Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 553.20 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.b.277.20 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −4.82966 | + | 1.29396i | −0.965933 | + | 0.258793i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 5.84802 | − | 5.84802i | 0.835432 | − | 0.835432i | −0.152822 | − | 0.988254i | \(-0.548836\pi\) |
0.988254 | + | 0.152822i | \(0.0488360\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 3.53570 | − | 6.12363i | 0.353570 | − | 0.612363i | ||||
\(11\) | −1.76345 | −0.160313 | −0.0801567 | − | 0.996782i | \(-0.525542\pi\) | ||||
−0.0801567 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | 5.00063 | + | 5.00063i | 0.384664 | + | 0.384664i | 0.872779 | − | 0.488115i | \(-0.162315\pi\) |
−0.488115 | + | 0.872779i | \(0.662315\pi\) | |||||||
\(14\) | 11.6960i | 0.835432i | ||||||||
\(15\) | −7.49988 | − | 4.33033i | −0.499992 | − | 0.288689i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −8.50993 | + | 8.50993i | −0.500584 | + | 0.500584i | −0.911619 | − | 0.411035i | \(-0.865167\pi\) |
0.411035 | + | 0.911619i | \(0.365167\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | − | 22.3969i | − | 1.17879i | −0.807847 | − | 0.589393i | \(-0.799367\pi\) | ||
0.807847 | − | 0.589393i | \(-0.200633\pi\) | |||||||
\(20\) | 2.58793 | + | 9.65933i | 0.129396 | + | 0.482966i | ||||
\(21\) | 14.3247 | 0.682127 | ||||||||
\(22\) | 1.76345 | − | 1.76345i | 0.0801567 | − | 0.0801567i | ||||
\(23\) | 3.39116 | + | 3.39116i | 0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 21.6513 | − | 12.4988i | 0.866053 | − | 0.499953i | ||||
\(26\) | −10.0013 | −0.384664 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | −11.6960 | − | 11.6960i | −0.417716 | − | 0.417716i | ||||
\(29\) | − | 38.8089i | − | 1.33824i | −0.743155 | − | 0.669120i | \(-0.766671\pi\) | ||
0.743155 | − | 0.669120i | \(-0.233329\pi\) | |||||||
\(30\) | 11.8302 | − | 3.16955i | 0.394340 | − | 0.105652i | ||||
\(31\) | 15.0913 | 0.486815 | 0.243407 | − | 0.969924i | \(-0.421735\pi\) | ||||
0.243407 | + | 0.969924i | \(0.421735\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | −2.15977 | − | 2.15977i | −0.0654476 | − | 0.0654476i | ||||
\(34\) | − | 17.0199i | − | 0.500584i | ||||||
\(35\) | −20.6769 | + | 35.8111i | −0.590768 | + | 1.02318i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 28.5900 | − | 28.5900i | 0.772702 | − | 0.772702i | −0.205876 | − | 0.978578i | \(-0.566004\pi\) |
0.978578 | + | 0.205876i | \(0.0660044\pi\) | |||||||
\(38\) | 22.3969 | + | 22.3969i | 0.589393 | + | 0.589393i | ||||
\(39\) | 12.2490i | 0.314077i | ||||||||
\(40\) | −12.2473 | − | 7.07140i | −0.306181 | − | 0.176785i | ||||
\(41\) | 63.9487 | 1.55972 | 0.779862 | − | 0.625951i | \(-0.215289\pi\) | ||||
0.779862 | + | 0.625951i | \(0.215289\pi\) | |||||||
\(42\) | −14.3247 | + | 14.3247i | −0.341064 | + | 0.341064i | ||||
\(43\) | 34.7533 | + | 34.7533i | 0.808217 | + | 0.808217i | 0.984364 | − | 0.176147i | \(-0.0563634\pi\) |
−0.176147 | + | 0.984364i | \(0.556363\pi\) | |||||||
\(44\) | 3.52689i | 0.0801567i | ||||||||
\(45\) | −3.88189 | − | 14.4890i | −0.0862642 | − | 0.321978i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 2.22777 | − | 2.22777i | 0.0473994 | − | 0.0473994i | −0.683010 | − | 0.730409i | \(-0.739329\pi\) |
0.730409 | + | 0.683010i | \(0.239329\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 19.3988i | − | 0.395894i | ||||||
\(50\) | −9.15250 | + | 34.1501i | −0.183050 | + | 0.683003i | ||||
\(51\) | −20.8450 | −0.408725 | ||||||||
\(52\) | 10.0013 | − | 10.0013i | 0.192332 | − | 0.192332i | ||||
\(53\) | 67.8328 | + | 67.8328i | 1.27986 | + | 1.27986i | 0.940743 | + | 0.339121i | \(0.110129\pi\) |
0.339121 | + | 0.940743i | \(0.389871\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 8.51686 | − | 2.28183i | 0.154852 | − | 0.0414879i | ||||
\(56\) | 23.3921 | 0.417716 | ||||||||
\(57\) | 27.4305 | − | 27.4305i | 0.481237 | − | 0.481237i | ||||
\(58\) | 38.8089 | + | 38.8089i | 0.669120 | + | 0.669120i | ||||
\(59\) | 29.3548i | 0.497538i | 0.968563 | + | 0.248769i | \(0.0800260\pi\) | ||||
−0.968563 | + | 0.248769i | \(0.919974\pi\) | |||||||
\(60\) | −8.66066 | + | 14.9998i | −0.144344 | + | 0.249996i | ||||
\(61\) | 54.6267 | 0.895520 | 0.447760 | − | 0.894154i | \(-0.352222\pi\) | ||||
0.447760 | + | 0.894154i | \(0.352222\pi\) | |||||||
\(62\) | −15.0913 | + | 15.0913i | −0.243407 | + | 0.243407i | ||||
\(63\) | 17.5441 | + | 17.5441i | 0.278477 | + | 0.278477i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −30.6220 | − | 17.6807i | −0.471108 | − | 0.272011i | ||||
\(66\) | 4.31954 | 0.0654476 | ||||||||
\(67\) | 14.0005 | − | 14.0005i | 0.208963 | − | 0.208963i | −0.594864 | − | 0.803826i | \(-0.702794\pi\) |
0.803826 | + | 0.594864i | \(0.202794\pi\) | |||||||
\(68\) | 17.0199 | + | 17.0199i | 0.250292 | + | 0.250292i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | −15.1343 | − | 56.4880i | −0.216204 | − | 0.806971i | ||||
\(71\) | −36.0984 | −0.508428 | −0.254214 | − | 0.967148i | \(-0.581817\pi\) | ||||
−0.254214 | + | 0.967148i | \(0.581817\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −58.7921 | − | 58.7921i | −0.805371 | − | 0.805371i | 0.178558 | − | 0.983929i | \(-0.442857\pi\) |
−0.983929 | + | 0.178558i | \(0.942857\pi\) | |||||||
\(74\) | 57.1799i | 0.772702i | ||||||||
\(75\) | 41.8252 | + | 11.2095i | 0.557669 | + | 0.149460i | ||||
\(76\) | −44.7938 | −0.589393 | ||||||||
\(77\) | −10.3127 | + | 10.3127i | −0.133931 | + | 0.133931i | ||||
\(78\) | −12.2490 | − | 12.2490i | −0.157038 | − | 0.157038i | ||||
\(79\) | 128.176i | 1.62248i | 0.584713 | + | 0.811240i | \(0.301207\pi\) | ||||
−0.584713 | + | 0.811240i | \(0.698793\pi\) | |||||||
\(80\) | 19.3187 | − | 5.17585i | 0.241483 | − | 0.0646982i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −63.9487 | + | 63.9487i | −0.779862 | + | 0.779862i | ||||
\(83\) | −68.9222 | − | 68.9222i | −0.830389 | − | 0.830389i | 0.157181 | − | 0.987570i | \(-0.449759\pi\) |
−0.987570 | + | 0.157181i | \(0.949759\pi\) | |||||||
\(84\) | − | 28.6494i | − | 0.341064i | ||||||
\(85\) | 30.0886 | − | 52.1116i | 0.353983 | − | 0.613078i | ||||
\(86\) | −69.5066 | −0.808217 | ||||||||
\(87\) | 47.5310 | − | 47.5310i | 0.546334 | − | 0.546334i | ||||
\(88\) | −3.52689 | − | 3.52689i | −0.0400783 | − | 0.0400783i | ||||
\(89\) | 19.7288i | 0.221672i | 0.993839 | + | 0.110836i | \(0.0353529\pi\) | ||||
−0.993839 | + | 0.110836i | \(0.964647\pi\) | |||||||
\(90\) | 18.3709 | + | 10.6071i | 0.204121 | + | 0.117857i | ||||
\(91\) | 58.4876 | 0.642721 | ||||||||
\(92\) | 6.78233 | − | 6.78233i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | 18.4829 | + | 18.4829i | 0.198741 | + | 0.198741i | ||||
\(94\) | 4.45554i | 0.0473994i | ||||||||
\(95\) | 28.9808 | + | 108.170i | 0.305061 | + | 1.13863i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 85.9628 | − | 85.9628i | 0.886215 | − | 0.886215i | −0.107942 | − | 0.994157i | \(-0.534426\pi\) |
0.994157 | + | 0.107942i | \(0.0344262\pi\) | |||||||
\(98\) | 19.3988 | + | 19.3988i | 0.197947 | + | 0.197947i | ||||
\(99\) | − | 5.29034i | − | 0.0534378i | ||||||
\(100\) | −24.9976 | − | 43.3026i | −0.249976 | − | 0.433026i | ||||
\(101\) | −9.56680 | −0.0947207 | −0.0473604 | − | 0.998878i | \(-0.515081\pi\) | ||||
−0.0473604 | + | 0.998878i | \(0.515081\pi\) | |||||||
\(102\) | 20.8450 | − | 20.8450i | 0.204363 | − | 0.204363i | ||||
\(103\) | 52.1473 | + | 52.1473i | 0.506284 | + | 0.506284i | 0.913384 | − | 0.407100i | \(-0.133460\pi\) |
−0.407100 | + | 0.913384i | \(0.633460\pi\) | |||||||
\(104\) | 20.0025i | 0.192332i | ||||||||
\(105\) | −69.1834 | + | 18.5356i | −0.658889 | + | 0.176530i | ||||
\(106\) | −135.666 | −1.27986 | ||||||||
\(107\) | 125.340 | − | 125.340i | 1.17140 | − | 1.17140i | 0.189525 | − | 0.981876i | \(-0.439305\pi\) |
0.981876 | − | 0.189525i | \(-0.0606947\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 65.7207i | 0.602942i | 0.953475 | + | 0.301471i | \(0.0974777\pi\) | ||||
−0.953475 | + | 0.301471i | \(0.902522\pi\) | |||||||
\(110\) | −6.23502 | + | 10.7987i | −0.0566820 | + | 0.0981699i | ||||
\(111\) | 70.0308 | 0.630908 | ||||||||
\(112\) | −23.3921 | + | 23.3921i | −0.208858 | + | 0.208858i | ||||
\(113\) | 50.2423 | + | 50.2423i | 0.444622 | + | 0.444622i | 0.893562 | − | 0.448940i | \(-0.148198\pi\) |
−0.448940 | + | 0.893562i | \(0.648198\pi\) | |||||||
\(114\) | 54.8610i | 0.481237i | ||||||||
\(115\) | −20.7662 | − | 11.9901i | −0.180576 | − | 0.104262i | ||||
\(116\) | −77.6179 | −0.669120 | ||||||||
\(117\) | −15.0019 | + | 15.0019i | −0.128221 | + | 0.128221i | ||||
\(118\) | −29.3548 | − | 29.3548i | −0.248769 | − | 0.248769i | ||||
\(119\) | 99.5325i | 0.836408i | ||||||||
\(120\) | −6.33910 | − | 23.6604i | −0.0528258 | − | 0.197170i | ||||
\(121\) | −117.890 | −0.974300 | ||||||||
\(122\) | −54.6267 | + | 54.6267i | −0.447760 | + | 0.447760i | ||||
\(123\) | 78.3209 | + | 78.3209i | 0.636755 | + | 0.636755i | ||||
\(124\) | − | 30.1825i | − | 0.243407i | ||||||
\(125\) | −88.3956 | + | 88.3811i | −0.707165 | + | 0.707049i | ||||
