Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,3,Mod(26,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.26");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.h (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: | \(0.953680925261\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 19 x^{10} - 26 x^{9} + 244 x^{8} - 338 x^{7} + 1249 x^{6} - 986 x^{5} + 3532 x^{4} + \cdots + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Root | \(1.18241 + 2.04800i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.26 |
Dual form | 35.3.h.a.31.2 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18241 | + | 2.04800i | −0.591207 | + | 1.02400i | 0.402864 | + | 0.915260i | \(0.368015\pi\) |
−0.994070 | + | 0.108740i | \(0.965318\pi\) | |||||||
\(3\) | 4.45439 | − | 2.57174i | 1.48480 | − | 0.857247i | 0.484946 | − | 0.874544i | \(-0.338839\pi\) |
0.999850 | + | 0.0172969i | \(0.00550606\pi\) | |||||||
\(4\) | −0.796202 | − | 1.37906i | −0.199051 | − | 0.344766i | ||||
\(5\) | −1.93649 | − | 1.11803i | −0.387298 | − | 0.223607i | ||||
\(6\) | 12.1634i | 2.02724i | ||||||||
\(7\) | −1.42520 | + | 6.85338i | −0.203600 | + | 0.979054i | ||||
\(8\) | −5.69355 | −0.711693 | ||||||||
\(9\) | 8.72772 | − | 15.1168i | 0.969746 | − | 1.67965i | ||||
\(10\) | 4.57947 | − | 2.64396i | 0.457947 | − | 0.264396i | ||||
\(11\) | −6.86467 | − | 11.8900i | −0.624061 | − | 1.08091i | −0.988722 | − | 0.149765i | \(-0.952148\pi\) |
0.364661 | − | 0.931140i | \(-0.381185\pi\) | |||||||
\(12\) | −7.09319 | − | 4.09525i | −0.591099 | − | 0.341271i | ||||
\(13\) | 6.14666i | 0.472820i | 0.971653 | + | 0.236410i | \(0.0759708\pi\) | ||||
−0.971653 | + | 0.236410i | \(0.924029\pi\) | |||||||
\(14\) | −12.3505 | − | 11.0223i | −0.882181 | − | 0.787310i | ||||
\(15\) | −11.5012 | −0.766745 | ||||||||
\(16\) | 9.91693 | − | 17.1766i | 0.619808 | − | 1.07354i | ||||
\(17\) | −1.74292 | + | 1.00628i | −0.102525 | + | 0.0591927i | −0.550386 | − | 0.834911i | \(-0.685519\pi\) |
0.447861 | + | 0.894103i | \(0.352186\pi\) | |||||||
\(18\) | 20.6395 | + | 35.7487i | 1.14664 | + | 1.98604i | ||||
\(19\) | −2.08213 | − | 1.20212i | −0.109586 | − | 0.0632692i | 0.444205 | − | 0.895925i | \(-0.353486\pi\) |
−0.553791 | + | 0.832656i | \(0.686819\pi\) | |||||||
\(20\) | 3.56072i | 0.178036i | ||||||||
\(21\) | 11.2767 | + | 34.1929i | 0.536987 | + | 1.62823i | ||||
\(22\) | 32.4675 | 1.47580 | ||||||||
\(23\) | −8.02550 | + | 13.9006i | −0.348935 | + | 0.604373i | −0.986061 | − | 0.166387i | \(-0.946790\pi\) |
0.637126 | + | 0.770760i | \(0.280123\pi\) | |||||||
\(24\) | −25.3613 | + | 14.6423i | −1.05672 | + | 0.610097i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | −12.5884 | − | 7.26789i | −0.484167 | − | 0.279534i | ||||
\(27\) | − | 43.4904i | − | 1.61075i | ||||||
\(28\) | 10.5860 | − | 3.49123i | 0.378071 | − | 0.124687i | ||||
\(29\) | 15.9780 | 0.550966 | 0.275483 | − | 0.961306i | \(-0.411162\pi\) | ||||
0.275483 | + | 0.961306i | \(0.411162\pi\) | |||||||
\(30\) | 13.5991 | − | 23.5544i | 0.453305 | − | 0.785147i | ||||
\(31\) | 17.9557 | − | 10.3667i | 0.579217 | − | 0.334411i | −0.181605 | − | 0.983371i | \(-0.558129\pi\) |
0.760822 | + | 0.648961i | \(0.224796\pi\) | |||||||
\(32\) | 12.0647 | + | 20.8967i | 0.377023 | + | 0.653023i | ||||
\(33\) | −61.1558 | − | 35.3083i | −1.85321 | − | 1.06995i | ||||
\(34\) | − | 4.75934i | − | 0.139981i | ||||||
\(35\) | 10.4222 | − | 11.6781i | 0.297777 | − | 0.333660i | ||||
\(36\) | −27.7961 | −0.772114 | ||||||||
\(37\) | −6.51335 | + | 11.2814i | −0.176036 | + | 0.304904i | −0.940519 | − | 0.339740i | \(-0.889661\pi\) |
0.764483 | + | 0.644644i | \(0.222994\pi\) | |||||||
\(38\) | 4.92387 | − | 2.84279i | 0.129575 | − | 0.0748104i | ||||
\(39\) | 15.8076 | + | 27.3796i | 0.405323 | + | 0.702041i | ||||
\(40\) | 11.0255 | + | 6.36558i | 0.275638 | + | 0.159139i | ||||
\(41\) | 55.2974i | 1.34872i | 0.738404 | + | 0.674358i | \(0.235580\pi\) | ||||
−0.738404 | + | 0.674358i | \(0.764420\pi\) | |||||||
\(42\) | −83.3607 | − | 17.3354i | −1.98478 | − | 0.412747i | ||||
\(43\) | 54.7172 | 1.27249 | 0.636246 | − | 0.771486i | \(-0.280486\pi\) | ||||
0.636246 | + | 0.771486i | \(0.280486\pi\) | |||||||
\(44\) | −10.9313 | + | 18.9336i | −0.248439 | + | 0.430310i | ||||
\(45\) | −33.8023 | + | 19.5158i | −0.751162 | + | 0.433684i | ||||
\(46\) | −18.9789 | − | 32.8724i | −0.412585 | − | 0.714618i | ||||
\(47\) | 61.9889 | + | 35.7893i | 1.31891 | + | 0.761475i | 0.983554 | − | 0.180615i | \(-0.0578089\pi\) |
0.335359 | + | 0.942090i | \(0.391142\pi\) | |||||||
\(48\) | − | 102.015i | − | 2.12532i | ||||||
\(49\) | −44.9376 | − | 19.5349i | −0.917094 | − | 0.398671i | ||||
\(50\) | −11.8241 | −0.236483 | ||||||||
\(51\) | −5.17577 | + | 8.96469i | −0.101486 | + | 0.175778i | ||||
\(52\) | 8.47662 | − | 4.89398i | 0.163012 | − | 0.0941150i | ||||
\(53\) | −33.6897 | − | 58.3523i | −0.635655 | − | 1.10099i | −0.986376 | − | 0.164507i | \(-0.947397\pi\) |
0.350721 | − | 0.936480i | \(-0.385937\pi\) | |||||||
\(54\) | 89.0683 | + | 51.4236i | 1.64941 | + | 0.952289i | ||||
\(55\) | 30.6997i | 0.558177i | ||||||||
\(56\) | 8.11445 | − | 39.0200i | 0.144901 | − | 0.696786i | ||||
\(57\) | −12.3661 | −0.216950 | ||||||||
\(58\) | −18.8926 | + | 32.7230i | −0.325735 | + | 0.564189i | ||||
\(59\) | 18.2612 | − | 10.5431i | 0.309511 | − | 0.178696i | −0.337196 | − | 0.941434i | \(-0.609479\pi\) |
0.646708 | + | 0.762738i | \(0.276145\pi\) | |||||||
\(60\) | 9.15727 | + | 15.8608i | 0.152621 | + | 0.264347i | ||||
\(61\) | −22.8803 | − | 13.2100i | −0.375088 | − | 0.216557i | 0.300591 | − | 0.953753i | \(-0.402816\pi\) |
−0.675679 | + | 0.737196i | \(0.736149\pi\) | |||||||
\(62\) | 49.0311i | 0.790824i | ||||||||
\(63\) | 91.1627 | + | 81.3589i | 1.44703 | + | 1.29141i | ||||
\(64\) | 22.2735 | 0.348023 | ||||||||
\(65\) | 6.87217 | − | 11.9029i | 0.105726 | − | 0.183122i | ||||
\(66\) | 144.623 | − | 83.4980i | 2.19126 | − | 1.26512i | ||||
\(67\) | −37.2194 | − | 64.4659i | −0.555513 | − | 0.962177i | −0.997863 | − | 0.0653349i | \(-0.979188\pi\) |
0.442350 | − | 0.896843i | \(-0.354145\pi\) | |||||||
\(68\) | 2.77544 | + | 1.60240i | 0.0408152 | + | 0.0235647i | ||||
\(69\) | 82.5581i | 1.19649i | ||||||||
\(70\) | 11.5934 | + | 35.1530i | 0.165620 | + | 0.502186i | ||||
\(71\) | −66.7438 | −0.940053 | −0.470027 | − | 0.882652i | \(-0.655756\pi\) | ||||
−0.470027 | + | 0.882652i | \(0.655756\pi\) | |||||||
\(72\) | −49.6916 | + | 86.0685i | −0.690162 | + | 1.19540i | ||||
\(73\) | −108.278 | + | 62.5145i | −1.48327 | + | 0.856363i | −0.999819 | − | 0.0190109i | \(-0.993948\pi\) |
−0.483446 | + | 0.875374i | \(0.660615\pi\) | |||||||
\(74\) | −15.4029 | − | 26.6787i | −0.208148 | − | 0.360522i | ||||
\(75\) | 22.2719 | + | 12.8587i | 0.296959 | + | 0.171449i | ||||
\(76\) | 3.82851i | 0.0503751i | ||||||||
\(77\) | 91.2699 | − | 30.1006i | 1.18532 | − | 0.390917i | ||||
\(78\) | −74.7645 | −0.958520 | ||||||||
\(79\) | 49.0504 | − | 84.9577i | 0.620891 | − | 1.07541i | −0.368430 | − | 0.929656i | \(-0.620104\pi\) |
0.989320 | − | 0.145758i | \(-0.0465622\pi\) | |||||||
\(80\) | −38.4081 | + | 22.1749i | −0.480101 | + | 0.277187i | ||||
\(81\) | −33.2966 | − | 57.6714i | −0.411069 | − | 0.711992i | ||||
\(82\) | −113.249 | − | 65.3844i | −1.38109 | − | 0.797370i | ||||
\(83\) | − | 78.1877i | − | 0.942020i | −0.882128 | − | 0.471010i | \(-0.843890\pi\) | ||
0.882128 | − | 0.471010i | \(-0.156110\pi\) | |||||||
\(84\) | 38.1755 | − | 42.7757i | 0.454471 | − | 0.509235i | ||||
\(85\) | 4.50020 | 0.0529436 | ||||||||
\(86\) | −64.6983 | + | 112.061i | −0.752306 | + | 1.30303i | ||||
\(87\) | 71.1723 | − | 41.0914i | 0.818072 | − | 0.472314i | ||||
\(88\) | 39.0843 | + | 67.6960i | 0.444140 | + | 0.769273i | ||||
\(89\) | 38.7285 | + | 22.3599i | 0.435151 | + | 0.251235i | 0.701539 | − | 0.712631i | \(-0.252497\pi\) |
−0.266388 | + | 0.963866i | \(0.585830\pi\) | |||||||
\(90\) | − | 92.3028i | − | 1.02559i | ||||||
\(91\) | −42.1254 | − | 8.76023i | −0.462916 | − | 0.0962662i | ||||
\(92\) | 25.5597 | 0.277823 | ||||||||
\(93\) | 53.3211 | − | 92.3549i | 0.573346 | − | 0.993064i | ||||
\(94\) | −146.593 | + | 84.6355i | −1.55950 | + | 0.900378i | ||||
\(95\) | 2.68801 | + | 4.65577i | 0.0282949 | + | 0.0490081i | ||||
\(96\) | 107.482 | + | 62.0548i | 1.11960 | + | 0.646404i | ||||
\(97\) | 31.6777i | 0.326574i | 0.986579 | + | 0.163287i | \(0.0522096\pi\) | ||||
−0.986579 | + | 0.163287i | \(0.947790\pi\) | |||||||
\(98\) | 93.1423 | − | 68.9339i | 0.950431 | − | 0.703407i | ||||
\(99\) | −239.652 | −2.42072 | ||||||||
\(100\) | 3.98101 | − | 6.89531i | 0.0398101 | − | 0.0689531i | ||||
\(101\) | −63.7153 | + | 36.7861i | −0.630845 | + | 0.364218i | −0.781079 | − | 0.624432i | \(-0.785330\pi\) |
0.150234 | + | 0.988650i | \(0.451997\pi\) | |||||||
\(102\) | −12.2398 | − | 21.1999i | −0.119998 | − | 0.207843i | ||||
\(103\) | 23.9642 | + | 13.8358i | 0.232663 | + | 0.134328i | 0.611800 | − | 0.791013i | \(-0.290446\pi\) |
−0.379137 | + | 0.925340i | \(0.623779\pi\) | |||||||
\(104\) | − | 34.9963i | − | 0.336503i | ||||||
\(105\) | 16.3915 | − | 78.8219i | 0.156110 | − | 0.750685i | ||||
\(106\) | 159.341 | 1.50321 | ||||||||
\(107\) | 41.1422 | − | 71.2603i | 0.384506 | − | 0.665984i | −0.607194 | − | 0.794553i | \(-0.707705\pi\) |
0.991701 | + | 0.128569i | \(0.0410384\pi\) | |||||||
\(108\) | −59.9759 | + | 34.6271i | −0.555333 | + | 0.320622i | ||||
\(109\) | 16.9306 | + | 29.3247i | 0.155327 | + | 0.269034i | 0.933178 | − | 0.359415i | \(-0.117024\pi\) |
−0.777851 | + | 0.628449i | \(0.783690\pi\) | |||||||
\(110\) | −62.8731 | − | 36.2998i | −0.571573 | − | 0.329998i | ||||
\(111\) | 67.0026i | 0.603627i | ||||||||
\(112\) | 103.584 | + | 92.4447i | 0.924860 | + | 0.825399i | ||||
