Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(929,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.929");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.i (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: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 929.4 | ||
Character | \(\chi\) | \(=\) | 960.929 |
Dual form | 960.3.i.b.929.7 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −2.90428 | − | 0.751787i | −0.968092 | − | 0.250596i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.38579 | + | 4.80412i | 0.277158 | + | 0.960824i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.03946i | − | 0.434208i | −0.976148 | − | 0.217104i | \(-0.930339\pi\) | ||
0.976148 | − | 0.217104i | \(-0.0696611\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.86963 | + | 4.36679i | 0.874404 | + | 0.485199i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.4633 | 1.04211 | 0.521057 | − | 0.853522i | \(-0.325538\pi\) | ||||
0.521057 | + | 0.853522i | \(0.325538\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.9968 | 1.30745 | 0.653724 | − | 0.756733i | \(-0.273206\pi\) | ||||
0.653724 | + | 0.756733i | \(0.273206\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.413034 | − | 14.9943i | −0.0275356 | − | 0.999621i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.1540 | −1.06789 | −0.533943 | − | 0.845521i | \(-0.679290\pi\) | ||||
−0.533943 | + | 0.845521i | \(0.679290\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 16.9311i | − | 0.891112i | −0.895254 | − | 0.445556i | \(-0.853006\pi\) | ||
0.895254 | − | 0.445556i | \(-0.146994\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.28502 | + | 8.82743i | −0.108811 | + | 0.420354i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −22.3489 | −0.971690 | −0.485845 | − | 0.874045i | \(-0.661488\pi\) | ||||
−0.485845 | + | 0.874045i | \(0.661488\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.1592 | + | 13.3150i | −0.846367 | + | 0.532600i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19.5727 | − | 18.5987i | −0.724914 | − | 0.688839i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.8986 | 0.617193 | 0.308596 | − | 0.951193i | \(-0.400141\pi\) | ||||
0.308596 | + | 0.951193i | \(0.400141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.9667 | 0.547314 | 0.273657 | − | 0.961827i | \(-0.411767\pi\) | ||||
0.273657 | + | 0.961827i | \(0.411767\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −33.2924 | − | 8.61792i | −1.00886 | − | 0.261149i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.6019 | − | 4.21205i | 0.417198 | − | 0.120344i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.21295 | 0.0327823 | 0.0163912 | − | 0.999866i | \(-0.494782\pi\) | ||||
0.0163912 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −49.3634 | − | 12.7780i | −1.26573 | − | 0.327641i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.0791i | 1.02632i | 0.858293 | + | 0.513160i | \(0.171525\pi\) | ||||
−0.858293 | + | 0.513160i | \(0.828475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.98640 | −0.0461954 | −0.0230977 | − | 0.999733i | \(-0.507353\pi\) | ||||
−0.0230977 | + | 0.999733i | \(0.507353\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.0730 | + | 43.8581i | −0.223844 | + | 0.974625i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 52.4557 | 1.11608 | 0.558039 | − | 0.829815i | \(-0.311554\pi\) | ||||
0.558039 | + | 0.829815i | \(0.311554\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 39.7617 | 0.811463 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.7244 | + | 13.6480i | 1.03381 | + | 0.267607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.58147i | 0.161915i | 0.996718 | + | 0.0809573i | \(0.0257977\pi\) | ||||
−0.996718 | + | 0.0809573i | \(0.974202\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.8856 | + | 55.0709i | 0.288830 | + | 1.00129i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.7286 | + | 49.1727i | −0.223309 | + | 0.862678i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 93.0686 | 1.57743 | 0.788717 | − | 0.614756i | \(-0.210746\pi\) | ||||
0.788717 | + | 0.614756i | \(0.210746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 80.4817i | − | 1.31937i | −0.751541 | − | 0.659686i | \(-0.770689\pi\) | ||
0.751541 | − | 0.659686i | \(-0.229311\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.2727 | − | 23.9194i | 0.210678 | − | 0.379673i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.5540 | + | 81.6548i | 0.362369 | + | 1.25623i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38.1420 | 0.569283 | 0.284642 | − | 0.958634i | \(-0.408125\pi\) | ||||
0.284642 | + | 0.958634i | \(0.408125\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 64.9073 | + | 16.8016i | 0.940685 | + | 0.243501i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 109.674i | − | 1.54470i | −0.635197 | − | 0.772350i | \(-0.719081\pi\) | ||
0.635197 | − | 0.772350i | \(-0.280919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28.2759i | 0.387341i | 0.981067 | + | 0.193671i | \(0.0620393\pi\) | ||||
−0.981067 | + | 0.193671i | \(0.937961\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 71.4621 | − | 22.7632i | 0.952828 | − | 0.303509i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 34.8421i | − | 0.452495i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −56.1781 | −0.711115 | −0.355558 | − | 0.934654i | \(-0.615709\pi\) | ||||
−0.355558 | + | 0.934654i | \(0.615709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 42.8623 | + | 68.7301i | 0.529164 | + | 0.848520i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 126.249i | 1.52108i | 0.649294 | + | 0.760538i | \(0.275065\pi\) | ||||
−0.649294 | + | 0.760538i | \(0.724935\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.1577 | − | 87.2143i | −0.295972 | − | 1.02605i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −51.9824 | − | 13.4559i | −0.597499 | − | 0.154666i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 126.786i | 1.42457i | 0.701892 | + | 0.712283i | \(0.252339\pi\) | ||||
−0.701892 | + | 0.712283i | \(0.747661\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 51.6611i | − | 0.567705i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −49.2761 | − | 12.7554i | −0.529850 | − | 0.137154i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 81.3392 | − | 23.4630i | 0.856202 | − | 0.246978i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 153.612i | − | 1.58363i | −0.610761 | − | 0.791815i | \(-0.709136\pi\) | ||
0.610761 | − | 0.791815i | \(-0.290864\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 90.2116 | + | 50.0576i | 0.911228 | + | 0.505633i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 170.074 | 1.68390 | 0.841948 | − | 0.539559i | \(-0.181409\pi\) | ||||
0.841948 | + | 0.539559i | \(0.181409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7993i | 0.143683i | 0.997416 | + | 0.0718415i | \(0.0228876\pi\) | ||||
−0.997416 | + | 0.0718415i | \(0.977112\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −45.5746 | + | 1.25540i | −0.434044 | + | 0.0119562i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 177.576i | 1.65959i | 0.558069 | + | 0.829795i | \(0.311543\pi\) | ||||
−0.558069 | + | 0.829795i | \(0.688457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 189.527i | 1.73878i | 0.494130 | + | 0.869388i | \(0.335487\pi\) | ||||
−0.494130 | + | 0.869388i | \(0.664513\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.52273 | − | 0.911877i | −0.0317363 | − | 0.00821511i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 107.567 | 0.951924 | 0.475962 | − | 0.879466i | \(-0.342100\pi\) | ||||
