Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,6,Mod(49,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.7566812231\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 3057 x^{16} + 14564 x^{15} + 3829838 x^{14} - 15907074 x^{13} - 2546775754 x^{12} + 7879525640 x^{11} + 976140188391 x^{10} + \cdots + 66\!\cdots\!83 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 273.8 | ||
Root | \(-21.8370 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.273 |
Dual form | 304.6.i.d.49.8 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 11.6685 | + | 20.2105i | 0.748535 | + | 1.29650i | 0.948525 | + | 0.316703i | \(0.102576\pi\) |
−0.199989 | + | 0.979798i | \(0.564091\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.2470 | − | 43.7291i | −0.451633 | − | 0.782251i | 0.546855 | − | 0.837227i | \(-0.315825\pi\) |
−0.998488 | + | 0.0549767i | \(0.982492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 187.942 | 1.44971 | 0.724853 | − | 0.688904i | \(-0.241908\pi\) | ||||
0.724853 | + | 0.688904i | \(0.241908\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −150.808 | + | 261.208i | −0.620610 | + | 1.07493i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −411.164 | −1.02455 | −0.512276 | − | 0.858821i | \(-0.671197\pi\) | ||||
−0.512276 | + | 0.858821i | \(0.671197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 286.794 | − | 496.742i | 0.470665 | − | 0.815216i | −0.528772 | − | 0.848764i | \(-0.677347\pi\) |
0.999437 | + | 0.0335480i | \(0.0106807\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 589.191 | − | 1020.51i | 0.676126 | − | 1.17108i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 559.243 | + | 968.637i | 0.469330 | + | 0.812903i | 0.999385 | − | 0.0350601i | \(-0.0111623\pi\) |
−0.530056 | + | 0.847963i | \(0.677829\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1048.98 | − | 1172.92i | 0.666630 | − | 0.745388i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2193.01 | + | 3798.40i | 1.08516 | + | 1.87955i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0483 | − | 124.791i | 0.0283991 | − | 0.0491886i | −0.851477 | − | 0.524393i | \(-0.824292\pi\) |
0.879876 | + | 0.475204i | \(0.157626\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 287.675 | − | 498.268i | 0.0920560 | − | 0.159446i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1367.94 | −0.361125 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2616.14 | + | 4531.29i | −0.577652 | + | 1.00052i | 0.418096 | + | 0.908403i | \(0.362697\pi\) |
−0.995748 | + | 0.0921194i | \(0.970636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6724.09 | 1.25669 | 0.628347 | − | 0.777934i | \(-0.283732\pi\) | ||||
0.628347 | + | 0.777934i | \(0.283732\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4797.68 | − | 8309.82i | −0.766913 | − | 1.32833i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4744.99 | − | 8218.56i | −0.654734 | − | 1.13403i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12337.9 | 1.48162 | 0.740811 | − | 0.671713i | \(-0.234441\pi\) | ||||
0.740811 | + | 0.671713i | \(0.234441\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13385.8 | 1.40924 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5964.03 | − | 10330.0i | −0.554090 | − | 0.959712i | −0.997974 | − | 0.0636278i | \(-0.979733\pi\) |
0.443884 | − | 0.896084i | \(-0.353600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2611.95 | + | 4524.03i | 0.215424 | + | 0.373125i | 0.953404 | − | 0.301698i | \(-0.0975534\pi\) |
−0.737980 | + | 0.674823i | \(0.764220\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15229.9 | 1.12115 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10457.1 | − | 18112.3i | 0.690507 | − | 1.19599i | −0.281165 | − | 0.959659i | \(-0.590721\pi\) |
0.971672 | − | 0.236333i | \(-0.0759458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18515.4 | 1.10165 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13051.1 | + | 22605.1i | −0.702620 | + | 1.21697i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4550.48 | − | 7881.66i | 0.222519 | − | 0.385414i | −0.733053 | − | 0.680171i | \(-0.761905\pi\) |
0.955572 | + | 0.294757i | \(0.0952387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10380.7 | + | 17979.9i | 0.462721 | + | 0.801456i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 35945.2 | + | 7514.28i | 1.46539 | + | 0.306338i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12030.3 | + | 20837.0i | 0.449930 | + | 0.779301i | 0.998381 | − | 0.0568813i | \(-0.0181157\pi\) |
−0.548451 | + | 0.836183i | \(0.684782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21555.9 | + | 37335.8i | −0.741721 | + | 1.28470i | 0.209990 | + | 0.977704i | \(0.432657\pi\) |
−0.951711 | + | 0.306995i | \(0.900676\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −28343.3 | + | 49092.0i | −0.899703 | + | 1.55833i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −28962.8 | −0.850271 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8051.46 | − | 13945.5i | 0.219123 | − | 0.379532i | −0.735417 | − | 0.677615i | \(-0.763014\pi\) |
0.954540 | + | 0.298083i | \(0.0963471\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3362.78 | 0.0850308 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 39902.4 | + | 69113.1i | 0.939407 | + | 1.62710i | 0.766581 | + | 0.642148i | \(0.221956\pi\) |
0.172826 | + | 0.984952i | \(0.444710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17210.0 | − | 29808.6i | −0.377985 | − | 0.654688i | 0.612784 | − | 0.790250i | \(-0.290049\pi\) |
−0.990769 | + | 0.135562i | \(0.956716\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13427.0 | 0.275629 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −77275.3 | −1.48530 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16379.2 | − | 28369.7i | −0.295274 | − | 0.511430i | 0.679774 | − | 0.733421i | \(-0.262078\pi\) |
−0.975049 | + | 0.221991i | \(0.928744\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20684.6 | + | 35826.8i | 0.350296 | + | 0.606730i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −49610.5 | −0.790457 | −0.395229 | − | 0.918583i | \(-0.629335\pi\) | ||||
−0.395229 | + | 0.918583i | \(0.629335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28238.4 | − | 48910.4i | 0.423929 | − | 0.734267i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −122106. | −1.72957 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −39238.1 | + | 67962.3i | −0.525089 | + | 0.909480i | 0.474484 | + | 0.880264i | \(0.342635\pi\) |
−0.999573 | + | 0.0292164i | \(0.990699\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 53900.8 | − | 93359.0i | 0.682326 | − | 1.18182i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 78460.1 | + | 135897.i | 0.940679 | + | 1.62930i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −77774.3 | − | 16258.6i | −0.884153 | − | 0.184830i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 62657.4 | + | 108526.i | 0.676149 | + | 1.17113i | 0.976131 | + | 0.217180i | \(0.0696860\pi\) |
−0.299982 | + | 0.953945i | \(0.596981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 62007.0 | − | 107399.i | 0.635847 | − | 1.10132i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −64376.2 | + | 111503.i | −0.627945 | + | 1.08763i | 0.360018 | + | 0.932945i | \(0.382770\pi\) |
−0.987963 | + | 0.154688i | \(0.950563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 185375. | 1.72170 | 0.860851 | − | 0.508857i | \(-0.169932\pi\) | ||||
0.860851 | + | 0.508857i | \(0.169932\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 110734. | − | 191797.i | 0.980184 | − | 1.69773i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 51720.8 | 0.436723 | 0.218361 | − | 0.975868i | \(-0.429929\pi\) | ||||
0.218361 | + | 0.975868i | \(0.429929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10666.1 | − | 18474.1i | −0.0859879 | − | 0.148935i | 0.819824 | − | 0.572616i | \(-0.194071\pi\) |