\(126\) | −35.0881 | −0.278477 | ||||||||
\(127\) | 87.1032 | − | 87.1032i | 0.685852 | − | 0.685852i | −0.275461 | − | 0.961312i | \(-0.588830\pi\) |
0.961312 | + | 0.275461i | \(0.0888304\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 85.1279i | 0.659906i | ||||||||
\(130\) | 48.3027 | − | 12.9413i | 0.371560 | − | 0.0995482i | ||||
\(131\) | 151.951 | 1.15993 | 0.579966 | − | 0.814641i | \(-0.303066\pi\) | ||||
0.579966 | + | 0.814641i | \(0.303066\pi\) | |||||||
\(132\) | −4.31954 | + | 4.31954i | −0.0327238 | + | 0.0327238i | ||||
\(133\) | −130.978 | − | 130.978i | −0.984795 | − | 0.984795i | ||||
\(134\) | 28.0010i | 0.208963i | ||||||||
\(135\) | 12.9910 | − | 22.4996i | 0.0962296 | − | 0.166664i | ||||
\(136\) | −34.0397 | −0.250292 | ||||||||
\(137\) | 67.2320 | − | 67.2320i | 0.490745 | − | 0.490745i | −0.417796 | − | 0.908541i | \(-0.637197\pi\) |
0.908541 | + | 0.417796i | \(0.137197\pi\) | |||||||
\(138\) | −8.30662 | − | 8.30662i | −0.0601929 | − | 0.0601929i | ||||
\(139\) | 147.787i | 1.06322i | 0.846990 | + | 0.531610i | \(0.178413\pi\) | ||||
−0.846990 | + | 0.531610i | \(0.821587\pi\) | |||||||
\(140\) | 71.6223 | + | 41.3537i | 0.511588 | + | 0.295384i | ||||
\(141\) | 5.45691 | 0.0387015 | ||||||||
\(142\) | 36.0984 | − | 36.0984i | 0.254214 | − | 0.254214i | ||||
\(143\) | −8.81835 | − | 8.81835i | −0.0616668 | − | 0.0616668i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 50.2173 | + | 187.434i | 0.346326 | + | 1.29265i | ||||
\(146\) | 117.584 | 0.805371 | ||||||||
\(147\) | 23.7586 | − | 23.7586i | 0.161623 | − | 0.161623i | ||||
\(148\) | −57.1799 | − | 57.1799i | −0.386351 | − | 0.386351i | ||||
\(149\) | − | 34.3711i | − | 0.230678i | −0.993326 | − | 0.115339i | \(-0.963205\pi\) | ||
0.993326 | − | 0.115339i | \(-0.0367955\pi\) | |||||||
\(150\) | −53.0347 | + | 30.6157i | −0.353565 | + | 0.204105i | ||||
\(151\) | −187.555 | −1.24208 | −0.621042 | − | 0.783777i | \(-0.713290\pi\) | ||||
−0.621042 | + | 0.783777i | \(0.713290\pi\) | |||||||
\(152\) | 44.7938 | − | 44.7938i | 0.294696 | − | 0.294696i | ||||
\(153\) | −25.5298 | − | 25.5298i | −0.166861 | − | 0.166861i | ||||
\(154\) | − | 20.6254i | − | 0.133931i | ||||||
\(155\) | −72.8857 | + | 19.5275i | −0.470230 | + | 0.125984i | ||||
\(156\) | 24.4980 | 0.157038 | ||||||||
\(157\) | 173.198 | − | 173.198i | 1.10317 | − | 1.10317i | 0.109147 | − | 0.994026i | \(-0.465188\pi\) |
0.994026 | − | 0.109147i | \(-0.0348120\pi\) | |||||||
\(158\) | −128.176 | − | 128.176i | −0.811240 | − | 0.811240i | ||||
\(159\) | 166.156i | 1.04500i | ||||||||
\(160\) | −14.1428 | + | 24.4945i | −0.0883925 | + | 0.153091i | ||||
\(161\) | 39.6632 | 0.246355 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −12.3280 | − | 12.3280i | −0.0756321 | − | 0.0756321i | 0.668279 | − | 0.743911i | \(-0.267031\pi\) |
−0.743911 | + | 0.668279i | \(0.767031\pi\) | |||||||
\(164\) | − | 127.897i | − | 0.779862i | ||||||
\(165\) | 13.2256 | + | 7.63631i | 0.0801554 | + | 0.0462807i | ||||
\(166\) | 137.844 | 0.830389 | ||||||||
\(167\) | 67.8791 | − | 67.8791i | 0.406461 | − | 0.406461i | −0.474041 | − | 0.880503i | \(-0.657205\pi\) |
0.880503 | + | 0.474041i | \(0.157205\pi\) | |||||||
\(168\) | 28.6494 | + | 28.6494i | 0.170532 | + | 0.170532i | ||||
\(169\) | − | 118.987i | − | 0.704067i | ||||||
\(170\) | 22.0231 | + | 82.2002i | 0.129547 | + | 0.483531i | ||||
\(171\) | 67.1908 | 0.392928 | ||||||||
\(172\) | 69.5066 | − | 69.5066i | 0.404108 | − | 0.404108i | ||||
\(173\) | 36.4436 | + | 36.4436i | 0.210656 | + | 0.210656i | 0.804546 | − | 0.593890i | \(-0.202409\pi\) |
−0.593890 | + | 0.804546i | \(0.702409\pi\) | |||||||
\(174\) | 95.0621i | 0.546334i | ||||||||
\(175\) | 53.5241 | − | 199.711i | 0.305852 | − | 1.14120i | ||||
\(176\) | 7.05379 | 0.0400783 | ||||||||
\(177\) | −35.9521 | + | 35.9521i | −0.203119 | + | 0.203119i | ||||
\(178\) | −19.7288 | − | 19.7288i | −0.110836 | − | 0.110836i | ||||
\(179\) | 96.1704i | 0.537265i | 0.963243 | + | 0.268633i | \(0.0865717\pi\) | ||||
−0.963243 | + | 0.268633i | \(0.913428\pi\) | |||||||
\(180\) | −28.9780 | + | 7.76378i | −0.160989 | + | 0.0431321i | ||||
\(181\) | 204.330 | 1.12889 | 0.564447 | − | 0.825469i | \(-0.309089\pi\) | ||||
0.564447 | + | 0.825469i | \(0.309089\pi\) | |||||||
\(182\) | −58.4876 | + | 58.4876i | −0.321361 | + | 0.321361i | ||||
\(183\) | 66.9038 | + | 66.9038i | 0.365594 | + | 0.365594i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −101.086 | + | 175.074i | −0.546409 | + | 0.946348i | ||||
\(186\) | −36.9659 | −0.198741 | ||||||||
\(187\) | 15.0068 | − | 15.0068i | 0.0802503 | − | 0.0802503i | ||||
\(188\) | −4.45554 | − | 4.45554i | −0.0236997 | − | 0.0236997i | ||||
\(189\) | 42.9740i | 0.227376i | ||||||||
\(190\) | −137.150 | − | 79.1888i | −0.721844 | − | 0.416783i | ||||
\(191\) | −103.300 | −0.540835 | −0.270418 | − | 0.962743i | \(-0.587162\pi\) | ||||
−0.270418 | + | 0.962743i | \(0.587162\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 21.4091 | + | 21.4091i | 0.110928 | + | 0.110928i | 0.760392 | − | 0.649464i | \(-0.225007\pi\) |
−0.649464 | + | 0.760392i | \(0.725007\pi\) | |||||||
\(194\) | 171.926i | 0.886215i | ||||||||
\(195\) | −15.8497 | − | 59.1585i | −0.0812807 | − | 0.303377i | ||||
\(196\) | −38.7976 | −0.197947 | ||||||||
\(197\) | 5.19419 | − | 5.19419i | 0.0263664 | − | 0.0263664i | −0.693801 | − | 0.720167i | \(-0.744065\pi\) |
0.720167 | + | 0.693801i | \(0.244065\pi\) | |||||||
\(198\) | 5.29034 | + | 5.29034i | 0.0267189 | + | 0.0267189i | ||||
\(199\) | − | 343.482i | − | 1.72604i | −0.505168 | − | 0.863021i | \(-0.668570\pi\) | ||
0.505168 | − | 0.863021i | \(-0.331430\pi\) | |||||||
\(200\) | 68.3003 | + | 18.3050i | 0.341501 | + | 0.0915250i | ||||
\(201\) | 34.2941 | 0.170617 | ||||||||
\(202\) | 9.56680 | − | 9.56680i | 0.0473604 | − | 0.0473604i | ||||
\(203\) | −226.956 | − | 226.956i | −1.11801 | − | 1.11801i | ||||
\(204\) | 41.6900i | 0.204363i | ||||||||
\(205\) | −308.851 | + | 82.7473i | −1.50659 | + | 0.403645i | ||||
\(206\) | −104.295 | −0.506284 | ||||||||
\(207\) | −10.1735 | + | 10.1735i | −0.0491473 | + | 0.0491473i | ||||
\(208\) | −20.0025 | − | 20.0025i | −0.0961660 | − | 0.0961660i | ||||
\(209\) | 39.4958i | 0.188975i | ||||||||
\(210\) | 50.6478 | − | 87.7190i | 0.241180 | − | 0.417709i | ||||
\(211\) | −203.788 | −0.965819 | −0.482910 | − | 0.875670i | \(-0.660420\pi\) | ||||
−0.482910 | + | 0.875670i | \(0.660420\pi\) | |||||||
\(212\) | 135.666 | − | 135.666i | 0.639932 | − | 0.639932i | ||||
\(213\) | −44.2113 | − | 44.2113i | −0.207565 | − | 0.207565i | ||||
\(214\) | 250.680i | 1.17140i | ||||||||
\(215\) | −212.816 | − | 122.877i | −0.989844 | − | 0.571523i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 88.2540 | − | 88.2540i | 0.406701 | − | 0.406701i | ||||
\(218\) | −65.7207 | − | 65.7207i | −0.301471 | − | 0.301471i | ||||
\(219\) | − | 144.011i | − | 0.657583i | ||||||
\(220\) | −4.56367 | − | 17.0337i | −0.0207440 | − | 0.0774260i | ||||
\(221\) | −85.1100 | −0.385113 | ||||||||
\(222\) | −70.0308 | + | 70.0308i | −0.315454 | + | 0.315454i | ||||
\(223\) | −232.124 | − | 232.124i | −1.04091 | − | 1.04091i | −0.999126 | − | 0.0417883i | \(-0.986694\pi\) |
−0.0417883 | − | 0.999126i | \(-0.513306\pi\) | |||||||
\(224\) | − | 46.7842i | − | 0.208858i | ||||||
\(225\) | 37.4964 | + | 64.9540i | 0.166651 | + | 0.288684i | ||||
\(226\) | −100.485 | −0.444622 | ||||||||
\(227\) | −184.343 | + | 184.343i | −0.812082 | + | 0.812082i | −0.984946 | − | 0.172863i | \(-0.944698\pi\) |
0.172863 | + | 0.984946i | \(0.444698\pi\) | |||||||
\(228\) | −54.8610 | − | 54.8610i | −0.240619 | − | 0.240619i | ||||
\(229\) | − | 223.254i | − | 0.974908i | −0.873149 | − | 0.487454i | \(-0.837926\pi\) | ||
0.873149 | − | 0.487454i | \(-0.162074\pi\) | |||||||
\(230\) | 32.7564 | − | 8.77608i | 0.142419 | − | 0.0381569i | ||||
\(231\) | −25.2608 | −0.109354 | ||||||||
\(232\) | 77.6179 | − | 77.6179i | 0.334560 | − | 0.334560i | ||||
\(233\) | −296.194 | − | 296.194i | −1.27122 | − | 1.27122i | −0.945449 | − | 0.325769i | \(-0.894377\pi\) |
−0.325769 | − | 0.945449i | \(-0.605623\pi\) | |||||||
\(234\) | − | 30.0038i | − | 0.128221i | ||||||
\(235\) | −7.87674 | + | 13.6420i | −0.0335180 | + | 0.0580513i | ||||
\(236\) | 58.7095 | 0.248769 | ||||||||
\(237\) | −156.983 | + | 156.983i | −0.662375 | + | 0.662375i | ||||
\(238\) | −99.5325 | − | 99.5325i | −0.418204 | − | 0.418204i | ||||
\(239\) | 2.15755i | 0.00902741i | 0.999990 | + | 0.00451370i | \(0.00143676\pi\) | ||||
−0.999990 | + | 0.00451370i | \(0.998563\pi\) | |||||||
\(240\) | 29.9995 | + | 17.3213i | 0.124998 | + | 0.0721722i | ||||
\(241\) | −136.072 | −0.564612 | −0.282306 | − | 0.959324i | \(-0.591099\pi\) | ||||
−0.282306 | + | 0.959324i | \(0.591099\pi\) | |||||||
\(242\) | 117.890 | − | 117.890i | 0.487150 | − | 0.487150i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 109.253i | − | 0.447760i | ||||||
\(245\) | 25.1013 | + | 93.6896i | 0.102454 | + | 0.382407i | ||||
\(246\) | −156.642 | −0.636755 | ||||||||
