Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.15 | ||
Character | \(\chi\) | \(=\) | 930.491 |
Dual form | 930.2.o.e.161.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.151443 | + | 1.72542i | −0.0874357 | + | 0.996170i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −1.72542 | − | 0.151443i | −0.704399 | − | 0.0618264i | ||||
\(7\) | −1.64767 | + | 2.85385i | −0.622762 | + | 1.07866i | 0.366207 | + | 0.930533i | \(0.380656\pi\) |
−0.988969 | + | 0.148122i | \(0.952677\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.95413 | − | 0.522605i | −0.984710 | − | 0.174202i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −2.34247 | − | 4.05727i | −0.706281 | − | 1.22331i | −0.966227 | − | 0.257691i | \(-0.917038\pi\) |
0.259947 | − | 0.965623i | \(-0.416295\pi\) | |||||||
\(12\) | 0.151443 | − | 1.72542i | 0.0437179 | − | 0.498085i | ||||
\(13\) | −3.57649 | + | 2.06489i | −0.991939 | + | 0.572696i | −0.905853 | − | 0.423592i | \(-0.860769\pi\) |
−0.0860855 | + | 0.996288i | \(0.527436\pi\) | |||||||
\(14\) | −2.85385 | − | 1.64767i | −0.762725 | − | 0.440359i | ||||
\(15\) | 0.731555 | + | 1.56998i | 0.188887 | + | 0.405366i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.02223 | − | 5.23465i | 0.732998 | − | 1.26959i | −0.222598 | − | 0.974910i | \(-0.571454\pi\) |
0.955596 | − | 0.294679i | \(-0.0952128\pi\) | |||||||
\(18\) | 0.522605 | − | 2.95413i | 0.123179 | − | 0.696295i | ||||
\(19\) | −1.11458 | + | 1.93051i | −0.255702 | + | 0.442889i | −0.965086 | − | 0.261933i | \(-0.915640\pi\) |
0.709384 | + | 0.704822i | \(0.248973\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | −4.67456 | − | 3.27512i | −1.02007 | − | 0.714690i | ||||
\(22\) | 4.05727 | − | 2.34247i | 0.865014 | − | 0.499416i | ||||
\(23\) | −0.244780 | −0.0510402 | −0.0255201 | − | 0.999674i | \(-0.508124\pi\) | ||||
−0.0255201 | + | 0.999674i | \(0.508124\pi\) | |||||||
\(24\) | 1.72542 | + | 0.151443i | 0.352199 | + | 0.0309132i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −2.06489 | − | 3.57649i | −0.404957 | − | 0.701407i | ||||
\(27\) | 1.34909 | − | 5.01796i | 0.259633 | − | 0.965707i | ||||
\(28\) | 1.64767 | − | 2.85385i | 0.311381 | − | 0.539328i | ||||
\(29\) | −2.05814 | −0.382188 | −0.191094 | − | 0.981572i | \(-0.561203\pi\) | ||||
−0.191094 | + | 0.981572i | \(0.561203\pi\) | |||||||
\(30\) | −1.56998 | + | 0.731555i | −0.286637 | + | 0.133563i | ||||
\(31\) | −5.16785 | + | 2.07204i | −0.928173 | + | 0.372149i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 7.35524 | − | 3.42729i | 1.28038 | − | 0.596614i | ||||
\(34\) | 5.23465 | + | 3.02223i | 0.897735 | + | 0.518308i | ||||
\(35\) | 3.29535i | 0.557015i | ||||||||
\(36\) | 2.95413 | + | 0.522605i | 0.492355 | + | 0.0871009i | ||||
\(37\) | −7.39979 | − | 4.27227i | −1.21652 | − | 0.702357i | −0.252347 | − | 0.967637i | \(-0.581202\pi\) |
−0.964172 | + | 0.265280i | \(0.914536\pi\) | |||||||
\(38\) | −1.93051 | − | 1.11458i | −0.313170 | − | 0.180809i | ||||
\(39\) | −3.02115 | − | 6.48364i | −0.483772 | − | 1.03821i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −6.83739 | + | 3.94757i | −1.06782 | + | 0.616507i | −0.927585 | − | 0.373611i | \(-0.878119\pi\) |
−0.140236 | + | 0.990118i | \(0.544786\pi\) | |||||||
\(42\) | 3.27512 | − | 4.67456i | 0.505362 | − | 0.721300i | ||||
\(43\) | 10.0366 | + | 5.79463i | 1.53057 | + | 0.883672i | 0.999336 | + | 0.0364445i | \(0.0116032\pi\) |
0.531230 | + | 0.847228i | \(0.321730\pi\) | |||||||
\(44\) | 2.34247 | + | 4.05727i | 0.353140 | + | 0.611657i | ||||
\(45\) | −2.81965 | + | 1.02448i | −0.420329 | + | 0.152720i | ||||
\(46\) | − | 0.244780i | − | 0.0360909i | ||||||
\(47\) | − | 3.99299i | − | 0.582437i | −0.956656 | − | 0.291219i | \(-0.905939\pi\) | ||
0.956656 | − | 0.291219i | \(-0.0940607\pi\) | |||||||
\(48\) | −0.151443 | + | 1.72542i | −0.0218589 | + | 0.249043i | ||||
\(49\) | −1.92965 | − | 3.34226i | −0.275665 | − | 0.477466i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | 8.57426 | + | 6.00736i | 1.20064 | + | 0.841198i | ||||
\(52\) | 3.57649 | − | 2.06489i | 0.495969 | − | 0.286348i | ||||
\(53\) | −0.996554 | − | 1.72608i | −0.136887 | − | 0.237096i | 0.789430 | − | 0.613841i | \(-0.210376\pi\) |
−0.926317 | + | 0.376746i | \(0.877043\pi\) | |||||||
\(54\) | 5.01796 | + | 1.34909i | 0.682858 | + | 0.183589i | ||||
\(55\) | −4.05727 | − | 2.34247i | −0.547083 | − | 0.315858i | ||||
\(56\) | 2.85385 | + | 1.64767i | 0.381362 | + | 0.220180i | ||||
\(57\) | −3.16214 | − | 2.21548i | −0.418835 | − | 0.293447i | ||||
\(58\) | − | 2.05814i | − | 0.270247i | ||||||
\(59\) | 0.641535 | + | 0.370390i | 0.0835207 | + | 0.0482207i | 0.541179 | − | 0.840908i | \(-0.317978\pi\) |
−0.457658 | + | 0.889128i | \(0.651312\pi\) | |||||||
\(60\) | −0.731555 | − | 1.56998i | −0.0944434 | − | 0.202683i | ||||
\(61\) | − | 6.30131i | − | 0.806801i | −0.915024 | − | 0.403400i | \(-0.867828\pi\) | ||
0.915024 | − | 0.403400i | \(-0.132172\pi\) | |||||||
\(62\) | −2.07204 | − | 5.16785i | −0.263149 | − | 0.656317i | ||||
\(63\) | 6.35888 | − | 7.56957i | 0.801144 | − | 0.953676i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.06489 | + | 3.57649i | −0.256117 | + | 0.443608i | ||||
\(66\) | 3.42729 | + | 7.35524i | 0.421870 | + | 0.905367i | ||||
\(67\) | 1.90767 | + | 3.30418i | 0.233059 | + | 0.403669i | 0.958707 | − | 0.284397i | \(-0.0917933\pi\) |
−0.725648 | + | 0.688066i | \(0.758460\pi\) | |||||||
\(68\) | −3.02223 | + | 5.23465i | −0.366499 | + | 0.634795i | ||||
\(69\) | 0.0370703 | − | 0.422348i | 0.00446273 | − | 0.0508447i | ||||
\(70\) | −3.29535 | −0.393869 | ||||||||
\(71\) | −8.36971 | + | 4.83225i | −0.993302 | + | 0.573483i | −0.906260 | − | 0.422722i | \(-0.861075\pi\) |
−0.0870422 | + | 0.996205i | \(0.527741\pi\) | |||||||
\(72\) | −0.522605 | + | 2.95413i | −0.0615896 | + | 0.348148i | ||||
\(73\) | 0.290365 | − | 0.167642i | 0.0339847 | − | 0.0196211i | −0.482911 | − | 0.875669i | \(-0.660421\pi\) |
0.516896 | + | 0.856048i | \(0.327087\pi\) | |||||||
\(74\) | 4.27227 | − | 7.39979i | 0.496642 | − | 0.860208i | ||||
\(75\) | 1.41853 | + | 0.993862i | 0.163798 | + | 0.114761i | ||||
\(76\) | 1.11458 | − | 1.93051i | 0.127851 | − | 0.221444i | ||||
\(77\) | 15.4385 | 1.75938 | ||||||||
\(78\) | 6.48364 | − | 3.02115i | 0.734128 | − | 0.342078i | ||||
\(79\) | −11.1206 | − | 6.42046i | −1.25116 | − | 0.722358i | −0.279820 | − | 0.960052i | \(-0.590275\pi\) |
−0.971340 | + | 0.237695i | \(0.923608\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 8.45377 | + | 3.08769i | 0.939308 | + | 0.343076i | ||||
\(82\) | −3.94757 | − | 6.83739i | −0.435936 | − | 0.755063i | ||||
\(83\) | 1.42255 | + | 2.46393i | 0.156145 | + | 0.270451i | 0.933475 | − | 0.358642i | \(-0.116760\pi\) |
−0.777330 | + | 0.629093i | \(0.783427\pi\) | |||||||
\(84\) | 4.67456 | + | 3.27512i | 0.510036 | + | 0.357345i | ||||
\(85\) | − | 6.04445i | − | 0.655613i | ||||||
\(86\) | −5.79463 | + | 10.0366i | −0.624851 | + | 1.08227i | ||||
\(87\) | 0.311692 | − | 3.55116i | 0.0334168 | − | 0.380724i | ||||
\(88\) | −4.05727 | + | 2.34247i | −0.432507 | + | 0.249708i | ||||
\(89\) | 0.149606 | 0.0158582 | 0.00792909 | − | 0.999969i | \(-0.497476\pi\) | ||||
0.00792909 | + | 0.999969i | \(0.497476\pi\) | |||||||
\(90\) | −1.02448 | − | 2.81965i | −0.107989 | − | 0.297218i | ||||
\(91\) | − | 13.6090i | − | 1.42661i | ||||||
\(92\) | 0.244780 | 0.0255201 | ||||||||
\(93\) | −2.79250 | − | 9.23049i | −0.289568 | − | 0.957157i | ||||
\(94\) | 3.99299 | 0.411845 | ||||||||
\(95\) | 2.22916i | 0.228707i | ||||||||
\(96\) | −1.72542 | − | 0.151443i | −0.176100 | − | 0.0154566i | ||||
\(97\) | −7.67331 | −0.779107 | −0.389553 | − | 0.921004i | \(-0.627371\pi\) | ||||
−0.389553 | + | 0.921004i | \(0.627371\pi\) | |||||||
\(98\) | 3.34226 | − | 1.92965i | 0.337619 | − | 0.194925i | ||||
\(99\) | 4.79960 | + | 13.2099i | 0.482378 | + | 1.32764i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | − | 5.06959i | − | 0.504443i | −0.967669 | − | 0.252222i | \(-0.918839\pi\) | ||
0.967669 | − | 0.252222i | \(-0.0811612\pi\) | |||||||
\(102\) | −6.00736 | + | 8.57426i | −0.594817 | + | 0.848978i | ||||
\(103\) | 9.37875 | + | 16.2445i | 0.924115 | + | 1.60061i | 0.792978 | + | 0.609251i | \(0.208530\pi\) |
0.131138 | + | 0.991364i | \(0.458137\pi\) | |||||||
\(104\) | 2.06489 | + | 3.57649i | 0.202479 | + | 0.350703i | ||||
\(105\) | −5.68585 | − | 0.499058i | −0.554882 | − | 0.0487030i | ||||
\(106\) | 1.72608 | − | 0.996554i | 0.167652 | − | 0.0967939i | ||||
\(107\) | 3.66151 | + | 2.11397i | 0.353971 | + | 0.204366i | 0.666433 | − | 0.745565i | \(-0.267820\pi\) |
−0.312462 | + | 0.949930i | \(0.601154\pi\) | |||||||
\(108\) | −1.34909 | + | 5.01796i | −0.129817 | + | 0.482854i | ||||
\(109\) | 5.84653 | 0.559996 | 0.279998 | − | 0.960001i | \(-0.409666\pi\) | ||||
0.279998 | + | 0.960001i | \(0.409666\pi\) | |||||||
\(110\) | 2.34247 | − | 4.05727i | 0.223346 | − | 0.386846i | ||||
\(111\) | 8.49210 | − | 12.1207i | 0.806034 | − | 1.15045i | ||||
\(112\) | −1.64767 | + | 2.85385i | −0.155690 | + | 0.269664i | ||||
\(113\) | −5.58805 | + | 3.22626i | −0.525679 | + | 0.303501i | −0.739255 | − | 0.673425i | \(-0.764822\pi\) |
0.213576 | + | 0.976926i | \(0.431489\pi\) | |||||||
\(114\) | 2.21548 | − | 3.16214i | 0.207498 | − | 0.296161i | ||||
\(115\) | −0.211986 | + | 0.122390i | −0.0197678 | + | 0.0114129i | ||||
\(116\) | 2.05814 | 0.191094 | ||||||||
\(117\) | 11.6445 | − | 4.23085i | 1.07654 | − | 0.391142i | ||||
\(118\) | −0.370390 | + | 0.641535i | −0.0340972 | + | 0.0590580i | ||||
\(119\) | 9.95929 | + | 17.2500i | 0.912966 | + | 1.58130i | ||||
\(120\) | 1.56998 | − | 0.731555i | 0.143319 | − | 0.0667815i | ||||
\(121\) | −5.47431 | + | 9.48178i | −0.497665 | + | 0.861980i | ||||
\(122\) | 6.30131 | 0.570494 | ||||||||
