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 | 553.17 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.b.277.17 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||
\(5\) | 2.08074 | + | 4.54648i | 0.416148 | + | 0.909297i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −1.45838 | + | 1.45838i | −0.208340 | + | 0.208340i | −0.803561 | − | 0.595222i | \(-0.797064\pi\) |
0.595222 | + | 0.803561i | \(0.297064\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −6.62723 | − | 2.46574i | −0.662723 | − | 0.246574i | ||||
\(11\) | 6.56968 | 0.597244 | 0.298622 | − | 0.954371i | \(-0.403473\pi\) | ||||
0.298622 | + | 0.954371i | \(0.403473\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | 16.0299 | + | 16.0299i | 1.23307 | + | 1.23307i | 0.962778 | + | 0.270292i | \(0.0871204\pi\) |
0.270292 | + | 0.962778i | \(0.412880\pi\) | |||||||
\(14\) | − | 2.91676i | − | 0.208340i | ||||||
\(15\) | −3.01990 | + | 8.11666i | −0.201327 | + | 0.541111i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 10.8651 | − | 10.8651i | 0.639121 | − | 0.639121i | −0.311218 | − | 0.950339i | \(-0.600737\pi\) |
0.950339 | + | 0.311218i | \(0.100737\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | − | 8.18603i | − | 0.430844i | −0.976521 | − | 0.215422i | \(-0.930887\pi\) | ||
0.976521 | − | 0.215422i | \(-0.0691126\pi\) | |||||||
\(20\) | 9.09297 | − | 4.16148i | 0.454648 | − | 0.208074i | ||||
\(21\) | −3.57228 | −0.170109 | ||||||||
\(22\) | −6.56968 | + | 6.56968i | −0.298622 | + | 0.298622i | ||||
\(23\) | 3.39116 | + | 3.39116i | 0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −16.3410 | + | 18.9201i | −0.653641 | + | 0.756805i | ||||
\(26\) | −32.0598 | −1.23307 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.91676 | + | 2.91676i | 0.104170 | + | 0.104170i | ||||
\(29\) | 6.33745i | 0.218533i | 0.994012 | + | 0.109266i | \(0.0348502\pi\) | ||||
−0.994012 | + | 0.109266i | \(0.965150\pi\) | |||||||
\(30\) | −5.09676 | − | 11.1366i | −0.169892 | − | 0.371219i | ||||
\(31\) | 27.7263 | 0.894397 | 0.447198 | − | 0.894435i | \(-0.352422\pi\) | ||||
0.447198 | + | 0.894435i | \(0.352422\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 8.04619 | + | 8.04619i | 0.243824 | + | 0.243824i | ||||
\(34\) | 21.7301i | 0.639121i | ||||||||
\(35\) | −9.66500 | − | 3.59598i | −0.276143 | − | 0.102742i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −14.1170 | + | 14.1170i | −0.381541 | + | 0.381541i | −0.871657 | − | 0.490116i | \(-0.836954\pi\) |
0.490116 | + | 0.871657i | \(0.336954\pi\) | |||||||
\(38\) | 8.18603 | + | 8.18603i | 0.215422 | + | 0.215422i | ||||
\(39\) | 39.2651i | 1.00680i | ||||||||
\(40\) | −4.93148 | + | 13.2545i | −0.123287 | + | 0.331361i | ||||
\(41\) | −69.6643 | −1.69913 | −0.849564 | − | 0.527485i | \(-0.823135\pi\) | ||||
−0.849564 | + | 0.527485i | \(0.823135\pi\) | |||||||
\(42\) | 3.57228 | − | 3.57228i | 0.0850543 | − | 0.0850543i | ||||
\(43\) | 17.6100 | + | 17.6100i | 0.409535 | + | 0.409535i | 0.881576 | − | 0.472042i | \(-0.156483\pi\) |
−0.472042 | + | 0.881576i | \(0.656483\pi\) | |||||||
\(44\) | − | 13.1394i | − | 0.298622i | ||||||
\(45\) | −13.6395 | + | 6.24223i | −0.303099 | + | 0.138716i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 22.1675 | − | 22.1675i | 0.471648 | − | 0.471648i | −0.430800 | − | 0.902448i | \(-0.641768\pi\) |
0.902448 | + | 0.430800i | \(0.141768\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | 44.7463i | 0.913189i | ||||||||
\(50\) | −2.57909 | − | 35.2611i | −0.0515818 | − | 0.705223i | ||||
\(51\) | 26.6138 | 0.521840 | ||||||||
\(52\) | 32.0598 | − | 32.0598i | 0.616535 | − | 0.616535i | ||||
\(53\) | −1.75313 | − | 1.75313i | −0.0330779 | − | 0.0330779i | 0.690374 | − | 0.723452i | \(-0.257446\pi\) |
−0.723452 | + | 0.690374i | \(0.757446\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 13.6698 | + | 29.8690i | 0.248542 | + | 0.543072i | ||||
\(56\) | −5.83351 | −0.104170 | ||||||||
\(57\) | 10.0258 | − | 10.0258i | 0.175891 | − | 0.175891i | ||||
\(58\) | −6.33745 | − | 6.33745i | −0.109266 | − | 0.109266i | ||||
\(59\) | − | 84.6547i | − | 1.43483i | −0.696649 | − | 0.717413i | \(-0.745326\pi\) | ||
0.696649 | − | 0.717413i | \(-0.254674\pi\) | |||||||
\(60\) | 16.2333 | + | 6.03981i | 0.270555 | + | 0.100663i | ||||
\(61\) | 30.9806 | 0.507879 | 0.253939 | − | 0.967220i | \(-0.418274\pi\) | ||||
0.253939 | + | 0.967220i | \(0.418274\pi\) | |||||||
\(62\) | −27.7263 | + | 27.7263i | −0.447198 | + | 0.447198i | ||||
\(63\) | −4.37513 | − | 4.37513i | −0.0694466 | − | 0.0694466i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −39.5256 | + | 106.234i | −0.608087 | + | 1.63437i | ||||
\(66\) | −16.0924 | −0.243824 | ||||||||
\(67\) | −30.7488 | + | 30.7488i | −0.458937 | + | 0.458937i | −0.898307 | − | 0.439369i | \(-0.855202\pi\) |
0.439369 | + | 0.898307i | \(0.355202\pi\) | |||||||
\(68\) | −21.7301 | − | 21.7301i | −0.319560 | − | 0.319560i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 13.2610 | − | 6.06902i | 0.189443 | − | 0.0867002i | ||||
\(71\) | −41.0485 | −0.578148 | −0.289074 | − | 0.957307i | \(-0.593347\pi\) | ||||
−0.289074 | + | 0.957307i | \(0.593347\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −37.1267 | − | 37.1267i | −0.508584 | − | 0.508584i | 0.405507 | − | 0.914092i | \(-0.367095\pi\) |
−0.914092 | + | 0.405507i | \(0.867095\pi\) | |||||||
\(74\) | − | 28.2340i | − | 0.381541i | ||||||
\(75\) | −43.1859 | + | 3.15873i | −0.575812 | + | 0.0421164i | ||||
\(76\) | −16.3721 | −0.215422 | ||||||||
\(77\) | −9.58108 | + | 9.58108i | −0.124430 | + | 0.124430i | ||||
\(78\) | −39.2651 | − | 39.2651i | −0.503399 | − | 0.503399i | ||||
\(79\) | 95.7052i | 1.21146i | 0.795671 | + | 0.605729i | \(0.207119\pi\) | ||||
−0.795671 | + | 0.605729i | \(0.792881\pi\) | |||||||
\(80\) | −8.32297 | − | 18.1859i | −0.104037 | − | 0.227324i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 69.6643 | − | 69.6643i | 0.849564 | − | 0.849564i | ||||
\(83\) | 44.3961 | + | 44.3961i | 0.534893 | + | 0.534893i | 0.922024 | − | 0.387132i | \(-0.126534\pi\) |
−0.387132 | + | 0.922024i | \(0.626534\pi\) | |||||||
\(84\) | 7.14456i | 0.0850543i | ||||||||
\(85\) | 72.0051 | + | 26.7904i | 0.847119 | + | 0.315181i | ||||
\(86\) | −35.2200 | −0.409535 | ||||||||
\(87\) | −7.76176 | + | 7.76176i | −0.0892157 | + | 0.0892157i | ||||
\(88\) | 13.1394 | + | 13.1394i | 0.149311 | + | 0.149311i | ||||
\(89\) | 142.109i | 1.59673i | 0.602173 | + | 0.798366i | \(0.294302\pi\) | ||||
−0.602173 | + | 0.798366i | \(0.705698\pi\) | |||||||
\(90\) | 7.39723 | − | 19.8817i | 0.0821914 | − | 0.220908i | ||||
\(91\) | −46.7554 | −0.513795 | ||||||||
\(92\) | 6.78233 | − | 6.78233i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | 33.9576 | + | 33.9576i | 0.365136 | + | 0.365136i | ||||
\(94\) | 44.3349i | 0.471648i | ||||||||
\(95\) | 37.2176 | − | 17.0330i | 0.391765 | − | 0.179295i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 99.3088 | − | 99.3088i | 1.02380 | − | 1.02380i | 0.0240920 | − | 0.999710i | \(-0.492331\pi\) |
0.999710 | − | 0.0240920i | \(-0.00766948\pi\) | |||||||
\(98\) | −44.7463 | − | 44.7463i | −0.456595 | − | 0.456595i | ||||
\(99\) | 19.7090i | 0.199081i | ||||||||
\(100\) | 37.8402 | + | 32.6821i | 0.378402 | + | 0.326821i | ||||
\(101\) | −120.819 | −1.19623 | −0.598114 | − | 0.801411i | \(-0.704083\pi\) | ||||
−0.598114 | + | 0.801411i | \(0.704083\pi\) | |||||||
\(102\) | −26.6138 | + | 26.6138i | −0.260920 | + | 0.260920i | ||||
\(103\) | −31.7941 | − | 31.7941i | −0.308681 | − | 0.308681i | 0.535717 | − | 0.844398i | \(-0.320041\pi\) |
−0.844398 | + | 0.535717i | \(0.820041\pi\) | |||||||
\(104\) | 64.1197i | 0.616535i | ||||||||
\(105\) | −7.43300 | − | 16.2413i | −0.0707904 | − | 0.154679i | ||||
\(106\) | 3.50625 | 0.0330779 | ||||||||
\(107\) | −118.422 | + | 118.422i | −1.10675 | + | 1.10675i | −0.113174 | + | 0.993575i | \(0.536102\pi\) |
−0.993575 | + | 0.113174i | \(0.963898\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 21.5303i | 0.197526i | 0.995111 | + | 0.0987628i | \(0.0314885\pi\) | ||||
−0.995111 | + | 0.0987628i | \(0.968511\pi\) | |||||||
\(110\) | −43.5388 | − | 16.1991i | −0.395807 | − | 0.147265i | ||||
\(111\) | −34.5795 | −0.311527 | ||||||||
\(112\) | 5.83351 | − | 5.83351i | 0.0520849 | − | 0.0520849i | ||||
\(113\) | −72.3235 | − | 72.3235i | −0.640031 | − | 0.640031i | 0.310532 | − | 0.950563i | \(-0.399493\pi\) |
−0.950563 | + | 0.310532i | \(0.899493\pi\) | |||||||
\(114\) | 20.0516i | 0.175891i | ||||||||
\(115\) | −8.36174 | + | 22.4740i | −0.0727108 | + | 0.195426i | ||||
\(116\) | 12.6749 | 0.109266 | ||||||||
\(117\) | −48.0898 | + | 48.0898i | −0.411024 | + | 0.411024i | ||||
\(118\) | 84.6547 | + | 84.6547i | 0.717413 | + | 0.717413i | ||||
\(119\) | 31.6907i | 0.266308i | ||||||||
\(120\) | −22.2731 | + | 10.1935i | −0.185609 | + | 0.0849459i | ||||
\(121\) | −77.8393 | −0.643300 | ||||||||
\(122\) | −30.9806 | + | 30.9806i | −0.253939 | + | 0.253939i | ||||
\(123\) | −85.3210 | − | 85.3210i | −0.693667 | − | 0.693667i | ||||
\(124\) | − | 55.4526i | − | 0.447198i | ||||||
