Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (of order \(12\), degree \(4\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 163.4 | ||
Character | \(\chi\) | \(=\) | 210.163 |
Dual form | 210.3.v.b.67.4 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 1.36603i | −0.183013 | − | 0.683013i | ||||
\(3\) | −0.448288 | + | 1.67303i | −0.149429 | + | 0.557678i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 4.60215 | + | 1.95454i | 0.920430 | + | 0.390907i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −2.49277 | − | 6.54111i | −0.356110 | − | 0.934444i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0.985440 | − | 7.00206i | 0.0985440 | − | 0.700206i | ||||
\(11\) | 1.59310 | + | 2.75932i | 0.144827 | + | 0.250848i | 0.929308 | − | 0.369305i | \(-0.120404\pi\) |
−0.784481 | + | 0.620152i | \(0.787071\pi\) | |||||||
\(12\) | −0.896575 | − | 3.34607i | −0.0747146 | − | 0.278839i | ||||
\(13\) | 16.7146 | + | 16.7146i | 1.28574 | + | 1.28574i | 0.937351 | + | 0.348386i | \(0.113270\pi\) |
0.348386 | + | 0.937351i | \(0.386730\pi\) | |||||||
\(14\) | −8.02290 | + | 5.79940i | −0.573064 | + | 0.414243i | ||||
\(15\) | −5.33309 | + | 6.82335i | −0.355539 | + | 0.454890i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.125000 | − | 0.216506i | ||||
\(17\) | 14.5470 | + | 3.89785i | 0.855704 | + | 0.229285i | 0.659896 | − | 0.751357i | \(-0.270600\pi\) |
0.195808 | + | 0.980642i | \(0.437267\pi\) | |||||||
\(18\) | −1.09808 | + | 4.09808i | −0.0610042 | + | 0.227671i | ||||
\(19\) | 13.5028 | + | 7.79585i | 0.710674 | + | 0.410308i | 0.811311 | − | 0.584615i | \(-0.198755\pi\) |
−0.100636 | + | 0.994923i | \(0.532088\pi\) | |||||||
\(20\) | −9.92569 | + | 1.21680i | −0.496285 | + | 0.0608398i | ||||
\(21\) | 12.0610 | − | 1.23819i | 0.574332 | − | 0.0589615i | ||||
\(22\) | 3.18619 | − | 3.18619i | 0.144827 | − | 0.144827i | ||||
\(23\) | 5.41879 | − | 1.45196i | 0.235600 | − | 0.0631287i | −0.139087 | − | 0.990280i | \(-0.544417\pi\) |
0.374687 | + | 0.927151i | \(0.377750\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 17.3596 | + | 17.9901i | 0.694383 | + | 0.719605i | ||||
\(26\) | 16.7146 | − | 28.9505i | 0.642869 | − | 1.11348i | ||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 10.8587 | + | 8.83676i | 0.387811 | + | 0.315598i | ||||
\(29\) | − | 47.4699i | − | 1.63689i | −0.574583 | − | 0.818446i | \(-0.694836\pi\) | ||
0.574583 | − | 0.818446i | \(-0.305164\pi\) | |||||||
\(30\) | 11.2729 | + | 4.78761i | 0.375764 | + | 0.159587i | ||||
\(31\) | 0.731778 | + | 1.26748i | 0.0236057 | + | 0.0408863i | 0.877587 | − | 0.479417i | \(-0.159152\pi\) |
−0.853981 | + | 0.520304i | \(0.825819\pi\) | |||||||
\(32\) | −5.46410 | − | 1.46410i | −0.170753 | − | 0.0457532i | ||||
\(33\) | −5.33061 | + | 1.42833i | −0.161533 | + | 0.0432828i | ||||
\(34\) | − | 21.2982i | − | 0.626419i | ||||||
\(35\) | 1.31271 | − | 34.9754i | 0.0375059 | − | 0.999296i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 14.3009 | + | 53.3715i | 0.386510 | + | 1.44247i | 0.835773 | + | 0.549074i | \(0.185020\pi\) |
−0.449264 | + | 0.893399i | \(0.648314\pi\) | |||||||
\(38\) | 5.70696 | − | 21.2987i | 0.150183 | − | 0.560491i | ||||
\(39\) | −35.4570 | + | 20.4711i | −0.909154 | + | 0.524900i | ||||
\(40\) | 5.29523 | + | 13.1134i | 0.132381 | + | 0.327834i | ||||
\(41\) | −27.2740 | −0.665219 | −0.332610 | − | 0.943065i | \(-0.607929\pi\) | ||||
−0.332610 | + | 0.943065i | \(0.607929\pi\) | |||||||
\(42\) | −6.10602 | − | 16.0224i | −0.145381 | − | 0.381485i | ||||
\(43\) | −16.8709 | − | 16.8709i | −0.392346 | − | 0.392346i | 0.483177 | − | 0.875523i | \(-0.339483\pi\) |
−0.875523 | + | 0.483177i | \(0.839483\pi\) | |||||||
\(44\) | −5.51865 | − | 3.18619i | −0.125424 | − | 0.0724135i | ||||
\(45\) | −9.02494 | − | 11.9813i | −0.200554 | − | 0.266250i | ||||
\(46\) | −3.96683 | − | 6.87075i | −0.0862355 | − | 0.149364i | ||||
\(47\) | −7.04479 | − | 26.2915i | −0.149889 | − | 0.559394i | −0.999489 | − | 0.0319661i | \(-0.989823\pi\) |
0.849600 | − | 0.527428i | \(-0.176844\pi\) | |||||||
\(48\) | 4.89898 | + | 4.89898i | 0.102062 | + | 0.102062i | ||||
\(49\) | −36.5722 | + | 32.6110i | −0.746371 | + | 0.665530i | ||||
\(50\) | 18.2209 | − | 30.2985i | 0.364419 | − | 0.605970i | ||||
\(51\) | −13.0425 | + | 22.5902i | −0.255734 | + | 0.442945i | ||||
\(52\) | −45.6651 | − | 12.2359i | −0.878175 | − | 0.235306i | ||||
\(53\) | −8.92325 | + | 33.3020i | −0.168363 | + | 0.628340i | 0.829224 | + | 0.558916i | \(0.188783\pi\) |
−0.997587 | + | 0.0694239i | \(0.977884\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 1.93848 | + | 15.8126i | 0.0352450 | + | 0.287502i | ||||
\(56\) | 8.09667 | − | 18.0678i | 0.144583 | − | 0.322639i | ||||
\(57\) | −19.0959 | + | 19.0959i | −0.335015 | + | 0.335015i | ||||
\(58\) | −64.8451 | + | 17.3752i | −1.11802 | + | 0.299572i | ||||
\(59\) | 46.3174 | − | 26.7414i | 0.785041 | − | 0.453243i | −0.0531731 | − | 0.998585i | \(-0.516933\pi\) |
0.838214 | + | 0.545342i | \(0.183600\pi\) | |||||||
\(60\) | 2.41383 | − | 17.1515i | 0.0402304 | − | 0.285858i | ||||
\(61\) | 20.4235 | − | 35.3745i | 0.334812 | − | 0.579911i | −0.648637 | − | 0.761098i | \(-0.724661\pi\) |
0.983449 | + | 0.181187i | \(0.0579940\pi\) | |||||||
\(62\) | 1.46356 | − | 1.46356i | 0.0236057 | − | 0.0236057i | ||||
\(63\) | −3.33525 | + | 20.7335i | −0.0529404 | + | 0.329102i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 44.2538 | + | 109.592i | 0.680828 | + | 1.68604i | ||||
\(66\) | 3.90227 | + | 6.75894i | 0.0591254 | + | 0.102408i | ||||
\(67\) | 59.1406 | + | 15.8467i | 0.882695 | + | 0.236517i | 0.671570 | − | 0.740941i | \(-0.265620\pi\) |
0.211126 | + | 0.977459i | \(0.432287\pi\) | |||||||
\(68\) | −29.0939 | + | 7.79570i | −0.427852 | + | 0.114643i | ||||
\(69\) | 9.71671i | 0.140822i | ||||||||
\(70\) | −48.2577 | + | 11.0087i | −0.689396 | + | 0.157267i | ||||
\(71\) | −102.469 | −1.44323 | −0.721616 | − | 0.692294i | \(-0.756600\pi\) | ||||
−0.721616 | + | 0.692294i | \(0.756600\pi\) | |||||||
\(72\) | −2.19615 | − | 8.19615i | −0.0305021 | − | 0.113835i | ||||
\(73\) | −7.92202 | + | 29.5654i | −0.108521 | + | 0.405005i | −0.998721 | − | 0.0505648i | \(-0.983898\pi\) |
0.890200 | + | 0.455570i | \(0.150565\pi\) | |||||||
\(74\) | 67.6724 | − | 39.0707i | 0.914492 | − | 0.527982i | ||||
\(75\) | −37.8802 | + | 20.9784i | −0.505069 | + | 0.279712i | ||||
\(76\) | −31.1834 | −0.410308 | ||||||||
\(77\) | 14.0778 | − | 17.2990i | 0.182829 | − | 0.224662i | ||||
\(78\) | 40.9422 | + | 40.9422i | 0.524900 | + | 0.524900i | ||||
\(79\) | −101.041 | − | 58.3361i | −1.27900 | − | 0.738431i | −0.302336 | − | 0.953202i | \(-0.597766\pi\) |
−0.976665 | + | 0.214770i | \(0.931100\pi\) | |||||||
\(80\) | 15.9750 | − | 12.0332i | 0.199688 | − | 0.150416i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 9.98297 | + | 37.2570i | 0.121744 | + | 0.454353i | ||||
\(83\) | −74.9073 | − | 74.9073i | −0.902497 | − | 0.902497i | 0.0931546 | − | 0.995652i | \(-0.470305\pi\) |
−0.995652 | + | 0.0931546i | \(0.970305\pi\) | |||||||
\(84\) | −19.6520 | + | 14.2056i | −0.233953 | + | 0.169114i | ||||
\(85\) | 59.3289 | + | 46.3711i | 0.697987 | + | 0.545542i | ||||
\(86\) | −16.8709 | + | 29.2212i | −0.196173 | + | 0.339782i | ||||
\(87\) | 79.4187 | + | 21.2802i | 0.912858 | + | 0.244600i | ||||
\(88\) | −2.33246 | + | 8.70484i | −0.0265052 | + | 0.0989187i | ||||
\(89\) | −91.7988 | − | 53.0001i | −1.03145 | − | 0.595506i | −0.114048 | − | 0.993475i | \(-0.536382\pi\) |
−0.917399 | + | 0.397969i | \(0.869715\pi\) | |||||||
\(90\) | −13.0633 | + | 16.7137i | −0.145148 | + | 0.185708i | ||||
\(91\) | 67.6662 | − | 150.998i | 0.743585 | − | 1.65931i | ||||
\(92\) | −7.93366 | + | 7.93366i | −0.0862355 | + | 0.0862355i | ||||
\(93\) | −2.44858 | + | 0.656094i | −0.0263288 | + | 0.00705478i | ||||
\(94\) | −33.3363 | + | 19.2467i | −0.354642 | + | 0.204752i | ||||
\(95\) | 46.9047 | + | 62.2694i | 0.493734 | + | 0.655467i | ||||
\(96\) | 4.89898 | − | 8.48528i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | −66.3214 | + | 66.3214i | −0.683725 | + | 0.683725i | −0.960838 | − | 0.277112i | \(-0.910623\pi\) |
0.277112 | + | 0.960838i | \(0.410623\pi\) | |||||||
\(98\) | 57.9338 | + | 38.0221i | 0.591161 | + | 0.387980i | ||||
\(99\) | − | 9.55858i | − | 0.0965513i | ||||||
\(100\) | −48.0578 | − | 13.8002i | −0.480578 | − | 0.138002i | ||||
\(101\) | −90.1553 | − | 156.154i | −0.892627 | − | 1.54608i | −0.836714 | − | 0.547640i | \(-0.815526\pi\) |
−0.0559130 | − | 0.998436i | \(-0.517807\pi\) | |||||||
\(102\) | 35.6327 | + | 9.54774i | 0.349340 | + | 0.0936053i | ||||
\(103\) | −76.7078 | + | 20.5538i | −0.744736 | + | 0.199551i | −0.611182 | − | 0.791490i | \(-0.709306\pi\) |
−0.133554 | + | 0.991042i | \(0.542639\pi\) | |||||||
\(104\) | 66.8583i | 0.642869i | ||||||||
\(105\) | 57.9265 | + | 17.8752i | 0.551681 | + | 0.170240i | ||||
\(106\) | 48.7576 | 0.459977 | ||||||||
\(107\) | 15.6342 | + | 58.3476i | 0.146114 | + | 0.545305i | 0.999703 | + | 0.0243583i | \(0.00775424\pi\) |
−0.853589 | + | 0.520947i | \(0.825579\pi\) | |||||||
\(108\) | −2.68973 | + | 10.0382i | −0.0249049 | + | 0.0929463i | ||||
\(109\) | −12.3921 | + | 7.15460i | −0.113689 | + | 0.0656385i | −0.555766 | − | 0.831339i | \(-0.687575\pi\) |
0.442077 | + | 0.896977i | \(0.354242\pi\) | |||||||
\(110\) | 20.8909 | − | 8.43582i | 0.189917 | − | 0.0766892i | ||||
\(111\) | −95.7032 | −0.862191 | ||||||||
\(112\) | −27.6446 | − | 4.44700i | −0.246827 | − | 0.0397053i | ||||
\(113\) | 66.0293 | + | 66.0293i | 0.584330 | + | 0.584330i | 0.936090 | − | 0.351760i | \(-0.114417\pi\) |
−0.351760 | + | 0.936090i | \(0.614417\pi\) | |||||||
\(114\) | 33.0750 | + | 19.0959i | 0.290132 | + | 0.167508i | ||||
\(115\) | 27.7760 | + | 3.90908i | 0.241530 | + | 0.0339920i | ||||
\(116\) | 47.4699 | + | 82.2202i | 0.409223 | + | 0.708795i | ||||
\(117\) | −18.3539 | − | 68.4976i | −0.156871 | − | 0.585450i | ||||
\(118\) | −53.4827 | − | 53.4827i | −0.453243 | − | 0.453243i | ||||
\(119\) | −10.7660 | − | 104.870i | −0.0904710 | − | 0.881259i | ||||
\(120\) | −24.3129 | + | 2.98053i | −0.202607 | + | 0.0248378i | ||||
