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 | 62.13 | ||
Character | \(\chi\) | \(=\) | 105.62 |
Dual form | 105.3.k.d.83.13 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
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 | 0.152108 | − | 0.988364i | \(-0.451394\pi\) |
0.988364 | − | 0.152108i | \(-0.0486063\pi\) | |||||||
\(3\) | −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 | ||||
\(7\) | −3.20922 | − | 6.22100i | −0.458460 | − | 0.888715i | ||||
\(8\) | −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 | \(0.169522\pi\) | ||||
−0.861506 | + | 0.507747i | \(0.830478\pi\) | |||||||
\(12\) | 6.88316 | + | 17.9412i | 0.573596 | + | 1.49510i | ||||
\(13\) | −5.82807 | − | 5.82807i | −0.448313 | − | 0.448313i | 0.446480 | − | 0.894794i | \(-0.352677\pi\) |
−0.894794 | + | 0.446480i | \(0.852677\pi\) | |||||||
\(14\) | −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 | \(-0.158150\pi\) |
−0.476652 | + | 0.879092i | \(0.658150\pi\) | |||||||
\(18\) | 1.53016 | − | 28.9913i | 0.0850091 | − | 1.61063i | ||||
\(19\) | 25.0261 | 1.31716 | 0.658581 | − | 0.752510i | \(-0.271157\pi\) | ||||
0.658581 | + | 0.752510i | \(0.271157\pi\) | |||||||
\(20\) | −29.8564 | − | 11.5900i | −1.49282 | − | 0.579500i | ||||
\(21\) | 15.6738 | + | 13.9761i | 0.746373 | + | 0.665528i | ||||
\(22\) | 25.4792 | + | 25.4792i | 1.15814 | + | 1.15814i | ||||
\(23\) | 23.3593 | + | 23.3593i | 1.01562 | + | 1.01562i | 0.999876 | + | 0.0157445i | \(0.00501183\pi\) |
0.0157445 | + | 0.999876i | \(0.494988\pi\) | |||||||
\(24\) | 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 | ||||
\(28\) | −39.8481 | + | 20.5564i | −1.42315 | + | 0.734157i | ||||
\(29\) | −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 | ||||||||
\(35\) | −34.8036 | + | 3.70223i | −0.994390 | + | 0.105778i | ||||
\(36\) | −38.5586 | − | 42.8557i | −1.07107 | − | 1.19044i | ||||
\(37\) | −20.8846 | − | 20.8846i | −0.564448 | − | 0.564448i | 0.366120 | − | 0.930568i | \(-0.380686\pi\) |
−0.930568 | + | 0.366120i | \(0.880686\pi\) | |||||||
\(38\) | 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 | \(-0.368313\pi\) | ||||
0.402005 | + | 0.915637i | \(0.368313\pi\) | |||||||
\(42\) | 67.6298 | − | 3.87246i | 1.61023 | − | 0.0922014i | ||||
\(43\) | 1.25060 | − | 1.25060i | 0.0290836 | − | 0.0290836i | −0.692415 | − | 0.721499i | \(-0.743453\pi\) |
0.721499 | + | 0.692415i | \(0.243453\pi\) | |||||||
\(44\) | 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 | −0.952173 | − | 0.305558i | \(-0.901157\pi\) |
−0.305558 | − | 0.952173i | \(-0.598843\pi\) | |||||||
\(48\) | −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 | 0.417293 | − | 0.908772i | \(-0.362979\pi\) |
−0.908772 | + | 0.417293i | \(0.862979\pi\) | |||||||
\(54\) | 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 | ||||
\(63\) | −58.9200 | − | 22.3033i | −0.935237 | − | 0.354021i | ||||
\(64\) | − | 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 | 0.659763 | − | 0.751473i | \(-0.270657\pi\) |
−0.751473 | + | 0.659763i | \(0.770657\pi\) | |||||||
\(68\) | 43.8225 | − | 43.8225i | 0.644448 | − | 0.644448i | ||||
\(69\) | −90.5294 | − | 40.3264i | −1.31202 | − | 0.584441i | ||||
\(70\) | −70.9406 | + | 87.8297i | −1.01344 | + | 1.25471i | ||||
\(71\) | 39.0498i | 0.549997i | 0.961445 | + | 0.274999i | \(0.0886774\pi\) | ||||
−0.961445 | + | 0.274999i | \(0.911323\pi\) | |||||||
\(72\) | −69.7361 | − | 3.68068i | −0.968557 | − | 0.0511205i | ||||
\(73\) | 51.1141 | + | 51.1141i | 0.700193 | + | 0.700193i | 0.964452 | − | 0.264259i | \(-0.0851274\pi\) |
−0.264259 | + | 0.964452i | \(0.585127\pi\) | |||||||
\(74\) | −95.2731 | −1.28747 | ||||||||
\(75\) | 69.8090 | + | 27.4172i | 0.930787 | + | 0.365563i | ||||
\(76\) | − | 160.302i | − | 2.10924i | ||||||
\(77\) | 69.4914 | − | 35.8484i | 0.902485 | − | 0.465564i | ||||
\(78\) | 74.4687 | − | 28.5700i | 0.954726 | − | 0.366282i | ||||
\(79\) | 16.8398i | 0.213162i | 0.994304 | + | 0.106581i | \(0.0339903\pi\) | ||||
−0.994304 | + | 0.106581i | \(0.966010\pi\) | |||||||
\(80\) | 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 | \(-0.836022\pi\) |
0.492667 | + | 0.870218i | \(0.336022\pi\) | |||||||
\(84\) | 89.5226 | − | 100.397i | 1.06575 | − | 1.19521i | ||||
\(85\) | 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 | 0.197101 | − | 0.980383i | \(-0.436847\pi\) |
0.980383 | − | 0.197101i | \(-0.0631528\pi\) | |||||||
\(98\) | 26.2933 | + | 155.859i | 0.268299 | + | 1.59040i | ||||
\(99\) | 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 | \(-0.587689\pi\) | ||||
−0.272012 | + | 0.962294i | \(0.587689\pi\) | |||||||
