Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.4 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.b.553.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 3.38334 | + | 3.68144i | 0.676669 | + | 0.736288i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −2.06971 | − | 2.06971i | −0.295672 | − | 0.295672i | 0.543644 | − | 0.839316i | \(-0.317044\pi\) |
−0.839316 | + | 0.543644i | \(0.817044\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0.298094 | − | 7.06478i | 0.0298094 | − | 0.706478i | ||||
\(11\) | 0.900062 | 0.0818238 | 0.0409119 | − | 0.999163i | \(-0.486974\pi\) | ||||
0.0409119 | + | 0.999163i | \(0.486974\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 6.37460 | − | 6.37460i | 0.490354 | − | 0.490354i | −0.418064 | − | 0.908418i | \(-0.637291\pi\) |
0.908418 | + | 0.418064i | \(0.137291\pi\) | |||||||
\(14\) | 4.13941i | 0.295672i | ||||||||
\(15\) | −8.65256 | − | 0.365089i | −0.576837 | − | 0.0243392i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −18.4729 | − | 18.4729i | −1.08664 | − | 1.08664i | −0.995872 | − | 0.0907667i | \(-0.971068\pi\) |
−0.0907667 | − | 0.995872i | \(-0.528932\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | − | 9.86457i | − | 0.519188i | −0.965718 | − | 0.259594i | \(-0.916411\pi\) | ||
0.965718 | − | 0.259594i | \(-0.0835888\pi\) | |||||||
\(20\) | −7.36288 | + | 6.76669i | −0.368144 | + | 0.338334i | ||||
\(21\) | 5.06972 | 0.241415 | ||||||||
\(22\) | −0.900062 | − | 0.900062i | −0.0409119 | − | 0.0409119i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −2.10597 | + | 24.9111i | −0.0842387 | + | 0.996446i | ||||
\(26\) | −12.7492 | −0.490354 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 4.13941 | − | 4.13941i | 0.147836 | − | 0.147836i | ||||
\(29\) | − | 7.79905i | − | 0.268933i | −0.990918 | − | 0.134466i | \(-0.957068\pi\) | ||
0.990918 | − | 0.134466i | \(-0.0429320\pi\) | |||||||
\(30\) | 8.28747 | + | 9.01764i | 0.276249 | + | 0.300588i | ||||
\(31\) | 18.5068 | 0.596995 | 0.298497 | − | 0.954410i | \(-0.403515\pi\) | ||||
0.298497 | + | 0.954410i | \(0.403515\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −1.10235 | + | 1.10235i | −0.0334044 | + | 0.0334044i | ||||
\(34\) | 36.9457i | 1.08664i | ||||||||
\(35\) | 0.616966 | − | 14.6220i | 0.0176276 | − | 0.417772i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −22.8521 | − | 22.8521i | −0.617623 | − | 0.617623i | 0.327298 | − | 0.944921i | \(-0.393862\pi\) |
−0.944921 | + | 0.327298i | \(0.893862\pi\) | |||||||
\(38\) | −9.86457 | + | 9.86457i | −0.259594 | + | 0.259594i | ||||
\(39\) | 15.6145i | 0.400372i | ||||||||
\(40\) | 14.1296 | + | 0.596187i | 0.353239 | + | 0.0149047i | ||||
\(41\) | 36.6804 | 0.894643 | 0.447322 | − | 0.894373i | \(-0.352378\pi\) | ||||
0.447322 | + | 0.894373i | \(0.352378\pi\) | |||||||
\(42\) | −5.06972 | − | 5.06972i | −0.120708 | − | 0.120708i | ||||
\(43\) | 14.6911 | − | 14.6911i | 0.341654 | − | 0.341654i | −0.515335 | − | 0.856989i | \(-0.672333\pi\) |
0.856989 | + | 0.515335i | \(0.172333\pi\) | |||||||
\(44\) | 1.80012i | 0.0409119i | ||||||||
\(45\) | 11.0443 | − | 10.1500i | 0.245429 | − | 0.225556i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 27.0328 | + | 27.0328i | 0.575166 | + | 0.575166i | 0.933568 | − | 0.358401i | \(-0.116678\pi\) |
−0.358401 | + | 0.933568i | \(0.616678\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 40.4326i | − | 0.825156i | ||||||
\(50\) | 27.0171 | − | 22.8052i | 0.540342 | − | 0.456103i | ||||
\(51\) | 45.2491 | 0.887237 | ||||||||
\(52\) | 12.7492 | + | 12.7492i | 0.245177 | + | 0.245177i | ||||
\(53\) | 51.0631 | − | 51.0631i | 0.963455 | − | 0.963455i | −0.0359002 | − | 0.999355i | \(-0.511430\pi\) |
0.999355 | + | 0.0359002i | \(0.0114298\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 3.04522 | + | 3.31352i | 0.0553676 | + | 0.0602459i | ||||
\(56\) | −8.27882 | −0.147836 | ||||||||
\(57\) | 12.0816 | + | 12.0816i | 0.211958 | + | 0.211958i | ||||
\(58\) | −7.79905 | + | 7.79905i | −0.134466 | + | 0.134466i | ||||
\(59\) | 91.7327i | 1.55479i | 0.629012 | + | 0.777396i | \(0.283460\pi\) | ||||
−0.629012 | + | 0.777396i | \(0.716540\pi\) | |||||||
\(60\) | 0.730177 | − | 17.3051i | 0.0121696 | − | 0.288419i | ||||
\(61\) | −44.5012 | −0.729528 | −0.364764 | − | 0.931100i | \(-0.618850\pi\) | ||||
−0.364764 | + | 0.931100i | \(0.618850\pi\) | |||||||
\(62\) | −18.5068 | − | 18.5068i | −0.298497 | − | 0.298497i | ||||
\(63\) | −6.20912 | + | 6.20912i | −0.0985574 | + | 0.0985574i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 45.0351 | + | 1.90023i | 0.692848 | + | 0.0292343i | ||||
\(66\) | 2.20469 | 0.0334044 | ||||||||
\(67\) | −21.6784 | − | 21.6784i | −0.323557 | − | 0.323557i | 0.526573 | − | 0.850130i | \(-0.323477\pi\) |
−0.850130 | + | 0.526573i | \(0.823477\pi\) | |||||||
\(68\) | 36.9457 | − | 36.9457i | 0.543319 | − | 0.543319i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | −15.2390 | + | 14.0051i | −0.217700 | + | 0.200072i | ||||
\(71\) | 84.1101 | 1.18465 | 0.592325 | − | 0.805699i | \(-0.298210\pi\) | ||||
0.592325 | + | 0.805699i | \(0.298210\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 77.0736 | − | 77.0736i | 1.05580 | − | 1.05580i | 0.0574543 | − | 0.998348i | \(-0.481702\pi\) |
0.998348 | − | 0.0574543i | \(-0.0182984\pi\) | |||||||
\(74\) | 45.7041i | 0.617623i | ||||||||
\(75\) | −27.9305 | − | 33.0891i | −0.372407 | − | 0.441188i | ||||
\(76\) | 19.7291 | 0.259594 | ||||||||
\(77\) | −1.86286 | − | 1.86286i | −0.0241930 | − | 0.0241930i | ||||
\(78\) | 15.6145 | − | 15.6145i | 0.200186 | − | 0.200186i | ||||
\(79\) | − | 31.3293i | − | 0.396574i | −0.980144 | − | 0.198287i | \(-0.936462\pi\) | ||
0.980144 | − | 0.198287i | \(-0.0635378\pi\) | |||||||
\(80\) | −13.5334 | − | 14.7258i | −0.169167 | − | 0.184072i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −36.6804 | − | 36.6804i | −0.447322 | − | 0.447322i | ||||
\(83\) | 8.70034 | − | 8.70034i | 0.104823 | − | 0.104823i | −0.652750 | − | 0.757573i | \(-0.726385\pi\) |
0.757573 | + | 0.652750i | \(0.226385\pi\) | |||||||
\(84\) | 10.1394i | 0.120708i | ||||||||
\(85\) | 5.50664 | − | 130.507i | 0.0647840 | − | 1.53537i | ||||
\(86\) | −29.3822 | −0.341654 | ||||||||
\(87\) | 9.55185 | + | 9.55185i | 0.109791 | + | 0.109791i | ||||
\(88\) | 1.80012 | − | 1.80012i | 0.0204560 | − | 0.0204560i | ||||
\(89\) | − | 32.1361i | − | 0.361079i | −0.983568 | − | 0.180540i | \(-0.942216\pi\) | ||
0.983568 | − | 0.180540i | \(-0.0577844\pi\) | |||||||
\(90\) | −21.1943 | − | 0.894281i | −0.235493 | − | 0.00993646i | ||||
\(91\) | −26.3871 | −0.289968 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | −22.6662 | + | 22.6662i | −0.243722 | + | 0.243722i | ||||
\(94\) | − | 54.0656i | − | 0.575166i | ||||||
\(95\) | 36.3158 | − | 33.3752i | 0.382272 | − | 0.351318i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −104.238 | − | 104.238i | −1.07461 | − | 1.07461i | −0.996982 | − | 0.0776323i | \(-0.975264\pi\) |
−0.0776323 | − | 0.996982i | \(-0.524736\pi\) | |||||||
\(98\) | −40.4326 | + | 40.4326i | −0.412578 | + | 0.412578i | ||||
\(99\) | − | 2.70019i | − | 0.0272746i | ||||||
\(100\) | −49.8223 | − | 4.21193i | −0.498223 | − | 0.0421193i | ||||
\(101\) | 62.2349 | 0.616187 | 0.308094 | − | 0.951356i | \(-0.400309\pi\) | ||||
0.308094 | + | 0.951356i | \(0.400309\pi\) | |||||||
\(102\) | −45.2491 | − | 45.2491i | −0.443618 | − | 0.443618i | ||||
\(103\) | 118.903 | − | 118.903i | 1.15440 | − | 1.15440i | 0.168738 | − | 0.985661i | \(-0.446031\pi\) |
0.985661 | − | 0.168738i | \(-0.0539692\pi\) | |||||||
\(104\) | − | 25.4984i | − | 0.245177i | ||||||
\(105\) | 17.1526 | + | 18.6639i | 0.163358 | + | 0.177751i | ||||
\(106\) | −102.126 | −0.963455 | ||||||||
\(107\) | −18.5364 | − | 18.5364i | −0.173237 | − | 0.173237i | 0.615163 | − | 0.788400i | \(-0.289090\pi\) |
−0.788400 | + | 0.615163i | \(0.789090\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 73.8874i | − | 0.677866i | −0.940811 | − | 0.338933i | \(-0.889934\pi\) | ||
0.940811 | − | 0.338933i | \(-0.110066\pi\) | |||||||
\(110\) | 0.268303 | − | 6.35874i | 0.00243912 | − | 0.0578067i | ||||
\(111\) | 55.9759 | 0.504287 | ||||||||
\(112\) | 8.27882 | + | 8.27882i | 0.0739181 | + | 0.0739181i | ||||
\(113\) | 80.0463 | − | 80.0463i | 0.708374 | − | 0.708374i | −0.257819 | − | 0.966193i | \(-0.583004\pi\) |
0.966193 | + | 0.257819i | \(0.0830038\pi\) | |||||||
\(114\) | − | 24.1632i | − | 0.211958i | ||||||
\(115\) | 23.9578 | + | 1.01088i | 0.208329 | + | 0.00879030i | ||||
\(116\) | 15.5981 | 0.134466 | ||||||||
\(117\) | −19.1238 | − | 19.1238i | −0.163451 | − | 0.163451i | ||||
\(118\) | 91.7327 | − | 91.7327i | 0.777396 | − | 0.777396i | ||||
\(119\) | 76.4668i | 0.642578i | ||||||||
\(120\) | −18.0353 | + | 16.5749i | −0.150294 | + | 0.138124i | ||||
\(121\) | −120.190 | −0.993305 | ||||||||
\(122\) | 44.5012 | + | 44.5012i | 0.364764 | + | 0.364764i | ||||
\(123\) | −44.9241 | + | 44.9241i | −0.365237 | + | 0.365237i | ||||
\(124\) | 37.0137i | 0.298497i | ||||||||
\(125\) | −98.8340 | + | 76.5300i | −0.790672 | + | 0.612240i | ||||
\(126\) | 12.4182 | 0.0985574 | ||||||||
