 | − | 0.648716i | \(-0.775306\pi\) |
0.181289 | + | 0.983430i | \(0.441973\pi\) | |||||||
\(242\) | − | 11.0000i | − | 0.707107i | ||||||
\(243\) | −7.79423 | − | 13.5000i | −0.500000 | − | 0.866025i | ||||
\(244\) | −10.5000 | − | 6.06218i | −0.672194 | − | 0.388091i | ||||
\(245\) | 22.5167 | + | 9.00000i | 1.43854 | + | 0.574989i | ||||
\(246\) | 12.0000i | 0.765092i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.73205 | 0.109985 | ||||||||
\(249\) | 10.5000 | − | 18.1865i | 0.665410 | − | 1.15252i | ||||
\(250\) | −6.00000 | − | 3.46410i | −0.379473 | − | 0.219089i | ||||
\(251\) | 9.52628 | + | 16.5000i | 0.601293 | + | 1.04147i | 0.992626 | + | 0.121221i | \(0.0386810\pi\) |
−0.391332 | + | 0.920250i | \(0.627986\pi\) | |||||||
\(252\) | −6.00000 | − | 5.19615i | −0.377964 | − | 0.327327i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −17.3205 | + | 10.0000i | −1.08679 | + | 0.627456i | ||||
\(255\) | −10.3923 | −0.650791 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.79423 | − | 13.5000i | 0.486191 | − | 0.842107i | −0.513683 | − | 0.857980i | \(-0.671719\pi\) |
0.999874 | + | 0.0158730i | \(0.00505273\pi\) | |||||||
\(258\) | 1.50000 | + | 0.866025i | 0.0933859 | + | 0.0539164i | ||||
\(259\) | 8.00000 | + | 6.92820i | 0.497096 | + | 0.430498i | ||||
\(260\) | 3.46410 | + | 12.0000i | 0.214834 | + | 0.744208i | ||||
\(261\) | 18.0000i | 1.11417i | ||||||||
\(262\) | 13.5000 | + | 7.79423i | 0.834033 | + | 0.481529i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 31.1769i | − | 1.91518i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.5000 | + | 23.3827i | 0.826187 | + | 1.43100i | ||||
\(268\) | 7.00000 | 0.427593 | ||||||||
\(269\) | −6.92820 | − | 12.0000i | −0.422420 | − | 0.731653i | 0.573756 | − | 0.819027i | \(-0.305486\pi\) |
−0.996176 | + | 0.0873736i | \(0.972153\pi\) | |||||||
\(270\) | −15.5885 | − | 9.00000i | −0.948683 | − | 0.547723i | ||||
\(271\) | −7.50000 | − | 4.33013i | −0.455593 | − | 0.263036i | 0.254597 | − | 0.967047i | \(-0.418057\pi\) |
−0.710189 | + | 0.704011i | \(0.751391\pi\) | |||||||
\(272\) | 1.73205 | 0.105021 | ||||||||
\(273\) | −9.52628 | − | 13.5000i | −0.576557 | − | 0.817057i | ||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.50000 | + | 2.59808i | 0.270868 | + | 0.156386i | ||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | −6.92820 | −0.415526 | ||||||||
\(279\) | −4.50000 | + | 2.59808i | −0.269408 | + | 0.155543i | ||||
\(280\) | −9.00000 | − | 1.73205i | −0.537853 | − | 0.103510i | ||||
\(281\) | 12.0000i | 0.715860i | 0.933748 | + | 0.357930i | \(0.116517\pi\) | ||||
−0.933748 | + | 0.357930i | \(0.883483\pi\) | |||||||
\(282\) | 5.19615 | − | 3.00000i | 0.309426 | − | 0.178647i | ||||
\(283\) | −21.0000 | − | 12.1244i | −1.24832 | − | 0.720718i | −0.277546 | − | 0.960712i | \(-0.589521\pi\) |
−0.970774 | + | 0.239994i | \(0.922854\pi\) | |||||||
\(284\) | −12.9904 | − | 7.50000i | −0.770837 | − | 0.445043i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.8564 | − | 12.0000i | −0.817918 | − | 0.708338i | ||||
\(288\) | 2.59808 | + | 1.50000i | 0.153093 | + | 0.0883883i | ||||
\(289\) | 7.00000 | − | 12.1244i | 0.411765 | − | 0.713197i | ||||
\(290\) | 10.3923 | + | 18.0000i | 0.610257 | + | 1.05700i | ||||
\(291\) | 30.0000i | 1.75863i | ||||||||
\(292\) | −12.0000 | + | 6.92820i | −0.702247 | + | 0.405442i | ||||
\(293\) | 8.66025 | + | 15.0000i | 0.505937 | + | 0.876309i | 0.999976 | + | 0.00686959i | \(0.00218668\pi\) |
−0.494039 | + | 0.869440i | \(0.664480\pi\) | |||||||
\(294\) | 12.0000 | − | 1.73205i | 0.699854 | − | 0.101015i | ||||
\(295\) | −3.00000 | − | 5.19615i | −0.174667 | − | 0.302532i | ||||
\(296\) | −3.46410 | − | 2.00000i | −0.201347 | − | 0.116248i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.0000 | 1.21650 | ||||||||
\(299\) | 7.79423 | + | 7.50000i | 0.450752 | + | 0.433736i | ||||
\(300\) | −12.1244 | −0.700000 | ||||||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | 13.8564 | + | 8.00000i | 0.797347 | + | 0.460348i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.3731 | − | 21.0000i | 2.08272 | − | 1.20246i | ||||
\(306\) | −4.50000 | + | 2.59808i | −0.257248 | + | 0.148522i | ||||
\(307\) | 24.2487i | 1.38395i | 0.721923 | + | 0.691974i | \(0.243259\pi\) | ||||
−0.721923 | + | 0.691974i | \(0.756741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9904 | + | 7.50000i | 0.738997 | + | 0.426660i | ||||
\(310\) | −3.00000 | + | 5.19615i | −0.170389 | + | 0.295122i | ||||
\(311\) | −13.8564 | −0.785725 | −0.392862 | − | 0.919597i | \(-0.628515\pi\) | ||||
−0.392862 | + | 0.919597i | \(0.628515\pi\) | |||||||
\(312\) | 4.50000 | + | 4.33013i | 0.254762 | + | 0.245145i | ||||
\(313\) | − | 3.46410i | − | 0.195803i | −0.995196 | − | 0.0979013i | \(-0.968787\pi\) | ||
0.995196 | − | 0.0979013i | \(-0.0312129\pi\) | |||||||
\(314\) | −6.92820 | + | 12.0000i | −0.390981 | + | 0.677199i | ||||
\(315\) | 25.9808 | − | 9.00000i | 1.46385 | − | 0.507093i | ||||
\(316\) | −5.00000 | − | 8.66025i | −0.281272 | − | 0.487177i | ||||
\(317\) | 3.00000i | 0.168497i | 0.996445 | + | 0.0842484i | \(0.0268489\pi\) | ||||
−0.996445 | + | 0.0842484i | \(0.973151\pi\) | |||||||
\(318\) | −7.79423 | − | 13.5000i | −0.437079 | − | 0.757042i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.46410 | 0.193649 | ||||||||
\(321\) | 27.0000 | − | 15.5885i | 1.50699 | − | 0.870063i | ||||
\(322\) | −7.50000 | + | 2.59808i | −0.417959 | + | 0.144785i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | −24.5000 | − | 6.06218i | −1.35902 | − | 0.336269i | ||||
\(326\) | 7.00000i | 0.387694i | ||||||||
\(327\) | −13.8564 | + | 24.0000i | −0.766261 | + | 1.32720i | ||||
\(328\) | 6.00000 | + | 3.46410i | 0.331295 | + | 0.191273i | ||||
\(329\) | −1.73205 | + | 9.00000i | −0.0954911 | + | 0.496186i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | −6.06218 | − | 10.5000i | −0.332705 | − | 0.576262i | ||||
\(333\) | 12.0000 | 0.657596 | ||||||||
\(334\) | −6.00000 | + | 3.46410i | −0.328305 | + | 0.189547i | ||||
\(335\) | −12.1244 | + | 21.0000i | −0.662424 | + | 1.14735i | ||||
\(336\) | −4.33013 | + | 1.50000i | −0.236228 | + | 0.0818317i | ||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 6.92820 | + | 11.0000i | 0.376845 | + | 0.598321i | ||||
\(339\) | − | 10.3923i | − | 0.564433i | ||||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0.866025 | − | 0.500000i | 0.0466930 | − | 0.0269582i | ||||
