Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.10 | ||
Root | \(0.813276 - 1.52924i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.239 |
Dual form | 546.2.p.d.281.10 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.65641 | + | 0.506265i | 0.956329 | + | 0.292292i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.645532 | + | 0.645532i | 0.288691 | + | 0.288691i | 0.836562 | − | 0.547872i | \(-0.184562\pi\) |
−0.547872 | + | 0.836562i | \(0.684562\pi\) | |||||||
\(6\) | 0.813276 | + | 1.52924i | 0.332018 | + | 0.624311i | ||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.48739 | + | 1.67717i | 0.829130 | + | 0.559055i | ||||
\(10\) | 0.912921i | 0.288691i | ||||||||
\(11\) | 0.346115 | − | 0.346115i | 0.104358 | − | 0.104358i | −0.653000 | − | 0.757358i | \(-0.726490\pi\) |
0.757358 | + | 0.653000i | \(0.226490\pi\) | |||||||
\(12\) | −0.506265 | + | 1.65641i | −0.146146 | + | 0.478165i | ||||
\(13\) | 0.964947 | − | 3.47403i | 0.267628 | − | 0.963522i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 0.742456 | + | 1.39608i | 0.191701 | + | 0.360466i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.74401 | −0.908055 | −0.454028 | − | 0.890988i | \(-0.650013\pi\) | ||||
−0.454028 | + | 0.890988i | \(0.650013\pi\) | |||||||
\(18\) | 0.572916 | + | 2.94479i | 0.135038 | + | 0.694093i | ||||
\(19\) | −0.564337 | + | 0.564337i | −0.129468 | + | 0.129468i | −0.768871 | − | 0.639404i | \(-0.779181\pi\) |
0.639404 | + | 0.768871i | \(0.279181\pi\) | |||||||
\(20\) | −0.645532 | + | 0.645532i | −0.144345 | + | 0.144345i | ||||
\(21\) | 0.813276 | + | 1.52924i | 0.177471 | + | 0.333708i | ||||
\(22\) | 0.489480 | 0.104358 | ||||||||
\(23\) | −2.93468 | −0.611922 | −0.305961 | − | 0.952044i | \(-0.598978\pi\) | ||||
−0.305961 | + | 0.952044i | \(0.598978\pi\) | |||||||
\(24\) | −1.52924 | + | 0.813276i | −0.312155 | + | 0.166009i | ||||
\(25\) | − | 4.16658i | − | 0.833315i | ||||||
\(26\) | 3.13883 | − | 1.77419i | 0.615575 | − | 0.347947i | ||||
\(27\) | 3.27105 | + | 4.03735i | 0.629514 | + | 0.776989i | ||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | 4.18850i | 0.777785i | 0.921283 | + | 0.388893i | \(0.127142\pi\) | ||||
−0.921283 | + | 0.388893i | \(0.872858\pi\) | |||||||
\(30\) | −0.462180 | + | 1.51217i | −0.0843821 | + | 0.276083i | ||||
\(31\) | −1.21118 | + | 1.21118i | −0.217534 | + | 0.217534i | −0.807459 | − | 0.589924i | \(-0.799158\pi\) |
0.589924 | + | 0.807459i | \(0.299158\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0.748534 | − | 0.398082i | 0.130303 | − | 0.0692973i | ||||
\(34\) | −2.64741 | − | 2.64741i | −0.454028 | − | 0.454028i | ||||
\(35\) | 0.912921i | 0.154312i | ||||||||
\(36\) | −1.67717 | + | 2.48739i | −0.279528 | + | 0.414565i | ||||
\(37\) | 2.17001 | + | 2.17001i | 0.356747 | + | 0.356747i | 0.862612 | − | 0.505866i | \(-0.168827\pi\) |
−0.505866 | + | 0.862612i | \(0.668827\pi\) | |||||||
\(38\) | −0.798093 | −0.129468 | ||||||||
\(39\) | 3.35713 | − | 5.26590i | 0.537571 | − | 0.843219i | ||||
\(40\) | −0.912921 | −0.144345 | ||||||||
\(41\) | −2.35038 | − | 2.35038i | −0.367068 | − | 0.367068i | 0.499339 | − | 0.866407i | \(-0.333576\pi\) |
−0.866407 | + | 0.499339i | \(0.833576\pi\) | |||||||
\(42\) | −0.506265 | + | 1.65641i | −0.0781184 | + | 0.255590i | ||||
\(43\) | − | 2.44891i | − | 0.373455i | −0.982412 | − | 0.186727i | \(-0.940212\pi\) | ||
0.982412 | − | 0.186727i | \(-0.0597881\pi\) | |||||||
\(44\) | 0.346115 | + | 0.346115i | 0.0521788 | + | 0.0521788i | ||||
\(45\) | 0.523027 | + | 2.68836i | 0.0779683 | + | 0.400757i | ||||
\(46\) | −2.07513 | − | 2.07513i | −0.305961 | − | 0.305961i | ||||
\(47\) | 7.22377 | − | 7.22377i | 1.05370 | − | 1.05370i | 0.0552213 | − | 0.998474i | \(-0.482414\pi\) |
0.998474 | − | 0.0552213i | \(-0.0175864\pi\) | |||||||
\(48\) | −1.65641 | − | 0.506265i | −0.239082 | − | 0.0730731i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 2.94621 | − | 2.94621i | 0.416658 | − | 0.416658i | ||||
\(51\) | −6.20161 | − | 1.89546i | −0.868400 | − | 0.265418i | ||||
\(52\) | 3.47403 | + | 0.964947i | 0.481761 | + | 0.133814i | ||||
\(53\) | − | 5.03273i | − | 0.691298i | −0.938364 | − | 0.345649i | \(-0.887659\pi\) | ||
0.938364 | − | 0.345649i | \(-0.112341\pi\) | |||||||
\(54\) | −0.541858 | + | 5.16782i | −0.0737376 | + | 0.703252i | ||||
\(55\) | 0.446857 | 0.0602542 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −1.22048 | + | 0.649069i | −0.161656 | + | 0.0859713i | ||||
\(58\) | −2.96172 | + | 2.96172i | −0.388893 | + | 0.388893i | ||||
\(59\) | −2.23605 | + | 2.23605i | −0.291109 | + | 0.291109i | −0.837518 | − | 0.546409i | \(-0.815994\pi\) |
0.546409 | + | 0.837518i | \(0.315994\pi\) | |||||||
\(60\) | −1.39608 | + | 0.742456i | −0.180233 | + | 0.0958507i | ||||
\(61\) | −4.58319 | −0.586818 | −0.293409 | − | 0.955987i | \(-0.594790\pi\) | ||||
−0.293409 | + | 0.955987i | \(0.594790\pi\) | |||||||
\(62\) | −1.71287 | −0.217534 | ||||||||
\(63\) | 0.572916 | + | 2.94479i | 0.0721806 | + | 0.371008i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 2.86550 | − | 1.61969i | 0.355422 | − | 0.200898i | ||||
\(66\) | 0.810780 | + | 0.247807i | 0.0998002 | + | 0.0305029i | ||||
\(67\) | 1.55654 | − | 1.55654i | 0.190162 | − | 0.190162i | −0.605604 | − | 0.795766i | \(-0.707069\pi\) |
0.795766 | + | 0.605604i | \(0.207069\pi\) | |||||||
\(68\) | − | 3.74401i | − | 0.454028i | ||||||
\(69\) | −4.86103 | − | 1.48572i | −0.585199 | − | 0.178860i | ||||
\(70\) | −0.645532 | + | 0.645532i | −0.0771559 | + | 0.0771559i | ||||
\(71\) | 1.98965 | + | 1.98965i | 0.236128 | + | 0.236128i | 0.815245 | − | 0.579117i | \(-0.196602\pi\) |
−0.579117 | + | 0.815245i | \(0.696602\pi\) | |||||||
\(72\) | −2.94479 | + | 0.572916i | −0.347046 | + | 0.0675188i | ||||
\(73\) | −2.94861 | − | 2.94861i | −0.345108 | − | 0.345108i | 0.513175 | − | 0.858284i | \(-0.328469\pi\) |
−0.858284 | + | 0.513175i | \(0.828469\pi\) | |||||||
\(74\) | 3.06885i | 0.356747i | ||||||||
\(75\) | 2.10939 | − | 6.90156i | 0.243572 | − | 0.796923i | ||||
\(76\) | −0.564337 | − | 0.564337i | −0.0647339 | − | 0.0647339i | ||||
\(77\) | 0.489480 | 0.0557815 | ||||||||
\(78\) | 6.09740 | − | 1.34971i | 0.690395 | − | 0.152824i | ||||
\(79\) | −5.80866 | −0.653525 | −0.326762 | − | 0.945106i | \(-0.605958\pi\) | ||||
−0.326762 | + | 0.945106i | \(0.605958\pi\) | |||||||
\(80\) | −0.645532 | − | 0.645532i | −0.0721727 | − | 0.0721727i | ||||
\(81\) | 3.37423 | + | 8.34353i | 0.374915 | + | 0.927059i | ||||
\(82\) | − | 3.32394i | − | 0.367068i | ||||||
\(83\) | −1.45281 | − | 1.45281i | −0.159467 | − | 0.159467i | 0.622864 | − | 0.782330i | \(-0.285969\pi\) |
−0.782330 | + | 0.622864i | \(0.785969\pi\) | |||||||
\(84\) | −1.52924 | + | 0.813276i | −0.166854 | + | 0.0887356i | ||||
\(85\) | −2.41688 | − | 2.41688i | −0.262147 | − | 0.262147i | ||||
\(86\) | 1.73164 | − | 1.73164i | 0.186727 | − | 0.186727i | ||||
\(87\) | −2.12049 | + | 6.93788i | −0.227341 | + | 0.743819i | ||||
\(88\) | 0.489480i | 0.0521788i | ||||||||
\(89\) | 12.0210 | − | 12.0210i | 1.27423 | − | 1.27423i | 0.330380 | − | 0.943848i | \(-0.392823\pi\) |
0.943848 | − | 0.330380i | \(-0.107177\pi\) | |||||||
\(90\) | −1.53112 | + | 2.27079i | −0.161394 | + | 0.239362i | ||||
\(91\) | 3.13883 | − | 1.77419i | 0.329039 | − | 0.185986i | ||||
\(92\) | − | 2.93468i | − | 0.305961i | ||||||
\(93\) | −2.61939 | + | 1.39303i | −0.271618 | + | 0.144451i | ||||
\(94\) | 10.2160 | 1.05370 | ||||||||
\(95\) | −0.728595 | −0.0747523 | ||||||||
\(96\) | −0.813276 | − | 1.52924i | −0.0830046 | − | 0.156078i | ||||
\(97\) | 6.69250 | − | 6.69250i | 0.679520 | − | 0.679520i | −0.280371 | − | 0.959892i | \(-0.590458\pi\) |
0.959892 | + | 0.280371i | \(0.0904576\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 1.44142 | − | 0.280431i | 0.144868 | − | 0.0281844i | ||||
\(100\) | 4.16658 | 0.416658 | ||||||||
\(101\) | −13.4516 | −1.33848 | −0.669241 | − | 0.743045i | \(-0.733381\pi\) | ||||
−0.669241 | + | 0.743045i | \(0.733381\pi\) | |||||||
\(102\) | −3.04491 | − | 5.72550i | −0.301491 | − | 0.566909i | ||||
\(103\) | 6.61463i | 0.651759i | 0.945411 | + | 0.325879i | \(0.105660\pi\) | ||||
−0.945411 | + | 0.325879i | \(0.894340\pi\) | |||||||
\(104\) | 1.77419 | + | 3.13883i | 0.173974 | + | 0.307788i | ||||
\(105\) | −0.462180 | + | 1.51217i | −0.0451041 | + | 0.147573i | ||||
\(106\) | 3.55868 | − | 3.55868i | 0.345649 | − | 0.345649i | ||||
\(107\) | 0.232092i | 0.0224372i | 0.999937 | + | 0.0112186i | \(0.00357107\pi\) | ||||
−0.999937 | + | 0.0112186i | \(0.996429\pi\) | |||||||
\(108\) | −4.03735 | + | 3.27105i | −0.388495 | + | 0.314757i | ||||
\(109\) | −8.15828 | + | 8.15828i | −0.781422 | + | 0.781422i | −0.980071 | − | 0.198649i | \(-0.936345\pi\) |
0.198649 | + | 0.980071i | \(0.436345\pi\) | |||||||
\(110\) | 0.315975 | + | 0.315975i | 0.0301271 | + | 0.0301271i | ||||
\(111\) | 2.49582 | + | 4.69302i | 0.236893 | + | 0.445441i | ||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | − | 9.58107i | − | 0.901311i | −0.892698 | − | 0.450656i | \(-0.851190\pi\) | ||
0.892698 | − | 0.450656i | \(-0.148810\pi\) | |||||||
\(114\) | −1.32197 | − | 0.404047i | −0.123814 | − | 0.0378424i | ||||
\(115\) | −1.89443 | − | 1.89443i | −0.176656 | − | 0.176656i | ||||
\(116\) | −4.18850 | −0.388893 | ||||||||
\(117\) | 8.22672 | − | 7.02289i | 0.760561 | − | 0.649267i | ||||
\(118\) | −3.16225 | −0.291109 | ||||||||
\(119\) | −2.64741 | − | 2.64741i | −0.242688 | − | 0.242688i | ||||
\(120\) | −1.51217 | − | 0.462180i | −0.138042 | − | 0.0421911i | ||||