0.475962 | + | 0.879466i | \(0.342100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −30.9708 | − | 107.367i | −0.269311 | − | 0.933624i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 133.759 | + | 74.2216i | 1.14324 | + | 0.634372i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 55.1785i | 0.463685i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4061 | 0.0860012 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 31.6345 | − | 122.209i | 0.257191 | − | 0.993572i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −93.2890 | − | 83.1996i | −0.746312 | − | 0.665597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 209.938i | − | 1.65305i | −0.562897 | − | 0.826527i | \(-0.690313\pi\) | ||
0.562897 | − | 0.826527i | \(-0.309687\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.76906 | + | 1.49335i | 0.0447214 | + | 0.0115764i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 28.0136 | 0.213844 | 0.106922 | − | 0.994267i | \(-0.465900\pi\) | ||||
0.106922 | + | 0.994267i | \(0.465900\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −51.4615 | −0.386928 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 62.2266 | − | 119.803i | 0.460938 | − | 0.887432i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 138.049 | 1.00766 | 0.503830 | − | 0.863803i | \(-0.331924\pi\) | ||||
0.503830 | + | 0.863803i | \(0.331924\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 162.141i | 1.16648i | 0.812299 | + | 0.583242i | \(0.198216\pi\) | ||||
−0.812299 | + | 0.583242i | \(0.801784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −152.346 | − | 39.4355i | −1.08047 | − | 0.279684i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 194.839 | 1.36251 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.8036 | + | 85.9870i | 0.171060 | + | 0.593014i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −115.479 | − | 29.8923i | −0.785571 | − | 0.203349i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 237.883 | 1.59653 | 0.798266 | − | 0.602306i | \(-0.205751\pi\) | ||||
0.798266 | + | 0.602306i | \(0.205751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 70.2302 | 0.465100 | 0.232550 | − | 0.972584i | \(-0.425293\pi\) | ||||
0.232550 | + | 0.972584i | \(0.425293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −142.866 | − | 79.2750i | −0.933763 | − | 0.518137i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.5123 | + | 81.5103i | 0.151692 | + | 0.525873i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 169.831 | 1.08173 | 0.540863 | − | 0.841111i | \(-0.318098\pi\) | ||||
0.540863 | + | 0.841111i | \(0.318098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.45144 | − | 24.9230i | 0.0405751 | − | 0.156748i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67.9285i | 0.421916i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 137.171 | 0.841538 | 0.420769 | − | 0.907168i | \(-0.361760\pi\) | ||||
0.420769 | + | 0.907168i | \(0.361760\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.73471 | − | 171.884i | −0.0286952 | − | 1.04172i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −121.223 | −0.725885 | −0.362943 | − | 0.931812i | \(-0.618228\pi\) | ||||
−0.362943 | + | 0.931812i | \(0.618228\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 119.892 | 0.709418 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 73.9347 | − | 133.242i | 0.432367 | − | 0.779192i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 21.4234i | − | 0.123835i | −0.998081 | − | 0.0619175i | \(-0.980278\pi\) | ||
0.998081 | − | 0.0619175i | \(-0.0197216\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 40.4704 | + | 64.3125i | 0.231259 | + | 0.367500i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −270.297 | − | 69.9678i | −1.52710 | − | 0.395298i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −29.4937 | −0.164769 | −0.0823847 | − | 0.996601i | \(-0.526254\pi\) | ||||
−0.0823847 | + | 0.996601i | \(0.526254\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.12992i | 0.0504416i | 0.999682 | + | 0.0252208i | \(0.00802888\pi\) | ||||
−0.999682 | + | 0.0252208i | \(0.991971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −60.5051 | + | 233.741i | −0.330629 | + | 1.27727i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.68089 | + | 5.82714i | 0.00908587 | + | 0.0314981i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −208.104 | −1.11286 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −56.5298 | + | 59.4904i | −0.299100 | + | 0.314764i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.76163i | 0.0458724i | 0.999737 | + | 0.0229362i | \(0.00730146\pi\) | ||||
−0.999737 | + | 0.0229362i | \(0.992699\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 292.061i | 1.51327i | 0.653839 | + | 0.756634i | \(0.273157\pi\) | ||||
−0.653839 | + | 0.756634i | \(0.726843\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.02026 | − | 254.856i | −0.0360013 | − | 1.30695i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 128.223i | − | 0.650877i | −0.945563 | − | 0.325438i | \(-0.894488\pi\) | ||
0.945563 | − | 0.325438i | \(-0.105512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −358.971 | −1.80387 | −0.901936 | − | 0.431869i | \(-0.857854\pi\) | ||||
−0.901936 | + | 0.431869i | \(0.857854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −110.775 | − | 28.6746i | −0.551118 | − | 0.142660i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 54.4020i | − | 0.267990i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −202.153 | + | 58.3127i | −0.986114 | + | 0.284452i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −175.877 | − | 97.5929i | −0.849650 | − | 0.471463i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 194.086i | − | 0.928640i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.4711i | − | 0.0922803i | −0.998935 | − | 0.0461402i | \(-0.985308\pi\) | ||
0.998935 | − | 0.0461402i | \(-0.0146921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −82.4513 | + | 318.523i | −0.387095 | + | 1.49541i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.75273 | − | 9.54293i | −0.0128034 | − | 0.0443857i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 51.5697i | − | 0.237648i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.2575 | − | 82.1210i | 0.0970660 | − | 0.374982i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −308.561 | −1.39620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 229.348i | 1.02847i | 0.857651 | + | 0.514233i | \(0.171923\pi\) | ||||
−0.857651 | + | 0.514233i | \(0.828077\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −224.659 | + | 12.3863i | −0.998484 | + | 0.0550503i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.21047i | 0.0317642i | 0.999874 | + | 0.0158821i | \(0.00505564\pi\) | ||||
−0.999874 | + | 0.0158821i | \(0.994944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.06181i | − | 0.0352044i | −0.999845 | − | 0.0176022i | \(-0.994397\pi\) | ||
0.999845 | − | 0.0176022i | \(-0.00560325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.1938 | + | 101.191i | −0.113393 | + | 0.438056i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 147.853 | 0.634563 | 0.317282 | − | 0.948331i | \(-0.397230\pi\) | ||||
0.317282 | + | 0.948331i | \(0.397230\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 72.6924 | + | 252.003i | 0.309329 | + | 1.07236i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 163.157 | + | 42.2340i | 0.688425 | + | 0.178202i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 225.695i | 0.944331i | 0.881510 | + | 0.472166i | \(0.156528\pi\) | ||||
−0.881510 | + | 0.472166i | \(0.843472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −288.529 | −1.19722 | −0.598608 | − | 0.801042i | \(-0.704279\pi\) | ||||
