Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(44,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.44");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.o (of order \(6\), 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: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 44.13 | ||
Character | \(\chi\) | \(=\) | 105.44 |
Dual form | 105.3.o.b.74.13 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.897800 | − | 1.55504i | 0.448900 | − | 0.777518i | −0.549415 | − | 0.835550i | \(-0.685149\pi\) |
0.998315 | + | 0.0580320i | \(0.0184826\pi\) | |||||||
\(3\) | −2.91099 | + | 0.725349i | −0.970330 | + | 0.241783i | ||||
\(4\) | 0.387909 | + | 0.671879i | 0.0969773 | + | 0.167970i | ||||
\(5\) | 3.31295 | + | 3.74491i | 0.662590 | + | 0.748983i | ||||
\(6\) | −1.48554 | + | 5.17791i | −0.247591 | + | 0.862986i | ||||
\(7\) | −1.39571 | + | 6.85945i | −0.199386 | + | 0.979921i | ||||
\(8\) | 8.57546 | 1.07193 | ||||||||
\(9\) | 7.94774 | − | 4.22297i | 0.883082 | − | 0.469219i | ||||
\(10\) | 8.79784 | − | 1.78957i | 0.879784 | − | 0.178957i | ||||
\(11\) | −1.00783 | + | 0.581870i | −0.0916208 | + | 0.0528973i | −0.545110 | − | 0.838364i | \(-0.683512\pi\) |
0.453490 | + | 0.891262i | \(0.350179\pi\) | |||||||
\(12\) | −1.61655 | − | 1.67446i | −0.134712 | − | 0.139539i | ||||
\(13\) | − | 12.4799i | − | 0.959993i | −0.877270 | − | 0.479996i | \(-0.840638\pi\) | ||
0.877270 | − | 0.479996i | \(-0.159362\pi\) | |||||||
\(14\) | 9.41362 | + | 8.32879i | 0.672401 | + | 0.594913i | ||||
\(15\) | −12.3603 | − | 8.49836i | −0.824022 | − | 0.566558i | ||||
\(16\) | 6.14742 | − | 10.6476i | 0.384213 | − | 0.665477i | ||||
\(17\) | 9.31485 | + | 16.1338i | 0.547933 | + | 0.949047i | 0.998416 | + | 0.0562623i | \(0.0179183\pi\) |
−0.450483 | + | 0.892785i | \(0.648748\pi\) | |||||||
\(18\) | 0.568609 | − | 16.1504i | 0.0315894 | − | 0.897244i | ||||
\(19\) | −15.2033 | + | 26.3329i | −0.800174 | + | 1.38594i | 0.119327 | + | 0.992855i | \(0.461926\pi\) |
−0.919501 | + | 0.393087i | \(0.871407\pi\) | |||||||
\(20\) | −1.23100 | + | 3.67859i | −0.0615502 | + | 0.183929i | ||||
\(21\) | −0.912610 | − | 20.9802i | −0.0434576 | − | 0.999055i | ||||
\(22\) | 2.08961i | 0.0949824i | ||||||||
\(23\) | 13.7201 | − | 23.7640i | 0.596527 | − | 1.03322i | −0.396802 | − | 0.917904i | \(-0.629880\pi\) |
0.993329 | − | 0.115311i | \(-0.0367865\pi\) | |||||||
\(24\) | −24.9631 | + | 6.22021i | −1.04013 | + | 0.259175i | ||||
\(25\) | −3.04875 | + | 24.8134i | −0.121950 | + | 0.992536i | ||||
\(26\) | −19.4067 | − | 11.2045i | −0.746412 | − | 0.430941i | ||||
\(27\) | −20.0727 | + | 18.0579i | −0.743432 | + | 0.668812i | ||||
\(28\) | −5.15012 | + | 1.72310i | −0.183933 | + | 0.0615392i | ||||
\(29\) | − | 52.6691i | − | 1.81617i | −0.418781 | − | 0.908087i | \(-0.637543\pi\) | ||
0.418781 | − | 0.908087i | \(-0.362457\pi\) | |||||||
\(30\) | −24.3124 | + | 11.5909i | −0.810412 | + | 0.386364i | ||||
\(31\) | −17.2838 | − | 29.9364i | −0.557542 | − | 0.965692i | −0.997701 | − | 0.0677718i | \(-0.978411\pi\) |
0.440158 | − | 0.897920i | \(-0.354922\pi\) | |||||||
\(32\) | 6.11262 | + | 10.5874i | 0.191019 | + | 0.330855i | ||||
\(33\) | 2.51172 | − | 2.42485i | 0.0761128 | − | 0.0734802i | ||||
\(34\) | 33.4515 | 0.983868 | ||||||||
\(35\) | −30.3119 | + | 17.4982i | −0.866055 | + | 0.499948i | ||||
\(36\) | 5.92032 | + | 3.70178i | 0.164453 | + | 0.102827i | ||||
\(37\) | 0.357210 | + | 0.206235i | 0.00965431 | + | 0.00557392i | 0.504819 | − | 0.863225i | \(-0.331559\pi\) |
−0.495165 | + | 0.868799i | \(0.664892\pi\) | |||||||
\(38\) | 27.2991 | + | 47.2834i | 0.718396 | + | 1.24430i | ||||
\(39\) | 9.05229 | + | 36.3289i | 0.232110 | + | 0.931510i | ||||
\(40\) | 28.4101 | + | 32.1144i | 0.710252 | + | 0.802859i | ||||
\(41\) | − | 17.2132i | − | 0.419835i | −0.977719 | − | 0.209918i | \(-0.932680\pi\) | ||
0.977719 | − | 0.209918i | \(-0.0673195\pi\) | |||||||
\(42\) | −33.4442 | − | 17.4169i | −0.796291 | − | 0.414687i | ||||
\(43\) | 7.86972i | 0.183017i | 0.995804 | + | 0.0915084i | \(0.0291688\pi\) | ||||
−0.995804 | + | 0.0915084i | \(0.970831\pi\) | |||||||
\(44\) | −0.781892 | − | 0.451426i | −0.0177703 | − | 0.0102597i | ||||
\(45\) | 42.1451 | + | 15.7731i | 0.936558 | + | 0.350513i | ||||
\(46\) | −24.6359 | − | 42.6706i | −0.535562 | − | 0.927621i | ||||
\(47\) | 17.4089 | − | 30.1530i | 0.370401 | − | 0.641554i | −0.619226 | − | 0.785213i | \(-0.712553\pi\) |
0.989627 | + | 0.143659i | \(0.0458868\pi\) | |||||||
\(48\) | −10.1718 | + | 35.4542i | −0.211913 | + | 0.738629i | ||||
\(49\) | −45.1040 | − | 19.1475i | −0.920490 | − | 0.390766i | ||||
\(50\) | 35.8486 | + | 27.0184i | 0.716971 | + | 0.540368i | ||||
\(51\) | −38.8181 | − | 40.2088i | −0.761139 | − | 0.788408i | ||||
\(52\) | 8.38498 | − | 4.84107i | 0.161250 | − | 0.0930975i | ||||
\(53\) | −17.8667 | − | 30.9460i | −0.337107 | − | 0.583886i | 0.646780 | − | 0.762676i | \(-0.276115\pi\) |
−0.983887 | + | 0.178790i | \(0.942782\pi\) | |||||||
\(54\) | 10.0595 | + | 47.4261i | 0.186286 | + | 0.878261i | ||||
\(55\) | −5.51794 | − | 1.84653i | −0.100326 | − | 0.0335732i | ||||
\(56\) | −11.9688 | + | 58.8229i | −0.213729 | + | 1.05041i | ||||
\(57\) | 25.1561 | − | 87.6825i | 0.441336 | − | 1.53829i | ||||
\(58\) | −81.9023 | − | 47.2863i | −1.41211 | − | 0.815281i | ||||
\(59\) | 32.3428 | − | 18.6731i | 0.548184 | − | 0.316494i | −0.200205 | − | 0.979754i | \(-0.564161\pi\) |
0.748389 | + | 0.663260i | \(0.230828\pi\) | |||||||
\(60\) | 0.915180 | − | 11.6012i | 0.0152530 | − | 0.193354i | ||||
\(61\) | 25.4414 | − | 44.0659i | 0.417073 | − | 0.722391i | −0.578571 | − | 0.815632i | \(-0.696389\pi\) |
0.995644 | + | 0.0932408i | \(0.0297226\pi\) | |||||||
\(62\) | −62.0697 | −1.00112 | ||||||||
\(63\) | 17.8745 | + | 60.4111i | 0.283723 | + | 0.958906i | ||||
\(64\) | 71.1310 | 1.11142 | ||||||||
\(65\) | 46.7362 | − | 41.3453i | 0.719018 | − | 0.636081i | ||||
\(66\) | −1.51570 | − | 6.08285i | −0.0229652 | − | 0.0921643i | ||||
\(67\) | 24.9784 | − | 14.4213i | 0.372812 | − | 0.215243i | −0.301874 | − | 0.953348i | \(-0.597612\pi\) |
0.674686 | + | 0.738105i | \(0.264279\pi\) | |||||||
\(68\) | −7.22664 | + | 12.5169i | −0.106274 | + | 0.184072i | ||||
\(69\) | −22.7020 | + | 79.1285i | −0.329014 | + | 1.14679i | ||||
\(70\) | −0.00374100 | + | 62.8460i | −5.34428e−5 | + | 0.897800i | ||||
\(71\) | 66.8477i | 0.941518i | 0.882262 | + | 0.470759i | \(0.156020\pi\) | ||||
−0.882262 | + | 0.470759i | \(0.843980\pi\) | |||||||
\(72\) | 68.1555 | − | 36.2139i | 0.946604 | − | 0.502971i | ||||
\(73\) | 46.7701 | − | 27.0027i | 0.640686 | − | 0.369900i | −0.144192 | − | 0.989550i | \(-0.546058\pi\) |
0.784879 | + | 0.619649i | \(0.212725\pi\) | |||||||
\(74\) | 0.641406 | − | 0.370316i | 0.00866765 | − | 0.00500427i | ||||
\(75\) | −9.12351 | − | 74.4430i | −0.121647 | − | 0.992573i | ||||
\(76\) | −23.5900 | −0.310395 | ||||||||
\(77\) | −2.58468 | − | 7.72527i | −0.0335672 | − | 0.100328i | ||||
\(78\) | 64.6199 | + | 18.5395i | 0.828460 | + | 0.237685i | ||||
\(79\) | −16.6402 | + | 28.8216i | −0.210635 | + | 0.364831i | −0.951914 | − | 0.306367i | \(-0.900887\pi\) |
0.741278 | + | 0.671198i | \(0.234220\pi\) | |||||||
\(80\) | 60.2405 | − | 12.2535i | 0.753007 | − | 0.153169i | ||||
\(81\) | 45.3330 | − | 67.1261i | 0.559667 | − | 0.828718i | ||||
\(82\) | −26.7672 | − | 15.4540i | −0.326429 | − | 0.188464i | ||||
\(83\) | −72.0714 | −0.868330 | −0.434165 | − | 0.900833i | \(-0.642957\pi\) | ||||
−0.434165 | + | 0.900833i | \(0.642957\pi\) | |||||||
\(84\) | 13.7421 | − | 8.75156i | 0.163597 | − | 0.104185i | ||||
\(85\) | −29.5601 | + | 88.3338i | −0.347765 | + | 1.03922i | ||||
\(86\) | 12.2377 | + | 7.06544i | 0.142299 | + | 0.0821562i | ||||
\(87\) | 38.2035 | + | 153.319i | 0.439120 | + | 1.76229i | ||||
\(88\) | −8.64260 | + | 4.98981i | −0.0982114 | + | 0.0567024i | ||||
\(89\) | 41.4850 | + | 23.9513i | 0.466123 | + | 0.269116i | 0.714615 | − | 0.699518i | \(-0.246602\pi\) |
−0.248492 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(90\) | 62.3656 | − | 51.3760i | 0.692951 | − | 0.570845i | ||||
\(91\) | 85.6053 | + | 17.4183i | 0.940717 | + | 0.191410i | ||||
\(92\) | 21.2887 | 0.231398 | ||||||||
\(93\) | 72.0274 | + | 74.6079i | 0.774488 | + | 0.802236i | ||||
\(94\) | −31.2594 | − | 54.1428i | −0.332546 | − | 0.575987i | ||||
\(95\) | −148.982 | + | 30.3045i | −1.56823 | + | 0.318994i | ||||
\(96\) | −25.4733 | − | 26.3860i | −0.265347 | − | 0.274854i | ||||
\(97\) | 66.7480i | 0.688124i | 0.938947 | + | 0.344062i | \(0.111803\pi\) | ||||
−0.938947 | + | 0.344062i | \(0.888197\pi\) | |||||||
\(98\) | −70.2695 | + | 52.9477i | −0.717036 | + | 0.540283i | ||||
\(99\) | −5.55274 | + | 8.88059i | −0.0560883 | + | 0.0897029i | ||||
\(100\) | −17.8542 | + | 7.57696i | −0.178542 | + | 0.0757696i | ||||
\(101\) | 19.3539 | − | 11.1740i | 0.191623 | − | 0.110633i | −0.401119 | − | 0.916026i | \(-0.631379\pi\) |
0.592742 | + | 0.805392i | \(0.298045\pi\) | |||||||
\(102\) | −97.3771 | + | 24.2640i | −0.954677 | + | 0.237883i | ||||
\(103\) | −12.8487 | − | 7.41823i | −0.124745 | − | 0.0720216i | 0.436329 | − | 0.899787i | \(-0.356278\pi\) |
−0.561074 | + | 0.827766i | \(0.689612\pi\) | |||||||
\(104\) | − | 107.021i | − | 1.02905i | ||||||
\(105\) | 75.5454 | − | 72.9238i | 0.719480 | − | 0.694513i | ||||
\(106\) | −64.1628 | −0.605309 | ||||||||
\(107\) | 16.9958 | − | 29.4376i | 0.158840 | − | 0.275118i | −0.775611 | − | 0.631211i | \(-0.782558\pi\) |
0.934450 | + | 0.356093i | \(0.115891\pi\) | |||||||
\(108\) | −19.9191 | − | 6.48156i | −0.184436 | − | 0.0600144i | ||||
\(109\) | 45.3155 | + | 78.4888i | 0.415739 | + | 0.720081i | 0.995506 | − | 0.0947015i | \(-0.0301897\pi\) |
−0.579767 | + | 0.814782i | \(0.696856\pi\) | |||||||
\(110\) | −7.82542 | + | 6.92278i | −0.0711402 | + | 0.0629344i | ||||
\(111\) | −1.18943 | − | 0.341247i | −0.0107156 | − | 0.00307429i | ||||
\(112\) | 64.4569 | + | 57.0288i | 0.575508 | + | 0.509186i | ||||
\(113\) | −76.2557 | −0.674830 | −0.337415 | − | 0.941356i | \(-0.609552\pi\) | ||||
−0.337415 | + | 0.941356i | \(0.609552\pi\) | |||||||
\(114\) | −113.764 | − | 117.840i | −0.997932 | − | 1.03368i | ||||
