Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(169,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.r (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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(0.939693 + 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.337 |
Dual form | 504.2.r.c.169.1 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.70574 | + | 0.300767i | −0.984808 | + | 0.173648i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.266044 | + | 0.460802i | −0.118979 | + | 0.206077i | −0.919363 | − | 0.393410i | \(-0.871295\pi\) |
0.800385 | + | 0.599487i | \(0.204629\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.81908 | − | 1.02606i | 0.939693 | − | 0.342020i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.11334 | + | 1.92836i | 0.335685 | + | 0.581423i | 0.983616 | − | 0.180276i | \(-0.0576989\pi\) |
−0.647931 | + | 0.761699i | \(0.724366\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.03209 | + | 1.78763i | −0.286250 | + | 0.495799i | −0.972912 | − | 0.231178i | \(-0.925742\pi\) |
0.686662 | + | 0.726977i | \(0.259075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.315207 | − | 0.866025i | 0.0813862 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.815207 | 0.197717 | 0.0988584 | − | 0.995102i | \(-0.468481\pi\) | ||||
0.0988584 | + | 0.995102i | \(0.468481\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.94356 | −1.82238 | −0.911189 | − | 0.411988i | \(-0.864834\pi\) | ||||
−0.911189 | + | 0.411988i | \(0.864834\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.11334 | + | 1.32683i | 0.242951 | + | 0.289538i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.40033 | + | 5.88954i | −0.709018 | + | 1.22805i | 0.256204 | + | 0.966623i | \(0.417528\pi\) |
−0.965222 | + | 0.261432i | \(0.915805\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.35844 | + | 4.08494i | 0.471688 | + | 0.816988i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | + | 2.59808i | −0.866025 | + | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.73783 | + | 6.47410i | 0.694097 | + | 1.20221i | 0.970484 | + | 0.241165i | \(0.0775294\pi\) |
−0.276387 | + | 0.961046i | \(0.589137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.14543 | + | 1.98394i | −0.205725 | + | 0.356327i | −0.950364 | − | 0.311142i | \(-0.899289\pi\) |
0.744638 | + | 0.667468i | \(0.232622\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.47906 | − | 2.95442i | −0.431548 | − | 0.514299i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.532089 | 0.0899394 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2909 | −1.69181 | −0.845903 | − | 0.533336i | \(-0.820938\pi\) | ||||
−0.845903 | + | 0.533336i | \(0.820938\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.22281 | − | 3.35965i | 0.195807 | − | 0.537974i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.29813 | − | 2.24843i | 0.202734 | − | 0.351146i | −0.746674 | − | 0.665190i | \(-0.768351\pi\) |
0.949409 | + | 0.314044i | \(0.101684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.145430 | − | 0.251892i | −0.0221778 | − | 0.0384131i | 0.854723 | − | 0.519084i | \(-0.173727\pi\) |
−0.876901 | + | 0.480670i | \(0.840393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.277189 | + | 1.57202i | −0.0413209 | + | 0.234342i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.213011 | − | 0.368946i | −0.0310709 | − | 0.0538163i | 0.850072 | − | 0.526667i | \(-0.176558\pi\) |
−0.881143 | + | 0.472850i | \(0.843225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.39053 | + | 0.245188i | −0.194713 | + | 0.0343332i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.41147 | 0.193881 | 0.0969404 | − | 0.995290i | \(-0.469094\pi\) | ||||
0.0969404 | + | 0.995290i | \(0.469094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18479 | −0.159757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.5496 | − | 2.38917i | 1.79469 | − | 0.316453i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.71554 | + | 2.97140i | −0.223344 | + | 0.386843i | −0.955821 | − | 0.293948i | \(-0.905031\pi\) |
0.732477 | + | 0.680791i | \(0.238364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.23783 | + | 9.07218i | 0.670635 | + | 1.16157i | 0.977724 | + | 0.209893i | \(0.0673116\pi\) |
−0.307089 | + | 0.951681i | \(0.599355\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.29813 | − | 1.92836i | −0.289538 | − | 0.242951i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.549163 | − | 0.951178i | −0.0681153 | − | 0.117979i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.10220 | − | 3.64111i | 0.256824 | − | 0.444833i | −0.708565 | − | 0.705645i | \(-0.750657\pi\) |
0.965389 | + | 0.260813i | \(0.0839905\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.02869 | − | 11.0687i | 0.484997 | − | 1.33252i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0865 | 1.43440 | 0.717200 | − | 0.696868i | \(-0.245423\pi\) | ||||
0.717200 | + | 0.696868i | \(0.245423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.09152 | −1.06408 | −0.532041 | − | 0.846719i | \(-0.678575\pi\) | ||||
−0.532041 | + | 0.846719i | \(0.678575\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.25150 | − | 6.25849i | −0.606391 | − | 0.722668i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.11334 | − | 1.92836i | 0.126877 | − | 0.219757i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.73055 | − | 6.46151i | −0.419720 | − | 0.726976i | 0.576191 | − | 0.817315i | \(-0.304538\pi\) |
−0.995911 | + | 0.0903388i | \(0.971205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.89440 | − | 5.78509i | 0.766044 | − | 0.642788i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.76264 | + | 15.1773i | 0.961825 | + | 1.66593i | 0.717914 | + | 0.696132i | \(0.245097\pi\) |
0.243911 | + | 0.969798i | \(0.421570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.216881 | + | 0.375650i | −0.0235241 | + | 0.0407449i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.32295 | − | 9.91890i | −0.892314 | − | 1.06342i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.09833 | −0.222422 | −0.111211 | − | 0.993797i | \(-0.535473\pi\) | ||||
−0.111211 | + | 0.993797i | \(0.535473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.06418 | 0.216385 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.35710 | − | 3.72859i | 0.140724 | − | 0.386637i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.11334 | − | 3.66041i | 0.216824 | − | 0.375551i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.94222 | − | 10.2922i | −0.603341 | − | 1.04502i | −0.992311 | − | 0.123767i | \(-0.960503\pi\) |
0.388970 | − | 0.921250i | \(-0.372831\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.11721 | + | 4.29385i | 0.514299 | + | 0.431548i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.68866 | − | 6.38895i | −0.367036 | − | 0.635724i | 0.622065 | − | 0.782966i | \(-0.286294\pi\) |
−0.989101 | + | 0.147241i | \(0.952961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.19594 | − | 5.53553i | 0.314905 | − | 0.545431i | −0.664512 | − | 0.747277i | \(-0.731361\pi\) |
0.979417 | + | 0.201846i | \(0.0646940\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.907604 | + | 0.160035i | −0.0885731 | + | 0.0156178i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0196004 | −0.00189484 | −0.000947419 | − | 1.00000i | \(-0.500302\pi\) | ||||
−0.000947419 | 1.00000i | \(0.500302\pi\) | ||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.24897 | 0.119630 | 0.0598148 | − | 0.998209i | \(-0.480949\pi\) | ||||
0.0598148 | + | 0.998209i | \(0.480949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.5535 | − | 3.09516i | 1.66610 | − | 0.293779i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.10607 | − | 10.5760i | 0.574410 | − | 0.994908i | −0.421695 | − | 0.906738i | \(-0.638565\pi\) |