−0.905812 | + | 0.423680i | \(0.860738\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 143965. | + | 249355.i | 1.10905 | + | 1.92093i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 181009. | 1.33353 | 0.666767 | − | 0.745266i | \(-0.267678\pi\) | ||||
0.666767 | + | 0.745266i | \(0.267678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7276.02 | −0.0513038 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 86501.9 | + | 149826.i | 0.584199 | + | 1.01186i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 105105. | + | 182048.i | 0.680390 | + | 1.17847i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8005.17 | 0.0497058 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 139183. | − | 241072.i | 0.829512 | − | 1.43676i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −186846. | −1.06957 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −909.283 | + | 1574.92i | −0.00500253 | + | 0.00866464i | −0.868516 | − | 0.495661i | \(-0.834926\pi\) |
0.863513 | + | 0.504326i | \(0.168259\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −60955.1 | + | 105577.i | −0.322504 | + | 0.558594i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 39930.7 | + | 69162.1i | 0.203296 | + | 0.352119i | 0.949589 | − | 0.313499i | \(-0.101501\pi\) |
−0.746292 | + | 0.665618i | \(0.768168\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 197149. | − | 220441.i | 0.966418 | − | 1.08059i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 34536.4 | + | 59818.8i | 0.163096 | + | 0.282490i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 99388.3 | − | 172146.i | 0.452412 | − | 0.783600i | −0.546123 | − | 0.837705i | \(-0.683897\pi\) |
0.998535 | + | 0.0541044i | \(0.0172304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 188358. | − | 326246.i | 0.826890 | − | 1.43222i | −0.0735761 | − | 0.997290i | \(-0.523441\pi\) |
0.900466 | − | 0.434926i | \(-0.143225\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 488077. | 2.06748 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −117920. | + | 204243.i | −0.482221 | + | 0.835231i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 264199. | 1.04355 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 216047. | + | 374204.i | 0.824622 | + | 1.42829i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −115828. | − | 200620.i | −0.427413 | − | 0.740300i | 0.569230 | − | 0.822179i | \(-0.307242\pi\) |
−0.996642 | + | 0.0818781i | \(0.973908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −465504. | −1.66143 | −0.830714 | − | 0.556700i | \(-0.812067\pi\) | ||||
−0.830714 | + | 0.556700i | \(0.812067\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −337354. | −1.16508 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −169763. | − | 294039.i | −0.567564 | − | 0.983049i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −256177. | − | 443712.i | −0.829451 | − | 1.43665i | −0.898469 | − | 0.439037i | \(-0.855320\pi\) |
0.0690177 | − | 0.997615i | \(-0.478013\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 212389. | 0.666254 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13540.9 | − | 23453.6i | 0.0411703 | − | 0.0713090i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −551349. | −1.62539 | −0.812694 | − | 0.582690i | \(-0.802000\pi\) | ||||
−0.812694 | + | 0.582690i | \(0.802000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −242254. | + | 419597.i | −0.692726 | + | 1.19984i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24265.6 | + | 42029.2i | −0.0673286 | + | 0.116617i | −0.897725 | − | 0.440557i | \(-0.854781\pi\) |
0.830396 | + | 0.557174i | \(0.188114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21144.6 | + | 36623.6i | 0.0569487 | + | 0.0986380i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 148179. | + | 450888.i | 0.387522 | + | 1.17918i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −84590.8 | − | 146516.i | −0.214886 | − | 0.372193i | 0.738351 | − | 0.674416i | \(-0.235605\pi\) |
−0.953237 | + | 0.302223i | \(0.902271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 54066.3 | − | 93645.7i | 0.133454 | − | 0.231149i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −280750. | + | 486274.i | −0.673577 | + | 1.16667i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 560804. | 1.30821 | 0.654106 | − | 0.756403i | \(-0.273045\pi\) | ||||
0.654106 | + | 0.756403i | \(0.273045\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 186731. | − | 323428.i | 0.423663 | − | 0.733806i | −0.572631 | − | 0.819813i | \(-0.694077\pi\) |
0.996295 | + | 0.0860068i | \(0.0274107\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00610e6 | −2.22082 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −311496. | − | 539526.i | −0.669149 | − | 1.15900i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −229941. | − | 398269.i | −0.480852 | − | 0.832861i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −257094. | −0.523525 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 603335. | 1.19667 | 0.598336 | − | 0.801245i | \(-0.295829\pi\) | ||||
0.598336 | + | 0.801245i | \(0.295829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 52.8895 | + | 91.6073i | 0.000102206 | + | 0.000177026i | 0.866077 | − | 0.499911i | \(-0.166634\pi\) |
−0.865974 | + | 0.500089i | \(0.833301\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −337953. | − | 585352.i | −0.636458 | − | 1.10238i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −704077. | −1.29257 | −0.646285 | − | 0.763096i | \(-0.723678\pi\) | ||||
−0.646285 | + | 0.763096i | \(0.723678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −81423.6 | + | 141030.i | −0.145753 | + | 0.252452i | −0.929654 | − | 0.368435i | \(-0.879894\pi\) |
0.783901 | + | 0.620886i | \(0.213227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 375794. | 0.656085 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −491684. | + | 851622.i | −0.837425 | + | 1.45046i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −301148. | + | 521604.i | −0.500490 | + | 0.866875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21731.0 | + | 37639.1i | 0.0352495 | + | 0.0610539i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −431305. | + | 482261.i | −0.682997 | + | 0.763689i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −349140. | − | 604728.i | −0.539875 | − | 0.935091i | −0.998910 | − | 0.0466728i | \(-0.985138\pi\) |
0.459035 | − | 0.888418i | \(-0.348195\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −931204. | + | 1.61289e6i | −1.40636 | + | 2.43588i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 131888. | − | 228436.i | 0.194585 | − | 0.337030i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.26374e6 | 1.82184 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 401630. | − | 695644.i | 0.565870 | − | 0.980115i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 641550. | 0.883588 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 93703.3 | + | 162299.i | 0.126181 | + | 0.218551i | 0.922194 | − | 0.386728i | \(-0.126395\pi\) |
−0.796013 | + | 0.605279i | \(0.793061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 86767.6 | + | 150286.i | 0.114262 | + | 0.197907i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −606601. | −0.781338 | −0.390669 | − | 0.920531i | \(-0.627756\pi\) | ||||
−0.390669 | + | 0.920531i | \(0.627756\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −215431. | −0.271469 | −0.135734 | − | 0.990745i | \(-0.543339\pi\) | ||||
−0.135734 | + | 0.990745i | \(0.543339\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −901687. | − | 1.56177e6i | −1.11180 | − | 1.92569i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −511411. | − | 885789.i | −0.617135 | − | 1.06891i | −0.990006 | − | 0.141026i | \(-0.954960\pi\) |