\(127\) | −27.4253 | − | 27.4253i | −0.215947 | − | 0.215947i | 0.590841 | − | 0.806788i | \(-0.298796\pi\) |
−0.806788 | + | 0.590841i | \(0.798796\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 35.9857i | 0.278959i | ||||||||
\(130\) | −43.1349 | − | 46.9354i | −0.331807 | − | 0.361041i | ||||
\(131\) | 80.5645 | 0.614996 | 0.307498 | − | 0.951549i | \(-0.400508\pi\) | ||||
0.307498 | + | 0.951549i | \(0.400508\pi\) | |||||||
\(132\) | −2.20469 | − | 2.20469i | −0.0167022 | − | 0.0167022i | ||||
\(133\) | −20.4168 | + | 20.4168i | −0.153510 | + | 0.153510i | ||||
\(134\) | 43.3567i | 0.323557i | ||||||||
\(135\) | −1.09527 | + | 25.9577i | −0.00811308 | + | 0.192279i | ||||
\(136\) | −73.8914 | −0.543319 | ||||||||
\(137\) | 54.9704 | + | 54.9704i | 0.401244 | + | 0.401244i | 0.878671 | − | 0.477427i | \(-0.158431\pi\) |
−0.477427 | + | 0.878671i | \(0.658431\pi\) | |||||||
\(138\) | 8.30662 | − | 8.30662i | 0.0601929 | − | 0.0601929i | ||||
\(139\) | 133.632i | 0.961379i | 0.876891 | + | 0.480690i | \(0.159614\pi\) | ||||
−0.876891 | + | 0.480690i | \(0.840386\pi\) | |||||||
\(140\) | 29.2440 | + | 1.23393i | 0.208886 | + | 0.00881380i | ||||
\(141\) | −66.2166 | −0.469621 | ||||||||
\(142\) | −84.1101 | − | 84.1101i | −0.592325 | − | 0.592325i | ||||
\(143\) | 5.73753 | − | 5.73753i | 0.0401226 | − | 0.0401226i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 28.7117 | − | 26.3869i | 0.198012 | − | 0.181979i | ||||
\(146\) | −154.147 | −1.05580 | ||||||||
\(147\) | 49.5197 | + | 49.5197i | 0.336868 | + | 0.336868i | ||||
\(148\) | 45.7041 | − | 45.7041i | 0.308812 | − | 0.308812i | ||||
\(149\) | 193.876i | 1.30118i | 0.759428 | + | 0.650591i | \(0.225479\pi\) | ||||
−0.759428 | + | 0.650591i | \(0.774521\pi\) | |||||||
\(150\) | −5.15854 | + | 61.0196i | −0.0343903 | + | 0.406797i | ||||
\(151\) | 211.812 | 1.40273 | 0.701364 | − | 0.712803i | \(-0.252575\pi\) | ||||
0.701364 | + | 0.712803i | \(0.252575\pi\) | |||||||
\(152\) | −19.7291 | − | 19.7291i | −0.129797 | − | 0.129797i | ||||
\(153\) | −55.4186 | + | 55.4186i | −0.362213 | + | 0.362213i | ||||
\(154\) | 3.72573i | 0.0241930i | ||||||||
\(155\) | 62.6150 | + | 68.1318i | 0.403968 | + | 0.439560i | ||||
\(156\) | −31.2290 | −0.200186 | ||||||||
\(157\) | −134.833 | − | 134.833i | −0.858809 | − | 0.858809i | 0.132389 | − | 0.991198i | \(-0.457735\pi\) |
−0.991198 | + | 0.132389i | \(0.957735\pi\) | |||||||
\(158\) | −31.3293 | + | 31.3293i | −0.198287 | + | 0.198287i | ||||
\(159\) | 125.079i | 0.786658i | ||||||||
\(160\) | −1.19237 | + | 28.2591i | −0.00745234 | + | 0.176620i | ||||
\(161\) | −14.0374 | −0.0871890 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −142.999 | + | 142.999i | −0.877293 | + | 0.877293i | −0.993254 | − | 0.115961i | \(-0.963005\pi\) |
0.115961 | + | 0.993254i | \(0.463005\pi\) | |||||||
\(164\) | 73.3608i | 0.447322i | ||||||||
\(165\) | −7.78784 | − | 0.328602i | −0.0471990 | − | 0.00199153i | ||||
\(166\) | −17.4007 | −0.104823 | ||||||||
\(167\) | −142.222 | − | 142.222i | −0.851630 | − | 0.851630i | 0.138704 | − | 0.990334i | \(-0.455706\pi\) |
−0.990334 | + | 0.138704i | \(0.955706\pi\) | |||||||
\(168\) | 10.1394 | − | 10.1394i | 0.0603539 | − | 0.0603539i | ||||
\(169\) | 87.7290i | 0.519107i | ||||||||
\(170\) | −136.013 | + | 125.000i | −0.800079 | + | 0.735295i | ||||
\(171\) | −29.5937 | −0.173063 | ||||||||
\(172\) | 29.3822 | + | 29.3822i | 0.170827 | + | 0.170827i | ||||
\(173\) | 147.140 | − | 147.140i | 0.850518 | − | 0.850518i | −0.139679 | − | 0.990197i | \(-0.544607\pi\) |
0.990197 | + | 0.139679i | \(0.0446071\pi\) | |||||||
\(174\) | − | 19.1037i | − | 0.109791i | ||||||
\(175\) | 55.9175 | − | 47.2000i | 0.319528 | − | 0.269714i | ||||
\(176\) | −3.60025 | −0.0204560 | ||||||||
\(177\) | −112.349 | − | 112.349i | −0.634741 | − | 0.634741i | ||||
\(178\) | −32.1361 | + | 32.1361i | −0.180540 | + | 0.180540i | ||||
\(179\) | 119.989i | 0.670327i | 0.942160 | + | 0.335164i | \(0.108792\pi\) | ||||
−0.942160 | + | 0.335164i | \(0.891208\pi\) | |||||||
\(180\) | 20.3001 | + | 22.0886i | 0.112778 | + | 0.122715i | ||||
\(181\) | 142.935 | 0.789695 | 0.394847 | − | 0.918747i | \(-0.370797\pi\) | ||||
0.394847 | + | 0.918747i | \(0.370797\pi\) | |||||||
\(182\) | 26.3871 | + | 26.3871i | 0.144984 | + | 0.144984i | ||||
\(183\) | 54.5026 | − | 54.5026i | 0.297828 | − | 0.297828i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 6.81206 | − | 161.445i | 0.0368219 | − | 0.872675i | ||||
\(186\) | 45.3323 | 0.243722 | ||||||||
\(187\) | −16.6267 | − | 16.6267i | −0.0889129 | − | 0.0889129i | ||||
\(188\) | −54.0656 | + | 54.0656i | −0.287583 | + | 0.287583i | ||||
\(189\) | − | 15.2092i | − | 0.0804718i | ||||||
\(190\) | −69.6911 | − | 2.94057i | −0.366795 | − | 0.0154767i | ||||
\(191\) | 71.7202 | 0.375499 | 0.187749 | − | 0.982217i | \(-0.439881\pi\) | ||||
0.187749 | + | 0.982217i | \(0.439881\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 15.6998 | − | 15.6998i | 0.0813462 | − | 0.0813462i | −0.665263 | − | 0.746609i | \(-0.731681\pi\) |
0.746609 | + | 0.665263i | \(0.231681\pi\) | |||||||
\(194\) | 208.475i | 1.07461i | ||||||||
\(195\) | −57.4838 | + | 52.8293i | −0.294789 | + | 0.270919i | ||||
\(196\) | 80.8653 | 0.412578 | ||||||||
\(197\) | 258.375 | + | 258.375i | 1.31155 | + | 1.31155i | 0.920274 | + | 0.391274i | \(0.127965\pi\) |
0.391274 | + | 0.920274i | \(0.372035\pi\) | |||||||
\(198\) | −2.70019 | + | 2.70019i | −0.0136373 | + | 0.0136373i | ||||
\(199\) | 17.1356i | 0.0861087i | 0.999073 | + | 0.0430544i | \(0.0137089\pi\) | ||||
−0.999073 | + | 0.0430544i | \(0.986291\pi\) | |||||||
\(200\) | 45.6103 | + | 54.0342i | 0.228052 | + | 0.270171i | ||||
\(201\) | 53.1009 | 0.264184 | ||||||||
\(202\) | −62.2349 | − | 62.2349i | −0.308094 | − | 0.308094i | ||||
\(203\) | −16.1417 | + | 16.1417i | −0.0795160 | + | 0.0795160i | ||||
\(204\) | 90.4982i | 0.443618i | ||||||||
\(205\) | 124.102 | + | 135.037i | 0.605377 | + | 0.658715i | ||||
\(206\) | −237.806 | −1.15440 | ||||||||
\(207\) | −10.1735 | − | 10.1735i | −0.0491473 | − | 0.0491473i | ||||
\(208\) | −25.4984 | + | 25.4984i | −0.122588 | + | 0.122588i | ||||
\(209\) | − | 8.87873i | − | 0.0424819i | ||||||
\(210\) | 1.51125 | − | 35.8165i | 0.00719644 | − | 0.170555i | ||||
\(211\) | −87.8965 | −0.416571 | −0.208286 | − | 0.978068i | \(-0.566788\pi\) | ||||
−0.208286 | + | 0.978068i | \(0.566788\pi\) | |||||||
\(212\) | 102.126 | + | 102.126i | 0.481728 | + | 0.481728i | ||||
\(213\) | −103.013 | + | 103.013i | −0.483631 | + | 0.483631i | ||||
\(214\) | 37.0728i | 0.173237i | ||||||||
\(215\) | 103.789 | + | 4.37933i | 0.482742 | + | 0.0203690i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −38.3037 | − | 38.3037i | −0.176515 | − | 0.176515i | ||||
\(218\) | −73.8874 | + | 73.8874i | −0.338933 | + | 0.338933i | ||||
\(219\) | 188.791i | 0.862059i | ||||||||
\(220\) | −6.62704 | + | 6.09044i | −0.0301229 | + | 0.0276838i | ||||
\(221\) | −235.514 | −1.06567 | ||||||||
\(222\) | −55.9759 | − | 55.9759i | −0.252144 | − | 0.252144i | ||||
\(223\) | −158.653 | + | 158.653i | −0.711447 | + | 0.711447i | −0.966838 | − | 0.255391i | \(-0.917796\pi\) |
0.255391 | + | 0.966838i | \(0.417796\pi\) | |||||||
\(224\) | − | 16.5576i | − | 0.0739181i | ||||||
\(225\) | 74.7334 | + | 6.31790i | 0.332149 | + | 0.0280796i | ||||
\(226\) | −160.093 | −0.708374 | ||||||||
\(227\) | 176.500 | + | 176.500i | 0.777531 | + | 0.777531i | 0.979410 | − | 0.201879i | \(-0.0647048\pi\) |
−0.201879 | + | 0.979410i | \(0.564705\pi\) | |||||||
\(228\) | −24.1632 | + | 24.1632i | −0.105979 | + | 0.105979i | ||||
\(229\) | − | 140.584i | − | 0.613902i | −0.951725 | − | 0.306951i | \(-0.900691\pi\) | ||
0.951725 | − | 0.306951i | \(-0.0993088\pi\) | |||||||
\(230\) | −22.9470 | − | 24.9687i | −0.0997694 | − | 0.108560i | ||||
\(231\) | 4.56306 | 0.0197535 | ||||||||
\(232\) | −15.5981 | − | 15.5981i | −0.0672332 | − | 0.0672332i | ||||
\(233\) | 23.4052 | − | 23.4052i | 0.100451 | − | 0.100451i | −0.655095 | − | 0.755546i | \(-0.727371\pi\) |
0.755546 | + | 0.655095i | \(0.227371\pi\) | |||||||
\(234\) | 38.2476i | 0.163451i | ||||||||
\(235\) | −8.05831 | + | 190.981i | −0.0342907 | + | 0.812685i | ||||
\(236\) | −183.465 | −0.777396 | ||||||||
\(237\) | 38.3704 | + | 38.3704i | 0.161901 | + | 0.161901i | ||||
\(238\) | 76.4668 | − | 76.4668i | 0.321289 | − | 0.321289i | ||||
\(239\) | − | 158.063i | − | 0.661349i | −0.943745 | − | 0.330675i | \(-0.892724\pi\) | ||
0.943745 | − | 0.330675i | \(-0.107276\pi\) | |||||||
\(240\) | 34.6102 | + | 1.46035i | 0.144209 | + | 0.00608481i | ||||
\(241\) | 148.164 | 0.614786 | 0.307393 | − | 0.951583i | \(-0.400543\pi\) | ||||
0.307393 | + | 0.951583i | \(0.400543\pi\) | |||||||
\(242\) | 120.190 | + | 120.190i | 0.496652 | + | 0.496652i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 89.0024i | − | 0.364764i | ||||||
\(245\) | 148.850 | − | 136.798i | 0.607552 | − | 0.558357i | ||||
\(246\) | 89.8482 | 0.365237 | ||||||||
\(247\) | −62.8827 | − | 62.8827i | −0.254586 | − | 0.254586i | ||||
\(248\) | 37.0137 | − | 37.0137i | 0.149249 | − | 0.149249i | ||||