\(115\) | 134.448 | − | 27.3481i | 1.16911 | − | 0.237809i | ||||
\(116\) | 35.3872 | − | 20.4308i | 0.305062 | − | 0.176128i | ||||
\(117\) | −52.7023 | − | 99.1870i | −0.450447 | − | 0.847752i | ||||
\(118\) | − | 67.0590i | − | 0.568297i | ||||||
\(119\) | −123.670 | + | 41.3767i | −1.03924 | + | 0.347703i | ||||
\(120\) | −105.996 | − | 72.8774i | −0.883296 | − | 0.607312i | ||||
\(121\) | −59.8229 | + | 103.616i | −0.494404 | + | 0.856332i | ||||
\(122\) | −45.6827 | − | 79.1247i | −0.374448 | − | 0.648563i | ||||
\(123\) | 12.4856 | + | 50.1076i | 0.101509 | + | 0.407379i | ||||
\(124\) | 13.4091 | − | 23.2253i | 0.108138 | − | 0.187300i | ||||
\(125\) | −103.024 | + | 70.7882i | −0.824195 | + | 0.566306i | ||||
\(126\) | 109.989 | + | 26.4415i | 0.872930 | + | 0.209854i | ||||
\(127\) | − | 0.573646i | − | 0.00451690i | −0.999997 | − | 0.00225845i | \(-0.999281\pi\) | ||
0.999997 | − | 0.00225845i | \(-0.000718888\pi\) | |||||||
\(128\) | 39.4109 | − | 68.2617i | 0.307898 | − | 0.533295i | ||||
\(129\) | −5.70830 | − | 22.9087i | −0.0442504 | − | 0.177587i | ||||
\(130\) | −22.3337 | − | 109.796i | −0.171797 | − | 0.844586i | ||||
\(131\) | −199.680 | − | 115.285i | −1.52427 | − | 0.880039i | −0.999587 | − | 0.0287429i | \(-0.990850\pi\) |
−0.524686 | − | 0.851296i | \(-0.675817\pi\) | |||||||
\(132\) | 2.60352 | + | 0.746951i | 0.0197237 | + | 0.00565872i | ||||
\(133\) | −159.410 | − | 141.039i | −1.19857 | − | 1.06045i | ||||
\(134\) | − | 51.7898i | − | 0.386491i | ||||||
\(135\) | −134.125 | − | 15.3454i | −0.993519 | − | 0.113670i | ||||
\(136\) | 79.8792 | + | 138.355i | 0.587347 | + | 1.01731i | ||||
\(137\) | 13.9490 | + | 24.1603i | 0.101817 | + | 0.176353i | 0.912433 | − | 0.409225i | \(-0.134201\pi\) |
−0.810616 | + | 0.585578i | \(0.800868\pi\) | |||||||
\(138\) | 102.666 | + | 106.344i | 0.743955 | + | 0.770609i | ||||
\(139\) | −130.478 | −0.938693 | −0.469346 | − | 0.883014i | \(-0.655510\pi\) | ||||
−0.469346 | + | 0.883014i | \(0.655510\pi\) | |||||||
\(140\) | −23.5149 | − | 13.5782i | −0.167964 | − | 0.0969873i | ||||
\(141\) | −28.8056 | + | 100.403i | −0.204295 | + | 0.712076i | ||||
\(142\) | 103.951 | + | 60.0159i | 0.732047 | + | 0.422647i | ||||
\(143\) | 7.26169 | + | 12.5776i | 0.0507810 | + | 0.0879553i | ||||
\(144\) | 3.89338 | − | 110.585i | 0.0270373 | − | 0.767951i | ||||
\(145\) | 197.241 | − | 174.490i | 1.36028 | − | 1.20338i | ||||
\(146\) | − | 96.9723i | − | 0.664194i | ||||||
\(147\) | 145.186 | + | 23.0221i | 0.987660 | + | 0.156613i | ||||
\(148\) | 0.320002i | 0.00216218i | ||||||||
\(149\) | 137.529 | + | 79.4024i | 0.923013 | + | 0.532902i | 0.884595 | − | 0.466360i | \(-0.154435\pi\) |
0.0384179 | + | 0.999262i | \(0.487768\pi\) | |||||||
\(150\) | −123.953 | − | 52.6476i | −0.826351 | − | 0.350984i | ||||
\(151\) | 24.0390 | + | 41.6367i | 0.159198 | + | 0.275740i | 0.934580 | − | 0.355753i | \(-0.115776\pi\) |
−0.775381 | + | 0.631493i | \(0.782442\pi\) | |||||||
\(152\) | −130.375 | + | 225.817i | −0.857733 | + | 1.48564i | ||||
\(153\) | 142.165 | + | 88.8908i | 0.929180 | + | 0.580986i | ||||
\(154\) | −14.3336 | − | 2.91649i | −0.0930753 | − | 0.0189382i | ||||
\(155\) | 54.8490 | − | 163.904i | 0.353865 | − | 1.05745i | ||||
\(156\) | −20.8971 | + | 20.1744i | −0.133956 | + | 0.129323i | ||||
\(157\) | −112.848 | + | 65.1528i | −0.718777 | + | 0.414986i | −0.814302 | − | 0.580441i | \(-0.802880\pi\) |
0.0955254 | + | 0.995427i | \(0.469547\pi\) | |||||||
\(158\) | 29.8791 | + | 51.7522i | 0.189108 | + | 0.327545i | ||||
\(159\) | 74.4564 | + | 77.1239i | 0.468279 | + | 0.485056i | ||||
\(160\) | −19.3980 | + | 57.9666i | −0.121237 | + | 0.362292i | ||||
\(161\) | 143.858 | + | 127.280i | 0.893530 | + | 0.790559i | ||||
\(162\) | −63.6835 | − | 130.760i | −0.393108 | − | 0.807163i | ||||
\(163\) | −121.121 | − | 69.9292i | −0.743073 | − | 0.429013i | 0.0801127 | − | 0.996786i | \(-0.474472\pi\) |
−0.823185 | + | 0.567773i | \(0.807805\pi\) | |||||||
\(164\) | 11.5652 | − | 6.67717i | 0.0705195 | − | 0.0407145i | ||||
\(165\) | 17.4020 | + | 1.37279i | 0.105467 | + | 0.00831991i | ||||
\(166\) | −64.7057 | + | 112.074i | −0.389794 | + | 0.675142i | ||||
\(167\) | 224.419 | 1.34383 | 0.671915 | − | 0.740629i | \(-0.265472\pi\) | ||||
0.671915 | + | 0.740629i | \(0.265472\pi\) | |||||||
\(168\) | −7.82605 | − | 179.915i | −0.0465836 | − | 1.07092i | ||||
\(169\) | 13.2519 | 0.0784136 | ||||||||
\(170\) | 110.823 | + | 125.273i | 0.651901 | + | 0.736900i | ||||
\(171\) | −9.62879 | + | 273.490i | −0.0563087 | + | 1.59936i | ||||
\(172\) | −5.28750 | + | 3.05274i | −0.0307413 | + | 0.0177485i | ||||
\(173\) | 146.827 | − | 254.312i | 0.848711 | − | 1.47001i | −0.0336474 | − | 0.999434i | \(-0.510712\pi\) |
0.882359 | − | 0.470577i | \(-0.155954\pi\) | |||||||
\(174\) | 272.716 | + | 78.2422i | 1.56733 | + | 0.449668i | ||||
\(175\) | −165.951 | − | 55.5449i | −0.948292 | − | 0.317400i | ||||
\(176\) | 14.3080i | 0.0812954i | ||||||||
\(177\) | −80.6051 | + | 77.8172i | −0.455396 | + | 0.439645i | ||||
\(178\) | 74.4904 | − | 43.0071i | 0.418485 | − | 0.241613i | ||||
\(179\) | −211.424 | + | 122.066i | −1.18114 | + | 0.681933i | −0.956278 | − | 0.292458i | \(-0.905527\pi\) |
−0.224863 | + | 0.974390i | \(0.572194\pi\) | |||||||
\(180\) | 5.75087 | + | 34.4349i | 0.0319493 | + | 0.191305i | ||||
\(181\) | 81.3669 | 0.449541 | 0.224771 | − | 0.974412i | \(-0.427837\pi\) | ||||
0.224771 | + | 0.974412i | \(0.427837\pi\) | |||||||
\(182\) | 103.942 | − | 117.481i | 0.571112 | − | 0.645501i | ||||
\(183\) | −42.0967 | + | 146.729i | −0.230036 | + | 0.801799i | ||||
\(184\) | 117.656 | − | 203.787i | 0.639437 | − | 1.10754i | ||||
\(185\) | 0.411085 | + | 2.02096i | 0.00222208 | + | 0.0109241i | ||||
\(186\) | 180.684 | − | 45.0222i | 0.971421 | − | 0.242055i | ||||
\(187\) | −18.7756 | − | 10.8401i | −0.100404 | − | 0.0579683i | ||||
\(188\) | 27.0122 | 0.143682 | ||||||||
\(189\) | −95.8518 | − | 162.891i | −0.507152 | − | 0.861856i | ||||
\(190\) | −86.6317 | + | 258.880i | −0.455956 | + | 1.36253i | ||||
\(191\) | 207.381 | + | 119.732i | 1.08577 | + | 0.626867i | 0.932446 | − | 0.361310i | \(-0.117670\pi\) |
0.153319 | + | 0.988177i | \(0.451004\pi\) | |||||||
\(192\) | −207.062 | + | 51.5948i | −1.07845 | + | 0.268723i | ||||
\(193\) | −1.39114 | + | 0.803175i | −0.00720798 | + | 0.00416153i | −0.503600 | − | 0.863937i | \(-0.667991\pi\) |
0.496392 | + | 0.868099i | \(0.334658\pi\) | |||||||
\(194\) | 103.796 | + | 59.9264i | 0.535029 | + | 0.308899i | ||||
\(195\) | −106.059 | + | 154.256i | −0.543891 | + | 0.791055i | ||||
\(196\) | −4.63145 | − | 37.7319i | −0.0236298 | − | 0.192510i | ||||
\(197\) | −286.325 | −1.45343 | −0.726713 | − | 0.686941i | \(-0.758953\pi\) | ||||
−0.726713 | + | 0.686941i | \(0.758953\pi\) | |||||||
\(198\) | 8.82438 | + | 16.6077i | 0.0445676 | + | 0.0838773i | ||||
\(199\) | −44.6292 | − | 77.3000i | −0.224267 | − | 0.388442i | 0.731832 | − | 0.681485i | \(-0.238665\pi\) |
−0.956099 | + | 0.293043i | \(0.905332\pi\) | |||||||
\(200\) | −26.1444 | + | 212.786i | −0.130722 | + | 1.06393i | ||||
\(201\) | −62.2515 | + | 60.0983i | −0.309709 | + | 0.298997i | ||||
\(202\) | − | 40.1280i | − | 0.198653i | ||||||
\(203\) | 361.281 | + | 73.5105i | 1.77971 | + | 0.362121i | ||||
\(204\) | 11.9575 | − | 41.6784i | 0.0586154 | − | 0.204306i | ||||
\(205\) | 64.4621 | − | 57.0266i | 0.314449 | − | 0.278178i | ||||
\(206\) | −23.0712 | + | 13.3202i | −0.111996 | + | 0.0646610i | ||||
\(207\) | 8.68944 | − | 246.809i | 0.0419780 | − | 1.19232i | ||||
\(208\) | −132.882 | − | 76.7192i | −0.638853 | − | 0.368842i | ||||
\(209\) | − | 35.3854i | − | 0.169308i | ||||||
\(210\) | −45.5744 | − | 182.947i | −0.217021 | − | 0.871176i | ||||
\(211\) | 174.205 | 0.825617 | 0.412808 | − | 0.910818i | \(-0.364548\pi\) | ||||
0.412808 | + | 0.910818i | \(0.364548\pi\) | |||||||
\(212\) | 13.8613 | − | 24.0085i | 0.0653835 | − | 0.113247i | ||||
\(213\) | −48.4880 | − | 194.593i | −0.227643 | − | 0.913583i | ||||
\(214\) | −30.5177 | − | 52.8582i | −0.142606 | − | 0.247001i | ||||
\(215\) | −29.4714 | + | 26.0720i | −0.137076 | + | 0.121265i | ||||
\(216\) | −172.132 | + | 154.855i | −0.796909 | + | 0.716921i | ||||
\(217\) | 229.471 | − | 76.7750i | 1.05747 | − | 0.353802i | ||||
\(218\) | 162.737 | 0.746501 | ||||||||
\(219\) | −116.561 | + | 112.529i | −0.532242 | + | 0.513833i | ||||
\(220\) | −0.899819 | − | 4.42367i | −0.00409009 | − | 0.0201076i | ||||
\(221\) | 201.348 | − | 116.249i | 0.911078 | − | 0.526011i | ||||
\(222\) | −1.59852 | + | 1.54323i | −0.00720053 | + | 0.00695148i | ||||
\(223\) | − | 149.196i | − | 0.669041i | −0.942388 | − | 0.334521i | \(-0.891426\pi\) | ||
0.942388 | − | 0.334521i | \(-0.108574\pi\) | |||||||
\(224\) | −81.1549 | + | 27.1523i | −0.362299 | + | 0.121216i | ||||
\(225\) | 80.5557 | + | 210.085i | 0.358025 | + | 0.933712i | ||||
\(226\) | −68.4624 | + | 118.580i | −0.302931 | + | 0.524692i | ||||
\(227\) | −46.1279 | − | 79.8959i | −0.203207 | − | 0.351964i | 0.746353 | − | 0.665550i | \(-0.231803\pi\) |
−0.949560 | + | 0.313586i | \(0.898470\pi\) | |||||||
\(228\) | 68.6703 | − | 17.1110i | 0.301186 | − | 0.0750482i | ||||
\(229\) | −74.0138 | + | 128.196i | −0.323205 | + | 0.559807i | −0.981147 | − | 0.193261i | \(-0.938094\pi\) |
0.657943 | + | 0.753068i | \(0.271427\pi\) | |||||||
\(230\) | 78.1802 | − | 233.625i | 0.339914 | − | 1.01576i | ||||
\(231\) | 13.1275 | + | 20.6134i | 0.0568290 | + | 0.0892355i | ||||
\(232\) | − | 451.661i | − | 1.94682i | ||||||
\(233\) | −201.616 | + | 349.210i | −0.865306 | + | 1.49875i | 0.00143686 | + | 0.999999i | \(0.499543\pi\) |
−0.866743 | + | 0.498755i | \(0.833791\pi\) | |||||||
\(234\) | −201.555 | − | 7.09619i | −0.861348 | − | 0.0303256i | ||||
\(235\) | 170.595 | − | 34.7008i | 0.725937 | − | 0.147663i | ||||
\(236\) | 25.0922 | + | 14.4870i | 0.106323 | + | 0.0613855i | ||||
\(237\) | 27.5337 | − | 95.9695i | 0.116176 | − | 0.404935i | ||||
\(238\) | −46.6885 | + | 229.459i | −0.196170 | + | 0.964113i | ||||
\(239\) | 42.1167i | 0.176220i | 0.996111 | + | 0.0881102i | \(0.0280828\pi\) | ||||
−0.996111 | + | 0.0881102i | \(0.971917\pi\) | |||||||