0.996105 | − | 0.0881703i | \(-0.0281020\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.80928 | − | 3.13376i | −0.168716 | − | 0.292225i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.07532 | + | 6.09845i | −0.0994136 | + | 0.563802i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.407604 | − | 0.705990i | −0.0373650 | − | 0.0647180i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.02094 | − | 5.23243i | 0.274631 | − | 0.475675i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.53802 | + | 4.22567i | −0.138678 | + | 0.381016i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.17024 | −0.462441 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.41921 | 0.125935 | 0.0629675 | − | 0.998016i | \(-0.479944\pi\) | ||||
0.0629675 | + | 0.998016i | \(0.479944\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.323826 | + | 0.385920i | 0.0285113 | + | 0.0339784i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.61721 | − | 7.99724i | 0.403408 | − | 0.698722i | −0.590727 | − | 0.806871i | \(-0.701159\pi\) |
0.994135 | + | 0.108149i | \(0.0344923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.97178 | + | 6.87933i | 0.344397 | + | 0.596513i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.76481i | − | 0.237957i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.975185 | + | 1.68907i | 0.0833157 | + | 0.144307i | 0.904672 | − | 0.426108i | \(-0.140116\pi\) |
−0.821357 | + | 0.570415i | \(0.806782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.05556 | − | 8.75649i | 0.428807 | − | 0.742715i | −0.567961 | − | 0.823056i | \(-0.692267\pi\) |
0.996767 | + | 0.0803403i | \(0.0256007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.474308 | + | 0.565258i | 0.0399439 | + | 0.0476033i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.59627 | −0.384359 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.97771 | −0.330331 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.592396 | − | 1.62760i | 0.0488600 | − | 0.134242i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.81567 | + | 11.8051i | −0.558362 | + | 0.967111i | 0.439272 | + | 0.898354i | \(0.355237\pi\) |
−0.997633 | + | 0.0687567i | \(0.978097\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.92262 | + | 8.52623i | 0.400597 | + | 0.693854i | 0.993798 | − | 0.111200i | \(-0.0354694\pi\) |
−0.593201 | + | 0.805054i | \(0.702136\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.29813 | − | 0.836452i | 0.185793 | − | 0.0676231i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.609470 | − | 1.05563i | −0.0489538 | − | 0.0847905i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.58765 | + | 13.1422i | −0.605560 | + | 1.04886i | 0.386402 | + | 0.922330i | \(0.373718\pi\) |
−0.991963 | + | 0.126531i | \(0.959616\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.40760 | + | 0.424525i | −0.190935 | + | 0.0336671i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.80066 | 0.535967 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.5699 | −1.68948 | −0.844741 | − | 0.535176i | \(-0.820245\pi\) | ||||
−0.844741 | + | 0.535176i | \(0.820245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.02094 | − | 0.356347i | 0.157330 | − | 0.0277416i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.97565 | + | 17.2783i | −0.771939 | + | 1.33704i | 0.164560 | + | 0.986367i | \(0.447380\pi\) |
−0.936499 | + | 0.350671i | \(0.885954\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.36959 | + | 7.56834i | 0.336122 | + | 0.582180i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.3935 | + | 8.15058i | −1.71248 | + | 0.623290i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.515015 | − | 0.892032i | −0.0391558 | − | 0.0678199i | 0.845783 | − | 0.533527i | \(-0.179134\pi\) |
−0.884939 | + | 0.465707i | \(0.845800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.35844 | − | 4.08494i | 0.178281 | − | 0.308792i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.03256 | − | 5.58440i | 0.152776 | − | 0.419749i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.4962 | 1.98042 | 0.990209 | − | 0.139593i | \(-0.0445794\pi\) | ||||
0.990209 | + | 0.139593i | \(0.0445794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.35504 | −0.100719 | −0.0503596 | − | 0.998731i | \(-0.516037\pi\) | ||||
−0.0503596 | + | 0.998731i | \(0.516037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6630 | − | 13.8994i | −0.862152 | − | 1.02747i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.73783 | − | 4.74205i | 0.201289 | − | 0.348643i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.907604 | + | 1.57202i | 0.0663706 | + | 0.114957i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.10354 | + | 5.37549i | 0.224564 | + | 0.388957i | 0.956189 | − | 0.292751i | \(-0.0945708\pi\) |
−0.731624 | + | 0.681708i | \(0.761237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.34864 | − | 5.80002i | 0.241040 | − | 0.417494i | −0.719971 | − | 0.694005i | \(-0.755845\pi\) |
0.961011 | + | 0.276510i | \(0.0891780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.22281 | + | 1.45729i | 0.0875673 | + | 0.104359i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.0223 | −1.35528 | −0.677641 | − | 0.735393i | \(-0.736998\pi\) | ||||
−0.677641 | + | 0.735393i | \(0.736998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.99319 | 0.566622 | 0.283311 | − | 0.959028i | \(-0.408567\pi\) | ||||
0.283311 | + | 0.959028i | \(0.408567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.49067 | + | 6.84305i | −0.175678 | + | 0.482672i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.73783 | − | 6.47410i | 0.262344 | − | 0.454393i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.690722 | + | 1.19637i | 0.0482421 | + | 0.0835578i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.54277 | + | 20.0920i | −0.246239 | + | 1.39649i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.84389 | − | 15.3181i | −0.611745 | − | 1.05957i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3648 | − | 19.6845i | 0.782388 | − | 1.35514i | −0.148160 | − | 0.988963i | \(-0.547335\pi\) |
0.930547 | − | 0.366172i | \(-0.119332\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.6163 | + | 3.63522i | −1.41261 | + | 0.249081i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.154763 | 0.0105548 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.29086 | 0.155514 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.5077 | − | 2.73443i | 1.04792 | − | 0.184776i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.841367 | + | 1.45729i | −0.0565964 | + | 0.0980279i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2442 | + | 17.7435i | 0.686004 | + | 1.18819i | 0.973120 | + | 0.230298i | \(0.0739700\pi\) |
−0.287116 | + | 0.957896i | \(0.592697\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.8400 | + | 9.09586i | 0.722668 | + | 0.606391i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.81655 | − | 10.0746i | −0.386058 | − | 0.668672i | 0.605857 | − | 0.795573i | \(-0.292830\pi\) |
−0.991915 | + | 0.126901i | \(0.959497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.20233 | + | 2.08250i | −0.0794524 | + | 0.137616i | −0.903014 | − | 0.429612i | \(-0.858651\pi\) |
0.823561 | + | 0.567227i | \(0.191984\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.31908 | + | 3.62414i | −0.0867890 | + | 0.238451i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.6313 | −1.08956 | −0.544778 | − | 0.838580i | \(-0.683386\pi\) | ||||
−0.544778 | + | 0.838580i | \(0.683386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.226682 | 0.0147871 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.30675 | + | 9.89960i | 0.539581 | + | 0.643048i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3229 | + | 23.0760i | −0.861790 | + | 1.49266i | 0.00840979 | + | 0.999965i | \(0.497323\pi\) |
−0.870200 | + | 0.492699i | \(0.836010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.27972 | + | 10.8768i | 0.404512 | + | 0.700635i | 0.994265 | − | 0.106949i | \(-0.0341081\pi\) |
