Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.14 | ||
Character | \(\chi\) | \(=\) | 1050.199 |
Dual form | 1050.3.q.e.649.13 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 6.50174 | − | 2.59373i | 0.928819 | − | 0.370533i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −1.50000 | − | 2.59808i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.13478 | + | 8.89370i | −0.466798 | + | 0.808518i | −0.999281 | − | 0.0379228i | \(-0.987926\pi\) |
0.532482 | + | 0.846441i | \(0.321259\pi\) | |||||||
\(12\) | 1.73205 | + | 3.00000i | 0.144338 | + | 0.250000i | ||||
\(13\) | 7.02340 | 0.540261 | 0.270131 | − | 0.962824i | \(-0.412933\pi\) | ||||
0.270131 | + | 0.962824i | \(0.412933\pi\) | |||||||
\(14\) | 6.12892 | − | 7.77408i | 0.437780 | − | 0.555291i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −15.8741 | + | 27.4947i | −0.933768 | + | 1.61733i | −0.156951 | + | 0.987606i | \(0.550167\pi\) |
−0.776816 | + | 0.629727i | \(0.783167\pi\) | |||||||
\(18\) | −3.67423 | − | 2.12132i | −0.204124 | − | 0.117851i | ||||
\(19\) | 26.9408 | − | 15.5543i | 1.41794 | − | 0.818648i | 0.421822 | − | 0.906679i | \(-0.361391\pi\) |
0.996118 | + | 0.0880311i | \(0.0280575\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74007 | + | 11.9988i | −0.0828607 | + | 0.571373i | ||||
\(22\) | 14.5234i | 0.660152i | ||||||||
\(23\) | 20.5146 | − | 11.8441i | 0.891940 | − | 0.514962i | 0.0173632 | − | 0.999849i | \(-0.494473\pi\) |
0.874576 | + | 0.484888i | \(0.161140\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.60187 | − | 4.96629i | 0.330841 | − | 0.191011i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 2.00927 | − | 13.8551i | 0.0717595 | − | 0.494824i | ||||
\(29\) | −9.19673 | −0.317129 | −0.158564 | − | 0.987349i | \(-0.550687\pi\) | ||||
−0.158564 | + | 0.987349i | \(0.550687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 17.4511 | + | 10.0754i | 0.562940 | + | 0.325013i | 0.754325 | − | 0.656502i | \(-0.227965\pi\) |
−0.191385 | + | 0.981515i | \(0.561298\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −8.89370 | − | 15.4043i | −0.269506 | − | 0.466798i | ||||
\(34\) | 44.8986i | 1.32055i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 41.7118 | − | 24.0823i | 1.12735 | − | 0.650874i | 0.184081 | − | 0.982911i | \(-0.441069\pi\) |
0.943266 | + | 0.332037i | \(0.107736\pi\) | |||||||
\(38\) | 21.9971 | − | 38.1001i | 0.578871 | − | 1.00263i | ||||
\(39\) | −6.08244 | + | 10.5351i | −0.155960 | + | 0.270131i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 65.1226i | 1.58836i | 0.607685 | + | 0.794178i | \(0.292098\pi\) | ||||
−0.607685 | + | 0.794178i | \(0.707902\pi\) | |||||||
\(42\) | 6.35331 | + | 15.9259i | 0.151269 | + | 0.379189i | ||||
\(43\) | 3.03497i | 0.0705807i | 0.999377 | + | 0.0352904i | \(0.0112356\pi\) | ||||
−0.999377 | + | 0.0352904i | \(0.988764\pi\) | |||||||
\(44\) | 10.2696 | + | 17.7874i | 0.233399 | + | 0.404259i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.7501 | − | 29.0120i | 0.364133 | − | 0.630697i | ||||
\(47\) | −30.9732 | − | 53.6472i | −0.659005 | − | 1.14143i | −0.980874 | − | 0.194645i | \(-0.937644\pi\) |
0.321869 | − | 0.946784i | \(-0.395689\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 35.5451 | − | 33.7275i | 0.725411 | − | 0.688316i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −27.4947 | − | 47.6222i | −0.539111 | − | 0.933768i | ||||
\(52\) | 7.02340 | − | 12.1649i | 0.135065 | − | 0.233940i | ||||
\(53\) | 1.19642 | + | 0.690751i | 0.0225739 | + | 0.0130330i | 0.511244 | − | 0.859435i | \(-0.329185\pi\) |
−0.488671 | + | 0.872468i | \(0.662518\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.33617 | − | 18.3897i | −0.131003 | − | 0.328387i | ||||
\(57\) | 53.8817i | 0.945293i | ||||||||
\(58\) | −11.2636 | + | 6.50307i | −0.194201 | + | 0.112122i | ||||
\(59\) | 95.1064 | + | 54.9097i | 1.61197 | + | 0.930673i | 0.988912 | + | 0.148500i | \(0.0474445\pi\) |
0.623061 | + | 0.782173i | \(0.285889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34.3741 | + | 19.8459i | −0.563510 | + | 0.325343i | −0.754553 | − | 0.656239i | \(-0.772146\pi\) |
0.191043 | + | 0.981582i | \(0.438813\pi\) | |||||||
\(62\) | 28.4976 | 0.459638 | ||||||||
\(63\) | −16.4913 | − | 13.0014i | −0.261767 | − | 0.206372i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −21.7850 | − | 12.5776i | −0.330076 | − | 0.190570i | ||||
\(67\) | −13.7863 | − | 7.95952i | −0.205765 | − | 0.118799i | 0.393576 | − | 0.919292i | \(-0.371238\pi\) |
−0.599342 | + | 0.800493i | \(0.704571\pi\) | |||||||
\(68\) | 31.7481 | + | 54.9893i | 0.466884 | + | 0.808667i | ||||
\(69\) | 41.0292i | 0.594626i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53.3489 | 0.751393 | 0.375696 | − | 0.926743i | \(-0.377404\pi\) | ||||
0.375696 | + | 0.926743i | \(0.377404\pi\) | |||||||
\(72\) | −7.34847 | + | 4.24264i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 36.1901 | − | 62.6830i | 0.495754 | − | 0.858672i | −0.504234 | − | 0.863567i | \(-0.668225\pi\) |
0.999988 | + | 0.00489557i | \(0.00155831\pi\) | |||||||
\(74\) | 34.0576 | − | 58.9894i | 0.460237 | − | 0.797155i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 62.2172i | − | 0.818648i | ||||||
\(77\) | −10.3171 | + | 71.1427i | −0.133989 | + | 0.923931i | ||||
\(78\) | 17.2037i | 0.220561i | ||||||||
\(79\) | 53.2229 | + | 92.1847i | 0.673707 | + | 1.16690i | 0.976845 | + | 0.213948i | \(0.0686325\pi\) |
−0.303138 | + | 0.952947i | \(0.598034\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 46.0486 | + | 79.7586i | 0.561569 | + | 0.972666i | ||||
\(83\) | −49.4298 | −0.595540 | −0.297770 | − | 0.954638i | \(-0.596243\pi\) | ||||
−0.297770 | + | 0.954638i | \(0.596243\pi\) | |||||||
\(84\) | 19.0425 | + | 15.0127i | 0.226697 | + | 0.178723i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.14605 | + | 3.71707i | 0.0249541 | + | 0.0432217i | ||||
\(87\) | 7.96460 | − | 13.7951i | 0.0915472 | − | 0.158564i | ||||
\(88\) | 25.1552 | + | 14.5234i | 0.285854 | + | 0.165038i | ||||
\(89\) | 142.807 | − | 82.4499i | 1.60458 | − | 0.926403i | 0.614022 | − | 0.789289i | \(-0.289551\pi\) |
0.990555 | − | 0.137114i | \(-0.0437826\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 45.6643 | − | 18.2168i | 0.501805 | − | 0.200185i | ||||
\(92\) | − | 47.3765i | − | 0.514962i | ||||||
\(93\) | −30.2262 | + | 17.4511i | −0.325013 | + | 0.187647i | ||||
\(94\) | −75.8686 | − | 43.8027i | −0.807113 | − | 0.465987i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | − | 4.89898i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | 49.4799 | 0.510102 | 0.255051 | − | 0.966928i | \(-0.417908\pi\) | ||||
0.255051 | + | 0.966928i | \(0.417908\pi\) | |||||||
\(98\) | 19.6848 | − | 66.4418i | 0.200865 | − | 0.677977i | ||||
\(99\) | 30.8087 | 0.311199 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 116.803 | + | 67.4364i | 1.15647 | + | 0.667687i | 0.950455 | − | 0.310863i | \(-0.100618\pi\) |
0.206012 | + | 0.978549i | \(0.433951\pi\) | |||||||
\(102\) | −67.3479 | − | 38.8833i | −0.660274 | − | 0.381209i | ||||
\(103\) | 18.7010 | + | 32.3911i | 0.181563 | + | 0.314477i | 0.942413 | − | 0.334451i | \(-0.108551\pi\) |
−0.760850 | + | 0.648928i | \(0.775218\pi\) | |||||||
\(104\) | − | 19.8652i | − | 0.191011i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.95374 | 0.0184315 | ||||||||
\(107\) | −21.4739 | + | 12.3980i | −0.200691 | + | 0.115869i | −0.596978 | − | 0.802258i | \(-0.703632\pi\) |
0.396287 | + | 0.918127i | \(0.370299\pi\) | |||||||
\(108\) | 5.19615 | − | 9.00000i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −28.1448 | + | 48.7483i | −0.258209 | + | 0.447232i | −0.965762 | − | 0.259429i | \(-0.916466\pi\) |
0.707553 | + | 0.706660i | \(0.249799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 83.4237i | 0.751565i | ||||||||
\(112\) | −21.9884 | − | 17.3352i | −0.196325 | − | 0.154779i | ||||
\(113\) | − | 74.9910i | − | 0.663637i | −0.943343 | − | 0.331818i | \(-0.892338\pi\) | ||
0.943343 | − | 0.331818i | \(-0.107662\pi\) | |||||||
\(114\) | 38.1001 | + | 65.9913i | 0.334212 | + | 0.578871i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.19673 | + | 15.9292i | −0.0792822 | + | 0.137321i | ||||
\(117\) | −10.5351 | − | 18.2473i | −0.0900436 | − | 0.155960i | ||||
\(118\) | 155.308 | 1.31617 | ||||||||
\(119\) | −31.8952 | + | 219.936i | −0.268027 | + | 1.84820i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.76807 | + | 13.4547i | 0.0641989 | + | 0.111196i | ||||
\(122\) | −28.0664 | + | 48.6124i | −0.230052 | + | 0.398462i | ||||
\(123\) | −97.6839 | − | 56.3978i | −0.794178 | − | 0.458519i | ||||
\(124\) | 34.9023 | − | 20.1508i | 0.281470 | − | 0.162507i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −29.3910 | − | 4.26229i | −0.233262 | − | 0.0338277i | ||||
\(127\) | 128.504i | 1.01184i | 0.862580 | + | 0.505921i | \(0.168847\pi\) | ||||