\(113\) | −36.7538 | −0.325255 | −0.162628 | − | 0.986688i | \(-0.551997\pi\) | ||||
−0.162628 | + | 0.986688i | \(0.551997\pi\) | |||||||
\(114\) | 14.6219 | − | 25.3258i | 0.128262 | − | 0.222156i | ||||
\(115\) | 31.0826 | − | 17.9456i | 0.270284 | − | 0.156048i | ||||
\(116\) | −12.7217 | − | 22.0347i | −0.109670 | − | 0.189954i | ||||
\(117\) | 92.9181 | + | 53.6463i | 0.794171 | + | 0.458515i | ||||
\(118\) | 49.8652i | 0.422586i | ||||||||
\(119\) | −4.41238 | − | 13.3790i | −0.0370788 | − | 0.112429i | ||||
\(120\) | 65.4825 | 0.545687 | ||||||||
\(121\) | −33.7474 | + | 58.4522i | −0.278904 | + | 0.483076i | ||||
\(122\) | 54.1081 | − | 31.2393i | 0.443509 | − | 0.256060i | ||||
\(123\) | 142.211 | + | 246.316i | 1.15618 | + | 2.00257i | ||||
\(124\) | −28.5928 | − | 16.5080i | −0.230587 | − | 0.133129i | ||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −274.415 | + | 90.5014i | −2.17790 | + | 0.718265i | ||||
\(127\) | −181.035 | −1.42547 | −0.712737 | − | 0.701431i | \(-0.752545\pi\) | ||||
−0.712737 | + | 0.701431i | \(0.752545\pi\) | |||||||
\(128\) | −74.5954 | + | 129.203i | −0.582776 | + | 1.00940i | ||||
\(129\) | 243.731 | − | 140.718i | 1.88939 | − | 1.09084i | ||||
\(130\) | 16.2515 | + | 28.1484i | 0.125011 | + | 0.216526i | ||||
\(131\) | 37.0813 | + | 21.4089i | 0.283063 | + | 0.163427i | 0.634809 | − | 0.772669i | \(-0.281079\pi\) |
−0.351746 | + | 0.936095i | \(0.614412\pi\) | |||||||
\(132\) | 112.450i | 0.851896i | ||||||||
\(133\) | 11.2060 | − | 12.5563i | 0.0842557 | − | 0.0944085i | ||||
\(134\) | 176.035 | 1.31369 | ||||||||
\(135\) | −48.6237 | + | 84.2187i | −0.360176 | + | 0.623843i | ||||
\(136\) | 9.92340 | − | 5.72928i | 0.0729662 | − | 0.0421271i | ||||
\(137\) | −50.5297 | − | 87.5200i | −0.368830 | − | 0.638832i | 0.620553 | − | 0.784165i | \(-0.286908\pi\) |
−0.989383 | + | 0.145332i | \(0.953575\pi\) | |||||||
\(138\) | −169.079 | − | 97.6178i | −1.22521 | − | 0.707375i | ||||
\(139\) | − | 132.591i | − | 0.953895i | −0.878932 | − | 0.476947i | \(-0.841743\pi\) | ||
0.878932 | − | 0.476947i | \(-0.158257\pi\) | |||||||
\(140\) | −24.4030 | − | 5.07475i | −0.174307 | − | 0.0362482i | ||||
\(141\) | 368.164 | 2.61109 | ||||||||
\(142\) | 78.9187 | − | 136.691i | 0.555766 | − | 0.962615i | ||||
\(143\) | 73.0835 | − | 42.1948i | 0.511073 | − | 0.295068i | ||||
\(144\) | −173.104 | − | 299.825i | −1.20211 | − | 2.08212i | ||||
\(145\) | −30.9413 | − | 17.8640i | −0.213388 | − | 0.123200i | ||||
\(146\) | − | 295.672i | − | 2.02515i | ||||||
\(147\) | −250.408 | + | 28.5519i | −1.70346 | + | 0.194231i | ||||
\(148\) | 20.7438 | 0.140161 | ||||||||
\(149\) | −71.8152 | + | 124.388i | −0.481981 | + | 0.834816i | −0.999786 | − | 0.0206830i | \(-0.993416\pi\) |
0.517805 | + | 0.855499i | \(0.326749\pi\) | |||||||
\(150\) | −52.6693 | + | 30.4086i | −0.351128 | + | 0.202724i | ||||
\(151\) | −73.0209 | − | 126.476i | −0.483582 | − | 0.837588i | 0.516240 | − | 0.856444i | \(-0.327331\pi\) |
−0.999822 | + | 0.0188554i | \(0.993998\pi\) | |||||||
\(152\) | 11.8547 | + | 6.84430i | 0.0779913 | + | 0.0450283i | ||||
\(153\) | 35.1300i | 0.229608i | ||||||||
\(154\) | −46.2727 | + | 222.512i | −0.300472 | + | 1.44488i | ||||
\(155\) | −46.3615 | −0.299106 | ||||||||
\(156\) | 25.1721 | − | 43.5994i | 0.161360 | − | 0.279483i | ||||
\(157\) | −172.624 | + | 99.6646i | −1.09952 | + | 0.634807i | −0.936094 | − | 0.351749i | \(-0.885587\pi\) |
−0.163423 | + | 0.986556i | \(0.552254\pi\) | |||||||
\(158\) | 115.996 | + | 200.910i | 0.734149 | + | 1.27158i | ||||
\(159\) | −300.134 | − | 173.283i | −1.88764 | − | 1.08983i | ||||
\(160\) | − | 53.9551i | − | 0.337220i | ||||||
\(161\) | −83.8279 | − | 74.8129i | −0.520670 | − | 0.464676i | ||||
\(162\) | 157.481 | 0.972107 | ||||||||
\(163\) | 64.0489 | − | 110.936i | 0.392938 | − | 0.680589i | −0.599897 | − | 0.800077i | \(-0.704792\pi\) |
0.992836 | + | 0.119488i | \(0.0381253\pi\) | |||||||
\(164\) | 76.2585 | − | 44.0279i | 0.464991 | − | 0.268463i | ||||
\(165\) | 78.9518 | + | 136.749i | 0.478496 | + | 0.828779i | ||||
\(166\) | 160.128 | + | 92.4501i | 0.964629 | + | 0.556929i | ||||
\(167\) | 300.506i | 1.79944i | 0.436469 | + | 0.899719i | \(0.356229\pi\) | ||||
−0.436469 | + | 0.899719i | \(0.643771\pi\) | |||||||
\(168\) | −64.2045 | − | 194.679i | −0.382170 | − | 1.15880i | ||||
\(169\) | 131.219 | 0.776442 | ||||||||
\(170\) | −5.32110 | + | 9.21642i | −0.0313006 | + | 0.0542142i | ||||
\(171\) | −36.3444 | + | 20.9834i | −0.212540 | + | 0.122710i | ||||
\(172\) | −43.5659 | − | 75.4584i | −0.253290 | − | 0.438712i | ||||
\(173\) | 96.8042 | + | 55.8899i | 0.559562 | + | 0.323063i | 0.752970 | − | 0.658055i | \(-0.228621\pi\) |
−0.193408 | + | 0.981118i | \(0.561954\pi\) | |||||||
\(174\) | 194.348i | 1.11694i | ||||||||
\(175\) | −33.2390 | + | 10.9621i | −0.189937 | + | 0.0626408i | ||||
\(176\) | −272.306 | −1.54719 | ||||||||
\(177\) | 54.2282 | − | 93.9261i | 0.306374 | − | 0.530656i | ||||
\(178\) | −91.5861 | + | 52.8772i | −0.514529 | + | 0.297063i | ||||
\(179\) | 176.173 | + | 305.141i | 0.984207 | + | 1.70470i | 0.645407 | + | 0.763839i | \(0.276688\pi\) |
0.338800 | + | 0.940858i | \(0.389979\pi\) | |||||||
\(180\) | 53.8269 | + | 31.0770i | 0.299038 | + | 0.172650i | ||||
\(181\) | 153.980i | 0.850718i | 0.905025 | + | 0.425359i | \(0.139852\pi\) | ||||
−0.905025 | + | 0.425359i | \(0.860148\pi\) | |||||||
\(182\) | 67.7505 | − | 75.9145i | 0.372256 | − | 0.417113i | ||||
\(183\) | −135.891 | −0.742572 | ||||||||
\(184\) | 45.6936 | − | 79.1436i | 0.248335 | − | 0.430128i | ||||
\(185\) | 25.2261 | − | 14.5643i | 0.136357 | − | 0.0787259i | ||||
\(186\) | 126.095 | + | 218.403i | 0.677932 | + | 1.17421i | ||||
\(187\) | 23.9292 | + | 13.8155i | 0.127963 | + | 0.0738797i | ||||
\(188\) | − | 113.982i | − | 0.606288i | ||||||
\(189\) | 298.056 | + | 61.9826i | 1.57702 | + | 0.327950i | ||||
\(190\) | −12.7134 | −0.0669124 | ||||||||
\(191\) | 38.4323 | − | 66.5667i | 0.201216 | − | 0.348517i | −0.747704 | − | 0.664032i | \(-0.768844\pi\) |
0.948921 | + | 0.315515i | \(0.102177\pi\) | |||||||
\(192\) | 99.2146 | − | 57.2816i | 0.516743 | − | 0.298342i | ||||
\(193\) | −166.261 | − | 287.973i | −0.861456 | − | 1.49209i | −0.870523 | − | 0.492127i | \(-0.836220\pi\) |
0.00906705 | − | 0.999959i | \(-0.497114\pi\) | |||||||
\(194\) | −64.8759 | − | 37.4561i | −0.334412 | − | 0.193073i | ||||
\(195\) | − | 70.6938i | − | 0.362532i | ||||||
\(196\) | 8.83957 | + | 77.5255i | 0.0450998 | + | 0.395538i | ||||
\(197\) | −122.760 | −0.623146 | −0.311573 | − | 0.950222i | \(-0.600856\pi\) | ||||
−0.311573 | + | 0.950222i | \(0.600856\pi\) | |||||||
\(198\) | 283.367 | − | 490.806i | 1.43115 | − | 2.47882i | ||||
\(199\) | 73.5085 | − | 42.4402i | 0.369390 | − | 0.213267i | −0.303802 | − | 0.952735i | \(-0.598256\pi\) |
0.673192 | + | 0.739468i | \(0.264923\pi\) | |||||||
\(200\) | −14.2339 | − | 24.6538i | −0.0711693 | − | 0.123269i | ||||
\(201\) | −331.579 | − | 191.437i | −1.64965 | − | 0.952425i | ||||
\(202\) | − | 173.985i | − | 0.861313i | ||||||
\(203\) | −22.7719 | + | 109.503i | −0.112177 | + | 0.539426i | ||||
\(204\) | 16.4838 | 0.0808031 | ||||||||
\(205\) | 61.8243 | − | 107.083i | 0.301582 | − | 0.522356i | ||||
\(206\) | −56.6713 | + | 32.7192i | −0.275103 | + | 0.158831i | ||||
\(207\) | 140.089 | + | 242.640i | 0.676756 | + | 1.17218i | ||||
\(208\) | 105.579 | + | 60.9560i | 0.507591 | + | 0.293058i | ||||
\(209\) | 33.0085i | 0.157935i | ||||||||
\(210\) | 142.046 | + | 126.770i | 0.676409 | + | 0.603666i | ||||
\(211\) | 142.536 | 0.675527 | 0.337763 | − | 0.941231i | \(-0.390330\pi\) | ||||
0.337763 | + | 0.941231i | \(0.390330\pi\) | |||||||
\(212\) | −53.6477 | + | 92.9205i | −0.253055 | + | 0.438304i | ||||
\(213\) | −297.303 | + | 171.648i | −1.39579 | + | 0.805858i | ||||
\(214\) | 97.2941 | + | 168.518i | 0.454645 | + | 0.787469i | ||||
\(215\) | −105.959 | − | 61.1756i | −0.492834 | − | 0.284538i | ||||
\(216\) | 247.614i | 1.14636i | ||||||||
\(217\) | 45.4567 | + | 137.832i | 0.209478 | + | 0.635171i | ||||
\(218\) | −80.0760 | −0.367321 | ||||||||
\(219\) | −321.543 | + | 556.928i | −1.46823 | + | 2.54305i | ||||
\(220\) | 42.3369 | − | 24.4432i | 0.192440 | − | 0.111105i | ||||
\(221\) | −6.18523 | − | 10.7131i | −0.0279875 | − | 0.0484757i | ||||
\(222\) | −137.221 | − | 79.2247i | −0.618114 | − | 0.356868i | ||||
\(223\) | − | 229.951i | − | 1.03117i | −0.856838 | − | 0.515585i | \(-0.827575\pi\) | ||
0.856838 | − | 0.515585i | \(-0.172425\pi\) | |||||||
\(224\) | −160.408 | + | 52.9021i | −0.716107 | + | 0.236170i | ||||
\(225\) | 87.2772 | 0.387898 | ||||||||
\(226\) | 43.4582 | − | 75.2719i | 0.192293 | − | 0.333061i | ||||
\(227\) | 297.681 | − | 171.866i | 1.31137 | − | 0.757121i | 0.329048 | − | 0.944313i | \(-0.393272\pi\) |
0.982323 | + | 0.187192i | \(0.0599387\pi\) | |||||||
\(228\) | 9.84594 | + | 17.0537i | 0.0431839 | + | 0.0747968i | ||||
\(229\) | 0.761259 | + | 0.439513i | 0.00332428 | + | 0.00191927i | 0.501661 | − | 0.865064i | \(-0.332722\pi\) |
−0.498337 | + | 0.866983i | \(0.666056\pi\) | |||||||
\(230\) | 84.8763i | 0.369027i | ||||||||
\(231\) | 329.141 | − | 368.802i | 1.42485 | − | 1.59655i | ||||
\(232\) | −90.9716 | −0.392119 | ||||||||
\(233\) | −51.9301 | + | 89.9455i | −0.222876 | + | 0.386032i | −0.955680 | − | 0.294407i | \(-0.904878\pi\) |
0.732804 | + | 0.680440i | \(0.238211\pi\) | |||||||
\(234\) | −219.735 | + | 126.864i | −0.939039 | + | 0.542154i | ||||
\(235\) | −80.0274 | − | 138.611i | −0.340542 | − | 0.589836i | ||||
\(236\) | −29.0792 | − | 16.7889i | −0.123217 | − | 0.0711393i | ||||
\(237\) | − | 504.580i | − | 2.12903i | ||||||
\(238\) | 32.6175 | + | 6.78302i | 0.137048 | + | 0.0285001i | ||||
\(239\) | −159.924 | −0.669140 | −0.334570 | − | 0.942371i | \(-0.608591\pi\) | ||||
