Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,3,Mod(577,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.577");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.6294988061\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(5.02578 - 5.02578i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.577 |
Dual form | 1014.3.f.j.775.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 6.39181 | − | 6.39181i | 1.27836 | − | 1.27836i | 0.336778 | − | 0.941584i | \(-0.390663\pi\) |
0.941584 | − | 0.336778i | \(-0.109337\pi\) | |||||||
\(6\) | −1.73205 | + | 1.73205i | −0.288675 | + | 0.288675i | ||||
\(7\) | 6.75784 | + | 6.75784i | 0.965405 | + | 0.965405i | 0.999421 | − | 0.0340162i | \(-0.0108298\pi\) |
−0.0340162 | + | 0.999421i | \(0.510830\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 12.7836i | − | 1.27836i | ||||||
\(11\) | −11.5157 | − | 11.5157i | −1.04688 | − | 1.04688i | −0.998846 | − | 0.0480334i | \(-0.984705\pi\) |
−0.0480334 | − | 0.998846i | \(-0.515295\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 13.5157 | 0.965405 | ||||||||
\(15\) | −11.0709 | + | 11.0709i | −0.738063 | + | 0.738063i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | − | 9.60634i | − | 0.565079i | −0.959256 | − | 0.282540i | \(-0.908823\pi\) | ||
0.959256 | − | 0.282540i | \(-0.0911768\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | −6.99865 | + | 6.99865i | −0.368350 | + | 0.368350i | −0.866875 | − | 0.498525i | \(-0.833875\pi\) |
0.498525 | + | 0.866875i | \(0.333875\pi\) | |||||||
\(20\) | −12.7836 | − | 12.7836i | −0.639181 | − | 0.639181i | ||||
\(21\) | −11.7049 | − | 11.7049i | −0.557377 | − | 0.557377i | ||||
\(22\) | −23.0313 | −1.04688 | ||||||||
\(23\) | − | 27.3583i | − | 1.18949i | −0.803915 | − | 0.594745i | \(-0.797253\pi\) | ||
0.803915 | − | 0.594745i | \(-0.202747\pi\) | |||||||
\(24\) | 3.46410 | + | 3.46410i | 0.144338 | + | 0.144338i | ||||
\(25\) | − | 56.7105i | − | 2.26842i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 13.5157 | − | 13.5157i | 0.482703 | − | 0.482703i | ||||
\(29\) | 27.6046 | 0.951884 | 0.475942 | − | 0.879477i | \(-0.342107\pi\) | ||||
0.475942 | + | 0.879477i | \(0.342107\pi\) | |||||||
\(30\) | 22.1419i | 0.738063i | ||||||||
\(31\) | −11.5613 | + | 11.5613i | −0.372946 | + | 0.372946i | −0.868549 | − | 0.495603i | \(-0.834947\pi\) |
0.495603 | + | 0.868549i | \(0.334947\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 19.9457 | + | 19.9457i | 0.604416 | + | 0.604416i | ||||
\(34\) | −9.60634 | − | 9.60634i | −0.282540 | − | 0.282540i | ||||
\(35\) | 86.3896 | 2.46827 | ||||||||
\(36\) | − | 6.00000i | − | 0.166667i | ||||||
\(37\) | 14.9065 | + | 14.9065i | 0.402878 | + | 0.402878i | 0.879246 | − | 0.476368i | \(-0.158047\pi\) |
−0.476368 | + | 0.879246i | \(0.658047\pi\) | |||||||
\(38\) | 13.9973i | 0.368350i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −25.5672 | −0.639181 | ||||||||
\(41\) | 28.6254 | − | 28.6254i | 0.698179 | − | 0.698179i | −0.265838 | − | 0.964018i | \(-0.585649\pi\) |
0.964018 | + | 0.265838i | \(0.0856487\pi\) | |||||||
\(42\) | −23.4098 | −0.557377 | ||||||||
\(43\) | 35.6912i | 0.830029i | 0.909815 | + | 0.415014i | \(0.136223\pi\) | ||||
−0.909815 | + | 0.415014i | \(0.863777\pi\) | |||||||
\(44\) | −23.0313 | + | 23.0313i | −0.523440 | + | 0.523440i | ||||
\(45\) | 19.1754 | − | 19.1754i | 0.426121 | − | 0.426121i | ||||
\(46\) | −27.3583 | − | 27.3583i | −0.594745 | − | 0.594745i | ||||
\(47\) | −25.5184 | − | 25.5184i | −0.542944 | − | 0.542944i | 0.381447 | − | 0.924391i | \(-0.375426\pi\) |
−0.924391 | + | 0.381447i | \(0.875426\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 42.3367i | 0.864014i | ||||||||
\(50\) | −56.7105 | − | 56.7105i | −1.13421 | − | 1.13421i | ||||
\(51\) | 16.6387i | 0.326249i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −39.0697 | −0.737165 | −0.368582 | − | 0.929595i | \(-0.620157\pi\) | ||||
−0.368582 | + | 0.929595i | \(0.620157\pi\) | |||||||
\(54\) | −5.19615 | + | 5.19615i | −0.0962250 | + | 0.0962250i | ||||
\(55\) | −147.212 | −2.67658 | ||||||||
\(56\) | − | 27.0313i | − | 0.482703i | ||||||
\(57\) | 12.1220 | − | 12.1220i | 0.212667 | − | 0.212667i | ||||
\(58\) | 27.6046 | − | 27.6046i | 0.475942 | − | 0.475942i | ||||
\(59\) | −33.6963 | − | 33.6963i | −0.571124 | − | 0.571124i | 0.361319 | − | 0.932442i | \(-0.382327\pi\) |
−0.932442 | + | 0.361319i | \(0.882327\pi\) | |||||||
\(60\) | 22.1419 | + | 22.1419i | 0.369031 | + | 0.369031i | ||||
\(61\) | 70.5433 | 1.15645 | 0.578224 | − | 0.815878i | \(-0.303746\pi\) | ||||
0.578224 | + | 0.815878i | \(0.303746\pi\) | |||||||
\(62\) | 23.1226i | 0.372946i | ||||||||
\(63\) | 20.2735 | + | 20.2735i | 0.321802 | + | 0.321802i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 39.8915 | 0.604416 | ||||||||
\(67\) | 28.3486 | − | 28.3486i | 0.423114 | − | 0.423114i | −0.463160 | − | 0.886274i | \(-0.653285\pi\) |
0.886274 | + | 0.463160i | \(0.153285\pi\) | |||||||
\(68\) | −19.2127 | −0.282540 | ||||||||
\(69\) | 47.3859i | 0.686752i | ||||||||
\(70\) | 86.3896 | − | 86.3896i | 1.23414 | − | 1.23414i | ||||
\(71\) | 22.6245 | − | 22.6245i | 0.318655 | − | 0.318655i | −0.529595 | − | 0.848250i | \(-0.677656\pi\) |
0.848250 | + | 0.529595i | \(0.177656\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 9.68320 | + | 9.68320i | 0.132647 | + | 0.132647i | 0.770313 | − | 0.637666i | \(-0.220100\pi\) |
−0.637666 | + | 0.770313i | \(0.720100\pi\) | |||||||
\(74\) | 29.8130 | 0.402878 | ||||||||
\(75\) | 98.2254i | 1.30967i | ||||||||
\(76\) | 13.9973 | + | 13.9973i | 0.184175 | + | 0.184175i | ||||
\(77\) | − | 155.642i | − | 2.02132i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −56.1543 | −0.710814 | −0.355407 | − | 0.934712i | \(-0.615658\pi\) | ||||
−0.355407 | + | 0.934712i | \(0.615658\pi\) | |||||||
\(80\) | −25.5672 | + | 25.5672i | −0.319591 | + | 0.319591i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 57.2507i | − | 0.698179i | ||||||
\(83\) | −4.59931 | + | 4.59931i | −0.0554133 | + | 0.0554133i | −0.734270 | − | 0.678857i | \(-0.762476\pi\) |
0.678857 | + | 0.734270i | \(0.262476\pi\) | |||||||
\(84\) | −23.4098 | + | 23.4098i | −0.278688 | + | 0.278688i | ||||
\(85\) | −61.4019 | − | 61.4019i | −0.722376 | − | 0.722376i | ||||
\(86\) | 35.6912 | + | 35.6912i | 0.415014 | + | 0.415014i | ||||
\(87\) | −47.8126 | −0.549570 | ||||||||
\(88\) | 46.0627i | 0.523440i | ||||||||
\(89\) | −81.8193 | − | 81.8193i | −0.919318 | − | 0.919318i | 0.0776620 | − | 0.996980i | \(-0.475255\pi\) |
−0.996980 | + | 0.0776620i | \(0.975255\pi\) | |||||||
\(90\) | − | 38.3509i | − | 0.426121i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −54.7165 | −0.594745 | ||||||||
\(93\) | 20.0248 | − | 20.0248i | 0.215320 | − | 0.215320i | ||||
\(94\) | −51.0367 | −0.542944 | ||||||||
\(95\) | 89.4681i | 0.941769i | ||||||||
\(96\) | 6.92820 | − | 6.92820i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 24.7045 | − | 24.7045i | 0.254686 | − | 0.254686i | −0.568203 | − | 0.822889i | \(-0.692361\pi\) |
0.822889 | + | 0.568203i | \(0.192361\pi\) | |||||||
\(98\) | 42.3367 | + | 42.3367i | 0.432007 | + | 0.432007i | ||||
\(99\) | −34.5470 | − | 34.5470i | −0.348960 | − | 0.348960i | ||||
\(100\) | −113.421 | −1.13421 | ||||||||
\(101\) | − | 117.169i | − | 1.16009i | −0.814584 | − | 0.580045i | \(-0.803035\pi\) | ||
0.814584 | − | 0.580045i | \(-0.196965\pi\) | |||||||
\(102\) | 16.6387 | + | 16.6387i | 0.163124 | + | 0.163124i | ||||
\(103\) | 184.178i | 1.78813i | 0.447933 | + | 0.894067i | \(0.352160\pi\) | ||||
−0.447933 | + | 0.894067i | \(0.647840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −149.631 | −1.42506 | ||||||||
\(106\) | −39.0697 | + | 39.0697i | −0.368582 | + | 0.368582i | ||||
\(107\) | 7.15198 | 0.0668410 | 0.0334205 | − | 0.999441i | \(-0.489360\pi\) | ||||
0.0334205 | + | 0.999441i | \(0.489360\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | −8.07627 | + | 8.07627i | −0.0740942 | + | 0.0740942i | −0.743183 | − | 0.669089i | \(-0.766685\pi\) |
0.669089 | + | 0.743183i | \(0.266685\pi\) | |||||||
\(110\) | −147.212 | + | 147.212i | −1.33829 | + | 1.33829i | ||||
\(111\) | −25.8188 | − | 25.8188i | −0.232602 | − | 0.232602i | ||||
\(112\) | −27.0313 | − | 27.0313i | −0.241351 | − | 0.241351i | ||||
\(113\) | −116.408 | −1.03015 | −0.515077 | − | 0.857144i | \(-0.672237\pi\) | ||||
−0.515077 | + | 0.857144i | \(0.672237\pi\) | |||||||
\(114\) | − | 24.2440i | − | 0.212667i | ||||||
\(115\) | −174.869 | − | 174.869i | −1.52060 | − | 1.52060i | ||||
\(116\) | − | 55.2093i | − | 0.475942i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −67.3926 | −0.571124 | ||||||||