−0.862580 | + | 0.505921i | \(0.831153\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −4.55246 | − | 2.62836i | −0.0352904 | − | 0.0203749i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 65.3818 | − | 37.7482i | 0.499098 | − | 0.288154i | −0.229243 | − | 0.973369i | \(-0.573625\pi\) |
0.728341 | + | 0.685215i | \(0.240292\pi\) | |||||||
\(132\) | −35.5748 | −0.269506 | ||||||||
\(133\) | 134.819 | − | 171.007i | 1.01367 | − | 1.28577i | ||||
\(134\) | −22.5129 | −0.168007 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 77.7667 | + | 44.8986i | 0.571814 | + | 0.330137i | ||||
\(137\) | −93.1121 | − | 53.7583i | −0.679650 | − | 0.392396i | 0.120073 | − | 0.992765i | \(-0.461687\pi\) |
−0.799723 | + | 0.600369i | \(0.795020\pi\) | |||||||
\(138\) | 29.0120 | + | 50.2503i | 0.210232 | + | 0.364133i | ||||
\(139\) | − | 272.004i | − | 1.95686i | −0.206576 | − | 0.978431i | \(-0.566232\pi\) | ||
0.206576 | − | 0.978431i | \(-0.433768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 107.294 | 0.760953 | ||||||||
\(142\) | 65.3388 | − | 37.7234i | 0.460132 | − | 0.265658i | ||||
\(143\) | −36.0636 | + | 62.4640i | −0.252193 | + | 0.436811i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 102.361i | − | 0.701102i | ||||||
\(147\) | 19.8082 | + | 82.5266i | 0.134750 | + | 0.561405i | ||||
\(148\) | − | 96.3294i | − | 0.650874i | ||||||
\(149\) | −41.7135 | − | 72.2498i | −0.279956 | − | 0.484898i | 0.691417 | − | 0.722456i | \(-0.256987\pi\) |
−0.971374 | + | 0.237557i | \(0.923653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −63.3973 | + | 109.807i | −0.419850 | + | 0.727201i | −0.995924 | − | 0.0901962i | \(-0.971251\pi\) |
0.576074 | + | 0.817397i | \(0.304584\pi\) | |||||||
\(152\) | −43.9942 | − | 76.2002i | −0.289436 | − | 0.501317i | ||||
\(153\) | 95.2443 | 0.622512 | ||||||||
\(154\) | 37.6696 | + | 94.4270i | 0.244608 | + | 0.613162i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 12.1649 | + | 21.0702i | 0.0779800 | + | 0.135065i | ||||
\(157\) | 49.6184 | − | 85.9416i | 0.316041 | − | 0.547399i | −0.663617 | − | 0.748072i | \(-0.730980\pi\) |
0.979658 | + | 0.200673i | \(0.0643130\pi\) | |||||||
\(158\) | 130.369 | + | 75.2685i | 0.825120 | + | 0.476383i | ||||
\(159\) | −2.07225 | + | 1.19642i | −0.0130330 | + | 0.00752463i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 102.660 | − | 130.217i | 0.637641 | − | 0.808799i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | −241.603 | + | 139.490i | −1.48223 | + | 0.855765i | −0.999797 | − | 0.0201678i | \(-0.993580\pi\) |
−0.482433 | + | 0.875933i | \(0.660247\pi\) | |||||||
\(164\) | 112.796 | + | 65.1226i | 0.687779 | + | 0.397089i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −60.5389 | + | 34.9522i | −0.364692 | + | 0.210555i | ||||
\(167\) | −29.9435 | −0.179302 | −0.0896511 | − | 0.995973i | \(-0.528575\pi\) | ||||
−0.0896511 | + | 0.995973i | \(0.528575\pi\) | |||||||
\(168\) | 33.9378 | + | 4.92167i | 0.202011 | + | 0.0292957i | ||||
\(169\) | −119.672 | −0.708118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −80.8225 | − | 46.6629i | −0.472646 | − | 0.272883i | ||||
\(172\) | 5.25673 | + | 3.03497i | 0.0305624 | + | 0.0176452i | ||||
\(173\) | −53.2530 | − | 92.2369i | −0.307821 | − | 0.533161i | 0.670065 | − | 0.742303i | \(-0.266266\pi\) |
−0.977885 | + | 0.209142i | \(0.932933\pi\) | |||||||
\(174\) | − | 22.5273i | − | 0.129467i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 41.0782 | 0.233399 | ||||||||
\(177\) | −164.729 | + | 95.1064i | −0.930673 | + | 0.537324i | ||||
\(178\) | 116.602 | − | 201.960i | 0.655066 | − | 1.13461i | ||||
\(179\) | −119.986 | + | 207.822i | −0.670315 | + | 1.16102i | 0.307500 | + | 0.951548i | \(0.400508\pi\) |
−0.977815 | + | 0.209471i | \(0.932826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 309.322i | 1.70896i | 0.519482 | + | 0.854482i | \(0.326125\pi\) | ||||
−0.519482 | + | 0.854482i | \(0.673875\pi\) | |||||||
\(182\) | 43.0459 | − | 54.6004i | 0.236516 | − | 0.300002i | ||||
\(183\) | − | 68.7483i | − | 0.375674i | ||||||
\(184\) | −33.5002 | − | 58.0241i | −0.182066 | − | 0.315348i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −24.6796 | + | 42.7464i | −0.132686 | + | 0.229819i | ||||
\(187\) | −163.020 | − | 282.358i | −0.871762 | − | 1.50994i | ||||
\(188\) | −123.893 | −0.659005 | ||||||||
\(189\) | 33.7840 | − | 13.4774i | 0.178751 | − | 0.0713091i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.54480 | − | 2.67567i | −0.00808796 | − | 0.0140088i | 0.861953 | − | 0.506988i | \(-0.169241\pi\) |
−0.870041 | + | 0.492979i | \(0.835908\pi\) | |||||||
\(192\) | 6.92820 | − | 12.0000i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −206.718 | − | 119.349i | −1.07108 | − | 0.618387i | −0.142602 | − | 0.989780i | \(-0.545547\pi\) |
−0.928476 | + | 0.371393i | \(0.878880\pi\) | |||||||
\(194\) | 60.6002 | − | 34.9875i | 0.312372 | − | 0.180348i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.8726 | − | 95.2935i | −0.116697 | − | 0.486191i | ||||
\(197\) | − | 291.539i | − | 1.47989i | −0.672666 | − | 0.739946i | \(-0.734851\pi\) | ||
0.672666 | − | 0.739946i | \(-0.265149\pi\) | |||||||
\(198\) | 37.7328 | − | 21.7850i | 0.190570 | − | 0.110025i | ||||
\(199\) | −209.224 | − | 120.796i | −1.05138 | − | 0.607013i | −0.128342 | − | 0.991730i | \(-0.540966\pi\) |
−0.923034 | + | 0.384717i | \(0.874299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.8785 | − | 13.7863i | 0.118799 | − | 0.0685885i | ||||
\(202\) | 190.739 | 0.944252 | ||||||||
\(203\) | −59.7947 | + | 23.8538i | −0.294555 | + | 0.117507i | ||||
\(204\) | −109.979 | −0.539111 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 45.8080 | + | 26.4473i | 0.222369 | + | 0.128385i | ||||
\(207\) | −61.5438 | − | 35.5324i | −0.297313 | − | 0.171654i | ||||
\(208\) | −14.0468 | − | 24.3298i | −0.0675327 | − | 0.116970i | ||||
\(209\) | 319.472i | 1.52857i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −263.018 | −1.24653 | −0.623266 | − | 0.782010i | \(-0.714195\pi\) | ||||
−0.623266 | + | 0.782010i | \(0.714195\pi\) | |||||||
\(212\) | 2.39283 | − | 1.38150i | 0.0112869 | − | 0.00651652i | ||||
\(213\) | −46.2015 | + | 80.0234i | −0.216908 | + | 0.375696i | ||||
\(214\) | −17.5334 | + | 30.3688i | −0.0819318 | + | 0.141910i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 139.596 | + | 20.2442i | 0.643297 | + | 0.0932911i | ||||
\(218\) | 79.6056i | 0.365163i | ||||||||
\(219\) | 62.6830 | + | 108.570i | 0.286224 | + | 0.495754i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −111.490 | + | 193.106i | −0.504479 | + | 0.873783i | ||||
\(222\) | 58.9894 | + | 102.173i | 0.265718 | + | 0.460237i | ||||
\(223\) | 112.658 | 0.505193 | 0.252597 | − | 0.967572i | \(-0.418715\pi\) | ||||
0.252597 | + | 0.967572i | \(0.418715\pi\) | |||||||
\(224\) | −39.1880 | − | 5.68306i | −0.174947 | − | 0.0253708i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −53.0266 | − | 91.8448i | −0.234631 | − | 0.406393i | ||||
\(227\) | −24.5102 | + | 42.4529i | −0.107974 | + | 0.187017i | −0.914950 | − | 0.403568i | \(-0.867770\pi\) |
0.806975 | + | 0.590585i | \(0.201103\pi\) | |||||||
\(228\) | 93.3258 | + | 53.8817i | 0.409324 | + | 0.236323i | ||||
\(229\) | −24.3476 | + | 14.0571i | −0.106321 | + | 0.0613846i | −0.552218 | − | 0.833700i | \(-0.686218\pi\) |
0.445896 | + | 0.895085i | \(0.352885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −97.7792 | − | 77.0871i | −0.423286 | − | 0.333710i | ||||
\(232\) | 26.0123i | 0.112122i | ||||||||
\(233\) | −152.596 | + | 88.1014i | −0.654919 | + | 0.378117i | −0.790338 | − | 0.612671i | \(-0.790095\pi\) |
0.135420 | + | 0.990788i | \(0.456762\pi\) | |||||||
\(234\) | −25.8056 | − | 14.8989i | −0.110280 | − | 0.0636704i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 190.213 | − | 109.819i | 0.805987 | − | 0.465337i | ||||
\(237\) | −184.369 | −0.777930 | ||||||||
\(238\) | 116.455 | + | 291.919i | 0.489306 | + | 1.22655i | ||||
\(239\) | −34.7150 | −0.145251 | −0.0726255 | − | 0.997359i | \(-0.523138\pi\) | ||||
−0.0726255 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −229.871 | − | 132.716i | −0.953823 | − | 0.550690i | −0.0595563 | − | 0.998225i | \(-0.518969\pi\) |
−0.894266 | + | 0.447535i | \(0.852302\pi\) | |||||||
\(242\) | 19.0278 | + | 10.9857i | 0.0786273 | + | 0.0453955i | ||||
\(243\) | −7.79423 | − | 13.5000i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 79.3837i | 0.325343i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −159.517 | −0.648444 | ||||||||
\(247\) | 189.216 | − | 109.244i | 0.766058 | − | 0.442284i | ||||
\(248\) | 28.4976 | − | 49.3592i | 0.114910 | − | 0.199029i | ||||
\(249\) | 42.8075 | − | 74.1447i | 0.171918 | − | 0.297770i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.1723i | 0.0963040i | 0.998840 | + | 0.0481520i | \(0.0153332\pi\) | ||||
