Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not 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: | \(14.4554679514\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.4.e.l.116.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | \(-0.548384\pi\) |
0.931749 | − | 0.363102i | \(-0.118282\pi\) | |||||||
\(3\) | 1.62132 | + | 2.80821i | 0.312023 | + | 0.540440i | 0.978800 | − | 0.204817i | \(-0.0656600\pi\) |
−0.666777 | + | 0.745257i | \(0.732327\pi\) | |||||||
\(4\) | −5.74264 | − | 9.94655i | −0.717830 | − | 1.24332i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 14.3137 | 0.973925 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −15.3848 | −0.679917 | ||||||||
\(9\) | 8.24264 | − | 14.2767i | 0.305283 | − | 0.528766i | ||||
\(10\) | −11.0355 | − | 19.1141i | −0.348974 | − | 0.604441i | ||||
\(11\) | 0.0710678 | + | 0.123093i | 0.00194798 | + | 0.00337400i | 0.866998 | − | 0.498312i | \(-0.166047\pi\) |
−0.865050 | + | 0.501686i | \(0.832713\pi\) | |||||||
\(12\) | 18.6213 | − | 32.2531i | 0.447959 | − | 0.775888i | ||||
\(13\) | 32.1421 | 0.685740 | 0.342870 | − | 0.939383i | \(-0.388601\pi\) | ||||
0.342870 | + | 0.939383i | \(0.388601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.2132 | 0.279082 | ||||||||
\(16\) | 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 | \(-0.470386\pi\) | |||||||
\(18\) | −36.3848 | − | 63.0203i | −0.476443 | − | 0.825223i | ||||
\(19\) | 21.6152 | − | 37.4387i | 0.260993 | − | 0.452054i | −0.705513 | − | 0.708697i | \(-0.749283\pi\) |
0.966506 | + | 0.256643i | \(0.0826166\pi\) | |||||||
\(20\) | −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 | \(0.413559\pi\) |
−0.968407 | + | 0.249375i | \(0.919775\pi\) | |||||||
\(24\) | −24.9437 | − | 43.2037i | −0.212150 | − | 0.367455i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 70.9411 | − | 122.874i | 0.535104 | − | 0.926827i | ||||
\(27\) | 141.007 | 1.00507 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −40.1472 | −0.257074 | −0.128537 | − | 0.991705i | \(-0.541028\pi\) | ||||
−0.128537 | + | 0.991705i | \(0.541028\pi\) | |||||||
\(30\) | 35.7843 | − | 61.9802i | 0.217776 | − | 0.377199i | ||||
\(31\) | 37.7107 | + | 65.3168i | 0.218485 | + | 0.378427i | 0.954345 | − | 0.298707i | \(-0.0965552\pi\) |
−0.735860 | + | 0.677134i | \(0.763222\pi\) | |||||||
\(32\) | −114.445 | − | 198.224i | −0.632224 | − | 1.09504i | ||||
\(33\) | −0.230447 | + | 0.399147i | −0.00121563 | + | 0.00210553i | ||||
\(34\) | −504.843 | −2.54647 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −189.338 | −0.876565 | ||||||||
\(37\) | 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 | ||||
\(39\) | 52.1127 | + | 90.2618i | 0.213967 | + | 0.370602i | ||||
\(40\) | −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 | ||||
\(45\) | −41.2132 | − | 71.3834i | −0.136527 | − | 0.236471i | ||||
\(46\) | 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 | \(0.170367\pi\) | |||||||
\(48\) | 77.7279 | 0.233730 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −110.355 | −0.312132 | ||||||||
\(51\) | 185.426 | − | 321.168i | 0.509115 | − | 0.881814i | ||||
\(52\) | −184.581 | − | 319.703i | −0.492245 | − | 0.852593i | ||||
\(53\) | 338.409 | + | 586.142i | 0.877058 | + | 1.51911i | 0.854554 | + | 0.519362i | \(0.173830\pi\) |
0.0225038 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(54\) | 311.218 | − | 539.045i | 0.784285 | − | 1.35842i | ||||
\(55\) | 0.710678 | 0.00174232 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 140.181 | 0.325744 | ||||||||
\(58\) | −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 | \(0.491929\pi\) | |||||||
\(60\) | −93.1066 | − | 161.265i | −0.200334 | − | 0.346988i | ||||
\(61\) | −378.551 | + | 655.669i | −0.794565 | + | 1.37623i | 0.128550 | + | 0.991703i | \(0.458968\pi\) |
−0.923115 | + | 0.384524i | \(0.874366\pi\) | |||||||
\(62\) | 332.926 | 0.681962 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −818.602 | −1.59883 | ||||||||
\(65\) | 80.3553 | − | 139.180i | 0.153336 | − | 0.265586i | ||||
\(66\) | 1.01724 | + | 1.76192i | 0.00189718 | + | 0.00328602i | ||||
\(67\) | 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 | ||||
\(69\) | −500.868 | −0.873876 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37.0253 | 0.0618886 | 0.0309443 | − | 0.999521i | \(-0.490149\pi\) | ||||
0.0309443 | + | 0.999521i | \(0.490149\pi\) | |||||||
\(72\) | −126.811 | + | 219.643i | −0.207567 | + | 0.359517i | ||||
\(73\) | 40.4386 | + | 70.0417i | 0.0648353 | + | 0.112298i | 0.896621 | − | 0.442799i | \(-0.146014\pi\) |
−0.831786 | + | 0.555097i | \(0.812681\pi\) | |||||||
\(74\) | −883.578 | − | 1530.40i | −1.38802 | − | 2.40413i | ||||
\(75\) | 40.5330 | − | 70.2052i | 0.0624046 | − | 0.108088i | ||||
\(76\) | −496.514 | −0.749395 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 460.073 | 0.667859 | ||||||||
\(79\) | 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 | ||||
\(81\) | 6.06645 | + | 10.5074i | 0.00832161 | + | 0.0144134i | ||||
\(82\) | 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 | ||||
\(87\) | −65.0914 | − | 112.742i | −0.0802131 | − | 0.138933i | ||||
\(88\) | −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 | \(0.0122166\pi\) | |||||||
\(90\) | −363.848 | −0.426144 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1774.05 | 2.01041 | ||||||||
\(93\) | −122.282 | + | 211.799i | −0.136345 | + | 0.236156i | ||||
\(94\) | 16.5320 | + | 28.6342i | 0.0181398 | + | 0.0314191i | ||||
\(95\) | −108.076 | − | 187.193i | −0.116720 | − | 0.202165i | ||||
\(96\) | 371.103 | − | 642.769i | 0.394537 | − | 0.683358i | ||||
\(97\) | −393.107 | −0.411484 | −0.205742 | − | 0.978606i | \(-0.565961\pi\) | ||||
−0.205742 | + | 0.978606i | \(0.565961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.34315 | 0.00237874 | ||||||||
\(100\) | −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 | \(0.761469\pi\) | |||||||
\(102\) | −818.512 | − | 1417.70i | −0.794556 | − | 1.37621i | ||||
\(103\) | −351.850 | + | 609.422i | −0.336590 | + | 0.582991i | −0.983789 | − | 0.179330i | \(-0.942607\pi\) |
0.647199 | + | 0.762321i | \(0.275940\pi\) | |||||||
\(104\) | −494.500 | −0.466247 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2987.62 | 2.73758 | ||||||||
\(107\) | −477.499 | + | 827.052i | −0.431416 | + | 0.747235i | −0.996996 | − | 0.0774592i | \(-0.975319\pi\) |
0.565579 | + | 0.824694i | \(0.308653\pi\) | |||||||
\(108\) | −809.753 | − | 1402.53i | −0.721468 | − | 1.24962i | ||||
\(109\) | −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 | ||||
\(111\) | 1298.14 | 1.11003 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1251.24 | 1.04165 | 0.520826 | − | 0.853663i | \(-0.325624\pi\) | ||||
0.520826 | + | 0.853663i | \(0.325624\pi\) | |||||||
\(114\) | 309.394 | − | 535.886i | 0.254188 | − | 0.440266i | ||||
\(115\) | 386.157 | + | 668.844i | 0.313125 | + | 0.542348i | ||||
\(116\) | 230.551 | + | 399.326i | 0.184535 | + | 0.319625i | ||||
