Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,3,Mod(31,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("78.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.f (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: | \(2.12534606201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.564373557504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 86x^{6} + 2523x^{4} - 28394x^{2} + 113569 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.4 | ||
Root | \(5.82017 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 78.73 |
Dual form | 78.3.f.b.31.4 |
$q$-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 \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(67\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 4.95414 | + | 4.95414i | 0.990829 | + | 0.990829i | 0.999958 | − | 0.00912980i | \(-0.00290615\pi\) |
−0.00912980 | + | 0.999958i | \(0.502906\pi\) | |||||||
\(6\) | −1.73205 | − | 1.73205i | −0.288675 | − | 0.288675i | ||||
\(7\) | −2.89463 | + | 2.89463i | −0.413519 | + | 0.413519i | −0.882963 | − | 0.469443i | \(-0.844455\pi\) |
0.469443 | + | 0.882963i | \(0.344455\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 9.90829i | − | 0.990829i | ||||||
\(11\) | 14.8823 | − | 14.8823i | 1.35294 | − | 1.35294i | 0.470587 | − | 0.882354i | \(-0.344042\pi\) |
0.882354 | − | 0.470587i | \(-0.155958\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | −6.40459 | + | 11.3129i | −0.492661 | + | 0.870221i | ||||
\(14\) | 5.78927 | 0.413519 | ||||||||
\(15\) | 8.58083 | + | 8.58083i | 0.572055 | + | 0.572055i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | − | 10.7175i | − | 0.630439i | −0.949019 | − | 0.315220i | \(-0.897922\pi\) | ||
0.949019 | − | 0.315220i | \(-0.102078\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | −13.7311 | − | 13.7311i | −0.722691 | − | 0.722691i | 0.246462 | − | 0.969152i | \(-0.420732\pi\) |
−0.969152 | + | 0.246462i | \(0.920732\pi\) | |||||||
\(20\) | −9.90829 | + | 9.90829i | −0.495414 | + | 0.495414i | ||||
\(21\) | −5.01365 | + | 5.01365i | −0.238745 | + | 0.238745i | ||||
\(22\) | −29.7647 | −1.35294 | ||||||||
\(23\) | 24.6929i | 1.07360i | 0.843708 | + | 0.536802i | \(0.180368\pi\) | ||||
−0.843708 | + | 0.536802i | \(0.819632\pi\) | |||||||
\(24\) | 3.46410 | − | 3.46410i | 0.144338 | − | 0.144338i | ||||
\(25\) | 24.0871i | 0.963482i | ||||||||
\(26\) | 17.7175 | − | 4.90829i | 0.681441 | − | 0.188780i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −5.78927 | − | 5.78927i | −0.206760 | − | 0.206760i | ||||
\(29\) | −50.5859 | −1.74434 | −0.872171 | − | 0.489201i | \(-0.837288\pi\) | ||||
−0.872171 | + | 0.489201i | \(0.837288\pi\) | |||||||
\(30\) | − | 17.1617i | − | 0.572055i | ||||||
\(31\) | −13.0137 | − | 13.0137i | −0.419795 | − | 0.419795i | 0.465338 | − | 0.885133i | \(-0.345933\pi\) |
−0.885133 | + | 0.465338i | \(0.845933\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 25.7770 | − | 25.7770i | 0.781121 | − | 0.781121i | ||||
\(34\) | −10.7175 | + | 10.7175i | −0.315220 | + | 0.315220i | ||||
\(35\) | −28.6809 | −0.819453 | ||||||||
\(36\) | 6.00000i | 0.166667i | ||||||||
\(37\) | 15.6656 | − | 15.6656i | 0.423394 | − | 0.423394i | −0.462976 | − | 0.886371i | \(-0.653219\pi\) |
0.886371 | + | 0.462976i | \(0.153219\pi\) | |||||||
\(38\) | 27.4622i | 0.722691i | ||||||||
\(39\) | −11.0931 | + | 19.5945i | −0.284438 | + | 0.502423i | ||||
\(40\) | 19.8166 | 0.495414 | ||||||||
\(41\) | −6.00136 | − | 6.00136i | −0.146375 | − | 0.146375i | 0.630122 | − | 0.776496i | \(-0.283005\pi\) |
−0.776496 | + | 0.630122i | \(0.783005\pi\) | |||||||
\(42\) | 10.0273 | 0.238745 | ||||||||
\(43\) | − | 10.3450i | − | 0.240582i | −0.992739 | − | 0.120291i | \(-0.961617\pi\) | ||
0.992739 | − | 0.120291i | \(-0.0383827\pi\) | |||||||
\(44\) | 29.7647 | + | 29.7647i | 0.676470 | + | 0.676470i | ||||
\(45\) | 14.8624 | + | 14.8624i | 0.330276 | + | 0.330276i | ||||
\(46\) | 24.6929 | − | 24.6929i | 0.536802 | − | 0.536802i | ||||
\(47\) | 49.4437 | − | 49.4437i | 1.05199 | − | 1.05199i | 0.0534213 | − | 0.998572i | \(-0.482987\pi\) |
0.998572 | − | 0.0534213i | \(-0.0170126\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 32.2422i | 0.658004i | ||||||||
\(50\) | 24.0871 | − | 24.0871i | 0.481741 | − | 0.481741i | ||||
\(51\) | − | 18.5632i | − | 0.363984i | ||||||
\(52\) | −22.6258 | − | 12.8092i | −0.435111 | − | 0.246330i | ||||
\(53\) | 4.69934 | 0.0886668 | 0.0443334 | − | 0.999017i | \(-0.485884\pi\) | ||||
0.0443334 | + | 0.999017i | \(0.485884\pi\) | |||||||
\(54\) | −5.19615 | − | 5.19615i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | 147.459 | 2.68106 | ||||||||
\(56\) | 11.5785i | 0.206760i | ||||||||
\(57\) | −23.7830 | − | 23.7830i | −0.417246 | − | 0.417246i | ||||
\(58\) | 50.5859 | + | 50.5859i | 0.872171 | + | 0.872171i | ||||
\(59\) | 40.3844 | − | 40.3844i | 0.684482 | − | 0.684482i | −0.276525 | − | 0.961007i | \(-0.589183\pi\) |
0.961007 | + | 0.276525i | \(0.0891828\pi\) | |||||||
\(60\) | −17.1617 | + | 17.1617i | −0.286028 | + | 0.286028i | ||||
\(61\) | −88.3293 | −1.44802 | −0.724010 | − | 0.689789i | \(-0.757703\pi\) | ||||
−0.724010 | + | 0.689789i | \(0.757703\pi\) | |||||||
\(62\) | 26.0273i | 0.419795i | ||||||||
\(63\) | −8.68390 | + | 8.68390i | −0.137840 | + | 0.137840i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −87.7749 | + | 24.3163i | −1.35038 | + | 0.374098i | ||||
\(66\) | −51.5540 | −0.781121 | ||||||||
\(67\) | −18.7237 | − | 18.7237i | −0.279459 | − | 0.279459i | 0.553434 | − | 0.832893i | \(-0.313317\pi\) |
−0.832893 | + | 0.553434i | \(0.813317\pi\) | |||||||
\(68\) | 21.4349 | 0.315220 | ||||||||
\(69\) | 42.7693i | 0.619846i | ||||||||
\(70\) | 28.6809 | + | 28.6809i | 0.409726 | + | 0.409726i | ||||
\(71\) | −75.9296 | − | 75.9296i | −1.06943 | − | 1.06943i | −0.997403 | − | 0.0720279i | \(-0.977053\pi\) |
−0.0720279 | − | 0.997403i | \(-0.522947\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −14.2029 | + | 14.2029i | −0.194560 | + | 0.194560i | −0.797663 | − | 0.603103i | \(-0.793931\pi\) |
0.603103 | + | 0.797663i | \(0.293931\pi\) | |||||||
\(74\) | −31.3312 | −0.423394 | ||||||||
\(75\) | 41.7200i | 0.556267i | ||||||||
\(76\) | 27.4622 | − | 27.4622i | 0.361345 | − | 0.361345i | ||||
\(77\) | 86.1579i | 1.11893i | ||||||||
\(78\) | 30.6876 | − | 8.50140i | 0.393430 | − | 0.108992i | ||||
\(79\) | 18.7698 | 0.237593 | 0.118796 | − | 0.992919i | \(-0.462096\pi\) | ||||
0.118796 | + | 0.992919i | \(0.462096\pi\) | |||||||
\(80\) | −19.8166 | − | 19.8166i | −0.247707 | − | 0.247707i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 12.0027i | 0.146375i | ||||||||
\(83\) | 53.7860 | + | 53.7860i | 0.648024 | + | 0.648024i | 0.952515 | − | 0.304491i | \(-0.0984865\pi\) |
−0.304491 | + | 0.952515i | \(0.598486\pi\) | |||||||
\(84\) | −10.0273 | − | 10.0273i | −0.119373 | − | 0.119373i | ||||
\(85\) | 53.0959 | − | 53.0959i | 0.624657 | − | 0.624657i | ||||
\(86\) | −10.3450 | + | 10.3450i | −0.120291 | + | 0.120291i | ||||
\(87\) | −87.6174 | −1.00710 | ||||||||
\(88\) | − | 59.5294i | − | 0.676470i | ||||||
\(89\) | −20.1329 | + | 20.1329i | −0.226213 | + | 0.226213i | −0.811108 | − | 0.584896i | \(-0.801135\pi\) |
0.584896 | + | 0.811108i | \(0.301135\pi\) | |||||||
\(90\) | − | 29.7249i | − | 0.330276i | ||||||
\(91\) | −14.2077 | − | 51.2856i | −0.156128 | − | 0.563578i | ||||
\(92\) | −49.3858 | −0.536802 | ||||||||
\(93\) | −22.5403 | − | 22.5403i | −0.242369 | − | 0.242369i | ||||
\(94\) | −98.8874 | −1.05199 | ||||||||
\(95\) | − | 136.052i | − | 1.43212i | ||||||
\(96\) | 6.92820 | + | 6.92820i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | 89.2469 | + | 89.2469i | 0.920071 | + | 0.920071i | 0.997034 | − | 0.0769633i | \(-0.0245224\pi\) |
−0.0769633 | + | 0.997034i | \(0.524522\pi\) | |||||||
\(98\) | 32.2422 | − | 32.2422i | 0.329002 | − | 0.329002i | ||||
\(99\) | 44.6470 | − | 44.6470i | 0.450980 | − | 0.450980i | ||||
\(100\) | −48.1741 | −0.481741 | ||||||||
\(101\) | 69.0811i | 0.683971i | 0.939705 | + | 0.341986i | \(0.111099\pi\) | ||||
−0.939705 | + | 0.341986i | \(0.888901\pi\) | |||||||
\(102\) | −18.5632 | + | 18.5632i | −0.181992 | + | 0.181992i | ||||
\(103\) | 97.2640i | 0.944311i | 0.881515 | + | 0.472156i | \(0.156524\pi\) | ||||
−0.881515 | + | 0.472156i | \(0.843476\pi\) | |||||||
\(104\) | 9.81657 | + | 35.4349i | 0.0943901 | + | 0.340721i | ||||
\(105\) | −49.6767 | −0.473111 | ||||||||
\(106\) | −4.69934 | − | 4.69934i | −0.0443334 | − | 0.0443334i | ||||
\(107\) | −37.7342 | −0.352656 | −0.176328 | − | 0.984331i | \(-0.556422\pi\) | ||||
−0.176328 | + | 0.984331i | \(0.556422\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | 100.492 | + | 100.492i | 0.921947 | + | 0.921947i | 0.997167 | − | 0.0752195i | \(-0.0239657\pi\) |
−0.0752195 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(110\) | −147.459 | − | 147.459i | −1.34053 | − | 1.34053i | ||||
\(111\) | 27.1336 | − | 27.1336i | 0.244447 | − | 0.244447i | ||||
\(112\) | 11.5785 | − | 11.5785i | 0.103380 | − | 0.103380i | ||||
\(113\) | 60.2534 | 0.533216 | 0.266608 | − | 0.963805i | \(-0.414097\pi\) | ||||