−0.589753 | + | 0.807584i | \(0.700775\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0201 | + | 11.9415i | −0.642788 | + | 0.766044i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.266044 | − | 0.460802i | −0.0169970 | − | 0.0294396i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.19846 | − | 14.2002i | 0.521656 | − | 0.903534i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.5116 | − | 23.2530i | −1.23650 | − | 1.47360i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7023 | 1.18048 | 0.590240 | − | 0.807228i | \(-0.299033\pi\) | ||||
0.590240 | + | 0.807228i | \(0.299033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.1429 | −0.952026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.256959 | − | 0.705990i | 0.0160914 | − | 0.0442108i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.57398 | − | 11.3865i | 0.410073 | − | 0.710268i | −0.584824 | − | 0.811160i | \(-0.698836\pi\) |
0.994897 | + | 0.100892i | \(0.0321697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.14543 | + | 8.91215i | 0.319721 | + | 0.553774i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1800 | + | 14.4158i | 1.06342 | + | 0.892314i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.4474 | − | 19.8275i | −0.705879 | − | 1.22262i | −0.966373 | − | 0.257143i | \(-0.917219\pi\) |
0.260494 | − | 0.965475i | \(-0.416114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.375515 | + | 0.650411i | −0.0230677 | + | 0.0399544i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.57919 | − | 0.631108i | 0.219043 | − | 0.0386232i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.3432 | −1.60617 | −0.803086 | − | 0.595863i | \(-0.796810\pi\) | ||||
−0.803086 | + | 0.595863i | \(0.796810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7246 | 0.651474 | 0.325737 | − | 0.945460i | \(-0.394388\pi\) | ||||
0.325737 | + | 0.945460i | \(0.394388\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.52094 | + | 0.620838i | −0.213097 | + | 0.0375748i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.25150 | + | 9.09586i | −0.316677 | + | 0.548501i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.49138 | + | 4.31520i | 0.149693 | + | 0.259275i | 0.931114 | − | 0.364729i | \(-0.118838\pi\) |
−0.781421 | + | 0.624004i | \(0.785505\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.19341 | + | 6.76817i | −0.0714476 | + | 0.405200i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.30928 | + | 7.46389i | 0.257070 | + | 0.445258i | 0.965456 | − | 0.260567i | \(-0.0839096\pi\) |
−0.708386 | + | 0.705826i | \(0.750576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.18227 | − | 2.04775i | 0.0702784 | − | 0.121726i | −0.828745 | − | 0.559627i | \(-0.810945\pi\) |
0.899023 | + | 0.437901i | \(0.144278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.50387 | + | 6.87933i | −0.148316 | + | 0.407496i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.59627 | −0.153253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3354 | −0.960908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.2314 | + | 15.7686i | 0.775640 | + | 0.924372i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.73783 | − | 15.1344i | 0.510469 | − | 0.884159i | −0.489457 | − | 0.872027i | \(-0.662805\pi\) |
0.999926 | − | 0.0121313i | \(-0.00386162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.912818 | − | 1.58105i | −0.0531463 | − | 0.0920522i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.0201 | − | 5.78509i | −0.581423 | − | 0.335685i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.01889 | − | 12.1571i | −0.405913 | − | 0.703061i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.145430 | + | 0.251892i | −0.00838243 | + | 0.0145188i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.21348 | + | 9.78844i | 0.471852 | + | 0.562331i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.57398 | −0.319165 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6928 | 1.46637 | 0.733184 | − | 0.680030i | \(-0.238033\pi\) | ||||
0.733184 | + | 0.680030i | \(0.238033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.78652 | + | 10.4034i | −0.215408 | + | 0.591828i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.91400 | − | 6.77925i | 0.221943 | − | 0.384416i | −0.733455 | − | 0.679738i | \(-0.762094\pi\) |
0.955398 | + | 0.295322i | \(0.0954269\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.51620 | + | 16.4825i | 0.537887 | + | 0.931648i | 0.999018 | + | 0.0443156i | \(0.0141107\pi\) |
−0.461130 | + | 0.887332i | \(0.652556\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.50000 | − | 0.545955i | 0.0845154 | − | 0.0307611i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.5890 | + | 27.0009i | 0.875565 | + | 1.51652i | 0.856160 | + | 0.516711i | \(0.172844\pi\) |
0.0194055 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.32295 | + | 14.4158i | −0.465996 | + | 0.807128i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0334331 | − | 0.00589515i | 0.00186605 | − | 0.000329035i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.47565 | −0.360315 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.73648 | −0.540083 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.13041 | + | 0.375650i | −0.117812 | + | 0.0207735i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.213011 | + | 0.368946i | −0.0117437 | + | 0.0203406i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4427 | − | 23.2834i | −0.738877 | − | 1.27977i | −0.953001 | − | 0.302966i | \(-0.902023\pi\) |
0.214125 | − | 0.976806i | \(-0.431310\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −29.0107 | + | 10.5590i | −1.58978 | + | 0.578632i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.11856 | + | 1.93739i | 0.0611132 | + | 0.105851i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.08512 | − | 5.34359i | 0.168057 | − | 0.291084i | −0.769679 | − | 0.638431i | \(-0.779584\pi\) |
0.937737 | + | 0.347347i | \(0.112917\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.23442 | + | 19.8764i | −0.392920 | + | 1.07954i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.10101 | −0.276235 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.02869 | + | 4.80120i | 0.216897 | + | 0.258488i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.06330 | − | 12.2340i | 0.379178 | − | 0.656755i | −0.611765 | − | 0.791040i | \(-0.709540\pi\) |
0.990943 | + | 0.134284i | \(0.0428735\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3628 | − | 21.4130i | −0.661764 | − | 1.14621i | −0.980152 | − | 0.198249i | \(-0.936475\pi\) |
0.318387 | − | 0.947961i | \(-0.396859\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 10.7258i | − | 0.572500i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.55097 | − | 16.5428i | −0.508347 | − | 0.880483i | −0.999953 | − | 0.00966532i | \(-0.996923\pi\) |
0.491606 | − | 0.870818i | \(-0.336410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.21554 | + | 5.56947i | −0.170663 | + | 0.295597i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.907604 | + | 1.08164i | 0.0480355 | + | 0.0572465i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.3233 | −1.01984 | −0.509921 | − | 0.860221i | \(-0.670325\pi\) | ||||
−0.509921 | + | 0.860221i | \(0.670325\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.1002 | 2.32106 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.57919 | + | 9.83375i | −0.187859 | + | 0.516138i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.41875 | − | 4.18939i | 0.126603 | − | 0.219283i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0180 | + | 29.4761i | 0.888333 | + | 1.53864i | 0.841845 | + | 0.539719i | \(0.181469\pi\) |
