Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,4,Mod(8,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([12]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.8");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.e (of order \(7\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.89109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Relative dimension: | \(13\) over \(\Q(\zeta_{7})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{7}]$ |
Embedding invariants
Embedding label | 8.5 | ||
Character | \(\chi\) | \(=\) | 49.8 |
Dual form | 49.4.e.a.43.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{6}{7}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46127 | − | 1.83238i | −0.516637 | − | 0.647843i | 0.453254 | − | 0.891382i | \(-0.350263\pi\) |
−0.969891 | + | 0.243539i | \(0.921692\pi\) | |||||||
\(3\) | 7.38411 | − | 3.55600i | 1.42107 | − | 0.684353i | 0.443759 | − | 0.896146i | \(-0.353645\pi\) |
0.977314 | + | 0.211794i | \(0.0679305\pi\) | |||||||
\(4\) | 0.557879 | − | 2.44423i | 0.0697348 | − | 0.305528i | ||||
\(5\) | −0.458224 | + | 0.220669i | −0.0409848 | + | 0.0197372i | −0.454264 | − | 0.890867i | \(-0.650098\pi\) |
0.413279 | + | 0.910604i | \(0.364383\pi\) | |||||||
\(6\) | −17.3061 | − | 8.33419i | −1.17753 | − | 0.567070i | ||||
\(7\) | 12.0280 | + | 14.0828i | 0.649453 | + | 0.760402i | ||||
\(8\) | −22.1867 | + | 10.6846i | −0.980525 | + | 0.472196i | ||||
\(9\) | 25.0457 | − | 31.4064i | 0.927620 | − | 1.16320i | ||||
\(10\) | 1.07394 | + | 0.517181i | 0.0339609 | + | 0.0163547i | ||||
\(11\) | −23.3352 | − | 29.2614i | −0.639620 | − | 0.802058i | 0.351335 | − | 0.936250i | \(-0.385728\pi\) |
−0.990955 | + | 0.134191i | \(0.957156\pi\) | |||||||
\(12\) | −4.57223 | − | 20.0323i | −0.109991 | − | 0.481901i | ||||
\(13\) | −8.07065 | − | 10.1203i | −0.172184 | − | 0.215912i | 0.688250 | − | 0.725473i | \(-0.258379\pi\) |
−0.860434 | + | 0.509561i | \(0.829808\pi\) | |||||||
\(14\) | 8.22883 | − | 42.6187i | 0.157089 | − | 0.813595i | ||||
\(15\) | −2.59888 | + | 3.25889i | −0.0447351 | + | 0.0560961i | ||||
\(16\) | 33.9286 | + | 16.3391i | 0.530134 | + | 0.255299i | ||||
\(17\) | 27.8294 | + | 121.929i | 0.397037 | + | 1.73953i | 0.638963 | + | 0.769238i | \(0.279364\pi\) |
−0.241926 | + | 0.970295i | \(0.577779\pi\) | |||||||
\(18\) | −94.1469 | −1.23281 | ||||||||
\(19\) | 59.9098 | 0.723382 | 0.361691 | − | 0.932298i | \(-0.382200\pi\) | ||||
0.361691 | + | 0.932298i | \(0.382200\pi\) | |||||||
\(20\) | 0.283731 | + | 1.24311i | 0.00317221 | + | 0.0138984i | ||||
\(21\) | 138.895 | + | 61.2175i | 1.44330 | + | 0.636131i | ||||
\(22\) | −19.5189 | + | 85.5177i | −0.189156 | + | 0.828747i | ||||
\(23\) | 2.99017 | − | 13.1008i | 0.0271084 | − | 0.118770i | −0.959563 | − | 0.281493i | \(-0.909171\pi\) |
0.986672 | + | 0.162723i | \(0.0520277\pi\) | |||||||
\(24\) | −125.835 | + | 157.792i | −1.07025 | + | 1.34205i | ||||
\(25\) | −77.7750 | + | 97.5267i | −0.622200 | + | 0.780214i | ||||
\(26\) | −6.75074 | + | 29.5769i | −0.0509204 | + | 0.223097i | ||||
\(27\) | 24.0189 | − | 105.234i | 0.171202 | − | 0.750083i | ||||
\(28\) | 41.1318 | − | 21.5427i | 0.277614 | − | 0.145400i | ||||
\(29\) | −23.4087 | − | 102.560i | −0.149893 | − | 0.656722i | −0.992913 | − | 0.118841i | \(-0.962082\pi\) |
0.843021 | − | 0.537881i | \(-0.180775\pi\) | |||||||
\(30\) | 9.76917 | 0.0594533 | ||||||||
\(31\) | 217.007 | 1.25728 | 0.628640 | − | 0.777696i | \(-0.283612\pi\) | ||||
0.628640 | + | 0.777696i | \(0.283612\pi\) | |||||||
\(32\) | 24.1980 | + | 106.018i | 0.133676 | + | 0.585674i | ||||
\(33\) | −276.363 | − | 133.089i | −1.45784 | − | 0.702058i | ||||
\(34\) | 182.753 | − | 229.165i | 0.921819 | − | 1.15592i | ||||
\(35\) | −8.61918 | − | 3.79888i | −0.0416259 | − | 0.0183465i | ||||
\(36\) | −62.7918 | − | 78.7384i | −0.290703 | − | 0.364530i | ||||
\(37\) | −21.6633 | − | 94.9130i | −0.0962546 | − | 0.421719i | 0.903725 | − | 0.428113i | \(-0.140822\pi\) |
−0.999980 | + | 0.00639464i | \(0.997965\pi\) | |||||||
\(38\) | −87.5445 | − | 109.777i | −0.373726 | − | 0.468638i | ||||
\(39\) | −95.5823 | − | 46.0300i | −0.392447 | − | 0.188992i | ||||
\(40\) | 7.80874 | − | 9.79185i | 0.0308667 | − | 0.0387057i | ||||
\(41\) | −160.772 | + | 77.4236i | −0.612398 | + | 0.294916i | −0.714257 | − | 0.699883i | \(-0.753235\pi\) |
0.101859 | + | 0.994799i | \(0.467521\pi\) | |||||||
\(42\) | −90.7897 | − | 343.963i | −0.333551 | − | 1.26368i | ||||
\(43\) | 379.002 | + | 182.518i | 1.34412 | + | 0.647295i | 0.961037 | − | 0.276419i | \(-0.0891477\pi\) |
0.383084 | + | 0.923714i | \(0.374862\pi\) | |||||||
\(44\) | −84.5397 | + | 40.7122i | −0.289655 | + | 0.139491i | ||||
\(45\) | −4.54614 | + | 19.9180i | −0.0150600 | + | 0.0659821i | ||||
\(46\) | −28.3750 | + | 13.6647i | −0.0909492 | + | 0.0437988i | ||||
\(47\) | −387.651 | − | 486.099i | −1.20308 | − | 1.50861i | −0.807166 | − | 0.590325i | \(-0.799000\pi\) |
−0.395913 | − | 0.918288i | \(-0.629572\pi\) | |||||||
\(48\) | 308.634 | 0.928073 | ||||||||
\(49\) | −53.6526 | + | 338.778i | −0.156422 | + | 0.987690i | ||||
\(50\) | 292.356 | 0.826907 | ||||||||
\(51\) | 639.074 | + | 801.374i | 1.75467 | + | 2.20029i | ||||
\(52\) | −29.2387 | + | 14.0806i | −0.0779745 | + | 0.0375506i | ||||
\(53\) | −21.6914 | + | 95.0364i | −0.0562179 | + | 0.246307i | −0.995227 | − | 0.0975851i | \(-0.968888\pi\) |
0.939009 | + | 0.343892i | \(0.111745\pi\) | |||||||
\(54\) | −227.926 | + | 109.763i | −0.574385 | + | 0.276609i | ||||
\(55\) | 17.1498 | + | 8.25892i | 0.0420451 | + | 0.0202479i | ||||
\(56\) | −417.332 | − | 183.938i | −0.995863 | − | 0.438924i | ||||
\(57\) | 442.381 | − | 213.039i | 1.02798 | − | 0.495048i | ||||
\(58\) | −153.722 | + | 192.762i | −0.348013 | + | 0.436394i | ||||
\(59\) | −583.525 | − | 281.011i | −1.28760 | − | 0.620076i | −0.340269 | − | 0.940328i | \(-0.610518\pi\) |
−0.947332 | + | 0.320252i | \(0.896232\pi\) | |||||||
\(60\) | 6.51560 | + | 8.17030i | 0.0140193 | + | 0.0175797i | ||||
\(61\) | −84.7554 | − | 371.338i | −0.177899 | − | 0.779425i | −0.982598 | − | 0.185743i | \(-0.940531\pi\) |
0.804700 | − | 0.593682i | \(-0.202326\pi\) | |||||||
\(62\) | −317.107 | − | 397.639i | −0.649558 | − | 0.814520i | ||||
\(63\) | 743.542 | − | 25.0419i | 1.48694 | − | 0.0500791i | ||||
\(64\) | 346.740 | − | 434.798i | 0.677226 | − | 0.849215i | ||||
\(65\) | 5.93139 | + | 2.85641i | 0.0113184 | + | 0.00545067i | ||||
\(66\) | 159.972 | + | 700.881i | 0.298351 | + | 1.30716i | ||||
\(67\) | −418.726 | −0.763515 | −0.381757 | − | 0.924263i | \(-0.624681\pi\) | ||||
−0.381757 | + | 0.924263i | \(0.624681\pi\) | |||||||
\(68\) | 313.547 | 0.559164 | ||||||||
\(69\) | −24.5066 | − | 107.371i | −0.0427573 | − | 0.187332i | ||||
\(70\) | 5.63399 | + | 21.3448i | 0.00961986 | + | 0.0364455i | ||||
\(71\) | −150.991 | + | 661.533i | −0.252384 | + | 1.10577i | 0.676805 | + | 0.736163i | \(0.263364\pi\) |
−0.929189 | + | 0.369605i | \(0.879493\pi\) | |||||||
\(72\) | −220.120 | + | 964.408i | −0.360297 | + | 1.57856i | ||||
\(73\) | 78.3249 | − | 98.2163i | 0.125579 | − | 0.157471i | −0.715068 | − | 0.699055i | \(-0.753604\pi\) |
0.840646 | + | 0.541585i | \(0.182176\pi\) | |||||||
\(74\) | −142.260 | + | 178.389i | −0.223479 | + | 0.280234i | ||||
\(75\) | −227.494 | + | 996.716i | −0.350250 | + | 1.53454i | ||||
\(76\) | 33.4224 | − | 146.433i | 0.0504449 | − | 0.221014i | ||||
\(77\) | 131.407 | − | 680.583i | 0.194483 | − | 1.00727i | ||||
\(78\) | 55.3274 | + | 242.405i | 0.0803153 | + | 0.351884i | ||||
\(79\) | −952.335 | −1.35628 | −0.678140 | − | 0.734933i | \(-0.737214\pi\) | ||||
−0.678140 | + | 0.734933i | \(0.737214\pi\) | |||||||
\(80\) | −19.1524 | −0.0267663 | ||||||||
\(81\) | 44.4926 | + | 194.935i | 0.0610324 | + | 0.267400i | ||||
\(82\) | 376.800 | + | 181.458i | 0.507447 | + | 0.244374i | ||||
\(83\) | −223.673 | + | 280.478i | −0.295799 | + | 0.370921i | −0.907416 | − | 0.420234i | \(-0.861948\pi\) |
0.611617 | + | 0.791154i | \(0.290520\pi\) | |||||||
\(84\) | 227.116 | − | 305.339i | 0.295005 | − | 0.396609i | ||||
\(85\) | −39.6580 | − | 49.7295i | −0.0506060 | − | 0.0634579i | ||||
\(86\) | −219.383 | − | 961.181i | −0.275078 | − | 1.20520i | ||||
\(87\) | −537.556 | − | 674.075i | −0.662438 | − | 0.830671i | ||||
\(88\) | 830.377 | + | 399.889i | 1.00589 | + | 0.484412i | ||||
\(89\) | 108.702 | − | 136.308i | 0.129465 | − | 0.162344i | −0.712874 | − | 0.701292i | \(-0.752607\pi\) |
0.842339 | + | 0.538948i | \(0.181178\pi\) | |||||||
\(90\) | 43.1403 | − | 20.7753i | 0.0505266 | − | 0.0243323i | ||||
\(91\) | 45.4481 | − | 235.385i | 0.0523544 | − | 0.271154i | ||||
\(92\) | −30.3531 | − | 14.6173i | −0.0343971 | − | 0.0165648i | ||||
\(93\) | 1602.41 | − | 771.679i | 1.78669 | − | 0.860423i | ||||
\(94\) | −324.253 | + | 1420.64i | −0.355789 | + | 1.55881i | ||||
\(95\) | −27.4521 | + | 13.2202i | −0.0296476 | + | 0.0142776i | ||||
\(96\) | 555.682 | + | 696.803i | 0.590771 | + | 0.740804i | ||||
\(97\) | −1351.05 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 699.169 | − | 396.735i | 0.720681 | − | 0.408941i | ||||
\(99\) | −1503.44 | −1.52628 | ||||||||
\(100\) | 194.988 | + | 244.508i | 0.194988 | + | 0.244508i | ||||
\(101\) | 843.641 | − | 406.276i | 0.831143 | − | 0.400257i | 0.0305993 | − | 0.999532i | \(-0.490258\pi\) |
0.800544 | + | 0.599274i | \(0.204544\pi\) | |||||||
\(102\) | 534.557 | − | 2342.05i | 0.518912 | − | 2.27350i | ||||
\(103\) | 829.007 | − | 399.229i | 0.793054 | − | 0.381914i | 0.00692390 | − | 0.999976i | \(-0.497796\pi\) |
0.786130 | + | 0.618062i | \(0.212082\pi\) | |||||||
\(104\) | 287.192 | + | 138.304i | 0.270784 | + | 0.130403i | ||||
\(105\) | −77.1538 | + | 2.59848i | −0.0717089 | + | 0.00241510i | ||||
\(106\) | 205.840 | − | 99.1271i | 0.188612 | − | 0.0908309i | ||||
\(107\) | 427.861 | − | 536.521i | 0.386569 | − | 0.484742i | −0.550030 | − | 0.835145i | \(-0.685384\pi\) |
0.936599 | + | 0.350402i | \(0.113955\pi\) | |||||||
\(108\) | −243.815 | − | 117.415i | −0.217233 | − | 0.104614i | ||||
\(109\) | −1127.77 | − | 1414.18i | −0.991016 | − | 1.24269i | −0.970048 | − | 0.242914i | \(-0.921897\pi\) |
−0.0209680 | − | 0.999780i | \(-0.506675\pi\) | |||||||