\(125\) | −120.021 | − | 34.9263i | −0.960172 | − | 0.279411i | ||||
\(126\) | 8.75027 | 0.0694466 | ||||||||
\(127\) | 74.6311 | − | 74.6311i | 0.587646 | − | 0.587646i | −0.349347 | − | 0.936993i | \(-0.613597\pi\) |
0.936993 | + | 0.349347i | \(0.113597\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 43.1355i | 0.334384i | ||||||||
\(130\) | −66.7082 | − | 145.760i | −0.513140 | − | 1.12123i | ||||
\(131\) | −159.638 | −1.21861 | −0.609304 | − | 0.792936i | \(-0.708551\pi\) | ||||
−0.609304 | + | 0.792936i | \(0.708551\pi\) | |||||||
\(132\) | 16.0924 | − | 16.0924i | 0.121912 | − | 0.121912i | ||||
\(133\) | 11.9383 | + | 11.9383i | 0.0897618 | + | 0.0897618i | ||||
\(134\) | − | 61.4976i | − | 0.458937i | ||||||
\(135\) | −24.3500 | − | 9.05971i | −0.180370 | − | 0.0671090i | ||||
\(136\) | 43.4602 | 0.319560 | ||||||||
\(137\) | 46.5130 | − | 46.5130i | 0.339511 | − | 0.339511i | −0.516672 | − | 0.856183i | \(-0.672829\pi\) |
0.856183 | + | 0.516672i | \(0.172829\pi\) | |||||||
\(138\) | −8.30662 | − | 8.30662i | −0.0601929 | − | 0.0601929i | ||||
\(139\) | − | 128.651i | − | 0.925547i | −0.886477 | − | 0.462774i | \(-0.846854\pi\) | ||
0.886477 | − | 0.462774i | \(-0.153146\pi\) | |||||||
\(140\) | −7.19197 | + | 19.3300i | −0.0513712 | + | 0.138071i | ||||
\(141\) | 54.2990 | 0.385099 | ||||||||
\(142\) | 41.0485 | − | 41.0485i | 0.289074 | − | 0.289074i | ||||
\(143\) | 105.311 | + | 105.311i | 0.736444 | + | 0.736444i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | −28.8131 | + | 13.1866i | −0.198711 | + | 0.0909421i | ||||
\(146\) | 74.2533 | 0.508584 | ||||||||
\(147\) | −54.8028 | + | 54.8028i | −0.372808 | + | 0.372808i | ||||
\(148\) | 28.2340 | + | 28.2340i | 0.190770 | + | 0.190770i | ||||
\(149\) | − | 93.9923i | − | 0.630821i | −0.948955 | − | 0.315410i | \(-0.897858\pi\) | ||
0.948955 | − | 0.315410i | \(-0.102142\pi\) | |||||||
\(150\) | 40.0272 | − | 46.3446i | 0.266848 | − | 0.308964i | ||||
\(151\) | 170.451 | 1.12881 | 0.564406 | − | 0.825497i | \(-0.309105\pi\) | ||||
0.564406 | + | 0.825497i | \(0.309105\pi\) | |||||||
\(152\) | 16.3721 | − | 16.3721i | 0.107711 | − | 0.107711i | ||||
\(153\) | 32.5952 | + | 32.5952i | 0.213040 | + | 0.213040i | ||||
\(154\) | − | 19.1622i | − | 0.124430i | ||||||
\(155\) | 57.6913 | + | 126.057i | 0.372202 | + | 0.813272i | ||||
\(156\) | 78.5302 | 0.503399 | ||||||||
\(157\) | 58.3661 | − | 58.3661i | 0.371758 | − | 0.371758i | −0.496359 | − | 0.868117i | \(-0.665330\pi\) |
0.868117 | + | 0.496359i | \(0.165330\pi\) | |||||||
\(158\) | −95.7052 | − | 95.7052i | −0.605729 | − | 0.605729i | ||||
\(159\) | − | 4.29427i | − | 0.0270080i | ||||||
\(160\) | 26.5089 | + | 9.86297i | 0.165681 | + | 0.0616435i | ||||
\(161\) | −9.89120 | −0.0614360 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 24.0343 | + | 24.0343i | 0.147450 | + | 0.147450i | 0.776978 | − | 0.629528i | \(-0.216752\pi\) |
−0.629528 | + | 0.776978i | \(0.716752\pi\) | |||||||
\(164\) | 139.329i | 0.849564i | ||||||||
\(165\) | −19.8398 | + | 53.3239i | −0.120241 | + | 0.323175i | ||||
\(166\) | −88.7922 | −0.534893 | ||||||||
\(167\) | 128.995 | − | 128.995i | 0.772426 | − | 0.772426i | −0.206104 | − | 0.978530i | \(-0.566078\pi\) |
0.978530 | + | 0.206104i | \(0.0660785\pi\) | |||||||
\(168\) | −7.14456 | − | 7.14456i | −0.0425272 | − | 0.0425272i | ||||
\(169\) | 344.917i | 2.04093i | ||||||||
\(170\) | −98.7956 | + | 45.2147i | −0.581150 | + | 0.265969i | ||||
\(171\) | 24.5581 | 0.143615 | ||||||||
\(172\) | 35.2200 | − | 35.2200i | 0.204767 | − | 0.204767i | ||||
\(173\) | −14.8434 | − | 14.8434i | −0.0858000 | − | 0.0858000i | 0.662904 | − | 0.748704i | \(-0.269324\pi\) |
−0.748704 | + | 0.662904i | \(0.769324\pi\) | |||||||
\(174\) | − | 15.5235i | − | 0.0892157i | ||||||
\(175\) | −3.76129 | − | 51.4241i | −0.0214931 | − | 0.293852i | ||||
\(176\) | −26.2787 | −0.149311 | ||||||||
\(177\) | 103.680 | − | 103.680i | 0.585765 | − | 0.585765i | ||||
\(178\) | −142.109 | − | 142.109i | −0.798366 | − | 0.798366i | ||||
\(179\) | − | 10.8323i | − | 0.0605158i | −0.999542 | − | 0.0302579i | \(-0.990367\pi\) | ||
0.999542 | − | 0.0302579i | \(-0.00963286\pi\) | |||||||
\(180\) | 12.4845 | + | 27.2789i | 0.0693581 | + | 0.151549i | ||||
\(181\) | −2.96458 | −0.0163789 | −0.00818944 | − | 0.999966i | \(-0.502607\pi\) | ||||
−0.00818944 | + | 0.999966i | \(0.502607\pi\) | |||||||
\(182\) | 46.7554 | − | 46.7554i | 0.256898 | − | 0.256898i | ||||
\(183\) | 37.9433 | + | 37.9433i | 0.207341 | + | 0.207341i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −93.5566 | − | 34.8089i | −0.505711 | − | 0.188156i | ||||
\(186\) | −67.9153 | −0.365136 | ||||||||
\(187\) | 71.3799 | − | 71.3799i | 0.381711 | − | 0.381711i | ||||
\(188\) | −44.3349 | − | 44.3349i | −0.235824 | − | 0.235824i | ||||
\(189\) | − | 10.7168i | − | 0.0567029i | ||||||
\(190\) | −20.1846 | + | 54.2507i | −0.106235 | + | 0.285530i | ||||
\(191\) | 225.451 | 1.18037 | 0.590186 | − | 0.807267i | \(-0.299054\pi\) | ||||
0.590186 | + | 0.807267i | \(0.299054\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 231.799 | + | 231.799i | 1.20103 | + | 1.20103i | 0.973854 | + | 0.227175i | \(0.0729490\pi\) |
0.227175 | + | 0.973854i | \(0.427051\pi\) | |||||||
\(194\) | 198.618i | 1.02380i | ||||||||
\(195\) | −178.518 | + | 81.7006i | −0.915478 | + | 0.418977i | ||||
\(196\) | 89.4925 | 0.456595 | ||||||||
\(197\) | 240.985 | − | 240.985i | 1.22327 | − | 1.22327i | 0.256811 | − | 0.966462i | \(-0.417328\pi\) |
0.966462 | − | 0.256811i | \(-0.0826717\pi\) | |||||||
\(198\) | −19.7090 | − | 19.7090i | −0.0995407 | − | 0.0995407i | ||||
\(199\) | 87.8703i | 0.441559i | 0.975324 | + | 0.220780i | \(0.0708602\pi\) | ||||
−0.975324 | + | 0.220780i | \(0.929140\pi\) | |||||||
\(200\) | −70.5223 | + | 5.15818i | −0.352611 | + | 0.0257909i | ||||
\(201\) | −75.3189 | −0.374721 | ||||||||
\(202\) | 120.819 | − | 120.819i | 0.598114 | − | 0.598114i | ||||
\(203\) | −9.24240 | − | 9.24240i | −0.0455291 | − | 0.0455291i | ||||
\(204\) | − | 53.2277i | − | 0.260920i | ||||||
\(205\) | −144.953 | − | 316.728i | −0.707090 | − | 1.54501i | ||||
\(206\) | 63.5882 | 0.308681 | ||||||||
\(207\) | −10.1735 | + | 10.1735i | −0.0491473 | + | 0.0491473i | ||||
\(208\) | −64.1197 | − | 64.1197i | −0.308268 | − | 0.308268i | ||||
\(209\) | − | 53.7796i | − | 0.257319i | ||||||
\(210\) | 23.6743 | + | 8.80832i | 0.112735 | + | 0.0419444i | ||||
\(211\) | 275.082 | 1.30371 | 0.651854 | − | 0.758345i | \(-0.273992\pi\) | ||||
0.651854 | + | 0.758345i | \(0.273992\pi\) | |||||||
\(212\) | −3.50625 | + | 3.50625i | −0.0165389 | + | 0.0165389i | ||||
\(213\) | −50.2739 | − | 50.2739i | −0.236028 | − | 0.236028i | ||||
\(214\) | − | 236.844i | − | 1.10675i | ||||||
\(215\) | −43.4217 | + | 116.705i | −0.201961 | + | 0.542816i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −40.4354 | + | 40.4354i | −0.186338 | + | 0.186338i | ||||
\(218\) | −21.5303 | − | 21.5303i | −0.0987628 | − | 0.0987628i | ||||
\(219\) | − | 90.9414i | − | 0.415257i | ||||||
\(220\) | 59.7379 | − | 27.3396i | 0.271536 | − | 0.124271i | ||||
\(221\) | 348.332 | 1.57616 | ||||||||
\(222\) | 34.5795 | − | 34.5795i | 0.155763 | − | 0.155763i | ||||
\(223\) | 75.3025 | + | 75.3025i | 0.337679 | + | 0.337679i | 0.855493 | − | 0.517814i | \(-0.173254\pi\) |
−0.517814 | + | 0.855493i | \(0.673254\pi\) | |||||||
\(224\) | 11.6670i | 0.0520849i | ||||||||
\(225\) | −56.7604 | − | 49.0231i | −0.252268 | − | 0.217880i | ||||
\(226\) | 144.647 | 0.640031 | ||||||||
\(227\) | 314.742 | − | 314.742i | 1.38653 | − | 1.38653i | 0.554038 | − | 0.832491i | \(-0.313086\pi\) |
0.832491 | − | 0.554038i | \(-0.186914\pi\) | |||||||
\(228\) | −20.0516 | − | 20.0516i | −0.0879456 | − | 0.0879456i | ||||
\(229\) | − | 101.559i | − | 0.443490i | −0.975105 | − | 0.221745i | \(-0.928825\pi\) | ||
0.975105 | − | 0.221745i | \(-0.0711752\pi\) | |||||||
\(230\) | −14.1123 | − | 30.8358i | −0.0613577 | − | 0.134068i | ||||
\(231\) | −23.4688 | −0.101596 | ||||||||
\(232\) | −12.6749 | + | 12.6749i | −0.0546332 | + | 0.0546332i | ||||
\(233\) | −195.602 | − | 195.602i | −0.839494 | − | 0.839494i | 0.149298 | − | 0.988792i | \(-0.452299\pi\) |
−0.988792 | + | 0.149298i | \(0.952299\pi\) | |||||||
\(234\) | − | 96.1795i | − | 0.411024i | ||||||
\(235\) | 146.909 | + | 54.6592i | 0.625144 | + | 0.232592i | ||||
\(236\) | −169.309 | −0.717413 | ||||||||
\(237\) | −117.215 | + | 117.215i | −0.494576 | + | 0.494576i | ||||
\(238\) | −31.6907 | − | 31.6907i | −0.133154 | − | 0.133154i | ||||
\(239\) | 262.676i | 1.09906i | 0.835473 | + | 0.549531i | \(0.185194\pi\) | ||||
−0.835473 | + | 0.549531i | \(0.814806\pi\) | |||||||
\(240\) | 12.0796 | − | 32.4666i | 0.0503317 | − | 0.135278i | ||||
\(241\) | 290.284 | 1.20450 | 0.602249 | − | 0.798308i | \(-0.294271\pi\) | ||||
0.602249 | + | 0.798308i | \(0.294271\pi\) | |||||||
\(242\) | 77.8393 | − | 77.8393i | 0.321650 | − | 0.321650i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 61.9612i | − | 0.253939i | ||||||
\(245\) | −203.438 | + | 93.1054i | −0.830360 | + | 0.380022i | ||||
\(246\) | 170.642 | 0.693667 | ||||||||