\(123\) | −5.77573 | − | 12.3952i | −0.520780 | − | 1.11764i | ||||
\(124\) | 5.16785 | − | 2.07204i | 0.464086 | − | 0.186075i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 7.56957 | + | 6.35888i | 0.674351 | + | 0.566494i | ||||
\(127\) | 0.366646 | + | 0.211683i | 0.0325346 | + | 0.0187839i | 0.516179 | − | 0.856481i | \(-0.327354\pi\) |
−0.483644 | + | 0.875265i | \(0.660687\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −11.5181 | + | 16.4397i | −1.01411 | + | 1.44744i | ||||
\(130\) | −3.57649 | − | 2.06489i | −0.313679 | − | 0.181102i | ||||
\(131\) | 1.79983 | + | 1.03913i | 0.157252 | + | 0.0907895i | 0.576561 | − | 0.817054i | \(-0.304394\pi\) |
−0.419309 | + | 0.907844i | \(0.637728\pi\) | |||||||
\(132\) | −7.35524 | + | 3.42729i | −0.640191 | + | 0.298307i | ||||
\(133\) | −3.67293 | − | 6.36169i | −0.318483 | − | 0.551629i | ||||
\(134\) | −3.30418 | + | 1.90767i | −0.285437 | + | 0.164797i | ||||
\(135\) | −1.34063 | − | 5.02023i | −0.115383 | − | 0.432073i | ||||
\(136\) | −5.23465 | − | 3.02223i | −0.448868 | − | 0.259154i | ||||
\(137\) | −9.76518 | − | 16.9138i | −0.834296 | − | 1.44504i | −0.894602 | − | 0.446863i | \(-0.852541\pi\) |
0.0603063 | − | 0.998180i | \(-0.480792\pi\) | |||||||
\(138\) | 0.422348 | + | 0.0370703i | 0.0359526 | + | 0.00315563i | ||||
\(139\) | 22.5295i | 1.91092i | 0.295114 | + | 0.955462i | \(0.404642\pi\) | ||||
−0.295114 | + | 0.955462i | \(0.595358\pi\) | |||||||
\(140\) | − | 3.29535i | − | 0.278508i | ||||||
\(141\) | 6.88957 | + | 0.604711i | 0.580207 | + | 0.0509258i | ||||
\(142\) | −4.83225 | − | 8.36971i | −0.405514 | − | 0.702370i | ||||
\(143\) | 16.7556 | + | 9.67385i | 1.40117 | + | 0.808968i | ||||
\(144\) | −2.95413 | − | 0.522605i | −0.246177 | − | 0.0435504i | ||||
\(145\) | −1.78240 | + | 1.02907i | −0.148021 | + | 0.0854597i | ||||
\(146\) | 0.167642 | + | 0.290365i | 0.0138742 | + | 0.0240308i | ||||
\(147\) | 6.05903 | − | 2.82330i | 0.499740 | − | 0.232862i | ||||
\(148\) | 7.39979 | + | 4.27227i | 0.608259 | + | 0.351179i | ||||
\(149\) | −13.4165 | − | 7.74601i | −1.09912 | − | 0.634578i | −0.163131 | − | 0.986604i | \(-0.552159\pi\) |
−0.935990 | + | 0.352027i | \(0.885493\pi\) | |||||||
\(150\) | −0.993862 | + | 1.41853i | −0.0811485 | + | 0.115823i | ||||
\(151\) | − | 18.2693i | − | 1.48673i | −0.668884 | − | 0.743367i | \(-0.733228\pi\) | ||
0.668884 | − | 0.743367i | \(-0.266772\pi\) | |||||||
\(152\) | 1.93051 | + | 1.11458i | 0.156585 | + | 0.0904043i | ||||
\(153\) | −11.6637 | + | 13.8844i | −0.942955 | + | 1.12249i | ||||
\(154\) | 15.4385i | 1.24407i | ||||||||
\(155\) | −3.43947 | + | 4.37836i | −0.276265 | + | 0.351679i | ||||
\(156\) | 3.02115 | + | 6.48364i | 0.241886 | + | 0.519107i | ||||
\(157\) | −18.3537 | −1.46478 | −0.732391 | − | 0.680885i | \(-0.761596\pi\) | ||||
−0.732391 | + | 0.680885i | \(0.761596\pi\) | |||||||
\(158\) | 6.42046 | − | 11.1206i | 0.510784 | − | 0.884704i | ||||
\(159\) | 3.12913 | − | 1.45807i | 0.248156 | − | 0.115632i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 0.403318 | − | 0.698566i | 0.0317859 | − | 0.0550548i | ||||
\(162\) | −3.08769 | + | 8.45377i | −0.242592 | + | 0.664191i | ||||
\(163\) | 1.70445 | 0.133503 | 0.0667515 | − | 0.997770i | \(-0.478737\pi\) | ||||
0.0667515 | + | 0.997770i | \(0.478737\pi\) | |||||||
\(164\) | 6.83739 | − | 3.94757i | 0.533910 | − | 0.308253i | ||||
\(165\) | 4.65618 | − | 6.64574i | 0.362483 | − | 0.517370i | ||||
\(166\) | −2.46393 | + | 1.42255i | −0.191238 | + | 0.110411i | ||||
\(167\) | −6.28618 | + | 10.8880i | −0.486439 | + | 0.842537i | −0.999878 | − | 0.0155887i | \(-0.995038\pi\) |
0.513439 | + | 0.858126i | \(0.328371\pi\) | |||||||
\(168\) | −3.27512 | + | 4.67456i | −0.252681 | + | 0.360650i | ||||
\(169\) | 2.02750 | − | 3.51174i | 0.155962 | − | 0.270134i | ||||
\(170\) | 6.04445 | 0.463588 | ||||||||
\(171\) | 4.30151 | − | 5.12049i | 0.328944 | − | 0.391573i | ||||
\(172\) | −10.0366 | − | 5.79463i | −0.765283 | − | 0.441836i | ||||
\(173\) | −2.25868 | + | 1.30405i | −0.171724 | + | 0.0991450i | −0.583399 | − | 0.812186i | \(-0.698277\pi\) |
0.411674 | + | 0.911331i | \(0.364944\pi\) | |||||||
\(174\) | 3.55116 | + | 0.311692i | 0.269212 | + | 0.0236293i | ||||
\(175\) | 1.64767 | + | 2.85385i | 0.124552 | + | 0.215731i | ||||
\(176\) | −2.34247 | − | 4.05727i | −0.176570 | − | 0.305828i | ||||
\(177\) | −0.736234 | + | 1.05082i | −0.0553387 | + | 0.0789846i | ||||
\(178\) | 0.149606i | 0.0112134i | ||||||||
\(179\) | −9.49768 | + | 16.4505i | −0.709890 | + | 1.22957i | 0.255008 | + | 0.966939i | \(0.417922\pi\) |
−0.964898 | + | 0.262626i | \(0.915411\pi\) | |||||||
\(180\) | 2.81965 | − | 1.02448i | 0.210165 | − | 0.0763599i | ||||
\(181\) | −14.3763 | + | 8.30014i | −1.06858 | + | 0.616944i | −0.927793 | − | 0.373096i | \(-0.878296\pi\) |
−0.140786 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(182\) | 13.6090 | 1.00877 | ||||||||
\(183\) | 10.8724 | + | 0.954291i | 0.803711 | + | 0.0705432i | ||||
\(184\) | 0.244780i | 0.0180454i | ||||||||
\(185\) | −8.54454 | −0.628207 | ||||||||
\(186\) | 9.23049 | − | 2.79250i | 0.676812 | − | 0.204756i | ||||
\(187\) | −28.3179 | −2.07081 | ||||||||
\(188\) | 3.99299i | 0.291219i | ||||||||
\(189\) | 12.0977 | + | 12.1181i | 0.879975 | + | 0.881461i | ||||
\(190\) | −2.22916 | −0.161720 | ||||||||
\(191\) | −14.6036 | + | 8.43140i | −1.05668 | + | 0.610074i | −0.924512 | − | 0.381153i | \(-0.875527\pi\) |
−0.132168 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(192\) | 0.151443 | − | 1.72542i | 0.0109295 | − | 0.124521i | ||||
\(193\) | −3.46345 | + | 5.99887i | −0.249305 | + | 0.431808i | −0.963333 | − | 0.268308i | \(-0.913535\pi\) |
0.714028 | + | 0.700117i | \(0.246869\pi\) | |||||||
\(194\) | − | 7.67331i | − | 0.550912i | ||||||
\(195\) | −5.85822 | − | 4.10442i | −0.419516 | − | 0.293924i | ||||
\(196\) | 1.92965 | + | 3.34226i | 0.137832 | + | 0.238733i | ||||
\(197\) | −7.40933 | − | 12.8333i | −0.527893 | − | 0.914337i | −0.999471 | − | 0.0325129i | \(-0.989649\pi\) |
0.471579 | − | 0.881824i | \(-0.343684\pi\) | |||||||
\(198\) | −13.2099 | + | 4.79960i | −0.938787 | + | 0.341093i | ||||
\(199\) | −16.4647 | + | 9.50589i | −1.16715 | + | 0.673855i | −0.953007 | − | 0.302947i | \(-0.902029\pi\) |
−0.214143 | + | 0.976802i | \(0.568696\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.0612372 | − | 0.0353553i | ||||
\(201\) | −5.98999 | + | 2.79113i | −0.422501 | + | 0.196871i | ||||
\(202\) | 5.06959 | 0.356695 | ||||||||
\(203\) | 3.39115 | − | 5.87364i | 0.238012 | − | 0.412249i | ||||
\(204\) | −8.57426 | − | 6.00736i | −0.600318 | − | 0.420599i | ||||
\(205\) | −3.94757 | + | 6.83739i | −0.275710 | + | 0.477544i | ||||
\(206\) | −16.2445 | + | 9.37875i | −1.13181 | + | 0.653448i | ||||
\(207\) | 0.723112 | + | 0.127923i | 0.0502598 | + | 0.00889129i | ||||
\(208\) | −3.57649 | + | 2.06489i | −0.247985 | + | 0.143174i | ||||
\(209\) | 10.4435 | 0.722390 | ||||||||
\(210\) | 0.499058 | − | 5.68585i | 0.0344382 | − | 0.392361i | ||||
\(211\) | −0.159771 | + | 0.276731i | −0.0109991 | + | 0.0190509i | −0.871473 | − | 0.490444i | \(-0.836835\pi\) |
0.860473 | + | 0.509495i | \(0.170168\pi\) | |||||||
\(212\) | 0.996554 | + | 1.72608i | 0.0684436 | + | 0.118548i | ||||
\(213\) | −7.07012 | − | 15.1731i | −0.484437 | − | 1.03964i | ||||
\(214\) | −2.11397 | + | 3.66151i | −0.144508 | + | 0.250296i | ||||
\(215\) | 11.5893 | 0.790381 | ||||||||
\(216\) | −5.01796 | − | 1.34909i | −0.341429 | − | 0.0917943i | ||||
\(217\) | 2.60163 | − | 18.1623i | 0.176610 | − | 1.23294i | ||||
\(218\) | 5.84653i | 0.395977i | ||||||||
\(219\) | 0.245279 | + | 0.526389i | 0.0165744 | + | 0.0355701i | ||||
\(220\) | 4.05727 | + | 2.34247i | 0.273541 | + | 0.157929i | ||||
\(221\) | 24.9622i | 1.67914i | ||||||||
\(222\) | 12.1207 | + | 8.49210i | 0.813490 | + | 0.569952i | ||||
\(223\) | −1.19955 | − | 0.692562i | −0.0803279 | − | 0.0463774i | 0.459298 | − | 0.888282i | \(-0.348101\pi\) |
−0.539626 | + | 0.841905i | \(0.681434\pi\) | |||||||
\(224\) | −2.85385 | − | 1.64767i | −0.190681 | − | 0.110090i | ||||
\(225\) | −1.92965 | + | 2.29705i | −0.128644 | + | 0.153137i | ||||
\(226\) | −3.22626 | − | 5.58805i | −0.214608 | − | 0.371711i | ||||
\(227\) | −7.88419 | + | 4.55194i | −0.523292 | + | 0.302123i | −0.738281 | − | 0.674494i | \(-0.764362\pi\) |
0.214988 | + | 0.976617i | \(0.431029\pi\) | |||||||
\(228\) | 3.16214 | + | 2.21548i | 0.209418 | + | 0.146724i | ||||
\(229\) | 6.91782 | + | 3.99401i | 0.457143 | + | 0.263931i | 0.710842 | − | 0.703352i | \(-0.248314\pi\) |
−0.253699 | + | 0.967283i | \(0.581647\pi\) | |||||||
\(230\) | −0.122390 | − | 0.211986i | −0.00807016 | − | 0.0139779i | ||||
\(231\) | −2.33805 | + | 26.6378i | −0.153833 | + | 1.75264i | ||||
\(232\) | 2.05814i | 0.135124i | ||||||||
\(233\) | 15.9529i | 1.04511i | 0.852606 | + | 0.522554i | \(0.175021\pi\) | ||||
−0.852606 | + | 0.522554i | \(0.824979\pi\) | |||||||
\(234\) | 4.23085 | + | 11.6445i | 0.276579 | + | 0.761226i | ||||
\(235\) | −1.99650 | − | 3.45803i | −0.130237 | − | 0.225577i | ||||
\(236\) | −0.641535 | − | 0.370390i | −0.0417603 | − | 0.0241103i | ||||
\(237\) | 12.7621 | − | 18.2153i | 0.828987 | − | 1.18321i | ||||
\(238\) | −17.2500 | + | 9.95929i | −1.11815 | + | 0.645565i | ||||
\(239\) | −4.52292 | − | 7.83393i | −0.292564 | − | 0.506735i | 0.681852 | − | 0.731491i | \(-0.261175\pi\) |
−0.974415 | + | 0.224756i | \(0.927842\pi\) | |||||||
\(240\) | 0.731555 | + | 1.56998i | 0.0472217 | + | 0.101342i | ||||
\(241\) | 13.3621 | + | 7.71462i | 0.860730 | + | 0.496943i | 0.864257 | − | 0.503051i | \(-0.167789\pi\) |
−0.00352685 | + | 0.999994i | \(0.501123\pi\) | |||||||
\(242\) | −9.48178 | − | 5.47431i | −0.609512 | − | 0.351902i | ||||
\(243\) | −6.60781 | + | 14.1187i | −0.423891 | + | 0.905713i | ||||
