Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(46,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.j (of order \(3\), 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: | \(18.5856016518\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.226 |
Dual form | 315.4.j.c.46.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.20711 | + | 3.82282i | −0.780330 | + | 1.35157i | 0.151419 | + | 0.988470i | \(0.451616\pi\) |
−0.931749 | + | 0.363102i | \(0.881718\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.74264 | − | 9.94655i | −0.717830 | − | 1.24332i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.1066 | + | 9.14207i | 0.869675 | + | 0.493625i | ||||
\(8\) | 15.3848 | 0.679917 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.0355 | + | 19.1141i | 0.348974 | + | 0.604441i | ||||
\(11\) | −0.0710678 | − | 0.123093i | −0.00194798 | − | 0.00337400i | 0.865050 | − | 0.501686i | \(-0.167287\pi\) |
−0.866998 | + | 0.498312i | \(0.833953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.1421 | −0.685740 | −0.342870 | − | 0.939383i | \(-0.611399\pi\) | ||||
−0.342870 | + | 0.939383i | \(0.611399\pi\) | |||||||
\(14\) | −70.4975 | + | 41.3951i | −1.34580 | + | 0.790237i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.9853 | − | 20.7591i | 0.187270 | − | 0.324361i | ||||
\(17\) | −57.1838 | − | 99.0452i | −0.815829 | − | 1.41306i | −0.908731 | − | 0.417383i | \(-0.862947\pi\) |
0.0929014 | − | 0.995675i | \(-0.470386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.6152 | + | 37.4387i | −0.260993 | + | 0.452054i | −0.966506 | − | 0.256643i | \(-0.917383\pi\) |
0.705513 | + | 0.708697i | \(0.250717\pi\) | |||||||
\(20\) | −57.4264 | −0.642047 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.627417 | 0.00608026 | ||||||||
\(23\) | 77.2315 | − | 133.769i | 0.700169 | − | 1.21273i | −0.268238 | − | 0.963353i | \(-0.586441\pi\) |
0.968407 | − | 0.249375i | \(-0.0802252\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 70.9411 | − | 122.874i | 0.535104 | − | 0.926827i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.56245 | − | 212.705i | −0.0105455 | − | 1.43562i | ||||
\(29\) | 40.1472 | 0.257074 | 0.128537 | − | 0.991705i | \(-0.458972\pi\) | ||||
0.128537 | + | 0.991705i | \(0.458972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.7107 | − | 65.3168i | −0.218485 | − | 0.378427i | 0.735860 | − | 0.677134i | \(-0.236778\pi\) |
−0.954345 | + | 0.298707i | \(0.903445\pi\) | |||||||
\(32\) | 114.445 | + | 198.224i | 0.632224 | + | 1.09504i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 504.843 | 2.54647 | ||||||||
\(35\) | 79.8528 | − | 46.8885i | 0.385645 | − | 0.226446i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 200.167 | − | 346.699i | 0.889383 | − | 1.54046i | 0.0487770 | − | 0.998810i | \(-0.484468\pi\) |
0.840606 | − | 0.541647i | \(-0.182199\pi\) | |||||||
\(38\) | −95.4142 | − | 165.262i | −0.407322 | − | 0.705502i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 38.4619 | − | 66.6180i | 0.152034 | − | 0.263331i | ||||
\(41\) | 95.4264 | 0.363490 | 0.181745 | − | 0.983346i | \(-0.441825\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −340.071 | −1.20605 | −0.603027 | − | 0.797721i | \(-0.706039\pi\) | ||||
−0.603027 | + | 0.797721i | \(0.706039\pi\) | |||||||
\(44\) | −0.816234 | + | 1.41376i | −0.00279663 | + | 0.00484391i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 340.916 | + | 590.484i | 1.09273 | + | 1.89266i | ||||
\(47\) | −3.74517 | + | 6.48682i | −0.0116232 | + | 0.0201319i | −0.871778 | − | 0.489900i | \(-0.837033\pi\) |
0.860155 | + | 0.510032i | \(0.170367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 175.845 | + | 294.495i | 0.512668 | + | 0.858587i | ||||
\(50\) | 110.355 | 0.312132 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 184.581 | + | 319.703i | 0.492245 | + | 0.852593i | ||||
\(53\) | −338.409 | − | 586.142i | −0.877058 | − | 1.51911i | −0.854554 | − | 0.519362i | \(-0.826170\pi\) |
−0.0225038 | − | 0.999747i | \(-0.507164\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.710678 | −0.00174232 | ||||||||
\(56\) | 247.796 | + | 140.649i | 0.591307 | + | 0.335624i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −88.6091 | + | 153.476i | −0.200603 | + | 0.347454i | ||||
\(59\) | 398.090 | + | 689.513i | 0.878423 | + | 1.52147i | 0.853071 | + | 0.521795i | \(0.174737\pi\) |
0.0253519 | + | 0.999679i | \(0.491929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 378.551 | − | 655.669i | 0.794565 | − | 1.37623i | −0.128550 | − | 0.991703i | \(-0.541032\pi\) |
0.923115 | − | 0.384524i | \(-0.125634\pi\) | |||||||
\(62\) | 332.926 | 0.681962 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −818.602 | −1.59883 | ||||||||
\(65\) | −80.3553 | + | 139.180i | −0.153336 | + | 0.265586i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 370.290 | + | 641.362i | 0.675197 | + | 1.16947i | 0.976411 | + | 0.215918i | \(0.0692745\pi\) |
−0.301215 | + | 0.953556i | \(0.597392\pi\) | |||||||
\(68\) | −656.772 | + | 1137.56i | −1.17125 | + | 2.02867i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.00253 | + | 408.751i | 0.00512672 | + | 0.697930i | ||||
\(71\) | −37.0253 | −0.0618886 | −0.0309443 | − | 0.999521i | \(-0.509851\pi\) | ||||
−0.0309443 | + | 0.999521i | \(0.509851\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −40.4386 | − | 70.0417i | −0.0648353 | − | 0.112298i | 0.831786 | − | 0.555097i | \(-0.187319\pi\) |
−0.896621 | + | 0.442799i | \(0.853986\pi\) | |||||||
\(74\) | 883.578 | + | 1530.40i | 1.38802 | + | 2.40413i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 496.514 | 0.749395 | ||||||||
\(77\) | −0.0193360 | − | 2.63232i | −2.86174e−5 | − | 0.00389585i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 158.679 | − | 274.840i | 0.225985 | − | 0.391417i | −0.730630 | − | 0.682774i | \(-0.760773\pi\) |
0.956614 | + | 0.291357i | \(0.0941067\pi\) | |||||||
\(80\) | −59.9264 | − | 103.796i | −0.0837497 | − | 0.145059i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −210.616 | + | 364.798i | −0.283642 | + | 0.491283i | ||||
\(83\) | 945.929 | 1.25095 | 0.625477 | − | 0.780243i | \(-0.284904\pi\) | ||||
0.625477 | + | 0.780243i | \(0.284904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −571.838 | −0.729700 | ||||||||
\(86\) | 750.573 | − | 1300.03i | 0.941121 | − | 1.63007i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.09336 | − | 1.89376i | −0.00132446 | − | 0.00229404i | ||||
\(89\) | 391.603 | − | 678.276i | 0.466402 | − | 0.807832i | −0.532861 | − | 0.846203i | \(-0.678883\pi\) |
0.999264 | + | 0.0383703i | \(0.0122166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −517.701 | − | 293.846i | −0.596371 | − | 0.338499i | ||||
\(92\) | −1774.05 | −2.01041 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16.5320 | − | 28.6342i | −0.0181398 | − | 0.0314191i | ||||
\(95\) | 108.076 | + | 187.193i | 0.116720 | + | 0.202165i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 393.107 | 0.411484 | 0.205742 | − | 0.978606i | \(-0.434039\pi\) | ||||
0.205742 | + | 0.978606i | \(0.434039\pi\) | |||||||
\(98\) | −1513.91 | + | 22.2424i | −1.56049 | + | 0.0229268i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −143.566 | + | 248.664i | −0.143566 | + | 0.248664i | ||||
\(101\) | 227.221 | + | 393.558i | 0.223855 | + | 0.387728i | 0.955975 | − | 0.293448i | \(-0.0948026\pi\) |
−0.732121 | + | 0.681175i | \(0.761469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 351.850 | − | 609.422i | 0.336590 | − | 0.582991i | −0.647199 | − | 0.762321i | \(-0.724060\pi\) |
0.983789 | + | 0.179330i | \(0.0573930\pi\) | |||||||
\(104\) | −494.500 | −0.466247 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2987.62 | 2.73758 | ||||||||
\(107\) | 477.499 | − | 827.052i | 0.431416 | − | 0.747235i | −0.565579 | − | 0.824694i | \(-0.691347\pi\) |
0.996996 | + | 0.0774592i | \(0.0246808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −144.463 | − | 250.218i | −0.126946 | − | 0.219876i | 0.795546 | − | 0.605893i | \(-0.207184\pi\) |
−0.922492 | + | 0.386017i | \(0.873851\pi\) | |||||||
\(110\) | 1.56854 | − | 2.71680i | 0.00135959 | − | 0.00235488i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 382.823 | − | 224.789i | 0.322977 | − | 0.189648i | ||||
\(113\) | −1251.24 | −1.04165 | −0.520826 | − | 0.853663i | \(-0.674376\pi\) | ||||
−0.520826 | + | 0.853663i | \(0.674376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −386.157 | − | 668.844i | −0.313125 | − | 0.542348i | ||||