\(121\) | 10.7604i | 0.978219i | ||||||||
\(122\) | −3.24081 | − | 3.24081i | −0.293409 | − | 0.293409i | ||||
\(123\) | −2.70328 | − | 5.08311i | −0.243747 | − | 0.458329i | ||||
\(124\) | −1.21118 | − | 1.21118i | −0.108767 | − | 0.108767i | ||||
\(125\) | 5.91732 | − | 5.91732i | 0.529261 | − | 0.529261i | ||||
\(126\) | −1.67717 | + | 2.48739i | −0.149414 | + | 0.221594i | ||||
\(127\) | 16.8593i | 1.49602i | 0.663686 | + | 0.748012i | \(0.268991\pi\) | ||||
−0.663686 | + | 0.748012i | \(0.731009\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 1.23980 | − | 4.05640i | 0.109158 | − | 0.357146i | ||||
\(130\) | 3.17151 | + | 0.880920i | 0.278160 | + | 0.0772618i | ||||
\(131\) | − | 21.4186i | − | 1.87135i | −0.352862 | − | 0.935676i | \(-0.614791\pi\) | ||
0.352862 | − | 0.935676i | \(-0.385209\pi\) | |||||||
\(132\) | 0.398082 | + | 0.748534i | 0.0346486 | + | 0.0651515i | ||||
\(133\) | −0.798093 | −0.0692034 | ||||||||
\(134\) | 2.20128 | 0.190162 | ||||||||
\(135\) | −0.494674 | + | 4.71781i | −0.0425747 | + | 0.406045i | ||||
\(136\) | 2.64741 | − | 2.64741i | 0.227014 | − | 0.227014i | ||||
\(137\) | −4.89961 | + | 4.89961i | −0.418602 | + | 0.418602i | −0.884722 | − | 0.466120i | \(-0.845652\pi\) |
0.466120 | + | 0.884722i | \(0.345652\pi\) | |||||||
\(138\) | −2.38670 | − | 4.48783i | −0.203169 | − | 0.382030i | ||||
\(139\) | 4.43061 | 0.375799 | 0.187900 | − | 0.982188i | \(-0.439832\pi\) | ||||
0.187900 | + | 0.982188i | \(0.439832\pi\) | |||||||
\(140\) | −0.912921 | −0.0771559 | ||||||||
\(141\) | 15.6227 | − | 8.30839i | 1.31567 | − | 0.699692i | ||||
\(142\) | 2.81379i | 0.236128i | ||||||||
\(143\) | −0.868431 | − | 1.53640i | −0.0726218 | − | 0.128480i | ||||
\(144\) | −2.48739 | − | 1.67717i | −0.207283 | − | 0.139764i | ||||
\(145\) | −2.70381 | + | 2.70381i | −0.224540 | + | 0.224540i | ||||
\(146\) | − | 4.16996i | − | 0.345108i | ||||||
\(147\) | −0.506265 | + | 1.65641i | −0.0417560 | + | 0.136618i | ||||
\(148\) | −2.17001 | + | 2.17001i | −0.178373 | + | 0.178373i | ||||
\(149\) | 7.00938 | + | 7.00938i | 0.574231 | + | 0.574231i | 0.933308 | − | 0.359077i | \(-0.116909\pi\) |
−0.359077 | + | 0.933308i | \(0.616909\pi\) | |||||||
\(150\) | 6.37171 | − | 3.38857i | 0.520248 | − | 0.276676i | ||||
\(151\) | 6.30515 | + | 6.30515i | 0.513105 | + | 0.513105i | 0.915477 | − | 0.402371i | \(-0.131814\pi\) |
−0.402371 | + | 0.915477i | \(0.631814\pi\) | |||||||
\(152\) | − | 0.798093i | − | 0.0647339i | ||||||
\(153\) | −9.31281 | − | 6.27932i | −0.752896 | − | 0.507653i | ||||
\(154\) | 0.346115 | + | 0.346115i | 0.0278907 | + | 0.0278907i | ||||
\(155\) | −1.56371 | −0.125600 | ||||||||
\(156\) | 5.26590 | + | 3.35713i | 0.421609 | + | 0.268785i | ||||
\(157\) | −19.2209 | −1.53400 | −0.766998 | − | 0.641649i | \(-0.778250\pi\) | ||||
−0.766998 | + | 0.641649i | \(0.778250\pi\) | |||||||
\(158\) | −4.10734 | − | 4.10734i | −0.326762 | − | 0.326762i | ||||
\(159\) | 2.54789 | − | 8.33626i | 0.202061 | − | 0.661109i | ||||
\(160\) | − | 0.912921i | − | 0.0721727i | ||||||
\(161\) | −2.07513 | − | 2.07513i | −0.163543 | − | 0.163543i | ||||
\(162\) | −3.51383 | + | 8.28571i | −0.276072 | + | 0.650987i | ||||
\(163\) | 9.47285 | + | 9.47285i | 0.741971 | + | 0.741971i | 0.972957 | − | 0.230986i | \(-0.0741953\pi\) |
−0.230986 | + | 0.972957i | \(0.574195\pi\) | |||||||
\(164\) | 2.35038 | − | 2.35038i | 0.183534 | − | 0.183534i | ||||
\(165\) | 0.740178 | + | 0.226228i | 0.0576228 | + | 0.0176118i | ||||
\(166\) | − | 2.05459i | − | 0.159467i | ||||||
\(167\) | 17.0105 | − | 17.0105i | 1.31631 | − | 1.31631i | 0.399636 | − | 0.916674i | \(-0.369137\pi\) |
0.916674 | − | 0.399636i | \(-0.130863\pi\) | |||||||
\(168\) | −1.65641 | − | 0.506265i | −0.127795 | − | 0.0390592i | ||||
\(169\) | −11.1378 | − | 6.70451i | −0.856750 | − | 0.515731i | ||||
\(170\) | − | 3.41798i | − | 0.262147i | ||||||
\(171\) | −2.35021 | + | 0.457240i | −0.179725 | + | 0.0349660i | ||||
\(172\) | 2.44891 | 0.186727 | ||||||||
\(173\) | 0.945226 | 0.0718642 | 0.0359321 | − | 0.999354i | \(-0.488560\pi\) | ||||
0.0359321 | + | 0.999354i | \(0.488560\pi\) | |||||||
\(174\) | −6.40524 | + | 3.40641i | −0.485580 | + | 0.258239i | ||||
\(175\) | 2.94621 | − | 2.94621i | 0.222713 | − | 0.222713i | ||||
\(176\) | −0.346115 | + | 0.346115i | −0.0260894 | + | 0.0260894i | ||||
\(177\) | −4.83585 | + | 2.57178i | −0.363485 | + | 0.193307i | ||||
\(178\) | 17.0003 | 1.27423 | ||||||||
\(179\) | −18.1644 | −1.35767 | −0.678834 | − | 0.734292i | \(-0.737515\pi\) | ||||
−0.678834 | + | 0.734292i | \(0.737515\pi\) | |||||||
\(180\) | −2.68836 | + | 0.523027i | −0.200378 | + | 0.0389841i | ||||
\(181\) | − | 18.4772i | − | 1.37340i | −0.726940 | − | 0.686701i | \(-0.759058\pi\) | ||
0.726940 | − | 0.686701i | \(-0.240942\pi\) | |||||||
\(182\) | 3.47403 | + | 0.964947i | 0.257512 | + | 0.0715266i | ||||
\(183\) | −7.59165 | − | 2.32031i | −0.561191 | − | 0.171522i | ||||
\(184\) | 2.07513 | − | 2.07513i | 0.152981 | − | 0.152981i | ||||
\(185\) | 2.80162i | 0.205979i | ||||||||
\(186\) | −2.83721 | − | 0.867164i | −0.208034 | − | 0.0635836i | ||||
\(187\) | −1.29586 | + | 1.29586i | −0.0947625 | + | 0.0947625i | ||||
\(188\) | 7.22377 | + | 7.22377i | 0.526848 | + | 0.526848i | ||||
\(189\) | −0.541858 | + | 5.16782i | −0.0394144 | + | 0.375904i | ||||
\(190\) | −0.515195 | − | 0.515195i | −0.0373762 | − | 0.0373762i | ||||
\(191\) | 14.1792i | 1.02597i | 0.858398 | + | 0.512984i | \(0.171460\pi\) | ||||
−0.858398 | + | 0.512984i | \(0.828540\pi\) | |||||||
\(192\) | 0.506265 | − | 1.65641i | 0.0365365 | − | 0.119541i | ||||
\(193\) | 3.37846 | + | 3.37846i | 0.243187 | + | 0.243187i | 0.818167 | − | 0.574980i | \(-0.194990\pi\) |
−0.574980 | + | 0.818167i | \(0.694990\pi\) | |||||||
\(194\) | 9.46462 | 0.679520 | ||||||||
\(195\) | 5.56644 | − | 1.23217i | 0.398621 | − | 0.0882378i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −1.50781 | − | 1.50781i | −0.107427 | − | 0.107427i | 0.651350 | − | 0.758777i | \(-0.274203\pi\) |
−0.758777 | + | 0.651350i | \(0.774203\pi\) | |||||||
\(198\) | 1.21753 | + | 0.820940i | 0.0865260 | + | 0.0583416i | ||||
\(199\) | 11.1999i | 0.793937i | 0.917832 | + | 0.396968i | \(0.129938\pi\) | ||||
−0.917832 | + | 0.396968i | \(0.870062\pi\) | |||||||
\(200\) | 2.94621 | + | 2.94621i | 0.208329 | + | 0.208329i | ||||
\(201\) | 3.36629 | − | 1.79025i | 0.237440 | − | 0.126274i | ||||
\(202\) | −9.51170 | − | 9.51170i | −0.669241 | − | 0.669241i | ||||
\(203\) | −2.96172 | + | 2.96172i | −0.207872 | + | 0.207872i | ||||
\(204\) | 1.89546 | − | 6.20161i | 0.132709 | − | 0.434200i | ||||
\(205\) | − | 3.03449i | − | 0.211938i | ||||||
\(206\) | −4.67725 | + | 4.67725i | −0.325879 | + | 0.325879i | ||||
\(207\) | −7.29969 | − | 4.92194i | −0.507364 | − | 0.342098i | ||||
\(208\) | −0.964947 | + | 3.47403i | −0.0669070 | + | 0.240881i | ||||
\(209\) | 0.390651i | 0.0270219i | ||||||||
\(210\) | −1.39608 | + | 0.742456i | −0.0963385 | + | 0.0512343i | ||||
\(211\) | 16.7046 | 1.14999 | 0.574997 | − | 0.818156i | \(-0.305003\pi\) | ||||
0.574997 | + | 0.818156i | \(0.305003\pi\) | |||||||
\(212\) | 5.03273 | 0.345649 | ||||||||
\(213\) | 2.28839 | + | 4.30297i | 0.156798 | + | 0.294834i | ||||
\(214\) | −0.164114 | + | 0.164114i | −0.0112186 | + | 0.0112186i | ||||
\(215\) | 1.58085 | − | 1.58085i | 0.107813 | − | 0.107813i | ||||
\(216\) | −5.16782 | − | 0.541858i | −0.351626 | − | 0.0368688i | ||||
\(217\) | −1.71287 | −0.116277 | ||||||||
\(218\) | −11.5376 | −0.781422 | ||||||||
\(219\) | −3.39133 | − | 6.37688i | −0.229165 | − | 0.430910i | ||||
\(220\) | 0.446857i | 0.0301271i | ||||||||
\(221\) | −3.61277 | + | 13.0068i | −0.243021 | + | 0.874932i | ||||
\(222\) | −1.55365 | + | 5.08328i | −0.104274 | + | 0.341167i | ||||
\(223\) | −16.2269 | + | 16.2269i | −1.08663 | + | 1.08663i | −0.0907580 | + | 0.995873i | \(0.528929\pi\) |
−0.995873 | + | 0.0907580i | \(0.971071\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 6.98804 | − | 10.3639i | 0.465869 | − | 0.690927i | ||||
\(226\) | 6.77484 | − | 6.77484i | 0.450656 | − | 0.450656i | ||||
\(227\) | 18.5844 | + | 18.5844i | 1.23349 | + | 1.23349i | 0.962616 | + | 0.270871i | \(0.0873117\pi\) |
0.270871 | + | 0.962616i | \(0.412688\pi\) | |||||||
\(228\) | −0.649069 | − | 1.22048i | −0.0429857 | − | 0.0808281i | ||||
\(229\) | −10.3015 | − | 10.3015i | −0.680741 | − | 0.680741i | 0.279426 | − | 0.960167i | \(-0.409856\pi\) |
−0.960167 | + | 0.279426i | \(0.909856\pi\) | |||||||
\(230\) | − | 2.67913i | − | 0.176656i | ||||||
\(231\) | 0.810780 | + | 0.247807i | 0.0533454 | + | 0.0163045i | ||||
\(232\) | −2.96172 | − | 2.96172i | −0.194446 | − | 0.194446i | ||||
\(233\) | −29.5763 | −1.93761 | −0.968803 | − | 0.247830i | \(-0.920282\pi\) | ||||
−0.968803 | + | 0.247830i | \(0.920282\pi\) | |||||||
\(234\) | 10.7831 | + | 0.851235i | 0.704914 | + | 0.0556470i | ||||
\(235\) | 9.32636 | 0.608384 | ||||||||
\(236\) | −2.23605 | − | 2.23605i | −0.145555 | − | 0.145555i | ||||
\(237\) | −9.62152 | − | 2.94072i | −0.624985 | − | 0.191020i | ||||
\(238\) | − | 3.74401i | − | 0.242688i | ||||||
\(239\) | 4.42519 | + | 4.42519i | 0.286242 | + | 0.286242i | 0.835592 | − | 0.549350i | \(-0.185125\pi\) |
−0.549350 | + | 0.835592i | \(0.685125\pi\) | |||||||
\(240\) | −0.742456 | − | 1.39608i | −0.0479253 | − | 0.0901164i | ||||
\(241\) | −11.6682 | − | 11.6682i | −0.751615 | − | 0.751615i | 0.223165 | − | 0.974781i | \(-0.428361\pi\) |
−0.974781 | + | 0.223165i | \(0.928361\pi\) | |||||||
\(242\) | −7.60876 | + | 7.60876i | −0.489109 | + | 0.489109i | ||||