\(244\) | 6.30131i | 0.403400i | ||||||||
\(245\) | −3.34226 | − | 1.92965i | −0.213529 | − | 0.123281i | ||||
\(246\) | 12.3952 | − | 5.77573i | 0.790288 | − | 0.368247i | ||||
\(247\) | − | 9.20591i | − | 0.585758i | ||||||
\(248\) | 2.07204 | + | 5.16785i | 0.131575 | + | 0.328159i | ||||
\(249\) | −4.46673 | + | 2.08134i | −0.283068 | + | 0.131900i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 1.89792 | − | 3.28729i | 0.119795 | − | 0.207492i | −0.799891 | − | 0.600145i | \(-0.795109\pi\) |
0.919687 | + | 0.392653i | \(0.128443\pi\) | |||||||
\(252\) | −6.35888 | + | 7.56957i | −0.400572 | + | 0.476838i | ||||
\(253\) | 0.573389 | + | 0.993140i | 0.0360487 | + | 0.0624382i | ||||
\(254\) | −0.211683 | + | 0.366646i | −0.0132822 | + | 0.0230054i | ||||
\(255\) | 10.4292 | + | 0.915391i | 0.653102 | + | 0.0573240i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.8650 | − | 15.5105i | 1.67579 | − | 0.967518i | 0.711495 | − | 0.702691i | \(-0.248018\pi\) |
0.964296 | − | 0.264828i | \(-0.0853150\pi\) | |||||||
\(258\) | −16.4397 | − | 11.5181i | −1.02349 | − | 0.717087i | ||||
\(259\) | 24.3849 | − | 14.0786i | 1.51520 | − | 0.874803i | ||||
\(260\) | 2.06489 | − | 3.57649i | 0.128059 | − | 0.221804i | ||||
\(261\) | 6.08002 | + | 1.07560i | 0.376344 | + | 0.0665777i | ||||
\(262\) | −1.03913 | + | 1.79983i | −0.0641979 | + | 0.111194i | ||||
\(263\) | 21.5086 | 1.32627 | 0.663137 | − | 0.748498i | \(-0.269225\pi\) | ||||
0.663137 | + | 0.748498i | \(0.269225\pi\) | |||||||
\(264\) | −3.42729 | − | 7.35524i | −0.210935 | − | 0.452684i | ||||
\(265\) | −1.72608 | − | 0.996554i | −0.106032 | − | 0.0612178i | ||||
\(266\) | 6.36169 | − | 3.67293i | 0.390060 | − | 0.225202i | ||||
\(267\) | −0.0226568 | + | 0.258132i | −0.00138657 | + | 0.0157975i | ||||
\(268\) | −1.90767 | − | 3.30418i | −0.116529 | − | 0.201835i | ||||
\(269\) | 13.5212 | + | 23.4194i | 0.824401 | + | 1.42791i | 0.902376 | + | 0.430950i | \(0.141821\pi\) |
−0.0779746 | + | 0.996955i | \(0.524845\pi\) | |||||||
\(270\) | 5.02023 | − | 1.34063i | 0.305521 | − | 0.0815882i | ||||
\(271\) | − | 16.9825i | − | 1.03162i | −0.856704 | − | 0.515808i | \(-0.827492\pi\) | ||
0.856704 | − | 0.515808i | \(-0.172508\pi\) | |||||||
\(272\) | 3.02223 | − | 5.23465i | 0.183249 | − | 0.317397i | ||||
\(273\) | 23.4812 | + | 2.06099i | 1.42115 | + | 0.124737i | ||||
\(274\) | 16.9138 | − | 9.76518i | 1.02180 | − | 0.589936i | ||||
\(275\) | −4.68494 | −0.282512 | ||||||||
\(276\) | −0.0370703 | + | 0.422348i | −0.00223137 | + | 0.0254223i | ||||
\(277\) | 23.1214i | 1.38923i | 0.719381 | + | 0.694616i | \(0.244426\pi\) | ||||
−0.719381 | + | 0.694616i | \(0.755574\pi\) | |||||||
\(278\) | −22.5295 | −1.35123 | ||||||||
\(279\) | 16.3494 | − | 3.42033i | 0.978810 | − | 0.204770i | ||||
\(280\) | 3.29535 | 0.196935 | ||||||||
\(281\) | − | 26.0722i | − | 1.55534i | −0.628674 | − | 0.777669i | \(-0.716402\pi\) | ||
0.628674 | − | 0.777669i | \(-0.283598\pi\) | |||||||
\(282\) | −0.604711 | + | 6.88957i | −0.0360100 | + | 0.410268i | ||||
\(283\) | 14.5905 | 0.867315 | 0.433657 | − | 0.901078i | \(-0.357223\pi\) | ||||
0.433657 | + | 0.901078i | \(0.357223\pi\) | |||||||
\(284\) | 8.36971 | − | 4.83225i | 0.496651 | − | 0.286742i | ||||
\(285\) | −3.84623 | − | 0.337591i | −0.227831 | − | 0.0199972i | ||||
\(286\) | −9.67385 | + | 16.7556i | −0.572027 | + | 0.990780i | ||||
\(287\) | − | 26.0172i | − | 1.53575i | ||||||
\(288\) | 0.522605 | − | 2.95413i | 0.0307948 | − | 0.174074i | ||||
\(289\) | −9.76772 | − | 16.9182i | −0.574571 | − | 0.995187i | ||||
\(290\) | −1.02907 | − | 1.78240i | −0.0604292 | − | 0.104666i | ||||
\(291\) | 1.16207 | − | 13.2397i | 0.0681218 | − | 0.776123i | ||||
\(292\) | −0.290365 | + | 0.167642i | −0.0169923 | + | 0.00981053i | ||||
\(293\) | −24.7303 | − | 14.2780i | −1.44476 | − | 0.834132i | −0.446598 | − | 0.894735i | \(-0.647364\pi\) |
−0.998162 | + | 0.0606026i | \(0.980698\pi\) | |||||||
\(294\) | 2.82330 | + | 6.05903i | 0.164658 | + | 0.353370i | ||||
\(295\) | 0.740780 | 0.0431299 | ||||||||
\(296\) | −4.27227 | + | 7.39979i | −0.248321 | + | 0.430104i | ||||
\(297\) | −23.5195 | + | 6.28077i | −1.36474 | + | 0.364447i | ||||
\(298\) | 7.74601 | − | 13.4165i | 0.448714 | − | 0.777196i | ||||
\(299\) | 0.875452 | − | 0.505443i | 0.0506287 | − | 0.0292305i | ||||
\(300\) | −1.41853 | − | 0.993862i | −0.0818991 | − | 0.0573807i | ||||
\(301\) | −33.0740 | + | 19.0953i | −1.90636 | + | 1.10064i | ||||
\(302\) | 18.2693 | 1.05128 | ||||||||
\(303\) | 8.74716 | + | 0.767755i | 0.502511 | + | 0.0441064i | ||||
\(304\) | −1.11458 | + | 1.93051i | −0.0639255 | + | 0.110722i | ||||
\(305\) | −3.15066 | − | 5.45710i | −0.180406 | − | 0.312473i | ||||
\(306\) | −13.8844 | − | 11.6637i | −0.793719 | − | 0.666770i | ||||
\(307\) | 4.69037 | − | 8.12397i | 0.267694 | − | 0.463659i | −0.700572 | − | 0.713582i | \(-0.747072\pi\) |
0.968266 | + | 0.249922i | \(0.0804051\pi\) | |||||||
\(308\) | −15.4385 | −0.879689 | ||||||||
\(309\) | −29.4488 | + | 13.7221i | −1.67529 | + | 0.780625i | ||||
\(310\) | −4.37836 | − | 3.43947i | −0.248674 | − | 0.195349i | ||||
\(311\) | 1.63457i | 0.0926879i | 0.998926 | + | 0.0463440i | \(0.0147570\pi\) | ||||
−0.998926 | + | 0.0463440i | \(0.985243\pi\) | |||||||
\(312\) | −6.48364 | + | 3.02115i | −0.367064 | + | 0.171039i | ||||
\(313\) | 10.6934 | + | 6.17384i | 0.604427 | + | 0.348966i | 0.770781 | − | 0.637100i | \(-0.219866\pi\) |
−0.166354 | + | 0.986066i | \(0.553200\pi\) | |||||||
\(314\) | − | 18.3537i | − | 1.03576i | ||||||
\(315\) | 1.72217 | − | 9.73488i | 0.0970330 | − | 0.548498i | ||||
\(316\) | 11.1206 | + | 6.42046i | 0.625580 | + | 0.361179i | ||||
\(317\) | 29.5244 | + | 17.0459i | 1.65825 | + | 0.957393i | 0.973521 | + | 0.228598i | \(0.0734141\pi\) |
0.684732 | + | 0.728795i | \(0.259919\pi\) | |||||||
\(318\) | 1.45807 | + | 3.12913i | 0.0817644 | + | 0.175473i | ||||
\(319\) | 4.82113 | + | 8.35045i | 0.269932 | + | 0.467535i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −4.20200 | + | 5.99748i | −0.234533 | + | 0.334747i | ||||
\(322\) | 0.698566 | + | 0.403318i | 0.0389296 | + | 0.0224760i | ||||
\(323\) | 6.73702 | + | 11.6689i | 0.374858 | + | 0.649273i | ||||
\(324\) | −8.45377 | − | 3.08769i | −0.469654 | − | 0.171538i | ||||
\(325\) | 4.12977i | 0.229078i | ||||||||
\(326\) | 1.70445i | 0.0944009i | ||||||||
\(327\) | −0.885417 | + | 10.0877i | −0.0489636 | + | 0.557851i | ||||
\(328\) | 3.94757 | + | 6.83739i | 0.217968 | + | 0.377532i | ||||
\(329\) | 11.3954 | + | 6.57914i | 0.628249 | + | 0.362720i | ||||
\(330\) | 6.64574 | + | 4.65618i | 0.365836 | + | 0.256314i | ||||
\(331\) | 19.1972 | − | 11.0835i | 1.05517 | − | 0.609205i | 0.131080 | − | 0.991372i | \(-0.458155\pi\) |
0.924093 | + | 0.382167i | \(0.124822\pi\) | |||||||
\(332\) | −1.42255 | − | 2.46393i | −0.0780725 | − | 0.135225i | ||||
\(333\) | 19.6272 | + | 16.4880i | 1.07557 | + | 0.903538i | ||||
\(334\) | −10.8880 | − | 6.28618i | −0.595764 | − | 0.343964i | ||||
\(335\) | 3.30418 | + | 1.90767i | 0.180526 | + | 0.104227i | ||||
\(336\) | −4.67456 | − | 3.27512i | −0.255018 | − | 0.178672i | ||||
\(337\) | − | 24.0073i | − | 1.30776i | −0.756597 | − | 0.653881i | \(-0.773140\pi\) | ||
0.756597 | − | 0.653881i | \(-0.226860\pi\) | |||||||
\(338\) | 3.51174 | + | 2.02750i | 0.191013 | + | 0.110282i | ||||
\(339\) | −4.72038 | − | 10.1303i | −0.256376 | − | 0.550203i | ||||
\(340\) | 6.04445i | 0.327807i | ||||||||
\(341\) | 20.5123 | + | 16.1137i | 1.11081 | + | 0.872605i | ||||
\(342\) | 5.12049 | + | 4.30151i | 0.276884 | + | 0.232599i | ||||
\(343\) | −10.3497 | −0.558829 | ||||||||
\(344\) | 5.79463 | − | 10.0366i | 0.312425 | − | 0.541137i | ||||
\(345\) | −0.179070 | − | 0.384299i | −0.00964081 | − | 0.0206900i | ||||
\(346\) | −1.30405 | − | 2.25868i | −0.0701061 | − | 0.121427i | ||||
\(347\) | −14.1185 | + | 24.4539i | −0.757919 | + | 1.31275i | 0.185992 | + | 0.982551i | \(0.440450\pi\) |
−0.943910 | + | 0.330202i | \(0.892883\pi\) | |||||||
\(348\) | −0.311692 | + | 3.55116i | −0.0167084 | + | 0.190362i | ||||
\(349\) | 14.1084 | 0.755205 | 0.377602 | − | 0.925968i | \(-0.376749\pi\) | ||||
0.377602 | + | 0.925968i | \(0.376749\pi\) | |||||||
\(350\) | −2.85385 | + | 1.64767i | −0.152545 | + | 0.0880718i | ||||
\(351\) | 5.53650 | + | 20.7324i | 0.295516 | + | 1.10661i | ||||
\(352\) | 4.05727 | − | 2.34247i | 0.216253 | − | 0.124854i | ||||
\(353\) | −11.1592 | + | 19.3283i | −0.593943 | + | 1.02874i | 0.399752 | + | 0.916623i | \(0.369096\pi\) |
−0.993695 | + | 0.112116i | \(0.964237\pi\) | |||||||
\(354\) | −1.05082 | − | 0.736234i | −0.0558506 | − | 0.0391304i | ||||
\(355\) | −4.83225 | + | 8.36971i | −0.256469 | + | 0.444218i | ||||
\(356\) | −0.149606 | −0.00792909 | ||||||||
\(357\) | −31.2717 | + | 14.5715i | −1.65507 | + | 0.771207i | ||||
\(358\) | −16.4505 | − | 9.49768i | −0.869434 | − | 0.501968i | ||||
\(359\) | −4.93899 | + | 2.85152i | −0.260670 | + | 0.150498i | −0.624640 | − | 0.780913i | \(-0.714754\pi\) |
0.363970 | + | 0.931411i | \(0.381421\pi\) | |||||||
\(360\) | 1.02448 | + | 2.81965i | 0.0539946 | + | 0.148609i | ||||
\(361\) | 7.01543 | + | 12.1511i | 0.369233 | + | 0.639530i | ||||
\(362\) | −8.30014 | − | 14.3763i | −0.436245 | − | 0.755599i | ||||
\(363\) | −15.5310 | − | 10.8814i | −0.815166 | − | 0.571127i | ||||
\(364\) | 13.6090i | 0.713307i | ||||||||
\(365\) | 0.167642 | − | 0.290365i | 0.00877480 | − | 0.0151984i | ||||
\(366\) | −0.954291 | + | 10.8724i | −0.0498816 | + | 0.568309i | ||||
\(367\) | 27.7580 | − | 16.0261i | 1.44896 | − | 0.836555i | 0.450537 | − | 0.892758i | \(-0.351233\pi\) |
0.998419 | + | 0.0562025i | \(0.0178992\pi\) | |||||||
\(368\) | −0.244780 | −0.0127600 | ||||||||
\(369\) | 22.2616 | − | 8.08838i | 1.15889 | − | 0.421064i | ||||
\(370\) | − | 8.54454i | − | 0.444210i | ||||||
