Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(22,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.l (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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 22.7 | ||
Character | \(\chi\) | \(=\) | 105.22 |
Dual form | 105.3.l.a.43.7 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.675544 | + | 0.675544i | 0.337772 | + | 0.337772i | 0.855528 | − | 0.517756i | \(-0.173233\pi\) |
−0.517756 | + | 0.855528i | \(0.673233\pi\) | |||||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | − | 3.08728i | − | 0.771820i | ||||||
\(5\) | 3.39488 | + | 3.67080i | 0.678976 | + | 0.734160i | ||||
\(6\) | 1.65474 | 0.275790 | ||||||||
\(7\) | −1.87083 | − | 1.87083i | −0.267261 | − | 0.267261i | ||||
\(8\) | 4.78777 | − | 4.78777i | 0.598471 | − | 0.598471i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −0.186396 | + | 4.77318i | −0.0186396 | + | 0.477318i | ||||
\(11\) | 7.59829 | 0.690754 | 0.345377 | − | 0.938464i | \(-0.387751\pi\) | ||||
0.345377 | + | 0.938464i | \(0.387751\pi\) | |||||||
\(12\) | −3.78113 | − | 3.78113i | −0.315094 | − | 0.315094i | ||||
\(13\) | 1.12200 | − | 1.12200i | 0.0863074 | − | 0.0863074i | −0.662635 | − | 0.748942i | \(-0.730562\pi\) |
0.748942 | + | 0.662635i | \(0.230562\pi\) | |||||||
\(14\) | − | 2.52765i | − | 0.180547i | ||||||
\(15\) | 8.65366 | + | 0.337932i | 0.576911 | + | 0.0225288i | ||||
\(16\) | −5.88043 | −0.367527 | ||||||||
\(17\) | −3.43635 | − | 3.43635i | −0.202138 | − | 0.202138i | 0.598777 | − | 0.800916i | \(-0.295653\pi\) |
−0.800916 | + | 0.598777i | \(0.795653\pi\) | |||||||
\(18\) | 2.02663 | − | 2.02663i | 0.112591 | − | 0.112591i | ||||
\(19\) | 26.3120i | 1.38484i | 0.721494 | + | 0.692420i | \(0.243456\pi\) | ||||
−0.721494 | + | 0.692420i | \(0.756544\pi\) | |||||||
\(20\) | 11.3328 | − | 10.4810i | 0.566640 | − | 0.524048i | ||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | 5.13298 | + | 5.13298i | 0.233317 | + | 0.233317i | ||||
\(23\) | −24.2663 | + | 24.2663i | −1.05506 | + | 1.05506i | −0.0566642 | + | 0.998393i | \(0.518046\pi\) |
−0.998393 | + | 0.0566642i | \(0.981954\pi\) | |||||||
\(24\) | − | 11.7276i | − | 0.488650i | ||||||
\(25\) | −1.94957 | + | 24.9239i | −0.0779827 | + | 0.996955i | ||||
\(26\) | 1.51592 | 0.0583044 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | −5.77577 | + | 5.77577i | −0.206278 | + | 0.206278i | ||||
\(29\) | − | 22.3579i | − | 0.770962i | −0.922716 | − | 0.385481i | \(-0.874035\pi\) | ||
0.922716 | − | 0.385481i | \(-0.125965\pi\) | |||||||
\(30\) | 5.61764 | + | 6.07421i | 0.187255 | + | 0.202474i | ||||
\(31\) | −18.3927 | −0.593314 | −0.296657 | − | 0.954984i | \(-0.595872\pi\) | ||||
−0.296657 | + | 0.954984i | \(0.595872\pi\) | |||||||
\(32\) | −23.1236 | − | 23.1236i | −0.722611 | − | 0.722611i | ||||
\(33\) | 9.30597 | − | 9.30597i | 0.281999 | − | 0.281999i | ||||
\(34\) | − | 4.64281i | − | 0.136553i | ||||||
\(35\) | 0.516200 | − | 13.2187i | 0.0147486 | − | 0.377677i | ||||
\(36\) | −9.26184 | −0.257273 | ||||||||
\(37\) | −34.4244 | − | 34.4244i | −0.930388 | − | 0.930388i | 0.0673418 | − | 0.997730i | \(-0.478548\pi\) |
−0.997730 | + | 0.0673418i | \(0.978548\pi\) | |||||||
\(38\) | −17.7749 | + | 17.7749i | −0.467760 | + | 0.467760i | ||||
\(39\) | − | 2.74832i | − | 0.0704697i | ||||||
\(40\) | 33.8289 | + | 1.32104i | 0.845721 | + | 0.0330261i | ||||
\(41\) | 37.4590 | 0.913633 | 0.456817 | − | 0.889561i | \(-0.348990\pi\) | ||||
0.456817 | + | 0.889561i | \(0.348990\pi\) | |||||||
\(42\) | −3.09573 | − | 3.09573i | −0.0737079 | − | 0.0737079i | ||||
\(43\) | −55.1278 | + | 55.1278i | −1.28204 | + | 1.28204i | −0.342537 | + | 0.939504i | \(0.611286\pi\) |
−0.939504 | + | 0.342537i | \(0.888714\pi\) | |||||||
\(44\) | − | 23.4581i | − | 0.533138i | ||||||
\(45\) | 11.0124 | − | 10.1846i | 0.244720 | − | 0.226325i | ||||
\(46\) | −32.7859 | −0.712738 | ||||||||
\(47\) | 40.8541 | + | 40.8541i | 0.869236 | + | 0.869236i | 0.992388 | − | 0.123151i | \(-0.0393001\pi\) |
−0.123151 | + | 0.992388i | \(0.539300\pi\) | |||||||
\(48\) | −7.20203 | + | 7.20203i | −0.150042 | + | 0.150042i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −18.1542 | + | 15.5201i | −0.363084 | + | 0.310403i | ||||
\(51\) | −8.41731 | −0.165045 | ||||||||
\(52\) | −3.46392 | − | 3.46392i | −0.0666138 | − | 0.0666138i | ||||
\(53\) | −9.39948 | + | 9.39948i | −0.177349 | + | 0.177349i | −0.790199 | − | 0.612850i | \(-0.790023\pi\) |
0.612850 | + | 0.790199i | \(0.290023\pi\) | |||||||
\(54\) | − | 4.96421i | − | 0.0919299i | ||||||
\(55\) | 25.7953 | + | 27.8918i | 0.469005 | + | 0.507124i | ||||
\(56\) | −17.9142 | −0.319896 | ||||||||
\(57\) | 32.2255 | + | 32.2255i | 0.565359 | + | 0.565359i | ||||
\(58\) | 15.1037 | − | 15.1037i | 0.260409 | − | 0.260409i | ||||
\(59\) | − | 49.7795i | − | 0.843720i | −0.906661 | − | 0.421860i | \(-0.861377\pi\) | ||
0.906661 | − | 0.421860i | \(-0.138623\pi\) | |||||||
\(60\) | 1.04329 | − | 26.7163i | 0.0173882 | − | 0.445271i | ||||
\(61\) | 88.3465 | 1.44830 | 0.724152 | − | 0.689641i | \(-0.242232\pi\) | ||||
0.724152 | + | 0.689641i | \(0.242232\pi\) | |||||||
\(62\) | −12.4251 | − | 12.4251i | −0.200405 | − | 0.200405i | ||||
\(63\) | −5.61249 | + | 5.61249i | −0.0890871 | + | 0.0890871i | ||||
\(64\) | − | 7.72024i | − | 0.120629i | ||||||
\(65\) | 7.92767 | + | 0.309582i | 0.121964 | + | 0.00476280i | ||||
\(66\) | 12.5732 | 0.190503 | ||||||||
\(67\) | −40.5887 | − | 40.5887i | −0.605802 | − | 0.605802i | 0.336044 | − | 0.941846i | \(-0.390911\pi\) |
−0.941846 | + | 0.336044i | \(0.890911\pi\) | |||||||
\(68\) | −10.6090 | + | 10.6090i | −0.156014 | + | 0.156014i | ||||
\(69\) | 59.4401i | 0.861451i | ||||||||
\(70\) | 9.27851 | − | 8.58108i | 0.132550 | − | 0.122587i | ||||
\(71\) | 136.425 | 1.92148 | 0.960740 | − | 0.277451i | \(-0.0894897\pi\) | ||||
0.960740 | + | 0.277451i | \(0.0894897\pi\) | |||||||
\(72\) | −14.3633 | − | 14.3633i | −0.199490 | − | 0.199490i | ||||
\(73\) | 5.85157 | − | 5.85157i | 0.0801585 | − | 0.0801585i | −0.665891 | − | 0.746049i | \(-0.731948\pi\) |
0.746049 | + | 0.665891i | \(0.231948\pi\) | |||||||
\(74\) | − | 46.5103i | − | 0.628518i | ||||||
\(75\) | 28.1377 | + | 32.9131i | 0.375169 | + | 0.438841i | ||||
\(76\) | 81.2325 | 1.06885 | ||||||||
\(77\) | −14.2151 | − | 14.2151i | −0.184612 | − | 0.184612i | ||||
\(78\) | 1.85661 | − | 1.85661i | 0.0238027 | − | 0.0238027i | ||||
\(79\) | − | 66.4377i | − | 0.840984i | −0.907296 | − | 0.420492i | \(-0.861857\pi\) | ||
0.907296 | − | 0.420492i | \(-0.138143\pi\) | |||||||
\(80\) | −19.9634 | − | 21.5859i | −0.249542 | − | 0.269824i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 25.3052 | + | 25.3052i | 0.308600 | + | 0.308600i | ||||
\(83\) | −34.8615 | + | 34.8615i | −0.420018 | + | 0.420018i | −0.885210 | − | 0.465192i | \(-0.845985\pi\) |
0.465192 | + | 0.885210i | \(0.345985\pi\) | |||||||
\(84\) | 14.1477i | 0.168425i | ||||||||
\(85\) | 0.948160 | − | 24.2802i | 0.0111548 | − | 0.285649i | ||||
\(86\) | −74.4824 | −0.866075 | ||||||||
\(87\) | −27.3827 | − | 27.3827i | −0.314744 | − | 0.314744i | ||||
\(88\) | 36.3789 | − | 36.3789i | 0.413396 | − | 0.413396i | ||||
\(89\) | 2.03390i | 0.0228528i | 0.999935 | + | 0.0114264i | \(0.00363721\pi\) | ||||
−0.999935 | + | 0.0114264i | \(0.996363\pi\) | |||||||
\(90\) | 14.3195 | + | 0.559189i | 0.159106 | + | 0.00621321i | ||||
\(91\) | −4.19813 | −0.0461332 | ||||||||
\(92\) | 74.9170 | + | 74.9170i | 0.814315 | + | 0.814315i | ||||
\(93\) | −22.5264 | + | 22.5264i | −0.242220 | + | 0.242220i | ||||
\(94\) | 55.1975i | 0.587207i | ||||||||
\(95\) | −96.5860 | + | 89.3260i | −1.01670 | + | 0.940274i | ||||
\(96\) | −56.6409 | −0.590010 | ||||||||
\(97\) | −58.4649 | − | 58.4649i | −0.602731 | − | 0.602731i | 0.338305 | − | 0.941036i | \(-0.390146\pi\) |
−0.941036 | + | 0.338305i | \(0.890146\pi\) | |||||||
\(98\) | −4.72881 | + | 4.72881i | −0.0482531 | + | 0.0482531i | ||||
\(99\) | − | 22.7949i | − | 0.230251i | ||||||
\(100\) | 76.9470 | + | 6.01886i | 0.769470 | + | 0.0601886i | ||||
\(101\) | 72.4773 | 0.717597 | 0.358798 | − | 0.933415i | \(-0.383187\pi\) | ||||
0.358798 | + | 0.933415i | \(0.383187\pi\) | |||||||
\(102\) | −5.68626 | − | 5.68626i | −0.0557476 | − | 0.0557476i | ||||
\(103\) | 96.7717 | − | 96.7717i | 0.939531 | − | 0.939531i | −0.0587421 | − | 0.998273i | \(-0.518709\pi\) |
0.998273 | + | 0.0587421i | \(0.0187090\pi\) | |||||||
\(104\) | − | 10.7437i | − | 0.103305i | ||||||
\(105\) | −15.5573 | − | 16.8217i | −0.148165 | − | 0.160207i | ||||
\(106\) | −12.6995 | −0.119807 | ||||||||
\(107\) | 12.4803 | + | 12.4803i | 0.116638 | + | 0.116638i | 0.763017 | − | 0.646379i | \(-0.223717\pi\) |
−0.646379 | + | 0.763017i | \(0.723717\pi\) | |||||||
\(108\) | −11.3434 | + | 11.3434i | −0.105031 | + | 0.105031i | ||||
\(109\) | − | 87.3675i | − | 0.801537i | −0.916179 | − | 0.400769i | \(-0.868743\pi\) | ||
0.916179 | − | 0.400769i | \(-0.131257\pi\) | |||||||
\(110\) | −1.41629 | + | 36.2680i | −0.0128754 | + | 0.329709i | ||||
\(111\) | −84.3221 | −0.759659 | ||||||||
\(112\) | 11.0013 | + | 11.0013i | 0.0982257 | + | 0.0982257i | ||||
\(113\) | 21.7147 | − | 21.7147i | 0.192165 | − | 0.192165i | −0.604466 | − | 0.796631i | \(-0.706613\pi\) |
0.796631 | + | 0.604466i | \(0.206613\pi\) | |||||||
