Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(68,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.l (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.95633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 117.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.117 |
Dual form | 245.2.l.a.178.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86603 | + | 0.500000i | −1.31948 | + | 0.353553i | −0.848783 | − | 0.528742i | \(-0.822664\pi\) |
−0.470696 | + | 0.882295i | \(0.655997\pi\) | |||||||
\(3\) | 0.500000 | − | 1.86603i | 0.288675 | − | 1.07735i | −0.657437 | − | 0.753510i | \(-0.728359\pi\) |
0.946112 | − | 0.323840i | \(-0.104974\pi\) | |||||||
\(4\) | 1.50000 | − | 0.866025i | 0.750000 | − | 0.433013i | ||||
\(5\) | 0.133975 | − | 2.23205i | 0.0599153 | − | 0.998203i | ||||
\(6\) | 3.73205i | 1.52360i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.366025 | − | 0.366025i | 0.129410 | − | 0.129410i | ||||
\(9\) | −0.633975 | − | 0.366025i | −0.211325 | − | 0.122008i | ||||
\(10\) | 0.866025 | + | 4.23205i | 0.273861 | + | 1.33829i | ||||
\(11\) | −0.366025 | − | 0.633975i | −0.110361 | − | 0.191151i | 0.805555 | − | 0.592521i | \(-0.201867\pi\) |
−0.915916 | + | 0.401371i | \(0.868534\pi\) | |||||||
\(12\) | −0.866025 | − | 3.23205i | −0.250000 | − | 0.933013i | ||||
\(13\) | −2.00000 | − | 2.00000i | −0.554700 | − | 0.554700i | 0.373094 | − | 0.927794i | \(-0.378297\pi\) |
−0.927794 | + | 0.373094i | \(0.878297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.09808 | − | 1.36603i | −1.05812 | − | 0.352706i | ||||
\(16\) | −2.23205 | + | 3.86603i | −0.558013 | + | 0.966506i | ||||
\(17\) | −1.00000 | − | 0.267949i | −0.242536 | − | 0.0649872i | 0.135503 | − | 0.990777i | \(-0.456735\pi\) |
−0.378039 | + | 0.925790i | \(0.623401\pi\) | |||||||
\(18\) | 1.36603 | + | 0.366025i | 0.321975 | + | 0.0862730i | ||||
\(19\) | −1.36603 | + | 2.36603i | −0.313388 | + | 0.542803i | −0.979093 | − | 0.203411i | \(-0.934797\pi\) |
0.665706 | + | 0.746214i | \(0.268131\pi\) | |||||||
\(20\) | −1.73205 | − | 3.46410i | −0.387298 | − | 0.774597i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | + | 1.00000i | 0.213201 | + | 0.213201i | ||||
\(23\) | −1.86603 | − | 6.96410i | −0.389093 | − | 1.45212i | −0.831612 | − | 0.555357i | \(-0.812582\pi\) |
0.442519 | − | 0.896759i | \(-0.354085\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −4.96410 | − | 0.598076i | −0.992820 | − | 0.119615i | ||||
\(26\) | 4.73205 | + | 2.73205i | 0.928032 | + | 0.535799i | ||||
\(27\) | 3.09808 | − | 3.09808i | 0.596225 | − | 0.596225i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | 8.33013 | + | 0.500000i | 1.52087 | + | 0.0912871i | ||||
\(31\) | −0.464102 | + | 0.267949i | −0.0833551 | + | 0.0481251i | −0.541098 | − | 0.840959i | \(-0.681991\pi\) |
0.457743 | + | 0.889085i | \(0.348658\pi\) | |||||||
\(32\) | 1.96410 | − | 7.33013i | 0.347207 | − | 1.29580i | ||||
\(33\) | −1.36603 | + | 0.366025i | −0.237795 | + | 0.0637168i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.26795 | −0.211325 | ||||||||
\(37\) | 4.73205 | − | 1.26795i | 0.777944 | − | 0.208450i | 0.152066 | − | 0.988370i | \(-0.451407\pi\) |
0.625878 | + | 0.779921i | \(0.284741\pi\) | |||||||
\(38\) | 1.36603 | − | 5.09808i | 0.221599 | − | 0.827017i | ||||
\(39\) | −4.73205 | + | 2.73205i | −0.757735 | + | 0.437478i | ||||
\(40\) | −0.767949 | − | 0.866025i | −0.121423 | − | 0.136931i | ||||
\(41\) | 0.464102i | 0.0724805i | 0.999343 | + | 0.0362402i | \(0.0115382\pi\) | ||||
−0.999343 | + | 0.0362402i | \(0.988462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.83013 | + | 5.83013i | −0.889086 | + | 0.889086i | −0.994435 | − | 0.105349i | \(-0.966404\pi\) |
0.105349 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(44\) | −1.09808 | − | 0.633975i | −0.165541 | − | 0.0955753i | ||||
\(45\) | −0.901924 | + | 1.36603i | −0.134451 | + | 0.203635i | ||||
\(46\) | 6.96410 | + | 12.0622i | 1.02680 | + | 1.77847i | ||||
\(47\) | −0.169873 | − | 0.633975i | −0.0247785 | − | 0.0924747i | 0.952429 | − | 0.304760i | \(-0.0985762\pi\) |
−0.977208 | + | 0.212285i | \(0.931909\pi\) | |||||||
\(48\) | 6.09808 | + | 6.09808i | 0.880181 | + | 0.880181i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.56218 | − | 1.36603i | 1.35230 | − | 0.193185i | ||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | −4.73205 | − | 1.26795i | −0.656217 | − | 0.175833i | ||||
\(53\) | 6.83013 | + | 1.83013i | 0.938190 | + | 0.251387i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(54\) | −4.23205 | + | 7.33013i | −0.575909 | + | 0.997504i | ||||
\(55\) | −1.46410 | + | 0.732051i | −0.197419 | + | 0.0987097i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.73205 | + | 3.73205i | 0.494322 | + | 0.494322i | ||||
\(58\) | 1.50000 | + | 5.59808i | 0.196960 | + | 0.735063i | ||||
\(59\) | 1.09808 | + | 1.90192i | 0.142957 | + | 0.247609i | 0.928609 | − | 0.371060i | \(-0.121005\pi\) |
−0.785652 | + | 0.618669i | \(0.787672\pi\) | |||||||
\(60\) | −7.33013 | + | 1.50000i | −0.946315 | + | 0.193649i | ||||
\(61\) | 7.33013 | + | 4.23205i | 0.938527 | + | 0.541859i | 0.889498 | − | 0.456939i | \(-0.151054\pi\) |
0.0490285 | + | 0.998797i | \(0.484387\pi\) | |||||||
\(62\) | 0.732051 | − | 0.732051i | 0.0929705 | − | 0.0929705i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.73205i | 0.716506i | ||||||||
\(65\) | −4.73205 | + | 4.19615i | −0.586939 | + | 0.520469i | ||||
\(66\) | 2.36603 | − | 1.36603i | 0.291238 | − | 0.168146i | ||||
\(67\) | −0.303848 | + | 1.13397i | −0.0371209 | + | 0.138537i | −0.981999 | − | 0.188884i | \(-0.939513\pi\) |
0.944878 | + | 0.327421i | \(0.106180\pi\) | |||||||
\(68\) | −1.73205 | + | 0.464102i | −0.210042 | + | 0.0562806i | ||||
\(69\) | −13.9282 | −1.67676 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.73205 | 0.561591 | 0.280796 | − | 0.959768i | \(-0.409402\pi\) | ||||
0.280796 | + | 0.959768i | \(0.409402\pi\) | |||||||
\(72\) | −0.366025 | + | 0.0980762i | −0.0431365 | + | 0.0115584i | ||||
\(73\) | −0.928203 | + | 3.46410i | −0.108638 | + | 0.405442i | −0.998732 | − | 0.0503336i | \(-0.983972\pi\) |
0.890094 | + | 0.455776i | \(0.150638\pi\) | |||||||
\(74\) | −8.19615 | + | 4.73205i | −0.952783 | + | 0.550090i | ||||
\(75\) | −3.59808 | + | 8.96410i | −0.415470 | + | 1.03509i | ||||
\(76\) | 4.73205i | 0.542803i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.46410 | − | 7.46410i | 0.845143 | − | 0.845143i | ||||
\(79\) | 5.83013 | + | 3.36603i | 0.655941 | + | 0.378707i | 0.790728 | − | 0.612167i | \(-0.209702\pi\) |
−0.134788 | + | 0.990874i | \(0.543035\pi\) | |||||||
\(80\) | 8.33013 | + | 5.50000i | 0.931337 | + | 0.614919i | ||||
\(81\) | −5.33013 | − | 9.23205i | −0.592236 | − | 1.02578i | ||||
\(82\) | −0.232051 | − | 0.866025i | −0.0256257 | − | 0.0956365i | ||||
\(83\) | 3.09808 | + | 3.09808i | 0.340058 | + | 0.340058i | 0.856389 | − | 0.516331i | \(-0.172703\pi\) |
−0.516331 | + | 0.856389i | \(0.672703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.732051 | + | 2.19615i | −0.0794021 | + | 0.238206i | ||||
\(86\) | 7.96410 | − | 13.7942i | 0.858791 | − | 1.48747i | ||||
\(87\) | −5.59808 | − | 1.50000i | −0.600177 | − | 0.160817i | ||||
\(88\) | −0.366025 | − | 0.0980762i | −0.0390184 | − | 0.0104550i | ||||
\(89\) | 8.33013 | − | 14.4282i | 0.882992 | − | 1.52939i | 0.0349934 | − | 0.999388i | \(-0.488859\pi\) |
0.847998 | − | 0.529999i | \(-0.177808\pi\) | |||||||
\(90\) | 1.00000 | − | 3.00000i | 0.105409 | − | 0.316228i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.83013 | − | 8.83013i | −0.920604 | − | 0.920604i | ||||
\(93\) | 0.267949 | + | 1.00000i | 0.0277850 | + | 0.103695i | ||||
\(94\) | 0.633975 | + | 1.09808i | 0.0653895 | + | 0.113258i | ||||
\(95\) | 5.09808 | + | 3.36603i | 0.523052 | + | 0.345347i | ||||
\(96\) | −12.6962 | − | 7.33013i | −1.29580 | − | 0.748128i | ||||
\(97\) | 7.92820 | − | 7.92820i | 0.804987 | − | 0.804987i | −0.178883 | − | 0.983870i | \(-0.557248\pi\) |
0.983870 | + | 0.178883i | \(0.0572484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.535898i | 0.0538598i | ||||||||
\(100\) | −7.96410 | + | 3.40192i | −0.796410 | + | 0.340192i | ||||
\(101\) | 10.1603 | − | 5.86603i | 1.01098 | − | 0.583691i | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) |
0.911479 | + | 0.411346i | \(0.134941\pi\) | |||||||
\(102\) | 1.00000 | − | 3.73205i | 0.0990148 | − | 0.369528i | ||||
\(103\) | 2.23205 | − | 0.598076i | 0.219931 | − | 0.0589302i | −0.147171 | − | 0.989111i | \(-0.547017\pi\) |
0.367102 | + | 0.930181i | \(0.380350\pi\) | |||||||
\(104\) | −1.46410 | −0.143567 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.6603 | −1.32680 | ||||||||
\(107\) | −8.59808 | + | 2.30385i | −0.831207 | + | 0.222721i | −0.649240 | − | 0.760583i | \(-0.724913\pi\) |
−0.181967 | + | 0.983305i | \(0.558246\pi\) | |||||||
\(108\) | 1.96410 | − | 7.33013i | 0.188996 | − | 0.705342i | ||||
\(109\) | 12.2321 | − | 7.06218i | 1.17162 | − | 0.676434i | 0.217557 | − | 0.976048i | \(-0.430191\pi\) |
0.954061 | + | 0.299614i | \(0.0968578\pi\) | |||||||
\(110\) | 2.36603 | − | 2.09808i | 0.225592 | − | 0.200044i | ||||
\(111\) | − | 9.46410i | − | 0.898293i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.26795 | + | 4.26795i | −0.401495 | + | 0.401495i | −0.878760 | − | 0.477265i | \(-0.841628\pi\) |
0.477265 | + | 0.878760i | \(0.341628\pi\) | |||||||
\(114\) | −8.83013 | − | 5.09808i | −0.827017 | − | 0.477479i | ||||
\(115\) | −15.7942 | + | 3.23205i | −1.47282 | + | 0.301390i | ||||
\(116\) | −2.59808 | − | 4.50000i | −0.241225 | − | 0.417815i | ||||
\(117\) | 0.535898 | + | 2.00000i | 0.0495438 | + | 0.184900i | ||||
