Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(343,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.g (of order \(2\), degree \(1\), 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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.10 | ||
Root | \(-0.0607713 - 1.99908i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.b.343.9 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0607713 | + | 1.99908i | 0.0303857 | + | 0.999538i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.99261 | + | 0.242973i | −0.998153 | + | 0.0607433i | ||||
\(5\) | 5.82257 | 1.16451 | 0.582257 | − | 0.813005i | \(-0.302170\pi\) | ||||
0.582257 | + | 0.813005i | \(0.302170\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.45132i | 0.778760i | 0.921077 | + | 0.389380i | \(0.127311\pi\) | ||||
−0.921077 | + | 0.389380i | \(0.872689\pi\) | |||||||
\(8\) | −0.728358 | − | 7.96677i | −0.0910448 | − | 0.995847i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.353845 | + | 11.6398i | 0.0353845 | + | 1.16398i | ||||
\(11\) | − | 1.60915i | − | 0.146286i | −0.997321 | − | 0.0731431i | \(-0.976697\pi\) | ||
0.997321 | − | 0.0731431i | \(-0.0233030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23.5274 | 1.80980 | 0.904901 | − | 0.425622i | \(-0.139945\pi\) | ||||
0.904901 | + | 0.425622i | \(0.139945\pi\) | |||||||
\(14\) | −10.8976 | + | 0.331284i | −0.778401 | + | 0.0236631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.8819 | − | 1.94019i | 0.992621 | − | 0.121262i | ||||
\(17\) | 5.92676 | 0.348633 | 0.174316 | − | 0.984690i | \(-0.444228\pi\) | ||||
0.174316 | + | 0.984690i | \(0.444228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.35890i | − | 0.229416i | ||||||
\(20\) | −23.2473 | + | 1.41473i | −1.16236 | + | 0.0707364i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.21681 | − | 0.0977900i | 0.146219 | − | 0.00444500i | ||||
\(23\) | − | 26.6121i | − | 1.15705i | −0.815665 | − | 0.578524i | \(-0.803629\pi\) | ||
0.815665 | − | 0.578524i | \(-0.196371\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.90234 | 0.356094 | ||||||||
\(26\) | 1.42979 | + | 47.0331i | 0.0549920 | + | 1.80897i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.32452 | − | 21.7650i | −0.0473044 | − | 0.777322i | ||||
\(29\) | 1.49241 | 0.0514625 | 0.0257313 | − | 0.999669i | \(-0.491809\pi\) | ||||
0.0257313 | + | 0.999669i | \(0.491809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.3933i | 1.01269i | 0.862332 | + | 0.506343i | \(0.169003\pi\) | ||||
−0.862332 | + | 0.506343i | \(0.830997\pi\) | |||||||
\(32\) | 4.84376 | + | 31.6313i | 0.151368 | + | 0.988478i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.360177 | + | 11.8480i | 0.0105934 | + | 0.348472i | ||||
\(35\) | 31.7407i | 0.906877i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.8255 | 0.725015 | 0.362507 | − | 0.931981i | \(-0.381921\pi\) | ||||
0.362507 | + | 0.931981i | \(0.381921\pi\) | |||||||
\(38\) | 8.71377 | − | 0.264896i | 0.229310 | − | 0.00697095i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.24092 | − | 46.3871i | −0.106023 | − | 1.15968i | ||||
\(41\) | 44.0382 | 1.07410 | 0.537051 | − | 0.843550i | \(-0.319538\pi\) | ||||
0.537051 | + | 0.843550i | \(0.319538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.8586i | 0.647875i | 0.946079 | + | 0.323937i | \(0.105007\pi\) | ||||
−0.946079 | + | 0.323937i | \(0.894993\pi\) | |||||||
\(44\) | 0.390980 | + | 6.42471i | 0.00888590 | + | 0.146016i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 53.1996 | − | 1.61725i | 1.15651 | − | 0.0351577i | ||||
\(47\) | 32.5166i | 0.691843i | 0.938264 | + | 0.345921i | \(0.112434\pi\) | ||||
−0.938264 | + | 0.345921i | \(0.887566\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.2831 | 0.393533 | ||||||||
\(50\) | 0.541007 | + | 17.7965i | 0.0108201 | + | 0.355929i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −93.9360 | + | 5.71653i | −1.80646 | + | 0.109933i | ||||
\(53\) | −76.7637 | −1.44837 | −0.724186 | − | 0.689605i | \(-0.757784\pi\) | ||||
−0.724186 | + | 0.689605i | \(0.757784\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.36938i | − | 0.170352i | ||||||
\(56\) | 43.4294 | − | 3.97051i | 0.775526 | − | 0.0709020i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.0906959 | + | 2.98345i | 0.00156372 | + | 0.0514388i | ||||
\(59\) | 33.8895i | 0.574398i | 0.957871 | + | 0.287199i | \(0.0927241\pi\) | ||||
−0.957871 | + | 0.287199i | \(0.907276\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 53.0162 | 0.869118 | 0.434559 | − | 0.900643i | \(-0.356904\pi\) | ||||
0.434559 | + | 0.900643i | \(0.356904\pi\) | |||||||
\(62\) | −62.7575 | + | 1.90781i | −1.01222 | + | 0.0307711i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −62.9390 | + | 11.6053i | −0.983422 | + | 0.181333i | ||||
\(65\) | 136.990 | 2.10754 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 76.1917i | 1.13719i | 0.822618 | + | 0.568594i | \(0.192513\pi\) | ||||
−0.822618 | + | 0.568594i | \(0.807487\pi\) | |||||||
\(68\) | −23.6632 | + | 1.44004i | −0.347989 | + | 0.0211771i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −63.4521 | + | 1.92892i | −0.906459 | + | 0.0275561i | ||||
\(71\) | − | 59.9326i | − | 0.844121i | −0.906568 | − | 0.422060i | \(-0.861307\pi\) | ||
0.906568 | − | 0.422060i | \(-0.138693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −49.8188 | −0.682450 | −0.341225 | − | 0.939982i | \(-0.610842\pi\) | ||||
−0.341225 | + | 0.939982i | \(0.610842\pi\) | |||||||
\(74\) | 1.63022 | + | 53.6263i | 0.0220301 | + | 0.724680i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.05909 | + | 17.4034i | 0.0139355 | + | 0.228992i | ||||
\(77\) | 8.77198 | 0.113922 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 23.3990i | − | 0.296190i | −0.988973 | − | 0.148095i | \(-0.952686\pi\) | ||
0.988973 | − | 0.148095i | \(-0.0473141\pi\) | |||||||
\(80\) | 92.4737 | − | 11.2969i | 1.15592 | − | 0.141212i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.67626 | + | 88.0358i | 0.0326373 | + | 1.07361i | ||||
\(83\) | 137.116i | 1.65200i | 0.563667 | + | 0.826002i | \(0.309390\pi\) | ||||
−0.563667 | + | 0.826002i | \(0.690610\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 34.5090 | 0.405988 | ||||||||
\(86\) | −55.6915 | + | 1.69300i | −0.647576 | + | 0.0196861i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.8197 | + | 1.17204i | −0.145679 | + | 0.0133186i | ||||
\(89\) | −116.608 | −1.31020 | −0.655101 | − | 0.755541i | \(-0.727374\pi\) | ||||
−0.655101 | + | 0.755541i | \(0.727374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 128.256i | 1.40940i | ||||||||
\(92\) | 6.46602 | + | 106.252i | 0.0702828 | + | 1.15491i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −65.0032 | + | 1.97608i | −0.691523 | + | 0.0210221i | ||||
\(95\) | − | 25.3800i | − | 0.267158i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −65.7341 | −0.677671 | −0.338836 | − | 0.940846i | \(-0.610033\pi\) | ||||
−0.338836 | + | 0.940846i | \(0.610033\pi\) | |||||||
\(98\) | 1.17186 | + | 38.5484i | 0.0119577 | + | 0.393351i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −35.5436 | + | 2.16303i | −0.355436 | + | 0.0216303i | ||||
\(101\) | −1.81406 | −0.0179609 | −0.00898047 | − | 0.999960i | \(-0.502859\pi\) | ||||
−0.00898047 | + | 0.999960i | \(0.502859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.494673i | − | 0.00480265i | −0.999997 | − | 0.00240133i | \(-0.999236\pi\) | ||
0.999997 | − | 0.00240133i | \(-0.000764367\pi\) | |||||||
\(104\) | −17.1364 | − | 187.438i | −0.164773 | − | 1.80229i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.66503 | − | 153.457i | −0.0440097 | − | 1.44770i | ||||
\(107\) | 11.7361i | 0.109684i | 0.998495 | + | 0.0548418i | \(0.0174654\pi\) | ||||
−0.998495 | + | 0.0548418i | \(0.982535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −28.9819 | −0.265889 | −0.132945 | − | 0.991123i | \(-0.542443\pi\) | ||||
−0.132945 | + | 0.991123i | \(0.542443\pi\) | |||||||
\(110\) | 18.7301 | − | 0.569390i | 0.170274 | − | 0.00517627i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.5766 | + | 86.5775i | 0.0944341 | + | 0.773013i | ||||
