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: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.a.553.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 2.69807 | + | 4.20956i | 0.539614 | + | 0.841912i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −5.61863 | − | 5.61863i | −0.802661 | − | 0.802661i | 0.180849 | − | 0.983511i | \(-0.442115\pi\) |
−0.983511 | + | 0.180849i | \(0.942115\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −1.51149 | + | 6.90763i | −0.151149 | + | 0.690763i | ||||
\(11\) | −12.8664 | −1.16967 | −0.584837 | − | 0.811151i | \(-0.698842\pi\) | ||||
−0.584837 | + | 0.811151i | \(0.698842\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 9.49626 | − | 9.49626i | 0.730481 | − | 0.730481i | −0.240234 | − | 0.970715i | \(-0.577224\pi\) |
0.970715 | + | 0.240234i | \(0.0772241\pi\) | |||||||
\(14\) | − | 11.2373i | − | 0.802661i | ||||||
\(15\) | −8.46009 | − | 1.85119i | −0.564006 | − | 0.123413i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −16.0031 | − | 16.0031i | −0.941358 | − | 0.941358i | 0.0570149 | − | 0.998373i | \(-0.481842\pi\) |
−0.998373 | + | 0.0570149i | \(0.981842\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | − | 27.2561i | − | 1.43453i | −0.696800 | − | 0.717265i | \(-0.745394\pi\) | ||
0.696800 | − | 0.717265i | \(-0.254606\pi\) | |||||||
\(20\) | −8.41912 | + | 5.39614i | −0.420956 | + | 0.269807i | ||||
\(21\) | 13.7628 | 0.655370 | ||||||||
\(22\) | −12.8664 | − | 12.8664i | −0.584837 | − | 0.584837i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | −10.4408 | + | 22.7154i | −0.417633 | + | 0.908616i | ||||
\(26\) | 18.9925 | 0.730481 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 11.2373 | − | 11.2373i | 0.401331 | − | 0.401331i | ||||
\(29\) | 10.8625i | 0.374569i | 0.982306 | + | 0.187284i | \(0.0599686\pi\) | ||||
−0.982306 | + | 0.187284i | \(0.940031\pi\) | |||||||
\(30\) | −6.60890 | − | 10.3113i | −0.220297 | − | 0.343709i | ||||
\(31\) | 11.1289 | 0.358997 | 0.179499 | − | 0.983758i | \(-0.442552\pi\) | ||||
0.179499 | + | 0.983758i | \(0.442552\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 15.7581 | − | 15.7581i | 0.477518 | − | 0.477518i | ||||
\(34\) | − | 32.0062i | − | 0.941358i | ||||||
\(35\) | 8.49251 | − | 38.8114i | 0.242643 | − | 1.10890i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 23.3287 | + | 23.3287i | 0.630504 | + | 0.630504i | 0.948195 | − | 0.317690i | \(-0.102907\pi\) |
−0.317690 | + | 0.948195i | \(0.602907\pi\) | |||||||
\(38\) | 27.2561 | − | 27.2561i | 0.717265 | − | 0.717265i | ||||
\(39\) | 23.2610i | 0.596435i | ||||||||
\(40\) | −13.8153 | − | 3.02298i | −0.345382 | − | 0.0755746i | ||||
\(41\) | −48.0560 | −1.17210 | −0.586049 | − | 0.810276i | \(-0.699317\pi\) | ||||
−0.586049 | + | 0.810276i | \(0.699317\pi\) | |||||||
\(42\) | 13.7628 | + | 13.7628i | 0.327685 | + | 0.327685i | ||||
\(43\) | 19.0800 | − | 19.0800i | 0.443721 | − | 0.443721i | −0.449540 | − | 0.893260i | \(-0.648412\pi\) |
0.893260 | + | 0.449540i | \(0.148412\pi\) | |||||||
\(44\) | − | 25.7328i | − | 0.584837i | ||||||
\(45\) | 12.6287 | − | 8.09421i | 0.280637 | − | 0.179871i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | −56.5992 | − | 56.5992i | −1.20424 | − | 1.20424i | −0.972865 | − | 0.231374i | \(-0.925678\pi\) |
−0.231374 | − | 0.972865i | \(-0.574322\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 14.1380i | 0.288530i | ||||||||
\(50\) | −33.1562 | + | 12.2746i | −0.663124 | + | 0.245491i | ||||
\(51\) | 39.1994 | 0.768616 | ||||||||
\(52\) | 18.9925 | + | 18.9925i | 0.365241 | + | 0.365241i | ||||
\(53\) | −40.7367 | + | 40.7367i | −0.768617 | + | 0.768617i | −0.977863 | − | 0.209246i | \(-0.932899\pi\) |
0.209246 | + | 0.977863i | \(0.432899\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | −34.7145 | − | 54.1620i | −0.631173 | − | 0.984764i | ||||
\(56\) | 22.4745 | 0.401331 | ||||||||
\(57\) | 33.3817 | + | 33.3817i | 0.585644 | + | 0.585644i | ||||
\(58\) | −10.8625 | + | 10.8625i | −0.187284 | + | 0.187284i | ||||
\(59\) | − | 63.6669i | − | 1.07910i | −0.841954 | − | 0.539550i | \(-0.818594\pi\) | ||
0.841954 | − | 0.539550i | \(-0.181406\pi\) | |||||||
\(60\) | 3.70238 | − | 16.9202i | 0.0617064 | − | 0.282003i | ||||
\(61\) | 104.528 | 1.71358 | 0.856788 | − | 0.515670i | \(-0.172457\pi\) | ||||
0.856788 | + | 0.515670i | \(0.172457\pi\) | |||||||
\(62\) | 11.1289 | + | 11.1289i | 0.179499 | + | 0.179499i | ||||
\(63\) | −16.8559 | + | 16.8559i | −0.267554 | + | 0.267554i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 65.5967 | + | 14.3535i | 1.00918 | + | 0.220823i | ||||
\(66\) | 31.5162 | 0.477518 | ||||||||
\(67\) | −3.47681 | − | 3.47681i | −0.0518926 | − | 0.0518926i | 0.680684 | − | 0.732577i | \(-0.261683\pi\) |
−0.732577 | + | 0.680684i | \(0.761683\pi\) | |||||||
\(68\) | 32.0062 | − | 32.0062i | 0.470679 | − | 0.470679i | ||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | 47.3039 | − | 30.3189i | 0.675771 | − | 0.433127i | ||||
\(71\) | −90.8333 | −1.27934 | −0.639671 | − | 0.768649i | \(-0.720930\pi\) | ||||
−0.639671 | + | 0.768649i | \(0.720930\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 6.81243 | − | 6.81243i | 0.0933210 | − | 0.0933210i | −0.658905 | − | 0.752226i | \(-0.728980\pi\) |
0.752226 | + | 0.658905i | \(0.228980\pi\) | |||||||
\(74\) | 46.6573i | 0.630504i | ||||||||
\(75\) | −15.0332 | − | 40.6079i | −0.200443 | − | 0.541439i | ||||
\(76\) | 54.5121 | 0.717265 | ||||||||
\(77\) | 72.2917 | + | 72.2917i | 0.938853 | + | 0.938853i | ||||
\(78\) | −23.2610 | + | 23.2610i | −0.298218 | + | 0.298218i | ||||
\(79\) | 103.414i | 1.30904i | 0.756045 | + | 0.654520i | \(0.227129\pi\) | ||||
−0.756045 | + | 0.654520i | \(0.772871\pi\) | |||||||
\(80\) | −10.7923 | − | 16.8382i | −0.134904 | − | 0.210478i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −48.0560 | − | 48.0560i | −0.586049 | − | 0.586049i | ||||
\(83\) | 87.6868 | − | 87.6868i | 1.05647 | − | 1.05647i | 0.0581608 | − | 0.998307i | \(-0.481476\pi\) |
0.998307 | − | 0.0581608i | \(-0.0185236\pi\) | |||||||
\(84\) | 27.5255i | 0.327685i | ||||||||
\(85\) | 24.1885 | − | 110.543i | 0.284571 | − | 1.30051i | ||||
\(86\) | 38.1600 | 0.443721 | ||||||||
\(87\) | −13.3038 | − | 13.3038i | −0.152917 | − | 0.152917i | ||||
\(88\) | 25.7328 | − | 25.7328i | 0.292419 | − | 0.292419i | ||||
\(89\) | 65.1773i | 0.732329i | 0.930550 | + | 0.366165i | \(0.119329\pi\) | ||||
−0.930550 | + | 0.366165i | \(0.880671\pi\) | |||||||
\(90\) | 20.7229 | + | 4.53448i | 0.230254 | + | 0.0503831i | ||||
\(91\) | −106.712 | −1.17266 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | −13.6301 | + | 13.6301i | −0.146560 | + | 0.146560i | ||||
\(94\) | − | 113.198i | − | 1.20424i | ||||||
\(95\) | 114.736 | − | 73.5388i | 1.20775 | − | 0.774093i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −121.933 | − | 121.933i | −1.25704 | − | 1.25704i | −0.952497 | − | 0.304547i | \(-0.901495\pi\) |
−0.304547 | − | 0.952497i | \(-0.598505\pi\) | |||||||
\(98\) | −14.1380 | + | 14.1380i | −0.144265 | + | 0.144265i | ||||
\(99\) | 38.5993i | 0.389892i | ||||||||
\(100\) | −45.4308 | − | 20.8817i | −0.454308 | − | 0.208817i | ||||
\(101\) | −129.221 | −1.27941 | −0.639705 | − | 0.768620i | \(-0.720944\pi\) | ||||
−0.639705 | + | 0.768620i | \(0.720944\pi\) | |||||||
\(102\) | 39.1994 | + | 39.1994i | 0.384308 | + | 0.384308i | ||||
\(103\) | −4.11421 | + | 4.11421i | −0.0399438 | + | 0.0399438i | −0.726797 | − | 0.686853i | \(-0.758992\pi\) |
0.686853 | + | 0.726797i | \(0.258992\pi\) | |||||||
\(104\) | 37.9850i | 0.365241i | ||||||||
\(105\) | 37.1329 | + | 57.9353i | 0.353647 | + | 0.551764i | ||||
\(106\) | −81.4734 | −0.768617 | ||||||||
\(107\) | 24.7912 | + | 24.7912i | 0.231693 | + | 0.231693i | 0.813399 | − | 0.581706i | \(-0.197615\pi\) |
−0.581706 | + | 0.813399i | \(0.697615\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 0.116226i | 0.00106629i | 1.00000 | 0.000533145i | \(0.000169705\pi\) | |||||
−1.00000 | 0.000533145i | \(0.999830\pi\) | ||||||||
\(110\) | 19.4475 | − | 88.8765i | 0.176795 | − | 0.807968i | ||||
\(111\) | −57.1433 | −0.514805 | ||||||||
\(112\) | 22.4745 | + | 22.4745i | 0.200665 | + | 0.200665i | ||||
\(113\) | 150.629 | − | 150.629i | 1.33300 | − | 1.33300i | 0.430335 | − | 0.902669i | \(-0.358396\pi\) |
0.902669 | − | 0.430335i | \(-0.141604\pi\) | |||||||
\(114\) | 66.7635i | 0.585644i | ||||||||
\(115\) | −23.4249 | − | 5.12572i | −0.203695 | − | 0.0445715i | ||||
\(116\) | −21.7250 | −0.187284 | ||||||||
\(117\) | −28.4888 | − | 28.4888i | −0.243494 | − | 0.243494i | ||||
\(118\) | 63.6669 | − | 63.6669i | 0.539550 | − | 0.539550i | ||||
\(119\) | 179.831i | 1.51118i | ||||||||
\(120\) | 20.6226 | − | 13.2178i | 0.171855 | − | 0.110148i | ||||
\(121\) | 44.5449 | 0.368139 | ||||||||
\(122\) | 104.528 | + | 104.528i | 0.856788 | + | 0.856788i | ||||
\(123\) | 58.8564 | − | 58.8564i | 0.478507 | − | 0.478507i | ||||
\(124\) | 22.2578i | 0.179499i | ||||||||
\(125\) | −123.792 | + | 17.3364i | −0.990336 | + | 0.138691i | ||||
\(126\) | −33.7118 | −0.267554 | ||||||||