\(249\) | 21.3114i | 0.0855879i | ||||||||
\(250\) | 175.364 | + | 22.3040i | 0.701456 | + | 0.0892162i | ||||
\(251\) | −222.580 | −0.886771 | −0.443386 | − | 0.896331i | \(-0.646223\pi\) | ||||
−0.443386 | + | 0.896331i | \(0.646223\pi\) | |||||||
\(252\) | −12.4182 | − | 12.4182i | −0.0492787 | − | 0.0492787i | ||||
\(253\) | 3.05226 | − | 3.05226i | 0.0120643 | − | 0.0120643i | ||||
\(254\) | 54.8505i | 0.215947i | ||||||||
\(255\) | 153.093 | + | 166.582i | 0.600366 | + | 0.653262i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −281.297 | − | 281.297i | −1.09454 | − | 1.09454i | −0.995037 | − | 0.0995018i | \(-0.968275\pi\) |
−0.0995018 | − | 0.995037i | \(-0.531725\pi\) | |||||||
\(258\) | 35.9857 | − | 35.9857i | 0.139480 | − | 0.139480i | ||||
\(259\) | 94.5941i | 0.365228i | ||||||||
\(260\) | −3.80045 | + | 90.0703i | −0.0146171 | + | 0.346424i | ||||
\(261\) | −23.3972 | −0.0896443 | ||||||||
\(262\) | −80.5645 | − | 80.5645i | −0.307498 | − | 0.307498i | ||||
\(263\) | −177.629 | + | 177.629i | −0.675394 | + | 0.675394i | −0.958954 | − | 0.283560i | \(-0.908484\pi\) |
0.283560 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(264\) | 4.40938i | 0.0167022i | ||||||||
\(265\) | 360.750 | + | 15.2216i | 1.36132 | + | 0.0574400i | ||||
\(266\) | 40.8335 | 0.153510 | ||||||||
\(267\) | 39.3585 | + | 39.3585i | 0.147410 | + | 0.147410i | ||||
\(268\) | 43.3567 | − | 43.3567i | 0.161779 | − | 0.161779i | ||||
\(269\) | 93.2801i | 0.346766i | 0.984854 | + | 0.173383i | \(0.0554699\pi\) | ||||
−0.984854 | + | 0.173383i | \(0.944530\pi\) | |||||||
\(270\) | 27.0529 | − | 24.8624i | 0.100196 | − | 0.0920830i | ||||
\(271\) | −351.552 | −1.29724 | −0.648620 | − | 0.761113i | \(-0.724653\pi\) | ||||
−0.648620 | + | 0.761113i | \(0.724653\pi\) | |||||||
\(272\) | 73.8914 | + | 73.8914i | 0.271660 | + | 0.271660i | ||||
\(273\) | 32.3174 | − | 32.3174i | 0.118379 | − | 0.118379i | ||||
\(274\) | − | 109.941i | − | 0.401244i | ||||||
\(275\) | −1.89550 | + | 22.4216i | −0.00689273 | + | 0.0815330i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | −211.987 | − | 211.987i | −0.765297 | − | 0.765297i | 0.211977 | − | 0.977275i | \(-0.432010\pi\) |
−0.977275 | + | 0.211977i | \(0.932010\pi\) | |||||||
\(278\) | 133.632 | − | 133.632i | 0.480690 | − | 0.480690i | ||||
\(279\) | − | 55.5205i | − | 0.198998i | ||||||
\(280\) | −28.0101 | − | 30.4780i | −0.100036 | − | 0.108850i | ||||
\(281\) | −135.367 | −0.481732 | −0.240866 | − | 0.970558i | \(-0.577431\pi\) | ||||
−0.240866 | + | 0.970558i | \(0.577431\pi\) | |||||||
\(282\) | 66.2166 | + | 66.2166i | 0.234811 | + | 0.234811i | ||||
\(283\) | 107.157 | − | 107.157i | 0.378648 | − | 0.378648i | −0.491966 | − | 0.870614i | \(-0.663722\pi\) |
0.870614 | + | 0.491966i | \(0.163722\pi\) | |||||||
\(284\) | 168.220i | 0.592325i | ||||||||
\(285\) | −3.60144 | + | 85.3538i | −0.0126366 | + | 0.299487i | ||||
\(286\) | −11.4751 | −0.0401226 | ||||||||
\(287\) | −75.9176 | − | 75.9176i | −0.264521 | − | 0.264521i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 393.493i | 1.36157i | ||||||||
\(290\) | −55.0986 | − | 2.32485i | −0.189995 | − | 0.00801672i | ||||
\(291\) | 255.329 | 0.877419 | ||||||||
\(292\) | 154.147 | + | 154.147i | 0.527901 | + | 0.527901i | ||||
\(293\) | −130.004 | + | 130.004i | −0.443700 | + | 0.443700i | −0.893253 | − | 0.449553i | \(-0.851583\pi\) |
0.449553 | + | 0.893253i | \(0.351583\pi\) | |||||||
\(294\) | − | 99.0393i | − | 0.336868i | ||||||
\(295\) | −337.708 | + | 310.363i | −1.14477 | + | 1.05208i | ||||
\(296\) | −91.4083 | −0.308812 | ||||||||
\(297\) | 3.30704 | + | 3.30704i | 0.0111348 | + | 0.0111348i | ||||
\(298\) | 193.876 | − | 193.876i | 0.650591 | − | 0.650591i | ||||
\(299\) | − | 43.2346i | − | 0.144597i | ||||||
\(300\) | 66.1781 | − | 55.8610i | 0.220594 | − | 0.186203i | ||||
\(301\) | −60.8126 | −0.202035 | ||||||||
\(302\) | −211.812 | − | 211.812i | −0.701364 | − | 0.701364i | ||||
\(303\) | −76.2219 | + | 76.2219i | −0.251557 | + | 0.251557i | ||||
\(304\) | 39.4583i | 0.129797i | ||||||||
\(305\) | −150.563 | − | 163.828i | −0.493649 | − | 0.537142i | ||||
\(306\) | 110.837 | 0.362213 | ||||||||
\(307\) | 6.52034 | + | 6.52034i | 0.0212389 | + | 0.0212389i | 0.717646 | − | 0.696408i | \(-0.245219\pi\) |
−0.696408 | + | 0.717646i | \(0.745219\pi\) | |||||||
\(308\) | 3.72573 | − | 3.72573i | 0.0120965 | − | 0.0120965i | ||||
\(309\) | 291.252i | 0.942563i | ||||||||
\(310\) | 5.51677 | − | 130.747i | 0.0177960 | − | 0.421764i | ||||
\(311\) | 21.8579 | 0.0702825 | 0.0351412 | − | 0.999382i | \(-0.488812\pi\) | ||||
0.0351412 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(312\) | 31.2290 | + | 31.2290i | 0.100093 | + | 0.100093i | ||||
\(313\) | 329.807 | − | 329.807i | 1.05369 | − | 1.05369i | 0.0552208 | − | 0.998474i | \(-0.482414\pi\) |
0.998474 | − | 0.0552208i | \(-0.0175863\pi\) | |||||||
\(314\) | 269.666i | 0.858809i | ||||||||
\(315\) | −43.8661 | − | 1.85090i | −0.139257 | − | 0.00587587i | ||||
\(316\) | 62.6586 | 0.198287 | ||||||||
\(317\) | −187.213 | − | 187.213i | −0.590579 | − | 0.590579i | 0.347209 | − | 0.937788i | \(-0.387129\pi\) |
−0.937788 | + | 0.347209i | \(0.887129\pi\) | |||||||
\(318\) | 125.079 | − | 125.079i | 0.393329 | − | 0.393329i | ||||
\(319\) | − | 7.01963i | − | 0.0220051i | ||||||
\(320\) | 29.4515 | − | 27.0668i | 0.0920359 | − | 0.0845836i | ||||
\(321\) | 45.4047 | 0.141448 | ||||||||
\(322\) | 14.0374 | + | 14.0374i | 0.0435945 | + | 0.0435945i | ||||
\(323\) | −182.227 | + | 182.227i | −0.564170 | + | 0.564170i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 145.374 | + | 172.223i | 0.447304 | + | 0.529917i | ||||
\(326\) | 285.998 | 0.877293 | ||||||||
\(327\) | 90.4932 | + | 90.4932i | 0.276738 | + | 0.276738i | ||||
\(328\) | 73.3608 | − | 73.3608i | 0.223661 | − | 0.223661i | ||||
\(329\) | − | 111.900i | − | 0.340122i | ||||||
\(330\) | 7.45923 | + | 8.11644i | 0.0226037 | + | 0.0245953i | ||||
\(331\) | −514.692 | −1.55496 | −0.777480 | − | 0.628908i | \(-0.783502\pi\) | ||||
−0.777480 | + | 0.628908i | \(0.783502\pi\) | |||||||
\(332\) | 17.4007 | + | 17.4007i | 0.0524117 | + | 0.0524117i | ||||
\(333\) | −68.5562 | + | 68.5562i | −0.205874 | + | 0.205874i | ||||
\(334\) | 284.444i | 0.851630i | ||||||||
\(335\) | 6.46218 | − | 153.153i | 0.0192901 | − | 0.457173i | ||||
\(336\) | −20.2789 | −0.0603539 | ||||||||
\(337\) | −131.193 | − | 131.193i | −0.389296 | − | 0.389296i | 0.485140 | − | 0.874436i | \(-0.338769\pi\) |
−0.874436 | + | 0.485140i | \(0.838769\pi\) | |||||||
\(338\) | 87.7290 | − | 87.7290i | 0.259553 | − | 0.259553i | ||||
\(339\) | 196.073i | 0.578385i | ||||||||
\(340\) | 261.013 | + | 11.0133i | 0.767687 | + | 0.0323920i | ||||
\(341\) | 16.6573 | 0.0488484 | ||||||||
\(342\) | 29.5937 | + | 29.5937i | 0.0865313 | + | 0.0865313i | ||||
\(343\) | −185.099 | + | 185.099i | −0.539648 | + | 0.539648i | ||||
\(344\) | − | 58.7644i | − | 0.170827i | ||||||
\(345\) | −30.5803 | + | 28.1042i | −0.0886386 | + | 0.0814614i | ||||
\(346\) | −294.279 | −0.850518 | ||||||||
\(347\) | 8.51905 | + | 8.51905i | 0.0245506 | + | 0.0245506i | 0.719276 | − | 0.694725i | \(-0.244474\pi\) |
−0.694725 | + | 0.719276i | \(0.744474\pi\) | |||||||
\(348\) | −19.1037 | + | 19.1037i | −0.0548957 | + | 0.0548957i | ||||
\(349\) | − | 141.333i | − | 0.404965i | −0.979286 | − | 0.202482i | \(-0.935099\pi\) | ||
0.979286 | − | 0.202482i | \(-0.0649009\pi\) | |||||||
\(350\) | −103.117 | − | 8.71746i | −0.294621 | − | 0.0249070i | ||||
\(351\) | 46.8435 | 0.133457 | ||||||||
\(352\) | 3.60025 | + | 3.60025i | 0.0102280 | + | 0.0102280i | ||||
\(353\) | −358.841 | + | 358.841i | −1.01655 | + | 1.01655i | −0.0166867 | + | 0.999861i | \(0.505312\pi\) |
−0.999861 | + | 0.0166867i | \(0.994688\pi\) | |||||||
\(354\) | 224.698i | 0.634741i | ||||||||
\(355\) | 284.574 | + | 309.646i | 0.801616 | + | 0.872243i | ||||
\(356\) | 64.2721 | 0.180540 | ||||||||
\(357\) | −93.6523 | − | 93.6523i | −0.262331 | − | 0.262331i | ||||
\(358\) | 119.989 | − | 119.989i | 0.335164 | − | 0.335164i | ||||
\(359\) | − | 233.537i | − | 0.650520i | −0.945625 | − | 0.325260i | \(-0.894548\pi\) | ||
0.945625 | − | 0.325260i | \(-0.105452\pi\) | |||||||
\(360\) | 1.78856 | − | 42.3887i | 0.00496823 | − | 0.117746i | ||||
\(361\) | 263.690 | 0.730444 | ||||||||
\(362\) | −142.935 | − | 142.935i | −0.394847 | − | 0.394847i | ||||
\(363\) | 147.202 | − | 147.202i | 0.405515 | − | 0.405515i | ||||
\(364\) | − | 52.7742i | − | 0.144984i | ||||||
\(365\) | 544.508 | + | 22.9751i | 1.49180 | + | 0.0629456i | ||||
\(366\) | −109.005 | −0.297828 | ||||||||
\(367\) | −41.8520 | − | 41.8520i | −0.114038 | − | 0.114038i | 0.647785 | − | 0.761823i | \(-0.275696\pi\) |
−0.761823 | + | 0.647785i | \(0.775696\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | − | 110.041i | − | 0.298214i | ||||||
\(370\) | −168.257 | + | 154.633i | −0.454748 | + | 0.417926i | ||||
\(371\) | −211.371 | −0.569734 | ||||||||
\(372\) | −45.3323 | − | 45.3323i | −0.121861 | − | 0.121861i | ||||
\(373\) | 238.065 | − | 238.065i | 0.638243 | − | 0.638243i | −0.311879 | − | 0.950122i | \(-0.600958\pi\) |
