Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(4,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.e (of order \(7\), degree \(6\), 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: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{7})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{7}]$ |
Embedding invariants
Embedding label | 11.5 | ||
Character | \(\chi\) | \(=\) | 43.11 |
Dual form | 43.4.e.a.4.5 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{7}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.873702 | − | 1.09559i | −0.308900 | − | 0.387349i | 0.603013 | − | 0.797731i | \(-0.293967\pi\) |
−0.911913 | + | 0.410383i | \(0.865395\pi\) | |||||||
\(3\) | 4.80787 | − | 6.02888i | 0.925275 | − | 1.16026i | −0.0614914 | − | 0.998108i | \(-0.519586\pi\) |
0.986766 | − | 0.162150i | \(-0.0518429\pi\) | |||||||
\(4\) | 1.34321 | − | 5.88499i | 0.167901 | − | 0.735624i | ||||
\(5\) | −14.6785 | + | 7.06881i | −1.31289 | + | 0.632254i | −0.953629 | − | 0.300984i | \(-0.902685\pi\) |
−0.359259 | + | 0.933238i | \(0.616971\pi\) | |||||||
\(6\) | −10.8058 | −0.735242 | ||||||||
\(7\) | 16.8292 | 0.908691 | 0.454346 | − | 0.890825i | \(-0.349873\pi\) | ||||
0.454346 | + | 0.890825i | \(0.349873\pi\) | |||||||
\(8\) | −17.7214 | + | 8.53416i | −0.783181 | + | 0.377160i | ||||
\(9\) | −7.22369 | − | 31.6490i | −0.267544 | − | 1.17219i | ||||
\(10\) | 20.5692 | + | 9.90558i | 0.650454 | + | 0.313242i | ||||
\(11\) | −3.70017 | − | 16.2115i | −0.101422 | − | 0.444360i | −0.999985 | − | 0.00551443i | \(-0.998245\pi\) |
0.898563 | − | 0.438845i | \(-0.144612\pi\) | |||||||
\(12\) | −29.0219 | − | 36.3923i | −0.698158 | − | 0.875463i | ||||
\(13\) | 72.4170 | − | 34.8742i | 1.54499 | − | 0.744028i | 0.549199 | − | 0.835691i | \(-0.314933\pi\) |
0.995790 | + | 0.0916636i | \(0.0292184\pi\) | |||||||
\(14\) | −14.7037 | − | 18.4379i | −0.280695 | − | 0.351980i | ||||
\(15\) | −27.9555 | + | 122.481i | −0.481205 | + | 2.10830i | ||||
\(16\) | −18.6753 | − | 8.99355i | −0.291801 | − | 0.140524i | ||||
\(17\) | 77.8953 | + | 37.5124i | 1.11132 | + | 0.535182i | 0.897199 | − | 0.441626i | \(-0.145598\pi\) |
0.214117 | + | 0.976808i | \(0.431312\pi\) | |||||||
\(18\) | −28.3629 | + | 35.5660i | −0.371400 | + | 0.465721i | ||||
\(19\) | −29.9127 | + | 131.056i | −0.361182 | + | 1.58244i | 0.389018 | + | 0.921230i | \(0.372814\pi\) |
−0.750200 | + | 0.661211i | \(0.770043\pi\) | |||||||
\(20\) | 21.8835 | + | 95.8779i | 0.244665 | + | 1.07195i | ||||
\(21\) | 80.9126 | − | 101.461i | 0.840789 | − | 1.05432i | ||||
\(22\) | −14.5283 | + | 18.2179i | −0.140793 | + | 0.176549i | ||||
\(23\) | −20.6519 | − | 90.4819i | −0.187227 | − | 0.820295i | −0.978070 | − | 0.208276i | \(-0.933215\pi\) |
0.790843 | − | 0.612019i | \(-0.209642\pi\) | |||||||
\(24\) | −33.7506 | + | 147.871i | −0.287055 | + | 1.25767i | ||||
\(25\) | 87.5551 | − | 109.791i | 0.700441 | − | 0.878325i | ||||
\(26\) | −101.479 | − | 48.8695i | −0.765446 | − | 0.368619i | ||||
\(27\) | −37.9542 | − | 18.2778i | −0.270529 | − | 0.130280i | ||||
\(28\) | 22.6052 | − | 99.0397i | 0.152571 | − | 0.668455i | ||||
\(29\) | 30.9122 | + | 38.7627i | 0.197940 | + | 0.248208i | 0.870889 | − | 0.491480i | \(-0.163544\pi\) |
−0.672949 | + | 0.739689i | \(0.734973\pi\) | |||||||
\(30\) | 158.613 | − | 76.3842i | 0.965290 | − | 0.464859i | ||||
\(31\) | −37.2757 | − | 46.7423i | −0.215965 | − | 0.270812i | 0.662034 | − | 0.749474i | \(-0.269693\pi\) |
−0.877999 | + | 0.478662i | \(0.841122\pi\) | |||||||
\(32\) | 41.4779 | + | 181.727i | 0.229135 | + | 1.00391i | ||||
\(33\) | −115.527 | − | 55.6350i | −0.609415 | − | 0.293479i | ||||
\(34\) | −26.9591 | − | 118.116i | −0.135984 | − | 0.595785i | ||||
\(35\) | −247.028 | + | 118.962i | −1.19301 | + | 0.574523i | ||||
\(36\) | −195.957 | −0.907209 | ||||||||
\(37\) | −128.973 | −0.573053 | −0.286526 | − | 0.958072i | \(-0.592501\pi\) | ||||
−0.286526 | + | 0.958072i | \(0.592501\pi\) | |||||||
\(38\) | 169.718 | − | 81.7321i | 0.724525 | − | 0.348913i | ||||
\(39\) | 137.919 | − | 604.264i | 0.566276 | − | 2.48102i | ||||
\(40\) | 199.797 | − | 250.538i | 0.789768 | − | 0.990338i | ||||
\(41\) | 152.540 | + | 191.279i | 0.581043 | + | 0.728605i | 0.982290 | − | 0.187365i | \(-0.0599947\pi\) |
−0.401248 | + | 0.915970i | \(0.631423\pi\) | |||||||
\(42\) | −181.853 | −0.668108 | ||||||||
\(43\) | −48.3873 | + | 277.787i | −0.171605 | + | 0.985166i | ||||
\(44\) | −100.375 | −0.343911 | ||||||||
\(45\) | 329.754 | + | 413.499i | 1.09237 | + | 1.36979i | ||||
\(46\) | −81.0872 | + | 101.680i | −0.259906 | + | 0.325911i | ||||
\(47\) | −17.3079 | + | 75.8307i | −0.0537151 | + | 0.235341i | −0.994658 | − | 0.103223i | \(-0.967084\pi\) |
0.940943 | + | 0.338565i | \(0.109941\pi\) | |||||||
\(48\) | −144.009 | + | 69.3512i | −0.433041 | + | 0.208541i | ||||
\(49\) | −59.7780 | −0.174280 | ||||||||
\(50\) | −196.782 | −0.556584 | ||||||||
\(51\) | 600.668 | − | 289.266i | 1.64922 | − | 0.794223i | ||||
\(52\) | −107.963 | − | 473.017i | −0.287919 | − | 1.26145i | ||||
\(53\) | −400.073 | − | 192.665i | −1.03687 | − | 0.499332i | −0.163582 | − | 0.986530i | \(-0.552305\pi\) |
−0.873292 | + | 0.487198i | \(0.838019\pi\) | |||||||
\(54\) | 13.1357 | + | 57.5515i | 0.0331028 | + | 0.145033i | ||||
\(55\) | 168.909 | + | 211.806i | 0.414104 | + | 0.519270i | ||||
\(56\) | −298.236 | + | 143.623i | −0.711670 | + | 0.342722i | ||||
\(57\) | 646.306 | + | 810.442i | 1.50185 | + | 1.88326i | ||||
\(58\) | 15.4598 | − | 67.7340i | 0.0349996 | − | 0.153343i | ||||
\(59\) | −485.882 | − | 233.988i | −1.07214 | − | 0.516317i | −0.187346 | − | 0.982294i | \(-0.559989\pi\) |
−0.884797 | + | 0.465977i | \(0.845703\pi\) | |||||||
\(60\) | 683.249 | + | 329.036i | 1.47012 | + | 0.707972i | ||||
\(61\) | 391.056 | − | 490.369i | 0.820813 | − | 1.02927i | −0.178162 | − | 0.984001i | \(-0.557015\pi\) |
0.998975 | − | 0.0452662i | \(-0.0144136\pi\) | |||||||
\(62\) | −18.6424 | + | 81.6776i | −0.0381869 | + | 0.167308i | ||||
\(63\) | −121.569 | − | 532.628i | −0.243115 | − | 1.06516i | ||||
\(64\) | 59.4685 | − | 74.5712i | 0.116149 | − | 0.145647i | ||||
\(65\) | −816.457 | + | 1023.80i | −1.55798 | + | 1.95365i | ||||
\(66\) | 39.9834 | + | 175.179i | 0.0745699 | + | 0.326712i | ||||
\(67\) | −121.667 | + | 533.057i | −0.221850 | + | 0.971989i | 0.734234 | + | 0.678896i | \(0.237541\pi\) |
−0.956084 | + | 0.293092i | \(0.905316\pi\) | |||||||
\(68\) | 325.390 | − | 408.026i | 0.580284 | − | 0.727653i | ||||
\(69\) | −644.796 | − | 310.517i | −1.12499 | − | 0.541767i | ||||
\(70\) | 346.162 | + | 166.703i | 0.591062 | + | 0.284640i | ||||
\(71\) | −50.5040 | + | 221.273i | −0.0844186 | + | 0.369862i | −0.999437 | − | 0.0335499i | \(-0.989319\pi\) |
0.915018 | + | 0.403412i | \(0.132176\pi\) | |||||||
\(72\) | 398.112 | + | 499.216i | 0.651637 | + | 0.817127i | ||||
\(73\) | −663.422 | + | 319.487i | −1.06367 | + | 0.512235i | −0.882060 | − | 0.471137i | \(-0.843844\pi\) |
−0.181606 | + | 0.983371i | \(0.558130\pi\) | |||||||
\(74\) | 112.683 | + | 141.301i | 0.177016 | + | 0.221971i | ||||
\(75\) | −240.961 | − | 1055.72i | −0.370983 | − | 1.62538i | ||||
\(76\) | 731.086 | + | 352.072i | 1.10344 | + | 0.531388i | ||||
\(77\) | −62.2710 | − | 272.827i | −0.0921615 | − | 0.403786i | ||||
\(78\) | −782.524 | + | 376.844i | −1.13594 | + | 0.547040i | ||||
\(79\) | 440.716 | 0.627651 | 0.313826 | − | 0.949481i | \(-0.398389\pi\) | ||||
0.313826 | + | 0.949481i | \(0.398389\pi\) | |||||||
\(80\) | 337.700 | 0.471950 | ||||||||
\(81\) | 497.025 | − | 239.355i | 0.681791 | − | 0.328333i | ||||
\(82\) | 76.2885 | − | 334.242i | 0.102740 | − | 0.450132i | ||||
\(83\) | −53.2813 | + | 66.8126i | −0.0704624 | + | 0.0883571i | −0.815814 | − | 0.578315i | \(-0.803710\pi\) |
0.745351 | + | 0.666672i | \(0.232282\pi\) | |||||||
\(84\) | −488.415 | − | 612.454i | −0.634411 | − | 0.795526i | ||||
\(85\) | −1408.56 | −1.79740 | ||||||||
\(86\) | 346.616 | − | 189.690i | 0.434611 | − | 0.237847i | ||||
\(87\) | 382.317 | 0.471134 | ||||||||
\(88\) | 203.924 | + | 255.713i | 0.247027 | + | 0.309762i | ||||
\(89\) | 550.122 | − | 689.831i | 0.655200 | − | 0.821595i | −0.337611 | − | 0.941286i | \(-0.609619\pi\) |
0.992811 | + | 0.119691i | \(0.0381904\pi\) | |||||||
\(90\) | 164.917 | − | 722.549i | 0.193153 | − | 0.846259i | ||||
\(91\) | 1218.72 | − | 586.905i | 1.40392 | − | 0.676092i | ||||
\(92\) | −560.225 | −0.634864 | ||||||||
\(93\) | −461.020 | −0.514038 | ||||||||
\(94\) | 98.2010 | − | 47.2911i | 0.107752 | − | 0.0518905i | ||||
\(95\) | −487.337 | − | 2135.16i | −0.526313 | − | 2.30593i | ||||
\(96\) | 1295.03 | + | 623.653i | 1.37681 | + | 0.663035i | ||||
\(97\) | 1.55579 | + | 6.81635i | 0.00162852 | + | 0.00713501i | 0.975736 | − | 0.218952i | \(-0.0702638\pi\) |
−0.974107 | + | 0.226087i | \(0.927407\pi\) | |||||||
\(98\) | 52.2281 | + | 65.4920i | 0.0538351 | + | 0.0675071i | ||||
\(99\) | −486.350 | + | 234.214i | −0.493738 | + | 0.237772i | ||||
\(100\) | −528.512 | − | 662.733i | −0.528512 | − | 0.662733i | ||||
\(101\) | −168.615 | + | 738.750i | −0.166117 | + | 0.727805i | 0.821408 | + | 0.570341i | \(0.193189\pi\) |
−0.987525 | + | 0.157464i | \(0.949668\pi\) | |||||||
\(102\) | −841.721 | − | 405.351i | −0.817086 | − | 0.393488i | ||||
\(103\) | −646.749 | − | 311.458i | −0.618700 | − | 0.297950i | 0.0981564 | − | 0.995171i | \(-0.468705\pi\) |
−0.716857 | + | 0.697221i | \(0.754420\pi\) | |||||||
\(104\) | −985.706 | + | 1236.04i | −0.929389 | + | 1.16542i | ||||
\(105\) | −470.468 | + | 2061.26i | −0.437267 | + | 1.91579i | ||||
\(106\) | 138.463 | + | 606.647i | 0.126875 | + | 0.555875i | ||||
\(107\) | 0.347739 | − | 0.436051i | 0.000314180 | − | 0.000393969i | −0.781674 | − | 0.623687i | \(-0.785634\pi\) |
0.781989 | + | 0.623293i | \(0.214206\pi\) | |||||||
\(108\) | −158.545 | + | 198.809i | −0.141259 | + | 0.177134i | ||||
\(109\) | 268.156 | + | 1174.87i | 0.235640 | + | 1.03240i | 0.944875 | + | 0.327432i | \(0.106183\pi\) |
−0.709235 | + | 0.704972i | \(0.750959\pi\) | |||||||
\(110\) | 84.4751 | − | 370.110i | 0.0732217 | − | 0.320805i | ||||