\(127\) | −153.452 | − | 153.452i | −1.20829 | − | 1.20829i | −0.971582 | − | 0.236705i | \(-0.923932\pi\) |
−0.236705 | − | 0.971582i | \(-0.576068\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 46.7362i | 0.362296i | ||||||||
\(130\) | 51.2431 | + | 79.9502i | 0.394178 | + | 0.615001i | ||||
\(131\) | −233.897 | −1.78548 | −0.892738 | − | 0.450576i | \(-0.851219\pi\) | ||||
−0.892738 | + | 0.450576i | \(0.851219\pi\) | |||||||
\(132\) | 31.5162 | + | 31.5162i | 0.238759 | + | 0.238759i | ||||
\(133\) | −153.142 | + | 153.142i | −1.15144 | + | 1.15144i | ||||
\(134\) | − | 6.95361i | − | 0.0518926i | ||||||
\(135\) | −5.55358 | + | 25.3803i | −0.0411376 | + | 0.188002i | ||||
\(136\) | 64.0124 | 0.470679 | ||||||||
\(137\) | 40.9626 | + | 40.9626i | 0.298997 | + | 0.298997i | 0.840621 | − | 0.541624i | \(-0.182190\pi\) |
−0.541624 | + | 0.840621i | \(0.682190\pi\) | |||||||
\(138\) | 8.30662 | − | 8.30662i | 0.0601929 | − | 0.0601929i | ||||
\(139\) | − | 148.538i | − | 1.06862i | −0.845290 | − | 0.534308i | \(-0.820572\pi\) | ||
0.845290 | − | 0.534308i | \(-0.179428\pi\) | |||||||
\(140\) | 77.6229 | + | 16.9850i | 0.554449 | + | 0.121322i | ||||
\(141\) | 138.639 | 0.983257 | ||||||||
\(142\) | −90.8333 | − | 90.8333i | −0.639671 | − | 0.639671i | ||||
\(143\) | −122.183 | + | 122.183i | −0.854426 | + | 0.854426i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −45.7264 | + | 29.3078i | −0.315354 | + | 0.202123i | ||||
\(146\) | 13.6249 | 0.0933210 | ||||||||
\(147\) | −17.3154 | − | 17.3154i | −0.117792 | − | 0.117792i | ||||
\(148\) | −46.6573 | + | 46.6573i | −0.315252 | + | 0.315252i | ||||
\(149\) | 10.9701i | 0.0736249i | 0.999322 | + | 0.0368125i | \(0.0117204\pi\) | ||||
−0.999322 | + | 0.0368125i | \(0.988280\pi\) | |||||||
\(150\) | 25.5747 | − | 55.6411i | 0.170498 | − | 0.370941i | ||||
\(151\) | −109.516 | −0.725269 | −0.362635 | − | 0.931931i | \(-0.618123\pi\) | ||||
−0.362635 | + | 0.931931i | \(0.618123\pi\) | |||||||
\(152\) | 54.5121 | + | 54.5121i | 0.358633 | + | 0.358633i | ||||
\(153\) | −48.0093 | + | 48.0093i | −0.313786 | + | 0.313786i | ||||
\(154\) | 144.583i | 0.938853i | ||||||||
\(155\) | 30.0266 | + | 46.8479i | 0.193720 | + | 0.302244i | ||||
\(156\) | −46.5220 | −0.298218 | ||||||||
\(157\) | 91.3919 | + | 91.3919i | 0.582114 | + | 0.582114i | 0.935484 | − | 0.353370i | \(-0.114964\pi\) |
−0.353370 | + | 0.935484i | \(0.614964\pi\) | |||||||
\(158\) | −103.414 | + | 103.414i | −0.654520 | + | 0.654520i | ||||
\(159\) | − | 99.7841i | − | 0.627573i | ||||||
\(160\) | 6.04597 | − | 27.6305i | 0.0377873 | − | 0.172691i | ||||
\(161\) | 38.1074 | 0.236692 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 48.2405 | − | 48.2405i | 0.295954 | − | 0.295954i | −0.543473 | − | 0.839427i | \(-0.682891\pi\) |
0.839427 | + | 0.543473i | \(0.182891\pi\) | |||||||
\(164\) | − | 96.1120i | − | 0.586049i | ||||||
\(165\) | 108.851 | + | 23.8182i | 0.659704 | + | 0.144353i | ||||
\(166\) | 175.374 | 1.05647 | ||||||||
\(167\) | 194.552 | + | 194.552i | 1.16498 | + | 1.16498i | 0.983371 | + | 0.181609i | \(0.0581305\pi\) |
0.181609 | + | 0.983371i | \(0.441869\pi\) | |||||||
\(168\) | −27.5255 | + | 27.5255i | −0.163843 | + | 0.163843i | ||||
\(169\) | − | 11.3578i | − | 0.0672057i | ||||||
\(170\) | 134.732 | − | 86.3549i | 0.792541 | − | 0.507970i | ||||
\(171\) | −81.7682 | −0.478177 | ||||||||
\(172\) | 38.1600 | + | 38.1600i | 0.221860 | + | 0.221860i | ||||
\(173\) | −126.996 | + | 126.996i | −0.734081 | + | 0.734081i | −0.971426 | − | 0.237344i | \(-0.923723\pi\) |
0.237344 | + | 0.971426i | \(0.423723\pi\) | |||||||
\(174\) | − | 26.6076i | − | 0.152917i | ||||||
\(175\) | 186.293 | − | 68.9662i | 1.06453 | − | 0.394093i | ||||
\(176\) | 51.4657 | 0.292419 | ||||||||
\(177\) | 77.9757 | + | 77.9757i | 0.440541 | + | 0.440541i | ||||
\(178\) | −65.1773 | + | 65.1773i | −0.366165 | + | 0.366165i | ||||
\(179\) | 281.606i | 1.57322i | 0.617453 | + | 0.786608i | \(0.288165\pi\) | ||||
−0.617453 | + | 0.786608i | \(0.711835\pi\) | |||||||
\(180\) | 16.1884 | + | 25.2574i | 0.0899357 | + | 0.140319i | ||||
\(181\) | −153.271 | −0.846803 | −0.423402 | − | 0.905942i | \(-0.639164\pi\) | ||||
−0.423402 | + | 0.905942i | \(0.639164\pi\) | |||||||
\(182\) | −106.712 | − | 106.712i | −0.586329 | − | 0.586329i | ||||
\(183\) | −128.020 | + | 128.020i | −0.699564 | + | 0.699564i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | −35.2611 | + | 161.146i | −0.190600 | + | 0.871059i | ||||
\(186\) | −27.2602 | −0.146560 | ||||||||
\(187\) | 205.903 | + | 205.903i | 1.10108 | + | 1.10108i | ||||
\(188\) | 113.198 | − | 113.198i | 0.602119 | − | 0.602119i | ||||
\(189\) | − | 41.2883i | − | 0.218457i | ||||||
\(190\) | 188.275 | + | 41.1973i | 0.990921 | + | 0.216828i | ||||
\(191\) | −326.257 | −1.70815 | −0.854076 | − | 0.520148i | \(-0.825877\pi\) | ||||
−0.854076 | + | 0.520148i | \(0.825877\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 113.315 | − | 113.315i | 0.587123 | − | 0.587123i | −0.349728 | − | 0.936851i | \(-0.613726\pi\) |
0.936851 | + | 0.349728i | \(0.113726\pi\) | |||||||
\(194\) | − | 243.867i | − | 1.25704i | ||||||
\(195\) | −97.9186 | + | 62.7598i | −0.502146 | + | 0.321845i | ||||
\(196\) | −28.2760 | −0.144265 | ||||||||
\(197\) | 62.0545 | + | 62.0545i | 0.314997 | + | 0.314997i | 0.846842 | − | 0.531845i | \(-0.178501\pi\) |
−0.531845 | + | 0.846842i | \(0.678501\pi\) | |||||||
\(198\) | −38.5993 | + | 38.5993i | −0.194946 | + | 0.194946i | ||||
\(199\) | 132.815i | 0.667412i | 0.942677 | + | 0.333706i | \(0.108299\pi\) | ||||
−0.942677 | + | 0.333706i | \(0.891701\pi\) | |||||||
\(200\) | −24.5491 | − | 66.3124i | −0.122746 | − | 0.331562i | ||||
\(201\) | 8.51640 | 0.0423702 | ||||||||
\(202\) | −129.221 | − | 129.221i | −0.639705 | − | 0.639705i | ||||
\(203\) | 61.0324 | − | 61.0324i | 0.300652 | − | 0.300652i | ||||
\(204\) | 78.3988i | 0.384308i | ||||||||
\(205\) | −129.659 | − | 202.295i | −0.632481 | − | 0.986804i | ||||
\(206\) | −8.22842 | −0.0399438 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | −37.9850 | + | 37.9850i | −0.182620 | + | 0.182620i | ||||
\(209\) | 350.688i | 1.67793i | ||||||||
\(210\) | −20.8023 | + | 95.0682i | −0.0990587 | + | 0.452706i | ||||
\(211\) | −202.742 | −0.960861 | −0.480430 | − | 0.877033i | \(-0.659520\pi\) | ||||
−0.480430 | + | 0.877033i | \(0.659520\pi\) | |||||||
\(212\) | −81.4734 | − | 81.4734i | −0.384308 | − | 0.384308i | ||||
\(213\) | 111.248 | − | 111.248i | 0.522289 | − | 0.522289i | ||||
\(214\) | 49.5823i | 0.231693i | ||||||||
\(215\) | 131.798 | + | 28.8392i | 0.613012 | + | 0.134136i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −62.5293 | − | 62.5293i | −0.288153 | − | 0.288153i | ||||
\(218\) | −0.116226 | + | 0.116226i | −0.000533145 | + | 0.000533145i | ||||
\(219\) | 16.6870i | 0.0761962i | ||||||||
\(220\) | 108.324 | − | 69.4290i | 0.492382 | − | 0.315587i | ||||
\(221\) | −303.939 | −1.37529 | ||||||||
\(222\) | −57.1433 | − | 57.1433i | −0.257402 | − | 0.257402i | ||||
\(223\) | −11.5319 | + | 11.5319i | −0.0517127 | + | 0.0517127i | −0.732490 | − | 0.680778i | \(-0.761642\pi\) |
0.680778 | + | 0.732490i | \(0.261642\pi\) | |||||||
\(224\) | 44.9490i | 0.200665i | ||||||||
\(225\) | 68.1462 | + | 31.3225i | 0.302872 | + | 0.139211i | ||||
\(226\) | 301.259 | 1.33300 | ||||||||
\(227\) | 163.407 | + | 163.407i | 0.719853 | + | 0.719853i | 0.968575 | − | 0.248722i | \(-0.0800105\pi\) |
−0.248722 | + | 0.968575i | \(0.580011\pi\) | |||||||
\(228\) | −66.7635 | + | 66.7635i | −0.292822 | + | 0.292822i | ||||
\(229\) | 154.404i | 0.674251i | 0.941460 | + | 0.337126i | \(0.109455\pi\) | ||||
−0.941460 | + | 0.337126i | \(0.890545\pi\) | |||||||
\(230\) | −18.2992 | − | 28.5506i | −0.0795618 | − | 0.124133i | ||||
\(231\) | −177.078 | −0.766570 | ||||||||
\(232\) | −21.7250 | − | 21.7250i | −0.0936422 | − | 0.0936422i | ||||
\(233\) | −259.278 | + | 259.278i | −1.11278 | + | 1.11278i | −0.120009 | + | 0.992773i | \(0.538292\pi\) |
−0.992773 | + | 0.120009i | \(0.961708\pi\) | |||||||
\(234\) | − | 56.9775i | − | 0.243494i | ||||||
\(235\) | 85.5493 | − | 390.967i | 0.364039 | − | 1.66369i | ||||
\(236\) | 127.334 | 0.539550 | ||||||||
\(237\) | −126.656 | − | 126.656i | −0.534413 | − | 0.534413i | ||||
\(238\) | −179.831 | + | 179.831i | −0.755592 | + | 0.755592i | ||||
\(239\) | − | 89.5241i | − | 0.374578i | −0.982305 | − | 0.187289i | \(-0.940030\pi\) | ||
0.982305 | − | 0.187289i | \(-0.0599701\pi\) | |||||||
\(240\) | 33.8404 | + | 7.40477i | 0.141001 | + | 0.0308532i | ||||
\(241\) | −153.366 | −0.636373 | −0.318187 | − | 0.948028i | \(-0.603074\pi\) | ||||
−0.318187 | + | 0.948028i | \(0.603074\pi\) | |||||||
\(242\) | 44.5449 | + | 44.5449i | 0.184070 | + | 0.184070i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 209.056i | 0.856788i | ||||||||
\(245\) | −59.5148 | + | 38.1453i | −0.242917 | + | 0.155695i | ||||
\(246\) | 117.713 | 0.478507 | ||||||||
\(247\) | −258.831 | − | 258.831i | −1.04790 | − | 1.04790i | ||||
\(248\) | −22.2578 | + | 22.2578i | −0.0897493 | + | 0.0897493i | ||||