\(118\) | −3.00000 | − | 3.00000i | −0.276172 | − | 0.276172i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.00000 | + | 1.00000i | −0.182574 | + | 0.0912871i | ||||
\(121\) | 5.23205 | − | 9.06218i | 0.475641 | − | 0.823834i | ||||
\(122\) | −15.7942 | − | 4.23205i | −1.42994 | − | 0.383152i | ||||
\(123\) | 0.866025 | + | 0.232051i | 0.0780869 | + | 0.0209233i | ||||
\(124\) | −0.464102 | + | 0.803848i | −0.0416776 | + | 0.0721876i | ||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.46410 | − | 6.46410i | −0.573596 | − | 0.573596i | 0.359535 | − | 0.933132i | \(-0.382935\pi\) |
−0.933132 | + | 0.359535i | \(0.882935\pi\) | |||||||
\(128\) | 1.06218 | + | 3.96410i | 0.0938841 | + | 0.350380i | ||||
\(129\) | 7.96410 | + | 13.7942i | 0.701200 | + | 1.21451i | ||||
\(130\) | 6.73205 | − | 10.1962i | 0.590440 | − | 0.894262i | ||||
\(131\) | −7.39230 | − | 4.26795i | −0.645869 | − | 0.372892i | 0.141003 | − | 0.990009i | \(-0.454967\pi\) |
−0.786872 | + | 0.617117i | \(0.788301\pi\) | |||||||
\(132\) | −1.73205 | + | 1.73205i | −0.150756 | + | 0.150756i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.26795i | − | 0.195921i | ||||||
\(135\) | −6.50000 | − | 7.33013i | −0.559431 | − | 0.630877i | ||||
\(136\) | −0.464102 | + | 0.267949i | −0.0397964 | + | 0.0229765i | ||||
\(137\) | 2.80385 | − | 10.4641i | 0.239549 | − | 0.894009i | −0.736496 | − | 0.676441i | \(-0.763521\pi\) |
0.976045 | − | 0.217567i | \(-0.0698121\pi\) | |||||||
\(138\) | 25.9904 | − | 6.96410i | 2.21245 | − | 0.592824i | ||||
\(139\) | 11.6603 | 0.989010 | 0.494505 | − | 0.869175i | \(-0.335349\pi\) | ||||
0.494505 | + | 0.869175i | \(0.335349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.26795 | −0.106781 | ||||||||
\(142\) | −8.83013 | + | 2.36603i | −0.741008 | + | 0.198552i | ||||
\(143\) | −0.535898 | + | 2.00000i | −0.0448141 | + | 0.167248i | ||||
\(144\) | 2.83013 | − | 1.63397i | 0.235844 | − | 0.136165i | ||||
\(145\) | −6.69615 | − | 0.401924i | −0.556085 | − | 0.0333780i | ||||
\(146\) | − | 6.92820i | − | 0.573382i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | − | 6.00000i | 0.493197 | − | 0.493197i | ||||
\(149\) | 9.69615 | + | 5.59808i | 0.794340 | + | 0.458612i | 0.841488 | − | 0.540276i | \(-0.181680\pi\) |
−0.0471484 | + | 0.998888i | \(0.515013\pi\) | |||||||
\(150\) | 2.23205 | − | 18.5263i | 0.182246 | − | 1.51266i | ||||
\(151\) | 6.92820 | + | 12.0000i | 0.563809 | + | 0.976546i | 0.997159 | + | 0.0753205i | \(0.0239980\pi\) |
−0.433350 | + | 0.901226i | \(0.642669\pi\) | |||||||
\(152\) | 0.366025 | + | 1.36603i | 0.0296886 | + | 0.110799i | ||||
\(153\) | 0.535898 | + | 0.535898i | 0.0433248 | + | 0.0433248i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.535898 | + | 1.07180i | 0.0430444 | + | 0.0860888i | ||||
\(156\) | −4.73205 | + | 8.19615i | −0.378867 | + | 0.656217i | ||||
\(157\) | 23.7583 | + | 6.36603i | 1.89612 | + | 0.508064i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) |
0.898513 | + | 0.438948i | \(0.144649\pi\) | |||||||
\(158\) | −12.5622 | − | 3.36603i | −0.999393 | − | 0.267787i | ||||
\(159\) | 6.83013 | − | 11.8301i | 0.541664 | − | 0.938190i | ||||
\(160\) | −16.0981 | − | 5.36603i | −1.27266 | − | 0.424222i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 14.5622 | + | 14.5622i | 1.14411 | + | 1.14411i | ||||
\(163\) | 1.43782 | + | 5.36603i | 0.112619 | + | 0.420300i | 0.999098 | − | 0.0424696i | \(-0.0135226\pi\) |
−0.886479 | + | 0.462769i | \(0.846856\pi\) | |||||||
\(164\) | 0.401924 | + | 0.696152i | 0.0313850 | + | 0.0543604i | ||||
\(165\) | 0.633975 | + | 3.09808i | 0.0493549 | + | 0.241185i | ||||
\(166\) | −7.33013 | − | 4.23205i | −0.568928 | − | 0.328471i | ||||
\(167\) | −10.7583 | + | 10.7583i | −0.832505 | + | 0.832505i | −0.987859 | − | 0.155354i | \(-0.950348\pi\) |
0.155354 | + | 0.987859i | \(0.450348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0.267949 | − | 4.46410i | 0.0205508 | − | 0.342381i | ||||
\(171\) | 1.73205 | − | 1.00000i | 0.132453 | − | 0.0764719i | ||||
\(172\) | −3.69615 | + | 13.7942i | −0.281829 | + | 1.05180i | ||||
\(173\) | −22.6603 | + | 6.07180i | −1.72283 | + | 0.461630i | −0.978511 | − | 0.206197i | \(-0.933891\pi\) |
−0.744317 | + | 0.667827i | \(0.767225\pi\) | |||||||
\(174\) | 11.1962 | 0.848778 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.26795 | 0.246331 | ||||||||
\(177\) | 4.09808 | − | 1.09808i | 0.308030 | − | 0.0825365i | ||||
\(178\) | −8.33013 | + | 31.0885i | −0.624369 | + | 2.33018i | ||||
\(179\) | −17.1962 | + | 9.92820i | −1.28530 | + | 0.742069i | −0.977812 | − | 0.209483i | \(-0.932822\pi\) |
−0.307488 | + | 0.951552i | \(0.599489\pi\) | |||||||
\(180\) | −0.169873 | + | 2.83013i | −0.0126616 | + | 0.210945i | ||||
\(181\) | 9.19615i | 0.683545i | 0.939783 | + | 0.341772i | \(0.111027\pi\) | ||||
−0.939783 | + | 0.341772i | \(0.888973\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5622 | − | 11.5622i | 0.854701 | − | 0.854701i | ||||
\(184\) | −3.23205 | − | 1.86603i | −0.238270 | − | 0.137565i | ||||
\(185\) | −2.19615 | − | 10.7321i | −0.161464 | − | 0.789036i | ||||
\(186\) | −1.00000 | − | 1.73205i | −0.0733236 | − | 0.127000i | ||||
\(187\) | 0.196152 | + | 0.732051i | 0.0143441 | + | 0.0535329i | ||||
\(188\) | −0.803848 | − | 0.803848i | −0.0586266 | − | 0.0586266i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.1962 | − | 3.73205i | −0.812254 | − | 0.270751i | ||||
\(191\) | −8.36603 | + | 14.4904i | −0.605344 | + | 1.04849i | 0.386653 | + | 0.922225i | \(0.373631\pi\) |
−0.991997 | + | 0.126262i | \(0.959702\pi\) | |||||||
\(192\) | 10.6962 | + | 2.86603i | 0.771928 | + | 0.206838i | ||||
\(193\) | −3.09808 | − | 0.830127i | −0.223004 | − | 0.0597539i | 0.145587 | − | 0.989346i | \(-0.453493\pi\) |
−0.368591 | + | 0.929592i | \(0.620160\pi\) | |||||||
\(194\) | −10.8301 | + | 18.7583i | −0.777558 | + | 1.34677i | ||||
\(195\) | 5.46410 | + | 10.9282i | 0.391292 | + | 0.782585i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1244 | + | 14.1244i | 1.00632 | + | 1.00632i | 0.999980 | + | 0.00633876i | \(0.00201770\pi\) |
0.00633876 | + | 0.999980i | \(0.497982\pi\) | |||||||
\(198\) | −0.267949 | − | 1.00000i | −0.0190423 | − | 0.0710669i | ||||
\(199\) | −12.4641 | − | 21.5885i | −0.883557 | − | 1.53037i | −0.847359 | − | 0.531021i | \(-0.821809\pi\) |
−0.0361978 | − | 0.999345i | \(-0.511525\pi\) | |||||||
\(200\) | −2.03590 | + | 1.59808i | −0.143960 | + | 0.113001i | ||||
\(201\) | 1.96410 | + | 1.13397i | 0.138537 | + | 0.0799844i | ||||
\(202\) | −16.0263 | + | 16.0263i | −1.12761 | + | 1.12761i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.46410i | 0.242536i | ||||||||
\(205\) | 1.03590 | + | 0.0621778i | 0.0723503 | + | 0.00434269i | ||||
\(206\) | −3.86603 | + | 2.23205i | −0.269359 | + | 0.155514i | ||||
\(207\) | −1.36603 | + | 5.09808i | −0.0949453 | + | 0.354341i | ||||
\(208\) | 12.1962 | − | 3.26795i | 0.845651 | − | 0.226592i | ||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1962 | 0.701932 | 0.350966 | − | 0.936388i | \(-0.385853\pi\) | ||||
0.350966 | + | 0.936388i | \(0.385853\pi\) | |||||||
\(212\) | 11.8301 | − | 3.16987i | 0.812496 | − | 0.217708i | ||||
\(213\) | 2.36603 | − | 8.83013i | 0.162117 | − | 0.605030i | ||||
\(214\) | 14.8923 | − | 8.59808i | 1.01802 | − | 0.587752i | ||||
\(215\) | 12.2321 | + | 13.7942i | 0.834219 | + | 0.940759i | ||||
\(216\) | − | 2.26795i | − | 0.154314i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −19.2942 | + | 19.2942i | −1.30677 | + | 1.30677i | ||||
\(219\) | 6.00000 | + | 3.46410i | 0.405442 | + | 0.234082i | ||||
\(220\) | −1.56218 | + | 2.36603i | −0.105322 | + | 0.159517i | ||||
\(221\) | 1.46410 | + | 2.53590i | 0.0984861 | + | 0.170583i | ||||
\(222\) | 4.73205 | + | 17.6603i | 0.317594 | + | 1.18528i | ||||
\(223\) | −6.12436 | − | 6.12436i | −0.410117 | − | 0.410117i | 0.471662 | − | 0.881779i | \(-0.343654\pi\) |
−0.881779 | + | 0.471662i | \(0.843654\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.92820 | + | 2.19615i | 0.195214 | + | 0.146410i | ||||
\(226\) | 5.83013 | − | 10.0981i | 0.387814 | − | 0.671714i | ||||
\(227\) | −0.0980762 | − | 0.0262794i | −0.00650955 | − | 0.00174423i | 0.255563 | − | 0.966792i | \(-0.417739\pi\) |
−0.262072 | + | 0.965048i | \(0.584406\pi\) | |||||||
\(228\) | 8.83013 | + | 2.36603i | 0.584789 | + | 0.156694i | ||||
\(229\) | 1.19615 | − | 2.07180i | 0.0790440 | − | 0.136908i | −0.823794 | − | 0.566890i | \(-0.808147\pi\) |
0.902838 | + | 0.429981i | \(0.141480\pi\) | |||||||
\(230\) | 27.8564 | − | 13.9282i | 1.83680 | − | 0.918399i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.09808 | − | 1.09808i | −0.0720922 | − | 0.0720922i | ||||
\(233\) | −0.464102 | − | 1.73205i | −0.0304043 | − | 0.113470i | 0.949056 | − | 0.315107i | \(-0.102041\pi\) |
−0.979460 | + | 0.201637i | \(0.935374\pi\) | |||||||
\(234\) | −2.00000 | − | 3.46410i | −0.130744 | − | 0.226455i | ||||
\(235\) | −1.43782 | + | 0.294229i | −0.0937932 | + | 0.0191934i | ||||
\(236\) | 3.29423 | + | 1.90192i | 0.214436 | + | 0.123805i | ||||
\(237\) | 9.19615 | − | 9.19615i | 0.597354 | − | 0.597354i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.3923i | − | 1.18970i | −0.803837 | − | 0.594850i | \(-0.797212\pi\) | ||
0.803837 | − | 0.594850i | \(-0.202788\pi\) | |||||||
\(240\) | 14.4282 | − | 12.7942i | 0.931337 | − | 0.825864i | ||||
\(241\) | −14.5359 | + | 8.39230i | −0.936340 | + | 0.540596i | −0.888811 | − | 0.458274i | \(-0.848468\pi\) |
−0.0475286 | + | 0.998870i | \(0.515135\pi\) | |||||||
\(242\) | −5.23205 | + | 19.5263i | −0.336329 | + | 1.25520i | ||||
\(243\) | −7.19615 | + | 1.92820i | −0.461633 | + | 0.123694i | ||||
\(244\) | 14.6603 | 0.938527 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.73205 | −0.110432 | ||||||||
