Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.01834519640\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.163 |
Dual form | 378.2.g.d.109.1 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 1.73205i | 0.316228 | + | 0.547723i | ||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.00000 | 1.06600 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 3.00000 | − | 5.19615i | 0.588348 | − | 1.01905i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | − | 1.73205i | 0.377964 | − | 0.327327i | ||||
\(29\) | −7.00000 | −1.29987 | −0.649934 | − | 0.759991i | \(-0.725203\pi\) | ||||
−0.649934 | + | 0.759991i | \(0.725203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −5.00000 | − | 1.73205i | −0.845154 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | −2.00000 | − | 3.46410i | −0.324443 | − | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | − | 1.73205i | 0.158114 | − | 0.273861i | ||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 2.50000 | − | 4.33013i | 0.376889 | − | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | − | 5.19615i | −0.416025 | − | 0.720577i | ||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0000 | −1.34840 | ||||||||
\(56\) | −0.500000 | − | 2.59808i | −0.0668153 | − | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.50000 | + | 6.06218i | −0.459573 | + | 0.796003i | ||||
\(59\) | 3.50000 | + | 6.06218i | 0.455661 | + | 0.789228i | 0.998726 | − | 0.0504625i | \(-0.0160695\pi\) |
−0.543065 | + | 0.839691i | \(0.682736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | −3.00000 | −0.381000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.00000 | + | 10.3923i | −0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | − | 8.66025i | −0.610847 | − | 1.05802i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.380251 | − | 0.924883i | \(-0.375838\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.00000 | + | 3.46410i | −0.478091 | + | 0.414039i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.50000 | − | 11.2583i | −0.760767 | − | 1.31769i | −0.942455 | − | 0.334332i | \(-0.891489\pi\) |
0.181688 | − | 0.983356i | \(-0.441844\pi\) | |||||||
\(74\) | 4.00000 | + | 6.92820i | 0.464991 | + | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | −10.0000 | + | 8.66025i | −1.13961 | + | 0.986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | − | 2.59808i | 0.168763 | − | 0.292306i | −0.769222 | − | 0.638982i | \(-0.779356\pi\) |
0.937985 | + | 0.346675i | \(0.112689\pi\) | |||||||
\(80\) | −1.00000 | − | 1.73205i | −0.111803 | − | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | 7.00000 | 0.768350 | 0.384175 | − | 0.923260i | \(-0.374486\pi\) | ||||
0.384175 | + | 0.923260i | \(0.374486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.50000 | − | 4.33013i | −0.266501 | − | 0.461593i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | + | 15.5885i | 0.314485 | + | 1.63411i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | − | 5.19615i | −0.309426 | − | 0.535942i | ||||
\(95\) | 4.00000 | + | 6.92820i | 0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | −0.507673 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | −1.00000 | + | 6.92820i | −0.101015 | + | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −2.50000 | − | 4.33013i | −0.248759 | − | 0.430864i | 0.714423 | − | 0.699715i | \(-0.246689\pi\) |
−0.963182 | + | 0.268851i | \(0.913356\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 6.00000 | − | 10.3923i | 0.580042 | − | 1.00466i | −0.415432 | − | 0.909624i | \(-0.636370\pi\) |
0.995474 | − | 0.0950377i | \(-0.0302972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | − | 13.8564i | −0.766261 | − | 1.32720i | −0.939577 | − | 0.342337i | \(-0.888782\pi\) |
0.173316 | − | 0.984866i | \(-0.444552\pi\) | |||||||
\(110\) | −5.00000 | + | 8.66025i | −0.476731 | + | 0.825723i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.50000 | − | 0.866025i | −0.236228 | − | 0.0818317i | ||||
\(113\) | −4.00000 | −0.376288 | −0.188144 | − | 0.982141i | \(-0.560247\pi\) | ||||
−0.188144 | + | 0.982141i | \(0.560247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | − | 6.92820i | −0.373002 | − | 0.646058i | ||||
\(116\) | 3.50000 | + | 6.06218i | 0.324967 | + | 0.562859i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | 8.00000 | − | 6.92820i | 0.733359 | − | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.50000 | + | 2.59808i | −0.134704 | + | 0.233314i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | + | 10.3923i | 0.526235 | + | 0.911465i | ||||
\(131\) | 6.50000 | − | 11.2583i | 0.567908 | − | 0.983645i | −0.428865 | − | 0.903369i | \(-0.641086\pi\) |
0.996773 | − | 0.0802763i | \(-0.0255803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0000 | + | 3.46410i | 0.867110 | + | 0.300376i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | −4.00000 | − | 6.92820i | −0.341743 | − | 0.591916i | 0.643013 | − | 0.765855i | \(-0.277684\pi\) |
−0.984757 | + | 0.173939i | \(0.944351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 1.00000 | + | 5.19615i | 0.0845154 | + | 0.439155i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | − | 3.46410i | 0.167836 | − | 0.290701i | ||||
\(143\) | 15.0000 | + | 25.9808i | 1.25436 | + | 2.17262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.00000 | − | 12.1244i | 0.581318 | − | 1.00687i | ||||
\(146\) | −13.0000 | −1.07589 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | + | 14.7224i | 0.691720 | + | 1.19809i | 0.971274 | + | 0.237964i | \(0.0764802\pi\) |
−0.279554 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(152\) | −2.00000 | + | 3.46410i | −0.162221 | + | 0.280976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.50000 | + | 12.9904i | 0.201456 | + | 1.04679i | ||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | −1.50000 | − | 2.59808i | −0.119334 | − | 0.206692i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | −10.0000 | − | 3.46410i | −0.788110 | − | 0.273009i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | + | 1.73205i | −0.0783260 | + | 0.135665i | −0.902528 | − | 0.430632i | \(-0.858291\pi\) |
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.50000 | − | 6.06218i | 0.271653 | − | 0.470516i | ||||
\(167\) | 14.0000 | 1.08335 | 0.541676 | − | 0.840587i | \(-0.317790\pi\) | ||||