\(247\) | 111.999 | − | 111.999i | 0.453436 | − | 0.453436i | ||||
\(248\) | 30.1825 | + | 30.1825i | 0.121704 | + | 0.121704i | ||||
\(249\) | − | 168.824i | − | 0.678009i | ||||||
\(250\) | 0.0145100 | − | 176.777i | 5.80400e−5 | − | 0.707107i | ||||
\(251\) | 191.977 | 0.764848 | 0.382424 | − | 0.923987i | \(-0.375089\pi\) | ||||
0.382424 | + | 0.923987i | \(0.375089\pi\) | |||||||
\(252\) | 35.0881 | − | 35.0881i | 0.139239 | − | 0.139239i | ||||
\(253\) | −5.98014 | − | 5.98014i | −0.0236369 | − | 0.0236369i | ||||
\(254\) | 174.206i | 0.685852i | ||||||||
\(255\) | 100.674 | − | 26.9726i | 0.394801 | − | 0.105775i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 100.820 | − | 100.820i | 0.392294 | − | 0.392294i | −0.483210 | − | 0.875504i | \(-0.660529\pi\) |
0.875504 | + | 0.483210i | \(0.160529\pi\) | |||||||
\(258\) | −85.1279 | − | 85.1279i | −0.329953 | − | 0.329953i | ||||
\(259\) | − | 334.390i | − | 1.29108i | ||||||
\(260\) | −35.3615 | + | 61.2440i | −0.136006 | + | 0.235554i | ||||
\(261\) | 116.427 | 0.446080 | ||||||||
\(262\) | −151.951 | + | 151.951i | −0.579966 | + | 0.579966i | ||||
\(263\) | −162.391 | − | 162.391i | −0.617455 | − | 0.617455i | 0.327423 | − | 0.944878i | \(-0.393820\pi\) |
−0.944878 | + | 0.327423i | \(0.893820\pi\) | |||||||
\(264\) | − | 8.63909i | − | 0.0327238i | ||||||
\(265\) | −415.383 | − | 239.836i | −1.56748 | − | 0.905043i | ||||
\(266\) | 261.955 | 0.984795 | ||||||||
\(267\) | −24.1628 | + | 24.1628i | −0.0904973 | + | 0.0904973i | ||||
\(268\) | −28.0010 | − | 28.0010i | −0.104481 | − | 0.104481i | ||||
\(269\) | 166.072i | 0.617366i | 0.951165 | + | 0.308683i | \(0.0998883\pi\) | ||||
−0.951165 | + | 0.308683i | \(0.900112\pi\) | |||||||
\(270\) | 9.50865 | + | 35.4906i | 0.0352172 | + | 0.131447i | ||||
\(271\) | −309.336 | −1.14146 | −0.570731 | − | 0.821137i | \(-0.693340\pi\) | ||||
−0.570731 | + | 0.821137i | \(0.693340\pi\) | |||||||
\(272\) | 34.0397 | − | 34.0397i | 0.125146 | − | 0.125146i | ||||
\(273\) | 71.6324 | + | 71.6324i | 0.262390 | + | 0.262390i | ||||
\(274\) | 134.464i | 0.490745i | ||||||||
\(275\) | −38.1809 | + | 22.0410i | −0.138840 | + | 0.0801491i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | −265.998 | + | 265.998i | −0.960281 | + | 0.960281i | −0.999241 | − | 0.0389595i | \(-0.987596\pi\) |
0.0389595 | + | 0.999241i | \(0.487596\pi\) | |||||||
\(278\) | −147.787 | − | 147.787i | −0.531610 | − | 0.531610i | ||||
\(279\) | 45.2738i | 0.162272i | ||||||||
\(280\) | −112.976 | + | 30.2685i | −0.403486 | + | 0.108102i | ||||
\(281\) | 57.9240 | 0.206135 | 0.103068 | − | 0.994674i | \(-0.467134\pi\) | ||||
0.103068 | + | 0.994674i | \(0.467134\pi\) | |||||||
\(282\) | −5.45691 | + | 5.45691i | −0.0193507 | + | 0.0193507i | ||||
\(283\) | −116.179 | − | 116.179i | −0.410525 | − | 0.410525i | 0.471396 | − | 0.881922i | \(-0.343750\pi\) |
−0.881922 | + | 0.471396i | \(0.843750\pi\) | |||||||
\(284\) | 72.1968i | 0.254214i | ||||||||
\(285\) | −96.9861 | + | 167.974i | −0.340302 | + | 0.589383i | ||||
\(286\) | 17.6367 | 0.0616668 | ||||||||
\(287\) | 373.974 | − | 373.974i | 1.30304 | − | 1.30304i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 144.162i | 0.498831i | ||||||||
\(290\) | −237.651 | − | 137.217i | −0.819488 | − | 0.473161i | ||||
\(291\) | 210.565 | 0.723591 | ||||||||
\(292\) | −117.584 | + | 117.584i | −0.402686 | + | 0.402686i | ||||
\(293\) | 189.001 | + | 189.001i | 0.645056 | + | 0.645056i | 0.951794 | − | 0.306738i | \(-0.0992376\pi\) |
−0.306738 | + | 0.951794i | \(0.599238\pi\) | |||||||
\(294\) | 47.5171i | 0.161623i | ||||||||
\(295\) | −37.9840 | − | 141.774i | −0.128759 | − | 0.480588i | ||||
\(296\) | 114.360 | 0.386351 | ||||||||
\(297\) | 6.47932 | − | 6.47932i | 0.0218159 | − | 0.0218159i | ||||
\(298\) | 34.3711 | + | 34.3711i | 0.115339 | + | 0.115339i | ||||
\(299\) | 33.9159i | 0.113431i | ||||||||
\(300\) | 22.4190 | − | 83.6504i | 0.0747299 | − | 0.278835i | ||||
\(301\) | 406.477 | 1.35042 | ||||||||
\(302\) | 187.555 | − | 187.555i | 0.621042 | − | 0.621042i | ||||
\(303\) | −11.7169 | − | 11.7169i | −0.0386696 | − | 0.0386696i | ||||
\(304\) | 89.5877i | 0.294696i | ||||||||
\(305\) | −263.829 | + | 70.6849i | −0.865012 | + | 0.231754i | ||||
\(306\) | 51.0596 | 0.166861 | ||||||||
\(307\) | 307.822 | − | 307.822i | 1.00268 | − | 1.00268i | 0.00268029 | − | 0.999996i | \(-0.499147\pi\) |
0.999996 | − | 0.00268029i | \(-0.000853164\pi\) | |||||||
\(308\) | 20.6254 | + | 20.6254i | 0.0669655 | + | 0.0669655i | ||||
\(309\) | 127.734i | 0.413379i | ||||||||
\(310\) | 53.3582 | − | 92.4132i | 0.172123 | − | 0.298107i | ||||
\(311\) | −529.789 | −1.70350 | −0.851750 | − | 0.523948i | \(-0.824459\pi\) | ||||
−0.851750 | + | 0.523948i | \(0.824459\pi\) | |||||||
\(312\) | −24.4980 | + | 24.4980i | −0.0785192 | + | 0.0785192i | ||||
\(313\) | 64.3377 | + | 64.3377i | 0.205552 | + | 0.205552i | 0.802374 | − | 0.596822i | \(-0.203570\pi\) |
−0.596822 | + | 0.802374i | \(0.703570\pi\) | |||||||
\(314\) | 346.396i | 1.10317i | ||||||||
\(315\) | −107.433 | − | 62.0306i | −0.341058 | − | 0.196923i | ||||
\(316\) | 256.352 | 0.811240 | ||||||||
\(317\) | −393.031 | + | 393.031i | −1.23985 | + | 1.23985i | −0.279781 | + | 0.960064i | \(0.590262\pi\) |
−0.960064 | + | 0.279781i | \(0.909738\pi\) | |||||||
\(318\) | −166.156 | − | 166.156i | −0.522502 | − | 0.522502i | ||||
\(319\) | 68.4375i | 0.214538i | ||||||||
\(320\) | −10.3517 | − | 38.6373i | −0.0323491 | − | 0.120742i | ||||
\(321\) | 307.019 | 0.956445 | ||||||||
\(322\) | −39.6632 | + | 39.6632i | −0.123178 | + | 0.123178i | ||||
\(323\) | 190.596 | + | 190.596i | 0.590081 | + | 0.590081i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 170.772 | + | 45.7683i | 0.525453 | + | 0.140826i | ||||
\(326\) | 24.6561 | 0.0756321 | ||||||||
\(327\) | −80.4911 | + | 80.4911i | −0.246150 | + | 0.246150i | ||||
\(328\) | 127.897 | + | 127.897i | 0.389931 | + | 0.389931i | ||||
\(329\) | − | 26.0561i | − | 0.0791980i | ||||||
\(330\) | −20.8620 | + | 5.58933i | −0.0632180 | + | 0.0169374i | ||||
\(331\) | 179.754 | 0.543064 | 0.271532 | − | 0.962429i | \(-0.412470\pi\) | ||||
0.271532 | + | 0.962429i | \(0.412470\pi\) | |||||||
\(332\) | −137.844 | + | 137.844i | −0.415194 | + | 0.415194i | ||||
\(333\) | 85.7699 | + | 85.7699i | 0.257567 | + | 0.257567i | ||||
\(334\) | 135.758i | 0.406461i | ||||||||
\(335\) | −49.5016 | + | 85.7338i | −0.147766 | + | 0.255922i | ||||
\(336\) | −57.2987 | −0.170532 | ||||||||
\(337\) | −118.371 | + | 118.371i | −0.351251 | + | 0.351251i | −0.860575 | − | 0.509324i | \(-0.829895\pi\) |
0.509324 | + | 0.860575i | \(0.329895\pi\) | |||||||
\(338\) | 118.987 | + | 118.987i | 0.352034 | + | 0.352034i | ||||
\(339\) | 123.068i | 0.363033i | ||||||||
\(340\) | −104.223 | − | 60.1771i | −0.306539 | − | 0.176992i | ||||
\(341\) | −26.6126 | −0.0780429 | ||||||||
\(342\) | −67.1908 | + | 67.1908i | −0.196464 | + | 0.196464i | ||||
\(343\) | 173.109 | + | 173.109i | 0.504690 | + | 0.504690i | ||||
\(344\) | 139.013i | 0.404108i | ||||||||
\(345\) | −10.7485 | − | 40.1182i | −0.0311550 | − | 0.116285i | ||||
\(346\) | −72.8871 | −0.210656 | ||||||||
\(347\) | 379.530 | − | 379.530i | 1.09375 | − | 1.09375i | 0.0986223 | − | 0.995125i | \(-0.468556\pi\) |
0.995125 | − | 0.0986223i | \(-0.0314436\pi\) | |||||||
\(348\) | −95.0621 | − | 95.0621i | −0.273167 | − | 0.273167i | ||||
\(349\) | 540.641i | 1.54912i | 0.632503 | + | 0.774558i | \(0.282027\pi\) | ||||
−0.632503 | + | 0.774558i | \(0.717973\pi\) | |||||||
\(350\) | 146.187 | + | 253.235i | 0.417676 | + | 0.723528i | ||||
\(351\) | −36.7470 | −0.104692 | ||||||||
\(352\) | −7.05379 | + | 7.05379i | −0.0200392 | + | 0.0200392i | ||||
\(353\) | 51.2669 | + | 51.2669i | 0.145232 | + | 0.145232i | 0.775984 | − | 0.630752i | \(-0.217254\pi\) |
−0.630752 | + | 0.775984i | \(0.717254\pi\) | |||||||
\(354\) | − | 71.9042i | − | 0.203119i | ||||||
\(355\) | 174.343 | − | 46.7100i | 0.491107 | − | 0.131577i | ||||
\(356\) | 39.4577 | 0.110836 | ||||||||
\(357\) | −121.902 | + | 121.902i | −0.341462 | + | 0.341462i | ||||
\(358\) | −96.1704 | − | 96.1704i | −0.268633 | − | 0.268633i | ||||
\(359\) | − | 217.517i | − | 0.605898i | −0.953007 | − | 0.302949i | \(-0.902029\pi\) | ||
0.953007 | − | 0.302949i | \(-0.0979712\pi\) | |||||||
\(360\) | 21.2142 | − | 36.7418i | 0.0589284 | − | 0.102060i | ||||
\(361\) | −140.622 | −0.389534 | ||||||||
\(362\) | −204.330 | + | 204.330i | −0.564447 | + | 0.564447i | ||||
\(363\) | −144.385 | − | 144.385i | −0.397756 | − | 0.397756i | ||||
\(364\) | − | 116.975i | − | 0.321361i | ||||||
\(365\) | 360.021 | + | 207.871i | 0.986358 | + | 0.569510i | ||||
\(366\) | −133.808 | −0.365594 | ||||||||
\(367\) | −391.093 | + | 391.093i | −1.06565 | + | 1.06565i | −0.0679602 | + | 0.997688i | \(0.521649\pi\) |
−0.997688 | + | 0.0679602i | \(0.978351\pi\) | |||||||
\(368\) | −13.5647 | − | 13.5647i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 191.846i | 0.519908i | ||||||||
\(370\) | −73.9887 | − | 276.160i | −0.199970 | − | 0.746378i | ||||
\(371\) | 793.375 | 2.13848 | ||||||||