\(113\) | 140.725 | 1.24536 | 0.622678 | − | 0.782478i | \(-0.286045\pi\) | ||||
0.622678 | + | 0.782478i | \(0.286045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 154.951i | − | 1.34740i | ||||||
\(116\) | −5.95863 | + | 0.362616i | −0.0513675 | + | 0.00312600i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −67.7477 | + | 2.05951i | −0.574133 | + | 0.0174535i | ||||
\(119\) | 32.3086i | 0.271501i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 118.411 | 0.978600 | ||||||||
\(122\) | 3.22186 | + | 105.983i | 0.0264087 | + | 0.868716i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.62772 | − | 125.341i | −0.0615138 | − | 1.01082i | ||||
\(125\) | −93.7298 | −0.749838 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 50.4262i | − | 0.397056i | −0.980095 | − | 0.198528i | \(-0.936384\pi\) | ||
0.980095 | − | 0.198528i | \(-0.0636161\pi\) | |||||||
\(128\) | −27.0248 | − | 125.115i | −0.211131 | − | 0.977458i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.32507 | + | 273.854i | 0.0640390 | + | 2.10657i | ||||
\(131\) | − | 124.954i | − | 0.953847i | −0.878945 | − | 0.476924i | \(-0.841752\pi\) | ||
0.878945 | − | 0.476924i | \(-0.158248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.7618 | 0.178660 | ||||||||
\(134\) | −152.313 | + | 4.63027i | −1.13666 | + | 0.0345542i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.31680 | − | 47.2171i | −0.0317412 | − | 0.347185i | ||||
\(137\) | −137.151 | −1.00110 | −0.500551 | − | 0.865707i | \(-0.666869\pi\) | ||||
−0.500551 | + | 0.865707i | \(0.666869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 89.6885i | − | 0.645241i | −0.946528 | − | 0.322621i | \(-0.895436\pi\) | ||
0.946528 | − | 0.322621i | \(-0.104564\pi\) | |||||||
\(140\) | −7.71214 | − | 126.728i | −0.0550867 | − | 0.905203i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 119.810 | − | 3.64218i | 0.843731 | − | 0.0256492i | ||||
\(143\) | − | 37.8591i | − | 0.264749i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.68969 | 0.0599289 | ||||||||
\(146\) | −3.02756 | − | 99.5917i | −0.0207367 | − | 0.682135i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −107.104 | + | 6.51788i | −0.723676 | + | 0.0440398i | ||||
\(149\) | −18.9194 | −0.126976 | −0.0634878 | − | 0.997983i | \(-0.520222\pi\) | ||||
−0.0634878 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 269.061i | − | 1.78186i | −0.454141 | − | 0.890930i | \(-0.650054\pi\) | ||
0.454141 | − | 0.890930i | \(-0.349946\pi\) | |||||||
\(152\) | −34.7264 | + | 3.17484i | −0.228463 | + | 0.0208871i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.533085 | + | 17.5359i | 0.00346159 | + | 0.113869i | ||||
\(155\) | 182.790i | 1.17929i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4972 | 0.0732305 | 0.0366153 | − | 0.999329i | \(-0.488342\pi\) | ||||
0.0366153 | + | 0.999329i | \(0.488342\pi\) | |||||||
\(158\) | 46.7764 | − | 1.42199i | 0.296053 | − | 0.00899993i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28.2032 | + | 184.175i | 0.176270 | + | 1.15110i | ||||
\(161\) | 145.071 | 0.901063 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 126.564i | − | 0.776465i | −0.921562 | − | 0.388232i | \(-0.873086\pi\) | ||
0.921562 | − | 0.388232i | \(-0.126914\pi\) | |||||||
\(164\) | −175.828 | + | 10.7001i | −1.07212 | + | 0.0652445i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −274.106 | + | 8.33274i | −1.65124 | + | 0.0501972i | ||||
\(167\) | 14.2424i | 0.0852836i | 0.999090 | + | 0.0426418i | \(0.0135774\pi\) | ||||
−0.999090 | + | 0.0426418i | \(0.986423\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 384.540 | 2.27539 | ||||||||
\(170\) | 2.09715 | + | 68.9860i | 0.0123362 | + | 0.405800i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.76889 | − | 111.229i | −0.0393540 | − | 0.646678i | ||||
\(173\) | 217.817 | 1.25906 | 0.629528 | − | 0.776978i | \(-0.283248\pi\) | ||||
0.629528 | + | 0.776978i | \(0.283248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 48.5295i | 0.277312i | ||||||||
\(176\) | −3.12206 | − | 25.5564i | −0.0177390 | − | 0.145207i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.08642 | − | 233.108i | −0.0398114 | − | 1.30960i | ||||
\(179\) | − | 180.223i | − | 1.00684i | −0.864043 | − | 0.503418i | \(-0.832076\pi\) | ||
0.864043 | − | 0.503418i | \(-0.167924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −95.0637 | −0.525214 | −0.262607 | − | 0.964903i | \(-0.584582\pi\) | ||||
−0.262607 | + | 0.964903i | \(0.584582\pi\) | |||||||
\(182\) | −256.393 | + | 7.79426i | −1.40875 | + | 0.0428256i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −212.013 | + | 19.3831i | −1.15224 | + | 0.105343i | ||||
\(185\) | 156.194 | 0.844290 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.53703i | − | 0.0510001i | ||||||
\(188\) | −7.90066 | − | 129.826i | −0.0420248 | − | 0.690565i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 50.7366 | − | 1.54238i | 0.267035 | − | 0.00811777i | ||||
\(191\) | 25.4789i | 0.133397i | 0.997773 | + | 0.0666987i | \(0.0212466\pi\) | ||||
−0.997773 | + | 0.0666987i | \(0.978753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 339.566 | 1.75941 | 0.879705 | − | 0.475520i | \(-0.157740\pi\) | ||||
0.879705 | + | 0.475520i | \(0.157740\pi\) | |||||||
\(194\) | −3.99475 | − | 131.407i | −0.0205915 | − | 0.677358i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −76.9900 | + | 4.68527i | −0.392806 | + | 0.0239045i | ||||
\(197\) | −136.859 | −0.694717 | −0.347358 | − | 0.937732i | \(-0.612921\pi\) | ||||
−0.347358 | + | 0.937732i | \(0.612921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 199.411i | 1.00207i | 0.865428 | + | 0.501034i | \(0.167047\pi\) | ||||
−0.865428 | + | 0.501034i | \(0.832953\pi\) | |||||||
\(200\) | −6.48409 | − | 70.9230i | −0.0324205 | − | 0.354615i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.110243 | − | 3.62644i | −0.000545755 | − | 0.0179527i | ||||
\(203\) | 8.13563i | 0.0400770i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 256.416 | 1.25081 | ||||||||
\(206\) | 0.988890 | − | 0.0300619i | 0.00480044 | − | 0.000145932i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 373.661 | − | 45.6478i | 1.79645 | − | 0.219461i | ||||
\(209\) | −7.01411 | −0.0335604 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 363.655i | 1.72348i | 0.507347 | + | 0.861742i | \(0.330626\pi\) | ||||
−0.507347 | + | 0.861742i | \(0.669374\pi\) | |||||||
\(212\) | 306.488 | − | 18.6515i | 1.44570 | − | 0.0879788i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.4614 | + | 0.713221i | −0.109633 | + | 0.00333281i | ||||
\(215\) | 162.209i | 0.754460i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −171.135 | −0.788640 | ||||||||
\(218\) | −1.76127 | − | 57.9371i | −0.00807922 | − | 0.265766i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.27651 | + | 37.4083i | 0.0103478 | + | 0.170038i | ||||
\(221\) | 139.441 | 0.630956 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 268.968i | − | 1.20614i | −0.797690 | − | 0.603068i | \(-0.793945\pi\) | ||
0.797690 | − | 0.603068i | \(-0.206055\pi\) | |||||||
\(224\) | −172.432 | + | 26.4049i | −0.769787 | + | 0.117879i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.55206 | + | 281.320i | 0.0378410 | + | 1.24478i | ||||
\(227\) | − | 79.9913i | − | 0.352384i | −0.984356 | − | 0.176192i | \(-0.943622\pi\) | ||
0.984356 | − | 0.176192i | \(-0.0563780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 297.342 | 1.29843 | 0.649217 | − | 0.760603i | \(-0.275097\pi\) | ||||
0.649217 | + | 0.760603i | \(0.275097\pi\) | |||||||
\(230\) | 309.759 | − | 9.41657i | 1.34678 | − | 0.0409416i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.08701 | − | 11.8897i | −0.00468539 | − | 0.0512488i | ||||
\(233\) | 255.975 | 1.09860 | 0.549302 | − | 0.835624i | \(-0.314894\pi\) | ||||
0.549302 | + | 0.835624i | \(0.314894\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 189.330i | 0.805661i | ||||||||