\(121\) | 55.4241 | − | 95.9973i | 0.458050 | − | 0.793366i | ||||
\(122\) | −55.7980 | − | 14.9510i | −0.457361 | − | 0.122550i | ||||
\(123\) | 12.2266 | − | 45.6303i | 0.0994032 | − | 0.370978i | ||||
\(124\) | −2.53495 | − | 1.46356i | −0.0204432 | − | 0.0118029i | ||||
\(125\) | 44.7291 | + | 116.723i | 0.357833 | + | 0.933786i | ||||
\(126\) | 29.5432 | − | 3.03294i | 0.234470 | − | 0.0240709i | ||||
\(127\) | 150.156 | − | 150.156i | 1.18233 | − | 1.18233i | 0.203192 | − | 0.979139i | \(-0.434868\pi\) |
0.979139 | − | 0.203192i | \(-0.0651317\pi\) | |||||||
\(128\) | 10.9282 | − | 2.92820i | 0.0853766 | − | 0.0228766i | ||||
\(129\) | 35.7885 | − | 20.6625i | 0.277431 | − | 0.160175i | ||||
\(130\) | 133.508 | − | 100.565i | 1.02698 | − | 0.773580i | ||||
\(131\) | 118.435 | − | 205.135i | 0.904084 | − | 1.56592i | 0.0819423 | − | 0.996637i | \(-0.473888\pi\) |
0.822142 | − | 0.569283i | \(-0.192779\pi\) | |||||||
\(132\) | 7.80455 | − | 7.80455i | 0.0591254 | − | 0.0591254i | ||||
\(133\) | 17.3341 | − | 107.757i | 0.130331 | − | 0.810200i | ||||
\(134\) | − | 86.5878i | − | 0.646178i | ||||||
\(135\) | 24.0908 | − | 9.72796i | 0.178450 | − | 0.0720590i | ||||
\(136\) | 21.2982 | + | 36.8896i | 0.156605 | + | 0.271247i | ||||
\(137\) | 103.535 | + | 27.7420i | 0.755727 | + | 0.202496i | 0.616057 | − | 0.787702i | \(-0.288729\pi\) |
0.139670 | + | 0.990198i | \(0.455396\pi\) | |||||||
\(138\) | 13.2733 | − | 3.55656i | 0.0961832 | − | 0.0257722i | ||||
\(139\) | 259.949i | 1.87014i | 0.354464 | + | 0.935070i | \(0.384663\pi\) | ||||
−0.354464 | + | 0.935070i | \(0.615337\pi\) | |||||||
\(140\) | 32.7017 | + | 61.8918i | 0.233584 | + | 0.442085i | ||||
\(141\) | 47.1447 | 0.334359 | ||||||||
\(142\) | 37.5064 | + | 139.976i | 0.264130 | + | 0.985745i | ||||
\(143\) | −19.4930 | + | 72.7489i | −0.136315 | + | 0.508734i | ||||
\(144\) | −10.3923 | + | 6.00000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 92.7815 | − | 218.464i | 0.639873 | − | 1.50665i | ||||
\(146\) | 43.2867 | 0.296484 | ||||||||
\(147\) | −38.1644 | − | 75.8055i | −0.259622 | − | 0.515684i | ||||
\(148\) | −78.1413 | − | 78.1413i | −0.527982 | − | 0.527982i | ||||
\(149\) | 26.3910 | + | 15.2369i | 0.177121 | + | 0.102261i | 0.585939 | − | 0.810355i | \(-0.300726\pi\) |
−0.408818 | + | 0.912616i | \(0.634059\pi\) | |||||||
\(150\) | 42.5221 | + | 44.0666i | 0.283481 | + | 0.293778i | ||||
\(151\) | 46.5201 | + | 80.5751i | 0.308080 | + | 0.533610i | 0.977942 | − | 0.208875i | \(-0.0669803\pi\) |
−0.669862 | + | 0.742485i | \(0.733647\pi\) | |||||||
\(152\) | 11.4139 | + | 42.5973i | 0.0750916 | + | 0.280246i | ||||
\(153\) | −31.9474 | − | 31.9474i | −0.208806 | − | 0.208806i | ||||
\(154\) | −28.7837 | − | 12.8988i | −0.186907 | − | 0.0837583i | ||||
\(155\) | 0.890425 | + | 7.26341i | 0.00574468 | + | 0.0468607i | ||||
\(156\) | 40.9422 | − | 70.9140i | 0.262450 | − | 0.454577i | ||||
\(157\) | 43.2837 | + | 11.5978i | 0.275692 | + | 0.0738715i | 0.394016 | − | 0.919104i | \(-0.371085\pi\) |
−0.118324 | + | 0.992975i | \(0.537752\pi\) | |||||||
\(158\) | −42.7050 | + | 159.377i | −0.270285 | + | 1.00872i | ||||
\(159\) | −51.7152 | − | 29.8578i | −0.325253 | − | 0.187785i | ||||
\(160\) | −22.2850 | − | 17.4178i | −0.139281 | − | 0.108861i | ||||
\(161\) | −23.0052 | − | 31.8255i | −0.142890 | − | 0.197674i | ||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −132.967 | + | 35.6285i | −0.815750 | + | 0.218580i | −0.642488 | − | 0.766296i | \(-0.722098\pi\) |
−0.173263 | + | 0.984876i | \(0.555431\pi\) | |||||||
\(164\) | 47.2399 | − | 27.2740i | 0.288048 | − | 0.166305i | ||||
\(165\) | −27.3240 | − | 3.84546i | −0.165600 | − | 0.0233058i | ||||
\(166\) | −74.9073 | + | 129.743i | −0.451249 | + | 0.781585i | ||||
\(167\) | −44.3224 | + | 44.3224i | −0.265404 | + | 0.265404i | −0.827245 | − | 0.561841i | \(-0.810093\pi\) |
0.561841 | + | 0.827245i | \(0.310093\pi\) | |||||||
\(168\) | 26.5983 | + | 21.6455i | 0.158323 | + | 0.128843i | ||||
\(169\) | 389.755i | 2.30624i | ||||||||
\(170\) | 41.6282 | − | 98.0177i | 0.244872 | − | 0.576575i | ||||
\(171\) | −23.3876 | − | 40.5084i | −0.136769 | − | 0.236891i | ||||
\(172\) | 46.0921 | + | 12.3503i | 0.267977 | + | 0.0718043i | ||||
\(173\) | 107.039 | − | 28.6810i | 0.618723 | − | 0.165786i | 0.0641758 | − | 0.997939i | \(-0.479558\pi\) |
0.554547 | + | 0.832152i | \(0.312891\pi\) | |||||||
\(174\) | − | 116.277i | − | 0.668258i | ||||||
\(175\) | 74.4019 | − | 158.396i | 0.425154 | − | 0.905121i | ||||
\(176\) | 12.7448 | 0.0724135 | ||||||||
\(177\) | 23.9756 | + | 89.4783i | 0.135456 | + | 0.505527i | ||||
\(178\) | −38.7987 | + | 144.799i | −0.217970 | + | 0.813477i | ||||
\(179\) | −250.216 | + | 144.462i | −1.39785 | + | 0.807050i | −0.994167 | − | 0.107848i | \(-0.965604\pi\) |
−0.403685 | + | 0.914898i | \(0.632271\pi\) | |||||||
\(180\) | 27.6129 | + | 11.7272i | 0.153405 | + | 0.0651512i | ||||
\(181\) | 119.317 | 0.659212 | 0.329606 | − | 0.944119i | \(-0.393084\pi\) | ||||
0.329606 | + | 0.944119i | \(0.393084\pi\) | |||||||
\(182\) | −231.034 | − | 37.1648i | −1.26942 | − | 0.204202i | ||||
\(183\) | 50.0272 | + | 50.0272i | 0.273372 | + | 0.273372i | ||||
\(184\) | 13.7415 | + | 7.93366i | 0.0746821 | + | 0.0431177i | ||||
\(185\) | −38.5018 | + | 273.575i | −0.208118 | + | 1.47879i | ||||
\(186\) | 1.79248 | + | 3.10467i | 0.00963700 | + | 0.0166918i | ||||
\(187\) | 12.4193 | + | 46.3495i | 0.0664134 | + | 0.247858i | ||||
\(188\) | 38.4935 | + | 38.4935i | 0.204752 | + | 0.204752i | ||||
\(189\) | −33.1926 | − | 14.8745i | −0.175622 | − | 0.0787012i | ||||
\(190\) | 67.8933 | − | 86.8652i | 0.357333 | − | 0.457185i | ||||
\(191\) | 63.4019 | − | 109.815i | 0.331947 | − | 0.574950i | −0.650946 | − | 0.759124i | \(-0.725628\pi\) |
0.982894 | + | 0.184174i | \(0.0589610\pi\) | |||||||
\(192\) | −13.3843 | − | 3.58630i | −0.0697097 | − | 0.0186787i | ||||
\(193\) | 74.2715 | − | 277.185i | 0.384827 | − | 1.43619i | −0.453613 | − | 0.891199i | \(-0.649865\pi\) |
0.838440 | − | 0.544994i | \(-0.183468\pi\) | |||||||
\(194\) | 114.872 | + | 66.3214i | 0.592123 | + | 0.341863i | ||||
\(195\) | −203.190 | + | 24.9092i | −1.04200 | + | 0.127739i | ||||
\(196\) | 30.7339 | − | 93.0561i | 0.156805 | − | 0.474776i | ||||
\(197\) | 3.41904 | − | 3.41904i | 0.0173555 | − | 0.0173555i | −0.698376 | − | 0.715731i | \(-0.746094\pi\) |
0.715731 | + | 0.698376i | \(0.246094\pi\) | |||||||
\(198\) | −13.0573 | + | 3.49868i | −0.0659458 | + | 0.0176701i | ||||
\(199\) | 190.157 | − | 109.787i | 0.955563 | − | 0.551694i | 0.0607582 | − | 0.998153i | \(-0.480648\pi\) |
0.894805 | + | 0.446458i | \(0.147315\pi\) | |||||||
\(200\) | −1.26109 | + | 70.6994i | −0.00630545 | + | 0.353497i | ||||
\(201\) | −53.0240 | + | 91.8402i | −0.263801 | + | 0.456917i | ||||
\(202\) | −180.311 | + | 180.311i | −0.892627 | + | 0.892627i | ||||
\(203\) | −310.506 | + | 118.332i | −1.52958 | + | 0.582914i | ||||
\(204\) | − | 52.1698i | − | 0.255734i | ||||||
\(205\) | −125.519 | − | 53.3080i | −0.612288 | − | 0.260039i | ||||
\(206\) | 56.1540 | + | 97.2616i | 0.272592 | + | 0.472144i | ||||
\(207\) | −16.2564 | − | 4.35588i | −0.0785332 | − | 0.0210429i | ||||
\(208\) | 91.3302 | − | 24.4719i | 0.439087 | − | 0.117653i | ||||
\(209\) | 49.6782i | 0.237695i | ||||||||
\(210\) | 3.21546 | − | 85.6718i | 0.0153117 | − | 0.407961i | ||||
\(211\) | −210.755 | −0.998840 | −0.499420 | − | 0.866360i | \(-0.666453\pi\) | ||||
−0.499420 | + | 0.866360i | \(0.666453\pi\) | |||||||
\(212\) | −17.8465 | − | 66.6041i | −0.0841816 | − | 0.314170i | ||||
\(213\) | 45.9358 | − | 171.435i | 0.215661 | − | 0.804858i | ||||
\(214\) | 73.9818 | − | 42.7134i | 0.345709 | − | 0.199595i | ||||
\(215\) | −44.6676 | − | 110.617i | −0.207756 | − | 0.514498i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 6.46654 | − | 7.94617i | 0.0297997 | − | 0.0366183i | ||||
\(218\) | 14.3092 | + | 14.3092i | 0.0656385 | + | 0.0656385i | ||||
\(219\) | −45.9125 | − | 26.5076i | −0.209646 | − | 0.121039i | ||||
\(220\) | −19.1701 | − | 25.4497i | −0.0871369 | − | 0.115681i | ||||
\(221\) | 177.996 | + | 308.298i | 0.805410 | + | 1.39501i | ||||
\(222\) | 35.0298 | + | 130.733i | 0.157792 | + | 0.588887i | ||||
\(223\) | −306.751 | − | 306.751i | −1.37557 | − | 1.37557i | −0.851960 | − | 0.523607i | \(-0.824586\pi\) |
−0.523607 | − | 0.851960i | \(-0.675414\pi\) | |||||||
\(224\) | 4.04392 | + | 39.3909i | 0.0180532 | + | 0.175852i | ||||
\(225\) | −18.1163 | − | 72.7791i | −0.0805170 | − | 0.323463i | ||||
\(226\) | 66.0293 | − | 114.366i | 0.292165 | − | 0.506044i | ||||
\(227\) | −17.9726 | − | 4.81575i | −0.0791745 | − | 0.0212147i | 0.219014 | − | 0.975722i | \(-0.429716\pi\) |
−0.298189 | + | 0.954507i | \(0.596383\pi\) | |||||||
\(228\) | 13.9791 | − | 52.1708i | 0.0613120 | − | 0.228820i | ||||
\(229\) | 53.2936 | + | 30.7691i | 0.232723 | + | 0.134363i | 0.611828 | − | 0.790991i | \(-0.290435\pi\) |
−0.379104 | + | 0.925354i | \(0.623768\pi\) | |||||||
\(230\) | −4.82683 | − | 39.3736i | −0.0209862 | − | 0.171189i | ||||
\(231\) | 22.6309 | + | 31.3076i | 0.0979691 | + | 0.135531i | ||||
\(232\) | 94.9398 | − | 94.9398i | 0.409223 | − | 0.409223i | ||||
\(233\) | 241.844 | − | 64.8020i | 1.03796 | − | 0.278120i | 0.300691 | − | 0.953722i | \(-0.402783\pi\) |
0.737267 | + | 0.675602i | \(0.236116\pi\) | |||||||
\(234\) | −86.8515 | + | 50.1438i | −0.371160 | + | 0.214290i | ||||
\(235\) | 18.9665 | − | 134.767i | 0.0807085 | − | 0.573476i | ||||
\(236\) | −53.4827 | + | 92.6348i | −0.226622 | + | 0.392520i | ||||
\(237\) | 142.894 | − | 142.894i | 0.602927 | − | 0.602927i | ||||
\(238\) | −139.314 | + | 53.0917i | −0.585353 | + | 0.223074i | ||||
\(239\) | − | 19.0275i | − | 0.0796128i | −0.999207 | − | 0.0398064i | \(-0.987326\pi\) | ||
0.999207 | − | 0.0398064i | \(-0.0126741\pi\) | |||||||
\(240\) | 12.9706 | + | 32.1211i | 0.0540442 | + | 0.133838i | ||||
\(241\) | 148.159 | + | 256.620i | 0.614769 | + | 1.06481i | 0.990425 | + | 0.138052i | \(0.0440841\pi\) |
−0.375656 | + | 0.926759i | \(0.622583\pi\) | |||||||
\(242\) | −151.421 | − | 40.5732i | −0.625708 | − | 0.167658i | ||||