0.266608 | + | 0.963805i | \(0.414097\pi\) | |||||||
\(114\) | 47.5660i | 0.417246i | ||||||||
\(115\) | −122.332 | + | 122.332i | −1.06376 | + | 1.06376i | ||||
\(116\) | − | 101.172i | − | 0.872171i | ||||||
\(117\) | −19.2138 | + | 33.9386i | −0.164220 | + | 0.290074i | ||||
\(118\) | −80.7689 | −0.684482 | ||||||||
\(119\) | 31.0231 | + | 31.0231i | 0.260699 | + | 0.260699i | ||||
\(120\) | 34.3233 | 0.286028 | ||||||||
\(121\) | − | 321.968i | − | 2.66090i | ||||||
\(122\) | 88.3293 | + | 88.3293i | 0.724010 | + | 0.724010i | ||||
\(123\) | −10.3947 | − | 10.3947i | −0.0845095 | − | 0.0845095i | ||||
\(124\) | 26.0273 | − | 26.0273i | 0.209898 | − | 0.209898i | ||||
\(125\) | 4.52285 | − | 4.52285i | 0.0361828 | − | 0.0361828i | ||||
\(126\) | 17.3678 | 0.137840 | ||||||||
\(127\) | 40.6683i | 0.320223i | 0.987099 | + | 0.160111i | \(0.0511854\pi\) | ||||
−0.987099 | + | 0.160111i | \(0.948815\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 17.9181i | − | 0.138900i | ||||||
\(130\) | 112.091 | + | 63.4585i | 0.862240 | + | 0.488143i | ||||
\(131\) | 214.111 | 1.63444 | 0.817218 | − | 0.576328i | \(-0.195515\pi\) | ||||
0.817218 | + | 0.576328i | \(0.195515\pi\) | |||||||
\(132\) | 51.5540 | + | 51.5540i | 0.390560 | + | 0.390560i | ||||
\(133\) | 79.4931 | 0.597693 | ||||||||
\(134\) | 37.4475i | 0.279459i | ||||||||
\(135\) | 25.7425 | + | 25.7425i | 0.190685 | + | 0.190685i | ||||
\(136\) | −21.4349 | − | 21.4349i | −0.157610 | − | 0.157610i | ||||
\(137\) | −118.462 | + | 118.462i | −0.864685 | + | 0.864685i | −0.991878 | − | 0.127193i | \(-0.959403\pi\) |
0.127193 | + | 0.991878i | \(0.459403\pi\) | |||||||
\(138\) | 42.7693 | − | 42.7693i | 0.309923 | − | 0.309923i | ||||
\(139\) | −54.6810 | −0.393388 | −0.196694 | − | 0.980465i | \(-0.563021\pi\) | ||||
−0.196694 | + | 0.980465i | \(0.563021\pi\) | |||||||
\(140\) | − | 57.3617i | − | 0.409726i | ||||||
\(141\) | 85.6390 | − | 85.6390i | 0.607369 | − | 0.607369i | ||||
\(142\) | 151.859i | 1.06943i | ||||||||
\(143\) | 73.0468 | + | 263.678i | 0.510817 | + | 1.84390i | ||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −250.610 | − | 250.610i | −1.72834 | − | 1.72834i | ||||
\(146\) | 28.4057 | 0.194560 | ||||||||
\(147\) | 55.8451i | 0.379899i | ||||||||
\(148\) | 31.3312 | + | 31.3312i | 0.211697 | + | 0.211697i | ||||
\(149\) | 123.029 | + | 123.029i | 0.825699 | + | 0.825699i | 0.986919 | − | 0.161220i | \(-0.0515428\pi\) |
−0.161220 | + | 0.986919i | \(0.551543\pi\) | |||||||
\(150\) | 41.7200 | − | 41.7200i | 0.278133 | − | 0.278133i | ||||
\(151\) | −29.7840 | + | 29.7840i | −0.197245 | + | 0.197245i | −0.798818 | − | 0.601573i | \(-0.794541\pi\) |
0.601573 | + | 0.798818i | \(0.294541\pi\) | |||||||
\(152\) | −54.9245 | −0.361345 | ||||||||
\(153\) | − | 32.1524i | − | 0.210146i | ||||||
\(154\) | 86.1579 | − | 86.1579i | 0.559467 | − | 0.559467i | ||||
\(155\) | − | 128.943i | − | 0.831890i | ||||||
\(156\) | −39.1890 | − | 22.1862i | −0.251211 | − | 0.142219i | ||||
\(157\) | 171.846 | 1.09456 | 0.547281 | − | 0.836949i | \(-0.315663\pi\) | ||||
0.547281 | + | 0.836949i | \(0.315663\pi\) | |||||||
\(158\) | −18.7698 | − | 18.7698i | −0.118796 | − | 0.118796i | ||||
\(159\) | 8.13950 | 0.0511918 | ||||||||
\(160\) | 39.6331i | 0.247707i | ||||||||
\(161\) | −71.4769 | − | 71.4769i | −0.443956 | − | 0.443956i | ||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −165.153 | + | 165.153i | −1.01321 | + | 1.01321i | −0.0132972 | + | 0.999912i | \(0.504233\pi\) |
−0.999912 | + | 0.0132972i | \(0.995767\pi\) | |||||||
\(164\) | 12.0027 | − | 12.0027i | 0.0731874 | − | 0.0731874i | ||||
\(165\) | 255.406 | 1.54791 | ||||||||
\(166\) | − | 107.572i | − | 0.648024i | ||||||
\(167\) | 65.6217 | − | 65.6217i | 0.392944 | − | 0.392944i | −0.482791 | − | 0.875735i | \(-0.660377\pi\) |
0.875735 | + | 0.482791i | \(0.160377\pi\) | |||||||
\(168\) | 20.0546i | 0.119373i | ||||||||
\(169\) | −86.9624 | − | 144.909i | −0.514570 | − | 0.857448i | ||||
\(170\) | −106.192 | −0.624657 | ||||||||
\(171\) | −41.1934 | − | 41.1934i | −0.240897 | − | 0.240897i | ||||
\(172\) | 20.6900 | 0.120291 | ||||||||
\(173\) | − | 216.560i | − | 1.25179i | −0.779906 | − | 0.625897i | \(-0.784733\pi\) | ||
0.779906 | − | 0.625897i | \(-0.215267\pi\) | |||||||
\(174\) | 87.6174 | + | 87.6174i | 0.503548 | + | 0.503548i | ||||
\(175\) | −69.7232 | − | 69.7232i | −0.398418 | − | 0.398418i | ||||
\(176\) | −59.5294 | + | 59.5294i | −0.338235 | + | 0.338235i | ||||
\(177\) | 69.9479 | − | 69.9479i | 0.395186 | − | 0.395186i | ||||
\(178\) | 40.2658 | 0.226213 | ||||||||
\(179\) | 22.1128i | 0.123535i | 0.998091 | + | 0.0617676i | \(0.0196738\pi\) | ||||
−0.998091 | + | 0.0617676i | \(0.980326\pi\) | |||||||
\(180\) | −29.7249 | + | 29.7249i | −0.165138 | + | 0.165138i | ||||
\(181\) | 41.5239i | 0.229414i | 0.993399 | + | 0.114707i | \(0.0365929\pi\) | ||||
−0.993399 | + | 0.114707i | \(0.963407\pi\) | |||||||
\(182\) | −37.0779 | + | 65.4933i | −0.203725 | + | 0.359853i | ||||
\(183\) | −152.991 | −0.836015 | ||||||||
\(184\) | 49.3858 | + | 49.3858i | 0.268401 | + | 0.268401i | ||||
\(185\) | 155.219 | 0.839022 | ||||||||
\(186\) | 45.0806i | 0.242369i | ||||||||
\(187\) | −159.501 | − | 159.501i | −0.852947 | − | 0.852947i | ||||
\(188\) | 98.8874 | + | 98.8874i | 0.525997 | + | 0.525997i | ||||
\(189\) | −15.0410 | + | 15.0410i | −0.0795818 | + | 0.0795818i | ||||
\(190\) | −136.052 | + | 136.052i | −0.716062 | + | 0.716062i | ||||
\(191\) | −221.663 | −1.16054 | −0.580269 | − | 0.814425i | \(-0.697053\pi\) | ||||
−0.580269 | + | 0.814425i | \(0.697053\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | −255.579 | + | 255.579i | −1.32424 | + | 1.32424i | −0.413937 | + | 0.910305i | \(0.635847\pi\) |
−0.910305 | + | 0.413937i | \(0.864153\pi\) | |||||||
\(194\) | − | 178.494i | − | 0.920071i | ||||||
\(195\) | −152.031 | + | 42.1171i | −0.779644 | + | 0.215985i | ||||
\(196\) | −64.4844 | −0.329002 | ||||||||
\(197\) | 138.728 | + | 138.728i | 0.704204 | + | 0.704204i | 0.965310 | − | 0.261106i | \(-0.0840873\pi\) |
−0.261106 | + | 0.965310i | \(0.584087\pi\) | |||||||
\(198\) | −89.2941 | −0.450980 | ||||||||
\(199\) | 258.963i | 1.30132i | 0.759369 | + | 0.650660i | \(0.225508\pi\) | ||||
−0.759369 | + | 0.650660i | \(0.774492\pi\) | |||||||
\(200\) | 48.1741 | + | 48.1741i | 0.240871 | + | 0.240871i | ||||
\(201\) | −32.4305 | − | 32.4305i | −0.161346 | − | 0.161346i | ||||
\(202\) | 69.0811 | − | 69.0811i | 0.341986 | − | 0.341986i | ||||
\(203\) | 146.428 | − | 146.428i | 0.721319 | − | 0.721319i | ||||
\(204\) | 37.1264 | 0.181992 | ||||||||
\(205\) | − | 59.4632i | − | 0.290065i | ||||||
\(206\) | 97.2640 | − | 97.2640i | 0.472156 | − | 0.472156i | ||||
\(207\) | 74.0787i | 0.357868i | ||||||||
\(208\) | 25.6184 | − | 45.2515i | 0.123165 | − | 0.217555i | ||||
\(209\) | −408.703 | −1.95551 | ||||||||
\(210\) | 49.6767 | + | 49.6767i | 0.236556 | + | 0.236556i | ||||
\(211\) | −220.454 | −1.04480 | −0.522402 | − | 0.852699i | \(-0.674964\pi\) | ||||
−0.522402 | + | 0.852699i | \(0.674964\pi\) | |||||||
\(212\) | 9.39868i | 0.0443334i | ||||||||
\(213\) | −131.514 | − | 131.514i | −0.617436 | − | 0.617436i | ||||
\(214\) | 37.7342 | + | 37.7342i | 0.176328 | + | 0.176328i | ||||
\(215\) | 51.2507 | − | 51.2507i | 0.238375 | − | 0.238375i | ||||
\(216\) | 10.3923 | − | 10.3923i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | 75.3395 | 0.347187 | ||||||||
\(218\) | − | 200.985i | − | 0.921947i | ||||||
\(219\) | −24.6001 | + | 24.6001i | −0.112329 | + | 0.112329i | ||||
\(220\) | 294.917i | 1.34053i | ||||||||
\(221\) | 121.245 | + | 68.6410i | 0.548622 | + | 0.310593i | ||||
\(222\) | −54.2672 | −0.244447 | ||||||||
\(223\) | −163.765 | − | 163.765i | −0.734370 | − | 0.734370i | 0.237112 | − | 0.971482i | \(-0.423799\pi\) |
−0.971482 | + | 0.237112i | \(0.923799\pi\) | |||||||
\(224\) | −23.1571 | −0.103380 | ||||||||
\(225\) | 72.2612i | 0.321161i | ||||||||
\(226\) | −60.2534 | − | 60.2534i | −0.266608 | − | 0.266608i | ||||
\(227\) | 113.077 | + | 113.077i | 0.498136 | + | 0.498136i | 0.910857 | − | 0.412721i | \(-0.135422\pi\) |
−0.412721 | + | 0.910857i | \(0.635422\pi\) | |||||||
\(228\) | 47.5660 | − | 47.5660i | 0.208623 | − | 0.208623i | ||||
\(229\) | 34.8308 | − | 34.8308i | 0.152100 | − | 0.152100i | −0.626955 | − | 0.779055i | \(-0.715699\pi\) |
0.779055 | + | 0.626955i | \(0.215699\pi\) | |||||||
\(230\) | 244.664 | 1.06376 | ||||||||
\(231\) | 149.230i | 0.646016i | ||||||||
\(232\) | −101.172 | + | 101.172i | −0.436086 | + | 0.436086i | ||||
\(233\) | − | 222.050i | − | 0.953004i | −0.879173 | − | 0.476502i | \(-0.841905\pi\) | ||
0.879173 | − | 0.476502i | \(-0.158095\pi\) | |||||||
\(234\) | 53.1524 | − | 14.7249i | 0.227147 | − | 0.0629267i | ||||
\(235\) | 489.902 | 2.08469 | ||||||||
\(236\) | 80.7689 | + | 80.7689i | 0.342241 | + | 0.342241i | ||||
\(237\) | 32.5103 | 0.137174 | ||||||||
\(238\) | − | 62.0463i | − | 0.260699i | ||||||
\(239\) | −269.828 | − | 269.828i | −1.12899 | − | 1.12899i | −0.990342 | − | 0.138644i | \(-0.955725\pi\) |