−0.334570 | + | 0.942371i | \(0.608591\pi\) | |||||||
\(240\) | −114.056 | + | 197.552i | −0.475235 | + | 0.823131i | ||||
\(241\) | 223.306 | − | 128.926i | 0.926583 | − | 0.534963i | 0.0408535 | − | 0.999165i | \(-0.486992\pi\) |
0.885729 | + | 0.464202i | \(0.153659\pi\) | |||||||
\(242\) | −79.8067 | − | 138.229i | −0.329780 | − | 0.571195i | ||||
\(243\) | 42.3421 | + | 24.4462i | 0.174247 | + | 0.100602i | ||||
\(244\) | 42.0712i | 0.172423i | ||||||||
\(245\) | 65.1806 | + | 88.0709i | 0.266043 | + | 0.359473i | ||||
\(246\) | −672.607 | −2.73417 | ||||||||
\(247\) | 7.38899 | − | 12.7981i | 0.0299149 | − | 0.0518142i | ||||
\(248\) | −102.232 | + | 59.0235i | −0.412225 | + | 0.237998i | ||||
\(249\) | −201.079 | − | 348.278i | −0.807544 | − | 1.39871i | ||||
\(250\) | 22.8973 | + | 13.2198i | 0.0915893 | + | 0.0528791i | ||||
\(251\) | 148.025i | 0.589740i | 0.955537 | + | 0.294870i | \(0.0952763\pi\) | ||||
−0.955537 | + | 0.294870i | \(0.904724\pi\) | |||||||
\(252\) | 39.6151 | − | 190.497i | 0.157203 | − | 0.755941i | ||||
\(253\) | 220.370 | 0.871026 | ||||||||
\(254\) | 214.059 | − | 370.760i | 0.842750 | − | 1.45969i | ||||
\(255\) | 20.0457 | − | 11.5734i | 0.0786104 | − | 0.0453857i | ||||
\(256\) | −131.858 | − | 228.385i | −0.515071 | − | 0.892129i | ||||
\(257\) | 59.0535 | + | 34.0946i | 0.229780 | + | 0.132664i | 0.610471 | − | 0.792039i | \(-0.290980\pi\) |
−0.380690 | + | 0.924703i | \(0.624314\pi\) | |||||||
\(258\) | 665.549i | 2.57965i | ||||||||
\(259\) | −68.0332 | − | 60.7168i | −0.262676 | − | 0.234428i | ||||
\(260\) | −21.8865 | −0.0841790 | ||||||||
\(261\) | 139.452 | − | 241.537i | 0.534297 | − | 0.925430i | ||||
\(262\) | −87.6909 | + | 50.6283i | −0.334698 | + | 0.193238i | ||||
\(263\) | −137.599 | − | 238.329i | −0.523191 | − | 0.906193i | −0.999636 | − | 0.0269887i | \(-0.991408\pi\) |
0.476445 | − | 0.879204i | \(-0.341925\pi\) | |||||||
\(264\) | 348.193 | + | 201.030i | 1.31891 | + | 0.761476i | ||||
\(265\) | 150.665i | 0.568547i | ||||||||
\(266\) | 12.4652 | + | 37.7967i | 0.0468618 | + | 0.142093i | ||||
\(267\) | 230.015 | 0.861481 | ||||||||
\(268\) | −59.2683 | + | 102.656i | −0.221151 | + | 0.383044i | ||||
\(269\) | 198.847 | − | 114.804i | 0.739207 | − | 0.426782i | −0.0825736 | − | 0.996585i | \(-0.526314\pi\) |
0.821781 | + | 0.569803i | \(0.192981\pi\) | |||||||
\(270\) | −114.987 | − | 199.163i | −0.425876 | − | 0.737640i | ||||
\(271\) | 451.013 | + | 260.393i | 1.66425 | + | 0.960858i | 0.970648 | + | 0.240504i | \(0.0773128\pi\) |
0.693607 | + | 0.720354i | \(0.256021\pi\) | |||||||
\(272\) | 39.9167i | 0.146753i | ||||||||
\(273\) | −210.172 | + | 69.3141i | −0.769860 | + | 0.253898i | ||||
\(274\) | 238.988 | 0.872219 | ||||||||
\(275\) | 34.3233 | − | 59.4498i | 0.124812 | − | 0.216181i | ||||
\(276\) | 113.853 | − | 65.7329i | 0.412510 | − | 0.238163i | ||||
\(277\) | 193.738 | + | 335.564i | 0.699414 | + | 1.21142i | 0.968670 | + | 0.248352i | \(0.0798891\pi\) |
−0.269255 | + | 0.963069i | \(0.586778\pi\) | |||||||
\(278\) | 271.547 | + | 156.778i | 0.976788 | + | 0.563949i | ||||
\(279\) | − | 361.912i | − | 1.29717i | ||||||
\(280\) | −59.3393 | + | 66.4897i | −0.211926 | + | 0.237463i | ||||
\(281\) | −157.972 | −0.562180 | −0.281090 | − | 0.959681i | \(-0.590696\pi\) | ||||
−0.281090 | + | 0.959681i | \(0.590696\pi\) | |||||||
\(282\) | −435.322 | + | 753.999i | −1.54369 | + | 2.67376i | ||||
\(283\) | −39.0701 | + | 22.5571i | −0.138057 | + | 0.0797072i | −0.567438 | − | 0.823416i | \(-0.692065\pi\) |
0.429381 | + | 0.903124i | \(0.358732\pi\) | |||||||
\(284\) | 53.1415 | + | 92.0439i | 0.187118 | + | 0.324098i | ||||
\(285\) | 23.9469 | + | 13.8257i | 0.0840242 | + | 0.0485114i | ||||
\(286\) | 199.567i | 0.697785i | ||||||||
\(287\) | −378.974 | − | 78.8099i | −1.32047 | − | 0.274599i | ||||
\(288\) | 421.190 | 1.46247 | ||||||||
\(289\) | −142.475 | + | 246.774i | −0.492992 | + | 0.853888i | ||||
\(290\) | 73.1708 | − | 42.2452i | 0.252313 | − | 0.145673i | ||||
\(291\) | 81.4668 | + | 141.105i | 0.279955 | + | 0.484896i | ||||
\(292\) | 172.423 | + | 99.5484i | 0.590489 | + | 0.340919i | ||||
\(293\) | − | 54.4900i | − | 0.185973i | −0.995667 | − | 0.0929864i | \(-0.970359\pi\) | ||
0.995667 | − | 0.0929864i | \(-0.0296413\pi\) | |||||||
\(294\) | 237.612 | − | 546.596i | 0.808203 | − | 1.85917i | ||||
\(295\) | −47.1501 | −0.159831 | ||||||||
\(296\) | 37.0840 | − | 64.2314i | 0.125284 | − | 0.216998i | ||||
\(297\) | −517.099 | + | 298.547i | −1.74107 | + | 1.00521i | ||||
\(298\) | −169.830 | − | 294.155i | −0.569901 | − | 0.987097i | ||||
\(299\) | −85.4420 | − | 49.3300i | −0.285759 | − | 0.164983i | ||||
\(300\) | − | 40.9525i | − | 0.136508i | ||||||
\(301\) | −77.9830 | + | 374.997i | −0.259080 | + | 1.24584i | ||||
\(302\) | 345.363 | 1.14359 | ||||||||
\(303\) | −189.208 | + | 327.719i | −0.624450 | + | 1.08158i | ||||
\(304\) | −41.2966 | + | 23.8426i | −0.135844 | + | 0.0784296i | ||||
\(305\) | 29.5384 | + | 51.1620i | 0.0968472 | + | 0.167744i | ||||
\(306\) | −71.9462 | − | 41.5381i | −0.235118 | − | 0.135746i | ||||
\(307\) | − | 176.942i | − | 0.576357i | −0.957577 | − | 0.288178i | \(-0.906950\pi\) | ||
0.957577 | − | 0.288178i | \(-0.0930496\pi\) | |||||||
\(308\) | −114.180 | − | 101.901i | −0.370714 | − | 0.330847i | ||||
\(309\) | 142.328 | 0.460609 | ||||||||
\(310\) | 54.8184 | − | 94.9483i | 0.176834 | − | 0.306285i | ||||
\(311\) | −189.438 | + | 109.372i | −0.609125 | + | 0.351678i | −0.772623 | − | 0.634865i | \(-0.781056\pi\) |
0.163498 | + | 0.986544i | \(0.447722\pi\) | |||||||
\(312\) | −90.0014 | − | 155.887i | −0.288466 | − | 0.499638i | ||||
\(313\) | 132.570 | + | 76.5394i | 0.423547 | + | 0.244535i | 0.696594 | − | 0.717466i | \(-0.254698\pi\) |
−0.273047 | + | 0.962001i | \(0.588031\pi\) | |||||||
\(314\) | − | 471.379i | − | 1.50121i | ||||||
\(315\) | −85.5738 | − | 259.474i | −0.271663 | − | 0.823726i | ||||
\(316\) | −156.216 | −0.494354 | ||||||||
\(317\) | 64.6285 | − | 111.940i | 0.203875 | − | 0.353122i | −0.745898 | − | 0.666060i | \(-0.767980\pi\) |
0.949774 | + | 0.312937i | \(0.101313\pi\) | |||||||
\(318\) | 709.765 | − | 409.783i | 2.23197 | − | 1.28863i | ||||
\(319\) | −109.684 | − | 189.978i | −0.343836 | − | 0.595542i | ||||
\(320\) | −43.1324 | − | 24.9025i | −0.134789 | − | 0.0778203i | ||||
\(321\) | − | 423.228i | − | 1.31847i | ||||||
\(322\) | 252.336 | − | 83.2198i | 0.783652 | − | 0.258447i | ||||
\(323\) | 4.83864 | 0.0149803 | ||||||||
\(324\) | −53.0216 | + | 91.8362i | −0.163647 | + | 0.283445i | ||||
\(325\) | −26.6158 | + | 15.3666i | −0.0818948 | + | 0.0472820i | ||||
\(326\) | 151.465 | + | 262.344i | 0.464615 | + | 0.804737i | ||||
\(327\) | 150.831 | + | 87.0825i | 0.461258 | + | 0.266307i | ||||
\(328\) | − | 314.838i | − | 0.959872i | ||||||
\(329\) | −333.624 | + | 373.827i | −1.01406 | + | 1.13625i | ||||
\(330\) | −373.415 | −1.13156 | ||||||||
\(331\) | −289.516 | + | 501.457i | −0.874672 | + | 1.51498i | −0.0175606 | + | 0.999846i | \(0.505590\pi\) |
−0.857112 | + | 0.515131i | \(0.827743\pi\) | |||||||
\(332\) | −107.826 | + | 62.2532i | −0.324776 | + | 0.187510i | ||||
\(333\) | 113.693 | + | 196.922i | 0.341421 | + | 0.591359i | ||||
\(334\) | −615.437 | − | 355.323i | −1.84262 | − | 1.06384i | ||||
\(335\) | 166.450i | 0.496866i | ||||||||
\(336\) | 699.149 | + | 145.392i | 2.08080 | + | 0.432715i | ||||
\(337\) | −14.2685 | −0.0423397 | −0.0211698 | − | 0.999776i | \(-0.506739\pi\) | ||||
−0.0211698 | + | 0.999776i | \(0.506739\pi\) | |||||||
\(338\) | −155.155 | + | 268.736i | −0.459037 | + | 0.795076i | ||||
\(339\) | −163.716 | + | 94.5214i | −0.482938 | + | 0.278824i | ||||
\(340\) | −3.58307 | − | 6.20606i | −0.0105384 | − | 0.0182531i | ||||
\(341\) | −246.520 | − | 142.328i | −0.722933 | − | 0.417385i | ||||
\(342\) | − | 99.2444i | − | 0.290188i | ||||||
\(343\) | 197.925 | − | 280.133i | 0.577041 | − | 0.816715i | ||||
\(344\) | −311.535 | −0.905624 | ||||||||
\(345\) | 92.3027 | − | 159.873i | 0.267544 | − | 0.463400i | ||||
\(346\) | −228.925 | + | 132.170i | −0.661633 | + | 0.381994i | ||||
\(347\) | 94.0286 | + | 162.862i | 0.270976 | + | 0.469344i | 0.969112 | − | 0.246621i | \(-0.0793203\pi\) |
−0.698136 | + | 0.715965i | \(0.745987\pi\) | |||||||
\(348\) | −113.335 | − | 65.4340i | −0.325676 | − | 0.188029i | ||||
\(349\) | − | 297.734i | − | 0.853106i | −0.904463 | − | 0.426553i | \(-0.859728\pi\) | ||
0.904463 | − | 0.426553i | \(-0.140272\pi\) | |||||||
\(350\) | 16.8518 | − | 81.0353i | 0.0481479 | − | 0.231529i | ||||
\(351\) | 267.320 | 0.761596 | ||||||||
\(352\) | 165.641 | − | 286.898i | 0.470571 | − | 0.815052i | ||||
\(353\) | 384.830 | − | 222.182i | 1.09017 | − | 0.629410i | 0.156549 | − | 0.987670i | \(-0.449963\pi\) |
0.933622 | + | 0.358260i | \(0.116630\pi\) | |||||||
\(354\) | 128.240 | + | 222.119i | 0.362261 | + | 0.627454i | ||||
\(355\) | 129.249 | + | 74.6218i | 0.364081 | + | 0.210202i | ||||
\(356\) | − | 71.2120i | − | 0.200034i | ||||||
\(357\) | −54.0619 | − | 48.2480i | −0.151434 | − | 0.135148i | ||||
\(358\) | −833.238 | −2.32748 | ||||||||
\(359\) | 208.158 | − | 360.540i | 0.579827 | − | 1.00429i | −0.415672 | − | 0.909515i | \(-0.636453\pi\) |
0.995499 | − | 0.0947753i | \(-0.0302132\pi\) | |||||||
\(360\) | 192.455 | − | 111.114i | 0.534597 | − | 0.308650i | ||||
\(361\) | −177.610 | − | 307.629i | −0.491994 | − | 0.852159i | ||||
\(362\) | −315.351 | − | 182.068i | −0.871135 | − | 0.502950i | ||||
\(363\) | 347.158i | 0.956358i | ||||||||
\(364\) | 21.4594 | + | 65.0684i | 0.0589544 | + | 0.178759i | ||||
\(365\) | 279.573 | 0.765955 | ||||||||
\(366\) | 160.679 | − | 278.304i | 0.439013 | − | 0.760393i | ||||
\(367\) | −460.868 | + | 266.082i | −1.25577 | + | 0.725019i | −0.972249 | − | 0.233947i | \(-0.924836\pi\) |