\(236\) | −8.23423 | − | 135.308i | −0.0348908 | − | 0.573337i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −64.5875 | + | 1.96344i | −0.271376 | + | 0.00824974i | ||||
\(239\) | − | 148.674i | − | 0.622067i | −0.950399 | − | 0.311034i | \(-0.899325\pi\) | ||
0.950399 | − | 0.311034i | \(-0.100675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −330.295 | −1.37052 | −0.685259 | − | 0.728299i | \(-0.740311\pi\) | ||||
−0.685259 | + | 0.728299i | \(0.740311\pi\) | |||||||
\(242\) | 7.19597 | + | 236.712i | 0.0297354 | + | 0.978148i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −211.673 | + | 12.8815i | −0.867513 | + | 0.0527930i | ||||
\(245\) | 112.277 | 0.458274 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 102.554i | − | 0.415197i | ||||||
\(248\) | 250.103 | − | 22.8655i | 1.00848 | − | 0.0921997i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.69608 | − | 187.373i | −0.0227843 | − | 0.749492i | ||||
\(251\) | − | 253.493i | − | 1.00993i | −0.863139 | − | 0.504966i | \(-0.831505\pi\) | ||
0.863139 | − | 0.504966i | \(-0.168495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.8228 | −0.169260 | ||||||||
\(254\) | 100.806 | − | 3.06446i | 0.396873 | − | 0.0120648i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 248.471 | − | 61.6281i | 0.970591 | − | 0.240735i | ||||
\(257\) | −254.160 | −0.988950 | −0.494475 | − | 0.869192i | \(-0.664640\pi\) | ||||
−0.494475 | + | 0.869192i | \(0.664640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 146.235i | 0.564613i | ||||||||
\(260\) | −546.949 | + | 33.2849i | −2.10365 | + | 0.128019i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 249.793 | − | 7.59362i | 0.953407 | − | 0.0289833i | ||||
\(263\) | − | 190.047i | − | 0.722613i | −0.932447 | − | 0.361306i | \(-0.882331\pi\) | ||
0.932447 | − | 0.361306i | \(-0.117669\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −446.962 | −1.68665 | ||||||||
\(266\) | 1.44403 | + | 47.5016i | 0.00542870 | + | 0.178577i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.5125 | − | 304.204i | −0.0690766 | − | 1.13509i | ||||
\(269\) | −233.427 | −0.867758 | −0.433879 | − | 0.900971i | \(-0.642855\pi\) | ||||
−0.433879 | + | 0.900971i | \(0.642855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.73196i | − | 0.0100810i | −0.999987 | − | 0.00504051i | \(-0.998396\pi\) | ||
0.999987 | − | 0.00504051i | \(-0.00160445\pi\) | |||||||
\(272\) | 94.1283 | − | 11.4991i | 0.346060 | − | 0.0422760i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.33485 | − | 274.175i | −0.0304192 | − | 1.00064i | ||||
\(275\) | − | 14.3252i | − | 0.0520916i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.4896 | −0.0739697 | −0.0369848 | − | 0.999316i | \(-0.511775\pi\) | ||||
−0.0369848 | + | 0.999316i | \(0.511775\pi\) | |||||||
\(278\) | 179.294 | − | 5.45049i | 0.644943 | − | 0.0196061i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 252.871 | − | 23.1186i | 0.903111 | − | 0.0825664i | ||||
\(281\) | 285.339 | 1.01544 | 0.507721 | − | 0.861522i | \(-0.330488\pi\) | ||||
0.507721 | + | 0.861522i | \(0.330488\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.45505i | − | 0.0157422i | −0.999969 | − | 0.00787112i | \(-0.997495\pi\) | ||
0.999969 | − | 0.00787112i | \(-0.00250548\pi\) | |||||||
\(284\) | 14.5620 | + | 239.288i | 0.0512746 | + | 0.842562i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 75.6833 | − | 2.30075i | 0.264627 | − | 0.00804458i | ||||
\(287\) | 240.066i | 0.836468i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −253.874 | −0.878455 | ||||||||
\(290\) | 0.528084 | + | 17.3713i | 0.00182098 | + | 0.0599012i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 198.907 | − | 12.1046i | 0.681190 | − | 0.0414542i | ||||
\(293\) | −326.981 | −1.11598 | −0.557988 | − | 0.829849i | \(-0.688426\pi\) | ||||
−0.557988 | + | 0.829849i | \(0.688426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 197.324i | 0.668895i | ||||||||
\(296\) | −19.5386 | − | 213.713i | −0.0660088 | − | 0.722004i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.14975 | − | 37.8213i | −0.00385824 | − | 0.126917i | ||||
\(299\) | − | 626.114i | − | 2.09403i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −151.866 | −0.504539 | ||||||||
\(302\) | 537.873 | − | 16.3512i | 1.78104 | − | 0.0541430i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.45711 | − | 69.2277i | −0.0278195 | − | 0.227723i | ||||
\(305\) | 308.690 | 1.01210 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 352.091i | − | 1.14688i | −0.819249 | − | 0.573438i | \(-0.805609\pi\) | ||
0.819249 | − | 0.573438i | \(-0.194391\pi\) | |||||||
\(308\) | −35.0231 | + | 2.13136i | −0.113711 | + | 0.00691998i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −365.410 | + | 11.1084i | −1.17874 | + | 0.0358334i | ||||
\(311\) | 75.4387i | 0.242568i | 0.992618 | + | 0.121284i | \(0.0387012\pi\) | ||||
−0.992618 | + | 0.121284i | \(0.961299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.1951 | −0.0421569 | −0.0210784 | − | 0.999778i | \(-0.506710\pi\) | ||||
−0.0210784 | + | 0.999778i | \(0.506710\pi\) | |||||||
\(314\) | 0.698699 | + | 22.9838i | 0.00222516 | + | 0.0731967i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.68533 | + | 93.4232i | 0.0179915 | + | 0.295643i | ||||
\(317\) | −276.427 | −0.872011 | −0.436005 | − | 0.899944i | \(-0.643607\pi\) | ||||
−0.436005 | + | 0.899944i | \(0.643607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.40151i | − | 0.00752826i | ||||||
\(320\) | −366.467 | + | 67.5729i | −1.14521 | + | 0.211165i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.81616 | + | 290.008i | 0.0273794 | + | 0.900647i | ||||
\(323\) | − | 25.8341i | − | 0.0799818i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 209.449 | 0.644459 | ||||||||
\(326\) | 253.011 | − | 7.69145i | 0.776106 | − | 0.0235934i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −32.0756 | − | 350.843i | −0.0977914 | − | 1.06964i | ||||
\(329\) | −177.258 | −0.538779 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 550.110i | − | 1.66196i | −0.556301 | − | 0.830981i | \(-0.687780\pi\) | ||
0.556301 | − | 0.830981i | \(-0.312220\pi\) | |||||||
\(332\) | −33.3156 | − | 547.453i | −0.100348 | − | 1.64895i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.4716 | + | 0.865527i | −0.0852442 | + | 0.00259140i | ||||
\(335\) | 443.631i | 1.32427i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −179.034 | −0.531259 | −0.265630 | − | 0.964075i | \(-0.585580\pi\) | ||||
−0.265630 | + | 0.964075i | \(0.585580\pi\) | |||||||
\(338\) | 23.3690 | + | 768.725i | 0.0691391 | + | 2.27433i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −137.781 | + | 8.38475i | −0.405238 | + | 0.0246610i | ||||
\(341\) | 50.5164 | 0.148142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.233i | 1.08523i | ||||||||
\(344\) | 221.943 | − | 20.2910i | 0.645184 | − | 0.0589856i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.2370 | + | 435.432i | 0.0382573 | + | 1.25848i | ||||
\(347\) | 161.757i | 0.466157i | 0.972458 | + | 0.233079i | \(0.0748800\pi\) | ||||
−0.972458 | + | 0.233079i | \(0.925120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −472.810 | −1.35476 | −0.677378 | − | 0.735635i | \(-0.736884\pi\) | ||||
−0.677378 | + | 0.735635i | \(0.736884\pi\) | |||||||
\(350\) | −97.0142 | + | 2.94920i | −0.277184 | + | 0.00842629i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 50.8994 | − | 7.79433i | 0.144601 | − | 0.0221430i | ||||
\(353\) | −319.200 | −0.904249 | −0.452125 | − | 0.891955i | \(-0.649334\pi\) | ||||
−0.452125 | + | 0.891955i | \(0.649334\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 348.962i | − | 0.982991i | ||||||
\(356\) | 465.571 | − | 28.3326i | 1.30778 | − | 0.0795860i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 360.281 | − | 10.9524i | 1.00637 | − | 0.0305933i | ||||
\(359\) | − | 545.770i | − | 1.52025i | −0.649776 | − | 0.760126i | \(-0.725137\pi\) | ||
0.649776 | − | 0.760126i | \(-0.274863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | −5.77715 | − | 190.040i | −0.0159590 | − | 0.524971i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −31.1626 | − | 512.075i | −0.0856117 | − | 1.40680i | ||||