−0.138644 | − | 0.990342i | \(-0.544275\pi\) | |||||||
\(240\) | −34.3233 | − | 34.3233i | −0.143014 | − | 0.143014i | ||||
\(241\) | 281.175 | − | 281.175i | 1.16670 | − | 1.16670i | 0.183721 | − | 0.982978i | \(-0.441186\pi\) |
0.982978 | − | 0.183721i | \(-0.0588142\pi\) | |||||||
\(242\) | −321.968 | + | 321.968i | −1.33045 | + | 1.33045i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 176.659i | − | 0.724010i | ||||||
\(245\) | −159.732 | + | 159.732i | −0.651969 | + | 0.651969i | ||||
\(246\) | 20.7893i | 0.0845095i | ||||||||
\(247\) | 243.281 | − | 67.3963i | 0.984942 | − | 0.272859i | ||||
\(248\) | −52.0546 | −0.209898 | ||||||||
\(249\) | 93.1600 | + | 93.1600i | 0.374137 | + | 0.374137i | ||||
\(250\) | −9.04569 | −0.0361828 | ||||||||
\(251\) | 172.399i | 0.686847i | 0.939181 | + | 0.343423i | \(0.111587\pi\) | ||||
−0.939181 | + | 0.343423i | \(0.888413\pi\) | |||||||
\(252\) | −17.3678 | − | 17.3678i | −0.0689198 | − | 0.0689198i | ||||
\(253\) | 367.488 | + | 367.488i | 1.45252 | + | 1.45252i | ||||
\(254\) | 40.6683 | − | 40.6683i | 0.160111 | − | 0.160111i | ||||
\(255\) | 91.9648 | − | 91.9648i | 0.360646 | − | 0.360646i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 136.658i | 0.531743i | 0.964008 | + | 0.265871i | \(0.0856597\pi\) | ||||
−0.964008 | + | 0.265871i | \(0.914340\pi\) | |||||||
\(258\) | −17.9181 | + | 17.9181i | −0.0694500 | + | 0.0694500i | ||||
\(259\) | 90.6923i | 0.350163i | ||||||||
\(260\) | −48.6327 | − | 175.550i | −0.187049 | − | 0.675191i | ||||
\(261\) | −151.758 | −0.581447 | ||||||||
\(262\) | −214.111 | − | 214.111i | −0.817218 | − | 0.817218i | ||||
\(263\) | −242.846 | −0.923369 | −0.461684 | − | 0.887044i | \(-0.652755\pi\) | ||||
−0.461684 | + | 0.887044i | \(0.652755\pi\) | |||||||
\(264\) | − | 103.108i | − | 0.390560i | ||||||
\(265\) | 23.2812 | + | 23.2812i | 0.0878536 | + | 0.0878536i | ||||
\(266\) | −79.4931 | − | 79.4931i | −0.298846 | − | 0.298846i | ||||
\(267\) | −34.8712 | + | 34.8712i | −0.130604 | + | 0.130604i | ||||
\(268\) | 37.4475 | − | 37.4475i | 0.139729 | − | 0.139729i | ||||
\(269\) | 266.841 | 0.991975 | 0.495988 | − | 0.868330i | \(-0.334806\pi\) | ||||
0.495988 | + | 0.868330i | \(0.334806\pi\) | |||||||
\(270\) | − | 51.4850i | − | 0.190685i | ||||||
\(271\) | 353.211 | − | 353.211i | 1.30336 | − | 1.30336i | 0.377247 | − | 0.926113i | \(-0.376871\pi\) |
0.926113 | − | 0.377247i | \(-0.123129\pi\) | |||||||
\(272\) | 42.8699i | 0.157610i | ||||||||
\(273\) | −24.6084 | − | 88.8292i | −0.0901408 | − | 0.325382i | ||||
\(274\) | 236.924 | 0.864685 | ||||||||
\(275\) | 358.472 | + | 358.472i | 1.30353 | + | 1.30353i | ||||
\(276\) | −85.5387 | −0.309923 | ||||||||
\(277\) | 318.494i | 1.14980i | 0.818225 | + | 0.574898i | \(0.194958\pi\) | ||||
−0.818225 | + | 0.574898i | \(0.805042\pi\) | |||||||
\(278\) | 54.6810 | + | 54.6810i | 0.196694 | + | 0.196694i | ||||
\(279\) | −39.0410 | − | 39.0410i | −0.139932 | − | 0.139932i | ||||
\(280\) | −57.3617 | + | 57.3617i | −0.204863 | + | 0.204863i | ||||
\(281\) | 62.1237 | − | 62.1237i | 0.221081 | − | 0.221081i | −0.587873 | − | 0.808954i | \(-0.700034\pi\) |
0.808954 | + | 0.587873i | \(0.200034\pi\) | |||||||
\(282\) | −171.278 | −0.607369 | ||||||||
\(283\) | − | 99.5260i | − | 0.351682i | −0.984419 | − | 0.175841i | \(-0.943736\pi\) | ||
0.984419 | − | 0.175841i | \(-0.0562645\pi\) | |||||||
\(284\) | 151.859 | − | 151.859i | 0.534715 | − | 0.534715i | ||||
\(285\) | − | 235.649i | − | 0.826838i | ||||||
\(286\) | 190.631 | − | 336.724i | 0.666541 | − | 1.17736i | ||||
\(287\) | 34.7435 | 0.121057 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 174.136 | 0.602546 | ||||||||
\(290\) | 501.220i | 1.72834i | ||||||||
\(291\) | 154.580 | + | 154.580i | 0.531203 | + | 0.531203i | ||||
\(292\) | −28.4057 | − | 28.4057i | −0.0972799 | − | 0.0972799i | ||||
\(293\) | −10.4011 | + | 10.4011i | −0.0354987 | + | 0.0354987i | −0.724633 | − | 0.689135i | \(-0.757991\pi\) |
0.689135 | + | 0.724633i | \(0.257991\pi\) | |||||||
\(294\) | 55.8451 | − | 55.8451i | 0.189949 | − | 0.189949i | ||||
\(295\) | 400.140 | 1.35641 | ||||||||
\(296\) | − | 62.6624i | − | 0.211697i | ||||||
\(297\) | 77.3309 | − | 77.3309i | 0.260374 | − | 0.260374i | ||||
\(298\) | − | 246.058i | − | 0.825699i | ||||||
\(299\) | −279.348 | − | 158.148i | −0.934273 | − | 0.528923i | ||||
\(300\) | −83.4400 | −0.278133 | ||||||||
\(301\) | 29.9450 | + | 29.9450i | 0.0994851 | + | 0.0994851i | ||||
\(302\) | 59.5680 | 0.197245 | ||||||||
\(303\) | 119.652i | 0.394891i | ||||||||
\(304\) | 54.9245 | + | 54.9245i | 0.180673 | + | 0.180673i | ||||
\(305\) | −437.596 | − | 437.596i | −1.43474 | − | 1.43474i | ||||
\(306\) | −32.1524 | + | 32.1524i | −0.105073 | + | 0.105073i | ||||
\(307\) | −308.228 | + | 308.228i | −1.00400 | + | 1.00400i | −0.00400658 | + | 0.999992i | \(0.501275\pi\) |
−0.999992 | + | 0.00400658i | \(0.998725\pi\) | |||||||
\(308\) | −172.316 | −0.559467 | ||||||||
\(309\) | 168.466i | 0.545198i | ||||||||
\(310\) | −128.943 | + | 128.943i | −0.415945 | + | 0.415945i | ||||
\(311\) | − | 51.6238i | − | 0.165993i | −0.996550 | − | 0.0829965i | \(-0.973551\pi\) | ||
0.996550 | − | 0.0829965i | \(-0.0264490\pi\) | |||||||
\(312\) | 17.0028 | + | 61.3751i | 0.0544961 | + | 0.196715i | ||||
\(313\) | 188.224 | 0.601354 | 0.300677 | − | 0.953726i | \(-0.402787\pi\) | ||||
0.300677 | + | 0.953726i | \(0.402787\pi\) | |||||||
\(314\) | −171.846 | − | 171.846i | −0.547281 | − | 0.547281i | ||||
\(315\) | −86.0426 | −0.273151 | ||||||||
\(316\) | 37.5397i | 0.118796i | ||||||||
\(317\) | −154.717 | − | 154.717i | −0.488067 | − | 0.488067i | 0.419629 | − | 0.907696i | \(-0.362160\pi\) |
−0.907696 | + | 0.419629i | \(0.862160\pi\) | |||||||
\(318\) | −8.13950 | − | 8.13950i | −0.0255959 | − | 0.0255959i | ||||
\(319\) | −752.837 | + | 752.837i | −2.35999 | + | 2.35999i | ||||
\(320\) | 39.6331 | − | 39.6331i | 0.123854 | − | 0.123854i | ||||
\(321\) | −65.3575 | −0.203606 | ||||||||
\(322\) | 142.954i | 0.443956i | ||||||||
\(323\) | −147.163 | + | 147.163i | −0.455613 | + | 0.455613i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | −272.494 | − | 154.268i | −0.838443 | − | 0.474670i | ||||
\(326\) | 330.306 | 1.01321 | ||||||||
\(327\) | 174.058 | + | 174.058i | 0.532287 | + | 0.532287i | ||||
\(328\) | −24.0055 | −0.0731874 | ||||||||
\(329\) | 286.243i | 0.870039i | ||||||||
\(330\) | −255.406 | − | 255.406i | −0.773957 | − | 0.773957i | ||||
\(331\) | 112.730 | + | 112.730i | 0.340575 | + | 0.340575i | 0.856584 | − | 0.516008i | \(-0.172583\pi\) |
−0.516008 | + | 0.856584i | \(0.672583\pi\) | |||||||
\(332\) | −107.572 | + | 107.572i | −0.324012 | + | 0.324012i | ||||
\(333\) | 46.9968 | − | 46.9968i | 0.141131 | − | 0.141131i | ||||
\(334\) | −131.243 | −0.392944 | ||||||||
\(335\) | − | 185.520i | − | 0.553791i | ||||||
\(336\) | 20.0546 | − | 20.0546i | 0.0596863 | − | 0.0596863i | ||||
\(337\) | − | 322.005i | − | 0.955504i | −0.878495 | − | 0.477752i | \(-0.841452\pi\) | ||
0.878495 | − | 0.477752i | \(-0.158548\pi\) | |||||||
\(338\) | −57.9463 | + | 231.871i | −0.171439 | + | 0.686009i | ||||
\(339\) | 104.362 | 0.307853 | ||||||||
\(340\) | 106.192 | + | 106.192i | 0.312329 | + | 0.312329i | ||||
\(341\) | −387.347 | −1.13592 | ||||||||
\(342\) | 82.3867i | 0.240897i | ||||||||
\(343\) | −235.166 | − | 235.166i | −0.685616 | − | 0.685616i | ||||
\(344\) | −20.6900 | − | 20.6900i | −0.0601454 | − | 0.0601454i | ||||
\(345\) | −211.885 | + | 211.885i | −0.614161 | + | 0.614161i | ||||
\(346\) | −216.560 | + | 216.560i | −0.625897 | + | 0.625897i | ||||
\(347\) | 181.180 | 0.522133 | 0.261066 | − | 0.965321i | \(-0.415926\pi\) | ||||
0.261066 | + | 0.965321i | \(0.415926\pi\) | |||||||
\(348\) | − | 175.235i | − | 0.503548i | ||||||
\(349\) | 57.1882 | − | 57.1882i | 0.163863 | − | 0.163863i | −0.620413 | − | 0.784276i | \(-0.713035\pi\) |
0.784276 | + | 0.620413i | \(0.213035\pi\) | |||||||
\(350\) | 139.446i | 0.398418i | ||||||||
\(351\) | −33.2792 | + | 58.7834i | −0.0948126 | + | 0.167474i | ||||
\(352\) | 119.059 | 0.338235 | ||||||||
\(353\) | 187.552 | + | 187.552i | 0.531309 | + | 0.531309i | 0.920962 | − | 0.389653i | \(-0.127405\pi\) |
−0.389653 | + | 0.920962i | \(0.627405\pi\) | |||||||
\(354\) | −139.896 | −0.395186 | ||||||||
\(355\) | − | 752.332i | − | 2.11924i | ||||||
\(356\) | −40.2658 | − | 40.2658i | −0.113106 | − | 0.113106i | ||||
\(357\) | 53.7337 | + | 53.7337i | 0.150514 | + | 0.150514i | ||||
\(358\) | 22.1128 | − | 22.1128i | 0.0617676 | − | 0.0617676i | ||||
\(359\) | 139.842 | − | 139.842i | 0.389532 | − | 0.389532i | −0.484989 | − | 0.874520i | \(-0.661176\pi\) |
0.874520 | + | 0.484989i | \(0.161176\pi\) | |||||||
\(360\) | 59.4497 | 0.165138 | ||||||||
\(361\) | 16.0874i | 0.0445635i | ||||||||
\(362\) | 41.5239 | − | 41.5239i | 0.114707 | − | 0.114707i | ||||
\(363\) | − | 557.666i | − | 1.53627i | ||||||
\(364\) | 102.571 | − | 28.4154i | 0.281789 | − | 0.0780642i | ||||
\(365\) | −140.726 | −0.385551 | ||||||||
\(366\) | 152.991 | + | 152.991i | 0.418008 | + | 0.418008i | ||||
