Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.i (of order \(3\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.3636603.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 811.3 | ||
Root | \(1.34370 + 1.48137i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.811 |
Dual form | 930.2.i.n.211.3 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 0.954758 | − | 1.65369i | 0.360865 | − | 0.625036i | −0.627239 | − | 0.778827i | \(-0.715815\pi\) |
0.988103 | + | 0.153791i | \(0.0491483\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 3.18740 | + | 5.52074i | 0.961037 | + | 1.66457i | 0.719905 | + | 0.694073i | \(0.244185\pi\) |
0.241132 | + | 0.970492i | \(0.422481\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 2.90952 | + | 5.03943i | 0.806955 | + | 1.39769i | 0.914964 | + | 0.403536i | \(0.132219\pi\) |
−0.108009 | + | 0.994150i | \(0.534448\pi\) | |||||||
\(14\) | −0.954758 | + | 1.65369i | −0.255170 | + | 0.441967i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.45476 | + | 5.98382i | −0.837902 | + | 1.45129i | 0.0537438 | + | 0.998555i | \(0.482885\pi\) |
−0.891646 | + | 0.452734i | \(0.850449\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −1.22212 | + | 2.11677i | −0.280373 | + | 0.485620i | −0.971477 | − | 0.237136i | \(-0.923791\pi\) |
0.691104 | + | 0.722756i | \(0.257125\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | −0.954758 | − | 1.65369i | −0.208345 | − | 0.360865i | ||||
\(22\) | −3.18740 | − | 5.52074i | −0.679556 | − | 1.17703i | ||||
\(23\) | −0.909516 | −0.189647 | −0.0948236 | − | 0.995494i | \(-0.530229\pi\) | ||||
−0.0948236 | + | 0.995494i | \(0.530229\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −2.90952 | − | 5.03943i | −0.570603 | − | 0.988313i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.954758 | − | 1.65369i | 0.180432 | − | 0.312518i | ||||
\(29\) | 5.46528 | 1.01488 | 0.507439 | − | 0.861688i | \(-0.330592\pi\) | ||||
0.507439 | + | 0.861688i | \(0.330592\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 4.42004 | − | 3.38574i | 0.793863 | − | 0.608097i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.37480 | 1.10971 | ||||||||
\(34\) | 3.45476 | − | 5.98382i | 0.592486 | − | 1.02622i | ||||
\(35\) | −1.90952 | −0.322767 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 4.45476 | − | 7.71587i | 0.732358 | − | 1.26848i | −0.223515 | − | 0.974700i | \(-0.571753\pi\) |
0.955873 | − | 0.293780i | \(-0.0949134\pi\) | |||||||
\(38\) | 1.22212 | − | 2.11677i | 0.198253 | − | 0.343385i | ||||
\(39\) | 5.81903 | 0.931791 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 3.59692 | + | 6.23004i | 0.561744 | + | 0.972969i | 0.997344 | + | 0.0728288i | \(0.0232027\pi\) |
−0.435601 | + | 0.900140i | \(0.643464\pi\) | |||||||
\(42\) | 0.954758 | + | 1.65369i | 0.147322 | + | 0.255170i | ||||
\(43\) | 0.232642 | − | 0.402947i | 0.0354775 | − | 0.0614488i | −0.847741 | − | 0.530410i | \(-0.822038\pi\) |
0.883219 | + | 0.468961i | \(0.155371\pi\) | |||||||
\(44\) | 3.18740 | + | 5.52074i | 0.480519 | + | 0.832283i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 0.909516 | 0.134101 | ||||||||
\(47\) | −8.72855 | −1.27319 | −0.636595 | − | 0.771198i | \(-0.719658\pi\) | ||||
−0.636595 | + | 0.771198i | \(0.719658\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 1.67687 | + | 2.90443i | 0.239553 | + | 0.414919i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | 3.45476 | + | 5.98382i | 0.483763 | + | 0.837902i | ||||
\(52\) | 2.90952 | + | 5.03943i | 0.403477 | + | 0.698843i | ||||
\(53\) | −3.64216 | − | 6.30840i | −0.500289 | − | 0.866526i | −1.00000 | 0.000333526i | \(-0.999894\pi\) | |
0.499711 | − | 0.866192i | \(-0.333439\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.18740 | − | 5.52074i | 0.429789 | − | 0.744416i | ||||
\(56\) | −0.954758 | + | 1.65369i | −0.127585 | + | 0.220984i | ||||
\(57\) | 1.22212 | + | 2.11677i | 0.161873 | + | 0.280373i | ||||
\(58\) | −5.46528 | −0.717627 | ||||||||
\(59\) | 2.86427 | − | 4.96107i | 0.372897 | − | 0.645876i | −0.617113 | − | 0.786874i | \(-0.711698\pi\) |
0.990010 | + | 0.140998i | \(0.0450312\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −4.44423 | −0.569026 | −0.284513 | − | 0.958672i | \(-0.591832\pi\) | ||||
−0.284513 | + | 0.958672i | \(0.591832\pi\) | |||||||
\(62\) | −4.42004 | + | 3.38574i | −0.561346 | + | 0.429989i | ||||
\(63\) | −1.90952 | −0.240576 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.90952 | − | 5.03943i | 0.360881 | − | 0.625064i | ||||
\(66\) | −6.37480 | −0.784684 | ||||||||
\(67\) | −4.45476 | − | 7.71587i | −0.544235 | − | 0.942643i | −0.998655 | − | 0.0518553i | \(-0.983487\pi\) |
0.454419 | − | 0.890788i | \(-0.349847\pi\) | |||||||
\(68\) | −3.45476 | + | 5.98382i | −0.418951 | + | 0.725644i | ||||
\(69\) | −0.454758 | + | 0.787664i | −0.0547464 | + | 0.0948236i | ||||
\(70\) | 1.90952 | 0.228231 | ||||||||
\(71\) | 4.90952 | + | 8.50353i | 0.582652 | + | 1.00918i | 0.995164 | + | 0.0982310i | \(0.0313184\pi\) |
−0.412511 | + | 0.910952i | \(0.635348\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 1.00000 | + | 1.73205i | 0.117041 | + | 0.202721i | 0.918594 | − | 0.395203i | \(-0.129326\pi\) |
−0.801553 | + | 0.597924i | \(0.795992\pi\) | |||||||
\(74\) | −4.45476 | + | 7.71587i | −0.517855 | + | 0.896951i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | −1.22212 | + | 2.11677i | −0.140186 | + | 0.242810i | ||||
\(77\) | 12.1728 | 1.38722 | ||||||||
\(78\) | −5.81903 | −0.658876 | ||||||||
\(79\) | 0.232642 | − | 0.402947i | 0.0261742 | − | 0.0453351i | −0.852642 | − | 0.522496i | \(-0.825001\pi\) |
0.878816 | + | 0.477161i | \(0.158334\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.59692 | − | 6.23004i | −0.397213 | − | 0.687993i | ||||
\(83\) | 6.32956 | + | 10.9631i | 0.694759 | + | 1.20336i | 0.970262 | + | 0.242058i | \(0.0778224\pi\) |
−0.275503 | + | 0.961300i | \(0.588844\pi\) | |||||||
\(84\) | −0.954758 | − | 1.65369i | −0.104173 | − | 0.180432i | ||||
\(85\) | 6.90952 | 0.749442 | ||||||||
\(86\) | −0.232642 | + | 0.402947i | −0.0250864 | + | 0.0434509i | ||||
\(87\) | 2.73264 | − | 4.73307i | 0.292970 | − | 0.507439i | ||||
\(88\) | −3.18740 | − | 5.52074i | −0.339778 | − | 0.588513i | ||||
\(89\) | −15.8190 | −1.67681 | −0.838407 | − | 0.545045i | \(-0.816513\pi\) | ||||
−0.838407 | + | 0.545045i | \(0.816513\pi\) | |||||||
\(90\) | 0.500000 | − | 0.866025i | 0.0527046 | − | 0.0912871i | ||||
\(91\) | 11.1115 | 1.16481 | ||||||||
\(92\) | −0.909516 | −0.0948236 | ||||||||
\(93\) | −0.722116 | − | 5.52074i | −0.0748800 | − | 0.572474i | ||||
\(94\) | 8.72855 | 0.900281 | ||||||||
\(95\) | 2.44423 | 0.250773 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 18.1728 | 1.84517 | 0.922583 | − | 0.385798i | \(-0.126074\pi\) | ||||
0.922583 | + | 0.385798i | \(0.126074\pi\) | |||||||
\(98\) | −1.67687 | − | 2.90443i | −0.169390 | − | 0.293392i | ||||
\(99\) | 3.18740 | − | 5.52074i | 0.320346 | − | 0.554855i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 1.93057 | 0.192099 | 0.0960493 | − | 0.995377i | \(-0.469379\pi\) | ||||
0.0960493 | + | 0.995377i | \(0.469379\pi\) | |||||||
\(102\) | −3.45476 | − | 5.98382i | −0.342072 | − | 0.592486i | ||||
\(103\) | 1.86427 | + | 3.22902i | 0.183692 | + | 0.318165i | 0.943135 | − | 0.332410i | \(-0.107862\pi\) |
−0.759443 | + | 0.650574i | \(0.774528\pi\) | |||||||
\(104\) | −2.90952 | − | 5.03943i | −0.285302 | − | 0.494157i | ||||
\(105\) | −0.954758 | + | 1.65369i | −0.0931748 | + | 0.161384i | ||||
\(106\) | 3.64216 | + | 6.30840i | 0.353758 | + | 0.612726i | ||||
\(107\) | 0.954758 | − | 1.65369i | 0.0922999 | − | 0.159868i | −0.816179 | − | 0.577800i | \(-0.803911\pi\) |
0.908479 | + | 0.417932i | \(0.137245\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.44423 | −0.234115 | −0.117058 | − | 0.993125i | \(-0.537346\pi\) | ||||
−0.117058 | + | 0.993125i | \(0.537346\pi\) | |||||||
\(110\) | −3.18740 | + | 5.52074i | −0.303907 | + | 0.526382i | ||||
\(111\) | −4.45476 | − | 7.71587i | −0.422827 | − | 0.732358i | ||||
\(112\) | 0.954758 | − | 1.65369i | 0.0902161 | − | 0.156259i | ||||
\(113\) | −4.67687 | − | 8.10058i | −0.439963 | − | 0.762039i | 0.557723 | − | 0.830027i | \(-0.311675\pi\) |
−0.997686 | + | 0.0679884i | \(0.978342\pi\) | |||||||
\(114\) | −1.22212 | − | 2.11677i | −0.114462 | − | 0.198253i | ||||
\(115\) | 0.454758 | + | 0.787664i | 0.0424064 | + | 0.0734500i | ||||
\(116\) | 5.46528 | 0.507439 | ||||||||
\(117\) | 2.90952 | − | 5.03943i | 0.268985 | − | 0.465895i | ||||
\(118\) | −2.86427 | + | 4.96107i | −0.263678 | + | 0.456703i | ||||
\(119\) | 6.59692 | + | 11.4262i | 0.604738 | + | 1.04744i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −14.8190 | + | 25.6673i | −1.34718 | + | 2.33339i | ||||
\(122\) | 4.44423 | 0.402362 | ||||||||
\(123\) | 7.19383 | 0.648646 | ||||||||
\(124\) | 4.42004 | − | 3.38574i | 0.396931 | − | 0.304048i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.90952 | 0.170113 | ||||||||
\(127\) | 7.32956 | − | 12.6952i | 0.650393 | − | 1.12651i | −0.332635 | − | 0.943056i | \(-0.607938\pi\) |