\(102\) | −87.4175 | + | 33.5378i | −0.857034 | + | 0.328802i | ||||
\(103\) | −109.306 | − | 109.306i | −1.06123 | − | 1.06123i | −0.997999 | − | 0.0632258i | \(-0.979861\pi\) |
−0.0632258 | − | 0.997999i | \(-0.520139\pi\) | |||||||
\(104\) | 63.9528i | 0.614931i | ||||||||
\(105\) | 93.5046 | − | 47.7692i | 0.890520 | − | 0.454944i | ||||
\(106\) | −118.830 | −1.12103 | ||||||||
\(107\) | −89.1318 | + | 89.1318i | −0.833007 | + | 0.833007i | −0.987927 | − | 0.154920i | \(-0.950488\pi\) |
0.154920 | + | 0.987927i | \(0.450488\pi\) | |||||||
\(108\) | 154.052 | + | 78.6017i | 1.42641 | + | 0.727794i | ||||
\(109\) | − | 91.2226i | − | 0.836904i | −0.908239 | − | 0.418452i | \(-0.862573\pi\) | ||
0.908239 | − | 0.418452i | \(-0.137427\pi\) | |||||||
\(110\) | 164.864 | − | 72.6592i | 1.49876 | − | 0.660538i | ||||
\(111\) | 80.9387 | + | 36.0542i | 0.729177 | + | 0.324813i | ||||
\(112\) | −1.90092 | − | 3.68489i | −0.0169725 | − | 0.0329008i | ||||
\(113\) | 98.3921 | + | 98.3921i | 0.870726 | + | 0.870726i | 0.992552 | − | 0.121825i | \(-0.0388747\pi\) |
−0.121825 | + | 0.992552i | \(0.538875\pi\) | |||||||
\(114\) | −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 | ||||
\(126\) | −185.266 | + | 83.5204i | −1.47036 | + | 0.662861i | ||||
\(127\) | 172.312 | + | 172.312i | 1.35679 | + | 1.35679i | 0.877843 | + | 0.478948i | \(0.158982\pi\) |
0.478948 | + | 0.877843i | \(0.341018\pi\) | |||||||
\(128\) | −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 | \(-0.411822\pi\) | ||||
0.273489 | + | 0.961875i | \(0.411822\pi\) | |||||||
\(132\) | −200.411 | + | 76.8879i | −1.51826 | + | 0.582484i | ||||
\(133\) | −80.3142 | − | 155.687i | −0.603866 | − | 1.17058i | ||||
\(134\) | −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 | −0.884141 | − | 0.467220i | \(-0.845256\pi\) |
0.467220 | + | 0.884141i | \(0.345256\pi\) | |||||||
\(138\) | −298.475 | + | 114.510i | −2.16286 | + | 0.829784i | ||||
\(139\) | −41.4536 | −0.298227 | −0.149113 | − | 0.988820i | \(-0.547642\pi\) | ||||
−0.149113 | + | 0.988820i | \(0.547642\pi\) | |||||||
\(140\) | 23.7143 | + | 222.932i | 0.169388 | + | 1.59237i | ||||
\(141\) | 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 | ||||||||
\(147\) | 36.6445 | − | 142.359i | 0.249282 | − | 0.968431i | ||||
\(148\) | −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 | −0.482284 | + | 0.876015i | \(0.660193\pi\) |
−0.876015 | + | 0.482284i | \(0.839807\pi\) | |||||||
\(158\) | 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 | −0.764458 | − | 0.644673i | \(-0.776993\pi\) |
0.644673 | + | 0.764458i | \(0.276993\pi\) | |||||||
\(164\) | − | 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 | \(-0.472424\pi\) |
−0.996250 | + | 0.0865247i | \(0.972424\pi\) | |||||||
\(168\) | −9.31486 | − | 162.678i | −0.0554456 | − | 0.968320i | ||||
\(169\) | − | 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 | \(-0.775866\pi\) |
0.647378 | + | 0.762169i | \(0.275866\pi\) | |||||||
\(174\) | 41.8793 | − | 94.0154i | 0.240685 | − | 0.540319i | ||||
\(175\) | −45.7175 | + | 168.923i | −0.261243 | + | 0.965273i | ||||
\(176\) | 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 | \(0.948065\pi\) | |||||||
\(182\) | 85.3236 | + | 165.398i | 0.468811 | + | 0.908780i | ||||
\(183\) | −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 | ||||
\(189\) | 188.998 | − | 0.844085i | 0.999990 | − | 0.00446606i | ||||
\(190\) | −162.784 | − | 369.358i | −0.856760 | − | 1.94399i | ||||
\(191\) | − | 8.99622i | − | 0.0471007i | −0.999723 | − | 0.0235503i | \(-0.992503\pi\) | ||
0.999723 | − | 0.0235503i | \(-0.00749699\pi\) | |||||||
\(192\) | 111.662 | + | 291.050i | 0.581571 | + | 1.51588i | ||||
\(193\) | 96.1055 | − | 96.1055i | 0.497956 | − | 0.497956i | −0.412845 | − | 0.910801i | \(-0.635465\pi\) |
0.910801 | + | 0.412845i | \(0.135465\pi\) | |||||||
\(194\) | − | 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 | −0.933351 | − | 0.358965i | \(-0.883130\pi\) |
0.358965 | + | 0.933351i | \(0.383130\pi\) | |||||||
\(198\) | 323.846 | + | 17.0926i | 1.63559 | + | 0.0863262i | ||||
\(199\) | −122.026 | −0.613196 | −0.306598 | − | 0.951839i | \(-0.599191\pi\) | ||||
−0.306598 | + | 0.951839i | \(0.599191\pi\) | |||||||
\(200\) | 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 | ||||
\(203\) | 34.1314 | + | 66.1629i | 0.168135 | + | 0.325926i | ||||
\(204\) | −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 | ||||||||
\(210\) | 104.320 | − | 322.238i | 0.496762 | − | 1.53446i | ||||
\(211\) | −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 | ||||
\(217\) | 167.637 | − | 86.4788i | 0.772522 | − | 0.398520i | ||||