\(111\) | −620.083 | + | 777.559i | −0.530231 | + | 0.664889i | ||||
\(112\) | −314.290 | − | 151.354i | −0.265157 | − | 0.127693i | ||||
\(113\) | 1679.36 | + | 808.736i | 1.39806 | + | 0.673270i | 0.972767 | − | 0.231786i | \(-0.0744570\pi\) |
0.425292 | + | 0.905056i | \(0.360171\pi\) | |||||||
\(114\) | 323.231 | − | 1416.17i | 0.265556 | − | 1.16348i | ||||
\(115\) | 942.739 | + | 1182.16i | 0.764443 | + | 0.958581i | ||||
\(116\) | 269.640 | − | 129.852i | 0.215822 | − | 0.103935i | ||||
\(117\) | −1626.85 | − | 2040.01i | −1.28549 | − | 1.61196i | ||||
\(118\) | 168.161 | + | 736.762i | 0.131191 | + | 0.574784i | ||||
\(119\) | 1310.92 | + | 631.304i | 1.00984 | + | 0.486315i | ||||
\(120\) | −549.863 | − | 2409.11i | −0.418295 | − | 1.83267i | ||||
\(121\) | 950.067 | − | 457.528i | 0.713800 | − | 0.343748i | ||||
\(122\) | −878.908 | −0.652235 | ||||||||
\(123\) | 1886.59 | 1.38299 | ||||||||
\(124\) | −325.147 | + | 156.583i | −0.235476 | + | 0.113399i | ||||
\(125\) | −55.9292 | + | 245.042i | −0.0400197 | + | 0.175338i | ||||
\(126\) | −477.325 | + | 598.547i | −0.337488 | + | 0.423197i | ||||
\(127\) | −1547.04 | − | 1939.92i | −1.08092 | − | 1.35544i | −0.930281 | − | 0.366848i | \(-0.880437\pi\) |
−0.150644 | − | 0.988588i | \(-0.548135\pi\) | |||||||
\(128\) | 1357.54 | 0.937431 | ||||||||
\(129\) | 1442.10 | + | 1627.28i | 0.984265 | + | 1.11065i | ||||
\(130\) | 1835.01 | 1.23801 | ||||||||
\(131\) | 600.223 | + | 752.656i | 0.400319 | + | 0.501984i | 0.940608 | − | 0.339496i | \(-0.110256\pi\) |
−0.540289 | + | 0.841480i | \(0.681685\pi\) | |||||||
\(132\) | −482.589 | + | 605.147i | −0.318212 | + | 0.399025i | ||||
\(133\) | −503.408 | + | 2205.57i | −0.328203 | + | 1.43795i | ||||
\(134\) | 690.311 | − | 332.436i | 0.445028 | − | 0.214314i | ||||
\(135\) | 686.314 | 0.437545 | ||||||||
\(136\) | −1700.55 | −1.07221 | ||||||||
\(137\) | 70.4394 | − | 33.9218i | 0.0439273 | − | 0.0211543i | −0.411791 | − | 0.911278i | \(-0.635097\pi\) |
0.455718 | + | 0.890124i | \(0.349382\pi\) | |||||||
\(138\) | 223.160 | + | 977.730i | 0.137657 | + | 0.603115i | ||||
\(139\) | −1838.73 | − | 885.487i | −1.12201 | − | 0.540331i | −0.221496 | − | 0.975161i | \(-0.571094\pi\) |
−0.900512 | + | 0.434830i | \(0.856808\pi\) | |||||||
\(140\) | 368.282 | + | 1613.55i | 0.222325 | + | 0.974070i | ||||
\(141\) | 373.960 | + | 468.931i | 0.223355 | + | 0.280079i | ||||
\(142\) | 286.549 | − | 137.995i | 0.169343 | − | 0.0815511i | ||||
\(143\) | −833.319 | − | 1044.95i | −0.487312 | − | 0.611070i | ||||
\(144\) | −149.733 | + | 656.021i | −0.0866508 | + | 0.379642i | ||||
\(145\) | −727.752 | − | 350.467i | −0.416803 | − | 0.200722i | ||||
\(146\) | 929.658 | + | 447.700i | 0.526980 | + | 0.253780i | ||||
\(147\) | −287.405 | + | 360.394i | −0.161257 | + | 0.202210i | ||||
\(148\) | −173.237 | + | 759.002i | −0.0962163 | + | 0.421551i | ||||
\(149\) | −74.8941 | − | 328.132i | −0.0411783 | − | 0.180414i | 0.950157 | − | 0.311773i | \(-0.100923\pi\) |
−0.991335 | + | 0.131359i | \(0.958066\pi\) | |||||||
\(150\) | −946.103 | + | 1186.38i | −0.514993 | + | 0.645781i | ||||
\(151\) | 843.211 | − | 1057.35i | 0.454434 | − | 0.569842i | −0.500849 | − | 0.865535i | \(-0.666979\pi\) |
0.955283 | + | 0.295692i | \(0.0955503\pi\) | |||||||
\(152\) | −588.361 | − | 2577.78i | −0.313963 | − | 1.37556i | ||||
\(153\) | 624.540 | − | 2736.29i | 0.330007 | − | 1.44585i | ||||
\(154\) | −244.499 | + | 306.593i | −0.127937 | + | 0.160428i | ||||
\(155\) | 877.565 | + | 422.613i | 0.454760 | + | 0.219001i | ||||
\(156\) | −3370.83 | − | 1623.31i | −1.73002 | − | 0.833132i | ||||
\(157\) | −197.376 | + | 864.759i | −0.100333 | + | 0.439588i | 0.899662 | + | 0.436586i | \(0.143813\pi\) |
−0.999995 | + | 0.00300170i | \(0.999045\pi\) | |||||||
\(158\) | −385.054 | − | 482.843i | −0.193882 | − | 0.243120i | ||||
\(159\) | −3085.05 | + | 1485.68i | −1.53875 | + | 0.741022i | ||||
\(160\) | −1893.43 | − | 2374.28i | −0.935554 | − | 1.17315i | ||||
\(161\) | −347.555 | − | 1522.74i | −0.170132 | − | 0.745395i | ||||
\(162\) | −696.486 | − | 335.410i | −0.337785 | − | 0.162669i | ||||
\(163\) | 48.5252 | + | 212.603i | 0.0233177 | + | 0.102162i | 0.985248 | − | 0.171135i | \(-0.0547433\pi\) |
−0.961930 | + | 0.273296i | \(0.911886\pi\) | |||||||
\(164\) | 1330.57 | − | 640.769i | 0.633537 | − | 0.305095i | ||||
\(165\) | 2089.04 | 0.985647 | ||||||||
\(166\) | 119.751 | 0.0559908 | ||||||||
\(167\) | 2492.94 | − | 1200.54i | 1.15515 | − | 0.556289i | 0.244571 | − | 0.969631i | \(-0.421353\pi\) |
0.910576 | + | 0.413342i | \(0.135639\pi\) | |||||||
\(168\) | −567.996 | + | 2488.55i | −0.260844 | + | 1.14283i | ||||
\(169\) | 2658.21 | − | 3333.29i | 1.20993 | − | 1.51720i | ||||
\(170\) | 1230.66 | + | 1543.20i | 0.555219 | + | 0.696222i | ||||
\(171\) | 4363.89 | 1.95155 | ||||||||
\(172\) | 1569.78 | + | 657.886i | 0.695899 | + | 0.291647i | ||||
\(173\) | −2722.10 | −1.19628 | −0.598142 | − | 0.801390i | \(-0.704094\pi\) | ||||
−0.598142 | + | 0.801390i | \(0.704094\pi\) | |||||||
\(174\) | −334.031 | − | 418.862i | −0.145533 | − | 0.182493i | ||||
\(175\) | 1473.48 | − | 1847.69i | 0.636485 | − | 0.798126i | ||||
\(176\) | −76.6973 | + | 336.033i | −0.0328481 | + | 0.143917i | ||||
\(177\) | −3746.74 | + | 1804.34i | −1.59109 | + | 0.766227i | ||||
\(178\) | −1236.41 | −0.520635 | ||||||||
\(179\) | −4376.37 | −1.82741 | −0.913703 | − | 0.406383i | \(-0.866790\pi\) | ||||
−0.913703 | + | 0.406383i | \(0.866790\pi\) | |||||||
\(180\) | 2876.36 | − | 1385.18i | 1.19106 | − | 0.573586i | ||||
\(181\) | 412.543 | + | 1807.47i | 0.169415 | + | 0.742254i | 0.986233 | + | 0.165360i | \(0.0528784\pi\) |
−0.816819 | + | 0.576894i | \(0.804264\pi\) | |||||||
\(182\) | −1707.80 | − | 822.435i | −0.695554 | − | 0.334961i | ||||
\(183\) | −1076.23 | − | 4715.26i | −0.434738 | − | 1.90471i | ||||
\(184\) | 1138.17 | + | 1427.22i | 0.456015 | + | 0.571825i | ||||
\(185\) | 1893.13 | − | 911.682i | 0.752354 | − | 0.362315i | ||||
\(186\) | 402.794 | + | 505.088i | 0.158787 | + | 0.199112i | ||||
\(187\) | 319.907 | − | 1401.60i | 0.125101 | − | 0.548104i | ||||
\(188\) | 423.015 | + | 203.713i | 0.164104 | + | 0.0790283i | ||||
\(189\) | −638.739 | − | 307.600i | −0.245828 | − | 0.118384i | ||||
\(190\) | −1913.47 | + | 2399.41i | −0.730619 | + | 0.916167i | ||||
\(191\) | 252.867 | − | 1107.88i | 0.0957950 | − | 0.419705i | −0.904177 | − | 0.427157i | \(-0.859515\pi\) |
0.999972 | + | 0.00745222i | \(0.00237214\pi\) | |||||||
\(192\) | −163.664 | − | 717.057i | −0.0615177 | − | 0.269527i | ||||
\(193\) | −1708.15 | + | 2141.96i | −0.637075 | + | 0.798867i | −0.990634 | − | 0.136545i | \(-0.956400\pi\) |
0.353559 | + | 0.935412i | \(0.384972\pi\) | |||||||
\(194\) | 6.10861 | − | 7.65996i | 0.00226068 | − | 0.00283481i | ||||
\(195\) | 2246.97 | + | 9844.63i | 0.825175 | + | 3.61533i | ||||
\(196\) | −80.2945 | + | 351.793i | −0.0292618 | + | 0.128204i | ||||
\(197\) | 1784.99 | − | 2238.31i | 0.645560 | − | 0.809507i | −0.346126 | − | 0.938188i | \(-0.612503\pi\) |
0.991686 | + | 0.128681i | \(0.0410745\pi\) | |||||||
\(198\) | 681.527 | + | 328.206i | 0.244616 | + | 0.117801i | ||||
\(199\) | 14.0497 | + | 6.76597i | 0.00500480 | + | 0.00241018i | 0.436384 | − | 0.899760i | \(-0.356259\pi\) |
−0.431380 | + | 0.902170i | \(0.641973\pi\) | |||||||
\(200\) | −614.625 | + | 2692.85i | −0.217303 | + | 0.952066i | ||||
\(201\) | 2628.78 | + | 3296.38i | 0.922485 | + | 1.15676i | ||||
\(202\) | 956.684 | − | 460.714i | 0.333228 | − | 0.160474i | ||||
\(203\) | 520.228 | + | 652.345i | 0.179866 | + | 0.225545i | ||||
\(204\) | −895.507 | − | 3923.47i | −0.307343 | − | 1.34656i | ||||
\(205\) | −3591.18 | − | 1729.42i | −1.22351 | − | 0.589210i | ||||
\(206\) | 223.836 | + | 980.692i | 0.0757060 | + | 0.331689i | ||||
\(207\) | −2714.48 | + | 1307.23i | −0.911447 | + | 0.438930i | ||||
\(208\) | −1666.05 | −0.555384 | ||||||||
\(209\) | 2235.31 | 0.739805 | ||||||||
\(210\) | 2669.34 | − | 1285.48i | 0.877151 | − | 0.422414i | ||||
\(211\) | −947.022 | + | 4149.17i | −0.308984 | + | 1.35375i | 0.547167 | + | 0.837023i | \(0.315706\pi\) |
−0.856151 | + | 0.516725i | \(0.827151\pi\) | |||||||
\(212\) | −1671.22 | + | 2095.64i | −0.541413 | + | 0.678911i | ||||
\(213\) | 1091.21 | + | 1368.33i | 0.351025 | + | 0.440172i | ||||
\(214\) | −0.781553 | −0.000249653 | ||||||||
\(215\) | −1253.37 | − | 4419.55i | −0.397577 | − | 1.40191i | ||||
\(216\) | 828.586 | 0.261010 | ||||||||
\(217\) | −627.321 | − | 786.635i | −0.196246 | − | 0.246084i | ||||
\(218\) | 1052.88 | − | 1320.27i | 0.327111 | − | 0.410185i | ||||
\(219\) | −1263.50 | + | 5535.74i | −0.389859 | + | 1.70808i | ||||
\(220\) | 1473.35 | − | 709.530i | 0.451516 | − | 0.217439i | ||||
\(221\) | 6949.16 | 2.11516 | ||||||||
\(222\) | 1393.65 | 0.421332 | ||||||||
\(223\) | −485.678 | + | 233.890i | −0.145845 | + | 0.0702352i | −0.505383 | − | 0.862895i | \(-0.668649\pi\) |
0.359538 | + | 0.933131i | \(0.382934\pi\) | |||||||
\(224\) | 698.041 | + | 3058.32i | 0.208213 | + | 0.912243i | ||||
\(225\) | −4107.24 | − | 1977.94i | −1.21696 | − | 0.586057i | ||||
\(226\) | −581.217 | − | 2546.48i | −0.171071 | − | 0.749509i | ||||
\(227\) | −3736.04 | − | 4684.84i | −1.09238 | − | 1.36980i | −0.923248 | − | 0.384204i | \(-0.874476\pi\) |
−0.169129 | − | 0.985594i | \(-0.554095\pi\) | |||||||
\(228\) | 5637.57 | − | 2714.91i | 1.63753 | − | 0.788593i | ||||
\(229\) | 1157.39 | + | 1451.32i | 0.333984 | + | 0.418802i | 0.920259 | − | 0.391309i | \(-0.127978\pi\) |
−0.586275 | + | 0.810112i | \(0.699406\pi\) | |||||||
\(230\) | 471.484 | − | 2065.71i | 0.135168 | − | 0.592211i | ||||
\(231\) | −1944.23 | − | 936.292i | −0.553771 | − | 0.266682i | ||||
\(232\) | −878.613 | − | 423.118i | −0.248637 | − | 0.119737i | ||||
\(233\) | −1451.55 | + | 1820.19i | −0.408130 | + | 0.511779i | −0.942835 | − | 0.333260i | \(-0.891851\pi\) |
0.534705 | + | 0.845039i | \(0.320423\pi\) | |||||||
\(234\) | −813.623 | + | 3564.72i | −0.227300 | + | 0.995867i | ||||
\(235\) | −281.979 | − | 1235.43i | −0.0782735 | − | 0.342938i | ||||