\(249\) | 214.788i | 0.862603i | ||||||||
\(250\) | −141.128 | − | 106.456i | −0.564513 | − | 0.425822i | ||||
\(251\) | −190.513 | −0.759016 | −0.379508 | − | 0.925188i | \(-0.623907\pi\) | ||||
−0.379508 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(252\) | −33.7118 | − | 33.7118i | −0.133777 | − | 0.133777i | ||||
\(253\) | 43.6322 | − | 43.6322i | 0.172459 | − | 0.172459i | ||||
\(254\) | − | 306.905i | − | 1.20829i | ||||||
\(255\) | 105.763 | + | 165.012i | 0.414756 | + | 0.647107i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −116.546 | − | 116.546i | −0.453486 | − | 0.453486i | 0.443024 | − | 0.896510i | \(-0.353906\pi\) |
−0.896510 | + | 0.443024i | \(0.853906\pi\) | |||||||
\(258\) | −46.7362 | + | 46.7362i | −0.181148 | + | 0.181148i | ||||
\(259\) | − | 262.150i | − | 1.01216i | ||||||
\(260\) | −28.7070 | + | 131.193i | −0.110412 | + | 0.504590i | ||||
\(261\) | 32.5875 | 0.124856 | ||||||||
\(262\) | −233.897 | − | 233.897i | −0.892738 | − | 0.892738i | ||||
\(263\) | 267.847 | − | 267.847i | 1.01843 | − | 1.01843i | 0.0186010 | − | 0.999827i | \(-0.494079\pi\) |
0.999827 | − | 0.0186010i | \(-0.00592123\pi\) | |||||||
\(264\) | 63.0323i | 0.238759i | ||||||||
\(265\) | −281.394 | − | 61.5732i | −1.06186 | − | 0.232352i | ||||
\(266\) | −306.284 | −1.15144 | ||||||||
\(267\) | −79.8256 | − | 79.8256i | −0.298972 | − | 0.298972i | ||||
\(268\) | 6.95361 | − | 6.95361i | 0.0259463 | − | 0.0259463i | ||||
\(269\) | − | 161.335i | − | 0.599757i | −0.953977 | − | 0.299879i | \(-0.903054\pi\) | ||
0.953977 | − | 0.299879i | \(-0.0969462\pi\) | |||||||
\(270\) | −30.9338 | + | 19.8267i | −0.114570 | + | 0.0734322i | ||||
\(271\) | 182.280 | 0.672620 | 0.336310 | − | 0.941751i | \(-0.390821\pi\) | ||||
0.336310 | + | 0.941751i | \(0.390821\pi\) | |||||||
\(272\) | 64.0124 | + | 64.0124i | 0.235340 | + | 0.235340i | ||||
\(273\) | 130.695 | − | 130.695i | 0.478736 | − | 0.478736i | ||||
\(274\) | 81.9252i | 0.298997i | ||||||||
\(275\) | 134.336 | − | 292.266i | 0.488495 | − | 1.06278i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | 211.687 | + | 211.687i | 0.764215 | + | 0.764215i | 0.977081 | − | 0.212867i | \(-0.0682800\pi\) |
−0.212867 | + | 0.977081i | \(0.568280\pi\) | |||||||
\(278\) | 148.538 | − | 148.538i | 0.534308 | − | 0.534308i | ||||
\(279\) | − | 33.3868i | − | 0.119666i | ||||||
\(280\) | 60.6378 | + | 94.6079i | 0.216564 | + | 0.337885i | ||||
\(281\) | 195.698 | 0.696433 | 0.348216 | − | 0.937414i | \(-0.386787\pi\) | ||||
0.348216 | + | 0.937414i | \(0.386787\pi\) | |||||||
\(282\) | 138.639 | + | 138.639i | 0.491628 | + | 0.491628i | ||||
\(283\) | 282.722 | − | 282.722i | 0.999016 | − | 0.999016i | −0.000983541 | − | 1.00000i | \(-0.500313\pi\) |
1.00000 | 0.000983541i | \(0.000313071\pi\) | ||||||||
\(284\) | − | 181.667i | − | 0.639671i | ||||||
\(285\) | −50.4562 | + | 230.589i | −0.177039 | + | 0.809083i | ||||
\(286\) | −244.366 | −0.854426 | ||||||||
\(287\) | 270.009 | + | 270.009i | 0.940798 | + | 0.940798i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 223.198i | 0.772311i | ||||||||
\(290\) | −75.0342 | − | 16.4186i | −0.258738 | − | 0.0566158i | ||||
\(291\) | 298.674 | 1.02637 | ||||||||
\(292\) | 13.6249 | + | 13.6249i | 0.0466605 | + | 0.0466605i | ||||
\(293\) | 303.769 | − | 303.769i | 1.03676 | − | 1.03676i | 0.0374575 | − | 0.999298i | \(-0.488074\pi\) |
0.999298 | − | 0.0374575i | \(-0.0119259\pi\) | |||||||
\(294\) | − | 34.6309i | − | 0.117792i | ||||||
\(295\) | 268.010 | − | 171.778i | 0.908508 | − | 0.582298i | ||||
\(296\) | −93.3147 | −0.315252 | ||||||||
\(297\) | −47.2743 | − | 47.2743i | −0.159173 | − | 0.159173i | ||||
\(298\) | −10.9701 | + | 10.9701i | −0.0368125 | + | 0.0368125i | ||||
\(299\) | 64.4067i | 0.215407i | ||||||||
\(300\) | 81.2158 | − | 30.0664i | 0.270719 | − | 0.100221i | ||||
\(301\) | −214.407 | −0.712315 | ||||||||
\(302\) | −109.516 | − | 109.516i | −0.362635 | − | 0.362635i | ||||
\(303\) | 158.262 | − | 158.262i | 0.522317 | − | 0.522317i | ||||
\(304\) | 109.024i | 0.358633i | ||||||||
\(305\) | 282.024 | + | 440.017i | 0.924669 | + | 1.44268i | ||||
\(306\) | −96.0186 | −0.313786 | ||||||||
\(307\) | −381.391 | − | 381.391i | −1.24231 | − | 1.24231i | −0.959038 | − | 0.283276i | \(-0.908579\pi\) |
−0.283276 | − | 0.959038i | \(-0.591421\pi\) | |||||||
\(308\) | −144.583 | + | 144.583i | −0.469426 | + | 0.469426i | ||||
\(309\) | − | 10.0777i | − | 0.0326139i | ||||||
\(310\) | −16.8213 | + | 76.8745i | −0.0542622 | + | 0.247982i | ||||
\(311\) | 34.0026 | 0.109333 | 0.0546666 | − | 0.998505i | \(-0.482590\pi\) | ||||
0.0546666 | + | 0.998505i | \(0.482590\pi\) | |||||||
\(312\) | −46.5220 | − | 46.5220i | −0.149109 | − | 0.149109i | ||||
\(313\) | −62.9469 | + | 62.9469i | −0.201108 | + | 0.201108i | −0.800475 | − | 0.599366i | \(-0.795419\pi\) |
0.599366 | + | 0.800475i | \(0.295419\pi\) | |||||||
\(314\) | 182.784i | 0.582114i | ||||||||
\(315\) | −116.434 | − | 25.4775i | −0.369633 | − | 0.0808811i | ||||
\(316\) | −206.828 | −0.654520 | ||||||||
\(317\) | −144.059 | − | 144.059i | −0.454444 | − | 0.454444i | 0.442383 | − | 0.896826i | \(-0.354133\pi\) |
−0.896826 | + | 0.442383i | \(0.854133\pi\) | |||||||
\(318\) | 99.7841 | − | 99.7841i | 0.313786 | − | 0.313786i | ||||
\(319\) | − | 139.762i | − | 0.438124i | ||||||
\(320\) | 33.6765 | − | 21.5846i | 0.105239 | − | 0.0674518i | ||||
\(321\) | −60.7257 | −0.189177 | ||||||||
\(322\) | 38.1074 | + | 38.1074i | 0.118346 | + | 0.118346i | ||||
\(323\) | −436.181 | + | 436.181i | −1.35041 | + | 1.35041i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 116.562 | + | 314.860i | 0.358653 | + | 0.968800i | ||||
\(326\) | 96.4810 | 0.295954 | ||||||||
\(327\) | −0.142347 | − | 0.142347i | −0.000435311 | − | 0.000435311i | ||||
\(328\) | 96.1120 | − | 96.1120i | 0.293025 | − | 0.293025i | ||||
\(329\) | 636.020i | 1.93319i | ||||||||
\(330\) | 85.0329 | + | 132.669i | 0.257675 | + | 0.402028i | ||||
\(331\) | 133.019 | 0.401871 | 0.200936 | − | 0.979604i | \(-0.435602\pi\) | ||||
0.200936 | + | 0.979604i | \(0.435602\pi\) | |||||||
\(332\) | 175.374 | + | 175.374i | 0.528234 | + | 0.528234i | ||||
\(333\) | 69.9860 | − | 69.9860i | 0.210168 | − | 0.210168i | ||||
\(334\) | 389.103i | 1.16498i | ||||||||
\(335\) | 5.25517 | − | 24.0165i | 0.0156871 | − | 0.0716911i | ||||
\(336\) | −55.0511 | −0.163843 | ||||||||
\(337\) | 221.295 | + | 221.295i | 0.656662 | + | 0.656662i | 0.954589 | − | 0.297926i | \(-0.0962950\pi\) |
−0.297926 | + | 0.954589i | \(0.596295\pi\) | |||||||
\(338\) | 11.3578 | − | 11.3578i | 0.0336028 | − | 0.0336028i | ||||
\(339\) | 368.965i | 1.08839i | ||||||||
\(340\) | 221.087 | + | 48.3771i | 0.650256 | + | 0.142286i | ||||
\(341\) | −143.189 | −0.419910 | ||||||||
\(342\) | −81.7682 | − | 81.7682i | −0.239088 | − | 0.239088i | ||||
\(343\) | −195.877 | + | 195.877i | −0.571069 | + | 0.571069i | ||||
\(344\) | 76.3199i | 0.221860i | ||||||||
\(345\) | 34.9673 | − | 22.4119i | 0.101354 | − | 0.0649619i | ||||
\(346\) | −253.992 | −0.734081 | ||||||||
\(347\) | 5.64579 | + | 5.64579i | 0.0162703 | + | 0.0162703i | 0.715195 | − | 0.698925i | \(-0.246338\pi\) |
−0.698925 | + | 0.715195i | \(0.746338\pi\) | |||||||
\(348\) | 26.6076 | − | 26.6076i | 0.0764586 | − | 0.0764586i | ||||
\(349\) | − | 356.420i | − | 1.02126i | −0.859800 | − | 0.510631i | \(-0.829412\pi\) | ||
0.859800 | − | 0.510631i | \(-0.170588\pi\) | |||||||
\(350\) | 255.259 | + | 117.326i | 0.729311 | + | 0.335218i | ||||
\(351\) | 69.7829 | 0.198812 | ||||||||
\(352\) | 51.4657 | + | 51.4657i | 0.146209 | + | 0.146209i | ||||
\(353\) | 220.393 | − | 220.393i | 0.624341 | − | 0.624341i | −0.322297 | − | 0.946639i | \(-0.604455\pi\) |
0.946639 | + | 0.322297i | \(0.104455\pi\) | |||||||
\(354\) | 155.951i | 0.440541i | ||||||||
\(355\) | −245.075 | − | 382.369i | −0.690351 | − | 1.07709i | ||||
\(356\) | −130.355 | −0.366165 | ||||||||
\(357\) | −220.247 | − | 220.247i | −0.616938 | − | 0.616938i | ||||
\(358\) | −281.606 | + | 281.606i | −0.786608 | + | 0.786608i | ||||
\(359\) | 339.199i | 0.944844i | 0.881373 | + | 0.472422i | \(0.156620\pi\) | ||||
−0.881373 | + | 0.472422i | \(0.843380\pi\) | |||||||
\(360\) | −9.06895 | + | 41.4458i | −0.0251915 | + | 0.115127i | ||||
\(361\) | −381.893 | −1.05788 | ||||||||
\(362\) | −153.271 | − | 153.271i | −0.423402 | − | 0.423402i | ||||
\(363\) | −54.5561 | + | 54.5561i | −0.150292 | + | 0.150292i | ||||
\(364\) | − | 213.424i | − | 0.586329i | ||||||
\(365\) | 47.0578 | + | 10.2969i | 0.128925 | + | 0.0282108i | ||||
\(366\) | −256.040 | −0.699564 | ||||||||
\(367\) | 34.4028 | + | 34.4028i | 0.0937407 | + | 0.0937407i | 0.752422 | − | 0.658681i | \(-0.228885\pi\) |
−0.658681 | + | 0.752422i | \(0.728885\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 144.168i | 0.390699i | ||||||||
\(370\) | −196.407 | + | 125.885i | −0.530830 | + | 0.340229i | ||||
\(371\) | 457.769 | 1.23388 | ||||||||
\(372\) | −27.2602 | − | 27.2602i | −0.0732800 | − | 0.0732800i | ||||
\(373\) | 76.1551 | − | 76.1551i | 0.204169 | − | 0.204169i | −0.597614 | − | 0.801784i | \(-0.703885\pi\) |