0.541676 | + | 0.840587i | \(0.317790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 4.00000 | − | 6.92820i | 0.306786 | − | 0.531369i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | 0.500000 | − | 0.866025i | 0.0380143 | − | 0.0658427i | −0.846392 | − | 0.532560i | \(-0.821230\pi\) |
0.884407 | + | 0.466717i | \(0.154563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 1.73205i | −0.151186 | + | 0.130931i | ||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | −7.50000 | − | 12.9904i | −0.560576 | − | 0.970947i | −0.997446 | − | 0.0714220i | \(-0.977246\pi\) |
0.436870 | − | 0.899525i | \(-0.356087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 15.0000 | + | 5.19615i | 1.11187 | + | 0.385164i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | −8.00000 | − | 13.8564i | −0.588172 | − | 1.01874i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0000 | − | 17.3205i | 0.731272 | − | 1.26660i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.50000 | + | 16.4545i | 0.683825 | + | 1.18442i | 0.973805 | + | 0.227387i | \(0.0730182\pi\) |
−0.289980 | + | 0.957033i | \(0.593649\pi\) | |||||||
\(194\) | −2.50000 | + | 4.33013i | −0.179490 | + | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 25.0000 | 1.78118 | 0.890588 | − | 0.454811i | \(-0.150293\pi\) | ||||
0.890588 | + | 0.454811i | \(0.150293\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.50000 | + | 16.4545i | 0.673437 | + | 1.16643i | 0.976923 | + | 0.213591i | \(0.0685161\pi\) |
−0.303486 | + | 0.952836i | \(0.598151\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.00000 | −0.351799 | ||||||||
\(203\) | −3.50000 | − | 18.1865i | −0.245652 | − | 1.27644i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | + | 10.3923i | −0.419058 | + | 0.725830i | ||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | + | 5.19615i | −0.208013 | + | 0.360288i | ||||
\(209\) | 20.0000 | 1.38343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | −8.00000 | + | 13.8564i | −0.545595 | + | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | − | 5.19615i | 0.407307 | − | 0.352738i | ||||
\(218\) | −16.0000 | −1.08366 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.00000 | + | 8.66025i | 0.337100 | + | 0.583874i | ||||
\(221\) | −12.0000 | − | 20.7846i | −0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | −0.0334825 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334825 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.00000 | + | 3.46410i | −0.133038 | + | 0.230429i | ||||
\(227\) | −13.5000 | − | 23.3827i | −0.896026 | − | 1.55196i | −0.832529 | − | 0.553981i | \(-0.813108\pi\) |
−0.0634974 | − | 0.997982i | \(-0.520225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | + | 3.46410i | −0.132164 | + | 0.228914i | −0.924510 | − | 0.381157i | \(-0.875526\pi\) |
0.792347 | + | 0.610071i | \(0.208859\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.00000 | 0.459573 | ||||||||
\(233\) | −11.0000 | + | 19.0526i | −0.720634 | + | 1.24817i | 0.240112 | + | 0.970745i | \(0.422816\pi\) |
−0.960746 | + | 0.277429i | \(0.910518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | + | 10.3923i | 0.391397 | + | 0.677919i | ||||
\(236\) | 3.50000 | − | 6.06218i | 0.227831 | − | 0.394614i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.00000 | − | 10.3923i | −0.129641 | − | 0.673633i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 7.00000 | + | 12.1244i | 0.449977 | + | 0.779383i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | − | 13.8564i | 0.127775 | − | 0.885253i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | − | 20.7846i | 0.763542 | − | 1.32249i | ||||
\(248\) | 1.50000 | + | 2.59808i | 0.0952501 | + | 0.164978i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.00000 | + | 10.3923i | −0.379473 | + | 0.657267i | ||||
\(251\) | 21.0000 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.0000 | − | 6.92820i | −1.24274 | − | 0.430498i | ||||
\(260\) | 12.0000 | 0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.50000 | − | 11.2583i | −0.401571 | − | 0.695542i | ||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 8.00000 | − | 6.92820i | 0.490511 | − | 0.424795i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.00000 | + | 8.66025i | −0.305424 | + | 0.529009i | ||||
\(269\) | 15.5000 | + | 26.8468i | 0.945052 | + | 1.63688i | 0.755648 | + | 0.654978i | \(0.227322\pi\) |
0.189404 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.00000 | −0.483298 | ||||||||
\(275\) | −2.50000 | + | 4.33013i | −0.150756 | + | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | −4.00000 | + | 6.92820i | −0.239904 | + | 0.415526i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.00000 | + | 1.73205i | 0.298807 | + | 0.103510i | ||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | − | 13.8564i | −0.475551 | − | 0.823678i | 0.524057 | − | 0.851683i | \(-0.324418\pi\) |
−0.999608 | + | 0.0280052i | \(0.991084\pi\) | |||||||
\(284\) | −2.00000 | − | 3.46410i | −0.118678 | − | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 30.0000 | 1.77394 | ||||||||
\(287\) | 3.00000 | + | 15.5885i | 0.177084 | + | 0.920158i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | −7.00000 | − | 12.1244i | −0.411054 | − | 0.711967i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.50000 | + | 11.2583i | −0.380384 | + | 0.658844i | ||||
\(293\) | −27.0000 | −1.57736 | −0.788678 | − | 0.614806i | \(-0.789234\pi\) | ||||
−0.788678 | + | 0.614806i | \(0.789234\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0000 | −0.815112 | ||||||||
\(296\) | 4.00000 | − | 6.92820i | 0.232495 | − | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.50000 | − | 7.79423i | −0.260678 | − | 0.451508i | ||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 20.7846i | 0.230556 | + | 1.19800i | ||||
\(302\) | 17.0000 | 0.978240 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | + | 3.46410i | 0.114708 | + | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 12.5000 | + | 4.33013i | 0.712254 | + | 0.246732i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.00000 | − | 5.19615i | 0.170389 | − | 0.295122i | ||||
\(311\) | 11.0000 | + | 19.0526i | 0.623753 | + | 1.08037i | 0.988781 | + | 0.149375i | \(0.0477261\pi\) |