0.0464873 | + | 0.998919i | \(0.485197\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.35251 | − | 7.67047i | 0.0704089 | − | 0.399309i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.705737 | − | 1.22237i | −0.0366400 | − | 0.0634624i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5765 | − | 18.3190i | 0.547631 | − | 0.948524i | −0.450806 | − | 0.892622i | \(-0.648863\pi\) |
0.998436 | − | 0.0559019i | \(-0.0178034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.81908 | − | 1.55504i | 0.455415 | − | 0.0803020i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.4311 | −0.794741 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4757 | −0.589465 | −0.294732 | − | 0.955580i | \(-0.595230\pi\) | ||||
−0.294732 | + | 0.955580i | \(0.595230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.42081 | + | 0.426854i | −0.124022 | + | 0.0218684i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.41400 | − | 4.18117i | 0.123350 | − | 0.213648i | −0.797737 | − | 0.603006i | \(-0.793970\pi\) |
0.921087 | + | 0.389358i | \(0.127303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.592396 | + | 1.02606i | 0.0301913 | + | 0.0522929i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.668434 | − | 0.560882i | −0.0339784 | − | 0.0285113i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.01367 | − | 13.8801i | −0.406309 | − | 0.703748i | 0.588164 | − | 0.808742i | \(-0.299851\pi\) |
−0.994473 | + | 0.104994i | \(0.966518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.77197 | + | 4.80120i | −0.140185 | + | 0.242807i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.47044 | + | 15.0299i | −0.275947 | + | 0.758158i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.96997 | 0.199751 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.5827 | 1.78584 | 0.892921 | − | 0.450213i | \(-0.148652\pi\) | ||||
0.892921 | + | 0.450213i | \(0.148652\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.84389 | − | 10.5397i | −0.442748 | − | 0.527647i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.0792 | + | 24.3859i | −0.703081 | + | 1.21777i | 0.264298 | + | 0.964441i | \(0.414860\pi\) |
−0.967380 | + | 0.253332i | \(0.918474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.36437 | − | 4.09521i | −0.117778 | − | 0.203997i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.831566 | + | 4.71605i | 0.0413209 | + | 0.234342i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.4572 | − | 19.8445i | −0.567914 | − | 0.983656i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3969 | − | 23.2042i | 0.662435 | − | 1.14737i | −0.317538 | − | 0.948245i | \(-0.602856\pi\) |
0.979974 | − | 0.199126i | \(-0.0638104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.17143 | − | 2.58781i | −0.107109 | − | 0.127647i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.43107 | 0.168832 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.32501 | −0.457747 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.98979 | + | 16.4568i | −0.293321 | + | 0.805893i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0608 | + | 17.4258i | −0.491501 | + | 0.851305i | −0.999952 | − | 0.00978617i | \(-0.996885\pi\) |
0.508451 | + | 0.861091i | \(0.330218\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.52616 | + | 7.83954i | 0.220591 | + | 0.382076i | 0.954988 | − | 0.296645i | \(-0.0958679\pi\) |
−0.734396 | + | 0.678721i | \(0.762535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.979055 | − | 0.821525i | −0.0476033 | − | 0.0399439i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.92262 | + | 3.33007i | 0.0932607 | + | 0.161532i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.23783 | − | 9.07218i | 0.253476 | − | 0.439034i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.84002 | − | 1.38241i | 0.378520 | − | 0.0667433i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.1952 | −0.924601 | −0.462301 | − | 0.886723i | \(-0.652976\pi\) | ||||
−0.462301 | + | 0.886723i | \(0.652976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5080 | −1.22584 | −0.612919 | − | 0.790146i | \(-0.710005\pi\) | ||||
−0.612919 | + | 0.790146i | \(0.710005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.78493 | − | 1.19637i | 0.325312 | − | 0.0573614i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.0107 | − | 46.7840i | 1.29210 | − | 2.23798i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.45471 | + | 16.3760i | 0.451249 | + | 0.781585i | 0.998464 | − | 0.0554064i | \(-0.0176455\pi\) |
−0.547215 | + | 0.836992i | \(0.684312\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.520945 | + | 2.95442i | −0.0248069 | + | 0.140687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3131 | − | 17.8629i | −0.489992 | − | 0.848692i | 0.509941 | − | 0.860209i | \(-0.329667\pi\) |
−0.999934 | + | 0.0115174i | \(0.996334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.558248 | − | 0.966914i | 0.0264635 | − | 0.0458361i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.07516 | − | 22.1863i | 0.381942 | − | 1.04938i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.3327 | 1.62026 | 0.810131 | − | 0.586248i | \(-0.199396\pi\) | ||||
0.810131 | + | 0.586248i | \(0.199396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.78106 | 0.272219 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.9611 | − | 13.0629i | −0.514998 | − | 0.613750i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.549163 | + | 0.951178i | −0.0257452 | + | 0.0445919i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.922152 | + | 1.59721i | 0.0431364 | + | 0.0747145i | 0.886788 | − | 0.462177i | \(-0.152932\pi\) |
−0.843651 | + | 0.536892i | \(0.819598\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.66843 | + | 2.11797i | −0.171228 | + | 0.0988584i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.5582 | + | 28.6797i | 0.771194 | + | 1.33575i | 0.936909 | + | 0.349574i | \(0.113674\pi\) |
−0.165714 | + | 0.986174i | \(0.552993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.14631 | − | 3.71751i | 0.0997473 | − | 0.172767i | −0.811833 | − | 0.583890i | \(-0.801530\pi\) |
0.911580 | + | 0.411123i | \(0.134863\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.35710 | + | 1.61732i | 0.0629338 | + | 0.0750016i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.7347 | 1.46851 | 0.734254 | − | 0.678875i | \(-0.237532\pi\) | ||||
0.734254 | + | 0.678875i | \(0.237532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.20439 | −0.194141 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.98979 | − | 24.6992i | 0.414228 | − | 1.13808i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.323826 | − | 0.560882i | 0.0148895 | − | 0.0257894i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7344 | − | 32.4490i | −0.859594 | − | 1.48886i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.97906 | − | 1.44826i | 0.182188 | − | 0.0663112i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.54845 | + | 16.5384i | 0.436280 | + | 0.755659i | 0.997399 | − | 0.0720762i | \(-0.0229625\pi\) |
−0.561119 | + | 0.827735i | \(0.689629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.6211 | − | 18.3963i | 0.484280 | − | 0.838797i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.6001 | + | 2.04542i | −0.527825 | + | 0.0930697i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.32358 | 0.287139 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.40198 | −0.0635297 | −0.0317649 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317649 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.7925 | − | 6.48751i | 1.66381 | − | 0.293375i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4586 | − | 18.1148i | 0.471989 | − | 0.817509i | −0.527497 | − | 0.849557i | \(-0.676870\pi\) |
0.999486 | + | 0.0320477i | \(0.0102029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.04710 | + | 5.27774i | 0.137235 | + | 0.237697i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.34002 | + | 1.21567i | −0.150123 | + | 0.0546402i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.04323 | − | 10.4672i | −0.271076 | − | 0.469518i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3105 | − | 19.5903i | 0.506326 | − | 0.876982i | −0.493647 | − | 0.869662i | \(-0.664337\pi\) |