\(236\) | −2029.66 | + | 2545.12i | −0.559829 | + | 0.702004i | ||||
\(237\) | 2118.91 | − | 2657.02i | 0.580750 | − | 0.728237i | ||||
\(238\) | −453.701 | − | 1987.79i | −0.123567 | − | 0.541384i | ||||
\(239\) | 13.6992 | − | 60.0200i | 0.00370764 | − | 0.0162442i | −0.973040 | − | 0.230635i | \(-0.925920\pi\) |
0.976748 | + | 0.214391i | \(0.0687767\pi\) | |||||||
\(240\) | 1623.62 | − | 2035.95i | 0.436683 | − | 0.547583i | ||||
\(241\) | −1834.95 | − | 883.666i | −0.490455 | − | 0.236191i | 0.172275 | − | 0.985049i | \(-0.444888\pi\) |
−0.662730 | + | 0.748858i | \(0.730602\pi\) | |||||||
\(242\) | −1331.34 | − | 641.138i | −0.353643 | − | 0.170305i | ||||
\(243\) | 1199.69 | − | 5256.18i | 0.316708 | − | 1.38759i | ||||
\(244\) | −2360.55 | − | 2960.03i | −0.619338 | − | 0.776625i | ||||
\(245\) | 877.454 | − | 422.559i | 0.228810 | − | 0.110189i | ||||
\(246\) | −1648.32 | − | 2066.93i | −0.427207 | − | 0.535701i | ||||
\(247\) | 2404.29 | + | 10533.9i | 0.619358 | + | 2.71358i | ||||
\(248\) | 1059.48 | + | 510.220i | 0.271279 | + | 0.130641i | ||||
\(249\) | 146.636 | + | 642.453i | 0.0373199 | + | 0.163509i | ||||
\(250\) | 317.330 | − | 152.818i | 0.0802789 | − | 0.0386603i | ||||
\(251\) | 3260.59 | 0.819946 | 0.409973 | − | 0.912098i | \(-0.365538\pi\) | ||||
0.409973 | + | 0.912098i | \(0.365538\pi\) | |||||||
\(252\) | −3297.80 | −0.824373 | ||||||||
\(253\) | −1390.43 | + | 669.598i | −0.345517 | + | 0.166392i | ||||
\(254\) | −773.706 | + | 3389.83i | −0.191129 | + | 0.837389i | ||||
\(255\) | −6772.16 | + | 8492.01i | −1.66309 | + | 2.08545i | ||||
\(256\) | −1661.84 | − | 2083.88i | −0.405722 | − | 0.508759i | ||||
\(257\) | −2352.03 | −0.570878 | −0.285439 | − | 0.958397i | \(-0.592139\pi\) | ||||
−0.285439 | + | 0.958397i | \(0.592139\pi\) | |||||||
\(258\) | 522.864 | − | 3001.71i | 0.126171 | − | 0.724335i | ||||
\(259\) | −2170.50 | −0.520728 | ||||||||
\(260\) | 4928.40 | + | 6180.02i | 1.17556 | + | 1.47411i | ||||
\(261\) | 1003.50 | − | 1258.35i | 0.237989 | − | 0.298429i | ||||
\(262\) | 300.184 | − | 1315.19i | 0.0707842 | − | 0.310126i | ||||
\(263\) | −1671.09 | + | 804.753i | −0.391801 | + | 0.188681i | −0.619404 | − | 0.785073i | \(-0.712626\pi\) |
0.227603 | + | 0.973754i | \(0.426911\pi\) | |||||||
\(264\) | 2522.10 | 0.587971 | ||||||||
\(265\) | 7234.41 | 1.67700 | ||||||||
\(266\) | 2856.23 | − | 1375.49i | 0.658370 | − | 0.317054i | ||||
\(267\) | −1513.99 | − | 6633.23i | −0.347022 | − | 1.52040i | ||||
\(268\) | 2973.61 | + | 1432.02i | 0.677769 | + | 0.326396i | ||||
\(269\) | −1641.80 | − | 7193.19i | −0.372127 | − | 1.63040i | −0.720795 | − | 0.693149i | \(-0.756223\pi\) |
0.348667 | − | 0.937246i | \(-0.386634\pi\) | |||||||
\(270\) | −599.634 | − | 751.917i | −0.135158 | − | 0.169482i | ||||
\(271\) | −215.740 | + | 103.895i | −0.0483589 | + | 0.0232884i | −0.457907 | − | 0.889000i | \(-0.651401\pi\) |
0.409548 | + | 0.912289i | \(0.365686\pi\) | |||||||
\(272\) | −1117.35 | − | 1401.11i | −0.249078 | − | 0.312334i | ||||
\(273\) | 2321.07 | − | 10169.3i | 0.514570 | − | 2.25448i | ||||
\(274\) | −98.7073 | − | 47.5349i | −0.0217632 | − | 0.0104806i | ||||
\(275\) | −2103.84 | − | 1013.16i | −0.461333 | − | 0.222166i | ||||
\(276\) | −2693.49 | + | 3377.53i | −0.587424 | + | 0.736606i | ||||
\(277\) | −1023.69 | + | 4485.08i | −0.222049 | + | 0.972861i | 0.733884 | + | 0.679275i | \(0.237706\pi\) |
−0.955933 | + | 0.293585i | \(0.905151\pi\) | |||||||
\(278\) | 636.375 | + | 2788.14i | 0.137292 | + | 0.601517i | ||||
\(279\) | −1210.08 | + | 1517.39i | −0.259662 | + | 0.325605i | ||||
\(280\) | 3362.43 | − | 4216.35i | 0.717656 | − | 0.899912i | ||||
\(281\) | −748.559 | − | 3279.65i | −0.158916 | − | 0.696255i | −0.990112 | − | 0.140276i | \(-0.955201\pi\) |
0.831197 | − | 0.555978i | \(-0.187656\pi\) | |||||||
\(282\) | 187.025 | − | 819.411i | 0.0394936 | − | 0.173033i | ||||
\(283\) | 1737.60 | − | 2178.89i | 0.364982 | − | 0.457673i | −0.565101 | − | 0.825021i | \(-0.691163\pi\) |
0.930083 | + | 0.367349i | \(0.119734\pi\) | |||||||
\(284\) | 1234.35 | + | 594.431i | 0.257905 | + | 0.124201i | ||||
\(285\) | −15215.7 | − | 7327.49i | −3.16245 | − | 1.52296i | ||||
\(286\) | −416.761 | + | 1825.95i | −0.0861664 | + | 0.377519i | ||||
\(287\) | 2567.13 | + | 3219.08i | 0.527989 | + | 0.662077i | ||||
\(288\) | 5451.85 | − | 2625.47i | 1.11546 | − | 0.537179i | ||||
\(289\) | 1597.29 | + | 2002.94i | 0.325115 | + | 0.407681i | ||||
\(290\) | 251.871 | + | 1103.52i | 0.0510013 | + | 0.223451i | ||||
\(291\) | 48.5750 | + | 23.3925i | 0.00978527 | + | 0.00471234i | ||||
\(292\) | 989.063 | + | 4333.37i | 0.198221 | + | 0.868463i | ||||
\(293\) | −1395.48 | + | 672.029i | −0.278242 | + | 0.133994i | −0.567801 | − | 0.823166i | \(-0.692206\pi\) |
0.289559 | + | 0.957160i | \(0.406491\pi\) | |||||||
\(294\) | 645.949 | 0.128138 | ||||||||
\(295\) | 8786.06 | 1.73405 | ||||||||
\(296\) | 2285.57 | − | 1100.67i | 0.448804 | − | 0.216133i | ||||
\(297\) | −155.874 | + | 682.927i | −0.0304535 | + | 0.133426i | ||||
\(298\) | −294.063 | + | 368.743i | −0.0571630 | + | 0.0716802i | ||||
\(299\) | −4651.03 | − | 5832.21i | −0.899586 | − | 1.12805i | ||||
\(300\) | −6536.55 | −1.25796 | ||||||||
\(301\) | −814.320 | + | 4674.93i | −0.155936 | + | 0.895212i | ||||
\(302\) | −1895.14 | −0.361102 | ||||||||
\(303\) | 3643.15 | + | 4568.37i | 0.690738 | + | 0.866158i | ||||
\(304\) | 1737.29 | − | 2178.49i | 0.327765 | − | 0.411004i | ||||
\(305\) | −2273.81 | + | 9962.20i | −0.426878 | + | 1.87028i | ||||
\(306\) | −3543.50 | + | 1706.46i | −0.661989 | + | 0.318797i | ||||
\(307\) | 702.537 | 0.130605 | 0.0653027 | − | 0.997865i | \(-0.479199\pi\) | ||||
0.0653027 | + | 0.997865i | \(0.479199\pi\) | |||||||
\(308\) | −1689.23 | −0.312509 | ||||||||
\(309\) | −4987.23 | + | 2401.72i | −0.918167 | + | 0.442166i | ||||
\(310\) | −303.721 | − | 1330.69i | −0.0556457 | − | 0.243800i | ||||
\(311\) | 4576.00 | + | 2203.69i | 0.834345 | + | 0.401800i | 0.801743 | − | 0.597669i | \(-0.203906\pi\) |
0.0326023 | + | 0.999468i | \(0.489621\pi\) | |||||||
\(312\) | 2712.77 | + | 11885.4i | 0.492244 | + | 2.15666i | ||||
\(313\) | −3237.12 | − | 4059.22i | −0.584578 | − | 0.733037i | 0.398308 | − | 0.917252i | \(-0.369597\pi\) |
−0.982886 | + | 0.184214i | \(0.941026\pi\) | |||||||
\(314\) | 1119.87 | − | 539.299i | 0.201267 | − | 0.0969249i | ||||
\(315\) | 5549.50 | + | 6958.85i | 0.992631 | + | 1.24472i | ||||
\(316\) | 591.975 | − | 2593.61i | 0.105383 | − | 0.461715i | ||||
\(317\) | −333.269 | − | 160.494i | −0.0590481 | − | 0.0284361i | 0.404127 | − | 0.914703i | \(-0.367575\pi\) |
−0.463175 | + | 0.886267i | \(0.653290\pi\) | |||||||
\(318\) | 4323.11 | + | 2081.90i | 0.762353 | + | 0.367130i | ||||
\(319\) | 514.021 | − | 644.562i | 0.0902184 | − | 0.113130i | ||||
\(320\) | −345.781 | + | 1514.97i | −0.0604055 | + | 0.264654i | ||||
\(321\) | −0.957015 | − | 4.19295i | −0.000166403 | − | 0.000729059i | ||||
\(322\) | −1364.63 | + | 1711.20i | −0.236174 | + | 0.296153i | ||||
\(323\) | −7246.30 | + | 9086.57i | −1.24828 | + | 1.56529i | ||||
\(324\) | −740.991 | − | 3246.49i | −0.127056 | − | 0.556669i | ||||
\(325\) | 2511.62 | − | 11004.1i | 0.428676 | − | 1.87815i | ||||
\(326\) | 190.528 | − | 238.915i | 0.0323693 | − | 0.0405898i | ||||
\(327\) | 8372.40 | + | 4031.94i | 1.41589 | + | 0.681855i | ||||
\(328\) | −4335.63 | − | 2087.93i | −0.729863 | − | 0.351483i | ||||
\(329\) | −291.277 | + | 1276.17i | −0.0488105 | + | 0.213853i | ||||
\(330\) | −1825.20 | − | 2288.73i | −0.304467 | − | 0.381789i | ||||
\(331\) | 5084.57 | − | 2448.60i | 0.844329 | − | 0.406608i | 0.0388598 | − | 0.999245i | \(-0.487627\pi\) |
0.805470 | + | 0.592637i | \(0.201913\pi\) | |||||||
\(332\) | 321.624 | + | 403.303i | 0.0531669 | + | 0.0666691i | ||||
\(333\) | 931.657 | + | 4081.86i | 0.153317 | + | 0.671725i | ||||
\(334\) | −3493.38 | − | 1682.32i | −0.572303 | − | 0.275607i | ||||
\(335\) | −1982.19 | − | 8684.53i | −0.323279 | − | 1.41638i | ||||
\(336\) | −2423.56 | + | 1167.13i | −0.393500 | + | 0.189500i | ||||
\(337\) | 11132.1 | 1.79942 | 0.899711 | − | 0.436486i | \(-0.143777\pi\) | ||||
0.899711 | + | 0.436486i | \(0.143777\pi\) | |||||||
\(338\) | −5974.38 | −0.961431 | ||||||||
\(339\) | 12949.9 | − | 6236.34i | 2.07476 | − | 0.999149i | ||||
\(340\) | −1891.99 | + | 8289.34i | −0.301787 | + | 1.32221i | ||||
\(341\) | −619.837 | + | 777.251i | −0.0984342 | + | 0.123433i | ||||
\(342\) | −3812.73 | − | 4781.02i | −0.602833 | − | 0.755929i | ||||
\(343\) | −6778.43 | −1.06706 | ||||||||
\(344\) | −1513.19 | − | 5335.71i | −0.237168 | − | 0.836286i | ||||
\(345\) | 11659.6 | 1.81952 | ||||||||
\(346\) | 2378.30 | + | 2982.29i | 0.369532 | + | 0.463379i | ||||
\(347\) | −7173.49 | + | 8995.27i | −1.10978 | + | 1.39162i | −0.198363 | + | 0.980129i | \(0.563562\pi\) |
−0.911415 | + | 0.411489i | \(0.865009\pi\) | |||||||
\(348\) | 513.532 | − | 2249.93i | 0.0791041 | − | 0.346578i | ||||
\(349\) | −2576.94 | + | 1240.99i | −0.395245 | + | 0.190340i | −0.620940 | − | 0.783858i | \(-0.713249\pi\) |
0.225695 | + | 0.974198i | \(0.427535\pi\) | |||||||
\(350\) | −3311.69 | −0.505763 | ||||||||
\(351\) | −3385.95 | −0.514897 | ||||||||
\(352\) | 2792.59 | − | 1344.84i | 0.422857 | − | 0.203637i | ||||
\(353\) | 2682.46 | + | 11752.6i | 0.404456 | + | 1.77204i | 0.608989 | + | 0.793178i | \(0.291575\pi\) |
−0.204533 | + | 0.978860i | \(0.565568\pi\) | |||||||
\(354\) | 5250.34 | + | 2528.43i | 0.788284 | + | 0.379618i | ||||
\(355\) | −822.809 | − | 3604.96i | −0.123014 | − | 0.538962i | ||||
\(356\) | −3320.72 | − | 4164.05i | −0.494376 | − | 0.619927i | ||||
\(357\) | 10108.8 | − | 4868.12i | 1.49863 | − | 0.721704i | ||||
\(358\) | 3823.64 | + | 4794.70i | 0.564486 | + | 0.707843i | ||||
\(359\) | 332.895 | − | 1458.51i | 0.0489402 | − | 0.214421i | −0.944545 | − | 0.328382i | \(-0.893497\pi\) |
0.993485 | + | 0.113961i | \(0.0363539\pi\) | |||||||
\(360\) | −9372.56 | − | 4513.59i | −1.37216 | − | 0.660797i | ||||
\(361\) | −10101.2 | − | 4864.50i | −1.47270 | − | 0.709214i | ||||