\(365\) | −290.074 | −0.794723 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 90.4491i | 0.246455i | 0.992378 | + | 0.123228i | \(0.0393246\pi\) | ||||
−0.992378 | + | 0.123228i | \(0.960675\pi\) | |||||||
\(368\) | −51.6327 | − | 422.651i | −0.140306 | − | 1.14851i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.49210 | + | 312.243i | 0.0256543 | + | 0.843900i | ||||
\(371\) | − | 418.464i | − | 1.12793i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 468.975 | 1.25731 | 0.628653 | − | 0.777686i | \(-0.283606\pi\) | ||||
0.628653 | + | 0.777686i | \(0.283606\pi\) | |||||||
\(374\) | 19.0652 | − | 0.579578i | 0.0509766 | − | 0.00154967i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 259.052 | − | 23.6837i | 0.688969 | − | 0.0629886i | ||||
\(377\) | 35.1127 | 0.0931370 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 196.529i | 0.518545i | 0.965804 | + | 0.259273i | \(0.0834828\pi\) | ||||
−0.965804 | + | 0.259273i | \(0.916517\pi\) | |||||||
\(380\) | 6.16666 | + | 101.333i | 0.0162280 | + | 0.266665i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −50.9342 | + | 1.54839i | −0.133336 | + | 0.00405337i | ||||
\(383\) | − | 24.8045i | − | 0.0647637i | −0.999476 | − | 0.0323819i | \(-0.989691\pi\) | ||
0.999476 | − | 0.0323819i | \(-0.0103093\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 51.0755 | 0.132664 | ||||||||
\(386\) | 20.6359 | + | 678.819i | 0.0534608 | + | 1.75860i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 262.451 | − | 15.9716i | 0.676420 | − | 0.0411639i | ||||
\(389\) | 126.462 | 0.325095 | 0.162547 | − | 0.986701i | \(-0.448029\pi\) | ||||
0.162547 | + | 0.986701i | \(0.448029\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 157.723i | − | 0.403385i | ||||||
\(392\) | −14.0450 | − | 153.624i | −0.0358291 | − | 0.391898i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.31712 | − | 273.592i | −0.0211094 | − | 0.694396i | ||||
\(395\) | − | 136.242i | − | 0.344917i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 403.878 | 1.01732 | 0.508662 | − | 0.860966i | \(-0.330140\pi\) | ||||
0.508662 | + | 0.860966i | \(0.330140\pi\) | |||||||
\(398\) | −398.639 | + | 12.1185i | −1.00160 | + | 0.0304485i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 141.386 | − | 17.2723i | 0.353466 | − | 0.0431807i | ||||
\(401\) | −345.608 | −0.861865 | −0.430933 | − | 0.902384i | \(-0.641815\pi\) | ||||
−0.430933 | + | 0.902384i | \(0.641815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 738.603i | 1.83276i | ||||||||
\(404\) | 7.24282 | − | 0.440767i | 0.0179278 | − | 0.00109101i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.2637 | + | 0.494413i | −0.0400585 | + | 0.00121777i | ||||
\(407\) | − | 43.1663i | − | 0.106060i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −429.506 | −1.05014 | −0.525069 | − | 0.851060i | \(-0.675960\pi\) | ||||
−0.525069 | + | 0.851060i | \(0.675960\pi\) | |||||||
\(410\) | 15.5827 | + | 512.595i | 0.0380066 | + | 1.25023i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.120192 | + | 1.97504i | 0.000291729 | + | 0.00479378i | ||||
\(413\) | −184.742 | −0.447318 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 798.370i | 1.92378i | ||||||||
\(416\) | 113.961 | + | 744.203i | 0.273945 | + | 1.78895i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.426257 | − | 14.0218i | −0.00101975 | − | 0.0335449i | ||||
\(419\) | 345.206i | 0.823881i | 0.911211 | + | 0.411940i | \(0.135149\pi\) | ||||
−0.911211 | + | 0.411940i | \(0.864851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −195.468 | −0.464295 | −0.232148 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232148 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(422\) | −726.974 | + | 22.0998i | −1.72269 | + | 0.0523692i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 55.9115 | + | 611.559i | 0.131867 | + | 1.44236i | ||||
\(425\) | 52.7620 | 0.124146 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 289.008i | 0.676834i | ||||||||
\(428\) | −2.85157 | − | 46.8579i | −0.00666254 | − | 0.109481i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −324.268 | + | 9.85764i | −0.754111 | + | 0.0229247i | ||||
\(431\) | 643.698i | 1.49350i | 0.665106 | + | 0.746749i | \(0.268386\pi\) | ||||
−0.665106 | + | 0.746749i | \(0.731614\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −755.385 | −1.74454 | −0.872269 | − | 0.489026i | \(-0.837352\pi\) | ||||
−0.872269 | + | 0.489026i | \(0.837352\pi\) | |||||||
\(434\) | −10.4001 | − | 342.112i | −0.0239633 | − | 0.788275i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 115.714 | − | 7.04183i | 0.265398 | − | 0.0161510i | ||||
\(437\) | −115.999 | −0.265445 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 522.862i | − | 1.19103i | −0.803345 | − | 0.595514i | \(-0.796948\pi\) | ||
0.803345 | − | 0.595514i | \(-0.203052\pi\) | |||||||
\(440\) | −74.6437 | + | 6.82426i | −0.169645 | + | 0.0155097i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.47403 | + | 278.754i | 0.0191720 | + | 0.630665i | ||||
\(443\) | 5.86286i | 0.0132345i | 0.999978 | + | 0.00661723i | \(0.00210634\pi\) | ||||
−0.999978 | + | 0.00661723i | \(0.997894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −678.959 | −1.52575 | ||||||||
\(446\) | 537.688 | − | 16.3455i | 1.20558 | − | 0.0366492i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −63.2644 | − | 343.101i | −0.141215 | − | 0.765850i | ||||
\(449\) | −626.982 | −1.39640 | −0.698199 | − | 0.715904i | \(-0.746015\pi\) | ||||
−0.698199 | + | 0.715904i | \(0.746015\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 70.8640i | − | 0.157126i | ||||||
\(452\) | −561.861 | + | 34.1924i | −1.24306 | + | 0.0756470i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 159.909 | − | 4.86117i | 0.352222 | − | 0.0107074i | ||||
\(455\) | 746.777i | 1.64127i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −451.537 | −0.988046 | −0.494023 | − | 0.869449i | \(-0.664474\pi\) | ||||
−0.494023 | + | 0.869449i | \(0.664474\pi\) | |||||||
\(458\) | 18.0698 | + | 594.408i | 0.0394538 | + | 1.29784i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 37.6489 | + | 618.659i | 0.0818454 | + | 1.34491i | ||||
\(461\) | −50.7723 | −0.110135 | −0.0550675 | − | 0.998483i | \(-0.517537\pi\) | ||||
−0.0550675 | + | 0.998483i | \(0.517537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 69.7862i | − | 0.150726i | −0.997156 | − | 0.0753631i | \(-0.975988\pi\) | ||
0.997156 | − | 0.0753631i | \(-0.0240116\pi\) | |||||||
\(464\) | 23.7024 | − | 2.89557i | 0.0510828 | − | 0.00624046i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.5559 | + | 511.713i | 0.0333818 | + | 1.09810i | ||||
\(467\) | 461.829i | 0.988927i | 0.869198 | + | 0.494464i | \(0.164635\pi\) | ||||
−0.869198 | + | 0.494464i | \(0.835365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −415.345 | −0.885597 | ||||||||
\(470\) | −378.486 | + | 11.5058i | −0.805289 | + | 0.0244805i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 269.990 | − | 24.6837i | 0.572012 | − | 0.0522959i | ||||
\(473\) | 44.8286 | 0.0947751 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 38.8044i | − | 0.0816935i | ||||||
\(476\) | −7.85013 | − | 128.996i | −0.0164919 | − | 0.271000i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 297.211 | − | 9.03512i | 0.621780 | − | 0.0189019i | ||||
\(479\) | 814.201i | 1.69979i | 0.526949 | + | 0.849897i | \(0.323336\pi\) | ||||
−0.526949 | + | 0.849897i | \(0.676664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 631.136 | 1.31213 | ||||||||
\(482\) | −20.0725 | − | 660.285i | −0.0416441 | − | 1.36989i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −472.768 | + | 28.7706i | −0.976793 | + | 0.0594434i | ||||
\(485\) | −382.742 | −0.789158 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 149.015i | 0.305986i | 0.988227 | + | 0.152993i | \(0.0488912\pi\) | ||||
−0.988227 | + | 0.152993i | \(0.951109\pi\) | |||||||
