Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [861,2,Mod(419,861)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(861, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("861.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 861 = 3 \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 861.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.87511961403\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Relative dimension: | \(108\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 524.16 | ||
Character | \(\chi\) | \(=\) | 861.524 |
Dual form | 861.2.l.a.419.16 |
$q$-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 \(\left(\mathbb{Z}/861\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(493\) | \(575\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09764 | −1.48325 | −0.741626 | − | 0.670813i | \(-0.765945\pi\) | ||||
−0.741626 | + | 0.670813i | \(0.765945\pi\) | |||||||
\(3\) | 0.839690 | + | 1.51490i | 0.484795 | + | 0.874628i | ||||
\(4\) | 2.40008 | 1.20004 | ||||||||
\(5\) | 2.02468i | 0.905465i | 0.891646 | + | 0.452733i | \(0.149551\pi\) | ||||
−0.891646 | + | 0.452733i | \(0.850449\pi\) | |||||||
\(6\) | −1.76136 | − | 3.17771i | −0.719074 | − | 1.29729i | ||||
\(7\) | 2.04936 | − | 1.67336i | 0.774584 | − | 0.632472i | ||||
\(8\) | −0.839219 | −0.296709 | ||||||||
\(9\) | −1.58984 | + | 2.54409i | −0.529947 | + | 0.848031i | ||||
\(10\) | − | 4.24705i | − | 1.34303i | ||||||
\(11\) | −1.97738 | − | 1.97738i | −0.596203 | − | 0.596203i | 0.343097 | − | 0.939300i | \(-0.388524\pi\) |
−0.939300 | + | 0.343097i | \(0.888524\pi\) | |||||||
\(12\) | 2.01532 | + | 3.63588i | 0.581774 | + | 1.04959i | ||||
\(13\) | −0.746924 | − | 0.746924i | −0.207160 | − | 0.207160i | 0.595900 | − | 0.803059i | \(-0.296796\pi\) |
−0.803059 | + | 0.595900i | \(0.796796\pi\) | |||||||
\(14\) | −4.29880 | + | 3.51011i | −1.14890 | + | 0.938115i | ||||
\(15\) | −3.06719 | + | 1.70011i | −0.791945 | + | 0.438965i | ||||
\(16\) | −3.03978 | −0.759945 | ||||||||
\(17\) | 4.42368 | + | 4.42368i | 1.07290 | + | 1.07290i | 0.997125 | + | 0.0757755i | \(0.0241432\pi\) |
0.0757755 | + | 0.997125i | \(0.475857\pi\) | |||||||
\(18\) | 3.33491 | − | 5.33658i | 0.786045 | − | 1.25784i | ||||
\(19\) | −3.72167 | + | 3.72167i | −0.853810 | + | 0.853810i | −0.990600 | − | 0.136790i | \(-0.956322\pi\) |
0.136790 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(20\) | 4.85939i | 1.08659i | ||||||||
\(21\) | 4.25580 | + | 1.69946i | 0.928692 | + | 0.370853i | ||||
\(22\) | 4.14783 | + | 4.14783i | 0.884320 | + | 0.884320i | ||||
\(23\) | 1.99753i | 0.416514i | 0.978074 | + | 0.208257i | \(0.0667791\pi\) | ||||
−0.978074 | + | 0.208257i | \(0.933221\pi\) | |||||||
\(24\) | −0.704684 | − | 1.27133i | −0.143843 | − | 0.259510i | ||||
\(25\) | 0.900666 | 0.180133 | ||||||||
\(26\) | 1.56678 | + | 1.56678i | 0.307270 | + | 0.307270i | ||||
\(27\) | −5.18902 | − | 0.272199i | −0.998627 | − | 0.0523847i | ||||
\(28\) | 4.91861 | − | 4.01620i | 0.929531 | − | 0.758991i | ||||
\(29\) | −2.41447 | − | 2.41447i | −0.448355 | − | 0.448355i | 0.446452 | − | 0.894807i | \(-0.352687\pi\) |
−0.894807 | + | 0.446452i | \(0.852687\pi\) | |||||||
\(30\) | 6.43385 | − | 3.56620i | 1.17465 | − | 0.651097i | ||||
\(31\) | 6.69591i | 1.20262i | 0.799016 | + | 0.601310i | \(0.205354\pi\) | ||||
−0.799016 | + | 0.601310i | \(0.794646\pi\) | |||||||
\(32\) | 8.05479 | 1.42390 | ||||||||
\(33\) | 1.33515 | − | 4.65593i | 0.232419 | − | 0.810493i | ||||
\(34\) | −9.27928 | − | 9.27928i | −1.59138 | − | 1.59138i | ||||
\(35\) | 3.38803 | + | 4.14929i | 0.572681 | + | 0.701358i | ||||
\(36\) | −3.81574 | + | 6.10602i | −0.635957 | + | 1.01767i | ||||
\(37\) | −0.270291 | −0.0444356 | −0.0222178 | − | 0.999753i | \(-0.507073\pi\) | ||||
−0.0222178 | + | 0.999753i | \(0.507073\pi\) | |||||||
\(38\) | 7.80672 | − | 7.80672i | 1.26642 | − | 1.26642i | ||||
\(39\) | 0.504330 | − | 1.75870i | 0.0807574 | − | 0.281617i | ||||
\(40\) | − | 1.69915i | − | 0.268660i | ||||||
\(41\) | 0.494936 | + | 6.38397i | 0.0772961 | + | 0.997008i | ||||
\(42\) | −8.92712 | − | 3.56485i | −1.37748 | − | 0.550069i | ||||
\(43\) | 9.03578i | 1.37794i | 0.724788 | + | 0.688972i | \(0.241938\pi\) | ||||
−0.724788 | + | 0.688972i | \(0.758062\pi\) | |||||||
\(44\) | −4.74587 | − | 4.74587i | −0.715468 | − | 0.715468i | ||||
\(45\) | −5.15098 | − | 3.21892i | −0.767862 | − | 0.479848i | ||||
\(46\) | − | 4.19010i | − | 0.617796i | ||||||
\(47\) | −3.64140 | − | 3.64140i | −0.531153 | − | 0.531153i | 0.389762 | − | 0.920916i | \(-0.372557\pi\) |
−0.920916 | + | 0.389762i | \(0.872557\pi\) | |||||||
\(48\) | −2.55247 | − | 4.60496i | −0.368418 | − | 0.664669i | ||||
\(49\) | 1.39972 | − | 6.85863i | 0.199960 | − | 0.979804i | ||||
\(50\) | −1.88927 | −0.267183 | ||||||||
\(51\) | −2.98691 | + | 10.4160i | −0.418251 | + | 1.45853i | ||||
\(52\) | −1.79268 | − | 1.79268i | −0.248600 | − | 0.248600i | ||||
\(53\) | −2.30499 | − | 2.30499i | −0.316615 | − | 0.316615i | 0.530851 | − | 0.847465i | \(-0.321873\pi\) |
−0.847465 | + | 0.530851i | \(0.821873\pi\) | |||||||
\(54\) | 10.8847 | + | 0.570974i | 1.48122 | + | 0.0776998i | ||||
\(55\) | 4.00357 | − | 4.00357i | 0.539841 | − | 0.539841i | ||||
\(56\) | −1.71986 | + | 1.40432i | −0.229826 | + | 0.187660i | ||||
\(57\) | −8.76301 | − | 2.51291i | −1.16069 | − | 0.332843i | ||||
\(58\) | 5.06467 | + | 5.06467i | 0.665024 | + | 0.665024i | ||||
\(59\) | 2.66949 | 0.347538 | 0.173769 | − | 0.984786i | \(-0.444405\pi\) | ||||
0.173769 | + | 0.984786i | \(0.444405\pi\) | |||||||
\(60\) | −7.36149 | + | 4.08039i | −0.950365 | + | 0.526776i | ||||
\(61\) | 0.289048 | 0.0370088 | 0.0185044 | − | 0.999829i | \(-0.494110\pi\) | ||||
0.0185044 | + | 0.999829i | \(0.494110\pi\) | |||||||
\(62\) | − | 14.0456i | − | 1.78379i | ||||||
\(63\) | 0.999040 | + | 7.87413i | 0.125867 | + | 0.992047i | ||||
\(64\) | −10.8165 | −1.35206 | ||||||||
\(65\) | 1.51228 | − | 1.51228i | 0.187576 | − | 0.187576i | ||||
\(66\) | −2.80065 | + | 9.76644i | −0.344737 | + | 1.20217i | ||||
\(67\) | −5.92249 | − | 5.92249i | −0.723548 | − | 0.723548i | 0.245778 | − | 0.969326i | \(-0.420956\pi\) |
−0.969326 | + | 0.245778i | \(0.920956\pi\) | |||||||
\(68\) | 10.6172 | + | 10.6172i | 1.28752 | + | 1.28752i | ||||
\(69\) | −3.02606 | + | 1.67731i | −0.364295 | + | 0.201924i | ||||
\(70\) | −7.10685 | − | 8.70371i | −0.849431 | − | 1.04029i | ||||
\(71\) | 6.99899 | + | 6.99899i | 0.830628 | + | 0.830628i | 0.987603 | − | 0.156975i | \(-0.0501741\pi\) |
−0.156975 | + | 0.987603i | \(0.550174\pi\) | |||||||
\(72\) | 1.33423 | − | 2.13505i | 0.157240 | − | 0.251618i | ||||
\(73\) | 0.182166 | 0.0213209 | 0.0106604 | − | 0.999943i | \(-0.496607\pi\) | ||||
0.0106604 | + | 0.999943i | \(0.496607\pi\) | |||||||
\(74\) | 0.566972 | 0.0659092 | ||||||||
\(75\) | 0.756280 | + | 1.36442i | 0.0873277 | + | 0.157549i | ||||
\(76\) | −8.93231 | + | 8.93231i | −1.02461 | + | 1.02461i | ||||
\(77\) | −7.36124 | − | 0.743483i | −0.838891 | − | 0.0847277i | ||||
\(78\) | −1.05790 | + | 3.68911i | −0.119784 | + | 0.417710i | ||||
\(79\) | −10.5205 | + | 10.5205i | −1.18365 | + | 1.18365i | −0.204863 | + | 0.978791i | \(0.565675\pi\) |
−0.978791 | + | 0.204863i | \(0.934325\pi\) | |||||||
\(80\) | − | 6.15459i | − | 0.688104i | ||||||
\(81\) | −3.94481 | − | 8.08940i | −0.438313 | − | 0.898823i | ||||
\(82\) | −1.03820 | − | 13.3912i | −0.114650 | − | 1.47882i | ||||
\(83\) | 5.98025 | 0.656418 | 0.328209 | − | 0.944605i | \(-0.393555\pi\) | ||||
0.328209 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(84\) | 10.2143 | + | 4.07884i | 1.11447 | + | 0.445038i | ||||
\(85\) | −8.95655 | + | 8.95655i | −0.971474 | + | 0.971474i | ||||
\(86\) | − | 18.9538i | − | 2.04384i | ||||||
\(87\) | 1.63027 | − | 5.68508i | 0.174783 | − | 0.609505i | ||||
\(88\) | 1.65946 | + | 1.65946i | 0.176899 | + | 0.176899i | ||||
\(89\) | −3.63097 | + | 3.63097i | −0.384882 | + | 0.384882i | −0.872857 | − | 0.487975i | \(-0.837736\pi\) |
0.487975 | + | 0.872857i | \(0.337736\pi\) | |||||||
\(90\) | 10.8049 | + | 6.75212i | 1.13893 | + | 0.711736i | ||||
\(91\) | −2.78059 | − | 0.280839i | −0.291485 | − | 0.0294399i | ||||
\(92\) | 4.79424i | 0.499834i | ||||||||
\(93\) | −10.1436 | + | 5.62249i | −1.05184 | + | 0.583025i | ||||
\(94\) | 7.63834 | + | 7.63834i | 0.787835 | + | 0.787835i | ||||
\(95\) | −7.53520 | − | 7.53520i | −0.773095 | − | 0.773095i | ||||
\(96\) | 6.76353 | + | 12.2022i | 0.690300 | + | 1.24538i | ||||
\(97\) | 4.74709 | − | 4.74709i | 0.481994 | − | 0.481994i | −0.423774 | − | 0.905768i | \(-0.639295\pi\) |
0.905768 | + | 0.423774i | \(0.139295\pi\) | |||||||
\(98\) | −2.93610 | + | 14.3869i | −0.296591 | + | 1.45330i | ||||
\(99\) | 8.17437 | − | 1.88692i | 0.821555 | − | 0.189643i | ||||
\(100\) | 2.16167 | 0.216167 | ||||||||
\(101\) | −12.8845 | − | 12.8845i | −1.28205 | − | 1.28205i | −0.939499 | − | 0.342553i | \(-0.888708\pi\) |
−0.342553 | − | 0.939499i | \(-0.611292\pi\) | |||||||
\(102\) | 6.26545 | − | 21.8489i | 0.620372 | − | 2.16336i | ||||
\(103\) | 3.44740 | 0.339682 | 0.169841 | − | 0.985471i | \(-0.445675\pi\) | ||||
0.169841 | + | 0.985471i | \(0.445675\pi\) | |||||||
\(104\) | 0.626833 | + | 0.626833i | 0.0614661 | + | 0.0614661i | ||||
\(105\) | −3.44087 | + | 8.61664i | −0.335794 | + | 0.840898i | ||||
\(106\) | 4.83503 | + | 4.83503i | 0.469620 | + | 0.469620i | ||||
\(107\) | 10.6153i | 1.02622i | 0.858322 | + | 0.513111i | \(0.171507\pi\) | ||||
−0.858322 | + | 0.513111i | \(0.828493\pi\) | |||||||
\(108\) | −12.4541 | − | 0.653299i | −1.19839 | − | 0.0628637i | ||||
\(109\) | 1.84035 | + | 1.84035i | 0.176274 | + | 0.176274i | 0.789729 | − | 0.613456i | \(-0.210221\pi\) |
−0.613456 | + | 0.789729i | \(0.710221\pi\) | |||||||