\(240\) | −166.472 | + | 79.3654i | −0.693632 | + | 0.330689i | ||||
\(241\) | −133.166 | − | 230.650i | −0.552554 | − | 0.957052i | −0.998089 | − | 0.0617877i | \(-0.980320\pi\) |
0.445535 | − | 0.895265i | \(-0.353014\pi\) | |||||||
\(242\) | 107.418 | + | 186.053i | 0.443876 | + | 0.768815i | ||||
\(243\) | −83.2741 | + | 228.286i | −0.342692 | + | 0.939448i | ||||
\(244\) | 39.4759 | 0.161786 | ||||||||
\(245\) | −77.7214 | − | 232.345i | −0.317230 | − | 0.948349i | ||||
\(246\) | 89.1286 | + | 25.5710i | 0.362312 | + | 0.103947i | ||||
\(247\) | 328.632 | + | 189.736i | 1.33049 | + | 0.768161i | ||||
\(248\) | −148.217 | − | 256.719i | −0.597648 | − | 1.03516i | ||||
\(249\) | 209.799 | − | 52.2770i | 0.842567 | − | 0.209948i | ||||
\(250\) | 17.5829 | + | 223.760i | 0.0703316 | + | 0.895041i | ||||
\(251\) | − | 426.902i | − | 1.70081i | −0.526133 | − | 0.850403i | \(-0.676358\pi\) | ||
0.526133 | − | 0.850403i | \(-0.323642\pi\) | |||||||
\(252\) | −33.6552 | + | 35.4435i | −0.133552 | + | 0.140649i | ||||
\(253\) | 31.9333i | 0.126219i | ||||||||
\(254\) | −0.892041 | − | 0.515020i | −0.00351197 | − | 0.00202764i | ||||
\(255\) | 21.9762 | − | 278.580i | 0.0861811 | − | 1.09247i | ||||
\(256\) | 71.4957 | + | 123.834i | 0.279280 | + | 0.483727i | ||||
\(257\) | −8.35527 | + | 14.4718i | −0.0325108 | + | 0.0563103i | −0.881823 | − | 0.471581i | \(-0.843684\pi\) |
0.849312 | + | 0.527891i | \(0.177017\pi\) | |||||||
\(258\) | −40.7487 | − | 11.6908i | −0.157941 | − | 0.0453132i | ||||
\(259\) | −1.91322 | + | 2.16242i | −0.00738694 | + | 0.00834910i | ||||
\(260\) | 45.9084 | + | 15.3628i | 0.176571 | + | 0.0590877i | ||||
\(261\) | −222.420 | − | 418.600i | −0.852183 | − | 1.60383i | ||||
\(262\) | −358.545 | + | 207.006i | −1.36849 | + | 0.790099i | ||||
\(263\) | 0.756335 | + | 1.31001i | 0.00287580 | + | 0.00498103i | 0.867460 | − | 0.497507i | \(-0.165751\pi\) |
−0.864584 | + | 0.502488i | \(0.832418\pi\) | |||||||
\(264\) | 21.5392 | − | 20.7942i | 0.0815878 | − | 0.0787659i | ||||
\(265\) | 56.6986 | − | 169.432i | 0.213957 | − | 0.639364i | ||||
\(266\) | −362.439 | + | 121.263i | −1.36255 | + | 0.455875i | ||||
\(267\) | −138.135 | − | 39.6311i | −0.517361 | − | 0.148431i | ||||
\(268\) | 19.3787 | + | 11.1883i | 0.0723087 | + | 0.0417474i | ||||
\(269\) | −10.5890 | + | 6.11353i | −0.0393641 | + | 0.0227269i | −0.519553 | − | 0.854438i | \(-0.673901\pi\) |
0.480189 | + | 0.877165i | \(0.340568\pi\) | |||||||
\(270\) | −144.280 | + | 194.792i | −0.534371 | + | 0.721452i | ||||
\(271\) | −117.307 | + | 203.182i | −0.432868 | + | 0.749749i | −0.997119 | − | 0.0758540i | \(-0.975832\pi\) |
0.564251 | + | 0.825603i | \(0.309165\pi\) | |||||||
\(272\) | 229.049 | 0.842092 | ||||||||
\(273\) | −261.830 | + | 11.3893i | −0.959086 | + | 0.0417190i | ||||
\(274\) | 50.0935 | 0.182823 | ||||||||
\(275\) | −11.3656 | − | 26.7816i | −0.0413293 | − | 0.0973878i | ||||
\(276\) | −61.9711 | + | 15.4417i | −0.224533 | + | 0.0559482i | ||||
\(277\) | −427.929 | + | 247.065i | −1.54487 | + | 0.891930i | −0.546348 | + | 0.837558i | \(0.683982\pi\) |
−0.998521 | + | 0.0543719i | \(0.982684\pi\) | |||||||
\(278\) | −117.143 | + | 202.898i | −0.421379 | + | 0.729850i | ||||
\(279\) | −263.788 | − | 164.938i | −0.945477 | − | 0.591175i | ||||
\(280\) | −259.939 | + | 150.055i | −0.928353 | + | 0.535911i | ||||
\(281\) | 67.0586i | 0.238643i | 0.992856 | + | 0.119321i | \(0.0380719\pi\) | ||||
−0.992856 | + | 0.119321i | \(0.961928\pi\) | |||||||
\(282\) | 130.268 | + | 134.935i | 0.461944 | + | 0.478494i | ||||
\(283\) | −118.530 | + | 68.4334i | −0.418834 | + | 0.241814i | −0.694579 | − | 0.719417i | \(-0.744409\pi\) |
0.275744 | + | 0.961231i | \(0.411076\pi\) | |||||||
\(284\) | −44.9136 | + | 25.9309i | −0.158146 | + | 0.0913058i | ||||
\(285\) | 411.704 | − | 196.280i | 1.44458 | − | 0.688702i | ||||
\(286\) | 26.0782 | 0.0911825 | ||||||||
\(287\) | 118.073 | + | 24.0246i | 0.411405 | + | 0.0837094i | ||||
\(288\) | 93.2917 | + | 58.3322i | 0.323929 | + | 0.202542i | ||||
\(289\) | −29.0330 | + | 50.2867i | −0.100460 | + | 0.174002i | ||||
\(290\) | −94.2549 | − | 463.374i | −0.325017 | − | 1.59784i | ||||
\(291\) | −48.4156 | − | 194.303i | −0.166377 | − | 0.667707i | ||||
\(292\) | 36.2851 | + | 20.9492i | 0.124264 | + | 0.0717439i | ||||
\(293\) | −98.9599 | −0.337747 | −0.168874 | − | 0.985638i | \(-0.554013\pi\) | ||||
−0.168874 | + | 0.985638i | \(0.554013\pi\) | |||||||
\(294\) | 166.148 | − | 205.100i | 0.565130 | − | 0.697620i | ||||
\(295\) | 177.079 | + | 59.2579i | 0.600269 | + | 0.200874i | ||||
\(296\) | 3.06324 | + | 1.76856i | 0.0103488 | + | 0.00597487i | ||||
\(297\) | 9.72244 | − | 29.8790i | 0.0327355 | − | 0.100603i | ||||
\(298\) | 246.947 | − | 142.575i | 0.828681 | − | 0.478439i | ||||
\(299\) | −296.572 | − | 171.226i | −0.991879 | − | 0.572662i | ||||
\(300\) | 46.4776 | − | 35.0070i | 0.154925 | − | 0.116690i | ||||
\(301\) | −53.9819 | − | 10.9838i | −0.179342 | − | 0.0364911i | ||||
\(302\) | 86.3287 | 0.285857 | ||||||||
\(303\) | −48.2339 | + | 46.5657i | −0.159188 | + | 0.153682i | ||||
\(304\) | 186.922 | + | 323.759i | 0.614875 | + | 1.06500i | ||||
\(305\) | 249.309 | − | 50.7120i | 0.817407 | − | 0.166269i | ||||
\(306\) | 265.864 | − | 141.265i | 0.868836 | − | 0.461650i | ||||
\(307\) | 441.330i | 1.43756i | 0.695239 | + | 0.718778i | \(0.255298\pi\) | ||||
−0.695239 | + | 0.718778i | \(0.744702\pi\) | |||||||
\(308\) | 4.18782 | − | 4.73329i | 0.0135968 | − | 0.0153678i | ||||
\(309\) | 42.7834 | + | 12.2746i | 0.138458 | + | 0.0397235i | ||||
\(310\) | −205.634 | − | 232.445i | −0.663334 | − | 0.749824i | ||||
\(311\) | −19.4380 | + | 11.2225i | −0.0625015 | + | 0.0360853i | −0.530925 | − | 0.847419i | \(-0.678155\pi\) |
0.468424 | + | 0.883504i | \(0.344822\pi\) | |||||||
\(312\) | 77.6276 | + | 311.537i | 0.248806 | + | 0.998516i | ||||
\(313\) | 217.506 | + | 125.577i | 0.694908 | + | 0.401206i | 0.805448 | − | 0.592666i | \(-0.201925\pi\) |
−0.110540 | + | 0.993872i | \(0.535258\pi\) | |||||||
\(314\) | 233.977i | 0.745149i | ||||||||
\(315\) | −167.017 | + | 267.077i | −0.530212 | + | 0.847865i | ||||
\(316\) | −25.8195 | −0.0817074 | ||||||||
\(317\) | 17.4496 | − | 30.2237i | 0.0550462 | − | 0.0953428i | −0.837189 | − | 0.546913i | \(-0.815803\pi\) |
0.892235 | + | 0.451570i | \(0.149136\pi\) | |||||||
\(318\) | 186.777 | − | 46.5405i | 0.587350 | − | 0.146354i | ||||
\(319\) | 30.6466 | + | 53.0814i | 0.0960707 | + | 0.166399i | ||||
\(320\) | 235.653 | + | 266.379i | 0.736416 | + | 0.832435i | ||||
\(321\) | −28.1221 | + | 98.0206i | −0.0876079 | + | 0.305360i | ||||
\(322\) | 327.081 | − | 109.433i | 1.01578 | − | 0.339854i | ||||
\(323\) | −566.466 | −1.75377 | ||||||||
\(324\) | 62.6857 | + | 4.41944i | 0.193474 | + | 0.0136403i | ||||
\(325\) | 309.669 | + | 38.0481i | 0.952828 | + | 0.117071i | ||||
\(326\) | −217.485 | + | 125.565i | −0.667131 | + | 0.385168i | ||||
\(327\) | −188.845 | − | 195.611i | −0.577508 | − | 0.598198i | ||||
\(328\) | − | 147.611i | − | 0.450035i | ||||||
\(329\) | 182.535 | + | 161.500i | 0.554819 | + | 0.490881i | ||||
\(330\) | 17.7583 | − | 25.8283i | 0.0538130 | − | 0.0782676i | ||||
\(331\) | 136.010 | − | 235.577i | 0.410908 | − | 0.711713i | −0.584082 | − | 0.811695i | \(-0.698545\pi\) |
0.994989 | + | 0.0999821i | \(0.0318786\pi\) | |||||||
\(332\) | −27.9572 | − | 48.4232i | −0.0842083 | − | 0.145853i | ||||
\(333\) | 3.70993 | + | 0.130616i | 0.0111409 | + | 0.000392240i | ||||
\(334\) | 201.484 | − | 348.980i | 0.603245 | − | 1.04485i | ||||
\(335\) | 136.759 | + | 45.7650i | 0.408235 | + | 0.136612i | ||||
\(336\) | −228.999 | − | 119.257i | −0.681546 | − | 0.354930i | ||||
\(337\) | − | 600.523i | − | 1.78197i | −0.454036 | − | 0.890983i | \(-0.650016\pi\) | ||
0.454036 | − | 0.890983i | \(-0.349984\pi\) | |||||||
\(338\) | 11.8976 | − | 20.6072i | 0.0351999 | − | 0.0609680i | ||||
\(339\) | 221.980 | − | 55.3121i | 0.654808 | − | 0.163162i | ||||
\(340\) | −70.8162 | + | 14.4047i | −0.208283 | + | 0.0423668i | ||||
\(341\) | 34.8383 | + | 20.1139i | 0.102165 | + | 0.0589850i | ||||
\(342\) | 416.642 | + | 260.513i | 1.21825 | + | 0.761733i | ||||
\(343\) | 194.293 | − | 282.664i | 0.566453 | − | 0.824094i | ||||
\(344\) | 67.4865i | 0.196182i | ||||||||
\(345\) | −371.540 | + | 177.132i | −1.07693 | + | 0.513425i | ||||
\(346\) | −263.643 | − | 456.643i | −0.761973 | − | 1.31978i | ||||
\(347\) | −77.0212 | − | 133.405i | −0.221963 | − | 0.384451i | 0.733441 | − | 0.679753i | \(-0.237913\pi\) |
−0.955404 | + | 0.295302i | \(0.904580\pi\) | |||||||
\(348\) | −88.1924 | + | 85.1420i | −0.253426 | + | 0.244661i | ||||
\(349\) | −20.2324 | −0.0579726 | −0.0289863 | − | 0.999580i | \(-0.509228\pi\) | ||||
−0.0289863 | + | 0.999580i | \(0.509228\pi\) | |||||||
\(350\) | −235.365 | + | 208.192i | −0.672472 | + | 0.594833i | ||||
\(351\) | 225.361 | + | 250.505i | 0.642055 | + | 0.713689i | ||||
\(352\) | −12.3210 | − | 7.11351i | −0.0350027 | − | 0.0202088i | ||||
\(353\) | 162.715 | + | 281.830i | 0.460948 | + | 0.798386i | 0.999008 | − | 0.0445203i | \(-0.0141760\pi\) |
−0.538060 | + | 0.842907i | \(0.680843\pi\) | |||||||
\(354\) | 48.6412 | + | 195.208i | 0.137405 | + | 0.551436i | ||||
\(355\) | −250.339 | + | 221.463i | −0.705180 | + | 0.623840i | ||||
\(356\) | 37.1638i | 0.104393i | ||||||||
\(357\) | 329.989 | − | 210.151i | 0.924339 | − | 0.588658i | ||||
\(358\) | 438.363i | 1.22448i | ||||||||
\(359\) | 499.939 | + | 288.640i | 1.39259 | + | 0.804011i | 0.993601 | − | 0.112945i | \(-0.0360285\pi\) |
0.398987 | + | 0.916957i | \(0.369362\pi\) | |||||||
\(360\) | 361.414 | + | 135.262i | 1.00393 | + | 0.375727i | ||||
\(361\) | −281.781 | − | 488.059i | −0.780556 | − | 1.35196i | ||||
\(362\) | 73.0513 | − | 126.528i | 0.201799 | − | 0.349526i | ||||
\(363\) | 98.9858 | − | 345.018i | 0.272688 | − | 0.950464i | ||||
\(364\) | 21.5041 | + | 64.2730i | 0.0590772 | + | 0.176574i | ||||
\(365\) | 256.070 | + | 85.6913i | 0.701561 | + | 0.234771i | ||||
\(366\) | 190.375 | + | 197.195i | 0.520150 | + | 0.538785i | ||||
\(367\) | −435.739 | + | 251.574i | −1.18730 | + | 0.685487i | −0.957692 | − | 0.287796i | \(-0.907077\pi\) |