0.372871 | − | 0.927883i | \(-0.378373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.05605e6 | −1.24742 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 382242. | − | 662063.i | 0.442047 | − | 0.765647i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.31113e6 | 1.48474 | 0.742371 | − | 0.669989i | \(-0.233701\pi\) | ||||
0.742371 | + | 0.669989i | \(0.233701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4784.45 | − | 8286.91i | 0.00530627 | − | 0.00919073i | −0.863360 | − | 0.504588i | \(-0.831644\pi\) |
0.868666 | + | 0.495398i | \(0.164978\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −648922. | + | 1.12397e6i | −0.704980 | + | 1.22106i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −467458. | − | 809662.i | −0.497540 | − | 0.861764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −281794. | − | 857460.i | −0.293893 | − | 0.894276i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −578881. | − | 1.00265e6i | −0.591685 | − | 1.02483i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 228222. | − | 395293.i | 0.228651 | − | 0.396036i | −0.728757 | − | 0.684772i | \(-0.759902\pi\) |
0.957409 | + | 0.288736i | \(0.0932351\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29623.7 | + | 51309.7i | −0.0290963 | + | 0.0503963i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.31800e6 | 1.26930 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 259837. | − | 450050.i | 0.245396 | − | 0.425038i | −0.716847 | − | 0.697231i | \(-0.754415\pi\) |
0.962243 | + | 0.272192i | \(0.0877487\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.31882e6 | 2.14792 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −789072. | − | 1.36671e6i | −0.716993 | − | 1.24187i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 159146. | + | 275650.i | 0.141876 | + | 0.245736i | 0.928203 | − | 0.372074i | \(-0.121353\pi\) |
−0.786327 | + | 0.617810i | \(0.788020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −459544. | −0.401987 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.83140e6 | −1.57219 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −71668.3 | − | 124133.i | −0.0603874 | − | 0.104594i | 0.834251 | − | 0.551385i | \(-0.185900\pi\) |
−0.894639 | + | 0.446790i | \(0.852567\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −304619. | − | 527616.i | −0.251961 | − | 0.436410i | 0.712104 | − | 0.702074i | \(-0.247742\pi\) |
−0.964066 | + | 0.265664i | \(0.914409\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.51577e6 | 2.04298 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −118282. | + | 204870.i | −0.0943161 | + | 0.163360i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.94146e6 | −1.52030 | −0.760151 | − | 0.649746i | \(-0.774875\pi\) | ||||
−0.760151 | + | 0.649746i | \(0.774875\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.01405e6 | + | 1.75638e6i | −0.779917 | + | 1.35086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −286688. | + | 496557.i | −0.216592 | + | 0.375149i | −0.953764 | − | 0.300557i | \(-0.902828\pi\) |
0.737172 | + | 0.675706i | \(0.236161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.04413e6 | + | 1.80849e6i | 0.774977 | + | 1.34230i | 0.934808 | + | 0.355155i | \(0.115572\pi\) |
−0.159831 | + | 0.987144i | \(0.551095\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −578917. | − | 1.76157e6i | −0.422187 | − | 1.28466i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.12090e6 | − | 1.94145e6i | −0.803268 | − | 1.39130i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 84423.8 | − | 146226.i | 0.0594593 | − | 0.102987i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.46224e6 | + | 2.53267e6i | −1.01224 | + | 1.75326i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −598199. | −0.407077 | −0.203538 | − | 0.979067i | \(-0.565244\pi\) | ||||
−0.203538 | + | 0.979067i | \(0.565244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 607456. | − | 1.05215e6i | 0.406406 | − | 0.703916i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 562448. | 0.369991 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −41326.0 | − | 71578.8i | −0.0267329 | − | 0.0463027i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 490896. | + | 850257.i | 0.312301 | + | 0.540921i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00470e6 | −1.88016 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.17689e6 | 1.33994 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −71331.2 | − | 123549.i | −0.0431950 | − | 0.0748159i | 0.843620 | − | 0.536941i | \(-0.180420\pi\) |
−0.886815 | + | 0.462125i | \(0.847087\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.16305e6 | + | 3.74651e6i | 1.28876 | + | 2.23219i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.33734e6 | 1.95659 | 0.978294 | − | 0.207219i | \(-0.0664414\pi\) | ||||
0.978294 | + | 0.207219i | \(0.0664414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.12350e6 | − | 1.94596e6i | 0.648205 | − | 1.12272i | −0.335347 | − | 0.942095i | \(-0.608854\pi\) |
0.983551 | − | 0.180628i | \(-0.0578131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.86234e6 | 1.62534 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29587.8 | + | 51247.6i | −0.0165373 | + | 0.0286434i | −0.874176 | − | 0.485610i | \(-0.838598\pi\) |
0.857638 | + | 0.514253i | \(0.171931\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.07566e6 | − | 1.86310e6i | 0.591834 | − | 1.02509i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 603505. | + | 1.04530e6i | 0.326902 | + | 0.566212i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.72277e6 | + | 360141.i | 0.918798 | + | 0.192073i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −165007. | − | 285801.i | −0.0866551 | − | 0.150091i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 248914. | − | 431132.i | 0.128730 | − | 0.222967i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.96534e6 | − | 3.40407e6i | 1.00103 | − | 1.73384i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.35196e6 | −1.17994 | −0.589970 | − | 0.807425i | \(-0.700860\pi\) | ||||
−0.589970 | + | 0.807425i | \(0.700860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.86066e6 | + | 3.22276e6i | −0.919510 | + | 1.59264i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −813102. | −0.395852 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −82853.0 | − | 143506.i | −0.0397405 | − | 0.0688326i | 0.845471 | − | 0.534021i | \(-0.179320\pi\) |
−0.885212 | + | 0.465189i | \(0.845986\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.11211e6 | + | 3.65827e6i | 0.998197 | + | 1.72893i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.76471e6 | −1.28755 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 321077. | 0.147358 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −84900.3 | − | 147052.i | −0.0384027 | − | 0.0665154i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −407820. | − | 706365.i | −0.181821 | − | 0.314924i | 0.760679 | − | 0.649128i | \(-0.224866\pi\) |
−0.942501 | + | 0.334204i | \(0.891533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.07255e6 | 0.471359 | 0.235680 | − | 0.971831i | \(-0.424268\pi\) | ||||
0.235680 | + | 0.971831i | \(0.424268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −392317. | + | 679513.i | −0.169969 | + | 0.294395i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.70760e6 | −1.58364 | −0.791819 | − | 0.610756i | \(-0.790866\pi\) | ||||
−0.791819 | + | 0.610756i | \(0.790866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.01484e6 | − | 3.48980e6i | 0.848533 | − | 1.46970i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.45285e6 | + | 4.24846e6i | −1.01859 | + | 1.76425i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 440125. | + | 762318.i | 0.180235 | + | 0.312176i | 0.941961 | − | 0.335724i | \(-0.108981\pi\) |
