Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,3,Mod(12,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.12");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.c (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: | \(0.790192766645\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(-1.35225i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.17 |
Dual form | 29.3.c.a.12.3 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.909588 | − | 0.909588i | 0.454794 | − | 0.454794i | −0.442148 | − | 0.896942i | \(-0.645783\pi\) |
0.896942 | + | 0.442148i | \(0.145783\pi\) | |||||||
\(3\) | 0.442660 | − | 0.442660i | 0.147553 | − | 0.147553i | −0.629471 | − | 0.777024i | \(-0.716728\pi\) |
0.777024 | + | 0.629471i | \(0.216728\pi\) | |||||||
\(4\) | 2.34530i | 0.586324i | ||||||||
\(5\) | − | 4.16447i | − | 0.832895i | −0.909160 | − | 0.416447i | \(-0.863275\pi\) | ||
0.909160 | − | 0.416447i | \(-0.136725\pi\) | |||||||
\(6\) | − | 0.805276i | − | 0.134213i | ||||||
\(7\) | −9.68815 | −1.38402 | −0.692011 | − | 0.721887i | \(-0.743275\pi\) | ||||
−0.692011 | + | 0.721887i | \(0.743275\pi\) | |||||||
\(8\) | 5.77161 | + | 5.77161i | 0.721451 | + | 0.721451i | ||||
\(9\) | 8.60810i | 0.956456i | ||||||||
\(10\) | −3.78796 | − | 3.78796i | −0.378796 | − | 0.378796i | ||||
\(11\) | −0.334930 | + | 0.334930i | −0.0304481 | + | 0.0304481i | −0.722167 | − | 0.691719i | \(-0.756854\pi\) |
0.691719 | + | 0.722167i | \(0.256854\pi\) | |||||||
\(12\) | 1.03817 | + | 1.03817i | 0.0865141 | + | 0.0865141i | ||||
\(13\) | − | 12.2282i | − | 0.940628i | −0.882499 | − | 0.470314i | \(-0.844141\pi\) | ||
0.882499 | − | 0.470314i | \(-0.155859\pi\) | |||||||
\(14\) | −8.81223 | + | 8.81223i | −0.629445 | + | 0.629445i | ||||
\(15\) | −1.84345 | − | 1.84345i | −0.122896 | − | 0.122896i | ||||
\(16\) | 1.11839 | 0.0698991 | ||||||||
\(17\) | 6.80978 | − | 6.80978i | 0.400575 | − | 0.400575i | −0.477861 | − | 0.878436i | \(-0.658588\pi\) |
0.878436 | + | 0.477861i | \(0.158588\pi\) | |||||||
\(18\) | 7.82983 | + | 7.82983i | 0.434991 | + | 0.434991i | ||||
\(19\) | 14.6673 | − | 14.6673i | 0.771963 | − | 0.771963i | −0.206486 | − | 0.978449i | \(-0.566203\pi\) |
0.978449 | + | 0.206486i | \(0.0662029\pi\) | |||||||
\(20\) | 9.76693 | 0.488347 | ||||||||
\(21\) | −4.28855 | + | 4.28855i | −0.204217 | + | 0.204217i | ||||
\(22\) | 0.609296i | 0.0276953i | ||||||||
\(23\) | −10.0844 | −0.438454 | −0.219227 | − | 0.975674i | \(-0.570353\pi\) | ||||
−0.219227 | + | 0.975674i | \(0.570353\pi\) | |||||||
\(24\) | 5.10972 | 0.212905 | ||||||||
\(25\) | 7.65715 | 0.306286 | ||||||||
\(26\) | −11.1226 | − | 11.1226i | −0.427792 | − | 0.427792i | ||||
\(27\) | 7.79440 | + | 7.79440i | 0.288681 | + | 0.288681i | ||||
\(28\) | − | 22.7216i | − | 0.811485i | ||||||
\(29\) | 28.1041 | + | 7.15263i | 0.969107 | + | 0.246642i | ||||
\(30\) | −3.35355 | −0.111785 | ||||||||
\(31\) | −37.3099 | + | 37.3099i | −1.20355 | + | 1.20355i | −0.230466 | + | 0.973080i | \(0.574025\pi\) |
−0.973080 | + | 0.230466i | \(0.925975\pi\) | |||||||
\(32\) | −22.0692 | + | 22.0692i | −0.689661 | + | 0.689661i | ||||
\(33\) | 0.296520i | 0.00898545i | ||||||||
\(34\) | − | 12.3882i | − | 0.364359i | ||||||
\(35\) | 40.3460i | 1.15274i | ||||||||
\(36\) | −20.1886 | −0.560794 | ||||||||
\(37\) | −45.0215 | − | 45.0215i | −1.21680 | − | 1.21680i | −0.968747 | − | 0.248050i | \(-0.920210\pi\) |
−0.248050 | − | 0.968747i | \(-0.579790\pi\) | |||||||
\(38\) | − | 26.6824i | − | 0.702169i | ||||||
\(39\) | −5.41292 | − | 5.41292i | −0.138793 | − | 0.138793i | ||||
\(40\) | 24.0357 | − | 24.0357i | 0.600893 | − | 0.600893i | ||||
\(41\) | 22.8142 | + | 22.8142i | 0.556443 | + | 0.556443i | 0.928293 | − | 0.371850i | \(-0.121276\pi\) |
−0.371850 | + | 0.928293i | \(0.621276\pi\) | |||||||
\(42\) | 7.80164i | 0.185753i | ||||||||
\(43\) | −17.5030 | + | 17.5030i | −0.407048 | + | 0.407048i | −0.880708 | − | 0.473660i | \(-0.842933\pi\) |
0.473660 | + | 0.880708i | \(0.342933\pi\) | |||||||
\(44\) | −0.785510 | − | 0.785510i | −0.0178525 | − | 0.0178525i | ||||
\(45\) | 35.8482 | 0.796627 | ||||||||
\(46\) | −9.17268 | + | 9.17268i | −0.199406 | + | 0.199406i | ||||
\(47\) | 2.20999 | + | 2.20999i | 0.0470210 | + | 0.0470210i | 0.730226 | − | 0.683205i | \(-0.239415\pi\) |
−0.683205 | + | 0.730226i | \(0.739415\pi\) | |||||||
\(48\) | 0.495064 | − | 0.495064i | 0.0103138 | − | 0.0103138i | ||||
\(49\) | 44.8602 | 0.915514 | ||||||||
\(50\) | 6.96485 | − | 6.96485i | 0.139297 | − | 0.139297i | ||||
\(51\) | − | 6.02883i | − | 0.118212i | ||||||
\(52\) | 28.6787 | 0.551513 | ||||||||
\(53\) | 90.1375 | 1.70071 | 0.850354 | − | 0.526212i | \(-0.176388\pi\) | ||||
0.850354 | + | 0.526212i | \(0.176388\pi\) | |||||||
\(54\) | 14.1794 | 0.262581 | ||||||||
\(55\) | 1.39481 | + | 1.39481i | 0.0253601 | + | 0.0253601i | ||||
\(56\) | −55.9162 | − | 55.9162i | −0.998504 | − | 0.998504i | ||||
\(57\) | − | 12.9852i | − | 0.227811i | ||||||
\(58\) | 32.0691 | − | 19.0572i | 0.552916 | − | 0.328573i | ||||
\(59\) | −90.4223 | −1.53258 | −0.766291 | − | 0.642494i | \(-0.777900\pi\) | ||||
−0.766291 | + | 0.642494i | \(0.777900\pi\) | |||||||
\(60\) | 4.32343 | − | 4.32343i | 0.0720572 | − | 0.0720572i | ||||
\(61\) | −29.4354 | + | 29.4354i | −0.482548 | + | 0.482548i | −0.905944 | − | 0.423397i | \(-0.860838\pi\) |
0.423397 | + | 0.905944i | \(0.360838\pi\) | |||||||
\(62\) | 67.8734i | 1.09473i | ||||||||
\(63\) | − | 83.3966i | − | 1.32376i | ||||||
\(64\) | 44.6213i | 0.697207i | ||||||||
\(65\) | −50.9239 | −0.783445 | ||||||||
\(66\) | 0.269711 | + | 0.269711i | 0.00408653 | + | 0.00408653i | ||||
\(67\) | 31.5543i | 0.470960i | 0.971879 | + | 0.235480i | \(0.0756662\pi\) | ||||
−0.971879 | + | 0.235480i | \(0.924334\pi\) | |||||||
\(68\) | 15.9710 | + | 15.9710i | 0.234867 | + | 0.234867i | ||||
\(69\) | −4.46397 | + | 4.46397i | −0.0646953 | + | 0.0646953i | ||||
\(70\) | 36.6983 | + | 36.6983i | 0.524261 | + | 0.524261i | ||||
\(71\) | − | 99.8673i | − | 1.40658i | −0.710902 | − | 0.703291i | \(-0.751713\pi\) | ||
0.710902 | − | 0.703291i | \(-0.248287\pi\) | |||||||
\(72\) | −49.6826 | + | 49.6826i | −0.690036 | + | 0.690036i | ||||
\(73\) | −3.96285 | − | 3.96285i | −0.0542856 | − | 0.0542856i | 0.679443 | − | 0.733728i | \(-0.262222\pi\) |
−0.733728 | + | 0.679443i | \(0.762222\pi\) | |||||||
\(74\) | −81.9020 | −1.10678 | ||||||||
\(75\) | 3.38951 | − | 3.38951i | 0.0451935 | − | 0.0451935i | ||||
\(76\) | 34.3992 | + | 34.3992i | 0.452621 | + | 0.452621i | ||||
\(77\) | 3.24485 | − | 3.24485i | 0.0421409 | − | 0.0421409i | ||||
\(78\) | −9.84706 | −0.126244 | ||||||||
\(79\) | −40.3117 | + | 40.3117i | −0.510275 | + | 0.510275i | −0.914611 | − | 0.404335i | \(-0.867503\pi\) |
0.404335 | + | 0.914611i | \(0.367503\pi\) | |||||||
\(80\) | − | 4.65749i | − | 0.0582186i | ||||||
\(81\) | −70.5724 | −0.871264 | ||||||||
\(82\) | 41.5030 | 0.506134 | ||||||||
\(83\) | 137.714 | 1.65921 | 0.829604 | − | 0.558352i | \(-0.188566\pi\) | ||||
0.829604 | + | 0.558352i | \(0.188566\pi\) | |||||||
\(84\) | −10.0579 | − | 10.0579i | −0.119737 | − | 0.119737i | ||||
\(85\) | −28.3592 | − | 28.3592i | −0.333637 | − | 0.333637i | ||||
\(86\) | 31.8411i | 0.370246i | ||||||||
\(87\) | 15.6067 | − | 9.27437i | 0.179388 | − | 0.106602i | ||||
\(88\) | −3.86616 | −0.0439337 | ||||||||
\(89\) | 83.1506 | − | 83.1506i | 0.934276 | − | 0.934276i | −0.0636936 | − | 0.997969i | \(-0.520288\pi\) |
0.997969 | + | 0.0636936i | \(0.0202880\pi\) | |||||||
\(90\) | 32.6071 | − | 32.6071i | 0.362302 | − | 0.362302i | ||||
\(91\) | 118.468i | 1.30185i | ||||||||
\(92\) | − | 23.6510i | − | 0.257076i | ||||||
\(93\) | 33.0312i | 0.355174i | ||||||||
\(94\) | 4.02036 | 0.0427698 | ||||||||
\(95\) | −61.0816 | − | 61.0816i | −0.642964 | − | 0.642964i | ||||
\(96\) | 19.5383i | 0.203524i | ||||||||
\(97\) | −79.9850 | − | 79.9850i | −0.824588 | − | 0.824588i | 0.162174 | − | 0.986762i | \(-0.448149\pi\) |
−0.986762 | + | 0.162174i | \(0.948149\pi\) | |||||||
\(98\) | 40.8043 | − | 40.8043i | 0.416371 | − | 0.416371i | ||||
\(99\) | −2.88311 | − | 2.88311i | −0.0291223 | − | 0.0291223i | ||||
\(100\) | 17.9583i | 0.179583i | ||||||||
\(101\) | −52.1216 | + | 52.1216i | −0.516055 | + | 0.516055i | −0.916375 | − | 0.400320i | \(-0.868899\pi\) |
0.400320 | + | 0.916375i | \(0.368899\pi\) | |||||||
\(102\) | −5.48375 | − | 5.48375i | −0.0537623 | − | 0.0537623i | ||||
\(103\) | 139.377 | 1.35318 | 0.676588 | − | 0.736361i | \(-0.263458\pi\) | ||||
0.676588 | + | 0.736361i | \(0.263458\pi\) | |||||||
\(104\) | 70.5762 | − | 70.5762i | 0.678617 | − | 0.678617i | ||||
\(105\) | 17.8596 | + | 17.8596i | 0.170091 | + | 0.170091i | ||||
\(106\) | 81.9880 | − | 81.9880i | 0.773472 | − | 0.773472i | ||||
\(107\) | −14.9646 | −0.139856 | −0.0699282 | − | 0.997552i | \(-0.522277\pi\) | ||||
−0.0699282 | + | 0.997552i | \(0.522277\pi\) | |||||||
\(108\) | −18.2802 | + | 18.2802i | −0.169261 | + | 0.169261i | ||||
\(109\) | 38.6223i | 0.354333i | 0.984181 | + | 0.177167i | \(0.0566931\pi\) | ||||
−0.984181 | + | 0.177167i | \(0.943307\pi\) | |||||||