\(110\) | −9.92709 | − | 43.4934i | −0.00860465 | − | 0.0376994i | ||||
\(111\) | −497.475 | − | 623.813i | −0.425389 | − | 0.533421i | ||||
\(112\) | 177.993 | + | 674.338i | 0.150167 | + | 0.568919i | ||||
\(113\) | 383.611 | − | 481.033i | 0.319355 | − | 0.400458i | −0.596080 | − | 0.802925i | \(-0.703276\pi\) |
0.915434 | + | 0.402467i | \(0.131847\pi\) | |||||||
\(114\) | −1036.81 | − | 499.300i | −0.851806 | − | 0.410208i | ||||
\(115\) | 1.52077 | + | 6.66292i | 0.00123315 | + | 0.00540279i | ||||
\(116\) | −263.739 | −0.211100 | ||||||||
\(117\) | −519.976 | −0.410870 | ||||||||
\(118\) | 337.771 | + | 1479.87i | 0.263511 | + | 1.15452i | ||||
\(119\) | −1382.37 | + | 1858.48i | −1.06489 | + | 1.43165i | ||||
\(120\) | 22.8408 | − | 100.072i | 0.0173756 | − | 0.0761273i | ||||
\(121\) | −15.5231 | + | 68.0111i | −0.0116627 | + | 0.0510977i | ||||
\(122\) | −556.580 | + | 697.929i | −0.413036 | + | 0.517931i | ||||
\(123\) | −911.838 | + | 1143.41i | −0.668437 | + | 0.838193i | ||||
\(124\) | 121.064 | − | 530.415i | 0.0876762 | − | 0.384135i | ||||
\(125\) | 28.2637 | − | 123.831i | 0.0202239 | − | 0.0886065i | ||||
\(126\) | −1132.40 | − | 1325.86i | −0.800654 | − | 0.937433i | ||||
\(127\) | 522.607 | + | 2289.69i | 0.365149 | + | 1.59982i | 0.739914 | + | 0.672701i | \(0.234866\pi\) |
−0.374765 | + | 0.927120i | \(0.622277\pi\) | |||||||
\(128\) | −433.437 | −0.299303 | ||||||||
\(129\) | 3447.62 | 2.35307 | ||||||||
\(130\) | −3.43336 | − | 15.0425i | −0.00231635 | − | 0.0101486i | ||||
\(131\) | 59.0007 | + | 28.4132i | 0.0393505 | + | 0.0189502i | 0.453456 | − | 0.891279i | \(-0.350191\pi\) |
−0.414105 | + | 0.910229i | \(0.635905\pi\) | |||||||
\(132\) | −479.478 | + | 601.246i | −0.316161 | + | 0.396453i | ||||
\(133\) | 720.598 | + | 843.700i | 0.469803 | + | 0.550061i | ||||
\(134\) | 611.872 | + | 767.263i | 0.394460 | + | 0.494638i | ||||
\(135\) | 12.2158 | + | 53.5208i | 0.00778790 | + | 0.0341210i | ||||
\(136\) | −1920.20 | − | 2407.85i | −1.21070 | − | 1.51818i | ||||
\(137\) | 2483.82 | + | 1196.15i | 1.54896 | + | 0.745938i | 0.996174 | − | 0.0873870i | \(-0.0278517\pi\) |
0.552783 | + | 0.833325i | \(0.313566\pi\) | |||||||
\(138\) | −160.933 | + | 201.803i | −0.0992716 | + | 0.124483i | ||||
\(139\) | 1435.89 | − | 691.486i | 0.876189 | − | 0.421950i | 0.0589578 | − | 0.998260i | \(-0.481222\pi\) |
0.817231 | + | 0.576310i | \(0.195508\pi\) | |||||||
\(140\) | −14.0938 | + | 18.9479i | −0.00850815 | + | 0.0114385i | ||||
\(141\) | −4591.03 | − | 2210.92i | −2.74209 | − | 1.32052i | ||||
\(142\) | 1432.82 | − | 690.008i | 0.846755 | − | 0.407776i | ||||
\(143\) | −107.803 | + | 472.317i | −0.0630417 | + | 0.276204i | ||||
\(144\) | 1362.92 | − | 656.347i | 0.788726 | − | 0.379830i | ||||
\(145\) | 33.3583 | + | 41.8299i | 0.0191052 | + | 0.0239572i | ||||
\(146\) | −294.423 | −0.166895 | ||||||||
\(147\) | 808.517 | + | 2692.36i | 0.453642 | + | 1.51063i | ||||
\(148\) | −244.074 | −0.135559 | ||||||||
\(149\) | −1023.05 | − | 1282.86i | −0.562492 | − | 0.705342i | 0.416525 | − | 0.909124i | \(-0.363248\pi\) |
−0.979016 | + | 0.203782i | \(0.934677\pi\) | |||||||
\(150\) | 2158.79 | − | 1039.62i | 1.17510 | − | 0.565896i | ||||
\(151\) | −505.231 | + | 2213.56i | −0.272285 | + | 1.19296i | 0.635022 | + | 0.772494i | \(0.280991\pi\) |
−0.907308 | + | 0.420467i | \(0.861866\pi\) | |||||||
\(152\) | −1329.20 | + | 640.111i | −0.709294 | + | 0.341578i | ||||
\(153\) | 4526.34 | + | 2179.77i | 2.39172 | + | 1.15179i | ||||
\(154\) | −1439.10 | + | 753.729i | −0.753028 | + | 0.394398i | ||||
\(155\) | −99.4380 | + | 47.8868i | −0.0515294 | + | 0.0248152i | ||||
\(156\) | −165.831 | + | 207.946i | −0.0851097 | + | 0.106724i | ||||
\(157\) | −1191.57 | − | 573.831i | −0.605719 | − | 0.291699i | 0.105776 | − | 0.994390i | \(-0.466267\pi\) |
−0.711495 | + | 0.702691i | \(0.751982\pi\) | |||||||
\(158\) | 1391.62 | + | 1745.04i | 0.700705 | + | 0.878656i | ||||
\(159\) | 177.778 | + | 778.894i | 0.0886709 | + | 0.388493i | ||||
\(160\) | −34.4830 | − | 43.2404i | −0.0170383 | − | 0.0213653i | ||||
\(161\) | 220.462 | − | 115.467i | 0.107918 | − | 0.0565220i | ||||
\(162\) | 292.178 | − | 366.380i | 0.141702 | − | 0.177688i | ||||
\(163\) | −1369.93 | − | 659.721i | −0.658287 | − | 0.317015i | 0.0747505 | − | 0.997202i | \(-0.476184\pi\) |
−0.733038 | + | 0.680188i | \(0.761898\pi\) | |||||||
\(164\) | 99.5497 | + | 436.156i | 0.0473995 | + | 0.207671i | ||||
\(165\) | 156.005 | 0.0736058 | ||||||||
\(166\) | 840.788 | 0.393119 | ||||||||
\(167\) | 196.298 | + | 860.038i | 0.0909581 | + | 0.398513i | 0.999828 | − | 0.0185671i | \(-0.00591044\pi\) |
−0.908870 | + | 0.417081i | \(0.863053\pi\) | |||||||
\(168\) | −3735.71 | + | 125.816i | −1.71557 | + | 0.0577791i | ||||
\(169\) | 451.594 | − | 1978.56i | 0.205550 | − | 0.900575i | ||||
\(170\) | −33.1721 | + | 145.337i | −0.0149658 | + | 0.0655695i | ||||
\(171\) | 1500.49 | − | 1881.55i | 0.671023 | − | 0.841437i | ||||
\(172\) | 657.551 | − | 824.543i | 0.291499 | − | 0.365528i | ||||
\(173\) | 344.179 | − | 1507.95i | 0.151257 | − | 0.662700i | −0.841264 | − | 0.540625i | \(-0.818188\pi\) |
0.992521 | − | 0.122075i | \(-0.0389550\pi\) | |||||||
\(174\) | −449.642 | + | 1970.01i | −0.195904 | + | 0.858311i | ||||
\(175\) | −2308.93 | + | 77.7630i | −0.997365 | + | 0.0335905i | ||||
\(176\) | −313.623 | − | 1374.07i | −0.134320 | − | 0.588493i | ||||
\(177\) | −5308.09 | −2.25413 | ||||||||
\(178\) | −408.610 | −0.172060 | ||||||||
\(179\) | 652.476 | + | 2858.68i | 0.272449 | + | 1.19368i | 0.907113 | + | 0.420888i | \(0.138281\pi\) |
−0.634664 | + | 0.772788i | \(0.718861\pi\) | |||||||
\(180\) | 46.1478 | + | 22.2236i | 0.0191092 | + | 0.00920250i | ||||
\(181\) | 1501.79 | − | 1883.18i | 0.616724 | − | 0.773348i | −0.371155 | − | 0.928571i | \(-0.621038\pi\) |
0.987879 | + | 0.155223i | \(0.0496096\pi\) | |||||||
\(182\) | −497.725 | + | 260.683i | −0.202713 | + | 0.106171i | ||||
\(183\) | −1946.32 | − | 2440.61i | −0.786209 | − | 0.985874i | ||||
\(184\) | 73.6341 | + | 322.612i | 0.0295021 | + | 0.129257i | ||||
\(185\) | 30.8710 | + | 38.7110i | 0.0122685 | + | 0.0153843i | ||||
\(186\) | −3755.56 | − | 1808.58i | −1.48049 | − | 0.712966i | ||||
\(187\) | 2918.40 | − | 3659.56i | 1.14125 | − | 1.43109i | ||||
\(188\) | −1404.40 | + | 676.322i | −0.544820 | + | 0.262372i | ||||
\(189\) | 1770.89 | − | 927.501i | 0.681552 | − | 0.356962i | ||||
\(190\) | 64.3394 | + | 30.9842i | 0.0245667 | + | 0.0118307i | ||||
\(191\) | 4185.55 | − | 2015.65i | 1.58563 | − | 0.763600i | 0.586699 | − | 0.809805i | \(-0.300427\pi\) |
0.998932 | + | 0.0462050i | \(0.0147127\pi\) | |||||||
\(192\) | 1014.22 | − | 4443.61i | 0.381226 | − | 1.67026i | ||||
\(193\) | 2400.63 | − | 1156.08i | 0.895342 | − | 0.431174i | 0.0711376 | − | 0.997467i | \(-0.477337\pi\) |
0.824204 | + | 0.566293i | \(0.191623\pi\) | |||||||
\(194\) | 1974.26 | + | 2475.64i | 0.730636 | + | 0.916188i | ||||
\(195\) | 53.9555 | 0.0198145 | ||||||||
\(196\) | 798.118 | + | 320.136i | 0.290859 | + | 0.116668i | ||||
\(197\) | 1234.85 | 0.446598 | 0.223299 | − | 0.974750i | \(-0.428317\pi\) | ||||
0.223299 | + | 0.974750i | \(0.428317\pi\) | |||||||
\(198\) | 2196.94 | + | 2754.87i | 0.788532 | + | 0.988788i | ||||
\(199\) | −2224.23 | + | 1071.13i | −0.792318 | + | 0.381560i | −0.785849 | − | 0.618419i | \(-0.787774\pi\) |
−0.00646926 | + | 0.999979i | \(0.502059\pi\) | |||||||
\(200\) | 683.542 | − | 2994.79i | 0.241668 | − | 1.05882i | ||||
\(201\) | −3091.92 | + | 1488.99i | −1.08501 | + | 0.522513i | ||||
\(202\) | −1977.24 | − | 952.188i | −0.688703 | − | 0.331662i | ||||
\(203\) | 1162.78 | − | 1563.26i | 0.402025 | − | 0.540489i | ||||
\(204\) | 2315.26 | − | 1114.97i | 0.794612 | − | 0.382665i | ||||
\(205\) | 56.5845 | − | 70.9547i | 0.0192782 | − | 0.0241741i | ||||
\(206\) | −1942.94 | − | 935.672i | −0.657142 | − | 0.316463i | ||||
\(207\) | −336.557 | − | 422.029i | −0.113006 | − | 0.141705i | ||||
\(208\) | −108.469 | − | 475.234i | −0.0361585 | − | 0.158421i | ||||
\(209\) | −1398.01 | − | 1753.04i | −0.462690 | − | 0.580194i | ||||
\(210\) | 117.504 | + | 137.578i | 0.0386121 | + | 0.0452084i | ||||
\(211\) | −2024.88 | + | 2539.12i | −0.660657 | + | 0.828438i | −0.993415 | − | 0.114574i | \(-0.963450\pi\) |
0.332757 | + | 0.943012i | \(0.392021\pi\) | |||||||
\(212\) | 220.189 | + | 106.038i | 0.0713333 | + | 0.0343523i | ||||
\(213\) | 1237.48 | + | 5421.76i | 0.398079 | + | 1.74410i | ||||
\(214\) | −1608.33 | −0.513753 | ||||||||
\(215\) | −213.944 | −0.0678643 | ||||||||
\(216\) | 591.476 | + | 2591.42i | 0.186319 | + | 0.816315i | ||||
\(217\) | 2610.17 | + | 3056.08i | 0.816545 | + | 0.956038i | ||||
\(218\) | −943.329 | + | 4133.00i | −0.293075 | + | 1.28404i | ||||
\(219\) | 229.102 | − | 1003.76i | 0.0706909 | − | 0.309717i | ||||
\(220\) | 29.7542 | − | 37.3106i | 0.00911830 | − | 0.0114340i | ||||
\(221\) | 1009.35 | − | 1265.69i | 0.307223 | − | 0.385245i | ||||
\(222\) | −416.116 | + | 1823.12i | −0.125801 | + | 0.551171i | ||||
\(223\) | 528.605 | − | 2315.97i | 0.158735 | − | 0.695465i | −0.831438 | − | 0.555618i | \(-0.812482\pi\) |
0.990173 | − | 0.139847i | \(-0.0446611\pi\) | |||||||
\(224\) | −1201.98 | + | 1615.97i | −0.358531 | + | 0.482015i | ||||
\(225\) | 1115.03 | + | 4885.26i | 0.330379 | + | 1.44748i | ||||
\(226\) | −1441.99 | −0.424424 | ||||||||
\(227\) | 2838.00 | 0.829799 | 0.414900 | − | 0.909867i | \(-0.363817\pi\) | ||||
0.414900 | + | 0.909867i | \(0.363817\pi\) | |||||||
\(228\) | −273.922 | − | 1200.13i | −0.0795653 | − | 0.348599i | ||||
\(229\) | −1608.45 | − | 774.588i | −0.464145 | − | 0.223521i | 0.187170 | − | 0.982327i | \(-0.440068\pi\) |
−0.651316 | + | 0.758807i | \(0.725783\pi\) | |||||||
\(230\) | 9.98673 | − | 12.5230i | 0.00286307 | − | 0.00359017i | ||||
\(231\) | −1449.83 | − | 5492.78i | −0.412951 | − | 1.56450i | ||||
\(232\) | 1615.17 | + | 2025.36i | 0.457075 | + | 0.573154i | ||||
\(233\) | 534.684 | + | 2342.60i | 0.150336 | + | 0.658665i | 0.992787 | + | 0.119892i | \(0.0382548\pi\) |
−0.842451 | + | 0.538773i | \(0.818888\pi\) | |||||||
\(234\) | 759.827 | + | 952.792i | 0.212271 | + | 0.266179i | ||||
\(235\) | 284.898 | + | 137.200i | 0.0790838 | + | 0.0380847i | ||||