−0.598608 | + | 0.801042i | \(0.704279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −72.8134 | − | 231.834i | −0.299644 | − | 0.954051i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 55.1013 | + | 191.020i | 0.224903 | + | 0.779674i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 287.775i | − | 1.16508i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 94.9125 | − | 366.663i | 0.381175 | − | 1.47254i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −431.712 | −1.71997 | −0.859984 | − | 0.510321i | \(-0.829527\pi\) | ||||
−0.859984 | + | 0.510321i | \(0.829527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −256.191 | −1.01261 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.49824 | + | 272.207i | 0.0294049 | + | 1.06748i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 130.084 | 0.506162 | 0.253081 | − | 0.967445i | \(-0.418556\pi\) | ||||
0.253081 | + | 0.967445i | \(0.418556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.68670i | − | 0.0142344i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 140.855 | + | 78.1594i | 0.539676 | + | 0.299461i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 94.7069 | 0.360102 | 0.180051 | − | 0.983657i | \(-0.442374\pi\) | ||||
0.180051 | + | 0.983657i | \(0.442374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −41.2265 | + | 11.8921i | −0.155572 | + | 0.0448759i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 95.3164 | − | 368.223i | 0.356990 | − | 1.37911i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −470.172 | −1.74785 | −0.873926 | − | 0.486059i | \(-0.838434\pi\) | ||||
−0.873926 | + | 0.486059i | \(0.838434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 110.731 | 0.408602 | 0.204301 | − | 0.978908i | \(-0.434508\pi\) | ||||
0.204301 | + | 0.978908i | \(0.434508\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38.8381 | + | 150.038i | −0.142264 | + | 0.549590i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −242.553 | + | 152.633i | −0.882011 | + | 0.555029i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 455.593 | 1.64474 | 0.822371 | − | 0.568952i | \(-0.192651\pi\) | ||||
0.822371 | + | 0.568952i | \(0.192651\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 133.522 | + | 74.0902i | 0.478573 | + | 0.265556i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 209.415i | − | 0.745250i | −0.927982 | − | 0.372625i | \(-0.878458\pi\) | ||
0.927982 | − | 0.372625i | \(-0.121542\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4631 | 0.0581734 | 0.0290867 | − | 0.999577i | \(-0.490740\pi\) | ||||
0.0290867 | + | 0.999577i | \(0.490740\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −253.871 | + | 6.99313i | −0.890774 | + | 0.0245373i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 127.898 | 0.445637 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.5695 | 0.140379 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −115.484 | + | 446.132i | −0.396851 | + | 1.53310i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 284.977i | − | 0.972616i | −0.873787 | − | 0.486308i | \(-0.838343\pi\) | ||
0.873787 | − | 0.486308i | \(-0.161657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 128.973 | + | 447.113i | 0.437198 | + | 1.51564i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −224.367 | − | 213.201i | −0.755443 | − | 0.717849i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −379.860 | −1.27043 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.03759i | 0.0200584i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −493.940 | − | 127.859i | −1.63017 | − | 0.421977i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 386.644 | − | 111.531i | 1.26769 | − | 0.365674i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −517.938 | −1.68710 | −0.843548 | − | 0.537054i | \(-0.819537\pi\) | ||||
−0.843548 | + | 0.537054i | \(0.819537\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1259 | − | 42.9814i | 0.0360063 | − | 0.139098i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 309.426i | 0.994940i | 0.867481 | + | 0.497470i | \(0.165738\pi\) | ||||
−0.867481 | + | 0.497470i | \(0.834262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 335.046i | − | 1.07043i | −0.844715 | − | 0.535217i | \(-0.820230\pi\) | ||
0.844715 | − | 0.535217i | \(-0.179770\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 133.305 | + | 30.6164i | 0.423190 | + | 0.0971948i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 589.116i | − | 1.85841i | −0.369564 | − | 0.929205i | \(-0.620493\pi\) | ||
0.369564 | − | 0.929205i | \(-0.379507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 205.176 | 0.643185 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 133.499 | − | 515.730i | 0.415886 | − | 1.60664i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 307.369i | 0.951605i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −359.639 | + | 226.312i | −1.10658 | + | 0.696346i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 142.484 | − | 550.437i | 0.435730 | − | 1.68329i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 159.437i | − | 0.484611i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 259.902i | − | 0.785203i | −0.919709 | − | 0.392602i | \(-0.871575\pi\) | ||
0.919709 | − | 0.392602i | \(-0.128425\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.54544 | + | 5.29668i | 0.0286650 | + | 0.0159060i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 52.8567 | + | 183.239i | 0.157781 | + | 0.546981i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 313.844i | − | 0.931288i | −0.884972 | − | 0.465644i | \(-0.845823\pi\) | ||
0.884972 | − | 0.465644i | \(-0.154177\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −312.405 | − | 80.8677i | −0.921550 | − | 0.238548i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 194.494 | 0.570363 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 269.788i | − | 0.786553i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.23085 | + | 335.106i | 0.0267561 | + | 0.971322i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 372.311i | 1.07294i | 0.843919 | + | 0.536471i | \(0.180243\pi\) | ||||
−0.843919 | + | 0.536471i | \(0.819757\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 67.3243i | − | 0.192906i | −0.995338 | − | 0.0964531i | \(-0.969250\pi\) | ||
0.995338 | − | 0.0964531i | \(-0.0307498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −332.673 | − | 316.118i | −0.947787 | − | 0.900621i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 359.038 | 1.01710 | 0.508552 | − | 0.861031i | \(-0.330181\pi\) | ||||
0.508552 | + | 0.861031i | \(0.330181\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 526.886 | − | 151.985i | 1.48419 | − | 0.428126i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 41.4825 | − | 160.254i | 0.116197 | − | 0.448889i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 59.4869i | 0.165702i | 0.996562 | + | 0.0828509i | \(0.0264025\pi\) | ||||
−0.996562 | + | 0.0828509i | \(0.973597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 74.3369 | 0.205919 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.2223 | − | 7.82320i | −0.0832571 | − | 0.0215515i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −135.841 | + | 39.1844i | −0.372167 | + | 0.107355i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 337.187i | − | 0.918766i | −0.888238 | − | 0.459383i | \(-0.848071\pi\) | ||
0.888238 | − | 0.459383i | \(-0.151929\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −183.751 | + | 331.147i | −0.497970 | + | 0.897418i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.0830 | 0.0703047 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 128.860 | 0.345469 | 0.172734 | − | 0.984968i | \(-0.444740\pi\) | ||||