\(117\) | 264.936 | − | 458.883i | 0.209345 | − | 0.362596i | ||||
\(118\) | 3514.51 | 2.74184 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −249.437 | −0.189753 | ||||||||
\(121\) | 665.490 | − | 1152.66i | 0.499992 | − | 0.866012i | ||||
\(122\) | 1671.00 | + | 2894.26i | 1.24005 | + | 2.14782i | ||||
\(123\) | 154.717 | + | 267.977i | 0.113417 | + | 0.196445i | ||||
\(124\) | 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 | ||||
\(129\) | −551.364 | − | 954.991i | −0.376317 | − | 0.651800i | ||||
\(130\) | −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 | \(0.0514771\pi\) | |||||||
\(132\) | 5.29351 | 0.00349046 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3269.08 | 2.10750 | ||||||||
\(135\) | 352.518 | − | 610.579i | 0.224740 | − | 0.389261i | ||||
\(136\) | 879.759 | + | 1523.79i | 0.554697 | + | 0.960763i | ||||
\(137\) | 719.671 | + | 1246.51i | 0.448800 | + | 0.777345i | 0.998308 | − | 0.0581435i | \(-0.0185181\pi\) |
−0.549508 | + | 0.835489i | \(0.685185\pi\) | |||||||
\(138\) | −1105.47 | + | 1914.73i | −0.681911 | + | 1.18111i | ||||
\(139\) | −662.132 | −0.404038 | −0.202019 | − | 0.979382i | \(-0.564750\pi\) | ||||
−0.202019 | + | 0.979382i | \(0.564750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.2885 | −0.0145068 | ||||||||
\(142\) | 81.7187 | − | 141.541i | 0.0482935 | − | 0.0836468i | ||||
\(143\) | 2.28427 | + | 3.95647i | 0.00133581 | + | 0.00231369i | ||||
\(144\) | −197.581 | − | 342.220i | −0.114341 | − | 0.198044i | ||||
\(145\) | −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 | −0.737315 | − | 0.675549i | \(-0.763907\pi\) |
0.953700 | + | 0.300760i | \(0.0972402\pi\) | |||||||
\(150\) | −178.921 | − | 309.901i | −0.0973925 | − | 0.168689i | ||||
\(151\) | 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 | ||||
\(153\) | −1885.38 | −0.996235 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 377.107 | 0.195419 | ||||||||
\(156\) | 598.529 | − | 1036.68i | 0.307184 | − | 0.532058i | ||||
\(157\) | 477.461 | + | 826.987i | 0.242710 | + | 0.420387i | 0.961485 | − | 0.274856i | \(-0.0886302\pi\) |
−0.718775 | + | 0.695243i | \(0.755297\pi\) | |||||||
\(158\) | −700.444 | − | 1213.20i | −0.352685 | − | 0.610869i | ||||
\(159\) | −1097.34 | + | 1900.65i | −0.547325 | + | 0.947995i | ||||
\(160\) | −1144.45 | −0.565478 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 53.5572 | 0.0259744 | ||||||||
\(163\) | 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 | ||||
\(165\) | 1.15224 | + | 1.99573i | 0.000543646 | + | 0.000941622i | ||||
\(166\) | 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 | ||||
\(171\) | −356.333 | − | 617.187i | −0.159354 | − | 0.276009i | ||||
\(172\) | 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 | \(0.829323\pi\) | |||||||
\(174\) | −574.655 | −0.250371 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.40707 | 0.00145919 | ||||||||
\(177\) | −1290.86 | + | 2235.84i | −0.548177 | + | 0.949470i | ||||
\(178\) | −1728.62 | − | 2994.05i | −0.727895 | − | 1.26075i | ||||
\(179\) | 552.976 | + | 957.782i | 0.230901 | + | 0.399933i | 0.958074 | − | 0.286522i | \(-0.0924992\pi\) |
−0.727172 | + | 0.686455i | \(0.759166\pi\) | |||||||
\(180\) | −473.345 | + | 819.858i | −0.196006 | + | 0.339492i | ||||
\(181\) | 117.214 | 0.0481349 | 0.0240674 | − | 0.999710i | \(-0.492338\pi\) | ||||
0.0240674 | + | 0.999710i | \(0.492338\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2455.01 | −0.991691 | ||||||||
\(184\) | 1188.19 | − | 2058.00i | 0.476057 | − | 0.824555i | ||||
\(185\) | −1000.83 | − | 1733.49i | −0.397744 | − | 0.688913i | ||||
\(186\) | 539.780 | + | 934.926i | 0.212788 | + | 0.368560i | ||||
\(187\) | 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 | −0.945220 | − | 0.326434i | \(-0.894153\pi\) |
0.755310 | + | 0.655368i | \(0.227486\pi\) | |||||||
\(192\) | −1327.22 | − | 2298.81i | −0.498873 | − | 0.864073i | ||||
\(193\) | −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 | ||||
\(195\) | 521.127 | 0.191378 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −41.6955 | −0.0150796 | −0.00753981 | − | 0.999972i | \(-0.502400\pi\) | ||||
−0.00753981 | + | 0.999972i | \(0.502400\pi\) | |||||||
\(198\) | 5.17157 | − | 8.95743i | 0.00185620 | − | 0.00321503i | ||||
\(199\) | 1202.81 | + | 2083.32i | 0.428466 | + | 0.742125i | 0.996737 | − | 0.0807167i | \(-0.0257209\pi\) |
−0.568271 | + | 0.822841i | \(0.692388\pi\) | |||||||
\(200\) | 192.310 | + | 333.090i | 0.0679917 | + | 0.117765i | ||||
\(201\) | −1200.72 | + | 2079.71i | −0.421354 | + | 0.729807i | ||||
\(202\) | 2006.00 | 0.698722 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4259.35 | −1.46183 | ||||||||
\(205\) | 238.566 | − | 413.208i | 0.0812789 | − | 0.140779i | ||||
\(206\) | 1553.14 | + | 2690.12i | 0.525303 | + | 0.909851i | ||||
\(207\) | 1273.18 | + | 2205.22i | 0.427499 | + | 0.740450i | ||||
\(208\) | 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 | ||||
\(213\) | 60.0298 | + | 103.975i | 0.0193107 | + | 0.0334471i | ||||
\(214\) | 2107.78 | + | 3650.78i | 0.673294 | + | 1.16618i | ||||
\(215\) | −850.178 | + | 1472.55i | −0.269682 | + | 0.467103i | ||||
\(216\) | −2169.36 | −0.683363 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1275.38 | −0.396238 | ||||||||
\(219\) | −131.128 | + | 227.120i | −0.0404603 | + | 0.0700792i | ||||
\(220\) | −4.08117 | − | 7.06879i | −0.00125069 | − | 0.00216626i | ||||
\(221\) | −1838.01 | − | 3183.52i | −0.559447 | − | 0.968991i | ||||
\(222\) | 2865.13 | − | 4962.54i | 0.866192 | − | 1.50029i | ||||
\(223\) | −4164.99 | −1.25071 | −0.625354 | − | 0.780341i | \(-0.715046\pi\) | ||||
−0.625354 | + | 0.780341i | \(0.715046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −412.132 | −0.122113 | ||||||||
\(226\) | 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 | \(0.721392\pi\) | |||||||
\(228\) | −805.008 | − | 1394.31i | −0.233829 | − | 0.405003i | ||||
\(229\) | 2172.58 | − | 3763.02i | 0.626935 | − | 1.08588i | −0.361228 | − | 0.932477i | \(-0.617642\pi\) |
0.988163 | − | 0.153406i | \(-0.0490242\pi\) | |||||||
\(230\) | 3409.16 | 0.977363 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 617.655 | 0.174789 | ||||||||
\(233\) | −1229.12 | + | 2128.91i | −0.345591 | + | 0.598581i | −0.985461 | − | 0.169902i | \(-0.945655\pi\) |
0.639870 | + | 0.768483i | \(0.278988\pi\) | |||||||
\(234\) | −1169.48 | − | 2025.61i | −0.326716 | − | 0.565889i | ||||
\(235\) | 18.7258 | + | 32.4341i | 0.00519804 | + | 0.00900326i | ||||
\(236\) | 4572.18 | − | 7919.25i | 1.26112 | − | 2.18432i | ||||
\(237\) | 1029.08 | 0.282050 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 322.304 | 0.0872307 | 0.0436154 | − | 0.999048i | \(-0.486112\pi\) | ||||
0.0436154 | + | 0.999048i | \(0.486112\pi\) | |||||||
\(240\) | 194.320 | − | 336.572i | 0.0522637 | − | 0.0905234i | ||||
\(241\) | −2505.62 | − | 4339.86i | −0.669714 | − | 1.15998i | −0.977984 | − | 0.208680i | \(-0.933083\pi\) |
0.308270 | − | 0.951299i | \(-0.400250\pi\) | |||||||