\(218\) | −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 | \(-0.214618\pi\) |
−0.624306 | + | 0.781180i | \(0.714618\pi\) | |||||||
\(224\) | −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 | \(-0.226916\pi\) |
−0.654014 | + | 0.756482i | \(0.726916\pi\) | |||||||
\(228\) | 172.258 | + | 448.997i | 0.755519 | + | 1.96929i | ||||
\(229\) | 91.1105 | 0.397862 | 0.198931 | − | 0.980013i | \(-0.436253\pi\) | ||||
0.198931 | + | 0.980013i | \(0.436253\pi\) | |||||||
\(230\) | 192.815 | − | 496.700i | 0.838326 | − | 2.15957i | ||||
\(231\) | −156.119 | + | 175.084i | −0.675840 | + | 0.757938i | ||||
\(232\) | 58.3524 | + | 58.3524i | 0.251519 | + | 0.251519i | ||||
\(233\) | 90.6015 | + | 90.6015i | 0.388847 | + | 0.388847i | 0.874276 | − | 0.485429i | \(-0.161336\pi\) |
−0.485429 | + | 0.874276i | \(0.661336\pi\) | |||||||
\(234\) | −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 | ||||
\(238\) | −100.160 | − | 194.158i | −0.420840 | − | 0.815789i | ||||
\(239\) | −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 | ||||||||
\(245\) | 134.724 | + | 204.632i | 0.549895 | + | 0.835234i | ||||
\(246\) | −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 | \(-0.581943\pi\) | ||||
−0.254597 | + | 0.967047i | \(0.581943\pi\) | |||||||
\(252\) | −142.862 | + | 377.407i | −0.566913 | + | 1.49765i | ||||
\(253\) | −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 | \(-0.161186\pi\) |
−0.485015 | + | 0.874506i | \(0.661186\pi\) | |||||||
\(258\) | 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 | 0.499306 | − | 0.866426i | \(-0.333588\pi\) |
−0.866426 | + | 0.499306i | \(0.833588\pi\) | |||||||
\(264\) | −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 | ||||
\(273\) | −9.89457 | − | 172.802i | −0.0362439 | − | 0.632974i | ||||
\(274\) | 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 | 0.451144 | − | 0.892451i | \(-0.351016\pi\) |
−0.892451 | + | 0.451144i | \(0.851016\pi\) | |||||||
\(278\) | −94.5532 | + | 94.5532i | −0.340120 | + | 0.340120i | ||||
\(279\) | 162.213 | + | 180.290i | 0.581407 | + | 0.646200i | ||||
\(280\) | 211.267 | + | 170.641i | 0.754525 | + | 0.609434i | ||||
\(281\) | − | 262.680i | − | 0.934803i | −0.884045 | − | 0.467401i | \(-0.845190\pi\) | ||
0.884045 | − | 0.467401i | \(-0.154810\pi\) | |||||||
\(282\) | 755.326 | − | 289.782i | 2.67846 | − | 1.02759i | ||||
\(283\) | 266.792 | + | 266.792i | 0.942728 | + | 0.942728i | 0.998446 | − | 0.0557189i | \(-0.0177451\pi\) |
−0.0557189 | + | 0.998446i | \(0.517745\pi\) | |||||||
\(284\) | 250.130 | 0.880740 | ||||||||
\(285\) | −1.48354 | + | 375.388i | −0.00520541 | + | 1.31715i | ||||
\(286\) | − | 296.989i | − | 1.03842i | ||||||
\(287\) | −105.790 | − | 205.072i | −0.368607 | − | 0.714536i | ||||
\(288\) | 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 | \(-0.508972\pi\) |
0.999603 | + | 0.0281818i | \(0.00897172\pi\) | |||||||
\(294\) | −241.130 | − | 408.298i | −0.820169 | − | 1.38877i | ||||
\(295\) | 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 | \(-0.945958\pi\) |
0.168965 | + | 0.985622i | \(0.445958\pi\) | |||||||
\(308\) | −229.624 | − | 445.121i | −0.745532 | − | 1.44520i | ||||
\(309\) | 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 | \(-0.341943\pi\) | ||||
0.476397 | + | 0.879230i | \(0.341943\pi\) | |||||||
\(312\) | −68.7226 | − | 179.128i | −0.220265 | − | 0.574128i | ||||
\(313\) | −195.491 | − | 195.491i | −0.624573 | − | 0.624573i | 0.322124 | − | 0.946697i | \(-0.395603\pi\) |
−0.946697 | + | 0.322124i | \(0.895603\pi\) | |||||||
\(314\) | 972.836i | 3.09820i | ||||||||
\(315\) | −210.569 | + | 234.277i | −0.668472 | + | 0.743737i | ||||
\(316\) | 107.866 | 0.341348 | ||||||||
\(317\) | −43.8360 | + | 43.8360i | −0.138284 | + | 0.138284i | −0.772860 | − | 0.634576i | \(-0.781175\pi\) |
0.634576 | + | 0.772860i | \(0.281175\pi\) | |||||||
\(318\) | 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 | ||||
\(322\) | −341.982 | − | 662.925i | −1.06206 | − | 2.05877i | ||||
\(323\) | 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 | ||||
\(336\) | 9.28408 | + | 8.27845i | 0.0276312 | + | 0.0246383i | ||||
\(337\) | 203.621 | + | 203.621i | 0.604218 | + | 0.604218i | 0.941429 | − | 0.337211i | \(-0.109484\pi\) |
−0.337211 | + | 0.941429i | \(0.609484\pi\) | |||||||
\(338\) | −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 | ||||
\(343\) | 339.547 | + | 48.5462i | 0.989933 | + | 0.141534i | ||||
\(344\) | −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 | −0.0348116 | + | 0.999394i | \(0.511083\pi\) |
−0.999394 | + | 0.0348116i | \(0.988917\pi\) | |||||||
\(348\) | −73.2051 | − | 190.812i | −0.210360 | − | 0.548310i | ||||
