Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (of order \(2\), degree \(1\), 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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.2 | ||
Root | \(-1.92254 - 0.551226i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.3.b.b.39.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92254 | + | 0.551226i | −0.961269 | + | 0.275613i | ||||
\(3\) | − | 0.644704i | − | 0.214901i | −0.994210 | − | 0.107451i | \(-0.965731\pi\) | ||
0.994210 | − | 0.107451i | \(-0.0342688\pi\) | |||||||
\(4\) | 3.39230 | − | 2.11950i | 0.848075 | − | 0.529876i | ||||
\(5\) | −2.32715 | −0.465431 | −0.232715 | − | 0.972545i | \(-0.574761\pi\) | ||||
−0.232715 | + | 0.972545i | \(0.574761\pi\) | |||||||
\(6\) | 0.355377 | + | 1.23947i | 0.0592296 | + | 0.206578i | ||||
\(7\) | − | 8.62924i | − | 1.23275i | −0.787453 | − | 0.616374i | \(-0.788601\pi\) | ||
0.787453 | − | 0.616374i | \(-0.211399\pi\) | |||||||
\(8\) | −5.35350 | + | 5.94475i | −0.669187 | + | 0.743094i | ||||
\(9\) | 8.58436 | 0.953817 | ||||||||
\(10\) | 4.47404 | − | 1.28279i | 0.447404 | − | 0.128279i | ||||
\(11\) | − | 19.2717i | − | 1.75197i | −0.482334 | − | 0.875987i | \(-0.660211\pi\) | ||
0.482334 | − | 0.875987i | \(-0.339789\pi\) | |||||||
\(12\) | −1.36645 | − | 2.18703i | −0.113871 | − | 0.182252i | ||||
\(13\) | 13.8067 | 1.06205 | 0.531025 | − | 0.847356i | \(-0.321807\pi\) | ||||
0.531025 | + | 0.847356i | \(0.321807\pi\) | |||||||
\(14\) | 4.75666 | + | 16.5900i | 0.339761 | + | 1.18500i | ||||
\(15\) | 1.50032i | 0.100022i | ||||||||
\(16\) | 7.01540 | − | 14.3800i | 0.438463 | − | 0.898749i | ||||
\(17\) | −12.5180 | −0.736353 | −0.368177 | − | 0.929756i | \(-0.620018\pi\) | ||||
−0.368177 | + | 0.929756i | \(0.620018\pi\) | |||||||
\(18\) | −16.5037 | + | 4.73192i | −0.916875 | + | 0.262884i | ||||
\(19\) | − | 4.35890i | − | 0.229416i | ||||||
\(20\) | −7.89440 | + | 4.93241i | −0.394720 | + | 0.246621i | ||||
\(21\) | −5.56330 | −0.264919 | ||||||||
\(22\) | 10.6231 | + | 37.0506i | 0.482867 | + | 1.68412i | ||||
\(23\) | 37.4981i | 1.63035i | 0.579214 | + | 0.815175i | \(0.303360\pi\) | ||||
−0.579214 | + | 0.815175i | \(0.696640\pi\) | |||||||
\(24\) | 3.83260 | + | 3.45142i | 0.159692 | + | 0.143809i | ||||
\(25\) | −19.5844 | −0.783374 | ||||||||
\(26\) | −26.5438 | + | 7.61058i | −1.02092 | + | 0.292715i | ||||
\(27\) | − | 11.3367i | − | 0.419878i | ||||||
\(28\) | −18.2897 | − | 29.2730i | −0.653204 | − | 1.04546i | ||||
\(29\) | −6.36930 | −0.219631 | −0.109816 | − | 0.993952i | \(-0.535026\pi\) | ||||
−0.109816 | + | 0.993952i | \(0.535026\pi\) | |||||||
\(30\) | −0.827018 | − | 2.88443i | −0.0275673 | − | 0.0961477i | ||||
\(31\) | 5.44851i | 0.175758i | 0.996131 | + | 0.0878791i | \(0.0280089\pi\) | ||||
−0.996131 | + | 0.0878791i | \(0.971991\pi\) | |||||||
\(32\) | −5.56075 | + | 31.5131i | −0.173774 | + | 0.984786i | ||||
\(33\) | −12.4245 | −0.376502 | ||||||||
\(34\) | 24.0663 | − | 6.90025i | 0.707833 | − | 0.202948i | ||||
\(35\) | 20.0816i | 0.573759i | ||||||||
\(36\) | 29.1207 | − | 18.1946i | 0.808909 | − | 0.505405i | ||||
\(37\) | 20.9250 | 0.565542 | 0.282771 | − | 0.959187i | \(-0.408746\pi\) | ||||
0.282771 | + | 0.959187i | \(0.408746\pi\) | |||||||
\(38\) | 2.40274 | + | 8.38015i | 0.0632299 | + | 0.220530i | ||||
\(39\) | − | 8.90120i | − | 0.228236i | ||||||
\(40\) | 12.4584 | − | 13.8343i | 0.311460 | − | 0.345859i | ||||
\(41\) | 72.8337 | 1.77643 | 0.888216 | − | 0.459425i | \(-0.151945\pi\) | ||||
0.888216 | + | 0.459425i | \(0.151945\pi\) | |||||||
\(42\) | 10.6957 | − | 3.06664i | 0.254659 | − | 0.0730152i | ||||
\(43\) | − | 10.1553i | − | 0.236171i | −0.993003 | − | 0.118085i | \(-0.962324\pi\) | ||
0.993003 | − | 0.118085i | \(-0.0376757\pi\) | |||||||
\(44\) | −40.8465 | − | 65.3755i | −0.928329 | − | 1.48581i | ||||
\(45\) | −19.9771 | −0.443936 | ||||||||
\(46\) | −20.6699 | − | 72.0914i | −0.449346 | − | 1.56721i | ||||
\(47\) | 32.4450i | 0.690318i | 0.938544 | + | 0.345159i | \(0.112175\pi\) | ||||
−0.938544 | + | 0.345159i | \(0.887825\pi\) | |||||||
\(48\) | −9.27083 | − | 4.52286i | −0.193142 | − | 0.0942262i | ||||
\(49\) | −25.4638 | −0.519669 | ||||||||
\(50\) | 37.6517 | − | 10.7954i | 0.753033 | − | 0.215908i | ||||
\(51\) | 8.07040i | 0.158243i | ||||||||
\(52\) | 46.8363 | − | 29.2633i | 0.900698 | − | 0.562755i | ||||
\(53\) | −42.9339 | −0.810074 | −0.405037 | − | 0.914300i | \(-0.632741\pi\) | ||||
−0.405037 | + | 0.914300i | \(0.632741\pi\) | |||||||
\(54\) | 6.24908 | + | 21.7952i | 0.115724 | + | 0.403615i | ||||
\(55\) | 44.8482i | 0.815423i | ||||||||
\(56\) | 51.2987 | + | 46.1966i | 0.916048 | + | 0.824940i | ||||
\(57\) | −2.81020 | −0.0493017 | ||||||||
\(58\) | 12.2452 | − | 3.51092i | 0.211125 | − | 0.0605332i | ||||
\(59\) | − | 38.9728i | − | 0.660556i | −0.943884 | − | 0.330278i | \(-0.892858\pi\) | ||
0.943884 | − | 0.330278i | \(-0.107142\pi\) | |||||||
\(60\) | 3.17994 | + | 5.08955i | 0.0529991 | + | 0.0848258i | ||||
\(61\) | 25.5611 | 0.419034 | 0.209517 | − | 0.977805i | \(-0.432811\pi\) | ||||
0.209517 | + | 0.977805i | \(0.432811\pi\) | |||||||
\(62\) | −3.00336 | − | 10.4750i | −0.0484412 | − | 0.168951i | ||||
\(63\) | − | 74.0765i | − | 1.17582i | ||||||
\(64\) | −6.68010 | − | 63.6504i | −0.104377 | − | 0.994538i | ||||
\(65\) | −32.1302 | −0.494311 | ||||||||
\(66\) | 23.8867 | − | 6.84873i | 0.361919 | − | 0.103769i | ||||
\(67\) | 65.3183i | 0.974900i | 0.873151 | + | 0.487450i | \(0.162073\pi\) | ||||
−0.873151 | + | 0.487450i | \(0.837927\pi\) | |||||||
\(68\) | −42.4648 | + | 26.5320i | −0.624483 | + | 0.390176i | ||||
\(69\) | 24.1751 | 0.350364 | ||||||||
\(70\) | −11.0695 | − | 38.6076i | −0.158135 | − | 0.551537i | ||||
\(71\) | 18.7557i | 0.264165i | 0.991239 | + | 0.132083i | \(0.0421665\pi\) | ||||
−0.991239 | + | 0.132083i | \(0.957834\pi\) | |||||||
\(72\) | −45.9563 | + | 51.0319i | −0.638283 | + | 0.708776i | ||||
\(73\) | 72.8251 | 0.997604 | 0.498802 | − | 0.866716i | \(-0.333773\pi\) | ||||
0.498802 | + | 0.866716i | \(0.333773\pi\) | |||||||
\(74\) | −40.2292 | + | 11.5344i | −0.543638 | + | 0.155871i | ||||
\(75\) | 12.6261i | 0.168348i | ||||||||
\(76\) | −9.23871 | − | 14.7867i | −0.121562 | − | 0.194562i | ||||
\(77\) | −166.300 | −2.15974 | ||||||||
\(78\) | 4.90657 | + | 17.1129i | 0.0629048 | + | 0.219396i | ||||
\(79\) | 139.874i | 1.77056i | 0.465060 | + | 0.885279i | \(0.346033\pi\) | ||||
−0.465060 | + | 0.885279i | \(0.653967\pi\) | |||||||
\(80\) | −16.3259 | + | 33.4644i | −0.204074 | + | 0.418306i | ||||
\(81\) | 69.9504 | 0.863585 | ||||||||
\(82\) | −140.026 | + | 40.1478i | −1.70763 | + | 0.489608i | ||||
\(83\) | − | 94.7116i | − | 1.14110i | −0.821262 | − | 0.570552i | \(-0.806729\pi\) | ||
0.821262 | − | 0.570552i | \(-0.193271\pi\) | |||||||
\(84\) | −18.8724 | + | 11.7914i | −0.224671 | + | 0.140374i | ||||
\(85\) | 29.1313 | 0.342721 | ||||||||
\(86\) | 5.59789 | + | 19.5240i | 0.0650917 | + | 0.227024i | ||||
\(87\) | 4.10631i | 0.0471990i | ||||||||
\(88\) | 114.566 | + | 103.171i | 1.30188 | + | 1.17240i | ||||
\(89\) | 33.3546 | 0.374770 | 0.187385 | − | 0.982287i | \(-0.439999\pi\) | ||||
0.187385 | + | 0.982287i | \(0.439999\pi\) | |||||||
\(90\) | 38.4068 | − | 11.0119i | 0.426742 | − | 0.122354i | ||||
\(91\) | − | 119.141i | − | 1.30924i | ||||||
\(92\) | 79.4773 | + | 127.205i | 0.863884 | + | 1.38266i | ||||
\(93\) | 3.51267 | 0.0377707 | ||||||||
\(94\) | −17.8845 | − | 62.3766i | −0.190261 | − | 0.663581i | ||||
\(95\) | 10.1438i | 0.106777i | ||||||||
\(96\) | 20.3166 | + | 3.58504i | 0.211632 | + | 0.0373441i | ||||
\(97\) | −150.817 | −1.55482 | −0.777408 | − | 0.628996i | \(-0.783466\pi\) | ||||
−0.777408 | + | 0.628996i | \(0.783466\pi\) | |||||||
\(98\) | 48.9551 | − | 14.0363i | 0.499542 | − | 0.143228i | ||||
\(99\) | − | 165.435i | − | 1.67106i | ||||||
\(100\) | −66.4360 | + | 41.5091i | −0.664360 | + | 0.415091i | ||||
\(101\) | 77.7745 | 0.770045 | 0.385022 | − | 0.922907i | \(-0.374194\pi\) | ||||
0.385022 | + | 0.922907i | \(0.374194\pi\) | |||||||
\(102\) | −4.44862 | − | 15.5157i | −0.0436139 | − | 0.152114i | ||||
\(103\) | 14.9481i | 0.145127i | 0.997364 | + | 0.0725637i | \(0.0231180\pi\) | ||||
−0.997364 | + | 0.0725637i | \(0.976882\pi\) | |||||||
\(104\) | −73.9139 | + | 82.0771i | −0.710711 | + | 0.789203i | ||||
\(105\) | 12.9467 | 0.123302 | ||||||||
\(106\) | 82.5420 | − | 23.6663i | 0.778698 | − | 0.223267i | ||||
\(107\) | 80.5205i | 0.752528i | 0.926512 | + | 0.376264i | \(0.122792\pi\) | ||||
−0.926512 | + | 0.376264i | \(0.877208\pi\) | |||||||
\(108\) | −24.0282 | − | 38.4575i | −0.222483 | − | 0.356088i | ||||
\(109\) | 53.8512 | 0.494048 | 0.247024 | − | 0.969009i | \(-0.420547\pi\) | ||||
0.247024 | + | 0.969009i | \(0.420547\pi\) | |||||||
\(110\) | −24.7215 | − | 86.2224i | −0.224741 | − | 0.783840i | ||||
\(111\) | − | 13.4905i | − | 0.121536i | ||||||
\(112\) | −124.088 | − | 60.5376i | −1.10793 | − | 0.540514i | ||||
\(113\) | 105.921 | 0.937355 | 0.468677 | − | 0.883369i | \(-0.344731\pi\) | ||||