\(371\) | 6.56798 | 0.340993 | ||||||||
\(372\) | 2.79250 | + | 9.23049i | 0.144784 | + | 0.478579i | ||||
\(373\) | −22.0309 | −1.14072 | −0.570359 | − | 0.821396i | \(-0.693196\pi\) | ||||
−0.570359 | + | 0.821396i | \(0.693196\pi\) | |||||||
\(374\) | − | 28.3179i | − | 1.46428i | ||||||
\(375\) | 1.72542 | + | 0.151443i | 0.0891002 | + | 0.00782049i | ||||
\(376\) | −3.99299 | −0.205923 | ||||||||
\(377\) | 7.36092 | − | 4.24983i | 0.379107 | − | 0.218877i | ||||
\(378\) | −12.1181 | + | 12.0977i | −0.623287 | + | 0.622237i | ||||
\(379\) | 11.4743 | − | 19.8741i | 0.589397 | − | 1.02087i | −0.404915 | − | 0.914355i | \(-0.632699\pi\) |
0.994312 | − | 0.106511i | \(-0.0339679\pi\) | |||||||
\(380\) | − | 2.22916i | − | 0.114353i | ||||||
\(381\) | −0.420768 | + | 0.600560i | −0.0215566 | + | 0.0307676i | ||||
\(382\) | −8.43140 | − | 14.6036i | −0.431388 | − | 0.747186i | ||||
\(383\) | −5.15835 | − | 8.93453i | −0.263579 | − | 0.456533i | 0.703611 | − | 0.710585i | \(-0.251570\pi\) |
−0.967190 | + | 0.254052i | \(0.918236\pi\) | |||||||
\(384\) | 1.72542 | + | 0.151443i | 0.0880498 | + | 0.00772830i | ||||
\(385\) | 13.3701 | − | 7.71924i | 0.681404 | − | 0.393409i | ||||
\(386\) | −5.99887 | − | 3.46345i | −0.305335 | − | 0.176285i | ||||
\(387\) | −26.6211 | − | 22.3633i | −1.35323 | − | 1.13679i | ||||
\(388\) | 7.67331 | 0.389553 | ||||||||
\(389\) | 12.7371 | − | 22.0613i | 0.645798 | − | 1.11855i | −0.338319 | − | 0.941031i | \(-0.609858\pi\) |
0.984117 | − | 0.177523i | \(-0.0568083\pi\) | |||||||
\(390\) | 4.10442 | − | 5.85822i | 0.207836 | − | 0.296642i | ||||
\(391\) | −0.739781 | + | 1.28134i | −0.0374123 | + | 0.0648001i | ||||
\(392\) | −3.34226 | + | 1.92965i | −0.168810 | + | 0.0974623i | ||||
\(393\) | −2.06551 | + | 2.94809i | −0.104191 | + | 0.148711i | ||||
\(394\) | 12.8333 | − | 7.40933i | 0.646534 | − | 0.373276i | ||||
\(395\) | −12.8409 | −0.646096 | ||||||||
\(396\) | −4.79960 | − | 13.2099i | −0.241189 | − | 0.663822i | ||||
\(397\) | 3.16333 | − | 5.47906i | 0.158763 | − | 0.274986i | −0.775660 | − | 0.631151i | \(-0.782583\pi\) |
0.934423 | + | 0.356165i | \(0.115916\pi\) | |||||||
\(398\) | −9.50589 | − | 16.4647i | −0.476487 | − | 0.825300i | ||||
\(399\) | 11.5328 | − | 5.37389i | 0.577363 | − | 0.269031i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −25.4504 | −1.27093 | −0.635465 | − | 0.772130i | \(-0.719192\pi\) | ||||
−0.635465 | + | 0.772130i | \(0.719192\pi\) | |||||||
\(402\) | −2.79113 | − | 5.98999i | −0.139209 | − | 0.298753i | ||||
\(403\) | 14.2042 | − | 18.0816i | 0.707562 | − | 0.900710i | ||||
\(404\) | 5.06959i | 0.252222i | ||||||||
\(405\) | 8.86502 | − | 1.55287i | 0.440506 | − | 0.0771626i | ||||
\(406\) | 5.87364 | + | 3.39115i | 0.291504 | + | 0.168300i | ||||
\(407\) | 40.0306i | 1.98425i | ||||||||
\(408\) | 6.00736 | − | 8.57426i | 0.297408 | − | 0.424489i | ||||
\(409\) | 31.9037 | + | 18.4196i | 1.57754 | + | 0.910790i | 0.995202 | + | 0.0978399i | \(0.0311933\pi\) |
0.582333 | + | 0.812950i | \(0.302140\pi\) | |||||||
\(410\) | −6.83739 | − | 3.94757i | −0.337675 | − | 0.194957i | ||||
\(411\) | 30.6622 | − | 14.2875i | 1.51246 | − | 0.704752i | ||||
\(412\) | −9.37875 | − | 16.2445i | −0.462058 | − | 0.800307i | ||||
\(413\) | −2.11408 | + | 1.22056i | −0.104027 | + | 0.0600600i | ||||
\(414\) | −0.127923 | + | 0.723112i | −0.00628709 | + | 0.0355390i | ||||
\(415\) | 2.46393 | + | 1.42255i | 0.120949 | + | 0.0698301i | ||||
\(416\) | −2.06489 | − | 3.57649i | −0.101239 | − | 0.175352i | ||||
\(417\) | −38.8727 | − | 3.41193i | −1.90361 | − | 0.167083i | ||||
\(418\) | 10.4435i | 0.510807i | ||||||||
\(419\) | 8.72337i | 0.426164i | 0.977034 | + | 0.213082i | \(0.0683502\pi\) | ||||
−0.977034 | + | 0.213082i | \(0.931650\pi\) | |||||||
\(420\) | 5.68585 | + | 0.499058i | 0.277441 | + | 0.0243515i | ||||
\(421\) | −2.19810 | − | 3.80721i | −0.107129 | − | 0.185552i | 0.807477 | − | 0.589899i | \(-0.200832\pi\) |
−0.914606 | + | 0.404347i | \(0.867499\pi\) | |||||||
\(422\) | −0.276731 | − | 0.159771i | −0.0134711 | − | 0.00777752i | ||||
\(423\) | −2.08676 | + | 11.7958i | −0.101462 | + | 0.573532i | ||||
\(424\) | −1.72608 | + | 0.996554i | −0.0838260 | + | 0.0483969i | ||||
\(425\) | −3.02223 | − | 5.23465i | −0.146600 | − | 0.253918i | ||||
\(426\) | 15.1731 | − | 7.07012i | 0.735137 | − | 0.342548i | ||||
\(427\) | 17.9830 | + | 10.3825i | 0.870260 | + | 0.502445i | ||||
\(428\) | −3.66151 | − | 2.11397i | −0.176986 | − | 0.102183i | ||||
\(429\) | −19.2290 | + | 27.4454i | −0.928383 | + | 1.32508i | ||||
\(430\) | 11.5893i | 0.558883i | ||||||||
\(431\) | −12.3311 | − | 7.11935i | −0.593967 | − | 0.342927i | 0.172698 | − | 0.984975i | \(-0.444752\pi\) |
−0.766665 | + | 0.642048i | \(0.778085\pi\) | |||||||
\(432\) | 1.34909 | − | 5.01796i | 0.0649084 | − | 0.241427i | ||||
\(433\) | 16.3649i | 0.786448i | 0.919443 | + | 0.393224i | \(0.128640\pi\) | ||||
−0.919443 | + | 0.393224i | \(0.871360\pi\) | |||||||
\(434\) | 18.1623 | + | 2.60163i | 0.871820 | + | 0.124882i | ||||
\(435\) | −1.50564 | − | 3.23124i | −0.0721901 | − | 0.154926i | ||||
\(436\) | −5.84653 | −0.279998 | ||||||||
\(437\) | 0.272827 | − | 0.472550i | 0.0130511 | − | 0.0226051i | ||||
\(438\) | −0.526389 | + | 0.245279i | −0.0251519 | + | 0.0117199i | ||||
\(439\) | −6.66688 | − | 11.5474i | −0.318193 | − | 0.551126i | 0.661918 | − | 0.749576i | \(-0.269743\pi\) |
−0.980111 | + | 0.198450i | \(0.936409\pi\) | |||||||
\(440\) | −2.34247 | + | 4.05727i | −0.111673 | + | 0.193423i | ||||
\(441\) | 3.95377 | + | 10.8819i | 0.188275 | + | 0.518186i | ||||
\(442\) | −24.9622 | −1.18733 | ||||||||
\(443\) | 18.7900 | − | 10.8484i | 0.892742 | − | 0.515425i | 0.0179037 | − | 0.999840i | \(-0.494301\pi\) |
0.874838 | + | 0.484415i | \(0.160967\pi\) | |||||||
\(444\) | −8.49210 | + | 12.1207i | −0.403017 | + | 0.575224i | ||||
\(445\) | 0.129562 | − | 0.0748029i | 0.00614185 | − | 0.00354600i | ||||
\(446\) | 0.692562 | − | 1.19955i | 0.0327937 | − | 0.0568004i | ||||
\(447\) | 15.3969 | − | 21.9759i | 0.728250 | − | 1.03943i | ||||
\(448\) | 1.64767 | − | 2.85385i | 0.0778452 | − | 0.134832i | ||||
\(449\) | 5.51787 | 0.260405 | 0.130202 | − | 0.991487i | \(-0.458437\pi\) | ||||
0.130202 | + | 0.991487i | \(0.458437\pi\) | |||||||
\(450\) | −2.29705 | − | 1.92965i | −0.108284 | − | 0.0909648i | ||||
\(451\) | 32.0327 | + | 18.4941i | 1.50836 | + | 0.870854i | ||||
\(452\) | 5.58805 | − | 3.22626i | 0.262840 | − | 0.151751i | ||||
\(453\) | 31.5221 | + | 2.76676i | 1.48104 | + | 0.129994i | ||||
\(454\) | −4.55194 | − | 7.88419i | −0.213633 | − | 0.370024i | ||||
\(455\) | −6.80451 | − | 11.7858i | −0.319000 | − | 0.552525i | ||||
\(456\) | −2.21548 | + | 3.16214i | −0.103749 | + | 0.148081i | ||||
\(457\) | 17.8127i | 0.833241i | 0.909081 | + | 0.416620i | \(0.136786\pi\) | ||||
−0.909081 | + | 0.416620i | \(0.863214\pi\) | |||||||
\(458\) | −3.99401 | + | 6.91782i | −0.186628 | + | 0.323249i | ||||
\(459\) | −22.1900 | − | 22.2275i | −1.03574 | − | 1.03749i | ||||
\(460\) | 0.211986 | − | 0.122390i | 0.00988389 | − | 0.00570646i | ||||
\(461\) | −10.7060 | −0.498630 | −0.249315 | − | 0.968422i | \(-0.580205\pi\) | ||||
−0.249315 | + | 0.968422i | \(0.580205\pi\) | |||||||
\(462\) | −26.6378 | − | 2.33805i | −1.23930 | − | 0.108776i | ||||
\(463\) | 23.2499i | 1.08051i | 0.841500 | + | 0.540257i | \(0.181673\pi\) | ||||
−0.841500 | + | 0.540257i | \(0.818327\pi\) | |||||||
\(464\) | −2.05814 | −0.0955469 | ||||||||
\(465\) | −7.03362 | − | 6.59759i | −0.326176 | − | 0.305956i | ||||
\(466\) | −15.9529 | −0.739003 | ||||||||
\(467\) | − | 1.78177i | − | 0.0824507i | −0.999150 | − | 0.0412253i | \(-0.986874\pi\) | ||
0.999150 | − | 0.0412253i | \(-0.0131262\pi\) | |||||||
\(468\) | −11.6445 | + | 4.23085i | −0.538268 | + | 0.195571i | ||||
\(469\) | −12.5728 | −0.580560 | ||||||||
\(470\) | 3.45803 | − | 1.99650i | 0.159507 | − | 0.0920914i | ||||
\(471\) | 2.77954 | − | 31.6677i | 0.128074 | − | 1.45917i | ||||
\(472\) | 0.370390 | − | 0.641535i | 0.0170486 | − | 0.0295290i | ||||
\(473\) | − | 54.2949i | − | 2.49648i | ||||||
\(474\) | 18.2153 | + | 12.7621i | 0.836655 | + | 0.586183i | ||||
\(475\) | 1.11458 | + | 1.93051i | 0.0511404 | + | 0.0885778i | ||||
\(476\) | −9.95929 | − | 17.2500i | −0.456483 | − | 0.790652i | ||||
\(477\) | 2.04189 | + | 5.61988i | 0.0934917 | + | 0.257316i | ||||
\(478\) | 7.83393 | − | 4.52292i | 0.358316 | − | 0.206874i | ||||
\(479\) | −30.8844 | − | 17.8311i | −1.41115 | − | 0.814725i | −0.415649 | − | 0.909525i | \(-0.636445\pi\) |
−0.995496 | + | 0.0948002i | \(0.969779\pi\) | |||||||
\(480\) | −1.56998 | + | 0.731555i | −0.0716593 | + | 0.0333908i | ||||
\(481\) | 35.2870 | 1.60895 | ||||||||
\(482\) | −7.71462 | + | 13.3621i | −0.351391 | + | 0.608628i | ||||
\(483\) | 1.14424 | + | 0.801684i | 0.0520647 | + | 0.0364779i | ||||
\(484\) | 5.47431 | − | 9.48178i | 0.248832 | − | 0.430990i | ||||
\(485\) | −6.64528 | + | 3.83666i | −0.301747 | + | 0.174214i | ||||
\(486\) | −14.1187 | − | 6.60781i | −0.640436 | − | 0.299737i | ||||
\(487\) | 9.14547 | − | 5.28014i | 0.414421 | − | 0.239266i | −0.278267 | − | 0.960504i | \(-0.589760\pi\) |
0.692687 | + | 0.721238i | \(0.256427\pi\) | |||||||
\(488\) | −6.30131 | −0.285247 | ||||||||
\(489\) | −0.258128 | + | 2.94089i | −0.0116729 | + | 0.132992i | ||||
\(490\) | 1.92965 | − | 3.34226i | 0.0871729 | − | 0.150988i | ||||
\(491\) | −8.01143 | − | 13.8762i | −0.361551 | − | 0.626224i | 0.626665 | − | 0.779288i | \(-0.284419\pi\) |
−0.988216 | + | 0.153064i | \(0.951086\pi\) | |||||||
\(492\) | 5.77573 | + | 12.3952i | 0.260390 | + | 0.558818i | ||||
\(493\) | −6.22018 | + | 10.7737i | −0.280143 | + | 0.485221i | ||||
\(494\) | 9.20591 | 0.414194 | ||||||||
\(495\) | 10.7615 | + | 9.04031i | 0.483695 | + | 0.406332i | ||||