−0.283521 | + | 0.958966i | \(0.591503\pi\) | |||||||
\(368\) | 159.177 | + | 275.702i | 0.432545 | + | 0.749191i | ||||
\(369\) | 835.922 | + | 482.620i | 2.26537 | + | 1.30791i | ||||
\(370\) | 68.8840i | 0.186173i | ||||||||
\(371\) | 447.925 | − | 147.725i | 1.20735 | − | 0.398180i | ||||
\(372\) | −169.818 | −0.456499 | ||||||||
\(373\) | −254.610 | + | 440.997i | −0.682600 | + | 1.18230i | 0.291584 | + | 0.956545i | \(0.405818\pi\) |
−0.974185 | + | 0.225753i | \(0.927516\pi\) | |||||||
\(374\) | −56.5883 | + | 32.6713i | −0.151306 | + | 0.0873564i | ||||
\(375\) | −28.7530 | − | 49.8016i | −0.0766745 | − | 0.132804i | ||||
\(376\) | −352.937 | − | 203.768i | −0.938662 | − | 0.541937i | ||||
\(377\) | 98.2114i | 0.260508i | ||||||||
\(378\) | −479.366 | + | 537.130i | −1.26816 | + | 1.42098i | ||||
\(379\) | 166.742 | 0.439953 | 0.219976 | − | 0.975505i | \(-0.429402\pi\) | ||||
0.219976 | + | 0.975505i | \(0.429402\pi\) | |||||||
\(380\) | 4.28040 | − | 7.41387i | 0.0112642 | − | 0.0195102i | ||||
\(381\) | −806.401 | + | 465.576i | −2.11654 | + | 1.22198i | ||||
\(382\) | 90.8858 | + | 157.419i | 0.237921 | + | 0.412091i | ||||
\(383\) | −295.194 | − | 170.430i | −0.770742 | − | 0.444988i | 0.0623972 | − | 0.998051i | \(-0.480125\pi\) |
−0.833139 | + | 0.553063i | \(0.813459\pi\) | |||||||
\(384\) | 767.360i | 1.99833i | ||||||||
\(385\) | −210.397 | − | 43.7533i | −0.546485 | − | 0.113645i | ||||
\(386\) | 786.357 | 2.03719 | ||||||||
\(387\) | 477.556 | − | 827.151i | 1.23399 | − | 2.13734i | ||||
\(388\) | 43.6855 | − | 25.2218i | 0.112591 | − | 0.0650047i | ||||
\(389\) | 14.9678 | + | 25.9249i | 0.0384775 | + | 0.0666450i | 0.884623 | − | 0.466307i | \(-0.154416\pi\) |
−0.846145 | + | 0.532952i | \(0.821083\pi\) | |||||||
\(390\) | 144.781 | + | 83.5893i | 0.371233 | + | 0.214332i | ||||
\(391\) | − | 32.3035i | − | 0.0826176i | ||||||
\(392\) | 255.854 | + | 111.223i | 0.652690 | + | 0.283732i | ||||
\(393\) | 220.233 | 0.560389 | ||||||||
\(394\) | 145.153 | − | 251.412i | 0.368408 | − | 0.638102i | ||||
\(395\) | −189.971 | + | 109.680i | −0.480940 | + | 0.277671i | ||||
\(396\) | 190.811 | + | 330.494i | 0.481846 | + | 0.834582i | ||||
\(397\) | 415.166 | + | 239.696i | 1.04576 | + | 0.603769i | 0.921459 | − | 0.388476i | \(-0.126998\pi\) |
0.124300 | + | 0.992245i | \(0.460332\pi\) | |||||||
\(398\) | 200.727i | 0.504340i | ||||||||
\(399\) | 17.6242 | − | 84.7497i | 0.0441710 | − | 0.212405i | ||||
\(400\) | 99.1693 | 0.247923 | ||||||||
\(401\) | 304.548 | − | 527.492i | 0.759470 | − | 1.31544i | −0.183651 | − | 0.982991i | \(-0.558792\pi\) |
0.943121 | − | 0.332449i | \(-0.107875\pi\) | |||||||
\(402\) | 784.127 | − | 452.716i | 1.95057 | − | 1.12616i | ||||
\(403\) | 63.7208 | + | 110.368i | 0.158116 | + | 0.273865i | ||||
\(404\) | 101.461 | + | 58.5783i | 0.251140 | + | 0.144996i | ||||
\(405\) | 148.907i | 0.367671i | ||||||||
\(406\) | −197.337 | − | 176.115i | −0.486052 | − | 0.433781i | ||||
\(407\) | 178.848 | 0.439430 | ||||||||
\(408\) | 29.4685 | − | 51.0409i | 0.0722266 | − | 0.125100i | ||||
\(409\) | −438.488 | + | 253.161i | −1.07210 | + | 0.618976i | −0.928754 | − | 0.370696i | \(-0.879119\pi\) |
−0.143344 | + | 0.989673i | \(0.545786\pi\) | |||||||
\(410\) | 146.204 | + | 253.232i | 0.356595 | + | 0.617640i | ||||
\(411\) | −450.158 | − | 259.899i | −1.09527 | − | 0.632357i | ||||
\(412\) | − | 44.0643i | − | 0.106952i | ||||||
\(413\) | 46.2300 | + | 140.177i | 0.111937 | + | 0.339411i | ||||
\(414\) | −662.570 | −1.60041 | ||||||||
\(415\) | −87.4165 | + | 151.410i | −0.210642 | + | 0.364843i | ||||
\(416\) | −128.445 | + | 74.1578i | −0.308762 | + | 0.178264i | ||||
\(417\) | −340.991 | − | 590.613i | −0.817724 | − | 1.41634i | ||||
\(418\) | −67.6014 | − | 39.0297i | −0.161726 | − | 0.0933725i | ||||
\(419\) | 600.983i | 1.43433i | 0.696905 | + | 0.717163i | \(0.254560\pi\) | ||||
−0.696905 | + | 0.717163i | \(0.745440\pi\) | |||||||
\(420\) | −121.751 | + | 40.1533i | −0.289884 | + | 0.0956031i | ||||
\(421\) | −277.147 | −0.658307 | −0.329153 | − | 0.944276i | \(-0.606763\pi\) | ||||
−0.329153 | + | 0.944276i | \(0.606763\pi\) | |||||||
\(422\) | −168.537 | + | 291.914i | −0.399376 | + | 0.691739i | ||||
\(423\) | 1082.04 | − | 624.718i | 2.55802 | − | 1.47687i | ||||
\(424\) | 191.814 | + | 332.232i | 0.452392 | + | 0.783565i | ||||
\(425\) | −8.71461 | − | 5.03138i | −0.0205050 | − | 0.0118385i | ||||
\(426\) | − | 811.835i | − | 1.90571i | ||||||
\(427\) | 123.142 | − | 137.981i | 0.288389 | − | 0.323140i | ||||
\(428\) | −131.030 | −0.306145 | ||||||||
\(429\) | 217.028 | − | 375.904i | 0.505893 | − | 0.876232i | ||||
\(430\) | 250.575 | − | 144.670i | 0.582733 | − | 0.336441i | ||||
\(431\) | 203.623 | + | 352.686i | 0.472444 | + | 0.818296i | 0.999503 | − | 0.0315322i | \(-0.0100387\pi\) |
−0.527059 | + | 0.849829i | \(0.676705\pi\) | |||||||
\(432\) | −747.018 | − | 431.291i | −1.72921 | − | 0.998359i | ||||
\(433\) | 312.356i | 0.721377i | 0.932686 | + | 0.360689i | \(0.117458\pi\) | ||||
−0.932686 | + | 0.360689i | \(0.882542\pi\) | |||||||
\(434\) | −336.028 | − | 69.8792i | −0.774259 | − | 0.161012i | ||||
\(435\) | −183.766 | −0.422451 | ||||||||
\(436\) | 26.9604 | − | 46.6968i | 0.0618358 | − | 0.107103i | ||||
\(437\) | 33.4202 | − | 19.2952i | 0.0764764 | − | 0.0441537i | ||||
\(438\) | −760.392 | − | 1317.04i | −1.73606 | − | 3.00694i | ||||
\(439\) | −184.053 | − | 106.263i | −0.419255 | − | 0.242057i | 0.275504 | − | 0.961300i | \(-0.411155\pi\) |
−0.694758 | + | 0.719243i | \(0.744489\pi\) | |||||||
\(440\) | − | 174.790i | − | 0.397251i | ||||||
\(441\) | −687.509 | + | 508.820i | −1.55898 | + | 1.15379i | ||||
\(442\) | 29.2540 | 0.0661855 | ||||||||
\(443\) | 185.709 | − | 321.658i | 0.419208 | − | 0.726089i | −0.576652 | − | 0.816990i | \(-0.695641\pi\) |
0.995860 | + | 0.0909005i | \(0.0289745\pi\) | |||||||
\(444\) | 92.4008 | − | 53.3476i | 0.208110 | − | 0.120152i | ||||
\(445\) | −49.9982 | − | 86.5995i | −0.112356 | − | 0.194606i | ||||
\(446\) | 470.940 | + | 271.897i | 1.05592 | + | 0.609635i | ||||
\(447\) | 738.760i | 1.65271i | ||||||||
\(448\) | −31.7442 | + | 152.648i | −0.0708575 | + | 0.340733i | ||||
\(449\) | 4.22975 | 0.00942037 | 0.00471018 | − | 0.999989i | \(-0.498501\pi\) | ||||
0.00471018 | + | 0.999989i | \(0.498501\pi\) | |||||||
\(450\) | −103.198 | + | 178.744i | −0.229328 | + | 0.397208i | ||||
\(451\) | 657.483 | − | 379.598i | 1.45783 | − | 0.841681i | ||||
\(452\) | 29.2635 | + | 50.6859i | 0.0647422 | + | 0.112137i | ||||
\(453\) | −650.527 | − | 375.582i | −1.43604 | − | 0.829099i | ||||
\(454\) | 812.869i | 1.79046i | ||||||||
\(455\) | 71.7812 | + | 64.0617i | 0.157761 | + | 0.140795i | ||||
\(456\) | 70.4071 | 0.154402 | ||||||||
\(457\) | −250.605 | + | 434.061i | −0.548371 | + | 0.949806i | 0.450016 | + | 0.893021i | \(0.351418\pi\) |
−0.998386 | + | 0.0567855i | \(0.981915\pi\) | |||||||
\(458\) | −1.80025 | + | 1.03937i | −0.00393067 | + | 0.00226937i | ||||
\(459\) | 43.7633 | + | 75.8003i | 0.0953449 | + | 0.165142i | ||||
\(460\) | −49.4961 | − | 28.5766i | −0.107600 | − | 0.0621230i | ||||
\(461\) | − | 300.121i | − | 0.651022i | −0.945538 | − | 0.325511i | \(-0.894464\pi\) | ||
0.945538 | − | 0.325511i | \(-0.105536\pi\) | |||||||
\(462\) | 366.127 | + | 1110.16i | 0.792483 | + | 2.40294i | ||||
\(463\) | 571.548 | 1.23444 | 0.617222 | − | 0.786789i | \(-0.288258\pi\) | ||||
0.617222 | + | 0.786789i | \(0.288258\pi\) | |||||||
\(464\) | 158.453 | − | 274.449i | 0.341493 | − | 0.591484i | ||||
\(465\) | −206.512 | + | 119.230i | −0.444112 | + | 0.256408i | ||||
\(466\) | −122.806 | − | 212.706i | −0.263531 | − | 0.456450i | ||||
\(467\) | −771.238 | − | 445.274i | −1.65147 | − | 0.953478i | −0.976467 | − | 0.215665i | \(-0.930808\pi\) |
−0.675005 | − | 0.737813i | \(-0.735858\pi\) | |||||||
\(468\) | − | 170.853i | − | 0.365071i | ||||||
\(469\) | 494.854 | − | 163.202i | 1.05513 | − | 0.347978i | ||||
\(470\) | 378.502 | 0.805323 | ||||||||
\(471\) | −512.623 | + | 887.890i | −1.08837 | + | 1.88512i | ||||
\(472\) | −103.971 | + | 60.0276i | −0.220277 | + | 0.127177i | ||||
\(473\) | −375.615 | − | 650.585i | −0.794112 | − | 1.37544i | ||||
\(474\) | 1033.38 | + | 596.621i | 2.18012 | + | 1.25870i | ||||
\(475\) | − | 12.0212i | − | 0.0253077i | ||||||
\(476\) | −14.9374 | + | 16.7374i | −0.0313811 | + | 0.0351625i | ||||
\(477\) | −1176.14 | −2.46570 | ||||||||
\(478\) | 189.097 | − | 327.525i | 0.395600 | − | 0.685199i | ||||
\(479\) | −28.6660 | + | 16.5503i | −0.0598456 | + | 0.0345519i | −0.529624 | − | 0.848232i | \(-0.677667\pi\) |
0.469779 | + | 0.882784i | \(0.344334\pi\) | |||||||
\(480\) | −138.759 | − | 240.337i | −0.289081 | − | 0.500702i | ||||
\(481\) | −69.3432 | − | 40.0353i | −0.144165 | − | 0.0832335i | ||||
\(482\) | 609.775i | 1.26509i | ||||||||
\(483\) | −565.802 | − | 117.662i | −1.17143 | − | 0.243606i | ||||
\(484\) | 107.479 | 0.222064 | ||||||||
\(485\) | 35.4167 | − | 61.3435i | 0.0730241 | − | 0.126482i | ||||
\(486\) | −100.132 | + | 57.8110i | −0.206032 | + | 0.118953i | ||||
\(487\) | 307.943 | + | 533.374i | 0.632327 | + | 1.09522i | 0.987075 | + | 0.160261i | \(0.0512335\pi\) |
−0.354747 | + | 0.934962i | \(0.615433\pi\) | |||||||
\(488\) | 130.270 | + | 75.2116i | 0.266947 | + | 0.154122i | ||||
\(489\) | − | 658.869i | − | 1.34738i | ||||||
\(490\) | −257.440 | + | 29.3536i | −0.525387 | + | 0.0599054i | ||||
\(491\) | −223.560 | −0.455316 | −0.227658 | − | 0.973741i | \(-0.573107\pi\) | ||||
−0.227658 | + | 0.973741i | \(0.573107\pi\) | |||||||
\(492\) | 226.457 | − | 392.235i | 0.460278 | − | 0.797225i | ||||
\(493\) | −27.8484 | + | 16.0783i | −0.0564877 | + | 0.0326132i | ||||
\(494\) | 17.4737 | + | 30.2653i | 0.0353718 | + | 0.0612658i | ||||
\(495\) | 464.083 | + | 267.939i | 0.937542 | + | 0.541290i | ||||