\(110\) | 2.53740 | 0.0230673 | ||||||||
\(111\) | −39.8584 | −0.359085 | ||||||||
\(112\) | −10.8351 | −0.0967418 | ||||||||
\(113\) | −20.2695 | − | 20.2695i | −0.179376 | − | 0.179376i | 0.611708 | − | 0.791084i | \(-0.290483\pi\) |
−0.791084 | + | 0.611708i | \(0.790483\pi\) | |||||||
\(114\) | −11.8112 | − | 11.8112i | −0.103607 | − | 0.103607i | ||||
\(115\) | 41.9964i | 0.365186i | ||||||||
\(116\) | −16.7750 | + | 65.9125i | −0.144612 | + | 0.568211i | ||||
\(117\) | 105.261 | 0.899670 | ||||||||
\(118\) | −82.2471 | + | 82.2471i | −0.697009 | + | 0.697009i | ||||
\(119\) | −65.9741 | + | 65.9741i | −0.554405 | + | 0.554405i | ||||
\(120\) | − | 21.2793i | − | 0.177327i | ||||||
\(121\) | 120.776i | 0.998146i | ||||||||
\(122\) | 53.5482i | 0.438920i | ||||||||
\(123\) | 20.1978 | 0.164210 | ||||||||
\(124\) | −87.5029 | − | 87.5029i | −0.705669 | − | 0.705669i | ||||
\(125\) | − | 136.000i | − | 1.08800i | ||||||
\(126\) | −75.8566 | − | 75.8566i | −0.602036 | − | 0.602036i | ||||
\(127\) | 52.2215 | − | 52.2215i | 0.411193 | − | 0.411193i | −0.470961 | − | 0.882154i | \(-0.656093\pi\) |
0.882154 | + | 0.470961i | \(0.156093\pi\) | |||||||
\(128\) | −47.6897 | − | 47.6897i | −0.372576 | − | 0.372576i | ||||
\(129\) | 15.4958i | 0.120122i | ||||||||
\(130\) | −46.3198 | + | 46.3198i | −0.356306 | + | 0.356306i | ||||
\(131\) | 25.3821 | + | 25.3821i | 0.193756 | + | 0.193756i | 0.797317 | − | 0.603561i | \(-0.206252\pi\) |
−0.603561 | + | 0.797317i | \(0.706252\pi\) | |||||||
\(132\) | −0.695427 | −0.00526839 | ||||||||
\(133\) | −142.099 | + | 142.099i | −1.06841 | + | 1.06841i | ||||
\(134\) | 28.7014 | + | 28.7014i | 0.214190 | + | 0.214190i | ||||
\(135\) | 32.4596 | − | 32.4596i | 0.240441 | − | 0.240441i | ||||
\(136\) | 78.6068 | 0.577991 | ||||||||
\(137\) | −117.179 | + | 117.179i | −0.855320 | + | 0.855320i | −0.990782 | − | 0.135462i | \(-0.956748\pi\) |
0.135462 | + | 0.990782i | \(0.456748\pi\) | |||||||
\(138\) | 8.12075i | 0.0588460i | ||||||||
\(139\) | 62.2884 | 0.448118 | 0.224059 | − | 0.974576i | \(-0.428069\pi\) | ||||
0.224059 | + | 0.974576i | \(0.428069\pi\) | |||||||
\(140\) | −94.6235 | −0.675882 | ||||||||
\(141\) | 1.95655 | 0.0138762 | ||||||||
\(142\) | −90.8381 | − | 90.8381i | −0.639705 | − | 0.639705i | ||||
\(143\) | 4.09558 | + | 4.09558i | 0.0286404 | + | 0.0286404i | ||||
\(144\) | 9.62718i | 0.0668554i | ||||||||
\(145\) | 29.7869 | − | 117.039i | 0.205427 | − | 0.807164i | ||||
\(146\) | −7.20912 | −0.0493776 | ||||||||
\(147\) | 19.8578 | − | 19.8578i | 0.135087 | − | 0.135087i | ||||
\(148\) | 105.589 | − | 105.589i | 0.713438 | − | 0.713438i | ||||
\(149\) | 140.996i | 0.946284i | 0.880986 | + | 0.473142i | \(0.156880\pi\) | ||||
−0.880986 | + | 0.473142i | \(0.843120\pi\) | |||||||
\(150\) | − | 6.16612i | − | 0.0411075i | ||||||
\(151\) | − | 269.100i | − | 1.78212i | −0.453889 | − | 0.891058i | \(-0.649964\pi\) | ||
0.453889 | − | 0.891058i | \(-0.350036\pi\) | |||||||
\(152\) | 169.308 | 1.11387 | ||||||||
\(153\) | 58.6193 | + | 58.6193i | 0.383133 | + | 0.383133i | ||||
\(154\) | − | 5.90295i | − | 0.0383308i | ||||||
\(155\) | 155.376 | + | 155.376i | 1.00243 | + | 1.00243i | ||||
\(156\) | 12.6949 | − | 12.6949i | 0.0813776 | − | 0.0813776i | ||||
\(157\) | −82.6681 | − | 82.6681i | −0.526549 | − | 0.526549i | 0.392993 | − | 0.919541i | \(-0.371440\pi\) |
−0.919541 | + | 0.392993i | \(0.871440\pi\) | |||||||
\(158\) | 73.3342i | 0.464140i | ||||||||
\(159\) | 39.9002 | − | 39.9002i | 0.250945 | − | 0.250945i | ||||
\(160\) | 91.9065 | + | 91.9065i | 0.574416 | + | 0.574416i | ||||
\(161\) | 97.6995 | 0.606829 | ||||||||
\(162\) | −64.1918 | + | 64.1918i | −0.396246 | + | 0.396246i | ||||
\(163\) | 16.1649 | + | 16.1649i | 0.0991711 | + | 0.0991711i | 0.754952 | − | 0.655780i | \(-0.227660\pi\) |
−0.655780 | + | 0.754952i | \(0.727660\pi\) | |||||||
\(164\) | −53.5060 | + | 53.5060i | −0.326256 | + | 0.326256i | ||||
\(165\) | 1.23485 | 0.00748393 | ||||||||
\(166\) | 125.263 | − | 125.263i | 0.754598 | − | 0.754598i | ||||
\(167\) | − | 134.528i | − | 0.805558i | −0.915297 | − | 0.402779i | \(-0.868044\pi\) | ||
0.915297 | − | 0.402779i | \(-0.131956\pi\) | |||||||
\(168\) | −49.5037 | −0.294665 | ||||||||
\(169\) | 19.4719 | 0.115218 | ||||||||
\(170\) | −51.5903 | −0.303472 | ||||||||
\(171\) | 126.258 | + | 126.258i | 0.738349 | + | 0.738349i | ||||
\(172\) | −41.0499 | − | 41.0499i | −0.238662 | − | 0.238662i | ||||
\(173\) | − | 94.1756i | − | 0.544368i | −0.962245 | − | 0.272184i | \(-0.912254\pi\) | ||
0.962245 | − | 0.272184i | \(-0.0877459\pi\) | |||||||
\(174\) | 5.75984 | − | 22.6316i | 0.0331025 | − | 0.130066i | ||||
\(175\) | −74.1836 | −0.423906 | ||||||||
\(176\) | −0.374580 | + | 0.374580i | −0.00212830 | + | 0.00212830i | ||||
\(177\) | −40.0263 | + | 40.0263i | −0.226137 | + | 0.226137i | ||||
\(178\) | − | 151.266i | − | 0.849806i | ||||||
\(179\) | − | 55.6892i | − | 0.311113i | −0.987827 | − | 0.155557i | \(-0.950283\pi\) | ||
0.987827 | − | 0.155557i | \(-0.0497171\pi\) | |||||||
\(180\) | 84.0748i | 0.467082i | ||||||||
\(181\) | −131.878 | −0.728610 | −0.364305 | − | 0.931280i | \(-0.618693\pi\) | ||||
−0.364305 | + | 0.931280i | \(0.618693\pi\) | |||||||
\(182\) | 107.757 | + | 107.757i | 0.592074 | + | 0.592074i | ||||
\(183\) | 26.0598i | 0.142403i | ||||||||
\(184\) | −58.2034 | − | 58.2034i | −0.316323 | − | 0.316323i | ||||
\(185\) | −187.491 | + | 187.491i | −1.01346 | + | 1.01346i | ||||
\(186\) | 30.0448 | + | 30.0448i | 0.161531 | + | 0.161531i | ||||
\(187\) | 4.56159i | 0.0243935i | ||||||||
\(188\) | −5.18308 | + | 5.18308i | −0.0275696 | + | 0.0275696i | ||||
\(189\) | −75.5133 | − | 75.5133i | −0.399541 | − | 0.399541i | ||||
\(190\) | −111.118 | −0.584833 | ||||||||
\(191\) | 122.543 | − | 122.543i | 0.641588 | − | 0.641588i | −0.309358 | − | 0.950946i | \(-0.600114\pi\) |
0.950946 | + | 0.309358i | \(0.100114\pi\) | |||||||
\(192\) | 19.7520 | + | 19.7520i | 0.102875 | + | 0.102875i | ||||
\(193\) | −175.959 | + | 175.959i | −0.911702 | + | 0.911702i | −0.996406 | − | 0.0847039i | \(-0.973006\pi\) |
0.0847039 | + | 0.996406i | \(0.473006\pi\) | |||||||
\(194\) | −145.507 | −0.750036 | ||||||||
\(195\) | −22.5420 | + | 22.5420i | −0.115600 | + | 0.115600i | ||||
\(196\) | 105.211i | 0.536789i | ||||||||
\(197\) | 42.7699 | 0.217106 | 0.108553 | − | 0.994091i | \(-0.465378\pi\) | ||||
0.108553 | + | 0.994091i | \(0.465378\pi\) | |||||||
\(198\) | −5.24488 | −0.0264893 | ||||||||
\(199\) | −101.732 | −0.511216 | −0.255608 | − | 0.966781i | \(-0.582276\pi\) | ||||
−0.255608 | + | 0.966781i | \(0.582276\pi\) | |||||||
\(200\) | 44.1941 | + | 44.1941i | 0.220970 | + | 0.220970i | ||||
\(201\) | 13.9678 | + | 13.9678i | 0.0694916 | + | 0.0694916i | ||||
\(202\) | 94.8184i | 0.469398i | ||||||||
\(203\) | −272.277 | − | 69.2957i | −1.34126 | − | 0.341358i | ||||
\(204\) | 14.1394 | 0.0693108 | ||||||||
\(205\) | 95.0090 | − | 95.0090i | 0.463459 | − | 0.463459i | ||||
\(206\) | 126.776 | − | 126.776i | 0.615417 | − | 0.615417i | ||||
\(207\) | − | 86.8078i | − | 0.419362i | ||||||
\(208\) | − | 13.6758i | − | 0.0657491i | ||||||
\(209\) | 9.82502i | 0.0470097i | ||||||||
\(210\) | 32.4897 | 0.154713 | ||||||||
\(211\) | 84.0454 | + | 84.0454i | 0.398319 | + | 0.398319i | 0.877640 | − | 0.479321i | \(-0.159117\pi\) |
−0.479321 | + | 0.877640i | \(0.659117\pi\) | |||||||
\(212\) | 211.399i | 0.997166i | ||||||||
\(213\) | −44.2072 | − | 44.2072i | −0.207546 | − | 0.207546i | ||||
\(214\) | −13.6117 | + | 13.6117i | −0.0636058 | + | 0.0636058i | ||||
\(215\) | 72.8910 | + | 72.8910i | 0.339028 | + | 0.339028i | ||||
\(216\) | 89.9725i | 0.416539i | ||||||||
\(217\) | 361.464 | − | 361.464i | 1.66573 | − | 1.66573i | ||||
\(218\) | 35.1304 | + | 35.1304i | 0.161149 | + | 0.161149i | ||||
\(219\) | −3.50839 | −0.0160200 | ||||||||
\(220\) | −3.27123 | + | 3.27123i | −0.0148692 | + | 0.0148692i | ||||
\(221\) | −83.2711 | − | 83.2711i | −0.376792 | − | 0.376792i | ||||
\(222\) | −36.2547 | + | 36.2547i | −0.163310 | + | 0.163310i | ||||
\(223\) | −306.140 | −1.37283 | −0.686413 | − | 0.727212i | \(-0.740816\pi\) | ||||
−0.686413 | + | 0.727212i | \(0.740816\pi\) | |||||||
\(224\) | 213.809 | − | 213.809i | 0.954506 | − | 0.954506i | ||||
\(225\) | 65.9135i | 0.292949i | ||||||||
\(226\) | −36.8739 | −0.163159 | ||||||||
\(227\) | 19.8257 | 0.0873379 | 0.0436689 | − | 0.999046i | \(-0.486095\pi\) | ||||
0.0436689 | + | 0.999046i | \(0.486095\pi\) | |||||||
\(228\) | 30.4543 | 0.133571 | ||||||||
\(229\) | 150.087 | + | 150.087i | 0.655402 | + | 0.655402i | 0.954289 | − | 0.298887i | \(-0.0966153\pi\) |
−0.298887 | + | 0.954289i | \(0.596615\pi\) | |||||||
\(230\) | 38.1994 | + | 38.1994i | 0.166084 | + | 0.166084i | ||||
\(231\) | − | 2.87273i | − | 0.0124360i | ||||||
\(232\) | 120.924 | + | 203.488i | 0.521223 | + | 0.877103i | ||||
\(233\) | 132.431 | 0.568375 | 0.284187 | − | 0.958769i | \(-0.408276\pi\) | ||||
0.284187 | + | 0.958769i | \(0.408276\pi\) | |||||||
\(234\) | 95.7445 | − | 95.7445i | 0.409165 | − | 0.409165i | ||||
\(235\) | 9.20344 | − | 9.20344i | 0.0391636 | − | 0.0391636i | ||||