−0.761725 | + | 0.647900i | \(0.775647\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −275361. | − | 2.46074e6i | −0.111208 | − | 0.993797i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 93408.4 | + | 161788.i | 0.0372066 | + | 0.0644437i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −869003. | + | 1.50516e6i | −0.341420 | + | 0.591357i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.32405e6 | + | 2.29332e6i | −0.513143 | + | 0.888789i | 0.486741 | + | 0.873546i | \(0.338186\pi\) |
−0.999884 | + | 0.0152431i | \(0.995148\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.59770e6 | 1.37550 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 855228. | − | 1.48130e6i | 0.322587 | − | 0.558737i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.42105e6 | 0.528856 | 0.264428 | − | 0.964405i | \(-0.414817\pi\) | ||||
0.264428 | + | 0.964405i | \(0.414817\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.18021e6 | − | 3.77624e6i | −0.800609 | − | 1.38670i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.50059e6 | + | 2.59909e6i | 0.543761 | + | 0.941822i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.14092e6 | −1.48081 | −0.740405 | − | 0.672161i | \(-0.765366\pi\) | ||||
−0.740405 | + | 0.672161i | \(0.765366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −42439.9 | −0.0149783 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −932604. | − | 1.61532e6i | −0.324863 | − | 0.562679i | 0.656622 | − | 0.754220i | \(-0.271985\pi\) |
−0.981485 | + | 0.191541i | \(0.938652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.95097e6 | + | 3.37918e6i | 0.670809 | + | 1.16188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.57561e6 | −0.534777 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −225886. | + | 391246.i | −0.0756859 | + | 0.131092i | −0.901384 | − | 0.433020i | \(-0.857448\pi\) |
0.825698 | + | 0.564112i | \(0.190781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 161170. | 0.0533141 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −931865. | + | 1.61404e6i | −0.304349 | + | 0.527147i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −827054. | + | 1.43250e6i | −0.266711 | + | 0.461957i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 387696. | + | 671509.i | 0.123457 | + | 0.213833i | 0.921129 | − | 0.389258i | \(-0.127269\pi\) |
−0.797672 | + | 0.603092i | \(0.793935\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.75564e6 | + | 1.41225e6i | 2.12439 | + | 0.444099i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.11762e6 | − | 5.39987e6i | −0.968193 | − | 1.67696i | −0.700781 | − | 0.713376i | \(-0.747165\pi\) |
−0.267412 | − | 0.963582i | \(-0.586168\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.92843e6 | − | 3.34014e6i | 0.591482 | − | 1.02448i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.04445e6 | − | 1.80904e6i | 0.316410 | − | 0.548038i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.07291e6 | −1.51800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.43708e6 | + | 4.22114e6i | −0.720379 | + | 1.24773i | 0.240468 | + | 0.970657i | \(0.422699\pi\) |
−0.960848 | + | 0.277077i | \(0.910634\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.63886e6 | 1.35459 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.26100e6 | + | 3.91616e6i | 0.652266 | + | 1.12976i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.25252e6 | + | 2.16942e6i | 0.356996 | + | 0.618336i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.79144e6 | 2.47583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.11548e6 | −0.866943 | −0.433471 | − | 0.901167i | \(-0.642711\pi\) | ||||
−0.433471 | + | 0.901167i | \(0.642711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.17883e6 | − | 3.77384e6i | −0.599125 | − | 1.03771i | −0.992951 | − | 0.118529i | \(-0.962182\pi\) |
0.393826 | − | 0.919185i | \(-0.371151\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.15405e6 | + | 5.46297e6i | 0.857071 | + | 1.48449i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 643520. | 0.172818 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.05126e6 | + | 7.01699e6i | −1.07528 | + | 1.86244i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.50378e6 | −1.44384 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.39109e6 | + | 5.87353e6i | −0.879317 | + | 1.52302i | −0.0272262 | + | 0.999629i | \(0.508667\pi\) |
−0.852091 | + | 0.523393i | \(0.824666\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16420.8 | + | 28441.7i | −0.00420896 | + | 0.00729014i | −0.868122 | − | 0.496351i | \(-0.834673\pi\) |
0.863913 | + | 0.503641i | \(0.168006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.08281e6 | + | 5.33958e6i | 0.781131 | + | 1.35296i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −70792.0 | − | 215411.i | −0.0177329 | − | 0.0539589i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.63969e6 | + | 4.57208e6i | 0.653720 | + | 1.13228i | 0.982213 | + | 0.187770i | \(0.0601259\pi\) |
−0.328493 | + | 0.944506i | \(0.606541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.79227e6 | + | 4.83636e6i | −0.683694 | + | 1.18419i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.86131e6 | − | 6.68798e6i | 0.934813 | − | 1.61914i | 0.159846 | − | 0.987142i | \(-0.448900\pi\) |
0.774967 | − | 0.632002i | \(-0.217767\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.96258e6 | 0.948589 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.70308e6 | − | 4.68187e6i | 0.639867 | − | 1.10828i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.68110e6 | 1.56398 | 0.781992 | − | 0.623288i | \(-0.214204\pi\) | ||||
0.781992 | + | 0.623288i | \(0.214204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.45220e6 | + | 4.24733e6i | 0.567694 | + | 0.983275i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.43174e6 | − | 9.40806e6i | −1.24364 | − | 2.15404i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.44334e6 | −1.23264 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.15454e6 | −0.258593 | −0.129297 | − | 0.991606i | \(-0.541272\pi\) | ||||
−0.129297 | + | 0.991606i | \(0.541272\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −765010. | − | 1.32504e6i | −0.169487 | − | 0.293559i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.99643e6 | + | 6.92202e6i | 0.875830 | + | 1.51698i | 0.855876 | + | 0.517181i | \(0.173019\pi\) |
0.0199544 | + | 0.999801i | \(0.493648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.73362e6 | 1.02622 | 0.513111 | − | 0.858322i | \(-0.328493\pi\) | ||||
0.513111 | + | 0.858322i | \(0.328493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.96177e6 | − | 6.86199e6i | 0.849683 | − | 1.47169i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.37127e6 | 0.715322 | 0.357661 | − | 0.933851i | \(-0.383574\pi\) | ||||
0.357661 | + | 0.933851i | \(0.383574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.51321e6 | − | 2.62096e6i | 0.317664 | − | 0.550210i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.97841e6 | − | 1.03549e7i | 1.24175 | − | 2.15077i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.07394e6 | − | 1.86012e6i | −0.220713 | − | 0.382285i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −282659. | − | 860093.i | −0.0574816 | − | 0.174909i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.37250e6 | + | 2.37724e6i | 0.276195 | + | 0.478384i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.45446e6 | + | 5.98330e6i | −0.687925 | + | 1.19152i | 0.284583 | + | 0.958652i | \(0.408145\pi\) |
−0.972508 | + | 0.232870i | \(0.925188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.53844e6 | − | 6.12876e6i | 0.697348 | − | 1.20784i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 632010. | 0.123270 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.16382e6 | − | 5.47990e6i | 0.610742 | − | 1.05784i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.84736e6 | 0.735089 | 0.367545 | − | 0.930006i | \(-0.380199\pi\) | ||||