\(372\) | 36.9659 | − | 36.9659i | 0.0993706 | − | 0.0993706i | ||||
\(373\) | 281.397 | + | 281.397i | 0.754414 | + | 0.754414i | 0.975300 | − | 0.220885i | \(-0.0708947\pi\) |
−0.220885 | + | 0.975300i | \(0.570895\pi\) | |||||||
\(374\) | 30.0136i | 0.0802503i | ||||||||
\(375\) | −216.506 | − | 0.0177710i | −0.577350 | − | 4.73894e-5i | ||||
\(376\) | 8.91109 | 0.0236997 | ||||||||
\(377\) | 194.069 | − | 194.069i | 0.514772 | − | 0.514772i | ||||
\(378\) | −42.9740 | − | 42.9740i | −0.113688 | − | 0.113688i | ||||
\(379\) | 450.647i | 1.18904i | 0.804080 | + | 0.594521i | \(0.202658\pi\) | ||||
−0.804080 | + | 0.594521i | \(0.797342\pi\) | |||||||
\(380\) | 216.339 | − | 57.9616i | 0.569314 | − | 0.152530i | ||||
\(381\) | 213.358 | 0.559996 | ||||||||
\(382\) | 103.300 | − | 103.300i | 0.270418 | − | 0.270418i | ||||
\(383\) | −120.781 | − | 120.781i | −0.315354 | − | 0.315354i | 0.531625 | − | 0.846980i | \(-0.321581\pi\) |
−0.846980 | + | 0.531625i | \(0.821581\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 36.4626 | − | 63.1510i | 0.0947079 | − | 0.164029i | ||||
\(386\) | −42.8181 | −0.110928 | ||||||||
\(387\) | −104.260 | + | 104.260i | −0.269406 | + | 0.269406i | ||||
\(388\) | −171.926 | − | 171.926i | −0.443107 | − | 0.443107i | ||||
\(389\) | − | 136.553i | − | 0.351035i | −0.984476 | − | 0.175518i | \(-0.943840\pi\) | ||
0.984476 | − | 0.175518i | \(-0.0561599\pi\) | |||||||
\(390\) | 75.0083 | + | 43.3088i | 0.192329 | + | 0.111048i | ||||
\(391\) | −57.7171 | −0.147614 | ||||||||
\(392\) | 38.7976 | − | 38.7976i | 0.0989734 | − | 0.0989734i | ||||
\(393\) | 186.101 | + | 186.101i | 0.473540 | + | 0.473540i | ||||
\(394\) | 10.3884i | 0.0263664i | ||||||||
\(395\) | −165.855 | − | 619.047i | −0.419886 | − | 1.56721i | ||||
\(396\) | −10.5807 | −0.0267189 | ||||||||
\(397\) | −11.6153 | + | 11.6153i | −0.0292576 | + | 0.0292576i | −0.721584 | − | 0.692327i | \(-0.756586\pi\) |
0.692327 | + | 0.721584i | \(0.256586\pi\) | |||||||
\(398\) | 343.482 | + | 343.482i | 0.863021 | + | 0.863021i | ||||
\(399\) | − | 320.829i | − | 0.804082i | ||||||
\(400\) | −86.6053 | + | 49.9953i | −0.216513 | + | 0.124988i | ||||
\(401\) | −325.917 | −0.812760 | −0.406380 | − | 0.913704i | \(-0.633209\pi\) | ||||
−0.406380 | + | 0.913704i | \(0.633209\pi\) | |||||||
\(402\) | −34.2941 | + | 34.2941i | −0.0853086 | + | 0.0853086i | ||||
\(403\) | 75.4658 | + | 75.4658i | 0.187260 | + | 0.187260i | ||||
\(404\) | 19.1336i | 0.0473604i | ||||||||
\(405\) | 43.4670 | − | 11.6457i | 0.107326 | − | 0.0287547i | ||||
\(406\) | 453.911 | 1.11801 | ||||||||
\(407\) | −50.4169 | + | 50.4169i | −0.123874 | + | 0.123874i | ||||
\(408\) | −41.6900 | − | 41.6900i | −0.102181 | − | 0.102181i | ||||
\(409\) | 447.168i | 1.09332i | 0.837354 | + | 0.546661i | \(0.184101\pi\) | ||||
−0.837354 | + | 0.546661i | \(0.815899\pi\) | |||||||
\(410\) | 226.104 | − | 391.598i | 0.551472 | − | 0.955117i | ||||
\(411\) | 164.684 | 0.400691 | ||||||||
\(412\) | 104.295 | − | 104.295i | 0.253142 | − | 0.253142i | ||||
\(413\) | 171.667 | + | 171.667i | 0.415659 | + | 0.415659i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | 422.054 | + | 243.688i | 1.01700 | + | 0.587201i | ||||
\(416\) | 40.0050 | 0.0961660 | ||||||||
\(417\) | −181.002 | + | 181.002i | −0.434057 | + | 0.434057i | ||||
\(418\) | −39.4958 | − | 39.4958i | −0.0944875 | − | 0.0944875i | ||||
\(419\) | − | 356.216i | − | 0.850157i | −0.905157 | − | 0.425078i | \(-0.860247\pi\) | ||
0.905157 | − | 0.425078i | \(-0.139753\pi\) | |||||||
\(420\) | 37.0712 | + | 138.367i | 0.0882648 | + | 0.329445i | ||||
\(421\) | 415.752 | 0.987534 | 0.493767 | − | 0.869594i | \(-0.335620\pi\) | ||||
0.493767 | + | 0.869594i | \(0.335620\pi\) | |||||||
\(422\) | 203.788 | − | 203.788i | 0.482910 | − | 0.482910i | ||||
\(423\) | 6.68332 | + | 6.68332i | 0.0157998 | + | 0.0157998i | ||||
\(424\) | 271.331i | 0.639932i | ||||||||
\(425\) | −77.8872 | + | 290.615i | −0.183264 | + | 0.683801i | ||||
\(426\) | 88.4227 | 0.207565 | ||||||||
\(427\) | 319.458 | − | 319.458i | 0.748146 | − | 0.748146i | ||||
\(428\) | −250.680 | − | 250.680i | −0.585700 | − | 0.585700i | ||||
\(429\) | − | 21.6004i | − | 0.0503507i | ||||||
\(430\) | 335.694 | − | 89.9390i | 0.780683 | − | 0.209161i | ||||
\(431\) | −456.460 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −56.6111 | − | 56.6111i | −0.130741 | − | 0.130741i | 0.638708 | − | 0.769449i | \(-0.279469\pi\) |
−0.769449 | + | 0.638708i | \(0.779469\pi\) | |||||||
\(434\) | 176.508i | 0.406701i | ||||||||
\(435\) | −168.056 | + | 291.062i | −0.386335 | + | 0.669109i | ||||
\(436\) | 131.441 | 0.301471 | ||||||||
\(437\) | 75.9516 | − | 75.9516i | 0.173802 | − | 0.173802i | ||||
\(438\) | 144.011 | + | 144.011i | 0.328791 | + | 0.328791i | ||||
\(439\) | 533.763i | 1.21586i | 0.793990 | + | 0.607931i | \(0.208000\pi\) | ||||
−0.793990 | + | 0.607931i | \(0.792000\pi\) | |||||||
\(440\) | 21.5974 | + | 12.4700i | 0.0490850 | + | 0.0283410i | ||||
\(441\) | 58.1964 | 0.131965 | ||||||||
\(442\) | 85.1100 | − | 85.1100i | 0.192557 | − | 0.192557i | ||||
\(443\) | −308.316 | − | 308.316i | −0.695973 | − | 0.695973i | 0.267567 | − | 0.963539i | \(-0.413780\pi\) |
−0.963539 | + | 0.267567i | \(0.913780\pi\) | |||||||
\(444\) | − | 140.062i | − | 0.315454i | ||||||
\(445\) | −25.5284 | − | 95.2836i | −0.0573671 | − | 0.214121i | ||||
\(446\) | 464.248 | 1.04091 | ||||||||
\(447\) | 42.0958 | − | 42.0958i | 0.0941740 | − | 0.0941740i | ||||
\(448\) | 46.7842 | + | 46.7842i | 0.104429 | + | 0.104429i | ||||
\(449\) | − | 479.262i | − | 1.06740i | −0.845674 | − | 0.533699i | \(-0.820801\pi\) | ||
0.845674 | − | 0.533699i | \(-0.179199\pi\) | |||||||
\(450\) | −102.450 | − | 27.4575i | −0.227668 | − | 0.0610167i | ||||
\(451\) | −112.770 | −0.250045 | ||||||||
\(452\) | 100.485 | − | 100.485i | 0.222311 | − | 0.222311i | ||||
\(453\) | −229.707 | − | 229.707i | −0.507079 | − | 0.507079i | ||||
\(454\) | − | 368.685i | − | 0.812082i | ||||||
\(455\) | −282.476 | + | 75.6808i | −0.620825 | + | 0.166331i | ||||
\(456\) | 109.722 | 0.240619 | ||||||||
\(457\) | 121.058 | − | 121.058i | 0.264898 | − | 0.264898i | −0.562142 | − | 0.827040i | \(-0.690023\pi\) |
0.827040 | + | 0.562142i | \(0.190023\pi\) | |||||||
\(458\) | 223.254 | + | 223.254i | 0.487454 | + | 0.487454i | ||||
\(459\) | − | 62.5350i | − | 0.136242i | ||||||
\(460\) | −23.9803 | + | 41.5325i | −0.0521311 | + | 0.0902880i | ||||
\(461\) | −130.197 | −0.282423 | −0.141211 | − | 0.989979i | \(-0.545100\pi\) | ||||
−0.141211 | + | 0.989979i | \(0.545100\pi\) | |||||||
\(462\) | 25.2608 | − | 25.2608i | 0.0546771 | − | 0.0546771i | ||||
\(463\) | −84.8852 | − | 84.8852i | −0.183337 | − | 0.183337i | 0.609471 | − | 0.792808i | \(-0.291382\pi\) |
−0.792808 | + | 0.609471i | \(0.791382\pi\) | |||||||
\(464\) | 155.236i | 0.334560i | ||||||||
\(465\) | −113.183 | − | 65.3501i | −0.243403 | − | 0.140538i | ||||
\(466\) | 592.388 | 1.27122 | ||||||||
\(467\) | 93.2186 | − | 93.2186i | 0.199612 | − | 0.199612i | −0.600222 | − | 0.799834i | \(-0.704921\pi\) |
0.799834 | + | 0.600222i | \(0.204921\pi\) | |||||||
\(468\) | 30.0038 | + | 30.0038i | 0.0641107 | + | 0.0641107i | ||||
\(469\) | − | 163.751i | − | 0.349148i | ||||||
\(470\) | −5.76531 | − | 21.5188i | −0.0122666 | − | 0.0457846i | ||||
\(471\) | 424.247 | 0.900737 | ||||||||
\(472\) | −58.7095 | + | 58.7095i | −0.124385 | + | 0.124385i | ||||
\(473\) | −61.2856 | − | 61.2856i | −0.129568 | − | 0.129568i | ||||
\(474\) | − | 313.966i | − | 0.662375i | ||||||
\(475\) | −279.935 | − | 484.923i | −0.589337 | − | 1.02089i | ||||
\(476\) | 199.065 | 0.418204 | ||||||||
\(477\) | −203.498 | + | 203.498i | −0.426621 | + | 0.426621i | ||||
\(478\) | −2.15755 | − | 2.15755i | −0.00451370 | − | 0.00451370i | ||||
\(479\) | − | 376.346i | − | 0.785690i | −0.919605 | − | 0.392845i | \(-0.871491\pi\) | ||
0.919605 | − | 0.392845i | \(-0.128509\pi\) | |||||||
\(480\) | −47.3209 | + | 12.6782i | −0.0985851 | + | 0.0264129i | ||||
\(481\) | 285.936 | 0.594461 | ||||||||
\(482\) | 136.072 | − | 136.072i | 0.282306 | − | 0.282306i | ||||
\(483\) | 48.5773 | + | 48.5773i | 0.100574 | + | 0.100574i | ||||
\(484\) | 235.781i | 0.487150i | ||||||||
\(485\) | −303.939 | + | 526.404i | −0.626678 | + | 1.08537i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −331.105 | + | 331.105i | −0.679887 | + | 0.679887i | −0.959974 | − | 0.280088i | \(-0.909636\pi\) |
0.280088 | + | 0.959974i | \(0.409636\pi\) | |||||||
\(488\) | 109.253 | + | 109.253i | 0.223880 | + | 0.223880i | ||||
\(489\) | − | 30.1974i | − | 0.0617533i | ||||||
\(490\) | −118.791 | − | 68.5883i | −0.242430 | − | 0.139976i | ||||
\(491\) | 95.5294 | 0.194561 | 0.0972805 | − | 0.995257i | \(-0.468986\pi\) | ||||
0.0972805 | + | 0.995257i | \(0.468986\pi\) | |||||||
\(492\) | 156.642 | − | 156.642i | 0.318377 | − | 0.318377i | ||||
\(493\) | 330.261 | + | 330.261i | 0.669901 | + | 0.669901i | ||||
\(494\) | 223.997i | 0.453436i | ||||||||
\(495\) | 6.84550 | + | 25.5506i | 0.0138293 | + | 0.0516173i | ||||
\(496\) | −60.3650 | −0.121704 | ||||||||