\(349\) | −51.4939 | −0.147547 | −0.0737735 | − | 0.997275i | \(-0.523504\pi\) | ||||
−0.0737735 | + | 0.997275i | \(0.523504\pi\) | |||||||
\(350\) | 281.025 | + | 489.582i | 0.802927 | + | 1.39881i | ||||
\(351\) | 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 | \(-0.610355\pi\) |
0.940502 | + | 0.339788i | \(0.110355\pi\) | |||||||
\(354\) | −620.616 | − | 276.454i | −1.75315 | − | 0.780944i | ||||
\(355\) | 182.016 | + | 70.6570i | 0.512721 | + | 0.199034i | ||||
\(356\) | 454.077 | 1.27550 | ||||||||
\(357\) | 11.6151 | + | 202.849i | 0.0325352 | + | 0.568205i | ||||
\(358\) | 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 | \(-0.560371\pi\) |
0.982068 | + | 0.188526i | \(0.0603710\pi\) | |||||||
\(368\) | 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 | −0.652000 | − | 0.758219i | \(-0.726070\pi\) |
0.758219 | + | 0.652000i | \(0.226070\pi\) | |||||||
\(374\) | 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 | ||||
\(378\) | 429.169 | − | 433.019i | 1.13537 | − | 1.14555i | ||||
\(379\) | − | 391.187i | − | 1.03216i | −0.856541 | − | 0.516078i | \(-0.827391\pi\) | ||
0.856541 | − | 0.516078i | \(-0.172609\pi\) | |||||||
\(380\) | −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 | \(-0.753713\pi\) |
0.698810 | + | 0.715307i | \(0.253713\pi\) | |||||||
\(384\) | 557.401 | + | 248.295i | 1.45157 | + | 0.646602i | ||||
\(385\) | −41.3555 | − | 388.772i | −0.107417 | − | 1.00980i | ||||
\(386\) | − | 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 | ||||||||
\(392\) | 374.906 | − | 63.2462i | 0.956392 | − | 0.161342i | ||||
\(393\) | −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 | \(-0.893198\pi\) |
0.329269 | + | 0.944236i | \(0.393198\pi\) | |||||||
\(398\) | −278.335 | + | 278.335i | −0.699333 | + | 0.699333i | ||||
\(399\) | 392.254 | + | 349.767i | 0.983094 | + | 0.876608i | ||||
\(400\) | −10.9297 | − | 9.99126i | −0.0273243 | − | 0.0249782i | ||||
\(401\) | 255.719i | 0.637703i | 0.947805 | + | 0.318851i | \(0.103297\pi\) | ||||
−0.947805 | + | 0.318851i | \(0.896703\pi\) | |||||||
\(402\) | 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 | \(-0.265664\pi\) | ||||
0.671469 | + | 0.741033i | \(0.265664\pi\) | |||||||
\(410\) | −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 | ||||
\(413\) | 436.756 | − | 225.309i | 1.05752 | − | 0.545541i | ||||
\(414\) | 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 | \(-0.192444\pi\) | |||||||
\(420\) | −305.981 | − | 598.936i | −0.728527 | − | 1.42604i | ||||
\(421\) | −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 | ||||
\(427\) | 88.1615 | − | 45.4798i | 0.206467 | − | 0.106510i | ||||
\(428\) | 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 | \(0.0355010\pi\) | ||||
−0.993787 | + | 0.111299i | \(0.964499\pi\) | |||||||
\(432\) | −7.26856 | + | 14.2457i | −0.0168254 | + | 0.0329762i | ||||
\(433\) | 273.161 | + | 273.161i | 0.630857 | + | 0.630857i | 0.948283 | − | 0.317426i | \(-0.102818\pi\) |
−0.317426 | + | 0.948283i | \(0.602818\pi\) | |||||||
\(434\) | 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 | \(-0.350859\pi\) | ||||
0.451585 | + | 0.892228i | \(0.350859\pi\) | |||||||
\(440\) | −174.775 | − | 396.565i | −0.397217 | − | 0.901284i | ||||
\(441\) | 50.3379 | + | 438.118i | 0.114145 | + | 0.993464i | ||||
\(442\) | −181.894 | − | 181.894i | −0.411526 | − | 0.411526i | ||||
\(443\) | −214.203 | − | 214.203i | −0.483528 | − | 0.483528i | 0.422728 | − | 0.906256i | \(-0.361072\pi\) |
−0.906256 | + | 0.422728i | \(0.861072\pi\) | |||||||
\(444\) | 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 | ||||
\(448\) | −646.433 | + | 333.475i | −1.44293 | + | 0.744363i | ||||
\(449\) | 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 | ||||||||
\(455\) | 224.415 | + | 181.261i | 0.493220 | + | 0.398376i | ||||
\(456\) | 532.142 | + | 237.043i | 1.16698 | + | 0.519832i | ||||
\(457\) | 18.8754 | + | 18.8754i | 0.0413028 | + | 0.0413028i | 0.727457 | − | 0.686154i | \(-0.240702\pi\) |
−0.686154 | + | 0.727457i | \(0.740702\pi\) | |||||||
\(458\) | 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 | \(-0.433426\pi\) | ||||
0.207628 | + | 0.978208i | \(0.433426\pi\) | |||||||
\(462\) | 43.2571 | + | 755.455i | 0.0936300 | + | 1.63518i | ||||
\(463\) | 362.672 | − | 362.672i | 0.783309 | − | 0.783309i | −0.197079 | − | 0.980388i | \(-0.563145\pi\) |
0.980388 | + | 0.197079i | \(0.0631454\pi\) | |||||||
\(464\) | −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 | \(-0.279709\pi\) |
−0.769931 | + | 0.638128i | \(0.779709\pi\) | |||||||
\(468\) | −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 | ||||