−0.229607 | + | 0.973283i | \(0.573744\pi\) | |||||||
\(368\) | −168.687 | − | 292.174i | −0.458388 | − | 0.793950i | ||||
\(369\) | −72.6910 | − | 136.806i | −0.196995 | − | 0.370749i | ||||
\(370\) | 3.51174 | + | 1.17517i | 0.00949120 | + | 0.00317614i | ||||
\(371\) | 237.209 | − | 79.3640i | 0.639377 | − | 0.213919i | ||||
\(372\) | −22.1874 | + | 77.3348i | −0.0596434 | + | 0.207889i | ||||
\(373\) | 185.731 | + | 107.232i | 0.497938 | + | 0.287484i | 0.727861 | − | 0.685724i | \(-0.240514\pi\) |
−0.229924 | + | 0.973209i | \(0.573848\pi\) | |||||||
\(374\) | −33.7134 | + | 19.4644i | −0.0901428 | + | 0.0520440i | ||||
\(375\) | 248.557 | − | 280.793i | 0.662818 | − | 0.748780i | ||||
\(376\) | 149.289 | − | 258.576i | 0.397045 | − | 0.687703i | ||||
\(377\) | −657.305 | −1.74351 | ||||||||
\(378\) | −339.357 | + | 2.80951i | −0.897770 | + | 0.00743255i | ||||
\(379\) | −505.361 | −1.33341 | −0.666704 | − | 0.745323i | \(-0.732295\pi\) | ||||
−0.666704 | + | 0.745323i | \(0.732295\pi\) | |||||||
\(380\) | −78.1525 | − | 88.3425i | −0.205664 | − | 0.232480i | ||||
\(381\) | 0.416094 | + | 1.66988i | 0.00109211 | + | 0.00438289i | ||||
\(382\) | 372.374 | − | 214.990i | 0.974800 | − | 0.562801i | ||||
\(383\) | 202.429 | − | 350.617i | 0.528535 | − | 0.915449i | −0.470912 | − | 0.882180i | \(-0.656075\pi\) |
0.999446 | − | 0.0332689i | \(-0.0105918\pi\) | |||||||
\(384\) | −65.2112 | + | 227.296i | −0.169821 | + | 0.591917i | ||||
\(385\) | 20.3676 | − | 35.2728i | 0.0529028 | − | 0.0916177i | ||||
\(386\) | 2.88436i | 0.00747244i | ||||||||
\(387\) | 33.2336 | + | 62.5465i | 0.0858749 | + | 0.161619i | ||||
\(388\) | −44.8466 | + | 25.8922i | −0.115584 | + | 0.0667324i | ||||
\(389\) | −168.810 | + | 97.4627i | −0.433960 | + | 0.250547i | −0.701032 | − | 0.713130i | \(-0.747277\pi\) |
0.267072 | + | 0.963676i | \(0.413944\pi\) | |||||||
\(390\) | 144.654 | + | 303.416i | 0.370907 | + | 0.777990i | ||||
\(391\) | 511.204 | 1.30743 | ||||||||
\(392\) | −386.788 | − | 164.199i | −0.986703 | − | 0.418875i | ||||
\(393\) | 664.888 | + | 190.756i | 1.69183 | + | 0.485385i | ||||
\(394\) | −257.063 | + | 445.245i | −0.652443 | + | 1.13006i | ||||
\(395\) | −163.063 | + | 33.1686i | −0.412817 | + | 0.0839711i | ||||
\(396\) | −8.12063 | − | 0.285904i | −0.0205067 | − | 0.000721980i | ||||
\(397\) | −500.171 | − | 288.774i | −1.25988 | − | 0.727390i | −0.286826 | − | 0.957983i | \(-0.592600\pi\) |
−0.973050 | + | 0.230593i | \(0.925933\pi\) | |||||||
\(398\) | −160.272 | −0.402694 | ||||||||
\(399\) | 566.343 | + | 294.936i | 1.41941 | + | 0.739188i | ||||
\(400\) | 245.462 | + | 185.000i | 0.613656 | + | 0.462501i | ||||
\(401\) | −199.268 | − | 115.047i | −0.496927 | − | 0.286901i | 0.230517 | − | 0.973068i | \(-0.425958\pi\) |
−0.727443 | + | 0.686168i | \(0.759292\pi\) | |||||||
\(402\) | 37.5657 | + | 150.760i | 0.0934470 | + | 0.375024i | ||||
\(403\) | −373.604 | + | 215.700i | −0.927057 | + | 0.535237i | ||||
\(404\) | 15.0151 | + | 8.66897i | 0.0371661 | + | 0.0214579i | ||||
\(405\) | 401.567 | − | 52.6171i | 0.991525 | − | 0.129919i | ||||
\(406\) | 438.669 | − | 495.806i | 1.08047 | − | 1.22120i | ||||
\(407\) | −0.480008 | −0.00117938 | ||||||||
\(408\) | −332.883 | − | 344.809i | −0.815890 | − | 0.845121i | ||||
\(409\) | 290.480 | + | 503.125i | 0.710219 | + | 1.23014i | 0.964775 | + | 0.263077i | \(0.0847375\pi\) |
−0.254556 | + | 0.967058i | \(0.581929\pi\) | |||||||
\(410\) | −30.8043 | − | 151.439i | −0.0751324 | − | 0.369364i | ||||
\(411\) | −58.1300 | − | 60.2126i | −0.141435 | − | 0.146503i | ||||
\(412\) | − | 11.5104i | − | 0.0279378i | ||||||
\(413\) | 82.9464 | + | 247.916i | 0.200839 | + | 0.600281i | ||||
\(414\) | −375.996 | − | 235.098i | −0.908203 | − | 0.567869i | ||||
\(415\) | −238.769 | − | 269.901i | −0.575347 | − | 0.650364i | ||||
\(416\) | 132.129 | − | 76.2850i | 0.317619 | − | 0.183377i | ||||
\(417\) | 379.821 | − | 94.6424i | 0.910842 | − | 0.226960i | ||||
\(418\) | −55.0256 | − | 31.7690i | −0.131640 | − | 0.0760025i | ||||
\(419\) | − | 220.813i | − | 0.527000i | −0.964659 | − | 0.263500i | \(-0.915123\pi\) | ||
0.964659 | − | 0.263500i | \(-0.0848769\pi\) | |||||||
\(420\) | 78.3007 | + | 22.4695i | 0.186430 | + | 0.0534989i | ||||
\(421\) | −747.852 | −1.77637 | −0.888185 | − | 0.459486i | \(-0.848033\pi\) | ||||
−0.888185 | + | 0.459486i | \(0.848033\pi\) | |||||||
\(422\) | 156.401 | − | 270.895i | 0.370620 | − | 0.641932i | ||||
\(423\) | 11.0257 | − | 313.166i | 0.0260654 | − | 0.740344i | ||||
\(424\) | −153.215 | − | 265.376i | −0.361356 | − | 0.625887i | ||||
\(425\) | −428.733 | + | 181.945i | −1.00878 | + | 0.428107i | ||||
\(426\) | −346.132 | − | 99.3053i | −0.812516 | − | 0.233111i | ||||
\(427\) | 266.759 | + | 236.017i | 0.624728 | + | 0.552734i | ||||
\(428\) | 26.3714 | 0.0616153 | ||||||||
\(429\) | −30.2619 | − | 31.3461i | −0.0705405 | − | 0.0730677i | ||||
\(430\) | 14.0834 | + | 69.2365i | 0.0327521 | + | 0.161015i | ||||
\(431\) | −310.115 | + | 179.045i | −0.719523 | + | 0.415417i | −0.814577 | − | 0.580055i | \(-0.803031\pi\) |
0.0950539 | + | 0.995472i | \(0.469698\pi\) | |||||||
\(432\) | 68.8792 | + | 324.736i | 0.159443 | + | 0.751703i | ||||
\(433\) | 622.750i | 1.43822i | 0.694896 | + | 0.719110i | \(0.255450\pi\) | ||||
−0.694896 | + | 0.719110i | \(0.744550\pi\) | |||||||
\(434\) | 86.6310 | − | 425.764i | 0.199611 | − | 0.981022i | ||||
\(435\) | −447.601 | + | 651.007i | −1.02897 | + | 1.49657i | ||||
\(436\) | −35.1566 | + | 60.8931i | −0.0806345 | + | 0.139663i | ||||
\(437\) | 417.182 | + | 722.581i | 0.954651 | + | 1.65350i | ||||
\(438\) | 70.3388 | + | 282.285i | 0.160591 | + | 0.644487i | ||||
\(439\) | 194.411 | − | 336.729i | 0.442849 | − | 0.767036i | −0.555051 | − | 0.831816i | \(-0.687301\pi\) |
0.997900 | + | 0.0647799i | \(0.0206345\pi\) | |||||||
\(440\) | −47.3189 | − | 15.8348i | −0.107543 | − | 0.0359882i | ||||
\(441\) | −439.334 | + | 38.2934i | −0.996223 | + | 0.0868331i | ||||
\(442\) | − | 417.472i | − | 0.944506i | ||||||
\(443\) | 192.113 | − | 332.750i | 0.433664 | − | 0.751128i | −0.563522 | − | 0.826101i | \(-0.690554\pi\) |
0.997186 | + | 0.0749733i | \(0.0238872\pi\) | |||||||
\(444\) | −0.232113 | − | 0.931523i | −0.000522778 | − | 0.00209802i | ||||
\(445\) | 47.7418 | + | 234.707i | 0.107285 | + | 0.527432i | ||||
\(446\) | −232.005 | − | 133.948i | −0.520191 | − | 0.300333i | ||||
\(447\) | −457.940 | − | 131.383i | −1.02447 | − | 0.293922i | ||||
\(448\) | −99.2779 | + | 487.919i | −0.221602 | + | 1.08911i | ||||
\(449\) | − | 33.9684i | − | 0.0756535i | −0.999284 | − | 0.0378267i | \(-0.987957\pi\) | ||
0.999284 | − | 0.0378267i | \(-0.0120435\pi\) | |||||||
\(450\) | 399.013 | + | 63.3476i | 0.886695 | + | 0.140772i | ||||
\(451\) | 10.0159 | + | 17.3480i | 0.0222081 | + | 0.0384656i | ||||
\(452\) | −29.5803 | − | 51.2346i | −0.0654432 | − | 0.113351i | ||||
\(453\) | −100.178 | − | 103.767i | −0.221144 | − | 0.229067i | ||||
\(454\) | −165.655 | −0.364878 | ||||||||
\(455\) | 218.376 | + | 378.290i | 0.479947 | + | 0.831407i | ||||
\(456\) | 215.725 | − | 751.918i | 0.473082 | − | 1.64894i | ||||
\(457\) | 432.197 | + | 249.529i | 0.945726 | + | 0.546015i | 0.891751 | − | 0.452527i | \(-0.149477\pi\) |
0.0539752 | + | 0.998542i | \(0.482811\pi\) | |||||||
\(458\) | 132.899 | + | 230.188i | 0.290173 | + | 0.502595i | ||||
\(459\) | −478.317 | − | 155.641i | −1.04208 | − | 0.339088i | ||||
\(460\) | 70.5282 | + | 79.7241i | 0.153322 | + | 0.173313i | ||||
\(461\) | 816.492i | 1.77113i | 0.464513 | + | 0.885566i | \(0.346229\pi\) | ||||
−0.464513 | + | 0.885566i | \(0.653771\pi\) | |||||||
\(462\) | 43.8404 | − | 1.90700i | 0.0948927 | − | 0.00412771i | ||||
\(463\) | − | 353.851i | − | 0.764258i | −0.924109 | − | 0.382129i | \(-0.875191\pi\) | ||
0.924109 | − | 0.382129i | \(-0.124809\pi\) | |||||||
\(464\) | −560.801 | − | 323.779i | −1.20862 | − | 0.697799i | ||||
\(465\) | −40.7771 | + | 516.909i | −0.0876926 | + | 1.11163i | ||||
\(466\) | 362.022 | + | 627.041i | 0.776872 | + | 1.34558i | ||||
\(467\) | −127.057 | + | 220.068i | −0.272070 | + | 0.471238i | −0.969392 | − | 0.245520i | \(-0.921041\pi\) |
0.697322 | + | 0.716758i | \(0.254375\pi\) | |||||||
\(468\) | 46.1979 | − | 73.8851i | 0.0987135 | − | 0.157874i | ||||
\(469\) | 64.0596 | + | 191.466i | 0.136588 | + | 0.408243i | ||||
\(470\) | 99.1994 | − | 296.436i | 0.211063 | − | 0.630715i | ||||
\(471\) | 281.241 | − | 271.513i | 0.597114 | − | 0.576462i | ||||
\(472\) | 277.355 | − | 160.131i | 0.587616 | − | 0.339260i | ||||
\(473\) | −4.57916 | − | 7.93133i | −0.00968109 | − | 0.0167681i | ||||
\(474\) | −124.516 | − | 128.977i | −0.262693 | − | 0.272104i | ||||
\(475\) | −607.058 | − | 457.528i | −1.27802 | − | 0.963217i | ||||
\(476\) | −75.7728 | − | 67.0406i | −0.159186 | − | 0.140842i | ||||
\(477\) | −272.684 | − | 170.500i | −0.571664 | − | 0.357442i | ||||
\(478\) | 65.4930 | + | 37.8124i | 0.137015 | + | 0.0791054i | ||||
\(479\) | 220.662 | − | 127.400i | 0.460673 | − | 0.265970i | −0.251654 | − | 0.967817i | \(-0.580975\pi\) |
0.712327 | + | 0.701847i | \(0.247641\pi\) | |||||||
\(480\) | 14.4213 | − | 182.811i | 0.0300443 | − | 0.380856i | ||||
\(481\) | 2.57379 | − | 4.45794i | 0.00535092 | − | 0.00926807i | ||||
\(482\) | −478.224 | −0.992167 | ||||||||
\(483\) | −511.093 | − | 266.163i | −1.05816 | − | 0.551062i | ||||
\(484\) | −92.8234 | −0.191784 | ||||||||
\(485\) | −249.966 | + | 221.133i | −0.515393 | + | 0.455944i | ||||
\(486\) | 280.229 | + | 334.449i | 0.576603 | + | 0.688167i | ||||
\(487\) | −144.819 | + | 83.6115i | −0.297370 | + | 0.171687i | −0.641261 | − | 0.767323i | \(-0.721588\pi\) |
0.343891 | + | 0.939010i | \(0.388255\pi\) | |||||||
\(488\) | 218.172 | − | 377.885i | 0.447074 | − | 0.774355i | ||||
\(489\) | 403.305 | + | 115.708i | 0.824754 | + | 0.236622i | ||||
\(490\) | −431.084 | − | 87.7402i | −0.879763 | − | 0.179062i | ||||
\(491\) | − | 663.001i | − | 1.35031i | −0.737677 | − | 0.675154i | \(-0.764077\pi\) | ||
0.737677 | − | 0.675154i | \(-0.235923\pi\) | |||||||
\(492\) | −28.8229 | + | 27.8260i | −0.0585832 | + | 0.0565569i | ||||