\(242\) | −2937.61 | − | 5088.10i | −0.780318 | − | 1.35155i | ||||
\(243\) | 1883.93 | − | 3263.05i | 0.497341 | − | 0.861420i | ||||
\(244\) | 8695.53 | 2.28145 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1365.91 | 0.354012 | ||||||||
\(247\) | 694.759 | − | 1203.36i | 0.178974 | − | 0.309991i | ||||
\(248\) | −580.170 | − | 1004.88i | −0.148552 | − | 0.257299i | ||||
\(249\) | 1533.65 | + | 2656.37i | 0.390327 | + | 0.676066i | ||||
\(250\) | −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 | ||||
\(255\) | −927.132 | − | 1605.84i | −0.227683 | − | 0.394359i | ||||
\(256\) | 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 | \(0.311711\pi\) | |||||||
\(258\) | −4867.68 | −1.17461 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1845.81 | −0.440277 | ||||||||
\(261\) | −330.919 | + | 573.168i | −0.0784803 | + | 0.135932i | ||||
\(262\) | −2343.16 | − | 4058.48i | −0.552523 | − | 0.956999i | ||||
\(263\) | 393.278 | + | 681.177i | 0.0922074 | + | 0.159708i | 0.908440 | − | 0.418016i | \(-0.137274\pi\) |
−0.816232 | + | 0.577724i | \(0.803941\pi\) | |||||||
\(264\) | 3.54538 | − | 6.14078i | 0.000826527 | − | 0.00143159i | ||||
\(265\) | 3384.09 | 0.784465 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2539.65 | 0.582113 | ||||||||
\(268\) | 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 | \(0.681225\pi\) | |||||||
\(270\) | −1556.09 | − | 2695.23i | −0.350743 | − | 0.607504i | ||||
\(271\) | 1449.71 | − | 2510.97i | 0.324958 | − | 0.562844i | −0.656546 | − | 0.754286i | \(-0.727983\pi\) |
0.981504 | + | 0.191442i | \(0.0613165\pi\) | |||||||
\(272\) | −2741.45 | −0.611122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6353.56 | 1.40085 | ||||||||
\(275\) | 1.77670 | − | 3.07733i | 0.000389595 | − | 0.000674799i | ||||
\(276\) | 2876.30 | + | 4981.91i | 0.627294 | + | 1.08651i | ||||
\(277\) | −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 | ||||
\(279\) | 1243.34 | 0.266799 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2359.40 | 0.500890 | 0.250445 | − | 0.968131i | \(-0.419423\pi\) | ||||
0.250445 | + | 0.968131i | \(0.419423\pi\) | |||||||
\(282\) | −53.6072 | + | 92.8504i | −0.0113201 | + | 0.0196070i | ||||
\(283\) | −1440.67 | − | 2495.32i | −0.302612 | − | 0.524139i | 0.674115 | − | 0.738626i | \(-0.264525\pi\) |
−0.976727 | + | 0.214487i | \(0.931192\pi\) | |||||||
\(284\) | −212.623 | − | 368.273i | −0.0444255 | − | 0.0769472i | ||||
\(285\) | 350.452 | − | 607.001i | 0.0728385 | − | 0.126160i | ||||
\(286\) | 20.1665 | 0.00416948 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3773.31 | −0.772028 | ||||||||
\(289\) | −4083.47 | + | 7072.77i | −0.831155 | + | 1.43960i | ||||
\(290\) | 443.046 | + | 767.378i | 0.0897122 | + | 0.155386i | ||||
\(291\) | −637.352 | − | 1103.93i | −0.128393 | − | 0.222382i | ||||
\(292\) | 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 | ||||
\(297\) | 10.0211 | + | 17.3570i | 0.00195785 | + | 0.00339110i | ||||
\(298\) | −1737.24 | − | 3008.98i | −0.337703 | − | 0.584918i | ||||
\(299\) | −2482.39 | + | 4299.62i | −0.480134 | + | 0.831616i | ||||
\(300\) | −931.066 | −0.179184 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3744.82 | 0.713544 | ||||||||
\(303\) | −736.795 | + | 1276.17i | −0.139696 | + | 0.241960i | ||||
\(304\) | −518.129 | − | 897.426i | −0.0977524 | − | 0.169312i | ||||
\(305\) | 1892.75 | + | 3278.35i | 0.355340 | + | 0.615467i | ||||
\(306\) | −4161.24 | + | 7207.47i | −0.777392 | + | 1.34648i | ||||
\(307\) | 4968.57 | 0.923685 | 0.461842 | − | 0.886962i | \(-0.347189\pi\) | ||||
0.461842 | + | 0.886962i | \(0.347189\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2281.84 | −0.420096 | ||||||||
\(310\) | 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 | \(0.985098\pi\) | |||||||
\(312\) | −801.742 | − | 1388.66i | −0.145480 | − | 0.251978i | ||||
\(313\) | 1799.60 | − | 3117.00i | 0.324983 | − | 0.562886i | −0.656526 | − | 0.754303i | \(-0.727975\pi\) |
0.981509 | + | 0.191417i | \(0.0613082\pi\) | |||||||
\(314\) | 4215.23 | 0.757577 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3644.95 | −0.648875 | ||||||||
\(317\) | −1770.78 | + | 3067.08i | −0.313744 | + | 0.543420i | −0.979170 | − | 0.203044i | \(-0.934917\pi\) |
0.665426 | + | 0.746464i | \(0.268250\pi\) | |||||||
\(318\) | 4843.89 | + | 8389.86i | 0.854188 | + | 1.47950i | ||||
\(319\) | −2.85317 | − | 4.94184i | −0.000500774 | − | 0.000867367i | ||||
\(320\) | −2046.51 | + | 3544.65i | −0.357510 | + | 0.619225i | ||||
\(321\) | −3096.71 | −0.538447 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4944.16 | −0.851704 | ||||||||
\(324\) | 69.6749 | − | 120.680i | 0.0119470 | − | 0.0206928i | ||||
\(325\) | −401.777 | − | 695.898i | −0.0685740 | − | 0.118774i | ||||
\(326\) | −16.2536 | − | 28.1521i | −0.00276136 | − | 0.00478282i | ||||
\(327\) | 468.443 | − | 811.367i | 0.0792200 | − | 0.137213i | ||||
\(328\) | −1468.11 | −0.247143 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.1724 | 0.00169689 | ||||||||
\(331\) | 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 | ||||
\(333\) | −3299.80 | − | 5715.42i | −0.543027 | − | 0.940550i | ||||
\(334\) | −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 | ||||
\(339\) | 2028.66 | + | 3513.74i | 0.325020 | + | 0.562950i | ||||
\(340\) | 3283.86 | + | 5687.81i | 0.523801 | + | 0.907249i | ||||
\(341\) | −5.36003 | + | 9.28385i | −0.000851208 | + | 0.00147434i | ||||
\(342\) | −3145.86 | −0.497394 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5231.92 | 0.820018 | ||||||||
\(345\) | −1252.17 | + | 2168.82i | −0.195405 | + | 0.338451i | ||||
\(346\) | 8761.26 | + | 15174.9i | 1.36130 | + | 2.35783i | ||||
\(347\) | 2723.89 | + | 4717.92i | 0.421401 | + | 0.729889i | 0.996077 | − | 0.0884927i | \(-0.0282050\pi\) |
−0.574675 | + | 0.818381i | \(0.694872\pi\) | |||||||
\(348\) | −747.594 | + | 1294.87i | −0.115159 | + | 0.199461i | ||||
\(349\) | 1227.84 | 0.188324 | 0.0941618 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941618 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4532.27 | 0.689216 | ||||||||
\(352\) | 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 | \(0.785596\pi\) | |||||||
\(354\) | 5698.15 | + | 9869.49i | 0.855518 | + | 1.48180i | ||||
\(355\) | 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 | \(-0.478273\pi\) |
0.829906 | − | 0.557904i | \(-0.188394\pi\) | |||||||
\(360\) | 634.056 | + | 1098.22i | 0.0928269 | + | 0.160781i | ||||
\(361\) | 2495.06 | + | 4321.58i | 0.363765 | + | 0.630059i | ||||
\(362\) | 258.703 | − | 448.086i | 0.0375611 | − | 0.0650577i | ||||
\(363\) | 4315.89 | 0.624037 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 404.386 | 0.0579905 | ||||||||
\(366\) | −5418.47 | + | 9385.06i | −0.773846 | + | 1.34034i | ||||
\(367\) | 6823.85 | + | 11819.3i | 0.970577 | + | 1.68109i | 0.693818 | + | 0.720150i | \(0.255927\pi\) |
0.276759 | + | 0.960939i | \(0.410740\pi\) | |||||||
\(368\) | 1851.28 | + | 3206.52i | 0.262241 | + | 0.454215i | ||||