\(236\) | −1012.39 | + | 1269.50i | −0.279241 | + | 0.350158i | ||||
\(237\) | −7032.15 | + | 3386.51i | −1.92737 | + | 0.928174i | ||||
\(238\) | 5425.45 | − | 182.725i | 1.47765 | − | 0.0497659i | ||||
\(239\) | −1300.88 | − | 626.471i | −0.352080 | − | 0.169553i | 0.249481 | − | 0.968380i | \(-0.419740\pi\) |
−0.601561 | + | 0.798827i | \(0.705454\pi\) | |||||||
\(240\) | −141.424 | + | 68.1060i | −0.0380369 | + | 0.0183176i | ||||
\(241\) | 69.6937 | − | 305.348i | 0.0186281 | − | 0.0816149i | −0.964759 | − | 0.263133i | \(-0.915244\pi\) |
0.983388 | + | 0.181518i | \(0.0581012\pi\) | |||||||
\(242\) | 147.305 | − | 70.9385i | 0.0391287 | − | 0.0188434i | ||||
\(243\) | 2838.81 | + | 3559.76i | 0.749424 | + | 0.939747i | ||||
\(244\) | −954.917 | −0.250542 | ||||||||
\(245\) | −50.1728 | − | 167.075i | −0.0130834 | − | 0.0435676i | ||||
\(246\) | 3427.60 | 0.888357 | ||||||||
\(247\) | −483.511 | − | 606.304i | −0.124555 | − | 0.156187i | ||||
\(248\) | −4814.69 | + | 2318.63i | −1.23279 | + | 0.593682i | ||||
\(249\) | −654.251 | + | 2866.46i | −0.166512 | + | 0.729536i | ||||
\(250\) | −268.207 | + | 129.162i | −0.0678515 | + | 0.0326756i | ||||
\(251\) | 1442.18 | + | 694.519i | 0.362669 | + | 0.174652i | 0.606339 | − | 0.795206i | \(-0.292637\pi\) |
−0.243671 | + | 0.969858i | \(0.578352\pi\) | |||||||
\(252\) | 353.598 | − | 1831.35i | 0.0883912 | − | 0.457796i | ||||
\(253\) | −453.123 | + | 218.213i | −0.112599 | + | 0.0542249i | ||||
\(254\) | 3431.91 | − | 4303.47i | 0.847783 | − | 1.06309i | ||||
\(255\) | −469.677 | − | 226.185i | −0.115342 | − | 0.0555460i | ||||
\(256\) | −2140.55 | − | 2684.17i | −0.522595 | − | 0.655314i | ||||
\(257\) | −361.984 | − | 1585.96i | −0.0878597 | − | 0.384938i | 0.911811 | − | 0.410611i | \(-0.134684\pi\) |
−0.999670 | + | 0.0256723i | \(0.991827\pi\) | |||||||
\(258\) | −5037.91 | − | 6317.34i | −1.21569 | − | 1.52442i | ||||
\(259\) | 1076.08 | − | 1446.70i | 0.258163 | − | 0.347079i | ||||
\(260\) | 10.2907 | − | 12.9041i | 0.00245462 | − | 0.00307800i | ||||
\(261\) | −3807.33 | − | 1833.51i | −0.902942 | − | 0.434834i | ||||
\(262\) | −34.1523 | − | 149.631i | −0.00805319 | − | 0.0352833i | ||||
\(263\) | 2602.75 | 0.610236 | 0.305118 | − | 0.952314i | \(-0.401304\pi\) | ||||
0.305118 | + | 0.952314i | \(0.401304\pi\) | |||||||
\(264\) | 7553.60 | 1.76095 | ||||||||
\(265\) | −11.0321 | − | 48.3346i | −0.00255733 | − | 0.0112044i | ||||
\(266\) | 492.988 | − | 2553.28i | 0.113635 | − | 0.588540i | ||||
\(267\) | 317.956 | − | 1393.06i | 0.0728786 | − | 0.319302i | ||||
\(268\) | −233.598 | + | 1023.46i | −0.0532436 | + | 0.233275i | ||||
\(269\) | −4345.33 | + | 5448.88i | −0.984906 | + | 1.23503i | −0.0129390 | + | 0.999916i | \(0.504119\pi\) |
−0.971967 | + | 0.235117i | \(0.924453\pi\) | |||||||
\(270\) | 80.2197 | − | 100.592i | 0.0180815 | − | 0.0226735i | ||||
\(271\) | −925.977 | + | 4056.97i | −0.207561 | + | 0.909385i | 0.758623 | + | 0.651530i | \(0.225873\pi\) |
−0.966184 | + | 0.257854i | \(0.916984\pi\) | |||||||
\(272\) | −1048.00 | + | 4591.57i | −0.233618 | + | 1.02355i | ||||
\(273\) | −501.434 | − | 1899.72i | −0.111166 | − | 0.421159i | ||||
\(274\) | −1437.75 | − | 6299.19i | −0.316998 | − | 1.38886i | ||||
\(275\) | 4668.66 | 1.02375 | ||||||||
\(276\) | −276.110 | −0.0602169 | ||||||||
\(277\) | −1303.68 | − | 5711.77i | −0.282781 | − | 1.23894i | −0.894211 | − | 0.447645i | \(-0.852263\pi\) |
0.611431 | − | 0.791298i | \(-0.290594\pi\) | |||||||
\(278\) | −3365.28 | − | 1620.63i | −0.726029 | − | 0.349637i | ||||
\(279\) | 5435.11 | − | 6815.42i | 1.16628 | − | 1.46247i | ||||
\(280\) | 231.821 | − | 7.80754i | 0.0494784 | − | 0.00166639i | ||||
\(281\) | −346.731 | − | 434.788i | −0.0736095 | − | 0.0923034i | 0.743663 | − | 0.668554i | \(-0.233087\pi\) |
−0.817273 | + | 0.576251i | \(0.804515\pi\) | |||||||
\(282\) | 2657.49 | + | 11643.2i | 0.561175 | + | 2.45867i | ||||
\(283\) | 1340.23 | + | 1680.59i | 0.281513 | + | 0.353006i | 0.902404 | − | 0.430891i | \(-0.141801\pi\) |
−0.620891 | + | 0.783897i | \(0.713229\pi\) | |||||||
\(284\) | 1532.70 | + | 738.110i | 0.320243 | + | 0.154221i | ||||
\(285\) | −155.698 | + | 195.239i | −0.0323606 | + | 0.0405789i | ||||
\(286\) | 1022.99 | − | 492.647i | 0.211506 | − | 0.101856i | ||||
\(287\) | −3024.11 | − | 1332.87i | −0.621978 | − | 0.274135i | ||||
\(288\) | 3935.71 | + | 1895.34i | 0.805256 | + | 0.387791i | ||||
\(289\) | −9665.67 | + | 4654.74i | −1.96737 | + | 0.947433i | ||||
\(290\) | 27.9027 | − | 122.250i | 0.00565001 | − | 0.0247543i | ||||
\(291\) | −9976.33 | + | 4804.35i | −2.00970 | + | 0.967821i | ||||
\(292\) | −196.367 | − | 246.236i | −0.0393545 | − | 0.0493490i | ||||
\(293\) | 5583.29 | 1.11324 | 0.556620 | − | 0.830767i | \(-0.312098\pi\) | ||||
0.556620 | + | 0.830767i | \(0.312098\pi\) | |||||||
\(294\) | 3751.96 | − | 5415.78i | 0.744281 | − | 1.07434i | ||||
\(295\) | 329.395 | 0.0650106 | ||||||||
\(296\) | 1494.74 | + | 1874.35i | 0.293514 | + | 0.368055i | ||||
\(297\) | −3639.77 | + | 1752.82i | −0.711114 | + | 0.342455i | ||||
\(298\) | −855.733 | + | 3749.21i | −0.166347 | + | 0.728812i | ||||
\(299\) | −156.716 | + | 75.4705i | −0.0303114 | + | 0.0145972i | ||||
\(300\) | 2309.28 | + | 1112.09i | 0.444422 | + | 0.214022i | ||||
\(301\) | 1988.28 | + | 7532.75i | 0.380740 | + | 1.44246i | ||||
\(302\) | 4794.36 | − | 2308.84i | 0.913524 | − | 0.439930i | ||||
\(303\) | 4784.82 | − | 5999.98i | 0.907198 | − | 1.13759i | ||||
\(304\) | 2032.65 | + | 978.875i | 0.383489 | + | 0.184679i | ||||
\(305\) | 120.780 | + | 151.453i | 0.0226748 | + | 0.0284333i | ||||
\(306\) | −2620.05 | − | 11479.2i | −0.489472 | − | 2.14452i | ||||
\(307\) | −4641.84 | − | 5820.68i | −0.862943 | − | 1.08210i | −0.995854 | − | 0.0909685i | \(-0.971004\pi\) |
0.132911 | − | 0.991128i | \(-0.457568\pi\) | |||||||
\(308\) | −1590.19 | − | 700.871i | −0.294186 | − | 0.129662i | ||||
\(309\) | 4701.82 | − | 5895.90i | 0.865623 | − | 1.08546i | ||||
\(310\) | 233.053 | + | 112.232i | 0.0426984 | + | 0.0205624i | ||||
\(311\) | −1179.03 | − | 5165.69i | −0.214974 | − | 0.941863i | −0.961131 | − | 0.276093i | \(-0.910960\pi\) |
0.746157 | − | 0.665770i | \(-0.231897\pi\) | |||||||
\(312\) | 2612.47 | 0.474045 | ||||||||
\(313\) | −3197.95 | −0.577504 | −0.288752 | − | 0.957404i | \(-0.593240\pi\) | ||||
−0.288752 | + | 0.957404i | \(0.593240\pi\) | |||||||
\(314\) | 689.736 | + | 3021.93i | 0.123962 | + | 0.543113i | ||||
\(315\) | −335.183 | + | 175.551i | −0.0599536 | + | 0.0314006i | ||||
\(316\) | −531.288 | + | 2327.72i | −0.0945799 | + | 0.414382i | ||||
\(317\) | 841.840 | − | 3688.34i | 0.149156 | − | 0.653495i | −0.843965 | − | 0.536399i | \(-0.819784\pi\) |
0.993121 | − | 0.117096i | \(-0.0373586\pi\) | |||||||
\(318\) | 1167.45 | − | 1463.93i | 0.205872 | − | 0.258155i | ||||
\(319\) | −2454.81 | + | 3078.23i | −0.430855 | + | 0.540276i | ||||
\(320\) | −62.9380 | + | 275.750i | −0.0109948 | + | 0.0481715i | ||||
\(321\) | 1251.51 | − | 5483.21i | 0.217608 | − | 0.953404i | ||||
\(322\) | −533.733 | − | 235.241i | −0.0923720 | − | 0.0407127i | ||||
\(323\) | 1667.26 | + | 7304.72i | 0.287209 | + | 1.25835i | ||||
\(324\) | 501.286 | 0.0859544 | ||||||||
\(325\) | 1614.69 | 0.275591 | ||||||||
\(326\) | 792.975 | + | 3474.25i | 0.134720 | + | 0.590248i | ||||
\(327\) | −13356.4 | − | 6432.10i | −2.25875 | − | 1.08776i | ||||
\(328\) | 2739.76 | − | 3435.56i | 0.461214 | − | 0.578344i | ||||
\(329\) | 2182.97 | − | 11306.0i | 0.365809 | − | 1.89460i | ||||
\(330\) | −227.965 | − | 285.860i | −0.0380275 | − | 0.0476850i | ||||
\(331\) | 2575.97 | + | 11286.1i | 0.427759 | + | 1.87414i | 0.482930 | + | 0.875659i | \(0.339573\pi\) |
−0.0551709 | + | 0.998477i | \(0.517570\pi\) | |||||||
\(332\) | 560.768 | + | 703.181i | 0.0926992 | + | 0.116241i | ||||
\(333\) | −3523.44 | − | 1696.80i | −0.579830 | − | 0.279232i | ||||
\(334\) | 1289.07 | − | 1616.44i | 0.211182 | − | 0.264813i | ||||
\(335\) | 191.870 | − | 92.3998i | 0.0312925 | − | 0.0150697i | ||||
\(336\) | 3712.26 | + | 4346.45i | 0.602740 | + | 0.705709i | ||||
\(337\) | 7035.45 | + | 3388.10i | 1.13723 | + | 0.547660i | 0.905173 | − | 0.425043i | \(-0.139741\pi\) |
0.232054 | + | 0.972703i | \(0.425455\pi\) | |||||||
\(338\) | −4285.37 | + | 2063.73i | −0.689626 | + | 0.332106i | ||||
\(339\) | 1122.07 | − | 4916.12i | 0.179772 | − | 0.787631i | ||||
\(340\) | −143.675 | + | 69.1900i | −0.0229172 | + | 0.0110363i | ||||
\(341\) | −5063.91 | − | 6349.94i | −0.804182 | − | 1.00841i | ||||
\(342\) | −5640.32 | −0.891795 | ||||||||
\(343\) | −5416.29 | + | 3319.25i | −0.852630 | + | 0.522515i | ||||
\(344\) | −10358.9 | −1.62359 | ||||||||
\(345\) | 34.9229 | + | 43.7919i | 0.00544981 | + | 0.00683385i | ||||
\(346\) | −3266.07 | + | 1572.85i | −0.507471 | + | 0.244385i | ||||
\(347\) | −265.526 | + | 1163.35i | −0.0410783 | + | 0.179976i | −0.991305 | − | 0.131583i | \(-0.957994\pi\) |
0.950227 | + | 0.311559i | \(0.100851\pi\) | |||||||
\(348\) | −1947.48 | + | 937.858i | −0.299988 | + | 0.144467i | ||||
\(349\) | 9346.38 | + | 4500.98i | 1.43353 | + | 0.690349i | 0.979650 | − | 0.200716i | \(-0.0643267\pi\) |
0.453876 | + | 0.891065i | \(0.350041\pi\) | |||||||
\(350\) | 3516.47 | + | 4117.20i | 0.537038 | + | 0.628782i | ||||
\(351\) | −1258.84 | + | 606.226i | −0.191430 | + | 0.0921880i | ||||
\(352\) | 2537.58 | − | 3182.02i | 0.384243 | − | 0.481825i | ||||
\(353\) | 5954.96 | + | 2867.76i | 0.897876 | + | 0.432394i | 0.825121 | − | 0.564955i | \(-0.191107\pi\) |
0.0727549 | + | 0.997350i | \(0.476821\pi\) | |||||||
\(354\) | 7756.55 | + | 9726.41i | 1.16457 | + | 1.46032i | ||||
\(355\) | −76.7923 | − | 336.449i | −0.0114809 | − | 0.0503010i | ||||
\(356\) | −272.525 | − | 341.735i | −0.0405724 | − | 0.0508762i | ||||
\(357\) | −3598.81 | + | 18638.9i | −0.533527 | + | 2.76324i | ||||
\(358\) | 4284.74 | − | 5372.89i | 0.632557 | − | 0.793202i | ||||
\(359\) | −656.739 | − | 316.269i | −0.0965497 | − | 0.0464959i | 0.384986 | − | 0.922923i | \(-0.374206\pi\) |
−0.481535 | + | 0.876427i | \(0.659921\pi\) | |||||||
\(360\) | −111.951 | − | 490.488i | −0.0163898 | − | 0.0718083i | ||||
\(361\) | −3269.81 | −0.476719 | ||||||||