\(345\) | −15.5885 | + | 9.00000i | −0.839254 | + | 0.484544i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.3923 | + | 6.00000i | −0.557888 | + | 0.322097i | −0.752297 | − | 0.658824i | \(-0.771054\pi\) |
0.194409 | + | 0.980921i | \(0.437721\pi\) | |||||||
\(348\) | 9.00000 | + | 5.19615i | 0.482451 | + | 0.278543i | ||||
\(349\) | −25.5000 | − | 14.7224i | −1.36498 | − | 0.788074i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | 12.1244 | − | 14.0000i | 0.648074 | − | 0.748331i | ||||
\(351\) | −18.1865 | − | 4.50000i | −0.970725 | − | 0.240192i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.06218 | + | 10.5000i | −0.322657 | + | 0.558859i | −0.981035 | − | 0.193829i | \(-0.937909\pi\) |
0.658378 | + | 0.752687i | \(0.271243\pi\) | |||||||
\(354\) | −2.59808 | − | 1.50000i | −0.138086 | − | 0.0797241i | ||||
\(355\) | 45.0000 | − | 25.9808i | 2.38835 | − | 1.37892i | ||||
\(356\) | 15.5885 | 0.826187 | ||||||||
\(357\) | 1.50000 | − | 7.79423i | 0.0793884 | − | 0.412514i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.0000i | − | 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | −9.00000 | + | 5.19615i | −0.474342 | + | 0.273861i | ||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.0526 | 1.00000 | ||||||||
\(364\) | −9.50000 | + | 0.866025i | −0.497935 | + | 0.0453921i | ||||
\(365\) | − | 48.0000i | − | 2.51243i | ||||||
\(366\) | 10.5000 | − | 18.1865i | 0.548844 | − | 0.950625i | ||||
\(367\) | −10.5000 | − | 6.06218i | −0.548096 | − | 0.316443i | 0.200258 | − | 0.979743i | \(-0.435822\pi\) |
−0.748354 | + | 0.663300i | \(0.769155\pi\) | |||||||
\(368\) | 2.59808 | − | 1.50000i | 0.135434 | − | 0.0781929i | ||||
\(369\) | −20.7846 | −1.08200 | ||||||||
\(370\) | 12.0000 | − | 6.92820i | 0.623850 | − | 0.360180i | ||||
\(371\) | 23.3827 | + | 4.50000i | 1.21397 | + | 0.233628i | ||||
\(372\) | 3.00000i | 0.155543i | ||||||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.00000 | − | 10.3923i | 0.309839 | − | 0.536656i | ||||
\(376\) | − | 3.46410i | − | 0.178647i | ||||||
\(377\) | 15.5885 | + | 15.0000i | 0.802846 | + | 0.772539i | ||||
\(378\) | 9.00000 | − | 10.3923i | 0.462910 | − | 0.534522i | ||||
\(379\) | 10.0000 | − | 17.3205i | 0.513665 | − | 0.889695i | −0.486209 | − | 0.873843i | \(-0.661621\pi\) |
0.999874 | − | 0.0158521i | \(-0.00504609\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3205 | − | 30.0000i | −0.887357 | − | 1.53695i | ||||
\(382\) | 15.0000 | 0.767467 | ||||||||
\(383\) | −12.1244 | − | 21.0000i | −0.619526 | − | 1.07305i | −0.989572 | − | 0.144037i | \(-0.953992\pi\) |
0.370047 | − | 0.929013i | \(-0.379342\pi\) | |||||||
\(384\) | 1.50000 | − | 0.866025i | 0.0765466 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.1244 | − | 7.00000i | 0.617113 | − | 0.356291i | ||||
\(387\) | −1.50000 | + | 2.59808i | −0.0762493 | + | 0.132068i | ||||
\(388\) | 15.0000 | + | 8.66025i | 0.761510 | + | 0.439658i | ||||
\(389\) | − | 9.00000i | − | 0.456318i | −0.973624 | − | 0.228159i | \(-0.926729\pi\) | ||
0.973624 | − | 0.228159i | \(-0.0732706\pi\) | |||||||
\(390\) | −20.7846 | + | 6.00000i | −1.05247 | + | 0.303822i | ||||
\(391\) | 5.19615i | 0.262781i | ||||||||
\(392\) | 2.59808 | − | 6.50000i | 0.131223 | − | 0.328300i | ||||
\(393\) | −13.5000 | + | 23.3827i | −0.680985 | + | 1.17950i | ||||
\(394\) | −7.50000 | − | 12.9904i | −0.377845 | − | 0.654446i | ||||
\(395\) | 34.6410 | 1.74298 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5000 | + | 6.06218i | −0.526980 | + | 0.304252i | −0.739786 | − | 0.672843i | \(-0.765073\pi\) |
0.212806 | + | 0.977095i | \(0.431740\pi\) | |||||||
\(398\) | 1.73205 | 0.0868199 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.50000 | + | 6.06218i | −0.175000 | + | 0.303109i | ||||
\(401\) | −15.5885 | − | 9.00000i | −0.778450 | − | 0.449439i | 0.0574304 | − | 0.998350i | \(-0.481709\pi\) |
−0.835881 | + | 0.548911i | \(0.815043\pi\) | |||||||
\(402\) | 12.1244i | 0.604708i | ||||||||
\(403\) | −1.50000 | + | 6.06218i | −0.0747203 | + | 0.301979i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.5885 | − | 27.0000i | 0.774597 | − | 1.34164i | ||||
\(406\) | −15.0000 | + | 5.19615i | −0.744438 | + | 0.257881i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.00000i | 0.148522i | ||||||||
\(409\) | −12.0000 | + | 6.92820i | −0.593362 | + | 0.342578i | −0.766426 | − | 0.642333i | \(-0.777967\pi\) |
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(410\) | −20.7846 | + | 12.0000i | −1.02648 | + | 0.592638i | ||||
\(411\) | 20.7846i | 1.02523i | ||||||||
\(412\) | 7.50000 | − | 4.33013i | 0.369498 | − | 0.213330i | ||||
\(413\) | 4.33013 | − | 1.50000i | 0.213072 | − | 0.0738102i | ||||
\(414\) | −4.50000 | + | 7.79423i | −0.221163 | + | 0.383065i | ||||
\(415\) | 42.0000 | 2.06170 | ||||||||
\(416\) | 3.46410 | − | 1.00000i | 0.169842 | − | 0.0490290i | ||||
\(417\) | − | 12.0000i | − | 0.587643i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.52628 | − | 16.5000i | 0.465389 | − | 0.806078i | −0.533830 | − | 0.845592i | \(-0.679248\pi\) |
0.999219 | + | 0.0395142i | \(0.0125810\pi\) | |||||||
\(420\) | 3.00000 | − | 15.5885i | 0.146385 | − | 0.760639i | ||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 17.3205 | − | 10.0000i | 0.843149 | − | 0.486792i | ||||
\(423\) | 5.19615 | + | 9.00000i | 0.252646 | + | 0.437595i | ||||
\(424\) | −9.00000 | −0.437079 | ||||||||
\(425\) | −6.06218 | − | 10.5000i | −0.294059 | − | 0.509325i | ||||
\(426\) | 12.9904 | − | 22.5000i | 0.629386 | − | 1.09013i | ||||
\(427\) | 10.5000 | + | 30.3109i | 0.508131 | + | 1.46685i | ||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.46410i | 0.167054i | ||||||||
\(431\) | 2.59808 | + | 1.50000i | 0.125145 | + | 0.0722525i | 0.561266 | − | 0.827636i | \(-0.310315\pi\) |
−0.436121 | + | 0.899888i | \(0.643648\pi\) | |||||||
\(432\) | −2.59808 | + | 4.50000i | −0.125000 | + | 0.216506i | ||||
\(433\) | 6.00000 | − | 3.46410i | 0.288342 | − | 0.166474i | −0.348852 | − | 0.937178i | \(-0.613428\pi\) |
0.637194 | + | 0.770704i | \(0.280095\pi\) | |||||||
\(434\) | −3.46410 | − | 3.00000i | −0.166282 | − | 0.144005i | ||||
\(435\) | −31.1769 | + | 18.0000i | −1.49482 | + | 0.863034i | ||||
\(436\) | 8.00000 | + | 13.8564i | 0.383131 | + | 0.663602i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −12.0000 | − | 20.7846i | −0.573382 | − | 0.993127i | ||||
\(439\) | −3.00000 | − | 1.73205i | −0.143182 | − | 0.0826663i | 0.426698 | − | 0.904394i | \(-0.359677\pi\) |
−0.569880 | + | 0.821728i | \(0.693010\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | + | 20.7846i | 0.142857 | + | 0.989743i | ||||