0.468677 | + | 0.883369i | \(0.344731\pi\) | |||||||
\(114\) | 5.40271 | − | 1.54905i | 0.0473922 | − | 0.0135882i | ||||
\(115\) | − | 87.2638i | − | 0.758815i | ||||||
\(116\) | −21.6066 | + | 13.4998i | −0.186264 | + | 0.116377i | ||||
\(117\) | 118.521 | 1.01300 | ||||||||
\(118\) | 21.4828 | + | 74.9266i | 0.182058 | + | 0.634972i | ||||
\(119\) | 108.021i | 0.907739i | ||||||||
\(120\) | −8.91905 | − | 8.03199i | −0.0743254 | − | 0.0669332i | ||||
\(121\) | −250.399 | −2.06941 | ||||||||
\(122\) | −49.1421 | + | 14.0899i | −0.402804 | + | 0.115491i | ||||
\(123\) | − | 46.9562i | − | 0.381758i | ||||||
\(124\) | 11.5481 | + | 18.4830i | 0.0931301 | + | 0.149056i | ||||
\(125\) | 103.755 | 0.830037 | ||||||||
\(126\) | 40.8329 | + | 142.415i | 0.324070 | + | 1.13028i | ||||
\(127\) | − | 17.1409i | − | 0.134968i | −0.997720 | − | 0.0674839i | \(-0.978503\pi\) | ||
0.997720 | − | 0.0674839i | \(-0.0214971\pi\) | |||||||
\(128\) | 47.9285 | + | 118.688i | 0.374441 | + | 0.927251i | ||||
\(129\) | −6.54719 | −0.0507534 | ||||||||
\(130\) | 61.7715 | − | 17.7110i | 0.475166 | − | 0.136238i | ||||
\(131\) | − | 229.336i | − | 1.75066i | −0.483526 | − | 0.875330i | \(-0.660644\pi\) | ||
0.483526 | − | 0.875330i | \(-0.339356\pi\) | |||||||
\(132\) | −42.1478 | + | 26.3339i | −0.319302 | + | 0.199499i | ||||
\(133\) | −37.6140 | −0.282812 | ||||||||
\(134\) | −36.0051 | − | 125.577i | −0.268695 | − | 0.937141i | ||||
\(135\) | 26.3822i | 0.195424i | ||||||||
\(136\) | 67.0151 | − | 74.4164i | 0.492758 | − | 0.547179i | ||||
\(137\) | −120.567 | −0.880054 | −0.440027 | − | 0.897985i | \(-0.645031\pi\) | ||||
−0.440027 | + | 0.897985i | \(0.645031\pi\) | |||||||
\(138\) | −46.4776 | + | 13.3260i | −0.336794 | + | 0.0965650i | ||||
\(139\) | 145.864i | 1.04938i | 0.851292 | + | 0.524692i | \(0.175819\pi\) | ||||
−0.851292 | + | 0.524692i | \(0.824181\pi\) | |||||||
\(140\) | 42.5630 | + | 68.1227i | 0.304021 | + | 0.486591i | ||||
\(141\) | 20.9174 | 0.148350 | ||||||||
\(142\) | −10.3387 | − | 36.0586i | −0.0728074 | − | 0.253934i | ||||
\(143\) | − | 266.078i | − | 1.86069i | ||||||
\(144\) | 60.2227 | − | 123.443i | 0.418213 | − | 0.857243i | ||||
\(145\) | 14.8223 | 0.102223 | ||||||||
\(146\) | −140.009 | + | 40.1431i | −0.958966 | + | 0.274953i | ||||
\(147\) | 16.4166i | 0.111678i | ||||||||
\(148\) | 70.9840 | − | 44.3507i | 0.479622 | − | 0.299667i | ||||
\(149\) | 19.2547 | 0.129226 | 0.0646132 | − | 0.997910i | \(-0.479419\pi\) | ||||
0.0646132 | + | 0.997910i | \(0.479419\pi\) | |||||||
\(150\) | −6.95984 | − | 24.2742i | −0.0463989 | − | 0.161828i | ||||
\(151\) | 165.526i | 1.09620i | 0.836414 | + | 0.548099i | \(0.184648\pi\) | ||||
−0.836414 | + | 0.548099i | \(0.815352\pi\) | |||||||
\(152\) | 25.9126 | + | 23.3354i | 0.170477 | + | 0.153522i | ||||
\(153\) | −107.459 | −0.702347 | ||||||||
\(154\) | 319.719 | − | 91.6690i | 2.07609 | − | 0.595253i | ||||
\(155\) | − | 12.6795i | − | 0.0818033i | ||||||
\(156\) | −18.8661 | − | 30.1956i | −0.120937 | − | 0.193561i | ||||
\(157\) | 149.449 | 0.951907 | 0.475954 | − | 0.879470i | \(-0.342103\pi\) | ||||
0.475954 | + | 0.879470i | \(0.342103\pi\) | |||||||
\(158\) | −77.1022 | − | 268.913i | −0.487989 | − | 1.70198i | ||||
\(159\) | 27.6796i | 0.174086i | ||||||||
\(160\) | 12.9407 | − | 73.3359i | 0.0808795 | − | 0.458349i | ||||
\(161\) | 323.580 | 2.00981 | ||||||||
\(162\) | −134.482 | + | 38.5585i | −0.830137 | + | 0.238015i | ||||
\(163\) | 146.763i | 0.900384i | 0.892932 | + | 0.450192i | \(0.148644\pi\) | ||||
−0.892932 | + | 0.450192i | \(0.851356\pi\) | |||||||
\(164\) | 247.074 | − | 154.371i | 1.50655 | − | 0.941289i | ||||
\(165\) | 28.9138 | 0.175235 | ||||||||
\(166\) | 52.2075 | + | 182.087i | 0.314503 | + | 1.09691i | ||||
\(167\) | 213.493i | 1.27840i | 0.769040 | + | 0.639201i | \(0.220735\pi\) | ||||
−0.769040 | + | 0.639201i | \(0.779265\pi\) | |||||||
\(168\) | 29.7831 | − | 33.0724i | 0.177281 | − | 0.196860i | ||||
\(169\) | 21.6237 | 0.127951 | ||||||||
\(170\) | −56.0061 | + | 16.0579i | −0.329447 | + | 0.0944584i | ||||
\(171\) | − | 37.4183i | − | 0.218821i | ||||||
\(172\) | −21.5243 | − | 34.4500i | −0.125141 | − | 0.200291i | ||||
\(173\) | −280.715 | −1.62263 | −0.811314 | − | 0.584610i | \(-0.801247\pi\) | ||||
−0.811314 | + | 0.584610i | \(0.801247\pi\) | |||||||
\(174\) | −2.26351 | − | 7.89454i | −0.0130087 | − | 0.0453709i | ||||
\(175\) | 168.998i | 0.965704i | ||||||||
\(176\) | −277.127 | − | 135.199i | −1.57459 | − | 0.768175i | ||||
\(177\) | −25.1259 | −0.141954 | ||||||||
\(178\) | −64.1254 | + | 18.3859i | −0.360255 | + | 0.103292i | ||||
\(179\) | − | 35.1878i | − | 0.196580i | −0.995158 | − | 0.0982899i | \(-0.968663\pi\) | ||
0.995158 | − | 0.0982899i | \(-0.0313372\pi\) | |||||||
\(180\) | −67.7684 | + | 42.3416i | −0.376491 | + | 0.235231i | ||||
\(181\) | −345.539 | −1.90906 | −0.954529 | − | 0.298120i | \(-0.903641\pi\) | ||||
−0.954529 | + | 0.298120i | \(0.903641\pi\) | |||||||
\(182\) | 65.6736 | + | 229.053i | 0.360844 | + | 1.25853i | ||||
\(183\) | − | 16.4793i | − | 0.0900509i | ||||||
\(184\) | −222.917 | − | 200.746i | −1.21150 | − | 1.09101i | ||||
\(185\) | −48.6958 | −0.263220 | ||||||||
\(186\) | −6.75324 | + | 1.93628i | −0.0363078 | + | 0.0104101i | ||||
\(187\) | 241.244i | 1.29007i | ||||||||
\(188\) | 68.7672 | + | 110.063i | 0.365783 | + | 0.585442i | ||||
\(189\) | −97.8271 | −0.517604 | ||||||||
\(190\) | −5.59154 | − | 19.5019i | −0.0294292 | − | 0.102642i | ||||
\(191\) | − | 100.233i | − | 0.524782i | −0.964962 | − | 0.262391i | \(-0.915489\pi\) | ||
0.964962 | − | 0.262391i | \(-0.0845110\pi\) | |||||||
\(192\) | −41.0357 | + | 4.30669i | −0.213727 | + | 0.0224307i | ||||
\(193\) | 168.119 | 0.871085 | 0.435543 | − | 0.900168i | \(-0.356557\pi\) | ||||
0.435543 | + | 0.900168i | \(0.356557\pi\) | |||||||
\(194\) | 289.952 | − | 83.1343i | 1.49460 | − | 0.428528i | ||||
\(195\) | 20.7145i | 0.106228i | ||||||||
\(196\) | −86.3808 | + | 53.9706i | −0.440719 | + | 0.275360i | ||||
\(197\) | 216.705 | 1.10002 | 0.550012 | − | 0.835157i | \(-0.314623\pi\) | ||||
0.550012 | + | 0.835157i | \(0.314623\pi\) | |||||||
\(198\) | 91.1922 | + | 318.056i | 0.460567 | + | 1.60634i | ||||
\(199\) | 82.2545i | 0.413339i | 0.978411 | + | 0.206670i | \(0.0662625\pi\) | ||||
−0.978411 | + | 0.206670i | \(0.933738\pi\) | |||||||
\(200\) | 104.845 | − | 116.424i | 0.524224 | − | 0.582121i | ||||
\(201\) | 42.1109 | 0.209507 | ||||||||
\(202\) | −149.524 | + | 42.8713i | −0.740220 | + | 0.212234i | ||||
\(203\) | 54.9623i | 0.270750i | ||||||||
\(204\) | 17.1053 | + | 27.3772i | 0.0838493 | + | 0.134202i | ||||
\(205\) | −169.495 | −0.826806 | ||||||||
\(206\) | −8.23978 | − | 28.7383i | −0.0399990 | − | 0.139506i | ||||
\(207\) | 321.897i | 1.55506i | ||||||||
\(208\) | 96.8592 | − | 198.540i | 0.465669 | − | 0.954517i | ||||
\(209\) | −84.0035 | −0.401931 | ||||||||
\(210\) | −24.8904 | + | 7.13653i | −0.118526 | + | 0.0339835i | ||||
\(211\) | 16.4195i | 0.0778173i | 0.999243 | + | 0.0389087i | \(0.0123881\pi\) | ||||
−0.999243 | + | 0.0389087i | \(0.987612\pi\) | |||||||
\(212\) | −145.645 | + | 90.9986i | −0.687003 | + | 0.429239i | ||||
\(213\) | 12.0919 | 0.0567695 | ||||||||
\(214\) | −44.3850 | − | 154.804i | −0.207407 | − | 0.723382i | ||||
\(215\) | 23.6331i | 0.109921i | ||||||||
\(216\) | 67.3938 | + | 60.6910i | 0.312009 | + | 0.280977i | ||||
\(217\) | 47.0165 | 0.216666 | ||||||||
\(218\) | −103.531 | + | 29.6842i | −0.474913 | + | 0.136166i | ||||
\(219\) | − | 46.9506i | − | 0.214386i | ||||||
\(220\) | 95.0561 | + | 152.139i | 0.432073 | + | 0.691540i | ||||
\(221\) | −172.832 | −0.782044 | ||||||||
\(222\) | 7.43629 | + | 25.9359i | 0.0334968 | + | 0.116828i | ||||
\(223\) | − | 195.225i | − | 0.875450i | −0.899109 | − | 0.437725i | \(-0.855784\pi\) | ||
0.899109 | − | 0.437725i | \(-0.144216\pi\) | |||||||
\(224\) | 271.934 | + | 47.9851i | 1.21399 | + | 0.214219i | ||||
\(225\) | −168.119 | −0.747196 | ||||||||
\(226\) | −203.637 | + | 58.3864i | −0.901050 | + | 0.258347i | ||||
\(227\) | − | 305.403i | − | 1.34539i | −0.739920 | − | 0.672695i | \(-0.765137\pi\) | ||
0.739920 | − | 0.672695i | \(-0.234863\pi\) | |||||||
\(228\) | −9.53304 | + | 5.95623i | −0.0418116 | + | 0.0261238i | ||||
\(229\) | −229.686 | −1.00300 | −0.501499 | − | 0.865158i | \(-0.667218\pi\) | ||||
−0.501499 | + | 0.865158i | \(0.667218\pi\) | |||||||
\(230\) | 48.1020 | + | 167.768i | 0.209139 | + | 0.729425i | ||||
\(231\) | 107.214i | 0.464132i | ||||||||
\(232\) | 34.0981 | − | 37.8639i | 0.146974 | − | 0.163207i | ||||
\(233\) | 187.667 | 0.805436 | 0.402718 | − | 0.915324i | \(-0.368065\pi\) | ||||
0.402718 | + | 0.915324i | \(0.368065\pi\) | |||||||
\(234\) | −227.862 | + | 65.3320i | −0.973767 | + | 0.279196i | ||||
\(235\) | − | 75.5044i | − | 0.321295i | ||||||
\(236\) | −82.6030 | − | 132.207i | −0.350013 | − | 0.560201i | ||||
\(237\) | 90.1774 | 0.380495 | ||||||||
\(238\) | −59.5439 | − | 207.674i | −0.250184 | − | 0.872581i | ||||