\(114\) | 43.5394i | 0.381925i | ||||||||
\(115\) | −171.458 | − | 6.69558i | −1.49094 | − | 0.0582224i | ||||
\(116\) | −69.0251 | −0.595044 | ||||||||
\(117\) | −3.36599 | − | 3.36599i | −0.0287691 | − | 0.0287691i | ||||
\(118\) | 33.6282 | − | 33.6282i | 0.284985 | − | 0.284985i | ||||
\(119\) | 12.8576i | 0.108047i | ||||||||
\(120\) | 43.0497 | − | 39.8138i | 0.358747 | − | 0.331781i | ||||
\(121\) | −63.2659 | −0.522859 | ||||||||
\(122\) | 59.6819 | + | 59.6819i | 0.489196 | + | 0.489196i | ||||
\(123\) | 45.8777 | − | 45.8777i | 0.372989 | − | 0.372989i | ||||
\(124\) | 56.7836i | 0.457932i | ||||||||
\(125\) | −98.1091 | + | 77.4571i | −0.784873 | + | 0.619657i | ||||
\(126\) | −7.58296 | −0.0601822 | ||||||||
\(127\) | −82.7648 | − | 82.7648i | −0.651692 | − | 0.651692i | 0.301709 | − | 0.953400i | \(-0.402443\pi\) |
−0.953400 | + | 0.301709i | \(0.902443\pi\) | |||||||
\(128\) | −87.2789 | + | 87.2789i | −0.681866 | + | 0.681866i | ||||
\(129\) | 135.035i | 1.04678i | ||||||||
\(130\) | 5.14635 | + | 5.56462i | 0.0395873 | + | 0.0428048i | ||||
\(131\) | −190.287 | −1.45257 | −0.726285 | − | 0.687394i | \(-0.758755\pi\) | ||||
−0.726285 | + | 0.687394i | \(0.758755\pi\) | |||||||
\(132\) | −28.7301 | − | 28.7301i | −0.217653 | − | 0.217653i | ||||
\(133\) | 49.2252 | − | 49.2252i | 0.370114 | − | 0.370114i | ||||
\(134\) | − | 54.8390i | − | 0.409246i | ||||||
\(135\) | 1.01380 | − | 25.9610i | 0.00750961 | − | 0.192304i | ||||
\(136\) | −32.9049 | −0.241948 | ||||||||
\(137\) | 122.593 | + | 122.593i | 0.894841 | + | 0.894841i | 0.994974 | − | 0.100133i | \(-0.0319268\pi\) |
−0.100133 | + | 0.994974i | \(0.531927\pi\) | |||||||
\(138\) | −40.1544 | + | 40.1544i | −0.290974 | + | 0.290974i | ||||
\(139\) | 149.073i | 1.07247i | 0.844070 | + | 0.536233i | \(0.180153\pi\) | ||||
−0.844070 | + | 0.536233i | \(0.819847\pi\) | |||||||
\(140\) | −40.8098 | − | 1.59366i | −0.291498 | − | 0.0113833i | ||||
\(141\) | 100.072 | 0.709729 | ||||||||
\(142\) | 92.1611 | + | 92.1611i | 0.649022 | + | 0.649022i | ||||
\(143\) | 8.52526 | − | 8.52526i | 0.0596172 | − | 0.0596172i | ||||
\(144\) | 17.6413i | 0.122509i | ||||||||
\(145\) | 82.0714 | − | 75.9024i | 0.566010 | − | 0.523465i | ||||
\(146\) | 7.90599 | 0.0541506 | ||||||||
\(147\) | 8.57321 | + | 8.57321i | 0.0583212 | + | 0.0583212i | ||||
\(148\) | −106.278 | + | 106.278i | −0.718093 | + | 0.718093i | ||||
\(149\) | − | 157.639i | − | 1.05798i | −0.848628 | − | 0.528990i | \(-0.822571\pi\) | ||
0.848628 | − | 0.528990i | \(-0.177429\pi\) | |||||||
\(150\) | −3.22602 | + | 41.2425i | −0.0215068 | + | 0.274950i | ||||
\(151\) | −234.309 | −1.55172 | −0.775858 | − | 0.630908i | \(-0.782682\pi\) | ||||
−0.775858 | + | 0.630908i | \(0.782682\pi\) | |||||||
\(152\) | 125.976 | + | 125.976i | 0.828787 | + | 0.828787i | ||||
\(153\) | −10.3091 | + | 10.3091i | −0.0673794 | + | 0.0673794i | ||||
\(154\) | − | 19.2059i | − | 0.124713i | ||||||
\(155\) | −62.4412 | − | 67.5161i | −0.402846 | − | 0.435588i | ||||
\(156\) | −8.48483 | −0.0543899 | ||||||||
\(157\) | −75.2106 | − | 75.2106i | −0.479048 | − | 0.479048i | 0.425779 | − | 0.904827i | \(-0.360000\pi\) |
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(158\) | 44.8816 | − | 44.8816i | 0.284061 | − | 0.284061i | ||||
\(159\) | 23.0239i | 0.144805i | ||||||||
\(160\) | 6.38027 | − | 163.384i | 0.0398767 | − | 1.02115i | ||||
\(161\) | 90.7963 | 0.563952 | ||||||||
\(162\) | −6.07989 | − | 6.07989i | −0.0375302 | − | 0.0375302i | ||||
\(163\) | 124.557 | − | 124.557i | 0.764153 | − | 0.764153i | −0.212918 | − | 0.977070i | \(-0.568297\pi\) |
0.977070 | + | 0.212918i | \(0.0682966\pi\) | |||||||
\(164\) | − | 115.646i | − | 0.705161i | ||||||
\(165\) | 65.7530 | + | 2.56771i | 0.398503 | + | 0.0155619i | ||||
\(166\) | −47.1010 | −0.283741 | ||||||||
\(167\) | −136.411 | − | 136.411i | −0.816834 | − | 0.816834i | 0.168814 | − | 0.985648i | \(-0.446006\pi\) |
−0.985648 | + | 0.168814i | \(0.946006\pi\) | |||||||
\(168\) | −21.9403 | + | 21.9403i | −0.130597 | + | 0.130597i | ||||
\(169\) | 166.482i | 0.985102i | ||||||||
\(170\) | 17.0428 | − | 15.7618i | 0.100252 | − | 0.0927164i | ||||
\(171\) | 78.9359 | 0.461614 | ||||||||
\(172\) | 170.195 | + | 170.195i | 0.989505 | + | 0.989505i | ||||
\(173\) | 121.020 | − | 121.020i | 0.699538 | − | 0.699538i | −0.264773 | − | 0.964311i | \(-0.585297\pi\) |
0.964311 | + | 0.264773i | \(0.0852969\pi\) | |||||||
\(174\) | − | 36.9965i | − | 0.212623i | ||||||
\(175\) | 50.2756 | − | 42.9810i | 0.287289 | − | 0.245606i | ||||
\(176\) | −44.6812 | −0.253871 | ||||||||
\(177\) | −60.9672 | − | 60.9672i | −0.344447 | − | 0.344447i | ||||
\(178\) | −1.37399 | + | 1.37399i | −0.00771902 | + | 0.00771902i | ||||
\(179\) | 57.2144i | 0.319634i | 0.987147 | + | 0.159817i | \(0.0510904\pi\) | ||||
−0.987147 | + | 0.159817i | \(0.948910\pi\) | |||||||
\(180\) | −31.4429 | − | 33.9984i | −0.174683 | − | 0.188880i | ||||
\(181\) | 294.230 | 1.62558 | 0.812791 | − | 0.582555i | \(-0.197947\pi\) | ||||
0.812791 | + | 0.582555i | \(0.197947\pi\) | |||||||
\(182\) | −2.83602 | − | 2.83602i | −0.0155825 | − | 0.0155825i | ||||
\(183\) | 108.202 | − | 108.202i | 0.591267 | − | 0.591267i | ||||
\(184\) | 232.363i | 1.26284i | ||||||||
\(185\) | 9.49839 | − | 243.232i | 0.0513427 | − | 1.31477i | ||||
\(186\) | −30.4352 | −0.163630 | ||||||||
\(187\) | −26.1104 | − | 26.1104i | −0.139628 | − | 0.139628i | ||||
\(188\) | 126.128 | − | 126.128i | 0.670894 | − | 0.670894i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | −125.592 | − | 4.90446i | −0.661009 | − | 0.0258129i | ||||
\(191\) | 246.643 | 1.29133 | 0.645663 | − | 0.763622i | \(-0.276581\pi\) | ||||
0.645663 | + | 0.763622i | \(0.276581\pi\) | |||||||
\(192\) | −9.45532 | − | 9.45532i | −0.0492465 | − | 0.0492465i | ||||
\(193\) | 100.720 | − | 100.720i | 0.521867 | − | 0.521867i | −0.396268 | − | 0.918135i | \(-0.629695\pi\) |
0.918135 | + | 0.396268i | \(0.129695\pi\) | |||||||
\(194\) | − | 78.9913i | − | 0.407171i | ||||||
\(195\) | 10.0885 | − | 9.33021i | 0.0517361 | − | 0.0478472i | ||||
\(196\) | 21.6110 | 0.110260 | ||||||||
\(197\) | −14.9915 | − | 14.9915i | −0.0760991 | − | 0.0760991i | 0.668033 | − | 0.744132i | \(-0.267137\pi\) |
−0.744132 | + | 0.668033i | \(0.767137\pi\) | |||||||
\(198\) | 15.3989 | − | 15.3989i | 0.0777724 | − | 0.0777724i | ||||
\(199\) | 287.332i | 1.44388i | 0.691957 | + | 0.721939i | \(0.256749\pi\) | ||||
−0.691957 | + | 0.721939i | \(0.743251\pi\) | |||||||
\(200\) | 109.996 | + | 128.664i | 0.549978 | + | 0.643319i | ||||
\(201\) | −99.4217 | −0.494635 | ||||||||
\(202\) | 48.9616 | + | 48.9616i | 0.242384 | + | 0.242384i | ||||
\(203\) | −41.8278 | + | 41.8278i | −0.206048 | + | 0.206048i | ||||
\(204\) | 25.9866i | 0.127385i | ||||||||
\(205\) | 127.169 | + | 137.504i | 0.620335 | + | 0.670753i | ||||
\(206\) | 130.747 | 0.634694 | ||||||||
\(207\) | 72.7990 | + | 72.7990i | 0.351686 | + | 0.351686i | ||||
\(208\) | −6.59782 | + | 6.59782i | −0.0317203 | + | 0.0317203i | ||||
\(209\) | 199.926i | 0.956584i | ||||||||
\(210\) | 0.854176 | − | 21.8734i | 0.00406750 | − | 0.104159i | ||||
\(211\) | −399.559 | −1.89365 | −0.946823 | − | 0.321755i | \(-0.895727\pi\) | ||||
−0.946823 | + | 0.321755i | \(0.895727\pi\) | |||||||
\(212\) | 29.0188 | + | 29.0188i | 0.136881 | + | 0.136881i | ||||
\(213\) | 167.086 | − | 167.086i | 0.784441 | − | 0.784441i | ||||
\(214\) | 16.8619i | 0.0787940i | ||||||||
\(215\) | −389.515 | − | 15.2109i | −1.81170 | − | 0.0707483i | ||||
\(216\) | −35.1828 | −0.162883 | ||||||||
\(217\) | 34.4097 | + | 34.4097i | 0.158570 | + | 0.158570i | ||||
\(218\) | 59.0206 | − | 59.0206i | 0.270737 | − | 0.270737i | ||||
\(219\) | − | 14.3334i | − | 0.0654492i | ||||||
\(220\) | 86.1099 | − | 79.6373i | 0.391409 | − | 0.361988i | ||||
\(221\) | −7.71115 | −0.0348921 | ||||||||
\(222\) | −56.9633 | − | 56.9633i | −0.256591 | − | 0.256591i | ||||
\(223\) | −210.325 | + | 210.325i | −0.943162 | + | 0.943162i | −0.998469 | − | 0.0553078i | \(-0.982386\pi\) |
0.0553078 | + | 0.998469i | \(0.482386\pi\) | |||||||
\(224\) | 86.5204i | 0.386252i | ||||||||
\(225\) | 74.7716 | + | 5.84870i | 0.332318 | + | 0.0259942i | ||||
\(226\) | 29.3384 | 0.129816 | ||||||||
\(227\) | 130.724 | + | 130.724i | 0.575877 | + | 0.575877i | 0.933765 | − | 0.357888i | \(-0.116503\pi\) |
−0.357888 | + | 0.933765i | \(0.616503\pi\) | |||||||
\(228\) | 99.4891 | − | 99.4891i | 0.436356 | − | 0.436356i | ||||
\(229\) | − | 256.942i | − | 1.12202i | −0.827809 | − | 0.561010i | \(-0.810413\pi\) | ||
0.827809 | − | 0.561010i | \(-0.189587\pi\) | |||||||
\(230\) | −111.304 | − | 120.351i | −0.483932 | − | 0.523264i | ||||
\(231\) | −34.8198 | −0.150735 | ||||||||
\(232\) | −107.044 | − | 107.044i | −0.461399 | − | 0.461399i | ||||
\(233\) | −60.6918 | + | 60.6918i | −0.260480 | + | 0.260480i | −0.825249 | − | 0.564769i | \(-0.808965\pi\) |
0.564769 | + | 0.825249i | \(0.308965\pi\) | |||||||
\(234\) | − | 4.54775i | − | 0.0194348i | ||||||
\(235\) | −11.2725 | + | 288.662i | −0.0479680 | + | 1.22835i | ||||
\(236\) | −153.683 | −0.651200 | ||||||||
\(237\) | −81.3693 | − | 81.3693i | −0.343330 | − | 0.343330i | ||||
\(238\) | −8.68591 | + | 8.68591i | −0.0364954 | + | 0.0364954i | ||||
\(239\) | − | 66.9426i | − | 0.280095i | −0.990145 | − | 0.140047i | \(-0.955275\pi\) | ||