\(236\) | − | 212.067i | − | 0.898590i | ||||||
\(237\) | 35.6888i | 0.150586i | ||||||||
\(238\) | 120.019i | 0.504280i | ||||||||
\(239\) | 176.690 | 0.739288 | 0.369644 | − | 0.929173i | \(-0.379480\pi\) | ||||
0.369644 | + | 0.929173i | \(0.379480\pi\) | |||||||
\(240\) | −2.06168 | − | 2.06168i | −0.00859034 | − | 0.00859034i | ||||
\(241\) | − | 161.010i | − | 0.668093i | −0.942557 | − | 0.334046i | \(-0.891586\pi\) | ||
0.942557 | − | 0.334046i | \(-0.108414\pi\) | |||||||
\(242\) | 109.856 | + | 109.856i | 0.453951 | + | 0.453951i | ||||
\(243\) | −101.389 | + | 101.389i | −0.417239 | + | 0.417239i | ||||
\(244\) | −69.0348 | − | 69.0348i | −0.282930 | − | 0.282930i | ||||
\(245\) | − | 186.819i | − | 0.762527i | ||||||
\(246\) | 18.3717 | − | 18.3717i | 0.0746817 | − | 0.0746817i | ||||
\(247\) | −179.354 | − | 179.354i | −0.726130 | − | 0.726130i | ||||
\(248\) | −430.677 | −1.73660 | ||||||||
\(249\) | 60.9606 | − | 60.9606i | 0.244822 | − | 0.244822i | ||||
\(250\) | −123.704 | − | 123.704i | −0.494816 | − | 0.494816i | ||||
\(251\) | 136.621 | − | 136.621i | 0.544306 | − | 0.544306i | −0.380482 | − | 0.924788i | \(-0.624242\pi\) |
0.924788 | + | 0.380482i | \(0.124242\pi\) | |||||||
\(252\) | 195.590 | 0.776150 | ||||||||
\(253\) | 3.37757 | − | 3.37757i | 0.0133501 | − | 0.0133501i | ||||
\(254\) | − | 95.0001i | − | 0.374016i | ||||||
\(255\) | −25.1069 | −0.0984585 | ||||||||
\(256\) | −265.241 | −1.03610 | ||||||||
\(257\) | −275.616 | −1.07244 | −0.536218 | − | 0.844079i | \(-0.680148\pi\) | ||||
−0.536218 | + | 0.844079i | \(0.680148\pi\) | |||||||
\(258\) | 14.0948 | + | 14.0948i | 0.0546310 | + | 0.0546310i | ||||
\(259\) | 436.175 | + | 436.175i | 1.68407 | + | 1.68407i | ||||
\(260\) | − | 119.432i | − | 0.459353i | ||||||
\(261\) | −61.5706 | + | 241.923i | −0.235903 | + | 0.926908i | ||||
\(262\) | 46.1744 | 0.176238 | ||||||||
\(263\) | −242.820 | + | 242.820i | −0.923269 | + | 0.923269i | −0.997259 | − | 0.0739900i | \(-0.976427\pi\) |
0.0739900 | + | 0.997259i | \(0.476427\pi\) | |||||||
\(264\) | −1.71140 | + | 1.71140i | −0.00648256 | + | 0.00648256i | ||||
\(265\) | − | 375.375i | − | 1.41651i | ||||||
\(266\) | 258.503i | 0.971816i | ||||||||
\(267\) | − | 73.6148i | − | 0.275711i | ||||||
\(268\) | −74.0042 | −0.276135 | ||||||||
\(269\) | 167.754 | + | 167.754i | 0.623620 | + | 0.623620i | 0.946455 | − | 0.322836i | \(-0.104636\pi\) |
−0.322836 | + | 0.946455i | \(0.604636\pi\) | |||||||
\(270\) | − | 59.0497i | − | 0.218703i | ||||||
\(271\) | 282.361 | + | 282.361i | 1.04192 | + | 1.04192i | 0.999082 | + | 0.0428420i | \(0.0136412\pi\) |
0.0428420 | + | 0.999082i | \(0.486359\pi\) | |||||||
\(272\) | 7.61596 | − | 7.61596i | 0.0279998 | − | 0.0279998i | ||||
\(273\) | 52.4412 | + | 52.4412i | 0.192092 | + | 0.192092i | ||||
\(274\) | 213.169i | 0.777989i | ||||||||
\(275\) | −2.56461 | + | 2.56461i | −0.00932584 | + | 0.00932584i | ||||
\(276\) | −10.4693 | − | 10.4693i | −0.0379324 | − | 0.0379324i | ||||
\(277\) | 30.5322 | 0.110224 | 0.0551122 | − | 0.998480i | \(-0.482448\pi\) | ||||
0.0551122 | + | 0.998480i | \(0.482448\pi\) | |||||||
\(278\) | 56.6568 | − | 56.6568i | 0.203802 | − | 0.203802i | ||||
\(279\) | −321.168 | − | 321.168i | −1.15114 | − | 1.15114i | ||||
\(280\) | −232.862 | + | 232.862i | −0.831649 | + | 0.831649i | ||||
\(281\) | −2.92201 | −0.0103986 | −0.00519931 | − | 0.999986i | \(-0.501655\pi\) | ||||
−0.00519931 | + | 0.999986i | \(0.501655\pi\) | |||||||
\(282\) | 1.77965 | − | 1.77965i | 0.00631082 | − | 0.00631082i | ||||
\(283\) | − | 26.9414i | − | 0.0951993i | −0.998866 | − | 0.0475997i | \(-0.984843\pi\) | ||
0.998866 | − | 0.0475997i | \(-0.0151572\pi\) | |||||||
\(284\) | 234.219 | 0.824713 | ||||||||
\(285\) | −54.0767 | −0.189743 | ||||||||
\(286\) | 7.45058 | 0.0260510 | ||||||||
\(287\) | −221.027 | − | 221.027i | −0.770129 | − | 0.770129i | ||||
\(288\) | −189.974 | − | 189.974i | −0.659631 | − | 0.659631i | ||||
\(289\) | 196.254i | 0.679079i | ||||||||
\(290\) | −79.3633 | − | 133.551i | −0.273666 | − | 0.460521i | ||||
\(291\) | −70.8123 | −0.243341 | ||||||||
\(292\) | 9.29406 | − | 9.29406i | 0.0318290 | − | 0.0318290i | ||||
\(293\) | −255.770 | + | 255.770i | −0.872934 | + | 0.872934i | −0.992791 | − | 0.119857i | \(-0.961756\pi\) |
0.119857 | + | 0.992791i | \(0.461756\pi\) | |||||||
\(294\) | − | 36.1249i | − | 0.122874i | ||||||
\(295\) | 376.561i | 1.27648i | ||||||||
\(296\) | − | 519.693i | − | 1.75572i | ||||||
\(297\) | −5.22115 | −0.0175796 | ||||||||
\(298\) | 128.249 | + | 128.249i | 0.430364 | + | 0.430364i | ||||
\(299\) | 123.314i | 0.412422i | ||||||||
\(300\) | 7.94942 | + | 7.94942i | 0.0264981 | + | 0.0264981i | ||||
\(301\) | 169.572 | − | 169.572i | 0.563362 | − | 0.563362i | ||||
\(302\) | −244.770 | − | 244.770i | −0.810496 | − | 0.810496i | ||||
\(303\) | 46.1443i | 0.152291i | ||||||||
\(304\) | 16.4037 | − | 16.4037i | 0.0539595 | − | 0.0539595i | ||||
\(305\) | 122.583 | + | 122.583i | 0.401912 | + | 0.401912i | ||||
\(306\) | 106.639 | 0.348493 | ||||||||
\(307\) | −9.20371 | + | 9.20371i | −0.0299795 | + | 0.0299795i | −0.721938 | − | 0.691958i | \(-0.756748\pi\) |
0.691958 | + | 0.721938i | \(0.256748\pi\) | |||||||
\(308\) | 7.61013 | + | 7.61013i | 0.0247082 | + | 0.0247082i | ||||
\(309\) | 61.6967 | − | 61.6967i | 0.199666 | − | 0.199666i | ||||
\(310\) | 282.657 | 0.911796 | ||||||||
\(311\) | 94.0902 | − | 94.0902i | 0.302541 | − | 0.302541i | −0.539466 | − | 0.842007i | \(-0.681374\pi\) |
0.842007 | + | 0.539466i | \(0.181374\pi\) | |||||||
\(312\) | − | 62.4825i | − | 0.200264i | ||||||
\(313\) | 133.762 | 0.427356 | 0.213678 | − | 0.976904i | \(-0.431456\pi\) | ||||
0.213678 | + | 0.976904i | \(0.431456\pi\) | |||||||
\(314\) | −150.388 | −0.478942 | ||||||||
\(315\) | −347.303 | −1.10255 | ||||||||
\(316\) | −94.5431 | − | 94.5431i | −0.299187 | − | 0.299187i | ||||
\(317\) | 405.329 | + | 405.329i | 1.27864 | + | 1.27864i | 0.941428 | + | 0.337213i | \(0.109484\pi\) |
0.337213 | + | 0.941428i | \(0.390516\pi\) | |||||||
\(318\) | − | 72.5856i | − | 0.228257i | ||||||
\(319\) | −11.8085 | + | 7.01726i | −0.0370173 | + | 0.0219977i | ||||
\(320\) | 185.824 | 0.580700 | ||||||||
\(321\) | −6.62424 | + | 6.62424i | −0.0206363 | + | 0.0206363i | ||||
\(322\) | 88.8663 | − | 88.8663i | 0.275982 | − | 0.275982i | ||||
\(323\) | − | 199.762i | − | 0.618458i | ||||||
\(324\) | − | 165.513i | − | 0.510844i | ||||||
\(325\) | − | 93.6329i | − | 0.288101i | ||||||
\(326\) | 29.4068 | 0.0902049 | ||||||||
\(327\) | 17.0965 | + | 17.0965i | 0.0522830 | + | 0.0522830i | ||||
\(328\) | 263.349i | 0.802893i | ||||||||
\(329\) | −21.4107 | − | 21.4107i | −0.0650781 | − | 0.0650781i | ||||
\(330\) | 1.12320 | − | 1.12320i | 0.00340365 | − | 0.00340365i | ||||
\(331\) | 185.108 | + | 185.108i | 0.559238 | + | 0.559238i | 0.929090 | − | 0.369853i | \(-0.120592\pi\) |
−0.369853 | + | 0.929090i | \(0.620592\pi\) | |||||||
\(332\) | 322.981i | 0.972834i | ||||||||
\(333\) | 387.550 | − | 387.550i | 1.16381 | − | 1.16381i | ||||
\(334\) | −122.365 | − | 122.365i | −0.366363 | − | 0.366363i | ||||
\(335\) | 131.407 | 0.392260 | ||||||||
\(336\) | −4.79626 | + | 4.79626i | −0.0142746 | + | 0.0142746i | ||||
\(337\) | −71.8022 | − | 71.8022i | −0.213063 | − | 0.213063i | 0.592504 | − | 0.805567i | \(-0.298139\pi\) |
−0.805567 | + | 0.592504i | \(0.798139\pi\) | |||||||
\(338\) | 17.7114 | − | 17.7114i | 0.0524006 | − | 0.0524006i | ||||
\(339\) | −17.9450 | −0.0529351 | ||||||||
\(340\) | 66.5107 | − | 66.5107i | 0.195620 | − | 0.195620i | ||||
\(341\) | − | 24.9924i | − | 0.0732915i | ||||||
\(342\) | 229.685 | 0.671593 | ||||||||
\(343\) | 40.1069 | 0.116930 | ||||||||
\(344\) | −202.041 | −0.587330 | ||||||||
\(345\) | 18.5901 | + | 18.5901i | 0.0538843 | + | 0.0538843i | ||||
\(346\) | −85.6610 | − | 85.6610i | −0.247575 | − | 0.247575i | ||||
\(347\) | − | 181.565i | − | 0.523241i | −0.965171 | − | 0.261621i | \(-0.915743\pi\) | ||
0.965171 | − | 0.261621i | \(-0.0842569\pi\) | |||||||
\(348\) | 21.7512 | + | 36.6024i | 0.0625033 | + | 0.105179i | ||||
\(349\) | 205.399 | 0.588536 | 0.294268 | − | 0.955723i | \(-0.404924\pi\) | ||||
0.294268 | + | 0.955723i | \(0.404924\pi\) | |||||||
\(350\) | −67.4765 | + | 67.4765i | −0.192790 | + | 0.192790i | ||||
\(351\) | 95.3112 | − | 95.3112i | 0.271542 | − | 0.271542i | ||||
\(352\) | − | 14.7832i | − | 0.0419978i | ||||||
\(353\) | − | 150.904i | − | 0.427489i | −0.976890 | − | 0.213745i | \(-0.931434\pi\) | ||
0.976890 | − | 0.213745i | \(-0.0685660\pi\) | |||||||
\(354\) | 72.8149i | 0.205692i | ||||||||
\(355\) | −415.895 | −1.17153 | ||||||||
\(356\) | 195.013 | + | 195.013i | 0.547789 | + | 0.547789i | ||||
\(357\) | 58.4082i | 0.163608i | ||||||||
\(358\) | −50.6543 | − | 50.6543i | −0.141492 | − | 0.141492i | ||||
\(359\) | −366.501 | + | 366.501i | −1.02089 | + | 1.02089i | −0.0211170 | + | 0.999777i | \(0.506722\pi\) |
−0.999777 | + | 0.0211170i | \(0.993278\pi\) | |||||||
\(360\) | 206.902 | + | 206.902i | 0.574728 | + | 0.574728i | ||||
\(361\) | − | 69.2592i | − | 0.191854i | ||||||