\(247\) | 7.46410 | − | 2.00000i | 0.474929 | − | 0.127257i | ||||
\(248\) | −0.0717968 | + | 0.267949i | −0.00455910 | + | 0.0170148i | ||||
\(249\) | 7.33013 | − | 4.23205i | 0.464528 | − | 0.268195i | ||||
\(250\) | −1.76795 | − | 21.5263i | −0.111815 | − | 1.36144i | ||||
\(251\) | − | 5.85641i | − | 0.369653i | −0.982771 | − | 0.184827i | \(-0.940828\pi\) | ||
0.982771 | − | 0.184827i | \(-0.0591723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.73205 | + | 3.73205i | −0.234632 | + | 0.234632i | ||||
\(254\) | 15.2942 | + | 8.83013i | 0.959645 | + | 0.554051i | ||||
\(255\) | 3.73205 | + | 2.46410i | 0.233710 | + | 0.154308i | ||||
\(256\) | −9.69615 | − | 16.7942i | −0.606010 | − | 1.04964i | ||||
\(257\) | −0.732051 | − | 2.73205i | −0.0456641 | − | 0.170421i | 0.939328 | − | 0.343020i | \(-0.111450\pi\) |
−0.984992 | + | 0.172600i | \(0.944783\pi\) | |||||||
\(258\) | −21.7583 | − | 21.7583i | −1.35461 | − | 1.35461i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.46410 | + | 10.3923i | −0.214834 | + | 0.644503i | ||||
\(261\) | −1.09808 | + | 1.90192i | −0.0679692 | + | 0.117726i | ||||
\(262\) | 15.9282 | + | 4.26795i | 0.984048 | + | 0.263675i | ||||
\(263\) | −8.06218 | − | 2.16025i | −0.497135 | − | 0.133207i | 0.00153494 | − | 0.999999i | \(-0.499511\pi\) |
−0.498670 | + | 0.866792i | \(0.666178\pi\) | |||||||
\(264\) | −0.366025 | + | 0.633975i | −0.0225273 | + | 0.0390184i | ||||
\(265\) | 5.00000 | − | 15.0000i | 0.307148 | − | 0.921443i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.7583 | − | 22.7583i | −1.39279 | − | 1.39279i | ||||
\(268\) | 0.526279 | + | 1.96410i | 0.0321476 | + | 0.119977i | ||||
\(269\) | −2.42820 | − | 4.20577i | −0.148050 | − | 0.256430i | 0.782457 | − | 0.622705i | \(-0.213966\pi\) |
−0.930507 | + | 0.366275i | \(0.880633\pi\) | |||||||
\(270\) | 15.7942 | + | 10.4282i | 0.961206 | + | 0.634640i | ||||
\(271\) | 21.4186 | + | 12.3660i | 1.30109 | + | 0.751183i | 0.980590 | − | 0.196067i | \(-0.0628171\pi\) |
0.320496 | + | 0.947250i | \(0.396150\pi\) | |||||||
\(272\) | 3.26795 | − | 3.26795i | 0.198149 | − | 0.198149i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.9282i | 1.26432i | ||||||||
\(275\) | 1.43782 | + | 3.36603i | 0.0867039 | + | 0.202979i | ||||
\(276\) | −20.8923 | + | 12.0622i | −1.25757 | + | 0.726058i | ||||
\(277\) | −5.19615 | + | 19.3923i | −0.312207 | + | 1.16517i | 0.614356 | + | 0.789029i | \(0.289416\pi\) |
−0.926562 | + | 0.376141i | \(0.877251\pi\) | |||||||
\(278\) | −21.7583 | + | 5.83013i | −1.30498 | + | 0.349668i | ||||
\(279\) | 0.392305 | 0.0234867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9282 | 0.771232 | 0.385616 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385616 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(282\) | 2.36603 | − | 0.633975i | 0.140895 | − | 0.0377526i | ||||
\(283\) | 7.09808 | − | 26.4904i | 0.421937 | − | 1.57469i | −0.348586 | − | 0.937277i | \(-0.613338\pi\) |
0.770523 | − | 0.637413i | \(-0.219995\pi\) | |||||||
\(284\) | 7.09808 | − | 4.09808i | 0.421193 | − | 0.243176i | ||||
\(285\) | 8.83013 | − | 7.83013i | 0.523052 | − | 0.463817i | ||||
\(286\) | − | 4.00000i | − | 0.236525i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.92820 | + | 3.92820i | −0.231472 | + | 0.231472i | ||||
\(289\) | −13.7942 | − | 7.96410i | −0.811425 | − | 0.468477i | ||||
\(290\) | 12.6962 | − | 2.59808i | 0.745544 | − | 0.152564i | ||||
\(291\) | −10.8301 | − | 18.7583i | −0.634873 | − | 1.09963i | ||||
\(292\) | 1.60770 | + | 6.00000i | 0.0940832 | + | 0.351123i | ||||
\(293\) | 18.3923 | + | 18.3923i | 1.07449 | + | 1.07449i | 0.996993 | + | 0.0774974i | \(0.0246929\pi\) |
0.0774974 | + | 0.996993i | \(0.475307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.39230 | − | 2.19615i | 0.255730 | − | 0.127865i | ||||
\(296\) | 1.26795 | − | 2.19615i | 0.0736980 | − | 0.127649i | ||||
\(297\) | −3.09808 | − | 0.830127i | −0.179769 | − | 0.0481689i | ||||
\(298\) | −20.8923 | − | 5.59808i | −1.21026 | − | 0.324288i | ||||
\(299\) | −10.1962 | + | 17.6603i | −0.589659 | + | 1.02132i | ||||
\(300\) | 2.36603 | + | 16.5622i | 0.136603 | + | 0.956218i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −18.9282 | − | 18.9282i | −1.08920 | − | 1.08920i | ||||
\(303\) | −5.86603 | − | 21.8923i | −0.336994 | − | 1.25768i | ||||
\(304\) | −6.09808 | − | 10.5622i | −0.349749 | − | 0.605782i | ||||
\(305\) | 10.4282 | − | 15.7942i | 0.597117 | − | 0.904375i | ||||
\(306\) | −1.26795 | − | 0.732051i | −0.0724838 | − | 0.0418486i | ||||
\(307\) | −9.29423 | + | 9.29423i | −0.530450 | + | 0.530450i | −0.920706 | − | 0.390257i | \(-0.872386\pi\) |
0.390257 | + | 0.920706i | \(0.372386\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.46410i | − | 0.253954i | ||||||
\(310\) | −1.53590 | − | 1.73205i | −0.0872332 | − | 0.0983739i | ||||
\(311\) | −16.2224 | + | 9.36603i | −0.919890 | + | 0.531099i | −0.883600 | − | 0.468243i | \(-0.844887\pi\) |
−0.0362898 | + | 0.999341i | \(0.511554\pi\) | |||||||
\(312\) | −0.732051 | + | 2.73205i | −0.0414442 | + | 0.154672i | ||||
\(313\) | −19.3923 | + | 5.19615i | −1.09612 | + | 0.293704i | −0.761183 | − | 0.648537i | \(-0.775381\pi\) |
−0.334935 | + | 0.942241i | \(0.608714\pi\) | |||||||
\(314\) | −47.5167 | −2.68152 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.6603 | 0.655941 | ||||||||
\(317\) | 4.46410 | − | 1.19615i | 0.250729 | − | 0.0671826i | −0.131265 | − | 0.991347i | \(-0.541904\pi\) |
0.381994 | + | 0.924165i | \(0.375237\pi\) | |||||||
\(318\) | −6.83013 | + | 25.4904i | −0.383015 | + | 1.42943i | ||||
\(319\) | −1.90192 | + | 1.09808i | −0.106487 | + | 0.0614805i | ||||
\(320\) | 12.7942 | + | 0.767949i | 0.715219 | + | 0.0429297i | ||||
\(321\) | 17.1962i | 0.959796i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | − | 2.00000i | 0.111283 | − | 0.111283i | ||||
\(324\) | −15.9904 | − | 9.23205i | −0.888355 | − | 0.512892i | ||||
\(325\) | 8.73205 | + | 11.1244i | 0.484367 | + | 0.617068i | ||||
\(326\) | −5.36603 | − | 9.29423i | −0.297197 | − | 0.514760i | ||||
\(327\) | −7.06218 | − | 26.3564i | −0.390539 | − | 1.45751i | ||||
\(328\) | 0.169873 | + | 0.169873i | 0.00937967 | + | 0.00937967i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.73205 | − | 5.46410i | −0.150394 | − | 0.300789i | ||||
\(331\) | −12.9282 | + | 22.3923i | −0.710598 | + | 1.23079i | 0.254035 | + | 0.967195i | \(0.418242\pi\) |
−0.964633 | + | 0.263597i | \(0.915091\pi\) | |||||||
\(332\) | 7.33013 | + | 1.96410i | 0.402293 | + | 0.107794i | ||||
\(333\) | −3.46410 | − | 0.928203i | −0.189832 | − | 0.0508652i | ||||
\(334\) | 14.6962 | − | 25.4545i | 0.804138 | − | 1.39281i | ||||
\(335\) | 2.49038 | + | 0.830127i | 0.136064 | + | 0.0453547i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4641 | + | 16.4641i | 0.896857 | + | 0.896857i | 0.995157 | − | 0.0983001i | \(-0.0313405\pi\) |
−0.0983001 | + | 0.995157i | \(0.531340\pi\) | |||||||
\(338\) | 2.50000 | + | 9.33013i | 0.135982 | + | 0.507492i | ||||
\(339\) | 5.83013 | + | 10.0981i | 0.316649 | + | 0.548452i | ||||
\(340\) | 0.803848 | + | 3.92820i | 0.0435948 | + | 0.213037i | ||||
\(341\) | 0.339746 | + | 0.196152i | 0.0183983 | + | 0.0106222i | ||||
\(342\) | −2.73205 | + | 2.73205i | −0.147732 | + | 0.147732i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.26795i | 0.230112i | ||||||||
\(345\) | −1.86603 | + | 31.0885i | −0.100463 | + | 1.67375i | ||||
\(346\) | 39.2487 | − | 22.6603i | 2.11002 | − | 1.21822i | ||||
\(347\) | −2.08846 | + | 7.79423i | −0.112114 | + | 0.418416i | −0.999055 | − | 0.0434674i | \(-0.986160\pi\) |
0.886941 | + | 0.461884i | \(0.152826\pi\) | |||||||
\(348\) | −9.69615 | + | 2.59808i | −0.519768 | + | 0.139272i | ||||
\(349\) | 9.73205 | 0.520945 | 0.260472 | − | 0.965481i | \(-0.416122\pi\) | ||||
0.260472 | + | 0.965481i | \(0.416122\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3923 | −0.661452 | ||||||||
\(352\) | −5.36603 | + | 1.43782i | −0.286010 | + | 0.0766362i | ||||
\(353\) | −1.43782 | + | 5.36603i | −0.0765276 | + | 0.285605i | −0.993575 | − | 0.113173i | \(-0.963899\pi\) |
0.917048 | + | 0.398777i | \(0.130565\pi\) | |||||||
\(354\) | −7.09808 | + | 4.09808i | −0.377258 | + | 0.217810i | ||||
\(355\) | 0.633975 | − | 10.5622i | 0.0336479 | − | 0.560582i | ||||
\(356\) | − | 28.8564i | − | 1.52939i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.1244 | − | 27.1244i | 1.43357 | − | 1.43357i | ||||
\(359\) | −12.3397 | − | 7.12436i | −0.651267 | − | 0.376009i | 0.137675 | − | 0.990478i | \(-0.456037\pi\) |
−0.788941 | + | 0.614468i | \(0.789371\pi\) | |||||||
\(360\) | 0.169873 | + | 0.830127i | 0.00895309 | + | 0.0437515i | ||||
\(361\) | 5.76795 | + | 9.99038i | 0.303576 | + | 0.525810i | ||||
\(362\) | −4.59808 | − | 17.1603i | −0.241670 | − | 0.901923i | ||||
\(363\) | −14.2942 | − | 14.2942i | −0.750252 | − | 0.750252i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.60770 | + | 2.53590i | 0.398205 | + | 0.132735i | ||||
\(366\) | −15.7942 | + | 27.3564i | −0.825578 | + | 1.42994i | ||||
\(367\) | −1.86603 | − | 0.500000i | −0.0974057 | − | 0.0260998i | 0.209787 | − | 0.977747i | \(-0.432723\pi\) |
−0.307193 | + | 0.951647i | \(0.599390\pi\) | |||||||
\(368\) | 31.0885 | + | 8.33013i | 1.62060 | + | 0.434238i | ||||
\(369\) | 0.169873 | − | 0.294229i | 0.00884323 | − | 0.0153169i | ||||
\(370\) | 9.46410 | + | 18.9282i | 0.492015 | + | 0.984030i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.26795 | + | 1.26795i | 0.0657401 | + | 0.0657401i | ||||
\(373\) | −4.26795 | − | 15.9282i | −0.220986 | − | 0.824731i | −0.983973 | − | 0.178317i | \(-0.942935\pi\) |
0.762987 | − | 0.646414i | \(-0.223732\pi\) | |||||||
\(374\) | −0.732051 | − | 1.26795i | −0.0378534 | − | 0.0655641i | ||||