−0.365028 | + | 0.930997i | \(0.618941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | + | 8.66025i | −0.282617 | + | 0.489506i | −0.972028 | − | 0.234863i | \(-0.924536\pi\) |
0.689412 | + | 0.724370i | \(0.257869\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | −0.168763 | ||||||||
\(317\) | −16.5000 | + | 28.5788i | −0.926732 | + | 1.60515i | −0.137981 | + | 0.990435i | \(0.544061\pi\) |
−0.788751 | + | 0.614713i | \(0.789272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.5000 | − | 30.3109i | −0.979812 | − | 1.69708i | ||||
\(320\) | −1.00000 | + | 1.73205i | −0.0559017 | + | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00000 | + | 6.92820i | −0.445823 | + | 0.386094i | ||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | + | 5.19615i | 0.166410 | + | 0.288231i | ||||
\(326\) | 1.00000 | + | 1.73205i | 0.0553849 | + | 0.0959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 15.0000 | + | 5.19615i | 0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | + | 27.7128i | −0.879440 | + | 1.52323i | −0.0274825 | + | 0.999622i | \(0.508749\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | −3.50000 | − | 6.06218i | −0.192087 | − | 0.332705i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.00000 | − | 12.1244i | 0.383023 | − | 0.663415i | ||||
\(335\) | 20.0000 | 1.09272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0000 | −1.47078 | −0.735392 | − | 0.677642i | \(-0.763002\pi\) | ||||
−0.735392 | + | 0.677642i | \(0.763002\pi\) | |||||||
\(338\) | 11.5000 | − | 19.9186i | 0.625518 | − | 1.08343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.00000 | − | 6.92820i | −0.216930 | − | 0.375735i | ||||
\(341\) | 7.50000 | − | 12.9904i | 0.406148 | − | 0.703469i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.500000 | − | 0.866025i | −0.0268802 | − | 0.0465578i | ||||
\(347\) | −13.5000 | − | 23.3827i | −0.724718 | − | 1.25525i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.234372 | − | 0.972147i | \(-0.424697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 0.500000 | + | 2.59808i | 0.0267261 | + | 0.138873i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.50000 | + | 4.33013i | −0.133250 | + | 0.230797i | ||||
\(353\) | −15.0000 | − | 25.9808i | −0.798369 | − | 1.38282i | −0.920677 | − | 0.390324i | \(-0.872363\pi\) |
0.122308 | − | 0.992492i | \(-0.460970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | + | 6.92820i | −0.212298 | + | 0.367711i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.0000 | −0.792775 | ||||||||
\(359\) | 8.00000 | − | 13.8564i | 0.422224 | − | 0.731313i | −0.573933 | − | 0.818902i | \(-0.694583\pi\) |
0.996157 | + | 0.0875892i | \(0.0279163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0000 | − | 10.3923i | 0.628971 | − | 0.544705i | ||||
\(365\) | 26.0000 | 1.36090 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | −2.00000 | − | 3.46410i | −0.104257 | − | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.0000 | −0.831800 | ||||||||
\(371\) | 12.0000 | − | 10.3923i | 0.623009 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | − | 17.3205i | 0.517780 | − | 0.896822i | −0.482006 | − | 0.876168i | \(-0.660092\pi\) |
0.999787 | − | 0.0206542i | \(-0.00657489\pi\) | |||||||
\(374\) | −10.0000 | − | 17.3205i | −0.517088 | − | 0.895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | + | 5.19615i | −0.154713 | + | 0.267971i | ||||
\(377\) | −42.0000 | −2.16311 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 4.00000 | − | 6.92820i | 0.205196 | − | 0.355409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.00000 | + | 15.5885i | 0.460480 | + | 0.797575i | ||||
\(383\) | −2.00000 | + | 3.46410i | −0.102195 | + | 0.177007i | −0.912589 | − | 0.408879i | \(-0.865920\pi\) |
0.810394 | + | 0.585886i | \(0.199253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.00000 | − | 25.9808i | −0.254824 | − | 1.32410i | ||||
\(386\) | 19.0000 | 0.967075 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.50000 | + | 4.33013i | 0.126918 | + | 0.219829i | ||||
\(389\) | 0.500000 | + | 0.866025i | 0.0253510 | + | 0.0439092i | 0.878423 | − | 0.477885i | \(-0.158596\pi\) |
−0.853072 | + | 0.521794i | \(0.825263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 6.50000 | − | 2.59808i | 0.328300 | − | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5000 | − | 21.6506i | 0.629741 | − | 1.09074i | ||||
\(395\) | 3.00000 | + | 5.19615i | 0.150946 | + | 0.261447i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.00000 | − | 15.5885i | 0.451697 | − | 0.782362i | −0.546795 | − | 0.837267i | \(-0.684152\pi\) |
0.998492 | + | 0.0549046i | \(0.0174855\pi\) | |||||||
\(398\) | 19.0000 | 0.952384 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | − | 15.5885i | −0.448322 | − | 0.776516i | ||||
\(404\) | −2.50000 | + | 4.33013i | −0.124380 | + | 0.215432i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5000 | − | 6.06218i | −0.868510 | − | 0.300861i | ||||
\(407\) | −40.0000 | −1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 6.00000 | + | 10.3923i | 0.296319 | + | 0.513239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | −14.0000 | + | 12.1244i | −0.688895 | + | 0.596601i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.00000 | + | 12.1244i | −0.343616 | + | 0.595161i | ||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.0000 | − | 17.3205i | 0.489116 | − | 0.847174i | ||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | 13.0000 | − | 22.5167i | 0.632830 | − | 1.09609i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | + | 5.19615i | 0.145693 | + | 0.252347i | ||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | + | 13.8564i | 0.385794 | + | 0.668215i | ||||
\(431\) | −9.00000 | − | 15.5885i | −0.433515 | − | 0.750870i | 0.563658 | − | 0.826008i | \(-0.309393\pi\) |
−0.997173 | + | 0.0751385i | \(0.976060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | −0.336399 | −0.168199 | − | 0.985753i | \(-0.553795\pi\) | ||||
−0.168199 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(434\) | −1.50000 | − | 7.79423i | −0.0720023 | − | 0.374135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | + | 13.8564i | −0.383131 | + | 0.663602i | ||||