\(243\) | −15.0573 | + | 4.03459i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | 81.6940i | 0.334812i | ||||||||
\(245\) | −232.050 | + | 78.5991i | −0.947143 | + | 0.320813i | ||||
\(246\) | −66.8073 | −0.271575 | ||||||||
\(247\) | 95.3894 | + | 355.998i | 0.386192 | + | 1.44129i | ||||
\(248\) | −1.07140 | + | 3.99851i | −0.00432015 | + | 0.0161230i | ||||
\(249\) | 158.902 | − | 91.7423i | 0.638162 | − | 0.368443i | ||||
\(250\) | 143.075 | − | 103.825i | 0.572300 | − | 0.415299i | ||||
\(251\) | −431.580 | −1.71944 | −0.859721 | − | 0.510763i | \(-0.829363\pi\) | ||||
−0.859721 | + | 0.510763i | \(0.829363\pi\) | |||||||
\(252\) | −14.9566 | − | 39.2466i | −0.0593517 | − | 0.155741i | ||||
\(253\) | 12.6391 | + | 12.6391i | 0.0499569 | + | 0.0499569i | ||||
\(254\) | −260.078 | − | 150.156i | −1.02393 | − | 0.591166i | ||||
\(255\) | −104.177 | + | 78.4716i | −0.408536 | + | 0.307732i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −80.0190 | − | 298.635i | −0.311358 | − | 1.16200i | −0.927333 | − | 0.374238i | \(-0.877904\pi\) |
0.615975 | − | 0.787766i | \(-0.288762\pi\) | |||||||
\(258\) | −41.3251 | − | 41.3251i | −0.160175 | − | 0.160175i | ||||
\(259\) | 313.460 | − | 226.587i | 1.21027 | − | 0.874851i | ||||
\(260\) | −186.242 | − | 145.566i | −0.716316 | − | 0.559868i | ||||
\(261\) | −71.2048 | + | 123.330i | −0.272815 | + | 0.472530i | ||||
\(262\) | −323.571 | − | 86.7005i | −1.23500 | − | 0.330918i | ||||
\(263\) | −66.3382 | + | 247.577i | −0.252236 | + | 0.941359i | 0.717371 | + | 0.696692i | \(0.245345\pi\) |
−0.969607 | + | 0.244667i | \(0.921321\pi\) | |||||||
\(264\) | −13.5179 | − | 7.80455i | −0.0512041 | − | 0.0295627i | ||||
\(265\) | −106.156 | + | 135.820i | −0.400589 | + | 0.512529i | ||||
\(266\) | −153.543 | + | 15.7629i | −0.577229 | + | 0.0592590i | ||||
\(267\) | 129.823 | − | 129.823i | 0.486229 | − | 0.486229i | ||||
\(268\) | −118.281 | + | 31.6933i | −0.441348 | + | 0.118259i | ||||
\(269\) | 165.231 | − | 95.3963i | 0.614242 | − | 0.354633i | −0.160382 | − | 0.987055i | \(-0.551272\pi\) |
0.774624 | + | 0.632422i | \(0.217939\pi\) | |||||||
\(270\) | −22.1065 | − | 29.3480i | −0.0818759 | − | 0.108696i | ||||
\(271\) | −86.4705 | + | 149.771i | −0.319080 | + | 0.552662i | −0.980296 | − | 0.197533i | \(-0.936707\pi\) |
0.661217 | + | 0.750195i | \(0.270040\pi\) | |||||||
\(272\) | 42.5965 | − | 42.5965i | 0.156605 | − | 0.156605i | ||||
\(273\) | 222.290 | + | 180.898i | 0.814249 | + | 0.662631i | ||||
\(274\) | − | 151.585i | − | 0.553230i | ||||||
\(275\) | −21.9851 | + | 76.5607i | −0.0799458 | + | 0.278403i | ||||
\(276\) | −9.71671 | − | 16.8298i | −0.0352055 | − | 0.0609777i | ||||
\(277\) | −442.182 | − | 118.482i | −1.59633 | − | 0.427734i | −0.652395 | − | 0.757879i | \(-0.726236\pi\) |
−0.943930 | + | 0.330145i | \(0.892903\pi\) | |||||||
\(278\) | 355.097 | − | 95.1481i | 1.27733 | − | 0.342259i | ||||
\(279\) | − | 4.39067i | − | 0.0157372i | ||||||
\(280\) | 72.5762 | − | 67.3253i | 0.259201 | − | 0.240448i | ||||
\(281\) | −268.170 | −0.954340 | −0.477170 | − | 0.878811i | \(-0.658337\pi\) | ||||
−0.477170 | + | 0.878811i | \(0.658337\pi\) | |||||||
\(282\) | −17.2561 | − | 64.4008i | −0.0611920 | − | 0.228372i | ||||
\(283\) | 36.2210 | − | 135.179i | 0.127989 | − | 0.477663i | −0.871939 | − | 0.489614i | \(-0.837138\pi\) |
0.999929 | + | 0.0119513i | \(0.00380432\pi\) | |||||||
\(284\) | 177.482 | − | 102.469i | 0.624938 | − | 0.360808i | ||||
\(285\) | −125.206 | + | 50.5585i | −0.439318 | + | 0.177398i | ||||
\(286\) | 106.512 | 0.372419 | ||||||||
\(287\) | 67.9878 | + | 178.402i | 0.236891 | + | 0.621610i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | −53.8601 | − | 31.0962i | −0.186367 | − | 0.107599i | ||||
\(290\) | −332.387 | − | 46.7787i | −1.14616 | − | 0.161306i | ||||
\(291\) | −81.2267 | − | 140.689i | −0.279130 | − | 0.483467i | ||||
\(292\) | −15.8440 | − | 59.1307i | −0.0542604 | − | 0.202503i | ||||
\(293\) | 98.0721 | + | 98.0721i | 0.334717 | + | 0.334717i | 0.854375 | − | 0.519657i | \(-0.173940\pi\) |
−0.519657 | + | 0.854375i | \(0.673940\pi\) | |||||||
\(294\) | −89.5831 | + | 79.8803i | −0.304705 | + | 0.271702i | ||||
\(295\) | 265.427 | − | 32.5388i | 0.899751 | − | 0.110301i | ||||
\(296\) | −78.1413 | + | 135.345i | −0.263991 | + | 0.457246i | ||||
\(297\) | 15.9918 | + | 4.28499i | 0.0538445 | + | 0.0144276i | ||||
\(298\) | 11.1542 | − | 41.6279i | 0.0374301 | − | 0.139691i | ||||
\(299\) | 114.842 | + | 66.3039i | 0.384086 | + | 0.221752i | ||||
\(300\) | 44.6320 | − | 74.2158i | 0.148773 | − | 0.247386i | ||||
\(301\) | −68.2990 | + | 152.410i | −0.226907 | + | 0.506344i | ||||
\(302\) | 93.0401 | − | 93.0401i | 0.308080 | − | 0.308080i | ||||
\(303\) | 301.666 | − | 80.8311i | 0.995596 | − | 0.266769i | ||||
\(304\) | 54.0112 | − | 31.1834i | 0.177669 | − | 0.102577i | ||||
\(305\) | 163.133 | − | 122.881i | 0.534862 | − | 0.402887i | ||||
\(306\) | −31.9474 | + | 55.3345i | −0.104403 | + | 0.180832i | ||||
\(307\) | 256.782 | − | 256.782i | 0.836422 | − | 0.836422i | −0.151964 | − | 0.988386i | \(-0.548560\pi\) |
0.988386 | + | 0.151964i | \(0.0485598\pi\) | |||||||
\(308\) | −7.08449 | + | 44.0405i | −0.0230016 | + | 0.142989i | ||||
\(309\) | − | 137.549i | − | 0.445141i | ||||||
\(310\) | 9.59608 | − | 3.87493i | 0.0309551 | − | 0.0124998i | ||||
\(311\) | 103.111 | + | 178.593i | 0.331545 | + | 0.574253i | 0.982815 | − | 0.184593i | \(-0.0590968\pi\) |
−0.651270 | + | 0.758846i | \(0.725763\pi\) | |||||||
\(312\) | −111.856 | − | 29.9718i | −0.358513 | − | 0.0960634i | ||||
\(313\) | −486.861 | + | 130.454i | −1.55547 | + | 0.416786i | −0.931225 | − | 0.364445i | \(-0.881259\pi\) |
−0.624242 | + | 0.781231i | \(0.714592\pi\) | |||||||
\(314\) | − | 63.3717i | − | 0.201821i | ||||||
\(315\) | −55.8736 | + | 88.8996i | −0.177376 | + | 0.282221i | ||||
\(316\) | 233.344 | 0.738431 | ||||||||
\(317\) | 51.2938 | + | 191.431i | 0.161810 | + | 0.603884i | 0.998426 | + | 0.0560930i | \(0.0178643\pi\) |
−0.836615 | + | 0.547791i | \(0.815469\pi\) | |||||||
\(318\) | −21.8574 | + | 81.5730i | −0.0687340 | + | 0.256519i | ||||
\(319\) | 130.985 | − | 75.6241i | 0.410611 | − | 0.237066i | ||||
\(320\) | −15.6363 | + | 36.8172i | −0.0488634 | + | 0.115054i | ||||
\(321\) | −104.626 | −0.325938 | ||||||||
\(322\) | −35.0539 | + | 43.0747i | −0.108863 | + | 0.133772i | ||||
\(323\) | 166.038 | + | 166.038i | 0.514049 | + | 0.514049i | ||||
\(324\) | −15.5885 | − | 9.00000i | −0.0481125 | − | 0.0277778i | ||||
\(325\) | −10.5393 | + | 590.856i | −0.0324286 | + | 1.81802i | ||||
\(326\) | 97.3388 | + | 168.596i | 0.298585 | + | 0.517165i | ||||
\(327\) | −6.41464 | − | 23.9398i | −0.0196166 | − | 0.0732103i | ||||
\(328\) | −54.5480 | − | 54.5480i | −0.166305 | − | 0.166305i | ||||
\(329\) | −154.415 | + | 111.620i | −0.469345 | + | 0.339269i | ||||
\(330\) | 4.74827 | + | 38.7328i | 0.0143887 | + | 0.117372i | ||||
\(331\) | 40.5455 | − | 70.2269i | 0.122494 | − | 0.212166i | −0.798257 | − | 0.602317i | \(-0.794244\pi\) |
0.920751 | + | 0.390152i | \(0.127577\pi\) | |||||||
\(332\) | 204.650 | + | 54.8359i | 0.616417 | + | 0.165168i | ||||
\(333\) | 42.9026 | − | 160.115i | 0.128837 | − | 0.480825i | ||||
\(334\) | 76.7687 | + | 44.3224i | 0.229846 | + | 0.132702i | ||||
\(335\) | 241.201 | + | 188.521i | 0.720003 | + | 0.562750i | ||||
\(336\) | 19.8327 | − | 44.2568i | 0.0590259 | − | 0.131717i | ||||
\(337\) | −440.171 | + | 440.171i | −1.30614 | + | 1.30614i | −0.381969 | + | 0.924175i | \(0.624754\pi\) |
−0.924175 | + | 0.381969i | \(0.875246\pi\) | |||||||
\(338\) | 532.415 | − | 142.660i | 1.57519 | − | 0.422071i | ||||
\(339\) | −140.069 | + | 80.8690i | −0.413184 | + | 0.238552i | ||||
\(340\) | −149.132 | − | 20.9882i | −0.438623 | − | 0.0617299i | ||||
\(341\) | −2.33159 | + | 4.03843i | −0.00683750 | + | 0.0118429i | ||||
\(342\) | −46.7751 | + | 46.7751i | −0.136769 | + | 0.136769i | ||||
\(343\) | 304.478 | + | 157.931i | 0.887691 | + | 0.460439i | ||||
\(344\) | − | 67.4835i | − | 0.196173i | ||||||
\(345\) | −18.9917 | + | 44.7178i | −0.0550483 | + | 0.129617i | ||||
\(346\) | −78.3581 | − | 135.720i | −0.226468 | − | 0.392255i | ||||
\(347\) | −65.0860 | − | 17.4397i | −0.187568 | − | 0.0502586i | 0.163812 | − | 0.986492i | \(-0.447621\pi\) |
−0.351380 | + | 0.936233i | \(0.614288\pi\) | |||||||
\(348\) | −158.837 | + | 42.5603i | −0.456429 | + | 0.122300i | ||||
\(349\) | 28.9513i | 0.0829550i | 0.999139 | + | 0.0414775i | \(0.0132065\pi\) | ||||
−0.999139 | + | 0.0414775i | \(0.986794\pi\) | |||||||
\(350\) | −243.606 | − | 43.6578i | −0.696018 | − | 0.124737i | ||||
\(351\) | 122.827 | 0.349933 | ||||||||
\(352\) | −4.66491 | − | 17.4097i | −0.0132526 | − | 0.0494593i | ||||
\(353\) | 166.352 | − | 620.833i | 0.471251 | − | 1.75873i | −0.164032 | − | 0.986455i | \(-0.552450\pi\) |
0.635284 | − | 0.772279i | \(-0.280883\pi\) | |||||||
\(354\) | 113.454 | − | 65.5027i | 0.320492 | − | 0.185036i | ||||
\(355\) | −471.580 | − | 200.280i | −1.32839 | − | 0.564169i | ||||
\(356\) | 212.000 | 0.595506 | ||||||||
\(357\) | 180.277 | + | 28.9999i | 0.504977 | + | 0.0812322i | ||||
\(358\) | 288.924 | + | 288.924i | 0.807050 | + | 0.807050i | ||||
\(359\) | −61.7189 | − | 35.6334i | −0.171919 | − | 0.0992575i | 0.411571 | − | 0.911378i | \(-0.364980\pi\) |
−0.583490 | + | 0.812120i | \(0.698313\pi\) | |||||||
\(360\) | 5.91264 | − | 42.0124i | 0.0164240 | − | 0.116701i | ||||
\(361\) | −58.9494 | − | 102.103i | −0.163295 | − | 0.282835i | ||||
\(362\) | −43.6732 | − | 162.991i | −0.120644 | − | 0.450250i | ||||
\(363\) | 135.761 | + | 135.761i | 0.373997 | + | 0.373997i | ||||
\(364\) | 33.7962 | + | 329.202i | 0.0928467 | + | 0.904400i | ||||
\(365\) | −94.2449 | + | 120.580i | −0.258205 | + | 0.330357i | ||||
\(366\) | 50.0272 | − | 86.6496i | 0.136686 | − | 0.236747i | ||||
\(367\) | 226.363 | + | 60.6537i | 0.616792 | + | 0.165269i | 0.553669 | − | 0.832737i | \(-0.313227\pi\) |
0.0631229 | + | 0.998006i | \(0.479894\pi\) | |||||||
\(368\) | 5.80784 | − | 21.6752i | 0.0157822 | − | 0.0588999i | ||||
\(369\) | 70.8599 | + | 40.9110i | 0.192032 | + | 0.110870i | ||||