\(442\) | −1.50000 | + | 6.06218i | −0.0713477 | + | 0.288348i | ||||
\(443\) | 18.0000i | 0.855206i | 0.903967 | + | 0.427603i | \(0.140642\pi\) | ||||
−0.903967 | + | 0.427603i | \(0.859358\pi\) | |||||||
\(444\) | 3.46410 | − | 6.00000i | 0.164399 | − | 0.284747i | ||||
\(445\) | −27.0000 | + | 46.7654i | −1.27992 | + | 2.21689i | ||||
\(446\) | −2.59808 | − | 4.50000i | −0.123022 | − | 0.213081i | ||||
\(447\) | 36.3731i | 1.72039i | ||||||||
\(448\) | −0.500000 | + | 2.59808i | −0.0236228 | + | 0.122748i | ||||
\(449\) | 5.19615 | − | 3.00000i | 0.245222 | − | 0.141579i | −0.372353 | − | 0.928091i | \(-0.621449\pi\) |
0.617574 | + | 0.786513i | \(0.288115\pi\) | |||||||
\(450\) | − | 21.0000i | − | 0.989949i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.19615 | − | 3.00000i | −0.244406 | − | 0.141108i | ||||
\(453\) | −13.8564 | + | 24.0000i | −0.651031 | + | 1.12762i | ||||
\(454\) | − | 10.3923i | − | 0.487735i | ||||||
\(455\) | 13.8564 | − | 30.0000i | 0.649598 | − | 1.40642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5000 | + | 26.8468i | −0.725059 | + | 1.25584i | 0.233890 | + | 0.972263i | \(0.424854\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | −7.79423 | + | 13.5000i | −0.364200 | + | 0.630814i | ||||
\(459\) | −4.50000 | − | 7.79423i | −0.210042 | − | 0.363803i | ||||
\(460\) | 10.3923i | 0.484544i | ||||||||
\(461\) | 3.46410 | + | 6.00000i | 0.161339 | + | 0.279448i | 0.935349 | − | 0.353726i | \(-0.115085\pi\) |
−0.774010 | + | 0.633173i | \(0.781752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 5.19615 | − | 3.00000i | 0.241225 | − | 0.139272i | ||||
\(465\) | −9.00000 | − | 5.19615i | −0.417365 | − | 0.240966i | ||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | −15.5885 | −0.721348 | −0.360674 | − | 0.932692i | \(-0.617453\pi\) | ||||
−0.360674 | + | 0.932692i | \(0.617453\pi\) | |||||||
\(468\) | −7.50000 | + | 7.79423i | −0.346688 | + | 0.360288i | ||||
\(469\) | −14.0000 | − | 12.1244i | −0.646460 | − | 0.559851i | ||||
\(470\) | 10.3923 | + | 6.00000i | 0.479361 | + | 0.276759i | ||||
\(471\) | −20.7846 | − | 12.0000i | −0.957704 | − | 0.552931i | ||||
\(472\) | −1.50000 | + | 0.866025i | −0.0690431 | + | 0.0398621i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 15.0000 | − | 8.66025i | 0.688973 | − | 0.397779i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.46410 | − | 3.00000i | −0.158777 | − | 0.137505i | ||||
\(477\) | 23.3827 | − | 13.5000i | 1.07062 | − | 0.618123i | ||||
\(478\) | 10.5000 | − | 18.1865i | 0.480259 | − | 0.831833i | ||||
\(479\) | −12.1244 | + | 21.0000i | −0.553976 | + | 0.959514i | 0.444006 | + | 0.896024i | \(0.353557\pi\) |
−0.997982 | + | 0.0634909i | \(0.979777\pi\) | |||||||
\(480\) | 6.00000i | 0.273861i | ||||||||
\(481\) | 10.0000 | − | 10.3923i | 0.455961 | − | 0.473848i | ||||
\(482\) | −10.3923 | −0.473357 | ||||||||
\(483\) | −4.50000 | − | 12.9904i | −0.204757 | − | 0.591083i | ||||
\(484\) | 5.50000 | − | 9.52628i | 0.250000 | − | 0.433013i | ||||
\(485\) | −51.9615 | + | 30.0000i | −2.35945 | + | 1.36223i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | 1.00000 | + | 1.73205i | 0.0453143 | + | 0.0784867i | 0.887793 | − | 0.460243i | \(-0.152238\pi\) |
−0.842479 | + | 0.538730i | \(0.818904\pi\) | |||||||
\(488\) | −6.06218 | − | 10.5000i | −0.274422 | − | 0.475313i | ||||
\(489\) | −12.1244 | −0.548282 | ||||||||
\(490\) | 15.0000 | + | 19.0526i | 0.677631 | + | 0.860707i | ||||
\(491\) | 31.1769 | + | 18.0000i | 1.40699 | + | 0.812329i | 0.995097 | − | 0.0989017i | \(-0.0315329\pi\) |
0.411897 | + | 0.911230i | \(0.364866\pi\) | |||||||
\(492\) | −6.00000 | + | 10.3923i | −0.270501 | + | 0.468521i | ||||
\(493\) | 10.3923i | 0.468046i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | + | 0.866025i | 0.0673520 | + | 0.0388857i | ||||
\(497\) | 12.9904 | + | 37.5000i | 0.582698 | + | 1.68210i | ||||
\(498\) | 18.1865 | − | 10.5000i | 0.814958 | − | 0.470516i | ||||
\(499\) | −17.0000 | −0.761025 | −0.380512 | − | 0.924776i | \(-0.624252\pi\) | ||||
−0.380512 | + | 0.924776i | \(0.624252\pi\) | |||||||
\(500\) | −3.46410 | − | 6.00000i | −0.154919 | − | 0.268328i | ||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 19.0526i | 0.850357i | ||||||||
\(503\) | 3.46410 | + | 6.00000i | 0.154457 | + | 0.267527i | 0.932861 | − | 0.360236i | \(-0.117304\pi\) |
−0.778404 | + | 0.627763i | \(0.783971\pi\) | |||||||
\(504\) | −2.59808 | − | 7.50000i | −0.115728 | − | 0.334077i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.0526 | + | 12.0000i | −0.846154 | + | 0.532939i | ||||
\(508\) | −20.0000 | −0.887357 | ||||||||
\(509\) | −1.73205 | + | 3.00000i | −0.0767718 | + | 0.132973i | −0.901855 | − | 0.432038i | \(-0.857795\pi\) |
0.825084 | + | 0.565011i | \(0.191128\pi\) | |||||||
\(510\) | −9.00000 | − | 5.19615i | −0.398527 | − | 0.230089i | ||||
\(511\) | 36.0000 | + | 6.92820i | 1.59255 | + | 0.306486i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.5000 | − | 7.79423i | 0.595459 | − | 0.343789i | ||||
\(515\) | 30.0000i | 1.32196i | ||||||||
\(516\) | 0.866025 | + | 1.50000i | 0.0381246 | + | 0.0660338i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.46410 | + | 10.0000i | 0.152204 | + | 0.439375i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.00000 | + | 12.1244i | −0.131559 | + | 0.531688i | ||||
\(521\) | 13.8564 | 0.607060 | 0.303530 | − | 0.952822i | \(-0.401835\pi\) | ||||
0.303530 | + | 0.952822i | \(0.401835\pi\) | |||||||
\(522\) | −9.00000 | + | 15.5885i | −0.393919 | + | 0.682288i | ||||
\(523\) | −18.0000 | − | 10.3923i | −0.787085 | − | 0.454424i | 0.0518503 | − | 0.998655i | \(-0.483488\pi\) |
−0.838935 | + | 0.544231i | \(0.816821\pi\) | |||||||
\(524\) | 7.79423 | + | 13.5000i | 0.340492 | + | 0.589750i | ||||
\(525\) | 24.2487 | + | 21.0000i | 1.05830 | + | 0.916515i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.59808 | + | 1.50000i | −0.113174 | + | 0.0653410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 15.5885 | − | 27.0000i | 0.677119 | − | 1.17281i | ||||
\(531\) | 2.59808 | − | 4.50000i | 0.112747 | − | 0.195283i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.3205 | + | 18.0000i | −0.750234 | + | 0.779667i | ||||
\(534\) | 27.0000i | 1.16840i | ||||||||
\(535\) | 54.0000 | + | 31.1769i | 2.33462 | + | 1.34790i | ||||