\(247\) | 131.221 | − | 131.221i | 0.531261 | − | 0.531261i | ||||
\(248\) | 55.4526 | + | 55.4526i | 0.223599 | + | 0.223599i | ||||
\(249\) | 108.748i | 0.436738i | ||||||||
\(250\) | 154.948 | − | 85.0951i | 0.619791 | − | 0.340381i | ||||
\(251\) | 77.4485 | 0.308560 | 0.154280 | − | 0.988027i | \(-0.450694\pi\) | ||||
0.154280 | + | 0.988027i | \(0.450694\pi\) | |||||||
\(252\) | −8.75027 | + | 8.75027i | −0.0347233 | + | 0.0347233i | ||||
\(253\) | 22.2789 | + | 22.2789i | 0.0880588 | + | 0.0880588i | ||||
\(254\) | 149.262i | 0.587646i | ||||||||
\(255\) | 55.3765 | + | 120.999i | 0.217163 | + | 0.474507i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 214.236 | − | 214.236i | 0.833602 | − | 0.833602i | −0.154406 | − | 0.988008i | \(-0.549346\pi\) |
0.988008 | + | 0.154406i | \(0.0493463\pi\) | |||||||
\(258\) | −43.1355 | − | 43.1355i | −0.167192 | − | 0.167192i | ||||
\(259\) | − | 41.1758i | − | 0.158980i | ||||||
\(260\) | 212.468 | + | 79.0513i | 0.817184 | + | 0.304043i | ||||
\(261\) | −19.0124 | −0.0728443 | ||||||||
\(262\) | 159.638 | − | 159.638i | 0.609304 | − | 0.609304i | ||||
\(263\) | −208.462 | − | 208.462i | −0.792632 | − | 0.792632i | 0.189289 | − | 0.981921i | \(-0.439382\pi\) |
−0.981921 | + | 0.189289i | \(0.939382\pi\) | |||||||
\(264\) | 32.1847i | 0.121912i | ||||||||
\(265\) | 4.32276 | − | 11.6184i | 0.0163123 | − | 0.0438429i | ||||
\(266\) | −23.8766 | −0.0897618 | ||||||||
\(267\) | −174.047 | + | 174.047i | −0.651863 | + | 0.651863i | ||||
\(268\) | 61.4976 | + | 61.4976i | 0.229469 | + | 0.229469i | ||||
\(269\) | − | 177.937i | − | 0.661474i | −0.943723 | − | 0.330737i | \(-0.892703\pi\) | ||
0.943723 | − | 0.330737i | \(-0.107297\pi\) | |||||||
\(270\) | 33.4097 | − | 15.2903i | 0.123740 | − | 0.0566306i | ||||
\(271\) | 196.940 | 0.726717 | 0.363359 | − | 0.931649i | \(-0.381630\pi\) | ||||
0.363359 | + | 0.931649i | \(0.381630\pi\) | |||||||
\(272\) | −43.4602 | + | 43.4602i | −0.159780 | + | 0.159780i | ||||
\(273\) | −57.2634 | − | 57.2634i | −0.209756 | − | 0.209756i | ||||
\(274\) | 93.0261i | 0.339511i | ||||||||
\(275\) | −107.355 | + | 124.299i | −0.390383 | + | 0.451997i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | 35.9249 | − | 35.9249i | 0.129693 | − | 0.129693i | −0.639281 | − | 0.768973i | \(-0.720768\pi\) |
0.768973 | + | 0.639281i | \(0.220768\pi\) | |||||||
\(278\) | 128.651 | + | 128.651i | 0.462774 | + | 0.462774i | ||||
\(279\) | 83.1789i | 0.298132i | ||||||||
\(280\) | −12.1380 | − | 26.5220i | −0.0433501 | − | 0.0947213i | ||||
\(281\) | −308.880 | −1.09922 | −0.549609 | − | 0.835422i | \(-0.685223\pi\) | ||||
−0.549609 | + | 0.835422i | \(0.685223\pi\) | |||||||
\(282\) | −54.2990 | + | 54.2990i | −0.192549 | + | 0.192549i | ||||
\(283\) | −145.332 | − | 145.332i | −0.513541 | − | 0.513541i | 0.402068 | − | 0.915610i | \(-0.368291\pi\) |
−0.915610 | + | 0.402068i | \(0.868291\pi\) | |||||||
\(284\) | 82.0970i | 0.289074i | ||||||||
\(285\) | 66.4432 | + | 24.7210i | 0.233134 | + | 0.0867404i | ||||
\(286\) | −210.623 | −0.736444 | ||||||||
\(287\) | 101.597 | − | 101.597i | 0.353996 | − | 0.353996i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 52.9013i | 0.183050i | ||||||||
\(290\) | 15.6265 | − | 41.9997i | 0.0538846 | − | 0.144827i | ||||
\(291\) | 243.256 | 0.835931 | ||||||||
\(292\) | −74.2533 | + | 74.2533i | −0.254292 | + | 0.254292i | ||||
\(293\) | −241.012 | − | 241.012i | −0.822568 | − | 0.822568i | 0.163908 | − | 0.986476i | \(-0.447590\pi\) |
−0.986476 | + | 0.163908i | \(0.947590\pi\) | |||||||
\(294\) | − | 109.606i | − | 0.372808i | ||||||
\(295\) | 384.881 | − | 176.145i | 1.30468 | − | 0.597100i | ||||
\(296\) | −56.4680 | −0.190770 | ||||||||
\(297\) | −24.1386 | + | 24.1386i | −0.0812746 | + | 0.0812746i | ||||
\(298\) | 93.9923 | + | 93.9923i | 0.315410 | + | 0.315410i | ||||
\(299\) | 108.720i | 0.363613i | ||||||||
\(300\) | 6.31746 | + | 86.3718i | 0.0210582 | + | 0.287906i | ||||
\(301\) | −51.3640 | −0.170645 | ||||||||
\(302\) | −170.451 | + | 170.451i | −0.564406 | + | 0.564406i | ||||
\(303\) | −147.973 | − | 147.973i | −0.488358 | − | 0.488358i | ||||
\(304\) | 32.7441i | 0.107711i | ||||||||
\(305\) | 64.4626 | + | 140.853i | 0.211353 | + | 0.461812i | ||||
\(306\) | −65.1903 | −0.213040 | ||||||||
\(307\) | 68.9379 | − | 68.9379i | 0.224553 | − | 0.224553i | −0.585859 | − | 0.810413i | \(-0.699243\pi\) |
0.810413 | + | 0.585859i | \(0.199243\pi\) | |||||||
\(308\) | 19.1622 | + | 19.1622i | 0.0622148 | + | 0.0622148i | ||||
\(309\) | − | 77.8793i | − | 0.252037i | ||||||
\(310\) | −183.748 | − | 68.3659i | −0.592737 | − | 0.220535i | ||||
\(311\) | 516.333 | 1.66024 | 0.830118 | − | 0.557588i | \(-0.188273\pi\) | ||||
0.830118 | + | 0.557588i | \(0.188273\pi\) | |||||||
\(312\) | −78.5302 | + | 78.5302i | −0.251700 | + | 0.251700i | ||||
\(313\) | −41.6424 | − | 41.6424i | −0.133043 | − | 0.133043i | 0.637449 | − | 0.770492i | \(-0.279989\pi\) |
−0.770492 | + | 0.637449i | \(0.779989\pi\) | |||||||
\(314\) | 116.732i | 0.371758i | ||||||||
\(315\) | 10.7879 | − | 28.9950i | 0.0342475 | − | 0.0920476i | ||||
\(316\) | 191.410 | 0.605729 | ||||||||
\(317\) | 132.540 | − | 132.540i | 0.418106 | − | 0.418106i | −0.466444 | − | 0.884551i | \(-0.654465\pi\) |
0.884551 | + | 0.466444i | \(0.154465\pi\) | |||||||
\(318\) | 4.29427 | + | 4.29427i | 0.0135040 | + | 0.0135040i | ||||
\(319\) | 41.6351i | 0.130517i | ||||||||
\(320\) | −36.3719 | + | 16.6459i | −0.113662 | + | 0.0520185i | ||||
\(321\) | −290.074 | −0.903657 | ||||||||
\(322\) | 9.89120 | − | 9.89120i | 0.0307180 | − | 0.0307180i | ||||
\(323\) | −88.9416 | − | 88.9416i | −0.275361 | − | 0.275361i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | −565.233 | + | 41.3426i | −1.73918 | + | 0.127208i | ||||
\(326\) | −48.0687 | −0.147450 | ||||||||
\(327\) | −26.3691 | + | 26.3691i | −0.0806395 | + | 0.0806395i | ||||
\(328\) | −139.329 | − | 139.329i | −0.424782 | − | 0.424782i | ||||
\(329\) | 64.6570i | 0.196526i | ||||||||
\(330\) | −33.4841 | − | 73.1637i | −0.101467 | − | 0.221708i | ||||
\(331\) | −345.899 | −1.04501 | −0.522506 | − | 0.852635i | \(-0.675003\pi\) | ||||
−0.522506 | + | 0.852635i | \(0.675003\pi\) | |||||||
\(332\) | 88.7922 | − | 88.7922i | 0.267446 | − | 0.267446i | ||||
\(333\) | −42.3510 | − | 42.3510i | −0.127180 | − | 0.127180i | ||||
\(334\) | 257.990i | 0.772426i | ||||||||
\(335\) | −203.779 | − | 75.8186i | −0.608296 | − | 0.226324i | ||||
\(336\) | 14.2891 | 0.0425272 | ||||||||
\(337\) | −257.263 | + | 257.263i | −0.763393 | + | 0.763393i | −0.976934 | − | 0.213541i | \(-0.931500\pi\) |
0.213541 | + | 0.976934i | \(0.431500\pi\) | |||||||
\(338\) | −344.917 | − | 344.917i | −1.02046 | − | 1.02046i | ||||
\(339\) | − | 177.156i | − | 0.522583i | ||||||
\(340\) | 53.5808 | − | 144.010i | 0.157591 | − | 0.423560i | ||||
\(341\) | 182.153 | 0.534173 | ||||||||
\(342\) | −24.5581 | + | 24.5581i | −0.0718073 | + | 0.0718073i | ||||
\(343\) | −136.717 | − | 136.717i | −0.398593 | − | 0.398593i | ||||
\(344\) | 70.4399i | 0.204767i | ||||||||
\(345\) | −37.7659 | + | 17.2839i | −0.109466 | + | 0.0500984i | ||||
\(346\) | 29.6868 | 0.0858000 | ||||||||
\(347\) | 212.920 | − | 212.920i | 0.613601 | − | 0.613601i | −0.330281 | − | 0.943883i | \(-0.607144\pi\) |
0.943883 | + | 0.330281i | \(0.107144\pi\) | |||||||
\(348\) | 15.5235 | + | 15.5235i | 0.0446078 | + | 0.0446078i | ||||
\(349\) | 377.789i | 1.08249i | 0.840865 | + | 0.541244i | \(0.182047\pi\) | ||||
−0.840865 | + | 0.541244i | \(0.817953\pi\) | |||||||
\(350\) | 55.1854 | + | 47.6628i | 0.157672 | + | 0.136179i | ||||
\(351\) | −117.795 | −0.335599 | ||||||||
\(352\) | 26.2787 | − | 26.2787i | 0.0746555 | − | 0.0746555i | ||||
\(353\) | 96.2068 | + | 96.2068i | 0.272541 | + | 0.272541i | 0.830122 | − | 0.557582i | \(-0.188271\pi\) |
−0.557582 | + | 0.830122i | \(0.688271\pi\) | |||||||
\(354\) | 207.361i | 0.585765i | ||||||||
\(355\) | −85.4113 | − | 186.626i | −0.240595 | − | 0.525708i | ||||
\(356\) | 284.218 | 0.798366 | ||||||||
\(357\) | −38.8130 | + | 38.8130i | −0.108720 | + | 0.108720i | ||||
\(358\) | 10.8323 | + | 10.8323i | 0.0302579 | + | 0.0302579i | ||||
\(359\) | − | 181.790i | − | 0.506380i | −0.967417 | − | 0.253190i | \(-0.918520\pi\) | ||
0.967417 | − | 0.253190i | \(-0.0814798\pi\) | |||||||
\(360\) | −39.7634 | − | 14.7945i | −0.110454 | − | 0.0410957i | ||||
\(361\) | 293.989 | 0.814374 | ||||||||
\(362\) | 2.96458 | − | 2.96458i | 0.00818944 | − | 0.00818944i | ||||
\(363\) | −95.3332 | − | 95.3332i | −0.262626 | − | 0.262626i | ||||
\(364\) | 93.5107i | 0.256898i | ||||||||
\(365\) | 91.5447 | − | 246.047i | 0.250808 | − | 0.674101i | ||||
\(366\) | −75.8867 | −0.207341 | ||||||||
\(367\) | 28.4702 | − | 28.4702i | 0.0775756 | − | 0.0775756i | −0.667254 | − | 0.744830i | \(-0.732531\pi\) |
0.744830 | + | 0.667254i | \(0.232531\pi\) | |||||||
\(368\) | −13.5647 | − | 13.5647i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 208.993i | − | 0.566376i | ||||||
\(370\) | 128.365 | − | 58.7477i | 0.346934 | − | 0.158778i | ||||
\(371\) | 5.11344 | 0.0137829 | ||||||||