\(362\) | −5645.22 | −0.819631 | ||||||||
\(363\) | 127.223 | + | 557.401i | 0.0183953 | + | 0.0805950i | ||||
\(364\) | −549.979 | − | 242.401i | −0.0791943 | − | 0.0349046i | ||||
\(365\) | −14.2170 | + | 62.2889i | −0.00203878 | + | 0.00893247i | ||||
\(366\) | −1628.01 | + | 7132.78i | −0.232507 | + | 1.01868i | ||||
\(367\) | 5932.66 | − | 7439.32i | 0.843821 | − | 1.05812i | −0.153725 | − | 0.988114i | \(-0.549127\pi\) |
0.997547 | − | 0.0700047i | \(-0.0223014\pi\) | |||||||
\(368\) | 315.507 | − | 395.634i | 0.0446928 | − | 0.0560430i | ||||
\(369\) | −1595.05 | + | 6988.39i | −0.225028 | + | 0.985911i | ||||
\(370\) | 25.8222 | − | 113.134i | 0.00362820 | − | 0.0158962i | ||||
\(371\) | −1599.29 | + | 837.625i | −0.223803 | + | 0.117216i | ||||
\(372\) | −992.208 | − | 4347.15i | −0.138289 | − | 0.605885i | ||||
\(373\) | −353.047 | −0.0490083 | −0.0245041 | − | 0.999700i | \(-0.507801\pi\) | ||||
−0.0245041 | + | 0.999700i | \(0.507801\pi\) | |||||||
\(374\) | −10970.3 | −1.51673 | ||||||||
\(375\) | −231.642 | − | 1014.89i | −0.0318985 | − | 0.139757i | ||||
\(376\) | 13794.5 | + | 6643.07i | 1.89201 | + | 0.911143i | ||||
\(377\) | −849.014 | + | 1064.63i | −0.115985 | + | 0.145441i | ||||
\(378\) | −4287.28 | − | 1889.61i | −0.583370 | − | 0.257119i | ||||
\(379\) | 836.559 | + | 1049.01i | 0.113380 | + | 0.142174i | 0.835283 | − | 0.549820i | \(-0.185304\pi\) |
−0.721903 | + | 0.691994i | \(0.756732\pi\) | |||||||
\(380\) | 16.9983 | + | 74.4744i | 0.00229472 | + | 0.0100538i | ||||
\(381\) | 12001.1 | + | 15048.9i | 1.61374 | + | 2.02357i | ||||
\(382\) | −9809.66 | − | 4724.08i | −1.31389 | − | 0.632736i | ||||
\(383\) | 1033.11 | − | 1295.48i | 0.137832 | − | 0.172836i | −0.708125 | − | 0.706087i | \(-0.750459\pi\) |
0.845957 | + | 0.533251i | \(0.179030\pi\) | |||||||
\(384\) | −3200.55 | + | 1541.30i | −0.425331 | + | 0.204829i | ||||
\(385\) | 89.9697 | + | 340.857i | 0.0119098 | + | 0.0451212i | ||||
\(386\) | −5626.34 | − | 2709.50i | −0.741900 | − | 0.357280i | ||||
\(387\) | 15224.6 | − | 7331.78i | 1.99977 | − | 0.963037i | ||||
\(388\) | −753.724 | + | 3302.28i | −0.0986199 | + | 0.432082i | ||||
\(389\) | 2519.00 | − | 1213.08i | 0.328324 | − | 0.158113i | −0.262458 | − | 0.964943i | \(-0.584533\pi\) |
0.590783 | + | 0.806831i | \(0.298819\pi\) | |||||||
\(390\) | −78.8436 | − | 98.8667i | −0.0102369 | − | 0.0128367i | ||||
\(391\) | 1680.58 | 0.217367 | ||||||||
\(392\) | −2429.32 | − | 8089.63i | −0.313008 | − | 1.04232i | ||||
\(393\) | 536.705 | 0.0688885 | ||||||||
\(394\) | −1804.46 | − | 2262.72i | −0.230729 | − | 0.289325i | ||||
\(395\) | 436.383 | − | 210.151i | 0.0555868 | − | 0.0267692i | ||||
\(396\) | −838.738 | + | 3674.75i | −0.106435 | + | 0.466321i | ||||
\(397\) | 2680.07 | − | 1290.65i | 0.338813 | − | 0.163164i | −0.256739 | − | 0.966481i | \(-0.582648\pi\) |
0.595551 | + | 0.803317i | \(0.296934\pi\) | |||||||
\(398\) | 5212.91 | + | 2510.41i | 0.656532 | + | 0.316169i | ||||
\(399\) | 8321.17 | + | 3667.53i | 1.04406 | + | 0.460166i | ||||
\(400\) | −4232.29 | + | 2038.17i | −0.529037 | + | 0.254771i | ||||
\(401\) | 5030.78 | − | 6308.40i | 0.626497 | − | 0.785602i | −0.362745 | − | 0.931888i | \(-0.618161\pi\) |
0.989242 | + | 0.146286i | \(0.0467320\pi\) | |||||||
\(402\) | 7246.52 | + | 3489.74i | 0.899063 | + | 0.432966i | ||||
\(403\) | −1751.39 | − | 2196.18i | −0.216484 | − | 0.271462i | ||||
\(404\) | −522.381 | − | 2288.70i | −0.0643303 | − | 0.281850i | ||||
\(405\) | −63.4036 | − | 79.5056i | −0.00777914 | − | 0.00975473i | ||||
\(406\) | −4563.61 | + | 153.699i | −0.557853 | + | 0.0187880i | ||||
\(407\) | −2271.77 | + | 2848.71i | −0.276677 | + | 0.346942i | ||||
\(408\) | −22741.3 | − | 10951.6i | −2.75947 | − | 1.32889i | ||||
\(409\) | −1697.77 | − | 7438.42i | −0.205255 | − | 0.899281i | −0.967675 | − | 0.252199i | \(-0.918846\pi\) |
0.762420 | − | 0.647082i | \(-0.224011\pi\) | |||||||
\(410\) | −212.701 | −0.0256209 | ||||||||
\(411\) | 22594.3 | 2.71167 | ||||||||
\(412\) | −513.320 | − | 2249.00i | −0.0613822 | − | 0.268933i | ||||
\(413\) | −3061.23 | − | 11597.7i | −0.364730 | − | 1.38180i | ||||
\(414\) | −281.515 | + | 1233.40i | −0.0334196 | + | 0.146421i | ||||
\(415\) | 40.5998 | − | 177.879i | 0.00480232 | − | 0.0210404i | ||||
\(416\) | 877.641 | − | 1100.53i | 0.103437 | − | 0.129706i | ||||
\(417\) | 8143.82 | − | 10212.0i | 0.956366 | − | 1.19924i | ||||
\(418\) | −1169.37 | + | 5123.35i | −0.136832 | + | 0.599500i | ||||
\(419\) | −2581.08 | + | 11308.4i | −0.300940 | + | 1.31851i | 0.567771 | + | 0.823187i | \(0.307806\pi\) |
−0.868711 | + | 0.495319i | \(0.835051\pi\) | |||||||
\(420\) | −36.6912 | + | 190.031i | −0.00426273 | + | 0.0220775i | ||||
\(421\) | −445.909 | − | 1953.65i | −0.0516206 | − | 0.226165i | 0.942537 | − | 0.334101i | \(-0.108433\pi\) |
−0.994158 | + | 0.107937i | \(0.965576\pi\) | |||||||
\(422\) | 7611.53 | 0.878018 | ||||||||
\(423\) | −24975.6 | −2.87082 | ||||||||
\(424\) | −534.161 | − | 2340.31i | −0.0611820 | − | 0.268056i | ||||
\(425\) | −14055.7 | − | 6768.89i | −1.60424 | − | 0.772563i | ||||
\(426\) | 8126.40 | − | 10190.2i | 0.924238 | − | 1.15896i | ||||
\(427\) | 4210.05 | − | 5660.06i | 0.477139 | − | 0.641474i | ||||
\(428\) | −1072.68 | − | 1345.10i | −0.121145 | − | 0.151911i | ||||
\(429\) | 883.528 | + | 3870.99i | 0.0994339 | + | 0.435648i | ||||
\(430\) | 312.630 | + | 392.025i | 0.0350612 | + | 0.0439654i | ||||
\(431\) | 2866.48 | + | 1380.43i | 0.320356 | + | 0.154276i | 0.587150 | − | 0.809478i | \(-0.300250\pi\) |
−0.266794 | + | 0.963754i | \(0.585964\pi\) | |||||||
\(432\) | 2534.35 | − | 3177.98i | 0.282255 | − | 0.353937i | ||||
\(433\) | −5583.54 | + | 2688.89i | −0.619695 | + | 0.298429i | −0.717266 | − | 0.696799i | \(-0.754607\pi\) |
0.0975712 | + | 0.995229i | \(0.468893\pi\) | |||||||
\(434\) | 1785.72 | − | 9248.58i | 0.197505 | − | 1.02292i | ||||
\(435\) | 395.068 | + | 190.255i | 0.0435450 | + | 0.0209702i | ||||
\(436\) | −4085.73 | + | 1967.58i | −0.448787 | + | 0.216124i | ||||
\(437\) | 179.140 | − | 784.865i | 0.0196097 | − | 0.0859158i | ||||
\(438\) | −2174.05 | + | 1046.97i | −0.237170 | + | 0.114215i | ||||
\(439\) | 2908.86 | + | 3647.60i | 0.316247 | + | 0.396561i | 0.914394 | − | 0.404825i | \(-0.132668\pi\) |
−0.598147 | + | 0.801386i | \(0.704096\pi\) | |||||||
\(440\) | −468.741 | −0.0507872 | ||||||||
\(441\) | 9296.01 | + | 10170.0i | 1.00378 | + | 1.09815i | ||||
\(442\) | −3794.15 | −0.408301 | ||||||||
\(443\) | −8139.18 | − | 10206.2i | −0.872921 | − | 1.09461i | −0.994778 | − | 0.102061i | \(-0.967456\pi\) |
0.121857 | − | 0.992548i | \(-0.461115\pi\) | |||||||
\(444\) | −1802.27 | + | 867.928i | −0.192640 | + | 0.0927704i | ||||
\(445\) | −19.7309 | + | 86.4466i | −0.00210187 | + | 0.00920891i | ||||
\(446\) | −5016.16 | + | 2415.66i | −0.532561 | + | 0.256468i | ||||
\(447\) | −12116.1 | − | 5834.83i | −1.28204 | − | 0.617400i | ||||
\(448\) | 10293.8 | − | 346.687i | 1.08557 | − | 0.0365612i | ||||
\(449\) | −12418.4 | + | 5980.41i | −1.30526 | + | 0.628581i | −0.951757 | − | 0.306852i | \(-0.900724\pi\) |
−0.353504 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(450\) | 7322.27 | − | 9181.84i | 0.767056 | − | 0.961858i | ||||
\(451\) | 6017.16 | + | 2897.71i | 0.628242 | + | 0.302545i | ||||
\(452\) | −961.745 | − | 1205.99i | −0.100081 | − | 0.125498i | ||||
\(453\) | 4140.74 | + | 18141.8i | 0.429468 | + | 1.88162i | ||||
\(454\) | −4147.08 | − | 5200.28i | −0.428705 | − | 0.537580i | ||||
\(455\) | 31.1167 | + | 117.888i | 0.00320609 | + | 0.0121465i | ||||
\(456\) | −7538.75 | + | 9453.30i | −0.774198 | + | 0.970814i | ||||
\(457\) | 1000.97 | + | 482.042i | 0.102458 | + | 0.0493413i | 0.484411 | − | 0.874841i | \(-0.339034\pi\) |
−0.381953 | + | 0.924182i | \(0.624748\pi\) | |||||||
\(458\) | 931.043 | + | 4079.17i | 0.0949887 | + | 0.416172i | ||||
\(459\) | 13499.4 | 1.37277 | ||||||||
\(460\) | 17.1341 | 0.00173670 | ||||||||
\(461\) | 1151.87 | + | 5046.67i | 0.116373 | + | 0.509863i | 0.999194 | + | 0.0401526i | \(0.0127844\pi\) |
−0.882821 | + | 0.469710i | \(0.844358\pi\) | |||||||
\(462\) | −7946.25 | + | 10683.1i | −0.800201 | + | 1.07580i | ||||
\(463\) | 1307.35 | − | 5727.87i | 0.131226 | − | 0.574939i | −0.865969 | − | 0.500097i | \(-0.833298\pi\) |
0.997195 | − | 0.0748419i | \(-0.0238452\pi\) | |||||||
\(464\) | 881.521 | − | 3862.20i | 0.0881974 | − | 0.386418i | ||||
\(465\) | −563.976 | + | 707.203i | −0.0562446 | + | 0.0705285i | ||||
\(466\) | 3511.21 | − | 4402.92i | 0.349042 | − | 0.437685i | ||||
\(467\) | 444.656 | − | 1948.17i | 0.0440605 | − | 0.193042i | −0.948108 | − | 0.317948i | \(-0.897006\pi\) |
0.992168 | + | 0.124907i | \(0.0398632\pi\) | |||||||
\(468\) | −290.084 | + | 1270.94i | −0.0286520 | + | 0.125532i | ||||
\(469\) | −5036.45 | − | 5896.85i | −0.495867 | − | 0.580578i | ||||
\(470\) | −164.912 | − | 722.526i | −0.0161847 | − | 0.0709098i | ||||
\(471\) | −10839.2 | −1.06040 | ||||||||
\(472\) | 15949.0 | 1.55532 | ||||||||
\(473\) | −3503.35 | − | 15349.2i | −0.340559 | − | 1.49209i | ||||
\(474\) | 16481.2 | + | 7936.94i | 1.59706 | + | 0.769105i | ||||
\(475\) | −4659.48 | + | 5842.81i | −0.450088 | + | 0.564392i | ||||
\(476\) | 3771.35 | + | 4415.63i | 0.363150 | + | 0.425189i | ||||
\(477\) | 2441.47 | + | 3061.51i | 0.234355 | + | 0.293872i | ||||
\(478\) | 753.009 | + | 3299.15i | 0.0720540 | + | 0.315689i | ||||
\(479\) | −7189.42 | − | 9015.25i | −0.685789 | − | 0.859952i | 0.310084 | − | 0.950709i | \(-0.399643\pi\) |
−0.995873 | + | 0.0907569i | \(0.971071\pi\) | |||||||
\(480\) | −408.389 | − | 196.670i | −0.0388340 | − | 0.0187015i | ||||
\(481\) | −785.709 | + | 985.248i | −0.0744807 | + | 0.0933959i | ||||
\(482\) | −661.354 | + | 318.491i | −0.0624976 | + | 0.0300972i | ||||
\(483\) | 1217.32 | − | 1636.58i | 0.114679 | − | 0.154176i | ||||
\(484\) | 157.574 | + | 75.8838i | 0.0147985 | + | 0.00712658i | ||||
\(485\) | 619.085 | − | 298.136i | 0.0579612 | − | 0.0279127i | ||||
\(486\) | 2374.54 | − | 10403.5i | 0.221628 | − | 0.971017i | ||||
\(487\) | 1569.12 | − | 755.646i | 0.146003 | − | 0.0703113i | −0.359456 | − | 0.933162i | \(-0.617038\pi\) |
0.505459 | + | 0.862851i | \(0.331323\pi\) | |||||||