\(536\) | 6.06218 | + | 3.50000i | 0.261846 | + | 0.151177i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 13.8564i | − | 0.597392i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.00000 | − | 15.5885i | −0.387298 | − | 0.670820i | ||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | −4.33013 | − | 7.50000i | −0.185995 | − | 0.322153i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.50000 | + | 0.866025i | 0.0643120 | + | 0.0371305i | ||||
\(545\) | −55.4256 | −2.37417 | ||||||||
\(546\) | −1.50000 | − | 16.4545i | −0.0641941 | − | 0.704187i | ||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 10.3923 | + | 6.00000i | 0.443937 | + | 0.256307i | ||||
\(549\) | 31.5000 | + | 18.1865i | 1.34439 | + | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.59808 | + | 4.50000i | 0.110581 | + | 0.191533i | ||||
\(553\) | −5.00000 | + | 25.9808i | −0.212622 | + | 1.10481i | ||||
\(554\) | − | 2.00000i | − | 0.0849719i | ||||||
\(555\) | 12.0000 | + | 20.7846i | 0.509372 | + | 0.882258i | ||||
\(556\) | −6.00000 | − | 3.46410i | −0.254457 | − | 0.146911i | ||||
\(557\) | 18.1865 | + | 10.5000i | 0.770588 | + | 0.444899i | 0.833084 | − | 0.553146i | \(-0.186573\pi\) |
−0.0624962 | + | 0.998045i | \(0.519906\pi\) | |||||||
\(558\) | −5.19615 | −0.219971 | ||||||||
\(559\) | 1.00000 | + | 3.46410i | 0.0422955 | + | 0.146516i | ||||
\(560\) | −6.92820 | − | 6.00000i | −0.292770 | − | 0.253546i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | ||||
\(563\) | 5.19615 | + | 9.00000i | 0.218992 | + | 0.379305i | 0.954500 | − | 0.298211i | \(-0.0963899\pi\) |
−0.735508 | + | 0.677516i | \(0.763057\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | 18.0000 | − | 10.3923i | 0.757266 | − | 0.437208i | ||||
\(566\) | −12.1244 | − | 21.0000i | −0.509625 | − | 0.882696i | ||||
\(567\) | 18.0000 | + | 15.5885i | 0.755929 | + | 0.654654i | ||||
\(568\) | −7.50000 | − | 12.9904i | −0.314693 | − | 0.545064i | ||||
\(569\) | 15.5885 | + | 9.00000i | 0.653502 | + | 0.377300i | 0.789797 | − | 0.613369i | \(-0.210186\pi\) |
−0.136295 | + | 0.990668i | \(0.543519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.0000 | −1.54840 | −0.774201 | − | 0.632940i | \(-0.781848\pi\) | ||||
−0.774201 | + | 0.632940i | \(0.781848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.9808i | 1.08536i | ||||||||
\(574\) | −6.00000 | − | 17.3205i | −0.250435 | − | 0.722944i | ||||
\(575\) | −18.1865 | − | 10.5000i | −0.758431 | − | 0.437880i | ||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | − | 10.3923i | − | 0.432637i | −0.976323 | − | 0.216319i | \(-0.930595\pi\) | ||
0.976323 | − | 0.216319i | \(-0.0694050\pi\) | |||||||
\(578\) | 12.1244 | − | 7.00000i | 0.504307 | − | 0.291162i | ||||
\(579\) | 12.1244 | + | 21.0000i | 0.503871 | + | 0.872730i | ||||
\(580\) | 20.7846i | 0.863034i | ||||||||
\(581\) | −6.06218 | + | 31.5000i | −0.251502 | + | 1.30684i | ||||
\(582\) | −15.0000 | + | 25.9808i | −0.621770 | + | 1.07694i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −13.8564 | −0.573382 | ||||||||
\(585\) | −10.3923 | − | 36.0000i | −0.429669 | − | 1.48842i | ||||
\(586\) | 17.3205i | 0.715504i | ||||||||
\(587\) | 2.59808 | − | 4.50000i | 0.107234 | − | 0.185735i | −0.807415 | − | 0.589984i | \(-0.799134\pi\) |
0.914649 | + | 0.404249i | \(0.132467\pi\) | |||||||
\(588\) | 11.2583 | + | 4.50000i | 0.464286 | + | 0.185577i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − | 6.00000i | − | 0.247016i | ||||||
\(591\) | 22.5000 | − | 12.9904i | 0.925526 | − | 0.534353i | ||||
\(592\) | −2.00000 | − | 3.46410i | −0.0821995 | − | 0.142374i | ||||
\(593\) | 39.8372 | 1.63592 | 0.817958 | − | 0.575278i | \(-0.195106\pi\) | ||||
0.817958 | + | 0.575278i | \(0.195106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0000 | − | 5.19615i | 0.614940 | − | 0.213021i | ||||
\(596\) | 18.1865 | + | 10.5000i | 0.744949 | + | 0.430097i | ||||
\(597\) | 3.00000i | 0.122782i | ||||||||
\(598\) | 3.00000 | + | 10.3923i | 0.122679 | + | 0.424973i | ||||
\(599\) | 33.0000i | 1.34834i | 0.738575 | + | 0.674172i | \(0.235499\pi\) | ||||
−0.738575 | + | 0.674172i | \(0.764501\pi\) | |||||||
\(600\) | −10.5000 | − | 6.06218i | −0.428661 | − | 0.247487i | ||||
\(601\) | 27.0000 | + | 15.5885i | 1.10135 | + | 0.635866i | 0.936576 | − | 0.350464i | \(-0.113976\pi\) |
0.164777 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(602\) | −2.59808 | − | 0.500000i | −0.105890 | − | 0.0203785i | ||||
\(603\) | −21.0000 | −0.855186 | ||||||||
\(604\) | 8.00000 | + | 13.8564i | 0.325515 | + | 0.563809i | ||||
\(605\) | 19.0526 | + | 33.0000i | 0.774597 | + | 1.34164i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50000 | − | 2.59808i | 0.182649 | − | 0.105453i | −0.405887 | − | 0.913923i | \(-0.633038\pi\) |
0.588537 | + | 0.808470i | \(0.299704\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.00000 | − | 25.9808i | −0.364698 | − | 1.05279i | ||||
\(610\) | 42.0000 | 1.70053 | ||||||||
\(611\) | 12.1244 | + | 3.00000i | 0.490499 | + | 0.121367i | ||||
\(612\) | −5.19615 | −0.210042 | ||||||||
\(613\) | 5.00000 | − | 8.66025i | 0.201948 | − | 0.349784i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
0.949156 | + | 0.314806i | \(0.101939\pi\) | |||||||
\(614\) | −12.1244 | + | 21.0000i | −0.489299 | + | 0.847491i | ||||
\(615\) | −20.7846 | − | 36.0000i | −0.838116 | − | 1.45166i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.5692 | + | 24.0000i | −1.67351 | + | 0.966204i | −0.707867 | + | 0.706346i | \(0.750342\pi\) |
−0.965647 | + | 0.259858i | \(0.916324\pi\) | |||||||
\(618\) | 7.50000 | + | 12.9904i | 0.301694 | + | 0.522550i | ||||
\(619\) | − | 38.1051i | − | 1.53157i | −0.643094 | − | 0.765787i | \(-0.722350\pi\) | ||
0.643094 | − | 0.765787i | \(-0.277650\pi\) | |||||||
\(620\) | −5.19615 | + | 3.00000i | −0.208683 | + | 0.120483i | ||||
\(621\) | −13.5000 | − | 7.79423i | −0.541736 | − | 0.312772i | ||||
\(622\) | −12.0000 | − | 6.92820i | −0.481156 | − | 0.277796i | ||||
\(623\) | −31.1769 | − | 27.0000i | −1.24908 | − | 1.08173i | ||||
\(624\) | 1.73205 | + | 6.00000i | 0.0693375 | + | 0.240192i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 1.73205 | − | 3.00000i | 0.0692267 | − | 0.119904i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.0000 | + | 6.92820i | −0.478852 | + | 0.276465i | ||||
\(629\) | 6.92820 | 0.276246 | ||||||||
\(630\) | 27.0000 | + | 5.19615i | 1.07571 | + | 0.207020i | ||||
\(631\) | −10.0000 | − | 17.3205i | −0.398094 | − | 0.689519i | 0.595397 | − | 0.803432i | \(-0.296995\pi\) |
−0.993491 | + | 0.113913i | \(0.963661\pi\) | |||||||
\(632\) | − | 10.0000i | − | 0.397779i | ||||||