\(239\) | − | 69.8504i | − | 0.292261i | −0.989265 | − | 0.146130i | \(-0.953318\pi\) | ||
0.989265 | − | 0.146130i | \(-0.0466819\pi\) | |||||||
\(240\) | 21.5747 | + | 10.5254i | 0.0898944 | + | 0.0438557i | ||||
\(241\) | 297.561 | 1.23469 | 0.617346 | − | 0.786691i | \(-0.288208\pi\) | ||||
0.617346 | + | 0.786691i | \(0.288208\pi\) | |||||||
\(242\) | 481.402 | − | 138.026i | 1.98926 | − | 0.570357i | ||||
\(243\) | − | 147.128i | − | 0.605463i | ||||||
\(244\) | 86.7109 | − | 54.1768i | 0.355372 | − | 0.222036i | ||||
\(245\) | 59.2582 | 0.241870 | ||||||||
\(246\) | 25.8835 | + | 90.2750i | 0.105217 | + | 0.366972i | ||||
\(247\) | − | 60.1818i | − | 0.243651i | ||||||
\(248\) | −32.3900 | − | 29.1686i | −0.130605 | − | 0.117615i | ||||
\(249\) | −61.0609 | −0.245225 | ||||||||
\(250\) | −199.472 | + | 57.1922i | −0.797889 | + | 0.228769i | ||||
\(251\) | − | 36.4667i | − | 0.145286i | −0.997358 | − | 0.0726429i | \(-0.976857\pi\) | ||
0.997358 | − | 0.0726429i | \(-0.0231433\pi\) | |||||||
\(252\) | −157.005 | − | 251.290i | −0.623037 | − | 0.997181i | ||||
\(253\) | 722.652 | 2.85633 | ||||||||
\(254\) | 9.44851 | + | 32.9540i | 0.0371988 | + | 0.129740i | ||||
\(255\) | − | 18.7811i | − | 0.0736513i | ||||||
\(256\) | −157.568 | − | 201.763i | −0.615501 | − | 0.788136i | ||||
\(257\) | −175.943 | −0.684604 | −0.342302 | − | 0.939590i | \(-0.611207\pi\) | ||||
−0.342302 | + | 0.939590i | \(0.611207\pi\) | |||||||
\(258\) | 12.5872 | − | 3.60898i | 0.0487877 | − | 0.0139883i | ||||
\(259\) | − | 180.567i | − | 0.697171i | ||||||
\(260\) | −108.995 | + | 68.1001i | −0.419213 | + | 0.261924i | ||||
\(261\) | −54.6764 | −0.209488 | ||||||||
\(262\) | 126.416 | + | 440.908i | 0.482504 | + | 1.68285i | ||||
\(263\) | − | 444.887i | − | 1.69158i | −0.533512 | − | 0.845792i | \(-0.679128\pi\) | ||
0.533512 | − | 0.845792i | \(-0.320872\pi\) | |||||||
\(264\) | 66.5148 | − | 73.8608i | 0.251950 | − | 0.279776i | ||||
\(265\) | 99.9138 | 0.377033 | ||||||||
\(266\) | 72.3143 | − | 20.7338i | 0.271858 | − | 0.0779466i | ||||
\(267\) | − | 21.5038i | − | 0.0805386i | ||||||
\(268\) | 138.442 | + | 221.579i | 0.516576 | + | 0.826788i | ||||
\(269\) | 149.744 | 0.556670 | 0.278335 | − | 0.960484i | \(-0.410217\pi\) | ||||
0.278335 | + | 0.960484i | \(0.410217\pi\) | |||||||
\(270\) | −14.5426 | − | 50.7208i | −0.0538614 | − | 0.187855i | ||||
\(271\) | − | 439.685i | − | 1.62245i | −0.584731 | − | 0.811227i | \(-0.698800\pi\) | ||
0.584731 | − | 0.811227i | \(-0.301200\pi\) | |||||||
\(272\) | −87.8188 | + | 180.009i | −0.322863 | + | 0.661797i | ||||
\(273\) | −76.8106 | −0.281358 | ||||||||
\(274\) | 231.795 | − | 66.4598i | 0.845968 | − | 0.242554i | ||||
\(275\) | 377.424i | 1.37245i | ||||||||
\(276\) | 82.0094 | − | 51.2393i | 0.297135 | − | 0.185650i | ||||
\(277\) | 83.2452 | 0.300524 | 0.150262 | − | 0.988646i | \(-0.451988\pi\) | ||||
0.150262 | + | 0.988646i | \(0.451988\pi\) | |||||||
\(278\) | −80.4042 | − | 280.430i | −0.289224 | − | 1.00874i | ||||
\(279\) | 46.7719i | 0.167641i | ||||||||
\(280\) | −119.380 | − | 107.507i | −0.426357 | − | 0.383952i | ||||
\(281\) | −12.9851 | −0.0462105 | −0.0231052 | − | 0.999733i | \(-0.507355\pi\) | ||||
−0.0231052 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(282\) | −40.2144 | + | 11.5302i | −0.142604 | + | 0.0408872i | ||||
\(283\) | − | 111.022i | − | 0.392303i | −0.980574 | − | 0.196152i | \(-0.937156\pi\) | ||
0.980574 | − | 0.196152i | \(-0.0628445\pi\) | |||||||
\(284\) | 39.7529 | + | 63.6251i | 0.139975 | + | 0.224032i | ||||
\(285\) | 6.53976 | 0.0229465 | ||||||||
\(286\) | 146.669 | + | 511.545i | 0.512829 | + | 1.78862i | ||||
\(287\) | − | 628.500i | − | 2.18990i | ||||||
\(288\) | −47.7355 | + | 270.520i | −0.165748 | + | 0.939306i | ||||
\(289\) | −132.300 | −0.457784 | ||||||||
\(290\) | −28.4965 | + | 8.17046i | −0.0982639 | + | 0.0281740i | ||||
\(291\) | 97.2324i | 0.334132i | ||||||||
\(292\) | 247.045 | − | 154.353i | 0.846043 | − | 0.528607i | ||||
\(293\) | −141.572 | −0.483179 | −0.241590 | − | 0.970378i | \(-0.577669\pi\) | ||||
−0.241590 | + | 0.970378i | \(0.577669\pi\) | |||||||
\(294\) | −9.04926 | − | 31.5615i | −0.0307798 | − | 0.107352i | ||||
\(295\) | 90.6956i | 0.307443i | ||||||||
\(296\) | −112.022 | + | 124.394i | −0.378453 | + | 0.420251i | ||||
\(297\) | −218.478 | −0.735615 | ||||||||
\(298\) | −37.0179 | + | 10.6137i | −0.124221 | + | 0.0356165i | ||||
\(299\) | 517.723i | 1.73151i | ||||||||
\(300\) | 26.7611 | + | 42.8315i | 0.0892036 | + | 0.142772i | ||||
\(301\) | −87.6329 | −0.291139 | ||||||||
\(302\) | −91.2421 | − | 318.229i | −0.302126 | − | 1.05374i | ||||
\(303\) | − | 50.1415i | − | 0.165484i | ||||||
\(304\) | −62.6809 | − | 30.5794i | −0.206187 | − | 0.100590i | ||||
\(305\) | −59.4846 | −0.195031 | ||||||||
\(306\) | 206.594 | − | 59.2342i | 0.675144 | − | 0.193576i | ||||
\(307\) | − | 357.744i | − | 1.16529i | −0.812727 | − | 0.582645i | \(-0.802018\pi\) | ||
0.812727 | − | 0.582645i | \(-0.197982\pi\) | |||||||
\(308\) | −564.141 | + | 352.474i | −1.83163 | + | 1.14440i | ||||
\(309\) | 9.63710 | 0.0311880 | ||||||||
\(310\) | 6.98927 | + | 24.3768i | 0.0225460 | + | 0.0786349i | ||||
\(311\) | 472.383i | 1.51892i | 0.650557 | + | 0.759458i | \(0.274536\pi\) | ||||
−0.650557 | + | 0.759458i | \(0.725464\pi\) | |||||||
\(312\) | 52.9154 | + | 47.6526i | 0.169601 | + | 0.152733i | ||||
\(313\) | 63.7596 | 0.203705 | 0.101852 | − | 0.994800i | \(-0.467523\pi\) | ||||
0.101852 | + | 0.994800i | \(0.467523\pi\) | |||||||
\(314\) | −287.322 | + | 82.3804i | −0.915039 | + | 0.262358i | ||||
\(315\) | 172.387i | 0.547261i | ||||||||
\(316\) | 296.464 | + | 474.495i | 0.938177 | + | 1.50157i | ||||
\(317\) | 198.721 | 0.626880 | 0.313440 | − | 0.949608i | \(-0.398519\pi\) | ||||
0.313440 | + | 0.949608i | \(0.398519\pi\) | |||||||
\(318\) | −15.2577 | − | 53.2151i | −0.0479803 | − | 0.167343i | ||||
\(319\) | 122.747i | 0.384788i | ||||||||
\(320\) | 15.5456 | + | 148.124i | 0.0485801 | + | 0.462888i | ||||
\(321\) | 51.9119 | 0.161719 | ||||||||
\(322\) | −622.094 | + | 178.366i | −1.93197 | + | 0.553930i | ||||
\(323\) | 54.5647i | 0.168931i | ||||||||
\(324\) | 237.293 | − | 148.260i | 0.732385 | − | 0.457593i | ||||
\(325\) | −270.394 | −0.831983 | ||||||||
\(326\) | −80.8993 | − | 282.156i | −0.248157 | − | 0.865511i | ||||
\(327\) | − | 34.7181i | − | 0.106172i | ||||||
\(328\) | −389.915 | + | 432.978i | −1.18877 | + | 1.32006i | ||||
\(329\) | 279.975 | 0.850989 | ||||||||
\(330\) | −55.5879 | + | 15.9380i | −0.168448 | + | 0.0482971i | ||||
\(331\) | 438.736i | 1.32549i | 0.748846 | + | 0.662744i | \(0.230608\pi\) | ||||
−0.748846 | + | 0.662744i | \(0.769392\pi\) | |||||||
\(332\) | −200.742 | − | 321.290i | −0.604644 | − | 0.967742i | ||||
\(333\) | 179.628 | 0.539424 | ||||||||
\(334\) | −117.683 | − | 410.449i | −0.352344 | − | 1.22889i | ||||
\(335\) | − | 152.006i | − | 0.453748i | ||||||
\(336\) | −39.0288 | + | 80.0003i | −0.116157 | + | 0.238096i | ||||
\(337\) | −538.699 | −1.59851 | −0.799257 | − | 0.600989i | \(-0.794773\pi\) | ||||
−0.799257 | + | 0.600989i | \(0.794773\pi\) | |||||||
\(338\) | −41.5724 | + | 11.9196i | −0.122995 | + | 0.0352650i | ||||
\(339\) | − | 68.2877i | − | 0.201439i | ||||||
\(340\) | 98.8222 | − | 61.7440i | 0.290653 | − | 0.181600i | ||||
\(341\) | 105.002 | 0.307924 | ||||||||
\(342\) | 20.6260 | + | 71.9382i | 0.0603098 | + | 0.210346i | ||||
\(343\) | − | 203.100i | − | 0.592127i | ||||||
\(344\) | 60.3710 | + | 54.3666i | 0.175497 | + | 0.158043i | ||||
\(345\) | −56.2593 | −0.163070 | ||||||||
\(346\) | 539.685 | − | 154.737i | 1.55978 | − | 0.447217i | ||||
\(347\) | 584.405i | 1.68417i | 0.539349 | + | 0.842083i | \(0.318671\pi\) | ||||
−0.539349 | + | 0.842083i | \(0.681329\pi\) | |||||||
\(348\) | 8.70335 | + | 13.9299i | 0.0250096 | + | 0.0400283i | ||||
\(349\) | −300.832 | −0.861983 | −0.430991 | − | 0.902356i | \(-0.641836\pi\) | ||||
−0.430991 | + | 0.902356i | \(0.641836\pi\) | |||||||
\(350\) | −93.1561 | − | 324.905i | −0.266160 | − | 0.928301i | ||||
\(351\) | − | 156.522i | − | 0.445931i | ||||||
\(352\) | 607.312 | + | 107.165i | 1.72532 | + | 0.304447i | ||||
\(353\) | −316.023 | −0.895250 | −0.447625 | − | 0.894221i | \(-0.647730\pi\) | ||||
−0.447625 | + | 0.894221i | \(0.647730\pi\) | |||||||
\(354\) | 48.3055 | − | 13.8500i | 0.136456 | − | 0.0391244i | ||||
\(355\) | − | 43.6475i | − | 0.122951i | ||||||
\(356\) | 113.149 | − | 70.6951i | 0.317833 | − | 0.198582i | ||||
\(357\) | 69.6415 | 0.195074 | ||||||||
\(358\) | 19.3964 | + | 67.6498i | 0.0541799 | + | 0.188966i | ||||
\(359\) | 116.055i | 0.323272i | 0.986850 | + | 0.161636i | \(0.0516770\pi\) | ||||
−0.986850 | + | 0.161636i | \(0.948323\pi\) | |||||||
\(360\) | 106.947 | − | 118.759i | 0.297076 | − | 0.329886i | ||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 664.312 | − | 190.470i | 1.83512 | − | 0.526161i | ||||
\(363\) | 161.433i | 0.444720i | ||||||||
\(364\) | −252.520 | − | 404.162i | −0.693736 | − | 1.11033i | ||||