\(496\) | − | 411.225i | − | 0.829083i | ||||||
\(497\) | 95.1234 | − | 457.420i | 0.191395 | − | 0.920363i | ||||
\(498\) | 951.032 | 1.90970 | ||||||||
\(499\) | 410.782 | − | 711.496i | 0.823211 | − | 1.42584i | −0.0800672 | − | 0.996789i | \(-0.525513\pi\) |
0.903279 | − | 0.429054i | \(-0.141153\pi\) | |||||||
\(500\) | −15.4184 | + | 8.90181i | −0.0308368 | + | 0.0178036i | ||||
\(501\) | 772.825 | + | 1338.57i | 1.54256 | + | 2.67180i | ||||
\(502\) | −303.155 | − | 175.026i | −0.603893 | − | 0.348658i | ||||
\(503\) | − | 173.706i | − | 0.345340i | −0.984980 | − | 0.172670i | \(-0.944761\pi\) | ||
0.984980 | − | 0.172670i | \(-0.0552394\pi\) | |||||||
\(504\) | −519.039 | − | 463.221i | −1.02984 | − | 0.919088i | ||||
\(505\) | 164.512 | 0.325767 | ||||||||
\(506\) | −260.568 | + | 451.317i | −0.514956 | + | 0.891931i | ||||
\(507\) | 584.499 | − | 337.460i | 1.15286 | − | 0.665602i | ||||
\(508\) | 144.141 | + | 249.659i | 0.283742 | + | 0.491455i | ||||
\(509\) | −397.384 | − | 229.430i | −0.780715 | − | 0.450746i | 0.0559685 | − | 0.998433i | \(-0.482175\pi\) |
−0.836684 | + | 0.547686i | \(0.815509\pi\) | |||||||
\(510\) | 54.7380i | 0.107329i | ||||||||
\(511\) | −274.117 | − | 831.168i | −0.536433 | − | 1.62655i | ||||
\(512\) | 26.8805 | 0.0525010 | ||||||||
\(513\) | −52.2805 | + | 90.5524i | −0.101911 | + | 0.176515i | ||||
\(514\) | −139.651 | + | 80.6278i | −0.271695 | + | 0.156863i | ||||
\(515\) | −30.9377 | − | 53.5857i | −0.0600732 | − | 0.104050i | ||||
\(516\) | −388.119 | − | 224.081i | −0.752169 | − | 0.434265i | ||||
\(517\) | − | 982.727i | − | 1.90083i | ||||||
\(518\) | 204.791 | − | 67.5397i | 0.395350 | − | 0.130385i | ||||
\(519\) | 574.938 | 1.10778 | ||||||||
\(520\) | −39.1270 | + | 67.7700i | −0.0752443 | + | 0.130327i | ||||
\(521\) | 388.712 | − | 224.423i | 0.746089 | − | 0.430755i | −0.0781902 | − | 0.996938i | \(-0.524914\pi\) |
0.824279 | + | 0.566184i | \(0.191581\pi\) | |||||||
\(522\) | 329.779 | + | 571.194i | 0.631760 | + | 1.09424i | ||||
\(523\) | 330.871 | + | 191.028i | 0.632640 | + | 0.365255i | 0.781774 | − | 0.623562i | \(-0.214315\pi\) |
−0.149134 | + | 0.988817i | \(0.547649\pi\) | |||||||
\(524\) | − | 68.1833i | − | 0.130121i | ||||||
\(525\) | −119.868 | + | 134.312i | −0.228319 | + | 0.255832i | ||||
\(526\) | 650.796 | 1.23726 | ||||||||
\(527\) | −20.8636 | + | 36.1368i | −0.0395894 | + | 0.0685708i | ||||
\(528\) | −1212.96 | + | 700.300i | −2.29727 | + | 1.32633i | ||||
\(529\) | 135.683 | + | 235.009i | 0.256489 | + | 0.444252i | ||||
\(530\) | −308.562 | − | 178.148i | −0.582192 | − | 0.336129i | ||||
\(531\) | − | 368.068i | − | 0.693161i | ||||||
\(532\) | −26.2382 | − | 5.45640i | −0.0493200 | − | 0.0102564i | ||||
\(533\) | −339.894 | −0.637700 | ||||||||
\(534\) | −271.973 | + | 471.072i | −0.509313 | + | 0.882156i | ||||
\(535\) | −159.343 | + | 91.9967i | −0.297837 | + | 0.171956i | ||||
\(536\) | 211.910 | + | 367.040i | 0.395355 | + | 0.684775i | ||||
\(537\) | 1569.49 | + | 906.144i | 2.92269 | + | 1.68742i | ||||
\(538\) | 542.984i | 1.00926i | ||||||||
\(539\) | 76.2127 | + | 668.407i | 0.141396 | + | 1.24009i | ||||
\(540\) | 154.857 | 0.286773 | ||||||||
\(541\) | −102.522 | + | 177.573i | −0.189504 | + | 0.328231i | −0.945085 | − | 0.326825i | \(-0.894021\pi\) |
0.755581 | + | 0.655055i | \(0.227355\pi\) | |||||||
\(542\) | −1066.57 | + | 615.783i | −1.96784 | + | 1.13613i | ||||
\(543\) | 395.997 | + | 685.886i | 0.729276 | + | 1.26314i | ||||
\(544\) | −42.0558 | − | 24.2809i | −0.0773084 | − | 0.0446340i | ||||
\(545\) | − | 75.7161i | − | 0.138929i | ||||||
\(546\) | 106.555 | − | 512.390i | 0.195155 | − | 0.938443i | ||||
\(547\) | −182.754 | −0.334102 | −0.167051 | − | 0.985948i | \(-0.553424\pi\) | ||||
−0.167051 | + | 0.985948i | \(0.553424\pi\) | |||||||
\(548\) | −80.4637 | + | 139.367i | −0.146832 | + | 0.254320i | ||||
\(549\) | −399.386 | + | 230.586i | −0.727480 | + | 0.420011i | ||||
\(550\) | 81.1688 | + | 140.588i | 0.147580 | + | 0.255615i | ||||
\(551\) | −33.2682 | − | 19.2074i | −0.0603779 | − | 0.0348592i | ||||
\(552\) | − | 470.048i | − | 0.851536i | ||||||
\(553\) | 512.341 | + | 457.243i | 0.926475 | + | 0.826840i | ||||
\(554\) | −916.312 | −1.65399 | ||||||||
\(555\) | 74.9112 | − | 129.750i | 0.134975 | − | 0.233784i | ||||
\(556\) | −182.852 | + | 105.570i | −0.328870 | + | 0.189873i | ||||
\(557\) | −405.832 | − | 702.922i | −0.728604 | − | 1.26198i | −0.957473 | − | 0.288522i | \(-0.906836\pi\) |
0.228870 | − | 0.973457i | \(-0.426497\pi\) | |||||||
\(558\) | 741.195 | + | 427.929i | 1.32831 | + | 0.766898i | ||||
\(559\) | 336.328i | 0.601659i | ||||||||
\(560\) | −97.2339 | − | 294.829i | −0.173632 | − | 0.526481i | ||||
\(561\) | 142.120 | 0.253333 | ||||||||
\(562\) | 186.789 | − | 323.528i | 0.332364 | − | 0.575672i | ||||
\(563\) | −275.702 | + | 159.176i | −0.489701 | + | 0.282729i | −0.724450 | − | 0.689327i | \(-0.757906\pi\) |
0.234749 | + | 0.972056i | \(0.424573\pi\) | |||||||
\(564\) | −293.133 | − | 507.721i | −0.519739 | − | 0.900214i | ||||
\(565\) | 71.1735 | + | 41.0921i | 0.125971 | + | 0.0727293i | ||||
\(566\) | − | 106.687i | − | 0.188494i | ||||||
\(567\) | 442.698 | − | 146.001i | 0.780773 | − | 0.257497i | ||||
\(568\) | 380.009 | 0.669030 | ||||||||
\(569\) | −299.181 | + | 518.196i | −0.525801 | + | 0.910714i | 0.473747 | + | 0.880661i | \(0.342901\pi\) |
−0.999548 | + | 0.0300533i | \(0.990432\pi\) | |||||||
\(570\) | −56.6303 | + | 32.6955i | −0.0993513 | + | 0.0573605i | ||||
\(571\) | −436.429 | − | 755.917i | −0.764324 | − | 1.32385i | −0.940603 | − | 0.339508i | \(-0.889740\pi\) |
0.176279 | − | 0.984340i | \(-0.443594\pi\) | |||||||
\(572\) | −116.378 | − | 67.1911i | −0.203459 | − | 0.117467i | ||||
\(573\) | − | 395.352i | − | 0.689969i | ||||||
\(574\) | 609.506 | − | 682.953i | 1.06186 | − | 1.18981i | ||||
\(575\) | −80.2550 | −0.139574 | ||||||||
\(576\) | 194.396 | − | 336.704i | 0.337494 | − | 0.584556i | ||||
\(577\) | 639.833 | − | 369.408i | 1.10890 | − | 0.640222i | 0.170353 | − | 0.985383i | \(-0.445509\pi\) |
0.938543 | + | 0.345162i | \(0.112176\pi\) | |||||||
\(578\) | −336.928 | − | 583.577i | −0.582921 | − | 1.00965i | ||||
\(579\) | −1481.18 | − | 855.161i | −2.55817 | − | 1.47696i | ||||
\(580\) | 56.8933i | 0.0980919i | ||||||||
\(581\) | 535.850 | + | 111.433i | 0.922289 | + | 0.191796i | ||||
\(582\) | −385.310 | −0.662044 | ||||||||
\(583\) | −462.538 | + | 801.139i | −0.793375 | + | 1.37417i | ||||
\(584\) | 616.488 | − | 355.929i | 1.05563 | − | 0.609468i | ||||
\(585\) | −119.957 | − | 207.771i | −0.205054 | − | 0.355164i | ||||
\(586\) | 111.596 | + | 64.4297i | 0.190436 | + | 0.109948i | ||||
\(587\) | 149.507i | 0.254697i | 0.991858 | + | 0.127349i | \(0.0406467\pi\) | ||||
−0.991858 | + | 0.127349i | \(0.959353\pi\) | |||||||
\(588\) | 238.750 | + | 322.596i | 0.406038 | + | 0.548632i | ||||
\(589\) | −49.8481 | −0.0846317 | ||||||||
\(590\) | 55.7510 | − | 96.5635i | 0.0944931 | − | 0.163667i | ||||
\(591\) | −546.820 | + | 315.706i | −0.925245 | + | 0.534190i | ||||
\(592\) | 129.185 | + | 223.755i | 0.218218 | + | 0.377964i | ||||
\(593\) | −219.713 | − | 126.851i | −0.370511 | − | 0.213914i | 0.303171 | − | 0.952936i | \(-0.401955\pi\) |
−0.673682 | + | 0.739022i | \(0.735288\pi\) | |||||||
\(594\) | − | 1412.02i | − | 2.37714i | ||||||
\(595\) | −6.41370 | + | 30.8416i | −0.0107793 | + | 0.0518346i | ||||
\(596\) | 228.718 | 0.383754 | ||||||||
\(597\) | 218.290 | − | 378.090i | 0.365645 | − | 0.633316i | ||||
\(598\) | 202.056 | − | 116.657i | 0.337886 | − | 0.195078i | ||||
\(599\) | −261.282 | − | 452.554i | −0.436197 | − | 0.755515i | 0.561196 | − | 0.827683i | \(-0.310342\pi\) |
−0.997392 | + | 0.0721679i | \(0.977008\pi\) | |||||||
\(600\) | −126.806 | − | 73.2117i | −0.211344 | − | 0.122019i | ||||
\(601\) | 956.828i | 1.59206i | 0.605258 | + | 0.796030i | \(0.293070\pi\) | ||||
−0.605258 | + | 0.796030i | \(0.706930\pi\) | |||||||
\(602\) | −675.786 | − | 603.111i | −1.12257 | − | 1.00185i | ||||
\(603\) | −1299.36 | −2.15483 | ||||||||
\(604\) | −116.279 | + | 201.401i | −0.192514 | + | 0.333445i | ||||
\(605\) | 130.703 | − | 75.4614i | 0.216038 | − | 0.124730i | ||||
\(606\) | −447.445 | − | 774.998i | −0.738358 | − | 1.27887i | ||||
\(607\) | −239.609 | − | 138.338i | −0.394743 | − | 0.227905i | 0.289470 | − | 0.957187i | \(-0.406521\pi\) |
−0.684213 | + | 0.729282i | \(0.739854\pi\) | |||||||
\(608\) | − | 58.0128i | − | 0.0954158i | ||||||
\(609\) | 180.180 | + | 546.334i | 0.295862 | + | 0.897101i | ||||
\(610\) | −139.706 | −0.229027 | ||||||||
\(611\) | −219.985 | + | 381.025i | −0.360040 | + | 0.623608i | ||||
\(612\) | 48.4464 | − | 27.9706i | 0.0791608 | − | 0.0457035i | ||||
\(613\) | 107.119 | + | 185.535i | 0.174745 | + | 0.302668i | 0.940073 | − | 0.340973i | \(-0.110756\pi\) |
−0.765328 | + | 0.643641i | \(0.777423\pi\) | |||||||
\(614\) | 362.376 | + | 209.218i | 0.590189 | + | 0.340746i | ||||
\(615\) | − | 635.985i | − | 1.03412i | ||||||
\(616\) | −519.649 | + | 171.379i | −0.843587 | + | 0.278213i | ||||
\(617\) | 1133.85 | 1.83769 | 0.918844 | − | 0.394620i | \(-0.129124\pi\) | ||||
0.918844 | + | 0.394620i | \(0.129124\pi\) | |||||||
\(618\) | −168.291 | + | 291.488i | −0.272315 | + | 0.471663i | ||||
\(619\) | 646.950 | − | 373.517i | 1.04515 | − | 0.603420i | 0.123865 | − | 0.992299i | \(-0.460471\pi\) |
0.921289 | + | 0.388879i | \(0.127138\pi\) | |||||||
\(620\) | 36.9131 | + | 63.9354i | 0.0595372 | + | 0.103122i | ||||
\(621\) | 604.541 | + | 349.032i | 0.973496 | + | 0.562048i | ||||
\(622\) | − | 517.292i | − | 0.831658i | ||||||
\(623\) | −208.437 | + | 233.553i | −0.334569 | + | 0.374885i | ||||
\(624\) | 627.052 | 1.00489 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −313.505 | + | 181.002i | −0.500807 | + | 0.289141i | ||||