\(367\) | 54.5159 | 0.148545 | 0.0742724 | − | 0.997238i | \(-0.476337\pi\) | ||||
0.0742724 | + | 0.997238i | \(0.476337\pi\) | |||||||
\(368\) | − | 98.7716i | − | 0.268401i | ||||||
\(369\) | −18.0041 | − | 18.0041i | −0.0487916 | − | 0.0487916i | ||||
\(370\) | −155.219 | − | 155.219i | −0.419511 | − | 0.419511i | ||||
\(371\) | −13.6029 | + | 13.6029i | −0.0366654 | + | 0.0366654i | ||||
\(372\) | 45.0806 | − | 45.0806i | 0.121184 | − | 0.121184i | ||||
\(373\) | −236.635 | −0.634410 | −0.317205 | − | 0.948357i | \(-0.602744\pi\) | ||||
−0.317205 | + | 0.948357i | \(0.602744\pi\) | |||||||
\(374\) | 319.002i | 0.852947i | ||||||||
\(375\) | 7.83380 | − | 7.83380i | 0.0208901 | − | 0.0208901i | ||||
\(376\) | − | 197.775i | − | 0.525997i | ||||||
\(377\) | 323.982 | − | 572.272i | 0.859369 | − | 1.51796i | ||||
\(378\) | 30.0819 | 0.0795818 | ||||||||
\(379\) | 81.9661 | + | 81.9661i | 0.216269 | + | 0.216269i | 0.806924 | − | 0.590655i | \(-0.201131\pi\) |
−0.590655 | + | 0.806924i | \(0.701131\pi\) | |||||||
\(380\) | 272.104 | 0.716062 | ||||||||
\(381\) | 70.4396i | 0.184881i | ||||||||
\(382\) | 221.663 | + | 221.663i | 0.580269 | + | 0.580269i | ||||
\(383\) | −314.234 | − | 314.234i | −0.820453 | − | 0.820453i | 0.165720 | − | 0.986173i | \(-0.447005\pi\) |
−0.986173 | + | 0.165720i | \(0.947005\pi\) | |||||||
\(384\) | −13.8564 | + | 13.8564i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −426.838 | + | 426.838i | −1.10867 | + | 1.10867i | ||||
\(386\) | 511.158 | 1.32424 | ||||||||
\(387\) | − | 31.0350i | − | 0.0801939i | ||||||
\(388\) | −178.494 | + | 178.494i | −0.460035 | + | 0.460035i | ||||
\(389\) | 328.370i | 0.844138i | 0.906564 | + | 0.422069i | \(0.138696\pi\) | ||||
−0.906564 | + | 0.422069i | \(0.861304\pi\) | |||||||
\(390\) | 194.148 | + | 109.913i | 0.497815 | + | 0.281829i | ||||
\(391\) | 264.645 | 0.676842 | ||||||||
\(392\) | 64.4844 | + | 64.4844i | 0.164501 | + | 0.164501i | ||||
\(393\) | 370.852 | 0.943643 | ||||||||
\(394\) | − | 277.456i | − | 0.704204i | ||||||
\(395\) | 92.9885 | + | 92.9885i | 0.235414 | + | 0.235414i | ||||
\(396\) | 89.2941 | + | 89.2941i | 0.225490 | + | 0.225490i | ||||
\(397\) | −48.4976 | + | 48.4976i | −0.122160 | + | 0.122160i | −0.765544 | − | 0.643384i | \(-0.777530\pi\) |
0.643384 | + | 0.765544i | \(0.277530\pi\) | |||||||
\(398\) | 258.963 | − | 258.963i | 0.650660 | − | 0.650660i | ||||
\(399\) | 137.686 | 0.345078 | ||||||||
\(400\) | − | 96.3482i | − | 0.240871i | ||||||
\(401\) | −176.776 | + | 176.776i | −0.440839 | + | 0.440839i | −0.892294 | − | 0.451455i | \(-0.850905\pi\) |
0.451455 | + | 0.892294i | \(0.350905\pi\) | |||||||
\(402\) | 64.8609i | 0.161346i | ||||||||
\(403\) | 230.569 | − | 63.8747i | 0.572131 | − | 0.158498i | ||||
\(404\) | −138.162 | −0.341986 | ||||||||
\(405\) | 44.5873 | + | 44.5873i | 0.110092 | + | 0.110092i | ||||
\(406\) | −292.855 | −0.721319 | ||||||||
\(407\) | − | 466.281i | − | 1.14565i | ||||||
\(408\) | −37.1264 | − | 37.1264i | −0.0909961 | − | 0.0909961i | ||||
\(409\) | −137.725 | − | 137.725i | −0.336735 | − | 0.336735i | 0.518402 | − | 0.855137i | \(-0.326527\pi\) |
−0.855137 | + | 0.518402i | \(0.826527\pi\) | |||||||
\(410\) | −59.4632 | + | 59.4632i | −0.145032 | + | 0.145032i | ||||
\(411\) | −205.182 | + | 205.182i | −0.499226 | + | 0.499226i | ||||
\(412\) | −194.528 | −0.472156 | ||||||||
\(413\) | 233.796i | 0.566093i | ||||||||
\(414\) | 74.0787 | − | 74.0787i | 0.178934 | − | 0.178934i | ||||
\(415\) | 532.927i | 1.28416i | ||||||||
\(416\) | −70.8699 | + | 19.6331i | −0.170360 | + | 0.0471951i | ||||
\(417\) | −94.7103 | −0.227123 | ||||||||
\(418\) | 408.703 | + | 408.703i | 0.977757 | + | 0.977757i | ||||
\(419\) | −54.8057 | −0.130801 | −0.0654006 | − | 0.997859i | \(-0.520833\pi\) | ||||
−0.0654006 | + | 0.997859i | \(0.520833\pi\) | |||||||
\(420\) | − | 99.3534i | − | 0.236556i | ||||||
\(421\) | −399.548 | − | 399.548i | −0.949046 | − | 0.949046i | 0.0497174 | − | 0.998763i | \(-0.484168\pi\) |
−0.998763 | + | 0.0497174i | \(0.984168\pi\) | |||||||
\(422\) | 220.454 | + | 220.454i | 0.522402 | + | 0.522402i | ||||
\(423\) | 148.331 | − | 148.331i | 0.350664 | − | 0.350664i | ||||
\(424\) | 9.39868 | − | 9.39868i | 0.0221667 | − | 0.0221667i | ||||
\(425\) | 258.152 | 0.607417 | ||||||||
\(426\) | 263.028i | 0.617436i | ||||||||
\(427\) | 255.681 | − | 255.681i | 0.598784 | − | 0.598784i | ||||
\(428\) | − | 75.4683i | − | 0.176328i | ||||||
\(429\) | 126.521 | + | 456.703i | 0.294920 | + | 1.06458i | ||||
\(430\) | −102.501 | −0.238375 | ||||||||
\(431\) | 266.968 | + | 266.968i | 0.619416 | + | 0.619416i | 0.945382 | − | 0.325965i | \(-0.105689\pi\) |
−0.325965 | + | 0.945382i | \(0.605689\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | 783.673i | 1.80987i | 0.425551 | + | 0.904934i | \(0.360080\pi\) | ||||
−0.425551 | + | 0.904934i | \(0.639920\pi\) | |||||||
\(434\) | −75.3395 | − | 75.3395i | −0.173593 | − | 0.173593i | ||||
\(435\) | −434.069 | − | 434.069i | −0.997860 | − | 0.997860i | ||||
\(436\) | −200.985 | + | 200.985i | −0.460974 | + | 0.460974i | ||||
\(437\) | 339.061 | − | 339.061i | 0.775884 | − | 0.775884i | ||||
\(438\) | 49.2001 | 0.112329 | ||||||||
\(439\) | − | 411.297i | − | 0.936895i | −0.883491 | − | 0.468447i | \(-0.844814\pi\) | ||
0.883491 | − | 0.468447i | \(-0.155186\pi\) | |||||||
\(440\) | 294.917 | − | 294.917i | 0.670266 | − | 0.670266i | ||||
\(441\) | 96.7266i | 0.219335i | ||||||||
\(442\) | −52.6044 | − | 189.886i | −0.119014 | − | 0.429607i | ||||
\(443\) | 166.429 | 0.375686 | 0.187843 | − | 0.982199i | \(-0.439850\pi\) | ||||
0.187843 | + | 0.982199i | \(0.439850\pi\) | |||||||
\(444\) | 54.2672 | + | 54.2672i | 0.122223 | + | 0.122223i | ||||
\(445\) | −199.483 | −0.448276 | ||||||||
\(446\) | 327.529i | 0.734370i | ||||||||
\(447\) | 213.093 | + | 213.093i | 0.476717 | + | 0.476717i | ||||
\(448\) | 23.1571 | + | 23.1571i | 0.0516899 | + | 0.0516899i | ||||
\(449\) | 280.017 | − | 280.017i | 0.623645 | − | 0.623645i | −0.322817 | − | 0.946462i | \(-0.604630\pi\) |
0.946462 | + | 0.322817i | \(0.104630\pi\) | |||||||
\(450\) | 72.2612 | − | 72.2612i | 0.160580 | − | 0.160580i | ||||
\(451\) | −178.629 | −0.396073 | ||||||||
\(452\) | 120.507i | 0.266608i | ||||||||
\(453\) | −51.5874 | + | 51.5874i | −0.113879 | + | 0.113879i | ||||
\(454\) | − | 226.154i | − | 0.498136i | ||||||
\(455\) | 183.689 | − | 324.463i | 0.403712 | − | 0.713105i | ||||
\(456\) | −95.1320 | −0.208623 | ||||||||
\(457\) | −392.456 | − | 392.456i | −0.858766 | − | 0.858766i | 0.132427 | − | 0.991193i | \(-0.457723\pi\) |
−0.991193 | + | 0.132427i | \(0.957723\pi\) | |||||||
\(458\) | −69.6617 | −0.152100 | ||||||||
\(459\) | − | 55.6896i | − | 0.121328i | ||||||
\(460\) | −244.664 | − | 244.664i | −0.531879 | − | 0.531879i | ||||
\(461\) | 474.185 | + | 474.185i | 1.02860 | + | 1.02860i | 0.999579 | + | 0.0290214i | \(0.00923909\pi\) |
0.0290214 | + | 0.999579i | \(0.490761\pi\) | |||||||
\(462\) | 149.230 | − | 149.230i | 0.323008 | − | 0.323008i | ||||
\(463\) | −218.266 | + | 218.266i | −0.471418 | + | 0.471418i | −0.902373 | − | 0.430955i | \(-0.858177\pi\) |
0.430955 | + | 0.902373i | \(0.358177\pi\) | |||||||
\(464\) | 202.344 | 0.436086 | ||||||||
\(465\) | − | 223.336i | − | 0.480292i | ||||||
\(466\) | −222.050 | + | 222.050i | −0.476502 | + | 0.476502i | ||||
\(467\) | − | 170.592i | − | 0.365293i | −0.983179 | − | 0.182646i | \(-0.941534\pi\) | ||
0.983179 | − | 0.182646i | \(-0.0584664\pi\) | |||||||
\(468\) | −67.8773 | − | 38.4276i | −0.145037 | − | 0.0821102i | ||||
\(469\) | 108.397 | 0.231123 | ||||||||
\(470\) | −489.902 | − | 489.902i | −1.04235 | − | 1.04235i | ||||
\(471\) | 297.646 | 0.631945 | ||||||||
\(472\) | − | 161.538i | − | 0.342241i | ||||||
\(473\) | −153.958 | − | 153.958i | −0.325493 | − | 0.325493i | ||||
\(474\) | −32.5103 | − | 32.5103i | −0.0685872 | − | 0.0685872i | ||||
\(475\) | 330.742 | − | 330.742i | 0.696300 | − | 0.696300i | ||||
\(476\) | −62.0463 | + | 62.0463i | −0.130349 | + | 0.130349i | ||||
\(477\) | 14.0980 | 0.0295556 | ||||||||
\(478\) | 539.656i | 1.12899i | ||||||||
\(479\) | −40.5687 | + | 40.5687i | −0.0846946 | + | 0.0846946i | −0.748185 | − | 0.663490i | \(-0.769074\pi\) |
0.663490 | + | 0.748185i | \(0.269074\pi\) | |||||||
\(480\) | 68.6466i | 0.143014i | ||||||||
\(481\) | 76.8912 | + | 277.555i | 0.159857 | + | 0.577037i | ||||
\(482\) | −562.349 | −1.16670 | ||||||||
\(483\) | −123.802 | − | 123.802i | −0.256318 | − | 0.256318i | ||||
\(484\) | 643.937 | 1.33045 | ||||||||
\(485\) | 884.283i | 1.82326i | ||||||||
\(486\) | −15.5885 | − | 15.5885i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | −112.692 | − | 112.692i | −0.231399 | − | 0.231399i | 0.581877 | − | 0.813277i | \(-0.302318\pi\) |
−0.813277 | + | 0.581877i | \(0.802318\pi\) | |||||||
\(488\) | −176.659 | + | 176.659i | −0.362005 | + | 0.362005i | ||||
\(489\) | −286.053 | + | 286.053i | −0.584976 | + | 0.584976i | ||||
\(490\) | 319.465 | 0.651969 | ||||||||
\(491\) | 400.234i | 0.815140i | 0.913174 | + | 0.407570i | \(0.133624\pi\) | ||||
−0.913174 | + | 0.407570i | \(0.866376\pi\) | |||||||