\(370\) | 387.804 | − | 47.5411i | 1.04812 | − | 0.128489i | ||||
\(371\) | 240.076 | − | 24.6465i | 0.647105 | − | 0.0664325i | ||||
\(372\) | 3.58497 | − | 3.58497i | 0.00963700 | − | 0.00963700i | ||||
\(373\) | 94.5060 | − | 25.3228i | 0.253367 | − | 0.0678895i | −0.129900 | − | 0.991527i | \(-0.541466\pi\) |
0.383267 | + | 0.923638i | \(0.374799\pi\) | |||||||
\(374\) | 58.7688 | − | 33.9302i | 0.157136 | − | 0.0907224i | ||||
\(375\) | −215.333 | + | 22.5076i | −0.574222 | + | 0.0600204i | ||||
\(376\) | 38.4935 | − | 66.6726i | 0.102376 | − | 0.177321i | ||||
\(377\) | 793.439 | − | 793.439i | 2.10461 | − | 2.10461i | ||||
\(378\) | −8.16965 | + | 50.7864i | −0.0216128 | + | 0.134356i | ||||
\(379\) | 415.479i | 1.09625i | 0.836396 | + | 0.548126i | \(0.184658\pi\) | ||||
−0.836396 | + | 0.548126i | \(0.815342\pi\) | |||||||
\(380\) | −143.511 | − | 60.9491i | −0.377660 | − | 0.160392i | ||||
\(381\) | 183.903 | + | 318.529i | 0.482685 | + | 0.836034i | ||||
\(382\) | −173.217 | − | 46.4134i | −0.453449 | − | 0.121501i | ||||
\(383\) | 254.473 | − | 68.1859i | 0.664421 | − | 0.178031i | 0.0891805 | − | 0.996015i | \(-0.471575\pi\) |
0.575240 | + | 0.817984i | \(0.304909\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 98.5997 | − | 52.0970i | 0.256103 | − | 0.135317i | ||||
\(386\) | −405.827 | −1.05137 | ||||||||
\(387\) | 18.5255 | + | 69.1382i | 0.0478695 | + | 0.178652i | ||||
\(388\) | 48.5506 | − | 181.193i | 0.125130 | − | 0.466993i | ||||
\(389\) | −100.478 | + | 58.0113i | −0.258299 | + | 0.149129i | −0.623559 | − | 0.781777i | \(-0.714314\pi\) |
0.365259 | + | 0.930906i | \(0.380980\pi\) | |||||||
\(390\) | 108.399 | + | 268.445i | 0.277947 | + | 0.688321i | ||||
\(391\) | 84.4865 | 0.216078 | ||||||||
\(392\) | −138.366 | − | 7.92236i | −0.352975 | − | 0.0202101i | ||||
\(393\) | 290.105 | + | 290.105i | 0.738182 | + | 0.738182i | ||||
\(394\) | −5.92194 | − | 3.41904i | −0.0150303 | − | 0.00867776i | ||||
\(395\) | −350.986 | − | 465.960i | −0.888573 | − | 1.17964i | ||||
\(396\) | 9.55858 | + | 16.5559i | 0.0241378 | + | 0.0418079i | ||||
\(397\) | −138.287 | − | 516.094i | −0.348330 | − | 1.29998i | −0.888674 | − | 0.458540i | \(-0.848373\pi\) |
0.540344 | − | 0.841444i | \(-0.318294\pi\) | |||||||
\(398\) | −219.574 | − | 219.574i | −0.551694 | − | 0.551694i | ||||
\(399\) | 172.510 | + | 77.3064i | 0.432355 | + | 0.193750i | ||||
\(400\) | 97.0388 | − | 24.1551i | 0.242597 | − | 0.0603878i | ||||
\(401\) | 222.706 | − | 385.738i | 0.555376 | − | 0.961939i | −0.442498 | − | 0.896769i | \(-0.645908\pi\) |
0.997874 | − | 0.0651700i | \(-0.0207590\pi\) | |||||||
\(402\) | 144.864 | + | 38.8163i | 0.360359 | + | 0.0965578i | ||||
\(403\) | −8.95398 | + | 33.4167i | −0.0222183 | + | 0.0829199i | ||||
\(404\) | 312.307 | + | 180.311i | 0.773038 | + | 0.446314i | ||||
\(405\) | 5.47559 | + | 44.6656i | 0.0135200 | + | 0.110285i | ||||
\(406\) | 275.297 | + | 380.846i | 0.678071 | + | 0.938045i | ||||
\(407\) | −124.487 | + | 124.487i | −0.305864 | + | 0.305864i | ||||
\(408\) | −71.2653 | + | 19.0955i | −0.174670 | + | 0.0468027i | ||||
\(409\) | −244.715 | + | 141.286i | −0.598326 | + | 0.345444i | −0.768383 | − | 0.639991i | \(-0.778938\pi\) |
0.170057 | + | 0.985434i | \(0.445605\pi\) | |||||||
\(410\) | −26.8769 | + | 190.974i | −0.0655534 | + | 0.465791i | ||||
\(411\) | −92.8266 | + | 160.780i | −0.225855 | + | 0.391193i | ||||
\(412\) | 112.308 | − | 112.308i | 0.272592 | − | 0.272592i | ||||
\(413\) | −290.377 | − | 236.307i | −0.703092 | − | 0.572172i | ||||
\(414\) | 23.8010i | 0.0574903i | ||||||||
\(415\) | −198.326 | − | 491.143i | −0.477893 | − | 1.18348i | ||||
\(416\) | −66.8583 | − | 115.802i | −0.160717 | − | 0.278370i | ||||
\(417\) | −434.904 | − | 116.532i | −1.04293 | − | 0.279453i | ||||
\(418\) | 67.8616 | − | 18.1835i | 0.162348 | − | 0.0435011i | ||||
\(419\) | − | 128.452i | − | 0.306567i | −0.988182 | − | 0.153283i | \(-0.951015\pi\) | ||
0.988182 | − | 0.153283i | \(-0.0489848\pi\) | |||||||
\(420\) | −118.207 | + | 26.9657i | −0.281445 | + | 0.0642040i | ||||
\(421\) | −432.680 | −1.02774 | −0.513872 | − | 0.857867i | \(-0.671789\pi\) | ||||
−0.513872 | + | 0.857867i | \(0.671789\pi\) | |||||||
\(422\) | 77.1418 | + | 287.897i | 0.182800 | + | 0.682220i | ||||
\(423\) | −21.1344 | + | 78.8746i | −0.0499631 | + | 0.186465i | ||||
\(424\) | −84.4506 | + | 48.7576i | −0.199176 | + | 0.114994i | ||||
\(425\) | 182.407 | + | 329.367i | 0.429192 | + | 0.774981i | ||||
\(426\) | −250.998 | −0.589197 | ||||||||
\(427\) | −282.300 | − | 45.4116i | −0.661124 | − | 0.106350i | ||||
\(428\) | −85.4268 | − | 85.4268i | −0.199595 | − | 0.199595i | ||||
\(429\) | −112.973 | − | 65.2249i | −0.263340 | − | 0.152039i | ||||
\(430\) | −134.756 | + | 101.506i | −0.313387 | + | 0.236060i | ||||
\(431\) | 204.635 | + | 354.438i | 0.474791 | + | 0.822362i | 0.999583 | − | 0.0288683i | \(-0.00919033\pi\) |
−0.524792 | + | 0.851230i | \(0.675857\pi\) | |||||||
\(432\) | −5.37945 | − | 20.0764i | −0.0124524 | − | 0.0464731i | ||||
\(433\) | 74.6999 | + | 74.6999i | 0.172517 | + | 0.172517i | 0.788084 | − | 0.615567i | \(-0.211073\pi\) |
−0.615567 | + | 0.788084i | \(0.711073\pi\) | |||||||
\(434\) | −13.2216 | − | 5.92496i | −0.0304645 | − | 0.0136520i | ||||
\(435\) | 323.904 | + | 253.161i | 0.744606 | + | 0.581979i | ||||
\(436\) | 14.3092 | − | 24.7843i | 0.0328193 | − | 0.0568446i | ||||
\(437\) | 84.4882 | + | 22.6385i | 0.193337 | + | 0.0518044i | ||||
\(438\) | −19.4049 | + | 72.4201i | −0.0443034 | + | 0.165343i | ||||
\(439\) | 348.826 | + | 201.395i | 0.794592 | + | 0.458758i | 0.841577 | − | 0.540138i | \(-0.181628\pi\) |
−0.0469848 | + | 0.998896i | \(0.514961\pi\) | |||||||
\(440\) | −27.7482 | + | 35.5021i | −0.0630642 | + | 0.0806867i | ||||
\(441\) | 143.934 | − | 29.8676i | 0.326380 | − | 0.0677269i | ||||
\(442\) | 355.991 | − | 355.991i | 0.805410 | − | 0.805410i | ||||
\(443\) | 99.0413 | − | 26.5380i | 0.223569 | − | 0.0599053i | −0.145295 | − | 0.989388i | \(-0.546413\pi\) |
0.368865 | + | 0.929483i | \(0.379747\pi\) | |||||||
\(444\) | 165.763 | − | 95.7032i | 0.373340 | − | 0.215548i | ||||
\(445\) | −318.881 | − | 423.338i | −0.716588 | − | 0.951322i | ||||
\(446\) | −306.751 | + | 531.309i | −0.687784 | + | 1.19128i | ||||
\(447\) | −37.3226 | + | 37.3226i | −0.0834957 | + | 0.0834957i | ||||
\(448\) | 52.3289 | − | 19.9422i | 0.116805 | − | 0.0445138i | ||||
\(449\) | − | 435.242i | − | 0.969359i | −0.874692 | − | 0.484680i | \(-0.838936\pi\) | ||
0.874692 | − | 0.484680i | \(-0.161064\pi\) | |||||||
\(450\) | −92.7871 | + | 51.3864i | −0.206193 | + | 0.114192i | ||||
\(451\) | −43.4501 | − | 75.2578i | −0.0963417 | − | 0.166869i | ||||
\(452\) | −180.395 | − | 48.3368i | −0.399105 | − | 0.106940i | ||||
\(453\) | −155.659 | + | 41.7087i | −0.343618 | + | 0.0920723i | ||||
\(454\) | 26.3137i | 0.0579598i | ||||||||
\(455\) | 606.540 | − | 562.658i | 1.33306 | − | 1.23661i | ||||
\(456\) | −76.3834 | −0.167508 | ||||||||
\(457\) | 32.0021 | + | 119.433i | 0.0700264 | + | 0.261342i | 0.992060 | − | 0.125769i | \(-0.0401397\pi\) |
−0.922033 | + | 0.387111i | \(0.873473\pi\) | |||||||
\(458\) | 22.5245 | − | 84.0627i | 0.0491802 | − | 0.183543i | ||||
\(459\) | 67.7706 | − | 39.1274i | 0.147648 | − | 0.0852448i | ||||
\(460\) | −52.0185 | + | 21.0053i | −0.113084 | + | 0.0456637i | ||||
\(461\) | 721.106 | 1.56422 | 0.782110 | − | 0.623140i | \(-0.214143\pi\) | ||||
0.782110 | + | 0.623140i | \(0.214143\pi\) | |||||||
\(462\) | 34.4834 | − | 42.3737i | 0.0746395 | − | 0.0917179i | ||||
\(463\) | −190.901 | − | 190.901i | −0.412313 | − | 0.412313i | 0.470231 | − | 0.882544i | \(-0.344171\pi\) |
−0.882544 | + | 0.470231i | \(0.844171\pi\) | |||||||
\(464\) | −164.440 | − | 94.9398i | −0.354398 | − | 0.204612i | ||||
\(465\) | −12.5511 | − | 1.76638i | −0.0269916 | − | 0.00379868i | ||||
\(466\) | −177.042 | − | 306.646i | −0.379919 | − | 0.658039i | ||||
\(467\) | −44.6556 | − | 166.657i | −0.0956222 | − | 0.356867i | 0.901491 | − | 0.432798i | \(-0.142474\pi\) |
−0.997113 | + | 0.0759313i | \(0.975807\pi\) | |||||||
\(468\) | 100.288 | + | 100.288i | 0.214290 | + | 0.214290i | ||||
\(469\) | −43.7693 | − | 426.347i | −0.0933246 | − | 0.909055i | ||||
\(470\) | −191.037 | + | 23.4194i | −0.406462 | + | 0.0498284i | ||||
\(471\) | −38.8071 | + | 67.2159i | −0.0823930 | + | 0.142709i | ||||
\(472\) | 146.118 | + | 39.1521i | 0.309571 | + | 0.0829493i | ||||
\(473\) | 19.6753 | − | 73.4292i | 0.0415968 | − | 0.155241i | ||||
\(474\) | −247.499 | − | 142.894i | −0.522150 | − | 0.301463i | ||||
\(475\) | 94.1548 | + | 378.250i | 0.198221 | + | 0.796316i | ||||
\(476\) | 123.517 | + | 170.874i | 0.259490 | + | 0.358978i | ||||
\(477\) | 73.1364 | − | 73.1364i | 0.153326 | − | 0.153326i | ||||
\(478\) | −25.9920 | + | 6.96454i | −0.0543766 | + | 0.0145702i | ||||
\(479\) | 330.041 | − | 190.549i | 0.689021 | − | 0.397806i | −0.114224 | − | 0.993455i | \(-0.536438\pi\) |
0.803245 | + | 0.595649i | \(0.203105\pi\) | |||||||
\(480\) | 39.1306 | − | 29.4753i | 0.0815221 | − | 0.0614069i | ||||
\(481\) | −653.050 | + | 1131.12i | −1.35769 | + | 2.35159i | ||||
\(482\) | 296.319 | − | 296.319i | 0.614769 | − | 0.614769i | ||||
\(483\) | 63.5581 | − | 24.2216i | 0.131590 | − | 0.0501481i | ||||
\(484\) | 221.696i | 0.458050i | ||||||||
\(485\) | −434.848 | + | 175.593i | −0.896594 | + | 0.362048i | ||||
\(486\) | 11.0227 | + | 19.0919i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 233.660 | + | 62.6089i | 0.479794 | + | 0.128560i | 0.490607 | − | 0.871381i | \(-0.336775\pi\) |
−0.0108128 | + | 0.999942i | \(0.503442\pi\) | |||||||
\(488\) | 111.596 | − | 29.9021i | 0.228681 | − | 0.0612748i | ||||
\(489\) | − | 238.430i | − | 0.487588i | ||||||
\(490\) | 192.305 | + | 288.217i | 0.392458 | + | 0.588198i | ||||
\(491\) | −899.374 | −1.83172 | −0.915860 | − | 0.401498i | \(-0.868490\pi\) | ||||
−0.915860 | + | 0.401498i | \(0.868490\pi\) | |||||||
\(492\) | 24.4532 | + | 91.2605i | 0.0497016 | + | 0.185489i | ||||
\(493\) | 185.030 | − | 690.543i | 0.375315 | − | 1.40070i | ||||
\(494\) | 451.388 | − | 260.609i | 0.913740 | − | 0.527548i | ||||