\(365\) | −169.475 | −0.464316 | ||||||||
\(366\) | 9.08383 | + | 31.6821i | 0.0248192 | + | 0.0865632i | ||||
\(367\) | 67.8773i | 0.184952i | 0.995715 | + | 0.0924759i | \(0.0294781\pi\) | ||||
−0.995715 | + | 0.0924759i | \(0.970522\pi\) | |||||||
\(368\) | 539.222 | + | 263.064i | 1.46528 | + | 0.714848i | ||||
\(369\) | 625.231 | 1.69439 | ||||||||
\(370\) | 93.6195 | − | 26.8424i | 0.253026 | − | 0.0725470i | ||||
\(371\) | 370.487i | 0.998617i | ||||||||
\(372\) | 11.9160 | − | 7.44512i | 0.0320324 | − | 0.0200138i | ||||
\(373\) | −267.337 | −0.716721 | −0.358361 | − | 0.933583i | \(-0.616664\pi\) | ||||
−0.358361 | + | 0.933583i | \(0.616664\pi\) | |||||||
\(374\) | −132.980 | − | 463.800i | −0.355561 | − | 1.24011i | ||||
\(375\) | − | 66.8910i | − | 0.178376i | ||||||
\(376\) | −192.877 | − | 173.694i | −0.512971 | − | 0.461952i | ||||
\(377\) | −87.9388 | −0.233259 | ||||||||
\(378\) | 188.076 | − | 53.9248i | 0.497556 | − | 0.142658i | ||||
\(379\) | 372.834i | 0.983731i | 0.870671 | + | 0.491866i | \(0.163685\pi\) | ||||
−0.870671 | + | 0.491866i | \(0.836315\pi\) | |||||||
\(380\) | 21.4999 | + | 34.4109i | 0.0565786 | + | 0.0905550i | ||||
\(381\) | −11.0508 | −0.0290047 | ||||||||
\(382\) | 55.2512 | + | 192.702i | 0.144637 | + | 0.504457i | ||||
\(383\) | − | 19.6246i | − | 0.0512392i | −0.999672 | − | 0.0256196i | \(-0.991844\pi\) | ||
0.999672 | − | 0.0256196i | \(-0.00815587\pi\) | |||||||
\(384\) | 76.5186 | − | 30.8997i | 0.199267 | − | 0.0804679i | ||||
\(385\) | 387.006 | 1.00521 | ||||||||
\(386\) | −323.216 | + | 92.6718i | −0.837347 | + | 0.240082i | ||||
\(387\) | − | 87.1771i | − | 0.225264i | ||||||
\(388\) | −511.617 | + | 319.658i | −1.31860 | + | 0.823860i | ||||
\(389\) | 198.727 | 0.510867 | 0.255434 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255434 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(390\) | −11.4183 | − | 39.8243i | −0.0292778 | − | 0.102114i | ||||
\(391\) | − | 469.401i | − | 1.20051i | ||||||
\(392\) | 136.320 | − | 151.376i | 0.347756 | − | 0.386163i | ||||
\(393\) | −147.854 | −0.376219 | ||||||||
\(394\) | −416.623 | + | 119.453i | −1.05742 | + | 0.303181i | ||||
\(395\) | − | 325.509i | − | 0.824072i | ||||||
\(396\) | −350.641 | − | 561.206i | −0.885457 | − | 1.41719i | ||||
\(397\) | 295.448 | 0.744203 | 0.372101 | − | 0.928192i | \(-0.378637\pi\) | ||||
0.372101 | + | 0.928192i | \(0.378637\pi\) | |||||||
\(398\) | −45.3408 | − | 158.137i | −0.113922 | − | 0.397330i | ||||
\(399\) | 24.2499i | 0.0607766i | ||||||||
\(400\) | −137.392 | + | 281.623i | −0.343480 | + | 0.704057i | ||||
\(401\) | −63.9986 | −0.159597 | −0.0797987 | − | 0.996811i | \(-0.525428\pi\) | ||||
−0.0797987 | + | 0.996811i | \(0.525428\pi\) | |||||||
\(402\) | −80.9599 | + | 23.2126i | −0.201393 | + | 0.0577429i | ||||
\(403\) | 75.2256i | 0.186664i | ||||||||
\(404\) | 263.835 | − | 164.843i | 0.653056 | − | 0.408028i | ||||
\(405\) | −162.785 | −0.401939 | ||||||||
\(406\) | −30.2966 | − | 105.667i | −0.0746222 | − | 0.260264i | ||||
\(407\) | − | 403.262i | − | 0.990815i | ||||||
\(408\) | −47.9765 | − | 43.2049i | −0.117590 | − | 0.105894i | ||||
\(409\) | 504.473 | 1.23343 | 0.616715 | − | 0.787186i | \(-0.288463\pi\) | ||||
0.616715 | + | 0.787186i | \(0.288463\pi\) | |||||||
\(410\) | 325.861 | − | 93.4302i | 0.794783 | − | 0.227878i | ||||
\(411\) | 77.7302i | 0.189125i | ||||||||
\(412\) | 31.6826 | + | 50.7085i | 0.0768995 | + | 0.123079i | ||||
\(413\) | −336.306 | −0.814299 | ||||||||
\(414\) | −177.438 | − | 618.859i | −0.428594 | − | 1.49483i | ||||
\(415\) | 220.408i | 0.531105i | ||||||||
\(416\) | −76.7754 | + | 435.091i | −0.184556 | + | 1.04589i | ||||
\(417\) | 94.0393 | 0.225514 | ||||||||
\(418\) | 161.500 | − | 46.3049i | 0.386363 | − | 0.110777i | ||||
\(419\) | 470.299i | 1.12243i | 0.827670 | + | 0.561215i | \(0.189666\pi\) | ||||
−0.827670 | + | 0.561215i | \(0.810334\pi\) | |||||||
\(420\) | 43.9190 | − | 27.4405i | 0.104569 | − | 0.0653345i | ||||
\(421\) | −470.034 | −1.11647 | −0.558235 | − | 0.829683i | \(-0.688521\pi\) | ||||
−0.558235 | + | 0.829683i | \(0.688521\pi\) | |||||||
\(422\) | −9.05083 | − | 31.5670i | −0.0214475 | − | 0.0748033i | ||||
\(423\) | 278.519i | 0.658437i | ||||||||
\(424\) | 229.847 | − | 255.231i | 0.542091 | − | 0.601961i | ||||
\(425\) | 245.157 | 0.576840 | ||||||||
\(426\) | −23.2471 | + | 6.66537i | −0.0545707 | + | 0.0156464i | ||||
\(427\) | − | 220.573i | − | 0.516564i | ||||||
\(428\) | 170.664 | + | 273.150i | 0.398747 | + | 0.638201i | ||||
\(429\) | −171.541 | −0.399864 | ||||||||
\(430\) | −13.0271 | − | 45.4354i | −0.0302957 | − | 0.105664i | ||||
\(431\) | 224.005i | 0.519733i | 0.965645 | + | 0.259866i | \(0.0836785\pi\) | ||||
−0.965645 | + | 0.259866i | \(0.916321\pi\) | |||||||
\(432\) | −163.022 | − | 79.5315i | −0.377365 | − | 0.184101i | ||||
\(433\) | 180.128 | 0.415999 | 0.207999 | − | 0.978129i | \(-0.433305\pi\) | ||||
0.207999 | + | 0.978129i | \(0.433305\pi\) | |||||||
\(434\) | −90.3909 | + | 25.9167i | −0.208274 | + | 0.0597159i | ||||
\(435\) | − | 9.55602i | − | 0.0219679i | ||||||
\(436\) | 182.680 | − | 114.138i | 0.418990 | − | 0.261784i | ||||
\(437\) | 163.450 | 0.374028 | ||||||||
\(438\) | 25.8804 | + | 90.2643i | 0.0590877 | + | 0.206083i | ||||
\(439\) | 590.004i | 1.34397i | 0.740563 | + | 0.671987i | \(0.234559\pi\) | ||||
−0.740563 | + | 0.671987i | \(0.765441\pi\) | |||||||
\(440\) | −266.612 | − | 240.095i | −0.605936 | − | 0.545671i | ||||
\(441\) | −218.590 | −0.495670 | ||||||||
\(442\) | 332.276 | − | 95.2693i | 0.751755 | − | 0.215541i | ||||
\(443\) | 157.459i | 0.355439i | 0.984081 | + | 0.177719i | \(0.0568720\pi\) | ||||
−0.984081 | + | 0.177719i | \(0.943128\pi\) | |||||||
\(444\) | −28.5931 | − | 45.7637i | −0.0643988 | − | 0.103071i | ||||
\(445\) | −77.6212 | −0.174430 | ||||||||
\(446\) | 107.613 | + | 375.328i | 0.241285 | + | 0.841543i | ||||
\(447\) | − | 12.4136i | − | 0.0277709i | ||||||
\(448\) | −549.255 | + | 57.6442i | −1.22602 | + | 0.128670i | ||||
\(449\) | −715.434 | −1.59339 | −0.796697 | − | 0.604379i | \(-0.793421\pi\) | ||||
−0.796697 | + | 0.604379i | \(0.793421\pi\) | |||||||
\(450\) | 323.215 | − | 92.6716i | 0.718256 | − | 0.205937i | ||||
\(451\) | − | 1403.63i | − | 3.11226i | ||||||
\(452\) | 359.316 | − | 224.500i | 0.794947 | − | 0.496682i | ||||
\(453\) | 106.715 | 0.235574 | ||||||||
\(454\) | 168.346 | + | 587.149i | 0.370807 | + | 1.29328i | ||||
\(455\) | 277.259i | 0.609361i | ||||||||
\(456\) | 15.0444 | − | 16.7059i | 0.0329921 | − | 0.0366358i | ||||
\(457\) | 31.3497 | 0.0685988 | 0.0342994 | − | 0.999412i | \(-0.489080\pi\) | ||||
0.0342994 | + | 0.999412i | \(0.489080\pi\) | |||||||
\(458\) | 441.581 | − | 126.609i | 0.964150 | − | 0.276439i | ||||
\(459\) | 141.913i | 0.309178i | ||||||||
\(460\) | −184.956 | − | 296.025i | −0.402078 | − | 0.643532i | ||||
\(461\) | 368.719 | 0.799824 | 0.399912 | − | 0.916554i | \(-0.369041\pi\) | ||||
0.399912 | + | 0.916554i | \(0.369041\pi\) | |||||||
\(462\) | −59.0994 | − | 206.124i | −0.127921 | − | 0.446155i | ||||
\(463\) | − | 817.405i | − | 1.76545i | −0.469887 | − | 0.882726i | \(-0.655705\pi\) | ||
0.469887 | − | 0.882726i | \(-0.344295\pi\) | |||||||
\(464\) | −44.6832 | + | 91.5905i | −0.0963001 | + | 0.197393i | ||||
\(465\) | −8.17453 | −0.0175796 | ||||||||
\(466\) | −360.796 | + | 103.447i | −0.774241 | + | 0.221989i | ||||
\(467\) | 86.9194i | 0.186123i | 0.995660 | + | 0.0930614i | \(0.0296653\pi\) | ||||
−0.995660 | + | 0.0930614i | \(0.970335\pi\) | |||||||
\(468\) | 402.060 | − | 251.206i | 0.859102 | − | 0.536766i | ||||
\(469\) | 563.647 | 1.20181 | ||||||||
\(470\) | 41.6200 | + | 145.160i | 0.0885531 | + | 0.308851i | ||||
\(471\) | − | 96.3506i | − | 0.204566i | ||||||
\(472\) | 231.683 | + | 208.641i | 0.490855 | + | 0.442036i | ||||
\(473\) | −195.711 | −0.413765 | ||||||||
\(474\) | −173.369 | + | 49.7081i | −0.365758 | + | 0.104869i | ||||
\(475\) | 85.3662i | 0.179718i | ||||||||
\(476\) | 228.951 | + | 366.439i | 0.480989 | + | 0.769830i | ||||
\(477\) | −368.560 | −0.772662 | ||||||||
\(478\) | 38.5033 | + | 134.290i | 0.0805509 | + | 0.280941i | ||||
\(479\) | − | 333.107i | − | 0.695421i | −0.937602 | − | 0.347710i | \(-0.886959\pi\) | ||
0.937602 | − | 0.347710i | \(-0.113041\pi\) | |||||||
\(480\) | −47.2799 | − | 8.34293i | −0.0984999 | − | 0.0173811i | ||||
\(481\) | 288.905 | 0.600634 | ||||||||
\(482\) | −572.072 | + | 164.023i | −1.18687 | + | 0.340297i | ||||
\(483\) | − | 208.613i | − | 0.431911i | ||||||
\(484\) | −849.429 | + | 530.722i | −1.75502 | + | 1.09653i | ||||
\(485\) | 350.975 | 0.723659 | ||||||||
\(486\) | 81.1005 | + | 282.858i | 0.166873 | + | 0.582013i | ||||
\(487\) | − | 264.690i | − | 0.543511i | −0.962366 | − | 0.271755i | \(-0.912396\pi\) | ||
0.962366 | − | 0.271755i | \(-0.0876042\pi\) | |||||||
\(488\) | −136.841 | + | 151.954i | −0.280412 | + | 0.311382i | ||||
\(489\) | 94.6183 | 0.193494 | ||||||||
\(490\) | −113.926 | + | 32.6646i | −0.232502 | + | 0.0666625i | ||||