\(243\) | 1.36507 | + | 15.5286i | 0.0875694 | + | 0.996158i | ||||
\(244\) | − | 4.58319i | − | 0.293409i | ||||||
\(245\) | −0.645532 | + | 0.645532i | −0.0412416 | + | 0.0412416i | ||||
\(246\) | 1.68280 | − | 5.50581i | 0.107291 | − | 0.351038i | ||||
\(247\) | 1.41597 | + | 2.50508i | 0.0900958 | + | 0.159394i | ||||
\(248\) | − | 1.71287i | − | 0.108767i | ||||||
\(249\) | −1.67094 | − | 3.14196i | −0.105892 | − | 0.199114i | ||||
\(250\) | 8.36836 | 0.529261 | ||||||||
\(251\) | 14.2635 | 0.900304 | 0.450152 | − | 0.892952i | \(-0.351370\pi\) | ||||
0.450152 | + | 0.892952i | \(0.351370\pi\) | |||||||
\(252\) | −2.94479 | + | 0.572916i | −0.185504 | + | 0.0360903i | ||||
\(253\) | −1.01574 | + | 1.01574i | −0.0638587 | + | 0.0638587i | ||||
\(254\) | −11.9213 | + | 11.9213i | −0.748012 | + | 0.748012i | ||||
\(255\) | −2.77976 | − | 5.22692i | −0.174075 | − | 0.327323i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.5921 | 0.910229 | 0.455114 | − | 0.890433i | \(-0.349598\pi\) | ||||
0.455114 | + | 0.890433i | \(0.349598\pi\) | |||||||
\(258\) | 3.74497 | − | 1.99164i | 0.233152 | − | 0.123994i | ||||
\(259\) | 3.06885i | 0.190689i | ||||||||
\(260\) | 1.61969 | + | 2.86550i | 0.100449 | + | 0.177711i | ||||
\(261\) | −7.02481 | + | 10.4184i | −0.434825 | + | 0.644886i | ||||
\(262\) | 15.1452 | − | 15.1452i | 0.935676 | − | 0.935676i | ||||
\(263\) | 26.6102i | 1.64086i | 0.571749 | + | 0.820429i | \(0.306265\pi\) | ||||
−0.571749 | + | 0.820429i | \(0.693735\pi\) | |||||||
\(264\) | −0.247807 | + | 0.810780i | −0.0152515 | + | 0.0499001i | ||||
\(265\) | 3.24879 | − | 3.24879i | 0.199571 | − | 0.199571i | ||||
\(266\) | −0.564337 | − | 0.564337i | −0.0346017 | − | 0.0346017i | ||||
\(267\) | 25.9976 | − | 13.8259i | 1.59103 | − | 0.846134i | ||||
\(268\) | 1.55654 | + | 1.55654i | 0.0950808 | + | 0.0950808i | ||||
\(269\) | 27.5224i | 1.67807i | 0.544078 | + | 0.839035i | \(0.316880\pi\) | ||||
−0.544078 | + | 0.839035i | \(0.683120\pi\) | |||||||
\(270\) | −3.68578 | + | 2.98621i | −0.224310 | + | 0.181735i | ||||
\(271\) | 11.2423 | + | 11.2423i | 0.682924 | + | 0.682924i | 0.960658 | − | 0.277734i | \(-0.0895834\pi\) |
−0.277734 | + | 0.960658i | \(0.589583\pi\) | |||||||
\(272\) | 3.74401 | 0.227014 | ||||||||
\(273\) | 6.09740 | − | 1.34971i | 0.369031 | − | 0.0816879i | ||||
\(274\) | −6.92909 | −0.418602 | ||||||||
\(275\) | −1.44211 | − | 1.44211i | −0.0869627 | − | 0.0869627i | ||||
\(276\) | 1.48572 | − | 4.86103i | 0.0894301 | − | 0.292600i | ||||
\(277\) | 24.6439i | 1.48071i | 0.672216 | + | 0.740355i | \(0.265343\pi\) | ||||
−0.672216 | + | 0.740355i | \(0.734657\pi\) | |||||||
\(278\) | 3.13291 | + | 3.13291i | 0.187900 | + | 0.187900i | ||||
\(279\) | −5.04402 | + | 0.981329i | −0.301978 | + | 0.0587506i | ||||
\(280\) | −0.645532 | − | 0.645532i | −0.0385779 | − | 0.0385779i | ||||
\(281\) | −23.3880 | + | 23.3880i | −1.39521 | + | 1.39521i | −0.582087 | + | 0.813126i | \(0.697764\pi\) |
−0.813126 | + | 0.582087i | \(0.802236\pi\) | |||||||
\(282\) | 16.9218 | + | 5.17198i | 1.00768 | + | 0.307987i | ||||
\(283\) | 9.52921i | 0.566453i | 0.959053 | + | 0.283226i | \(0.0914048\pi\) | ||||
−0.959053 | + | 0.283226i | \(0.908595\pi\) | |||||||
\(284\) | −1.98965 | + | 1.98965i | −0.118064 | + | 0.118064i | ||||
\(285\) | −1.20685 | − | 0.368862i | −0.0714878 | − | 0.0218495i | ||||
\(286\) | 0.472323 | − | 1.70047i | 0.0279290 | − | 0.100551i | ||||
\(287\) | − | 3.32394i | − | 0.196206i | ||||||
\(288\) | −0.572916 | − | 2.94479i | −0.0337594 | − | 0.173523i | ||||
\(289\) | −2.98240 | −0.175435 | ||||||||
\(290\) | −3.82377 | −0.224540 | ||||||||
\(291\) | 14.4737 | − | 7.69735i | 0.848464 | − | 0.451227i | ||||
\(292\) | 2.94861 | − | 2.94861i | 0.172554 | − | 0.172554i | ||||
\(293\) | −6.68662 | + | 6.68662i | −0.390636 | + | 0.390636i | −0.874914 | − | 0.484278i | \(-0.839082\pi\) |
0.484278 | + | 0.874914i | \(0.339082\pi\) | |||||||
\(294\) | −1.52924 | + | 0.813276i | −0.0891872 | + | 0.0474312i | ||||
\(295\) | −2.88689 | −0.168081 | ||||||||
\(296\) | −3.06885 | −0.178373 | ||||||||
\(297\) | 2.52955 | + | 0.265229i | 0.146779 | + | 0.0153901i | ||||
\(298\) | 9.91276i | 0.574231i | ||||||||
\(299\) | −2.83181 | + | 10.1952i | −0.163768 | + | 0.589601i | ||||
\(300\) | 6.90156 | + | 2.10939i | 0.398462 | + | 0.121786i | ||||
\(301\) | 1.73164 | − | 1.73164i | 0.0998100 | − | 0.0998100i | ||||
\(302\) | 8.91682i | 0.513105i | ||||||||
\(303\) | −22.2813 | − | 6.81006i | −1.28003 | − | 0.391228i | ||||
\(304\) | 0.564337 | − | 0.564337i | 0.0323669 | − | 0.0323669i | ||||
\(305\) | −2.95860 | − | 2.95860i | −0.169409 | − | 0.169409i | ||||
\(306\) | −2.14500 | − | 11.0253i | −0.122622 | − | 0.630275i | ||||
\(307\) | 17.6200 | + | 17.6200i | 1.00563 | + | 1.00563i | 0.999984 | + | 0.00564240i | \(0.00179604\pi\) |
0.00564240 | + | 0.999984i | \(0.498204\pi\) | |||||||
\(308\) | 0.489480i | 0.0278907i | ||||||||
\(309\) | −3.34876 | + | 10.9565i | −0.190504 | + | 0.623296i | ||||
\(310\) | −1.10571 | − | 1.10571i | −0.0628001 | − | 0.0628001i | ||||
\(311\) | −4.11610 | −0.233403 | −0.116701 | − | 0.993167i | \(-0.537232\pi\) | ||||
−0.116701 | + | 0.993167i | \(0.537232\pi\) | |||||||
\(312\) | 1.34971 | + | 6.09740i | 0.0764120 | + | 0.345197i | ||||
\(313\) | −15.1426 | −0.855910 | −0.427955 | − | 0.903800i | \(-0.640766\pi\) | ||||
−0.427955 | + | 0.903800i | \(0.640766\pi\) | |||||||
\(314\) | −13.5912 | − | 13.5912i | −0.766998 | − | 0.766998i | ||||
\(315\) | −1.53112 | + | 2.27079i | −0.0862688 | + | 0.127945i | ||||
\(316\) | − | 5.80866i | − | 0.326762i | ||||||
\(317\) | 15.8113 | + | 15.8113i | 0.888053 | + | 0.888053i | 0.994336 | − | 0.106283i | \(-0.0338949\pi\) |
−0.106283 | + | 0.994336i | \(0.533895\pi\) | |||||||
\(318\) | 7.69626 | − | 4.09299i | 0.431585 | − | 0.229524i | ||||
\(319\) | 1.44970 | + | 1.44970i | 0.0811678 | + | 0.0811678i | ||||
\(320\) | 0.645532 | − | 0.645532i | 0.0360864 | − | 0.0360864i | ||||
\(321\) | −0.117500 | + | 0.384440i | −0.00655823 | + | 0.0214574i | ||||
\(322\) | − | 2.93468i | − | 0.163543i | ||||||
\(323\) | 2.11288 | − | 2.11288i | 0.117564 | − | 0.117564i | ||||
\(324\) | −8.34353 | + | 3.37423i | −0.463530 | + | 0.187457i | ||||
\(325\) | −14.4748 | − | 4.02052i | −0.802918 | − | 0.223019i | ||||
\(326\) | 13.3966i | 0.741971i | ||||||||
\(327\) | −17.6437 | + | 9.38321i | −0.975700 | + | 0.518893i | ||||
\(328\) | 3.32394 | 0.183534 | ||||||||
\(329\) | 10.2160 | 0.563224 | ||||||||
\(330\) | 0.363418 | + | 0.683352i | 0.0200055 | + | 0.0376173i | ||||
\(331\) | 11.5195 | − | 11.5195i | 0.633169 | − | 0.633169i | −0.315693 | − | 0.948861i | \(-0.602237\pi\) |
0.948861 | + | 0.315693i | \(0.102237\pi\) | |||||||
\(332\) | 1.45281 | − | 1.45281i | 0.0797334 | − | 0.0797334i | ||||
\(333\) | 1.75819 | + | 9.03711i | 0.0963484 | + | 0.495231i | ||||
\(334\) | 24.0564 | 1.31631 | ||||||||
\(335\) | 2.00959 | 0.109796 | ||||||||
\(336\) | −0.813276 | − | 1.52924i | −0.0443678 | − | 0.0834270i | ||||
\(337\) | − | 29.3517i | − | 1.59889i | −0.600740 | − | 0.799444i | \(-0.705127\pi\) | ||
0.600740 | − | 0.799444i | \(-0.294873\pi\) | |||||||
\(338\) | −3.13478 | − | 12.6164i | −0.170510 | − | 0.686241i | ||||
\(339\) | 4.85056 | − | 15.8702i | 0.263446 | − | 0.861950i | ||||
\(340\) | 2.41688 | − | 2.41688i | 0.131074 | − | 0.131074i | ||||
\(341\) | 0.838414i | 0.0454027i | ||||||||
\(342\) | −1.98517 | − | 1.33853i | −0.107346 | − | 0.0723796i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 1.73164 | + | 1.73164i | 0.0933637 | + | 0.0933637i | ||||
\(345\) | −2.17887 | − | 4.09704i | −0.117306 | − | 0.220577i | ||||
\(346\) | 0.668376 | + | 0.668376i | 0.0359321 | + | 0.0359321i | ||||
\(347\) | 11.4483i | 0.614575i | 0.951617 | + | 0.307287i | \(0.0994212\pi\) | ||||
−0.951617 | + | 0.307287i | \(0.900579\pi\) | |||||||
\(348\) | −6.93788 | − | 2.12049i | −0.371909 | − | 0.113670i | ||||
\(349\) | −3.56656 | − | 3.56656i | −0.190914 | − | 0.190914i | 0.605177 | − | 0.796091i | \(-0.293102\pi\) |
−0.796091 | + | 0.605177i | \(0.793102\pi\) | |||||||
\(350\) | 4.16658 | 0.222713 | ||||||||
\(351\) | 17.1823 | − | 7.46789i | 0.917122 | − | 0.398607i | ||||
\(352\) | −0.489480 | −0.0260894 | ||||||||
\(353\) | −3.64816 | − | 3.64816i | −0.194172 | − | 0.194172i | 0.603324 | − | 0.797496i | \(-0.293843\pi\) |
−0.797496 | + | 0.603324i | \(0.793843\pi\) | |||||||
\(354\) | −5.23799 | − | 1.60094i | −0.278396 | − | 0.0850889i | ||||
\(355\) | 2.56877i | 0.136336i | ||||||||
\(356\) | 12.0210 | + | 12.0210i | 0.637114 | + | 0.637114i | ||||
\(357\) | −3.04491 | − | 5.72550i | −0.161154 | − | 0.303025i | ||||
\(358\) | −12.8441 | − | 12.8441i | −0.678834 | − | 0.678834i | ||||
\(359\) | 0.169016 | − | 0.169016i | 0.00892035 | − | 0.00892035i | −0.702633 | − | 0.711553i | \(-0.747992\pi\) |
0.711553 | + | 0.702633i | \(0.247992\pi\) | |||||||
\(360\) | −2.27079 | − | 1.53112i | −0.119681 | − | 0.0806971i | ||||
\(361\) | 18.3630i | 0.966476i | ||||||||
\(362\) | 13.0654 | − | 13.0654i | 0.686701 | − | 0.686701i | ||||
\(363\) | −5.44762 | + | 17.8237i | −0.285926 | + | 0.935499i | ||||
\(364\) | 1.77419 | + | 3.13883i | 0.0929928 | + | 0.164519i | ||||
\(365\) | − | 3.80684i | − | 0.199259i | ||||||
\(366\) | −3.72740 | − | 7.00881i | −0.194834 | − | 0.366357i | ||||
\(367\) | −19.5827 | −1.02221 | −0.511104 | − | 0.859519i | \(-0.670763\pi\) | ||||
−0.511104 | + | 0.859519i | \(0.670763\pi\) | |||||||
\(368\) | 2.93468 | 0.152981 | ||||||||
\(369\) | −1.90434 | − | 9.78830i | −0.0991359 | − | 0.509558i | ||||