\(495\) | 18.6826 | − | 43.9900i | 0.0377426 | − | 0.0888687i | ||||
\(496\) | 5.85422 | 0.0118029 | ||||||||
\(497\) | 255.433 | + | 670.264i | 0.513950 | + | 1.34862i | ||||
\(498\) | −183.485 | − | 183.485i | −0.368443 | − | 0.368443i | ||||
\(499\) | 128.915 | + | 74.4290i | 0.258346 | + | 0.149156i | 0.623580 | − | 0.781760i | \(-0.285678\pi\) |
−0.365234 | + | 0.930916i | \(0.619011\pi\) | |||||||
\(500\) | −194.196 | − | 157.441i | −0.388393 | − | 0.314883i | ||||
\(501\) | −54.2837 | − | 94.0221i | −0.108351 | − | 0.187669i | ||||
\(502\) | 157.969 | + | 589.549i | 0.314680 | + | 1.17440i | ||||
\(503\) | 306.658 | + | 306.658i | 0.609658 | + | 0.609658i | 0.942857 | − | 0.333199i | \(-0.108128\pi\) |
−0.333199 | + | 0.942857i | \(0.608128\pi\) | |||||||
\(504\) | −48.1374 | + | 34.7964i | −0.0955107 | + | 0.0690405i | ||||
\(505\) | −109.701 | − | 894.854i | −0.217229 | − | 1.77199i | ||||
\(506\) | 12.6391 | − | 21.8915i | 0.0249784 | − | 0.0432639i | ||||
\(507\) | −652.072 | − | 174.722i | −1.28614 | − | 0.344620i | ||||
\(508\) | −109.922 | + | 410.234i | −0.216382 | + | 0.807547i | ||||
\(509\) | 1.24200 | + | 0.717067i | 0.00244007 | + | 0.00140878i | 0.501220 | − | 0.865320i | \(-0.332885\pi\) |
−0.498779 | + | 0.866729i | \(0.666218\pi\) | |||||||
\(510\) | 145.325 | + | 113.585i | 0.284952 | + | 0.222717i | ||||
\(511\) | 213.138 | − | 21.8810i | 0.417100 | − | 0.0428199i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 78.2563 | − | 20.9687i | 0.152546 | − | 0.0408747i | ||||
\(514\) | −378.654 | + | 218.616i | −0.736681 | + | 0.425323i | ||||
\(515\) | −393.194 | − | 55.3364i | −0.763483 | − | 0.107449i | ||||
\(516\) | −41.3251 | + | 71.5771i | −0.0800873 | + | 0.138715i | ||||
\(517\) | 61.3238 | − | 61.3238i | 0.118615 | − | 0.118615i | ||||
\(518\) | −424.257 | − | 345.258i | −0.819030 | − | 0.666521i | ||||
\(519\) | 191.937i | 0.369821i | ||||||||
\(520\) | −130.677 | + | 307.692i | −0.251302 | + | 0.591716i | ||||
\(521\) | −457.957 | − | 793.205i | −0.878996 | − | 1.52247i | −0.852444 | − | 0.522819i | \(-0.824880\pi\) |
−0.0265527 | − | 0.999647i | \(-0.508453\pi\) | |||||||
\(522\) | 194.535 | + | 52.1255i | 0.372673 | + | 0.0998574i | ||||
\(523\) | 39.3228 | − | 10.5365i | 0.0751870 | − | 0.0201463i | −0.221029 | − | 0.975267i | \(-0.570942\pi\) |
0.296216 | + | 0.955121i | \(0.404275\pi\) | |||||||
\(524\) | 473.740i | 0.904084i | ||||||||
\(525\) | 231.649 | + | 195.484i | 0.441235 | + | 0.372350i | ||||
\(526\) | 362.478 | 0.689123 | ||||||||
\(527\) | 5.70472 | + | 21.2903i | 0.0108249 | + | 0.0403991i | ||||
\(528\) | −5.71333 | + | 21.3224i | −0.0108207 | + | 0.0403834i | ||||
\(529\) | −430.872 | + | 248.764i | −0.814503 | + | 0.470254i | ||||
\(530\) | 224.390 | + | 95.2984i | 0.423377 | + | 0.179808i | ||||
\(531\) | −160.448 | −0.302162 | ||||||||
\(532\) | 77.7331 | + | 203.974i | 0.146115 | + | 0.383410i | ||||
\(533\) | −455.873 | − | 455.873i | −0.855297 | − | 0.855297i | ||||
\(534\) | −224.860 | − | 129.823i | −0.421087 | − | 0.243114i | ||||
\(535\) | −42.0915 | + | 299.082i | −0.0786757 | + | 0.559032i | ||||
\(536\) | 86.5878 | + | 149.974i | 0.161544 | + | 0.279803i | ||||
\(537\) | −129.521 | − | 483.379i | −0.241194 | − | 0.900148i | ||||
\(538\) | −190.793 | − | 190.793i | −0.354633 | − | 0.354633i | ||||
\(539\) | −148.247 | − | 48.9620i | −0.275041 | − | 0.0908386i | ||||
\(540\) | −31.9985 | + | 40.9401i | −0.0592565 | + | 0.0758150i | ||||
\(541\) | 301.769 | − | 522.680i | 0.557799 | − | 0.966137i | −0.439881 | − | 0.898056i | \(-0.644979\pi\) |
0.997680 | − | 0.0680803i | \(-0.0216874\pi\) | |||||||
\(542\) | 236.242 | + | 63.3008i | 0.435871 | + | 0.116791i | ||||
\(543\) | −53.4885 | + | 199.622i | −0.0985055 | + | 0.367628i | ||||
\(544\) | −73.7793 | − | 42.5965i | −0.135624 | − | 0.0783024i | ||||
\(545\) | −71.0144 | + | 8.70569i | −0.130302 | + | 0.0159737i | ||||
\(546\) | 165.748 | − | 369.867i | 0.303567 | − | 0.677412i | ||||
\(547\) | −518.562 | + | 518.562i | −0.948010 | + | 0.948010i | −0.998714 | − | 0.0507035i | \(-0.983854\pi\) |
0.0507035 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(548\) | −207.069 | + | 55.4840i | −0.377863 | + | 0.101248i | ||||
\(549\) | −106.124 | + | 61.2705i | −0.193304 | + | 0.111604i | ||||
\(550\) | 112.631 | + | 2.00904i | 0.204784 | + | 0.00365279i | ||||
\(551\) | 370.068 | − | 640.977i | 0.671630 | − | 1.16330i | ||||
\(552\) | −19.4334 | + | 19.4334i | −0.0352055 | + | 0.0352055i | ||||
\(553\) | −129.710 | + | 806.339i | −0.234557 | + | 1.45812i | ||||
\(554\) | 647.400i | 1.16859i | ||||||||
\(555\) | −440.441 | − | 187.055i | −0.793587 | − | 0.337037i | ||||
\(556\) | −259.949 | − | 450.245i | −0.467535 | − | 0.809794i | ||||
\(557\) | −835.705 | − | 223.927i | −1.50037 | − | 0.402023i | −0.587145 | − | 0.809482i | \(-0.699748\pi\) |
−0.913223 | + | 0.407459i | \(0.866415\pi\) | |||||||
\(558\) | −5.99776 | + | 1.60710i | −0.0107487 | + | 0.00288010i | ||||
\(559\) | − | 563.980i | − | 1.00891i | ||||||
\(560\) | −118.533 | − | 74.4981i | −0.211666 | − | 0.133032i | ||||
\(561\) | −83.1116 | −0.148149 | ||||||||
\(562\) | 98.1569 | + | 366.326i | 0.174656 | + | 0.651826i | ||||
\(563\) | −137.803 | + | 514.289i | −0.244766 | + | 0.913480i | 0.728734 | + | 0.684796i | \(0.240109\pi\) |
−0.973501 | + | 0.228684i | \(0.926558\pi\) | |||||||
\(564\) | −81.6570 | + | 47.1447i | −0.144782 | + | 0.0835898i | ||||
\(565\) | 174.820 | + | 432.933i | 0.309416 | + | 0.766253i | ||||
\(566\) | −197.915 | −0.349673 | ||||||||
\(567\) | 39.7654 | − | 48.8642i | 0.0701330 | − | 0.0861803i | ||||
\(568\) | −204.939 | − | 204.939i | −0.360808 | − | 0.360808i | ||||
\(569\) | −758.601 | − | 437.979i | −1.33322 | − | 0.769734i | −0.347427 | − | 0.937707i | \(-0.612945\pi\) |
−0.985792 | + | 0.167973i | \(0.946278\pi\) | |||||||
\(570\) | 114.893 | + | 152.528i | 0.201566 | + | 0.267593i | ||||
\(571\) | 92.9859 | + | 161.056i | 0.162847 | + | 0.282060i | 0.935889 | − | 0.352296i | \(-0.114599\pi\) |
−0.773041 | + | 0.634356i | \(0.781266\pi\) | |||||||
\(572\) | −38.9860 | − | 145.498i | −0.0681574 | − | 0.254367i | ||||
\(573\) | 155.302 | + | 155.302i | 0.271034 | + | 0.271034i | ||||
\(574\) | 218.816 | − | 158.173i | 0.381213 | − | 0.275562i | ||||
\(575\) | 120.189 | + | 72.2793i | 0.209024 | + | 0.125703i | ||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −38.0669 | − | 10.2000i | −0.0659739 | − | 0.0176776i | 0.225681 | − | 0.974201i | \(-0.427539\pi\) |
−0.291655 | + | 0.956524i | \(0.594206\pi\) | |||||||
\(578\) | −22.7640 | + | 84.9563i | −0.0393840 | + | 0.146983i | ||||
\(579\) | 430.445 | + | 248.517i | 0.743428 | + | 0.429218i | ||||
\(580\) | 57.7612 | + | 471.171i | 0.0995883 | + | 0.812365i | ||||
\(581\) | −303.250 | + | 676.703i | −0.521944 | + | 1.16472i | ||||
\(582\) | −162.453 | + | 162.453i | −0.279130 | + | 0.279130i | ||||
\(583\) | −106.107 | + | 28.4312i | −0.182001 | + | 0.0487671i | ||||
\(584\) | −74.9748 | + | 43.2867i | −0.128381 | + | 0.0741211i | ||||
\(585\) | 49.4137 | − | 351.110i | 0.0844678 | − | 0.600188i | ||||
\(586\) | 98.0721 | − | 169.866i | 0.167359 | − | 0.289874i | ||||
\(587\) | −269.361 | + | 269.361i | −0.458878 | + | 0.458878i | −0.898287 | − | 0.439409i | \(-0.855188\pi\) |
0.439409 | + | 0.898287i | \(0.355188\pi\) | |||||||
\(588\) | 141.908 | + | 93.1346i | 0.241340 | + | 0.158392i | ||||
\(589\) | 22.8193i | 0.0387425i | ||||||||
\(590\) | −141.602 | − | 350.669i | −0.240003 | − | 0.594355i | ||||
\(591\) | 4.18745 | + | 7.25287i | 0.00708536 | + | 0.0122722i | ||||
\(592\) | 213.486 | + | 57.2034i | 0.360618 | + | 0.0966274i | ||||
\(593\) | −583.511 | + | 156.351i | −0.983998 | + | 0.263661i | −0.714727 | − | 0.699403i | \(-0.753449\pi\) |
−0.269270 | + | 0.963065i | \(0.586783\pi\) | |||||||
\(594\) | − | 23.4136i | − | 0.0394169i | ||||||
\(595\) | 155.425 | − | 503.669i | 0.261218 | − | 0.846503i | ||||
\(596\) | −60.9475 | −0.102261 | ||||||||
\(597\) | 98.4325 | + | 367.355i | 0.164879 | + | 0.615335i | ||||
\(598\) | 48.5378 | − | 181.146i | 0.0811670 | − | 0.302919i | ||||
\(599\) | −373.767 | + | 215.794i | −0.623985 | + | 0.360258i | −0.778419 | − | 0.627745i | \(-0.783978\pi\) |
0.154434 | + | 0.988003i | \(0.450645\pi\) | |||||||
\(600\) | −117.717 | − | 33.8035i | −0.196195 | − | 0.0563392i | ||||
\(601\) | 473.060 | 0.787121 | 0.393560 | − | 0.919299i | \(-0.371243\pi\) | ||||
0.393560 | + | 0.919299i | \(0.371243\pi\) | |||||||
\(602\) | 233.194 | + | 37.5124i | 0.387366 | + | 0.0623129i | ||||
\(603\) | −129.882 | − | 129.882i | −0.215393 | − | 0.215393i | ||||
\(604\) | −161.150 | − | 93.0401i | −0.266805 | − | 0.154040i | ||||
\(605\) | 442.700 | − | 333.466i | 0.731736 | − | 0.551183i | ||||
\(606\) | −220.835 | − | 382.497i | −0.364414 | − | 0.631183i | ||||
\(607\) | 296.215 | + | 1105.49i | 0.487999 | + | 1.82124i | 0.566160 | + | 0.824296i | \(0.308429\pi\) |
−0.0781609 | + | 0.996941i | \(0.524905\pi\) | |||||||
\(608\) | −62.3668 | − | 62.3668i | −0.102577 | − | 0.102577i | ||||
\(609\) | −58.7768 | − | 572.533i | −0.0965137 | − | 0.940119i | ||||
\(610\) | −227.569 | − | 177.866i | −0.373063 | − | 0.291584i | ||||
\(611\) | 321.701 | − | 557.203i | 0.526516 | − | 0.911952i | ||||
\(612\) | 87.2818 | + | 23.3871i | 0.142617 | + | 0.0382142i | ||||
\(613\) | −36.9829 | + | 138.022i | −0.0603310 | + | 0.225158i | −0.989508 | − | 0.144476i | \(-0.953850\pi\) |
0.929177 | + | 0.369634i | \(0.120517\pi\) | |||||||
\(614\) | −444.759 | − | 256.782i | −0.724363 | − | 0.418211i | ||||
\(615\) | 145.455 | − | 186.100i | 0.236512 | − | 0.302602i | ||||
\(616\) | 62.7536 | − | 6.44235i | 0.101873 | − | 0.0104584i | ||||
\(617\) | 341.819 | − | 341.819i | 0.554002 | − | 0.554002i | −0.373591 | − | 0.927593i | \(-0.621874\pi\) |
0.927593 | + | 0.373591i | \(0.121874\pi\) | |||||||
\(618\) | −187.895 | + | 50.3463i | −0.304037 | + | 0.0814665i | ||||
\(619\) | 260.991 | − | 150.683i | 0.421633 | − | 0.243430i | −0.274143 | − | 0.961689i | \(-0.588394\pi\) |
0.695776 | + | 0.718259i | \(0.255061\pi\) | |||||||
\(620\) | −8.80567 | − | 11.6902i | −0.0142027 | − | 0.0188551i | ||||