\(496\) | −5.16785 | + | 2.07204i | −0.232043 | + | 0.0930373i | ||||
\(497\) | − | 31.8479i | − | 1.42857i | ||||||
\(498\) | −2.08134 | − | 4.46673i | −0.0932673 | − | 0.200159i | ||||
\(499\) | 15.8026 | + | 9.12364i | 0.707422 | + | 0.408430i | 0.810106 | − | 0.586284i | \(-0.199410\pi\) |
−0.102684 | + | 0.994714i | \(0.532743\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −17.8343 | − | 12.4952i | −0.796778 | − | 0.558244i | ||||
\(502\) | 3.28729 | + | 1.89792i | 0.146719 | + | 0.0847082i | ||||
\(503\) | −30.0423 | − | 17.3449i | −1.33952 | − | 0.773371i | −0.352782 | − | 0.935706i | \(-0.614764\pi\) |
−0.986736 | + | 0.162335i | \(0.948098\pi\) | |||||||
\(504\) | −7.56957 | − | 6.35888i | −0.337176 | − | 0.283247i | ||||
\(505\) | −2.53480 | − | 4.39040i | −0.112797 | − | 0.195370i | ||||
\(506\) | −0.993140 | + | 0.573389i | −0.0441504 | + | 0.0254903i | ||||
\(507\) | 5.75216 | + | 4.03011i | 0.255462 | + | 0.178984i | ||||
\(508\) | −0.366646 | − | 0.211683i | −0.0162673 | − | 0.00939193i | ||||
\(509\) | −9.89991 | − | 17.1472i | −0.438806 | − | 0.760034i | 0.558792 | − | 0.829308i | \(-0.311265\pi\) |
−0.997598 | + | 0.0692738i | \(0.977932\pi\) | |||||||
\(510\) | −0.915391 | + | 10.4292i | −0.0405342 | + | 0.461813i | ||||
\(511\) | 1.10488i | 0.0488770i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 8.18354 | + | 8.19736i | 0.361312 | + | 0.361922i | ||||
\(514\) | 15.5105 | + | 26.8650i | 0.684139 | + | 1.18496i | ||||
\(515\) | 16.2445 | + | 9.37875i | 0.715817 | + | 0.413277i | ||||
\(516\) | 11.5181 | − | 16.4397i | 0.507057 | − | 0.723720i | ||||
\(517\) | −16.2007 | + | 9.35345i | −0.712504 | + | 0.411364i | ||||
\(518\) | 14.0786 | + | 24.3849i | 0.618579 | + | 1.07141i | ||||
\(519\) | −1.90797 | − | 4.09465i | −0.0837505 | − | 0.179735i | ||||
\(520\) | 3.57649 | + | 2.06489i | 0.156839 | + | 0.0905512i | ||||
\(521\) | 27.2181 | + | 15.7144i | 1.19245 | + | 0.688460i | 0.958861 | − | 0.283876i | \(-0.0916204\pi\) |
0.233587 | + | 0.972336i | \(0.424954\pi\) | |||||||
\(522\) | −1.07560 | + | 6.08002i | −0.0470776 | + | 0.266115i | ||||
\(523\) | − | 30.9522i | − | 1.35345i | −0.736237 | − | 0.676723i | \(-0.763399\pi\) | ||
0.736237 | − | 0.676723i | \(-0.236601\pi\) | |||||||
\(524\) | −1.79983 | − | 1.03913i | −0.0786260 | − | 0.0453947i | ||||
\(525\) | −5.17362 | + | 2.41073i | −0.225795 | + | 0.105213i | ||||
\(526\) | 21.5086i | 0.937818i | ||||||||
\(527\) | −4.77201 | + | 33.3141i | −0.207872 | + | 1.45118i | ||||
\(528\) | 7.35524 | − | 3.42729i | 0.320096 | − | 0.149154i | ||||
\(529\) | −22.9401 | −0.997395 | ||||||||
\(530\) | 0.996554 | − | 1.72608i | 0.0432875 | − | 0.0749762i | ||||
\(531\) | −1.70161 | − | 1.42945i | −0.0738435 | − | 0.0620328i | ||||
\(532\) | 3.67293 | + | 6.36169i | 0.159242 | + | 0.275814i | ||||
\(533\) | 16.3026 | − | 28.2369i | 0.706142 | − | 1.22307i | ||||
\(534\) | −0.258132 | − | 0.0226568i | −0.0111705 | − | 0.000980454i | ||||
\(535\) | 4.22795 | 0.182790 | ||||||||
\(536\) | 3.30418 | − | 1.90767i | 0.142719 | − | 0.0823987i | ||||
\(537\) | −26.9456 | − | 18.8788i | −1.16279 | − | 0.814679i | ||||
\(538\) | −23.4194 | + | 13.5212i | −1.00968 | + | 0.582940i | ||||
\(539\) | −9.04031 | + | 15.6583i | −0.389394 | + | 0.674449i | ||||
\(540\) | 1.34063 | + | 5.02023i | 0.0576916 | + | 0.216036i | ||||
\(541\) | 21.6449 | − | 37.4901i | 0.930588 | − | 1.61183i | 0.148270 | − | 0.988947i | \(-0.452630\pi\) |
0.782318 | − | 0.622879i | \(-0.214037\pi\) | |||||||
\(542\) | 16.9825 | 0.729463 | ||||||||
\(543\) | −12.1440 | − | 26.0620i | −0.521149 | − | 1.11843i | ||||
\(544\) | 5.23465 | + | 3.02223i | 0.224434 | + | 0.129577i | ||||
\(545\) | 5.06324 | − | 2.92326i | 0.216885 | − | 0.125219i | ||||
\(546\) | −2.06099 | + | 23.4812i | −0.0882024 | + | 1.00490i | ||||
\(547\) | 2.09475 | + | 3.62821i | 0.0895650 | + | 0.155131i | 0.907327 | − | 0.420425i | \(-0.138119\pi\) |
−0.817762 | + | 0.575556i | \(0.804786\pi\) | |||||||
\(548\) | 9.76518 | + | 16.9138i | 0.417148 | + | 0.722522i | ||||
\(549\) | −3.29310 | + | 18.6149i | −0.140546 | + | 0.794465i | ||||
\(550\) | − | 4.68494i | − | 0.199766i | ||||||
\(551\) | 2.29396 | − | 3.97326i | 0.0977261 | − | 0.169267i | ||||
\(552\) | −0.422348 | − | 0.0370703i | −0.0179763 | − | 0.00157781i | ||||
\(553\) | 36.6461 | − | 21.1576i | 1.55835 | − | 0.899714i | ||||
\(554\) | −23.1214 | −0.982336 | ||||||||
\(555\) | 1.29401 | − | 14.7429i | 0.0549278 | − | 0.625801i | ||||
\(556\) | − | 22.5295i | − | 0.955462i | ||||||
\(557\) | 33.3611 | 1.41356 | 0.706778 | − | 0.707435i | \(-0.250148\pi\) | ||||
0.706778 | + | 0.707435i | \(0.250148\pi\) | |||||||
\(558\) | 3.42033 | + | 16.3494i | 0.144794 | + | 0.692123i | ||||
\(559\) | −47.8610 | −2.02430 | ||||||||
\(560\) | 3.29535i | 0.139254i | ||||||||
\(561\) | 4.28855 | − | 48.8602i | 0.181063 | − | 2.06288i | ||||
\(562\) | 26.0722 | 1.09979 | ||||||||
\(563\) | 3.50089 | − | 2.02124i | 0.147545 | − | 0.0851851i | −0.424410 | − | 0.905470i | \(-0.639518\pi\) |
0.571955 | + | 0.820285i | \(0.306185\pi\) | |||||||
\(564\) | −6.88957 | − | 0.604711i | −0.290103 | − | 0.0254629i | ||||
\(565\) | −3.22626 | + | 5.58805i | −0.135730 | + | 0.235091i | ||||
\(566\) | 14.5905i | 0.613284i | ||||||||
\(567\) | −22.7409 | + | 19.0383i | −0.955026 | + | 0.799534i | ||||
\(568\) | 4.83225 | + | 8.36971i | 0.202757 | + | 0.351185i | ||||
\(569\) | −1.92967 | − | 3.34229i | −0.0808961 | − | 0.140116i | 0.822739 | − | 0.568419i | \(-0.192445\pi\) |
−0.903635 | + | 0.428303i | \(0.859112\pi\) | |||||||
\(570\) | 0.337591 | − | 3.84623i | 0.0141401 | − | 0.161101i | ||||
\(571\) | 27.2167 | − | 15.7136i | 1.13898 | − | 0.657593i | 0.192805 | − | 0.981237i | \(-0.438241\pi\) |
0.946179 | + | 0.323644i | \(0.104908\pi\) | |||||||
\(572\) | −16.7556 | − | 9.67385i | −0.700587 | − | 0.404484i | ||||
\(573\) | −12.3361 | − | 26.4742i | −0.515346 | − | 1.10598i | ||||
\(574\) | 26.0172 | 1.08594 | ||||||||
\(575\) | −0.122390 | + | 0.211986i | −0.00510402 | + | 0.00884042i | ||||
\(576\) | 2.95413 | + | 0.522605i | 0.123089 | + | 0.0217752i | ||||
\(577\) | 0.696828 | − | 1.20694i | 0.0290093 | − | 0.0502457i | −0.851156 | − | 0.524912i | \(-0.824098\pi\) |
0.880166 | + | 0.474667i | \(0.157431\pi\) | |||||||
\(578\) | 16.9182 | − | 9.76772i | 0.703703 | − | 0.406283i | ||||
\(579\) | −9.82604 | − | 6.88438i | −0.408356 | − | 0.286105i | ||||
\(580\) | 1.78240 | − | 1.02907i | 0.0740103 | − | 0.0427299i | ||||
\(581\) | −9.37558 | −0.388965 | ||||||||
\(582\) | 13.2397 | + | 1.16207i | 0.548802 | + | 0.0481694i | ||||
\(583\) | −4.66879 | + | 8.08658i | −0.193362 | + | 0.334912i | ||||
\(584\) | −0.167642 | − | 0.290365i | −0.00693709 | − | 0.0120154i | ||||
\(585\) | 7.96903 | − | 9.48628i | 0.329479 | − | 0.392210i | ||||
\(586\) | 14.2780 | − | 24.7303i | 0.589821 | − | 1.02160i | ||||
\(587\) | 44.2243 | 1.82533 | 0.912666 | − | 0.408706i | \(-0.134020\pi\) | ||||
0.912666 | + | 0.408706i | \(0.134020\pi\) | |||||||
\(588\) | −6.05903 | + | 2.82330i | −0.249870 | + | 0.116431i | ||||
\(589\) | 1.75989 | − | 12.2860i | 0.0725149 | − | 0.506237i | ||||
\(590\) | 0.740780i | 0.0304974i | ||||||||
\(591\) | 23.2649 | − | 10.8407i | 0.956992 | − | 0.445925i | ||||
\(592\) | −7.39979 | − | 4.27227i | −0.304130 | − | 0.175589i | ||||
\(593\) | − | 14.8656i | − | 0.610459i | −0.952279 | − | 0.305229i | \(-0.901267\pi\) | ||
0.952279 | − | 0.305229i | \(-0.0987332\pi\) | |||||||
\(594\) | −6.28077 | − | 23.5195i | −0.257703 | − | 0.965015i | ||||
\(595\) | 17.2500 | + | 9.95929i | 0.707181 | + | 0.408291i | ||||
\(596\) | 13.4165 | + | 7.74601i | 0.549560 | + | 0.317289i | ||||
\(597\) | −13.9082 | − | 29.8481i | −0.569223 | − | 1.22160i | ||||
\(598\) | 0.505443 | + | 0.875452i | 0.0206691 | + | 0.0357999i | ||||
\(599\) | −23.8479 | + | 13.7686i | −0.974397 | + | 0.562568i | −0.900574 | − | 0.434703i | \(-0.856853\pi\) |
−0.0738230 | + | 0.997271i | \(0.523520\pi\) | |||||||
\(600\) | 0.993862 | − | 1.41853i | 0.0405743 | − | 0.0579114i | ||||
\(601\) | −30.8947 | − | 17.8371i | −1.26022 | − | 0.727589i | −0.287105 | − | 0.957899i | \(-0.592693\pi\) |
−0.973117 | + | 0.230310i | \(0.926026\pi\) | |||||||
\(602\) | −19.0953 | − | 33.0740i | −0.778266 | − | 1.34800i | ||||
\(603\) | −3.90872 | − | 10.7579i | −0.159175 | − | 0.438096i | ||||
\(604\) | 18.2693i | 0.743367i | ||||||||
\(605\) | 10.9486i | 0.445125i | ||||||||
\(606\) | −0.767755 | + | 8.74716i | −0.0311879 | + | 0.355329i | ||||
\(607\) | 22.4644 | + | 38.9094i | 0.911801 | + | 1.57929i | 0.811519 | + | 0.584327i | \(0.198641\pi\) |
0.100282 | + | 0.994959i | \(0.468025\pi\) | |||||||
\(608\) | −1.93051 | − | 1.11458i | −0.0782924 | − | 0.0452022i | ||||
\(609\) | 9.62091 | + | 6.74067i | 0.389859 | + | 0.273146i | ||||
\(610\) | 5.45710 | − | 3.15066i | 0.220951 | − | 0.127566i | ||||
\(611\) | 8.24507 | + | 14.2809i | 0.333560 | + | 0.577742i | ||||
\(612\) | 11.6637 | − | 13.8844i | 0.471477 | − | 0.561244i | ||||
\(613\) | 36.0994 | + | 20.8420i | 1.45804 | + | 0.841800i | 0.998915 | − | 0.0465721i | \(-0.0148297\pi\) |
0.459125 | + | 0.888372i | \(0.348163\pi\) | |||||||
\(614\) | 8.12397 | + | 4.69037i | 0.327857 | + | 0.189288i | ||||
\(615\) | −11.1995 | − | 7.84668i | −0.451608 | − | 0.316409i | ||||
\(616\) | − | 15.4385i | − | 0.622034i | ||||||
\(617\) | −37.6159 | − | 21.7175i | −1.51436 | − | 0.874316i | −0.999858 | − | 0.0168256i | \(-0.994644\pi\) |
−0.514501 | − | 0.857490i | \(-0.672023\pi\) | |||||||
\(618\) | −13.7221 | − | 29.4488i | −0.551985 | − | 1.18461i | ||||
\(619\) | − | 38.4345i | − | 1.54481i | −0.635129 | − | 0.772406i | \(-0.719053\pi\) | ||
0.635129 | − | 0.772406i | \(-0.280947\pi\) | |||||||
\(620\) | 3.43947 | − | 4.37836i | 0.138132 | − | 0.175839i | ||||
\(621\) | −0.330231 | + | 1.22830i | −0.0132517 | + | 0.0492899i | ||||