\(375\) | 19.5263 | + | 9.23205i | 1.00833 | + | 0.476741i | ||||
\(376\) | −0.294229 | − | 0.169873i | −0.0151737 | − | 0.00876053i | ||||
\(377\) | −6.00000 | + | 6.00000i | −0.309016 | + | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.6603i | 1.00988i | 0.863155 | + | 0.504940i | \(0.168485\pi\) | ||||
−0.863155 | + | 0.504940i | \(0.831515\pi\) | |||||||
\(380\) | 10.5622 | + | 0.633975i | 0.541828 | + | 0.0325222i | ||||
\(381\) | −15.2942 | + | 8.83013i | −0.783547 | + | 0.452381i | ||||
\(382\) | 8.36603 | − | 31.2224i | 0.428043 | − | 1.59748i | ||||
\(383\) | 28.1865 | − | 7.55256i | 1.44026 | − | 0.385918i | 0.547638 | − | 0.836715i | \(-0.315527\pi\) |
0.892626 | + | 0.450797i | \(0.148860\pi\) | |||||||
\(384\) | 7.92820 | 0.404584 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.19615 | 0.315376 | ||||||||
\(387\) | 5.83013 | − | 1.56218i | 0.296362 | − | 0.0794100i | ||||
\(388\) | 5.02628 | − | 18.7583i | 0.255171 | − | 0.952310i | ||||
\(389\) | 7.73205 | − | 4.46410i | 0.392031 | − | 0.226339i | −0.291009 | − | 0.956720i | \(-0.593991\pi\) |
0.683040 | + | 0.730381i | \(0.260658\pi\) | |||||||
\(390\) | −15.6603 | − | 17.6603i | −0.792988 | − | 0.894262i | ||||
\(391\) | 7.46410i | 0.377476i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.6603 | + | 11.6603i | −0.588182 | + | 0.588182i | ||||
\(394\) | −33.4186 | − | 19.2942i | −1.68360 | − | 0.972029i | ||||
\(395\) | 8.29423 | − | 12.5622i | 0.417328 | − | 0.632072i | ||||
\(396\) | 0.464102 | + | 0.803848i | 0.0233220 | + | 0.0403949i | ||||
\(397\) | 5.36603 | + | 20.0263i | 0.269313 | + | 1.00509i | 0.959557 | + | 0.281514i | \(0.0908365\pi\) |
−0.690244 | + | 0.723577i | \(0.742497\pi\) | |||||||
\(398\) | 34.0526 | + | 34.0526i | 1.70690 | + | 1.70690i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.3923 | − | 17.8564i | 0.669615 | − | 0.892820i | ||||
\(401\) | −5.50000 | + | 9.52628i | −0.274657 | + | 0.475720i | −0.970049 | − | 0.242911i | \(-0.921898\pi\) |
0.695392 | + | 0.718631i | \(0.255231\pi\) | |||||||
\(402\) | −4.23205 | − | 1.13397i | −0.211076 | − | 0.0565575i | ||||
\(403\) | 1.46410 | + | 0.392305i | 0.0729321 | + | 0.0195421i | ||||
\(404\) | 10.1603 | − | 17.5981i | 0.505492 | − | 0.875537i | ||||
\(405\) | −21.3205 | + | 10.6603i | −1.05942 | + | 0.529712i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.53590 | − | 2.53590i | −0.125700 | − | 0.125700i | ||||
\(408\) | 0.267949 | + | 1.00000i | 0.0132655 | + | 0.0495074i | ||||
\(409\) | 3.42820 | + | 5.93782i | 0.169514 | + | 0.293606i | 0.938249 | − | 0.345961i | \(-0.112447\pi\) |
−0.768735 | + | 0.639567i | \(0.779114\pi\) | |||||||
\(410\) | −1.96410 | + | 0.401924i | −0.0970001 | + | 0.0198496i | ||||
\(411\) | −18.1244 | − | 10.4641i | −0.894009 | − | 0.516156i | ||||
\(412\) | 2.83013 | − | 2.83013i | 0.139430 | − | 0.139430i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 10.1962i | − | 0.501114i | ||||||
\(415\) | 7.33013 | − | 6.50000i | 0.359822 | − | 0.319072i | ||||
\(416\) | −18.5885 | + | 10.7321i | −0.911374 | + | 0.526182i | ||||
\(417\) | 5.83013 | − | 21.7583i | 0.285503 | − | 1.06551i | ||||
\(418\) | −3.73205 | + | 1.00000i | −0.182541 | + | 0.0489116i | ||||
\(419\) | −3.85641 | −0.188398 | −0.0941989 | − | 0.995553i | \(-0.530029\pi\) | ||||
−0.0941989 | + | 0.995553i | \(0.530029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.6603 | −1.68924 | −0.844619 | − | 0.535368i | \(-0.820173\pi\) | ||||
−0.844619 | + | 0.535368i | \(0.820173\pi\) | |||||||
\(422\) | −19.0263 | + | 5.09808i | −0.926185 | + | 0.248170i | ||||
\(423\) | −0.124356 | + | 0.464102i | −0.00604638 | + | 0.0225654i | ||||
\(424\) | 3.16987 | − | 1.83013i | 0.153943 | − | 0.0888788i | ||||
\(425\) | 4.80385 | + | 1.92820i | 0.233021 | + | 0.0935316i | ||||
\(426\) | 17.6603i | 0.855642i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.9019 | + | 10.9019i | −0.526964 | + | 0.526964i | ||||
\(429\) | 3.46410 | + | 2.00000i | 0.167248 | + | 0.0965609i | ||||
\(430\) | −29.7224 | − | 19.6244i | −1.43334 | − | 0.946370i | ||||
\(431\) | 2.09808 | + | 3.63397i | 0.101061 | + | 0.175042i | 0.912122 | − | 0.409919i | \(-0.134443\pi\) |
−0.811061 | + | 0.584961i | \(0.801110\pi\) | |||||||
\(432\) | 5.06218 | + | 18.8923i | 0.243554 | + | 0.908956i | ||||
\(433\) | −24.4641 | − | 24.4641i | −1.17567 | − | 1.17567i | −0.980836 | − | 0.194833i | \(-0.937583\pi\) |
−0.194833 | − | 0.980836i | \(-0.562417\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.09808 | + | 12.2942i | −0.196488 | + | 0.589463i | ||||
\(436\) | 12.2321 | − | 21.1865i | 0.585809 | − | 1.01465i | ||||
\(437\) | 19.0263 | + | 5.09808i | 0.910150 | + | 0.243874i | ||||
\(438\) | −12.9282 | − | 3.46410i | −0.617733 | − | 0.165521i | ||||
\(439\) | −15.6603 | + | 27.1244i | −0.747423 | + | 1.29457i | 0.201631 | + | 0.979462i | \(0.435376\pi\) |
−0.949054 | + | 0.315113i | \(0.897957\pi\) | |||||||
\(440\) | −0.267949 | + | 0.803848i | −0.0127740 | + | 0.0383219i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | − | 4.00000i | −0.190261 | − | 0.190261i | ||||
\(443\) | 0.937822 | + | 3.50000i | 0.0445573 | + | 0.166290i | 0.984619 | − | 0.174713i | \(-0.0558999\pi\) |
−0.940062 | + | 0.341003i | \(0.889233\pi\) | |||||||
\(444\) | −8.19615 | − | 14.1962i | −0.388972 | − | 0.673720i | ||||
\(445\) | −31.0885 | − | 20.5263i | −1.47373 | − | 0.973039i | ||||
\(446\) | 14.4904 | + | 8.36603i | 0.686139 | + | 0.396143i | ||||
\(447\) | 15.2942 | − | 15.2942i | 0.723392 | − | 0.723392i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.05256i | 0.238445i | 0.992868 | + | 0.119222i | \(0.0380402\pi\) | ||||
−0.992868 | + | 0.119222i | \(0.961960\pi\) | |||||||
\(450\) | −6.56218 | − | 2.63397i | −0.309344 | − | 0.124167i | ||||
\(451\) | 0.294229 | − | 0.169873i | 0.0138547 | − | 0.00799901i | ||||
\(452\) | −2.70577 | + | 10.0981i | −0.127269 | + | 0.474974i | ||||
\(453\) | 25.8564 | − | 6.92820i | 1.21484 | − | 0.325515i | ||||
\(454\) | 0.196152 | 0.00920589 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.73205 | 0.127940 | ||||||||
\(457\) | 30.8564 | − | 8.26795i | 1.44340 | − | 0.386758i | 0.549678 | − | 0.835376i | \(-0.314750\pi\) |
0.893724 | + | 0.448618i | \(0.148084\pi\) | |||||||
\(458\) | −1.19615 | + | 4.46410i | −0.0558925 | + | 0.208594i | ||||
\(459\) | −3.92820 | + | 2.26795i | −0.183353 | + | 0.105859i | ||||
\(460\) | −20.8923 | + | 18.5263i | −0.974109 | + | 0.863792i | ||||
\(461\) | − | 26.3923i | − | 1.22921i | −0.788834 | − | 0.614606i | \(-0.789315\pi\) | ||
0.788834 | − | 0.614606i | \(-0.210685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7583 | − | 17.7583i | 0.825300 | − | 0.825300i | −0.161563 | − | 0.986862i | \(-0.551653\pi\) |
0.986862 | + | 0.161563i | \(0.0516534\pi\) | |||||||
\(464\) | 11.5981 | + | 6.69615i | 0.538427 | + | 0.310861i | ||||
\(465\) | 2.26795 | − | 0.464102i | 0.105174 | − | 0.0215222i | ||||
\(466\) | 1.73205 | + | 3.00000i | 0.0802357 | + | 0.138972i | ||||
\(467\) | −8.40192 | − | 31.3564i | −0.388795 | − | 1.45100i | −0.832097 | − | 0.554629i | \(-0.812860\pi\) |
0.443303 | − | 0.896372i | \(-0.353807\pi\) | |||||||
\(468\) | 2.53590 | + | 2.53590i | 0.117222 | + | 0.117222i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.53590 | − | 1.26795i | 0.116972 | − | 0.0584861i | ||||
\(471\) | 23.7583 | − | 41.1506i | 1.09473 | − | 1.89612i | ||||
\(472\) | 1.09808 | + | 0.294229i | 0.0505431 | + | 0.0135430i | ||||
\(473\) | 5.83013 | + | 1.56218i | 0.268070 | + | 0.0718290i | ||||
\(474\) | −12.5622 | + | 21.7583i | −0.577000 | + | 0.999393i | ||||
\(475\) | 8.19615 | − | 10.9282i | 0.376065 | − | 0.501420i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.66025 | − | 3.66025i | −0.167592 | − | 0.167592i | ||||
\(478\) | 9.19615 | + | 34.3205i | 0.420622 | + | 1.56978i | ||||
\(479\) | 13.4641 | + | 23.3205i | 0.615191 | + | 1.06554i | 0.990351 | + | 0.138581i | \(0.0442542\pi\) |
−0.375161 | + | 0.926960i | \(0.622412\pi\) | |||||||
\(480\) | −18.0622 | + | 27.3564i | −0.824422 | + | 1.24864i | ||||
\(481\) | −12.0000 | − | 6.92820i | −0.547153 | − | 0.315899i | ||||
\(482\) | 22.9282 | − | 22.9282i | 1.04435 | − | 1.04435i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 18.1244i | − | 0.823834i | ||||||
\(485\) | −16.6340 | − | 18.7583i | −0.755310 | − | 0.851772i | ||||
\(486\) | 12.4641 | − | 7.19615i | 0.565383 | − | 0.326424i | ||||
\(487\) | 2.22243 | − | 8.29423i | 0.100708 | − | 0.375847i | −0.897115 | − | 0.441797i | \(-0.854341\pi\) |
0.997823 | + | 0.0659498i | \(0.0210077\pi\) | |||||||
\(488\) | 4.23205 | − | 1.13397i | 0.191576 | − | 0.0513326i | ||||
\(489\) | 10.7321 | 0.485320 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7128 | −0.799368 | −0.399684 | − | 0.916653i | \(-0.630880\pi\) | ||||
−0.399684 | + | 0.916653i | \(0.630880\pi\) | |||||||
\(492\) | 1.50000 | − | 0.401924i | 0.0676252 | − | 0.0181201i | ||||
\(493\) | −0.803848 | + | 3.00000i | −0.0362035 | + | 0.135113i | ||||
\(494\) | −12.9282 | + | 7.46410i | −0.581667 | + | 0.335826i | ||||
\(495\) | 1.19615 | + | 0.0717968i | 0.0537631 | + | 0.00322702i | ||||
\(496\) | − | 2.39230i | − | 0.107418i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −11.5622 | + | 11.5622i | −0.518114 | + | 0.518114i | ||||
\(499\) | 29.0263 | + | 16.7583i | 1.29939 | + | 0.750206i | 0.980300 | − | 0.197517i | \(-0.0632877\pi\) |
0.319095 | + | 0.947723i | \(0.396621\pi\) | |||||||
\(500\) | 6.52628 | + | 18.2321i | 0.291864 | + | 0.815362i | ||||
\(501\) | 14.6962 | + | 25.4545i | 0.656576 | + | 1.13722i | ||||
\(502\) | 2.92820 | + | 10.9282i | 0.130692 | + | 0.487750i | ||||
\(503\) | −19.3660 | − | 19.3660i | −0.863488 | − | 0.863488i | 0.128253 | − | 0.991741i | \(-0.459063\pi\) |