\(497\) | −211.104 | + | 211.104i | −0.424757 | + | 0.424757i | ||||
\(498\) | 168.824 | + | 168.824i | 0.339005 | + | 0.339005i | ||||
\(499\) | 134.022i | 0.268581i | 0.990942 | + | 0.134291i | \(0.0428756\pi\) | ||||
−0.990942 | + | 0.134291i | \(0.957124\pi\) | |||||||
\(500\) | 176.762 | + | 176.791i | 0.353524 | + | 0.353582i | ||||
\(501\) | 166.269 | 0.331874 | ||||||||
\(502\) | −191.977 | + | 191.977i | −0.382424 | + | 0.382424i | ||||
\(503\) | −474.271 | − | 474.271i | −0.942885 | − | 0.942885i | 0.0555696 | − | 0.998455i | \(-0.482303\pi\) |
−0.998455 | + | 0.0555696i | \(0.982303\pi\) | |||||||
\(504\) | 70.1763i | 0.139239i | ||||||||
\(505\) | 46.2044 | − | 12.3791i | 0.0914939 | − | 0.0245130i | ||||
\(506\) | 11.9603 | 0.0236369 | ||||||||
\(507\) | 145.729 | − | 145.729i | 0.287434 | − | 0.287434i | ||||
\(508\) | −174.206 | − | 174.206i | −0.342926 | − | 0.342926i | ||||
\(509\) | 447.848i | 0.879859i | 0.898032 | + | 0.439930i | \(0.144997\pi\) | ||||
−0.898032 | + | 0.439930i | \(0.855003\pi\) | |||||||
\(510\) | −73.7016 | + | 127.647i | −0.144513 | + | 0.250288i | ||||
\(511\) | −687.635 | −1.34567 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 82.2915 | + | 82.2915i | 0.160412 | + | 0.160412i | ||||
\(514\) | 201.639i | 0.392294i | ||||||||
\(515\) | −319.330 | − | 184.377i | −0.620059 | − | 0.358014i | ||||
\(516\) | 170.256 | 0.329953 | ||||||||
\(517\) | −3.92856 | + | 3.92856i | −0.00759876 | + | 0.00759876i | ||||
\(518\) | 334.390 | + | 334.390i | 0.645540 | + | 0.645540i | ||||
\(519\) | 89.2681i | 0.172000i | ||||||||
\(520\) | −25.8825 | − | 96.6055i | −0.0497741 | − | 0.185780i | ||||
\(521\) | 348.685 | 0.669261 | 0.334631 | − | 0.942349i | \(-0.391388\pi\) | ||||
0.334631 | + | 0.942349i | \(0.391388\pi\) | |||||||
\(522\) | −116.427 | + | 116.427i | −0.223040 | + | 0.223040i | ||||
\(523\) | 550.982 | + | 550.982i | 1.05350 | + | 1.05350i | 0.998485 | + | 0.0550166i | \(0.0175212\pi\) |
0.0550166 | + | 0.998485i | \(0.482479\pi\) | |||||||
\(524\) | − | 303.902i | − | 0.579966i | ||||||
\(525\) | 310.148 | − | 179.041i | 0.590758 | − | 0.341031i | ||||
\(526\) | 324.781 | 0.617455 | ||||||||
\(527\) | −128.426 | + | 128.426i | −0.243692 | + | 0.243692i | ||||
\(528\) | 8.63909 | + | 8.63909i | 0.0163619 | + | 0.0163619i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | 655.219 | − | 175.546i | 1.23626 | − | 0.331219i | ||||
\(531\) | −88.0643 | −0.165846 | ||||||||
\(532\) | −261.955 | + | 261.955i | −0.492397 | + | 0.492397i | ||||
\(533\) | 319.784 | + | 319.784i | 0.599970 | + | 0.599970i | ||||
\(534\) | − | 48.3256i | − | 0.0904973i | ||||||
\(535\) | −443.164 | + | 767.535i | −0.828345 | + | 1.43464i | ||||
\(536\) | 56.0020 | 0.104481 | ||||||||
\(537\) | −117.784 | + | 117.784i | −0.219338 | + | 0.219338i | ||||
\(538\) | −166.072 | − | 166.072i | −0.308683 | − | 0.308683i | ||||
\(539\) | 34.2087i | 0.0634670i | ||||||||
\(540\) | −44.9993 | − | 25.9820i | −0.0833320 | − | 0.0481148i | ||||
\(541\) | 353.593 | 0.653591 | 0.326795 | − | 0.945095i | \(-0.394031\pi\) | ||||
0.326795 | + | 0.945095i | \(0.394031\pi\) | |||||||
\(542\) | 309.336 | − | 309.336i | 0.570731 | − | 0.570731i | ||||
\(543\) | 250.252 | + | 250.252i | 0.460869 | + | 0.460869i | ||||
\(544\) | 68.0794i | 0.125146i | ||||||||
\(545\) | −85.0401 | − | 317.409i | −0.156037 | − | 0.582402i | ||||
\(546\) | −143.265 | −0.262390 | ||||||||
\(547\) | −39.6840 | + | 39.6840i | −0.0725485 | + | 0.0725485i | −0.742450 | − | 0.669901i | \(-0.766336\pi\) |
0.669901 | + | 0.742450i | \(0.266336\pi\) | |||||||
\(548\) | −134.464 | − | 134.464i | −0.245372 | − | 0.245372i | ||||
\(549\) | 163.880i | 0.298507i | ||||||||
\(550\) | 16.1400 | − | 60.2219i | 0.0293454 | − | 0.109494i | ||||
\(551\) | −869.201 | −1.57750 | ||||||||
\(552\) | −16.6132 | + | 16.6132i | −0.0300965 | + | 0.0300965i | ||||
\(553\) | 749.576 | + | 749.576i | 1.35547 | + | 1.35547i | ||||
\(554\) | − | 531.996i | − | 0.960281i | ||||||
\(555\) | −338.225 | + | 90.6173i | −0.609415 | + | 0.163274i | ||||
\(556\) | 295.575 | 0.531610 | ||||||||
\(557\) | −162.116 | + | 162.116i | −0.291052 | + | 0.291052i | −0.837496 | − | 0.546444i | \(-0.815981\pi\) |
0.546444 | + | 0.837496i | \(0.315981\pi\) | |||||||
\(558\) | −45.2738 | − | 45.2738i | −0.0811358 | − | 0.0811358i | ||||
\(559\) | 347.577i | 0.621784i | ||||||||
\(560\) | 82.7075 | − | 143.245i | 0.147692 | − | 0.255794i | ||||
\(561\) | 36.7590 | 0.0655241 | ||||||||
\(562\) | −57.9240 | + | 57.9240i | −0.103068 | + | 0.103068i | ||||
\(563\) | 99.3830 | + | 99.3830i | 0.176524 | + | 0.176524i | 0.789839 | − | 0.613315i | \(-0.210164\pi\) |
−0.613315 | + | 0.789839i | \(0.710164\pi\) | |||||||
\(564\) | − | 10.9138i | − | 0.0193507i | ||||||
\(565\) | −307.665 | − | 177.642i | −0.544540 | − | 0.314410i | ||||
\(566\) | 232.357 | 0.410525 | ||||||||
\(567\) | −52.6322 | + | 52.6322i | −0.0928258 | + | 0.0928258i | ||||
\(568\) | −72.1968 | − | 72.1968i | −0.127107 | − | 0.127107i | ||||
\(569\) | 1021.63i | 1.79548i | 0.440530 | + | 0.897738i | \(0.354790\pi\) | ||||
−0.440530 | + | 0.897738i | \(0.645210\pi\) | |||||||
\(570\) | −70.9881 | − | 264.960i | −0.124541 | − | 0.464843i | ||||
\(571\) | −454.037 | −0.795161 | −0.397580 | − | 0.917567i | \(-0.630150\pi\) | ||||
−0.397580 | + | 0.917567i | \(0.630150\pi\) | |||||||
\(572\) | −17.6367 | + | 17.6367i | −0.0308334 | + | 0.0308334i | ||||
\(573\) | −126.516 | − | 126.516i | −0.220795 | − | 0.220795i | ||||
\(574\) | 747.947i | 1.30304i | ||||||||
\(575\) | 115.809 | + | 31.0377i | 0.201407 | + | 0.0539785i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 112.620 | − | 112.620i | 0.195182 | − | 0.195182i | −0.602749 | − | 0.797931i | \(-0.705928\pi\) |
0.797931 | + | 0.602749i | \(0.205928\pi\) | |||||||
\(578\) | −144.162 | − | 144.162i | −0.249416 | − | 0.249416i | ||||
\(579\) | 52.4413i | 0.0905721i | ||||||||
\(580\) | 374.868 | − | 100.435i | 0.646325 | − | 0.173163i | ||||
\(581\) | −806.118 | −1.38747 | ||||||||
\(582\) | −210.565 | + | 210.565i | −0.361796 | + | 0.361796i | ||||
\(583\) | −119.619 | − | 119.619i | −0.205179 | − | 0.205179i | ||||
\(584\) | − | 235.168i | − | 0.402686i | ||||||
\(585\) | 53.0422 | − | 91.8660i | 0.0906704 | − | 0.157036i | ||||
\(586\) | −378.003 | −0.645056 | ||||||||
\(587\) | 760.222 | − | 760.222i | 1.29510 | − | 1.29510i | 0.363505 | − | 0.931592i | \(-0.381580\pi\) |
0.931592 | − | 0.363505i | \(-0.118420\pi\) | |||||||
\(588\) | −47.5171 | − | 47.5171i | −0.0808114 | − | 0.0808114i | ||||
\(589\) | − | 337.998i | − | 0.573850i | ||||||
\(590\) | 179.758 | + | 103.790i | 0.304674 | + | 0.175915i | ||||
\(591\) | 12.7231 | 0.0215281 | ||||||||
\(592\) | −114.360 | + | 114.360i | −0.193175 | + | 0.193175i | ||||
\(593\) | −623.009 | − | 623.009i | −1.05061 | − | 1.05061i | −0.998649 | − | 0.0519559i | \(-0.983454\pi\) |
−0.0519559 | − | 0.998649i | \(-0.516546\pi\) | |||||||
\(594\) | 12.9586i | 0.0218159i | ||||||||
\(595\) | −128.791 | − | 480.709i | −0.216456 | − | 0.807914i | ||||
\(596\) | −68.7421 | −0.115339 | ||||||||
\(597\) | 420.678 | − | 420.678i | 0.704653 | − | 0.704653i | ||||
\(598\) | −33.9159 | − | 33.9159i | −0.0567156 | − | 0.0567156i | ||||
\(599\) | 320.986i | 0.535870i | 0.963437 | + | 0.267935i | \(0.0863412\pi\) | ||||
−0.963437 | + | 0.267935i | \(0.913659\pi\) | |||||||
\(600\) | 61.2314 | + | 106.069i | 0.102052 | + | 0.176782i | ||||
\(601\) | −7.35941 | −0.0122453 | −0.00612264 | − | 0.999981i | \(-0.501949\pi\) | ||||
−0.00612264 | + | 0.999981i | \(0.501949\pi\) | |||||||
\(602\) | −406.477 | + | 406.477i | −0.675210 | + | 0.675210i | ||||
\(603\) | 42.0015 | + | 42.0015i | 0.0696542 | + | 0.0696542i | ||||
\(604\) | 375.109i | 0.621042i | ||||||||
\(605\) | 569.370 | − | 152.546i | 0.941108 | − | 0.252142i | ||||
\(606\) | 23.4338 | 0.0386696 | ||||||||
\(607\) | −360.752 | + | 360.752i | −0.594319 | + | 0.594319i | −0.938795 | − | 0.344476i | \(-0.888057\pi\) |
0.344476 | + | 0.938795i | \(0.388057\pi\) | |||||||
\(608\) | −89.5877 | − | 89.5877i | −0.147348 | − | 0.147348i | ||||
\(609\) | − | 555.925i | − | 0.912850i | ||||||
\(610\) | 193.144 | − | 334.514i | 0.316629 | − | 0.548383i | ||||
\(611\) | 22.2805 | 0.0364657 | ||||||||
\(612\) | −51.0596 | + | 51.0596i | −0.0834307 | + | 0.0834307i | ||||
\(613\) | 649.344 | + | 649.344i | 1.05929 | + | 1.05929i | 0.998128 | + | 0.0611606i | \(0.0194802\pi\) |
0.0611606 | + | 0.998128i | \(0.480520\pi\) | |||||||
\(614\) | 615.643i | 1.00268i | ||||||||
\(615\) | −479.608 | − | 276.919i | −0.779850 | − | 0.450275i | ||||
\(616\) | −41.2507 | −0.0669655 | ||||||||
\(617\) | 686.962 | − | 686.962i | 1.11339 | − | 1.11339i | 0.120701 | − | 0.992689i | \(-0.461486\pi\) |
0.992689 | − | 0.120701i | \(-0.0385143\pi\) | |||||||
\(618\) | −127.734 | − | 127.734i | −0.206690 | − | 0.206690i | ||||
\(619\) | 246.527i | 0.398267i | 0.979972 | + | 0.199133i | \(0.0638127\pi\) | ||||
−0.979972 | + | 0.199133i | \(0.936187\pi\) | |||||||
\(620\) | 39.0551 | + | 145.771i | 0.0629920 | + | 0.235115i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | 529.789 | − | 529.789i | 0.851750 | − | 0.851750i | ||||