−0.998840 | + | 0.0481520i | \(0.984667\pi\) | |||||||
\(252\) | −39.0104 | + | 15.5624i | −0.154803 | + | 0.0617555i | ||||
\(253\) | 243.268i | 0.961533i | ||||||||
\(254\) | 90.8659 | + | 157.384i | 0.357740 | + | 0.619624i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.76874 | − | 8.25969i | −0.0185554 | − | 0.0321389i | 0.856599 | − | 0.515983i | \(-0.172573\pi\) |
−0.875154 | + | 0.483844i | \(0.839240\pi\) | |||||||
\(258\) | −7.43413 | −0.0288145 | ||||||||
\(259\) | 208.736 | − | 264.766i | 0.805932 | − | 1.02226i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.7951 | + | 23.8938i | 0.0528548 | + | 0.0915472i | ||||
\(262\) | 53.3840 | − | 92.4639i | 0.203756 | − | 0.352916i | ||||
\(263\) | −114.197 | − | 65.9316i | −0.434209 | − | 0.250691i | 0.266929 | − | 0.963716i | \(-0.413991\pi\) |
−0.701138 | + | 0.713026i | \(0.747324\pi\) | |||||||
\(264\) | −43.5701 | + | 25.1552i | −0.165038 | + | 0.0952848i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 44.1980 | − | 304.771i | 0.166158 | − | 1.14576i | ||||
\(267\) | 285.615i | 1.06972i | ||||||||
\(268\) | −27.5726 | + | 15.9190i | −0.102883 | + | 0.0593994i | ||||
\(269\) | 32.8041 | + | 18.9395i | 0.121949 | + | 0.0704070i | 0.559733 | − | 0.828673i | \(-0.310904\pi\) |
−0.437785 | + | 0.899080i | \(0.644237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 313.801 | − | 181.173i | 1.15794 | − | 0.668535i | 0.207128 | − | 0.978314i | \(-0.433588\pi\) |
0.950809 | + | 0.309779i | \(0.100255\pi\) | |||||||
\(272\) | 126.992 | 0.466884 | ||||||||
\(273\) | −12.2212 | + | 84.2726i | −0.0447664 | + | 0.308691i | ||||
\(274\) | −152.051 | −0.554932 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 71.0647 | + | 41.0292i | 0.257481 | + | 0.148657i | ||||
\(277\) | 98.1197 | + | 56.6495i | 0.354223 | + | 0.204511i | 0.666544 | − | 0.745466i | \(-0.267773\pi\) |
−0.312321 | + | 0.949977i | \(0.601106\pi\) | |||||||
\(278\) | −192.336 | − | 333.135i | −0.691855 | − | 1.19833i | ||||
\(279\) | − | 60.4525i | − | 0.216676i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −178.735 | −0.636069 | −0.318034 | − | 0.948079i | \(-0.603023\pi\) | ||||
−0.318034 | + | 0.948079i | \(0.603023\pi\) | |||||||
\(282\) | 131.408 | − | 75.8686i | 0.465987 | − | 0.269038i | ||||
\(283\) | 21.5843 | − | 37.3850i | 0.0762695 | − | 0.132103i | −0.825368 | − | 0.564595i | \(-0.809032\pi\) |
0.901638 | + | 0.432492i | \(0.142366\pi\) | |||||||
\(284\) | 53.3489 | − | 92.4030i | 0.187848 | − | 0.325363i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 102.003i | 0.356655i | ||||||||
\(287\) | 168.910 | + | 423.410i | 0.588538 | + | 1.47530i | ||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | −359.471 | − | 622.622i | −1.24384 | − | 2.15440i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −42.8508 | + | 74.2198i | −0.147254 | + | 0.255051i | ||||
\(292\) | −72.3801 | − | 125.366i | −0.247877 | − | 0.429336i | ||||
\(293\) | 15.4426 | 0.0527050 | 0.0263525 | − | 0.999653i | \(-0.491611\pi\) | ||||
0.0263525 | + | 0.999653i | \(0.491611\pi\) | |||||||
\(294\) | 82.6151 | + | 87.0675i | 0.281004 | + | 0.296148i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −68.1151 | − | 117.979i | −0.230119 | − | 0.398577i | ||||
\(297\) | −26.6811 | + | 46.2130i | −0.0898354 | + | 0.155599i | ||||
\(298\) | −102.177 | − | 58.9917i | −0.342875 | − | 0.197959i | ||||
\(299\) | 144.082 | − | 83.1859i | 0.481881 | − | 0.278214i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.87189 | + | 19.7326i | 0.0261525 | + | 0.0655568i | ||||
\(302\) | 179.315i | 0.593757i | ||||||||
\(303\) | −202.309 | + | 116.803i | −0.667687 | + | 0.385489i | ||||
\(304\) | −107.763 | − | 62.2172i | −0.354485 | − | 0.204662i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 116.650 | − | 67.3479i | 0.381209 | − | 0.220091i | ||||
\(307\) | 234.648 | 0.764327 | 0.382163 | − | 0.924095i | \(-0.375179\pi\) | ||||
0.382163 | + | 0.924095i | \(0.375179\pi\) | |||||||
\(308\) | 112.906 | + | 89.0125i | 0.366577 | + | 0.289002i | ||||
\(309\) | −64.7823 | −0.209651 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −345.352 | − | 199.389i | −1.11045 | − | 0.641121i | −0.171508 | − | 0.985183i | \(-0.554864\pi\) |
−0.938947 | + | 0.344061i | \(0.888197\pi\) | |||||||
\(312\) | 29.7978 | + | 17.2037i | 0.0955056 | + | 0.0551402i | ||||
\(313\) | −64.6002 | − | 111.891i | −0.206390 | − | 0.357479i | 0.744184 | − | 0.667974i | \(-0.232838\pi\) |
−0.950575 | + | 0.310495i | \(0.899505\pi\) | |||||||
\(314\) | − | 140.342i | − | 0.446949i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 212.892 | 0.673707 | ||||||||
\(317\) | −348.632 | + | 201.283i | −1.09979 | + | 0.634961i | −0.936165 | − | 0.351562i | \(-0.885651\pi\) |
−0.163621 | + | 0.986523i | \(0.552317\pi\) | |||||||
\(318\) | −1.69199 | + | 2.93061i | −0.00532072 | + | 0.00921575i | ||||
\(319\) | 47.2232 | − | 81.7930i | 0.148035 | − | 0.256404i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 42.9479i | − | 0.133794i | ||||||
\(322\) | 33.6554 | − | 232.074i | 0.104520 | − | 0.720726i | ||||
\(323\) | 987.640i | 3.05771i | ||||||||
\(324\) | 9.00000 | + | 15.5885i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −197.268 | + | 341.679i | −0.605118 | + | 1.04809i | ||||
\(327\) | −48.7483 | − | 84.4345i | −0.149077 | − | 0.258209i | ||||
\(328\) | 184.195 | 0.561569 | ||||||||
\(329\) | −340.526 | − | 268.464i | −1.03503 | − | 0.815999i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 83.4463 | + | 144.533i | 0.252104 | + | 0.436656i | 0.964105 | − | 0.265522i | \(-0.0855443\pi\) |
−0.712001 | + | 0.702178i | \(0.752211\pi\) | |||||||
\(332\) | −49.4298 | + | 85.6150i | −0.148885 | + | 0.257876i | ||||
\(333\) | −125.136 | − | 72.2470i | −0.375782 | − | 0.216958i | ||||
\(334\) | −36.6731 | + | 21.1732i | −0.109800 | + | 0.0633929i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 45.0453 | − | 17.9699i | 0.134064 | − | 0.0534818i | ||||
\(337\) | − | 541.392i | − | 1.60651i | −0.595638 | − | 0.803253i | \(-0.703101\pi\) | ||
0.595638 | − | 0.803253i | \(-0.296899\pi\) | |||||||
\(338\) | −146.568 | + | 84.6208i | −0.433632 | + | 0.250357i | ||||
\(339\) | 112.486 | + | 64.9441i | 0.331818 | + | 0.191575i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −179.215 | + | 103.470i | −0.525558 | + | 0.303431i | ||||
\(342\) | −131.983 | −0.385914 | ||||||||
\(343\) | 143.625 | − | 311.482i | 0.418732 | − | 0.908110i | ||||
\(344\) | 8.58420 | 0.0249541 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −130.443 | − | 75.3111i | −0.377002 | − | 0.217662i | ||||
\(347\) | −371.251 | − | 214.342i | −1.06989 | − | 0.617700i | −0.141737 | − | 0.989904i | \(-0.545269\pi\) |
−0.928151 | + | 0.372204i | \(0.878602\pi\) | |||||||
\(348\) | −15.9292 | − | 27.5902i | −0.0457736 | − | 0.0792822i | ||||
\(349\) | − | 74.6851i | − | 0.213998i | −0.994259 | − | 0.106999i | \(-0.965876\pi\) | ||
0.994259 | − | 0.106999i | \(-0.0341241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.4946 | 0.103973 | ||||||||
\(352\) | 50.3104 | − | 29.0467i | 0.142927 | − | 0.0825190i | ||||
\(353\) | 182.956 | − | 316.890i | 0.518290 | − | 0.897705i | −0.481484 | − | 0.876455i | \(-0.659902\pi\) |
0.999774 | − | 0.0212499i | \(-0.00676457\pi\) | |||||||
\(354\) | −134.501 | + | 232.962i | −0.379946 | + | 0.658085i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 329.799i | − | 0.926403i | ||||||
\(357\) | −302.282 | − | 238.313i | −0.846728 | − | 0.667543i | ||||
\(358\) | 339.373i | 0.947968i | ||||||||
\(359\) | −248.793 | − | 430.922i | −0.693017 | − | 1.20034i | −0.970845 | − | 0.239710i | \(-0.922948\pi\) |
0.277828 | − | 0.960631i | \(-0.410386\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 303.373 | − | 525.457i | 0.840368 | − | 1.45556i | ||||
\(362\) | 218.724 | + | 378.841i | 0.604210 | + | 1.04652i | ||||
\(363\) | −26.9094 | −0.0741305 | ||||||||
\(364\) | 14.1119 | − | 97.3096i | 0.0387689 | − | 0.267334i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −48.6124 | − | 84.1991i | −0.132821 | − | 0.230052i | ||||
\(367\) | −69.6861 | + | 120.700i | −0.189880 | + | 0.328882i | −0.945210 | − | 0.326462i | \(-0.894143\pi\) |
0.755330 | + | 0.655345i | \(0.227477\pi\) | |||||||
\(368\) | −82.0584 | − | 47.3765i | −0.222985 | − | 0.128740i | ||||
\(369\) | 169.194 | − | 97.6839i | 0.458519 | − | 0.264726i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.57040 | + | 1.38790i | 0.0257962 | + | 0.00374098i | ||||
\(372\) | 69.8045i | 0.187647i | ||||||||
\(373\) | −300.961 | + | 173.760i | −0.806865 | + | 0.465844i | −0.845866 | − | 0.533395i | \(-0.820916\pi\) |
0.0390009 | + | 0.999239i | \(0.487582\pi\) | |||||||
\(374\) | −399.315 | − | 230.544i | −1.06769 | − | 0.616429i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −151.737 | + | 87.6055i | −0.403556 | + | 0.232993i | ||||
