Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,3,Mod(47,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.e (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: | \(2.77929869648\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{18} + 149 x^{16} - 800 x^{14} - 1986 x^{12} + 2844 x^{10} - 160866 x^{8} + \cdots + 3486784401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 89.9 | ||
Root | \(2.98496 + 0.299984i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 102.89 |
Dual form | 102.3.e.b.47.9 |
$q$-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 \(\left(\mathbb{Z}/102\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 2.32281 | − | 1.89857i | 0.774270 | − | 0.632856i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −3.05768 | − | 3.05768i | −0.611536 | − | 0.611536i | 0.331810 | − | 0.943346i | \(-0.392341\pi\) |
−0.943346 | + | 0.331810i | \(0.892341\pi\) | |||||||
\(6\) | 3.28495 | − | 2.68498i | 0.547491 | − | 0.447497i | ||||
\(7\) | 3.50287 | + | 3.50287i | 0.500410 | + | 0.500410i | 0.911565 | − | 0.411156i | \(-0.134875\pi\) |
−0.411156 | + | 0.911565i | \(0.634875\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 1.79088 | − | 8.82002i | 0.198987 | − | 0.980002i | ||||
\(10\) | −4.32421 | − | 4.32421i | −0.432421 | − | 0.432421i | ||||
\(11\) | −6.44580 | + | 6.44580i | −0.585981 | + | 0.585981i | −0.936541 | − | 0.350559i | \(-0.885992\pi\) |
0.350559 | + | 0.936541i | \(0.385992\pi\) | |||||||
\(12\) | 4.64562 | − | 3.79713i | 0.387135 | − | 0.316428i | ||||
\(13\) | 2.26456 | 0.174197 | 0.0870985 | − | 0.996200i | \(-0.472241\pi\) | ||||
0.0870985 | + | 0.996200i | \(0.472241\pi\) | |||||||
\(14\) | 4.95380 | + | 4.95380i | 0.353843 | + | 0.353843i | ||||
\(15\) | −12.9076 | − | 1.29720i | −0.860508 | − | 0.0864797i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −6.83994 | + | 15.5633i | −0.402349 | + | 0.915486i | ||||
\(18\) | 2.53269 | − | 12.4734i | 0.140705 | − | 0.692966i | ||||
\(19\) | 16.3812i | 0.862169i | 0.902312 | + | 0.431085i | \(0.141869\pi\) | ||||
−0.902312 | + | 0.431085i | \(0.858131\pi\) | |||||||
\(20\) | −6.11536 | − | 6.11536i | −0.305768 | − | 0.305768i | ||||
\(21\) | 14.7869 | + | 1.48606i | 0.704139 | + | 0.0707649i | ||||
\(22\) | −9.11573 | + | 9.11573i | −0.414351 | + | 0.414351i | ||||
\(23\) | 7.15696 | − | 7.15696i | 0.311172 | − | 0.311172i | −0.534191 | − | 0.845364i | \(-0.679384\pi\) |
0.845364 | + | 0.534191i | \(0.179384\pi\) | |||||||
\(24\) | 6.56990 | − | 5.36996i | 0.273746 | − | 0.223748i | ||||
\(25\) | − | 6.30119i | − | 0.252048i | ||||||
\(26\) | 3.20257 | 0.123176 | ||||||||
\(27\) | −12.5855 | − | 23.8873i | −0.466130 | − | 0.884716i | ||||
\(28\) | 7.00573 | + | 7.00573i | 0.250205 | + | 0.250205i | ||||
\(29\) | 6.56388 | + | 6.56388i | 0.226341 | + | 0.226341i | 0.811162 | − | 0.584821i | \(-0.198835\pi\) |
−0.584821 | + | 0.811162i | \(0.698835\pi\) | |||||||
\(30\) | −18.2541 | − | 1.83451i | −0.608471 | − | 0.0611504i | ||||
\(31\) | −22.2472 | + | 22.2472i | −0.717651 | + | 0.717651i | −0.968124 | − | 0.250473i | \(-0.919414\pi\) |
0.250473 | + | 0.968124i | \(0.419414\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | −2.73458 | + | 27.2101i | −0.0828659 | + | 0.824549i | ||||
\(34\) | −9.67314 | + | 22.0098i | −0.284504 | + | 0.647346i | ||||
\(35\) | − | 21.4213i | − | 0.612037i | ||||||
\(36\) | 3.58177 | − | 17.6400i | 0.0994936 | − | 0.490001i | ||||
\(37\) | −49.6392 | + | 49.6392i | −1.34160 | + | 1.34160i | −0.447134 | + | 0.894467i | \(0.647555\pi\) |
−0.894467 | + | 0.447134i | \(0.852445\pi\) | |||||||
\(38\) | 23.1665i | 0.609646i | ||||||||
\(39\) | 5.26014 | − | 4.29942i | 0.134875 | − | 0.110242i | ||||
\(40\) | −8.64842 | − | 8.64842i | −0.216211 | − | 0.216211i | ||||
\(41\) | 16.9856 | − | 16.9856i | 0.414283 | − | 0.414283i | −0.468945 | − | 0.883227i | \(-0.655366\pi\) |
0.883227 | + | 0.468945i | \(0.155366\pi\) | |||||||
\(42\) | 20.9119 | + | 2.10161i | 0.497902 | + | 0.0500383i | ||||
\(43\) | − | 18.0836i | − | 0.420548i | −0.977643 | − | 0.210274i | \(-0.932564\pi\) | ||
0.977643 | − | 0.210274i | \(-0.0674356\pi\) | |||||||
\(44\) | −12.8916 | + | 12.8916i | −0.292991 | + | 0.292991i | ||||
\(45\) | −32.4447 | + | 21.4928i | −0.720994 | + | 0.477619i | ||||
\(46\) | 10.1215 | − | 10.1215i | 0.220032 | − | 0.220032i | ||||
\(47\) | − | 79.1555i | − | 1.68416i | −0.539353 | − | 0.842080i | \(-0.681331\pi\) | ||
0.539353 | − | 0.842080i | \(-0.318669\pi\) | |||||||
\(48\) | 9.29124 | − | 7.59427i | 0.193567 | − | 0.158214i | ||||
\(49\) | − | 24.4598i | − | 0.499180i | ||||||
\(50\) | − | 8.91123i | − | 0.178225i | ||||||
\(51\) | 13.6600 | + | 49.1366i | 0.267844 | + | 0.963462i | ||||
\(52\) | 4.52912 | 0.0870985 | ||||||||
\(53\) | −68.2420 | −1.28759 | −0.643793 | − | 0.765200i | \(-0.722640\pi\) | ||||
−0.643793 | + | 0.765200i | \(0.722640\pi\) | |||||||
\(54\) | −17.7986 | − | 33.7818i | −0.329604 | − | 0.625589i | ||||
\(55\) | 39.4184 | 0.716697 | ||||||||
\(56\) | 9.90760 | + | 9.90760i | 0.176922 | + | 0.176922i | ||||
\(57\) | 31.1008 | + | 38.0504i | 0.545629 | + | 0.667551i | ||||
\(58\) | 9.28273 | + | 9.28273i | 0.160047 | + | 0.160047i | ||||
\(59\) | 108.015 | 1.83075 | 0.915377 | − | 0.402597i | \(-0.131892\pi\) | ||||
0.915377 | + | 0.402597i | \(0.131892\pi\) | |||||||
\(60\) | −25.8152 | − | 2.59439i | −0.430254 | − | 0.0432399i | ||||
\(61\) | 9.60289 | + | 9.60289i | 0.157424 | + | 0.157424i | 0.781424 | − | 0.624000i | \(-0.214493\pi\) |
−0.624000 | + | 0.781424i | \(0.714493\pi\) | |||||||
\(62\) | −31.4622 | + | 31.4622i | −0.507456 | + | 0.507456i | ||||
\(63\) | 37.1686 | − | 24.6221i | 0.589978 | − | 0.390827i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −6.92430 | − | 6.92430i | −0.106528 | − | 0.106528i | ||||
\(66\) | −3.86727 | + | 38.4809i | −0.0585951 | + | 0.583044i | ||||
\(67\) | 60.5593 | 0.903870 | 0.451935 | − | 0.892051i | \(-0.350734\pi\) | ||||
0.451935 | + | 0.892051i | \(0.350734\pi\) | |||||||
\(68\) | −13.6799 | + | 31.1265i | −0.201175 | + | 0.457743i | ||||
\(69\) | 3.03628 | − | 30.2122i | 0.0440041 | − | 0.437858i | ||||
\(70\) | − | 30.2943i | − | 0.432775i | ||||||
\(71\) | −9.60666 | − | 9.60666i | −0.135305 | − | 0.135305i | 0.636210 | − | 0.771516i | \(-0.280501\pi\) |
−0.771516 | + | 0.636210i | \(0.780501\pi\) | |||||||
\(72\) | 5.06539 | − | 24.9468i | 0.0703526 | − | 0.346483i | ||||
\(73\) | 70.3897 | − | 70.3897i | 0.964243 | − | 0.964243i | −0.0351395 | − | 0.999382i | \(-0.511188\pi\) |
0.999382 | + | 0.0351395i | \(0.0111875\pi\) | |||||||
\(74\) | −70.2005 | + | 70.2005i | −0.948655 | + | 0.948655i | ||||
\(75\) | −11.9632 | − | 14.6365i | −0.159510 | − | 0.195153i | ||||
\(76\) | 32.7624i | 0.431085i | ||||||||
\(77\) | −45.1575 | −0.586461 | ||||||||
\(78\) | 7.43896 | − | 6.08030i | 0.0953713 | − | 0.0779525i | ||||
\(79\) | −81.2199 | − | 81.2199i | −1.02810 | − | 1.02810i | −0.999594 | − | 0.0285069i | \(-0.990925\pi\) |
−0.0285069 | − | 0.999594i | \(-0.509075\pi\) | |||||||
\(80\) | −12.2307 | − | 12.2307i | −0.152884 | − | 0.152884i | ||||
\(81\) | −74.5855 | − | 31.5913i | −0.920808 | − | 0.390016i | ||||
\(82\) | 24.0212 | − | 24.0212i | 0.292942 | − | 0.292942i | ||||
\(83\) | 165.328 | 1.99190 | 0.995951 | − | 0.0899016i | \(-0.0286552\pi\) | ||||
0.995951 | + | 0.0899016i | \(0.0286552\pi\) | |||||||
\(84\) | 29.5738 | + | 2.97213i | 0.352070 | + | 0.0353824i | ||||
\(85\) | 68.5018 | − | 26.6731i | 0.805904 | − | 0.313802i | ||||
\(86\) | − | 25.5740i | − | 0.297372i | ||||||
\(87\) | 27.7086 | + | 2.78467i | 0.318490 | + | 0.0320077i | ||||
\(88\) | −18.2315 | + | 18.2315i | −0.207176 | + | 0.207176i | ||||
\(89\) | − | 40.2790i | − | 0.452573i | −0.974061 | − | 0.226287i | \(-0.927341\pi\) | ||
0.974061 | − | 0.226287i | \(-0.0726586\pi\) | |||||||
\(90\) | −45.8838 | + | 30.3955i | −0.509820 | + | 0.337727i | ||||
\(91\) | 7.93245 | + | 7.93245i | 0.0871698 | + | 0.0871698i | ||||
\(92\) | 14.3139 | − | 14.3139i | 0.155586 | − | 0.155586i | ||||
\(93\) | −9.43818 | + | 93.9137i | −0.101486 | + | 1.00982i | ||||
\(94\) | − | 111.943i | − | 1.19088i | ||||||
\(95\) | 50.0885 | − | 50.0885i | 0.527247 | − | 0.527247i | ||||
\(96\) | 13.1398 | − | 10.7399i | 0.136873 | − | 0.111874i | ||||
\(97\) | −28.5480 | + | 28.5480i | −0.294309 | + | 0.294309i | −0.838780 | − | 0.544471i | \(-0.816731\pi\) |
0.544471 | + | 0.838780i | \(0.316731\pi\) | |||||||
\(98\) | − | 34.5914i | − | 0.352974i | ||||||
\(99\) | 45.3084 | + | 68.3957i | 0.457660 | + | 0.690866i | ||||
\(100\) | − | 12.6024i | − | 0.126024i | ||||||
\(101\) | 167.151i | 1.65496i | 0.561492 | + | 0.827482i | \(0.310227\pi\) | ||||
−0.561492 | + | 0.827482i | \(0.689773\pi\) | |||||||
\(102\) | 19.3182 | + | 69.4896i | 0.189394 | + | 0.681271i | ||||
\(103\) | −22.3187 | −0.216686 | −0.108343 | − | 0.994114i | \(-0.534555\pi\) | ||||
−0.108343 | + | 0.994114i | \(0.534555\pi\) | |||||||
\(104\) | 6.40514 | 0.0615879 | ||||||||
\(105\) | −40.6698 | − | 49.7576i | −0.387331 | − | 0.473882i | ||||
\(106\) | −96.5088 | −0.910460 | ||||||||
\(107\) | −104.198 | − | 104.198i | −0.973816 | − | 0.973816i | 0.0258498 | − | 0.999666i | \(-0.491771\pi\) |
−0.999666 | + | 0.0258498i | \(0.991771\pi\) | |||||||
\(108\) | −25.1710 | − | 47.7747i | −0.233065 | − | 0.442358i | ||||
\(109\) | −60.2159 | − | 60.2159i | −0.552440 | − | 0.552440i | 0.374704 | − | 0.927144i | \(-0.377744\pi\) |
−0.927144 | + | 0.374704i | \(0.877744\pi\) | |||||||
\(110\) | 55.7460 | 0.506782 | ||||||||
\(111\) | −21.0590 | + | 209.546i | −0.189721 | + | 1.88780i | ||||
\(112\) | 14.0115 | + | 14.0115i | 0.125102 | + | 0.125102i | ||||