0.990145 | − | 0.140047i | \(-0.0447255\pi\) | |||||||
\(240\) | −50.8872 | − | 1.98719i | −0.212030 | − | 0.00827995i | ||||
\(241\) | 82.5830 | 0.342668 | 0.171334 | − | 0.985213i | \(-0.445192\pi\) | ||||
0.171334 | + | 0.985213i | \(0.445192\pi\) | |||||||
\(242\) | −42.7389 | − | 42.7389i | −0.176607 | − | 0.176607i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 272.750i | − | 1.11783i | ||||||
\(245\) | −25.6956 | + | 23.7642i | −0.104880 | + | 0.0969966i | ||||
\(246\) | 61.9848 | 0.251971 | ||||||||
\(247\) | 29.5219 | + | 29.5219i | 0.119522 | + | 0.119522i | ||||
\(248\) | −88.0602 | + | 88.0602i | −0.355081 | + | 0.355081i | ||||
\(249\) | 85.3929i | 0.342943i | ||||||||
\(250\) | −118.603 | − | 13.9514i | −0.474411 | − | 0.0558054i | ||||
\(251\) | 197.943 | 0.788619 | 0.394309 | − | 0.918978i | \(-0.370984\pi\) | ||||
0.394309 | + | 0.918978i | \(0.370984\pi\) | |||||||
\(252\) | 17.3273 | + | 17.3273i | 0.0687592 | + | 0.0687592i | ||||
\(253\) | −184.383 | + | 184.383i | −0.728785 | + | 0.728785i | ||||
\(254\) | − | 111.823i | − | 0.440246i | ||||||
\(255\) | −28.5758 | − | 30.8983i | −0.112062 | − | 0.121170i | ||||
\(256\) | −148.802 | −0.581259 | ||||||||
\(257\) | −206.394 | − | 206.394i | −0.803091 | − | 0.803091i | 0.180487 | − | 0.983577i | \(-0.442233\pi\) |
−0.983577 | + | 0.180487i | \(0.942233\pi\) | |||||||
\(258\) | −91.2220 | + | 91.2220i | −0.353574 | + | 0.353574i | ||||
\(259\) | 128.804i | 0.497313i | ||||||||
\(260\) | 0.955766 | − | 24.4749i | 0.00367602 | − | 0.0941344i | ||||
\(261\) | −67.0737 | −0.256987 | ||||||||
\(262\) | −128.547 | − | 128.547i | −0.490637 | − | 0.490637i | ||||
\(263\) | 235.719 | − | 235.719i | 0.896270 | − | 0.896270i | −0.0988340 | − | 0.995104i | \(-0.531511\pi\) |
0.995104 | + | 0.0988340i | \(0.0315113\pi\) | |||||||
\(264\) | − | 89.1097i | − | 0.337537i | ||||||
\(265\) | −66.4137 | − | 2.59351i | −0.250618 | − | 0.00978683i | ||||
\(266\) | 66.5076 | 0.250028 | ||||||||
\(267\) | 2.49100 | + | 2.49100i | 0.00932960 | + | 0.00932960i | ||||
\(268\) | −125.309 | + | 125.309i | −0.467570 | + | 0.467570i | ||||
\(269\) | 379.956i | 1.41248i | 0.707974 | + | 0.706238i | \(0.249609\pi\) | ||||
−0.707974 | + | 0.706238i | \(0.750391\pi\) | |||||||
\(270\) | 18.2226 | − | 16.8529i | 0.0674913 | − | 0.0624182i | ||||
\(271\) | −239.134 | −0.882414 | −0.441207 | − | 0.897405i | \(-0.645450\pi\) | ||||
−0.441207 | + | 0.897405i | \(0.645450\pi\) | |||||||
\(272\) | 20.2072 | + | 20.2072i | 0.0742913 | + | 0.0742913i | ||||
\(273\) | −5.14163 | + | 5.14163i | −0.0188338 | + | 0.0188338i | ||||
\(274\) | 165.634i | 0.604504i | ||||||||
\(275\) | −14.8134 | + | 189.379i | −0.0538668 | + | 0.688650i | ||||
\(276\) | 183.508 | 0.664885 | ||||||||
\(277\) | 118.114 | + | 118.114i | 0.426403 | + | 0.426403i | 0.887401 | − | 0.460998i | \(-0.152509\pi\) |
−0.460998 | + | 0.887401i | \(0.652509\pi\) | |||||||
\(278\) | −100.705 | + | 100.705i | −0.362249 | + | 0.362249i | ||||
\(279\) | 55.1782i | 0.197771i | ||||||||
\(280\) | −60.8165 | − | 65.7594i | −0.217202 | − | 0.234855i | ||||
\(281\) | 337.248 | 1.20017 | 0.600086 | − | 0.799936i | \(-0.295133\pi\) | ||||
0.600086 | + | 0.799936i | \(0.295133\pi\) | |||||||
\(282\) | 67.6028 | + | 67.6028i | 0.239726 | + | 0.239726i | ||||
\(283\) | −91.9392 | + | 91.9392i | −0.324873 | + | 0.324873i | −0.850633 | − | 0.525760i | \(-0.823781\pi\) |
0.525760 | + | 0.850633i | \(0.323781\pi\) | |||||||
\(284\) | − | 421.182i | − | 1.48304i | ||||||
\(285\) | −8.89167 | + | 227.695i | −0.0311988 | + | 0.798929i | ||||
\(286\) | 11.5184 | 0.0402740 | ||||||||
\(287\) | −70.0793 | − | 70.0793i | −0.244179 | − | 0.244179i | ||||
\(288\) | −69.3707 | + | 69.3707i | −0.240870 | + | 0.240870i | ||||
\(289\) | − | 265.383i | − | 0.918280i | ||||||
\(290\) | 106.718 | + | 4.16743i | 0.367994 | + | 0.0143705i | ||||
\(291\) | −143.209 | −0.492128 | ||||||||
\(292\) | −18.0654 | − | 18.0654i | −0.0618680 | − | 0.0618680i | ||||
\(293\) | −348.854 | + | 348.854i | −1.19063 | + | 1.19063i | −0.213736 | + | 0.976891i | \(0.568563\pi\) |
−0.976891 | + | 0.213736i | \(0.931437\pi\) | |||||||
\(294\) | 11.5832i | 0.0393985i | ||||||||
\(295\) | 182.731 | − | 168.995i | 0.619426 | − | 0.572866i | ||||
\(296\) | −329.632 | −1.11362 | ||||||||
\(297\) | −27.9179 | − | 27.9179i | −0.0939997 | − | 0.0939997i | ||||
\(298\) | 106.492 | − | 106.492i | 0.357356 | − | 0.357356i | ||||
\(299\) | 54.4534i | 0.182119i | ||||||||
\(300\) | 101.612 | − | 86.8689i | 0.338707 | − | 0.289563i | ||||
\(301\) | 206.269 | 0.685280 | ||||||||
\(302\) | −158.286 | − | 158.286i | −0.524126 | − | 0.524126i | ||||
\(303\) | 88.7662 | − | 88.7662i | 0.292958 | − | 0.292958i | ||||
\(304\) | − | 154.726i | − | 0.508966i | ||||||
\(305\) | 299.926 | + | 324.302i | 0.983363 | + | 1.06329i | ||||
\(306\) | −13.9284 | −0.0455178 | ||||||||
\(307\) | 306.607 | + | 306.607i | 0.998720 | + | 0.998720i | 0.999999 | − | 0.00127914i | \(-0.000407163\pi\) |
−0.00127914 | + | 0.999999i | \(0.500407\pi\) | |||||||
\(308\) | −43.8860 | + | 43.8860i | −0.142487 | + | 0.142487i | ||||
\(309\) | − | 237.041i | − | 0.767124i | ||||||
\(310\) | 3.42834 | − | 87.7918i | 0.0110592 | − | 0.283199i | ||||
\(311\) | −74.8228 | −0.240588 | −0.120294 | − | 0.992738i | \(-0.538384\pi\) | ||||
−0.120294 | + | 0.992738i | \(0.538384\pi\) | |||||||
\(312\) | −13.1583 | − | 13.1583i | −0.0421741 | − | 0.0421741i | ||||
\(313\) | 101.601 | − | 101.601i | 0.324605 | − | 0.324605i | −0.525925 | − | 0.850531i | \(-0.676281\pi\) |
0.850531 | + | 0.525925i | \(0.176281\pi\) | |||||||
\(314\) | − | 101.616i | − | 0.323618i | ||||||
\(315\) | −39.6560 | − | 1.54860i | −0.125892 | − | 0.00491619i | ||||
\(316\) | −205.112 | −0.649089 | ||||||||
\(317\) | 124.097 | + | 124.097i | 0.391475 | + | 0.391475i | 0.875213 | − | 0.483738i | \(-0.160721\pi\) |
−0.483738 | + | 0.875213i | \(0.660721\pi\) | |||||||
\(318\) | −15.5537 | + | 15.5537i | −0.0489109 | + | 0.0489109i | ||||
\(319\) | − | 169.882i | − | 0.532545i | ||||||
\(320\) | 28.3395 | − | 26.2093i | 0.0885608 | − | 0.0819040i | ||||
\(321\) | 30.5703 | 0.0952345 | ||||||||
\(322\) | 61.3369 | + | 61.3369i | 0.190487 | + | 0.190487i | ||||
\(323\) | 90.4172 | − | 90.4172i | 0.279929 | − | 0.279929i | ||||
\(324\) | 27.7855i | 0.0857578i | ||||||||
\(325\) | 25.7771 | + | 30.1519i | 0.0793141 | + | 0.0927751i | ||||
\(326\) | 168.287 | 0.516219 | ||||||||
\(327\) | −107.003 | − | 107.003i | −0.327226 | − | 0.327226i | ||||
\(328\) | 179.345 | − | 179.345i | 0.546783 | − | 0.546783i | ||||
\(329\) | − | 152.862i | − | 0.464626i | ||||||
\(330\) | 42.6844 | + | 46.1536i | 0.129347 | + | 0.139860i | ||||
\(331\) | 397.089 | 1.19966 | 0.599832 | − | 0.800126i | \(-0.295234\pi\) | ||||
0.599832 | + | 0.800126i | \(0.295234\pi\) | |||||||
\(332\) | 107.627 | + | 107.627i | 0.324179 | + | 0.324179i | ||||
\(333\) | −103.273 | + | 103.273i | −0.310129 | + | 0.310129i | ||||
\(334\) | − | 184.304i | − | 0.551807i | ||||||
\(335\) | 11.1993 | − | 286.787i | 0.0334307 | − | 0.856081i | ||||
\(336\) | 26.9475 | 0.0802009 | ||||||||
\(337\) | −185.463 | − | 185.463i | −0.550334 | − | 0.550334i | 0.376203 | − | 0.926537i | \(-0.377230\pi\) |
−0.926537 | + | 0.376203i | \(0.877230\pi\) | |||||||
\(338\) | −112.466 | + | 112.466i | −0.332740 | + | 0.332740i | ||||
\(339\) | − | 53.1898i | − | 0.156902i | ||||||
\(340\) | −74.9597 | − | 2.92724i | −0.220470 | − | 0.00860952i | ||||
\(341\) | −139.753 | −0.409834 | ||||||||
\(342\) | 53.3247 | + | 53.3247i | 0.155920 | + | 0.155920i | ||||
\(343\) | 13.0958 | − | 13.0958i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 527.878i | 1.53453i | ||||||||
\(345\) | −218.193 | + | 201.792i | −0.632443 | + | 0.584905i | ||||
\(346\) | 163.509 | 0.472569 | ||||||||
\(347\) | −182.221 | − | 182.221i | −0.525133 | − | 0.525133i | 0.393984 | − | 0.919117i | \(-0.371097\pi\) |
−0.919117 | + | 0.393984i | \(0.871097\pi\) | |||||||
\(348\) | −84.5382 | + | 84.5382i | −0.242926 | + | 0.242926i | ||||
\(349\) | − | 416.140i | − | 1.19238i | −0.802844 | − | 0.596189i | \(-0.796681\pi\) | ||
0.802844 | − | 0.596189i | \(-0.203319\pi\) | |||||||
\(350\) | 62.9989 | + | 4.92783i | 0.179997 | + | 0.0140795i | ||||
\(351\) | −8.24495 | −0.0234899 | ||||||||
\(352\) | −175.700 | − | 175.700i | −0.499147 | − | 0.499147i | ||||
\(353\) | −402.531 | + | 402.531i | −1.14031 | + | 1.14031i | −0.151921 | + | 0.988393i | \(0.548546\pi\) |
−0.988393 | + | 0.151921i | \(0.951454\pi\) | |||||||
\(354\) | − | 82.3720i | − | 0.232689i | ||||||
\(355\) | 463.147 | + | 500.789i | 1.30464 | + | 1.41067i | ||||
\(356\) | 6.27921 | 0.0176382 | ||||||||
\(357\) | 15.7473 | + | 15.7473i | 0.0441102 | + | 0.0441102i | ||||
\(358\) | −38.6508 | + | 38.6508i | −0.107963 | + | 0.107963i | ||||
\(359\) | − | 120.174i | − | 0.334747i | −0.985894 | − | 0.167373i | \(-0.946471\pi\) | ||
0.985894 | − | 0.167373i | \(-0.0535285\pi\) | |||||||
\(360\) | 3.96313 | − | 101.487i | 0.0110087 | − | 0.281907i | ||||
\(361\) | −331.320 | −0.917785 | ||||||||
\(362\) | 198.766 | + | 198.766i | 0.549076 | + | 0.549076i | ||||
\(363\) | −77.4846 | + | 77.4846i | −0.213456 | + | 0.213456i | ||||
\(364\) | 12.9608i | 0.0356066i | ||||||||
\(365\) | 41.3453 | + | 1.61457i | 0.113275 | + | 0.00442348i | ||||
\(366\) | 146.190 | 0.399427 | ||||||||