\(483\) | 39.6580 | + | 692.601i | 0.0821078 | + | 1.43396i | ||||
\(484\) | 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 | 0.971689 | − | 0.236262i | \(-0.0759224\pi\) |
−0.236262 | + | 0.971689i | \(0.575922\pi\) | |||||||
\(488\) | 77.7540 | − | 77.7540i | 0.159332 | − | 0.159332i | ||||
\(489\) | 33.7071 | − | 75.6696i | 0.0689307 | − | 0.154744i | ||||
\(490\) | 774.053 | + | 159.457i | 1.57970 | + | 0.325422i | ||||
\(491\) | − | 644.045i | − | 1.31170i | −0.754891 | − | 0.655850i | \(-0.772310\pi\) | ||
0.754891 | − | 0.655850i | \(-0.227690\pi\) | |||||||
\(492\) | 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 | ||||||||
\(497\) | 242.929 | − | 125.319i | 0.488791 | − | 0.252152i | ||||
\(498\) | −153.617 | − | 400.408i | −0.308468 | − | 0.804032i | ||||
\(499\) | − | 530.323i | − | 1.06277i | −0.847130 | − | 0.531386i | \(-0.821672\pi\) | ||
0.847130 | − | 0.531386i | \(-0.178328\pi\) | |||||||
\(500\) | 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 | −0.0247567 | + | 0.999694i | \(0.507881\pi\) |
−0.999694 | + | 0.0247567i | \(0.992119\pi\) | |||||||
\(504\) | 200.901 | + | 445.641i | 0.398614 | + | 0.884208i | ||||
\(505\) | −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 | ||||
\(518\) | 305.752 | + | 592.694i | 0.590256 | + | 1.14420i | ||||
\(519\) | 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 | \(-0.439942\pi\) | ||||
0.187561 | + | 0.982253i | \(0.439942\pi\) | |||||||
\(522\) | −16.2739 | + | 308.334i | −0.0311761 | + | 0.590679i | ||||
\(523\) | −516.575 | − | 516.575i | −0.987715 | − | 0.987715i | 0.0122109 | − | 0.999925i | \(-0.496113\pi\) |
−0.999925 | + | 0.0122109i | \(0.996113\pi\) | |||||||
\(524\) | − | 458.975i | − | 0.875906i | ||||||
\(525\) | −53.4699 | − | 522.270i | −0.101847 | − | 0.994800i | ||||
\(526\) | −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 | ||||
\(532\) | −997.242 | + | 514.446i | −1.87451 | + | 0.967003i | ||||
\(533\) | −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 | ||||
\(546\) | −416.720 | − | 371.583i | −0.763224 | − | 0.680554i | ||||
\(547\) | −259.758 | − | 259.758i | −0.474878 | − | 0.474878i | 0.428611 | − | 0.903489i | \(-0.359003\pi\) |
−0.903489 | + | 0.428611i | \(0.859003\pi\) | |||||||
\(548\) | 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 | ||||
\(553\) | 104.760 | − | 54.0426i | 0.189440 | − | 0.0977263i | ||||
\(554\) | −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 | −0.592984 | − | 0.805214i | \(-0.702050\pi\) |
0.805214 | + | 0.592984i | \(0.202050\pi\) | |||||||
\(558\) | 781.229 | + | 41.2333i | 1.40005 | + | 0.0738947i | ||||
\(559\) | −14.5771 | −0.0260772 | ||||||||
\(560\) | −20.6152 | + | 2.19294i | −0.0368129 | + | 0.00391597i | ||||
\(561\) | 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 | −0.0112552 | + | 0.999937i | \(0.503583\pi\) |
−0.999937 | + | 0.0112552i | \(0.996417\pi\) | |||||||
\(564\) | 653.678 | − | 1467.45i | 1.15900 | − | 2.60186i | ||||
\(565\) | 636.649 | − | 280.586i | 1.12681 | − | 0.496612i | ||||
\(566\) | 1217.08 | 2.15031 | ||||||||
\(567\) | −528.465 | + | 205.459i | −0.932038 | + | 0.362361i | ||||
\(568\) | 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 | \(-0.724884\pi\) |
0.760643 | + | 0.649170i | \(0.224884\pi\) | |||||||
\(578\) | −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 | \(-0.461720\pi\) |
−0.992777 | + | 0.119971i | \(0.961720\pi\) | |||||||
\(588\) | −911.870 | − | 234.723i | −1.55080 | − | 0.399189i | ||||
\(589\) | 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 | \(-0.675238\pi\) |
0.852250 | + | 0.523135i | \(0.175238\pi\) | |||||||
\(594\) | −925.441 | + | 300.124i | −1.55798 | + | 0.505260i | ||||
\(595\) | −263.437 | − | 212.779i | −0.442751 | − | 0.357613i | ||||
\(596\) | 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 | \(0.987462\pi\) | |||||||
\(602\) | −35.4913 | + | 18.3089i | −0.0589557 | + | 0.0304134i | ||||
\(603\) | −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 | −0.354769 | + | 0.934954i | \(0.615440\pi\) |
−0.934954 | + | 0.354769i | \(0.884560\pi\) | |||||||
\(608\) | 583.046 | − | 583.046i | 0.958957 | − | 0.958957i | ||||
\(609\) | −166.697 | − | 148.641i | −0.273723 | − | 0.244074i | ||||
\(610\) | 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 | −0.0414311 | − | 0.999141i | \(-0.513192\pi\) |
0.999141 | + | 0.0414311i | \(0.0131917\pi\) | |||||||
\(614\) | 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 | −0.303150 | − | 0.952943i | \(-0.598038\pi\) |
0.952943 | + | 0.303150i | \(0.0980383\pi\) | |||||||
\(618\) | 1396.67 | − | 535.833i | 2.25998 | − | 0.867044i | ||||