0.367545 | + | 0.930006i | \(0.380199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.43342e6 | − | 1.11430e7i | −1.21666 | − | 2.10732i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.95587e6 | − | 8.58382e6i | −0.927719 | − | 1.60686i | −0.787129 | − | 0.616788i | \(-0.788433\pi\) |
−0.140590 | − | 0.990068i | \(-0.544900\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.85223e6 | −1.08444 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.26197e6 | −1.14868 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.49937e6 | + | 1.29893e7i | 1.36186 | + | 2.35882i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.50894e6 | + | 6.07766e6i | 0.630847 | + | 1.09266i | 0.987379 | + | 0.158376i | \(0.0506259\pi\) |
−0.356532 | + | 0.934283i | \(0.616041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.13257e6 | −0.201591 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.11612e6 | + | 1.93318e6i | −0.196694 | + | 0.340684i | −0.947455 | − | 0.319890i | \(-0.896354\pi\) |
0.750760 | + | 0.660575i | \(0.229687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.50123e6 | 1.13440 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −493453. | + | 854686.i | −0.0852562 | + | 0.147668i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 787950. | − | 1.36477e6i | 0.134804 | − | 0.233488i | −0.790718 | − | 0.612180i | \(-0.790293\pi\) |
0.925523 | + | 0.378692i | \(0.123626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.23449e6 | − | 5.60231e6i | −0.547966 | − | 0.949106i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.43495e6 | + | 1.60448e6i | −0.240737 | + | 0.269178i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.68017e6 | − | 8.10629e6i | −0.777577 | − | 1.34680i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.29960e6 | + | 7.44713e6i | −0.707460 | + | 1.22536i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.97410e6 | − | 3.41924e6i | 0.321700 | − | 0.557200i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.35615e6 | −0.703086 | −0.351543 | − | 0.936172i | \(-0.614343\pi\) | ||||
−0.351543 | + | 0.936172i | \(0.614343\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.64694e6 | − | 4.58464e6i | 0.423146 | − | 0.732911i | −0.573099 | − | 0.819486i | \(-0.694259\pi\) |
0.996245 | + | 0.0865752i | \(0.0275923\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.52350e6 | 0.399580 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.76040e6 | + | 6.51320e6i | 0.589803 | + | 1.02157i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.20779e6 | + | 5.55605e6i | 0.498387 | + | 0.863232i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.25705e6 | −1.11692 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.84180e6 | −1.04316 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.30580e6 | − | 2.26171e6i | −0.197238 | − | 0.341627i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.54374e6 | + | 1.13341e7i | 0.979243 | + | 1.69610i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.61286e6 | −1.12869 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.45983e6 | + | 9.45670e6i | −0.802021 | + | 1.38914i | 0.116263 | + | 0.993218i | \(0.462909\pi\) |
−0.918284 | + | 0.395923i | \(0.870425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.71551e6 | 1.26851 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −538572. | + | 932835.i | −0.0776699 | + | 0.134528i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.49890e6 | − | 2.59617e6i | 0.214192 | − | 0.370992i | −0.738830 | − | 0.673892i | \(-0.764621\pi\) |
0.953022 | + | 0.302900i | \(0.0979548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.50161e6 | − | 1.12611e7i | −0.920640 | − | 1.59460i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.57053e6 | + | 7.82176e6i | 0.360697 | + | 1.09755i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.07835e6 | − | 5.33186e6i | −0.428061 | − | 0.741423i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.26938e6 | − | 1.25909e7i | 1.00176 | − | 1.73510i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 197093. | − | 341375.i | 0.0269174 | − | 0.0466223i | −0.852253 | − | 0.523130i | \(-0.824764\pi\) |
0.879170 | + | 0.476508i | \(0.158098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.99637e6 | 0.405569 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.36613e6 | − | 9.29441e6i | 0.719870 | − | 1.24685i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.10461e7 | −1.46872 | −0.734361 | − | 0.678760i | \(-0.762518\pi\) | ||||
−0.734361 | + | 0.678760i | \(0.762518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.56994e6 | − | 7.91537e6i | −0.602267 | − | 1.04316i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.88752e6 | + | 6.73338e6i | 0.507826 | + | 0.879580i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.21256e6 | −0.933918 | −0.466959 | − | 0.884279i | \(-0.654651\pi\) | ||||
−0.466959 | + | 0.884279i | \(0.654651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.09113e6 | −0.396760 | −0.198380 | − | 0.980125i | \(-0.563568\pi\) | ||||
−0.198380 | + | 0.980125i | \(0.563568\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.04003e6 | + | 1.21937e7i | 0.895752 | + | 1.55149i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −41453.0 | − | 71798.6i | −0.00522861 | − | 0.00905621i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.16381e6 | −0.270570 | −0.135285 | − | 0.990807i | \(-0.543195\pi\) | ||||
−0.135285 | + | 0.990807i | \(0.543195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1234.28 | + | 2137.84i | −0.000153009 | + | 0.000265020i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.32392e6 | −1.14593 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.87099e6 | + | 3.24066e6i | −0.227982 | + | 0.394877i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.36783e6 | − | 7.56531e6i | 0.527687 | − | 0.913981i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 632835. | + | 1.09610e6i | 0.0758045 | + | 0.131297i | 0.901436 | − | 0.432913i | \(-0.142514\pi\) |
−0.825631 | + | 0.564210i | \(0.809181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.05347e6 | − | 7.88679e6i | 0.837750 | − | 0.936725i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.21553e6 | − | 1.42297e7i | −0.967535 | − | 1.67582i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.38325e6 | + | 1.45202e7i | −0.978984 | + | 1.69565i | −0.312878 | + | 0.949793i | \(0.601293\pi\) |
−0.666106 | + | 0.745857i | \(0.732040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.30720e6 | − | 9.19234e6i | 0.614573 | − | 1.06447i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.80037e6 | −0.436405 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.31238e6 | + | 4.00516e6i | −0.263325 | + | 0.456092i | −0.967123 | − | 0.254308i | \(-0.918152\pi\) |
0.703798 | + | 0.710400i | \(0.251486\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −568699. | −0.0642238 | −0.0321119 | − | 0.999484i | \(-0.510223\pi\) | ||||
−0.0321119 | + | 0.999484i | \(0.510223\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.42846e6 | + | 4.20621e6i | 0.271980 | + | 0.471083i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −202107. | − | 350059.i | −0.0224488 | − | 0.0388824i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.98344e6 | −1.09979 | −0.549893 | − | 0.835235i | \(-0.685332\pi\) | ||||
−0.549893 | + | 0.835235i | \(0.685332\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.29489e7 | −2.50737 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.99809e6 | − | 1.03890e7i | −0.649995 | − | 1.12582i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.93664e6 | − | 5.08641e6i | −0.315645 | − | 0.546714i | 0.663929 | − | 0.747796i | \(-0.268888\pi\) |
−0.979574 | + | 0.201082i | \(0.935554\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.40558e7 | −1.49854 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.31577e6 | + | 7.47513e6i | −0.456400 | + | 0.790508i | −0.998767 | − | 0.0496336i | \(-0.984195\pi\) |