\(369\) | 786.566 | − | 1362.37i | 0.110967 | − | 0.192201i | ||||
\(370\) | −8835.78 | −1.24149 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2808.89 | 0.391490 | ||||||||
\(373\) | 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 | ||||
\(375\) | −202.665 | − | 351.026i | −0.0279082 | − | 0.0483384i | ||||
\(376\) | 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 | ||||
\(381\) | −3157.72 | − | 5469.34i | −0.424607 | − | 0.735440i | ||||
\(382\) | 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 | \(0.0404210\pi\) | |||||||
\(384\) | −5779.58 | −0.768068 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14380.5 | −1.89623 | ||||||||
\(387\) | −2803.08 | + | 4855.08i | −0.368188 | + | 0.637720i | ||||
\(388\) | 2257.47 | + | 3910.05i | 0.295376 | + | 0.511606i | ||||
\(389\) | −758.496 | − | 1313.75i | −0.0988619 | − | 0.171234i | 0.812352 | − | 0.583168i | \(-0.198187\pi\) |
−0.911214 | + | 0.411934i | \(0.864854\pi\) | |||||||
\(390\) | 1150.18 | − | 1992.18i | 0.149338 | − | 0.258661i | ||||
\(391\) | 17665.6 | 2.28487 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3442.53 | 0.441865 | ||||||||
\(394\) | −92.0265 | + | 159.395i | −0.0117671 | + | 0.0203812i | ||||
\(395\) | −793.396 | − | 1374.20i | −0.101063 | − | 0.175047i | ||||
\(396\) | −13.4558 | − | 23.3062i | −0.00170753 | − | 0.00295753i | ||||
\(397\) | −3937.47 | + | 6819.90i | −0.497773 | + | 0.862169i | −0.999997 | − | 0.00256925i | \(-0.999182\pi\) |
0.502223 | + | 0.864738i | \(0.332516\pi\) | |||||||
\(398\) | 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 | \(-0.590125\pi\) |
0.971228 | − | 0.238151i | \(-0.0765412\pi\) | |||||||
\(402\) | 5300.23 | + | 9180.26i | 0.657590 | + | 1.13898i | ||||
\(403\) | 1212.10 | + | 2099.42i | 0.149824 | + | 0.259503i | ||||
\(404\) | 2609.69 | − | 4520.12i | 0.321379 | − | 0.556645i | ||||
\(405\) | 60.6645 | 0.00744307 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 56.9016 | 0.00692999 | ||||||||
\(408\) | −2852.74 | + | 4941.10i | −0.346157 | + | 0.599561i | ||||
\(409\) | −5355.07 | − | 9275.25i | −0.647411 | − | 1.12135i | −0.983739 | − | 0.179603i | \(-0.942519\pi\) |
0.336328 | − | 0.941745i | \(-0.390815\pi\) | |||||||
\(410\) | −1053.08 | − | 1823.99i | −0.126849 | − | 0.219708i | ||||
\(411\) | −2333.63 | + | 4041.97i | −0.280072 | + | 0.485099i | ||||
\(412\) | 8082.19 | 0.966458 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11240.2 | 1.33436 | ||||||||
\(415\) | 2364.82 | − | 4095.99i | 0.279722 | − | 0.484492i | ||||
\(416\) | −3678.50 | − | 6371.34i | −0.433541 | − | 0.750915i | ||||
\(417\) | −1073.53 | − | 1859.41i | −0.126069 | − | 0.218358i | ||||
\(418\) | 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 | ||||
\(423\) | 61.7401 | + | 106.937i | 0.00709671 | + | 0.0122919i | ||||
\(424\) | −5206.35 | − | 9017.66i | −0.596327 | − | 1.03287i | ||||
\(425\) | −1429.59 | + | 2476.13i | −0.163166 | + | 0.282612i | ||||
\(426\) | 529.969 | 0.0602748 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10968.4 | 1.23873 | ||||||||
\(429\) | −7.40707 | + | 12.8294i | −0.000833605 | + | 0.00144385i | ||||
\(430\) | 3752.87 | + | 6500.15i | 0.420882 | + | 0.728989i | ||||
\(431\) | −3085.32 | − | 5343.93i | −0.344814 | − | 0.597235i | 0.640506 | − | 0.767953i | \(-0.278725\pi\) |
−0.985320 | + | 0.170718i | \(0.945391\pi\) | |||||||
\(432\) | 1690.01 | − | 2927.18i | 0.188219 | − | 0.326005i | ||||
\(433\) | −14001.1 | −1.55392 | −0.776961 | − | 0.629548i | \(-0.783240\pi\) | ||||
−0.776961 | + | 0.629548i | \(0.783240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −650.914 | −0.0717447 | ||||||||
\(436\) | −1659.20 | + | 2873.82i | −0.182251 | + | 0.315668i | ||||
\(437\) | 3338.75 | + | 5782.89i | 0.365479 | + | 0.633028i | ||||
\(438\) | 578.826 | + | 1002.56i | 0.0631447 | + | 0.109370i | ||||
\(439\) | 6103.49 | − | 10571.6i | 0.663562 | − | 1.14932i | −0.316111 | − | 0.948722i | \(-0.602377\pi\) |
0.979673 | − | 0.200601i | \(-0.0642893\pi\) | |||||||
\(440\) | −10.9336 | −0.00118464 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16226.7 | −1.74621 | ||||||||
\(443\) | −613.882 | + | 1063.27i | −0.0658384 | + | 0.114035i | −0.897066 | − | 0.441897i | \(-0.854306\pi\) |
0.831227 | + | 0.555933i | \(0.187639\pi\) | |||||||
\(444\) | −7454.73 | − | 12912.0i | −0.796815 | − | 1.38012i | ||||
\(445\) | −1958.01 | − | 3391.38i | −0.208581 | − | 0.361274i | ||||
\(446\) | −9192.57 | + | 15922.0i | −0.975966 | + | 1.69042i | ||||
\(447\) | 2552.32 | 0.270068 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1151.70 | −0.121051 | −0.0605257 | − | 0.998167i | \(-0.519278\pi\) | ||||
−0.0605257 | + | 0.998167i | \(0.519278\pi\) | |||||||
\(450\) | −909.619 | + | 1575.51i | −0.0952886 | + | 0.165045i | ||||
\(451\) | 6.78175 | + | 11.7463i | 0.000708071 | + | 0.00122641i | ||||
\(452\) | −7185.41 | − | 12445.5i | −0.747729 | − | 1.29510i | ||||
\(453\) | −1375.46 | + | 2382.36i | −0.142659 | + | 0.247093i | ||||
\(454\) | 10401.0 | 1.07520 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2156.65 | −0.221479 | ||||||||
\(457\) | −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 | ||||
\(459\) | −8063.32 | − | 13966.1i | −0.819964 | − | 1.42022i | ||||
\(460\) | 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 | ||||
\(465\) | 611.411 | + | 1058.99i | 0.0609753 | + | 0.105612i | ||||
\(466\) | 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 | \(-0.133668\pi\) | |||||||
\(468\) | −6085.73 | −0.601096 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 165.320 | 0.0162247 | ||||||||
\(471\) | −1548.23 | + | 2681.62i | −0.151463 | + | 0.262341i | ||||
\(472\) | −6124.53 | − | 10608.0i | −0.597255 | − | 1.03448i | ||||
\(473\) | −24.1681 | − | 41.8604i | −0.00234937 | − | 0.00406922i | ||||
\(474\) | 2271.29 | − | 3933.98i | 0.220092 | − | 0.381211i | ||||
\(475\) | −1080.76 | −0.104397 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11157.5 | 1.07100 | ||||||||
\(478\) | 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 | \(0.794808\pi\) | |||||||
\(480\) | −1855.52 | − | 3213.85i | −0.176442 | − | 0.305607i | ||||
\(481\) | 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 | ||||
\(486\) | −8316.05 | − | 14403.8i | −0.776180 | − | 1.34438i | ||||
\(487\) | 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 | ||||
\(489\) | 23.8795 | 0.00220832 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15223.9 | −1.39928 | −0.699640 | − | 0.714496i | \(-0.746656\pi\) | ||||
−0.699640 | + | 0.714496i | \(0.746656\pi\) | |||||||
\(492\) | 1776.97 | − | 3077.79i | 0.162829 | − | 0.282028i | ||||
\(493\) | 2295.77 | + | 3976.39i | 0.209729 | + | 0.363260i | ||||
\(494\) | −3066.82 | − | 5311.88i | −0.279317 | − | 0.483791i | ||||
\(495\) | 5.85786 | − | 10.1461i | 0.000531902 | − | 0.000921281i | ||||
\(496\) | 1807.89 | 0.163663 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13539.8 | 1.21833 | ||||||||
\(499\) | 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 | ||||