\(113\) | −92.3651 | + | 92.3651i | −0.817391 | + | 0.817391i | −0.985729 | − | 0.168339i | \(-0.946160\pi\) |
0.168339 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(114\) | 43.9832 | + | 53.8114i | 0.385818 | + | 0.472030i | ||||
\(115\) | −43.7674 | −0.380586 | ||||||||
\(116\) | 13.1278 | + | 13.1278i | 0.113170 | + | 0.113170i | ||||
\(117\) | 4.05557 | − | 19.9735i | 0.0346630 | − | 0.170713i | ||||
\(118\) | 152.756 | 1.29454 | ||||||||
\(119\) | −78.4755 | + | 30.5567i | −0.659458 | + | 0.256779i | ||||
\(120\) | −36.5083 | − | 3.66902i | −0.304235 | − | 0.0305752i | ||||
\(121\) | 37.9034i | 0.313252i | ||||||||
\(122\) | 13.5805 | + | 13.5805i | 0.111316 | + | 0.111316i | ||||
\(123\) | 7.20600 | − | 71.7026i | 0.0585853 | − | 0.582948i | ||||
\(124\) | −44.4943 | + | 44.4943i | −0.358825 | + | 0.358825i | ||||
\(125\) | −95.7090 | + | 95.7090i | −0.765672 | + | 0.765672i | ||||
\(126\) | 52.5643 | − | 34.8209i | 0.417177 | − | 0.276357i | ||||
\(127\) | 42.9662i | 0.338317i | 0.985589 | + | 0.169158i | \(0.0541049\pi\) | ||||
−0.985589 | + | 0.169158i | \(0.945895\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | −34.3328 | − | 42.0046i | −0.266146 | − | 0.325617i | ||||
\(130\) | −9.79244 | − | 9.79244i | −0.0753265 | − | 0.0753265i | ||||
\(131\) | −10.1739 | − | 10.1739i | −0.0776631 | − | 0.0776631i | 0.667208 | − | 0.744871i | \(-0.267489\pi\) |
−0.744871 | + | 0.667208i | \(0.767489\pi\) | |||||||
\(132\) | −5.46915 | + | 54.4203i | −0.0414330 | + | 0.412275i | ||||
\(133\) | −57.3812 | + | 57.3812i | −0.431438 | + | 0.431438i | ||||
\(134\) | 85.6438 | 0.639133 | ||||||||
\(135\) | −34.5573 | + | 111.522i | −0.255980 | + | 0.826091i | ||||
\(136\) | −19.3463 | + | 44.0196i | −0.142252 | + | 0.323673i | ||||
\(137\) | − | 105.475i | − | 0.769892i | −0.922939 | − | 0.384946i | \(-0.874220\pi\) | ||
0.922939 | − | 0.384946i | \(-0.125780\pi\) | |||||||
\(138\) | 4.29395 | − | 42.7265i | 0.0311156 | − | 0.309612i | ||||
\(139\) | 3.58670 | − | 3.58670i | 0.0258036 | − | 0.0258036i | −0.694087 | − | 0.719891i | \(-0.744192\pi\) |
0.719891 | + | 0.694087i | \(0.244192\pi\) | |||||||
\(140\) | − | 42.8426i | − | 0.306018i | ||||||
\(141\) | −150.282 | − | 183.863i | −1.06583 | − | 1.30399i | ||||
\(142\) | −13.5859 | − | 13.5859i | −0.0956751 | − | 0.0956751i | ||||
\(143\) | −14.5969 | + | 14.5969i | −0.102076 | + | 0.102076i | ||||
\(144\) | 7.16354 | − | 35.2801i | 0.0497468 | − | 0.245001i | ||||
\(145\) | − | 40.1405i | − | 0.276831i | ||||||
\(146\) | 99.5461 | − | 99.5461i | 0.681823 | − | 0.681823i | ||||
\(147\) | −46.4387 | − | 56.8155i | −0.315909 | − | 0.386500i | ||||
\(148\) | −99.2785 | + | 99.2785i | −0.670800 | + | 0.670800i | ||||
\(149\) | 243.101i | 1.63155i | 0.578368 | + | 0.815776i | \(0.303690\pi\) | ||||
−0.578368 | + | 0.815776i | \(0.696310\pi\) | |||||||
\(150\) | −16.9186 | − | 20.6991i | −0.112790 | − | 0.137994i | ||||
\(151\) | − | 135.072i | − | 0.894520i | −0.894404 | − | 0.447260i | \(-0.852400\pi\) | ||
0.894404 | − | 0.447260i | \(-0.147600\pi\) | |||||||
\(152\) | 46.3331i | 0.304823i | ||||||||
\(153\) | 125.019 | + | 88.2004i | 0.817116 | + | 0.576473i | ||||
\(154\) | −63.8624 | −0.414691 | ||||||||
\(155\) | 136.049 | 0.877738 | ||||||||
\(156\) | 10.5203 | − | 8.59884i | 0.0674377 | − | 0.0551208i | ||||
\(157\) | 102.595 | 0.653469 | 0.326734 | − | 0.945116i | \(-0.394052\pi\) | ||||
0.326734 | + | 0.945116i | \(0.394052\pi\) | |||||||
\(158\) | −114.862 | − | 114.862i | −0.726977 | − | 0.726977i | ||||
\(159\) | −158.513 | + | 129.562i | −0.996938 | + | 0.814856i | ||||
\(160\) | −17.2968 | − | 17.2968i | −0.108105 | − | 0.108105i | ||||
\(161\) | 50.1397 | 0.311427 | ||||||||
\(162\) | −105.480 | − | 44.6768i | −0.651110 | − | 0.275783i | ||||
\(163\) | 90.8715 | + | 90.8715i | 0.557494 | + | 0.557494i | 0.928593 | − | 0.371099i | \(-0.121019\pi\) |
−0.371099 | + | 0.928593i | \(0.621019\pi\) | |||||||
\(164\) | 33.9712 | − | 33.9712i | 0.207141 | − | 0.207141i | ||||
\(165\) | 91.5613 | − | 74.8384i | 0.554917 | − | 0.453566i | ||||
\(166\) | 233.809 | 1.40849 | ||||||||
\(167\) | −90.3104 | − | 90.3104i | −0.540781 | − | 0.540781i | 0.382977 | − | 0.923758i | \(-0.374899\pi\) |
−0.923758 | + | 0.382977i | \(0.874899\pi\) | |||||||
\(168\) | 41.8237 | + | 4.20322i | 0.248951 | + | 0.0250192i | ||||
\(169\) | −163.872 | −0.969655 | ||||||||
\(170\) | 96.8762 | − | 37.7215i | 0.569860 | − | 0.221891i | ||||
\(171\) | 144.483 | + | 29.3369i | 0.844927 | + | 0.171561i | ||||
\(172\) | − | 36.1671i | − | 0.210274i | ||||||
\(173\) | −19.5661 | − | 19.5661i | −0.113099 | − | 0.113099i | 0.648292 | − | 0.761391i | \(-0.275483\pi\) |
−0.761391 | + | 0.648292i | \(0.775483\pi\) | |||||||
\(174\) | 39.1859 | + | 3.93812i | 0.225206 | + | 0.0226329i | ||||
\(175\) | 22.0722 | − | 22.0722i | 0.126127 | − | 0.126127i | ||||
\(176\) | −25.7832 | + | 25.7832i | −0.146495 | + | 0.146495i | ||||
\(177\) | 250.897 | − | 205.073i | 1.41750 | − | 1.15860i | ||||
\(178\) | − | 56.9632i | − | 0.320018i | ||||||
\(179\) | −163.486 | −0.913328 | −0.456664 | − | 0.889639i | \(-0.650956\pi\) | ||||
−0.456664 | + | 0.889639i | \(0.650956\pi\) | |||||||
\(180\) | −64.8895 | + | 42.9857i | −0.360497 | + | 0.238809i | ||||
\(181\) | 122.461 | + | 122.461i | 0.676579 | + | 0.676579i | 0.959224 | − | 0.282645i | \(-0.0912120\pi\) |
−0.282645 | + | 0.959224i | \(0.591212\pi\) | |||||||
\(182\) | 11.2182 | + | 11.2182i | 0.0616384 | + | 0.0616384i | ||||
\(183\) | 40.5374 | + | 4.07395i | 0.221516 | + | 0.0222620i | ||||
\(184\) | 20.2429 | − | 20.2429i | 0.110016 | − | 0.110016i | ||||
\(185\) | 303.562 | 1.64087 | ||||||||
\(186\) | −13.3476 | + | 132.814i | −0.0717613 | + | 0.714054i | ||||
\(187\) | −56.2288 | − | 144.406i | −0.300689 | − | 0.772227i | ||||
\(188\) | − | 158.311i | − | 0.842080i | ||||||
\(189\) | 39.5888 | − | 127.760i | 0.209464 | − | 0.675976i | ||||
\(190\) | 70.8358 | − | 70.8358i | 0.372820 | − | 0.372820i | ||||
\(191\) | − | 92.3252i | − | 0.483378i | −0.970354 | − | 0.241689i | \(-0.922299\pi\) | ||
0.970354 | − | 0.241689i | \(-0.0777013\pi\) | |||||||
\(192\) | 18.5825 | − | 15.1885i | 0.0967837 | − | 0.0791070i | ||||
\(193\) | 218.951 | + | 218.951i | 1.13446 | + | 1.13446i | 0.989427 | + | 0.145033i | \(0.0463289\pi\) |
0.145033 | + | 0.989427i | \(0.453671\pi\) | |||||||
\(194\) | −40.3730 | + | 40.3730i | −0.208108 | + | 0.208108i | ||||
\(195\) | −29.2301 | − | 2.93758i | −0.149898 | − | 0.0150645i | ||||
\(196\) | − | 48.9197i | − | 0.249590i | ||||||
\(197\) | 71.3747 | − | 71.3747i | 0.362308 | − | 0.362308i | −0.502354 | − | 0.864662i | \(-0.667533\pi\) |
0.864662 | + | 0.502354i | \(0.167533\pi\) | |||||||
\(198\) | 64.0757 | + | 96.7261i | 0.323615 | + | 0.488516i | ||||
\(199\) | 110.195 | − | 110.195i | 0.553744 | − | 0.553744i | −0.373775 | − | 0.927519i | \(-0.621937\pi\) |
0.927519 | + | 0.373775i | \(0.121937\pi\) | |||||||
\(200\) | − | 17.8225i | − | 0.0891123i | ||||||
\(201\) | 140.668 | − | 114.976i | 0.699839 | − | 0.572019i | ||||
\(202\) | 236.388i | 1.17024i | ||||||||
\(203\) | 45.9848i | 0.226526i | ||||||||
\(204\) | 27.3201 | + | 98.2732i | 0.133922 | + | 0.481731i | ||||
\(205\) | −103.873 | −0.506697 | ||||||||
\(206\) | −31.5634 | −0.153220 | ||||||||
\(207\) | −50.3072 | − | 75.9418i | −0.243030 | − | 0.366868i | ||||
\(208\) | 9.05824 | 0.0435492 | ||||||||
\(209\) | −105.590 | − | 105.590i | −0.505215 | − | 0.505215i | ||||
\(210\) | −57.5157 | − | 70.3678i | −0.273884 | − | 0.335085i | ||||
\(211\) | 48.0391 | + | 48.0391i | 0.227674 | + | 0.227674i | 0.811720 | − | 0.584047i | \(-0.198531\pi\) |
−0.584047 | + | 0.811720i | \(0.698531\pi\) | |||||||
\(212\) | −136.484 | −0.643793 | ||||||||
\(213\) | −40.5533 | − | 4.07555i | −0.190391 | − | 0.0191340i | ||||
\(214\) | −147.359 | − | 147.359i | −0.688592 | − | 0.688592i | ||||
\(215\) | −55.2937 | + | 55.2937i | −0.257180 | + | 0.257180i | ||||
\(216\) | −35.5972 | − | 67.5636i | −0.164802 | − | 0.312794i | ||||
\(217\) | −155.858 | −0.718238 | ||||||||
\(218\) | −85.1582 | − | 85.1582i | −0.390634 | − | 0.390634i | ||||
\(219\) | 29.8623 | − | 297.142i | 0.136357 | − | 1.35681i | ||||
\(220\) | 78.8367 | 0.358349 | ||||||||
\(221\) | −15.4895 | + | 35.2440i | −0.0700880 | + | 0.159475i | ||||
\(222\) | −29.7820 | + | 296.343i | −0.134153 | + | 1.33488i | ||||
\(223\) | 343.681i | 1.54117i | 0.637337 | + | 0.770585i | \(0.280036\pi\) | ||||
−0.637337 | + | 0.770585i | \(0.719964\pi\) | |||||||
\(224\) | 19.8152 | + | 19.8152i | 0.0884608 | + | 0.0884608i | ||||
\(225\) | −55.5766 | − | 11.2847i | −0.247007 | − | 0.0501542i | ||||
\(226\) | −130.624 | + | 130.624i | −0.577982 | + | 0.577982i | ||||
\(227\) | −266.074 | + | 266.074i | −1.17213 | + | 1.17213i | −0.190433 | + | 0.981700i | \(0.560989\pi\) |
−0.981700 | + | 0.190433i | \(0.939011\pi\) | |||||||
\(228\) | 62.2017 | + | 76.1009i | 0.272814 | + | 0.333776i | ||||
\(229\) | − | 276.854i | − | 1.20897i | −0.796617 | − | 0.604484i | \(-0.793379\pi\) | ||
0.796617 | − | 0.604484i | \(-0.206621\pi\) | |||||||
\(230\) | −61.8964 | −0.269115 | ||||||||
\(231\) | −104.892 | + | 85.7346i | −0.454079 | + | 0.371145i | ||||
\(232\) | 18.5655 | + | 18.5655i | 0.0800235 | + | 0.0800235i | ||||
\(233\) | 212.257 | + | 212.257i | 0.910974 | + | 0.910974i | 0.996349 | − | 0.0853750i | \(-0.0272088\pi\) |
−0.0853750 | + | 0.996349i | \(0.527209\pi\) | |||||||
\(234\) | 5.73544 | − | 28.2467i | 0.0245104 | − | 0.120713i | ||||
\(235\) | −242.032 | + | 242.032i | −1.02992 | + | 1.02992i | ||||
\(236\) | 216.029 | 0.915377 | ||||||||