\(488\) | 5848.03 | + | 7333.20i | 0.542475 | + | 0.680242i | ||||
\(489\) | −12461.7 | −1.15242 | ||||||||
\(490\) | −232.829 | + | 336.078i | −0.0214656 | + | 0.0309846i | ||||
\(491\) | 12623.9 | 1.16030 | 0.580152 | − | 0.814508i | \(-0.302993\pi\) | ||||
0.580152 | + | 0.814508i | \(0.302993\pi\) | |||||||
\(492\) | 2286.06 | + | 2866.62i | 0.209478 | + | 0.262678i | ||||
\(493\) | 11853.6 | − | 5708.38i | 1.08288 | − | 0.521486i | ||||
\(494\) | −404.436 | + | 1771.95i | −0.0368349 | + | 0.161384i | ||||
\(495\) | 688.912 | − | 331.763i | 0.0625542 | − | 0.0301245i | ||||
\(496\) | 7362.75 | + | 3545.71i | 0.666527 | + | 0.320982i | ||||
\(497\) | −11132.4 | + | 5830.57i | −1.00474 | + | 0.526231i | ||||
\(498\) | 6208.47 | − | 2989.84i | 0.558651 | − | 0.269032i | ||||
\(499\) | −5972.25 | + | 7488.97i | −0.535781 | + | 0.671848i | −0.973876 | − | 0.227081i | \(-0.927082\pi\) |
0.438095 | + | 0.898929i | \(0.355653\pi\) | |||||||
\(500\) | −286.904 | − | 138.166i | −0.0256615 | − | 0.0123579i | ||||
\(501\) | 4507.78 | + | 5652.58i | 0.401982 | + | 0.504069i | ||||
\(502\) | −834.801 | − | 3657.50i | −0.0742211 | − | 0.325184i | ||||
\(503\) | 9712.22 | + | 12178.7i | 0.860927 | + | 1.07957i | 0.996055 | + | 0.0887404i | \(0.0282842\pi\) |
−0.135128 | + | 0.990828i | \(0.543144\pi\) | |||||||
\(504\) | −16229.2 | + | 8500.02i | −1.43434 | + | 0.751232i | ||||
\(505\) | −296.924 | + | 372.331i | −0.0261642 | + | 0.0328089i | ||||
\(506\) | 1061.98 | + | 511.424i | 0.0933022 | + | 0.0449320i | ||||
\(507\) | −3701.15 | − | 16215.8i | −0.324209 | − | 1.42045i | ||||
\(508\) | 5888.08 | 0.514254 | ||||||||
\(509\) | 3010.35 | 0.262144 | 0.131072 | − | 0.991373i | \(-0.458158\pi\) | ||||
0.131072 | + | 0.991373i | \(0.458158\pi\) | |||||||
\(510\) | 271.870 | + | 1191.14i | 0.0236051 | + | 0.103421i | ||||
\(511\) | 2325.26 | − | 78.3128i | 0.201298 | − | 0.00677956i | ||||
\(512\) | −2562.07 | + | 11225.1i | −0.221149 | + | 0.968918i | ||||
\(513\) | 1438.97 | − | 6304.53i | 0.123844 | − | 0.542596i | ||||
\(514\) | −2377.11 | + | 2980.80i | −0.203988 | + | 0.255793i | ||||
\(515\) | −291.773 | + | 365.872i | −0.0249652 | + | 0.0313054i | ||||
\(516\) | 1923.36 | − | 8426.77i | 0.164091 | − | 0.718930i | ||||
\(517\) | −5178.03 | + | 22686.4i | −0.440482 | + | 1.92988i | ||||
\(518\) | −4223.33 | + | 142.239i | −0.358229 | + | 0.0120649i | ||||
\(519\) | −2820.81 | − | 12358.8i | −0.238573 | − | 1.04526i | ||||
\(520\) | −162.118 | −0.0136718 | ||||||||
\(521\) | 1065.01 | 0.0895567 | 0.0447784 | − | 0.998997i | \(-0.485742\pi\) | ||||
0.0447784 | + | 0.998997i | \(0.485742\pi\) | |||||||
\(522\) | 2203.86 | + | 9655.72i | 0.184790 | + | 0.809616i | ||||
\(523\) | −4202.52 | − | 2023.83i | −0.351364 | − | 0.169208i | 0.249873 | − | 0.968279i | \(-0.419611\pi\) |
−0.601237 | + | 0.799071i | \(0.705325\pi\) | |||||||
\(524\) | 102.364 | − | 128.360i | 0.00853392 | − | 0.0107012i | ||||
\(525\) | −16772.9 | + | 8784.78i | −1.39434 | + | 0.730284i | ||||
\(526\) | −3803.32 | − | 4769.21i | −0.315271 | − | 0.395337i | ||||
\(527\) | 6039.19 | + | 26459.4i | 0.499187 | + | 2.18708i | ||||
\(528\) | −7202.04 | − | 9031.07i | −0.593614 | − | 0.744369i | ||||
\(529\) | 10799.4 | + | 5200.72i | 0.887598 | + | 0.427444i | ||||
\(530\) | −72.4463 | + | 90.8448i | −0.00593748 | + | 0.00744537i | ||||
\(531\) | −23440.3 | + | 11288.3i | −1.91568 | + | 0.922541i | ||||
\(532\) | 2464.20 | − | 1290.62i | 0.200821 | − | 0.105180i | ||||
\(533\) | 2081.08 | + | 1002.20i | 0.169121 | + | 0.0814445i | ||||
\(534\) | −3017.22 | + | 1453.02i | −0.244509 | + | 0.117750i | ||||
\(535\) | −77.6626 | + | 340.262i | −0.00627598 | + | 0.0274969i | ||||
\(536\) | 9290.16 | − | 4473.90i | 0.748645 | − | 0.360528i | ||||
\(537\) | 14983.4 | + | 18788.6i | 1.20407 | + | 1.50985i | ||||
\(538\) | 16334.1 | 1.30895 | ||||||||
\(539\) | 11165.1 | − | 6335.49i | 0.892236 | − | 0.506288i | ||||
\(540\) | 137.632 | 0.0109680 | ||||||||
\(541\) | −702.598 | − | 881.030i | −0.0558356 | − | 0.0700156i | 0.753130 | − | 0.657872i | \(-0.228543\pi\) |
−0.808965 | + | 0.587857i | \(0.799972\pi\) | |||||||
\(542\) | 8787.00 | − | 4231.59i | 0.696372 | − | 0.335355i | ||||
\(543\) | 4392.78 | − | 19246.0i | 0.347168 | − | 1.52104i | ||||
\(544\) | −12253.3 | + | 5900.86i | −0.965724 | + | 0.465068i | ||||
\(545\) | 828.836 | + | 399.146i | 0.0651439 | + | 0.0313717i | ||||
\(546\) | −2748.27 | + | 3694.82i | −0.215412 | + | 0.289604i | ||||
\(547\) | −7581.27 | + | 3650.94i | −0.592599 | + | 0.285380i | −0.706049 | − | 0.708163i | \(-0.749524\pi\) |
0.113450 | + | 0.993544i | \(0.463810\pi\) | |||||||
\(548\) | 4309.32 | − | 5403.72i | 0.335922 | − | 0.421232i | ||||
\(549\) | −13785.1 | − | 6638.57i | −1.07165 | − | 0.516079i | ||||
\(550\) | −6822.18 | − | 8554.74i | −0.528907 | − | 0.663228i | ||||
\(551\) | −1402.41 | − | 6144.36i | −0.108430 | − | 0.475061i | ||||
\(552\) | 1690.93 | + | 2120.36i | 0.130382 | + | 0.163494i | ||||
\(553\) | −11454.7 | − | 13411.6i | −0.880840 | − | 1.03132i | ||||
\(554\) | −8561.09 | + | 10735.3i | −0.656545 | + | 0.823282i | ||||
\(555\) | 365.611 | + | 176.069i | 0.0279627 | + | 0.0134661i | ||||
\(556\) | −889.098 | − | 3895.40i | −0.0678169 | − | 0.297125i | ||||
\(557\) | −7064.06 | −0.537367 | −0.268684 | − | 0.963228i | \(-0.586589\pi\) | ||||
−0.268684 | + | 0.963228i | \(0.586589\pi\) | |||||||
\(558\) | −20430.6 | −1.54999 | ||||||||
\(559\) | −1211.66 | − | 5308.64i | −0.0916777 | − | 0.401666i | ||||
\(560\) | −230.366 | − | 269.720i | −0.0173835 | − | 0.0203531i | ||||
\(561\) | 8536.40 | − | 37400.4i | 0.642437 | − | 2.81470i | ||||
\(562\) | −290.026 | + | 1270.69i | −0.0217687 | + | 0.0953748i | ||||
\(563\) | −8341.32 | + | 10459.7i | −0.624413 | + | 0.782990i | −0.988958 | − | 0.148196i | \(-0.952653\pi\) |
0.364545 | + | 0.931186i | \(0.381225\pi\) | |||||||
\(564\) | −7965.23 | + | 9988.08i | −0.594675 | + | 0.745699i | ||||
\(565\) | −69.6306 | + | 305.072i | −0.00518475 | + | 0.0227159i | ||||
\(566\) | 1121.04 | − | 4911.59i | 0.0832523 | − | 0.364752i | ||||
\(567\) | −2210.08 | + | 2971.27i | −0.163694 | + | 0.220073i | ||||
\(568\) | −3718.21 | − | 16290.5i | −0.274670 | − | 1.20341i | ||||
\(569\) | −18967.1 | −1.39744 | −0.698718 | − | 0.715397i | \(-0.746246\pi\) | ||||
−0.698718 | + | 0.715397i | \(0.746246\pi\) | |||||||
\(570\) | 585.269 | 0.0430074 | ||||||||
\(571\) | 4627.84 | + | 20275.9i | 0.339176 | + | 1.48603i | 0.800790 | + | 0.598945i | \(0.204413\pi\) |
−0.461615 | + | 0.887080i | \(0.652730\pi\) | |||||||
\(572\) | 1094.31 | + | 526.991i | 0.0799918 | + | 0.0385220i | ||||
\(573\) | 23738.9 | − | 29767.6i | 1.73073 | − | 2.17026i | ||||
\(574\) | 1976.73 | + | 7489.00i | 0.143741 | + | 0.544573i | ||||
\(575\) | 1045.12 | + | 1310.53i | 0.0757988 | + | 0.0950487i | ||||
\(576\) | −4971.07 | − | 21779.7i | −0.359597 | − | 1.57550i | ||||
\(577\) | −1580.07 | − | 1981.34i | −0.114002 | − | 0.142954i | 0.721556 | − | 0.692356i | \(-0.243427\pi\) |
−0.835558 | + | 0.549402i | \(0.814856\pi\) | |||||||
\(578\) | 22653.4 | + | 10909.3i | 1.63020 | + | 0.785064i | ||||
\(579\) | 13615.5 | − | 17073.3i | 0.977271 | − | 1.22546i | ||||
\(580\) | 120.852 | − | 58.1991i | 0.00865188 | − | 0.00416653i | ||||
\(581\) | −6640.27 | + | 223.639i | −0.474156 | + | 0.0159692i | ||||
\(582\) | 23381.5 | + | 11259.9i | 1.66528 | + | 0.801958i | ||||
\(583\) | 3287.07 | − | 1582.97i | 0.233511 | − | 0.112453i | ||||
\(584\) | −688.375 | + | 3015.97i | −0.0487759 | + | 0.213701i | ||||
\(585\) | 238.266 | − | 114.743i | 0.0168394 | − | 0.00810944i | ||||
\(586\) | −8158.70 | − | 10230.7i | −0.575141 | − | 0.721204i | ||||
\(587\) | 24973.2 | 1.75597 | 0.877985 | − | 0.478687i | \(-0.158887\pi\) | ||||
0.877985 | + | 0.478687i | \(0.158887\pi\) | |||||||
\(588\) | 7031.79 | − | 474.188i | 0.493174 | − | 0.0332571i | ||||
\(589\) | 13000.9 | 0.909494 | ||||||||
\(590\) | −481.336 | − | 603.576i | −0.0335869 | − | 0.0421167i | ||||
\(591\) | 9118.30 | − | 4391.14i | 0.634648 | − | 0.305630i | ||||
\(592\) | 815.792 | − | 3574.22i | 0.0566366 | − | 0.248141i | ||||
\(593\) | 3658.73 | − | 1761.95i | 0.253366 | − | 0.122015i | −0.302890 | − | 0.953025i | \(-0.597952\pi\) |
0.556256 | + | 0.831011i | \(0.312237\pi\) | |||||||
\(594\) | 8530.52 | + | 4108.08i | 0.589245 | + | 0.283765i | ||||
\(595\) | 223.325 | − | 1156.65i | 0.0153873 | − | 0.0796938i | ||||
\(596\) | −3706.33 | + | 1784.88i | −0.254727 | + | 0.122670i | ||||
\(597\) | −12615.0 | + | 15818.7i | −0.864820 | + | 1.08445i | ||||
\(598\) | 367.295 | + | 176.880i | 0.0251167 | + | 0.0120956i | ||||
\(599\) | 4060.22 | + | 5091.36i | 0.276955 | + | 0.347291i | 0.900782 | − | 0.434272i | \(-0.142994\pi\) |
−0.623827 | + | 0.781563i | \(0.714423\pi\) | |||||||
\(600\) | −5602.13 | − | 24544.5i | −0.381177 | − | 1.67004i | ||||
\(601\) | −13008.1 | − | 16311.6i | −0.882880 | − | 1.10710i | −0.993568 | − | 0.113241i | \(-0.963877\pi\) |
0.110688 | − | 0.993855i | \(-0.464695\pi\) | |||||||
\(602\) | 10897.4 | − | 14650.7i | 0.737783 | − | 0.991888i | ||||
\(603\) | −10487.3 | + | 13150.7i | −0.708252 | + | 0.888119i | ||||
\(604\) | 5128.59 | + | 2469.80i | 0.345495 | + | 0.166382i | ||||
\(605\) | −7.89489 | − | 34.5898i | −0.000530533 | − | 0.00232442i | ||||
\(606\) | −17986.1 | −1.20567 | ||||||||
\(607\) | 2087.96 | 0.139617 | 0.0698087 | − | 0.997560i | \(-0.477761\pi\) | ||||
0.0698087 | + | 0.997560i | \(0.477761\pi\) | |||||||
\(608\) | 1449.70 | + | 6351.54i | 0.0966990 | + | 0.423666i | ||||
\(609\) | 3027.13 | − | 15678.1i | 0.201421 | − | 1.04320i | ||||
\(610\) | 101.027 | − | 442.628i | 0.00670567 | − | 0.0293794i | ||||
\(611\) | −1790.86 | + | 7846.27i | −0.118577 | + | 0.519519i | ||||
\(612\) | 7853.01 | − | 9847.36i | 0.518691 | − | 0.650418i | ||||
\(613\) | −12599.8 | + | 15799.7i | −0.830183 | + | 1.04102i | 0.168288 | + | 0.985738i | \(0.446176\pi\) |
−0.998471 | + | 0.0552790i | \(0.982395\pi\) | |||||||
\(614\) | −3882.69 | + | 17011.2i | −0.255200 | + | 1.11810i | ||||
\(615\) | 165.511 | − | 725.152i | 0.0108521 | − | 0.0475462i | ||||
\(616\) | 4356.24 | + | 16503.9i | 0.284932 | + | 1.07948i | ||||