\(362\) | −119.955 | + | 119.955i | −0.331368 | + | 0.331368i | ||||
\(363\) | 53.4625 | + | 53.4625i | 0.147280 | + | 0.147280i | ||||
\(364\) | −277.843 | −0.763306 | ||||||||
\(365\) | −16.5032 | + | 16.5032i | −0.0452142 | + | 0.0452142i | ||||
\(366\) | 23.7037 | + | 23.7037i | 0.0647641 | + | 0.0647641i | ||||
\(367\) | −84.3213 | + | 84.3213i | −0.229758 | + | 0.229758i | −0.812592 | − | 0.582833i | \(-0.801944\pi\) |
0.582833 | + | 0.812592i | \(0.301944\pi\) | |||||||
\(368\) | −11.2783 | −0.0306475 | ||||||||
\(369\) | −196.387 | + | 196.387i | −0.532213 | + | 0.532213i | ||||
\(370\) | 341.079i | 0.921835i | ||||||||
\(371\) | −873.265 | −2.35381 | ||||||||
\(372\) | −77.4680 | −0.208247 | ||||||||
\(373\) | 91.4080 | 0.245062 | 0.122531 | − | 0.992465i | \(-0.460899\pi\) | ||||
0.122531 | + | 0.992465i | \(0.460899\pi\) | |||||||
\(374\) | 4.14917 | + | 4.14917i | 0.0110940 | + | 0.0110940i | ||||
\(375\) | −60.2017 | − | 60.2017i | −0.160538 | − | 0.160538i | ||||
\(376\) | 25.5104i | 0.0678468i | ||||||||
\(377\) | 87.4635 | − | 343.662i | 0.231999 | − | 0.911569i | ||||
\(378\) | −137.372 | −0.363418 | ||||||||
\(379\) | 178.021 | − | 178.021i | 0.469713 | − | 0.469713i | −0.432108 | − | 0.901822i | \(-0.642230\pi\) |
0.901822 | + | 0.432108i | \(0.142230\pi\) | |||||||
\(380\) | 143.255 | − | 143.255i | 0.376986 | − | 0.376986i | ||||
\(381\) | − | 46.2327i | − | 0.121346i | ||||||
\(382\) | − | 222.928i | − | 0.583581i | ||||||
\(383\) | − | 142.083i | − | 0.370973i | −0.982647 | − | 0.185486i | \(-0.940614\pi\) | ||
0.982647 | − | 0.185486i | \(-0.0593860\pi\) | |||||||
\(384\) | −42.2206 | −0.109950 | ||||||||
\(385\) | −13.5131 | − | 13.5131i | −0.0350989 | − | 0.0350989i | ||||
\(386\) | 320.100i | 0.829274i | ||||||||
\(387\) | −150.668 | − | 150.668i | −0.389323 | − | 0.389323i | ||||
\(388\) | 187.589 | − | 187.589i | 0.483476 | − | 0.483476i | ||||
\(389\) | −339.694 | − | 339.694i | −0.873250 | − | 0.873250i | 0.119575 | − | 0.992825i | \(-0.461847\pi\) |
−0.992825 | + | 0.119575i | \(0.961847\pi\) | |||||||
\(390\) | 41.0078i | 0.105148i | ||||||||
\(391\) | −68.6727 | + | 68.6727i | −0.175634 | + | 0.175634i | ||||
\(392\) | 258.916 | + | 258.916i | 0.660499 | + | 0.660499i | ||||
\(393\) | 22.4712 | 0.0571787 | ||||||||
\(394\) | 38.9030 | − | 38.9030i | 0.0987386 | − | 0.0987386i | ||||
\(395\) | 167.877 | + | 167.877i | 0.425006 | + | 0.425006i | ||||
\(396\) | 6.76175 | − | 6.76175i | 0.0170751 | − | 0.0170751i | ||||
\(397\) | −657.787 | −1.65689 | −0.828447 | − | 0.560068i | \(-0.810775\pi\) | ||||
−0.828447 | + | 0.560068i | \(0.810775\pi\) | |||||||
\(398\) | −92.5342 | + | 92.5342i | −0.232498 | + | 0.232498i | ||||
\(399\) | 125.803i | 0.315296i | ||||||||
\(400\) | 8.56364 | 0.0214091 | ||||||||
\(401\) | 343.872 | 0.857537 | 0.428768 | − | 0.903414i | \(-0.358948\pi\) | ||||
0.428768 | + | 0.903414i | \(0.358948\pi\) | |||||||
\(402\) | 25.4099 | 0.0632088 | ||||||||
\(403\) | 456.232 | + | 456.232i | 1.13209 | + | 1.13209i | ||||
\(404\) | −122.241 | − | 122.241i | −0.302576 | − | 0.302576i | ||||
\(405\) | 293.897i | 0.725672i | ||||||||
\(406\) | −310.690 | + | 184.629i | −0.765247 | + | 0.454751i | ||||
\(407\) | 30.1581 | 0.0740984 | ||||||||
\(408\) | 34.7961 | − | 34.7961i | 0.0852844 | − | 0.0852844i | ||||
\(409\) | 219.662 | − | 219.662i | 0.537072 | − | 0.537072i | −0.385596 | − | 0.922668i | \(-0.626004\pi\) |
0.922668 | + | 0.385596i | \(0.126004\pi\) | |||||||
\(410\) | − | 172.838i | − | 0.421557i | ||||||
\(411\) | 103.741i | 0.252411i | ||||||||
\(412\) | 326.881i | 0.793401i | ||||||||
\(413\) | 876.024 | 2.12112 | ||||||||
\(414\) | −78.9594 | − | 78.9594i | −0.190723 | − | 0.190723i | ||||
\(415\) | − | 573.508i | − | 1.38195i | ||||||
\(416\) | 269.866 | + | 269.866i | 0.648715 | + | 0.648715i | ||||
\(417\) | 27.5726 | − | 27.5726i | 0.0661213 | − | 0.0661213i | ||||
\(418\) | 8.93673 | + | 8.93673i | 0.0213797 | + | 0.0213797i | ||||
\(419\) | − | 512.017i | − | 1.22200i | −0.791631 | − | 0.610999i | \(-0.790768\pi\) | ||
0.791631 | − | 0.610999i | \(-0.209232\pi\) | |||||||
\(420\) | −41.8860 | + | 41.8860i | −0.0997286 | + | 0.0997286i | ||||
\(421\) | −426.710 | − | 426.710i | −1.01356 | − | 1.01356i | −0.999907 | − | 0.0136572i | \(-0.995653\pi\) |
−0.0136572 | − | 0.999907i | \(-0.504347\pi\) | |||||||
\(422\) | 152.893 | 0.362307 | ||||||||
\(423\) | −19.0238 | + | 19.0238i | −0.0449735 | + | 0.0449735i | ||||
\(424\) | 520.238 | + | 520.238i | 1.22698 | + | 1.22698i | ||||
\(425\) | 52.1435 | − | 52.1435i | 0.122691 | − | 0.122691i | ||||
\(426\) | −80.4208 | −0.188781 | ||||||||
\(427\) | 285.175 | − | 285.175i | 0.667857 | − | 0.667857i | ||||
\(428\) | − | 35.0965i | − | 0.0820012i | ||||||
\(429\) | 3.62589 | 0.00845197 | ||||||||
\(430\) | 132.602 | 0.308376 | ||||||||
\(431\) | 596.638 | 1.38431 | 0.692156 | − | 0.721748i | \(-0.256661\pi\) | ||||
0.692156 | + | 0.721748i | \(0.256661\pi\) | |||||||
\(432\) | 8.71714 | + | 8.71714i | 0.0201786 | + | 0.0201786i | ||||
\(433\) | −41.8737 | − | 41.8737i | −0.0967059 | − | 0.0967059i | 0.657099 | − | 0.753805i | \(-0.271783\pi\) |
−0.753805 | + | 0.657099i | \(0.771783\pi\) | |||||||
\(434\) | − | 657.567i | − | 1.51513i | ||||||
\(435\) | −38.6229 | − | 64.9938i | −0.0887882 | − | 0.149411i | ||||
\(436\) | −90.5808 | −0.207754 | ||||||||
\(437\) | −147.911 | + | 147.911i | −0.338470 | + | 0.338470i | ||||
\(438\) | −3.19119 | + | 3.19119i | −0.00728582 | + | 0.00728582i | ||||
\(439\) | 344.567i | 0.784891i | 0.919775 | + | 0.392445i | \(0.128371\pi\) | ||||
−0.919775 | + | 0.392445i | \(0.871629\pi\) | |||||||
\(440\) | 16.1005i | 0.0365922i | ||||||||
\(441\) | 386.161i | 0.875649i | ||||||||
\(442\) | −151.485 | −0.342726 | ||||||||
\(443\) | −124.564 | − | 124.564i | −0.281184 | − | 0.281184i | 0.552397 | − | 0.833581i | \(-0.313713\pi\) |
−0.833581 | + | 0.552397i | \(0.813713\pi\) | |||||||
\(444\) | − | 93.4798i | − | 0.210540i | ||||||
\(445\) | −346.278 | − | 346.278i | −0.778154 | − | 0.778154i | ||||
\(446\) | −278.462 | + | 278.462i | −0.624353 | + | 0.624353i | ||||
\(447\) | 62.4134 | + | 62.4134i | 0.139627 | + | 0.139627i | ||||
\(448\) | − | 432.297i | − | 0.964949i | ||||||
\(449\) | −562.904 | + | 562.904i | −1.25368 | + | 1.25368i | −0.299628 | + | 0.954056i | \(0.596863\pi\) |
−0.954056 | + | 0.299628i | \(0.903137\pi\) | |||||||
\(450\) | 59.9542 | + | 59.9542i | 0.133232 | + | 0.133232i | ||||
\(451\) | −15.2823 | −0.0338853 | ||||||||
\(452\) | 47.5381 | − | 47.5381i | 0.105173 | − | 0.105173i | ||||
\(453\) | −119.120 | − | 119.120i | −0.262957 | − | 0.262957i | ||||
\(454\) | 18.0332 | − | 18.0332i | 0.0397208 | − | 0.0397208i | ||||
\(455\) | 493.358 | 1.08430 | ||||||||
\(456\) | 74.9458 | − | 74.9458i | 0.164355 | − | 0.164355i | ||||
\(457\) | − | 377.138i | − | 0.825247i | −0.910902 | − | 0.412623i | \(-0.864613\pi\) | ||
0.910902 | − | 0.412623i | \(-0.135387\pi\) | |||||||
\(458\) | 273.035 | 0.596146 | ||||||||
\(459\) | 106.156 | 0.231277 | ||||||||
\(460\) | −98.4940 | −0.214117 | ||||||||
\(461\) | −40.0863 | − | 40.0863i | −0.0869552 | − | 0.0869552i | 0.662291 | − | 0.749246i | \(-0.269584\pi\) |
−0.749246 | + | 0.662291i | \(0.769584\pi\) | |||||||
\(462\) | −2.61300 | − | 2.61300i | −0.00565584 | − | 0.00565584i | ||||
\(463\) | 410.934i | 0.887546i | 0.896139 | + | 0.443773i | \(0.146360\pi\) | ||||
−0.896139 | + | 0.443773i | \(0.853640\pi\) | |||||||
\(464\) | 31.4312 | + | 7.99939i | 0.0677397 | + | 0.0172401i | ||||
\(465\) | 137.558 | 0.295823 | ||||||||
\(466\) | 120.458 | − | 120.458i | 0.258494 | − | 0.258494i | ||||
\(467\) | −427.051 | + | 427.051i | −0.914455 | + | 0.914455i | −0.996619 | − | 0.0821634i | \(-0.973817\pi\) |
0.0821634 | + | 0.996619i | \(0.473817\pi\) | |||||||
\(468\) | 246.869i | 0.527498i | ||||||||
\(469\) | − | 305.703i | − | 0.651818i | ||||||
\(470\) | − | 16.7427i | − | 0.0356227i | ||||||
\(471\) | −73.1877 | −0.155388 | ||||||||
\(472\) | −521.882 | − | 521.882i | −1.10568 | − | 1.10568i | ||||
\(473\) | − | 11.7246i | − | 0.0247877i | ||||||
\(474\) | 32.4621 | + | 32.4621i | 0.0684854 | + | 0.0684854i | ||||
\(475\) | 112.310 | − | 112.310i | 0.236441 | − | 0.236441i | ||||
\(476\) | −154.729 | − | 154.729i | −0.325061 | − | 0.325061i | ||||
\(477\) | 775.913i | 1.62665i | ||||||||
\(478\) | 160.715 | − | 160.715i | 0.336224 | − | 0.336224i | ||||
\(479\) | 223.602 | + | 223.602i | 0.466811 | + | 0.466811i | 0.900880 | − | 0.434069i | \(-0.142923\pi\) |
−0.434069 | + | 0.900880i | \(0.642923\pi\) | |||||||
\(480\) | 81.3666 | 0.169514 | ||||||||
\(481\) | −550.530 | + | 550.530i | −1.14455 | + | 1.14455i | ||||
\(482\) | −146.453 | − | 146.453i | −0.303845 | − | 0.303845i | ||||
\(483\) | 43.2476 | − | 43.2476i | 0.0895396 | − | 0.0895396i | ||||
\(484\) | −283.255 | −0.585237 | ||||||||
\(485\) | −333.096 | + | 333.096i | −0.686795 | + | 0.686795i | ||||
\(486\) | 184.445i | 0.379516i | ||||||||
\(487\) | 397.009 | 0.815214 | 0.407607 | − | 0.913157i | \(-0.366363\pi\) | ||||
0.407607 | + | 0.913157i | \(0.366363\pi\) | |||||||
\(488\) | −339.780 | −0.696270 | ||||||||
\(489\) | 14.3111 | 0.0292661 | ||||||||