\(488\) | −38.6148 | − | 422.368i | −0.0791286 | − | 0.865508i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.82323 | + | 224.451i | 0.0139250 | + | 0.458063i | ||||
\(491\) | 367.294i | 0.748053i | 0.927418 | + | 0.374027i | \(0.122023\pi\) | ||||
−0.927418 | + | 0.374027i | \(0.877977\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.84517 | 0.0179415 | ||||||||
\(494\) | 205.013 | − | 6.23232i | 0.415005 | − | 0.0126160i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 60.9091 | + | 498.586i | 0.122801 | + | 1.00521i | ||||
\(497\) | 326.712 | 0.657368 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 138.107i | − | 0.276767i | −0.990379 | − | 0.138384i | \(-0.955809\pi\) | ||
0.990379 | − | 0.138384i | \(-0.0441907\pi\) | |||||||
\(500\) | 374.227 | − | 22.7738i | 0.748454 | − | 0.0455476i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 506.752 | − | 15.4051i | 1.00947 | − | 0.0306875i | ||||
\(503\) | − | 31.6936i | − | 0.0630092i | −0.999504 | − | 0.0315046i | \(-0.989970\pi\) | ||
0.999504 | − | 0.0315046i | \(-0.0100299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5625 | −0.0209158 | ||||||||
\(506\) | −2.60240 | − | 85.6061i | −0.00514308 | − | 0.169182i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.2522 | + | 201.332i | 0.0241185 | + | 0.396323i | ||||
\(509\) | 564.839 | 1.10970 | 0.554852 | − | 0.831949i | \(-0.312775\pi\) | ||||
0.554852 | + | 0.831949i | \(0.312775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 271.578i | − | 0.531465i | ||||||
\(512\) | 138.299 | + | 492.968i | 0.270116 | + | 0.962828i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.4457 | − | 508.086i | −0.0300499 | − | 0.988494i | ||||
\(515\) | − | 2.88027i | − | 0.00559276i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 52.3240 | 0.101207 | ||||||||
\(518\) | −292.334 | + | 8.88687i | −0.564352 | + | 0.0171561i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −99.7779 | − | 1091.37i | −0.191881 | − | 2.09879i | ||||
\(521\) | 304.845 | 0.585114 | 0.292557 | − | 0.956248i | \(-0.405494\pi\) | ||||
0.292557 | + | 0.956248i | \(0.405494\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 812.948i | − | 1.55439i | −0.629257 | − | 0.777197i | \(-0.716641\pi\) | ||
0.629257 | − | 0.777197i | \(-0.283359\pi\) | |||||||
\(524\) | 30.3604 | + | 498.893i | 0.0579398 | + | 0.952086i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 379.919 | − | 11.5494i | 0.722279 | − | 0.0219571i | ||||
\(527\) | 186.060i | 0.353055i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −179.204 | −0.338759 | ||||||||
\(530\) | −27.1625 | − | 893.512i | −0.0512500 | − | 1.68587i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −94.8715 | + | 5.77347i | −0.178330 | + | 0.0108524i | ||||
\(533\) | 1036.11 | 1.94391 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 68.3345i | 0.127728i | ||||||||
\(536\) | 607.002 | − | 55.4948i | 1.13247 | − | 0.103535i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.1857 | − | 466.638i | −0.0263674 | − | 0.867357i | ||||
\(539\) | − | 31.0294i | − | 0.0575684i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −396.300 | −0.732532 | −0.366266 | − | 0.930510i | \(-0.619364\pi\) | ||||
−0.366266 | + | 0.930510i | \(0.619364\pi\) | |||||||
\(542\) | 5.46139 | − | 0.166025i | 0.0100764 | − | 0.000306319i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.7078 | + | 187.471i | 0.0527717 | + | 0.344616i | ||||
\(545\) | −168.749 | −0.309632 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 526.396i | − | 0.962333i | −0.876629 | − | 0.481167i | \(-0.840213\pi\) | ||
0.876629 | − | 0.481167i | \(-0.159787\pi\) | |||||||
\(548\) | 547.591 | − | 33.3240i | 0.999254 | − | 0.0608102i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 28.6371 | − | 0.870560i | 0.0520675 | − | 0.00158284i | ||||
\(551\) | − | 6.50528i | − | 0.0118063i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 127.555 | 0.230661 | ||||||||
\(554\) | −1.24518 | − | 40.9603i | −0.00224762 | − | 0.0739355i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.7919 | + | 358.092i | 0.0391940 | + | 0.644050i | ||||
\(557\) | −68.8105 | −0.123538 | −0.0617688 | − | 0.998090i | \(-0.519674\pi\) | ||||
−0.0617688 | + | 0.998090i | \(0.519674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 655.442i | 1.17253i | ||||||||
\(560\) | 61.5832 | + | 504.104i | 0.109970 | + | 0.900185i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.3404 | + | 570.415i | 0.0308549 | + | 1.01497i | ||||
\(563\) | − | 588.997i | − | 1.04618i | −0.852279 | − | 0.523088i | \(-0.824780\pi\) | ||
0.852279 | − | 0.523088i | \(-0.175220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 819.383 | 1.45023 | ||||||||
\(566\) | 8.90599 | − | 0.270739i | 0.0157350 | − | 0.000478338i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −477.469 | + | 43.6524i | −0.840615 | + | 0.0768528i | ||||
\(569\) | 421.857 | 0.741401 | 0.370700 | − | 0.928752i | \(-0.379118\pi\) | ||||
0.370700 | + | 0.928752i | \(0.379118\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 393.676i | 0.689451i | 0.938704 | + | 0.344725i | \(0.112028\pi\) | ||||
−0.938704 | + | 0.344725i | \(0.887972\pi\) | |||||||
\(572\) | 9.19875 | + | 151.157i | 0.0160817 | + | 0.264260i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −479.911 | + | 14.5892i | −0.836082 | + | 0.0254166i | ||||
\(575\) | − | 236.910i | − | 0.412017i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 703.416 | 1.21909 | 0.609546 | − | 0.792751i | \(-0.291352\pi\) | ||||
0.609546 | + | 0.792751i | \(0.291352\pi\) | |||||||
\(578\) | −15.4282 | − | 507.513i | −0.0266924 | − | 0.878050i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −34.6946 | + | 2.11136i | −0.0598182 | + | 0.00364027i | ||||
\(581\) | −747.465 | −1.28651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 123.524i | 0.211877i | ||||||||
\(584\) | 36.2860 | + | 396.895i | 0.0621335 | + | 0.679615i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.8711 | − | 653.660i | −0.0339097 | − | 1.11546i | ||||
\(587\) | 56.2392i | 0.0958078i | 0.998852 | + | 0.0479039i | \(0.0152541\pi\) | ||||
−0.998852 | + | 0.0479039i | \(0.984746\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 136.840 | 0.232326 | ||||||||
\(590\) | −394.466 | + | 11.9916i | −0.668586 | + | 0.0203248i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 426.041 | − | 52.0468i | 0.719665 | − | 0.0879169i | ||||
\(593\) | −553.916 | −0.934090 | −0.467045 | − | 0.884233i | \(-0.654681\pi\) | ||||
−0.467045 | + | 0.884233i | \(0.654681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 188.119i | 0.316167i | ||||||||
\(596\) | 75.5377 | − | 4.59690i | 0.126741 | − | 0.00771291i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1251.65 | − | 38.0498i | 2.09306 | − | 0.0636284i | ||||
\(599\) | − | 724.179i | − | 1.20898i | −0.796613 | − | 0.604490i | \(-0.793377\pi\) | ||
0.796613 | − | 0.604490i | \(-0.206623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −393.734 | −0.655132 | −0.327566 | − | 0.944828i | \(-0.606228\pi\) | ||||
−0.327566 | + | 0.944828i | \(0.606228\pi\) | |||||||
\(602\) | −9.22911 | − | 303.592i | −0.0153308 | − | 0.504306i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 65.3745 | + | 1074.26i | 0.108236 | + | 1.77857i | ||||
\(605\) | 689.454 | 1.13959 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 860.362i | − | 1.41740i | −0.705510 | − | 0.708700i | \(-0.749282\pi\) | ||
0.705510 | − | 0.708700i | \(-0.250718\pi\) | |||||||
\(608\) | 137.878 | − | 21.1135i | 0.226772 | − | 0.0347261i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.7595 | + | 617.096i | 0.0307533 | + | 1.01163i | ||||
\(611\) | 765.032i | 1.25210i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 563.747 | 0.919652 | 0.459826 | − | 0.888009i | \(-0.347912\pi\) | ||||
0.459826 | + | 0.888009i | \(0.347912\pi\) | |||||||
\(614\) | 703.856 | − | 21.3970i | 1.14635 | − | 0.0348486i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.38914 | − | 69.8844i | −0.0103720 | − | 0.113449i | ||||
\(617\) | 677.849 | 1.09862 | 0.549310 | − | 0.835619i | \(-0.314891\pi\) | ||||