\(110\) | −8.39803 | + | 8.39803i | −0.800721 | + | 0.800721i | ||||
\(111\) | −0.226961 | − | 0.409464i | −0.0215422 | − | 0.0388646i | ||||
\(112\) | −6.22959 | + | 5.08665i | −0.588641 | + | 0.480644i | ||||
\(113\) | 16.8845i | 1.58836i | 0.607685 | + | 0.794178i | \(0.292098\pi\) | ||||
−0.607685 | + | 0.794178i | \(0.707902\pi\) | |||||||
\(114\) | 18.3816 | + | 5.27117i | 1.72160 | + | 0.493690i | ||||
\(115\) | −4.04437 | −0.377139 | ||||||||
\(116\) | −5.79491 | − | 5.79491i | −0.538044 | − | 0.538044i | ||||
\(117\) | 3.08773 | − | 0.712754i | 0.285461 | − | 0.0658941i | ||||
\(118\) | −5.59962 | −0.515487 | ||||||||
\(119\) | 16.4681 | + | 1.66327i | 1.50963 | + | 0.152472i | ||||
\(120\) | 2.57404 | − | 1.42676i | 0.234977 | − | 0.130245i | ||||
\(121\) | − | 3.17991i | − | 0.289083i | ||||||
\(122\) | −0.606317 | −0.0548934 | ||||||||
\(123\) | −9.25548 | + | 6.11033i | −0.834538 | + | 0.550950i | ||||
\(124\) | 16.0707i | 1.44319i | ||||||||
\(125\) | 11.9470i | 1.06857i | ||||||||
\(126\) | −2.09562 | − | 16.5171i | −0.186693 | − | 1.47146i | ||||
\(127\) | −20.2414 | −1.79613 | −0.898065 | − | 0.439862i | \(-0.855027\pi\) | ||||
−0.898065 | + | 0.439862i | \(0.855027\pi\) | |||||||
\(128\) | 6.57943 | 0.581545 | ||||||||
\(129\) | −13.6883 | + | 7.58726i | −1.20519 | + | 0.668021i | ||||
\(130\) | −3.17222 | + | 3.17222i | −0.278222 | + | 0.278222i | ||||
\(131\) | 0.739441i | 0.0646053i | 0.999478 | + | 0.0323026i | \(0.0102840\pi\) | ||||
−0.999478 | + | 0.0323026i | \(0.989716\pi\) | |||||||
\(132\) | 3.20446 | − | 11.1746i | 0.278912 | − | 0.972623i | ||||
\(133\) | −1.39932 | + | 13.8547i | −0.121337 | + | 1.20136i | ||||
\(134\) | 12.4232 | + | 12.4232i | 1.07320 | + | 1.07320i | ||||
\(135\) | 0.551116 | − | 10.5061i | 0.0474325 | − | 0.904222i | ||||
\(136\) | −3.71244 | − | 3.71244i | −0.318339 | − | 0.318339i | ||||
\(137\) | −1.12158 | + | 1.12158i | −0.0958226 | + | 0.0958226i | −0.753393 | − | 0.657570i | \(-0.771584\pi\) |
0.657570 | + | 0.753393i | \(0.271584\pi\) | |||||||
\(138\) | 6.34758 | − | 3.51838i | 0.540342 | − | 0.299505i | ||||
\(139\) | 1.50267i | 0.127455i | 0.997967 | + | 0.0637273i | \(0.0202988\pi\) | ||||
−0.997967 | + | 0.0637273i | \(0.979701\pi\) | |||||||
\(140\) | 8.13153 | + | 9.95863i | 0.687239 | + | 0.841658i | ||||
\(141\) | 2.45871 | − | 8.57401i | 0.207061 | − | 0.722062i | ||||
\(142\) | −14.6813 | − | 14.6813i | −1.23203 | − | 1.23203i | ||||
\(143\) | 2.95391i | 0.247018i | ||||||||
\(144\) | 4.83277 | − | 7.73348i | 0.402730 | − | 0.644457i | ||||
\(145\) | 4.88853 | − | 4.88853i | 0.405970 | − | 0.405970i | ||||
\(146\) | −0.382117 | −0.0316242 | ||||||||
\(147\) | 11.5655 | − | 3.63869i | 0.953903 | − | 0.300114i | ||||
\(148\) | −0.648720 | −0.0533244 | ||||||||
\(149\) | 1.30698 | − | 1.30698i | 0.107072 | − | 0.107072i | −0.651541 | − | 0.758613i | \(-0.725877\pi\) |
0.758613 | + | 0.651541i | \(0.225877\pi\) | |||||||
\(150\) | −1.58640 | − | 2.86205i | −0.129529 | − | 0.233686i | ||||
\(151\) | 4.62897 | − | 4.62897i | 0.376701 | − | 0.376701i | −0.493210 | − | 0.869910i | \(-0.664177\pi\) |
0.869910 | + | 0.493210i | \(0.164177\pi\) | |||||||
\(152\) | 3.12330 | − | 3.12330i | 0.253333 | − | 0.253333i | ||||
\(153\) | −18.2872 | + | 4.22131i | −1.47843 | + | 0.341272i | ||||
\(154\) | 15.4412 | + | 1.55956i | 1.24429 | + | 0.125673i | ||||
\(155\) | −13.5571 | −1.08893 | ||||||||
\(156\) | 1.21043 | − | 4.22102i | 0.0969121 | − | 0.337952i | ||||
\(157\) | −6.56100 | − | 6.56100i | −0.523625 | − | 0.523625i | 0.395039 | − | 0.918664i | \(-0.370731\pi\) |
−0.918664 | + | 0.395039i | \(0.870731\pi\) | |||||||
\(158\) | 22.0683 | − | 22.0683i | 1.75566 | − | 1.75566i | ||||
\(159\) | 1.55635 | − | 5.42731i | 0.123427 | − | 0.430414i | ||||
\(160\) | 16.3084i | 1.28929i | ||||||||
\(161\) | 3.34260 | + | 4.09366i | 0.263434 | + | 0.322625i | ||||
\(162\) | 8.27479 | + | 16.9686i | 0.650129 | + | 1.33318i | ||||
\(163\) | 13.4110 | 1.05043 | 0.525217 | − | 0.850968i | \(-0.323984\pi\) | ||||
0.525217 | + | 0.850968i | \(0.323984\pi\) | |||||||
\(164\) | 1.18789 | + | 15.3220i | 0.0927583 | + | 1.19645i | ||||
\(165\) | 9.42677 | + | 2.70325i | 0.733873 | + | 0.210448i | ||||
\(166\) | −12.5444 | −0.973634 | ||||||||
\(167\) | −1.56671 | + | 1.56671i | −0.121235 | + | 0.121235i | −0.765121 | − | 0.643886i | \(-0.777321\pi\) |
0.643886 | + | 0.765121i | \(0.277321\pi\) | |||||||
\(168\) | −3.57155 | − | 1.42622i | −0.275551 | − | 0.110035i | ||||
\(169\) | − | 11.8842i | − | 0.914170i | ||||||
\(170\) | 18.7876 | − | 18.7876i | 1.44094 | − | 1.44094i | ||||
\(171\) | −3.55141 | − | 15.3851i | −0.271583 | − | 1.17653i | ||||
\(172\) | 21.6866i | 1.65359i | ||||||||
\(173\) | − | 5.85099i | − | 0.444842i | −0.974951 | − | 0.222421i | \(-0.928604\pi\) | ||
0.974951 | − | 0.222421i | \(-0.0713960\pi\) | |||||||
\(174\) | −3.41971 | + | 11.9252i | −0.259248 | + | 0.904049i | ||||
\(175\) | 1.84578 | − | 1.50714i | 0.139528 | − | 0.113929i | ||||
\(176\) | 6.01081 | + | 6.01081i | 0.453082 | + | 0.453082i | ||||
\(177\) | 2.24155 | + | 4.04401i | 0.168485 | + | 0.303967i | ||||
\(178\) | 7.61646 | − | 7.61646i | 0.570878 | − | 0.570878i | ||||
\(179\) | 2.75075 | − | 2.75075i | 0.205601 | − | 0.205601i | −0.596794 | − | 0.802395i | \(-0.703559\pi\) |
0.802395 | + | 0.596794i | \(0.203559\pi\) | |||||||
\(180\) | −12.3627 | − | 7.72566i | −0.921465 | − | 0.575837i | ||||
\(181\) | 14.9636 | − | 14.9636i | 1.11224 | − | 1.11224i | 0.119388 | − | 0.992848i | \(-0.461907\pi\) |
0.992848 | − | 0.119388i | \(-0.0380931\pi\) | |||||||
\(182\) | 5.83266 | + | 0.589097i | 0.432346 | + | 0.0436668i | ||||
\(183\) | 0.242711 | + | 0.437878i | 0.0179417 | + | 0.0323689i | ||||
\(184\) | − | 1.67637i | − | 0.123584i | ||||||
\(185\) | − | 0.547253i | − | 0.0402349i | ||||||
\(186\) | 21.2776 | − | 11.7939i | 1.56015 | − | 0.864773i | ||||
\(187\) | − | 17.4946i | − | 1.27933i | ||||||
\(188\) | −8.73966 | − | 8.73966i | −0.637405 | − | 0.637405i | ||||
\(189\) | −11.0896 | + | 8.12527i | −0.806652 | + | 0.591027i | ||||
\(190\) | 15.8061 | + | 15.8061i | 1.14670 | + | 1.14670i | ||||
\(191\) | 13.0600 | − | 13.0600i | 0.944989 | − | 0.944989i | −0.0535744 | − | 0.998564i | \(-0.517061\pi\) |
0.998564 | + | 0.0535744i | \(0.0170614\pi\) | |||||||
\(192\) | −9.08248 | − | 16.3859i | −0.655472 | − | 1.18255i | ||||
\(193\) | 17.8816 | − | 17.8816i | 1.28715 | − | 1.28715i | 0.350633 | − | 0.936513i | \(-0.385966\pi\) |
0.936513 | − | 0.350633i | \(-0.114034\pi\) | |||||||
\(194\) | −9.95766 | + | 9.95766i | −0.714918 | + | 0.714918i | ||||
\(195\) | 3.56081 | + | 1.02111i | 0.254995 | + | 0.0731230i | ||||
\(196\) | 3.35943 | − | 16.4612i | 0.239959 | − | 1.17580i | ||||
\(197\) | 10.7115 | 0.763160 | 0.381580 | − | 0.924336i | \(-0.375380\pi\) | ||||
0.381580 | + | 0.924336i | \(0.375380\pi\) | |||||||
\(198\) | −17.1469 | + | 3.95808i | −1.21857 | + | 0.281288i | ||||
\(199\) | 11.8741 | − | 11.8741i | 0.841730 | − | 0.841730i | −0.147354 | − | 0.989084i | \(-0.547076\pi\) |
0.989084 | + | 0.147354i | \(0.0470756\pi\) | |||||||
\(200\) | −0.755856 | −0.0534471 | ||||||||
\(201\) | 3.99892 | − | 13.9450i | 0.282062 | − | 0.983607i | ||||
\(202\) | 27.0269 | + | 27.0269i | 1.90161 | + | 1.90161i | ||||
\(203\) | −8.98838 | − | 0.907824i | −0.630861 | − | 0.0637167i | ||||
\(204\) | −7.16882 | + | 24.9991i | −0.501918 | + | 1.75029i | ||||
\(205\) | −12.9255 | + | 1.00209i | −0.902756 | + | 0.0699889i | ||||
\(206\) | −7.23139 | −0.503835 | ||||||||
\(207\) | −5.08191 | − | 3.17576i | −0.353217 | − | 0.220731i | ||||
\(208\) | 2.27049 | + | 2.27049i | 0.157430 | + | 0.157430i | ||||
\(209\) | 14.7183 | 1.01809 | ||||||||
\(210\) | 7.21769 | − | 18.0746i | 0.498068 | − | 1.24726i | ||||
\(211\) | 18.9647 | + | 18.9647i | 1.30558 | + | 1.30558i | 0.924571 | + | 0.381010i | \(0.124424\pi\) |
0.381010 | + | 0.924571i | \(0.375576\pi\) | |||||||
\(212\) | −5.53216 | − | 5.53216i | −0.379950 | − | 0.379950i | ||||
\(213\) | −4.72579 | + | 16.4798i | −0.323805 | + | 1.12917i | ||||
\(214\) | − | 22.2671i | − | 1.52215i | ||||||
\(215\) | −18.2946 | −1.24768 | ||||||||
\(216\) | 4.35472 | + | 0.228435i | 0.296301 | + | 0.0155430i | ||||
\(217\) | 11.2047 | + | 13.7223i | 0.760623 | + | 0.931530i | ||||
\(218\) | −3.86039 | − | 3.86039i | −0.261458 | − | 0.261458i | ||||
\(219\) | 0.152963 | + | 0.275963i | 0.0103363 | + | 0.0186478i | ||||
\(220\) | 9.60888 | − | 9.60888i | 0.647831 | − | 0.647831i | ||||
\(221\) | − | 6.60831i | − | 0.444523i | ||||||
\(222\) | 0.476081 | + | 0.858906i | 0.0319525 | + | 0.0576460i | ||||
\(223\) | 3.63008i | 0.243088i | 0.992586 | + | 0.121544i | \(0.0387845\pi\) | ||||
−0.992586 | + | 0.121544i | \(0.961215\pi\) | |||||||
\(224\) | 16.5071 | − | 13.4786i | 1.10293 | − | 0.900576i | ||||
\(225\) | −1.43191 | + | 2.29138i | −0.0954610 | + | 0.152758i | ||||
\(226\) | − | 35.4175i | − | 2.35593i | ||||||
\(227\) | −0.712916 | − | 0.712916i | −0.0473179 | − | 0.0473179i | 0.683052 | − | 0.730370i | \(-0.260652\pi\) |
−0.730370 | + | 0.683052i | \(0.760652\pi\) | |||||||
\(228\) | −21.0319 | − | 6.03118i | −1.39287 | − | 0.399424i | ||||
\(229\) | −15.7588 | + | 15.7588i | −1.04137 | + | 1.04137i | −0.0422653 | + | 0.999106i | \(0.513457\pi\) |
−0.999106 | + | 0.0422653i | \(0.986543\pi\) | |||||||
\(230\) | 8.48361 | 0.559393 | ||||||||
\(231\) | −5.05486 | − | 11.7758i | −0.332585 | − | 0.774793i | ||||
\(232\) | 2.02627 | + | 2.02627i | 0.133031 | + | 0.133031i | ||||
\(233\) | −5.53838 | − | 5.53838i | −0.362831 | − | 0.362831i | 0.502023 | − | 0.864854i | \(-0.332589\pi\) |
−0.864854 | + | 0.502023i | \(0.832589\pi\) | |||||||
\(234\) | −6.47694 | + | 1.49510i | −0.423411 | + | 0.0977376i | ||||
\(235\) | 7.37268 | − | 7.37268i | 0.480941 | − | 0.480941i | ||||