\(437\) | 8.00000 | + | 13.8564i | 0.382692 | + | 0.662842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.50000 | + | 2.59808i | −0.0715911 | + | 0.123999i | −0.899599 | − | 0.436717i | \(-0.856141\pi\) |
0.828008 | + | 0.560717i | \(0.189474\pi\) | |||||||
\(440\) | 10.0000 | 0.476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | 5.50000 | − | 9.52628i | 0.261313 | − | 0.452607i | −0.705278 | − | 0.708931i | \(-0.749178\pi\) |
0.966591 | + | 0.256323i | \(0.0825112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | + | 10.3923i | 0.284427 | + | 0.492642i | ||||
\(446\) | −0.500000 | + | 0.866025i | −0.0236757 | + | 0.0410075i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | + | 2.59808i | 0.0236228 | + | 0.122748i | ||||
\(449\) | 14.0000 | 0.660701 | 0.330350 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0000 | + | 25.9808i | 0.706322 | + | 1.22339i | ||||
\(452\) | 2.00000 | + | 3.46410i | 0.0940721 | + | 0.162938i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27.0000 | −1.26717 | ||||||||
\(455\) | −30.0000 | − | 10.3923i | −1.40642 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | − | 22.5167i | 0.608114 | − | 1.05328i | −0.383437 | − | 0.923567i | \(-0.625260\pi\) |
0.991551 | − | 0.129718i | \(-0.0414071\pi\) | |||||||
\(458\) | 2.00000 | + | 3.46410i | 0.0934539 | + | 0.161867i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | + | 6.92820i | −0.186501 | + | 0.323029i | ||||
\(461\) | 23.0000 | 1.07122 | 0.535608 | − | 0.844466i | \(-0.320082\pi\) | ||||
0.535608 | + | 0.844466i | \(0.320082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.0000 | −1.34774 | −0.673872 | − | 0.738848i | \(-0.735370\pi\) | ||||
−0.673872 | + | 0.738848i | \(0.735370\pi\) | |||||||
\(464\) | 3.50000 | − | 6.06218i | 0.162483 | − | 0.281430i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.0000 | + | 19.0526i | 0.509565 | + | 0.882593i | ||||
\(467\) | 3.50000 | − | 6.06218i | 0.161961 | − | 0.280524i | −0.773611 | − | 0.633661i | \(-0.781552\pi\) |
0.935572 | + | 0.353137i | \(0.114885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | − | 17.3205i | 0.923514 | − | 0.799787i | ||||
\(470\) | 12.0000 | 0.553519 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.50000 | − | 6.06218i | −0.161101 | − | 0.279034i | ||||
\(473\) | 20.0000 | + | 34.6410i | 0.919601 | + | 1.59280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | −10.0000 | − | 3.46410i | −0.458349 | − | 0.158777i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.0000 | + | 22.5167i | 0.593985 | + | 1.02881i | 0.993689 | + | 0.112168i | \(0.0357796\pi\) |
−0.399704 | + | 0.916644i | \(0.630887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | + | 41.5692i | −1.09431 | + | 1.89539i | ||||
\(482\) | 1.00000 | 0.0455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | 5.00000 | − | 8.66025i | 0.227038 | − | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50000 | + | 11.2583i | 0.294543 | + | 0.510164i | 0.974879 | − | 0.222737i | \(-0.0714992\pi\) |
−0.680335 | + | 0.732901i | \(0.738166\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.0000 | − | 8.66025i | −0.496929 | − | 0.391230i | ||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.0000 | + | 24.2487i | 0.630528 | + | 1.09211i | ||||
\(494\) | −12.0000 | − | 20.7846i | −0.539906 | − | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | 2.00000 | + | 10.3923i | 0.0897123 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | − | 6.92820i | 0.179065 | − | 0.310149i | −0.762496 | − | 0.646993i | \(-0.776026\pi\) |
0.941560 | + | 0.336844i | \(0.109360\pi\) | |||||||
\(500\) | 6.00000 | + | 10.3923i | 0.268328 | + | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.5000 | − | 18.1865i | 0.468638 | − | 0.811705i | ||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | −10.0000 | + | 17.3205i | −0.444554 | + | 0.769991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.50000 | − | 2.59808i | 0.0664863 | − | 0.115158i | −0.830866 | − | 0.556473i | \(-0.812154\pi\) |
0.897352 | + | 0.441315i | \(0.145488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.0000 | − | 22.5167i | 1.15017 | − | 0.996078i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | − | 13.8564i | −0.352522 | − | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.0000 | 1.31940 | ||||||||
\(518\) | −16.0000 | + | 13.8564i | −0.703000 | + | 0.608816i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | − | 10.3923i | 0.263117 | − | 0.455733i | ||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0000 | + | 22.5167i | −0.568450 | + | 0.984585i | 0.428269 | + | 0.903651i | \(0.359124\pi\) |
−0.996719 | + | 0.0809336i | \(0.974210\pi\) | |||||||
\(524\) | −13.0000 | −0.567908 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | 0.523225 | ||||||||
\(527\) | −6.00000 | + | 10.3923i | −0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 6.00000 | − | 10.3923i | 0.260623 | − | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | − | 10.3923i | −0.0867110 | − | 0.450564i | ||||
\(533\) | 36.0000 | 1.55933 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | + | 20.7846i | 0.518805 | + | 0.898597i | ||||
\(536\) | 5.00000 | + | 8.66025i | 0.215967 | + | 0.374066i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.0000 | 1.33650 | ||||||||
\(539\) | −27.5000 | − | 21.6506i | −1.18451 | − | 0.932559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0000 | − | 25.9808i | 0.644900 | − | 1.11700i | −0.339424 | − | 0.940633i | \(-0.610232\pi\) |
0.984325 | − | 0.176367i | \(-0.0564345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | − | 3.46410i | 0.0857493 | − | 0.148522i | ||||
\(545\) | 32.0000 | 1.37073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.0000 | −0.769624 | −0.384812 | − | 0.922995i | \(-0.625734\pi\) | ||||
−0.384812 | + | 0.922995i | \(0.625734\pi\) | |||||||
\(548\) | −4.00000 | + | 6.92820i | −0.170872 | + | 0.295958i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.50000 | + | 4.33013i | 0.106600 | + | 0.184637i | ||||
\(551\) | −14.0000 | + | 24.2487i | −0.596420 | + | 1.03303i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50000 | + | 2.59808i | 0.318932 | + | 0.110481i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | + | 6.92820i | 0.169638 | + | 0.293821i | ||||
\(557\) | −5.50000 | − | 9.52628i | −0.233042 | − | 0.403641i | 0.725660 | − | 0.688054i | \(-0.241535\pi\) |