\(367\) | 162.325 | + | 162.325i | 0.442301 | + | 0.442301i | 0.892785 | − | 0.450483i | \(-0.148748\pi\) |
−0.450483 | + | 0.892785i | \(0.648748\pi\) | |||||||
\(368\) | 142.696 | − | 142.696i | 0.387762 | − | 0.387762i | ||||
\(369\) | − | 112.377i | − | 0.304544i | ||||||
\(370\) | 170.730 | − | 157.897i | 0.461433 | − | 0.426749i | ||||
\(371\) | 35.1696 | 0.0947968 | ||||||||
\(372\) | 69.5454 | + | 69.5454i | 0.186950 | + | 0.186950i | ||||
\(373\) | 306.523 | − | 306.523i | 0.821776 | − | 0.821776i | −0.164586 | − | 0.986363i | \(-0.552629\pi\) |
0.986363 | + | 0.164586i | \(0.0526289\pi\) | |||||||
\(374\) | − | 35.2774i | − | 0.0943247i | ||||||
\(375\) | −25.2935 | + | 215.024i | −0.0674493 | + | 0.573397i | ||||
\(376\) | 391.200 | 1.04043 | ||||||||
\(377\) | −25.0855 | − | 25.0855i | −0.0665398 | − | 0.0665398i | ||||
\(378\) | −9.28719 | + | 9.28719i | −0.0245693 | + | 0.0245693i | ||||
\(379\) | − | 126.143i | − | 0.332830i | −0.986056 | − | 0.166415i | \(-0.946781\pi\) | ||
0.986056 | − | 0.166415i | \(-0.0532192\pi\) | |||||||
\(380\) | 275.775 | + | 298.188i | 0.725723 | + | 0.784706i | ||||
\(381\) | −202.732 | −0.532104 | ||||||||
\(382\) | 166.618 | + | 166.618i | 0.436174 | + | 0.436174i | ||||
\(383\) | 349.571 | − | 349.571i | 0.912717 | − | 0.912717i | −0.0837685 | − | 0.996485i | \(-0.526696\pi\) |
0.996485 | + | 0.0837685i | \(0.0266956\pi\) | |||||||
\(384\) | 213.789i | 0.556742i | ||||||||
\(385\) | 3.92224 | − | 100.439i | 0.0101876 | − | 0.260882i | ||||
\(386\) | 136.082 | 0.352544 | ||||||||
\(387\) | 165.383 | + | 165.383i | 0.427347 | + | 0.427347i | ||||
\(388\) | −180.498 | + | 180.498i | −0.465200 | + | 0.465200i | ||||
\(389\) | − | 165.348i | − | 0.425060i | −0.977155 | − | 0.212530i | \(-0.931830\pi\) | ||
0.977155 | − | 0.212530i | \(-0.0681704\pi\) | |||||||
\(390\) | 13.1182 | + | 0.512277i | 0.0336364 | + | 0.00131353i | ||||
\(391\) | 166.775 | 0.426535 | ||||||||
\(392\) | 33.5144 | + | 33.5144i | 0.0854959 | + | 0.0854959i | ||||
\(393\) | −233.053 | + | 233.053i | −0.593009 | + | 0.593009i | ||||
\(394\) | − | 20.2549i | − | 0.0514083i | ||||||
\(395\) | 243.880 | − | 225.548i | 0.617417 | − | 0.571008i | ||||
\(396\) | −70.3742 | −0.177713 | ||||||||
\(397\) | −42.7811 | − | 42.7811i | −0.107761 | − | 0.107761i | 0.651171 | − | 0.758931i | \(-0.274278\pi\) |
−0.758931 | + | 0.651171i | \(0.774278\pi\) | |||||||
\(398\) | −194.105 | + | 194.105i | −0.487701 | + | 0.487701i | ||||
\(399\) | − | 120.577i | − | 0.302197i | ||||||
\(400\) | 11.4643 | − | 146.563i | 0.0286607 | − | 0.366408i | ||||
\(401\) | 92.5492 | 0.230796 | 0.115398 | − | 0.993319i | \(-0.463186\pi\) | ||||
0.115398 | + | 0.993319i | \(0.463186\pi\) | |||||||
\(402\) | −67.1637 | − | 67.1637i | −0.167074 | − | 0.167074i | ||||
\(403\) | −20.6366 | + | 20.6366i | −0.0512074 | + | 0.0512074i | ||||
\(404\) | − | 223.758i | − | 0.553856i | ||||||
\(405\) | −30.5539 | − | 33.0372i | −0.0754418 | − | 0.0815734i | ||||
\(406\) | −56.5130 | −0.139195 | ||||||||
\(407\) | −261.566 | − | 261.566i | −0.642669 | − | 0.642669i | ||||
\(408\) | −40.3001 | + | 40.3001i | −0.0987748 | + | 0.0987748i | ||||
\(409\) | − | 71.7158i | − | 0.175344i | −0.996149 | − | 0.0876721i | \(-0.972057\pi\) | ||
0.996149 | − | 0.0876721i | \(-0.0279428\pi\) | |||||||
\(410\) | −6.98222 | + | 178.798i | −0.0170298 | + | 0.436094i | ||||
\(411\) | 300.291 | 0.730635 | ||||||||
\(412\) | −298.761 | − | 298.761i | −0.725149 | − | 0.725149i | ||||
\(413\) | −93.1289 | + | 93.1289i | −0.225494 | + | 0.225494i | ||||
\(414\) | 98.3578i | 0.237579i | ||||||||
\(415\) | −246.320 | − | 9.61901i | −0.593543 | − | 0.0231783i | ||||
\(416\) | −51.8891 | −0.124733 | ||||||||
\(417\) | 182.576 | + | 182.576i | 0.437832 | + | 0.437832i | ||||
\(418\) | −135.059 | + | 135.059i | −0.323107 | + | 0.323107i | ||||
\(419\) | 472.026i | 1.12655i | 0.826268 | + | 0.563277i | \(0.190460\pi\) | ||||
−0.826268 | + | 0.563277i | \(0.809540\pi\) | |||||||
\(420\) | −51.9334 | + | 48.0298i | −0.123651 | + | 0.114357i | ||||
\(421\) | 746.988 | 1.77432 | 0.887159 | − | 0.461464i | \(-0.152676\pi\) | ||||
0.887159 | + | 0.461464i | \(0.152676\pi\) | |||||||
\(422\) | −269.920 | − | 269.920i | −0.639620 | − | 0.639620i | ||||
\(423\) | 122.562 | − | 122.562i | 0.289745 | − | 0.289745i | ||||
\(424\) | 90.0051i | 0.212276i | ||||||||
\(425\) | 92.3466 | − | 78.9478i | 0.217286 | − | 0.185759i | ||||
\(426\) | 225.748 | 0.529924 | ||||||||
\(427\) | −165.281 | − | 165.281i | −0.387075 | − | 0.387075i | ||||
\(428\) | 38.5301 | − | 38.5301i | 0.0900235 | − | 0.0900235i | ||||
\(429\) | − | 20.8825i | − | 0.0486772i | ||||||
\(430\) | −252.859 | − | 273.410i | −0.588044 | − | 0.635838i | ||||
\(431\) | −754.426 | −1.75041 | −0.875204 | − | 0.483754i | \(-0.839273\pi\) | ||||
−0.875204 | + | 0.483754i | \(0.839273\pi\) | |||||||
\(432\) | 21.6061 | + | 21.6061i | 0.0500141 | + | 0.0500141i | ||||
\(433\) | −344.305 | + | 344.305i | −0.795162 | + | 0.795162i | −0.982328 | − | 0.187166i | \(-0.940070\pi\) |
0.187166 | + | 0.982328i | \(0.440070\pi\) | |||||||
\(434\) | 46.4905i | 0.107121i | ||||||||
\(435\) | 7.55546 | − | 193.478i | 0.0173689 | − | 0.444776i | ||||
\(436\) | −269.728 | −0.618643 | ||||||||
\(437\) | −638.495 | − | 638.495i | −1.46109 | − | 1.46109i | ||||
\(438\) | 9.68282 | − | 9.68282i | 0.0221069 | − | 0.0221069i | ||||
\(439\) | − | 49.1546i | − | 0.111970i | −0.998432 | − | 0.0559848i | \(-0.982170\pi\) | ||
0.998432 | − | 0.0559848i | \(-0.0178298\pi\) | |||||||
\(440\) | 257.042 | + | 10.0377i | 0.584185 | + | 0.0228129i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −5.20922 | − | 5.20922i | −0.0117856 | − | 0.0117856i | ||||
\(443\) | 117.289 | − | 117.289i | 0.264762 | − | 0.264762i | −0.562224 | − | 0.826985i | \(-0.690054\pi\) |
0.826985 | + | 0.562224i | \(0.190054\pi\) | |||||||
\(444\) | 260.326i | 0.586320i | ||||||||
\(445\) | −7.46603 | + | 6.90484i | −0.0167776 | + | 0.0155165i | ||||
\(446\) | −284.168 | −0.637147 | ||||||||
\(447\) | −193.068 | − | 193.068i | −0.431918 | − | 0.431918i | ||||
\(448\) | −14.4432 | + | 14.4432i | −0.0322394 | + | 0.0322394i | ||||
\(449\) | 296.976i | 0.661416i | 0.943733 | + | 0.330708i | \(0.107288\pi\) | ||||
−0.943733 | + | 0.330708i | \(0.892712\pi\) | |||||||
\(450\) | 46.5604 | + | 54.4625i | 0.103468 | + | 0.121028i | ||||
\(451\) | 284.624 | 0.631096 | ||||||||
\(452\) | −67.0393 | − | 67.0393i | −0.148317 | − | 0.148317i | ||||
\(453\) | −286.969 | + | 286.969i | −0.633485 | + | 0.633485i | ||||
\(454\) | 176.620i | 0.389030i | ||||||||
\(455\) | −14.2521 | − | 15.4105i | −0.0313234 | − | 0.0338692i | ||||
\(456\) | 308.576 | 0.676702 | ||||||||
\(457\) | −257.425 | − | 257.425i | −0.563293 | − | 0.563293i | 0.366948 | − | 0.930241i | \(-0.380403\pi\) |
−0.930241 | + | 0.366948i | \(0.880403\pi\) | |||||||
\(458\) | 173.576 | − | 173.576i | 0.378987 | − | 0.378987i | ||||
\(459\) | 25.2519i | 0.0550151i | ||||||||
\(460\) | −20.6711 | + | 529.339i | −0.0449372 | + | 1.15074i | ||||
\(461\) | −357.600 | −0.775704 | −0.387852 | − | 0.921722i | \(-0.626783\pi\) | ||||
−0.387852 | + | 0.921722i | \(0.626783\pi\) | |||||||
\(462\) | −23.5223 | − | 23.5223i | −0.0509140 | − | 0.0509140i | ||||
\(463\) | 78.7851 | − | 78.7851i | 0.170162 | − | 0.170162i | −0.616888 | − | 0.787051i | \(-0.711607\pi\) |
0.787051 | + | 0.616888i | \(0.211607\pi\) | |||||||
\(464\) | 131.474i | 0.283349i | ||||||||
\(465\) | −159.165 | − | 6.21550i | −0.342289 | − | 0.0133667i | ||||
\(466\) | −81.9999 | −0.175965 | ||||||||
\(467\) | 654.767 | + | 654.767i | 1.40207 | + | 1.40207i | 0.793500 | + | 0.608570i | \(0.208257\pi\) |
0.608570 | + | 0.793500i | \(0.291743\pi\) | |||||||
\(468\) | −10.3918 | + | 10.3918i | −0.0222046 | + | 0.0222046i | ||||
\(469\) | 151.869i | 0.323815i | ||||||||
\(470\) | −202.619 | + | 187.389i | −0.431104 | + | 0.398700i | ||||
\(471\) | −184.228 | −0.391141 | ||||||||
\(472\) | −238.333 | − | 238.333i | −0.504942 | − | 0.504942i | ||||
\(473\) | −418.877 | + | 418.877i | −0.885575 | + | 0.885575i | ||||
\(474\) | − | 109.937i | − | 0.231935i | ||||||
\(475\) | −655.796 | − | 51.2970i | −1.38062 | − | 0.107994i | ||||
\(476\) | 39.6952 | 0.0833932 | ||||||||
\(477\) | 28.1984 | + | 28.1984i | 0.0591162 | + | 0.0591162i | ||||
\(478\) | 45.2227 | − | 45.2227i | 0.0946081 | − | 0.0946081i | ||||
\(479\) | − | 262.707i | − | 0.548449i | −0.961666 | − | 0.274225i | \(-0.911579\pi\) | ||
0.961666 | − | 0.274225i | \(-0.0884212\pi\) | |||||||
\(480\) | −192.289 | − | 207.918i | −0.400603 | − | 0.433162i | ||||
\(481\) | −77.2480 | −0.160599 | ||||||||
\(482\) | 55.7884 | + | 55.7884i | 0.115744 | + | 0.115744i | ||||
\(483\) | 111.202 | − | 111.202i | 0.230232 | − | 0.230232i | ||||
\(484\) | 195.320i | 0.403553i | ||||||||
\(485\) | 16.1317 | − | 413.095i | 0.0332612 | − | 0.851742i | ||||
\(486\) | −14.8926 | −0.0306433 | ||||||||
\(487\) | −42.8848 | − | 42.8848i | −0.0880591 | − | 0.0880591i | 0.661705 | − | 0.749764i | \(-0.269833\pi\) |
−0.749764 | + | 0.661705i | \(0.769833\pi\) | |||||||
\(488\) | 422.983 | − | 422.983i | 0.866768 | − | 0.866768i | ||||
\(489\) | − | 305.101i | − | 0.623928i | ||||||
\(490\) | −33.4122 | − | 1.30478i | −0.0681883 | − | 0.00266281i | ||||
\(491\) | −58.5988 | −0.119346 | −0.0596730 | − | 0.998218i | \(-0.519006\pi\) | ||||