\(491\) | 402.874i | 0.820518i | 0.911969 | + | 0.410259i | \(0.134562\pi\) | ||||
−0.911969 | + | 0.410259i | \(0.865438\pi\) | |||||||
\(492\) | −99.5238 | − | 159.289i | −0.202284 | − | 0.323759i | ||||
\(493\) | 79.7310 | 0.161726 | ||||||||
\(494\) | 33.1738 | + | 115.702i | 0.0671534 | + | 0.234214i | ||||
\(495\) | 384.993i | 0.777764i | ||||||||
\(496\) | 78.3495 | + | 38.2235i | 0.157963 | + | 0.0770634i | ||||
\(497\) | 161.848 | 0.325650 | ||||||||
\(498\) | 117.392 | − | 33.6584i | 0.235727 | − | 0.0675871i | ||||
\(499\) | 350.536i | 0.702477i | 0.936286 | + | 0.351238i | \(0.114239\pi\) | ||||
−0.936286 | + | 0.351238i | \(0.885761\pi\) | |||||||
\(500\) | 351.967 | − | 219.908i | 0.703934 | − | 0.439817i | ||||
\(501\) | 137.640 | 0.274730 | ||||||||
\(502\) | 20.1014 | + | 70.1086i | 0.0400426 | + | 0.139659i | ||||
\(503\) | − | 339.615i | − | 0.675179i | −0.941293 | − | 0.337589i | \(-0.890388\pi\) | ||
0.941293 | − | 0.337589i | \(-0.109612\pi\) | |||||||
\(504\) | 440.366 | + | 396.568i | 0.873742 | + | 0.786842i | ||||
\(505\) | −180.993 | −0.358403 | ||||||||
\(506\) | −1389.33 | + | 398.345i | −2.74570 | + | 0.787242i | ||||
\(507\) | − | 13.9409i | − | 0.0274969i | ||||||
\(508\) | −36.3302 | − | 58.1471i | −0.0715162 | − | 0.114463i | ||||
\(509\) | −933.003 | −1.83301 | −0.916506 | − | 0.400020i | \(-0.869003\pi\) | ||||
−0.916506 | + | 0.400020i | \(0.869003\pi\) | |||||||
\(510\) | 10.3526 | + | 36.1073i | 0.0202992 | + | 0.0707986i | ||||
\(511\) | − | 628.426i | − | 1.22980i | ||||||
\(512\) | 414.148 | + | 301.041i | 0.808882 | + | 0.587971i | ||||
\(513\) | −49.4155 | −0.0963266 | ||||||||
\(514\) | 338.257 | − | 96.9844i | 0.658088 | − | 0.188686i | ||||
\(515\) | − | 34.7866i | − | 0.0675467i | ||||||
\(516\) | −22.2100 | + | 13.8768i | −0.0430427 | + | 0.0268930i | ||||
\(517\) | 625.270 | 1.20942 | ||||||||
\(518\) | 99.5333 | + | 347.147i | 0.192149 | + | 0.670169i | ||||
\(519\) | 180.978i | 0.348705i | ||||||||
\(520\) | 172.009 | − | 191.006i | 0.330787 | − | 0.367319i | ||||
\(521\) | −415.284 | −0.797091 | −0.398545 | − | 0.917149i | \(-0.630485\pi\) | ||||
−0.398545 | + | 0.917149i | \(0.630485\pi\) | |||||||
\(522\) | 105.117 | − | 30.1390i | 0.201374 | − | 0.0577376i | ||||
\(523\) | − | 241.598i | − | 0.461947i | −0.972960 | − | 0.230973i | \(-0.925809\pi\) | ||
0.972960 | − | 0.230973i | \(-0.0741911\pi\) | |||||||
\(524\) | −486.080 | − | 777.978i | −0.927633 | − | 1.48469i | ||||
\(525\) | 108.954 | 0.207531 | ||||||||
\(526\) | 245.233 | + | 855.311i | 0.466223 | + | 1.62607i | ||||
\(527\) | − | 68.2044i | − | 0.129420i | ||||||
\(528\) | −87.1632 | + | 178.665i | −0.165082 | + | 0.338381i | ||||
\(529\) | −877.105 | −1.65804 | ||||||||
\(530\) | −192.088 | + | 55.0750i | −0.362430 | + | 0.103915i | ||||
\(531\) | − | 334.556i | − | 0.630050i | ||||||
\(532\) | −127.598 | + | 79.7230i | −0.239846 | + | 0.149855i | ||||
\(533\) | 1005.59 | 1.88666 | ||||||||
\(534\) | 11.8535 | + | 41.3419i | 0.0221975 | + | 0.0774192i | ||||
\(535\) | − | 187.384i | − | 0.350250i | ||||||
\(536\) | −388.301 | − | 349.681i | −0.724442 | − | 0.652391i | ||||
\(537\) | −22.6857 | −0.0422452 | ||||||||
\(538\) | −287.889 | + | 82.5428i | −0.535109 | + | 0.153425i | ||||
\(539\) | 490.731i | 0.910447i | ||||||||
\(540\) | 55.9173 | + | 89.4965i | 0.103551 | + | 0.165734i | ||||
\(541\) | −304.787 | −0.563377 | −0.281689 | − | 0.959506i | \(-0.590894\pi\) | ||||
−0.281689 | + | 0.959506i | \(0.590894\pi\) | |||||||
\(542\) | 242.366 | + | 845.311i | 0.447169 | + | 1.55961i | ||||
\(543\) | 222.770i | 0.410259i | ||||||||
\(544\) | 69.6095 | − | 394.482i | 0.127959 | − | 0.725150i | ||||
\(545\) | −125.320 | −0.229945 | ||||||||
\(546\) | 147.671 | − | 42.3400i | 0.270460 | − | 0.0775458i | ||||
\(547\) | 555.915i | 1.01630i | 0.861269 | + | 0.508149i | \(0.169670\pi\) | ||||
−0.861269 | + | 0.508149i | \(0.830330\pi\) | |||||||
\(548\) | −409.001 | + | 255.543i | −0.746352 | + | 0.466319i | ||||
\(549\) | 219.425 | 0.399682 | ||||||||
\(550\) | −208.046 | − | 725.612i | −0.378265 | − | 1.31930i | ||||
\(551\) | 27.7632i | 0.0503869i | ||||||||
\(552\) | −129.422 | + | 143.715i | −0.234459 | + | 0.260354i | ||||
\(553\) | 1207.01 | 2.18265 | ||||||||
\(554\) | −160.042 | + | 45.8869i | −0.288885 | + | 0.0828283i | ||||
\(555\) | 31.3944i | 0.0565664i | ||||||||
\(556\) | 309.160 | + | 494.816i | 0.556043 | + | 0.889956i | ||||
\(557\) | −192.055 | −0.344802 | −0.172401 | − | 0.985027i | \(-0.555152\pi\) | ||||
−0.172401 | + | 0.985027i | \(0.555152\pi\) | |||||||
\(558\) | −25.7819 | − | 89.9208i | −0.0462041 | − | 0.161148i | ||||
\(559\) | − | 140.211i | − | 0.250825i | ||||||
\(560\) | 288.773 | + | 140.880i | 0.515666 | + | 0.251572i | ||||
\(561\) | 155.531 | 0.277238 | ||||||||
\(562\) | 24.9644 | − | 7.15775i | 0.0444207 | − | 0.0127362i | ||||
\(563\) | − | 107.771i | − | 0.191423i | −0.995409 | − | 0.0957114i | \(-0.969487\pi\) | ||
0.995409 | − | 0.0957114i | \(-0.0305126\pi\) | |||||||
\(564\) | 70.9580 | − | 44.3345i | 0.125812 | − | 0.0786072i | ||||
\(565\) | −246.495 | −0.436274 | ||||||||
\(566\) | 61.1981 | + | 213.444i | 0.108124 | + | 0.377109i | ||||
\(567\) | − | 603.619i | − | 1.06458i | ||||||
\(568\) | −111.498 | − | 100.409i | −0.196300 | − | 0.176776i | ||||
\(569\) | −647.934 | −1.13872 | −0.569362 | − | 0.822087i | \(-0.692810\pi\) | ||||
−0.569362 | + | 0.822087i | \(0.692810\pi\) | |||||||
\(570\) | −12.5729 | + | 3.60489i | −0.0220578 | + | 0.00632436i | ||||
\(571\) | − | 285.402i | − | 0.499828i | −0.968268 | − | 0.249914i | \(-0.919598\pi\) | ||
0.968268 | − | 0.249914i | \(-0.0804023\pi\) | |||||||
\(572\) | −563.953 | − | 902.616i | −0.985933 | − | 1.57800i | ||||
\(573\) | −64.6208 | −0.112776 | ||||||||
\(574\) | 346.445 | + | 1208.31i | 0.603563 | + | 2.10508i | ||||
\(575\) | − | 734.376i | − | 1.27717i | ||||||
\(576\) | −57.3444 | − | 546.398i | −0.0995562 | − | 0.948608i | ||||
\(577\) | −92.4624 | −0.160247 | −0.0801234 | − | 0.996785i | \(-0.525531\pi\) | ||||
−0.0801234 | + | 0.996785i | \(0.525531\pi\) | |||||||
\(578\) | 254.351 | − | 72.9269i | 0.440053 | − | 0.126171i | ||||
\(579\) | − | 108.387i | − | 0.187197i | ||||||
\(580\) | 50.2819 | − | 31.4160i | 0.0866929 | − | 0.0541656i | ||||
\(581\) | −817.289 | −1.40669 | ||||||||
\(582\) | −53.5970 | − | 186.933i | −0.0920911 | − | 0.321191i | ||||
\(583\) | 827.410i | 1.41923i | ||||||||
\(584\) | −389.869 | + | 432.927i | −0.667584 | + | 0.741314i | ||||
\(585\) | −275.817 | −0.471482 | ||||||||
\(586\) | 272.177 | − | 78.0379i | 0.464465 | − | 0.133170i | ||||
\(587\) | 654.717i | 1.11536i | 0.830056 | + | 0.557681i | \(0.188309\pi\) | ||||
−0.830056 | + | 0.557681i | \(0.811691\pi\) | |||||||
\(588\) | 34.7951 | + | 55.6901i | 0.0591753 | + | 0.0947110i | ||||
\(589\) | 23.7495 | 0.0403217 | ||||||||
\(590\) | −49.9938 | − | 174.366i | −0.0847352 | − | 0.295535i | ||||
\(591\) | − | 139.710i | − | 0.236396i | ||||||
\(592\) | 146.798 | − | 300.902i | 0.247969 | − | 0.508280i | ||||
\(593\) | 106.297 | 0.179253 | 0.0896264 | − | 0.995975i | \(-0.471433\pi\) | ||||
0.0896264 | + | 0.995975i | \(0.471433\pi\) | |||||||
\(594\) | 420.032 | − | 120.431i | 0.707124 | − | 0.202745i | ||||
\(595\) | − | 251.381i | − | 0.422489i | ||||||
\(596\) | 65.3178 | − | 40.8105i | 0.109594 | − | 0.0684740i | ||||
\(597\) | 53.0298 | 0.0888271 | ||||||||
\(598\) | −285.382 | − | 995.342i | −0.477228 | − | 1.66445i | ||||
\(599\) | 478.675i | 0.799124i | 0.916706 | + | 0.399562i | \(0.130838\pi\) | ||||
−0.916706 | + | 0.399562i | \(0.869162\pi\) | |||||||
\(600\) | −75.0591 | − | 67.5939i | −0.125098 | − | 0.112656i | ||||
\(601\) | 808.024 | 1.34447 | 0.672233 | − | 0.740340i | \(-0.265335\pi\) | ||||
0.672233 | + | 0.740340i | \(0.265335\pi\) | |||||||
\(602\) | 168.478 | − | 48.3055i | 0.279863 | − | 0.0802418i | ||||
\(603\) | 560.715i | 0.929876i | ||||||||
\(604\) | 350.833 | + | 561.513i | 0.580849 | + | 0.929657i | ||||
\(605\) | 582.717 | 0.963169 | ||||||||
\(606\) | 27.6393 | + | 96.3990i | 0.0456094 | + | 0.159074i | ||||
\(607\) | − | 694.694i | − | 1.14447i | −0.820089 | − | 0.572236i | \(-0.806076\pi\) | ||
0.820089 | − | 0.572236i | \(-0.193924\pi\) | |||||||
\(608\) | 137.363 | + | 24.2388i | 0.225925 | + | 0.0398664i | ||||
\(609\) | 35.4344 | 0.0581845 | ||||||||
\(610\) | 114.361 | − | 32.7894i | 0.187478 | − | 0.0537531i | ||||
\(611\) | 447.956i | 0.733153i | ||||||||
\(612\) | −364.533 | + | 227.760i | −0.595643 | + | 0.372157i | ||||
\(613\) | −496.830 | −0.810489 | −0.405245 | − | 0.914208i | \(-0.632814\pi\) | ||||
−0.405245 | + | 0.914208i | \(0.632814\pi\) | |||||||
\(614\) | 197.198 | + | 687.776i | 0.321169 | + | 1.12016i | ||||
\(615\) | 109.274i | 0.177682i | ||||||||
\(616\) | 890.289 | − | 988.614i | 1.44527 | − | 1.60489i | ||||
\(617\) | 387.951 | 0.628770 | 0.314385 | − | 0.949296i | \(-0.398202\pi\) | ||||
0.314385 | + | 0.949296i | \(0.398202\pi\) | |||||||
\(618\) | −18.5277 | + | 5.31222i | −0.0299801 | + | 0.00859583i | ||||