\(236\) | 6.40699 | 0.417060 | ||||||||
\(237\) | −24.7716 | − | 7.10357i | −1.60909 | − | 0.461426i | ||||
\(238\) | −34.5441 | − | 3.48895i | −2.23916 | − | 0.226155i | ||||
\(239\) | −9.25443 | − | 9.25443i | −0.598620 | − | 0.598620i | 0.341326 | − | 0.939945i | \(-0.389124\pi\) |
−0.939945 | + | 0.341326i | \(0.889124\pi\) | |||||||
\(240\) | 9.32358 | − | 5.16795i | 0.601834 | − | 0.333589i | ||||
\(241\) | 23.2848 | 1.49990 | 0.749952 | − | 0.661493i | \(-0.230077\pi\) | ||||
0.749952 | + | 0.661493i | \(0.230077\pi\) | |||||||
\(242\) | 6.67030i | 0.428783i | ||||||||
\(243\) | 8.94221 | − | 12.7686i | 0.573643 | − | 0.819105i | ||||
\(244\) | 0.693738 | 0.0444120 | ||||||||
\(245\) | 13.8865 | + | 2.83398i | 0.887178 | + | 0.181056i | ||||
\(246\) | 19.4146 | − | 12.8173i | 1.23783 | − | 0.817199i | ||||
\(247\) | 5.55962 | 0.353750 | ||||||||
\(248\) | − | 5.61934i | − | 0.356828i | ||||||
\(249\) | 5.02156 | + | 9.05948i | 0.318228 | + | 0.574121i | ||||
\(250\) | − | 25.0604i | − | 1.58496i | ||||||
\(251\) | − | 11.6411i | − | 0.734777i | −0.930067 | − | 0.367389i | \(-0.880252\pi\) | ||
0.930067 | − | 0.367389i | \(-0.119748\pi\) | |||||||
\(252\) | 2.39777 | + | 18.8985i | 0.151046 | + | 1.19050i | ||||
\(253\) | 3.94989 | − | 3.94989i | 0.248327 | − | 0.248327i | ||||
\(254\) | 42.4590 | 2.66412 | ||||||||
\(255\) | −21.0890 | − | 6.04754i | −1.32064 | − | 0.378712i | ||||
\(256\) | 7.83168 | 0.489480 | ||||||||
\(257\) | −9.52431 | + | 9.52431i | −0.594110 | + | 0.594110i | −0.938739 | − | 0.344629i | \(-0.888005\pi\) |
0.344629 | + | 0.938739i | \(0.388005\pi\) | |||||||
\(258\) | 28.7131 | − | 15.9153i | 1.78760 | − | 0.990844i | ||||
\(259\) | −0.553922 | + | 0.452295i | −0.0344191 | + | 0.0281042i | ||||
\(260\) | 3.62960 | − | 3.62960i | 0.225098 | − | 0.225098i | ||||
\(261\) | 9.98125 | − | 2.30401i | 0.617824 | − | 0.142615i | ||||
\(262\) | − | 1.55108i | − | 0.0958260i | ||||||
\(263\) | −20.0529 | + | 20.0529i | −1.23652 | + | 1.23652i | −0.275103 | + | 0.961415i | \(0.588712\pi\) |
−0.961415 | + | 0.275103i | \(0.911288\pi\) | |||||||
\(264\) | −1.12048 | + | 3.90734i | −0.0689609 | + | 0.240480i | ||||
\(265\) | 4.66687 | − | 4.66687i | 0.286684 | − | 0.286684i | ||||
\(266\) | 2.93527 | − | 29.0622i | 0.179973 | − | 1.78192i | ||||
\(267\) | −8.54945 | − | 2.45166i | −0.523218 | − | 0.150039i | ||||
\(268\) | −14.2144 | − | 14.2144i | −0.868286 | − | 0.868286i | ||||
\(269\) | 14.6784 | 0.894960 | 0.447480 | − | 0.894294i | \(-0.352322\pi\) | ||||
0.447480 | + | 0.894294i | \(0.352322\pi\) | |||||||
\(270\) | −1.15604 | + | 22.0380i | −0.0703544 | + | 1.34119i | ||||
\(271\) | 27.6481i | 1.67950i | 0.542974 | + | 0.839750i | \(0.317298\pi\) | ||||
−0.542974 | + | 0.839750i | \(0.682702\pi\) | |||||||
\(272\) | −13.4470 | − | 13.4470i | −0.815345 | − | 0.815345i | ||||
\(273\) | −1.90939 | − | 4.44813i | −0.115562 | − | 0.269213i | ||||
\(274\) | 2.35266 | − | 2.35266i | 0.142129 | − | 0.142129i | ||||
\(275\) | −1.78096 | − | 1.78096i | −0.107396 | − | 0.107396i | ||||
\(276\) | −7.26279 | + | 4.02567i | −0.437168 | + | 0.242317i | ||||
\(277\) | 14.0195 | 0.842353 | 0.421176 | − | 0.906979i | \(-0.361617\pi\) | ||||
0.421176 | + | 0.906979i | \(0.361617\pi\) | |||||||
\(278\) | − | 3.15205i | − | 0.189047i | ||||||
\(279\) | −17.0350 | − | 10.6454i | −1.01986 | − | 0.637325i | ||||
\(280\) | −2.84330 | − | 3.48217i | −0.169919 | − | 0.208099i | ||||
\(281\) | 15.4895 | − | 15.4895i | 0.924025 | − | 0.924025i | −0.0732859 | − | 0.997311i | \(-0.523349\pi\) |
0.997311 | + | 0.0732859i | \(0.0233486\pi\) | |||||||
\(282\) | −5.15748 | + | 17.9852i | −0.307123 | + | 1.07100i | ||||
\(283\) | 24.3610i | 1.44811i | 0.689741 | + | 0.724056i | \(0.257725\pi\) | ||||
−0.689741 | + | 0.724056i | \(0.742275\pi\) | |||||||
\(284\) | 16.7981 | + | 16.7981i | 0.996786 | + | 0.996786i | ||||
\(285\) | 5.08784 | − | 17.7423i | 0.301377 | − | 1.05096i | ||||
\(286\) | − | 6.19623i | − | 0.366391i | ||||||
\(287\) | 11.6970 | + | 12.2548i | 0.690452 | + | 0.723379i | ||||
\(288\) | −12.8058 | + | 20.4921i | −0.754591 | + | 1.20751i | ||||
\(289\) | 22.1379i | 1.30223i | ||||||||
\(290\) | −10.2544 | + | 10.2544i | −0.602156 | + | 0.602156i | ||||
\(291\) | 11.1774 | + | 3.20528i | 0.655233 | + | 0.187897i | ||||
\(292\) | 0.437212 | 0.0255859 | ||||||||
\(293\) | −0.456694 | − | 0.456694i | −0.0266803 | − | 0.0266803i | 0.693641 | − | 0.720321i | \(-0.256006\pi\) |
−0.720321 | + | 0.693641i | \(0.756006\pi\) | |||||||
\(294\) | −24.2601 | + | 7.63266i | −1.41488 | + | 0.445145i | ||||
\(295\) | 5.40487i | 0.314684i | ||||||||
\(296\) | 0.226833 | 0.0131844 | ||||||||
\(297\) | 9.72243 | + | 10.7989i | 0.564153 | + | 0.626617i | ||||
\(298\) | −2.74156 | + | 2.74156i | −0.158814 | + | 0.158814i | ||||
\(299\) | 1.49201 | − | 1.49201i | 0.0862849 | − | 0.0862849i | ||||
\(300\) | 1.81513 | + | 3.27471i | 0.104797 | + | 0.189065i | ||||
\(301\) | 15.1201 | + | 18.5175i | 0.871510 | + | 1.06733i | ||||
\(302\) | −9.70991 | + | 9.70991i | −0.558742 | + | 0.558742i | ||||
\(303\) | 8.69970 | − | 30.3376i | 0.499785 | − | 1.74285i | ||||
\(304\) | 11.3131 | − | 11.3131i | 0.648849 | − | 0.648849i | ||||
\(305\) | 0.585230i | 0.0335102i | ||||||||
\(306\) | 38.3599 | − | 8.85477i | 2.19289 | − | 0.506193i | ||||
\(307\) | −1.98590 | −0.113342 | −0.0566708 | − | 0.998393i | \(-0.518049\pi\) | ||||
−0.0566708 | + | 0.998393i | \(0.518049\pi\) | |||||||
\(308\) | −17.6676 | − | 1.78442i | −1.00670 | − | 0.101677i | ||||
\(309\) | 2.89475 | + | 5.22246i | 0.164676 | + | 0.297096i | ||||
\(310\) | 28.4378 | 1.61516 | ||||||||
\(311\) | 21.3389 | + | 21.3389i | 1.21002 | + | 1.21002i | 0.971020 | + | 0.238999i | \(0.0768191\pi\) |
0.238999 | + | 0.971020i | \(0.423181\pi\) | |||||||
\(312\) | −0.423244 | + | 1.47594i | −0.0239615 | + | 0.0835584i | ||||
\(313\) | −13.3139 | + | 13.3139i | −0.752545 | + | 0.752545i | −0.974954 | − | 0.222409i | \(-0.928608\pi\) |
0.222409 | + | 0.974954i | \(0.428608\pi\) | |||||||
\(314\) | 13.7626 | + | 13.7626i | 0.776668 | + | 0.776668i | ||||
\(315\) | −15.9426 | + | 2.02274i | −0.898264 | + | 0.113968i | ||||
\(316\) | −25.2501 | + | 25.2501i | −1.42043 | + | 1.42043i | ||||
\(317\) | 2.25572 | + | 2.25572i | 0.126694 | + | 0.126694i | 0.767610 | − | 0.640917i | \(-0.221446\pi\) |
−0.640917 | + | 0.767610i | \(0.721446\pi\) | |||||||
\(318\) | −3.26466 | + | 11.3845i | −0.183073 | + | 0.638412i | ||||
\(319\) | 9.54865i | 0.534622i | ||||||||
\(320\) | − | 21.8999i | − | 1.22424i | ||||||
\(321\) | −16.0811 | + | 8.91358i | −0.897561 | + | 0.497507i | ||||
\(322\) | −7.01155 | − | 8.58700i | −0.390739 | − | 0.478535i | ||||
\(323\) | −32.9270 | −1.83211 | ||||||||
\(324\) | −9.46786 | − | 19.4152i | −0.525992 | − | 1.07862i | ||||
\(325\) | −0.672729 | − | 0.672729i | −0.0373163 | − | 0.0373163i | ||||
\(326\) | −28.1315 | −1.55806 | ||||||||
\(327\) | −1.24262 | + | 4.33327i | −0.0687171 | + | 0.239630i | ||||
\(328\) | −0.415360 | − | 5.35755i | −0.0229344 | − | 0.295821i | ||||
\(329\) | −13.5559 | − | 1.36914i | −0.747362 | − | 0.0754833i | ||||
\(330\) | −19.7739 | − | 5.67043i | −1.08852 | − | 0.312147i | ||||
\(331\) | −0.756244 | + | 0.756244i | −0.0415669 | + | 0.0415669i | −0.727585 | − | 0.686018i | \(-0.759357\pi\) |
0.686018 | + | 0.727585i | \(0.259357\pi\) | |||||||
\(332\) | 14.3531 | 0.787728 | ||||||||
\(333\) | 0.429720 | − | 0.687645i | 0.0235485 | − | 0.0376827i | ||||
\(334\) | 3.28638 | − | 3.28638i | 0.179823 | − | 0.179823i | ||||
\(335\) | 11.9912 | − | 11.9912i | 0.655147 | − | 0.655147i | ||||
\(336\) | −12.9367 | − | 5.16599i | −0.705755 | − | 0.281828i | ||||
\(337\) | − | 24.2200i | − | 1.31935i | −0.751553 | − | 0.659673i | \(-0.770695\pi\) | ||
0.751553 | − | 0.659673i | \(-0.229305\pi\) | |||||||
\(338\) | 24.9287i | 1.35595i | ||||||||
\(339\) | −25.5783 | + | 14.1777i | −1.38922 | + | 0.770028i | ||||
\(340\) | −21.4964 | + | 21.4964i | −1.16581 | + | 1.16581i | ||||
\(341\) | 13.2404 | − | 13.2404i | 0.717006 | − | 0.717006i | ||||
\(342\) | 7.44957 | + | 32.2724i | 0.402827 | + | 1.74509i | ||||
\(343\) | −8.60845 | − | 16.3980i | −0.464813 | − | 0.885409i | ||||
\(344\) | − | 7.58300i | − | 0.408848i | ||||||
\(345\) | −3.39602 | − | 6.12681i | −0.182835 | − | 0.329856i | ||||
\(346\) | 12.2732i | 0.659813i | ||||||||
\(347\) | −24.5046 | + | 24.5046i | −1.31547 | + | 1.31547i | −0.398158 | + | 0.917317i | \(0.630350\pi\) |
−0.917317 | + | 0.398158i | \(0.869650\pi\) | |||||||
\(348\) | 3.91278 | − | 13.6446i | 0.209747 | − | 0.731429i | ||||
\(349\) | 36.0130 | 1.92773 | 0.963865 | − | 0.266391i | \(-0.0858311\pi\) | ||||
0.963865 | + | 0.266391i | \(0.0858311\pi\) | |||||||
\(350\) | −3.87178 | + | 3.16143i | −0.206956 | + | 0.168986i | ||||
\(351\) | 3.67249 | + | 4.07912i | 0.196023 | + | 0.217727i | ||||
\(352\) | −15.9274 | − | 15.9274i | −0.848934 | − | 0.848934i | ||||
\(353\) | 32.7351 | 1.74231 | 0.871157 | − | 0.491005i | \(-0.163370\pi\) | ||||
0.871157 | + | 0.491005i | \(0.163370\pi\) | |||||||
\(354\) | −4.70195 | − | 8.48287i | −0.249906 | − | 0.450859i | ||||
\(355\) | −14.1707 | + | 14.1707i | −0.752104 | + | 0.752104i | ||||
\(356\) | −8.71461 | + | 8.71461i | −0.461874 | + | 0.461874i | ||||
\(357\) | 11.3084 | + | 26.3442i | 0.598505 | + | 1.39428i | ||||
\(358\) | −5.77008 | + | 5.77008i | −0.304958 | + | 0.304958i | ||||
\(359\) | − | 18.7389i | − | 0.989003i | −0.869177 | − | 0.494501i | \(-0.835351\pi\) | ||
0.869177 | − | 0.494501i | \(-0.164649\pi\) | |||||||
\(360\) | 4.32280 | + | 2.70138i | 0.227832 | + | 0.142375i | ||||
\(361\) | − | 8.70170i | − | 0.457984i | ||||||
\(362\) | −31.3882 | + | 31.3882i | −1.64973 | + | 1.64973i | ||||
\(363\) | 4.81725 | − | 2.67014i | 0.252840 | − | 0.140146i | ||||