\(119\) | 64.9181 | − | 64.9181i | 0.545530 | − | 0.545530i | ||||
\(120\) | 44.2838 | 0.369031 | ||||||||
\(121\) | 144.221i | 1.19191i | ||||||||
\(122\) | 70.5433 | − | 70.5433i | 0.578224 | − | 0.578224i | ||||
\(123\) | −49.5806 | + | 49.5806i | −0.403094 | + | 0.403094i | ||||
\(124\) | 23.1226 | + | 23.1226i | 0.186473 | + | 0.186473i | ||||
\(125\) | −202.687 | − | 202.687i | −1.62150 | − | 1.62150i | ||||
\(126\) | 40.5470 | 0.321802 | ||||||||
\(127\) | − | 27.0182i | − | 0.212742i | −0.994327 | − | 0.106371i | \(-0.966077\pi\) | ||
0.994327 | − | 0.106371i | \(-0.0339230\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 61.8190i | − | 0.479217i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −64.5682 | −0.492887 | −0.246444 | − | 0.969157i | \(-0.579262\pi\) | ||||
−0.246444 | + | 0.969157i | \(0.579262\pi\) | |||||||
\(132\) | 39.8915 | − | 39.8915i | 0.302208 | − | 0.302208i | ||||
\(133\) | −94.5914 | −0.711214 | ||||||||
\(134\) | − | 56.6973i | − | 0.423114i | ||||||
\(135\) | −33.2128 | + | 33.2128i | −0.246021 | + | 0.246021i | ||||
\(136\) | −19.2127 | + | 19.2127i | −0.141270 | + | 0.141270i | ||||
\(137\) | 144.369 | + | 144.369i | 1.05379 | + | 1.05379i | 0.998469 | + | 0.0553206i | \(0.0176181\pi\) |
0.0553206 | + | 0.998469i | \(0.482382\pi\) | |||||||
\(138\) | 47.3859 | + | 47.3859i | 0.343376 | + | 0.343376i | ||||
\(139\) | 63.6113 | 0.457635 | 0.228818 | − | 0.973469i | \(-0.426514\pi\) | ||||
0.228818 | + | 0.973469i | \(0.426514\pi\) | |||||||
\(140\) | − | 172.779i | − | 1.23414i | ||||||
\(141\) | 44.1991 | + | 44.1991i | 0.313469 | + | 0.313469i | ||||
\(142\) | − | 45.2490i | − | 0.318655i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 176.444 | − | 176.444i | 1.21685 | − | 1.21685i | ||||
\(146\) | 19.3664 | 0.132647 | ||||||||
\(147\) | − | 73.3293i | − | 0.498839i | ||||||
\(148\) | 29.8130 | − | 29.8130i | 0.201439 | − | 0.201439i | ||||
\(149\) | −20.5202 | + | 20.5202i | −0.137720 | + | 0.137720i | −0.772606 | − | 0.634886i | \(-0.781047\pi\) |
0.634886 | + | 0.772606i | \(0.281047\pi\) | |||||||
\(150\) | 98.2254 | + | 98.2254i | 0.654836 | + | 0.654836i | ||||
\(151\) | −31.6350 | − | 31.6350i | −0.209503 | − | 0.209503i | 0.594553 | − | 0.804056i | \(-0.297329\pi\) |
−0.804056 | + | 0.594553i | \(0.797329\pi\) | |||||||
\(152\) | 27.9946 | 0.184175 | ||||||||
\(153\) | − | 28.8190i | − | 0.188360i | ||||||
\(154\) | −155.642 | − | 155.642i | −1.01066 | − | 1.01066i | ||||
\(155\) | 147.796i | 0.953520i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 242.423 | 1.54409 | 0.772047 | − | 0.635566i | \(-0.219233\pi\) | ||||
0.772047 | + | 0.635566i | \(0.219233\pi\) | |||||||
\(158\) | −56.1543 | + | 56.1543i | −0.355407 | + | 0.355407i | ||||
\(159\) | 67.6707 | 0.425602 | ||||||||
\(160\) | 51.1345i | 0.319591i | ||||||||
\(161\) | 184.883 | − | 184.883i | 1.14834 | − | 1.14834i | ||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −11.0402 | − | 11.0402i | −0.0677314 | − | 0.0677314i | 0.672430 | − | 0.740161i | \(-0.265251\pi\) |
−0.740161 | + | 0.672430i | \(0.765251\pi\) | |||||||
\(164\) | −57.2507 | − | 57.2507i | −0.349090 | − | 0.349090i | ||||
\(165\) | 254.979 | 1.54532 | ||||||||
\(166\) | 9.19861i | 0.0554133i | ||||||||
\(167\) | −35.0077 | − | 35.0077i | −0.209627 | − | 0.209627i | 0.594482 | − | 0.804109i | \(-0.297357\pi\) |
−0.804109 | + | 0.594482i | \(0.797357\pi\) | |||||||
\(168\) | 46.8197i | 0.278688i | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −122.804 | −0.722376 | ||||||||
\(171\) | −20.9959 | + | 20.9959i | −0.122783 | + | 0.122783i | ||||
\(172\) | 71.3825 | 0.415014 | ||||||||
\(173\) | 168.425i | 0.973553i | 0.873527 | + | 0.486776i | \(0.161827\pi\) | ||||
−0.873527 | + | 0.486776i | \(0.838173\pi\) | |||||||
\(174\) | −47.8126 | + | 47.8126i | −0.274785 | + | 0.274785i | ||||
\(175\) | 383.240 | − | 383.240i | 2.18994 | − | 2.18994i | ||||
\(176\) | 46.0627 | + | 46.0627i | 0.261720 | + | 0.261720i | ||||
\(177\) | 58.3637 | + | 58.3637i | 0.329738 | + | 0.329738i | ||||
\(178\) | −163.639 | −0.919318 | ||||||||
\(179\) | 313.047i | 1.74886i | 0.485148 | + | 0.874432i | \(0.338766\pi\) | ||||
−0.485148 | + | 0.874432i | \(0.661234\pi\) | |||||||
\(180\) | −38.3509 | − | 38.3509i | −0.213060 | − | 0.213060i | ||||
\(181\) | 19.4795i | 0.107622i | 0.998551 | + | 0.0538108i | \(0.0171368\pi\) | ||||
−0.998551 | + | 0.0538108i | \(0.982863\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −122.185 | −0.667675 | ||||||||
\(184\) | −54.7165 | + | 54.7165i | −0.297372 | + | 0.297372i | ||||
\(185\) | 190.559 | 1.03005 | ||||||||
\(186\) | − | 40.0496i | − | 0.215320i | ||||||
\(187\) | −110.623 | + | 110.623i | −0.591569 | + | 0.591569i | ||||
\(188\) | −51.0367 | + | 51.0367i | −0.271472 | + | 0.271472i | ||||
\(189\) | −35.1147 | − | 35.1147i | −0.185792 | − | 0.185792i | ||||
\(190\) | 89.4681 | + | 89.4681i | 0.470885 | + | 0.470885i | ||||
\(191\) | 142.951 | 0.748435 | 0.374218 | − | 0.927341i | \(-0.377911\pi\) | ||||
0.374218 | + | 0.927341i | \(0.377911\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | 118.662 | + | 118.662i | 0.614830 | + | 0.614830i | 0.944201 | − | 0.329370i | \(-0.106836\pi\) |
−0.329370 | + | 0.944201i | \(0.606836\pi\) | |||||||
\(194\) | − | 49.4091i | − | 0.254686i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 84.6734 | 0.432007 | ||||||||
\(197\) | 120.481 | − | 120.481i | 0.611580 | − | 0.611580i | −0.331778 | − | 0.943358i | \(-0.607648\pi\) |
0.943358 | + | 0.331778i | \(0.107648\pi\) | |||||||
\(198\) | −69.0940 | −0.348960 | ||||||||
\(199\) | − | 161.726i | − | 0.812693i | −0.913719 | − | 0.406346i | \(-0.866803\pi\) | ||
0.913719 | − | 0.406346i | \(-0.133197\pi\) | |||||||
\(200\) | −113.421 | + | 113.421i | −0.567105 | + | 0.567105i | ||||
\(201\) | −49.1013 | + | 49.1013i | −0.244285 | + | 0.244285i | ||||
\(202\) | −117.169 | − | 117.169i | −0.580045 | − | 0.580045i | ||||
\(203\) | 186.548 | + | 186.548i | 0.918953 | + | 0.918953i | ||||
\(204\) | 33.2773 | 0.163124 | ||||||||
\(205\) | − | 365.936i | − | 1.78505i | ||||||
\(206\) | 184.178 | + | 184.178i | 0.894067 | + | 0.894067i | ||||
\(207\) | − | 82.0748i | − | 0.396497i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 161.188 | 0.771236 | ||||||||
\(210\) | −149.631 | + | 149.631i | −0.712529 | + | 0.712529i | ||||
\(211\) | −179.875 | −0.852490 | −0.426245 | − | 0.904608i | \(-0.640164\pi\) | ||||
−0.426245 | + | 0.904608i | \(0.640164\pi\) | |||||||
\(212\) | 78.1394i | 0.368582i | ||||||||
\(213\) | −39.1868 | + | 39.1868i | −0.183975 | + | 0.183975i | ||||
\(214\) | 7.15198 | − | 7.15198i | 0.0334205 | − | 0.0334205i | ||||
\(215\) | 228.132 | + | 228.132i | 1.06108 | + | 1.06108i | ||||
\(216\) | 10.3923 | + | 10.3923i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | −156.259 | −0.720088 | ||||||||
\(218\) | 16.1525i | 0.0740942i | ||||||||
\(219\) | −16.7718 | − | 16.7718i | −0.0765836 | − | 0.0765836i | ||||
\(220\) | 294.424i | 1.33829i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −51.6376 | −0.232602 | ||||||||
\(223\) | 275.631 | − | 275.631i | 1.23602 | − | 1.23602i | 0.274399 | − | 0.961616i | \(-0.411521\pi\) |
0.961616 | − | 0.274399i | \(-0.0884790\pi\) | |||||||
\(224\) | −54.0627 | −0.241351 | ||||||||
\(225\) | − | 170.131i | − | 0.756140i | ||||||
\(226\) | −116.408 | + | 116.408i | −0.515077 | + | 0.515077i | ||||
\(227\) | −94.2749 | + | 94.2749i | −0.415308 | + | 0.415308i | −0.883583 | − | 0.468275i | \(-0.844876\pi\) |
0.468275 | + | 0.883583i | \(0.344876\pi\) | |||||||
\(228\) | −24.2440 | − | 24.2440i | −0.106333 | − | 0.106333i | ||||
\(229\) | 304.866 | + | 304.866i | 1.33129 | + | 1.33129i | 0.904215 | + | 0.427077i | \(0.140457\pi\) |
0.427077 | + | 0.904215i | \(0.359543\pi\) | |||||||
\(230\) | −349.738 | −1.52060 | ||||||||
\(231\) | 269.580i | 1.16701i | ||||||||
\(232\) | −55.2093 | − | 55.2093i | −0.237971 | − | 0.237971i | ||||
\(233\) | − | 44.1414i | − | 0.189448i | −0.995504 | − | 0.0947240i | \(-0.969803\pi\) | ||
0.995504 | − | 0.0947240i | \(-0.0301969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −326.217 | −1.38816 | ||||||||
\(236\) | −67.3926 | + | 67.3926i | −0.285562 | + | 0.285562i | ||||
\(237\) | 97.2622 | 0.410389 | ||||||||
\(238\) | − | 129.836i | − | 0.545530i | ||||||
\(239\) | 15.8448 | − | 15.8448i | 0.0662964 | − | 0.0662964i | −0.673181 | − | 0.739478i | \(-0.735073\pi\) |
0.739478 | + | 0.673181i | \(0.235073\pi\) | |||||||
\(240\) | 44.2838 | − | 44.2838i | 0.184516 | − | 0.184516i | ||||
\(241\) | −340.106 | − | 340.106i | −1.41123 | − | 1.41123i | −0.751541 | − | 0.659686i | \(-0.770689\pi\) |
−0.659686 | − | 0.751541i | \(-0.729311\pi\) | |||||||