0.549310 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 997.063i | − | 1.61076i | −0.592756 | − | 0.805382i | \(-0.701960\pi\) | ||
0.592756 | − | 0.805382i | \(-0.298040\pi\) | |||||||
\(620\) | −44.4129 | − | 729.808i | −0.0716338 | − | 1.17711i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −150.808 | + | 4.58451i | −0.242456 | + | 0.00737060i | ||||
\(623\) | − | 635.668i | − | 1.02033i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −768.307 | −1.22929 | ||||||||
\(626\) | −0.801884 | − | 26.3780i | −0.00128096 | − | 0.0421374i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −45.9038 | + | 2.79351i | −0.0730953 | + | 0.00444826i | ||||
\(629\) | 158.988 | 0.252764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1071.78i | 1.69854i | 0.527959 | + | 0.849270i | \(0.322958\pi\) | ||||
−0.527959 | + | 0.849270i | \(0.677042\pi\) | |||||||
\(632\) | −186.415 | + | 17.0429i | −0.294960 | + | 0.0269665i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.7989 | − | 552.599i | −0.0264966 | − | 0.871608i | ||||
\(635\) | − | 293.610i | − | 0.462378i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 453.682 | 0.712216 | ||||||||
\(638\) | 4.80081 | − | 0.145943i | 0.00752478 | − | 0.000228751i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −157.354 | − | 728.489i | −0.245866 | − | 1.13826i | ||||
\(641\) | 627.241 | 0.978536 | 0.489268 | − | 0.872134i | \(-0.337264\pi\) | ||||
0.489268 | + | 0.872134i | \(0.337264\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 620.131i | 0.964433i | 0.876052 | + | 0.482217i | \(0.160168\pi\) | ||||
−0.876052 | + | 0.482217i | \(0.839832\pi\) | |||||||
\(644\) | −579.213 | + | 35.2484i | −0.899399 | + | 0.0547335i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 51.6444 | − | 1.56997i | 0.0799449 | − | 0.00243030i | ||||
\(647\) | 1270.23i | 1.96327i | 0.190778 | + | 0.981633i | \(0.438899\pi\) | ||||
−0.190778 | + | 0.981633i | \(0.561101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.5332 | 0.0840265 | ||||||||
\(650\) | 12.7285 | + | 418.705i | 0.0195823 | + | 0.644162i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.7516 | + | 505.320i | 0.0471650 | + | 0.775031i | ||||
\(653\) | −775.383 | −1.18742 | −0.593708 | − | 0.804681i | \(-0.702337\pi\) | ||||
−0.593708 | + | 0.804681i | \(0.702337\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 727.554i | − | 1.11077i | ||||||
\(656\) | 699.412 | − | 85.4427i | 1.06618 | − | 0.130248i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.7722 | − | 354.353i | −0.0163712 | − | 0.538531i | ||||
\(659\) | − | 516.735i | − | 0.784119i | −0.919940 | − | 0.392060i | \(-0.871763\pi\) | ||
0.919940 | − | 0.392060i | \(-0.128237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −987.675 | −1.49421 | −0.747107 | − | 0.664704i | \(-0.768558\pi\) | ||||
−0.747107 | + | 0.664704i | \(0.768558\pi\) | |||||||
\(662\) | 1099.71 | − | 33.4309i | 1.66119 | − | 0.0504998i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1092.37 | − | 99.8698i | 1.64514 | − | 0.150406i | ||||
\(665\) | 138.355 | 0.208052 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 39.7163i | − | 0.0595446i | ||||||
\(668\) | −3.46051 | − | 56.8643i | −0.00518041 | − | 0.0851261i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −886.853 | + | 26.9601i | −1.32366 | + | 0.0402389i | ||||
\(671\) | − | 85.3109i | − | 0.127140i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −237.022 | −0.352187 | −0.176094 | − | 0.984373i | \(-0.556346\pi\) | ||||
−0.176094 | + | 0.984373i | \(0.556346\pi\) | |||||||
\(674\) | −10.8802 | − | 357.904i | −0.0161427 | − | 0.531014i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1535.32 | + | 93.4329i | −2.27118 | + | 0.138214i | ||||
\(677\) | −894.692 | −1.32155 | −0.660777 | − | 0.750582i | \(-0.729773\pi\) | ||||
−0.660777 | + | 0.750582i | \(0.729773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 358.338i | − | 0.527743i | ||||||
\(680\) | −25.1349 | − | 274.925i | −0.0369631 | − | 0.404302i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.06995 | + | 100.986i | 0.00450139 | + | 0.148074i | ||||
\(683\) | − | 1327.94i | − | 1.94427i | −0.234421 | − | 0.972135i | \(-0.575320\pi\) | ||
0.234421 | − | 0.972135i | \(-0.424680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −798.572 | −1.16580 | ||||||||
\(686\) | −744.122 | + | 22.6211i | −1.08473 | + | 0.0329754i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 54.0511 | + | 442.449i | 0.0785627 | + | 0.643094i | ||||
\(689\) | −1806.05 | −2.62127 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 552.974i | − | 0.800252i | −0.916460 | − | 0.400126i | \(-0.868966\pi\) | ||
0.916460 | − | 0.400126i | \(-0.131034\pi\) | |||||||
\(692\) | −869.658 | + | 52.9236i | −1.25673 | + | 0.0764792i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −323.364 | + | 9.83016i | −0.465942 | + | 0.0141645i | ||||
\(695\) | − | 522.218i | − | 0.751393i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 261.004 | 0.374467 | ||||||||
\(698\) | −28.7333 | − | 945.183i | −0.0411652 | − | 1.35413i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.7914 | − | 193.760i | −0.0168448 | − | 0.276799i | ||||
\(701\) | −815.608 | −1.16349 | −0.581746 | − | 0.813370i | \(-0.697630\pi\) | ||||
−0.581746 | + | 0.813370i | \(0.697630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 116.930i | − | 0.166330i | ||||||
\(704\) | 18.6747 | + | 101.278i | 0.0265266 | + | 0.143861i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.3982 | − | 638.105i | −0.0274762 | − | 0.903832i | ||||
\(707\) | − | 9.88900i | − | 0.0139873i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 764.747 | 1.07863 | 0.539314 | − | 0.842105i | \(-0.318684\pi\) | ||||
0.539314 | + | 0.842105i | \(0.318684\pi\) | |||||||
\(710\) | 697.601 | − | 21.2069i | 0.982537 | − | 0.0298688i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 84.9324 | + | 928.990i | 0.119287 | + | 1.30476i | ||||
\(713\) | 835.441 | 1.17173 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 220.437i | − | 0.308304i | ||||||
\(716\) | 43.7894 | + | 719.563i | 0.0611584 | + | 1.00498i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1091.04 | − | 33.1672i | 1.51955 | − | 0.0461938i | ||||
\(719\) | 713.170i | 0.991892i | 0.868353 | + | 0.495946i | \(0.165179\pi\) | ||||
−0.868353 | + | 0.495946i | \(0.834821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.69662 | 0.00374011 | ||||||||
\(722\) | −1.15465 | − | 37.9825i | −0.00159925 | − | 0.0526073i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 379.553 | − | 23.0979i | 0.524244 | − | 0.0319032i | ||||
\(725\) | 13.2860 | 0.0183255 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 890.749i | 1.22524i | 0.790378 | + | 0.612619i | \(0.209884\pi\) | ||||
−0.790378 | + | 0.612619i | \(0.790116\pi\) | |||||||
\(728\) | 1021.78 | − | 93.4160i | 1.40355 | − | 0.128319i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.6282 | − | 579.880i | −0.0241482 | − | 0.794356i | ||||
\(731\) | 165.111i | 0.225870i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −221.785 | −0.302572 | −0.151286 | − | 0.988490i | \(-0.548341\pi\) | ||||
−0.151286 | + | 0.988490i | \(0.548341\pi\) | |||||||
\(734\) | −180.815 | + | 5.49671i | −0.246342 | + | 0.00748871i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 841.775 | − | 128.903i | 1.14372 | − | 0.175140i | ||||
\(737\) | 122.604 | 0.166355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 635.372i | 0.859772i | 0.902883 | + | 0.429886i | \(0.141446\pi\) | ||||
−0.902883 | + | 0.429886i | \(0.858554\pi\) | |||||||
\(740\) | −623.621 | + | 37.9508i | −0.842731 | + | 0.0512849i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 836.541 | − | 25.4306i | 1.12741 | − | 0.0342730i | ||||
\(743\) | 795.274i | 1.07036i | 0.844740 | + | 0.535178i | \(0.179755\pi\) | ||||
−0.844740 | + | 0.535178i | \(0.820245\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −110.159 | −0.147865 | ||||||||
\(746\) | 28.5002 | + | 937.518i | 0.0382041 | + | 1.25673i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.31724 | + | 38.0777i | 0.00309791 | + | 0.0509060i | ||||