−0.0596730 | + | 0.998218i | \(0.519006\pi\) | |||||||
\(492\) | −141.637 | − | 141.637i | −0.287881 | − | 0.287881i | ||||
\(493\) | −76.8296 | + | 76.8296i | −0.155841 | + | 0.155841i | ||||
\(494\) | 39.8867i | 0.0807424i | ||||||||
\(495\) | 83.6755 | − | 77.3859i | 0.169041 | − | 0.156335i | ||||
\(496\) | 108.157 | 0.218059 | ||||||||
\(497\) | −255.228 | − | 255.228i | −0.513537 | − | 0.513537i | ||||
\(498\) | −57.6867 | + | 57.6867i | −0.115837 | + | 0.115837i | ||||
\(499\) | 421.048i | 0.843784i | 0.906646 | + | 0.421892i | \(0.138634\pi\) | ||||
−0.906646 | + | 0.421892i | \(0.861366\pi\) | |||||||
\(500\) | 239.132 | + | 302.890i | 0.478264 | + | 0.605781i | ||||
\(501\) | −334.138 | −0.666942 | ||||||||
\(502\) | 133.719 | + | 133.719i | 0.266373 | + | 0.266373i | ||||
\(503\) | 357.650 | − | 357.650i | 0.711034 | − | 0.711034i | −0.255718 | − | 0.966751i | \(-0.582312\pi\) |
0.966751 | + | 0.255718i | \(0.0823118\pi\) | |||||||
\(504\) | 53.7426i | 0.106632i | ||||||||
\(505\) | 246.052 | + | 266.050i | 0.487231 | + | 0.526831i | ||||
\(506\) | −249.117 | −0.492326 | ||||||||
\(507\) | 203.898 | + | 203.898i | 0.402166 | + | 0.402166i | ||||
\(508\) | −255.518 | + | 255.518i | −0.502989 | + | 0.502989i | ||||
\(509\) | 934.911i | 1.83676i | 0.395700 | + | 0.918380i | \(0.370502\pi\) | ||||
−0.395700 | + | 0.918380i | \(0.629498\pi\) | |||||||
\(510\) | 1.56896 | − | 40.1773i | 0.00307638 | − | 0.0787790i | ||||
\(511\) | −21.8946 | −0.0428465 | ||||||||
\(512\) | 248.593 | + | 248.593i | 0.485533 | + | 0.485533i | ||||
\(513\) | 96.6764 | − | 96.6764i | 0.188453 | − | 0.188453i | ||||
\(514\) | − | 278.857i | − | 0.542523i | ||||||
\(515\) | 683.758 | + | 26.7013i | 1.32769 | + | 0.0518472i | ||||
\(516\) | 416.891 | 0.807928 | ||||||||
\(517\) | 310.421 | + | 310.421i | 0.600428 | + | 0.600428i | ||||
\(518\) | −87.0129 | + | 87.0129i | −0.167978 | + | 0.167978i | ||||
\(519\) | − | 296.438i | − | 0.571171i | ||||||
\(520\) | 39.4381 | − | 36.4736i | 0.0758424 | − | 0.0701416i | ||||
\(521\) | −73.1865 | −0.140473 | −0.0702366 | − | 0.997530i | \(-0.522375\pi\) | ||||
−0.0702366 | + | 0.997530i | \(0.522375\pi\) | |||||||
\(522\) | −45.3112 | − | 45.3112i | −0.0868031 | − | 0.0868031i | ||||
\(523\) | 53.6581 | − | 53.6581i | 0.102597 | − | 0.102597i | −0.653945 | − | 0.756542i | \(-0.726887\pi\) |
0.756542 | + | 0.653945i | \(0.226887\pi\) | |||||||
\(524\) | 587.469i | 1.12112i | ||||||||
\(525\) | 8.93404 | − | 114.216i | 0.0170172 | − | 0.217553i | ||||
\(526\) | 318.477 | 0.605470 | ||||||||
\(527\) | 63.2039 | + | 63.2039i | 0.119932 | + | 0.119932i | ||||
\(528\) | −54.7231 | + | 54.7231i | −0.103642 | + | 0.103642i | ||||
\(529\) | − | 648.709i | − | 1.22629i | ||||||
\(530\) | −43.1134 | − | 46.6174i | −0.0813460 | − | 0.0879574i | ||||
\(531\) | −149.338 | −0.281240 | ||||||||
\(532\) | −151.972 | − | 151.972i | −0.285662 | − | 0.285662i | ||||
\(533\) | 42.0288 | − | 42.0288i | 0.0788533 | − | 0.0788533i | ||||
\(534\) | 3.36556i | 0.00630256i | ||||||||
\(535\) | −3.44356 | + | 88.1816i | −0.00643656 | + | 0.164825i | ||||
\(536\) | −388.659 | −0.725110 | ||||||||
\(537\) | 70.0731 | + | 70.0731i | 0.130490 | + | 0.130490i | ||||
\(538\) | −256.677 | + | 256.677i | −0.477095 | + | 0.477095i | ||||
\(539\) | 53.1880i | 0.0986791i | ||||||||
\(540\) | −80.1488 | − | 3.12988i | −0.148424 | − | 0.00579607i | ||||
\(541\) | −1071.71 | −1.98098 | −0.990490 | − | 0.137581i | \(-0.956067\pi\) | ||||
−0.990490 | + | 0.137581i | \(0.956067\pi\) | |||||||
\(542\) | −161.546 | − | 161.546i | −0.298055 | − | 0.298055i | ||||
\(543\) | 360.357 | − | 360.357i | 0.663641 | − | 0.663641i | ||||
\(544\) | 158.921i | 0.292135i | ||||||||
\(545\) | 320.709 | − | 296.602i | 0.588457 | − | 0.544225i | ||||
\(546\) | −6.94680 | −0.0127231 | ||||||||
\(547\) | 601.898 | + | 601.898i | 1.10036 | + | 1.10036i | 0.994367 | + | 0.105994i | \(0.0338026\pi\) |
0.105994 | + | 0.994367i | \(0.466197\pi\) | |||||||
\(548\) | 378.480 | − | 378.480i | 0.690656 | − | 0.690656i | ||||
\(549\) | − | 265.039i | − | 0.482768i | ||||||
\(550\) | −137.941 | + | 117.927i | −0.250801 | + | 0.214412i | ||||
\(551\) | 588.281 | 1.06766 | ||||||||
\(552\) | 284.586 | + | 284.586i | 0.515553 | + | 0.515553i | ||||
\(553\) | −124.294 | + | 124.294i | −0.224762 | + | 0.224762i | ||||
\(554\) | 159.582i | 0.288054i | ||||||||
\(555\) | −286.264 | − | 309.530i | −0.515790 | − | 0.557711i | ||||
\(556\) | 460.229 | 0.827751 | ||||||||
\(557\) | −242.099 | − | 242.099i | −0.434648 | − | 0.434648i | 0.455558 | − | 0.890206i | \(-0.349440\pi\) |
−0.890206 | + | 0.455558i | \(0.849440\pi\) | |||||||
\(558\) | −37.2753 | + | 37.2753i | −0.0668016 | + | 0.0668016i | ||||
\(559\) | 123.706i | 0.221299i | ||||||||
\(560\) | −3.03548 | + | 77.7315i | −0.00542050 | + | 0.138806i | ||||
\(561\) | −63.9572 | −0.114006 | ||||||||
\(562\) | 227.826 | + | 227.826i | 0.405384 | + | 0.405384i | ||||
\(563\) | 76.1930 | − | 76.1930i | 0.135334 | − | 0.135334i | −0.636195 | − | 0.771529i | \(-0.719492\pi\) |
0.771529 | + | 0.636195i | \(0.219492\pi\) | |||||||
\(564\) | − | 308.950i | − | 0.547783i | ||||||
\(565\) | 153.429 | + | 5.99152i | 0.271556 | + | 0.0106045i | ||||
\(566\) | −124.218 | −0.219466 | ||||||||
\(567\) | 16.8375 | + | 16.8375i | 0.0296957 | + | 0.0296957i | ||||
\(568\) | 653.172 | − | 653.172i | 1.14995 | − | 1.14995i | ||||
\(569\) | − | 319.028i | − | 0.560683i | −0.959900 | − | 0.280341i | \(-0.909552\pi\) | ||
0.959900 | − | 0.280341i | \(-0.0904476\pi\) | |||||||
\(570\) | −159.825 | + | 147.811i | −0.280394 | + | 0.259318i | ||||
\(571\) | −26.8933 | −0.0470987 | −0.0235493 | − | 0.999723i | \(-0.507497\pi\) | ||||
−0.0235493 | + | 0.999723i | \(0.507497\pi\) | |||||||
\(572\) | −26.3199 | − | 26.3199i | −0.0460137 | − | 0.0460137i | ||||
\(573\) | 302.075 | − | 302.075i | 0.527182 | − | 0.527182i | ||||
\(574\) | − | 94.6833i | − | 0.164953i | ||||||
\(575\) | −557.502 | − | 652.119i | −0.969568 | − | 1.13412i | ||||
\(576\) | −23.1607 | −0.0402096 | ||||||||
\(577\) | 302.359 | + | 302.359i | 0.524019 | + | 0.524019i | 0.918783 | − | 0.394764i | \(-0.129174\pi\) |
−0.394764 | + | 0.918783i | \(0.629174\pi\) | |||||||
\(578\) | 179.278 | − | 179.278i | 0.310169 | − | 0.310169i | ||||
\(579\) | − | 246.713i | − | 0.426102i | ||||||
\(580\) | −234.332 | − | 253.378i | −0.404021 | − | 0.436858i | ||||
\(581\) | 130.440 | 0.224509 | ||||||||
\(582\) | −96.7441 | − | 96.7441i | −0.166227 | − | 0.166227i | ||||
\(583\) | −71.4200 | + | 71.4200i | −0.122504 | + | 0.122504i | ||||
\(584\) | − | 56.0319i | − | 0.0959451i | ||||||
\(585\) | 0.928746 | − | 23.7830i | 0.00158760 | − | 0.0406547i | ||||
\(586\) | −471.332 | −0.804321 | ||||||||
\(587\) | 16.9036 | + | 16.9036i | 0.0287966 | + | 0.0287966i | 0.721358 | − | 0.692562i | \(-0.243518\pi\) |
−0.692562 | + | 0.721358i | \(0.743518\pi\) | |||||||
\(588\) | 26.4679 | − | 26.4679i | 0.0450135 | − | 0.0450135i | ||||
\(589\) | − | 483.949i | − | 0.821646i | ||||||
\(590\) | 237.606 | + | 9.27872i | 0.402723 | + | 0.0157266i | ||||
\(591\) | −36.7216 | −0.0621347 | ||||||||
\(592\) | 202.430 | + | 202.430i | 0.341943 | + | 0.341943i | ||||
\(593\) | 411.219 | − | 411.219i | 0.693456 | − | 0.693456i | −0.269535 | − | 0.962991i | \(-0.586870\pi\) |
0.962991 | + | 0.269535i | \(0.0868699\pi\) | |||||||
\(594\) | − | 37.7195i | − | 0.0635009i | ||||||
\(595\) | −47.1979 | + | 43.6502i | −0.0793242 | + | 0.0733617i | ||||
\(596\) | −486.676 | −0.816570 | ||||||||
\(597\) | 351.908 | + | 351.908i | 0.589461 | + | 0.589461i | ||||
\(598\) | −36.7857 | + | 36.7857i | −0.0615145 | + | 0.0615145i | ||||
\(599\) | − | 637.724i | − | 1.06465i | −0.846541 | − | 0.532324i | \(-0.821319\pi\) | ||
0.846541 | − | 0.532324i | \(-0.178681\pi\) | |||||||
\(600\) | 292.297 | + | 22.8637i | 0.487162 | + | 0.0381062i | ||||
\(601\) | 576.764 | 0.959674 | 0.479837 | − | 0.877358i | \(-0.340696\pi\) | ||||
0.479837 | + | 0.877358i | \(0.340696\pi\) | |||||||
\(602\) | 139.344 | + | 139.344i | 0.231468 | + | 0.231468i | ||||
\(603\) | −121.766 | + | 121.766i | −0.201934 | + | 0.201934i | ||||
\(604\) | 723.378i | 1.19765i | ||||||||
\(605\) | −214.780 | − | 232.237i | −0.355009 | − | 0.383862i | ||||
\(606\) | 119.931 | 0.197906 | ||||||||
\(607\) | −144.949 | − | 144.949i | −0.238796 | − | 0.238796i | 0.577555 | − | 0.816352i | \(-0.304007\pi\) |
−0.816352 | + | 0.577555i | \(0.804007\pi\) | |||||||
\(608\) | 608.427 | − | 608.427i | 1.00070 | − | 1.00070i | ||||
\(609\) | 102.457i | 0.168238i | ||||||||
\(610\) | −16.4675 | + | 421.694i | −0.0269959 | + | 0.691301i | ||||
\(611\) | 91.6763 | 0.150043 | ||||||||
\(612\) | 31.8269 | + | 31.8269i | 0.0520048 | + | 0.0520048i | ||||
\(613\) | 588.190 | − | 588.190i | 0.959527 | − | 0.959527i | −0.0396852 | − | 0.999212i | \(-0.512636\pi\) |
0.999212 | + | 0.0396852i | \(0.0126355\pi\) | |||||||
\(614\) | 414.253i | 0.674679i | ||||||||
\(615\) | 324.157 | + | 12.6586i | 0.527085 | + | 0.0205831i | ||||
\(616\) | −136.117 | −0.220970 | ||||||||
\(617\) | 688.254 | + | 688.254i | 1.11548 | + | 1.11548i | 0.992396 | + | 0.123088i | \(0.0392798\pi\) |
0.123088 | + | 0.992396i | \(0.460720\pi\) | |||||||
\(618\) | 160.132 | − | 160.132i | 0.259113 | − | 0.259113i | ||||