\(617\) | 2255.74 | + | 9883.06i | 0.147184 | + | 0.644857i | 0.993660 | + | 0.112429i | \(0.0358631\pi\) |
−0.846475 | + | 0.532428i | \(0.821280\pi\) | |||||||
\(618\) | −17674.2 | −1.15042 | ||||||||
\(619\) | 8513.93 | 0.552833 | 0.276416 | − | 0.961038i | \(-0.410853\pi\) | ||||
0.276416 | + | 0.961038i | \(0.410853\pi\) | |||||||
\(620\) | 61.5719 | + | 269.764i | 0.00398836 | + | 0.0174742i | ||||
\(621\) | −1306.82 | − | 629.333i | −0.0844460 | − | 0.0406671i | ||||
\(622\) | −7742.60 | + | 9708.91i | −0.499115 | + | 0.625871i | ||||
\(623\) | 3227.07 | − | 108.685i | 0.207528 | − | 0.00698938i | ||||
\(624\) | −2490.88 | − | 3123.46i | −0.159800 | − | 0.200382i | ||||
\(625\) | −3455.32 | − | 15138.7i | −0.221140 | − | 0.968880i | ||||
\(626\) | 4673.07 | + | 5859.84i | 0.298360 | + | 0.374132i | ||||
\(627\) | −16556.9 | − | 7973.37i | −1.05457 | − | 0.507856i | ||||
\(628\) | −2067.33 | + | 2592.34i | −0.131362 | + | 0.164723i | ||||
\(629\) | 10969.7 | − | 5282.75i | 0.695377 | − | 0.334876i | ||||
\(630\) | 811.469 | + | 357.652i | 0.0513170 | + | 0.0226178i | ||||
\(631\) | −27414.1 | − | 13201.9i | −1.72954 | − | 0.832901i | −0.986522 | − | 0.163627i | \(-0.947681\pi\) |
−0.743015 | − | 0.669274i | \(-0.766605\pi\) | |||||||
\(632\) | 21129.2 | − | 10175.3i | 1.32987 | − | 0.640430i | ||||
\(633\) | −5922.84 | + | 25949.7i | −0.371898 | + | 1.62939i | ||||
\(634\) | −7988.59 | + | 3847.10i | −0.500422 | + | 0.240990i | ||||
\(635\) | −744.735 | − | 933.868i | −0.0465416 | − | 0.0583613i | ||||
\(636\) | 2002.97 | 0.124879 | ||||||||
\(637\) | 3861.54 | − | 2191.18i | 0.240188 | − | 0.136291i | ||||
\(638\) | 9227.62 | 0.572610 | ||||||||
\(639\) | 16994.7 | + | 21310.6i | 1.05211 | + | 1.31931i | ||||
\(640\) | 198.611 | − | 95.6460i | 0.0122669 | − | 0.00590741i | ||||
\(641\) | −1151.33 | + | 5044.30i | −0.0709435 | + | 0.310824i | −0.997933 | − | 0.0642637i | \(-0.979530\pi\) |
0.926989 | + | 0.375087i | \(0.122387\pi\) | |||||||
\(642\) | −11876.1 | + | 5719.22i | −0.730080 | + | 0.351588i | ||||
\(643\) | −18830.8 | − | 9068.41i | −1.15492 | − | 0.556179i | −0.244411 | − | 0.969672i | \(-0.578595\pi\) |
−0.910508 | + | 0.413492i | \(0.864309\pi\) | |||||||
\(644\) | −159.235 | − | 603.275i | −0.00974341 | − | 0.0369136i | ||||
\(645\) | −1579.78 | + | 760.783i | −0.0964401 | + | 0.0464431i | ||||
\(646\) | 10948.7 | − | 13729.2i | 0.666827 | − | 0.836175i | ||||
\(647\) | −20770.3 | − | 10002.4i | −1.26208 | − | 0.607784i | −0.321354 | − | 0.946959i | \(-0.604138\pi\) |
−0.940723 | + | 0.339175i | \(0.889852\pi\) | |||||||
\(648\) | −3069.94 | − | 3849.58i | −0.186109 | − | 0.233373i | ||||
\(649\) | 5393.89 | + | 23632.2i | 0.326239 | + | 1.42934i | ||||
\(650\) | −2359.50 | − | 2958.72i | −0.142380 | − | 0.178539i | ||||
\(651\) | 30141.2 | + | 13284.7i | 1.81464 | + | 0.799796i | ||||
\(652\) | −2376.76 | + | 2980.36i | −0.142762 | + | 0.179018i | ||||
\(653\) | 10790.8 | + | 5196.56i | 0.646670 | + | 0.311420i | 0.728316 | − | 0.685242i | \(-0.240303\pi\) |
−0.0816459 | + | 0.996661i | \(0.526018\pi\) | |||||||
\(654\) | 7731.29 | + | 33873.0i | 0.462259 | + | 2.02529i | ||||
\(655\) | −33.3054 | −0.00198680 | ||||||||
\(656\) | −6719.79 | −0.399945 | ||||||||
\(657\) | −1122.91 | − | 4919.80i | −0.0666803 | − | 0.292146i | ||||
\(658\) | −23906.8 | + | 12521.2i | −1.41639 | + | 0.741833i | ||||
\(659\) | −854.158 | + | 3742.31i | −0.0504906 | + | 0.221214i | −0.993879 | − | 0.110477i | \(-0.964762\pi\) |
0.943388 | + | 0.331691i | \(0.107619\pi\) | |||||||
\(660\) | 87.0318 | − | 381.311i | 0.00513289 | − | 0.0224887i | ||||
\(661\) | 3.89646 | − | 4.88601i | 0.000229281 | − | 0.000287509i | −0.781717 | − | 0.623634i | \(-0.785656\pi\) |
0.781946 | + | 0.623346i | \(0.214227\pi\) | |||||||
\(662\) | 16916.1 | − | 21212.2i | 0.993149 | − | 1.24537i | ||||
\(663\) | 2952.38 | − | 12935.2i | 0.172942 | − | 0.757710i | ||||
\(664\) | 1965.80 | − | 8612.74i | 0.114891 | − | 0.503372i | ||||
\(665\) | −516.373 | − | 227.590i | −0.0301114 | − | 0.0132715i | ||||
\(666\) | 2039.53 | + | 8935.76i | 0.118664 | + | 0.519901i | ||||
\(667\) | −1413.61 | −0.0820620 | ||||||||
\(668\) | 2211.64 | 0.128100 | ||||||||
\(669\) | −4332.31 | − | 18981.1i | −0.250369 | − | 1.09694i | ||||
\(670\) | −449.685 | − | 216.557i | −0.0259296 | − | 0.0124871i | ||||
\(671\) | −8888.08 | + | 11145.3i | −0.511357 | + | 0.641221i | ||||
\(672\) | −3129.20 | + | 16206.7i | −0.179630 | + | 0.930341i | ||||
\(673\) | 9562.15 | + | 11990.6i | 0.547688 | + | 0.686779i | 0.976229 | − | 0.216744i | \(-0.0695436\pi\) |
−0.428541 | + | 0.903522i | \(0.640972\pi\) | |||||||
\(674\) | −4072.44 | − | 17842.5i | −0.232737 | − | 1.01969i | ||||
\(675\) | 8395.03 | + | 10527.0i | 0.478703 | + | 0.600275i | ||||
\(676\) | −4584.12 | − | 2207.60i | −0.260817 | − | 0.125603i | ||||
\(677\) | 4724.84 | − | 5924.76i | 0.268228 | − | 0.336347i | −0.629416 | − | 0.777068i | \(-0.716706\pi\) |
0.897644 | + | 0.440721i | \(0.145277\pi\) | |||||||
\(678\) | −10647.8 | + | 5127.73i | −0.603138 | + | 0.290456i | ||||
\(679\) | −16250.5 | − | 19026.7i | −0.918465 | − | 1.07537i | ||||
\(680\) | 1411.22 | + | 679.608i | 0.0795850 | + | 0.0383261i | ||||
\(681\) | 20956.1 | − | 10091.9i | 1.17921 | − | 0.567875i | ||||
\(682\) | −4235.74 | + | 18558.0i | −0.237822 | + | 1.04197i | ||||
\(683\) | −3004.51 | + | 1446.89i | −0.168322 | + | 0.0810598i | −0.516148 | − | 0.856500i | \(-0.672634\pi\) |
0.347825 | + | 0.937559i | \(0.386920\pi\) | |||||||
\(684\) | −3761.84 | − | 4717.20i | −0.210289 | − | 0.263694i | ||||
\(685\) | −1402.10 | −0.0782064 | ||||||||
\(686\) | 13996.8 | + | 5074.35i | 0.779008 | + | 0.282419i | ||||
\(687\) | −14631.4 | −0.812552 | ||||||||
\(688\) | 9876.80 | + | 12385.1i | 0.547310 | + | 0.686306i | ||||
\(689\) | 1136.86 | − | 547.482i | 0.0628605 | − | 0.0302720i | ||||
\(690\) | 29.2115 | − | 127.984i | 0.00161168 | − | 0.00706124i | ||||
\(691\) | 4296.41 | − | 2069.04i | 0.236531 | − | 0.113908i | −0.311864 | − | 0.950127i | \(-0.600953\pi\) |
0.548395 | + | 0.836219i | \(0.315239\pi\) | |||||||
\(692\) | −3493.75 | − | 1682.50i | −0.191926 | − | 0.0924266i | ||||
\(693\) | −18083.4 | − | 21172.7i | −0.991246 | − | 1.16058i | ||||
\(694\) | 2519.69 | − | 1213.42i | 0.137819 | − | 0.0663700i | ||||
\(695\) | −505.368 | + | 633.711i | −0.0275823 | + | 0.0345871i | ||||
\(696\) | 19128.8 | + | 9211.96i | 1.04178 | + | 0.501693i | ||||
\(697\) | −13914.3 | − | 17448.0i | −0.756160 | − | 0.948195i | ||||
\(698\) | −5410.11 | − | 23703.2i | −0.293375 | − | 1.28536i | ||||
\(699\) | 12278.5 | + | 15396.7i | 0.664398 | + | 0.833128i | ||||
\(700\) | −1098.03 | + | 5686.94i | −0.0592883 | + | 0.307066i | ||||
\(701\) | 6232.25 | − | 7814.99i | 0.335790 | − | 0.421067i | −0.585057 | − | 0.810992i | \(-0.698928\pi\) |
0.920847 | + | 0.389925i | \(0.127499\pi\) | |||||||
\(702\) | 2950.34 | + | 1420.81i | 0.158623 | + | 0.0763890i | ||||
\(703\) | −1297.84 | − | 5686.22i | −0.0696288 | − | 0.305064i | ||||
\(704\) | −20814.0 | −1.11429 | ||||||||
\(705\) | 2591.60 | 0.138447 | ||||||||
\(706\) | −3447.00 | − | 15102.3i | −0.183753 | − | 0.805074i | ||||
\(707\) | 15868.9 | + | 6994.16i | 0.844145 | + | 0.372054i | ||||
\(708\) | −2961.27 | + | 12974.2i | −0.157191 | + | 0.688699i | ||||
\(709\) | 2198.34 | − | 9631.56i | 0.116446 | − | 0.510184i | −0.882740 | − | 0.469861i | \(-0.844304\pi\) |
0.999187 | − | 0.0403234i | \(-0.0128388\pi\) | |||||||
\(710\) | −504.287 | + | 632.356i | −0.0266557 | + | 0.0334252i | ||||
\(711\) | −23851.9 | + | 29909.4i | −1.25811 | + | 1.57762i | ||||
\(712\) | −955.350 | + | 4185.66i | −0.0502855 | + | 0.220315i | ||||
\(713\) | 648.889 | − | 2842.97i | 0.0340828 | − | 0.149327i | ||||
\(714\) | 39412.4 | − | 20642.2i | 2.06578 | − | 1.08195i | ||||
\(715\) | −54.8277 | − | 240.216i | −0.00286775 | − | 0.0125644i | ||||
\(716\) | 7351.27 | 0.383701 | ||||||||
\(717\) | −11833.6 | −0.616364 | ||||||||
\(718\) | 380.150 | + | 1665.55i | 0.0197592 | + | 0.0865706i | ||||
\(719\) | −7317.47 | − | 3523.91i | −0.379549 | − | 0.182781i | 0.234375 | − | 0.972146i | \(-0.424696\pi\) |
−0.613924 | + | 0.789365i | \(0.710410\pi\) | |||||||
\(720\) | −479.686 | + | 601.508i | −0.0248290 | + | 0.0311345i | ||||
\(721\) | 15593.6 | + | 6872.83i | 0.805460 | + | 0.355004i | ||||
\(722\) | 4778.09 | + | 5991.53i | 0.246291 | + | 0.308839i | ||||
\(723\) | −571.192 | − | 2502.55i | −0.0293815 | − | 0.128729i | ||||
\(724\) | −3765.11 | − | 4721.30i | −0.193272 | − | 0.242356i | ||||
\(725\) | 11823.0 | + | 5693.64i | 0.605647 | + | 0.291664i | ||||
\(726\) | 835.462 | − | 1047.64i | 0.0427092 | − | 0.0535557i | ||||
\(727\) | −7204.98 | + | 3469.73i | −0.367562 | + | 0.177009i | −0.608542 | − | 0.793521i | \(-0.708245\pi\) |
0.240980 | + | 0.970530i | \(0.422531\pi\) | |||||||
\(728\) | 1506.64 | + | 5708.01i | 0.0767030 | + | 0.290595i | ||||
\(729\) | 28756.6 | + | 13848.5i | 1.46099 | + | 0.703575i | ||||
\(730\) | 134.912 | − | 64.9700i | 0.00684014 | − | 0.00329404i | ||||
\(731\) | −11706.7 | + | 51290.5i | −0.592324 | + | 2.59514i | ||||
\(732\) | −7051.21 | + | 3395.68i | −0.356039 | + | 0.171459i | ||||
\(733\) | 366.857 | + | 460.024i | 0.0184859 | + | 0.0231806i | 0.790989 | − | 0.611831i | \(-0.209567\pi\) |
−0.772503 | + | 0.635012i | \(0.780995\pi\) | |||||||
\(734\) | −22300.9 | −1.12144 | ||||||||
\(735\) | −964.602 | − | 1055.29i | −0.0484080 | − | 0.0529591i | ||||
\(736\) | 1461.28 | 0.0731840 | ||||||||
\(737\) | 9771.04 | + | 12252.5i | 0.488360 | + | 0.612383i | ||||
\(738\) | 15136.2 | − | 7289.19i | 0.754973 | − | 0.363576i | ||||
\(739\) | −799.196 | + | 3501.51i | −0.0397820 | + | 0.174296i | −0.990916 | − | 0.134482i | \(-0.957063\pi\) |
0.951134 | + | 0.308778i | \(0.0999201\pi\) | |||||||
\(740\) | 111.841 | − | 53.8596i | 0.00555587 | − | 0.00267557i | ||||
\(741\) | −5726.32 | − | 2757.65i | −0.283889 | − | 0.136714i | ||||
\(742\) | 3871.84 | + | 1706.50i | 0.191563 | + | 0.0844307i | ||||
\(743\) | −14481.1 | + | 6973.72i | −0.715019 | + | 0.344335i | −0.755773 | − | 0.654834i | \(-0.772738\pi\) |
0.0407534 | + | 0.999169i | \(0.487024\pi\) | |||||||
\(744\) | −27307.1 | + | 34242.1i | −1.34560 | + | 1.68733i | ||||
\(745\) | 751.871 | + | 362.082i | 0.0369751 | + | 0.0178063i | ||||
