Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(62,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.62");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 83.14 | ||
Character | \(\chi\) | \(=\) | 105.83 |
Dual form | 105.3.k.d.62.14 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.28094 | + | 2.28094i | 1.14047 | + | 1.14047i | 0.988364 | + | 0.152108i | \(0.0486063\pi\) |
0.152108 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(3\) | 2.80094 | + | 1.07458i | 0.933647 | + | 0.358195i | ||||
\(4\) | 6.40541i | 1.60135i | ||||||||
\(5\) | −1.80941 | − | 4.66112i | −0.361882 | − | 0.932224i | ||||
\(6\) | 3.93772 | + | 8.83986i | 0.656287 | + | 1.47331i | ||||
\(7\) | −6.22100 | + | 3.20922i | −0.888715 | + | 0.458460i | ||||
\(8\) | −5.48661 | + | 5.48661i | −0.685827 | + | 0.685827i | ||||
\(9\) | 6.69054 | + | 6.01969i | 0.743393 | + | 0.668855i | ||||
\(10\) | 6.50460 | − | 14.7589i | 0.650460 | − | 1.47589i | ||||
\(11\) | − | 11.1704i | − | 1.01549i | −0.861506 | − | 0.507747i | \(-0.830478\pi\) | ||
0.861506 | − | 0.507747i | \(-0.169522\pi\) | |||||||
\(12\) | −6.88316 | + | 17.9412i | −0.573596 | + | 1.49510i | ||||
\(13\) | 5.82807 | − | 5.82807i | 0.448313 | − | 0.448313i | −0.446480 | − | 0.894794i | \(-0.647323\pi\) |
0.894794 | + | 0.446480i | \(0.147323\pi\) | |||||||
\(14\) | −21.5098 | − | 6.86971i | −1.53642 | − | 0.490694i | ||||
\(15\) | −0.0592799 | − | 14.9999i | −0.00395199 | − | 0.999992i | ||||
\(16\) | 0.592330 | 0.0370206 | ||||||||
\(17\) | −6.84147 | + | 6.84147i | −0.402440 | + | 0.402440i | −0.879092 | − | 0.476652i | \(-0.841850\pi\) |
0.476652 | + | 0.879092i | \(0.341850\pi\) | |||||||
\(18\) | 1.53016 | + | 28.9913i | 0.0850091 | + | 1.61063i | ||||
\(19\) | −25.0261 | −1.31716 | −0.658581 | − | 0.752510i | \(-0.728843\pi\) | ||||
−0.658581 | + | 0.752510i | \(0.728843\pi\) | |||||||
\(20\) | 29.8564 | − | 11.5900i | 1.49282 | − | 0.579500i | ||||
\(21\) | −20.8732 | + | 2.30385i | −0.993964 | + | 0.109707i | ||||
\(22\) | 25.4792 | − | 25.4792i | 1.15814 | − | 1.15814i | ||||
\(23\) | 23.3593 | − | 23.3593i | 1.01562 | − | 1.01562i | 0.0157445 | − | 0.999876i | \(-0.494988\pi\) |
0.999876 | − | 0.0157445i | \(-0.00501183\pi\) | |||||||
\(24\) | −21.2635 | + | 9.47185i | −0.885980 | + | 0.394661i | ||||
\(25\) | −18.4521 | + | 16.8677i | −0.738083 | + | 0.674710i | ||||
\(26\) | 26.5870 | 1.02258 | ||||||||
\(27\) | 12.2711 | + | 24.0503i | 0.454487 | + | 0.890754i | ||||
\(28\) | −20.5564 | − | 39.8481i | −0.734157 | − | 1.42315i | ||||
\(29\) | −10.6354 | −0.366738 | −0.183369 | − | 0.983044i | \(-0.558700\pi\) | ||||
−0.183369 | + | 0.983044i | \(0.558700\pi\) | |||||||
\(30\) | 34.0787 | − | 34.3491i | 1.13596 | − | 1.14497i | ||||
\(31\) | 26.9470i | 0.869257i | 0.900610 | + | 0.434629i | \(0.143120\pi\) | ||||
−0.900610 | + | 0.434629i | \(0.856880\pi\) | |||||||
\(32\) | 23.2975 | + | 23.2975i | 0.728048 | + | 0.728048i | ||||
\(33\) | 12.0036 | − | 31.2877i | 0.363745 | − | 0.948113i | ||||
\(34\) | −31.2100 | −0.917942 | ||||||||
\(35\) | 26.2149 | + | 23.1901i | 0.748997 | + | 0.662573i | ||||
\(36\) | −38.5586 | + | 42.8557i | −1.07107 | + | 1.19044i | ||||
\(37\) | −20.8846 | + | 20.8846i | −0.564448 | + | 0.564448i | −0.930568 | − | 0.366120i | \(-0.880686\pi\) |
0.366120 | + | 0.930568i | \(0.380686\pi\) | |||||||
\(38\) | −57.0831 | − | 57.0831i | −1.50219 | − | 1.50219i | ||||
\(39\) | 22.5868 | − | 10.0613i | 0.579150 | − | 0.257983i | ||||
\(40\) | 35.5013 | + | 15.6462i | 0.887532 | + | 0.391156i | ||||
\(41\) | −32.9644 | −0.804010 | −0.402005 | − | 0.915637i | \(-0.631687\pi\) | ||||
−0.402005 | + | 0.915637i | \(0.631687\pi\) | |||||||
\(42\) | −52.8657 | − | 42.3558i | −1.25871 | − | 1.00847i | ||||
\(43\) | 1.25060 | + | 1.25060i | 0.0290836 | + | 0.0290836i | 0.721499 | − | 0.692415i | \(-0.243453\pi\) |
−0.692415 | + | 0.721499i | \(0.743453\pi\) | |||||||
\(44\) | 71.5513 | 1.62617 | ||||||||
\(45\) | 15.9526 | − | 42.0775i | 0.354502 | − | 0.935055i | ||||
\(46\) | 106.562 | 2.31657 | ||||||||
\(47\) | 59.1134 | − | 59.1134i | 1.25773 | − | 1.25773i | 0.305558 | − | 0.952173i | \(-0.401157\pi\) |
0.952173 | − | 0.305558i | \(-0.0988431\pi\) | |||||||
\(48\) | 1.65908 | + | 0.636508i | 0.0345642 | + | 0.0132606i | ||||
\(49\) | 28.4018 | − | 39.9292i | 0.579629 | − | 0.814881i | ||||
\(50\) | −80.5625 | − | 3.61381i | −1.61125 | − | 0.0722761i | ||||
\(51\) | −26.5143 | + | 11.8108i | −0.519888 | + | 0.231585i | ||||
\(52\) | 37.3312 | + | 37.3312i | 0.717908 | + | 0.717908i | ||||
\(53\) | −26.0484 | + | 26.0484i | −0.491478 | + | 0.491478i | −0.908772 | − | 0.417293i | \(-0.862979\pi\) |
0.417293 | + | 0.908772i | \(0.362979\pi\) | |||||||
\(54\) | −26.8677 | + | 82.8473i | −0.497550 | + | 1.53421i | ||||
\(55\) | −52.0668 | + | 20.2119i | −0.946669 | + | 0.367489i | ||||
\(56\) | 16.5245 | − | 51.7400i | 0.295080 | − | 0.923929i | ||||
\(57\) | −70.0965 | − | 26.8926i | −1.22976 | − | 0.471800i | ||||
\(58\) | −24.2588 | − | 24.2588i | −0.418254 | − | 0.418254i | ||||
\(59\) | 70.2066i | 1.18994i | 0.803747 | + | 0.594971i | \(0.202837\pi\) | ||||
−0.803747 | + | 0.594971i | \(0.797163\pi\) | |||||||
\(60\) | 96.0805 | − | 0.379712i | 1.60134 | − | 0.00632854i | ||||
\(61\) | 14.1716i | 0.232321i | 0.993230 | + | 0.116161i | \(0.0370587\pi\) | ||||
−0.993230 | + | 0.116161i | \(0.962941\pi\) | |||||||
\(62\) | −61.4646 | + | 61.4646i | −0.991364 | + | 0.991364i | ||||
\(63\) | −60.9404 | − | 15.9771i | −0.967308 | − | 0.253605i | ||||
\(64\) | 103.911i | 1.62362i | ||||||||
\(65\) | −37.7107 | − | 16.6200i | −0.580165 | − | 0.255692i | ||||
\(66\) | 98.7451 | − | 43.9861i | 1.49614 | − | 0.666456i | ||||
\(67\) | −6.14458 | + | 6.14458i | −0.0917101 | + | 0.0917101i | −0.751473 | − | 0.659763i | \(-0.770657\pi\) |
0.659763 | + | 0.751473i | \(0.270657\pi\) | |||||||
\(68\) | −43.8225 | − | 43.8225i | −0.644448 | − | 0.644448i | ||||
\(69\) | 90.5294 | − | 40.3264i | 1.31202 | − | 0.584441i | ||||
\(70\) | 6.89950 | + | 112.690i | 0.0985643 | + | 1.60986i | ||||
\(71\) | − | 39.0498i | − | 0.549997i | −0.961445 | − | 0.274999i | \(-0.911323\pi\) | ||
0.961445 | − | 0.274999i | \(-0.0886774\pi\) | |||||||
\(72\) | −69.7361 | + | 3.68068i | −0.968557 | + | 0.0511205i | ||||
\(73\) | −51.1141 | + | 51.1141i | −0.700193 | + | 0.700193i | −0.964452 | − | 0.264259i | \(-0.914873\pi\) |
0.264259 | + | 0.964452i | \(0.414873\pi\) | |||||||
\(74\) | −95.2731 | −1.28747 | ||||||||
\(75\) | −69.8090 | + | 27.4172i | −0.930787 | + | 0.365563i | ||||
\(76\) | − | 160.302i | − | 2.10924i | ||||||
\(77\) | 35.8484 | + | 69.4914i | 0.465564 | + | 0.902485i | ||||
\(78\) | 74.4687 | + | 28.5700i | 0.954726 | + | 0.366282i | ||||
\(79\) | − | 16.8398i | − | 0.213162i | −0.994304 | − | 0.106581i | \(-0.966010\pi\) | ||
0.994304 | − | 0.106581i | \(-0.0339903\pi\) | |||||||
\(80\) | −1.07177 | − | 2.76092i | −0.0133971 | − | 0.0345115i | ||||
\(81\) | 8.52661 | + | 80.5500i | 0.105267 | + | 0.994444i | ||||
\(82\) | −75.1900 | − | 75.1900i | −0.916951 | − | 0.916951i | ||||
\(83\) | 31.3367 | + | 31.3367i | 0.377551 | + | 0.377551i | 0.870218 | − | 0.492667i | \(-0.163978\pi\) |
−0.492667 | + | 0.870218i | \(0.663978\pi\) | |||||||
\(84\) | −14.7571 | − | 133.702i | −0.175680 | − | 1.59169i | ||||
\(85\) | 44.2679 | + | 19.5099i | 0.520799 | + | 0.229528i | ||||
\(86\) | 5.70508i | 0.0663381i | ||||||||
\(87\) | −29.7891 | − | 11.4286i | −0.342404 | − | 0.131364i | ||||
\(88\) | 61.2879 | + | 61.2879i | 0.696453 | + | 0.696453i | ||||
\(89\) | 70.8895i | 0.796511i | 0.917274 | + | 0.398256i | \(0.130384\pi\) | ||||
−0.917274 | + | 0.398256i | \(0.869616\pi\) | |||||||
\(90\) | 132.363 | − | 59.5894i | 1.47070 | − | 0.662105i | ||||
\(91\) | −17.5529 | + | 54.9600i | −0.192889 | + | 0.603957i | ||||
\(92\) | 149.626 | + | 149.626i | 1.62637 | + | 1.62637i | ||||
\(93\) | −28.9568 | + | 75.4769i | −0.311363 | + | 0.811579i | ||||
\(94\) | 269.669 | 2.86882 | ||||||||
\(95\) | 45.2824 | + | 116.650i | 0.476657 | + | 1.22789i | ||||
\(96\) | 40.2198 | + | 90.2902i | 0.418957 | + | 0.940522i | ||||
\(97\) | −114.216 | − | 114.216i | −1.17748 | − | 1.17748i | −0.980383 | − | 0.197101i | \(-0.936847\pi\) |
−0.197101 | − | 0.980383i | \(-0.563153\pi\) | |||||||
\(98\) | 155.859 | − | 26.2933i | 1.59040 | − | 0.268299i | ||||
\(99\) | 67.2426 | − | 74.7363i | 0.679218 | − | 0.754912i | ||||
\(100\) | −108.045 | − | 118.193i | −1.08045 | − | 1.18193i | ||||
\(101\) | 54.9464 | 0.544024 | 0.272012 | − | 0.962294i | \(-0.412311\pi\) | ||||
0.272012 | + | 0.962294i | \(0.412311\pi\) | |||||||
\(102\) | −87.4175 | − | 33.5378i | −0.857034 | − | 0.328802i | ||||
\(103\) | 109.306 | − | 109.306i | 1.06123 | − | 1.06123i | 0.0632258 | − | 0.997999i | \(-0.479861\pi\) |
0.997999 | − | 0.0632258i | \(-0.0201388\pi\) | |||||||
\(104\) | 63.9528i | 0.614931i | ||||||||
\(105\) | 48.5067 | + | 93.1241i | 0.461969 | + | 0.886896i | ||||
\(106\) | −118.830 | −1.12103 | ||||||||
\(107\) | −89.1318 | − | 89.1318i | −0.833007 | − | 0.833007i | 0.154920 | − | 0.987927i | \(-0.450488\pi\) |
−0.987927 | + | 0.154920i | \(0.950488\pi\) | |||||||
\(108\) | −154.052 | + | 78.6017i | −1.42641 | + | 0.727794i | ||||
\(109\) | 91.2226i | 0.836904i | 0.908239 | + | 0.418452i | \(0.137427\pi\) | ||||
−0.908239 | + | 0.418452i | \(0.862573\pi\) | |||||||
\(110\) | −164.864 | − | 72.6592i | −1.49876 | − | 0.660538i | ||||
\(111\) | −80.9387 | + | 36.0542i | −0.729177 | + | 0.324813i | ||||
\(112\) | −3.68489 | + | 1.90092i | −0.0329008 | + | 0.0169725i | ||||
\(113\) | 98.3921 | − | 98.3921i | 0.870726 | − | 0.870726i | −0.121825 | − | 0.992552i | \(-0.538875\pi\) |
0.992552 | + | 0.121825i | \(0.0388747\pi\) | |||||||
\(114\) | −98.5457 | − | 221.227i | −0.864436 | − | 1.94059i | ||||
\(115\) | −151.147 | − | 66.6139i | −1.31432 | − | 0.579251i | ||||