\(362\) | 1619.80 | − | 2031.16i | 0.235179 | − | 0.294905i | ||||
\(363\) | 1809.42 | − | 7927.57i | 0.261625 | − | 1.14625i | ||||
\(364\) | −1816.93 | − | 7960.49i | −0.261629 | − | 1.14627i | ||||
\(365\) | 7479.66 | − | 9379.20i | 1.07261 | − | 1.34501i | ||||
\(366\) | −4225.68 | + | 5298.83i | −0.603496 | + | 0.756760i | ||||
\(367\) | 1659.50 | + | 7270.76i | 0.236036 | + | 1.03414i | 0.944530 | + | 0.328426i | \(0.106518\pi\) |
−0.708493 | + | 0.705717i | \(0.750625\pi\) | |||||||
\(368\) | −428.073 | + | 1875.51i | −0.0606382 | + | 0.265673i | ||||
\(369\) | 4951.90 | − | 6209.49i | 0.698606 | − | 0.876024i | ||||
\(370\) | −2652.86 | − | 1277.55i | −0.372744 | − | 0.179504i | ||||
\(371\) | −6732.92 | − | 3242.40i | −0.942198 | − | 0.453739i | ||||
\(372\) | −619.247 | + | 2713.10i | −0.0863077 | + | 0.378139i | ||||
\(373\) | 4481.76 | + | 5619.95i | 0.622137 | + | 0.780135i | 0.988643 | − | 0.150281i | \(-0.0480178\pi\) |
−0.366507 | + | 0.930415i | \(0.619446\pi\) | |||||||
\(374\) | −1815.08 | + | 874.098i | −0.250951 | + | 0.120852i | ||||
\(375\) | 1208.43 | + | 1515.32i | 0.166408 | + | 0.208669i | ||||
\(376\) | −340.432 | − | 1491.53i | −0.0466927 | − | 0.204574i | ||||
\(377\) | 3590.39 | + | 1729.04i | 0.490489 | + | 0.236207i | ||||
\(378\) | 221.064 | + | 968.545i | 0.0300802 | + | 0.131790i | ||||
\(379\) | −7406.19 | + | 3566.63i | −1.00377 | + | 0.483392i | −0.862218 | − | 0.506538i | \(-0.830925\pi\) |
−0.141556 | + | 0.989930i | \(0.545211\pi\) | |||||||
\(380\) | −13220.0 | −1.78466 | ||||||||
\(381\) | −19133.5 | −2.57281 | ||||||||
\(382\) | −1434.71 | + | 690.922i | −0.192163 | + | 0.0925410i | ||||
\(383\) | 1371.30 | − | 6008.06i | 0.182951 | − | 0.801560i | −0.797265 | − | 0.603629i | \(-0.793721\pi\) |
0.980216 | − | 0.197931i | \(-0.0634221\pi\) | |||||||
\(384\) | 6526.90 | − | 8184.47i | 0.867381 | − | 1.08766i | ||||
\(385\) | 2842.61 | + | 3564.52i | 0.376293 | + | 0.471856i | ||||
\(386\) | 3839.11 | 0.506233 | ||||||||
\(387\) | 9141.23 | − | 475.234i | 1.20071 | − | 0.0624225i | ||||
\(388\) | 42.2039 | 0.00552211 | ||||||||
\(389\) | −2946.64 | − | 3694.98i | −0.384064 | − | 0.481601i | 0.551793 | − | 0.833981i | \(-0.313944\pi\) |
−0.935857 | + | 0.352380i | \(0.885372\pi\) | |||||||
\(390\) | 8822.47 | − | 11063.0i | 1.14549 | − | 1.43641i | ||||
\(391\) | 1785.51 | − | 7822.82i | 0.230939 | − | 1.01181i | ||||
\(392\) | 1059.35 | − | 510.155i | 0.136493 | − | 0.0657315i | ||||
\(393\) | 7423.46 | 0.952835 | ||||||||
\(394\) | −4011.81 | −0.512975 | ||||||||
\(395\) | −6469.07 | + | 3115.34i | −0.824036 | + | 0.396835i | ||||
\(396\) | 725.076 | + | 3176.77i | 0.0920112 | + | 0.403127i | ||||
\(397\) | −10940.6 | − | 5268.73i | −1.38311 | − | 0.666070i | −0.413448 | − | 0.910528i | \(-0.635676\pi\) |
−0.969660 | + | 0.244458i | \(0.921390\pi\) | |||||||
\(398\) | −4.86252 | − | 21.3041i | −0.000612402 | − | 0.00268311i | ||||
\(399\) | 10876.8 | + | 13639.1i | 1.36472 | + | 1.71130i | ||||
\(400\) | −2622.52 | + | 1262.94i | −0.327815 | + | 0.157868i | ||||
\(401\) | −2628.51 | − | 3296.05i | −0.327336 | − | 0.410466i | 0.590746 | − | 0.806858i | \(-0.298834\pi\) |
−0.918082 | + | 0.396391i | \(0.870262\pi\) | |||||||
\(402\) | 1314.71 | − | 5760.11i | 0.163113 | − | 0.714647i | ||||
\(403\) | −4329.50 | − | 2084.98i | −0.535155 | − | 0.257717i | ||||
\(404\) | 4121.05 | + | 1984.59i | 0.507500 | + | 0.244399i | ||||
\(405\) | −5603.65 | + | 7026.76i | −0.687525 | + | 0.862129i | ||||
\(406\) | 260.177 | − | 1139.91i | 0.0318038 | − | 0.139342i | ||||
\(407\) | 477.221 | + | 2090.84i | 0.0581203 | + | 0.254642i | ||||
\(408\) | −8176.01 | + | 10252.4i | −0.992090 | + | 1.24404i | ||||
\(409\) | 149.590 | − | 187.580i | 0.0180850 | − | 0.0226779i | −0.772707 | − | 0.634763i | \(-0.781098\pi\) |
0.790792 | + | 0.612085i | \(0.209669\pi\) | |||||||
\(410\) | 1242.89 | + | 5445.45i | 0.149712 | + | 0.655931i | ||||
\(411\) | 134.153 | − | 587.762i | 0.0161004 | − | 0.0705405i | ||||
\(412\) | −2701.65 | + | 3387.76i | −0.323060 | + | 0.405104i | ||||
\(413\) | −8177.01 | − | 3937.84i | −0.974247 | − | 0.469173i | ||||
\(414\) | 3803.83 | + | 1831.83i | 0.451565 | + | 0.217462i | ||||
\(415\) | 309.806 | − | 1357.35i | 0.0366452 | − | 0.160553i | ||||
\(416\) | 9341.28 | + | 11713.6i | 1.10095 | + | 1.38054i | ||||
\(417\) | −14178.9 | + | 6828.18i | −1.66509 | + | 0.801865i | ||||
\(418\) | −1952.99 | − | 2448.97i | −0.228526 | − | 0.286562i | ||||
\(419\) | 7.00489 | + | 30.6905i | 0.000816734 | + | 0.00357835i | 0.975335 | − | 0.220731i | \(-0.0708444\pi\) |
−0.974518 | + | 0.224310i | \(0.927987\pi\) | |||||||
\(420\) | 11498.5 | + | 5537.41i | 1.33588 | + | 0.643328i | ||||
\(421\) | −209.339 | − | 917.176i | −0.0242342 | − | 0.106177i | 0.961364 | − | 0.275279i | \(-0.0887703\pi\) |
−0.985598 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(422\) | 5373.20 | − | 2587.60i | 0.619818 | − | 0.298489i | ||||
\(423\) | 2524.99 | 0.290235 | ||||||||
\(424\) | 8734.08 | 1.00039 | ||||||||
\(425\) | 10938.6 | − | 5267.77i | 1.24848 | − | 0.601234i | ||||
\(426\) | 545.736 | − | 2391.03i | 0.0620681 | − | 0.271938i | ||||
\(427\) | 6581.16 | − | 8252.52i | 0.745866 | − | 0.935286i | ||||
\(428\) | −2.09907 | − | 2.63215i | −0.000237062 | − | 0.000297266i | ||||
\(429\) | −10306.4 | −1.15990 | ||||||||
\(430\) | −3746.93 | + | 5234.54i | −0.420216 | + | 0.587051i | ||||
\(431\) | 2818.53 | 0.314997 | 0.157499 | − | 0.987519i | \(-0.449657\pi\) | ||||
0.157499 | + | 0.987519i | \(0.449657\pi\) | |||||||
\(432\) | 544.424 | + | 682.686i | 0.0606333 | + | 0.0760318i | ||||
\(433\) | 9279.84 | − | 11636.6i | 1.02993 | − | 1.29149i | 0.0742042 | − | 0.997243i | \(-0.476358\pi\) |
0.955728 | − | 0.294251i | \(-0.0950702\pi\) | |||||||
\(434\) | −313.736 | + | 1374.57i | −0.0347001 | + | 0.152031i | ||||
\(435\) | −5611.85 | + | 2702.53i | −0.618547 | + | 0.297876i | ||||
\(436\) | 7274.29 | 0.799026 | ||||||||
\(437\) | 12476.0 | 1.36569 | ||||||||
\(438\) | 7168.80 | − | 3452.31i | 0.782052 | − | 0.376616i | ||||
\(439\) | −809.577 | − | 3546.99i | −0.0880159 | − | 0.385623i | 0.911664 | − | 0.410937i | \(-0.134798\pi\) |
−0.999680 | + | 0.0253143i | \(0.991941\pi\) | |||||||
\(440\) | −4800.89 | − | 2311.99i | −0.520167 | − | 0.250499i | ||||
\(441\) | 431.818 | + | 1891.92i | 0.0466275 | + | 0.204289i | ||||
\(442\) | −6071.49 | − | 7613.41i | −0.653374 | − | 0.819305i | ||||
\(443\) | −5167.64 | + | 2488.60i | −0.554226 | + | 0.266901i | −0.689964 | − | 0.723844i | \(-0.742374\pi\) |
0.135738 | + | 0.990745i | \(0.456659\pi\) | |||||||
\(444\) | 3743.03 | + | 4693.61i | 0.400082 | + | 0.501686i | ||||
\(445\) | −3198.70 | + | 14014.4i | −0.340748 | + | 1.49291i | ||||
\(446\) | 680.585 | + | 327.752i | 0.0722570 | + | 0.0347971i | ||||
\(447\) | −2338.35 | − | 1126.09i | −0.247428 | − | 0.119155i | ||||
\(448\) | 1000.81 | − | 1254.97i | 0.105544 | − | 0.132348i | ||||
\(449\) | −3037.70 | + | 13309.0i | −0.319283 | + | 1.39887i | 0.519532 | + | 0.854451i | \(0.326106\pi\) |
−0.838815 | + | 0.544417i | \(0.816751\pi\) | |||||||
\(450\) | 1421.49 | + | 6227.97i | 0.148911 | + | 0.652420i | ||||
\(451\) | 2536.50 | − | 3180.67i | 0.264832 | − | 0.332089i | ||||
\(452\) | 7015.14 | − | 8796.70i | 0.730009 | − | 0.915403i | ||||
\(453\) | −2320.60 | − | 10167.2i | −0.240688 | − | 1.05452i | ||||
\(454\) | −1868.47 | + | 8186.31i | −0.193154 | + | 0.846261i | ||||
\(455\) | −13740.3 | + | 17229.8i | −1.41573 | + | 1.77527i | ||||
\(456\) | −18369.9 | − | 8846.46i | −1.88651 | − | 0.908494i | ||||
\(457\) | 16266.8 | + | 7833.70i | 1.66506 | + | 0.801849i | 0.998404 | + | 0.0564816i | \(0.0179882\pi\) |
0.666654 | + | 0.745368i | \(0.267726\pi\) | |||||||
\(458\) | 578.834 | − | 2536.04i | 0.0590548 | − | 0.258736i | ||||
\(459\) | −2270.81 | − | 2847.51i | −0.230920 | − | 0.289565i | ||||
\(460\) | 8223.29 | − | 3960.13i | 0.833506 | − | 0.401395i | ||||
\(461\) | −4831.33 | − | 6058.30i | −0.488107 | − | 0.612067i | 0.475393 | − | 0.879773i | \(-0.342306\pi\) |
−0.963501 | + | 0.267706i | \(0.913734\pi\) | |||||||
\(462\) | 672.888 | + | 2948.11i | 0.0677610 | + | 0.296880i | ||||
\(463\) | 5343.01 | + | 2573.06i | 0.536308 | + | 0.258272i | 0.682375 | − | 0.731002i | \(-0.260947\pi\) |
−0.146067 | + | 0.989275i | \(0.546661\pi\) | |||||||
\(464\) | −228.680 | − | 1001.91i | −0.0228798 | − | 0.100243i | ||||
\(465\) | 6767.10 | − | 3258.86i | 0.674875 | − | 0.325003i | ||||
\(466\) | 3262.40 | 0.324308 | ||||||||
\(467\) | −3326.65 | −0.329634 | −0.164817 | − | 0.986324i | \(-0.552703\pi\) | ||||
−0.164817 | + | 0.986324i | \(0.552703\pi\) | |||||||
\(468\) | −14190.6 | + | 6833.85i | −1.40163 | + | 0.674989i | ||||
\(469\) | −2047.55 | + | 8970.92i | −0.201593 | + | 0.883238i | ||||
\(470\) | −1107.16 | + | 1388.33i | −0.108658 | + | 0.136253i | ||||
\(471\) | 4264.57 | + | 5347.60i | 0.417200 | + | 0.523152i | ||||
\(472\) | 10607.4 | 1.03442 | ||||||||
\(473\) | 4682.39 | − | 243.428i | 0.455173 | − | 0.0236635i | ||||
\(474\) | −4762.29 | −0.461475 | ||||||||
\(475\) | 11769.7 | + | 14758.8i | 1.13691 | + | 1.42564i | ||||
\(476\) | 5476.05 | − | 6866.75i | 0.527299 | − | 0.661212i | ||||
\(477\) | −3207.66 | + | 14053.7i | −0.307901 | + | 1.34900i | ||||
\(478\) | −77.7261 | + | 37.4309i | −0.00743746 | + | 0.00358169i | ||||
\(479\) | −3999.59 | −0.381516 | −0.190758 | − | 0.981637i | \(-0.561094\pi\) | ||||
−0.190758 | + | 0.981637i | \(0.561094\pi\) | |||||||
\(480\) | −23417.6 | −2.22680 | ||||||||
\(481\) | −9339.80 | + | 4497.81i | −0.885360 | + | 0.426367i | ||||
\(482\) | 635.067 | + | 2782.41i | 0.0600135 | + | 0.262936i | ||||
\(483\) | −10851.4 | − | 5225.76i | −1.02227 | − | 0.492299i | ||||
\(484\) | −1416.41 | − | 6205.69i | −0.133021 | − | 0.582804i | ||||
\(485\) | −71.0202 | − | 89.0565i | −0.00664920 | − | 0.00833783i | ||||
\(486\) | −6806.77 | + | 3277.97i | −0.635311 | + | 0.305950i | ||||
\(487\) | −11045.1 | − | 13850.1i | −1.02772 | − | 1.28872i | −0.956646 | − | 0.291254i | \(-0.905928\pi\) |
−0.0710774 | − | 0.997471i | \(-0.522644\pi\) | |||||||