0.801784 | + | 0.597614i | \(0.203885\pi\) | |||||||
\(374\) | 411.805i | 1.10108i | ||||||||
\(375\) | 130.381 | − | 172.846i | 0.347682 | − | 0.460923i | ||||
\(376\) | 226.397 | 0.602119 | ||||||||
\(377\) | 103.153 | + | 103.153i | 0.273616 | + | 0.273616i | ||||
\(378\) | 41.2883 | − | 41.2883i | 0.109228 | − | 0.109228i | ||||
\(379\) | − | 101.960i | − | 0.269024i | −0.990912 | − | 0.134512i | \(-0.957053\pi\) | ||
0.990912 | − | 0.134512i | \(-0.0429468\pi\) | |||||||
\(380\) | 147.078 | + | 229.472i | 0.387046 | + | 0.603874i | ||||
\(381\) | 375.880 | 0.986562 | ||||||||
\(382\) | −326.257 | − | 326.257i | −0.854076 | − | 0.854076i | ||||
\(383\) | 523.069 | − | 523.069i | 1.36572 | − | 1.36572i | 0.499267 | − | 0.866448i | \(-0.333603\pi\) |
0.866448 | − | 0.499267i | \(-0.166397\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −109.268 | + | 499.364i | −0.283814 | + | 1.29705i | ||||
\(386\) | 226.630 | 0.587123 | ||||||||
\(387\) | −57.2400 | − | 57.2400i | −0.147907 | − | 0.147907i | ||||
\(388\) | 243.867 | − | 243.867i | 0.628522 | − | 0.628522i | ||||
\(389\) | 8.10447i | 0.0208341i | 0.999946 | + | 0.0104171i | \(0.00331591\pi\) | ||||
−0.999946 | + | 0.0104171i | \(0.996684\pi\) | |||||||
\(390\) | −160.678 | − | 35.1588i | −0.411996 | − | 0.0901507i | ||||
\(391\) | 108.538 | 0.277591 | ||||||||
\(392\) | −28.2760 | − | 28.2760i | −0.0721326 | − | 0.0721326i | ||||
\(393\) | 286.465 | − | 286.465i | 0.728917 | − | 0.728917i | ||||
\(394\) | 124.109i | 0.314997i | ||||||||
\(395\) | −435.328 | + | 279.019i | −1.10210 | + | 0.706376i | ||||
\(396\) | −77.1985 | −0.194946 | ||||||||
\(397\) | −46.7570 | − | 46.7570i | −0.117776 | − | 0.117776i | 0.645763 | − | 0.763538i | \(-0.276540\pi\) |
−0.763538 | + | 0.645763i | \(0.776540\pi\) | |||||||
\(398\) | −132.815 | + | 132.815i | −0.333706 | + | 0.333706i | ||||
\(399\) | − | 375.119i | − | 0.940148i | ||||||
\(400\) | 41.7633 | − | 90.8616i | 0.104408 | − | 0.227154i | ||||
\(401\) | 212.655 | 0.530311 | 0.265156 | − | 0.964206i | \(-0.414577\pi\) | ||||
0.265156 | + | 0.964206i | \(0.414577\pi\) | |||||||
\(402\) | 8.51640 | + | 8.51640i | 0.0211851 | + | 0.0211851i | ||||
\(403\) | 105.683 | − | 105.683i | 0.262241 | − | 0.262241i | ||||
\(404\) | − | 258.441i | − | 0.639705i | ||||||
\(405\) | −24.2826 | − | 37.8861i | −0.0599571 | − | 0.0935458i | ||||
\(406\) | 122.065 | 0.300652 | ||||||||
\(407\) | −300.156 | − | 300.156i | −0.737485 | − | 0.737485i | ||||
\(408\) | −78.3988 | + | 78.3988i | −0.192154 | + | 0.192154i | ||||
\(409\) | 201.150i | 0.491810i | 0.969294 | + | 0.245905i | \(0.0790852\pi\) | ||||
−0.969294 | + | 0.245905i | \(0.920915\pi\) | |||||||
\(410\) | 72.6363 | − | 331.953i | 0.177162 | − | 0.809642i | ||||
\(411\) | −100.337 | −0.244130 | ||||||||
\(412\) | −8.22842 | − | 8.22842i | −0.0199719 | − | 0.0199719i | ||||
\(413\) | −357.721 | + | 357.721i | −0.866152 | + | 0.866152i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 605.709 | + | 132.538i | 1.45954 | + | 0.319369i | ||||
\(416\) | −75.9700 | −0.182620 | ||||||||
\(417\) | 181.921 | + | 181.921i | 0.436260 | + | 0.436260i | ||||
\(418\) | −350.688 | + | 350.688i | −0.838967 | + | 0.838967i | ||||
\(419\) | − | 284.817i | − | 0.679753i | −0.940470 | − | 0.339877i | \(-0.889615\pi\) | ||
0.940470 | − | 0.339877i | \(-0.110385\pi\) | |||||||
\(420\) | −115.871 | + | 74.2659i | −0.275882 | + | 0.176824i | ||||
\(421\) | −162.868 | −0.386860 | −0.193430 | − | 0.981114i | \(-0.561961\pi\) | ||||
−0.193430 | + | 0.981114i | \(0.561961\pi\) | |||||||
\(422\) | −202.742 | − | 202.742i | −0.480430 | − | 0.480430i | ||||
\(423\) | −169.798 | + | 169.798i | −0.401413 | + | 0.401413i | ||||
\(424\) | − | 162.947i | − | 0.384308i | ||||||
\(425\) | 530.602 | − | 196.431i | 1.24848 | − | 0.462190i | ||||
\(426\) | 222.495 | 0.522289 | ||||||||
\(427\) | −587.305 | − | 587.305i | −1.37542 | − | 1.37542i | ||||
\(428\) | −49.5823 | + | 49.5823i | −0.115847 | + | 0.115847i | ||||
\(429\) | − | 299.286i | − | 0.697636i | ||||||
\(430\) | 102.958 | + | 160.637i | 0.239438 | + | 0.373574i | ||||
\(431\) | 740.079 | 1.71712 | 0.858561 | − | 0.512712i | \(-0.171359\pi\) | ||||
0.858561 | + | 0.512712i | \(0.171359\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 542.660 | − | 542.660i | 1.25326 | − | 1.25326i | 0.299003 | − | 0.954252i | \(-0.403346\pi\) |
0.954252 | − | 0.299003i | \(-0.0966541\pi\) | |||||||
\(434\) | − | 125.059i | − | 0.288153i | ||||||
\(435\) | 20.1086 | − | 91.8977i | 0.0462266 | − | 0.211259i | ||||
\(436\) | −0.232451 | −0.000533145 | ||||||||
\(437\) | 92.4298 | + | 92.4298i | 0.211510 | + | 0.211510i | ||||
\(438\) | −16.6870 | + | 16.6870i | −0.0380981 | + | 0.0380981i | ||||
\(439\) | 484.445i | 1.10352i | 0.834003 | + | 0.551760i | \(0.186043\pi\) | ||||
−0.834003 | + | 0.551760i | \(0.813957\pi\) | |||||||
\(440\) | 177.753 | + | 38.8950i | 0.403984 | + | 0.0883977i | ||||
\(441\) | 42.4140 | 0.0961768 | ||||||||
\(442\) | −303.939 | − | 303.939i | −0.687645 | − | 0.687645i | ||||
\(443\) | 526.218 | − | 526.218i | 1.18785 | − | 1.18785i | 0.210190 | − | 0.977661i | \(-0.432592\pi\) |
0.977661 | − | 0.210190i | \(-0.0674082\pi\) | |||||||
\(444\) | − | 114.287i | − | 0.257402i | ||||||
\(445\) | −274.368 | + | 175.853i | −0.616557 | + | 0.395175i | ||||
\(446\) | −23.0638 | −0.0517127 | ||||||||
\(447\) | −13.4356 | − | 13.4356i | −0.0300572 | − | 0.0300572i | ||||
\(448\) | −44.9490 | + | 44.9490i | −0.100333 | + | 0.100333i | ||||
\(449\) | − | 620.540i | − | 1.38205i | −0.722831 | − | 0.691025i | \(-0.757160\pi\) | ||
0.722831 | − | 0.691025i | \(-0.242840\pi\) | |||||||
\(450\) | 36.8237 | + | 99.4687i | 0.0818304 | + | 0.221041i | ||||
\(451\) | 618.309 | 1.37097 | ||||||||
\(452\) | 301.259 | + | 301.259i | 0.666502 | + | 0.666502i | ||||
\(453\) | 134.129 | − | 134.129i | 0.296090 | − | 0.296090i | ||||
\(454\) | 326.813i | 0.719853i | ||||||||
\(455\) | −287.916 | − | 449.210i | −0.632783 | − | 0.987275i | ||||
\(456\) | −133.527 | −0.292822 | ||||||||
\(457\) | −2.93906 | − | 2.93906i | −0.00643119 | − | 0.00643119i | 0.703884 | − | 0.710315i | \(-0.251448\pi\) |
−0.710315 | + | 0.703884i | \(0.751448\pi\) | |||||||
\(458\) | −154.404 | + | 154.404i | −0.337126 | + | 0.337126i | ||||
\(459\) | − | 117.598i | − | 0.256205i | ||||||
\(460\) | 10.2514 | − | 46.8498i | 0.0222857 | − | 0.101847i | ||||
\(461\) | 336.573 | 0.730093 | 0.365046 | − | 0.930989i | \(-0.381053\pi\) | ||||
0.365046 | + | 0.930989i | \(0.381053\pi\) | |||||||
\(462\) | −177.078 | − | 177.078i | −0.383285 | − | 0.383285i | ||||
\(463\) | −592.717 | + | 592.717i | −1.28017 | + | 1.28017i | −0.339595 | + | 0.940572i | \(0.610290\pi\) |
−0.940572 | + | 0.339595i | \(0.889710\pi\) | |||||||
\(464\) | − | 43.4500i | − | 0.0936422i | ||||||
\(465\) | −94.1516 | − | 20.6018i | −0.202477 | − | 0.0443049i | ||||
\(466\) | −518.556 | −1.11278 | ||||||||
\(467\) | −352.885 | − | 352.885i | −0.755642 | − | 0.755642i | 0.219884 | − | 0.975526i | \(-0.429432\pi\) |
−0.975526 | + | 0.219884i | \(0.929432\pi\) | |||||||
\(468\) | 56.9775 | − | 56.9775i | 0.121747 | − | 0.121747i | ||||
\(469\) | 39.0698i | 0.0833044i | ||||||||
\(470\) | 476.516 | − | 305.417i | 1.01386 | − | 0.649824i | ||||
\(471\) | −223.864 | −0.475294 | ||||||||
\(472\) | 127.334 | + | 127.334i | 0.269775 | + | 0.269775i | ||||
\(473\) | −245.491 | + | 245.491i | −0.519009 | + | 0.519009i | ||||
\(474\) | − | 253.312i | − | 0.534413i | ||||||
\(475\) | 619.132 | + | 284.576i | 1.30344 | + | 0.599107i | ||||
\(476\) | −359.662 | −0.755592 | ||||||||
\(477\) | 122.210 | + | 122.210i | 0.256206 | + | 0.256206i | ||||
\(478\) | 89.5241 | − | 89.5241i | 0.187289 | − | 0.187289i | ||||
\(479\) | 160.749i | 0.335593i | 0.985822 | + | 0.167797i | \(0.0536652\pi\) | ||||
−0.985822 | + | 0.167797i | \(0.946335\pi\) | |||||||
\(480\) | 26.4356 | + | 41.2451i | 0.0550741 | + | 0.0859273i | ||||
\(481\) | 443.070 | 0.921143 | ||||||||
\(482\) | −153.366 | − | 153.366i | −0.318187 | − | 0.318187i | ||||
\(483\) | −46.6718 | + | 46.6718i | −0.0966291 | + | 0.0966291i | ||||
\(484\) | 89.0897i | 0.184070i | ||||||||
\(485\) | 184.301 | − | 842.270i | 0.380002 | − | 1.73664i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −212.553 | − | 212.553i | −0.436454 | − | 0.436454i | 0.454363 | − | 0.890817i | \(-0.349867\pi\) |
−0.890817 | + | 0.454363i | \(0.849867\pi\) | |||||||
\(488\) | −209.056 | + | 209.056i | −0.428394 | + | 0.428394i | ||||
\(489\) | 118.165i | 0.241645i | ||||||||
\(490\) | −97.6601 | − | 21.3695i | −0.199306 | − | 0.0436111i | ||||
\(491\) | −399.924 | −0.814510 | −0.407255 | − | 0.913314i | \(-0.633514\pi\) | ||||
−0.407255 | + | 0.913314i | \(0.633514\pi\) | |||||||
\(492\) | 117.713 | + | 117.713i | 0.239254 | + | 0.239254i | ||||
\(493\) | 173.834 | − | 173.834i | 0.352604 | − | 0.352604i | ||||
\(494\) | − | 517.661i | − | 1.04790i | ||||||
\(495\) | −162.486 | + | 104.144i | −0.328255 | + | 0.210391i | ||||
\(496\) | −44.5157 | −0.0897493 | ||||||||