\(377\) | −64.5923 | −0.171332 | ||||||||
\(378\) | 31.8468 | − | 40.3953i | 0.0842509 | − | 0.106866i | ||||
\(379\) | −307.387 | −0.811048 | −0.405524 | − | 0.914084i | \(-0.632911\pi\) | ||||
−0.405524 | + | 0.914084i | \(0.632911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −192.756 | − | 111.288i | −0.505921 | − | 0.292093i | ||||
\(382\) | −3.78397 | − | 2.18468i | −0.00990569 | − | 0.00571905i | ||||
\(383\) | 254.364 | + | 440.572i | 0.664136 | + | 1.15032i | 0.979519 | + | 0.201353i | \(0.0645339\pi\) |
−0.315382 | + | 0.948965i | \(0.602133\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −337.569 | −0.874531 | ||||||||
\(387\) | 7.88509 | − | 4.55246i | 0.0203749 | − | 0.0117635i | ||||
\(388\) | 49.4799 | − | 85.7016i | 0.127525 | − | 0.220880i | ||||
\(389\) | −85.4840 | + | 148.063i | −0.219753 | + | 0.380624i | −0.954732 | − | 0.297466i | \(-0.903859\pi\) |
0.734979 | + | 0.678090i | \(0.237192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 752.057i | 1.92342i | ||||||||
\(392\) | −95.3957 | − | 100.537i | −0.243356 | − | 0.256472i | ||||
\(393\) | 130.764i | 0.332732i | ||||||||
\(394\) | −206.149 | − | 357.061i | −0.523221 | − | 0.906245i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 30.8087 | − | 53.3622i | 0.0777997 | − | 0.134753i | ||||
\(397\) | 318.249 | + | 551.223i | 0.801634 | + | 1.38847i | 0.918540 | + | 0.395328i | \(0.129369\pi\) |
−0.116906 | + | 0.993143i | \(0.537298\pi\) | |||||||
\(398\) | −341.661 | −0.858446 | ||||||||
\(399\) | 139.755 | + | 350.325i | 0.350262 | + | 0.878006i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 296.110 | + | 512.878i | 0.738429 | + | 1.27900i | 0.953202 | + | 0.302333i | \(0.0977654\pi\) |
−0.214773 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(402\) | 19.4968 | − | 33.7694i | 0.0484994 | − | 0.0840034i | ||||
\(403\) | 122.566 | + | 70.7636i | 0.304135 | + | 0.175592i | ||||
\(404\) | 233.606 | − | 134.873i | 0.578234 | − | 0.333843i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −56.3661 | + | 71.4961i | −0.138833 | + | 0.176099i | ||||
\(407\) | 494.630i | 1.21531i | ||||||||
\(408\) | −134.696 | + | 77.7667i | −0.330137 | + | 0.190605i | ||||
\(409\) | 245.717 | + | 141.865i | 0.600776 | + | 0.346858i | 0.769347 | − | 0.638831i | \(-0.220582\pi\) |
−0.168571 | + | 0.985690i | \(0.553915\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 161.275 | − | 93.1121i | 0.392396 | − | 0.226550i | ||||
\(412\) | 74.8041 | 0.181563 | ||||||||
\(413\) | 760.778 | + | 110.328i | 1.84208 | + | 0.267138i | ||||
\(414\) | −100.501 | −0.242755 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −34.4075 | − | 19.8652i | −0.0827103 | − | 0.0477528i | ||||
\(417\) | 408.006 | + | 235.562i | 0.978431 | + | 0.564897i | ||||
\(418\) | 225.901 | + | 391.271i | 0.540432 | + | 0.936056i | ||||
\(419\) | 482.511i | 1.15158i | 0.817599 | + | 0.575789i | \(0.195305\pi\) | ||||
−0.817599 | + | 0.575789i | \(0.804695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 762.080 | 1.81017 | 0.905083 | − | 0.425234i | \(-0.139808\pi\) | ||||
0.905083 | + | 0.425234i | \(0.139808\pi\) | |||||||
\(422\) | −322.130 | + | 185.982i | −0.763342 | + | 0.440716i | ||||
\(423\) | −92.9197 | + | 160.942i | −0.219668 | + | 0.380476i | ||||
\(424\) | 1.95374 | − | 3.38397i | 0.00460787 | − | 0.00798107i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 130.678i | 0.306755i | ||||||||
\(427\) | −172.017 | + | 218.190i | −0.402849 | + | 0.510984i | ||||
\(428\) | 49.5920i | 0.115869i | ||||||||
\(429\) | −62.4640 | − | 108.191i | −0.145604 | − | 0.252193i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −128.008 | + | 221.717i | −0.297003 | + | 0.514424i | −0.975449 | − | 0.220226i | \(-0.929320\pi\) |
0.678446 | + | 0.734650i | \(0.262654\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −646.579 | −1.49325 | −0.746627 | − | 0.665243i | \(-0.768328\pi\) | ||||
−0.746627 | + | 0.665243i | \(0.768328\pi\) | |||||||
\(434\) | 185.284 | − | 73.9150i | 0.426921 | − | 0.170311i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 56.2897 | + | 97.4966i | 0.129105 | + | 0.223616i | ||||
\(437\) | 368.454 | − | 638.181i | 0.843144 | − | 1.46037i | ||||
\(438\) | 153.541 | + | 88.6472i | 0.350551 | + | 0.202391i | ||||
\(439\) | −290.352 | + | 167.635i | −0.661394 | + | 0.381856i | −0.792808 | − | 0.609472i | \(-0.791382\pi\) |
0.131414 | + | 0.991328i | \(0.458048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −140.944 | − | 41.7578i | −0.319602 | − | 0.0946888i | ||||
\(442\) | 315.341i | 0.713441i | ||||||||
\(443\) | 243.400 | − | 140.527i | 0.549435 | − | 0.317216i | −0.199459 | − | 0.979906i | \(-0.563919\pi\) |
0.748894 | + | 0.662690i | \(0.230585\pi\) | |||||||
\(444\) | 144.494 | + | 83.4237i | 0.325437 | + | 0.187891i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 137.977 | − | 79.6613i | 0.309366 | − | 0.178613i | ||||
\(447\) | 144.500 | 0.323265 | ||||||||
\(448\) | −52.0139 | + | 20.7498i | −0.116102 | + | 0.0463166i | ||||
\(449\) | −47.2320 | −0.105194 | −0.0525969 | − | 0.998616i | \(-0.516750\pi\) | ||||
−0.0525969 | + | 0.998616i | \(0.516750\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −579.181 | − | 334.390i | −1.28422 | − | 0.741442i | ||||
\(452\) | −129.888 | − | 74.9910i | −0.287363 | − | 0.165909i | ||||
\(453\) | −109.807 | − | 190.192i | −0.242400 | − | 0.419850i | ||||
\(454\) | 69.3253i | 0.152699i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 152.400 | 0.334212 | ||||||||
\(457\) | 509.909 | − | 294.396i | 1.11578 | − | 0.644193i | 0.175456 | − | 0.984487i | \(-0.443860\pi\) |
0.940319 | + | 0.340294i | \(0.110527\pi\) | |||||||
\(458\) | −19.8797 | + | 34.4327i | −0.0434055 | + | 0.0751805i | ||||
\(459\) | −82.4840 | + | 142.866i | −0.179704 | + | 0.311256i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 60.5606i | − | 0.131368i | −0.997840 | − | 0.0656839i | \(-0.979077\pi\) | ||
0.997840 | − | 0.0656839i | \(-0.0209229\pi\) | |||||||
\(462\) | −174.263 | − | 25.2717i | −0.377193 | − | 0.0547007i | ||||
\(463\) | − | 88.7592i | − | 0.191704i | −0.995396 | − | 0.0958522i | \(-0.969442\pi\) | ||
0.995396 | − | 0.0958522i | \(-0.0305576\pi\) | |||||||
\(464\) | 18.3935 | + | 31.8584i | 0.0396411 | + | 0.0686604i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −124.594 | + | 215.803i | −0.267369 | + | 0.463097i | ||||
\(467\) | 151.112 | + | 261.733i | 0.323580 | + | 0.560457i | 0.981224 | − | 0.192872i | \(-0.0617802\pi\) |
−0.657644 | + | 0.753329i | \(0.728447\pi\) | |||||||
\(468\) | −42.1404 | −0.0900436 | ||||||||
\(469\) | −110.280 | − | 15.9928i | −0.235138 | − | 0.0340997i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 85.9416 | + | 148.855i | 0.182466 | + | 0.316041i | ||||
\(472\) | 155.308 | − | 269.002i | 0.329043 | − | 0.569919i | ||||
\(473\) | −26.9921 | − | 15.5839i | −0.0570658 | − | 0.0329470i | ||||
\(474\) | −225.806 | + | 130.369i | −0.476383 | + | 0.275040i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 349.045 | + | 275.180i | 0.733288 | + | 0.578110i | ||||
\(477\) | − | 4.14451i | − | 0.00868869i | ||||||
\(478\) | −42.5170 | + | 24.5472i | −0.0889478 | + | 0.0513540i | ||||
\(479\) | −30.4237 | − | 17.5651i | −0.0635151 | − | 0.0366704i | 0.467906 | − | 0.883778i | \(-0.345009\pi\) |
−0.531421 | + | 0.847108i | \(0.678342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 292.959 | − | 169.140i | 0.609062 | − | 0.351642i | ||||
\(482\) | −375.378 | −0.778793 | ||||||||
\(483\) | 106.419 | + | 266.761i | 0.220329 | + | 0.552301i | ||||
\(484\) | 31.0723 | 0.0641989 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | − | 11.0227i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | −55.9741 | − | 32.3167i | −0.114937 | − | 0.0663586i | 0.441430 | − | 0.897296i | \(-0.354471\pi\) |
−0.556366 | + | 0.830937i | \(0.687805\pi\) | |||||||
\(488\) | 56.1327 | + | 97.2247i | 0.115026 | + | 0.199231i | ||||
\(489\) | − | 483.207i | − | 0.988153i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 241.365 | 0.491578 | 0.245789 | − | 0.969323i | \(-0.420953\pi\) | ||||
0.245789 | + | 0.969323i | \(0.420953\pi\) | |||||||
\(492\) | −195.368 | + | 112.796i | −0.397089 | + | 0.229260i | ||||
\(493\) | 145.989 | − | 252.861i | 0.296125 | − | 0.512903i | ||||
\(494\) | 154.494 | − | 267.592i | 0.312742 | − | 0.541685i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 80.6033i | − | 0.162507i | ||||||
\(497\) | 346.860 | − | 138.373i | 0.697908 | − | 0.278416i | ||||
\(498\) | − | 121.078i | − | 0.243128i | ||||||
\(499\) | −95.8123 | − | 165.952i | −0.192009 | − | 0.332569i | 0.753907 | − | 0.656981i | \(-0.228167\pi\) |
−0.945916 | + | 0.324412i | \(0.894834\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.9318 | − | 44.9152i | 0.0517601 | − | 0.0896511i | ||||
\(502\) | 17.0924 | + | 29.6049i | 0.0340486 | + | 0.0589739i | ||||