\(116\) | −230.551 | − | 399.326i | −0.184535 | − | 0.319625i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3514.51 | −2.74184 | ||||||||
\(119\) | −15.5584 | − | 2118.06i | −0.0119852 | − | 1.63161i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 665.490 | − | 1152.66i | 0.499992 | − | 0.866012i | ||||
\(122\) | 1671.00 | + | 2894.26i | 1.24005 | + | 2.14782i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −433.118 | + | 750.182i | −0.313670 | + | 0.543293i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1947.62 | −1.36082 | −0.680408 | − | 0.732833i | \(-0.738198\pi\) | ||||
−0.680408 | + | 0.732833i | \(0.738198\pi\) | |||||||
\(128\) | 891.185 | − | 1543.58i | 0.615393 | − | 1.06589i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −354.706 | − | 614.368i | −0.239306 | − | 0.414490i | ||||
\(131\) | 530.823 | − | 919.412i | 0.354032 | − | 0.613201i | −0.632920 | − | 0.774217i | \(-0.718144\pi\) |
0.986952 | + | 0.161016i | \(0.0514771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −690.415 | + | 405.402i | −0.450124 | + | 0.264307i | ||||
\(134\) | −3269.08 | −2.10750 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −879.759 | − | 1523.79i | −0.554697 | − | 0.960763i | ||||
\(137\) | −719.671 | − | 1246.51i | −0.448800 | − | 0.777345i | 0.549508 | − | 0.835489i | \(-0.314815\pi\) |
−0.998308 | + | 0.0581435i | \(0.981482\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 662.132 | 0.404038 | 0.202019 | − | 0.979382i | \(-0.435250\pi\) | ||||
0.202019 | + | 0.979382i | \(0.435250\pi\) | |||||||
\(140\) | −924.944 | − | 524.996i | −0.558372 | − | 0.316930i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 81.7187 | − | 141.541i | 0.0482935 | − | 0.0836468i | ||||
\(143\) | 2.28427 | + | 3.95647i | 0.00133581 | + | 0.00231369i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 100.368 | − | 173.842i | 0.0574835 | − | 0.0995643i | ||||
\(146\) | 357.009 | 0.202372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4597.94 | −2.55370 | ||||||||
\(149\) | −393.555 | + | 681.657i | −0.216384 | + | 0.374789i | −0.953700 | − | 0.300760i | \(-0.902760\pi\) |
0.737315 | + | 0.675549i | \(0.236093\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 424.177 | + | 734.697i | 0.228603 | + | 0.395952i | 0.957394 | − | 0.288784i | \(-0.0932509\pi\) |
−0.728791 | + | 0.684736i | \(0.759918\pi\) | |||||||
\(152\) | −332.545 | + | 575.985i | −0.177454 | + | 0.307359i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.1056 | + | 5.73589i | 0.00528785 | + | 0.00300137i | ||||
\(155\) | −377.107 | −0.195419 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −477.461 | − | 826.987i | −0.242710 | − | 0.420387i | 0.718775 | − | 0.695243i | \(-0.244703\pi\) |
−0.961485 | + | 0.274856i | \(0.911370\pi\) | |||||||
\(158\) | 700.444 | + | 1213.20i | 0.352685 | + | 0.610869i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1144.45 | 0.565478 | ||||||||
\(161\) | 2466.86 | − | 1448.51i | 1.20755 | − | 0.709058i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.68211 | − | 6.37760i | 0.00176936 | − | 0.00306461i | −0.865139 | − | 0.501532i | \(-0.832770\pi\) |
0.866909 | + | 0.498467i | \(0.166103\pi\) | |||||||
\(164\) | −548.000 | − | 949.163i | −0.260924 | − | 0.451934i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2087.77 | + | 3616.12i | −0.976157 | + | 1.69075i | ||||
\(167\) | −2921.40 | −1.35368 | −0.676841 | − | 0.736129i | \(-0.736651\pi\) | ||||
−0.676841 | + | 0.736129i | \(0.736651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1163.88 | −0.529760 | ||||||||
\(170\) | 1262.11 | − | 2186.03i | 0.569407 | − | 0.986242i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1952.91 | + | 3382.53i | 0.865742 | + | 1.49951i | ||||
\(173\) | −1984.78 | + | 3437.75i | −0.872256 | + | 1.51079i | −0.0125990 | + | 0.999921i | \(0.504011\pi\) |
−0.859657 | + | 0.510871i | \(0.829323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.40097 | − | 462.994i | −0.00146908 | − | 0.199995i | ||||
\(176\) | −3.40707 | −0.00145919 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1728.62 | + | 2994.05i | 0.727895 | + | 1.26075i | ||||
\(179\) | −552.976 | − | 957.782i | −0.230901 | − | 0.399933i | 0.727172 | − | 0.686455i | \(-0.240834\pi\) |
−0.958074 | + | 0.286522i | \(0.907501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −117.214 | −0.0481349 | −0.0240674 | − | 0.999710i | \(-0.507662\pi\) | ||||
−0.0240674 | + | 0.999710i | \(0.507662\pi\) | |||||||
\(182\) | 2265.94 | − | 1330.53i | 0.922871 | − | 0.541897i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1188.19 | − | 2058.00i | 0.476057 | − | 0.824555i | ||||
\(185\) | −1000.83 | − | 1733.49i | −0.397744 | − | 0.688913i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.12785 | + | 14.0778i | −0.00317843 | + | 0.00550521i | ||||
\(188\) | 86.0286 | 0.0333738 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −954.142 | −0.364320 | ||||||||
\(191\) | 501.300 | − | 868.277i | 0.189910 | − | 0.328933i | −0.755310 | − | 0.655368i | \(-0.772514\pi\) |
0.945220 | + | 0.326434i | \(0.105847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1628.88 | − | 2821.30i | −0.607510 | − | 1.05224i | −0.991649 | − | 0.128963i | \(-0.958835\pi\) |
0.384140 | − | 0.923275i | \(-0.374498\pi\) | |||||||
\(194\) | −867.629 | + | 1502.78i | −0.321093 | + | 0.556150i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1919.39 | − | 3440.23i | 0.699488 | − | 1.25373i | ||||
\(197\) | 41.6955 | 0.0150796 | 0.00753981 | − | 0.999972i | \(-0.497600\pi\) | ||||
0.00753981 | + | 0.999972i | \(0.497600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1202.81 | − | 2083.32i | −0.428466 | − | 0.742125i | 0.568271 | − | 0.822841i | \(-0.307612\pi\) |
−0.996737 | + | 0.0807167i | \(0.974279\pi\) | |||||||
\(200\) | −192.310 | − | 333.090i | −0.0679917 | − | 0.117765i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2006.00 | −0.698722 | ||||||||
\(203\) | 646.635 | + | 367.028i | 0.223571 | + | 0.126898i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 238.566 | − | 413.208i | 0.0812789 | − | 0.140779i | ||||
\(206\) | 1553.14 | + | 2690.12i | 0.525303 | + | 0.909851i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −385.233 | + | 667.242i | −0.128419 | + | 0.222428i | ||||
\(209\) | 6.14459 | 0.00203364 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1211.24 | 0.395190 | 0.197595 | − | 0.980284i | \(-0.436687\pi\) | ||||
0.197595 | + | 0.980284i | \(0.436687\pi\) | |||||||
\(212\) | −3886.72 | + | 6732.00i | −1.25916 | + | 2.18092i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2107.78 | + | 3650.78i | 0.673294 | + | 1.16618i | ||||
\(215\) | −850.178 | + | 1472.55i | −0.269682 | + | 0.467103i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.2602 | − | 1396.79i | −0.00320973 | − | 0.436958i | ||||
\(218\) | 1275.38 | 0.396238 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.08117 | + | 7.06879i | 0.00125069 | + | 0.00216626i | ||||
\(221\) | 1838.01 | + | 3183.52i | 0.559447 | + | 0.968991i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4164.99 | 1.25071 | 0.625354 | − | 0.780341i | \(-0.284954\pi\) | ||||
0.625354 | + | 0.780341i | \(0.284954\pi\) | |||||||
\(224\) | 31.1379 | + | 4238.98i | 0.00928789 | + | 1.26441i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2761.62 | − | 4783.26i | 0.812832 | − | 1.40787i | ||||
\(227\) | 1178.12 | + | 2040.57i | 0.344470 | + | 0.596639i | 0.985257 | − | 0.171079i | \(-0.0547254\pi\) |
−0.640788 | + | 0.767718i | \(0.721392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2172.58 | + | 3763.02i | −0.626935 | + | 1.08588i | 0.361228 | + | 0.932477i | \(0.382358\pi\) |
−0.988163 | + | 0.153406i | \(0.950976\pi\) | |||||||
\(230\) | 3409.16 | 0.977363 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 617.655 | 0.174789 | ||||||||
\(233\) | 1229.12 | − | 2128.91i | 0.345591 | − | 0.598581i | −0.639870 | − | 0.768483i | \(-0.721012\pi\) |
0.985461 | + | 0.169902i | \(0.0543452\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.7258 | + | 32.4341i | 0.00519804 | + | 0.00900326i | ||||
\(236\) | 4572.18 | − | 7919.25i | 1.26112 | − | 2.18432i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8131.30 | + | 4615.31i | 2.21460 | + | 1.25700i | ||||
\(239\) | −322.304 | −0.0872307 | −0.0436154 | − | 0.999048i | \(-0.513888\pi\) | ||||
−0.0436154 | + | 0.999048i | \(0.513888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2505.62 | + | 4339.86i | 0.669714 | + | 1.15998i | 0.977984 | + | 0.208680i | \(0.0669168\pi\) |
−0.308270 | + | 0.951299i | \(0.599750\pi\) | |||||||