\(746\) | 515.897 | + | 646.915i | 0.0253195 | + | 0.0317496i | ||||
\(747\) | 3206.71 | + | 14049.5i | 0.157065 | + | 0.688147i | ||||
\(748\) | −7316.67 | − | 9174.81i | −0.357652 | − | 0.448482i | ||||
\(749\) | 12702.1 | − | 427.795i | 0.619657 | − | 0.0208696i | ||||
\(750\) | −1521.17 | + | 1907.49i | −0.0740603 | + | 0.0928687i | ||||
\(751\) | 4488.91 | + | 2161.74i | 0.218113 | + | 0.105038i | 0.539750 | − | 0.841825i | \(-0.318519\pi\) |
−0.321637 | + | 0.946863i | \(0.604233\pi\) | |||||||
\(752\) | −5210.00 | − | 22826.5i | −0.252645 | − | 1.10691i | ||||
\(753\) | 13119.0 | 0.634902 | ||||||||
\(754\) | 3191.44 | 0.154145 | ||||||||
\(755\) | −256.955 | − | 1125.79i | −0.0123862 | − | 0.0542674i | ||||
\(756\) | −1279.08 | − | 4845.89i | −0.0615340 | − | 0.233126i | ||||
\(757\) | −310.080 | + | 1358.55i | −0.0148878 | + | 0.0652277i | −0.981826 | − | 0.189783i | \(-0.939222\pi\) |
0.966938 | + | 0.255010i | \(0.0820788\pi\) | |||||||
\(758\) | 699.745 | − | 3065.78i | 0.0335302 | − | 0.146905i | ||||
\(759\) | −2569.95 | + | 3222.61i | −0.122903 | + | 0.154115i | ||||
\(760\) | 467.820 | − | 586.628i | 0.0223284 | − | 0.0279990i | ||||
\(761\) | 2343.63 | − | 10268.1i | 0.111638 | − | 0.489118i | −0.887937 | − | 0.459965i | \(-0.847862\pi\) |
0.999575 | − | 0.0291527i | \(-0.00928091\pi\) | |||||||
\(762\) | 10038.4 | − | 43981.2i | 0.477236 | − | 2.09091i | ||||
\(763\) | 6350.79 | − | 32892.0i | 0.301329 | − | 1.56064i | ||||
\(764\) | −2591.68 | − | 11354.9i | −0.122728 | − | 0.537705i | ||||
\(765\) | −2555.09 | −0.120757 | ||||||||
\(766\) | −3883.47 | −0.183180 | ||||||||
\(767\) | 1865.52 | + | 8173.37i | 0.0878226 | + | 0.384776i | ||||
\(768\) | −25351.0 | − | 12208.4i | −1.19111 | − | 0.573609i | ||||
\(769\) | 22320.1 | − | 27988.5i | 1.04666 | − | 1.31247i | 0.0983419 | − | 0.995153i | \(-0.468646\pi\) |
0.948319 | − | 0.317319i | \(-0.102782\pi\) | |||||||
\(770\) | 493.107 | − | 662.942i | 0.0230784 | − | 0.0310270i | ||||
\(771\) | −8312.59 | − | 10423.7i | −0.388289 | − | 0.486899i | ||||
\(772\) | −1486.47 | − | 6512.63i | −0.0692993 | − | 0.303620i | ||||
\(773\) | −11136.2 | − | 13964.3i | −0.518163 | − | 0.649756i | 0.452055 | − | 0.891990i | \(-0.350691\pi\) |
−0.970218 | + | 0.242234i | \(0.922120\pi\) | |||||||
\(774\) | −35681.8 | − | 17183.5i | −1.65705 | − | 0.797993i | ||||
\(775\) | −16877.7 | + | 21164.0i | −0.782279 | + | 0.980947i | ||||
\(776\) | 29975.5 | − | 14435.4i | 1.38667 | − | 0.667786i | ||||
\(777\) | 2801.42 | − | 14509.1i | 0.129344 | − | 0.669899i | ||||
\(778\) | −5903.76 | − | 2843.10i | −0.272057 | − | 0.131016i | ||||
\(779\) | −9631.81 | + | 4638.43i | −0.442998 | + | 0.213337i | ||||
\(780\) | 30.1006 | − | 131.879i | 0.00138176 | − | 0.00605389i | ||||
\(781\) | 22880.8 | − | 11018.8i | 1.04832 | − | 0.504845i | ||||
\(782\) | −2455.78 | − | 3079.45i | −0.112300 | − | 0.140819i | ||||
\(783\) | −11355.0 | −0.518258 | ||||||||
\(784\) | −7355.69 | + | 10617.6i | −0.335081 | + | 0.483674i | ||||
\(785\) | 672.633 | 0.0305826 | ||||||||
\(786\) | −784.272 | − | 983.446i | −0.0355904 | − | 0.0446289i | ||||
\(787\) | 12089.8 | − | 5822.13i | 0.547591 | − | 0.263706i | −0.139569 | − | 0.990212i | \(-0.544572\pi\) |
0.687160 | + | 0.726507i | \(0.258857\pi\) | |||||||
\(788\) | 688.899 | − | 3018.26i | 0.0311434 | − | 0.136448i | ||||
\(789\) | 19219.0 | − | 9255.36i | 0.867190 | − | 0.417617i | ||||
\(790\) | −1022.75 | − | 492.530i | −0.0460605 | − | 0.0221816i | ||||
\(791\) | 11388.4 | − | 383.552i | 0.511915 | − | 0.0172409i | ||||
\(792\) | 33356.5 | − | 16063.6i | 1.49655 | − | 0.720702i | ||||
\(793\) | −3074.01 | + | 3854.68i | −0.137656 | + | 0.172615i | ||||
\(794\) | −6281.27 | − | 3024.90i | −0.280748 | − | 0.135201i | ||||
\(795\) | −253.340 | − | 317.678i | −0.0113019 | − | 0.0141722i | ||||
\(796\) | 1377.24 | + | 6034.07i | 0.0613253 | + | 0.268684i | ||||
\(797\) | −9426.62 | − | 11820.6i | −0.418956 | − | 0.525354i | 0.526906 | − | 0.849924i | \(-0.323352\pi\) |
−0.945862 | + | 0.324569i | \(0.894781\pi\) | |||||||
\(798\) | −5439.19 | − | 20606.8i | −0.241285 | − | 0.914125i | ||||
\(799\) | 48481.3 | − | 60793.6i | 2.14661 | − | 2.69177i | ||||
\(800\) | −12221.6 | − | 5885.62i | −0.540124 | − | 0.260110i | ||||
\(801\) | −1558.42 | − | 6827.86i | −0.0687439 | − | 0.301187i | ||||
\(802\) | −18910.7 | −0.832619 | ||||||||
\(803\) | −4701.67 | −0.206623 | ||||||||
\(804\) | 1914.51 | + | 8388.02i | 0.0839796 | + | 0.367939i | ||||
\(805\) | −75.5410 | + | 101.559i | −0.00330742 | + | 0.00444655i | ||||
\(806\) | −1464.96 | + | 6418.42i | −0.0640212 | + | 0.280495i | ||||
\(807\) | −12710.2 | + | 55687.1i | −0.554425 | + | 2.42910i | ||||
\(808\) | −14376.8 | + | 18027.9i | −0.625956 | + | 0.784924i | ||||
\(809\) | −6111.52 | + | 7663.60i | −0.265599 | + | 0.333051i | −0.896691 | − | 0.442658i | \(-0.854036\pi\) |
0.631092 | + | 0.775708i | \(0.282607\pi\) | |||||||
\(810\) | −53.0343 | + | 232.359i | −0.00230054 | + | 0.0100793i | ||||
\(811\) | −8491.55 | + | 37203.9i | −0.367668 | + | 1.61086i | 0.365501 | + | 0.930811i | \(0.380898\pi\) |
−0.733169 | + | 0.680047i | \(0.761959\pi\) | |||||||
\(812\) | −3172.27 | − | 3714.20i | −0.137100 | − | 0.160521i | ||||
\(813\) | 7589.07 | + | 33249.9i | 0.327380 | + | 1.43435i | ||||
\(814\) | 8539.58 | 0.367705 | ||||||||
\(815\) | 773.312 | 0.0332368 | ||||||||
\(816\) | 8589.11 | + | 37631.4i | 0.368479 | + | 1.61441i | ||||
\(817\) | 22705.9 | + | 10934.6i | 0.972313 | + | 0.468241i | ||||
\(818\) | −11149.1 | + | 13980.5i | −0.476550 | + | 0.597575i | ||||
\(819\) | −6254.30 | − | 7322.74i | −0.266841 | − | 0.312427i | ||||
\(820\) | −141.862 | − | 177.889i | −0.00604151 | − | 0.00757581i | ||||
\(821\) | −4388.23 | − | 19226.1i | −0.186541 | − | 0.817289i | −0.978422 | − | 0.206615i | \(-0.933755\pi\) |
0.791881 | − | 0.610675i | \(-0.209102\pi\) | |||||||
\(822\) | −33016.4 | − | 41401.3i | −1.40095 | − | 1.75673i | ||||
\(823\) | 33674.0 | + | 16216.6i | 1.42625 | + | 0.686845i | 0.978296 | − | 0.207212i | \(-0.0664391\pi\) |
0.447952 | + | 0.894057i | \(0.352153\pi\) | |||||||
\(824\) | −14127.4 | + | 17715.2i | −0.597270 | + | 0.748953i | ||||
\(825\) | 34473.9 | − | 16601.8i | 1.45482 | − | 0.700605i | ||||
\(826\) | −16778.0 | + | 22556.7i | −0.706759 | + | 0.950179i | ||||
\(827\) | −1241.30 | − | 597.780i | −0.0521938 | − | 0.0251352i | 0.407605 | − | 0.913158i | \(-0.366364\pi\) |
−0.459799 | + | 0.888023i | \(0.652078\pi\) | |||||||
\(828\) | −1219.29 | + | 587.180i | −0.0511755 | + | 0.0246448i | ||||
\(829\) | 4904.69 | − | 21488.9i | 0.205485 | − | 0.900288i | −0.762043 | − | 0.647526i | \(-0.775804\pi\) |
0.967528 | − | 0.252762i | \(-0.0813391\pi\) | |||||||
\(830\) | −385.269 | + | 185.536i | −0.0161119 | + | 0.00775908i | ||||
\(831\) | −29937.6 | − | 37540.5i | −1.24973 | − | 1.56711i | ||||
\(832\) | −7198.69 | −0.299964 | ||||||||
\(833\) | −42799.9 | + | 2886.20i | −1.78022 | + | 0.120049i | ||||
\(834\) | −30612.6 | −1.27102 | ||||||||
\(835\) | −279.732 | − | 350.773i | −0.0115934 | − | 0.0145377i | ||||
\(836\) | −5064.76 | + | 2439.06i | −0.209531 | + | 0.100905i | ||||
\(837\) | 5212.28 | − | 22836.5i | 0.215248 | − | 0.943064i | ||||
\(838\) | 24493.0 | − | 11795.2i | 1.00966 | − | 0.486227i | ||||
\(839\) | −1972.93 | − | 950.111i | −0.0811835 | − | 0.0390959i | 0.392851 | − | 0.919602i | \(-0.371489\pi\) |
−0.474035 | + | 0.880506i | \(0.657203\pi\) | |||||||
\(840\) | 1684.03 | − | 882.007i | 0.0691720 | − | 0.0362287i | ||||
\(841\) | 12003.1 | − | 5780.39i | 0.492152 | − | 0.237008i | ||||
\(842\) | −2928.24 | + | 3671.89i | −0.119850 | + | 0.150287i | ||||
\(843\) | −4106.41 | − | 1977.54i | −0.167773 | − | 0.0807950i | ||||
\(844\) | 5076.55 | + | 6365.79i | 0.207040 | + | 0.259620i | ||||
\(845\) | 229.676 | + | 1006.28i | 0.00935041 | + | 0.0409668i | ||||
\(846\) | 36496.1 | + | 45764.7i | 1.48317 | + | 1.85984i | ||||
\(847\) | −1144.50 | + | 599.431i | −0.0464292 | + | 0.0243172i | ||||
\(848\) | −2288.77 | + | 2870.03i | −0.0926849 | + | 0.116223i | ||||
\(849\) | 15872.6 | + | 7643.82i | 0.641631 | + | 0.308993i | ||||
\(850\) | 8136.10 | + | 35646.6i | 0.328313 | + | 1.43843i | ||||
\(851\) | −1308.21 | −0.0526967 | ||||||||
\(852\) | 13942.4 | 0.560631 | ||||||||
\(853\) | 1195.89 | + | 5239.55i | 0.0480030 | + | 0.210315i | 0.993242 | − | 0.116065i | \(-0.0370282\pi\) |
−0.945239 | + | 0.326380i | \(0.894171\pi\) | |||||||
\(854\) | −16523.4 | + | 556.494i | −0.662083 | + | 0.0222984i | ||||
\(855\) | −272.359 | + | 1193.28i | −0.0108941 | + | 0.0477302i | ||||
\(856\) | −3760.35 | + | 16475.2i | −0.150147 | + | 0.657838i | ||||
\(857\) | −4304.69 | + | 5397.91i | −0.171582 | + | 0.215157i | −0.860186 | − | 0.509981i | \(-0.829652\pi\) |
0.688604 | + | 0.725138i | \(0.258224\pi\) | |||||||
\(858\) | 5802.03 | − | 7275.52i | 0.230860 | − | 0.289490i | ||||
\(859\) | 3228.59 | − | 14145.4i | 0.128240 | − | 0.561855i | −0.869456 | − | 0.494010i | \(-0.835531\pi\) |
0.997696 | − | 0.0678448i | \(-0.0216123\pi\) | |||||||
\(860\) | −119.355 | + | 522.926i | −0.00473251 | + | 0.0207345i | ||||
\(861\) | −27070.1 | + | 911.698i | −1.07148 | + | 0.0360866i | ||||
\(862\) | −1659.25 | − | 7269.65i | −0.0655618 | − | 0.287245i | ||||
\(863\) | 19735.6 | 0.778455 | 0.389228 | − | 0.921142i | \(-0.372742\pi\) | ||||
0.389228 | + | 0.921142i | \(0.372742\pi\) | |||||||
\(864\) | 11737.9 | 0.462189 | ||||||||
\(865\) | 175.046 | + | 766.927i | 0.00688063 | + | 0.0301460i | ||||
\(866\) | 13086.1 | + | 6301.95i | 0.513493 | + | 0.247285i | ||||
\(867\) | −54820.1 | + | 68742.2i | −2.14739 | + | 2.69274i | ||||
\(868\) | 8925.91 | − | 4674.93i | 0.349038 | − | 0.182808i | ||||
\(869\) | 22222.9 | + | 27866.7i | 0.867504 | + | 1.08782i | ||||
\(870\) | −228.684 | − | 1001.93i | −0.00891161 | − | 0.0390443i | ||||
\(871\) | 3379.39 | + | 4237.62i | 0.131465 | + | 0.164852i | ||||
\(872\) | 40131.4 | + | 19326.3i | 1.55851 | + | 0.750539i | ||||
\(873\) | −33838.1 | + | 42431.7i | −1.31185 | + | 1.64501i | ||||
\(874\) | −1699.94 | + | 818.648i | −0.0657910 | + | 0.0316833i | ||||
\(875\) | 2083.85 | − | 1091.42i | 0.0805110 | − | 0.0421675i | ||||