\(623\) | 115.375 | + | 115.375i | 0.185192 | + | 0.185192i | ||||
\(624\) | − | 48.9960i | − | 0.0785192i | ||||||
\(625\) | 312.559 | − | 541.232i | 0.500095 | − | 0.865971i | ||||
\(626\) | −128.675 | −0.205552 | ||||||||
\(627\) | −48.3722 | + | 48.3722i | −0.0771487 | + | 0.0771487i | ||||
\(628\) | −346.396 | − | 346.396i | −0.551586 | − | 0.551586i | ||||
\(629\) | 486.597i | 0.773605i | ||||||||
\(630\) | 169.464 | − | 45.4028i | 0.268990 | − | 0.0720679i | ||||
\(631\) | 807.068 | 1.27903 | 0.639515 | − | 0.768778i | \(-0.279135\pi\) | ||||
0.639515 | + | 0.768778i | \(0.279135\pi\) | |||||||
\(632\) | −256.352 | + | 256.352i | −0.405620 | + | 0.405620i | ||||
\(633\) | −249.588 | − | 249.588i | −0.394294 | − | 0.394294i | ||||
\(634\) | − | 786.062i | − | 1.23985i | ||||||
\(635\) | −307.971 | + | 533.387i | −0.484993 | + | 0.839980i | ||||
\(636\) | 332.311 | 0.522502 | ||||||||
\(637\) | 97.0062 | − | 97.0062i | 0.152286 | − | 0.152286i | ||||
\(638\) | −68.4375 | − | 68.4375i | −0.107269 | − | 0.107269i | ||||
\(639\) | − | 108.295i | − | 0.169476i | ||||||
\(640\) | 48.9890 | + | 28.2856i | 0.0765453 | + | 0.0441963i | ||||
\(641\) | −926.142 | −1.44484 | −0.722420 | − | 0.691455i | \(-0.756970\pi\) | ||||
−0.722420 | + | 0.691455i | \(0.756970\pi\) | |||||||
\(642\) | −307.019 | + | 307.019i | −0.478222 | + | 0.478222i | ||||
\(643\) | 387.838 | + | 387.838i | 0.603170 | + | 0.603170i | 0.941152 | − | 0.337982i | \(-0.109744\pi\) |
−0.337982 | + | 0.941152i | \(0.609744\pi\) | |||||||
\(644\) | − | 79.3265i | − | 0.123178i | ||||||
\(645\) | −110.152 | − | 411.139i | −0.170779 | − | 0.637425i | ||||
\(646\) | −381.192 | −0.590081 | ||||||||
\(647\) | 873.903 | − | 873.903i | 1.35070 | − | 1.35070i | 0.465822 | − | 0.884878i | \(-0.345759\pi\) |
0.884878 | − | 0.465822i | \(-0.154241\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 51.7655i | − | 0.0797620i | ||||||
\(650\) | −216.541 | + | 125.004i | −0.333139 | + | 0.192314i | ||||
\(651\) | 216.177 | 0.332070 | ||||||||
\(652\) | −24.6561 | + | 24.6561i | −0.0378160 | + | 0.0378160i | ||||
\(653\) | −697.096 | − | 697.096i | −1.06753 | − | 1.06753i | −0.997548 | − | 0.0699794i | \(-0.977707\pi\) |
−0.0699794 | − | 0.997548i | \(-0.522293\pi\) | |||||||
\(654\) | − | 160.982i | − | 0.246150i | ||||||
\(655\) | −733.872 | + | 196.619i | −1.12042 | + | 0.300182i | ||||
\(656\) | −255.795 | −0.389931 | ||||||||
\(657\) | 176.376 | − | 176.376i | 0.268457 | − | 0.268457i | ||||
\(658\) | 26.0561 | + | 26.0561i | 0.0395990 | + | 0.0395990i | ||||
\(659\) | 1089.85i | 1.65380i | 0.562352 | + | 0.826898i | \(0.309897\pi\) | ||||
−0.562352 | + | 0.826898i | \(0.690103\pi\) | |||||||
\(660\) | 15.2726 | − | 26.4513i | 0.0231403 | − | 0.0400777i | ||||
\(661\) | −374.443 | −0.566480 | −0.283240 | − | 0.959049i | \(-0.591409\pi\) | ||||
−0.283240 | + | 0.959049i | \(0.591409\pi\) | |||||||
\(662\) | −179.754 | + | 179.754i | −0.271532 | + | 0.271532i | ||||
\(663\) | −104.238 | − | 104.238i | −0.157222 | − | 0.157222i | ||||
\(664\) | − | 275.689i | − | 0.415194i | ||||||
\(665\) | 802.059 | + | 463.098i | 1.20610 | + | 0.696388i | ||||
\(666\) | −171.540 | −0.257567 | ||||||||
\(667\) | 131.608 | − | 131.608i | 0.197313 | − | 0.197313i | ||||
\(668\) | −135.758 | − | 135.758i | −0.203231 | − | 0.203231i | ||||
\(669\) | − | 568.585i | − | 0.849903i | ||||||
\(670\) | −36.2323 | − | 135.235i | −0.0540780 | − | 0.201844i | ||||
\(671\) | −96.3313 | −0.143564 | ||||||||
\(672\) | 57.2987 | − | 57.2987i | 0.0852659 | − | 0.0852659i | ||||
\(673\) | 356.156 | + | 356.156i | 0.529206 | + | 0.529206i | 0.920336 | − | 0.391130i | \(-0.127916\pi\) |
−0.391130 | + | 0.920336i | \(0.627916\pi\) | |||||||
\(674\) | − | 236.743i | − | 0.351251i | ||||||
\(675\) | −33.6284 | + | 125.476i | −0.0498199 | + | 0.185890i | ||||
\(676\) | −237.975 | −0.352034 | ||||||||
\(677\) | −372.658 | + | 372.658i | −0.550455 | + | 0.550455i | −0.926572 | − | 0.376117i | \(-0.877259\pi\) |
0.376117 | + | 0.926572i | \(0.377259\pi\) | |||||||
\(678\) | −123.068 | − | 123.068i | −0.181516 | − | 0.181516i | ||||
\(679\) | − | 1005.43i | − | 1.48074i | ||||||
\(680\) | 164.400 | − | 44.0461i | 0.241765 | − | 0.0647737i | ||||
\(681\) | −451.546 | −0.663062 | ||||||||
\(682\) | 26.6126 | − | 26.6126i | 0.0390214 | − | 0.0390214i | ||||
\(683\) | 282.250 | + | 282.250i | 0.413250 | + | 0.413250i | 0.882869 | − | 0.469619i | \(-0.155609\pi\) |
−0.469619 | + | 0.882869i | \(0.655609\pi\) | |||||||
\(684\) | − | 134.382i | − | 0.196464i | ||||||
\(685\) | −237.712 | + | 411.704i | −0.347025 | + | 0.601028i | ||||
\(686\) | −346.217 | −0.504690 | ||||||||
\(687\) | 273.429 | − | 273.429i | 0.398005 | − | 0.398005i | ||||
\(688\) | −139.013 | − | 139.013i | −0.202054 | − | 0.202054i | ||||
\(689\) | 678.413i | 0.984635i | ||||||||
\(690\) | 50.8667 | + | 29.3697i | 0.0737198 | + | 0.0425648i | ||||
\(691\) | −560.128 | −0.810605 | −0.405303 | − | 0.914183i | \(-0.632834\pi\) | ||||
−0.405303 | + | 0.914183i | \(0.632834\pi\) | |||||||
\(692\) | 72.8871 | − | 72.8871i | 0.105328 | − | 0.105328i | ||||
\(693\) | −30.9380 | − | 30.9380i | −0.0446436 | − | 0.0446436i | ||||
\(694\) | 759.061i | 1.09375i | ||||||||
\(695\) | −191.232 | − | 713.764i | −0.275153 | − | 1.02700i | ||||
\(696\) | 190.124 | 0.273167 | ||||||||
\(697\) | −544.199 | + | 544.199i | −0.780773 | + | 0.780773i | ||||
\(698\) | −540.641 | − | 540.641i | −0.774558 | − | 0.774558i | ||||
\(699\) | − | 725.524i | − | 1.03795i | ||||||
\(700\) | −399.422 | − | 107.048i | −0.570602 | − | 0.152926i | ||||
\(701\) | 149.533 | 0.213314 | 0.106657 | − | 0.994296i | \(-0.465985\pi\) | ||||
0.106657 | + | 0.994296i | \(0.465985\pi\) | |||||||
\(702\) | 36.7470 | − | 36.7470i | 0.0523461 | − | 0.0523461i | ||||
\(703\) | −640.327 | − | 640.327i | −0.910850 | − | 0.910850i | ||||
\(704\) | − | 14.1076i | − | 0.0200392i | ||||||
\(705\) | −26.3550 | + | 7.06103i | −0.0373830 | + | 0.0100157i | ||||
\(706\) | −102.534 | −0.145232 | ||||||||
\(707\) | −55.9469 | + | 55.9469i | −0.0791328 | + | 0.0791328i | ||||
\(708\) | 71.9042 | + | 71.9042i | 0.101560 | + | 0.101560i | ||||
\(709\) | − | 790.988i | − | 1.11564i | −0.829963 | − | 0.557819i | \(-0.811638\pi\) | ||
0.829963 | − | 0.557819i | \(-0.188362\pi\) | |||||||
\(710\) | −127.633 | + | 221.053i | −0.179765 | + | 0.311342i | ||||
\(711\) | −384.528 | −0.540827 | ||||||||
\(712\) | −39.4577 | + | 39.4577i | −0.0554181 | + | 0.0554181i | ||||
\(713\) | 51.1769 | + | 51.1769i | 0.0717769 | + | 0.0717769i | ||||
\(714\) | − | 243.804i | − | 0.341462i | ||||||
\(715\) | 54.0003 | + | 31.1790i | 0.0755248 | + | 0.0436070i | ||||
\(716\) | 192.341 | 0.268633 | ||||||||
\(717\) | −2.64245 | + | 2.64245i | −0.00368542 | + | 0.00368542i | ||||
\(718\) | 217.517 | + | 217.517i | 0.302949 | + | 0.302949i | ||||
\(719\) | 279.928i | 0.389330i | 0.980870 | + | 0.194665i | \(0.0623620\pi\) | ||||
−0.980870 | + | 0.194665i | \(0.937638\pi\) | |||||||
\(720\) | 15.5276 | + | 57.9560i | 0.0215661 | + | 0.0804944i | ||||
\(721\) | 609.917 | 0.845932 | ||||||||
\(722\) | 140.622 | − | 140.622i | 0.194767 | − | 0.194767i | ||||
\(723\) | −166.653 | − | 166.653i | −0.230502 | − | 0.230502i | ||||
\(724\) | − | 408.660i | − | 0.564447i | ||||||
\(725\) | −485.066 | − | 840.265i | −0.669056 | − | 1.15899i | ||||
\(726\) | 288.771 | 0.397756 | ||||||||
\(727\) | 738.912 | − | 738.912i | 1.01639 | − | 1.01639i | 0.0165221 | − | 0.999864i | \(-0.494741\pi\) |
0.999864 | − | 0.0165221i | \(-0.00525940\pi\) | |||||||
\(728\) | 116.975 | + | 116.975i | 0.160680 | + | 0.160680i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −567.892 | + | 152.150i | −0.777934 | + | 0.208424i | ||||
\(731\) | −591.497 | −0.809161 | ||||||||
\(732\) | 133.808 | − | 133.808i | 0.182797 | − | 0.182797i | ||||
\(733\) | 709.411 | + | 709.411i | 0.967819 | + | 0.967819i | 0.999498 | − | 0.0316790i | \(-0.0100854\pi\) |
−0.0316790 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(734\) | − | 782.186i | − | 1.06565i | ||||||
\(735\) | −84.0032 | + | 145.489i | −0.114290 | + | 0.197944i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −24.6891 | + | 24.6891i | −0.0334995 | + | 0.0334995i | ||||
\(738\) | −191.846 | − | 191.846i | −0.259954 | − | 0.259954i | ||||
\(739\) | − | 233.841i | − | 0.316429i | −0.987405 | − | 0.158214i | \(-0.949426\pi\) | ||
0.987405 | − | 0.158214i | \(-0.0505737\pi\) | |||||||
\(740\) | 350.149 | + | 202.171i | 0.473174 | + | 0.273204i | ||||
\(741\) | 274.340 | 0.370229 | ||||||||
\(742\) | −793.375 | + | 793.375i | −1.06924 | + | 1.06924i | ||||
\(743\) | −201.785 | − | 201.785i | −0.271581 | − | 0.271581i | 0.558155 | − | 0.829736i | \(-0.311509\pi\) |
−0.829736 | + | 0.558155i | \(0.811509\pi\) | |||||||
\(744\) | 73.9317i | 0.0993706i | ||||||||
\(745\) | 44.4749 | + | 166.001i | 0.0596978 | + | 0.222820i | ||||
\(746\) | −562.793 | −0.754414 | ||||||||
\(747\) | 206.767 | − | 206.767i | 0.276796 | − | 0.276796i | ||||
\(748\) | −30.0136 | − | 30.0136i | −0.0401251 | − | 0.0401251i | ||||