0.950122 | + | 0.311879i | \(0.100958\pi\) | |||||||
\(374\) | 33.2534i | 0.0889129i | ||||||||
\(375\) | 27.3168 | − | 214.776i | 0.0728447 | − | 0.572736i | ||||
\(376\) | 108.131 | 0.287583 | ||||||||
\(377\) | −49.7158 | − | 49.7158i | −0.131872 | − | 0.131872i | ||||
\(378\) | −15.2092 | + | 15.2092i | −0.0402359 | + | 0.0402359i | ||||
\(379\) | 253.908i | 0.669941i | 0.942229 | + | 0.334970i | \(0.108726\pi\) | ||||
−0.942229 | + | 0.334970i | \(0.891274\pi\) | |||||||
\(380\) | 66.7505 | + | 72.6316i | 0.175659 | + | 0.191136i | ||||
\(381\) | 67.1779 | 0.176320 | ||||||||
\(382\) | −71.7202 | − | 71.7202i | −0.187749 | − | 0.187749i | ||||
\(383\) | −68.9077 | + | 68.9077i | −0.179916 | + | 0.179916i | −0.791319 | − | 0.611403i | \(-0.790605\pi\) |
0.611403 | + | 0.791319i | \(0.290605\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0.555308 | − | 13.1607i | 0.00144236 | − | 0.0341837i | ||||
\(386\) | −31.3996 | −0.0813462 | ||||||||
\(387\) | −44.0733 | − | 44.0733i | −0.113885 | − | 0.113885i | ||||
\(388\) | 208.475 | − | 208.475i | 0.537307 | − | 0.537307i | ||||
\(389\) | 34.7594i | 0.0893557i | 0.999001 | + | 0.0446778i | \(0.0142261\pi\) | ||||
−0.999001 | + | 0.0446778i | \(0.985774\pi\) | |||||||
\(390\) | 110.313 | + | 4.65459i | 0.282854 | + | 0.0119348i | ||||
\(391\) | −125.289 | −0.320432 | ||||||||
\(392\) | −80.8653 | − | 80.8653i | −0.206289 | − | 0.206289i | ||||
\(393\) | −98.6709 | + | 98.6709i | −0.251071 | + | 0.251071i | ||||
\(394\) | − | 516.750i | − | 1.31155i | ||||||
\(395\) | 115.337 | − | 105.998i | 0.291992 | − | 0.268349i | ||||
\(396\) | 5.40037 | 0.0136373 | ||||||||
\(397\) | −490.772 | − | 490.772i | −1.23620 | − | 1.23620i | −0.961542 | − | 0.274659i | \(-0.911435\pi\) |
−0.274659 | − | 0.961542i | \(-0.588565\pi\) | |||||||
\(398\) | 17.1356 | − | 17.1356i | 0.0430544 | − | 0.0430544i | ||||
\(399\) | − | 50.0107i | − | 0.125340i | ||||||
\(400\) | 8.42387 | − | 99.6446i | 0.0210597 | − | 0.249111i | ||||
\(401\) | −473.229 | −1.18012 | −0.590061 | − | 0.807358i | \(-0.700896\pi\) | ||||
−0.590061 | + | 0.807358i | \(0.700896\pi\) | |||||||
\(402\) | −53.1009 | − | 53.1009i | −0.132092 | − | 0.132092i | ||||
\(403\) | 117.974 | − | 117.974i | 0.292739 | − | 0.292739i | ||||
\(404\) | 124.470i | 0.308094i | ||||||||
\(405\) | −30.4501 | − | 33.1329i | −0.0751854 | − | 0.0818097i | ||||
\(406\) | 32.2835 | 0.0795160 | ||||||||
\(407\) | −20.5683 | − | 20.5683i | −0.0505363 | − | 0.0505363i | ||||
\(408\) | 90.4982 | − | 90.4982i | 0.221809 | − | 0.221809i | ||||
\(409\) | − | 285.348i | − | 0.697671i | −0.937184 | − | 0.348836i | \(-0.886577\pi\) | ||
0.937184 | − | 0.348836i | \(-0.113423\pi\) | |||||||
\(410\) | 10.9342 | − | 259.139i | 0.0266688 | − | 0.632046i | ||||
\(411\) | −134.650 | −0.327614 | ||||||||
\(412\) | 237.806 | + | 237.806i | 0.577200 | + | 0.577200i | ||||
\(413\) | 189.860 | − | 189.860i | 0.459709 | − | 0.459709i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 61.4660 | + | 2.59352i | 0.148111 | + | 0.00624944i | ||||
\(416\) | 50.9968 | 0.122588 | ||||||||
\(417\) | −163.665 | − | 163.665i | −0.392481 | − | 0.392481i | ||||
\(418\) | −8.87873 | + | 8.87873i | −0.0212410 | + | 0.0212410i | ||||
\(419\) | − | 290.087i | − | 0.692331i | −0.938173 | − | 0.346165i | \(-0.887484\pi\) | ||
0.938173 | − | 0.346165i | \(-0.112516\pi\) | |||||||
\(420\) | −37.3277 | + | 34.3052i | −0.0888756 | + | 0.0816791i | ||||
\(421\) | −442.922 | −1.05207 | −0.526035 | − | 0.850463i | \(-0.676322\pi\) | ||||
−0.526035 | + | 0.850463i | \(0.676322\pi\) | |||||||
\(422\) | 87.8965 | + | 87.8965i | 0.208286 | + | 0.208286i | ||||
\(423\) | 81.0985 | − | 81.0985i | 0.191722 | − | 0.191722i | ||||
\(424\) | − | 204.252i | − | 0.481728i | ||||||
\(425\) | 499.083 | − | 421.277i | 1.17431 | − | 0.991240i | ||||
\(426\) | 206.027 | 0.483631 | ||||||||
\(427\) | 92.1044 | + | 92.1044i | 0.215701 | + | 0.215701i | ||||
\(428\) | 37.0728 | − | 37.0728i | 0.0866187 | − | 0.0866187i | ||||
\(429\) | 14.0540i | 0.0327600i | ||||||||
\(430\) | −99.4102 | − | 108.169i | −0.231186 | − | 0.251555i | ||||
\(431\) | 377.479 | 0.875821 | 0.437910 | − | 0.899019i | \(-0.355719\pi\) | ||||
0.437910 | + | 0.899019i | \(0.355719\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −567.756 | + | 567.756i | −1.31121 | + | 1.31121i | −0.390695 | + | 0.920520i | \(0.627765\pi\) |
−0.920520 | + | 0.390695i | \(0.872235\pi\) | |||||||
\(434\) | 76.6074i | 0.176515i | ||||||||
\(435\) | −2.84735 | + | 67.4818i | −0.00654562 | + | 0.155130i | ||||
\(436\) | 147.775 | 0.338933 | ||||||||
\(437\) | −33.4524 | − | 33.4524i | −0.0765501 | − | 0.0765501i | ||||
\(438\) | 188.791 | − | 188.791i | 0.431030 | − | 0.431030i | ||||
\(439\) | 295.256i | 0.672564i | 0.941761 | + | 0.336282i | \(0.109170\pi\) | ||||
−0.941761 | + | 0.336282i | \(0.890830\pi\) | |||||||
\(440\) | 12.7175 | + | 0.536606i | 0.0289034 | + | 0.00121956i | ||||
\(441\) | −121.298 | −0.275052 | ||||||||
\(442\) | 235.514 | + | 235.514i | 0.532837 | + | 0.532837i | ||||
\(443\) | 419.157 | − | 419.157i | 0.946179 | − | 0.946179i | −0.0524451 | − | 0.998624i | \(-0.516701\pi\) |
0.998624 | + | 0.0524451i | \(0.0167014\pi\) | |||||||
\(444\) | 111.952i | 0.252144i | ||||||||
\(445\) | 118.307 | − | 108.727i | 0.265858 | − | 0.244331i | ||||
\(446\) | 317.306 | 0.711447 | ||||||||
\(447\) | −237.449 | − | 237.449i | −0.531206 | − | 0.531206i | ||||
\(448\) | −16.5576 | + | 16.5576i | −0.0369590 | + | 0.0369590i | ||||
\(449\) | − | 646.254i | − | 1.43932i | −0.694328 | − | 0.719659i | \(-0.744298\pi\) | ||
0.694328 | − | 0.719659i | \(-0.255702\pi\) | |||||||
\(450\) | −68.4155 | − | 81.0513i | −0.152034 | − | 0.180114i | ||||
\(451\) | 33.0146 | 0.0732031 | ||||||||
\(452\) | 160.093 | + | 160.093i | 0.354187 | + | 0.354187i | ||||
\(453\) | −259.416 | + | 259.416i | −0.572661 | + | 0.572661i | ||||
\(454\) | − | 352.999i | − | 0.777531i | ||||||
\(455\) | −89.2766 | − | 97.1424i | −0.196212 | − | 0.213500i | ||||
\(456\) | 48.3263 | 0.105979 | ||||||||
\(457\) | 117.758 | + | 117.758i | 0.257677 | + | 0.257677i | 0.824109 | − | 0.566432i | \(-0.191677\pi\) |
−0.566432 | + | 0.824109i | \(0.691677\pi\) | |||||||
\(458\) | −140.584 | + | 140.584i | −0.306951 | + | 0.306951i | ||||
\(459\) | − | 135.747i | − | 0.295746i | ||||||
\(460\) | −2.02177 | + | 47.9157i | −0.00439515 | + | 0.104165i | ||||
\(461\) | 638.280 | 1.38456 | 0.692278 | − | 0.721631i | \(-0.256607\pi\) | ||||
0.692278 | + | 0.721631i | \(0.256607\pi\) | |||||||
\(462\) | −4.56306 | − | 4.56306i | −0.00987676 | − | 0.00987676i | ||||
\(463\) | 243.006 | − | 243.006i | 0.524851 | − | 0.524851i | −0.394182 | − | 0.919033i | \(-0.628972\pi\) |
0.919033 | + | 0.394182i | \(0.128972\pi\) | |||||||
\(464\) | 31.1962i | 0.0672332i | ||||||||
\(465\) | −160.131 | − | 6.75664i | −0.344369 | − | 0.0145304i | ||||
\(466\) | −46.8103 | −0.100451 | ||||||||
\(467\) | −180.259 | − | 180.259i | −0.385994 | − | 0.385994i | 0.487262 | − | 0.873256i | \(-0.337996\pi\) |
−0.873256 | + | 0.487262i | \(0.837996\pi\) | |||||||
\(468\) | 38.2476 | − | 38.2476i | 0.0817256 | − | 0.0817256i | ||||
\(469\) | 89.7356i | 0.191334i | ||||||||
\(470\) | 199.039 | − | 182.923i | 0.423488 | − | 0.389197i | ||||
\(471\) | 330.272 | 0.701214 | ||||||||
\(472\) | 183.465 | + | 183.465i | 0.388698 | + | 0.388698i | ||||
\(473\) | 13.2229 | − | 13.2229i | 0.0279554 | − | 0.0279554i | ||||
\(474\) | − | 76.7409i | − | 0.161901i | ||||||
\(475\) | 245.738 | + | 20.7745i | 0.517343 | + | 0.0437357i | ||||
\(476\) | −152.934 | −0.321289 | ||||||||
\(477\) | −153.189 | − | 153.189i | −0.321152 | − | 0.321152i | ||||
\(478\) | −158.063 | + | 158.063i | −0.330675 | + | 0.330675i | ||||
\(479\) | 521.944i | 1.08965i | 0.838549 | + | 0.544827i | \(0.183405\pi\) | ||||
−0.838549 | + | 0.544827i | \(0.816595\pi\) | |||||||
\(480\) | −33.1499 | − | 36.0706i | −0.0690622 | − | 0.0751470i | ||||
\(481\) | −291.345 | −0.605708 | ||||||||
\(482\) | −148.164 | − | 148.164i | −0.307393 | − | 0.307393i | ||||
\(483\) | 17.1923 | − | 17.1923i | 0.0355948 | − | 0.0355948i | ||||
\(484\) | − | 240.380i | − | 0.496652i | ||||||
\(485\) | 31.0726 | − | 736.416i | 0.0640672 | − | 1.51838i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −173.549 | − | 173.549i | −0.356364 | − | 0.356364i | 0.506107 | − | 0.862471i | \(-0.331084\pi\) |
−0.862471 | + | 0.506107i | \(0.831084\pi\) | |||||||
\(488\) | −89.0024 | + | 89.0024i | −0.182382 | + | 0.182382i | ||||
\(489\) | − | 350.274i | − | 0.716307i | ||||||
\(490\) | −285.648 | − | 12.0527i | −0.582955 | − | 0.0245974i | ||||
\(491\) | −261.292 | −0.532164 | −0.266082 | − | 0.963950i | \(-0.585729\pi\) | ||||
−0.266082 | + | 0.963950i | \(0.585729\pi\) | |||||||
\(492\) | −89.8482 | − | 89.8482i | −0.182618 | − | 0.182618i | ||||
\(493\) | −144.071 | + | 144.071i | −0.292233 | + | 0.292233i | ||||
\(494\) | 125.765i | 0.254586i | ||||||||
\(495\) | 9.94057 | − | 9.13566i | 0.0200820 | − | 0.0184559i | ||||
\(496\) | −74.0274 | −0.149249 | ||||||||
\(497\) | −174.083 | − | 174.083i | −0.350268 | − | 0.350268i | ||||