−0.958702 | + | 0.284413i | \(0.908201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.0000 | 2.03018 | ||||||||
\(560\) | 4.00000 | − | 3.46410i | 0.169031 | − | 0.146385i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.00000 | + | 1.73205i | −0.0421825 | + | 0.0730622i | ||||
\(563\) | 10.0000 | + | 17.3205i | 0.421450 | + | 0.729972i | 0.996082 | − | 0.0884397i | \(-0.0281881\pi\) |
−0.574632 | + | 0.818412i | \(0.694855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | − | 6.92820i | 0.168281 | − | 0.291472i | ||||
\(566\) | −16.0000 | −0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −6.00000 | + | 10.3923i | −0.251533 | + | 0.435668i | −0.963948 | − | 0.266090i | \(-0.914268\pi\) |
0.712415 | + | 0.701758i | \(0.247601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(572\) | 15.0000 | − | 25.9808i | 0.627182 | − | 1.08631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.0000 | + | 5.19615i | 0.626088 | + | 0.216883i | ||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.5000 | − | 37.2391i | −0.895057 | − | 1.55028i | −0.833734 | − | 0.552166i | \(-0.813802\pi\) |
−0.0613223 | − | 0.998118i | \(-0.519532\pi\) | |||||||
\(578\) | −0.500000 | − | 0.866025i | −0.0207973 | − | 0.0360219i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.0000 | −0.581318 | ||||||||
\(581\) | 3.50000 | + | 18.1865i | 0.145204 | + | 0.754505i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0000 | − | 25.9808i | 0.621237 | − | 1.07601i | ||||
\(584\) | 6.50000 | + | 11.2583i | 0.268972 | + | 0.465873i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.5000 | + | 23.3827i | −0.557680 | + | 0.965930i | ||||
\(587\) | −20.0000 | −0.825488 | −0.412744 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | −7.00000 | + | 12.1244i | −0.288185 | + | 0.499152i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | 18.0000 | − | 31.1769i | 0.739171 | − | 1.28028i | −0.213697 | − | 0.976900i | \(-0.568551\pi\) |
0.952869 | − | 0.303383i | \(-0.0981160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | + | 20.7846i | 0.163984 | + | 0.852086i | ||||
\(596\) | −9.00000 | −0.368654 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000 | + | 20.7846i | 0.490716 | + | 0.849946i | ||||
\(599\) | 15.0000 | + | 25.9808i | 0.612883 | + | 1.06155i | 0.990752 | + | 0.135686i | \(0.0433238\pi\) |
−0.377869 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 20.0000 | + | 6.92820i | 0.815139 | + | 0.282372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.50000 | − | 14.7224i | 0.345860 | − | 0.599047i | ||||
\(605\) | −14.0000 | − | 24.2487i | −0.569181 | − | 0.985850i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50000 | − | 7.79423i | 0.182649 | − | 0.316358i | −0.760133 | − | 0.649768i | \(-0.774866\pi\) |
0.942782 | + | 0.333410i | \(0.108199\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | − | 31.1769i | 0.728202 | − | 1.26128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | + | 5.19615i | 0.121169 | + | 0.209871i | 0.920229 | − | 0.391381i | \(-0.128002\pi\) |
−0.799060 | + | 0.601251i | \(0.794669\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.0000 | − | 8.66025i | 0.402911 | − | 0.348932i | ||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.00000 | − | 3.46410i | −0.0803868 | − | 0.139234i | 0.823029 | − | 0.567999i | \(-0.192282\pi\) |
−0.903416 | + | 0.428765i | \(0.858949\pi\) | |||||||
\(620\) | −3.00000 | − | 5.19615i | −0.120483 | − | 0.208683i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.0000 | 0.882120 | ||||||||
\(623\) | 15.0000 | + | 5.19615i | 0.600962 | + | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 5.00000 | + | 8.66025i | 0.199840 | + | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.00000 | + | 12.1244i | −0.279330 | + | 0.483814i | ||||
\(629\) | 32.0000 | 1.27592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | −1.50000 | + | 2.59808i | −0.0596668 | + | 0.103346i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.5000 | + | 28.5788i | 0.655299 | + | 1.13501i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.0000 | + | 15.5885i | −1.54524 | + | 0.617637i | ||||
\(638\) | −35.0000 | −1.38566 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | + | 1.73205i | 0.0395285 | + | 0.0684653i | ||||
\(641\) | 7.00000 | + | 12.1244i | 0.276483 | + | 0.478883i | 0.970508 | − | 0.241068i | \(-0.0774976\pi\) |
−0.694025 | + | 0.719951i | \(0.744164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0000 | 0.552106 | 0.276053 | − | 0.961142i | \(-0.410973\pi\) | ||||
0.276053 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(644\) | 2.00000 | + | 10.3923i | 0.0788110 | + | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | + | 13.8564i | −0.314756 | + | 0.545173i | ||||
\(647\) | −9.00000 | − | 15.5885i | −0.353827 | − | 0.612845i | 0.633090 | − | 0.774078i | \(-0.281786\pi\) |
−0.986916 | + | 0.161233i | \(0.948453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5000 | + | 30.3109i | −0.686935 | + | 1.18981i | ||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.0000 | + | 22.5167i | 0.507952 | + | 0.879799i | ||||
\(656\) | −3.00000 | + | 5.19615i | −0.117130 | + | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0000 | − | 10.3923i | 0.467809 | − | 0.405134i | ||||
\(659\) | −41.0000 | −1.59713 | −0.798567 | − | 0.601906i | \(-0.794408\pi\) | ||||
−0.798567 | + | 0.601906i | \(0.794408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0000 | + | 32.9090i | 0.739014 | + | 1.28001i | 0.952940 | + | 0.303160i | \(0.0980418\pi\) |
−0.213925 | + | 0.976850i | \(0.568625\pi\) | |||||||
\(662\) | 16.0000 | + | 27.7128i | 0.621858 | + | 1.07709i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.00000 | −0.271653 | ||||||||
\(665\) | −16.0000 | + | 13.8564i | −0.620453 | + | 0.537328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0000 | − | 24.2487i | 0.542082 | − | 0.938914i | ||||
\(668\) | −7.00000 | − | 12.1244i | −0.270838 | − | 0.469105i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0000 | − | 17.3205i | 0.386334 | − | 0.669150i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | −13.5000 | + | 23.3827i | −0.520001 | + | 0.900667i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5000 | − | 19.9186i | −0.442308 | − | 0.766099i | ||||