\(116\) | − | 68.1242i | − | 0.587277i | ||||||
\(117\) | 74.0762 | − | 3.90974i | 0.633129 | − | 0.0334166i | ||||
\(118\) | −160.137 | + | 160.137i | −1.35710 | + | 1.35710i | ||||
\(119\) | 20.6050 | − | 64.5166i | 0.173152 | − | 0.542157i | ||||
\(120\) | 82.6238 | + | 81.9733i | 0.688532 | + | 0.683111i | ||||
\(121\) | −3.77875 | −0.0312293 | ||||||||
\(122\) | −32.3246 | + | 32.3246i | −0.264956 | + | 0.264956i | ||||
\(123\) | −92.3314 | − | 35.4230i | −0.750661 | − | 0.287992i | ||||
\(124\) | −172.607 | −1.39199 | ||||||||
\(125\) | 112.010 | + | 55.4868i | 0.896079 | + | 0.443894i | ||||
\(126\) | −102.559 | − | 175.445i | −0.813958 | − | 1.39242i | ||||
\(127\) | 172.312 | − | 172.312i | 1.35679 | − | 1.35679i | 0.478948 | − | 0.877843i | \(-0.341018\pi\) |
0.877843 | − | 0.478948i | \(-0.158982\pi\) | |||||||
\(128\) | −143.826 | + | 143.826i | −1.12364 | + | 1.12364i | ||||
\(129\) | 2.15897 | + | 4.84672i | 0.0167362 | + | 0.0375714i | ||||
\(130\) | −48.1068 | − | 123.925i | −0.370052 | − | 0.953271i | ||||
\(131\) | −71.6542 | −0.546979 | −0.273489 | − | 0.961875i | \(-0.588178\pi\) | ||||
−0.273489 | + | 0.961875i | \(0.588178\pi\) | |||||||
\(132\) | 200.411 | + | 76.8879i | 1.51826 | + | 0.582484i | ||||
\(133\) | 155.687 | − | 80.3142i | 1.17058 | − | 0.603866i | ||||
\(134\) | −28.0309 | −0.209186 | ||||||||
\(135\) | 89.8981 | − | 100.714i | 0.665912 | − | 0.746031i | ||||
\(136\) | − | 75.0730i | − | 0.552008i | ||||||
\(137\) | −57.1182 | − | 57.1182i | −0.416921 | − | 0.416921i | 0.467220 | − | 0.884141i | \(-0.345256\pi\) |
−0.884141 | + | 0.467220i | \(0.845256\pi\) | |||||||
\(138\) | 298.475 | + | 114.510i | 2.16286 | + | 0.829784i | ||||
\(139\) | 41.4536 | 0.298227 | 0.149113 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149113 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(140\) | −148.542 | + | 167.917i | −1.06101 | + | 1.19941i | ||||
\(141\) | 229.095 | − | 102.051i | 1.62479 | − | 0.723765i | ||||
\(142\) | 89.0704 | − | 89.0704i | 0.627256 | − | 0.627256i | ||||
\(143\) | −65.1021 | − | 65.1021i | −0.455260 | − | 0.455260i | ||||
\(144\) | 3.96301 | + | 3.56564i | 0.0275209 | + | 0.0247614i | ||||
\(145\) | 19.2438 | + | 49.5729i | 0.132716 | + | 0.341882i | ||||
\(146\) | −233.177 | −1.59710 | ||||||||
\(147\) | 122.459 | − | 81.3191i | 0.833054 | − | 0.553191i | ||||
\(148\) | −133.774 | − | 133.774i | −0.903880 | − | 0.903880i | ||||
\(149\) | −62.9077 | −0.422199 | −0.211100 | − | 0.977465i | \(-0.567704\pi\) | ||||
−0.211100 | + | 0.977465i | \(0.567704\pi\) | |||||||
\(150\) | −221.768 | − | 96.6933i | −1.47845 | − | 0.644622i | ||||
\(151\) | −20.6412 | −0.136697 | −0.0683484 | − | 0.997662i | \(-0.521773\pi\) | ||||
−0.0683484 | + | 0.997662i | \(0.521773\pi\) | |||||||
\(152\) | 137.308 | − | 137.308i | 0.903345 | − | 0.903345i | ||||
\(153\) | −86.9567 | + | 4.58958i | −0.568344 | + | 0.0299972i | ||||
\(154\) | −76.7377 | + | 240.274i | −0.498297 | + | 1.56022i | ||||
\(155\) | 125.603 | − | 48.7581i | 0.810343 | − | 0.314568i | ||||
\(156\) | 64.4470 | + | 144.678i | 0.413122 | + | 0.927423i | ||||
\(157\) | 213.253 | + | 213.253i | 1.35830 | + | 1.35830i | 0.876015 | + | 0.482284i | \(0.160193\pi\) |
0.482284 | + | 0.876015i | \(0.339807\pi\) | |||||||
\(158\) | 38.4106 | − | 38.4106i | 0.243105 | − | 0.243105i | ||||
\(159\) | −100.951 | + | 44.9687i | −0.634912 | + | 0.282822i | ||||
\(160\) | 66.4378 | − | 150.747i | 0.415237 | − | 0.942171i | ||||
\(161\) | −70.3531 | + | 220.283i | −0.436976 | + | 1.36822i | ||||
\(162\) | −164.281 | + | 203.179i | −1.01408 | + | 1.25419i | ||||
\(163\) | −19.5250 | − | 19.5250i | −0.119785 | − | 0.119785i | 0.644673 | − | 0.764458i | \(-0.276993\pi\) |
−0.764458 | + | 0.644673i | \(0.776993\pi\) | |||||||
\(164\) | − | 211.151i | − | 1.28750i | ||||||
\(165\) | −167.555 | + | 0.662183i | −1.01549 | + | 0.00401323i | ||||
\(166\) | 142.955i | 0.861173i | ||||||||
\(167\) | 151.924 | − | 151.924i | 0.909725 | − | 0.909725i | −0.0865247 | − | 0.996250i | \(-0.527576\pi\) |
0.996250 | + | 0.0865247i | \(0.0275761\pi\) | |||||||
\(168\) | 101.883 | − | 127.164i | 0.606447 | − | 0.756927i | ||||
\(169\) | 101.067i | 0.598030i | ||||||||
\(170\) | 56.4717 | + | 145.474i | 0.332186 | + | 0.855728i | ||||
\(171\) | −167.438 | − | 150.649i | −0.979169 | − | 0.880990i | ||||
\(172\) | −8.01059 | + | 8.01059i | −0.0465732 | + | 0.0465732i | ||||
\(173\) | 19.8589 | + | 19.8589i | 0.114791 | + | 0.114791i | 0.762169 | − | 0.647378i | \(-0.224134\pi\) |
−0.647378 | + | 0.762169i | \(0.724134\pi\) | |||||||
\(174\) | −41.8793 | − | 94.0154i | −0.240685 | − | 0.540319i | ||||
\(175\) | 60.6582 | − | 164.151i | 0.346618 | − | 0.938006i | ||||
\(176\) | − | 6.61658i | − | 0.0375942i | ||||||
\(177\) | −75.4429 | + | 196.645i | −0.426231 | + | 1.11099i | ||||
\(178\) | −161.695 | + | 161.695i | −0.908399 | + | 0.908399i | ||||
\(179\) | 157.790 | 0.881508 | 0.440754 | − | 0.897628i | \(-0.354711\pi\) | ||||
0.440754 | + | 0.897628i | \(0.354711\pi\) | |||||||
\(180\) | 269.524 | + | 102.183i | 1.49735 | + | 0.567683i | ||||
\(181\) | 58.8019i | 0.324872i | 0.986719 | + | 0.162436i | \(0.0519351\pi\) | ||||
−0.986719 | + | 0.162436i | \(0.948065\pi\) | |||||||
\(182\) | −165.398 | + | 85.3236i | −0.908780 | + | 0.468811i | ||||
\(183\) | −15.2286 | + | 39.6938i | −0.0832162 | + | 0.216906i | ||||
\(184\) | 256.327i | 1.39308i | ||||||||
\(185\) | 135.134 | + | 59.5568i | 0.730455 | + | 0.321928i | ||||
\(186\) | −238.207 | + | 106.110i | −1.28068 | + | 0.570483i | ||||
\(187\) | 76.4223 | + | 76.4223i | 0.408675 | + | 0.408675i | ||||
\(188\) | 378.646 | + | 378.646i | 2.01407 | + | 2.01407i | ||||
\(189\) | −153.522 | − | 110.237i | −0.812284 | − | 0.583262i | ||||
\(190\) | −162.784 | + | 369.358i | −0.856760 | + | 1.94399i | ||||
\(191\) | 8.99622i | 0.0471007i | 0.999723 | + | 0.0235503i | \(0.00749699\pi\) | ||||
−0.999723 | + | 0.0235503i | \(0.992503\pi\) | |||||||
\(192\) | −111.662 | + | 291.050i | −0.581571 | + | 1.51588i | ||||
\(193\) | 96.1055 | + | 96.1055i | 0.497956 | + | 0.497956i | 0.910801 | − | 0.412845i | \(-0.135465\pi\) |
−0.412845 | + | 0.910801i | \(0.635465\pi\) | |||||||
\(194\) | − | 521.041i | − | 2.68578i | ||||||
\(195\) | −87.7659 | − | 87.0749i | −0.450082 | − | 0.446538i | ||||
\(196\) | 255.763 | + | 181.925i | 1.30491 | + | 0.928190i | ||||
\(197\) | −113.154 | − | 113.154i | −0.574386 | − | 0.574386i | 0.358965 | − | 0.933351i | \(-0.383130\pi\) |
−0.933351 | + | 0.358965i | \(0.883130\pi\) | |||||||
\(198\) | 323.846 | − | 17.0926i | 1.63559 | − | 0.0863262i | ||||
\(199\) | 122.026 | 0.613196 | 0.306598 | − | 0.951839i | \(-0.400809\pi\) | ||||
0.306598 | + | 0.951839i | \(0.400809\pi\) | |||||||
\(200\) | 8.69270 | − | 193.786i | 0.0434635 | − | 0.968931i | ||||
\(201\) | −23.8135 | + | 10.6077i | −0.118475 | + | 0.0527748i | ||||
\(202\) | 125.330 | + | 125.330i | 0.620444 | + | 0.620444i | ||||
\(203\) | 66.1629 | − | 34.1314i | 0.325926 | − | 0.168135i | ||||
\(204\) | −75.6532 | − | 169.835i | −0.370849 | − | 0.832525i | ||||
\(205\) | 59.6461 | + | 153.651i | 0.290956 | + | 0.749517i | ||||
\(206\) | 498.643 | 2.42060 | ||||||||
\(207\) | 296.902 | − | 15.6705i | 1.43431 | − | 0.0757028i | ||||
\(208\) | 3.45214 | − | 3.45214i | 0.0165968 | − | 0.0165968i | ||||
\(209\) | 279.552i | 1.33757i | ||||||||
\(210\) | −101.770 | + | 323.052i | −0.484618 | + | 1.53834i | ||||
\(211\) | −4.27938 | −0.0202814 | −0.0101407 | − | 0.999949i | \(-0.503228\pi\) | ||||
−0.0101407 | + | 0.999949i | \(0.503228\pi\) | |||||||
\(212\) | −166.850 | − | 166.850i | −0.787031 | − | 0.787031i | ||||
\(213\) | 41.9623 | − | 109.376i | 0.197006 | − | 0.513503i | ||||
\(214\) | − | 406.609i | − | 1.90004i | ||||||
\(215\) | 3.56634 | − | 8.09202i | 0.0165876 | − | 0.0376373i | ||||
\(216\) | −199.282 | − | 64.6280i | −0.922602 | − | 0.299204i | ||||
\(217\) | −86.4788 | − | 167.637i | −0.398520 | − | 0.772522i | ||||
\(218\) | −208.074 | + | 208.074i | −0.954466 | + | 0.954466i | ||||
\(219\) | −198.094 | + | 88.2411i | −0.904538 | + | 0.402928i | ||||
\(220\) | −129.465 | − | 333.509i | −0.588480 | − | 1.51595i | ||||
\(221\) | 79.7452i | 0.360838i | ||||||||
\(222\) | −266.854 | − | 102.379i | −1.20205 | − | 0.461166i | ||||
\(223\) | −34.9829 | + | 34.9829i | −0.156874 | + | 0.156874i | −0.781180 | − | 0.624306i | \(-0.785382\pi\) |
0.624306 | + | 0.781180i | \(0.285382\pi\) | |||||||
\(224\) | −219.701 | − | 70.1671i | −0.980808 | − | 0.313246i | ||||
\(225\) | −224.993 | + | 1.77838i | −0.999969 | + | 0.00790392i | ||||
\(226\) | 448.854 | 1.98608 | ||||||||
\(227\) | −23.2602 | + | 23.2602i | −0.102468 | + | 0.102468i | −0.756482 | − | 0.654014i | \(-0.773084\pi\) |
0.654014 | + | 0.756482i | \(0.273084\pi\) | |||||||
\(228\) | 172.258 | − | 448.997i | 0.755519 | − | 1.96929i | ||||
\(229\) | −91.1105 | −0.397862 | −0.198931 | − | 0.980013i | \(-0.563747\pi\) | ||||
−0.198931 | + | 0.980013i | \(0.563747\pi\) | |||||||
\(230\) | −192.815 | − | 496.700i | −0.838326 | − | 2.15957i | ||||
\(231\) | 25.7350 | + | 233.163i | 0.111407 | + | 1.00937i | ||||
\(232\) | 58.3524 | − | 58.3524i | 0.251519 | − | 0.251519i | ||||
\(233\) | 90.6015 | − | 90.6015i | 0.388847 | − | 0.388847i | −0.485429 | − | 0.874276i | \(-0.661336\pi\) |
0.874276 | + | 0.485429i | \(0.161336\pi\) | |||||||
\(234\) | 177.881 | + | 160.046i | 0.760177 | + | 0.683956i | ||||
\(235\) | −382.495 | − | 168.574i | −1.62764 | − | 0.717338i | ||||
\(236\) | −449.702 | −1.90552 | ||||||||
\(237\) | 18.0958 | − | 47.1673i | 0.0763535 | − | 0.199018i | ||||
\(238\) | 194.158 | − | 100.160i | 0.815789 | − | 0.420840i | ||||
\(239\) | −406.988 | −1.70288 | −0.851439 | − | 0.524454i | \(-0.824269\pi\) | ||||
−0.851439 | + | 0.524454i | \(0.824269\pi\) | |||||||
\(240\) | −0.0351132 | − | 8.88488i | −0.000146305 | − | 0.0370203i | ||||