\(370\) | −1.98104 | + | 1.98104i | −0.102989 | + | 0.102989i | ||||
\(371\) | 3.55868 | − | 3.55868i | 0.184757 | − | 0.184757i | ||||
\(372\) | −1.39303 | − | 2.61939i | −0.0722254 | − | 0.135809i | ||||
\(373\) | −26.8148 | −1.38842 | −0.694210 | − | 0.719773i | \(-0.744246\pi\) | ||||
−0.694210 | + | 0.719773i | \(0.744246\pi\) | |||||||
\(374\) | −1.83262 | −0.0947625 | ||||||||
\(375\) | 12.7972 | − | 6.80578i | 0.660847 | − | 0.351449i | ||||
\(376\) | 10.2160i | 0.526848i | ||||||||
\(377\) | 14.5510 | + | 4.04168i | 0.749414 | + | 0.208157i | ||||
\(378\) | −4.03735 | + | 3.27105i | −0.207659 | + | 0.168245i | ||||
\(379\) | 0.249109 | − | 0.249109i | 0.0127959 | − | 0.0127959i | −0.700680 | − | 0.713476i | \(-0.747120\pi\) |
0.713476 | + | 0.700680i | \(0.247120\pi\) | |||||||
\(380\) | − | 0.728595i | − | 0.0373762i | ||||||
\(381\) | −8.53529 | + | 27.9260i | −0.437276 | + | 1.43069i | ||||
\(382\) | −10.0262 | + | 10.0262i | −0.512984 | + | 0.512984i | ||||
\(383\) | 2.01331 | + | 2.01331i | 0.102875 | + | 0.102875i | 0.756671 | − | 0.653796i | \(-0.226824\pi\) |
−0.653796 | + | 0.756671i | \(0.726824\pi\) | |||||||
\(384\) | 1.52924 | − | 0.813276i | 0.0780388 | − | 0.0415023i | ||||
\(385\) | 0.315975 | + | 0.315975i | 0.0161036 | + | 0.0161036i | ||||
\(386\) | 4.77786i | 0.243187i | ||||||||
\(387\) | 4.10722 | − | 6.09139i | 0.208782 | − | 0.309643i | ||||
\(388\) | 6.69250 | + | 6.69250i | 0.339760 | + | 0.339760i | ||||
\(389\) | 6.62477 | 0.335889 | 0.167945 | − | 0.985796i | \(-0.446287\pi\) | ||||
0.167945 | + | 0.985796i | \(0.446287\pi\) | |||||||
\(390\) | 4.80735 | + | 3.06479i | 0.243430 | + | 0.155192i | ||||
\(391\) | 10.9875 | 0.555659 | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 10.8435 | − | 35.4780i | 0.546981 | − | 1.78963i | ||||
\(394\) | − | 2.13237i | − | 0.107427i | ||||||
\(395\) | −3.74968 | − | 3.74968i | −0.188667 | − | 0.188667i | ||||
\(396\) | 0.280431 | + | 1.44142i | 0.0140922 | + | 0.0724338i | ||||
\(397\) | −16.9697 | − | 16.9697i | −0.851684 | − | 0.851684i | 0.138657 | − | 0.990341i | \(-0.455722\pi\) |
−0.990341 | + | 0.138657i | \(0.955722\pi\) | |||||||
\(398\) | −7.91950 | + | 7.91950i | −0.396968 | + | 0.396968i | ||||
\(399\) | −1.32197 | − | 0.404047i | −0.0661812 | − | 0.0202276i | ||||
\(400\) | 4.16658i | 0.208329i | ||||||||
\(401\) | 19.1843 | − | 19.1843i | 0.958019 | − | 0.958019i | −0.0411346 | − | 0.999154i | \(-0.513097\pi\) |
0.999154 | + | 0.0411346i | \(0.0130973\pi\) | |||||||
\(402\) | 3.64622 | + | 1.11443i | 0.181857 | + | 0.0555828i | ||||
\(403\) | 3.03895 | + | 5.37640i | 0.151381 | + | 0.267817i | ||||
\(404\) | − | 13.4516i | − | 0.669241i | ||||||
\(405\) | −3.20785 | + | 7.56420i | −0.159399 | + | 0.375868i | ||||
\(406\) | −4.18850 | −0.207872 | ||||||||
\(407\) | 1.50214 | 0.0744584 | ||||||||
\(408\) | 5.72550 | − | 3.04491i | 0.283454 | − | 0.150746i | ||||
\(409\) | 6.18510 | − | 6.18510i | 0.305834 | − | 0.305834i | −0.537457 | − | 0.843291i | \(-0.680615\pi\) |
0.843291 | + | 0.537457i | \(0.180615\pi\) | |||||||
\(410\) | 2.14571 | − | 2.14571i | 0.105969 | − | 0.105969i | ||||
\(411\) | −10.5963 | + | 5.63526i | −0.522675 | + | 0.277967i | ||||
\(412\) | −6.61463 | −0.325879 | ||||||||
\(413\) | −3.16225 | −0.155604 | ||||||||
\(414\) | −1.68132 | − | 8.64200i | −0.0826325 | − | 0.424731i | ||||
\(415\) | − | 1.87567i | − | 0.0920732i | ||||||
\(416\) | −3.13883 | + | 1.77419i | −0.153894 | + | 0.0869868i | ||||
\(417\) | 7.33891 | + | 2.24306i | 0.359388 | + | 0.109843i | ||||
\(418\) | −0.276232 | + | 0.276232i | −0.0135109 | + | 0.0135109i | ||||
\(419\) | − | 21.7419i | − | 1.06216i | −0.847321 | − | 0.531080i | \(-0.821786\pi\) | ||
0.847321 | − | 0.531080i | \(-0.178214\pi\) | |||||||
\(420\) | −1.51217 | − | 0.462180i | −0.0737864 | − | 0.0225521i | ||||
\(421\) | 20.0060 | − | 20.0060i | 0.975035 | − | 0.975035i | −0.0246608 | − | 0.999696i | \(-0.507851\pi\) |
0.999696 | + | 0.0246608i | \(0.00785059\pi\) | |||||||
\(422\) | 11.8119 | + | 11.8119i | 0.574997 | + | 0.574997i | ||||
\(423\) | 30.0838 | − | 5.85289i | 1.46272 | − | 0.284577i | ||||
\(424\) | 3.55868 | + | 3.55868i | 0.172825 | + | 0.172825i | ||||
\(425\) | 15.5997i | 0.756696i | ||||||||
\(426\) | −1.42452 | + | 4.66079i | −0.0690184 | + | 0.225816i | ||||
\(427\) | −3.24081 | − | 3.24081i | −0.156834 | − | 0.156834i | ||||
\(428\) | −0.232092 | −0.0112186 | ||||||||
\(429\) | −0.660654 | − | 2.98456i | −0.0318967 | − | 0.144096i | ||||
\(430\) | 2.23566 | 0.107813 | ||||||||
\(431\) | −19.5706 | − | 19.5706i | −0.942682 | − | 0.942682i | 0.0557616 | − | 0.998444i | \(-0.482241\pi\) |
−0.998444 | + | 0.0557616i | \(0.982241\pi\) | |||||||
\(432\) | −3.27105 | − | 4.03735i | −0.157378 | − | 0.194247i | ||||
\(433\) | 1.51276i | 0.0726985i | 0.999339 | + | 0.0363493i | \(0.0115729\pi\) | ||||
−0.999339 | + | 0.0363493i | \(0.988427\pi\) | |||||||
\(434\) | −1.21118 | − | 1.21118i | −0.0581385 | − | 0.0581385i | ||||
\(435\) | −5.84747 | + | 3.10978i | −0.280365 | + | 0.149102i | ||||
\(436\) | −8.15828 | − | 8.15828i | −0.390711 | − | 0.390711i | ||||
\(437\) | 1.65615 | − | 1.65615i | 0.0792242 | − | 0.0792242i | ||||
\(438\) | 2.11111 | − | 6.90717i | 0.100873 | − | 0.330037i | ||||
\(439\) | − | 3.57755i | − | 0.170747i | −0.996349 | − | 0.0853737i | \(-0.972792\pi\) | ||
0.996349 | − | 0.0853737i | \(-0.0272084\pi\) | |||||||
\(440\) | −0.315975 | + | 0.315975i | −0.0150635 | + | 0.0150635i | ||||
\(441\) | −1.67717 | + | 2.48739i | −0.0798650 | + | 0.118447i | ||||
\(442\) | −11.7518 | + | 6.64258i | −0.558976 | + | 0.315955i | ||||
\(443\) | − | 2.53190i | − | 0.120294i | −0.998190 | − | 0.0601472i | \(-0.980843\pi\) | ||
0.998190 | − | 0.0601472i | \(-0.0191570\pi\) | |||||||
\(444\) | −4.69302 | + | 2.49582i | −0.222721 | + | 0.118446i | ||||
\(445\) | 15.5199 | 0.735716 | ||||||||
\(446\) | −22.9482 | −1.08663 | ||||||||
\(447\) | 8.06181 | + | 15.1590i | 0.381310 | + | 0.716997i | ||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | −12.5933 | + | 12.5933i | −0.594314 | + | 0.594314i | −0.938794 | − | 0.344480i | \(-0.888055\pi\) |
0.344480 | + | 0.938794i | \(0.388055\pi\) | |||||||
\(450\) | 12.2697 | − | 2.38710i | 0.578398 | − | 0.112529i | ||||
\(451\) | −1.62700 | −0.0766126 | ||||||||
\(452\) | 9.58107 | 0.450656 | ||||||||
\(453\) | 7.25183 | + | 13.6360i | 0.340721 | + | 0.640674i | ||||
\(454\) | 26.2822i | 1.23349i | ||||||||
\(455\) | 3.17151 | + | 0.880920i | 0.148683 | + | 0.0412982i | ||||
\(456\) | 0.404047 | − | 1.32197i | 0.0189212 | − | 0.0619069i | ||||
\(457\) | 2.80065 | − | 2.80065i | 0.131009 | − | 0.131009i | −0.638562 | − | 0.769571i | \(-0.720470\pi\) |
0.769571 | + | 0.638562i | \(0.220470\pi\) | |||||||
\(458\) | − | 14.5685i | − | 0.680741i | ||||||
\(459\) | −12.2468 | − | 15.1159i | −0.571634 | − | 0.705549i | ||||
\(460\) | 1.89443 | − | 1.89443i | 0.0883282 | − | 0.0883282i | ||||
\(461\) | −1.30086 | − | 1.30086i | −0.0605872 | − | 0.0605872i | 0.676164 | − | 0.736751i | \(-0.263641\pi\) |
−0.736751 | + | 0.676164i | \(0.763641\pi\) | |||||||
\(462\) | 0.398082 | + | 0.748534i | 0.0185205 | + | 0.0348250i | ||||
\(463\) | 8.21976 | + | 8.21976i | 0.382005 | + | 0.382005i | 0.871824 | − | 0.489819i | \(-0.162937\pi\) |
−0.489819 | + | 0.871824i | \(0.662937\pi\) | |||||||
\(464\) | − | 4.18850i | − | 0.194446i | ||||||
\(465\) | −2.59015 | − | 0.791652i | −0.120115 | − | 0.0367120i | ||||
\(466\) | −20.9136 | − | 20.9136i | −0.968803 | − | 0.968803i | ||||
\(467\) | 32.5141 | 1.50457 | 0.752286 | − | 0.658837i | \(-0.228951\pi\) | ||||
0.752286 | + | 0.658837i | \(0.228951\pi\) | |||||||
\(468\) | 7.02289 | + | 8.22672i | 0.324633 | + | 0.380280i | ||||
\(469\) | 2.20128 | 0.101646 | ||||||||
\(470\) | 6.59473 | + | 6.59473i | 0.304192 | + | 0.304192i | ||||
\(471\) | −31.8377 | − | 9.73088i | −1.46701 | − | 0.448375i | ||||
\(472\) | − | 3.16225i | − | 0.145555i | ||||||
\(473\) | −0.847603 | − | 0.847603i | −0.0389728 | − | 0.0389728i | ||||
\(474\) | −4.72404 | − | 8.88285i | −0.216982 | − | 0.408003i | ||||
\(475\) | 2.35135 | + | 2.35135i | 0.107887 | + | 0.107887i | ||||
\(476\) | 2.64741 | − | 2.64741i | 0.121344 | − | 0.121344i | ||||
\(477\) | 8.44072 | − | 12.5184i | 0.386474 | − | 0.573176i | ||||
\(478\) | 6.25816i | 0.286242i | ||||||||
\(479\) | −22.3153 | + | 22.3153i | −1.01961 | + | 1.01961i | −0.0198079 | + | 0.999804i | \(0.506305\pi\) |
−0.999804 | + | 0.0198079i | \(0.993695\pi\) | |||||||
\(480\) | 0.462180 | − | 1.51217i | 0.0210955 | − | 0.0690209i | ||||
\(481\) | 9.63260 | − | 5.44472i | 0.439209 | − | 0.248258i | ||||
\(482\) | − | 16.5013i | − | 0.751615i | ||||||
\(483\) | −2.38670 | − | 4.48783i | −0.108599 | − | 0.204203i | ||||
\(484\) | −10.7604 | −0.489109 | ||||||||
\(485\) | 8.64045 | 0.392343 | ||||||||
\(486\) | −10.0151 | + | 11.9456i | −0.454295 | + | 0.541864i | ||||
\(487\) | −7.39827 | + | 7.39827i | −0.335247 | + | 0.335247i | −0.854575 | − | 0.519328i | \(-0.826182\pi\) |
0.519328 | + | 0.854575i | \(0.326182\pi\) | |||||||
\(488\) | 3.24081 | − | 3.24081i | 0.146704 | − | 0.146704i | ||||
\(489\) | 10.8952 | + | 20.4867i | 0.492696 | + | 0.926440i | ||||
\(490\) | −0.912921 | −0.0412416 | ||||||||
\(491\) | −22.4035 | −1.01106 | −0.505528 | − | 0.862810i | \(-0.668702\pi\) | ||||
−0.505528 | + | 0.862810i | \(0.668702\pi\) | |||||||
\(492\) | 5.08311 | − | 2.70328i | 0.229164 | − | 0.121873i | ||||
\(493\) | − | 15.6818i | − | 0.706272i | ||||||
\(494\) | −0.770117 | + | 2.77260i | −0.0346492 | + | 0.124745i | ||||