\(677\) | 4.50000 | − | 7.79423i | 0.172949 | − | 0.299557i | −0.766501 | − | 0.642244i | \(-0.778004\pi\) |
0.939450 | + | 0.342687i | \(0.111337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.50000 | − | 12.9904i | −0.0959412 | − | 0.498525i | ||||
\(680\) | −8.00000 | −0.306786 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.50000 | − | 12.9904i | −0.287190 | − | 0.497427i | ||||
\(683\) | 10.5000 | + | 18.1865i | 0.401771 | + | 0.695888i | 0.993940 | − | 0.109926i | \(-0.0350613\pi\) |
−0.592168 | + | 0.805814i | \(0.701728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0000 | 0.611329 | ||||||||
\(686\) | −18.5000 | + | 0.866025i | −0.706333 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | −18.0000 | − | 31.1769i | −0.685745 | − | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | −1.00000 | −0.0380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.0000 | −1.02491 | ||||||||
\(695\) | 8.00000 | − | 13.8564i | 0.303457 | − | 0.525603i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0000 | − | 20.7846i | −0.454532 | − | 0.787273i | ||||
\(698\) | −10.0000 | + | 17.3205i | −0.378506 | + | 0.655591i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.50000 | + | 0.866025i | 0.0944911 | + | 0.0327327i | ||||
\(701\) | 14.0000 | 0.528773 | 0.264386 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264386 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | + | 27.7128i | 0.603451 | + | 1.04521i | ||||
\(704\) | 2.50000 | + | 4.33013i | 0.0942223 | + | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.0000 | −1.12906 | ||||||||
\(707\) | 10.0000 | − | 8.66025i | 0.376089 | − | 0.325702i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | + | 6.92820i | −0.150223 | + | 0.260194i | −0.931309 | − | 0.364229i | \(-0.881333\pi\) |
0.781086 | + | 0.624423i | \(0.214666\pi\) | |||||||
\(710\) | 4.00000 | + | 6.92820i | 0.150117 | + | 0.260011i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | 12.0000 | 0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −60.0000 | −2.24387 | ||||||||
\(716\) | −7.50000 | + | 12.9904i | −0.280288 | + | 0.485473i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.00000 | − | 13.8564i | −0.298557 | − | 0.517116i | ||||
\(719\) | 3.00000 | − | 5.19615i | 0.111881 | − | 0.193784i | −0.804648 | − | 0.593753i | \(-0.797646\pi\) |
0.916529 | + | 0.399969i | \(0.130979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.0000 | − | 6.92820i | −0.744839 | − | 0.258020i | ||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.50000 | − | 6.06218i | −0.129987 | − | 0.225144i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | −3.00000 | − | 15.5885i | −0.111187 | − | 0.577747i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.0000 | − | 22.5167i | 0.481152 | − | 0.833379i | ||||
\(731\) | −16.0000 | − | 27.7128i | −0.591781 | − | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0000 | − | 31.1769i | 0.664845 | − | 1.15155i | −0.314482 | − | 0.949263i | \(-0.601831\pi\) |
0.979327 | − | 0.202282i | \(-0.0648358\pi\) | |||||||
\(734\) | 4.00000 | 0.147643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 25.0000 | − | 43.3013i | 0.920887 | − | 1.59502i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.00000 | + | 5.19615i | 0.110357 | + | 0.191144i | 0.915914 | − | 0.401374i | \(-0.131467\pi\) |
−0.805557 | + | 0.592518i | \(0.798134\pi\) | |||||||
\(740\) | −8.00000 | + | 13.8564i | −0.294086 | + | 0.509372i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.00000 | − | 15.5885i | −0.110133 | − | 0.572270i | ||||
\(743\) | 6.00000 | 0.220119 | 0.110059 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110059 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | −10.0000 | − | 17.3205i | −0.366126 | − | 0.634149i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.0000 | −0.731272 | ||||||||
\(749\) | 30.0000 | + | 10.3923i | 1.09618 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.00000 | + | 10.3923i | −0.218943 | + | 0.379221i | −0.954485 | − | 0.298259i | \(-0.903594\pi\) |
0.735542 | + | 0.677479i | \(0.236928\pi\) | |||||||
\(752\) | 3.00000 | + | 5.19615i | 0.109399 | + | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21.0000 | + | 36.3731i | −0.764775 | + | 1.32463i | ||||
\(755\) | −34.0000 | −1.23739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 5.00000 | − | 8.66025i | 0.181608 | − | 0.314555i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.00000 | − | 6.92820i | −0.145095 | − | 0.251312i | ||||
\(761\) | 4.00000 | − | 6.92820i | 0.145000 | − | 0.251147i | −0.784373 | − | 0.620289i | \(-0.787015\pi\) |
0.929373 | + | 0.369142i | \(0.120348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.0000 | − | 27.7128i | 1.15848 | − | 1.00327i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.00000 | + | 3.46410i | 0.0722629 | + | 0.125163i | ||||
\(767\) | 21.0000 | + | 36.3731i | 0.758266 | + | 1.31336i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | 0.0360609 | 0.0180305 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180305 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(770\) | −25.0000 | − | 8.66025i | −0.900937 | − | 0.312094i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.50000 | − | 16.4545i | 0.341912 | − | 0.592210i | ||||
\(773\) | −19.0000 | − | 32.9090i | −0.683383 | − | 1.18365i | −0.973942 | − | 0.226796i | \(-0.927175\pi\) |
0.290560 | − | 0.956857i | \(-0.406159\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50000 | − | 2.59808i | 0.0538816 | − | 0.0933257i | ||||
\(776\) | 5.00000 | 0.179490 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.00000 | 0.0358517 | ||||||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | + | 17.3205i | 0.357828 | + | 0.619777i | ||||
\(782\) | 8.00000 | − | 13.8564i | 0.286079 | − | 0.495504i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | 28.0000 | 0.999363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.00000 | − | 15.5885i | −0.320815 | − | 0.555668i | 0.659841 | − | 0.751405i | \(-0.270624\pi\) |
−0.980656 | + | 0.195737i | \(0.937290\pi\) | |||||||
\(788\) | −12.5000 | − | 21.6506i | −0.445294 | − | 0.771272i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.00000 | 0.213470 | ||||||||