\(621\) | 14.5751 | − | 25.2448i | 0.0234703 | − | 0.0406518i | ||||
\(622\) | 206.221 | − | 206.221i | 0.331545 | − | 0.331545i | ||||
\(623\) | −117.846 | + | 732.583i | −0.189158 | + | 1.17590i | ||||
\(624\) | 163.769i | 0.262450i | ||||||||
\(625\) | −22.2896 | + | 624.602i | −0.0356633 | + | 0.999364i | ||||
\(626\) | 356.407 | + | 617.315i | 0.569340 | + | 0.986127i | ||||
\(627\) | −83.1132 | − | 22.2701i | −0.132557 | − | 0.0355185i | ||||
\(628\) | −86.5674 | + | 23.1957i | −0.137846 | + | 0.0369358i | ||||
\(629\) | 832.137i | 1.32295i | ||||||||
\(630\) | 141.890 | + | 43.7852i | 0.225223 | + | 0.0695003i | ||||
\(631\) | 866.914 | 1.37387 | 0.686937 | − | 0.726717i | \(-0.258955\pi\) | ||||
0.686937 | + | 0.726717i | \(0.258955\pi\) | |||||||
\(632\) | −85.4099 | − | 318.754i | −0.135142 | − | 0.504358i | ||||
\(633\) | 94.4790 | − | 352.600i | 0.149256 | − | 0.557031i | ||||
\(634\) | 242.725 | − | 140.137i | 0.382847 | − | 0.221037i | ||||
\(635\) | 984.526 | − | 397.556i | 1.55044 | − | 0.626072i | ||||
\(636\) | 119.431 | 0.187785 | ||||||||
\(637\) | −1156.37 | − | 66.2094i | −1.81533 | − | 0.103939i | ||||
\(638\) | −151.248 | − | 151.248i | −0.237066 | − | 0.237066i | ||||
\(639\) | 266.223 | + | 153.704i | 0.416625 | + | 0.240539i | ||||
\(640\) | 56.0165 | + | 7.88352i | 0.0875258 | + | 0.0123180i | ||||
\(641\) | 263.616 | + | 456.597i | 0.411258 | + | 0.712319i | 0.995028 | − | 0.0996000i | \(-0.0317563\pi\) |
−0.583770 | + | 0.811919i | \(0.698423\pi\) | |||||||
\(642\) | 38.2958 | + | 142.922i | 0.0596508 | + | 0.222620i | ||||
\(643\) | −831.612 | − | 831.612i | −1.29333 | − | 1.29333i | −0.932714 | − | 0.360617i | \(-0.882566\pi\) |
−0.360617 | − | 0.932714i | \(-0.617434\pi\) | |||||||
\(644\) | 71.6717 | + | 32.1181i | 0.111292 | + | 0.0498729i | ||||
\(645\) | 205.090 | − | 25.1421i | 0.317969 | − | 0.0389800i | ||||
\(646\) | 166.038 | − | 287.586i | 0.257025 | − | 0.445180i | ||||
\(647\) | 80.8644 | + | 21.6675i | 0.124984 | + | 0.0334893i | 0.320769 | − | 0.947158i | \(-0.396059\pi\) |
−0.195785 | + | 0.980647i | \(0.562725\pi\) | |||||||
\(648\) | −6.58846 | + | 24.5885i | −0.0101674 | + | 0.0379452i | ||||
\(649\) | 147.576 | + | 85.2032i | 0.227390 | + | 0.131284i | ||||
\(650\) | 810.982 | − | 201.871i | 1.24766 | − | 0.310571i | ||||
\(651\) | 10.3953 | + | 14.3809i | 0.0159682 | + | 0.0220905i | ||||
\(652\) | 194.678 | − | 194.678i | 0.298585 | − | 0.298585i | ||||
\(653\) | 328.360 | − | 87.9837i | 0.502848 | − | 0.134738i | 0.00152651 | − | 0.999999i | \(-0.499514\pi\) |
0.501321 | + | 0.865261i | \(0.332847\pi\) | |||||||
\(654\) | −30.3544 | + | 17.5251i | −0.0464134 | + | 0.0267968i | ||||
\(655\) | 946.000 | − | 712.579i | 1.44428 | − | 1.08791i | ||||
\(656\) | −54.5480 | + | 94.4799i | −0.0831524 | + | 0.144024i | ||||
\(657\) | 64.9301 | − | 64.9301i | 0.0988281 | − | 0.0988281i | ||||
\(658\) | 208.995 | + | 170.079i | 0.317621 | + | 0.258478i | ||||
\(659\) | 286.236i | 0.434349i | 0.976133 | + | 0.217174i | \(0.0696840\pi\) | ||||
−0.976133 | + | 0.217174i | \(0.930316\pi\) | |||||||
\(660\) | 51.1720 | − | 20.6634i | 0.0775333 | − | 0.0313082i | ||||
\(661\) | −287.474 | − | 497.920i | −0.434908 | − | 0.753283i | 0.562380 | − | 0.826879i | \(-0.309886\pi\) |
−0.997288 | + | 0.0735962i | \(0.976552\pi\) | |||||||
\(662\) | −110.772 | − | 29.6814i | −0.167330 | − | 0.0448359i | ||||
\(663\) | −595.585 | + | 159.587i | −0.898318 | + | 0.240704i | ||||
\(664\) | − | 299.629i | − | 0.451249i | ||||||
\(665\) | 290.388 | − | 462.032i | 0.436674 | − | 0.694785i | ||||
\(666\) | −234.424 | −0.351988 | ||||||||
\(667\) | −68.9244 | − | 257.229i | −0.103335 | − | 0.385651i | ||||
\(668\) | 32.4463 | − | 121.091i | 0.0485723 | − | 0.181274i | ||||
\(669\) | 650.718 | − | 375.692i | 0.972673 | − | 0.561573i | ||||
\(670\) | 169.239 | − | 398.490i | 0.252595 | − | 0.594761i | ||||
\(671\) | 130.146 | 0.193959 | ||||||||
\(672\) | −67.7152 | − | 10.8929i | −0.100767 | − | 0.0162096i | ||||
\(673\) | 95.3384 | + | 95.3384i | 0.141662 | + | 0.141662i | 0.774381 | − | 0.632719i | \(-0.218061\pi\) |
−0.632719 | + | 0.774381i | \(0.718061\pi\) | |||||||
\(674\) | 762.398 | + | 440.171i | 1.13115 | + | 0.653072i | ||||
\(675\) | 129.883 | + | 2.31677i | 0.192419 | + | 0.00343225i | ||||
\(676\) | −389.755 | − | 675.075i | −0.576560 | − | 0.998632i | ||||
\(677\) | 67.6328 | + | 252.409i | 0.0999008 | + | 0.372835i | 0.997717 | − | 0.0675358i | \(-0.0215137\pi\) |
−0.897816 | + | 0.440371i | \(0.854847\pi\) | |||||||
\(678\) | 161.738 | + | 161.738i | 0.238552 | + | 0.238552i | ||||
\(679\) | 599.139 | + | 268.491i | 0.882385 | + | 0.395421i | ||||
\(680\) | 25.9156 | + | 211.400i | 0.0381112 | + | 0.310882i | ||||
\(681\) | 16.1138 | − | 27.9099i | 0.0236620 | − | 0.0409837i | ||||
\(682\) | 6.37001 | + | 1.70684i | 0.00934019 | + | 0.00250270i | ||||
\(683\) | −197.660 | + | 737.678i | −0.289400 | + | 1.08005i | 0.656164 | + | 0.754618i | \(0.272178\pi\) |
−0.945564 | + | 0.325437i | \(0.894489\pi\) | |||||||
\(684\) | 81.0169 | + | 46.7751i | 0.118446 | + | 0.0683847i | ||||
\(685\) | 422.259 | + | 330.035i | 0.616437 | + | 0.481803i | ||||
\(686\) | 104.291 | − | 473.731i | 0.152027 | − | 0.690571i | ||||
\(687\) | −75.3686 | + | 75.3686i | −0.109707 | + | 0.109707i | ||||
\(688\) | −92.1842 | + | 24.7007i | −0.133989 | + | 0.0359022i | ||||
\(689\) | −705.778 | + | 407.481i | −1.02435 | + | 0.591410i | ||||
\(690\) | 68.0370 | + | 9.57524i | 0.0986044 | + | 0.0138772i | ||||
\(691\) | 103.948 | − | 180.043i | 0.150431 | − | 0.260555i | −0.780955 | − | 0.624588i | \(-0.785267\pi\) |
0.931386 | + | 0.364033i | \(0.118600\pi\) | |||||||
\(692\) | −156.716 | + | 156.716i | −0.226468 | + | 0.226468i | ||||
\(693\) | −62.5237 | + | 23.8274i | −0.0902218 | + | 0.0343829i | ||||
\(694\) | 95.2925i | 0.137309i | ||||||||
\(695\) | −508.080 | + | 1196.33i | −0.731050 | + | 1.72133i | ||||
\(696\) | 116.277 | + | 201.398i | 0.167065 | + | 0.289364i | ||||
\(697\) | −396.754 | − | 106.310i | −0.569231 | − | 0.152525i | ||||
\(698\) | 39.5482 | − | 10.5969i | 0.0566593 | − | 0.0151818i | ||||
\(699\) | 433.663i | 0.620405i | ||||||||
\(700\) | 29.5284 | + | 348.752i | 0.0421834 | + | 0.498217i | ||||
\(701\) | 1201.88 | 1.71453 | 0.857263 | − | 0.514879i | \(-0.172163\pi\) | ||||
0.857263 | + | 0.514879i | \(0.172163\pi\) | |||||||
\(702\) | −44.9577 | − | 167.784i | −0.0640423 | − | 0.239009i | ||||
\(703\) | −222.975 | + | 832.153i | −0.317176 | + | 1.18372i | ||||
\(704\) | −22.0746 | + | 12.7448i | −0.0313560 | + | 0.0181034i | ||||
\(705\) | 216.967 | + | 92.1459i | 0.307754 | + | 0.130703i | ||||
\(706\) | −908.963 | −1.28748 | ||||||||
\(707\) | −796.681 | + | 978.971i | −1.12685 | + | 1.38468i | ||||
\(708\) | −131.005 | − | 131.005i | −0.185036 | − | 0.185036i | ||||
\(709\) | −284.619 | − | 164.325i | −0.401437 | − | 0.231770i | 0.285667 | − | 0.958329i | \(-0.407785\pi\) |
−0.687104 | + | 0.726559i | \(0.741118\pi\) | |||||||
\(710\) | −100.978 | + | 717.498i | −0.142222 | + | 1.01056i | ||||
\(711\) | 175.008 | + | 303.123i | 0.246144 | + | 0.426333i | ||||
\(712\) | −77.5975 | − | 289.598i | −0.108985 | − | 0.406738i | ||||
\(713\) | 5.80568 | + | 5.80568i | 0.00814261 | + | 0.00814261i | ||||
\(714\) | −26.3713 | − | 256.877i | −0.0369346 | − | 0.359772i | ||||
\(715\) | −231.900 | + | 296.702i | −0.324336 | + | 0.414967i | ||||
\(716\) | 288.924 | − | 500.431i | 0.403525 | − | 0.698926i | ||||
\(717\) | 31.8336 | + | 8.52978i | 0.0443983 | + | 0.0118965i | ||||
\(718\) | −26.0855 | + | 97.3523i | −0.0363308 | + | 0.135588i | ||||
\(719\) | −18.0139 | − | 10.4003i | −0.0250540 | − | 0.0144650i | 0.487421 | − | 0.873167i | \(-0.337938\pi\) |
−0.512475 | + | 0.858702i | \(0.671271\pi\) | |||||||
\(720\) | −59.5542 | + | 7.30078i | −0.0827141 | + | 0.0101400i | ||||
\(721\) | 325.660 | + | 450.518i | 0.451678 | + | 0.624851i | ||||
\(722\) | −117.899 | + | 117.899i | −0.163295 | + | 0.163295i | ||||
\(723\) | −495.751 | + | 132.836i | −0.685686 | + | 0.183729i | ||||
\(724\) | −206.664 | + | 119.317i | −0.285447 | + | 0.164803i | ||||
\(725\) | 853.989 | − | 824.057i | 1.17792 | − | 1.13663i | ||||
\(726\) | 135.761 | − | 235.144i | 0.186998 | − | 0.323890i | ||||
\(727\) | 869.829 | − | 869.829i | 1.19646 | − | 1.19646i | 0.221245 | − | 0.975218i | \(-0.428988\pi\) |
0.975218 | − | 0.221245i | \(-0.0710121\pi\) | |||||||
\(728\) | 437.328 | − | 166.663i | 0.600725 | − | 0.228932i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 199.212 | + | 84.6054i | 0.272893 | + | 0.115898i | ||||
\(731\) | −179.660 | − | 311.180i | −0.245773 | − | 0.425691i | ||||
\(732\) | −136.677 | − | 36.6224i | −0.186717 | − | 0.0500306i | ||||
\(733\) | 895.402 | − | 239.922i | 1.22156 | − | 0.327315i | 0.410271 | − | 0.911964i | \(-0.365434\pi\) |
0.811287 | + | 0.584648i | \(0.198767\pi\) | |||||||
\(734\) | − | 331.418i | − | 0.451523i | ||||||
\(735\) | −27.4737 | − | 423.462i | −0.0373792 | − | 0.576139i | ||||
\(736\) | −31.7346 | −0.0431177 | ||||||||
\(737\) | 50.4906 | + | 188.433i | 0.0685082 | + | 0.255676i | ||||
\(738\) | 29.9489 | − | 111.771i | 0.0405812 | − | 0.151451i | ||||
\(739\) | 2.96458 | − | 1.71160i | 0.00401160 | − | 0.00231610i | −0.497993 | − | 0.867181i | \(-0.665929\pi\) |
0.502004 | + | 0.864865i | \(0.332596\pi\) | |||||||
\(740\) | −206.888 | − | 512.348i | −0.279579 | − | 0.692362i | ||||
\(741\) | −638.359 | −0.861483 | ||||||||
\(742\) | −121.542 | − | 318.928i | −0.163803 | − | 0.429823i | ||||
\(743\) | −72.5388 | − | 72.5388i | −0.0976296 | − | 0.0976296i | 0.656605 | − | 0.754235i | \(-0.271992\pi\) |
−0.754235 | + | 0.656605i | \(0.771992\pi\) | |||||||
\(744\) | −6.20934 | − | 3.58497i | −0.00834589 | − | 0.00481850i | ||||
\(745\) | 91.6746 | + | 121.705i | 0.123053 | + | 0.163362i | ||||
\(746\) | −69.1832 | − | 119.829i | −0.0927388 | − | 0.160628i | ||||
\(747\) | 82.2539 | + | 306.976i | 0.110112 | + | 0.410945i | ||||
\(748\) | −67.8603 | − | 67.8603i | −0.0907224 | − | 0.0907224i | ||||
\(749\) | 342.685 | − | 247.712i | 0.457524 | − | 0.330724i | ||||
\(750\) | 109.563 | + | 285.912i | 0.146085 | + | 0.381216i | ||||