\(497\) | 510.359 | + | 510.359i | 1.02688 | + | 1.02688i | ||||
\(498\) | −214.788 | + | 214.788i | −0.431301 | + | 0.431301i | ||||
\(499\) | 284.551i | 0.570242i | 0.958492 | + | 0.285121i | \(0.0920338\pi\) | ||||
−0.958492 | + | 0.285121i | \(0.907966\pi\) | |||||||
\(500\) | −34.6728 | − | 247.584i | −0.0693456 | − | 0.495168i | ||||
\(501\) | −476.552 | −0.951202 | ||||||||
\(502\) | −190.513 | − | 190.513i | −0.379508 | − | 0.379508i | ||||
\(503\) | −123.416 | + | 123.416i | −0.245359 | + | 0.245359i | −0.819063 | − | 0.573704i | \(-0.805506\pi\) |
0.573704 | + | 0.819063i | \(0.305506\pi\) | |||||||
\(504\) | − | 67.4236i | − | 0.133777i | ||||||
\(505\) | −348.646 | − | 543.962i | −0.690388 | − | 1.07715i | ||||
\(506\) | 87.2643 | 0.172459 | ||||||||
\(507\) | 13.9104 | + | 13.9104i | 0.0274366 | + | 0.0274366i | ||||
\(508\) | 306.905 | − | 306.905i | 0.604143 | − | 0.604143i | ||||
\(509\) | 501.577i | 0.985416i | 0.870195 | + | 0.492708i | \(0.163993\pi\) | ||||
−0.870195 | + | 0.492708i | \(0.836007\pi\) | |||||||
\(510\) | −59.2496 | + | 270.775i | −0.116176 | + | 0.530932i | ||||
\(511\) | −76.5530 | −0.149810 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 100.145 | − | 100.145i | 0.195215 | − | 0.195215i | ||||
\(514\) | − | 233.092i | − | 0.453486i | ||||||
\(515\) | −28.4194 | − | 6.21859i | −0.0551834 | − | 0.0120749i | ||||
\(516\) | −93.4724 | −0.181148 | ||||||||
\(517\) | 728.230 | + | 728.230i | 1.40857 | + | 1.40857i | ||||
\(518\) | 262.150 | − | 262.150i | 0.506082 | − | 0.506082i | ||||
\(519\) | − | 311.076i | − | 0.599375i | ||||||
\(520\) | −159.900 | + | 102.486i | −0.307501 | + | 0.197089i | ||||
\(521\) | −622.530 | −1.19488 | −0.597438 | − | 0.801915i | \(-0.703814\pi\) | ||||
−0.597438 | + | 0.801915i | \(0.703814\pi\) | |||||||
\(522\) | 32.5875 | + | 32.5875i | 0.0624282 | + | 0.0624282i | ||||
\(523\) | −271.805 | + | 271.805i | −0.519703 | + | 0.519703i | −0.917481 | − | 0.397779i | \(-0.869781\pi\) |
0.397779 | + | 0.917481i | \(0.369781\pi\) | |||||||
\(524\) | − | 467.795i | − | 0.892738i | ||||||
\(525\) | −143.695 | + | 312.627i | −0.273704 | + | 0.595480i | ||||
\(526\) | 535.693 | 1.01843 | ||||||||
\(527\) | −178.097 | − | 178.097i | −0.337945 | − | 0.337945i | ||||
\(528\) | −63.0323 | + | 63.0323i | −0.119379 | + | 0.119379i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −219.821 | − | 342.967i | −0.414756 | − | 0.647108i | ||||
\(531\) | −191.001 | −0.359700 | ||||||||
\(532\) | −306.284 | − | 306.284i | −0.575721 | − | 0.575721i | ||||
\(533\) | −456.352 | + | 456.352i | −0.856196 | + | 0.856196i | ||||
\(534\) | − | 159.651i | − | 0.298972i | ||||||
\(535\) | −37.4716 | + | 171.248i | −0.0700404 | + | 0.320090i | ||||
\(536\) | 13.9072 | 0.0259463 | ||||||||
\(537\) | −344.895 | − | 344.895i | −0.642263 | − | 0.642263i | ||||
\(538\) | 161.335 | − | 161.335i | 0.299879 | − | 0.299879i | ||||
\(539\) | − | 181.905i | − | 0.337487i | ||||||
\(540\) | −50.7605 | − | 11.1072i | −0.0940010 | − | 0.0205688i | ||||
\(541\) | 1017.17 | 1.88017 | 0.940085 | − | 0.340940i | \(-0.110745\pi\) | ||||
0.940085 | + | 0.340940i | \(0.110745\pi\) | |||||||
\(542\) | 182.280 | + | 182.280i | 0.336310 | + | 0.336310i | ||||
\(543\) | 187.718 | − | 187.718i | 0.345706 | − | 0.345706i | ||||
\(544\) | 128.025i | 0.235340i | ||||||||
\(545\) | −0.489259 | + | 0.313585i | −0.000897722 | + | 0.000575385i | ||||
\(546\) | 261.390 | 0.478736 | ||||||||
\(547\) | −533.088 | − | 533.088i | −0.974567 | − | 0.974567i | 0.0251176 | − | 0.999685i | \(-0.492004\pi\) |
−0.999685 | + | 0.0251176i | \(0.992004\pi\) | |||||||
\(548\) | −81.9252 | + | 81.9252i | −0.149498 | + | 0.149498i | ||||
\(549\) | − | 313.584i | − | 0.571192i | ||||||
\(550\) | 426.602 | − | 157.930i | 0.775640 | − | 0.287145i | ||||
\(551\) | 296.069 | 0.537330 | ||||||||
\(552\) | 16.6132 | + | 16.6132i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | 581.046 | − | 581.046i | 1.05072 | − | 1.05072i | ||||
\(554\) | 423.375i | 0.764215i | ||||||||
\(555\) | −154.177 | − | 240.548i | −0.277796 | − | 0.433421i | ||||
\(556\) | 297.075 | 0.534308 | ||||||||
\(557\) | −359.466 | − | 359.466i | −0.645361 | − | 0.645361i | 0.306507 | − | 0.951868i | \(-0.400840\pi\) |
−0.951868 | + | 0.306507i | \(0.900840\pi\) | |||||||
\(558\) | 33.3868 | − | 33.3868i | 0.0598329 | − | 0.0598329i | ||||
\(559\) | − | 362.377i | − | 0.648259i | ||||||
\(560\) | −33.9701 | + | 155.246i | −0.0606608 | + | 0.277224i | ||||
\(561\) | −504.356 | −0.899031 | ||||||||
\(562\) | 195.698 | + | 195.698i | 0.348216 | + | 0.348216i | ||||
\(563\) | −342.658 | + | 342.658i | −0.608628 | + | 0.608628i | −0.942587 | − | 0.333959i | \(-0.891615\pi\) |
0.333959 | + | 0.942587i | \(0.391615\pi\) | |||||||
\(564\) | 277.278i | 0.491628i | ||||||||
\(565\) | 1040.49 | + | 227.675i | 1.84158 | + | 0.402965i | ||||
\(566\) | 565.443 | 0.999016 | ||||||||
\(567\) | 50.5677 | + | 50.5677i | 0.0891846 | + | 0.0891846i | ||||
\(568\) | 181.667 | − | 181.667i | 0.319836 | − | 0.319836i | ||||
\(569\) | 236.879i | 0.416307i | 0.978096 | + | 0.208154i | \(0.0667454\pi\) | ||||
−0.978096 | + | 0.208154i | \(0.933255\pi\) | |||||||
\(570\) | −281.045 | + | 180.133i | −0.493061 | + | 0.316022i | ||||
\(571\) | 402.396 | 0.704722 | 0.352361 | − | 0.935864i | \(-0.385379\pi\) | ||||
0.352361 | + | 0.935864i | \(0.385379\pi\) | |||||||
\(572\) | −244.366 | − | 244.366i | −0.427213 | − | 0.427213i | ||||
\(573\) | 399.582 | − | 399.582i | 0.697350 | − | 0.697350i | ||||
\(574\) | 540.018i | 0.940798i | ||||||||
\(575\) | −41.6251 | − | 112.438i | −0.0723914 | − | 0.195545i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 255.514 | + | 255.514i | 0.442832 | + | 0.442832i | 0.892963 | − | 0.450131i | \(-0.148623\pi\) |
−0.450131 | + | 0.892963i | \(0.648623\pi\) | |||||||
\(578\) | −223.198 | + | 223.198i | −0.386156 | + | 0.386156i | ||||
\(579\) | 277.564i | 0.479384i | ||||||||
\(580\) | −58.6156 | − | 91.4527i | −0.101061 | − | 0.157677i | ||||
\(581\) | −985.360 | −1.69597 | ||||||||
\(582\) | 298.674 | + | 298.674i | 0.513186 | + | 0.513186i | ||||
\(583\) | 524.135 | − | 524.135i | 0.899032 | − | 0.899032i | ||||
\(584\) | 27.2497i | 0.0466605i | ||||||||
\(585\) | 43.0605 | − | 196.790i | 0.0736078 | − | 0.336393i | ||||
\(586\) | 607.539 | 1.03676 | ||||||||
\(587\) | 533.089 | + | 533.089i | 0.908158 | + | 0.908158i | 0.996124 | − | 0.0879655i | \(-0.0280365\pi\) |
−0.0879655 | + | 0.996124i | \(0.528037\pi\) | |||||||
\(588\) | 34.6309 | − | 34.6309i | 0.0588960 | − | 0.0588960i | ||||
\(589\) | − | 303.331i | − | 0.514992i | ||||||
\(590\) | 439.788 | + | 96.2320i | 0.745403 | + | 0.163105i | ||||
\(591\) | −152.002 | −0.257194 | ||||||||
\(592\) | −93.3147 | − | 93.3147i | −0.157626 | − | 0.157626i | ||||
\(593\) | 433.233 | − | 433.233i | 0.730579 | − | 0.730579i | −0.240156 | − | 0.970734i | \(-0.577199\pi\) |
0.970734 | + | 0.240156i | \(0.0771985\pi\) | |||||||
\(594\) | − | 94.5485i | − | 0.159173i | ||||||
\(595\) | −757.009 | + | 485.196i | −1.27228 | + | 0.815456i | ||||
\(596\) | −21.9402 | −0.0368125 | ||||||||
\(597\) | −162.664 | − | 162.664i | −0.272470 | − | 0.272470i | ||||
\(598\) | −64.4067 | + | 64.4067i | −0.107704 | + | 0.107704i | ||||
\(599\) | 111.533i | 0.186198i | 0.995657 | + | 0.0930989i | \(0.0296773\pi\) | ||||
−0.995657 | + | 0.0930989i | \(0.970323\pi\) | |||||||
\(600\) | 111.282 | + | 51.1494i | 0.185470 | + | 0.0852490i | ||||
\(601\) | 523.677 | 0.871343 | 0.435671 | − | 0.900106i | \(-0.356511\pi\) | ||||
0.435671 | + | 0.900106i | \(0.356511\pi\) | |||||||
\(602\) | −214.407 | − | 214.407i | −0.356157 | − | 0.356157i | ||||
\(603\) | −10.4304 | + | 10.4304i | −0.0172975 | + | 0.0172975i | ||||
\(604\) | − | 219.031i | − | 0.362635i | ||||||
\(605\) | 120.185 | + | 187.514i | 0.198653 | + | 0.309941i | ||||
\(606\) | 316.524 | 0.522317 | ||||||||
\(607\) | 3.99156 | + | 3.99156i | 0.00657588 | + | 0.00657588i | 0.710387 | − | 0.703811i | \(-0.248520\pi\) |
−0.703811 | + | 0.710387i | \(0.748520\pi\) | |||||||
\(608\) | −109.024 | + | 109.024i | −0.179316 | + | 0.179316i | ||||
\(609\) | 149.498i | 0.245481i | ||||||||
\(610\) | −157.993 | + | 722.042i | −0.259005 | + | 1.18367i | ||||
\(611\) | −1074.96 | −1.75935 | ||||||||
\(612\) | −96.0186 | − | 96.0186i | −0.156893 | − | 0.156893i | ||||
\(613\) | 87.2893 | − | 87.2893i | 0.142397 | − | 0.142397i | −0.632315 | − | 0.774712i | \(-0.717895\pi\) |
0.774712 | + | 0.632315i | \(0.217895\pi\) | |||||||
\(614\) | − | 762.781i | − | 1.24231i | ||||||
\(615\) | 406.558 | + | 88.9609i | 0.661070 | + | 0.144652i | ||||
\(616\) | −289.167 | −0.469426 | ||||||||
\(617\) | −416.059 | − | 416.059i | −0.674325 | − | 0.674325i | 0.284385 | − | 0.958710i | \(-0.408211\pi\) |
−0.958710 | + | 0.284385i | \(0.908211\pi\) | |||||||
\(618\) | 10.0777 | − | 10.0777i | 0.0163070 | − | 0.0163070i | ||||
\(619\) | − | 248.948i | − | 0.402178i | −0.979573 | − | 0.201089i | \(-0.935552\pi\) | ||
0.979573 | − | 0.201089i | \(-0.0644480\pi\) | |||||||