\(749\) | −63.9775 | −0.0854172 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 84.7437i | 0.112841i | 0.998407 | + | 0.0564206i | \(0.0179688\pi\) | ||||
−0.998407 | + | 0.0564206i | \(0.982031\pi\) | |||||||
\(752\) | 63.0885 | + | 516.426i | 0.0838943 | + | 0.686737i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.13384 | + | 70.1929i | 0.00283003 | + | 0.0930940i | ||||
\(755\) | − | 1566.63i | − | 2.07500i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1207.44 | 1.59503 | 0.797514 | − | 0.603301i | \(-0.206148\pi\) | ||||
0.797514 | + | 0.603301i | \(0.206148\pi\) | |||||||
\(758\) | −392.876 | + | 11.9433i | −0.518306 | + | 0.0157563i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −202.197 | + | 18.4857i | −0.266048 | + | 0.0243233i | ||||
\(761\) | −524.706 | −0.689495 | −0.344748 | − | 0.938695i | \(-0.612035\pi\) | ||||
−0.344748 | + | 0.938695i | \(0.612035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 157.990i | − | 0.207064i | ||||||
\(764\) | −6.19068 | − | 101.727i | −0.00810299 | − | 0.133151i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 49.5861 | − | 1.50740i | 0.0647338 | − | 0.00196789i | ||||
\(767\) | 797.332i | 1.03955i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 531.656 | 0.691360 | 0.345680 | − | 0.938352i | \(-0.387648\pi\) | ||||
0.345680 | + | 0.938352i | \(0.387648\pi\) | |||||||
\(770\) | 3.10393 | + | 102.104i | 0.00403107 | + | 0.132602i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1355.76 | + | 82.5054i | −1.75616 | + | 0.106872i | ||||
\(773\) | 249.261 | 0.322459 | 0.161229 | − | 0.986917i | \(-0.448454\pi\) | ||||
0.161229 | + | 0.986917i | \(0.448454\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 279.474i | 0.360611i | ||||||||
\(776\) | 47.8780 | + | 523.689i | 0.0616984 | + | 0.674857i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.68525 | + | 252.807i | 0.00987821 | + | 0.324944i | ||||
\(779\) | − | 191.958i | − | 0.246416i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −96.4404 | −0.123483 | ||||||||
\(782\) | 315.301 | − | 9.58506i | 0.403198 | − | 0.0122571i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 306.253 | − | 37.4130i | 0.390629 | − | 0.0477206i | ||||
\(785\) | 66.9432 | 0.0852780 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 226.270i | 0.287509i | 0.989613 | + | 0.143755i | \(0.0459176\pi\) | ||||
−0.989613 | + | 0.143755i | \(0.954082\pi\) | |||||||
\(788\) | 546.426 | − | 33.2531i | 0.693434 | − | 0.0421994i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 272.359 | − | 8.27963i | 0.344758 | − | 0.0104805i | ||||
\(791\) | 767.138i | 0.969833i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1247.33 | 1.57293 | ||||||||
\(794\) | 24.5442 | + | 807.383i | 0.0309121 | + | 1.01685i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −48.4516 | − | 796.173i | −0.0608688 | − | 1.00022i | ||||
\(797\) | 874.323 | 1.09702 | 0.548509 | − | 0.836145i | \(-0.315196\pi\) | ||||
0.548509 | + | 0.836145i | \(0.315196\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 192.718i | 0.241199i | ||||||||
\(800\) | 43.1208 | + | 281.592i | 0.0539010 | + | 0.351991i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.0031 | − | 690.897i | −0.0261883 | − | 0.861467i | ||||
\(803\) | 80.1659i | 0.0998330i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 844.687 | 1.04930 | ||||||||
\(806\) | −1476.52 | + | 44.8859i | −1.83192 | + | 0.0556897i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.32128 | + | 14.4522i | 0.00163525 | + | 0.0178864i | ||||
\(809\) | 314.242 | 0.388433 | 0.194216 | − | 0.980959i | \(-0.437784\pi\) | ||||
0.194216 | + | 0.980959i | \(0.437784\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1244.45i | − | 1.53446i | −0.641371 | − | 0.767231i | \(-0.721634\pi\) | ||
0.641371 | − | 0.767231i | \(-0.278366\pi\) | |||||||
\(812\) | −1.97674 | − | 32.4824i | −0.00243441 | − | 0.0400030i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 86.2927 | − | 2.62327i | 0.106011 | − | 0.00322269i | ||||
\(815\) | − | 736.927i | − | 0.904204i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 121.433 | 0.148633 | ||||||||
\(818\) | −26.1017 | − | 858.616i | −0.0319091 | − | 1.04965i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1023.77 | + | 62.3021i | −1.24850 | + | 0.0759782i | ||||
\(821\) | −406.689 | −0.495358 | −0.247679 | − | 0.968842i | \(-0.579668\pi\) | ||||
−0.247679 | + | 0.968842i | \(0.579668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1354.51i | 1.64582i | 0.568171 | + | 0.822910i | \(0.307651\pi\) | ||||
−0.568171 | + | 0.822910i | \(0.692349\pi\) | |||||||
\(824\) | −3.94095 | + | 0.360299i | −0.00478271 | + | 0.000437256i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.2270 | − | 369.314i | −0.0135921 | − | 0.447112i | ||||
\(827\) | − | 465.660i | − | 0.563072i | −0.959551 | − | 0.281536i | \(-0.909156\pi\) | ||
0.959551 | − | 0.281536i | \(-0.0908439\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1349.16 | −1.62745 | −0.813727 | − | 0.581248i | \(-0.802565\pi\) | ||||
−0.813727 | + | 0.581248i | \(0.802565\pi\) | |||||||
\(830\) | −1596.00 | + | 48.5180i | −1.92289 | + | 0.0584554i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1480.79 | + | 273.044i | −1.77980 | + | 0.328177i | ||||
\(833\) | 114.286 | 0.137198 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 82.9272i | 0.0993140i | ||||||||
\(836\) | 28.0046 | − | 1.70424i | 0.0334984 | − | 0.00203857i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −690.093 | + | 20.9786i | −0.823500 | + | 0.0250342i | ||||
\(839\) | − | 860.694i | − | 1.02586i | −0.858431 | − | 0.512929i | \(-0.828561\pi\) | ||
0.858431 | − | 0.512929i | \(-0.171439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −838.773 | −0.997352 | ||||||||
\(842\) | −11.8789 | − | 390.756i | −0.0141079 | − | 0.464081i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −88.3584 | − | 1451.93i | −0.104690 | − | 1.72030i | ||||
\(845\) | 2239.01 | 2.64972 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 645.494i | 0.762095i | ||||||||
\(848\) | −1219.16 | + | 148.937i | −1.43768 | + | 0.175633i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.20642 | + | 105.475i | 0.00377225 | + | 0.124089i | ||||
\(851\) | − | 713.884i | − | 0.838877i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −279.325 | −0.327462 | −0.163731 | − | 0.986505i | \(-0.552353\pi\) | ||||
−0.163731 | + | 0.986505i | \(0.552353\pi\) | |||||||
\(854\) | −577.749 | + | 17.5634i | −0.676522 | + | 0.0205660i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 93.4992 | − | 8.54811i | 0.109228 | − | 0.00998611i | ||||
\(857\) | −548.748 | −0.640313 | −0.320157 | − | 0.947365i | \(-0.603736\pi\) | ||||
−0.320157 | + | 0.947365i | \(0.603736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 241.447i | − | 0.281079i | −0.990075 | − | 0.140539i | \(-0.955116\pi\) | ||
0.990075 | − | 0.140539i | \(-0.0448837\pi\) | |||||||
\(860\) | −39.4124 | − | 647.637i | −0.0458283 | − | 0.753066i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1286.80 | + | 39.1184i | −1.49281 | + | 0.0453809i | ||||
\(863\) | − | 316.519i | − | 0.366766i | −0.983042 | − | 0.183383i | \(-0.941295\pi\) | ||
0.983042 | − | 0.183383i | \(-0.0587048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1268.25 | 1.46619 | ||||||||
\(866\) | −45.9058 | − | 1510.07i | −0.0530090 | − | 1.74373i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 683.275 | − | 41.5811i | 0.787183 | − | 0.0479045i | ||||
\(869\) | −37.6525 | −0.0433285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1792.59i | 2.05809i | ||||||||
\(872\) | 21.1092 | + | 230.892i | 0.0242078 | + | 0.264785i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.04944 | − | 231.892i | −0.00806572 | − | 0.265322i | ||||
\(875\) | − | 510.951i | − | 0.583944i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 883.893 | 1.00786 | 0.503930 | − | 0.863744i | \(-0.331887\pi\) | ||||
0.503930 | + | 0.863744i | \(0.331887\pi\) | |||||||