\(490\) | −169.929 | − | 169.929i | −0.346793 | − | 0.346793i | ||||
\(491\) | −441.208 | − | 441.208i | −0.898591 | − | 0.898591i | 0.0967208 | − | 0.995312i | \(-0.469165\pi\) |
−0.995312 | + | 0.0967208i | \(0.969165\pi\) | |||||||
\(492\) | 47.3699i | 0.0962803i | ||||||||
\(493\) | 240.090 | − | 142.675i | 0.486999 | − | 0.289401i | ||||
\(494\) | −326.277 | −0.660480 | ||||||||
\(495\) | −12.0066 | + | 12.0066i | −0.0242558 | + | 0.0242558i | ||||
\(496\) | −41.7269 | + | 41.7269i | −0.0841268 | + | 0.0841268i | ||||
\(497\) | 967.529i | 1.94674i | ||||||||
\(498\) | − | 110.898i | − | 0.222687i | ||||||
\(499\) | − | 94.9470i | − | 0.190275i | −0.995464 | − | 0.0951373i | \(-0.969671\pi\) | ||
0.995464 | − | 0.0951373i | \(-0.0303290\pi\) | |||||||
\(500\) | 318.960 | 0.637920 | ||||||||
\(501\) | −59.5502 | − | 59.5502i | −0.118863 | − | 0.118863i | ||||
\(502\) | − | 248.537i | − | 0.495094i | ||||||
\(503\) | −35.4061 | − | 35.4061i | −0.0703899 | − | 0.0703899i | 0.671035 | − | 0.741425i | \(-0.265850\pi\) |
−0.741425 | + | 0.671035i | \(0.765850\pi\) | |||||||
\(504\) | 481.333 | − | 481.333i | 0.955025 | − | 0.955025i | ||||
\(505\) | 217.059 | + | 217.059i | 0.429820 | + | 0.429820i | ||||
\(506\) | − | 6.14440i | − | 0.0121431i | ||||||
\(507\) | 8.61942 | − | 8.61942i | 0.0170008 | − | 0.0170008i | ||||
\(508\) | 122.475 | + | 122.475i | 0.241092 | + | 0.241092i | ||||
\(509\) | 215.741 | 0.423852 | 0.211926 | − | 0.977286i | \(-0.432026\pi\) | ||||
0.211926 | + | 0.977286i | \(0.432026\pi\) | |||||||
\(510\) | −22.8370 | + | 22.8370i | −0.0447783 | + | 0.0447783i | ||||
\(511\) | 38.3927 | + | 38.3927i | 0.0751324 | + | 0.0751324i | ||||
\(512\) | −50.5014 | + | 50.5014i | −0.0986355 | + | 0.0986355i | ||||
\(513\) | 228.646 | 0.445703 | ||||||||
\(514\) | −250.697 | + | 250.697i | −0.487738 | + | 0.487738i | ||||
\(515\) | − | 580.433i | − | 1.12705i | ||||||
\(516\) | −36.3422 | −0.0704307 | ||||||||
\(517\) | −1.48038 | −0.00286341 | ||||||||
\(518\) | 793.479 | 1.53181 | ||||||||
\(519\) | −41.6878 | − | 41.6878i | −0.0803232 | − | 0.0803232i | ||||
\(520\) | −293.913 | − | 293.913i | −0.565217 | − | 0.565217i | ||||
\(521\) | 279.099i | 0.535700i | 0.963461 | + | 0.267850i | \(0.0863131\pi\) | ||||
−0.963461 | + | 0.267850i | \(0.913687\pi\) | |||||||
\(522\) | 164.046 | + | 276.054i | 0.314265 | + | 0.528839i | ||||
\(523\) | −135.622 | −0.259316 | −0.129658 | − | 0.991559i | \(-0.541388\pi\) | ||||
−0.129658 | + | 0.991559i | \(0.541388\pi\) | |||||||
\(524\) | −59.5285 | + | 59.5285i | −0.113604 | + | 0.113604i | ||||
\(525\) | −32.8381 | + | 32.8381i | −0.0625488 | + | 0.0625488i | ||||
\(526\) | 441.732i | 0.839795i | ||||||||
\(527\) | 508.145i | 0.964221i | ||||||||
\(528\) | 0.331623i | 0.000628074i | ||||||||
\(529\) | −427.304 | −0.807758 | ||||||||
\(530\) | −341.437 | − | 341.437i | −0.644221 | − | 0.644221i | ||||
\(531\) | − | 778.365i | − | 1.46585i | ||||||
\(532\) | −333.264 | − | 333.264i | −0.626437 | − | 0.626437i | ||||
\(533\) | 278.975 | − | 278.975i | 0.523406 | − | 0.523406i | ||||
\(534\) | −66.9592 | − | 66.9592i | −0.125392 | − | 0.125392i | ||||
\(535\) | 62.3198i | 0.116486i | ||||||||
\(536\) | −182.119 | + | 182.119i | −0.339774 | + | 0.339774i | ||||
\(537\) | −24.6514 | − | 24.6514i | −0.0459057 | − | 0.0459057i | ||||
\(538\) | 305.174 | 0.567237 | ||||||||
\(539\) | −15.0250 | + | 15.0250i | −0.0278757 | + | 0.0278757i | ||||
\(540\) | 76.1274 | + | 76.1274i | 0.140977 | + | 0.140977i | ||||
\(541\) | 381.445 | − | 381.445i | 0.705074 | − | 0.705074i | −0.260421 | − | 0.965495i | \(-0.583861\pi\) |
0.965495 | + | 0.260421i | \(0.0838614\pi\) | |||||||
\(542\) | 513.665 | 0.947722 | ||||||||
\(543\) | −58.3773 | + | 58.3773i | −0.107509 | + | 0.107509i | ||||
\(544\) | 300.572i | 0.552523i | ||||||||
\(545\) | 160.842 | 0.295122 | ||||||||
\(546\) | 95.3997 | 0.174725 | ||||||||
\(547\) | 104.335 | 0.190739 | 0.0953697 | − | 0.995442i | \(-0.469597\pi\) | ||||
0.0953697 | + | 0.995442i | \(0.469597\pi\) | |||||||
\(548\) | −274.819 | − | 274.819i | −0.501495 | − | 0.501495i | ||||
\(549\) | −253.383 | − | 253.383i | −0.461536 | − | 0.461536i | ||||
\(550\) | 4.66547i | 0.00848268i | ||||||||
\(551\) | 517.121 | − | 307.301i | 0.938513 | − | 0.557716i | ||||
\(552\) | −51.5286 | −0.0933489 | ||||||||
\(553\) | 390.546 | − | 390.546i | 0.706232 | − | 0.706232i | ||||
\(554\) | 27.7717 | − | 27.7717i | 0.0501295 | − | 0.0501295i | ||||
\(555\) | 165.989i | 0.299080i | ||||||||
\(556\) | 146.085i | 0.262743i | ||||||||
\(557\) | 132.616i | 0.238090i | 0.992889 | + | 0.119045i | \(0.0379833\pi\) | ||||
−0.992889 | + | 0.119045i | \(0.962017\pi\) | |||||||
\(558\) | −584.261 | −1.04706 | ||||||||
\(559\) | 214.030 | + | 214.030i | 0.382880 | + | 0.382880i | ||||
\(560\) | 45.1224i | 0.0805758i | ||||||||
\(561\) | 2.01923 | + | 2.01923i | 0.00359935 | + | 0.00359935i | ||||
\(562\) | −2.65783 | + | 2.65783i | −0.00472923 | + | 0.00472923i | ||||
\(563\) | 253.583 | + | 253.583i | 0.450413 | + | 0.450413i | 0.895492 | − | 0.445078i | \(-0.146824\pi\) |
−0.445078 | + | 0.895492i | \(0.646824\pi\) | |||||||
\(564\) | 4.58868i | 0.00813596i | ||||||||
\(565\) | −84.4120 | + | 84.4120i | −0.149402 | + | 0.149402i | ||||
\(566\) | −24.5056 | − | 24.5056i | −0.0432961 | − | 0.0432961i | ||||
\(567\) | 683.716 | 1.20585 | ||||||||
\(568\) | 576.395 | − | 576.395i | 1.01478 | − | 1.01478i | ||||
\(569\) | 216.864 | + | 216.864i | 0.381133 | + | 0.381133i | 0.871510 | − | 0.490377i | \(-0.163141\pi\) |
−0.490377 | + | 0.871510i | \(0.663141\pi\) | |||||||
\(570\) | −49.1876 | + | 49.1876i | −0.0862940 | + | 0.0862940i | ||||
\(571\) | 398.256 | 0.697472 | 0.348736 | − | 0.937221i | \(-0.386611\pi\) | ||||
0.348736 | + | 0.937221i | \(0.386611\pi\) | |||||||
\(572\) | −9.60534 | + | 9.60534i | −0.0167926 | + | 0.0167926i | ||||
\(573\) | − | 108.490i | − | 0.189337i | ||||||
\(574\) | −402.087 | −0.700500 | ||||||||
\(575\) | −77.2180 | −0.134292 | ||||||||
\(576\) | −384.104 | −0.666848 | ||||||||
\(577\) | −504.599 | − | 504.599i | −0.874521 | − | 0.874521i | 0.118440 | − | 0.992961i | \(-0.462211\pi\) |
−0.992961 | + | 0.118440i | \(0.962211\pi\) | |||||||
\(578\) | 178.510 | + | 178.510i | 0.308841 | + | 0.308841i | ||||
\(579\) | 155.780i | 0.269049i | ||||||||
\(580\) | 274.491 | + | 69.8592i | 0.473260 | + | 0.120447i | ||||
\(581\) | −1334.20 | −2.29638 | ||||||||
\(582\) | −64.4101 | + | 64.4101i | −0.110670 | + | 0.110670i | ||||
\(583\) | −30.1897 | + | 30.1897i | −0.0517834 | + | 0.0517834i | ||||
\(584\) | − | 45.7440i | − | 0.0783288i | ||||||
\(585\) | − | 438.358i | − | 0.749330i | ||||||
\(586\) | 465.290i | 0.794011i | ||||||||
\(587\) | 110.932 | 0.188982 | 0.0944911 | − | 0.995526i | \(-0.469878\pi\) | ||||
0.0944911 | + | 0.995526i | \(0.469878\pi\) | |||||||
\(588\) | 46.5725 | + | 46.5725i | 0.0792049 | + | 0.0792049i | ||||
\(589\) | 1094.47i | 1.85819i | ||||||||
\(590\) | 342.516 | + | 342.516i | 0.580535 | + | 0.580535i | ||||
\(591\) | 18.9325 | − | 18.9325i | 0.0320347 | − | 0.0320347i | ||||
\(592\) | −50.3514 | − | 50.3514i | −0.0850530 | − | 0.0850530i | ||||
\(593\) | − | 988.969i | − | 1.66774i | −0.551962 | − | 0.833870i | \(-0.686121\pi\) | ||
0.551962 | − | 0.833870i | \(-0.313879\pi\) | |||||||
\(594\) | −4.74910 | + | 4.74910i | −0.00799511 | + | 0.00799511i | ||||
\(595\) | 274.748 | + | 274.748i | 0.461761 | + | 0.461761i | ||||
\(596\) | −330.678 | −0.554829 | ||||||||
\(597\) | −45.0326 | + | 45.0326i | −0.0754315 | + | 0.0754315i | ||||
\(598\) | 112.165 | + | 112.165i | 0.187567 | + | 0.187567i | ||||
\(599\) | 262.125 | − | 262.125i | 0.437604 | − | 0.437604i | −0.453601 | − | 0.891205i | \(-0.649861\pi\) |
0.891205 | + | 0.453601i | \(0.149861\pi\) | |||||||
\(600\) | 39.1259 | 0.0652098 | ||||||||
\(601\) | −496.848 | + | 496.848i | −0.826702 | + | 0.826702i | −0.987059 | − | 0.160357i | \(-0.948735\pi\) |
0.160357 | + | 0.987059i | \(0.448735\pi\) | |||||||
\(602\) | − | 308.482i | − | 0.512428i | ||||||
\(603\) | −271.623 | −0.450452 | ||||||||
\(604\) | 631.119 | 1.04490 | ||||||||
\(605\) | 502.967 | 0.831351 | ||||||||
\(606\) | 41.9723 | + | 41.9723i | 0.0692612 | + | 0.0692612i | ||||
\(607\) | −466.144 | − | 466.144i | −0.767947 | − | 0.767947i | 0.209798 | − | 0.977745i | \(-0.432719\pi\) |
−0.977745 | + | 0.209798i | \(0.932719\pi\) | |||||||
\(608\) | 647.390i | 1.06479i | ||||||||
\(609\) | −151.200 | + | 89.8515i | −0.248276 | + | 0.147539i | ||||
\(610\) | 223.000 | 0.365574 | ||||||||
\(611\) | 27.0241 | − | 27.0241i | 0.0442293 | − | 0.0442293i | ||||
\(612\) | −137.480 | + | 137.480i | −0.224640 | + | 0.224640i | ||||
\(613\) | 581.681i | 0.948908i | 0.880280 | + | 0.474454i | \(0.157355\pi\) | ||||
−0.880280 | + | 0.474454i | \(0.842645\pi\) | |||||||
\(614\) | 16.7432i | 0.0272690i | ||||||||
\(615\) | − | 84.1133i | − | 0.136770i | ||||||
\(616\) | 37.4560 | 0.0608052 | ||||||||
\(617\) | −546.898 | − | 546.898i | −0.886383 | − | 0.886383i | 0.107791 | − | 0.994174i | \(-0.465622\pi\) |
−0.994174 | + | 0.107791i | \(0.965622\pi\) | |||||||