\(749\) | − | 1465.98i | − | 1.95725i | ||||||
\(750\) | 216.524 | − | 216.489i | 0.288699 | − | 0.288651i | ||||
\(751\) | 76.6521 | 0.102067 | 0.0510333 | − | 0.998697i | \(-0.483749\pi\) | ||||
0.0510333 | + | 0.998697i | \(0.483749\pi\) | |||||||
\(752\) | −8.91109 | + | 8.91109i | −0.0118499 | + | 0.0118499i | ||||
\(753\) | 235.123 | + | 235.123i | 0.312248 | + | 0.312248i | ||||
\(754\) | 388.138i | 0.514772i | ||||||||
\(755\) | 905.826 | − | 242.689i | 1.19977 | − | 0.321442i | ||||
\(756\) | 85.9481 | 0.113688 | ||||||||
\(757\) | −971.333 | + | 971.333i | −1.28314 | + | 1.28314i | −0.344262 | + | 0.938874i | \(0.611871\pi\) |
−0.938874 | + | 0.344262i | \(0.888129\pi\) | |||||||
\(758\) | −450.647 | − | 450.647i | −0.594521 | − | 0.594521i | ||||
\(759\) | − | 14.6483i | − | 0.0192995i | ||||||
\(760\) | −158.378 | + | 274.301i | −0.208392 | + | 0.360922i | ||||
\(761\) | 806.466 | 1.05975 | 0.529873 | − | 0.848077i | \(-0.322240\pi\) | ||||
0.529873 | + | 0.848077i | \(0.322240\pi\) | |||||||
\(762\) | −213.358 | + | 213.358i | −0.279998 | + | 0.279998i | ||||
\(763\) | 384.336 | + | 384.336i | 0.503717 | + | 0.503717i | ||||
\(764\) | 206.599i | 0.270418i | ||||||||
\(765\) | 156.335 | + | 90.2657i | 0.204359 | + | 0.117994i | ||||
\(766\) | 241.562 | 0.315354 | ||||||||
\(767\) | −146.792 | + | 146.792i | −0.191385 | + | 0.191385i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 919.455i | − | 1.19565i | −0.801626 | − | 0.597825i | \(-0.796032\pi\) | ||
0.801626 | − | 0.597825i | \(-0.203968\pi\) | |||||||
\(770\) | 26.6885 | + | 99.6136i | 0.0346603 | + | 0.129368i | ||||
\(771\) | 246.956 | 0.320307 | ||||||||
\(772\) | 42.8181 | − | 42.8181i | 0.0554639 | − | 0.0554639i | ||||
\(773\) | 604.542 | + | 604.542i | 0.782073 | + | 0.782073i | 0.980180 | − | 0.198107i | \(-0.0634794\pi\) |
−0.198107 | + | 0.980180i | \(0.563479\pi\) | |||||||
\(774\) | − | 208.520i | − | 0.269406i | ||||||
\(775\) | 326.746 | − | 188.623i | 0.421607 | − | 0.243384i | ||||
\(776\) | 343.851 | 0.443107 | ||||||||
\(777\) | 409.542 | − | 409.542i | 0.527081 | − | 0.527081i | ||||
\(778\) | 136.553 | + | 136.553i | 0.175518 | + | 0.175518i | ||||
\(779\) | − | 1432.25i | − | 1.83858i | ||||||
\(780\) | −118.317 | + | 31.6995i | −0.151689 | + | 0.0406404i | ||||
\(781\) | 63.6576 | 0.0815078 | ||||||||
\(782\) | 57.7171 | − | 57.7171i | 0.0738071 | − | 0.0738071i | ||||
\(783\) | 142.593 | + | 142.593i | 0.182111 | + | 0.182111i | ||||
\(784\) | 77.5951i | 0.0989734i | ||||||||
\(785\) | −612.377 | + | 1060.60i | −0.780098 | + | 1.35108i | ||||
\(786\) | −372.202 | −0.473540 | ||||||||
\(787\) | −586.515 | + | 586.515i | −0.745254 | + | 0.745254i | −0.973584 | − | 0.228330i | \(-0.926673\pi\) |
0.228330 | + | 0.973584i | \(0.426673\pi\) | |||||||
\(788\) | −10.3884 | − | 10.3884i | −0.0131832 | − | 0.0131832i | ||||
\(789\) | − | 397.774i | − | 0.504150i | ||||||
\(790\) | 784.901 | + | 453.192i | 0.993546 | + | 0.573660i | ||||
\(791\) | 587.637 | 0.742904 | ||||||||
\(792\) | 10.5807 | − | 10.5807i | 0.0133594 | − | 0.0133594i | ||||
\(793\) | 273.168 | + | 273.168i | 0.344474 | + | 0.344474i | ||||
\(794\) | − | 23.2306i | − | 0.0292576i | ||||||
\(795\) | −214.999 | − | 802.476i | −0.270439 | − | 1.00940i | ||||
\(796\) | −686.965 | −0.863021 | ||||||||
\(797\) | −619.264 | + | 619.264i | −0.776993 | + | 0.776993i | −0.979318 | − | 0.202325i | \(-0.935150\pi\) |
0.202325 | + | 0.979318i | \(0.435150\pi\) | |||||||
\(798\) | 320.829 | + | 320.829i | 0.402041 | + | 0.402041i | ||||
\(799\) | 37.9164i | 0.0474548i | ||||||||
\(800\) | 36.6100 | − | 136.601i | 0.0457625 | − | 0.170751i | ||||
\(801\) | −59.1865 | −0.0738908 | ||||||||
\(802\) | 325.917 | − | 325.917i | 0.406380 | − | 0.406380i | ||||
\(803\) | 103.677 | + | 103.677i | 0.129112 | + | 0.129112i | ||||
\(804\) | − | 68.5881i | − | 0.0853086i | ||||||
\(805\) | −191.560 | + | 51.3228i | −0.237963 | + | 0.0637550i | ||||
\(806\) | −150.932 | −0.187260 | ||||||||
\(807\) | −203.395 | + | 203.395i | −0.252039 | + | 0.252039i | ||||
\(808\) | −19.1336 | − | 19.1336i | −0.0236802 | − | 0.0236802i | ||||
\(809\) | 1363.50i | 1.68541i | 0.538375 | + | 0.842705i | \(0.319038\pi\) | ||||
−0.538375 | + | 0.842705i | \(0.680962\pi\) | |||||||
\(810\) | −31.8213 | + | 55.1126i | −0.0392856 | + | 0.0680403i | ||||
\(811\) | 1102.47 | 1.35940 | 0.679698 | − | 0.733492i | \(-0.262111\pi\) | ||||
0.679698 | + | 0.733492i | \(0.262111\pi\) | |||||||
\(812\) | −453.911 | + | 453.911i | −0.559004 | + | 0.559004i | ||||
\(813\) | −378.858 | − | 378.858i | −0.466000 | − | 0.466000i | ||||
\(814\) | − | 100.834i | − | 0.123874i | ||||||
\(815\) | 75.4922 | + | 43.5882i | 0.0926285 | + | 0.0534825i | ||||
\(816\) | 83.3799 | 0.102181 | ||||||||
\(817\) | 778.367 | − | 778.367i | 0.952714 | − | 0.952714i | ||||
\(818\) | −447.168 | − | 447.168i | −0.546661 | − | 0.546661i | ||||
\(819\) | 175.463i | 0.214240i | ||||||||
\(820\) | 165.495 | + | 617.702i | 0.201823 | + | 0.753295i | ||||
\(821\) | −1282.68 | −1.56234 | −0.781169 | − | 0.624319i | \(-0.785376\pi\) | ||||
−0.781169 | + | 0.624319i | \(0.785376\pi\) | |||||||
\(822\) | −164.684 | + | 164.684i | −0.200346 | + | 0.200346i | ||||
\(823\) | −151.442 | − | 151.442i | −0.184013 | − | 0.184013i | 0.609089 | − | 0.793102i | \(-0.291535\pi\) |
−0.793102 | + | 0.609089i | \(0.791535\pi\) | |||||||
\(824\) | 208.589i | 0.253142i | ||||||||
\(825\) | −73.7565 | − | 19.7673i | −0.0894018 | − | 0.0239604i | ||||
\(826\) | −343.335 | −0.415659 | ||||||||
\(827\) | 424.578 | − | 424.578i | 0.513396 | − | 0.513396i | −0.402169 | − | 0.915565i | \(-0.631744\pi\) |
0.915565 | + | 0.402169i | \(0.131744\pi\) | |||||||
\(828\) | 20.3470 | + | 20.3470i | 0.0245737 | + | 0.0245737i | ||||
\(829\) | 171.099i | 0.206392i | 0.994661 | + | 0.103196i | \(0.0329069\pi\) | ||||
−0.994661 | + | 0.103196i | \(0.967093\pi\) | |||||||
\(830\) | −665.743 | + | 178.366i | −0.802100 | + | 0.214898i | ||||
\(831\) | −651.559 | −0.784066 | ||||||||
\(832\) | −40.0050 | + | 40.0050i | −0.0480830 | + | 0.0480830i | ||||
\(833\) | 165.082 | + | 165.082i | 0.198178 | + | 0.198178i | ||||
\(834\) | − | 362.004i | − | 0.434057i | ||||||
\(835\) | −240.000 | + | 415.666i | −0.287425 | + | 0.497804i | ||||
\(836\) | 78.9915 | 0.0944875 | ||||||||
\(837\) | −55.4488 | + | 55.4488i | −0.0662471 | + | 0.0662471i | ||||
\(838\) | 356.216 | + | 356.216i | 0.425078 | + | 0.425078i | ||||
\(839\) | − | 1019.44i | − | 1.21507i | −0.794294 | − | 0.607533i | \(-0.792159\pi\) | ||
0.794294 | − | 0.607533i | \(-0.207841\pi\) | |||||||
\(840\) | −175.438 | − | 101.296i | −0.208855 | − | 0.120590i | ||||
\(841\) | −665.134 | −0.790884 | ||||||||
\(842\) | −415.752 | + | 415.752i | −0.493767 | + | 0.493767i | ||||
\(843\) | 70.9421 | + | 70.9421i | 0.0841544 | + | 0.0841544i | ||||
\(844\) | 407.576i | 0.482910i | ||||||||
\(845\) | 153.965 | + | 574.669i | 0.182207 | + | 0.680082i | ||||
\(846\) | −13.3666 | −0.0157998 | ||||||||
\(847\) | −689.425 | + | 689.425i | −0.813961 | + | 0.813961i | ||||
\(848\) | −271.331 | − | 271.331i | −0.319966 | − | 0.319966i | ||||
\(849\) | − | 284.578i | − | 0.335192i | ||||||
\(850\) | −212.728 | − | 368.502i | −0.250268 | − | 0.433532i | ||||
\(851\) | 193.907 | 0.227857 | ||||||||
\(852\) | −88.4227 | + | 88.4227i | −0.103782 | + | 0.103782i | ||||
\(853\) | 435.813 | + | 435.813i | 0.510918 | + | 0.510918i | 0.914808 | − | 0.403890i | \(-0.132342\pi\) |
−0.403890 | + | 0.914808i | \(0.632342\pi\) | |||||||
\(854\) | 638.917i | 0.748146i | ||||||||
\(855\) | −324.509 | + | 86.9424i | −0.379542 | + | 0.101687i | ||||
\(856\) | 501.360 | 0.585700 | ||||||||
\(857\) | −601.838 | + | 601.838i | −0.702261 | + | 0.702261i | −0.964896 | − | 0.262634i | \(-0.915409\pi\) |
0.262634 | + | 0.964896i | \(0.415409\pi\) | |||||||
\(858\) | 21.6004 | + | 21.6004i | 0.0251753 | + | 0.0251753i | ||||
\(859\) | − | 1343.67i | − | 1.56422i | −0.623138 | − | 0.782112i | \(-0.714142\pi\) | ||
0.623138 | − | 0.782112i | \(-0.285858\pi\) | |||||||
\(860\) | −245.755 | + | 425.633i | −0.285761 | + | 0.494922i | ||||
\(861\) | 916.045 | 1.06393 | ||||||||
\(862\) | 456.460 | − | 456.460i | 0.529536 | − | 0.529536i | ||||
\(863\) | −645.537 | − | 645.537i | −0.748015 | − | 0.748015i | 0.226091 | − | 0.974106i | \(-0.427405\pi\) |
−0.974106 | + | 0.226091i | \(0.927405\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −223.167 | − | 128.854i | −0.257996 | − | 0.148964i | ||||
\(866\) | 113.222 | 0.130741 | ||||||||
\(867\) | −176.562 | + | 176.562i | −0.203647 | + | 0.203647i | ||||
\(868\) | −176.508 | − | 176.508i | −0.203350 | − | 0.203350i | ||||
\(869\) | − | 226.031i | − | 0.260105i | ||||||
\(870\) | −123.007 | − | 459.118i | −0.141387 | − | 0.527722i | ||||
\(871\) | 140.023 | 0.160761 | ||||||||
\(872\) | −131.441 | + | 131.441i | −0.150736 | + | 0.150736i | ||||
\(873\) | 257.889 | + | 257.889i | 0.295405 | + | 0.295405i | ||||
\(874\) | 151.903i | 0.173802i | ||||||||
\(875\) | −0.0848548 | + | 1033.79i | −9.69769e−5 | + | 1.18148i | ||||
\(876\) | −288.021 | −0.328791 | ||||||||