0.999973 | − | 0.00731977i | \(-0.00232998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.8191 | − | 32.4726i | 0.528037 | − | 1.45077i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.2327 | −0.946718 | −0.473359 | − | 0.880870i | \(-0.656959\pi\) | ||||
−0.473359 | + | 0.880870i | \(0.656959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.92539 | 0.174678 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.72967 | − | 11.5954i | −0.432110 | − | 0.514969i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.94697 | − | 5.10430i | 0.130622 | − | 0.226244i | −0.793295 | − | 0.608838i | \(-0.791636\pi\) |
0.923917 | + | 0.382594i | \(0.124969\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.54576 | + | 7.87349i | 0.201093 | + | 0.348303i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.7460 | − | 20.6380i | 1.57823 | − | 0.911189i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.70052 | + | 2.94539i | 0.0749340 | + | 0.129789i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.474308 | − | 0.821525i | 0.0208600 | − | 0.0361306i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.14677 | + | 1.36667i | 0.0503378 | + | 0.0599902i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.5039 | 1.86213 | 0.931065 | − | 0.364852i | \(-0.118881\pi\) | ||||
0.931065 | + | 0.364852i | \(0.118881\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.7716 | −1.03946 | −0.519729 | − | 0.854331i | \(-0.673967\pi\) | ||||
−0.519729 | + | 0.854331i | \(0.673967\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.79426 | + | 7.67717i | −0.121952 | + | 0.335059i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.933763 | + | 1.61732i | −0.0406753 | + | 0.0704518i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6245 | − | 20.1342i | −0.505412 | − | 0.875400i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.78740 | + | 10.1368i | −0.0775665 | + | 0.439902i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.67958 | + | 4.64117i | 0.116065 | + | 0.201031i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.00521457 | − | 0.00903189i | 0.000225445 | − | 0.000390483i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −45.1955 | + | 7.96919i | −1.95033 | + | 0.343896i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.22668 | −0.0959100 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.6560 | 0.974058 | 0.487029 | − | 0.873386i | \(-0.338081\pi\) | ||||
0.487029 | + | 0.873386i | \(0.338081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.31134 | − | 0.407551i | 0.0991890 | − | 0.0174897i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.332282 | + | 0.575529i | −0.0142334 | + | 0.0246529i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.13176 | + | 3.69232i | 0.0911474 | + | 0.157872i | 0.907994 | − | 0.418983i | \(-0.137613\pi\) |
−0.816847 | + | 0.576855i | \(0.804280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.0744 | + | 20.2009i | 1.02747 | + | 0.862152i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.6917 | − | 51.4275i | −1.26491 | − | 2.19088i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.73055 | + | 6.46151i | −0.158639 | + | 0.274771i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.24376 | + | 8.91215i | −0.137690 | + | 0.378300i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.90404 | −0.123048 | −0.0615240 | − | 0.998106i | \(-0.519596\pi\) | ||||
−0.0615240 | + | 0.998106i | \(0.519596\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.600385 | 0.0253936 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.02094 | − | 2.40847i | −0.0853243 | − | 0.101686i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.16978 | + | 8.95432i | −0.217880 | + | 0.377380i | −0.954160 | − | 0.299298i | \(-0.903248\pi\) |
0.736280 | + | 0.676678i | \(0.236581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.24897 | + | 5.62738i | 0.136685 | + | 0.236746i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.45723 | − | 3.07818i | −0.355170 | − | 0.129271i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.3530 | + | 30.0562i | 0.727475 | + | 1.26002i | 0.957947 | + | 0.286944i | \(0.0926395\pi\) |
−0.230473 | + | 0.973079i | \(0.574027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2135 | + | 36.7428i | −0.887756 | + | 1.53764i | −0.0452350 | + | 0.998976i | \(0.514404\pi\) |
−0.842521 | + | 0.538663i | \(0.818930\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.91060 | − | 8.23573i | −0.288694 | − | 0.344052i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.0779 | −1.33774 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7811 | 0.990018 | 0.495009 | − | 0.868888i | \(-0.335165\pi\) | ||||
0.495009 | + | 0.868888i | \(0.335165\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.96744 | + | 10.9005i | −0.164881 | + | 0.453008i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.76264 | − | 15.1773i | 0.363536 | − | 0.629662i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.57145 | + | 2.72183i | 0.0650829 | + | 0.112727i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.52410 | − | 2.11797i | −0.104359 | − | 0.0875673i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.10560 | − | 10.5752i | −0.252005 | − | 0.436486i | 0.712073 | − | 0.702106i | \(-0.247757\pi\) |
−0.964078 | + | 0.265620i | \(0.914423\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.09879 | − | 15.7596i | 0.374909 | − | 0.649362i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.4470 | − | 5.72129i | 1.33469 | − | 0.235342i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.2139 | −0.583694 | −0.291847 | − | 0.956465i | \(-0.594270\pi\) | ||||
−0.291847 | + | 0.956465i | \(0.594270\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.433763 | 0.0177825 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.6343 | + | 2.40409i | −0.558014 | + | 0.0983930i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.34730 | − | 16.1900i | 0.381920 | − | 0.661505i | −0.609417 | − | 0.792850i | \(-0.708596\pi\) |
0.991337 | + | 0.131345i | \(0.0419296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.7096 | − | 34.1380i | −0.803972 | − | 1.39252i | −0.916983 | − | 0.398926i | \(-0.869383\pi\) |
0.113011 | − | 0.993594i | \(-0.463950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.19026 | − | 12.4216i | 0.0891941 | − | 0.505845i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.60741 | + | 2.78412i | 0.0653506 | + | 0.113190i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.1682 | + | 26.2721i | −0.615658 | + | 1.06635i | 0.374611 | + | 0.927182i | \(0.377776\pi\) |
−0.990269 | + | 0.139168i | \(0.955557\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.42855 | + | 12.1673i | −0.179454 | + | 0.493045i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.879385 | 0.0355761 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.91622 | 0.198564 | 0.0992822 | − | 0.995059i | \(-0.468345\pi\) | ||||
0.0992822 | + | 0.995059i | \(0.468345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.53802 | − | 1.83294i | −0.0620189 | − | 0.0739112i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.9440 | + | 27.6159i | −0.641882 | + | 1.11177i | 0.343130 | + | 0.939288i | \(0.388513\pi\) |
−0.985012 | + | 0.172485i | \(0.944820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.109470 | + | 0.189608i | 0.00439999 | + | 0.00762100i | 0.868217 | − | 0.496185i | \(-0.165266\pi\) |