\(364\) | −6.67363 | − | 0.674035i | −0.349793 | − | 0.0353290i | ||||
\(365\) | 0.368827i | 0.0193053i | ||||||||
\(366\) | −0.509119 | − | 0.918510i | −0.0266121 | − | 0.0480113i | ||||
\(367\) | 16.5886 | 0.865919 | 0.432959 | − | 0.901413i | \(-0.357469\pi\) | ||||
0.432959 | + | 0.901413i | \(0.357469\pi\) | |||||||
\(368\) | − | 6.07206i | − | 0.316528i | ||||||
\(369\) | −17.0283 | − | 8.89033i | −0.886457 | − | 0.462812i | ||||
\(370\) | 1.14794i | 0.0596785i | ||||||||
\(371\) | −8.58083 | − | 0.866661i | −0.445495 | − | 0.0449948i | ||||
\(372\) | −24.3455 | + | 13.4944i | −1.26226 | + | 0.699653i | ||||
\(373\) | −5.77490 | −0.299013 | −0.149507 | − | 0.988761i | \(-0.547768\pi\) | ||||
−0.149507 | + | 0.988761i | \(0.547768\pi\) | |||||||
\(374\) | 36.6974i | 1.89758i | ||||||||
\(375\) | −18.0985 | + | 10.0318i | −0.934600 | + | 0.518037i | ||||
\(376\) | 3.05594 | + | 3.05594i | 0.157598 | + | 0.157598i | ||||
\(377\) | 3.60685i | 0.185762i | ||||||||
\(378\) | 23.2620 | − | 17.0439i | 1.19647 | − | 0.876642i | ||||
\(379\) | −14.3455 | −0.736879 | −0.368440 | − | 0.929652i | \(-0.620108\pi\) | ||||
−0.368440 | + | 0.929652i | \(0.620108\pi\) | |||||||
\(380\) | −18.0851 | − | 18.0851i | −0.927745 | − | 0.927745i | ||||
\(381\) | −16.9965 | − | 30.6636i | −0.870756 | − | 1.57095i | ||||
\(382\) | −27.3952 | + | 27.3952i | −1.40166 | + | 1.40166i | ||||
\(383\) | −12.8310 | − | 12.8310i | −0.655633 | − | 0.655633i | 0.298711 | − | 0.954344i | \(-0.403443\pi\) |
−0.954344 | + | 0.298711i | \(0.903443\pi\) | |||||||
\(384\) | 5.52468 | + | 9.96717i | 0.281930 | + | 0.508635i | ||||
\(385\) | 1.50532 | − | 14.9042i | 0.0767180 | − | 0.759586i | ||||
\(386\) | −37.5091 | + | 37.5091i | −1.90916 | + | 1.90916i | ||||
\(387\) | −22.9879 | − | 14.3655i | −1.16854 | − | 0.730237i | ||||
\(388\) | 11.3934 | − | 11.3934i | 0.578411 | − | 0.578411i | ||||
\(389\) | −8.45760 | −0.428817 | −0.214409 | − | 0.976744i | \(-0.568782\pi\) | ||||
−0.214409 | + | 0.976744i | \(0.568782\pi\) | |||||||
\(390\) | −7.46928 | − | 2.14191i | −0.378222 | − | 0.108460i | ||||
\(391\) | −8.83645 | + | 8.83645i | −0.446879 | + | 0.446879i | ||||
\(392\) | −1.17467 | + | 5.75589i | −0.0593298 | + | 0.290717i | ||||
\(393\) | −1.12018 | + | 0.620902i | −0.0565056 | + | 0.0313203i | ||||
\(394\) | −22.4688 | −1.13196 | ||||||||
\(395\) | −21.3008 | − | 21.3008i | −1.07176 | − | 1.07176i | ||||
\(396\) | 19.6191 | − | 4.52876i | 0.985898 | − | 0.227579i | ||||
\(397\) | −2.63287 | − | 2.63287i | −0.132140 | − | 0.132140i | 0.637943 | − | 0.770083i | \(-0.279785\pi\) |
−0.770083 | + | 0.637943i | \(0.779785\pi\) | |||||||
\(398\) | −24.9075 | + | 24.9075i | −1.24850 | + | 1.24850i | ||||
\(399\) | −22.1635 | + | 9.51385i | −1.10956 | + | 0.476288i | ||||
\(400\) | −2.73783 | −0.136891 | ||||||||
\(401\) | 14.8737 | 0.742756 | 0.371378 | − | 0.928482i | \(-0.378885\pi\) | ||||
0.371378 | + | 0.928482i | \(0.378885\pi\) | |||||||
\(402\) | −8.38828 | + | 29.2516i | −0.418370 | + | 1.45894i | ||||
\(403\) | 5.00133 | − | 5.00133i | 0.249134 | − | 0.249134i | ||||
\(404\) | −30.9237 | − | 30.9237i | −1.53851 | − | 1.53851i | ||||
\(405\) | 16.3785 | − | 7.98699i | 0.813852 | − | 0.396877i | ||||
\(406\) | 18.8544 | + | 1.90428i | 0.935726 | + | 0.0945080i | ||||
\(407\) | 0.534469 | + | 0.534469i | 0.0264926 | + | 0.0264926i | ||||
\(408\) | 2.50667 | − | 8.74127i | 0.124099 | − | 0.432757i | ||||
\(409\) | 36.2004i | 1.78999i | 0.446073 | + | 0.894997i | \(0.352822\pi\) | ||||
−0.446073 | + | 0.894997i | \(0.647178\pi\) | |||||||
\(410\) | 27.1130 | − | 2.10202i | 1.33902 | − | 0.103811i | ||||
\(411\) | −2.64085 | − | 0.757298i | −0.130264 | − | 0.0373548i | ||||
\(412\) | 8.27403 | 0.407632 | ||||||||
\(413\) | 5.47074 | − | 4.46703i | 0.269197 | − | 0.219808i | ||||
\(414\) | 10.6600 | + | 6.66159i | 0.523910 | + | 0.327399i | ||||
\(415\) | 12.1081i | 0.594364i | ||||||||
\(416\) | −6.01632 | − | 6.01632i | −0.294974 | − | 0.294974i | ||||
\(417\) | −2.27639 | + | 1.26177i | −0.111475 | + | 0.0617894i | ||||
\(418\) | −30.8737 | −1.51008 | ||||||||
\(419\) | 13.2363i | 0.646637i | 0.946290 | + | 0.323319i | \(0.104799\pi\) | ||||
−0.946290 | + | 0.323319i | \(0.895201\pi\) | |||||||
\(420\) | −8.25835 | + | 20.6806i | −0.402966 | + | 1.00911i | ||||
\(421\) | 17.6887 | − | 17.6887i | 0.862093 | − | 0.862093i | −0.129488 | − | 0.991581i | \(-0.541333\pi\) |
0.991581 | + | 0.129488i | \(0.0413332\pi\) | |||||||
\(422\) | −39.7810 | − | 39.7810i | −1.93651 | − | 1.93651i | ||||
\(423\) | 15.0533 | − | 3.47482i | 0.731918 | − | 0.168951i | ||||
\(424\) | 1.93439 | + | 1.93439i | 0.0939424 | + | 0.0939424i | ||||
\(425\) | 3.98426 | + | 3.98426i | 0.193265 | + | 0.193265i | ||||
\(426\) | 9.91298 | − | 34.5685i | 0.480285 | − | 1.67485i | ||||
\(427\) | 0.592362 | − | 0.483682i | 0.0286664 | − | 0.0234070i | ||||
\(428\) | 25.4776i | 1.23151i | ||||||||
\(429\) | −4.47488 | + | 2.48037i | −0.216049 | + | 0.119753i | ||||
\(430\) | 38.3754 | 1.85062 | ||||||||
\(431\) | 24.6794 | 1.18877 | 0.594383 | − | 0.804182i | \(-0.297396\pi\) | ||||
0.594383 | + | 0.804182i | \(0.297396\pi\) | |||||||
\(432\) | 15.7735 | + | 0.827425i | 0.758902 | + | 0.0398095i | ||||
\(433\) | − | 20.0591i | − | 0.963978i | −0.876177 | − | 0.481989i | \(-0.839914\pi\) | ||
0.876177 | − | 0.481989i | \(-0.160086\pi\) | |||||||
\(434\) | −23.5033 | − | 28.7844i | −1.12820 | − | 1.38169i | ||||
\(435\) | 11.5105 | + | 3.30078i | 0.551885 | + | 0.158260i | ||||
\(436\) | 4.41699 | + | 4.41699i | 0.211535 | + | 0.211535i | ||||
\(437\) | −7.43417 | − | 7.43417i | −0.355624 | − | 0.355624i | ||||
\(438\) | −0.320860 | − | 0.578869i | −0.0153313 | − | 0.0276594i | ||||
\(439\) | 5.00937 | + | 5.00937i | 0.239084 | + | 0.239084i | 0.816471 | − | 0.577387i | \(-0.195927\pi\) |
−0.577387 | + | 0.816471i | \(0.695927\pi\) | |||||||
\(440\) | −3.35987 | + | 3.35987i | −0.160176 | + | 0.160176i | ||||
\(441\) | 15.2237 | + | 14.4651i | 0.724936 | + | 0.688816i | ||||
\(442\) | 13.8618i | 0.659340i | ||||||||
\(443\) | 17.0431 | 0.809743 | 0.404872 | − | 0.914374i | \(-0.367316\pi\) | ||||
0.404872 | + | 0.914374i | \(0.367316\pi\) | |||||||
\(444\) | −0.544724 | − | 0.982745i | −0.0258514 | − | 0.0466390i | ||||
\(445\) | −7.35156 | − | 7.35156i | −0.348497 | − | 0.348497i | ||||
\(446\) | − | 7.61458i | − | 0.360561i | ||||||
\(447\) | 3.07739 | + | 0.882482i | 0.145556 | + | 0.0417400i | ||||
\(448\) | −22.1668 | + | 18.0999i | −1.04728 | + | 0.855138i | ||||
\(449\) | 24.0362 | 1.13434 | 0.567170 | − | 0.823601i | \(-0.308038\pi\) | ||||
0.567170 | + | 0.823601i | \(0.308038\pi\) | |||||||
\(450\) | 3.00364 | − | 4.80648i | 0.141593 | − | 0.226579i | ||||
\(451\) | 11.6449 | − | 13.6022i | 0.548335 | − | 0.640504i | ||||
\(452\) | 40.5240i | 1.90609i | ||||||||
\(453\) | 10.8993 | + | 3.12553i | 0.512095 | + | 0.146850i | ||||
\(454\) | 1.49544 | + | 1.49544i | 0.0701844 | + | 0.0701844i | ||||
\(455\) | 0.568609 | − | 5.62980i | 0.0266568 | − | 0.263929i | ||||
\(456\) | 7.35409 | + | 2.10888i | 0.344387 | + | 0.0987574i | ||||
\(457\) | 2.87058 | + | 2.87058i | 0.134280 | + | 0.134280i | 0.771052 | − | 0.636772i | \(-0.219731\pi\) |
−0.636772 | + | 0.771052i | \(0.719731\pi\) | |||||||
\(458\) | 33.0563 | − | 33.0563i | 1.54462 | − | 1.54462i | ||||
\(459\) | −21.7504 | − | 24.1587i | −1.01522 | − | 1.12763i | ||||
\(460\) | −9.70680 | −0.452582 | ||||||||
\(461\) | −26.4473 | −1.23177 | −0.615887 | − | 0.787834i | \(-0.711202\pi\) | ||||
−0.615887 | + | 0.787834i | \(0.711202\pi\) | |||||||
\(462\) | 10.6033 | + | 24.7014i | 0.493308 | + | 1.14921i | ||||
\(463\) | −3.77660 | + | 3.77660i | −0.175514 | + | 0.175514i | −0.789397 | − | 0.613883i | \(-0.789607\pi\) |
0.613883 | + | 0.789397i | \(0.289607\pi\) | |||||||
\(464\) | 7.33945 | + | 7.33945i | 0.340725 | + | 0.340725i | ||||
\(465\) | −11.3837 | − | 20.5376i | −0.527909 | − | 0.952409i | ||||
\(466\) | 11.6175 | + | 11.6175i | 0.538171 | + | 0.538171i | ||||
\(467\) | 25.0661 | 1.15992 | 0.579959 | − | 0.814645i | \(-0.303068\pi\) | ||||
0.579959 | + | 0.814645i | \(0.303068\pi\) | |||||||
\(468\) | 7.41081 | − | 1.71067i | 0.342565 | − | 0.0790755i | ||||
\(469\) | −22.0478 | − | 2.22682i | −1.01807 | − | 0.102825i | ||||
\(470\) | −15.4652 | + | 15.4652i | −0.713357 | + | 0.713357i | ||||
\(471\) | 4.43005 | − | 15.4485i | 0.204126 | − | 0.711828i | ||||
\(472\) | −2.24029 | −0.103118 | ||||||||
\(473\) | 17.8672 | − | 17.8672i | 0.821535 | − | 0.821535i | ||||
\(474\) | 51.9617 | + | 14.9007i | 2.38668 | + | 0.684412i | ||||
\(475\) | −3.35198 | + | 3.35198i | −0.153800 | + | 0.153800i | ||||
\(476\) | 39.5248 | + | 3.99199i | 1.81162 | + | 0.182973i | ||||
\(477\) | 9.52868 | − | 2.19954i | 0.436288 | − | 0.100710i | ||||
\(478\) | 19.4124 | + | 19.4124i | 0.887904 | + | 0.887904i | ||||
\(479\) | −2.40299 | + | 2.40299i | −0.109795 | + | 0.109795i | −0.759870 | − | 0.650075i | \(-0.774738\pi\) |
0.650075 | + | 0.759870i | \(0.274738\pi\) | |||||||
\(480\) | −24.7056 | + | 13.6940i | −1.12765 | + | 0.625042i | ||||
\(481\) | 0.201887 | + | 0.201887i | 0.00920525 | + | 0.00920525i | ||||
\(482\) | −48.8430 | −2.22474 | ||||||||
\(483\) | −3.39473 | + | 8.50110i | −0.154466 | + | 0.386813i | ||||
\(484\) | − | 7.63204i | − | 0.346911i | ||||||
\(485\) | 9.61134 | + | 9.61134i | 0.436428 | + | 0.436428i | ||||
\(486\) | −18.7575 | + | 26.7839i | −0.850858 | + | 1.21494i | ||||
\(487\) | 17.8432i | 0.808552i | 0.914637 | + | 0.404276i | \(0.132476\pi\) | ||||
−0.914637 | + | 0.404276i | \(0.867524\pi\) | |||||||
\(488\) | −0.242575 | −0.0109808 | ||||||||
\(489\) | 11.2611 | + | 20.3164i | 0.509245 | + | 0.918738i | ||||
\(490\) | −29.1289 | − | 5.94466i | −1.31591 | − | 0.268552i | ||||