\(492\) | 20.7893 | − | 20.7893i | 0.0422547 | − | 0.0422547i | ||||
\(493\) | 542.153i | 1.09970i | ||||||||
\(494\) | −310.677 | − | 175.884i | −0.628901 | − | 0.356041i | ||||
\(495\) | 442.376 | 0.893688 | ||||||||
\(496\) | 52.0546 | + | 52.0546i | 0.104949 | + | 0.104949i | ||||
\(497\) | 439.577 | 0.884460 | ||||||||
\(498\) | − | 186.320i | − | 0.374137i | ||||||
\(499\) | 395.751 | + | 395.751i | 0.793087 | + | 0.793087i | 0.981995 | − | 0.188908i | \(-0.0604947\pi\) |
−0.188908 | + | 0.981995i | \(0.560495\pi\) | |||||||
\(500\) | 9.04569 | + | 9.04569i | 0.0180914 | + | 0.0180914i | ||||
\(501\) | 113.660 | − | 113.660i | 0.226866 | − | 0.226866i | ||||
\(502\) | 172.399 | − | 172.399i | 0.343423 | − | 0.343423i | ||||
\(503\) | −186.068 | −0.369917 | −0.184958 | − | 0.982746i | \(-0.559215\pi\) | ||||
−0.184958 | + | 0.982746i | \(0.559215\pi\) | |||||||
\(504\) | 34.7356i | 0.0689198i | ||||||||
\(505\) | −342.238 | + | 342.238i | −0.677698 | + | 0.677698i | ||||
\(506\) | − | 734.976i | − | 1.45252i | ||||||
\(507\) | −150.623 | − | 250.989i | −0.297087 | − | 0.495048i | ||||
\(508\) | −81.3366 | −0.160111 | ||||||||
\(509\) | −713.760 | − | 713.760i | −1.40228 | − | 1.40228i | −0.792808 | − | 0.609472i | \(-0.791382\pi\) |
−0.609472 | − | 0.792808i | \(-0.708618\pi\) | |||||||
\(510\) | −183.930 | −0.360646 | ||||||||
\(511\) | − | 82.2241i | − | 0.160908i | ||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −71.3490 | − | 71.3490i | −0.139082 | − | 0.139082i | ||||
\(514\) | 136.658 | − | 136.658i | 0.265871 | − | 0.265871i | ||||
\(515\) | −481.860 | + | 481.860i | −0.935650 | + | 0.935650i | ||||
\(516\) | 35.8362 | 0.0694500 | ||||||||
\(517\) | − | 1471.68i | − | 2.84657i | ||||||
\(518\) | 90.6923 | − | 90.6923i | 0.175082 | − | 0.175082i | ||||
\(519\) | − | 375.094i | − | 0.722724i | ||||||
\(520\) | −126.917 | + | 224.182i | −0.244071 | + | 0.431120i | ||||
\(521\) | −949.290 | −1.82205 | −0.911027 | − | 0.412347i | \(-0.864709\pi\) | ||||
−0.911027 | + | 0.412347i | \(0.864709\pi\) | |||||||
\(522\) | 151.758 | + | 151.758i | 0.290724 | + | 0.290724i | ||||
\(523\) | 253.311 | 0.484342 | 0.242171 | − | 0.970234i | \(-0.422140\pi\) | ||||
0.242171 | + | 0.970234i | \(0.422140\pi\) | |||||||
\(524\) | 428.222i | 0.817218i | ||||||||
\(525\) | −120.764 | − | 120.764i | −0.230027 | − | 0.230027i | ||||
\(526\) | 242.846 | + | 242.846i | 0.461684 | + | 0.461684i | ||||
\(527\) | −139.473 | + | 139.473i | −0.264655 | + | 0.264655i | ||||
\(528\) | −103.108 | + | 103.108i | −0.195280 | + | 0.195280i | ||||
\(529\) | −80.7391 | −0.152626 | ||||||||
\(530\) | − | 46.5624i | − | 0.0878536i | ||||||
\(531\) | 121.153 | − | 121.153i | 0.228161 | − | 0.228161i | ||||
\(532\) | 158.986i | 0.298846i | ||||||||
\(533\) | 106.329 | − | 29.4564i | 0.199492 | − | 0.0552653i | ||||
\(534\) | 69.7425 | 0.130604 | ||||||||
\(535\) | −186.940 | − | 186.940i | −0.349421 | − | 0.349421i | ||||
\(536\) | −74.8949 | −0.139729 | ||||||||
\(537\) | 38.3005i | 0.0713231i | ||||||||
\(538\) | −266.841 | − | 266.841i | −0.495988 | − | 0.495988i | ||||
\(539\) | 479.840 | + | 479.840i | 0.890240 | + | 0.890240i | ||||
\(540\) | −51.4850 | + | 51.4850i | −0.0953425 | + | 0.0953425i | ||||
\(541\) | 305.522 | − | 305.522i | 0.564735 | − | 0.564735i | −0.365914 | − | 0.930649i | \(-0.619243\pi\) |
0.930649 | + | 0.365914i | \(0.119243\pi\) | |||||||
\(542\) | −706.421 | −1.30336 | ||||||||
\(543\) | 71.9215i | 0.132452i | ||||||||
\(544\) | 42.8699 | − | 42.8699i | 0.0788049 | − | 0.0788049i | ||||
\(545\) | 995.706i | 1.82698i | ||||||||
\(546\) | −64.2208 | + | 113.438i | −0.117620 | + | 0.207761i | ||||
\(547\) | −550.333 | −1.00609 | −0.503047 | − | 0.864259i | \(-0.667788\pi\) | ||||
−0.503047 | + | 0.864259i | \(0.667788\pi\) | |||||||
\(548\) | −236.924 | − | 236.924i | −0.432342 | − | 0.432342i | ||||
\(549\) | −264.988 | −0.482674 | ||||||||
\(550\) | − | 716.944i | − | 1.30353i | ||||||
\(551\) | 694.601 | + | 694.601i | 1.26062 | + | 1.26062i | ||||
\(552\) | 85.5387 | + | 85.5387i | 0.154961 | + | 0.154961i | ||||
\(553\) | −54.3318 | + | 54.3318i | −0.0982492 | + | 0.0982492i | ||||
\(554\) | 318.494 | − | 318.494i | 0.574898 | − | 0.574898i | ||||
\(555\) | 268.847 | 0.484410 | ||||||||
\(556\) | − | 109.362i | − | 0.196694i | ||||||
\(557\) | −8.16464 | + | 8.16464i | −0.0146582 | + | 0.0146582i | −0.714398 | − | 0.699740i | \(-0.753299\pi\) |
0.699740 | + | 0.714398i | \(0.253299\pi\) | |||||||
\(558\) | 78.0819i | 0.139932i | ||||||||
\(559\) | 117.032 | + | 66.2556i | 0.209359 | + | 0.118525i | ||||
\(560\) | 114.723 | 0.204863 | ||||||||
\(561\) | −276.264 | − | 276.264i | −0.492449 | − | 0.492449i | ||||
\(562\) | −124.247 | −0.221081 | ||||||||
\(563\) | − | 613.374i | − | 1.08947i | −0.838607 | − | 0.544737i | \(-0.816629\pi\) | ||
0.838607 | − | 0.544737i | \(-0.183371\pi\) | |||||||
\(564\) | 171.278 | + | 171.278i | 0.303684 | + | 0.303684i | ||||
\(565\) | 298.504 | + | 298.504i | 0.528326 | + | 0.528326i | ||||
\(566\) | −99.5260 | + | 99.5260i | −0.175841 | + | 0.175841i | ||||
\(567\) | −26.0517 | + | 26.0517i | −0.0459466 | + | 0.0459466i | ||||
\(568\) | −303.718 | −0.534715 | ||||||||
\(569\) | 292.821i | 0.514624i | 0.966328 | + | 0.257312i | \(0.0828367\pi\) | ||||
−0.966328 | + | 0.257312i | \(0.917163\pi\) | |||||||
\(570\) | −235.649 | + | 235.649i | −0.413419 | + | 0.413419i | ||||
\(571\) | − | 208.583i | − | 0.365295i | −0.983179 | − | 0.182647i | \(-0.941533\pi\) | ||
0.983179 | − | 0.182647i | \(-0.0584666\pi\) | |||||||
\(572\) | −527.355 | + | 146.094i | −0.921949 | + | 0.255408i | ||||
\(573\) | −383.931 | −0.670037 | ||||||||
\(574\) | −34.7435 | − | 34.7435i | −0.0605287 | − | 0.0605287i | ||||
\(575\) | −594.779 | −1.03440 | ||||||||
\(576\) | − | 24.0000i | − | 0.0416667i | ||||||
\(577\) | 495.420 | + | 495.420i | 0.858614 | + | 0.858614i | 0.991175 | − | 0.132561i | \(-0.0423201\pi\) |
−0.132561 | + | 0.991175i | \(0.542320\pi\) | |||||||
\(578\) | −174.136 | − | 174.136i | −0.301273 | − | 0.301273i | ||||
\(579\) | −442.676 | + | 442.676i | −0.764552 | + | 0.764552i | ||||
\(580\) | 501.220 | − | 501.220i | 0.864172 | − | 0.864172i | ||||
\(581\) | −311.381 | −0.535940 | ||||||||
\(582\) | − | 309.160i | − | 0.531203i | ||||||
\(583\) | 69.9372 | − | 69.9372i | 0.119961 | − | 0.119961i | ||||
\(584\) | 56.8114i | 0.0972799i | ||||||||
\(585\) | −263.325 | + | 72.9490i | −0.450128 | + | 0.124699i | ||||
\(586\) | 20.8022 | 0.0354987 | ||||||||
\(587\) | 242.505 | + | 242.505i | 0.413126 | + | 0.413126i | 0.882826 | − | 0.469700i | \(-0.155638\pi\) |
−0.469700 | + | 0.882826i | \(0.655638\pi\) | |||||||
\(588\) | −111.690 | −0.189949 | ||||||||
\(589\) | 357.384i | 0.606764i | ||||||||
\(590\) | −400.140 | − | 400.140i | −0.678204 | − | 0.678204i | ||||
\(591\) | 240.284 | + | 240.284i | 0.406572 | + | 0.406572i | ||||
\(592\) | −62.6624 | + | 62.6624i | −0.105849 | + | 0.105849i | ||||
\(593\) | 661.970 | − | 661.970i | 1.11631 | − | 1.11631i | 0.124029 | − | 0.992279i | \(-0.460418\pi\) |
0.992279 | − | 0.124029i | \(-0.0395816\pi\) | |||||||
\(594\) | −154.662 | −0.260374 | ||||||||
\(595\) | 307.386i | 0.516615i | ||||||||
\(596\) | −246.058 | + | 246.058i | −0.412849 | + | 0.412849i | ||||
\(597\) | 448.537i | 0.751318i | ||||||||
\(598\) | 121.200 | + | 437.496i | 0.202675 | + | 0.731598i | ||||
\(599\) | −592.427 | −0.989027 | −0.494514 | − | 0.869170i | \(-0.664654\pi\) | ||||
−0.494514 | + | 0.869170i | \(0.664654\pi\) | |||||||
\(600\) | 83.4400 | + | 83.4400i | 0.139067 | + | 0.139067i | ||||
\(601\) | 3.03593 | 0.00505147 | 0.00252573 | − | 0.999997i | \(-0.499196\pi\) | ||||
0.00252573 | + | 0.999997i | \(0.499196\pi\) | |||||||
\(602\) | − | 59.8900i | − | 0.0994851i | ||||||
\(603\) | −56.1712 | − | 56.1712i | −0.0931529 | − | 0.0931529i | ||||
\(604\) | −59.5680 | − | 59.5680i | −0.0986225 | − | 0.0986225i | ||||
\(605\) | 1595.08 | − | 1595.08i | 2.63649 | − | 2.63649i | ||||
\(606\) | 119.652 | − | 119.652i | 0.197446 | − | 0.197446i | ||||
\(607\) | 365.518 | 0.602171 | 0.301085 | − | 0.953597i | \(-0.402651\pi\) | ||||
0.301085 | + | 0.953597i | \(0.402651\pi\) | |||||||
\(608\) | − | 109.849i | − | 0.180673i | ||||||
\(609\) | 253.620 | − | 253.620i | 0.416454 | − | 0.416454i | ||||
\(610\) | 875.191i | 1.43474i | ||||||||
\(611\) | 242.684 | + | 876.017i | 0.397191 | + | 1.43374i | ||||
\(612\) | 64.3048 | 0.105073 | ||||||||
\(613\) | 787.305 | + | 787.305i | 1.28435 | + | 1.28435i | 0.938168 | + | 0.346180i | \(0.112521\pi\) |
0.346180 | + | 0.938168i | \(0.387479\pi\) | |||||||
\(614\) | 616.455 | 1.00400 | ||||||||
\(615\) | − | 102.993i | − | 0.167469i | ||||||
\(616\) | 172.316 | + | 172.316i | 0.279733 | + | 0.279733i | ||||
\(617\) | 181.253 | + | 181.253i | 0.293765 | + | 0.293765i | 0.838566 | − | 0.544801i | \(-0.183395\pi\) |
−0.544801 | + | 0.838566i | \(0.683395\pi\) | |||||||
\(618\) | 168.466 | − | 168.466i | 0.272599 | − | 0.272599i | ||||
\(619\) | 475.455 | − | 475.455i | 0.768102 | − | 0.768102i | −0.209671 | − | 0.977772i | \(-0.567239\pi\) |