0.172734 | + | 0.984968i | \(0.444740\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 208.389 | + | 311.768i | 0.555703 | + | 0.831381i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 304.219 | 0.806947 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 146.179i | 0.385697i | 0.981229 | + | 0.192848i | \(0.0617725\pi\) | ||||
−0.981229 | + | 0.192848i | \(0.938227\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −157.829 | + | 609.718i | −0.414248 | + | 1.60031i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 108.089 | 0.282216 | 0.141108 | − | 0.989994i | \(-0.454934\pi\) | ||||
0.141108 | + | 0.989994i | \(0.454934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 167.386 | − | 48.2837i | 0.434768 | − | 0.125412i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.6323 | − | 8.67421i | −0.0403935 | − | 0.0224140i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 344.945 | 0.886748 | 0.443374 | − | 0.896337i | \(-0.353781\pi\) | ||||
0.443374 | + | 0.896337i | \(0.353781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 405.723 | 1.03765 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −81.3591 | − | 21.0602i | −0.207021 | − | 0.0535884i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −77.8509 | − | 269.886i | −0.197091 | − | 0.683257i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 651.573 | 1.64124 | 0.820621 | − | 0.571473i | \(-0.193628\pi\) | ||||
0.820621 | + | 0.571473i | \(0.193628\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 149.458 | + | 38.6881i | 0.374582 | + | 0.0969625i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 35.6227i | − | 0.0888346i | −0.999013 | − | 0.0444173i | \(-0.985857\pi\) | ||
0.999013 | − | 0.0444173i | \(-0.0141431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 288.380 | 0.715584 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −270.790 | + | 301.161i | −0.668617 | + | 0.743607i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.9043 | 0.0341629 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −583.841 | −1.42748 | −0.713742 | − | 0.700409i | \(-0.753001\pi\) | ||||
−0.713742 | + | 0.700409i | \(0.753001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −400.934 | − | 103.784i | −0.975508 | − | 0.252515i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 282.878i | − | 0.684935i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −606.517 | + | 174.955i | −1.46149 | + | 0.421578i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 121.896 | − | 470.903i | 0.292316 | − | 1.12926i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −349.798 | −0.834840 | −0.417420 | − | 0.908714i | \(-0.637066\pi\) | ||||
−0.417420 | + | 0.908714i | \(0.637066\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 801.589i | − | 1.90401i | −0.306078 | − | 0.952006i | \(-0.599017\pi\) | ||
0.306078 | − | 0.952006i | \(-0.400983\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 412.807 | + | 229.063i | 0.975903 | + | 0.541520i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 384.125 | − | 241.721i | 0.903823 | − | 0.568755i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −244.621 | −0.572883 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −565.865 | − | 146.477i | −1.31903 | − | 0.341439i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 536.485i | 1.24474i | 0.782721 | + | 0.622372i | \(0.213831\pi\) | ||||
−0.782721 | + | 0.622372i | \(0.786169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 147.436i | 0.340499i | 0.985401 | + | 0.170249i | \(0.0544574\pi\) | ||||
−0.985401 | + | 0.170249i | \(0.945543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.39273 | − | 268.377i | −0.0169948 | − | 0.616959i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 378.392i | 0.865885i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 668.581 | 1.52296 | 0.761482 | − | 0.648187i | \(-0.224472\pi\) | ||||
0.761482 | + | 0.648187i | \(0.224472\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 312.910 | + | 173.631i | 0.709546 | + | 0.393721i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 198.439i | 0.447944i | 0.974596 | + | 0.223972i | \(0.0719025\pi\) | ||||
−0.974596 | + | 0.223972i | \(0.928098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −609.098 | + | 175.699i | −1.36876 | + | 0.394829i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −690.878 | − | 178.837i | −1.54559 | − | 0.400084i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 44.5024i | 0.0991144i | 0.998771 | + | 0.0495572i | \(0.0157810\pi\) | ||||
−0.998771 | + | 0.0495572i | \(0.984219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 482.364i | 1.06954i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −203.968 | − | 52.7981i | −0.450260 | − | 0.116552i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 248.186 | − | 71.5914i | 0.545465 | − | 0.157344i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.70201i | 0.00591250i | 0.999996 | + | 0.00295625i | \(0.000941005\pi\) | ||||
−0.999996 | + | 0.00295625i | \(0.999059\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 355.324 | + | 337.641i | 0.774125 | + | 0.735601i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −530.641 | −1.15107 | −0.575533 | − | 0.817779i | \(-0.695205\pi\) | ||||
−0.575533 | + | 0.817779i | \(0.695205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 775.407i | 1.67475i | 0.546632 | + | 0.837373i | \(0.315910\pi\) | ||||
−0.546632 | + | 0.837373i | \(0.684090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.00784 | − | 254.404i | −0.0150706 | − | 0.547106i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 333.335i | 0.713779i | 0.934147 | + | 0.356890i | \(0.116163\pi\) | ||||
−0.934147 | + | 0.356890i | \(0.883837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 115.931i | − | 0.247187i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −493.236 | − | 127.677i | −1.04721 | − | 0.271076i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.7706 | −0.0481409 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 225.438 | + | 358.249i | 0.474606 | + | 0.754208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −37.4735 | + | 67.5331i | −0.0785608 | + | 0.141579i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 698.275i | − | 1.45778i | −0.684632 | − | 0.728889i | \(-0.740037\pi\) | ||
0.684632 | − | 0.728889i | \(-0.259963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.6162 | 0.0428612 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 51.0677 | − | 197.283i | 0.105730 | − | 0.408454i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 737.971 | − | 212.874i | 1.52159 | − | 0.438915i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 409.379i | − | 0.840614i | −0.907382 | − | 0.420307i | \(-0.861922\pi\) | ||
0.907382 | − | 0.420307i | \(-0.138078\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −398.381 | − | 103.123i | −0.814686 | − | 0.210886i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 275.334 | 0.560763 | 0.280381 | − | 0.959889i | \(-0.409539\pi\) | ||||
0.280381 | + | 0.959889i | \(0.409539\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −324.932 | −0.659091 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −115.469 | + | 502.757i | −0.233270 | + | 1.01567i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −333.349 | −0.670722 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 421.784i | − | 0.845258i | −0.906303 | − | 0.422629i | \(-0.861107\pi\) | ||