\(237\) | −342.860 | − | 34.4569i | −1.44667 | − | 0.145388i | ||||
\(238\) | −110.981 | + | 43.2136i | −0.466307 | + | 0.181570i | ||||
\(239\) | − | 164.670i | − | 0.688995i | −0.938787 | − | 0.344497i | \(-0.888049\pi\) | ||
0.938787 | − | 0.344497i | \(-0.111951\pi\) | |||||||
\(240\) | −51.6305 | − | 5.18878i | −0.215127 | − | 0.0216199i | ||||
\(241\) | −102.383 | + | 102.383i | −0.424826 | + | 0.424826i | −0.886862 | − | 0.462035i | \(-0.847119\pi\) |
0.462035 | + | 0.886862i | \(0.347119\pi\) | |||||||
\(242\) | 53.6036i | 0.221502i | ||||||||
\(243\) | −233.226 | + | 68.2250i | −0.959778 | + | 0.280761i | ||||
\(244\) | 19.2058 | + | 19.2058i | 0.0787122 | + | 0.0787122i | ||||
\(245\) | −74.7904 | + | 74.7904i | −0.305267 | + | 0.305267i | ||||
\(246\) | 10.1908 | − | 101.403i | 0.0414261 | − | 0.412206i | ||||
\(247\) | 37.0962i | 0.150187i | ||||||||
\(248\) | −62.9245 | + | 62.9245i | −0.253728 | + | 0.253728i | ||||
\(249\) | 384.025 | − | 313.886i | 1.54227 | − | 1.26059i | ||||
\(250\) | −135.353 | + | 135.353i | −0.541412 | + | 0.541412i | ||||
\(251\) | − | 14.5020i | − | 0.0577769i | −0.999583 | − | 0.0288885i | \(-0.990803\pi\) | ||
0.999583 | − | 0.0288885i | \(-0.00919677\pi\) | |||||||
\(252\) | 74.3372 | − | 49.2442i | 0.294989 | − | 0.195414i | ||||
\(253\) | 92.2646i | 0.364682i | ||||||||
\(254\) | 60.7634i | 0.239226i | ||||||||
\(255\) | 108.476 | − | 192.012i | 0.425396 | − | 0.752988i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 268.938 | 1.04645 | 0.523225 | − | 0.852194i | \(-0.324729\pi\) | ||||
0.523225 | + | 0.852194i | \(0.324729\pi\) | |||||||
\(258\) | −48.5540 | − | 59.4035i | −0.188194 | − | 0.230246i | ||||
\(259\) | −347.759 | −1.34270 | ||||||||
\(260\) | −13.8486 | − | 13.8486i | −0.0532638 | − | 0.0532638i | ||||
\(261\) | 69.6487 | − | 46.1384i | 0.266853 | − | 0.176775i | ||||
\(262\) | −14.3880 | − | 14.3880i | −0.0549161 | − | 0.0549161i | ||||
\(263\) | 291.070 | 1.10673 | 0.553365 | − | 0.832939i | \(-0.313343\pi\) | ||||
0.553365 | + | 0.832939i | \(0.313343\pi\) | |||||||
\(264\) | −7.73455 | + | 76.9619i | −0.0292975 | + | 0.291522i | ||||
\(265\) | 208.662 | + | 208.662i | 0.787405 | + | 0.787405i | ||||
\(266\) | −81.1493 | + | 81.1493i | −0.305072 | + | 0.305072i | ||||
\(267\) | −76.4725 | − | 93.5605i | −0.286414 | − | 0.350414i | ||||
\(268\) | 121.119 | 0.451935 | ||||||||
\(269\) | −207.923 | − | 207.923i | −0.772947 | − | 0.772947i | 0.205673 | − | 0.978621i | \(-0.434062\pi\) |
−0.978621 | + | 0.205673i | \(0.934062\pi\) | |||||||
\(270\) | −48.8715 | + | 157.716i | −0.181005 | + | 0.584135i | ||||
\(271\) | 30.6638 | 0.113151 | 0.0565754 | − | 0.998398i | \(-0.481982\pi\) | ||||
0.0565754 | + | 0.998398i | \(0.481982\pi\) | |||||||
\(272\) | −27.3598 | + | 62.2531i | −0.100587 | + | 0.228872i | ||||
\(273\) | 33.4859 | + | 3.36528i | 0.122659 | + | 0.0123270i | ||||
\(274\) | − | 149.165i | − | 0.544396i | ||||||
\(275\) | 40.6162 | + | 40.6162i | 0.147695 | + | 0.147695i | ||||
\(276\) | 6.07256 | − | 60.4244i | 0.0220020 | − | 0.218929i | ||||
\(277\) | 48.6256 | − | 48.6256i | 0.175544 | − | 0.175544i | −0.613866 | − | 0.789410i | \(-0.710387\pi\) |
0.789410 | + | 0.613866i | \(0.210387\pi\) | |||||||
\(278\) | 5.07235 | − | 5.07235i | 0.0182459 | − | 0.0182459i | ||||
\(279\) | 156.378 | + | 236.063i | 0.560496 | + | 0.846102i | ||||
\(280\) | − | 60.5886i | − | 0.216388i | ||||||
\(281\) | 69.2460 | 0.246427 | 0.123214 | − | 0.992380i | \(-0.460680\pi\) | ||||
0.123214 | + | 0.992380i | \(0.460680\pi\) | |||||||
\(282\) | −212.531 | − | 260.022i | −0.753656 | − | 0.922063i | ||||
\(283\) | 212.579 | + | 212.579i | 0.751164 | + | 0.751164i | 0.974697 | − | 0.223532i | \(-0.0717588\pi\) |
−0.223532 | + | 0.974697i | \(0.571759\pi\) | |||||||
\(284\) | −19.2133 | − | 19.2133i | −0.0676525 | − | 0.0676525i | ||||
\(285\) | 21.2496 | − | 211.442i | 0.0745601 | − | 0.741903i | ||||
\(286\) | −20.6431 | + | 20.6431i | −0.0721788 | + | 0.0721788i | ||||
\(287\) | 118.997 | 0.414622 | ||||||||
\(288\) | 10.1308 | − | 49.8936i | 0.0351763 | − | 0.173242i | ||||
\(289\) | −195.430 | − | 212.904i | −0.676230 | − | 0.736691i | ||||
\(290\) | − | 56.7672i | − | 0.195749i | ||||||
\(291\) | −12.1113 | + | 120.512i | −0.0416195 | + | 0.414130i | ||||
\(292\) | 140.779 | − | 140.779i | 0.482121 | − | 0.482121i | ||||
\(293\) | 175.749i | 0.599825i | 0.953967 | + | 0.299913i | \(0.0969576\pi\) | ||||
−0.953967 | + | 0.299913i | \(0.903042\pi\) | |||||||
\(294\) | −65.6742 | − | 80.3493i | −0.223382 | − | 0.273297i | ||||
\(295\) | −330.274 | − | 330.274i | −1.11957 | − | 1.11957i | ||||
\(296\) | −140.401 | + | 140.401i | −0.474327 | + | 0.474327i | ||||
\(297\) | 235.097 | + | 72.8492i | 0.791571 | + | 0.245284i | ||||
\(298\) | 343.797i | 1.15368i | ||||||||
\(299\) | 16.2074 | − | 16.2074i | 0.0542052 | − | 0.0542052i | ||||
\(300\) | −23.9265 | − | 29.2729i | −0.0797549 | − | 0.0975764i | ||||
\(301\) | 63.3443 | − | 63.3443i | 0.210446 | − | 0.210446i | ||||
\(302\) | − | 191.021i | − | 0.632521i | ||||||
\(303\) | 317.348 | + | 388.261i | 1.04735 | + | 1.28139i | ||||
\(304\) | 65.5248i | 0.215542i | ||||||||
\(305\) | − | 58.7251i | − | 0.192541i | ||||||
\(306\) | 176.803 | + | 124.734i | 0.577788 | + | 0.407628i | ||||
\(307\) | 526.455 | 1.71484 | 0.857419 | − | 0.514619i | \(-0.172067\pi\) | ||||
0.857419 | + | 0.514619i | \(0.172067\pi\) | |||||||
\(308\) | −90.3151 | −0.293231 | ||||||||
\(309\) | −51.8421 | + | 42.3735i | −0.167774 | + | 0.137131i | ||||
\(310\) | 192.403 | 0.620655 | ||||||||
\(311\) | 168.301 | + | 168.301i | 0.541160 | + | 0.541160i | 0.923869 | − | 0.382709i | \(-0.125009\pi\) |
−0.382709 | + | 0.923869i | \(0.625009\pi\) | |||||||
\(312\) | 14.8779 | − | 12.1606i | 0.0476857 | − | 0.0389763i | ||||
\(313\) | −313.933 | − | 313.933i | −1.00298 | − | 1.00298i | −0.999996 | − | 0.00298652i | \(-0.999049\pi\) |
−0.00298652 | − | 0.999996i | \(-0.500951\pi\) | |||||||
\(314\) | 145.091 | 0.462072 | ||||||||
\(315\) | −188.936 | − | 38.3631i | −0.599797 | − | 0.121787i | ||||
\(316\) | −162.440 | − | 162.440i | −0.514050 | − | 0.514050i | ||||
\(317\) | −412.404 | + | 412.404i | −1.30096 | + | 1.30096i | −0.373216 | + | 0.927745i | \(0.621745\pi\) |
−0.927745 | + | 0.373216i | \(0.878255\pi\) | |||||||
\(318\) | −224.172 | + | 183.228i | −0.704942 | + | 0.576190i | ||||
\(319\) | −84.6189 | −0.265263 | ||||||||
\(320\) | −24.4614 | − | 24.4614i | −0.0764420 | − | 0.0764420i | ||||
\(321\) | −439.860 | − | 44.2053i | −1.37028 | − | 0.137711i | ||||
\(322\) | 70.9083 | 0.220212 | ||||||||
\(323\) | −254.945 | − | 112.047i | −0.789304 | − | 0.346893i | ||||
\(324\) | −149.171 | − | 63.1825i | −0.460404 | − | 0.195008i | ||||
\(325\) | − | 14.2694i | − | 0.0439059i | ||||||
\(326\) | 128.512 | + | 128.512i | 0.394208 | + | 0.394208i | ||||
\(327\) | −254.194 | − | 25.5461i | −0.777352 | − | 0.0781227i | ||||
\(328\) | 48.0425 | − | 48.0425i | 0.146471 | − | 0.146471i | ||||
\(329\) | 277.271 | − | 277.271i | 0.842769 | − | 0.842769i | ||||
\(330\) | 129.487 | − | 105.837i | 0.392386 | − | 0.320720i | ||||
\(331\) | − | 195.845i | − | 0.591676i | −0.955238 | − | 0.295838i | \(-0.904401\pi\) | ||
0.955238 | − | 0.295838i | \(-0.0955989\pi\) | |||||||
\(332\) | 330.656 | 0.995951 | ||||||||
\(333\) | 348.921 | + | 526.717i | 1.04781 | + | 1.58173i | ||||
\(334\) | −127.718 | − | 127.718i | −0.382390 | − | 0.382390i | ||||
\(335\) | −185.171 | − | 185.171i | −0.552749 | − | 0.552749i | ||||
\(336\) | 59.1477 | + | 5.94425i | 0.176035 | + | 0.0176912i | ||||
\(337\) | 358.030 | − | 358.030i | 1.06240 | − | 1.06240i | 0.0644838 | − | 0.997919i | \(-0.479460\pi\) |
0.997919 | − | 0.0644838i | \(-0.0205401\pi\) | |||||||
\(338\) | −231.750 | −0.685650 | ||||||||
\(339\) | −39.1852 | + | 389.908i | −0.115590 | + | 1.15017i | ||||
\(340\) | 137.004 | − | 53.3463i | 0.402952 | − | 0.156901i | ||||
\(341\) | − | 286.801i | − | 0.841060i | ||||||
\(342\) | 204.329 | + | 41.4886i | 0.597454 | + | 0.121312i | ||||
\(343\) | 257.320 | − | 257.320i | 0.750204 | − | 0.750204i | ||||
\(344\) | − | 51.1480i | − | 0.148686i | ||||||
\(345\) | −101.663 | + | 83.0953i | −0.294676 | + | 0.240856i | ||||
\(346\) | −27.6707 | − | 27.6707i | −0.0799731 | − | 0.0799731i | ||||
\(347\) | −61.9535 | + | 61.9535i | −0.178540 | + | 0.178540i | −0.790719 | − | 0.612179i | \(-0.790293\pi\) |
0.612179 | + | 0.790719i | \(0.290293\pi\) | |||||||
\(348\) | 55.4172 | + | 5.56934i | 0.159245 | + | 0.0160039i | ||||
\(349\) | − | 165.579i | − | 0.474439i | −0.971456 | − | 0.237220i | \(-0.923764\pi\) | ||
0.971456 | − | 0.237220i | \(-0.0762361\pi\) | |||||||
\(350\) | 31.2148 | − | 31.2148i | 0.0891853 | − | 0.0891853i | ||||
\(351\) | −28.5007 | − | 54.0943i | −0.0811985 | − | 0.154115i | ||||
\(352\) | −36.4629 | + | 36.4629i | −0.103588 | + | 0.103588i | ||||
\(353\) | − | 41.8884i | − | 0.118664i | −0.998238 | − | 0.0593319i | \(-0.981103\pi\) | ||
0.998238 | − | 0.0593319i | \(-0.0188970\pi\) | |||||||
\(354\) | 354.822 | − | 290.017i | 1.00232 | − | 0.819256i | ||||
\(355\) | 58.7482i | 0.165488i | ||||||||
\(356\) | − | 80.5581i | − | 0.226287i | ||||||
\(357\) | −124.270 | + | 219.968i | −0.348094 | + | 0.616157i | ||||
\(358\) | −231.204 | −0.645821 | ||||||||
\(359\) | −404.427 | −1.12654 | −0.563269 | − | 0.826274i | \(-0.690456\pi\) | ||||
−0.563269 | + | 0.826274i | \(0.690456\pi\) | |||||||
\(360\) | −91.7676 | + | 60.7909i | −0.254910 | + | 0.168864i | ||||
\(361\) | 92.6559 | 0.256665 | ||||||||
\(362\) | 173.186 | + | 173.186i | 0.478414 | + | 0.478414i | ||||
\(363\) | 71.9622 | + | 88.0425i | 0.198243 | + | 0.242541i | ||||