\(241\) | − | 117.108i | − | 0.485924i | −0.970036 | − | 0.242962i | \(-0.921881\pi\) | ||
0.970036 | − | 0.242962i | \(-0.0781191\pi\) | |||||||
\(242\) | −8.61911 | − | 8.61911i | −0.0356161 | − | 0.0356161i | ||||
\(243\) | −62.6752 | + | 234.778i | −0.257923 | + | 0.966166i | ||||
\(244\) | −90.7749 | −0.372028 | ||||||||
\(245\) | −237.505 | − | 60.1360i | −0.969408 | − | 0.245453i | ||||
\(246\) | −129.805 | − | 291.401i | −0.527662 | − | 1.18456i | ||||
\(247\) | −145.854 | + | 145.854i | −0.590501 | + | 0.590501i | ||||
\(248\) | −147.848 | − | 147.848i | −0.596160 | − | 0.596160i | ||||
\(249\) | 54.0984 | + | 121.446i | 0.217263 | + | 0.487736i | ||||
\(250\) | 128.926 | + | 382.051i | 0.515705 | + | 1.52820i | ||||
\(251\) | 127.808 | 0.509195 | 0.254597 | − | 0.967047i | \(-0.418057\pi\) | ||||
0.254597 | + | 0.967047i | \(0.418057\pi\) | |||||||
\(252\) | 102.340 | − | 390.348i | 0.406111 | − | 1.54900i | ||||
\(253\) | −260.933 | − | 260.933i | −1.03136 | − | 1.03136i | ||||
\(254\) | 786.070 | 3.09477 | ||||||||
\(255\) | 103.027 | + | 102.216i | 0.404027 | + | 0.400846i | ||||
\(256\) | −240.473 | −0.939346 | ||||||||
\(257\) | −100.099 | + | 100.099i | −0.389491 | + | 0.389491i | −0.874506 | − | 0.485015i | \(-0.838814\pi\) |
0.485015 | + | 0.874506i | \(0.338814\pi\) | |||||||
\(258\) | −6.13059 | + | 15.9796i | −0.0237620 | + | 0.0619364i | ||||
\(259\) | 62.8998 | − | 196.946i | 0.242856 | − | 0.760410i | ||||
\(260\) | 106.458 | − | 241.553i | 0.409453 | − | 0.929049i | ||||
\(261\) | −71.1566 | − | 64.0218i | −0.272631 | − | 0.245294i | ||||
\(262\) | −163.439 | − | 163.439i | −0.623814 | − | 0.623814i | ||||
\(263\) | −96.5525 | + | 96.5525i | −0.367120 | + | 0.367120i | −0.866426 | − | 0.499306i | \(-0.833588\pi\) |
0.499306 | + | 0.866426i | \(0.333588\pi\) | |||||||
\(264\) | 105.805 | + | 237.523i | 0.400776 | + | 0.899708i | ||||
\(265\) | 168.547 | + | 74.2824i | 0.636025 | + | 0.280311i | ||||
\(266\) | 538.306 | + | 171.922i | 2.02371 | + | 0.646323i | ||||
\(267\) | −76.1767 | + | 198.557i | −0.285306 | + | 0.743660i | ||||
\(268\) | −39.3586 | − | 39.3586i | −0.146860 | − | 0.146860i | ||||
\(269\) | − | 213.738i | − | 0.794565i | −0.917696 | − | 0.397282i | \(-0.869953\pi\) | ||
0.917696 | − | 0.397282i | \(-0.130047\pi\) | |||||||
\(270\) | 434.776 | − | 24.6709i | 1.61028 | − | 0.0913736i | ||||
\(271\) | − | 525.042i | − | 1.93743i | −0.248184 | − | 0.968713i | \(-0.579834\pi\) | ||
0.248184 | − | 0.968713i | \(-0.420166\pi\) | |||||||
\(272\) | −4.05241 | + | 4.05241i | −0.0148986 | + | 0.0148986i | ||||
\(273\) | −108.224 | + | 135.078i | −0.396424 | + | 0.494790i | ||||
\(274\) | − | 260.567i | − | 0.950974i | ||||||
\(275\) | 188.420 | + | 206.118i | 0.685164 | + | 0.749520i | ||||
\(276\) | 258.308 | + | 579.879i | 0.935897 | + | 2.10101i | ||||
\(277\) | −122.242 | + | 122.242i | −0.441307 | + | 0.441307i | −0.892451 | − | 0.451144i | \(-0.851016\pi\) |
0.451144 | + | 0.892451i | \(0.351016\pi\) | |||||||
\(278\) | 94.5532 | + | 94.5532i | 0.340120 | + | 0.340120i | ||||
\(279\) | −162.213 | + | 180.290i | −0.581407 | + | 0.646200i | ||||
\(280\) | −271.066 | + | 16.5962i | −0.968093 | + | 0.0592720i | ||||
\(281\) | 262.680i | 0.934803i | 0.884045 | + | 0.467401i | \(0.154810\pi\) | ||||
−0.884045 | + | 0.467401i | \(0.845190\pi\) | |||||||
\(282\) | 755.326 | + | 289.782i | 2.67846 | + | 1.02759i | ||||
\(283\) | −266.792 | + | 266.792i | −0.942728 | + | 0.942728i | −0.998446 | − | 0.0557189i | \(-0.982255\pi\) |
0.0557189 | + | 0.998446i | \(0.482255\pi\) | |||||||
\(284\) | 250.130 | 0.880740 | ||||||||
\(285\) | 1.48354 | + | 375.388i | 0.00520541 | + | 1.31715i | ||||
\(286\) | − | 296.989i | − | 1.03842i | ||||||
\(287\) | 205.072 | − | 105.790i | 0.714536 | − | 0.368607i | ||||
\(288\) | 15.6291 | + | 296.117i | 0.0542676 | + | 1.02818i | ||||
\(289\) | 195.389i | 0.676085i | ||||||||
\(290\) | −69.1790 | + | 156.967i | −0.238548 | + | 0.541266i | ||||
\(291\) | −197.178 | − | 442.647i | −0.677586 | − | 1.52112i | ||||
\(292\) | −327.407 | − | 327.407i | −1.12126 | − | 1.12126i | ||||
\(293\) | −284.626 | − | 284.626i | −0.971421 | − | 0.971421i | 0.0281818 | − | 0.999603i | \(-0.491028\pi\) |
−0.999603 | + | 0.0281818i | \(0.991028\pi\) | |||||||
\(294\) | 464.806 | + | 93.8378i | 1.58097 | + | 0.319176i | ||||
\(295\) | 327.241 | − | 127.032i | 1.10929 | − | 0.430618i | ||||
\(296\) | − | 229.171i | − | 0.774227i | ||||||
\(297\) | 268.653 | − | 137.074i | 0.904555 | − | 0.461529i | ||||
\(298\) | −143.489 | − | 143.489i | −0.481507 | − | 0.481507i | ||||
\(299\) | − | 272.279i | − | 0.910632i | ||||||
\(300\) | −175.619 | − | 447.156i | −0.585395 | − | 1.49052i | ||||
\(301\) | −11.7934 | − | 3.76652i | −0.0391807 | − | 0.0125134i | ||||
\(302\) | −47.0815 | − | 47.0815i | −0.155899 | − | 0.155899i | ||||
\(303\) | 153.902 | + | 59.0445i | 0.507926 | + | 0.194867i | ||||
\(304\) | −14.8237 | −0.0487621 | ||||||||
\(305\) | 66.0555 | − | 25.6422i | 0.216575 | − | 0.0840727i | ||||
\(306\) | −208.812 | − | 187.875i | −0.682392 | − | 0.613970i | ||||
\(307\) | 250.714 | + | 250.714i | 0.816657 | + | 0.816657i | 0.985622 | − | 0.168965i | \(-0.0540424\pi\) |
−0.168965 | + | 0.985622i | \(0.554042\pi\) | |||||||
\(308\) | −445.121 | + | 229.624i | −1.44520 | + | 0.745532i | ||||
\(309\) | 423.619 | − | 188.701i | 1.37093 | − | 0.610684i | ||||
\(310\) | 397.708 | + | 175.279i | 1.28293 | + | 0.565417i | ||||
\(311\) | −296.319 | −0.952794 | −0.476397 | − | 0.879230i | \(-0.658057\pi\) | ||||
−0.476397 | + | 0.879230i | \(0.658057\pi\) | |||||||
\(312\) | −68.7226 | + | 179.128i | −0.220265 | + | 0.574128i | ||||
\(313\) | 195.491 | − | 195.491i | 0.624573 | − | 0.624573i | −0.322124 | − | 0.946697i | \(-0.604397\pi\) |
0.946697 | + | 0.322124i | \(0.104397\pi\) | |||||||
\(314\) | 972.836i | 3.09820i | ||||||||
\(315\) | 35.7948 | + | 312.960i | 0.113634 | + | 0.993523i | ||||
\(316\) | 107.866 | 0.341348 | ||||||||
\(317\) | −43.8360 | − | 43.8360i | −0.138284 | − | 0.138284i | 0.634576 | − | 0.772860i | \(-0.281175\pi\) |
−0.772860 | + | 0.634576i | \(0.781175\pi\) | |||||||
\(318\) | −332.835 | − | 127.692i | −1.04665 | − | 0.401549i | ||||
\(319\) | 118.802i | 0.372420i | ||||||||
\(320\) | 484.344 | − | 188.018i | 1.51357 | − | 0.587557i | ||||
\(321\) | −153.873 | − | 345.432i | −0.479356 | − | 1.07611i | ||||
\(322\) | −662.925 | + | 341.982i | −2.05877 | + | 1.06206i | ||||
\(323\) | 171.215 | − | 171.215i | 0.530078 | − | 0.530078i | ||||
\(324\) | −515.956 | + | 54.6165i | −1.59246 | + | 0.168569i | ||||
\(325\) | −9.23369 | + | 205.846i | −0.0284113 | + | 0.633374i | ||||
\(326\) | − | 89.0709i | − | 0.273224i | ||||||
\(327\) | −98.0263 | + | 255.509i | −0.299775 | + | 0.781373i | ||||
\(328\) | 180.863 | − | 180.863i | 0.551412 | − | 0.551412i | ||||
\(329\) | −178.037 | + | 557.453i | −0.541145 | + | 1.69438i | ||||
\(330\) | −383.695 | − | 380.674i | −1.16271 | − | 1.15356i | ||||
\(331\) | −452.094 | −1.36584 | −0.682922 | − | 0.730492i | \(-0.739291\pi\) | ||||
−0.682922 | + | 0.730492i | \(0.739291\pi\) | |||||||
\(332\) | −200.725 | + | 200.725i | −0.604593 | + | 0.604593i | ||||
\(333\) | −265.448 | + | 14.0103i | −0.797140 | + | 0.0420731i | ||||
\(334\) | 693.061 | 2.07503 | ||||||||
\(335\) | 39.7587 | + | 17.5226i | 0.118683 | + | 0.0523062i | ||||
\(336\) | −12.3638 | + | 1.36464i | −0.0367972 | + | 0.00406142i | ||||
\(337\) | 203.621 | − | 203.621i | 0.604218 | − | 0.604218i | −0.337211 | − | 0.941429i | \(-0.609484\pi\) |
0.941429 | + | 0.337211i | \(0.109484\pi\) | |||||||
\(338\) | −230.529 | + | 230.529i | −0.682037 | + | 0.682037i | ||||
\(339\) | 381.321 | − | 169.860i | 1.12484 | − | 0.501061i | ||||
\(340\) | −124.969 | + | 283.554i | −0.367556 | + | 0.833984i | ||||
\(341\) | 301.010 | 0.882726 | ||||||||
\(342\) | −38.2940 | − | 725.539i | −0.111971 | − | 2.12146i | ||||
\(343\) | −48.5462 | + | 339.547i | −0.141534 | + | 0.989933i | ||||
\(344\) | −13.7231 | −0.0398927 | ||||||||
\(345\) | −351.771 | − | 349.002i | −1.01963 | − | 1.01160i | ||||
\(346\) | 90.5940i | 0.261832i | ||||||||
\(347\) | −358.869 | − | 358.869i | −1.03421 | − | 1.03421i | −0.999394 | − | 0.0348116i | \(-0.988917\pi\) |
−0.0348116 | − | 0.999394i | \(-0.511083\pi\) | |||||||
\(348\) | 73.2051 | − | 190.812i | 0.210360 | − | 0.548310i | ||||
\(349\) | 51.4939 | 0.147547 | 0.0737735 | − | 0.997275i | \(-0.476496\pi\) | ||||
0.0737735 | + | 0.997275i | \(0.476496\pi\) | |||||||
\(350\) | 512.777 | − | 236.062i | 1.46508 | − | 0.674462i | ||||
\(351\) | 211.684 | + | 68.6501i | 0.603089 | + | 0.195584i | ||||
\(352\) | 260.244 | − | 260.244i | 0.739329 | − | 0.739329i | ||||
\(353\) | −212.052 | − | 212.052i | −0.600714 | − | 0.600714i | 0.339788 | − | 0.940502i | \(-0.389645\pi\) |
−0.940502 | + | 0.339788i | \(0.889645\pi\) | |||||||
\(354\) | −620.616 | + | 276.454i | −1.75315 | + | 0.780944i | ||||
\(355\) | −182.016 | + | 70.6570i | −0.512721 | + | 0.199034i | ||||
\(356\) | −454.077 | −1.27550 | ||||||||
\(357\) | 127.042 | − | 158.565i | 0.355860 | − | 0.444161i | ||||
\(358\) | 359.910 | + | 359.910i | 1.00534 | + | 1.00534i | ||||
\(359\) | −194.091 | −0.540643 | −0.270321 | − | 0.962770i | \(-0.587130\pi\) | ||||
−0.270321 | + | 0.962770i | \(0.587130\pi\) | |||||||
\(360\) | 143.337 | + | 318.389i | 0.398159 | + | 0.884413i | ||||
\(361\) | 265.304 | 0.734915 | ||||||||
\(362\) | −134.124 | + | 134.124i | −0.370508 | + | 0.370508i | ||||
\(363\) | −10.5840 | − | 4.06058i | −0.0291571 | − | 0.0111862i | ||||
\(364\) | −352.042 | − | 112.434i | −0.967148 | − | 0.308883i | ||||
\(365\) | 330.735 | + | 145.763i | 0.906123 | + | 0.399350i | ||||
\(366\) | −125.275 | + | 55.8038i | −0.342281 | + | 0.152469i | ||||
\(367\) | −291.230 | − | 291.230i | −0.793542 | − | 0.793542i | 0.188526 | − | 0.982068i | \(-0.439629\pi\) |