\(491\) | − | 26.6222i | − | 1.20144i | −0.799458 | − | 0.600722i | \(-0.794880\pi\) | ||
0.799458 | − | 0.600722i | \(-0.205120\pi\) | |||||||
\(492\) | −22.2139 | + | 14.6653i | −1.00148 | + | 0.661162i | ||||
\(493\) | − | 21.3617i | − | 0.962081i | ||||||
\(494\) | −11.6621 | −0.524701 | ||||||||
\(495\) | 3.82041 | + | 16.5505i | 0.171715 | + | 0.743889i | ||||
\(496\) | − | 20.3541i | − | 0.913925i | ||||||
\(497\) | 26.0553 | + | 2.63158i | 1.16874 | + | 0.118042i | ||||
\(498\) | −10.5334 | − | 19.0035i | −0.472013 | − | 0.851567i | ||||
\(499\) | −8.28943 | + | 8.28943i | −0.371086 | + | 0.371086i | −0.867873 | − | 0.496787i | \(-0.834513\pi\) |
0.496787 | + | 0.867873i | \(0.334513\pi\) | |||||||
\(500\) | 28.6737i | 1.28233i | ||||||||
\(501\) | −3.68895 | − | 1.05786i | −0.164810 | − | 0.0472615i | ||||
\(502\) | 24.4187i | 1.08986i | ||||||||
\(503\) | −27.5862 | + | 27.5862i | −1.23001 | + | 1.23001i | −0.266048 | + | 0.963960i | \(0.585718\pi\) |
−0.963960 | + | 0.266048i | \(0.914282\pi\) | |||||||
\(504\) | −0.838414 | − | 6.60812i | −0.0373459 | − | 0.294349i | ||||
\(505\) | 26.0869 | − | 26.0869i | 1.16085 | − | 1.16085i | ||||
\(506\) | −8.28543 | + | 8.28543i | −0.368332 | + | 0.368332i | ||||
\(507\) | 18.0034 | − | 9.97905i | 0.799558 | − | 0.443185i | ||||
\(508\) | −48.5809 | −2.15543 | ||||||||
\(509\) | 20.4064 | + | 20.4064i | 0.904499 | + | 0.904499i | 0.995821 | − | 0.0913223i | \(-0.0291094\pi\) |
−0.0913223 | + | 0.995821i | \(0.529109\pi\) | |||||||
\(510\) | 44.2370 | + | 12.6855i | 1.95885 | + | 0.561725i | ||||
\(511\) | 0.373322 | − | 0.304829i | 0.0165148 | − | 0.0134848i | ||||
\(512\) | −29.5869 | −1.30757 | ||||||||
\(513\) | 20.3249 | − | 18.2988i | 0.897365 | − | 0.807911i | ||||
\(514\) | 19.9785 | − | 19.9785i | 0.881215 | − | 0.881215i | ||||
\(515\) | 6.97988i | 0.307570i | ||||||||
\(516\) | −32.8530 | + | 18.2100i | −1.44627 | + | 0.801651i | ||||
\(517\) | 14.4009i | 0.633351i | ||||||||
\(518\) | 1.16193 | − | 0.948750i | 0.0510522 | − | 0.0416857i | ||||
\(519\) | 8.86365 | − | 4.91302i | 0.389071 | − | 0.215657i | ||||
\(520\) | −1.26914 | + | 1.26914i | −0.0556554 | + | 0.0556554i | ||||
\(521\) | −26.5644 | + | 26.5644i | −1.16381 | + | 1.16381i | −0.180171 | + | 0.983635i | \(0.557665\pi\) |
−0.983635 | + | 0.180171i | \(0.942335\pi\) | |||||||
\(522\) | −20.9370 | + | 4.83298i | −0.916389 | + | 0.211534i | ||||
\(523\) | − | 22.8925i | − | 1.00102i | −0.865731 | − | 0.500510i | \(-0.833146\pi\) | ||
0.865731 | − | 0.500510i | \(-0.166854\pi\) | |||||||
\(524\) | 1.77472i | 0.0775289i | ||||||||
\(525\) | 3.83305 | + | 1.53065i | 0.167288 | + | 0.0668029i | ||||
\(526\) | 42.0638 | − | 42.0638i | 1.83407 | − | 1.83407i | ||||
\(527\) | −29.6206 | + | 29.6206i | −1.29029 | + | 1.29029i | ||||
\(528\) | −4.05855 | + | 14.1530i | −0.176626 | + | 0.615930i | ||||
\(529\) | 19.0099 | 0.826516 | ||||||||
\(530\) | −9.78940 | + | 9.78940i | −0.425224 | + | 0.425224i | ||||
\(531\) | −4.24407 | + | 6.79143i | −0.184177 | + | 0.294723i | ||||
\(532\) | −3.35849 | + | 33.2525i | −0.145609 | + | 1.44168i | ||||
\(533\) | 4.39866 | − | 5.13802i | 0.190527 | − | 0.222552i | ||||
\(534\) | 17.9336 | + | 5.14270i | 0.776064 | + | 0.222546i | ||||
\(535\) | −21.4926 | −0.929207 | ||||||||
\(536\) | 4.97027 | + | 4.97027i | 0.214683 | + | 0.214683i | ||||
\(537\) | 6.47690 | + | 1.85733i | 0.279499 | + | 0.0801499i | ||||
\(538\) | −30.7900 | −1.32745 | ||||||||
\(539\) | −16.3299 | + | 10.7944i | −0.703379 | + | 0.464946i | ||||
\(540\) | 1.32272 | − | 25.2155i | 0.0569209 | − | 1.08510i | ||||
\(541\) | 0.180347i | 0.00775374i | 0.999992 | + | 0.00387687i | \(0.00123405\pi\) | ||||
−0.999992 | + | 0.00387687i | \(0.998766\pi\) | |||||||
\(542\) | − | 57.9956i | − | 2.49112i | ||||||
\(543\) | 35.2331 | + | 10.1036i | 1.51200 | + | 0.433585i | ||||
\(544\) | 35.6318 | + | 35.6318i | 1.52770 | + | 1.52770i | ||||
\(545\) | −3.72612 | + | 3.72612i | −0.159610 | + | 0.159610i | ||||
\(546\) | 4.00521 | + | 9.33056i | 0.171407 | + | 0.399311i | ||||
\(547\) | 5.59800 | + | 5.59800i | 0.239353 | + | 0.239353i | 0.816582 | − | 0.577229i | \(-0.195866\pi\) |
−0.577229 | + | 0.816582i | \(0.695866\pi\) | |||||||
\(548\) | −2.69187 | + | 2.69187i | −0.114991 | + | 0.114991i | ||||
\(549\) | −0.459540 | + | 0.735365i | −0.0196127 | + | 0.0313846i | ||||
\(550\) | 3.73581 | + | 3.73581i | 0.159295 | + | 0.159295i | ||||
\(551\) | 17.9717 | 0.765621 | ||||||||
\(552\) | 2.53953 | − | 1.40763i | 0.108090 | − | 0.0599127i | ||||
\(553\) | −3.95566 | + | 39.1650i | −0.168212 | + | 1.66547i | ||||
\(554\) | −29.4079 | −1.24942 | ||||||||
\(555\) | 0.829034 | − | 0.459523i | 0.0351905 | − | 0.0195057i | ||||
\(556\) | 3.60652i | 0.152950i | ||||||||
\(557\) | 17.6104 | − | 17.6104i | 0.746179 | − | 0.746179i | −0.227581 | − | 0.973759i | \(-0.573082\pi\) |
0.973759 | + | 0.227581i | \(0.0730815\pi\) | |||||||
\(558\) | 35.7332 | + | 22.3302i | 1.51271 | + | 0.945314i | ||||
\(559\) | 6.74904 | − | 6.74904i | 0.285454 | − | 0.285454i | ||||
\(560\) | −10.2989 | − | 12.6129i | −0.435206 | − | 0.532994i | ||||
\(561\) | 26.5026 | − | 14.6901i | 1.11894 | − | 0.620215i | ||||
\(562\) | −32.4913 | + | 32.4913i | −1.37056 | + | 1.37056i | ||||
\(563\) | −16.4094 | + | 16.4094i | −0.691572 | + | 0.691572i | −0.962578 | − | 0.271006i | \(-0.912644\pi\) |
0.271006 | + | 0.962578i | \(0.412644\pi\) | |||||||
\(564\) | 5.90110 | − | 20.5783i | 0.248481 | − | 0.866503i | ||||
\(565\) | −34.1856 | −1.43820 | ||||||||
\(566\) | − | 51.1006i | − | 2.14792i | ||||||
\(567\) | −21.6208 | − | 9.97696i | −0.907989 | − | 0.418993i | ||||
\(568\) | −5.87369 | − | 5.87369i | −0.246455 | − | 0.246455i | ||||
\(569\) | 17.7056 | 0.742258 | 0.371129 | − | 0.928581i | \(-0.378971\pi\) | ||||
0.371129 | + | 0.928581i | \(0.378971\pi\) | |||||||
\(570\) | −10.6724 | + | 37.2169i | −0.447019 | + | 1.55884i | ||||
\(571\) | 11.8022 | − | 11.8022i | 0.493907 | − | 0.493907i | −0.415628 | − | 0.909535i | \(-0.636438\pi\) |
0.909535 | + | 0.415628i | \(0.136438\pi\) | |||||||
\(572\) | 7.08962i | 0.296432i | ||||||||
\(573\) | 30.7510 | + | 8.81824i | 1.28464 | + | 0.368387i | ||||
\(574\) | −24.5360 | − | 25.7061i | −1.02411 | − | 1.07295i | ||||
\(575\) | 1.79911i | 0.0750281i | ||||||||
\(576\) | 17.1965 | − | 27.5181i | 0.716519 | − | 1.14659i | ||||
\(577\) | 7.53826 | + | 7.53826i | 0.313822 | + | 0.313822i | 0.846388 | − | 0.532566i | \(-0.178772\pi\) |
−0.532566 | + | 0.846388i | \(0.678772\pi\) | |||||||
\(578\) | − | 46.4373i | − | 1.93154i | ||||||
\(579\) | 42.1038 | + | 12.0738i | 1.74978 | + | 0.501771i | ||||
\(580\) | 11.7328 | − | 11.7328i | 0.487180 | − | 0.487180i | ||||
\(581\) | 12.2557 | − | 10.0071i | 0.508451 | − | 0.415166i | ||||
\(582\) | −23.4462 | − | 6.72350i | −0.971877 | − | 0.278698i | ||||
\(583\) | 9.11570i | 0.377534i | ||||||||
\(584\) | −0.152877 | −0.00632609 | ||||||||
\(585\) | 1.44310 | + | 6.25168i | 0.0596648 | + | 0.258475i | ||||
\(586\) | 0.957978 | + | 0.957978i | 0.0395737 | + | 0.0395737i | ||||
\(587\) | −0.248981 | + | 0.248981i | −0.0102765 | + | 0.0102765i | −0.712226 | − | 0.701950i | \(-0.752313\pi\) |
0.701950 | + | 0.712226i | \(0.252313\pi\) | |||||||
\(588\) | 27.7580 | − | 8.73315i | 1.14472 | − | 0.360149i | ||||
\(589\) | −24.9200 | − | 24.9200i | −1.02681 | − | 1.02681i | ||||
\(590\) | − | 11.3375i | − | 0.466756i | ||||||
\(591\) | 8.99431 | + | 16.2268i | 0.369977 | + | 0.667481i | ||||
\(592\) | 0.821625 | 0.0337686 | ||||||||
\(593\) | −5.71596 | − | 5.71596i | −0.234726 | − | 0.234726i | 0.579936 | − | 0.814662i | \(-0.303078\pi\) |
−0.814662 | + | 0.579936i | \(0.803078\pi\) | |||||||
\(594\) | −20.3941 | − | 22.6522i | −0.836781 | − | 0.929431i | ||||
\(595\) | −3.36760 | + | 33.3427i | −0.138058 | + | 1.36692i | ||||
\(596\) | 3.13684 | − | 3.13684i | 0.128490 | − | 0.128490i | ||||
\(597\) | 27.9585 | + | 8.01748i | 1.14427 | + | 0.328133i | ||||
\(598\) | −3.12969 | + | 3.12969i | −0.127982 | + | 0.127982i | ||||
\(599\) | − | 22.2767i | − | 0.910201i | −0.890440 | − | 0.455101i | \(-0.849603\pi\) | ||
0.890440 | − | 0.455101i | \(-0.150397\pi\) | |||||||
\(600\) | −0.634685 | − | 1.14505i | −0.0259109 | − | 0.0467463i | ||||
\(601\) | −8.30614 | + | 8.30614i | −0.338814 | + | 0.338814i | −0.855921 | − | 0.517107i | \(-0.827009\pi\) |
0.517107 | + | 0.855921i | \(0.327009\pi\) | |||||||
\(602\) | −31.7165 | − | 38.8430i | −1.29267 | − | 1.58312i | ||||
\(603\) | 24.4832 | − | 5.65155i | 0.997033 | − | 0.230149i | ||||
\(604\) | 11.1099 | − | 11.1099i | 0.452056 | − | 0.452056i | ||||
\(605\) | 6.43831 | 0.261755 | ||||||||
\(606\) | −18.2488 | + | 63.6373i | −0.741307 | + | 2.58509i | ||||
\(607\) | 4.35516 | 0.176771 | 0.0883853 | − | 0.996086i | \(-0.471829\pi\) | ||||
0.0883853 | + | 0.996086i | \(0.471829\pi\) | |||||||
\(608\) | −29.9773 | + | 29.9773i | −1.21574 | + | 1.21574i | ||||
\(609\) | −6.17219 | − | 14.3788i | −0.250110 | − | 0.582658i | ||||
\(610\) | − | 1.22760i | − | 0.0497040i | ||||||
\(611\) | 5.43971i | 0.220067i | ||||||||
\(612\) | −43.8907 | + | 10.1315i | −1.77418 | + | 0.409540i | ||||
\(613\) | − | 28.9830i | − | 1.17061i | −0.810812 | − | 0.585307i | \(-0.800974\pi\) | ||
0.810812 | − | 0.585307i | \(-0.199026\pi\) | |||||||
\(614\) | 4.16570 | 0.168114 | ||||||||
\(615\) | −12.3715 | − | 18.7394i | −0.498866 | − | 0.755645i | ||||
\(616\) | 6.17769 | + | 0.623945i | 0.248906 | + | 0.0251395i | ||||
\(617\) | 17.7686 | 0.715335 | 0.357668 | − | 0.933849i | \(-0.383572\pi\) | ||||
0.357668 | + | 0.933849i | \(0.383572\pi\) | |||||||
\(618\) | −6.07213 | − | 10.9548i | −0.244257 | − | 0.440668i | ||||
\(619\) | − | 46.7719i | − | 1.87992i | −0.341283 | − | 0.939961i | \(-0.610861\pi\) | ||
0.341283 | − | 0.939961i | \(-0.389139\pi\) | |||||||