0.983028 | − | 0.183458i | \(-0.0587291\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.232642 | − | 0.402947i | −0.0204829 | − | 0.0354775i | ||||
\(130\) | −2.90952 | + | 5.03943i | −0.255181 | + | 0.441987i | ||||
\(131\) | −1.14216 | + | 1.97827i | −0.0997908 | + | 0.172843i | −0.911598 | − | 0.411083i | \(-0.865151\pi\) |
0.811807 | + | 0.583926i | \(0.198484\pi\) | |||||||
\(132\) | 6.37480 | 0.554855 | ||||||||
\(133\) | 2.33365 | + | 4.04200i | 0.202353 | + | 0.350486i | ||||
\(134\) | 4.45476 | + | 7.71587i | 0.384832 | + | 0.666549i | ||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 3.45476 | − | 5.98382i | 0.296243 | − | 0.513108i | ||||
\(137\) | −9.73907 | − | 16.8686i | −0.832065 | − | 1.44118i | −0.896398 | − | 0.443251i | \(-0.853825\pi\) |
0.0643326 | − | 0.997929i | \(-0.479508\pi\) | |||||||
\(138\) | 0.454758 | − | 0.787664i | 0.0387116 | − | 0.0670504i | ||||
\(139\) | 11.3748 | 0.964798 | 0.482399 | − | 0.875952i | \(-0.339766\pi\) | ||||
0.482399 | + | 0.875952i | \(0.339766\pi\) | |||||||
\(140\) | −1.90952 | −0.161384 | ||||||||
\(141\) | −4.36427 | + | 7.55914i | −0.367538 | + | 0.636595i | ||||
\(142\) | −4.90952 | − | 8.50353i | −0.411997 | − | 0.713600i | ||||
\(143\) | −18.5476 | + | 32.1254i | −1.55103 | + | 2.68646i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −2.73264 | − | 4.73307i | −0.226934 | − | 0.393060i | ||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | 3.35375 | 0.276613 | ||||||||
\(148\) | 4.45476 | − | 7.71587i | 0.366179 | − | 0.634240i | ||||
\(149\) | 3.35784 | − | 5.81595i | 0.275085 | − | 0.476461i | −0.695071 | − | 0.718941i | \(-0.744627\pi\) |
0.970157 | + | 0.242479i | \(0.0779606\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | −4.55577 | −0.370743 | −0.185372 | − | 0.982669i | \(-0.559349\pi\) | ||||
−0.185372 | + | 0.982669i | \(0.559349\pi\) | |||||||
\(152\) | 1.22212 | − | 2.11677i | 0.0991267 | − | 0.171693i | ||||
\(153\) | 6.90952 | 0.558601 | ||||||||
\(154\) | −12.1728 | −0.980911 | ||||||||
\(155\) | −5.14216 | − | 2.13500i | −0.413028 | − | 0.171487i | ||||
\(156\) | 5.81903 | 0.465895 | ||||||||
\(157\) | −17.9434 | −1.43204 | −0.716021 | − | 0.698079i | \(-0.754038\pi\) | ||||
−0.716021 | + | 0.698079i | \(0.754038\pi\) | |||||||
\(158\) | −0.232642 | + | 0.402947i | −0.0185080 | + | 0.0320567i | ||||
\(159\) | −7.28432 | −0.577684 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −0.868368 | + | 1.50406i | −0.0684370 | + | 0.118536i | ||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 5.79798 | 0.454133 | 0.227066 | − | 0.973879i | \(-0.427087\pi\) | ||||
0.227066 | + | 0.973879i | \(0.427087\pi\) | |||||||
\(164\) | 3.59692 | + | 6.23004i | 0.280872 | + | 0.486484i | ||||
\(165\) | −3.18740 | − | 5.52074i | −0.248139 | − | 0.429789i | ||||
\(166\) | −6.32956 | − | 10.9631i | −0.491269 | − | 0.850903i | ||||
\(167\) | 8.06220 | − | 13.9641i | 0.623872 | − | 1.08058i | −0.364886 | − | 0.931052i | \(-0.618892\pi\) |
0.988758 | − | 0.149525i | \(-0.0477745\pi\) | |||||||
\(168\) | 0.954758 | + | 1.65369i | 0.0736612 | + | 0.127585i | ||||
\(169\) | −10.4306 | + | 18.0663i | −0.802351 | + | 1.38971i | ||||
\(170\) | −6.90952 | −0.529936 | ||||||||
\(171\) | 2.44423 | 0.186915 | ||||||||
\(172\) | 0.232642 | − | 0.402947i | 0.0177388 | − | 0.0307244i | ||||
\(173\) | 0.732642 | + | 1.26897i | 0.0557017 | + | 0.0964782i | 0.892532 | − | 0.450985i | \(-0.148927\pi\) |
−0.836830 | + | 0.547463i | \(0.815594\pi\) | |||||||
\(174\) | −2.73264 | + | 4.73307i | −0.207161 | + | 0.358813i | ||||
\(175\) | 0.954758 | + | 1.65369i | 0.0721729 | + | 0.125007i | ||||
\(176\) | 3.18740 | + | 5.52074i | 0.240259 | + | 0.416141i | ||||
\(177\) | −2.86427 | − | 4.96107i | −0.215292 | − | 0.372897i | ||||
\(178\) | 15.8190 | 1.18569 | ||||||||
\(179\) | 8.00643 | − | 13.8675i | 0.598429 | − | 1.03651i | −0.394624 | − | 0.918843i | \(-0.629125\pi\) |
0.993053 | − | 0.117667i | \(-0.0375414\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | 1.46528 | + | 2.53794i | 0.108914 | + | 0.188644i | 0.915330 | − | 0.402704i | \(-0.131929\pi\) |
−0.806417 | + | 0.591348i | \(0.798596\pi\) | |||||||
\(182\) | −11.1115 | −0.823642 | ||||||||
\(183\) | −2.22212 | + | 3.84882i | −0.164264 | + | 0.284513i | ||||
\(184\) | 0.909516 | 0.0670504 | ||||||||
\(185\) | −8.90952 | −0.655041 | ||||||||
\(186\) | 0.722116 | + | 5.52074i | 0.0529481 | + | 0.404800i | ||||
\(187\) | −44.0468 | −3.22102 | ||||||||
\(188\) | −8.72855 | −0.636595 | ||||||||
\(189\) | −0.954758 | + | 1.65369i | −0.0694484 | + | 0.120288i | ||||
\(190\) | −2.44423 | −0.177323 | ||||||||
\(191\) | 0.222116 | + | 0.384717i | 0.0160718 | + | 0.0278371i | 0.873949 | − | 0.486017i | \(-0.161551\pi\) |
−0.857878 | + | 0.513854i | \(0.828217\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −8.73264 | + | 15.1254i | −0.628589 | + | 1.08875i | 0.359246 | + | 0.933243i | \(0.383034\pi\) |
−0.987835 | + | 0.155506i | \(0.950299\pi\) | |||||||
\(194\) | −18.1728 | −1.30473 | ||||||||
\(195\) | −2.90952 | − | 5.03943i | −0.208355 | − | 0.360881i | ||||
\(196\) | 1.67687 | + | 2.90443i | 0.119777 | + | 0.207459i | ||||
\(197\) | 5.28432 | + | 9.15270i | 0.376492 | + | 0.652103i | 0.990549 | − | 0.137158i | \(-0.0437969\pi\) |
−0.614057 | + | 0.789261i | \(0.710464\pi\) | |||||||
\(198\) | −3.18740 | + | 5.52074i | −0.226519 | + | 0.392342i | ||||
\(199\) | 4.32956 | + | 7.49901i | 0.306914 | + | 0.531591i | 0.977686 | − | 0.210073i | \(-0.0673702\pi\) |
−0.670772 | + | 0.741664i | \(0.734037\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −8.90952 | −0.628429 | ||||||||
\(202\) | −1.93057 | −0.135834 | ||||||||
\(203\) | 5.21802 | − | 9.03788i | 0.366233 | − | 0.634335i | ||||
\(204\) | 3.45476 | + | 5.98382i | 0.241881 | + | 0.418951i | ||||
\(205\) | 3.59692 | − | 6.23004i | 0.251219 | − | 0.435125i | ||||
\(206\) | −1.86427 | − | 3.22902i | −0.129890 | − | 0.224976i | ||||
\(207\) | 0.454758 | + | 0.787664i | 0.0316079 | + | 0.0547464i | ||||
\(208\) | 2.90952 | + | 5.03943i | 0.201739 | + | 0.349422i | ||||
\(209\) | −15.5815 | −1.07779 | ||||||||
\(210\) | 0.954758 | − | 1.65369i | 0.0658846 | − | 0.114115i | ||||
\(211\) | 5.22212 | − | 9.04497i | 0.359505 | − | 0.622681i | −0.628373 | − | 0.777912i | \(-0.716279\pi\) |
0.987878 | + | 0.155231i | \(0.0496121\pi\) | |||||||
\(212\) | −3.64216 | − | 6.30840i | −0.250144 | − | 0.433263i | ||||
\(213\) | 9.81903 | 0.672789 | ||||||||
\(214\) | −0.954758 | + | 1.65369i | −0.0652659 | + | 0.113044i | ||||
\(215\) | −0.465283 | −0.0317320 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.37889 | − | 10.5419i | −0.0936053 | − | 0.715633i | ||||
\(218\) | 2.44423 | 0.165544 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 3.18740 | − | 5.52074i | 0.214894 | − | 0.372208i | ||||
\(221\) | −40.2067 | −2.70459 | ||||||||
\(222\) | 4.45476 | + | 7.71587i | 0.298984 | + | 0.517855i | ||||
\(223\) | 7.42004 | − | 12.8519i | 0.496883 | − | 0.860626i | −0.503111 | − | 0.864222i | \(-0.667811\pi\) |
0.999994 | + | 0.00359581i | \(0.00114458\pi\) | |||||||
\(224\) | −0.954758 | + | 1.65369i | −0.0637925 | + | 0.110492i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 4.67687 | + | 8.10058i | 0.311101 | + | 0.538843i | ||||
\(227\) | −1.48947 | − | 2.57985i | −0.0988599 | − | 0.171230i | 0.812353 | − | 0.583166i | \(-0.198186\pi\) |
−0.911213 | + | 0.411935i | \(0.864853\pi\) | |||||||
\(228\) | 1.22212 | + | 2.11677i | 0.0809366 | + | 0.140186i | ||||
\(229\) | 3.75683 | − | 6.50703i | 0.248259 | − | 0.429996i | −0.714784 | − | 0.699345i | \(-0.753475\pi\) |
0.963043 | + | 0.269349i | \(0.0868084\pi\) | |||||||
\(230\) | −0.454758 | − | 0.787664i | −0.0299859 | − | 0.0519370i | ||||
\(231\) | 6.08639 | − | 10.5419i | 0.400455 | − | 0.693609i | ||||
\(232\) | −5.46528 | −0.358813 | ||||||||
\(233\) | 12.9095 | 0.845731 | 0.422865 | − | 0.906193i | \(-0.361024\pi\) | ||||
0.422865 | + | 0.906193i | \(0.361024\pi\) | |||||||
\(234\) | −2.90952 | + | 5.03943i | −0.190201 | + | 0.329438i | ||||
\(235\) | 4.36427 | + | 7.55914i | 0.284694 | + | 0.493104i | ||||
\(236\) | 2.86427 | − | 4.96107i | 0.186448 | − | 0.322938i | ||||
\(237\) | −0.232642 | − | 0.402947i | −0.0151117 | − | 0.0261742i | ||||
\(238\) | −6.59692 | − | 11.4262i | −0.427615 | − | 0.740650i | ||||
\(239\) | 6.46528 | + | 11.1982i | 0.418204 | + | 0.724351i | 0.995759 | − | 0.0920008i | \(-0.0293262\pi\) |
−0.577555 | + | 0.816352i | \(0.695993\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 5.35784 | − | 9.28006i | 0.345129 | − | 0.597781i | −0.640248 | − | 0.768168i | \(-0.721169\pi\) |
0.985377 | + | 0.170387i | \(0.0545018\pi\) | |||||||
\(242\) | 14.8190 | − | 25.6673i | 0.952603 | − | 1.64996i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −4.44423 | −0.284513 | ||||||||
\(245\) | 1.67687 | − | 2.90443i | 0.107132 | − | 0.185557i | ||||
\(246\) | −7.19383 | −0.458662 | ||||||||
\(247\) | −14.2231 | −0.904992 | ||||||||
\(248\) | −4.42004 | + | 3.38574i | −0.280673 | + | 0.214995i | ||||
\(249\) | 12.6591 | 0.802239 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −1.76736 | + | 3.06115i | −0.111555 | + | 0.193218i | −0.916397 | − | 0.400270i | \(-0.868916\pi\) |
0.804843 | + | 0.593488i | \(0.202250\pi\) | |||||||