\(619\) | − | 882.105i | − | 1.42505i | −0.701647 | − | 0.712525i | \(-0.747552\pi\) | ||
0.701647 | − | 0.712525i | \(-0.252448\pi\) | |||||||
\(620\) | −26.8743 | − | 43.0127i | −0.0433456 | − | 0.0693753i | ||||
\(621\) | 425.104 | 0.684548 | ||||||||
\(622\) | −260.389 | − | 908.173i | −0.418633 | − | 1.46009i | ||||
\(623\) | − | 287.824i | − | 0.461998i | ||||||
\(624\) | −127.999 | − | 62.4455i | −0.205127 | − | 0.100073i | ||||
\(625\) | 248.156 | 0.397050 | ||||||||
\(626\) | −122.580 | + | 35.1459i | −0.195815 | + | 0.0561437i | ||||
\(627\) | 54.1574i | 0.0863754i | ||||||||
\(628\) | 506.977 | − | 316.759i | 0.807289 | − | 0.504393i | ||||
\(629\) | −261.940 | −0.416439 | ||||||||
\(630\) | −95.0243 | − | 331.421i | −0.150832 | − | 0.526065i | ||||
\(631\) | 502.601i | 0.796515i | 0.917274 | + | 0.398258i | \(0.130385\pi\) | ||||
−0.917274 | + | 0.398258i | \(0.869615\pi\) | |||||||
\(632\) | −831.517 | − | 748.816i | −1.31569 | − | 1.18484i | ||||
\(633\) | 10.5857 | 0.0167230 | ||||||||
\(634\) | −382.048 | + | 109.540i | −0.602600 | + | 0.172776i | ||||
\(635\) | 39.8895i | 0.0628181i | ||||||||
\(636\) | 58.6671 | + | 93.8977i | 0.0922439 | + | 0.147638i | ||||
\(637\) | −351.570 | −0.551915 | ||||||||
\(638\) | −67.6616 | − | 235.987i | −0.106053 | − | 0.369885i | ||||
\(639\) | 161.006i | 0.251966i | ||||||||
\(640\) | −111.537 | − | 276.205i | −0.174277 | − | 0.431571i | ||||
\(641\) | 385.625 | 0.601600 | 0.300800 | − | 0.953687i | \(-0.402746\pi\) | ||||
0.300800 | + | 0.953687i | \(0.402746\pi\) | |||||||
\(642\) | −99.8026 | + | 28.6152i | −0.155456 | + | 0.0445719i | ||||
\(643\) | − | 925.293i | − | 1.43902i | −0.694480 | − | 0.719512i | \(-0.744365\pi\) | ||
0.694480 | − | 0.719512i | \(-0.255635\pi\) | |||||||
\(644\) | 1097.68 | − | 685.829i | 1.70447 | − | 1.06495i | ||||
\(645\) | 15.2363 | 0.0236222 | ||||||||
\(646\) | −30.0775 | − | 104.903i | −0.0465596 | − | 0.162388i | ||||
\(647\) | 656.956i | 1.01539i | 0.861538 | + | 0.507694i | \(0.169502\pi\) | ||||
−0.861538 | + | 0.507694i | \(0.830498\pi\) | |||||||
\(648\) | −374.479 | + | 415.838i | −0.577900 | + | 0.641725i | ||||
\(649\) | −751.073 | −1.15728 | ||||||||
\(650\) | 519.843 | − | 149.048i | 0.799759 | − | 0.229305i | ||||
\(651\) | − | 30.3117i | − | 0.0465617i | ||||||
\(652\) | 311.064 | + | 497.863i | 0.477092 | + | 0.763593i | ||||
\(653\) | 392.897 | 0.601680 | 0.300840 | − | 0.953675i | \(-0.402733\pi\) | ||||
0.300840 | + | 0.953675i | \(0.402733\pi\) | |||||||
\(654\) | 19.1375 | + | 66.7468i | 0.0292622 | + | 0.102059i | ||||
\(655\) | 533.701i | 0.814811i | ||||||||
\(656\) | 510.958 | − | 1047.35i | 0.778899 | − | 1.59657i | ||||
\(657\) | 625.157 | 0.951533 | ||||||||
\(658\) | −538.263 | + | 154.330i | −0.818029 | + | 0.234543i | ||||
\(659\) | − | 695.576i | − | 1.05550i | −0.849399 | − | 0.527751i | \(-0.823035\pi\) | ||
0.849399 | − | 0.527751i | \(-0.176965\pi\) | |||||||
\(660\) | 98.0844 | − | 61.2830i | 0.148613 | − | 0.0928530i | ||||
\(661\) | 1179.05 | 1.78373 | 0.891866 | − | 0.452299i | \(-0.149396\pi\) | ||||
0.891866 | + | 0.452299i | \(0.149396\pi\) | |||||||
\(662\) | −241.843 | − | 843.487i | −0.365322 | − | 1.27415i | ||||
\(663\) | 111.425i | 0.168062i | ||||||||
\(664\) | 563.037 | + | 507.038i | 0.847947 | + | 0.763612i | ||||
\(665\) | 87.5335 | 0.131629 | ||||||||
\(666\) | −345.342 | + | 99.0156i | −0.518531 | + | 0.148672i | ||||
\(667\) | − | 238.837i | − | 0.358076i | ||||||
\(668\) | 452.500 | + | 724.233i | 0.677395 | + | 1.08418i | ||||
\(669\) | −125.863 | −0.188135 | ||||||||
\(670\) | 83.7894 | + | 292.237i | 0.125059 | + | 0.436174i | ||||
\(671\) | − | 492.606i | − | 0.734137i | ||||||
\(672\) | 30.9362 | − | 175.317i | 0.0460359 | − | 0.260889i | ||||
\(673\) | −881.170 | −1.30932 | −0.654658 | − | 0.755925i | \(-0.727187\pi\) | ||||
−0.654658 | + | 0.755925i | \(0.727187\pi\) | |||||||
\(674\) | 1035.67 | − | 296.945i | 1.53660 | − | 0.440571i | ||||
\(675\) | 222.022i | 0.328921i | ||||||||
\(676\) | 73.3542 | − | 45.8316i | 0.108512 | − | 0.0677982i | ||||
\(677\) | −126.536 | −0.186907 | −0.0934533 | − | 0.995624i | \(-0.529791\pi\) | ||||
−0.0934533 | + | 0.995624i | \(0.529791\pi\) | |||||||
\(678\) | 37.6420 | + | 131.286i | 0.0555191 | + | 0.193637i | ||||
\(679\) | 1301.44i | 1.91670i | ||||||||
\(680\) | −155.954 | + | 173.178i | −0.229345 | + | 0.254674i | ||||
\(681\) | −196.895 | −0.289126 | ||||||||
\(682\) | −201.870 | + | 57.8798i | −0.295998 | + | 0.0848678i | ||||
\(683\) | 873.042i | 1.27825i | 0.769105 | + | 0.639123i | \(0.220702\pi\) | ||||
−0.769105 | + | 0.639123i | \(0.779298\pi\) | |||||||
\(684\) | −79.3083 | − | 126.934i | −0.115948 | − | 0.185576i | ||||
\(685\) | 280.579 | 0.409604 | ||||||||
\(686\) | 111.954 | + | 390.467i | 0.163198 | + | 0.569193i | ||||
\(687\) | 148.080i | 0.215545i | ||||||||
\(688\) | −146.034 | − | 71.2439i | −0.212258 | − | 0.103552i | ||||
\(689\) | −592.774 | −0.860339 | ||||||||
\(690\) | 108.161 | − | 31.0116i | 0.156754 | − | 0.0449443i | ||||
\(691\) | 610.841i | 0.883996i | 0.897016 | + | 0.441998i | \(0.145730\pi\) | ||||
−0.897016 | + | 0.441998i | \(0.854270\pi\) | |||||||
\(692\) | −952.269 | + | 594.976i | −1.37611 | + | 0.859792i | ||||
\(693\) | −1427.58 | −2.06000 | ||||||||
\(694\) | −322.139 | − | 1123.54i | −0.464178 | − | 1.61894i | ||||
\(695\) | − | 339.449i | − | 0.488415i | ||||||
\(696\) | −24.4110 | − | 21.9831i | −0.0350733 | − | 0.0315850i | ||||
\(697\) | −911.733 | −1.30808 | ||||||||
\(698\) | 578.361 | − | 165.826i | 0.828597 | − | 0.237574i | ||||
\(699\) | − | 120.989i | − | 0.173089i | ||||||
\(700\) | 358.192 | + | 573.292i | 0.511703 | + | 0.818989i | ||||
\(701\) | −506.393 | −0.722387 | −0.361193 | − | 0.932491i | \(-0.617631\pi\) | ||||
−0.361193 | + | 0.932491i | \(0.617631\pi\) | |||||||
\(702\) | 86.2789 | + | 300.919i | 0.122904 | + | 0.428660i | ||||
\(703\) | − | 91.2102i | − | 0.129744i | ||||||
\(704\) | −1226.65 | + | 128.737i | −1.74241 | + | 0.182865i | ||||
\(705\) | −48.6780 | −0.0690467 | ||||||||
\(706\) | 607.566 | − | 174.200i | 0.860576 | − | 0.246742i | ||||
\(707\) | − | 671.135i | − | 0.949272i | ||||||
\(708\) | −85.2346 | + | 53.2545i | −0.120388 | + | 0.0752182i | ||||
\(709\) | −1036.42 | −1.46180 | −0.730902 | − | 0.682483i | \(-0.760900\pi\) | ||||
−0.730902 | + | 0.682483i | \(0.760900\pi\) | |||||||
\(710\) | 24.0596 | + | 83.9140i | 0.0338868 | + | 0.118189i | ||||
\(711\) | 1200.73i | 1.68879i | ||||||||
\(712\) | −178.564 | + | 198.284i | −0.250792 | + | 0.278489i | ||||
\(713\) | −204.308 | −0.286548 | ||||||||
\(714\) | −133.888 | + | 38.3882i | −0.187519 | + | 0.0537649i | ||||
\(715\) | 619.204i | 0.866020i | ||||||||
\(716\) | −74.5806 | − | 119.367i | −0.104163 | − | 0.166714i | ||||
\(717\) | −45.0328 | −0.0628072 | ||||||||
\(718\) | −63.9722 | − | 223.119i | −0.0890978 | − | 0.310751i | ||||
\(719\) | 834.943i | 1.16126i | 0.814169 | + | 0.580628i | \(0.197193\pi\) | ||||
−0.814169 | + | 0.580628i | \(0.802807\pi\) | |||||||
\(720\) | −140.148 | + | 287.271i | −0.194649 | + | 0.398987i | ||||
\(721\) | 128.991 | 0.178905 | ||||||||
\(722\) | 36.5282 | − | 10.4733i | 0.0505931 | − | 0.0145059i | ||||
\(723\) | − | 191.839i | − | 0.265337i | ||||||
\(724\) | −1172.17 | + | 732.372i | −1.61902 | + | 1.01156i | ||||
\(725\) | 124.739 | 0.172053 | ||||||||
\(726\) | −88.9862 | − | 310.362i | −0.122571 | − | 0.427495i | ||||
\(727\) | 225.252i | 0.309838i | 0.987927 | + | 0.154919i | \(0.0495116\pi\) | ||||
−0.987927 | + | 0.154919i | \(0.950488\pi\) | |||||||
\(728\) | 708.263 | + | 637.821i | 0.972889 | + | 0.876128i | ||||
\(729\) | 534.700 | 0.733470 | ||||||||
\(730\) | 325.822 | − | 93.4191i | 0.446332 | − | 0.127971i | ||||
\(731\) | 127.125i | 0.173905i | ||||||||
\(732\) | −34.9280 | − | 55.9028i | −0.0477158 | − | 0.0763700i | ||||
\(733\) | 697.401 | 0.951434 | 0.475717 | − | 0.879598i | \(-0.342189\pi\) | ||||
0.475717 | + | 0.879598i | \(0.342189\pi\) | |||||||
\(734\) | −37.4157 | − | 130.497i | −0.0509751 | − | 0.177788i | ||||
\(735\) | − | 38.2040i | − | 0.0519782i | ||||||
\(736\) | −1181.68 | − | 208.517i | −1.60555 | − | 0.283312i | ||||
\(737\) | 1258.80 | 1.70800 | ||||||||
\(738\) | −1202.03 | + | 344.643i | −1.62877 | + | 0.466996i | ||||
\(739\) | 1065.87i | 1.44231i | 0.692772 | + | 0.721157i | \(0.256389\pi\) | ||||
−0.692772 | + | 0.721157i | \(0.743611\pi\) | |||||||
\(740\) | −165.191 | + | 103.211i | −0.223231 | + | 0.139474i | ||||
\(741\) | −38.7994 | −0.0523609 | ||||||||
\(742\) | −204.222 | − | 712.275i | −0.275232 | − | 0.959939i | ||||
\(743\) | 1050.43i | 1.41376i | 0.707332 | + | 0.706881i | \(0.249898\pi\) | ||||
−0.707332 | + | 0.706881i | \(0.750102\pi\) | |||||||
\(744\) | −18.8051 | + | 20.8820i | −0.0252756 | + | 0.0280671i | ||||
\(745\) | −44.8087 | −0.0601459 | ||||||||
\(746\) | 513.966 | − | 147.363i | 0.688962 | − | 0.197538i | ||||
\(747\) | − | 813.038i | − | 1.08840i | ||||||
\(748\) | 511.317 | + | 818.370i | 0.683578 | + | 1.09408i | ||||