−0.982068 | + | 0.188526i | \(0.939629\pi\) | |||||||
\(368\) | 13.8364 | − | 13.8364i | 0.0375989 | − | 0.0375989i | ||||
\(369\) | −220.550 | − | 198.436i | −0.597696 | − | 0.537766i | ||||
\(370\) | 172.388 | + | 444.079i | 0.465913 | + | 1.20021i | ||||
\(371\) | 78.4520 | − | 245.642i | 0.211461 | − | 0.662107i | ||||
\(372\) | −483.461 | − | 185.480i | −1.29963 | − | 0.498603i | ||||
\(373\) | 39.6194 | + | 39.6194i | 0.106218 | + | 0.106218i | 0.758219 | − | 0.652000i | \(-0.226070\pi\) |
−0.652000 | + | 0.758219i | \(0.726070\pi\) | |||||||
\(374\) | 348.630i | 0.932165i | ||||||||
\(375\) | 254.108 | + | 275.779i | 0.677621 | + | 0.735411i | ||||
\(376\) | 648.665i | 1.72517i | ||||||||
\(377\) | −61.9839 | + | 61.9839i | −0.164414 | + | 0.164414i | ||||
\(378\) | −98.7311 | − | 601.618i | −0.261193 | − | 1.59158i | ||||
\(379\) | 391.187i | 1.03216i | 0.856541 | + | 0.516078i | \(0.172609\pi\) | ||||
−0.856541 | + | 0.516078i | \(0.827391\pi\) | |||||||
\(380\) | −747.188 | + | 290.052i | −1.96629 | + | 0.763296i | ||||
\(381\) | 667.801 | − | 297.473i | 1.75276 | − | 0.780769i | ||||
\(382\) | −20.5199 | + | 20.5199i | −0.0537170 | + | 0.0537170i | ||||
\(383\) | 6.31835 | + | 6.31835i | 0.0164970 | + | 0.0164970i | 0.715307 | − | 0.698810i | \(-0.246287\pi\) |
−0.698810 | + | 0.715307i | \(0.746287\pi\) | |||||||
\(384\) | −557.401 | + | 248.295i | −1.45157 | + | 0.646602i | ||||
\(385\) | 259.043 | − | 292.832i | 0.672839 | − | 0.760603i | ||||
\(386\) | 438.422i | 1.13581i | ||||||||
\(387\) | 0.838958 | + | 15.8954i | 0.00216785 | + | 0.0410733i | ||||
\(388\) | 731.601 | − | 731.601i | 1.88557 | − | 1.88557i | ||||
\(389\) | 234.607 | 0.603103 | 0.301551 | − | 0.953450i | \(-0.402496\pi\) | ||||
0.301551 | + | 0.953450i | \(0.402496\pi\) | |||||||
\(390\) | −1.57608 | − | 398.802i | −0.00404122 | − | 1.02257i | ||||
\(391\) | 319.624i | 0.817452i | ||||||||
\(392\) | 63.2462 | + | 374.906i | 0.161342 | + | 0.956392i | ||||
\(393\) | −200.699 | − | 76.9985i | −0.510685 | − | 0.195925i | ||||
\(394\) | − | 516.196i | − | 1.31014i | ||||||
\(395\) | −78.4923 | + | 30.4701i | −0.198715 | + | 0.0771394i | ||||
\(396\) | 478.717 | + | 430.717i | 1.20888 | + | 1.08767i | ||||
\(397\) | 244.142 | + | 244.142i | 0.614967 | + | 0.614967i | 0.944236 | − | 0.329269i | \(-0.106802\pi\) |
−0.329269 | + | 0.944236i | \(0.606802\pi\) | |||||||
\(398\) | 278.335 | + | 278.335i | 0.699333 | + | 0.699333i | ||||
\(399\) | 522.375 | − | 57.6562i | 1.30921 | − | 0.144502i | ||||
\(400\) | −10.9297 | + | 9.99126i | −0.0273243 | + | 0.0249782i | ||||
\(401\) | − | 255.719i | − | 0.637703i | −0.947805 | − | 0.318851i | \(-0.896703\pi\) | ||
0.947805 | − | 0.318851i | \(-0.103297\pi\) | |||||||
\(402\) | −78.5128 | − | 30.1215i | −0.195306 | − | 0.0749292i | ||||
\(403\) | 157.049 | + | 157.049i | 0.389700 | + | 0.389700i | ||||
\(404\) | 351.955i | 0.871175i | ||||||||
\(405\) | 360.025 | − | 185.491i | 0.888951 | − | 0.458003i | ||||
\(406\) | 228.766 | + | 73.0621i | 0.563462 | + | 0.179956i | ||||
\(407\) | 233.290 | + | 233.290i | 0.573194 | + | 0.573194i | ||||
\(408\) | 80.6723 | − | 210.275i | 0.197726 | − | 0.515380i | ||||
\(409\) | −549.262 | −1.34294 | −0.671469 | − | 0.741033i | \(-0.734336\pi\) | ||||
−0.671469 | + | 0.741033i | \(0.734336\pi\) | |||||||
\(410\) | −214.420 | + | 486.519i | −0.522976 | + | 1.18663i | ||||
\(411\) | −98.6064 | − | 221.363i | −0.239918 | − | 0.538596i | ||||
\(412\) | 700.151 | + | 700.151i | 1.69940 | + | 1.69940i | ||||
\(413\) | −225.309 | − | 436.756i | −0.545541 | − | 1.05752i | ||||
\(414\) | 712.960 | + | 641.473i | 1.72213 | + | 1.54945i | ||||
\(415\) | 89.3634 | − | 202.765i | 0.215333 | − | 0.488591i | ||||
\(416\) | 271.559 | 0.652787 | ||||||||
\(417\) | 116.109 | + | 44.5453i | 0.278439 | + | 0.106823i | ||||
\(418\) | −637.643 | + | 637.643i | −1.52546 | + | 1.52546i | ||||
\(419\) | − | 476.333i | − | 1.13683i | −0.822741 | − | 0.568417i | \(-0.807556\pi\) | ||
0.822741 | − | 0.568417i | \(-0.192444\pi\) | |||||||
\(420\) | −596.498 | + | 310.706i | −1.42023 | + | 0.739775i | ||||
\(421\) | −736.969 | −1.75052 | −0.875261 | − | 0.483652i | \(-0.839310\pi\) | ||||
−0.875261 | + | 0.483652i | \(0.839310\pi\) | |||||||
\(422\) | −9.76103 | − | 9.76103i | −0.0231304 | − | 0.0231304i | ||||
\(423\) | 751.345 | − | 39.6560i | 1.77623 | − | 0.0937494i | ||||
\(424\) | − | 285.835i | − | 0.674138i | ||||||
\(425\) | 10.8393 | − | 241.640i | 0.0255041 | − | 0.568564i | ||||
\(426\) | 345.195 | − | 153.767i | 0.810316 | − | 0.360956i | ||||
\(427\) | −45.4798 | − | 88.1615i | −0.106510 | − | 0.206467i | ||||
\(428\) | 570.926 | − | 570.926i | 1.33394 | − | 1.33394i | ||||
\(429\) | −112.390 | − | 252.305i | −0.261980 | − | 0.588123i | ||||
\(430\) | 26.5921 | − | 10.3228i | 0.0618420 | − | 0.0240066i | ||||
\(431\) | − | 95.9393i | − | 0.222597i | −0.993787 | − | 0.111299i | \(-0.964499\pi\) | ||
0.993787 | − | 0.111299i | \(-0.0355010\pi\) | |||||||
\(432\) | 7.26856 | + | 14.2457i | 0.0168254 | + | 0.0329762i | ||||
\(433\) | −273.161 | + | 273.161i | −0.630857 | + | 0.630857i | −0.948283 | − | 0.317426i | \(-0.897182\pi\) |
0.317426 | + | 0.948283i | \(0.397182\pi\) | |||||||
\(434\) | 185.118 | − | 579.625i | 0.426539 | − | 1.33554i | ||||
\(435\) | 0.630465 | + | 159.530i | 0.00144935 | + | 0.366735i | ||||
\(436\) | −584.318 | −1.34018 | ||||||||
\(437\) | −584.591 | + | 584.591i | −1.33774 | + | 1.33774i | ||||
\(438\) | −653.114 | − | 250.568i | −1.49113 | − | 0.572073i | ||||
\(439\) | −396.491 | −0.903169 | −0.451585 | − | 0.892228i | \(-0.649141\pi\) | ||||
−0.451585 | + | 0.892228i | \(0.649141\pi\) | |||||||
\(440\) | 174.775 | − | 396.565i | 0.397217 | − | 0.901284i | ||||
\(441\) | 430.385 | − | 96.1775i | 0.975929 | − | 0.218090i | ||||
\(442\) | −181.894 | + | 181.894i | −0.411526 | + | 0.411526i | ||||
\(443\) | −214.203 | + | 214.203i | −0.483528 | + | 0.483528i | −0.906256 | − | 0.422728i | \(-0.861072\pi\) |
0.422728 | + | 0.906256i | \(0.361072\pi\) | |||||||
\(444\) | −230.942 | − | 518.446i | −0.520140 | − | 1.16767i | ||||
\(445\) | 330.425 | − | 128.268i | 0.742527 | − | 0.288243i | ||||
\(446\) | −159.588 | −0.357821 | ||||||||
\(447\) | −176.201 | − | 67.5996i | −0.394185 | − | 0.151230i | ||||
\(448\) | −333.475 | − | 646.433i | −0.744363 | − | 1.44293i | ||||
\(449\) | 147.297 | 0.328055 | 0.164027 | − | 0.986456i | \(-0.447551\pi\) | ||||
0.164027 | + | 0.986456i | \(0.447551\pi\) | |||||||
\(450\) | −517.253 | − | 509.140i | −1.14945 | − | 1.13142i | ||||
\(451\) | 368.227i | 0.816468i | ||||||||
\(452\) | 630.242 | + | 630.242i | 1.39434 | + | 1.39434i | ||||
\(453\) | −57.8148 | − | 22.1807i | −0.127627 | − | 0.0489641i | ||||
\(454\) | −106.110 | −0.233723 | ||||||||
\(455\) | 287.936 | − | 17.6290i | 0.632826 | − | 0.0387451i | ||||
\(456\) | 532.142 | − | 237.043i | 1.16698 | − | 0.519832i | ||||
\(457\) | 18.8754 | − | 18.8754i | 0.0413028 | − | 0.0413028i | −0.686154 | − | 0.727457i | \(-0.740702\pi\) |
0.727457 | + | 0.686154i | \(0.240702\pi\) | |||||||
\(458\) | −207.818 | − | 207.818i | −0.453751 | − | 0.453751i | ||||
\(459\) | −248.492 | − | 80.5871i | −0.541378 | − | 0.175571i | ||||
\(460\) | 426.690 | − | 968.158i | 0.927586 | − | 2.10469i | ||||
\(461\) | −191.433 | −0.415256 | −0.207628 | − | 0.978208i | \(-0.566574\pi\) | ||||
−0.207628 | + | 0.978208i | \(0.566574\pi\) | |||||||
\(462\) | −473.132 | + | 590.533i | −1.02410 | + | 1.27821i | ||||
\(463\) | 362.672 | + | 362.672i | 0.783309 | + | 0.783309i | 0.980388 | − | 0.197079i | \(-0.0631454\pi\) |
−0.197079 | + | 0.980388i | \(0.563145\pi\) | |||||||
\(464\) | −6.29967 | −0.0135769 | ||||||||
\(465\) | 404.201 | − | 1.59741i | 0.869251 | − | 0.00343530i | ||||
\(466\) | 413.314 | 0.886939 | ||||||||
\(467\) | 61.5519 | − | 61.5519i | 0.131803 | − | 0.131803i | −0.638128 | − | 0.769931i | \(-0.720291\pi\) |
0.769931 | + | 0.638128i | \(0.220291\pi\) | |||||||
\(468\) | 25.0435 | + | 474.488i | 0.0535118 | + | 1.01386i | ||||
\(469\) | 18.5061 | − | 57.9448i | 0.0394587 | − | 0.123550i | ||||
\(470\) | −487.941 | − | 1256.96i | −1.03817 | − | 2.67438i | ||||
\(471\) | 368.151 | + | 826.467i | 0.781636 | + | 1.75471i | ||||
\(472\) | −385.197 | − | 385.197i | −0.816094 | − | 0.816094i | ||||
\(473\) | 13.9697 | − | 13.9697i | 0.0295343 | − | 0.0295343i | ||||
\(474\) | 148.861 | − | 66.3104i | 0.314053 | − | 0.139895i | ||||
\(475\) | 461.783 | − | 422.133i | 0.972175 | − | 0.888701i | ||||
\(476\) | 413.256 | + | 131.984i | 0.868184 | + | 0.277277i | ||||
\(477\) | −331.081 | + | 17.4744i | −0.694089 | + | 0.0366340i | ||||
\(478\) | −928.316 | − | 928.316i | −1.94208 | − | 1.94208i | ||||
\(479\) | − | 572.620i | − | 1.19545i | −0.801702 | − | 0.597724i | \(-0.796072\pi\) | ||
0.801702 | − | 0.597724i | \(-0.203928\pi\) | |||||||
\(480\) | 348.079 | − | 350.841i | 0.725165 | − | 0.730919i | ||||
\(481\) | 243.434i | 0.506099i | ||||||||
\(482\) | 267.116 | − | 267.116i | 0.554183 | − | 0.554183i | ||||
\(483\) | −433.768 | + | 541.400i | −0.898070 | + | 1.12091i | ||||
\(484\) | − | 24.2044i | − | 0.0500092i | ||||||
\(485\) | −325.711 | + | 739.038i | −0.671569 | + | 1.52379i | ||||
\(486\) | −678.475 | + | 392.558i | −1.39604 | + | 0.807732i | ||||
\(487\) | 358.153 | − | 358.153i | 0.735427 | − | 0.735427i | −0.236262 | − | 0.971689i | \(-0.575922\pi\) |
0.971689 | + | 0.236262i | \(0.0759224\pi\) | |||||||
\(488\) | −77.7540 | − | 77.7540i | −0.159332 | − | 0.159332i | ||||
\(489\) | −33.7071 | − | 75.6696i | −0.0689307 | − | 0.154744i | ||||
\(490\) | −404.569 | − | 678.903i | −0.825651 | − | 1.38552i | ||||
\(491\) | 644.045i | 1.31170i | 0.754891 | + | 0.655850i | \(0.227690\pi\) | ||||
−0.754891 | + | 0.655850i | \(0.772310\pi\) | |||||||
\(492\) | 226.899 | − | 591.421i | 0.461177 | − | 1.20207i | ||||
\(493\) | 72.7618 | − | 72.7618i | 0.147590 | − | 0.147590i | ||||