\(252\) | −1.90952 | −0.120288 | ||||||||
\(253\) | −2.89899 | − | 5.02120i | −0.182258 | − | 0.315680i | ||||
\(254\) | −7.32956 | + | 12.6952i | −0.459897 | + | 0.796566i | ||||
\(255\) | 3.45476 | − | 5.98382i | 0.216345 | − | 0.374721i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2948 | − | 21.2953i | −0.766931 | − | 1.32836i | −0.939220 | − | 0.343317i | \(-0.888449\pi\) |
0.172289 | − | 0.985047i | \(-0.444884\pi\) | |||||||
\(258\) | 0.232642 | + | 0.402947i | 0.0144836 | + | 0.0250864i | ||||
\(259\) | −8.50643 | − | 14.7336i | −0.528564 | − | 0.915500i | ||||
\(260\) | 2.90952 | − | 5.03943i | 0.180441 | − | 0.312532i | ||||
\(261\) | −2.73264 | − | 4.73307i | −0.169146 | − | 0.292970i | ||||
\(262\) | 1.14216 | − | 1.97827i | 0.0705627 | − | 0.122218i | ||||
\(263\) | −1.53472 | −0.0946347 | −0.0473173 | − | 0.998880i | \(-0.515067\pi\) | ||||
−0.0473173 | + | 0.998880i | \(0.515067\pi\) | |||||||
\(264\) | −6.37480 | −0.392342 | ||||||||
\(265\) | −3.64216 | + | 6.30840i | −0.223736 | + | 0.387522i | ||||
\(266\) | −2.33365 | − | 4.04200i | −0.143085 | − | 0.247831i | ||||
\(267\) | −7.90952 | + | 13.6997i | −0.484055 | + | 0.838407i | ||||
\(268\) | −4.45476 | − | 7.71587i | −0.272118 | − | 0.471322i | ||||
\(269\) | 7.96119 | + | 13.7892i | 0.485402 | + | 0.840741i | 0.999859 | − | 0.0167747i | \(-0.00533982\pi\) |
−0.514457 | + | 0.857516i | \(0.672006\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | 16.4781 | 1.00098 | 0.500488 | − | 0.865743i | \(-0.333154\pi\) | ||||
0.500488 | + | 0.865743i | \(0.333154\pi\) | |||||||
\(272\) | −3.45476 | + | 5.98382i | −0.209475 | + | 0.362822i | ||||
\(273\) | 5.55577 | − | 9.62287i | 0.336250 | − | 0.582403i | ||||
\(274\) | 9.73907 | + | 16.8686i | 0.588359 | + | 1.01907i | ||||
\(275\) | −6.37480 | −0.384415 | ||||||||
\(276\) | −0.454758 | + | 0.787664i | −0.0273732 | + | 0.0474118i | ||||
\(277\) | −25.6591 | −1.54171 | −0.770853 | − | 0.637013i | \(-0.780170\pi\) | ||||
−0.770853 | + | 0.637013i | \(0.780170\pi\) | |||||||
\(278\) | −11.3748 | −0.682215 | ||||||||
\(279\) | −5.14216 | − | 2.13500i | −0.307853 | − | 0.127819i | ||||
\(280\) | 1.90952 | 0.114115 | ||||||||
\(281\) | −31.1373 | −1.85749 | −0.928747 | − | 0.370715i | \(-0.879113\pi\) | ||||
−0.928747 | + | 0.370715i | \(0.879113\pi\) | |||||||
\(282\) | 4.36427 | − | 7.55914i | 0.259889 | − | 0.450140i | ||||
\(283\) | −16.9918 | −1.01006 | −0.505029 | − | 0.863102i | \(-0.668518\pi\) | ||||
−0.505029 | + | 0.863102i | \(0.668518\pi\) | |||||||
\(284\) | 4.90952 | + | 8.50353i | 0.291326 | + | 0.504592i | ||||
\(285\) | 1.22212 | − | 2.11677i | 0.0723919 | − | 0.125386i | ||||
\(286\) | 18.5476 | − | 32.1254i | 1.09674 | − | 1.89961i | ||||
\(287\) | 13.7367 | 0.810854 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −15.3707 | − | 26.6228i | −0.904159 | − | 1.56605i | ||||
\(290\) | 2.73264 | + | 4.73307i | 0.160466 | + | 0.277936i | ||||
\(291\) | 9.08639 | − | 15.7381i | 0.532654 | − | 0.922583i | ||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | −13.4612 | + | 23.3155i | −0.786411 | + | 1.36210i | 0.141741 | + | 0.989904i | \(0.454730\pi\) |
−0.928152 | + | 0.372200i | \(0.878603\pi\) | |||||||
\(294\) | −3.35375 | −0.195595 | ||||||||
\(295\) | −5.72855 | −0.333529 | ||||||||
\(296\) | −4.45476 | + | 7.71587i | −0.258928 | + | 0.448476i | ||||
\(297\) | −3.18740 | − | 5.52074i | −0.184952 | − | 0.320346i | ||||
\(298\) | −3.35784 | + | 5.81595i | −0.194515 | + | 0.336909i | ||||
\(299\) | −2.64625 | − | 4.58344i | −0.153037 | − | 0.265067i | ||||
\(300\) | 0.500000 | + | 0.866025i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | −0.444233 | − | 0.769434i | −0.0256052 | − | 0.0443494i | ||||
\(302\) | 4.55577 | 0.262155 | ||||||||
\(303\) | 0.965283 | − | 1.67192i | 0.0554541 | − | 0.0960493i | ||||
\(304\) | −1.22212 | + | 2.11677i | −0.0700932 | + | 0.121405i | ||||
\(305\) | 2.22212 | + | 3.84882i | 0.127238 | + | 0.220383i | ||||
\(306\) | −6.90952 | −0.394991 | ||||||||
\(307\) | −9.97171 | + | 17.2715i | −0.569116 | + | 0.985738i | 0.427538 | + | 0.903997i | \(0.359381\pi\) |
−0.996654 | + | 0.0817401i | \(0.973952\pi\) | |||||||
\(308\) | 12.1728 | 0.693609 | ||||||||
\(309\) | 3.72855 | 0.212110 | ||||||||
\(310\) | 5.14216 | + | 2.13500i | 0.292055 | + | 0.121260i | ||||
\(311\) | 24.5686 | 1.39316 | 0.696580 | − | 0.717480i | \(-0.254704\pi\) | ||||
0.696580 | + | 0.717480i | \(0.254704\pi\) | |||||||
\(312\) | −5.81903 | −0.329438 | ||||||||
\(313\) | −11.9265 | + | 20.6573i | −0.674124 | + | 1.16762i | 0.302600 | + | 0.953118i | \(0.402145\pi\) |
−0.976724 | + | 0.214500i | \(0.931188\pi\) | |||||||
\(314\) | 17.9434 | 1.01261 | ||||||||
\(315\) | 0.954758 | + | 1.65369i | 0.0537945 | + | 0.0931748i | ||||
\(316\) | 0.232642 | − | 0.402947i | 0.0130871 | − | 0.0226675i | ||||
\(317\) | 7.55167 | − | 13.0799i | 0.424144 | − | 0.734639i | −0.572196 | − | 0.820117i | \(-0.693908\pi\) |
0.996340 | + | 0.0854776i | \(0.0272416\pi\) | |||||||
\(318\) | 7.28432 | 0.408484 | ||||||||
\(319\) | 17.4200 | + | 30.1724i | 0.975335 | + | 1.68933i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −0.954758 | − | 1.65369i | −0.0532894 | − | 0.0922999i | ||||
\(322\) | 0.868368 | − | 1.50406i | 0.0483922 | − | 0.0838178i | ||||
\(323\) | −8.44423 | − | 14.6258i | −0.469850 | − | 0.813804i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −5.81903 | −0.322782 | ||||||||
\(326\) | −5.79798 | −0.321121 | ||||||||
\(327\) | −1.22212 | + | 2.11677i | −0.0675832 | + | 0.117058i | ||||
\(328\) | −3.59692 | − | 6.23004i | −0.198606 | − | 0.343996i | ||||
\(329\) | −8.33365 | + | 14.4343i | −0.459449 | + | 0.795789i | ||||
\(330\) | 3.18740 | + | 5.52074i | 0.175461 | + | 0.303907i | ||||
\(331\) | −0.0621987 | − | 0.107731i | −0.00341875 | − | 0.00592145i | 0.864311 | − | 0.502958i | \(-0.167755\pi\) |
−0.867730 | + | 0.497036i | \(0.834422\pi\) | |||||||
\(332\) | 6.32956 | + | 10.9631i | 0.347380 | + | 0.601679i | ||||
\(333\) | −8.90952 | −0.488238 | ||||||||
\(334\) | −8.06220 | + | 13.9641i | −0.441144 | + | 0.764084i | ||||
\(335\) | −4.45476 | + | 7.71587i | −0.243389 | + | 0.421563i | ||||
\(336\) | −0.954758 | − | 1.65369i | −0.0520863 | − | 0.0902161i | ||||
\(337\) | −11.4653 | −0.624554 | −0.312277 | − | 0.949991i | \(-0.601092\pi\) | ||||
−0.312277 | + | 0.949991i | \(0.601092\pi\) | |||||||
\(338\) | 10.4306 | − | 18.0663i | 0.567348 | − | 0.982676i | ||||
\(339\) | −9.35375 | −0.508026 | ||||||||
\(340\) | 6.90952 | 0.374721 | ||||||||
\(341\) | 32.7802 | + | 13.6102i | 1.77515 | + | 0.737033i | ||||
\(342\) | −2.44423 | −0.132169 | ||||||||
\(343\) | 19.7706 | 1.06751 | ||||||||
\(344\) | −0.232642 | + | 0.402947i | −0.0125432 | + | 0.0217254i | ||||
\(345\) | 0.909516 | 0.0489667 | ||||||||
\(346\) | −0.732642 | − | 1.26897i | −0.0393871 | − | 0.0682204i | ||||
\(347\) | −2.48947 | + | 4.31190i | −0.133642 | + | 0.231475i | −0.925078 | − | 0.379777i | \(-0.876001\pi\) |
0.791436 | + | 0.611252i | \(0.209334\pi\) | |||||||
\(348\) | 2.73264 | − | 4.73307i | 0.146485 | − | 0.253719i | ||||
\(349\) | −26.1244 | −1.39841 | −0.699203 | − | 0.714923i | \(-0.746462\pi\) | ||||
−0.699203 | + | 0.714923i | \(0.746462\pi\) | |||||||
\(350\) | −0.954758 | − | 1.65369i | −0.0510340 | − | 0.0883934i | ||||
\(351\) | −2.90952 | − | 5.03943i | −0.155298 | − | 0.268985i | ||||
\(352\) | −3.18740 | − | 5.52074i | −0.169889 | − | 0.294256i | ||||
\(353\) | 14.4054 | − | 24.9509i | 0.766723 | − | 1.32800i | −0.172607 | − | 0.984991i | \(-0.555219\pi\) |
0.939331 | − | 0.343013i | \(-0.111447\pi\) | |||||||
\(354\) | 2.86427 | + | 4.96107i | 0.152234 | + | 0.263678i | ||||
\(355\) | 4.90952 | − | 8.50353i | 0.260570 | − | 0.451321i | ||||
\(356\) | −15.8190 | −0.838407 | ||||||||
\(357\) | 13.1938 | 0.698292 | ||||||||
\(358\) | −8.00643 | + | 13.8675i | −0.423153 | + | 0.732923i | ||||
\(359\) | −3.31260 | − | 5.73759i | −0.174832 | − | 0.302819i | 0.765271 | − | 0.643708i | \(-0.222605\pi\) |
−0.940103 | + | 0.340890i | \(0.889272\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 6.51286 | + | 11.2806i | 0.342782 | + | 0.593716i | ||||
\(362\) | −1.46528 | − | 2.53794i | −0.0770136 | − | 0.133391i | ||||
\(363\) | 14.8190 | + | 25.6673i | 0.777797 | + | 1.34718i | ||||
\(364\) | 11.1115 | 0.582403 | ||||||||
\(365\) | 1.00000 | − | 1.73205i | 0.0523424 | − | 0.0906597i | ||||
\(366\) | 2.22212 | − | 3.84882i | 0.116152 | − | 0.201181i | ||||
\(367\) | 12.0000 | + | 20.7846i | 0.626395 | + | 1.08495i | 0.988269 | + | 0.152721i | \(0.0488036\pi\) |
−0.361874 | + | 0.932227i | \(0.617863\pi\) | |||||||
\(368\) | −0.909516 | −0.0474118 | ||||||||
\(369\) | 3.59692 | − | 6.23004i | 0.187248 | − | 0.324323i | ||||
\(370\) | 8.90952 | 0.463184 | ||||||||
\(371\) | −13.9095 | −0.722146 | ||||||||
\(372\) | −0.722116 | − | 5.52074i | −0.0374400 | − | 0.286237i | ||||
\(373\) | −27.4360 | −1.42058 | −0.710292 | − | 0.703907i | \(-0.751437\pi\) | ||||
−0.710292 | + | 0.703907i | \(0.751437\pi\) | |||||||
\(374\) | 44.0468 | 2.27760 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 8.72855 | 0.450140 | ||||||||
\(377\) | 15.9013 | + | 27.5419i | 0.818960 | + | 1.41848i | ||||