\(498\) | 21.3114 | − | 21.3114i | 0.0427940 | − | 0.0427940i | ||||
\(499\) | − | 391.452i | − | 0.784473i | −0.919864 | − | 0.392237i | \(-0.871701\pi\) | ||
0.919864 | − | 0.392237i | \(-0.128299\pi\) | |||||||
\(500\) | −153.060 | − | 197.668i | −0.306120 | − | 0.395336i | ||||
\(501\) | 348.372 | 0.695353 | ||||||||
\(502\) | 222.580 | + | 222.580i | 0.443386 | + | 0.443386i | ||||
\(503\) | −451.156 | + | 451.156i | −0.896930 | + | 0.896930i | −0.995163 | − | 0.0982331i | \(-0.968681\pi\) |
0.0982331 | + | 0.995163i | \(0.468681\pi\) | |||||||
\(504\) | 24.8365i | 0.0492787i | ||||||||
\(505\) | 210.562 | + | 229.114i | 0.416955 | + | 0.453691i | ||||
\(506\) | −6.10452 | −0.0120643 | ||||||||
\(507\) | −107.446 | − | 107.446i | −0.211924 | − | 0.211924i | ||||
\(508\) | 54.8505 | − | 54.8505i | 0.107973 | − | 0.107973i | ||||
\(509\) | − | 15.5183i | − | 0.0304878i | −0.999884 | − | 0.0152439i | \(-0.995148\pi\) | ||
0.999884 | − | 0.0152439i | \(-0.00485247\pi\) | |||||||
\(510\) | 13.4885 | − | 319.675i | 0.0264480 | − | 0.626814i | ||||
\(511\) | −319.039 | −0.624343 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 36.2448 | − | 36.2448i | 0.0706526 | − | 0.0706526i | ||||
\(514\) | 562.593i | 1.09454i | ||||||||
\(515\) | 840.024 | + | 35.4443i | 1.63112 | + | 0.0688238i | ||||
\(516\) | −71.9714 | −0.139480 | ||||||||
\(517\) | 24.3312 | + | 24.3312i | 0.0470623 | + | 0.0470623i | ||||
\(518\) | 94.5941 | − | 94.5941i | 0.182614 | − | 0.182614i | ||||
\(519\) | 360.417i | 0.694445i | ||||||||
\(520\) | 93.8707 | − | 86.2698i | 0.180521 | − | 0.165904i | ||||
\(521\) | −573.680 | −1.10111 | −0.550556 | − | 0.834798i | \(-0.685584\pi\) | ||||
−0.550556 | + | 0.834798i | \(0.685584\pi\) | |||||||
\(522\) | 23.3972 | + | 23.3972i | 0.0448222 | + | 0.0448222i | ||||
\(523\) | 159.178 | − | 159.178i | 0.304356 | − | 0.304356i | −0.538359 | − | 0.842715i | \(-0.680956\pi\) |
0.842715 | + | 0.538359i | \(0.180956\pi\) | |||||||
\(524\) | 161.129i | 0.307498i | ||||||||
\(525\) | −10.6767 | + | 126.293i | −0.0203365 | + | 0.240557i | ||||
\(526\) | 355.257 | 0.675394 | ||||||||
\(527\) | −341.874 | − | 341.874i | −0.648718 | − | 0.648718i | ||||
\(528\) | 4.40938 | − | 4.40938i | 0.00835111 | − | 0.00835111i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −345.528 | − | 375.971i | −0.651940 | − | 0.709380i | ||||
\(531\) | 275.198 | 0.518264 | ||||||||
\(532\) | −40.8335 | − | 40.8335i | −0.0767548 | − | 0.0767548i | ||||
\(533\) | 233.823 | − | 233.823i | 0.438692 | − | 0.438692i | ||||
\(534\) | − | 78.7170i | − | 0.147410i | ||||||
\(535\) | 5.52559 | − | 130.956i | 0.0103282 | − | 0.244777i | ||||
\(536\) | −86.7134 | −0.161779 | ||||||||
\(537\) | −146.955 | − | 146.955i | −0.273660 | − | 0.273660i | ||||
\(538\) | 93.2801 | − | 93.2801i | 0.173383 | − | 0.173383i | ||||
\(539\) | − | 36.3919i | − | 0.0675174i | ||||||
\(540\) | −51.9153 | − | 2.19053i | −0.0961395 | − | 0.00405654i | ||||
\(541\) | 19.0291 | 0.0351740 | 0.0175870 | − | 0.999845i | \(-0.494402\pi\) | ||||
0.0175870 | + | 0.999845i | \(0.494402\pi\) | |||||||
\(542\) | 351.552 | + | 351.552i | 0.648620 | + | 0.648620i | ||||
\(543\) | −175.059 | + | 175.059i | −0.322392 | + | 0.322392i | ||||
\(544\) | − | 147.783i | − | 0.271660i | ||||||
\(545\) | 272.012 | − | 249.986i | 0.499104 | − | 0.458691i | ||||
\(546\) | −64.6349 | −0.118379 | ||||||||
\(547\) | −18.2605 | − | 18.2605i | −0.0333830 | − | 0.0333830i | 0.690218 | − | 0.723601i | \(-0.257515\pi\) |
−0.723601 | + | 0.690218i | \(0.757515\pi\) | |||||||
\(548\) | −109.941 | + | 109.941i | −0.200622 | + | 0.200622i | ||||
\(549\) | 133.504i | 0.243176i | ||||||||
\(550\) | 24.3171 | − | 20.5261i | 0.0442129 | − | 0.0373201i | ||||
\(551\) | −76.9344 | −0.139627 | ||||||||
\(552\) | 16.6132 | + | 16.6132i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | −64.8425 | + | 64.8425i | −0.117256 | + | 0.117256i | ||||
\(554\) | 423.975i | 0.765297i | ||||||||
\(555\) | 189.386 | + | 206.072i | 0.341236 | + | 0.371301i | ||||
\(556\) | −267.263 | −0.480690 | ||||||||
\(557\) | 602.059 | + | 602.059i | 1.08090 | + | 1.08090i | 0.996426 | + | 0.0844703i | \(0.0269198\pi\) |
0.0844703 | + | 0.996426i | \(0.473080\pi\) | |||||||
\(558\) | −55.5205 | + | 55.5205i | −0.0994991 | + | 0.0994991i | ||||
\(559\) | − | 187.300i | − | 0.335062i | ||||||
\(560\) | −2.46787 | + | 58.4881i | −0.00440690 | + | 0.104443i | ||||
\(561\) | 40.7270 | 0.0725971 | ||||||||
\(562\) | 135.367 | + | 135.367i | 0.240866 | + | 0.240866i | ||||
\(563\) | −208.664 | + | 208.664i | −0.370628 | + | 0.370628i | −0.867706 | − | 0.497078i | \(-0.834406\pi\) |
0.497078 | + | 0.867706i | \(0.334406\pi\) | |||||||
\(564\) | − | 132.433i | − | 0.234811i | ||||||
\(565\) | 565.510 | + | 23.8613i | 1.00090 | + | 0.0422324i | ||||
\(566\) | −214.315 | −0.378648 | ||||||||
\(567\) | 18.6274 | + | 18.6274i | 0.0328525 | + | 0.0328525i | ||||
\(568\) | 168.220 | − | 168.220i | 0.296162 | − | 0.296162i | ||||
\(569\) | − | 375.263i | − | 0.659513i | −0.944066 | − | 0.329756i | \(-0.893033\pi\) | ||
0.944066 | − | 0.329756i | \(-0.106967\pi\) | |||||||
\(570\) | 88.9552 | − | 81.7523i | 0.156062 | − | 0.143425i | ||||
\(571\) | 999.501 | 1.75044 | 0.875219 | − | 0.483726i | \(-0.160717\pi\) | ||||
0.875219 | + | 0.483726i | \(0.160717\pi\) | |||||||
\(572\) | 11.4751 | + | 11.4751i | 0.0200613 | + | 0.0200613i | ||||
\(573\) | −87.8390 | + | 87.8390i | −0.153297 | + | 0.153297i | ||||
\(574\) | 151.835i | 0.264521i | ||||||||
\(575\) | 77.3361 | + | 91.6195i | 0.134498 | + | 0.159338i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 503.643 | + | 503.643i | 0.872866 | + | 0.872866i | 0.992784 | − | 0.119918i | \(-0.0382632\pi\) |
−0.119918 | + | 0.992784i | \(0.538263\pi\) | |||||||
\(578\) | 393.493 | − | 393.493i | 0.680784 | − | 0.680784i | ||||
\(579\) | 38.4566i | 0.0664189i | ||||||||
\(580\) | 52.7738 | + | 57.4235i | 0.0909893 | + | 0.0990060i | ||||
\(581\) | −36.0143 | −0.0619867 | ||||||||
\(582\) | −255.329 | − | 255.329i | −0.438709 | − | 0.438709i | ||||
\(583\) | 45.9600 | − | 45.9600i | 0.0788336 | − | 0.0788336i | ||||
\(584\) | − | 308.294i | − | 0.527901i | ||||||
\(585\) | 5.70068 | − | 135.105i | 0.00974475 | − | 0.230949i | ||||
\(586\) | 260.008 | 0.443700 | ||||||||
\(587\) | 422.350 | + | 422.350i | 0.719506 | + | 0.719506i | 0.968504 | − | 0.248998i | \(-0.0801013\pi\) |
−0.248998 | + | 0.968504i | \(0.580101\pi\) | |||||||
\(588\) | −99.0393 | + | 99.0393i | −0.168434 | + | 0.168434i | ||||
\(589\) | − | 182.562i | − | 0.309953i | ||||||
\(590\) | 648.071 | + | 27.3449i | 1.09843 | + | 0.0463473i | ||||
\(591\) | −632.887 | −1.07087 | ||||||||
\(592\) | 91.4083 | + | 91.4083i | 0.154406 | + | 0.154406i | ||||
\(593\) | −228.691 | + | 228.691i | −0.385651 | + | 0.385651i | −0.873133 | − | 0.487482i | \(-0.837916\pi\) |
0.487482 | + | 0.873133i | \(0.337916\pi\) | |||||||
\(594\) | − | 6.61408i | − | 0.0111348i | ||||||
\(595\) | −281.508 | + | 258.713i | −0.473122 | + | 0.434812i | ||||
\(596\) | −387.752 | −0.650591 | ||||||||
\(597\) | −20.9868 | − | 20.9868i | −0.0351537 | − | 0.0351537i | ||||
\(598\) | −43.2346 | + | 43.2346i | −0.0722987 | + | 0.0722987i | ||||
\(599\) | − | 277.402i | − | 0.463108i | −0.972822 | − | 0.231554i | \(-0.925619\pi\) | ||
0.972822 | − | 0.231554i | \(-0.0743811\pi\) | |||||||
\(600\) | −122.039 | − | 10.3171i | −0.203399 | − | 0.0171951i | ||||
\(601\) | −535.528 | −0.891062 | −0.445531 | − | 0.895266i | \(-0.646985\pi\) | ||||
−0.445531 | + | 0.895266i | \(0.646985\pi\) | |||||||
\(602\) | 60.8126 | + | 60.8126i | 0.101018 | + | 0.101018i | ||||
\(603\) | −65.0351 | + | 65.0351i | −0.107852 | + | 0.107852i | ||||
\(604\) | 423.624i | 0.701364i | ||||||||
\(605\) | −406.644 | − | 442.472i | −0.672138 | − | 0.731358i | ||||
\(606\) | 152.444 | 0.251557 | ||||||||
\(607\) | 689.127 | + | 689.127i | 1.13530 | + | 1.13530i | 0.989282 | + | 0.146018i | \(0.0466458\pi\) |
0.146018 | + | 0.989282i | \(0.453354\pi\) | |||||||
\(608\) | 39.4583 | − | 39.4583i | 0.0648985 | − | 0.0648985i | ||||
\(609\) | − | 39.5391i | − | 0.0649245i | ||||||
\(610\) | −13.2655 | + | 314.391i | −0.0217468 | + | 0.515395i | ||||
\(611\) | 344.647 | 0.564070 | ||||||||
\(612\) | −110.837 | − | 110.837i | −0.181106 | − | 0.181106i | ||||
\(613\) | 212.580 | − | 212.580i | 0.346787 | − | 0.346787i | −0.512124 | − | 0.858911i | \(-0.671141\pi\) |
0.858911 | + | 0.512124i | \(0.171141\pi\) | |||||||
\(614\) | − | 13.0407i | − | 0.0212389i | ||||||
\(615\) | −317.379 | − | 13.3916i | −0.516063 | − | 0.0217749i | ||||
\(616\) | −7.45145 | −0.0120965 | ||||||||
\(617\) | 743.093 | + | 743.093i | 1.20437 | + | 1.20437i | 0.972825 | + | 0.231540i | \(0.0743763\pi\) |
0.231540 | + | 0.972825i | \(0.425624\pi\) | |||||||
\(618\) | 291.252 | − | 291.252i | 0.471281 | − | 0.471281i | ||||
\(619\) | 837.046i | 1.35225i | 0.736785 | + | 0.676127i | \(0.236343\pi\) | ||||
−0.736785 | + | 0.676127i | \(0.763657\pi\) | |||||||
\(620\) | −136.264 | + | 125.230i | −0.219780 | + | 0.201984i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | −21.8579 | − | 21.8579i | −0.0351412 | − | 0.0351412i | ||||