\(364\) | 15.8649 | + | 15.8649i | 0.0435849 | + | 0.0435849i | ||||
\(365\) | −430.459 | −1.17934 | ||||||||
\(366\) | 57.3286 | + | 5.76143i | 0.156635 | + | 0.0157416i | ||||
\(367\) | 248.887 | + | 248.887i | 0.678167 | + | 0.678167i | 0.959585 | − | 0.281418i | \(-0.0908048\pi\) |
−0.281418 | + | 0.959585i | \(0.590805\pi\) | |||||||
\(368\) | 28.6278 | − | 28.6278i | 0.0777930 | − | 0.0777930i | ||||
\(369\) | −119.394 | − | 180.232i | −0.323561 | − | 0.488435i | ||||
\(370\) | 429.301 | 1.16027 | ||||||||
\(371\) | −239.043 | − | 239.043i | −0.644320 | − | 0.644320i | ||||
\(372\) | −18.8764 | + | 187.827i | −0.0507429 | + | 0.504912i | ||||
\(373\) | 63.0002 | 0.168901 | 0.0844507 | − | 0.996428i | \(-0.473086\pi\) | ||||
0.0844507 | + | 0.996428i | \(0.473086\pi\) | |||||||
\(374\) | −79.5195 | − | 204.222i | −0.212619 | − | 0.546047i | ||||
\(375\) | −40.6038 | + | 404.024i | −0.108277 | + | 1.07740i | ||||
\(376\) | − | 223.886i | − | 0.595440i | ||||||
\(377\) | 14.8643 | + | 14.8643i | 0.0394279 | + | 0.0394279i | ||||
\(378\) | 55.9870 | − | 180.679i | 0.148114 | − | 0.477988i | ||||
\(379\) | 340.542 | − | 340.542i | 0.898527 | − | 0.898527i | −0.0967791 | − | 0.995306i | \(-0.530854\pi\) |
0.995306 | + | 0.0967791i | \(0.0308540\pi\) | |||||||
\(380\) | 100.177 | − | 100.177i | 0.263624 | − | 0.263624i | ||||
\(381\) | 81.5743 | + | 99.8023i | 0.214106 | + | 0.261948i | ||||
\(382\) | − | 130.567i | − | 0.341800i | ||||||
\(383\) | 507.354 | 1.32468 | 0.662342 | − | 0.749202i | \(-0.269563\pi\) | ||||
0.662342 | + | 0.749202i | \(0.269563\pi\) | |||||||
\(384\) | 26.2796 | − | 21.4798i | 0.0684364 | − | 0.0559371i | ||||
\(385\) | 138.077 | + | 138.077i | 0.358642 | + | 0.358642i | ||||
\(386\) | 309.643 | + | 309.643i | 0.802184 | + | 0.802184i | ||||
\(387\) | −159.497 | − | 32.3856i | −0.412138 | − | 0.0836836i | ||||
\(388\) | −57.0960 | + | 57.0960i | −0.147155 | + | 0.147155i | ||||
\(389\) | −23.5326 | −0.0604952 | −0.0302476 | − | 0.999542i | \(-0.509630\pi\) | ||||
−0.0302476 | + | 0.999542i | \(0.509630\pi\) | |||||||
\(390\) | −41.3376 | − | 4.15436i | −0.105994 | − | 0.0106522i | ||||
\(391\) | 62.4325 | + | 160.339i | 0.159674 | + | 0.410074i | ||||
\(392\) | − | 69.1829i | − | 0.176487i | ||||||
\(393\) | −42.9477 | − | 4.31618i | −0.109282 | − | 0.0109826i | ||||
\(394\) | 100.939 | − | 100.939i | 0.256190 | − | 0.256190i | ||||
\(395\) | 496.689i | 1.25744i | ||||||||
\(396\) | 90.6167 | + | 136.791i | 0.228830 | + | 0.345433i | ||||
\(397\) | 269.112 | + | 269.112i | 0.677863 | + | 0.677863i | 0.959516 | − | 0.281653i | \(-0.0908827\pi\) |
−0.281653 | + | 0.959516i | \(0.590883\pi\) | |||||||
\(398\) | 155.839 | − | 155.839i | 0.391556 | − | 0.391556i | ||||
\(399\) | −24.3435 | + | 242.228i | −0.0610113 | + | 0.607087i | ||||
\(400\) | − | 25.2048i | − | 0.0630119i | ||||||
\(401\) | 305.035 | − | 305.035i | 0.760687 | − | 0.760687i | −0.215760 | − | 0.976447i | \(-0.569223\pi\) |
0.976447 | + | 0.215760i | \(0.0692227\pi\) | |||||||
\(402\) | 198.934 | − | 162.600i | 0.494861 | − | 0.404479i | ||||
\(403\) | −50.3801 | + | 50.3801i | −0.125013 | + | 0.125013i | ||||
\(404\) | 334.303i | 0.827482i | ||||||||
\(405\) | 131.462 | + | 324.654i | 0.324599 | + | 0.801616i | ||||
\(406\) | 65.0323i | 0.160178i | ||||||||
\(407\) | − | 639.929i | − | 1.57231i | ||||||
\(408\) | 38.6364 | + | 138.979i | 0.0946971 | + | 0.340635i | ||||
\(409\) | −439.207 | −1.07386 | −0.536928 | − | 0.843628i | \(-0.680415\pi\) | ||||
−0.536928 | + | 0.843628i | \(0.680415\pi\) | |||||||
\(410\) | −146.899 | −0.358289 | ||||||||
\(411\) | −200.252 | − | 244.999i | −0.487231 | − | 0.596104i | ||||
\(412\) | −44.6374 | −0.108343 | ||||||||
\(413\) | 378.360 | + | 378.360i | 0.916127 | + | 0.916127i | ||||
\(414\) | −71.1451 | − | 107.398i | −0.171848 | − | 0.259415i | ||||
\(415\) | −505.519 | − | 505.519i | −1.21812 | − | 1.21812i | ||||
\(416\) | 12.8103 | 0.0307940 | ||||||||
\(417\) | 1.52163 | − | 15.1408i | 0.00364898 | − | 0.0363089i | ||||
\(418\) | −149.327 | − | 149.327i | −0.357241 | − | 0.357241i | ||||
\(419\) | −54.5759 | + | 54.5759i | −0.130253 | + | 0.130253i | −0.769228 | − | 0.638975i | \(-0.779359\pi\) |
0.638975 | + | 0.769228i | \(0.279359\pi\) | |||||||
\(420\) | −81.3395 | − | 99.5151i | −0.193666 | − | 0.236941i | ||||
\(421\) | −718.243 | −1.70604 | −0.853020 | − | 0.521878i | \(-0.825232\pi\) | ||||
−0.853020 | + | 0.521878i | \(0.825232\pi\) | |||||||
\(422\) | 67.9376 | + | 67.9376i | 0.160990 | + | 0.160990i | ||||
\(423\) | −698.153 | − | 141.758i | −1.65048 | − | 0.335126i | ||||
\(424\) | −193.018 | −0.455230 | ||||||||
\(425\) | 98.0671 | + | 43.0998i | 0.230746 | + | 0.101411i | ||||
\(426\) | −57.3511 | − | 5.76369i | −0.134627 | − | 0.0135298i | ||||
\(427\) | 67.2753i | 0.157553i | ||||||||
\(428\) | −208.397 | − | 208.397i | −0.486908 | − | 0.486908i | ||||
\(429\) | −6.19261 | + | 61.6190i | −0.0144350 | + | 0.143634i | ||||
\(430\) | −78.1971 | + | 78.1971i | −0.181854 | + | 0.181854i | ||||
\(431\) | 486.540 | − | 486.540i | 1.12886 | − | 1.12886i | 0.138501 | − | 0.990362i | \(-0.455772\pi\) |
0.990362 | − | 0.138501i | \(-0.0442284\pi\) | |||||||
\(432\) | −50.3421 | − | 95.5493i | −0.116533 | − | 0.221179i | ||||
\(433\) | 401.213i | 0.926589i | 0.886204 | + | 0.463295i | \(0.153333\pi\) | ||||
−0.886204 | + | 0.463295i | \(0.846667\pi\) | |||||||
\(434\) | −220.416 | −0.507871 | ||||||||
\(435\) | −76.2094 | − | 93.2387i | −0.175194 | − | 0.214342i | ||||
\(436\) | −120.432 | − | 120.432i | −0.276220 | − | 0.276220i | ||||
\(437\) | 117.240 | + | 117.240i | 0.268283 | + | 0.268283i | ||||
\(438\) | 42.2316 | − | 420.222i | 0.0964192 | − | 0.959410i | ||||
\(439\) | −224.591 | + | 224.591i | −0.511596 | + | 0.511596i | −0.915015 | − | 0.403419i | \(-0.867822\pi\) |
0.403419 | + | 0.915015i | \(0.367822\pi\) | |||||||
\(440\) | 111.492 | 0.253391 | ||||||||
\(441\) | −215.736 | − | 43.8048i | −0.489198 | − | 0.0993305i | ||||
\(442\) | −21.9054 | + | 49.8425i | −0.0495597 | + | 0.112766i | ||||
\(443\) | − | 224.083i | − | 0.505832i | −0.967488 | − | 0.252916i | \(-0.918610\pi\) | ||
0.967488 | − | 0.252916i | \(-0.0813896\pi\) | |||||||
\(444\) | −42.1181 | + | 419.092i | −0.0948605 | + | 0.943900i | ||||
\(445\) | −123.160 | + | 123.160i | −0.276765 | + | 0.276765i | ||||
\(446\) | 486.038i | 1.08977i | ||||||||
\(447\) | 461.544 | + | 564.678i | 1.03254 | + | 1.26326i | ||||
\(448\) | 28.0229 | + | 28.0229i | 0.0625512 | + | 0.0625512i | ||||
\(449\) | −166.816 | + | 166.816i | −0.371527 | + | 0.371527i | −0.868033 | − | 0.496506i | \(-0.834616\pi\) |
0.496506 | + | 0.868033i | \(0.334616\pi\) | |||||||
\(450\) | −78.5972 | − | 15.9590i | −0.174660 | − | 0.0354644i | ||||
\(451\) | 218.971i | 0.485524i | ||||||||
\(452\) | −184.730 | + | 184.730i | −0.408695 | + | 0.408695i | ||||
\(453\) | −256.444 | − | 313.748i | −0.566102 | − | 0.692599i | ||||
\(454\) | −376.286 | + | 376.286i | −0.828823 | + | 0.828823i | ||||
\(455\) | − | 48.5098i | − | 0.106615i | ||||||
\(456\) | 87.9664 | + | 107.623i | 0.192909 | + | 0.236015i | ||||
\(457\) | − | 358.924i | − | 0.785391i | −0.919669 | − | 0.392695i | \(-0.871543\pi\) | ||
0.919669 | − | 0.392695i | \(-0.128457\pi\) | |||||||
\(458\) | − | 391.530i | − | 0.854870i | ||||||
\(459\) | 457.849 | − | 32.4838i | 0.997493 | − | 0.0707708i | ||||
\(460\) | −87.5347 | −0.190293 | ||||||||
\(461\) | −666.524 | −1.44582 | −0.722911 | − | 0.690941i | \(-0.757196\pi\) | ||||
−0.722911 | + | 0.690941i | \(0.757196\pi\) | |||||||
\(462\) | −148.340 | + | 121.247i | −0.321083 | + | 0.262439i | ||||
\(463\) | −175.521 | −0.379096 | −0.189548 | − | 0.981871i | \(-0.560702\pi\) | ||||
−0.189548 | + | 0.981871i | \(0.560702\pi\) | |||||||
\(464\) | 26.2555 | + | 26.2555i | 0.0565852 | + | 0.0565852i | ||||
\(465\) | 316.017 | − | 258.299i | 0.679606 | − | 0.555482i | ||||
\(466\) | 300.177 | + | 300.177i | 0.644156 | + | 0.644156i | ||||
\(467\) | −314.564 | −0.673585 | −0.336793 | − | 0.941579i | \(-0.609342\pi\) | ||||
−0.336793 | + | 0.941579i | \(0.609342\pi\) | |||||||
\(468\) | 8.11113 | − | 39.9469i | 0.0173315 | − | 0.0853567i | ||||
\(469\) | 212.131 | + | 212.131i | 0.452305 | + | 0.452305i | ||||
\(470\) | −342.285 | + | 342.285i | −0.728266 | + | 0.728266i | ||||
\(471\) | 238.308 | − | 194.783i | 0.505961 | − | 0.413552i | ||||
\(472\) | 305.511 | 0.647269 | ||||||||
\(473\) | 116.563 | + | 116.563i | 0.246433 | + | 0.246433i | ||||
\(474\) | −484.877 | − | 48.7294i | −1.02295 | − | 0.102805i | ||||
\(475\) | 103.221 | 0.217308 | ||||||||
\(476\) | −156.951 | + | 61.1133i | −0.329729 | + | 0.128389i | ||||
\(477\) | −122.214 | + | 601.896i | −0.256213 | + | 1.26184i | ||||
\(478\) | − | 232.878i | − | 0.487193i | ||||||
\(479\) | 317.240 | + | 317.240i | 0.662297 | + | 0.662297i | 0.955921 | − | 0.293624i | \(-0.0948614\pi\) |
−0.293624 | + | 0.955921i | \(0.594861\pi\) | |||||||
\(480\) | −73.0165 | − | 7.33805i | −0.152118 | − | 0.0152876i | ||||
\(481\) | −112.411 | + | 112.411i | −0.233703 | + | 0.233703i | ||||
\(482\) | −144.792 | + | 144.792i | −0.300398 | + | 0.300398i | ||||
\(483\) | 116.465 | − | 95.1937i | 0.241128 | − | 0.197088i | ||||
\(484\) | 75.8069i | 0.156626i | ||||||||
\(485\) | 174.581 | 0.359962 | ||||||||
\(486\) | −329.831 | + | 96.4848i | −0.678665 | + | 0.198528i | ||||
\(487\) | 319.242 | + | 319.242i | 0.655528 | + | 0.655528i | 0.954319 | − | 0.298790i | \(-0.0965832\pi\) |
−0.298790 | + | 0.954319i | \(0.596583\pi\) | |||||||
\(488\) | 27.1611 | + | 27.1611i | 0.0556580 | + | 0.0556580i | ||||