\(242\) | 144.221 | + | 144.221i | 0.595956 | + | 0.595956i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 141.087i | − | 0.578224i | ||||||
\(245\) | 270.608 | + | 270.608i | 1.10452 | + | 1.10452i | ||||
\(246\) | 99.1611i | 0.403094i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 46.2453 | 0.186473 | ||||||||
\(249\) | 7.96623 | − | 7.96623i | 0.0319929 | − | 0.0319929i | ||||
\(250\) | −405.375 | −1.62150 | ||||||||
\(251\) | 211.776i | 0.843729i | 0.906659 | + | 0.421865i | \(0.138624\pi\) | ||||
−0.906659 | + | 0.421865i | \(0.861376\pi\) | |||||||
\(252\) | 40.5470 | − | 40.5470i | 0.160901 | − | 0.160901i | ||||
\(253\) | −315.049 | + | 315.049i | −1.24525 | + | 1.24525i | ||||
\(254\) | −27.0182 | − | 27.0182i | −0.106371 | − | 0.106371i | ||||
\(255\) | 106.351 | + | 106.351i | 0.417064 | + | 0.417064i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 272.421i | 1.06000i | 0.847997 | + | 0.530002i | \(0.177809\pi\) | ||||
−0.847997 | + | 0.530002i | \(0.822191\pi\) | |||||||
\(258\) | −61.8190 | − | 61.8190i | −0.239609 | − | 0.239609i | ||||
\(259\) | 201.471i | 0.777881i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 82.8139 | 0.317295 | ||||||||
\(262\) | −64.5682 | + | 64.5682i | −0.246444 | + | 0.246444i | ||||
\(263\) | 236.343 | 0.898643 | 0.449321 | − | 0.893370i | \(-0.351666\pi\) | ||||
0.449321 | + | 0.893370i | \(0.351666\pi\) | |||||||
\(264\) | − | 79.7829i | − | 0.302208i | ||||||
\(265\) | −249.726 | + | 249.726i | −0.942363 | + | 0.942363i | ||||
\(266\) | −94.5914 | + | 94.5914i | −0.355607 | + | 0.355607i | ||||
\(267\) | 141.715 | + | 141.715i | 0.530768 | + | 0.530768i | ||||
\(268\) | −56.6973 | − | 56.6973i | −0.211557 | − | 0.211557i | ||||
\(269\) | 466.361 | 1.73368 | 0.866842 | − | 0.498583i | \(-0.166146\pi\) | ||||
0.866842 | + | 0.498583i | \(0.166146\pi\) | |||||||
\(270\) | 66.4256i | 0.246021i | ||||||||
\(271\) | 326.130 | + | 326.130i | 1.20343 | + | 1.20343i | 0.973116 | + | 0.230315i | \(0.0739757\pi\) |
0.230315 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(272\) | 38.4254i | 0.141270i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 288.738 | 1.05379 | ||||||||
\(275\) | −653.059 | + | 653.059i | −2.37476 | + | 2.37476i | ||||
\(276\) | 94.7718 | 0.343376 | ||||||||
\(277\) | 24.5533i | 0.0886400i | 0.999017 | + | 0.0443200i | \(0.0141121\pi\) | ||||
−0.999017 | + | 0.0443200i | \(0.985888\pi\) | |||||||
\(278\) | 63.6113 | − | 63.6113i | 0.228818 | − | 0.228818i | ||||
\(279\) | −34.6840 | + | 34.6840i | −0.124315 | + | 0.124315i | ||||
\(280\) | −172.779 | − | 172.779i | −0.617069 | − | 0.617069i | ||||
\(281\) | −276.591 | − | 276.591i | −0.984311 | − | 0.984311i | 0.0155674 | − | 0.999879i | \(-0.495045\pi\) |
−0.999879 | + | 0.0155674i | \(0.995045\pi\) | |||||||
\(282\) | 88.3982 | 0.313469 | ||||||||
\(283\) | 391.711i | 1.38414i | 0.721832 | + | 0.692068i | \(0.243300\pi\) | ||||
−0.721832 | + | 0.692068i | \(0.756700\pi\) | |||||||
\(284\) | −45.2490 | − | 45.2490i | −0.159327 | − | 0.159327i | ||||
\(285\) | − | 154.963i | − | 0.543731i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 386.891 | 1.34805 | ||||||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 196.718 | 0.680686 | ||||||||
\(290\) | − | 352.887i | − | 1.21685i | ||||||
\(291\) | −42.7895 | + | 42.7895i | −0.147043 | + | 0.147043i | ||||
\(292\) | 19.3664 | − | 19.3664i | 0.0663233 | − | 0.0663233i | ||||
\(293\) | 209.571 | + | 209.571i | 0.715261 | + | 0.715261i | 0.967631 | − | 0.252370i | \(-0.0812100\pi\) |
−0.252370 | + | 0.967631i | \(0.581210\pi\) | |||||||
\(294\) | −73.3293 | − | 73.3293i | −0.249419 | − | 0.249419i | ||||
\(295\) | −430.761 | −1.46021 | ||||||||
\(296\) | − | 59.6260i | − | 0.201439i | ||||||
\(297\) | 59.8372 | + | 59.8372i | 0.201472 | + | 0.201472i | ||||
\(298\) | 41.0405i | 0.137720i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 196.451 | 0.654836 | ||||||||
\(301\) | −241.195 | + | 241.195i | −0.801314 | + | 0.801314i | ||||
\(302\) | −63.2700 | −0.209503 | ||||||||
\(303\) | 202.943i | 0.669779i | ||||||||
\(304\) | 27.9946 | − | 27.9946i | 0.0920875 | − | 0.0920875i | ||||
\(305\) | 450.899 | − | 450.899i | 1.47836 | − | 1.47836i | ||||
\(306\) | −28.8190 | − | 28.8190i | −0.0941798 | − | 0.0941798i | ||||
\(307\) | −221.215 | − | 221.215i | −0.720571 | − | 0.720571i | 0.248150 | − | 0.968722i | \(-0.420177\pi\) |
−0.968722 | + | 0.248150i | \(0.920177\pi\) | |||||||
\(308\) | −311.284 | −1.01066 | ||||||||
\(309\) | − | 319.005i | − | 1.03238i | ||||||
\(310\) | 147.796 | + | 147.796i | 0.476760 | + | 0.476760i | ||||
\(311\) | 12.5556i | 0.0403716i | 0.999796 | + | 0.0201858i | \(0.00642578\pi\) | ||||
−0.999796 | + | 0.0201858i | \(0.993574\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 590.956 | 1.88804 | 0.944018 | − | 0.329893i | \(-0.107013\pi\) | ||||
0.944018 | + | 0.329893i | \(0.107013\pi\) | |||||||
\(314\) | 242.423 | − | 242.423i | 0.772047 | − | 0.772047i | ||||
\(315\) | 259.169 | 0.822758 | ||||||||
\(316\) | 112.309i | 0.355407i | ||||||||
\(317\) | −54.7137 | + | 54.7137i | −0.172598 | + | 0.172598i | −0.788120 | − | 0.615522i | \(-0.788945\pi\) |
0.615522 | + | 0.788120i | \(0.288945\pi\) | |||||||
\(318\) | 67.6707 | − | 67.6707i | 0.212801 | − | 0.212801i | ||||
\(319\) | −317.886 | − | 317.886i | −0.996507 | − | 0.996507i | ||||
\(320\) | 51.1345 | + | 51.1345i | 0.159795 | + | 0.159795i | ||||
\(321\) | −12.3876 | −0.0385906 | ||||||||
\(322\) | − | 369.765i | − | 1.14834i | ||||||
\(323\) | 67.2314 | + | 67.2314i | 0.208147 | + | 0.208147i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.0804 | −0.0677314 | ||||||||
\(327\) | 13.9885 | − | 13.9885i | 0.0427783 | − | 0.0427783i | ||||
\(328\) | −114.501 | −0.349090 | ||||||||
\(329\) | − | 344.898i | − | 1.04832i | ||||||
\(330\) | 254.979 | − | 254.979i | 0.772662 | − | 0.772662i | ||||
\(331\) | 14.4546 | − | 14.4546i | 0.0436693 | − | 0.0436693i | −0.684935 | − | 0.728604i | \(-0.740169\pi\) |
0.728604 | + | 0.684935i | \(0.240169\pi\) | |||||||
\(332\) | 9.19861 | + | 9.19861i | 0.0277067 | + | 0.0277067i | ||||
\(333\) | 44.7195 | + | 44.7195i | 0.134293 | + | 0.134293i | ||||
\(334\) | −70.0153 | −0.209627 | ||||||||
\(335\) | − | 362.398i | − | 1.08179i | ||||||
\(336\) | 46.8197 | + | 46.8197i | 0.139344 | + | 0.139344i | ||||
\(337\) | − | 202.326i | − | 0.600375i | −0.953880 | − | 0.300188i | \(-0.902951\pi\) | ||
0.953880 | − | 0.300188i | \(-0.0970493\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 201.624 | 0.594760 | ||||||||
\(340\) | −122.804 | + | 122.804i | −0.361188 | + | 0.361188i | ||||
\(341\) | 266.273 | 0.780858 | ||||||||
\(342\) | 41.9919i | 0.122783i | ||||||||
\(343\) | 45.0296 | − | 45.0296i | 0.131282 | − | 0.131282i | ||||
\(344\) | 71.3825 | − | 71.3825i | 0.207507 | − | 0.207507i | ||||
\(345\) | 302.882 | + | 302.882i | 0.877918 | + | 0.877918i | ||||
\(346\) | 168.425 | + | 168.425i | 0.486776 | + | 0.486776i | ||||
\(347\) | 556.526 | 1.60382 | 0.801911 | − | 0.597444i | \(-0.203817\pi\) | ||||
0.801911 | + | 0.597444i | \(0.203817\pi\) | |||||||
\(348\) | 95.6252i | 0.274785i | ||||||||
\(349\) | −327.786 | − | 327.786i | −0.939216 | − | 0.939216i | 0.0590400 | − | 0.998256i | \(-0.481196\pi\) |
−0.998256 | + | 0.0590400i | \(0.981196\pi\) | |||||||
\(350\) | − | 766.480i | − | 2.18994i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 92.1254 | 0.261720 | ||||||||
\(353\) | −199.807 | + | 199.807i | −0.566025 | + | 0.566025i | −0.931012 | − | 0.364987i | \(-0.881073\pi\) |
0.364987 | + | 0.931012i | \(0.381073\pi\) | |||||||
\(354\) | 116.727 | 0.329738 | ||||||||
\(355\) | − | 289.223i | − | 0.814713i | ||||||
\(356\) | −163.639 | + | 163.639i | −0.459659 | + | 0.459659i | ||||
\(357\) | −112.441 | + | 112.441i | −0.314962 | + | 0.314962i | ||||
\(358\) | 313.047 | + | 313.047i | 0.874432 | + | 0.874432i | ||||
\(359\) | 280.398 | + | 280.398i | 0.781054 | + | 0.781054i | 0.980009 | − | 0.198955i | \(-0.0637547\pi\) |
−0.198955 | + | 0.980009i | \(0.563755\pi\) | |||||||
\(360\) | −76.7017 | −0.213060 | ||||||||
\(361\) | 263.038i | 0.728637i | ||||||||
\(362\) | 19.4795 | + | 19.4795i | 0.0538108 | + | 0.0538108i | ||||
\(363\) | − | 249.799i | − | 0.688151i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 123.786 | 0.339141 | ||||||||
\(366\) | −122.185 | + | 122.185i | −0.333838 | + | 0.333838i | ||||
\(367\) | 591.886 | 1.61277 | 0.806384 | − | 0.591392i | \(-0.201421\pi\) | ||||
0.806384 | + | 0.591392i | \(0.201421\pi\) | |||||||
\(368\) | 109.433i | 0.297372i | ||||||||
\(369\) | 85.8761 | − | 85.8761i | 0.232726 | − | 0.232726i | ||||
\(370\) | 190.559 | − | 190.559i | 0.515024 | − | 0.515024i | ||||