\(378\) | 0.954758 | − | 1.65369i | 0.0491075 | − | 0.0850566i | ||||
\(379\) | −9.26326 | + | 16.0444i | −0.475822 | + | 0.824148i | −0.999616 | − | 0.0276969i | \(-0.991183\pi\) |
0.523794 | + | 0.851845i | \(0.324516\pi\) | |||||||
\(380\) | 2.44423 | 0.125386 | ||||||||
\(381\) | −7.32956 | − | 12.6952i | −0.375505 | − | 0.650393i | ||||
\(382\) | −0.222116 | − | 0.384717i | −0.0113645 | − | 0.0196838i | ||||
\(383\) | −1.36427 | − | 2.36299i | −0.0697111 | − | 0.120743i | 0.829063 | − | 0.559155i | \(-0.188874\pi\) |
−0.898774 | + | 0.438412i | \(0.855541\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −6.08639 | − | 10.5419i | −0.310191 | − | 0.537267i | ||||
\(386\) | 8.73264 | − | 15.1254i | 0.444480 | − | 0.769862i | ||||
\(387\) | −0.465283 | −0.0236517 | ||||||||
\(388\) | 18.1728 | 0.922583 | ||||||||
\(389\) | 8.87071 | − | 15.3645i | 0.449763 | − | 0.779012i | −0.548608 | − | 0.836080i | \(-0.684842\pi\) |
0.998370 | + | 0.0570682i | \(0.0181753\pi\) | |||||||
\(390\) | 2.90952 | + | 5.03943i | 0.147329 | + | 0.255181i | ||||
\(391\) | 3.14216 | − | 5.44238i | 0.158906 | − | 0.275233i | ||||
\(392\) | −1.67687 | − | 2.90443i | −0.0846949 | − | 0.146696i | ||||
\(393\) | 1.14216 | + | 1.97827i | 0.0576142 | + | 0.0997908i | ||||
\(394\) | −5.28432 | − | 9.15270i | −0.266220 | − | 0.461106i | ||||
\(395\) | −0.465283 | −0.0234109 | ||||||||
\(396\) | 3.18740 | − | 5.52074i | 0.160173 | − | 0.277428i | ||||
\(397\) | 5.85784 | − | 10.1461i | 0.293997 | − | 0.509217i | −0.680754 | − | 0.732512i | \(-0.738348\pi\) |
0.974751 | + | 0.223295i | \(0.0716812\pi\) | |||||||
\(398\) | −4.32956 | − | 7.49901i | −0.217021 | − | 0.375892i | ||||
\(399\) | 4.66730 | 0.233657 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 14.7075 | 0.734457 | 0.367229 | − | 0.930131i | \(-0.380307\pi\) | ||||
0.367229 | + | 0.930131i | \(0.380307\pi\) | |||||||
\(402\) | 8.90952 | 0.444366 | ||||||||
\(403\) | 29.9224 | + | 12.4236i | 1.49054 | + | 0.618865i | ||||
\(404\) | 1.93057 | 0.0960493 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −5.21802 | + | 9.03788i | −0.258966 | + | 0.448542i | ||||
\(407\) | 56.7964 | 2.81529 | ||||||||
\(408\) | −3.45476 | − | 5.98382i | −0.171036 | − | 0.296243i | ||||
\(409\) | 11.6938 | − | 20.2543i | 0.578223 | − | 1.00151i | −0.417461 | − | 0.908695i | \(-0.637080\pi\) |
0.995683 | − | 0.0928161i | \(-0.0295869\pi\) | |||||||
\(410\) | −3.59692 | + | 6.23004i | −0.177639 | + | 0.307680i | ||||
\(411\) | −19.4781 | −0.960786 | ||||||||
\(412\) | 1.86427 | + | 3.22902i | 0.0918462 | + | 0.159082i | ||||
\(413\) | −5.46938 | − | 9.47324i | −0.269130 | − | 0.466148i | ||||
\(414\) | −0.454758 | − | 0.787664i | −0.0223501 | − | 0.0387116i | ||||
\(415\) | 6.32956 | − | 10.9631i | 0.310706 | − | 0.538158i | ||||
\(416\) | −2.90952 | − | 5.03943i | −0.142651 | − | 0.247078i | ||||
\(417\) | 5.68740 | − | 9.85087i | 0.278513 | − | 0.482399i | ||||
\(418\) | 15.5815 | 0.762116 | ||||||||
\(419\) | −14.3748 | −0.702255 | −0.351127 | − | 0.936328i | \(-0.614202\pi\) | ||||
−0.351127 | + | 0.936328i | \(0.614202\pi\) | |||||||
\(420\) | −0.954758 | + | 1.65369i | −0.0465874 | + | 0.0806918i | ||||
\(421\) | 7.15268 | + | 12.3888i | 0.348600 | + | 0.603794i | 0.986001 | − | 0.166739i | \(-0.0533237\pi\) |
−0.637401 | + | 0.770533i | \(0.719990\pi\) | |||||||
\(422\) | −5.22212 | + | 9.04497i | −0.254209 | + | 0.440302i | ||||
\(423\) | 4.36427 | + | 7.55914i | 0.212198 | + | 0.367538i | ||||
\(424\) | 3.64216 | + | 6.30840i | 0.176879 | + | 0.306363i | ||||
\(425\) | −3.45476 | − | 5.98382i | −0.167580 | − | 0.290258i | ||||
\(426\) | −9.81903 | −0.475734 | ||||||||
\(427\) | −4.24317 | + | 7.34938i | −0.205341 | + | 0.355661i | ||||
\(428\) | 0.954758 | − | 1.65369i | 0.0461500 | − | 0.0799341i | ||||
\(429\) | 18.5476 | + | 32.1254i | 0.895486 | + | 1.55103i | ||||
\(430\) | 0.465283 | 0.0224379 | ||||||||
\(431\) | 11.3255 | − | 19.6163i | 0.545528 | − | 0.944883i | −0.453045 | − | 0.891488i | \(-0.649662\pi\) |
0.998573 | − | 0.0533953i | \(-0.0170043\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 26.5686 | 1.27681 | 0.638403 | − | 0.769702i | \(-0.279595\pi\) | ||||
0.638403 | + | 0.769702i | \(0.279595\pi\) | |||||||
\(434\) | 1.37889 | + | 10.5419i | 0.0661890 | + | 0.506029i | ||||
\(435\) | −5.46528 | −0.262040 | ||||||||
\(436\) | −2.44423 | −0.117058 | ||||||||
\(437\) | 1.11153 | − | 1.92523i | 0.0531719 | − | 0.0920964i | ||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | 3.91595 | + | 6.78262i | 0.186898 | + | 0.323717i | 0.944214 | − | 0.329331i | \(-0.106823\pi\) |
−0.757316 | + | 0.653048i | \(0.773490\pi\) | |||||||
\(440\) | −3.18740 | + | 5.52074i | −0.151953 | + | 0.263191i | ||||
\(441\) | 1.67687 | − | 2.90443i | 0.0798512 | − | 0.138306i | ||||
\(442\) | 40.2067 | 1.91244 | ||||||||
\(443\) | 9.35375 | + | 16.2012i | 0.444410 | + | 0.769741i | 0.998011 | − | 0.0630414i | \(-0.0200800\pi\) |
−0.553601 | + | 0.832782i | \(0.686747\pi\) | |||||||
\(444\) | −4.45476 | − | 7.71587i | −0.211413 | − | 0.366179i | ||||
\(445\) | 7.90952 | + | 13.6997i | 0.374947 | + | 0.649427i | ||||
\(446\) | −7.42004 | + | 12.8519i | −0.351349 | + | 0.608555i | ||||
\(447\) | −3.35784 | − | 5.81595i | −0.158820 | − | 0.275085i | ||||
\(448\) | 0.954758 | − | 1.65369i | 0.0451081 | − | 0.0781295i | ||||
\(449\) | −14.8885 | −0.702630 | −0.351315 | − | 0.936257i | \(-0.614265\pi\) | ||||
−0.351315 | + | 0.936257i | \(0.614265\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −22.9296 | + | 39.7153i | −1.07971 | + | 1.87012i | ||||
\(452\) | −4.67687 | − | 8.10058i | −0.219982 | − | 0.381019i | ||||
\(453\) | −2.27788 | + | 3.94541i | −0.107024 | + | 0.185372i | ||||
\(454\) | 1.48947 | + | 2.57985i | 0.0699045 | + | 0.121078i | ||||
\(455\) | −5.55577 | − | 9.62287i | −0.260458 | − | 0.451127i | ||||
\(456\) | −1.22212 | − | 2.11677i | −0.0572308 | − | 0.0991267i | ||||
\(457\) | −14.2067 | −0.664561 | −0.332281 | − | 0.943181i | \(-0.607818\pi\) | ||||
−0.332281 | + | 0.943181i | \(0.607818\pi\) | |||||||
\(458\) | −3.75683 | + | 6.50703i | −0.175545 | + | 0.304053i | ||||
\(459\) | 3.45476 | − | 5.98382i | 0.161254 | − | 0.279301i | ||||
\(460\) | 0.454758 | + | 0.787664i | 0.0212032 | + | 0.0367250i | ||||
\(461\) | 22.6802 | 1.05632 | 0.528160 | − | 0.849145i | \(-0.322882\pi\) | ||||
0.528160 | + | 0.849145i | \(0.322882\pi\) | |||||||
\(462\) | −6.08639 | + | 10.5419i | −0.283165 | + | 0.490455i | ||||
\(463\) | −22.6170 | −1.05110 | −0.525551 | − | 0.850762i | \(-0.676141\pi\) | ||||
−0.525551 | + | 0.850762i | \(0.676141\pi\) | |||||||
\(464\) | 5.46528 | 0.253719 | ||||||||
\(465\) | −4.42004 | + | 3.38574i | −0.204974 | + | 0.157010i | ||||
\(466\) | −12.9095 | −0.598022 | ||||||||
\(467\) | 35.5897 | 1.64689 | 0.823447 | − | 0.567393i | \(-0.192048\pi\) | ||||
0.823447 | + | 0.567393i | \(0.192048\pi\) | |||||||
\(468\) | 2.90952 | − | 5.03943i | 0.134492 | − | 0.232948i | ||||
\(469\) | −17.0129 | −0.785581 | ||||||||
\(470\) | −4.36427 | − | 7.55914i | −0.201309 | − | 0.348677i | ||||
\(471\) | −8.97171 | + | 15.5395i | −0.413395 | + | 0.716021i | ||||
\(472\) | −2.86427 | + | 4.96107i | −0.131839 | + | 0.228352i | ||||
\(473\) | 2.96609 | 0.136381 | ||||||||
\(474\) | 0.232642 | + | 0.402947i | 0.0106856 | + | 0.0185080i | ||||
\(475\) | −1.22212 | − | 2.11677i | −0.0560745 | − | 0.0971240i | ||||
\(476\) | 6.59692 | + | 11.4262i | 0.302369 | + | 0.523719i | ||||
\(477\) | −3.64216 | + | 6.30840i | −0.166763 | + | 0.288842i | ||||
\(478\) | −6.46528 | − | 11.1982i | −0.295715 | − | 0.512194i | ||||
\(479\) | 1.24317 | − | 2.15323i | 0.0568017 | − | 0.0983835i | −0.836226 | − | 0.548384i | \(-0.815243\pi\) |
0.893028 | + | 0.450001i | \(0.148576\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 51.8448 | 2.36392 | ||||||||
\(482\) | −5.35784 | + | 9.28006i | −0.244043 | + | 0.422695i | ||||
\(483\) | 0.868368 | + | 1.50406i | 0.0395121 | + | 0.0684370i | ||||
\(484\) | −14.8190 | + | 25.6673i | −0.673592 | + | 1.16670i | ||||
\(485\) | −9.08639 | − | 15.7381i | −0.412592 | − | 0.714630i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 4.51053 | + | 7.81246i | 0.204391 | + | 0.354016i | 0.949939 | − | 0.312436i | \(-0.101145\pi\) |
−0.745547 | + | 0.666453i | \(0.767812\pi\) | |||||||
\(488\) | 4.44423 | 0.201181 | ||||||||
\(489\) | 2.89899 | − | 5.02120i | 0.131097 | − | 0.227066i | ||||
\(490\) | −1.67687 | + | 2.90443i | −0.0757535 | + | 0.131209i | ||||
\(491\) | −9.07587 | − | 15.7199i | −0.409588 | − | 0.709427i | 0.585255 | − | 0.810849i | \(-0.300994\pi\) |
−0.994844 | + | 0.101422i | \(0.967661\pi\) | |||||||
\(492\) | 7.19383 | 0.324323 | ||||||||
\(493\) | −18.8812 | + | 32.7033i | −0.850368 | + | 1.47288i | ||||
\(494\) | 14.2231 | 0.639926 | ||||||||
\(495\) | −6.37480 | −0.286526 | ||||||||
\(496\) | 4.42004 | − | 3.38574i | 0.198466 | − | 0.152024i | ||||
\(497\) | 18.7496 | 0.841034 | ||||||||
\(498\) | −12.6591 | −0.567268 | ||||||||
\(499\) | 15.5759 | − | 26.9782i | 0.697271 | − | 1.20771i | −0.272137 | − | 0.962258i | \(-0.587731\pi\) |