\(791\) | −2.00000 | − | 10.3923i | −0.0711118 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.00000 | − | 15.5885i | −0.319398 | − | 0.553214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.50000 | − | 16.4545i | 0.336719 | − | 0.583214i | ||||
\(797\) | −33.0000 | −1.16892 | −0.584460 | − | 0.811423i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811423i | \(0.698694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.00000 | + | 15.5885i | 0.317801 | + | 0.550448i | ||||
\(803\) | 32.5000 | − | 56.2917i | 1.14690 | − | 1.98649i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | − | 13.8564i | 0.563926 | − | 0.488374i | ||||
\(806\) | −18.0000 | −0.634023 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.50000 | + | 4.33013i | 0.0879497 | + | 0.152333i | ||||
\(809\) | 17.0000 | + | 29.4449i | 0.597688 | + | 1.03523i | 0.993161 | + | 0.116749i | \(0.0372472\pi\) |
−0.395473 | + | 0.918477i | \(0.629419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.0000 | −1.75574 | −0.877869 | − | 0.478901i | \(-0.841035\pi\) | ||||
−0.877869 | + | 0.478901i | \(0.841035\pi\) | |||||||
\(812\) | −14.0000 | + | 12.1244i | −0.491304 | + | 0.425481i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.0000 | + | 34.6410i | −0.701000 | + | 1.21417i | ||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | − | 27.7128i | 0.559769 | − | 0.969549i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | −24.5000 | + | 42.4352i | −0.855056 | + | 1.48100i | 0.0215373 | + | 0.999768i | \(0.493144\pi\) |
−0.876593 | + | 0.481232i | \(0.840189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.50000 | − | 11.2583i | −0.226576 | − | 0.392441i | 0.730215 | − | 0.683217i | \(-0.239420\pi\) |
−0.956791 | + | 0.290776i | \(0.906086\pi\) | |||||||
\(824\) | 4.00000 | − | 6.92820i | 0.139347 | − | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.50000 | + | 18.1865i | 0.121781 | + | 0.632790i | ||||
\(827\) | −51.0000 | −1.77344 | −0.886722 | − | 0.462303i | \(-0.847023\pi\) | ||||
−0.886722 | + | 0.462303i | \(0.847023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0000 | − | 19.0526i | −0.382046 | − | 0.661723i | 0.609309 | − | 0.792933i | \(-0.291447\pi\) |
−0.991355 | + | 0.131210i | \(0.958114\pi\) | |||||||
\(830\) | 7.00000 | + | 12.1244i | 0.242974 | + | 0.420843i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | 22.0000 | + | 17.3205i | 0.762255 | + | 0.600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | + | 24.2487i | −0.484490 | + | 0.839161i | ||||
\(836\) | −10.0000 | − | 17.3205i | −0.345857 | − | 0.599042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | + | 10.3923i | −0.207267 | + | 0.358996i | ||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −9.00000 | + | 15.5885i | −0.310160 | + | 0.537214i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.0000 | − | 22.5167i | −0.447478 | − | 0.775055i | ||||
\(845\) | −23.0000 | + | 39.8372i | −0.791224 | + | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0000 | − | 12.1244i | −1.20261 | − | 0.416598i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.00000 | − | 3.46410i | −0.0685994 | − | 0.118818i | ||||
\(851\) | −16.0000 | − | 27.7128i | −0.548473 | − | 0.949983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.0000 | −1.57501 | −0.787505 | − | 0.616308i | \(-0.788628\pi\) | ||||
−0.787505 | + | 0.616308i | \(0.788628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | 15.0000 | + | 25.9808i | 0.512390 | + | 0.887486i | 0.999897 | + | 0.0143666i | \(0.00457319\pi\) |
−0.487507 | + | 0.873119i | \(0.662093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.00000 | − | 13.8564i | 0.272956 | − | 0.472774i | −0.696661 | − | 0.717400i | \(-0.745332\pi\) |
0.969618 | + | 0.244626i | \(0.0786652\pi\) | |||||||
\(860\) | 16.0000 | 0.545595 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.0000 | −0.613082 | ||||||||
\(863\) | −19.0000 | + | 32.9090i | −0.646768 | + | 1.12023i | 0.337123 | + | 0.941461i | \(0.390546\pi\) |
−0.983890 | + | 0.178774i | \(0.942787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | + | 1.73205i | 0.0340010 | + | 0.0588915i | ||||
\(866\) | −3.50000 | + | 6.06218i | −0.118935 | + | 0.206001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.50000 | − | 2.59808i | −0.254567 | − | 0.0881845i | ||||
\(869\) | 15.0000 | 0.508840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.0000 | − | 51.9615i | −1.01651 | − | 1.76065i | ||||
\(872\) | 8.00000 | + | 13.8564i | 0.270914 | + | 0.469237i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.0000 | 0.541208 | ||||||||
\(875\) | −6.00000 | − | 31.1769i | −0.202837 | − | 1.05397i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.0000 | + | 29.4449i | −0.574049 | + | 0.994282i | 0.422095 | + | 0.906552i | \(0.361295\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | 1.50000 | + | 2.59808i | 0.0506225 | + | 0.0876808i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.00000 | − | 8.66025i | 0.168550 | − | 0.291937i | ||||
\(881\) | 54.0000 | 1.81931 | 0.909653 | − | 0.415369i | \(-0.136347\pi\) | ||||
0.909653 | + | 0.415369i | \(0.136347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | −12.0000 | + | 20.7846i | −0.403604 | + | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.50000 | − | 9.52628i | −0.184776 | − | 0.320042i | ||||
\(887\) | −21.0000 | + | 36.3731i | −0.705111 | + | 1.22129i | 0.261540 | + | 0.965193i | \(0.415770\pi\) |
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.500000 | + | 0.866025i | 0.0167412 | + | 0.0289967i | ||||
\(893\) | −12.0000 | − | 20.7846i | −0.401565 | − | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.0000 | 1.00279 | ||||||||
\(896\) | 2.50000 | + | 0.866025i | 0.0835191 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.00000 | − | 12.1244i | 0.233593 | − | 0.404595i | ||||
\(899\) | 10.5000 | + | 18.1865i | 0.350195 | + | 0.606555i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | + | 20.7846i | −0.399778 | + | 0.692436i | ||||
\(902\) | 30.0000 | 0.998891 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.00000 | 0.133038 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.0000 | + | 36.3731i | 0.697294 | + | 1.20775i | 0.969401 | + | 0.245481i | \(0.0789459\pi\) |