\(503\) | −919.711 | −1.82845 | −0.914226 | − | 0.405205i | \(-0.867200\pi\) | ||||
−0.914226 | + | 0.405205i | \(0.867200\pi\) | |||||||
\(504\) | −36.7735 | + | 46.6445i | −0.0729634 | + | 0.0925485i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 172.016 | + | 297.941i | 0.339953 | + | 0.588816i | ||||
\(507\) | 103.639 | − | 179.508i | 0.204416 | − | 0.354059i | ||||
\(508\) | 222.575 | + | 128.504i | 0.438140 | + | 0.252960i | ||||
\(509\) | −250.976 | + | 144.901i | −0.493076 | + | 0.284678i | −0.725850 | − | 0.687853i | \(-0.758553\pi\) |
0.232773 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 72.7154 | − | 501.416i | 0.142300 | − | 0.981244i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 139.989 | − | 80.8225i | 0.272883 | − | 0.157549i | ||||
\(514\) | −11.6810 | − | 6.74401i | −0.0227256 | − | 0.0131206i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.10492 | + | 5.25673i | −0.0176452 | + | 0.0101875i | ||||
\(517\) | 636.163 | 1.23049 | ||||||||
\(518\) | 68.4307 | − | 471.870i | 0.132106 | − | 0.910946i | ||||
\(519\) | 184.474 | 0.355441 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −653.176 | − | 377.112i | −1.25370 | − | 0.723823i | −0.281856 | − | 0.959457i | \(-0.590950\pi\) |
−0.971842 | + | 0.235634i | \(0.924283\pi\) | |||||||
\(522\) | 33.7909 | + | 19.5092i | 0.0647336 | + | 0.0373740i | ||||
\(523\) | −37.8638 | − | 65.5821i | −0.0723974 | − | 0.125396i | 0.827554 | − | 0.561386i | \(-0.189732\pi\) |
−0.899952 | + | 0.435990i | \(0.856398\pi\) | |||||||
\(524\) | − | 150.993i | − | 0.288154i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −186.483 | −0.354530 | ||||||||
\(527\) | −554.040 | + | 319.875i | −1.05131 | + | 0.606974i | ||||
\(528\) | −35.5748 | + | 61.6174i | −0.0673765 | + | 0.116700i | ||||
\(529\) | 16.0662 | − | 27.8275i | 0.0303709 | − | 0.0526039i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 329.458i | − | 0.620449i | ||||||
\(532\) | −161.375 | − | 404.520i | −0.303336 | − | 0.760376i | ||||
\(533\) | 457.382i | 0.858128i | ||||||||
\(534\) | 201.960 | + | 349.805i | 0.378202 | + | 0.655066i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −22.5129 | + | 38.9935i | −0.0420017 | + | 0.0727491i | ||||
\(537\) | −207.822 | − | 359.959i | −0.387007 | − | 0.670315i | ||||
\(538\) | 53.5689 | 0.0995705 | ||||||||
\(539\) | 117.446 | + | 489.311i | 0.217895 | + | 0.907813i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −493.177 | − | 854.207i | −0.911602 | − | 1.57894i | −0.811802 | − | 0.583933i | \(-0.801513\pi\) |
−0.0998002 | − | 0.995007i | \(-0.531820\pi\) | |||||||
\(542\) | 256.217 | − | 443.782i | 0.472726 | − | 0.818785i | ||||
\(543\) | −463.984 | − | 267.881i | −0.854482 | − | 0.493335i | ||||
\(544\) | 155.533 | − | 89.7972i | 0.285907 | − | 0.165068i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 44.6218 | + | 111.854i | 0.0817250 | + | 0.204861i | ||||
\(547\) | 346.700i | 0.633820i | 0.948456 | + | 0.316910i | \(0.102645\pi\) | ||||
−0.948456 | + | 0.316910i | \(0.897355\pi\) | |||||||
\(548\) | −186.224 | + | 107.517i | −0.339825 | + | 0.196198i | ||||
\(549\) | 103.122 | + | 59.5377i | 0.187837 | + | 0.108448i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −247.768 | + | 143.049i | −0.449669 | + | 0.259617i | ||||
\(552\) | 116.048 | 0.210232 | ||||||||
\(553\) | 585.143 | + | 461.315i | 1.05813 | + | 0.834204i | ||||
\(554\) | 160.229 | 0.289222 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −471.124 | − | 272.004i | −0.847346 | − | 0.489215i | ||||
\(557\) | 132.891 | + | 76.7246i | 0.238583 | + | 0.137746i | 0.614525 | − | 0.788897i | \(-0.289348\pi\) |
−0.375942 | + | 0.926643i | \(0.622681\pi\) | |||||||
\(558\) | −42.7464 | − | 74.0389i | −0.0766064 | − | 0.132686i | ||||
\(559\) | 21.3158i | 0.0381320i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 564.716 | 1.00662 | ||||||||
\(562\) | −218.905 | + | 126.385i | −0.389511 | + | 0.224884i | ||||
\(563\) | 87.0695 | − | 150.809i | 0.154653 | − | 0.267866i | −0.778280 | − | 0.627918i | \(-0.783907\pi\) |
0.932933 | + | 0.360051i | \(0.117241\pi\) | |||||||
\(564\) | 107.294 | − | 185.839i | 0.190238 | − | 0.329502i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 61.0495i | − | 0.107861i | ||||||
\(567\) | −9.04169 | + | 62.3478i | −0.0159465 | + | 0.109961i | ||||
\(568\) | − | 150.893i | − | 0.265658i | ||||||
\(569\) | −109.591 | − | 189.817i | −0.192603 | − | 0.333597i | 0.753509 | − | 0.657437i | \(-0.228359\pi\) |
−0.946112 | + | 0.323840i | \(0.895026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −478.914 | + | 829.504i | −0.838729 | + | 1.45272i | 0.0522282 | + | 0.998635i | \(0.483368\pi\) |
−0.890958 | + | 0.454087i | \(0.849966\pi\) | |||||||
\(572\) | 72.1272 | + | 124.928i | 0.126097 | + | 0.218406i | ||||
\(573\) | 5.35135 | 0.00933917 | ||||||||
\(574\) | 506.268 | + | 399.132i | 0.882001 | + | 0.695351i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 518.944 | − | 898.838i | 0.899384 | − | 1.55778i | 0.0710997 | − | 0.997469i | \(-0.477349\pi\) |
0.828284 | − | 0.560309i | \(-0.189318\pi\) | |||||||
\(578\) | −880.521 | − | 508.369i | −1.52339 | − | 0.879531i | ||||
\(579\) | 358.046 | − | 206.718i | 0.618387 | − | 0.357026i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −321.380 | + | 128.208i | −0.553149 | + | 0.220667i | ||||
\(582\) | 121.200i | 0.208248i | ||||||||
\(583\) | −12.2867 | + | 7.09371i | −0.0210749 | + | 0.0121676i | ||||
\(584\) | −177.294 | − | 102.361i | −0.303586 | − | 0.175276i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.9132 | − | 10.9195i | 0.0322751 | − | 0.0186340i | ||||
\(587\) | −819.162 | −1.39551 | −0.697753 | − | 0.716339i | \(-0.745817\pi\) | ||||
−0.697753 | + | 0.716339i | \(0.745817\pi\) | |||||||
\(588\) | 162.748 | + | 48.2177i | 0.276783 | + | 0.0820029i | ||||
\(589\) | 626.864 | 1.06429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 437.308 | + | 252.480i | 0.739946 | + | 0.427208i | ||||
\(592\) | −166.847 | − | 96.3294i | −0.281837 | − | 0.162719i | ||||
\(593\) | −266.689 | − | 461.919i | −0.449729 | − | 0.778953i | 0.548639 | − | 0.836059i | \(-0.315146\pi\) |
−0.998368 | + | 0.0571059i | \(0.981813\pi\) | |||||||
\(594\) | 75.4655i | 0.127046i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −166.854 | −0.279956 | ||||||||
\(597\) | 362.387 | − | 209.224i | 0.607013 | − | 0.350459i | ||||
\(598\) | 117.643 | − | 203.763i | 0.196727 | − | 0.340741i | ||||
\(599\) | −171.452 | + | 296.963i | −0.286230 | + | 0.495765i | −0.972907 | − | 0.231198i | \(-0.925735\pi\) |
0.686677 | + | 0.726963i | \(0.259069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 418.941i | − | 0.697073i | −0.937295 | − | 0.348536i | \(-0.886679\pi\) | ||
0.937295 | − | 0.348536i | \(-0.113321\pi\) | |||||||
\(602\) | 23.5941 | + | 18.6011i | 0.0391929 | + | 0.0308989i | ||||
\(603\) | 47.7571i | 0.0791992i | ||||||||
\(604\) | 126.795 | + | 219.615i | 0.209925 | + | 0.363601i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −165.185 | + | 286.108i | −0.272582 | + | 0.472126i | ||||
\(607\) | 70.7875 | + | 122.608i | 0.116619 | + | 0.201989i | 0.918426 | − | 0.395594i | \(-0.129461\pi\) |
−0.801807 | + | 0.597583i | \(0.796128\pi\) | |||||||
\(608\) | −175.977 | −0.289436 | ||||||||
\(609\) | 16.0030 | − | 110.350i | 0.0262775 | − | 0.181199i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −217.537 | − | 376.786i | −0.356035 | − | 0.616670i | ||||
\(612\) | 95.2443 | − | 164.968i | 0.155628 | − | 0.269556i | ||||
\(613\) | −257.244 | − | 148.520i | −0.419647 | − | 0.242284i | 0.275279 | − | 0.961364i | \(-0.411230\pi\) |
−0.694926 | + | 0.719081i | \(0.744563\pi\) | |||||||
\(614\) | 287.384 | − | 165.921i | 0.468053 | − | 0.270230i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 201.222 | + | 29.1813i | 0.326659 | + | 0.0473722i | ||||
\(617\) | − | 674.329i | − | 1.09292i | −0.837486 | − | 0.546458i | \(-0.815976\pi\) | ||
0.837486 | − | 0.546458i | \(-0.184024\pi\) | |||||||
\(618\) | −79.3418 | + | 45.8080i | −0.128385 | + | 0.0741230i | ||||
\(619\) | 833.055 | + | 480.965i | 1.34581 | + | 0.777003i | 0.987653 | − | 0.156659i | \(-0.0500724\pi\) |
0.358156 | + | 0.933662i | \(0.383406\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 106.597 | − | 61.5438i | 0.171654 | − | 0.0991044i | ||||
\(622\) | −563.957 | −0.906683 | ||||||||
\(623\) | 714.643 | − | 906.471i | 1.14710 | − | 1.45501i | ||||
\(624\) | 48.6595 | 0.0779800 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −158.238 | − | 91.3585i | −0.252776 | − | 0.145940i | ||||
\(627\) | −479.208 | − | 276.671i | −0.764287 | − | 0.441261i | ||||
\(628\) | −99.2368 | − | 171.883i | −0.158020 | − | 0.273699i | ||||
\(629\) | 1529.14i | 2.43106i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1185.17 | 1.87824 | 0.939122 | − | 0.343584i | \(-0.111641\pi\) | ||||