\(623\) | −66.5122 | + | 66.5122i | −0.106761 | + | 0.106761i | ||||
\(624\) | − | 62.4580i | − | 0.100093i | ||||||
\(625\) | −616.130 | − | 104.924i | −0.985808 | − | 0.167879i | ||||
\(626\) | −659.613 | −1.05369 | ||||||||
\(627\) | 10.8742 | + | 10.8742i | 0.0173432 | + | 0.0173432i | ||||
\(628\) | 269.666 | − | 269.666i | 0.429404 | − | 0.429404i | ||||
\(629\) | 844.286i | 1.34227i | ||||||||
\(630\) | 42.0152 | + | 45.7170i | 0.0666907 | + | 0.0725666i | ||||
\(631\) | 455.081 | 0.721206 | 0.360603 | − | 0.932719i | \(-0.382571\pi\) | ||||
0.360603 | + | 0.932719i | \(0.382571\pi\) | |||||||
\(632\) | −62.6586 | − | 62.6586i | −0.0991434 | − | 0.0991434i | ||||
\(633\) | 107.651 | − | 107.651i | 0.170064 | − | 0.170064i | ||||
\(634\) | 374.427i | 0.590579i | ||||||||
\(635\) | 8.17530 | − | 193.754i | 0.0128745 | − | 0.305124i | ||||
\(636\) | −250.157 | −0.393329 | ||||||||
\(637\) | −257.742 | − | 257.742i | −0.404618 | − | 0.404618i | ||||
\(638\) | −7.01963 | + | 7.01963i | −0.0110026 | + | 0.0110026i | ||||
\(639\) | − | 252.330i | − | 0.394883i | ||||||
\(640\) | −56.5183 | − | 2.38475i | −0.0883098 | − | 0.00372617i | ||||
\(641\) | 295.317 | 0.460713 | 0.230357 | − | 0.973106i | \(-0.426011\pi\) | ||||
0.230357 | + | 0.973106i | \(0.426011\pi\) | |||||||
\(642\) | −45.4047 | − | 45.4047i | −0.0707239 | − | 0.0707239i | ||||
\(643\) | 5.55950 | − | 5.55950i | 0.00864619 | − | 0.00864619i | −0.702770 | − | 0.711417i | \(-0.748054\pi\) |
0.711417 | + | 0.702770i | \(0.248054\pi\) | |||||||
\(644\) | − | 28.0749i | − | 0.0435945i | ||||||
\(645\) | −132.479 | + | 121.752i | −0.205394 | + | 0.188763i | ||||
\(646\) | 364.454 | 0.564170 | ||||||||
\(647\) | 220.812 | + | 220.812i | 0.341286 | + | 0.341286i | 0.856851 | − | 0.515565i | \(-0.172418\pi\) |
−0.515565 | + | 0.856851i | \(0.672418\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 82.5651i | 0.127219i | ||||||||
\(650\) | 26.8494 | − | 317.597i | 0.0413067 | − | 0.488611i | ||||
\(651\) | 93.8246 | 0.144124 | ||||||||
\(652\) | −285.998 | − | 285.998i | −0.438647 | − | 0.438647i | ||||
\(653\) | −643.901 | + | 643.901i | −0.986065 | + | 0.986065i | −0.999904 | − | 0.0138390i | \(-0.995595\pi\) |
0.0138390 | + | 0.999904i | \(0.495595\pi\) | |||||||
\(654\) | − | 180.986i | − | 0.276738i | ||||||
\(655\) | 272.577 | + | 296.593i | 0.416149 | + | 0.452814i | ||||
\(656\) | −146.722 | −0.223661 | ||||||||
\(657\) | −231.221 | − | 231.221i | −0.351934 | − | 0.351934i | ||||
\(658\) | −111.900 | + | 111.900i | −0.170061 | + | 0.170061i | ||||
\(659\) | − | 576.226i | − | 0.874395i | −0.899366 | − | 0.437198i | \(-0.855971\pi\) | ||
0.899366 | − | 0.437198i | \(-0.144029\pi\) | |||||||
\(660\) | 0.657205 | − | 15.5757i | 0.000995765 | − | 0.0235995i | ||||
\(661\) | −82.0390 | −0.124113 | −0.0620567 | − | 0.998073i | \(-0.519766\pi\) | ||||
−0.0620567 | + | 0.998073i | \(0.519766\pi\) | |||||||
\(662\) | 514.692 | + | 514.692i | 0.777480 | + | 0.777480i | ||||
\(663\) | 288.445 | − | 288.445i | 0.435060 | − | 0.435060i | ||||
\(664\) | − | 34.8014i | − | 0.0524117i | ||||||
\(665\) | −144.240 | − | 6.08611i | −0.216902 | − | 0.00915204i | ||||
\(666\) | 137.112 | 0.205874 | ||||||||
\(667\) | −26.4479 | − | 26.4479i | −0.0396520 | − | 0.0396520i | ||||
\(668\) | 284.444 | − | 284.444i | 0.425815 | − | 0.425815i | ||||
\(669\) | − | 388.618i | − | 0.580894i | ||||||
\(670\) | −159.615 | + | 146.691i | −0.238231 | + | 0.218941i | ||||
\(671\) | −40.0538 | −0.0596927 | ||||||||
\(672\) | 20.2789 | + | 20.2789i | 0.0301769 | + | 0.0301769i | ||||
\(673\) | −187.726 | + | 187.726i | −0.278939 | + | 0.278939i | −0.832685 | − | 0.553747i | \(-0.813198\pi\) |
0.553747 | + | 0.832685i | \(0.313198\pi\) | |||||||
\(674\) | 262.385i | 0.389296i | ||||||||
\(675\) | −99.2672 | + | 83.7916i | −0.147063 | + | 0.124136i | ||||
\(676\) | −175.458 | −0.259553 | ||||||||
\(677\) | −155.129 | − | 155.129i | −0.229142 | − | 0.229142i | 0.583192 | − | 0.812334i | \(-0.301803\pi\) |
−0.812334 | + | 0.583192i | \(0.801803\pi\) | |||||||
\(678\) | 196.073 | − | 196.073i | 0.289193 | − | 0.289193i | ||||
\(679\) | 431.482i | 0.635467i | ||||||||
\(680\) | −250.000 | − | 272.027i | −0.367647 | − | 0.400039i | ||||
\(681\) | −432.334 | −0.634852 | ||||||||
\(682\) | −16.6573 | − | 16.6573i | −0.0244242 | − | 0.0244242i | ||||
\(683\) | −574.764 | + | 574.764i | −0.841529 | + | 0.841529i | −0.989058 | − | 0.147529i | \(-0.952868\pi\) |
0.147529 | + | 0.989058i | \(0.452868\pi\) | |||||||
\(684\) | − | 59.1874i | − | 0.0865313i | ||||||
\(685\) | −16.3863 | + | 388.354i | −0.0239217 | + | 0.566940i | ||||
\(686\) | 370.199 | 0.539648 | ||||||||
\(687\) | 172.179 | + | 172.179i | 0.250625 | + | 0.250625i | ||||
\(688\) | −58.7644 | + | 58.7644i | −0.0854134 | + | 0.0854134i | ||||
\(689\) | − | 651.014i | − | 0.944868i | ||||||
\(690\) | 58.6845 | + | 2.47615i | 0.0850500 | + | 0.00358863i | ||||
\(691\) | −806.478 | −1.16712 | −0.583559 | − | 0.812071i | \(-0.698340\pi\) | ||||
−0.583559 | + | 0.812071i | \(0.698340\pi\) | |||||||
\(692\) | 294.279 | + | 294.279i | 0.425259 | + | 0.425259i | ||||
\(693\) | −5.58859 | + | 5.58859i | −0.00806434 | + | 0.00806434i | ||||
\(694\) | − | 17.0381i | − | 0.0245506i | ||||||
\(695\) | −491.957 | + | 452.122i | −0.707851 | + | 0.650535i | ||||
\(696\) | 38.2074 | 0.0548957 | ||||||||
\(697\) | −677.592 | − | 677.592i | −0.972154 | − | 0.972154i | ||||
\(698\) | −141.333 | + | 141.333i | −0.202482 | + | 0.202482i | ||||
\(699\) | 57.3307i | 0.0820182i | ||||||||
\(700\) | 94.4000 | + | 111.835i | 0.134857 | + | 0.159764i | ||||
\(701\) | 909.201 | 1.29701 | 0.648503 | − | 0.761212i | \(-0.275395\pi\) | ||||
0.648503 | + | 0.761212i | \(0.275395\pi\) | |||||||
\(702\) | −46.8435 | − | 46.8435i | −0.0667287 | − | 0.0667287i | ||||
\(703\) | −225.426 | + | 225.426i | −0.320663 | + | 0.320663i | ||||
\(704\) | − | 7.20050i | − | 0.0102280i | ||||||
\(705\) | −224.034 | − | 243.772i | −0.317778 | − | 0.345776i | ||||
\(706\) | 717.683 | 1.01655 | ||||||||
\(707\) | −128.808 | − | 128.808i | −0.182189 | − | 0.182189i | ||||
\(708\) | 224.698 | − | 224.698i | 0.317370 | − | 0.317370i | ||||
\(709\) | 425.987i | 0.600827i | 0.953809 | + | 0.300414i | \(0.0971248\pi\) | ||||
−0.953809 | + | 0.300414i | \(0.902875\pi\) | |||||||
\(710\) | 25.0727 | − | 594.220i | 0.0353137 | − | 0.836929i | ||||
\(711\) | −93.9880 | −0.132191 | ||||||||
\(712\) | −64.2721 | − | 64.2721i | −0.0902699 | − | 0.0902699i | ||||
\(713\) | 62.7598 | − | 62.7598i | 0.0880221 | − | 0.0880221i | ||||
\(714\) | 187.305i | 0.262331i | ||||||||
\(715\) | 40.5344 | + | 1.71032i | 0.0566915 | + | 0.00239206i | ||||
\(716\) | −239.977 | −0.335164 | ||||||||
\(717\) | 193.586 | + | 193.586i | 0.269995 | + | 0.269995i | ||||
\(718\) | −233.537 | + | 233.537i | −0.325260 | + | 0.325260i | ||||
\(719\) | − | 1319.34i | − | 1.83497i | −0.397776 | − | 0.917483i | \(-0.630218\pi\) | ||
0.397776 | − | 0.917483i | \(-0.369782\pi\) | |||||||
\(720\) | −44.1773 | + | 40.6001i | −0.0613573 | + | 0.0563891i | ||||
\(721\) | −492.189 | −0.682648 | ||||||||
\(722\) | −263.690 | − | 263.690i | −0.365222 | − | 0.365222i | ||||
\(723\) | −181.463 | + | 181.463i | −0.250985 | + | 0.250985i | ||||
\(724\) | 285.870i | 0.394847i | ||||||||
\(725\) | 194.283 | + | 16.4246i | 0.267977 | + | 0.0226546i | ||||
\(726\) | −294.404 | −0.405515 | ||||||||
\(727\) | 951.508 | + | 951.508i | 1.30881 | + | 1.30881i | 0.922271 | + | 0.386544i | \(0.126331\pi\) |
0.386544 | + | 0.922271i | \(0.373669\pi\) | |||||||
\(728\) | −52.7742 | + | 52.7742i | −0.0724920 | + | 0.0724920i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −521.533 | − | 567.483i | −0.714429 | − | 0.777374i | ||||
\(731\) | −542.774 | −0.742508 | ||||||||
\(732\) | 109.005 | + | 109.005i | 0.148914 | + | 0.148914i | ||||
\(733\) | 191.910 | − | 191.910i | 0.261814 | − | 0.261814i | −0.563977 | − | 0.825791i | \(-0.690729\pi\) |
0.825791 | + | 0.563977i | \(0.190729\pi\) | |||||||
\(734\) | 83.7040i | 0.114038i | ||||||||
\(735\) | −14.7615 | + | 349.846i | −0.0200837 | + | 0.475980i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −19.5119 | − | 19.5119i | −0.0264747 | − | 0.0264747i | ||||
\(738\) | −110.041 | + | 110.041i | −0.149107 | + | 0.149107i | ||||
\(739\) | 673.498i | 0.911363i | 0.890143 | + | 0.455682i | \(0.150604\pi\) | ||||
−0.890143 | + | 0.455682i | \(0.849396\pi\) | |||||||
\(740\) | 322.890 | + | 13.6241i | 0.436337 | + | 0.0184110i | ||||
\(741\) | 154.030 | 0.207868 | ||||||||
\(742\) | 211.371 | + | 211.371i | 0.284867 | + | 0.284867i | ||||
\(743\) | 122.642 | − | 122.642i | 0.165063 | − | 0.165063i | −0.619743 | − | 0.784805i | \(-0.712763\pi\) |
0.784805 | + | 0.619743i | \(0.212763\pi\) | |||||||
\(744\) | 90.6646i | 0.121861i | ||||||||
\(745\) | −713.743 | + | 655.950i | −0.958044 | + | 0.880470i | ||||
\(746\) | −476.129 | −0.638243 | ||||||||
\(747\) | −26.1010 | − | 26.1010i | −0.0349411 | − | 0.0349411i | ||||
\(748\) | 33.2534 | − | 33.2534i | 0.0444565 | − | 0.0444565i | ||||
\(749\) | 76.7298i | 0.102443i | ||||||||