\(620\) | −32.5381 | −1.30676 | ||||||||
\(621\) | 0.543726 | − | 10.3652i | 0.0218190 | − | 0.415943i | ||||
\(622\) | −44.7613 | − | 44.7613i | −1.79476 | − | 1.79476i | ||||
\(623\) | −1.36522 | + | 13.5171i | −0.0546964 | + | 0.541550i | ||||
\(624\) | −1.53305 | + | 5.34606i | −0.0613712 | + | 0.214014i | ||||
\(625\) | −19.6855 | −0.787419 | ||||||||
\(626\) | 27.9277 | − | 27.9277i | 1.11621 | − | 1.11621i | ||||
\(627\) | 12.3589 | + | 22.2968i | 0.493565 | + | 0.890449i | ||||
\(628\) | −15.7469 | − | 15.7469i | −0.628370 | − | 0.628370i | ||||
\(629\) | −1.19568 | − | 1.19568i | −0.0476749 | − | 0.0476749i | ||||
\(630\) | 33.4418 | − | 4.24297i | 1.33235 | − | 0.169044i | ||||
\(631\) | 28.0636 | 1.11720 | 0.558598 | − | 0.829439i | \(-0.311340\pi\) | ||||
0.558598 | + | 0.829439i | \(0.311340\pi\) | |||||||
\(632\) | 8.82905 | − | 8.82905i | 0.351201 | − | 0.351201i | ||||
\(633\) | −12.8051 | + | 44.6540i | −0.508958 | + | 1.77484i | ||||
\(634\) | −4.73167 | − | 4.73167i | −0.187919 | − | 0.187919i | ||||
\(635\) | − | 40.9823i | − | 1.62633i | ||||||
\(636\) | 3.73537 | − | 13.0260i | 0.148117 | − | 0.516513i | ||||
\(637\) | −6.16836 | + | 4.07739i | −0.244399 | + | 0.161552i | ||||
\(638\) | − | 20.0296i | − | 0.792980i | ||||||
\(639\) | −28.9334 | + | 6.67880i | −1.14459 | + | 0.264209i | ||||
\(640\) | 13.3212i | 0.526568i | ||||||||
\(641\) | −6.94341 | + | 6.94341i | −0.274248 | + | 0.274248i | −0.830808 | − | 0.556559i | \(-0.812121\pi\) |
0.556559 | + | 0.830808i | \(0.312121\pi\) | |||||||
\(642\) | 33.7324 | − | 18.6974i | 1.33131 | − | 0.737929i | ||||
\(643\) | −26.5169 | − | 26.5169i | −1.04573 | − | 1.04573i | −0.998903 | − | 0.0468220i | \(-0.985091\pi\) |
−0.0468220 | − | 0.998903i | \(-0.514909\pi\) | |||||||
\(644\) | 8.02250 | + | 9.82510i | 0.316131 | + | 0.387163i | ||||
\(645\) | −15.3618 | − | 27.7144i | −0.604869 | − | 1.09126i | ||||
\(646\) | 69.0689 | 2.71748 | ||||||||
\(647\) | − | 42.1882i | − | 1.65859i | −0.558813 | − | 0.829294i | \(-0.688743\pi\) | ||
0.558813 | − | 0.829294i | \(-0.311257\pi\) | |||||||
\(648\) | 3.31056 | + | 6.78878i | 0.130051 | + | 0.266689i | ||||
\(649\) | −5.27861 | − | 5.27861i | −0.207203 | − | 0.207203i | ||||
\(650\) | 1.41114 | + | 1.41114i | 0.0553495 | + | 0.0553495i | ||||
\(651\) | −11.3794 | + | 28.4964i | −0.445995 | + | 1.11686i | ||||
\(652\) | 32.1876 | 1.26056 | ||||||||
\(653\) | −29.7126 | − | 29.7126i | −1.16275 | − | 1.16275i | −0.983872 | − | 0.178873i | \(-0.942755\pi\) |
−0.178873 | − | 0.983872i | \(-0.557245\pi\) | |||||||
\(654\) | 2.60657 | − | 9.08962i | 0.101925 | − | 0.355432i | ||||
\(655\) | −1.49713 | −0.0584978 | ||||||||
\(656\) | −1.50450 | − | 19.4059i | −0.0587408 | − | 0.757671i | ||||
\(657\) | −0.289614 | + | 0.463446i | −0.0112989 | + | 0.0180808i | ||||
\(658\) | 28.4354 | + | 2.87197i | 1.10853 | + | 0.111961i | ||||
\(659\) | 10.2150 | + | 10.2150i | 0.397918 | + | 0.397918i | 0.877498 | − | 0.479580i | \(-0.159211\pi\) |
−0.479580 | + | 0.877498i | \(0.659211\pi\) | |||||||
\(660\) | 22.6250 | + | 6.48801i | 0.880676 | + | 0.252545i | ||||
\(661\) | 16.9744 | 0.660227 | 0.330114 | − | 0.943941i | \(-0.392913\pi\) | ||||
0.330114 | + | 0.943941i | \(0.392913\pi\) | |||||||
\(662\) | 1.58632 | − | 1.58632i | 0.0616543 | − | 0.0616543i | ||||
\(663\) | 10.0109 | − | 5.54893i | 0.388792 | − | 0.215503i | ||||
\(664\) | −5.01875 | −0.194765 | ||||||||
\(665\) | −28.0514 | − | 2.83319i | −1.08779 | − | 0.109866i | ||||
\(666\) | −0.901396 | + | 1.44243i | −0.0349284 | + | 0.0558930i | ||||
\(667\) | 4.82298 | − | 4.82298i | 0.186746 | − | 0.186746i | ||||
\(668\) | −3.76022 | + | 3.76022i | −0.145487 | + | 0.145487i | ||||
\(669\) | −5.49920 | + | 3.04814i | −0.212611 | + | 0.117848i | ||||
\(670\) | −25.1531 | + | 25.1531i | −0.971749 | + | 0.971749i | ||||
\(671\) | −0.571558 | − | 0.571558i | −0.0220648 | − | 0.0220648i | ||||
\(672\) | 34.2796 | + | 13.6888i | 1.32236 | + | 0.528057i | ||||
\(673\) | 10.9588 | + | 10.9588i | 0.422429 | + | 0.422429i | 0.886039 | − | 0.463610i | \(-0.153446\pi\) |
−0.463610 | + | 0.886039i | \(0.653446\pi\) | |||||||
\(674\) | 50.8047i | 1.95692i | ||||||||
\(675\) | −4.67357 | − | 0.245160i | −0.179886 | − | 0.00943622i | ||||
\(676\) | − | 28.5230i | − | 1.09704i | ||||||
\(677\) | − | 3.40048i | − | 0.130691i | −0.997863 | − | 0.0653455i | \(-0.979185\pi\) | ||
0.997863 | − | 0.0653455i | \(-0.0208150\pi\) | |||||||
\(678\) | 53.6539 | − | 29.7397i | 2.06056 | − | 1.14215i | ||||
\(679\) | 1.78487 | − | 17.6721i | 0.0684971 | − | 0.678192i | ||||
\(680\) | 7.51651 | − | 7.51651i | 0.288245 | − | 0.288245i | ||||
\(681\) | 0.481367 | − | 1.67862i | 0.0184460 | − | 0.0643250i | ||||
\(682\) | −27.7735 | + | 27.7735i | −1.06350 | + | 1.06350i | ||||
\(683\) | −5.94637 | + | 5.94637i | −0.227532 | + | 0.227532i | −0.811661 | − | 0.584129i | \(-0.801436\pi\) |
0.584129 | + | 0.811661i | \(0.301436\pi\) | |||||||
\(684\) | −8.52367 | − | 36.9256i | −0.325911 | − | 1.41188i | ||||
\(685\) | −2.27083 | − | 2.27083i | −0.0867641 | − | 0.0867641i | ||||
\(686\) | 18.0574 | + | 34.3971i | 0.689435 | + | 1.31329i | ||||
\(687\) | −37.1055 | − | 10.6405i | −1.41566 | − | 0.405960i | ||||
\(688\) | − | 27.4668i | − | 1.04716i | ||||||
\(689\) | 3.44331i | 0.131180i | ||||||||
\(690\) | 7.12361 | + | 12.8518i | 0.271191 | + | 0.489261i | ||||
\(691\) | 16.5238 | − | 16.5238i | 0.628596 | − | 0.628596i | −0.319119 | − | 0.947715i | \(-0.603387\pi\) |
0.947715 | + | 0.319119i | \(0.103387\pi\) | |||||||
\(692\) | − | 14.0428i | − | 0.533828i | ||||||
\(693\) | 13.5947 | − | 17.5457i | 0.516419 | − | 0.666504i | ||||
\(694\) | 51.4017 | − | 51.4017i | 1.95118 | − | 1.95118i | ||||
\(695\) | −3.04242 | −0.115406 | ||||||||
\(696\) | −1.36815 | + | 4.77103i | −0.0518598 | + | 0.180845i | ||||
\(697\) | −26.0512 | + | 30.4301i | −0.986760 | + | 1.15262i | ||||
\(698\) | −75.5421 | −2.85931 | ||||||||
\(699\) | 3.73957 | − | 13.0406i | 0.141443 | − | 0.493241i | ||||
\(700\) | 4.43003 | − | 3.61725i | 0.167439 | − | 0.136719i | ||||
\(701\) | − | 15.4407i | − | 0.583188i | −0.956542 | − | 0.291594i | \(-0.905814\pi\) | ||
0.956542 | − | 0.291594i | \(-0.0941857\pi\) | |||||||
\(702\) | −7.70355 | − | 8.55650i | −0.290752 | − | 0.322944i | ||||
\(703\) | 1.00593 | − | 1.00593i | 0.0379395 | − | 0.0379395i | ||||
\(704\) | 21.3883 | + | 21.3883i | 0.806102 | + | 0.806102i | ||||
\(705\) | 17.3596 | + | 4.97810i | 0.653802 | + | 0.187486i | ||||
\(706\) | −68.6663 | −2.58429 | ||||||||
\(707\) | −47.9652 | − | 4.84447i | −1.80392 | − | 0.182195i | ||||
\(708\) | 5.37989 | + | 9.70595i | 0.202189 | + | 0.364772i | ||||
\(709\) | −17.2082 | + | 17.2082i | −0.646268 | + | 0.646268i | −0.952089 | − | 0.305821i | \(-0.901069\pi\) |
0.305821 | + | 0.952089i | \(0.401069\pi\) | |||||||
\(710\) | 29.7250 | − | 29.7250i | 1.11556 | − | 1.11556i | ||||
\(711\) | −10.0393 | − | 43.4912i | −0.376501 | − | 1.63105i | ||||
\(712\) | 3.04718 | − | 3.04718i | 0.114198 | − | 0.114198i | ||||
\(713\) | −13.3753 | −0.500909 | ||||||||
\(714\) | −23.7210 | − | 55.2605i | −0.887735 | − | 2.06807i | ||||
\(715\) | −5.98073 | −0.223667 | ||||||||
\(716\) | 6.60202 | − | 6.60202i | 0.246729 | − | 0.246729i | ||||
\(717\) | 6.24868 | − | 21.7904i | 0.233361 | − | 0.813777i | ||||
\(718\) | 39.3075i | 1.46694i | ||||||||
\(719\) | 18.4919 | + | 18.4919i | 0.689631 | + | 0.689631i | 0.962150 | − | 0.272520i | \(-0.0878569\pi\) |
−0.272520 | + | 0.962150i | \(0.587857\pi\) | |||||||
\(720\) | 15.6578 | + | 9.78481i | 0.583533 | + | 0.364658i | ||||
\(721\) | 7.06495 | − | 5.76875i | 0.263112 | − | 0.214839i | ||||
\(722\) | 18.2530i | 0.679306i | ||||||||
\(723\) | 19.5520 | + | 35.2741i | 0.727146 | + | 1.31186i | ||||
\(724\) | 35.9138 | − | 35.9138i | 1.33473 | − | 1.33473i | ||||
\(725\) | −2.17463 | − | 2.17463i | −0.0807636 | − | 0.0807636i | ||||
\(726\) | −10.1048 | + | 5.60099i | −0.375026 | + | 0.207872i | ||||
\(727\) | 7.97693 | + | 7.97693i | 0.295848 | + | 0.295848i | 0.839385 | − | 0.543537i | \(-0.182915\pi\) |
−0.543537 | + | 0.839385i | \(0.682915\pi\) | |||||||
\(728\) | 2.33352 | + | 0.235685i | 0.0864861 | + | 0.00873507i | ||||
\(729\) | 26.8518 | + | 2.82489i | 0.994512 | + | 0.104626i | ||||
\(730\) | − | 0.773665i | − | 0.0286346i | ||||||
\(731\) | −39.9714 | + | 39.9714i | −1.47840 | + | 1.47840i | ||||
\(732\) | 0.582525 | + | 1.05094i | 0.0215307 | + | 0.0388440i | ||||
\(733\) | −35.3200 | −1.30457 | −0.652287 | − | 0.757972i | \(-0.726190\pi\) | ||||
−0.652287 | + | 0.757972i | \(0.726190\pi\) | |||||||
\(734\) | −34.7969 | −1.28438 | ||||||||
\(735\) | 7.36719 | + | 23.4164i | 0.271743 | + | 0.863726i | ||||
\(736\) | 16.0897i | 0.593075i | ||||||||
\(737\) | 23.4221i | 0.862763i | ||||||||
\(738\) | 35.7191 | + | 18.6487i | 1.31484 | + | 0.686467i | ||||
\(739\) | −39.8911 | −1.46742 | −0.733709 | − | 0.679464i | \(-0.762212\pi\) | ||||
−0.733709 | + | 0.679464i | \(0.762212\pi\) | |||||||
\(740\) | − | 1.31345i | − | 0.0482834i | ||||||
\(741\) | 4.66835 | + | 8.42226i | 0.171496 | + | 0.309399i | ||||
\(742\) | 17.9995 | + | 1.81794i | 0.660781 | + | 0.0667387i | ||||
\(743\) | 45.3144 | 1.66243 | 0.831213 | − | 0.555954i | \(-0.187647\pi\) | ||||
0.831213 | + | 0.555954i | \(0.187647\pi\) | |||||||
\(744\) | 8.51273 | − | 4.71850i | 0.312092 | − | 0.172989i | ||||
\(745\) | 2.64621 | + | 2.64621i | 0.0969496 | + | 0.0969496i | ||||
\(746\) | 12.1136 | 0.443512 | ||||||||
\(747\) | −9.50765 | + | 15.2143i | −0.347867 | + | 0.556663i | ||||
\(748\) | − | 41.9885i | − | 1.53525i | ||||||
\(749\) | 17.7633 | + | 21.7546i | 0.649056 | + | 0.794894i | ||||
\(750\) | 37.9640 | − | 21.0430i | 1.38625 | − | 0.768381i | ||||