\(619\) | −382.132 | −0.617338 | −0.308669 | − | 0.951170i | \(-0.599883\pi\) | ||||
−0.308669 | + | 0.951170i | \(0.599883\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 441.004 | − | 227.500i | 0.707872 | − | 0.365169i | ||||
\(624\) | 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 | ||||||
\(630\) | 54.0773 | + | 1014.67i | 0.0858370 | + | 1.61059i | ||||
\(631\) | 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 | ||||
\(637\) | 398.238 | − | 67.1823i | 0.625177 | − | 0.105467i | ||||
\(638\) | −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 | \(-0.965713\pi\) | ||
0.994204 | − | 0.107509i | \(-0.0342873\pi\) | |||||||
\(642\) | −436.936 | − | 1138.89i | −0.680585 | − | 1.77397i | ||||
\(643\) | 340.846 | + | 340.846i | 0.530087 | + | 0.530087i | 0.920598 | − | 0.390511i | \(-0.127702\pi\) |
−0.390511 | + | 0.920598i | \(0.627702\pi\) | |||||||
\(644\) | −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 | \(-0.317470\pi\) |
−0.840043 | + | 0.542520i | \(0.817470\pi\) | |||||||
\(648\) | −488.729 | + | 395.164i | −0.754211 | + | 0.609822i | ||||
\(649\) | −784.239 | −1.20838 | ||||||||
\(650\) | 490.586 | + | 448.463i | 0.754748 | + | 0.689943i | ||||
\(651\) | −376.613 | + | 422.362i | −0.578515 | + | 0.648790i | ||||
\(652\) | 125.066 | + | 125.066i | 0.191819 | + | 0.191819i | ||||
\(653\) | 178.554 | + | 178.554i | 0.273436 | + | 0.273436i | 0.830482 | − | 0.557046i | \(-0.188065\pi\) |
−0.557046 | + | 0.830482i | \(0.688065\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | 865.427 | + | 1677.61i | 1.31524 | + | 2.54956i | ||||
\(659\) | −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 | ||||||||
\(665\) | −870.998 | + | 92.6523i | −1.30977 | + | 0.139327i | ||||
\(666\) | −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 | ||||||||
\(672\) | 690.770 | − | 39.5532i | 1.02793 | − | 0.0588590i | ||||
\(673\) | −770.416 | + | 770.416i | −1.14475 | + | 1.14475i | −0.157179 | + | 0.987570i | \(0.550240\pi\) |
−0.987570 | + | 0.157179i | \(0.949760\pi\) | |||||||
\(674\) | 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 | \(-0.101388\pi\) |
−0.313162 | + | 0.949700i | \(0.601388\pi\) | |||||||
\(678\) | −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 | 0.813319 | + | 0.581818i | \(0.197658\pi\) |
0.581818 | + | 0.813319i | \(0.302342\pi\) | |||||||
\(684\) | −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 | ||||
\(693\) | 249.138 | − | 658.162i | 0.359507 | − | 0.949728i | ||||
\(694\) | 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 | ||||
\(700\) | 1082.02 | + | 292.839i | 1.54574 | + | 0.418342i | ||||
\(701\) | 1086.06i | 1.54929i | 0.632393 | + | 0.774647i | \(0.282073\pi\) | ||||
−0.632393 | + | 0.774647i | \(0.717927\pi\) | |||||||
\(702\) | 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 | ||||||
\(707\) | 176.335 | + | 341.822i | 0.249413 | + | 0.483482i | ||||
\(708\) | −1259.59 | + | 483.243i | −1.77908 | + | 0.682547i | ||||
\(709\) | 384.594i | 0.542446i | 0.962516 | + | 0.271223i | \(0.0874281\pi\) | ||||
−0.962516 | + | 0.271223i | \(0.912572\pi\) | |||||||
\(710\) | 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 | ||||
\(714\) | 489.181 | + | 436.194i | 0.685127 | + | 0.610916i | ||||
\(715\) | −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 | \(-0.530124\pi\) |
0.995525 | + | 0.0944960i | \(0.0301240\pi\) | |||||||
\(728\) | 397.851 | − | 205.239i | 0.546498 | − | 0.281921i | ||||
\(729\) | −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 | \(-0.318864\pi\) |
−0.842410 | + | 0.538838i | \(0.818864\pi\) | |||||||
\(734\) | − | 1328.56i | − | 1.81003i | ||||||
\(735\) | −597.249 | − | 428.391i | −0.812584 | − | 0.582844i | ||||
\(736\) | 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 | \(0.0745899\pi\) | ||||
−0.972670 | + | 0.232192i | \(0.925410\pi\) | |||||||
\(740\) | 381.486 | + | 865.590i | 0.515521 | + | 1.16972i | ||||
\(741\) | 565.260 | + | 251.796i | 0.762834 | + | 0.339805i | ||||
\(742\) | 381.351 | + | 739.240i | 0.513950 | + | 0.996280i | ||||
\(743\) | 54.5399 | + | 54.5399i | 0.0734050 | + | 0.0734050i | 0.742856 | − | 0.669451i | \(-0.233471\pi\) |
−0.669451 | + | 0.742856i | \(0.733471\pi\) | |||||||
\(744\) | −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 | ||||
\(756\) | −5.40671 | − | 1210.61i | −0.00715174 | − | 1.60134i | ||||
\(757\) | −881.940 | − | 881.940i | −1.16505 | − | 1.16505i | −0.983356 | − | 0.181690i | \(-0.941843\pi\) |
−0.181690 | − | 0.983356i | \(-0.558157\pi\) | |||||||
\(758\) | −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 | \(-0.780673\pi\) | ||||
−0.771859 | + | 0.635794i | \(0.780673\pi\) | |||||||