−0.863817 | + | 0.503806i | \(0.831933\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 35.3373i | − | 1.41804i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.04916 | + | 1.81720i | 0.0420338 | + | 0.0728047i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4167 | + | 18.0422i | −0.416668 | + | 0.721689i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.6925 | + | 23.4686i | 0.786444 | + | 0.937247i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.38919 | −0.334499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.1685 | −0.882514 | −0.441257 | − | 0.897381i | \(-0.645467\pi\) | ||||
−0.441257 | + | 0.897381i | \(0.645467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.4650 | + | 36.9947i | −0.535185 | + | 1.47041i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.377574 | + | 0.653978i | −0.0149836 | + | 0.0259523i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.03209 | − | 1.78763i | −0.0408929 | − | 0.0708285i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.0727 | − | 12.4014i | 1.34789 | − | 0.490594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.4996 | + | 26.8461i | 0.612197 | + | 1.06036i | 0.990869 | + | 0.134825i | \(0.0430474\pi\) |
−0.378672 | + | 0.925531i | \(0.623619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6591 | + | 37.5147i | −0.854152 | + | 1.47943i | 0.0232784 | + | 0.999729i | \(0.492590\pi\) |
−0.877430 | + | 0.479705i | \(0.840744\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.263985 | + | 0.0465477i | −0.0103944 | + | 0.00183281i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.8658 | 0.977574 | 0.488787 | − | 0.872403i | \(-0.337439\pi\) | ||||
0.488787 | + | 0.872403i | \(0.337439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.63991 | −0.299893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.90760 | + | 0.689016i | −0.153151 | + | 0.0270047i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.8883 | + | 18.8591i | −0.426092 | + | 0.738014i | −0.996522 | − | 0.0833330i | \(-0.973443\pi\) |
0.570429 | + | 0.821347i | \(0.306777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.45677 | + | 4.25524i | 0.0959938 | + | 0.166266i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.6297 | + | 9.32845i | −0.999910 | + | 0.363937i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.6177 | + | 35.7109i | 0.803151 | + | 1.39110i | 0.917532 | + | 0.397661i | \(0.130178\pi\) |
−0.114382 | + | 0.993437i | \(0.536489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.6959 | + | 20.2580i | −0.454919 | + | 0.787943i | −0.998684 | − | 0.0512948i | \(-0.983665\pi\) |
0.543764 | + | 0.839238i | \(0.316999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.996845 | − | 2.73881i | 0.0387142 | − | 0.106367i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.22668 | −0.163904 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.8394 | −1.96851 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.8106 | − | 27.1846i | −0.881910 | − | 1.05102i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.6630 | + | 20.2009i | −0.450244 | + | 0.779845i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.22621 | + | 3.85592i | 0.0858143 | + | 0.148635i | 0.905738 | − | 0.423838i | \(-0.139317\pi\) |
−0.819924 | + | 0.572473i | \(0.805984\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.2260 | − | 12.2548i | −0.816988 | − | 0.471688i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6172 | + | 37.4421i | 0.830817 | + | 1.43902i | 0.897391 | + | 0.441236i | \(0.145460\pi\) |
−0.0665744 | + | 0.997781i | \(0.521207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.94222 | + | 10.2922i | −0.228041 | + | 0.394979i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.9516 | + | 15.4351i | 0.496307 | + | 0.591475i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.79797 | 0.0687975 | 0.0343987 | − | 0.999408i | \(-0.489048\pi\) | ||||
0.0343987 | + | 0.999408i | \(0.489048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.03777 | −0.0396512 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.42452 | − | 3.91382i | 0.0543487 | − | 0.149322i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.45677 | + | 2.52319i | −0.0554984 | + | 0.0961260i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.78833 | + | 4.82953i | 0.106073 | + | 0.183724i | 0.914176 | − | 0.405317i | \(-0.132839\pi\) |
−0.808103 | + | 0.589041i | \(0.799506\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.15998 | − | 6.57856i | 0.0440639 | − | 0.249899i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.69001 | + | 4.65923i | 0.102038 | + | 0.176735i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.05825 | − | 1.83294i | 0.0400840 | − | 0.0694275i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.3687 | − | 5.00217i | 1.07300 | − | 0.189199i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.3737 | −0.429579 | −0.214789 | − | 0.976660i | \(-0.568907\pi\) | ||||
−0.214789 | + | 0.976660i | \(0.568907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.7461 | 3.08311 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.386659 | + | 0.0681784i | −0.0145624 | + | 0.00256775i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.68866 | + | 6.38895i | −0.138726 | + | 0.240281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.2053 | − | 40.1928i | −0.871494 | − | 1.50947i | −0.860451 | − | 0.509533i | \(-0.829818\pi\) |
−0.0110435 | − | 0.999939i | \(-0.503515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.1466 | − | 14.3877i | −0.643048 | − | 0.539581i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.78968 | − | 13.4921i | −0.291726 | − | 0.505284i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.22281 | − | 2.11797i | 0.0457305 | − | 0.0792076i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.7849 | − | 43.3687i | 0.589499 | − | 1.61964i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.6878 | 1.10717 | 0.553584 | − | 0.832793i | \(-0.313260\pi\) | ||||
0.553584 | + | 0.832793i | \(0.313260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.39187 | −0.238046 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.9829 | − | 16.6642i | −0.520031 | − | 0.619748i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.6309 | + | 30.5376i | −0.654795 | + | 1.13414i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.7904 | − | 25.6177i | −0.548545 | − | 0.950108i | −0.998375 | − | 0.0569937i | \(-0.981848\pi\) |
0.449829 | − | 0.893115i | \(-0.351485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.118555 | − | 0.205344i | −0.00438493 | − | 0.00759492i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.31790 | − | 4.01471i | 0.0856134 | − | 0.148287i | −0.820039 | − | 0.572308i | \(-0.806048\pi\) |
0.905652 | + | 0.424021i | \(0.139382\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.592396 | + | 0.705990i | 0.0218509 | + | 0.0260408i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.36184 | 0.344848 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.3492 | −1.15320 | −0.576599 | − | 0.817027i | \(-0.695620\pi\) | ||||
−0.576599 | + | 0.817027i | \(0.695620\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.71348 | + | 26.6876i | −0.356834 | + | 0.980392i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.9183 | + | 34.4996i | −0.730733 | + | 1.26567i | 0.225837 | + | 0.974165i | \(0.427488\pi\) |
−0.956570 | + | 0.291502i | \(0.905845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.62654 | − | 6.28136i | −0.132866 | − | 0.230131i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.2754 | + | 33.7951i | 1.47360 | + | 1.23650i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.00980018 | + | 0.0169744i | 0.000358091 | + | 0.000620231i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.20115 | + | 7.27661i | −0.153302 | + | 0.265527i | −0.932440 | − | 0.361326i | \(-0.882324\pi\) |
0.779137 | + | 0.626853i | \(0.215657\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.9013 | + | 5.62505i | −1.16255 | + | 0.204988i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.23854 | −0.190650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9299 | −1.26955 | −0.634775 | − | 0.772697i | \(-0.718907\pi\) | ||||