\(489\) | 383.603 | + | 38.5515i | 0.784464 | + | 0.0788374i | ||||
\(490\) | −105.770 | + | 105.770i | −0.215856 | + | 0.215856i | ||||
\(491\) | 148.054 | 0.301537 | 0.150768 | − | 0.988569i | \(-0.451825\pi\) | ||||
0.150768 | + | 0.988569i | \(0.451825\pi\) | |||||||
\(492\) | 14.4120 | − | 143.405i | 0.0292927 | − | 0.291474i | ||||
\(493\) | −147.052 | + | 57.2589i | −0.298280 | + | 0.116144i | ||||
\(494\) | 52.4620i | 0.106198i | ||||||||
\(495\) | 70.5937 | − | 347.671i | 0.142614 | − | 0.702365i | ||||
\(496\) | −88.9887 | + | 88.9887i | −0.179413 | + | 0.179413i | ||||
\(497\) | − | 67.3017i | − | 0.135416i | ||||||
\(498\) | 543.093 | − | 443.902i | 1.09055 | − | 0.891369i | ||||
\(499\) | −383.524 | − | 383.524i | −0.768585 | − | 0.768585i | 0.209272 | − | 0.977857i | \(-0.432891\pi\) |
−0.977857 | + | 0.209272i | \(0.932891\pi\) | |||||||
\(500\) | −191.418 | + | 191.418i | −0.382836 | + | 0.382836i | ||||
\(501\) | −381.234 | − | 38.3134i | −0.760946 | − | 0.0764739i | ||||
\(502\) | − | 20.5089i | − | 0.0408545i | ||||||
\(503\) | 43.5758 | − | 43.5758i | 0.0866319 | − | 0.0866319i | −0.662463 | − | 0.749095i | \(-0.730489\pi\) |
0.749095 | + | 0.662463i | \(0.230489\pi\) | |||||||
\(504\) | 105.129 | − | 69.6419i | 0.208589 | − | 0.138178i | ||||
\(505\) | 511.095 | − | 511.095i | 1.01207 | − | 1.01207i | ||||
\(506\) | 130.482i | 0.257869i | ||||||||
\(507\) | −380.643 | + | 311.122i | −0.750775 | + | 0.613652i | ||||
\(508\) | 85.9325i | 0.169158i | ||||||||
\(509\) | − | 786.816i | − | 1.54581i | −0.634524 | − | 0.772904i | \(-0.718804\pi\) | ||
0.634524 | − | 0.772904i | \(-0.281196\pi\) | |||||||
\(510\) | 153.408 | − | 271.546i | 0.300800 | − | 0.532443i | ||||
\(511\) | 493.132 | 0.965033 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 391.303 | − | 206.166i | 0.762775 | − | 0.401883i | ||||
\(514\) | 380.336 | 0.739952 | ||||||||
\(515\) | 68.2434 | + | 68.2434i | 0.132511 | + | 0.132511i | ||||
\(516\) | −68.6657 | − | 84.0093i | −0.133073 | − | 0.162809i | ||||
\(517\) | 510.220 | + | 510.220i | 0.986886 | + | 0.986886i | ||||
\(518\) | −491.806 | −0.949432 | ||||||||
\(519\) | −82.5961 | − | 8.30078i | −0.159145 | − | 0.0159938i | ||||
\(520\) | −19.5849 | − | 19.5849i | −0.0376632 | − | 0.0376632i | ||||
\(521\) | 167.182 | − | 167.182i | 0.320888 | − | 0.320888i | −0.528220 | − | 0.849108i | \(-0.677140\pi\) |
0.849108 | + | 0.528220i | \(0.177140\pi\) | |||||||
\(522\) | 98.4981 | − | 65.2495i | 0.188694 | − | 0.124999i | ||||
\(523\) | −641.177 | −1.22596 | −0.612980 | − | 0.790099i | \(-0.710029\pi\) | ||||
−0.612980 | + | 0.790099i | \(0.710029\pi\) | |||||||
\(524\) | −20.3477 | − | 20.3477i | −0.0388315 | − | 0.0388315i | ||||
\(525\) | 9.36396 | − | 93.1752i | 0.0178361 | − | 0.177477i | ||||
\(526\) | 411.635 | 0.782577 | ||||||||
\(527\) | −194.069 | − | 498.408i | −0.368253 | − | 0.945745i | ||||
\(528\) | −10.9383 | + | 108.841i | −0.0207165 | + | 0.206137i | ||||
\(529\) | 426.556i | 0.806344i | ||||||||
\(530\) | 295.093 | + | 295.093i | 0.556779 | + | 0.556779i | ||||
\(531\) | 193.442 | − | 952.690i | 0.364297 | − | 1.79414i | ||||
\(532\) | −114.762 | + | 114.762i | −0.215719 | + | 0.215719i | ||||
\(533\) | 38.4649 | − | 38.4649i | 0.0721668 | − | 0.0721668i | ||||
\(534\) | −108.148 | − | 132.315i | −0.202525 | − | 0.247780i | ||||
\(535\) | 637.210i | 1.19105i | ||||||||
\(536\) | 171.288 | 0.319566 | ||||||||
\(537\) | −379.746 | + | 310.389i | −0.707162 | + | 0.578005i | ||||
\(538\) | −294.047 | − | 294.047i | −0.546556 | − | 0.546556i | ||||
\(539\) | 157.663 | + | 157.663i | 0.292510 | + | 0.292510i | ||||
\(540\) | −69.1147 | + | 223.045i | −0.127990 | + | 0.413046i | ||||
\(541\) | 171.204 | − | 171.204i | 0.316458 | − | 0.316458i | −0.530947 | − | 0.847405i | \(-0.678164\pi\) |
0.847405 | + | 0.530947i | \(0.178164\pi\) | |||||||
\(542\) | 43.3652 | 0.0800096 | ||||||||
\(543\) | 516.953 | + | 51.9530i | 0.952031 | + | 0.0956777i | ||||
\(544\) | −38.6925 | + | 88.0391i | −0.0711260 | + | 0.161837i | ||||
\(545\) | 368.242i | 0.675674i | ||||||||
\(546\) | 47.3562 | + | 4.75922i | 0.0867329 | + | 0.00871653i | ||||
\(547\) | −284.575 | + | 284.575i | −0.520247 | + | 0.520247i | −0.917646 | − | 0.397399i | \(-0.869913\pi\) |
0.397399 | + | 0.917646i | \(0.369913\pi\) | |||||||
\(548\) | − | 210.951i | − | 0.384946i | ||||||
\(549\) | 101.895 | − | 67.5000i | 0.185602 | − | 0.122951i | ||||
\(550\) | 57.4399 | + | 57.4399i | 0.104436 | + | 0.104436i | ||||
\(551\) | −107.524 | + | 107.524i | −0.195144 | + | 0.195144i | ||||
\(552\) | 8.58790 | − | 85.4530i | 0.0155578 | − | 0.154806i | ||||
\(553\) | − | 569.005i | − | 1.02894i | ||||||
\(554\) | 68.7670 | − | 68.7670i | 0.124128 | − | 0.124128i | ||||
\(555\) | 705.116 | − | 576.332i | 1.27048 | − | 1.03844i | ||||
\(556\) | 7.17339 | − | 7.17339i | 0.0129018 | − | 0.0129018i | ||||
\(557\) | 383.754i | 0.688966i | 0.938793 | + | 0.344483i | \(0.111946\pi\) | ||||
−0.938793 | + | 0.344483i | \(0.888054\pi\) | |||||||
\(558\) | 221.152 | + | 333.843i | 0.396330 | + | 0.598285i | ||||
\(559\) | − | 40.9513i | − | 0.0732581i | ||||||
\(560\) | − | 85.6852i | − | 0.153009i | ||||||
\(561\) | −404.774 | − | 228.675i | −0.721522 | − | 0.407620i | ||||
\(562\) | 97.9286 | 0.174250 | ||||||||
\(563\) | 12.8676 | 0.0228555 | 0.0114277 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114277 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(564\) | −300.564 | − | 367.726i | −0.532915 | − | 0.651997i | ||||
\(565\) | 564.846 | 0.999727 | ||||||||
\(566\) | 300.633 | + | 300.633i | 0.531153 | + | 0.531153i | ||||
\(567\) | −150.603 | − | 371.923i | −0.265614 | − | 0.655949i | ||||
\(568\) | −27.1717 | − | 27.1717i | −0.0478376 | − | 0.0478376i | ||||
\(569\) | −516.933 | −0.908493 | −0.454247 | − | 0.890876i | \(-0.650092\pi\) | ||||
−0.454247 | + | 0.890876i | \(0.650092\pi\) | |||||||
\(570\) | 30.0515 | − | 299.025i | 0.0527220 | − | 0.524605i | ||||
\(571\) | −753.602 | − | 753.602i | −1.31979 | − | 1.31979i | −0.913936 | − | 0.405857i | \(-0.866973\pi\) |
−0.405857 | − | 0.913936i | \(-0.633027\pi\) | |||||||
\(572\) | −29.1938 | + | 29.1938i | −0.0510381 | + | 0.0510381i | ||||
\(573\) | −175.286 | − | 214.454i | −0.305908 | − | 0.374265i | ||||
\(574\) | 168.286 | 0.293182 | ||||||||
\(575\) | −45.0973 | − | 45.0973i | −0.0784302 | − | 0.0784302i | ||||
\(576\) | 14.3271 | − | 70.5602i | 0.0248734 | − | 0.122500i | ||||
\(577\) | −380.406 | −0.659283 | −0.329641 | − | 0.944106i | \(-0.606928\pi\) | ||||
−0.329641 | + | 0.944106i | \(0.606928\pi\) | |||||||
\(578\) | −276.380 | − | 301.091i | −0.478167 | − | 0.520919i | ||||
\(579\) | 924.274 | + | 92.8881i | 1.59633 | + | 0.160428i | ||||
\(580\) | − | 80.2810i | − | 0.138415i | ||||||
\(581\) | 579.121 | + | 579.121i | 0.996767 | + | 0.996767i | ||||
\(582\) | −17.1279 | + | 170.430i | −0.0294294 | + | 0.292834i | ||||
\(583\) | 439.874 | − | 439.874i | 0.754501 | − | 0.754501i | ||||
\(584\) | 199.092 | − | 199.092i | 0.340911 | − | 0.340911i | ||||
\(585\) | −73.4731 | + | 48.6718i | −0.125595 | + | 0.0831997i | ||||
\(586\) | 248.546i | 0.424141i | ||||||||
\(587\) | 857.140 | 1.46020 | 0.730102 | − | 0.683338i | \(-0.239472\pi\) | ||||
0.730102 | + | 0.683338i | \(0.239472\pi\) | |||||||
\(588\) | −92.8773 | − | 113.631i | −0.157955 | − | 0.193250i | ||||
\(589\) | −364.436 | − | 364.436i | −0.618736 | − | 0.618736i | ||||
\(590\) | −467.078 | − | 467.078i | −0.791657 | − | 0.791657i | ||||
\(591\) | 30.2801 | − | 301.299i | 0.0512354 | − | 0.509813i | ||||
\(592\) | −198.557 | + | 198.557i | −0.335400 | + | 0.335400i | ||||
\(593\) | −691.294 | −1.16576 | −0.582878 | − | 0.812559i | \(-0.698074\pi\) | ||||
−0.582878 | + | 0.812559i | \(0.698074\pi\) | |||||||
\(594\) | 332.477 | + | 103.024i | 0.559725 | + | 0.173442i | ||||
\(595\) | 333.385 | + | 146.520i | 0.560311 | + | 0.246253i | ||||
\(596\) | 486.202i | 0.815776i | ||||||||
\(597\) | 46.7494 | − | 465.175i | 0.0783072 | − | 0.779188i | ||||
\(598\) | 22.9207 | − | 22.9207i | 0.0383289 | − | 0.0383289i | ||||
\(599\) | 674.839i | 1.12661i | 0.826250 | + | 0.563304i | \(0.190470\pi\) | ||||
−0.826250 | + | 0.563304i | \(0.809530\pi\) | |||||||
\(600\) | −33.8371 | − | 41.3982i | −0.0563952 | − | 0.0689969i | ||||
\(601\) | 606.268 | + | 606.268i | 1.00877 | + | 1.00877i | 0.999961 | + | 0.00880462i | \(0.00280263\pi\) |
0.00880462 | + | 0.999961i | \(0.497197\pi\) | |||||||
\(602\) | 89.5823 | − | 89.5823i | 0.148808 | − | 0.148808i | ||||
\(603\) | 108.455 | − | 534.134i | 0.179859 | − | 0.885795i | ||||
\(604\) | − | 270.145i | − | 0.447260i | ||||||
\(605\) | 115.897 | − | 115.897i | 0.191565 | − | 0.191565i | ||||
\(606\) | 448.798 | + | 549.083i | 0.740591 | + | 0.906078i | ||||
\(607\) | −90.0709 | + | 90.0709i | −0.148387 | + | 0.148387i | −0.777397 | − | 0.629010i | \(-0.783460\pi\) |
0.629010 | + | 0.777397i | \(0.283460\pi\) | |||||||
\(608\) | 92.6661i | 0.152411i | ||||||||
\(609\) | 87.3052 | + | 106.814i | 0.143358 | + | 0.175392i | ||||
\(610\) | − | 83.0499i | − | 0.136147i | ||||||
\(611\) | − | 179.252i | − | 0.293375i | ||||||
\(612\) | 250.038 | + | 176.401i | 0.408558 | + | 0.288237i | ||||
\(613\) | −661.357 | −1.07889 | −0.539443 | − | 0.842022i | \(-0.681365\pi\) | ||||
−0.539443 | + | 0.842022i | \(0.681365\pi\) | |||||||
\(614\) | 744.520 | 1.21257 | ||||||||
\(615\) | −241.277 | + | 197.210i | −0.392320 | + | 0.320666i | ||||
\(616\) | −127.725 | −0.207345 | ||||||||
\(617\) | 296.006 | + | 296.006i | 0.479751 | + | 0.479751i | 0.905052 | − | 0.425301i | \(-0.139832\pi\) |
−0.425301 | + | 0.905052i | \(0.639832\pi\) | |||||||