\(751\) | 625.085 | − | 1082.68i | 0.832336 | − | 1.44165i | −0.0638447 | − | 0.997960i | \(-0.520336\pi\) |
0.896181 | − | 0.443689i | \(-0.146330\pi\) | |||||||
\(752\) | −105.166 | − | 28.1792i | −0.139849 | − | 0.0374723i | ||||
\(753\) | 193.472 | − | 722.048i | 0.256935 | − | 0.958895i | ||||
\(754\) | −1374.28 | − | 793.439i | −1.82265 | − | 1.05231i | ||||
\(755\) | 56.6055 | + | 461.744i | 0.0749741 | + | 0.611581i | ||||
\(756\) | 72.3658 | − | 7.42915i | 0.0957219 | − | 0.00982692i | ||||
\(757\) | 477.258 | − | 477.258i | 0.630460 | − | 0.630460i | −0.317723 | − | 0.948183i | \(-0.602918\pi\) |
0.948183 | + | 0.317723i | \(0.102918\pi\) | |||||||
\(758\) | 567.555 | − | 152.076i | 0.748754 | − | 0.200628i | ||||
\(759\) | −26.8116 | + | 15.4797i | −0.0353248 | + | 0.0203948i | ||||
\(760\) | −30.7294 | + | 218.348i | −0.0404334 | + | 0.287300i | ||||
\(761\) | 291.071 | − | 504.150i | 0.382485 | − | 0.662483i | −0.608932 | − | 0.793222i | \(-0.708402\pi\) |
0.991417 | + | 0.130739i | \(0.0417351\pi\) | |||||||
\(762\) | 367.806 | − | 367.806i | 0.482685 | − | 0.482685i | ||||
\(763\) | 77.6898 | + | 63.2234i | 0.101821 | + | 0.0828617i | ||||
\(764\) | 253.608i | 0.331947i | ||||||||
\(765\) | −84.5844 | − | 209.469i | −0.110568 | − | 0.273816i | ||||
\(766\) | −186.287 | − | 322.659i | −0.243195 | − | 0.421226i | ||||
\(767\) | 1221.15 | + | 327.205i | 1.59211 | + | 0.426604i | ||||
\(768\) | 26.7685 | − | 7.17260i | 0.0348548 | − | 0.00933933i | ||||
\(769\) | − | 932.077i | − | 1.21206i | −0.795440 | − | 0.606032i | \(-0.792760\pi\) | ||
0.795440 | − | 0.606032i | \(-0.207240\pi\) | |||||||
\(770\) | −107.256 | − | 115.621i | −0.139293 | − | 0.150157i | ||||
\(771\) | 535.498 | 0.694550 | ||||||||
\(772\) | 148.543 | + | 554.370i | 0.192413 | + | 0.718096i | ||||
\(773\) | −351.902 | + | 1313.32i | −0.455242 | + | 1.69899i | 0.232133 | + | 0.972684i | \(0.425430\pi\) |
−0.687375 | + | 0.726303i | \(0.741237\pi\) | |||||||
\(774\) | 87.6637 | − | 50.6127i | 0.113261 | − | 0.0653910i | ||||
\(775\) | −10.0987 | + | 35.1677i | −0.0130306 | + | 0.0453776i | ||||
\(776\) | −265.285 | −0.341863 | ||||||||
\(777\) | 238.566 | + | 626.005i | 0.307035 | + | 0.805669i | ||||
\(778\) | 116.023 | + | 116.023i | 0.149129 | + | 0.149129i | ||||
\(779\) | −368.275 | − | 212.624i | −0.472754 | − | 0.272945i | ||||
\(780\) | 327.026 | − | 246.334i | 0.419264 | − | 0.315813i | ||||
\(781\) | −163.244 | − | 282.746i | −0.209019 | − | 0.362031i | ||||
\(782\) | −30.9242 | − | 115.411i | −0.0395450 | − | 0.147584i | ||||
\(783\) | −174.415 | − | 174.415i | −0.222753 | − | 0.222753i | ||||
\(784\) | 39.8234 | + | 191.912i | 0.0507952 | + | 0.244785i | ||||
\(785\) | 176.530 | + | 137.974i | 0.224879 | + | 0.175764i | ||||
\(786\) | 290.105 | − | 502.477i | 0.369091 | − | 0.639284i | ||||
\(787\) | 633.106 | + | 169.640i | 0.804455 | + | 0.215553i | 0.637539 | − | 0.770418i | \(-0.279952\pi\) |
0.166916 | + | 0.985971i | \(0.446619\pi\) | |||||||
\(788\) | −2.50291 | + | 9.34098i | −0.00317628 | + | 0.0118540i | ||||
\(789\) | −384.466 | − | 221.972i | −0.487283 | − | 0.281333i | ||||
\(790\) | −508.043 | + | 650.009i | −0.643092 | + | 0.822796i | ||||
\(791\) | 267.309 | − | 596.500i | 0.337937 | − | 0.754109i | ||||
\(792\) | 19.1172 | − | 19.1172i | 0.0241378 | − | 0.0241378i | ||||
\(793\) | 932.641 | − | 249.900i | 1.17609 | − | 0.315133i | ||||
\(794\) | −654.381 | + | 377.807i | −0.824157 | + | 0.475827i | ||||
\(795\) | −179.643 | − | 238.489i | −0.225966 | − | 0.299986i | ||||
\(796\) | −219.574 | + | 380.314i | −0.275847 | + | 0.477781i | ||||
\(797\) | −315.934 | + | 315.934i | −0.396404 | + | 0.396404i | −0.876963 | − | 0.480559i | \(-0.840434\pi\) |
0.480559 | + | 0.876963i | \(0.340434\pi\) | |||||||
\(798\) | 42.4596 | − | 263.949i | 0.0532075 | − | 0.330763i | ||||
\(799\) | − | 409.922i | − | 0.513043i | ||||||
\(800\) | −68.5152 | − | 123.716i | −0.0856440 | − | 0.154645i | ||||
\(801\) | 159.000 | + | 275.396i | 0.198502 | + | 0.343816i | ||||
\(802\) | −608.443 | − | 163.032i | −0.758658 | − | 0.203282i | ||||
\(803\) | −94.2010 | + | 25.2411i | −0.117311 | + | 0.0314335i | ||||
\(804\) | − | 212.096i | − | 0.263801i | ||||||
\(805\) | −43.6696 | − | 191.430i | −0.0542479 | − | 0.237802i | ||||
\(806\) | 48.9255 | 0.0607016 | ||||||||
\(807\) | 85.5300 | + | 319.202i | 0.105985 | + | 0.395542i | ||||
\(808\) | 131.997 | − | 492.618i | 0.163362 | − | 0.609676i | ||||
\(809\) | −303.124 | + | 175.009i | −0.374690 | + | 0.216327i | −0.675505 | − | 0.737355i | \(-0.736075\pi\) |
0.300815 | + | 0.953682i | \(0.402741\pi\) | |||||||
\(810\) | 59.0102 | − | 23.8285i | 0.0728521 | − | 0.0294180i | ||||
\(811\) | −989.841 | −1.22052 | −0.610260 | − | 0.792202i | \(-0.708935\pi\) | ||||
−0.610260 | + | 0.792202i | \(0.708935\pi\) | |||||||
\(812\) | 419.480 | − | 515.462i | 0.516601 | − | 0.634805i | ||||
\(813\) | −211.809 | − | 211.809i | −0.260527 | − | 0.260527i | ||||
\(814\) | 215.617 | + | 124.487i | 0.264886 | + | 0.152932i | ||||
\(815\) | −681.573 | − | 95.9216i | −0.836285 | − | 0.117695i | ||||
\(816\) | 52.1698 | + | 90.3608i | 0.0639336 | + | 0.110736i | ||||
\(817\) | −96.2814 | − | 359.327i | −0.117848 | − | 0.439813i | ||||
\(818\) | 282.573 | + | 282.573i | 0.345444 | + | 0.345444i | ||||
\(819\) | −402.298 | + | 290.804i | −0.491207 | + | 0.355072i | ||||
\(820\) | 270.713 | − | 33.1869i | 0.330138 | − | 0.0404718i | ||||
\(821\) | −288.107 | + | 499.016i | −0.350922 | + | 0.607815i | −0.986411 | − | 0.164295i | \(-0.947465\pi\) |
0.635489 | + | 0.772110i | \(0.280798\pi\) | |||||||
\(822\) | 253.607 | + | 67.9538i | 0.308524 | + | 0.0826688i | ||||
\(823\) | −365.774 | + | 1365.09i | −0.444440 | + | 1.65867i | 0.272969 | + | 0.962023i | \(0.411994\pi\) |
−0.717410 | + | 0.696651i | \(0.754672\pi\) | |||||||
\(824\) | −194.523 | − | 112.308i | −0.236072 | − | 0.136296i | ||||
\(825\) | −118.233 | − | 71.1030i | −0.143313 | − | 0.0861855i | ||||
\(826\) | −216.516 | + | 483.157i | −0.262126 | + | 0.584935i | ||||
\(827\) | 326.116 | − | 326.116i | 0.394336 | − | 0.394336i | −0.481894 | − | 0.876230i | \(-0.660051\pi\) |
0.876230 | + | 0.481894i | \(0.160051\pi\) | |||||||
\(828\) | 32.5128 | − | 8.71177i | 0.0392666 | − | 0.0105215i | ||||
\(829\) | 153.724 | − | 88.7528i | 0.185433 | − | 0.107060i | −0.404410 | − | 0.914578i | \(-0.632523\pi\) |
0.589843 | + | 0.807518i | \(0.299190\pi\) | |||||||
\(830\) | −598.322 | + | 450.689i | −0.720870 | + | 0.542999i | ||||
\(831\) | 396.450 | − | 686.671i | 0.477076 | − | 0.826319i | ||||
\(832\) | −133.717 | + | 133.717i | −0.160717 | + | 0.160717i | ||||
\(833\) | −659.127 | + | 331.838i | −0.791269 | + | 0.398365i | ||||
\(834\) | 636.743i | 0.763481i | ||||||||
\(835\) | −290.608 | + | 117.349i | −0.348034 | + | 0.140537i | ||||
\(836\) | −49.6782 | − | 86.0451i | −0.0594237 | − | 0.102925i | ||||
\(837\) | 7.34573 | + | 1.96828i | 0.00877626 | + | 0.00235159i | ||||
\(838\) | −175.468 | + | 47.0165i | −0.209389 | + | 0.0561057i | ||||
\(839\) | 644.851i | 0.768595i | 0.923209 | + | 0.384297i | \(0.125556\pi\) | ||||
−0.923209 | + | 0.384297i | \(0.874444\pi\) | |||||||
\(840\) | 80.1025 | + | 151.603i | 0.0953601 | + | 0.180480i | ||||
\(841\) | −1412.39 | −1.67942 | ||||||||
\(842\) | 158.372 | + | 591.052i | 0.188090 | + | 0.701962i | ||||
\(843\) | 120.217 | − | 448.656i | 0.142606 | − | 0.532214i | ||||
\(844\) | 365.039 | − | 210.755i | 0.432510 | − | 0.249710i | ||||
\(845\) | −761.789 | + | 1793.71i | −0.901526 | + | 2.12273i | ||||
\(846\) | 115.480 | 0.136502 | ||||||||
\(847\) | −766.089 | − | 123.235i | −0.904473 | − | 0.145496i | ||||
\(848\) | 97.5151 | + | 97.5151i | 0.114994 | + | 0.114994i | ||||
\(849\) | 209.921 | + | 121.198i | 0.247256 | + | 0.142754i | ||||
\(850\) | 383.158 | − | 369.729i | 0.450774 | − | 0.434975i | ||||
\(851\) | 154.987 | + | 268.445i | 0.182123 | + | 0.315446i | ||||
\(852\) | 91.8716 | + | 342.869i | 0.107831 | + | 0.402429i | ||||
\(853\) | 701.059 | + | 701.059i | 0.821875 | + | 0.821875i | 0.986377 | − | 0.164502i | \(-0.0526016\pi\) |
−0.164502 | + | 0.986377i | \(0.552602\pi\) | |||||||
\(854\) | 41.2955 | + | 402.251i | 0.0483554 | + | 0.471019i | ||||
\(855\) | −28.4579 | − | 232.138i | −0.0332841 | − | 0.271506i | ||||
\(856\) | −85.4268 | + | 147.964i | −0.0997977 | + | 0.172855i | ||||
\(857\) | 373.395 | + | 100.051i | 0.435700 | + | 0.116745i | 0.470001 | − | 0.882666i | \(-0.344254\pi\) |
−0.0343006 | + | 0.999412i | \(0.510920\pi\) | |||||||
\(858\) | −47.7479 | + | 178.198i | −0.0556503 | + | 0.207690i | ||||
\(859\) | 145.790 | + | 84.1717i | 0.169720 | + | 0.0979880i | 0.582454 | − | 0.812864i | \(-0.302093\pi\) |
−0.412734 | + | 0.910852i | \(0.635426\pi\) | |||||||
\(860\) | 187.984 | + | 146.927i | 0.218586 | + | 0.170845i | ||||
\(861\) | −328.951 | + | 33.7704i | −0.382056 | + | 0.0392223i | ||||
\(862\) | 409.270 | − | 409.270i | 0.474791 | − | 0.474791i | ||||
\(863\) | −390.788 | + | 104.711i | −0.452825 | + | 0.121334i | −0.478021 | − | 0.878348i | \(-0.658646\pi\) |
0.0251958 | + | 0.999683i | \(0.491979\pi\) | |||||||
\(864\) | −25.4558 | + | 14.6969i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 548.668 | + | 77.2172i | 0.634298 | + | 0.0892684i | ||||
\(866\) | 74.6999 | − | 129.384i | 0.0862585 | − | 0.149404i | ||||
\(867\) | 76.1697 | − | 76.1697i | 0.0878544 | − | 0.0878544i | ||||
\(868\) | −3.25421 | + | 20.2297i | −0.00374909 | + | 0.0233061i | ||||
\(869\) | − | 371.740i | − | 0.427779i | ||||||
\(870\) | 227.267 | − | 535.124i | 0.261227 | − | 0.615085i | ||||
\(871\) | 723.640 | + | 1253.38i | 0.830815 | + | 1.43901i | ||||
\(872\) | −39.0935 | − | 10.4751i | −0.0448319 | − | 0.0120127i | ||||
\(873\) | 271.790 | − | 72.8259i | 0.311329 | − | 0.0834203i | ||||
\(874\) | − | 123.699i | − | 0.141532i | ||||||
\(875\) | 652.000 | − | 583.542i | 0.745142 | − | 0.666905i | ||||
\(876\) | 106.030 | 0.121039 | ||||||||
\(877\) | −85.5338 | − | 319.216i | −0.0975300 | − | 0.363987i | 0.899861 | − | 0.436177i | \(-0.143668\pi\) |
−0.997391 | + | 0.0721901i | \(0.977001\pi\) | |||||||