\(242\) | 2937.61 | + | 5088.10i | 0.780318 | + | 1.35155i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8695.53 | −2.28145 | ||||||||
\(245\) | 1714.81 | − | 25.1941i | 0.447165 | − | 0.00656976i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 694.759 | − | 1203.36i | 0.178974 | − | 0.309991i | ||||
\(248\) | −580.170 | − | 1004.88i | −0.148552 | − | 0.257299i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 275.888 | − | 477.853i | 0.0697948 | − | 0.120888i | ||||
\(251\) | −3936.95 | −0.990031 | −0.495015 | − | 0.868884i | \(-0.664838\pi\) | ||||
−0.495015 | + | 0.868884i | \(0.664838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.9547 | −0.00545565 | ||||||||
\(254\) | 4298.62 | − | 7445.42i | 1.06189 | − | 1.83924i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 659.471 | + | 1142.24i | 0.161004 | + | 0.278867i | ||||
\(257\) | −1813.08 | + | 3140.35i | −0.440066 | + | 0.762216i | −0.997694 | − | 0.0678748i | \(-0.978378\pi\) |
0.557628 | + | 0.830091i | \(0.311711\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6393.54 | − | 3754.20i | 1.53388 | − | 0.900674i | ||||
\(260\) | 1845.81 | 0.440277 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2343.16 | + | 4058.48i | 0.552523 | + | 0.956999i | ||||
\(263\) | −393.278 | − | 681.177i | −0.0922074 | − | 0.159708i | 0.816232 | − | 0.577724i | \(-0.196059\pi\) |
−0.908440 | + | 0.418016i | \(0.862726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3384.09 | −0.784465 | ||||||||
\(266\) | −25.9601 | − | 3534.10i | −0.00598389 | − | 0.814622i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4252.89 | − | 7366.22i | 0.969353 | − | 1.67897i | ||||
\(269\) | 2028.97 | + | 3514.28i | 0.459883 | + | 0.796541i | 0.998954 | − | 0.0457192i | \(-0.0145580\pi\) |
−0.539071 | + | 0.842260i | \(0.681225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1449.71 | + | 2510.97i | −0.324958 | + | 0.562844i | −0.981504 | − | 0.191442i | \(-0.938684\pi\) |
0.656546 | + | 0.754286i | \(0.272017\pi\) | |||||||
\(272\) | −2741.45 | −0.611122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6353.56 | 1.40085 | ||||||||
\(275\) | −1.77670 | + | 3.07733i | −0.000389595 | + | 0.000674799i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2646.98 | − | 4584.70i | −0.574157 | − | 0.994470i | −0.996133 | − | 0.0878623i | \(-0.971996\pi\) |
0.421975 | − | 0.906607i | \(-0.361337\pi\) | |||||||
\(278\) | −1461.40 | + | 2531.21i | −0.315283 | + | 0.546086i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1228.52 | − | 721.369i | 0.262207 | − | 0.153964i | ||||
\(281\) | −2359.40 | −0.500890 | −0.250445 | − | 0.968131i | \(-0.580577\pi\) | ||||
−0.250445 | + | 0.968131i | \(0.580577\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1440.67 | + | 2495.32i | 0.302612 | + | 0.524139i | 0.976727 | − | 0.214487i | \(-0.0688081\pi\) |
−0.674115 | + | 0.738626i | \(0.735475\pi\) | |||||||
\(284\) | 212.623 | + | 368.273i | 0.0444255 | + | 0.0769472i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.1665 | −0.00416948 | ||||||||
\(287\) | 1537.00 | + | 872.395i | 0.316118 | + | 0.179428i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4083.47 | + | 7072.77i | −0.831155 | + | 1.43960i | ||||
\(290\) | 443.046 | + | 767.378i | 0.0897122 | + | 0.155386i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −464.449 | + | 804.449i | −0.0930815 | + | 0.161222i | ||||
\(293\) | −760.730 | −0.151680 | −0.0758402 | − | 0.997120i | \(-0.524164\pi\) | ||||
−0.0758402 | + | 0.997120i | \(0.524164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3980.90 | 0.785685 | ||||||||
\(296\) | 3079.52 | − | 5333.88i | 0.604707 | − | 1.04738i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1737.24 | − | 3008.98i | −0.337703 | − | 0.584918i | ||||
\(299\) | −2482.39 | + | 4299.62i | −0.480134 | + | 0.831616i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5477.39 | − | 3108.95i | −1.04888 | − | 0.595339i | ||||
\(302\) | −3744.82 | −0.713544 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 518.129 | + | 897.426i | 0.0977524 | + | 0.169312i | ||||
\(305\) | −1892.75 | − | 3278.35i | −0.355340 | − | 0.615467i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4968.57 | −0.923685 | −0.461842 | − | 0.886962i | \(-0.652811\pi\) | ||||
−0.461842 | + | 0.886962i | \(0.652811\pi\) | |||||||
\(308\) | −26.0714 | + | 15.3088i | −0.00482324 | + | 0.00283214i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 832.315 | − | 1441.61i | 0.152491 | − | 0.264123i | ||||
\(311\) | −2516.98 | − | 4359.54i | −0.458922 | − | 0.794877i | 0.539982 | − | 0.841677i | \(-0.318431\pi\) |
−0.998904 | + | 0.0467998i | \(0.985098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1799.60 | + | 3117.00i | −0.324983 | + | 0.562886i | −0.981509 | − | 0.191417i | \(-0.938692\pi\) |
0.656526 | + | 0.754303i | \(0.272025\pi\) | |||||||
\(314\) | 4215.23 | 0.757577 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3644.95 | −0.648875 | ||||||||
\(317\) | 1770.78 | − | 3067.08i | 0.313744 | − | 0.543420i | −0.665426 | − | 0.746464i | \(-0.731750\pi\) |
0.979170 | + | 0.203044i | \(0.0650834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.85317 | − | 4.94184i | −0.000500774 | − | 0.000867367i | ||||
\(320\) | −2046.51 | + | 3544.65i | −0.357510 | + | 0.619225i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 92.7558 | + | 12627.4i | 0.0160530 | + | 2.18539i | ||||
\(323\) | 4944.16 | 0.851704 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 401.777 | + | 695.898i | 0.0685740 | + | 0.118774i | ||||
\(326\) | 16.2536 | + | 28.1521i | 0.00276136 | + | 0.00478282i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1468.11 | 0.247143 | ||||||||
\(329\) | −119.625 | + | 70.2420i | −0.0200460 | + | 0.0117707i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3678.98 | − | 6372.18i | 0.610922 | − | 1.05815i | −0.380164 | − | 0.924919i | \(-0.624132\pi\) |
0.991085 | − | 0.133228i | \(-0.0425342\pi\) | |||||||
\(332\) | −5432.13 | − | 9408.73i | −0.897972 | − | 1.55533i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6447.85 | − | 11168.0i | 1.05632 | − | 1.82960i | ||||
\(335\) | 3702.90 | 0.603914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2323.24 | −0.375534 | −0.187767 | − | 0.982214i | \(-0.560125\pi\) | ||||
−0.187767 | + | 0.982214i | \(0.560125\pi\) | |||||||
\(338\) | 2568.81 | − | 4449.32i | 0.413388 | − | 0.716009i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3283.86 | + | 5687.81i | 0.523801 | + | 0.907249i | ||||
\(341\) | −5.36003 | + | 9.28385i | −0.000851208 | + | 0.00147434i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 139.974 | + | 6350.91i | 0.0220347 | + | 0.999757i | ||||
\(344\) | −5231.92 | −0.820018 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8761.26 | − | 15174.9i | −1.36130 | − | 2.35783i | ||||
\(347\) | −2723.89 | − | 4717.92i | −0.421401 | − | 0.729889i | 0.574675 | − | 0.818381i | \(-0.305128\pi\) |
−0.996077 | + | 0.0884927i | \(0.971795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1227.84 | −0.188324 | −0.0941618 | − | 0.995557i | \(-0.530017\pi\) | ||||
−0.0941618 | + | 0.995557i | \(0.530017\pi\) | |||||||
\(350\) | 1777.45 | + | 1008.88i | 0.271453 | + | 0.154076i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2667 | − | 28.1747i | 0.00246311 | − | 0.00426624i | ||||
\(353\) | 990.931 | + | 1716.34i | 0.149411 | + | 0.258787i | 0.931010 | − | 0.364994i | \(-0.118929\pi\) |
−0.781599 | + | 0.623781i | \(0.785596\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −92.5631 | + | 160.324i | −0.0138387 | + | 0.0239693i | ||||
\(356\) | −8995.33 | −1.33919 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4881.90 | 0.720717 | ||||||||
\(359\) | −6109.03 | + | 10581.1i | −0.898112 | + | 1.55557i | −0.0682058 | + | 0.997671i | \(0.521727\pi\) |
−0.829906 | + | 0.557904i | \(0.811606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2495.06 | + | 4321.58i | 0.363765 | + | 0.630059i | ||||
\(362\) | 258.703 | − | 448.086i | 0.0375611 | − | 0.0650577i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 50.2203 | + | 6836.78i | 0.00723149 | + | 0.984464i | ||||
\(365\) | −404.386 | −0.0579905 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6823.85 | − | 11819.3i | −0.970577 | − | 1.68109i | −0.693818 | − | 0.720150i | \(-0.744073\pi\) |
−0.276759 | − | 0.960939i | \(-0.589260\pi\) | |||||||
\(368\) | −1851.28 | − | 3206.52i | −0.262241 | − | 0.454215i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8835.78 | 1.24149 | ||||||||