\(494\) | −665.369 | −1.34690 | ||||||||
\(495\) | −470.024 | − | 178.198i | −0.949544 | − | 0.359995i | ||||
\(496\) | 15.9615i | 0.0321804i | ||||||||
\(497\) | 125.319 | + | 242.929i | 0.252152 | + | 0.488791i | ||||
\(498\) | −153.617 | + | 400.408i | −0.308468 | + | 0.804032i | ||||
\(499\) | 530.323i | 1.06277i | 0.847130 | + | 0.531386i | \(0.178328\pi\) | ||||
−0.847130 | + | 0.531386i | \(0.821672\pi\) | |||||||
\(500\) | −355.416 | + | 717.470i | −0.710831 | + | 1.43494i | ||||
\(501\) | 588.786 | − | 262.275i | 1.17522 | − | 0.523503i | ||||
\(502\) | 291.523 | + | 291.523i | 0.580723 | + | 0.580723i | ||||
\(503\) | 515.298 | + | 515.298i | 1.02445 | + | 1.02445i | 0.999694 | + | 0.0247567i | \(0.00788111\pi\) |
0.0247567 | + | 0.999694i | \(0.492119\pi\) | |||||||
\(504\) | 422.017 | − | 246.696i | 0.837335 | − | 0.489477i | ||||
\(505\) | −99.4205 | − | 256.112i | −0.196872 | − | 0.507152i | ||||
\(506\) | − | 1190.35i | − | 2.35247i | ||||||
\(507\) | −108.605 | + | 283.083i | −0.214211 | + | 0.558349i | ||||
\(508\) | 1103.73 | + | 1103.73i | 2.17270 | + | 2.17270i | ||||
\(509\) | 648.378i | 1.27383i | 0.770935 | + | 0.636914i | \(0.219789\pi\) | ||||
−0.770935 | + | 0.636914i | \(0.780211\pi\) | |||||||
\(510\) | 1.85013 | + | 468.147i | 0.00362770 | + | 0.917935i | ||||
\(511\) | 153.945 | − | 482.017i | 0.301261 | − | 0.943282i | ||||
\(512\) | 26.7994 | + | 26.7994i | 0.0523425 | + | 0.0523425i | ||||
\(513\) | −307.098 | − | 601.886i | −0.598632 | − | 1.17327i | ||||
\(514\) | −456.642 | −0.888408 | ||||||||
\(515\) | −707.269 | − | 311.710i | −1.37334 | − | 0.605262i | ||||
\(516\) | −31.0452 | + | 13.8291i | −0.0601652 | + | 0.0268006i | ||||
\(517\) | −660.323 | − | 660.323i | −1.27722 | − | 1.27722i | ||||
\(518\) | 592.694 | − | 305.752i | 1.14420 | − | 0.590256i | ||||
\(519\) | 34.2835 | + | 76.9636i | 0.0660568 | + | 0.148292i | ||||
\(520\) | 298.092 | − | 115.717i | 0.573253 | − | 0.222532i | ||||
\(521\) | −195.439 | −0.375123 | −0.187561 | − | 0.982253i | \(-0.560058\pi\) | ||||
−0.187561 | + | 0.982253i | \(0.560058\pi\) | |||||||
\(522\) | −16.2739 | − | 308.334i | −0.0311761 | − | 0.590679i | ||||
\(523\) | 516.575 | − | 516.575i | 0.987715 | − | 0.987715i | −0.0122109 | − | 0.999925i | \(-0.503887\pi\) |
0.999925 | + | 0.0122109i | \(0.00388694\pi\) | |||||||
\(524\) | − | 458.975i | − | 0.875906i | ||||||
\(525\) | 346.294 | − | 394.595i | 0.659608 | − | 0.751610i | ||||
\(526\) | −440.462 | −0.837380 | ||||||||
\(527\) | −184.357 | − | 184.357i | −0.349824 | − | 0.349824i | ||||
\(528\) | 7.11008 | − | 18.5327i | 0.0134661 | − | 0.0350997i | ||||
\(529\) | − | 562.311i | − | 1.06297i | ||||||
\(530\) | 215.011 | + | 553.879i | 0.405682 | + | 1.04506i | ||||
\(531\) | −422.622 | + | 469.720i | −0.795899 | + | 0.884595i | ||||
\(532\) | 514.446 | + | 997.242i | 0.967003 | + | 1.87451i | ||||
\(533\) | −192.119 | + | 192.119i | −0.360448 | + | 0.360448i | ||||
\(534\) | −626.653 | + | 279.143i | −1.17351 | + | 0.522740i | ||||
\(535\) | −254.178 | + | 576.730i | −0.475099 | + | 1.07800i | ||||
\(536\) | − | 67.4259i | − | 0.125795i | ||||||
\(537\) | 441.960 | + | 169.559i | 0.823018 | + | 0.315752i | ||||
\(538\) | 487.524 | − | 487.524i | 0.906179 | − | 0.906179i | ||||
\(539\) | −446.026 | − | 317.261i | −0.827507 | − | 0.588610i | ||||
\(540\) | 645.116 | + | 575.834i | 1.19466 | + | 1.06636i | ||||
\(541\) | −165.071 | −0.305123 | −0.152561 | − | 0.988294i | \(-0.548752\pi\) | ||||
−0.152561 | + | 0.988294i | \(0.548752\pi\) | |||||||
\(542\) | 1197.59 | − | 1197.59i | 2.20958 | − | 2.20958i | ||||
\(543\) | −63.1875 | + | 164.701i | −0.116367 | + | 0.303316i | ||||
\(544\) | −318.779 | −0.585990 | ||||||||
\(545\) | 425.199 | − | 165.059i | 0.780182 | − | 0.302860i | ||||
\(546\) | −554.957 | + | 61.2524i | −1.01641 | + | 0.112184i | ||||
\(547\) | −259.758 | + | 259.758i | −0.474878 | + | 0.474878i | −0.903489 | − | 0.428611i | \(-0.859003\pi\) |
0.428611 | + | 0.903489i | \(0.359003\pi\) | |||||||
\(548\) | 365.866 | − | 365.866i | 0.667638 | − | 0.667638i | ||||
\(549\) | −85.3086 | + | 94.8155i | −0.155389 | + | 0.172706i | ||||
\(550\) | −40.3678 | + | 899.919i | −0.0733960 | + | 1.63622i | ||||
\(551\) | 266.162 | 0.483053 | ||||||||
\(552\) | −275.445 | + | 717.956i | −0.498994 | + | 1.30064i | ||||
\(553\) | 54.0426 | + | 104.760i | 0.0977263 | + | 0.189440i | ||||
\(554\) | −557.655 | −1.00660 | ||||||||
\(555\) | 314.504 | + | 312.028i | 0.566674 | + | 0.562213i | ||||
\(556\) | 265.527i | 0.477567i | ||||||||
\(557\) | 118.212 | + | 118.212i | 0.212230 | + | 0.212230i | 0.805214 | − | 0.592984i | \(-0.202050\pi\) |
−0.592984 | + | 0.805214i | \(0.702050\pi\) | |||||||
\(558\) | −781.229 | + | 41.2333i | −1.40005 | + | 0.0738947i | ||||
\(559\) | 14.5771 | 0.0260772 | ||||||||
\(560\) | 15.5279 | + | 13.7362i | 0.0277283 | + | 0.0245289i | ||||
\(561\) | 131.932 | + | 296.176i | 0.235173 | + | 0.527944i | ||||
\(562\) | −599.158 | + | 599.158i | −1.06612 | + | 1.06612i | ||||
\(563\) | 569.301 | + | 569.301i | 1.01119 | + | 1.01119i | 0.999937 | + | 0.0112552i | \(0.00358273\pi\) |
0.0112552 | + | 0.999937i | \(0.496417\pi\) | |||||||
\(564\) | 653.678 | + | 1467.45i | 1.15900 | + | 2.60186i | ||||
\(565\) | −636.649 | − | 280.586i | −1.12681 | − | 0.496612i | ||||
\(566\) | −1217.08 | −2.15031 | ||||||||
\(567\) | −311.547 | − | 473.738i | −0.549465 | − | 0.835517i | ||||
\(568\) | 214.251 | + | 214.251i | 0.377203 | + | 0.377203i | ||||
\(569\) | 602.118 | 1.05820 | 0.529102 | − | 0.848558i | \(-0.322529\pi\) | ||||
0.529102 | + | 0.848558i | \(0.322529\pi\) | |||||||
\(570\) | −852.855 | + | 859.623i | −1.49624 | + | 1.50811i | ||||
\(571\) | −883.761 | −1.54774 | −0.773871 | − | 0.633343i | \(-0.781682\pi\) | ||||
−0.773871 | + | 0.633343i | \(0.781682\pi\) | |||||||
\(572\) | 417.006 | − | 417.006i | 0.729032 | − | 0.729032i | ||||
\(573\) | −9.66720 | + | 25.1979i | −0.0168712 | + | 0.0439754i | ||||
\(574\) | 709.058 | + | 226.456i | 1.23529 | + | 0.394523i | ||||
\(575\) | −37.0092 | + | 825.045i | −0.0643638 | + | 1.43486i | ||||
\(576\) | −625.515 | + | 695.223i | −1.08596 | + | 1.20698i | ||||
\(577\) | −64.3197 | − | 64.3197i | −0.111473 | − | 0.111473i | 0.649170 | − | 0.760643i | \(-0.275116\pi\) |
−0.760643 | + | 0.649170i | \(0.775116\pi\) | |||||||
\(578\) | −445.670 | + | 445.670i | −0.771056 | + | 0.771056i | ||||
\(579\) | 165.912 | + | 372.459i | 0.286550 | + | 0.643280i | ||||
\(580\) | −317.535 | + | 123.264i | −0.547474 | + | 0.212525i | ||||
\(581\) | −295.513 | − | 94.3795i | −0.508627 | − | 0.162443i | ||||
\(582\) | 559.902 | − | 1459.40i | 0.962031 | − | 2.50757i | ||||
\(583\) | 290.972 | + | 290.972i | 0.499094 | + | 0.499094i | ||||
\(584\) | − | 560.886i | − | 0.960422i | ||||||
\(585\) | −152.258 | − | 338.204i | −0.260270 | − | 0.578126i | ||||
\(586\) | − | 1298.43i | − | 2.21576i | ||||||
\(587\) | 512.337 | − | 512.337i | 0.872806 | − | 0.872806i | −0.119971 | − | 0.992777i | \(-0.538280\pi\) |
0.992777 | + | 0.119971i | \(0.0382803\pi\) | |||||||
\(588\) | 520.882 | + | 784.400i | 0.885855 | + | 1.33401i | ||||
\(589\) | − | 674.377i | − | 1.14495i | ||||||
\(590\) | 1036.17 | + | 456.666i | 1.75623 | + | 0.774010i | ||||
\(591\) | −195.344 | − | 438.531i | −0.330532 | − | 0.742016i | ||||
\(592\) | −12.3706 | + | 12.3706i | −0.0208962 | + | 0.0208962i | ||||
\(593\) | −195.165 | − | 195.165i | −0.329114 | − | 0.329114i | 0.523135 | − | 0.852250i | \(-0.324762\pi\) |
−0.852250 | + | 0.523135i | \(0.824762\pi\) | |||||||
\(594\) | 925.441 | + | 300.124i | 1.55798 | + | 0.505260i | ||||
\(595\) | −338.003 | + | 20.6944i | −0.568072 | + | 0.0347805i | ||||
\(596\) | − | 402.950i | − | 0.676090i | ||||||
\(597\) | 341.788 | + | 131.127i | 0.572509 | + | 0.219644i | ||||
\(598\) | 621.053 | − | 621.053i | 1.03855 | − | 1.03855i | ||||
\(599\) | 93.4354 | 0.155986 | 0.0779928 | − | 0.996954i | \(-0.475149\pi\) | ||||
0.0779928 | + | 0.996954i | \(0.475149\pi\) | |||||||
\(600\) | 232.587 | − | 533.443i | 0.387646 | − | 0.889071i | ||||
\(601\) | 47.3325i | 0.0787563i | 0.999224 | + | 0.0393782i | \(0.0125377\pi\) | ||||
−0.999224 | + | 0.0393782i | \(0.987462\pi\) | |||||||
\(602\) | −18.3089 | − | 35.4913i | −0.0304134 | − | 0.0589557i | ||||
\(603\) | −78.0990 | + | 4.12207i | −0.129517 | + | 0.00683593i | ||||
\(604\) | − | 132.216i | − | 0.218900i | ||||||
\(605\) | 6.83729 | + | 17.6132i | 0.0113013 | + | 0.0291127i | ||||
\(606\) | 216.364 | + | 485.719i | 0.357036 | + | 0.801516i | ||||
\(607\) | 782.862 | + | 782.862i | 1.28972 | + | 1.28972i | 0.934954 | + | 0.354769i | \(0.115440\pi\) |
0.354769 | + | 0.934954i | \(0.384560\pi\) | |||||||
\(608\) | −583.046 | − | 583.046i | −0.958957 | − | 0.958957i | ||||
\(609\) | 221.995 | − | 24.5023i | 0.364524 | − | 0.0402337i | ||||
\(610\) | 209.157 | + | 92.1804i | 0.342881 | + | 0.151115i | ||||
\(611\) | − | 689.034i | − | 1.12772i | ||||||
\(612\) | −29.3981 | − | 556.994i | −0.0480362 | − | 0.910120i | ||||
\(613\) | 587.076 | + | 587.076i | 0.957710 | + | 0.957710i | 0.999141 | − | 0.0414311i | \(-0.0131917\pi\) |
−0.0414311 | + | 0.999141i | \(0.513192\pi\) | |||||||
\(614\) | 1143.73i | 1.86275i | ||||||||
\(615\) | 1.95413 | + | 494.462i | 0.00317744 | + | 0.804004i | ||||
\(616\) | −577.959 | − | 184.586i | −0.938245 | − | 0.299652i | ||||
\(617\) | 400.922 | + | 400.922i | 0.649793 | + | 0.649793i | 0.952943 | − | 0.303150i | \(-0.0980383\pi\) |
−0.303150 | + | 0.952943i | \(0.598038\pi\) | |||||||
\(618\) | 1396.67 | + | 535.833i | 2.25998 | + | 0.867044i | ||||
\(619\) | 382.132 | 0.617338 | 0.308669 | − | 0.951170i | \(-0.400117\pi\) | ||||
0.308669 | + | 0.951170i | \(0.400117\pi\) | |||||||
\(620\) | 312.316 | + | 804.540i | 0.503735 | + | 1.29764i | ||||
\(621\) | 848.443 | + | 275.154i | 1.36625 | + | 0.443082i | ||||