\(762\) | −2201.74 | + | 844.699i | −2.88942 | + | 1.10853i | ||||
\(763\) | −567.496 | + | 292.753i | −0.743769 | + | 0.383687i | ||||
\(764\) | −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 | \(-0.583175\pi\) | ||||
−0.258339 | + | 0.966054i | \(0.583175\pi\) | |||||||
\(770\) | −981.097 | − | 792.438i | −1.27415 | − | 1.02914i | ||||
\(771\) | −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 | \(-0.714298\pi\) |
0.781807 | + | 0.623520i | \(0.214298\pi\) | |||||||
\(774\) | −34.3428 | − | 38.1701i | −0.0443706 | − | 0.0493153i | ||||
\(775\) | 454.535 | − | 497.228i | 0.586496 | − | 0.641584i | ||||
\(776\) | −1253.32 | −1.61510 | ||||||||
\(777\) | −35.4566 | − | 619.226i | −0.0456327 | − | 0.796944i | ||||
\(778\) | 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 | \(-0.703090\pi\) |
0.803273 | + | 0.595610i | \(0.203090\pi\) | |||||||
\(788\) | 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 | \(-0.130757\pi\) |
−0.399329 | + | 0.916808i | \(0.630757\pi\) | |||||||
\(798\) | 1692.51 | − | 96.9124i | 2.12094 | − | 0.121444i | ||||
\(799\) | − | 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 | ||||
\(805\) | −899.469 | − | 726.506i | −1.11735 | − | 0.902492i | ||||
\(806\) | − | 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 | \(0.862213\pi\) | |||||||
\(812\) | 423.801 | − | 218.625i | 0.521922 | − | 0.269243i | ||||
\(813\) | 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 | ||||
\(819\) | 213.404 | + | 473.375i | 0.260567 | + | 0.577992i | ||||
\(820\) | −984.199 | − | 382.058i | −1.20024 | − | 0.465924i | ||||
\(821\) | − | 93.5358i | − | 0.113929i | −0.998376 | − | 0.0569646i | \(-0.981858\pi\) | ||
0.998376 | − | 0.0569646i | \(-0.0181422\pi\) | |||||||
\(822\) | −280.001 | − | 729.832i | −0.340634 | − | 0.887874i | ||||
\(823\) | −955.257 | + | 955.257i | −1.16070 | + | 1.16070i | −0.176378 | + | 0.984322i | \(0.556438\pi\) |
−0.984322 | + | 0.176378i | \(0.943562\pi\) | |||||||
\(824\) | 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 | −0.876585 | − | 0.481247i | \(-0.840184\pi\) |
0.481247 | + | 0.876585i | \(0.340184\pi\) | |||||||
\(828\) | 100.376 | − | 1901.78i | 0.121227 | − | 2.29683i | ||||
\(829\) | 502.107 | 0.605678 | 0.302839 | − | 0.953042i | \(-0.402066\pi\) | ||||
0.302839 | + | 0.953042i | \(0.402066\pi\) | |||||||
\(830\) | 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 | ||||
\(833\) | −467.484 | + | 78.8641i | −0.561206 | + | 0.0946748i | ||||
\(834\) | 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 | \(0.967621\pi\) | |||||||
\(840\) | −775.115 | − | 250.933i | −0.922756 | − | 0.298729i | ||||
\(841\) | −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 | ||||
\(847\) | 12.1268 | + | 23.5076i | 0.0143174 | + | 0.0277539i | ||||
\(848\) | −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 | \(-0.401954\pi\) |
−0.952936 | + | 0.303173i | \(0.901954\pi\) | |||||||
\(854\) | 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 | \(-0.122468\pi\) |
−0.375323 | + | 0.926894i | \(0.622468\pi\) | |||||||
\(858\) | 319.139 | + | 831.848i | 0.371957 | + | 0.969520i | ||||
\(859\) | 218.046 | 0.253837 | 0.126919 | − | 0.991913i | \(-0.459491\pi\) | ||||
0.126919 | + | 0.991913i | \(0.459491\pi\) | |||||||
\(860\) | −51.8327 | + | 22.8439i | −0.0602706 | + | 0.0265627i | ||||
\(861\) | 516.679 | + | 460.713i | 0.600091 | + | 0.535091i | ||||
\(862\) | 218.832 | + | 218.832i | 0.253866 | + | 0.253866i | ||||
\(863\) | −823.471 | − | 823.471i | −0.954196 | − | 0.954196i | 0.0447996 | − | 0.998996i | \(-0.485735\pi\) |
−0.998996 | + | 0.0447996i | \(0.985735\pi\) | |||||||
\(864\) | 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 | ||||
\(868\) | −553.933 | − | 1073.79i | −0.638171 | − | 1.23708i | ||||
\(869\) | −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 | ||||||||
\(875\) | 704.648 | + | 518.745i | 0.805312 | + | 0.592851i | ||||
\(876\) | −565.221 | + | 1268.87i | −0.645229 | + | 1.44849i | ||||
\(877\) | 601.564 | + | 601.564i | 0.685934 | + | 0.685934i | 0.961331 | − | 0.275397i | \(-0.0888092\pi\) |
−0.275397 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(878\) | 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 | \(-0.658659\pi\) | ||||
−0.478057 | + | 0.878329i | \(0.658659\pi\) | |||||||
\(882\) | 1114.14 | + | 884.504i | 1.26320 | + | 1.00284i | ||||
\(883\) | 918.430 | − | 918.430i | 1.04012 | − | 1.04012i | 0.0409643 | − | 0.999161i | \(-0.486957\pi\) |
0.999161 | − | 0.0409643i | \(-0.0130430\pi\) | |||||||
\(884\) | −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 | \(-0.379618\pi\) |
−0.929334 | + | 0.369239i | \(0.879618\pi\) | |||||||