\(371\) | −92.0737 | − | 12534.5i | −0.0128847 | − | 1.75407i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2772.01 | − | 4801.27i | 0.384797 | − | 0.666488i | −0.606944 | − | 0.794745i | \(-0.707605\pi\) |
0.991741 | + | 0.128256i | \(0.0409380\pi\) | |||||||
\(374\) | −35.8781 | − | 62.1426i | −0.00496046 | − | 0.00859176i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −57.6185 | + | 99.7982i | −0.00790279 | + | 0.0136880i | ||||
\(377\) | −1290.42 | −0.176286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −634.243 | −0.0859601 | −0.0429801 | − | 0.999076i | \(-0.513685\pi\) | ||||
−0.0429801 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(380\) | 1241.28 | − | 2149.97i | 0.167570 | − | 0.290240i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2212.84 | + | 3832.76i | 0.296385 | + | 0.513353i | ||||
\(383\) | 2895.47 | − | 5015.09i | 0.386296 | − | 0.669084i | −0.605652 | − | 0.795730i | \(-0.707088\pi\) |
0.991948 | + | 0.126645i | \(0.0404210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.4466 | − | 6.49707i | −0.00151526 | − | 0.000860055i | ||||
\(386\) | 14380.5 | 1.89623 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2257.47 | − | 3910.05i | −0.295376 | − | 0.511606i | ||||
\(389\) | 758.496 | + | 1313.75i | 0.0988619 | + | 0.171234i | 0.911214 | − | 0.411934i | \(-0.135146\pi\) |
−0.812352 | + | 0.583168i | \(0.801813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17665.6 | −2.28487 | ||||||||
\(392\) | 2705.34 | + | 4530.74i | 0.348572 | + | 0.583768i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −92.0265 | + | 159.395i | −0.0117671 | + | 0.0203812i | ||||
\(395\) | −793.396 | − | 1374.20i | −0.101063 | − | 0.175047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3937.47 | − | 6819.90i | 0.497773 | − | 0.862169i | −0.502223 | − | 0.864738i | \(-0.667484\pi\) |
0.999997 | + | 0.00256925i | \(0.000817820\pi\) | |||||||
\(398\) | 10618.9 | 1.33738 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −599.264 | −0.0749080 | ||||||||
\(401\) | −5555.64 | + | 9622.65i | −0.691859 | + | 1.19833i | 0.279369 | + | 0.960184i | \(0.409875\pi\) |
−0.971228 | + | 0.238151i | \(0.923459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1212.10 | + | 2099.42i | 0.149824 | + | 0.259503i | ||||
\(404\) | 2609.69 | − | 4520.12i | 0.321379 | − | 0.556645i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2830.28 | + | 1661.90i | −0.345971 | + | 0.203149i | ||||
\(407\) | −56.9016 | −0.00692999 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5355.07 | + | 9275.25i | 0.647411 | + | 1.12135i | 0.983739 | + | 0.179603i | \(0.0574814\pi\) |
−0.336328 | + | 0.941745i | \(0.609185\pi\) | |||||||
\(410\) | 1053.08 | + | 1823.99i | 0.126849 | + | 0.219708i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8082.19 | −0.966458 | ||||||||
\(413\) | 108.312 | + | 14745.1i | 0.0129048 | + | 1.75680i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2364.82 | − | 4095.99i | 0.279722 | − | 0.484492i | ||||
\(416\) | −3678.50 | − | 6371.34i | −0.433541 | − | 0.750915i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.5618 | + | 23.4897i | −0.00158691 | + | 0.00274860i | ||||
\(419\) | −8615.98 | −1.00458 | −0.502289 | − | 0.864700i | \(-0.667509\pi\) | ||||
−0.502289 | + | 0.864700i | \(0.667509\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6689.72 | 0.774435 | 0.387217 | − | 0.921988i | \(-0.373436\pi\) | ||||
0.387217 | + | 0.921988i | \(0.373436\pi\) | |||||||
\(422\) | −2673.33 | + | 4630.35i | −0.308379 | + | 0.534128i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5206.35 | − | 9017.66i | −0.596327 | − | 1.03287i | ||||
\(425\) | −1429.59 | + | 2476.13i | −0.163166 | + | 0.282612i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12091.3 | − | 7099.87i | 1.37035 | − | 0.804653i | ||||
\(428\) | −10968.4 | −1.23873 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3752.87 | − | 6500.15i | −0.420882 | − | 0.728989i | ||||
\(431\) | 3085.32 | + | 5343.93i | 0.344814 | + | 0.597235i | 0.985320 | − | 0.170718i | \(-0.0546088\pi\) |
−0.640506 | + | 0.767953i | \(0.721275\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14001.1 | 1.55392 | 0.776961 | − | 0.629548i | \(-0.216760\pi\) | ||||
0.776961 | + | 0.629548i | \(0.216760\pi\) | |||||||
\(434\) | 5362.31 | + | 3043.63i | 0.593085 | + | 0.336634i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1659.20 | + | 2873.82i | −0.182251 | + | 0.315668i | ||||
\(437\) | 3338.75 | + | 5782.89i | 0.365479 | + | 0.633028i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6103.49 | + | 10571.6i | −0.663562 | + | 1.14932i | 0.316111 | + | 0.948722i | \(0.397623\pi\) |
−0.979673 | + | 0.200601i | \(0.935711\pi\) | |||||||
\(440\) | −10.9336 | −0.00118464 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16226.7 | −1.74621 | ||||||||
\(443\) | 613.882 | − | 1063.27i | 0.0658384 | − | 0.114035i | −0.831227 | − | 0.555933i | \(-0.812361\pi\) |
0.897066 | + | 0.441897i | \(0.145694\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1958.01 | − | 3391.38i | −0.208581 | − | 0.361274i | ||||
\(446\) | −9192.57 | + | 15922.0i | −0.975966 | + | 1.69042i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13184.9 | − | 7483.72i | −1.39046 | − | 0.789224i | ||||
\(449\) | 1151.70 | 0.121051 | 0.0605257 | − | 0.998167i | \(-0.480722\pi\) | ||||
0.0605257 | + | 0.998167i | \(0.480722\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.78175 | − | 11.7463i | −0.000708071 | − | 0.00122641i | ||||
\(452\) | 7185.41 | + | 12445.5i | 0.747729 | + | 1.29510i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10401.0 | −1.07520 | ||||||||
\(455\) | −2566.64 | + | 1507.10i | −0.264453 | + | 0.155283i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9356.91 | + | 16206.6i | −0.957763 | + | 1.65889i | −0.229849 | + | 0.973226i | \(0.573823\pi\) |
−0.727914 | + | 0.685668i | \(0.759510\pi\) | |||||||
\(458\) | −9590.23 | − | 16610.8i | −0.978433 | − | 1.69470i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4435.13 | + | 7681.87i | −0.449541 | + | 0.778628i | ||||
\(461\) | 3154.57 | 0.318705 | 0.159352 | − | 0.987222i | \(-0.449059\pi\) | ||||
0.159352 | + | 0.987222i | \(0.449059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4051.11 | 0.406633 | 0.203316 | − | 0.979113i | \(-0.434828\pi\) | ||||
0.203316 | + | 0.979113i | \(0.434828\pi\) | |||||||
\(464\) | 481.175 | − | 833.420i | 0.0481422 | − | 0.0833848i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5425.62 | + | 9397.45i | 0.539350 | + | 0.934181i | ||||
\(467\) | 8170.80 | − | 14152.2i | 0.809635 | − | 1.40233i | −0.103482 | − | 0.994631i | \(-0.532998\pi\) |
0.913117 | − | 0.407697i | \(-0.133668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 100.748 | + | 13715.4i | 0.00991920 | + | 1.35036i | ||||
\(470\) | −165.320 | −0.0162247 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6124.53 | + | 10608.0i | 0.597255 | + | 1.03448i | ||||
\(473\) | 24.1681 | + | 41.8604i | 0.00234937 | + | 0.00406922i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1080.76 | 0.104397 | ||||||||
\(476\) | −20978.0 | + | 12318.0i | −2.02001 | + | 1.18612i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 711.360 | − | 1232.11i | 0.0680688 | − | 0.117899i | ||||
\(479\) | 1265.72 | + | 2192.30i | 0.120736 | + | 0.209121i | 0.920058 | − | 0.391782i | \(-0.128141\pi\) |
−0.799322 | + | 0.600903i | \(0.794808\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6433.78 | + | 11143.6i | −0.609886 | + | 1.05635i | ||||
\(482\) | −22120.7 | −2.09039 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15286.7 | −1.43564 | ||||||||
\(485\) | 982.767 | − | 1702.20i | 0.0920106 | − | 0.159367i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4221.09 | + | 7311.14i | 0.392763 | + | 0.680286i | 0.992813 | − | 0.119677i | \(-0.0381858\pi\) |
−0.600050 | + | 0.799963i | \(0.704852\pi\) | |||||||
\(488\) | 5823.92 | − | 10087.3i | 0.540239 | − | 0.935721i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3688.47 | + | 6611.04i | −0.340057 | + | 0.609502i | ||||
\(491\) | 15223.9 | 1.39928 | 0.699640 | − | 0.714496i | \(-0.253344\pi\) | ||||
0.699640 | + | 0.714496i | \(0.253344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2295.77 | − | 3976.39i | −0.209729 | − | 0.363260i | ||||
\(494\) | 3066.82 | + | 5311.88i | 0.279317 | + | 0.483791i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1807.89 | −0.163663 | ||||||||
\(497\) | −596.351 | − | 338.487i | −0.0538229 | − | 0.0305498i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8311.32 | − | 14395.6i | 0.745623 | − | 1.29146i | −0.204280 | − | 0.978913i | \(-0.565485\pi\) |