\(618\) | −73.3157 | + | 59.9252i | −0.118634 | + | 0.0969664i | ||||
\(619\) | 671.731 | + | 671.731i | 1.08519 | + | 1.08519i | 0.996016 | + | 0.0891716i | \(0.0284220\pi\) |
0.0891716 | + | 0.996016i | \(0.471578\pi\) | |||||||
\(620\) | 272.099 | 0.438869 | ||||||||
\(621\) | −261.035 | − | 80.8866i | −0.420346 | − | 0.130252i | ||||
\(622\) | 238.013 | + | 238.013i | 0.382658 | + | 0.382658i | ||||
\(623\) | 141.092 | − | 141.092i | 0.226472 | − | 0.226472i | ||||
\(624\) | 21.0406 | − | 17.1977i | 0.0337189 | − | 0.0275604i | ||||
\(625\) | 427.765 | 0.684424 | ||||||||
\(626\) | −443.969 | − | 443.969i | −0.709215 | − | 0.709215i | ||||
\(627\) | −445.735 | − | 44.7957i | −0.710901 | − | 0.0714444i | ||||
\(628\) | 205.189 | 0.326734 | ||||||||
\(629\) | −433.019 | − | 1112.08i | −0.688425 | − | 1.76801i | ||||
\(630\) | −267.196 | − | 54.2536i | −0.424121 | − | 0.0861168i | ||||
\(631\) | 425.417i | 0.674195i | 0.941470 | + | 0.337097i | \(0.109445\pi\) | ||||
−0.941470 | + | 0.337097i | \(0.890555\pi\) | |||||||
\(632\) | −229.725 | − | 229.725i | −0.363488 | − | 0.363488i | ||||
\(633\) | 202.791 | + | 20.3802i | 0.320365 | + | 0.0321962i | ||||
\(634\) | −583.228 | + | 583.228i | −0.919918 | + | 0.919918i | ||||
\(635\) | 131.377 | − | 131.377i | 0.206893 | − | 0.206893i | ||||
\(636\) | −317.026 | + | 259.124i | −0.498469 | + | 0.407428i | ||||
\(637\) | − | 55.3908i | − | 0.0869557i | ||||||
\(638\) | −119.669 | −0.187569 | ||||||||
\(639\) | −101.935 | + | 67.5265i | −0.159523 | + | 0.105675i | ||||
\(640\) | −34.5937 | − | 34.5937i | −0.0540527 | − | 0.0540527i | ||||
\(641\) | −441.841 | − | 441.841i | −0.689299 | − | 0.689299i | 0.272778 | − | 0.962077i | \(-0.412058\pi\) |
−0.962077 | + | 0.272778i | \(0.912058\pi\) | |||||||
\(642\) | −622.056 | − | 62.5157i | −0.968935 | − | 0.0973765i | ||||
\(643\) | 153.381 | − | 153.381i | 0.238540 | − | 0.238540i | −0.577705 | − | 0.816246i | \(-0.696052\pi\) |
0.816246 | + | 0.577705i | \(0.196052\pi\) | |||||||
\(644\) | 100.279 | 0.155713 | ||||||||
\(645\) | −23.4579 | + | 233.416i | −0.0363688 | + | 0.361885i | ||||
\(646\) | −360.547 | − | 158.458i | −0.558122 | − | 0.245291i | ||||
\(647\) | − | 159.259i | − | 0.246149i | −0.992397 | − | 0.123075i | \(-0.960725\pi\) | ||
0.992397 | − | 0.123075i | \(-0.0392755\pi\) | |||||||
\(648\) | −210.960 | − | 89.3536i | −0.325555 | − | 0.137891i | ||||
\(649\) | −696.239 | + | 696.239i | −1.07279 | + | 1.07279i | ||||
\(650\) | − | 20.1800i | − | 0.0310462i | ||||||
\(651\) | −362.028 | + | 295.906i | −0.556110 | + | 0.454541i | ||||
\(652\) | 181.743 | + | 181.743i | 0.278747 | + | 0.278747i | ||||
\(653\) | −793.451 | + | 793.451i | −1.21509 | + | 1.21509i | −0.245752 | + | 0.969333i | \(0.579035\pi\) |
−0.969333 | + | 0.245752i | \(0.920965\pi\) | |||||||
\(654\) | −359.485 | − | 36.1277i | −0.549671 | − | 0.0552411i | ||||
\(655\) | 62.2168i | 0.0949875i | ||||||||
\(656\) | 67.9424 | − | 67.9424i | 0.103571 | − | 0.103571i | ||||
\(657\) | −494.779 | − | 746.899i | −0.753088 | − | 1.13683i | ||||
\(658\) | 392.121 | − | 392.121i | 0.595928 | − | 0.595928i | ||||
\(659\) | 1134.84i | 1.72207i | 0.508546 | + | 0.861035i | \(0.330183\pi\) | ||||
−0.508546 | + | 0.861035i | \(0.669817\pi\) | |||||||
\(660\) | 183.123 | − | 149.677i | 0.277459 | − | 0.226783i | ||||
\(661\) | 540.175i | 0.817208i | 0.912712 | + | 0.408604i | \(0.133984\pi\) | ||||
−0.912712 | + | 0.408604i | \(0.866016\pi\) | |||||||
\(662\) | − | 276.966i | − | 0.418378i | ||||||
\(663\) | 30.9340 | + | 111.273i | 0.0466576 | + | 0.167832i | ||||
\(664\) | 467.618 | 0.704243 | ||||||||
\(665\) | 350.907 | 0.527679 | ||||||||
\(666\) | 493.449 | + | 744.890i | 0.740914 | + | 1.11845i | ||||
\(667\) | 93.9548 | 0.140862 | ||||||||
\(668\) | −180.621 | − | 180.621i | −0.270390 | − | 0.270390i | ||||
\(669\) | 652.501 | + | 798.305i | 0.975338 | + | 1.19328i | ||||
\(670\) | −261.871 | − | 261.871i | −0.390853 | − | 0.390853i | ||||
\(671\) | −123.797 | −0.184496 | ||||||||
\(672\) | 83.6475 | + | 8.40644i | 0.124475 | + | 0.0125096i | ||||
\(673\) | −174.135 | − | 174.135i | −0.258744 | − | 0.258744i | 0.565799 | − | 0.824543i | \(-0.308568\pi\) |
−0.824543 | + | 0.565799i | \(0.808568\pi\) | |||||||
\(674\) | 506.330 | − | 506.330i | 0.751232 | − | 0.751232i | ||||
\(675\) | −150.519 | + | 79.3037i | −0.222991 | + | 0.117487i | ||||
\(676\) | −327.744 | −0.484828 | ||||||||
\(677\) | −605.055 | − | 605.055i | −0.893729 | − | 0.893729i | 0.101143 | − | 0.994872i | \(-0.467750\pi\) |
−0.994872 | + | 0.101143i | \(0.967750\pi\) | |||||||
\(678\) | −55.4162 | + | 551.413i | −0.0817348 | + | 0.813294i | ||||
\(679\) | −200.000 | −0.294550 | ||||||||
\(680\) | 193.752 | − | 75.4430i | 0.284930 | − | 0.110946i | ||||
\(681\) | −112.880 | + | 1123.20i | −0.165756 | + | 1.64934i | ||||
\(682\) | − | 405.598i | − | 0.594719i | ||||||
\(683\) | 645.841 | + | 645.841i | 0.945595 | + | 0.945595i | 0.998595 | − | 0.0529996i | \(-0.0168782\pi\) |
−0.0529996 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(684\) | 288.965 | + | 58.6737i | 0.422464 | + | 0.0857803i | ||||
\(685\) | −322.510 | + | 322.510i | −0.470817 | + | 0.470817i | ||||
\(686\) | 363.906 | − | 363.906i | 0.530475 | − | 0.530475i | ||||
\(687\) | −525.625 | − | 643.078i | −0.765103 | − | 0.936068i | ||||
\(688\) | − | 72.3342i | − | 0.105137i | ||||||
\(689\) | −154.538 | −0.224293 | ||||||||
\(690\) | −143.774 | + | 117.514i | −0.208367 | + | 0.170311i | ||||
\(691\) | −572.002 | − | 572.002i | −0.827789 | − | 0.827789i | 0.159422 | − | 0.987211i | \(-0.449037\pi\) |
−0.987211 | + | 0.159422i | \(0.949037\pi\) | |||||||
\(692\) | −39.1323 | − | 39.1323i | −0.0565496 | − | 0.0565496i | ||||
\(693\) | −80.8719 | + | 398.290i | −0.116698 | + | 0.574733i | ||||
\(694\) | −87.6155 | + | 87.6155i | −0.126247 | + | 0.126247i | ||||
\(695\) | −21.9339 | −0.0315596 | ||||||||
\(696\) | 78.3718 | + | 7.87624i | 0.112603 | + | 0.0113164i | ||||
\(697\) | 148.171 | + | 380.532i | 0.212584 | + | 0.545956i | ||||
\(698\) | − | 234.164i | − | 0.335479i | ||||||
\(699\) | 896.016 | + | 90.0483i | 1.28185 | + | 0.128824i | ||||
\(700\) | 44.1445 | − | 44.1445i | 0.0630635 | − | 0.0630635i | ||||
\(701\) | − | 233.074i | − | 0.332488i | −0.986085 | − | 0.166244i | \(-0.946836\pi\) | ||
0.986085 | − | 0.166244i | \(-0.0531640\pi\) | |||||||
\(702\) | −40.3060 | − | 76.5009i | −0.0574160 | − | 0.108976i | ||||
\(703\) | −813.151 | − | 813.151i | −1.15669 | − | 1.15669i | ||||
\(704\) | −51.5664 | + | 51.5664i | −0.0732477 | + | 0.0732477i | ||||
\(705\) | −102.680 | + | 1021.71i | −0.145646 | + | 1.44923i | ||||
\(706\) | − | 59.2391i | − | 0.0839080i | ||||||
\(707\) | −585.509 | + | 585.509i | −0.828160 | + | 0.828160i | ||||
\(708\) | 501.794 | − | 410.146i | 0.708749 | − | 0.579302i | ||||
\(709\) | −112.143 | + | 112.143i | −0.158171 | + | 0.158171i | −0.781756 | − | 0.623585i | \(-0.785676\pi\) |
0.623585 | + | 0.781756i | \(0.285676\pi\) | |||||||
\(710\) | 83.0825i | 0.117018i | ||||||||
\(711\) | −861.817 | + | 570.906i | −1.21212 | + | 0.802962i | ||||
\(712\) | − | 113.926i | − | 0.160009i | ||||||
\(713\) | 318.444i | 0.446626i | ||||||||
\(714\) | −175.744 | + | 311.082i | −0.246140 | + | 0.435689i | ||||
\(715\) | 89.2652 | 0.124846 | ||||||||
\(716\) | −326.971 | −0.456664 | ||||||||
\(717\) | −312.637 | − | 382.496i | −0.436034 | − | 0.533468i | ||||
\(718\) | −571.946 | −0.796582 | ||||||||
\(719\) | −352.542 | − | 352.542i | −0.490323 | − | 0.490323i | 0.418085 | − | 0.908408i | \(-0.362701\pi\) |
−0.908408 | + | 0.418085i | \(0.862701\pi\) | |||||||
\(720\) | −129.779 | + | 85.9714i | −0.180249 | + | 0.119405i | ||||
\(721\) | −78.1794 | − | 78.1794i | −0.108432 | − | 0.108432i | ||||
\(722\) | 131.035 | 0.181489 | ||||||||
\(723\) | −43.4352 | + | 432.198i | −0.0600764 | + | 0.597784i | ||||
\(724\) | 244.922 | + | 244.922i | 0.338289 | + | 0.338289i | ||||
\(725\) | 41.3602 | − | 41.3602i | 0.0570486 | − | 0.0570486i | ||||
\(726\) | 101.770 | + | 124.511i | 0.140179 | + | 0.171503i | ||||
\(727\) | 560.698 | 0.771249 | 0.385625 | − | 0.922656i | \(-0.373986\pi\) | ||||
0.385625 | + | 0.922656i | \(0.373986\pi\) | |||||||
\(728\) | 22.4364 | + | 22.4364i | 0.0308192 | + | 0.0308192i | ||||
\(729\) | −412.210 | + | 601.269i | −0.565445 | + | 0.824786i | ||||
\(730\) | −608.760 | −0.833918 | ||||||||
\(731\) | 281.439 | + | 123.690i | 0.385006 | + | 0.169207i | ||||
\(732\) | 81.0749 | + | 8.14790i | 0.110758 | + | 0.0111310i | ||||
\(733\) | − | 715.196i | − | 0.975711i | −0.872924 | − | 0.487856i | \(-0.837779\pi\) | ||
0.872924 | − | 0.487856i | \(-0.162221\pi\) | |||||||
\(734\) | 351.980 | + | 351.980i | 0.479536 | + | 0.479536i | ||||
\(735\) | −31.7292 | + | 315.718i | −0.0431690 | + | 0.429549i | ||||
\(736\) | 40.4859 | − | 40.4859i | 0.0550080 | − | 0.0550080i | ||||
\(737\) | −390.353 | + | 390.353i | −0.529651 | + | 0.529651i | ||||
\(738\) | −168.849 | − | 254.887i | −0.228792 | − | 0.345376i | ||||
\(739\) | − | 553.000i | − | 0.748308i | −0.927366 | − | 0.374154i | \(-0.877933\pi\) | ||
0.927366 | − | 0.374154i | \(-0.122067\pi\) | |||||||
\(740\) | 607.123 | 0.820437 | ||||||||
\(741\) | 70.4297 | + | 86.1675i | 0.0950468 | + | 0.116285i | ||||
\(742\) | −338.058 | − | 338.058i | −0.455603 | − | 0.455603i | ||||
\(743\) | 5.84822 | + | 5.84822i | 0.00787109 | + | 0.00787109i | 0.711031 | − | 0.703160i | \(-0.248228\pi\) |
−0.703160 | + | 0.711031i | \(0.748228\pi\) | |||||||
\(744\) | −26.6952 | + | 265.628i | −0.0358806 | + | 0.357027i | ||||
\(745\) | 743.326 | − | 743.326i | 0.997753 | − | 0.997753i | ||||