\(618\) | − | 112.237i | − | 0.181614i | ||||||
\(619\) | −650.477 | − | 650.477i | −1.05085 | − | 1.05085i | −0.998636 | − | 0.0522157i | \(-0.983372\pi\) |
−0.0522157 | − | 0.998636i | \(-0.516628\pi\) | |||||||
\(620\) | −364.404 | + | 364.404i | −0.587748 | + | 0.587748i | ||||
\(621\) | −78.6021 | − | 78.6021i | −0.126573 | − | 0.126573i | ||||
\(622\) | − | 171.167i | − | 0.275188i | ||||||
\(623\) | −805.575 | + | 805.575i | −1.29306 | + | 1.29306i | ||||
\(624\) | −6.05373 | − | 6.05373i | −0.00970149 | − | 0.00970149i | ||||
\(625\) | −374.939 | −0.599903 | ||||||||
\(626\) | 121.669 | − | 121.669i | 0.194359 | − | 0.194359i | ||||
\(627\) | 4.34914 | + | 4.34914i | 0.00693643 | + | 0.00693643i | ||||
\(628\) | 193.881 | − | 193.881i | 0.308728 | − | 0.308728i | ||||
\(629\) | −613.173 | −0.974837 | ||||||||
\(630\) | −315.903 | + | 315.903i | −0.501433 | + | 0.501433i | ||||
\(631\) | 1020.55i | 1.61735i | 0.588253 | + | 0.808677i | \(0.299816\pi\) | ||||
−0.588253 | + | 0.808677i | \(0.700184\pi\) | |||||||
\(632\) | −465.327 | −0.736277 | ||||||||
\(633\) | 74.4070 | 0.117547 | ||||||||
\(634\) | 737.366 | 1.16304 | ||||||||
\(635\) | −217.475 | − | 217.475i | −0.342480 | − | 0.342480i | ||||
\(636\) | 93.5780 | + | 93.5780i | 0.147135 | + | 0.147135i | ||||
\(637\) | − | 548.558i | − | 0.861159i | ||||||
\(638\) | −4.35807 | + | 17.1237i | −0.00683083 | + | 0.0268397i | ||||
\(639\) | 859.668 | 1.34533 | ||||||||
\(640\) | −198.603 | + | 198.603i | −0.310316 | + | 0.310316i | ||||
\(641\) | 65.0163 | − | 65.0163i | 0.101430 | − | 0.101430i | −0.654571 | − | 0.756001i | \(-0.727151\pi\) |
0.756001 | + | 0.654571i | \(0.227151\pi\) | |||||||
\(642\) | 12.0507i | 0.0187705i | ||||||||
\(643\) | − | 590.198i | − | 0.917882i | −0.888467 | − | 0.458941i | \(-0.848229\pi\) | ||
0.888467 | − | 0.458941i | \(-0.151771\pi\) | |||||||
\(644\) | 229.134i | 0.355799i | ||||||||
\(645\) | 64.5318 | 0.100049 | ||||||||
\(646\) | −181.701 | − | 181.701i | −0.281271 | − | 0.281271i | ||||
\(647\) | − | 96.4448i | − | 0.149065i | −0.997219 | − | 0.0745323i | \(-0.976254\pi\) | ||
0.997219 | − | 0.0745323i | \(-0.0237464\pi\) | |||||||
\(648\) | −407.316 | − | 407.316i | −0.628575 | − | 0.628575i | ||||
\(649\) | 30.2851 | − | 30.2851i | 0.0466642 | − | 0.0466642i | ||||
\(650\) | −85.1674 | − | 85.1674i | −0.131027 | − | 0.131027i | ||||
\(651\) | − | 320.011i | − | 0.491569i | ||||||
\(652\) | −37.9115 | + | 37.9115i | −0.0581465 | + | 0.0581465i | ||||
\(653\) | −185.978 | − | 185.978i | −0.284806 | − | 0.284806i | 0.550216 | − | 0.835022i | \(-0.314545\pi\) |
−0.835022 | + | 0.550216i | \(0.814545\pi\) | |||||||
\(654\) | 31.1016 | 0.0475560 | ||||||||
\(655\) | 105.703 | − | 105.703i | 0.161379 | − | 0.161379i | ||||
\(656\) | 25.5150 | + | 25.5150i | 0.0388949 | + | 0.0388949i | ||||
\(657\) | 34.1126 | − | 34.1126i | 0.0519218 | − | 0.0519218i | ||||
\(658\) | −38.9498 | −0.0591943 | ||||||||
\(659\) | 811.110 | − | 811.110i | 1.23082 | − | 1.23082i | 0.267170 | − | 0.963649i | \(-0.413911\pi\) |
0.963649 | − | 0.267170i | \(-0.0860886\pi\) | |||||||
\(660\) | 2.89609i | 0.00438801i | ||||||||
\(661\) | 442.227 | 0.669027 | 0.334513 | − | 0.942391i | \(-0.391428\pi\) | ||||
0.334513 | + | 0.942391i | \(0.391428\pi\) | |||||||
\(662\) | 336.744 | 0.508676 | ||||||||
\(663\) | −73.7216 | −0.111194 | ||||||||
\(664\) | 794.833 | + | 794.833i | 1.19704 | + | 1.19704i | ||||
\(665\) | 591.767 | + | 591.767i | 0.889876 | + | 0.889876i | ||||
\(666\) | − | 705.021i | − | 1.05859i | ||||||
\(667\) | −283.414 | − | 72.1302i | −0.424908 | − | 0.108141i | ||||
\(668\) | 315.509 | 0.472318 | ||||||||
\(669\) | −135.516 | + | 135.516i | −0.202565 | + | 0.202565i | ||||
\(670\) | 119.526 | − | 119.526i | 0.178398 | − | 0.178398i | ||||
\(671\) | − | 19.7176i | − | 0.0293854i | ||||||
\(672\) | − | 189.290i | − | 0.281681i | ||||||
\(673\) | 725.102i | 1.07742i | 0.842492 | + | 0.538708i | \(0.181088\pi\) | ||||
−0.842492 | + | 0.538708i | \(0.818912\pi\) | |||||||
\(674\) | −130.621 | −0.193799 | ||||||||
\(675\) | 59.6829 | + | 59.6829i | 0.0884191 | + | 0.0884191i | ||||
\(676\) | 45.6673i | 0.0675552i | ||||||||
\(677\) | 650.790 | + | 650.790i | 0.961285 | + | 0.961285i | 0.999278 | − | 0.0379933i | \(-0.0120965\pi\) |
−0.0379933 | + | 0.999278i | \(0.512097\pi\) | |||||||
\(678\) | −16.3226 | + | 16.3226i | −0.0240746 | + | 0.0240746i | ||||
\(679\) | 774.907 | + | 774.907i | 1.14125 | + | 1.14125i | ||||
\(680\) | − | 327.356i | − | 0.481406i | ||||||
\(681\) | 8.77604 | − | 8.77604i | 0.0128870 | − | 0.0128870i | ||||
\(682\) | −22.7328 | − | 22.7328i | −0.0333325 | − | 0.0333325i | ||||
\(683\) | −791.357 | −1.15865 | −0.579324 | − | 0.815097i | \(-0.696683\pi\) | ||||
−0.579324 | + | 0.815097i | \(0.696683\pi\) | |||||||
\(684\) | −296.112 | + | 296.112i | −0.432912 | + | 0.432912i | ||||
\(685\) | 487.988 | + | 487.988i | 0.712392 | + | 0.712392i | ||||
\(686\) | 36.4808 | − | 36.4808i | 0.0531790 | − | 0.0531790i | ||||
\(687\) | 132.875 | 0.193413 | ||||||||
\(688\) | −19.5751 | + | 19.5751i | −0.0284522 | + | 0.0284522i | ||||
\(689\) | − | 1102.22i | − | 1.59973i | ||||||
\(690\) | 33.8187 | 0.0490126 | ||||||||
\(691\) | 646.166 | 0.935118 | 0.467559 | − | 0.883962i | \(-0.345134\pi\) | ||||
0.467559 | + | 0.883962i | \(0.345134\pi\) | |||||||
\(692\) | 220.870 | 0.319176 | ||||||||
\(693\) | 27.9320 | + | 27.9320i | 0.0403059 | + | 0.0403059i | ||||
\(694\) | −165.149 | − | 165.149i | −0.237967 | − | 0.237967i | ||||
\(695\) | − | 259.399i | − | 0.373235i | ||||||
\(696\) | 143.604 | + | 36.5479i | 0.206328 | + | 0.0525114i | ||||
\(697\) | 310.719 | 0.445795 | ||||||||
\(698\) | 186.829 | − | 186.829i | 0.267663 | − | 0.267663i | ||||
\(699\) | 58.6220 | − | 58.6220i | 0.0838656 | − | 0.0838656i | ||||
\(700\) | − | 173.983i | − | 0.248547i | ||||||
\(701\) | − | 738.399i | − | 1.05335i | −0.850066 | − | 0.526676i | \(-0.823438\pi\) | ||
0.850066 | − | 0.526676i | \(-0.176562\pi\) | |||||||
\(702\) | − | 173.388i | − | 0.246991i | ||||||
\(703\) | −1320.69 | −1.87864 | ||||||||
\(704\) | −14.9450 | − | 14.9450i | −0.0212287 | − | 0.0212287i | ||||
\(705\) | − | 8.14799i | − | 0.0115574i | ||||||
\(706\) | −137.260 | − | 137.260i | −0.194420 | − | 0.194420i | ||||
\(707\) | 504.962 | − | 504.962i | 0.714231 | − | 0.714231i | ||||
\(708\) | −93.8736 | − | 93.8736i | −0.132590 | − | 0.132590i | ||||
\(709\) | 211.506i | 0.298316i | 0.988813 | + | 0.149158i | \(0.0476564\pi\) | ||||
−0.988813 | + | 0.149158i | \(0.952344\pi\) | |||||||
\(710\) | −378.293 | + | 378.293i | −0.532807 | + | 0.532807i | ||||
\(711\) | −347.008 | − | 347.008i | −0.488056 | − | 0.488056i | ||||
\(712\) | 959.825 | 1.34807 | ||||||||
\(713\) | 376.249 | − | 376.249i | 0.527699 | − | 0.527699i | ||||
\(714\) | 53.1274 | + | 53.1274i | 0.0744081 | + | 0.0744081i | ||||
\(715\) | 17.0559 | − | 17.0559i | 0.0238544 | − | 0.0238544i | ||||
\(716\) | 130.608 | 0.182413 | ||||||||
\(717\) | 78.2135 | − | 78.2135i | 0.109084 | − | 0.109084i | ||||
\(718\) | 666.730i | 0.928593i | ||||||||
\(719\) | −479.844 | −0.667376 | −0.333688 | − | 0.942684i | \(-0.608293\pi\) | ||||
−0.333688 | + | 0.942684i | \(0.608293\pi\) | |||||||
\(720\) | 40.0921 | 0.0556835 | ||||||||
\(721\) | −1350.31 | −1.87283 | ||||||||
\(722\) | −62.9974 | − | 62.9974i | −0.0872540 | − | 0.0872540i | ||||
\(723\) | −71.2728 | − | 71.2728i | −0.0985792 | − | 0.0985792i | ||||
\(724\) | − | 309.294i | − | 0.427202i | ||||||
\(725\) | 215.197 | + | 54.7687i | 0.296824 | + | 0.0755431i | ||||
\(726\) | 97.2578 | 0.133964 | ||||||||
\(727\) | −943.499 | + | 943.499i | −1.29780 | + | 1.29780i | −0.367953 | + | 0.929844i | \(0.619941\pi\) |
−0.929844 | + | 0.367953i | \(0.880059\pi\) | |||||||
\(728\) | −683.753 | + | 683.753i | −0.939221 | + | 0.939221i | ||||
\(729\) | − | 545.390i | − | 0.748134i | ||||||
\(730\) | 30.0222i | 0.0411263i | ||||||||
\(731\) | 238.384i | 0.326106i | ||||||||
\(732\) | −61.1179 | −0.0834944 | ||||||||
\(733\) | 256.074 | + | 256.074i | 0.349350 | + | 0.349350i | 0.859868 | − | 0.510517i | \(-0.170546\pi\) |
−0.510517 | + | 0.859868i | \(0.670546\pi\) | |||||||
\(734\) | 153.395i | 0.208986i | ||||||||
\(735\) | −82.6973 | − | 82.6973i | −0.112513 | − | 0.112513i | ||||
\(736\) | 222.555 | − | 222.555i | 0.302385 | − | 0.302385i | ||||
\(737\) | −10.5685 | − | 10.5685i | −0.0143398 | − | 0.0143398i | ||||
\(738\) | 357.262i | 0.484095i | ||||||||
\(739\) | 9.12101 | − | 9.12101i | 0.0123424 | − | 0.0123424i | −0.700909 | − | 0.713251i | \(-0.747222\pi\) |
0.713251 | + | 0.700909i | \(0.247222\pi\) | |||||||
\(740\) | −439.722 | − | 439.722i | −0.594219 | − | 0.594219i | ||||
\(741\) | −158.786 | −0.214286 | ||||||||
\(742\) | −794.312 | + | 794.312i | −1.07050 | + | 1.07050i | ||||
\(743\) | −343.894 | − | 343.894i | −0.462845 | − | 0.462845i | 0.436742 | − | 0.899587i | \(-0.356132\pi\) |
−0.899587 | + | 0.436742i | \(0.856132\pi\) | |||||||
\(744\) | −190.643 | + | 190.643i | −0.256241 | + | 0.256241i | ||||
\(745\) | 587.175 | 0.788155 | ||||||||
\(746\) | 83.1437 | − | 83.1437i | 0.111453 | − | 0.111453i | ||||