0.949903 | − | 0.312545i | \(-0.101181\pi\) | |||||||
\(500\) | 717.830 | + | 1243.32i | 0.0642047 | + | 0.111206i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8689.26 | − | 15050.2i | 0.772551 | − | 1.33810i | ||||
\(503\) | 17506.6 | 1.55185 | 0.775923 | − | 0.630828i | \(-0.217285\pi\) | ||||
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2272.21 | 0.200222 | ||||||||
\(506\) | 48.4564 | − | 83.9289i | 0.00425721 | − | 0.00737370i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11184.5 | + | 19372.1i | 0.976835 | + | 1.69193i | ||||
\(509\) | 6191.58 | − | 10724.1i | 0.539169 | − | 0.933867i | −0.459780 | − | 0.888033i | \(-0.652072\pi\) |
0.998949 | − | 0.0458348i | \(-0.0145948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0025 | − | 1497.83i | −0.000952485 | − | 0.129667i | ||||
\(512\) | 8436.86 | 0.728242 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8003.33 | − | 13862.2i | −0.686793 | − | 1.18956i | ||||
\(515\) | −1759.25 | − | 3047.11i | −0.150528 | − | 0.260722i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.06464 | 9.05666e−5 | ||||||||
\(518\) | 240.402 | + | 32727.3i | 0.0203912 | + | 2.77597i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1236.25 | + | 2141.25i | −0.104256 | + | 0.180577i | ||||
\(521\) | −7489.50 | − | 12972.2i | −0.629790 | − | 1.09083i | −0.987594 | − | 0.157032i | \(-0.949807\pi\) |
0.357803 | − | 0.933797i | \(-0.383526\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1859.56 | + | 3220.85i | −0.155474 | + | 0.269288i | −0.933231 | − | 0.359276i | \(-0.883024\pi\) |
0.777758 | + | 0.628564i | \(0.216357\pi\) | |||||||
\(524\) | −12193.3 | −1.01654 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3472.02 | 0.287809 | ||||||||
\(527\) | −4312.88 | + | 7470.12i | −0.356493 | + | 0.617464i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5845.91 | − | 10125.4i | −0.480472 | − | 0.832203i | ||||
\(530\) | 7469.05 | − | 12936.8i | 0.612141 | − | 1.06026i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7997.15 | + | 4539.16i | 0.651730 | + | 0.369920i | ||||
\(533\) | −3067.21 | −0.249260 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2387.49 | − | 4135.26i | −0.192935 | − | 0.334173i | ||||
\(536\) | 5696.83 | + | 9867.21i | 0.459078 | + | 0.795146i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17912.6 | −1.43544 | ||||||||
\(539\) | 23.7534 | − | 42.5745i | 0.00189820 | − | 0.00340225i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 122.363 | − | 211.939i | 0.00972420 | − | 0.0168428i | −0.861122 | − | 0.508398i | \(-0.830238\pi\) |
0.870847 | + | 0.491555i | \(0.163571\pi\) | |||||||
\(542\) | −6399.33 | − | 11084.0i | −0.507149 | − | 0.878408i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13088.8 | − | 22670.4i | 1.03157 | − | 1.78674i | ||||
\(545\) | −1444.63 | −0.113544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12685.4 | −0.991568 | −0.495784 | − | 0.868446i | \(-0.665119\pi\) | ||||
−0.495784 | + | 0.868446i | \(0.665119\pi\) | |||||||
\(548\) | −8265.63 | + | 14316.5i | −0.644325 | + | 1.11600i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.84271 | − | 13.5840i | −0.000608026 | − | 0.00105313i | ||||
\(551\) | −867.790 | + | 1503.06i | −0.0670946 | + | 0.116211i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5068.39 | − | 2976.09i | 0.389747 | − | 0.228854i | ||||
\(554\) | 23368.7 | 1.79213 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3802.39 | − | 6585.93i | −0.290031 | − | 0.502348i | ||||
\(557\) | −11031.4 | − | 19106.9i | −0.839164 | − | 1.45347i | −0.890595 | − | 0.454798i | \(-0.849711\pi\) |
0.0514307 | − | 0.998677i | \(-0.483622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10930.6 | 0.827040 | ||||||||
\(560\) | −16.3047 | − | 2219.65i | −0.00123035 | − | 0.167495i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5207.45 | − | 9019.57i | 0.390859 | − | 0.676988i | ||||
\(563\) | 3931.10 | + | 6808.86i | 0.294274 | + | 0.509697i | 0.974816 | − | 0.223012i | \(-0.0715890\pi\) |
−0.680542 | + | 0.732709i | \(0.738256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3128.10 | + | 5418.02i | −0.232920 | + | 0.403430i | ||||
\(566\) | −12718.9 | −0.944549 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −569.625 | −0.0420791 | ||||||||
\(569\) | 10470.8 | − | 18135.9i | 0.771453 | − | 1.33620i | −0.165313 | − | 0.986241i | \(-0.552864\pi\) |
0.936766 | − | 0.349955i | \(-0.113803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3565.83 | + | 6176.20i | 0.261341 | + | 0.452655i | 0.966598 | − | 0.256296i | \(-0.0825021\pi\) |
−0.705258 | + | 0.708951i | \(0.749169\pi\) | |||||||
\(572\) | 26.2355 | − | 45.4412i | 0.00191776 | − | 0.00332167i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6727.32 | + | 3950.19i | −0.489186 | + | 0.287243i | ||||
\(575\) | −3861.57 | −0.280067 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7816.51 | + | 13538.6i | 0.563961 | + | 0.976809i | 0.997146 | + | 0.0755039i | \(0.0240565\pi\) |
−0.433184 | + | 0.901305i | \(0.642610\pi\) | |||||||
\(578\) | −18025.3 | − | 31220.7i | −1.29715 | − | 2.24673i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2305.51 | −0.165054 | ||||||||
\(581\) | 15235.7 | + | 8647.75i | 1.08792 | + | 0.617502i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −48.1000 | + | 83.3116i | −0.00341698 | + | 0.00591838i | ||||
\(584\) | −622.139 | − | 1077.58i | −0.0440827 | − | 0.0763534i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1679.01 | − | 2908.14i | 0.118361 | − | 0.205007i | ||||
\(587\) | 19406.2 | 1.36453 | 0.682266 | − | 0.731104i | \(-0.260995\pi\) | ||||
0.682266 | + | 0.731104i | \(0.260995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3260.50 | 0.228093 | ||||||||
\(590\) | −8786.28 | + | 15218.3i | −0.613094 | + | 1.06191i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4798.10 | − | 8310.56i | −0.333110 | − | 0.576963i | ||||
\(593\) | −7429.82 | + | 12868.8i | −0.514513 | + | 0.891162i | 0.485346 | + | 0.874322i | \(0.338694\pi\) |
−0.999858 | + | 0.0168395i | \(0.994640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9210.36 | − | 5227.78i | −0.634602 | − | 0.360198i | ||||
\(596\) | 9040.18 | 0.621309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10957.8 | − | 18979.4i | −0.749326 | − | 1.29787i | ||||
\(599\) | −5264.93 | − | 9119.13i | −0.359131 | − | 0.622032i | 0.628685 | − | 0.777660i | \(-0.283593\pi\) |
−0.987816 | + | 0.155627i | \(0.950260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11595.2 | 0.786984 | 0.393492 | − | 0.919328i | \(-0.371267\pi\) | ||||
0.393492 | + | 0.919328i | \(0.371267\pi\) | |||||||
\(602\) | 23974.2 | − | 14077.3i | 1.62311 | − | 0.953069i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4871.80 | − | 8438.20i | 0.328196 | − | 0.568453i | ||||
\(605\) | −3327.45 | − | 5763.31i | −0.223603 | − | 0.387292i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11641.0 | − | 20162.9i | 0.778411 | − | 1.34825i | −0.154446 | − | 0.988001i | \(-0.549359\pi\) |
0.932857 | − | 0.360246i | \(-0.117307\pi\) | |||||||
\(608\) | −9894.99 | −0.660024 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16710.0 | 1.10913 | ||||||||
\(611\) | 120.378 | − | 208.500i | 0.00797047 | − | 0.0138053i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3693.99 | + | 6398.18i | 0.243391 | + | 0.421566i | 0.961678 | − | 0.274181i | \(-0.0884068\pi\) |
−0.718287 | + | 0.695747i | \(0.755073\pi\) | |||||||
\(614\) | 10966.2 | − | 18993.9i | 0.720779 | − | 1.24843i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.297480 | − | 40.4976i | −1.94575e−5 | − | 0.00264886i | ||||
\(617\) | −667.085 | −0.0435265 | −0.0217632 | − | 0.999763i | \(-0.506928\pi\) | ||||
−0.0217632 | + | 0.999763i | \(0.506928\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4712.89 | + | 8162.96i | 0.306021 | + | 0.530044i | 0.977488 | − | 0.210990i | \(-0.0676689\pi\) |
−0.671467 | + | 0.741034i | \(0.734336\pi\) | |||||||
\(620\) | 2165.59 | + | 3750.91i | 0.140278 | + | 0.242968i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22221.0 | 1.43244 | ||||||||
\(623\) | 12508.2 | − | 7344.66i | 0.804385 | − | 0.472323i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −7943.83 | − | 13759.1i | −0.507187 | − | 0.878474i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5483.77 | + | 9498.17i | −0.348450 | + | 0.603532i | ||||
\(629\) | −45785.1 | −2.90234 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28047.3 | 1.76949 | 0.884744 | − | 0.466078i | \(-0.154333\pi\) | ||||
0.884744 | + | 0.466078i | \(0.154333\pi\) | |||||||