0.939122 | + | 0.343584i | \(0.111641\pi\) | |||||||
\(632\) | 260.738 | − | 150.537i | 0.412560 | − | 0.238191i | ||||
\(633\) | 227.781 | − | 394.527i | 0.359843 | − | 0.623266i | ||||
\(634\) | −284.657 | + | 493.040i | −0.448985 | + | 0.777666i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.78566i | 0.00752463i | ||||||||
\(637\) | 249.648 | − | 236.882i | 0.391912 | − | 0.371871i | ||||
\(638\) | − | 133.567i | − | 0.209353i | ||||||
\(639\) | −80.0234 | − | 138.605i | −0.125232 | − | 0.216908i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −203.549 | + | 352.557i | −0.317549 | + | 0.550011i | −0.979976 | − | 0.199115i | \(-0.936193\pi\) |
0.662427 | + | 0.749126i | \(0.269526\pi\) | |||||||
\(642\) | −30.3688 | − | 52.6002i | −0.0473034 | − | 0.0819318i | ||||
\(643\) | 1077.83 | 1.67626 | 0.838128 | − | 0.545474i | \(-0.183650\pi\) | ||||
0.838128 | + | 0.545474i | \(0.183650\pi\) | |||||||
\(644\) | −122.882 | − | 308.029i | −0.190810 | − | 0.478306i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 698.367 | + | 1209.61i | 1.08106 | + | 1.87246i | ||||
\(647\) | −588.349 | + | 1019.05i | −0.909350 | + | 1.57504i | −0.0943805 | + | 0.995536i | \(0.530087\pi\) |
−0.814969 | + | 0.579504i | \(0.803246\pi\) | |||||||
\(648\) | 22.0454 | + | 12.7279i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −976.701 | + | 563.899i | −1.50493 | + | 0.868873i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −151.260 | + | 191.861i | −0.232349 | + | 0.294718i | ||||
\(652\) | 557.959i | 0.855765i | ||||||||
\(653\) | 761.345 | − | 439.563i | 1.16592 | − | 0.673144i | 0.213204 | − | 0.977008i | \(-0.431610\pi\) |
0.952715 | + | 0.303864i | \(0.0982769\pi\) | |||||||
\(654\) | −119.408 | − | 68.9405i | −0.182582 | − | 0.105414i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 225.591 | − | 130.245i | 0.343889 | − | 0.198545i | ||||
\(657\) | −217.140 | −0.330503 | ||||||||
\(658\) | −606.890 | − | 88.0113i | −0.922325 | − | 0.133756i | ||||
\(659\) | −65.1550 | −0.0988696 | −0.0494348 | − | 0.998777i | \(-0.515742\pi\) | ||||
−0.0494348 | + | 0.998777i | \(0.515742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0376 | + | 12.7234i | 0.0333397 | + | 0.0192487i | 0.516577 | − | 0.856241i | \(-0.327206\pi\) |
−0.483237 | + | 0.875489i | \(0.660539\pi\) | |||||||
\(662\) | 204.401 | + | 118.011i | 0.308762 | + | 0.178264i | ||||
\(663\) | −193.106 | − | 334.469i | −0.291261 | − | 0.504479i | ||||
\(664\) | 139.809i | 0.210555i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −204.345 | −0.306825 | ||||||||
\(667\) | −188.667 | + | 108.927i | −0.282860 | + | 0.163309i | ||||
\(668\) | −29.9435 | + | 51.8636i | −0.0448256 | + | 0.0776401i | ||||
\(669\) | −97.5647 | + | 168.987i | −0.145837 | + | 0.252597i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 407.618i | − | 0.607478i | ||||||
\(672\) | 42.4624 | − | 53.8604i | 0.0631881 | − | 0.0801494i | ||||
\(673\) | − | 23.1893i | − | 0.0344566i | −0.999852 | − | 0.0172283i | \(-0.994516\pi\) | ||
0.999852 | − | 0.0172283i | \(-0.00548420\pi\) | |||||||
\(674\) | −382.822 | − | 663.068i | −0.567986 | − | 0.983780i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −119.672 | + | 207.278i | −0.177029 | + | 0.306624i | ||||
\(677\) | −71.0658 | − | 123.090i | −0.104972 | − | 0.181816i | 0.808755 | − | 0.588146i | \(-0.200142\pi\) |
−0.913727 | + | 0.406330i | \(0.866809\pi\) | |||||||
\(678\) | 183.690 | 0.270929 | ||||||||
\(679\) | 321.705 | − | 128.337i | 0.473792 | − | 0.189009i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.4529 | − | 73.5306i | −0.0623391 | − | 0.107974i | ||||
\(682\) | −146.329 | + | 253.449i | −0.214558 | + | 0.371626i | ||||
\(683\) | 568.722 | + | 328.352i | 0.832682 | + | 0.480749i | 0.854770 | − | 0.519007i | \(-0.173698\pi\) |
−0.0220879 | + | 0.999756i | \(0.507031\pi\) | |||||||
\(684\) | −161.645 | + | 93.3258i | −0.236323 | + | 0.136441i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −44.3466 | − | 483.044i | −0.0646452 | − | 0.704146i | ||||
\(687\) | − | 48.6951i | − | 0.0708808i | ||||||
\(688\) | 10.5135 | − | 6.06994i | 0.0152812 | − | 0.00882259i | ||||
\(689\) | 8.40290 | + | 4.85142i | 0.0121958 | + | 0.00704125i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 212.350 | − | 122.600i | 0.307308 | − | 0.177425i | −0.338413 | − | 0.940998i | \(-0.609890\pi\) |
0.645721 | + | 0.763573i | \(0.276557\pi\) | |||||||
\(692\) | −213.012 | −0.307821 | ||||||||
\(693\) | 200.310 | − | 79.9094i | 0.289047 | − | 0.115309i | ||||
\(694\) | −606.250 | −0.873560 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −39.0184 | − | 22.5273i | −0.0560610 | − | 0.0323668i | ||||
\(697\) | −1790.52 | − | 1033.76i | −2.56890 | − | 1.48316i | ||||
\(698\) | −52.8104 | − | 91.4702i | −0.0756595 | − | 0.131046i | ||||
\(699\) | − | 305.192i | − | 0.436612i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 379.419 | 0.541254 | 0.270627 | − | 0.962684i | \(-0.412769\pi\) | ||||
0.270627 | + | 0.962684i | \(0.412769\pi\) | |||||||
\(702\) | 44.6966 | − | 25.8056i | 0.0636704 | − | 0.0367601i | ||||
\(703\) | 749.168 | − | 1297.60i | 1.06567 | − | 1.84580i | ||||
\(704\) | 41.0782 | − | 71.1496i | 0.0583498 | − | 0.101065i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 517.479i | − | 0.732973i | ||||||
\(707\) | 934.335 | + | 135.498i | 1.32155 | + | 0.191651i | ||||
\(708\) | 380.426i | 0.537324i | ||||||||
\(709\) | −442.054 | − | 765.661i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 159.669 | − | 276.554i | 0.224569 | − | 0.388965i | ||||
\(712\) | −233.203 | − | 403.920i | −0.327533 | − | 0.567304i | ||||
\(713\) | 477.337 | 0.669477 | ||||||||
\(714\) | −538.731 | − | 78.1269i | −0.754525 | − | 0.109421i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 239.973 | + | 415.645i | 0.335157 | + | 0.580510i | ||||
\(717\) | 30.0641 | − | 52.0725i | 0.0419304 | − | 0.0726255i | ||||
\(718\) | −609.416 | − | 351.847i | −0.848769 | − | 0.490037i | ||||
\(719\) | 825.831 | − | 476.794i | 1.14858 | − | 0.663135i | 0.200042 | − | 0.979787i | \(-0.435892\pi\) |
0.948542 | + | 0.316653i | \(0.102559\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 205.603 | + | 162.093i | 0.285164 | + | 0.224817i | ||||
\(722\) | − | 858.068i | − | 1.18846i | ||||||
\(723\) | 398.149 | − | 229.871i | 0.550690 | − | 0.317941i | ||||
\(724\) | 535.762 | + | 309.322i | 0.740003 | + | 0.427241i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −32.9571 | + | 19.0278i | −0.0453955 | + | 0.0262091i | ||||
\(727\) | −1110.82 | −1.52795 | −0.763974 | − | 0.645248i | \(-0.776754\pi\) | ||||
−0.763974 | + | 0.645248i | \(0.776754\pi\) | |||||||
\(728\) | −51.5249 | − | 129.158i | −0.0707759 | − | 0.177415i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −83.4455 | − | 48.1773i | −0.114153 | − | 0.0659060i | ||||
\(732\) | −119.075 | − | 68.7483i | −0.162671 | − | 0.0939184i | ||||
\(733\) | −20.3571 | − | 35.2595i | −0.0277722 | − | 0.0481029i | 0.851805 | − | 0.523859i | \(-0.175508\pi\) |
−0.879577 | + | 0.475756i | \(0.842175\pi\) | |||||||
\(734\) | 197.102i | 0.268531i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −134.001 | −0.182066 | ||||||||
\(737\) | 141.579 | − | 81.7407i | 0.192102 | − | 0.110910i | ||||
\(738\) | 138.146 | − | 239.276i | 0.187190 | − | 0.324222i | ||||
\(739\) | 422.735 | − | 732.199i | 0.572037 | − | 0.990797i | −0.424320 | − | 0.905512i | \(-0.639487\pi\) |
0.996357 | − | 0.0852847i | \(-0.0271800\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 378.433i | 0.510705i | ||||||||
\(742\) | 12.7027 | − | 5.06747i | 0.0171195 | − | 0.00682947i | ||||
\(743\) | − | 355.319i | − | 0.478222i | −0.970992 | − | 0.239111i | \(-0.923144\pi\) | ||
0.970992 | − | 0.239111i | \(-0.0768559\pi\) | |||||||
\(744\) | 49.3592 | + | 85.4927i | 0.0663431 | + | 0.114910i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −245.733 | + | 425.623i | −0.329401 | + | 0.570540i | ||||
\(747\) | 74.1447 | + | 128.422i | 0.0992567 | + | 0.171918i | ||||
\(748\) | −652.078 | −0.871762 | ||||||||
\(749\) | −107.461 | + | 136.306i | −0.143473 | + | 0.181984i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −108.768 | − | 188.392i | −0.144831 | − | 0.250855i | 0.784479 | − | 0.620156i | \(-0.212931\pi\) |
−0.929310 | + | 0.369300i | \(0.879597\pi\) | |||||||
\(752\) | −123.893 | + | 214.589i | −0.164751 | + | 0.285357i | ||||
\(753\) | −36.2584 | − | 20.9338i | −0.0481520 | − | 0.0278006i | ||||
\(754\) | −79.1091 | + | 45.6737i | −0.104919 | + | 0.0605751i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.4404 | − | 71.9930i | 0.0138101 | − | 0.0952289i | ||||
\(757\) | 1178.25i | 1.55647i | 0.627975 | + | 0.778233i | \(0.283884\pi\) | ||||
−0.627975 | + | 0.778233i | \(0.716116\pi\) | |||||||
\(758\) | −376.471 | + | 217.356i | −0.496663 | + | 0.286749i | ||||