−0.991741 | + | 0.128253i | \(0.959063\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.7321 | − | 23.4641i | −0.522069 | − | 1.04414i | ||||
\(506\) | 5.09808 | − | 8.83013i | 0.226637 | − | 0.392547i | ||||
\(507\) | −9.33013 | − | 2.50000i | −0.414365 | − | 0.111029i | ||||
\(508\) | −15.2942 | − | 4.09808i | −0.678572 | − | 0.181823i | ||||
\(509\) | 13.4545 | − | 23.3038i | 0.596359 | − | 1.03292i | −0.396994 | − | 0.917821i | \(-0.629947\pi\) |
0.993353 | − | 0.115104i | \(-0.0367200\pi\) | |||||||
\(510\) | −8.19615 | − | 2.73205i | −0.362932 | − | 0.120977i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.6865 | + | 20.6865i | 0.914224 | + | 0.914224i | ||||
\(513\) | 3.09808 | + | 11.5622i | 0.136783 | + | 0.510483i | ||||
\(514\) | 2.73205 | + | 4.73205i | 0.120506 | + | 0.208722i | ||||
\(515\) | −1.03590 | − | 5.06218i | −0.0456471 | − | 0.223066i | ||||
\(516\) | 23.8923 | + | 13.7942i | 1.05180 | + | 0.607257i | ||||
\(517\) | −0.339746 | + | 0.339746i | −0.0149420 | + | 0.0149420i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.3205i | 1.98935i | ||||||||
\(520\) | −0.196152 | + | 3.26795i | −0.00860185 | + | 0.143309i | ||||
\(521\) | 3.33975 | − | 1.92820i | 0.146317 | − | 0.0844761i | −0.425054 | − | 0.905168i | \(-0.639745\pi\) |
0.571371 | + | 0.820692i | \(0.306412\pi\) | |||||||
\(522\) | 1.09808 | − | 4.09808i | 0.0480615 | − | 0.179368i | ||||
\(523\) | −14.4904 | + | 3.88269i | −0.633620 | + | 0.169778i | −0.561312 | − | 0.827604i | \(-0.689703\pi\) |
−0.0723082 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(524\) | −14.7846 | −0.645869 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.1244 | 0.703055 | ||||||||
\(527\) | 0.535898 | − | 0.143594i | 0.0233441 | − | 0.00625503i | ||||
\(528\) | 1.63397 | − | 6.09808i | 0.0711096 | − | 0.265385i | ||||
\(529\) | −25.0981 | + | 14.4904i | −1.09122 | + | 0.630017i | ||||
\(530\) | −1.83013 | + | 30.4904i | −0.0794956 | + | 1.32442i | ||||
\(531\) | − | 1.60770i | − | 0.0697680i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.928203 | − | 0.928203i | 0.0402049 | − | 0.0402049i | ||||
\(534\) | 53.8468 | + | 31.0885i | 2.33018 | + | 1.34533i | ||||
\(535\) | 3.99038 | + | 19.5000i | 0.172519 | + | 0.843059i | ||||
\(536\) | 0.303848 | + | 0.526279i | 0.0131242 | + | 0.0227318i | ||||
\(537\) | 9.92820 | + | 37.0526i | 0.428434 | + | 1.59894i | ||||
\(538\) | 6.63397 | + | 6.63397i | 0.286011 | + | 0.286011i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −16.0981 | − | 5.36603i | −0.692751 | − | 0.230917i | ||||
\(541\) | 9.35641 | − | 16.2058i | 0.402263 | − | 0.696741i | −0.591735 | − | 0.806132i | \(-0.701557\pi\) |
0.993999 | + | 0.109392i | \(0.0348903\pi\) | |||||||
\(542\) | −46.1506 | − | 12.3660i | −1.98234 | − | 0.531166i | ||||
\(543\) | 17.1603 | + | 4.59808i | 0.736417 | + | 0.197322i | ||||
\(544\) | −3.92820 | + | 6.80385i | −0.168420 | + | 0.291713i | ||||
\(545\) | −14.1244 | − | 28.2487i | −0.605021 | − | 1.21004i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.75833 | + | 5.75833i | 0.246208 | + | 0.246208i | 0.819413 | − | 0.573204i | \(-0.194300\pi\) |
−0.573204 | + | 0.819413i | \(0.694300\pi\) | |||||||
\(548\) | −4.85641 | − | 18.1244i | −0.207455 | − | 0.774234i | ||||
\(549\) | −3.09808 | − | 5.36603i | −0.132223 | − | 0.229016i | ||||
\(550\) | −4.36603 | − | 5.56218i | −0.186168 | − | 0.237172i | ||||
\(551\) | 7.09808 | + | 4.09808i | 0.302388 | + | 0.174584i | ||||
\(552\) | −5.09808 | + | 5.09808i | −0.216989 | + | 0.216989i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 38.7846i | − | 1.64780i | ||||||
\(555\) | −21.1244 | − | 1.26795i | −0.896679 | − | 0.0538214i | ||||
\(556\) | 17.4904 | − | 10.0981i | 0.741757 | − | 0.428254i | ||||
\(557\) | −1.77757 | + | 6.63397i | −0.0753180 | + | 0.281091i | −0.993305 | − | 0.115519i | \(-0.963147\pi\) |
0.917987 | + | 0.396610i | \(0.129813\pi\) | |||||||
\(558\) | −0.732051 | + | 0.196152i | −0.0309902 | + | 0.00830379i | ||||
\(559\) | 23.3205 | 0.986352 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.46410 | 0.0618144 | ||||||||
\(562\) | −24.1244 | + | 6.46410i | −1.01762 | + | 0.272672i | ||||
\(563\) | −5.72243 | + | 21.3564i | −0.241172 | + | 0.900065i | 0.734097 | + | 0.679044i | \(0.237606\pi\) |
−0.975269 | + | 0.221021i | \(0.929061\pi\) | |||||||
\(564\) | −1.90192 | + | 1.09808i | −0.0800854 | + | 0.0462373i | ||||
\(565\) | 8.95448 | + | 10.0981i | 0.376718 | + | 0.424829i | ||||
\(566\) | 52.9808i | 2.22695i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.73205 | − | 1.73205i | 0.0726752 | − | 0.0726752i | ||||
\(569\) | −13.0526 | − | 7.53590i | −0.547192 | − | 0.315921i | 0.200797 | − | 0.979633i | \(-0.435647\pi\) |
−0.747989 | + | 0.663712i | \(0.768980\pi\) | |||||||
\(570\) | −12.5622 | + | 19.0263i | −0.526172 | + | 0.796923i | ||||
\(571\) | −10.0263 | − | 17.3660i | −0.419587 | − | 0.726746i | 0.576311 | − | 0.817230i | \(-0.304492\pi\) |
−0.995898 | + | 0.0904849i | \(0.971158\pi\) | |||||||
\(572\) | 0.928203 | + | 3.46410i | 0.0388101 | + | 0.144841i | ||||
\(573\) | 22.8564 | + | 22.8564i | 0.954840 | + | 0.954840i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.09808 | + | 35.6865i | 0.212604 | + | 1.48823i | ||||
\(576\) | 2.09808 | − | 3.63397i | 0.0874198 | − | 0.151416i | ||||
\(577\) | −27.4904 | − | 7.36603i | −1.14444 | − | 0.306652i | −0.363705 | − | 0.931514i | \(-0.618488\pi\) |
−0.780735 | + | 0.624863i | \(0.785155\pi\) | |||||||
\(578\) | 29.7224 | + | 7.96410i | 1.23629 | + | 0.331263i | ||||
\(579\) | −3.09808 | + | 5.36603i | −0.128752 | + | 0.223004i | ||||
\(580\) | −10.3923 | + | 5.19615i | −0.431517 | + | 0.215758i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 29.5885 | + | 29.5885i | 1.22648 | + | 1.22648i | ||||
\(583\) | −1.33975 | − | 5.00000i | −0.0554866 | − | 0.207079i | ||||
\(584\) | 0.928203 | + | 1.60770i | 0.0384093 | + | 0.0665269i | ||||
\(585\) | 4.53590 | − | 0.928203i | 0.187536 | − | 0.0383765i | ||||
\(586\) | −43.5167 | − | 25.1244i | −1.79766 | − | 1.03788i | ||||
\(587\) | −25.7846 | + | 25.7846i | −1.06424 | + | 1.06424i | −0.0664553 | + | 0.997789i | \(0.521169\pi\) |
−0.997789 | + | 0.0664553i | \(0.978831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.46410i | − | 0.0603273i | ||||||
\(590\) | −7.09808 | + | 6.29423i | −0.292223 | + | 0.259129i | ||||
\(591\) | 33.4186 | − | 19.2942i | 1.37466 | − | 0.793659i | ||||
\(592\) | −5.66025 | + | 21.1244i | −0.232635 | + | 0.868206i | ||||
\(593\) | 6.56218 | − | 1.75833i | 0.269476 | − | 0.0722060i | −0.121550 | − | 0.992585i | \(-0.538787\pi\) |
0.391027 | + | 0.920379i | \(0.372120\pi\) | |||||||
\(594\) | 6.19615 | 0.254231 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.3923 | 0.794340 | ||||||||
\(597\) | −46.5167 | + | 12.4641i | −1.90380 | + | 0.510122i | ||||
\(598\) | 10.1962 | − | 38.0526i | 0.416952 | − | 1.55608i | ||||
\(599\) | 32.6603 | − | 18.8564i | 1.33446 | − | 0.770452i | 0.348482 | − | 0.937316i | \(-0.386697\pi\) |
0.985980 | + | 0.166864i | \(0.0533640\pi\) | |||||||
\(600\) | 1.96410 | + | 4.59808i | 0.0801841 | + | 0.187716i | ||||
\(601\) | 21.1769i | 0.863824i | 0.901916 | + | 0.431912i | \(0.142161\pi\) | ||||
−0.901916 | + | 0.431912i | \(0.857839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.607695 | − | 0.607695i | 0.0247473 | − | 0.0247473i | ||||
\(604\) | 20.7846 | + | 12.0000i | 0.845714 | + | 0.488273i | ||||
\(605\) | −19.5263 | − | 12.8923i | −0.793856 | − | 0.524147i | ||||
\(606\) | 21.8923 | + | 37.9186i | 0.889314 | + | 1.54034i | ||||
\(607\) | −2.30385 | − | 8.59808i | −0.0935103 | − | 0.348985i | 0.903279 | − | 0.429053i | \(-0.141153\pi\) |
−0.996789 | + | 0.0800683i | \(0.974486\pi\) | |||||||
\(608\) | 14.6603 | + | 14.6603i | 0.594552 | + | 0.594552i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.5622 | + | 34.6865i | −0.468139 | + | 1.40442i | ||||
\(611\) | −0.928203 | + | 1.60770i | −0.0375511 | + | 0.0650404i | ||||
\(612\) | 1.26795 | + | 0.339746i | 0.0512538 | + | 0.0137334i | ||||
\(613\) | −13.4641 | − | 3.60770i | −0.543810 | − | 0.145713i | −0.0235520 | − | 0.999723i | \(-0.507498\pi\) |
−0.520258 | + | 0.854009i | \(0.674164\pi\) | |||||||
\(614\) | 12.6962 | − | 21.9904i | 0.512375 | − | 0.887460i | ||||
\(615\) | 0.633975 | − | 1.90192i | 0.0255643 | − | 0.0766930i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.9090 | − | 31.9090i | −1.28461 | − | 1.28461i | −0.938017 | − | 0.346590i | \(-0.887340\pi\) |
−0.346590 | − | 0.938017i | \(-0.612660\pi\) | |||||||
\(618\) | 2.23205 | + | 8.33013i | 0.0897863 | + | 0.335087i | ||||
\(619\) | −0.0980762 | − | 0.169873i | −0.00394202 | − | 0.00682777i | 0.864048 | − | 0.503410i | \(-0.167921\pi\) |
−0.867990 | + | 0.496582i | \(0.834588\pi\) | |||||||
\(620\) | 1.73205 | + | 1.14359i | 0.0695608 | + | 0.0459278i | ||||
\(621\) | −27.3564 | − | 15.7942i | −1.09777 | − | 0.633801i | ||||
\(622\) | 25.5885 | − | 25.5885i | 1.02600 | − | 1.02600i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 24.3923i | − | 0.976474i | ||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 33.5885 | − | 19.3923i | 1.34246 | − | 0.775072i | ||||
\(627\) | 1.00000 | − | 3.73205i | 0.0399362 | − | 0.149044i | ||||
\(628\) | 41.1506 | − | 11.0263i | 1.64209 | − | 0.439996i | ||||
\(629\) | −5.07180 | −0.202226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.5885 | 1.05847 | 0.529235 | − | 0.848475i | \(-0.322479\pi\) | ||||
0.529235 | + | 0.848475i | \(0.322479\pi\) | |||||||
\(632\) | 3.36603 | − | 0.901924i | 0.133893 | − | 0.0358766i | ||||
\(633\) | 5.09808 | − | 19.0263i | 0.202630 | − | 0.756227i | ||||
\(634\) | −7.73205 | + | 4.46410i | −0.307079 | + | 0.177292i | ||||