\(888\) | −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 | ||||
\(903\) | 37.0801 | − | 2.12319i | 0.0410632 | − | 0.00235126i | ||||
\(904\) | − | 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 | 0.895281 | − | 0.445502i | \(-0.146975\pi\) |
−0.445502 | + | 0.895281i | \(0.646975\pi\) | |||||||
\(908\) | 148.991 | − | 148.991i | 0.164087 | − | 0.164087i | ||||
\(909\) | −367.621 | + | 330.761i | −0.404424 | + | 0.363873i | ||||
\(910\) | 925.325 | − | 98.4313i | 1.01684 | − | 0.108166i | ||||
\(911\) | 763.804i | 0.838424i | 0.907888 | + | 0.419212i | \(0.137694\pi\) | ||||
−0.907888 | + | 0.419212i | \(0.862306\pi\) | |||||||
\(912\) | −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 | ||||||
\(917\) | −229.954 | − | 445.761i | −0.250768 | − | 0.486108i | ||||
\(918\) | −382.983 | + | 750.612i | −0.417192 | + | 0.817660i | ||||
\(919\) | 369.412i | 0.401972i | 0.979594 | + | 0.200986i | \(0.0644145\pi\) | ||||
−0.979594 | + | 0.200986i | \(0.935585\pi\) | |||||||
\(920\) | −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 | ||||
\(924\) | 1121.48 | + | 1000.01i | 1.21373 | + | 1.08226i | ||||
\(925\) | 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 | \(-0.817410\pi\) |
0.542678 | + | 0.839941i | \(0.317410\pi\) | |||||||
\(938\) | 89.9573 | + | 174.380i | 0.0959033 | + | 0.185906i | ||||
\(939\) | 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 | \(-0.280413\pi\) | ||||
0.636423 | + | 0.771340i | \(0.280413\pi\) | |||||||
\(942\) | −1045.39 | − | 2724.86i | −1.10976 | − | 2.89263i | ||||
\(943\) | 770.025 | + | 770.025i | 0.816569 | + | 0.816569i | ||||
\(944\) | 41.5855i | 0.0440524i | ||||||||
\(945\) | 338.040 | − | 882.470i | 0.357715 | − | 0.933831i | ||||
\(946\) | 63.7283 | 0.0673660 | ||||||||
\(947\) | −99.0939 | + | 99.0939i | −0.104640 | + | 0.104640i | −0.757488 | − | 0.652849i | \(-0.773574\pi\) |
0.652849 | + | 0.757488i | \(0.273574\pi\) | |||||||
\(948\) | −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 | ||||
\(952\) | −467.030 | + | 240.926i | −0.490577 | + | 0.253074i | ||||
\(953\) | −294.311 | − | 294.311i | −0.308826 | − | 0.308826i | 0.535628 | − | 0.844454i | \(-0.320075\pi\) |
−0.844454 | + | 0.535628i | \(0.820075\pi\) | |||||||
\(954\) | −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 | ||||
\(966\) | 1670.24 | + | 1489.33i | 1.72903 | + | 1.54174i | ||||
\(967\) | 749.151 | + | 749.151i | 0.774716 | + | 0.774716i | 0.978927 | − | 0.204211i | \(-0.0654627\pi\) |
−0.204211 | + | 0.978927i | \(0.565463\pi\) | |||||||
\(968\) | 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 | \(-0.608296\pi\) | ||||
−0.333697 | + | 0.942680i | \(0.608296\pi\) | |||||||
\(972\) | 1503.85 | − | 401.460i | 1.54717 | − | 0.413025i | ||||
\(973\) | 133.034 | + | 257.883i | 0.136725 | + | 0.265039i | ||||
\(974\) | 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 | −0.636502 | − | 0.771275i | \(-0.719619\pi\) |
0.771275 | + | 0.636502i | \(0.219619\pi\) | |||||||
\(978\) | −95.7141 | − | 249.482i | −0.0978672 | − | 0.255094i | ||||
\(979\) | −791.867 | −0.808853 | ||||||||
\(980\) | 1310.75 | − | 862.964i | 1.33750 | − | 0.880576i | ||||
\(981\) | −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 | \(-0.975275\pi\) |
0.0775980 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(984\) | 700.939 | + | 312.234i | 0.712336 | + | 0.317311i | ||||
\(985\) | 322.683 | + | 732.167i | 0.327597 | + | 0.743316i | ||||
\(986\) | −331.931 | −0.336644 | ||||||||
\(987\) | −100.359 | − | 1752.71i | −0.101681 | − | 1.77579i | ||||
\(988\) | −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 | \(-0.797101\pi\) |
0.595128 | + | 0.803631i | \(0.297101\pi\) | |||||||
\(998\) | −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.62.13 | yes | 32 | |
3.2 | odd | 2 | inner | 105.3.k.d.62.4 | yes | 32 | |
5.3 | odd | 4 | inner | 105.3.k.d.83.3 | yes | 32 | |
7.6 | odd | 2 | inner | 105.3.k.d.62.14 | yes | 32 | |
15.8 | even | 4 | inner | 105.3.k.d.83.14 | yes | 32 | |
21.20 | even | 2 | inner | 105.3.k.d.62.3 | ✓ | 32 | |
35.13 | even | 4 | inner | 105.3.k.d.83.4 | yes | 32 | |
105.83 | odd | 4 | inner | 105.3.k.d.83.13 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.d.62.3 | ✓ | 32 | 21.20 | even | 2 | inner | |
105.3.k.d.62.4 | yes | 32 | 3.2 | odd | 2 | inner | |
105.3.k.d.62.13 | yes | 32 | 1.1 | even | 1 | trivial | |
105.3.k.d.62.14 | yes | 32 | 7.6 | odd | 2 | inner | |
105.3.k.d.83.3 | yes | 32 | 5.3 | odd | 4 | inner | |
105.3.k.d.83.4 | yes | 32 | 35.13 | even | 4 | inner | |
105.3.k.d.83.13 | yes | 32 | 105.83 | odd | 4 | inner | |
105.3.k.d.83.14 | yes | 32 | 15.8 | even | 4 | inner |