\(878\) | 147.431 | − | 550.220i | 0.167917 | − | 0.626675i | ||||
\(879\) | −208.042 | + | 120.113i | −0.236681 | + | 0.136648i | ||||
\(880\) | 58.6534 | + | 24.9101i | 0.0666516 | + | 0.0283069i | ||||
\(881\) | −1080.58 | −1.22654 | −0.613271 | − | 0.789873i | \(-0.710147\pi\) | ||||
−0.613271 | + | 0.789873i | \(0.710147\pi\) | |||||||
\(882\) | −93.4833 | − | 185.685i | −0.105990 | − | 0.210527i | ||||
\(883\) | 614.885 | + | 614.885i | 0.696359 | + | 0.696359i | 0.963623 | − | 0.267264i | \(-0.0861197\pi\) |
−0.267264 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(884\) | −616.595 | − | 355.991i | −0.697506 | − | 0.402705i | ||||
\(885\) | −64.5490 | + | 458.654i | −0.0729367 | + | 0.518253i | ||||
\(886\) | −72.5032 | − | 125.579i | −0.0818321 | − | 0.141737i | ||||
\(887\) | −290.975 | − | 1085.93i | −0.328043 | − | 1.22427i | −0.911217 | − | 0.411927i | \(-0.864856\pi\) |
0.583173 | − | 0.812348i | \(-0.301811\pi\) | |||||||
\(888\) | −191.406 | − | 191.406i | −0.215548 | − | 0.215548i | ||||
\(889\) | −1356.49 | − | 607.882i | −1.52586 | − | 0.683782i | ||||
\(890\) | −461.572 | + | 590.553i | −0.518620 | + | 0.663542i | ||||
\(891\) | −14.3379 | + | 24.8339i | −0.0160919 | + | 0.0278720i | ||||
\(892\) | 838.061 | + | 224.558i | 0.939530 | + | 0.251746i | ||||
\(893\) | 109.840 | − | 409.930i | 0.123001 | − | 0.459048i | ||||
\(894\) | 64.6446 | + | 37.3226i | 0.0723094 | + | 0.0417478i | ||||
\(895\) | −1433.89 | + | 175.781i | −1.60211 | + | 0.196403i | ||||
\(896\) | −46.3952 | − | 64.1832i | −0.0517804 | − | 0.0716330i | ||||
\(897\) | −162.411 | + | 162.411i | −0.181060 | + | 0.181060i | ||||
\(898\) | −594.552 | + | 159.310i | −0.662085 | + | 0.177405i | ||||
\(899\) | 60.1670 | − | 34.7374i | 0.0669265 | − | 0.0386401i | ||||
\(900\) | 104.158 | + | 107.941i | 0.115731 | + | 0.119934i | ||||
\(901\) | −259.613 | + | 449.662i | −0.288138 | + | 0.499070i | ||||
\(902\) | −86.9002 | + | 86.9002i | −0.0963417 | + | 0.0963417i | ||||
\(903\) | −224.369 | − | 182.590i | −0.248470 | − | 0.202203i | ||||
\(904\) | 264.117i | 0.292165i | ||||||||
\(905\) | 549.116 | + | 233.210i | 0.606759 | + | 0.257691i | ||||
\(906\) | 113.950 | + | 197.368i | 0.125773 | + | 0.217845i | ||||
\(907\) | 452.469 | + | 121.239i | 0.498863 | + | 0.133670i | 0.499472 | − | 0.866330i | \(-0.333527\pi\) |
−0.000609101 | 1.00000i | \(0.500194\pi\) | ||||||||
\(908\) | 35.9452 | − | 9.63149i | 0.0395873 | − | 0.0106074i | ||||
\(909\) | 540.932i | 0.595085i | ||||||||
\(910\) | −990.614 | − | 622.602i | −1.08859 | − | 0.684178i | ||||
\(911\) | 52.1757 | 0.0572730 | 0.0286365 | − | 0.999590i | \(-0.490883\pi\) | ||||
0.0286365 | + | 0.999590i | \(0.490883\pi\) | |||||||
\(912\) | 27.9583 | + | 104.342i | 0.0306560 | + | 0.114410i | ||||
\(913\) | 87.3589 | − | 326.028i | 0.0956834 | − | 0.357095i | ||||
\(914\) | 151.435 | − | 87.4313i | 0.165684 | − | 0.0956578i | ||||
\(915\) | 132.453 | + | 328.012i | 0.144757 | + | 0.358483i | ||||
\(916\) | −123.076 | −0.134363 | ||||||||
\(917\) | −1637.04 | − | 263.340i | −1.78522 | − | 0.287176i | ||||
\(918\) | −78.2548 | − | 78.2548i | −0.0852448 | − | 0.0852448i | ||||
\(919\) | 732.410 | + | 422.857i | 0.796964 | + | 0.460127i | 0.842409 | − | 0.538839i | \(-0.181137\pi\) |
−0.0454444 | + | 0.998967i | \(0.514470\pi\) | |||||||
\(920\) | 47.7339 | + | 63.3702i | 0.0518846 | + | 0.0688806i | ||||
\(921\) | 314.492 | + | 544.716i | 0.341468 | + | 0.591440i | ||||
\(922\) | −263.943 | − | 985.049i | −0.286272 | − | 1.06838i | ||||
\(923\) | −1712.73 | − | 1712.73i | −1.85562 | − | 1.85562i | ||||
\(924\) | −70.5053 | − | 31.5954i | −0.0763045 | − | 0.0341942i | ||||
\(925\) | −711.904 | + | 1183.78i | −0.769626 | + | 1.27976i | ||||
\(926\) | −190.901 | + | 330.650i | −0.206157 | + | 0.357074i | ||||
\(927\) | 230.123 | + | 61.6614i | 0.248245 | + | 0.0665171i | ||||
\(928\) | −69.5007 | + | 259.380i | −0.0748930 | + | 0.279505i | ||||
\(929\) | 820.740 | + | 473.855i | 0.883466 | + | 0.510070i | 0.871800 | − | 0.489862i | \(-0.162953\pi\) |
0.0116666 | + | 0.999932i | \(0.496286\pi\) | |||||||
\(930\) | 2.18109 | + | 17.7916i | 0.00234526 | + | 0.0191308i | ||||
\(931\) | −748.057 | + | 155.229i | −0.803499 | + | 0.166733i | ||||
\(932\) | −354.085 | + | 354.085i | −0.379919 | + | 0.379919i | ||||
\(933\) | −345.014 | + | 92.4463i | −0.369790 | + | 0.0990850i | ||||
\(934\) | −211.312 | + | 122.001i | −0.226245 | + | 0.130622i | ||||
\(935\) | −33.4362 | + | 237.581i | −0.0357606 | + | 0.254098i | ||||
\(936\) | 100.288 | − | 173.703i | 0.107145 | − | 0.185580i | ||||
\(937\) | −105.113 | + | 105.113i | −0.112180 | + | 0.112180i | −0.760969 | − | 0.648788i | \(-0.775276\pi\) |
0.648788 | + | 0.760969i | \(0.275276\pi\) | |||||||
\(938\) | −566.380 | + | 215.844i | −0.603817 | + | 0.230111i | ||||
\(939\) | − | 873.016i | − | 0.929729i | ||||||
\(940\) | 101.916 | + | 252.390i | 0.108421 | + | 0.268499i | ||||
\(941\) | −166.881 | − | 289.047i | −0.177345 | − | 0.307170i | 0.763626 | − | 0.645659i | \(-0.223417\pi\) |
−0.940970 | + | 0.338490i | \(0.890084\pi\) | |||||||
\(942\) | 106.023 | + | 28.4088i | 0.112551 | + | 0.0301579i | ||||
\(943\) | −147.792 | + | 39.6008i | −0.156725 | + | 0.0419944i | ||||
\(944\) | − | 213.931i | − | 0.226622i | ||||||
\(945\) | −123.685 | − | 133.331i | −0.130883 | − | 0.141091i | ||||
\(946\) | −107.508 | −0.113645 | ||||||||
\(947\) | 377.999 | + | 1410.71i | 0.399154 | + | 1.48966i | 0.814589 | + | 0.580039i | \(0.196963\pi\) |
−0.415435 | + | 0.909623i | \(0.636371\pi\) | |||||||
\(948\) | −104.605 | + | 390.393i | −0.110343 | + | 0.411806i | ||||
\(949\) | −626.586 | + | 361.760i | −0.660259 | + | 0.381201i | ||||
\(950\) | 482.236 | − | 267.067i | 0.507617 | − | 0.281123i | ||||
\(951\) | −343.265 | −0.360952 | ||||||||
\(952\) | 188.207 | − | 231.272i | 0.197697 | − | 0.242932i | ||||
\(953\) | −164.273 | − | 164.273i | −0.172374 | − | 0.172374i | 0.615647 | − | 0.788022i | \(-0.288895\pi\) |
−0.788022 | + | 0.615647i | \(0.788895\pi\) | |||||||
\(954\) | −126.676 | − | 73.1364i | −0.132784 | − | 0.0766628i | ||||
\(955\) | 506.423 | − | 381.466i | 0.530286 | − | 0.399440i | ||||
\(956\) | 19.0275 | + | 32.9565i | 0.0199032 | + | 0.0344734i | ||||
\(957\) | 67.8027 | + | 253.043i | 0.0708492 | + | 0.264413i | ||||
\(958\) | −381.098 | − | 381.098i | −0.397806 | − | 0.397806i | ||||
\(959\) | −76.6248 | − | 746.385i | −0.0799007 | − | 0.778295i | ||||
\(960\) | −54.5868 | − | 42.6647i | −0.0568613 | − | 0.0444424i | ||||
\(961\) | 479.429 | − | 830.395i | 0.498886 | − | 0.864095i | ||||
\(962\) | 1784.17 | + | 478.066i | 1.85464 | + | 0.496950i | ||||
\(963\) | 46.9026 | − | 175.043i | 0.0487047 | − | 0.181768i | ||||
\(964\) | −513.239 | − | 296.319i | −0.532406 | − | 0.307385i | ||||
\(965\) | 883.577 | − | 1130.48i | 0.915624 | − | 1.17148i | ||||
\(966\) | −56.3511 | − | 77.9562i | −0.0583345 | − | 0.0807000i | ||||
\(967\) | 409.994 | − | 409.994i | 0.423986 | − | 0.423986i | −0.462588 | − | 0.886573i | \(-0.653079\pi\) |
0.886573 | + | 0.462588i | \(0.153079\pi\) | |||||||
\(968\) | 302.843 | − | 81.1465i | 0.312854 | − | 0.0838290i | ||||
\(969\) | −352.220 | + | 203.354i | −0.363488 | + | 0.209860i | ||||
\(970\) | 399.031 | + | 529.742i | 0.411372 | + | 0.546126i | ||||
\(971\) | 334.655 | − | 579.640i | 0.344650 | − | 0.596952i | −0.640640 | − | 0.767841i | \(-0.721331\pi\) |
0.985290 | + | 0.170890i | \(0.0546642\pi\) | |||||||
\(972\) | 22.0454 | − | 22.0454i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 1700.36 | − | 647.995i | 1.74754 | − | 0.665976i | ||||
\(974\) | − | 342.101i | − | 0.351234i | ||||||
\(975\) | −983.796 | − | 282.506i | −1.00902 | − | 0.289750i | ||||
\(976\) | −81.6940 | − | 141.498i | −0.0837029 | − | 0.144978i | ||||
\(977\) | −612.440 | − | 164.103i | −0.626858 | − | 0.167966i | −0.0686143 | − | 0.997643i | \(-0.521858\pi\) |
−0.558243 | + | 0.829677i | \(0.688524\pi\) | |||||||
\(978\) | −325.702 | + | 87.2716i | −0.333029 | + | 0.0892348i | ||||
\(979\) | − | 337.737i | − | 0.344982i | ||||||
\(980\) | 323.323 | − | 368.188i | 0.329922 | − | 0.375702i | ||||
\(981\) | 42.9276 | 0.0437590 | ||||||||
\(982\) | 329.194 | + | 1228.57i | 0.335228 | + | 1.25109i | ||||
\(983\) | −3.87887 | + | 14.4761i | −0.00394595 | + | 0.0147265i | −0.967871 | − | 0.251448i | \(-0.919093\pi\) |
0.963925 | + | 0.266175i | \(0.0857598\pi\) | |||||||
\(984\) | 115.714 | − | 66.8073i | 0.117595 | − | 0.0678936i | ||||
\(985\) | 22.4175 | − | 9.05229i | 0.0227589 | − | 0.00919015i | ||||
\(986\) | −1011.03 | −1.02538 | ||||||||
\(987\) | −117.521 | − | 308.378i | −0.119069 | − | 0.312440i | ||||
\(988\) | −521.218 | − | 521.218i | −0.527548 | − | 0.527548i | ||||
\(989\) | −115.916 | − | 66.9239i | −0.117205 | − | 0.0676683i | ||||
\(990\) | −66.9298 | − | 9.41941i | −0.0676059 | − | 0.00951456i | ||||
\(991\) | 294.827 | + | 510.655i | 0.297504 | + | 0.515293i | 0.975564 | − | 0.219714i | \(-0.0705124\pi\) |
−0.678060 | + | 0.735007i | \(0.737179\pi\) | |||||||
\(992\) | −2.14279 | − | 7.99702i | −0.00216008 | − | 0.00806151i | ||||
\(993\) | 99.3158 | + | 99.3158i | 0.100016 | + | 0.100016i | ||||
\(994\) | 822.102 | − | 594.262i | 0.827065 | − | 0.597849i | ||||
\(995\) | 1089.71 | − | 133.589i | 1.09519 | − | 0.134260i | ||||
\(996\) | −183.485 | + | 317.805i | −0.184221 | + | 0.319081i | ||||
\(997\) | 565.774 | + | 151.599i | 0.567476 | + | 0.152055i | 0.531139 | − | 0.847285i | \(-0.321764\pi\) |
0.0363372 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(998\) | 54.4858 | − | 203.344i | 0.0545950 | − | 0.203751i | ||||
\(999\) | 248.644 | + | 143.555i | 0.248893 | + | 0.143698i |
(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 | 210.3.v.b.163.4 | yes | 32 | |
5.2 | odd | 4 | inner | 210.3.v.b.37.5 | ✓ | 32 | |
7.4 | even | 3 | inner | 210.3.v.b.193.5 | yes | 32 | |
35.32 | odd | 12 | inner | 210.3.v.b.67.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.b.37.5 | ✓ | 32 | 5.2 | odd | 4 | inner | |
210.3.v.b.67.4 | yes | 32 | 35.32 | odd | 12 | inner | |
210.3.v.b.163.4 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.b.193.5 | yes | 32 | 7.4 | even | 3 | inner |