\(746\) | 89.0958 | 0.119431 | ||||||||
\(747\) | 296.083 | − | 1458.19i | 0.396363 | − | 1.95207i | ||||
\(748\) | −112.458 | − | 288.813i | −0.150344 | − | 0.386114i | ||||
\(749\) | − | 729.986i | − | 0.974614i | ||||||
\(750\) | −57.4224 | + | 571.376i | −0.0765632 | + | 0.761835i | ||||
\(751\) | −157.647 | + | 157.647i | −0.209916 | + | 0.209916i | −0.804232 | − | 0.594316i | \(-0.797423\pi\) |
0.594316 | + | 0.804232i | \(0.297423\pi\) | |||||||
\(752\) | − | 316.622i | − | 0.421040i | ||||||
\(753\) | −27.5330 | − | 33.6854i | −0.0365645 | − | 0.0447349i | ||||
\(754\) | 21.0213 | + | 21.0213i | 0.0278797 | + | 0.0278797i | ||||
\(755\) | −413.008 | + | 413.008i | −0.547031 | + | 0.547031i | ||||
\(756\) | 79.1775 | − | 255.519i | 0.104732 | − | 0.337988i | ||||
\(757\) | − | 221.919i | − | 0.293156i | −0.989199 | − | 0.146578i | \(-0.953174\pi\) | ||
0.989199 | − | 0.146578i | \(-0.0468259\pi\) | |||||||
\(758\) | 481.599 | − | 481.599i | 0.635354 | − | 0.635354i | ||||
\(759\) | 175.170 | + | 214.313i | 0.230791 | + | 0.282362i | ||||
\(760\) | 141.672 | − | 141.672i | 0.186410 | − | 0.186410i | ||||
\(761\) | − | 433.531i | − | 0.569686i | −0.958574 | − | 0.284843i | \(-0.908059\pi\) | ||
0.958574 | − | 0.284843i | \(-0.0919415\pi\) | |||||||
\(762\) | 115.363 | + | 141.142i | 0.151396 | + | 0.185226i | ||||
\(763\) | − | 421.857i | − | 0.552892i | ||||||
\(764\) | − | 184.650i | − | 0.241689i | ||||||
\(765\) | −112.579 | − | 651.956i | −0.147162 | − | 0.852230i | ||||
\(766\) | 717.507 | 0.936693 | ||||||||
\(767\) | 244.605 | 0.318912 | ||||||||
\(768\) | 37.1649 | − | 30.3771i | 0.0483919 | − | 0.0395535i | ||||
\(769\) | −126.996 | −0.165144 | −0.0825722 | − | 0.996585i | \(-0.526314\pi\) | ||||
−0.0825722 | + | 0.996585i | \(0.526314\pi\) | |||||||
\(770\) | 195.271 | + | 195.271i | 0.253598 | + | 0.253598i | ||||
\(771\) | 624.691 | − | 510.597i | 0.810235 | − | 0.662252i | ||||
\(772\) | 437.902 | + | 437.902i | 0.567230 | + | 0.567230i | ||||
\(773\) | 374.560 | 0.484554 | 0.242277 | − | 0.970207i | \(-0.422106\pi\) | ||||
0.242277 | + | 0.970207i | \(0.422106\pi\) | |||||||
\(774\) | −225.563 | − | 45.8001i | −0.291425 | − | 0.0591732i | ||||
\(775\) | 140.184 | + | 140.184i | 0.180882 | + | 0.180882i | ||||
\(776\) | −80.7460 | + | 80.7460i | −0.104054 | + | 0.104054i | ||||
\(777\) | −807.778 | + | 660.244i | −1.03961 | + | 0.849735i | ||||
\(778\) | −33.2802 | −0.0427766 | ||||||||
\(779\) | 278.245 | + | 278.245i | 0.357182 | + | 0.357182i | ||||
\(780\) | −58.4602 | − | 5.87516i | −0.0749489 | − | 0.00753225i | ||||
\(781\) | 123.845 | 0.158572 | ||||||||
\(782\) | 88.2928 | + | 226.753i | 0.112906 | + | 0.289966i | ||||
\(783\) | 74.1838 | − | 239.403i | 0.0947430 | − | 0.305751i | ||||
\(784\) | − | 97.8394i | − | 0.124795i | ||||||
\(785\) | −313.702 | − | 313.702i | −0.399620 | − | 0.399620i | ||||
\(786\) | −60.7372 | − | 6.10400i | −0.0772738 | − | 0.00776590i | ||||
\(787\) | 778.915 | − | 778.915i | 0.989726 | − | 0.989726i | −0.0102216 | − | 0.999948i | \(-0.503254\pi\) |
0.999948 | + | 0.0102216i | \(0.00325369\pi\) | |||||||
\(788\) | 142.749 | − | 142.749i | 0.181154 | − | 0.181154i | ||||
\(789\) | 676.100 | − | 552.616i | 0.856908 | − | 0.700401i | ||||
\(790\) | 702.425i | 0.889145i | ||||||||
\(791\) | −647.086 | −0.818060 | ||||||||
\(792\) | 128.151 | + | 193.452i | 0.161807 | + | 0.244258i | ||||
\(793\) | 21.7463 | + | 21.7463i | 0.0274229 | + | 0.0274229i | ||||
\(794\) | 380.581 | + | 380.581i | 0.479322 | + | 0.479322i | ||||
\(795\) | 880.842 | + | 88.5233i | 1.10798 | + | 0.111350i | ||||
\(796\) | 220.390 | − | 220.390i | 0.276872 | − | 0.276872i | ||||
\(797\) | 1081.50 | 1.35696 | 0.678481 | − | 0.734618i | \(-0.262639\pi\) | ||||
0.678481 | + | 0.734618i | \(0.262639\pi\) | |||||||
\(798\) | −34.4269 | + | 342.562i | −0.0431415 | + | 0.429275i | ||||
\(799\) | 1231.92 | + | 541.419i | 1.54182 | + | 0.677620i | ||||
\(800\) | − | 35.6449i | − | 0.0445561i | ||||||
\(801\) | −355.262 | − | 72.1351i | −0.443523 | − | 0.0900563i | ||||
\(802\) | 431.385 | − | 431.385i | 0.537887 | − | 0.537887i | ||||
\(803\) | 907.436i | 1.13006i | ||||||||
\(804\) | 281.335 | − | 229.952i | 0.349920 | − | 0.286010i | ||||
\(805\) | −153.311 | − | 153.311i | −0.190449 | − | 0.190449i | ||||
\(806\) | −71.2482 | + | 71.2482i | −0.0883972 | + | 0.0883972i | ||||
\(807\) | −877.720 | − | 88.2095i | −1.08763 | − | 0.109306i | ||||
\(808\) | 472.775i | 0.585118i | ||||||||
\(809\) | −358.740 | + | 358.740i | −0.443437 | + | 0.443437i | −0.893165 | − | 0.449729i | \(-0.851521\pi\) |
0.449729 | + | 0.893165i | \(0.351521\pi\) | |||||||
\(810\) | 185.916 | + | 459.131i | 0.229526 | + | 0.566828i | ||||
\(811\) | 120.348 | − | 120.348i | 0.148394 | − | 0.148394i | −0.629006 | − | 0.777400i | \(-0.716538\pi\) |
0.777400 | + | 0.629006i | \(0.216538\pi\) | |||||||
\(812\) | 91.9696i | 0.113263i | ||||||||
\(813\) | 71.2262 | − | 58.2174i | 0.0876092 | − | 0.0716081i | ||||
\(814\) | − | 904.996i | − | 1.11179i | ||||||
\(815\) | − | 555.712i | − | 0.681855i | ||||||
\(816\) | 54.6401 | + | 196.546i | 0.0669609 | + | 0.240866i | ||||
\(817\) | 296.231 | 0.362583 | ||||||||
\(818\) | −621.133 | −0.759331 | ||||||||
\(819\) | 84.1705 | − | 55.7583i | 0.102772 | − | 0.0680809i | ||||
\(820\) | −207.746 | −0.253349 | ||||||||
\(821\) | 371.478 | + | 371.478i | 0.452471 | + | 0.452471i | 0.896174 | − | 0.443703i | \(-0.146336\pi\) |
−0.443703 | + | 0.896174i | \(0.646336\pi\) | |||||||
\(822\) | −283.199 | − | 346.481i | −0.344524 | − | 0.421509i | ||||
\(823\) | −455.455 | − | 455.455i | −0.553408 | − | 0.553408i | 0.374015 | − | 0.927423i | \(-0.377981\pi\) |
−0.927423 | + | 0.374015i | \(0.877981\pi\) | |||||||
\(824\) | −63.1268 | −0.0766102 | ||||||||
\(825\) | 171.456 | + | 17.2311i | 0.207826 | + | 0.0208862i | ||||
\(826\) | 535.083 | + | 535.083i | 0.647800 | + | 0.647800i | ||||
\(827\) | −235.576 | + | 235.576i | −0.284856 | + | 0.284856i | −0.835042 | − | 0.550186i | \(-0.814557\pi\) |
0.550186 | + | 0.835042i | \(0.314557\pi\) | |||||||
\(828\) | −100.614 | − | 151.884i | −0.121515 | − | 0.183434i | ||||
\(829\) | −206.893 | −0.249569 | −0.124785 | − | 0.992184i | \(-0.539824\pi\) | ||||
−0.124785 | + | 0.992184i | \(0.539824\pi\) | |||||||
\(830\) | −714.913 | − | 714.913i | −0.861340 | − | 0.861340i | ||||
\(831\) | 20.6290 | − | 205.267i | 0.0248243 | − | 0.247012i | ||||
\(832\) | 18.1165 | 0.0217746 | ||||||||
\(833\) | 380.675 | + | 167.304i | 0.456993 | + | 0.200845i | ||||
\(834\) | 2.15190 | − | 21.4123i | 0.00258022 | − | 0.0256742i | ||||
\(835\) | 552.280i | 0.661414i | ||||||||
\(836\) | −211.180 | − | 211.180i | −0.252608 | − | 0.252608i | ||||
\(837\) | 811.418 | + | 251.433i | 0.969436 | + | 0.300398i | ||||
\(838\) | −77.1819 | + | 77.1819i | −0.0921025 | + | 0.0921025i | ||||
\(839\) | −615.416 | + | 615.416i | −0.733511 | + | 0.733511i | −0.971314 | − | 0.237802i | \(-0.923573\pi\) |
0.237802 | + | 0.971314i | \(0.423573\pi\) | |||||||
\(840\) | −115.031 | − | 140.736i | −0.136942 | − | 0.167542i | ||||
\(841\) | − | 754.831i | − | 0.897540i | ||||||
\(842\) | −1015.75 | −1.20635 | ||||||||
\(843\) | 160.845 | − | 131.468i | 0.190801 | − | 0.155953i | ||||
\(844\) | 96.0782 | + | 96.0782i | 0.113837 | + | 0.113837i | ||||
\(845\) | 501.067 | + | 501.067i | 0.592979 | + | 0.592979i | ||||
\(846\) | −987.337 | − | 200.477i | −1.16707 | − | 0.236970i | ||||
\(847\) | −132.771 | + | 132.771i | −0.156754 | + | 0.156754i | ||||
\(848\) | −272.968 | −0.321896 | ||||||||
\(849\) | 897.378 | + | 90.1851i | 1.05698 | + | 0.106225i | ||||
\(850\) | 138.688 | + | 60.9523i | 0.163162 | + | 0.0717085i | ||||
\(851\) | 710.532i | 0.834937i | ||||||||
\(852\) | −81.1067 | − | 8.15109i | −0.0951956 | − | 0.00956701i | ||||
\(853\) | 940.089 | − | 940.089i | 1.10210 | − | 1.10210i | 0.107939 | − | 0.994157i | \(-0.465575\pi\) |
0.994157 | − | 0.107939i | \(-0.0344253\pi\) | |||||||
\(854\) | 95.1417i | 0.111407i | ||||||||
\(855\) | −352.079 | − | 531.484i | −0.411788 | − | 0.621619i | ||||
\(856\) | −294.717 | − | 294.717i | −0.344296 | − | 0.344296i | ||||
\(857\) | 219.073 | − | 219.073i | 0.255628 | − | 0.255628i | −0.567645 | − | 0.823273i | \(-0.692145\pi\) |
0.823273 | + | 0.567645i | \(0.192145\pi\) | |||||||
\(858\) | −8.75768 | + | 87.1424i | −0.0102071 | + | 0.101565i | ||||
\(859\) | 1089.87i | 1.26876i | 0.773021 | + | 0.634381i | \(0.218745\pi\) | ||||
−0.773021 | + | 0.634381i | \(0.781255\pi\) | |||||||
\(860\) | −110.587 | + | 110.587i | −0.128590 | + | 0.128590i | ||||
\(861\) | 276.406 | − | 225.923i | 0.321029 | − | 0.262396i | ||||
\(862\) | 688.072 | − | 688.072i | 0.798227 | − | 0.798227i | ||||
\(863\) | − | 624.771i | − | 0.723953i | −0.932187 | − | 0.361976i | \(-0.882102\pi\) | ||
0.932187 | − | 0.361976i | \(-0.117898\pi\) | |||||||
\(864\) | −71.1944 | − | 135.127i | −0.0824010 | − | 0.156397i | ||||
\(865\) | 119.654i | 0.138328i | ||||||||
\(866\) | 567.401i | 0.655197i | ||||||||
\(867\) | −858.159 | − | 123.497i | −0.989803 | − | 0.142441i | ||||
\(868\) | −311.715 | −0.359119 | ||||||||
\(869\) | 1047.05 | 1.20490 | ||||||||
\(870\) | −107.776 | − | 131.859i | −0.123881 | − | 0.151563i | ||||
\(871\) | 137.140 | 0.157451 | ||||||||
\(872\) | −170.316 | − | 170.316i | −0.195317 | − | 0.195317i | ||||
\(873\) | 200.668 | + | 302.920i | 0.229860 | + | 0.346988i | ||||
\(874\) | 165.802 | + | 165.802i | 0.189705 | + | 0.189705i | ||||
\(875\) | −670.512 | −0.766299 | ||||||||
\(876\) | 59.7245 | − | 594.283i | 0.0681787 | − | 0.678405i | ||||
\(877\) | −851.798 | − | 851.798i | −0.971264 | − | 0.971264i | 0.0283346 | − | 0.999598i | \(-0.490980\pi\) |