\(622\) | −675.887 | − | 675.887i | −1.08663 | − | 1.08663i | ||||
\(623\) | −227.500 | − | 441.004i | −0.365169 | − | 0.707872i | ||||
\(624\) | 13.3789 | − | 5.95963i | 0.0214405 | − | 0.00955068i | ||||
\(625\) | 55.9588 | − | 622.490i | 0.0895341 | − | 0.995984i | ||||
\(626\) | 891.810 | 1.42462 | ||||||||
\(627\) | −300.402 | + | 783.009i | −0.479111 | + | 1.24882i | ||||
\(628\) | −1365.97 | + | 1365.97i | −2.17512 | + | 2.17512i | ||||
\(629\) | − | 285.762i | − | 0.454312i | ||||||
\(630\) | −632.198 | + | 795.489i | −1.00349 | + | 1.26268i | ||||
\(631\) | 1097.98 | 1.74006 | 0.870031 | − | 0.492997i | \(-0.164099\pi\) | ||||
0.870031 | + | 0.492997i | \(0.164099\pi\) | |||||||
\(632\) | 92.3934 | + | 92.3934i | 0.146192 | + | 0.146192i | ||||
\(633\) | −11.9863 | − | 4.59856i | −0.0189357 | − | 0.00726470i | ||||
\(634\) | − | 199.975i | − | 0.315418i | ||||||
\(635\) | −1114.95 | − | 491.386i | −1.75583 | − | 0.773836i | ||||
\(636\) | −288.043 | − | 646.633i | −0.452898 | − | 1.01672i | ||||
\(637\) | −67.1823 | − | 398.238i | −0.105467 | − | 0.625177i | ||||
\(638\) | −270.981 | + | 270.981i | −0.424735 | + | 0.424735i | ||||
\(639\) | 235.068 | − | 261.264i | 0.367868 | − | 0.408864i | ||||
\(640\) | 930.630 | + | 410.150i | 1.45411 | + | 0.640860i | ||||
\(641\) | 137.826i | 0.215017i | 0.994204 | + | 0.107509i | \(0.0342873\pi\) | ||||
−0.994204 | + | 0.107509i | \(0.965713\pi\) | |||||||
\(642\) | 436.936 | − | 1138.89i | 0.680585 | − | 1.77397i | ||||
\(643\) | −340.846 | + | 340.846i | −0.530087 | + | 0.530087i | −0.920598 | − | 0.390511i | \(-0.872298\pi\) |
0.390511 | + | 0.920598i | \(0.372298\pi\) | |||||||
\(644\) | −1411.01 | − | 450.640i | −2.19100 | − | 0.699752i | ||||
\(645\) | 18.6847 | − | 18.8329i | 0.0289685 | − | 0.0291983i | ||||
\(646\) | 781.065 | 1.20908 | ||||||||
\(647\) | 192.497 | − | 192.497i | 0.297523 | − | 0.297523i | −0.542520 | − | 0.840043i | \(-0.682530\pi\) |
0.840043 | + | 0.542520i | \(0.182530\pi\) | |||||||
\(648\) | −488.729 | − | 395.164i | −0.754211 | − | 0.609822i | ||||
\(649\) | 784.239 | 1.20838 | ||||||||
\(650\) | −490.586 | + | 448.463i | −0.754748 | + | 0.689943i | ||||
\(651\) | −62.0817 | − | 562.471i | −0.0953636 | − | 0.864010i | ||||
\(652\) | 125.066 | − | 125.066i | 0.191819 | − | 0.191819i | ||||
\(653\) | 178.554 | − | 178.554i | 0.273436 | − | 0.273436i | −0.557046 | − | 0.830482i | \(-0.688065\pi\) |
0.830482 | + | 0.557046i | \(0.188065\pi\) | |||||||
\(654\) | −806.394 | + | 359.209i | −1.23302 | + | 0.549250i | ||||
\(655\) | 129.652 | + | 333.989i | 0.197942 | + | 0.509907i | ||||
\(656\) | −19.5258 | −0.0297649 | ||||||||
\(657\) | −649.672 | + | 34.2897i | −0.988846 | + | 0.0521913i | ||||
\(658\) | −1677.61 | + | 865.427i | −2.54956 | + | 1.31524i | ||||
\(659\) | −984.529 | −1.49397 | −0.746987 | − | 0.664838i | \(-0.768500\pi\) | ||||
−0.746987 | + | 0.664838i | \(0.768500\pi\) | |||||||
\(660\) | −4.24155 | − | 1073.26i | −0.00642660 | − | 1.62615i | ||||
\(661\) | 730.936i | 1.10580i | 0.833247 | + | 0.552901i | \(0.186479\pi\) | ||||
−0.833247 | + | 0.552901i | \(0.813521\pi\) | |||||||
\(662\) | −1031.20 | − | 1031.20i | −1.55771 | − | 1.55771i | ||||
\(663\) | −85.6929 | + | 223.362i | −0.129250 | + | 0.336895i | ||||
\(664\) | −343.865 | −0.517869 | ||||||||
\(665\) | −656.056 | − | 580.356i | −0.986550 | − | 0.872716i | ||||
\(666\) | −637.428 | − | 573.515i | −0.957099 | − | 0.861133i | ||||
\(667\) | −248.435 | + | 248.435i | −0.372467 | + | 0.372467i | ||||
\(668\) | 973.137 | + | 973.137i | 1.45679 | + | 1.45679i | ||||
\(669\) | −135.577 | + | 60.3930i | −0.202656 | + | 0.0902735i | ||||
\(670\) | 50.7193 | + | 130.655i | 0.0757004 | + | 0.195008i | ||||
\(671\) | 158.303 | 0.235921 | ||||||||
\(672\) | −539.969 | − | 432.621i | −0.803525 | − | 0.643781i | ||||
\(673\) | −770.416 | − | 770.416i | −1.14475 | − | 1.14475i | −0.987570 | − | 0.157179i | \(-0.949760\pi\) |
−0.157179 | − | 0.987570i | \(-0.550240\pi\) | |||||||
\(674\) | 928.898 | 1.37819 | ||||||||
\(675\) | −632.103 | − | 236.793i | −0.936449 | − | 0.350804i | ||||
\(676\) | −647.377 | −0.957658 | ||||||||
\(677\) | −430.936 | + | 430.936i | −0.636538 | + | 0.636538i | −0.949700 | − | 0.313162i | \(-0.898612\pi\) |
0.313162 | + | 0.949700i | \(0.398612\pi\) | |||||||
\(678\) | 1257.21 | + | 482.331i | 1.85430 | + | 0.711403i | ||||
\(679\) | 1077.08 | + | 343.994i | 1.58628 | + | 0.506618i | ||||
\(680\) | −349.924 | + | 135.838i | −0.514595 | + | 0.199761i | ||||
\(681\) | −90.1453 | + | 40.1553i | −0.132372 | + | 0.0589652i | ||||
\(682\) | 686.586 | + | 686.586i | 1.00672 | + | 1.00672i | ||||
\(683\) | 952.879 | − | 952.879i | 1.39514 | − | 1.39514i | 0.581818 | − | 0.813319i | \(-0.302342\pi\) |
0.813319 | − | 0.581818i | \(-0.197658\pi\) | |||||||
\(684\) | 964.971 | − | 1072.51i | 1.41078 | − | 1.56800i | ||||
\(685\) | −162.885 | + | 369.585i | −0.237788 | + | 0.539540i | ||||
\(686\) | −885.219 | + | 663.757i | −1.29041 | + | 0.967576i | ||||
\(687\) | −255.195 | − | 97.9059i | −0.371463 | − | 0.142512i | ||||
\(688\) | 0.740765 | + | 0.740765i | 0.00107669 | + | 0.00107669i | ||||
\(689\) | 303.623i | 0.440673i | ||||||||
\(690\) | −6.31701 | − | 1598.42i | −0.00915508 | − | 2.31656i | ||||
\(691\) | − | 428.205i | − | 0.619689i | −0.950787 | − | 0.309844i | \(-0.899723\pi\) | ||
0.950787 | − | 0.309844i | \(-0.100277\pi\) | |||||||
\(692\) | −127.204 | + | 127.204i | −0.183821 | + | 0.183821i | ||||
\(693\) | −178.471 | + | 680.731i | −0.257534 | + | 0.982296i | ||||
\(694\) | − | 1637.12i | − | 2.35897i | ||||||
\(695\) | −75.0064 | − | 193.220i | −0.107923 | − | 0.278014i | ||||
\(696\) | 226.146 | − | 100.737i | 0.324922 | − | 0.144737i | ||||
\(697\) | 225.525 | − | 225.525i | 0.323565 | − | 0.323565i | ||||
\(698\) | 117.455 | + | 117.455i | 0.168273 | + | 0.168273i | ||||
\(699\) | 351.128 | − | 156.410i | 0.502329 | − | 0.223763i | ||||
\(700\) | 1051.46 | + | 388.541i | 1.50208 | + | 0.555058i | ||||
\(701\) | − | 1086.06i | − | 1.54929i | −0.632393 | − | 0.774647i | \(-0.717927\pi\) | ||
0.632393 | − | 0.774647i | \(-0.282073\pi\) | |||||||
\(702\) | 326.253 | + | 639.427i | 0.464748 | + | 0.910865i | ||||
\(703\) | 522.659 | − | 522.659i | 0.743469 | − | 0.743469i | ||||
\(704\) | 1160.74 | 1.64877 | ||||||||
\(705\) | −890.198 | − | 883.190i | −1.26269 | − | 1.25275i | ||||
\(706\) | − | 967.358i | − | 1.37020i | ||||||
\(707\) | −341.822 | + | 176.335i | −0.483482 | + | 0.249413i | ||||
\(708\) | −1259.59 | − | 483.243i | −1.77908 | − | 0.682547i | ||||
\(709\) | − | 384.594i | − | 0.542446i | −0.962516 | − | 0.271223i | \(-0.912572\pi\) | ||
0.962516 | − | 0.271223i | \(-0.0874281\pi\) | |||||||
\(710\) | −576.333 | − | 254.003i | −0.811736 | − | 0.357751i | ||||
\(711\) | 101.370 | − | 112.667i | 0.142574 | − | 0.158463i | ||||
\(712\) | −388.943 | − | 388.943i | −0.546269 | − | 0.546269i | ||||
\(713\) | 629.462 | + | 629.462i | 0.882836 | + | 0.882836i | ||||
\(714\) | 651.455 | − | 71.9031i | 0.912401 | − | 0.100705i | ||||
\(715\) | −185.653 | + | 421.245i | −0.259654 | + | 0.589154i | ||||
\(716\) | 1010.71i | 1.41161i | ||||||||
\(717\) | −1139.95 | − | 437.342i | −1.58989 | − | 0.609961i | ||||
\(718\) | −442.710 | − | 442.710i | −0.616588 | − | 0.616588i | ||||
\(719\) | 160.221i | 0.222838i | 0.993773 | + | 0.111419i | \(0.0355396\pi\) | ||||
−0.993773 | + | 0.111419i | \(0.964460\pi\) | |||||||
\(720\) | 9.44920 | − | 24.9237i | 0.0131239 | − | 0.0346163i | ||||
\(721\) | −329.207 | + | 1030.78i | −0.456597 | + | 1.42966i | ||||
\(722\) | 605.144 | + | 605.144i | 0.838150 | + | 0.838150i | ||||
\(723\) | 125.842 | − | 328.012i | 0.174056 | − | 0.453682i | ||||
\(724\) | −376.650 | −0.520235 | ||||||||
\(725\) | 196.245 | − | 179.395i | 0.270683 | − | 0.247442i | ||||
\(726\) | −14.8797 | − | 33.4036i | −0.0204954 | − | 0.0460104i | ||||
\(727\) | −655.048 | − | 655.048i | −0.901029 | − | 0.901029i | 0.0944960 | − | 0.995525i | \(-0.469876\pi\) |
−0.995525 | + | 0.0944960i | \(0.969876\pi\) | |||||||
\(728\) | −205.239 | − | 397.851i | −0.281921 | − | 0.546498i | ||||
\(729\) | −427.838 | + | 590.250i | −0.586884 | + | 0.809671i | ||||
\(730\) | 421.912 | + | 1086.86i | 0.577961 | + | 1.48886i | ||||
\(731\) | −17.1118 | −0.0234088 | ||||||||
\(732\) | −254.255 | − | 97.5452i | −0.347343 | − | 0.133258i | ||||
\(733\) | 222.518 | − | 222.518i | 0.303572 | − | 0.303572i | −0.538838 | − | 0.842410i | \(-0.681136\pi\) |
0.842410 | + | 0.538838i | \(0.181136\pi\) | |||||||
\(734\) | − | 1328.56i | − | 1.81003i | ||||||
\(735\) | −600.616 | − | 423.657i | −0.817165 | − | 0.576404i | ||||
\(736\) | 1088.43 | 1.47884 | ||||||||
\(737\) | 68.6376 | + | 68.6376i | 0.0931311 | + | 0.0931311i | ||||
\(738\) | −50.4409 | − | 955.682i | −0.0683481 | − | 1.29496i | ||||
\(739\) | − | 343.180i | − | 0.464385i | −0.972670 | − | 0.232192i | \(-0.925410\pi\) | ||
0.972670 | − | 0.232192i | \(-0.0745899\pi\) | |||||||
\(740\) | −381.486 | + | 865.590i | −0.515521 | + | 1.16972i | ||||
\(741\) | −565.260 | + | 251.796i | −0.762834 | + | 0.339805i | ||||
\(742\) | 739.240 | − | 381.351i | 0.996280 | − | 0.513950i | ||||
\(743\) | 54.5399 | − | 54.5399i | 0.0734050 | − | 0.0734050i | −0.669451 | − | 0.742856i | \(-0.733471\pi\) |
0.742856 | + | 0.669451i | \(0.233471\pi\) | |||||||
\(744\) | −255.238 | − | 572.987i | −0.343062 | − | 0.770144i | ||||
\(745\) | 113.826 | + | 293.220i | 0.152786 | + | 0.393584i | ||||
\(746\) | 180.739i | 0.242278i | ||||||||
\(747\) | 21.0221 | + | 398.297i | 0.0281421 | + | 0.533196i | ||||
\(748\) | −489.516 | + | 489.516i | −0.654433 | + | 0.654433i | ||||
\(749\) | 840.533 | + | 268.446i | 1.12221 | + | 0.358405i | ||||
\(750\) | −49.4309 | + | 1208.64i | −0.0659079 | + | 1.61152i | ||||
\(751\) | 969.222 | 1.29057 | 0.645287 | − | 0.763940i | \(-0.276738\pi\) | ||||