\(371\) | −264.027 | − | 264.027i | −0.711662 | − | 0.711662i | ||||
\(372\) | −40.0496 | − | 40.0496i | −0.107660 | − | 0.107660i | ||||
\(373\) | −511.886 | −1.37235 | −0.686174 | − | 0.727437i | \(-0.740711\pi\) | ||||
−0.686174 | + | 0.727437i | \(0.740711\pi\) | |||||||
\(374\) | 221.247i | 0.591569i | ||||||||
\(375\) | 351.065 | + | 351.065i | 0.936173 | + | 0.936173i | ||||
\(376\) | 102.073i | 0.271472i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −70.2295 | −0.185792 | ||||||||
\(379\) | 144.716 | − | 144.716i | 0.381837 | − | 0.381837i | −0.489926 | − | 0.871764i | \(-0.662976\pi\) |
0.871764 | + | 0.489926i | \(0.162976\pi\) | |||||||
\(380\) | 178.936 | 0.470885 | ||||||||
\(381\) | 46.7968i | 0.122826i | ||||||||
\(382\) | 142.951 | − | 142.951i | 0.374218 | − | 0.374218i | ||||
\(383\) | −232.211 | + | 232.211i | −0.606295 | + | 0.606295i | −0.941976 | − | 0.335681i | \(-0.891034\pi\) |
0.335681 | + | 0.941976i | \(0.391034\pi\) | |||||||
\(384\) | −13.8564 | − | 13.8564i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | −994.834 | − | 994.834i | −2.58398 | − | 2.58398i | ||||
\(386\) | 237.325 | 0.614830 | ||||||||
\(387\) | 107.074i | 0.276676i | ||||||||
\(388\) | −49.4091 | − | 49.4091i | −0.127343 | − | 0.127343i | ||||
\(389\) | 393.984i | 1.01281i | 0.862295 | + | 0.506406i | \(0.169026\pi\) | ||||
−0.862295 | + | 0.506406i | \(0.830974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −262.813 | −0.672156 | ||||||||
\(392\) | 84.6734 | − | 84.6734i | 0.216003 | − | 0.216003i | ||||
\(393\) | 111.835 | 0.284569 | ||||||||
\(394\) | − | 240.963i | − | 0.611580i | ||||||
\(395\) | −358.928 | + | 358.928i | −0.908678 | + | 0.908678i | ||||
\(396\) | −69.0940 | + | 69.0940i | −0.174480 | + | 0.174480i | ||||
\(397\) | −84.9000 | − | 84.9000i | −0.213854 | − | 0.213854i | 0.592048 | − | 0.805902i | \(-0.298319\pi\) |
−0.805902 | + | 0.592048i | \(0.798319\pi\) | |||||||
\(398\) | −161.726 | − | 161.726i | −0.406346 | − | 0.406346i | ||||
\(399\) | 163.837 | 0.410619 | ||||||||
\(400\) | 226.842i | 0.567105i | ||||||||
\(401\) | −234.950 | − | 234.950i | −0.585910 | − | 0.585910i | 0.350611 | − | 0.936521i | \(-0.385974\pi\) |
−0.936521 | + | 0.350611i | \(0.885974\pi\) | |||||||
\(402\) | 98.2025i | 0.244285i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −234.338 | −0.580045 | ||||||||
\(405\) | 57.5263 | − | 57.5263i | 0.142040 | − | 0.142040i | ||||
\(406\) | 373.095 | 0.918953 | ||||||||
\(407\) | − | 343.316i | − | 0.843529i | ||||||
\(408\) | 33.2773 | − | 33.2773i | 0.0815621 | − | 0.0815621i | ||||
\(409\) | 311.016 | − | 311.016i | 0.760431 | − | 0.760431i | −0.215970 | − | 0.976400i | \(-0.569291\pi\) |
0.976400 | + | 0.215970i | \(0.0692912\pi\) | |||||||
\(410\) | −365.936 | − | 365.936i | −0.892526 | − | 0.892526i | ||||
\(411\) | −250.055 | − | 250.055i | −0.608406 | − | 0.608406i | ||||
\(412\) | 368.356 | 0.894067 | ||||||||
\(413\) | − | 455.428i | − | 1.10273i | ||||||
\(414\) | −82.0748 | − | 82.0748i | −0.198248 | − | 0.198248i | ||||
\(415\) | 58.7958i | 0.141677i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −110.178 | −0.264216 | ||||||||
\(418\) | 161.188 | − | 161.188i | 0.385618 | − | 0.385618i | ||||
\(419\) | −124.953 | −0.298217 | −0.149108 | − | 0.988821i | \(-0.547640\pi\) | ||||
−0.149108 | + | 0.988821i | \(0.547640\pi\) | |||||||
\(420\) | 299.262i | 0.712529i | ||||||||
\(421\) | −9.46318 | + | 9.46318i | −0.0224779 | + | 0.0224779i | −0.718256 | − | 0.695779i | \(-0.755060\pi\) |
0.695779 | + | 0.718256i | \(0.255060\pi\) | |||||||
\(422\) | −179.875 | + | 179.875i | −0.426245 | + | 0.426245i | ||||
\(423\) | −76.5551 | − | 76.5551i | −0.180981 | − | 0.180981i | ||||
\(424\) | 78.1394 | + | 78.1394i | 0.184291 | + | 0.184291i | ||||
\(425\) | −544.780 | −1.28184 | ||||||||
\(426\) | 78.3735i | 0.183975i | ||||||||
\(427\) | 476.720 | + | 476.720i | 1.11644 | + | 1.11644i | ||||
\(428\) | − | 14.3040i | − | 0.0334205i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 456.263 | 1.06108 | ||||||||
\(431\) | 511.221 | − | 511.221i | 1.18613 | − | 1.18613i | 0.207999 | − | 0.978129i | \(-0.433305\pi\) |
0.978129 | − | 0.207999i | \(-0.0666951\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | − | 40.9607i | − | 0.0945973i | −0.998881 | − | 0.0472987i | \(-0.984939\pi\) | ||
0.998881 | − | 0.0472987i | \(-0.0150613\pi\) | |||||||
\(434\) | −156.259 | + | 156.259i | −0.360044 | + | 0.360044i | ||||
\(435\) | −305.609 | + | 305.609i | −0.702550 | + | 0.702550i | ||||
\(436\) | 16.1525 | + | 16.1525i | 0.0370471 | + | 0.0370471i | ||||
\(437\) | 191.471 | + | 191.471i | 0.438148 | + | 0.438148i | ||||
\(438\) | −33.5436 | −0.0765836 | ||||||||
\(439\) | − | 665.355i | − | 1.51562i | −0.652478 | − | 0.757808i | \(-0.726271\pi\) | ||
0.652478 | − | 0.757808i | \(-0.273729\pi\) | |||||||
\(440\) | 294.424 | + | 294.424i | 0.669145 | + | 0.669145i | ||||
\(441\) | 127.010i | 0.288005i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 267.578 | 0.604013 | 0.302006 | − | 0.953306i | \(-0.402344\pi\) | ||||
0.302006 | + | 0.953306i | \(0.402344\pi\) | |||||||
\(444\) | −51.6376 | + | 51.6376i | −0.116301 | + | 0.116301i | ||||
\(445\) | −1045.95 | −2.35044 | ||||||||
\(446\) | − | 551.263i | − | 1.23602i | ||||||
\(447\) | 35.5421 | − | 35.5421i | 0.0795125 | − | 0.0795125i | ||||
\(448\) | −54.0627 | + | 54.0627i | −0.120676 | + | 0.120676i | ||||
\(449\) | −398.196 | − | 398.196i | −0.886850 | − | 0.886850i | 0.107369 | − | 0.994219i | \(-0.465757\pi\) |
−0.994219 | + | 0.107369i | \(0.965757\pi\) | |||||||
\(450\) | −170.131 | − | 170.131i | −0.378070 | − | 0.378070i | ||||
\(451\) | −659.280 | −1.46182 | ||||||||
\(452\) | 232.815i | 0.515077i | ||||||||
\(453\) | 54.7934 | + | 54.7934i | 0.120957 | + | 0.120957i | ||||
\(454\) | 188.550i | 0.415308i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −48.4881 | −0.106333 | ||||||||
\(457\) | −471.131 | + | 471.131i | −1.03092 | + | 1.03092i | −0.0314138 | + | 0.999506i | \(0.510001\pi\) |
−0.999506 | + | 0.0314138i | \(0.989999\pi\) | |||||||
\(458\) | 609.732 | 1.33129 | ||||||||
\(459\) | 49.9160i | 0.108750i | ||||||||
\(460\) | −349.738 | + | 349.738i | −0.760299 | + | 0.760299i | ||||
\(461\) | 253.308 | − | 253.308i | 0.549475 | − | 0.549475i | −0.376814 | − | 0.926289i | \(-0.622980\pi\) |
0.926289 | + | 0.376814i | \(0.122980\pi\) | |||||||
\(462\) | 269.580 | + | 269.580i | 0.583506 | + | 0.583506i | ||||
\(463\) | 630.292 | + | 630.292i | 1.36132 | + | 1.36132i | 0.872236 | + | 0.489084i | \(0.162669\pi\) |
0.489084 | + | 0.872236i | \(0.337331\pi\) | |||||||
\(464\) | −110.419 | −0.237971 | ||||||||
\(465\) | − | 255.989i | − | 0.550515i | ||||||
\(466\) | −44.1414 | − | 44.1414i | −0.0947240 | − | 0.0947240i | ||||
\(467\) | 425.264i | 0.910630i | 0.890331 | + | 0.455315i | \(0.150473\pi\) | ||||
−0.890331 | + | 0.455315i | \(0.849527\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 383.151 | 0.816953 | ||||||||
\(470\) | −326.217 | + | 326.217i | −0.694079 | + | 0.694079i | ||||
\(471\) | −419.888 | −0.891483 | ||||||||
\(472\) | 134.785i | 0.285562i | ||||||||
\(473\) | 411.009 | − | 411.009i | 0.868940 | − | 0.868940i | ||||
\(474\) | 97.2622 | − | 97.2622i | 0.205194 | − | 0.205194i | ||||
\(475\) | 396.897 | + | 396.897i | 0.835572 | + | 0.835572i | ||||
\(476\) | −129.836 | − | 129.836i | −0.272765 | − | 0.272765i | ||||
\(477\) | −117.209 | −0.245722 | ||||||||
\(478\) | − | 31.6897i | − | 0.0662964i | ||||||
\(479\) | 194.811 | + | 194.811i | 0.406704 | + | 0.406704i | 0.880588 | − | 0.473883i | \(-0.157148\pi\) |
−0.473883 | + | 0.880588i | \(0.657148\pi\) | |||||||
\(480\) | − | 88.5675i | − | 0.184516i | ||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −680.212 | −1.41123 | ||||||||
\(483\) | −320.226 | + | 320.226i | −0.662994 | + | 0.662994i | ||||
\(484\) | 288.443 | 0.595956 | ||||||||
\(485\) | − | 315.813i | − | 0.651162i | ||||||
\(486\) | −15.5885 | + | 15.5885i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 452.708 | − | 452.708i | 0.929585 | − | 0.929585i | −0.0680942 | − | 0.997679i | \(-0.521692\pi\) |
0.997679 | + | 0.0680942i | \(0.0216918\pi\) | |||||||
\(488\) | −141.087 | − | 141.087i | −0.289112 | − | 0.289112i | ||||
\(489\) | 19.1222 | + | 19.1222i | 0.0391048 | + | 0.0391048i | ||||
\(490\) | 541.216 | 1.10452 | ||||||||
\(491\) | 566.666i | 1.15411i | 0.816706 | + | 0.577053i | \(0.195798\pi\) | ||||
−0.816706 | + | 0.577053i | \(0.804202\pi\) | |||||||
\(492\) | 99.1611 | + | 99.1611i | 0.201547 | + | 0.201547i | ||||
\(493\) | − | 265.180i | − | 0.537890i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −441.636 | −0.892194 | ||||||||