\(488\) | −2745.16 | + | 12027.3i | −0.254647 | + | 1.11568i | ||||
\(489\) | 1515.06 | + | 729.614i | 0.140109 | + | 0.0674730i | ||||
\(490\) | −1229.58 | − | 592.136i | −0.113361 | − | 0.0545918i | ||||
\(491\) | 3960.14 | − | 4965.86i | 0.363989 | − | 0.456428i | −0.565788 | − | 0.824551i | \(-0.691428\pi\) |
0.929777 | + | 0.368123i | \(0.119999\pi\) | |||||||
\(492\) | 2534.09 | − | 11102.6i | 0.232206 | − | 1.01736i | ||||
\(493\) | 953.834 | + | 4179.02i | 0.0871370 | + | 0.381772i | ||||
\(494\) | 9440.16 | − | 11837.6i | 0.859783 | − | 1.07813i | ||||
\(495\) | 5483.29 | − | 6875.83i | 0.497890 | − | 0.624335i | ||||
\(496\) | 275.756 | + | 1208.17i | 0.0249633 | + | 0.109372i | ||||
\(497\) | −849.942 | + | 3723.84i | −0.0767105 | + | 0.336091i | ||||
\(498\) | 575.747 | − | 721.964i | 0.0518069 | − | 0.0649638i | ||||
\(499\) | −5041.62 | − | 2427.92i | −0.452293 | − | 0.217813i | 0.193847 | − | 0.981032i | \(-0.437903\pi\) |
−0.646140 | + | 0.763219i | \(0.723618\pi\) | |||||||
\(500\) | 1366.94 | + | 658.286i | 0.122263 | + | 0.0588789i | ||||
\(501\) | 4747.84 | − | 20801.7i | 0.423389 | − | 1.85499i | ||||
\(502\) | −2848.78 | − | 3572.26i | −0.253281 | − | 0.317605i | ||||
\(503\) | −5603.29 | + | 2698.40i | −0.496696 | + | 0.239196i | −0.665423 | − | 0.746467i | \(-0.731749\pi\) |
0.168727 | + | 0.985663i | \(0.446034\pi\) | |||||||
\(504\) | 6699.90 | + | 8401.41i | 0.592137 | + | 0.742517i | ||||
\(505\) | −2747.06 | − | 12035.7i | −0.242065 | − | 1.06055i | ||||
\(506\) | 1948.43 | + | 938.313i | 0.171182 | + | 0.0824370i | ||||
\(507\) | −7315.66 | − | 32052.0i | −0.640828 | − | 2.80765i | ||||
\(508\) | −13494.4 | + | 6498.58i | −1.17858 | + | 0.567574i | ||||
\(509\) | 18178.1 | 1.58297 | 0.791485 | − | 0.611188i | \(-0.209308\pi\) | ||||
0.791485 | + | 0.611188i | \(0.209308\pi\) | |||||||
\(510\) | 15220.6 | 1.32153 | ||||||||
\(511\) | −11164.9 | + | 5376.71i | −0.966544 | + | 0.465463i | ||||
\(512\) | 1585.54 | − | 6946.69i | 0.136858 | − | 0.599616i | ||||
\(513\) | 3530.73 | − | 4427.40i | 0.303871 | − | 0.381042i | ||||
\(514\) | 2054.97 | + | 2576.85i | 0.176344 | + | 0.221129i | ||||
\(515\) | 11695.0 | 1.00066 | ||||||||
\(516\) | 11513.6 | − | 6300.98i | 0.982283 | − | 0.537568i | ||||
\(517\) | 1293.37 | 0.110024 | ||||||||
\(518\) | 1896.37 | + | 2377.98i | 0.160853 | + | 0.201703i | ||||
\(519\) | −13087.5 | + | 16411.2i | −1.10689 | + | 1.38800i | ||||
\(520\) | 5731.42 | − | 25111.0i | 0.483345 | − | 2.11767i | ||||
\(521\) | 12977.7 | − | 6249.72i | 1.09129 | − | 0.525538i | 0.200380 | − | 0.979718i | \(-0.435782\pi\) |
0.890910 | + | 0.454181i | \(0.150068\pi\) | |||||||
\(522\) | −2255.39 | −0.189111 | ||||||||
\(523\) | −4841.59 | −0.404796 | −0.202398 | − | 0.979303i | \(-0.564873\pi\) | ||||
−0.202398 | + | 0.979303i | \(0.564873\pi\) | |||||||
\(524\) | 5235.60 | − | 2521.33i | 0.436485 | − | 0.210200i | ||||
\(525\) | −4055.18 | − | 17766.9i | −0.337109 | − | 1.47697i | ||||
\(526\) | 2341.71 | + | 1127.71i | 0.194113 | + | 0.0934798i | ||||
\(527\) | −1150.19 | − | 5039.31i | −0.0950721 | − | 0.416538i | ||||
\(528\) | 1657.15 | + | 2078.00i | 0.136587 | + | 0.171275i | ||||
\(529\) | 3201.61 | − | 1541.81i | 0.263139 | − | 0.126721i | ||||
\(530\) | −6320.71 | − | 7925.92i | −0.518027 | − | 0.649585i | ||||
\(531\) | −3895.65 | + | 17068.0i | −0.318374 | + | 1.39489i | ||||
\(532\) | 12303.6 | + | 5925.10i | 1.00269 | + | 0.482868i | ||||
\(533\) | 17717.2 | + | 8532.16i | 1.43981 | + | 0.693375i | ||||
\(534\) | −5944.51 | + | 7454.17i | −0.481730 | + | 0.604071i | ||||
\(535\) | −2.02194 | + | 8.85870i | −0.000163395 | + | 0.000715878i | ||||
\(536\) | −2393.09 | − | 10484.8i | −0.192847 | − | 0.844916i | ||||
\(537\) | −21041.0 | + | 26384.6i | −1.69085 | + | 2.12026i | ||||
\(538\) | −6446.32 | + | 8083.43i | −0.516581 | + | 0.647772i | ||||
\(539\) | 221.189 | + | 969.093i | 0.0176759 | + | 0.0774430i | ||||
\(540\) | 921.865 | − | 4038.95i | 0.0734643 | − | 0.321868i | ||||
\(541\) | −5375.13 | + | 6740.20i | −0.427163 | + | 0.535645i | −0.948109 | − | 0.317944i | \(-0.897008\pi\) |
0.520947 | + | 0.853589i | \(0.325579\pi\) | |||||||
\(542\) | 302.318 | + | 145.589i | 0.0239588 | + | 0.0115379i | ||||
\(543\) | 12880.4 | + | 6202.89i | 1.01796 | + | 0.490224i | ||||
\(544\) | −3586.07 | + | 15711.6i | −0.282631 | + | 1.23829i | ||||
\(545\) | −12241.1 | − | 15349.8i | −0.962110 | − | 1.20645i | ||||
\(546\) | −13169.2 | + | 6341.98i | −1.03222 | + | 0.497091i | ||||
\(547\) | −5034.63 | − | 6313.23i | −0.393538 | − | 0.493481i | 0.545107 | − | 0.838367i | \(-0.316489\pi\) |
−0.938645 | + | 0.344886i | \(0.887918\pi\) | |||||||
\(548\) | −105.015 | − | 460.099i | −0.00818614 | − | 0.0358658i | ||||
\(549\) | −18344.6 | − | 8834.28i | −1.42610 | − | 0.686772i | ||||
\(550\) | 728.129 | + | 3190.14i | 0.0564500 | + | 0.247324i | ||||
\(551\) | −6004.76 | + | 2891.74i | −0.464268 | + | 0.223579i | ||||
\(552\) | 14076.7 | 1.08540 | ||||||||
\(553\) | 7416.90 | 0.570341 | ||||||||
\(554\) | 5808.20 | − | 2797.08i | 0.445427 | − | 0.214506i | ||||
\(555\) | 3605.49 | − | 15796.7i | 0.275756 | − | 1.20817i | ||||
\(556\) | −7680.88 | + | 9631.52i | −0.585867 | + | 0.734654i | ||||
\(557\) | 3189.39 | + | 3999.37i | 0.242619 | + | 0.304235i | 0.888200 | − | 0.459457i | \(-0.151956\pi\) |
−0.645581 | + | 0.763692i | \(0.723385\pi\) | |||||||
\(558\) | 2719.68 | 0.206332 | ||||||||
\(559\) | 6183.54 | + | 21804.0i | 0.467863 | + | 1.64975i | ||||
\(560\) | 5683.21 | 0.428856 | ||||||||
\(561\) | −6912.03 | − | 8667.41i | −0.520189 | − | 0.652296i | ||||
\(562\) | −2939.13 | + | 3685.55i | −0.220604 | + | 0.276629i | ||||
\(563\) | 957.517 | − | 4195.16i | 0.0716777 | − | 0.314041i | −0.926361 | − | 0.376636i | \(-0.877081\pi\) |
0.998039 | + | 0.0625956i | \(0.0199378\pi\) | |||||||
\(564\) | 3261.96 | − | 1570.88i | 0.243534 | − | 0.117280i | ||||
\(565\) | −30367.3 | −2.26117 | ||||||||
\(566\) | −3905.31 | −0.290022 | ||||||||
\(567\) | 8364.54 | − | 4028.15i | 0.619537 | − | 0.298353i | ||||
\(568\) | −993.375 | − | 4352.26i | −0.0733822 | − | 0.321508i | ||||
\(569\) | 20232.7 | + | 9743.55i | 1.49068 | + | 0.717875i | 0.989101 | − | 0.147236i | \(-0.0470375\pi\) |
0.501581 | + | 0.865111i | \(0.332752\pi\) | |||||||
\(570\) | 5266.06 | + | 23072.1i | 0.386967 | + | 1.69541i | ||||
\(571\) | 1254.92 | + | 1573.61i | 0.0919730 | + | 0.115330i | 0.825688 | − | 0.564126i | \(-0.190787\pi\) |
−0.733715 | + | 0.679457i | \(0.762215\pi\) | |||||||
\(572\) | −7268.84 | + | 3500.49i | −0.531338 | + | 0.255879i | ||||
\(573\) | −5463.54 | − | 6851.07i | −0.398330 | − | 0.499490i | ||||
\(574\) | 1283.87 | − | 5625.02i | 0.0933587 | − | 0.409031i | ||||
\(575\) | −11742.2 | − | 5654.77i | −0.851627 | − | 0.410122i | ||||
\(576\) | −2789.69 | − | 1343.44i | −0.201800 | − | 0.0971819i | ||||
\(577\) | −4279.56 | + | 5366.40i | −0.308770 | + | 0.387186i | −0.911869 | − | 0.410480i | \(-0.865361\pi\) |
0.603099 | + | 0.797666i | \(0.293932\pi\) | |||||||
\(578\) | 798.839 | − | 3499.94i | 0.0574867 | − | 0.251866i | ||||
\(579\) | 4701.01 | + | 20596.5i | 0.337422 | + | 1.47834i | ||||
\(580\) | −3040.02 | + | 3812.06i | −0.217638 | + | 0.272909i | ||||
\(581\) | −896.682 | + | 1124.40i | −0.0640286 | + | 0.0802893i | ||||
\(582\) | −16.8115 | − | 73.6561i | −0.00119735 | − | 0.00524595i | ||||
\(583\) | −1643.06 | + | 7198.70i | −0.116721 | + | 0.511389i | ||||
\(584\) | 9030.18 | − | 11323.5i | 0.639849 | − | 0.802345i | ||||
\(585\) | 38300.2 | + | 18444.4i | 2.70687 | + | 1.30356i | ||||
\(586\) | 1955.50 | + | 941.720i | 0.137852 | + | 0.0663858i | ||||
\(587\) | 3847.54 | − | 16857.2i | 0.270537 | − | 1.18530i | −0.638845 | − | 0.769336i | \(-0.720587\pi\) |
0.909381 | − | 0.415963i | \(-0.136556\pi\) | |||||||
\(588\) | 1734.87 | + | 2175.46i | 0.121675 | + | 0.152576i | ||||
\(589\) | 7240.89 | − | 3487.03i | 0.506546 | − | 0.243940i | ||||
\(590\) | −7676.39 | − | 9625.89i | −0.535647 | − | 0.671681i | ||||
\(591\) | −4912.48 | − | 21523.0i | −0.341916 | − | 1.49803i | ||||
\(592\) | 2408.60 | + | 1159.92i | 0.167218 | + | 0.0805278i | ||||
\(593\) | 982.122 | + | 4302.96i | 0.0680116 | + | 0.297978i | 0.997482 | − | 0.0709180i | \(-0.0225928\pi\) |
−0.929471 | + | 0.368896i | \(0.879736\pi\) | |||||||
\(594\) | 884.393 | − | 425.901i | 0.0610893 | − | 0.0294191i | ||||
\(595\) | −23704.9 | −1.63329 | ||||||||
\(596\) | −2031.65 | −0.139631 | ||||||||
\(597\) | 108.340 | − | 52.1739i | 0.00742725 | − | 0.00357677i | ||||
\(598\) | −2326.08 | + | 10191.2i | −0.159064 | + | 0.696907i | ||||
\(599\) | 8790.80 | − | 11023.3i | 0.599637 | − | 0.751921i | −0.385685 | − | 0.922631i | \(-0.626035\pi\) |
0.985321 | + | 0.170710i | \(0.0546061\pi\) | |||||||
\(600\) | 13279.8 | + | 16652.4i | 0.903577 | + | 1.13305i | ||||
\(601\) | 3049.05 | 0.206944 | 0.103472 | − | 0.994632i | \(-0.467005\pi\) | ||||
0.103472 | + | 0.994632i | \(0.467005\pi\) | |||||||
\(602\) | 5833.27 | − | 3192.34i | 0.394928 | − | 0.216130i | ||||
\(603\) | 17749.6 | 1.19871 | ||||||||
\(604\) | −5089.91 | − | 6382.54i | −0.342890 | − | 0.429970i | ||||
\(605\) | −10711.4 | + | 13431.7i | −0.719803 | + | 0.902605i | ||||
\(606\) | 1822.02 | − | 7982.78i | 0.122136 | − | 0.535113i | ||||
\(607\) | 21857.1 | − | 10525.8i | 1.46154 | − | 0.703839i | 0.476981 | − | 0.878914i | \(-0.341731\pi\) |
0.984555 | + | 0.175075i | \(0.0560168\pi\) | |||||||
\(608\) | −25057.2 | −1.67138 | ||||||||
\(609\) | 6434.09 | 0.428116 | ||||||||
\(610\) | 12901.1 | − | 6212.84i | 0.856311 | − | 0.412378i | ||||
\(611\) | 1391.15 | + | 6095.03i | 0.0921112 | + | 0.403566i | ||||
\(612\) | −15264.1 | − | 7350.82i | −1.00820 | − | 0.485522i | ||||
\(613\) | −3829.10 | − | 16776.4i | −0.252293 | − | 1.10537i | −0.929281 | − | 0.369374i | \(-0.879572\pi\) |
0.676988 | − | 0.735994i | \(-0.263285\pi\) | |||||||
\(614\) | −613.807 | − | 769.690i | −0.0403440 | − | 0.0505898i | ||||
\(615\) | −27692.4 | + | 13336.0i | −1.81572 | + | 0.874403i | ||||
\(616\) | 3431.88 | + | 4303.44i | 0.224471 | + | 0.281478i | ||||
\(617\) | −4038.69 | + | 17694.6i | −0.263519 | + | 1.15455i | 0.653884 | + | 0.756595i | \(0.273139\pi\) |