\(372\) | 67.9153 | − | 67.9153i | 0.182568 | − | 0.182568i | ||||
\(373\) | −94.2294 | − | 94.2294i | −0.252626 | − | 0.252626i | 0.569421 | − | 0.822046i | \(-0.307168\pi\) |
−0.822046 | + | 0.569421i | \(0.807168\pi\) | |||||||
\(374\) | 142.760i | 0.381711i | ||||||||
\(375\) | −104.220 | − | 189.772i | −0.277920 | − | 0.506057i | ||||
\(376\) | 88.6698 | 0.235824 | ||||||||
\(377\) | −101.589 | + | 101.589i | −0.269466 | + | 0.269466i | ||||
\(378\) | 10.7168 | + | 10.7168i | 0.0283514 | + | 0.0283514i | ||||
\(379\) | 139.587i | 0.368302i | 0.982898 | + | 0.184151i | \(0.0589536\pi\) | ||||
−0.982898 | + | 0.184151i | \(0.941046\pi\) | |||||||
\(380\) | −34.0660 | − | 74.4353i | −0.0896474 | − | 0.195882i | ||||
\(381\) | 182.808 | 0.479811 | ||||||||
\(382\) | −225.451 | + | 225.451i | −0.590186 | + | 0.590186i | ||||
\(383\) | 115.635 | + | 115.635i | 0.301920 | + | 0.301920i | 0.841764 | − | 0.539845i | \(-0.181517\pi\) |
−0.539845 | + | 0.841764i | \(0.681517\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −63.4960 | − | 23.6245i | −0.164925 | − | 0.0613623i | ||||
\(386\) | −463.597 | −1.20103 | ||||||||
\(387\) | −52.8300 | + | 52.8300i | −0.136512 | + | 0.136512i | ||||
\(388\) | −198.618 | − | 198.618i | −0.511901 | − | 0.511901i | ||||
\(389\) | − | 443.439i | − | 1.13995i | −0.821663 | − | 0.569974i | \(-0.806953\pi\) | ||
0.821663 | − | 0.569974i | \(-0.193047\pi\) | |||||||
\(390\) | 96.8177 | − | 260.219i | 0.248250 | − | 0.667228i | ||||
\(391\) | 73.6904 | 0.188466 | ||||||||
\(392\) | −89.4925 | + | 89.4925i | −0.228297 | + | 0.228297i | ||||
\(393\) | −195.515 | − | 195.515i | −0.497495 | − | 0.497495i | ||||
\(394\) | 481.969i | 1.22327i | ||||||||
\(395\) | −435.122 | + | 199.138i | −1.10158 | + | 0.504147i | ||||
\(396\) | 39.4181 | 0.0995407 | ||||||||
\(397\) | −471.063 | + | 471.063i | −1.18656 | + | 1.18656i | −0.208544 | + | 0.978013i | \(0.566872\pi\) |
−0.978013 | + | 0.208544i | \(0.933128\pi\) | |||||||
\(398\) | −87.8703 | − | 87.8703i | −0.220780 | − | 0.220780i | ||||
\(399\) | 29.2428i | 0.0732902i | ||||||||
\(400\) | 65.3641 | − | 75.6805i | 0.163410 | − | 0.189201i | ||||
\(401\) | 736.854 | 1.83754 | 0.918771 | − | 0.394791i | \(-0.129183\pi\) | ||||
0.918771 | + | 0.394791i | \(0.129183\pi\) | |||||||
\(402\) | 75.3189 | − | 75.3189i | 0.187360 | − | 0.187360i | ||||
\(403\) | 444.450 | + | 444.450i | 1.10285 | + | 1.10285i | ||||
\(404\) | 241.638i | 0.598114i | ||||||||
\(405\) | −18.7267 | − | 40.9184i | −0.0462387 | − | 0.101033i | ||||
\(406\) | 18.4848 | 0.0455291 | ||||||||
\(407\) | −92.7442 | + | 92.7442i | −0.227873 | + | 0.227873i | ||||
\(408\) | 53.2277 | + | 53.2277i | 0.130460 | + | 0.130460i | ||||
\(409\) | − | 593.667i | − | 1.45151i | −0.687954 | − | 0.725754i | \(-0.741491\pi\) | ||
0.687954 | − | 0.725754i | \(-0.258509\pi\) | |||||||
\(410\) | 461.681 | + | 171.774i | 1.12605 | + | 0.418961i | ||||
\(411\) | 113.933 | 0.277210 | ||||||||
\(412\) | −63.5882 | + | 63.5882i | −0.154340 | + | 0.154340i | ||||
\(413\) | 123.459 | + | 123.459i | 0.298931 | + | 0.298931i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | −109.469 | + | 294.223i | −0.263781 | + | 0.708971i | ||||
\(416\) | 128.239 | 0.308268 | ||||||||
\(417\) | 157.565 | − | 157.565i | 0.377853 | − | 0.377853i | ||||
\(418\) | 53.7796 | + | 53.7796i | 0.128659 | + | 0.128659i | ||||
\(419\) | 450.030i | 1.07406i | 0.843564 | + | 0.537028i | \(0.180453\pi\) | ||||
−0.843564 | + | 0.537028i | \(0.819547\pi\) | |||||||
\(420\) | −32.4826 | + | 14.8660i | −0.0773396 | + | 0.0353952i | ||||
\(421\) | −715.043 | −1.69844 | −0.849220 | − | 0.528039i | \(-0.822928\pi\) | ||||
−0.849220 | + | 0.528039i | \(0.822928\pi\) | |||||||
\(422\) | −275.082 | + | 275.082i | −0.651854 | + | 0.651854i | ||||
\(423\) | 66.5024 | + | 66.5024i | 0.157216 | + | 0.157216i | ||||
\(424\) | − | 7.01251i | − | 0.0165389i | ||||||
\(425\) | 28.0220 | + | 383.114i | 0.0659340 | + | 0.901445i | ||||
\(426\) | 100.548 | 0.236028 | ||||||||
\(427\) | −45.1814 | + | 45.1814i | −0.105811 | + | 0.105811i | ||||
\(428\) | 236.844 | + | 236.844i | 0.553374 | + | 0.553374i | ||||
\(429\) | 257.959i | 0.601304i | ||||||||
\(430\) | −73.2837 | − | 160.127i | −0.170427 | − | 0.372388i | ||||
\(431\) | −643.338 | −1.49266 | −0.746332 | − | 0.665574i | \(-0.768187\pi\) | ||||
−0.746332 | + | 0.665574i | \(0.768187\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 198.297 | + | 198.297i | 0.457961 | + | 0.457961i | 0.897986 | − | 0.440025i | \(-0.145030\pi\) |
−0.440025 | + | 0.897986i | \(0.645030\pi\) | |||||||
\(434\) | − | 80.8708i | − | 0.186338i | ||||||
\(435\) | −51.4390 | − | 19.1385i | −0.118250 | − | 0.0439966i | ||||
\(436\) | 43.0606 | 0.0987628 | ||||||||
\(437\) | 27.7602 | − | 27.7602i | 0.0635244 | − | 0.0635244i | ||||
\(438\) | 90.9414 | + | 90.9414i | 0.207629 | + | 0.207629i | ||||
\(439\) | 337.344i | 0.768438i | 0.923242 | + | 0.384219i | \(0.125529\pi\) | ||||
−0.923242 | + | 0.384219i | \(0.874471\pi\) | |||||||
\(440\) | −32.3983 | + | 87.0775i | −0.0736325 | + | 0.197904i | ||||
\(441\) | −134.239 | −0.304396 | ||||||||
\(442\) | −348.332 | + | 348.332i | −0.788081 | + | 0.788081i | ||||
\(443\) | 109.373 | + | 109.373i | 0.246892 | + | 0.246892i | 0.819694 | − | 0.572802i | \(-0.194143\pi\) |
−0.572802 | + | 0.819694i | \(0.694143\pi\) | |||||||
\(444\) | 69.1589i | 0.155763i | ||||||||
\(445\) | −646.097 | + | 295.692i | −1.45190 | + | 0.664477i | ||||
\(446\) | −150.605 | −0.337679 | ||||||||
\(447\) | 115.117 | − | 115.117i | 0.257531 | − | 0.257531i | ||||
\(448\) | −11.6670 | − | 11.6670i | −0.0260425 | − | 0.0260425i | ||||
\(449\) | 372.277i | 0.829124i | 0.910021 | + | 0.414562i | \(0.136065\pi\) | ||||
−0.910021 | + | 0.414562i | \(0.863935\pi\) | |||||||
\(450\) | 105.783 | − | 7.73727i | 0.235074 | − | 0.0171939i | ||||
\(451\) | −457.672 | −1.01479 | ||||||||
\(452\) | −144.647 | + | 144.647i | −0.320016 | + | 0.320016i | ||||
\(453\) | 208.758 | + | 208.758i | 0.460835 | + | 0.460835i | ||||
\(454\) | 629.484i | 1.38653i | ||||||||
\(455\) | −97.2858 | − | 212.572i | −0.213815 | − | 0.467192i | ||||
\(456\) | 40.1032 | 0.0879456 | ||||||||
\(457\) | 10.4967 | − | 10.4967i | 0.0229688 | − | 0.0229688i | −0.695529 | − | 0.718498i | \(-0.744830\pi\) |
0.718498 | + | 0.695529i | \(0.244830\pi\) | |||||||
\(458\) | 101.559 | + | 101.559i | 0.221745 | + | 0.221745i | ||||
\(459\) | 79.8415i | 0.173947i | ||||||||
\(460\) | 44.9480 | + | 16.7235i | 0.0977131 | + | 0.0363554i | ||||
\(461\) | −833.333 | −1.80766 | −0.903832 | − | 0.427887i | \(-0.859258\pi\) | ||||
−0.903832 | + | 0.427887i | \(0.859258\pi\) | |||||||
\(462\) | 23.4688 | − | 23.4688i | 0.0507982 | − | 0.0507982i | ||||
\(463\) | 52.1194 | + | 52.1194i | 0.112569 | + | 0.112569i | 0.761148 | − | 0.648579i | \(-0.224636\pi\) |
−0.648579 | + | 0.761148i | \(0.724636\pi\) | |||||||
\(464\) | − | 25.3498i | − | 0.0546332i | ||||||
\(465\) | −83.7308 | + | 225.045i | −0.180066 | + | 0.483968i | ||||
\(466\) | 391.204 | 0.839494 | ||||||||
\(467\) | −185.727 | + | 185.727i | −0.397703 | + | 0.397703i | −0.877422 | − | 0.479719i | \(-0.840738\pi\) |
0.479719 | + | 0.877422i | \(0.340738\pi\) | |||||||
\(468\) | 96.1795 | + | 96.1795i | 0.205512 | + | 0.205512i | ||||
\(469\) | − | 89.6867i | − | 0.191230i | ||||||
\(470\) | −201.568 | + | 92.2495i | −0.428868 | + | 0.196276i | ||||
\(471\) | 142.967 | 0.303539 | ||||||||
\(472\) | 169.309 | − | 169.309i | 0.358706 | − | 0.358706i | ||||
\(473\) | 115.692 | + | 115.692i | 0.244592 | + | 0.244592i | ||||
\(474\) | − | 234.429i | − | 0.494576i | ||||||
\(475\) | 154.881 | + | 133.768i | 0.326064 | + | 0.281617i | ||||
\(476\) | 63.3814 | 0.133154 | ||||||||
\(477\) | 5.25938 | − | 5.25938i | 0.0110260 | − | 0.0110260i | ||||
\(478\) | −262.676 | − | 262.676i | −0.549531 | − | 0.549531i | ||||
\(479\) | − | 384.415i | − | 0.802536i | −0.915961 | − | 0.401268i | \(-0.868570\pi\) | ||
0.915961 | − | 0.401268i | \(-0.131430\pi\) | |||||||
\(480\) | 20.3870 | + | 44.5463i | 0.0424730 | + | 0.0928047i | ||||
\(481\) | −452.589 | −0.940933 | ||||||||
\(482\) | −290.284 | + | 290.284i | −0.602249 | + | 0.602249i | ||||
\(483\) | −12.1142 | − | 12.1142i | −0.0250811 | − | 0.0250811i | ||||
\(484\) | 155.679i | 0.321650i | ||||||||
\(485\) | 658.142 | + | 244.870i | 1.35699 | + | 0.504886i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 176.011 | − | 176.011i | 0.361420 | − | 0.361420i | −0.502916 | − | 0.864335i | \(-0.667739\pi\) |
0.864335 | + | 0.502916i | \(0.167739\pi\) | |||||||
\(488\) | 61.9612 | + | 61.9612i | 0.126970 | + | 0.126970i | ||||
\(489\) | 58.8719i | 0.120392i | ||||||||
\(490\) | 110.333 | − | 296.544i | 0.225169 | − | 0.605191i | ||||
\(491\) | 565.321 | 1.15137 | 0.575683 | − | 0.817673i | \(-0.304736\pi\) | ||||
0.575683 | + | 0.817673i | \(0.304736\pi\) | |||||||
\(492\) | −170.642 | + | 170.642i | −0.346833 | + | 0.346833i | ||||
\(493\) | 68.8568 | + | 68.8568i | 0.139669 | + | 0.139669i | ||||
\(494\) | 262.443i | 0.531261i | ||||||||
\(495\) | −89.6069 | + | 41.0094i | −0.181024 | + | 0.0828474i | ||||
\(496\) | −110.905 | −0.223599 | ||||||||