0.969409 | − | 0.245451i | \(-0.0789361\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −8.06220 | − | 13.9641i | −0.360192 | − | 0.623872i | ||||
\(502\) | 1.76736 | − | 3.06115i | 0.0788811 | − | 0.136626i | ||||
\(503\) | 13.4370 | − | 23.2736i | 0.599126 | − | 1.03772i | −0.393824 | − | 0.919186i | \(-0.628848\pi\) |
0.992950 | − | 0.118531i | \(-0.0378185\pi\) | |||||||
\(504\) | 1.90952 | 0.0850566 | ||||||||
\(505\) | −0.965283 | − | 1.67192i | −0.0429545 | − | 0.0743994i | ||||
\(506\) | 2.89899 | + | 5.02120i | 0.128876 | + | 0.223220i | ||||
\(507\) | 10.4306 | + | 18.0663i | 0.463238 | + | 0.802351i | ||||
\(508\) | 7.32956 | − | 12.6952i | 0.325197 | − | 0.563257i | ||||
\(509\) | −18.8877 | − | 32.7144i | −0.837181 | − | 1.45004i | −0.892242 | − | 0.451557i | \(-0.850869\pi\) |
0.0550614 | − | 0.998483i | \(-0.482465\pi\) | |||||||
\(510\) | −3.45476 | + | 5.98382i | −0.152979 | + | 0.264968i | ||||
\(511\) | 3.81903 | 0.168944 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.22212 | − | 2.11677i | 0.0539578 | − | 0.0934576i | ||||
\(514\) | 12.2948 | + | 21.2953i | 0.542302 | + | 0.939295i | ||||
\(515\) | 1.86427 | − | 3.22902i | 0.0821497 | − | 0.142287i | ||||
\(516\) | −0.232642 | − | 0.402947i | −0.0102415 | − | 0.0177388i | ||||
\(517\) | −27.8214 | − | 48.1880i | −1.22358 | − | 2.11931i | ||||
\(518\) | 8.50643 | + | 14.7336i | 0.373751 | + | 0.647356i | ||||
\(519\) | 1.46528 | 0.0643188 | ||||||||
\(520\) | −2.90952 | + | 5.03943i | −0.127591 | + | 0.220994i | ||||
\(521\) | 19.1938 | − | 33.2447i | 0.840897 | − | 1.45648i | −0.0482403 | − | 0.998836i | \(-0.515361\pi\) |
0.889137 | − | 0.457641i | \(-0.151305\pi\) | |||||||
\(522\) | 2.73264 | + | 4.73307i | 0.119604 | + | 0.207161i | ||||
\(523\) | 17.0339 | 0.744841 | 0.372421 | − | 0.928064i | \(-0.378528\pi\) | ||||
0.372421 | + | 0.928064i | \(0.378528\pi\) | |||||||
\(524\) | −1.14216 | + | 1.97827i | −0.0498954 | + | 0.0864213i | ||||
\(525\) | 1.90952 | 0.0833381 | ||||||||
\(526\) | 1.53472 | 0.0669168 | ||||||||
\(527\) | 4.98947 | + | 38.1456i | 0.217345 | + | 1.66165i | ||||
\(528\) | 6.37480 | 0.277428 | ||||||||
\(529\) | −22.1728 | −0.964034 | ||||||||
\(530\) | 3.64216 | − | 6.30840i | 0.158205 | − | 0.274019i | ||||
\(531\) | −5.72855 | −0.248598 | ||||||||
\(532\) | 2.33365 | + | 4.04200i | 0.101177 | + | 0.175243i | ||||
\(533\) | −20.9306 | + | 36.2528i | −0.906603 | + | 1.57028i | ||||
\(534\) | 7.90952 | − | 13.6997i | 0.342278 | − | 0.592843i | ||||
\(535\) | −1.90952 | −0.0825556 | ||||||||
\(536\) | 4.45476 | + | 7.71587i | 0.192416 | + | 0.333275i | ||||
\(537\) | −8.00643 | − | 13.8675i | −0.345503 | − | 0.598429i | ||||
\(538\) | −7.96119 | − | 13.7892i | −0.343231 | − | 0.594494i | ||||
\(539\) | −10.6897 | + | 18.5152i | −0.460440 | + | 0.797505i | ||||
\(540\) | 0.500000 | + | 0.866025i | 0.0215166 | + | 0.0372678i | ||||
\(541\) | 2.97171 | − | 5.14716i | 0.127764 | − | 0.221294i | −0.795046 | − | 0.606549i | \(-0.792553\pi\) |
0.922810 | + | 0.385255i | \(0.125887\pi\) | |||||||
\(542\) | −16.4781 | −0.707797 | ||||||||
\(543\) | 2.93057 | 0.125763 | ||||||||
\(544\) | 3.45476 | − | 5.98382i | 0.148122 | − | 0.256554i | ||||
\(545\) | 1.22212 | + | 2.11677i | 0.0523497 | + | 0.0906724i | ||||
\(546\) | −5.55577 | + | 9.62287i | −0.237765 | + | 0.411821i | ||||
\(547\) | 4.42647 | + | 7.66688i | 0.189262 | + | 0.327812i | 0.945005 | − | 0.327057i | \(-0.106057\pi\) |
−0.755742 | + | 0.654869i | \(0.772724\pi\) | |||||||
\(548\) | −9.73907 | − | 16.8686i | −0.416033 | − | 0.720590i | ||||
\(549\) | 2.22212 | + | 3.84882i | 0.0948376 | + | 0.164264i | ||||
\(550\) | 6.37480 | 0.271822 | ||||||||
\(551\) | −6.67921 | + | 11.5687i | −0.284544 | + | 0.492845i | ||||
\(552\) | 0.454758 | − | 0.787664i | 0.0193558 | − | 0.0335252i | ||||
\(553\) | −0.444233 | − | 0.769434i | −0.0188907 | − | 0.0327197i | ||||
\(554\) | 25.6591 | 1.09015 | ||||||||
\(555\) | −4.45476 | + | 7.71587i | −0.189094 | + | 0.327520i | ||||
\(556\) | 11.3748 | 0.482399 | ||||||||
\(557\) | −9.42318 | −0.399273 | −0.199637 | − | 0.979870i | \(-0.563976\pi\) | ||||
−0.199637 | + | 0.979870i | \(0.563976\pi\) | |||||||
\(558\) | 5.14216 | + | 2.13500i | 0.217685 | + | 0.0903817i | ||||
\(559\) | 2.70750 | 0.114515 | ||||||||
\(560\) | −1.90952 | −0.0806918 | ||||||||
\(561\) | −22.0234 | + | 38.1456i | −0.929828 | + | 1.61051i | ||||
\(562\) | 31.1373 | 1.31345 | ||||||||
\(563\) | −19.5023 | − | 33.7790i | −0.821926 | − | 1.42362i | −0.904246 | − | 0.427011i | \(-0.859567\pi\) |
0.0823209 | − | 0.996606i | \(-0.473767\pi\) | |||||||
\(564\) | −4.36427 | + | 7.55914i | −0.183769 | + | 0.318297i | ||||
\(565\) | −4.67687 | + | 8.10058i | −0.196758 | + | 0.340794i | ||||
\(566\) | 16.9918 | 0.714219 | ||||||||
\(567\) | 0.954758 | + | 1.65369i | 0.0400961 | + | 0.0694484i | ||||
\(568\) | −4.90952 | − | 8.50353i | −0.205999 | − | 0.356800i | ||||
\(569\) | −22.5897 | − | 39.1265i | −0.947009 | − | 1.64027i | −0.751679 | − | 0.659530i | \(-0.770756\pi\) |
−0.195330 | − | 0.980738i | \(-0.562578\pi\) | |||||||
\(570\) | −1.22212 | + | 2.11677i | −0.0511888 | + | 0.0886616i | ||||
\(571\) | −5.46528 | − | 9.46615i | −0.228715 | − | 0.396146i | 0.728713 | − | 0.684820i | \(-0.240119\pi\) |
−0.957428 | + | 0.288674i | \(0.906786\pi\) | |||||||
\(572\) | −18.5476 | + | 32.1254i | −0.775513 | + | 1.34323i | ||||
\(573\) | 0.444233 | 0.0185581 | ||||||||
\(574\) | −13.7367 | −0.573360 | ||||||||
\(575\) | 0.454758 | − | 0.787664i | 0.0189647 | − | 0.0328479i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −2.71568 | + | 4.70370i | −0.113055 | + | 0.195818i | −0.917001 | − | 0.398885i | \(-0.869397\pi\) |
0.803945 | + | 0.594703i | \(0.202730\pi\) | |||||||
\(578\) | 15.3707 | + | 26.6228i | 0.639337 | + | 1.10736i | ||||
\(579\) | 8.73264 | + | 15.1254i | 0.362916 | + | 0.628589i | ||||
\(580\) | −2.73264 | − | 4.73307i | −0.113467 | − | 0.196530i | ||||
\(581\) | 24.1728 | 1.00286 | ||||||||
\(582\) | −9.08639 | + | 15.7381i | −0.376643 | + | 0.652365i | ||||
\(583\) | 23.2180 | − | 40.2148i | 0.961592 | − | 1.66553i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | −5.81903 | −0.240587 | ||||||||
\(586\) | 13.4612 | − | 23.3155i | 0.556077 | − | 0.963153i | ||||
\(587\) | −39.9095 | −1.64724 | −0.823621 | − | 0.567141i | \(-0.808050\pi\) | ||||
−0.823621 | + | 0.567141i | \(0.808050\pi\) | |||||||
\(588\) | 3.35375 | 0.138306 | ||||||||
\(589\) | 1.76502 | + | 13.4940i | 0.0727264 | + | 0.556009i | ||||
\(590\) | 5.72855 | 0.235841 | ||||||||
\(591\) | 10.5686 | 0.434735 | ||||||||
\(592\) | 4.45476 | − | 7.71587i | 0.183089 | − | 0.317120i | ||||
\(593\) | 43.5394 | 1.78795 | 0.893974 | − | 0.448118i | \(-0.147906\pi\) | ||||
0.893974 | + | 0.448118i | \(0.147906\pi\) | |||||||
\(594\) | 3.18740 | + | 5.52074i | 0.130781 | + | 0.226519i | ||||
\(595\) | 6.59692 | − | 11.4262i | 0.270447 | − | 0.468428i | ||||
\(596\) | 3.35784 | − | 5.81595i | 0.137543 | − | 0.238231i | ||||
\(597\) | 8.65911 | 0.354394 | ||||||||
\(598\) | 2.64625 | + | 4.58344i | 0.108213 | + | 0.187431i | ||||
\(599\) | −6.28432 | − | 10.8848i | −0.256770 | − | 0.444739i | 0.708605 | − | 0.705606i | \(-0.249325\pi\) |
−0.965375 | + | 0.260867i | \(0.915992\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | 1.41361 | − | 2.44844i | 0.0576623 | − | 0.0998741i | −0.835753 | − | 0.549105i | \(-0.814969\pi\) |
0.893416 | + | 0.449231i | \(0.148302\pi\) | |||||||
\(602\) | 0.444233 | + | 0.769434i | 0.0181056 | + | 0.0313598i | ||||
\(603\) | −4.45476 | + | 7.71587i | −0.181412 | + | 0.314214i | ||||
\(604\) | −4.55577 | −0.185372 | ||||||||
\(605\) | 29.6381 | 1.20496 | ||||||||
\(606\) | −0.965283 | + | 1.67192i | −0.0392119 | + | 0.0679171i | ||||
\(607\) | 4.93057 | + | 8.53999i | 0.200126 | + | 0.346628i | 0.948569 | − | 0.316571i | \(-0.102532\pi\) |
−0.748443 | + | 0.663199i | \(0.769198\pi\) | |||||||
\(608\) | 1.22212 | − | 2.11677i | 0.0495634 | − | 0.0858463i | ||||
\(609\) | −5.21802 | − | 9.03788i | −0.211445 | − | 0.366233i | ||||
\(610\) | −2.22212 | − | 3.84882i | −0.0899709 | − | 0.155834i | ||||
\(611\) | −25.3958 | − | 43.9869i | −1.02741 | − | 1.77952i | ||||
\(612\) | 6.90952 | 0.279301 | ||||||||
\(613\) | −19.4781 | + | 33.7371i | −0.786715 | + | 1.36263i | 0.141254 | + | 0.989973i | \(0.454886\pi\) |
−0.927969 | + | 0.372657i | \(0.878447\pi\) | |||||||
\(614\) | 9.97171 | − | 17.2715i | 0.402426 | − | 0.697022i | ||||
\(615\) | −3.59692 | − | 6.23004i | −0.145042 | − | 0.251219i | ||||
\(616\) | −12.1728 | −0.490455 | ||||||||
\(617\) | −18.2738 | + | 31.6511i | −0.735675 | + | 1.27423i | 0.218751 | + | 0.975781i | \(0.429802\pi\) |
−0.954427 | + | 0.298446i | \(0.903532\pi\) | |||||||
\(618\) | −3.72855 | −0.149984 | ||||||||
\(619\) | −45.6802 | −1.83604 | −0.918020 | − | 0.396533i | \(-0.870213\pi\) | ||||
−0.918020 | + | 0.396533i | \(0.870213\pi\) | |||||||
\(620\) | −5.14216 | − | 2.13500i | −0.206514 | − | 0.0857436i | ||||
\(621\) | 0.909516 | 0.0364976 | ||||||||
\(622\) | −24.5686 | −0.985112 | ||||||||
\(623\) | −15.1033 | + | 26.1598i | −0.605103 | + | 1.04807i | ||||
\(624\) | 5.81903 | 0.232948 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 11.9265 | − | 20.6573i | 0.476678 | − | 0.825630i | ||||