\(501\) | −4736.53 | − | 8203.91i | −0.422380 | − | 0.731584i | ||||
\(502\) | −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 | ||||
\(507\) | −1887.03 | − | 3268.43i | −0.165297 | − | 0.286304i | ||||
\(508\) | 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 | \(-0.0145948\pi\) | |||||||
\(510\) | −8185.12 | −0.710673 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8436.86 | −0.728242 | ||||||||
\(513\) | 3047.90 | − | 5279.12i | 0.262316 | − | 0.454345i | ||||
\(514\) | 8003.33 | + | 13862.2i | 0.686793 | + | 1.18956i | ||||
\(515\) | 1759.25 | + | 3047.11i | 0.150528 | + | 0.260722i | ||||
\(516\) | −6332.57 | + | 10968.3i | −0.540263 | + | 0.935764i | ||||
\(517\) | −1.06464 | −9.05666e−5 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12871.9 | −1.08866 | ||||||||
\(520\) | −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 | \(-0.383526\pi\) | |||||||
\(522\) | 1460.75 | + | 2530.09i | 0.122481 | + | 0.212143i | ||||
\(523\) | 1859.56 | − | 3220.85i | 0.155474 | − | 0.269288i | −0.777758 | − | 0.628564i | \(-0.783643\pi\) |
0.933231 | + | 0.359276i | \(0.116976\pi\) | |||||||
\(524\) | −12193.3 | −1.01654 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3472.02 | 0.287809 | ||||||||
\(527\) | 4312.88 | − | 7470.12i | 0.356493 | − | 0.617464i | ||||
\(528\) | 5.52395 | + | 9.56777i | 0.000455302 | + | 0.000788605i | ||||
\(529\) | −5845.91 | − | 10125.4i | −0.480472 | − | 0.832203i | ||||
\(530\) | 7469.05 | − | 12936.8i | 0.612141 | − | 1.06026i | ||||
\(531\) | 13125.3 | 1.07267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3067.21 | 0.249260 | ||||||||
\(534\) | 5605.29 | − | 9708.64i | 0.454240 | − | 0.786768i | ||||
\(535\) | 2387.49 | + | 4135.26i | 0.192935 | + | 0.334173i | ||||
\(536\) | −5696.83 | − | 9867.21i | −0.459078 | − | 0.795146i | ||||
\(537\) | −1793.10 | + | 3105.74i | −0.144093 | + | 0.249577i | ||||
\(538\) | 17912.6 | 1.43544 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8097.53 | −0.645301 | ||||||||
\(541\) | 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 | ||||
\(543\) | 190.041 | + | 329.160i | 0.0150192 | + | 0.0260140i | ||||
\(544\) | −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 | ||||
\(549\) | 6240.52 | + | 10808.9i | 0.485134 | + | 0.840277i | ||||
\(550\) | −7.84271 | − | 13.5840i | −0.000608026 | − | 0.00105313i | ||||
\(551\) | −867.790 | + | 1503.06i | −0.0670946 | + | 0.116211i | ||||
\(552\) | 7705.74 | 0.594163 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −23368.7 | −1.79213 | ||||||||
\(555\) | 3245.34 | − | 5621.09i | 0.248211 | − | 0.429914i | ||||
\(556\) | 3802.39 | + | 6585.93i | 0.290031 | + | 0.502348i | ||||
\(557\) | 11031.4 | + | 19106.9i | 0.839164 | + | 1.45347i | 0.890595 | + | 0.454798i | \(0.150289\pi\) |
−0.0514307 | + | 0.998677i | \(0.516378\pi\) | |||||||
\(558\) | 2744.19 | − | 4753.08i | 0.208191 | − | 0.360598i | ||||
\(559\) | −10930.6 | −0.827040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.7114 | 0.00396698 | ||||||||
\(562\) | 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 | \(0.738256\pi\) | |||||||
\(564\) | 139.480 | + | 241.586i | 0.0104134 | + | 0.0180366i | ||||
\(565\) | 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 | \(0.447136\pi\) |
−0.936766 | + | 0.349955i | \(0.886197\pi\) | |||||||
\(570\) | −1546.97 | − | 2679.43i | −0.113676 | − | 0.196893i | ||||
\(571\) | 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 | ||||
\(573\) | −3251.07 | −0.237025 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3861.57 | 0.280067 | ||||||||
\(576\) | −6747.44 | + | 11686.9i | −0.488096 | + | 0.845408i | ||||
\(577\) | −7816.51 | − | 13538.6i | −0.563961 | − | 0.976809i | −0.997146 | − | 0.0755039i | \(-0.975943\pi\) |
0.433184 | − | 0.901305i | \(-0.357390\pi\) | |||||||
\(578\) | 18025.3 | + | 31220.7i | 1.29715 | + | 2.24673i | ||||
\(579\) | 5281.87 | − | 9148.47i | 0.379114 | − | 0.656645i | ||||
\(580\) | 2305.51 | 0.165054 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5626.82 | −0.400754 | ||||||||
\(583\) | −48.1000 | + | 83.3116i | −0.00341698 | + | 0.00591838i | ||||
\(584\) | −622.139 | − | 1077.58i | −0.0440827 | − | 0.0763534i | ||||
\(585\) | −1324.68 | − | 2294.41i | −0.0936219 | − | 0.162158i | ||||
\(586\) | −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 | ||||
\(591\) | −67.6018 | − | 117.090i | −0.00470519 | − | 0.00814963i | ||||
\(592\) | −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 | \(0.994640\pi\) | |||||||
\(594\) | 88.4703 | 0.00611108 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9040.18 | −0.621309 | ||||||||
\(597\) | −3900.27 | + | 6755.46i | −0.267383 | + | 0.463120i | ||||
\(598\) | 10957.8 | + | 18979.4i | 0.749326 | + | 1.29787i | ||||
\(599\) | 5264.93 | + | 9119.13i | 0.359131 | + | 0.622032i | 0.987816 | − | 0.155627i | \(-0.0497399\pi\) |
−0.628685 | + | 0.777660i | \(0.716407\pi\) | |||||||
\(600\) | −623.591 | + | 1080.09i | −0.0424300 | + | 0.0734909i | ||||
\(601\) | −11595.2 | −0.786984 | −0.393492 | − | 0.919328i | \(-0.628733\pi\) | ||||
−0.393492 | + | 0.919328i | \(0.628733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12208.7 | 0.824504 | ||||||||
\(604\) | 4871.80 | − | 8438.20i | 0.328196 | − | 0.568453i | ||||
\(605\) | −3327.45 | − | 5763.31i | −0.223603 | − | 0.387292i | ||||
\(606\) | 3252.37 | + | 5633.27i | 0.218017 | + | 0.377617i | ||||
\(607\) | −11641.0 | + | 20162.9i | −0.778411 | + | 1.34825i | 0.154446 | + | 0.988001i | \(0.450641\pi\) |
−0.932857 | + | 0.360246i | \(0.882693\pi\) | |||||||
\(608\) | −9894.99 | −0.660024 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16710.0 | 1.10913 | ||||||||
\(611\) | −120.378 | + | 208.500i | −0.00797047 | + | 0.0138053i | ||||
\(612\) | 10827.1 | + | 18753.0i | 0.715128 | + | 1.23864i | ||||
\(613\) | 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 | ||||
\(615\) | 1547.17 | 0.101444 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 667.085 | 0.0435265 | 0.0217632 | − | 0.999763i | \(-0.493072\pi\) | ||||
0.0217632 | + | 0.999763i | \(0.493072\pi\) | |||||||
\(618\) | −5036.27 | + | 8723.08i | −0.327813 | + | 0.567789i | ||||
\(619\) | −4712.89 | − | 8162.96i | −0.306021 | − | 0.530044i | 0.671467 | − | 0.741034i | \(-0.265664\pi\) |
−0.977488 | + | 0.210990i | \(0.932331\pi\) | |||||||
\(620\) | −2165.59 | − | 3750.91i | −0.140278 | − | 0.242968i | ||||
\(621\) | −10890.2 | + | 18862.4i | −0.703717 | + | 1.21887i | ||||
\(622\) | −22221.0 | −1.43244 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2498.34 | 0.160278 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −7943.83 | − | 13759.1i | −0.507187 | − | 0.878474i | ||||
\(627\) | 9.96234 | + | 17.2553i | 0.000634542 | + | 0.00109906i | ||||
\(628\) | 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 | ||||
\(633\) | 1963.81 | + | 3401.41i | 0.123309 | + | 0.213577i | ||||
\(634\) | 7816.59 | + | 13538.7i | 0.489647 | + | 0.848094i | ||||
\(635\) | −4869.06 | + | 8433.46i | −0.304288 | + | 0.527042i | ||||