\(493\) | 849.752 | − | 490.605i | 1.72363 | − | 0.995141i | ||||
\(494\) | 590.092 | − | 340.690i | 1.19452 | − | 0.689655i | ||||
\(495\) | −51.6530 | + | 8.62640i | −0.104349 | + | 0.0174271i | ||||
\(496\) | −425.003 | −0.856861 | ||||||||
\(497\) | −458.539 | − | 93.2998i | −0.922613 | − | 0.187726i | ||||
\(498\) | 107.065 | − | 373.180i | 0.214991 | − | 0.749357i | ||||
\(499\) | 213.627 | − | 370.012i | 0.428109 | − | 0.741507i | −0.568596 | − | 0.822617i | \(-0.692513\pi\) |
0.996705 | + | 0.0811099i | \(0.0258465\pi\) | |||||||
\(500\) | −87.5252 | − | 41.7605i | −0.175050 | − | 0.0835209i | ||||
\(501\) | −653.283 | + | 162.783i | −1.30396 | + | 0.324915i | ||||
\(502\) | −663.848 | − | 383.273i | −1.32241 | − | 0.763492i | ||||
\(503\) | 503.059 | 1.00012 | 0.500059 | − | 0.865991i | \(-0.333312\pi\) | ||||
0.500059 | + | 0.865991i | \(0.333312\pi\) | |||||||
\(504\) | 153.283 | + | 518.053i | 0.304132 | + | 1.02788i | ||||
\(505\) | 105.964 | + | 35.4598i | 0.209830 | + | 0.0702175i | ||||
\(506\) | 49.6575 | + | 28.6698i | 0.0981373 | + | 0.0566596i | ||||
\(507\) | −38.5762 | + | 9.61226i | −0.0760871 | + | 0.0189591i | ||||
\(508\) | 0.385421 | − | 0.222523i | 0.000758702 | − | 0.000438037i | ||||
\(509\) | −481.244 | − | 277.846i | −0.945469 | − | 0.545867i | −0.0537984 | − | 0.998552i | \(-0.517133\pi\) |
−0.891670 | + | 0.452685i | \(0.850466\pi\) | |||||||
\(510\) | −413.472 | − | 284.283i | −0.810729 | − | 0.557418i | ||||
\(511\) | 119.947 | + | 358.505i | 0.234729 | + | 0.701575i | ||||
\(512\) | 572.043 | 1.11727 | ||||||||
\(513\) | −170.347 | − | 803.111i | −0.332059 | − | 1.56552i | ||||
\(514\) | 15.0027 | + | 25.9855i | 0.0291882 | + | 0.0505554i | ||||
\(515\) | −14.7866 | − | 72.6936i | −0.0287119 | − | 0.141153i | ||||
\(516\) | 13.1776 | − | 12.7218i | 0.0255379 | − | 0.0246546i | ||||
\(517\) | 40.5188i | 0.0783729i | ||||||||
\(518\) | 1.64495 | + | 4.91654i | 0.00317557 | + | 0.00949139i | ||||
\(519\) | −242.947 | + | 846.801i | −0.468106 | + | 1.63160i | ||||
\(520\) | 400.784 | − | 354.555i | 0.770739 | − | 0.681836i | ||||
\(521\) | −209.107 | + | 120.728i | −0.401358 | + | 0.231724i | −0.687070 | − | 0.726591i | \(-0.741103\pi\) |
0.285712 | + | 0.958316i | \(0.407770\pi\) | |||||||
\(522\) | −850.626 | − | 29.9481i | −1.62955 | − | 0.0573718i | ||||
\(523\) | 683.792 | + | 394.788i | 1.30744 | + | 0.754852i | 0.981669 | − | 0.190596i | \(-0.0610421\pi\) |
0.325773 | + | 0.945448i | \(0.394375\pi\) | |||||||
\(524\) | − | 178.881i | − | 0.341375i | ||||||
\(525\) | 523.372 | + | 41.3183i | 0.996898 | + | 0.0787014i | ||||
\(526\) | 2.71615 | 0.00516379 | ||||||||
\(527\) | 321.992 | − | 557.707i | 0.610991 | − | 1.05827i | ||||
\(528\) | −10.3783 | − | 41.6505i | −0.0196559 | − | 0.0788834i | ||||
\(529\) | −111.984 | − | 193.961i | −0.211689 | − | 0.366656i | ||||
\(530\) | −212.568 | − | 240.284i | −0.401072 | − | 0.453366i | ||||
\(531\) | 178.196 | − | 284.992i | 0.335586 | − | 0.536708i | ||||
\(532\) | 32.9247 | − | 161.814i | 0.0618885 | − | 0.304162i | ||||
\(533\) | −214.820 | −0.403039 | ||||||||
\(534\) | −185.646 | + | 179.225i | −0.347651 | + | 0.335627i | ||||
\(535\) | 166.548 | − | 33.8775i | 0.311304 | − | 0.0633224i | ||||
\(536\) | 214.202 | − | 123.669i | 0.399630 | − | 0.230726i | ||||
\(537\) | 526.914 | − | 508.689i | 0.981218 | − | 0.947280i | ||||
\(538\) | 21.9549i | 0.0408084i | ||||||||
\(539\) | 56.5985 | − | 6.94725i | 0.105007 | − | 0.0128891i | ||||
\(540\) | −41.7181 | − | 96.0683i | −0.0772557 | − | 0.177904i | ||||
\(541\) | −394.171 | + | 682.723i | −0.728596 | + | 1.26197i | 0.228880 | + | 0.973455i | \(0.426494\pi\) |
−0.957477 | + | 0.288511i | \(0.906840\pi\) | |||||||
\(542\) | 210.637 | + | 364.834i | 0.388629 | + | 0.673125i | ||||
\(543\) | −236.858 | + | 59.0195i | −0.436203 | + | 0.108691i | ||||
\(544\) | −113.876 | + | 197.240i | −0.209332 | + | 0.362573i | ||||
\(545\) | −143.806 | + | 429.732i | −0.263864 | + | 0.788499i | ||||
\(546\) | −217.361 | + | 417.381i | −0.398097 | + | 0.764434i | ||||
\(547\) | − | 2.30392i | − | 0.00421191i | −0.999998 | − | 0.00210596i | \(-0.999330\pi\) | ||
0.999998 | − | 0.00210596i | \(-0.000670347\pi\) | |||||||
\(548\) | −10.8219 | + | 18.7440i | −0.0197479 | + | 0.0342044i | ||||
\(549\) | 16.1130 | − | 457.662i | 0.0293497 | − | 0.833629i | ||||
\(550\) | −51.8504 | − | 6.37070i | −0.0942735 | − | 0.0115831i | ||||
\(551\) | 1386.93 | + | 800.744i | 2.51711 | + | 1.45326i | ||||
\(552\) | −194.680 | + | 678.564i | −0.352681 | + | 1.22928i | ||||
\(553\) | −174.476 | − | 154.369i | −0.315508 | − | 0.279148i | ||||
\(554\) | 887.259i | 1.60155i | ||||||||
\(555\) | −2.66257 | − | 5.58483i | −0.00479742 | − | 0.0100628i | ||||
\(556\) | −50.6137 | − | 87.6656i | −0.0910319 | − | 0.157672i | ||||
\(557\) | 178.710 | + | 309.535i | 0.320844 | + | 0.555718i | 0.980662 | − | 0.195707i | \(-0.0627003\pi\) |
−0.659819 | + | 0.751425i | \(0.729367\pi\) | |||||||
\(558\) | −493.313 | + | 262.118i | −0.884074 | + | 0.469746i | ||||
\(559\) | 98.2134 | 0.175695 | ||||||||
\(560\) | −0.0256154 | + | 430.319i | −4.57417e−5 | + | 0.768427i | ||||
\(561\) | 62.5183 | + | 17.9365i | 0.111441 | + | 0.0319724i | ||||
\(562\) | 104.279 | + | 60.2052i | 0.185549 | + | 0.107127i | ||||
\(563\) | 331.223 | + | 573.695i | 0.588318 | + | 1.01900i | 0.994453 | + | 0.105183i | \(0.0335430\pi\) |
−0.406135 | + | 0.913813i | \(0.633124\pi\) | |||||||
\(564\) | −78.6324 | + | 19.5933i | −0.139419 | + | 0.0347399i | ||||
\(565\) | −252.631 | − | 285.571i | −0.447135 | − | 0.505436i | ||||
\(566\) | 245.758i | 0.434202i | ||||||||
\(567\) | 397.177 | + | 404.648i | 0.700488 | + | 0.713665i | ||||
\(568\) | 573.250i | 1.00924i | ||||||||
\(569\) | −286.622 | − | 165.481i | −0.503729 | − | 0.290828i | 0.226523 | − | 0.974006i | \(-0.427264\pi\) |
−0.730252 | + | 0.683178i | \(0.760597\pi\) | |||||||
\(570\) | 64.4057 | − | 816.435i | 0.112992 | − | 1.43234i | ||||
\(571\) | 420.825 | + | 728.890i | 0.736996 | + | 1.27651i | 0.953842 | + | 0.300309i | \(0.0970897\pi\) |
−0.216846 | + | 0.976206i | \(0.569577\pi\) | |||||||
\(572\) | −5.63375 | + | 9.75795i | −0.00984922 | + | 0.0170593i | ||||
\(573\) | −690.532 | − | 198.114i | −1.20512 | − | 0.345748i | ||||
\(574\) | 143.365 | − | 162.039i | 0.249765 | − | 0.282298i | ||||
\(575\) | 547.835 | + | 412.893i | 0.952757 | + | 0.718075i | ||||
\(576\) | 565.330 | − | 300.384i | 0.981476 | − | 0.521500i | ||||
\(577\) | −446.025 | + | 257.513i | −0.773007 | + | 0.446296i | −0.833946 | − | 0.551845i | \(-0.813924\pi\) |
0.0609390 | + | 0.998141i | \(0.480590\pi\) | |||||||
\(578\) | 52.1317 | + | 90.2948i | 0.0901933 | + | 0.156219i | ||||
\(579\) | 3.46701 | − | 3.34710i | 0.00598793 | − | 0.00578082i | ||||
\(580\) | 193.748 | + | 64.8358i | 0.334048 | + | 0.111786i | ||||
\(581\) | 100.590 | − | 494.370i | 0.173133 | − | 0.850895i | ||||
\(582\) | −345.615 | − | 99.1571i | −0.593841 | − | 0.170373i | ||||
\(583\) | 36.0131 | + | 20.7922i | 0.0617720 | + | 0.0356641i | ||||
\(584\) | 401.075 | − | 231.561i | 0.686773 | − | 0.396508i | ||||
\(585\) | 196.847 | − | 525.967i | 0.336490 | − | 0.899089i | ||||
\(586\) | −88.8462 | + | 153.886i | −0.151615 | + | 0.262604i | ||||
\(587\) | 935.242 | 1.59326 | 0.796629 | − | 0.604469i | \(-0.206615\pi\) | ||||
0.796629 | + | 0.604469i | \(0.206615\pi\) | |||||||
\(588\) | 40.8509 | + | 106.478i | 0.0694744 | + | 0.181085i | ||||
\(589\) | 1051.08 | 1.78452 | ||||||||
\(590\) | 251.130 | − | 222.163i | 0.425644 | − | 0.376548i | ||||
\(591\) | 833.489 | − | 207.686i | 1.41030 | − | 0.351414i | ||||
\(592\) | 4.39183 | − | 2.53563i | 0.00741863 | − | 0.00428315i | ||||
\(593\) | 244.872 | − | 424.131i | 0.412938 | − | 0.715229i | −0.582272 | − | 0.812994i | \(-0.697836\pi\) |
0.995210 | + | 0.0977651i | \(0.0311694\pi\) | |||||||
\(594\) | −37.7341 | − | 41.9441i | −0.0635254 | − | 0.0706130i | ||||
\(595\) | −564.664 | − | 326.054i | −0.949015 | − | 0.547989i | ||||
\(596\) | 123.204i | 0.206718i | ||||||||
\(597\) | 185.985 | + | 192.648i | 0.311532 | + | 0.322693i | ||||
\(598\) | −532.525 | + | 307.453i | −0.890510 | + | 0.514136i | ||||
\(599\) | 406.061 | − | 234.439i | 0.677898 | − | 0.391384i | −0.121165 | − | 0.992632i | \(-0.538663\pi\) |
0.799063 | + | 0.601248i | \(0.205330\pi\) | |||||||
\(600\) | −78.2384 | − | 638.383i | −0.130397 | − | 1.06397i | ||||
\(601\) | 679.264 | 1.13022 | 0.565112 | − | 0.825014i | \(-0.308833\pi\) | ||||
0.565112 | + | 0.825014i | \(0.308833\pi\) | |||||||
\(602\) | −65.5452 | + | 74.0825i | −0.108879 | + | 0.123061i | ||||
\(603\) | 137.621 | − | 220.100i | 0.228227 | − | 0.365008i | ||||
\(604\) | −18.6499 | + | 32.3025i | −0.0308773 | + | 0.0534810i | ||||
\(605\) | −586.224 | + | 119.244i | −0.968965 | + | 0.197097i | ||||
\(606\) | 29.1068 | + | 116.812i | 0.0480310 | + | 0.192759i | ||||
\(607\) | 530.707 | + | 306.404i | 0.874312 | + | 0.504784i | 0.868779 | − | 0.495201i | \(-0.164905\pi\) |
0.00553303 | + | 0.999985i | \(0.498239\pi\) | |||||||
\(608\) | −371.728 | −0.611395 | ||||||||
\(609\) | −1105.01 | + | 48.0663i | −1.81446 | + | 0.0789266i | ||||
\(610\) | 144.971 | − | 433.214i | 0.237657 | − | 0.710186i | ||||
\(611\) | −376.307 | − | 217.261i | −0.615887 | − | 0.355583i | ||||
\(612\) | −4.57689 | + | 129.999i | −0.00747857 | + | 0.212417i | ||||
\(613\) | 173.001 | − | 99.8821i | 0.282220 | − | 0.162940i | −0.352208 | − | 0.935922i | \(-0.614569\pi\) |
0.634428 | + | 0.772982i | \(0.281236\pi\) | |||||||
\(614\) | 686.284 | + | 396.226i | 1.11773 | + | 0.645319i | ||||
\(615\) | −146.284 | + | 212.761i | −0.237861 | + | 0.345953i | ||||
\(616\) | −22.1648 | − | 66.2478i | −0.0359818 | − | 0.107545i | ||||
\(617\) | 530.227 | 0.859363 | 0.429682 | − | 0.902980i | \(-0.358626\pi\) | ||||
0.429682 | + | 0.902980i | \(0.358626\pi\) | |||||||
\(618\) | 57.4983 | − | 55.5096i | 0.0930393 | − | 0.0898213i | ||||
\(619\) | −410.628 | − | 711.228i | −0.663373 | − | 1.14900i | −0.979724 | − | 0.200353i | \(-0.935791\pi\) |
0.316351 | − | 0.948642i | \(-0.397542\pi\) | |||||||
\(620\) | 131.400 | − | 26.7281i | 0.211936 | − | 0.0431099i | ||||