\(751\) | 13.5274 | − | 13.5274i | 0.493623 | − | 0.493623i | −0.415823 | − | 0.909446i | \(-0.636506\pi\) |
0.909446 | + | 0.415823i | \(0.136506\pi\) | |||||||
\(752\) | 11.0691 | + | 11.0691i | 0.403647 | + | 0.403647i | ||||
\(753\) | 17.6350 | − | 9.77489i | 0.642657 | − | 0.356217i | ||||
\(754\) | − | 7.56586i | − | 0.275532i | ||||||
\(755\) | 9.37220 | + | 9.37220i | 0.341089 | + | 0.341089i | ||||
\(756\) | −26.6160 | + | 19.5013i | −0.968014 | + | 0.709255i | ||||
\(757\) | −25.7757 | − | 25.7757i | −0.936834 | − | 0.936834i | 0.0612862 | − | 0.998120i | \(-0.480480\pi\) |
−0.998120 | + | 0.0612862i | \(0.980480\pi\) | |||||||
\(758\) | 30.0917 | 1.09298 | ||||||||
\(759\) | 9.30037 | + | 2.66700i | 0.337582 | + | 0.0968060i | ||||
\(760\) | 6.32369 | + | 6.32369i | 0.229384 | + | 0.229384i | ||||
\(761\) | 4.53345 | 0.164337 | 0.0821687 | − | 0.996618i | \(-0.473815\pi\) | ||||
0.0821687 | + | 0.996618i | \(0.473815\pi\) | |||||||
\(762\) | 35.6524 | + | 64.3212i | 1.29155 | + | 2.33011i | ||||
\(763\) | 6.85110 | + | 0.691959i | 0.248027 | + | 0.0250506i | ||||
\(764\) | 31.3451 | − | 31.3451i | 1.13402 | − | 1.13402i | ||||
\(765\) | −8.54680 | − | 37.0258i | −0.309010 | − | 1.33867i | ||||
\(766\) | 26.9147 | + | 26.9147i | 0.972469 | + | 0.972469i | ||||
\(767\) | −1.99391 | − | 1.99391i | −0.0719959 | − | 0.0719959i | ||||
\(768\) | 6.57619 | + | 11.8642i | 0.237298 | + | 0.428113i | ||||
\(769\) | 50.9062i | 1.83573i | 0.396898 | + | 0.917863i | \(0.370087\pi\) | ||||
−0.396898 | + | 0.917863i | \(0.629913\pi\) | |||||||
\(770\) | −3.15761 | + | 31.2635i | −0.113792 | + | 1.12666i | ||||
\(771\) | −22.4258 | − | 6.43090i | −0.807647 | − | 0.231603i | ||||
\(772\) | 42.9173 | − | 42.9173i | 1.54463 | − | 1.54463i | ||||
\(773\) | −2.67907 | − | 2.67907i | −0.0963594 | − | 0.0963594i | 0.657284 | − | 0.753643i | \(-0.271705\pi\) |
−0.753643 | + | 0.657284i | \(0.771705\pi\) | |||||||
\(774\) | 48.2202 | + | 30.1335i | 1.73324 | + | 1.08313i | ||||
\(775\) | 6.03077i | 0.216632i | ||||||||
\(776\) | −3.98385 | + | 3.98385i | −0.143012 | + | 0.143012i | ||||
\(777\) | −1.15030 | − | 0.459349i | −0.0412669 | − | 0.0164791i | ||||
\(778\) | 17.7410 | 0.636044 | ||||||||
\(779\) | −25.6010 | − | 21.9170i | −0.917252 | − | 0.785260i | ||||
\(780\) | 8.54622 | + | 2.45074i | 0.306004 | + | 0.0877505i | ||||
\(781\) | − | 27.6794i | − | 0.990446i | ||||||
\(782\) | 18.5357 | − | 18.5357i | 0.662834 | − | 0.662834i | ||||
\(783\) | 11.8715 | + | 13.1859i | 0.424253 | + | 0.471227i | ||||
\(784\) | −4.25483 | + | 20.8487i | −0.151958 | + | 0.744597i | ||||
\(785\) | 13.2839 | − | 13.2839i | 0.474124 | − | 0.474124i | ||||
\(786\) | 2.34973 | − | 1.30243i | 0.0838121 | − | 0.0464560i | ||||
\(787\) | 9.80042 | 0.349347 | 0.174674 | − | 0.984626i | \(-0.444113\pi\) | ||||
0.174674 | + | 0.984626i | \(0.444113\pi\) | |||||||
\(788\) | 25.7084 | 0.915823 | ||||||||
\(789\) | −47.2165 | − | 13.5399i | −1.68095 | − | 0.482034i | ||||
\(790\) | 44.6812 | + | 44.6812i | 1.58969 | + | 1.58969i | ||||
\(791\) | 28.2538 | + | 34.6023i | 1.00459 | + | 1.23031i | ||||
\(792\) | −6.86009 | + | 1.58354i | −0.243763 | + | 0.0562687i | ||||
\(793\) | −0.215897 | − | 0.215897i | −0.00766672 | − | 0.00766672i | ||||
\(794\) | 5.52281 | + | 5.52281i | 0.195997 | + | 0.195997i | ||||
\(795\) | 10.9886 | + | 3.15112i | 0.389724 | + | 0.111759i | ||||
\(796\) | 28.4987 | − | 28.4987i | 1.01011 | − | 1.01011i | ||||
\(797\) | 23.2344 | 0.823005 | 0.411503 | − | 0.911409i | \(-0.365004\pi\) | ||||
0.411503 | + | 0.911409i | \(0.365004\pi\) | |||||||
\(798\) | 46.4910 | − | 19.9566i | 1.64576 | − | 0.706456i | ||||
\(799\) | − | 32.2168i | − | 1.13975i | ||||||
\(800\) | 7.25467 | 0.256491 | ||||||||
\(801\) | −3.46486 | − | 15.0102i | −0.122425 | − | 0.530359i | ||||
\(802\) | −31.1996 | −1.10169 | ||||||||
\(803\) | −0.360211 | − | 0.360211i | −0.0127116 | − | 0.0127116i | ||||
\(804\) | 9.59773 | − | 33.4692i | 0.338486 | − | 1.18037i | ||||
\(805\) | −8.28835 | + | 6.76769i | −0.292126 | + | 0.238530i | ||||
\(806\) | −10.4910 | + | 10.4910i | −0.369529 | + | 0.369529i | ||||
\(807\) | 12.3253 | + | 22.2364i | 0.433873 | + | 0.782757i | ||||
\(808\) | 10.8129 | + | 10.8129i | 0.380396 | + | 0.380396i | ||||
\(809\) | 11.8811 | + | 11.8811i | 0.417718 | + | 0.417718i | 0.884416 | − | 0.466698i | \(-0.154557\pi\) |
−0.466698 | + | 0.884416i | \(0.654557\pi\) | |||||||
\(810\) | −34.3561 | + | 16.7538i | −1.20715 | + | 0.588669i | ||||
\(811\) | 23.3444 | 0.819734 | 0.409867 | − | 0.912145i | \(-0.365575\pi\) | ||||
0.409867 | + | 0.912145i | \(0.365575\pi\) | |||||||
\(812\) | −21.5728 | − | 2.17885i | −0.757058 | − | 0.0764626i | ||||
\(813\) | −41.8840 | + | 23.2158i | −1.46894 | + | 0.814214i | ||||
\(814\) | −1.12112 | − | 1.12112i | −0.0392953 | − | 0.0392953i | ||||
\(815\) | 27.1531i | 0.951131i | ||||||||
\(816\) | 9.07955 | − | 31.6622i | 0.317848 | − | 1.10840i | ||||
\(817\) | −33.6282 | − | 33.6282i | −1.17650 | − | 1.17650i | ||||
\(818\) | − | 75.9352i | − | 2.65501i | ||||||
\(819\) | 5.13517 | − | 6.62759i | 0.179437 | − | 0.231587i | ||||
\(820\) | −31.0222 | + | 2.40509i | −1.08334 | + | 0.0839894i | ||||
\(821\) | − | 32.9035i | − | 1.14834i | −0.818736 | − | 0.574170i | \(-0.805325\pi\) | ||
0.818736 | − | 0.574170i | \(-0.194675\pi\) | |||||||
\(822\) | 5.53954 | + | 1.58854i | 0.193214 | + | 0.0554065i | ||||
\(823\) | 15.6209 | − | 15.6209i | 0.544511 | − | 0.544511i | −0.380337 | − | 0.924848i | \(-0.624192\pi\) |
0.924848 | + | 0.380337i | \(0.124192\pi\) | |||||||
\(824\) | −2.89312 | −0.100787 | ||||||||
\(825\) | 1.20252 | − | 4.19343i | 0.0418664 | − | 0.145997i | ||||
\(826\) | −11.4756 | + | 9.37020i | −0.399288 | + | 0.326031i | ||||
\(827\) | −26.9798 | − | 26.9798i | −0.938178 | − | 0.938178i | 0.0600191 | − | 0.998197i | \(-0.480884\pi\) |
−0.998197 | + | 0.0600191i | \(0.980884\pi\) | |||||||
\(828\) | −12.1970 | − | 7.62207i | −0.423874 | − | 0.264885i | ||||
\(829\) | −52.2940 | −1.81625 | −0.908123 | − | 0.418704i | \(-0.862485\pi\) | ||||
−0.908123 | + | 0.418704i | \(0.862485\pi\) | |||||||
\(830\) | − | 25.3984i | − | 0.881592i | ||||||
\(831\) | 11.7721 | + | 21.2382i | 0.408369 | + | 0.736745i | ||||
\(832\) | 8.07908 | + | 8.07908i | 0.280092 | + | 0.280092i | ||||
\(833\) | 36.5323 | − | 24.1485i | 1.26577 | − | 0.836696i | ||||
\(834\) | 4.77504 | − | 2.64674i | 0.165346 | − | 0.0916493i | ||||
\(835\) | −3.17208 | − | 3.17208i | −0.109774 | − | 0.109774i | ||||
\(836\) | 35.3252 | 1.22175 | ||||||||
\(837\) | 1.82262 | − | 34.7452i | 0.0629989 | − | 1.20097i | ||||
\(838\) | − | 27.7650i | − | 0.959126i | ||||||
\(839\) | −20.5029 | − | 20.5029i | −0.707838 | − | 0.707838i | 0.258242 | − | 0.966080i | \(-0.416857\pi\) |
−0.966080 | + | 0.258242i | \(0.916857\pi\) | |||||||
\(840\) | 2.88764 | − | 7.23125i | 0.0996332 | − | 0.249502i | ||||
\(841\) | − | 17.3407i | − | 0.597955i | ||||||
\(842\) | −37.1044 | + | 37.1044i | −1.27870 | + | 1.27870i | ||||
\(843\) | 36.4714 | + | 10.4586i | 1.25614 | + | 0.360215i | ||||
\(844\) | 45.5167 | + | 45.5167i | 1.56675 | + | 1.56675i | ||||
\(845\) | 24.0617 | 0.827749 | ||||||||
\(846\) | −31.5764 | + | 7.28890i | −1.08562 | + | 0.250598i | ||||
\(847\) | −5.32115 | − | 6.51677i | −0.182837 | − | 0.223919i | ||||
\(848\) | 7.00667 | + | 7.00667i | 0.240610 | + | 0.240610i | ||||
\(849\) | −36.9045 | + | 20.4557i | −1.26656 | + | 0.702038i | ||||
\(850\) | −8.35752 | − | 8.35752i | −0.286661 | − | 0.286661i | ||||
\(851\) | − | 0.539915i | − | 0.0185081i | ||||||
\(852\) | −11.3423 | + | 39.5527i | −0.388579 | + | 1.35505i | ||||
\(853\) | 30.2203 | 1.03472 | 0.517362 | − | 0.855767i | \(-0.326914\pi\) | ||||
0.517362 | + | 0.855767i | \(0.326914\pi\) | |||||||
\(854\) | −1.24256 | + | 1.01459i | −0.0425195 | + | 0.0347185i | ||||
\(855\) | 31.1500 | − | 7.19048i | 1.06531 | − | 0.245909i | ||||
\(856\) | − | 8.90858i | − | 0.304489i | ||||||
\(857\) | 34.3852 | 1.17458 | 0.587289 | − | 0.809377i | \(-0.300195\pi\) | ||||
0.587289 | + | 0.809377i | \(0.300195\pi\) | |||||||
\(858\) | 9.38667 | − | 5.20291i | 0.320455 | − | 0.177625i | ||||
\(859\) | −50.9572 | −1.73864 | −0.869318 | − | 0.494253i | \(-0.835442\pi\) | ||||
−0.869318 | + | 0.494253i | \(0.835442\pi\) | |||||||
\(860\) | −43.9084 | −1.49726 | ||||||||
\(861\) | −8.74296 | + | 28.0100i | −0.297959 | + | 0.954579i | ||||
\(862\) | −51.7684 | −1.76324 | ||||||||
\(863\) | 26.2677 | 0.894162 | 0.447081 | − | 0.894494i | \(-0.352464\pi\) | ||||
0.447081 | + | 0.894494i | \(0.352464\pi\) | |||||||
\(864\) | −41.7965 | − | 2.19251i | −1.42194 | − | 0.0745906i | ||||
\(865\) | 11.8464 | 0.402789 | ||||||||
\(866\) | 42.0767i | 1.42982i | ||||||||
\(867\) | −33.5367 | + | 18.5890i | −1.13897 | + | 0.631315i | ||||
\(868\) | 26.8921 | + | 32.9346i | 0.912778 | + | 1.11787i | ||||
\(869\) | 41.6063 | 1.41140 | ||||||||
\(870\) | −24.1448 | − | 6.92383i | −0.818585 | − | 0.234740i | ||||
\(871\) | 8.84731i | 0.299780i | ||||||||
\(872\) | −1.54446 | − | 1.54446i | −0.0523019 | − | 0.0523019i | ||||
\(873\) | 4.52992 | + | 19.6241i | 0.153314 | + | 0.664176i | ||||
\(874\) | 15.5942 | + | 15.5942i | 0.527481 | + | 0.527481i | ||||
\(875\) | 19.9916 | + | 24.4836i | 0.675840 | + | 0.827696i | ||||
\(876\) | 0.367122 | + | 0.662332i | 0.0124039 | + | 0.0223781i | ||||
\(877\) | 3.17121 | 0.107084 | 0.0535420 | − | 0.998566i | \(-0.482949\pi\) | ||||
0.0535420 | + | 0.998566i | \(0.482949\pi\) | |||||||
\(878\) | −10.5078 | − | 10.5078i | −0.354622 | − | 0.354622i | ||||
\(879\) | 0.308364 | − | 1.07533i | 0.0104009 | − | 0.0362699i | ||||
\(880\) | −12.1700 | + | 12.1700i | −0.410250 | + | 0.410250i | ||||
\(881\) | − | 8.27262i | − | 0.278712i | −0.990242 | − | 0.139356i | \(-0.955497\pi\) | ||
0.990242 | − | 0.139356i | \(-0.0445032\pi\) | |||||||