0.906303 | − | 0.422629i | \(-0.138893\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 352.064 | + | 91.1337i | 0.702723 | + | 0.181904i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −190.452 | −0.378633 | −0.189316 | − | 0.981916i | \(-0.560627\pi\) | ||||
−0.189316 | + | 0.981916i | \(0.560627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 235.686 | + | 817.054i | 0.466705 | + | 1.61793i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −348.199 | − | 90.1330i | −0.686782 | − | 0.177777i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −300.150 | −0.589685 | −0.294843 | − | 0.955546i | \(-0.595267\pi\) | ||||
−0.294843 | + | 0.955546i | \(0.595267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 85.9435 | 0.168187 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −314.896 | + | 331.388i | −0.613833 | + | 0.645980i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −71.0979 | + | 20.5087i | −0.138054 | + | 0.0398228i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 601.313 | 1.16308 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.1059 | + | 62.2196i | −0.0310325 | + | 0.119884i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 232.372i | 0.446012i | 0.974817 | + | 0.223006i | \(0.0715870\pi\) | ||||
−0.974817 | + | 0.223006i | \(0.928413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 249.629 | 0.477303 | 0.238651 | − | 0.971105i | \(-0.423295\pi\) | ||||
0.238651 | + | 0.971105i | \(0.423295\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −69.1878 | − | 217.206i | −0.131786 | − | 0.413726i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −308.015 | −0.584468 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.5278 | −0.0558182 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 732.416 | + | 406.411i | 1.37931 | + | 0.765370i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 715.211i | 1.34186i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −853.097 | + | 246.083i | −1.59457 | + | 0.459968i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 85.6579 | + | 22.1730i | 0.159512 | + | 0.0412905i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 455.798 | 0.845637 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 349.843i | 0.646661i | 0.946286 | + | 0.323330i | \(0.104802\pi\) | ||||
−0.946286 | + | 0.323330i | \(0.895198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.86376 | − | 26.5158i | 0.0126404 | − | 0.0488321i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −910.509 | + | 262.644i | −1.67066 | + | 0.481915i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −116.234 | −0.212493 | −0.106247 | − | 0.994340i | \(-0.533883\pi\) | ||||
−0.106247 | + | 0.994340i | \(0.533883\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 351.447 | − | 633.362i | 0.640158 | − | 1.15366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 303.043i | − | 0.549988i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 170.751i | 0.308772i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.500988 | − | 18.1873i | −0.000902681 | − | 0.0327699i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 87.2444i | 0.156633i | 0.996929 | + | 0.0783163i | \(0.0249544\pi\) | ||||
−0.996929 | + | 0.0783163i | \(0.975046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.7625 | −0.0603981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 604.393 | + | 156.450i | 1.07735 | + | 0.278877i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 967.995i | − | 1.71935i | −0.510839 | − | 0.859676i | \(-0.670665\pi\) | ||
0.510839 | − | 0.859676i | \(-0.329335\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 149.066 | + | 516.767i | 0.263833 | + | 0.914632i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 208.902 | − | 130.278i | 0.368434 | − | 0.229767i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 827.215i | 1.45380i | 0.686741 | + | 0.726902i | \(0.259041\pi\) | ||||
−0.686741 | + | 0.726902i | \(0.740959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 862.968i | − | 1.51133i | −0.654960 | − | 0.755664i | \(-0.727314\pi\) | ||
0.654960 | − | 0.755664i | \(-0.272686\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.58688 | − | 25.4462i | 0.0114954 | − | 0.0444087i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 472.884 | − | 297.575i | 0.822407 | − | 0.517522i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 345.725i | − | 0.599176i | −0.954069 | − | 0.299588i | \(-0.903151\pi\) | ||
0.954069 | − | 0.299588i | \(-0.0968493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 219.567 | − | 848.225i | 0.379218 | − | 1.46498i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 383.729 | 0.660464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 98.3716i | 0.168733i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −171.208 | + | 745.448i | −0.292664 | + | 1.27427i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 231.353i | − | 0.394129i | −0.980391 | − | 0.197064i | \(-0.936859\pi\) | ||
0.980391 | − | 0.197064i | \(-0.0631408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 287.266i | − | 0.487718i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −96.3962 | + | 372.394i | −0.163107 | + | 0.630109i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −152.452 | −0.257087 | −0.128543 | − | 0.991704i | \(-0.541030\pi\) | ||||
−0.128543 | + | 0.991704i | \(0.541030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −265.084 | + | 76.4657i | −0.445520 | + | 0.128514i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1042.55 | + | 269.869i | 1.74631 | + | 0.452043i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 636.180i | − | 1.06207i | −0.847350 | − | 0.531035i | \(-0.821803\pi\) | ||
0.847350 | − | 0.531035i | \(-0.178197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −388.977 | −0.647217 | −0.323609 | − | 0.946191i | \(-0.604896\pi\) | ||||
−0.323609 | + | 0.946191i | \(0.604896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 300.163 | + | 166.558i | 0.497783 | + | 0.276216i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.4207 | + | 49.9924i | 0.0238359 | + | 0.0826321i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 913.941i | − | 1.50567i | −0.658210 | − | 0.752835i | \(-0.728686\pi\) | ||
0.658210 | − | 0.752835i | \(-0.271314\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −40.8987 | + | 157.998i | −0.0671572 | + | 0.259439i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 891.579 | 1.45921 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −854.218 | −1.39350 | −0.696752 | − | 0.717312i | \(-0.745372\pi\) | ||||
−0.696752 | + | 0.717312i | \(0.745372\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 630.948 | − | 17.3801i | 1.02593 | − | 0.0282603i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −992.683 | −1.60889 | −0.804443 | − | 0.594029i | \(-0.797536\pi\) | ||||
−0.804443 | + | 0.594029i | \(0.797536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 695.874i | − | 1.12419i | −0.827072 | − | 0.562095i | \(-0.809995\pi\) | ||
0.827072 | − | 0.562095i | \(-0.190005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 437.428 | + | 415.659i | 0.704392 | + | 0.669338i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 385.362 | 0.618559 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 270.422 | − | 563.469i | 0.432675 | − | 0.901550i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −145.911 | + | 563.679i | −0.232713 | + | 0.899009i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.0199 | −0.0350078 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −142.981 | −0.226594 | −0.113297 | − | 0.993561i | \(-0.536141\pi\) | ||||