−0.917403 | + | 0.397959i | \(0.869719\pi\) | |||||||
\(618\) | 6988.65 | + | 3365.55i | 0.454894 | + | 0.219065i | ||||
\(619\) | 1666.48 | + | 802.533i | 0.108209 | + | 0.0521107i | 0.487205 | − | 0.873288i | \(-0.338016\pi\) |
−0.378996 | + | 0.925398i | \(0.623731\pi\) | |||||||
\(620\) | 3665.83 | − | 4596.81i | 0.237457 | − | 0.297762i | ||||
\(621\) | −869.982 | + | 3811.64i | −0.0562177 | + | 0.246306i | ||||
\(622\) | −1583.73 | − | 6938.78i | −0.102093 | − | 0.447298i | ||||
\(623\) | 9258.11 | − | 11609.3i | 0.595374 | − | 0.746576i | ||||
\(624\) | −8010.16 | + | 10044.4i | −0.513883 | + | 0.644389i | ||||
\(625\) | 2994.81 | + | 13121.1i | 0.191668 | + | 0.839752i | ||||
\(626\) | −1618.95 | + | 7093.10i | −0.103365 | + | 0.452871i | ||||
\(627\) | 10747.1 | − | 13476.4i | 0.684523 | − | 0.858365i | ||||
\(628\) | 4823.98 | + | 2323.11i | 0.306525 | + | 0.147615i | ||||
\(629\) | −10046.4 | − | 4838.07i | −0.636843 | − | 0.306687i | ||||
\(630\) | 2775.42 | − | 12159.9i | 0.175517 | − | 0.768988i | ||||
\(631\) | −8183.73 | − | 10262.1i | −0.516306 | − | 0.647427i | 0.453514 | − | 0.891249i | \(-0.350170\pi\) |
−0.969820 | + | 0.243822i | \(0.921599\pi\) | |||||||
\(632\) | −7810.09 | + | 3761.14i | −0.491565 | + | 0.236725i | ||||
\(633\) | 20461.7 | + | 25658.2i | 1.28480 | + | 1.61109i | ||||
\(634\) | 115.343 | + | 505.349i | 0.00722530 | + | 0.0316561i | ||||
\(635\) | 36421.2 | + | 17539.5i | 2.27611 | + | 1.09612i | ||||
\(636\) | 4599.36 | + | 20151.1i | 0.286755 | + | 1.25636i | ||||
\(637\) | −4328.95 | + | 2084.71i | −0.269261 | + | 0.129669i | ||||
\(638\) | −1155.28 | −0.0716893 | ||||||||
\(639\) | 7367.89 | 0.456133 | ||||||||
\(640\) | −19926.8 | + | 9596.23i | −1.23074 | + | 0.592694i | ||||
\(641\) | −1989.46 | + | 8716.37i | −0.122588 | + | 0.537092i | 0.875919 | + | 0.482459i | \(0.160256\pi\) |
−0.998506 | + | 0.0546334i | \(0.982601\pi\) | |||||||
\(642\) | −3.75760 | + | 4.71188i | −0.000230998 | + | 0.000289662i | ||||
\(643\) | −8626.19 | − | 10816.9i | −0.529057 | − | 0.663417i | 0.443447 | − | 0.896300i | \(-0.353755\pi\) |
−0.972505 | + | 0.232884i | \(0.925184\pi\) | |||||||
\(644\) | −9428.14 | −0.576896 | ||||||||
\(645\) | −32670.9 | − | 13692.2i | −1.99445 | − | 0.835860i | ||||
\(646\) | 16286.2 | 0.991909 | ||||||||
\(647\) | −1375.53 | − | 1724.86i | −0.0835822 | − | 0.104809i | 0.738282 | − | 0.674492i | \(-0.235637\pi\) |
−0.821864 | + | 0.569683i | \(0.807066\pi\) | |||||||
\(648\) | −6765.28 | + | 8483.39i | −0.410132 | + | 0.514289i | ||||
\(649\) | −1995.46 | + | 8742.69i | −0.120691 | + | 0.528783i | ||||
\(650\) | −14250.4 | + | 6862.62i | −0.859917 | + | 0.414114i | ||||
\(651\) | −7758.60 | −0.467102 | ||||||||
\(652\) | 1316.35 | 0.0790676 | ||||||||
\(653\) | −5106.82 | + | 2459.32i | −0.306042 | + | 0.147382i | −0.580601 | − | 0.814188i | \(-0.697182\pi\) |
0.274559 | + | 0.961570i | \(0.411468\pi\) | |||||||
\(654\) | −2897.64 | − | 12695.4i | −0.173252 | − | 0.759067i | ||||
\(655\) | −14130.8 | − | 6805.02i | −0.842954 | − | 0.405945i | ||||
\(656\) | −1128.45 | − | 4944.07i | −0.0671626 | − | 0.294258i | ||||
\(657\) | 14903.8 | + | 18688.8i | 0.885012 | + | 1.10977i | ||||
\(658\) | 1652.65 | − | 795.872i | 0.0979131 | − | 0.0471525i | ||||
\(659\) | 3822.83 | + | 4793.67i | 0.225973 | + | 0.283361i | 0.881873 | − | 0.471486i | \(-0.156282\pi\) |
−0.655900 | + | 0.754847i | \(0.727711\pi\) | |||||||
\(660\) | 2806.03 | − | 12294.0i | 0.165492 | − | 0.725066i | ||||
\(661\) | 18007.4 | + | 8671.92i | 1.05962 | + | 0.510285i | 0.880747 | − | 0.473587i | \(-0.157041\pi\) |
0.178871 | + | 0.983872i | \(0.442755\pi\) | |||||||
\(662\) | −7125.05 | − | 3431.24i | −0.418312 | − | 0.201449i | ||||
\(663\) | 33410.6 | − | 41895.6i | 1.95711 | − | 2.45413i | ||||
\(664\) | 374.028 | − | 1638.72i | 0.0218601 | − | 0.0957752i | ||||
\(665\) | −8201.49 | − | 35933.1i | −0.478256 | − | 2.09538i | ||||
\(666\) | 3658.04 | − | 4587.03i | 0.212832 | − | 0.266883i | ||||
\(667\) | 2868.92 | − | 3597.52i | 0.166545 | − | 0.208840i | ||||
\(668\) | −3716.60 | − | 16283.5i | −0.215269 | − | 0.943155i | ||||
\(669\) | −924.981 | + | 4052.61i | −0.0534556 | + | 0.234204i | ||||
\(670\) | −7782.82 | + | 9759.35i | −0.448771 | + | 0.562741i | ||||
\(671\) | −9396.61 | − | 4525.17i | −0.540614 | − | 0.260346i | ||||
\(672\) | 21794.3 | + | 10495.6i | 1.25109 | + | 0.602494i | ||||
\(673\) | −1864.50 | + | 8168.92i | −0.106792 | + | 0.467888i | 0.893047 | + | 0.449964i | \(0.148563\pi\) |
−0.999839 | + | 0.0179247i | \(0.994294\pi\) | |||||||
\(674\) | −9726.15 | − | 12196.2i | −0.555842 | − | 0.697003i | ||||
\(675\) | −5329.81 | + | 2566.70i | −0.303918 | + | 0.146359i | ||||
\(676\) | −16045.8 | − | 20120.8i | −0.912939 | − | 1.14479i | ||||
\(677\) | 4700.72 | + | 20595.2i | 0.266859 | + | 1.16918i | 0.913645 | + | 0.406513i | \(0.133255\pi\) |
−0.646786 | + | 0.762671i | \(0.723887\pi\) | |||||||
\(678\) | −18146.8 | − | 8739.04i | −1.02791 | − | 0.495016i | ||||
\(679\) | 26.1827 | + | 114.714i | 0.00147982 | + | 0.00648352i | ||||
\(680\) | 24961.6 | − | 12020.8i | 1.40769 | − | 0.677910i | ||||
\(681\) | −46206.7 | −2.60007 | ||||||||
\(682\) | 1393.10 | 0.0782178 | ||||||||
\(683\) | 20594.3 | − | 9917.67i | 1.15376 | − | 0.555621i | 0.243598 | − | 0.969876i | \(-0.421672\pi\) |
0.910161 | + | 0.414255i | \(0.135958\pi\) | |||||||
\(684\) | 5861.62 | − | 25681.4i | 0.327668 | − | 1.43561i | ||||
\(685\) | −794.160 | + | 995.845i | −0.0442968 | + | 0.0555464i | ||||
\(686\) | 5922.33 | + | 7426.36i | 0.329614 | + | 0.413323i | ||||
\(687\) | 14314.4 | 0.794945 | ||||||||
\(688\) | 3401.94 | − | 4752.58i | 0.188514 | − | 0.263358i | ||||
\(689\) | −35691.2 | −1.97348 | ||||||||
\(690\) | −10187.1 | − | 12774.2i | −0.562050 | − | 0.704788i | ||||
\(691\) | 17689.5 | − | 22181.9i | 0.973865 | − | 1.22119i | −0.00136589 | − | 0.999999i | \(-0.500435\pi\) |
0.975231 | − | 0.221189i | \(-0.0709938\pi\) | |||||||
\(692\) | −3656.35 | + | 16019.5i | −0.200858 | + | 0.880015i | ||||
\(693\) | −8184.88 | + | 3941.63i | −0.448655 | + | 0.216061i | ||||
\(694\) | 16122.6 | 0.881851 | ||||||||
\(695\) | 33249.2 | 1.81470 | ||||||||
\(696\) | −6775.18 | + | 3262.76i | −0.368984 | + | 0.177693i | ||||
\(697\) | 4706.81 | + | 20621.9i | 0.255787 | + | 1.12067i | ||||
\(698\) | 3611.09 | + | 1739.01i | 0.195819 | + | 0.0943015i | ||||
\(699\) | 3994.82 | + | 17502.5i | 0.216163 | + | 0.947072i | ||||
\(700\) | −8894.43 | − | 11153.3i | −0.480254 | − | 0.602220i | ||||
\(701\) | 1889.20 | − | 909.789i | 0.101789 | − | 0.0490189i | −0.382297 | − | 0.924040i | \(-0.624867\pi\) |
0.484085 | + | 0.875021i | \(0.339152\pi\) | |||||||
\(702\) | 2958.31 | + | 3709.61i | 0.159052 | + | 0.199445i | ||||
\(703\) | 3857.92 | − | 16902.7i | 0.206976 | − | 0.906822i | ||||
\(704\) | −1428.96 | − | 688.149i | −0.0764998 | − | 0.0368403i | ||||
\(705\) | −8803.97 | − | 4239.77i | −0.470321 | − | 0.226495i | ||||
\(706\) | 10532.4 | − | 13207.2i | 0.561460 | − | 0.704048i | ||||
\(707\) | −2837.65 | + | 12432.6i | −0.150949 | + | 0.661350i | ||||
\(708\) | 5585.84 | + | 24473.2i | 0.296509 | + | 1.29909i | ||||
\(709\) | 12754.2 | − | 15993.3i | 0.675592 | − | 0.847165i | −0.319348 | − | 0.947637i | \(-0.603464\pi\) |
0.994940 | + | 0.100472i | \(0.0320354\pi\) | |||||||
\(710\) | −3230.66 | + | 4051.12i | −0.170767 | + | 0.214135i | ||||
\(711\) | −3183.60 | − | 13948.2i | −0.167924 | − | 0.735724i | ||||
\(712\) | −3861.78 | + | 16919.6i | −0.203267 | + | 0.890573i | ||||
\(713\) | −3459.52 | + | 4338.10i | −0.181711 | + | 0.227858i | ||||
\(714\) | −14165.5 | − | 6821.74i | −0.742479 | − | 0.357559i | ||||
\(715\) | 19618.5 | + | 9447.75i | 1.02614 | + | 0.494162i | ||||
\(716\) | −5878.39 | + | 25754.9i | −0.306824 | + | 1.34428i | ||||
\(717\) | −295.989 | − | 371.159i | −0.0154169 | − | 0.0193322i | ||||
\(718\) | −1888.77 | + | 909.585i | −0.0981732 | + | 0.0472777i | ||||
\(719\) | −9575.91 | − | 12007.8i | −0.496691 | − | 0.622831i | 0.468788 | − | 0.883311i | \(-0.344691\pi\) |
−0.965479 | + | 0.260479i | \(0.916119\pi\) | |||||||
\(720\) | −2439.44 | − | 10687.9i | −0.126267 | − | 0.553213i | ||||
\(721\) | −10884.3 | − | 5241.59i | −0.562207 | − | 0.270745i | ||||
\(722\) | 3495.98 | + | 15316.9i | 0.180204 | + | 0.789524i | ||||
\(723\) | −14149.7 | + | 6814.15i | −0.727848 | + | 0.350513i | ||||
\(724\) | 11191.1 | 0.574465 | ||||||||
\(725\) | 6962.30 | 0.356653 | ||||||||
\(726\) | −10266.2 | + | 4943.96i | −0.524815 | + | 0.252738i | ||||
\(727\) | 5138.97 | − | 22515.3i | 0.262165 | − | 1.14862i | −0.656733 | − | 0.754123i | \(-0.728062\pi\) |
0.918898 | − | 0.394496i | \(-0.129081\pi\) | |||||||
\(728\) | −16588.7 | + | 20801.5i | −0.844528 | + | 1.05900i | ||||
\(729\) | −16634.2 | − | 20858.6i | −0.845104 | − | 1.05973i | ||||
\(730\) | −16810.7 | −0.852319 | ||||||||
\(731\) | −14189.6 | + | 19823.2i | −0.717950 | + | 1.00299i | ||||
\(732\) | −29194.9 | −1.47414 | ||||||||
\(733\) | −15001.6 | − | 18811.4i | −0.755928 | − | 0.947904i | 0.243832 | − | 0.969818i | \(-0.421596\pi\) |
−0.999760 | + | 0.0219137i | \(0.993024\pi\) | |||||||
\(734\) | 6515.84 | − | 8170.60i | 0.327662 | − | 0.410875i | ||||
\(735\) | 1671.12 | − | 7321.67i | 0.0838644 | − | 0.367434i | ||||
\(736\) | 15586.4 | − | 7506.01i | 0.780601 | − | 0.375917i | ||||
\(737\) | 9091.85 | 0.454413 | ||||||||
\(738\) | −11129.5 | −0.555126 | ||||||||
\(739\) | −13662.5 | + | 6579.50i | −0.680084 | + | 0.327511i | −0.741837 | − | 0.670580i | \(-0.766045\pi\) |
0.0617531 | + | 0.998091i | \(0.480331\pi\) | |||||||
\(740\) | −2822.37 | − | 12365.6i | −0.140206 | − | 0.614283i | ||||
\(741\) | 75067.0 | + | 36150.4i | 3.72153 | + | 1.79220i | ||||
\(742\) | 2330.23 | + | 10209.4i | 0.115290 | + | 0.505119i | ||||
\(743\) | 12900.1 | + | 16176.2i | 0.636956 | + | 0.798718i | 0.990619 | − | 0.136655i | \(-0.0436352\pi\) |
−0.353662 | + | 0.935373i | \(0.615064\pi\) | |||||||
\(744\) | 8169.91 | − | 3934.42i | 0.402585 | − | 0.193875i | ||||
\(745\) | 3418.84 | + | 4287.09i | 0.168130 | + | 0.210828i | ||||