\(622\) | −1.63457 | −0.0655403 | ||||||||
\(623\) | −0.246502 | + | 0.426953i | −0.00987587 | + | 0.0171055i | ||||
\(624\) | −3.02115 | − | 6.48364i | −0.120943 | − | 0.259553i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −6.17384 | + | 10.6934i | −0.246756 | + | 0.427394i | ||||
\(627\) | −1.58159 | + | 18.0193i | −0.0631627 | + | 0.719623i | ||||
\(628\) | 18.3537 | 0.732391 | ||||||||
\(629\) | −44.7277 | + | 25.8236i | −1.78341 | + | 1.02965i | ||||
\(630\) | 9.73488 | + | 1.72217i | 0.387847 | + | 0.0686127i | ||||
\(631\) | 5.86942 | − | 3.38871i | 0.233658 | − | 0.134902i | −0.378601 | − | 0.925560i | \(-0.623595\pi\) |
0.612258 | + | 0.790658i | \(0.290261\pi\) | |||||||
\(632\) | −6.42046 | + | 11.1206i | −0.255392 | + | 0.442352i | ||||
\(633\) | −0.453280 | − | 0.317580i | −0.0180163 | − | 0.0126227i | ||||
\(634\) | −17.0459 | + | 29.5244i | −0.676979 | + | 1.17256i | ||||
\(635\) | 0.423367 | 0.0168008 | ||||||||
\(636\) | −3.12913 | + | 1.45807i | −0.124078 | + | 0.0578162i | ||||
\(637\) | 13.8028 | + | 7.96903i | 0.546885 | + | 0.315744i | ||||
\(638\) | −8.35045 | + | 4.82113i | −0.330597 | + | 0.190870i | ||||
\(639\) | 27.2506 | − | 9.90105i | 1.07802 | − | 0.391680i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 1.51314 | + | 2.62083i | 0.0597653 | + | 0.103517i | 0.894360 | − | 0.447348i | \(-0.147631\pi\) |
−0.834595 | + | 0.550865i | \(0.814298\pi\) | |||||||
\(642\) | −5.99748 | − | 4.20200i | −0.236702 | − | 0.165840i | ||||
\(643\) | − | 8.47085i | − | 0.334058i | −0.985952 | − | 0.167029i | \(-0.946583\pi\) | ||
0.985952 | − | 0.167029i | \(-0.0534173\pi\) | |||||||
\(644\) | −0.403318 | + | 0.698566i | −0.0158929 | + | 0.0275274i | ||||
\(645\) | −1.75511 | + | 19.9963i | −0.0691075 | + | 0.787354i | ||||
\(646\) | −11.6689 | + | 6.73702i | −0.459106 | + | 0.265065i | ||||
\(647\) | 30.7071 | 1.20722 | 0.603611 | − | 0.797279i | \(-0.293728\pi\) | ||||
0.603611 | + | 0.797279i | \(0.293728\pi\) | |||||||
\(648\) | 3.08769 | − | 8.45377i | 0.121296 | − | 0.332095i | ||||
\(649\) | − | 3.47051i | − | 0.136229i | ||||||
\(650\) | −4.12977 | −0.161983 | ||||||||
\(651\) | 30.9436 | + | 7.23945i | 1.21278 | + | 0.283737i | ||||
\(652\) | −1.70445 | −0.0667515 | ||||||||
\(653\) | 20.6155i | 0.806748i | 0.915035 | + | 0.403374i | \(0.132163\pi\) | ||||
−0.915035 | + | 0.403374i | \(0.867837\pi\) | |||||||
\(654\) | −10.0877 | − | 0.885417i | −0.394460 | − | 0.0346225i | ||||
\(655\) | 2.07827 | 0.0812046 | ||||||||
\(656\) | −6.83739 | + | 3.94757i | −0.266955 | + | 0.154127i | ||||
\(657\) | −0.945387 | + | 0.343491i | −0.0368831 | + | 0.0134009i | ||||
\(658\) | −6.57914 | + | 11.3954i | −0.256482 | + | 0.444239i | ||||
\(659\) | 45.9699i | 1.79073i | 0.445331 | + | 0.895366i | \(0.353086\pi\) | ||||
−0.445331 | + | 0.895366i | \(0.646914\pi\) | |||||||
\(660\) | −4.65618 | + | 6.64574i | −0.181242 | + | 0.258685i | ||||
\(661\) | −1.62902 | − | 2.82155i | −0.0633616 | − | 0.109745i | 0.832604 | − | 0.553868i | \(-0.186849\pi\) |
−0.895966 | + | 0.444123i | \(0.853515\pi\) | |||||||
\(662\) | 11.0835 | + | 19.1972i | 0.430773 | + | 0.746121i | ||||
\(663\) | −43.0702 | − | 3.78036i | −1.67271 | − | 0.146817i | ||||
\(664\) | 2.46393 | − | 1.42255i | 0.0956189 | − | 0.0552056i | ||||
\(665\) | −6.36169 | − | 3.67293i | −0.246696 | − | 0.142430i | ||||
\(666\) | −16.4880 | + | 19.6272i | −0.638898 | + | 0.760540i | ||||
\(667\) | 0.503792 | 0.0195069 | ||||||||
\(668\) | 6.28618 | − | 10.8880i | 0.243220 | − | 0.421269i | ||||
\(669\) | 1.37662 | − | 1.96484i | 0.0532233 | − | 0.0759653i | ||||
\(670\) | −1.90767 | + | 3.30418i | −0.0736996 | + | 0.127651i | ||||
\(671\) | −25.5662 | + | 14.7606i | −0.986970 | + | 0.569828i | ||||
\(672\) | 3.27512 | − | 4.67456i | 0.126341 | − | 0.180325i | ||||
\(673\) | −28.5117 | + | 16.4612i | −1.09905 | + | 0.634534i | −0.935970 | − | 0.352079i | \(-0.885475\pi\) |
−0.163076 | + | 0.986614i | \(0.552141\pi\) | |||||||
\(674\) | 24.0073 | 0.924727 | ||||||||
\(675\) | −3.67114 | − | 3.67733i | −0.141302 | − | 0.141541i | ||||
\(676\) | −2.02750 | + | 3.51174i | −0.0779808 | + | 0.135067i | ||||
\(677\) | 2.98095 | + | 5.16316i | 0.114567 | + | 0.198436i | 0.917607 | − | 0.397490i | \(-0.130118\pi\) |
−0.803039 | + | 0.595926i | \(0.796785\pi\) | |||||||
\(678\) | 10.1303 | − | 4.72038i | 0.389052 | − | 0.181285i | ||||
\(679\) | 12.6431 | − | 21.8985i | 0.485198 | − | 0.840388i | ||||
\(680\) | −6.04445 | −0.231794 | ||||||||
\(681\) | −6.65999 | − | 14.2929i | −0.255211 | − | 0.547705i | ||||
\(682\) | −16.1137 | + | 20.5123i | −0.617025 | + | 0.785458i | ||||
\(683\) | 32.4819i | 1.24289i | 0.783459 | + | 0.621443i | \(0.213453\pi\) | ||||
−0.783459 | + | 0.621443i | \(0.786547\pi\) | |||||||
\(684\) | −4.30151 | + | 5.12049i | −0.164472 | + | 0.195787i | ||||
\(685\) | −16.9138 | − | 9.76518i | −0.646243 | − | 0.373109i | ||||
\(686\) | − | 10.3497i | − | 0.395152i | ||||||
\(687\) | −7.93899 | + | 11.3313i | −0.302891 | + | 0.432315i | ||||
\(688\) | 10.0366 | + | 5.79463i | 0.382641 | + | 0.220918i | ||||
\(689\) | 7.12832 | + | 4.11554i | 0.271567 | + | 0.156790i | ||||
\(690\) | 0.384299 | − | 0.179070i | 0.0146300 | − | 0.00681708i | ||||
\(691\) | 8.97812 | + | 15.5506i | 0.341544 | + | 0.591571i | 0.984720 | − | 0.174147i | \(-0.0557169\pi\) |
−0.643176 | + | 0.765719i | \(0.722384\pi\) | |||||||
\(692\) | 2.25868 | − | 1.30405i | 0.0858621 | − | 0.0495725i | ||||
\(693\) | −45.6073 | − | 8.06823i | −1.73248 | − | 0.306487i | ||||
\(694\) | −24.4539 | − | 14.1185i | −0.928257 | − | 0.535929i | ||||
\(695\) | 11.2647 | + | 19.5111i | 0.427296 | + | 0.740098i | ||||
\(696\) | −3.55116 | − | 0.311692i | −0.134606 | − | 0.0118146i | ||||
\(697\) | 47.7218i | 1.80759i | ||||||||
\(698\) | 14.1084i | 0.534010i | ||||||||
\(699\) | −27.5254 | − | 2.41595i | −1.04110 | − | 0.0913797i | ||||
\(700\) | −1.64767 | − | 2.85385i | −0.0622762 | − | 0.107866i | ||||
\(701\) | −17.0045 | − | 9.81756i | −0.642251 | − | 0.370804i | 0.143230 | − | 0.989689i | \(-0.454251\pi\) |
−0.785481 | + | 0.618885i | \(0.787584\pi\) | |||||||
\(702\) | −20.7324 | + | 5.53650i | −0.782494 | + | 0.208962i | ||||
\(703\) | 16.4953 | − | 9.52357i | 0.622133 | − | 0.359188i | ||||
\(704\) | 2.34247 | + | 4.05727i | 0.0882851 | + | 0.152914i | ||||
\(705\) | 6.26890 | − | 2.92109i | 0.236100 | − | 0.110015i | ||||
\(706\) | −19.3283 | − | 11.1592i | −0.727428 | − | 0.419981i | ||||
\(707\) | 14.4679 | + | 8.35303i | 0.544120 | + | 0.314148i | ||||
\(708\) | 0.736234 | − | 1.05082i | 0.0276694 | − | 0.0394923i | ||||
\(709\) | 2.09339i | 0.0786187i | 0.999227 | + | 0.0393094i | \(0.0125158\pi\) | ||||
−0.999227 | + | 0.0393094i | \(0.987484\pi\) | |||||||
\(710\) | −8.36971 | − | 4.83225i | −0.314110 | − | 0.181351i | ||||
\(711\) | 29.4962 | + | 24.7785i | 1.10619 | + | 0.929267i | ||||
\(712\) | − | 0.149606i | − | 0.00560672i | ||||||
\(713\) | 1.26499 | − | 0.507194i | 0.0473741 | − | 0.0189946i | ||||
\(714\) | −14.5715 | − | 31.2717i | −0.545326 | − | 1.17031i | ||||
\(715\) | 19.3477 | 0.723563 | ||||||||
\(716\) | 9.49768 | − | 16.4505i | 0.354945 | − | 0.614783i | ||||
\(717\) | 14.2018 | − | 6.61753i | 0.530375 | − | 0.247136i | ||||
\(718\) | −2.85152 | − | 4.93899i | −0.106418 | − | 0.184321i | ||||
\(719\) | −4.88475 | + | 8.46063i | −0.182170 | + | 0.315528i | −0.942619 | − | 0.333869i | \(-0.891646\pi\) |
0.760449 | + | 0.649398i | \(0.224979\pi\) | |||||||
\(720\) | −2.81965 | + | 1.02448i | −0.105082 | + | 0.0381800i | ||||
\(721\) | −61.8124 | −2.30202 | ||||||||
\(722\) | −12.1511 | + | 7.01543i | −0.452216 | + | 0.261087i | ||||
\(723\) | −15.3345 | + | 21.8869i | −0.570298 | + | 0.813983i | ||||
\(724\) | 14.3763 | − | 8.30014i | 0.534289 | − | 0.308472i | ||||
\(725\) | −1.02907 | + | 1.78240i | −0.0382188 | + | 0.0661968i | ||||
\(726\) | 10.8814 | − | 15.5310i | 0.403847 | − | 0.576409i | ||||
\(727\) | −9.42776 | + | 16.3294i | −0.349656 | + | 0.605622i | −0.986188 | − | 0.165628i | \(-0.947035\pi\) |
0.636532 | + | 0.771250i | \(0.280368\pi\) | |||||||
\(728\) | −13.6090 | −0.504384 | ||||||||
\(729\) | −23.3599 | − | 13.5394i | −0.865181 | − | 0.501460i | ||||
\(730\) | 0.290365 | + | 0.167642i | 0.0107469 | + | 0.00620472i | ||||
\(731\) | 60.6657 | − | 35.0254i | 2.24380 | − | 1.29546i | ||||
\(732\) | −10.8724 | − | 0.954291i | −0.401855 | − | 0.0352716i | ||||
\(733\) | −7.30224 | − | 12.6479i | −0.269714 | − | 0.467159i | 0.699074 | − | 0.715050i | \(-0.253596\pi\) |
−0.968788 | + | 0.247891i | \(0.920263\pi\) | |||||||
\(734\) | 16.0261 | + | 27.7580i | 0.591534 | + | 1.02457i | ||||
\(735\) | 3.83562 | − | 5.47456i | 0.141479 | − | 0.201932i | ||||
\(736\) | − | 0.244780i | − | 0.00902271i | ||||||
\(737\) | 8.93730 | − | 15.4799i | 0.329210 | − | 0.570208i | ||||
\(738\) | 8.08838 | + | 22.2616i | 0.297737 | + | 0.819459i | ||||
\(739\) | −41.8282 | + | 24.1495i | −1.53868 | + | 0.888355i | −0.539759 | + | 0.841819i | \(0.681485\pi\) |
−0.998917 | + | 0.0465355i | \(0.985182\pi\) | |||||||
\(740\) | 8.54454 | 0.314104 | ||||||||
\(741\) | 15.8840 | + | 1.39417i | 0.583515 | + | 0.0512162i | ||||
\(742\) | 6.56798i | 0.241118i | ||||||||
\(743\) | 6.41688 | 0.235412 | 0.117706 | − | 0.993048i | \(-0.462446\pi\) | ||||
0.117706 | + | 0.993048i | \(0.462446\pi\) | |||||||
\(744\) | −9.23049 | + | 2.79250i | −0.338406 | + | 0.102378i | ||||
\(745\) | −15.4920 | −0.567584 | ||||||||
\(746\) | − | 22.0309i | − | 0.806609i | ||||||
\(747\) | −2.91473 | − | 8.02219i | −0.106644 | − | 0.293516i | ||||
\(748\) | 28.3179 | 1.03540 | ||||||||
\(749\) | −12.0659 | + | 6.96627i | −0.440880 | + | 0.254542i | ||||
\(750\) | −0.151443 | + | 1.72542i | −0.00552992 | + | 0.0630033i | ||||
\(751\) | −8.51988 | + | 14.7569i | −0.310895 | + | 0.538486i | −0.978556 | − | 0.205979i | \(-0.933962\pi\) |