\(621\) | 153.728 | + | 724.763i | 0.247549 | + | 1.16709i | ||||
\(622\) | 40.3023i | 0.0647947i | ||||||||
\(623\) | −222.194 | + | 251.135i | −0.356651 | + | 0.403106i | ||||
\(624\) | 442.465 | + | 126.943i | 0.709079 | + | 0.203435i | ||||
\(625\) | −606.410 | − | 151.300i | −0.970256 | − | 0.242079i | ||||
\(626\) | 390.555 | − | 225.487i | 0.623889 | − | 0.360202i | ||||
\(627\) | 25.6668 | + | 103.007i | 0.0409359 | + | 0.164285i | ||||
\(628\) | −87.5496 | − | 50.5468i | −0.139410 | − | 0.0804885i | ||||
\(629\) | 7.68420i | 0.0122165i | ||||||||
\(630\) | 265.367 | + | 499.499i | 0.421218 | + | 0.792856i | ||||
\(631\) | 314.044 | 0.497692 | 0.248846 | − | 0.968543i | \(-0.419949\pi\) | ||||
0.248846 | + | 0.968543i | \(0.419949\pi\) | |||||||
\(632\) | −142.697 | + | 247.159i | −0.225787 | + | 0.391074i | ||||
\(633\) | −507.110 | + | 126.360i | −0.801121 | + | 0.199620i | ||||
\(634\) | −31.3326 | − | 54.2697i | −0.0494205 | − | 0.0855988i | ||||
\(635\) | 2.14826 | − | 1.90046i | 0.00338308 | − | 0.00299285i | ||||
\(636\) | −22.9356 | + | 79.9427i | −0.0360622 | + | 0.125696i | ||||
\(637\) | −238.959 | + | 562.894i | −0.375133 | + | 0.883664i | ||||
\(638\) | 110.058 | 0.172505 | ||||||||
\(639\) | 282.296 | + | 531.288i | 0.441778 | + | 0.831437i | ||||
\(640\) | 386.201 | − | 78.5571i | 0.603438 | − | 0.122745i | ||||
\(641\) | −633.511 | + | 365.758i | −0.988317 | + | 0.570605i | −0.904771 | − | 0.425899i | \(-0.859958\pi\) |
−0.0835460 | + | 0.996504i | \(0.526625\pi\) | |||||||
\(642\) | 127.177 | + | 131.734i | 0.198096 | + | 0.205193i | ||||
\(643\) | 326.029i | 0.507044i | 0.967330 | + | 0.253522i | \(0.0815890\pi\) | ||||
−0.967330 | + | 0.253522i | \(0.918411\pi\) | |||||||
\(644\) | −29.7127 | + | 146.028i | −0.0461377 | + | 0.226752i | ||||
\(645\) | 66.8797 | − | 97.2724i | 0.103690 | − | 0.150810i | ||||
\(646\) | −508.574 | + | 880.875i | −0.787266 | + | 1.36358i | ||||
\(647\) | −286.539 | − | 496.301i | −0.442874 | − | 0.767080i | 0.555028 | − | 0.831832i | \(-0.312708\pi\) |
−0.997901 | + | 0.0647521i | \(0.979374\pi\) | |||||||
\(648\) | 388.752 | − | 575.638i | 0.599925 | − | 0.888330i | ||||
\(649\) | −21.7307 | + | 37.6387i | −0.0334834 | + | 0.0579949i | ||||
\(650\) | 337.187 | − | 447.387i | 0.518749 | − | 0.688287i | ||||
\(651\) | −612.298 | + | 389.938i | −0.940550 | + | 0.598982i | ||||
\(652\) | − | 108.505i | − | 0.166418i | ||||||
\(653\) | −451.271 | + | 781.625i | −0.691074 | + | 1.19698i | 0.280412 | + | 0.959880i | \(0.409529\pi\) |
−0.971486 | + | 0.237096i | \(0.923804\pi\) | |||||||
\(654\) | −473.727 | + | 118.041i | −0.724353 | + | 0.180491i | ||||
\(655\) | −229.796 | − | 1129.72i | −0.350833 | − | 1.72476i | ||||
\(656\) | −183.280 | − | 105.817i | −0.279391 | − | 0.161306i | ||||
\(657\) | 257.685 | − | 412.119i | 0.392214 | − | 0.627275i | ||||
\(658\) | 415.019 | − | 138.855i | 0.630727 | − | 0.211025i | ||||
\(659\) | − | 1144.56i | − | 1.73681i | −0.495855 | − | 0.868405i | \(-0.665145\pi\) | ||
0.495855 | − | 0.868405i | \(-0.334855\pi\) | |||||||
\(660\) | 5.82807 | + | 12.2246i | 0.00883041 | + | 0.0185221i | ||||
\(661\) | −374.330 | − | 648.358i | −0.566308 | − | 0.980875i | −0.996927 | − | 0.0783407i | \(-0.975038\pi\) |
0.430618 | − | 0.902534i | \(-0.358296\pi\) | |||||||
\(662\) | −244.220 | − | 423.002i | −0.368913 | − | 0.638976i | ||||
\(663\) | −501.802 | + | 484.446i | −0.756866 | + | 0.730688i | ||||
\(664\) | −618.046 | −0.930792 | ||||||||
\(665\) | 0.0633499 | − | 1064.23i | 9.52630e−5 | − | 1.60035i | ||||
\(666\) | 3.53389 | − | 5.65181i | 0.00530614 | − | 0.00848620i | ||||
\(667\) | −1251.62 | − | 722.626i | −1.87650 | − | 1.08340i | ||||
\(668\) | 87.0544 | + | 150.783i | 0.130321 | + | 0.225723i | ||||
\(669\) | 108.219 | + | 434.309i | 0.161763 | + | 0.649191i | ||||
\(670\) | 193.948 | − | 171.577i | 0.289475 | − | 0.256085i | ||||
\(671\) | 59.2145i | 0.0882481i | ||||||||
\(672\) | 216.546 | − | 137.906i | 0.322242 | − | 0.205217i | ||||
\(673\) | 351.912i | 0.522900i | 0.965217 | + | 0.261450i | \(0.0842007\pi\) | ||||
−0.965217 | + | 0.261450i | \(0.915799\pi\) | |||||||
\(674\) | −933.834 | − | 539.149i | −1.38551 | − | 0.799925i | ||||
\(675\) | −386.882 | − | 553.125i | −0.573158 | − | 0.819445i | ||||
\(676\) | 5.14054 | + | 8.90367i | 0.00760434 | + | 0.0131711i | ||||
\(677\) | −284.770 | + | 493.237i | −0.420636 | + | 0.728562i | −0.996002 | − | 0.0893336i | \(-0.971526\pi\) |
0.575366 | + | 0.817896i | \(0.304860\pi\) | |||||||
\(678\) | 113.281 | − | 394.846i | 0.167082 | − | 0.582368i | ||||
\(679\) | −457.854 | − | 93.1606i | −0.674307 | − | 0.137203i | ||||
\(680\) | −253.491 | + | 757.503i | −0.372781 | + | 1.11397i | ||||
\(681\) | 192.230 | + | 199.117i | 0.282277 | + | 0.292390i | ||||
\(682\) | 62.5556 | − | 36.1165i | 0.0917238 | − | 0.0529567i | ||||
\(683\) | −390.284 | − | 675.992i | −0.571426 | − | 0.989740i | −0.996420 | − | 0.0845432i | \(-0.973057\pi\) |
0.424993 | − | 0.905196i | \(-0.360276\pi\) | |||||||
\(684\) | −187.487 | + | 99.6199i | −0.274104 | + | 0.145643i | ||||
\(685\) | −44.2661 | + | 132.280i | −0.0646220 | + | 0.193109i | ||||
\(686\) | −265.116 | − | 555.909i | −0.386467 | − | 0.810363i | ||||
\(687\) | 122.467 | − | 426.863i | 0.178263 | − | 0.621343i | ||||
\(688\) | 83.7939 | + | 48.3784i | 0.121793 | + | 0.0703175i | ||||
\(689\) | −386.203 | + | 222.974i | −0.560527 | + | 0.323620i | ||||
\(690\) | −58.1225 | + | 736.787i | −0.0842355 | + | 1.06781i | ||||
\(691\) | −237.246 | + | 410.922i | −0.343337 | + | 0.594678i | −0.985050 | − | 0.172267i | \(-0.944891\pi\) |
0.641713 | + | 0.766945i | \(0.278224\pi\) | |||||||
\(692\) | 227.822 | 0.329223 | ||||||||
\(693\) | −53.1659 | − | 50.4834i | −0.0767185 | − | 0.0728476i | ||||
\(694\) | −276.599 | −0.398557 | ||||||||
\(695\) | −432.268 | − | 488.630i | −0.621968 | − | 0.703065i | ||||
\(696\) | 327.612 | + | 1314.78i | 0.470707 | + | 1.88906i | ||||
\(697\) | 277.715 | − | 160.339i | 0.398443 | − | 0.230041i | ||||
\(698\) | −18.1647 | + | 31.4621i | −0.0260239 | + | 0.0450747i | ||||
\(699\) | 333.604 | − | 1162.79i | 0.477259 | − | 1.66350i | ||||
\(700\) | −27.0545 | − | 133.045i | −0.0386493 | − | 0.190065i | ||||
\(701\) | − | 319.674i | − | 0.456025i | −0.973658 | − | 0.228013i | \(-0.926777\pi\) | ||
0.973658 | − | 0.228013i | \(-0.0732227\pi\) | |||||||
\(702\) | 591.873 | − | 125.541i | 0.843125 | − | 0.178834i | ||||
\(703\) | −10.8615 | + | 6.27091i | −0.0154503 | + | 0.00892021i | ||||
\(704\) | −71.6879 | + | 41.3890i | −0.101829 | + | 0.0587912i | ||||
\(705\) | −471.431 | + | 224.755i | −0.668696 | + | 0.318801i | ||||
\(706\) | 584.342 | 0.827679 | ||||||||
\(707\) | 49.6349 | + | 148.353i | 0.0702050 | + | 0.209834i | ||||
\(708\) | −83.5512 | − | 23.9709i | −0.118010 | − | 0.0338571i | ||||
\(709\) | 679.847 | − | 1177.53i | 0.958882 | − | 1.66083i | 0.233657 | − | 0.972319i | \(-0.424931\pi\) |
0.725225 | − | 0.688512i | \(-0.241736\pi\) | |||||||
\(710\) | 119.629 | + | 588.116i | 0.168491 | + | 0.828332i | ||||
\(711\) | −10.5388 | + | 299.338i | −0.0148225 | + | 0.421010i | ||||
\(712\) | 355.753 | + | 205.394i | 0.499653 | + | 0.288475i | ||||
\(713\) | −948.544 | −1.33036 | ||||||||
\(714\) | −30.5282 | − | 701.818i | −0.0427566 | − | 0.982939i | ||||
\(715\) | −23.0445 | + | 68.8634i | −0.0322300 | + | 0.0963124i | ||||
\(716\) | −164.027 | − | 94.7010i | −0.229088 | − | 0.132264i | ||||
\(717\) | −30.5493 | − | 122.601i | −0.0426071 | − | 0.170992i | ||||
\(718\) | 897.691 | − | 518.282i | 1.25027 | − | 0.721842i | ||||
\(719\) | −10.4725 | − | 6.04630i | −0.0145654 | − | 0.00840932i | 0.492700 | − | 0.870199i | \(-0.336010\pi\) |
−0.507265 | + | 0.861790i | \(0.669343\pi\) | |||||||
\(720\) | 427.030 | − | 351.782i | 0.593097 | − | 0.488586i | ||||
\(721\) | 68.8180 | − | 77.7816i | 0.0954480 | − | 0.107880i | ||||
\(722\) | −1011.93 | −1.40157 | ||||||||
\(723\) | 554.945 | + | 574.827i | 0.767559 | + | 0.795059i | ||||
\(724\) | 31.5630 | + | 54.6687i | 0.0435953 | + | 0.0755092i | ||||
\(725\) | 1306.90 | + | 160.575i | 1.80262 | + | 0.221482i | ||||
\(726\) | −447.646 | − | 463.684i | −0.616593 | − | 0.638683i | ||||
\(727\) | − | 806.023i | − | 1.10870i | −0.832284 | − | 0.554349i | \(-0.812967\pi\) | ||
0.832284 | − | 0.554349i | \(-0.187033\pi\) | |||||||
\(728\) | 734.105 | + | 149.370i | 1.00839 | + | 0.205178i | ||||
\(729\) | 76.8232 | − | 724.941i | 0.105382 | − | 0.994432i | ||||
\(730\) | 363.153 | − | 321.264i | 0.497469 | − | 0.440088i | ||||
\(731\) | −126.968 | + | 73.3053i | −0.173692 | + | 0.100281i | ||||
\(732\) | −114.914 | + | 28.6338i | −0.156986 | + | 0.0391172i | ||||
\(733\) | 229.808 | + | 132.680i | 0.313517 | + | 0.181009i | 0.648499 | − | 0.761215i | \(-0.275397\pi\) |
−0.334982 | + | 0.942224i | \(0.608730\pi\) | |||||||
\(734\) | 903.452i | 1.23086i | ||||||||
\(735\) | 394.778 | + | 619.980i | 0.537113 | + | 0.843510i | ||||
\(736\) | 335.464 | 0.455793 | ||||||||
\(737\) | −16.7827 | + | 29.0684i | −0.0227716 | + | 0.0394415i | ||||
\(738\) | −278.001 | − | 9.78760i | −0.376695 | − | 0.0132623i | ||||
\(739\) | 288.214 | + | 499.201i | 0.390005 | + | 0.675509i | 0.992450 | − | 0.122652i | \(-0.0391398\pi\) |
−0.602444 | + | 0.798161i | \(0.705807\pi\) | |||||||
\(740\) | −1.19838 | + | 1.06015i | −0.00161943 | + | 0.00143263i | ||||
\(741\) | −1094.27 | − | 313.946i | −1.47675 | − | 0.423679i | ||||
\(742\) | 89.5524 | − | 440.121i | 0.120691 | − | 0.593155i | ||||
\(743\) | −142.356 | −0.191596 | −0.0957979 | − | 0.995401i | \(-0.530540\pi\) | ||||
−0.0957979 | + | 0.995401i | \(0.530540\pi\) | |||||||
\(744\) | 617.668 | + | 639.797i | 0.830200 | + | 0.859943i | ||||
\(745\) | 158.271 | + | 778.090i | 0.212445 | + | 1.04442i | ||||
\(746\) | 333.498 | − | 192.545i | 0.447049 | − | 0.258104i | ||||
\(747\) | −572.805 | + | 304.356i | −0.766807 | + | 0.407437i | ||||
\(748\) | − | 16.8199i | − | 0.0224864i | ||||||
\(749\) | 178.205 | + | 157.668i | 0.237924 | + | 0.210505i | ||||
\(750\) | −213.488 | − | 638.610i | −0.284651 | − | 0.851481i | ||||
\(751\) | −39.6817 | + | 68.7308i | −0.0528385 | + | 0.0915190i | −0.891235 | − | 0.453542i | \(-0.850160\pi\) |