\(882\) | −31.9337 | − | 30.3426i | −1.07526 | − | 1.02169i | ||||
\(883\) | −27.3976 | − | 27.3976i | −0.922001 | − | 0.922001i | 0.0751695 | − | 0.997171i | \(-0.476050\pi\) |
−0.997171 | + | 0.0751695i | \(0.976050\pi\) | |||||||
\(884\) | − | 15.8605i | − | 0.533445i | ||||||
\(885\) | −8.18784 | + | 4.53842i | −0.275231 | + | 0.152557i | ||||
\(886\) | −35.7503 | −1.20105 | ||||||||
\(887\) | −8.33058 | − | 8.33058i | −0.279714 | − | 0.279714i | 0.553281 | − | 0.832995i | \(-0.313376\pi\) |
−0.832995 | + | 0.553281i | \(0.813376\pi\) | |||||||
\(888\) | 0.190470 | + | 0.343630i | 0.00639175 | + | 0.0115315i | ||||
\(889\) | −41.4818 | + | 33.8711i | −1.39125 | + | 1.13600i | ||||
\(890\) | 15.4209 | + | 15.4209i | 0.516910 | + | 0.516910i | ||||
\(891\) | −8.19544 | + | 23.7963i | −0.274558 | + | 0.797205i | ||||
\(892\) | 8.71247i | 0.291715i | ||||||||
\(893\) | 27.1042 | 0.907009 | ||||||||
\(894\) | −6.45525 | − | 1.85113i | −0.215896 | − | 0.0619109i | ||||
\(895\) | 5.56940 | + | 5.56940i | 0.186164 | + | 0.186164i | ||||
\(896\) | 13.4836 | − | 11.0098i | 0.450455 | − | 0.367810i | ||||
\(897\) | 3.51306 | + | 1.00742i | 0.117298 | + | 0.0336366i | ||||
\(898\) | −50.4192 | −1.68251 | ||||||||
\(899\) | 16.1670 | − | 16.1670i | 0.539201 | − | 0.539201i | ||||
\(900\) | −3.43671 | + | 5.49948i | −0.114557 | + | 0.183316i | ||||
\(901\) | − | 20.3931i | − | 0.679393i | ||||||
\(902\) | −24.4267 | + | 28.5325i | −0.813320 | + | 0.950029i | ||||
\(903\) | −15.3560 | + | 38.4545i | −0.511015 | + | 1.27968i | ||||
\(904\) | − | 14.1698i | − | 0.471279i | ||||||
\(905\) | 30.2965 | + | 30.2965i | 1.00709 | + | 1.00709i | ||||
\(906\) | −22.8628 | − | 6.55622i | −0.759567 | − | 0.217816i | ||||
\(907\) | 52.6134i | 1.74700i | 0.486825 | + | 0.873499i | \(0.338155\pi\) | ||||
−0.486825 | + | 0.873499i | \(0.661845\pi\) | |||||||
\(908\) | −1.71105 | − | 1.71105i | −0.0567833 | − | 0.0567833i | ||||
\(909\) | 53.2635 | − | 12.2950i | 1.76664 | − | 0.407800i | ||||
\(910\) | −1.19273 | + | 11.8093i | −0.0395387 | + | 0.391474i | ||||
\(911\) | −38.5428 | −1.27698 | −0.638491 | − | 0.769630i | \(-0.720441\pi\) | ||||
−0.638491 | + | 0.769630i | \(0.720441\pi\) | |||||||
\(912\) | 26.6376 | + | 7.63869i | 0.882060 | + | 0.252942i | ||||
\(913\) | −11.8253 | − | 11.8253i | −0.391359 | − | 0.391359i | ||||
\(914\) | −6.02142 | − | 6.02142i | −0.199171 | − | 0.199171i | ||||
\(915\) | −0.886564 | + | 0.491412i | −0.0293089 | + | 0.0162456i | ||||
\(916\) | −37.8224 | + | 37.8224i | −1.24969 | + | 1.24969i | ||||
\(917\) | 1.23735 | + | 1.51538i | 0.0408610 | + | 0.0500422i | ||||
\(918\) | 45.6245 | + | 50.6761i | 1.50583 | + | 1.67256i | ||||
\(919\) | −12.9944 | − | 12.9944i | −0.428645 | − | 0.428645i | 0.459521 | − | 0.888167i | \(-0.348021\pi\) |
−0.888167 | + | 0.459521i | \(0.848021\pi\) | |||||||
\(920\) | 3.39411 | 0.111901 | ||||||||
\(921\) | −1.66754 | − | 3.00844i | −0.0549474 | − | 0.0991316i | ||||
\(922\) | 55.4769 | 1.82703 | ||||||||
\(923\) | − | 10.4554i | − | 0.344145i | ||||||
\(924\) | −12.1321 | − | 28.2629i | −0.399115 | − | 0.929782i | ||||
\(925\) | −0.243442 | −0.00800432 | ||||||||
\(926\) | 7.92194 | − | 7.92194i | 0.260331 | − | 0.260331i | ||||
\(927\) | −5.48081 | + | 8.77050i | −0.180014 | + | 0.288061i | ||||
\(928\) | −19.4480 | − | 19.4480i | −0.638413 | − | 0.638413i | ||||
\(929\) | 23.8842 | + | 23.8842i | 0.783616 | + | 0.783616i | 0.980439 | − | 0.196823i | \(-0.0630626\pi\) |
−0.196823 | + | 0.980439i | \(0.563063\pi\) | |||||||
\(930\) | 23.8790 | + | 43.0804i | 0.783022 | + | 1.41266i | ||||
\(931\) | 20.3163 | + | 30.7349i | 0.665839 | + | 1.00729i | ||||
\(932\) | −13.2925 | − | 13.2925i | −0.435412 | − | 0.435412i | ||||
\(933\) | −14.4082 | + | 50.2444i | −0.471704 | + | 1.64493i | ||||
\(934\) | −52.5795 | −1.72045 | ||||||||
\(935\) | 35.4210 | 1.15839 | ||||||||
\(936\) | −2.59129 | + | 0.598157i | −0.0846989 | + | 0.0195514i | ||||
\(937\) | −9.00990 | + | 9.00990i | −0.294341 | + | 0.294341i | −0.838792 | − | 0.544452i | \(-0.816738\pi\) |
0.544452 | + | 0.838792i | \(0.316738\pi\) | |||||||
\(938\) | 46.2482 | + | 4.67105i | 1.51006 | + | 0.152515i | ||||
\(939\) | −31.3487 | − | 8.98965i | −1.02303 | − | 0.293366i | ||||
\(940\) | 17.6950 | − | 17.6950i | 0.577148 | − | 0.577148i | ||||
\(941\) | 12.3856i | 0.403760i | 0.979410 | + | 0.201880i | \(0.0647051\pi\) | ||||
−0.979410 | + | 0.201880i | \(0.935295\pi\) | |||||||
\(942\) | −9.29263 | + | 32.4053i | −0.302770 | + | 1.05582i | ||||
\(943\) | −12.7522 | + | 0.988652i | −0.415268 | + | 0.0321949i | ||||
\(944\) | −8.11467 | −0.264110 | ||||||||
\(945\) | −16.4511 | − | 22.4530i | −0.535154 | − | 0.730395i | ||||
\(946\) | −37.4789 | + | 37.4789i | −1.21854 | + | 1.21854i | ||||
\(947\) | 17.7611i | 0.577157i | 0.957456 | + | 0.288579i | \(0.0931827\pi\) | ||||
−0.957456 | + | 0.288579i | \(0.906817\pi\) | |||||||
\(948\) | −59.4537 | − | 17.0491i | −1.93097 | − | 0.553730i | ||||
\(949\) | −0.136064 | − | 0.136064i | −0.00441682 | − | 0.00441682i | ||||
\(950\) | 7.03124 | − | 7.03124i | 0.228124 | − | 0.228124i | ||||
\(951\) | −1.52308 | + | 5.31129i | −0.0493893 | + | 0.172230i | ||||
\(952\) | −13.8204 | − | 1.39585i | −0.447921 | − | 0.0452398i | ||||
\(953\) | − | 54.6021i | − | 1.76874i | −0.466790 | − | 0.884368i | \(-0.654589\pi\) | ||
0.466790 | − | 0.884368i | \(-0.345411\pi\) | |||||||
\(954\) | −19.9877 | + | 4.61384i | −0.647126 | + | 0.149379i | ||||
\(955\) | 26.4424 | + | 26.4424i | 0.855655 | + | 0.855655i | ||||
\(956\) | −22.2114 | − | 22.2114i | −0.718367 | − | 0.718367i | ||||
\(957\) | −14.4652 | + | 8.01791i | −0.467595 | + | 0.259182i | ||||
\(958\) | 5.04059 | − | 5.04059i | 0.162854 | − | 0.162854i | ||||
\(959\) | −0.421705 | + | 4.17531i | −0.0136176 | + | 0.134828i | ||||
\(960\) | 33.1761 | − | 18.3891i | 1.07076 | − | 0.593507i | ||||
\(961\) | −13.8352 | −0.446296 | ||||||||
\(962\) | −0.423485 | − | 0.423485i | −0.0136537 | − | 0.0136537i | ||||
\(963\) | −27.0063 | − | 16.8767i | −0.870267 | − | 0.543843i | ||||
\(964\) | 55.8853 | 1.79994 | ||||||||
\(965\) | 36.2046 | + | 36.2046i | 1.16547 | + | 1.16547i | ||||
\(966\) | 7.12091 | − | 17.8322i | 0.229112 | − | 0.573742i | ||||
\(967\) | 23.5981 | + | 23.5981i | 0.758862 | + | 0.758862i | 0.976115 | − | 0.217253i | \(-0.0697097\pi\) |
−0.217253 | + | 0.976115i | \(0.569710\pi\) | |||||||
\(968\) | 2.66865i | 0.0857735i | ||||||||
\(969\) | −27.6485 | − | 49.8811i | −0.888197 | − | 1.60241i | ||||
\(970\) | −20.1611 | − | 20.1611i | −0.647334 | − | 0.647334i | ||||
\(971\) | −17.2598 | + | 17.2598i | −0.553893 | + | 0.553893i | −0.927562 | − | 0.373669i | \(-0.878100\pi\) |
0.373669 | + | 0.927562i | \(0.378100\pi\) | |||||||
\(972\) | 21.4620 | − | 30.6456i | 0.688394 | − | 0.982959i | ||||
\(973\) | 2.51451 | + | 3.07950i | 0.0806114 | + | 0.0987242i | ||||
\(974\) | − | 37.4285i | − | 1.19929i | ||||||
\(975\) | 0.454233 | − | 1.58400i | 0.0145471 | − | 0.0507286i | ||||
\(976\) | −0.878642 | −0.0281246 | ||||||||
\(977\) | −11.8320 | − | 11.8320i | −0.378539 | − | 0.378539i | 0.492036 | − | 0.870575i | \(-0.336253\pi\) |
−0.870575 | + | 0.492036i | \(0.836253\pi\) | |||||||
\(978\) | −23.6217 | − | 42.6164i | −0.755340 | − | 1.36272i | ||||
\(979\) | 14.3596 | 0.458936 | ||||||||
\(980\) | 33.3288 | + | 6.80178i | 1.06465 | + | 0.217275i | ||||
\(981\) | −7.60788 | + | 1.75616i | −0.242901 | + | 0.0560698i | ||||
\(982\) | 55.8437i | 1.78205i | ||||||||
\(983\) | 9.95976 | 0.317667 | 0.158834 | − | 0.987305i | \(-0.449227\pi\) | ||||
0.158834 | + | 0.987305i | \(0.449227\pi\) | |||||||
\(984\) | 7.76737 | − | 5.12791i | 0.247615 | − | 0.163472i | ||||
\(985\) | 21.6873i | 0.691015i | ||||||||
\(986\) | 44.8090i | 1.42701i | ||||||||
\(987\) | −9.30866 | − | 21.6855i | −0.296298 | − | 0.690258i | ||||
\(988\) | 13.3435 | 0.424514 | ||||||||
\(989\) | −18.0493 | −0.573934 | ||||||||
\(990\) | −8.01384 | − | 34.7169i | −0.254697 | − | 1.10338i | ||||
\(991\) | 0.311106 | − | 0.311106i | 0.00988259 | − | 0.00988259i | −0.702148 | − | 0.712031i | \(-0.747776\pi\) |
0.712031 | + | 0.702148i | \(0.247776\pi\) | |||||||
\(992\) | 53.9341i | 1.71241i | ||||||||
\(993\) | −1.78064 | − | 0.510623i | −0.0565070 | − | 0.0162041i | ||||
\(994\) | −54.6545 | − | 5.52009i | −1.73354 | − | 0.175087i | ||||
\(995\) | 24.0412 | + | 24.0412i | 0.762157 | + | 0.762157i | ||||
\(996\) | 12.0521 | + | 21.7435i | 0.381887 | + | 0.688968i | ||||
\(997\) | −38.1817 | − | 38.1817i | −1.20923 | − | 1.20923i | −0.971278 | − | 0.237947i | \(-0.923525\pi\) |
−0.237947 | − | 0.971278i | \(-0.576475\pi\) | |||||||
\(998\) | 17.3882 | − | 17.3882i | 0.550414 | − | 0.550414i | ||||
\(999\) | 1.40254 | + | 0.0735729i | 0.0443746 | + | 0.00232774i |
(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 | 861.2.l.a.524.16 | yes | 216 | |
3.2 | odd | 2 | inner | 861.2.l.a.524.94 | yes | 216 | |
7.6 | odd | 2 | inner | 861.2.l.a.524.15 | yes | 216 | |
21.20 | even | 2 | inner | 861.2.l.a.524.93 | yes | 216 | |
41.9 | even | 4 | inner | 861.2.l.a.419.93 | yes | 216 | |
123.50 | odd | 4 | inner | 861.2.l.a.419.15 | ✓ | 216 | |
287.132 | odd | 4 | inner | 861.2.l.a.419.94 | yes | 216 | |
861.419 | even | 4 | inner | 861.2.l.a.419.16 | yes | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.l.a.419.15 | ✓ | 216 | 123.50 | odd | 4 | inner | |
861.2.l.a.419.16 | yes | 216 | 861.419 | even | 4 | inner | |
861.2.l.a.419.93 | yes | 216 | 41.9 | even | 4 | inner | |
861.2.l.a.419.94 | yes | 216 | 287.132 | odd | 4 | inner | |
861.2.l.a.524.15 | yes | 216 | 7.6 | odd | 2 | inner | |
861.2.l.a.524.16 | yes | 216 | 1.1 | even | 1 | trivial | |
861.2.l.a.524.93 | yes | 216 | 21.20 | even | 2 | inner | |
861.2.l.a.524.94 | yes | 216 | 3.2 | odd | 2 | inner |