\(627\) | −7.79075 | + | 13.4940i | −0.311132 | + | 0.538897i | ||||
\(628\) | −17.9434 | −0.716021 | ||||||||
\(629\) | 30.7802 | + | 53.3129i | 1.22729 | + | 2.12572i | ||||
\(630\) | −0.954758 | − | 1.65369i | −0.0380385 | − | 0.0658846i | ||||
\(631\) | 9.16635 | + | 15.8766i | 0.364907 | + | 0.632037i | 0.988761 | − | 0.149504i | \(-0.0477676\pi\) |
−0.623855 | + | 0.781540i | \(0.714434\pi\) | |||||||
\(632\) | −0.232642 | + | 0.402947i | −0.00925399 | + | 0.0160284i | ||||
\(633\) | −5.22212 | − | 9.04497i | −0.207560 | − | 0.359505i | ||||
\(634\) | −7.55167 | + | 13.0799i | −0.299915 | + | 0.519468i | ||||
\(635\) | −14.6591 | −0.581729 | ||||||||
\(636\) | −7.28432 | −0.288842 | ||||||||
\(637\) | −9.75779 | + | 16.9010i | −0.386618 | + | 0.669641i | ||||
\(638\) | −17.4200 | − | 30.1724i | −0.689666 | − | 1.19454i | ||||
\(639\) | 4.90952 | − | 8.50353i | 0.194217 | − | 0.336394i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −6.86837 | − | 11.8964i | −0.271284 | − | 0.469878i | 0.697907 | − | 0.716189i | \(-0.254115\pi\) |
−0.969191 | + | 0.246311i | \(0.920782\pi\) | |||||||
\(642\) | 0.954758 | + | 1.65369i | 0.0376813 | + | 0.0652659i | ||||
\(643\) | 40.6509 | 1.60312 | 0.801558 | − | 0.597917i | \(-0.204005\pi\) | ||||
0.801558 | + | 0.597917i | \(0.204005\pi\) | |||||||
\(644\) | −0.868368 | + | 1.50406i | −0.0342185 | + | 0.0592681i | ||||
\(645\) | −0.232642 | + | 0.402947i | −0.00916025 | + | 0.0158660i | ||||
\(646\) | 8.44423 | + | 14.6258i | 0.332234 | + | 0.575446i | ||||
\(647\) | 30.6930 | 1.20667 | 0.603334 | − | 0.797489i | \(-0.293839\pi\) | ||||
0.603334 | + | 0.797489i | \(0.293839\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 36.5183 | 1.43347 | ||||||||
\(650\) | 5.81903 | 0.228241 | ||||||||
\(651\) | −9.81903 | − | 4.07681i | −0.384838 | − | 0.159783i | ||||
\(652\) | 5.79798 | 0.227066 | ||||||||
\(653\) | −15.6463 | −0.612285 | −0.306143 | − | 0.951986i | \(-0.599038\pi\) | ||||
−0.306143 | + | 0.951986i | \(0.599038\pi\) | |||||||
\(654\) | 1.22212 | − | 2.11677i | 0.0477885 | − | 0.0827722i | ||||
\(655\) | 2.28432 | 0.0892556 | ||||||||
\(656\) | 3.59692 | + | 6.23004i | 0.140436 | + | 0.243242i | ||||
\(657\) | 1.00000 | − | 1.73205i | 0.0390137 | − | 0.0675737i | ||||
\(658\) | 8.33365 | − | 14.4343i | 0.324880 | − | 0.562708i | ||||
\(659\) | 27.8319 | 1.08418 | 0.542088 | − | 0.840321i | \(-0.317634\pi\) | ||||
0.542088 | + | 0.840321i | \(0.317634\pi\) | |||||||
\(660\) | −3.18740 | − | 5.52074i | −0.124069 | − | 0.214894i | ||||
\(661\) | 0.0411483 | + | 0.0712710i | 0.00160048 | + | 0.00277212i | 0.866825 | − | 0.498613i | \(-0.166157\pi\) |
−0.865224 | + | 0.501385i | \(0.832824\pi\) | |||||||
\(662\) | 0.0621987 | + | 0.107731i | 0.00241742 | + | 0.00418710i | ||||
\(663\) | −20.1033 | + | 34.8200i | −0.780749 | + | 1.35230i | ||||
\(664\) | −6.32956 | − | 10.9631i | −0.245634 | − | 0.425451i | ||||
\(665\) | 2.33365 | − | 4.04200i | 0.0904951 | − | 0.156742i | ||||
\(666\) | 8.90952 | 0.345237 | ||||||||
\(667\) | −4.97076 | −0.192469 | ||||||||
\(668\) | 8.06220 | − | 13.9641i | 0.311936 | − | 0.540289i | ||||
\(669\) | −7.42004 | − | 12.8519i | −0.286875 | − | 0.496883i | ||||
\(670\) | 4.45476 | − | 7.71587i | 0.172102 | − | 0.298090i | ||||
\(671\) | −14.1655 | − | 24.5354i | −0.546855 | − | 0.947180i | ||||
\(672\) | 0.954758 | + | 1.65369i | 0.0368306 | + | 0.0637925i | ||||
\(673\) | −4.73264 | − | 8.19718i | −0.182430 | − | 0.315978i | 0.760278 | − | 0.649598i | \(-0.225063\pi\) |
−0.942707 | + | 0.333620i | \(0.891730\pi\) | |||||||
\(674\) | 11.4653 | 0.441626 | ||||||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | −10.4306 | + | 18.0663i | −0.401176 | + | 0.694857i | ||||
\(677\) | −7.39176 | − | 12.8029i | −0.284088 | − | 0.492055i | 0.688299 | − | 0.725427i | \(-0.258358\pi\) |
−0.972388 | + | 0.233371i | \(0.925024\pi\) | |||||||
\(678\) | 9.35375 | 0.359229 | ||||||||
\(679\) | 17.3506 | − | 30.0521i | 0.665855 | − | 1.15330i | ||||
\(680\) | −6.90952 | −0.264968 | ||||||||
\(681\) | −2.97895 | −0.114154 | ||||||||
\(682\) | −32.7802 | − | 13.6102i | −1.25522 | − | 0.521161i | ||||
\(683\) | 11.5219 | 0.440871 | 0.220436 | − | 0.975401i | \(-0.429252\pi\) | ||||
0.220436 | + | 0.975401i | \(0.429252\pi\) | |||||||
\(684\) | 2.44423 | 0.0934576 | ||||||||
\(685\) | −9.73907 | + | 16.8686i | −0.372111 | + | 0.644515i | ||||
\(686\) | −19.7706 | −0.754847 | ||||||||
\(687\) | −3.75683 | − | 6.50703i | −0.143332 | − | 0.248259i | ||||
\(688\) | 0.232642 | − | 0.402947i | 0.00886938 | − | 0.0153622i | ||||
\(689\) | 21.1938 | − | 36.7088i | 0.807421 | − | 1.39849i | ||||
\(690\) | −0.909516 | −0.0346247 | ||||||||
\(691\) | 5.86837 | + | 10.1643i | 0.223243 | + | 0.386669i | 0.955791 | − | 0.294047i | \(-0.0950023\pi\) |
−0.732548 | + | 0.680716i | \(0.761669\pi\) | |||||||
\(692\) | 0.732642 | + | 1.26897i | 0.0278509 | + | 0.0482391i | ||||
\(693\) | −6.08639 | − | 10.5419i | −0.231203 | − | 0.400455i | ||||
\(694\) | 2.48947 | − | 4.31190i | 0.0944992 | − | 0.163677i | ||||
\(695\) | −5.68740 | − | 9.85087i | −0.215735 | − | 0.373665i | ||||
\(696\) | −2.73264 | + | 4.73307i | −0.103581 | + | 0.179407i | ||||
\(697\) | −49.7059 | −1.88274 | ||||||||
\(698\) | 26.1244 | 0.988823 | ||||||||
\(699\) | 6.45476 | − | 11.1800i | 0.244141 | − | 0.422865i | ||||
\(700\) | 0.954758 | + | 1.65369i | 0.0360865 | + | 0.0625036i | ||||
\(701\) | −6.68097 | + | 11.5718i | −0.252337 | + | 0.437060i | −0.964169 | − | 0.265290i | \(-0.914532\pi\) |
0.711832 | + | 0.702350i | \(0.247866\pi\) | |||||||
\(702\) | 2.90952 | + | 5.03943i | 0.109813 | + | 0.190201i | ||||
\(703\) | 10.8885 | + | 18.8594i | 0.410666 | + | 0.711295i | ||||
\(704\) | 3.18740 | + | 5.52074i | 0.120130 | + | 0.208071i | ||||
\(705\) | 8.72855 | 0.328736 | ||||||||
\(706\) | −14.4054 | + | 24.9509i | −0.542155 | + | 0.939040i | ||||
\(707\) | 1.84322 | − | 3.19256i | 0.0693216 | − | 0.120068i | ||||
\(708\) | −2.86427 | − | 4.96107i | −0.107646 | − | 0.186448i | ||||
\(709\) | −24.1665 | −0.907592 | −0.453796 | − | 0.891106i | \(-0.649930\pi\) | ||||
−0.453796 | + | 0.891106i | \(0.649930\pi\) | |||||||
\(710\) | −4.90952 | + | 8.50353i | −0.184251 | + | 0.319132i | ||||
\(711\) | −0.465283 | −0.0174495 | ||||||||
\(712\) | 15.8190 | 0.592843 | ||||||||
\(713\) | −4.02010 | + | 3.07938i | −0.150554 | + | 0.115324i | ||||
\(714\) | −13.1938 | −0.493767 | ||||||||
\(715\) | 37.0952 | 1.38728 | ||||||||
\(716\) | 8.00643 | − | 13.8675i | 0.299214 | − | 0.518255i | ||||
\(717\) | 12.9306 | 0.482901 | ||||||||
\(718\) | 3.31260 | + | 5.73759i | 0.123625 | + | 0.214125i | ||||
\(719\) | −5.84732 | + | 10.1279i | −0.218068 | + | 0.377705i | −0.954217 | − | 0.299114i | \(-0.903309\pi\) |
0.736149 | + | 0.676819i | \(0.236642\pi\) | |||||||
\(720\) | −0.500000 | + | 0.866025i | −0.0186339 | + | 0.0322749i | ||||
\(721\) | 7.11972 | 0.265152 | ||||||||
\(722\) | −6.51286 | − | 11.2806i | −0.242384 | − | 0.419821i | ||||
\(723\) | −5.35784 | − | 9.28006i | −0.199260 | − | 0.345129i | ||||
\(724\) | 1.46528 | + | 2.53794i | 0.0544568 | + | 0.0943220i | ||||
\(725\) | −2.73264 | + | 4.73307i | −0.101488 | + | 0.175782i | ||||
\(726\) | −14.8190 | − | 25.6673i | −0.549986 | − | 0.952603i | ||||
\(727\) | 11.8771 | − | 20.5718i | 0.440499 | − | 0.762966i | −0.557228 | − | 0.830360i | \(-0.688135\pi\) |
0.997726 | + | 0.0673936i | \(0.0214683\pi\) | |||||||
\(728\) | −11.1115 | −0.411821 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | + | 1.73205i | −0.0370117 | + | 0.0641061i | ||||
\(731\) | 1.60744 | + | 2.78417i | 0.0594533 | + | 0.102976i | ||||
\(732\) | −2.22212 | + | 3.84882i | −0.0821318 | + | 0.142256i | ||||
\(733\) | −24.0645 | − | 41.6810i | −0.888844 | − | 1.53952i | −0.841244 | − | 0.540656i | \(-0.818176\pi\) |
−0.0476004 | − | 0.998866i | \(-0.515157\pi\) | |||||||
\(734\) | −12.0000 | − | 20.7846i | −0.442928 | − | 0.767174i | ||||
\(735\) | −1.67687 | − | 2.90443i | −0.0618524 | − | 0.107132i | ||||
\(736\) | 0.909516 | 0.0335252 | ||||||||
\(737\) | 28.3982 | − | 49.1871i | 1.04606 | − | 1.81183i | ||||
\(738\) | −3.59692 | + | 6.23004i | −0.132404 | + | 0.229331i | ||||
\(739\) | 2.49357 | + | 4.31899i | 0.0917274 | + | 0.158877i | 0.908238 | − | 0.418454i | \(-0.137428\pi\) |
−0.816511 | + | 0.577330i | \(0.804094\pi\) | |||||||
\(740\) | −8.90952 | −0.327520 | ||||||||
\(741\) | −7.11153 | + | 12.3175i | −0.261249 | + | 0.452496i | ||||
\(742\) | 13.9095 | 0.510634 | ||||||||
\(743\) | −28.2843 | −1.03765 | −0.518825 | − | 0.854880i | \(-0.673631\pi\) | ||||
−0.518825 | + | 0.854880i | \(0.673631\pi\) | |||||||
\(744\) | 0.722116 | + | 5.52074i | 0.0264741 | + | 0.202400i | ||||
\(745\) | −6.71568 | −0.246044 | ||||||||
\(746\) | 27.4360 | 1.00450 | ||||||||
\(747\) | 6.32956 | − | 10.9631i | 0.231586 | − | 0.401119i | ||||
\(748\) | −44.0468 | −1.61051 | ||||||||
\(749\) | −1.82313 | − | 3.15775i | −0.0666156 | − | 0.115382i | ||||
\(750\) | −0.500000 | + | 0.866025i | −0.0182574 | + | 0.0316228i | ||||
\(751\) | 2.74317 | − | 4.75130i | 0.100100 | − | 0.173378i | −0.811626 | − | 0.584177i | \(-0.801417\pi\) |