\(635\) | −15.2942 | + | 13.5622i | −0.606933 | + | 0.538199i | ||||
\(636\) | − | 23.6603i | − | 0.938190i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.00000 | − | 3.00000i | 0.118771 | − | 0.118771i | ||||
\(639\) | −3.00000 | − | 1.73205i | −0.118678 | − | 0.0685189i | ||||
\(640\) | 8.99038 | − | 1.83975i | 0.355376 | − | 0.0727223i | ||||
\(641\) | 3.33013 | + | 5.76795i | 0.131532 | + | 0.227820i | 0.924267 | − | 0.381746i | \(-0.124677\pi\) |
−0.792735 | + | 0.609566i | \(0.791344\pi\) | |||||||
\(642\) | −8.59808 | − | 32.0885i | −0.339339 | − | 1.26643i | ||||
\(643\) | 24.4641 | + | 24.4641i | 0.964770 | + | 0.964770i | 0.999400 | − | 0.0346302i | \(-0.0110253\pi\) |
−0.0346302 | + | 0.999400i | \(0.511025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.8564 | − | 15.9282i | 1.25434 | − | 0.627172i | ||||
\(646\) | −2.73205 | + | 4.73205i | −0.107491 | + | 0.186180i | ||||
\(647\) | −5.40192 | − | 1.44744i | −0.212372 | − | 0.0569048i | 0.151065 | − | 0.988524i | \(-0.451730\pi\) |
−0.363436 | + | 0.931619i | \(0.618397\pi\) | |||||||
\(648\) | −5.33013 | − | 1.42820i | −0.209387 | − | 0.0561051i | ||||
\(649\) | 0.803848 | − | 1.39230i | 0.0315538 | − | 0.0546527i | ||||
\(650\) | −21.8564 | − | 16.3923i | −0.857279 | − | 0.642959i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.80385 | + | 6.80385i | 0.266459 | + | 0.266459i | ||||
\(653\) | 2.33975 | + | 8.73205i | 0.0915613 | + | 0.341712i | 0.996476 | − | 0.0838822i | \(-0.0267319\pi\) |
−0.904914 | + | 0.425594i | \(0.860065\pi\) | |||||||
\(654\) | 26.3564 | + | 45.6506i | 1.03062 | + | 1.78508i | ||||
\(655\) | −10.5167 | + | 15.9282i | −0.410920 | + | 0.622366i | ||||
\(656\) | −1.79423 | − | 1.03590i | −0.0700529 | − | 0.0404450i | ||||
\(657\) | 1.85641 | − | 1.85641i | 0.0724253 | − | 0.0724253i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.3397i | − | 0.402779i | −0.979511 | − | 0.201390i | \(-0.935454\pi\) | ||
0.979511 | − | 0.201390i | \(-0.0645457\pi\) | |||||||
\(660\) | 3.63397 | + | 4.09808i | 0.141452 | + | 0.159517i | ||||
\(661\) | 12.2776 | − | 7.08846i | 0.477542 | − | 0.275709i | −0.241850 | − | 0.970314i | \(-0.577754\pi\) |
0.719392 | + | 0.694605i | \(0.244421\pi\) | |||||||
\(662\) | 12.9282 | − | 48.2487i | 0.502469 | − | 1.87524i | ||||
\(663\) | 5.46410 | − | 1.46410i | 0.212208 | − | 0.0568610i | ||||
\(664\) | 2.26795 | 0.0880135 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.92820 | 0.268462 | ||||||||
\(667\) | −20.8923 | + | 5.59808i | −0.808953 | + | 0.216758i | ||||
\(668\) | −6.82051 | + | 25.4545i | −0.263893 | + | 0.984864i | ||||
\(669\) | −14.4904 | + | 8.36603i | −0.560230 | + | 0.323449i | ||||
\(670\) | −5.06218 | − | 0.303848i | −0.195569 | − | 0.0117387i | ||||
\(671\) | − | 6.19615i | − | 0.239200i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3923 | + | 16.3923i | −0.631877 | + | 0.631877i | −0.948539 | − | 0.316662i | \(-0.897438\pi\) |
0.316662 | + | 0.948539i | \(0.397438\pi\) | |||||||
\(674\) | −38.9545 | − | 22.4904i | −1.50047 | − | 0.866297i | ||||
\(675\) | −17.2321 | + | 13.5263i | −0.663262 | + | 0.520627i | ||||
\(676\) | −4.33013 | − | 7.50000i | −0.166543 | − | 0.288462i | ||||
\(677\) | −1.85641 | − | 6.92820i | −0.0713475 | − | 0.266272i | 0.921033 | − | 0.389485i | \(-0.127347\pi\) |
−0.992380 | + | 0.123213i | \(0.960680\pi\) | |||||||
\(678\) | −15.9282 | − | 15.9282i | −0.611719 | − | 0.611719i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.535898 | + | 1.07180i | 0.0205508 | + | 0.0411015i | ||||
\(681\) | −0.0980762 | + | 0.169873i | −0.00375829 | + | 0.00650955i | ||||
\(682\) | −0.732051 | − | 0.196152i | −0.0280317 | − | 0.00751106i | ||||
\(683\) | −18.4282 | − | 4.93782i | −0.705136 | − | 0.188941i | −0.111606 | − | 0.993753i | \(-0.535599\pi\) |
−0.593530 | + | 0.804812i | \(0.702266\pi\) | |||||||
\(684\) | 1.73205 | − | 3.00000i | 0.0662266 | − | 0.114708i | ||||
\(685\) | −22.9808 | − | 7.66025i | −0.878050 | − | 0.292683i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.26795 | − | 3.26795i | −0.124680 | − | 0.124680i | ||||
\(688\) | −9.52628 | − | 35.5526i | −0.363186 | − | 1.35543i | ||||
\(689\) | −10.0000 | − | 17.3205i | −0.380970 | − | 0.659859i | ||||
\(690\) | −12.0622 | − | 58.9449i | −0.459199 | − | 2.24399i | ||||
\(691\) | 24.9737 | + | 14.4186i | 0.950045 | + | 0.548509i | 0.893095 | − | 0.449868i | \(-0.148529\pi\) |
0.0569502 | + | 0.998377i | \(0.481862\pi\) | |||||||
\(692\) | −28.7321 | + | 28.7321i | −1.09223 | + | 1.09223i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 15.5885i | − | 0.591730i | ||||||
\(695\) | 1.56218 | − | 26.0263i | 0.0592568 | − | 0.987233i | ||||
\(696\) | −2.59808 | + | 1.50000i | −0.0984798 | + | 0.0568574i | ||||
\(697\) | 0.124356 | − | 0.464102i | 0.00471031 | − | 0.0175791i | ||||
\(698\) | −18.1603 | + | 4.86603i | −0.687376 | + | 0.184182i | ||||
\(699\) | −3.46410 | −0.131024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7321 | −0.896347 | −0.448174 | − | 0.893947i | \(-0.647925\pi\) | ||||
−0.448174 | + | 0.893947i | \(0.647925\pi\) | |||||||
\(702\) | 23.1244 | − | 6.19615i | 0.872773 | − | 0.233859i | ||||
\(703\) | −3.46410 | + | 12.9282i | −0.130651 | + | 0.487596i | ||||
\(704\) | 3.63397 | − | 2.09808i | 0.136961 | − | 0.0790742i | ||||
\(705\) | −0.169873 | + | 2.83013i | −0.00639779 | + | 0.106589i | ||||
\(706\) | − | 10.7321i | − | 0.403906i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.19615 | − | 5.19615i | 0.195283 | − | 0.195283i | ||||
\(709\) | 6.99038 | + | 4.03590i | 0.262529 | + | 0.151571i | 0.625488 | − | 0.780234i | \(-0.284900\pi\) |
−0.362959 | + | 0.931805i | \(0.618233\pi\) | |||||||
\(710\) | 4.09808 | + | 20.0263i | 0.153798 | + | 0.751573i | ||||
\(711\) | −2.46410 | − | 4.26795i | −0.0924110 | − | 0.160061i | ||||
\(712\) | −2.23205 | − | 8.33013i | −0.0836496 | − | 0.312185i | ||||
\(713\) | 2.73205 | + | 2.73205i | 0.102316 | + | 0.102316i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.39230 | + | 1.46410i | 0.164263 | + | 0.0547543i | ||||
\(716\) | −17.1962 | + | 29.7846i | −0.642650 | + | 1.11310i | ||||
\(717\) | −34.3205 | − | 9.19615i | −1.28172 | − | 0.343437i | ||||
\(718\) | 26.5885 | + | 7.12436i | 0.992272 | + | 0.265879i | ||||
\(719\) | 3.70577 | − | 6.41858i | 0.138202 | − | 0.239373i | −0.788614 | − | 0.614888i | \(-0.789201\pi\) |
0.926816 | + | 0.375516i | \(0.122534\pi\) | |||||||
\(720\) | −3.26795 | − | 6.53590i | −0.121789 | − | 0.243579i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.7583 | − | 15.7583i | −0.586464 | − | 0.586464i | ||||
\(723\) | 8.39230 | + | 31.3205i | 0.312113 | + | 1.16482i | ||||
\(724\) | 7.96410 | + | 13.7942i | 0.295984 | + | 0.512658i | ||||
\(725\) | −1.79423 | + | 14.8923i | −0.0666360 | + | 0.553086i | ||||
\(726\) | 33.8205 | + | 19.5263i | 1.25520 | + | 0.724688i | ||||
\(727\) | −4.90192 | + | 4.90192i | −0.181802 | + | 0.181802i | −0.792141 | − | 0.610338i | \(-0.791033\pi\) |
0.610338 | + | 0.792141i | \(0.291033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 17.5885i | − | 0.651424i | ||||||
\(730\) | −15.4641 | − | 0.928203i | −0.572352 | − | 0.0343543i | ||||
\(731\) | 7.39230 | − | 4.26795i | 0.273414 | − | 0.157856i | ||||
\(732\) | 7.33013 | − | 27.3564i | 0.270929 | − | 1.01112i | ||||
\(733\) | 9.83013 | − | 2.63397i | 0.363084 | − | 0.0972881i | −0.0726647 | − | 0.997356i | \(-0.523150\pi\) |
0.435749 | + | 0.900068i | \(0.356484\pi\) | |||||||
\(734\) | 3.73205 | 0.137753 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −54.7128 | −2.01674 | ||||||||
\(737\) | 0.830127 | − | 0.222432i | 0.0305781 | − | 0.00819338i | ||||
\(738\) | −0.169873 | + | 0.633975i | −0.00625311 | + | 0.0233369i | ||||
\(739\) | 7.43782 | − | 4.29423i | 0.273605 | − | 0.157966i | −0.356920 | − | 0.934135i | \(-0.616173\pi\) |
0.630525 | + | 0.776169i | \(0.282840\pi\) | |||||||
\(740\) | −12.5885 | − | 14.1962i | −0.462761 | − | 0.521861i | ||||
\(741\) | − | 14.9282i | − | 0.548401i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.8301 | + | 14.8301i | −0.544065 | + | 0.544065i | −0.924718 | − | 0.380653i | \(-0.875699\pi\) |
0.380653 | + | 0.924718i | \(0.375699\pi\) | |||||||
\(744\) | 0.464102 | + | 0.267949i | 0.0170148 | + | 0.00982349i | ||||
\(745\) | 13.7942 | − | 20.8923i | 0.505381 | − | 0.765435i | ||||
\(746\) | 15.9282 | + | 27.5885i | 0.583173 | + | 1.01009i | ||||
\(747\) | −0.830127 | − | 3.09808i | −0.0303728 | − | 0.113353i | ||||
\(748\) | 0.928203 | + | 0.928203i | 0.0339385 | + | 0.0339385i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −41.0526 | − | 7.46410i | −1.49903 | − | 0.272550i | ||||
\(751\) | −7.19615 | + | 12.4641i | −0.262591 | + | 0.454822i | −0.966930 | − | 0.255043i | \(-0.917910\pi\) |
0.704338 | + | 0.709864i | \(0.251244\pi\) | |||||||
\(752\) | 2.83013 | + | 0.758330i | 0.103204 | + | 0.0276535i | ||||
\(753\) | −10.9282 | − | 2.92820i | −0.398246 | − | 0.106710i | ||||
\(754\) | 8.19615 | − | 14.1962i | 0.298486 | − | 0.516993i | ||||
\(755\) | 27.7128 | − | 13.8564i | 1.00857 | − | 0.504286i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.26795 | + | 9.26795i | 0.336849 | + | 0.336849i | 0.855180 | − | 0.518331i | \(-0.173446\pi\) |
−0.518331 | + | 0.855180i | \(0.673446\pi\) | |||||||
\(758\) | −9.83013 | − | 36.6865i | −0.357046 | − | 1.33251i | ||||
\(759\) | 5.09808 | + | 8.83013i | 0.185048 | + | 0.320513i | ||||
\(760\) | 3.09808 | − | 0.633975i | 0.112379 | − | 0.0229967i | ||||
\(761\) | −11.0718 | − | 6.39230i | −0.401352 | − | 0.231721i | 0.285715 | − | 0.958315i | \(-0.407769\pi\) |
−0.687067 | + | 0.726594i | \(0.741102\pi\) | |||||||
\(762\) | 24.1244 | − | 24.1244i | 0.873933 | − | 0.873933i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 28.9808i | 1.04849i | ||||||||