\(749\) | 694.831 | 0.927678 | ||||||||
\(750\) | 36.8720 | + | 128.600i | 0.0491627 | + | 0.171467i | ||||
\(751\) | 26.6606i | 0.0355002i | 0.999842 | + | 0.0177501i | \(0.00565033\pi\) | ||||
−0.999842 | + | 0.0177501i | \(0.994350\pi\) | |||||||
\(752\) | 466.558 | + | 227.614i | 0.620423 | + | 0.302679i | ||||
\(753\) | −23.5102 | −0.0312221 | ||||||||
\(754\) | 169.066 | − | 48.4741i | 0.224225 | − | 0.0642893i | ||||
\(755\) | − | 385.204i | − | 0.510204i | ||||||
\(756\) | −331.859 | + | 207.345i | −0.438967 | + | 0.274266i | ||||
\(757\) | 445.989 | 0.589153 | 0.294577 | − | 0.955628i | \(-0.404821\pi\) | ||||
0.294577 | + | 0.955628i | \(0.404821\pi\) | |||||||
\(758\) | −205.516 | − | 716.788i | −0.271129 | − | 0.945630i | ||||
\(759\) | − | 465.897i | − | 0.613830i | ||||||
\(760\) | −60.3025 | − | 54.3050i | −0.0793454 | − | 0.0714539i | ||||
\(761\) | 294.799 | 0.387384 | 0.193692 | − | 0.981062i | \(-0.437954\pi\) | ||||
0.193692 | + | 0.981062i | \(0.437954\pi\) | |||||||
\(762\) | 21.2456 | − | 6.09149i | 0.0278813 | − | 0.00799408i | ||||
\(763\) | − | 464.695i | − | 0.609037i | ||||||
\(764\) | −212.445 | − | 340.022i | −0.278070 | − | 0.445055i | ||||
\(765\) | 250.074 | 0.326894 | ||||||||
\(766\) | 10.8176 | + | 37.7291i | 0.0141222 | + | 0.0492547i | ||||
\(767\) | − | 538.084i | − | 0.701543i | ||||||
\(768\) | −130.077 | + | 101.585i | −0.169371 | + | 0.132272i | ||||
\(769\) | −279.363 | −0.363281 | −0.181641 | − | 0.983365i | \(-0.558141\pi\) | ||||
−0.181641 | + | 0.983365i | \(0.558141\pi\) | |||||||
\(770\) | −744.034 | + | 213.328i | −0.966278 | + | 0.277049i | ||||
\(771\) | 113.431i | 0.147122i | ||||||||
\(772\) | 570.312 | − | 356.330i | 0.738746 | − | 0.461567i | ||||
\(773\) | −1092.48 | −1.41329 | −0.706647 | − | 0.707566i | \(-0.749793\pi\) | ||||
−0.706647 | + | 0.707566i | \(0.749793\pi\) | |||||||
\(774\) | 48.0543 | + | 167.601i | 0.0620856 | + | 0.216539i | ||||
\(775\) | − | 106.705i | − | 0.137684i | ||||||
\(776\) | 807.400 | − | 896.571i | 1.04046 | − | 1.15537i | ||||
\(777\) | −116.412 | −0.149823 | ||||||||
\(778\) | −382.061 | + | 109.544i | −0.491081 | + | 0.140802i | ||||
\(779\) | − | 317.475i | − | 0.407542i | ||||||
\(780\) | 43.9044 | + | 70.2697i | 0.0562877 | + | 0.0900893i | ||||
\(781\) | 361.456 | 0.462811 | ||||||||
\(782\) | 258.746 | + | 902.441i | 0.330877 | + | 1.15402i | ||||
\(783\) | 72.2069i | 0.0922183i | ||||||||
\(784\) | −178.639 | + | 366.169i | −0.227856 | + | 0.467052i | ||||
\(785\) | −347.792 | −0.443047 | ||||||||
\(786\) | 284.255 | − | 81.5010i | 0.361648 | − | 0.103691i | ||||
\(787\) | − | 231.147i | − | 0.293706i | −0.989158 | − | 0.146853i | \(-0.953086\pi\) | ||
0.989158 | − | 0.146853i | \(-0.0469145\pi\) | |||||||
\(788\) | 735.127 | − | 459.306i | 0.932903 | − | 0.582876i | ||||
\(789\) | −286.820 | −0.363524 | ||||||||
\(790\) | 179.429 | + | 625.802i | 0.227125 | + | 0.792155i | ||||
\(791\) | − | 914.019i | − | 1.15552i | ||||||
\(792\) | 983.472 | + | 885.658i | 1.24176 | + | 1.11825i | ||||
\(793\) | 352.913 | 0.445035 | ||||||||
\(794\) | −568.011 | + | 162.859i | −0.715379 | + | 0.205112i | ||||
\(795\) | − | 64.4148i | − | 0.0810249i | ||||||
\(796\) | 174.339 | + | 279.032i | 0.219018 | + | 0.350543i | ||||
\(797\) | 453.389 | 0.568869 | 0.284435 | − | 0.958695i | \(-0.408194\pi\) | ||||
0.284435 | + | 0.958695i | \(0.408194\pi\) | |||||||
\(798\) | −13.3672 | − | 46.6213i | −0.0167508 | − | 0.0584227i | ||||
\(799\) | − | 406.146i | − | 0.508318i | ||||||
\(800\) | 108.904 | − | 617.165i | 0.136130 | − | 0.771456i | ||||
\(801\) | 286.327 | 0.357462 | ||||||||
\(802\) | 123.040 | − | 35.2777i | 0.153416 | − | 0.0439871i | ||||
\(803\) | − | 1403.47i | − | 1.74778i | ||||||
\(804\) | 142.853 | − | 89.2543i | 0.177678 | − | 0.111013i | ||||
\(805\) | −753.020 | −0.935429 | ||||||||
\(806\) | −41.4663 | − | 144.624i | −0.0514470 | − | 0.179434i | ||||
\(807\) | − | 96.5406i | − | 0.119629i | ||||||
\(808\) | −416.366 | + | 462.350i | −0.515304 | + | 0.572216i | ||||
\(809\) | 528.874 | 0.653738 | 0.326869 | − | 0.945070i | \(-0.394006\pi\) | ||||
0.326869 | + | 0.945070i | \(0.394006\pi\) | |||||||
\(810\) | 312.961 | − | 89.7315i | 0.386371 | − | 0.110780i | ||||
\(811\) | − | 1185.82i | − | 1.46217i | −0.682287 | − | 0.731084i | \(-0.739015\pi\) | ||
0.682287 | − | 0.731084i | \(-0.260985\pi\) | |||||||
\(812\) | 116.493 | + | 186.449i | 0.143464 | + | 0.229616i | ||||
\(813\) | −283.467 | −0.348668 | ||||||||
\(814\) | 222.288 | + | 775.286i | 0.273081 | + | 0.952439i | ||||
\(815\) | − | 341.539i | − | 0.419066i | ||||||
\(816\) | 116.052 | + | 56.6171i | 0.142221 | + | 0.0693837i | ||||
\(817\) | −44.2661 | −0.0541813 | ||||||||
\(818\) | −969.868 | + | 278.079i | −1.18566 | + | 0.339949i | ||||
\(819\) | − | 1022.75i | − | 1.24878i | ||||||
\(820\) | −574.979 | + | 359.246i | −0.701194 | + | 0.438105i | ||||
\(821\) | −570.471 | −0.694849 | −0.347424 | − | 0.937708i | \(-0.612944\pi\) | ||||
−0.347424 | + | 0.937708i | \(0.612944\pi\) | |||||||
\(822\) | −42.8469 | − | 149.439i | −0.0521252 | − | 0.181800i | ||||
\(823\) | 1386.72i | 1.68496i | 0.538728 | + | 0.842480i | \(0.318905\pi\) | ||||
−0.538728 | + | 0.842480i | \(0.681095\pi\) | |||||||
\(824\) | −88.8628 | − | 80.0247i | −0.107843 | − | 0.0971174i | ||||
\(825\) | 243.327 | 0.294942 | ||||||||
\(826\) | 646.560 | − | 185.380i | 0.782760 | − | 0.224431i | ||||
\(827\) | − | 1073.59i | − | 1.29818i | −0.760712 | − | 0.649089i | \(-0.775150\pi\) | ||
0.760712 | − | 0.649089i | \(-0.224850\pi\) | |||||||
\(828\) | 682.262 | + | 1091.97i | 0.823988 | + | 1.31881i | ||||
\(829\) | 1109.24 | 1.33804 | 0.669021 | − | 0.743243i | \(-0.266713\pi\) | ||||
0.669021 | + | 0.743243i | \(0.266713\pi\) | |||||||
\(830\) | −121.495 | − | 423.743i | −0.146379 | − | 0.510534i | ||||
\(831\) | − | 53.6685i | − | 0.0645830i | ||||||
\(832\) | −92.2299 | − | 878.799i | −0.110853 | − | 1.05625i | ||||
\(833\) | 318.756 | 0.382660 | ||||||||
\(834\) | −180.794 | + | 51.8369i | −0.216779 | + | 0.0621545i | ||||
\(835\) | − | 496.831i | − | 0.595007i | ||||||
\(836\) | −284.965 | + | 178.046i | −0.340867 | + | 0.212973i | ||||
\(837\) | 61.7681 | 0.0737970 | ||||||||
\(838\) | −259.241 | − | 904.167i | −0.309356 | − | 1.07896i | ||||
\(839\) | − | 1547.29i | − | 1.84421i | −0.386943 | − | 0.922104i | \(-0.626469\pi\) | ||
0.386943 | − | 0.922104i | \(-0.373531\pi\) | |||||||
\(840\) | −69.3099 | + | 76.9647i | −0.0825118 | + | 0.0916246i | ||||
\(841\) | −800.432 | −0.951762 | ||||||||
\(842\) | 903.658 | − | 259.095i | 1.07323 | − | 0.307714i | ||||
\(843\) | 8.37157i | 0.00993069i | ||||||||
\(844\) | 34.8011 | + | 55.6997i | 0.0412335 | + | 0.0659949i | ||||
\(845\) | −50.3218 | −0.0595524 | ||||||||
\(846\) | −153.527 | − | 535.463i | −0.181474 | − | 0.632935i | ||||
\(847\) | 2160.76i | 2.55107i | ||||||||
\(848\) | −301.199 | + | 617.389i | −0.355187 | + | 0.728053i | ||||
\(849\) | −71.5762 | −0.0843065 | ||||||||
\(850\) | −471.324 | + | 135.137i | −0.554498 | + | 0.158985i | ||||
\(851\) | 784.649i | 0.922031i | ||||||||
\(852\) | 41.0194 | − | 25.6288i | 0.0481448 | − | 0.0300808i | ||||
\(853\) | −341.108 | −0.399892 | −0.199946 | − | 0.979807i | \(-0.564077\pi\) | ||||
−0.199946 | + | 0.979807i | \(0.564077\pi\) | |||||||
\(854\) | 121.585 | + | 424.059i | 0.142372 | + | 0.496557i | ||||
\(855\) | 87.0782i | 0.101846i | ||||||||
\(856\) | −478.674 | − | 431.067i | −0.559199 | − | 0.503583i | ||||
\(857\) | 1535.74 | 1.79200 | 0.896000 | − | 0.444054i | \(-0.146460\pi\) | ||||
0.896000 | + | 0.444054i | \(0.146460\pi\) | |||||||
\(858\) | 329.795 | − | 94.5581i | 0.384376 | − | 0.110208i | ||||
\(859\) | 1223.16i | 1.42393i | 0.702213 | + | 0.711967i | \(0.252196\pi\) | ||||
−0.702213 | + | 0.711967i | \(0.747804\pi\) | |||||||
\(860\) | 50.0904 | + | 80.1704i | 0.0582446 | + | 0.0932214i | ||||
\(861\) | −405.196 | −0.470611 | ||||||||
\(862\) | −123.477 | − | 430.658i | −0.143245 | − | 0.499603i | ||||
\(863\) | − | 672.603i | − | 0.779377i | −0.920947 | − | 0.389689i | \(-0.872583\pi\) | ||
0.920947 | − | 0.389689i | \(-0.127417\pi\) | |||||||
\(864\) | 357.255 | + | 63.0406i | 0.413490 | + | 0.0729636i | ||||
\(865\) | 653.266 | 0.755221 | ||||||||
\(866\) | −346.302 | + | 99.2909i | −0.399887 | + | 0.114655i | ||||
\(867\) | 85.2940i | 0.0983783i | ||||||||
\(868\) | 159.494 | − | 99.6516i | 0.183749 | − | 0.114806i | ||||
\(869\) | 2695.62 | 3.10197 | ||||||||
\(870\) | 5.26753 | + | 18.3718i | 0.00605463 | + | 0.0211170i | ||||
\(871\) | 901.827i | 1.03539i | ||||||||
\(872\) | −288.293 | + | 320.132i | −0.330611 | + | 0.367124i | ||||
\(873\) | −1294.67 | −1.48301 | ||||||||
\(874\) | −314.239 | + | 90.0980i | −0.359542 | + | 0.103087i | ||||
\(875\) | − | 895.324i | − | 1.02323i | ||||||
\(876\) | −99.5121 | − | 159.271i | −0.113598 | − | 0.181816i | ||||
\(877\) | −1328.68 | −1.51503 | −0.757514 | − | 0.652819i | \(-0.773586\pi\) | ||||
−0.757514 | + | 0.652819i | \(0.773586\pi\) | |||||||