\(619\) | 1033.56i | 1.66972i | 0.550459 | + | 0.834862i | \(0.314453\pi\) | ||||
−0.550459 | + | 0.834862i | \(0.685547\pi\) | |||||||
\(620\) | −208.441 | + | 192.773i | −0.336195 | + | 0.310925i | ||||
\(621\) | 178.320 | 0.287150 | ||||||||
\(622\) | −50.5461 | − | 50.5461i | −0.0812638 | − | 0.0812638i | ||||
\(623\) | 3.80507 | − | 3.80507i | 0.00610766 | − | 0.00610766i | ||||
\(624\) | 16.1613i | 0.0258995i | ||||||||
\(625\) | −617.398 | − | 97.1815i | −0.987837 | − | 0.155490i | ||||
\(626\) | 137.272 | 0.219285 | ||||||||
\(627\) | 244.858 | + | 244.858i | 0.390524 | + | 0.390524i | ||||
\(628\) | −232.196 | + | 232.196i | −0.369739 | + | 0.369739i | ||||
\(629\) | 236.588i | 0.376134i | ||||||||
\(630\) | −25.7432 | − | 27.8355i | −0.0408623 | − | 0.0441834i | ||||
\(631\) | −53.6569 | −0.0850346 | −0.0425173 | − | 0.999096i | \(-0.513538\pi\) | ||||
−0.0425173 | + | 0.999096i | \(0.513538\pi\) | |||||||
\(632\) | −318.089 | − | 318.089i | −0.503305 | − | 0.503305i | ||||
\(633\) | −489.358 | + | 489.358i | −0.773078 | + | 0.773078i | ||||
\(634\) | 167.666i | 0.264458i | ||||||||
\(635\) | 22.8365 | − | 584.790i | 0.0359630 | − | 0.920929i | ||||
\(636\) | 71.0813 | 0.111763 | ||||||||
\(637\) | 7.85397 | + | 7.85397i | 0.0123296 | + | 0.0123296i | ||||
\(638\) | 114.763 | − | 114.763i | 0.179879 | − | 0.179879i | ||||
\(639\) | − | 409.275i | − | 0.640493i | ||||||
\(640\) | −616.685 | − | 24.0820i | −0.963570 | − | 0.0376282i | ||||
\(641\) | −120.207 | −0.187531 | −0.0937653 | − | 0.995594i | \(-0.529890\pi\) | ||||
−0.0937653 | + | 0.995594i | \(0.529890\pi\) | |||||||
\(642\) | 20.6516 | + | 20.6516i | 0.0321675 | + | 0.0321675i | ||||
\(643\) | 18.2639 | − | 18.2639i | 0.0284042 | − | 0.0284042i | −0.692762 | − | 0.721166i | \(-0.743606\pi\) |
0.721166 | + | 0.692762i | \(0.243606\pi\) | |||||||
\(644\) | − | 280.314i | − | 0.435270i | ||||||
\(645\) | −495.686 | + | 458.427i | −0.768506 | + | 0.710740i | ||||
\(646\) | 122.162 | 0.189105 | ||||||||
\(647\) | 281.286 | + | 281.286i | 0.434754 | + | 0.434754i | 0.890242 | − | 0.455488i | \(-0.150535\pi\) |
−0.455488 | + | 0.890242i | \(0.650535\pi\) | |||||||
\(648\) | −43.0899 | + | 43.0899i | −0.0664968 | + | 0.0664968i | ||||
\(649\) | − | 378.239i | − | 0.582803i | ||||||
\(650\) | −2.95538 | + | 37.7825i | −0.00454674 | + | 0.0581269i | ||||
\(651\) | 84.2861 | 0.129472 | ||||||||
\(652\) | −384.542 | − | 384.542i | −0.589789 | − | 0.589789i | ||||
\(653\) | −554.289 | + | 554.289i | −0.848835 | + | 0.848835i | −0.989988 | − | 0.141152i | \(-0.954919\pi\) |
0.141152 | + | 0.989988i | \(0.454919\pi\) | |||||||
\(654\) | − | 144.570i | − | 0.221056i | ||||||
\(655\) | −646.001 | − | 698.505i | −0.986261 | − | 1.06642i | ||||
\(656\) | −220.275 | −0.335785 | ||||||||
\(657\) | −17.5547 | − | 17.5547i | −0.0267195 | − | 0.0267195i | ||||
\(658\) | 103.265 | − | 103.265i | 0.156938 | − | 0.156938i | ||||
\(659\) | 317.311i | 0.481504i | 0.970587 | + | 0.240752i | \(0.0773941\pi\) | ||||
−0.970587 | + | 0.240752i | \(0.922606\pi\) | |||||||
\(660\) | 7.92724 | − | 202.998i | 0.0120110 | − | 0.307573i | ||||
\(661\) | −533.264 | −0.806753 | −0.403377 | − | 0.915034i | \(-0.632164\pi\) | ||||
−0.403377 | + | 0.915034i | \(0.632164\pi\) | |||||||
\(662\) | 268.251 | + | 268.251i | 0.405213 | + | 0.405213i | ||||
\(663\) | −9.44419 | + | 9.44419i | −0.0142446 | + | 0.0142446i | ||||
\(664\) | 333.818i | 0.502738i | ||||||||
\(665\) | 347.810 | + | 13.5822i | 0.523022 | + | 0.0204244i | ||||
\(666\) | −139.531 | −0.209506 | ||||||||
\(667\) | 542.544 | + | 542.544i | 0.813410 | + | 0.813410i | ||||
\(668\) | −421.140 | + | 421.140i | −0.630449 | + | 0.630449i | ||||
\(669\) | 515.189i | 0.770088i | ||||||||
\(670\) | 201.303 | − | 186.172i | 0.300452 | − | 0.277868i | ||||
\(671\) | 671.282 | 1.00042 | ||||||||
\(672\) | 105.965 | + | 105.965i | 0.157687 | + | 0.157687i | ||||
\(673\) | −244.707 | + | 244.707i | −0.363606 | + | 0.363606i | −0.865139 | − | 0.501533i | \(-0.832770\pi\) |
0.501533 | + | 0.865139i | \(0.332770\pi\) | |||||||
\(674\) | − | 250.576i | − | 0.371775i | ||||||
\(675\) | 98.7393 | − | 84.4130i | 0.146280 | − | 0.125056i | ||||
\(676\) | 513.978 | 0.760322 | ||||||||
\(677\) | −380.155 | − | 380.155i | −0.561529 | − | 0.561529i | 0.368213 | − | 0.929742i | \(-0.379970\pi\) |
−0.929742 | + | 0.368213i | \(0.879970\pi\) | |||||||
\(678\) | 35.9321 | − | 35.9321i | 0.0529971 | − | 0.0529971i | ||||
\(679\) | 218.756i | 0.322173i | ||||||||
\(680\) | −111.708 | − | 120.787i | −0.164277 | − | 0.177629i | ||||
\(681\) | 320.207 | 0.470202 | ||||||||
\(682\) | −94.4096 | − | 94.4096i | −0.138430 | − | 0.138430i | ||||
\(683\) | −739.822 | + | 739.822i | −1.08319 | + | 1.08319i | −0.0869848 | + | 0.996210i | \(0.527723\pi\) |
−0.996210 | + | 0.0869848i | \(0.972277\pi\) | |||||||
\(684\) | − | 243.697i | − | 0.356283i | ||||||
\(685\) | −33.8260 | + | 866.205i | −0.0493810 | + | 1.26453i | ||||
\(686\) | 17.6936 | 0.0257924 | ||||||||
\(687\) | −314.689 | − | 314.689i | −0.458062 | − | 0.458062i | ||||
\(688\) | 324.175 | − | 324.175i | 0.471185 | − | 0.471185i | ||||
\(689\) | 21.0924i | 0.0306130i | ||||||||
\(690\) | −283.718 | − | 11.0794i | −0.411186 | − | 0.0160571i | ||||
\(691\) | −909.333 | −1.31597 | −0.657984 | − | 0.753032i | \(-0.728590\pi\) | ||||
−0.657984 | + | 0.753032i | \(0.728590\pi\) | |||||||
\(692\) | −373.623 | − | 373.623i | −0.539918 | − | 0.539918i | ||||
\(693\) | −42.6453 | + | 42.6453i | −0.0615372 | + | 0.0615372i | ||||
\(694\) | − | 246.197i | − | 0.354750i | ||||||
\(695\) | −547.216 | + | 506.084i | −0.787362 | + | 0.728179i | ||||
\(696\) | −262.204 | −0.376730 | ||||||||
\(697\) | −128.722 | − | 128.722i | −0.184680 | − | 0.184680i | ||||
\(698\) | 281.121 | − | 281.121i | 0.402752 | − | 0.402752i | ||||
\(699\) | 148.664i | 0.212681i | ||||||||
\(700\) | −132.694 | − | 155.215i | −0.189563 | − | 0.221736i | ||||
\(701\) | −794.647 | −1.13359 | −0.566795 | − | 0.823859i | \(-0.691817\pi\) | ||||
−0.566795 | + | 0.823859i | \(0.691817\pi\) | |||||||
\(702\) | −5.56983 | − | 5.56983i | −0.00793423 | − | 0.00793423i | ||||
\(703\) | 905.773 | − | 905.773i | 1.28844 | − | 1.28844i | ||||
\(704\) | − | 58.6606i | − | 0.0833248i | ||||||
\(705\) | 339.732 | + | 367.343i | 0.481889 | + | 0.521055i | ||||
\(706\) | −543.854 | −0.770332 | ||||||||
\(707\) | −135.593 | − | 135.593i | −0.191786 | − | 0.191786i | ||||
\(708\) | −188.223 | + | 188.223i | −0.265851 | + | 0.265851i | ||||
\(709\) | 281.184i | 0.396592i | 0.980142 | + | 0.198296i | \(0.0635407\pi\) | ||||
−0.980142 | + | 0.198296i | \(0.936459\pi\) | |||||||
\(710\) | −25.4291 | + | 651.181i | −0.0358157 | + | 0.917156i | ||||
\(711\) | −199.313 | −0.280328 | ||||||||
\(712\) | 9.73783 | + | 9.73783i | 0.0136767 | + | 0.0136767i | ||||
\(713\) | 446.324 | − | 446.324i | 0.625981 | − | 0.625981i | ||||
\(714\) | 21.2760i | 0.0297984i | ||||||||
\(715\) | 60.2368 | + | 2.35229i | 0.0842472 | + | 0.00328992i | ||||
\(716\) | 176.637 | 0.246700 | ||||||||
\(717\) | −81.9877 | − | 81.9877i | −0.114348 | − | 0.114348i | ||||
\(718\) | 81.1829 | − | 81.1829i | 0.113068 | − | 0.113068i | ||||
\(719\) | 1122.66i | 1.56143i | 0.624890 | + | 0.780713i | \(0.285144\pi\) | ||||
−0.624890 | + | 0.780713i | \(0.714856\pi\) | |||||||
\(720\) | −64.7577 | + | 59.8901i | −0.0899412 | + | 0.0831807i | ||||
\(721\) | −362.087 | −0.502201 | ||||||||
\(722\) | −223.821 | − | 223.821i | −0.310002 | − | 0.310002i | ||||
\(723\) | 101.143 | − | 101.143i | 0.139894 | − | 0.139894i | ||||
\(724\) | − | 908.372i | − | 1.25466i | ||||||
\(725\) | 557.245 | + | 43.5882i | 0.768614 | + | 0.0601217i | ||||
\(726\) | −104.689 | −0.144199 | ||||||||
\(727\) | −208.125 | − | 208.125i | −0.286279 | − | 0.286279i | 0.549328 | − | 0.835607i | \(-0.314884\pi\) |
−0.835607 | + | 0.549328i | \(0.814884\pi\) | |||||||
\(728\) | −20.0997 | + | 20.0997i | −0.0276094 | + | 0.0276094i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 26.8399 | + | 29.0213i | 0.0367670 | + | 0.0397552i | ||||
\(731\) | 378.877 | 0.518299 | ||||||||
\(732\) | −334.050 | − | 334.050i | −0.456352 | − | 0.456352i | ||||
\(733\) | −760.380 | + | 760.380i | −1.03735 | + | 1.03735i | −0.0380787 | + | 0.999275i | \(0.512124\pi\) |
−0.999275 | + | 0.0380787i | \(0.987876\pi\) | |||||||
\(734\) | 219.315i | 0.298794i | ||||||||
\(735\) | −2.36553 | + | 60.5756i | −0.00321840 | + | 0.0824158i | ||||
\(736\) | 1122.25 | 1.52479 | ||||||||
\(737\) | −308.405 | − | 308.405i | −0.418460 | − | 0.418460i | ||||
\(738\) | 75.9155 | − | 75.9155i | 0.102867 | − | 0.102867i | ||||
\(739\) | − | 425.934i | − | 0.576365i | −0.957575 | − | 0.288183i | \(-0.906949\pi\) | ||
0.957575 | − | 0.288183i | \(-0.0930510\pi\) | |||||||
\(740\) | −750.924 | − | 29.3242i | −1.01476 | − | 0.0396273i | ||||
\(741\) | 72.3137 | 0.0975893 | ||||||||
\(742\) | 23.7586 | + | 23.7586i | 0.0320197 | + | 0.0320197i | ||||
\(743\) | −325.298 | + | 325.298i | −0.437818 | + | 0.437818i | −0.891277 | − | 0.453459i | \(-0.850190\pi\) |
0.453459 | + | 0.891277i | \(0.350190\pi\) | |||||||
\(744\) | 215.703i | 0.289923i | ||||||||
\(745\) | 578.661 | − | 535.166i | 0.776727 | − | 0.718343i | ||||
\(746\) | 414.139 | 0.555146 | ||||||||
\(747\) | 104.585 | + | 104.585i | 0.140006 | + | 0.140006i | ||||
\(748\) | −80.6102 | + | 80.6102i | −0.107768 | + | 0.107768i | ||||