\(746\) | 2241.43 | − | 9820.33i | 0.110006 | − | 0.481967i | ||||
\(747\) | 2499.44 | + | 1203.67i | 0.122423 | + | 0.0589557i | ||||
\(748\) | −7818.72 | − | 3765.30i | −0.382194 | − | 0.184055i | ||||
\(749\) | 5.85217 | − | 7.33839i | 0.000285492 | − | 0.000357996i | ||||
\(750\) | 604.360 | − | 2647.87i | 0.0294241 | − | 0.128916i | ||||
\(751\) | −2106.13 | − | 9227.55i | −0.102335 | − | 0.448360i | −0.999971 | − | 0.00762171i | \(-0.997574\pi\) |
0.897636 | − | 0.440738i | \(-0.145283\pi\) | |||||||
\(752\) | 1005.22 | − | 1260.50i | 0.0487453 | − | 0.0611247i | ||||
\(753\) | 15676.5 | − | 19657.7i | 0.758675 | − | 0.951348i | ||||
\(754\) | −1242.61 | − | 5444.24i | −0.0600176 | − | 0.262954i | ||||
\(755\) | −4902.88 | + | 21480.9i | −0.236336 | + | 1.03546i | ||||
\(756\) | −2668.19 | + | 3345.80i | −0.128361 | + | 0.160960i | ||||
\(757\) | 9520.73 | + | 4584.94i | 0.457116 | + | 0.220135i | 0.648249 | − | 0.761429i | \(-0.275502\pi\) |
−0.191133 | + | 0.981564i | \(0.561216\pi\) | |||||||
\(758\) | 10378.4 | + | 4997.95i | 0.497307 | + | 0.239490i | ||||
\(759\) | −2648.10 | + | 11602.1i | −0.126640 | + | 0.554848i | ||||
\(760\) | 26858.1 | + | 33679.0i | 1.28190 | + | 1.60745i | ||||
\(761\) | 10185.9 | − | 4905.25i | 0.485199 | − | 0.233660i | −0.175259 | − | 0.984522i | \(-0.556076\pi\) |
0.660458 | + | 0.750863i | \(0.270362\pi\) | |||||||
\(762\) | 16717.0 | + | 20962.4i | 0.794741 | + | 0.996573i | ||||
\(763\) | 4512.86 | + | 19772.1i | 0.214124 | + | 0.938137i | ||||
\(764\) | −6180.24 | − | 2976.24i | −0.292661 | − | 0.140938i | ||||
\(765\) | 10175.0 | + | 44579.5i | 0.480885 | + | 2.10689i | ||||
\(766\) | −7780.46 | + | 3746.87i | −0.366997 | + | 0.176736i | ||||
\(767\) | −43346.3 | −2.04060 | ||||||||
\(768\) | −20553.3 | −0.965696 | ||||||||
\(769\) | −7159.65 | + | 3447.91i | −0.335740 | + | 0.161684i | −0.594156 | − | 0.804350i | \(-0.702514\pi\) |
0.258416 | + | 0.966034i | \(0.416799\pi\) | |||||||
\(770\) | 1421.65 | − | 6228.65i | 0.0665359 | − | 0.291513i | ||||
\(771\) | −11308.3 | + | 14180.1i | −0.528219 | + | 0.662366i | ||||
\(772\) | 10311.0 | + | 12929.6i | 0.480700 | + | 0.602779i | ||||
\(773\) | 1530.93 | 0.0712340 | 0.0356170 | − | 0.999366i | \(-0.488660\pi\) | ||||
0.0356170 | + | 0.999366i | \(0.488660\pi\) | |||||||
\(774\) | −8507.37 | − | 9599.80i | −0.395079 | − | 0.445811i | ||||
\(775\) | −8395.54 | −0.389131 | ||||||||
\(776\) | −85.7425 | − | 107.518i | −0.00396647 | − | 0.00497379i | ||||
\(777\) | −10435.5 | + | 13085.7i | −0.481817 | + | 0.604179i | ||||
\(778\) | −1473.68 | + | 6456.61i | −0.0679100 | + | 0.297533i | ||||
\(779\) | −29631.2 | + | 14269.7i | −1.36284 | + | 0.656307i | ||||
\(780\) | 60953.7 | 2.79807 | ||||||||
\(781\) | 3774.04 | 0.172914 | ||||||||
\(782\) | −10130.6 | + | 4878.63i | −0.463259 | + | 0.223094i | ||||
\(783\) | −464.752 | − | 2036.21i | −0.0212119 | − | 0.0929353i | ||||
\(784\) | 1116.37 | + | 537.616i | 0.0508551 | + | 0.0244905i | ||||
\(785\) | −3215.63 | − | 14088.6i | −0.146205 | − | 0.640566i | ||||
\(786\) | −6485.89 | − | 8133.05i | −0.294331 | − | 0.369079i | ||||
\(787\) | 16006.3 | − | 7708.21i | 0.724983 | − | 0.349134i | −0.0347256 | − | 0.999397i | \(-0.511056\pi\) |
0.759709 | + | 0.650263i | \(0.225341\pi\) | |||||||
\(788\) | −10774.8 | − | 13511.2i | −0.487102 | − | 0.610807i | ||||
\(789\) | −3182.61 | + | 13943.9i | −0.143604 | + | 0.629172i | ||||
\(790\) | 9065.16 | + | 4365.55i | 0.408258 | + | 0.196607i | ||||
\(791\) | 28262.2 | + | 13610.4i | 1.27040 | + | 0.611794i | ||||
\(792\) | 6619.97 | − | 8301.18i | 0.297008 | − | 0.372436i | ||||
\(793\) | 11217.9 | − | 49148.8i | 0.502345 | − | 2.20092i | ||||
\(794\) | 3786.49 | + | 16589.7i | 0.169241 | + | 0.741494i | ||||
\(795\) | 34782.1 | − | 43615.3i | 1.55169 | − | 1.94576i | ||||
\(796\) | 58.6893 | − | 73.5941i | 0.00261330 | − | 0.00327698i | ||||
\(797\) | −2771.98 | − | 12144.8i | −0.123198 | − | 0.539764i | −0.998428 | − | 0.0560571i | \(-0.982147\pi\) |
0.875230 | − | 0.483707i | \(-0.160710\pi\) | |||||||
\(798\) | 5439.72 | − | 23833.0i | 0.241308 | − | 1.05724i | ||||
\(799\) | −4192.79 | + | 5257.59i | −0.185645 | + | 0.232791i | ||||
\(800\) | 23583.5 | + | 11357.2i | 1.04225 | + | 0.501923i | ||||
\(801\) | −25806.4 | − | 12427.7i | −1.13836 | − | 0.548204i | ||||
\(802\) | −1314.58 | + | 5759.53i | −0.0578794 | + | 0.253586i | ||||
\(803\) | 7634.15 | + | 9572.92i | 0.335496 | + | 0.420699i | ||||
\(804\) | 22930.2 | − | 11042.6i | 1.00583 | − | 0.484381i | ||||
\(805\) | 15865.5 | + | 19894.8i | 0.694642 | + | 0.871054i | ||||
\(806\) | 1498.42 | + | 6564.99i | 0.0654832 | + | 0.286900i | ||||
\(807\) | −51260.4 | − | 24685.7i | −2.23600 | − | 1.07680i | ||||
\(808\) | −3316.52 | − | 14530.6i | −0.144400 | − | 0.632656i | ||||
\(809\) | 25554.4 | − | 12306.4i | 1.11056 | − | 0.534819i | 0.213598 | − | 0.976922i | \(-0.431482\pi\) |
0.896964 | + | 0.442103i | \(0.145767\pi\) | |||||||
\(810\) | 12594.3 | 0.546321 | ||||||||
\(811\) | −5605.49 | −0.242707 | −0.121354 | − | 0.992609i | \(-0.538723\pi\) | ||||
−0.121354 | + | 0.992609i | \(0.538723\pi\) | |||||||
\(812\) | 4537.82 | − | 2185.30i | 0.196116 | − | 0.0944445i | ||||
\(813\) | −410.879 | + | 1800.18i | −0.0177247 | + | 0.0776569i | ||||
\(814\) | 1873.75 | − | 2349.61i | 0.0806817 | − | 0.101172i | ||||
\(815\) | −2215.13 | − | 2777.68i | −0.0952056 | − | 0.119384i | ||||
\(816\) | −13819.2 | −0.592853 | ||||||||
\(817\) | −34958.4 | − | 14650.8i | −1.49699 | − | 0.627378i | ||||
\(818\) | −336.208 | −0.0143707 | ||||||||
\(819\) | −27378.6 | − | 34331.7i | −1.16812 | − | 1.46477i | ||||
\(820\) | −15001.3 | + | 18811.1i | −0.638865 | + | 0.801112i | ||||
\(821\) | 3839.86 | − | 16823.5i | 0.163230 | − | 0.715158i | −0.825370 | − | 0.564592i | \(-0.809033\pi\) |
0.988600 | − | 0.150565i | \(-0.0481094\pi\) | |||||||
\(822\) | −761.154 | + | 366.552i | −0.0322972 | + | 0.0155535i | ||||
\(823\) | −23660.3 | −1.00212 | −0.501060 | − | 0.865413i | \(-0.667056\pi\) | ||||
−0.501060 | + | 0.865413i | \(0.667056\pi\) | |||||||
\(824\) | 14119.3 | 0.596929 | ||||||||
\(825\) | −16223.2 | + | 7812.68i | −0.684629 | + | 0.329700i | ||||
\(826\) | 2830.02 | + | 12399.1i | 0.119212 | + | 0.522301i | ||||
\(827\) | −27822.1 | − | 13398.4i | −1.16985 | − | 0.563372i | −0.254915 | − | 0.966963i | \(-0.582047\pi\) |
−0.914939 | + | 0.403591i | \(0.867762\pi\) | |||||||
\(828\) | 4046.89 | + | 17730.6i | 0.169854 | + | 0.744179i | ||||
\(829\) | −15781.9 | − | 19789.9i | −0.661193 | − | 0.829109i | 0.332280 | − | 0.943181i | \(-0.392182\pi\) |
−0.993473 | + | 0.114072i | \(0.963611\pi\) | |||||||
\(830\) | −1757.77 | + | 846.497i | −0.0735097 | + | 0.0354004i | ||||
\(831\) | 22118.2 | + | 27735.4i | 0.923313 | + | 1.15780i | ||||
\(832\) | 1705.92 | − | 7474.14i | 0.0710844 | − | 0.311441i | ||||
\(833\) | −4656.43 | − | 2242.42i | −0.193680 | − | 0.0932715i | ||||
\(834\) | 19869.0 | + | 9568.39i | 0.824947 | + | 0.397274i | ||||
\(835\) | −28106.3 | + | 35244.2i | −1.16486 | + | 1.46069i | ||||
\(836\) | 3002.49 | − | 13154.8i | 0.124214 | − | 0.544218i | ||||
\(837\) | 560.425 | + | 2455.38i | 0.0231435 | + | 0.101398i | ||||
\(838\) | 27.5039 | − | 34.4888i | 0.00113378 | − | 0.00142171i | ||||
\(839\) | 828.774 | − | 1039.25i | 0.0341031 | − | 0.0427639i | −0.764488 | − | 0.644639i | \(-0.777008\pi\) |
0.798591 | + | 0.601875i | \(0.205579\pi\) | |||||||
\(840\) | −9253.75 | − | 40543.3i | −0.380101 | − | 1.66533i | ||||
\(841\) | 4880.08 | − | 21381.0i | 0.200094 | − | 0.876667i | ||||
\(842\) | −821.946 | + | 1030.69i | −0.0336415 | + | 0.0421851i | ||||
\(843\) | −23371.6 | − | 11255.2i | −0.954876 | − | 0.459844i | ||||
\(844\) | 23145.8 | + | 11146.4i | 0.943971 | + | 0.454592i | ||||
\(845\) | −15456.2 | + | 67718.1i | −0.629243 | + | 2.75689i | ||||
\(846\) | −2206.09 | − | 2766.35i | −0.0896537 | − | 0.112422i | ||||
\(847\) | 15988.9 | − | 7699.84i | 0.648624 | − | 0.312361i | ||||
\(848\) | 5738.74 | + | 7196.16i | 0.232393 | + | 0.291412i | ||||
\(849\) | −4782.07 | − | 20951.6i | −0.193310 | − | 0.846946i | ||||
\(850\) | −15328.4 | − | 7381.77i | −0.618541 | − | 0.297874i | ||||
\(851\) | 2663.53 | + | 11669.7i | 0.107291 | + | 0.470072i | ||||
\(852\) | 9518.34 | − | 4583.79i | 0.382738 | − | 0.184317i | ||||
\(853\) | 26615.5 | 1.06834 | 0.534171 | − | 0.845376i | \(-0.320624\pi\) | ||||
0.534171 | + | 0.845376i | \(0.320624\pi\) | |||||||
\(854\) | −14791.3 | −0.592680 | ||||||||
\(855\) | −64055.4 | + | 30847.5i | −2.56216 | + | 1.23387i | ||||
\(856\) | −2.44108 | + | 10.6951i | −9.74703e−5 | + | 0.000427045i | ||||
\(857\) | 24488.6 | − | 30707.8i | 0.976098 | − | 1.22399i | 0.00150647 | − | 0.999999i | \(-0.499520\pi\) |
0.974592 | − | 0.223989i | \(-0.0719081\pi\) | |||||||
\(858\) | 9004.68 | + | 11291.5i | 0.358292 | + | 0.449284i | ||||
\(859\) | 11705.3 | 0.464937 | 0.232468 | − | 0.972604i | \(-0.425320\pi\) | ||||
0.232468 | + | 0.972604i | \(0.425320\pi\) | |||||||
\(860\) | −27692.5 | + | 1439.68i | −1.09803 | + | 0.0570845i | ||||
\(861\) | 31749.8 | 1.25671 | ||||||||
\(862\) | −2462.56 | − | 3087.95i | −0.0973028 | − | 0.122014i | ||||
\(863\) | −23962.5 | + | 30048.0i | −0.945183 | + | 1.18522i | 0.0373820 | + | 0.999301i | \(0.488098\pi\) |
−0.982565 | + | 0.185921i | \(0.940473\pi\) | |||||||
\(864\) | 1747.30 | − | 7655.42i | 0.0688013 | − | 0.301438i | ||||
\(865\) | 39956.4 | − | 19242.0i | 1.57059 | − | 0.756355i | ||||
\(866\) | −20856.7 | −0.818405 | ||||||||
\(867\) | 19755.0 | 0.773836 | ||||||||
\(868\) | −5471.97 | + | 2635.16i | −0.213975 | + | 0.103045i | ||||
\(869\) | −1630.73 | − | 7144.68i | −0.0636578 | − | 0.278903i | ||||
\(870\) | 7863.94 | + | 3787.07i | 0.306451 | + | 0.147579i | ||||
\(871\) | 9779.18 | + | 42845.4i | 0.380431 | + | 1.66678i | ||||
\(872\) | −14778.6 | − | 18531.8i | −0.573930 | − | 0.719686i | ||||
\(873\) | 204.492 | − | 98.4783i | 0.00792786 | − | 0.00381785i | ||||
\(874\) | −10900.3 | − | 13668.5i | −0.421862 | − | 0.528999i | ||||
\(875\) | −941.244 | + | 4123.86i | −0.0363655 | + | 0.159328i | ||||