0.645287 | + | 0.763940i | \(0.276738\pi\) | |||||||
\(752\) | 35.0146 | − | 35.0146i | 0.0465620 | − | 0.0465620i | ||||
\(753\) | 357.982 | + | 137.340i | 0.475408 | + | 0.182391i | ||||
\(754\) | −282.764 | −0.375018 | ||||||||
\(755\) | 37.3484 | + | 96.2112i | 0.0494681 | + | 0.127432i | ||||
\(756\) | 706.111 | − | 983.370i | 0.934009 | − | 1.30075i | ||||
\(757\) | −881.940 | + | 881.940i | −1.16505 | + | 1.16505i | −0.181690 | + | 0.983356i | \(0.558157\pi\) |
−0.983356 | + | 0.181690i | \(0.941843\pi\) | |||||||
\(758\) | −892.277 | + | 892.277i | −1.17715 | + | 1.17715i | ||||
\(759\) | −450.464 | − | 1011.25i | −0.593497 | − | 1.33235i | ||||
\(760\) | −888.458 | − | 391.564i | −1.16902 | − | 0.515216i | ||||
\(761\) | 1174.77 | 1.54372 | 0.771859 | − | 0.635794i | \(-0.219327\pi\) | ||||
0.771859 | + | 0.635794i | \(0.219327\pi\) | |||||||
\(762\) | 2201.74 | + | 844.699i | 2.88942 | + | 1.10853i | ||||
\(763\) | −292.753 | − | 567.496i | −0.383687 | − | 0.743769i | ||||
\(764\) | −57.6245 | −0.0754248 | ||||||||
\(765\) | 178.733 | + | 397.011i | 0.233638 | + | 0.518969i | ||||
\(766\) | 28.8236i | 0.0376288i | ||||||||
\(767\) | 409.169 | + | 409.169i | 0.533467 | + | 0.533467i | ||||
\(768\) | −673.550 | − | 258.408i | −0.877018 | − | 0.336469i | ||||
\(769\) | 397.325 | 0.516678 | 0.258339 | − | 0.966054i | \(-0.416825\pi\) | ||||
0.258339 | + | 0.966054i | \(0.416825\pi\) | |||||||
\(770\) | 1258.80 | − | 77.0705i | 1.63480 | − | 0.100092i | ||||
\(771\) | −387.937 | + | 172.807i | −0.503161 | + | 0.224134i | ||||
\(772\) | −615.595 | + | 615.595i | −0.797403 | + | 0.797403i | ||||
\(773\) | −122.356 | − | 122.356i | −0.158287 | − | 0.158287i | 0.623520 | − | 0.781807i | \(-0.285702\pi\) |
−0.781807 | + | 0.623520i | \(0.785702\pi\) | |||||||
\(774\) | −34.3428 | + | 38.1701i | −0.0443706 | + | 0.0493153i | ||||
\(775\) | −454.535 | − | 497.228i | −0.586496 | − | 0.641584i | ||||
\(776\) | 1253.32 | 1.61510 | ||||||||
\(777\) | 387.814 | − | 484.043i | 0.499117 | − | 0.622965i | ||||
\(778\) | 535.125 | + | 535.125i | 0.687822 | + | 0.687822i | ||||
\(779\) | 824.970 | 1.05901 | ||||||||
\(780\) | 557.751 | − | 562.177i | 0.715065 | − | 0.720740i | ||||
\(781\) | −436.203 | −0.558519 | ||||||||
\(782\) | −729.044 | + | 729.044i | −0.932281 | + | 0.932281i | ||||
\(783\) | −130.508 | − | 255.785i | −0.166678 | − | 0.326673i | ||||
\(784\) | 16.8232 | − | 23.6512i | 0.0214582 | − | 0.0301674i | ||||
\(785\) | 608.136 | − | 1379.86i | 0.774695 | − | 1.75778i | ||||
\(786\) | −282.155 | − | 633.413i | −0.358975 | − | 0.805869i | ||||
\(787\) | −163.431 | − | 163.431i | −0.207663 | − | 0.207663i | 0.595610 | − | 0.803273i | \(-0.296910\pi\) |
−0.803273 | + | 0.595610i | \(0.796910\pi\) | |||||||
\(788\) | 724.799 | − | 724.799i | 0.919795 | − | 0.919795i | ||||
\(789\) | −374.192 | + | 166.684i | −0.474261 | + | 0.211260i | ||||
\(790\) | −248.537 | − | 109.536i | −0.314604 | − | 0.138653i | ||||
\(791\) | −296.336 | + | 927.860i | −0.374634 | + | 1.17302i | ||||
\(792\) | 41.1148 | + | 778.983i | 0.0519126 | + | 0.983565i | ||||
\(793\) | 82.5930 | + | 82.5930i | 0.104153 | + | 0.104153i | ||||
\(794\) | 1113.75i | 1.40270i | ||||||||
\(795\) | 392.266 | + | 389.178i | 0.493417 | + | 0.489532i | ||||
\(796\) | 781.627i | 0.981944i | ||||||||
\(797\) | −412.431 | + | 412.431i | −0.517479 | + | 0.517479i | −0.916808 | − | 0.399329i | \(-0.869243\pi\) |
0.399329 | + | 0.916808i | \(0.369243\pi\) | |||||||
\(798\) | 1323.02 | + | 1060.00i | 1.65792 | + | 1.32832i | ||||
\(799\) | 808.845i | 1.01232i | ||||||||
\(800\) | −822.865 | − | 36.9114i | −1.02858 | − | 0.0461392i | ||||
\(801\) | −426.733 | + | 474.289i | −0.532750 | + | 0.592121i | ||||
\(802\) | 583.280 | − | 583.280i | 0.727282 | − | 0.727282i | ||||
\(803\) | 570.967 | + | 570.967i | 0.711042 | + | 0.711042i | ||||
\(804\) | −67.9469 | − | 152.535i | −0.0845111 | − | 0.189720i | ||||
\(805\) | 1154.06 | − | 70.6581i | 1.43362 | − | 0.0877741i | ||||
\(806\) | 716.440i | 0.888883i | ||||||||
\(807\) | 229.679 | − | 598.667i | 0.284609 | − | 0.741843i | ||||
\(808\) | −301.470 | + | 301.470i | −0.373106 | + | 0.373106i | ||||
\(809\) | −677.677 | −0.837672 | −0.418836 | − | 0.908062i | \(-0.637562\pi\) | ||||
−0.418836 | + | 0.908062i | \(0.637562\pi\) | |||||||
\(810\) | 1244.29 | + | 398.101i | 1.53616 | + | 0.491483i | ||||
\(811\) | 680.395i | 0.838958i | 0.907765 | + | 0.419479i | \(0.137787\pi\) | ||||
−0.907765 | + | 0.419479i | \(0.862213\pi\) | |||||||
\(812\) | 218.625 | + | 423.801i | 0.269243 | + | 0.521922i | ||||
\(813\) | 564.202 | − | 1470.61i | 0.693976 | − | 1.80887i | ||||
\(814\) | 1064.24i | 1.30742i | ||||||||
\(815\) | −55.6797 | + | 126.337i | −0.0683186 | + | 0.155015i | ||||
\(816\) | −15.7052 | + | 6.99590i | −0.0192466 | + | 0.00857341i | ||||
\(817\) | −31.2975 | − | 31.2975i | −0.0383078 | − | 0.0383078i | ||||
\(818\) | −1252.84 | − | 1252.84i | −1.53158 | − | 1.53158i | ||||
\(819\) | −448.281 | + | 262.049i | −0.547351 | + | 0.319962i | ||||
\(820\) | −984.199 | + | 382.058i | −1.20024 | + | 0.465924i | ||||
\(821\) | 93.5358i | 0.113929i | 0.998376 | + | 0.0569646i | \(0.0181422\pi\) | ||||
−0.998376 | + | 0.0569646i | \(0.981858\pi\) | |||||||
\(822\) | 280.001 | − | 729.832i | 0.340634 | − | 0.887874i | ||||
\(823\) | −955.257 | − | 955.257i | −1.16070 | − | 1.16070i | −0.984322 | − | 0.176378i | \(-0.943562\pi\) |
−0.176378 | − | 0.984322i | \(-0.556438\pi\) | |||||||
\(824\) | 1199.44i | 1.45563i | ||||||||
\(825\) | 306.262 | + | 779.797i | 0.371227 | + | 0.945209i | ||||
\(826\) | 482.299 | − | 1510.13i | 0.583897 | − | 1.82825i | ||||
\(827\) | −326.945 | − | 326.945i | −0.395338 | − | 0.395338i | 0.481247 | − | 0.876585i | \(-0.340184\pi\) |
−0.876585 | + | 0.481247i | \(0.840184\pi\) | |||||||
\(828\) | 100.376 | + | 1901.78i | 0.121227 | + | 2.29683i | ||||
\(829\) | −502.107 | −0.605678 | −0.302839 | − | 0.953042i | \(-0.597934\pi\) | ||||
−0.302839 | + | 0.953042i | \(0.597934\pi\) | |||||||
\(830\) | 666.329 | − | 258.663i | 0.802806 | − | 0.311643i | ||||
\(831\) | −473.752 | + | 211.033i | −0.570099 | + | 0.253951i | ||||
\(832\) | 605.603 | + | 605.603i | 0.727889 | + | 0.727889i | ||||
\(833\) | 78.8641 | + | 467.484i | 0.0946748 | + | 0.561206i | ||||
\(834\) | 163.233 | + | 366.443i | 0.195723 | + | 0.439381i | ||||
\(835\) | −983.029 | − | 433.244i | −1.17728 | − | 0.518855i | ||||
\(836\) | −1790.65 | −2.14192 | ||||||||
\(837\) | −648.084 | + | 330.670i | −0.774294 | + | 0.395066i | ||||
\(838\) | 1086.49 | − | 1086.49i | 1.29653 | − | 1.29653i | ||||
\(839\) | 170.395i | 0.203092i | 0.994831 | + | 0.101546i | \(0.0323790\pi\) | ||||
−0.994831 | + | 0.101546i | \(0.967621\pi\) | |||||||
\(840\) | −777.074 | − | 244.798i | −0.925088 | − | 0.291427i | ||||
\(841\) | −727.888 | −0.865503 | ||||||||
\(842\) | −1680.99 | − | 1680.99i | −1.99642 | − | 1.99642i | ||||
\(843\) | −282.271 | + | 735.750i | −0.334841 | + | 0.872776i | ||||
\(844\) | − | 27.4112i | − | 0.0324777i | ||||||
\(845\) | 471.086 | − | 182.872i | 0.557498 | − | 0.216416i | ||||
\(846\) | 1804.23 | + | 1623.32i | 2.13266 | + | 1.91882i | ||||
\(847\) | 23.5076 | − | 12.1268i | 0.0277539 | − | 0.0143174i | ||||
\(848\) | −15.4292 | + | 15.4292i | −0.0181948 | + | 0.0181948i | ||||
\(849\) | −1033.96 | + | 460.578i | −1.21785 | + | 0.542495i | ||||
\(850\) | 575.890 | − | 526.443i | 0.677518 | − | 0.619344i | ||||
\(851\) | 975.697i | 1.14653i | ||||||||
\(852\) | 700.600 | + | 268.786i | 0.822300 | + | 0.315476i | ||||
\(853\) | 554.247 | − | 554.247i | 0.649763 | − | 0.649763i | −0.303173 | − | 0.952936i | \(-0.598046\pi\) |
0.952936 | + | 0.303173i | \(0.0980460\pi\) | |||||||
\(854\) | 97.3547 | − | 304.828i | 0.113998 | − | 0.356942i | ||||
\(855\) | −399.231 | + | 1053.03i | −0.466937 | + | 1.23162i | ||||
\(856\) | 978.063 | 1.14260 | ||||||||
\(857\) | −472.697 | + | 472.697i | −0.551572 | + | 0.551572i | −0.926894 | − | 0.375323i | \(-0.877532\pi\) |
0.375323 | + | 0.926894i | \(0.377532\pi\) | |||||||
\(858\) | 319.139 | − | 831.848i | 0.371957 | − | 0.969520i | ||||
\(859\) | −218.046 | −0.253837 | −0.126919 | − | 0.991913i | \(-0.540509\pi\) | ||||
−0.126919 | + | 0.991913i | \(0.540509\pi\) | |||||||
\(860\) | 51.8327 | + | 22.8439i | 0.0602706 | + | 0.0265627i | ||||
\(861\) | 688.074 | − | 75.9450i | 0.799157 | − | 0.0882055i | ||||
\(862\) | 218.832 | − | 218.832i | 0.253866 | − | 0.253866i | ||||
\(863\) | −823.471 | + | 823.471i | −0.954196 | + | 0.954196i | −0.998996 | − | 0.0447996i | \(-0.985735\pi\) |
0.0447996 | + | 0.998996i | \(0.485735\pi\) | |||||||
\(864\) | −274.426 | + | 846.201i | −0.317623 | + | 0.979399i | ||||
\(865\) | 56.6318 | − | 128.497i | 0.0654703 | − | 0.148552i | ||||
\(866\) | −1246.13 | −1.43895 | ||||||||
\(867\) | −209.961 | + | 547.272i | −0.242170 | + | 0.631225i | ||||
\(868\) | 1073.79 | − | 553.933i | 1.23708 | − | 0.638171i | ||||
\(869\) | −188.108 | −0.216465 | ||||||||
\(870\) | −362.441 | + | 365.317i | −0.416598 | + | 0.419904i | ||||
\(871\) | 71.6221i | 0.0822297i | ||||||||
\(872\) | −500.503 | − | 500.503i | −0.573971 | − | 0.573971i | ||||
\(873\) | −76.6214 | − | 1451.71i | −0.0877679 | − | 1.66290i | ||||
\(874\) | −2666.84 | −3.05130 | ||||||||
\(875\) | −874.883 | + | 14.2812i | −0.999867 | + | 0.0163214i | ||||
\(876\) | −565.221 | − | 1268.87i | −0.645229 | − | 1.44849i | ||||
\(877\) | 601.564 | − | 601.564i | 0.685934 | − | 0.685934i | −0.275397 | − | 0.961331i | \(-0.588809\pi\) |
0.961331 | + | 0.275397i | \(0.0888092\pi\) | |||||||
\(878\) | −904.375 | − | 904.375i | −1.03004 | − | 1.03004i | ||||
\(879\) | −491.367 | − | 1103.08i | −0.559006 | − | 1.25492i | ||||
\(880\) | −30.8407 | + | 11.9721i | −0.0350462 | + | 0.0136047i | ||||
\(881\) | 842.336 | 0.956113 | 0.478057 | − | 0.878329i | \(-0.341341\pi\) | ||||