−0.113297 | + | 0.993561i | \(0.536141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6381 | + | 56.5496i | −0.0231250 | + | 0.0893358i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1008.57 | − | 290.929i | 1.58830 | − | 0.458157i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 675.822 | 1.06095 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 478.922 | − | 863.092i | 0.749487 | − | 1.35069i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 658.955i | 1.02801i | 0.857787 | + | 0.514005i | \(0.171839\pi\) | ||||
−0.857787 | + | 0.514005i | \(0.828161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −986.709 | −1.53454 | −0.767270 | − | 0.641324i | \(-0.778385\pi\) | ||||
−0.767270 | + | 0.641324i | \(0.778385\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.820452 | + | 29.7848i | 0.00127202 | + | 0.0461779i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −875.183 | −1.35268 | −0.676339 | − | 0.736590i | \(-0.736435\pi\) | ||||
−0.676339 | + | 0.736590i | \(0.736435\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1066.87 | 1.64387 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.7694 | + | 149.773i | −0.0595536 | + | 0.230065i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 683.228i | 1.04629i | 0.852243 | + | 0.523145i | \(0.175242\pi\) | ||||
−0.852243 | + | 0.523145i | \(0.824758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.8209 | + | 134.581i | 0.0592685 | + | 0.205467i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −123.475 | + | 222.521i | −0.187938 | + | 0.338693i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 299.346 | 0.454242 | 0.227121 | − | 0.973866i | \(-0.427069\pi\) | ||||
0.227121 | + | 0.973866i | \(0.427069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 305.186i | − | 0.461704i | −0.972989 | − | 0.230852i | \(-0.925849\pi\) | ||
0.972989 | − | 0.230852i | \(-0.0741513\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 896.146 | + | 231.972i | 1.35165 | + | 0.349882i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −71.3147 | − | 247.227i | −0.107240 | − | 0.371770i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −400.013 | −0.599720 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 172.421 | − | 666.089i | 0.257729 | − | 0.995649i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 922.582i | − | 1.37494i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 725.482i | 1.07798i | 0.842312 | + | 0.538991i | \(0.181194\pi\) | ||||
−0.842312 | + | 0.538991i | \(0.818806\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 661.783 | + | 132.922i | 0.980419 | + | 0.196922i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 794.175i | − | 1.17308i | −0.809920 | − | 0.586540i | \(-0.800490\pi\) | ||
0.809920 | − | 0.586540i | \(-0.199510\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −466.898 | −0.687625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.42074 | − | 20.9412i | 0.00795996 | − | 0.0307506i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 697.731i | 1.02157i | 0.859709 | + | 0.510784i | \(0.170645\pi\) | ||||
−0.859709 | + | 0.510784i | \(0.829355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 191.307 | + | 663.207i | 0.279281 | + | 0.968185i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.06076 | + | 23.4137i | −0.00882207 | + | 0.0340811i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 145.858i | 0.211695i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 531.954i | 0.769832i | 0.922952 | + | 0.384916i | \(0.125770\pi\) | ||||
−0.922952 | + | 0.384916i | \(0.874230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 152.148 | − | 274.194i | 0.219550 | − | 0.395663i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −778.946 | + | 224.693i | −1.12079 | + | 0.323300i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 763.907i | − | 1.09599i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −429.406 | − | 111.154i | −0.614315 | − | 0.159019i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 880.504 | 1.25607 | 0.628034 | − | 0.778186i | \(-0.283860\pi\) | ||||
0.628034 | + | 0.778186i | \(0.283860\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 20.5366i | − | 0.0292127i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.6660 | − | 786.537i | −0.0307319 | − | 1.11565i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 516.931i | − | 0.731162i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 279.807i | 0.394650i | 0.980338 | + | 0.197325i | \(0.0632255\pi\) | ||||
−0.980338 | + | 0.197325i | \(0.936775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −442.101 | − | 245.318i | −0.621802 | − | 0.345032i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −379.187 | −0.531820 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 270.005 | + | 936.029i | 0.377630 | + | 1.30913i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 169.675 | − | 655.481i | 0.236645 | − | 0.914199i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1100.16i | 1.53013i | 0.643953 | + | 0.765065i | \(0.277293\pi\) | ||||
−0.643953 | + | 0.765065i | \(0.722707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.9820 | 0.0623883 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 837.968 | + | 216.912i | 1.15902 | + | 0.300017i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −378.719 | + | 238.319i | −0.522372 | + | 0.328717i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 595.579i | − | 0.819229i | −0.912259 | − | 0.409614i | \(-0.865663\pi\) | ||
0.912259 | − | 0.409614i | \(-0.134337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 37.1802 | + | 728.051i | 0.0510017 | + | 0.998699i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.0613 | 0.0493314 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 94.7325 | 0.129239 | 0.0646197 | − | 0.997910i | \(-0.479417\pi\) | ||||
0.0646197 | + | 0.997910i | \(0.479417\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.4229 | − | 596.199i | −0.0223441 | − | 0.811155i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 437.231 | 0.593258 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 618.484i | 0.836920i | 0.908235 | + | 0.418460i | \(0.137430\pi\) | ||||
−0.908235 | + | 0.418460i | \(0.862570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −216.346 | + | 835.779i | −0.291964 | + | 1.12791i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1000.33 | −1.34634 | −0.673172 | − | 0.739486i | \(-0.735069\pi\) | ||||
−0.673172 | + | 0.739486i | \(0.735069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 329.656 | + | 1142.82i | 0.442491 | + | 1.53399i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −551.304 | + | 993.535i | −0.738024 | + | 1.33003i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 539.735 | 0.720608 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 839.947 | 1.11844 | 0.559219 | − | 0.829020i | \(-0.311101\pi\) | ||||
0.559219 | + | 0.829020i | \(0.311101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1253.81 | + | 324.555i | 1.66509 | + | 0.431016i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 97.3241 | + | 337.394i | 0.128906 | + | 0.446880i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −994.763 | −1.31409 | −0.657043 | − | 0.753853i | \(-0.728193\pi\) | ||||
−0.657043 | + | 0.753853i | \(0.728193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 744.049 | + | 192.601i | 0.980301 | + | 0.253756i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 182.129i | − | 0.239329i | −0.992814 | − | 0.119665i | \(-0.961818\pi\) | ||