\(496\) | 46.2453 | − | 46.2453i | 0.0932365 | − | 0.0932365i | ||||
\(497\) | 305.785 | 0.615262 | ||||||||
\(498\) | − | 15.9325i | − | 0.0319929i | ||||||
\(499\) | 409.292 | − | 409.292i | 0.820224 | − | 0.820224i | −0.165916 | − | 0.986140i | \(-0.553058\pi\) |
0.986140 | + | 0.165916i | \(0.0530581\pi\) | |||||||
\(500\) | −405.375 | + | 405.375i | −0.810749 | + | 0.810749i | ||||
\(501\) | 60.6351 | + | 60.6351i | 0.121028 | + | 0.121028i | ||||
\(502\) | 211.776 | + | 211.776i | 0.421865 | + | 0.421865i | ||||
\(503\) | 223.242 | 0.443821 | 0.221910 | − | 0.975067i | \(-0.428771\pi\) | ||||
0.221910 | + | 0.975067i | \(0.428771\pi\) | |||||||
\(504\) | − | 81.0940i | − | 0.160901i | ||||||
\(505\) | −748.923 | − | 748.923i | −1.48302 | − | 1.48302i | ||||
\(506\) | 630.097i | 1.24525i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −54.0363 | −0.106371 | ||||||||
\(509\) | −303.312 | + | 303.312i | −0.595898 | + | 0.595898i | −0.939218 | − | 0.343320i | \(-0.888448\pi\) |
0.343320 | + | 0.939218i | \(0.388448\pi\) | |||||||
\(510\) | 212.702 | 0.417064 | ||||||||
\(511\) | 130.875i | 0.256115i | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 36.3660 | − | 36.3660i | 0.0708890 | − | 0.0708890i | ||||
\(514\) | 272.421 | + | 272.421i | 0.530002 | + | 0.530002i | ||||
\(515\) | 1177.23 | + | 1177.23i | 2.28588 | + | 2.28588i | ||||
\(516\) | −123.638 | −0.239609 | ||||||||
\(517\) | 587.722i | 1.13679i | ||||||||
\(518\) | 201.471 | + | 201.471i | 0.388941 | + | 0.388941i | ||||
\(519\) | − | 291.720i | − | 0.562081i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −470.908 | −0.903854 | −0.451927 | − | 0.892055i | \(-0.649263\pi\) | ||||
−0.451927 | + | 0.892055i | \(0.649263\pi\) | |||||||
\(522\) | 82.8139 | − | 82.8139i | 0.158647 | − | 0.158647i | ||||
\(523\) | −911.570 | −1.74296 | −0.871481 | − | 0.490428i | \(-0.836840\pi\) | ||||
−0.871481 | + | 0.490428i | \(0.836840\pi\) | |||||||
\(524\) | 129.136i | 0.246444i | ||||||||
\(525\) | −663.791 | + | 663.791i | −1.26436 | + | 1.26436i | ||||
\(526\) | 236.343 | − | 236.343i | 0.449321 | − | 0.449321i | ||||
\(527\) | 111.062 | + | 111.062i | 0.210744 | + | 0.210744i | ||||
\(528\) | −79.7829 | − | 79.7829i | −0.151104 | − | 0.151104i | ||||
\(529\) | −219.474 | −0.414885 | ||||||||
\(530\) | 499.452i | 0.942363i | ||||||||
\(531\) | −101.089 | − | 101.089i | −0.190375 | − | 0.190375i | ||||
\(532\) | 189.183i | 0.355607i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 283.430 | 0.530768 | ||||||||
\(535\) | 45.7141 | − | 45.7141i | 0.0854469 | − | 0.0854469i | ||||
\(536\) | −113.395 | −0.211557 | ||||||||
\(537\) | − | 542.213i | − | 1.00971i | ||||||
\(538\) | 466.361 | − | 466.361i | 0.866842 | − | 0.866842i | ||||
\(539\) | 487.535 | − | 487.535i | 0.904518 | − | 0.904518i | ||||
\(540\) | 66.4256 | + | 66.4256i | 0.123010 | + | 0.123010i | ||||
\(541\) | 393.572 | + | 393.572i | 0.727490 | + | 0.727490i | 0.970119 | − | 0.242629i | \(-0.0780099\pi\) |
−0.242629 | + | 0.970119i | \(0.578010\pi\) | |||||||
\(542\) | 652.260 | 1.20343 | ||||||||
\(543\) | − | 33.7395i | − | 0.0621353i | ||||||
\(544\) | 38.4254 | + | 38.4254i | 0.0706349 | + | 0.0706349i | ||||
\(545\) | 103.244i | 0.189438i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −388.679 | −0.710565 | −0.355283 | − | 0.934759i | \(-0.615615\pi\) | ||||
−0.355283 | + | 0.934759i | \(0.615615\pi\) | |||||||
\(548\) | 288.738 | − | 288.738i | 0.526895 | − | 0.526895i | ||||
\(549\) | 211.630 | 0.385483 | ||||||||
\(550\) | 1306.12i | 2.37476i | ||||||||
\(551\) | −193.195 | + | 193.195i | −0.350626 | + | 0.350626i | ||||
\(552\) | 94.7718 | − | 94.7718i | 0.171688 | − | 0.171688i | ||||
\(553\) | −379.482 | − | 379.482i | −0.686224 | − | 0.686224i | ||||
\(554\) | 24.5533 | + | 24.5533i | 0.0443200 | + | 0.0443200i | ||||
\(555\) | −330.058 | −0.594699 | ||||||||
\(556\) | − | 127.223i | − | 0.228818i | ||||||
\(557\) | −500.081 | − | 500.081i | −0.897811 | − | 0.897811i | 0.0974309 | − | 0.995242i | \(-0.468938\pi\) |
−0.995242 | + | 0.0974309i | \(0.968938\pi\) | |||||||
\(558\) | 69.3679i | 0.124315i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −345.558 | −0.617069 | ||||||||
\(561\) | 191.606 | − | 191.606i | 0.341543 | − | 0.341543i | ||||
\(562\) | −553.183 | −0.984311 | ||||||||
\(563\) | 594.275i | 1.05555i | 0.849384 | + | 0.527776i | \(0.176974\pi\) | ||||
−0.849384 | + | 0.527776i | \(0.823026\pi\) | |||||||
\(564\) | 88.3982 | − | 88.3982i | 0.156734 | − | 0.156734i | ||||
\(565\) | −744.055 | + | 744.055i | −1.31691 | + | 1.31691i | ||||
\(566\) | 391.711 | + | 391.711i | 0.692068 | + | 0.692068i | ||||
\(567\) | 60.8205 | + | 60.8205i | 0.107267 | + | 0.107267i | ||||
\(568\) | −90.4980 | −0.159327 | ||||||||
\(569\) | 116.935i | 0.205509i | 0.994707 | + | 0.102754i | \(0.0327656\pi\) | ||||
−0.994707 | + | 0.102754i | \(0.967234\pi\) | |||||||
\(570\) | −154.963 | − | 154.963i | −0.271865 | − | 0.271865i | ||||
\(571\) | 137.505i | 0.240815i | 0.992725 | + | 0.120408i | \(0.0384201\pi\) | ||||
−0.992725 | + | 0.120408i | \(0.961580\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −247.599 | −0.432109 | ||||||||
\(574\) | 386.891 | − | 386.891i | 0.674026 | − | 0.674026i | ||||
\(575\) | −1551.50 | −2.69826 | ||||||||
\(576\) | 24.0000i | 0.0416667i | ||||||||
\(577\) | 617.016 | − | 617.016i | 1.06935 | − | 1.06935i | 0.0719422 | − | 0.997409i | \(-0.477080\pi\) |
0.997409 | − | 0.0719422i | \(-0.0229197\pi\) | |||||||
\(578\) | 196.718 | − | 196.718i | 0.340343 | − | 0.340343i | ||||
\(579\) | −205.529 | − | 205.529i | −0.354972 | − | 0.354972i | ||||
\(580\) | −352.887 | − | 352.887i | −0.608426 | − | 0.608426i | ||||
\(581\) | −62.1627 | −0.106993 | ||||||||
\(582\) | 85.5790i | 0.147043i | ||||||||
\(583\) | 449.914 | + | 449.914i | 0.771722 | + | 0.771722i | ||||
\(584\) | − | 38.7328i | − | 0.0663233i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 419.143 | 0.715261 | ||||||||
\(587\) | 273.246 | − | 273.246i | 0.465495 | − | 0.465495i | −0.434956 | − | 0.900452i | \(-0.643236\pi\) |
0.900452 | + | 0.434956i | \(0.143236\pi\) | |||||||
\(588\) | −146.659 | −0.249419 | ||||||||
\(589\) | − | 161.827i | − | 0.274749i | ||||||
\(590\) | −430.761 | + | 430.761i | −0.730103 | + | 0.730103i | ||||
\(591\) | −208.680 | + | 208.680i | −0.353096 | + | 0.353096i | ||||
\(592\) | −59.6260 | − | 59.6260i | −0.100720 | − | 0.100720i | ||||
\(593\) | −536.353 | − | 536.353i | −0.904473 | − | 0.904473i | 0.0913459 | − | 0.995819i | \(-0.470883\pi\) |
−0.995819 | + | 0.0913459i | \(0.970883\pi\) | |||||||
\(594\) | 119.674 | 0.201472 | ||||||||
\(595\) | − | 829.888i | − | 1.39477i | ||||||
\(596\) | 41.0405 | + | 41.0405i | 0.0688598 | + | 0.0688598i | ||||
\(597\) | 280.117i | 0.469208i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 344.623 | 0.575331 | 0.287666 | − | 0.957731i | \(-0.407121\pi\) | ||||
0.287666 | + | 0.957731i | \(0.407121\pi\) | |||||||
\(600\) | 196.451 | − | 196.451i | 0.327418 | − | 0.327418i | ||||
\(601\) | 891.739 | 1.48376 | 0.741879 | − | 0.670533i | \(-0.233935\pi\) | ||||
0.741879 | + | 0.670533i | \(0.233935\pi\) | |||||||
\(602\) | 482.391i | 0.801314i | ||||||||
\(603\) | 85.0459 | − | 85.0459i | 0.141038 | − | 0.141038i | ||||
\(604\) | −63.2700 | + | 63.2700i | −0.104752 | + | 0.104752i | ||||
\(605\) | 921.835 | + | 921.835i | 1.52370 | + | 1.52370i | ||||
\(606\) | 202.943 | + | 202.943i | 0.334889 | + | 0.334889i | ||||
\(607\) | 465.467 | 0.766832 | 0.383416 | − | 0.923576i | \(-0.374748\pi\) | ||||
0.383416 | + | 0.923576i | \(0.374748\pi\) | |||||||
\(608\) | − | 55.9892i | − | 0.0920875i | ||||||
\(609\) | −323.110 | − | 323.110i | −0.530558 | − | 0.530558i | ||||
\(610\) | − | 901.799i | − | 1.47836i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −57.6381 | −0.0941798 | ||||||||
\(613\) | 623.188 | − | 623.188i | 1.01662 | − | 1.01662i | 0.0167601 | − | 0.999860i | \(-0.494665\pi\) |
0.999860 | − | 0.0167601i | \(-0.00533514\pi\) | |||||||
\(614\) | −442.431 | −0.720571 | ||||||||
\(615\) | 633.819i | 1.03060i | ||||||||
\(616\) | −311.284 | + | 311.284i | −0.505331 | + | 0.505331i | ||||
\(617\) | −802.642 | + | 802.642i | −1.30088 | + | 1.30088i | −0.373078 | + | 0.927800i | \(0.621697\pi\) |
−0.927800 | + | 0.373078i | \(0.878303\pi\) | |||||||
\(618\) | −319.005 | − | 319.005i | −0.516190 | − | 0.516190i | ||||
\(619\) | −69.6384 | − | 69.6384i | −0.112501 | − | 0.112501i | 0.648615 | − | 0.761117i | \(-0.275349\pi\) |
−0.761117 | + | 0.648615i | \(0.775349\pi\) | |||||||
\(620\) | 295.591 | 0.476760 | ||||||||
\(621\) | 142.158i | 0.228917i | ||||||||
\(622\) | 12.5556 | + | 12.5556i | 0.0201858 | + | 0.0201858i | ||||