\(632\) | 2441.24 | − | 4228.36i | 0.153651 | − | 0.266131i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7816.59 | + | 13538.7i | 0.489647 | + | 0.848094i | ||||
\(635\) | −4869.06 | + | 8433.46i | −0.304288 | + | 0.527042i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5652.04 | − | 9465.71i | −0.351557 | − | 0.588768i | ||||
\(638\) | 25.1890 | 0.00156308 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4455.92 | − | 7717.89i | −0.275212 | − | 0.476682i | ||||
\(641\) | 11604.2 | + | 20099.0i | 0.715034 | + | 1.23847i | 0.962947 | + | 0.269692i | \(0.0869220\pi\) |
−0.247913 | + | 0.968782i | \(0.579745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4294.22 | −0.263371 | −0.131686 | − | 0.991292i | \(-0.542039\pi\) | ||||
−0.131686 | + | 0.991292i | \(0.542039\pi\) | |||||||
\(644\) | −28573.9 | − | 16218.5i | −1.74840 | − | 0.992388i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10912.3 | + | 18900.6i | −0.664610 | + | 1.15114i | ||||
\(647\) | −8696.69 | − | 15063.1i | −0.528443 | − | 0.915289i | −0.999450 | − | 0.0331602i | \(-0.989443\pi\) |
0.471007 | − | 0.882129i | \(-0.343890\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.5828 | − | 98.0043i | 0.00342230 | − | 0.00592759i | ||||
\(650\) | −3547.06 | −0.214042 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −84.5801 | −0.00508039 | ||||||||
\(653\) | 7237.72 | − | 12536.1i | 0.433743 | − | 0.751265i | −0.563449 | − | 0.826151i | \(-0.690526\pi\) |
0.997192 | + | 0.0748861i | \(0.0238593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2654.11 | − | 4597.06i | −0.158328 | − | 0.274232i | ||||
\(656\) | 1143.71 | − | 1980.97i | 0.0680708 | − | 0.117902i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.49798 | − | 612.336i | −0.000266489 | − | 0.0362786i | ||||
\(659\) | −620.113 | −0.0366558 | −0.0183279 | − | 0.999832i | \(-0.505834\pi\) | ||||
−0.0183279 | + | 0.999832i | \(0.505834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3052.75 | − | 5287.52i | −0.179634 | − | 0.311135i | 0.762121 | − | 0.647434i | \(-0.224158\pi\) |
−0.941755 | + | 0.336299i | \(0.890825\pi\) | |||||||
\(662\) | 16239.8 | + | 28128.2i | 0.953441 | + | 1.65141i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14552.9 | 0.850546 | ||||||||
\(665\) | 29.4051 | + | 4003.09i | 0.00171471 | + | 0.233433i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3100.63 | − | 5370.44i | 0.179995 | − | 0.311761i | ||||
\(668\) | 16776.6 | + | 29057.9i | 0.971713 | + | 1.68306i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8172.70 | + | 14155.5i | −0.471252 | + | 0.816233i | ||||
\(671\) | −107.611 | −0.00619118 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16302.5 | −0.933754 | −0.466877 | − | 0.884322i | \(-0.654621\pi\) | ||||
−0.466877 | + | 0.884322i | \(0.654621\pi\) | |||||||
\(674\) | 5127.64 | − | 8881.33i | 0.293040 | − | 0.507561i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6683.76 | + | 11576.6i | 0.380278 | + | 0.658660i | ||||
\(677\) | −2409.55 | + | 4173.46i | −0.136789 | + | 0.236926i | −0.926280 | − | 0.376837i | \(-0.877012\pi\) |
0.789490 | + | 0.613763i | \(0.210345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6331.61 | + | 3593.81i | 0.357857 | + | 0.203119i | ||||
\(680\) | −8797.59 | −0.496136 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −23.6603 | − | 40.9809i | −0.00132845 | − | 0.00230094i | ||||
\(683\) | −4095.16 | − | 7093.03i | −0.229425 | − | 0.397375i | 0.728213 | − | 0.685351i | \(-0.240351\pi\) |
−0.957638 | + | 0.287976i | \(0.907018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7196.71 | −0.401419 | ||||||||
\(686\) | −24587.3 | − | 13482.0i | −1.36844 | − | 0.750359i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4075.85 | + | 7059.57i | −0.225858 | + | 0.391197i | ||||
\(689\) | 10877.2 | + | 18839.9i | 0.601434 | + | 1.04171i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −238.487 | + | 413.071i | −0.0131295 | + | 0.0227409i | −0.872515 | − | 0.488586i | \(-0.837513\pi\) |
0.859386 | + | 0.511327i | \(0.170846\pi\) | |||||||
\(692\) | 45591.6 | 2.50453 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24047.7 | 1.31533 | ||||||||
\(695\) | 1655.33 | − | 2867.12i | 0.0903457 | − | 0.156483i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5456.84 | − | 9451.53i | −0.296546 | − | 0.513633i | ||||
\(698\) | 2709.98 | − | 4693.82i | 0.146955 | − | 0.254533i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4585.66 | + | 2692.64i | −0.247602 | + | 0.145389i | ||||
\(701\) | 20366.7 | 1.09735 | 0.548673 | − | 0.836037i | \(-0.315133\pi\) | ||||
0.548673 | + | 0.836037i | \(0.315133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8653.29 | + | 14987.9i | 0.464246 | + | 0.804098i | ||||
\(704\) | 58.1763 | + | 100.764i | 0.00311449 | + | 0.00539445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8748.36 | −0.466358 | ||||||||
\(707\) | 61.8218 | + | 8416.15i | 0.00328861 | + | 0.447697i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11207.5 | + | 19412.0i | −0.593664 | + | 1.02826i | 0.400070 | + | 0.916484i | \(0.368986\pi\) |
−0.993734 | + | 0.111771i | \(0.964348\pi\) | |||||||
\(710\) | −408.593 | − | 707.705i | −0.0215975 | − | 0.0374080i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6024.72 | − | 10435.1i | 0.317115 | − | 0.549259i | ||||
\(713\) | −11649.8 | −0.611906 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.8427 | 0.00119478 | ||||||||
\(716\) | −6351.08 | + | 11000.4i | −0.331496 | + | 0.574168i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −26966.5 | − | 46707.4i | −1.40165 | − | 2.42772i | ||||
\(719\) | −13078.0 | + | 22651.7i | −0.678340 | + | 1.17492i | 0.297141 | + | 0.954834i | \(0.403967\pi\) |
−0.975481 | + | 0.220085i | \(0.929366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11238.5 | − | 6599.08i | 0.580503 | − | 0.340863i | ||||
\(722\) | −22027.5 | −1.13543 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 673.115 | + | 1165.87i | 0.0345527 | + | 0.0598470i | ||||
\(725\) | −501.840 | − | 869.212i | −0.0257074 | − | 0.0445265i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13666.2 | −0.697184 | −0.348592 | − | 0.937275i | \(-0.613340\pi\) | ||||
−0.348592 | + | 0.937275i | \(0.613340\pi\) | |||||||
\(728\) | −7964.71 | − | 4520.75i | −0.405483 | − | 0.230151i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 892.523 | − | 1545.90i | 0.0452517 | − | 0.0783783i | ||||
\(731\) | 19446.5 | + | 33682.4i | 0.983935 | + | 1.70423i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12519.1 | + | 21683.7i | −0.630836 | + | 1.09264i | 0.356545 | + | 0.934278i | \(0.383955\pi\) |
−0.987381 | + | 0.158362i | \(0.949379\pi\) | |||||||
\(734\) | 60243.8 | 3.02948 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35354.9 | 1.77065 | ||||||||
\(737\) | 52.6315 | − | 91.1603i | 0.00263054 | − | 0.00455622i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1627.60 | − | 2819.08i | −0.0810178 | − | 0.140327i | 0.822670 | − | 0.568520i | \(-0.192484\pi\) |
−0.903687 | + | 0.428193i | \(0.859150\pi\) | |||||||
\(740\) | −11494.8 | + | 19909.7i | −0.571026 | + | 0.989045i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 48120.4 | + | 27313.0i | 2.38080 | + | 1.35134i | ||||
\(743\) | 8366.48 | 0.413104 | 0.206552 | − | 0.978436i | \(-0.433776\pi\) | ||||
0.206552 | + | 0.978436i | \(0.433776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1967.78 | + | 3408.29i | 0.0967701 | + | 0.167611i | ||||
\(746\) | 12236.3 | + | 21193.8i | 0.600538 | + | 1.04016i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 186.701 | 0.00912630 | ||||||||
\(749\) | 15251.8 | − | 8955.67i | 0.744046 | − | 0.436893i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5082.23 | − | 8802.69i | 0.246942 | − | 0.427716i | −0.715734 | − | 0.698373i | \(-0.753908\pi\) |
0.962676 | + | 0.270657i | \(0.0872410\pi\) | |||||||
\(752\) | 89.7737 | + | 155.493i | 0.00435334 | + | 0.00754021i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2848.09 | − | 4933.03i | 0.137561 | − | 0.238263i | ||||
\(755\) | 4241.77 | 0.204469 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9031.23 | 0.433614 | 0.216807 | − | 0.976214i | \(-0.430436\pi\) | ||||
0.216807 | + | 0.976214i | \(0.430436\pi\) | |||||||
\(758\) | 1399.84 | − | 2424.60i | 0.0670773 | − | 0.116181i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1662.73 | + | 2879.93i | 0.0793598 | + | 0.137455i | ||||
\(761\) | −16217.3 | + | 28089.3i | −0.772508 | + | 1.33802i | 0.163677 | + | 0.986514i | \(0.447665\pi\) |