\(620\) | −93.6957 | + | 60.0532i | −0.151122 | + | 0.0968600i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | 34.0026 | + | 34.0026i | 0.0546666 | + | 0.0546666i | ||||
\(623\) | 366.207 | − | 366.207i | 0.587812 | − | 0.587812i | ||||
\(624\) | − | 93.0439i | − | 0.149109i | ||||||
\(625\) | −406.978 | − | 474.335i | −0.651165 | − | 0.758936i | ||||
\(626\) | −125.894 | −0.201108 | ||||||||
\(627\) | −429.504 | − | 429.504i | −0.685014 | − | 0.685014i | ||||
\(628\) | −182.784 | + | 182.784i | −0.291057 | + | 0.291057i | ||||
\(629\) | − | 746.662i | − | 1.18706i | ||||||
\(630\) | −90.9567 | − | 141.912i | −0.144376 | − | 0.225257i | ||||
\(631\) | 470.788 | 0.746098 | 0.373049 | − | 0.927812i | \(-0.378312\pi\) | ||||
0.373049 | + | 0.927812i | \(0.378312\pi\) | |||||||
\(632\) | −206.828 | − | 206.828i | −0.327260 | − | 0.327260i | ||||
\(633\) | 248.307 | − | 248.307i | 0.392270 | − | 0.392270i | ||||
\(634\) | − | 288.117i | − | 0.454444i | ||||||
\(635\) | 231.942 | − | 1059.99i | 0.365263 | − | 1.66928i | ||||
\(636\) | 199.568 | 0.313786 | ||||||||
\(637\) | 134.258 | + | 134.258i | 0.210766 | + | 0.210766i | ||||
\(638\) | 139.762 | − | 139.762i | 0.219062 | − | 0.219062i | ||||
\(639\) | 272.500i | 0.426448i | ||||||||
\(640\) | 55.2611 | + | 12.0919i | 0.0863454 | + | 0.0188936i | ||||
\(641\) | 1011.49 | 1.57799 | 0.788995 | − | 0.614400i | \(-0.210602\pi\) | ||||
0.788995 | + | 0.614400i | \(0.210602\pi\) | |||||||
\(642\) | −60.7257 | − | 60.7257i | −0.0945883 | − | 0.0945883i | ||||
\(643\) | −422.128 | + | 422.128i | −0.656498 | + | 0.656498i | −0.954550 | − | 0.298052i | \(-0.903663\pi\) |
0.298052 | + | 0.954550i | \(0.403663\pi\) | |||||||
\(644\) | 76.2148i | 0.118346i | ||||||||
\(645\) | −196.739 | + | 126.098i | −0.305022 | + | 0.195500i | ||||
\(646\) | −872.363 | −1.35041 | ||||||||
\(647\) | 482.452 | + | 482.452i | 0.745675 | + | 0.745675i | 0.973664 | − | 0.227989i | \(-0.0732149\pi\) |
−0.227989 | + | 0.973664i | \(0.573215\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 819.165i | 1.26220i | ||||||||
\(650\) | −198.298 | + | 431.422i | −0.305073 | + | 0.663727i | ||||
\(651\) | 153.165 | 0.235276 | ||||||||
\(652\) | 96.4810 | + | 96.4810i | 0.147977 | + | 0.147977i | ||||
\(653\) | 455.524 | − | 455.524i | 0.697586 | − | 0.697586i | −0.266303 | − | 0.963889i | \(-0.585802\pi\) |
0.963889 | + | 0.266303i | \(0.0858022\pi\) | |||||||
\(654\) | − | 0.284693i | − | 0.000435311i | ||||||
\(655\) | −631.071 | − | 984.605i | −0.963468 | − | 1.50321i | ||||
\(656\) | 192.224 | 0.293025 | ||||||||
\(657\) | −20.4373 | − | 20.4373i | −0.0311070 | − | 0.0311070i | ||||
\(658\) | −636.020 | + | 636.020i | −0.966596 | + | 0.966596i | ||||
\(659\) | 81.7349i | 0.124029i | 0.998075 | + | 0.0620143i | \(0.0197525\pi\) | ||||
−0.998075 | + | 0.0620143i | \(0.980248\pi\) | |||||||
\(660\) | −47.6364 | + | 217.702i | −0.0721764 | + | 0.329852i | ||||
\(661\) | −137.438 | −0.207925 | −0.103962 | − | 0.994581i | \(-0.533152\pi\) | ||||
−0.103962 | + | 0.994581i | \(0.533152\pi\) | |||||||
\(662\) | 133.019 | + | 133.019i | 0.200936 | + | 0.200936i | ||||
\(663\) | 372.248 | − | 372.248i | 0.561459 | − | 0.561459i | ||||
\(664\) | 350.747i | 0.528234i | ||||||||
\(665\) | −1057.85 | − | 231.473i | −1.59075 | − | 0.348079i | ||||
\(666\) | 139.972 | 0.210168 | ||||||||
\(667\) | −36.8365 | − | 36.8365i | −0.0552272 | − | 0.0552272i | ||||
\(668\) | −389.103 | + | 389.103i | −0.582490 | + | 0.582490i | ||||
\(669\) | − | 28.2473i | − | 0.0422232i | ||||||
\(670\) | 29.2717 | − | 18.7613i | 0.0436891 | − | 0.0280020i | ||||
\(671\) | −1344.90 | −2.00433 | ||||||||
\(672\) | −55.0511 | − | 55.0511i | −0.0819213 | − | 0.0819213i | ||||
\(673\) | −363.220 | + | 363.220i | −0.539702 | + | 0.539702i | −0.923441 | − | 0.383739i | \(-0.874636\pi\) |
0.383739 | + | 0.923441i | \(0.374636\pi\) | |||||||
\(674\) | 442.591i | 0.656662i | ||||||||
\(675\) | −121.824 | + | 45.0996i | −0.180480 | + | 0.0668142i | ||||
\(676\) | 22.7155 | 0.0336028 | ||||||||
\(677\) | 202.715 | + | 202.715i | 0.299431 | + | 0.299431i | 0.840791 | − | 0.541360i | \(-0.182090\pi\) |
−0.541360 | + | 0.840791i | \(0.682090\pi\) | |||||||
\(678\) | −368.965 | + | 368.965i | −0.544197 | + | 0.544197i | ||||
\(679\) | 1370.20i | 2.01796i | ||||||||
\(680\) | 172.710 | + | 269.464i | 0.253985 | + | 0.396271i | ||||
\(681\) | −400.263 | −0.587758 | ||||||||
\(682\) | −143.189 | − | 143.189i | −0.209955 | − | 0.209955i | ||||
\(683\) | −496.960 | + | 496.960i | −0.727614 | + | 0.727614i | −0.970144 | − | 0.242530i | \(-0.922023\pi\) |
0.242530 | + | 0.970144i | \(0.422023\pi\) | |||||||
\(684\) | − | 163.536i | − | 0.239088i | ||||||
\(685\) | −61.9146 | + | 282.954i | −0.0903863 | + | 0.413072i | ||||
\(686\) | −391.753 | −0.571069 | ||||||||
\(687\) | −189.105 | − | 189.105i | −0.275262 | − | 0.275262i | ||||
\(688\) | −76.3199 | + | 76.3199i | −0.110930 | + | 0.110930i | ||||
\(689\) | 773.692i | 1.12292i | ||||||||
\(690\) | 57.3791 | + | 12.5554i | 0.0831581 | + | 0.0181962i | ||||
\(691\) | 708.102 | 1.02475 | 0.512375 | − | 0.858762i | \(-0.328766\pi\) | ||||
0.512375 | + | 0.858762i | \(0.328766\pi\) | |||||||
\(692\) | −253.992 | − | 253.992i | −0.367041 | − | 0.367041i | ||||
\(693\) | 216.875 | − | 216.875i | 0.312951 | − | 0.312951i | ||||
\(694\) | 11.2916i | 0.0162703i | ||||||||
\(695\) | 625.278 | − | 400.765i | 0.899681 | − | 0.576640i | ||||
\(696\) | 53.2152 | 0.0764586 | ||||||||
\(697\) | 769.045 | + | 769.045i | 1.10336 | + | 1.10336i | ||||
\(698\) | 356.420 | − | 356.420i | 0.510631 | − | 0.510631i | ||||
\(699\) | − | 635.099i | − | 0.908583i | ||||||
\(700\) | 137.932 | + | 372.585i | 0.197046 | + | 0.532264i | ||||
\(701\) | −282.940 | −0.403624 | −0.201812 | − | 0.979424i | \(-0.564683\pi\) | ||||
−0.201812 | + | 0.979424i | \(0.564683\pi\) | |||||||
\(702\) | 69.7829 | + | 69.7829i | 0.0994059 | + | 0.0994059i | ||||
\(703\) | 635.848 | − | 635.848i | 0.904478 | − | 0.904478i | ||||
\(704\) | 102.931i | 0.146209i | ||||||||
\(705\) | 374.058 | + | 583.610i | 0.530579 | + | 0.827816i | ||||
\(706\) | 440.785 | 0.624341 | ||||||||
\(707\) | 726.042 | + | 726.042i | 1.02693 | + | 1.02693i | ||||
\(708\) | −155.951 | + | 155.951i | −0.220270 | + | 0.220270i | ||||
\(709\) | 348.639i | 0.491733i | 0.969304 | + | 0.245867i | \(0.0790725\pi\) | ||||
−0.969304 | + | 0.245867i | \(0.920927\pi\) | |||||||
\(710\) | 137.294 | − | 627.443i | 0.193372 | − | 0.883723i | ||||
\(711\) | 310.242 | 0.436347 | ||||||||
\(712\) | −130.355 | − | 130.355i | −0.183082 | − | 0.183082i | ||||
\(713\) | −37.7400 | + | 37.7400i | −0.0529313 | + | 0.0529313i | ||||
\(714\) | − | 440.494i | − | 0.616938i | ||||||
\(715\) | −843.994 | − | 184.678i | −1.18041 | − | 0.258291i | ||||
\(716\) | −563.211 | −0.786608 | ||||||||
\(717\) | 109.644 | + | 109.644i | 0.152921 | + | 0.152921i | ||||
\(718\) | −339.199 | + | 339.199i | −0.472422 | + | 0.472422i | ||||
\(719\) | − | 692.400i | − | 0.963003i | −0.876445 | − | 0.481502i | \(-0.840092\pi\) | ||
0.876445 | − | 0.481502i | \(-0.159908\pi\) | |||||||
\(720\) | −50.5147 | + | 32.3768i | −0.0701594 | + | 0.0449678i | ||||
\(721\) | 46.2324 | 0.0641226 | ||||||||
\(722\) | −381.893 | − | 381.893i | −0.528938 | − | 0.528938i | ||||
\(723\) | 187.834 | − | 187.834i | 0.259798 | − | 0.259798i | ||||
\(724\) | − | 306.543i | − | 0.423402i | ||||||
\(725\) | −246.746 | − | 113.414i | −0.340339 | − | 0.156432i | ||||
\(726\) | −109.112 | −0.150292 | ||||||||
\(727\) | 564.236 | + | 564.236i | 0.776116 | + | 0.776116i | 0.979168 | − | 0.203052i | \(-0.0650861\pi\) |
−0.203052 | + | 0.979168i | \(0.565086\pi\) | |||||||
\(728\) | 213.424 | − | 213.424i | 0.293165 | − | 0.293165i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 36.7608 | + | 57.3547i | 0.0503573 | + | 0.0785681i | ||||
\(731\) | −610.677 | −0.835400 | ||||||||
\(732\) | −256.040 | − | 256.040i | −0.349782 | − | 0.349782i | ||||
\(733\) | −591.205 | + | 591.205i | −0.806555 | + | 0.806555i | −0.984111 | − | 0.177556i | \(-0.943181\pi\) |
0.177556 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(734\) | 68.8057i | 0.0937407i | ||||||||
\(735\) | 26.1721 | − | 119.609i | 0.0356083 | − | 0.162733i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 44.7341 | + | 44.7341i | 0.0606975 | + | 0.0606975i | ||||
\(738\) | −144.168 | + | 144.168i | −0.195350 | + | 0.195350i | ||||
\(739\) | 258.804i | 0.350208i | 0.984550 | + | 0.175104i | \(0.0560262\pi\) | ||||
−0.984550 | + | 0.175104i | \(0.943974\pi\) | |||||||
\(740\) | −322.292 | − | 70.5222i | −0.435529 | − | 0.0953002i | ||||
\(741\) | 634.003 | 0.855605 | ||||||||
\(742\) | 457.769 | + | 457.769i | 0.616939 | + | 0.616939i | ||||
\(743\) | 49.1328 | − | 49.1328i | 0.0661276 | − | 0.0661276i | −0.673270 | − | 0.739397i | \(-0.735111\pi\) |
0.739397 | + | 0.673270i | \(0.235111\pi\) | |||||||
\(744\) | − | 54.5203i | − | 0.0732800i | ||||||
\(745\) | −46.1794 | + | 29.5981i | −0.0619857 | + | 0.0397290i | ||||
\(746\) | 152.310 | 0.204169 | ||||||||
\(747\) | −263.061 | − | 263.061i | −0.352156 | − | 0.352156i | ||||
\(748\) | −411.805 | + | 411.805i | −0.550542 | + | 0.550542i | ||||