0.992814 | − | 0.119665i | \(-0.0381819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 576.058 | 0.754991 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 182.865 | − | 796.203i | 0.239039 | − | 1.04079i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1581.87 | 2.06241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 238.214 | 0.309771 | 0.154886 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154886 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −377.799 | − | 97.7952i | −0.490012 | − | 0.126842i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 420.519i | 0.544009i | 0.962296 | + | 0.272004i | \(0.0876865\pi\) | ||||
−0.962296 | + | 0.272004i | \(0.912313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −359.002 | + | 225.912i | −0.463229 | + | 0.291499i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.77161 | + | 10.7072i | −0.00356707 | + | 0.0137802i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 712.447 | 0.914566 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1257.22i | − | 1.60975i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −350.323 | − | 332.890i | −0.447412 | − | 0.425146i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 235.350 | + | 815.888i | 0.299808 | + | 1.03935i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 746.996 | 0.949169 | 0.474585 | − | 0.880210i | \(-0.342598\pi\) | ||||
0.474585 | + | 0.880210i | \(0.342598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −275.055 | − | 71.1994i | −0.348612 | − | 0.0902401i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 326.947i | − | 0.413333i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1367.93i | − | 1.72501i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 128.673 | − | 3.54444i | 0.161853 | − | 0.00445842i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 598.627i | 0.751100i | 0.926802 | + | 0.375550i | \(0.122546\pi\) | ||||
−0.926802 | + | 0.375550i | \(0.877454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −952.283 | −1.19184 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −553.650 | + | 997.763i | −0.691198 | + | 1.24565i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 324.134i | 0.403654i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −326.337 | + | 94.1345i | −0.405387 | + | 0.116937i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1365.51 | + | 353.469i | 1.69208 | + | 0.438004i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 412.050i | 0.509332i | 0.967029 | + | 0.254666i | \(0.0819655\pi\) | ||||
−0.967029 | + | 0.254666i | \(0.918034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1455.03i | − | 1.79411i | −0.441915 | − | 0.897057i | \(-0.645701\pi\) | ||
0.441915 | − | 0.897057i | \(-0.354299\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −321.594 | − | 83.2463i | −0.395565 | − | 0.102394i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 190.089 | + | 658.985i | 0.233239 | + | 0.808570i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.6321i | 0.0411653i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 225.593 | − | 406.554i | 0.275450 | − | 0.496403i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −169.674 | −0.206668 | −0.103334 | − | 0.994647i | \(-0.532951\pi\) | ||||
−0.103334 | + | 0.994647i | \(0.532951\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 701.170i | 0.851968i | 0.904731 | + | 0.425984i | \(0.140072\pi\) | ||||
−0.904731 | + | 0.425984i | \(0.859928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 819.188 | − | 260.940i | 0.992956 | − | 0.316291i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 453.999i | − | 0.548972i | −0.961591 | − | 0.274486i | \(-0.911492\pi\) | ||
0.961591 | − | 0.274486i | \(-0.0885076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 400.990i | 0.483703i | 0.970313 | + | 0.241852i | \(0.0777547\pi\) | ||||
−0.970313 | + | 0.241852i | \(0.922245\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1323.17 | − | 342.509i | −1.59226 | − | 0.412165i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −721.836 | −0.866549 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −167.989 | − | 582.369i | −0.201185 | − | 0.697448i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −332.085 | − | 315.558i | −0.396756 | − | 0.377011i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 841.266i | − | 1.00270i | −0.865244 | − | 0.501351i | \(-0.832837\pi\) | ||
0.865244 | − | 0.501351i | \(-0.167163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −520.641 | −0.619073 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −157.436 | + | 608.199i | −0.186756 | + | 0.721470i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 166.144 | + | 575.974i | 0.196621 | + | 0.681627i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 31.6291i | − | 0.0373425i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −47.8133 | − | 12.3767i | −0.0563172 | − | 0.0145780i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.1080 | −0.0318543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 539.313 | 0.632255 | 0.316127 | − | 0.948717i | \(-0.397617\pi\) | ||||
0.316127 | + | 0.948717i | \(0.397617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 742.568 | + | 170.547i | 0.868500 | + | 0.199470i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −409.842 | −0.478228 | −0.239114 | − | 0.970991i | \(-0.576857\pi\) | ||||
−0.239114 | + | 0.970991i | \(0.576857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 831.792i | 0.968326i | 0.874978 | + | 0.484163i | \(0.160876\pi\) | ||||
−0.874978 | + | 0.484163i | \(0.839124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −371.450 | − | 96.1519i | −0.431417 | − | 0.111675i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1214.06 | 1.40679 | 0.703395 | − | 0.710799i | \(-0.251666\pi\) | ||||
0.703395 | + | 0.710799i | \(0.251666\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 102.921 | − | 29.6883i | 0.118984 | − | 0.0343218i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −117.825 | − | 30.4996i | −0.135900 | − | 0.0351783i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −643.984 | −0.741063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 648.292 | 0.744308 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 670.792 | − | 1208.87i | 0.768376 | − | 1.38473i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −252.882 | + | 283.548i | −0.289008 | + | 0.324055i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −343.642 | −0.391838 | −0.195919 | − | 0.980620i | \(-0.562769\pi\) | ||||
−0.195919 | + | 0.980620i | \(0.562769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −214.242 | + | 827.650i | −0.243733 | + | 0.941582i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 464.129i | − | 0.526821i | −0.964684 | − | 0.263410i | \(-0.915153\pi\) | ||
0.964684 | − | 0.263410i | \(-0.0848473\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 543.338 | 0.615332 | 0.307666 | − | 0.951494i | \(-0.400452\pi\) | ||||
0.307666 | + | 0.951494i | \(0.400452\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −38.4405 | − | 1395.50i | −0.0434356 | − | 1.57684i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1616.28 | −1.82219 | −0.911093 | − | 0.412200i | \(-0.864760\pi\) | ||||
−0.911093 | + | 0.412200i | \(0.864760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −638.098 | −0.717770 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 491.341 | + | 787.870i | 0.551449 | + | 0.884254i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 888.134i | − | 0.994551i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.8720 | − | 141.691i | −0.0456671 | − | 0.158314i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1103.22 | + | 285.573i | 1.22990 | + | 0.318365i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 303.680 | 0.337798 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 155.788i | − | 0.172906i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.53898 | − | 17.5348i | 0.00502656 | − | 0.0194184i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −43.8613 | + | 12.6521i | −0.0484655 | + | 0.0139803i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1189.11 | 1.31104 | 0.655521 | − | 0.755177i | \(-0.272449\pi\) | ||||