0.977772 | + | 0.209671i | \(0.0672391\pi\) | |||||||
\(620\) | 257.886 | 0.415945 | ||||||||
\(621\) | 128.308i | 0.206615i | ||||||||
\(622\) | −51.6238 | + | 51.6238i | −0.0829965 | + | 0.0829965i | ||||
\(623\) | − | 116.555i | − | 0.187086i | ||||||
\(624\) | 44.3723 | − | 78.3779i | 0.0711095 | − | 0.125606i | ||||
\(625\) | 646.990 | 1.03518 | ||||||||
\(626\) | −188.224 | − | 188.224i | −0.300677 | − | 0.300677i | ||||
\(627\) | −707.894 | −1.12902 | ||||||||
\(628\) | 343.692i | 0.547281i | ||||||||
\(629\) | −167.895 | − | 167.895i | −0.266924 | − | 0.266924i | ||||
\(630\) | 86.0426 | + | 86.0426i | 0.136575 | + | 0.136575i | ||||
\(631\) | 220.841 | − | 220.841i | 0.349985 | − | 0.349985i | −0.510119 | − | 0.860104i | \(-0.670399\pi\) |
0.860104 | + | 0.510119i | \(0.170399\pi\) | |||||||
\(632\) | 37.5397 | − | 37.5397i | 0.0593982 | − | 0.0593982i | ||||
\(633\) | −381.837 | −0.603218 | ||||||||
\(634\) | 309.435i | 0.488067i | ||||||||
\(635\) | −201.477 | + | 201.477i | −0.317286 | + | 0.317286i | ||||
\(636\) | 16.2790i | 0.0255959i | ||||||||
\(637\) | −364.752 | − | 206.498i | −0.572609 | − | 0.324173i | ||||
\(638\) | 1505.67 | 2.35999 | ||||||||
\(639\) | −227.789 | − | 227.789i | −0.356477 | − | 0.356477i | ||||
\(640\) | −79.2663 | −0.123854 | ||||||||
\(641\) | − | 1061.61i | − | 1.65618i | −0.560593 | − | 0.828091i | \(-0.689427\pi\) | ||
0.560593 | − | 0.828091i | \(-0.310573\pi\) | |||||||
\(642\) | 65.3575 | + | 65.3575i | 0.101803 | + | 0.101803i | ||||
\(643\) | −492.440 | − | 492.440i | −0.765847 | − | 0.765847i | 0.211526 | − | 0.977372i | \(-0.432157\pi\) |
−0.977372 | + | 0.211526i | \(0.932157\pi\) | |||||||
\(644\) | 142.954 | − | 142.954i | 0.221978 | − | 0.221978i | ||||
\(645\) | 88.7688 | − | 88.7688i | 0.137626 | − | 0.137626i | ||||
\(646\) | 294.326 | 0.455613 | ||||||||
\(647\) | − | 1042.77i | − | 1.61170i | −0.592119 | − | 0.805850i | \(-0.701709\pi\) | ||
0.592119 | − | 0.805850i | \(-0.298291\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 1202.03i | − | 1.85213i | ||||||
\(650\) | 118.226 | + | 426.762i | 0.181886 | + | 0.656556i | ||||
\(651\) | 130.492 | 0.200448 | ||||||||
\(652\) | −330.306 | − | 330.306i | −0.506604 | − | 0.506604i | ||||
\(653\) | −188.757 | −0.289061 | −0.144531 | − | 0.989500i | \(-0.546167\pi\) | ||||
−0.144531 | + | 0.989500i | \(0.546167\pi\) | |||||||
\(654\) | − | 348.115i | − | 0.532287i | ||||||
\(655\) | 1060.74 | + | 1060.74i | 1.61945 | + | 1.61945i | ||||
\(656\) | 24.0055 | + | 24.0055i | 0.0365937 | + | 0.0365937i | ||||
\(657\) | −42.6086 | + | 42.6086i | −0.0648532 | + | 0.0648532i | ||||
\(658\) | 286.243 | − | 286.243i | 0.435019 | − | 0.435019i | ||||
\(659\) | −134.577 | −0.204214 | −0.102107 | − | 0.994773i | \(-0.532558\pi\) | ||||
−0.102107 | + | 0.994773i | \(0.532558\pi\) | |||||||
\(660\) | 510.811i | 0.773957i | ||||||||
\(661\) | 110.259 | − | 110.259i | 0.166807 | − | 0.166807i | −0.618768 | − | 0.785574i | \(-0.712368\pi\) |
0.785574 | + | 0.618768i | \(0.212368\pi\) | |||||||
\(662\) | − | 225.461i | − | 0.340575i | ||||||
\(663\) | 210.003 | + | 118.890i | 0.316747 | + | 0.179321i | ||||
\(664\) | 215.144 | 0.324012 | ||||||||
\(665\) | 393.820 | + | 393.820i | 0.592211 | + | 0.592211i | ||||
\(666\) | −93.9935 | −0.141131 | ||||||||
\(667\) | − | 1249.11i | − | 1.87273i | ||||||
\(668\) | 131.243 | + | 131.243i | 0.196472 | + | 0.196472i | ||||
\(669\) | −283.648 | − | 283.648i | −0.423989 | − | 0.423989i | ||||
\(670\) | −185.520 | + | 185.520i | −0.276896 | + | 0.276896i | ||||
\(671\) | −1314.55 | + | 1314.55i | −1.95909 | + | 1.95909i | ||||
\(672\) | −40.1092 | −0.0596863 | ||||||||
\(673\) | 1027.47i | 1.52670i | 0.645984 | + | 0.763351i | \(0.276447\pi\) | ||||
−0.645984 | + | 0.763351i | \(0.723553\pi\) | |||||||
\(674\) | −322.005 | + | 322.005i | −0.477752 | + | 0.477752i | ||||
\(675\) | 125.160i | 0.185422i | ||||||||
\(676\) | 289.817 | − | 173.925i | 0.428724 | − | 0.257285i | ||||
\(677\) | 254.223 | 0.375514 | 0.187757 | − | 0.982216i | \(-0.439878\pi\) | ||||
0.187757 | + | 0.982216i | \(0.439878\pi\) | |||||||
\(678\) | −104.362 | − | 104.362i | −0.153926 | − | 0.153926i | ||||
\(679\) | −516.674 | −0.760933 | ||||||||
\(680\) | − | 212.383i | − | 0.312329i | ||||||
\(681\) | 195.855 | + | 195.855i | 0.287599 | + | 0.287599i | ||||
\(682\) | 387.347 | + | 387.347i | 0.567958 | + | 0.567958i | ||||
\(683\) | −179.840 | + | 179.840i | −0.263309 | + | 0.263309i | −0.826397 | − | 0.563088i | \(-0.809613\pi\) |
0.563088 | + | 0.826397i | \(0.309613\pi\) | |||||||
\(684\) | 82.3867 | − | 82.3867i | 0.120448 | − | 0.120448i | ||||
\(685\) | −1173.75 | −1.71351 | ||||||||
\(686\) | 470.333i | 0.685616i | ||||||||
\(687\) | 60.3288 | − | 60.3288i | 0.0878148 | − | 0.0878148i | ||||
\(688\) | 41.3801i | 0.0601454i | ||||||||
\(689\) | −30.0974 | + | 53.1631i | −0.0436827 | + | 0.0771597i | ||||
\(690\) | 423.771 | 0.614161 | ||||||||
\(691\) | −552.911 | − | 552.911i | −0.800160 | − | 0.800160i | 0.182960 | − | 0.983120i | \(-0.441432\pi\) |
−0.983120 | + | 0.182960i | \(0.941432\pi\) | |||||||
\(692\) | 433.121 | 0.625897 | ||||||||
\(693\) | 258.474i | 0.372978i | ||||||||
\(694\) | −181.180 | − | 181.180i | −0.261066 | − | 0.261066i | ||||
\(695\) | −270.897 | − | 270.897i | −0.389780 | − | 0.389780i | ||||
\(696\) | −175.235 | + | 175.235i | −0.251774 | + | 0.251774i | ||||
\(697\) | −64.3194 | + | 64.3194i | −0.0922804 | + | 0.0922804i | ||||
\(698\) | −114.376 | −0.163863 | ||||||||
\(699\) | − | 384.602i | − | 0.550217i | ||||||
\(700\) | 139.446 | − | 139.446i | 0.199209 | − | 0.199209i | ||||
\(701\) | 307.529i | 0.438701i | 0.975646 | + | 0.219350i | \(0.0703938\pi\) | ||||
−0.975646 | + | 0.219350i | \(0.929606\pi\) | |||||||
\(702\) | 92.0627 | − | 25.5042i | 0.131143 | − | 0.0363308i | ||||
\(703\) | −430.212 | −0.611966 | ||||||||
\(704\) | −119.059 | − | 119.059i | −0.169118 | − | 0.169118i | ||||
\(705\) | 848.535 | 1.20360 | ||||||||
\(706\) | − | 375.104i | − | 0.531309i | ||||||
\(707\) | −199.964 | − | 199.964i | −0.282835 | − | 0.282835i | ||||
\(708\) | 139.896 | + | 139.896i | 0.197593 | + | 0.197593i | ||||
\(709\) | 126.877 | − | 126.877i | 0.178952 | − | 0.178952i | −0.611947 | − | 0.790899i | \(-0.709613\pi\) |
0.790899 | + | 0.611947i | \(0.209613\pi\) | |||||||
\(710\) | −752.332 | + | 752.332i | −1.05962 | + | 1.05962i | ||||
\(711\) | 56.3095 | 0.0791976 | ||||||||
\(712\) | 80.5317i | 0.113106i | ||||||||
\(713\) | 321.345 | − | 321.345i | 0.450694 | − | 0.450694i | ||||
\(714\) | − | 107.467i | − | 0.150514i | ||||||
\(715\) | −944.412 | + | 1668.18i | −1.32086 | + | 2.33312i | ||||
\(716\) | −44.2256 | −0.0617676 | ||||||||
\(717\) | −467.355 | − | 467.355i | −0.651821 | − | 0.651821i | ||||
\(718\) | −279.684 | −0.389532 | ||||||||
\(719\) | 132.467i | 0.184238i | 0.995748 | + | 0.0921191i | \(0.0293640\pi\) | ||||
−0.995748 | + | 0.0921191i | \(0.970636\pi\) | |||||||
\(720\) | −59.4497 | − | 59.4497i | −0.0825690 | − | 0.0825690i | ||||
\(721\) | −281.544 | − | 281.544i | −0.390491 | − | 0.390491i | ||||
\(722\) | 16.0874 | − | 16.0874i | 0.0222817 | − | 0.0222817i | ||||
\(723\) | 487.009 | − | 487.009i | 0.673594 | − | 0.673594i | ||||
\(724\) | −83.0479 | −0.114707 | ||||||||
\(725\) | − | 1218.47i | − | 1.68064i | ||||||
\(726\) | −557.666 | + | 557.666i | −0.768135 | + | 0.768135i | ||||
\(727\) | − | 445.841i | − | 0.613261i | −0.951829 | − | 0.306630i | \(-0.900798\pi\) | ||
0.951829 | − | 0.306630i | \(-0.0992016\pi\) | |||||||
\(728\) | −130.987 | − | 74.1558i | −0.179927 | − | 0.101862i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 140.726 | + | 140.726i | 0.192775 | + | 0.192775i | ||||
\(731\) | −110.872 | −0.151672 | ||||||||
\(732\) | − | 305.982i | − | 0.418008i | ||||||
\(733\) | 213.665 | + | 213.665i | 0.291494 | + | 0.291494i | 0.837670 | − | 0.546177i | \(-0.183917\pi\) |
−0.546177 | + | 0.837670i | \(0.683917\pi\) | |||||||
\(734\) | −54.5159 | − | 54.5159i | −0.0742724 | − | 0.0742724i | ||||
\(735\) | −276.665 | + | 276.665i | −0.376415 | + | 0.376415i | ||||
\(736\) | −98.7716 | + | 98.7716i | −0.134201 | + | 0.134201i | ||||
\(737\) | −557.306 | −0.756182 | ||||||||
\(738\) | 36.0082i | 0.0487916i | ||||||||
\(739\) | 831.408 | − | 831.408i | 1.12505 | − | 1.12505i | 0.134074 | − | 0.990971i | \(-0.457194\pi\) |
0.990971 | − | 0.134074i | \(-0.0428059\pi\) | |||||||
\(740\) | 310.438i | 0.419511i | ||||||||
\(741\) | 421.375 | − | 116.734i | 0.568657 | − | 0.157535i | ||||
\(742\) | 27.2057 | 0.0366654 | ||||||||
\(743\) | 198.919 | + | 198.919i | 0.267724 | + | 0.267724i | 0.828182 | − | 0.560459i | \(-0.189375\pi\) |
−0.560459 | + | 0.828182i | \(0.689375\pi\) | |||||||
\(744\) | −90.1612 | −0.121184 | ||||||||
\(745\) | 1219.01i | 1.63625i | ||||||||
\(746\) | 236.635 | + | 236.635i | 0.317205 | + | 0.317205i | ||||
\(747\) | 161.358 | + | 161.358i | 0.216008 | + | 0.216008i | ||||
\(748\) | 319.002 | − | 319.002i | 0.426474 | − | 0.426474i | ||||
\(749\) | 109.227 | − | 109.227i | 0.145830 | − | 0.145830i | ||||
\(750\) | −15.6676 | −0.0208901 | ||||||||