\(497\) | 59.8642 | − | 59.8642i | 0.120451 | − | 0.120451i | ||||
\(498\) | −108.748 | − | 108.748i | −0.218369 | − | 0.218369i | ||||
\(499\) | − | 876.225i | − | 1.75596i | −0.478696 | − | 0.877981i | \(-0.658890\pi\) | ||
0.478696 | − | 0.877981i | \(-0.341110\pi\) | |||||||
\(500\) | −69.8527 | + | 240.043i | −0.139705 | + | 0.480086i | ||||
\(501\) | 315.972 | 0.630683 | ||||||||
\(502\) | −77.4485 | + | 77.4485i | −0.154280 | + | 0.154280i | ||||
\(503\) | 617.070 | + | 617.070i | 1.22678 | + | 1.22678i | 0.965175 | + | 0.261605i | \(0.0842516\pi\) |
0.261605 | + | 0.965175i | \(0.415748\pi\) | |||||||
\(504\) | − | 17.5005i | − | 0.0347233i | ||||||
\(505\) | −251.393 | − | 549.302i | −0.497809 | − | 1.08773i | ||||
\(506\) | −44.5578 | −0.0880588 | ||||||||
\(507\) | −422.435 | + | 422.435i | −0.833205 | + | 0.833205i | ||||
\(508\) | −149.262 | − | 149.262i | −0.293823 | − | 0.293823i | ||||
\(509\) | 466.623i | 0.916744i | 0.888760 | + | 0.458372i | \(0.151567\pi\) | ||||
−0.888760 | + | 0.458372i | \(0.848433\pi\) | |||||||
\(510\) | −176.376 | − | 65.6228i | −0.345835 | − | 0.128672i | ||||
\(511\) | 108.289 | 0.211917 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 30.0774 | + | 30.0774i | 0.0586304 | + | 0.0586304i | ||||
\(514\) | 428.471i | 0.833602i | ||||||||
\(515\) | 78.3961 | − | 210.707i | 0.152225 | − | 0.409139i | ||||
\(516\) | 86.2710 | 0.167192 | ||||||||
\(517\) | 145.633 | − | 145.633i | 0.281689 | − | 0.281689i | ||||
\(518\) | 41.1758 | + | 41.1758i | 0.0794900 | + | 0.0794900i | ||||
\(519\) | − | 36.3587i | − | 0.0700554i | ||||||
\(520\) | −291.519 | + | 133.416i | −0.560614 | + | 0.256570i | ||||
\(521\) | −562.863 | −1.08035 | −0.540176 | − | 0.841552i | \(-0.681642\pi\) | ||||
−0.540176 | + | 0.841552i | \(0.681642\pi\) | |||||||
\(522\) | 19.0124 | − | 19.0124i | 0.0364221 | − | 0.0364221i | ||||
\(523\) | 205.814 | + | 205.814i | 0.393526 | + | 0.393526i | 0.875942 | − | 0.482416i | \(-0.160241\pi\) |
−0.482416 | + | 0.875942i | \(0.660241\pi\) | |||||||
\(524\) | 319.275i | 0.609304i | ||||||||
\(525\) | 58.3747 | − | 67.5880i | 0.111190 | − | 0.128739i | ||||
\(526\) | 416.924 | 0.792632 | ||||||||
\(527\) | 301.248 | − | 301.248i | 0.571627 | − | 0.571627i | ||||
\(528\) | −32.1847 | − | 32.1847i | −0.0609560 | − | 0.0609560i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | 7.29561 | + | 15.9411i | 0.0137653 | + | 0.0300776i | ||||
\(531\) | 253.964 | 0.478275 | ||||||||
\(532\) | 23.8766 | − | 23.8766i | 0.0448809 | − | 0.0448809i | ||||
\(533\) | −1116.71 | − | 1116.71i | −2.09515 | − | 2.09515i | ||||
\(534\) | − | 348.095i | − | 0.651863i | ||||||
\(535\) | −784.810 | − | 291.998i | −1.46693 | − | 0.545791i | ||||
\(536\) | −122.995 | −0.229469 | ||||||||
\(537\) | 13.2668 | − | 13.2668i | 0.0247055 | − | 0.0247055i | ||||
\(538\) | 177.937 | + | 177.937i | 0.330737 | + | 0.330737i | ||||
\(539\) | 293.969i | 0.545397i | ||||||||
\(540\) | −18.1194 | + | 48.7000i | −0.0335545 | + | 0.0901851i | ||||
\(541\) | −152.262 | −0.281445 | −0.140723 | − | 0.990049i | \(-0.544943\pi\) | ||||
−0.140723 | + | 0.990049i | \(0.544943\pi\) | |||||||
\(542\) | −196.940 | + | 196.940i | −0.363359 | + | 0.363359i | ||||
\(543\) | −3.63085 | − | 3.63085i | −0.00668665 | − | 0.00668665i | ||||
\(544\) | − | 86.9204i | − | 0.159780i | ||||||
\(545\) | −97.8871 | + | 44.7990i | −0.179609 | + | 0.0822000i | ||||
\(546\) | 114.527 | 0.209756 | ||||||||
\(547\) | 486.325 | − | 486.325i | 0.889076 | − | 0.889076i | −0.105358 | − | 0.994434i | \(-0.533599\pi\) |
0.994434 | + | 0.105358i | \(0.0335989\pi\) | |||||||
\(548\) | −93.0261 | − | 93.0261i | −0.169756 | − | 0.169756i | ||||
\(549\) | 92.9418i | 0.169293i | ||||||||
\(550\) | −16.9438 | − | 231.655i | −0.0308069 | − | 0.421190i | ||||
\(551\) | 51.8786 | 0.0941535 | ||||||||
\(552\) | −16.6132 | + | 16.6132i | −0.0300965 | + | 0.0300965i | ||||
\(553\) | −139.574 | − | 139.574i | −0.252395 | − | 0.252395i | ||||
\(554\) | 71.8498i | 0.129693i | ||||||||
\(555\) | −71.9509 | − | 157.215i | −0.129641 | − | 0.283270i | ||||
\(556\) | −257.302 | −0.462774 | ||||||||
\(557\) | −93.7887 | + | 93.7887i | −0.168382 | + | 0.168382i | −0.786268 | − | 0.617886i | \(-0.787989\pi\) |
0.617886 | + | 0.786268i | \(0.287989\pi\) | |||||||
\(558\) | −83.1789 | − | 83.1789i | −0.149066 | − | 0.149066i | ||||
\(559\) | 564.573i | 1.00997i | ||||||||
\(560\) | 38.6600 | + | 14.3839i | 0.0690357 | + | 0.0256856i | ||||
\(561\) | 174.844 | 0.311666 | ||||||||
\(562\) | 308.880 | − | 308.880i | 0.549609 | − | 0.549609i | ||||
\(563\) | −4.76825 | − | 4.76825i | −0.00846936 | − | 0.00846936i | 0.702859 | − | 0.711329i | \(-0.251906\pi\) |
−0.711329 | + | 0.702859i | \(0.751906\pi\) | |||||||
\(564\) | − | 108.598i | − | 0.192549i | ||||||
\(565\) | 178.331 | − | 479.304i | 0.315630 | − | 0.848326i | ||||
\(566\) | 290.664 | 0.513541 | ||||||||
\(567\) | 13.1254 | − | 13.1254i | 0.0231489 | − | 0.0231489i | ||||
\(568\) | −82.0970 | − | 82.0970i | −0.144537 | − | 0.144537i | ||||
\(569\) | − | 993.556i | − | 1.74614i | −0.487591 | − | 0.873072i | \(-0.662124\pi\) | ||
0.487591 | − | 0.873072i | \(-0.337876\pi\) | |||||||
\(570\) | −91.1642 | + | 41.7222i | −0.159937 | + | 0.0731968i | ||||
\(571\) | 524.502 | 0.918567 | 0.459284 | − | 0.888290i | \(-0.348106\pi\) | ||||
0.459284 | + | 0.888290i | \(0.348106\pi\) | |||||||
\(572\) | 210.623 | − | 210.623i | 0.368222 | − | 0.368222i | ||||
\(573\) | 276.120 | + | 276.120i | 0.481885 | + | 0.481885i | ||||
\(574\) | 203.194i | 0.353996i | ||||||||
\(575\) | −119.576 | + | 8.74612i | −0.207959 | + | 0.0152107i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −441.957 | + | 441.957i | −0.765956 | + | 0.765956i | −0.977392 | − | 0.211435i | \(-0.932186\pi\) |
0.211435 | + | 0.977392i | \(0.432186\pi\) | |||||||
\(578\) | −52.9013 | − | 52.9013i | −0.0915248 | − | 0.0915248i | ||||
\(579\) | 567.788i | 0.980636i | ||||||||
\(580\) | 26.3732 | + | 57.6263i | 0.0454710 | + | 0.0993556i | ||||
\(581\) | −129.493 | −0.222879 | ||||||||
\(582\) | −243.256 | + | 243.256i | −0.417965 | + | 0.417965i | ||||
\(583\) | −11.5175 | − | 11.5175i | −0.0197556 | − | 0.0197556i | ||||
\(584\) | − | 148.507i | − | 0.254292i | ||||||
\(585\) | −318.702 | − | 118.577i | −0.544789 | − | 0.202696i | ||||
\(586\) | 482.025 | 0.822568 | ||||||||
\(587\) | 659.069 | − | 659.069i | 1.12278 | − | 1.12278i | 0.131453 | − | 0.991322i | \(-0.458036\pi\) |
0.991322 | − | 0.131453i | \(-0.0419644\pi\) | |||||||
\(588\) | 109.606 | + | 109.606i | 0.186404 | + | 0.186404i | ||||
\(589\) | − | 226.968i | − | 0.385345i | ||||||
\(590\) | −208.737 | + | 561.026i | −0.353791 | + | 0.950891i | ||||
\(591\) | 590.290 | 0.998798 | ||||||||
\(592\) | 56.4680 | − | 56.4680i | 0.0953852 | − | 0.0953852i | ||||
\(593\) | −224.731 | − | 224.731i | −0.378973 | − | 0.378973i | 0.491758 | − | 0.870732i | \(-0.336354\pi\) |
−0.870732 | + | 0.491758i | \(0.836354\pi\) | |||||||
\(594\) | − | 48.2771i | − | 0.0812746i | ||||||
\(595\) | −144.081 | + | 65.9402i | −0.242153 | + | 0.110824i | ||||
\(596\) | −187.985 | −0.315410 | ||||||||
\(597\) | −107.619 | + | 107.619i | −0.180266 | + | 0.180266i | ||||
\(598\) | −108.720 | − | 108.720i | −0.181806 | − | 0.181806i | ||||
\(599\) | − | 104.512i | − | 0.174477i | −0.996187 | − | 0.0872386i | \(-0.972196\pi\) | ||
0.996187 | − | 0.0872386i | \(-0.0278043\pi\) | |||||||
\(600\) | −92.6893 | − | 80.0544i | −0.154482 | − | 0.133424i | ||||
\(601\) | −368.220 | −0.612679 | −0.306340 | − | 0.951922i | \(-0.599104\pi\) | ||||
−0.306340 | + | 0.951922i | \(0.599104\pi\) | |||||||
\(602\) | 51.3640 | − | 51.3640i | 0.0853223 | − | 0.0853223i | ||||
\(603\) | −92.2464 | − | 92.2464i | −0.152979 | − | 0.152979i | ||||
\(604\) | − | 340.901i | − | 0.564406i | ||||||
\(605\) | −161.963 | − | 353.895i | −0.267708 | − | 0.584950i | ||||
\(606\) | 295.945 | 0.488358 | ||||||||
\(607\) | 697.004 | − | 697.004i | 1.14828 | − | 1.14828i | 0.161385 | − | 0.986891i | \(-0.448404\pi\) |
0.986891 | − | 0.161385i | \(-0.0515962\pi\) | |||||||
\(608\) | −32.7441 | − | 32.7441i | −0.0538554 | − | 0.0538554i | ||||
\(609\) | − | 22.6392i | − | 0.0371743i | ||||||
\(610\) | −205.315 | − | 76.3902i | −0.336583 | − | 0.125230i | ||||
\(611\) | 710.685 | 1.16315 | ||||||||
\(612\) | 65.1903 | − | 65.1903i | 0.106520 | − | 0.106520i | ||||
\(613\) | 314.788 | + | 314.788i | 0.513520 | + | 0.513520i | 0.915603 | − | 0.402083i | \(-0.131714\pi\) |
−0.402083 | + | 0.915603i | \(0.631714\pi\) | |||||||
\(614\) | 137.876i | 0.224553i | ||||||||
\(615\) | 210.379 | − | 565.441i | 0.342080 | − | 0.919417i | ||||
\(616\) | −38.3243 | −0.0622148 | ||||||||
\(617\) | −371.648 | + | 371.648i | −0.602346 | + | 0.602346i | −0.940935 | − | 0.338588i | \(-0.890051\pi\) |
0.338588 | + | 0.940935i | \(0.390051\pi\) | |||||||
\(618\) | 77.8793 | + | 77.8793i | 0.126018 | + | 0.126018i | ||||
\(619\) | 522.132i | 0.843509i | 0.906710 | + | 0.421755i | \(0.138586\pi\) | ||||
−0.906710 | + | 0.421755i | \(0.861414\pi\) | |||||||