\(876\) | −2325.61 | − | 1119.96i | −0.0896977 | − | 0.0431961i | ||||
\(877\) | −32839.9 | + | 15814.9i | −1.26445 | + | 0.608929i | −0.941349 | − | 0.337434i | \(-0.890441\pi\) |
−0.323105 | + | 0.946363i | \(0.604727\pi\) | |||||||
\(878\) | 2433.13 | − | 10660.3i | 0.0935243 | − | 0.409757i | ||||
\(879\) | 41227.6 | − | 19854.2i | 1.58199 | − | 0.761849i | ||||
\(880\) | 446.925 | + | 560.426i | 0.0171203 | + | 0.0214681i | ||||
\(881\) | 840.638 | 0.0321474 | 0.0160737 | − | 0.999871i | \(-0.494883\pi\) | ||||
0.0160737 | + | 0.999871i | \(0.494883\pi\) | |||||||
\(882\) | 5051.22 | − | 31894.9i | 0.192838 | − | 1.21764i | ||||
\(883\) | 19961.4 | 0.760763 | 0.380382 | − | 0.924830i | \(-0.375793\pi\) | ||||
0.380382 | + | 0.924830i | \(0.375793\pi\) | |||||||
\(884\) | −2530.53 | − | 3173.18i | −0.0962792 | − | 0.120730i | ||||
\(885\) | 2432.29 | − | 1171.33i | 0.0923848 | − | 0.0444902i | ||||
\(886\) | −6808.06 | + | 29828.1i | −0.258151 | + | 1.13103i | ||||
\(887\) | −7836.33 | + | 3773.78i | −0.296639 | + | 0.142854i | −0.576283 | − | 0.817250i | \(-0.695498\pi\) |
0.279645 | + | 0.960104i | \(0.409783\pi\) | |||||||
\(888\) | 17702.5 | + | 8525.08i | 0.668984 | + | 0.322166i | ||||
\(889\) | −25959.4 | + | 34900.3i | −0.979360 | + | 1.31667i | ||||
\(890\) | 187.235 | − | 90.1676i | 0.00705183 | − | 0.00339598i | ||||
\(891\) | 4665.82 | − | 5850.76i | 0.175433 | − | 0.219986i | ||||
\(892\) | −5365.85 | − | 2584.06i | −0.201415 | − | 0.0969963i | ||||
\(893\) | −23224.1 | − | 29122.1i | −0.870285 | − | 1.09130i | ||||
\(894\) | 7013.37 | + | 30727.6i | 0.262374 | + | 1.14954i | ||||
\(895\) | −929.802 | − | 1165.94i | −0.0347261 | − | 0.0435452i | ||||
\(896\) | −5213.39 | − | 6104.02i | −0.194383 | − | 0.227590i | ||||
\(897\) | −888.836 | + | 1114.56i | −0.0330851 | + | 0.0414874i | ||||
\(898\) | 29105.1 | + | 14016.3i | 1.08157 | + | 0.520856i | ||||
\(899\) | −5079.86 | − | 22256.3i | −0.188457 | − | 0.825684i | ||||
\(900\) | 12562.7 | 0.465286 | ||||||||
\(901\) | −12191.3 | −0.450779 | ||||||||
\(902\) | −3483.01 | − | 15260.0i | −0.128571 | − | 0.563308i | ||||
\(903\) | 41468.1 | + | 48552.3i | 1.52821 | + | 1.78928i | ||||
\(904\) | −3371.45 | + | 14771.3i | −0.124041 | + | 0.543457i | ||||
\(905\) | −272.595 | + | 1194.32i | −0.0100126 | + | 0.0438679i | ||||
\(906\) | 27191.8 | − | 34097.5i | 0.997117 | − | 1.25034i | ||||
\(907\) | 17257.3 | − | 21640.0i | 0.631775 | − | 0.792220i | −0.358173 | − | 0.933655i | \(-0.616600\pi\) |
0.989948 | + | 0.141435i | \(0.0451716\pi\) | |||||||
\(908\) | 1583.26 | − | 6936.70i | 0.0578659 | − | 0.253527i | ||||
\(909\) | 8369.96 | − | 36671.2i | 0.305406 | − | 1.33807i | ||||
\(910\) | 170.545 | − | 229.284i | 0.00621265 | − | 0.00835239i | ||||
\(911\) | −3633.60 | − | 15919.8i | −0.132148 | − | 0.578977i | −0.997031 | − | 0.0770037i | \(-0.975465\pi\) |
0.864883 | − | 0.501973i | \(-0.167392\pi\) | |||||||
\(912\) | 18490.2 | 0.671351 | ||||||||
\(913\) | 13426.6 | 0.486699 | ||||||||
\(914\) | −579.407 | − | 2538.55i | −0.0209684 | − | 0.0918684i | ||||
\(915\) | 1430.42 | + | 688.853i | 0.0516810 | + | 0.0248883i | ||||
\(916\) | −2790.59 | + | 3499.29i | −0.100659 | + | 0.126222i | ||||
\(917\) | 309.524 | + | 1172.65i | 0.0111465 | + | 0.0422294i | ||||
\(918\) | −19726.3 | − | 24736.1i | −0.709223 | − | 0.889337i | ||||
\(919\) | −6975.15 | − | 30560.1i | −0.250369 | − | 1.09694i | −0.931203 | − | 0.364500i | \(-0.881240\pi\) |
0.680835 | − | 0.732437i | \(-0.261617\pi\) | |||||||
\(920\) | −104.931 | − | 131.580i | −0.00376031 | − | 0.00471528i | ||||
\(921\) | −54974.2 | − | 26474.2i | −1.96684 | − | 0.947181i | ||||
\(922\) | 7564.20 | − | 9485.20i | 0.270188 | − | 0.338805i | ||||
\(923\) | 7913.49 | − | 3810.93i | 0.282205 | − | 0.135903i | ||||
\(924\) | −14234.4 | + | 479.404i | −0.506795 | + | 0.0170684i | ||||
\(925\) | 10941.4 | + | 5269.11i | 0.388920 | + | 0.187294i | ||||
\(926\) | −12406.0 | + | 5974.42i | −0.440266 | + | 0.212021i | ||||
\(927\) | 8224.77 | − | 36035.1i | 0.291410 | − | 1.27675i | ||||
\(928\) | 10306.8 | − | 4963.50i | 0.364588 | − | 0.175576i | ||||
\(929\) | −12975.0 | − | 16270.2i | −0.458231 | − | 0.574604i | 0.498014 | − | 0.867169i | \(-0.334063\pi\) |
−0.956246 | + | 0.292565i | \(0.905491\pi\) | |||||||
\(930\) | 2119.98 | 0.0747495 | ||||||||
\(931\) | −3214.32 | + | 20296.1i | −0.113152 | + | 0.714477i | ||||
\(932\) | 6024.14 | 0.211724 | ||||||||
\(933\) | −27075.3 | − | 33951.4i | −0.950060 | − | 1.19134i | ||||
\(934\) | −4219.54 | + | 2032.02i | −0.147824 | + | 0.0711882i | ||||
\(935\) | −529.729 | + | 2320.90i | −0.0185283 | + | 0.0811780i | ||||
\(936\) | 11536.6 | − | 5555.72i | 0.402868 | − | 0.194011i | ||||
\(937\) | −16397.7 | − | 7896.70i | −0.571706 | − | 0.275319i | 0.125614 | − | 0.992079i | \(-0.459910\pi\) |
−0.697320 | + | 0.716760i | \(0.745624\pi\) | |||||||
\(938\) | −3445.62 | + | 17845.6i | −0.119940 | + | 0.621192i | ||||
\(939\) | −23614.0 | + | 11371.9i | −0.820675 | + | 0.395216i | ||||
\(940\) | 494.285 | − | 619.814i | 0.0171509 | − | 0.0215065i | ||||
\(941\) | −17413.2 | − | 8385.74i | −0.603244 | − | 0.290507i | 0.107226 | − | 0.994235i | \(-0.465803\pi\) |
−0.710470 | + | 0.703728i | \(0.751518\pi\) | |||||||
\(942\) | 15839.1 | + | 19861.6i | 0.547840 | + | 0.686969i | ||||
\(943\) | 533.575 | + | 2337.74i | 0.0184259 | + | 0.0807290i | ||||
\(944\) | −15206.7 | − | 19068.6i | −0.524296 | − | 0.657446i | ||||
\(945\) | −606.793 | + | 815.783i | −0.0208878 | + | 0.0280819i | ||||
\(946\) | −23006.2 | + | 28848.8i | −0.790692 | + | 0.991496i | ||||
\(947\) | −37501.7 | − | 18059.9i | −1.28685 | − | 0.619712i | −0.339705 | − | 0.940532i | \(-0.610327\pi\) |
−0.947140 | + | 0.320820i | \(0.896042\pi\) | |||||||
\(948\) | 4354.30 | + | 19077.4i | 0.149178 | + | 0.653593i | ||||
\(949\) | −1626.11 | −0.0556225 | ||||||||
\(950\) | 17515.0 | 0.598170 | ||||||||
\(951\) | −6899.51 | − | 30228.7i | −0.235260 | − | 1.03074i | ||||
\(952\) | 10813.2 | − | 56003.6i | 0.368127 | − | 1.90660i | ||||
\(953\) | −4328.14 | + | 18962.8i | −0.147117 | + | 0.644561i | 0.846561 | + | 0.532292i | \(0.178669\pi\) |
−0.993678 | + | 0.112269i | \(0.964188\pi\) | |||||||
\(954\) | 2042.18 | − | 8947.38i | 0.0693062 | − | 0.303650i | ||||
\(955\) | −1473.13 | + | 1847.24i | −0.0499154 | + | 0.0625919i | ||||
\(956\) | −2256.97 | + | 2830.15i | −0.0763553 | + | 0.0957465i | ||||
\(957\) | −7180.38 | + | 31459.3i | −0.242538 | + | 1.06263i | ||||
\(958\) | −6013.63 | + | 26347.4i | −0.202810 | + | 0.888567i | ||||
\(959\) | 13030.4 | + | 49366.5i | 0.438762 | + | 1.66228i | ||||
\(960\) | 515.824 | + | 2259.97i | 0.0173418 | + | 0.0759795i | ||||
\(961\) | 17301.2 | 0.580754 | ||||||||
\(962\) | 2953.48 | 0.0989854 | ||||||||
\(963\) | −6134.07 | − | 26875.1i | −0.205262 | − | 0.899313i | ||||
\(964\) | −707.459 | − | 340.694i | −0.0236366 | − | 0.0113828i | ||||
\(965\) | −844.913 | + | 1059.49i | −0.0281852 | + | 0.0353431i | ||||
\(966\) | −4777.66 | + | 160.908i | −0.159129 | + | 0.00535934i | ||||
\(967\) | −9772.09 | − | 12253.8i | −0.324973 | − | 0.407504i | 0.592328 | − | 0.805697i | \(-0.298209\pi\) |
−0.917302 | + | 0.398193i | \(0.869637\pi\) | |||||||
\(968\) | −382.263 | − | 1674.80i | −0.0126925 | − | 0.0556097i | ||||
\(969\) | 38286.8 | + | 48010.1i | 1.26930 | + | 1.59165i | ||||
\(970\) | −1450.95 | − | 698.739i | −0.0480279 | − | 0.0231290i | ||||
\(971\) | 29304.5 | − | 36746.6i | 0.968512 | − | 1.21448i | −0.00821050 | − | 0.999966i | \(-0.502614\pi\) |
0.976722 | − | 0.214509i | \(-0.0688151\pi\) | |||||||
\(972\) | 10284.6 | − | 4952.79i | 0.339380 | − | 0.163437i | ||||
\(973\) | 27009.0 | + | 11904.1i | 0.889895 | + | 0.392219i | ||||
\(974\) | −3677.53 | − | 1771.01i | −0.120981 | − | 0.0582615i | ||||
\(975\) | 11923.1 | − | 5741.84i | 0.391634 | − | 0.188601i | ||||
\(976\) | 3191.71 | − | 13983.8i | 0.104676 | − | 0.458617i | ||||
\(977\) | −39123.9 | + | 18841.1i | −1.28115 | + | 0.616970i | −0.945686 | − | 0.325083i | \(-0.894608\pi\) |
−0.335465 | + | 0.942053i | \(0.608893\pi\) | |||||||
\(978\) | 18209.9 | + | 22834.4i | 0.595385 | + | 0.746590i | ||||
\(979\) | −6525.14 | −0.213018 | ||||||||
\(980\) | −436.361 | + | 29.4259i | −0.0142235 | + | 0.000959160i | ||||
\(981\) | −72660.0 | −2.36479 | ||||||||
\(982\) | −18447.0 | − | 23131.8i | −0.599456 | − | 0.751695i | ||||
\(983\) | −25446.9 | + | 12254.6i | −0.825667 | + | 0.397620i | −0.798488 | − | 0.602010i | \(-0.794367\pi\) |
−0.0271788 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(984\) | 8013.88 | − | 35111.1i | 0.259627 | − | 1.13750i | ||||
\(985\) | −565.840 | + | 272.494i | −0.0183037 | + | 0.00881460i | ||||
\(986\) | −27781.2 | − | 13378.7i | −0.897296 | − | 0.432115i | ||||
\(987\) | −24085.0 | − | 91247.7i | −0.776731 | − | 2.94270i | ||||
\(988\) | −1751.68 | + | 843.566i | −0.0564054 | + | 0.0271634i | ||||
\(989\) | 3524.40 | − | 4419.46i | 0.113316 | − | 0.142094i | ||||
\(990\) | −1614.60 | − | 777.551i | −0.0518338 | − | 0.0249618i | ||||
\(991\) | 15862.2 | + | 19890.6i | 0.508456 | + | 0.637583i | 0.968113 | − | 0.250513i | \(-0.0805993\pi\) |
−0.459658 | + | 0.888096i | \(0.652028\pi\) | |||||||
\(992\) | 5251.14 | + | 23006.8i | 0.168069 | + | 0.736356i | ||||
\(993\) | 59154.6 | + | 74177.5i | 1.89045 | + | 2.37055i | ||||
\(994\) | 26951.2 | + | 11878.7i | 0.860001 | + | 0.379043i | ||||
\(995\) | 782.828 | − | 981.636i | 0.0249420 | − | 0.0312763i | ||||
\(996\) | 6641.28 | + | 3198.27i | 0.211282 | + | 0.101748i | ||||
\(997\) | 3162.22 | + | 13854.6i | 0.100450 | + | 0.440100i | 0.999995 | + | 0.00327116i | \(0.00104124\pi\) |
−0.899545 | + | 0.436829i | \(0.856102\pi\) | |||||||
\(998\) | 22449.7 | 0.712056 | ||||||||
\(999\) | −10508.4 | −0.332803 |
(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 | 49.4.e.a.8.5 | ✓ | 78 | |
49.22 | even | 7 | 2401.4.a.d.1.12 | 39 | |||
49.27 | odd | 14 | 2401.4.a.c.1.12 | 39 | |||
49.43 | even | 7 | inner | 49.4.e.a.43.5 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.e.a.8.5 | ✓ | 78 | 1.1 | even | 1 | trivial | |
49.4.e.a.43.5 | yes | 78 | 49.43 | even | 7 | inner | |
2401.4.a.c.1.12 | 39 | 49.27 | odd | 14 | |||
2401.4.a.d.1.12 | 39 | 49.22 | even | 7 |