\(623\) | − | 1105.84i | − | 1.77503i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1173.32 | −1.87731 | ||||||||
\(626\) | 590.956 | − | 590.956i | 0.944018 | − | 0.944018i | ||||
\(627\) | −279.186 | −0.445273 | ||||||||
\(628\) | − | 484.845i | − | 0.772047i | ||||||
\(629\) | 143.197 | − | 143.197i | 0.227658 | − | 0.227658i | ||||
\(630\) | 259.169 | − | 259.169i | 0.411379 | − | 0.411379i | ||||
\(631\) | 451.647 | + | 451.647i | 0.715764 | + | 0.715764i | 0.967735 | − | 0.251971i | \(-0.0810786\pi\) |
−0.251971 | + | 0.967735i | \(0.581079\pi\) | |||||||
\(632\) | 112.309 | + | 112.309i | 0.177704 | + | 0.177704i | ||||
\(633\) | 311.553 | 0.492185 | ||||||||
\(634\) | 109.427i | 0.172598i | ||||||||
\(635\) | −172.695 | − | 172.695i | −0.271961 | − | 0.271961i | ||||
\(636\) | − | 135.341i | − | 0.212801i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −635.772 | −0.996507 | ||||||||
\(639\) | 67.8735 | − | 67.8735i | 0.106218 | − | 0.106218i | ||||
\(640\) | 102.269 | 0.159795 | ||||||||
\(641\) | 915.621i | 1.42843i | 0.699928 | + | 0.714213i | \(0.253215\pi\) | ||||
−0.699928 | + | 0.714213i | \(0.746785\pi\) | |||||||
\(642\) | −12.3876 | + | 12.3876i | −0.0192953 | + | 0.0192953i | ||||
\(643\) | −298.879 | + | 298.879i | −0.464819 | + | 0.464819i | −0.900231 | − | 0.435412i | \(-0.856603\pi\) |
0.435412 | + | 0.900231i | \(0.356603\pi\) | |||||||
\(644\) | −369.765 | − | 369.765i | −0.574170 | − | 0.574170i | ||||
\(645\) | −395.135 | − | 395.135i | −0.612613 | − | 0.612613i | ||||
\(646\) | 134.463 | 0.208147 | ||||||||
\(647\) | 643.609i | 0.994760i | 0.867533 | + | 0.497380i | \(0.165704\pi\) | ||||
−0.867533 | + | 0.497380i | \(0.834296\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 776.071i | 1.19579i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 270.649 | 0.415743 | ||||||||
\(652\) | −22.0804 | + | 22.0804i | −0.0338657 | + | 0.0338657i | ||||
\(653\) | −298.247 | −0.456733 | −0.228366 | − | 0.973575i | \(-0.573338\pi\) | ||||
−0.228366 | + | 0.973575i | \(0.573338\pi\) | |||||||
\(654\) | − | 27.9770i | − | 0.0427783i | ||||||
\(655\) | −412.708 | + | 412.708i | −0.630088 | + | 0.630088i | ||||
\(656\) | −114.501 | + | 114.501i | −0.174545 | + | 0.174545i | ||||
\(657\) | 29.0496 | + | 29.0496i | 0.0442155 | + | 0.0442155i | ||||
\(658\) | −344.898 | − | 344.898i | −0.524161 | − | 0.524161i | ||||
\(659\) | −645.888 | −0.980103 | −0.490052 | − | 0.871693i | \(-0.663022\pi\) | ||||
−0.490052 | + | 0.871693i | \(0.663022\pi\) | |||||||
\(660\) | − | 509.957i | − | 0.772662i | ||||||
\(661\) | −686.907 | − | 686.907i | −1.03919 | − | 1.03919i | −0.999200 | − | 0.0399930i | \(-0.987266\pi\) |
−0.0399930 | − | 0.999200i | \(-0.512734\pi\) | |||||||
\(662\) | − | 28.9091i | − | 0.0436693i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.3972 | 0.0277067 | ||||||||
\(665\) | −604.610 | + | 604.610i | −0.909189 | + | 0.909189i | ||||
\(666\) | 89.4389 | 0.134293 | ||||||||
\(667\) | − | 755.215i | − | 1.13226i | ||||||
\(668\) | −70.0153 | + | 70.0153i | −0.104813 | + | 0.104813i | ||||
\(669\) | −477.408 | + | 477.408i | −0.713614 | + | 0.713614i | ||||
\(670\) | −362.398 | − | 362.398i | −0.540893 | − | 0.540893i | ||||
\(671\) | −812.354 | − | 812.354i | −1.21066 | − | 1.21066i | ||||
\(672\) | 93.6393 | 0.139344 | ||||||||
\(673\) | − | 822.616i | − | 1.22231i | −0.791510 | − | 0.611156i | \(-0.790705\pi\) | ||
0.791510 | − | 0.611156i | \(-0.209295\pi\) | |||||||
\(674\) | −202.326 | − | 202.326i | −0.300188 | − | 0.300188i | ||||
\(675\) | 294.676i | 0.436557i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 195.713 | 0.289089 | 0.144544 | − | 0.989498i | \(-0.453828\pi\) | ||||
0.144544 | + | 0.989498i | \(0.453828\pi\) | |||||||
\(678\) | 201.624 | − | 201.624i | 0.297380 | − | 0.297380i | ||||
\(679\) | 333.898 | 0.491750 | ||||||||
\(680\) | 245.608i | 0.361188i | ||||||||
\(681\) | 163.289 | − | 163.289i | 0.239778 | − | 0.239778i | ||||
\(682\) | 266.273 | − | 266.273i | 0.390429 | − | 0.390429i | ||||
\(683\) | −460.017 | − | 460.017i | −0.673525 | − | 0.673525i | 0.285002 | − | 0.958527i | \(-0.408006\pi\) |
−0.958527 | + | 0.285002i | \(0.908006\pi\) | |||||||
\(684\) | 41.9919 | + | 41.9919i | 0.0613917 | + | 0.0613917i | ||||
\(685\) | 1845.56 | 2.69425 | ||||||||
\(686\) | − | 90.0592i | − | 0.131282i | ||||||
\(687\) | −528.043 | − | 528.043i | −0.768622 | − | 0.768622i | ||||
\(688\) | − | 142.765i | − | 0.207507i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 605.763 | 0.877918 | ||||||||
\(691\) | −222.362 | + | 222.362i | −0.321797 | + | 0.321797i | −0.849456 | − | 0.527659i | \(-0.823070\pi\) |
0.527659 | + | 0.849456i | \(0.323070\pi\) | |||||||
\(692\) | 336.849 | 0.486776 | ||||||||
\(693\) | − | 466.926i | − | 0.673775i | ||||||
\(694\) | 556.526 | − | 556.526i | 0.801911 | − | 0.801911i | ||||
\(695\) | 406.592 | − | 406.592i | 0.585024 | − | 0.585024i | ||||
\(696\) | 95.6252 | + | 95.6252i | 0.137393 | + | 0.137393i | ||||
\(697\) | −274.985 | − | 274.985i | −0.394526 | − | 0.394526i | ||||
\(698\) | −655.572 | −0.939216 | ||||||||
\(699\) | 76.4552i | 0.109378i | ||||||||
\(700\) | −766.480 | − | 766.480i | −1.09497 | − | 1.09497i | ||||
\(701\) | 769.901i | 1.09829i | 0.835727 | + | 0.549145i | \(0.185046\pi\) | ||||
−0.835727 | + | 0.549145i | \(0.814954\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −208.651 | −0.296800 | ||||||||
\(704\) | 92.1254 | − | 92.1254i | 0.130860 | − | 0.130860i | ||||
\(705\) | 565.025 | 0.801454 | ||||||||
\(706\) | 399.614i | 0.566025i | ||||||||
\(707\) | 791.810 | − | 791.810i | 1.11996 | − | 1.11996i | ||||
\(708\) | 116.727 | − | 116.727i | 0.164869 | − | 0.164869i | ||||
\(709\) | 672.423 | + | 672.423i | 0.948411 | + | 0.948411i | 0.998733 | − | 0.0503224i | \(-0.0160249\pi\) |
−0.0503224 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(710\) | −289.223 | − | 289.223i | −0.407356 | − | 0.407356i | ||||
\(711\) | −168.463 | −0.236938 | ||||||||
\(712\) | 327.277i | 0.459659i | ||||||||
\(713\) | 316.298 | + | 316.298i | 0.443615 | + | 0.443615i | ||||
\(714\) | 224.883i | 0.314962i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 626.093 | 0.874432 | ||||||||
\(717\) | −27.4441 | + | 27.4441i | −0.0382763 | + | 0.0382763i | ||||
\(718\) | 560.797 | 0.781054 | ||||||||
\(719\) | 1345.47i | 1.87130i | 0.352926 | + | 0.935651i | \(0.385187\pi\) | ||||
−0.352926 | + | 0.935651i | \(0.614813\pi\) | |||||||
\(720\) | −76.7017 | + | 76.7017i | −0.106530 | + | 0.106530i | ||||
\(721\) | −1244.64 | + | 1244.64i | −1.72627 | + | 1.72627i | ||||
\(722\) | 263.038 | + | 263.038i | 0.364318 | + | 0.364318i | ||||
\(723\) | 589.081 | + | 589.081i | 0.814773 | + | 0.814773i | ||||
\(724\) | 38.9590 | 0.0538108 | ||||||||
\(725\) | − | 1565.47i | − | 2.15927i | ||||||
\(726\) | −249.799 | − | 249.799i | −0.344075 | − | 0.344075i | ||||
\(727\) | − | 681.807i | − | 0.937837i | −0.883241 | − | 0.468918i | \(-0.844644\pi\) | ||
0.883241 | − | 0.468918i | \(-0.155356\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 123.786 | − | 123.786i | 0.169570 | − | 0.169570i | ||||
\(731\) | 342.862 | 0.469032 | ||||||||
\(732\) | 244.369i | 0.333838i | ||||||||
\(733\) | −760.545 | + | 760.545i | −1.03758 | + | 1.03758i | −0.0383126 | + | 0.999266i | \(0.512198\pi\) |
−0.999266 | + | 0.0383126i | \(0.987802\pi\) | |||||||
\(734\) | 591.886 | − | 591.886i | 0.806384 | − | 0.806384i | ||||
\(735\) | −468.707 | − | 468.707i | −0.637696 | − | 0.637696i | ||||
\(736\) | 109.433 | + | 109.433i | 0.148686 | + | 0.148686i | ||||
\(737\) | −652.907 | −0.885898 | ||||||||
\(738\) | − | 171.752i | − | 0.232726i | ||||||
\(739\) | −553.955 | − | 553.955i | −0.749601 | − | 0.749601i | 0.224803 | − | 0.974404i | \(-0.427826\pi\) |
−0.974404 | + | 0.224803i | \(0.927826\pi\) | |||||||
\(740\) | − | 381.118i | − | 0.515024i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −528.053 | −0.711662 | ||||||||
\(743\) | 570.731 | − | 570.731i | 0.768144 | − | 0.768144i | −0.209636 | − | 0.977780i | \(-0.567228\pi\) |
0.977780 | + | 0.209636i | \(0.0672278\pi\) | |||||||
\(744\) | −80.0992 | −0.107660 | ||||||||
\(745\) | 262.323i | 0.352111i | ||||||||
\(746\) | −511.886 | + | 511.886i | −0.686174 | + | 0.686174i | ||||
\(747\) | −13.7979 | + | 13.7979i | −0.0184711 | + | 0.0184711i | ||||
\(748\) | 221.247 | + | 221.247i | 0.295785 | + | 0.295785i | ||||
\(749\) | 48.3319 | + | 48.3319i | 0.0645286 | + | 0.0645286i | ||||
\(750\) | 702.129 | 0.936173 | ||||||||
\(751\) | 991.338i | 1.32002i | 0.751255 | + | 0.660012i | \(0.229449\pi\) | ||||
−0.751255 | + | 0.660012i | \(0.770551\pi\) | |||||||
\(752\) | 102.073 | + | 102.073i | 0.135736 | + | 0.135736i | ||||