−0.634775 | + | 0.772697i | \(0.718907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.8298 | − | 4.55449i | 0.937563 | − | 0.165318i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.01279 | + | 10.4145i | −0.217964 | + | 0.377524i | −0.954185 | − | 0.299216i | \(-0.903275\pi\) |
0.736222 | + | 0.676740i | \(0.236608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.624485 | − | 1.08164i | −0.0226079 | − | 0.0391580i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.225966 | + | 1.28152i | −0.00816983 | + | 0.0463334i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.54117 | − | 6.13349i | −0.127864 | − | 0.221468i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.1695 | + | 45.3270i | −0.943697 | + | 1.63453i | −0.185359 | + | 0.982671i | \(0.559345\pi\) |
−0.758339 | + | 0.651861i | \(0.773989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.78880 | + | 21.3996i | −0.280507 | + | 0.770686i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.2181 | 1.37461 | 0.687305 | − | 0.726369i | \(-0.258794\pi\) | ||||
0.687305 | + | 0.726369i | \(0.258794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.8057 | −0.388153 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.4572 | − | 13.6542i | −0.411026 | − | 0.489842i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.3118 | + | 17.8606i | −0.369459 | + | 0.639921i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4564 | + | 23.3071i | 0.481506 | + | 0.833993i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −33.6404 | − | 19.4223i | −1.20221 | − | 0.694097i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.03730 | − | 6.99281i | −0.144098 | − | 0.249584i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4809 | + | 33.7419i | −0.694418 | + | 1.20277i | 0.275959 | + | 0.961170i | \(0.411005\pi\) |
−0.970377 | + | 0.241598i | \(0.922329\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.4898 | + | 30.3775i | 0.907461 | + | 1.08147i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.2121 | −0.434213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.6236 | −0.767877 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.444907 | − | 1.22237i | 0.0157792 | − | 0.0433531i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4863 | − | 21.6270i | 0.442288 | − | 0.766066i | −0.555570 | − | 0.831469i | \(-0.687500\pi\) |
0.997859 | + | 0.0654034i | \(0.0208334\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.173648 | − | 0.300767i | −0.00614323 | − | 0.0106404i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.91534 | + | 2.15301i | −0.209008 | + | 0.0760728i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.1220 | − | 17.5317i | −0.357196 | − | 0.618682i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.80928 | + | 3.13376i | −0.0637687 | + | 0.110451i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.9345 | − | 7.92317i | 1.58177 | − | 0.278909i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.21450 | −0.218490 | −0.109245 | − | 0.994015i | \(-0.534843\pi\) | ||||
−0.109245 | + | 0.994015i | \(0.534843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.5689 | 1.03831 | 0.519153 | − | 0.854682i | \(-0.326248\pi\) | ||||
0.519153 | + | 0.854682i | \(0.326248\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2934 | + | 3.22562i | −0.641577 | + | 0.113127i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.73854 | − | 9.93944i | 0.201012 | − | 0.348164i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.15523 | + | 2.00092i | 0.0404164 | + | 0.0700032i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.81908 | − | 2.11797i | 0.203335 | − | 0.0740079i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.10788 | + | 15.7753i | 0.317867 | + | 0.550562i | 0.980043 | − | 0.198787i | \(-0.0637001\pi\) |
−0.662176 | + | 0.749349i | \(0.730367\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.7939 | + | 22.1596i | −0.445966 | + | 0.772435i | −0.998119 | − | 0.0613074i | \(-0.980473\pi\) |
0.552153 | + | 0.833743i | \(0.313806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.22193 | − | 17.0946i | 0.216620 | − | 0.595158i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.3432 | 1.12468 | 0.562341 | − | 0.826905i | \(-0.309901\pi\) | ||||
0.562341 | + | 0.826905i | \(0.309901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7314 | 0.476912 | 0.238456 | − | 0.971153i | \(-0.423359\pi\) | ||||
0.238456 | + | 0.971153i | \(0.423359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.54751 | − | 6.61127i | −0.192441 | − | 0.229342i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.407604 | + | 0.705990i | −0.0141226 | + | 0.0244611i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.30793 | − | 9.19361i | −0.183689 | − | 0.318158i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 11.9037i | − | 0.411450i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.5077 | + | 32.0563i | 0.638958 | + | 1.10671i | 0.985662 | + | 0.168733i | \(0.0539676\pi\) |
−0.346704 | + | 0.937975i | \(0.612699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4427 | + | 23.2834i | −0.463541 | + | 0.802876i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.59539 | − | 11.4353i | −0.330483 | − | 0.393854i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.65002 | −0.159965 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.04189 | −0.207602 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.40074 | + | 3.84850i | −0.0480733 | + | 0.132080i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.9923 | − | 60.6085i | 1.19952 | − | 2.07763i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4893 | − | 19.9001i | −0.393387 | − | 0.681366i | 0.599507 | − | 0.800370i | \(-0.295363\pi\) |
−0.992894 | + | 0.119003i | \(0.962030\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.20187 | − | 12.4874i | 0.0753023 | − | 0.427060i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.22328 | + | 3.85083i | 0.0759457 | + | 0.131542i | 0.901497 | − | 0.432785i | \(-0.142469\pi\) |
−0.825551 | + | 0.564327i | \(0.809136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5196 | − | 19.9525i | 0.393044 | − | 0.680772i | −0.599806 | − | 0.800146i | \(-0.704755\pi\) |
0.992849 | + | 0.119374i | \(0.0380888\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.42855 | − | 0.780873i | 0.150925 | − | 0.0266121i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.2395 | 0.723000 | 0.361500 | − | 0.932372i | \(-0.382265\pi\) | ||||
0.361500 | + | 0.932372i | \(0.382265\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.548067 | 0.0186348 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.8640 | − | 4.91317i | 0.946310 | − | 0.166860i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.30675 | − | 14.3877i | 0.281787 | − | 0.488070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.33931 | + | 7.51590i | 0.147032 | + | 0.254667i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.3120 | − | 22.9175i | −0.924372 | − | 0.775640i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.58512 | + | 4.47756i | 0.0873931 | + | 0.151369i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.2237 | − | 40.2247i | 0.784210 | − | 1.35829i | −0.145260 | − | 0.989394i | \(-0.546402\pi\) |
0.929470 | − | 0.368898i | \(-0.120265\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.3525 | + | 28.4433i | −0.349182 | + | 0.959368i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.3301 | 0.617555 | 0.308778 | − | 0.951134i | \(-0.400080\pi\) | ||||
0.308778 | + | 0.951134i | \(0.400080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4894 | 0.487606 | 0.243803 | − | 0.969825i | \(-0.421605\pi\) | ||||
0.243803 | + | 0.969825i | \(0.421605\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.03256 | + | 2.42231i | 0.0683236 | + | 0.0814249i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.49360 | + | 12.9793i | −0.251611 | + | 0.435802i | −0.963969 | − | 0.266013i | \(-0.914294\pi\) |