\(747\) | 1185.46i | 1.58696i | ||||||||
\(748\) | −10.6983 | −0.0143025 | ||||||||
\(749\) | 144.980 | 0.193564 | ||||||||
\(750\) | −109.517 | −0.146023 | ||||||||
\(751\) | 485.159 | + | 485.159i | 0.646017 | + | 0.646017i | 0.952028 | − | 0.306011i | \(-0.0989945\pi\) |
−0.306011 | + | 0.952028i | \(0.598994\pi\) | |||||||
\(752\) | 2.47162 | + | 2.47162i | 0.00328673 | + | 0.00328673i | ||||
\(753\) | − | 120.953i | − | 0.160628i | ||||||
\(754\) | −233.035 | − | 392.146i | −0.309065 | − | 0.520088i | ||||
\(755\) | −1120.66 | −1.48432 | ||||||||
\(756\) | 177.101 | − | 177.101i | 0.234261 | − | 0.234261i | ||||
\(757\) | −158.090 | + | 158.090i | −0.208838 | + | 0.208838i | −0.803773 | − | 0.594936i | \(-0.797178\pi\) |
0.594936 | + | 0.803773i | \(0.297178\pi\) | |||||||
\(758\) | − | 323.852i | − | 0.427246i | ||||||
\(759\) | − | 2.99023i | − | 0.00393970i | ||||||
\(760\) | − | 705.078i | − | 0.927734i | ||||||
\(761\) | 1412.54 | 1.85617 | 0.928084 | − | 0.372371i | \(-0.121455\pi\) | ||||
0.928084 | + | 0.372371i | \(0.121455\pi\) | |||||||
\(762\) | −42.0527 | − | 42.0527i | −0.0551873 | − | 0.0551873i | ||||
\(763\) | − | 374.179i | − | 0.490405i | ||||||
\(764\) | 287.400 | + | 287.400i | 0.376179 | + | 0.376179i | ||||
\(765\) | 244.119 | − | 244.119i | 0.319109 | − | 0.319109i | ||||
\(766\) | −129.237 | − | 129.237i | −0.168716 | − | 0.168716i | ||||
\(767\) | 1105.70i | 1.44159i | ||||||||
\(768\) | −117.412 | + | 117.412i | −0.152880 | + | 0.152880i | ||||
\(769\) | −137.717 | − | 137.717i | −0.179086 | − | 0.179086i | 0.611871 | − | 0.790957i | \(-0.290417\pi\) |
−0.790957 | + | 0.611871i | \(0.790417\pi\) | |||||||
\(770\) | −24.5827 | −0.0319256 | ||||||||
\(771\) | −122.004 | + | 122.004i | −0.158242 | + | 0.158242i | ||||
\(772\) | −412.675 | − | 412.675i | −0.534553 | − | 0.534553i | ||||
\(773\) | −349.001 | + | 349.001i | −0.451489 | + | 0.451489i | −0.895848 | − | 0.444360i | \(-0.853431\pi\) |
0.444360 | + | 0.895848i | \(0.353431\pi\) | |||||||
\(774\) | −274.092 | −0.354124 | ||||||||
\(775\) | −285.688 | + | 285.688i | −0.368629 | + | 0.368629i | ||||
\(776\) | − | 923.285i | − | 1.18980i | ||||||
\(777\) | 386.154 | 0.496981 | ||||||||
\(778\) | −617.964 | −0.794298 | ||||||||
\(779\) | 669.244 | 0.859107 | ||||||||
\(780\) | −52.8676 | − | 52.8676i | −0.0677790 | − | 0.0677790i | ||||
\(781\) | 33.4485 | + | 33.4485i | 0.0428278 | + | 0.0428278i | ||||
\(782\) | 124.928i | 0.159754i | ||||||||
\(783\) | 163.304 | + | 274.805i | 0.208562 | + | 0.350964i | ||||
\(784\) | 50.1710 | 0.0639936 | ||||||||
\(785\) | −344.269 | + | 344.269i | −0.438560 | + | 0.438560i | ||||
\(786\) | 20.4396 | − | 20.4396i | 0.0260045 | − | 0.0260045i | ||||
\(787\) | − | 880.918i | − | 1.11934i | −0.828717 | − | 0.559668i | \(-0.810929\pi\) | ||
0.828717 | − | 0.559668i | \(-0.189071\pi\) | |||||||
\(788\) | 100.308i | 0.127295i | ||||||||
\(789\) | 214.973i | 0.272463i | ||||||||
\(790\) | 305.398 | 0.386580 | ||||||||
\(791\) | 196.374 | + | 196.374i | 0.248261 | + | 0.248261i | ||||
\(792\) | − | 33.2804i | − | 0.0420206i | ||||||
\(793\) | 359.941 | + | 359.941i | 0.453898 | + | 0.453898i | ||||
\(794\) | −598.315 | + | 598.315i | −0.753545 | + | 0.753545i | ||||
\(795\) | −166.164 | − | 166.164i | −0.209011 | − | 0.209011i | ||||
\(796\) | − | 238.592i | − | 0.299738i | ||||||
\(797\) | 634.695 | − | 634.695i | 0.796356 | − | 0.796356i | −0.186163 | − | 0.982519i | \(-0.559605\pi\) |
0.982519 | + | 0.186163i | \(0.0596053\pi\) | |||||||
\(798\) | 114.429 | + | 114.429i | 0.143395 | + | 0.143395i | ||||
\(799\) | 30.0991 | 0.0376709 | ||||||||
\(800\) | −168.987 | + | 168.987i | −0.211234 | + | 0.211234i | ||||
\(801\) | 715.769 | + | 715.769i | 0.893594 | + | 0.893594i | ||||
\(802\) | 312.782 | − | 312.782i | 0.390003 | − | 0.390003i | ||||
\(803\) | 2.65455 | 0.00330579 | ||||||||
\(804\) | −32.7587 | + | 32.7587i | −0.0407446 | + | 0.0407446i | ||||
\(805\) | − | 406.867i | − | 0.505425i | ||||||
\(806\) | 829.967 | 1.02974 | ||||||||
\(807\) | 148.516 | 0.184034 | ||||||||
\(808\) | −601.651 | −0.744617 | ||||||||
\(809\) | −768.799 | − | 768.799i | −0.950308 | − | 0.950308i | 0.0485143 | − | 0.998822i | \(-0.484551\pi\) |
−0.998822 | + | 0.0485143i | \(0.984551\pi\) | |||||||
\(810\) | 267.325 | + | 267.325i | 0.330031 | + | 0.330031i | ||||
\(811\) | − | 615.818i | − | 0.759332i | −0.925124 | − | 0.379666i | \(-0.876039\pi\) | ||
0.925124 | − | 0.379666i | \(-0.123961\pi\) | |||||||
\(812\) | 162.519 | − | 638.570i | 0.200147 | − | 0.786416i | ||||
\(813\) | 249.980 | 0.307479 | ||||||||
\(814\) | 27.4314 | − | 27.4314i | 0.0336995 | − | 0.0336995i | ||||
\(815\) | 67.3183 | − | 67.3183i | 0.0825991 | − | 0.0825991i | ||||
\(816\) | − | 6.74256i | − | 0.00826294i | ||||||
\(817\) | 513.445i | 0.628451i | ||||||||
\(818\) | − | 399.605i | − | 0.488514i | ||||||
\(819\) | −1019.79 | −1.24516 | ||||||||
\(820\) | 222.824 | + | 222.824i | 0.271737 | + | 0.271737i | ||||
\(821\) | 998.934i | 1.21673i | 0.793658 | + | 0.608364i | \(0.208174\pi\) | ||||
−0.793658 | + | 0.608364i | \(0.791826\pi\) | |||||||
\(822\) | 94.3614 | + | 94.3614i | 0.114795 | + | 0.114795i | ||||
\(823\) | −117.268 | + | 117.268i | −0.142489 | + | 0.142489i | −0.774753 | − | 0.632264i | \(-0.782126\pi\) |
0.632264 | + | 0.774753i | \(0.282126\pi\) | |||||||
\(824\) | 804.431 | + | 804.431i | 0.976251 | + | 0.976251i | ||||
\(825\) | 2.27050i | 0.00275212i | ||||||||
\(826\) | 796.822 | − | 796.822i | 0.964675 | − | 0.964675i | ||||
\(827\) | 1079.32 | + | 1079.32i | 1.30510 | + | 1.30510i | 0.924906 | + | 0.380195i | \(0.124143\pi\) |
0.380195 | + | 0.924906i | \(0.375857\pi\) | |||||||
\(828\) | 203.590 | 0.245882 | ||||||||
\(829\) | 671.650 | − | 671.650i | 0.810192 | − | 0.810192i | −0.174470 | − | 0.984662i | \(-0.555821\pi\) |
0.984662 | + | 0.174470i | \(0.0558212\pi\) | |||||||
\(830\) | −521.656 | − | 521.656i | −0.628501 | − | 0.628501i | ||||
\(831\) | 13.5154 | − | 13.5154i | 0.0162640 | − | 0.0162640i | ||||
\(832\) | 545.636 | 0.655813 | ||||||||
\(833\) | 305.488 | − | 305.488i | 0.366732 | − | 0.366732i | ||||
\(834\) | − | 50.1594i | − | 0.0601432i | ||||||
\(835\) | −560.239 | −0.670945 | ||||||||
\(836\) | −23.0426 | −0.0275629 | ||||||||
\(837\) | −581.617 | −0.694883 | ||||||||
\(838\) | −465.725 | − | 465.725i | −0.555758 | − | 0.555758i | ||||
\(839\) | −100.846 | − | 100.846i | −0.120197 | − | 0.120197i | 0.644449 | − | 0.764647i | \(-0.277087\pi\) |
−0.764647 | + | 0.644449i | \(0.777087\pi\) | |||||||
\(840\) | 206.157i | 0.245425i | ||||||||
\(841\) | 738.680 | + | 402.036i | 0.878335 | + | 0.478045i | ||||
\(842\) | −776.262 | −0.921926 | ||||||||
\(843\) | −1.29346 | + | 1.29346i | −0.00153435 | + | 0.00153435i | ||||
\(844\) | −197.111 | + | 197.111i | −0.233544 | + | 0.233544i | ||||
\(845\) | − | 81.0901i | − | 0.0959646i | ||||||
\(846\) | 34.6077i | 0.0409074i | ||||||||
\(847\) | − | 1170.09i | − | 1.38145i | ||||||
\(848\) | 100.808 | 0.118878 | ||||||||
\(849\) | −11.9259 | − | 11.9259i | −0.0140470 | − | 0.0140470i | ||||
\(850\) | − | 94.8582i | − | 0.111598i | ||||||
\(851\) | 454.016 | + | 454.016i | 0.533509 | + | 0.533509i | ||||
\(852\) | 103.679 | − | 103.679i | 0.121689 | − | 0.121689i | ||||
\(853\) | −922.579 | − | 922.579i | −1.08157 | − | 1.08157i | −0.996363 | − | 0.0852066i | \(-0.972845\pi\) |
−0.0852066 | − | 0.996363i | \(-0.527155\pi\) | |||||||
\(854\) | − | 518.783i | − | 0.607475i | ||||||
\(855\) | 525.797 | − | 525.797i | 0.614967 | − | 0.614967i | ||||
\(856\) | −86.3700 | − | 86.3700i | −0.100900 | − | 0.100900i | ||||
\(857\) | −633.774 | −0.739527 | −0.369763 | − | 0.929126i | \(-0.620561\pi\) | ||||
−0.369763 | + | 0.929126i | \(0.620561\pi\) | |||||||
\(858\) | 3.29807 | − | 3.29807i | 0.00384390 | − | 0.00384390i | ||||
\(859\) | −834.541 | − | 834.541i | −0.971526 | − | 0.971526i | 0.0280796 | − | 0.999606i | \(-0.491061\pi\) |
−0.999606 | + | 0.0280796i | \(0.991061\pi\) | |||||||
\(860\) | −170.951 | + | 170.951i | −0.198780 | + | 0.198780i | ||||
\(861\) | −195.680 | −0.227270 | ||||||||
\(862\) | 542.695 | − | 542.695i | 0.629577 | − | 0.629577i | ||||
\(863\) | 805.408i | 0.933265i | 0.884451 | + | 0.466632i | \(0.154533\pi\) | ||||
−0.884451 | + | 0.466632i | \(0.845467\pi\) | |||||||
\(864\) | −344.032 | −0.398185 | ||||||||
\(865\) | −392.192 | −0.453401 | ||||||||
\(866\) | −76.1756 | −0.0879626 | ||||||||
\(867\) | 86.8737 | + | 86.8737i | 0.100200 | + | 0.100200i | ||||
\(868\) | 847.741 | + | 847.741i | 0.976660 | + | 0.976660i | ||||
\(869\) | − | 27.0032i | − | 0.0310739i | ||||||
\(870\) | −94.2486 | − | 23.9867i | −0.108332 | − | 0.0275709i | ||||
\(871\) | 385.851 | 0.442998 | ||||||||
\(872\) | −222.913 | + | 222.913i | −0.255634 | + | 0.255634i | ||||
\(873\) | 688.520 | − | 688.520i | 0.788682 | − | 0.788682i | ||||
\(874\) | 269.077i | 0.307868i | ||||||||
\(875\) | 1317.59i | 1.50581i | ||||||||
\(876\) | − | 8.22822i | − | 0.00939294i | ||||||
\(877\) | 427.725 | 0.487714 | 0.243857 | − | 0.969811i | \(-0.421587\pi\) | ||||
0.243857 | + | 0.969811i | \(0.421587\pi\) | |||||||