\(765\) | 1.26795 | − | 1.12436i | 0.0458428 | − | 0.0406512i | ||||
\(766\) | −48.8205 | + | 28.1865i | −1.76396 | + | 1.01842i | ||||
\(767\) | 1.60770 | − | 6.00000i | 0.0580505 | − | 0.216647i | ||||
\(768\) | −36.1865 | + | 9.69615i | −1.30577 | + | 0.349880i | ||||
\(769\) | −47.1769 | −1.70124 | −0.850622 | − | 0.525778i | \(-0.823774\pi\) | ||||
−0.850622 | + | 0.525778i | \(0.823774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.46410 | −0.196785 | ||||||||
\(772\) | −5.36603 | + | 1.43782i | −0.193127 | + | 0.0517484i | ||||
\(773\) | −4.80385 | + | 17.9282i | −0.172782 | + | 0.644833i | 0.824136 | + | 0.566391i | \(0.191661\pi\) |
−0.996919 | + | 0.0784412i | \(0.975006\pi\) | |||||||
\(774\) | −10.0981 | + | 5.83013i | −0.362968 | + | 0.209560i | ||||
\(775\) | 2.46410 | − | 1.05256i | 0.0885131 | − | 0.0378090i | ||||
\(776\) | − | 5.80385i | − | 0.208346i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.1962 | + | 12.1962i | −0.437253 | + | 0.437253i | ||||
\(779\) | −1.09808 | − | 0.633975i | −0.0393427 | − | 0.0227145i | ||||
\(780\) | 17.6603 | + | 11.6603i | 0.632339 | + | 0.417504i | ||||
\(781\) | −1.73205 | − | 3.00000i | −0.0619777 | − | 0.107348i | ||||
\(782\) | −3.73205 | − | 13.9282i | −0.133458 | − | 0.498072i | ||||
\(783\) | −9.29423 | − | 9.29423i | −0.332149 | − | 0.332149i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.3923 | − | 52.1769i | 0.620758 | − | 1.86227i | ||||
\(786\) | 15.9282 | − | 27.5885i | 0.568140 | − | 0.984048i | ||||
\(787\) | 19.3564 | + | 5.18653i | 0.689981 | + | 0.184880i | 0.586739 | − | 0.809776i | \(-0.300412\pi\) |
0.103243 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(788\) | 33.4186 | + | 8.95448i | 1.19049 | + | 0.318990i | ||||
\(789\) | −8.06218 | + | 13.9641i | −0.287021 | + | 0.497135i | ||||
\(790\) | −9.19615 | + | 27.5885i | −0.327184 | + | 0.981553i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.196152 | + | 0.196152i | 0.00696997 | + | 0.00696997i | ||||
\(793\) | −6.19615 | − | 23.1244i | −0.220032 | − | 0.821170i | ||||
\(794\) | −20.0263 | − | 34.6865i | −0.710706 | − | 1.23098i | ||||
\(795\) | −25.4904 | − | 16.8301i | −0.904051 | − | 0.596903i | ||||
\(796\) | −37.3923 | − | 21.5885i | −1.32534 | − | 0.765183i | ||||
\(797\) | 29.4641 | − | 29.4641i | 1.04367 | − | 1.04367i | 0.0446702 | − | 0.999002i | \(-0.485776\pi\) |
0.999002 | − | 0.0446702i | \(-0.0142237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.679492i | 0.0240387i | ||||||||
\(800\) | −14.1340 | + | 35.2128i | −0.499711 | + | 1.24496i | ||||
\(801\) | −10.5622 | + | 6.09808i | −0.373196 | + | 0.215465i | ||||
\(802\) | 5.50000 | − | 20.5263i | 0.194212 | − | 0.724808i | ||||
\(803\) | 2.53590 | − | 0.679492i | 0.0894899 | − | 0.0239787i | ||||
\(804\) | 3.92820 | 0.138537 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.92820 | −0.103142 | ||||||||
\(807\) | −9.06218 | + | 2.42820i | −0.319004 | + | 0.0854768i | ||||
\(808\) | 1.57180 | − | 5.86603i | 0.0552956 | − | 0.206366i | ||||
\(809\) | −21.9904 | + | 12.6962i | −0.773141 | + | 0.446373i | −0.833994 | − | 0.551774i | \(-0.813951\pi\) |
0.0608532 | + | 0.998147i | \(0.480618\pi\) | |||||||
\(810\) | 34.4545 | − | 30.5526i | 1.21061 | − | 1.07351i | ||||
\(811\) | 29.0718i | 1.02085i | 0.859923 | + | 0.510424i | \(0.170512\pi\) | ||||
−0.859923 | + | 0.510424i | \(0.829488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.7846 | − | 33.7846i | 1.18488 | − | 1.18488i | ||||
\(814\) | 6.00000 | + | 3.46410i | 0.210300 | + | 0.121417i | ||||
\(815\) | 12.1699 | − | 2.49038i | 0.426292 | − | 0.0872342i | ||||
\(816\) | −4.46410 | − | 7.73205i | −0.156275 | − | 0.270676i | ||||
\(817\) | −5.83013 | − | 21.7583i | −0.203970 | − | 0.761228i | ||||
\(818\) | −9.36603 | − | 9.36603i | −0.327475 | − | 0.327475i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.60770 | − | 0.803848i | 0.0561432 | − | 0.0280716i | ||||
\(821\) | 7.33975 | − | 12.7128i | 0.256159 | − | 0.443680i | −0.709051 | − | 0.705157i | \(-0.750876\pi\) |
0.965210 | + | 0.261477i | \(0.0842096\pi\) | |||||||
\(822\) | 39.0526 | + | 10.4641i | 1.36211 | + | 0.364977i | ||||
\(823\) | 24.6962 | + | 6.61731i | 0.860854 | + | 0.230665i | 0.662129 | − | 0.749390i | \(-0.269653\pi\) |
0.198725 | + | 0.980055i | \(0.436320\pi\) | |||||||
\(824\) | 0.598076 | − | 1.03590i | 0.0208350 | − | 0.0360872i | ||||
\(825\) | 7.00000 | − | 1.00000i | 0.243709 | − | 0.0348155i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.77757 | − | 3.77757i | −0.131359 | − | 0.131359i | 0.638370 | − | 0.769729i | \(-0.279609\pi\) |
−0.769729 | + | 0.638370i | \(0.779609\pi\) | |||||||
\(828\) | 2.36603 | + | 8.83013i | 0.0822251 | + | 0.306868i | ||||
\(829\) | −10.7321 | − | 18.5885i | −0.372740 | − | 0.645604i | 0.617246 | − | 0.786770i | \(-0.288248\pi\) |
−0.989986 | + | 0.141166i | \(0.954915\pi\) | |||||||
\(830\) | −10.4282 | + | 15.7942i | −0.361968 | + | 0.548226i | ||||
\(831\) | 33.5885 | + | 19.3923i | 1.16517 | + | 0.672712i | ||||
\(832\) | 11.4641 | − | 11.4641i | 0.397446 | − | 0.397446i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 43.5167i | 1.50686i | ||||||||
\(835\) | 22.5718 | + | 25.4545i | 0.781129 | + | 0.880889i | ||||
\(836\) | 3.00000 | − | 1.73205i | 0.103757 | − | 0.0599042i | ||||
\(837\) | −0.607695 | + | 2.26795i | −0.0210050 | + | 0.0783918i | ||||
\(838\) | 7.19615 | − | 1.92820i | 0.248587 | − | 0.0666087i | ||||
\(839\) | 31.1244 | 1.07453 | 0.537266 | − | 0.843413i | \(-0.319457\pi\) | ||||
0.537266 | + | 0.843413i | \(0.319457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 64.6769 | − | 17.3301i | 2.22891 | − | 0.597236i | ||||
\(843\) | 6.46410 | − | 24.1244i | 0.222635 | − | 0.830887i | ||||
\(844\) | 15.2942 | − | 8.83013i | 0.526449 | − | 0.303946i | ||||
\(845\) | −11.1603 | − | 0.669873i | −0.383924 | − | 0.0230443i | ||||
\(846\) | − | 0.928203i | − | 0.0319123i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −22.3205 | + | 22.3205i | −0.766489 | + | 0.766489i | ||||
\(849\) | −45.8827 | − | 26.4904i | −1.57469 | − | 0.909148i | ||||
\(850\) | −9.92820 | − | 1.19615i | −0.340535 | − | 0.0410277i | ||||
\(851\) | −17.6603 | − | 30.5885i | −0.605386 | − | 1.04856i | ||||
\(852\) | −4.09808 | − | 15.2942i | −0.140398 | − | 0.523972i | ||||
\(853\) | 6.12436 | + | 6.12436i | 0.209694 | + | 0.209694i | 0.804137 | − | 0.594443i | \(-0.202628\pi\) |
−0.594443 | + | 0.804137i | \(0.702628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.00000 | − | 4.00000i | −0.0683986 | − | 0.136797i | ||||
\(856\) | −2.30385 | + | 3.99038i | −0.0787439 | + | 0.136388i | ||||
\(857\) | 22.0263 | + | 5.90192i | 0.752403 | + | 0.201606i | 0.614584 | − | 0.788851i | \(-0.289324\pi\) |
0.137820 | + | 0.990457i | \(0.455991\pi\) | |||||||
\(858\) | −7.46410 | − | 2.00000i | −0.254820 | − | 0.0682789i | ||||
\(859\) | −10.5359 | + | 18.2487i | −0.359480 | + | 0.622638i | −0.987874 | − | 0.155257i | \(-0.950379\pi\) |
0.628394 | + | 0.777895i | \(0.283713\pi\) | |||||||
\(860\) | 30.2942 | + | 10.0981i | 1.03302 | + | 0.344342i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.73205 | − | 5.73205i | −0.195234 | − | 0.195234i | ||||
\(863\) | 8.94486 | + | 33.3827i | 0.304487 | + | 1.13636i | 0.933386 | + | 0.358873i | \(0.116839\pi\) |
−0.628900 | + | 0.777487i | \(0.716494\pi\) | |||||||
\(864\) | −16.6244 | − | 28.7942i | −0.565572 | − | 0.979600i | ||||
\(865\) | 10.5167 | + | 51.3923i | 0.357577 | + | 1.74739i | ||||
\(866\) | 57.8827 | + | 33.4186i | 1.96693 | + | 1.13561i | ||||
\(867\) | −21.7583 | + | 21.7583i | −0.738952 | + | 0.738952i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.92820i | − | 0.167178i | ||||||
\(870\) | 1.50000 | − | 24.9904i | 0.0508548 | − | 0.847253i | ||||
\(871\) | 2.87564 | − | 1.66025i | 0.0974375 | − | 0.0562556i | ||||
\(872\) | 1.89230 | − | 7.06218i | 0.0640815 | − | 0.239156i | ||||
\(873\) | −7.92820 | + | 2.12436i | −0.268329 | + | 0.0718985i | ||||
\(874\) | −38.0526 | −1.28715 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | −15.4904 | + | 4.15064i | −0.523073 | + | 0.140157i | −0.510688 | − | 0.859766i | \(-0.670609\pi\) |
−0.0123853 | + | 0.999923i | \(0.503942\pi\) | |||||||
\(878\) | 15.6603 | − | 58.4449i | 0.528508 | − | 1.97242i | ||||
\(879\) | 43.5167 | − | 25.1244i | 1.46778 | − | 0.847423i | ||||
\(880\) | 0.437822 | − | 7.29423i | 0.0147590 | − | 0.245888i | ||||
\(881\) | 52.8564i | 1.78078i | 0.455201 | + | 0.890389i | \(0.349567\pi\) | ||||
−0.455201 | + | 0.890389i | \(0.650433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.9282 | − | 21.9282i | 0.737943 | − | 0.737943i | −0.234237 | − | 0.972180i | \(-0.575259\pi\) |
0.972180 | + | 0.234237i | \(0.0752591\pi\) | |||||||
\(884\) | 4.39230 | + | 2.53590i | 0.147729 | + | 0.0852915i | ||||
\(885\) | −1.90192 | − | 9.29423i | −0.0639325 | − | 0.312422i | ||||
\(886\) | −3.50000 | − | 6.06218i | −0.117585 | − | 0.203663i | ||||
\(887\) | 9.89230 | + | 36.9186i | 0.332151 | + | 1.23960i | 0.906925 | + | 0.421292i | \(0.138423\pi\) |
−0.574774 | + | 0.818312i | \(0.694910\pi\) | |||||||
\(888\) | −3.46410 | − | 3.46410i | −0.116248 | − | 0.116248i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 68.2750 | + | 22.7583i | 2.28858 | + | 0.762861i | ||||
\(891\) | −3.90192 | + | 6.75833i | −0.130719 | + | 0.226413i | ||||
\(892\) | −14.4904 | − | 3.88269i | −0.485174 | − | 0.130002i | ||||
\(893\) | 1.73205 | + | 0.464102i | 0.0579609 | + | 0.0155306i | ||||
\(894\) | −20.8923 | + | 36.1865i | −0.698743 | + | 1.21026i | ||||
\(895\) | 19.8564 | + | 39.7128i | 0.663726 | + | 1.32745i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.8564 | + | 27.8564i | 0.930098 | + | 0.930098i | ||||