0.667661 | + | 0.744465i | \(0.267295\pi\) | |||||||
\(752\) | − | 3.99299i | − | 0.145609i | ||||||
\(753\) | 5.38452 | + | 3.77254i | 0.196223 | + | 0.137479i | ||||
\(754\) | 4.24983 | + | 7.36092i | 0.154770 | + | 0.268069i | ||||
\(755\) | −9.13464 | − | 15.8217i | −0.332444 | − | 0.575809i | ||||
\(756\) | −12.0977 | − | 12.1181i | −0.439988 | − | 0.440730i | ||||
\(757\) | 17.9616 | − | 10.3701i | 0.652826 | − | 0.376909i | −0.136712 | − | 0.990611i | \(-0.543653\pi\) |
0.789538 | + | 0.613701i | \(0.210320\pi\) | |||||||
\(758\) | 19.8741 | + | 11.4743i | 0.721861 | + | 0.416767i | ||||
\(759\) | −1.80042 | + | 0.838932i | −0.0653510 | + | 0.0304513i | ||||
\(760\) | 2.22916 | 0.0808601 | ||||||||
\(761\) | −11.5689 | + | 20.0379i | −0.419372 | + | 0.726373i | −0.995876 | − | 0.0907205i | \(-0.971083\pi\) |
0.576504 | + | 0.817094i | \(0.304416\pi\) | |||||||
\(762\) | −0.600560 | − | 0.420768i | −0.0217560 | − | 0.0152428i | ||||
\(763\) | −9.63317 | + | 16.6851i | −0.348744 | + | 0.604043i | ||||
\(764\) | 14.6036 | − | 8.43140i | 0.528340 | − | 0.305037i | ||||
\(765\) | −3.15886 | + | 17.8561i | −0.114209 | + | 0.645589i | ||||
\(766\) | 8.93453 | − | 5.15835i | 0.322818 | − | 0.186379i | ||||
\(767\) | −3.05925 | −0.110463 | ||||||||
\(768\) | −0.151443 | + | 1.72542i | −0.00546473 | + | 0.0622606i | ||||
\(769\) | 19.5619 | − | 33.8822i | 0.705420 | − | 1.22182i | −0.261120 | − | 0.965306i | \(-0.584092\pi\) |
0.966540 | − | 0.256517i | \(-0.0825749\pi\) | |||||||
\(770\) | 7.71924 | + | 13.3701i | 0.278182 | + | 0.481826i | ||||
\(771\) | 22.6936 | + | 48.7023i | 0.817289 | + | 1.75397i | ||||
\(772\) | 3.46345 | − | 5.99887i | 0.124652 | − | 0.215904i | ||||
\(773\) | 17.0109 | 0.611839 | 0.305920 | − | 0.952057i | \(-0.401036\pi\) | ||||
0.305920 | + | 0.952057i | \(0.401036\pi\) | |||||||
\(774\) | 22.3633 | − | 26.6211i | 0.803831 | − | 0.956875i | ||||
\(775\) | −0.789485 | + | 5.51151i | −0.0283592 | + | 0.197979i | ||||
\(776\) | 7.67331i | 0.275456i | ||||||||
\(777\) | 20.5986 | + | 44.2062i | 0.738969 | + | 1.58589i | ||||
\(778\) | 22.0613 | + | 12.7371i | 0.790937 | + | 0.456648i | ||||
\(779\) | − | 17.5995i | − | 0.630568i | ||||||
\(780\) | 5.85822 | + | 4.10442i | 0.209758 | + | 0.146962i | ||||
\(781\) | 39.2116 | + | 22.6388i | 1.40310 | + | 0.810080i | ||||
\(782\) | −1.28134 | − | 0.739781i | −0.0458206 | − | 0.0264545i | ||||
\(783\) | −2.77663 | + | 10.3277i | −0.0992286 | + | 0.369081i | ||||
\(784\) | −1.92965 | − | 3.34226i | −0.0689162 | − | 0.119366i | ||||
\(785\) | −15.8947 | + | 9.17683i | −0.567307 | + | 0.327535i | ||||
\(786\) | −2.94809 | − | 2.06551i | −0.105155 | − | 0.0736743i | ||||
\(787\) | 12.8119 | + | 7.39695i | 0.456695 | + | 0.263673i | 0.710653 | − | 0.703542i | \(-0.248399\pi\) |
−0.253959 | + | 0.967215i | \(0.581733\pi\) | |||||||
\(788\) | 7.40933 | + | 12.8333i | 0.263946 | + | 0.457168i | ||||
\(789\) | −3.25732 | + | 37.1112i | −0.115964 | + | 1.32120i | ||||
\(790\) | − | 12.8409i | − | 0.456859i | ||||||
\(791\) | − | 21.2633i | − | 0.756036i | ||||||
\(792\) | 13.2099 | − | 4.79960i | 0.469393 | − | 0.170546i | ||||
\(793\) | 13.0115 | + | 22.5366i | 0.462052 | + | 0.800297i | ||||
\(794\) | 5.47906 | + | 3.16333i | 0.194444 | + | 0.112263i | ||||
\(795\) | 1.98087 | − | 2.82729i | 0.0702544 | − | 0.100274i | ||||
\(796\) | 16.4647 | − | 9.50589i | 0.583575 | − | 0.336927i | ||||
\(797\) | 11.4621 | + | 19.8529i | 0.406007 | + | 0.703226i | 0.994438 | − | 0.105322i | \(-0.0335873\pi\) |
−0.588431 | + | 0.808548i | \(0.700254\pi\) | |||||||
\(798\) | 5.37389 | + | 11.5328i | 0.190234 | + | 0.408257i | ||||
\(799\) | −20.9019 | − | 12.0677i | −0.739456 | − | 0.426925i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | −0.441955 | − | 0.0781848i | −0.0156157 | − | 0.00276252i | ||||
\(802\) | − | 25.4504i | − | 0.898683i | ||||||
\(803\) | −1.36034 | − | 0.785394i | −0.0480054 | − | 0.0277159i | ||||
\(804\) | 5.98999 | − | 2.79113i | 0.211250 | − | 0.0984354i | ||||
\(805\) | − | 0.806635i | − | 0.0284302i | ||||||
\(806\) | 18.0816 | + | 14.2042i | 0.636898 | + | 0.500322i | ||||
\(807\) | −42.4559 | + | 19.7830i | −1.49452 | + | 0.696394i | ||||
\(808\) | −5.06959 | −0.178348 | ||||||||
\(809\) | 25.3510 | − | 43.9092i | 0.891294 | − | 1.54377i | 0.0529687 | − | 0.998596i | \(-0.483132\pi\) |
0.838325 | − | 0.545170i | \(-0.183535\pi\) | |||||||
\(810\) | 1.55287 | + | 8.86502i | 0.0545622 | + | 0.311485i | ||||
\(811\) | −8.64545 | − | 14.9744i | −0.303583 | − | 0.525821i | 0.673362 | − | 0.739313i | \(-0.264850\pi\) |
−0.976945 | + | 0.213492i | \(0.931516\pi\) | |||||||
\(812\) | −3.39115 | + | 5.87364i | −0.119006 | + | 0.206124i | ||||
\(813\) | 29.3020 | + | 2.57189i | 1.02767 | + | 0.0902001i | ||||
\(814\) | −40.0306 | −1.40307 | ||||||||
\(815\) | 1.47610 | − | 0.852226i | 0.0517055 | − | 0.0298522i | ||||
\(816\) | 8.57426 | + | 6.00736i | 0.300159 | + | 0.210299i | ||||
\(817\) | −22.3732 | + | 12.9171i | −0.782737 | + | 0.451914i | ||||
\(818\) | −18.4196 | + | 31.9037i | −0.644026 | + | 1.11549i | ||||
\(819\) | −7.11215 | + | 40.2028i | −0.248519 | + | 1.40480i | ||||
\(820\) | 3.94757 | − | 6.83739i | 0.137855 | − | 0.238772i | ||||
\(821\) | −37.4349 | −1.30649 | −0.653244 | − | 0.757147i | \(-0.726593\pi\) | ||||
−0.653244 | + | 0.757147i | \(0.726593\pi\) | |||||||
\(822\) | 14.2875 | + | 30.6622i | 0.498335 | + | 1.06947i | ||||
\(823\) | −28.5790 | − | 16.5001i | −0.996202 | − | 0.575157i | −0.0890794 | − | 0.996025i | \(-0.528393\pi\) |
−0.907122 | + | 0.420867i | \(0.861726\pi\) | |||||||
\(824\) | 16.2445 | − | 9.37875i | 0.565903 | − | 0.326724i | ||||
\(825\) | 0.709501 | − | 8.08347i | 0.0247017 | − | 0.281430i | ||||
\(826\) | −1.22056 | − | 2.11408i | −0.0424689 | − | 0.0735582i | ||||
\(827\) | −21.9755 | − | 38.0628i | −0.764165 | − | 1.32357i | −0.940687 | − | 0.339275i | \(-0.889818\pi\) |
0.176523 | − | 0.984297i | \(-0.443515\pi\) | |||||||
\(828\) | −0.723112 | − | 0.127923i | −0.0251299 | − | 0.00444564i | ||||
\(829\) | 8.72147i | 0.302909i | 0.988464 | + | 0.151455i | \(0.0483957\pi\) | ||||
−0.988464 | + | 0.151455i | \(0.951604\pi\) | |||||||
\(830\) | −1.42255 | + | 2.46393i | −0.0493774 | + | 0.0855241i | ||||
\(831\) | −39.8941 | − | 3.50158i | −1.38391 | − | 0.121469i | ||||
\(832\) | 3.57649 | − | 2.06489i | 0.123992 | − | 0.0715870i | ||||
\(833\) | −23.3274 | −0.808247 | ||||||||
\(834\) | 3.41193 | − | 38.8727i | 0.118146 | − | 1.34605i | ||||
\(835\) | 12.5724i | 0.435084i | ||||||||
\(836\) | −10.4435 | −0.361195 | ||||||||
\(837\) | 3.42550 | + | 28.7274i | 0.118403 | + | 0.992966i | ||||
\(838\) | −8.72337 | −0.301344 | ||||||||
\(839\) | − | 42.4663i | − | 1.46610i | −0.680175 | − | 0.733050i | \(-0.738096\pi\) | ||
0.680175 | − | 0.733050i | \(-0.261904\pi\) | |||||||
\(840\) | −0.499058 | + | 5.68585i | −0.0172191 | + | 0.196180i | ||||
\(841\) | −24.7640 | −0.853933 | ||||||||
\(842\) | 3.80721 | − | 2.19810i | 0.131205 | − | 0.0757514i | ||||
\(843\) | 44.9854 | + | 3.94846i | 1.54938 | + | 0.135992i | ||||
\(844\) | 0.159771 | − | 0.276731i | 0.00549953 | − | 0.00952547i | ||||
\(845\) | − | 4.05500i | − | 0.139496i | ||||||
\(846\) | −11.7958 | − | 2.08676i | −0.405548 | − | 0.0717442i | ||||
\(847\) | −18.0398 | − | 31.2458i | −0.619853 | − | 1.07362i | ||||
\(848\) | −0.996554 | − | 1.72608i | −0.0342218 | − | 0.0592739i | ||||
\(849\) | −2.20963 | + | 25.1747i | −0.0758343 | + | 0.863993i | ||||
\(850\) | 5.23465 | − | 3.02223i | 0.179547 | − | 0.103662i | ||||
\(851\) | 1.81132 | + | 1.04577i | 0.0620913 | + | 0.0358484i | ||||
\(852\) | 7.07012 | + | 15.1731i | 0.242218 | + | 0.519820i | ||||
\(853\) | 21.4819 | 0.735525 | 0.367762 | − | 0.929920i | \(-0.380124\pi\) | ||||
0.367762 | + | 0.929920i | \(0.380124\pi\) | |||||||
\(854\) | −10.3825 | + | 17.9830i | −0.355282 | + | 0.615367i | ||||
\(855\) | 1.16497 | − | 6.58523i | 0.0398411 | − | 0.225210i | ||||
\(856\) | 2.11397 | − | 3.66151i | 0.0722541 | − | 0.125148i | ||||
\(857\) | −16.4246 | + | 9.48276i | −0.561054 | + | 0.323925i | −0.753569 | − | 0.657369i | \(-0.771669\pi\) |
0.192514 | + | 0.981294i | \(0.438336\pi\) | |||||||
\(858\) | −27.4454 | − | 19.2290i | −0.936970 | − | 0.656466i | ||||
\(859\) | −30.8514 | + | 17.8121i | −1.05264 | + | 0.607741i | −0.923387 | − | 0.383871i | \(-0.874591\pi\) |
−0.129251 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(860\) | −11.5893 | −0.395190 | ||||||||
\(861\) | 44.8906 | + | 3.94013i | 1.52987 | + | 0.134279i | ||||
\(862\) | 7.11935 | − | 12.3311i | 0.242486 | − | 0.419998i | ||||
\(863\) | 2.53731 | + | 4.39475i | 0.0863710 | + | 0.149599i | 0.905975 | − | 0.423332i | \(-0.139140\pi\) |
−0.819604 | + | 0.572931i | \(0.805806\pi\) | |||||||
\(864\) | 5.01796 | + | 1.34909i | 0.170715 | + | 0.0458971i | ||||
\(865\) | −1.30405 | + | 2.25868i | −0.0443390 | + | 0.0767974i | ||||
\(866\) | −16.3649 | −0.556103 | ||||||||
\(867\) | 30.6702 | − | 14.2912i | 1.04161 | − | 0.485356i | ||||
\(868\) | −2.60163 | + | 18.1623i | −0.0883050 | + | 0.616470i | ||||
\(869\) | 60.1588i | 2.04075i | ||||||||
\(870\) | 3.23124 | − | 1.50564i | 0.109549 | − | 0.0510461i | ||||
\(871\) | −13.6455 | − | 7.87823i | −0.462360 | − | 0.266943i | ||||
\(872\) | − | 5.84653i | − | 0.197988i | ||||||
\(873\) | 22.6680 | + | 4.01011i | 0.767194 | + | 0.135722i | ||||
\(874\) | 0.472550 | + | 0.272827i | 0.0159842 | + | 0.00922851i | ||||
\(875\) | 2.85385 | + | 1.64767i | 0.0964779 | + | 0.0557015i | ||||
\(876\) | −0.245279 | − | 0.526389i | −0.00828722 | − | 0.0177850i | ||||
\(877\) | 17.7228 | + | 30.6968i | 0.598456 | + | 1.03656i | 0.993049 | + | 0.117700i | \(0.0375522\pi\) |
−0.394593 | + | 0.918856i | \(0.629114\pi\) | |||||||
\(878\) | 11.5474 | − | 6.66688i | 0.389705 | − | 0.224996i | ||||