0.712359 | + | 0.701815i | \(0.247627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.709607 | − | 1.22908i | −0.0237995 | − | 0.0412219i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.8316 | + | 6.85413i | 0.630881 | + | 0.229622i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.69207 | + | 2.93075i | 0.0566228 | + | 0.0980736i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.04916 | + | 12.2095i | −0.235628 | + | 0.408119i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.6288 | + | 18.6257i | 0.521831 | + | 0.621894i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.1257 | −0.571173 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.15064 | 0.0383335 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.172304 | − | 0.473401i | 0.00573392 | − | 0.0157538i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.360500 | − | 0.624404i | 0.0119834 | − | 0.0207559i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0790 | − | 22.6535i | −0.434282 | − | 0.752199i | 0.562955 | − | 0.826488i | \(-0.309665\pi\) |
−0.997237 | + | 0.0742892i | \(0.976331\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.9541 | − | 14.2262i | −0.562331 | − | 0.471852i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.0432 | − | 22.5915i | −0.432142 | − | 0.748491i | 0.564916 | − | 0.825148i | \(-0.308909\pi\) |
−0.997058 | + | 0.0766573i | \(0.975575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.5116 | + | 33.7951i | −0.645740 | + | 1.11845i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.50774 | − | 1.67647i | 0.314316 | − | 0.0554224i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.23442 | −0.304947 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.709141 | −0.0233924 | −0.0116962 | − | 0.999932i | \(-0.503723\pi\) | ||||
−0.0116962 | + | 0.999932i | \(0.503723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.8252 | + | 7.72757i | −1.44409 | + | 0.254632i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4743 | + | 21.6061i | −0.410597 | + | 0.711175i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.2704 | − | 42.0375i | −0.798005 | − | 1.38219i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.32981 | − | 18.8843i | 0.109365 | − | 0.620242i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.0929 | + | 34.8019i | 0.659225 | + | 1.14181i | 0.980816 | + | 0.194933i | \(0.0624490\pi\) |
−0.321591 | + | 0.946879i | \(0.604218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.97178 | − | 6.87933i | 0.130170 | − | 0.225461i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.63728 | + | 12.7408i | −0.151818 | + | 0.417116i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.965852 | −0.0315867 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.5389 | 0.964994 | 0.482497 | − | 0.875898i | \(-0.339730\pi\) | ||||
0.482497 | + | 0.875898i | \(0.339730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.1895 | − | 25.2527i | −0.691495 | − | 0.824091i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.512326 | − | 0.887375i | 0.0167014 | − | 0.0289276i | −0.857554 | − | 0.514394i | \(-0.828017\pi\) |
0.874255 | + | 0.485466i | \(0.161350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.82816 | + | 15.2908i | 0.287485 | + | 0.497938i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.39440 | + | 1.38241i | −0.0778898 | + | 0.0449697i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.1891 | + | 50.5571i | 0.948519 | + | 1.64288i | 0.748547 | + | 0.663082i | \(0.230752\pi\) |
0.199973 | + | 0.979801i | \(0.435915\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.38326 | − | 16.2523i | 0.304593 | − | 0.527571i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.7117 | − | 41.3678i | −1.12560 | − | 1.34144i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.7743 | −1.09406 | −0.547028 | − | 0.837115i | \(-0.684241\pi\) | ||||
−0.547028 | + | 0.837115i | \(0.684241\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.30272 | −0.106873 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.86097 | − | 27.0928i | 0.318760 | − | 0.875785i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.975185 | − | 1.68907i | 0.0314904 | − | 0.0545429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8760 | + | 22.3019i | 0.415354 | + | 0.719415i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0552549 | + | 0.0201112i | −0.00178057 | + | 0.000648073i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.78177 | + | 3.08612i | 0.0573573 | + | 0.0993458i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.28699 | + | 10.8894i | −0.202176 | + | 0.350179i | −0.949229 | − | 0.314585i | \(-0.898135\pi\) |
0.747053 | + | 0.664764i | \(0.231468\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.0458 | − | 1.94767i | 0.354841 | − | 0.0625680i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.92808 | −0.0939666 | −0.0469833 | − | 0.998896i | \(-0.514961\pi\) | ||||
−0.0469833 | + | 0.998896i | \(0.514961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.1111 | −0.324148 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.6079 | − | 2.92842i | 0.531878 | − | 0.0937844i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.3425 | + | 35.2343i | −0.650816 | + | 1.12725i | 0.332109 | + | 0.943241i | \(0.392240\pi\) |
−0.982925 | + | 0.184005i | \(0.941094\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.33615 | − | 4.04633i | −0.0746637 | − | 0.129321i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.52094 | − | 1.28152i | 0.112415 | − | 0.0409158i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.78446 | + | 4.82283i | 0.0888106 | + | 0.153824i | 0.907009 | − | 0.421112i | \(-0.138360\pi\) |
−0.818198 | + | 0.574936i | \(0.805027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.06077 | − | 8.76552i | 0.161250 | − | 0.279293i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.252374 | − | 0.693392i | 0.00803315 | − | 0.0220709i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.97804 | 0.0628979 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.1307 | −0.988900 | −0.494450 | − | 0.869206i | \(-0.664630\pi\) | ||||
−0.494450 | + | 0.869206i | \(0.664630\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.9326 | + | 35.6723i | 0.949882 | + | 1.13202i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.12654 | + | 3.68328i | −0.0674160 | + | 0.116768i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.2317 | − | 24.6501i | −0.450724 | − | 0.780676i | 0.547708 | − | 0.836670i | \(-0.315501\pi\) |
−0.998431 | + | 0.0559938i | \(0.982167\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 46.3089 | − | 26.7364i | 1.46515 | − | 0.845903i |
(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 | 504.2.r.c.337.1 | yes | 6 | |
3.2 | odd | 2 | 1512.2.r.c.1009.3 | 6 | |||
4.3 | odd | 2 | 1008.2.r.i.337.3 | 6 | |||
9.2 | odd | 6 | 1512.2.r.c.505.3 | 6 | |||
9.4 | even | 3 | 4536.2.a.s.1.3 | 3 | |||
9.5 | odd | 6 | 4536.2.a.v.1.1 | 3 | |||
9.7 | even | 3 | inner | 504.2.r.c.169.1 | ✓ | 6 | |
12.11 | even | 2 | 3024.2.r.h.1009.3 | 6 | |||
36.7 | odd | 6 | 1008.2.r.i.673.3 | 6 | |||
36.11 | even | 6 | 3024.2.r.h.2017.3 | 6 | |||
36.23 | even | 6 | 9072.2.a.cc.1.1 | 3 | |||
36.31 | odd | 6 | 9072.2.a.br.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.c.169.1 | ✓ | 6 | 9.7 | even | 3 | inner | |
504.2.r.c.337.1 | yes | 6 | 1.1 | even | 1 | trivial | |
1008.2.r.i.337.3 | 6 | 4.3 | odd | 2 | |||
1008.2.r.i.673.3 | 6 | 36.7 | odd | 6 | |||
1512.2.r.c.505.3 | 6 | 9.2 | odd | 6 | |||
1512.2.r.c.1009.3 | 6 | 3.2 | odd | 2 | |||
3024.2.r.h.1009.3 | 6 | 12.11 | even | 2 | |||
3024.2.r.h.2017.3 | 6 | 36.11 | even | 6 | |||
4536.2.a.s.1.3 | 3 | 9.4 | even | 3 | |||
4536.2.a.v.1.1 | 3 | 9.5 | odd | 6 | |||
9072.2.a.br.1.3 | 3 | 36.31 | odd | 6 | |||
9072.2.a.cc.1.1 | 3 | 36.23 | even | 6 |