\(753\) | − | 366.807i | − | 0.487127i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −404.410 | −0.535642 | ||||||||
\(756\) | −70.2295 | + | 70.2295i | −0.0928961 | + | 0.0928961i | ||||
\(757\) | 740.328 | 0.977976 | 0.488988 | − | 0.872290i | \(-0.337366\pi\) | ||||
0.488988 | + | 0.872290i | \(0.337366\pi\) | |||||||
\(758\) | − | 289.433i | − | 0.381837i | ||||||
\(759\) | 545.680 | − | 545.680i | 0.718946 | − | 0.718946i | ||||
\(760\) | 178.936 | − | 178.936i | 0.235442 | − | 0.235442i | ||||
\(761\) | 558.497 | + | 558.497i | 0.733898 | + | 0.733898i | 0.971390 | − | 0.237491i | \(-0.0763252\pi\) |
−0.237491 | + | 0.971390i | \(0.576325\pi\) | |||||||
\(762\) | 46.7968 | + | 46.7968i | 0.0614132 | + | 0.0614132i | ||||
\(763\) | −109.156 | −0.143062 | ||||||||
\(764\) | − | 285.902i | − | 0.374218i | ||||||
\(765\) | −184.206 | − | 184.206i | −0.240792 | − | 0.240792i | ||||
\(766\) | 464.422i | 0.606295i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 9.05118 | − | 9.05118i | 0.0117701 | − | 0.0117701i | −0.701197 | − | 0.712967i | \(-0.747351\pi\) |
0.712967 | + | 0.701197i | \(0.247351\pi\) | |||||||
\(770\) | −1989.67 | −2.58398 | ||||||||
\(771\) | − | 471.847i | − | 0.611993i | ||||||
\(772\) | 237.325 | − | 237.325i | 0.307415 | − | 0.307415i | ||||
\(773\) | −67.3318 | + | 67.3318i | −0.0871045 | + | 0.0871045i | −0.749317 | − | 0.662212i | \(-0.769618\pi\) |
0.662212 | + | 0.749317i | \(0.269618\pi\) | |||||||
\(774\) | 107.074 | + | 107.074i | 0.138338 | + | 0.138338i | ||||
\(775\) | 655.648 | + | 655.648i | 0.845997 | + | 0.845997i | ||||
\(776\) | −98.8182 | −0.127343 | ||||||||
\(777\) | − | 348.958i | − | 0.449110i | ||||||
\(778\) | 393.984 | + | 393.984i | 0.506406 | + | 0.506406i | ||||
\(779\) | 400.678i | 0.514349i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −521.072 | −0.667186 | ||||||||
\(782\) | −262.813 | + | 262.813i | −0.336078 | + | 0.336078i | ||||
\(783\) | −143.438 | −0.183190 | ||||||||
\(784\) | − | 169.347i | − | 0.216003i | ||||||
\(785\) | 1549.52 | − | 1549.52i | 1.97391 | − | 1.97391i | ||||
\(786\) | 111.835 | − | 111.835i | 0.142284 | − | 0.142284i | ||||
\(787\) | −636.463 | − | 636.463i | −0.808721 | − | 0.808721i | 0.175720 | − | 0.984440i | \(-0.443775\pi\) |
−0.984440 | + | 0.175720i | \(0.943775\pi\) | |||||||
\(788\) | −240.963 | − | 240.963i | −0.305790 | − | 0.305790i | ||||
\(789\) | −409.358 | −0.518832 | ||||||||
\(790\) | 717.856i | 0.908678i | ||||||||
\(791\) | −786.663 | − | 786.663i | −0.994517 | − | 0.994517i | ||||
\(792\) | 138.188i | 0.174480i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −169.800 | −0.213854 | ||||||||
\(795\) | 432.539 | − | 432.539i | 0.544074 | − | 0.544074i | ||||
\(796\) | −323.452 | −0.406346 | ||||||||
\(797\) | 646.448i | 0.811102i | 0.914072 | + | 0.405551i | \(0.132920\pi\) | ||||
−0.914072 | + | 0.405551i | \(0.867080\pi\) | |||||||
\(798\) | 163.837 | − | 163.837i | 0.205310 | − | 0.205310i | ||||
\(799\) | −245.138 | + | 245.138i | −0.306806 | + | 0.306806i | ||||
\(800\) | 226.842 | + | 226.842i | 0.283552 | + | 0.283552i | ||||
\(801\) | −245.458 | − | 245.458i | −0.306439 | − | 0.306439i | ||||
\(802\) | −469.900 | −0.585910 | ||||||||
\(803\) | − | 223.017i | − | 0.277730i | ||||||
\(804\) | 98.2025 | + | 98.2025i | 0.122142 | + | 0.122142i | ||||
\(805\) | − | 2363.47i | − | 2.93599i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −807.761 | −1.00094 | ||||||||
\(808\) | −234.338 | + | 234.338i | −0.290023 | + | 0.290023i | ||||
\(809\) | −1145.39 | −1.41581 | −0.707903 | − | 0.706310i | \(-0.750358\pi\) | ||||
−0.707903 | + | 0.706310i | \(0.750358\pi\) | |||||||
\(810\) | − | 115.053i | − | 0.142040i | ||||||
\(811\) | −394.302 | + | 394.302i | −0.486192 | + | 0.486192i | −0.907102 | − | 0.420910i | \(-0.861711\pi\) |
0.420910 | + | 0.907102i | \(0.361711\pi\) | |||||||
\(812\) | 373.095 | − | 373.095i | 0.459477 | − | 0.459477i | ||||
\(813\) | −564.873 | − | 564.873i | −0.694801 | − | 0.694801i | ||||
\(814\) | −343.316 | − | 343.316i | −0.421765 | − | 0.421765i | ||||
\(815\) | −141.134 | −0.173171 | ||||||||
\(816\) | − | 66.5547i | − | 0.0815621i | ||||||
\(817\) | −249.790 | − | 249.790i | −0.305741 | − | 0.305741i | ||||
\(818\) | − | 622.032i | − | 0.760431i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −731.871 | −0.892526 | ||||||||
\(821\) | −501.342 | + | 501.342i | −0.610648 | + | 0.610648i | −0.943115 | − | 0.332467i | \(-0.892119\pi\) |
0.332467 | + | 0.943115i | \(0.392119\pi\) | |||||||
\(822\) | −500.109 | −0.608406 | ||||||||
\(823\) | − | 554.185i | − | 0.673372i | −0.941617 | − | 0.336686i | \(-0.890694\pi\) | ||
0.941617 | − | 0.336686i | \(-0.109306\pi\) | |||||||
\(824\) | 368.356 | − | 368.356i | 0.447034 | − | 0.447034i | ||||
\(825\) | 1131.13 | − | 1131.13i | 1.37107 | − | 1.37107i | ||||
\(826\) | −455.428 | − | 455.428i | −0.551366 | − | 0.551366i | ||||
\(827\) | −140.395 | − | 140.395i | −0.169764 | − | 0.169764i | 0.617112 | − | 0.786876i | \(-0.288303\pi\) |
−0.786876 | + | 0.617112i | \(0.788303\pi\) | |||||||
\(828\) | −164.150 | −0.198248 | ||||||||
\(829\) | 515.600i | 0.621955i | 0.950417 | + | 0.310977i | \(0.100656\pi\) | ||||
−0.950417 | + | 0.310977i | \(0.899344\pi\) | |||||||
\(830\) | 58.7958 | + | 58.7958i | 0.0708383 | + | 0.0708383i | ||||
\(831\) | − | 42.5275i | − | 0.0511763i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 406.701 | 0.488236 | ||||||||
\(834\) | −110.178 | + | 110.178i | −0.132108 | + | 0.132108i | ||||
\(835\) | −447.525 | −0.535958 | ||||||||
\(836\) | − | 322.377i | − | 0.385618i | ||||||
\(837\) | 60.0744 | − | 60.0744i | 0.0717735 | − | 0.0717735i | ||||
\(838\) | −124.953 | + | 124.953i | −0.149108 | + | 0.149108i | ||||
\(839\) | −615.379 | − | 615.379i | −0.733467 | − | 0.733467i | 0.237838 | − | 0.971305i | \(-0.423561\pi\) |
−0.971305 | + | 0.237838i | \(0.923561\pi\) | |||||||
\(840\) | 299.262 | + | 299.262i | 0.356265 | + | 0.356265i | ||||
\(841\) | −78.9844 | −0.0939173 | ||||||||
\(842\) | 18.9264i | 0.0224779i | ||||||||
\(843\) | 479.071 | + | 479.071i | 0.568292 | + | 0.568292i | ||||
\(844\) | 359.751i | 0.426245i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −153.110 | −0.180981 | ||||||||
\(847\) | −974.624 | + | 974.624i | −1.15068 | + | 1.15068i | ||||
\(848\) | 156.279 | 0.184291 | ||||||||
\(849\) | − | 678.463i | − | 0.799131i | ||||||
\(850\) | −544.780 | + | 544.780i | −0.640918 | + | 0.640918i | ||||
\(851\) | 407.816 | − | 407.816i | 0.479219 | − | 0.479219i | ||||
\(852\) | 78.3735 | + | 78.3735i | 0.0919877 | + | 0.0919877i | ||||
\(853\) | 42.9256 | + | 42.9256i | 0.0503230 | + | 0.0503230i | 0.731820 | − | 0.681497i | \(-0.238671\pi\) |
−0.681497 | + | 0.731820i | \(0.738671\pi\) | |||||||
\(854\) | 953.440 | 1.11644 | ||||||||
\(855\) | 268.404i | 0.313923i | ||||||||
\(856\) | −14.3040 | − | 14.3040i | −0.0167102 | − | 0.0167102i | ||||
\(857\) | 236.541i | 0.276011i | 0.990431 | + | 0.138005i | \(0.0440692\pi\) | ||||
−0.990431 | + | 0.138005i | \(0.955931\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −646.957 | −0.753151 | −0.376575 | − | 0.926386i | \(-0.622898\pi\) | ||||
−0.376575 | + | 0.926386i | \(0.622898\pi\) | |||||||
\(860\) | 456.263 | − | 456.263i | 0.530539 | − | 0.530539i | ||||
\(861\) | −670.115 | −0.778298 | ||||||||
\(862\) | − | 1022.44i | − | 1.18613i | ||||||
\(863\) | 344.605 | − | 344.605i | 0.399310 | − | 0.399310i | −0.478680 | − | 0.877990i | \(-0.658884\pi\) |
0.877990 | + | 0.478680i | \(0.158884\pi\) | |||||||
\(864\) | 20.7846 | − | 20.7846i | 0.0240563 | − | 0.0240563i | ||||
\(865\) | 1076.54 | + | 1076.54i | 1.24455 | + | 1.24455i | ||||
\(866\) | −40.9607 | − | 40.9607i | −0.0472987 | − | 0.0472987i | ||||
\(867\) | −340.726 | −0.392994 | ||||||||
\(868\) | 312.518i | 0.360044i | ||||||||
\(869\) | 646.655 | + | 646.655i | 0.744137 | + | 0.744137i | ||||
\(870\) | 611.218i | 0.702550i | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 32.3051 | 0.0370471 | ||||||||
\(873\) | 74.1136 | − | 74.1136i | 0.0848953 | − | 0.0848953i | ||||
\(874\) | 382.942 | 0.438148 | ||||||||
\(875\) | − | 2739.45i | − | 3.13081i | ||||||
\(876\) | −33.5436 | + | 33.5436i | −0.0382918 | + | 0.0382918i | ||||
\(877\) | −622.004 | + | 622.004i | −0.709240 | + | 0.709240i | −0.966375 | − | 0.257135i | \(-0.917221\pi\) |
0.257135 | + | 0.966375i | \(0.417221\pi\) | |||||||
\(878\) | −665.355 | − | 665.355i | −0.757808 | − | 0.757808i | ||||
\(879\) | −362.988 | − | 362.988i | −0.412956 | − | 0.412956i | ||||
\(880\) | 588.848 | 0.669145 | ||||||||
\(881\) | 41.4598i | 0.0470599i | 0.999723 | + | 0.0235299i | \(0.00749050\pi\) | ||||
−0.999723 | + | 0.0235299i | \(0.992509\pi\) | |||||||