0.911726 | + | 0.410800i | \(0.134751\pi\) | |||||||
\(752\) | −8.72855 | −0.318297 | ||||||||
\(753\) | 1.76736 | + | 3.06115i | 0.0644061 | + | 0.111555i | ||||
\(754\) | −15.9013 | − | 27.5419i | −0.579092 | − | 1.00302i | ||||
\(755\) | 2.27788 | + | 3.94541i | 0.0829007 | + | 0.143588i | ||||
\(756\) | −0.954758 | + | 1.65369i | −0.0347242 | + | 0.0601441i | ||||
\(757\) | 1.12111 | + | 1.94181i | 0.0407473 | + | 0.0705765i | 0.885680 | − | 0.464297i | \(-0.153693\pi\) |
−0.844932 | + | 0.534873i | \(0.820359\pi\) | |||||||
\(758\) | 9.26326 | − | 16.0444i | 0.336457 | − | 0.582760i | ||||
\(759\) | −5.79798 | −0.210453 | ||||||||
\(760\) | −2.44423 | −0.0886616 | ||||||||
\(761\) | −11.9717 | + | 20.7356i | −0.433974 | + | 0.751666i | −0.997211 | − | 0.0746298i | \(-0.976222\pi\) |
0.563237 | + | 0.826295i | \(0.309556\pi\) | |||||||
\(762\) | 7.32956 | + | 12.6952i | 0.265522 | + | 0.459897i | ||||
\(763\) | −2.33365 | + | 4.04200i | −0.0844838 | + | 0.146330i | ||||
\(764\) | 0.222116 | + | 0.384717i | 0.00803589 | + | 0.0139186i | ||||
\(765\) | −3.45476 | − | 5.98382i | −0.124907 | − | 0.216345i | ||||
\(766\) | 1.36427 | + | 2.36299i | 0.0492932 | + | 0.0853784i | ||||
\(767\) | 33.3346 | 1.20364 | ||||||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −6.73264 | + | 11.6613i | −0.242785 | + | 0.420516i | −0.961507 | − | 0.274782i | \(-0.911394\pi\) |
0.718721 | + | 0.695298i | \(0.244728\pi\) | |||||||
\(770\) | 6.08639 | + | 10.5419i | 0.219338 | + | 0.379905i | ||||
\(771\) | −24.5897 | −0.885576 | ||||||||
\(772\) | −8.73264 | + | 15.1254i | −0.314295 | + | 0.544374i | ||||
\(773\) | −2.36194 | −0.0849529 | −0.0424765 | − | 0.999097i | \(-0.513525\pi\) | ||||
−0.0424765 | + | 0.999097i | \(0.513525\pi\) | |||||||
\(774\) | 0.465283 | 0.0167243 | ||||||||
\(775\) | 0.722116 | + | 5.52074i | 0.0259392 | + | 0.198311i | ||||
\(776\) | −18.1728 | −0.652365 | ||||||||
\(777\) | −17.0129 | −0.610333 | ||||||||
\(778\) | −8.87071 | + | 15.3645i | −0.318030 | + | 0.550844i | ||||
\(779\) | −17.5834 | −0.629991 | ||||||||
\(780\) | −2.90952 | − | 5.03943i | −0.104177 | − | 0.180441i | ||||
\(781\) | −31.2972 | + | 54.2083i | −1.11990 | + | 1.93973i | ||||
\(782\) | −3.14216 | + | 5.44238i | −0.112363 | + | 0.194619i | ||||
\(783\) | −5.46528 | −0.195313 | ||||||||
\(784\) | 1.67687 | + | 2.90443i | 0.0598884 | + | 0.103730i | ||||
\(785\) | 8.97171 | + | 15.5395i | 0.320214 | + | 0.554627i | ||||
\(786\) | −1.14216 | − | 1.97827i | −0.0407394 | − | 0.0705627i | ||||
\(787\) | 4.19149 | − | 7.25988i | 0.149411 | − | 0.258787i | −0.781599 | − | 0.623781i | \(-0.785596\pi\) |
0.931010 | + | 0.364994i | \(0.118929\pi\) | |||||||
\(788\) | 5.28432 | + | 9.15270i | 0.188246 | + | 0.326052i | ||||
\(789\) | −0.767358 | + | 1.32910i | −0.0273187 | + | 0.0473173i | ||||
\(790\) | 0.465283 | 0.0165540 | ||||||||
\(791\) | −17.8611 | −0.635069 | ||||||||
\(792\) | −3.18740 | + | 5.52074i | −0.113259 | + | 0.196171i | ||||
\(793\) | −12.9306 | − | 22.3964i | −0.459178 | − | 0.795319i | ||||
\(794\) | −5.85784 | + | 10.1461i | −0.207887 | + | 0.360071i | ||||
\(795\) | 3.64216 | + | 6.30840i | 0.129174 | + | 0.223736i | ||||
\(796\) | 4.32956 | + | 7.49901i | 0.153457 | + | 0.265795i | ||||
\(797\) | 4.08639 | + | 7.07784i | 0.144747 | + | 0.250710i | 0.929279 | − | 0.369379i | \(-0.120430\pi\) |
−0.784531 | + | 0.620089i | \(0.787096\pi\) | |||||||
\(798\) | −4.66730 | −0.165221 | ||||||||
\(799\) | 30.1550 | − | 52.2300i | 1.06681 | − | 1.84777i | ||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 7.90952 | + | 13.6997i | 0.279469 | + | 0.484055i | ||||
\(802\) | −14.7075 | −0.519340 | ||||||||
\(803\) | −6.37480 | + | 11.0415i | −0.224962 | + | 0.389645i | ||||
\(804\) | −8.90952 | −0.314214 | ||||||||
\(805\) | 1.73674 | 0.0612119 | ||||||||
\(806\) | −29.9224 | − | 12.4236i | −1.05397 | − | 0.437603i | ||||
\(807\) | 15.9224 | 0.560494 | ||||||||
\(808\) | −1.93057 | −0.0679171 | ||||||||
\(809\) | 8.11058 | − | 14.0479i | 0.285153 | − | 0.493899i | −0.687493 | − | 0.726191i | \(-0.741289\pi\) |
0.972646 | + | 0.232291i | \(0.0746223\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −19.2843 | − | 33.4014i | −0.677164 | − | 1.17288i | −0.975831 | − | 0.218525i | \(-0.929875\pi\) |
0.298667 | − | 0.954357i | \(-0.403458\pi\) | |||||||
\(812\) | 5.21802 | − | 9.03788i | 0.183117 | − | 0.317167i | ||||
\(813\) | 8.23907 | − | 14.2705i | 0.288957 | − | 0.500488i | ||||
\(814\) | −56.7964 | −1.99071 | ||||||||
\(815\) | −2.89899 | − | 5.02120i | −0.101547 | − | 0.175885i | ||||
\(816\) | 3.45476 | + | 5.98382i | 0.120941 | + | 0.209475i | ||||
\(817\) | 0.568630 | + | 0.984896i | 0.0198939 | + | 0.0344572i | ||||
\(818\) | −11.6938 | + | 20.2543i | −0.408865 | + | 0.708175i | ||||
\(819\) | −5.55577 | − | 9.62287i | −0.194134 | − | 0.336250i | ||||
\(820\) | 3.59692 | − | 6.23004i | 0.125610 | − | 0.217562i | ||||
\(821\) | −29.3877 | −1.02564 | −0.512818 | − | 0.858497i | \(-0.671399\pi\) | ||||
−0.512818 | + | 0.858497i | \(0.671399\pi\) | |||||||
\(822\) | 19.4781 | 0.679378 | ||||||||
\(823\) | 19.5928 | − | 33.9358i | 0.682963 | − | 1.18293i | −0.291110 | − | 0.956690i | \(-0.594024\pi\) |
0.974072 | − | 0.226237i | \(-0.0726423\pi\) | |||||||
\(824\) | −1.86427 | − | 3.22902i | −0.0649451 | − | 0.112488i | ||||
\(825\) | −3.18740 | + | 5.52074i | −0.110971 | + | 0.192207i | ||||
\(826\) | 5.46938 | + | 9.47324i | 0.190304 | + | 0.329616i | ||||
\(827\) | 0.180968 | + | 0.313446i | 0.00629288 | + | 0.0108996i | 0.869155 | − | 0.494540i | \(-0.164664\pi\) |
−0.862862 | + | 0.505440i | \(0.831330\pi\) | |||||||
\(828\) | 0.454758 | + | 0.787664i | 0.0158039 | + | 0.0273732i | ||||
\(829\) | 37.4005 | 1.29897 | 0.649487 | − | 0.760373i | \(-0.274984\pi\) | ||||
0.649487 | + | 0.760373i | \(0.274984\pi\) | |||||||
\(830\) | −6.32956 | + | 10.9631i | −0.219702 | + | 0.380535i | ||||
\(831\) | −12.8296 | + | 22.2214i | −0.445052 | + | 0.770853i | ||||
\(832\) | 2.90952 | + | 5.03943i | 0.100869 | + | 0.174711i | ||||
\(833\) | −23.1728 | −0.802889 | ||||||||
\(834\) | −5.68740 | + | 9.85087i | −0.196939 | + | 0.341108i | ||||
\(835\) | −16.1244 | −0.558008 | ||||||||
\(836\) | −15.5815 | −0.538897 | ||||||||
\(837\) | −4.42004 | + | 3.38574i | −0.152779 | + | 0.117028i | ||||
\(838\) | 14.3748 | 0.496569 | ||||||||
\(839\) | 49.4005 | 1.70550 | 0.852748 | − | 0.522323i | \(-0.174934\pi\) | ||||
0.852748 | + | 0.522323i | \(0.174934\pi\) | |||||||
\(840\) | 0.954758 | − | 1.65369i | 0.0329423 | − | 0.0570577i | ||||
\(841\) | 0.869320 | 0.0299766 | ||||||||
\(842\) | −7.15268 | − | 12.3888i | −0.246498 | − | 0.426947i | ||||
\(843\) | −15.5686 | + | 26.9657i | −0.536212 | + | 0.928747i | ||||
\(844\) | 5.22212 | − | 9.04497i | 0.179753 | − | 0.311341i | ||||
\(845\) | 20.8611 | 0.717645 | ||||||||
\(846\) | −4.36427 | − | 7.55914i | −0.150047 | − | 0.259889i | ||||
\(847\) | 28.2972 | + | 49.0122i | 0.972303 | + | 1.68408i | ||||
\(848\) | −3.64216 | − | 6.30840i | −0.125072 | − | 0.216631i | ||||
\(849\) | −8.49591 | + | 14.7153i | −0.291579 | + | 0.505029i | ||||
\(850\) | 3.45476 | + | 5.98382i | 0.118497 | + | 0.205243i | ||||
\(851\) | −4.05167 | + | 7.01770i | −0.138890 | + | 0.240564i | ||||
\(852\) | 9.81903 | 0.336394 | ||||||||
\(853\) | 11.5960 | 0.397038 | 0.198519 | − | 0.980097i | \(-0.436387\pi\) | ||||
0.198519 | + | 0.980097i | \(0.436387\pi\) | |||||||
\(854\) | 4.24317 | − | 7.34938i | 0.145198 | − | 0.251491i | ||||
\(855\) | −1.22212 | − | 2.11677i | −0.0417955 | − | 0.0723919i | ||||
\(856\) | −0.954758 | + | 1.65369i | −0.0326330 | + | 0.0565219i | ||||
\(857\) | 23.5298 | + | 40.7548i | 0.803763 | + | 1.39216i | 0.917123 | + | 0.398605i | \(0.130506\pi\) |
−0.113359 | + | 0.993554i | \(0.536161\pi\) | |||||||
\(858\) | −18.5476 | − | 32.1254i | −0.633204 | − | 1.09674i | ||||
\(859\) | 1.31260 | + | 2.27349i | 0.0447853 | + | 0.0775705i | 0.887549 | − | 0.460713i | \(-0.152406\pi\) |
−0.842764 | + | 0.538284i | \(0.819073\pi\) | |||||||
\(860\) | −0.465283 | −0.0158660 | ||||||||
\(861\) | 6.86837 | − | 11.8964i | 0.234073 | − | 0.405427i | ||||
\(862\) | −11.3255 | + | 19.6163i | −0.385747 | + | 0.668133i | ||||
\(863\) | −15.8497 | − | 27.4524i | −0.539529 | − | 0.934491i | −0.998929 | − | 0.0462618i | \(-0.985269\pi\) |
0.459401 | − | 0.888229i | \(-0.348064\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0.732642 | − | 1.26897i | 0.0249106 | − | 0.0431464i | ||||
\(866\) | −26.5686 | −0.902839 | ||||||||
\(867\) | −30.7414 | −1.04403 | ||||||||
\(868\) | −1.37889 | − | 10.5419i | −0.0468027 | − | 0.357817i | ||||
\(869\) | 2.96609 | 0.100618 | ||||||||
\(870\) | 5.46528 | 0.185290 | ||||||||
\(871\) | 25.9224 | − | 44.8989i | 0.878346 | − | 1.52134i | ||||
\(872\) | 2.44423 | 0.0827722 | ||||||||
\(873\) | −9.08639 | − | 15.7381i | −0.307528 | − | 0.532654i | ||||
\(874\) | −1.11153 | + | 1.92523i | −0.0375982 | + | 0.0651220i | ||||
\(875\) | 0.954758 | − | 1.65369i | 0.0322767 | − | 0.0559049i | ||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 15.8085 | + | 27.3811i | 0.533815 | + | 0.924595i | 0.999220 | + | 0.0394971i | \(0.0125756\pi\) |