\(751\) | 479.541i | 0.638537i | 0.947664 | + | 0.319268i | \(0.103437\pi\) | ||||
−0.947664 | + | 0.319268i | \(0.896563\pi\) | |||||||
\(752\) | −197.775 | + | 197.775i | −0.262998 | + | 0.262998i | ||||
\(753\) | 298.603i | 0.396551i | ||||||||
\(754\) | −896.254 | + | 248.290i | −1.18867 | + | 0.329297i | ||||
\(755\) | −295.108 | −0.390872 | ||||||||
\(756\) | −30.0819 | − | 30.0819i | −0.0397909 | − | 0.0397909i | ||||
\(757\) | 154.927 | 0.204660 | 0.102330 | − | 0.994751i | \(-0.467370\pi\) | ||||
0.102330 | + | 0.994751i | \(0.467370\pi\) | |||||||
\(758\) | − | 163.932i | − | 0.216269i | ||||||
\(759\) | 636.508 | + | 636.508i | 0.838614 | + | 0.838614i | ||||
\(760\) | −272.104 | − | 272.104i | −0.358031 | − | 0.358031i | ||||
\(761\) | −220.102 | + | 220.102i | −0.289228 | + | 0.289228i | −0.836775 | − | 0.547547i | \(-0.815562\pi\) |
0.547547 | + | 0.836775i | \(0.315562\pi\) | |||||||
\(762\) | 70.4396 | − | 70.4396i | 0.0924404 | − | 0.0924404i | ||||
\(763\) | −581.777 | −0.762486 | ||||||||
\(764\) | − | 443.326i | − | 0.580269i | ||||||
\(765\) | 159.288 | − | 159.288i | 0.208219 | − | 0.208219i | ||||
\(766\) | 628.467i | 0.820453i | ||||||||
\(767\) | 198.218 | + | 715.510i | 0.258433 | + | 0.932868i | ||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | −658.837 | − | 658.837i | −0.856745 | − | 0.856745i | 0.134208 | − | 0.990953i | \(-0.457151\pi\) |
−0.990953 | + | 0.134208i | \(0.957151\pi\) | |||||||
\(770\) | 853.677 | 1.10867 | ||||||||
\(771\) | 236.698i | 0.307002i | ||||||||
\(772\) | −511.158 | − | 511.158i | −0.662121 | − | 0.662121i | ||||
\(773\) | −415.757 | − | 415.757i | −0.537849 | − | 0.537849i | 0.385048 | − | 0.922897i | \(-0.374185\pi\) |
−0.922897 | + | 0.385048i | \(0.874185\pi\) | |||||||
\(774\) | −31.0350 | + | 31.0350i | −0.0400970 | + | 0.0400970i | ||||
\(775\) | 313.461 | − | 313.461i | 0.404465 | − | 0.404465i | ||||
\(776\) | 356.987 | 0.460035 | ||||||||
\(777\) | 157.084i | 0.202167i | ||||||||
\(778\) | 328.370 | − | 328.370i | 0.422069 | − | 0.422069i | ||||
\(779\) | 164.811i | 0.211567i | ||||||||
\(780\) | −84.2343 | − | 304.061i | −0.107993 | − | 0.389822i | ||||
\(781\) | −2260.02 | −2.89375 | ||||||||
\(782\) | −264.645 | − | 264.645i | −0.338421 | − | 0.338421i | ||||
\(783\) | −262.852 | −0.335699 | ||||||||
\(784\) | − | 128.969i | − | 0.164501i | ||||||
\(785\) | 851.350 | + | 851.350i | 1.08452 | + | 1.08452i | ||||
\(786\) | −370.852 | − | 370.852i | −0.471821 | − | 0.471821i | ||||
\(787\) | −550.553 | + | 550.553i | −0.699559 | + | 0.699559i | −0.964315 | − | 0.264756i | \(-0.914708\pi\) |
0.264756 | + | 0.964315i | \(0.414708\pi\) | |||||||
\(788\) | −277.456 | + | 277.456i | −0.352102 | + | 0.352102i | ||||
\(789\) | −420.621 | −0.533107 | ||||||||
\(790\) | − | 185.977i | − | 0.235414i | ||||||
\(791\) | −174.412 | + | 174.412i | −0.220495 | + | 0.220495i | ||||
\(792\) | − | 178.588i | − | 0.225490i | ||||||
\(793\) | 565.713 | − | 999.258i | 0.713383 | − | 1.26010i | ||||
\(794\) | 96.9952 | 0.122160 | ||||||||
\(795\) | 40.3242 | + | 40.3242i | 0.0507223 | + | 0.0507223i | ||||
\(796\) | −517.926 | −0.650660 | ||||||||
\(797\) | − | 542.210i | − | 0.680314i | −0.940369 | − | 0.340157i | \(-0.889520\pi\) | ||
0.940369 | − | 0.340157i | \(-0.110480\pi\) | |||||||
\(798\) | −137.686 | − | 137.686i | −0.172539 | − | 0.172539i | ||||
\(799\) | −529.911 | − | 529.911i | −0.663218 | − | 0.663218i | ||||
\(800\) | −96.3482 | + | 96.3482i | −0.120435 | + | 0.120435i | ||||
\(801\) | −60.3987 | + | 60.3987i | −0.0754042 | + | 0.0754042i | ||||
\(802\) | 353.553 | 0.440839 | ||||||||
\(803\) | 422.744i | 0.526455i | ||||||||
\(804\) | 64.8609 | − | 64.8609i | 0.0806728 | − | 0.0806728i | ||||
\(805\) | − | 708.213i | − | 0.879768i | ||||||
\(806\) | −294.444 | − | 166.694i | −0.365315 | − | 0.206817i | ||||
\(807\) | 462.183 | 0.572717 | ||||||||
\(808\) | 138.162 | + | 138.162i | 0.170993 | + | 0.170993i | ||||
\(809\) | 1593.57 | 1.96980 | 0.984900 | − | 0.173122i | \(-0.0553855\pi\) | ||||
0.984900 | + | 0.173122i | \(0.0553855\pi\) | |||||||
\(810\) | − | 89.1746i | − | 0.110092i | ||||||
\(811\) | 220.059 | + | 220.059i | 0.271342 | + | 0.271342i | 0.829640 | − | 0.558298i | \(-0.188545\pi\) |
−0.558298 | + | 0.829640i | \(0.688545\pi\) | |||||||
\(812\) | 292.855 | + | 292.855i | 0.360659 | + | 0.360659i | ||||
\(813\) | 611.779 | − | 611.779i | 0.752495 | − | 0.752495i | ||||
\(814\) | −466.281 | + | 466.281i | −0.572827 | + | 0.572827i | ||||
\(815\) | −1636.38 | −2.00783 | ||||||||
\(816\) | 74.2528i | 0.0909961i | ||||||||
\(817\) | −142.049 | + | 142.049i | −0.173866 | + | 0.173866i | ||||
\(818\) | 275.450i | 0.336735i | ||||||||
\(819\) | −42.6231 | − | 153.857i | −0.0520428 | − | 0.187859i | ||||
\(820\) | 118.926 | 0.145032 | ||||||||
\(821\) | −218.126 | − | 218.126i | −0.265684 | − | 0.265684i | 0.561675 | − | 0.827358i | \(-0.310157\pi\) |
−0.827358 | + | 0.561675i | \(0.810157\pi\) | |||||||
\(822\) | 410.364 | 0.499226 | ||||||||
\(823\) | 513.628i | 0.624092i | 0.950067 | + | 0.312046i | \(0.101014\pi\) | ||||
−0.950067 | + | 0.312046i | \(0.898986\pi\) | |||||||
\(824\) | 194.528 | + | 194.528i | 0.236078 | + | 0.236078i | ||||
\(825\) | 620.892 | + | 620.892i | 0.752596 | + | 0.752596i | ||||
\(826\) | 233.796 | − | 233.796i | 0.283046 | − | 0.283046i | ||||
\(827\) | 380.987 | − | 380.987i | 0.460686 | − | 0.460686i | −0.438195 | − | 0.898880i | \(-0.644382\pi\) |
0.898880 | + | 0.438195i | \(0.144382\pi\) | |||||||
\(828\) | −148.157 | −0.178934 | ||||||||
\(829\) | 1083.19i | 1.30662i | 0.757089 | + | 0.653312i | \(0.226621\pi\) | ||||
−0.757089 | + | 0.653312i | \(0.773379\pi\) | |||||||
\(830\) | 532.927 | − | 532.927i | 0.642080 | − | 0.642080i | ||||
\(831\) | 551.647i | 0.663835i | ||||||||
\(832\) | 90.5030 | + | 51.2367i | 0.108778 | + | 0.0615826i | ||||
\(833\) | 345.555 | 0.414832 | ||||||||
\(834\) | 94.7103 | + | 94.7103i | 0.113561 | + | 0.113561i | ||||
\(835\) | 650.198 | 0.778680 | ||||||||
\(836\) | − | 817.405i | − | 0.977757i | ||||||
\(837\) | −67.6209 | − | 67.6209i | −0.0807896 | − | 0.0807896i | ||||
\(838\) | 54.8057 | + | 54.8057i | 0.0654006 | + | 0.0654006i | ||||
\(839\) | 564.487 | − | 564.487i | 0.672810 | − | 0.672810i | −0.285553 | − | 0.958363i | \(-0.592177\pi\) |
0.958363 | + | 0.285553i | \(0.0921773\pi\) | |||||||
\(840\) | −99.3534 | + | 99.3534i | −0.118278 | + | 0.118278i | ||||
\(841\) | 1717.94 | 2.04273 | ||||||||
\(842\) | 799.097i | 0.949046i | ||||||||
\(843\) | 107.601 | − | 107.601i | 0.127641 | − | 0.127641i | ||||
\(844\) | − | 440.907i | − | 0.522402i | ||||||
\(845\) | 287.074 | − | 1148.72i | 0.339733 | − | 1.35944i | ||||
\(846\) | −296.662 | −0.350664 | ||||||||
\(847\) | 931.981 | + | 931.981i | 1.10033 | + | 1.10033i | ||||
\(848\) | −18.7974 | −0.0221667 | ||||||||
\(849\) | − | 172.384i | − | 0.203044i | ||||||
\(850\) | −258.152 | − | 258.152i | −0.303709 | − | 0.303709i | ||||
\(851\) | 386.829 | + | 386.829i | 0.454558 | + | 0.454558i | ||||
\(852\) | 263.028 | − | 263.028i | 0.308718 | − | 0.308718i | ||||
\(853\) | −78.1611 | + | 78.1611i | −0.0916309 | + | 0.0916309i | −0.751436 | − | 0.659806i | \(-0.770639\pi\) |
0.659806 | + | 0.751436i | \(0.270639\pi\) | |||||||
\(854\) | −511.362 | −0.598784 | ||||||||
\(855\) | − | 408.156i | − | 0.477375i | ||||||
\(856\) | −75.4683 | + | 75.4683i | −0.0881639 | + | 0.0881639i | ||||
\(857\) | 640.540i | 0.747422i | 0.927545 | + | 0.373711i | \(0.121915\pi\) | ||||
−0.927545 | + | 0.373711i | \(0.878085\pi\) | |||||||
\(858\) | 330.182 | − | 583.224i | 0.384828 | − | 0.679748i | ||||
\(859\) | −631.942 | −0.735671 | −0.367836 | − | 0.929891i | \(-0.619901\pi\) | ||||
−0.367836 | + | 0.929891i | \(0.619901\pi\) | |||||||
\(860\) | 102.501 | + | 102.501i | 0.119188 | + | 0.119188i | ||||
\(861\) | 60.1775 | 0.0698926 | ||||||||
\(862\) | − | 533.937i | − | 0.619416i | ||||||
\(863\) | −838.507 | − | 838.507i | −0.971619 | − | 0.971619i | 0.0279890 | − | 0.999608i | \(-0.491090\pi\) |
−0.999608 | + | 0.0279890i | \(0.991090\pi\) | |||||||
\(864\) | 20.7846 | + | 20.7846i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 1072.87 | − | 1072.87i | 1.24031 | − | 1.24031i | ||||
\(866\) | 783.673 | − | 783.673i | 0.904934 | − | 0.904934i | ||||
\(867\) | 301.612 | 0.347880 | ||||||||
\(868\) | 150.679i | 0.173593i | ||||||||
\(869\) | 279.339 | − | 279.339i | 0.321449 | − | 0.321449i | ||||
\(870\) | 868.138i | 0.997860i | ||||||||
\(871\) | 331.737 | − | 91.9014i | 0.380869 | − | 0.105513i | ||||
\(872\) | 401.969 | 0.460974 | ||||||||
\(873\) | 267.741 | + | 267.741i | 0.306690 | + | 0.306690i | ||||
\(874\) | −678.122 | −0.775884 | ||||||||
\(875\) | 26.1840i | 0.0299245i | ||||||||
\(876\) | −49.2001 | − | 49.2001i | −0.0561645 | − | 0.0561645i | ||||
\(877\) | 70.3069 | + | 70.3069i | 0.0801675 | + | 0.0801675i | 0.746054 | − | 0.665886i | \(-0.231946\pi\) |
−0.665886 | + | 0.746054i | \(0.731946\pi\) | |||||||
\(878\) | −411.297 | + | 411.297i | −0.468447 | + | 0.468447i | ||||
\(879\) | −18.0153 | + | 18.0153i | −0.0204952 | + | 0.0204952i | ||||
\(880\) | −589.834 | −0.670266 | ||||||||