\(759\) | −364.902 | − | 210.676i | −0.480766 | − | 0.277571i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 711.636 | − | 410.863i | 0.935133 | − | 0.539899i | 0.0467017 | − | 0.998909i | \(-0.485129\pi\) |
0.888431 | + | 0.459010i | \(0.151796\pi\) | |||||||
\(762\) | −314.769 | −0.413082 | ||||||||
\(763\) | −56.5504 | + | 389.948i | −0.0741159 | + | 0.511073i | ||||
\(764\) | −6.17920 | −0.00808796 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 623.063 | + | 359.725i | 0.813398 | + | 0.469615i | ||||
\(767\) | 667.970 | + | 385.653i | 0.870887 | + | 0.502807i | ||||
\(768\) | −13.8564 | − | 24.0000i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 230.888i | 0.300244i | 0.988667 | + | 0.150122i | \(0.0479667\pi\) | ||||
−0.988667 | + | 0.150122i | \(0.952033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.5194 | 0.0214259 | ||||||||
\(772\) | −413.436 | + | 238.697i | −0.535539 | + | 0.309193i | ||||
\(773\) | 337.234 | − | 584.107i | 0.436267 | − | 0.755636i | −0.561131 | − | 0.827727i | \(-0.689634\pi\) |
0.997398 | + | 0.0720908i | \(0.0229671\pi\) | |||||||
\(774\) | 6.43815 | − | 11.1512i | 0.00831802 | − | 0.0144072i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 139.950i | − | 0.180348i | ||||||
\(777\) | 216.378 | + | 542.399i | 0.278479 | + | 0.698068i | ||||
\(778\) | 241.785i | 0.310778i | ||||||||
\(779\) | 1012.94 | + | 1754.46i | 1.30030 | + | 2.25219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −273.935 | + | 474.469i | −0.350749 | + | 0.607515i | ||||
\(782\) | 531.784 | + | 921.077i | 0.680031 | + | 1.17785i | ||||
\(783\) | −47.7876 | −0.0610314 | ||||||||
\(784\) | −187.926 | − | 55.6770i | −0.239701 | − | 0.0710166i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 92.4639 | + | 160.152i | 0.117639 | + | 0.203756i | ||||
\(787\) | −311.445 | + | 539.438i | −0.395737 | + | 0.685436i | −0.993195 | − | 0.116464i | \(-0.962844\pi\) |
0.597458 | + | 0.801900i | \(0.296177\pi\) | |||||||
\(788\) | −504.960 | − | 291.539i | −0.640812 | − | 0.369973i | ||||
\(789\) | 197.795 | − | 114.197i | 0.250691 | − | 0.144736i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −194.506 | − | 487.571i | −0.245899 | − | 0.616399i | ||||
\(792\) | − | 87.1401i | − | 0.110025i | ||||||
\(793\) | −241.423 | + | 139.386i | −0.304443 | + | 0.175770i | ||||
\(794\) | 779.547 | + | 450.072i | 0.981797 | + | 0.566841i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −418.448 | + | 241.591i | −0.525688 | + | 0.303506i | ||||
\(797\) | 1322.28 | 1.65907 | 0.829537 | − | 0.558452i | \(-0.188604\pi\) | ||||
0.829537 | + | 0.558452i | \(0.188604\pi\) | |||||||
\(798\) | 418.881 | + | 330.237i | 0.524913 | + | 0.413831i | ||||
\(799\) | 1966.68 | 2.46143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −428.422 | − | 247.350i | −0.534859 | − | 0.308801i | ||||
\(802\) | 725.319 | + | 418.763i | 0.904387 | + | 0.522148i | ||||
\(803\) | 371.656 | + | 643.727i | 0.462834 | + | 0.801653i | ||||
\(804\) | − | 55.1451i | − | 0.0685885i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 200.150 | 0.248325 | ||||||||
\(807\) | −56.8185 | + | 32.8041i | −0.0704070 | + | 0.0406495i | ||||
\(808\) | 190.739 | − | 330.369i | 0.236063 | − | 0.408873i | ||||
\(809\) | 521.105 | − | 902.581i | 0.644135 | − | 1.11567i | −0.340366 | − | 0.940293i | \(-0.610551\pi\) |
0.984501 | − | 0.175381i | \(-0.0561158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 782.292i | 0.964602i | 0.876006 | + | 0.482301i | \(0.160199\pi\) | ||||
−0.876006 | + | 0.482301i | \(0.839801\pi\) | |||||||
\(812\) | −18.4787 | + | 127.421i | −0.0227570 | + | 0.156923i | ||||
\(813\) | 627.602i | 0.771958i | ||||||||
\(814\) | 349.756 | + | 605.796i | 0.429676 | + | 0.744221i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −109.979 | + | 190.489i | −0.134778 | + | 0.233442i | ||||
\(817\) | 47.2069 | + | 81.7647i | 0.0577808 | + | 0.100079i | ||||
\(818\) | 401.255 | 0.490532 | ||||||||
\(819\) | −115.825 | − | 91.3141i | −0.141423 | − | 0.111495i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 505.805 | + | 876.080i | 0.616084 | + | 1.06709i | 0.990193 | + | 0.139704i | \(0.0446153\pi\) |
−0.374109 | + | 0.927385i | \(0.622051\pi\) | |||||||
\(822\) | 131.680 | − | 228.077i | 0.160195 | − | 0.277466i | ||||
\(823\) | −965.106 | − | 557.204i | −1.17267 | − | 0.677040i | −0.218361 | − | 0.975868i | \(-0.570071\pi\) |
−0.954307 | + | 0.298828i | \(0.903404\pi\) | |||||||
\(824\) | 91.6160 | − | 52.8945i | 0.111184 | − | 0.0641924i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1009.77 | − | 402.827i | 1.22249 | − | 0.487684i | ||||
\(827\) | − | 1267.52i | − | 1.53267i | −0.642440 | − | 0.766336i | \(-0.722078\pi\) | ||
0.642440 | − | 0.766336i | \(-0.277922\pi\) | |||||||
\(828\) | −123.088 | + | 71.0647i | −0.148657 | + | 0.0858269i | ||||
\(829\) | 180.535 | + | 104.232i | 0.217775 | + | 0.125732i | 0.604919 | − | 0.796287i | \(-0.293205\pi\) |
−0.387145 | + | 0.922019i | \(0.626539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −169.948 | + | 98.1197i | −0.204511 | + | 0.118074i | ||||
\(832\) | −56.1872 | −0.0675327 | ||||||||
\(833\) | 363.081 | + | 1512.69i | 0.435871 | + | 1.81596i | ||||
\(834\) | 666.270 | 0.798885 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 553.341 | + | 319.472i | 0.661892 | + | 0.382143i | ||||
\(837\) | 90.6787 | + | 52.3534i | 0.108338 | + | 0.0625488i | ||||
\(838\) | 341.187 | + | 590.953i | 0.407144 | + | 0.705194i | ||||
\(839\) | − | 389.239i | − | 0.463932i | −0.972724 | − | 0.231966i | \(-0.925484\pi\) | ||
0.972724 | − | 0.231966i | \(-0.0745159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −756.420 | −0.899429 | ||||||||
\(842\) | 933.354 | − | 538.872i | 1.10850 | − | 0.639991i | ||||
\(843\) | 154.789 | − | 268.103i | 0.183617 | − | 0.318034i | ||||
\(844\) | −263.018 | + | 455.561i | −0.311633 | + | 0.539764i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 262.816i | 0.310658i | ||||||||
\(847\) | 85.4037 | + | 67.3305i | 0.100831 | + | 0.0794930i | ||||
\(848\) | − | 5.52601i | − | 0.00651652i | ||||||
\(849\) | 37.3850 | + | 64.7528i | 0.0440342 | + | 0.0762695i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 570.468 | − | 988.080i | 0.670350 | − | 1.16108i | ||||
\(852\) | 92.4030 | + | 160.047i | 0.108454 | + | 0.187848i | ||||
\(853\) | 1239.21 | 1.45277 | 0.726386 | − | 0.687287i | \(-0.241199\pi\) | ||||
0.726386 | + | 0.687287i | \(0.241199\pi\) | |||||||
\(854\) | −56.3928 | + | 388.861i | −0.0660337 | + | 0.455341i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.0668 | + | 60.7375i | 0.0409659 | + | 0.0709550i | ||||
\(857\) | −91.1334 | + | 157.848i | −0.106340 | + | 0.184186i | −0.914285 | − | 0.405072i | \(-0.867247\pi\) |
0.807945 | + | 0.589258i | \(0.200580\pi\) | |||||||
\(858\) | −153.005 | − | 88.3374i | −0.178327 | − | 0.102957i | ||||
\(859\) | 366.992 | − | 211.883i | 0.427232 | − | 0.246662i | −0.270935 | − | 0.962598i | \(-0.587333\pi\) |
0.698167 | + | 0.715935i | \(0.253999\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −781.396 | − | 113.318i | −0.907544 | − | 0.131612i | ||||
\(862\) | 362.062i | 0.420026i | ||||||||
\(863\) | 14.9502 | − | 8.63152i | 0.0173236 | − | 0.0100018i | −0.491313 | − | 0.870983i | \(-0.663483\pi\) |
0.508637 | + | 0.860981i | \(0.330150\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −791.895 | + | 457.201i | −0.914428 | + | 0.527945i | ||||
\(867\) | 1245.24 | 1.43627 | ||||||||
\(868\) | 174.659 | − | 221.542i | 0.201221 | − | 0.255233i | ||||
\(869\) | −1093.15 | −1.25794 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −96.8266 | − | 55.9028i | −0.111167 | − | 0.0641824i | ||||
\(872\) | 137.881 | + | 79.6056i | 0.158120 | + | 0.0912908i | ||||
\(873\) | −74.2198 | − | 128.552i | −0.0850169 | − | 0.147254i | ||||
\(874\) | − | 1042.15i | − | 1.19239i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 250.732 | 0.286224 | ||||||||
\(877\) | −318.122 | + | 183.668i | −0.362739 | + | 0.209428i | −0.670282 | − | 0.742107i | \(-0.733827\pi\) |
0.307542 | + | 0.951534i | \(0.400493\pi\) | |||||||
\(878\) | −237.071 | + | 410.620i | −0.270013 | + | 0.467676i | ||||
\(879\) | −13.3737 | + | 23.1638i | −0.0152146 | + | 0.0263525i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 376.890i | 0.427798i | 0.976856 | + | 0.213899i | \(0.0686164\pi\) | ||||
−0.976856 | + | 0.213899i | \(0.931384\pi\) | |||||||
\(882\) | −202.148 | + | 48.5201i | −0.229193 | + | 0.0550114i | ||||
\(883\) | 1101.06i | 1.24695i | 0.781842 | + | 0.623476i | \(0.214280\pi\) | ||||
−0.781842 | + | 0.623476i | \(0.785720\pi\) | |||||||
\(884\) | 222.980 | + | 386.212i | 0.252239 | + | 0.436891i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 198.735 | − | 344.219i | 0.224306 | − | 0.388509i | ||||
\(887\) | −60.6873 | − | 105.113i | −0.0684186 | − | 0.118504i | 0.829787 | − | 0.558081i | \(-0.188462\pi\) |