\(620\) | 252.114 | − | 115.383i | 0.406636 | − | 0.186101i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | −516.333 | + | 516.333i | −0.830118 | + | 0.830118i | ||||
\(623\) | −207.249 | − | 207.249i | −0.332663 | − | 0.332663i | ||||
\(624\) | − | 157.060i | − | 0.251700i | ||||||
\(625\) | −90.9417 | − | 618.348i | −0.145507 | − | 0.989357i | ||||
\(626\) | 83.2848 | 0.133043 | ||||||||
\(627\) | 65.8663 | − | 65.8663i | 0.105050 | − | 0.105050i | ||||
\(628\) | −116.732 | − | 116.732i | −0.185879 | − | 0.185879i | ||||
\(629\) | 306.764i | 0.487701i | ||||||||
\(630\) | 18.2070 | + | 39.7829i | 0.0289001 | + | 0.0631475i | ||||
\(631\) | −1205.43 | −1.91034 | −0.955171 | − | 0.296056i | \(-0.904329\pi\) | ||||
−0.955171 | + | 0.296056i | \(0.904329\pi\) | |||||||
\(632\) | −191.410 | + | 191.410i | −0.302865 | + | 0.302865i | ||||
\(633\) | 336.905 | + | 336.905i | 0.532236 | + | 0.532236i | ||||
\(634\) | 265.079i | 0.418106i | ||||||||
\(635\) | 494.597 | + | 184.021i | 0.778893 | + | 0.289797i | ||||
\(636\) | −8.58853 | −0.0135040 | ||||||||
\(637\) | −717.279 | + | 717.279i | −1.12603 | + | 1.12603i | ||||
\(638\) | −41.6351 | − | 41.6351i | −0.0652587 | − | 0.0652587i | ||||
\(639\) | − | 123.145i | − | 0.192716i | ||||||
\(640\) | 19.7259 | − | 53.0178i | 0.0308218 | − | 0.0828403i | ||||
\(641\) | 274.948 | 0.428936 | 0.214468 | − | 0.976731i | \(-0.431198\pi\) | ||||
0.214468 | + | 0.976731i | \(0.431198\pi\) | |||||||
\(642\) | 290.074 | − | 290.074i | 0.451828 | − | 0.451828i | ||||
\(643\) | −253.931 | − | 253.931i | −0.394916 | − | 0.394916i | 0.481520 | − | 0.876435i | \(-0.340085\pi\) |
−0.876435 | + | 0.481520i | \(0.840085\pi\) | |||||||
\(644\) | 19.7824i | 0.0307180i | ||||||||
\(645\) | −196.115 | + | 89.7538i | −0.304054 | + | 0.139153i | ||||
\(646\) | 177.883 | 0.275361 | ||||||||
\(647\) | 486.345 | − | 486.345i | 0.751693 | − | 0.751693i | −0.223102 | − | 0.974795i | \(-0.571618\pi\) |
0.974795 | + | 0.223102i | \(0.0716184\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 556.154i | − | 0.856941i | ||||||
\(650\) | 523.891 | − | 606.576i | 0.805986 | − | 0.933194i | ||||
\(651\) | −99.0461 | −0.152145 | ||||||||
\(652\) | 48.0687 | − | 48.0687i | 0.0737250 | − | 0.0737250i | ||||
\(653\) | 85.6860 | + | 85.6860i | 0.131219 | + | 0.131219i | 0.769666 | − | 0.638447i | \(-0.220423\pi\) |
−0.638447 | + | 0.769666i | \(0.720423\pi\) | |||||||
\(654\) | − | 52.7382i | − | 0.0806395i | ||||||
\(655\) | −332.165 | − | 725.790i | −0.507122 | − | 1.10808i | ||||
\(656\) | 278.657 | 0.424782 | ||||||||
\(657\) | 111.380 | − | 111.380i | 0.169528 | − | 0.169528i | ||||
\(658\) | −64.6570 | − | 64.6570i | −0.0982630 | − | 0.0982630i | ||||
\(659\) | − | 329.137i | − | 0.499450i | −0.968317 | − | 0.249725i | \(-0.919660\pi\) | ||
0.968317 | − | 0.249725i | \(-0.0803402\pi\) | |||||||
\(660\) | 106.648 | + | 39.6796i | 0.161588 | + | 0.0601207i | ||||
\(661\) | −845.705 | −1.27943 | −0.639717 | − | 0.768611i | \(-0.720948\pi\) | ||||
−0.639717 | + | 0.768611i | \(0.720948\pi\) | |||||||
\(662\) | 345.899 | − | 345.899i | 0.522506 | − | 0.522506i | ||||
\(663\) | 426.618 | + | 426.618i | 0.643465 | + | 0.643465i | ||||
\(664\) | 177.584i | 0.267446i | ||||||||
\(665\) | −29.4368 | + | 79.1179i | −0.0442659 | + | 0.118974i | ||||
\(666\) | 84.7020 | 0.127180 | ||||||||
\(667\) | −21.4913 | + | 21.4913i | −0.0322209 | + | 0.0322209i | ||||
\(668\) | −257.990 | − | 257.990i | −0.386213 | − | 0.386213i | ||||
\(669\) | 184.453i | 0.275714i | ||||||||
\(670\) | 279.598 | − | 127.961i | 0.417310 | − | 0.190986i | ||||
\(671\) | 203.533 | 0.303328 | ||||||||
\(672\) | −14.2891 | + | 14.2891i | −0.0212636 | + | 0.0212636i | ||||
\(673\) | 462.307 | + | 462.307i | 0.686935 | + | 0.686935i | 0.961553 | − | 0.274619i | \(-0.0885516\pi\) |
−0.274619 | + | 0.961553i | \(0.588552\pi\) | |||||||
\(674\) | − | 514.527i | − | 0.763393i | ||||||
\(675\) | −9.47619 | − | 129.558i | −0.0140388 | − | 0.191937i | ||||
\(676\) | 689.833 | 1.02046 | ||||||||
\(677\) | −324.228 | + | 324.228i | −0.478919 | + | 0.478919i | −0.904786 | − | 0.425867i | \(-0.859969\pi\) |
0.425867 | + | 0.904786i | \(0.359969\pi\) | |||||||
\(678\) | 177.156 | + | 177.156i | 0.261292 | + | 0.261292i | ||||
\(679\) | 289.659i | 0.426597i | ||||||||
\(680\) | 90.4295 | + | 197.591i | 0.132985 | + | 0.290575i | ||||
\(681\) | 770.958 | 1.13210 | ||||||||
\(682\) | −182.153 | + | 182.153i | −0.267086 | + | 0.267086i | ||||
\(683\) | 448.652 | + | 448.652i | 0.656884 | + | 0.656884i | 0.954642 | − | 0.297757i | \(-0.0962386\pi\) |
−0.297757 | + | 0.954642i | \(0.596239\pi\) | |||||||
\(684\) | − | 49.1162i | − | 0.0718073i | ||||||
\(685\) | 308.252 | + | 114.689i | 0.450004 | + | 0.167429i | ||||
\(686\) | 273.435 | 0.398593 | ||||||||
\(687\) | 124.384 | − | 124.384i | 0.181054 | − | 0.181054i | ||||
\(688\) | −70.4399 | − | 70.4399i | −0.102384 | − | 0.102384i | ||||
\(689\) | − | 56.2050i | − | 0.0815747i | ||||||
\(690\) | 20.4820 | − | 55.0499i | 0.0296840 | − | 0.0797824i | ||||
\(691\) | −570.580 | −0.825731 | −0.412866 | − | 0.910792i | \(-0.635472\pi\) | ||||
−0.412866 | + | 0.910792i | \(0.635472\pi\) | |||||||
\(692\) | −29.6868 | + | 29.6868i | −0.0429000 | + | 0.0429000i | ||||
\(693\) | −28.7432 | − | 28.7432i | −0.0414765 | − | 0.0414765i | ||||
\(694\) | 425.839i | 0.613601i | ||||||||
\(695\) | 584.910 | − | 267.690i | 0.841597 | − | 0.385165i | ||||
\(696\) | −31.0471 | −0.0446078 | ||||||||
\(697\) | −756.906 | + | 756.906i | −1.08595 | + | 1.08595i | ||||
\(698\) | −377.789 | − | 377.789i | −0.541244 | − | 0.541244i | ||||
\(699\) | − | 479.125i | − | 0.685444i | ||||||
\(700\) | −102.848 | + | 7.52258i | −0.146926 | + | 0.0107465i | ||||
\(701\) | −250.724 | −0.357666 | −0.178833 | − | 0.983879i | \(-0.557232\pi\) | ||||
−0.178833 | + | 0.983879i | \(0.557232\pi\) | |||||||
\(702\) | 117.795 | − | 117.795i | 0.167800 | − | 0.167800i | ||||
\(703\) | 115.562 | + | 115.562i | 0.164384 | + | 0.164384i | ||||
\(704\) | 52.5575i | 0.0746555i | ||||||||
\(705\) | 112.982 | + | 246.869i | 0.160258 | + | 0.350169i | ||||
\(706\) | −192.414 | −0.272541 | ||||||||
\(707\) | 176.200 | − | 176.200i | 0.249222 | − | 0.249222i | ||||
\(708\) | −207.361 | − | 207.361i | −0.292882 | − | 0.292882i | ||||
\(709\) | − | 1105.31i | − | 1.55898i | −0.626417 | − | 0.779488i | \(-0.715479\pi\) | ||
0.626417 | − | 0.779488i | \(-0.284521\pi\) | |||||||
\(710\) | 272.038 | + | 101.215i | 0.383152 | + | 0.142556i | ||||
\(711\) | −287.116 | −0.403820 | ||||||||
\(712\) | −284.218 | + | 284.218i | −0.399183 | + | 0.399183i | ||||
\(713\) | 94.0244 | + | 94.0244i | 0.131872 | + | 0.131872i | ||||
\(714\) | − | 77.6260i | − | 0.108720i | ||||||
\(715\) | −259.671 | + | 697.923i | −0.363176 | + | 0.976116i | ||||
\(716\) | −21.6647 | −0.0302579 | ||||||||
\(717\) | −321.711 | + | 321.711i | −0.448690 | + | 0.448690i | ||||
\(718\) | 181.790 | + | 181.790i | 0.253190 | + | 0.253190i | ||||
\(719\) | − | 693.532i | − | 0.964579i | −0.876012 | − | 0.482289i | \(-0.839805\pi\) | ||
0.876012 | − | 0.482289i | \(-0.160195\pi\) | |||||||
\(720\) | 54.5578 | − | 24.9689i | 0.0757747 | − | 0.0346790i | ||||
\(721\) | 92.7356 | 0.128621 | ||||||||
\(722\) | −293.989 | + | 293.989i | −0.407187 | + | 0.407187i | ||||
\(723\) | 355.524 | + | 355.524i | 0.491735 | + | 0.491735i | ||||
\(724\) | 5.92916i | 0.00818944i | ||||||||
\(725\) | −119.905 | − | 103.560i | −0.165387 | − | 0.142842i | ||||
\(726\) | 190.666 | 0.262626 | ||||||||
\(727\) | 508.634 | − | 508.634i | 0.699634 | − | 0.699634i | −0.264697 | − | 0.964332i | \(-0.585272\pi\) |
0.964332 | + | 0.264697i | \(0.0852721\pi\) | |||||||
\(728\) | −93.5107 | − | 93.5107i | −0.128449 | − | 0.128449i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 154.502 | + | 337.591i | 0.211647 | + | 0.462454i | ||||
\(731\) | 382.667 | 0.523484 | ||||||||
\(732\) | 75.8867 | − | 75.8867i | 0.103670 | − | 0.103670i | ||||
\(733\) | 685.681 | + | 685.681i | 0.935445 | + | 0.935445i | 0.998039 | − | 0.0625940i | \(-0.0199373\pi\) |
−0.0625940 | + | 0.998039i | \(0.519937\pi\) | |||||||
\(734\) | 56.9405i | 0.0775756i | ||||||||
\(735\) | −363.190 | − | 135.129i | −0.494136 | − | 0.183850i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −202.010 | + | 202.010i | −0.274098 | + | 0.274098i | ||||
\(738\) | 208.993 | + | 208.993i | 0.283188 | + | 0.283188i | ||||
\(739\) | − | 60.5009i | − | 0.0818686i | −0.999162 | − | 0.0409343i | \(-0.986967\pi\) | ||
0.999162 | − | 0.0409343i | \(-0.0130334\pi\) | |||||||
\(740\) | −69.6178 | + | 187.113i | −0.0940781 | + | 0.252856i | ||||
\(741\) | 321.425 | 0.433772 | ||||||||
\(742\) | −5.11344 | + | 5.11344i | −0.00689143 | + | 0.00689143i | ||||
\(743\) | −323.462 | − | 323.462i | −0.435346 | − | 0.435346i | 0.455096 | − | 0.890442i | \(-0.349605\pi\) |
−0.890442 | + | 0.455096i | \(0.849605\pi\) | |||||||
\(744\) | 135.831i | 0.182568i | ||||||||
\(745\) | 427.334 | − | 195.574i | 0.573603 | − | 0.262515i | ||||
\(746\) | 188.459 | 0.252626 | ||||||||
\(747\) | −133.188 | + | 133.188i | −0.178298 | + | 0.178298i | ||||
\(748\) | −142.760 | − | 142.760i | −0.190855 | − | 0.190855i | ||||