\(749\) | − | 278.585i | − | 0.371942i | ||||||
\(750\) | 303.227 | − | 42.4653i | 0.404303 | − | 0.0566204i | ||||
\(751\) | −1118.26 | −1.48903 | −0.744517 | − | 0.667604i | \(-0.767320\pi\) | ||||
−0.744517 | + | 0.667604i | \(0.767320\pi\) | |||||||
\(752\) | 226.397 | + | 226.397i | 0.301060 | + | 0.301060i | ||||
\(753\) | 233.330 | − | 233.330i | 0.309867 | − | 0.309867i | ||||
\(754\) | 206.306i | 0.273616i | ||||||||
\(755\) | −295.481 | − | 461.013i | −0.391365 | − | 0.610613i | ||||
\(756\) | 82.5766 | 0.109228 | ||||||||
\(757\) | −814.033 | − | 814.033i | −1.07534 | − | 1.07534i | −0.996920 | − | 0.0784198i | \(-0.975013\pi\) |
−0.0784198 | − | 0.996920i | \(-0.524987\pi\) | |||||||
\(758\) | 101.960 | − | 101.960i | 0.134512 | − | 0.134512i | ||||
\(759\) | 106.877i | 0.140812i | ||||||||
\(760\) | −82.3947 | + | 376.550i | −0.108414 | + | 0.495460i | ||||
\(761\) | −470.046 | −0.617669 | −0.308835 | − | 0.951116i | \(-0.599939\pi\) | ||||
−0.308835 | + | 0.951116i | \(0.599939\pi\) | |||||||
\(762\) | 375.880 | + | 375.880i | 0.493281 | + | 0.493281i | ||||
\(763\) | 0.653028 | − | 0.653028i | 0.000855869 | − | 0.000855869i | ||||
\(764\) | − | 652.514i | − | 0.854076i | ||||||
\(765\) | −331.630 | − | 72.5656i | −0.433504 | − | 0.0948570i | ||||
\(766\) | 1046.14 | 1.36572 | ||||||||
\(767\) | −604.597 | − | 604.597i | −0.788262 | − | 0.788262i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 694.030i | 0.902510i | 0.892395 | + | 0.451255i | \(0.149023\pi\) | ||||
−0.892395 | + | 0.451255i | \(0.850977\pi\) | |||||||
\(770\) | −608.633 | + | 390.096i | −0.790432 | + | 0.506618i | ||||
\(771\) | 285.478 | 0.370270 | ||||||||
\(772\) | 226.630 | + | 226.630i | 0.293562 | + | 0.293562i | ||||
\(773\) | −472.817 | + | 472.817i | −0.611665 | + | 0.611665i | −0.943380 | − | 0.331714i | \(-0.892373\pi\) |
0.331714 | + | 0.943380i | \(0.392373\pi\) | |||||||
\(774\) | − | 114.480i | − | 0.147907i | ||||||
\(775\) | −116.195 | + | 252.798i | −0.149929 | + | 0.326191i | ||||
\(776\) | 487.733 | 0.628522 | ||||||||
\(777\) | 321.067 | + | 321.067i | 0.413214 | + | 0.413214i | ||||
\(778\) | −8.10447 | + | 8.10447i | −0.0104171 | + | 0.0104171i | ||||
\(779\) | 1309.82i | 1.68141i | ||||||||
\(780\) | −125.520 | − | 195.837i | −0.160922 | − | 0.251073i | ||||
\(781\) | 1168.70 | 1.49641 | ||||||||
\(782\) | 108.538 | + | 108.538i | 0.138796 | + | 0.138796i | ||||
\(783\) | −39.9114 | + | 39.9114i | −0.0509724 | + | 0.0509724i | ||||
\(784\) | − | 56.5520i | − | 0.0721326i | ||||||
\(785\) | −138.138 | + | 631.302i | −0.175972 | + | 0.804206i | ||||
\(786\) | 572.929 | 0.728917 | ||||||||
\(787\) | −848.095 | − | 848.095i | −1.07763 | − | 1.07763i | −0.996721 | − | 0.0809093i | \(-0.974218\pi\) |
−0.0809093 | − | 0.996721i | \(-0.525782\pi\) | |||||||
\(788\) | −124.109 | + | 124.109i | −0.157499 | + | 0.157499i | ||||
\(789\) | 656.087i | 0.831543i | ||||||||
\(790\) | −714.347 | − | 156.310i | −0.904236 | − | 0.197860i | ||||
\(791\) | −1692.66 | −2.13990 | ||||||||
\(792\) | −77.1985 | − | 77.1985i | −0.0974729 | − | 0.0974729i | ||||
\(793\) | 992.625 | − | 992.625i | 1.25173 | − | 1.25173i | ||||
\(794\) | − | 93.5140i | − | 0.117776i | ||||||
\(795\) | 420.047 | − | 269.224i | 0.528361 | − | 0.338647i | ||||
\(796\) | −265.630 | −0.333706 | ||||||||
\(797\) | −146.099 | − | 146.099i | −0.183312 | − | 0.183312i | 0.609486 | − | 0.792797i | \(-0.291376\pi\) |
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(798\) | 375.119 | − | 375.119i | 0.470074 | − | 0.470074i | ||||
\(799\) | 1811.53i | 2.26724i | ||||||||
\(800\) | 132.625 | − | 49.0982i | 0.165781 | − | 0.0613728i | ||||
\(801\) | 195.532 | 0.244110 | ||||||||
\(802\) | 212.655 | + | 212.655i | 0.265156 | + | 0.265156i | ||||
\(803\) | −87.6516 | + | 87.6516i | −0.109155 | + | 0.109155i | ||||
\(804\) | 17.0328i | 0.0211851i | ||||||||
\(805\) | 102.816 | + | 160.415i | 0.127722 | + | 0.199274i | ||||
\(806\) | 211.366 | 0.262241 | ||||||||
\(807\) | 197.594 | + | 197.594i | 0.244850 | + | 0.244850i | ||||
\(808\) | 258.441 | − | 258.441i | 0.319853 | − | 0.319853i | ||||
\(809\) | 717.004i | 0.886284i | 0.896451 | + | 0.443142i | \(0.146136\pi\) | ||||
−0.896451 | + | 0.443142i | \(0.853864\pi\) | |||||||
\(810\) | 13.6034 | − | 62.1687i | 0.0167944 | − | 0.0767515i | ||||
\(811\) | 45.3065 | 0.0558650 | 0.0279325 | − | 0.999610i | \(-0.491108\pi\) | ||||
0.0279325 | + | 0.999610i | \(0.491108\pi\) | |||||||
\(812\) | 122.065 | + | 122.065i | 0.150326 | + | 0.150326i | ||||
\(813\) | −223.246 | + | 223.246i | −0.274596 | + | 0.274596i | ||||
\(814\) | − | 600.313i | − | 0.737485i | ||||||
\(815\) | 333.228 | + | 72.9151i | 0.408868 | + | 0.0894664i | ||||
\(816\) | −156.798 | −0.192154 | ||||||||
\(817\) | −520.045 | − | 520.045i | −0.636530 | − | 0.636530i | ||||
\(818\) | −201.150 | + | 201.150i | −0.245905 | + | 0.245905i | ||||
\(819\) | 320.136i | 0.390886i | ||||||||
\(820\) | 404.590 | − | 259.317i | 0.493402 | − | 0.316240i | ||||
\(821\) | 5.96649 | 0.00726734 | 0.00363367 | − | 0.999993i | \(-0.498843\pi\) | ||||
0.00363367 | + | 0.999993i | \(0.498843\pi\) | |||||||
\(822\) | −100.337 | − | 100.337i | −0.122065 | − | 0.122065i | ||||
\(823\) | −157.910 | + | 157.910i | −0.191872 | + | 0.191872i | −0.796504 | − | 0.604633i | \(-0.793320\pi\) |
0.604633 | + | 0.796504i | \(0.293320\pi\) | |||||||
\(824\) | − | 16.4568i | − | 0.0199719i | ||||||
\(825\) | 193.424 | + | 522.479i | 0.234453 | + | 0.633307i | ||||
\(826\) | −715.441 | −0.866152 | ||||||||
\(827\) | 932.001 | + | 932.001i | 1.12697 | + | 1.12697i | 0.990668 | + | 0.136299i | \(0.0435207\pi\) |
0.136299 | + | 0.990668i | \(0.456479\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | 1455.66i | 1.75592i | 0.478732 | + | 0.877961i | \(0.341097\pi\) | ||||
−0.478732 | + | 0.877961i | \(0.658903\pi\) | |||||||
\(830\) | 473.171 | + | 738.246i | 0.570085 | + | 0.889454i | ||||
\(831\) | −518.526 | −0.623979 | ||||||||
\(832\) | −75.9700 | − | 75.9700i | −0.0913102 | − | 0.0913102i | ||||
\(833\) | 226.252 | − | 226.252i | 0.271611 | − | 0.271611i | ||||
\(834\) | 363.841i | 0.436260i | ||||||||
\(835\) | −294.063 | + | 1343.89i | −0.352171 | + | 1.60945i | ||||
\(836\) | −701.376 | −0.838967 | ||||||||
\(837\) | 40.8903 | + | 40.8903i | 0.0488534 | + | 0.0488534i | ||||
\(838\) | 284.817 | − | 284.817i | 0.339877 | − | 0.339877i | ||||
\(839\) | − | 841.130i | − | 1.00254i | −0.865291 | − | 0.501270i | \(-0.832867\pi\) | ||
0.865291 | − | 0.501270i | \(-0.167133\pi\) | |||||||
\(840\) | −190.136 | − | 41.6046i | −0.226353 | − | 0.0495293i | ||||
\(841\) | 723.006 | 0.859698 | ||||||||
\(842\) | −162.868 | − | 162.868i | −0.193430 | − | 0.193430i | ||||
\(843\) | −239.680 | + | 239.680i | −0.284317 | + | 0.284317i | ||||
\(844\) | − | 405.483i | − | 0.480430i | ||||||
\(845\) | 47.8112 | − | 30.6440i | 0.0565813 | − | 0.0362651i | ||||
\(846\) | −339.595 | −0.401413 | ||||||||
\(847\) | −250.281 | − | 250.281i | −0.295491 | − | 0.295491i | ||||
\(848\) | 162.947 | − | 162.947i | 0.192154 | − | 0.192154i | ||||
\(849\) | 692.523i | 0.815693i | ||||||||
\(850\) | 727.033 | + | 334.171i | 0.855333 | + | 0.393143i | ||||
\(851\) | −158.223 | −0.185926 | ||||||||
\(852\) | 222.495 | + | 222.495i | 0.261145 | + | 0.261145i | ||||
\(853\) | 125.620 | − | 125.620i | 0.147269 | − | 0.147269i | −0.629628 | − | 0.776897i | \(-0.716793\pi\) |
0.776897 | + | 0.629628i | \(0.216793\pi\) | |||||||
\(854\) | − | 1174.61i | − | 1.37542i | ||||||
\(855\) | −220.616 | − | 344.208i | −0.258031 | − | 0.402583i | ||||
\(856\) | −99.1647 | −0.115847 | ||||||||
\(857\) | −397.770 | − | 397.770i | −0.464143 | − | 0.464143i | 0.435868 | − | 0.900011i | \(-0.356441\pi\) |
−0.900011 | + | 0.435868i | \(0.856441\pi\) | |||||||
\(858\) | 299.286 | − | 299.286i | 0.348818 | − | 0.348818i | ||||
\(859\) | − | 577.038i | − | 0.671756i | −0.941906 | − | 0.335878i | \(-0.890967\pi\) | ||
0.941906 | − | 0.335878i | \(-0.109033\pi\) | |||||||
\(860\) | −57.6785 | + | 263.595i | −0.0670680 | + | 0.306506i | ||||
\(861\) | −661.384 | −0.768158 | ||||||||
\(862\) | 740.079 | + | 740.079i | 0.858561 | + | 0.858561i | ||||
\(863\) | 440.196 | − | 440.196i | 0.510076 | − | 0.510076i | −0.404474 | − | 0.914550i | \(-0.632545\pi\) |
0.914550 | + | 0.404474i | \(0.132545\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | −877.242 | − | 191.954i | −1.01415 | − | 0.221912i | ||||
\(866\) | 1085.32 | 1.25326 | ||||||||
\(867\) | −273.361 | − | 273.361i | −0.315295 | − | 0.315295i | ||||
\(868\) | 125.059 | − | 125.059i | 0.144077 | − | 0.144077i | ||||
\(869\) | − | 1330.57i | − | 1.53115i | ||||||
\(870\) | 112.006 | − | 71.7891i | 0.128743 | − | 0.0825162i | ||||
\(871\) | −66.0333 | −0.0758132 | ||||||||
\(872\) | −0.232451 | − | 0.232451i | −0.000266572 | − | 0.000266572i | ||||
\(873\) | −365.800 | + | 365.800i | −0.419015 | + | 0.419015i | ||||
\(874\) | 184.860i | 0.211510i | ||||||||
\(875\) | 792.948 | + | 598.134i | 0.906226 | + | 0.683582i | ||||
\(876\) | −33.3740 | −0.0380981 | ||||||||