\(749\) | − | 46.6969i | − | 0.0623456i | ||||||
\(750\) | −162.345 | + | 128.171i | −0.216460 | + | 0.170895i | ||||
\(751\) | −107.270 | −0.142836 | −0.0714182 | − | 0.997446i | \(-0.522752\pi\) | ||||
−0.0714182 | + | 0.997446i | \(0.522752\pi\) | |||||||
\(752\) | −240.240 | − | 240.240i | −0.319468 | − | 0.319468i | ||||
\(753\) | 242.430 | − | 242.430i | 0.321952 | − | 0.321952i | ||||
\(754\) | − | 33.8927i | − | 0.0449505i | ||||||
\(755\) | −795.451 | − | 860.102i | −1.05358 | − | 1.13921i | ||||
\(756\) | 42.4431 | 0.0561417 | ||||||||
\(757\) | 537.483 | + | 537.483i | 0.710017 | + | 0.710017i | 0.966539 | − | 0.256521i | \(-0.0825764\pi\) |
−0.256521 | + | 0.966539i | \(0.582576\pi\) | |||||||
\(758\) | 85.2149 | − | 85.2149i | 0.112421 | − | 0.112421i | ||||
\(759\) | 451.643i | 0.595051i | ||||||||
\(760\) | −34.7593 | + | 890.104i | −0.0457359 | + | 1.17119i | ||||
\(761\) | −547.917 | −0.719996 | −0.359998 | − | 0.932953i | \(-0.617223\pi\) | ||||
−0.359998 | + | 0.932953i | \(0.617223\pi\) | |||||||
\(762\) | −136.954 | − | 136.954i | −0.179730 | − | 0.179730i | ||||
\(763\) | −163.450 | + | 163.450i | −0.214220 | + | 0.214220i | ||||
\(764\) | − | 761.458i | − | 0.996672i | ||||||
\(765\) | −72.8405 | − | 2.84448i | −0.0952163 | − | 0.00371828i | ||||
\(766\) | 472.300 | 0.616580 | ||||||||
\(767\) | −55.8524 | − | 55.8524i | −0.0728193 | − | 0.0728193i | ||||
\(768\) | −182.245 | + | 182.245i | −0.237298 | + | 0.237298i | ||||
\(769\) | − | 354.375i | − | 0.460826i | −0.973093 | − | 0.230413i | \(-0.925992\pi\) | ||
0.973093 | − | 0.230413i | \(-0.0740077\pi\) | |||||||
\(770\) | 70.5009 | − | 65.2016i | 0.0915596 | − | 0.0846774i | ||||
\(771\) | −505.561 | −0.655721 | ||||||||
\(772\) | −310.952 | − | 310.952i | −0.402787 | − | 0.402787i | ||||
\(773\) | −507.940 | + | 507.940i | −0.657103 | + | 0.657103i | −0.954694 | − | 0.297591i | \(-0.903817\pi\) |
0.297591 | + | 0.954694i | \(0.403817\pi\) | |||||||
\(774\) | 223.447i | 0.288692i | ||||||||
\(775\) | 35.8579 | − | 458.418i | 0.0462682 | − | 0.591507i | ||||
\(776\) | −559.833 | −0.721435 | ||||||||
\(777\) | 157.752 | + | 157.752i | 0.203027 | + | 0.203027i | ||||
\(778\) | 111.700 | − | 111.700i | 0.143573 | − | 0.143573i | ||||
\(779\) | 985.620i | 1.26524i | ||||||||
\(780\) | −28.8050 | − | 31.1461i | −0.0369295 | − | 0.0399309i | ||||
\(781\) | 1036.60 | 1.32727 | ||||||||
\(782\) | 112.664 | + | 112.664i | 0.144072 | + | 0.144072i | ||||
\(783\) | −82.1482 | + | 82.1482i | −0.104915 | + | 0.104915i | ||||
\(784\) | − | 41.1630i | − | 0.0525038i | ||||||
\(785\) | 20.7521 | − | 531.414i | 0.0264359 | − | 0.676960i | ||||
\(786\) | −314.875 | −0.400604 | ||||||||
\(787\) | 630.653 | + | 630.653i | 0.801338 | + | 0.801338i | 0.983305 | − | 0.181967i | \(-0.0582463\pi\) |
−0.181967 | + | 0.983305i | \(0.558246\pi\) | |||||||
\(788\) | −46.2831 | + | 46.2831i | −0.0587349 | + | 0.0587349i | ||||
\(789\) | − | 577.391i | − | 0.731801i | ||||||
\(790\) | 317.119 | + | 12.3838i | 0.401417 | + | 0.0156756i | ||||
\(791\) | −81.2488 | −0.102717 | ||||||||
\(792\) | −109.137 | − | 109.137i | −0.137799 | − | 0.137799i | ||||
\(793\) | 99.1244 | − | 99.1244i | 0.124999 | − | 0.124999i | ||||
\(794\) | − | 57.8010i | − | 0.0727972i | ||||||
\(795\) | −84.5163 | + | 78.1635i | −0.106310 | + | 0.0983189i | ||||
\(796\) | 887.074 | 1.11441 | ||||||||
\(797\) | 549.518 | + | 549.518i | 0.689483 | + | 0.689483i | 0.962118 | − | 0.272634i | \(-0.0878949\pi\) |
−0.272634 | + | 0.962118i | \(0.587895\pi\) | |||||||
\(798\) | 81.4548 | − | 81.4548i | 0.102074 | − | 0.102074i | ||||
\(799\) | − | 280.778i | − | 0.351412i | ||||||
\(800\) | 621.410 | − | 531.248i | 0.776762 | − | 0.664060i | ||||
\(801\) | 6.10169 | 0.00761759 | ||||||||
\(802\) | 62.5210 | + | 62.5210i | 0.0779564 | + | 0.0779564i | ||||
\(803\) | 44.4620 | − | 44.4620i | 0.0553698 | − | 0.0553698i | ||||
\(804\) | 306.943i | 0.381770i | ||||||||
\(805\) | 308.243 | + | 333.295i | 0.382910 | + | 0.414031i | ||||
\(806\) | −27.8818 | −0.0345928 | ||||||||
\(807\) | 465.350 | + | 465.350i | 0.576641 | + | 0.576641i | ||||
\(808\) | 347.004 | − | 347.004i | 0.429461 | − | 0.429461i | ||||
\(809\) | 1512.58i | 1.86970i | 0.355048 | + | 0.934848i | \(0.384464\pi\) | ||||
−0.355048 | + | 0.934848i | \(0.615536\pi\) | |||||||
\(810\) | 1.67757 | − | 42.9586i | 0.00207107 | − | 0.0530353i | ||||
\(811\) | −1045.50 | −1.28915 | −0.644573 | − | 0.764543i | \(-0.722965\pi\) | ||||
−0.644573 | + | 0.764543i | \(0.722965\pi\) | |||||||
\(812\) | 129.134 | + | 129.134i | 0.159032 | + | 0.159032i | ||||
\(813\) | −292.879 | + | 292.879i | −0.360244 | + | 0.360244i | ||||
\(814\) | − | 353.399i | − | 0.434151i | ||||||
\(815\) | 880.079 | + | 34.3678i | 1.07985 | + | 0.0421691i | ||||
\(816\) | 49.4974 | 0.0606586 | ||||||||
\(817\) | −1450.52 | − | 1450.52i | −1.77542 | − | 1.77542i | ||||
\(818\) | 48.4471 | − | 48.4471i | 0.0592263 | − | 0.0592263i | ||||
\(819\) | 12.5944i | 0.0153777i | ||||||||
\(820\) | 424.515 | − | 392.606i | 0.517701 | − | 0.478787i | ||||
\(821\) | 1039.41 | 1.26603 | 0.633013 | − | 0.774141i | \(-0.281818\pi\) | ||||
0.633013 | + | 0.774141i | \(0.281818\pi\) | |||||||
\(822\) | 202.860 | + | 202.860i | 0.246788 | + | 0.246788i | ||||
\(823\) | 631.240 | − | 631.240i | 0.766999 | − | 0.766999i | −0.210578 | − | 0.977577i | \(-0.567535\pi\) |
0.977577 | + | 0.210578i | \(0.0675346\pi\) | |||||||
\(824\) | − | 926.641i | − | 1.12456i | ||||||
\(825\) | 213.798 | + | 250.083i | 0.259149 | + | 0.303131i | ||||
\(826\) | −125.825 | −0.152331 | ||||||||
\(827\) | 363.393 | + | 363.393i | 0.439411 | + | 0.439411i | 0.891814 | − | 0.452403i | \(-0.149433\pi\) |
−0.452403 | + | 0.891814i | \(0.649433\pi\) | |||||||
\(828\) | 224.751 | − | 224.751i | 0.271438 | − | 0.271438i | ||||
\(829\) | − | 1037.80i | − | 1.25187i | −0.779876 | − | 0.625935i | \(-0.784718\pi\) | ||
0.779876 | − | 0.625935i | \(-0.215282\pi\) | |||||||
\(830\) | −159.902 | − | 172.898i | −0.192653 | − | 0.208311i | ||||
\(831\) | 289.318 | 0.348156 | ||||||||
\(832\) | −8.66208 | − | 8.66208i | −0.0104112 | − | 0.0104112i | ||||
\(833\) | 24.0545 | − | 24.0545i | 0.0288769 | − | 0.0288769i | ||||
\(834\) | 246.676i | 0.295775i | ||||||||
\(835\) | 37.6387 | − | 963.839i | 0.0450763 | − | 1.15430i | ||||
\(836\) | 617.228 | 0.738311 | ||||||||
\(837\) | 67.5792 | + | 67.5792i | 0.0807398 | + | 0.0807398i | ||||
\(838\) | −318.874 | + | 318.874i | −0.380518 | + | 0.380518i | ||||
\(839\) | − | 1350.36i | − | 1.60949i | −0.593622 | − | 0.804744i | \(-0.702302\pi\) | ||
0.593622 | − | 0.804744i | \(-0.297698\pi\) | |||||||
\(840\) | −155.023 | − | 6.05378i | −0.184552 | − | 0.00720689i | ||||
\(841\) | 341.124 | 0.405617 | ||||||||
\(842\) | 504.623 | + | 504.623i | 0.599315 | + | 0.599315i | ||||
\(843\) | 413.043 | − | 413.043i | 0.489968 | − | 0.489968i | ||||
\(844\) | 1233.55i | 1.46155i | ||||||||
\(845\) | −611.123 | + | 565.187i | −0.723223 | + | 0.668861i | ||||
\(846\) | 165.592 | 0.195736 | ||||||||
\(847\) | 118.360 | + | 118.360i | 0.139740 | + | 0.139740i | ||||
\(848\) | 55.2730 | − | 55.2730i | 0.0651804 | − | 0.0651804i | ||||
\(849\) | 225.204i | 0.265258i | ||||||||
\(850\) | 115.717 | + | 9.05147i | 0.136137 | + | 0.0106488i | ||||
\(851\) | 1670.71 | 1.96323 | ||||||||
\(852\) | −515.841 | − | 515.841i | −0.605447 | − | 0.605447i | ||||
\(853\) | −294.827 | + | 294.827i | −0.345636 | + | 0.345636i | −0.858481 | − | 0.512845i | \(-0.828591\pi\) |
0.512845 | + | 0.858481i | \(0.328591\pi\) | |||||||
\(854\) | − | 223.309i | − | 0.261486i | ||||||
\(855\) | 267.978 | + | 289.758i | 0.313425 | + | 0.338898i | ||||
\(856\) | 119.505 | 0.139609 | ||||||||
\(857\) | −839.471 | − | 839.471i | −0.979546 | − | 0.979546i | 0.0202485 | − | 0.999795i | \(-0.493554\pi\) |
−0.999795 | + | 0.0202485i | \(0.993554\pi\) | |||||||
\(858\) | 14.1071 | − | 14.1071i | 0.0164418 | − | 0.0164418i | ||||
\(859\) | − | 215.750i | − | 0.251164i | −0.992083 | − | 0.125582i | \(-0.959920\pi\) | ||
0.992083 | − | 0.125582i | \(-0.0400798\pi\) | |||||||
\(860\) | −46.9603 | + | 1202.54i | −0.0546050 | + | 1.39831i | ||||
\(861\) | −171.659 | −0.199371 | ||||||||
\(862\) | −509.648 | − | 509.648i | −0.591239 | − | 0.591239i | ||||
\(863\) | −503.739 | + | 503.739i | −0.583707 | + | 0.583707i | −0.935920 | − | 0.352213i | \(-0.885429\pi\) |
0.352213 | + | 0.935920i | \(0.385429\pi\) | |||||||
\(864\) | 169.923i | 0.196670i | ||||||||
\(865\) | 855.090 | + | 33.3919i | 0.988543 | + | 0.0386034i | ||||
\(866\) | −465.187 | −0.537167 | ||||||||
\(867\) | −325.026 | − | 325.026i | −0.374886 | − | 0.374886i | ||||
\(868\) | 106.232 | − | 106.232i | 0.122387 | − | 0.122387i | ||||
\(869\) | − | 504.813i | − | 0.580913i | ||||||
\(870\) | 135.807 | − | 125.599i | 0.156100 | − | 0.144366i | ||||
\(871\) | −91.0808 | −0.104570 | ||||||||
\(872\) | −418.296 | − | 418.296i | −0.479697 | − | 0.479697i | ||||
\(873\) | −175.395 | + | 175.395i | −0.200910 | + | 0.200910i | ||||
\(874\) | − | 862.663i | − | 0.987028i | ||||||
\(875\) | 328.454 | + | 38.6364i | 0.375376 | + | 0.0441559i | ||||
\(876\) | −44.2511 | −0.0505150 | ||||||||
\(877\) | 512.283 | + | 512.283i | 0.584131 | + | 0.584131i | 0.936036 | − | 0.351905i | \(-0.114466\pi\) |
−0.351905 | + | 0.936036i | \(0.614466\pi\) | |||||||