\(881\) | 824.918i | 0.936343i | 0.883638 | + | 0.468171i | \(0.155087\pi\) | ||||
−0.883638 | + | 0.468171i | \(0.844913\pi\) | |||||||
\(882\) | 96.7266 | − | 96.7266i | 0.109667 | − | 0.109667i | ||||
\(883\) | 1624.86i | 1.84016i | 0.391726 | + | 0.920082i | \(0.371878\pi\) | ||||
−0.391726 | + | 0.920082i | \(0.628122\pi\) | |||||||
\(884\) | −137.282 | + | 242.491i | −0.155296 | + | 0.274311i | ||||
\(885\) | 693.064 | 0.783123 | ||||||||
\(886\) | −166.429 | − | 166.429i | −0.187843 | − | 0.187843i | ||||
\(887\) | −494.247 | −0.557212 | −0.278606 | − | 0.960406i | \(-0.589872\pi\) | ||||
−0.278606 | + | 0.960406i | \(0.589872\pi\) | |||||||
\(888\) | − | 108.534i | − | 0.122223i | ||||||
\(889\) | −117.720 | − | 117.720i | −0.132418 | − | 0.132418i | ||||
\(890\) | 199.483 | + | 199.483i | 0.224138 | + | 0.224138i | ||||
\(891\) | 133.941 | − | 133.941i | 0.150327 | − | 0.150327i | ||||
\(892\) | 327.529 | − | 327.529i | 0.367185 | − | 0.367185i | ||||
\(893\) | −1357.83 | −1.52053 | ||||||||
\(894\) | − | 426.185i | − | 0.476717i | ||||||
\(895\) | −109.550 | + | 109.550i | −0.122402 | + | 0.122402i | ||||
\(896\) | − | 46.3141i | − | 0.0516899i | ||||||
\(897\) | −483.844 | − | 273.920i | −0.539403 | − | 0.305374i | ||||
\(898\) | −560.033 | −0.623645 | ||||||||
\(899\) | 658.308 | + | 658.308i | 0.732266 | + | 0.732266i | ||||
\(900\) | −144.522 | −0.160580 | ||||||||
\(901\) | − | 50.3650i | − | 0.0558990i | ||||||
\(902\) | 178.629 | + | 178.629i | 0.198036 | + | 0.198036i | ||||
\(903\) | 51.8663 | + | 51.8663i | 0.0574378 | + | 0.0574378i | ||||
\(904\) | 120.507 | − | 120.507i | 0.133304 | − | 0.133304i | ||||
\(905\) | −205.715 | + | 205.715i | −0.227310 | + | 0.227310i | ||||
\(906\) | 103.175 | 0.113879 | ||||||||
\(907\) | 553.094i | 0.609806i | 0.952383 | + | 0.304903i | \(0.0986240\pi\) | ||||
−0.952383 | + | 0.304903i | \(0.901376\pi\) | |||||||
\(908\) | −226.154 | + | 226.154i | −0.249068 | + | 0.249068i | ||||
\(909\) | 207.243i | 0.227990i | ||||||||
\(910\) | −508.152 | + | 140.774i | −0.558409 | + | 0.154696i | ||||
\(911\) | 991.642 | 1.08852 | 0.544260 | − | 0.838917i | \(-0.316810\pi\) | ||||
0.544260 | + | 0.838917i | \(0.316810\pi\) | |||||||
\(912\) | 95.1320 | + | 95.1320i | 0.104311 | + | 0.104311i | ||||
\(913\) | 1600.92 | 1.75348 | ||||||||
\(914\) | 784.912i | 0.858766i | ||||||||
\(915\) | −757.938 | − | 757.938i | −0.828348 | − | 0.828348i | ||||
\(916\) | 69.6617 | + | 69.6617i | 0.0760499 | + | 0.0760499i | ||||
\(917\) | −619.773 | + | 619.773i | −0.675871 | + | 0.675871i | ||||
\(918\) | −55.6896 | + | 55.6896i | −0.0606641 | + | 0.0606641i | ||||
\(919\) | 91.7872 | 0.0998773 | 0.0499386 | − | 0.998752i | \(-0.484097\pi\) | ||||
0.0499386 | + | 0.998752i | \(0.484097\pi\) | |||||||
\(920\) | 489.328i | 0.531879i | ||||||||
\(921\) | −533.866 | + | 533.866i | −0.579659 | + | 0.579659i | ||||
\(922\) | − | 948.369i | − | 1.02860i | ||||||
\(923\) | 1345.28 | − | 372.684i | 1.45751 | − | 0.403775i | ||||
\(924\) | −298.460 | −0.323008 | ||||||||
\(925\) | 377.338 | + | 377.338i | 0.407933 | + | 0.407933i | ||||
\(926\) | 436.533 | 0.471418 | ||||||||
\(927\) | 291.792i | 0.314770i | ||||||||
\(928\) | −202.344 | − | 202.344i | −0.218043 | − | 0.218043i | ||||
\(929\) | 343.654 | + | 343.654i | 0.369919 | + | 0.369919i | 0.867447 | − | 0.497529i | \(-0.165759\pi\) |
−0.497529 | + | 0.867447i | \(0.665759\pi\) | |||||||
\(930\) | −223.336 | + | 223.336i | −0.240146 | + | 0.240146i | ||||
\(931\) | 442.722 | − | 442.722i | 0.475533 | − | 0.475533i | ||||
\(932\) | 444.100 | 0.476502 | ||||||||
\(933\) | − | 89.4151i | − | 0.0958361i | ||||||
\(934\) | −170.592 | + | 170.592i | −0.182646 | + | 0.182646i | ||||
\(935\) | − | 1580.38i | − | 1.69025i | ||||||
\(936\) | 29.4497 | + | 106.305i | 0.0314634 | + | 0.113574i | ||||
\(937\) | −1140.31 | −1.21698 | −0.608488 | − | 0.793563i | \(-0.708223\pi\) | ||||
−0.608488 | + | 0.793563i | \(0.708223\pi\) | |||||||
\(938\) | −108.397 | − | 108.397i | −0.115562 | − | 0.115562i | ||||
\(939\) | 326.013 | 0.347192 | ||||||||
\(940\) | 979.804i | 1.04235i | ||||||||
\(941\) | −221.565 | − | 221.565i | −0.235457 | − | 0.235457i | 0.579509 | − | 0.814966i | \(-0.303244\pi\) |
−0.814966 | + | 0.579509i | \(0.803244\pi\) | |||||||
\(942\) | −297.646 | − | 297.646i | −0.315973 | − | 0.315973i | ||||
\(943\) | 148.191 | − | 148.191i | 0.157149 | − | 0.157149i | ||||
\(944\) | −161.538 | + | 161.538i | −0.171120 | + | 0.171120i | ||||
\(945\) | −149.030 | −0.157704 | ||||||||
\(946\) | 307.916i | 0.325493i | ||||||||
\(947\) | 169.150 | − | 169.150i | 0.178617 | − | 0.178617i | −0.612136 | − | 0.790753i | \(-0.709689\pi\) |
0.790753 | + | 0.612136i | \(0.209689\pi\) | |||||||
\(948\) | 65.0206i | 0.0685872i | ||||||||
\(949\) | −69.7117 | − | 251.639i | −0.0734580 | − | 0.265162i | ||||
\(950\) | −661.485 | −0.696300 | ||||||||
\(951\) | −267.978 | − | 267.978i | −0.281786 | − | 0.281786i | ||||
\(952\) | 124.093 | 0.130349 | ||||||||
\(953\) | 580.946i | 0.609598i | 0.952417 | + | 0.304799i | \(0.0985892\pi\) | ||||
−0.952417 | + | 0.304799i | \(0.901411\pi\) | |||||||
\(954\) | −14.0980 | − | 14.0980i | −0.0147778 | − | 0.0147778i | ||||
\(955\) | −1098.15 | − | 1098.15i | −1.14989 | − | 1.14989i | ||||
\(956\) | 539.656 | − | 539.656i | 0.564493 | − | 0.564493i | ||||
\(957\) | −1303.95 | + | 1303.95i | −1.36254 | + | 1.36254i | ||||
\(958\) | 81.1374 | 0.0846946 | ||||||||
\(959\) | − | 685.807i | − | 0.715127i | ||||||
\(960\) | 68.6466 | − | 68.6466i | 0.0715069 | − | 0.0715069i | ||||
\(961\) | − | 622.290i | − | 0.647544i | ||||||
\(962\) | 200.663 | − | 354.446i | 0.208590 | − | 0.368447i | ||||
\(963\) | −113.203 | −0.117552 | ||||||||
\(964\) | 562.349 | + | 562.349i | 0.583350 | + | 0.583350i | ||||
\(965\) | −2532.35 | −2.62419 | ||||||||
\(966\) | 247.603i | 0.256318i | ||||||||
\(967\) | 191.274 | + | 191.274i | 0.197802 | + | 0.197802i | 0.799057 | − | 0.601255i | \(-0.205332\pi\) |
−0.601255 | + | 0.799057i | \(0.705332\pi\) | |||||||
\(968\) | −643.937 | − | 643.937i | −0.665224 | − | 0.665224i | ||||
\(969\) | −254.894 | + | 254.894i | −0.263048 | + | 0.263048i | ||||
\(970\) | 884.283 | − | 884.283i | 0.911632 | − | 0.911632i | ||||
\(971\) | 1344.57 | 1.38473 | 0.692364 | − | 0.721549i | \(-0.256569\pi\) | ||||
0.692364 | + | 0.721549i | \(0.256569\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 158.281 | − | 158.281i | 0.162674 | − | 0.162674i | ||||
\(974\) | 225.383i | 0.231399i | ||||||||
\(975\) | −471.973 | − | 267.200i | −0.484075 | − | 0.274051i | ||||
\(976\) | 353.317 | 0.362005 | ||||||||
\(977\) | −1006.88 | − | 1006.88i | −1.03058 | − | 1.03058i | −0.999517 | − | 0.0310628i | \(-0.990111\pi\) |
−0.0310628 | − | 0.999517i | \(-0.509889\pi\) | |||||||
\(978\) | 572.107 | 0.584976 | ||||||||
\(979\) | 599.250i | 0.612104i | ||||||||
\(980\) | −319.465 | − | 319.465i | −0.325985 | − | 0.325985i | ||||
\(981\) | 301.477 | + | 301.477i | 0.307316 | + | 0.307316i | ||||
\(982\) | 400.234 | − | 400.234i | 0.407570 | − | 0.407570i | ||||
\(983\) | 541.766 | − | 541.766i | 0.551135 | − | 0.551135i | −0.375633 | − | 0.926768i | \(-0.622575\pi\) |
0.926768 | + | 0.375633i | \(0.122575\pi\) | |||||||
\(984\) | −41.5787 | −0.0422547 | ||||||||
\(985\) | 1374.56i | 1.39549i | ||||||||
\(986\) | 542.153 | − | 542.153i | 0.549851 | − | 0.549851i | ||||
\(987\) | 495.787i | 0.502317i | ||||||||
\(988\) | 134.793 | + | 486.561i | 0.136430 | + | 0.492471i | ||||
\(989\) | 255.448 | 0.258290 | ||||||||
\(990\) | −442.376 | − | 442.376i | −0.446844 | − | 0.446844i | ||||
\(991\) | −976.262 | −0.985128 | −0.492564 | − | 0.870276i | \(-0.663940\pi\) | ||||
−0.492564 | + | 0.870276i | \(0.663940\pi\) | |||||||
\(992\) | − | 104.109i | − | 0.104949i | ||||||
\(993\) | 195.255 | + | 195.255i | 0.196631 | + | 0.196631i | ||||
\(994\) | −439.577 | − | 439.577i | −0.442230 | − | 0.442230i | ||||
\(995\) | −1282.94 | + | 1282.94i | −1.28939 | + | 1.28939i | ||||
\(996\) | −186.320 | + | 186.320i | −0.187068 | + | 0.187068i | ||||
\(997\) | 859.899 | 0.862487 | 0.431243 | − | 0.902236i | \(-0.358075\pi\) | ||||
0.431243 | + | 0.902236i | \(0.358075\pi\) | |||||||
\(998\) | − | 791.501i | − | 0.793087i | ||||||
\(999\) | 81.4008 | − | 81.4008i | 0.0814823 | − | 0.0814823i |
(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 | 78.3.f.b.73.4 | yes | 8 | |
3.2 | odd | 2 | 234.3.i.e.73.1 | 8 | |||
4.3 | odd | 2 | 624.3.ba.c.385.2 | 8 | |||
13.5 | odd | 4 | inner | 78.3.f.b.31.4 | ✓ | 8 | |
13.8 | odd | 4 | 1014.3.f.i.577.3 | 8 | |||
13.12 | even | 2 | 1014.3.f.i.775.3 | 8 | |||
39.5 | even | 4 | 234.3.i.e.109.1 | 8 | |||
52.31 | even | 4 | 624.3.ba.c.577.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.f.b.31.4 | ✓ | 8 | 13.5 | odd | 4 | inner | |
78.3.f.b.73.4 | yes | 8 | 1.1 | even | 1 | trivial | |
234.3.i.e.73.1 | 8 | 3.2 | odd | 2 | |||
234.3.i.e.109.1 | 8 | 39.5 | even | 4 | |||
624.3.ba.c.385.2 | 8 | 4.3 | odd | 2 | |||
624.3.ba.c.577.2 | 8 | 52.31 | even | 4 | |||
1014.3.f.i.577.3 | 8 | 13.8 | odd | 4 | |||
1014.3.f.i.775.3 | 8 | 13.12 | even | 2 |