\(495\) | 1.11151 | + | 0.749453i | 0.0499586 | + | 0.0336854i | ||||
\(496\) | 1.21118 | − | 1.21118i | 0.0543836 | − | 0.0543836i | ||||
\(497\) | 2.81379i | 0.126216i | ||||||||
\(498\) | 1.04017 | − | 3.40324i | 0.0466109 | − | 0.152503i | ||||
\(499\) | 25.8150 | − | 25.8150i | 1.15564 | − | 1.15564i | 0.170232 | − | 0.985404i | \(-0.445548\pi\) |
0.985404 | − | 0.170232i | \(-0.0544517\pi\) | |||||||
\(500\) | 5.91732 | + | 5.91732i | 0.264631 | + | 0.264631i | ||||
\(501\) | 36.7881 | − | 19.5645i | 1.64357 | − | 0.874078i | ||||
\(502\) | 10.0858 | + | 10.0858i | 0.450152 | + | 0.450152i | ||||
\(503\) | 2.80539i | 0.125086i | 0.998042 | + | 0.0625430i | \(0.0199211\pi\) | ||||
−0.998042 | + | 0.0625430i | \(0.980079\pi\) | |||||||
\(504\) | −2.48739 | − | 1.67717i | −0.110797 | − | 0.0747069i | ||||
\(505\) | −8.68343 | − | 8.68343i | −0.386408 | − | 0.386408i | ||||
\(506\) | −1.43647 | −0.0638587 | ||||||||
\(507\) | −15.0544 | − | 16.7441i | −0.668591 | − | 0.743630i | ||||
\(508\) | −16.8593 | −0.748012 | ||||||||
\(509\) | −14.7980 | − | 14.7980i | −0.655912 | − | 0.655912i | 0.298499 | − | 0.954410i | \(-0.403514\pi\) |
−0.954410 | + | 0.298499i | \(0.903514\pi\) | |||||||
\(510\) | 1.73041 | − | 5.66158i | 0.0766236 | − | 0.250699i | ||||
\(511\) | − | 4.16996i | − | 0.184468i | ||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −4.12440 | − | 0.432453i | −0.182097 | − | 0.0190933i | ||||
\(514\) | 10.3182 | + | 10.3182i | 0.455114 | + | 0.455114i | ||||
\(515\) | −4.26996 | + | 4.26996i | −0.188157 | + | 0.188157i | ||||
\(516\) | 4.05640 | + | 1.23980i | 0.178573 | + | 0.0545790i | ||||
\(517\) | − | 5.00051i | − | 0.219922i | ||||||
\(518\) | −2.17001 | + | 2.17001i | −0.0953446 | + | 0.0953446i | ||||
\(519\) | 1.56568 | + | 0.478535i | 0.0687258 | + | 0.0210054i | ||||
\(520\) | −0.880920 | + | 3.17151i | −0.0386309 | + | 0.139080i | ||||
\(521\) | − | 41.1077i | − | 1.80096i | −0.434896 | − | 0.900481i | \(-0.643215\pi\) | ||
0.434896 | − | 0.900481i | \(-0.356785\pi\) | |||||||
\(522\) | −12.3342 | + | 2.39966i | −0.539855 | + | 0.105030i | ||||
\(523\) | −10.5444 | −0.461074 | −0.230537 | − | 0.973064i | \(-0.574048\pi\) | ||||
−0.230537 | + | 0.973064i | \(0.574048\pi\) | |||||||
\(524\) | 21.4186 | 0.935676 | ||||||||
\(525\) | 6.37171 | − | 3.38857i | 0.278084 | − | 0.147890i | ||||
\(526\) | −18.8163 | + | 18.8163i | −0.820429 | + | 0.820429i | ||||
\(527\) | 4.53467 | − | 4.53467i | 0.197533 | − | 0.197533i | ||||
\(528\) | −0.748534 | + | 0.398082i | −0.0325758 | + | 0.0173243i | ||||
\(529\) | −14.3877 | −0.625551 | ||||||||
\(530\) | 4.59448 | 0.199571 | ||||||||
\(531\) | −9.31216 | + | 1.81171i | −0.404113 | + | 0.0786214i | ||||
\(532\) | − | 0.798093i | − | 0.0346017i | ||||||
\(533\) | −10.4333 | + | 5.89730i | −0.451916 | + | 0.255440i | ||||
\(534\) | 28.1595 | + | 8.60667i | 1.21858 | + | 0.372447i | ||||
\(535\) | −0.149823 | + | 0.149823i | −0.00647742 | + | 0.00647742i | ||||
\(536\) | 2.20128i | 0.0950808i | ||||||||
\(537\) | −30.0876 | − | 9.19598i | −1.29838 | − | 0.396836i | ||||
\(538\) | −19.4613 | + | 19.4613i | −0.839035 | + | 0.839035i | ||||
\(539\) | 0.346115 | + | 0.346115i | 0.0149082 | + | 0.0149082i | ||||
\(540\) | −4.71781 | − | 0.494674i | −0.203022 | − | 0.0212874i | ||||
\(541\) | 9.48820 | + | 9.48820i | 0.407930 | + | 0.407930i | 0.881016 | − | 0.473086i | \(-0.156860\pi\) |
−0.473086 | + | 0.881016i | \(0.656860\pi\) | |||||||
\(542\) | 15.8991i | 0.682924i | ||||||||
\(543\) | 9.35438 | − | 30.6059i | 0.401435 | − | 1.31342i | ||||
\(544\) | 2.64741 | + | 2.64741i | 0.113507 | + | 0.113507i | ||||
\(545\) | −10.5329 | −0.451179 | ||||||||
\(546\) | 5.26590 | + | 3.35713i | 0.225360 | + | 0.143672i | ||||
\(547\) | 34.3778 | 1.46989 | 0.734945 | − | 0.678127i | \(-0.237208\pi\) | ||||
0.734945 | + | 0.678127i | \(0.237208\pi\) | |||||||
\(548\) | −4.89961 | − | 4.89961i | −0.209301 | − | 0.209301i | ||||
\(549\) | −11.4002 | − | 7.68677i | −0.486549 | − | 0.328064i | ||||
\(550\) | − | 2.03946i | − | 0.0869627i | ||||||
\(551\) | −2.36373 | − | 2.36373i | −0.100698 | − | 0.100698i | ||||
\(552\) | 4.48783 | − | 2.38670i | 0.191015 | − | 0.101585i | ||||
\(553\) | −4.10734 | − | 4.10734i | −0.174662 | − | 0.174662i | ||||
\(554\) | −17.4259 | + | 17.4259i | −0.740355 | + | 0.740355i | ||||
\(555\) | −1.41836 | + | 4.64063i | −0.0602061 | + | 0.196984i | ||||
\(556\) | 4.43061i | 0.187900i | ||||||||
\(557\) | 23.0785 | − | 23.0785i | 0.977867 | − | 0.977867i | −0.0218937 | − | 0.999760i | \(-0.506970\pi\) |
0.999760 | + | 0.0218937i | \(0.00696954\pi\) | |||||||
\(558\) | −4.26057 | − | 2.87276i | −0.180364 | − | 0.121614i | ||||
\(559\) | −8.50757 | − | 2.36307i | −0.359832 | − | 0.0999470i | ||||
\(560\) | − | 0.912921i | − | 0.0385779i | ||||||
\(561\) | −2.80252 | + | 1.49042i | −0.118322 | + | 0.0629258i | ||||
\(562\) | −33.0757 | −1.39521 | ||||||||
\(563\) | −19.8382 | −0.836082 | −0.418041 | − | 0.908428i | \(-0.637283\pi\) | ||||
−0.418041 | + | 0.908428i | \(0.637283\pi\) | |||||||
\(564\) | 8.30839 | + | 15.6227i | 0.349846 | + | 0.657833i | ||||
\(565\) | 6.18489 | − | 6.18489i | 0.260200 | − | 0.260200i | ||||
\(566\) | −6.73817 | + | 6.73817i | −0.283226 | + | 0.283226i | ||||
\(567\) | −3.51383 | + | 8.28571i | −0.147567 | + | 0.347967i | ||||
\(568\) | −2.81379 | −0.118064 | ||||||||
\(569\) | −6.55300 | −0.274716 | −0.137358 | − | 0.990521i | \(-0.543861\pi\) | ||||
−0.137358 | + | 0.990521i | \(0.543861\pi\) | |||||||
\(570\) | −0.592549 | − | 1.11420i | −0.0248191 | − | 0.0466687i | ||||
\(571\) | − | 30.9170i | − | 1.29384i | −0.762559 | − | 0.646919i | \(-0.776057\pi\) | ||
0.762559 | − | 0.646919i | \(-0.223943\pi\) | |||||||
\(572\) | 1.53640 | − | 0.868431i | 0.0642399 | − | 0.0363109i | ||||
\(573\) | −7.17841 | + | 23.4865i | −0.299882 | + | 0.981163i | ||||
\(574\) | 2.35038 | − | 2.35038i | 0.0981030 | − | 0.0981030i | ||||
\(575\) | 12.2276i | 0.509924i | ||||||||
\(576\) | 1.67717 | − | 2.48739i | 0.0698819 | − | 0.103641i | ||||
\(577\) | 10.8612 | − | 10.8612i | 0.452158 | − | 0.452158i | −0.443912 | − | 0.896070i | \(-0.646410\pi\) |
0.896070 | + | 0.443912i | \(0.146410\pi\) | |||||||
\(578\) | −2.10888 | − | 2.10888i | −0.0877177 | − | 0.0877177i | ||||
\(579\) | 3.88572 | + | 7.30651i | 0.161485 | + | 0.303648i | ||||
\(580\) | −2.70381 | − | 2.70381i | −0.112270 | − | 0.112270i | ||||
\(581\) | − | 2.05459i | − | 0.0852386i | ||||||
\(582\) | 15.6773 | + | 4.79161i | 0.649845 | + | 0.198619i | ||||
\(583\) | −1.74190 | − | 1.74190i | −0.0721422 | − | 0.0721422i | ||||
\(584\) | 4.16996 | 0.172554 | ||||||||
\(585\) | 9.84412 | + | 0.777110i | 0.407004 | + | 0.0321296i | ||||
\(586\) | −9.45631 | −0.390636 | ||||||||
\(587\) | 4.36741 | + | 4.36741i | 0.180262 | + | 0.180262i | 0.791470 | − | 0.611208i | \(-0.209316\pi\) |
−0.611208 | + | 0.791470i | \(0.709316\pi\) | |||||||
\(588\) | −1.65641 | − | 0.506265i | −0.0683092 | − | 0.0208780i | ||||
\(589\) | − | 1.36703i | − | 0.0563273i | ||||||
\(590\) | −2.04134 | − | 2.04134i | −0.0840405 | − | 0.0840405i | ||||
\(591\) | −1.73421 | − | 3.26091i | −0.0713357 | − | 0.134136i | ||||
\(592\) | −2.17001 | − | 2.17001i | −0.0891867 | − | 0.0891867i | ||||
\(593\) | −6.15560 | + | 6.15560i | −0.252780 | + | 0.252780i | −0.822109 | − | 0.569329i | \(-0.807203\pi\) |
0.569329 | + | 0.822109i | \(0.307203\pi\) | |||||||
\(594\) | 1.60112 | + | 1.97621i | 0.0656945 | + | 0.0810847i | ||||
\(595\) | − | 3.41798i | − | 0.140124i | ||||||
\(596\) | −7.00938 | + | 7.00938i | −0.287115 | + | 0.287115i | ||||
\(597\) | −5.67010 | + | 18.5516i | −0.232062 | + | 0.759265i | ||||
\(598\) | −9.21145 | + | 5.20667i | −0.376684 | + | 0.212917i | ||||
\(599\) | − | 31.1615i | − | 1.27323i | −0.771184 | − | 0.636613i | \(-0.780335\pi\) | ||
0.771184 | − | 0.636613i | \(-0.219665\pi\) | |||||||
\(600\) | 3.38857 | + | 6.37171i | 0.138338 | + | 0.260124i | ||||
\(601\) | 10.3915 | 0.423878 | 0.211939 | − | 0.977283i | \(-0.432022\pi\) | ||||
0.211939 | + | 0.977283i | \(0.432022\pi\) | |||||||
\(602\) | 2.44891 | 0.0998100 | ||||||||
\(603\) | 6.48230 | − | 1.26115i | 0.263980 | − | 0.0513579i | ||||
\(604\) | −6.30515 | + | 6.30515i | −0.256553 | + | 0.256553i | ||||
\(605\) | −6.94619 | + | 6.94619i | −0.282403 | + | 0.282403i | ||||
\(606\) | −10.9398 | − | 20.5707i | −0.444401 | − | 0.835629i | ||||
\(607\) | −19.5779 | −0.794643 | −0.397322 | − | 0.917679i | \(-0.630060\pi\) | ||||
−0.397322 | + | 0.917679i | \(0.630060\pi\) | |||||||
\(608\) | 0.798093 | 0.0323669 | ||||||||
\(609\) | −6.40524 | + | 3.40641i | −0.259553 | + | 0.138035i | ||||
\(610\) | − | 4.18409i | − | 0.169409i | ||||||
\(611\) | −18.1250 | − | 32.0661i | −0.733260 | − | 1.29726i | ||||
\(612\) | 6.27932 | − | 9.31281i | 0.253827 | − | 0.376448i | ||||
\(613\) | 6.71448 | − | 6.71448i | 0.271195 | − | 0.271195i | −0.558386 | − | 0.829581i | \(-0.688579\pi\) |
0.829581 | + | 0.558386i | \(0.188579\pi\) | |||||||
\(614\) | 24.9184i | 1.00563i | ||||||||
\(615\) | 1.53626 | − | 5.02637i | 0.0619479 | − | 0.202683i | ||||
\(616\) | −0.346115 | + | 0.346115i | −0.0139454 | + | 0.0139454i | ||||
\(617\) | 10.3723 | + | 10.3723i | 0.417575 | + | 0.417575i | 0.884367 | − | 0.466792i | \(-0.154590\pi\) |
−0.466792 | + | 0.884367i | \(0.654590\pi\) | |||||||
\(618\) | −10.1154 | + | 5.37952i | −0.406900 | + | 0.216396i | ||||
\(619\) | −17.7776 | − | 17.7776i | −0.714542 | − | 0.714542i | 0.252940 | − | 0.967482i | \(-0.418602\pi\) |
−0.967482 | + | 0.252940i | \(0.918602\pi\) | |||||||