\(636\) | 25206.5 | 1.57155 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.1890 | −0.00156308 | ||||||||
\(639\) | 305.186 | − | 528.597i | 0.0188935 | − | 0.0327246i | ||||
\(640\) | 4455.92 | + | 7717.89i | 0.275212 | + | 0.476682i | ||||
\(641\) | −11604.2 | − | 20099.0i | −0.715034 | − | 1.23847i | −0.962947 | − | 0.269692i | \(-0.913078\pi\) |
0.247913 | − | 0.968782i | \(-0.420255\pi\) | |||||||
\(642\) | −6834.77 | + | 11838.2i | −0.420167 | + | 0.727750i | ||||
\(643\) | 4294.22 | 0.263371 | 0.131686 | − | 0.991292i | \(-0.457961\pi\) | ||||
0.131686 | + | 0.991292i | \(0.457961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5513.64 | −0.336588 | ||||||||
\(646\) | −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 | \(-0.343890\pi\) | |||||||
\(648\) | −93.3310 | − | 161.654i | −0.00565801 | − | 0.00979995i | ||||
\(649\) | −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 | −0.997192 | − | 0.0748861i | \(-0.976141\pi\) |
0.563449 | + | 0.826151i | \(0.309474\pi\) | |||||||
\(654\) | −2067.81 | − | 3581.55i | −0.123636 | − | 0.214143i | ||||
\(655\) | −2654.11 | − | 4597.06i | −0.158328 | − | 0.274232i | ||||
\(656\) | 1143.71 | − | 1980.97i | 0.0680708 | − | 0.117902i | ||||
\(657\) | 1333.28 | 0.0791725 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 620.113 | 0.0366558 | 0.0183279 | − | 0.999832i | \(-0.494166\pi\) | ||||
0.0183279 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(660\) | 13.2338 | − | 22.9216i | 0.000780490 | − | 0.00135185i | ||||
\(661\) | 3052.75 | + | 5287.52i | 0.179634 | + | 0.311135i | 0.941755 | − | 0.336299i | \(-0.109175\pi\) |
−0.762121 | + | 0.647434i | \(0.775842\pi\) | |||||||
\(662\) | −16239.8 | − | 28128.2i | −0.953441 | − | 1.65141i | ||||
\(663\) | 5960.00 | − | 10323.0i | 0.349121 | − | 0.604695i | ||||
\(664\) | −14552.9 | −0.850546 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −29132.1 | −1.69496 | ||||||||
\(667\) | 3100.63 | − | 5370.44i | 0.179995 | − | 0.311761i | ||||
\(668\) | 16776.6 | + | 29057.9i | 0.971713 | + | 1.68306i | ||||
\(669\) | −6752.78 | − | 11696.2i | −0.390250 | − | 0.675933i | ||||
\(670\) | 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 | ||||
\(675\) | −1762.59 | − | 3052.89i | −0.100507 | − | 0.174083i | ||||
\(676\) | 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 | \(0.210345\pi\) | |||||||
\(678\) | 17909.9 | 1.01449 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8797.59 | 0.496136 | ||||||||
\(681\) | −3820.22 | + | 6616.82i | −0.214965 | + | 0.372331i | ||||
\(682\) | 23.6603 | + | 40.9809i | 0.00132845 | + | 0.00230094i | ||||
\(683\) | 4095.16 | + | 7093.03i | 0.229425 | + | 0.397375i | 0.957638 | − | 0.287976i | \(-0.0929822\pi\) |
−0.728213 | + | 0.685351i | \(0.759649\pi\) | |||||||
\(684\) | −4092.59 | + | 7088.57i | −0.228778 | + | 0.396255i | ||||
\(685\) | 7196.71 | 0.401419 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14089.8 | 0.782473 | ||||||||
\(688\) | −4075.85 | + | 7059.57i | −0.225858 | + | 0.391197i | ||||
\(689\) | 10877.2 | + | 18839.9i | 0.601434 | + | 1.04171i | ||||
\(690\) | 5527.35 | + | 9573.64i | 0.304960 | + | 0.528206i | ||||
\(691\) | 238.487 | − | 413.071i | 0.0131295 | − | 0.0227409i | −0.859386 | − | 0.511327i | \(-0.829154\pi\) |
0.872515 | + | 0.488586i | \(0.162487\pi\) | |||||||
\(692\) | 45591.6 | 2.50453 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24047.7 | 1.31533 | ||||||||
\(695\) | −1655.33 | + | 2867.12i | −0.0903457 | + | 0.156483i | ||||
\(696\) | 1001.42 | + | 1734.51i | 0.0545383 | + | 0.0944630i | ||||
\(697\) | −5456.84 | − | 9451.53i | −0.296546 | − | 0.513633i | ||||
\(698\) | 2709.98 | − | 4693.82i | 0.146955 | − | 0.254533i | ||||
\(699\) | −7971.22 | −0.431329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20366.7 | −1.09735 | −0.548673 | − | 0.836037i | \(-0.684867\pi\) | ||||
−0.548673 | + | 0.836037i | \(0.684867\pi\) | |||||||
\(702\) | 10003.2 | − | 17326.1i | 0.537816 | − | 0.931524i | ||||
\(703\) | −8653.29 | − | 14987.9i | −0.464246 | − | 0.804098i | ||||
\(704\) | −58.1763 | − | 100.764i | −0.00311449 | − | 0.00539445i | ||||
\(705\) | −60.7211 | + | 105.172i | −0.00324382 | + | 0.00561845i | ||||
\(706\) | 8748.36 | 0.466358 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 29651.9 | 1.57399 | ||||||||
\(709\) | −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 | ||||
\(711\) | −2615.87 | − | 4530.82i | −0.137979 | − | 0.238986i | ||||
\(712\) | −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 | ||||
\(717\) | 522.559 | + | 905.098i | 0.0272180 | + | 0.0471430i | ||||
\(718\) | −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 | \(0.929366\pi\) | |||||||
\(720\) | −1975.81 | −0.102269 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 22027.5 | 1.13543 | ||||||||
\(723\) | 8124.82 | − | 14072.6i | 0.417933 | − | 0.723881i | ||||
\(724\) | −673.115 | − | 1165.87i | −0.0345527 | − | 0.0598470i | ||||
\(725\) | 501.840 | + | 869.212i | 0.0257074 | + | 0.0445265i | ||||
\(726\) | 9525.63 | − | 16498.9i | 0.486955 | − | 0.843431i | ||||
\(727\) | 13666.2 | 0.697184 | 0.348592 | − | 0.937275i | \(-0.386660\pi\) | ||||
0.348592 | + | 0.937275i | \(0.386660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12545.4 | 0.637371 | ||||||||
\(730\) | 892.523 | − | 1545.90i | 0.0452517 | − | 0.0783783i | ||||
\(731\) | 19446.5 | + | 33682.4i | 0.983935 | + | 1.70423i | ||||
\(732\) | 14098.2 | + | 24418.9i | 0.711866 | + | 1.23299i | ||||
\(733\) | 12519.1 | − | 21683.7i | 0.630836 | − | 1.09264i | −0.356545 | − | 0.934278i | \(-0.616045\pi\) |
0.987381 | − | 0.158362i | \(-0.0506213\pi\) | |||||||
\(734\) | 60243.8 | 3.02948 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35354.9 | 1.77065 | ||||||||
\(737\) | −52.6315 | + | 91.1603i | −0.00263054 | + | 0.00455622i | ||||
\(738\) | −3472.07 | − | 6013.80i | −0.173182 | − | 0.299961i | ||||
\(739\) | −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 | ||||
\(741\) | 4505.71 | 0.223376 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8366.48 | −0.413104 | −0.206552 | − | 0.978436i | \(-0.566224\pi\) | ||||
−0.206552 | + | 0.978436i | \(0.566224\pi\) | |||||||
\(744\) | 1881.28 | − | 3258.48i | 0.0927032 | − | 0.160567i | ||||
\(745\) | −1967.78 | − | 3408.29i | −0.0967701 | − | 0.167611i | ||||
\(746\) | −12236.3 | − | 21193.8i | −0.600538 | − | 1.04016i | ||||
\(747\) | 7796.95 | − | 13504.7i | 0.381895 | − | 0.661462i | ||||
\(748\) | −186.701 | −0.00912630 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1789.21 | −0.0871105 | ||||||||
\(751\) | 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 | ||||
\(753\) | −6383.05 | − | 11055.8i | −0.308913 | − | 0.535052i | ||||
\(754\) | −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 | ||||
\(759\) | −35.5956 | − | 61.6534i | −0.00170229 | − | 0.00294845i | ||||
\(760\) | 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 | \(0.885669\pi\) | |||||||
\(762\) | −27877.7 | −1.32533 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11515.1 | 0.545292 | ||||||||