−0.936185 | + | 0.351509i | \(0.885669\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.3053 | − | 5350.86i | −0.00186494 | − | 0.253885i | ||||
\(764\) | −11515.1 | −0.545292 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12781.2 | + | 22137.7i | 0.602877 | + | 1.04421i | ||||
\(767\) | −12795.5 | − | 22162.4i | −0.602370 | − | 1.04334i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22629.4 | −1.06117 | −0.530583 | − | 0.847633i | \(-0.678027\pi\) | ||||
−0.530583 | + | 0.847633i | \(0.678027\pi\) | |||||||
\(770\) | 50.1010 | − | 29.4186i | 0.00234482 | − | 0.00137685i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18708.2 | + | 32403.5i | −0.872178 | + | 1.51066i | ||||
\(773\) | 1353.50 | + | 2344.34i | 0.0629782 | + | 0.109081i | 0.895795 | − | 0.444467i | \(-0.146607\pi\) |
−0.832817 | + | 0.553548i | \(0.813273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −942.767 | + | 1632.92i | −0.0436970 | + | 0.0756855i | ||||
\(776\) | 6047.86 | 0.279775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6696.33 | −0.308580 | ||||||||
\(779\) | −2062.66 | + | 3572.64i | −0.0948685 | + | 0.164317i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.63130 | + | 4.55755i | 0.000120558 | + | 0.000208812i | ||||
\(782\) | 38989.8 | − | 67532.2i | 1.78296 | − | 3.08817i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8221.02 | − | 120.783i | 0.374500 | − | 0.00550215i | ||||
\(785\) | −4774.61 | −0.217087 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12542.3 | + | 21723.9i | 0.568088 | + | 0.983958i | 0.996755 | + | 0.0804951i | \(0.0256501\pi\) |
−0.428667 | + | 0.903463i | \(0.641017\pi\) | |||||||
\(788\) | −239.442 | − | 414.726i | −0.0108246 | − | 0.0187488i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7004.44 | 0.315451 | ||||||||
\(791\) | −20153.2 | − | 11438.9i | −0.905898 | − | 0.514186i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12167.4 | + | 21074.6i | −0.544865 | + | 0.943734i | ||||
\(794\) | 17380.8 | + | 30104.5i | 0.776855 | + | 1.34555i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13814.6 | + | 23927.5i | −0.615131 | + | 1.06544i | ||||
\(797\) | −7374.99 | −0.327774 | −0.163887 | − | 0.986479i | \(-0.552403\pi\) | ||||
−0.163887 | + | 0.986479i | \(0.552403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 856.651 | 0.0379301 | ||||||||
\(800\) | 2861.12 | − | 4955.60i | 0.126445 | − | 0.219009i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24523.8 | − | 42476.4i | −1.07976 | − | 1.87019i | ||||
\(803\) | −5.74777 | + | 9.95542i | −0.000252596 | + | 0.000437508i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −105.065 | − | 14303.1i | −0.00460006 | − | 0.626233i | ||||
\(806\) | −10701.0 | −0.467649 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3495.74 | + | 6054.80i | 0.152203 | + | 0.263623i | ||||
\(809\) | 1157.19 | + | 2004.30i | 0.0502899 | + | 0.0871046i | 0.890075 | − | 0.455815i | \(-0.150652\pi\) |
−0.839785 | + | 0.542920i | \(0.817319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38300.1 | 1.65832 | 0.829160 | − | 0.559011i | \(-0.188819\pi\) | ||||
0.829160 | + | 0.559011i | \(0.188819\pi\) | |||||||
\(812\) | −62.7278 | − | 8539.49i | −0.00271098 | − | 0.369061i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 125.588 | − | 217.525i | 0.00540768 | − | 0.00936638i | ||||
\(815\) | −18.4105 | − | 31.8880i | −0.000791280 | − | 0.00137054i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7350.71 | − | 12731.8i | 0.314772 | − | 0.545201i | ||||
\(818\) | −47276.8 | −2.02078 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5480.00 | −0.233378 | ||||||||
\(821\) | 1971.47 | − | 3414.68i | 0.0838059 | − | 0.145156i | −0.821076 | − | 0.570819i | \(-0.806626\pi\) |
0.904882 | + | 0.425663i | \(0.139959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9251.41 | − | 16023.9i | −0.391839 | − | 0.678686i | 0.600853 | − | 0.799360i | \(-0.294828\pi\) |
−0.992692 | + | 0.120674i | \(0.961494\pi\) | |||||||
\(824\) | 5413.13 | − | 9375.81i | 0.228853 | − | 0.396386i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −56606.8 | − | 32129.9i | −2.38451 | − | 1.35344i | ||||
\(827\) | 11965.2 | 0.503110 | 0.251555 | − | 0.967843i | \(-0.419058\pi\) | ||||
0.251555 | + | 0.967843i | \(0.419058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17981.5 | + | 31144.8i | 0.753344 | + | 1.30483i | 0.946193 | + | 0.323602i | \(0.104894\pi\) |
−0.192849 | + | 0.981228i | \(0.561773\pi\) | |||||||
\(830\) | 10438.8 | + | 18080.6i | 0.436551 | + | 0.756128i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26311.6 | 1.09638 | ||||||||
\(833\) | 19112.8 | − | 34257.0i | 0.794983 | − | 1.42489i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7303.50 | + | 12650.0i | −0.302692 | + | 0.524279i | ||||
\(836\) | −35.2862 | − | 61.1174i | −0.00145981 | − | 0.00252846i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19016.4 | − | 32937.3i | 0.783902 | − | 1.35776i | ||||
\(839\) | 20174.0 | 0.830137 | 0.415069 | − | 0.909790i | \(-0.363758\pi\) | ||||
0.415069 | + | 0.909790i | \(0.363758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22777.2 | −0.933913 | ||||||||
\(842\) | −14764.9 | + | 25573.6i | −0.604315 | + | 1.04670i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6955.71 | − | 12047.6i | −0.283679 | − | 0.491347i | ||||
\(845\) | −2909.71 | + | 5039.76i | −0.118458 | + | 0.205175i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21256.5 | − | 12481.5i | 0.862316 | − | 0.506340i | ||||
\(848\) | −16223.7 | −0.656987 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6310.53 | − | 10930.2i | −0.254647 | − | 0.441061i | ||||
\(851\) | −30918.3 | − | 53552.1i | −1.24544 | − | 2.15716i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25297.5 | 1.01544 | 0.507719 | − | 0.861523i | \(-0.330489\pi\) | ||||
0.507719 | + | 0.861523i | \(0.330489\pi\) | |||||||
\(854\) | 454.643 | + | 61893.2i | 0.0182173 | + | 2.48003i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7346.21 | − | 12724.0i | 0.293327 | − | 0.508058i | ||||
\(857\) | 19634.5 | + | 34008.0i | 0.782617 | + | 1.35553i | 0.930412 | + | 0.366514i | \(0.119449\pi\) |
−0.147795 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7249.55 | − | 12556.6i | 0.287953 | − | 0.498749i | −0.685368 | − | 0.728197i | \(-0.740359\pi\) |
0.973321 | + | 0.229448i | \(0.0736921\pi\) | |||||||
\(860\) | 19529.1 | 0.774343 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27238.5 | −1.07627 | ||||||||
\(863\) | −12205.6 | + | 21140.8i | −0.481442 | + | 0.833882i | −0.999773 | − | 0.0212980i | \(-0.993220\pi\) |
0.518331 | + | 0.855180i | \(0.326553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9923.92 | + | 17188.7i | 0.390085 | + | 0.675647i | ||||
\(866\) | −30901.9 | + | 53523.6i | −1.21257 | + | 2.10024i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13834.3 | + | 8123.29i | −0.540974 | + | 0.317653i | ||||
\(869\) | −45.1079 | −0.00176085 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11901.9 | − | 20614.7i | −0.463010 | − | 0.801956i | ||||
\(872\) | −2222.54 | − | 3849.55i | −0.0863126 | − | 0.149498i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −29475.9 | −1.14078 | ||||||||
\(875\) | −2013.33 | − | 1142.76i | −0.0777861 | − | 0.0441512i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2528.32 | − | 4379.18i | 0.0973494 | − | 0.168614i | −0.813237 | − | 0.581932i | \(-0.802297\pi\) |
0.910587 | + | 0.413318i | \(0.135630\pi\) | |||||||
\(878\) | −26942.1 | − | 46665.1i | −1.03559 | − | 1.79370i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.51768 | + | 14.7530i | −0.000326285 | + | 0.000565142i | ||||
\(881\) | −13233.9 | −0.506086 | −0.253043 | − | 0.967455i | \(-0.581431\pi\) | ||||
−0.253043 | + | 0.967455i | \(0.581431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13824.2 | −0.526866 | −0.263433 | − | 0.964678i | \(-0.584855\pi\) | ||||
−0.263433 | + | 0.964678i | \(0.584855\pi\) | |||||||
\(884\) | 21110.0 | − | 36563.7i | 0.803176 | − | 1.39114i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2709.81 | + | 4693.52i | 0.102751 | + | 0.177971i | ||||
\(887\) | −18909.7 | + | 32752.5i | −0.715811 | + | 1.23982i | 0.246835 | + | 0.969057i | \(0.420609\pi\) |
−0.962646 | + | 0.270763i | \(0.912724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31369.6 | − | 17805.3i | −1.18347 | − | 0.671734i | ||||
\(890\) | 17286.2 | 0.651049 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23918.0 | − | 41427.2i | −0.897796 | − | 1.55503i | ||||
\(893\) | −161.905 | − | 280.428i | −0.00606713 | − | 0.0105086i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5529.76 | −0.206524 | ||||||||