\(620\) | − | 1.56371i | − | 0.0628001i | ||||||
\(621\) | −9.59948 | − | 11.8483i | −0.385214 | − | 0.475457i | ||||
\(622\) | −2.91052 | − | 2.91052i | −0.116701 | − | 0.116701i | ||||
\(623\) | 17.0003 | 0.681104 | ||||||||
\(624\) | −3.35713 | + | 5.26590i | −0.134393 | + | 0.210805i | ||||
\(625\) | −13.1932 | −0.527729 | ||||||||
\(626\) | −10.7074 | − | 10.7074i | −0.427955 | − | 0.427955i | ||||
\(627\) | −0.197773 | + | 0.647078i | −0.00789829 | + | 0.0258418i | ||||
\(628\) | − | 19.2209i | − | 0.766998i | ||||||
\(629\) | −8.12452 | − | 8.12452i | −0.323946 | − | 0.323946i | ||||
\(630\) | −2.68836 | + | 0.523027i | −0.107107 | + | 0.0208379i | ||||
\(631\) | 33.4192 | + | 33.4192i | 1.33040 | + | 1.33040i | 0.905011 | + | 0.425388i | \(0.139862\pi\) |
0.425388 | + | 0.905011i | \(0.360138\pi\) | |||||||
\(632\) | 4.10734 | − | 4.10734i | 0.163381 | − | 0.163381i | ||||
\(633\) | 27.6697 | + | 8.45697i | 1.09977 | + | 0.336134i | ||||
\(634\) | 22.3606i | 0.888053i | ||||||||
\(635\) | −10.8832 | + | 10.8832i | −0.431888 | + | 0.431888i | ||||
\(636\) | 8.33626 | + | 2.54789i | 0.330554 | + | 0.101031i | ||||
\(637\) | 3.47403 | + | 0.964947i | 0.137646 | + | 0.0382326i | ||||
\(638\) | 2.05019i | 0.0811678i | ||||||||
\(639\) | 1.61206 | + | 8.28601i | 0.0637723 | + | 0.327789i | ||||
\(640\) | 0.912921 | 0.0360864 | ||||||||
\(641\) | 33.1552 | 1.30955 | 0.654775 | − | 0.755823i | \(-0.272763\pi\) | ||||
0.654775 | + | 0.755823i | \(0.272763\pi\) | |||||||
\(642\) | −0.354926 | + | 0.188755i | −0.0140078 | + | 0.00744957i | ||||
\(643\) | 12.7533 | − | 12.7533i | 0.502941 | − | 0.502941i | −0.409410 | − | 0.912351i | \(-0.634265\pi\) |
0.912351 | + | 0.409410i | \(0.134265\pi\) | |||||||
\(644\) | 2.07513 | − | 2.07513i | 0.0817716 | − | 0.0817716i | ||||
\(645\) | 3.41886 | − | 1.81821i | 0.134618 | − | 0.0715918i | ||||
\(646\) | 2.98807 | 0.117564 | ||||||||
\(647\) | 25.5626 | 1.00497 | 0.502484 | − | 0.864586i | \(-0.332420\pi\) | ||||
0.502484 | + | 0.864586i | \(0.332420\pi\) | |||||||
\(648\) | −8.28571 | − | 3.51383i | −0.325493 | − | 0.138036i | ||||
\(649\) | 1.54786i | 0.0607589i | ||||||||
\(650\) | −7.39229 | − | 13.0782i | −0.289950 | − | 0.512968i | ||||
\(651\) | −2.83721 | − | 0.867164i | −0.111199 | − | 0.0339868i | ||||
\(652\) | −9.47285 | + | 9.47285i | −0.370985 | + | 0.370985i | ||||
\(653\) | − | 37.4482i | − | 1.46546i | −0.680520 | − | 0.732730i | \(-0.738246\pi\) | ||
0.680520 | − | 0.732730i | \(-0.261754\pi\) | |||||||
\(654\) | −19.1109 | − | 5.84106i | −0.747296 | − | 0.228404i | ||||
\(655\) | 13.8264 | − | 13.8264i | 0.540242 | − | 0.540242i | ||||
\(656\) | 2.35038 | + | 2.35038i | 0.0917670 | + | 0.0917670i | ||||
\(657\) | −2.38904 | − | 12.2796i | −0.0932052 | − | 0.479075i | ||||
\(658\) | 7.22377 | + | 7.22377i | 0.281612 | + | 0.281612i | ||||
\(659\) | 9.60599i | 0.374196i | 0.982341 | + | 0.187098i | \(0.0599082\pi\) | ||||
−0.982341 | + | 0.187098i | \(0.940092\pi\) | |||||||
\(660\) | −0.226228 | + | 0.740178i | −0.00880591 | + | 0.0288114i | ||||
\(661\) | 6.14906 | + | 6.14906i | 0.239171 | + | 0.239171i | 0.816507 | − | 0.577336i | \(-0.195908\pi\) |
−0.577336 | + | 0.816507i | \(0.695908\pi\) | |||||||
\(662\) | 16.2910 | 0.633169 | ||||||||
\(663\) | −12.5691 | + | 19.7156i | −0.488144 | + | 0.765689i | ||||
\(664\) | 2.05459 | 0.0797334 | ||||||||
\(665\) | −0.515195 | − | 0.515195i | −0.0199784 | − | 0.0199784i | ||||
\(666\) | −5.14697 | + | 7.63343i | −0.199441 | + | 0.295790i | ||||
\(667\) | − | 12.2919i | − | 0.475944i | ||||||
\(668\) | 17.0105 | + | 17.0105i | 0.658155 | + | 0.658155i | ||||
\(669\) | −35.0934 | + | 18.6632i | −1.35679 | + | 0.721563i | ||||
\(670\) | 1.42100 | + | 1.42100i | 0.0548979 | + | 0.0548979i | ||||
\(671\) | −1.58631 | + | 1.58631i | −0.0612389 | + | 0.0612389i | ||||
\(672\) | 0.506265 | − | 1.65641i | 0.0195296 | − | 0.0638974i | ||||
\(673\) | 6.96650i | 0.268539i | 0.990945 | + | 0.134269i | \(0.0428688\pi\) | ||||
−0.990945 | + | 0.134269i | \(0.957131\pi\) | |||||||
\(674\) | 20.7548 | − | 20.7548i | 0.799444 | − | 0.799444i | ||||
\(675\) | 16.8219 | − | 13.6291i | 0.647477 | − | 0.524584i | ||||
\(676\) | 6.70451 | − | 11.1378i | 0.257866 | − | 0.428375i | ||||
\(677\) | − | 5.13417i | − | 0.197322i | −0.995121 | − | 0.0986611i | \(-0.968544\pi\) | ||
0.995121 | − | 0.0986611i | \(-0.0314560\pi\) | |||||||
\(678\) | 14.6518 | − | 7.79205i | 0.562698 | − | 0.299252i | ||||
\(679\) | 9.46462 | 0.363219 | ||||||||
\(680\) | 3.41798 | 0.131074 | ||||||||
\(681\) | 21.3747 | + | 40.1919i | 0.819081 | + | 1.54016i | ||||
\(682\) | −0.592848 | + | 0.592848i | −0.0227013 | + | 0.0227013i | ||||
\(683\) | 15.1739 | − | 15.1739i | 0.580615 | − | 0.580615i | −0.354457 | − | 0.935072i | \(-0.615334\pi\) |
0.935072 | + | 0.354457i | \(0.115334\pi\) | |||||||
\(684\) | −0.457240 | − | 2.35021i | −0.0174830 | − | 0.0898626i | ||||
\(685\) | −6.32571 | −0.241693 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −11.8482 | − | 22.2788i | −0.452037 | − | 0.849988i | ||||
\(688\) | 2.44891i | 0.0933637i | ||||||||
\(689\) | −17.4838 | − | 4.85631i | −0.666081 | − | 0.185011i | ||||
\(690\) | 1.35635 | − | 4.43773i | 0.0516353 | − | 0.168942i | ||||
\(691\) | −19.4188 | + | 19.4188i | −0.738725 | + | 0.738725i | −0.972331 | − | 0.233607i | \(-0.924947\pi\) |
0.233607 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(692\) | 0.945226i | 0.0359321i | ||||||||
\(693\) | 1.21753 | + | 0.820940i | 0.0462501 | + | 0.0311849i | ||||
\(694\) | −8.09514 | + | 8.09514i | −0.307287 | + | 0.307287i | ||||
\(695\) | 2.86010 | + | 2.86010i | 0.108490 | + | 0.108490i | ||||
\(696\) | −3.40641 | − | 6.40524i | −0.129120 | − | 0.242790i | ||||
\(697\) | 8.79985 | + | 8.79985i | 0.333318 | + | 0.333318i | ||||
\(698\) | − | 5.04388i | − | 0.190914i | ||||||
\(699\) | −48.9905 | − | 14.9734i | −1.85299 | − | 0.566348i | ||||
\(700\) | 2.94621 | + | 2.94621i | 0.111356 | + | 0.111356i | ||||
\(701\) | −24.6973 | −0.932803 | −0.466402 | − | 0.884573i | \(-0.654450\pi\) | ||||
−0.466402 | + | 0.884573i | \(0.654450\pi\) | |||||||
\(702\) | 17.4303 | + | 6.86911i | 0.657864 | + | 0.259258i | ||||
\(703\) | −2.44923 | −0.0923744 | ||||||||
\(704\) | −0.346115 | − | 0.346115i | −0.0130447 | − | 0.0130447i | ||||
\(705\) | 15.4483 | + | 4.72161i | 0.581816 | + | 0.177826i | ||||
\(706\) | − | 5.15928i | − | 0.194172i | ||||||
\(707\) | −9.51170 | − | 9.51170i | −0.357724 | − | 0.357724i | ||||
\(708\) | −2.57178 | − | 4.83585i | −0.0966536 | − | 0.181743i | ||||
\(709\) | 15.9540 | + | 15.9540i | 0.599167 | + | 0.599167i | 0.940091 | − | 0.340924i | \(-0.110740\pi\) |
−0.340924 | + | 0.940091i | \(0.610740\pi\) | |||||||
\(710\) | −1.81639 | + | 1.81639i | −0.0681680 | + | 0.0681680i | ||||
\(711\) | −14.4484 | − | 9.74208i | −0.541857 | − | 0.365357i | ||||
\(712\) | 17.0003i | 0.637114i | ||||||||
\(713\) | 3.55442 | − | 3.55442i | 0.133114 | − | 0.133114i | ||||
\(714\) | 1.89546 | − | 6.20161i | 0.0709358 | − | 0.232090i | ||||
\(715\) | 0.431193 | − | 1.55239i | 0.0161257 | − | 0.0580562i | ||||
\(716\) | − | 18.1644i | − | 0.678834i | ||||||
\(717\) | 5.08961 | + | 9.57025i | 0.190075 | + | 0.357407i | ||||
\(718\) | 0.239025 | 0.00892035 | ||||||||
\(719\) | −10.8293 | −0.403865 | −0.201933 | − | 0.979399i | \(-0.564722\pi\) | ||||
−0.201933 | + | 0.979399i | \(0.564722\pi\) | |||||||
\(720\) | −0.523027 | − | 2.68836i | −0.0194921 | − | 0.100189i | ||||
\(721\) | −4.67725 | + | 4.67725i | −0.174190 | + | 0.174190i | ||||
\(722\) | −12.9846 | + | 12.9846i | −0.483238 | + | 0.483238i | ||||
\(723\) | −13.4201 | − | 25.2345i | −0.499100 | − | 0.938483i | ||||
\(724\) | 18.4772 | 0.686701 | ||||||||
\(725\) | 17.4517 | 0.648140 | ||||||||
\(726\) | −16.4553 | + | 8.75118i | −0.610713 | + | 0.324787i | ||||
\(727\) | 33.1488i | 1.22942i | 0.788753 | + | 0.614710i | \(0.210727\pi\) | ||||
−0.788753 | + | 0.614710i | \(0.789273\pi\) | |||||||
\(728\) | −0.964947 | + | 3.47403i | −0.0357633 | + | 0.128756i | ||||
\(729\) | −5.60046 | + | 26.4128i | −0.207424 | + | 0.978251i | ||||
\(730\) | 2.69185 | − | 2.69185i | 0.0996297 | − | 0.0996297i | ||||
\(731\) | 9.16873i | 0.339118i | ||||||||
\(732\) | 2.32031 | − | 7.59165i | 0.0857612 | − | 0.280595i | ||||
\(733\) | 16.6460 | − | 16.6460i | 0.614835 | − | 0.614835i | −0.329367 | − | 0.944202i | \(-0.606835\pi\) |
0.944202 | + | 0.329367i | \(0.106835\pi\) | |||||||
\(734\) | −13.8470 | − | 13.8470i | −0.511104 | − | 0.511104i | ||||
\(735\) | −1.39608 | + | 0.742456i | −0.0514951 | + | 0.0273859i | ||||
\(736\) | 2.07513 | + | 2.07513i | 0.0764903 | + | 0.0764903i | ||||
\(737\) | − | 1.07748i | − | 0.0396896i | ||||||
\(738\) | 5.57480 | − | 8.26794i | 0.205211 | − | 0.304347i | ||||
\(739\) | −31.1450 | − | 31.1450i | −1.14569 | − | 1.14569i | −0.987392 | − | 0.158294i | \(-0.949401\pi\) |
−0.158294 | − | 0.987392i | \(-0.550599\pi\) | |||||||
\(740\) | −2.80162 | −0.102989 | ||||||||
\(741\) | 1.07719 | + | 4.86629i | 0.0395716 | + | 0.178768i | ||||
\(742\) | 5.03273 | 0.184757 | ||||||||
\(743\) | −20.0711 | − | 20.0711i | −0.736339 | − | 0.736339i | 0.235529 | − | 0.971867i | \(-0.424318\pi\) |
−0.971867 | + | 0.235529i | \(0.924318\pi\) | |||||||
\(744\) | 0.867164 | − | 2.83721i | 0.0317918 | − | 0.104017i | ||||
\(745\) | 9.04956i | 0.331550i | ||||||||
\(746\) | −18.9610 | − | 18.9610i | −0.694210 | − | 0.694210i | ||||
\(747\) | −1.17711 | − | 6.05032i | −0.0430680 | − | 0.221369i | ||||
\(748\) | −1.29586 | − | 1.29586i | −0.0473812 | − | 0.0473812i | ||||