\(878\) | 33.2061 | − | 33.2061i | 0.0378202 | − | 0.0378202i | ||||
\(879\) | 854.514i | 0.972143i | ||||||||
\(880\) | −151.687 | − | 164.016i | −0.172372 | − | 0.186382i | ||||
\(881\) | −8.98563 | −0.0101993 | −0.00509967 | − | 0.999987i | \(-0.501623\pi\) | ||||
−0.00509967 | + | 0.999987i | \(0.501623\pi\) | |||||||
\(882\) | 14.1864 | + | 14.1864i | 0.0160844 | + | 0.0160844i | ||||
\(883\) | −51.0268 | + | 51.0268i | −0.0577880 | + | 0.0577880i | −0.735410 | − | 0.677622i | \(-0.763011\pi\) |
0.677622 | + | 0.735410i | \(0.263011\pi\) | |||||||
\(884\) | 23.8065i | 0.0269304i | ||||||||
\(885\) | 16.8221 | − | 430.775i | 0.0190080 | − | 0.486751i | ||||
\(886\) | 158.468 | 0.178858 | ||||||||
\(887\) | 502.029 | + | 502.029i | 0.565985 | + | 0.565985i | 0.931001 | − | 0.365016i | \(-0.118937\pi\) |
−0.365016 | + | 0.931001i | \(0.618937\pi\) | |||||||
\(888\) | −403.715 | + | 403.715i | −0.454634 | + | 0.454634i | ||||
\(889\) | 309.678i | 0.348344i | ||||||||
\(890\) | −9.70815 | − | 0.379111i | −0.0109080 | − | 0.000425967i | ||||
\(891\) | −68.3846 | −0.0767504 | ||||||||
\(892\) | 649.332 | + | 649.332i | 0.727951 | + | 0.727951i | ||||
\(893\) | −1074.95 | + | 1074.95i | −1.20375 | + | 1.20375i | ||||
\(894\) | − | 260.851i | − | 0.291780i | ||||||
\(895\) | −210.023 | + | 194.236i | −0.234662 | + | 0.217024i | ||||
\(896\) | 326.568 | 0.364473 | ||||||||
\(897\) | 66.6916 | + | 66.6916i | 0.0743496 | + | 0.0743496i | ||||
\(898\) | −200.620 | + | 200.620i | −0.223408 | + | 0.223408i | ||||
\(899\) | 411.223i | 0.457423i | ||||||||
\(900\) | 18.0566 | − | 230.841i | 0.0200629 | − | 0.256490i | ||||
\(901\) | 64.5998 | 0.0716979 | ||||||||
\(902\) | 192.276 | + | 192.276i | 0.213166 | + | 0.213166i | ||||
\(903\) | 252.627 | − | 252.627i | 0.279764 | − | 0.279764i | ||||
\(904\) | − | 207.930i | − | 0.230011i | ||||||
\(905\) | 998.877 | + | 1080.06i | 1.10373 | + | 1.19344i | ||||
\(906\) | −387.720 | −0.427947 | ||||||||
\(907\) | −185.954 | − | 185.954i | −0.205021 | − | 0.205021i | 0.597126 | − | 0.802147i | \(-0.296309\pi\) |
−0.802147 | + | 0.597126i | \(0.796309\pi\) | |||||||
\(908\) | 403.582 | − | 403.582i | 0.444474 | − | 0.444474i | ||||
\(909\) | − | 217.432i | − | 0.239199i | ||||||
\(910\) | 0.782516 | − | 20.0384i | 0.000859907 | − | 0.0220202i | ||||
\(911\) | −1184.97 | −1.30073 | −0.650365 | − | 0.759622i | \(-0.725384\pi\) | ||||
−0.650365 | + | 0.759622i | \(0.725384\pi\) | |||||||
\(912\) | −189.500 | − | 189.500i | −0.207785 | − | 0.207785i | ||||
\(913\) | −264.888 | + | 264.888i | −0.290129 | + | 0.290129i | ||||
\(914\) | − | 347.804i | − | 0.380529i | ||||||
\(915\) | 764.520 | + | 29.8551i | 0.835541 | + | 0.0326286i | ||||
\(916\) | −793.254 | −0.865997 | ||||||||
\(917\) | 355.994 | + | 355.994i | 0.388216 | + | 0.388216i | ||||
\(918\) | −17.0588 | + | 17.0588i | −0.0185825 | + | 0.0185825i | ||||
\(919\) | − | 244.007i | − | 0.265514i | −0.991149 | − | 0.132757i | \(-0.957617\pi\) | ||
0.991149 | − | 0.132757i | \(-0.0423830\pi\) | |||||||
\(920\) | −852.959 | + | 788.845i | −0.927129 | + | 0.857440i | ||||
\(921\) | 751.031 | 0.815451 | ||||||||
\(922\) | −241.574 | − | 241.574i | −0.262011 | − | 0.262011i | ||||
\(923\) | 153.068 | − | 153.068i | 0.165838 | − | 0.165838i | ||||
\(924\) | 107.498i | 0.116340i | ||||||||
\(925\) | 925.101 | − | 790.876i | 1.00011 | − | 0.855001i | ||||
\(926\) | 106.446 | 0.114952 | ||||||||
\(927\) | −290.315 | − | 290.315i | −0.313177 | − | 0.313177i | ||||
\(928\) | −516.994 | + | 516.994i | −0.557106 | + | 0.557106i | ||||
\(929\) | − | 319.725i | − | 0.344160i | −0.985083 | − | 0.172080i | \(-0.944951\pi\) | ||
0.985083 | − | 0.172080i | \(-0.0550488\pi\) | |||||||
\(930\) | −103.324 | − | 111.721i | −0.111101 | − | 0.120131i | ||||
\(931\) | −184.184 | −0.197834 | ||||||||
\(932\) | 187.373 | + | 187.373i | 0.201044 | + | 0.201044i | ||||
\(933\) | −91.6389 | + | 91.6389i | −0.0982196 | + | 0.0982196i | ||||
\(934\) | 884.647i | 0.947160i | ||||||||
\(935\) | 7.20440 | − | 184.488i | 0.00770524 | − | 0.197313i | ||||
\(936\) | −32.2312 | −0.0344350 | ||||||||
\(937\) | −815.691 | − | 815.691i | −0.870535 | − | 0.870535i | 0.121996 | − | 0.992531i | \(-0.461071\pi\) |
−0.992531 | + | 0.121996i | \(0.961071\pi\) | |||||||
\(938\) | −102.594 | + | 102.594i | −0.109376 | + | 0.109376i | ||||
\(939\) | − | 248.872i | − | 0.265039i | ||||||
\(940\) | 891.181 | + | 34.8013i | 0.948065 | + | 0.0370227i | ||||
\(941\) | −506.239 | −0.537980 | −0.268990 | − | 0.963143i | \(-0.586690\pi\) | ||||
−0.268990 | + | 0.963143i | \(0.586690\pi\) | |||||||
\(942\) | −124.454 | − | 124.454i | −0.132116 | − | 0.132116i | ||||
\(943\) | −908.992 | + | 908.992i | −0.963936 | + | 0.963936i | ||||
\(944\) | 292.725i | 0.310090i | ||||||||
\(945\) | −50.4652 | + | 46.6719i | −0.0534023 | + | 0.0493882i | ||||
\(946\) | −565.939 | −0.598245 | ||||||||
\(947\) | 164.875 | + | 164.875i | 0.174103 | + | 0.174103i | 0.788779 | − | 0.614677i | \(-0.210713\pi\) |
−0.614677 | + | 0.788779i | \(0.710713\pi\) | |||||||
\(948\) | −251.210 | + | 251.210i | −0.264989 | + | 0.264989i | ||||
\(949\) | − | 13.1309i | − | 0.0138365i | ||||||
\(950\) | −408.366 | − | 477.672i | −0.429859 | − | 0.502813i | ||||
\(951\) | 303.975 | 0.319638 | ||||||||
\(952\) | 61.5595 | + | 61.5595i | 0.0646633 | + | 0.0646633i | ||||
\(953\) | 232.231 | − | 232.231i | 0.243684 | − | 0.243684i | −0.574689 | − | 0.818372i | \(-0.694877\pi\) |
0.818372 | + | 0.574689i | \(0.194877\pi\) | |||||||
\(954\) | 38.0986i | 0.0399356i | ||||||||
\(955\) | 837.325 | + | 905.379i | 0.876780 | + | 0.948041i | ||||
\(956\) | −206.671 | −0.216183 | ||||||||
\(957\) | −208.062 | − | 208.062i | −0.217411 | − | 0.217411i | ||||
\(958\) | 177.470 | − | 177.470i | 0.185251 | − | 0.185251i | ||||
\(959\) | − | 458.702i | − | 0.478313i | ||||||
\(960\) | 2.60892 | − | 66.8083i | 0.00271762 | − | 0.0695920i | ||||
\(961\) | −622.707 | −0.647978 | ||||||||
\(962\) | −52.1844 | − | 52.1844i | −0.0542458 | − | 0.0542458i | ||||
\(963\) | 37.4408 | − | 37.4408i | 0.0388793 | − | 0.0388793i | ||||
\(964\) | − | 254.957i | − | 0.264478i | ||||||
\(965\) | 711.658 | + | 27.7908i | 0.737469 | + | 0.0287988i | ||||
\(966\) | 150.244 | 0.155532 | ||||||||
\(967\) | −625.445 | − | 625.445i | −0.646789 | − | 0.646789i | 0.305427 | − | 0.952216i | \(-0.401201\pi\) |
−0.952216 | + | 0.305427i | \(0.901201\pi\) | |||||||
\(968\) | −302.903 | + | 302.903i | −0.312916 | + | 0.312916i | ||||
\(969\) | − | 221.476i | − | 0.228561i | ||||||
\(970\) | 289.961 | − | 268.166i | 0.298929 | − | 0.276460i | ||||
\(971\) | −513.341 | −0.528673 | −0.264336 | − | 0.964431i | \(-0.585153\pi\) | ||||
−0.264336 | + | 0.964431i | \(0.585153\pi\) | |||||||
\(972\) | 34.0302 | + | 34.0302i | 0.0350105 | + | 0.0350105i | ||||
\(973\) | 278.890 | − | 278.890i | 0.286628 | − | 0.286628i | ||||
\(974\) | − | 57.9411i | − | 0.0594878i | ||||||
\(975\) | 68.4987 | + | 5.35803i | 0.0702551 | + | 0.00549542i | ||||
\(976\) | −519.515 | −0.532290 | ||||||||
\(977\) | −307.372 | − | 307.372i | −0.314608 | − | 0.314608i | 0.532084 | − | 0.846692i | \(-0.321409\pi\) |
−0.846692 | + | 0.532084i | \(0.821409\pi\) | |||||||
\(978\) | 206.109 | − | 206.109i | 0.210745 | − | 0.210745i | ||||
\(979\) | 15.4541i | 0.0157856i | ||||||||
\(980\) | 73.3667 | + | 79.3296i | 0.0748639 | + | 0.0809485i | ||||
\(981\) | −262.103 | −0.267179 | ||||||||
\(982\) | −39.5861 | − | 39.5861i | −0.0403117 | − | 0.0403117i | ||||
\(983\) | 810.191 | − | 810.191i | 0.824202 | − | 0.824202i | −0.162506 | − | 0.986708i | \(-0.551958\pi\) |
0.986708 | + | 0.162506i | \(0.0519576\pi\) | |||||||
\(984\) | − | 439.303i | − | 0.446447i | ||||||
\(985\) | 4.13647 | − | 105.925i | 0.00419946 | − | 0.107538i | ||||
\(986\) | −103.804 | −0.105277 | ||||||||
\(987\) | −187.217 | − | 187.217i | −0.189683 | − | 0.189683i | ||||
\(988\) | 91.1425 | − | 91.1425i | 0.0922495 | − | 0.0922495i | ||||
\(989\) | − | 2675.50i | − | 2.70525i | ||||||
\(990\) | 108.804 | + | 4.24888i | 0.109903 | + | 0.00429180i | ||||
\(991\) | −833.240 | −0.840807 | −0.420404 | − | 0.907337i | \(-0.638111\pi\) | ||||
−0.420404 | + | 0.907337i | \(0.638111\pi\) | |||||||
\(992\) | 425.306 | + | 425.306i | 0.428736 | + | 0.428736i | ||||
\(993\) | 486.332 | − | 486.332i | 0.489761 | − | 0.489761i | ||||
\(994\) | − | 344.835i | − | 0.346917i | ||||||
\(995\) | −1054.74 | + | 975.457i | −1.06004 | + | 0.980358i | ||||
\(996\) | 263.632 | 0.264691 | ||||||||
\(997\) | −119.981 | − | 119.981i | −0.120342 | − | 0.120342i | 0.644371 | − | 0.764713i | \(-0.277119\pi\) |
−0.764713 | + | 0.644371i | \(0.777119\pi\) | |||||||
\(998\) | −284.437 | + | 284.437i | −0.285007 | + | 0.285007i | ||||
\(999\) | 252.966i | 0.253220i |
(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 | 105.3.l.a.22.7 | ✓ | 24 | |
3.2 | odd | 2 | 315.3.o.b.127.6 | 24 | |||
5.2 | odd | 4 | 525.3.l.e.43.6 | 24 | |||
5.3 | odd | 4 | inner | 105.3.l.a.43.7 | yes | 24 | |
5.4 | even | 2 | 525.3.l.e.232.6 | 24 | |||
15.8 | even | 4 | 315.3.o.b.253.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
105.3.l.a.43.7 | yes | 24 | 5.3 | odd | 4 | inner | |
315.3.o.b.127.6 | 24 | 3.2 | odd | 2 | |||
315.3.o.b.253.6 | 24 | 15.8 | even | 4 | |||
525.3.l.e.43.6 | 24 | 5.2 | odd | 4 | |||
525.3.l.e.232.6 | 24 | 5.4 | even | 2 |