\(878\) | 313.414 | + | 313.414i | 0.356964 | + | 0.356964i | ||||
\(879\) | 226.438i | 0.257609i | ||||||||
\(880\) | 1.55993 | + | 1.55993i | 0.00177265 | + | 0.00177265i | ||||
\(881\) | −977.952 | + | 977.952i | −1.11005 | + | 1.11005i | −0.116905 | + | 0.993143i | \(0.537297\pi\) |
−0.993143 | + | 0.116905i | \(0.962703\pi\) | |||||||
\(882\) | 351.248 | + | 351.248i | 0.398240 | + | 0.398240i | ||||
\(883\) | 1215.83i | 1.37693i | 0.725270 | + | 0.688464i | \(0.241715\pi\) | ||||
−0.725270 | + | 0.688464i | \(0.758285\pi\) | |||||||
\(884\) | 195.296 | − | 195.296i | 0.220923 | − | 0.220923i | ||||
\(885\) | 166.689 | + | 166.689i | 0.188349 | + | 0.188349i | ||||
\(886\) | −226.604 | −0.255761 | ||||||||
\(887\) | 1221.32 | − | 1221.32i | 1.37691 | − | 1.37691i | 0.527122 | − | 0.849790i | \(-0.323271\pi\) |
0.849790 | − | 0.527122i | \(-0.176729\pi\) | |||||||
\(888\) | −230.047 | − | 230.047i | −0.259062 | − | 0.259062i | ||||
\(889\) | −505.929 | + | 505.929i | −0.569099 | + | 0.569099i | ||||
\(890\) | −629.942 | −0.707800 | ||||||||
\(891\) | 23.6368 | − | 23.6368i | 0.0265284 | − | 0.0265284i | ||||
\(892\) | − | 717.990i | − | 0.804922i | ||||||
\(893\) | 64.8291 | 0.0725970 | ||||||||
\(894\) | 113.541 | 0.127003 | ||||||||
\(895\) | −231.916 | −0.259124 | ||||||||
\(896\) | 462.025 | + | 462.025i | 0.515653 | + | 0.515653i | ||||
\(897\) | 54.5862 | + | 54.5862i | 0.0608542 | + | 0.0608542i | ||||
\(898\) | 1024.02i | 1.14034i | ||||||||
\(899\) | −1315.43 | + | 781.698i | −1.46321 | + | 0.869519i | ||||
\(900\) | −154.587 | −0.171763 | ||||||||
\(901\) | 613.816 | − | 613.816i | 0.681261 | − | 0.681261i | ||||
\(902\) | −13.9006 | + | 13.9006i | −0.0154108 | + | 0.0154108i | ||||
\(903\) | − | 150.125i | − | 0.166252i | ||||||
\(904\) | − | 233.976i | − | 0.258823i | ||||||
\(905\) | 549.204i | 0.606856i | ||||||||
\(906\) | −216.700 | −0.239183 | ||||||||
\(907\) | −236.820 | − | 236.820i | −0.261103 | − | 0.261103i | 0.564399 | − | 0.825502i | \(-0.309108\pi\) |
−0.825502 | + | 0.564399i | \(0.809108\pi\) | |||||||
\(908\) | 46.4972i | 0.0512083i | ||||||||
\(909\) | −448.668 | − | 448.668i | −0.493584 | − | 0.493584i | ||||
\(910\) | 448.753 | − | 448.753i | 0.493135 | − | 0.493135i | ||||
\(911\) | −807.445 | − | 807.445i | −0.886328 | − | 0.886328i | 0.107840 | − | 0.994168i | \(-0.465606\pi\) |
−0.994168 | + | 0.107840i | \(0.965606\pi\) | |||||||
\(912\) | − | 14.5225i | − | 0.0159238i | ||||||
\(913\) | −46.1246 | + | 46.1246i | −0.0505198 | + | 0.0505198i | ||||
\(914\) | −343.040 | − | 343.040i | −0.375317 | − | 0.375317i | ||||
\(915\) | 108.525 | 0.118607 | ||||||||
\(916\) | −351.999 | + | 351.999i | −0.384278 | + | 0.384278i | ||||
\(917\) | −245.905 | − | 245.905i | −0.268163 | − | 0.268163i | ||||
\(918\) | 96.5585 | − | 96.5585i | 0.105184 | − | 0.105184i | ||||
\(919\) | −791.267 | −0.861009 | −0.430504 | − | 0.902589i | \(-0.641664\pi\) | ||||
−0.430504 | + | 0.902589i | \(0.641664\pi\) | |||||||
\(920\) | −242.387 | + | 242.387i | −0.263464 | + | 0.263464i | ||||
\(921\) | 8.14823i | 0.00884715i | ||||||||
\(922\) | −72.9241 | −0.0790934 | ||||||||
\(923\) | −1221.19 | −1.32307 | ||||||||
\(924\) | 6.73740 | 0.00729156 | ||||||||
\(925\) | −344.736 | − | 344.736i | −0.372688 | − | 0.372688i | ||||
\(926\) | 373.781 | + | 373.781i | 0.403651 | + | 0.403651i | ||||
\(927\) | 1199.77i | 1.29425i | ||||||||
\(928\) | −778.086 | + | 462.381i | −0.838455 | + | 0.498256i | ||||
\(929\) | 1491.46 | 1.60545 | 0.802724 | − | 0.596351i | \(-0.203383\pi\) | ||||
0.802724 | + | 0.596351i | \(0.203383\pi\) | |||||||
\(930\) | 125.121 | − | 125.121i | 0.134539 | − | 0.134539i | ||||
\(931\) | 657.978 | − | 657.978i | 0.706743 | − | 0.706743i | ||||
\(932\) | 310.591i | 0.333252i | ||||||||
\(933\) | − | 83.2999i | − | 0.0892818i | ||||||
\(934\) | 776.881i | 0.831778i | ||||||||
\(935\) | 18.9966 | 0.0203173 | ||||||||
\(936\) | 607.527 | + | 607.527i | 0.649068 | + | 0.649068i | ||||
\(937\) | − | 910.587i | − | 0.971811i | −0.874011 | − | 0.485905i | \(-0.838490\pi\) | ||
0.874011 | − | 0.485905i | \(-0.161510\pi\) | |||||||
\(938\) | −278.064 | − | 278.064i | −0.296443 | − | 0.296443i | ||||
\(939\) | 59.2113 | − | 59.2113i | 0.0630578 | − | 0.0630578i | ||||
\(940\) | 21.5848 | + | 21.5848i | 0.0229626 | + | 0.0229626i | ||||
\(941\) | − | 1302.28i | − | 1.38393i | −0.721929 | − | 0.691967i | \(-0.756744\pi\) | ||
0.721929 | − | 0.691967i | \(-0.243256\pi\) | |||||||
\(942\) | −66.5707 | + | 66.5707i | −0.0706695 | + | 0.0706695i | ||||
\(943\) | −230.068 | − | 230.068i | −0.243974 | − | 0.243974i | ||||
\(944\) | −101.127 | −0.107126 | ||||||||
\(945\) | −314.473 | + | 314.473i | −0.332776 | + | 0.332776i | ||||
\(946\) | −10.6645 | − | 10.6645i | −0.0112733 | − | 0.0112733i | ||||
\(947\) | −455.078 | + | 455.078i | −0.480547 | + | 0.480547i | −0.905306 | − | 0.424759i | \(-0.860359\pi\) |
0.424759 | + | 0.905306i | \(0.360359\pi\) | |||||||
\(948\) | −83.7008 | −0.0882920 | ||||||||
\(949\) | −48.4584 | + | 48.4584i | −0.0510626 | + | 0.0510626i | ||||
\(950\) | − | 204.311i | − | 0.215064i | ||||||
\(951\) | 358.846 | 0.377335 | ||||||||
\(952\) | −761.554 | −0.799952 | ||||||||
\(953\) | 299.880 | 0.314670 | 0.157335 | − | 0.987545i | \(-0.449710\pi\) | ||||
0.157335 | + | 0.987545i | \(0.449710\pi\) | |||||||
\(954\) | 705.761 | + | 705.761i | 0.739792 | + | 0.739792i | ||||
\(955\) | −510.328 | − | 510.328i | −0.534375 | − | 0.534375i | ||||
\(956\) | 414.391i | 0.433463i | ||||||||
\(957\) | −2.12090 | + | 8.33342i | −0.00221619 | + | 0.00870785i | ||||
\(958\) | 406.772 | 0.424606 | ||||||||
\(959\) | 1135.25 | − | 1135.25i | 1.18378 | − | 1.18378i | ||||
\(960\) | 82.2569 | − | 82.2569i | 0.0856842 | − | 0.0856842i | ||||
\(961\) | − | 1823.06i | − | 1.89705i | ||||||
\(962\) | 1001.51i | 1.04107i | ||||||||
\(963\) | − | 128.817i | − | 0.133766i | ||||||
\(964\) | 377.617 | 0.391719 | ||||||||
\(965\) | 732.775 | + | 732.775i | 0.759352 | + | 0.759352i | ||||
\(966\) | − | 78.6751i | − | 0.0814442i | ||||||
\(967\) | 136.707 | + | 136.707i | 0.141372 | + | 0.141372i | 0.774251 | − | 0.632879i | \(-0.218127\pi\) |
−0.632879 | + | 0.774251i | \(0.718127\pi\) | |||||||
\(968\) | −697.070 | + | 697.070i | −0.720113 | + | 0.720113i | ||||
\(969\) | −88.4266 | − | 88.4266i | −0.0912556 | − | 0.0912556i | ||||
\(970\) | 605.960i | 0.624701i | ||||||||
\(971\) | 225.421 | − | 225.421i | 0.232153 | − | 0.232153i | −0.581438 | − | 0.813591i | \(-0.697510\pi\) |
0.813591 | + | 0.581438i | \(0.197510\pi\) | |||||||
\(972\) | −237.788 | − | 237.788i | −0.244638 | − | 0.244638i | ||||
\(973\) | −603.459 | −0.620205 | ||||||||
\(974\) | 361.115 | − | 361.115i | 0.370755 | − | 0.370755i | ||||
\(975\) | −41.4475 | − | 41.4475i | −0.0425103 | − | 0.0425103i | ||||
\(976\) | −32.9201 | + | 32.9201i | −0.0337297 | + | 0.0337297i | ||||
\(977\) | 119.816 | 0.122637 | 0.0613186 | − | 0.998118i | \(-0.480469\pi\) | ||||
0.0613186 | + | 0.998118i | \(0.480469\pi\) | |||||||
\(978\) | 13.0172 | − | 13.0172i | 0.0133100 | − | 0.0133100i | ||||
\(979\) | 55.6992i | 0.0568939i | ||||||||
\(980\) | 438.147 | 0.447088 | ||||||||
\(981\) | −332.465 | −0.338904 | ||||||||
\(982\) | −802.635 | −0.817348 | ||||||||
\(983\) | 727.465 | + | 727.465i | 0.740046 | + | 0.740046i | 0.972587 | − | 0.232540i | \(-0.0747038\pi\) |
−0.232540 | + | 0.972587i | \(0.574704\pi\) | |||||||
\(984\) | 116.574 | + | 116.574i | 0.118469 | + | 0.118469i | ||||
\(985\) | − | 178.114i | − | 0.180827i | ||||||
\(986\) | 88.6081 | − | 348.159i | 0.0898662 | − | 0.353102i | ||||
\(987\) | −18.9553 | −0.0192050 | ||||||||
\(988\) | 420.639 | − | 420.639i | 0.425748 | − | 0.425748i | ||||
\(989\) | 176.508 | − | 176.508i | 0.178471 | − | 0.178471i | ||||
\(990\) | 21.8422i | 0.0220628i | ||||||||
\(991\) | − | 76.7646i | − | 0.0774617i | −0.999250 | − | 0.0387309i | \(-0.987669\pi\) | ||
0.999250 | − | 0.0387309i | \(-0.0123315\pi\) | |||||||
\(992\) | − | 1646.80i | − | 1.66008i | ||||||
\(993\) | 163.879 | 0.165035 | ||||||||
\(994\) | 880.053 | + | 880.053i | 0.885365 | + | 0.885365i | ||||
\(995\) | 423.660i | 0.425789i | ||||||||
\(996\) | 142.971 | + | 142.971i | 0.143545 | + | 0.143545i | ||||
\(997\) | −352.075 | + | 352.075i | −0.353135 | + | 0.353135i | −0.861275 | − | 0.508140i | \(-0.830333\pi\) |
0.508140 | + | 0.861275i | \(0.330333\pi\) | |||||||
\(998\) | −86.3627 | − | 86.3627i | −0.0865358 | − | 0.0865358i | ||||
\(999\) | − | 701.831i | − | 0.702533i |
(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 | 29.3.c.a.17.3 | yes | 8 | |
3.2 | odd | 2 | 261.3.f.a.46.2 | 8 | |||
4.3 | odd | 2 | 464.3.l.c.17.2 | 8 | |||
29.12 | odd | 4 | inner | 29.3.c.a.12.3 | ✓ | 8 | |
87.41 | even | 4 | 261.3.f.a.244.2 | 8 | |||
116.99 | even | 4 | 464.3.l.c.273.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.3.c.a.12.3 | ✓ | 8 | 29.12 | odd | 4 | inner | |
29.3.c.a.17.3 | yes | 8 | 1.1 | even | 1 | trivial | |
261.3.f.a.46.2 | 8 | 3.2 | odd | 2 | |||
261.3.f.a.244.2 | 8 | 87.41 | even | 4 | |||
464.3.l.c.17.2 | 8 | 4.3 | odd | 2 | |||
464.3.l.c.273.2 | 8 | 116.99 | even | 4 |