\(749\) | −0.164114 | + | 0.164114i | −0.00599660 | + | 0.00599660i | ||||
\(750\) | 13.8614 | + | 4.23661i | 0.506148 | + | 0.154699i | ||||
\(751\) | − | 5.53789i | − | 0.202080i | −0.994882 | − | 0.101040i | \(-0.967783\pi\) | ||
0.994882 | − | 0.101040i | \(-0.0322171\pi\) | |||||||
\(752\) | −7.22377 | + | 7.22377i | −0.263424 | + | 0.263424i | ||||
\(753\) | 23.6262 | + | 7.22111i | 0.860987 | + | 0.263152i | ||||
\(754\) | 7.43119 | + | 13.1470i | 0.270628 | + | 0.478785i | ||||
\(755\) | 8.14035i | 0.296258i | ||||||||
\(756\) | −5.16782 | − | 0.541858i | −0.187952 | − | 0.0197072i | ||||
\(757\) | 37.7422 | 1.37176 | 0.685882 | − | 0.727713i | \(-0.259417\pi\) | ||||
0.685882 | + | 0.727713i | \(0.259417\pi\) | |||||||
\(758\) | 0.352294 | 0.0127959 | ||||||||
\(759\) | −2.19671 | + | 1.16824i | −0.0797354 | + | 0.0424045i | ||||
\(760\) | 0.515195 | − | 0.515195i | 0.0186881 | − | 0.0186881i | ||||
\(761\) | −13.0324 | + | 13.0324i | −0.472423 | + | 0.472423i | −0.902698 | − | 0.430275i | \(-0.858417\pi\) |
0.430275 | + | 0.902698i | \(0.358417\pi\) | |||||||
\(762\) | −25.7820 | + | 13.7113i | −0.933983 | + | 0.496707i | ||||
\(763\) | −11.5376 | −0.417687 | ||||||||
\(764\) | −14.1792 | −0.512984 | ||||||||
\(765\) | −1.95822 | − | 10.0652i | −0.0707995 | − | 0.363909i | ||||
\(766\) | 2.84725i | 0.102875i | ||||||||
\(767\) | 5.61044 | + | 9.92578i | 0.202581 | + | 0.358399i | ||||
\(768\) | 1.65641 | + | 0.506265i | 0.0597706 | + | 0.0182683i | ||||
\(769\) | −8.01862 | + | 8.01862i | −0.289159 | + | 0.289159i | −0.836748 | − | 0.547589i | \(-0.815546\pi\) |
0.547589 | + | 0.836748i | \(0.315546\pi\) | |||||||
\(770\) | 0.446857i | 0.0161036i | ||||||||
\(771\) | 24.1705 | + | 7.38746i | 0.870478 | + | 0.266053i | ||||
\(772\) | −3.37846 | + | 3.37846i | −0.121593 | + | 0.121593i | ||||
\(773\) | 27.9230 | + | 27.9230i | 1.00432 | + | 1.00432i | 0.999991 | + | 0.00433086i | \(0.00137856\pi\) |
0.00433086 | + | 0.999991i | \(0.498621\pi\) | |||||||
\(774\) | 7.21151 | − | 1.40302i | 0.259212 | − | 0.0504304i | ||||
\(775\) | 5.04647 | + | 5.04647i | 0.181275 | + | 0.181275i | ||||
\(776\) | 9.46462i | 0.339760i | ||||||||
\(777\) | −1.55365 | + | 5.08328i | −0.0557370 | + | 0.182362i | ||||
\(778\) | 4.68442 | + | 4.68442i | 0.167945 | + | 0.167945i | ||||
\(779\) | 2.65281 | 0.0950469 | ||||||||
\(780\) | 1.23217 | + | 5.56644i | 0.0441189 | + | 0.199311i | ||||
\(781\) | 1.37729 | 0.0492835 | ||||||||
\(782\) | 7.76930 | + | 7.76930i | 0.277830 | + | 0.277830i | ||||
\(783\) | −16.9105 | + | 13.7008i | −0.604331 | + | 0.489627i | ||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −12.4077 | − | 12.4077i | −0.442851 | − | 0.442851i | ||||
\(786\) | 32.7542 | − | 17.4192i | 1.16830 | − | 0.621323i | ||||
\(787\) | 10.8587 | + | 10.8587i | 0.387072 | + | 0.387072i | 0.873642 | − | 0.486570i | \(-0.161752\pi\) |
−0.486570 | + | 0.873642i | \(0.661752\pi\) | |||||||
\(788\) | 1.50781 | − | 1.50781i | 0.0537137 | − | 0.0537137i | ||||
\(789\) | −13.4718 | + | 44.0775i | −0.479610 | + | 1.56920i | ||||
\(790\) | − | 5.30284i | − | 0.188667i | ||||||
\(791\) | 6.77484 | − | 6.77484i | 0.240886 | − | 0.240886i | ||||
\(792\) | −0.820940 | + | 1.21753i | −0.0291708 | + | 0.0432630i | ||||
\(793\) | −4.42254 | + | 15.9221i | −0.157049 | + | 0.565412i | ||||
\(794\) | − | 23.9988i | − | 0.851684i | ||||||
\(795\) | 7.02608 | − | 3.73658i | 0.249189 | − | 0.132523i | ||||
\(796\) | −11.1999 | −0.396968 | ||||||||
\(797\) | 20.7467 | 0.734884 | 0.367442 | − | 0.930046i | \(-0.380234\pi\) | ||||
0.367442 | + | 0.930046i | \(0.380234\pi\) | |||||||
\(798\) | −0.649069 | − | 1.22048i | −0.0229768 | − | 0.0432044i | ||||
\(799\) | −27.0459 | + | 27.0459i | −0.956814 | + | 0.956814i | ||||
\(800\) | −2.94621 | + | 2.94621i | −0.104164 | + | 0.104164i | ||||
\(801\) | 50.0623 | − | 9.73976i | 1.76887 | − | 0.344137i | ||||
\(802\) | 27.1307 | 0.958019 | ||||||||
\(803\) | −2.04111 | −0.0720294 | ||||||||
\(804\) | 1.79025 | + | 3.36629i | 0.0631371 | + | 0.118720i | ||||
\(805\) | − | 2.67913i | − | 0.0944268i | ||||||
\(806\) | −1.65282 | + | 5.95055i | −0.0582183 | + | 0.209599i | ||||
\(807\) | −13.9336 | + | 45.5884i | −0.490487 | + | 1.60479i | ||||
\(808\) | 9.51170 | − | 9.51170i | 0.334621 | − | 0.334621i | ||||
\(809\) | 8.50252i | 0.298933i | 0.988767 | + | 0.149466i | \(0.0477556\pi\) | ||||
−0.988767 | + | 0.149466i | \(0.952244\pi\) | |||||||
\(810\) | −7.61698 | + | 3.08041i | −0.267634 | + | 0.108234i | ||||
\(811\) | 30.5279 | − | 30.5279i | 1.07198 | − | 1.07198i | 0.0747808 | − | 0.997200i | \(-0.476174\pi\) |
0.997200 | − | 0.0747808i | \(-0.0238257\pi\) | |||||||
\(812\) | −2.96172 | − | 2.96172i | −0.103936 | − | 0.103936i | ||||
\(813\) | 12.9303 | + | 24.3135i | 0.453487 | + | 0.852713i | ||||
\(814\) | 1.06217 | + | 1.06217i | 0.0372292 | + | 0.0372292i | ||||
\(815\) | 12.2301i | 0.428400i | ||||||||
\(816\) | 6.20161 | + | 1.89546i | 0.217100 | + | 0.0663544i | ||||
\(817\) | 1.38201 | + | 1.38201i | 0.0483504 | + | 0.0483504i | ||||
\(818\) | 8.74706 | 0.305834 | ||||||||
\(819\) | 10.7831 | + | 0.851235i | 0.376792 | + | 0.0297446i | ||||
\(820\) | 3.03449 | 0.105969 | ||||||||
\(821\) | 19.1767 | + | 19.1767i | 0.669270 | + | 0.669270i | 0.957547 | − | 0.288277i | \(-0.0930825\pi\) |
−0.288277 | + | 0.957547i | \(0.593082\pi\) | |||||||
\(822\) | −11.4774 | − | 3.50796i | −0.400321 | − | 0.122354i | ||||
\(823\) | − | 15.6058i | − | 0.543984i | −0.962300 | − | 0.271992i | \(-0.912318\pi\) | ||
0.962300 | − | 0.271992i | \(-0.0876824\pi\) | |||||||
\(824\) | −4.67725 | − | 4.67725i | −0.162940 | − | 0.162940i | ||||
\(825\) | −1.65864 | − | 3.11882i | −0.0577465 | − | 0.108584i | ||||
\(826\) | −2.23605 | − | 2.23605i | −0.0778022 | − | 0.0778022i | ||||
\(827\) | −10.6978 | + | 10.6978i | −0.371999 | + | 0.371999i | −0.868205 | − | 0.496206i | \(-0.834726\pi\) |
0.496206 | + | 0.868205i | \(0.334726\pi\) | |||||||
\(828\) | 4.92194 | − | 7.29969i | 0.171049 | − | 0.253682i | ||||
\(829\) | 28.2914i | 0.982601i | 0.870990 | + | 0.491301i | \(0.163478\pi\) | ||||
−0.870990 | + | 0.491301i | \(0.836522\pi\) | |||||||
\(830\) | 1.32630 | − | 1.32630i | 0.0460366 | − | 0.0460366i | ||||
\(831\) | −12.4764 | + | 40.8205i | −0.432800 | + | 1.41605i | ||||
\(832\) | −3.47403 | − | 0.964947i | −0.120440 | − | 0.0334535i | ||||
\(833\) | − | 3.74401i | − | 0.129722i | ||||||
\(834\) | 3.60331 | + | 6.77548i | 0.124772 | + | 0.234616i | ||||
\(835\) | 21.9616 | 0.760013 | ||||||||
\(836\) | −0.390651 | −0.0135109 | ||||||||
\(837\) | −8.85179 | − | 0.928131i | −0.305963 | − | 0.0320809i | ||||
\(838\) | 15.3738 | − | 15.3738i | 0.531080 | − | 0.531080i | ||||
\(839\) | −39.8387 | + | 39.8387i | −1.37539 | + | 1.37539i | −0.523137 | + | 0.852249i | \(0.675238\pi\) |
−0.852249 | + | 0.523137i | \(0.824762\pi\) | |||||||
\(840\) | −0.742456 | − | 1.39608i | −0.0256172 | − | 0.0481692i | ||||
\(841\) | 11.4564 | 0.395050 | ||||||||
\(842\) | 28.2928 | 0.975035 | ||||||||
\(843\) | −50.5807 | + | 26.8996i | −1.74209 | + | 0.926473i | ||||
\(844\) | 16.7046i | 0.574997i | ||||||||
\(845\) | −2.86181 | − | 11.5178i | −0.0984491 | − | 0.396223i | ||||
\(846\) | 25.4111 | + | 17.1339i | 0.873651 | + | 0.589074i | ||||
\(847\) | −7.60876 | + | 7.60876i | −0.261440 | + | 0.261440i | ||||
\(848\) | 5.03273i | 0.172825i | ||||||||
\(849\) | −4.82431 | + | 15.7843i | −0.165570 | + | 0.541715i | ||||
\(850\) | −11.0307 | + | 11.0307i | −0.378348 | + | 0.378348i | ||||
\(851\) | −6.36826 | − | 6.36826i | −0.218301 | − | 0.218301i | ||||
\(852\) | −4.30297 | + | 2.28839i | −0.147417 | + | 0.0783988i | ||||
\(853\) | 33.9837 | + | 33.9837i | 1.16358 | + | 1.16358i | 0.983686 | + | 0.179894i | \(0.0575756\pi\) |
0.179894 | + | 0.983686i | \(0.442424\pi\) | |||||||
\(854\) | − | 4.58319i | − | 0.156834i | ||||||
\(855\) | −1.81230 | − | 1.22198i | −0.0619794 | − | 0.0417907i | ||||
\(856\) | −0.164114 | − | 0.164114i | −0.00560930 | − | 0.00560930i | ||||
\(857\) | 36.2526 | 1.23836 | 0.619182 | − | 0.785247i | \(-0.287464\pi\) | ||||
0.619182 | + | 0.785247i | \(0.287464\pi\) | |||||||
\(858\) | 1.64325 | − | 2.57755i | 0.0560996 | − | 0.0879963i | ||||
\(859\) | 23.8722 | 0.814510 | 0.407255 | − | 0.913314i | \(-0.366486\pi\) | ||||
0.407255 | + | 0.913314i | \(0.366486\pi\) | |||||||
\(860\) | 1.58085 | + | 1.58085i | 0.0539065 | + | 0.0539065i | ||||
\(861\) | 1.68280 | − | 5.50581i | 0.0573495 | − | 0.187638i | ||||
\(862\) | − | 27.6770i | − | 0.942682i | ||||||
\(863\) | 9.11408 | + | 9.11408i | 0.310247 | + | 0.310247i | 0.845005 | − | 0.534758i | \(-0.179597\pi\) |
−0.534758 | + | 0.845005i | \(0.679597\pi\) | |||||||
\(864\) | 0.541858 | − | 5.16782i | 0.0184344 | − | 0.175813i | ||||
\(865\) | 0.610174 | + | 0.610174i | 0.0207465 | + | 0.0207465i | ||||
\(866\) | −1.06968 | + | 1.06968i | −0.0363493 | + | 0.0363493i | ||||
\(867\) | −4.94008 | − | 1.50989i | −0.167774 | − | 0.0512784i | ||||
\(868\) | − | 1.71287i | − | 0.0581385i | ||||||
\(869\) | −2.01046 | + | 2.01046i | −0.0682003 | + | 0.0682003i | ||||
\(870\) | −6.33373 | − | 1.93584i | −0.214734 | − | 0.0656312i | ||||
\(871\) | −3.90549 | − | 6.90944i | −0.132332 | − | 0.234118i | ||||
\(872\) | − | 11.5376i | − | 0.390711i | ||||||
\(873\) | 27.8713 | − | 5.42244i | 0.943300 | − | 0.183522i | ||||
\(874\) | 2.34214 | 0.0792242 | ||||||||
\(875\) | 8.36836 | 0.282902 | ||||||||
\(876\) | 6.37688 | − | 3.39133i | 0.215455 | − | 0.114582i | ||||
\(877\) | 34.8819 | − | 34.8819i | 1.17788 | − | 1.17788i | 0.197594 | − | 0.980284i | \(-0.436687\pi\) |