\(877\) | 1080.01 | + | 1080.01i | 1.23148 | + | 1.23148i | 0.963395 | + | 0.268086i | \(0.0863912\pi\) |
0.268086 | + | 0.963395i | \(0.413609\pi\) | |||||||
\(878\) | −484.445 | + | 484.445i | −0.551760 | + | 0.551760i | ||||
\(879\) | 744.080i | 0.846508i | ||||||||
\(880\) | 138.858 | + | 216.648i | 0.157793 | + | 0.246191i | ||||
\(881\) | −134.518 | −0.152688 | −0.0763440 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763440 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(882\) | 42.4140 | + | 42.4140i | 0.0480884 | + | 0.0480884i | ||||
\(883\) | 448.543 | − | 448.543i | 0.507976 | − | 0.507976i | −0.405929 | − | 0.913905i | \(-0.633052\pi\) |
0.913905 | + | 0.405929i | \(0.133052\pi\) | |||||||
\(884\) | − | 607.878i | − | 0.687645i | ||||||
\(885\) | −117.860 | + | 538.628i | −0.133175 | + | 0.608619i | ||||
\(886\) | 1052.44 | 1.18785 | ||||||||
\(887\) | 728.517 | + | 728.517i | 0.821327 | + | 0.821327i | 0.986298 | − | 0.164971i | \(-0.0527532\pi\) |
−0.164971 | + | 0.986298i | \(0.552753\pi\) | |||||||
\(888\) | 114.287 | − | 114.287i | 0.128701 | − | 0.128701i | ||||
\(889\) | 1724.38i | 1.93969i | ||||||||
\(890\) | −450.221 | − | 98.5150i | −0.505866 | − | 0.110691i | ||||
\(891\) | 115.798 | 0.129964 | ||||||||
\(892\) | −23.0638 | − | 23.0638i | −0.0258563 | − | 0.0258563i | ||||
\(893\) | −1542.67 | + | 1542.67i | −1.72752 | + | 1.72752i | ||||
\(894\) | − | 26.8712i | − | 0.0300572i | ||||||
\(895\) | −1185.44 | + | 759.792i | −1.32451 | + | 0.848929i | ||||
\(896\) | −89.8981 | −0.100333 | ||||||||
\(897\) | −78.8818 | − | 78.8818i | −0.0879396 | − | 0.0879396i | ||||
\(898\) | 620.540 | − | 620.540i | 0.691025 | − | 0.691025i | ||||
\(899\) | 120.888i | 0.134469i | ||||||||
\(900\) | −62.6450 | + | 136.292i | −0.0696055 | + | 0.151436i | ||||
\(901\) | 1303.83 | 1.44709 | ||||||||
\(902\) | 618.309 | + | 618.309i | 0.685487 | + | 0.685487i | ||||
\(903\) | 262.594 | − | 262.594i | 0.290801 | − | 0.290801i | ||||
\(904\) | 602.518i | 0.666502i | ||||||||
\(905\) | −413.537 | − | 645.205i | −0.456947 | − | 0.712934i | ||||
\(906\) | 268.257 | 0.296090 | ||||||||
\(907\) | 176.709 | + | 176.709i | 0.194828 | + | 0.194828i | 0.797779 | − | 0.602951i | \(-0.206008\pi\) |
−0.602951 | + | 0.797779i | \(0.706008\pi\) | |||||||
\(908\) | −326.813 | + | 326.813i | −0.359927 | + | 0.359927i | ||||
\(909\) | 387.662i | 0.426470i | ||||||||
\(910\) | 161.294 | − | 737.127i | 0.177246 | − | 0.810029i | ||||
\(911\) | −1311.05 | −1.43914 | −0.719569 | − | 0.694421i | \(-0.755661\pi\) | ||||
−0.719569 | + | 0.694421i | \(0.755661\pi\) | |||||||
\(912\) | −133.527 | − | 133.527i | −0.146411 | − | 0.146411i | ||||
\(913\) | −1128.22 | + | 1128.22i | −1.23572 | + | 1.23572i | ||||
\(914\) | − | 5.87811i | − | 0.00643119i | ||||||
\(915\) | −884.317 | − | 193.502i | −0.966466 | − | 0.211477i | ||||
\(916\) | −308.807 | −0.337126 | ||||||||
\(917\) | 1314.18 | + | 1314.18i | 1.43313 | + | 1.43313i | ||||
\(918\) | 117.598 | − | 117.598i | 0.128103 | − | 0.128103i | ||||
\(919\) | − | 782.706i | − | 0.851693i | −0.904795 | − | 0.425847i | \(-0.859976\pi\) | ||
0.904795 | − | 0.425847i | \(-0.140024\pi\) | |||||||
\(920\) | 57.1013 | − | 36.5984i | 0.0620666 | − | 0.0397809i | ||||
\(921\) | 934.212 | 1.01435 | ||||||||
\(922\) | 336.573 | + | 336.573i | 0.365046 | + | 0.365046i | ||||
\(923\) | −862.576 | + | 862.576i | −0.934536 | + | 0.934536i | ||||
\(924\) | − | 354.155i | − | 0.383285i | ||||||
\(925\) | −773.490 | + | 286.349i | −0.836206 | + | 0.309567i | ||||
\(926\) | −1185.43 | −1.28017 | ||||||||
\(927\) | 12.3426 | + | 12.3426i | 0.0133146 | + | 0.0133146i | ||||
\(928\) | 43.4500 | − | 43.4500i | 0.0468211 | − | 0.0468211i | ||||
\(929\) | − | 1258.54i | − | 1.35473i | −0.735647 | − | 0.677365i | \(-0.763122\pi\) | ||
0.735647 | − | 0.677365i | \(-0.236878\pi\) | |||||||
\(930\) | −73.5499 | − | 114.753i | −0.0790859 | − | 0.123391i | ||||
\(931\) | 385.346 | 0.413906 | ||||||||
\(932\) | −518.556 | − | 518.556i | −0.556391 | − | 0.556391i | ||||
\(933\) | −41.6445 | + | 41.6445i | −0.0446351 | + | 0.0446351i | ||||
\(934\) | − | 705.769i | − | 0.755642i | ||||||
\(935\) | −311.220 | + | 1422.30i | −0.332856 | + | 1.52118i | ||||
\(936\) | 113.955 | 0.121747 | ||||||||
\(937\) | −223.347 | − | 223.347i | −0.238364 | − | 0.238364i | 0.577808 | − | 0.816172i | \(-0.303908\pi\) |
−0.816172 | + | 0.577808i | \(0.803908\pi\) | |||||||
\(938\) | −39.0698 | + | 39.0698i | −0.0416522 | + | 0.0416522i | ||||
\(939\) | − | 154.188i | − | 0.164204i | ||||||
\(940\) | 781.933 | + | 171.099i | 0.831844 | + | 0.182020i | ||||
\(941\) | 1007.84 | 1.07104 | 0.535518 | − | 0.844524i | \(-0.320116\pi\) | ||||
0.535518 | + | 0.844524i | \(0.320116\pi\) | |||||||
\(942\) | −223.864 | − | 223.864i | −0.237647 | − | 0.237647i | ||||
\(943\) | 162.966 | − | 162.966i | 0.172816 | − | 0.172816i | ||||
\(944\) | 254.668i | 0.269775i | ||||||||
\(945\) | 173.806 | − | 111.399i | 0.183921 | − | 0.117882i | ||||
\(946\) | −490.982 | −0.519009 | ||||||||
\(947\) | 515.759 | + | 515.759i | 0.544624 | + | 0.544624i | 0.924881 | − | 0.380257i | \(-0.124164\pi\) |
−0.380257 | + | 0.924881i | \(0.624164\pi\) | |||||||
\(948\) | 253.312 | − | 253.312i | 0.267207 | − | 0.267207i | ||||
\(949\) | − | 129.385i | − | 0.136338i | ||||||
\(950\) | 334.556 | + | 903.708i | 0.352165 | + | 0.951272i | ||||
\(951\) | 352.870 | 0.371052 | ||||||||
\(952\) | −359.662 | − | 359.662i | −0.377796 | − | 0.377796i | ||||
\(953\) | −969.316 | + | 969.316i | −1.01712 | + | 1.01712i | −0.0172703 | + | 0.999851i | \(0.505498\pi\) |
−0.999851 | + | 0.0172703i | \(0.994502\pi\) | |||||||
\(954\) | 244.420i | 0.256206i | ||||||||
\(955\) | −880.265 | − | 1373.40i | −0.921743 | − | 1.43812i | ||||
\(956\) | 179.048 | 0.187289 | ||||||||
\(957\) | 171.172 | + | 171.172i | 0.178863 | + | 0.178863i | ||||
\(958\) | −160.749 | + | 160.749i | −0.167797 | + | 0.167797i | ||||
\(959\) | − | 460.307i | − | 0.479987i | ||||||
\(960\) | −14.8095 | + | 67.6807i | −0.0154266 | + | 0.0705007i | ||||
\(961\) | −837.147 | −0.871121 | ||||||||
\(962\) | 443.070 | + | 443.070i | 0.460572 | + | 0.460572i | ||||
\(963\) | 74.3735 | − | 74.3735i | 0.0772310 | − | 0.0772310i | ||||
\(964\) | − | 306.732i | − | 0.318187i | ||||||
\(965\) | 782.737 | + | 171.274i | 0.811127 | + | 0.177486i | ||||
\(966\) | −93.3437 | −0.0966291 | ||||||||
\(967\) | 293.239 | + | 293.239i | 0.303246 | + | 0.303246i | 0.842283 | − | 0.539036i | \(-0.181211\pi\) |
−0.539036 | + | 0.842283i | \(0.681211\pi\) | |||||||
\(968\) | −89.0897 | + | 89.0897i | −0.0920348 | + | 0.0920348i | ||||
\(969\) | − | 1068.42i | − | 1.10260i | ||||||
\(970\) | 1026.57 | − | 657.969i | 1.05832 | − | 0.678319i | ||||
\(971\) | 1223.41 | 1.25995 | 0.629976 | − | 0.776615i | \(-0.283065\pi\) | ||||
0.629976 | + | 0.776615i | \(0.283065\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −834.577 | + | 834.577i | −0.857736 | + | 0.857736i | ||||
\(974\) | − | 425.106i | − | 0.436454i | ||||||
\(975\) | −528.382 | − | 242.864i | −0.541931 | − | 0.249091i | ||||
\(976\) | −418.112 | −0.428394 | ||||||||
\(977\) | −143.186 | − | 143.186i | −0.146556 | − | 0.146556i | 0.630021 | − | 0.776578i | \(-0.283046\pi\) |
−0.776578 | + | 0.630021i | \(0.783046\pi\) | |||||||
\(978\) | −118.165 | + | 118.165i | −0.120823 | + | 0.120823i | ||||
\(979\) | − | 838.599i | − | 0.856587i | ||||||
\(980\) | −76.2906 | − | 119.030i | −0.0778475 | − | 0.121459i | ||||
\(981\) | 0.348677 | 0.000355430 | ||||||||
\(982\) | −399.924 | − | 399.924i | −0.407255 | − | 0.407255i | ||||
\(983\) | 1069.62 | − | 1069.62i | 1.08811 | − | 1.08811i | 0.0923919 | − | 0.995723i | \(-0.470549\pi\) |
0.995723 | − | 0.0923919i | \(-0.0294513\pi\) | |||||||
\(984\) | 235.425i | 0.239254i | ||||||||
\(985\) | −93.7948 | + | 428.649i | −0.0952232 | + | 0.435177i | ||||
\(986\) | 347.667 | 0.352604 | ||||||||
\(987\) | −778.962 | − | 778.962i | −0.789222 | − | 0.789222i | ||||
\(988\) | 517.661 | − | 517.661i | 0.523949 | − | 0.523949i | ||||
\(989\) | 129.407i | 0.130846i | ||||||||
\(990\) | −266.630 | − | 58.3425i | −0.269323 | − | 0.0589318i | ||||
\(991\) | 135.844 | 0.137078 | 0.0685388 | − | 0.997648i | \(-0.478166\pi\) | ||||
0.0685388 | + | 0.997648i | \(0.478166\pi\) | |||||||
\(992\) | −44.5157 | − | 44.5157i | −0.0448747 | − | 0.0448747i | ||||
\(993\) | −162.915 | + | 162.915i | −0.164063 | + | 0.164063i | ||||
\(994\) | 1020.72i | 1.02688i | ||||||||
\(995\) | −559.093 | + | 358.344i | −0.561902 | + | 0.360145i | ||||
\(996\) | −429.576 | −0.431301 | ||||||||
\(997\) | −85.6067 | − | 85.6067i | −0.0858643 | − | 0.0858643i | 0.662870 | − | 0.748734i | \(-0.269338\pi\) |
−0.748734 | + | 0.662870i | \(0.769338\pi\) | |||||||
\(998\) | −284.551 | + | 284.551i | −0.285121 | + | 0.285121i | ||||
\(999\) | 171.430i | 0.171602i |
(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.a.277.2 | ✓ | 40 | |
5.3 | odd | 4 | inner | 690.3.k.a.553.2 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.2 | ✓ | 40 | 1.1 | even | 1 | trivial | |
690.3.k.a.553.2 | yes | 40 | 5.3 | odd | 4 | inner |