0.478057 | + | 0.878329i | \(0.341341\pi\) | |||||||
\(882\) | 1201.06 | + | 762.308i | 1.36174 | + | 0.864294i | ||||
\(883\) | 918.430 | + | 918.430i | 1.04012 | + | 1.04012i | 0.999161 | + | 0.0409643i | \(0.0130430\pi\) |
0.0409643 | + | 0.999161i | \(0.486957\pi\) | |||||||
\(884\) | −510.801 | −0.577829 | ||||||||
\(885\) | 1053.09 | − | 4.16184i | 1.18993 | − | 0.00470264i | ||||
\(886\) | −977.170 | −1.10290 | ||||||||
\(887\) | 496.805 | − | 496.805i | 0.560095 | − | 0.560095i | −0.369239 | − | 0.929334i | \(-0.620382\pi\) |
0.929334 | + | 0.369239i | \(0.120382\pi\) | |||||||
\(888\) | 246.264 | − | 641.895i | 0.277324 | − | 0.722855i | ||||
\(889\) | −518.968 | + | 1624.95i | −0.583766 | + | 1.82784i | ||||
\(890\) | 1046.25 | + | 461.108i | 1.17556 | + | 0.518099i | ||||
\(891\) | 899.779 | − | 95.2460i | 1.00985 | − | 0.106898i | ||||
\(892\) | −224.080 | − | 224.080i | −0.251211 | − | 0.251211i | ||||
\(893\) | −1479.38 | + | 1479.38i | −1.65664 | + | 1.65664i | ||||
\(894\) | −247.713 | − | 556.095i | −0.277084 | − | 0.622030i | ||||
\(895\) | −285.507 | − | 735.478i | −0.319002 | − | 0.821763i | ||||
\(896\) | 433.173 | − | 1356.31i | 0.483452 | − | 1.51374i | ||||
\(897\) | 292.587 | − | 762.638i | 0.326184 | − | 0.850209i | ||||
\(898\) | 335.975 | + | 335.975i | 0.374137 | + | 0.374137i | ||||
\(899\) | − | 286.592i | − | 0.318790i | ||||||
\(900\) | −11.3913 | − | 1441.17i | −0.0126570 | − | 1.60130i | ||||
\(901\) | − | 356.418i | − | 0.395581i | ||||||
\(902\) | −839.905 | + | 839.905i | −0.931159 | + | 0.931159i | ||||
\(903\) | −28.9852 | − | 23.2228i | −0.0320988 | − | 0.0257174i | ||||
\(904\) | 1079.68i | 1.19434i | ||||||||
\(905\) | 274.083 | − | 106.397i | 0.302854 | − | 0.117565i | ||||
\(906\) | −81.2794 | − | 182.465i | −0.0897124 | − | 0.201397i | ||||
\(907\) | 407.949 | − | 407.949i | 0.449778 | − | 0.449778i | −0.445502 | − | 0.895281i | \(-0.646975\pi\) |
0.895281 | + | 0.445502i | \(0.146975\pi\) | |||||||
\(908\) | −148.991 | − | 148.991i | −0.164087 | − | 0.164087i | ||||
\(909\) | 367.621 | + | 330.761i | 0.404424 | + | 0.363873i | ||||
\(910\) | 696.976 | + | 616.555i | 0.765908 | + | 0.677532i | ||||
\(911\) | − | 763.804i | − | 0.838424i | −0.907888 | − | 0.419212i | \(-0.862306\pi\) | ||
0.907888 | − | 0.419212i | \(-0.137694\pi\) | |||||||
\(912\) | −41.5203 | − | 15.9293i | −0.0455266 | − | 0.0174663i | ||||
\(913\) | 350.045 | − | 350.045i | 0.383401 | − | 0.383401i | ||||
\(914\) | 86.1073 | 0.0942093 | ||||||||
\(915\) | 212.572 | − | 0.840090i | 0.232319 | − | 0.000918131i | ||||
\(916\) | − | 583.600i | − | 0.637118i | ||||||
\(917\) | 445.761 | − | 229.954i | 0.486108 | − | 0.250768i | ||||
\(918\) | −382.983 | − | 750.612i | −0.417192 | − | 0.817660i | ||||
\(919\) | − | 369.412i | − | 0.401972i | −0.979594 | − | 0.200986i | \(-0.935585\pi\) | ||
0.979594 | − | 0.200986i | \(-0.0644145\pi\) | |||||||
\(920\) | 1194.77 | − | 463.800i | 1.29866 | − | 0.504130i | ||||
\(921\) | 432.821 | + | 971.648i | 0.469947 | + | 1.05499i | ||||
\(922\) | −436.648 | − | 436.648i | −0.473587 | − | 0.473587i | ||||
\(923\) | −227.585 | − | 227.585i | −0.246571 | − | 0.246571i | ||||
\(924\) | −1493.51 | + | 164.843i | −1.61635 | + | 0.178402i | ||||
\(925\) | 33.0884 | − | 737.639i | 0.0357712 | − | 0.797448i | ||||
\(926\) | 1654.47i | 1.78668i | ||||||||
\(927\) | 1389.31 | − | 73.3276i | 1.49871 | − | 0.0791021i | ||||
\(928\) | −247.779 | − | 247.779i | −0.267003 | − | 0.267003i | ||||
\(929\) | − | 443.766i | − | 0.477682i | −0.971059 | − | 0.238841i | \(-0.923233\pi\) | ||
0.971059 | − | 0.238841i | \(-0.0767674\pi\) | |||||||
\(930\) | 925.605 | + | 918.317i | 0.995274 | + | 0.987438i | ||||
\(931\) | −710.785 | + | 999.270i | −0.763464 | + | 1.07333i | ||||
\(932\) | 580.340 | + | 580.340i | 0.622682 | + | 0.622682i | ||||
\(933\) | −829.972 | − | 318.420i | −0.889573 | − | 0.341286i | ||||
\(934\) | 280.793 | 0.300635 | ||||||||
\(935\) | 217.934 | − | 494.492i | 0.233085 | − | 0.528869i | ||||
\(936\) | −384.976 | + | 427.879i | −0.411299 | + | 0.457135i | ||||
\(937\) | 278.535 | + | 278.535i | 0.297263 | + | 0.297263i | 0.839941 | − | 0.542678i | \(-0.182590\pi\) |
−0.542678 | + | 0.839941i | \(0.682590\pi\) | |||||||
\(938\) | 174.380 | − | 89.9573i | 0.185906 | − | 0.0959033i | ||||
\(939\) | 757.632 | − | 337.488i | 0.806849 | − | 0.359412i | ||||
\(940\) | 1079.79 | − | 2450.04i | 1.14871 | − | 2.60642i | ||||
\(941\) | −1197.75 | −1.27285 | −0.636423 | − | 0.771340i | \(-0.719587\pi\) | ||||
−0.636423 | + | 0.771340i | \(0.719587\pi\) | |||||||
\(942\) | −1045.39 | + | 2724.86i | −1.10976 | + | 2.89263i | ||||
\(943\) | −770.025 | + | 770.025i | −0.816569 | + | 0.816569i | ||||
\(944\) | 41.5855i | 0.0440524i | ||||||||
\(945\) | −236.042 | + | 915.046i | −0.249780 | + | 0.968303i | ||||
\(946\) | 63.7283 | 0.0673660 | ||||||||
\(947\) | −99.0939 | − | 99.0939i | −0.104640 | − | 0.104640i | 0.652849 | − | 0.757488i | \(-0.273574\pi\) |
−0.757488 | + | 0.652849i | \(0.773574\pi\) | |||||||
\(948\) | 302.126 | + | 115.911i | 0.318698 | + | 0.122269i | ||||
\(949\) | 595.793i | 0.627811i | ||||||||
\(950\) | 2016.16 | + | 90.4393i | 2.12228 | + | 0.0951993i | ||||
\(951\) | −75.6766 | − | 169.888i | −0.0795758 | − | 0.178641i | ||||
\(952\) | 240.926 | + | 467.030i | 0.253074 | + | 0.490577i | ||||
\(953\) | −294.311 | + | 294.311i | −0.308826 | + | 0.308826i | −0.844454 | − | 0.535628i | \(-0.820075\pi\) |
0.535628 | + | 0.844454i | \(0.320075\pi\) | |||||||
\(954\) | −795.035 | − | 715.318i | −0.833370 | − | 0.749809i | ||||
\(955\) | 41.9325 | − | 16.2778i | 0.0439084 | − | 0.0170449i | ||||
\(956\) | − | 2606.92i | − | 2.72691i | ||||||
\(957\) | −127.663 | + | 332.758i | −0.133399 | + | 0.347709i | ||||
\(958\) | 1306.11 | − | 1306.11i | 1.36338 | − | 1.36338i | ||||
\(959\) | 538.637 | + | 172.028i | 0.561666 | + | 0.179382i | ||||
\(960\) | 1558.66 | − | 6.15986i | 1.62360 | − | 0.00641652i | ||||
\(961\) | 234.860 | 0.244392 | ||||||||
\(962\) | −555.258 | + | 555.258i | −0.577192 | + | 0.577192i | ||||
\(963\) | −59.7937 | − | 1132.89i | −0.0620911 | − | 1.17641i | ||||
\(964\) | 750.124 | 0.778137 | ||||||||
\(965\) | 274.065 | − | 621.853i | 0.284005 | − | 0.644407i | ||||
\(966\) | −2224.30 | + | 245.503i | −2.30259 | + | 0.254144i | ||||
\(967\) | 749.151 | − | 749.151i | 0.774716 | − | 0.774716i | −0.204211 | − | 0.978927i | \(-0.565463\pi\) |
0.978927 | + | 0.204211i | \(0.0654627\pi\) | |||||||
\(968\) | 20.7325 | − | 20.7325i | 0.0214179 | − | 0.0214179i | ||||
\(969\) | 663.549 | − | 295.578i | 0.684777 | − | 0.305035i | ||||
\(970\) | −2428.63 | + | 942.775i | −2.50375 | + | 0.971933i | ||||
\(971\) | 648.040 | 0.667394 | 0.333697 | − | 0.942680i | \(-0.391704\pi\) | ||||
0.333697 | + | 0.942680i | \(0.391704\pi\) | |||||||
\(972\) | −1503.85 | − | 401.460i | −1.54717 | − | 0.413025i | ||||
\(973\) | −257.883 | + | 133.034i | −0.265039 | + | 0.136725i | ||||
\(974\) | 1633.85 | 1.67747 | ||||||||
\(975\) | −247.062 | + | 566.641i | −0.253397 | + | 0.581171i | ||||
\(976\) | 8.39425i | 0.00860067i | ||||||||
\(977\) | 131.673 | + | 131.673i | 0.134773 | + | 0.134773i | 0.771275 | − | 0.636502i | \(-0.219619\pi\) |
−0.636502 | + | 0.771275i | \(0.719619\pi\) | |||||||
\(978\) | 95.7141 | − | 249.482i | 0.0978672 | − | 0.255094i | ||||
\(979\) | 791.867 | 0.808853 | ||||||||
\(980\) | 385.196 | − | 1521.32i | 0.393057 | − | 1.55237i | ||||
\(981\) | −549.132 | + | 610.328i | −0.559767 | + | 0.622149i | ||||
\(982\) | −1469.03 | + | 1469.03i | −1.49596 | + | 1.49596i | ||||
\(983\) | 903.757 | + | 903.757i | 0.919387 | + | 0.919387i | 0.996985 | − | 0.0775980i | \(-0.0247251\pi\) |
−0.0775980 | + | 0.996985i | \(0.524725\pi\) | |||||||
\(984\) | 700.939 | − | 312.234i | 0.712336 | − | 0.317311i | ||||
\(985\) | −322.683 | + | 732.167i | −0.327597 | + | 0.743316i | ||||
\(986\) | 331.931 | 0.336644 | ||||||||
\(987\) | −1097.70 | + | 1370.08i | −1.11216 | + | 1.38812i | ||||
\(988\) | −934.254 | − | 934.254i | −0.945601 | − | 0.945601i | ||||
\(989\) | 58.4260 | 0.0590759 | ||||||||
\(990\) | −665.640 | − | 1478.56i | −0.672364 | − | 1.49349i | ||||
\(991\) | −628.425 | −0.634132 | −0.317066 | − | 0.948403i | \(-0.602698\pi\) | ||||
−0.317066 | + | 0.948403i | \(0.602698\pi\) | |||||||
\(992\) | −627.798 | + | 627.798i | −0.632861 | + | 0.632861i | ||||
\(993\) | −1266.29 | − | 485.813i | −1.27522 | − | 0.489238i | ||||
\(994\) | −268.261 | + | 839.954i | −0.269880 | + | 0.845024i | ||||
\(995\) | −220.795 | − | 568.778i | −0.221904 | − | 0.571636i | ||||
\(996\) | −777.914 | + | 346.523i | −0.781038 | + | 0.347914i | ||||
\(997\) | 207.877 | + | 207.877i | 0.208503 | + | 0.208503i | 0.803631 | − | 0.595128i | \(-0.202899\pi\) |
−0.595128 | + | 0.803631i | \(0.702899\pi\) | |||||||
\(998\) | −1209.64 | + | 1209.64i | −1.21206 | + | 1.21206i | ||||
\(999\) | −758.558 | − | 246.004i | −0.759318 | − | 0.246250i |
(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 | 105.3.k.d.83.14 | yes | 32 | |
3.2 | odd | 2 | inner | 105.3.k.d.83.3 | yes | 32 | |
5.2 | odd | 4 | inner | 105.3.k.d.62.4 | yes | 32 | |
7.6 | odd | 2 | inner | 105.3.k.d.83.13 | yes | 32 | |
15.2 | even | 4 | inner | 105.3.k.d.62.13 | yes | 32 | |
21.20 | even | 2 | inner | 105.3.k.d.83.4 | yes | 32 | |
35.27 | even | 4 | inner | 105.3.k.d.62.3 | ✓ | 32 | |
105.62 | odd | 4 | inner | 105.3.k.d.62.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.d.62.3 | ✓ | 32 | 35.27 | even | 4 | inner | |
105.3.k.d.62.4 | yes | 32 | 5.2 | odd | 4 | inner | |
105.3.k.d.62.13 | yes | 32 | 15.2 | even | 4 | inner | |
105.3.k.d.62.14 | yes | 32 | 105.62 | odd | 4 | inner | |
105.3.k.d.83.3 | yes | 32 | 3.2 | odd | 2 | inner | |
105.3.k.d.83.4 | yes | 32 | 21.20 | even | 2 | inner | |
105.3.k.d.83.13 | yes | 32 | 7.6 | odd | 2 | inner | |
105.3.k.d.83.14 | yes | 32 | 1.1 | even | 1 | trivial |