\(896\) | 28465.4 | − | 16714.5i | 1.06134 | − | 0.623206i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2541.92 | + | 4402.74i | −0.0944600 | + | 0.163609i | ||||
\(899\) | −1513.98 | − | 2622.29i | −0.0561668 | − | 0.0972838i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38703.0 | + | 67035.6i | −1.43106 | + | 2.47867i | ||||
\(902\) | 59.8721 | 0.00221012 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19250.0 | −0.708237 | ||||||||
\(905\) | −293.034 | + | 507.550i | −0.0107633 | + | 0.0186426i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −526.377 | − | 911.711i | −0.0192702 | − | 0.0333769i | 0.856230 | − | 0.516596i | \(-0.172801\pi\) |
−0.875500 | + | 0.483219i | \(0.839468\pi\) | |||||||
\(908\) | 13531.1 | − | 23436.5i | 0.494542 | − | 0.856571i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −96.5076 | − | 13138.1i | −0.00351560 | − | 0.478598i | ||||
\(911\) | −7854.40 | −0.285651 | −0.142825 | − | 0.989748i | \(-0.545619\pi\) | ||||
−0.142825 | + | 0.989748i | \(0.545619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67.2251 | − | 116.437i | −0.00243683 | − | 0.00422071i | ||||
\(914\) | −41303.4 | − | 71539.6i | −1.49474 | − | 2.58897i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 49905.4 | 1.80013 | ||||||||
\(917\) | 16955.1 | − | 9955.78i | 0.610584 | − | 0.358527i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2467.92 | + | 4274.57i | −0.0885846 | + | 0.153433i | −0.906913 | − | 0.421318i | \(-0.861568\pi\) |
0.818328 | + | 0.574751i | \(0.194901\pi\) | |||||||
\(920\) | −5940.95 | − | 10290.0i | −0.212899 | − | 0.368752i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6962.47 | + | 12059.4i | −0.248695 | + | 0.430752i | ||||
\(923\) | 1190.07 | 0.0424395 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10008.3 | −0.355753 | ||||||||
\(926\) | −8941.22 | + | 15486.7i | −0.317308 | + | 0.549593i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4594.63 | + | 7958.14i | 0.162528 | + | 0.281507i | ||||
\(929\) | −7852.51 | + | 13600.9i | −0.277322 | + | 0.480336i | −0.970718 | − | 0.240220i | \(-0.922780\pi\) |
0.693396 | + | 0.720557i | \(0.256114\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14826.4 | + | 217.830i | −0.521930 | + | 0.00766821i | ||||
\(932\) | −28233.7 | −0.992302 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36067.7 | + | 62471.0i | 1.26356 | + | 2.18856i | ||||
\(935\) | 40.6393 | + | 70.3892i | 0.00142144 | + | 0.00246200i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43806.5 | −1.52732 | −0.763658 | − | 0.645621i | \(-0.776599\pi\) | ||||
−0.763658 | + | 0.645621i | \(0.776599\pi\) | |||||||
\(938\) | −52653.8 | − | 29886.2i | −1.83284 | − | 1.04032i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 215.071 | − | 372.515i | 0.00746261 | − | 0.0129256i | ||||
\(941\) | 2031.21 | + | 3518.16i | 0.0703672 | + | 0.121880i | 0.899062 | − | 0.437821i | \(-0.144250\pi\) |
−0.828695 | + | 0.559700i | \(0.810916\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7369.92 | − | 12765.1i | 0.254504 | − | 0.440815i | ||||
\(944\) | 19084.9 | 0.658009 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −213.366 | −0.00733313 | ||||||||
\(947\) | −2430.06 | + | 4208.99i | −0.0833859 | + | 0.144429i | −0.904702 | − | 0.426044i | \(-0.859907\pi\) |
0.821316 | + | 0.570473i | \(0.193240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1299.78 | + | 2251.29i | 0.0444602 | + | 0.0770073i | ||||
\(950\) | −2385.36 | + | 4131.56i | −0.0814644 | + | 0.141100i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −239.363 | − | 32585.9i | −0.00814895 | − | 1.10936i | ||||
\(953\) | 18999.6 | 0.645811 | 0.322906 | − | 0.946431i | \(-0.395340\pi\) | ||||
0.322906 | + | 0.946431i | \(0.395340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2506.50 | − | 4341.38i | −0.0849303 | − | 0.147104i | ||||
\(956\) | 1850.88 | + | 3205.82i | 0.0626168 | + | 0.108456i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11174.4 | −0.376855 | ||||||||
\(959\) | −195.807 | − | 26656.3i | −0.00659325 | − | 0.897577i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12051.3 | − | 20873.5i | 0.404529 | − | 0.700664i | ||||
\(962\) | −28400.1 | − | 49190.4i | −0.951825 | − | 1.64861i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28777.7 | − | 49844.5i | 0.961482 | − | 1.66534i | ||||
\(965\) | −16288.8 | −0.543373 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32695.1 | −1.08728 | −0.543641 | − | 0.839318i | \(-0.682955\pi\) | ||||
−0.543641 | + | 0.839318i | \(0.682955\pi\) | |||||||
\(968\) | 10238.4 | − | 17733.5i | 0.339954 | − | 0.588817i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4338.14 | + | 7513.88i | 0.143597 | + | 0.248718i | ||||
\(971\) | −3094.85 | + | 5360.43i | −0.102285 | + | 0.177162i | −0.912626 | − | 0.408797i | \(-0.865949\pi\) |
0.810341 | + | 0.585959i | \(0.199282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10664.7 | + | 6053.26i | 0.351382 | + | 0.199443i | ||||
\(974\) | −37265.6 | −1.22594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9074.08 | − | 15716.8i | −0.297596 | − | 0.515452i | ||||
\(977\) | 1071.22 | + | 1855.41i | 0.0350782 | + | 0.0607572i | 0.883032 | − | 0.469314i | \(-0.155499\pi\) |
−0.847953 | + | 0.530071i | \(0.822165\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −111.321 | −0.00363416 | ||||||||
\(980\) | −10098.2 | − | 16911.8i | −0.329157 | − | 0.551253i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33600.8 | + | 58198.4i | −1.09190 | + | 1.89123i | ||||
\(983\) | 8404.11 | + | 14556.4i | 0.272685 | + | 0.472305i | 0.969549 | − | 0.244899i | \(-0.0787549\pi\) |
−0.696863 | + | 0.717204i | \(0.745422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 104.239 | − | 180.547i | 0.00337190 | − | 0.00584031i | ||||
\(986\) | 20268.0 | 0.654630 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15959.0 | −0.513891 | ||||||||
\(989\) | −26264.2 | + | 45490.9i | −0.844442 | + | 1.46262i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10625.4 | − | 18403.7i | −0.340593 | − | 0.589924i | 0.643950 | − | 0.765067i | \(-0.277294\pi\) |
−0.984543 | + | 0.175144i | \(0.943961\pi\) | |||||||
\(992\) | 8631.57 | − | 14950.3i | 0.276263 | − | 0.478501i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2610.19 | − | 1532.67i | 0.0832898 | − | 0.0489066i | ||||
\(995\) | −12028.1 | −0.383231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18820.0 | + | 32597.1i | 0.597828 | + | 1.03547i | 0.993141 | + | 0.116922i | \(0.0373028\pi\) |
−0.395313 | + | 0.918546i | \(0.629364\pi\) | |||||||
\(998\) | 36688.0 | + | 63545.4i | 1.16366 | + | 2.01553i | ||||
\(999\) | 0 | 0 |
(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 | 315.4.j.c.226.1 | 4 | ||
3.2 | odd | 2 | 35.4.e.b.16.2 | yes | 4 | ||
7.2 | even | 3 | 2205.4.a.bf.1.2 | 2 | |||
7.4 | even | 3 | inner | 315.4.j.c.46.1 | 4 | ||
7.5 | odd | 6 | 2205.4.a.bg.1.2 | 2 | |||
12.11 | even | 2 | 560.4.q.i.401.2 | 4 | |||
15.2 | even | 4 | 175.4.k.c.149.4 | 8 | |||
15.8 | even | 4 | 175.4.k.c.149.1 | 8 | |||
15.14 | odd | 2 | 175.4.e.c.51.1 | 4 | |||
21.2 | odd | 6 | 245.4.a.g.1.1 | 2 | |||
21.5 | even | 6 | 245.4.a.h.1.1 | 2 | |||
21.11 | odd | 6 | 35.4.e.b.11.2 | ✓ | 4 | ||
21.17 | even | 6 | 245.4.e.l.116.2 | 4 | |||
21.20 | even | 2 | 245.4.e.l.226.2 | 4 | |||
84.11 | even | 6 | 560.4.q.i.81.2 | 4 | |||
105.32 | even | 12 | 175.4.k.c.74.1 | 8 | |||
105.44 | odd | 6 | 1225.4.a.x.1.2 | 2 | |||
105.53 | even | 12 | 175.4.k.c.74.4 | 8 | |||
105.74 | odd | 6 | 175.4.e.c.151.1 | 4 | |||
105.89 | even | 6 | 1225.4.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.b.11.2 | ✓ | 4 | 21.11 | odd | 6 | ||
35.4.e.b.16.2 | yes | 4 | 3.2 | odd | 2 | ||
175.4.e.c.51.1 | 4 | 15.14 | odd | 2 | |||
175.4.e.c.151.1 | 4 | 105.74 | odd | 6 | |||
175.4.k.c.74.1 | 8 | 105.32 | even | 12 | |||
175.4.k.c.74.4 | 8 | 105.53 | even | 12 | |||
175.4.k.c.149.1 | 8 | 15.8 | even | 4 | |||
175.4.k.c.149.4 | 8 | 15.2 | even | 4 | |||
245.4.a.g.1.1 | 2 | 21.2 | odd | 6 | |||
245.4.a.h.1.1 | 2 | 21.5 | even | 6 | |||
245.4.e.l.116.2 | 4 | 21.17 | even | 6 | |||
245.4.e.l.226.2 | 4 | 21.20 | even | 2 | |||
315.4.j.c.46.1 | 4 | 7.4 | even | 3 | inner | ||
315.4.j.c.226.1 | 4 | 1.1 | even | 1 | trivial | ||
560.4.q.i.81.2 | 4 | 84.11 | even | 6 | |||
560.4.q.i.401.2 | 4 | 12.11 | even | 2 | |||
1225.4.a.v.1.2 | 2 | 105.89 | even | 6 | |||
1225.4.a.x.1.2 | 2 | 105.44 | odd | 6 | |||
2205.4.a.bf.1.2 | 2 | 7.2 | even | 3 | |||
2205.4.a.bg.1.2 | 2 | 7.5 | odd | 6 |