−0.465404 | + | 0.885098i | \(0.654091\pi\) | |||||||
\(878\) | −3.91595 | − | 6.78262i | −0.132157 | − | 0.228902i | ||||
\(879\) | 13.4612 | + | 23.3155i | 0.454035 | + | 0.786411i | ||||
\(880\) | 3.18740 | − | 5.52074i | 0.107447 | − | 0.186104i | ||||
\(881\) | −26.9507 | − | 46.6799i | −0.907991 | − | 1.57269i | −0.816851 | − | 0.576848i | \(-0.804282\pi\) |
−0.0911397 | − | 0.995838i | \(-0.529051\pi\) | |||||||
\(882\) | −1.67687 | + | 2.90443i | −0.0564633 | + | 0.0977973i | ||||
\(883\) | −44.5055 | −1.49773 | −0.748864 | − | 0.662723i | \(-0.769401\pi\) | ||||
−0.748864 | + | 0.662723i | \(0.769401\pi\) | |||||||
\(884\) | −40.2067 | −1.35230 | ||||||||
\(885\) | −2.86427 | + | 4.96107i | −0.0962815 | + | 0.166764i | ||||
\(886\) | −9.35375 | − | 16.2012i | −0.314245 | − | 0.544289i | ||||
\(887\) | −16.0645 | + | 27.8246i | −0.539394 | + | 0.934258i | 0.459542 | + | 0.888156i | \(0.348013\pi\) |
−0.998937 | + | 0.0461026i | \(0.985320\pi\) | |||||||
\(888\) | 4.45476 | + | 7.71587i | 0.149492 | + | 0.258928i | ||||
\(889\) | −13.9959 | − | 24.2416i | −0.469408 | − | 0.813038i | ||||
\(890\) | −7.90952 | − | 13.6997i | −0.265128 | − | 0.459214i | ||||
\(891\) | −6.37480 | −0.213564 | ||||||||
\(892\) | 7.42004 | − | 12.8519i | 0.248441 | − | 0.430313i | ||||
\(893\) | 10.6673 | − | 18.4763i | 0.356968 | − | 0.618286i | ||||
\(894\) | 3.35784 | + | 5.81595i | 0.112303 | + | 0.194515i | ||||
\(895\) | −16.0129 | −0.535251 | ||||||||
\(896\) | −0.954758 | + | 1.65369i | −0.0318962 | + | 0.0552459i | ||||
\(897\) | −5.29250 | −0.176712 | ||||||||
\(898\) | 14.8885 | 0.496835 | ||||||||
\(899\) | 24.1568 | − | 18.5040i | 0.805674 | − | 0.617144i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 50.3311 | 1.67677 | ||||||||
\(902\) | 22.9296 | − | 39.7153i | 0.763473 | − | 1.32237i | ||||
\(903\) | −0.888466 | −0.0295663 | ||||||||
\(904\) | 4.67687 | + | 8.10058i | 0.155551 | + | 0.269421i | ||||
\(905\) | 1.46528 | − | 2.53794i | 0.0487077 | − | 0.0843641i | ||||
\(906\) | 2.27788 | − | 3.94541i | 0.0756776 | − | 0.131077i | ||||
\(907\) | 24.3619 | 0.808925 | 0.404462 | − | 0.914555i | \(-0.367459\pi\) | ||||
0.404462 | + | 0.914555i | \(0.367459\pi\) | |||||||
\(908\) | −1.48947 | − | 2.57985i | −0.0494300 | − | 0.0856152i | ||||
\(909\) | −0.965283 | − | 1.67192i | −0.0320164 | − | 0.0554541i | ||||
\(910\) | 5.55577 | + | 9.62287i | 0.184172 | + | 0.318995i | ||||
\(911\) | −11.7084 | + | 20.2796i | −0.387918 | + | 0.671894i | −0.992169 | − | 0.124900i | \(-0.960139\pi\) |
0.604251 | + | 0.796794i | \(0.293472\pi\) | |||||||
\(912\) | 1.22212 | + | 2.11677i | 0.0404683 | + | 0.0700932i | ||||
\(913\) | −40.3497 | + | 69.8877i | −1.33538 | + | 2.31294i | ||||
\(914\) | 14.2067 | 0.469916 | ||||||||
\(915\) | 4.44423 | 0.146922 | ||||||||
\(916\) | 3.75683 | − | 6.50703i | 0.124129 | − | 0.214998i | ||||
\(917\) | 2.18097 | + | 3.77755i | 0.0720219 | + | 0.124746i | ||||
\(918\) | −3.45476 | + | 5.98382i | −0.114024 | + | 0.197495i | ||||
\(919\) | −4.11797 | − | 7.13253i | −0.135839 | − | 0.235280i | 0.790079 | − | 0.613006i | \(-0.210040\pi\) |
−0.925918 | + | 0.377725i | \(0.876706\pi\) | |||||||
\(920\) | −0.454758 | − | 0.787664i | −0.0149929 | − | 0.0259685i | ||||
\(921\) | 9.97171 | + | 17.2715i | 0.328579 | + | 0.569116i | ||||
\(922\) | −22.6802 | −0.746931 | ||||||||
\(923\) | −28.5686 | + | 49.4823i | −0.940348 | + | 1.62873i | ||||
\(924\) | 6.08639 | − | 10.5419i | 0.200228 | − | 0.346804i | ||||
\(925\) | 4.45476 | + | 7.71587i | 0.146472 | + | 0.253696i | ||||
\(926\) | 22.6170 | 0.743241 | ||||||||
\(927\) | 1.86427 | − | 3.22902i | 0.0612308 | − | 0.106055i | ||||
\(928\) | −5.46528 | −0.179407 | ||||||||
\(929\) | −34.8062 | −1.14195 | −0.570977 | − | 0.820966i | \(-0.693435\pi\) | ||||
−0.570977 | + | 0.820966i | \(0.693435\pi\) | |||||||
\(930\) | 4.42004 | − | 3.38574i | 0.144939 | − | 0.111023i | ||||
\(931\) | −8.19734 | −0.268657 | ||||||||
\(932\) | 12.9095 | 0.422865 | ||||||||
\(933\) | 12.2843 | − | 21.2771i | 0.402170 | − | 0.696580i | ||||
\(934\) | −35.5897 | −1.16453 | ||||||||
\(935\) | 22.0234 | + | 38.1456i | 0.720242 | + | 1.24750i | ||||
\(936\) | −2.90952 | + | 5.03943i | −0.0951005 | + | 0.164719i | ||||
\(937\) | 11.8885 | − | 20.5914i | 0.388379 | − | 0.672693i | −0.603852 | − | 0.797096i | \(-0.706368\pi\) |
0.992232 | + | 0.124404i | \(0.0397017\pi\) | |||||||
\(938\) | 17.0129 | 0.555490 | ||||||||
\(939\) | 11.9265 | + | 20.6573i | 0.389206 | + | 0.674124i | ||||
\(940\) | 4.36427 | + | 7.55914i | 0.142347 | + | 0.246552i | ||||
\(941\) | −6.59048 | − | 11.4151i | −0.214844 | − | 0.372120i | 0.738381 | − | 0.674384i | \(-0.235591\pi\) |
−0.953224 | + | 0.302264i | \(0.902258\pi\) | |||||||
\(942\) | 8.97171 | − | 15.5395i | 0.292314 | − | 0.506303i | ||||
\(943\) | −3.27145 | − | 5.66632i | −0.106533 | − | 0.184521i | ||||
\(944\) | 2.86427 | − | 4.96107i | 0.0932242 | − | 0.161469i | ||||
\(945\) | 1.90952 | 0.0621166 | ||||||||
\(946\) | −2.96609 | −0.0964358 | ||||||||
\(947\) | −24.7285 | + | 42.8311i | −0.803570 | + | 1.39182i | 0.113682 | + | 0.993517i | \(0.463735\pi\) |
−0.917252 | + | 0.398307i | \(0.869598\pi\) | |||||||
\(948\) | −0.232642 | − | 0.402947i | −0.00755585 | − | 0.0130871i | ||||
\(949\) | −5.81903 | + | 10.0789i | −0.188894 | + | 0.327174i | ||||
\(950\) | 1.22212 | + | 2.11677i | 0.0396507 | + | 0.0686770i | ||||
\(951\) | −7.55167 | − | 13.0799i | −0.244880 | − | 0.424144i | ||||
\(952\) | −6.59692 | − | 11.4262i | −0.213807 | − | 0.370325i | ||||
\(953\) | 36.4442 | 1.18054 | 0.590272 | − | 0.807204i | \(-0.299020\pi\) | ||||
0.590272 | + | 0.807204i | \(0.299020\pi\) | |||||||
\(954\) | 3.64216 | − | 6.30840i | 0.117919 | − | 0.204242i | ||||
\(955\) | 0.222116 | − | 0.384717i | 0.00718752 | − | 0.0124491i | ||||
\(956\) | 6.46528 | + | 11.1982i | 0.209102 | + | 0.362176i | ||||
\(957\) | 34.8401 | 1.12622 | ||||||||
\(958\) | −1.24317 | + | 2.15323i | −0.0401649 | + | 0.0695676i | ||||
\(959\) | −37.1938 | −1.20105 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 8.07353 | − | 29.9302i | 0.260436 | − | 0.965491i | ||||
\(962\) | −51.8448 | −1.67154 | ||||||||
\(963\) | −1.90952 | −0.0615333 | ||||||||
\(964\) | 5.35784 | − | 9.28006i | 0.172564 | − | 0.298890i | ||||
\(965\) | 17.4653 | 0.562227 | ||||||||
\(966\) | −0.868368 | − | 1.50406i | −0.0279393 | − | 0.0483922i | ||||
\(967\) | −29.2761 | + | 50.7077i | −0.941457 | + | 1.63065i | −0.178762 | + | 0.983892i | \(0.557209\pi\) |
−0.762695 | + | 0.646759i | \(0.776124\pi\) | |||||||
\(968\) | 14.8190 | − | 25.6673i | 0.476302 | − | 0.824979i | ||||
\(969\) | −16.8885 | −0.542536 | ||||||||
\(970\) | 9.08639 | + | 15.7381i | 0.291746 | + | 0.505320i | ||||
\(971\) | 17.0969 | + | 29.6127i | 0.548666 | + | 0.950318i | 0.998366 | + | 0.0571380i | \(0.0181975\pi\) |
−0.449700 | + | 0.893180i | \(0.648469\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 10.8602 | − | 18.8104i | 0.348161 | − | 0.603033i | ||||
\(974\) | −4.51053 | − | 7.81246i | −0.144527 | − | 0.250327i | ||||
\(975\) | −2.90952 | + | 5.03943i | −0.0931791 | + | 0.161391i | ||||
\(976\) | −4.44423 | −0.142256 | ||||||||
\(977\) | −22.1810 | −0.709632 | −0.354816 | − | 0.934936i | \(-0.615456\pi\) | ||||
−0.354816 | + | 0.934936i | \(0.615456\pi\) | |||||||
\(978\) | −2.89899 | + | 5.02120i | −0.0926995 | + | 0.160560i | ||||
\(979\) | −50.4216 | − | 87.3327i | −1.61148 | − | 2.79117i | ||||
\(980\) | 1.67687 | − | 2.90443i | 0.0535658 | − | 0.0927787i | ||||
\(981\) | 1.22212 | + | 2.11677i | 0.0390192 | + | 0.0675832i | ||||
\(982\) | 9.07587 | + | 15.7199i | 0.289622 | + | 0.501641i | ||||
\(983\) | 4.53472 | + | 7.85436i | 0.144635 | + | 0.250515i | 0.929237 | − | 0.369485i | \(-0.120466\pi\) |
−0.784602 | + | 0.620000i | \(0.787133\pi\) | |||||||
\(984\) | −7.19383 | −0.229331 | ||||||||
\(985\) | 5.28432 | − | 9.15270i | 0.168372 | − | 0.291629i | ||||
\(986\) | 18.8812 | − | 32.7033i | 0.601301 | − | 1.04148i | ||||
\(987\) | 8.33365 | + | 14.4343i | 0.265263 | + | 0.459449i | ||||
\(988\) | −14.2231 | −0.452496 | ||||||||
\(989\) | −0.211591 | + | 0.366487i | −0.00672821 | + | 0.0116536i | ||||
\(990\) | 6.37480 | 0.202604 | ||||||||
\(991\) | 34.3877 | 1.09236 | 0.546180 | − | 0.837668i | \(-0.316081\pi\) | ||||
0.546180 | + | 0.837668i | \(0.316081\pi\) | |||||||
\(992\) | −4.42004 | + | 3.38574i | −0.140336 | + | 0.107497i | ||||
\(993\) | −0.124397 | −0.00394763 | ||||||||
\(994\) | −18.7496 | −0.594701 | ||||||||
\(995\) | 4.32956 | − | 7.49901i | 0.137256 | − | 0.237735i | ||||
\(996\) | 12.6591 | 0.401119 | ||||||||
\(997\) | −16.9296 | − | 29.3230i | −0.536166 | − | 0.928667i | −0.999106 | − | 0.0422774i | \(-0.986539\pi\) |
0.462940 | − | 0.886390i | \(-0.346795\pi\) | |||||||
\(998\) | −15.5759 | + | 26.9782i | −0.493045 | + | 0.853980i | ||||
\(999\) | −4.45476 | + | 7.71587i | −0.140942 | + | 0.244119i |
(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 | 930.2.i.n.811.3 | yes | 6 | |
31.25 | even | 3 | inner | 930.2.i.n.211.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.n.211.3 | ✓ | 6 | 31.25 | even | 3 | inner | |
930.2.i.n.811.3 | yes | 6 | 1.1 | even | 1 | trivial |