\(633\) | 17.3205 | + | 30.0000i | 0.688428 | + | 1.19239i | ||||
\(634\) | −1.50000 | + | 2.59808i | −0.0595726 | + | 0.103183i | ||||
\(635\) | 34.6410 | − | 60.0000i | 1.37469 | − | 2.38103i | ||||
\(636\) | − | 15.5885i | − | 0.618123i | ||||||
\(637\) | 20.5000 | + | 14.7224i | 0.812240 | + | 0.583324i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.9711 | + | 22.5000i | 1.54167 | + | 0.890086i | ||||
\(640\) | 3.00000 | + | 1.73205i | 0.118585 | + | 0.0684653i | ||||
\(641\) | −10.3923 | + | 6.00000i | −0.410471 | + | 0.236986i | −0.690992 | − | 0.722862i | \(-0.742826\pi\) |
0.280521 | + | 0.959848i | \(0.409493\pi\) | |||||||
\(642\) | 31.1769 | 1.23045 | ||||||||
\(643\) | −6.00000 | + | 3.46410i | −0.236617 | + | 0.136611i | −0.613621 | − | 0.789601i | \(-0.710288\pi\) |
0.377004 | + | 0.926212i | \(0.376954\pi\) | |||||||
\(644\) | −7.79423 | − | 1.50000i | −0.307136 | − | 0.0591083i | ||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.3923 | − | 18.0000i | 0.408564 | − | 0.707653i | −0.586165 | − | 0.810191i | \(-0.699363\pi\) |
0.994729 | + | 0.102538i | \(0.0326965\pi\) | |||||||
\(648\) | −7.79423 | − | 4.50000i | −0.306186 | − | 0.176777i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −18.1865 | − | 17.5000i | −0.713335 | − | 0.686406i | ||||
\(651\) | 5.19615 | − | 6.00000i | 0.203653 | − | 0.235159i | ||||
\(652\) | −3.50000 | + | 6.06218i | −0.137071 | + | 0.237413i | ||||
\(653\) | −33.7750 | − | 19.5000i | −1.32172 | − | 0.763094i | −0.337715 | − | 0.941248i | \(-0.609654\pi\) |
−0.984003 | + | 0.178154i | \(0.942987\pi\) | |||||||
\(654\) | −24.0000 | + | 13.8564i | −0.938474 | + | 0.541828i | ||||
\(655\) | −54.0000 | −2.10995 | ||||||||
\(656\) | 3.46410 | + | 6.00000i | 0.135250 | + | 0.234261i | ||||
\(657\) | 36.0000 | − | 20.7846i | 1.40449 | − | 0.810885i | ||||
\(658\) | −6.00000 | + | 6.92820i | −0.233904 | + | 0.270089i | ||||
\(659\) | 5.19615 | − | 3.00000i | 0.202413 | − | 0.116863i | −0.395367 | − | 0.918523i | \(-0.629383\pi\) |
0.597781 | + | 0.801660i | \(0.296049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5000 | + | 6.06218i | 0.408403 | + | 0.235791i | 0.690103 | − | 0.723711i | \(-0.257565\pi\) |
−0.281701 | + | 0.959502i | \(0.590898\pi\) | |||||||
\(662\) | − | 28.0000i | − | 1.08825i | ||||||
\(663\) | −10.5000 | − | 2.59808i | −0.407786 | − | 0.100901i | ||||
\(664\) | − | 12.1244i | − | 0.470516i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.3923 | + | 6.00000i | 0.402694 | + | 0.232495i | ||||
\(667\) | 9.00000 | + | 15.5885i | 0.348481 | + | 0.603587i | ||||
\(668\) | −6.92820 | −0.268060 | ||||||||
\(669\) | 7.79423 | − | 4.50000i | 0.301342 | − | 0.173980i | ||||
\(670\) | −21.0000 | + | 12.1244i | −0.811301 | + | 0.468405i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.50000 | − | 0.866025i | −0.173591 | − | 0.0334077i | ||||
\(673\) | 20.5000 | − | 35.5070i | 0.790217 | − | 1.36870i | −0.135615 | − | 0.990762i | \(-0.543301\pi\) |
0.925832 | − | 0.377934i | \(-0.123365\pi\) | |||||||
\(674\) | −12.1244 | − | 7.00000i | −0.467013 | − | 0.269630i | ||||
\(675\) | 36.3731 | 1.40000 | ||||||||
\(676\) | 0.500000 | + | 12.9904i | 0.0192308 | + | 0.499630i | ||||
\(677\) | 20.7846 | 0.798817 | 0.399409 | − | 0.916773i | \(-0.369215\pi\) | ||||
0.399409 | + | 0.916773i | \(0.369215\pi\) | |||||||
\(678\) | 5.19615 | − | 9.00000i | 0.199557 | − | 0.345643i | ||||
\(679\) | −15.0000 | − | 43.3013i | −0.575647 | − | 1.66175i | ||||
\(680\) | −5.19615 | + | 3.00000i | −0.199263 | + | 0.115045i | ||||
\(681\) | 18.0000 | 0.689761 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.3923 | + | 6.00000i | −0.397650 | + | 0.229584i | −0.685470 | − | 0.728101i | \(-0.740403\pi\) |
0.287819 | + | 0.957685i | \(0.407070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | + | 20.7846i | −1.37549 | + | 0.794139i | ||||
\(686\) | −16.4545 | + | 8.50000i | −0.628235 | + | 0.324532i | ||||
\(687\) | −23.3827 | − | 13.5000i | −0.892105 | − | 0.515057i | ||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 7.79423 | − | 31.5000i | 0.296936 | − | 1.20005i | ||||
\(690\) | −18.0000 | −0.685248 | ||||||||
\(691\) | −39.0000 | − | 22.5167i | −1.48363 | − | 0.856574i | −0.483803 | − | 0.875177i | \(-0.660745\pi\) |
−0.999827 | + | 0.0186028i | \(0.994078\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 20.7846 | − | 12.0000i | 0.788405 | − | 0.455186i | ||||
\(696\) | 5.19615 | + | 9.00000i | 0.196960 | + | 0.341144i | ||||
\(697\) | −12.0000 | −0.454532 | ||||||||
\(698\) | −14.7224 | − | 25.5000i | −0.557252 | − | 0.965189i | ||||
\(699\) | −27.0000 | − | 15.5885i | −1.02123 | − | 0.589610i | ||||
\(700\) | 17.5000 | − | 6.06218i | 0.661438 | − | 0.229129i | ||||
\(701\) | − | 33.0000i | − | 1.24639i | −0.782065 | − | 0.623196i | \(-0.785834\pi\) | ||
0.782065 | − | 0.623196i | \(-0.214166\pi\) | |||||||
\(702\) | −13.5000 | − | 12.9904i | −0.509525 | − | 0.490290i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.3923 | + | 18.0000i | −0.391397 | + | 0.677919i | ||||
\(706\) | −10.5000 | + | 6.06218i | −0.395173 | + | 0.228153i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.50000 | − | 2.59808i | −0.0563735 | − | 0.0976417i | ||||
\(709\) | −14.0000 | − | 24.2487i | −0.525781 | − | 0.910679i | −0.999549 | − | 0.0300298i | \(-0.990440\pi\) |
0.473768 | − | 0.880650i | \(-0.342894\pi\) | |||||||
\(710\) | 51.9615 | 1.95008 | ||||||||
\(711\) | 15.0000 | + | 25.9808i | 0.562544 | + | 0.974355i | ||||
\(712\) | 13.5000 | + | 7.79423i | 0.505934 | + | 0.292101i | ||||
\(713\) | −2.59808 | + | 4.50000i | −0.0972987 | + | 0.168526i | ||||
\(714\) | 5.19615 | − | 6.00000i | 0.194461 | − | 0.224544i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.5000 | + | 18.1865i | 1.17639 | + | 0.679189i | ||||
\(718\) | 12.0000 | − | 20.7846i | 0.447836 | − | 0.775675i | ||||
\(719\) | −12.1244 | − | 21.0000i | −0.452162 | − | 0.783168i | 0.546358 | − | 0.837552i | \(-0.316014\pi\) |
−0.998520 | + | 0.0543839i | \(0.982681\pi\) | |||||||
\(720\) | −10.3923 | −0.387298 | ||||||||
\(721\) | −22.5000 | − | 4.33013i | −0.837944 | − | 0.161262i | ||||
\(722\) | −16.4545 | + | 9.50000i | −0.612372 | + | 0.353553i | ||||
\(723\) | − | 18.0000i | − | 0.669427i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36.3731 | − | 21.0000i | −1.35086 | − | 0.779920i | ||||
\(726\) | 16.5000 | + | 9.52628i | 0.612372 | + | 0.353553i | ||||
\(727\) | 12.1244i | 0.449667i | 0.974397 | + | 0.224834i | \(0.0721839\pi\) | ||||
−0.974397 | + | 0.224834i | \(0.927816\pi\) | |||||||