\(878\) | 1045.24 | − | 31.7750i | 1.19048 | − | 0.0361902i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −18.1784 | − | 148.804i | −0.0206573 | − | 0.169095i | ||||
\(881\) | 823.058 | 0.934231 | 0.467116 | − | 0.884196i | \(-0.345293\pi\) | ||||
0.467116 | + | 0.884196i | \(0.345293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1295.31i | − | 1.46694i | −0.679721 | − | 0.733470i | \(-0.737899\pi\) | ||
0.679721 | − | 0.733470i | \(-0.262101\pi\) | |||||||
\(884\) | −556.735 | + | 33.8805i | −0.629791 | + | 0.0383263i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.7203 | + | 0.356294i | −0.0132283 | + | 0.000402138i | ||||
\(887\) | − | 229.109i | − | 0.258297i | −0.991625 | − | 0.129148i | \(-0.958776\pi\) | ||
0.991625 | − | 0.129148i | \(-0.0412244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 274.889 | 0.309212 | ||||||||
\(890\) | −41.2612 | − | 1357.29i | −0.0463609 | − | 1.52505i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 65.3520 | + | 1073.89i | 0.0732646 | + | 1.20391i | ||||
\(893\) | 141.737 | 0.158720 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1049.36i | − | 1.17247i | ||||||
\(896\) | 682.040 | − | 147.321i | 0.761205 | − | 0.164421i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.1025 | − | 1253.39i | −0.0424304 | − | 1.39575i | ||||
\(899\) | 46.8517i | 0.0521154i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −454.960 | −0.504950 | ||||||||
\(902\) | 141.663 | − | 4.30650i | 0.157054 | − | 0.00477439i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −102.498 | − | 1121.13i | −0.113383 | − | 1.24018i | ||||
\(905\) | −553.515 | −0.611619 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1024.23i | − | 1.12925i | −0.825347 | − | 0.564626i | \(-0.809020\pi\) | ||
0.825347 | − | 0.564626i | \(-0.190980\pi\) | |||||||
\(908\) | 19.4357 | + | 319.374i | 0.0214050 | + | 0.351734i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1492.87 | + | 45.3826i | −1.64051 | + | 0.0498710i | ||||
\(911\) | − | 596.394i | − | 0.654659i | −0.944910 | − | 0.327329i | \(-0.893851\pi\) | ||
0.944910 | − | 0.327329i | \(-0.106149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 220.640 | 0.241665 | ||||||||
\(914\) | −27.4405 | − | 902.657i | −0.0300224 | − | 0.987590i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1187.17 | + | 72.2460i | −1.29604 | + | 0.0788711i | ||||
\(917\) | 681.164 | 0.742818 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1761.71i | 1.91699i | 0.285116 | + | 0.958493i | \(0.407968\pi\) | ||||
−0.285116 | + | 0.958493i | \(0.592032\pi\) | |||||||
\(920\) | −1234.46 | + | 112.860i | −1.34180 | + | 0.122674i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.08550 | − | 101.498i | −0.00334653 | − | 0.110084i | ||||
\(923\) | − | 1410.06i | − | 1.52769i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 238.810 | 0.258173 | ||||||||
\(926\) | 139.508 | − | 4.24100i | 0.150657 | − | 0.00457991i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.22890 | + | 47.2070i | 0.00778976 | + | 0.0508696i | ||||
\(929\) | −146.570 | −0.157771 | −0.0788857 | − | 0.996884i | \(-0.525136\pi\) | ||||
−0.0788857 | + | 0.996884i | \(0.525136\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 84.0531i | − | 0.0902826i | ||||||
\(932\) | −1022.01 | + | 62.1950i | −1.09658 | + | 0.0667328i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −923.232 | + | 28.0660i | −0.988471 | + | 0.0300492i | ||||
\(935\) | − | 55.5300i | − | 0.0593904i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 813.237 | 0.867915 | 0.433958 | − | 0.900933i | \(-0.357117\pi\) | ||||
0.433958 | + | 0.900933i | \(0.357117\pi\) | |||||||
\(938\) | −25.2411 | − | 830.307i | −0.0269095 | − | 0.885188i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −46.0021 | − | 755.922i | −0.0489384 | − | 0.804173i | ||||
\(941\) | −573.885 | −0.609867 | −0.304934 | − | 0.952374i | \(-0.598634\pi\) | ||||
−0.304934 | + | 0.952374i | \(0.598634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1171.95i | − | 1.24279i | ||||||
\(944\) | 65.7522 | + | 538.230i | 0.0696527 | + | 0.570159i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.72430 | + | 89.6159i | 0.00287981 | + | 0.0947314i | ||||
\(947\) | 1186.01i | 1.25239i | 0.779666 | + | 0.626195i | \(0.215389\pi\) | ||||
−0.779666 | + | 0.626195i | \(0.784611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1172.11 | −1.23510 | ||||||||
\(950\) | 77.5730 | − | 2.35819i | 0.0816558 | − | 0.00248231i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 257.396 | − | 23.5323i | 0.270374 | − | 0.0247188i | ||||
\(953\) | −132.421 | −0.138951 | −0.0694757 | − | 0.997584i | \(-0.522133\pi\) | ||||
−0.0694757 | + | 0.997584i | \(0.522133\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 148.353i | 0.155343i | ||||||||
\(956\) | 36.1238 | + | 593.598i | 0.0377864 | + | 0.620918i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1627.65 | + | 49.4801i | −1.69901 | + | 0.0516493i | ||||
\(959\) | − | 747.654i | − | 0.779619i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5372 | −0.0255330 | ||||||||
\(962\) | 38.3550 | + | 1261.69i | 0.0398700 | + | 1.31153i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1318.74 | − | 80.2528i | 1.36799 | − | 0.0832498i | ||||
\(965\) | 1977.15 | 2.04886 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 949.146i | − | 0.981536i | −0.871290 | − | 0.490768i | \(-0.836716\pi\) | ||
0.871290 | − | 0.490768i | \(-0.163284\pi\) | |||||||
\(968\) | −86.2453 | − | 943.351i | −0.0890964 | − | 0.974536i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.2597 | − | 765.130i | −0.0239791 | − | 0.788793i | ||||
\(971\) | − | 1700.58i | − | 1.75137i | −0.482883 | − | 0.875685i | \(-0.660410\pi\) | ||
0.482883 | − | 0.875685i | \(-0.339590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 488.921 | 0.502488 | ||||||||
\(974\) | −297.893 | + | 9.05585i | −0.305845 | + | 0.00929759i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 841.999 | − | 102.862i | 0.862704 | − | 0.105391i | ||||
\(977\) | −1288.94 | −1.31929 | −0.659643 | − | 0.751579i | \(-0.729293\pi\) | ||||
−0.659643 | + | 0.751579i | \(0.729293\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 187.640i | 0.191665i | ||||||||
\(980\) | −448.280 | + | 27.2803i | −0.457428 | + | 0.0278371i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −734.249 | + | 22.3209i | −0.747708 | + | 0.0227301i | ||||
\(983\) | 1526.52i | 1.55292i | 0.630168 | + | 0.776459i | \(0.282986\pi\) | ||||
−0.630168 | + | 0.776459i | \(0.717014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −796.873 | −0.809008 | ||||||||
\(986\) | 0.537533 | + | 17.6822i | 0.000545165 | + | 0.0179332i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.9178 | + | 409.457i | 0.0252204 | + | 0.414430i | ||||
\(989\) | 741.376 | 0.749622 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 613.326i | 0.618896i | 0.950916 | + | 0.309448i | \(0.100144\pi\) | ||||
−0.950916 | + | 0.309448i | \(0.899856\pi\) | |||||||
\(992\) | −993.009 | + | 152.062i | −1.00102 | + | 0.153288i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.8547 | + | 653.122i | 0.0199745 | + | 0.657064i | ||||
\(995\) | 1161.09i | 1.16692i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.6625 | −0.0347668 | −0.0173834 | − | 0.999849i | \(-0.505534\pi\) | ||||
−0.0173834 | + | 0.999849i | \(0.505534\pi\) | |||||||
\(998\) | 276.086 | − | 8.39293i | 0.276639 | − | 0.00840975i | ||||
\(999\) | 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 | 684.3.g.b.343.10 | 14 | ||
3.2 | odd | 2 | 76.3.b.b.39.5 | ✓ | 14 | ||
4.3 | odd | 2 | inner | 684.3.g.b.343.9 | 14 | ||
12.11 | even | 2 | 76.3.b.b.39.6 | yes | 14 | ||
24.5 | odd | 2 | 1216.3.d.d.191.1 | 14 | |||
24.11 | even | 2 | 1216.3.d.d.191.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.b.b.39.5 | ✓ | 14 | 3.2 | odd | 2 | ||
76.3.b.b.39.6 | yes | 14 | 12.11 | even | 2 | ||
684.3.g.b.343.9 | 14 | 4.3 | odd | 2 | inner | ||
684.3.g.b.343.10 | 14 | 1.1 | even | 1 | trivial | ||
1216.3.d.d.191.1 | 14 | 24.5 | odd | 2 | |||
1216.3.d.d.191.14 | 14 | 24.11 | even | 2 |