\(765\) | −4713.45 | + | 8163.94i | −0.222765 | + | 0.385840i | ||||
\(766\) | −12781.2 | − | 22137.7i | −0.602877 | − | 1.04421i | ||||
\(767\) | 12795.5 | + | 22162.4i | 0.602370 | + | 1.04334i | ||||
\(768\) | −2138.43 | + | 3703.87i | −0.100474 | + | 0.174026i | ||||
\(769\) | 22629.4 | 1.06117 | 0.530583 | − | 0.847633i | \(-0.321973\pi\) | ||||
0.530583 | + | 0.847633i | \(0.321973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11758.3 | −0.549243 | ||||||||
\(772\) | −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 | \(0.813273\pi\) | |||||||
\(774\) | 12373.4 | + | 21431.4i | 0.574616 | + | 0.995265i | ||||
\(775\) | 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 | ||||
\(780\) | −2992.65 | − | 5183.41i | −0.137377 | − | 0.237944i | ||||
\(781\) | 2.63130 | + | 4.55755i | 0.000120558 | + | 0.000208812i | ||||
\(782\) | 38989.8 | − | 67532.2i | 1.78296 | − | 3.08817i | ||||
\(783\) | −5661.04 | −0.258377 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4774.61 | 0.217087 | ||||||||
\(786\) | 7598.04 | − | 13160.2i | 0.344800 | − | 0.597212i | ||||
\(787\) | −12542.3 | − | 21723.9i | −0.568088 | − | 0.983958i | −0.996755 | − | 0.0804951i | \(-0.974350\pi\) |
0.428667 | − | 0.903463i | \(-0.358983\pi\) | |||||||
\(788\) | 239.442 | + | 414.726i | 0.0108246 | + | 0.0187488i | ||||
\(789\) | −1275.26 | + | 2208.81i | −0.0575417 | + | 0.0996651i | ||||
\(790\) | −7004.44 | −0.315451 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36.0488 | −0.00161735 | ||||||||
\(793\) | −12167.4 | + | 21074.6i | −0.544865 | + | 0.943734i | ||||
\(794\) | 17380.8 | + | 30104.5i | 0.776855 | + | 1.34555i | ||||
\(795\) | 5486.70 | + | 9503.24i | 0.244771 | + | 0.423956i | ||||
\(796\) | 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 | ||||
\(801\) | −6455.68 | − | 11181.6i | −0.284769 | − | 0.493235i | ||||
\(802\) | −24523.8 | − | 42476.4i | −1.07976 | − | 1.87019i | ||||
\(803\) | −5.74777 | + | 9.95542i | −0.000252596 | + | 0.000437508i | ||||
\(804\) | 27581.2 | 1.20984 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10701.0 | 0.467649 | ||||||||
\(807\) | −6579.23 | + | 11395.6i | −0.286988 | + | 0.497079i | ||||
\(808\) | −3495.74 | − | 6054.80i | −0.152203 | − | 0.263623i | ||||
\(809\) | −1157.19 | − | 2004.30i | −0.0502899 | − | 0.0871046i | 0.839785 | − | 0.542920i | \(-0.182681\pi\) |
−0.890075 | + | 0.455815i | \(0.849348\pi\) | |||||||
\(810\) | 133.893 | − | 231.910i | 0.00580805 | − | 0.0100598i | ||||
\(811\) | −38300.1 | −1.65832 | −0.829160 | − | 0.559011i | \(-0.811181\pi\) | ||||
−0.829160 | + | 0.559011i | \(0.811181\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9401.78 | 0.405578 | ||||||||
\(814\) | 125.588 | − | 217.525i | 0.00540768 | − | 0.00936638i | ||||
\(815\) | −18.4105 | − | 31.8880i | −0.000791280 | − | 0.00137054i | ||||
\(816\) | −4444.78 | − | 7698.58i | −0.190684 | − | 0.330275i | ||||
\(817\) | −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 | −0.904882 | − | 0.425663i | \(-0.860041\pi\) |
0.821076 | + | 0.570819i | \(0.193374\pi\) | |||||||
\(822\) | 10301.2 | + | 17842.1i | 0.437098 | + | 0.757075i | ||||
\(823\) | −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 | ||||
\(825\) | 11.5224 | 0.000486251 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11965.2 | −0.503110 | −0.251555 | − | 0.967843i | \(-0.580942\pi\) | ||||
−0.251555 | + | 0.967843i | \(0.580942\pi\) | |||||||
\(828\) | 14622.9 | − | 25327.5i | 0.613744 | − | 1.06303i | ||||
\(829\) | −17981.5 | − | 31144.8i | −0.753344 | − | 1.30483i | −0.946193 | − | 0.323602i | \(-0.895106\pi\) |
0.192849 | − | 0.981228i | \(-0.438227\pi\) | |||||||
\(830\) | −10438.8 | − | 18080.6i | −0.436551 | − | 0.756128i | ||||
\(831\) | 8583.20 | − | 14866.5i | 0.358301 | − | 0.620595i | ||||
\(832\) | −26311.6 | −1.09638 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9477.56 | −0.393503 | ||||||||
\(835\) | −7303.50 | + | 12650.0i | −0.302692 | + | 0.524279i | ||||
\(836\) | −35.2862 | − | 61.1174i | −0.00145981 | − | 0.00252846i | ||||
\(837\) | 5317.47 | + | 9210.14i | 0.219592 | + | 0.380345i | ||||
\(838\) | −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 | ||||
\(843\) | 3825.35 | + | 6625.69i | 0.156289 | + | 0.270701i | ||||
\(844\) | −6955.71 | − | 12047.6i | −0.283679 | − | 0.491347i | ||||
\(845\) | −2909.71 | + | 5039.76i | −0.118458 | + | 0.205175i | ||||
\(846\) | 545.068 | 0.0221511 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16223.7 | 0.656987 | ||||||||
\(849\) | 4671.59 | − | 8091.43i | 0.188844 | − | 0.327087i | ||||
\(850\) | 6310.53 | + | 10930.2i | 0.254647 | + | 0.441061i | ||||
\(851\) | 30918.3 | + | 53552.1i | 1.24544 | + | 2.15716i | ||||
\(852\) | 689.459 | − | 1194.18i | 0.0277236 | − | 0.0480186i | ||||
\(853\) | −25297.5 | −1.01544 | −0.507719 | − | 0.861523i | \(-0.669511\pi\) | ||||
−0.507719 | + | 0.861523i | \(0.669511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3563.33 | −0.142530 | ||||||||
\(856\) | 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 | \(0.547218\pi\) | |||||||
\(858\) | 32.6964 | + | 56.6318i | 0.00130097 | + | 0.00225335i | ||||
\(859\) | −7249.55 | + | 12556.6i | −0.287953 | + | 0.498749i | −0.973321 | − | 0.229448i | \(-0.926308\pi\) |
0.685368 | + | 0.728197i | \(0.259641\pi\) | |||||||
\(860\) | 19529.1 | 0.774343 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27238.5 | −1.07627 | ||||||||
\(863\) | 12205.6 | − | 21140.8i | 0.481442 | − | 0.833882i | −0.518331 | − | 0.855180i | \(-0.673447\pi\) |
0.999773 | + | 0.0212980i | \(0.00677986\pi\) | |||||||
\(864\) | −16137.5 | − | 27951.0i | −0.635428 | − | 1.10059i | ||||
\(865\) | 9923.92 | + | 17188.7i | 0.390085 | + | 0.675647i | ||||
\(866\) | −30901.9 | + | 53523.6i | −1.21257 | + | 2.10024i | ||||
\(867\) | −26482.4 | −1.03736 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.1079 | 0.00176085 | ||||||||
\(870\) | −1436.64 | + | 2488.33i | −0.0559846 | + | 0.0969681i | ||||
\(871\) | 11901.9 | + | 20614.7i | 0.463010 | + | 0.801956i | ||||
\(872\) | 2222.54 | + | 3849.55i | 0.0863126 | + | 0.149498i | ||||
\(873\) | −3240.24 | + | 5612.26i | −0.125619 | + | 0.217579i | ||||
\(874\) | 29475.9 | 1.14078 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3012.08 | 0.116174 | ||||||||
\(877\) | 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 | ||||
\(879\) | −1233.39 | − | 2136.29i | −0.0473278 | − | 0.0819741i | ||||
\(880\) | 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 | ||||
\(885\) | 6454.32 | + | 11179.2i | 0.245152 | + | 0.424616i | ||||
\(886\) | 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 | \(0.912724\pi\) | |||||||
\(888\) | −19971.5 | −0.754731 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −17286.2 | −0.651049 | ||||||||
\(891\) | −0.862259 | + | 1.49348i | −3.24206e−5 | + | 5.61541e-5i | ||||
\(892\) | 23918.0 | + | 41427.2i | 0.897796 | + | 1.55503i | ||||
\(893\) | 161.905 | + | 280.428i | 0.00606713 | + | 0.0105086i | ||||