\(749\) | − | 345.408i | − | 0.461159i | ||||||
\(750\) | 293.991 | + | 85.5517i | 0.391988 | + | 0.114069i | ||||
\(751\) | −20.9996 | −0.0279622 | −0.0139811 | − | 0.999902i | \(-0.504450\pi\) | ||||
−0.0139811 | + | 0.999902i | \(0.504450\pi\) | |||||||
\(752\) | −88.6698 | + | 88.6698i | −0.117912 | + | 0.117912i | ||||
\(753\) | 94.8546 | + | 94.8546i | 0.125969 | + | 0.125969i | ||||
\(754\) | − | 203.178i | − | 0.269466i | ||||||
\(755\) | 354.664 | + | 774.951i | 0.469753 | + | 1.02642i | ||||
\(756\) | −21.4337 | −0.0283514 | ||||||||
\(757\) | −315.246 | + | 315.246i | −0.416441 | + | 0.416441i | −0.883975 | − | 0.467534i | \(-0.845143\pi\) |
0.467534 | + | 0.883975i | \(0.345143\pi\) | |||||||
\(758\) | −139.587 | − | 139.587i | −0.184151 | − | 0.184151i | ||||
\(759\) | 54.5719i | 0.0718997i | ||||||||
\(760\) | 108.501 | + | 40.3693i | 0.142765 | + | 0.0531174i | ||||
\(761\) | −828.712 | −1.08898 | −0.544489 | − | 0.838768i | \(-0.683276\pi\) | ||||
−0.544489 | + | 0.838768i | \(0.683276\pi\) | |||||||
\(762\) | −182.808 | + | 182.808i | −0.239906 | + | 0.239906i | ||||
\(763\) | −31.3993 | − | 31.3993i | −0.0411524 | − | 0.0411524i | ||||
\(764\) | − | 450.902i | − | 0.590186i | ||||||
\(765\) | −80.3712 | + | 216.015i | −0.105060 | + | 0.282373i | ||||
\(766\) | −231.270 | −0.301920 | ||||||||
\(767\) | 1357.01 | − | 1357.01i | 1.76924 | − | 1.76924i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | 968.106i | 1.25892i | 0.777035 | + | 0.629458i | \(0.216723\pi\) | ||||
−0.777035 | + | 0.629458i | \(0.783277\pi\) | |||||||
\(770\) | 87.1204 | − | 39.8715i | 0.113143 | − | 0.0517812i | ||||
\(771\) | 524.768 | 0.680633 | ||||||||
\(772\) | 463.597 | − | 463.597i | 0.600515 | − | 0.600515i | ||||
\(773\) | −74.5415 | − | 74.5415i | −0.0964314 | − | 0.0964314i | 0.657245 | − | 0.753677i | \(-0.271722\pi\) |
−0.753677 | + | 0.657245i | \(0.771722\pi\) | |||||||
\(774\) | − | 105.660i | − | 0.136512i | ||||||
\(775\) | −453.076 | + | 524.585i | −0.584614 | + | 0.676884i | ||||
\(776\) | 397.235 | 0.511901 | ||||||||
\(777\) | 50.4299 | − | 50.4299i | 0.0649033 | − | 0.0649033i | ||||
\(778\) | 443.439 | + | 443.439i | 0.569974 | + | 0.569974i | ||||
\(779\) | 570.274i | 0.732059i | ||||||||
\(780\) | 163.401 | + | 357.036i | 0.209489 | + | 0.457739i | ||||
\(781\) | −269.676 | −0.345295 | ||||||||
\(782\) | −73.6904 | + | 73.6904i | −0.0942332 | + | 0.0942332i | ||||
\(783\) | −23.2853 | − | 23.2853i | −0.0297386 | − | 0.0297386i | ||||
\(784\) | − | 178.985i | − | 0.228297i | ||||||
\(785\) | 386.805 | + | 143.916i | 0.492745 | + | 0.183332i | ||||
\(786\) | 391.031 | 0.497495 | ||||||||
\(787\) | −669.944 | + | 669.944i | −0.851263 | + | 0.851263i | −0.990289 | − | 0.139026i | \(-0.955603\pi\) |
0.139026 | + | 0.990289i | \(0.455603\pi\) | |||||||
\(788\) | −481.969 | − | 481.969i | −0.611636 | − | 0.611636i | ||||
\(789\) | − | 510.626i | − | 0.647181i | ||||||
\(790\) | 235.984 | − | 634.260i | 0.298714 | − | 0.802861i | ||||
\(791\) | 210.950 | 0.266688 | ||||||||
\(792\) | −39.4181 | + | 39.4181i | −0.0497703 | + | 0.0497703i | ||||
\(793\) | 496.617 | + | 496.617i | 0.626250 | + | 0.626250i | ||||
\(794\) | − | 942.126i | − | 1.18656i | ||||||
\(795\) | 19.5238 | − | 8.93526i | 0.0245582 | − | 0.0112393i | ||||
\(796\) | 175.741 | 0.220780 | ||||||||
\(797\) | 852.114 | − | 852.114i | 1.06915 | − | 1.06915i | 0.0717269 | − | 0.997424i | \(-0.477149\pi\) |
0.997424 | − | 0.0717269i | \(-0.0228510\pi\) | |||||||
\(798\) | −29.2428 | − | 29.2428i | −0.0366451 | − | 0.0366451i | ||||
\(799\) | − | 481.701i | − | 0.602880i | ||||||
\(800\) | 10.3164 | + | 141.045i | 0.0128955 | + | 0.176306i | ||||
\(801\) | −426.327 | −0.532244 | ||||||||
\(802\) | −736.854 | + | 736.854i | −0.918771 | + | 0.918771i | ||||
\(803\) | −243.910 | − | 243.910i | −0.303749 | − | 0.303749i | ||||
\(804\) | 150.638i | 0.187360i | ||||||||
\(805\) | −20.5810 | − | 44.9702i | −0.0255665 | − | 0.0558636i | ||||
\(806\) | −888.901 | −1.10285 | ||||||||
\(807\) | 217.927 | − | 217.927i | 0.270046 | − | 0.270046i | ||||
\(808\) | −241.638 | − | 241.638i | −0.299057 | − | 0.299057i | ||||
\(809\) | 119.855i | 0.148152i | 0.997253 | + | 0.0740761i | \(0.0236008\pi\) | ||||
−0.997253 | + | 0.0740761i | \(0.976399\pi\) | |||||||
\(810\) | 59.6450 | + | 22.1917i | 0.0736358 | + | 0.0273971i | ||||
\(811\) | 865.405 | 1.06708 | 0.533542 | − | 0.845773i | \(-0.320861\pi\) | ||||
0.533542 | + | 0.845773i | \(0.320861\pi\) | |||||||
\(812\) | −18.4848 | + | 18.4848i | −0.0227645 | + | 0.0227645i | ||||
\(813\) | 241.202 | + | 241.202i | 0.296681 | + | 0.296681i | ||||
\(814\) | − | 185.488i | − | 0.227873i | ||||||
\(815\) | −59.2625 | + | 159.281i | −0.0727147 | + | 0.195437i | ||||
\(816\) | −106.455 | −0.130460 | ||||||||
\(817\) | 144.156 | − | 144.156i | 0.176445 | − | 0.176445i | ||||
\(818\) | 593.667 | + | 593.667i | 0.725754 | + | 0.725754i | ||||
\(819\) | − | 140.266i | − | 0.171265i | ||||||
\(820\) | −633.455 | + | 289.907i | −0.772506 | + | 0.353545i | ||||
\(821\) | −45.9137 | −0.0559241 | −0.0279620 | − | 0.999609i | \(-0.508902\pi\) | ||||
−0.0279620 | + | 0.999609i | \(0.508902\pi\) | |||||||
\(822\) | −113.933 | + | 113.933i | −0.138605 | + | 0.138605i | ||||
\(823\) | 442.133 | + | 442.133i | 0.537221 | + | 0.537221i | 0.922712 | − | 0.385491i | \(-0.125968\pi\) |
−0.385491 | + | 0.922712i | \(0.625968\pi\) | |||||||
\(824\) | − | 127.176i | − | 0.154340i | ||||||
\(825\) | −283.718 | + | 20.7518i | −0.343900 | + | 0.0251538i | ||||
\(826\) | −246.917 | −0.298931 | ||||||||
\(827\) | −21.4492 | + | 21.4492i | −0.0259361 | + | 0.0259361i | −0.719956 | − | 0.694020i | \(-0.755838\pi\) |
0.694020 | + | 0.719956i | \(0.255838\pi\) | |||||||
\(828\) | 20.3470 | + | 20.3470i | 0.0245737 | + | 0.0245737i | ||||
\(829\) | − | 671.387i | − | 0.809876i | −0.914344 | − | 0.404938i | \(-0.867293\pi\) | ||
0.914344 | − | 0.404938i | \(-0.132707\pi\) | |||||||
\(830\) | −184.754 | − | 403.692i | −0.222595 | − | 0.486376i | ||||
\(831\) | 87.9976 | 0.105894 | ||||||||
\(832\) | −128.239 | + | 128.239i | −0.154134 | + | 0.154134i | ||||
\(833\) | 486.171 | + | 486.171i | 0.583638 | + | 0.583638i | ||||
\(834\) | 315.129i | 0.377853i | ||||||||
\(835\) | 854.880 | + | 318.069i | 1.02381 | + | 0.380921i | ||||
\(836\) | −107.559 | −0.128659 | ||||||||
\(837\) | −101.873 | + | 101.873i | −0.121712 | + | 0.121712i | ||||
\(838\) | −450.030 | − | 450.030i | −0.537028 | − | 0.537028i | ||||
\(839\) | 1314.79i | 1.56709i | 0.621332 | + | 0.783547i | \(0.286592\pi\) | ||||
−0.621332 | + | 0.783547i | \(0.713408\pi\) | |||||||
\(840\) | 17.6166 | − | 47.3486i | 0.0209722 | − | 0.0563674i | ||||
\(841\) | 800.837 | 0.952243 | ||||||||
\(842\) | 715.043 | − | 715.043i | 0.849220 | − | 0.849220i | ||||
\(843\) | −378.299 | − | 378.299i | −0.448754 | − | 0.448754i | ||||
\(844\) | − | 550.164i | − | 0.651854i | ||||||
\(845\) | −1568.16 | + | 717.682i | −1.85581 | + | 0.849328i | ||||
\(846\) | −133.005 | −0.157216 | ||||||||
\(847\) | 113.519 | − | 113.519i | 0.134025 | − | 0.134025i | ||||
\(848\) | 7.01251 | + | 7.01251i | 0.00826947 | + | 0.00826947i | ||||
\(849\) | − | 355.990i | − | 0.419305i | ||||||
\(850\) | −411.136 | − | 355.092i | −0.483690 | − | 0.417756i | ||||
\(851\) | −95.7462 | −0.112510 | ||||||||
\(852\) | −100.548 | + | 100.548i | −0.118014 | + | 0.118014i | ||||
\(853\) | 1140.91 | + | 1140.91i | 1.33753 | + | 1.33753i | 0.898447 | + | 0.439081i | \(0.144696\pi\) |
0.439081 | + | 0.898447i | \(0.355304\pi\) | |||||||
\(854\) | − | 90.3628i | − | 0.105811i | ||||||
\(855\) | 51.0990 | + | 111.653i | 0.0597650 | + | 0.130588i | ||||
\(856\) | −473.689 | −0.553374 | ||||||||
\(857\) | 238.411 | − | 238.411i | 0.278192 | − | 0.278192i | −0.554195 | − | 0.832387i | \(-0.686974\pi\) |
0.832387 | + | 0.554195i | \(0.186974\pi\) | |||||||
\(858\) | −257.959 | − | 257.959i | −0.300652 | − | 0.300652i | ||||
\(859\) | − | 1134.94i | − | 1.32124i | −0.750721 | − | 0.660619i | \(-0.770294\pi\) | ||
0.750721 | − | 0.660619i | \(-0.229706\pi\) | |||||||
\(860\) | 233.411 | + | 86.8434i | 0.271408 | + | 0.100981i | ||||
\(861\) | 248.860 | 0.289037 | ||||||||
\(862\) | 643.338 | − | 643.338i | 0.746332 | − | 0.746332i | ||||
\(863\) | 308.927 | + | 308.927i | 0.357968 | + | 0.357968i | 0.863064 | − | 0.505095i | \(-0.168543\pi\) |
−0.505095 | + | 0.863064i | \(0.668543\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 36.6000 | − | 98.3705i | 0.0423121 | − | 0.113723i | ||||
\(866\) | −396.594 | −0.457961 | ||||||||
\(867\) | −64.7906 | + | 64.7906i | −0.0747297 | + | 0.0747297i | ||||
\(868\) | 80.8708 | + | 80.8708i | 0.0931692 | + | 0.0931692i | ||||
\(869\) | 628.753i | 0.723536i | ||||||||
\(870\) | 70.5775 | − | 32.3005i | 0.0811235 | − | 0.0371270i | ||||
\(871\) | −985.802 | −1.13180 | ||||||||
\(872\) | −43.0606 | + | 43.0606i | −0.0493814 | + | 0.0493814i | ||||
\(873\) | 297.926 | + | 297.926i | 0.341267 | + | 0.341267i | ||||
\(874\) | 55.5203i | 0.0635244i | ||||||||
\(875\) | 225.972 | − | 124.101i | 0.258254 | − | 0.141830i | ||||
\(876\) | −181.883 | −0.207629 | ||||||||