\(877\) | −1132.84 | + | 1132.84i | −1.29172 | + | 1.29172i | −0.358004 | + | 0.933720i | \(0.616543\pi\) |
−0.933720 | + | 0.358004i | \(0.883457\pi\) | |||||||
\(878\) | −533.763 | − | 533.763i | −0.607931 | − | 0.607931i | ||||
\(879\) | 462.957i | 0.526686i | ||||||||
\(880\) | −34.0674 | + | 9.12734i | −0.0387130 | + | 0.0103720i | ||||
\(881\) | 1591.02 | 1.80592 | 0.902960 | − | 0.429725i | \(-0.141389\pi\) | ||||
0.902960 | + | 0.429725i | \(0.141389\pi\) | |||||||
\(882\) | −58.1964 | + | 58.1964i | −0.0659823 | + | 0.0659823i | ||||
\(883\) | −129.734 | − | 129.734i | −0.146924 | − | 0.146924i | 0.629819 | − | 0.776742i | \(-0.283129\pi\) |
−0.776742 | + | 0.629819i | \(0.783129\pi\) | |||||||
\(884\) | 170.220i | 0.192557i | ||||||||
\(885\) | 127.116 | − | 220.157i | 0.143634 | − | 0.248765i | ||||
\(886\) | 616.632 | 0.695973 | ||||||||
\(887\) | 488.248 | − | 488.248i | 0.550449 | − | 0.550449i | −0.376122 | − | 0.926570i | \(-0.622743\pi\) |
0.926570 | + | 0.376122i | \(0.122743\pi\) | |||||||
\(888\) | 140.062 | + | 140.062i | 0.157727 | + | 0.157727i | ||||
\(889\) | − | 1018.76i | − | 1.14597i | ||||||
\(890\) | 120.812 | + | 69.7553i | 0.135744 | + | 0.0783767i | ||||
\(891\) | 15.8710 | 0.0178126 | ||||||||
\(892\) | −464.248 | + | 464.248i | −0.520457 | + | 0.520457i | ||||
\(893\) | −49.8952 | − | 49.8952i | −0.0558737 | − | 0.0558737i | ||||
\(894\) | 84.1915i | 0.0941740i | ||||||||
\(895\) | −124.441 | − | 464.471i | −0.139040 | − | 0.518962i | ||||
\(896\) | −93.5684 | −0.104429 | ||||||||
\(897\) | −41.5384 | + | 41.5384i | −0.0463081 | + | 0.0463081i | ||||
\(898\) | 479.262 | + | 479.262i | 0.533699 | + | 0.533699i | ||||
\(899\) | − | 585.676i | − | 0.651474i | ||||||
\(900\) | 129.908 | − | 74.9929i | 0.144342 | − | 0.0833254i | ||||
\(901\) | −1154.50 | −1.28136 | ||||||||
\(902\) | 112.770 | − | 112.770i | 0.125022 | − | 0.125022i | ||||
\(903\) | 497.830 | + | 497.830i | 0.551307 | + | 0.551307i | ||||
\(904\) | 200.969i | 0.222311i | ||||||||
\(905\) | −986.845 | + | 264.395i | −1.09044 | + | 0.292150i | ||||
\(906\) | 459.413 | 0.507079 | ||||||||
\(907\) | 717.440 | − | 717.440i | 0.791003 | − | 0.791003i | −0.190654 | − | 0.981657i | \(-0.561061\pi\) |
0.981657 | + | 0.190654i | \(0.0610609\pi\) | |||||||
\(908\) | 368.685 | + | 368.685i | 0.406041 | + | 0.406041i | ||||
\(909\) | − | 28.7004i | − | 0.0315736i | ||||||
\(910\) | 206.795 | − | 358.156i | 0.227247 | − | 0.393578i | ||||
\(911\) | −1469.66 | −1.61324 | −0.806618 | − | 0.591073i | \(-0.798704\pi\) | ||||
−0.806618 | + | 0.591073i | \(0.798704\pi\) | |||||||
\(912\) | −109.722 | + | 109.722i | −0.120309 | + | 0.120309i | ||||
\(913\) | 121.541 | + | 121.541i | 0.133122 | + | 0.133122i | ||||
\(914\) | 242.117i | 0.264898i | ||||||||
\(915\) | −409.694 | − | 236.552i | −0.447753 | − | 0.258527i | ||||
\(916\) | −446.508 | −0.487454 | ||||||||
\(917\) | 888.613 | − | 888.613i | 0.969044 | − | 0.969044i | ||||
\(918\) | 62.5350 | + | 62.5350i | 0.0681209 | + | 0.0681209i | ||||
\(919\) | 1596.20i | 1.73689i | 0.495786 | + | 0.868445i | \(0.334880\pi\) | ||||
−0.495786 | + | 0.868445i | \(0.665120\pi\) | |||||||
\(920\) | −17.5522 | − | 65.5128i | −0.0190784 | − | 0.0712095i | ||||
\(921\) | 754.006 | 0.818682 | ||||||||
\(922\) | 130.197 | − | 130.197i | 0.141211 | − | 0.141211i | ||||
\(923\) | −180.515 | − | 180.515i | −0.195574 | − | 0.195574i | ||||
\(924\) | 50.5216i | 0.0546771i | ||||||||
\(925\) | 261.670 | − | 976.351i | 0.282886 | − | 1.05552i | ||||
\(926\) | 169.770 | 0.183337 | ||||||||
\(927\) | −156.442 | + | 156.442i | −0.168761 | + | 0.168761i | ||||
\(928\) | −155.236 | − | 155.236i | −0.167280 | − | 0.167280i | ||||
\(929\) | − | 1330.70i | − | 1.43240i | −0.697895 | − | 0.716200i | \(-0.745880\pi\) | ||
0.697895 | − | 0.716200i | \(-0.254120\pi\) | |||||||
\(930\) | 178.533 | − | 47.8325i | 0.191971 | − | 0.0514328i | ||||
\(931\) | −434.473 | −0.466673 | ||||||||
\(932\) | −592.388 | + | 592.388i | −0.635609 | + | 0.635609i | ||||
\(933\) | −648.856 | − | 648.856i | −0.695451 | − | 0.695451i | ||||
\(934\) | 186.437i | 0.199612i | ||||||||
\(935\) | −53.0596 | + | 91.8961i | −0.0567482 | + | 0.0982846i | ||||
\(936\) | −60.0076 | −0.0641107 | ||||||||
\(937\) | 1149.86 | − | 1149.86i | 1.22717 | − | 1.22717i | 0.262138 | − | 0.965030i | \(-0.415572\pi\) |
0.965030 | − | 0.262138i | \(-0.0844276\pi\) | |||||||
\(938\) | 163.751 | + | 163.751i | 0.174574 | + | 0.174574i | ||||
\(939\) | 157.594i | 0.167832i | ||||||||
\(940\) | 27.2841 | + | 15.7535i | 0.0290256 | + | 0.0167590i | ||||
\(941\) | −1043.38 | −1.10880 | −0.554399 | − | 0.832251i | \(-0.687052\pi\) | ||||
−0.554399 | + | 0.832251i | \(0.687052\pi\) | |||||||
\(942\) | −424.247 | + | 424.247i | −0.450368 | + | 0.450368i | ||||
\(943\) | 216.861 | + | 216.861i | 0.229969 | + | 0.229969i | ||||
\(944\) | − | 117.419i | − | 0.124385i | ||||||
\(945\) | −55.6068 | − | 207.550i | −0.0588432 | − | 0.219630i | ||||
\(946\) | 122.571 | 0.129568 | ||||||||
\(947\) | 235.405 | − | 235.405i | 0.248580 | − | 0.248580i | −0.571808 | − | 0.820388i | \(-0.693758\pi\) |
0.820388 | + | 0.571808i | \(0.193758\pi\) | |||||||
\(948\) | 313.966 | + | 313.966i | 0.331187 | + | 0.331187i | ||||
\(949\) | − | 587.995i | − | 0.619594i | ||||||
\(950\) | 764.858 | + | 204.988i | 0.805113 | + | 0.215777i | ||||
\(951\) | −962.725 | −1.01233 | ||||||||
\(952\) | −199.065 | + | 199.065i | −0.209102 | + | 0.209102i | ||||
\(953\) | 614.995 | + | 614.995i | 0.645325 | + | 0.645325i | 0.951860 | − | 0.306534i | \(-0.0991695\pi\) |
−0.306534 | + | 0.951860i | \(0.599169\pi\) | |||||||
\(954\) | − | 406.997i | − | 0.426621i | ||||||
\(955\) | 498.902 | − | 133.666i | 0.522410 | − | 0.139964i | ||||
\(956\) | 4.31510 | 0.00451370 | ||||||||
\(957\) | −83.8185 | + | 83.8185i | −0.0875846 | + | 0.0875846i | ||||
\(958\) | 376.346 | + | 376.346i | 0.392845 | + | 0.392845i | ||||
\(959\) | − | 786.349i | − | 0.819968i | ||||||
\(960\) | 34.6427 | − | 59.9991i | 0.0360861 | − | 0.0624990i | ||||
\(961\) | −733.254 | −0.763011 | ||||||||
\(962\) | −285.936 | + | 285.936i | −0.297231 | + | 0.297231i | ||||
\(963\) | 376.020 | + | 376.020i | 0.390467 | + | 0.390467i | ||||
\(964\) | 272.143i | 0.282306i | ||||||||
\(965\) | −131.101 | − | 75.6960i | −0.135856 | − | 0.0784415i | ||||
\(966\) | −97.1547 | −0.100574 | ||||||||
\(967\) | −567.252 | + | 567.252i | −0.586610 | + | 0.586610i | −0.936712 | − | 0.350101i | \(-0.886147\pi\) |
0.350101 | + | 0.936712i | \(0.386147\pi\) | |||||||
\(968\) | −235.781 | − | 235.781i | −0.243575 | − | 0.243575i | ||||
\(969\) | 466.863i | 0.481799i | ||||||||
\(970\) | −222.465 | − | 830.343i | −0.229346 | − | 0.856024i | ||||
\(971\) | −315.250 | −0.324666 | −0.162333 | − | 0.986736i | \(-0.551902\pi\) | ||||
−0.162333 | + | 0.986736i | \(0.551902\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 864.265 | + | 864.265i | 0.888247 | + | 0.888247i | ||||
\(974\) | − | 662.210i | − | 0.679887i | ||||||
\(975\) | 153.098 | + | 265.207i | 0.157023 | + | 0.272007i | ||||
\(976\) | −218.507 | −0.223880 | ||||||||
\(977\) | −570.296 | + | 570.296i | −0.583722 | + | 0.583722i | −0.935924 | − | 0.352202i | \(-0.885433\pi\) |
0.352202 | + | 0.935924i | \(0.385433\pi\) | |||||||
\(978\) | 30.1974 | + | 30.1974i | 0.0308767 | + | 0.0308767i | ||||
\(979\) | − | 34.7907i | − | 0.0355370i | ||||||
\(980\) | 187.379 | − | 50.2026i | 0.191203 | − | 0.0512272i | ||||
\(981\) | −197.162 | −0.200981 | ||||||||
\(982\) | −95.5294 | + | 95.5294i | −0.0972805 | + | 0.0972805i | ||||
\(983\) | 246.193 | + | 246.193i | 0.250451 | + | 0.250451i | 0.821156 | − | 0.570704i | \(-0.193330\pi\) |
−0.570704 | + | 0.821156i | \(0.693330\pi\) | |||||||
\(984\) | 313.283i | 0.318377i | ||||||||
\(985\) | −18.3651 | + | 31.8073i | −0.0186448 | + | 0.0322916i | ||||
\(986\) | −660.523 | −0.669901 | ||||||||
\(987\) | 31.9121 | − | 31.9121i | 0.0323324 | − | 0.0323324i | ||||
\(988\) | −223.997 | − | 223.997i | −0.226718 | − | 0.226718i | ||||
\(989\) | 235.709i | 0.238330i | ||||||||
\(990\) | −32.3961 | − | 18.7051i | −0.0327233 | − | 0.0188940i | ||||
\(991\) | 1027.66 | 1.03699 | 0.518495 | − | 0.855080i | \(-0.326492\pi\) | ||||
0.518495 | + | 0.855080i | \(0.326492\pi\) | |||||||
\(992\) | 60.3650 | − | 60.3650i | 0.0608518 | − | 0.0608518i | ||||
\(993\) | 220.153 | + | 220.153i | 0.221705 | + | 0.221705i | ||||
\(994\) | − | 422.209i | − | 0.424757i | ||||||
\(995\) | 444.453 | + | 1658.90i | 0.446687 | + | 1.66724i | ||||
\(996\) | −337.649 | −0.339005 | ||||||||
\(997\) | −121.459 | + | 121.459i | −0.121825 | + | 0.121825i | −0.765391 | − | 0.643566i | \(-0.777454\pi\) |
0.643566 | + | 0.765391i | \(0.277454\pi\) | |||||||
\(998\) | −134.022 | − | 134.022i | −0.134291 | − | 0.134291i | ||||
\(999\) | 210.093i | 0.210303i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.3.k.b.553.20 | yes | 48 | |
5.2 | odd | 4 | inner | 690.3.k.b.277.20 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.20 | ✓ | 48 | 5.2 | odd | 4 | inner | |
690.3.k.b.553.20 | yes | 48 | 1.1 | even | 1 | trivial |