\(894\) | 5633.23 | − | 9757.04i | 0.210742 | − | 0.365016i | ||||
\(895\) | 5529.76 | 0.206524 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16099.0 | −0.599252 | ||||||||
\(898\) | −2541.92 | + | 4402.74i | −0.0944600 | + | 0.163609i | ||||
\(899\) | −1513.98 | − | 2622.29i | −0.0561668 | − | 0.0972838i | ||||
\(900\) | 2366.73 | + | 4099.29i | 0.0876565 | + | 0.151826i | ||||
\(901\) | 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 | ||||
\(906\) | 6071.55 | + | 10516.2i | 0.222642 | + | 0.385628i | ||||
\(907\) | −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 | ||||
\(909\) | 7491.60 | 0.273356 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7854.40 | 0.285651 | 0.142825 | − | 0.989748i | \(-0.454381\pi\) | ||||
0.142825 | + | 0.989748i | \(0.454381\pi\) | |||||||
\(912\) | 1680.11 | − | 2910.03i | 0.0610021 | − | 0.105659i | ||||
\(913\) | 67.2251 | + | 116.437i | 0.00243683 | + | 0.00422071i | ||||
\(914\) | 41303.4 | + | 71539.6i | 1.49474 | + | 2.58897i | ||||
\(915\) | −6137.52 | + | 10630.5i | −0.221749 | + | 0.384080i | ||||
\(916\) | −49905.4 | −1.80013 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −71186.4 | −2.55937 | ||||||||
\(919\) | −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 | ||||
\(921\) | 8055.64 | + | 13952.8i | 0.288211 | + | 0.499196i | ||||
\(922\) | 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 | ||||
\(927\) | 5800.34 | + | 10046.5i | 0.205510 | + | 0.355955i | ||||
\(928\) | 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 | \(0.256114\pi\) | |||||||
\(930\) | 5397.80 | 0.190323 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28233.7 | 0.992302 | ||||||||
\(933\) | 8161.66 | − | 14136.4i | 0.286389 | − | 0.496040i | ||||
\(934\) | −36067.7 | − | 62471.0i | −1.26356 | − | 2.18856i | ||||
\(935\) | −40.6393 | − | 70.3892i | −0.00142144 | − | 0.00246200i | ||||
\(936\) | −4075.98 | + | 7059.81i | −0.142337 | + | 0.246535i | ||||
\(937\) | 43806.5 | 1.52732 | 0.763658 | − | 0.645621i | \(-0.223401\pi\) | ||||
0.763658 | + | 0.645621i | \(0.223401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11670.9 | 0.405608 | ||||||||
\(940\) | 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 | \(0.810916\pi\) | |||||||
\(942\) | 6834.24 | + | 11837.2i | 0.236382 | + | 0.409425i | ||||
\(943\) | −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 | −0.821316 | − | 0.570473i | \(-0.806760\pi\) |
0.904702 | + | 0.426044i | \(0.140093\pi\) | |||||||
\(948\) | −5909.63 | − | 10235.8i | −0.202464 | − | 0.350678i | ||||
\(949\) | 1299.78 | + | 2251.29i | 0.0444602 | + | 0.0770073i | ||||
\(950\) | −2385.36 | + | 4131.56i | −0.0814644 | + | 0.141100i | ||||
\(951\) | −11484.0 | −0.391581 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18999.6 | −0.645811 | −0.322906 | − | 0.946431i | \(-0.604660\pi\) | ||||
−0.322906 | + | 0.946431i | \(0.604660\pi\) | |||||||
\(954\) | 24625.9 | − | 42653.3i | 0.835736 | − | 1.44754i | ||||
\(955\) | 2506.50 | + | 4341.38i | 0.0849303 | + | 0.147104i | ||||
\(956\) | −1850.88 | − | 3205.82i | −0.0626168 | − | 0.108456i | ||||
\(957\) | 9.25181 | − | 16.0246i | 0.000312506 | − | 0.000541277i | ||||
\(958\) | 11174.4 | 0.376855 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13272.2 | −0.446205 | ||||||||
\(961\) | 12051.3 | − | 20873.5i | 0.404529 | − | 0.700664i | ||||
\(962\) | −28400.1 | − | 49190.4i | −0.951825 | − | 1.64861i | ||||
\(963\) | 7871.70 | + | 13634.2i | 0.263408 | + | 0.456236i | ||||
\(964\) | −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 | ||||
\(969\) | −8016.07 | − | 13884.2i | −0.265751 | − | 0.460295i | ||||
\(970\) | 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 | \(0.199282\pi\) | |||||||
\(972\) | −43274.8 | −1.42803 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37265.6 | 1.22594 | ||||||||
\(975\) | 1302.82 | − | 2256.55i | 0.0427934 | − | 0.0741203i | ||||
\(976\) | 9074.08 | + | 15716.8i | 0.297596 | + | 0.515452i | ||||
\(977\) | −1071.22 | − | 1855.41i | −0.0350782 | − | 0.0607572i | 0.847953 | − | 0.530071i | \(-0.177835\pi\) |
−0.883032 | + | 0.469314i | \(0.844501\pi\) | |||||||
\(978\) | 52.7046 | − | 91.2871i | 0.00172322 | − | 0.00298470i | ||||
\(979\) | 111.321 | 0.00363416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4763.04 | −0.155018 | ||||||||
\(982\) | −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 | \(0.745422\pi\) | |||||||
\(984\) | −2380.28 | − | 4122.77i | −0.0771145 | − | 0.133566i | ||||
\(985\) | −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 | ||||
\(990\) | −25.8579 | − | 44.7871i | −0.000830118 | − | 0.00143781i | ||||
\(991\) | −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 | ||||
\(993\) | 23859.2 | 0.762487 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12028.1 | 0.383231 | ||||||||
\(996\) | 17614.4 | − | 30509.1i | 0.560377 | − | 0.970601i | ||||
\(997\) | −18820.0 | − | 32597.1i | −0.597828 | − | 1.03547i | −0.993141 | − | 0.116922i | \(-0.962697\pi\) |
0.395313 | − | 0.918546i | \(-0.370636\pi\) | |||||||
\(998\) | −36688.0 | − | 63545.4i | −1.16366 | − | 2.01553i | ||||
\(999\) | 28224.9 | − | 48887.0i | 0.893891 | − | 1.54826i |
(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 | 245.4.e.l.226.2 | 4 | ||
7.2 | even | 3 | 245.4.a.h.1.1 | 2 | |||
7.3 | odd | 6 | 35.4.e.b.11.2 | ✓ | 4 | ||
7.4 | even | 3 | inner | 245.4.e.l.116.2 | 4 | ||
7.5 | odd | 6 | 245.4.a.g.1.1 | 2 | |||
7.6 | odd | 2 | 35.4.e.b.16.2 | yes | 4 | ||
21.2 | odd | 6 | 2205.4.a.bg.1.2 | 2 | |||
21.5 | even | 6 | 2205.4.a.bf.1.2 | 2 | |||
21.17 | even | 6 | 315.4.j.c.46.1 | 4 | |||
21.20 | even | 2 | 315.4.j.c.226.1 | 4 | |||
28.3 | even | 6 | 560.4.q.i.81.2 | 4 | |||
28.27 | even | 2 | 560.4.q.i.401.2 | 4 | |||
35.3 | even | 12 | 175.4.k.c.74.4 | 8 | |||
35.9 | even | 6 | 1225.4.a.v.1.2 | 2 | |||
35.13 | even | 4 | 175.4.k.c.149.1 | 8 | |||
35.17 | even | 12 | 175.4.k.c.74.1 | 8 | |||
35.19 | odd | 6 | 1225.4.a.x.1.2 | 2 | |||
35.24 | odd | 6 | 175.4.e.c.151.1 | 4 | |||
35.27 | even | 4 | 175.4.k.c.149.4 | 8 | |||
35.34 | odd | 2 | 175.4.e.c.51.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.b.11.2 | ✓ | 4 | 7.3 | odd | 6 | ||
35.4.e.b.16.2 | yes | 4 | 7.6 | odd | 2 | ||
175.4.e.c.51.1 | 4 | 35.34 | odd | 2 | |||
175.4.e.c.151.1 | 4 | 35.24 | odd | 6 | |||
175.4.k.c.74.1 | 8 | 35.17 | even | 12 | |||
175.4.k.c.74.4 | 8 | 35.3 | even | 12 | |||
175.4.k.c.149.1 | 8 | 35.13 | even | 4 | |||
175.4.k.c.149.4 | 8 | 35.27 | even | 4 | |||
245.4.a.g.1.1 | 2 | 7.5 | odd | 6 | |||
245.4.a.h.1.1 | 2 | 7.2 | even | 3 | |||
245.4.e.l.116.2 | 4 | 7.4 | even | 3 | inner | ||
245.4.e.l.226.2 | 4 | 1.1 | even | 1 | trivial | ||
315.4.j.c.46.1 | 4 | 21.17 | even | 6 | |||
315.4.j.c.226.1 | 4 | 21.20 | even | 2 | |||
560.4.q.i.81.2 | 4 | 28.3 | even | 6 | |||
560.4.q.i.401.2 | 4 | 28.27 | even | 2 | |||
1225.4.a.v.1.2 | 2 | 35.9 | even | 6 | |||
1225.4.a.x.1.2 | 2 | 35.19 | odd | 6 | |||
2205.4.a.bf.1.2 | 2 | 21.5 | even | 6 | |||
2205.4.a.bg.1.2 | 2 | 21.2 | odd | 6 |