0.980284 | − | 0.197594i | \(-0.0633129\pi\) | |||||||
\(878\) | 2.52971 | − | 2.52971i | 0.0853737 | − | 0.0853737i | ||||
\(879\) | −14.4610 | + | 7.69058i | −0.487757 | + | 0.259397i | ||||
\(880\) | −0.446857 | −0.0150635 | ||||||||
\(881\) | −5.86477 | −0.197589 | −0.0987946 | − | 0.995108i | \(-0.531499\pi\) | ||||
−0.0987946 | + | 0.995108i | \(0.531499\pi\) | |||||||
\(882\) | −2.94479 | + | 0.572916i | −0.0991561 | + | 0.0192911i | ||||
\(883\) | 29.2851i | 0.985523i | 0.870165 | + | 0.492761i | \(0.164012\pi\) | ||||
−0.870165 | + | 0.492761i | \(0.835988\pi\) | |||||||
\(884\) | −13.0068 | − | 3.61277i | −0.437466 | − | 0.121511i | ||||
\(885\) | −4.78187 | − | 1.46153i | −0.160741 | − | 0.0491288i | ||||
\(886\) | 1.79033 | − | 1.79033i | 0.0601472 | − | 0.0601472i | ||||
\(887\) | 31.3717i | 1.05336i | 0.850064 | + | 0.526680i | \(0.176563\pi\) | ||||
−0.850064 | + | 0.526680i | \(0.823437\pi\) | |||||||
\(888\) | −5.08328 | − | 1.55365i | −0.170584 | − | 0.0521371i | ||||
\(889\) | −11.9213 | + | 11.9213i | −0.399829 | + | 0.399829i | ||||
\(890\) | 10.9743 | + | 10.9743i | 0.367858 | + | 0.367858i | ||||
\(891\) | 4.05569 | + | 1.71995i | 0.135871 | + | 0.0576205i | ||||
\(892\) | −16.2269 | − | 16.2269i | −0.543315 | − | 0.543315i | ||||
\(893\) | 8.15328i | 0.272839i | ||||||||
\(894\) | −5.01848 | + | 16.4196i | −0.167843 | + | 0.549154i | ||||
\(895\) | −11.7257 | − | 11.7257i | −0.391946 | − | 0.391946i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −9.85209 | + | 15.4537i | −0.328952 | + | 0.515984i | ||||
\(898\) | −17.8096 | −0.594314 | ||||||||
\(899\) | −5.07303 | − | 5.07303i | −0.169195 | − | 0.169195i | ||||
\(900\) | 10.3639 | + | 6.98804i | 0.345463 | + | 0.232935i | ||||
\(901\) | 18.8426i | 0.627737i | ||||||||
\(902\) | −1.15047 | − | 1.15047i | −0.0383063 | − | 0.0383063i | ||||
\(903\) | 3.74497 | − | 1.99164i | 0.124625 | − | 0.0662775i | ||||
\(904\) | 6.77484 | + | 6.77484i | 0.225328 | + | 0.225328i | ||||
\(905\) | 11.9276 | − | 11.9276i | 0.396488 | − | 0.396488i | ||||
\(906\) | −4.51428 | + | 14.7699i | −0.149977 | + | 0.490698i | ||||
\(907\) | − | 50.4013i | − | 1.67355i | −0.547548 | − | 0.836775i | \(-0.684438\pi\) | ||
0.547548 | − | 0.836775i | \(-0.315562\pi\) | |||||||
\(908\) | −18.5844 | + | 18.5844i | −0.616743 | + | 0.616743i | ||||
\(909\) | −33.4593 | − | 22.5605i | −1.10978 | − | 0.748285i | ||||
\(910\) | 1.61969 | + | 2.86550i | 0.0536923 | + | 0.0949905i | ||||
\(911\) | 31.2810i | 1.03639i | 0.855264 | + | 0.518193i | \(0.173395\pi\) | ||||
−0.855264 | + | 0.518193i | \(0.826605\pi\) | |||||||
\(912\) | 1.22048 | − | 0.649069i | 0.0404140 | − | 0.0214928i | ||||
\(913\) | −1.00568 | −0.0332831 | ||||||||
\(914\) | 3.96071 | 0.131009 | ||||||||
\(915\) | −3.40282 | − | 6.39849i | −0.112494 | − | 0.211528i | ||||
\(916\) | 10.3015 | − | 10.3015i | 0.340371 | − | 0.340371i | ||||
\(917\) | 15.1452 | − | 15.1452i | 0.500140 | − | 0.500140i | ||||
\(918\) | 2.02872 | − | 19.3484i | 0.0669578 | − | 0.638591i | ||||
\(919\) | −22.5225 | −0.742948 | −0.371474 | − | 0.928443i | \(-0.621148\pi\) | ||||
−0.371474 | + | 0.928443i | \(0.621148\pi\) | |||||||
\(920\) | 2.67913 | 0.0883282 | ||||||||
\(921\) | 20.2656 | + | 38.1063i | 0.667773 | + | 1.25565i | ||||
\(922\) | − | 1.83970i | − | 0.0605872i | ||||||
\(923\) | 8.83200 | − | 4.99219i | 0.290709 | − | 0.164320i | ||||
\(924\) | −0.247807 | + | 0.810780i | −0.00815225 | + | 0.0266727i | ||||
\(925\) | 9.04149 | − | 9.04149i | 0.297282 | − | 0.297282i | ||||
\(926\) | 11.6245i | 0.382005i | ||||||||
\(927\) | −11.0938 | + | 16.4532i | −0.364369 | + | 0.540393i | ||||
\(928\) | 2.96172 | − | 2.96172i | 0.0972232 | − | 0.0972232i | ||||
\(929\) | −5.35331 | − | 5.35331i | −0.175636 | − | 0.175636i | 0.613814 | − | 0.789451i | \(-0.289634\pi\) |
−0.789451 | + | 0.613814i | \(0.789634\pi\) | |||||||
\(930\) | −1.27173 | − | 2.39129i | −0.0417016 | − | 0.0784136i | ||||
\(931\) | −0.564337 | − | 0.564337i | −0.0184954 | − | 0.0184954i | ||||
\(932\) | − | 29.5763i | − | 0.968803i | ||||||
\(933\) | −6.81795 | − | 2.08384i | −0.223210 | − | 0.0682218i | ||||
\(934\) | 22.9909 | + | 22.9909i | 0.752286 | + | 0.752286i | ||||
\(935\) | −1.67304 | −0.0547141 | ||||||||
\(936\) | −0.851235 | + | 10.7831i | −0.0278235 | + | 0.352457i | ||||
\(937\) | 16.9581 | 0.553998 | 0.276999 | − | 0.960870i | \(-0.410660\pi\) | ||||
0.276999 | + | 0.960870i | \(0.410660\pi\) | |||||||
\(938\) | 1.55654 | + | 1.55654i | 0.0508228 | + | 0.0508228i | ||||
\(939\) | −25.0823 | − | 7.66616i | −0.818531 | − | 0.250176i | ||||
\(940\) | 9.32636i | 0.304192i | ||||||||
\(941\) | −29.5920 | − | 29.5920i | −0.964672 | − | 0.964672i | 0.0347252 | − | 0.999397i | \(-0.488944\pi\) |
−0.999397 | + | 0.0347252i | \(0.988944\pi\) | |||||||
\(942\) | −15.6319 | − | 29.3934i | −0.509315 | − | 0.957690i | ||||
\(943\) | 6.89761 | + | 6.89761i | 0.224617 | + | 0.224617i | ||||
\(944\) | 2.23605 | − | 2.23605i | 0.0727773 | − | 0.0727773i | ||||
\(945\) | −3.68578 | + | 2.98621i | −0.119899 | + | 0.0971414i | ||||
\(946\) | − | 1.19869i | − | 0.0389728i | ||||||
\(947\) | 21.1614 | − | 21.1614i | 0.687653 | − | 0.687653i | −0.274060 | − | 0.961713i | \(-0.588367\pi\) |
0.961713 | + | 0.274060i | \(0.0883667\pi\) | |||||||
\(948\) | 2.94072 | − | 9.62152i | 0.0955101 | − | 0.312492i | ||||
\(949\) | −13.0888 | + | 7.39830i | −0.424880 | + | 0.240159i | ||||
\(950\) | 3.32531i | 0.107887i | ||||||||
\(951\) | 18.1853 | + | 34.1948i | 0.589700 | + | 1.10884i | ||||
\(952\) | 3.74401 | 0.121344 | ||||||||
\(953\) | 5.31495 | 0.172168 | 0.0860841 | − | 0.996288i | \(-0.472565\pi\) | ||||
0.0860841 | + | 0.996288i | \(0.472565\pi\) | |||||||
\(954\) | 14.8203 | − | 2.88333i | 0.479825 | − | 0.0933513i | ||||
\(955\) | −9.15310 | + | 9.15310i | −0.296187 | + | 0.296187i | ||||
\(956\) | −4.42519 | + | 4.42519i | −0.143121 | + | 0.143121i | ||||
\(957\) | 1.66737 | + | 3.13524i | 0.0538984 | + | 0.101348i | ||||
\(958\) | −31.5586 | −1.01961 | ||||||||
\(959\) | −6.92909 | −0.223752 | ||||||||
\(960\) | 1.39608 | − | 0.742456i | 0.0450582 | − | 0.0239627i | ||||
\(961\) | 28.0661i | 0.905358i | ||||||||
\(962\) | 10.6613 | + | 2.96128i | 0.343733 | + | 0.0954754i | ||||
\(963\) | −0.389257 | + | 0.577305i | −0.0125436 | + | 0.0186034i | ||||
\(964\) | 11.6682 | − | 11.6682i | 0.375808 | − | 0.375808i | ||||
\(965\) | 4.36181i | 0.140412i | ||||||||
\(966\) | 1.48572 | − | 4.86103i | 0.0478024 | − | 0.156401i | ||||
\(967\) | −25.6241 | + | 25.6241i | −0.824017 | + | 0.824017i | −0.986681 | − | 0.162665i | \(-0.947991\pi\) |
0.162665 | + | 0.986681i | \(0.447991\pi\) | |||||||
\(968\) | −7.60876 | − | 7.60876i | −0.244555 | − | 0.244555i | ||||
\(969\) | 4.56948 | − | 2.43012i | 0.146793 | − | 0.0780667i | ||||
\(970\) | 6.10972 | + | 6.10972i | 0.196171 | + | 0.196171i | ||||
\(971\) | − | 7.76748i | − | 0.249270i | −0.992203 | − | 0.124635i | \(-0.960224\pi\) | ||
0.992203 | − | 0.124635i | \(-0.0397760\pi\) | |||||||
\(972\) | −15.5286 | + | 1.36507i | −0.498079 | + | 0.0437847i | ||||
\(973\) | 3.13291 | + | 3.13291i | 0.100437 | + | 0.100437i | ||||
\(974\) | −10.4627 | −0.335247 | ||||||||
\(975\) | −21.9408 | − | 13.9877i | −0.702667 | − | 0.447966i | ||||
\(976\) | 4.58319 | 0.146704 | ||||||||
\(977\) | 4.94323 | + | 4.94323i | 0.158148 | + | 0.158148i | 0.781746 | − | 0.623598i | \(-0.214330\pi\) |
−0.623598 | + | 0.781746i | \(0.714330\pi\) | |||||||
\(978\) | −6.78225 | + | 22.1903i | −0.216872 | + | 0.709568i | ||||
\(979\) | − | 8.32133i | − | 0.265951i | ||||||
\(980\) | −0.645532 | − | 0.645532i | −0.0206208 | − | 0.0206208i | ||||
\(981\) | −33.9756 | + | 6.61005i | −1.08476 | + | 0.211043i | ||||
\(982\) | −15.8417 | − | 15.8417i | −0.505528 | − | 0.505528i | ||||
\(983\) | 30.0897 | − | 30.0897i | 0.959713 | − | 0.959713i | −0.0395061 | − | 0.999219i | \(-0.512578\pi\) |
0.999219 | + | 0.0395061i | \(0.0125785\pi\) | |||||||
\(984\) | 5.50581 | + | 1.68280i | 0.175519 | + | 0.0536456i | ||||
\(985\) | − | 1.94669i | − | 0.0620266i | ||||||
\(986\) | 11.0887 | − | 11.0887i | 0.353136 | − | 0.353136i | ||||
\(987\) | 16.9218 | + | 5.17198i | 0.538627 | + | 0.164626i | ||||
\(988\) | −2.50508 | + | 1.41597i | −0.0796971 | + | 0.0450479i | ||||
\(989\) | 7.18675i | 0.228525i | ||||||||
\(990\) | 0.256011 | + | 1.31590i | 0.00813658 | + | 0.0418220i | ||||
\(991\) | −21.8501 | −0.694092 | −0.347046 | − | 0.937848i | \(-0.612815\pi\) | ||||
−0.347046 | + | 0.937848i | \(0.612815\pi\) | |||||||
\(992\) | 1.71287 | 0.0543836 | ||||||||
\(993\) | 24.9129 | − | 13.2491i | 0.790588 | − | 0.420447i | ||||
\(994\) | −1.98965 | + | 1.98965i | −0.0631078 | + | 0.0631078i | ||||
\(995\) | −7.22987 | + | 7.22987i | −0.229202 | + | 0.229202i | ||||
\(996\) | 3.14196 | − | 1.67094i | 0.0995568 | − | 0.0529459i | ||||
\(997\) | 7.97068 | 0.252434 | 0.126217 | − | 0.992003i | \(-0.459716\pi\) | ||||
0.126217 | + | 0.992003i | \(0.459716\pi\) | |||||||
\(998\) | 36.5079 | 1.15564 | ||||||||
\(999\) | −1.66288 | + | 15.8593i | −0.0526113 | + | 0.501765i |
(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 | 546.2.p.d.239.10 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.c.239.5 | ✓ | 20 | ||
13.8 | odd | 4 | 546.2.p.c.281.5 | yes | 20 | ||
39.8 | even | 4 | inner | 546.2.p.d.281.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.5 | ✓ | 20 | 3.2 | odd | 2 | ||
546.2.p.c.281.5 | yes | 20 | 13.8 | odd | 4 | ||
546.2.p.d.239.10 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.p.d.281.10 | yes | 20 | 39.8 | even | 4 | inner |