\(750\) | −242.093 | + | 187.459i | −0.322791 | + | 0.249946i | ||||
\(751\) | 532.663 | 0.709272 | 0.354636 | − | 0.935005i | \(-0.384605\pi\) | ||||
0.354636 | + | 0.935005i | \(0.384605\pi\) | |||||||
\(752\) | −108.131 | − | 108.131i | −0.143792 | − | 0.143792i | ||||
\(753\) | 272.603 | − | 272.603i | 0.362023 | − | 0.362023i | ||||
\(754\) | 99.4317i | 0.131872i | ||||||||
\(755\) | 716.633 | + | 779.773i | 0.949182 | + | 1.03281i | ||||
\(756\) | 30.4183 | 0.0402359 | ||||||||
\(757\) | −786.166 | − | 786.166i | −1.03853 | − | 1.03853i | −0.999227 | − | 0.0393009i | \(-0.987487\pi\) |
−0.0393009 | − | 0.999227i | \(-0.512513\pi\) | |||||||
\(758\) | 253.908 | − | 253.908i | 0.334970 | − | 0.334970i | ||||
\(759\) | 7.47648i | 0.00985043i | ||||||||
\(760\) | 5.88113 | − | 139.382i | 0.00773833 | − | 0.183398i | ||||
\(761\) | 54.7150 | 0.0718989 | 0.0359494 | − | 0.999354i | \(-0.488554\pi\) | ||||
0.0359494 | + | 0.999354i | \(0.488554\pi\) | |||||||
\(762\) | −67.1779 | − | 67.1779i | −0.0881600 | − | 0.0881600i | ||||
\(763\) | −152.925 | + | 152.925i | −0.200426 | + | 0.200426i | ||||
\(764\) | 143.440i | 0.187749i | ||||||||
\(765\) | −391.520 | − | 16.5199i | −0.511791 | − | 0.0215947i | ||||
\(766\) | 137.815 | 0.179916 | ||||||||
\(767\) | 584.759 | + | 584.759i | 0.762397 | + | 0.762397i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 4.86567i | 0.00632727i | 0.999995 | + | 0.00316363i | \(0.00100702\pi\) | ||||
−0.999995 | + | 0.00316363i | \(0.998993\pi\) | |||||||
\(770\) | −13.7160 | + | 12.6054i | −0.0178130 | + | 0.0163707i | ||||
\(771\) | 689.033 | 0.893688 | ||||||||
\(772\) | 31.3996 | + | 31.3996i | 0.0406731 | + | 0.0406731i | ||||
\(773\) | −764.339 | + | 764.339i | −0.988795 | + | 0.988795i | −0.999938 | − | 0.0111426i | \(-0.996453\pi\) |
0.0111426 | + | 0.999938i | \(0.496453\pi\) | |||||||
\(774\) | 88.1467i | 0.113885i | ||||||||
\(775\) | −38.9748 | + | 461.027i | −0.0502901 | + | 0.594873i | ||||
\(776\) | −416.950 | −0.537307 | ||||||||
\(777\) | −115.854 | − | 115.854i | −0.149104 | − | 0.149104i | ||||
\(778\) | 34.7594 | − | 34.7594i | 0.0446778 | − | 0.0446778i | ||||
\(779\) | − | 361.836i | − | 0.464488i | ||||||
\(780\) | −105.659 | − | 114.968i | −0.135460 | − | 0.147394i | ||||
\(781\) | 75.7043 | 0.0969326 | ||||||||
\(782\) | 125.289 | + | 125.289i | 0.160216 | + | 0.160216i | ||||
\(783\) | 28.6556 | − | 28.6556i | 0.0365971 | − | 0.0365971i | ||||
\(784\) | 161.731i | 0.206289i | ||||||||
\(785\) | 40.1928 | − | 952.565i | 0.0512011 | − | 1.21346i | ||||
\(786\) | 197.342 | 0.251071 | ||||||||
\(787\) | 702.992 | + | 702.992i | 0.893256 | + | 0.893256i | 0.994828 | − | 0.101572i | \(-0.0323873\pi\) |
−0.101572 | + | 0.994828i | \(0.532387\pi\) | |||||||
\(788\) | −516.750 | + | 516.750i | −0.655774 | + | 0.655774i | ||||
\(789\) | − | 435.100i | − | 0.551457i | ||||||
\(790\) | −221.335 | − | 9.33907i | −0.280171 | − | 0.0118216i | ||||
\(791\) | −331.345 | −0.418893 | ||||||||
\(792\) | −5.40037 | − | 5.40037i | −0.00681865 | − | 0.00681865i | ||||
\(793\) | −283.677 | + | 283.677i | −0.357727 | + | 0.357727i | ||||
\(794\) | 981.544i | 1.23620i | ||||||||
\(795\) | −460.469 | + | 423.184i | −0.579206 | + | 0.532307i | ||||
\(796\) | −34.2713 | −0.0430544 | ||||||||
\(797\) | −307.310 | − | 307.310i | −0.385583 | − | 0.385583i | 0.487525 | − | 0.873109i | \(-0.337900\pi\) |
−0.873109 | + | 0.487525i | \(0.837900\pi\) | |||||||
\(798\) | −50.0107 | + | 50.0107i | −0.0626700 | + | 0.0626700i | ||||
\(799\) | − | 998.747i | − | 1.25000i | ||||||
\(800\) | −108.068 | + | 91.2207i | −0.135086 | + | 0.114026i | ||||
\(801\) | −96.4082 | −0.120360 | ||||||||
\(802\) | 473.229 | + | 473.229i | 0.590061 | + | 0.590061i | ||||
\(803\) | 69.3710 | − | 69.3710i | 0.0863898 | − | 0.0863898i | ||||
\(804\) | 106.202i | 0.132092i | ||||||||
\(805\) | −47.4934 | − | 51.6779i | −0.0589981 | − | 0.0641962i | ||||
\(806\) | −235.947 | −0.292739 | ||||||||
\(807\) | −114.244 | − | 114.244i | −0.141567 | − | 0.141567i | ||||
\(808\) | 124.470 | − | 124.470i | 0.154047 | − | 0.154047i | ||||
\(809\) | − | 697.617i | − | 0.862321i | −0.902275 | − | 0.431160i | \(-0.858104\pi\) | ||
0.902275 | − | 0.431160i | \(-0.141896\pi\) | |||||||
\(810\) | −2.68284 | + | 63.5830i | −0.00331215 | + | 0.0784976i | ||||
\(811\) | 1305.11 | 1.60927 | 0.804633 | − | 0.593773i | \(-0.202362\pi\) | ||||
0.804633 | + | 0.593773i | \(0.202362\pi\) | |||||||
\(812\) | −32.2835 | − | 32.2835i | −0.0397580 | − | 0.0397580i | ||||
\(813\) | 430.561 | − | 430.561i | 0.529596 | − | 0.529596i | ||||
\(814\) | 41.1365i | 0.0505363i | ||||||||
\(815\) | −1010.26 | − | 42.6270i | −1.23958 | − | 0.0523031i | ||||
\(816\) | −180.996 | −0.221809 | ||||||||
\(817\) | −144.922 | − | 144.922i | −0.177383 | − | 0.177383i | ||||
\(818\) | −285.348 | + | 285.348i | −0.348836 | + | 0.348836i | ||||
\(819\) | 79.1613i | 0.0966560i | ||||||||
\(820\) | −270.073 | + | 248.205i | −0.329357 | + | 0.302689i | ||||
\(821\) | −959.958 | −1.16925 | −0.584627 | − | 0.811302i | \(-0.698759\pi\) | ||||
−0.584627 | + | 0.811302i | \(0.698759\pi\) | |||||||
\(822\) | 134.650 | + | 134.650i | 0.163807 | + | 0.163807i | ||||
\(823\) | −382.034 | + | 382.034i | −0.464197 | + | 0.464197i | −0.900028 | − | 0.435831i | \(-0.856454\pi\) |
0.435831 | + | 0.900028i | \(0.356454\pi\) | |||||||
\(824\) | − | 475.612i | − | 0.577200i | ||||||
\(825\) | −25.1392 | − | 29.7822i | −0.0304718 | − | 0.0360996i | ||||
\(826\) | −379.719 | −0.459709 | ||||||||
\(827\) | −815.819 | − | 815.819i | −0.986481 | − | 0.986481i | 0.0134292 | − | 0.999910i | \(-0.495725\pi\) |
−0.999910 | + | 0.0134292i | \(0.995725\pi\) | |||||||
\(828\) | 20.3470 | − | 20.3470i | 0.0245737 | − | 0.0245737i | ||||
\(829\) | 14.4275i | 0.0174035i | 0.999962 | + | 0.00870173i | \(0.00276988\pi\) | ||||
−0.999962 | + | 0.00870173i | \(0.997230\pi\) | |||||||
\(830\) | −58.8725 | − | 64.0595i | −0.0709307 | − | 0.0771802i | ||||
\(831\) | 519.261 | 0.624863 | ||||||||
\(832\) | −50.9968 | − | 50.9968i | −0.0612942 | − | 0.0612942i | ||||
\(833\) | −746.906 | + | 746.906i | −0.896646 | + | 0.896646i | ||||
\(834\) | 327.329i | 0.392481i | ||||||||
\(835\) | 42.3955 | − | 1004.77i | 0.0507731 | − | 1.20332i | ||||
\(836\) | 17.7575 | 0.0212410 | ||||||||
\(837\) | 67.9985 | + | 67.9985i | 0.0812407 | + | 0.0812407i | ||||
\(838\) | −290.087 | + | 290.087i | −0.346165 | + | 0.346165i | ||||
\(839\) | 283.559i | 0.337972i | 0.985618 | + | 0.168986i | \(0.0540493\pi\) | ||||
−0.985618 | + | 0.168986i | \(0.945951\pi\) | |||||||
\(840\) | 71.6330 | + | 3.02251i | 0.0852774 | + | 0.00359822i | ||||
\(841\) | 780.175 | 0.927675 | ||||||||
\(842\) | 442.922 | + | 442.922i | 0.526035 | + | 0.526035i | ||||
\(843\) | 165.790 | − | 165.790i | 0.196666 | − | 0.196666i | ||||
\(844\) | − | 175.793i | − | 0.208286i | ||||||
\(845\) | −322.969 | + | 296.817i | −0.382212 | + | 0.351263i | ||||
\(846\) | −162.197 | −0.191722 | ||||||||
\(847\) | 248.758 | + | 248.758i | 0.293693 | + | 0.293693i | ||||
\(848\) | −204.252 | + | 204.252i | −0.240864 | + | 0.240864i | ||||
\(849\) | 262.481i | 0.309165i | ||||||||
\(850\) | −920.360 | − | 77.8065i | −1.08278 | − | 0.0915370i | ||||
\(851\) | −154.990 | −0.182127 | ||||||||
\(852\) | −206.027 | − | 206.027i | −0.241816 | − | 0.241816i | ||||
\(853\) | −190.843 | + | 190.843i | −0.223732 | + | 0.223732i | −0.810068 | − | 0.586336i | \(-0.800570\pi\) |
0.586336 | + | 0.810068i | \(0.300570\pi\) | |||||||
\(854\) | − | 184.209i | − | 0.215701i | ||||||
\(855\) | −100.126 | − | 108.947i | −0.117106 | − | 0.127424i | ||||
\(856\) | −74.1456 | −0.0866187 | ||||||||
\(857\) | 966.259 | + | 966.259i | 1.12749 | + | 1.12749i | 0.990584 | + | 0.136907i | \(0.0437160\pi\) |
0.136907 | + | 0.990584i | \(0.456284\pi\) | |||||||
\(858\) | 14.0540 | − | 14.0540i | 0.0163800 | − | 0.0163800i | ||||
\(859\) | 1296.14i | 1.50889i | 0.656361 | + | 0.754447i | \(0.272095\pi\) | ||||
−0.656361 | + | 0.754447i | \(0.727905\pi\) | |||||||
\(860\) | −8.75865 | + | 207.579i | −0.0101845 | + | 0.241371i | ||||
\(861\) | 185.959 | 0.215981 | ||||||||
\(862\) | −377.479 | − | 377.479i | −0.437910 | − | 0.437910i | ||||
\(863\) | 283.162 | − | 283.162i | 0.328113 | − | 0.328113i | −0.523755 | − | 0.851869i | \(-0.675469\pi\) |
0.851869 | + | 0.523755i | \(0.175469\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 1039.51 | + | 43.8614i | 1.20174 | + | 0.0507068i | ||||
\(866\) | 1135.51 | 1.31121 | ||||||||
\(867\) | −481.929 | − | 481.929i | −0.555858 | − | 0.555858i | ||||
\(868\) | 76.6074 | − | 76.6074i | 0.0882574 | − | 0.0882574i | ||||
\(869\) | − | 28.1983i | − | 0.0324492i | ||||||
\(870\) | 70.3291 | − | 64.6344i | 0.0808380 | − | 0.0742924i | ||||
\(871\) | −276.382 | −0.317315 | ||||||||
\(872\) | −147.775 | − | 147.775i | −0.169466 | − | 0.169466i | ||||
\(873\) | −312.713 | + | 312.713i | −0.358205 | + | 0.358205i | ||||
\(874\) | 66.9048i | 0.0765501i | ||||||||
\(875\) | 362.952 | + | 46.1628i | 0.414802 | + | 0.0527575i | ||||
\(876\) | −377.582 | −0.431030 | ||||||||