−0.999598 | + | 0.0283346i | \(0.990980\pi\) | |||||||
\(878\) | −317.619 | + | 317.619i | −0.361753 | + | 0.361753i | ||||
\(879\) | 333.671 | + | 408.231i | 0.379603 | + | 0.464427i | ||||
\(880\) | 157.673 | 0.179174 | ||||||||
\(881\) | −131.718 | − | 131.718i | −0.149509 | − | 0.149509i | 0.628390 | − | 0.777899i | \(-0.283714\pi\) |
−0.777899 | + | 0.628390i | \(0.783714\pi\) | |||||||
\(882\) | −305.097 | − | 61.9493i | −0.345915 | − | 0.0702373i | ||||
\(883\) | −456.928 | −0.517472 | −0.258736 | − | 0.965948i | \(-0.583306\pi\) | ||||
−0.258736 | + | 0.965948i | \(0.583306\pi\) | |||||||
\(884\) | −30.9789 | + | 70.4879i | −0.0350440 | + | 0.0797374i | ||||
\(885\) | −1394.21 | − | 140.116i | −1.57538 | − | 0.158323i | ||||
\(886\) | − | 316.902i | − | 0.357677i | ||||||
\(887\) | −841.913 | − | 841.913i | −0.949169 | − | 0.949169i | 0.0496005 | − | 0.998769i | \(-0.484205\pi\) |
−0.998769 | + | 0.0496005i | \(0.984205\pi\) | |||||||
\(888\) | −59.5640 | + | 592.685i | −0.0670765 | + | 0.667438i | ||||
\(889\) | −150.505 | + | 150.505i | −0.169297 | + | 0.169297i | ||||
\(890\) | −174.175 | + | 174.175i | −0.195702 | + | 0.195702i | ||||
\(891\) | 684.394 | − | 277.132i | 0.768118 | − | 0.311035i | ||||
\(892\) | 687.362i | 0.770585i | ||||||||
\(893\) | 1296.66 | 1.45203 | ||||||||
\(894\) | 652.722 | + | 798.575i | 0.730114 | + | 0.893261i | ||||
\(895\) | 499.887 | + | 499.887i | 0.558533 | + | 0.558533i | ||||
\(896\) | 39.6304 | + | 39.6304i | 0.0442304 | + | 0.0442304i | ||||
\(897\) | 6.87584 | − | 68.4174i | 0.00766537 | − | 0.0762735i | ||||
\(898\) | −235.913 | + | 235.913i | −0.262710 | + | 0.262710i | ||||
\(899\) | −292.055 | −0.324867 | ||||||||
\(900\) | −111.153 | − | 22.5694i | −0.123504 | − | 0.0250771i | ||||
\(901\) | 466.771 | − | 1062.07i | 0.518059 | − | 1.17877i | ||||
\(902\) | 309.672i | 0.343317i | ||||||||
\(903\) | 26.8733 | − | 267.400i | 0.0297600 | − | 0.296124i | ||||
\(904\) | −261.248 | + | 261.248i | −0.288991 | + | 0.288991i | ||||
\(905\) | − | 748.892i | − | 0.827505i | ||||||
\(906\) | −362.667 | − | 443.706i | −0.400294 | − | 0.489742i | ||||
\(907\) | −215.244 | − | 215.244i | −0.237314 | − | 0.237314i | 0.578423 | − | 0.815737i | \(-0.303668\pi\) |
−0.815737 | + | 0.578423i | \(0.803668\pi\) | |||||||
\(908\) | −532.149 | + | 532.149i | −0.586067 | + | 0.586067i | ||||
\(909\) | 1474.28 | + | 299.349i | 1.62187 | + | 0.329317i | ||||
\(910\) | − | 68.6032i | − | 0.0753882i | ||||||
\(911\) | 244.858 | − | 244.858i | 0.268780 | − | 0.268780i | −0.559829 | − | 0.828608i | \(-0.689133\pi\) |
0.828608 | + | 0.559829i | \(0.189133\pi\) | |||||||
\(912\) | 124.403 | + | 152.202i | 0.136407 | + | 0.166888i | ||||
\(913\) | −1065.67 | + | 1065.67i | −1.16722 | + | 1.16722i | ||||
\(914\) | − | 507.595i | − | 0.555355i | ||||||
\(915\) | −111.494 | − | 136.407i | −0.121851 | − | 0.149079i | ||||
\(916\) | − | 553.708i | − | 0.604484i | ||||||
\(917\) | − | 71.2754i | − | 0.0777267i | ||||||
\(918\) | 647.496 | − | 45.9390i | 0.705334 | − | 0.0500425i | ||||
\(919\) | −1243.12 | −1.35268 | −0.676342 | − | 0.736588i | \(-0.736436\pi\) | ||||
−0.676342 | + | 0.736588i | \(0.736436\pi\) | |||||||
\(920\) | −123.793 | −0.134557 | ||||||||
\(921\) | 1222.85 | − | 999.510i | 1.32775 | − | 1.08524i | ||||
\(922\) | −942.607 | −1.02235 | ||||||||
\(923\) | −21.7549 | − | 21.7549i | −0.0235697 | − | 0.0235697i | ||||
\(924\) | −209.785 | + | 171.469i | −0.227040 | + | 0.185573i | ||||
\(925\) | 312.786 | + | 312.786i | 0.338147 | + | 0.338147i | ||||
\(926\) | −248.225 | −0.268061 | ||||||||
\(927\) | −39.9702 | + | 196.851i | −0.0431178 | + | 0.212353i | ||||
\(928\) | 37.1309 | + | 37.1309i | 0.0400118 | + | 0.0400118i | ||||
\(929\) | −85.2682 | + | 85.2682i | −0.0917849 | + | 0.0917849i | −0.751508 | − | 0.659723i | \(-0.770673\pi\) |
0.659723 | + | 0.751508i | \(0.270673\pi\) | |||||||
\(930\) | 446.915 | − | 365.290i | 0.480554 | − | 0.392785i | ||||
\(931\) | 400.682 | 0.430378 | ||||||||
\(932\) | 424.514 | + | 424.514i | 0.455487 | + | 0.455487i | ||||
\(933\) | 710.460 | + | 71.4002i | 0.761479 | + | 0.0765275i | ||||
\(934\) | −444.861 | −0.476297 | ||||||||
\(935\) | −269.619 | + | 613.478i | −0.288363 | + | 0.656127i | ||||
\(936\) | 11.4709 | − | 56.4935i | 0.0122552 | − | 0.0603563i | ||||
\(937\) | 467.613i | 0.499053i | 0.968368 | + | 0.249527i | \(0.0802750\pi\) | ||||
−0.968368 | + | 0.249527i | \(0.919725\pi\) | |||||||
\(938\) | 299.999 | + | 299.999i | 0.319828 | + | 0.319828i | ||||
\(939\) | −1325.23 | − | 133.184i | −1.41132 | − | 0.141836i | ||||
\(940\) | −484.064 | + | 484.064i | −0.514962 | + | 0.514962i | ||||
\(941\) | 729.906 | − | 729.906i | 0.775670 | − | 0.775670i | −0.203421 | − | 0.979091i | \(-0.565206\pi\) |
0.979091 | + | 0.203421i | \(0.0652061\pi\) | |||||||
\(942\) | 337.018 | − | 275.464i | 0.357769 | − | 0.292425i | ||||
\(943\) | − | 243.130i | − | 0.257826i | ||||||
\(944\) | 432.058 | 0.457689 | ||||||||
\(945\) | −511.698 | + | 269.598i | −0.541479 | + | 0.285289i | ||||
\(946\) | 164.845 | + | 164.845i | 0.174255 | + | 0.174255i | ||||
\(947\) | 447.287 | + | 447.287i | 0.472320 | + | 0.472320i | 0.902665 | − | 0.430345i | \(-0.141608\pi\) |
−0.430345 | + | 0.902665i | \(0.641608\pi\) | |||||||
\(948\) | −685.720 | − | 68.9138i | −0.723333 | − | 0.0726939i | ||||
\(949\) | 159.402 | − | 159.402i | 0.167968 | − | 0.167968i | ||||
\(950\) | 145.977 | 0.153660 | ||||||||
\(951\) | −174.959 | + | 1740.91i | −0.183974 | + | 1.83061i | ||||
\(952\) | −221.962 | + | 86.4273i | −0.233153 | + | 0.0907849i | ||||
\(953\) | − | 837.817i | − | 0.879136i | −0.898209 | − | 0.439568i | \(-0.855132\pi\) | ||
0.898209 | − | 0.439568i | \(-0.144868\pi\) | |||||||
\(954\) | −172.836 | + | 851.209i | −0.181170 | + | 0.892253i | ||||
\(955\) | −282.301 | + | 282.301i | −0.295603 | + | 0.295603i | ||||
\(956\) | − | 329.340i | − | 0.344497i | ||||||
\(957\) | −196.553 | + | 160.655i | −0.205385 | + | 0.167873i | ||||
\(958\) | 448.645 | + | 448.645i | 0.468315 | + | 0.468315i | ||||
\(959\) | 369.466 | − | 369.466i | 0.385262 | − | 0.385262i | ||||
\(960\) | −103.261 | − | 10.3776i | −0.107563 | − | 0.0108100i | ||||
\(961\) | − | 28.8729i | − | 0.0300447i | ||||||
\(962\) | −158.973 | + | 158.973i | −0.165253 | + | 0.165253i | ||||
\(963\) | −1105.64 | + | 732.424i | −1.14812 | + | 0.760565i | ||||
\(964\) | −204.766 | + | 204.766i | −0.212413 | + | 0.212413i | ||||
\(965\) | − | 1338.96i | − | 1.38753i | ||||||
\(966\) | 164.706 | − | 134.624i | 0.170504 | − | 0.139363i | ||||
\(967\) | 1140.58i | 1.17950i | 0.807585 | + | 0.589751i | \(0.200774\pi\) | ||||
−0.807585 | + | 0.589751i | \(0.799226\pi\) | |||||||
\(968\) | 107.207i | 0.110751i | ||||||||
\(969\) | −804.917 | + | 223.768i | −0.830667 | + | 0.230927i | ||||
\(970\) | 246.895 | 0.254531 | ||||||||
\(971\) | −1208.99 | −1.24509 | −0.622547 | − | 0.782582i | \(-0.713902\pi\) | ||||
−0.622547 | + | 0.782582i | \(0.713902\pi\) | |||||||
\(972\) | −466.452 | + | 136.450i | −0.479889 | + | 0.140381i | ||||
\(973\) | 25.1274 | 0.0258247 | ||||||||
\(974\) | 451.477 | + | 451.477i | 0.463529 | + | 0.463529i | ||||
\(975\) | −27.0915 | − | 33.1451i | −0.0277861 | − | 0.0339950i | ||||
\(976\) | 38.4116 | + | 38.4116i | 0.0393561 | + | 0.0393561i | ||||
\(977\) | 1782.73 | 1.82469 | 0.912347 | − | 0.409417i | \(-0.134268\pi\) | ||||
0.912347 | + | 0.409417i | \(0.134268\pi\) | |||||||
\(978\) | 542.496 | + | 54.5200i | 0.554700 | + | 0.0557465i | ||||
\(979\) | 259.630 | + | 259.630i | 0.265200 | + | 0.265200i | ||||
\(980\) | −149.581 | + | 149.581i | −0.152633 | + | 0.152633i | ||||
\(981\) | −638.946 | + | 423.266i | −0.651321 | + | 0.431464i | ||||
\(982\) | 209.381 | 0.213219 | ||||||||
\(983\) | 496.507 | + | 496.507i | 0.505094 | + | 0.505094i | 0.913017 | − | 0.407923i | \(-0.133747\pi\) |
−0.407923 | + | 0.913017i | \(0.633747\pi\) | |||||||
\(984\) | 20.3816 | − | 202.805i | 0.0207130 | − | 0.206103i | ||||
\(985\) | −436.482 | −0.443129 | ||||||||
\(986\) | −207.963 | + | 80.9763i | −0.210916 | + | 0.0821260i | ||||
\(987\) | 117.630 | − | 1170.47i | 0.119179 | − | 1.18588i | ||||
\(988\) | 74.1925i | 0.0750936i | ||||||||
\(989\) | −129.423 | − | 129.423i | −0.130863 | − | 0.130863i | ||||
\(990\) | 99.8346 | − | 491.681i | 0.100843 | − | 0.496647i | ||||
\(991\) | 11.1339 | − | 11.1339i | 0.0112350 | − | 0.0112350i | −0.701467 | − | 0.712702i | \(-0.747471\pi\) |
0.712702 | + | 0.701467i | \(0.247471\pi\) | |||||||
\(992\) | −125.849 | + | 125.849i | −0.126864 | + | 0.126864i | ||||
\(993\) | −371.825 | − | 454.910i | −0.374446 | − | 0.458117i | ||||
\(994\) | − | 95.1790i | − | 0.0957535i | ||||||
\(995\) | −673.883 | −0.677269 | ||||||||
\(996\) | 768.050 | − | 627.772i | 0.771134 | − | 0.630293i | ||||
\(997\) | 1232.84 | + | 1232.84i | 1.23655 | + | 1.23655i | 0.961402 | + | 0.275149i | \(0.0887272\pi\) |
0.275149 | + | 0.961402i | \(0.411273\pi\) | |||||||
\(998\) | −542.385 | − | 542.385i | −0.543472 | − | 0.543472i | ||||
\(999\) | 1810.48 | + | 561.014i | 1.81230 | + | 0.561575i |
(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 | 102.3.e.b.89.9 | yes | 20 | |
3.2 | odd | 2 | inner | 102.3.e.b.89.4 | yes | 20 | |
17.13 | even | 4 | inner | 102.3.e.b.47.4 | ✓ | 20 | |
51.47 | odd | 4 | inner | 102.3.e.b.47.9 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.3.e.b.47.4 | ✓ | 20 | 17.13 | even | 4 | inner | |
102.3.e.b.47.9 | yes | 20 | 51.47 | odd | 4 | inner | |
102.3.e.b.89.4 | yes | 20 | 3.2 | odd | 2 | inner | |
102.3.e.b.89.9 | yes | 20 | 1.1 | even | 1 | trivial |