\(627\) | 84.8894 | + | 147.033i | 0.135390 | + | 0.234502i | ||||
\(628\) | 274.888 | + | 158.706i | 0.437719 | + | 0.252717i | ||||
\(629\) | − | 26.2169i | − | 0.0416803i | ||||||
\(630\) | 632.586 | + | 131.550i | 1.00410 | + | 0.208810i | ||||
\(631\) | −879.471 | −1.39377 | −0.696887 | − | 0.717181i | \(-0.745432\pi\) | ||||
−0.696887 | + | 0.717181i | \(0.745432\pi\) | |||||||
\(632\) | −279.270 | + | 483.711i | −0.441884 | + | 0.765365i | ||||
\(633\) | 634.911 | − | 366.566i | 1.00302 | − | 0.579093i | ||||
\(634\) | 152.835 | + | 264.718i | 0.241065 | + | 0.417537i | ||||
\(635\) | 350.573 | + | 202.404i | 0.552084 | + | 0.318746i | ||||
\(636\) | 551.872i | 0.867723i | ||||||||
\(637\) | 120.074 | − | 276.216i | 0.188500 | − | 0.433620i | ||||
\(638\) | 518.766 | 0.813114 | ||||||||
\(639\) | −582.521 | + | 1008.96i | −0.911613 | + | 1.57896i | ||||
\(640\) | 288.907 | − | 166.800i | 0.451417 | − | 0.260625i | ||||
\(641\) | 146.735 | + | 254.153i | 0.228916 | + | 0.396494i | 0.957487 | − | 0.288476i | \(-0.0931485\pi\) |
−0.728571 | + | 0.684970i | \(0.759815\pi\) | |||||||
\(642\) | 866.771 | + | 500.431i | 1.35011 | + | 0.779487i | ||||
\(643\) | 401.514i | 0.624439i | 0.950010 | + | 0.312219i | \(0.101072\pi\) | ||||
−0.950010 | + | 0.312219i | \(0.898928\pi\) | |||||||
\(644\) | −36.4277 | + | 175.170i | −0.0565648 | + | 0.272003i | ||||
\(645\) | −629.312 | −0.975677 | ||||||||
\(646\) | −5.72127 | + | 9.90954i | −0.00885646 | + | 0.0153398i | ||||
\(647\) | −783.686 | + | 452.461i | −1.21126 | + | 0.699322i | −0.963034 | − | 0.269380i | \(-0.913181\pi\) |
−0.248227 | + | 0.968702i | \(0.579848\pi\) | |||||||
\(648\) | 189.576 | + | 328.355i | 0.292555 | + | 0.506720i | ||||
\(649\) | −250.714 | − | 144.750i | −0.386308 | − | 0.223035i | ||||
\(650\) | − | 72.6789i | − | 0.111814i | ||||||
\(651\) | 556.950 | + | 497.054i | 0.855530 | + | 0.763525i | ||||
\(652\) | −203.984 | −0.312858 | ||||||||
\(653\) | 216.459 | − | 374.918i | 0.331484 | − | 0.574148i | −0.651319 | − | 0.758804i | \(-0.725784\pi\) |
0.982803 | + | 0.184657i | \(0.0591173\pi\) | |||||||
\(654\) | −356.690 | + | 205.935i | −0.545397 | + | 0.314885i | ||||
\(655\) | −47.8718 | − | 82.9163i | −0.0730867 | − | 0.126590i | ||||
\(656\) | 949.823 | + | 548.380i | 1.44790 | + | 0.835946i | ||||
\(657\) | 2182.44i | 3.32182i | ||||||||
\(658\) | −371.115 | − | 1125.28i | −0.564004 | − | 1.71015i | ||||
\(659\) | 358.497 | 0.544002 | 0.272001 | − | 0.962297i | \(-0.412315\pi\) | ||||
0.272001 | + | 0.962297i | \(0.412315\pi\) | |||||||
\(660\) | 125.723 | − | 217.759i | 0.190490 | − | 0.329938i | ||||
\(661\) | 804.899 | − | 464.709i | 1.21770 | − | 0.703039i | 0.253274 | − | 0.967395i | \(-0.418492\pi\) |
0.964425 | + | 0.264355i | \(0.0851592\pi\) | |||||||
\(662\) | −684.656 | − | 1185.86i | −1.03422 | − | 1.79133i | ||||
\(663\) | −55.1029 | − | 31.8137i | −0.0831114 | − | 0.0479844i | ||||
\(664\) | 445.165i | 0.670429i | ||||||||
\(665\) | −35.7387 | + | 11.7865i | −0.0537425 | + | 0.0177241i | ||||
\(666\) | −537.730 | −0.807402 | ||||||||
\(667\) | −128.232 | + | 222.104i | −0.192251 | + | 0.332989i | ||||
\(668\) | 414.417 | − | 239.264i | 0.620385 | − | 0.358179i | ||||
\(669\) | −591.375 | − | 1024.29i | −0.883968 | − | 1.53108i | ||||
\(670\) | −340.890 | − | 196.813i | −0.508791 | − | 0.293751i | ||||
\(671\) | 362.728i | 0.540579i | ||||||||
\(672\) | −578.468 | + | 648.174i | −0.860816 | + | 0.964545i | ||||
\(673\) | −853.958 | −1.26888 | −0.634442 | − | 0.772971i | \(-0.718770\pi\) | ||||
−0.634442 | + | 0.772971i | \(0.718770\pi\) | |||||||
\(674\) | 16.8712 | − | 29.2218i | 0.0250315 | − | 0.0433558i | ||||
\(675\) | 188.319 | − | 108.726i | 0.278991 | − | 0.161075i | ||||
\(676\) | −104.477 | − | 180.959i | −0.154551 | − | 0.267690i | ||||
\(677\) | 321.116 | + | 185.396i | 0.474321 | + | 0.273850i | 0.718047 | − | 0.695995i | \(-0.245036\pi\) |
−0.243726 | + | 0.969844i | \(0.578370\pi\) | |||||||
\(678\) | − | 447.054i | − | 0.659371i | ||||||
\(679\) | −217.099 | − | 45.1471i | −0.319734 | − | 0.0664905i | ||||
\(680\) | −25.6221 | −0.0376796 | ||||||||
\(681\) | 883.992 | − | 1531.12i | 1.29808 | − | 2.24834i | ||||
\(682\) | 582.977 | − | 336.582i | 0.854805 | − | 0.493522i | ||||
\(683\) | 364.738 | + | 631.744i | 0.534023 | + | 0.924955i | 0.999210 | + | 0.0397422i | \(0.0126537\pi\) |
−0.465187 | + | 0.885212i | \(0.654013\pi\) | |||||||
\(684\) | 57.8750 | + | 33.4141i | 0.0846125 | + | 0.0488511i | ||||
\(685\) | 225.976i | 0.329892i | ||||||||
\(686\) | 339.683 | + | 736.584i | 0.495165 | + | 1.07374i | ||||
\(687\) | 4.52126 | 0.00658116 | ||||||||
\(688\) | 542.626 | − | 939.856i | 0.788701 | − | 1.36607i | ||||
\(689\) | 358.672 | − | 207.079i | 0.520568 | − | 0.300550i | ||||
\(690\) | 218.280 | + | 378.072i | 0.316348 | + | 0.547930i | ||||
\(691\) | 4.35725 | + | 2.51566i | 0.00630572 | + | 0.00364061i | 0.503150 | − | 0.864199i | \(-0.332174\pi\) |
−0.496844 | + | 0.867840i | \(0.665508\pi\) | |||||||
\(692\) | − | 177.999i | − | 0.257224i | ||||||
\(693\) | 341.552 | − | 1642.42i | 0.492860 | − | 2.37002i | ||||
\(694\) | −444.723 | −0.640811 | ||||||||
\(695\) | −148.242 | + | 256.762i | −0.213297 | + | 0.369442i | ||||
\(696\) | −405.223 | + | 233.955i | −0.582217 | + | 0.336143i | ||||
\(697\) | −55.6444 | − | 96.3790i | −0.0798342 | − | 0.138277i | ||||
\(698\) | 609.759 | + | 352.045i | 0.873581 | + | 0.504362i | ||||
\(699\) | 534.203i | 0.764239i | ||||||||
\(700\) | 41.5824 | + | 37.1106i | 0.0594035 | + | 0.0530151i | ||||
\(701\) | −132.748 | −0.189370 | −0.0946850 | − | 0.995507i | \(-0.530184\pi\) | ||||
−0.0946850 | + | 0.995507i | \(0.530184\pi\) | |||||||
\(702\) | −316.083 | + | 547.472i | −0.450261 | + | 0.779875i | ||||
\(703\) | 27.1232 | − | 15.6596i | 0.0385821 | − | 0.0222754i | ||||
\(704\) | −152.900 | − | 264.830i | −0.217187 | − | 0.376180i | ||||
\(705\) | −712.946 | − | 411.619i | −1.01127 | − | 0.583857i | ||||
\(706\) | 1050.84i | 1.48845i | ||||||||
\(707\) | −161.302 | − | 489.093i | −0.228149 | − | 0.691786i | ||||
\(708\) | −172.707 | −0.243936 | ||||||||
\(709\) | 81.9066 | − | 141.866i | 0.115524 | − | 0.200094i | −0.802465 | − | 0.596699i | \(-0.796479\pi\) |
0.917989 | + | 0.396606i | \(0.129812\pi\) | |||||||
\(710\) | −305.651 | + | 176.468i | −0.430494 | + | 0.248546i | ||||
\(711\) | −856.195 | − | 1482.97i | −1.20421 | − | 2.08576i | ||||
\(712\) | −220.502 | − | 127.307i | −0.309694 | − | 0.178802i | ||||
\(713\) | 332.793i | 0.466750i | ||||||||
\(714\) | 162.735 | − | 53.6697i | 0.227921 | − | 0.0751677i | ||||
\(715\) | −188.701 | −0.263917 | ||||||||
\(716\) | 280.539 | − | 485.908i | 0.391814 | − | 0.678642i | ||||
\(717\) | −712.365 | + | 411.284i | −0.993536 | + | 0.573618i | ||||
\(718\) | 492.257 | + | 852.615i | 0.685595 | + | 1.18749i | ||||
\(719\) | 1229.91 | + | 710.091i | 1.71059 | + | 0.987609i | 0.933762 | + | 0.357895i | \(0.116505\pi\) |
0.776827 | + | 0.629714i | \(0.216828\pi\) | |||||||
\(720\) | 774.146i | 1.07520i | ||||||||
\(721\) | −128.976 | + | 144.517i | −0.178884 | + | 0.200440i | ||||
\(722\) | 840.033 | 1.16348 | ||||||||
\(723\) | 663.129 | − | 1148.57i | 0.917191 | − | 1.58862i | ||||
\(724\) | 212.348 | − | 122.599i | 0.293298 | − | 0.169336i | ||||
\(725\) | 39.9451 | + | 69.1869i | 0.0550966 | + | 0.0954302i | ||||
\(726\) | −710.980 | − | 410.484i | −0.979311 | − | 0.565405i | ||||
\(727\) | − | 1115.52i | − | 1.53441i | −0.641403 | − | 0.767204i | \(-0.721647\pi\) | ||
0.641403 | − | 0.767204i | \(-0.278353\pi\) | |||||||
\(728\) | 239.843 | + | 49.8767i | 0.329454 | + | 0.0685120i | ||||
\(729\) | 850.816 | 1.16710 | ||||||||
\(730\) | −330.571 | + | 572.566i | −0.452838 | + | 0.784338i | ||||
\(731\) | −95.3677 | + | 55.0606i | −0.130462 | + | 0.0753223i | ||||
\(732\) | 108.196 | + | 187.402i | 0.147809 | + | 0.256013i | ||||
\(733\) | −532.598 | − | 307.496i | −0.726600 | − | 0.419503i | 0.0905770 | − | 0.995889i | \(-0.471129\pi\) |
−0.817177 | + | 0.576387i | \(0.804462\pi\) | |||||||
\(734\) | − | 1258.48i | − | 1.71454i | ||||||
\(735\) | 516.835 | + | 224.674i | 0.703177 | + | 0.305679i | ||||
\(736\) | −387.302 | −0.526226 | ||||||||
\(737\) | −510.998 | + | 885.074i | −0.693348 | + | 1.20091i | ||||
\(738\) | −1976.81 | + | 1141.31i | −2.67860 | + | 1.54649i | ||||
\(739\) | 169.560 | + | 293.687i | 0.229446 | + | 0.397412i | 0.957644 | − | 0.287955i | \(-0.0929753\pi\) |
−0.728198 | + | 0.685367i | \(0.759642\pi\) | |||||||
\(740\) | −40.1701 | − | 23.1922i | −0.0542839 | − | 0.0313409i | ||||
\(741\) | − | 76.0103i | − | 0.102578i | ||||||
\(742\) | −227.093 | + | 1092.02i | −0.306055 | + | 1.47173i | ||||
\(743\) | −1032.93 | −1.39021 | −0.695105 | − | 0.718909i | \(-0.744642\pi\) | ||||
−0.695105 | + | 0.718909i | \(0.744642\pi\) | |||||||
\(744\) | −303.586 | + | 525.827i | −0.408046 | + | 0.706757i | ||||
\(745\) | 278.139 | − | 160.584i | 0.373341 | − | 0.215548i | ||||
\(746\) | −602.108 | − | 1042.88i | −0.807115 | − | 1.39796i | ||||
\(747\) | −1181.95 | − | 682.400i | −1.58226 | − | 0.913520i | ||||
\(748\) | − | 43.9997i | − | 0.0588232i | ||||||
\(749\) | 429.738 | + | 383.523i | 0.573749 | + | 0.512047i | ||||
\(750\) | 135.991 | 0.181322 | ||||||||
\(751\) | 273.235 | − | 473.257i | 0.363829 | − | 0.630170i | −0.624759 | − | 0.780818i | \(-0.714803\pi\) |
0.988587 | + | 0.150648i | \(0.0481361\pi\) | |||||||
\(752\) | 1229.48 | − | 709.841i | 1.63495 | − | 0.943937i | ||||
\(753\) | 380.681 | + | 659.359i | 0.505553 | + | 0.875643i | ||||
\(754\) | −201.137 | − | 116.126i | −0.266760 | − | 0.154014i | ||||
\(755\) | 326.559i | 0.432529i | ||||||||
\(756\) | −151.835 | − | 460.389i | −0.200840 | − | 0.608980i | ||||
\(757\) | 191.558 | 0.253049 | 0.126524 | − | 0.991964i | \(-0.459618\pi\) | ||||