\(728\) | −8.66025 | − | 4.00000i | −0.320970 | − | 0.148250i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 24.0000 | − | 41.5692i | 0.888280 | − | 1.53855i | ||||
\(731\) | −0.866025 | + | 1.50000i | −0.0320311 | + | 0.0554795i | ||||
\(732\) | 18.1865 | − | 10.5000i | 0.672194 | − | 0.388091i | ||||
\(733\) | − | 8.66025i | − | 0.319874i | −0.987127 | − | 0.159937i | \(-0.948871\pi\) | ||
0.987127 | − | 0.159937i | \(-0.0511291\pi\) | |||||||
\(734\) | −6.06218 | − | 10.5000i | −0.223759 | − | 0.387562i | ||||
\(735\) | −33.0000 | + | 25.9808i | −1.21722 | + | 0.958315i | ||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −18.0000 | − | 10.3923i | −0.662589 | − | 0.382546i | ||||
\(739\) | 3.50000 | − | 6.06218i | 0.128750 | − | 0.223001i | −0.794443 | − | 0.607339i | \(-0.792237\pi\) |
0.923192 | + | 0.384338i | \(0.125570\pi\) | |||||||
\(740\) | 13.8564 | 0.509372 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.0000 | + | 15.5885i | 0.660801 | + | 0.572270i | ||||
\(743\) | 23.3827 | + | 13.5000i | 0.857828 | + | 0.495267i | 0.863284 | − | 0.504718i | \(-0.168404\pi\) |
−0.00545664 | + | 0.999985i | \(0.501737\pi\) | |||||||
\(744\) | −1.50000 | + | 2.59808i | −0.0549927 | + | 0.0952501i | ||||
\(745\) | −63.0000 | + | 36.3731i | −2.30814 | + | 1.33261i | ||||
\(746\) | − | 14.0000i | − | 0.512576i | ||||||
\(747\) | 18.1865 | + | 31.5000i | 0.665410 | + | 1.15252i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.1769 | + | 36.0000i | −1.13918 | + | 1.31541i | ||||
\(750\) | 10.3923 | − | 6.00000i | 0.379473 | − | 0.219089i | ||||
\(751\) | −2.00000 | + | 3.46410i | −0.0729810 | + | 0.126407i | −0.900207 | − | 0.435463i | \(-0.856585\pi\) |
0.827225 | + | 0.561870i | \(0.189918\pi\) | |||||||
\(752\) | 1.73205 | − | 3.00000i | 0.0631614 | − | 0.109399i | ||||
\(753\) | −33.0000 | −1.20259 | ||||||||
\(754\) | 6.00000 | + | 20.7846i | 0.218507 | + | 0.756931i | ||||
\(755\) | −55.4256 | −2.01715 | ||||||||
\(756\) | 12.9904 | − | 4.50000i | 0.472456 | − | 0.163663i | ||||
\(757\) | −11.0000 | + | 19.0526i | −0.399802 | + | 0.692477i | −0.993701 | − | 0.112062i | \(-0.964254\pi\) |
0.593899 | + | 0.804539i | \(0.297588\pi\) | |||||||
\(758\) | 17.3205 | − | 10.0000i | 0.629109 | − | 0.363216i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2487 | + | 42.0000i | 0.879015 | + | 1.52250i | 0.852423 | + | 0.522852i | \(0.175132\pi\) |
0.0265919 | + | 0.999646i | \(0.491535\pi\) | |||||||
\(762\) | − | 34.6410i | − | 1.25491i | ||||||
\(763\) | 8.00000 | − | 41.5692i | 0.289619 | − | 1.50491i | ||||
\(764\) | 12.9904 | + | 7.50000i | 0.469975 | + | 0.271340i | ||||
\(765\) | 9.00000 | − | 15.5885i | 0.325396 | − | 0.563602i | ||||
\(766\) | − | 24.2487i | − | 0.876142i | ||||||
\(767\) | −1.73205 | − | 6.00000i | −0.0625407 | − | 0.216647i | ||||
\(768\) | 1.73205 | 0.0625000 | ||||||||
\(769\) | 36.0000 | + | 20.7846i | 1.29819 | + | 0.749512i | 0.980092 | − | 0.198545i | \(-0.0636214\pi\) |
0.318101 | + | 0.948057i | \(0.396955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.5000 | + | 23.3827i | 0.486191 | + | 0.842107i | ||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 17.3205 | + | 30.0000i | 0.622975 | + | 1.07903i | 0.988929 | + | 0.148392i | \(0.0474097\pi\) |
−0.365953 | + | 0.930633i | \(0.619257\pi\) | |||||||
\(774\) | −2.59808 | + | 1.50000i | −0.0933859 | + | 0.0539164i | ||||
\(775\) | − | 12.1244i | − | 0.435520i | ||||||
\(776\) | 8.66025 | + | 15.0000i | 0.310885 | + | 0.538469i | ||||
\(777\) | −17.3205 | + | 6.00000i | −0.621370 | + | 0.215249i | ||||
\(778\) | 4.50000 | − | 7.79423i | 0.161333 | − | 0.279437i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −21.0000 | − | 5.19615i | −0.751921 | − | 0.186052i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.59808 | + | 4.50000i | −0.0929070 | + | 0.160920i | ||||
\(783\) | −27.0000 | − | 15.5885i | −0.964901 | − | 0.557086i | ||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | − | 48.0000i | − | 1.71319i | ||||||
\(786\) | −23.3827 | + | 13.5000i | −0.834033 | + | 0.481529i | ||||
\(787\) | 33.0000 | − | 19.0526i | 1.17632 | − | 0.679150i | 0.221162 | − | 0.975237i | \(-0.429015\pi\) |
0.955161 | + | 0.296087i | \(0.0956817\pi\) | |||||||
\(788\) | − | 15.0000i | − | 0.534353i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 30.0000 | + | 17.3205i | 1.06735 | + | 0.616236i | ||||
\(791\) | 5.19615 | + | 15.0000i | 0.184754 | + | 0.533339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.0000 | − | 12.1244i | 1.49146 | − | 0.430548i | ||||
\(794\) | −12.1244 | −0.430277 | ||||||||
\(795\) | 46.7654 | + | 27.0000i | 1.65860 | + | 0.957591i | ||||
\(796\) | 1.50000 | + | 0.866025i | 0.0531661 | + | 0.0306955i | ||||
\(797\) | −15.5885 | − | 27.0000i | −0.552171 | − | 0.956389i | −0.998118 | − | 0.0613293i | \(-0.980466\pi\) |
0.445946 | − | 0.895060i | \(-0.352867\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00000 | + | 5.19615i | 0.106132 | + | 0.183827i | ||||
\(800\) | −6.06218 | + | 3.50000i | −0.214330 | + | 0.123744i | ||||
\(801\) | −46.7654 | −1.65237 | ||||||||
\(802\) | −9.00000 | − | 15.5885i | −0.317801 | − | 0.550448i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.06218 | + | 10.5000i | −0.213797 | + | 0.370306i | ||||
\(805\) | 18.0000 | − | 20.7846i | 0.634417 | − | 0.732561i | ||||
\(806\) | −4.33013 | + | 4.50000i | −0.152522 | + | 0.158506i | ||||
\(807\) | 24.0000 | 0.844840 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 27.0000 | − | 15.5885i | 0.948683 | − | 0.547723i | ||||
\(811\) | − | 48.4974i | − | 1.70297i | −0.524375 | − | 0.851487i | \(-0.675701\pi\) | ||
0.524375 | − | 0.851487i | \(-0.324299\pi\) | |||||||
\(812\) | −15.5885 | − | 3.00000i | −0.547048 | − | 0.105279i | ||||
\(813\) | 12.9904 | − | 7.50000i | 0.455593 | − | 0.263036i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1244 | − | 21.0000i | −0.424698 | − | 0.735598i | ||||
\(816\) | −1.50000 | + | 2.59808i | −0.0525105 | + | 0.0909509i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −13.8564 | −0.484478 | ||||||||
\(819\) | 28.5000 | − | 2.59808i | 0.995871 | − | 0.0907841i | ||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | 2.59808 | + | 1.50000i | 0.0906735 | + | 0.0523504i | 0.544651 | − | 0.838663i | \(-0.316662\pi\) |
−0.453978 | + | 0.891013i | \(0.649995\pi\) | |||||||
\(822\) | −10.3923 | + | 18.0000i | −0.362473 | + | 0.627822i | ||||
\(823\) | −13.0000 | − | 22.5167i | −0.453152 | − | 0.784881i | 0.545428 | − | 0.838157i | \(-0.316367\pi\) |