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(908\) | −13.5000 | + | 23.3827i | −0.448013 | + | 0.775982i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.0000 | + | 20.7846i | −0.795592 | + | 0.689003i | ||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.5000 | + | 30.3109i | 0.579165 | + | 1.00314i | ||||
\(914\) | −13.0000 | − | 22.5167i | −0.430002 | − | 0.744785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.00000 | 0.132164 | ||||||||
\(917\) | 32.5000 | + | 11.2583i | 1.07324 | + | 0.371783i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.50000 | + | 11.2583i | −0.214415 | + | 0.371378i | −0.953092 | − | 0.302682i | \(-0.902118\pi\) |
0.738676 | + | 0.674060i | \(0.235451\pi\) | |||||||
\(920\) | 4.00000 | + | 6.92820i | 0.131876 | + | 0.228416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.5000 | − | 19.9186i | 0.378732 | − | 0.655984i | ||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | −14.5000 | + | 25.1147i | −0.476500 | + | 0.825321i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.50000 | − | 6.06218i | −0.114893 | − | 0.199001i | ||||
\(929\) | 18.0000 | − | 31.1769i | 0.590561 | − | 1.02288i | −0.403596 | − | 0.914937i | \(-0.632240\pi\) |
0.994157 | − | 0.107944i | \(-0.0344268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | + | 27.7128i | −0.131095 | + | 0.908251i | ||||
\(932\) | 22.0000 | 0.720634 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.50000 | − | 6.06218i | −0.114523 | − | 0.198361i | ||||
\(935\) | 20.0000 | + | 34.6410i | 0.654070 | + | 1.13288i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | −5.00000 | − | 25.9808i | −0.163256 | − | 0.848302i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00000 | − | 10.3923i | 0.195698 | − | 0.338960i | ||||
\(941\) | 6.50000 | + | 11.2583i | 0.211894 | + | 0.367011i | 0.952307 | − | 0.305141i | \(-0.0987035\pi\) |
−0.740413 | + | 0.672152i | \(0.765370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | + | 20.7846i | −0.390774 | + | 0.676840i | ||||
\(944\) | −7.00000 | −0.227831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0000 | 1.30051 | ||||||||
\(947\) | 12.5000 | − | 21.6506i | 0.406195 | − | 0.703551i | −0.588264 | − | 0.808669i | \(-0.700189\pi\) |
0.994460 | + | 0.105118i | \(0.0335219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.0000 | − | 67.5500i | −1.26599 | − | 2.19277i | ||||
\(950\) | 2.00000 | − | 3.46410i | 0.0648886 | − | 0.112390i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.00000 | + | 6.92820i | −0.259281 | + | 0.224544i | ||||
\(953\) | −2.00000 | −0.0647864 | −0.0323932 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323932 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.0000 | − | 31.1769i | −0.582466 | − | 1.00886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.0000 | 0.840022 | ||||||||
\(959\) | 16.0000 | − | 13.8564i | 0.516667 | − | 0.447447i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 24.0000 | + | 41.5692i | 0.773791 | + | 1.34025i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.500000 | − | 0.866025i | 0.0161039 | − | 0.0278928i | ||||
\(965\) | −38.0000 | −1.22326 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | 7.00000 | − | 12.1244i | 0.224989 | − | 0.389692i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.00000 | − | 8.66025i | −0.160540 | − | 0.278064i | ||||
\(971\) | 6.00000 | − | 10.3923i | 0.192549 | − | 0.333505i | −0.753545 | − | 0.657396i | \(-0.771658\pi\) |
0.946094 | + | 0.323891i | \(0.104991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00000 | − | 20.7846i | −0.128234 | − | 0.666324i | ||||
\(974\) | 13.0000 | 0.416547 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | 0.958804 | ||||||||
\(980\) | −13.0000 | + | 5.19615i | −0.415270 | + | 0.165985i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.00000 | + | 10.3923i | −0.191468 | + | 0.331632i | ||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.0000 | + | 43.3013i | −0.796566 | + | 1.37969i | ||||
\(986\) | 28.0000 | 0.891702 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.0000 | −0.763542 | ||||||||
\(989\) | −16.0000 | + | 27.7128i | −0.508770 | + | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | − | 6.92820i | −0.127064 | − | 0.220082i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.922538 | + | 0.385906i | \(0.873889\pi\) | |||||||
\(992\) | 1.50000 | − | 2.59808i | 0.0476250 | − | 0.0824890i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.0000 | + | 3.46410i | 0.317181 | + | 0.109875i | ||||
\(995\) | −38.0000 | −1.20468 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0000 | + | 50.2295i | 0.918439 | + | 1.59078i | 0.801786 | + | 0.597611i | \(0.203883\pi\) |
0.116653 | + | 0.993173i | \(0.462784\pi\) | |||||||
\(998\) | −4.00000 | − | 6.92820i | −0.126618 | − | 0.219308i | ||||
\(999\) | 0 | 0 |
(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 | 378.2.g.d.163.1 | yes | 2 | |
3.2 | odd | 2 | 378.2.g.c.163.1 | yes | 2 | ||
7.2 | even | 3 | 2646.2.a.k.1.1 | 1 | |||
7.4 | even | 3 | inner | 378.2.g.d.109.1 | yes | 2 | |
7.5 | odd | 6 | 2646.2.a.c.1.1 | 1 | |||
9.2 | odd | 6 | 1134.2.e.o.919.1 | 2 | |||
9.4 | even | 3 | 1134.2.h.o.541.1 | 2 | |||
9.5 | odd | 6 | 1134.2.h.b.541.1 | 2 | |||
9.7 | even | 3 | 1134.2.e.b.919.1 | 2 | |||
21.2 | odd | 6 | 2646.2.a.t.1.1 | 1 | |||
21.5 | even | 6 | 2646.2.a.bb.1.1 | 1 | |||
21.11 | odd | 6 | 378.2.g.c.109.1 | ✓ | 2 | ||
63.4 | even | 3 | 1134.2.e.b.865.1 | 2 | |||
63.11 | odd | 6 | 1134.2.h.b.109.1 | 2 | |||
63.25 | even | 3 | 1134.2.h.o.109.1 | 2 | |||
63.32 | odd | 6 | 1134.2.e.o.865.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.c.109.1 | ✓ | 2 | 21.11 | odd | 6 | ||
378.2.g.c.163.1 | yes | 2 | 3.2 | odd | 2 | ||
378.2.g.d.109.1 | yes | 2 | 7.4 | even | 3 | inner | |
378.2.g.d.163.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1134.2.e.b.865.1 | 2 | 63.4 | even | 3 | |||
1134.2.e.b.919.1 | 2 | 9.7 | even | 3 | |||
1134.2.e.o.865.1 | 2 | 63.32 | odd | 6 | |||
1134.2.e.o.919.1 | 2 | 9.2 | odd | 6 | |||
1134.2.h.b.109.1 | 2 | 63.11 | odd | 6 | |||
1134.2.h.b.541.1 | 2 | 9.5 | odd | 6 | |||
1134.2.h.o.109.1 | 2 | 63.25 | even | 3 | |||
1134.2.h.o.541.1 | 2 | 9.4 | even | 3 | |||
2646.2.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
2646.2.a.k.1.1 | 1 | 7.2 | even | 3 | |||
2646.2.a.t.1.1 | 1 | 21.2 | odd | 6 | |||
2646.2.a.bb.1.1 | 1 | 21.5 | even | 6 |