0.126524 | + | 0.991964i | \(0.459618\pi\) | |||||||
\(758\) | −197.158 | + | 341.488i | −0.260103 | + | 0.450511i | ||||
\(759\) | 981.612 | − | 566.734i | 1.29330 | − | 0.746685i | ||||
\(760\) | −15.3043 | − | 26.5079i | −0.0201373 | − | 0.0348788i | ||||
\(761\) | −471.813 | − | 272.401i | −0.619990 | − | 0.357952i | 0.156875 | − | 0.987618i | \(-0.449858\pi\) |
−0.776865 | + | 0.629667i | \(0.783191\pi\) | |||||||
\(762\) | − | 2202.01i | − | 2.88978i | ||||||
\(763\) | −225.103 | + | 74.2384i | −0.295024 | + | 0.0972980i | ||||
\(764\) | −122.400 | −0.160209 | ||||||||
\(765\) | 39.2765 | − | 68.0289i | 0.0513418 | − | 0.0889267i | ||||
\(766\) | 698.083 | − | 403.038i | 0.911336 | − | 0.526160i | ||||
\(767\) | 64.8048 | + | 112.245i | 0.0844912 | + | 0.146343i | ||||
\(768\) | −1174.70 | − | 678.211i | −1.52955 | − | 0.883087i | ||||
\(769\) | − | 120.495i | − | 0.156691i | −0.996926 | − | 0.0783453i | \(-0.975036\pi\) | ||
0.996926 | − | 0.0783453i | \(-0.0249637\pi\) | |||||||
\(770\) | 338.383 | − | 379.158i | 0.439458 | − | 0.492413i | ||||
\(771\) | 350.730 | 0.454903 | ||||||||
\(772\) | −264.755 | + | 458.569i | −0.342947 | + | 0.594001i | ||||
\(773\) | −1146.74 | + | 662.070i | −1.48349 | + | 0.856495i | −0.999824 | − | 0.0187565i | \(-0.994029\pi\) |
−0.483668 | + | 0.875251i | \(0.660696\pi\) | |||||||
\(774\) | 1129.34 | + | 1956.07i | 1.45909 | + | 2.52722i | ||||
\(775\) | 89.7786 | + | 51.8337i | 0.115843 | + | 0.0668822i | ||||
\(776\) | − | 180.358i | − | 0.232420i | ||||||
\(777\) | −459.194 | − | 95.4922i | −0.590983 | − | 0.122899i | ||||
\(778\) | −70.7923 | −0.0909926 | ||||||||
\(779\) | 66.4738 | − | 115.136i | 0.0853323 | − | 0.147800i | ||||
\(780\) | −97.4912 | + | 56.2866i | −0.124989 | + | 0.0721623i | ||||
\(781\) | 458.174 | + | 793.581i | 0.586650 | + | 1.01611i | ||||
\(782\) | 66.1575 | + | 38.1961i | 0.0846004 | + | 0.0488441i | ||||
\(783\) | − | 694.890i | − | 0.887471i | ||||||
\(784\) | −781.187 | + | 578.150i | −0.996412 | + | 0.737437i | ||||
\(785\) | 445.714 | 0.567788 | ||||||||
\(786\) | −260.406 | + | 451.037i | −0.331305 | + | 0.573838i | ||||
\(787\) | −1131.71 | + | 653.396i | −1.43801 | + | 0.830236i | −0.997712 | − | 0.0676145i | \(-0.978461\pi\) |
−0.440300 | + | 0.897851i | \(0.645128\pi\) | |||||||
\(788\) | 97.7416 | + | 169.293i | 0.124038 | + | 0.214839i | ||||
\(789\) | −1225.84 | − | 707.739i | −1.55366 | − | 0.897008i | ||||
\(790\) | − | 518.748i | − | 0.656643i | ||||||
\(791\) | 52.3817 | − | 251.888i | 0.0662221 | − | 0.318443i | ||||
\(792\) | 1364.47 | 1.72281 | ||||||||
\(793\) | 81.1972 | − | 140.638i | 0.102392 | − | 0.177349i | ||||
\(794\) | −981.796 | + | 566.840i | −1.23652 | + | 0.713904i | ||||
\(795\) | 387.472 | + | 671.121i | 0.487386 | + | 0.844177i | ||||
\(796\) | −117.055 | − | 67.5819i | −0.147054 | − | 0.0849019i | ||||
\(797\) | 263.263i | 0.330317i | 0.986267 | + | 0.165159i | \(0.0528136\pi\) | ||||
−0.986267 | + | 0.165159i | \(0.947186\pi\) | |||||||
\(798\) | 152.728 | + | 136.304i | 0.191389 | + | 0.170807i | ||||
\(799\) | −144.056 | −0.180295 | ||||||||
\(800\) | −60.3237 | + | 104.484i | −0.0754046 | + | 0.130605i | ||||
\(801\) | 676.022 | − | 390.301i | 0.843972 | − | 0.487268i | ||||
\(802\) | 720.202 | + | 1247.43i | 0.898007 | + | 1.55539i | ||||
\(803\) | 1486.59 | + | 858.283i | 1.85130 | + | 1.06885i | ||||
\(804\) | 609.691i | 0.758323i | ||||||||
\(805\) | 78.6887 | + | 238.597i | 0.0977500 | + | 0.296394i | ||||
\(806\) | −301.377 | −0.373917 | ||||||||
\(807\) | 590.494 | − | 1022.77i | 0.731715 | − | 1.26737i | ||||
\(808\) | 362.766 | − | 209.443i | 0.448968 | − | 0.259212i | ||||
\(809\) | 296.062 | + | 512.795i | 0.365961 | + | 0.633863i | 0.988930 | − | 0.148384i | \(-0.0474071\pi\) |
−0.622969 | + | 0.782247i | \(0.714074\pi\) | |||||||
\(810\) | −304.961 | − | 176.069i | −0.376495 | − | 0.217370i | ||||
\(811\) | 34.9609i | 0.0431083i | 0.999768 | + | 0.0215542i | \(0.00686144\pi\) | ||||
−0.999768 | + | 0.0215542i | \(0.993139\pi\) | |||||||
\(812\) | 169.143 | − | 55.7830i | 0.208304 | − | 0.0686983i | ||||
\(813\) | 2678.65 | 3.29477 | ||||||||
\(814\) | −211.472 | + | 366.280i | −0.259794 | + | 0.449976i | ||||
\(815\) | −248.060 | + | 143.218i | −0.304369 | + | 0.175727i | ||||
\(816\) | 102.655 | + | 177.804i | 0.125803 | + | 0.217898i | ||||
\(817\) | −113.928 | − | 65.7763i | −0.139447 | − | 0.0805096i | ||||
\(818\) | − | 1197.37i | − | 1.46377i | ||||||
\(819\) | −500.085 | + | 560.346i | −0.610605 | + | 0.684183i | ||||
\(820\) | −196.899 | −0.240120 | ||||||||
\(821\) | 412.442 | − | 714.371i | 0.502365 | − | 0.870122i | −0.497631 | − | 0.867389i | \(-0.665797\pi\) |
0.999996 | − | 0.00273351i | \(-0.000870103\pi\) | |||||||
\(822\) | 1064.55 | − | 614.616i | 1.29507 | − | 0.747707i | ||||
\(823\) | −421.891 | − | 730.737i | −0.512626 | − | 0.887894i | −0.999893 | − | 0.0146410i | \(-0.995339\pi\) |
0.487267 | − | 0.873253i | \(-0.337994\pi\) | |||||||
\(824\) | −136.442 | − | 78.7745i | −0.165584 | − | 0.0956002i | ||||
\(825\) | − | 353.083i | − | 0.427980i | ||||||
\(826\) | −341.745 | − | 71.0679i | −0.413735 | − | 0.0860387i | ||||
\(827\) | 359.972 | 0.435274 | 0.217637 | − | 0.976030i | \(-0.430165\pi\) | ||||
0.217637 | + | 0.976030i | \(0.430165\pi\) | |||||||
\(828\) | 223.078 | − | 386.382i | 0.269417 | − | 0.466645i | ||||
\(829\) | −1290.05 | + | 744.811i | −1.55615 | + | 0.898446i | −0.558534 | + | 0.829481i | \(0.688636\pi\) |
−0.997619 | + | 0.0689641i | \(0.978031\pi\) | |||||||
\(830\) | −206.725 | − | 358.058i | −0.249066 | − | 0.431395i | ||||
\(831\) | 1725.97 | + | 996.487i | 2.07698 | + | 1.19914i | ||||
\(832\) | 136.907i | 0.164552i | ||||||||
\(833\) | 97.9802 | − | 11.1718i | 0.117623 | − | 0.0134116i | ||||
\(834\) | 1612.77 | 1.93378 | ||||||||
\(835\) | 335.976 | − | 581.928i | 0.402367 | − | 0.696920i | ||||
\(836\) | 45.5208 | − | 26.2814i | 0.0544507 | − | 0.0314371i | ||||
\(837\) | −450.853 | − | 780.901i | −0.538654 | − | 0.932976i | ||||
\(838\) | −1230.81 | − | 710.610i | −1.46875 | − | 0.847983i | ||||
\(839\) | − | 778.799i | − | 0.928247i | −0.885770 | − | 0.464124i | \(-0.846369\pi\) | ||
0.885770 | − | 0.464124i | \(-0.153631\pi\) | |||||||
\(840\) | −93.3258 | + | 448.776i | −0.111102 | + | 0.534258i | ||||
\(841\) | −585.703 | −0.696436 | ||||||||
\(842\) | 327.703 | − | 567.597i | 0.389195 | − | 0.674106i | ||||
\(843\) | −703.671 | + | 406.264i | −0.834722 | + | 0.481927i | ||||
\(844\) | −113.488 | − | 196.566i | −0.134464 | − | 0.232898i | ||||
\(845\) | −254.104 | − | 146.707i | −0.300715 | − | 0.173618i | ||||
\(846\) | 2954.70i | 3.49255i | ||||||||
\(847\) | −352.498 | − | 314.590i | −0.416172 | − | 0.371416i | ||||
\(848\) | −1336.40 | −1.57594 | ||||||||
\(849\) | −116.022 | + | 200.957i | −0.136658 | + | 0.236698i | ||||
\(850\) | 20.6085 | − | 11.8983i | 0.0242453 | − | 0.0139981i | ||||
\(851\) | −104.546 | − | 181.078i | −0.122850 | − | 0.212783i | ||||
\(852\) | 473.426 | + | 273.333i | 0.555665 | + | 0.320813i | ||||
\(853\) | − | 496.640i | − | 0.582228i | −0.956688 | − | 0.291114i | \(-0.905974\pi\) | ||
0.956688 | − | 0.291114i | \(-0.0940259\pi\) | |||||||
\(854\) | 136.980 | + | 415.345i | 0.160398 | + | 0.486353i | ||||
\(855\) | 93.8408 | 0.109755 | ||||||||
\(856\) | −234.245 | + | 405.724i | −0.273650 | + | 0.473977i | ||||
\(857\) | −112.697 | + | 65.0654i | −0.131501 | + | 0.0759223i | −0.564307 | − | 0.825565i | \(-0.690857\pi\) |
0.432806 | + | 0.901487i | \(0.357523\pi\) | |||||||
\(858\) | 513.234 | + | 888.947i | 0.598175 | + | 1.03607i | ||||
\(859\) | 762.753 | + | 440.376i | 0.887954 | + | 0.512661i | 0.873273 | − | 0.487232i | \(-0.161993\pi\) |
0.0146815 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(860\) | 194.833i | 0.226550i | ||||||||
\(861\) | −1890.78 | + | 623.573i | −2.19602 | + | 0.724243i | ||||
\(862\) | −963.067 | −1.11725 | ||||||||
\(863\) | 389.409 | − | 674.477i | 0.451227 | − | 0.781549i | −0.547235 | − | 0.836979i | \(-0.684320\pi\) |
0.998463 | + | 0.0554301i | \(0.0176530\pi\) | |||||||
\(864\) | 908.807 | − | 524.700i | 1.05186 | − | 0.607291i | ||||
\(865\) | −124.974 | − | 216.461i | −0.144478 | − | 0.250244i | ||||
\(866\) | −639.706 | − | 369.334i | −0.738690 | − | 0.426483i | ||||
\(867\) | 1465.63i | 1.69047i | ||||||||
\(868\) | 153.886 | − | 172.430i | 0.177288 | − | 0.198652i | ||||
\(869\) | −1346.86 | −1.54989 | ||||||||
\(870\) | 217.287 | − | 376.353i | 0.249756 | − | 0.432590i | ||||
\(871\) | 396.250 | − | 228.775i | 0.454936 | − | 0.262658i | ||||
\(872\) | −96.3953 | − | 166.962i | −0.110545 | − | 0.191470i | ||||
\(873\) | 478.866 | + | 276.474i | 0.548530 | + | 0.316694i | ||||
\(874\) | 91.2594i | 0.104416i | ||||||||
\(875\) | 76.6231 | + | 15.9342i | 0.0875693 | + | 0.0182106i | ||||
\(876\) | 1024.05 | 1.16901 | ||||||||
\(877\) | 31.3183 | − | 54.2449i | 0.0357107 | − | 0.0618528i | −0.847618 | − | 0.530607i | \(-0.821964\pi\) |
0.883328 | + | 0.468755i | \(0.155297\pi\) | |||||||
\(878\) | 435.253 | − | 251.293i | 0.495732 | − | 0.286211i | ||||
\(879\) | −140.134 | − | 242.720i | −0.159425 | − | 0.276132i | ||||
\(880\) | 527.318 | + | 304.447i | 0.599225 | + | 0.345963i | ||||
\(881\) | − | 1073.96i | − | 1.21902i | −0.792777 | − | 0.609512i | \(-0.791365\pi\) | ||
0.792777 | − | 0.609512i | \(-0.208635\pi\) | |||||||
\(882\) | −229.144 | − | 2009.65i | −0.259800 | − | 2.27852i | ||||
\(883\) | 61.5102 | 0.0696605 | 0.0348303 | − | 0.999393i | \(-0.488911\pi\) | ||||
0.0348303 | + | 0.999393i | \(0.488911\pi\) | |||||||
\(884\) | −9.84939 | + | 17.0597i | −0.0111418 | + | 0.0192982i | ||||
\(885\) | −210.025 | + | 121.258i | −0.237316 | + | 0.137015i | ||||
\(886\) | 439.170 | + | 760.664i | 0.495677 | + | 0.858538i | ||||