\(878\) | −325.226 | − | 1134.31i | −0.370416 | − | 1.29192i | ||||
\(879\) | 91.2717i | 0.103836i | ||||||||
\(880\) | 644.917 | + | 314.629i | 0.732861 | + | 0.357532i | ||||
\(881\) | 372.924 | 0.423296 | 0.211648 | − | 0.977346i | \(-0.432117\pi\) | ||||
0.211648 | + | 0.977346i | \(0.432117\pi\) | |||||||
\(882\) | 420.248 | − | 120.493i | 0.476472 | − | 0.136613i | ||||
\(883\) | − | 669.314i | − | 0.758000i | −0.925397 | − | 0.379000i | \(-0.876268\pi\) | ||
0.925397 | − | 0.379000i | \(-0.123732\pi\) | |||||||
\(884\) | −586.297 | + | 366.318i | −0.663232 | + | 0.414387i | ||||
\(885\) | 58.4718 | 0.0660699 | ||||||||
\(886\) | −86.7957 | − | 302.722i | −0.0979635 | − | 0.341672i | ||||
\(887\) | − | 874.225i | − | 0.985598i | −0.870143 | − | 0.492799i | \(-0.835974\pi\) | ||
0.870143 | − | 0.492799i | \(-0.164026\pi\) | |||||||
\(888\) | 80.1974 | + | 72.2211i | 0.0903124 | + | 0.0813301i | ||||
\(889\) | −147.913 | −0.166381 | ||||||||
\(890\) | 149.230 | − | 42.7868i | 0.167674 | − | 0.0480750i | ||||
\(891\) | − | 1348.06i | − | 1.51298i | ||||||
\(892\) | −413.781 | − | 662.263i | −0.463880 | − | 0.742448i | ||||
\(893\) | 141.424 | 0.158370 | ||||||||
\(894\) | 6.84270 | + | 23.8656i | 0.00765402 | + | 0.0266953i | ||||
\(895\) | 81.8873i | 0.0914942i | ||||||||
\(896\) | 1024.19 | − | 413.587i | 1.14307 | − | 0.461592i | ||||
\(897\) | 333.778 | 0.372105 | ||||||||
\(898\) | 1375.45 | − | 394.366i | 1.53168 | − | 0.439160i | ||||
\(899\) | − | 34.7032i | − | 0.0386020i | ||||||
\(900\) | −570.311 | + | 356.329i | −0.633678 | + | 0.395921i | ||||
\(901\) | 537.447 | 0.596500 | ||||||||
\(902\) | 773.718 | + | 2698.53i | 0.857780 | + | 2.99172i | ||||
\(903\) | 56.4973i | 0.0625662i | ||||||||
\(904\) | −567.048 | + | 629.674i | −0.627266 | + | 0.696543i | ||||
\(905\) | 804.123 | 0.888534 | ||||||||
\(906\) | −205.164 | + | 58.8241i | −0.226450 | + | 0.0649273i | ||||
\(907\) | − | 33.1952i | − | 0.0365989i | −0.999833 | − | 0.0182994i | \(-0.994175\pi\) | ||
0.999833 | − | 0.0182994i | \(-0.00582522\pi\) | |||||||
\(908\) | −647.304 | − | 1036.02i | −0.712890 | − | 1.14099i | ||||
\(909\) | 667.644 | 0.734482 | ||||||||
\(910\) | −152.832 | − | 533.041i | −0.167948 | − | 0.585760i | ||||
\(911\) | 25.4273i | 0.0279114i | 0.999903 | + | 0.0139557i | \(0.00444238\pi\) | ||||
−0.999903 | + | 0.0139557i | \(0.995558\pi\) | |||||||
\(912\) | −19.7147 | + | 40.4106i | −0.0216170 | + | 0.0443099i | ||||
\(913\) | −1825.26 | −1.99918 | ||||||||
\(914\) | −60.2709 | + | 17.2807i | −0.0659419 | + | 0.0189067i | ||||
\(915\) | 38.3499i | 0.0419125i | ||||||||
\(916\) | −779.165 | + | 486.821i | −0.850617 | + | 0.531464i | ||||
\(917\) | −1979.00 | −2.15812 | ||||||||
\(918\) | −78.2260 | − | 272.833i | −0.0852135 | − | 0.297204i | ||||
\(919\) | − | 445.408i | − | 0.484666i | −0.970193 | − | 0.242333i | \(-0.922087\pi\) | ||
0.970193 | − | 0.242333i | \(-0.0779126\pi\) | |||||||
\(920\) | 518.761 | + | 467.166i | 0.563871 | + | 0.507790i | ||||
\(921\) | −230.639 | −0.250422 | ||||||||
\(922\) | −708.875 | + | 203.247i | −0.768845 | + | 0.220442i | ||||
\(923\) | 258.954i | 0.280557i | ||||||||
\(924\) | 227.241 | + | 363.704i | 0.245932 | + | 0.393619i | ||||
\(925\) | −409.804 | −0.443031 | ||||||||
\(926\) | 450.575 | + | 1571.49i | 0.486582 | + | 1.69707i | ||||
\(927\) | 128.320i | 0.138425i | ||||||||
\(928\) | 35.4181 | − | 200.717i | 0.0381661 | − | 0.216290i | ||||
\(929\) | −408.473 | −0.439691 | −0.219846 | − | 0.975535i | \(-0.570555\pi\) | ||||
−0.219846 | + | 0.975535i | \(0.570555\pi\) | |||||||
\(930\) | 15.7158 | − | 4.50601i | 0.0168987 | − | 0.00484517i | ||||
\(931\) | 110.994i | 0.119220i | ||||||||
\(932\) | 636.622 | − | 397.760i | 0.683070 | − | 0.426781i | ||||
\(933\) | 304.547 | 0.326417 | ||||||||
\(934\) | −47.9122 | − | 167.106i | −0.0512979 | − | 0.178914i | ||||
\(935\) | − | 561.411i | − | 0.600439i | ||||||
\(936\) | −634.503 | + | 704.579i | −0.677888 | + | 0.752756i | ||||
\(937\) | −1101.68 | −1.17576 | −0.587878 | − | 0.808950i | \(-0.700037\pi\) | ||||
−0.587878 | + | 0.808950i | \(0.700037\pi\) | |||||||
\(938\) | −1083.63 | + | 310.697i | −1.15526 | + | 0.331233i | ||||
\(939\) | − | 41.1060i | − | 0.0437764i | ||||||
\(940\) | −160.032 | − | 256.134i | −0.170247 | − | 0.272482i | ||||
\(941\) | −1342.45 | −1.42662 | −0.713309 | − | 0.700850i | \(-0.752804\pi\) | ||||
−0.713309 | + | 0.700850i | \(0.752804\pi\) | |||||||
\(942\) | 53.1109 | + | 185.238i | 0.0563810 | + | 0.196643i | ||||
\(943\) | 2731.12i | 2.89621i | ||||||||
\(944\) | −560.428 | − | 273.410i | −0.593674 | − | 0.289629i | ||||
\(945\) | 227.659 | 0.240909 | ||||||||
\(946\) | 376.262 | − | 107.881i | 0.397740 | − | 0.114039i | ||||
\(947\) | 786.294i | 0.830300i | 0.909753 | + | 0.415150i | \(0.136271\pi\) | ||||
−0.909753 | + | 0.415150i | \(0.863729\pi\) | |||||||
\(948\) | 305.909 | − | 191.131i | 0.322689 | − | 0.201615i | ||||
\(949\) | 1005.47 | 1.05951 | ||||||||
\(950\) | −47.0561 | − | 164.120i | −0.0495327 | − | 0.172758i | ||||
\(951\) | − | 128.116i | − | 0.134717i | ||||||
\(952\) | −642.157 | − | 578.290i | −0.674535 | − | 0.607447i | ||||
\(953\) | 1134.64 | 1.19060 | 0.595301 | − | 0.803503i | \(-0.297033\pi\) | ||||
0.595301 | + | 0.803503i | \(0.297033\pi\) | |||||||
\(954\) | 708.570 | − | 203.160i | 0.742736 | − | 0.212956i | ||||
\(955\) | 233.258i | 0.244250i | ||||||||
\(956\) | −148.048 | − | 236.953i | −0.154862 | − | 0.247859i | ||||
\(957\) | 79.1357 | 0.0826915 | ||||||||
\(958\) | 183.617 | + | 640.410i | 0.191667 | + | 0.668486i | ||||
\(959\) | 1040.40i | 1.08488i | ||||||||
\(960\) | 95.4963 | − | 10.0223i | 0.0994753 | − | 0.0104399i | ||||
\(961\) | 931.314 | 0.969109 | ||||||||
\(962\) | −555.430 | + | 159.252i | −0.577371 | + | 0.165542i | ||||
\(963\) | 691.217i | 0.717775i | ||||||||
\(964\) | 1009.42 | − | 630.682i | 1.04711 | − | 0.654234i | ||||
\(965\) | −391.240 | −0.405430 | ||||||||
\(966\) | 114.993 | + | 401.067i | 0.119040 | + | 0.415183i | ||||
\(967\) | − | 963.333i | − | 0.996208i | −0.867117 | − | 0.498104i | \(-0.834030\pi\) | ||
0.867117 | − | 0.498104i | \(-0.165970\pi\) | |||||||
\(968\) | 1340.51 | − | 1488.56i | 1.38483 | − | 1.53777i | ||||
\(969\) | 35.1781 | 0.0363035 | ||||||||
\(970\) | −674.762 | + | 193.466i | −0.695631 | + | 0.199450i | ||||
\(971\) | 1320.90i | 1.36035i | 0.733050 | + | 0.680174i | \(0.238096\pi\) | ||||
−0.733050 | + | 0.680174i | \(0.761904\pi\) | |||||||
\(972\) | −311.838 | − | 499.101i | −0.320821 | − | 0.513478i | ||||
\(973\) | 1258.70 | 1.29363 | ||||||||
\(974\) | 145.904 | + | 508.876i | 0.149799 | + | 0.522460i | ||||
\(975\) | 174.324i | 0.178794i | ||||||||
\(976\) | 179.321 | − | 367.568i | 0.183731 | − | 0.376607i | ||||
\(977\) | −1159.80 | −1.18710 | −0.593550 | − | 0.804797i | \(-0.702274\pi\) | ||||
−0.593550 | + | 0.804797i | \(0.702274\pi\) | |||||||
\(978\) | −181.907 | + | 52.1561i | −0.185999 | + | 0.0533293i | ||||
\(979\) | − | 642.800i | − | 0.656588i | ||||||
\(980\) | 201.021 | − | 125.598i | 0.205124 | − | 0.128161i | ||||
\(981\) | 462.278 | 0.471232 | ||||||||
\(982\) | −222.075 | − | 774.541i | −0.226145 | − | 0.788738i | ||||
\(983\) | − | 8.37645i | − | 0.00852131i | −0.999991 | − | 0.00426065i | \(-0.998644\pi\) | ||
0.999991 | − | 0.00426065i | \(-0.00135621\pi\) | |||||||
\(984\) | 279.143 | + | 251.380i | 0.283682 | + | 0.255467i | ||||
\(985\) | −504.305 | −0.511985 | ||||||||
\(986\) | −153.286 | + | 43.9498i | −0.155462 | + | 0.0445738i | ||||
\(987\) | − | 180.501i | − | 0.182879i | ||||||
\(988\) | −127.556 | − | 204.155i | −0.129105 | − | 0.206634i | ||||
\(989\) | 380.806 | 0.385041 | ||||||||
\(990\) | −212.218 | − | 740.164i | −0.214362 | − | 0.747641i | ||||
\(991\) | 854.355i | 0.862114i | 0.902325 | + | 0.431057i | \(0.141859\pi\) | ||||
−0.902325 | + | 0.431057i | \(0.858141\pi\) | |||||||
\(992\) | −171.700 | − | 30.2978i | −0.173084 | − | 0.0305421i | ||||
\(993\) | 282.855 | 0.284849 | ||||||||
\(994\) | −311.159 | + | 89.2147i | −0.313037 | + | 0.0897532i | ||||
\(995\) | − | 191.419i | − | 0.192381i | ||||||
\(996\) | −207.137 | + | 129.419i | −0.207969 | + | 0.129939i | ||||
\(997\) | −77.4664 | −0.0776995 | −0.0388497 | − | 0.999245i | \(-0.512369\pi\) | ||||
−0.0388497 | + | 0.999245i | \(0.512369\pi\) | |||||||
\(998\) | −193.224 | − | 673.918i | −0.193612 | − | 0.675269i | ||||
\(999\) | − | 237.221i | − | 0.237458i |
(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 | 76.3.b.b.39.2 | yes | 14 | |
3.2 | odd | 2 | 684.3.g.b.343.13 | 14 | |||
4.3 | odd | 2 | inner | 76.3.b.b.39.1 | ✓ | 14 | |
8.3 | odd | 2 | 1216.3.d.d.191.7 | 14 | |||
8.5 | even | 2 | 1216.3.d.d.191.8 | 14 | |||
12.11 | even | 2 | 684.3.g.b.343.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.b.b.39.1 | ✓ | 14 | 4.3 | odd | 2 | inner | |
76.3.b.b.39.2 | yes | 14 | 1.1 | even | 1 | trivial | |
684.3.g.b.343.13 | 14 | 3.2 | odd | 2 | |||
684.3.g.b.343.14 | 14 | 12.11 | even | 2 | |||
1216.3.d.d.191.7 | 14 | 8.3 | odd | 2 | |||
1216.3.d.d.191.8 | 14 | 8.5 | even | 2 |