\(879\) | 28.3808 | − | 40.5078i | 0.957261 | − | 1.36629i | ||||
\(880\) | −4.05727 | − | 2.34247i | −0.136771 | − | 0.0789646i | ||||
\(881\) | −3.31664 | − | 5.74459i | −0.111741 | − | 0.193540i | 0.804732 | − | 0.593639i | \(-0.202309\pi\) |
−0.916472 | + | 0.400099i | \(0.868976\pi\) | |||||||
\(882\) | −10.8819 | + | 3.95377i | −0.366413 | + | 0.133130i | ||||
\(883\) | − | 35.2519i | − | 1.18632i | −0.805084 | − | 0.593160i | \(-0.797880\pi\) | ||
0.805084 | − | 0.593160i | \(-0.202120\pi\) | |||||||
\(884\) | − | 24.9622i | − | 0.839570i | ||||||
\(885\) | −0.112186 | + | 1.27816i | −0.00377109 | + | 0.0429647i | ||||
\(886\) | 10.8484 | + | 18.7900i | 0.364460 | + | 0.631264i | ||||
\(887\) | 2.63299 | + | 1.52016i | 0.0884070 | + | 0.0510418i | 0.543552 | − | 0.839376i | \(-0.317079\pi\) |
−0.455145 | + | 0.890417i | \(0.650412\pi\) | |||||||
\(888\) | −12.1207 | − | 8.49210i | −0.406745 | − | 0.284976i | ||||
\(889\) | −1.20823 | + | 0.697570i | −0.0405226 | + | 0.0233957i | ||||
\(890\) | 0.0748029 | + | 0.129562i | 0.00250740 | + | 0.00434294i | ||||
\(891\) | −7.27509 | − | 41.5321i | −0.243725 | − | 1.39138i | ||||
\(892\) | 1.19955 | + | 0.692562i | 0.0401640 | + | 0.0231887i | ||||
\(893\) | 7.70850 | + | 4.45050i | 0.257955 | + | 0.148930i | ||||
\(894\) | 21.9759 | + | 15.3969i | 0.734986 | + | 0.514950i | ||||
\(895\) | 18.9954i | 0.634945i | ||||||||
\(896\) | 2.85385 | + | 1.64767i | 0.0953406 | + | 0.0550449i | ||||
\(897\) | 0.739518 | + | 1.58707i | 0.0246918 | + | 0.0529906i | ||||
\(898\) | 5.51787i | 0.184134i | ||||||||
\(899\) | 10.6362 | − | 4.26455i | 0.354736 | − | 0.142231i | ||||
\(900\) | 1.92965 | − | 2.29705i | 0.0643218 | − | 0.0765683i | ||||
\(901\) | −12.0473 | −0.401352 | ||||||||
\(902\) | −18.4941 | + | 32.0327i | −0.615786 | + | 1.06657i | ||||
\(903\) | −27.9385 | − | 59.9584i | −0.929736 | − | 1.99529i | ||||
\(904\) | 3.22626 | + | 5.58805i | 0.107304 | + | 0.185856i | ||||
\(905\) | −8.30014 | + | 14.3763i | −0.275906 | + | 0.477883i | ||||
\(906\) | −2.76676 | + | 31.5221i | −0.0919194 | + | 1.04725i | ||||
\(907\) | −7.96679 | −0.264533 | −0.132267 | − | 0.991214i | \(-0.542225\pi\) | ||||
−0.132267 | + | 0.991214i | \(0.542225\pi\) | |||||||
\(908\) | 7.88419 | − | 4.55194i | 0.261646 | − | 0.151061i | ||||
\(909\) | −2.64940 | + | 14.9762i | −0.0878749 | + | 0.496730i | ||||
\(910\) | 11.7858 | − | 6.80451i | 0.390694 | − | 0.225567i | ||||
\(911\) | −21.6226 | + | 37.4515i | −0.716390 | + | 1.24082i | 0.246031 | + | 0.969262i | \(0.420873\pi\) |
−0.962421 | + | 0.271561i | \(0.912460\pi\) | |||||||
\(912\) | −3.16214 | − | 2.21548i | −0.104709 | − | 0.0733618i | ||||
\(913\) | 6.66455 | − | 11.5433i | 0.220564 | − | 0.382029i | ||||
\(914\) | −17.8127 | −0.589190 | ||||||||
\(915\) | 9.89292 | − | 4.60976i | 0.327050 | − | 0.152394i | ||||
\(916\) | −6.91782 | − | 3.99401i | −0.228571 | − | 0.131966i | ||||
\(917\) | −5.93107 | + | 3.42430i | −0.195861 | + | 0.113080i | ||||
\(918\) | 22.2275 | − | 22.1900i | 0.733616 | − | 0.732379i | ||||
\(919\) | 8.39359 | + | 14.5381i | 0.276879 | + | 0.479569i | 0.970607 | − | 0.240668i | \(-0.0773665\pi\) |
−0.693728 | + | 0.720237i | \(0.744033\pi\) | |||||||
\(920\) | 0.122390 | + | 0.211986i | 0.00403508 | + | 0.00698896i | ||||
\(921\) | 13.3069 | + | 9.32317i | 0.438478 | + | 0.307209i | ||||
\(922\) | − | 10.7060i | − | 0.352585i | ||||||
\(923\) | 19.9561 | − | 34.5650i | 0.656863 | − | 1.13772i | ||||
\(924\) | 2.33805 | − | 26.6378i | 0.0769163 | − | 0.876320i | ||||
\(925\) | −7.39979 | + | 4.27227i | −0.243304 | + | 0.140471i | ||||
\(926\) | −23.2499 | −0.764038 | ||||||||
\(927\) | −19.2166 | − | 52.8896i | −0.631156 | − | 1.73712i | ||||
\(928\) | − | 2.05814i | − | 0.0675618i | ||||||
\(929\) | 27.8352 | 0.913242 | 0.456621 | − | 0.889661i | \(-0.349060\pi\) | ||||
0.456621 | + | 0.889661i | \(0.349060\pi\) | |||||||
\(930\) | 6.59759 | − | 7.03362i | 0.216344 | − | 0.230641i | ||||
\(931\) | 8.60301 | 0.281952 | ||||||||
\(932\) | − | 15.9529i | − | 0.522554i | ||||||
\(933\) | −2.82031 | − | 0.247544i | −0.0923330 | − | 0.00810424i | ||||
\(934\) | 1.78177 | 0.0583014 | ||||||||
\(935\) | −24.5240 | + | 14.1589i | −0.802021 | + | 0.463047i | ||||
\(936\) | −4.23085 | − | 11.6445i | −0.138290 | − | 0.380613i | ||||
\(937\) | 19.2733 | − | 33.3823i | 0.629630 | − | 1.09055i | −0.357996 | − | 0.933723i | \(-0.616540\pi\) |
0.987626 | − | 0.156828i | \(-0.0501267\pi\) | |||||||
\(938\) | − | 12.5728i | − | 0.410518i | ||||||
\(939\) | −12.2719 | + | 17.5156i | −0.400478 | + | 0.571600i | ||||
\(940\) | 1.99650 | + | 3.45803i | 0.0651185 | + | 0.112789i | ||||
\(941\) | 6.88657 | + | 11.9279i | 0.224496 | + | 0.388838i | 0.956168 | − | 0.292818i | \(-0.0945931\pi\) |
−0.731672 | + | 0.681657i | \(0.761260\pi\) | |||||||
\(942\) | 31.6677 | + | 2.77954i | 1.03179 | + | 0.0905622i | ||||
\(943\) | 1.67366 | − | 0.966286i | 0.0545018 | − | 0.0314666i | ||||
\(944\) | 0.641535 | + | 0.370390i | 0.0208802 | + | 0.0120552i | ||||
\(945\) | 16.5359 | + | 4.44573i | 0.537914 | + | 0.144620i | ||||
\(946\) | 54.2949 | 1.76528 | ||||||||
\(947\) | −10.9849 | + | 19.0264i | −0.356960 | + | 0.618273i | −0.987451 | − | 0.157923i | \(-0.949520\pi\) |
0.630491 | + | 0.776196i | \(0.282854\pi\) | |||||||
\(948\) | −12.7621 | + | 18.2153i | −0.414494 | + | 0.591604i | ||||
\(949\) | −0.692325 | + | 1.19914i | −0.0224738 | + | 0.0389258i | ||||
\(950\) | −1.93051 | + | 1.11458i | −0.0626340 | + | 0.0361617i | ||||
\(951\) | −33.8825 | + | 48.3603i | −1.09872 | + | 1.56819i | ||||
\(952\) | 17.2500 | − | 9.95929i | 0.559075 | − | 0.322782i | ||||
\(953\) | 44.4966 | 1.44138 | 0.720692 | − | 0.693255i | \(-0.243824\pi\) | ||||
0.720692 | + | 0.693255i | \(0.243824\pi\) | |||||||
\(954\) | −5.61988 | + | 2.04189i | −0.181950 | + | 0.0661086i | ||||
\(955\) | −8.43140 | + | 14.6036i | −0.272834 | + | 0.472562i | ||||
\(956\) | 4.52292 | + | 7.83393i | 0.146282 | + | 0.253367i | ||||
\(957\) | −15.1381 | + | 7.05385i | −0.489346 | + | 0.228019i | ||||
\(958\) | 17.8311 | − | 30.8844i | 0.576098 | − | 0.997830i | ||||
\(959\) | 64.3593 | 2.07827 | ||||||||
\(960\) | −0.731555 | − | 1.56998i | −0.0236108 | − | 0.0506708i | ||||
\(961\) | 22.4133 | − | 21.4160i | 0.723010 | − | 0.690838i | ||||
\(962\) | 35.2870i | 1.13770i | ||||||||
\(963\) | −9.71180 | − | 8.15848i | −0.312958 | − | 0.262903i | ||||
\(964\) | −13.3621 | − | 7.71462i | −0.430365 | − | 0.248471i | ||||
\(965\) | 6.92690i | 0.222985i | ||||||||
\(966\) | −0.801684 | + | 1.14424i | −0.0257938 | + | 0.0368153i | ||||
\(967\) | −46.3539 | − | 26.7624i | −1.49064 | − | 0.860621i | −0.490697 | − | 0.871330i | \(-0.663258\pi\) |
−0.999943 | + | 0.0107092i | \(0.996591\pi\) | |||||||
\(968\) | 9.48178 | + | 5.47431i | 0.304756 | + | 0.175951i | ||||
\(969\) | −21.1539 | + | 9.85701i | −0.679563 | + | 0.316653i | ||||
\(970\) | −3.83666 | − | 6.64528i | −0.123188 | − | 0.213367i | ||||
\(971\) | −42.9055 | + | 24.7715i | −1.37690 | + | 0.794955i | −0.991785 | − | 0.127912i | \(-0.959172\pi\) |
−0.385118 | + | 0.922868i | \(0.625839\pi\) | |||||||
\(972\) | 6.60781 | − | 14.1187i | 0.211946 | − | 0.452856i | ||||
\(973\) | −64.2958 | − | 37.1212i | −2.06123 | − | 1.19005i | ||||
\(974\) | 5.28014 | + | 9.14547i | 0.169187 | + | 0.293040i | ||||
\(975\) | −7.12558 | − | 0.625425i | −0.228201 | − | 0.0200296i | ||||
\(976\) | − | 6.30131i | − | 0.201700i | ||||||
\(977\) | − | 9.46739i | − | 0.302888i | −0.988466 | − | 0.151444i | \(-0.951608\pi\) | ||
0.988466 | − | 0.151444i | \(-0.0483924\pi\) | |||||||
\(978\) | −2.94089 | − | 0.258128i | −0.0940393 | − | 0.00825401i | ||||
\(979\) | −0.350447 | − | 0.606992i | −0.0112003 | − | 0.0193995i | ||||
\(980\) | 3.34226 | + | 1.92965i | 0.106765 | + | 0.0616405i | ||||
\(981\) | −17.2714 | − | 3.05543i | −0.551433 | − | 0.0975522i | ||||
\(982\) | 13.8762 | − | 8.01143i | 0.442807 | − | 0.255655i | ||||
\(983\) | −10.1810 | − | 17.6341i | −0.324725 | − | 0.562440i | 0.656732 | − | 0.754124i | \(-0.271938\pi\) |
−0.981457 | + | 0.191684i | \(0.938605\pi\) | |||||||
\(984\) | −12.3952 | + | 5.77573i | −0.395144 | + | 0.184124i | ||||
\(985\) | −12.8333 | − | 7.40933i | −0.408904 | − | 0.236081i | ||||
\(986\) | −10.7737 | − | 6.22018i | −0.343103 | − | 0.198091i | ||||
\(987\) | −13.0775 | + | 18.6655i | −0.416262 | + | 0.594129i | ||||
\(988\) | 9.20591i | 0.292879i | ||||||||
\(989\) | −2.45676 | − | 1.41841i | −0.0781203 | − | 0.0451028i | ||||
\(990\) | −9.04031 | + | 10.7615i | −0.287320 | + | 0.342024i | ||||
\(991\) | 53.4053i | 1.69647i | 0.529617 | + | 0.848237i | \(0.322336\pi\) | ||||
−0.529617 | + | 0.848237i | \(0.677664\pi\) | |||||||
\(992\) | −2.07204 | − | 5.16785i | −0.0657873 | − | 0.164079i | ||||
\(993\) | 16.2164 | + | 34.8017i | 0.514612 | + | 1.10440i | ||||
\(994\) | 31.8479 | 1.01015 | ||||||||
\(995\) | −9.50589 | + | 16.4647i | −0.301357 | + | 0.521966i | ||||
\(996\) | 4.46673 | − | 2.08134i | 0.141534 | − | 0.0659499i | ||||
\(997\) | 27.9449 | + | 48.4020i | 0.885024 | + | 1.53291i | 0.845686 | + | 0.533680i | \(0.179191\pi\) |
0.0393377 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(998\) | −9.12364 | + | 15.8026i | −0.288804 | + | 0.500223i | ||||
\(999\) | −31.4211 | + | 31.3682i | −0.994120 | + | 0.992445i |
(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 | 930.2.o.e.491.15 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.491.9 | yes | 40 | |
31.6 | odd | 6 | inner | 930.2.o.e.161.19 | yes | 40 | |
93.68 | even | 6 | inner | 930.2.o.e.161.5 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.5 | ✓ | 40 | 93.68 | even | 6 | inner | |
930.2.o.e.161.19 | yes | 40 | 31.6 | odd | 6 | inner | |
930.2.o.e.491.9 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.491.15 | yes | 40 | 1.1 | even | 1 | trivial |