0.542368 | + | 0.840141i | \(0.317528\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.29725e6 | 0.660578 | 0.330289 | − | 0.943880i | \(-0.392854\pi\) | ||||
0.330289 | + | 0.943880i | \(0.392854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −98557.6 | + | 170707.i | −0.0102556 | + | 0.0177632i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.37450e6 | + | 1.27730e7i | −0.761224 | + | 1.31848i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.81831e6 | + | 6.61351e6i | 0.390995 | + | 0.677224i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.47794e7 | − | 3.08961e6i | −1.50137 | − | 0.313859i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.89989e6 | + | 1.19510e7i | 0.695369 | + | 1.20441i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.14448e6 | + | 3.71434e6i | −0.214411 | + | 0.371371i | −0.953090 | − | 0.302686i | \(-0.902117\pi\) |
0.738679 | + | 0.674057i | \(0.235450\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.14788e6 | − | 1.41125e7i | 0.808231 | − | 1.39990i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 91826.8 | 0.00903723 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.31010e6 | − | 9.19737e6i | 0.518507 | − | 0.898080i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.40705e7 | −2.33202 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.61057e6 | − | 9.71779e6i | −0.539339 | − | 0.934163i | −0.998940 | − | 0.0460372i | \(-0.985341\pi\) |
0.459600 | − | 0.888126i | \(-0.347993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.20567e6 | + | 3.82032e6i | 0.210384 | + | 0.364395i | 0.951835 | − | 0.306612i | \(-0.0991953\pi\) |
−0.741451 | + | 0.671007i | \(0.765862\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.15574e6 | 0.582614 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.20279e6 | −0.676457 | −0.338229 | − | 0.941064i | \(-0.609828\pi\) | ||||
−0.338229 | + | 0.941064i | \(0.609828\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.94641e6 | − | 8.56744e6i | −0.460976 | − | 0.798434i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.47460e7 | + | 2.55408e7i | 1.36371 | + | 2.36201i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.23537e6 | −0.388695 | −0.194347 | − | 0.980933i | \(-0.562259\pi\) | ||||
−0.194347 | + | 0.980933i | \(0.562259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.01627e6 | − | 3.49227e6i | 0.183630 | − | 0.318057i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.03817e7 | 0.938325 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.24491e6 | − | 5.62036e6i | 0.291065 | − | 0.504139i | −0.682997 | − | 0.730421i | \(-0.739324\pi\) |
0.974062 | + | 0.226282i | \(0.0726572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.60734e6 | + | 9.71219e6i | −0.499175 | + | 0.864597i | −1.00000 | 0.000952002i | \(-0.999697\pi\) | |
0.500824 | + | 0.865549i | \(0.333030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.48594e6 | + | 1.29660e7i | 0.661397 | + | 1.14557i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.46171e7 | − | 3.05568e6i | −1.28176 | − | 0.267950i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 376977. | + | 652943.i | 0.0328095 | + | 0.0568278i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.18676e6 | + | 3.78757e6i | −0.188901 | + | 0.327187i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.86300e6 | − | 1.53512e7i | 0.759932 | − | 1.31624i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 301881. | 0.0256920 | 0.0128460 | − | 0.999917i | \(-0.495911\pi\) | ||||
0.0128460 | + | 0.999917i | \(0.495911\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −393522. | + | 681600.i | −0.0332437 | + | 0.0575798i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −470872. | −0.0394849 | −0.0197424 | − | 0.999805i | \(-0.506285\pi\) | ||||
−0.0197424 | + | 0.999805i | \(0.506285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.17760e7 | + | 2.03966e7i | 0.980218 | + | 1.69779i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.07813e6 | − | 1.22597e7i | −0.584859 | − | 1.01301i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.01992e7 | 0.836589 | 0.418295 | − | 0.908311i | \(-0.362628\pi\) | ||||
0.418295 | + | 0.908311i | \(0.362628\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00370e7 | −0.817296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.51376e6 | − | 4.35396e6i | −0.203204 | − | 0.351960i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.61010e6 | − | 4.52083e6i | −0.209464 | − | 0.362802i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.81669e6 | −0.383754 | −0.191877 | − | 0.981419i | \(-0.561458\pi\) | ||||
−0.191877 | + | 0.981419i | \(0.561458\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.16538e7 | − | 2.01849e7i | 0.921792 | − | 1.59659i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.90220e7 | −1.49380 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.67068e6 | − | 1.15540e7i | 0.520102 | − | 0.900843i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.19348e7 | − | 2.06717e7i | 0.923895 | − | 1.60023i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.09052e6 | + | 3.62088e6i | 0.160679 | + | 0.278304i | 0.935112 | − | 0.354351i | \(-0.115298\pi\) |
−0.774434 | + | 0.632655i | \(0.781965\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.29423e7 | − | 1.44713e7i | 0.987694 | − | 1.10438i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.23225e7 | − | 2.13432e7i | −0.933739 | − | 1.61728i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.20990e7 | + | 2.09561e7i | −0.910336 | + | 1.57675i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.41436e6 | + | 7.64589e6i | −0.329801 | + | 0.571232i | −0.982472 | − | 0.186409i | \(-0.940315\pi\) |
0.652671 | + | 0.757641i | \(0.273648\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.88050e6 | 0.733001 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 484459. | − | 839107.i | 0.0356889 | − | 0.0618150i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.19085e7 | 0.871146 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.52989e7 | + | 2.64985e7i | 1.11138 | + | 1.92497i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.62278e6 | + | 4.54279e6i | 0.189208 | + | 0.327718i | 0.944986 | − | 0.327109i | \(-0.106075\pi\) |
−0.755778 | + | 0.654828i | \(0.772741\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.48398e7 | 2.49596 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 223310. | 0.0158877 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50520e6 | + | 2.60708e6i | 0.106353 | + | 0.184208i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.18888e6 | − | 1.59156e7i | −0.644802 | − | 1.11683i | −0.984347 | − | 0.176241i | \(-0.943606\pi\) |
0.339545 | − | 0.940590i | \(-0.389727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.02351e7 | −1.41022 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.92142e6 | + | 5.06006e6i | −0.202209 | + | 0.350237i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.42837e7 | 1.66938 | 0.834689 | − | 0.550721i | \(-0.185647\pi\) | ||||
0.834689 | + | 0.550721i | \(0.185647\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.09091e7 | − | 1.88951e7i | 0.744852 | − | 1.29012i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.31048e6 | + | 5.73391e6i | −0.224503 | + | 0.388850i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.29261e6 | + | 2.23886e6i | 0.0870674 | + | 0.150805i | 0.906270 | − | 0.422699i | \(-0.138917\pi\) |
−0.819203 | + | 0.573504i | \(0.805584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.40415e7 | − | 1.57005e7i | 0.939441 | − | 1.05043i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.08526e6 | − | 1.57361e7i | −0.603761 | − | 1.04575i | −0.992246 | − | 0.124290i | \(-0.960335\pi\) |