\(877\) | 52.6873 | − | 52.6873i | 0.0600767 | − | 0.0600767i | −0.676430 | − | 0.736507i | \(-0.736474\pi\) |
0.736507 | + | 0.676430i | \(0.236474\pi\) | |||||||
\(878\) | −337.344 | − | 337.344i | −0.384219 | − | 0.384219i | ||||
\(879\) | − | 590.358i | − | 0.671624i | ||||||
\(880\) | −54.6793 | − | 119.476i | −0.0621355 | − | 0.135768i | ||||
\(881\) | −1442.03 | −1.63681 | −0.818404 | − | 0.574644i | \(-0.805141\pi\) | ||||
−0.818404 | + | 0.574644i | \(0.805141\pi\) | |||||||
\(882\) | 134.239 | − | 134.239i | 0.152198 | − | 0.152198i | ||||
\(883\) | −517.014 | − | 517.014i | −0.585520 | − | 0.585520i | 0.350895 | − | 0.936415i | \(-0.385877\pi\) |
−0.936415 | + | 0.350895i | \(0.885877\pi\) | |||||||
\(884\) | − | 696.664i | − | 0.788081i | ||||||
\(885\) | 687.113 | + | 255.649i | 0.776399 | + | 0.288869i | ||||
\(886\) | −218.747 | −0.246892 | ||||||||
\(887\) | 645.843 | − | 645.843i | 0.728121 | − | 0.728121i | −0.242124 | − | 0.970245i | \(-0.577844\pi\) |
0.970245 | + | 0.242124i | \(0.0778442\pi\) | |||||||
\(888\) | −69.1589 | − | 69.1589i | −0.0778817 | − | 0.0778817i | ||||
\(889\) | 217.681i | 0.244860i | ||||||||
\(890\) | 350.404 | − | 941.789i | 0.393713 | − | 1.05819i | ||||
\(891\) | −59.1271 | −0.0663604 | ||||||||
\(892\) | 150.605 | − | 150.605i | 0.168840 | − | 0.168840i | ||||
\(893\) | −181.463 | − | 181.463i | −0.203207 | − | 0.203207i | ||||
\(894\) | 230.233i | 0.257531i | ||||||||
\(895\) | 49.2490 | − | 22.5393i | 0.0550268 | − | 0.0251836i | ||||
\(896\) | 23.3340 | 0.0260425 | ||||||||
\(897\) | −133.155 | + | 133.155i | −0.148444 | + | 0.148444i | ||||
\(898\) | −372.277 | − | 372.277i | −0.414562 | − | 0.414562i | ||||
\(899\) | 175.714i | 0.195455i | ||||||||
\(900\) | −98.0462 | + | 113.521i | −0.108940 | + | 0.126134i | ||||
\(901\) | −38.0956 | −0.0422815 | ||||||||
\(902\) | 457.672 | − | 457.672i | 0.507397 | − | 0.507397i | ||||
\(903\) | −62.9078 | − | 62.9078i | −0.0696654 | − | 0.0696654i | ||||
\(904\) | − | 289.294i | − | 0.320016i | ||||||
\(905\) | −6.16852 | − | 13.4784i | −0.00681605 | − | 0.0148933i | ||||
\(906\) | −417.517 | −0.460835 | ||||||||
\(907\) | −258.058 | + | 258.058i | −0.284518 | + | 0.284518i | −0.834908 | − | 0.550390i | \(-0.814479\pi\) |
0.550390 | + | 0.834908i | \(0.314479\pi\) | |||||||
\(908\) | −629.484 | − | 629.484i | −0.693265 | − | 0.693265i | ||||
\(909\) | − | 362.457i | − | 0.398743i | ||||||
\(910\) | 309.858 | + | 115.287i | 0.340504 | + | 0.126689i | ||||
\(911\) | −1486.36 | −1.63157 | −0.815784 | − | 0.578357i | \(-0.803694\pi\) | ||||
−0.815784 | + | 0.578357i | \(0.803694\pi\) | |||||||
\(912\) | −40.1032 | + | 40.1032i | −0.0439728 | + | 0.0439728i | ||||
\(913\) | 291.668 | + | 291.668i | 0.319461 | + | 0.319461i | ||||
\(914\) | 20.9935i | 0.0229688i | ||||||||
\(915\) | −93.5585 | + | 251.459i | −0.102250 | + | 0.274819i | ||||
\(916\) | −203.118 | −0.221745 | ||||||||
\(917\) | 232.812 | − | 232.812i | 0.253885 | − | 0.253885i | ||||
\(918\) | −79.8415 | − | 79.8415i | −0.0869733 | − | 0.0869733i | ||||
\(919\) | − | 1545.07i | − | 1.68125i | −0.541614 | − | 0.840627i | \(-0.682187\pi\) | ||
0.541614 | − | 0.840627i | \(-0.317813\pi\) | |||||||
\(920\) | −61.6715 | + | 28.2246i | −0.0670342 | + | 0.0306789i | ||||
\(921\) | 168.863 | 0.183347 | ||||||||
\(922\) | 833.333 | − | 833.333i | 0.903832 | − | 0.903832i | ||||
\(923\) | −658.004 | − | 658.004i | −0.712897 | − | 0.712897i | ||||
\(924\) | 46.9375i | 0.0507982i | ||||||||
\(925\) | −36.4090 | − | 497.782i | −0.0393611 | − | 0.538142i | ||||
\(926\) | −104.239 | −0.112569 | ||||||||
\(927\) | 95.3823 | − | 95.3823i | 0.102894 | − | 0.102894i | ||||
\(928\) | 25.3498 | + | 25.3498i | 0.0273166 | + | 0.0273166i | ||||
\(929\) | − | 1408.56i | − | 1.51621i | −0.652130 | − | 0.758107i | \(-0.726124\pi\) | ||
0.652130 | − | 0.758107i | \(-0.273876\pi\) | |||||||
\(930\) | −141.314 | − | 308.776i | −0.151951 | − | 0.332017i | ||||
\(931\) | 366.294 | 0.393442 | ||||||||
\(932\) | −391.204 | + | 391.204i | −0.419747 | + | 0.419747i | ||||
\(933\) | 632.377 | + | 632.377i | 0.677789 | + | 0.677789i | ||||
\(934\) | − | 371.454i | − | 0.397703i | ||||||
\(935\) | 473.051 | + | 176.005i | 0.505937 | + | 0.188240i | ||||
\(936\) | −192.359 | −0.205512 | ||||||||
\(937\) | −1156.07 | + | 1156.07i | −1.23380 | + | 1.23380i | −0.271306 | + | 0.962493i | \(0.587456\pi\) |
−0.962493 | + | 0.271306i | \(0.912544\pi\) | |||||||
\(938\) | 89.6867 | + | 89.6867i | 0.0956149 | + | 0.0956149i | ||||
\(939\) | − | 102.003i | − | 0.108629i | ||||||
\(940\) | 109.318 | − | 293.817i | 0.116296 | − | 0.312572i | ||||
\(941\) | −539.273 | −0.573085 | −0.286543 | − | 0.958068i | \(-0.592506\pi\) | ||||
−0.286543 | + | 0.958068i | \(0.592506\pi\) | |||||||
\(942\) | −142.967 | + | 142.967i | −0.151770 | + | 0.151770i | ||||
\(943\) | −236.243 | − | 236.243i | −0.250523 | − | 0.250523i | ||||
\(944\) | 338.619i | 0.358706i | ||||||||
\(945\) | 48.7240 | − | 22.2990i | 0.0515597 | − | 0.0235968i | ||||
\(946\) | −231.384 | −0.244592 | ||||||||
\(947\) | 60.4452 | − | 60.4452i | 0.0638281 | − | 0.0638281i | −0.674472 | − | 0.738300i | \(-0.735629\pi\) |
0.738300 | + | 0.674472i | \(0.235629\pi\) | |||||||
\(948\) | 234.429 | + | 234.429i | 0.247288 | + | 0.247288i | ||||
\(949\) | − | 1190.27i | − | 1.25424i | ||||||
\(950\) | −288.649 | + | 21.1125i | −0.303841 | + | 0.0222237i | ||||
\(951\) | 324.655 | 0.341382 | ||||||||
\(952\) | −63.3814 | + | 63.3814i | −0.0665771 | + | 0.0665771i | ||||
\(953\) | 397.881 | + | 397.881i | 0.417503 | + | 0.417503i | 0.884342 | − | 0.466839i | \(-0.154607\pi\) |
−0.466839 | + | 0.884342i | \(0.654607\pi\) | |||||||
\(954\) | 10.5188i | 0.0110260i | ||||||||
\(955\) | 469.106 | + | 1025.01i | 0.491210 | + | 1.07331i | ||||
\(956\) | 525.351 | 0.549531 | ||||||||
\(957\) | −50.9923 | + | 50.9923i | −0.0532835 | + | 0.0532835i | ||||
\(958\) | 384.415 | + | 384.415i | 0.401268 | + | 0.401268i | ||||
\(959\) | 135.667i | 0.141467i | ||||||||
\(960\) | −64.9333 | − | 24.1592i | −0.0676388 | − | 0.0251659i | ||||
\(961\) | −192.252 | −0.200055 | ||||||||
\(962\) | 452.589 | − | 452.589i | 0.470467 | − | 0.470467i | ||||
\(963\) | −355.266 | − | 355.266i | −0.368916 | − | 0.368916i | ||||
\(964\) | − | 580.568i | − | 0.602249i | ||||||
\(965\) | −571.555 | + | 1536.18i | −0.592285 | + | 1.59190i | ||||
\(966\) | 24.2284 | 0.0250811 | ||||||||
\(967\) | 627.872 | − | 627.872i | 0.649299 | − | 0.649299i | −0.303525 | − | 0.952823i | \(-0.598164\pi\) |
0.952823 | + | 0.303525i | \(0.0981636\pi\) | |||||||
\(968\) | −155.679 | − | 155.679i | −0.160825 | − | 0.160825i | ||||
\(969\) | − | 217.862i | − | 0.224831i | ||||||
\(970\) | −903.011 | + | 413.272i | −0.930940 | + | 0.426053i | ||||
\(971\) | −191.624 | −0.197347 | −0.0986735 | − | 0.995120i | \(-0.531460\pi\) | ||||
−0.0986735 | + | 0.995120i | \(0.531460\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 187.622 | + | 187.622i | 0.192828 | + | 0.192828i | ||||
\(974\) | 352.023i | 0.361420i | ||||||||
\(975\) | −742.901 | − | 641.632i | −0.761949 | − | 0.658085i | ||||
\(976\) | −123.922 | −0.126970 | ||||||||
\(977\) | −1008.83 | + | 1008.83i | −1.03258 | + | 1.03258i | −0.0331267 | + | 0.999451i | \(0.510546\pi\) |
−0.999451 | + | 0.0331267i | \(0.989454\pi\) | |||||||
\(978\) | −58.8719 | − | 58.8719i | −0.0601962 | − | 0.0601962i | ||||
\(979\) | 933.612i | 0.953638i | ||||||||
\(980\) | 186.211 | + | 406.876i | 0.190011 | + | 0.415180i | ||||
\(981\) | −64.5909 | −0.0658419 | ||||||||
\(982\) | −565.321 | + | 565.321i | −0.575683 | + | 0.575683i | ||||
\(983\) | 308.876 | + | 308.876i | 0.314218 | + | 0.314218i | 0.846541 | − | 0.532323i | \(-0.178681\pi\) |
−0.532323 | + | 0.846541i | \(0.678681\pi\) | |||||||
\(984\) | − | 341.284i | − | 0.346833i | ||||||
\(985\) | 1597.06 | + | 594.206i | 1.62138 | + | 0.603255i | ||||
\(986\) | −137.714 | −0.139669 | ||||||||
\(987\) | −79.1884 | + | 79.1884i | −0.0802314 | + | 0.0802314i | ||||
\(988\) | −262.443 | − | 262.443i | −0.265630 | − | 0.265630i | ||||
\(989\) | 119.437i | 0.120765i | ||||||||
\(990\) | 48.5974 | − | 130.616i | 0.0490883 | − | 0.131936i | ||||
\(991\) | −273.887 | −0.276374 | −0.138187 | − | 0.990406i | \(-0.544128\pi\) | ||||
−0.138187 | + | 0.990406i | \(0.544128\pi\) | |||||||
\(992\) | 110.905 | − | 110.905i | 0.111800 | − | 0.111800i | ||||
\(993\) | −423.638 | − | 423.638i | −0.426625 | − | 0.426625i | ||||
\(994\) | 119.728i | 0.120451i | ||||||||
\(995\) | −399.501 | + | 182.835i | −0.401509 | + | 0.183754i | ||||
\(996\) | 217.495 | 0.218369 | ||||||||
\(997\) | 276.311 | − | 276.311i | 0.277142 | − | 0.277142i | −0.554825 | − | 0.831967i | \(-0.687215\pi\) |
0.831967 | + | 0.554825i | \(0.187215\pi\) | |||||||
\(998\) | 876.225 | + | 876.225i | 0.877981 | + | 0.877981i | ||||
\(999\) | − | 103.738i | − | 0.103842i |
(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.553.17 | yes | 48 | |
5.2 | odd | 4 | inner | 690.3.k.b.277.17 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.17 | ✓ | 48 | 5.2 | odd | 4 | inner | |
690.3.k.b.553.17 | yes | 48 | 1.1 | even | 1 | trivial |