−0.998580 | + | 0.0532760i | \(0.983034\pi\) | |||||||
\(824\) | 8.66025 | 0.301694 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.50000 | + | 0.866025i | 0.156575 | + | 0.0301329i | ||||
\(827\) | 42.0000i | 1.46048i | 0.683189 | + | 0.730242i | \(0.260592\pi\) | ||||
−0.683189 | + | 0.730242i | \(0.739408\pi\) | |||||||
\(828\) | −7.79423 | + | 4.50000i | −0.270868 | + | 0.156386i | ||||
\(829\) | −24.0000 | − | 13.8564i | −0.833554 | − | 0.481253i | 0.0215137 | − | 0.999769i | \(-0.493151\pi\) |
−0.855068 | + | 0.518516i | \(0.826485\pi\) | |||||||
\(830\) | 36.3731 | + | 21.0000i | 1.26253 | + | 0.728921i | ||||
\(831\) | 3.46410 | 0.120168 | ||||||||
\(832\) | 3.50000 | + | 0.866025i | 0.121341 | + | 0.0300240i | ||||
\(833\) | 1.73205 | + | 12.0000i | 0.0600120 | + | 0.415775i | ||||
\(834\) | 6.00000 | − | 10.3923i | 0.207763 | − | 0.359856i | ||||
\(835\) | 12.0000 | − | 20.7846i | 0.415277 | − | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.00000i | − | 0.311086i | ||||||
\(838\) | 16.5000 | − | 9.52628i | 0.569983 | − | 0.329080i | ||||
\(839\) | −8.66025 | − | 15.0000i | −0.298985 | − | 0.517858i | 0.676919 | − | 0.736058i | \(-0.263315\pi\) |
−0.975904 | + | 0.218200i | \(0.929981\pi\) | |||||||
\(840\) | 10.3923 | − | 12.0000i | 0.358569 | − | 0.414039i | ||||
\(841\) | 3.50000 | + | 6.06218i | 0.120690 | + | 0.209041i | ||||
\(842\) | 12.1244 | + | 7.00000i | 0.417833 | + | 0.241236i | ||||
\(843\) | −18.0000 | − | 10.3923i | −0.619953 | − | 0.357930i | ||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | −39.8372 | − | 21.0000i | −1.37044 | − | 0.722422i | ||||
\(846\) | 10.3923i | 0.357295i | ||||||||
\(847\) | −27.5000 | + | 9.52628i | −0.944911 | + | 0.327327i | ||||
\(848\) | −7.79423 | − | 4.50000i | −0.267655 | − | 0.154531i | ||||
\(849\) | 36.3731 | − | 21.0000i | 1.24832 | − | 0.720718i | ||||
\(850\) | − | 12.1244i | − | 0.415862i | ||||||
\(851\) | 10.3923 | − | 6.00000i | 0.356244 | − | 0.205677i | ||||
\(852\) | 22.5000 | − | 12.9904i | 0.770837 | − | 0.445043i | ||||
\(853\) | − | 12.1244i | − | 0.415130i | −0.978221 | − | 0.207565i | \(-0.933446\pi\) | ||
0.978221 | − | 0.207565i | \(-0.0665539\pi\) | |||||||
\(854\) | −6.06218 | + | 31.5000i | −0.207443 | + | 1.07791i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | − | 15.5885i | 0.307614 | − | 0.532803i | ||||
\(857\) | −34.6410 | −1.18331 | −0.591657 | − | 0.806190i | \(-0.701526\pi\) | ||||
−0.591657 | + | 0.806190i | \(0.701526\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 27.7128i | − | 0.945549i | −0.881183 | − | 0.472774i | \(-0.843253\pi\) | ||
0.881183 | − | 0.472774i | \(-0.156747\pi\) | |||||||
\(860\) | −1.73205 | + | 3.00000i | −0.0590624 | + | 0.102299i | ||||
\(861\) | 30.0000 | − | 10.3923i | 1.02240 | − | 0.354169i | ||||
\(862\) | 1.50000 | + | 2.59808i | 0.0510902 | + | 0.0884908i | ||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | −4.50000 | + | 2.59808i | −0.153093 | + | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.92820 | 0.235430 | ||||||||
\(867\) | 12.1244 | + | 21.0000i | 0.411765 | + | 0.713197i | ||||
\(868\) | −1.50000 | − | 4.33013i | −0.0509133 | − | 0.146974i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −36.0000 | −1.22051 | ||||||||
\(871\) | −17.5000 | + | 18.1865i | −0.592965 | + | 0.616227i | ||||
\(872\) | 16.0000i | 0.541828i | ||||||||
\(873\) | −45.0000 | − | 25.9808i | −1.52302 | − | 0.879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.46410 | + | 18.0000i | −0.117108 | + | 0.608511i | ||||
\(876\) | − | 24.0000i | − | 0.810885i | ||||||
\(877\) | 14.0000 | + | 24.2487i | 0.472746 | + | 0.818821i | 0.999514 | − | 0.0311889i | \(-0.00992933\pi\) |
−0.526767 | + | 0.850010i | \(0.676596\pi\) | |||||||
\(878\) | −1.73205 | − | 3.00000i | −0.0584539 | − | 0.101245i | ||||
\(879\) | −30.0000 | −1.01187 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.59808 | − | 4.50000i | 0.0875314 | − | 0.151609i | −0.818936 | − | 0.573885i | \(-0.805436\pi\) |
0.906467 | + | 0.422276i | \(0.138769\pi\) | |||||||
\(882\) | −7.79423 | + | 19.5000i | −0.262445 | + | 0.656599i | ||||
\(883\) | −47.0000 | −1.58168 | −0.790838 | − | 0.612026i | \(-0.790355\pi\) | ||||
−0.790838 | + | 0.612026i | \(0.790355\pi\) | |||||||
\(884\) | −4.33013 | + | 4.50000i | −0.145638 | + | 0.151351i | ||||
\(885\) | 10.3923 | 0.349334 | ||||||||
\(886\) | −9.00000 | + | 15.5885i | −0.302361 | + | 0.523704i | ||||
\(887\) | 22.5167 | − | 39.0000i | 0.756035 | − | 1.30949i | −0.188822 | − | 0.982011i | \(-0.560467\pi\) |
0.944858 | − | 0.327481i | \(-0.106200\pi\) | |||||||
\(888\) | 6.00000 | − | 3.46410i | 0.201347 | − | 0.116248i | ||||
\(889\) | 40.0000 | + | 34.6410i | 1.34156 | + | 1.16182i | ||||
\(890\) | −46.7654 | + | 27.0000i | −1.56758 | + | 0.905042i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 5.19615i | − | 0.173980i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −18.1865 | + | 31.5000i | −0.608249 | + | 1.05352i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.73205 | + | 2.00000i | −0.0578638 | + | 0.0668153i | ||||
\(897\) | −18.0000 | + | 5.19615i | −0.601003 | + | 0.173494i | ||||
\(898\) | 6.00000 | 0.200223 | ||||||||
\(899\) | −5.19615 | + | 9.00000i | −0.173301 | + | 0.300167i | ||||
\(900\) | 10.5000 | − | 18.1865i | 0.350000 | − | 0.606218i | ||||
\(901\) | 13.5000 | − | 7.79423i | 0.449750 | − | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.866025 | − | 4.50000i | 0.0288195 | − | 0.149751i | ||||
\(904\) | −3.00000 | − | 5.19615i | −0.0997785 | − | 0.172821i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.0000 | + | 13.8564i | −0.797347 | + | 0.460348i | ||||
\(907\) | −3.50000 | + | 6.06218i | −0.116216 | + | 0.201291i | −0.918265 | − | 0.395966i | \(-0.870410\pi\) |
0.802049 | + | 0.597258i | \(0.203743\pi\) | |||||||
\(908\) | 5.19615 | − | 9.00000i | 0.172440 | − | 0.298675i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 27.0000 | − | 19.0526i | 0.895041 | − | 0.631586i | ||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.8468 | + | 15.5000i | −0.888013 | + | 0.512694i | ||||
\(915\) | 72.7461i | 2.40491i | ||||||||
\(916\) | −13.5000 | + | 7.79423i | −0.446053 | + | 0.257529i | ||||
\(917\) | 7.79423 | − | 40.5000i | 0.257388 | − | 1.33743i | ||||
\(918\) | − | 9.00000i | − | 0.297044i | ||||||
\(919\) | 7.00000 | + | 12.1244i | 0.230909 | + | 0.399946i | 0.958076 | − | 0.286515i | \(-0.0924968\pi\) |
−0.727167 | + | 0.686461i | \(0.759163\pi\) | |||||||