\(887\) | 112.273 | + | 64.8207i | 0.126576 | + | 0.0730786i | 0.561951 | − | 0.827171i | \(-0.310051\pi\) |
−0.435375 | + | 0.900249i | \(0.643384\pi\) | |||||||
\(888\) | − | 381.482i | − | 0.429597i | ||||||
\(889\) | 258.012 | − | 1240.70i | 0.290227 | − | 1.39562i | ||||
\(890\) | 236.474 | 0.265701 | ||||||||
\(891\) | −457.140 | + | 791.790i | −0.513064 | + | 0.888653i | ||||
\(892\) | −317.117 | + | 183.087i | −0.355512 | + | 0.205255i | ||||
\(893\) | −86.0458 | − | 149.036i | −0.0963559 | − | 0.166893i | ||||
\(894\) | −1512.98 | − | 873.520i | −1.69237 | − | 0.977092i | ||||
\(895\) | − | 787.870i | − | 0.880302i | ||||||
\(896\) | −779.163 | − | 695.371i | −0.869602 | − | 0.776083i | ||||
\(897\) | −507.456 | −0.565726 | ||||||||
\(898\) | −5.00131 | + | 8.66252i | −0.00556938 | + | 0.00964646i | ||||
\(899\) | 286.897 | − | 165.640i | 0.319129 | − | 0.184249i | ||||
\(900\) | −69.4903 | − | 120.361i | −0.0772114 | − | 0.133734i | ||||
\(901\) | 117.437 | + | 67.8023i | 0.130341 | + | 0.0752523i | ||||
\(902\) | 1795.37i | 1.99043i | ||||||||
\(903\) | 617.030 | + | 1870.94i | 0.683311 | + | 2.07191i | ||||
\(904\) | 209.260 | 0.231482 | ||||||||
\(905\) | 172.155 | − | 298.181i | 0.190226 | − | 0.329482i | ||||
\(906\) | 1538.38 | − | 888.185i | 1.69799 | − | 0.980337i | ||||
\(907\) | 700.954 | + | 1214.09i | 0.772827 | + | 1.33858i | 0.936008 | + | 0.351979i | \(0.114491\pi\) |
−0.163181 | + | 0.986596i | \(0.552175\pi\) | |||||||
\(908\) | −474.029 | − | 273.681i | −0.522059 | − | 0.301411i | ||||
\(909\) | 1284.23i | 1.41280i | ||||||||
\(910\) | −216.073 | + | 71.2605i | −0.237443 | + | 0.0783082i | ||||
\(911\) | −1235.23 | −1.35590 | −0.677950 | − | 0.735108i | \(-0.737132\pi\) | ||||
−0.677950 | + | 0.735108i | \(0.737132\pi\) | |||||||
\(912\) | −122.634 | + | 212.408i | −0.134467 | + | 0.232904i | ||||
\(913\) | −929.648 | + | 536.732i | −1.01823 | + | 0.587878i | ||||
\(914\) | −592.639 | − | 1026.48i | −0.648401 | − | 1.12306i | ||||
\(915\) | 263.151 | + | 151.930i | 0.287597 | + | 0.166044i | ||||
\(916\) | − | 1.39977i | − | 0.00152813i | ||||||
\(917\) | −199.572 | + | 223.620i | −0.217635 | + | 0.243861i | ||||
\(918\) | −206.985 | −0.225474 | ||||||||
\(919\) | −341.200 | + | 590.976i | −0.371273 | + | 0.643064i | −0.989762 | − | 0.142730i | \(-0.954412\pi\) |
0.618488 | + | 0.785794i | \(0.287745\pi\) | |||||||
\(920\) | −176.970 | + | 102.174i | −0.192359 | + | 0.111059i | ||||
\(921\) | −455.048 | − | 788.166i | −0.494080 | − | 0.855772i | ||||
\(922\) | 614.648 | + | 354.867i | 0.666646 | + | 0.384889i | ||||
\(923\) | − | 410.251i | − | 0.444476i | ||||||
\(924\) | −770.664 | − | 160.264i | −0.834052 | − | 0.173446i | ||||
\(925\) | −65.1335 | −0.0704146 | ||||||||
\(926\) | −675.805 | + | 1170.53i | −0.729811 | + | 1.26407i | ||||
\(927\) | 418.306 | − | 241.509i | 0.451247 | − | 0.260528i | ||||
\(928\) | 192.771 | + | 333.888i | 0.207727 | + | 0.359794i | ||||
\(929\) | 109.020 | + | 62.9427i | 0.117352 | + | 0.0677531i | 0.557527 | − | 0.830159i | \(-0.311750\pi\) |
−0.440175 | + | 0.897912i | \(0.645084\pi\) | |||||||
\(930\) | − | 563.915i | − | 0.606360i | ||||||
\(931\) | 70.0825 | + | 94.6943i | 0.0752766 | + | 0.101712i | ||||
\(932\) | 165.387 | 0.177454 | ||||||||
\(933\) | −562.553 | + | 974.371i | −0.602951 | + | 1.04434i | ||||
\(934\) | 1823.84 | − | 1053.00i | 1.95272 | − | 1.12740i | ||||
\(935\) | −30.8924 | − | 53.5072i | −0.0330400 | − | 0.0572270i | ||||
\(936\) | −529.033 | − | 305.437i | −0.565206 | − | 0.326322i | ||||
\(937\) | 235.260i | 0.251078i | 0.992089 | + | 0.125539i | \(0.0400660\pi\) | ||||
−0.992089 | + | 0.125539i | \(0.959934\pi\) | |||||||
\(938\) | −250.885 | + | 1206.43i | −0.267468 | + | 1.28618i | ||||
\(939\) | 787.358 | 0.838507 | ||||||||
\(940\) | −127.436 | + | 220.725i | −0.135570 | + | 0.234814i | ||||
\(941\) | 300.317 | − | 173.388i | 0.319147 | − | 0.184260i | −0.331865 | − | 0.943327i | \(-0.607678\pi\) |
0.651012 | + | 0.759067i | \(0.274345\pi\) | |||||||
\(942\) | −1212.27 | − | 2099.71i | −1.28691 | − | 2.22899i | ||||
\(943\) | −768.665 | − | 443.789i | −0.815128 | − | 0.470614i | ||||
\(944\) | − | 418.221i | − | 0.443030i | ||||||
\(945\) | −507.884 | − | 453.265i | −0.537444 | − | 0.479646i | ||||
\(946\) | 1776.53 | 1.87794 | ||||||||
\(947\) | 347.003 | − | 601.027i | 0.366424 | − | 0.634665i | −0.622580 | − | 0.782556i | \(-0.713915\pi\) |
0.989004 | + | 0.147892i | \(0.0472487\pi\) | |||||||
\(948\) | −695.847 | + | 401.747i | −0.734016 | + | 0.423784i | ||||
\(949\) | −384.255 | − | 665.550i | −0.404906 | − | 0.701317i | ||||
\(950\) | 24.6193 | + | 14.2140i | 0.0259151 | + | 0.0149621i | ||||
\(951\) | − | 664.831i | − | 0.699086i | ||||||
\(952\) | 25.1221 | + | 76.1742i | 0.0263887 | + | 0.0800149i | ||||
\(953\) | 1530.11 | 1.60557 | 0.802786 | − | 0.596267i | \(-0.203350\pi\) | ||||
0.802786 | + | 0.596267i | \(0.203350\pi\) | |||||||
\(954\) | 1390.68 | − | 2408.73i | 1.45774 | − | 2.52487i | ||||
\(955\) | −148.848 | + | 85.9373i | −0.155861 | + | 0.0899867i | ||||
\(956\) | 127.332 | + | 220.546i | 0.133193 | + | 0.230696i | ||||
\(957\) | −977.149 | − | 564.157i | −1.02105 | − | 0.589506i | ||||
\(958\) | − | 78.2774i | − | 0.0817091i | ||||||
\(959\) | 671.823 | − | 221.566i | 0.700545 | − | 0.231038i | ||||
\(960\) | −256.171 | −0.266845 | ||||||||
\(961\) | −265.562 | + | 459.966i | −0.276339 | + | 0.478633i | ||||
\(962\) | 163.985 | − | 94.6765i | 0.170462 | − | 0.0984164i | ||||
\(963\) | −718.154 | − | 1243.88i | −0.745747 | − | 1.29167i | ||||
\(964\) | −355.594 | − | 205.302i | −0.368874 | − | 0.212969i | ||||
\(965\) | 743.542i | 0.770510i | ||||||||
\(966\) | 909.983 | − | 1019.64i | 0.942011 | − | 1.05552i | ||||
\(967\) | 66.4870 | 0.0687560 | 0.0343780 | − | 0.999409i | \(-0.489055\pi\) | ||||
0.0343780 | + | 0.999409i | \(0.489055\pi\) | |||||||
\(968\) | 192.142 | − | 332.800i | 0.198494 | − | 0.343802i | ||||
\(969\) | 21.5532 | − | 12.4437i | 0.0222427 | − | 0.0128418i | ||||
\(970\) | 83.7544 | + | 145.067i | 0.0863447 | + | 0.149553i | ||||
\(971\) | −527.453 | − | 304.525i | −0.543206 | − | 0.313620i | 0.203171 | − | 0.979143i | \(-0.434875\pi\) |
−0.746377 | + | 0.665523i | \(0.768208\pi\) | |||||||
\(972\) | − | 77.8565i | − | 0.0800993i | ||||||
\(973\) | 908.699 | + | 188.969i | 0.933915 | + | 0.194213i | ||||
\(974\) | −1456.47 | −1.49534 | ||||||||
\(975\) | −79.0381 | + | 136.898i | −0.0810647 | + | 0.140408i | ||||
\(976\) | −453.806 | + | 262.005i | −0.464965 | + | 0.268448i | ||||
\(977\) | 635.780 | + | 1101.20i | 0.650748 | + | 1.12713i | 0.982942 | + | 0.183917i | \(0.0588777\pi\) |
−0.332194 | + | 0.943211i | \(0.607789\pi\) | |||||||
\(978\) | 1349.36 | + | 779.056i | 1.37972 | + | 0.796581i | ||||
\(979\) | − | 613.973i | − | 0.627143i | ||||||
\(980\) | 69.5584 | − | 160.010i | 0.0709779 | − | 0.163276i | ||||
\(981\) | 591.063 | 0.602511 | ||||||||
\(982\) | 264.340 | − | 457.851i | 0.269186 | − | 0.466243i | ||||
\(983\) | 147.832 | − | 85.3509i | 0.150389 | − | 0.0868270i | −0.422917 | − | 0.906168i | \(-0.638994\pi\) |
0.573306 | + | 0.819341i | \(0.305661\pi\) | |||||||
\(984\) | −809.683 | − | 1402.41i | −0.822848 | − | 1.42521i | ||||
\(985\) | 237.723 | + | 137.250i | 0.241343 | + | 0.139340i | ||||
\(986\) | − | 76.0448i | − | 0.0771245i | ||||||
\(987\) | −524.707 | + | 2523.16i | −0.531618 | + | 2.55640i | ||||
\(988\) | −23.5325 | −0.0238183 | ||||||||
\(989\) | −439.133 | + | 760.600i | −0.444017 | + | 0.769060i | ||||
\(990\) | −1097.48 | + | 633.628i | −1.10856 | + | 0.640028i | ||||
\(991\) | 11.7052 | + | 20.2740i | 0.0118115 | + | 0.0204581i | 0.871871 | − | 0.489736i | \(-0.162907\pi\) |
−0.860059 | + | 0.510194i | \(0.829574\pi\) | |||||||
\(992\) | 433.262 | + | 250.144i | 0.436756 | + | 0.252161i | ||||
\(993\) | 2978.25i | 2.99924i | ||||||||
\(994\) | 824.322 | + | 735.673i | 0.829298 | + | 0.740113i | ||||
\(995\) | −189.798 | −0.190752 | ||||||||
\(996\) | −320.198 | + | 554.600i | −0.321484 | + | 0.556827i | ||||
\(997\) | 1576.72 | − | 910.318i | 1.58146 | − | 0.913057i | 0.586815 | − | 0.809721i | \(-0.300382\pi\) |
0.994647 | − | 0.103336i | \(-0.0329516\pi\) | |||||||
\(998\) | 971.429 | + | 1682.56i | 0.973376 | + | 1.68594i | ||||
\(999\) | 490.634 | + | 283.268i | 0.491125 | + | 0.283551i |
(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 | 35.3.h.a.26.2 | ✓ | 12 | |
3.2 | odd | 2 | 315.3.w.c.271.5 | 12 | |||
4.3 | odd | 2 | 560.3.bx.c.481.1 | 12 | |||
5.2 | odd | 4 | 175.3.j.b.124.3 | 24 | |||
5.3 | odd | 4 | 175.3.j.b.124.10 | 24 | |||
5.4 | even | 2 | 175.3.i.d.26.5 | 12 | |||
7.2 | even | 3 | 245.3.d.a.146.10 | 12 | |||
7.3 | odd | 6 | inner | 35.3.h.a.31.2 | yes | 12 | |
7.4 | even | 3 | 245.3.h.c.31.2 | 12 | |||
7.5 | odd | 6 | 245.3.d.a.146.9 | 12 | |||
7.6 | odd | 2 | 245.3.h.c.166.2 | 12 | |||
21.17 | even | 6 | 315.3.w.c.136.5 | 12 | |||
28.3 | even | 6 | 560.3.bx.c.241.1 | 12 | |||
35.3 | even | 12 | 175.3.j.b.24.3 | 24 | |||
35.17 | even | 12 | 175.3.j.b.24.10 | 24 | |||
35.24 | odd | 6 | 175.3.i.d.101.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.3.h.a.26.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
35.3.h.a.31.2 | yes | 12 | 7.3 | odd | 6 | inner | |
175.3.i.d.26.5 | 12 | 5.4 | even | 2 | |||
175.3.i.d.101.5 | 12 | 35.24 | odd | 6 | |||
175.3.j.b.24.3 | 24 | 35.3 | even | 12 | |||
175.3.j.b.24.10 | 24 | 35.17 | even | 12 | |||
175.3.j.b.124.3 | 24 | 5.2 | odd | 4 | |||
175.3.j.b.124.10 | 24 | 5.3 | odd | 4 | |||
245.3.d.a.146.9 | 12 | 7.5 | odd | 6 | |||
245.3.d.a.146.10 | 12 | 7.2 | even | 3 | |||
245.3.h.c.31.2 | 12 | 7.4 | even | 3 | |||
245.3.h.c.166.2 | 12 | 7.6 | odd | 2 | |||
315.3.w.c.136.5 | 12 | 21.17 | even | 6 | |||
315.3.w.c.271.5 | 12 | 3.2 | odd | 2 | |||
560.3.bx.c.241.1 | 12 | 28.3 | even | 6 | |||
560.3.bx.c.481.1 | 12 | 4.3 | odd | 2 |