0.838396 | + | 0.545061i | \(0.183494\pi\) | |||||||
\(752\) | −214.039 | − | 370.726i | −0.284626 | − | 0.492987i | ||||
\(753\) | 309.653 | + | 1242.71i | 0.411226 | + | 1.65034i | ||||
\(754\) | −590.129 | + | 1022.13i | −0.782664 | + | 1.35561i | ||||
\(755\) | −76.2860 | + | 227.964i | −0.101041 | + | 0.301939i | ||||
\(756\) | 72.2611 | − | 127.588i | 0.0955834 | − | 0.168767i | ||||
\(757\) | 1310.05i | 1.73058i | 0.501268 | + | 0.865292i | \(0.332867\pi\) | ||||
−0.501268 | + | 0.865292i | \(0.667133\pi\) | |||||||
\(758\) | −453.714 | + | 785.855i | −0.598567 | + | 1.03675i | ||||
\(759\) | −23.1628 | − | 92.9576i | −0.0305176 | − | 0.122474i | ||||
\(760\) | −1277.59 | + | 259.875i | −1.68104 | + | 0.341941i | ||||
\(761\) | −363.973 | − | 210.140i | −0.478283 | − | 0.276137i | 0.241418 | − | 0.970421i | \(-0.422388\pi\) |
−0.719701 | + | 0.694284i | \(0.755721\pi\) | |||||||
\(762\) | 2.97029 | + | 0.852177i | 0.00389802 | + | 0.00111834i | ||||
\(763\) | −601.637 | + | 201.292i | −0.788515 | + | 0.263817i | ||||
\(764\) | 185.780i | 0.243167i | ||||||||
\(765\) | 138.095 | + | 826.885i | 0.180517 | + | 1.08090i | ||||
\(766\) | −363.481 | − | 629.568i | −0.474519 | − | 0.821891i | ||||
\(767\) | −233.039 | − | 403.636i | −0.303832 | − | 0.526252i | ||||
\(768\) | −297.946 | − | 308.621i | −0.387951 | − | 0.401850i | ||||
\(769\) | −564.796 | −0.734455 | −0.367227 | − | 0.930131i | \(-0.619693\pi\) | ||||
−0.367227 | + | 0.930131i | \(0.619693\pi\) | |||||||
\(770\) | −36.5645 | − | 63.3402i | −0.0474863 | − | 0.0822600i | ||||
\(771\) | 13.8250 | − | 48.1876i | 0.0179313 | − | 0.0625002i | ||||
\(772\) | −1.07927 | − | 0.623118i | −0.00139802 | − | 0.000807147i | ||||
\(773\) | −279.388 | − | 483.914i | −0.361433 | − | 0.626021i | 0.626764 | − | 0.779209i | \(-0.284379\pi\) |
−0.988197 | + | 0.153189i | \(0.951046\pi\) | |||||||
\(774\) | 127.099 | + | 4.47479i | 0.164211 | + | 0.00578139i | ||||
\(775\) | 795.519 | − | 337.602i | 1.02648 | − | 0.435615i | ||||
\(776\) | 572.395i | 0.737623i | ||||||||
\(777\) | 4.00085 | − | 7.68253i | 0.00514910 | − | 0.00988742i | ||||
\(778\) | 350.008i | 0.449882i | ||||||||
\(779\) | 453.274 | + | 261.698i | 0.581867 | + | 0.335941i | ||||
\(780\) | −144.782 | − | 11.4214i | −0.185618 | − | 0.0146428i | ||||
\(781\) | −38.8967 | − | 67.3711i | −0.0498037 | − | 0.0862626i | ||||
\(782\) | 458.959 | − | 794.940i | 0.586904 | − | 1.01655i | ||||
\(783\) | 951.093 | + | 1057.21i | 1.21468 | + | 1.35020i | ||||
\(784\) | −481.149 | + | 362.543i | −0.613711 | + | 0.462428i | ||||
\(785\) | −617.851 | − | 206.758i | −0.787072 | − | 0.263386i | ||||
\(786\) | 893.569 | − | 862.663i | 1.13686 | − | 1.09754i | ||||
\(787\) | 1010.07 | − | 583.163i | 1.28344 | − | 0.740995i | 0.305965 | − | 0.952043i | \(-0.401021\pi\) |
0.977476 | + | 0.211047i | \(0.0676875\pi\) | |||||||
\(788\) | −111.068 | − | 192.376i | −0.140949 | − | 0.244131i | ||||
\(789\) | −3.15190 | − | 3.26482i | −0.00399481 | − | 0.00413793i | ||||
\(790\) | −94.8194 | + | 283.347i | −0.120024 | + | 0.358667i | ||||
\(791\) | 106.431 | − | 523.072i | 0.134552 | − | 0.661280i | ||||
\(792\) | −47.6173 | + | 76.1551i | −0.0601229 | + | 0.0961555i | ||||
\(793\) | −549.938 | − | 317.507i | −0.693491 | − | 0.400387i | ||||
\(794\) | −898.107 | + | 518.522i | −1.13112 | + | 0.653051i | ||||
\(795\) | −42.1522 | + | 534.340i | −0.0530216 | + | 0.672126i | ||||
\(796\) | 34.6241 | − | 59.9708i | 0.0434977 | − | 0.0753402i | ||||
\(797\) | 290.985 | 0.365100 | 0.182550 | − | 0.983197i | \(-0.441565\pi\) | ||||
0.182550 | + | 0.983197i | \(0.441565\pi\) | |||||||
\(798\) | 967.099 | − | 615.890i | 1.21190 | − | 0.771792i | ||||
\(799\) | 648.644 | 0.811820 | ||||||||
\(800\) | −281.345 | + | 119.397i | −0.351681 | + | 0.149246i | ||||
\(801\) | 430.857 | + | 15.1692i | 0.537899 | + | 0.0189379i | ||||
\(802\) | −357.805 | + | 206.579i | −0.446141 | + | 0.257579i | ||||
\(803\) | −31.4242 | + | 54.4283i | −0.0391335 | + | 0.0677812i | ||||
\(804\) | −64.5267 | − | 18.5127i | −0.0802571 | − | 0.0230258i | ||||
\(805\) | −0.0571697 | + | 960.409i | −7.10182e−5 | + | 1.19305i | ||||
\(806\) | 774.624i | 0.961072i | ||||||||
\(807\) | 26.3899 | − | 25.4771i | 0.0327012 | − | 0.0315702i | ||||
\(808\) | 165.969 | − | 95.8220i | 0.205407 | − | 0.118592i | ||||
\(809\) | 201.885 | − | 116.559i | 0.249549 | − | 0.144077i | −0.370009 | − | 0.929028i | \(-0.620645\pi\) |
0.619558 | + | 0.784951i | \(0.287312\pi\) | |||||||
\(810\) | 278.706 | − | 671.691i | 0.344081 | − | 0.829249i | ||||
\(811\) | 704.253 | 0.868377 | 0.434188 | − | 0.900822i | \(-0.357035\pi\) | ||||
0.434188 | + | 0.900822i | \(0.357035\pi\) | |||||||
\(812\) | 90.7539 | + | 271.252i | 0.111766 | + | 0.334054i | ||||
\(813\) | 194.102 | − | 676.550i | 0.238748 | − | 0.832165i | ||||
\(814\) | −0.430952 | + | 0.746430i | −0.000529425 | + | 0.000916990i | ||||
\(815\) | −139.389 | − | 685.259i | −0.171029 | − | 0.840808i | ||||
\(816\) | −666.760 | + | 166.141i | −0.817108 | + | 0.203604i | ||||
\(817\) | −207.232 | − | 119.646i | −0.253651 | − | 0.146445i | ||||
\(818\) | 1043.17 | 1.27527 | ||||||||
\(819\) | 753.925 | − | 223.073i | 0.920543 | − | 0.272372i | ||||
\(820\) | 63.3204 | + | 21.1896i | 0.0772199 | + | 0.0258409i | ||||
\(821\) | 681.324 | + | 393.363i | 0.829871 | + | 0.479126i | 0.853808 | − | 0.520587i | \(-0.174287\pi\) |
−0.0239375 | + | 0.999713i | \(0.507620\pi\) | |||||||
\(822\) | −145.822 | + | 36.3353i | −0.177399 | + | 0.0442036i | ||||
\(823\) | −1214.48 | + | 701.183i | −1.47568 | + | 0.851984i | −0.999624 | − | 0.0274304i | \(-0.991268\pi\) |
−0.476056 | + | 0.879415i | \(0.657934\pi\) | |||||||
\(824\) | −110.184 | − | 63.6147i | −0.133718 | − | 0.0772023i | ||||
\(825\) | 52.5111 | + | 69.7171i | 0.0636499 | + | 0.0845056i | ||||
\(826\) | 459.988 | + | 93.5946i | 0.556886 | + | 0.113311i | ||||
\(827\) | −413.959 | −0.500555 | −0.250277 | − | 0.968174i | \(-0.580522\pi\) | ||||
−0.250277 | + | 0.968174i | \(0.580522\pi\) | |||||||
\(828\) | 169.197 | − | 89.9014i | 0.204344 | − | 0.108577i | ||||
\(829\) | 298.625 | + | 517.233i | 0.360223 | + | 0.623924i | 0.987997 | − | 0.154471i | \(-0.0493674\pi\) |
−0.627775 | + | 0.778395i | \(0.716034\pi\) | |||||||
\(830\) | −634.073 | + | 128.977i | −0.763943 | + | 0.155394i | ||||
\(831\) | 1066.49 | − | 1029.60i | 1.28338 | − | 1.23899i | ||||
\(832\) | − | 887.708i | − | 1.06696i | ||||||
\(833\) | −111.215 | − | 906.056i | −0.133511 | − | 1.08770i | ||||
\(834\) | 193.831 | − | 675.605i | 0.232412 | − | 0.810078i | ||||
\(835\) | 743.490 | + | 840.432i | 0.890407 | + | 1.00650i | ||||
\(836\) | 23.7747 | − | 13.7263i | 0.0284386 | − | 0.0164191i | ||||
\(837\) | 887.522 | + | 288.794i | 1.06036 | + | 0.345035i | ||||
\(838\) | −343.372 | − | 198.246i | −0.409752 | − | 0.236570i | ||||
\(839\) | 534.770i | 0.637389i | 0.947857 | + | 0.318695i | \(0.103244\pi\) | ||||
−0.947857 | + | 0.318695i | \(0.896756\pi\) | |||||||
\(840\) | 647.837 | − | 625.356i | 0.771235 | − | 0.744471i | ||||
\(841\) | −1933.03 | −2.29849 | ||||||||
\(842\) | −671.421 | + | 1162.94i | −0.797413 | + | 1.38116i | ||||
\(843\) | −48.6409 | − | 195.207i | −0.0576998 | − | 0.231562i | ||||
\(844\) | 67.5758 | + | 117.045i | 0.0800661 | + | 0.138679i | ||||
\(845\) | 43.9029 | + | 49.6272i | 0.0519561 | + | 0.0587305i | ||||
\(846\) | −477.085 | − | 298.305i | −0.563930 | − | 0.352607i | ||||
\(847\) | −627.255 | − | 554.969i | −0.740561 | − | 0.655218i | ||||
\(848\) | −439.335 | −0.518084 | ||||||||
\(849\) | 295.402 | − | 285.185i | 0.347941 | − | 0.335907i | ||||
\(850\) | −101.985 | + | 830.046i | −0.119983 | + | 0.976525i | ||||
\(851\) | 9.80192 | − | 5.65914i | 0.0115181 | − | 0.00664999i | ||||
\(852\) | 111.934 | − | 108.063i | 0.131378 | − | 0.126834i | ||||
\(853\) | − | 1067.16i | − | 1.25107i | −0.780197 | − | 0.625534i | \(-0.784881\pi\) | ||
0.780197 | − | 0.625534i | \(-0.215119\pi\) | |||||||
\(854\) | 606.511 | − | 202.923i | 0.710201 | − | 0.237615i | ||||
\(855\) | −1056.10 | + | 869.999i | −1.23520 | + | 1.01754i | ||||
\(856\) | 145.747 | − | 252.441i | 0.170265 | − | 0.294908i | ||||
\(857\) | −666.543 | − | 1154.49i | −0.777763 | − | 1.34713i | −0.933228 | − | 0.359284i | \(-0.883021\pi\) |
0.155465 | − | 0.987841i | \(-0.450312\pi\) | |||||||
\(858\) | −75.9134 | + | 18.9158i | −0.0884771 | + | 0.0220464i | ||||
\(859\) | 106.833 | − | 185.040i | 0.124369 | − | 0.215414i | −0.797117 | − | 0.603825i | \(-0.793643\pi\) |
0.921486 | + | 0.388411i | \(0.126976\pi\) | |||||||
\(860\) | −28.9494 | − | 9.68765i | −0.0336621 | − | 0.0112647i | ||||
\(861\) | −361.136 | + | 15.7090i | −0.419438 | + | 0.0182450i | ||||
\(862\) | 642.986i | 0.745923i | ||||||||
\(863\) | 654.750 | − | 1134.06i | 0.758690 | − | 1.31409i | −0.184829 | − | 0.982771i | \(-0.559173\pi\) |
0.943519 | − | 0.331319i | \(-0.107494\pi\) | |||||||
\(864\) | −313.882 | − | 102.135i | −0.363290 | − | 0.118212i | ||||
\(865\) | 1438.81 | − | 292.668i | 1.66336 | − | 0.338344i | ||||
\(866\) | 968.398 | + | 559.105i | 1.11824 | + | 0.645618i | ||||
\(867\) | 48.0395 | − | 167.443i | 0.0554088 | − | 0.193129i | ||||
\(868\) | 140.597 | + | 124.395i | 0.161978 | + | 0.143312i | ||||
\(869\) | − | 38.7297i | − | 0.0445682i | ||||||
\(870\) | 610.483 | + | 1280.51i | 0.701705 | + | 1.47185i | ||||
\(871\) | −179.976 | − | 311.728i | −0.206632 | − | 0.357897i | ||||
\(872\) | 388.602 | + | 673.078i | 0.445644 | + | 0.771878i | ||||
\(873\) | 281.875 | + | 530.496i | 0.322881 | + | 0.607670i | ||||
\(874\) | 1498.19 | 1.71417 | ||||||||
\(875\) | −341.776 | − | 805.490i | −0.390602 | − | 0.920560i | ||||
\(876\) | −120.821 | − | 34.6636i | −0.137924 | − | 0.0395703i | ||||
\(877\) | 953.678 | + | 550.606i | 1.08743 | + | 0.627829i | 0.932892 | − | 0.360157i | \(-0.117277\pi\) |
0.154541 | + | 0.987986i | \(0.450610\pi\) | |||||||
\(878\) | −349.084 | − | 604.631i | −0.397590 | − | 0.688646i | ||||
\(879\) | 288.071 | − | 71.7805i | 0.327726 | − | 0.0816616i | ||||
\(880\) | −53.5822 | + | 47.4017i | −0.0608889 | + | 0.0538655i | ||||
\(881\) | 295.122i | 0.334985i | 0.985873 | + | 0.167492i | \(0.0535670\pi\) | ||||