\(898\) | −2.52628 | − | 9.42820i | −0.0843030 | − | 0.314623i | ||||
\(899\) | 0.803848 | + | 1.39230i | 0.0268098 | + | 0.0464360i | ||||
\(900\) | 6.29423 | + | 0.758330i | 0.209808 | + | 0.0252777i | ||||
\(901\) | −6.33975 | − | 3.66025i | −0.211208 | − | 0.121941i | ||||
\(902\) | −0.464102 | + | 0.464102i | −0.0154529 | + | 0.0154529i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.12436i | 0.103915i | ||||||||
\(905\) | 20.5263 | + | 1.23205i | 0.682317 | + | 0.0409548i | ||||
\(906\) | −44.7846 | + | 25.8564i | −1.48787 | + | 0.859022i | ||||
\(907\) | −0.454483 | + | 1.69615i | −0.0150908 | + | 0.0563198i | −0.973061 | − | 0.230549i | \(-0.925948\pi\) |
0.957970 | + | 0.286869i | \(0.0926144\pi\) | |||||||
\(908\) | −0.169873 | + | 0.0455173i | −0.00563743 | + | 0.00151055i | ||||
\(909\) | −8.58846 | −0.284861 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5167 | 1.24298 | 0.621491 | − | 0.783421i | \(-0.286527\pi\) | ||||
0.621491 | + | 0.783421i | \(0.286527\pi\) | |||||||
\(912\) | −22.7583 | + | 6.09808i | −0.753604 | + | 0.201927i | ||||
\(913\) | 0.830127 | − | 3.09808i | 0.0274732 | − | 0.102531i | ||||
\(914\) | −53.4449 | + | 30.8564i | −1.76780 | + | 1.02064i | ||||
\(915\) | −24.2583 | − | 27.3564i | −0.801956 | − | 0.904375i | ||||
\(916\) | − | 4.14359i | − | 0.136908i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.19615 | − | 6.19615i | 0.204504 | − | 0.204504i | ||||
\(919\) | −39.6673 | − | 22.9019i | −1.30850 | − | 0.755465i | −0.326657 | − | 0.945143i | \(-0.605922\pi\) |
−0.981846 | + | 0.189678i | \(0.939256\pi\) | |||||||
\(920\) | −4.59808 | + | 6.96410i | −0.151594 | + | 0.229600i | ||||
\(921\) | 12.6962 | + | 21.9904i | 0.418352 | + | 0.724608i | ||||
\(922\) | 13.1962 | + | 49.2487i | 0.434592 | + | 1.62192i | ||||
\(923\) | −9.46410 | − | 9.46410i | −0.311515 | − | 0.311515i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.2487 | + | 3.46410i | −0.797293 | + | 0.113899i | ||||
\(926\) | −24.2583 | + | 42.0167i | −0.797178 | + | 1.38075i | ||||
\(927\) | −1.63397 | − | 0.437822i | −0.0536668 | − | 0.0143800i | ||||
\(928\) | −21.9904 | − | 5.89230i | −0.721870 | − | 0.193424i | ||||
\(929\) | −0.839746 | + | 1.45448i | −0.0275512 | + | 0.0477200i | −0.879472 | − | 0.475950i | \(-0.842104\pi\) |
0.851921 | + | 0.523670i | \(0.175438\pi\) | |||||||
\(930\) | −4.00000 | + | 2.00000i | −0.131165 | + | 0.0655826i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.19615 | − | 2.19615i | −0.0719374 | − | 0.0719374i | ||||
\(933\) | 9.36603 | + | 34.9545i | 0.306630 | + | 1.14436i | ||||
\(934\) | 31.3564 | + | 54.3109i | 1.02601 | + | 1.77711i | ||||
\(935\) | 1.66025 | − | 0.339746i | 0.0542961 | − | 0.0111109i | ||||
\(936\) | 0.928203 | + | 0.535898i | 0.0303393 | + | 0.0175164i | ||||
\(937\) | 30.9282 | − | 30.9282i | 1.01038 | − | 1.01038i | 0.0104348 | − | 0.999946i | \(-0.496678\pi\) |
0.999946 | − | 0.0104348i | \(-0.00332156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.7846i | 1.26569i | ||||||||
\(940\) | −1.90192 | + | 1.68653i | −0.0620339 | + | 0.0550087i | ||||
\(941\) | −24.8038 | + | 14.3205i | −0.808582 | + | 0.466835i | −0.846463 | − | 0.532447i | \(-0.821273\pi\) |
0.0378810 | + | 0.999282i | \(0.487939\pi\) | |||||||
\(942\) | −23.7583 | + | 88.6673i | −0.774088 | + | 2.88894i | ||||
\(943\) | 3.23205 | − | 0.866025i | 0.105250 | − | 0.0282017i | ||||
\(944\) | −9.80385 | −0.319088 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.6603 | −0.379108 | ||||||||
\(947\) | 43.6506 | − | 11.6962i | 1.41846 | − | 0.380074i | 0.533520 | − | 0.845788i | \(-0.320869\pi\) |
0.884935 | + | 0.465714i | \(0.154202\pi\) | |||||||
\(948\) | 5.83013 | − | 21.7583i | 0.189354 | − | 0.706678i | ||||
\(949\) | 8.78461 | − | 5.07180i | 0.285160 | − | 0.164637i | ||||
\(950\) | −9.83013 | + | 24.4904i | −0.318931 | + | 0.794573i | ||||
\(951\) | − | 8.92820i | − | 0.289517i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.1436 | + | 10.1436i | −0.328583 | + | 0.328583i | −0.852048 | − | 0.523464i | \(-0.824639\pi\) |
0.523464 | + | 0.852048i | \(0.324639\pi\) | |||||||
\(954\) | 8.66025 | + | 5.00000i | 0.280386 | + | 0.161881i | ||||
\(955\) | 31.2224 | + | 20.6147i | 1.01033 | + | 0.667077i | ||||
\(956\) | −15.9282 | − | 27.5885i | −0.515155 | − | 0.892274i | ||||
\(957\) | 1.09808 | + | 4.09808i | 0.0354958 | + | 0.132472i | ||||
\(958\) | −36.7846 | − | 36.7846i | −1.18846 | − | 1.18846i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7.83013 | − | 23.4904i | 0.252716 | − | 0.758149i | ||||
\(961\) | −15.3564 | + | 26.5981i | −0.495368 | + | 0.858002i | ||||
\(962\) | 25.8564 | + | 6.92820i | 0.833644 | + | 0.223374i | ||||
\(963\) | 6.29423 | + | 1.68653i | 0.202829 | + | 0.0543478i | ||||
\(964\) | −14.5359 | + | 25.1769i | −0.468170 | + | 0.810894i | ||||
\(965\) | −2.26795 | + | 6.80385i | −0.0730079 | + | 0.219024i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.43782 | − | 1.43782i | −0.0462372 | − | 0.0462372i | 0.683610 | − | 0.729847i | \(-0.260409\pi\) |
−0.729847 | + | 0.683610i | \(0.760409\pi\) | |||||||
\(968\) | −1.40192 | − | 5.23205i | −0.0450595 | − | 0.168164i | ||||
\(969\) | −2.73205 | − | 4.73205i | −0.0877661 | − | 0.152015i | ||||
\(970\) | 40.4186 | + | 26.6865i | 1.29776 | + | 0.856853i | ||||
\(971\) | −42.9282 | − | 24.7846i | −1.37763 | − | 0.795376i | −0.385758 | − | 0.922600i | \(-0.626060\pi\) |
−0.991874 | + | 0.127224i | \(0.959393\pi\) | |||||||
\(972\) | −9.12436 | + | 9.12436i | −0.292664 | + | 0.292664i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.5885i | 0.531528i | ||||||||
\(975\) | 25.1244 | − | 10.7321i | 0.804623 | − | 0.343701i | ||||
\(976\) | −32.7224 | + | 18.8923i | −1.04742 | + | 0.604728i | ||||
\(977\) | −11.5622 | + | 43.1506i | −0.369907 | + | 1.38051i | 0.490739 | + | 0.871307i | \(0.336727\pi\) |
−0.860646 | + | 0.509204i | \(0.829940\pi\) | |||||||
\(978\) | −20.0263 | + | 5.36603i | −0.640370 | + | 0.171587i | ||||
\(979\) | −12.1962 | −0.389791 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3397 | −0.330123 | ||||||||
\(982\) | 33.0526 | − | 8.85641i | 1.05475 | − | 0.282619i | ||||
\(983\) | −3.88526 | + | 14.5000i | −0.123921 | + | 0.462478i | −0.999799 | − | 0.0200540i | \(-0.993616\pi\) |
0.875878 | + | 0.482532i | \(0.160283\pi\) | |||||||
\(984\) | 0.401924 | − | 0.232051i | 0.0128129 | − | 0.00739751i | ||||
\(985\) | 33.4186 | − | 29.6340i | 1.06480 | − | 0.944217i | ||||
\(986\) | − | 6.00000i | − | 0.191079i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.46410 | − | 9.46410i | 0.301093 | − | 0.301093i | ||||
\(989\) | 51.4808 | + | 29.7224i | 1.63699 | + | 0.945118i | ||||
\(990\) | −2.26795 | + | 0.464102i | −0.0720802 | + | 0.0147501i | ||||
\(991\) | 11.8564 | + | 20.5359i | 0.376631 | + | 0.652344i | 0.990570 | − | 0.137009i | \(-0.0437491\pi\) |
−0.613939 | + | 0.789354i | \(0.710416\pi\) | |||||||
\(992\) | 1.05256 | + | 3.92820i | 0.0334188 | + | 0.124721i | ||||
\(993\) | 35.3205 | + | 35.3205i | 1.12086 | + | 1.12086i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.8564 | + | 24.9282i | −1.58055 | + | 0.790277i | ||||
\(996\) | 7.33013 | − | 12.6962i | 0.232264 | − | 0.402293i | ||||
\(997\) | −25.6865 | − | 6.88269i | −0.813501 | − | 0.217977i | −0.171998 | − | 0.985097i | \(-0.555022\pi\) |
−0.641503 | + | 0.767121i | \(0.721689\pi\) | |||||||
\(998\) | −62.5429 | − | 16.7583i | −1.97976 | − | 0.530476i | ||||
\(999\) | 10.7321 | − | 18.5885i | 0.339547 | − | 0.588113i |
(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 | 245.2.l.a.117.1 | 4 | ||
5.3 | odd | 4 | 245.2.l.b.68.1 | 4 | |||
7.2 | even | 3 | 245.2.f.b.97.2 | 4 | |||
7.3 | odd | 6 | 245.2.l.b.227.1 | 4 | |||
7.4 | even | 3 | 35.2.k.b.17.1 | yes | 4 | ||
7.5 | odd | 6 | 245.2.f.a.97.2 | 4 | |||
7.6 | odd | 2 | 35.2.k.a.12.1 | yes | 4 | ||
21.11 | odd | 6 | 315.2.bz.a.262.1 | 4 | |||
21.20 | even | 2 | 315.2.bz.b.82.1 | 4 | |||
28.11 | odd | 6 | 560.2.ci.b.17.1 | 4 | |||
28.27 | even | 2 | 560.2.ci.a.257.1 | 4 | |||
35.3 | even | 12 | inner | 245.2.l.a.178.1 | 4 | ||
35.4 | even | 6 | 175.2.o.a.157.1 | 4 | |||
35.13 | even | 4 | 35.2.k.b.33.1 | yes | 4 | ||
35.18 | odd | 12 | 35.2.k.a.3.1 | ✓ | 4 | ||
35.23 | odd | 12 | 245.2.f.a.48.2 | 4 | |||
35.27 | even | 4 | 175.2.o.a.68.1 | 4 | |||
35.32 | odd | 12 | 175.2.o.b.143.1 | 4 | |||
35.33 | even | 12 | 245.2.f.b.48.2 | 4 | |||
35.34 | odd | 2 | 175.2.o.b.82.1 | 4 | |||
105.53 | even | 12 | 315.2.bz.b.73.1 | 4 | |||
105.83 | odd | 4 | 315.2.bz.a.208.1 | 4 | |||
140.83 | odd | 4 | 560.2.ci.b.33.1 | 4 | |||
140.123 | even | 12 | 560.2.ci.a.353.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.k.a.3.1 | ✓ | 4 | 35.18 | odd | 12 | ||
35.2.k.a.12.1 | yes | 4 | 7.6 | odd | 2 | ||
35.2.k.b.17.1 | yes | 4 | 7.4 | even | 3 | ||
35.2.k.b.33.1 | yes | 4 | 35.13 | even | 4 | ||
175.2.o.a.68.1 | 4 | 35.27 | even | 4 | |||
175.2.o.a.157.1 | 4 | 35.4 | even | 6 | |||
175.2.o.b.82.1 | 4 | 35.34 | odd | 2 | |||
175.2.o.b.143.1 | 4 | 35.32 | odd | 12 | |||
245.2.f.a.48.2 | 4 | 35.23 | odd | 12 | |||
245.2.f.a.97.2 | 4 | 7.5 | odd | 6 | |||
245.2.f.b.48.2 | 4 | 35.33 | even | 12 | |||
245.2.f.b.97.2 | 4 | 7.2 | even | 3 | |||
245.2.l.a.117.1 | 4 | 1.1 | even | 1 | trivial | ||
245.2.l.a.178.1 | 4 | 35.3 | even | 12 | inner | ||
245.2.l.b.68.1 | 4 | 5.3 | odd | 4 | |||
245.2.l.b.227.1 | 4 | 7.3 | odd | 6 | |||
315.2.bz.a.208.1 | 4 | 105.83 | odd | 4 | |||
315.2.bz.a.262.1 | 4 | 21.11 | odd | 6 | |||
315.2.bz.b.73.1 | 4 | 105.53 | even | 12 | |||
315.2.bz.b.82.1 | 4 | 21.20 | even | 2 | |||
560.2.ci.a.257.1 | 4 | 28.27 | even | 2 | |||
560.2.ci.a.353.1 | 4 | 140.123 | even | 12 | |||
560.2.ci.b.17.1 | 4 | 28.11 | odd | 6 | |||
560.2.ci.b.33.1 | 4 | 140.83 | odd | 4 |