\(877\) | 704.197 | + | 704.197i | 0.802961 | + | 0.802961i | 0.983557 | − | 0.180596i | \(-0.0578027\pi\) |
−0.180596 | + | 0.983557i | \(0.557803\pi\) | |||||||
\(878\) | 295.256 | − | 295.256i | 0.336282 | − | 0.336282i | ||||
\(879\) | − | 318.444i | − | 0.362280i | ||||||
\(880\) | −12.1809 | − | 13.2541i | −0.0138419 | − | 0.0150615i | ||||
\(881\) | −210.859 | −0.239341 | −0.119670 | − | 0.992814i | \(-0.538184\pi\) | ||||
−0.119670 | + | 0.992814i | \(0.538184\pi\) | |||||||
\(882\) | 121.298 | + | 121.298i | 0.137526 | + | 0.137526i | ||||
\(883\) | −439.742 | + | 439.742i | −0.498009 | + | 0.498009i | −0.910818 | − | 0.412809i | \(-0.864548\pi\) |
0.412809 | + | 0.910818i | \(0.364548\pi\) | |||||||
\(884\) | − | 471.028i | − | 0.532837i | ||||||
\(885\) | 33.4906 | − | 793.722i | 0.0378424 | − | 0.896861i | ||||
\(886\) | −838.314 | −0.946179 | ||||||||
\(887\) | 189.904 | + | 189.904i | 0.214097 | + | 0.214097i | 0.806005 | − | 0.591908i | \(-0.201625\pi\) |
−0.591908 | + | 0.806005i | \(0.701625\pi\) | |||||||
\(888\) | 111.952 | − | 111.952i | 0.126072 | − | 0.126072i | ||||
\(889\) | 113.524i | 0.127699i | ||||||||
\(890\) | −227.034 | − | 9.57956i | −0.255095 | − | 0.0107636i | ||||
\(891\) | −8.10056 | −0.00909153 | ||||||||
\(892\) | −317.306 | − | 317.306i | −0.355724 | − | 0.355724i | ||||
\(893\) | 266.667 | − | 266.667i | 0.298620 | − | 0.298620i | ||||
\(894\) | 474.898i | 0.531206i | ||||||||
\(895\) | −441.730 | + | 405.962i | −0.493553 | + | 0.453589i | ||||
\(896\) | 33.1153 | 0.0369590 | ||||||||
\(897\) | 52.9514 | + | 52.9514i | 0.0590316 | + | 0.0590316i | ||||
\(898\) | −646.254 | + | 646.254i | −0.719659 | + | 0.719659i | ||||
\(899\) | − | 144.336i | − | 0.160552i | ||||||
\(900\) | −12.6358 | + | 149.467i | −0.0140398 | + | 0.166074i | ||||
\(901\) | −1886.56 | −2.09386 | ||||||||
\(902\) | −33.0146 | − | 33.0146i | −0.0366016 | − | 0.0366016i | ||||
\(903\) | 74.4799 | − | 74.4799i | 0.0824805 | − | 0.0824805i | ||||
\(904\) | − | 320.185i | − | 0.354187i | ||||||
\(905\) | 483.598 | + | 526.205i | 0.534362 | + | 0.581443i | ||||
\(906\) | 518.831 | 0.572661 | ||||||||
\(907\) | 79.6022 | + | 79.6022i | 0.0877642 | + | 0.0877642i | 0.749626 | − | 0.661862i | \(-0.230233\pi\) |
−0.661862 | + | 0.749626i | \(0.730233\pi\) | |||||||
\(908\) | −352.999 | + | 352.999i | −0.388766 | + | 0.388766i | ||||
\(909\) | − | 186.705i | − | 0.205396i | ||||||
\(910\) | −7.86582 | + | 186.419i | −0.00864376 | + | 0.204856i | ||||
\(911\) | 599.614 | 0.658193 | 0.329096 | − | 0.944296i | \(-0.393256\pi\) | ||||
0.329096 | + | 0.944296i | \(0.393256\pi\) | |||||||
\(912\) | −48.3263 | − | 48.3263i | −0.0529894 | − | 0.0529894i | ||||
\(913\) | 7.83085 | − | 7.83085i | 0.00857705 | − | 0.00857705i | ||||
\(914\) | − | 235.516i | − | 0.257677i | ||||||
\(915\) | 385.049 | + | 16.2469i | 0.420819 | + | 0.0177562i | ||||
\(916\) | 281.167 | 0.306951 | ||||||||
\(917\) | −166.745 | − | 166.745i | −0.181837 | − | 0.181837i | ||||
\(918\) | −135.747 | + | 135.747i | −0.147873 | + | 0.147873i | ||||
\(919\) | − | 694.185i | − | 0.755370i | −0.925934 | − | 0.377685i | \(-0.876720\pi\) | ||
0.925934 | − | 0.377685i | \(-0.123280\pi\) | |||||||
\(920\) | 49.9375 | − | 45.8939i | 0.0542798 | − | 0.0498847i | ||||
\(921\) | −15.9715 | −0.0173415 | ||||||||
\(922\) | −638.280 | − | 638.280i | −0.692278 | − | 0.692278i | ||||
\(923\) | 536.168 | − | 536.168i | 0.580897 | − | 0.580897i | ||||
\(924\) | 9.12613i | 0.00987676i | ||||||||
\(925\) | 617.397 | − | 521.145i | 0.667456 | − | 0.563400i | ||||
\(926\) | −486.012 | −0.524851 | ||||||||
\(927\) | −356.709 | − | 356.709i | −0.384800 | − | 0.384800i | ||||
\(928\) | 31.1962 | − | 31.1962i | 0.0336166 | − | 0.0336166i | ||||
\(929\) | − | 988.592i | − | 1.06415i | −0.846699 | − | 0.532073i | \(-0.821413\pi\) | ||
0.846699 | − | 0.532073i | \(-0.178587\pi\) | |||||||
\(930\) | 153.375 | + | 166.888i | 0.164919 | + | 0.179450i | ||||
\(931\) | −398.851 | −0.428411 | ||||||||
\(932\) | 46.8103 | + | 46.8103i | 0.0502257 | + | 0.0502257i | ||||
\(933\) | −26.7703 | + | 26.7703i | −0.0286927 | + | 0.0286927i | ||||
\(934\) | 360.518i | 0.385994i | ||||||||
\(935\) | 4.95632 | − | 117.464i | 0.00530088 | − | 0.125630i | ||||
\(936\) | −76.4952 | −0.0817256 | ||||||||
\(937\) | −585.244 | − | 585.244i | −0.624594 | − | 0.624594i | 0.322109 | − | 0.946703i | \(-0.395608\pi\) |
−0.946703 | + | 0.322109i | \(0.895608\pi\) | |||||||
\(938\) | 89.7356 | − | 89.7356i | 0.0956670 | − | 0.0956670i | ||||
\(939\) | 807.858i | 0.860338i | ||||||||
\(940\) | −381.962 | − | 16.1166i | −0.406342 | − | 0.0171453i | ||||
\(941\) | 437.656 | 0.465097 | 0.232548 | − | 0.972585i | \(-0.425294\pi\) | ||||
0.232548 | + | 0.972585i | \(0.425294\pi\) | |||||||
\(942\) | −330.272 | − | 330.272i | −0.350607 | − | 0.350607i | ||||
\(943\) | 124.389 | − | 124.389i | 0.131908 | − | 0.131908i | ||||
\(944\) | − | 366.931i | − | 0.388698i | ||||||
\(945\) | 55.9916 | − | 51.4579i | 0.0592504 | − | 0.0544528i | ||||
\(946\) | −26.4458 | −0.0279554 | ||||||||
\(947\) | 386.988 | + | 386.988i | 0.408646 | + | 0.408646i | 0.881266 | − | 0.472620i | \(-0.156692\pi\) |
−0.472620 | + | 0.881266i | \(0.656692\pi\) | |||||||
\(948\) | −76.7409 | + | 76.7409i | −0.0809503 | + | 0.0809503i | ||||
\(949\) | − | 982.626i | − | 1.03543i | ||||||
\(950\) | −224.963 | − | 266.512i | −0.236803 | − | 0.280539i | ||||
\(951\) | 458.577 | 0.482205 | ||||||||
\(952\) | 152.934 | + | 152.934i | 0.160645 | + | 0.160645i | ||||
\(953\) | 354.062 | − | 354.062i | 0.371524 | − | 0.371524i | −0.496508 | − | 0.868032i | \(-0.665385\pi\) |
0.868032 | + | 0.496508i | \(0.165385\pi\) | |||||||
\(954\) | 306.379i | 0.321152i | ||||||||
\(955\) | 242.654 | + | 264.034i | 0.254088 | + | 0.276475i | ||||
\(956\) | 316.125 | 0.330675 | ||||||||
\(957\) | 8.59726 | + | 8.59726i | 0.00898355 | + | 0.00898355i | ||||
\(958\) | 521.944 | − | 521.944i | 0.544827 | − | 0.544827i | ||||
\(959\) | − | 227.545i | − | 0.237273i | ||||||
\(960\) | −2.92071 | + | 69.2204i | −0.00304241 | + | 0.0721046i | ||||
\(961\) | −618.497 | −0.643597 | ||||||||
\(962\) | 291.345 | + | 291.345i | 0.302854 | + | 0.302854i | ||||
\(963\) | −55.6092 | + | 55.6092i | −0.0577458 | + | 0.0577458i | ||||
\(964\) | 296.327i | 0.307393i | ||||||||
\(965\) | 110.916 | + | 4.68002i | 0.114939 | + | 0.00484976i | ||||
\(966\) | −34.3845 | −0.0355948 | ||||||||
\(967\) | −1153.10 | − | 1153.10i | −1.19245 | − | 1.19245i | −0.976377 | − | 0.216075i | \(-0.930674\pi\) |
−0.216075 | − | 0.976377i | \(-0.569326\pi\) | |||||||
\(968\) | −240.380 | + | 240.380i | −0.248326 | + | 0.248326i | ||||
\(969\) | − | 446.363i | − | 0.460643i | ||||||
\(970\) | −767.488 | + | 705.343i | −0.791225 | + | 0.727158i | ||||
\(971\) | −96.6570 | −0.0995438 | −0.0497719 | − | 0.998761i | \(-0.515849\pi\) | ||||
−0.0497719 | + | 0.998761i | \(0.515849\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 276.578 | − | 276.578i | 0.284253 | − | 0.284253i | ||||
\(974\) | 347.098i | 0.356364i | ||||||||
\(975\) | −388.975 | − | 32.8836i | −0.398949 | − | 0.0337268i | ||||
\(976\) | 178.005 | 0.182382 | ||||||||
\(977\) | 1227.96 | + | 1227.96i | 1.25687 | + | 1.25687i | 0.952578 | + | 0.304295i | \(0.0984209\pi\) |
0.304295 | + | 0.952578i | \(0.401579\pi\) | |||||||
\(978\) | −350.274 | + | 350.274i | −0.358153 | + | 0.358153i | ||||
\(979\) | − | 28.9245i | − | 0.0295449i | ||||||
\(980\) | 273.595 | + | 297.700i | 0.279179 | + | 0.303776i | ||||
\(981\) | −221.662 | −0.225955 | ||||||||
\(982\) | 261.292 | + | 261.292i | 0.266082 | + | 0.266082i | ||||
\(983\) | −1081.37 | + | 1081.37i | −1.10007 | + | 1.10007i | −0.105665 | + | 0.994402i | \(0.533697\pi\) |
−0.994402 | + | 0.105665i | \(0.966303\pi\) | |||||||
\(984\) | 179.696i | 0.182618i | ||||||||
\(985\) | −77.0199 | + | 1825.36i | −0.0781928 | + | 1.85316i | ||||
\(986\) | 288.142 | 0.292233 | ||||||||
\(987\) | 137.049 | + | 137.049i | 0.138854 | + | 0.138854i | ||||
\(988\) | 125.765 | − | 125.765i | 0.127293 | − | 0.127293i | ||||
\(989\) | − | 99.6400i | − | 0.100748i | ||||||
\(990\) | −19.0762 | − | 0.804908i | −0.0192689 | − | 0.000813039i | ||||
\(991\) | 582.750 | 0.588043 | 0.294021 | − | 0.955799i | \(-0.405006\pi\) | ||||
0.294021 | + | 0.955799i | \(0.405006\pi\) | |||||||
\(992\) | 74.0274 | + | 74.0274i | 0.0746244 | + | 0.0746244i | ||||
\(993\) | 630.366 | − | 630.366i | 0.634810 | − | 0.634810i | ||||
\(994\) | 348.167i | 0.350268i | ||||||||
\(995\) | −63.0838 | + | 57.9758i | −0.0634008 | + | 0.0582671i | ||||
\(996\) | −42.6228 | −0.0427940 | ||||||||
\(997\) | 648.095 | + | 648.095i | 0.650045 | + | 0.650045i | 0.953004 | − | 0.302959i | \(-0.0979745\pi\) |
−0.302959 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(998\) | −391.452 | + | 391.452i | −0.392237 | + | 0.392237i | ||||
\(999\) | − | 167.928i | − | 0.168096i |
(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 | 690.3.k.b.277.4 | ✓ | 48 | |
5.3 | odd | 4 | inner | 690.3.k.b.553.4 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.4 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.k.b.553.4 | yes | 48 | 5.3 | odd | 4 | inner |