0.655521 | + | 0.755177i | \(0.272449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1338.42 | + | 742.676i | 1.47241 | + | 0.817025i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1003.01i | 1.10100i | 0.834834 | + | 0.550502i | \(0.185564\pi\) | ||||
−0.834834 | + | 0.550502i | \(0.814436\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1447.23i | 1.58513i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1206.77 | + | 33.2417i | −1.31887 | + | 0.0363297i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 85.1461i | − | 0.0928529i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −118.618 | −0.129073 | −0.0645363 | − | 0.997915i | \(-0.520557\pi\) | ||||
−0.0645363 | + | 0.997915i | \(0.520557\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1504.24 | + | 389.379i | 1.63326 | + | 0.422779i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1864.10i | − | 2.01961i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.6650 | + | 16.1504i | −0.0277459 | + | 0.0174599i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −64.6256 | + | 116.465i | −0.0697148 | + | 0.125637i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1417.18i | − | 1.52549i | −0.646699 | − | 0.762745i | \(-0.723851\pi\) | ||
0.646699 | − | 0.762745i | \(-0.276149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 673.210i | − | 0.723105i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 232.623 | − | 898.659i | 0.249328 | − | 0.963193i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −288.389 | − | 999.759i | −0.308437 | − | 1.06926i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 495.393i | 0.528701i | 0.964427 | + | 0.264351i | \(0.0851576\pi\) | ||||
−0.964427 | + | 0.264351i | \(0.914842\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −251.883 | + | 973.065i | −0.268246 | + | 1.03628i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 120.337 | 0.127883 | 0.0639413 | − | 0.997954i | \(-0.479633\pi\) | ||||
0.0639413 | + | 0.997954i | \(0.479633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 940.421i | − | 0.997265i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −364.137 | − | 189.135i | −0.385331 | − | 0.200143i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 119.186i | − | 0.125857i | −0.998018 | − | 0.0629283i | \(-0.979956\pi\) | ||
0.998018 | − | 0.0629283i | \(-0.0200439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 480.600i | 0.506428i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −442.890 | + | 1710.96i | −0.465710 | + | 1.79911i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −617.067 | −0.647499 | −0.323750 | − | 0.946143i | \(-0.604944\pi\) | ||||
−0.323750 | + | 0.946143i | \(0.604944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.0919 | + | 12.1418i | −0.0440753 | + | 0.0127139i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −595.888 | − | 154.249i | −0.622662 | − | 0.161179i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 419.596i | − | 0.437535i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −673.130 | −0.700447 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −775.438 | + | 1397.46i | −0.805231 | + | 1.45115i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1403.10 | + | 404.734i | −1.45398 | + | 0.419414i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 784.649i | 0.811426i | 0.914001 | + | 0.405713i | \(0.132977\pi\) | ||||
−0.914001 | + | 0.405713i | \(0.867023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 231.076 | − | 892.683i | 0.238468 | − | 0.921241i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1364.14 | −1.40488 | −0.702440 | − | 0.711743i | \(-0.747906\pi\) | ||||
−0.702440 | + | 0.711743i | \(0.747906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 492.822 | 0.506497 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1214.63 | − | 386.902i | 1.24577 | − | 0.396822i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1116.73 | −1.14302 | −0.571511 | − | 0.820595i | \(-0.693642\pi\) | ||||
−0.571511 | + | 0.820595i | \(0.693642\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1453.38i | 1.48456i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −827.623 | + | 1491.50i | −0.843652 | + | 1.52039i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1737.11 | −1.76715 | −0.883574 | − | 0.468292i | \(-0.844870\pi\) | ||||
−0.883574 | + | 0.468292i | \(0.844870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 615.998 | − | 177.690i | 0.625378 | − | 0.180395i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −119.863 | + | 463.049i | −0.121441 | + | 0.469147i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.3939 | 0.0448877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1343.20 | 1.35540 | 0.677699 | − | 0.735339i | \(-0.262977\pi\) | ||||
0.677699 | + | 0.735339i | \(0.262977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −195.391 | + | 754.828i | −0.196768 | + | 0.760149i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −497.457 | − | 1724.54i | −0.499957 | − | 1.73321i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 281.483 | 0.282330 | 0.141165 | − | 0.989986i | \(-0.454915\pi\) | ||||
0.141165 | + | 0.989986i | \(0.454915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.7406 | − | 22.5592i | −0.0237644 | − | 0.0225818i |
(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 | 960.3.i.b.929.4 | yes | 64 | |
3.2 | odd | 2 | inner | 960.3.i.b.929.5 | yes | 64 | |
4.3 | odd | 2 | inner | 960.3.i.b.929.64 | yes | 64 | |
5.4 | even | 2 | inner | 960.3.i.b.929.63 | yes | 64 | |
8.3 | odd | 2 | inner | 960.3.i.b.929.1 | ✓ | 64 | |
8.5 | even | 2 | inner | 960.3.i.b.929.61 | yes | 64 | |
12.11 | even | 2 | inner | 960.3.i.b.929.57 | yes | 64 | |
15.14 | odd | 2 | inner | 960.3.i.b.929.58 | yes | 64 | |
20.19 | odd | 2 | inner | 960.3.i.b.929.3 | yes | 64 | |
24.5 | odd | 2 | inner | 960.3.i.b.929.60 | yes | 64 | |
24.11 | even | 2 | inner | 960.3.i.b.929.8 | yes | 64 | |
40.19 | odd | 2 | inner | 960.3.i.b.929.62 | yes | 64 | |
40.29 | even | 2 | inner | 960.3.i.b.929.2 | yes | 64 | |
60.59 | even | 2 | inner | 960.3.i.b.929.6 | yes | 64 | |
120.29 | odd | 2 | inner | 960.3.i.b.929.7 | yes | 64 | |
120.59 | even | 2 | inner | 960.3.i.b.929.59 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
960.3.i.b.929.1 | ✓ | 64 | 8.3 | odd | 2 | inner | |
960.3.i.b.929.2 | yes | 64 | 40.29 | even | 2 | inner | |
960.3.i.b.929.3 | yes | 64 | 20.19 | odd | 2 | inner | |
960.3.i.b.929.4 | yes | 64 | 1.1 | even | 1 | trivial | |
960.3.i.b.929.5 | yes | 64 | 3.2 | odd | 2 | inner | |
960.3.i.b.929.6 | yes | 64 | 60.59 | even | 2 | inner | |
960.3.i.b.929.7 | yes | 64 | 120.29 | odd | 2 | inner | |
960.3.i.b.929.8 | yes | 64 | 24.11 | even | 2 | inner | |
960.3.i.b.929.57 | yes | 64 | 12.11 | even | 2 | inner | |
960.3.i.b.929.58 | yes | 64 | 15.14 | odd | 2 | inner | |
960.3.i.b.929.59 | yes | 64 | 120.59 | even | 2 | inner | |
960.3.i.b.929.60 | yes | 64 | 24.5 | odd | 2 | inner | |
960.3.i.b.929.61 | yes | 64 | 8.5 | even | 2 | inner | |
960.3.i.b.929.62 | yes | 64 | 40.19 | odd | 2 | inner | |
960.3.i.b.929.63 | yes | 64 | 5.4 | even | 2 | inner | |
960.3.i.b.929.64 | yes | 64 | 4.3 | odd | 2 | inner |