0.388485 | − | 0.921455i | \(-0.372999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.84862e6 | + | 1.01301e7i | −0.386067 | + | 0.668688i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.48168e6 | − | 1.29586e7i | 0.490566 | − | 0.849685i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.72054e6 | 0.633120 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.21562e6 | − | 1.24978e7i | 0.466846 | − | 0.808601i | −0.532437 | − | 0.846470i | \(-0.678724\pi\) |
0.999283 | + | 0.0378689i | \(0.0120569\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.06521e7 | 0.684615 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.17526e7 | + | 2.03561e7i | 0.750355 | + | 1.29965i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.51265e6 | − | 2.61999e6i | −0.0959399 | − | 0.166173i | 0.814061 | − | 0.580780i | \(-0.197252\pi\) |
−0.910001 | + | 0.414607i | \(0.863919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.38266e6 | −0.0871184 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.91756e7 | 1.20029 | 0.600147 | − | 0.799890i | \(-0.295109\pi\) | ||||
0.600147 | + | 0.799890i | \(0.295109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00460e6 | − | 3.47208e6i | −0.124657 | − | 0.215913i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.51718e6 | + | 1.47522e7i | 0.526190 | + | 0.911387i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.38008e7 | 0.847065 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.08868e7 | + | 1.88565e7i | −0.663872 | + | 1.14986i | 0.315718 | + | 0.948853i | \(0.397755\pi\) |
−0.979590 | + | 0.201007i | \(0.935579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.21276e7 | 0.734750 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.04601e6 | − | 1.81174e6i | 0.0629631 | − | 0.109055i | −0.832826 | − | 0.553536i | \(-0.813278\pi\) |
0.895789 | + | 0.444480i | \(0.146612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.93435e6 | − | 3.35040e6i | 0.115686 | − | 0.200374i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.70572e7 | + | 4.68644e7i | 1.60779 | + | 2.78478i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.83724e7 | − | 3.84072e6i | −1.08473 | − | 0.226761i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.64065e7 | − | 2.84168e7i | −0.962471 | − | 1.66705i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.57872e6 | − | 6.19852e6i | 0.208604 | − | 0.361313i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.29354e7 | + | 2.24048e7i | −0.749215 | + | 1.29768i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.41901e7 | −1.96772 | −0.983860 | − | 0.178942i | \(-0.942733\pi\) | ||||
−0.983860 | + | 0.178942i | \(0.942733\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.71400e6 | + | 6.43284e6i | −0.212398 | + | 0.367884i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.40193e7 | 1.93323 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.23642e7 | + | 2.14154e7i | 0.698205 | + | 1.20933i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.36220e6 | − | 9.28759e6i | −0.300902 | − | 0.521177i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.39978e7 | −0.780573 | −0.390287 | − | 0.920693i | \(-0.627624\pi\) | ||||
−0.390287 | + | 0.920693i | \(0.627624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.33923e7 | 1.29630 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.18349e7 | − | 2.04986e7i | −0.651751 | − | 1.12887i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.07614e6 | + | 1.22562e7i | 0.387265 | + | 0.670762i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.36747e6 | −0.0743754 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.67253e6 | − | 2.89690e6i | 0.0904043 | − | 0.156585i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.41687e6 | −0.398428 | −0.199214 | − | 0.979956i | \(-0.563839\pi\) | ||||
−0.199214 | + | 0.979956i | \(0.563839\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.16311e7 | + | 2.01456e7i | −0.620965 | + | 1.07554i | 0.368341 | + | 0.929691i | \(0.379926\pi\) |
−0.989306 | + | 0.145852i | \(0.953408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.10890e6 | − | 1.23130e7i | 0.377204 | − | 0.653337i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.39199e7 | + | 2.41100e7i | 0.734079 | + | 1.27146i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.04619e6 | + | 1.68204e6i | 0.421731 | + | 0.0881620i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.62574e7 | + | 2.81586e7i | 0.846917 | + | 1.46690i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.30361e6 | − | 7.45407e6i | 0.222831 | − | 0.385954i | −0.732836 | − | 0.680406i | \(-0.761804\pi\) |
0.955666 | + | 0.294452i | \(0.0951370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.89709e6 | + | 1.36782e7i | −0.406413 | + | 0.703928i | −0.994485 | − | 0.104881i | \(-0.966554\pi\) |
0.588072 | + | 0.808809i | \(0.299887\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.52069e6 | −0.282396 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.47559e6 | + | 1.12161e7i | −0.329242 | + | 0.570264i | −0.982362 | − | 0.186990i | \(-0.940127\pi\) |
0.653119 | + | 0.757255i | \(0.273460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.28769e7 | −0.650765 | −0.325383 | − | 0.945582i | \(-0.605493\pi\) | ||||
−0.325383 | + | 0.945582i | \(0.605493\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.26540e7 | − | 3.92379e7i | −1.13800 | − | 1.97107i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.03546e7 | + | 1.79347e7i | 0.517036 | + | 0.895532i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.45054e6 | 0.121631 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.19814e6 | −0.453823 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.39980e7 | + | 2.42452e7i | 0.686530 | + | 1.18911i | 0.972953 | + | 0.231002i | \(0.0742003\pi\) |
−0.286423 | + | 0.958103i | \(0.592466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.43281e6 | − | 5.94580e6i | −0.167363 | − | 0.289881i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.33809e7 | −0.648508 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.06768e6 | − | 1.84927e6i | 0.0514398 | − | 0.0890963i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.50451e6 | 0.0720588 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.43669e7 | + | 4.22047e7i | −1.16020 | + | 2.00952i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 888925. | − | 1.53966e6i | 0.0420767 | − | 0.0728789i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.33528e6 | + | 1.27051e7i | 0.345179 | + | 0.597867i | 0.985386 | − | 0.170335i | \(-0.0544850\pi\) |
−0.640208 | + | 0.768202i | \(0.721152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.59759e7 | − | 1.78633e7i | 0.747394 | − | 0.835693i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.31078e7 | − | 2.27033e7i | −0.609645 | − | 1.05594i | −0.991299 | − | 0.131631i | \(-0.957979\pi\) |
0.381653 | − | 0.924306i | \(-0.375355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.60178e7 | + | 2.77437e7i | −0.740664 | + | 1.28287i | 0.211530 | + | 0.977372i | \(0.432156\pi\) |
−0.952193 | + | 0.305496i | \(0.901178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.61584e7 | − | 4.53076e7i | 1.20255 | − | 2.08288i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.79175e6 | 0.127600 | 0.0637998 | − | 0.997963i | \(-0.479678\pi\) | ||||
0.0637998 | + | 0.997963i | \(0.479678\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.27133e6 | + | 7.39817e6i | −0.194099 | + | 0.336189i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.94040e6 | 0.178030 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.73456e6 | + | 1.16646e7i | 0.302524 | + | 0.523986i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.61823e6 | − | 7.99900e6i | −0.206267 | − | 0.357265i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.77970e7 | −1.67850 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.51162e7 | −1.55056 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.02849e7 | + | 1.78139e7i | 0.451543 | + | 0.782096i | 0.998482 | − | 0.0550767i | \(-0.0175403\pi\) |