−0.898205 | + | 0.439576i | \(0.855129\pi\) | |||||||
\(888\) | 235.958 | 0.265718 | ||||||||
\(889\) | 333.304 | + | 835.498i | 0.374920 | + | 0.939818i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.2130 | − | 80.0433i | −0.0518665 | − | 0.0898354i | ||||
\(892\) | 112.658 | − | 195.129i | 0.126298 | − | 0.218755i | ||||
\(893\) | −1668.89 | − | 963.534i | −1.86886 | − | 1.07899i | ||||
\(894\) | 176.975 | − | 102.177i | 0.197959 | − | 0.114292i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −49.0314 | + | 62.1926i | −0.0547225 | + | 0.0694114i | ||||
\(897\) | 288.165i | 0.321254i | ||||||||
\(898\) | −57.8472 | + | 33.3981i | −0.0644178 | + | 0.0371916i | ||||
\(899\) | −160.493 | − | 92.6609i | −0.178524 | − | 0.103071i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.9839 | + | 21.9300i | −0.0421575 | + | 0.0243397i | ||||
\(902\) | −945.799 | −1.04856 | ||||||||
\(903\) | −36.4161 | − | 5.28108i | −0.0403279 | − | 0.00584837i | ||||
\(904\) | −212.106 | −0.234631 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −268.972 | − | 155.291i | −0.296879 | − | 0.171403i | ||||
\(907\) | −67.6459 | − | 39.0554i | −0.0745820 | − | 0.0430599i | 0.462245 | − | 0.886752i | \(-0.347044\pi\) |
−0.536827 | + | 0.843692i | \(0.680377\pi\) | |||||||
\(908\) | 49.0204 | + | 84.9058i | 0.0539872 | + | 0.0935086i | ||||
\(909\) | − | 404.618i | − | 0.445124i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 863.281 | 0.947619 | 0.473809 | − | 0.880627i | \(-0.342879\pi\) | ||||
0.473809 | + | 0.880627i | \(0.342879\pi\) | |||||||
\(912\) | 186.652 | − | 107.763i | 0.204662 | − | 0.118162i | ||||
\(913\) | 253.811 | − | 439.614i | 0.277997 | − | 0.481505i | ||||
\(914\) | 416.339 | − | 721.121i | 0.455513 | − | 0.788973i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 56.2283i | 0.0613846i | ||||||||
\(917\) | 327.187 | − | 415.012i | 0.356801 | − | 0.452575i | ||||
\(918\) | 233.300i | 0.254139i | ||||||||
\(919\) | 678.926 | + | 1175.93i | 0.738766 | + | 1.27958i | 0.953051 | + | 0.302810i | \(0.0979247\pi\) |
−0.214285 | + | 0.976771i | \(0.568742\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −203.211 | + | 351.973i | −0.220642 | + | 0.382163i | ||||
\(922\) | −42.8228 | − | 74.1712i | −0.0464455 | − | 0.0804460i | ||||
\(923\) | 374.691 | 0.405949 | ||||||||
\(924\) | −231.298 | + | 92.2714i | −0.250322 | + | 0.0998608i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −62.7622 | − | 108.707i | −0.0677778 | − | 0.117395i | ||||
\(927\) | 56.1031 | − | 97.1734i | 0.0605211 | − | 0.104826i | ||||
\(928\) | 45.0546 | + | 26.0123i | 0.0485502 | + | 0.0280305i | ||||
\(929\) | −800.920 | + | 462.411i | −0.862131 | + | 0.497752i | −0.864725 | − | 0.502245i | \(-0.832508\pi\) |
0.00259410 | + | 0.999997i | \(0.499174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 433.009 | − | 1461.53i | 0.465101 | − | 1.56985i | ||||
\(932\) | 352.405i | 0.378117i | ||||||||
\(933\) | 598.166 | − | 345.352i | 0.641121 | − | 0.370152i | ||||
\(934\) | 370.147 | + | 213.704i | 0.396303 | + | 0.228806i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −51.6112 | + | 29.7978i | −0.0551402 | + | 0.0318352i | ||||
\(937\) | −270.668 | −0.288867 | −0.144433 | − | 0.989515i | \(-0.546136\pi\) | ||||
−0.144433 | + | 0.989515i | \(0.546136\pi\) | |||||||
\(938\) | −146.373 | + | 58.3924i | −0.156048 | + | 0.0622520i | ||||
\(939\) | 223.782 | 0.238319 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −395.174 | − | 228.154i | −0.419952 | − | 0.242459i | 0.275105 | − | 0.961414i | \(-0.411287\pi\) |
−0.695057 | + | 0.718955i | \(0.744621\pi\) | |||||||
\(942\) | 210.513 | + | 121.540i | 0.223475 | + | 0.129023i | ||||
\(943\) | 771.320 | + | 1335.97i | 0.817943 | + | 1.41672i | ||||
\(944\) | − | 439.278i | − | 0.465337i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.0780 | −0.0465940 | ||||||||
\(947\) | −860.460 | + | 496.787i | −0.908617 | + | 0.524590i | −0.879986 | − | 0.475000i | \(-0.842448\pi\) |
−0.0286308 | + | 0.999590i | \(0.509115\pi\) | |||||||
\(948\) | −184.369 | + | 319.337i | −0.194483 | + | 0.336854i | ||||
\(949\) | 254.177 | − | 440.248i | 0.267837 | − | 0.463907i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 697.264i | − | 0.733190i | ||||||
\(952\) | 622.073 | + | 90.2132i | 0.653438 | + | 0.0947618i | ||||
\(953\) | 206.385i | 0.216563i | 0.994120 | + | 0.108281i | \(0.0345348\pi\) | ||||
−0.994120 | + | 0.108281i | \(0.965465\pi\) | |||||||
\(954\) | −2.93061 | − | 5.07596i | −0.00307192 | − | 0.00532072i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −34.7150 | + | 60.1282i | −0.0363128 | + | 0.0628956i | ||||
\(957\) | 81.7930 | + | 141.670i | 0.0854681 | + | 0.148035i | ||||
\(958\) | −49.6817 | −0.0518598 | ||||||||
\(959\) | −744.825 | − | 108.015i | −0.776668 | − | 0.112633i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −277.472 | − | 480.596i | −0.288733 | − | 0.500100i | ||||
\(962\) | 239.200 | − | 414.306i | 0.248649 | − | 0.430672i | ||||
\(963\) | 64.4218 | + | 37.1940i | 0.0668970 | + | 0.0386230i | ||||
\(964\) | −459.743 | + | 265.432i | −0.476911 | + | 0.275345i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 318.964 | + | 251.465i | 0.330191 | + | 0.260316i | ||||
\(967\) | 169.282i | 0.175058i | 0.996162 | + | 0.0875292i | \(0.0278971\pi\) | ||||
−0.996162 | + | 0.0875292i | \(0.972103\pi\) | |||||||
\(968\) | 38.0556 | − | 21.9714i | 0.0393136 | − | 0.0226977i | ||||
\(969\) | −1481.46 | − | 855.321i | −1.52885 | − | 0.882684i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −122.891 | + | 70.9512i | −0.126561 | + | 0.0730702i | −0.561944 | − | 0.827175i | \(-0.689946\pi\) |
0.435383 | + | 0.900245i | \(0.356613\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | −705.504 | − | 1768.50i | −0.725081 | − | 1.81757i | ||||
\(974\) | −91.4053 | −0.0938453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 137.497 | + | 79.3837i | 0.140878 | + | 0.0813357i | ||||
\(977\) | 1219.19 | + | 703.901i | 1.24789 | + | 0.720472i | 0.970689 | − | 0.240339i | \(-0.0772588\pi\) |
0.277204 | + | 0.960811i | \(0.410592\pi\) | |||||||
\(978\) | −341.679 | − | 591.805i | −0.349365 | − | 0.605118i | ||||
\(979\) | 1693.45i | 1.72977i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 168.869 | 0.172140 | ||||||||
\(982\) | 295.610 | − | 170.671i | 0.301029 | − | 0.173799i | ||||
\(983\) | 448.890 | − | 777.500i | 0.456653 | − | 0.790946i | −0.542129 | − | 0.840296i | \(-0.682381\pi\) |
0.998782 | + | 0.0493494i | \(0.0157148\pi\) | |||||||
\(984\) | −159.517 | + | 276.292i | −0.162111 | + | 0.280784i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 412.920i | − | 0.418783i | ||||||
\(987\) | 697.600 | − | 278.293i | 0.706788 | − | 0.281958i | ||||
\(988\) | − | 436.976i | − | 0.442284i | ||||||
\(989\) | 35.9466 | + | 62.2613i | 0.0363464 | + | 0.0629538i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −762.140 | + | 1320.06i | −0.769061 | + | 1.33205i | 0.169011 | + | 0.985614i | \(0.445943\pi\) |
−0.938072 | + | 0.346439i | \(0.887391\pi\) | |||||||
\(992\) | −56.9951 | − | 98.7185i | −0.0574548 | − | 0.0995146i | ||||
\(993\) | −289.066 | −0.291104 | ||||||||
\(994\) | 326.971 | − | 414.739i | 0.328945 | − | 0.417242i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −85.6150 | − | 148.289i | −0.0859588 | − | 0.148885i | ||||
\(997\) | −444.935 | + | 770.649i | −0.446273 | + | 0.772968i | −0.998140 | − | 0.0609641i | \(-0.980582\pi\) |
0.551866 | + | 0.833932i | \(0.313916\pi\) | |||||||
\(998\) | −234.691 | − | 135.499i | −0.235162 | − | 0.135771i | ||||
\(999\) | 216.741 | − | 125.136i | 0.216958 | − | 0.125261i |
(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 | 1050.3.q.e.199.14 | 32 | ||
5.2 | odd | 4 | 1050.3.p.i.451.7 | 16 | |||
5.3 | odd | 4 | 210.3.o.b.31.1 | ✓ | 16 | ||
5.4 | even | 2 | inner | 1050.3.q.e.199.3 | 32 | ||
7.5 | odd | 6 | inner | 1050.3.q.e.649.3 | 32 | ||
15.8 | even | 4 | 630.3.v.c.451.7 | 16 | |||
35.3 | even | 12 | 1470.3.f.d.391.12 | 16 | |||
35.12 | even | 12 | 1050.3.p.i.901.7 | 16 | |||
35.18 | odd | 12 | 1470.3.f.d.391.14 | 16 | |||
35.19 | odd | 6 | inner | 1050.3.q.e.649.13 | 32 | ||
35.33 | even | 12 | 210.3.o.b.61.1 | yes | 16 | ||
105.68 | odd | 12 | 630.3.v.c.271.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.1 | ✓ | 16 | 5.3 | odd | 4 | ||
210.3.o.b.61.1 | yes | 16 | 35.33 | even | 12 | ||
630.3.v.c.271.7 | 16 | 105.68 | odd | 12 | |||
630.3.v.c.451.7 | 16 | 15.8 | even | 4 | |||
1050.3.p.i.451.7 | 16 | 5.2 | odd | 4 | |||
1050.3.p.i.901.7 | 16 | 35.12 | even | 12 | |||
1050.3.q.e.199.3 | 32 | 5.4 | even | 2 | inner | ||
1050.3.q.e.199.14 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.q.e.649.3 | 32 | 7.5 | odd | 6 | inner | ||
1050.3.q.e.649.13 | 32 | 35.19 | odd | 6 | inner | ||
1470.3.f.d.391.12 | 16 | 35.3 | even | 12 | |||
1470.3.f.d.391.14 | 16 | 35.18 | odd | 12 |