−0.985873 | + | 0.167492i | \(0.946433\pi\) | |||||||
\(882\) | −334.887 | + | 717.560i | −0.379690 | + | 0.813560i | ||||
\(883\) | − | 1192.92i | − | 1.35098i | −0.737368 | − | 0.675491i | \(-0.763932\pi\) | ||
0.737368 | − | 0.675491i | \(-0.236068\pi\) | |||||||
\(884\) | 156.210 | + | 90.1878i | 0.176708 | + | 0.102022i | ||||
\(885\) | −558.459 | − | 44.0549i | −0.631028 | − | 0.0497795i | ||||
\(886\) | −344.958 | − | 597.486i | −0.389344 | − | 0.674363i | ||||
\(887\) | −530.626 | + | 919.071i | −0.598225 | + | 1.03616i | 0.394858 | + | 0.918742i | \(0.370794\pi\) |
−0.993083 | + | 0.117414i | \(0.962539\pi\) | |||||||
\(888\) | −10.1999 | − | 2.92635i | −0.0114864 | − | 0.00329544i | ||||
\(889\) | 3.93490 | + | 0.800642i | 0.00442621 | + | 0.000900609i | ||||
\(890\) | 407.841 | + | 136.480i | 0.458248 | + | 0.153348i | ||||
\(891\) | −6.62924 | + | 94.0296i | −0.00744022 | + | 0.105533i | ||||
\(892\) | 100.242 | − | 57.8746i | 0.112379 | − | 0.0648818i | ||||
\(893\) | 529.344 | + | 916.852i | 0.592771 | + | 1.02671i | ||||
\(894\) | −615.444 | + | 594.157i | −0.688416 | + | 0.664605i | ||||
\(895\) | −1157.56 | − | 387.368i | −1.29337 | − | 0.432813i | ||||
\(896\) | 413.232 | + | 365.610i | 0.461196 | + | 0.408047i | ||||
\(897\) | 987.517 | + | 283.319i | 1.10091 | + | 0.315851i | ||||
\(898\) | −52.8221 | − | 30.4969i | −0.0588219 | − | 0.0339609i | ||||
\(899\) | −1576.72 | + | 910.322i | −1.75386 | + | 1.01259i | ||||
\(900\) | −109.903 | + | 135.618i | −0.122115 | + | 0.150686i | ||||
\(901\) | 332.851 | − | 576.515i | 0.369424 | − | 0.639861i | ||||
\(902\) | 35.9690 | 0.0398770 | ||||||||
\(903\) | 165.108 | − | 7.18198i | 0.182844 | − | 0.00795347i | ||||
\(904\) | −653.928 | −0.723372 | ||||||||
\(905\) | 269.564 | + | 304.712i | 0.297861 | + | 0.336698i | ||||
\(906\) | −251.302 | + | 62.6185i | −0.277375 | + | 0.0691153i | ||||
\(907\) | 58.1760 | − | 33.5879i | 0.0641411 | − | 0.0370319i | −0.467586 | − | 0.883947i | \(-0.654876\pi\) |
0.531728 | + | 0.846915i | \(0.321543\pi\) | |||||||
\(908\) | 35.7869 | − | 61.9847i | 0.0394129 | − | 0.0682651i | ||||
\(909\) | 106.632 | − | 170.539i | 0.117307 | − | 0.187611i | ||||
\(910\) | 784.313 | + | 0.0466873i | 0.861882 | + | 5.13047e-5i | ||||
\(911\) | − | 184.755i | − | 0.202805i | −0.994845 | − | 0.101402i | \(-0.967667\pi\) | ||
0.994845 | − | 0.101402i | \(-0.0323330\pi\) | |||||||
\(912\) | −778.966 | − | 806.874i | −0.854130 | − | 0.884731i | ||||
\(913\) | 72.6357 | − | 41.9362i | 0.0795571 | − | 0.0459323i | ||||
\(914\) | 776.053 | − | 448.054i | 0.849073 | − | 0.490212i | ||||
\(915\) | −688.953 | + | 328.458i | −0.752954 | + | 0.358971i | ||||
\(916\) | −114.843 | −0.125374 | ||||||||
\(917\) | 1069.49 | − | 1208.79i | 1.16629 | − | 1.31820i | ||||
\(918\) | −671.461 | + | 604.065i | −0.731439 | + | 0.658023i | ||||
\(919\) | −366.654 | + | 635.064i | −0.398971 | + | 0.691038i | −0.993599 | − | 0.112963i | \(-0.963966\pi\) |
0.594628 | + | 0.804001i | \(0.297299\pi\) | |||||||
\(920\) | 1152.95 | − | 234.522i | 1.25321 | − | 0.254916i | ||||
\(921\) | −320.118 | − | 1284.71i | −0.347577 | − | 1.39490i | ||||
\(922\) | 1269.67 | + | 733.047i | 1.37709 | + | 0.795062i | ||||
\(923\) | 834.254 | 0.903850 | ||||||||
\(924\) | −8.75742 | + | 16.8162i | −0.00947773 | + | 0.0181994i | ||||
\(925\) | −6.20644 | + | 8.23483i | −0.00670966 | + | 0.00890252i | ||||
\(926\) | −550.252 | − | 317.688i | −0.594224 | − | 0.343076i | ||||
\(927\) | −133.445 | − | 4.69823i | −0.143954 | − | 0.00506820i | ||||
\(928\) | 557.627 | − | 321.946i | 0.600891 | − | 0.346925i | ||||
\(929\) | 738.216 | + | 426.209i | 0.794635 | + | 0.458783i | 0.841592 | − | 0.540114i | \(-0.181619\pi\) |
−0.0469566 | + | 0.998897i | \(0.514952\pi\) | |||||||
\(930\) | 767.202 | + | 527.491i | 0.824948 | + | 0.567194i | ||||
\(931\) | 1189.94 | − | 896.613i | 1.27813 | − | 0.963065i | ||||
\(932\) | −312.835 | −0.335660 | ||||||||
\(933\) | 48.4435 | − | 46.7680i | 0.0519223 | − | 0.0501265i | ||||
\(934\) | 228.143 | + | 395.155i | 0.244264 | + | 0.423078i | ||||
\(935\) | −21.6073 | − | 106.225i | −0.0231094 | − | 0.113610i | ||||
\(936\) | −451.947 | − | 850.575i | −0.482849 | − | 0.908733i | ||||
\(937\) | 962.292i | 1.02699i | 0.858092 | + | 0.513496i | \(0.171650\pi\) | ||||
−0.858092 | + | 0.513496i | \(0.828350\pi\) | |||||||
\(938\) | 355.249 | + | 72.2833i | 0.378731 | + | 0.0770611i | ||||
\(939\) | −724.246 | − | 207.786i | −0.771295 | − | 0.221285i | ||||
\(940\) | 89.4901 | + | 101.158i | 0.0952023 | + | 0.107615i | ||||
\(941\) | −1201.16 | + | 693.492i | −1.27648 | + | 0.736974i | −0.976199 | − | 0.216879i | \(-0.930412\pi\) |
−0.300277 | + | 0.953852i | \(0.597079\pi\) | |||||||
\(942\) | −169.715 | − | 681.104i | −0.180165 | − | 0.723041i | ||||
\(943\) | −409.054 | − | 236.168i | −0.433780 | − | 0.250443i | ||||
\(944\) | − | 459.166i | − | 0.486405i | ||||||
\(945\) | 292.460 | − | 898.606i | 0.309482 | − | 0.950905i | ||||
\(946\) | −16.4447 | −0.0173834 | ||||||||
\(947\) | −538.877 | + | 933.363i | −0.569036 | + | 0.985599i | 0.427626 | + | 0.903956i | \(0.359350\pi\) |
−0.996662 | + | 0.0816434i | \(0.973983\pi\) | |||||||
\(948\) | 75.1604 | − | 18.7282i | 0.0792831 | − | 0.0197555i | ||||
\(949\) | −336.992 | − | 583.687i | −0.355102 | − | 0.615054i | ||||
\(950\) | −1256.49 | + | 533.228i | −1.32262 | + | 0.561292i | ||||
\(951\) | −28.8730 | + | 100.638i | −0.0303607 | + | 0.105823i | ||||
\(952\) | −1060.53 | + | 354.824i | −1.11400 | + | 0.372715i | ||||
\(953\) | 522.489 | 0.548257 | 0.274129 | − | 0.961693i | \(-0.411611\pi\) | ||||
0.274129 | + | 0.961693i | \(0.411611\pi\) | |||||||
\(954\) | −509.949 | + | 270.958i | −0.534538 | + | 0.284023i | ||||
\(955\) | 238.659 | + | 1173.29i | 0.249904 | + | 1.22857i | ||||
\(956\) | −28.2973 | + | 16.3375i | −0.0295997 | + | 0.0170894i | ||||
\(957\) | −127.714 | − | 132.290i | −0.133453 | − | 0.138234i | ||||
\(958\) | − | 457.517i | − | 0.477576i | ||||||
\(959\) | −185.195 | + | 61.9615i | −0.193113 | + | 0.0646105i | ||||
\(960\) | −879.203 | − | 604.497i | −0.915836 | − | 0.629684i | ||||
\(961\) | −116.961 | + | 202.582i | −0.121707 | + | 0.210803i | ||||
\(962\) | −4.62151 | − | 8.00468i | −0.00480406 | − | 0.00832088i | ||||
\(963\) | 10.7641 | − | 305.735i | 0.0111776 | − | 0.317482i | ||||
\(964\) | 103.312 | − | 178.942i | 0.107170 | − | 0.185625i | ||||
\(965\) | −7.61659 | − | 2.54882i | −0.00789284 | − | 0.00264126i | ||||
\(966\) | −872.752 | + | 555.806i | −0.903470 | + | 0.575368i | ||||
\(967\) | 1319.89i | 1.36493i | 0.730919 | + | 0.682465i | \(0.239092\pi\) | ||||
−0.730919 | + | 0.682465i | \(0.760908\pi\) | |||||||
\(968\) | −513.009 | + | 888.557i | −0.529968 | + | 0.917931i | ||||
\(969\) | 1648.98 | − | 410.886i | 1.70173 | − | 0.424031i | ||||
\(970\) | 119.450 | + | 587.238i | 0.123145 | + | 0.605400i | ||||
\(971\) | −1471.76 | − | 849.722i | −1.51572 | − | 0.875100i | −0.999830 | − | 0.0184437i | \(-0.994129\pi\) |
−0.515888 | − | 0.856656i | \(-0.672538\pi\) | |||||||
\(972\) | −185.683 | + | 32.6041i | −0.191032 | + | 0.0335433i | ||||
\(973\) | 182.109 | − | 895.009i | 0.187163 | − | 0.919845i | ||||
\(974\) | 300.266i | 0.308281i | ||||||||
\(975\) | −929.042 | + | 113.861i | −0.952863 | + | 0.116780i | ||||
\(976\) | −312.798 | − | 541.783i | −0.320490 | − | 0.555105i | ||||
\(977\) | −0.666368 | − | 1.15418i | −0.000682055 | − | 0.00118135i | 0.865684 | − | 0.500591i | \(-0.166884\pi\) |
−0.866366 | + | 0.499409i | \(0.833550\pi\) | |||||||
\(978\) | 542.018 | − | 523.270i | 0.554210 | − | 0.535041i | ||||
\(979\) | −55.7463 | −0.0569421 | ||||||||
\(980\) | 125.959 | − | 142.348i | 0.128530 | − | 0.145253i | ||||
\(981\) | 691.612 | + | 432.442i | 0.705007 | + | 0.440818i | ||||
\(982\) | −1030.99 | − | 595.242i | −1.04989 | − | 0.606153i | ||||
\(983\) | −169.240 | − | 293.133i | −0.172167 | − | 0.298202i | 0.767010 | − | 0.641635i | \(-0.221744\pi\) |
−0.939177 | + | 0.343433i | \(0.888410\pi\) | |||||||
\(984\) | 107.070 | + | 429.696i | 0.108811 | + | 0.436683i | ||||
\(985\) | −948.579 | − | 1072.26i | −0.963025 | − | 1.08859i | ||||
\(986\) | − | 1761.86i | − | 1.78688i | ||||||
\(987\) | −648.503 | − | 337.723i | −0.657045 | − | 0.342171i | ||||
\(988\) | 294.401i | 0.297977i | ||||||||
\(989\) | 187.016 | + | 107.974i | 0.189096 | + | 0.109174i | ||||
\(990\) | −32.9597 | + | 88.0670i | −0.0332926 | + | 0.0889565i | ||||
\(991\) | 82.0512 | + | 142.117i | 0.0827963 | + | 0.143407i | 0.904450 | − | 0.426580i | \(-0.140282\pi\) |
−0.821654 | + | 0.569987i | \(0.806948\pi\) | |||||||
\(992\) | 211.299 | − | 365.980i | 0.213003 | − | 0.368932i | ||||
\(993\) | −225.049 | + | 784.417i | −0.226636 | + | 0.789947i | ||||
\(994\) | −556.761 | + | 629.279i | −0.560121 | + | 0.633078i | ||||
\(995\) | 141.628 | − | 423.223i | 0.142339 | − | 0.425350i | ||||
\(996\) | 116.507 | + | 120.681i | 0.116975 | + | 0.121166i | ||||
\(997\) | 34.3128 | − | 19.8105i | 0.0344161 | − | 0.0198701i | −0.482693 | − | 0.875789i | \(-0.660341\pi\) |
0.517109 | + | 0.855919i | \(0.327008\pi\) | |||||||
\(998\) | −383.588 | − | 664.394i | −0.384357 | − | 0.665725i | ||||
\(999\) | −10.8943 | + | 2.31078i | −0.0109052 | + | 0.00231309i |
(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.o.b.44.13 | yes | 40 | |
3.2 | odd | 2 | inner | 105.3.o.b.44.7 | ✓ | 40 | |
5.4 | even | 2 | inner | 105.3.o.b.44.8 | yes | 40 | |
7.4 | even | 3 | inner | 105.3.o.b.74.14 | yes | 40 | |
15.14 | odd | 2 | inner | 105.3.o.b.44.14 | yes | 40 | |
21.11 | odd | 6 | inner | 105.3.o.b.74.8 | yes | 40 | |
35.4 | even | 6 | inner | 105.3.o.b.74.7 | yes | 40 | |
105.74 | odd | 6 | inner | 105.3.o.b.74.13 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.o.b.44.7 | ✓ | 40 | 3.2 | odd | 2 | inner | |
105.3.o.b.44.8 | yes | 40 | 5.4 | even | 2 | inner | |
105.3.o.b.44.13 | yes | 40 | 1.1 | even | 1 | trivial | |
105.3.o.b.44.14 | yes | 40 | 15.14 | odd | 2 | inner | |
105.3.o.b.74.7 | yes | 40 | 35.4 | even | 6 | inner | |
105.3.o.b.74.8 | yes | 40 | 21.11 | odd | 6 | inner | |
105.3.o.b.74.13 | yes | 40 | 105.74 | odd | 6 | inner | |
105.3.o.b.74.14 | yes | 40 | 7.4 | even | 3 | inner |