\(882\) | 127.010 | + | 127.010i | 0.144002 | + | 0.144002i | ||||
\(883\) | − | 28.0736i | − | 0.0317934i | −0.999874 | − | 0.0158967i | \(-0.994940\pi\) | ||
0.999874 | − | 0.0158967i | \(-0.00506029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 746.099 | 0.843050 | ||||||||
\(886\) | 267.578 | − | 267.578i | 0.302006 | − | 0.302006i | ||||
\(887\) | 137.864 | 0.155427 | 0.0777135 | − | 0.996976i | \(-0.475238\pi\) | ||||
0.0777135 | + | 0.996976i | \(0.475238\pi\) | |||||||
\(888\) | 103.275i | 0.116301i | ||||||||
\(889\) | 182.584 | − | 182.584i | 0.205382 | − | 0.205382i | ||||
\(890\) | −1045.95 | + | 1045.95i | −1.17522 | + | 1.17522i | ||||
\(891\) | −103.641 | − | 103.641i | −0.116320 | − | 0.116320i | ||||
\(892\) | −551.263 | − | 551.263i | −0.618008 | − | 0.618008i | ||||
\(893\) | 357.188 | 0.399987 | ||||||||
\(894\) | − | 71.0842i | − | 0.0795125i | ||||||
\(895\) | 2000.94 | + | 2000.94i | 2.23568 | + | 2.23568i | ||||
\(896\) | 108.125i | 0.120676i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −796.391 | −0.886850 | ||||||||
\(899\) | −319.146 | + | 319.146i | −0.355001 | + | 0.355001i | ||||
\(900\) | −340.263 | −0.378070 | ||||||||
\(901\) | 375.317i | 0.416556i | ||||||||
\(902\) | −659.280 | + | 659.280i | −0.730909 | + | 0.730909i | ||||
\(903\) | 417.763 | − | 417.763i | 0.462639 | − | 0.462639i | ||||
\(904\) | 232.815 | + | 232.815i | 0.257539 | + | 0.257539i | ||||
\(905\) | 124.509 | + | 124.509i | 0.137579 | + | 0.137579i | ||||
\(906\) | 109.587 | 0.120957 | ||||||||
\(907\) | 896.456i | 0.988375i | 0.869355 | + | 0.494187i | \(0.164534\pi\) | ||||
−0.869355 | + | 0.494187i | \(0.835466\pi\) | |||||||
\(908\) | 188.550 | + | 188.550i | 0.207654 | + | 0.207654i | ||||
\(909\) | − | 351.507i | − | 0.386697i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −318.659 | −0.349791 | −0.174895 | − | 0.984587i | \(-0.555959\pi\) | ||||
−0.174895 | + | 0.984587i | \(0.555959\pi\) | |||||||
\(912\) | −48.4881 | + | 48.4881i | −0.0531667 | + | 0.0531667i | ||||
\(913\) | 105.928 | 0.116022 | ||||||||
\(914\) | 942.261i | 1.03092i | ||||||||
\(915\) | −780.981 | + | 780.981i | −0.853531 | + | 0.853531i | ||||
\(916\) | 609.732 | − | 609.732i | 0.665646 | − | 0.665646i | ||||
\(917\) | −436.341 | − | 436.341i | −0.475836 | − | 0.475836i | ||||
\(918\) | 49.9160 | + | 49.9160i | 0.0543748 | + | 0.0543748i | ||||
\(919\) | −100.528 | −0.109389 | −0.0546944 | − | 0.998503i | \(-0.517418\pi\) | ||||
−0.0546944 | + | 0.998503i | \(0.517418\pi\) | |||||||
\(920\) | 699.475i | 0.760299i | ||||||||
\(921\) | 383.156 | + | 383.156i | 0.416022 | + | 0.416022i | ||||
\(922\) | − | 506.616i | − | 0.549475i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 539.160 | 0.583506 | ||||||||
\(925\) | 845.354 | − | 845.354i | 0.913896 | − | 0.913896i | ||||
\(926\) | 1260.58 | 1.36132 | ||||||||
\(927\) | 552.534i | 0.596045i | ||||||||
\(928\) | −110.419 | + | 110.419i | −0.118985 | + | 0.118985i | ||||
\(929\) | 786.064 | − | 786.064i | 0.846140 | − | 0.846140i | −0.143509 | − | 0.989649i | \(-0.545839\pi\) |
0.989649 | + | 0.143509i | \(0.0458387\pi\) | |||||||
\(930\) | −255.989 | − | 255.989i | −0.275257 | − | 0.275257i | ||||
\(931\) | −296.300 | − | 296.300i | −0.318259 | − | 0.318259i | ||||
\(932\) | −88.2828 | −0.0947240 | ||||||||
\(933\) | − | 21.7469i | − | 0.0233086i | ||||||
\(934\) | 425.264 | + | 425.264i | 0.455315 | + | 0.455315i | ||||
\(935\) | 1414.17i | 1.51248i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −99.5793 | −0.106275 | −0.0531373 | − | 0.998587i | \(-0.516922\pi\) | ||||
−0.0531373 | + | 0.998587i | \(0.516922\pi\) | |||||||
\(938\) | 383.151 | − | 383.151i | 0.408476 | − | 0.408476i | ||||
\(939\) | −1023.57 | −1.09006 | ||||||||
\(940\) | 652.434i | 0.694079i | ||||||||
\(941\) | −795.092 | + | 795.092i | −0.844943 | + | 0.844943i | −0.989497 | − | 0.144554i | \(-0.953825\pi\) |
0.144554 | + | 0.989497i | \(0.453825\pi\) | |||||||
\(942\) | −419.888 | + | 419.888i | −0.445741 | + | 0.445741i | ||||
\(943\) | −783.140 | − | 783.140i | −0.830477 | − | 0.830477i | ||||
\(944\) | 134.785 | + | 134.785i | 0.142781 | + | 0.142781i | ||||
\(945\) | −448.894 | −0.475020 | ||||||||
\(946\) | − | 822.017i | − | 0.868940i | ||||||
\(947\) | −258.294 | − | 258.294i | −0.272750 | − | 0.272750i | 0.557456 | − | 0.830206i | \(-0.311777\pi\) |
−0.830206 | + | 0.557456i | \(0.811777\pi\) | |||||||
\(948\) | − | 194.524i | − | 0.205194i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 793.793 | 0.835572 | ||||||||
\(951\) | 94.7669 | − | 94.7669i | 0.0996497 | − | 0.0996497i | ||||
\(952\) | −259.672 | −0.272765 | ||||||||
\(953\) | 302.820i | 0.317755i | 0.987298 | + | 0.158877i | \(0.0507875\pi\) | ||||
−0.987298 | + | 0.158877i | \(0.949213\pi\) | |||||||
\(954\) | −117.209 | + | 117.209i | −0.122861 | + | 0.122861i | ||||
\(955\) | 913.716 | − | 913.716i | 0.956771 | − | 0.956771i | ||||
\(956\) | −31.6897 | − | 31.6897i | −0.0331482 | − | 0.0331482i | ||||
\(957\) | 550.594 | + | 550.594i | 0.575334 | + | 0.575334i | ||||
\(958\) | 389.623 | 0.406704 | ||||||||
\(959\) | 1951.25i | 2.03467i | ||||||||
\(960\) | −88.5675 | − | 88.5675i | −0.0922578 | − | 0.0922578i | ||||
\(961\) | 693.672i | 0.721823i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.4559 | 0.0222803 | ||||||||
\(964\) | −680.212 | + | 680.212i | −0.705614 | + | 0.705614i | ||||
\(965\) | 1516.93 | 1.57195 | ||||||||
\(966\) | 640.452i | 0.662994i | ||||||||
\(967\) | −228.726 | + | 228.726i | −0.236532 | + | 0.236532i | −0.815412 | − | 0.578881i | \(-0.803490\pi\) |
0.578881 | + | 0.815412i | \(0.303490\pi\) | |||||||
\(968\) | 288.443 | − | 288.443i | 0.297978 | − | 0.297978i | ||||
\(969\) | −116.448 | − | 116.448i | −0.120174 | − | 0.120174i | ||||
\(970\) | −315.813 | − | 315.813i | −0.325581 | − | 0.325581i | ||||
\(971\) | −595.549 | −0.613335 | −0.306668 | − | 0.951817i | \(-0.599214\pi\) | ||||
−0.306668 | + | 0.951817i | \(0.599214\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 429.875 | + | 429.875i | 0.441804 | + | 0.441804i | ||||
\(974\) | − | 905.415i | − | 0.929585i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −282.173 | −0.289112 | ||||||||
\(977\) | 675.329 | − | 675.329i | 0.691227 | − | 0.691227i | −0.271275 | − | 0.962502i | \(-0.587445\pi\) |
0.962502 | + | 0.271275i | \(0.0874453\pi\) | |||||||
\(978\) | 38.2444 | 0.0391048 | ||||||||
\(979\) | 1884.41i | 1.92483i | ||||||||
\(980\) | 541.216 | − | 541.216i | 0.552261 | − | 0.552261i | ||||
\(981\) | −24.2288 | + | 24.2288i | −0.0246981 | + | 0.0246981i | ||||
\(982\) | 566.666 | + | 566.666i | 0.577053 | + | 0.577053i | ||||
\(983\) | −265.546 | − | 265.546i | −0.270138 | − | 0.270138i | 0.559018 | − | 0.829156i | \(-0.311178\pi\) |
−0.829156 | + | 0.559018i | \(0.811178\pi\) | |||||||
\(984\) | 198.322 | 0.201547 | ||||||||
\(985\) | − | 1540.19i | − | 1.56364i | ||||||
\(986\) | −265.180 | − | 265.180i | −0.268945 | − | 0.268945i | ||||
\(987\) | 597.381i | 0.605249i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 976.450 | 0.987310 | ||||||||
\(990\) | −441.636 | + | 441.636i | −0.446097 | + | 0.446097i | ||||
\(991\) | 145.155 | 0.146473 | 0.0732366 | − | 0.997315i | \(-0.476667\pi\) | ||||
0.0732366 | + | 0.997315i | \(0.476667\pi\) | |||||||
\(992\) | − | 92.4906i | − | 0.0932365i | ||||||
\(993\) | −25.0360 | + | 25.0360i | −0.0252125 | + | 0.0252125i | ||||
\(994\) | 305.785 | − | 305.785i | 0.307631 | − | 0.307631i | ||||
\(995\) | −1033.72 | − | 1033.72i | −1.03892 | − | 1.03892i | ||||
\(996\) | −15.9325 | − | 15.9325i | −0.0159965 | − | 0.0159965i | ||||
\(997\) | 584.322 | 0.586081 | 0.293040 | − | 0.956100i | \(-0.405333\pi\) | ||||
0.293040 | + | 0.956100i | \(0.405333\pi\) | |||||||
\(998\) | − | 818.583i | − | 0.820224i | ||||||
\(999\) | −77.4564 | − | 77.4564i | −0.0775339 | − | 0.0775339i |
(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 | 1014.3.f.j.577.2 | 8 | ||
13.2 | odd | 12 | 78.3.l.c.7.1 | ✓ | 8 | ||
13.4 | even | 6 | 78.3.l.c.67.1 | yes | 8 | ||
13.5 | odd | 4 | 1014.3.f.h.775.1 | 8 | |||
13.8 | odd | 4 | inner | 1014.3.f.j.775.2 | 8 | ||
13.12 | even | 2 | 1014.3.f.h.577.1 | 8 | |||
39.2 | even | 12 | 234.3.bb.d.163.2 | 8 | |||
39.17 | odd | 6 | 234.3.bb.d.145.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.l.c.7.1 | ✓ | 8 | 13.2 | odd | 12 | ||
78.3.l.c.67.1 | yes | 8 | 13.4 | even | 6 | ||
234.3.bb.d.145.2 | 8 | 39.17 | odd | 6 | |||
234.3.bb.d.163.2 | 8 | 39.2 | even | 12 | |||
1014.3.f.h.577.1 | 8 | 13.12 | even | 2 | |||
1014.3.f.h.775.1 | 8 | 13.5 | odd | 4 | |||
1014.3.f.j.577.2 | 8 | 1.1 | even | 1 | trivial | ||
1014.3.f.j.775.2 | 8 | 13.8 | odd | 4 | inner |