−0.546939 | + | 0.837173i | \(0.684207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.98009e6 | − | 1.20899e7i | −0.304711 | − | 0.527776i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −884571. | −0.0383966 | −0.0191983 | − | 0.999816i | \(-0.506111\pi\) | ||||
−0.0191983 | + | 0.999816i | \(0.506111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.71324e6 | + | 4.69946e6i | −0.117108 | + | 0.202837i | −0.918620 | − | 0.395141i | \(-0.870696\pi\) |
0.801513 | + | 0.597978i | \(0.204029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.83524e7 | 1.21684 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.62216e6 | + | 1.32020e7i | −0.325289 | + | 0.563417i | −0.981571 | − | 0.191099i | \(-0.938795\pi\) |
0.656282 | + | 0.754516i | \(0.272128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −170893. | + | 295995.i | −0.00725220 | + | 0.0125612i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.50478e6 | − | 1.47307e7i | −0.358896 | − | 0.621626i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.02748e7 | − | 3.12648e7i | −0.431166 | − | 1.31198i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.41586e7 | − | 2.45235e7i | −0.590831 | − | 1.02335i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 964427. | − | 1.67044e6i | 0.0400210 | − | 0.0693185i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.75912e7 | + | 3.04688e7i | −0.725931 | + | 1.25735i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01793e7 | 0.417739 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.14560e7 | + | 1.98425e7i | −0.467536 | + | 0.809797i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.88576e7 | −0.765360 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.62809e6 | − | 6.28404e6i | −0.146440 | − | 0.253642i | 0.783469 | − | 0.621431i | \(-0.213448\pi\) |
−0.929909 | + | 0.367789i | \(0.880115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.94169e7 | − | 3.36311e7i | −0.779419 | − | 1.34999i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.21717e6 | −0.128433 | −0.0642166 | − | 0.997936i | \(-0.520455\pi\) | ||||
−0.0642166 | + | 0.997936i | \(0.520455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.03981e7 | 0.809864 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.54010e7 | + | 4.39959e7i | 1.00299 | + | 1.73724i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.50468e6 | + | 1.29985e7i | 0.294720 | + | 0.510469i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.78840e6 | 0.226084 | 0.113042 | − | 0.993590i | \(-0.463941\pi\) | ||||
0.113042 | + | 0.993590i | \(0.463941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.66466e6 | − | 2.88327e6i | 0.0646660 | − | 0.112005i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.57752e7 | 1.76858 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54931e6 | − | 6.14758e6i | 0.136392 | − | 0.236238i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.79561e7 | + | 4.84214e7i | −1.06851 | + | 1.85071i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.26109e7 | − | 2.18428e7i | −0.479411 | − | 0.830364i | 0.520310 | − | 0.853977i | \(-0.325816\pi\) |
−0.999721 | + | 0.0236130i | \(0.992483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.94223e7 | − | 2.17170e7i | 0.734391 | − | 0.821155i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.89418e7 | + | 6.74492e7i | 1.46458 | + | 2.53672i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.16106e7 | + | 2.01102e7i | −0.434337 | + | 0.752294i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.25018e7 | − | 2.16537e7i | 0.465182 | − | 0.805719i | −0.534027 | − | 0.845467i | \(-0.679322\pi\) |
0.999210 | + | 0.0397478i | \(0.0126555\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.24383e7 | 1.94082 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.25003e7 | + | 2.16511e7i | −0.460198 | + | 0.797087i | −0.998970 | − | 0.0453646i | \(-0.985555\pi\) |
0.538772 | + | 0.842452i | \(0.318888\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.71879e6 | −0.0629425 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.49085e6 | + | 1.12425e7i | 0.236441 | + | 0.409527i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 155598. | + | 269504.i | 0.00563806 | + | 0.00976540i | 0.868831 | − | 0.495109i | \(-0.164872\pi\) |
−0.863193 | + | 0.504875i | \(0.831539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.97429e7 | −0.711617 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.38098e6 | −0.0495150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.37486e7 | − | 4.11338e7i | −0.847045 | − | 1.46712i | −0.883834 | − | 0.467802i | \(-0.845046\pi\) |
0.0367888 | − | 0.999323i | \(-0.488287\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.52324e7 | − | 2.63833e7i | −0.540456 | − | 0.936098i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.02056e7 | 1.77203 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.86793e7 | − | 3.23535e7i | 0.655864 | − | 1.13599i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.65842e7 | 0.579278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.79993e6 | + | 1.35099e7i | −0.271035 | + | 0.469446i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2670.60 | − | 4625.62i | 9.23190e−5 | − | 0.000159901i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.00225e7 | + | 1.73594e7i | 0.344674 | + | 0.596992i | 0.985294 | − | 0.170865i | \(-0.0546562\pi\) |
−0.640621 | + | 0.767857i | \(0.721323\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.28235e7 | + | 3.90202e7i | 0.438730 | + | 1.33500i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.33282e7 | − | 2.30850e7i | −0.453651 | − | 0.785747i | 0.544959 | − | 0.838463i | \(-0.316545\pi\) |
−0.998610 | + | 0.0527164i | \(0.983212\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.54005e7 | − | 6.13155e7i | 1.19875 | − | 2.07629i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.85077e6 | − | 6.66973e6i | 0.129729 | − | 0.224697i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.83585e7 | −0.950487 | −0.475243 | − | 0.879854i | \(-0.657640\pi\) | ||||
−0.475243 | + | 0.879854i | \(0.657640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.61333e7 | − | 2.79437e7i | 0.537980 | − | 0.931809i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.43412e6 | 0.213460 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.09422e6 | − | 1.40196e7i | −0.267172 | − | 0.462756i | 0.700958 | − | 0.713202i | \(-0.252756\pi\) |
−0.968130 | + | 0.250446i | \(0.919423\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.77758e7 | + | 3.07887e7i | 0.583767 | + | 1.01111i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.17303e7 | 2.99723 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 752745. | 0.0244713 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.72685e7 | + | 2.99099e7i | 0.558561 | + | 0.967456i | 0.997617 | + | 0.0689965i | \(0.0219797\pi\) |
−0.439056 | + | 0.898460i | \(0.644687\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.74439e7 | − | 4.75342e7i | −0.883227 | − | 1.52979i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.22282e6 | 0.263307 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.12806e7 | − | 1.95385e7i | 0.359412 | − | 0.622521i | −0.628450 | − | 0.777850i | \(-0.716310\pi\) |
0.987863 | + | 0.155329i | \(0.0496438\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.68775e7 | −0.535050 |
(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 | 304.6.i.d.273.8 | 18 | ||
4.3 | odd | 2 | 76.6.e.a.45.2 | ✓ | 18 | ||
12.11 | even | 2 | 684.6.k.f.577.8 | 18 | |||
19.11 | even | 3 | inner | 304.6.i.d.49.8 | 18 | ||
76.11 | odd | 6 | 76.6.e.a.49.2 | yes | 18 | ||
228.11 | even | 6 | 684.6.k.f.505.8 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.2 | ✓ | 18 | 4.3 | odd | 2 | ||
76.6.e.a.49.2 | yes | 18 | 76.11 | odd | 6 | ||
304.6.i.d.49.8 | 18 | 19.11 | even | 3 | inner | ||
304.6.i.d.273.8 | 18 | 1.1 | even | 1 | trivial | ||
684.6.k.f.505.8 | 18 | 228.11 | even | 6 | |||
684.6.k.f.577.8 | 18 | 12.11 | even | 2 |