\(920\) | −5.19615 | + | 9.00000i | −0.171312 | + | 0.296721i | ||||
\(921\) | −36.3731 | − | 21.0000i | −1.19853 | − | 0.691974i | ||||
\(922\) | 6.92820i | 0.228168i | ||||||||
\(923\) | 51.9615 | − | 15.0000i | 1.71033 | − | 0.493731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | + | 24.2487i | −0.460317 | + | 0.797293i | ||||
\(926\) | 12.1244 | + | 7.00000i | 0.398431 | + | 0.230034i | ||||
\(927\) | −22.5000 | + | 12.9904i | −0.738997 | + | 0.426660i | ||||
\(928\) | 6.00000 | 0.196960 | ||||||||
\(929\) | −26.8468 | − | 46.5000i | −0.880815 | − | 1.52562i | −0.850437 | − | 0.526077i | \(-0.823662\pi\) |
−0.0303776 | − | 0.999538i | \(-0.509671\pi\) | |||||||
\(930\) | −5.19615 | − | 9.00000i | −0.170389 | − | 0.295122i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.5885 | + | 9.00000i | −0.510617 | + | 0.294805i | ||||
\(933\) | 12.0000 | − | 20.7846i | 0.392862 | − | 0.680458i | ||||
\(934\) | −13.5000 | − | 7.79423i | −0.441733 | − | 0.255035i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.3923 | + | 3.00000i | −0.339683 | + | 0.0980581i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | −6.06218 | − | 17.5000i | −0.197937 | − | 0.571395i | ||||
\(939\) | 5.19615 | + | 3.00000i | 0.169570 | + | 0.0979013i | ||||
\(940\) | 6.00000 | + | 10.3923i | 0.195698 | + | 0.338960i | ||||
\(941\) | −38.1051 | −1.24219 | −0.621096 | − | 0.783735i | \(-0.713312\pi\) | ||||
−0.621096 | + | 0.783735i | \(0.713312\pi\) | |||||||
\(942\) | −12.0000 | − | 20.7846i | −0.390981 | − | 0.677199i | ||||
\(943\) | −18.0000 | + | 10.3923i | −0.586161 | + | 0.338420i | ||||
\(944\) | −1.73205 | −0.0563735 | ||||||||
\(945\) | −9.00000 | + | 46.7654i | −0.292770 | + | 1.52128i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.5885 | + | 9.00000i | 0.506557 | + | 0.292461i | 0.731417 | − | 0.681930i | \(-0.238859\pi\) |
−0.224860 | + | 0.974391i | \(0.572193\pi\) | |||||||
\(948\) | 17.3205 | 0.562544 | ||||||||
\(949\) | 12.0000 | − | 48.4974i | 0.389536 | − | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.50000 | − | 2.59808i | −0.145922 | − | 0.0842484i | ||||
\(952\) | −1.50000 | − | 4.33013i | −0.0486153 | − | 0.140340i | ||||
\(953\) | −31.1769 | + | 18.0000i | −1.00992 | + | 0.583077i | −0.911168 | − | 0.412035i | \(-0.864818\pi\) |
−0.0987513 | + | 0.995112i | \(0.531485\pi\) | |||||||
\(954\) | 27.0000 | 0.874157 | ||||||||
\(955\) | −45.0000 | + | 25.9808i | −1.45617 | + | 0.840718i | ||||
\(956\) | 18.1865 | − | 10.5000i | 0.588195 | − | 0.339594i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.0000 | + | 12.1244i | −0.678479 | + | 0.391720i | ||||
\(959\) | −10.3923 | − | 30.0000i | −0.335585 | − | 0.968751i | ||||
\(960\) | −3.00000 | + | 5.19615i | −0.0968246 | + | 0.167705i | ||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 13.8564 | − | 4.00000i | 0.446748 | − | 0.128965i | ||||
\(963\) | 54.0000i | 1.74013i | ||||||||
\(964\) | −9.00000 | − | 5.19615i | −0.289870 | − | 0.167357i | ||||
\(965\) | −24.2487 | + | 42.0000i | −0.780594 | + | 1.35203i | ||||
\(966\) | 2.59808 | − | 13.5000i | 0.0835917 | − | 0.434355i | ||||
\(967\) | 14.0000 | 0.450210 | 0.225105 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225105 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(968\) | 9.52628 | − | 5.50000i | 0.306186 | − | 0.176777i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −60.0000 | −1.92648 | ||||||||
\(971\) | 6.06218 | + | 10.5000i | 0.194545 | + | 0.336961i | 0.946751 | − | 0.321966i | \(-0.104344\pi\) |
−0.752207 | + | 0.658927i | \(0.771010\pi\) | |||||||
\(972\) | 7.79423 | − | 13.5000i | 0.250000 | − | 0.433013i | ||||
\(973\) | 6.00000 | + | 17.3205i | 0.192351 | + | 0.555270i | ||||
\(974\) | 2.00000i | 0.0640841i | ||||||||
\(975\) | 30.3109 | − | 31.5000i | 0.970725 | − | 1.00881i | ||||
\(976\) | − | 12.1244i | − | 0.388091i | ||||||
\(977\) | −20.7846 | − | 12.0000i | −0.664959 | − | 0.383914i | 0.129205 | − | 0.991618i | \(-0.458757\pi\) |
−0.794164 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(978\) | −10.5000 | − | 6.06218i | −0.335753 | − | 0.193847i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.46410 | + | 24.0000i | 0.110657 | + | 0.766652i | ||||
\(981\) | −24.0000 | − | 41.5692i | −0.766261 | − | 1.32720i | ||||
\(982\) | 18.0000 | + | 31.1769i | 0.574403 | + | 0.994895i | ||||
\(983\) | 13.8564 | 0.441951 | 0.220975 | − | 0.975279i | \(-0.429076\pi\) | ||||
0.220975 | + | 0.975279i | \(0.429076\pi\) | |||||||
\(984\) | −10.3923 | + | 6.00000i | −0.331295 | + | 0.191273i | ||||
\(985\) | 45.0000 | + | 25.9808i | 1.43382 | + | 0.827816i | ||||
\(986\) | −5.19615 | + | 9.00000i | −0.165479 | + | 0.286618i | ||||
\(987\) | −12.0000 | − | 10.3923i | −0.381964 | − | 0.330791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.00000i | 0.0953945i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.00000 | − | 12.1244i | 0.222362 | − | 0.385143i | −0.733163 | − | 0.680053i | \(-0.761957\pi\) |
0.955525 | + | 0.294911i | \(0.0952899\pi\) | |||||||
\(992\) | 0.866025 | + | 1.50000i | 0.0274963 | + | 0.0476250i | ||||
\(993\) | 48.4974 | 1.53902 | ||||||||
\(994\) | −7.50000 | + | 38.9711i | −0.237886 | + | 1.23609i | ||||
\(995\) | −5.19615 | + | 3.00000i | −0.164729 | + | 0.0951064i | ||||
\(996\) | 21.0000 | 0.665410 | ||||||||
\(997\) | 43.5000 | − | 25.1147i | 1.37766 | − | 0.795392i | 0.385782 | − | 0.922590i | \(-0.373932\pi\) |
0.991877 | + | 0.127198i | \(0.0405985\pi\) | |||||||
\(998\) | −14.7224 | − | 8.50000i | −0.466030 | − | 0.269063i | ||||
\(999\) | −10.3923 | + | 18.0000i | −0.328798 | + | 0.569495i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 546.2.bq.a.503.2 | yes | 4 | |
3.2 | odd | 2 | inner | 546.2.bq.a.503.1 | yes | 4 | |
7.6 | odd | 2 | 546.2.bq.b.503.2 | yes | 4 | ||
13.3 | even | 3 | 546.2.bq.b.419.1 | yes | 4 | ||
21.20 | even | 2 | 546.2.bq.b.503.1 | yes | 4 | ||
39.29 | odd | 6 | 546.2.bq.b.419.2 | yes | 4 | ||
91.55 | odd | 6 | inner | 546.2.bq.a.419.1 | ✓ | 4 | |
273.146 | even | 6 | inner | 546.2.bq.a.419.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bq.a.419.1 | ✓ | 4 | 91.55 | odd | 6 | inner | |
546.2.bq.a.419.2 | yes | 4 | 273.146 | even | 6 | inner | |
546.2.bq.a.503.1 | yes | 4 | 3.2 | odd | 2 | inner | |
546.2.bq.a.503.2 | yes | 4 | 1.1 | even | 1 | trivial | |
546.2.bq.b.419.1 | yes | 4 | 13.3 | even | 3 | ||
546.2.bq.b.419.2 | yes | 4 | 39.29 | odd | 6 | ||
546.2.bq.b.503.1 | yes | 4 | 21.20 | even | 2 | ||
546.2.bq.b.503.2 | yes | 4 | 7.6 | odd | 2 |