\(876\) | 30880.6 | + | 14871.3i | 1.19105 | + | 0.573579i | ||||
\(877\) | −15440.8 | − | 7435.89i | −0.594525 | − | 0.286308i | 0.112325 | − | 0.993672i | \(-0.464170\pi\) |
−0.706850 | + | 0.707363i | \(0.749885\pi\) | |||||||
\(878\) | −3178.71 | + | 3985.97i | −0.122182 | + | 0.153212i | ||||
\(879\) | −2657.72 | + | 11644.2i | −0.101982 | + | 0.446814i | ||||
\(880\) | −1249.55 | − | 5474.63i | −0.0478662 | − | 0.209715i | ||||
\(881\) | −5669.11 | + | 7108.84i | −0.216796 | + | 0.271853i | −0.878323 | − | 0.478068i | \(-0.841337\pi\) |
0.661527 | + | 0.749921i | \(0.269909\pi\) | |||||||
\(882\) | 1695.48 | − | 2126.06i | 0.0647276 | − | 0.0811659i | ||||
\(883\) | 6572.72 | + | 28797.0i | 0.250498 | + | 1.09750i | 0.931075 | + | 0.364827i | \(0.118872\pi\) |
−0.680578 | + | 0.732676i | \(0.738271\pi\) | |||||||
\(884\) | 9334.18 | − | 40895.7i | 0.355139 | − | 1.55596i | ||||
\(885\) | 42242.2 | − | 52970.0i | 1.60447 | − | 2.01194i | ||||
\(886\) | 7241.46 | + | 3487.30i | 0.274584 | + | 0.132233i | ||||
\(887\) | −37867.1 | − | 18235.8i | −1.43343 | − | 0.690304i | −0.453798 | − | 0.891105i | \(-0.649931\pi\) |
−0.979632 | + | 0.200801i | \(0.935646\pi\) | |||||||
\(888\) | 4352.90 | − | 19071.3i | 0.164497 | − | 0.720711i | ||||
\(889\) | −26035.4 | − | 32647.4i | −0.982227 | − | 1.23167i | ||||
\(890\) | 18148.7 | − | 8739.96i | 0.683535 | − | 0.329173i | ||||
\(891\) | −5719.39 | − | 7171.89i | −0.215047 | − | 0.269660i | ||||
\(892\) | 724.074 | + | 3172.37i | 0.0271791 | + | 0.119080i | ||||
\(893\) | −9420.37 | − | 4536.61i | −0.353013 | − | 0.170002i | ||||
\(894\) | 809.291 | + | 3545.73i | 0.0302760 | + | 0.132648i | ||||
\(895\) | 64238.8 | − | 30935.8i | 2.39918 | − | 1.15538i | ||||
\(896\) | 22846.4 | 0.851835 | ||||||||
\(897\) | −57523.2 | −2.14119 | ||||||||
\(898\) | 17235.2 | − | 8300.05i | 0.640476 | − | 0.308437i | ||||
\(899\) | 659.581 | − | 2889.81i | 0.0244697 | − | 0.107209i | ||||
\(900\) | −17157.1 | + | 21514.3i | −0.635446 | + | 0.796825i | ||||
\(901\) | −23936.5 | − | 30015.4i | −0.885062 | − | 1.10983i | ||||
\(902\) | −5700.85 | −0.210441 | ||||||||
\(903\) | 24269.5 | + | 27385.9i | 0.894393 | + | 1.00924i | ||||
\(904\) | −36662.4 | −1.34886 | ||||||||
\(905\) | −18832.2 | − | 23614.8i | −0.691715 | − | 0.867383i | ||||
\(906\) | −9111.57 | + | 11425.6i | −0.334119 | + | 0.418972i | ||||
\(907\) | 932.893 | − | 4087.27i | 0.0341524 | − | 0.149631i | −0.954977 | − | 0.296680i | \(-0.904120\pi\) |
0.989129 | + | 0.147049i | \(0.0469775\pi\) | |||||||
\(908\) | −32588.6 | + | 15693.8i | −1.19107 | + | 0.573588i | ||||
\(909\) | 24598.7 | 0.897567 | ||||||||
\(910\) | 30881.7 | 1.12496 | ||||||||
\(911\) | 6396.64 | − | 3080.46i | 0.232635 | − | 0.112031i | −0.313935 | − | 0.949444i | \(-0.601648\pi\) |
0.546570 | + | 0.837413i | \(0.315933\pi\) | |||||||
\(912\) | −4781.20 | − | 20947.8i | −0.173598 | − | 0.760583i | ||||
\(913\) | 1280.28 | + | 616.553i | 0.0464088 | + | 0.0223493i | ||||
\(914\) | −5629.87 | − | 24666.1i | −0.203741 | − | 0.892649i | ||||
\(915\) | 49128.7 | + | 61605.4i | 1.77502 | + | 2.22581i | ||||
\(916\) | 10095.6 | − | 4861.79i | 0.364157 | − | 0.175369i | ||||
\(917\) | 10101.3 | + | 12666.6i | 0.363766 | + | 0.456148i | ||||
\(918\) | −1135.68 | + | 4975.74i | −0.0408312 | + | 0.178893i | ||||
\(919\) | 33504.0 | + | 16134.7i | 1.20261 | + | 0.579145i | 0.924418 | − | 0.381382i | \(-0.124552\pi\) |
0.278188 | + | 0.960527i | \(0.410266\pi\) | |||||||
\(920\) | −26795.4 | − | 12904.0i | −0.960236 | − | 0.462425i | ||||
\(921\) | 3377.70 | − | 4235.51i | 0.120846 | − | 0.151536i | ||||
\(922\) | −2416.25 | + | 10586.3i | −0.0863069 | + | 0.378135i | ||||
\(923\) | 4059.35 | + | 17785.2i | 0.144762 | + | 0.634243i | ||||
\(924\) | −8121.58 | + | 10184.1i | −0.289156 | + | 0.362591i | ||||
\(925\) | −11292.2 | + | 14160.0i | −0.401390 | + | 0.503327i | ||||
\(926\) | −1849.19 | − | 8101.81i | −0.0656242 | − | 0.287519i | ||||
\(927\) | −5185.43 | + | 22718.9i | −0.183724 | + | 0.804947i | ||||
\(928\) | −5762.04 | + | 7225.37i | −0.203824 | + | 0.255587i | ||||
\(929\) | 22429.2 | + | 10801.4i | 0.792120 | + | 0.381465i | 0.785773 | − | 0.618515i | \(-0.212265\pi\) |
0.00634696 | + | 0.999980i | \(0.497980\pi\) | |||||||
\(930\) | −9482.80 | − | 4566.67i | −0.334358 | − | 0.161018i | ||||
\(931\) | 1788.12 | − | 7834.29i | 0.0629467 | − | 0.275788i | ||||
\(932\) | 8762.05 | + | 10987.3i | 0.307951 | + | 0.386159i | ||||
\(933\) | 35286.6 | − | 16993.1i | 1.23819 | − | 0.596281i | ||||
\(934\) | 2906.50 | + | 3644.63i | 0.101824 | + | 0.127683i | ||||
\(935\) | 5211.91 | + | 22834.9i | 0.182297 | + | 0.798695i | ||||
\(936\) | 46239.8 | + | 22267.9i | 1.61474 | + | 0.777617i | ||||
\(937\) | 8540.50 | + | 37418.4i | 0.297765 | + | 1.30459i | 0.873446 | + | 0.486921i | \(0.161880\pi\) |
−0.575681 | + | 0.817674i | \(0.695263\pi\) | |||||||
\(938\) | 11617.4 | − | 5594.63i | 0.404393 | − | 0.194745i | ||||
\(939\) | −40036.2 | −1.39141 | ||||||||
\(940\) | −7649.25 | −0.265416 | ||||||||
\(941\) | −30252.9 | + | 14569.0i | −1.04805 | + | 0.504715i | −0.876972 | − | 0.480542i | \(-0.840440\pi\) |
−0.171080 | + | 0.985257i | \(0.554726\pi\) | |||||||
\(942\) | 2132.80 | − | 9344.42i | 0.0737691 | − | 0.323203i | ||||
\(943\) | 14157.1 | − | 17752.4i | 0.488884 | − | 0.613041i | ||||
\(944\) | 6969.60 | + | 8739.61i | 0.240298 | + | 0.301324i | ||||
\(945\) | 11550.1 | 0.397593 | ||||||||
\(946\) | −4357.71 | − | 4917.29i | −0.149769 | − | 0.169001i | ||||
\(947\) | −40210.2 | −1.37978 | −0.689892 | − | 0.723913i | \(-0.742342\pi\) | ||||
−0.689892 | + | 0.723913i | \(0.742342\pi\) | |||||||
\(948\) | −12790.4 | − | 16038.7i | −0.438200 | − | 0.549485i | ||||
\(949\) | −36901.2 | + | 46272.6i | −1.26224 | + | 1.58279i | ||||
\(950\) | 5886.30 | − | 25789.5i | 0.201028 | − | 0.880762i | ||||
\(951\) | −2569.91 | + | 1237.60i | −0.0876289 | + | 0.0421998i | ||||
\(952\) | −28618.9 | −0.974309 | ||||||||
\(953\) | 18846.5 | 0.640607 | 0.320303 | − | 0.947315i | \(-0.396215\pi\) | ||||
0.320303 | + | 0.947315i | \(0.396215\pi\) | |||||||
\(954\) | 18199.6 | − | 8764.46i | 0.617645 | − | 0.297442i | ||||
\(955\) | 4119.70 | + | 18049.6i | 0.139592 | + | 0.611593i | ||||
\(956\) | −334.816 | − | 161.239i | −0.0113271 | − | 0.00545485i | ||||
\(957\) | −1414.64 | − | 6197.94i | −0.0477835 | − | 0.209353i | ||||
\(958\) | 3494.45 | + | 4381.90i | 0.117850 | + | 0.147779i | ||||
\(959\) | 1185.44 | − | 570.877i | 0.0399164 | − | 0.0192227i | ||||
\(960\) | 7471.08 | + | 9368.44i | 0.251175 | + | 0.314964i | ||||
\(961\) | 5833.76 | − | 25559.4i | 0.195823 | − | 0.857956i | ||||
\(962\) | 13087.9 | + | 6302.82i | 0.438641 | + | 0.211238i | ||||
\(963\) | −16.3126 | − | 7.85572i | −0.000545862 | − | 0.000262873i | ||||
\(964\) | −7665.09 | + | 9611.72i | −0.256096 | + | 0.321134i | ||||
\(965\) | 9932.10 | − | 43515.4i | 0.331322 | − | 1.45162i | ||||
\(966\) | 3755.61 | + | 16454.4i | 0.125088 | + | 0.548046i | ||||
\(967\) | 741.765 | − | 930.143i | 0.0246676 | − | 0.0309322i | −0.769345 | − | 0.638834i | \(-0.779417\pi\) |
0.794012 | + | 0.607902i | \(0.207989\pi\) | |||||||
\(968\) | −12931.9 | + | 16216.1i | −0.429386 | + | 0.538434i | ||||
\(969\) | 19942.6 | + | 87374.1i | 0.661143 | + | 2.89666i | ||||
\(970\) | −35.5187 | + | 155.618i | −0.00117571 | + | 0.00515111i | ||||
\(971\) | −28664.3 | + | 35943.9i | −0.947356 | + | 1.18795i | 0.0347080 | + | 0.999397i | \(0.488950\pi\) |
−0.982064 | + | 0.188549i | \(0.939622\pi\) | |||||||
\(972\) | −29321.1 | − | 14120.3i | −0.967567 | − | 0.465956i | ||||
\(973\) | −30944.4 | − | 14902.0i | −1.01956 | − | 0.490994i | ||||
\(974\) | −5523.89 | + | 24201.7i | −0.181722 | + | 0.796174i | ||||
\(975\) | −54267.0 | − | 68048.6i | −1.78250 | − | 2.23518i | ||||
\(976\) | −11713.2 | + | 5640.80i | −0.384151 | + | 0.184998i | ||||
\(977\) | 26616.9 | + | 33376.5i | 0.871597 | + | 1.09295i | 0.994929 | + | 0.100583i | \(0.0320707\pi\) |
−0.123332 | + | 0.992366i | \(0.539358\pi\) | |||||||
\(978\) | −524.354 | − | 2297.34i | −0.0171442 | − | 0.0751134i | ||||
\(979\) | −13218.8 | − | 6365.82i | −0.431535 | − | 0.207817i | ||||
\(980\) | −1308.15 | − | 5731.39i | −0.0426402 | − | 0.186819i | ||||
\(981\) | 35246.4 | − | 16973.8i | 1.14713 | − | 0.552427i | ||||
\(982\) | −8900.52 | −0.289233 | ||||||||
\(983\) | 19065.0 | 0.618596 | 0.309298 | − | 0.950965i | \(-0.399906\pi\) | ||||
0.309298 | + | 0.950965i | \(0.399906\pi\) | |||||||
\(984\) | −33433.0 | + | 16100.5i | −1.08313 | + | 0.521610i | ||||
\(985\) | −10378.9 | + | 45472.8i | −0.335735 | + | 1.47095i | ||||
\(986\) | 3745.11 | − | 4696.22i | 0.120962 | − | 0.151682i | ||||
\(987\) | 6293.45 | + | 7891.73i | 0.202961 | + | 0.254505i | ||||
\(988\) | 65221.3 | 2.10017 | ||||||||
\(989\) | 26134.0 | − | 1358.66i | 0.840256 | − | 0.0436832i | ||||
\(990\) | −12323.8 | −0.395634 | ||||||||
\(991\) | 32082.8 | + | 40230.5i | 1.02840 | + | 1.28957i | 0.956367 | + | 0.292169i | \(0.0943771\pi\) |
0.0720325 | + | 0.997402i | \(0.477051\pi\) | |||||||
\(992\) | 6948.20 | − | 8712.77i | 0.222385 | − | 0.278862i | ||||
\(993\) | 9683.63 | − | 42426.8i | 0.309467 | − | 1.35586i | ||||
\(994\) | 4822.39 | − | 2322.34i | 0.153880 | − | 0.0741047i | ||||
\(995\) | −254.056 | −0.00809459 | ||||||||
\(996\) | 3977.79 | 0.126547 | ||||||||
\(997\) | −2678.30 | + | 1289.80i | −0.0850777 | + | 0.0409713i | −0.475939 | − | 0.879478i | \(-0.657892\pi\) |
0.390861 | + | 0.920450i | \(0.372177\pi\) | |||||||
\(998\) | 1744.88 | + | 7644.81i | 0.0553438 | + | 0.242477i | ||||
\(999\) | 4895.05 | + | 2357.33i | 0.155028 | + | 0.0746573i |
(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 | 43.4.e.a.11.5 | yes | 60 | |
43.2 | odd | 14 | 1849.4.a.g.1.19 | 30 | |||
43.4 | even | 7 | inner | 43.4.e.a.4.5 | ✓ | 60 | |
43.41 | even | 7 | 1849.4.a.h.1.12 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.5 | ✓ | 60 | 43.4 | even | 7 | inner | |
43.4.e.a.11.5 | yes | 60 | 1.1 | even | 1 | trivial | |
1849.4.a.g.1.19 | 30 | 43.2 | odd | 14 | |||
1849.4.a.h.1.12 | 30 | 43.41 | even | 7 |